LMFDB - Embedded newform 420.2.n.b.71.18

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			71.18
Character	$\chi$	$=$	420.71
Dual form			420.2.n.b.71.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09123 + 0.899566i) q^{2} +(-0.826488 + 1.52214i) q^{3} +(0.381563 + 1.96327i) q^{4} +1.00000i q^{5} +(-2.27116 + 0.917526i) q^{6} +1.00000i q^{7} +(-1.34971 + 2.48561i) q^{8} +(-1.63383 - 2.51607i) q^{9} +O(q^{10})$	\(q+(1.09123 + 0.899566i) q^{2} +(-0.826488 + 1.52214i) q^{3} +(0.381563 + 1.96327i) q^{4} +1.00000i q^{5} +(-2.27116 + 0.917526i) q^{6} +1.00000i q^{7} +(-1.34971 + 2.48561i) q^{8} +(-1.63383 - 2.51607i) q^{9} +(-0.899566 + 1.09123i) q^{10} -2.07669 q^{11} +(-3.30373 - 1.04182i) q^{12} +3.88750 q^{13} +(-0.899566 + 1.09123i) q^{14} +(-1.52214 - 0.826488i) q^{15} +(-3.70882 + 1.49822i) q^{16} -1.08277i q^{17} +(0.480479 - 4.21535i) q^{18} +1.74609i q^{19} +(-1.96327 + 0.381563i) q^{20} +(-1.52214 - 0.826488i) q^{21} +(-2.26615 - 1.86812i) q^{22} +0.0176032 q^{23} +(-2.66794 - 4.10879i) q^{24} -1.00000 q^{25} +(4.24215 + 3.49706i) q^{26} +(5.18015 - 0.407427i) q^{27} +(-1.96327 + 0.381563i) q^{28} -9.28540i q^{29} +(-0.917526 - 2.27116i) q^{30} +10.8667i q^{31} +(-5.39492 - 1.70143i) q^{32} +(1.71636 - 3.16102i) q^{33} +(0.974026 - 1.18155i) q^{34} -1.00000 q^{35} +(4.31629 - 4.16769i) q^{36} +6.46752 q^{37} +(-1.57073 + 1.90539i) q^{38} +(-3.21297 + 5.91732i) q^{39} +(-2.48561 - 1.34971i) q^{40} +9.66961i q^{41} +(-0.917526 - 2.27116i) q^{42} -3.43356i q^{43} +(-0.792388 - 4.07709i) q^{44} +(2.51607 - 1.63383i) q^{45} +(0.0192092 + 0.0158353i) q^{46} +0.213241 q^{47} +(0.784794 - 6.88361i) q^{48} -1.00000 q^{49} +(-1.09123 - 0.899566i) q^{50} +(1.64814 + 0.894900i) q^{51} +(1.48333 + 7.63218i) q^{52} +7.93599i q^{53} +(6.01924 + 4.21529i) q^{54} -2.07669i q^{55} +(-2.48561 - 1.34971i) q^{56} +(-2.65780 - 1.44313i) q^{57} +(8.35283 - 10.1325i) q^{58} +2.98100 q^{59} +(1.04182 - 3.30373i) q^{60} +8.36640 q^{61} +(-9.77528 + 11.8580i) q^{62} +(2.51607 - 1.63383i) q^{63} +(-4.35655 - 6.70973i) q^{64} +3.88750i q^{65} +(4.71649 - 1.90542i) q^{66} -7.12183i q^{67} +(2.12577 - 0.413147i) q^{68} +(-0.0145489 + 0.0267946i) q^{69} +(-1.09123 - 0.899566i) q^{70} +4.44568 q^{71} +(8.45917 - 0.665112i) q^{72} +5.62152 q^{73} +(7.05755 + 5.81796i) q^{74} +(0.826488 - 1.52214i) q^{75} +(-3.42805 + 0.666245i) q^{76} -2.07669i q^{77} +(-8.82911 + 3.56688i) q^{78} +2.33735i q^{79} +(-1.49822 - 3.70882i) q^{80} +(-3.66118 + 8.22167i) q^{81} +(-8.69845 + 10.5518i) q^{82} +3.90649 q^{83} +(1.04182 - 3.30373i) q^{84} +1.08277 q^{85} +(3.08871 - 3.74680i) q^{86} +(14.1337 + 7.67428i) q^{87} +(2.80294 - 5.16185i) q^{88} -1.16319i q^{89} +(4.21535 + 0.480479i) q^{90} +3.88750i q^{91} +(0.00671675 + 0.0345598i) q^{92} +(-16.5406 - 8.98117i) q^{93} +(0.232695 + 0.191824i) q^{94} -1.74609 q^{95} +(7.04865 - 6.80563i) q^{96} +11.4536 q^{97} +(-1.09123 - 0.899566i) q^{98} +(3.39297 + 5.22509i) 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 $

$2$	1.09123	+	0.899566i	0.771616	+	0.636089i
$2$	1.09123	+	0.899566i	0.771616	+	0.636089i
$3$	−0.826488	+	1.52214i	−0.477173	+	0.878809i
$3$	−0.826488	+	1.52214i	−0.477173	+	0.878809i
$4$	0.381563	+	1.96327i	0.190782	+	0.981633i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−2.27116	+	0.917526i	−0.927195	+	0.374578i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−1.34971	+	2.48561i	−0.477196	+	0.878797i
$9$	−1.63383	−	2.51607i	−0.544611	−	0.838689i
$10$	−0.899566	+	1.09123i	−0.284468	+	0.345077i
$11$	−2.07669			−0.626146			−0.313073	−	0.949729i	$-0.601358\pi$
$11$	−2.07669			−0.626146			−0.313073	+	0.949729i	$0.601358\pi$
$12$	−3.30373	−	1.04182i	−0.953704	−	0.300748i
$13$	3.88750			1.07820			0.539099	−	0.842243i	$-0.318765\pi$
$13$	3.88750			1.07820			0.539099	+	0.842243i	$0.318765\pi$
$14$	−0.899566	+	1.09123i	−0.240419	+	0.291643i
$15$	−1.52214	−	0.826488i	−0.393015	−	0.213398i
$16$	−3.70882	+	1.49822i	−0.927205	+	0.374555i
$17$		−	1.08277i		−	0.262611i	−0.991342	−	0.131306i	$-0.958083\pi$
$17$		−	1.08277i		−	0.262611i	0.991342	−	0.131306i	$-0.0419169\pi$
$18$	0.480479	−	4.21535i	0.113250	−	0.993567i
$19$			1.74609i			0.400582i	0.979737	+	0.200291i	$0.0641887\pi$
$19$			1.74609i			0.400582i	−0.979737	+	0.200291i	$0.935811\pi$
$20$	−1.96327	+	0.381563i	−0.438999	+	0.0853201i
$21$	−1.52214	−	0.826488i	−0.332159	−	0.180355i
$22$	−2.26615	−	1.86812i	−0.483144	−	0.398284i
$23$	0.0176032			0.00367053			0.00183526	−	0.999998i	$-0.499416\pi$
$23$	0.0176032			0.00367053			0.00183526	+	0.999998i	$0.499416\pi$
$24$	−2.66794	−	4.10879i	−0.544590	−	0.838702i
$25$	−1.00000			−0.200000
$26$	4.24215	+	3.49706i	0.831954	+	0.685829i
$27$	5.18015	−	0.407427i	0.996921	−	0.0784095i
$28$	−1.96327	+	0.381563i	−0.371022	+	0.0721087i
$29$		−	9.28540i		−	1.72426i	−0.506691	−	0.862128i	$-0.669131\pi$
$29$		−	9.28540i		−	1.72426i	0.506691	−	0.862128i	$-0.330869\pi$
$30$	−0.917526	−	2.27116i	−0.167516	−	0.414654i
$31$			10.8667i			1.95171i	0.218419	+	0.975855i	$0.429910\pi$
$31$			10.8667i			1.95171i	−0.218419	+	0.975855i	$0.570090\pi$
$32$	−5.39492	−	1.70143i	−0.953696	−	0.300772i
$33$	1.71636	−	3.16102i	0.298780	−	0.550262i
$34$	0.974026	−	1.18155i	0.167044	−	0.202635i
$35$	−1.00000			−0.169031
$36$	4.31629	−	4.16769i	0.719382	−	0.694614i
$37$	6.46752			1.06325			0.531627	−	0.846978i	$-0.321581\pi$
$37$	6.46752			1.06325			0.531627	+	0.846978i	$0.321581\pi$
$38$	−1.57073	+	1.90539i	−0.254805	+	0.309095i
$39$	−3.21297	+	5.91732i	−0.514487	+	0.947530i
$40$	−2.48561	−	1.34971i	−0.393010	−	0.213408i
$41$			9.66961i			1.51014i	0.655645	+	0.755069i	$0.272397\pi$
$41$			9.66961i			1.51014i	−0.655645	+	0.755069i	$0.727603\pi$
$42$	−0.917526	−	2.27116i	−0.141577	−	0.350447i
$43$		−	3.43356i		−	0.523613i	−0.965120	−	0.261807i	$-0.915682\pi$
$43$		−	3.43356i		−	0.523613i	0.965120	−	0.261807i	$-0.0843183\pi$
$44$	−0.792388	−	4.07709i	−0.119457	−	0.614645i
$45$	2.51607	−	1.63383i	0.375073	−	0.243558i
$46$	0.0192092	+	0.0158353i	0.00283224	+	0.00233478i
$47$	0.213241			0.0311044			0.0155522	−	0.999879i	$-0.495049\pi$
$47$	0.213241			0.0311044			0.0155522	+	0.999879i	$0.495049\pi$
$48$	0.784794	−	6.88361i	0.113275	−	0.993564i
$49$	−1.00000			−0.142857
$50$	−1.09123	−	0.899566i	−0.154323	−	0.127218i
$51$	1.64814	+	0.894900i	0.230785	+	0.125311i
$52$	1.48333	+	7.63218i	0.205700	+	1.05839i
$53$			7.93599i			1.09009i	0.838406	+	0.545046i	$0.183488\pi$
$53$			7.93599i			1.09009i	−0.838406	+	0.545046i	$0.816512\pi$
$54$	6.01924	+	4.21529i	0.819115	+	0.573629i
$55$		−	2.07669i		−	0.280021i
$56$	−2.48561	−	1.34971i	−0.332154	−	0.180363i
$57$	−2.65780	−	1.44313i	−0.352035	−	0.191147i
$58$	8.35283	−	10.1325i	1.09678	−	1.33046i
$59$	2.98100			0.388093			0.194046	−	0.980992i	$-0.437839\pi$
$59$	2.98100			0.388093			0.194046	+	0.980992i	$0.437839\pi$
$60$	1.04182	−	3.30373i	0.134499	−	0.426509i
$61$	8.36640			1.07121			0.535604	−	0.844469i	$-0.320084\pi$
$61$	8.36640			1.07121			0.535604	+	0.844469i	$0.320084\pi$
$62$	−9.77528	+	11.8580i	−1.24146	+	1.50597i
$63$	2.51607	−	1.63383i	0.316995	−	0.205844i
$64$	−4.35655	−	6.70973i	−0.544569	−	0.838716i
$65$			3.88750i			0.482184i
$66$	4.71649	−	1.90542i	0.580559	−	0.234541i
$67$		−	7.12183i		−	0.870070i	−0.900414	−	0.435035i	$-0.856736\pi$
$67$		−	7.12183i		−	0.870070i	0.900414	−	0.435035i	$-0.143264\pi$
$68$	2.12577	−	0.413147i	0.257788	−	0.0501014i
$69$	−0.0145489	+	0.0267946i	−0.00175148	+	0.00322569i
$70$	−1.09123	−	0.899566i	−0.130427	−	0.107519i
$71$	4.44568			0.527605			0.263803	−	0.964577i	$-0.415023\pi$
$71$	4.44568			0.527605			0.263803	+	0.964577i	$0.415023\pi$
$72$	8.45917	−	0.665112i	0.996923	−	0.0783842i
$73$	5.62152			0.657950			0.328975	−	0.944339i	$-0.393297\pi$
$73$	5.62152			0.657950			0.328975	+	0.944339i	$0.393297\pi$
$74$	7.05755	+	5.81796i	0.820424	+	0.676324i
$75$	0.826488	−	1.52214i	0.0954347	−	0.175762i
$76$	−3.42805	+	0.666245i	−0.393224	+	0.0764236i
$77$		−	2.07669i		−	0.236661i
$78$	−8.82911	+	3.56688i	−0.999699	+	0.403869i
$79$			2.33735i			0.262972i	0.991318	+	0.131486i	$0.0419748\pi$
$79$			2.33735i			0.262972i	−0.991318	+	0.131486i	$0.958025\pi$
$80$	−1.49822	−	3.70882i	−0.167506	−	0.414659i
$81$	−3.66118	+	8.22167i	−0.406797	+	0.913518i
$82$	−8.69845	+	10.5518i	−0.960583	+	1.16525i
$83$	3.90649			0.428793			0.214397	−	0.976747i	$-0.431222\pi$
$83$	3.90649			0.428793			0.214397	+	0.976747i	$0.431222\pi$
$84$	1.04182	−	3.30373i	0.113672	−	0.360466i
$85$	1.08277			0.117443
$86$	3.08871	−	3.74680i	0.333065	−	0.404028i
$87$	14.1337	+	7.67428i	1.51529	+	0.822769i
$88$	2.80294	−	5.16185i	0.298794	−	0.550255i
$89$		−	1.16319i		−	0.123297i	−0.998098	−	0.0616487i	$-0.980364\pi$
$89$		−	1.16319i		−	0.123297i	0.998098	−	0.0616487i	$-0.0196358\pi$
$90$	4.21535	+	0.480479i	0.444336	+	0.0506470i
$91$			3.88750i			0.407520i
$92$	0.00671675	+	0.0345598i	0.000700269	+	0.00360311i
$93$	−16.5406	−	8.98117i	−1.71518	−	0.931304i
$94$	0.232695	+	0.191824i	0.0240006	+	0.0197852i
$95$	−1.74609			−0.179146
$96$	7.04865	−	6.80563i	0.719400	−	0.694596i
$97$	11.4536			1.16294			0.581470	−	0.813568i	$-0.302478\pi$
$97$	11.4536			1.16294			0.581470	+	0.813568i	$0.302478\pi$
$98$	−1.09123	−	0.899566i	−0.110231	−	0.0908699i
$99$	3.39297	+	5.22509i	0.341006	+	0.525141i
$100$	−0.381563	−	1.96327i	−0.0381563	−	0.196327i
$101$		−	1.81896i		−	0.180993i	−0.995897	−	0.0904966i	$-0.971155\pi$
$101$		−	1.81896i		−	0.180993i	0.995897	−	0.0904966i	$-0.0288454\pi$
$102$	0.993473	+	2.45915i	0.0983684	+	0.243492i
$103$		−	19.5278i		−	1.92413i	−0.272826	−	0.962063i	$-0.587958\pi$
$103$		−	19.5278i		−	1.92413i	0.272826	−	0.962063i	$-0.412042\pi$
$104$	−5.24700	+	9.66281i	−0.514511	+	0.947517i
$105$	0.826488	−	1.52214i	0.0806570	−	0.148546i
$106$	−7.13894	+	8.65998i	−0.693395	+	0.841132i
$107$	17.1849			1.66133			0.830666	−	0.556771i	$-0.187960\pi$
$107$	17.1849			1.66133			0.830666	+	0.556771i	$0.187960\pi$
$108$	2.77644	+	10.0146i	0.267163	+	0.963651i
$109$	−17.4510			−1.67150			−0.835750	−	0.549110i	$-0.814967\pi$
$109$	−17.4510			−1.67150			−0.835750	+	0.549110i	$0.814967\pi$
$110$	1.86812	−	2.26615i	0.178118	−	0.216068i
$111$	−5.34533	+	9.84449i	−0.507357	+	0.934398i
$112$	−1.49822	−	3.70882i	−0.141568	−	0.350450i
$113$			3.38532i			0.318464i	0.987241	+	0.159232i	$0.0509018\pi$
$113$			3.38532i			0.318464i	−0.987241	+	0.159232i	$0.949098\pi$
$114$	−1.60209	−	3.96565i	−0.150049	−	0.371417i
$115$			0.0176032i			0.00164151i
$116$	18.2297	−	3.54297i	1.69259	−	0.328956i
$117$	−6.35152	−	9.78120i	−0.587198	−	0.904272i
$118$	3.25295	+	2.68160i	0.299458	+	0.246862i
$119$	1.08277			0.0992577
$120$	4.10879	−	2.66794i	0.375079	−	0.243548i
$121$	−6.68736			−0.607942
$122$	9.12966	+	7.52613i	0.826561	+	0.681384i
$123$	−14.7185	−	7.99182i	−1.32712	−	0.720598i
$124$	−21.3341	+	4.14632i	−1.91586	+	0.372350i
$125$		−	1.00000i		−	0.0894427i
$126$	4.21535	+	0.480479i	0.375533	+	0.0428045i
$127$		−	15.8920i		−	1.41019i	−0.709113	−	0.705095i	$-0.750904\pi$
$127$		−	15.8920i		−	1.41019i	0.709113	−	0.705095i	$-0.249096\pi$
$128$	1.28185	−	11.2409i	0.113300	−	0.993561i
$129$	5.22637	+	2.83780i	0.460156	+	0.249854i
$130$	−3.49706	+	4.24215i	−0.306712	+	0.372061i
$131$	−13.2810			−1.16036			−0.580182	−	0.814487i	$-0.697019\pi$
$131$	−13.2810			−1.16036			−0.580182	+	0.814487i	$0.697019\pi$
$132$	6.86081	+	2.16354i	0.597157	+	0.188312i
$133$	−1.74609			−0.151406
$134$	6.40655	−	7.77155i	0.553442	−	0.671360i
$135$	0.407427	+	5.18015i	0.0350658	+	0.445837i
$136$	2.69136	+	1.46143i	0.230782	+	0.125317i
$137$			15.2183i			1.30019i	0.759853	+	0.650095i	$0.225271\pi$
$137$			15.2183i			1.30019i	−0.759853	+	0.650095i	$0.774729\pi$
$138$	−0.0399797	+	0.0161514i	−0.00340330	+	0.00137490i
$139$		−	13.5504i		−	1.14933i	−0.818390	−	0.574664i	$-0.805133\pi$
$139$		−	13.5504i		−	1.14933i	0.818390	−	0.574664i	$-0.194867\pi$
$140$	−0.381563	−	1.96327i	−0.0322480	−	0.165926i
$141$	−0.176241	+	0.324583i	−0.0148422	+	0.0273348i
$142$	4.85126	+	3.99918i	0.407108	+	0.335604i
$143$	−8.07312			−0.675108
$144$	9.82921	+	6.88379i	0.819101	+	0.573649i
$145$	9.28540			0.771111
$146$	6.13437	+	5.05693i	0.507684	+	0.418514i
$147$	0.826488	−	1.52214i	0.0681676	−	0.125544i
$148$	2.46777	+	12.6975i	0.202849	+	1.04373i
$149$			4.07558i			0.333885i	0.985967	+	0.166942i	$0.0533894\pi$
$149$			4.07558i			0.333885i	−0.985967	+	0.166942i	$0.946611\pi$
$150$	2.27116	−	0.917526i	0.185439	−	0.0749157i
$151$			6.96098i			0.566477i	0.959050	+	0.283238i	$0.0914087\pi$
$151$			6.96098i			0.566477i	−0.959050	+	0.283238i	$0.908591\pi$
$152$	−4.34012	−	2.35673i	−0.352030	−	0.191156i
$153$	−2.72433	+	1.76907i	−0.220249	+	0.143021i
$154$	1.86812	−	2.26615i	0.150537	−	0.182611i
$155$	−10.8667			−0.872831
$156$	−12.8432	−	4.05008i	−1.02828	−	0.324266i
$157$	−18.2695			−1.45806			−0.729031	−	0.684481i	$-0.760029\pi$
$157$	−18.2695			−1.45806			−0.729031	+	0.684481i	$0.760029\pi$
$158$	−2.10260	+	2.55058i	−0.167274	+	0.202913i
$159$	−12.0797	−	6.55900i	−0.957983	−	0.520163i
$160$	1.70143	−	5.39492i	0.134510	−	0.426506i
$161$			0.0176032i			0.00138733i
$162$	−11.3911	+	5.67826i	−0.894970	+	0.446126i
$163$		−	4.26875i		−	0.334354i	−0.985927	−	0.167177i	$-0.946535\pi$
$163$		−	4.26875i		−	0.334354i	0.985927	−	0.167177i	$-0.0534652\pi$
$164$	−18.9840	+	3.68957i	−1.48240	+	0.288107i
$165$	3.16102	+	1.71636i	0.246085	+	0.133618i
$166$	4.26288	+	3.51415i	0.330864	+	0.272751i
$167$	−19.7862			−1.53110			−0.765550	−	0.643376i	$-0.777533\pi$
$167$	−19.7862			−1.53110			−0.765550	+	0.643376i	$0.777533\pi$
$168$	4.10879	−	2.66794i	0.317000	−	0.205836i
$169$	2.11262			0.162509
$170$	1.18155	+	0.974026i	0.0906211	+	0.0747044i
$171$	4.39329	−	2.85283i	0.335963	−	0.218161i
$172$	6.74099	−	1.31012i	0.513996	−	0.0998958i
$173$		−	15.7824i		−	1.19991i	−0.800032	−	0.599957i	$-0.795184\pi$
$173$		−	15.7824i		−	1.19991i	0.800032	−	0.599957i	$-0.204816\pi$
$174$	8.51959	+	21.0886i	0.645869	+	1.59872i
$175$		−	1.00000i		−	0.0755929i
$176$	7.70207	−	3.11134i	0.580565	−	0.234526i
$177$	−2.46376	+	4.53750i	−0.185188	+	0.341059i
$178$	1.04636	−	1.26930i	0.0784281	−	0.0951382i
$179$	21.5974			1.61427			0.807134	−	0.590369i	$-0.201018\pi$
$179$	21.5974			1.61427			0.807134	+	0.590369i	$0.201018\pi$
$180$	4.16769	+	4.31629i	0.310641	+	0.321718i
$181$	21.1987			1.57569			0.787845	−	0.615874i	$-0.211197\pi$
$181$	21.1987			1.57569			0.787845	+	0.615874i	$0.211197\pi$
$182$	−3.49706	+	4.24215i	−0.259219	+	0.314449i
$183$	−6.91473	+	12.7349i	−0.511152	+	0.941387i
$184$	−0.0237593	+	0.0437549i	−0.00175156	+	0.00322565i
$185$			6.46752i			0.475502i
$186$	−9.97044	−	24.6799i	−0.731068	−	1.80962i
$187$			2.24859i			0.164433i
$188$	0.0813649	+	0.418648i	0.00593414	+	0.0305331i
$189$	0.407427	+	5.18015i	0.0296360	+	0.376801i
$190$	−1.90539	−	1.57073i	−0.138231	−	0.113952i
$191$	−19.1594			−1.38633			−0.693164	−	0.720780i	$-0.743784\pi$
$191$	−19.1594			−1.38633			−0.693164	+	0.720780i	$0.743784\pi$
$192$	13.8138	−	1.08577i	0.996925	−	0.0783590i
$193$	11.6629			0.839516			0.419758	−	0.907636i	$-0.362115\pi$
$193$	11.6629			0.839516			0.419758	+	0.907636i	$0.362115\pi$
$194$	12.4985	+	10.3033i	0.897343	+	0.739734i
$195$	−5.91732	−	3.21297i	−0.423748	−	0.230086i
$196$	−0.381563	−	1.96327i	−0.0272545	−	0.140233i
$197$		−	24.8253i		−	1.76873i	−0.466796	−	0.884365i	$-0.654592\pi$
$197$		−	24.8253i		−	1.76873i	0.466796	−	0.884365i	$-0.345408\pi$
$198$	−0.997807	+	8.75397i	−0.0709110	+	0.622117i
$199$		−	23.6092i		−	1.67361i	−0.547502	−	0.836804i	$-0.684421\pi$
$199$		−	23.6092i		−	1.67361i	0.547502	−	0.836804i	$-0.315579\pi$
$200$	1.34971	−	2.48561i	0.0954391	−	0.175759i
$201$	10.8404	+	5.88611i	0.764626	+	0.415174i
$202$	1.63627	−	1.98490i	0.115128	−	0.139657i
$203$	9.28540			0.651707
$204$	−1.12806	+	3.57719i	−0.0789799	+	0.250453i
$205$	−9.66961			−0.675355
$206$	17.5665	−	21.3093i	1.22392	−	1.48469i
$207$	−0.0287608	−	0.0442909i	−0.00199901	−	0.00307843i
$208$	−14.4180	+	5.82432i	−0.999710	+	0.403844i
$209$		−	3.62610i		−	0.250822i
$210$	2.27116	−	0.917526i	0.156725	−	0.0633153i
$211$		−	13.6589i		−	0.940318i	−0.882582	−	0.470159i	$-0.844197\pi$
$211$		−	13.6589i		−	0.940318i	0.882582	−	0.470159i	$-0.155803\pi$
$212$	−15.5804	+	3.02808i	−1.07007	+	0.207969i
$213$	−3.67430	+	6.76696i	−0.251759	+	0.463664i
$214$	18.7527	+	15.4590i	1.28191	+	1.05675i
$215$	3.43356			0.234167
$216$	−5.97901	+	13.4258i	−0.406820	+	0.913508i
$217$	−10.8667			−0.737677
$218$	−19.0430	−	15.6983i	−1.28976	−	1.06322i
$219$	−4.64612	+	8.55676i	−0.313956	+	0.578212i
$220$	4.07709	−	0.792388i	0.274878	−	0.0534228i
$221$		−	4.20928i		−	0.283147i
$222$	−14.6888	+	5.93412i	−0.985845	+	0.398272i
$223$			20.4231i			1.36763i	0.729655	+	0.683816i	$0.239681\pi$
$223$			20.4231i			1.36763i	−0.729655	+	0.683816i	$0.760319\pi$
$224$	1.70143	−	5.39492i	0.113681	−	0.360463i
$225$	1.63383	+	2.51607i	0.108922	+	0.167738i
$226$	−3.04532	+	3.69416i	−0.202572	+	0.245732i
$227$	−0.876538			−0.0581778			−0.0290889	−	0.999577i	$-0.509261\pi$
$227$	−0.876538			−0.0581778			−0.0290889	+	0.999577i	$0.509261\pi$
$228$	1.81912	−	5.76862i	0.120474	−	0.382036i
$229$	−6.67620			−0.441176			−0.220588	−	0.975367i	$-0.570798\pi$
$229$	−6.67620			−0.441176			−0.220588	+	0.975367i	$0.570798\pi$
$230$	−0.0158353	+	0.0192092i	−0.00104415	+	0.00126662i
$231$	3.16102	+	1.71636i	0.207980	+	0.112928i
$232$	23.0799	+	12.5326i	1.51527	+	0.822807i
$233$		−	6.09775i		−	0.399477i	−0.979849	−	0.199739i	$-0.935991\pi$
$233$		−	6.09775i		−	0.399477i	0.979849	−	0.199739i	$-0.0640093\pi$
$234$	1.86786	−	16.3871i	0.122106	−	1.07126i
$235$			0.213241i			0.0139103i
$236$	1.13744	+	5.85249i	0.0740409	+	0.380964i
$237$	−3.55777	−	1.93179i	−0.231102	−	0.125483i
$238$	1.18155	+	0.974026i	0.0765888	+	0.0631367i
$239$	1.02568			0.0663460			0.0331730	−	0.999450i	$-0.489439\pi$
$239$	1.02568			0.0663460			0.0331730	+	0.999450i	$0.489439\pi$
$240$	6.88361	+	0.784794i	0.444335	+	0.0506582i
$241$	−3.40650			−0.219432			−0.109716	−	0.993963i	$-0.534994\pi$
$241$	−3.40650			−0.219432			−0.109716	+	0.993963i	$0.534994\pi$
$242$	−7.29744	−	6.01572i	−0.469097	−	0.386705i
$243$	−9.48863	−	12.3679i	−0.608696	−	0.793404i
$244$	3.19231	+	16.4255i	0.204367	+	1.05153i
$245$		−	1.00000i		−	0.0638877i
$246$	−8.87211	−	21.9612i	−0.565665	−	1.40019i
$247$			6.78793i			0.431906i
$248$	−27.0103	−	14.6669i	−1.71516	−	0.931347i
$249$	−3.22867	+	5.94624i	−0.204609	+	0.376827i
$250$	0.899566	−	1.09123i	0.0568935	−	0.0690154i
$251$	−15.1214			−0.954451			−0.477226	−	0.878781i	$-0.658358\pi$
$251$	−15.1214			−0.954451			−0.477226	+	0.878781i	$0.658358\pi$
$252$	4.16769	+	4.31629i	0.262540	+	0.271901i
$253$	−0.0365565			−0.00229829
$254$	14.2959	−	17.3418i	0.897006	−	1.08812i
$255$	−0.894900	+	1.64814i	−0.0560408	+	0.103210i
$256$	11.5107	−	11.1132i	0.719417	−	0.694578i
$257$			7.85725i			0.490122i	0.969508	+	0.245061i	$0.0788079\pi$
$257$			7.85725i			0.490122i	−0.969508	+	0.245061i	$0.921192\pi$
$258$	3.15038	+	7.79815i	0.196134	+	0.485492i
$259$			6.46752i			0.401872i
$260$	−7.63218	+	1.48333i	−0.473328	+	0.0919919i
$261$	−23.3627	+	15.1708i	−1.44611	+	0.939049i
$262$	−14.4926	−	11.9471i	−0.895355	−	0.738095i
$263$	12.1722			0.750573			0.375286	−	0.926909i	$-0.377544\pi$
$263$	12.1722			0.750573			0.375286	+	0.926909i	$0.377544\pi$
$264$	5.54047	+	8.53267i	0.340993	+	0.525150i
$265$	−7.93599			−0.487504
$266$	−1.90539	−	1.57073i	−0.116827	−	0.0963074i
$267$	1.77053	+	0.961359i	0.108355	+	0.0588342i
$268$	13.9820	−	2.71743i	0.854089	−	0.165993i
$269$			8.80637i			0.536934i	0.963289	+	0.268467i	$0.0865170\pi$
$269$			8.80637i			0.536934i	−0.963289	+	0.268467i	$0.913483\pi$
$270$	−4.21529	+	6.01924i	−0.256535	+	0.366320i
$271$			1.27004i			0.0771494i	0.999256	+	0.0385747i	$0.0122818\pi$
$271$			1.27004i			0.0771494i	−0.999256	+	0.0385747i	$0.987718\pi$
$272$	1.62223	+	4.01581i	0.0983623	+	0.243494i
$273$	−5.91732	−	3.21297i	−0.358133	−	0.194458i
$274$	−13.6899	+	16.6067i	−0.827037	+	1.00325i
$275$	2.07669			0.125229
$276$	−0.0581563	−	0.0183395i	−0.00350060	−	0.00110391i
$277$	−19.7185			−1.18477			−0.592384	−	0.805656i	$-0.701813\pi$
$277$	−19.7185			−1.18477			−0.592384	+	0.805656i	$0.701813\pi$
$278$	12.1894	−	14.7866i	0.731074	−	0.886839i
$279$	27.3412	−	17.7543i	1.63688	−	1.06292i
$280$	1.34971	−	2.48561i	0.0806608	−	0.148544i
$281$		−	7.41059i		−	0.442079i	−0.975265	−	0.221039i	$-0.929055\pi$
$281$		−	7.41059i		−	0.442079i	0.975265	−	0.221039i	$-0.0709449\pi$
$282$	−0.484303	+	0.195654i	−0.0288398	+	0.0116510i
$283$			5.40388i			0.321227i	0.987017	+	0.160614i	$0.0513473\pi$
$283$			5.40388i			0.321227i	−0.987017	+	0.160614i	$0.948653\pi$
$284$	1.69631	+	8.72805i	0.100657	+	0.517914i
$285$	1.44313	−	2.65780i	0.0854835	−	0.157435i
$286$	−8.80963	−	7.26230i	−0.520924	−	0.429429i
$287$	−9.66961			−0.570779
$288$	4.53350	+	16.3538i	0.267139	+	0.963658i
$289$	15.8276			0.931035
$290$	10.1325	+	8.35283i	0.595001	+	0.490495i
$291$	−9.46630	+	17.4341i	−0.554924	+	1.02200i
$292$	2.14497	+	11.0365i	0.125525	+	0.645865i
$293$			20.9154i			1.22189i	0.791672	+	0.610946i	$0.209211\pi$
$293$			20.9154i			1.22189i	−0.791672	+	0.610946i	$0.790789\pi$
$294$	2.27116	−	0.917526i	0.132456	−	0.0535112i
$295$			2.98100i			0.173560i
$296$	−8.72930	+	16.0758i	−0.507380	+	0.934385i
$297$	−10.7576	+	0.846101i	−0.624218	+	0.0490957i
$298$	−3.66626	+	4.44740i	−0.212381	+	0.257631i
$299$	0.0684325			0.00395755
$300$	3.30373	+	1.04182i	0.190741	+	0.0601497i
$301$	3.43356			0.197907
$302$	−6.26186	+	7.59603i	−0.360330	+	0.437102i
$303$	2.76872	+	1.50335i	0.159059	+	0.0863652i
$304$	−2.61603	−	6.47595i	−0.150040	−	0.371421i
$305$			8.36640i			0.479059i
$306$	−4.56427	−	0.520250i	−0.260922	−	0.0297407i
$307$			11.4504i			0.653508i	0.945109	+	0.326754i	$0.105955\pi$
$307$			11.4504i			0.653508i	−0.945109	+	0.326754i	$0.894045\pi$
$308$	4.07709	−	0.792388i	0.232314	−	0.0451505i
$309$	29.7240	+	16.1395i	1.69094	+	0.918142i
$310$	−11.8580	−	9.77528i	−0.673490	−	0.555198i
$311$	−11.4635			−0.650037			−0.325018	−	0.945708i	$-0.605370\pi$
$311$	−11.4635			−0.650037			−0.325018	+	0.945708i	$0.605370\pi$
$312$	−10.3716	−	15.9729i	−0.587175	−	0.904287i
$313$	10.7557			0.607949			0.303975	−	0.952680i	$-0.401686\pi$
$313$	10.7557			0.607949			0.303975	+	0.952680i	$0.401686\pi$
$314$	−19.9362	−	16.4346i	−1.12506	−	0.927457i
$315$	1.63383	+	2.51607i	0.0920561	+	0.141764i
$316$	−4.58883	+	0.891845i	−0.258142	+	0.0501702i
$317$		−	29.2336i		−	1.64192i	−0.570985	−	0.820960i	$-0.693439\pi$
$317$		−	29.2336i		−	1.64192i	0.570985	−	0.820960i	$-0.306561\pi$
$318$	−7.28147	−	18.0239i	−0.408325	−	1.01073i
$319$			19.2829i			1.07964i
$320$	6.70973	−	4.35655i	0.375085	−	0.243539i
$321$	−14.2032	+	26.1579i	−0.792743	+	1.45999i
$322$	−0.0158353	+	0.0192092i	−0.000882465	+	0.00107049i
$323$	1.89062			0.105197
$324$	−17.5383	−	4.05077i	−0.974349	−	0.225043i
$325$	−3.88750			−0.215639
$326$	3.84002	−	4.65818i	0.212679	−	0.257993i
$327$	14.4230	−	26.5629i	0.797596	−	1.46893i
$328$	−24.0349	−	13.0512i	−1.32711	−	0.720632i
$329$			0.213241i			0.0117563i
$330$	1.90542	+	4.71649i	0.104890	+	0.259634i
$331$			3.93597i			0.216340i	0.994132	+	0.108170i	$0.0344991\pi$
$331$			3.93597i			0.216340i	−0.994132	+	0.108170i	$0.965501\pi$
$332$	1.49057	+	7.66948i	0.0818058	+	0.420917i
$333$	−10.5669	−	16.2727i	−0.579060	−	0.891739i
$334$	−21.5913	−	17.7990i	−1.18142	−	0.973916i
$335$	7.12183			0.389107
$336$	6.88361	+	0.784794i	0.375532	+	0.0428140i
$337$	−2.52822			−0.137721			−0.0688605	−	0.997626i	$-0.521936\pi$
$337$	−2.52822			−0.137721			−0.0688605	+	0.997626i	$0.521936\pi$
$338$	2.30536	+	1.90044i	0.125395	+	0.103370i
$339$	−5.15294	−	2.79793i	−0.279869	−	0.151963i
$340$	0.413147	+	2.12577i	0.0224060	+	0.115286i
$341$		−	22.5667i		−	1.22205i
$342$	7.36039	+	0.838962i	0.398004	+	0.0453659i
$343$		−	1.00000i		−	0.0539949i
$344$	8.53451	+	4.63432i	0.460150	+	0.249866i
$345$	−0.0267946	−	0.0145489i	−0.00144257	−	0.000783285i
$346$	14.1973	−	17.2222i	0.763252	−	0.925872i
$347$	32.6521			1.75286			0.876428	−	0.481533i	$-0.159920\pi$
$347$	32.6521			1.75286			0.876428	+	0.481533i	$0.159920\pi$
$348$	−9.67374	+	30.6764i	−0.518567	+	1.64443i
$349$	−0.574408			−0.0307474			−0.0153737	−	0.999882i	$-0.504894\pi$
$349$	−0.574408			−0.0307474			−0.0153737	+	0.999882i	$0.504894\pi$
$350$	0.899566	−	1.09123i	0.0480838	−	0.0583287i
$351$	20.1378	−	1.58387i	1.07488	−	0.0845409i
$352$	11.2036	+	3.53333i	0.597153	+	0.188327i
$353$			15.2498i			0.811664i	0.913948	+	0.405832i	$0.133018\pi$
$353$			15.2498i			0.811664i	−0.913948	+	0.405832i	$0.866982\pi$
$354$	−6.77031	+	2.73514i	−0.359838	+	0.145371i
$355$			4.44568i			0.235952i
$356$	2.28364	−	0.443829i	0.121033	−	0.0235229i
$357$	−0.894900	+	1.64814i	−0.0473631	+	0.0872286i
$358$	23.5677	+	19.4283i	1.24559	+	1.02682i
$359$	−6.80601			−0.359207			−0.179604	−	0.983739i	$-0.557482\pi$
$359$	−6.80601			−0.359207			−0.179604	+	0.983739i	$0.557482\pi$
$360$	0.665112	+	8.45917i	0.0350545	+	0.445838i
$361$	15.9512			0.839534
$362$	23.1327	+	19.0697i	1.21583	+	1.00228i
$363$	5.52703	−	10.1791i	0.290094	−	0.534265i
$364$	−7.63218	+	1.48333i	−0.400035	+	0.0777474i
$365$			5.62152i			0.294244i
$366$	−19.0014	+	7.67639i	−0.993219	+	0.401251i
$367$			3.82872i			0.199857i	0.994995	+	0.0999287i	$0.0318615\pi$
$367$			3.82872i			0.199857i	−0.994995	+	0.0999287i	$0.968139\pi$
$368$	−0.0652872	+	0.0263735i	−0.00340333	+	0.00137481i
$369$	24.3294	−	15.7985i	1.26654	−	0.822439i
$370$	−5.81796	+	7.05755i	−0.302462	+	0.366905i
$371$	−7.93599			−0.412016
$372$	11.3211	−	35.9005i	0.586973	−	1.86135i
$373$	−1.52917			−0.0791777			−0.0395888	−	0.999216i	$-0.512605\pi$
$373$	−1.52917			−0.0791777			−0.0395888	+	0.999216i	$0.512605\pi$
$374$	−2.02275	+	2.45372i	−0.104594	+	0.126879i
$375$	1.52214	+	0.826488i	0.0786031	+	0.0426797i
$376$	−0.287814	+	0.530034i	−0.0148429	+	0.0273344i
$377$		−	36.0970i		−	1.85909i
$378$	−4.21529	+	6.01924i	−0.216811	+	0.309597i
$379$		−	14.1473i		−	0.726697i	−0.931653	−	0.363348i	$-0.881634\pi$
$379$		−	14.1473i		−	0.726697i	0.931653	−	0.363348i	$-0.118366\pi$
$380$	−0.666245	−	3.42805i	−0.0341777	−	0.175855i
$381$	24.1899	+	13.1346i	1.23929	+	0.672905i
$382$	−20.9073	−	17.2352i	−1.06971	−	0.881827i
$383$	27.7958			1.42030			0.710149	−	0.704051i	$-0.248628\pi$
$383$	27.7958			1.42030			0.710149	+	0.704051i	$0.248628\pi$
$384$	16.0508	+	11.2416i	0.819086	+	0.573670i
$385$	2.07669			0.105838
$386$	12.7269	+	10.4916i	0.647784	+	0.534007i
$387$	−8.63907	+	5.60987i	−0.439149	+	0.285166i
$388$	4.37029	+	22.4865i	0.221868	+	1.14158i
$389$		−	34.8498i		−	1.76696i	−0.468472	−	0.883478i	$-0.655195\pi$
$389$		−	34.8498i		−	1.76696i	0.468472	−	0.883478i	$-0.344805\pi$
$390$	−3.56688	−	8.82911i	−0.180616	−	0.447079i
$391$		−	0.0190603i		−	0.000963922i
$392$	1.34971	−	2.48561i	0.0681708	−	0.125542i
$393$	10.9766	−	20.2155i	0.553695	−	1.01974i
$394$	22.3320	−	27.0901i	1.12507	−	1.36478i
$395$	−2.33735			−0.117605
$396$	−8.96360	+	8.65499i	−0.450438	+	0.434930i
$397$	31.4624			1.57905			0.789525	−	0.613718i	$-0.210327\pi$
$397$	31.4624			1.57905			0.789525	+	0.613718i	$0.210327\pi$
$398$	21.2380	−	25.7630i	1.06456	−	1.29138i
$399$	1.44313	−	2.65780i	0.0722467	−	0.133057i
$400$	3.70882	−	1.49822i	0.185441	−	0.0749110i
$401$			29.4959i			1.47295i	0.676463	+	0.736477i	$0.263512\pi$
$401$			29.4959i			1.47295i	−0.676463	+	0.736477i	$0.736488\pi$
$402$	6.53446	+	16.1748i	0.325909	+	0.806725i
$403$			42.2441i			2.10433i
$404$	3.57110	−	0.694048i	0.177669	−	0.0345302i
$405$	−8.22167	−	3.66118i	−0.408538	−	0.181925i
$406$	10.1325	+	8.35283i	0.502868	+	0.414544i
$407$	−13.4310			−0.665752
$408$	−4.44889	+	2.88877i	−0.220253	+	0.143015i
$409$	−31.3821			−1.55174			−0.775872	−	0.630890i	$-0.782690\pi$
$409$	−31.3821			−1.55174			−0.775872	+	0.630890i	$0.782690\pi$
$410$	−10.5518	−	8.69845i	−0.521114	−	0.429586i
$411$	−23.1645	−	12.5778i	−1.14262	−	0.620416i
$412$	38.3382	−	7.45107i	1.88879	−	0.367088i
$413$			2.98100i			0.146685i
$414$	0.00845799	−	0.0742037i	0.000415688	−	0.00364691i
$415$			3.90649i			0.191762i
$416$	−20.9727	−	6.61428i	−1.02827	−	0.324292i
$417$	20.6256	+	11.1992i	1.01004	+	0.548428i
$418$	3.26191	−	3.95690i	0.159545	−	0.193538i
$419$	4.89374			0.239075			0.119537	−	0.992830i	$-0.461859\pi$
$419$	4.89374			0.239075			0.119537	+	0.992830i	$0.461859\pi$
$420$	3.30373	+	1.04182i	0.161205	+	0.0508357i
$421$	−14.1782			−0.691004			−0.345502	−	0.938418i	$-0.612291\pi$
$421$	−14.1782			−0.691004			−0.345502	+	0.938418i	$0.612291\pi$
$422$	12.2871	−	14.9050i	0.598126	−	0.725564i
$423$	−0.348400	−	0.536528i	−0.0169398	−	0.0260869i
$424$	−19.7258	−	10.7113i	−0.957969	−	0.520187i
$425$			1.08277i			0.0525222i
$426$	−10.0968	+	4.07903i	−0.489193	+	0.197629i
$427$			8.36640i			0.404879i
$428$	6.55714	+	33.7386i	0.316951	+	1.63082i
$429$	6.67234	−	12.2884i	0.322144	−	0.593292i
$430$	3.74680	+	3.08871i	0.180687	+	0.148951i
$431$	15.9143			0.766564			0.383282	−	0.923631i	$-0.374794\pi$
$431$	15.9143			0.766564			0.383282	+	0.923631i	$0.374794\pi$
$432$	−18.6018	+	9.27208i	−0.894982	+	0.446103i
$433$	23.8485			1.14609			0.573043	−	0.819525i	$-0.305763\pi$
$433$	23.8485			1.14609			0.573043	+	0.819525i	$0.305763\pi$
$434$	−11.8580	−	9.77528i	−0.569203	−	0.469228i
$435$	−7.67428	+	14.1337i	−0.367953	+	0.677659i
$436$	−6.65865	−	34.2609i	−0.318892	−	1.64080i
$437$			0.0307369i			0.00147035i
$438$	−12.7674	+	5.15789i	−0.610048	+	0.246454i
$439$			3.11342i			0.148596i	0.997236	+	0.0742978i	$0.0236715\pi$
$439$			3.11342i			0.148596i	−0.997236	+	0.0742978i	$0.976328\pi$
$440$	5.16185	+	2.80294i	0.246081	+	0.133625i
$441$	1.63383	+	2.51607i	0.0778016	+	0.119813i
$442$	3.78652	−	4.59329i	0.180106	−	0.218480i
$443$	35.4423			1.68391			0.841957	−	0.539545i	$-0.181404\pi$
$443$	35.4423			1.68391			0.841957	+	0.539545i	$0.181404\pi$
$444$	−21.3669	−	6.73801i	−1.01403	−	0.319772i
$445$	1.16319			0.0551403
$446$	−18.3719	+	22.2863i	−0.869935	+	1.05529i
$447$	−6.20362	−	3.36842i	−0.293421	−	0.159321i
$448$	6.70973	−	4.35655i	0.317005	−	0.205828i
$449$			25.4194i			1.19961i	0.800145	+	0.599807i	$0.204756\pi$
$449$			25.4194i			1.19961i	−0.800145	+	0.599807i	$0.795244\pi$
$450$	−0.480479	+	4.21535i	−0.0226500	+	0.198713i
$451$		−	20.0808i		−	0.945567i
$452$	−6.64628	+	1.29171i	−0.312615	+	0.0607571i
$453$	−10.5956	−	5.75317i	−0.497825	−	0.270308i
$454$	−0.956504	−	0.788503i	−0.0448909	−	0.0370063i
$455$	−3.88750			−0.182249
$456$	7.17433	−	4.65847i	0.335969	−	0.218153i
$457$	11.5206			0.538912			0.269456	−	0.963013i	$-0.413156\pi$
$457$	11.5206			0.538912			0.269456	+	0.963013i	$0.413156\pi$
$458$	−7.28526	−	6.00568i	−0.340418	−	0.280627i
$459$	−0.441152	−	5.60894i	−0.0205912	−	0.261803i
$460$	−0.0345598	+	0.00671675i	−0.00161136	+	0.000313170i
$461$		−	11.5780i		−	0.539240i	−0.962967	−	0.269620i	$-0.913102\pi$
$461$		−	11.5780i		−	0.539240i	0.962967	−	0.269620i	$-0.0868982\pi$
$462$	1.90542	+	4.71649i	0.0886480	+	0.219431i
$463$		−	16.8353i		−	0.782404i	−0.920305	−	0.391202i	$-0.872059\pi$
$463$		−	16.8353i		−	0.782404i	0.920305	−	0.391202i	$-0.127941\pi$
$464$	13.9116	+	34.4379i	0.645828	+	1.59874i
$465$	8.98117	−	16.5406i	0.416492	−	0.767052i
$466$	5.48533	−	6.65405i	0.254103	−	0.308243i
$467$	−8.52455			−0.394469			−0.197235	−	0.980356i	$-0.563196\pi$
$467$	−8.52455			−0.394469			−0.197235	+	0.980356i	$0.563196\pi$
$468$	16.7796	−	16.2019i	0.775636	−	0.748931i
$469$	7.12183			0.328856
$470$	−0.191824	+	0.232695i	−0.00884819	+	0.0107334i
$471$	15.0995	−	27.8087i	0.695748	−	1.28136i
$472$	−4.02349	+	7.40961i	−0.185196	+	0.341055i
$473$			7.13044i			0.327858i
$474$	−2.14457	−	5.30847i	−0.0985036	−	0.243826i
$475$		−	1.74609i		−	0.0801163i
$476$	0.413147	+	2.12577i	0.0189365	+	0.0974346i
$477$	19.9675	−	12.9661i	0.914247	−	0.593676i
$478$	1.11926	+	0.922670i	0.0511936	+	0.0422019i
$479$	−8.18702			−0.374074			−0.187037	−	0.982353i	$-0.559889\pi$
$479$	−8.18702			−0.374074			−0.187037	+	0.982353i	$0.559889\pi$
$480$	6.80563	+	7.04865i	0.310633	+	0.321725i
$481$	25.1425			1.14640
$482$	−3.71727	−	3.06437i	−0.169317	−	0.139578i
$483$	−0.0267946	−	0.0145489i	−0.00121920	−	0.000661997i
$484$	−2.55165	−	13.1291i	−0.115984	−	0.596775i
$485$			11.4536i			0.520083i
$486$	0.771510	−	22.0319i	0.0349964	−	0.999387i
$487$		−	9.64886i		−	0.437231i	−0.975811	−	0.218616i	$-0.929846\pi$
$487$		−	9.64886i		−	0.437231i	0.975811	−	0.218616i	$-0.0701541\pi$
$488$	−11.2922	+	20.7956i	−0.511176	+	0.941374i
$489$	6.49764	+	3.52807i	0.293834	+	0.159545i
$490$	0.899566	−	1.09123i	0.0406382	−	0.0492967i
$491$	−10.3699			−0.467987			−0.233993	−	0.972238i	$-0.575179\pi$
$491$	−10.3699			−0.467987			−0.233993	+	0.972238i	$0.575179\pi$
$492$	10.0740	−	31.9457i	0.454172	−	1.44022i
$493$	−10.0540			−0.452809
$494$	−6.10619	+	7.40719i	−0.274731	+	0.333265i
$495$	−5.22509	+	3.39297i	−0.234850	+	0.152502i
$496$	−16.2806	−	40.3025i	−0.731022	−	1.80963i
$497$			4.44568i			0.199416i
$498$	−8.87225	+	3.58431i	−0.397575	+	0.160617i
$499$			28.8552i			1.29174i	0.763449	+	0.645868i	$0.223504\pi$
$499$			28.8552i			1.29174i	−0.763449	+	0.645868i	$0.776496\pi$
$500$	1.96327	−	0.381563i	0.0877999	−	0.0170640i
$501$	16.3531	−	30.1174i	0.730601	−	1.34555i
$502$	−16.5009	−	13.6027i	−0.736470	−	0.607116i
$503$	−4.78556			−0.213378			−0.106689	−	0.994292i	$-0.534025\pi$
$503$	−4.78556			−0.213378			−0.106689	+	0.994292i	$0.534025\pi$
$504$	0.665112	+	8.45917i	0.0296265	+	0.376802i
$505$	1.81896			0.0809427
$506$	−0.0398915	−	0.0328849i	−0.00177339	−	0.00146191i
$507$	−1.74606	+	3.21571i	−0.0775451	+	0.142815i
$508$	31.2003	−	6.06381i	1.38429	−	0.269038i
$509$		−	11.5277i		−	0.510958i	−0.966815	−	0.255479i	$-0.917767\pi$
$509$		−	11.5277i		−	0.510958i	0.966815	−	0.255479i	$-0.0822331\pi$
$510$	−2.45915	+	0.993473i	−0.108893	+	0.0439917i
$511$			5.62152i			0.248682i
$512$	22.5579	−	1.77249i	0.996927	−	0.0783338i
$513$	0.711407	+	9.04504i	0.0314094	+	0.399348i
$514$	−7.06811	+	8.57406i	−0.311761	+	0.378186i
$515$	19.5278			0.860496
$516$	−3.57716	+	11.3435i	−0.157476	+	0.499372i
$517$	−0.442835			−0.0194759
$518$	−5.81796	+	7.05755i	−0.255627	+	0.310091i
$519$	24.0231	+	13.0440i	1.05449	+	0.572567i
$520$	−9.66281	−	5.24700i	−0.423742	−	0.230096i
$521$		−	28.5564i		−	1.25108i	−0.780193	−	0.625539i	$-0.784879\pi$
$521$		−	28.5564i		−	1.25108i	0.780193	−	0.625539i	$-0.215121\pi$
$522$	−39.1412	−	4.46144i	−1.71316	−	0.195272i
$523$			23.0389i			1.00742i	0.863873	+	0.503710i	$0.168032\pi$
$523$			23.0389i			1.00742i	−0.863873	+	0.503710i	$0.831968\pi$
$524$	−5.06753	−	26.0741i	−0.221376	−	1.13905i
$525$	1.52214	+	0.826488i	0.0664317	+	0.0360709i
$526$	13.2827	+	10.9497i	0.579154	+	0.477431i
$527$	11.7661			0.512541
$528$	−1.62977	+	14.2951i	−0.0709268	+	0.622115i
$529$	−22.9997			−0.999987
$530$	−8.65998	−	7.13894i	−0.376166	−	0.310096i
$531$	−4.87045	−	7.50038i	−0.211360	−	0.325489i
$532$	−0.666245	−	3.42805i	−0.0288854	−	0.148625i
$533$			37.5906i			1.62823i
$534$	1.06725	+	2.64177i	0.0461845	+	0.114321i
$535$			17.1849i			0.742970i
$536$	17.7021	+	9.61243i	0.764615	+	0.415194i
$537$	−17.8500	+	32.8743i	−0.770285	+	1.41863i
$538$	−7.92191	+	9.60977i	−0.341538	+	0.414306i
$539$	2.07669			0.0894494
$540$	−10.0146	+	2.77644i	−0.430958	+	0.119479i
$541$	−30.0318			−1.29117			−0.645584	−	0.763689i	$-0.723386\pi$
$541$	−30.0318			−1.29117			−0.645584	+	0.763689i	$0.723386\pi$
$542$	−1.14248	+	1.38590i	−0.0490739	+	0.0595297i
$543$	−17.5205	+	32.2675i	−0.751877	+	1.38473i
$544$	−1.84226	+	5.84148i	−0.0789862	+	0.250451i
$545$		−	17.4510i		−	0.747518i
$546$	−3.56688	−	8.82911i	−0.152648	−	0.377851i
$547$			16.6927i			0.713730i	0.934156	+	0.356865i	$0.116154\pi$
$547$			16.6927i			0.713730i	−0.934156	+	0.356865i	$0.883846\pi$
$548$	−29.8776	+	5.80676i	−1.27631	+	0.248052i
$549$	−13.6693	−	21.0504i	−0.583392	−	0.898410i
$550$	2.26615	+	1.86812i	0.0966288	+	0.0796569i
$551$	16.2132			0.690705
$552$	−0.0469643	−	0.0723279i	−0.00199893	−	0.00307848i
$553$	−2.33735			−0.0993940
$554$	−21.5174	−	17.7381i	−0.914186	−	0.753618i
$555$	−9.84449	−	5.34533i	−0.417875	−	0.226897i
$556$	26.6030	−	5.17032i	1.12822	−	0.219270i
$557$			7.22921i			0.306311i	0.988202	+	0.153156i	$0.0489436\pi$
$557$			7.22921i			0.306311i	−0.988202	+	0.153156i	$0.951056\pi$
$558$	45.8067	+	5.22121i	1.93915	+	0.221031i
$559$		−	13.3480i		−	0.564558i
$560$	3.70882	−	1.49822i	0.156726	−	0.0633113i
$561$	−3.42267	−	1.85843i	−0.144505	−	0.0784630i
$562$	6.66631	−	8.08665i	0.281201	−	0.341115i
$563$	−0.606001			−0.0255399			−0.0127699	−	0.999918i	$-0.504065\pi$
$563$	−0.606001			−0.0255399			−0.0127699	+	0.999918i	$0.504065\pi$
$564$	−0.704489	−	0.222159i	−0.0296644	−	0.00935459i
$565$	−3.38532			−0.142421
$566$	−4.86114	+	5.89687i	−0.204329	+	0.247864i
$567$	−8.22167	−	3.66118i	−0.345278	−	0.153755i
$568$	−6.00039	+	11.0502i	−0.251771	+	0.463658i
$569$			4.54488i			0.190531i	0.995452	+	0.0952657i	$0.0303701\pi$
$569$			4.54488i			0.190531i	−0.995452	+	0.0952657i	$0.969630\pi$
$570$	3.96565	−	1.60209i	0.166103	−	0.0671040i
$571$		−	26.1093i		−	1.09264i	−0.837577	−	0.546320i	$-0.816028\pi$
$571$		−	26.1093i		−	1.09264i	0.837577	−	0.546320i	$-0.183972\pi$
$572$	−3.08041	−	15.8497i	−0.128798	−	0.662708i
$573$	15.8350	−	29.1634i	0.661518	−	1.21832i
$574$	−10.5518	−	8.69845i	−0.440422	−	0.363066i
$575$	−0.0176032			−0.000734106
$576$	−9.76424	+	21.9239i	−0.406844	+	0.913498i
$577$	−27.2597			−1.13484			−0.567419	−	0.823429i	$-0.692058\pi$
$577$	−27.2597			−1.13484			−0.567419	+	0.823429i	$0.692058\pi$
$578$	17.2715	+	14.2380i	0.718402	+	0.592221i
$579$	−9.63927	+	17.7526i	−0.400595	+	0.737774i
$580$	3.54297	+	18.2297i	0.147114	+	0.756947i
$581$			3.90649i			0.162069i
$582$	−26.0130	+	10.5090i	−1.07827	+	0.435612i
$583$		−	16.4806i		−	0.682556i
$584$	−7.58744	+	13.9729i	−0.313971	+	0.578204i
$585$	9.78120	−	6.35152i	0.404403	−	0.262603i
$586$	−18.8148	+	22.8235i	−0.777232	+	0.942831i
$587$	−13.8384			−0.571170			−0.285585	−	0.958353i	$-0.592188\pi$
$587$	−13.8384			−0.571170			−0.285585	+	0.958353i	$0.592188\pi$
$588$	3.30373	+	1.04182i	0.136243	+	0.0429640i
$589$	−18.9742			−0.781819
$590$	−2.68160	+	3.25295i	−0.110400	+	0.133922i
$591$	37.7877	+	20.5178i	1.55438	+	0.843991i
$592$	−23.9869	+	9.68977i	−0.985855	+	0.398247i
$593$			9.50707i			0.390409i	0.980763	+	0.195204i	$0.0625370\pi$
$593$			9.50707i			0.390409i	−0.980763	+	0.195204i	$0.937463\pi$
$594$	−12.5001	−	8.75386i	−0.512886	−	0.359175i
$595$			1.08277i			0.0443894i
$596$	−8.00145	+	1.55509i	−0.327752	+	0.0636991i
$597$	35.9365	+	19.5127i	1.47078	+	0.798601i
$598$	0.0746756	+	0.0615595i	0.00305371	+	0.00251736i
$599$	−41.0068			−1.67549			−0.837747	−	0.546059i	$-0.816128\pi$
$599$	−41.0068			−1.67549			−0.837747	+	0.546059i	$0.816128\pi$
$600$	2.66794	+	4.10879i	0.108918	+	0.167740i
$601$	−37.2130			−1.51795			−0.758974	−	0.651121i	$-0.774299\pi$
$601$	−37.2130			−1.51795			−0.758974	+	0.651121i	$0.774299\pi$
$602$	3.74680	+	3.08871i	0.152708	+	0.125887i
$603$	−17.9190	+	11.6359i	−0.729718	+	0.473850i
$604$	−13.6663	+	2.65605i	−0.556072	+	0.108073i
$605$		−	6.68736i		−	0.271880i
$606$	1.66894	+	4.13114i	0.0677961	+	0.167816i
$607$		−	4.07839i		−	0.165537i	−0.996569	−	0.0827685i	$-0.973624\pi$
$607$		−	4.07839i		−	0.165537i	0.996569	−	0.0827685i	$-0.0263762\pi$
$608$	2.97085	−	9.42004i	0.120484	−	0.382033i
$609$	−7.67428	+	14.1337i	−0.310977	+	0.572726i
$610$	−7.52613	+	9.12966i	−0.304724	+	0.369649i
$611$	0.828973			0.0335367
$612$	−4.51266	−	4.67357i	−0.182414	−	0.188918i
$613$	−42.0474			−1.69828			−0.849139	−	0.528169i	$-0.822879\pi$
$613$	−42.0474			−1.69828			−0.849139	+	0.528169i	$0.822879\pi$
$614$	−10.3004	+	12.4950i	−0.415689	+	0.504257i
$615$	7.99182	−	14.7185i	0.322261	−	0.593508i
$616$	5.16185	+	2.80294i	0.207977	+	0.112933i
$617$			16.9882i			0.683917i	0.939715	+	0.341959i	$0.111090\pi$
$617$			16.9882i			0.683917i	−0.939715	+	0.341959i	$0.888910\pi$
$618$	17.9172	+	44.3506i	0.720736	+	1.78404i
$619$			18.8674i			0.758344i	0.925326	+	0.379172i	$0.123791\pi$
$619$			18.8674i			0.758344i	−0.925326	+	0.379172i	$0.876209\pi$
$620$	−4.14632	−	21.3341i	−0.166520	−	0.856800i
$621$	0.0911875	−	0.00717204i	0.00365923	−	0.000287804i
$622$	−12.5093	−	10.3122i	−0.501578	−	0.413481i
$623$	1.16319			0.0466020
$624$	3.05088	−	26.7600i	0.122133	−	1.07126i
$625$	1.00000			0.0400000
$626$	11.7370	+	9.67548i	0.469103	+	0.386710i
$627$	5.51943	+	2.99693i	0.220425	+	0.119686i
$628$	−6.97095	−	35.8678i	−0.278171	−	1.43128i
$629$		−	7.00287i		−	0.279223i
$630$	−0.480479	+	4.21535i	−0.0191428	+	0.167943i
$631$		−	19.6701i		−	0.783055i	−0.920166	−	0.391528i	$-0.871947\pi$
$631$		−	19.6701i		−	0.783055i	0.920166	−	0.391528i	$-0.128053\pi$
$632$	−5.80974	−	3.15475i	−0.231099	−	0.125489i
$633$	20.7908	+	11.2889i	0.826360	+	0.448695i
$634$	26.2975	−	31.9005i	1.04441	−	1.26693i
$635$	15.8920			0.630656
$636$	8.26789	−	26.2183i	0.327843	−	1.03962i
$637$	−3.88750			−0.154028
$638$	−17.3462	+	21.0421i	−0.686744	+	0.833063i
$639$	−7.26350	−	11.1856i	−0.287340	−	0.442496i
$640$	11.2409	+	1.28185i	0.444334	+	0.0506695i
$641$			9.20814i			0.363700i	0.983326	+	0.181850i	$0.0582085\pi$
$641$			9.20814i			0.363700i	−0.983326	+	0.181850i	$0.941792\pi$
$642$	−39.0297	+	15.7676i	−1.54038	+	0.622299i
$643$			25.9331i			1.02270i	0.859372	+	0.511351i	$0.170855\pi$
$643$			25.9331i			1.02270i	−0.859372	+	0.511351i	$0.829145\pi$
$644$	−0.0345598	+	0.00671675i	−0.00136185	+	0.000264677i
$645$	−2.83780	+	5.22637i	−0.111738	+	0.205788i
$646$	2.06311	+	1.70074i	0.0811718	+	0.0669148i
$647$	−27.5894			−1.08465			−0.542326	−	0.840168i	$-0.682456\pi$
$647$	−27.5894			−1.08465			−0.542326	+	0.840168i	$0.682456\pi$
$648$	−15.4943	−	20.1972i	−0.608676	−	0.793419i
$649$	−6.19061			−0.243003
$650$	−4.24215	−	3.49706i	−0.166391	−	0.137166i
$651$	8.98117	−	16.5406i	0.352000	−	0.648277i
$652$	8.38069	−	1.62880i	0.328213	−	0.0637886i
$653$			14.0786i			0.550939i	0.961310	+	0.275470i	$0.0888333\pi$
$653$			14.0786i			0.550939i	−0.961310	+	0.275470i	$0.911167\pi$
$654$	39.6339	−	16.0117i	1.54981	−	0.626108i
$655$		−	13.2810i		−	0.518930i
$656$	−14.4872	−	35.8628i	−0.565630	−	1.40021i
$657$	−9.18463	−	14.1441i	−0.358327	−	0.551815i
$658$	−0.191824	+	0.232695i	−0.00747808	+	0.00907138i
$659$	−34.5048			−1.34412			−0.672058	−	0.740499i	$-0.734589\pi$
$659$	−34.5048			−1.34412			−0.672058	+	0.740499i	$0.734589\pi$
$660$	−2.16354	+	6.86081i	−0.0842158	+	0.267057i
$661$	40.0292			1.55695			0.778477	−	0.627673i	$-0.215993\pi$
$661$	40.0292			1.55695			0.778477	+	0.627673i	$0.215993\pi$
$662$	−3.54066	+	4.29504i	−0.137612	+	0.166932i
$663$	6.40712	+	3.47892i	0.248832	+	0.135110i
$664$	−5.27264	+	9.71003i	−0.204618	+	0.376822i
$665$		−	1.74609i		−	0.0677106i
$666$	3.10751	−	27.2629i	0.120414	−	1.05641i
$667$		−	0.163453i		−	0.00632893i
$668$	−7.54968	−	38.8455i	−0.292106	−	1.50298i
$669$	−31.0868	−	16.8794i	−1.20189	−	0.652597i
$670$	7.77155	+	6.40655i	0.300241	+	0.247507i
$671$	−17.3744			−0.670732
$672$	6.80563	+	7.04865i	0.262533	+	0.271908i
$673$	−4.17387			−0.160891			−0.0804454	−	0.996759i	$-0.525634\pi$
$673$	−4.17387			−0.160891			−0.0804454	+	0.996759i	$0.525634\pi$
$674$	−2.75887	−	2.27430i	−0.106268	−	0.0876028i
$675$	−5.18015	+	0.407427i	−0.199384	+	0.0156819i
$676$	0.806099	+	4.14764i	0.0310038	+	0.159525i
$677$			49.7553i			1.91225i	0.292956	+	0.956126i	$0.405361\pi$
$677$			49.7553i			1.91225i	−0.292956	+	0.956126i	$0.594639\pi$
$678$	−3.10612	−	7.68859i	−0.119290	−	0.295278i
$679$			11.4536i			0.439550i
$680$	−1.46143	+	2.69136i	−0.0560434	+	0.103209i
$681$	0.724448	−	1.33421i	0.0277609	−	0.0511272i
$682$	20.3002	−	24.6254i	0.777335	−	0.942957i
$683$	0.268279			0.0102654			0.00513270	−	0.999987i	$-0.498366\pi$
$683$	0.268279			0.0102654			0.00513270	+	0.999987i	$0.498366\pi$
$684$	7.27717	+	7.53666i	0.278250	+	0.288171i
$685$	−15.2183			−0.581463
$686$	0.899566	−	1.09123i	0.0343456	−	0.0416633i
$687$	5.51780	−	10.1621i	0.210517	−	0.387709i
$688$	5.14423	+	12.7345i	0.196122	+	0.485497i
$689$			30.8511i			1.17533i
$690$	−0.0161514	−	0.0399797i	−0.000614874	−	0.00152200i
$691$			40.1141i			1.52601i	0.646392	+	0.763006i	$0.276277\pi$
$691$			40.1141i			1.52601i	−0.646392	+	0.763006i	$0.723723\pi$
$692$	30.9850	−	6.02198i	1.17787	−	0.228921i
$693$	−5.22509	+	3.39297i	−0.198485	+	0.128888i
$694$	35.6309	+	29.3727i	1.35253	+	1.11497i
$695$	13.5504			0.513995
$696$	−38.1517	+	24.7728i	−1.44614	+	0.939012i
$697$	10.4700			0.396579
$698$	−0.626811	−	0.516718i	−0.0237252	−	0.0195581i
$699$	9.28165	+	5.03972i	0.351064	+	0.190620i
$700$	1.96327	−	0.381563i	0.0742044	−	0.0144217i
$701$		−	12.1460i		−	0.458748i	−0.973338	−	0.229374i	$-0.926332\pi$
$701$		−	12.1460i		−	0.458748i	0.973338	−	0.229374i	$-0.0736678\pi$
$702$	23.3998	+	16.3869i	0.883168	+	0.618485i
$703$			11.2929i			0.425920i
$704$	9.04720	+	13.9340i	0.340979	+	0.525158i
$705$	−0.324583	−	0.176241i	−0.0122245	−	0.00663762i
$706$	−13.7182	+	16.6410i	−0.516291	+	0.626293i
$707$	1.81896			0.0684090
$708$	−9.84840	−	3.10567i	−0.370125	−	0.116718i
$709$	19.4332			0.729829			0.364915	−	0.931041i	$-0.381098\pi$
$709$	19.4332			0.729829			0.364915	+	0.931041i	$0.381098\pi$
$710$	−3.99918	+	4.85126i	−0.150087	+	0.182064i
$711$	5.88091	−	3.81883i	0.220552	−	0.143217i
$712$	2.89123	+	1.56997i	0.108353	+	0.0588370i
$713$			0.191288i			0.00716381i
$714$	−2.45915	+	0.993473i	−0.0920313	+	0.0371798i
$715$		−	8.07312i		−	0.301918i
$716$	8.24078	+	42.4015i	0.307972	+	1.58462i
$717$	−0.847716	+	1.56124i	−0.0316585	+	0.0583054i
$718$	−7.42691	−	6.12245i	−0.277170	−	0.228488i
$719$	−40.9225			−1.52615			−0.763076	−	0.646309i	$-0.776312\pi$
$719$	−40.9225			−1.52615			−0.763076	+	0.646309i	$0.776312\pi$
$720$	−6.88379	+	9.82921i	−0.256544	+	0.366313i
$721$	19.5278			0.727252
$722$	17.4064	+	14.3491i	0.647798	+	0.534019i
$723$	2.81543	−	5.18518i	0.104707	−	0.192839i
$724$	8.08866	+	41.6187i	0.300613	+	1.54675i
$725$			9.28540i			0.344851i
$726$	15.1880	−	6.13582i	0.563681	−	0.227722i
$727$		−	8.73982i		−	0.324142i	−0.986779	−	0.162071i	$-0.948183\pi$
$727$		−	8.73982i		−	0.324142i	0.986779	−	0.162071i	$-0.0518173\pi$
$728$	−9.66281	−	5.24700i	−0.358128	−	0.194467i
$729$	26.6680	−	4.22107i	0.987704	−	0.156336i
$730$	−5.05693	+	6.13437i	−0.187165	+	0.227043i
$731$	−3.71777			−0.137507
$732$	−27.6403	−	8.71631i	−1.02161	−	0.322164i
$733$	−28.1014			−1.03795			−0.518974	−	0.854790i	$-0.673686\pi$
$733$	−28.1014			−1.03795			−0.518974	+	0.854790i	$0.673686\pi$
$734$	−3.44418	+	4.17801i	−0.127127	+	0.154213i
$735$	1.52214	+	0.826488i	0.0561451	+	0.0304855i
$736$	−0.0949681	−	0.0299506i	−0.00350057	−	0.00110399i
$737$			14.7898i			0.544791i
$738$	40.7607	+	4.64605i	1.50042	+	0.171023i
$739$		−	40.7137i		−	1.49768i	−0.662751	−	0.748840i	$-0.730611\pi$
$739$		−	40.7137i		−	1.49768i	0.662751	−	0.748840i	$-0.269389\pi$
$740$	−12.6975	+	2.46777i	−0.466768	+	0.0907170i
$741$	−10.3322	−	5.61015i	−0.379563	−	0.206094i
$742$	−8.65998	−	7.13894i	−0.317918	−	0.262079i
$743$	−13.9305			−0.511062			−0.255531	−	0.966801i	$-0.582250\pi$
$743$	−13.9305			−0.511062			−0.255531	+	0.966801i	$0.582250\pi$
$744$	44.6488	−	28.9915i	1.63690	−	1.06288i
$745$	−4.07558			−0.149318
$746$	−1.66868	−	1.37559i	−0.0610947	−	0.0503640i
$747$	−6.38256	−	9.82899i	−0.233526	−	0.359624i
$748$	−4.41457	+	0.857977i	−0.161413	+	0.0313708i
$749$			17.1849i			0.627924i
$750$	0.917526	+	2.27116i	0.0335033	+	0.0829309i
$751$			35.7046i			1.30288i	0.758700	+	0.651440i	$0.225835\pi$
$751$			35.7046i			1.30288i	−0.758700	+	0.651440i	$0.774165\pi$
$752$	−0.790872	+	0.319482i	−0.0288401	+	0.0116503i
$753$	12.4976	−	23.0169i	0.455439	−	0.838781i
$754$	32.4716	−	39.3901i	1.18255	−	1.43450i
$755$	−6.96098			−0.253336
$756$	−10.0146	+	2.77644i	−0.364226	+	0.100978i
$757$	1.44168			0.0523987			0.0261994	−	0.999657i	$-0.491660\pi$
$757$	1.44168			0.0523987			0.0261994	+	0.999657i	$0.491660\pi$
$758$	12.7264	−	15.4379i	0.462244	−	0.560730i
$759$	0.0302135	−	0.0556441i	0.00109668	−	0.00201975i
$760$	2.35673	−	4.34012i	0.0854874	−	0.157433i
$761$		−	29.6645i		−	1.07534i	−0.843156	−	0.537670i	$-0.819305\pi$
$761$		−	29.6645i		−	1.07534i	0.843156	−	0.537670i	$-0.180695\pi$
$762$	14.5813	+	36.0933i	0.528226	+	1.30752i
$763$		−	17.4510i		−	0.631768i
$764$	−7.31053	−	37.6150i	−0.264486	−	1.36086i
$765$	−1.76907	−	2.72433i	−0.0639609	−	0.0984984i
$766$	30.3316	+	25.0041i	1.09592	+	0.903436i
$767$	11.5886			0.418441
$768$	7.40250	+	26.7059i	0.267115	+	0.963665i
$769$	−30.7667			−1.10948			−0.554739	−	0.832025i	$-0.687182\pi$
$769$	−30.7667			−1.10948			−0.554739	+	0.832025i	$0.687182\pi$
$770$	2.26615	+	1.86812i	0.0816662	+	0.0673223i
$771$	−11.9598	−	6.49392i	−0.430723	−	0.233873i
$772$	4.45014	+	22.8974i	0.160164	+	0.824096i
$773$		−	9.78554i		−	0.351962i	−0.984394	−	0.175981i	$-0.943690\pi$
$773$		−	9.78554i		−	0.351962i	0.984394	−	0.175981i	$-0.0563097\pi$
$774$	−14.4737	−	1.64976i	−0.520245	−	0.0592992i
$775$		−	10.8667i		−	0.390342i
$776$	−15.4591	+	28.4693i	−0.554950	+	1.02199i
$777$	−9.84449	−	5.34533i	−0.353169	−	0.191763i
$778$	31.3497	−	38.0292i	1.12394	−	1.36341i
$779$	−16.8840			−0.604934
$780$	4.05008	−	12.8432i	0.145016	−	0.459861i
$781$	−9.23230			−0.330358
$782$	0.0171460	−	0.0207992i	0.000613140	−	0.000743777i
$783$	−3.78313	−	48.0998i	−0.135198	−	1.71895i
$784$	3.70882	−	1.49822i	0.132458	−	0.0535078i
$785$		−	18.2695i		−	0.652065i
$786$	30.1631	−	12.1856i	1.07588	−	0.434647i
$787$		−	29.5634i		−	1.05382i	−0.849920	−	0.526911i	$-0.823350\pi$
$787$		−	29.5634i		−	1.05382i	0.849920	−	0.526911i	$-0.176650\pi$
$788$	48.7387	−	9.47242i	1.73624	−	0.337441i
$789$	−10.0602	+	18.5279i	−0.358153	+	0.659610i
$790$	−2.55058	−	2.10260i	−0.0907456	−	0.0748070i
$791$	−3.38532			−0.120368
$792$	−17.5671	+	1.38123i	−0.624219	+	0.0490799i
$793$	32.5243			1.15497
$794$	34.3327	+	28.3025i	1.21842	+	1.00442i
$795$	6.55900	−	12.0797i	0.232624	−	0.428423i
$796$	46.3510	−	9.00838i	1.64287	−	0.319294i
$797$			11.0944i			0.392985i	0.980505	+	0.196492i	$0.0629551\pi$
$797$			11.0944i			0.392985i	−0.980505	+	0.196492i	$0.937045\pi$
$798$	3.96565	−	1.60209i	0.140383	−	0.0567132i
$799$		−	0.230892i		−	0.00816836i
$800$	5.39492	+	1.70143i	0.190739	+	0.0601545i
$801$	−2.92665	+	1.90045i	−0.103408	+	0.0671491i
$802$	−26.5335	+	32.1868i	−0.936930	+	1.13655i
$803$	−11.6742			−0.411972
$804$	−7.41968	+	23.5286i	−0.261672	+	0.829789i
$805$	−0.0176032			−0.000620433
$806$	−38.0013	+	46.0980i	−1.33854	+	1.62373i
$807$	−13.4045	−	7.27836i	−0.471862	−	0.256210i
$808$	4.52123	+	2.45507i	0.159056	+	0.0863692i
$809$		−	36.6219i		−	1.28756i	−0.765211	−	0.643779i	$-0.777366\pi$
$809$		−	36.6219i		−	1.28756i	0.765211	−	0.643779i	$-0.222634\pi$
$810$	−5.67826	−	11.3911i	−0.199514	−	0.400243i
$811$		−	3.51939i		−	0.123583i	−0.998089	−	0.0617913i	$-0.980319\pi$
$811$		−	3.51939i		−	0.123583i	0.998089	−	0.0617913i	$-0.0196813\pi$
$812$	3.54297	+	18.2297i	0.124334	+	0.639737i
$813$	−1.93318	−	1.04967i	−0.0677996	−	0.0368136i
$814$	−14.6563	−	12.0821i	−0.513705	−	0.423478i
$815$	4.26875			0.149528
$816$	−7.45339	−	0.849754i	−0.260921	−	0.0297473i
$817$	5.99532			0.209750
$818$	−34.2450	−	28.2302i	−1.19735	−	0.987047i
$819$	9.78120	−	6.35152i	0.341783	−	0.221940i
$820$	−3.68957	−	18.9840i	−0.128845	−	0.662950i
$821$		−	11.5056i		−	0.401549i	−0.979637	−	0.200775i	$-0.935654\pi$
$821$		−	11.5056i		−	0.401549i	0.979637	−	0.200775i	$-0.0643459\pi$
$822$	−13.9632	−	34.5632i	−0.487023	−	1.20553i
$823$		−	11.6775i		−	0.407051i	−0.979070	−	0.203525i	$-0.934760\pi$
$823$		−	11.6775i		−	0.407051i	0.979070	−	0.203525i	$-0.0652399\pi$
$824$	48.5385	+	26.3569i	1.69092	+	0.918185i
$825$	−1.71636	+	3.16102i	−0.0597560	+	0.110052i
$826$	−2.68160	+	3.25295i	−0.0933049	+	0.113185i
$827$	0.702333			0.0244225			0.0122113	−	0.999925i	$-0.496113\pi$
$827$	0.702333			0.0244225			0.0122113	+	0.999925i	$0.496113\pi$
$828$	0.0759808	−	0.0733648i	0.00264051	−	0.00254960i
$829$	36.4866			1.26723			0.633615	−	0.773648i	$-0.281570\pi$
$829$	36.4866			1.26723			0.633615	+	0.773648i	$0.281570\pi$
$830$	−3.51415	+	4.26288i	−0.121978	+	0.147967i
$831$	16.2971	−	30.0143i	0.565340	−	1.04119i
$832$	−16.9361	−	26.0840i	−0.587153	−	0.904302i
$833$			1.08277i			0.0375159i
$834$	12.4328	+	30.7750i	0.430513	+	1.06565i
$835$		−	19.7862i		−	0.684729i
$836$	7.11899	−	1.38358i	0.246215	−	0.0478523i
$837$	4.42738	+	56.2910i	0.153033	+	1.94570i
$838$	5.34020	+	4.40224i	0.184474	+	0.152073i
$839$	31.6506			1.09270			0.546349	−	0.837557i	$-0.316017\pi$
$839$	31.6506			1.09270			0.546349	+	0.837557i	$0.316017\pi$
$840$	2.66794	+	4.10879i	0.0920525	+	0.141767i
$841$	−57.2187			−1.97306
$842$	−15.4717	−	12.7542i	−0.533189	−	0.439540i
$843$	11.2800	+	6.12477i	0.388503	+	0.210948i
$844$	26.8161	−	5.21174i	0.923047	−	0.179395i
$845$			2.11262i			0.0726764i
$846$	0.102458	−	0.898884i	0.00352257	−	0.0309043i
$847$		−	6.68736i		−	0.229780i
$848$	−11.8898	−	29.4331i	−0.408299	−	1.01074i
$849$	−8.22547	−	4.46624i	−0.282297	−	0.153281i
$850$	−0.974026	+	1.18155i	−0.0334088	+	0.0405270i
$851$	0.113849			0.00390271
$852$	−14.6873	−	4.63161i	−0.503179	−	0.158676i
$853$	−5.58114			−0.191094			−0.0955472	−	0.995425i	$-0.530460\pi$
$853$	−5.58114			−0.191094			−0.0955472	+	0.995425i	$0.530460\pi$
$854$	−7.52613	+	9.12966i	−0.257539	+	0.312411i
$855$	2.85283	+	4.39329i	0.0975646	+	0.150247i
$856$	−23.1947	+	42.7151i	−0.792780	+	1.45997i
$857$		−	40.4096i		−	1.38036i	−0.723636	−	0.690182i	$-0.757530\pi$
$857$		−	40.4096i		−	1.38036i	0.723636	−	0.690182i	$-0.242470\pi$
$858$	18.3353	−	7.40730i	0.625957	−	0.252881i
$859$			3.55494i			0.121293i	0.998159	+	0.0606465i	$0.0193162\pi$
$859$			3.55494i			0.121293i	−0.998159	+	0.0606465i	$0.980684\pi$
$860$	1.31012	+	6.74099i	0.0446747	+	0.229866i
$861$	7.99182	−	14.7185i	0.272360	−	0.501606i
$862$	17.3661	+	14.3159i	0.591493	+	0.487603i
$863$	−39.1611			−1.33306			−0.666530	−	0.745479i	$-0.732221\pi$
$863$	−39.1611			−1.33306			−0.666530	+	0.745479i	$0.732221\pi$
$864$	−28.6397	−	6.61561i	−0.974343	−	0.225068i
$865$	15.7824			0.536618
$866$	26.0242	+	21.4533i	0.884338	+	0.729013i
$867$	−13.0813	+	24.0919i	−0.444265	+	0.818202i
$868$	−4.14632	−	21.3341i	−0.140735	−	0.724128i
$869$		−	4.85394i		−	0.164659i
$870$	−21.0886	+	8.51959i	−0.714970	+	0.288841i
$871$		−	27.6861i		−	0.938107i
$872$	23.5538	−	43.3764i	0.797633	−	1.46891i
$873$	−18.7133	−	28.8181i	−0.633350	−	0.975345i
$874$	−0.0276499	+	0.0335410i	−0.000935271	+	0.00113454i
$875$	1.00000			0.0338062
$876$	−18.5720	−	5.85663i	−0.627489	−	0.197877i
$877$	30.8860			1.04295			0.521473	−	0.853268i	$-0.325383\pi$
$877$	30.8860			1.04295			0.521473	+	0.853268i	$0.325383\pi$
$878$	−2.80073	+	3.39746i	−0.0945200	+	0.114659i
$879$	−31.8362	−	17.2863i	−1.07381	−	0.583054i
$880$	3.11134	+	7.70207i	0.104883	+	0.259637i
$881$		−	12.3355i		−	0.415594i	−0.978172	−	0.207797i	$-0.933371\pi$
$881$		−	12.3355i		−	0.415594i	0.978172	−	0.207797i	$-0.0666293\pi$
$882$	−0.480479	+	4.21535i	−0.0161786	+	0.141938i
$883$		−	51.1513i		−	1.72138i	−0.509130	−	0.860690i	$-0.670033\pi$
$883$		−	51.1513i		−	1.72138i	0.509130	−	0.860690i	$-0.329967\pi$
$884$	8.26393	−	1.60611i	0.277946	−	0.0540192i
$885$	−4.53750	−	2.46376i	−0.152526	−	0.0828184i
$886$	38.6757	+	31.8827i	1.29933	+	1.07112i
$887$	4.10786			0.137928			0.0689642	−	0.997619i	$-0.478031\pi$
$887$	4.10786			0.137928			0.0689642	+	0.997619i	$0.478031\pi$
$888$	−17.2549	−	26.5737i	−0.579038	−	0.891754i
$889$	15.8920			0.533002
$890$	1.26930	+	1.04636i	0.0425471	+	0.0350741i
$891$	7.60313	−	17.0739i	0.254714	−	0.571996i
$892$	−40.0959	+	7.79270i	−1.34251	+	0.260919i
$893$			0.372339i			0.0124598i
$894$	−3.73945	−	9.25629i	−0.125066	−	0.309577i
$895$			21.5974i			0.721922i
$896$	11.2409	+	1.28185i	0.375531	+	0.0428235i
$897$	−0.0565587	+	0.104164i	−0.00188844	+	0.00347794i
$898$	−22.8664	+	27.7384i	−0.763061	+	0.925641i
$899$	100.901			3.36525
$900$	−4.31629	+	4.16769i	−0.143876	+	0.138923i
$901$	8.59288			0.286270
$902$	18.0640	−	21.9127i	0.601465	−	0.729614i
$903$	−2.83780	+	5.22637i	−0.0944360	+	0.173923i
$904$	−8.41460	−	4.56921i	−0.279865	−	0.151970i
$905$			21.1987i			0.704670i
$906$	−6.38688	−	15.8095i	−0.212190	−	0.525234i
$907$		−	28.5278i		−	0.947252i	−0.880726	−	0.473626i	$-0.842945\pi$
$907$		−	28.5278i		−	0.947252i	0.880726	−	0.473626i	$-0.157055\pi$
$908$	−0.334454	−	1.72088i	−0.0110993	−	0.0571093i
$909$	−4.57662	+	2.97188i	−0.151797	+	0.0985710i
$910$	−4.24215	−	3.49706i	−0.140626	−	0.115926i
$911$	31.7510			1.05196			0.525979	−	0.850497i	$-0.323699\pi$
$911$	31.7510			1.05196			0.525979	+	0.850497i	$0.323699\pi$
$912$	12.0194	+	1.37032i	0.398003	+	0.0453760i
$913$	−8.11257			−0.268487
$914$	12.5716	+	10.3636i	0.415833	+	0.342796i
$915$	−12.7349	−	6.91473i	−0.421001	−	0.228594i
$916$	−2.54739	−	13.1071i	−0.0841682	−	0.433072i
$917$		−	13.2810i		−	0.438576i
$918$	4.56421	−	6.51748i	0.150641	−	0.215109i
$919$			48.0995i			1.58665i	0.608795	+	0.793327i	$0.291653\pi$
$919$			48.0995i			1.58665i	−0.608795	+	0.793327i	$0.708347\pi$
$920$	−0.0437549	−	0.0237593i	−0.00144255	−	0.000783322i
$921$	−17.4291	−	9.46361i	−0.574309	−	0.311837i
$922$	10.4152	−	12.6342i	0.343005	−	0.416086i
$923$	17.2826			0.568862
$924$	−2.16354	+	6.86081i	−0.0711753	+	0.225704i
$925$	−6.46752			−0.212651
$926$	15.1445	−	18.3712i	0.497679	−	0.603716i
$927$	−49.1331	+	31.9051i	−1.61374	+	1.04790i
$928$	−15.7984	+	50.0940i	−0.518609	+	1.64442i
$929$			41.1804i			1.35108i	0.737321	+	0.675542i	$0.236090\pi$
$929$			41.1804i			1.35108i	−0.737321	+	0.675542i	$0.763910\pi$
$930$	24.6799	−	9.97044i	0.809285	−	0.326944i
$931$		−	1.74609i		−	0.0572259i
$932$	11.9715	−	2.32668i	0.392140	−	0.0762129i
$933$	9.47447	−	17.4491i	0.310180	−	0.571258i
$934$	−9.30224	−	7.66840i	−0.304379	−	0.250918i
$935$	−2.24859			−0.0735366
$936$	32.8850	−	2.58562i	1.07488	−	0.0845137i
$937$	11.5893			0.378606			0.189303	−	0.981919i	$-0.439377\pi$
$937$	11.5893			0.378606			0.189303	+	0.981919i	$0.439377\pi$
$938$	7.77155	+	6.40655i	0.253750	+	0.209181i
$939$	−8.88948	+	16.3717i	−0.290097	+	0.534271i
$940$	−0.418648	+	0.0813649i	−0.0136548	+	0.00265383i
$941$		−	31.7808i		−	1.03602i	−0.855373	−	0.518012i	$-0.826672\pi$
$941$		−	31.7808i		−	1.03602i	0.855373	−	0.518012i	$-0.173328\pi$
$942$	41.4928	−	16.7627i	1.35191	−	0.546158i
$943$			0.170216i			0.00554301i
$944$	−11.0560	+	4.46619i	−0.359841	+	0.145362i
$945$	−5.18015	+	0.407427i	−0.168510	+	0.0132536i
$946$	−6.41430	+	7.78095i	−0.208547	+	0.252980i
$947$	−0.973758			−0.0316429			−0.0158214	−	0.999875i	$-0.505036\pi$
$947$	−0.973758			−0.0316429			−0.0158214	+	0.999875i	$0.505036\pi$
$948$	2.43510	−	7.72195i	0.0790883	−	0.250797i
$949$	21.8536			0.709399
$950$	1.57073	−	1.90539i	0.0509611	−	0.0618190i
$951$	44.4976	+	24.1612i	1.44293	+	0.783481i
$952$	−1.46143	+	2.69136i	−0.0473653	+	0.0872274i
$953$			19.4218i			0.629133i	0.949235	+	0.314566i	$0.101859\pi$
$953$			19.4218i			0.629133i	−0.949235	+	0.314566i	$0.898141\pi$
$954$	33.4529	+	3.81308i	1.08308	+	0.123453i
$955$		−	19.1594i		−	0.619984i
$956$	0.391363	+	2.01369i	0.0126576	+	0.0651274i
$957$	−29.3513	−	15.9371i	−0.948793	−	0.515173i
$958$	−8.93392	−	7.36476i	−0.288642	−	0.237945i
$959$	−15.2183			−0.491426
$960$	1.08577	+	13.8138i	0.0350432	+	0.445839i
$961$	−87.0843			−2.80917
$962$	27.4362	+	22.6173i	0.884579	+	0.729211i
$963$	−28.0773	−	43.2385i	−0.904780	−	1.39334i
$964$	−1.29979	−	6.68786i	−0.0418636	−	0.215402i
$965$			11.6629i			0.375443i
$966$	−0.0161514	−	0.0399797i	−0.000519664	−	0.00128633i
$967$			27.4809i			0.883728i	0.897082	+	0.441864i	$0.145683\pi$
$967$			27.4809i			0.883728i	−0.897082	+	0.441864i	$0.854317\pi$
$968$	9.02601	−	16.6222i	0.290107	−	0.534257i
$969$	−1.56258	+	2.87780i	−0.0501973	+	0.0924483i
$970$	−10.3033	+	12.4985i	−0.330819	+	0.401304i
$971$	38.6485			1.24029			0.620144	−	0.784488i	$-0.287074\pi$
$971$	38.6485			1.24029			0.620144	+	0.784488i	$0.287074\pi$
$972$	20.6610	−	23.3478i	0.662703	−	0.748882i
$973$	13.5504			0.434405
$974$	8.67978	−	10.5291i	0.278118	−	0.337375i
$975$	3.21297	−	5.91732i	0.102897	−	0.189506i
$976$	−31.0295	+	12.5347i	−0.993229	+	0.401226i
$977$			51.1792i			1.63737i	0.574243	+	0.818685i	$0.305296\pi$
$977$			51.1792i			1.63737i	−0.574243	+	0.818685i	$0.694704\pi$
$978$	3.91669	+	9.69499i	0.125242	+	0.310012i
$979$			2.41558i			0.0772021i
$980$	1.96327	−	0.381563i	0.0627142	−	0.0121886i
$981$	28.5120	+	43.9078i	0.910318	+	1.40187i
$982$	−11.3159	−	9.32840i	−0.361106	−	0.297681i
$983$	6.19182			0.197489			0.0987443	−	0.995113i	$-0.468517\pi$
$983$	6.19182			0.197489			0.0987443	+	0.995113i	$0.468517\pi$
$984$	39.7303	−	25.7979i	1.26656	−	0.822407i
$985$	24.8253			0.791000
$986$	−10.9712	−	9.04422i	−0.349394	−	0.288027i
$987$	−0.324583	−	0.176241i	−0.0103316	−	0.00560982i
$988$	−13.3265	+	2.59003i	−0.423973	+	0.0823997i
$989$		−	0.0604418i		−	0.00192194i
$990$	−8.75397	−	0.997807i	−0.278219	−	0.0317124i
$991$			5.68339i			0.180539i	0.995917	+	0.0902695i	$0.0287728\pi$
$991$			5.68339i			0.180539i	−0.995917	+	0.0902695i	$0.971227\pi$
$992$	18.4888	−	58.6248i	0.587021	−	1.86134i
$993$	−5.99110	−	3.25303i	−0.190122	−	0.103232i
$994$	−3.99918	+	4.85126i	−0.126846	+	0.153873i
$995$	23.6092			0.748460
$996$	−12.9060	−	4.06987i	−0.408942	−	0.128959i
$997$	15.0648			0.477106			0.238553	−	0.971129i	$-0.423327\pi$
$997$	15.0648			0.477106			0.238553	+	0.971129i	$0.423327\pi$
$998$	−25.9572	+	31.4876i	−0.821659	+	0.996724i
$999$	33.5028	−	2.63505i	1.05998	−	0.0833692i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.n.b.71.18	yes	24
3.2	odd	2		420.2.n.a.71.7	✓	24
4.3	odd	2		420.2.n.a.71.8	yes	24
12.11	even	2	inner	420.2.n.b.71.17	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.n.a.71.7	✓	24	3.2	odd	2
420.2.n.a.71.8	yes	24	4.3	odd	2
420.2.n.b.71.17	yes	24	12.11	even	2	inner
420.2.n.b.71.18	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)

\(f(q)\)	\(=\)	\(q+(1.09123 + 0.899566i) q^{2} +(-0.826488 + 1.52214i) q^{3} +(0.381563 + 1.96327i) q^{4} +1.00000i q^{5} +(-2.27116 + 0.917526i) q^{6} +1.00000i q^{7} +(-1.34971 + 2.48561i) q^{8} +(-1.63383 - 2.51607i) q^{9} +O(q^{10})\)	\(q+(1.09123 + 0.899566i) q^{2} +(-0.826488 + 1.52214i) q^{3} +(0.381563 + 1.96327i) q^{4} +1.00000i q^{5} +(-2.27116 + 0.917526i) q^{6} +1.00000i q^{7} +(-1.34971 + 2.48561i) q^{8} +(-1.63383 - 2.51607i) q^{9} +(-0.899566 + 1.09123i) q^{10} -2.07669 q^{11} +(-3.30373 - 1.04182i) q^{12} +3.88750 q^{13} +(-0.899566 + 1.09123i) q^{14} +(-1.52214 - 0.826488i) q^{15} +(-3.70882 + 1.49822i) q^{16} -1.08277i q^{17} +(0.480479 - 4.21535i) q^{18} +1.74609i q^{19} +(-1.96327 + 0.381563i) q^{20} +(-1.52214 - 0.826488i) q^{21} +(-2.26615 - 1.86812i) q^{22} +0.0176032 q^{23} +(-2.66794 - 4.10879i) q^{24} -1.00000 q^{25} +(4.24215 + 3.49706i) q^{26} +(5.18015 - 0.407427i) q^{27} +(-1.96327 + 0.381563i) q^{28} -9.28540i q^{29} +(-0.917526 - 2.27116i) q^{30} +10.8667i q^{31} +(-5.39492 - 1.70143i) q^{32} +(1.71636 - 3.16102i) q^{33} +(0.974026 - 1.18155i) q^{34} -1.00000 q^{35} +(4.31629 - 4.16769i) q^{36} +6.46752 q^{37} +(-1.57073 + 1.90539i) q^{38} +(-3.21297 + 5.91732i) q^{39} +(-2.48561 - 1.34971i) q^{40} +9.66961i q^{41} +(-0.917526 - 2.27116i) q^{42} -3.43356i q^{43} +(-0.792388 - 4.07709i) q^{44} +(2.51607 - 1.63383i) q^{45} +(0.0192092 + 0.0158353i) q^{46} +0.213241 q^{47} +(0.784794 - 6.88361i) q^{48} -1.00000 q^{49} +(-1.09123 - 0.899566i) q^{50} +(1.64814 + 0.894900i) q^{51} +(1.48333 + 7.63218i) q^{52} +7.93599i q^{53} +(6.01924 + 4.21529i) q^{54} -2.07669i q^{55} +(-2.48561 - 1.34971i) q^{56} +(-2.65780 - 1.44313i) q^{57} +(8.35283 - 10.1325i) q^{58} +2.98100 q^{59} +(1.04182 - 3.30373i) q^{60} +8.36640 q^{61} +(-9.77528 + 11.8580i) q^{62} +(2.51607 - 1.63383i) q^{63} +(-4.35655 - 6.70973i) q^{64} +3.88750i q^{65} +(4.71649 - 1.90542i) q^{66} -7.12183i q^{67} +(2.12577 - 0.413147i) q^{68} +(-0.0145489 + 0.0267946i) q^{69} +(-1.09123 - 0.899566i) q^{70} +4.44568 q^{71} +(8.45917 - 0.665112i) q^{72} +5.62152 q^{73} +(7.05755 + 5.81796i) q^{74} +(0.826488 - 1.52214i) q^{75} +(-3.42805 + 0.666245i) q^{76} -2.07669i q^{77} +(-8.82911 + 3.56688i) q^{78} +2.33735i q^{79} +(-1.49822 - 3.70882i) q^{80} +(-3.66118 + 8.22167i) q^{81} +(-8.69845 + 10.5518i) q^{82} +3.90649 q^{83} +(1.04182 - 3.30373i) q^{84} +1.08277 q^{85} +(3.08871 - 3.74680i) q^{86} +(14.1337 + 7.67428i) q^{87} +(2.80294 - 5.16185i) q^{88} -1.16319i q^{89} +(4.21535 + 0.480479i) q^{90} +3.88750i q^{91} +(0.00671675 + 0.0345598i) q^{92} +(-16.5406 - 8.98117i) q^{93} +(0.232695 + 0.191824i) q^{94} -1.74609 q^{95} +(7.04865 - 6.80563i) q^{96} +11.4536 q^{97} +(-1.09123 - 0.899566i) q^{98} +(3.39297 + 5.22509i) 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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