LMFDB - Embedded newform 420.2.n.b.71.7

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			71.7
Character	$\chi$	$=$	420.71
Dual form			420.2.n.b.71.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.859821 - 1.12281i) q^{2} +(-1.72451 - 0.161413i) q^{3} +(-0.521414 + 1.93084i) q^{4} -1.00000i q^{5} +(1.30154 + 2.07509i) q^{6} -1.00000i q^{7} +(2.61629 - 1.07472i) q^{8} +(2.94789 + 0.556719i) q^{9} +O(q^{10})$	\(q+(-0.859821 - 1.12281i) q^{2} +(-1.72451 - 0.161413i) q^{3} +(-0.521414 + 1.93084i) q^{4} -1.00000i q^{5} +(1.30154 + 2.07509i) q^{6} -1.00000i q^{7} +(2.61629 - 1.07472i) q^{8} +(2.94789 + 0.556719i) q^{9} +(-1.12281 + 0.859821i) q^{10} -5.30518 q^{11} +(1.21085 - 3.24559i) q^{12} -3.33407 q^{13} +(-1.12281 + 0.859821i) q^{14} +(-0.161413 + 1.72451i) q^{15} +(-3.45625 - 2.01353i) q^{16} +0.634962i q^{17} +(-1.90957 - 3.78861i) q^{18} +5.08185i q^{19} +(1.93084 + 0.521414i) q^{20} +(-0.161413 + 1.72451i) q^{21} +(4.56151 + 5.95672i) q^{22} +8.45161 q^{23} +(-4.68530 + 1.43107i) q^{24} -1.00000 q^{25} +(2.86670 + 3.74353i) q^{26} +(-4.99382 - 1.43590i) q^{27} +(1.93084 + 0.521414i) q^{28} +10.4606i q^{29} +(2.07509 - 1.30154i) q^{30} +4.35430i q^{31} +(0.710944 + 5.61200i) q^{32} +(9.14886 + 0.856327i) q^{33} +(0.712943 - 0.545954i) q^{34} -1.00000 q^{35} +(-2.61201 + 5.40161i) q^{36} -0.255252 q^{37} +(5.70596 - 4.36948i) q^{38} +(5.74965 + 0.538164i) q^{39} +(-1.07472 - 2.61629i) q^{40} +5.20097i q^{41} +(2.07509 - 1.30154i) q^{42} -6.21029i q^{43} +(2.76620 - 10.2434i) q^{44} +(0.556719 - 2.94789i) q^{45} +(-7.26687 - 9.48957i) q^{46} -13.0438 q^{47} +(5.63535 + 4.03025i) q^{48} -1.00000 q^{49} +(0.859821 + 1.12281i) q^{50} +(0.102491 - 1.09500i) q^{51} +(1.73843 - 6.43754i) q^{52} +8.71720i q^{53} +(2.68155 + 6.84173i) q^{54} +5.30518i q^{55} +(-1.07472 - 2.61629i) q^{56} +(0.820279 - 8.76372i) q^{57} +(11.7453 - 8.99428i) q^{58} +1.82137 q^{59} +(-3.24559 - 1.21085i) q^{60} -1.58269 q^{61} +(4.88906 - 3.74392i) q^{62} +(0.556719 - 2.94789i) q^{63} +(5.68994 - 5.62358i) q^{64} +3.33407i q^{65} +(-6.90489 - 11.0087i) q^{66} +9.38729i q^{67} +(-1.22601 - 0.331078i) q^{68} +(-14.5749 - 1.36420i) q^{69} +(0.859821 + 1.12281i) q^{70} -2.69785 q^{71} +(8.31086 - 1.71163i) q^{72} -9.27865 q^{73} +(0.219471 + 0.286600i) q^{74} +(1.72451 + 0.161413i) q^{75} +(-9.81222 - 2.64975i) q^{76} +5.30518i q^{77} +(-4.33941 - 6.91850i) q^{78} -5.23327i q^{79} +(-2.01353 + 3.45625i) q^{80} +(8.38013 + 3.28229i) q^{81} +(5.83972 - 4.47191i) q^{82} +4.47848 q^{83} +(-3.24559 - 1.21085i) q^{84} +0.634962 q^{85} +(-6.97299 + 5.33974i) q^{86} +(1.68849 - 18.0395i) q^{87} +(-13.8799 + 5.70160i) q^{88} -11.3607i q^{89} +(-3.78861 + 1.90957i) q^{90} +3.33407i q^{91} +(-4.40679 + 16.3187i) q^{92} +(0.702843 - 7.50905i) q^{93} +(11.2154 + 14.6458i) q^{94} +5.08185 q^{95} +(-0.320181 - 9.79273i) q^{96} -10.9809 q^{97} +(0.859821 + 1.12281i) q^{98} +(-15.6391 - 2.95350i) 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 $

$2$	−0.859821	−	1.12281i	−0.607986	−	0.793948i
$2$	−0.859821	−	1.12281i	−0.607986	−	0.793948i
$3$	−1.72451	−	0.161413i	−0.995648	−	0.0931921i
$3$	−1.72451	−	0.161413i	−0.995648	−	0.0931921i
$4$	−0.521414	+	1.93084i	−0.260707	+	0.965418i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	1.30154	+	2.07509i	0.531350	+	0.847152i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.61629	−	1.07472i	0.924998	−	0.379972i
$9$	2.94789	+	0.556719i	0.982630	+	0.185573i
$10$	−1.12281	+	0.859821i	−0.355064	+	0.271899i
$11$	−5.30518			−1.59957			−0.799786	−	0.600285i	$-0.795054\pi$
$11$	−5.30518			−1.59957			−0.799786	+	0.600285i	$0.795054\pi$
$12$	1.21085	−	3.24559i	0.349542	−	0.936921i
$13$	−3.33407			−0.924705			−0.462352	−	0.886696i	$-0.652994\pi$
$13$	−3.33407			−0.924705			−0.462352	+	0.886696i	$0.652994\pi$
$14$	−1.12281	+	0.859821i	−0.300084	+	0.229797i
$15$	−0.161413	+	1.72451i	−0.0416768	+	0.445267i
$16$	−3.45625	−	2.01353i	−0.864064	−	0.503383i
$17$			0.634962i			0.154001i	0.997031	+	0.0770004i	$0.0245343\pi$
$17$			0.634962i			0.154001i	−0.997031	+	0.0770004i	$0.975466\pi$
$18$	−1.90957	−	3.78861i	−0.450090	−	0.892983i
$19$			5.08185i			1.16586i	0.812524	+	0.582928i	$0.198093\pi$
$19$			5.08185i			1.16586i	−0.812524	+	0.582928i	$0.801907\pi$
$20$	1.93084	+	0.521414i	0.431748	+	0.116592i
$21$	−0.161413	+	1.72451i	−0.0352233	+	0.376320i
$22$	4.56151	+	5.95672i	0.972517	+	1.26998i
$23$	8.45161			1.76228			0.881141	−	0.472853i	$-0.156776\pi$
$23$	8.45161			1.76228			0.881141	+	0.472853i	$0.156776\pi$
$24$	−4.68530	+	1.43107i	−0.956383	+	0.292116i
$25$	−1.00000			−0.200000
$26$	2.86670	+	3.74353i	0.562207	+	0.734167i
$27$	−4.99382	−	1.43590i	−0.961060	−	0.276339i
$28$	1.93084	+	0.521414i	0.364894	+	0.0985380i
$29$			10.4606i			1.94249i	0.238081	+	0.971245i	$0.423482\pi$
$29$			10.4606i			1.94249i	−0.238081	+	0.971245i	$0.576518\pi$
$30$	2.07509	−	1.30154i	0.378858	−	0.237627i
$31$			4.35430i			0.782056i	0.920379	+	0.391028i	$0.127880\pi$
$31$			4.35430i			0.782056i	−0.920379	+	0.391028i	$0.872120\pi$
$32$	0.710944	+	5.61200i	0.125678	+	0.992071i
$33$	9.14886	+	0.856327i	1.59261	+	0.149067i
$34$	0.712943	−	0.545954i	0.122269	−	0.0936303i
$35$	−1.00000			−0.169031
$36$	−2.61201	+	5.40161i	−0.435334	+	0.900269i
$37$	−0.255252			−0.0419632			−0.0209816	−	0.999780i	$-0.506679\pi$
$37$	−0.255252			−0.0419632			−0.0209816	+	0.999780i	$0.506679\pi$
$38$	5.70596	−	4.36948i	0.925629	−	0.708824i
$39$	5.74965	+	0.538164i	0.920680	+	0.0861751i
$40$	−1.07472	−	2.61629i	−0.169929	−	0.413672i
$41$			5.20097i			0.812255i	0.913816	+	0.406128i	$0.133121\pi$
$41$			5.20097i			0.812255i	−0.913816	+	0.406128i	$0.866879\pi$
$42$	2.07509	−	1.30154i	0.320194	−	0.200831i
$43$		−	6.21029i		−	0.947061i	−0.880778	−	0.473530i	$-0.842979\pi$
$43$		−	6.21029i		−	0.947061i	0.880778	−	0.473530i	$-0.157021\pi$
$44$	2.76620	−	10.2434i	0.417020	−	1.54426i
$45$	0.556719	−	2.94789i	0.0829908	−	0.439446i
$46$	−7.26687	−	9.48957i	−1.07144	−	1.39916i
$47$	−13.0438			−1.90264			−0.951319	−	0.308207i	$-0.900271\pi$
$47$	−13.0438			−1.90264			−0.951319	+	0.308207i	$0.900271\pi$
$48$	5.63535	+	4.03025i	0.813392	+	0.581716i
$49$	−1.00000			−0.142857
$50$	0.859821	+	1.12281i	0.121597	+	0.158790i
$51$	0.102491	−	1.09500i	0.0143517	−	0.153331i
$52$	1.73843	−	6.43754i	0.241077	−	0.892726i
$53$			8.71720i			1.19740i	0.800973	+	0.598700i	$0.204316\pi$
$53$			8.71720i			1.19740i	−0.800973	+	0.598700i	$0.795684\pi$
$54$	2.68155	+	6.84173i	0.364912	+	0.931042i
$55$			5.30518i			0.715351i
$56$	−1.07472	−	2.61629i	−0.143616	−	0.349616i
$57$	0.820279	−	8.76372i	0.108649	−	1.16078i
$58$	11.7453	−	8.99428i	1.54224	−	1.18101i
$59$	1.82137			0.237122			0.118561	−	0.992947i	$-0.462172\pi$
$59$	1.82137			0.237122			0.118561	+	0.992947i	$0.462172\pi$
$60$	−3.24559	−	1.21085i	−0.419004	−	0.156320i
$61$	−1.58269			−0.202642			−0.101321	−	0.994854i	$-0.532307\pi$
$61$	−1.58269			−0.202642			−0.101321	+	0.994854i	$0.532307\pi$
$62$	4.88906	−	3.74392i	0.620912	−	0.475479i
$63$	0.556719	−	2.94789i	0.0701400	−	0.371399i
$64$	5.68994	−	5.62358i	0.711242	−	0.702947i
$65$			3.33407i			0.413540i
$66$	−6.90489	−	11.0087i	−0.849933	−	1.35508i
$67$			9.38729i			1.14684i	0.819262	+	0.573420i	$0.194384\pi$
$67$			9.38729i			1.14684i	−0.819262	+	0.573420i	$0.805616\pi$
$68$	−1.22601	−	0.331078i	−0.148675	−	0.0401491i
$69$	−14.5749	−	1.36420i	−1.75461	−	0.164231i
$70$	0.859821	+	1.12281i	0.102768	+	0.134202i
$71$	−2.69785			−0.320176			−0.160088	−	0.987103i	$-0.551178\pi$
$71$	−2.69785			−0.320176			−0.160088	+	0.987103i	$0.551178\pi$
$72$	8.31086	−	1.71163i	0.979444	−	0.201718i
$73$	−9.27865			−1.08598			−0.542992	−	0.839738i	$-0.682709\pi$
$73$	−9.27865			−1.08598			−0.542992	+	0.839738i	$0.682709\pi$
$74$	0.219471	+	0.286600i	0.0255130	+	0.0333166i
$75$	1.72451	+	0.161413i	0.199130	+	0.0186384i
$76$	−9.81222	−	2.64975i	−1.12554	−	0.303947i
$77$			5.30518i			0.604582i
$78$	−4.33941	−	6.91850i	−0.491342	−	0.783366i
$79$		−	5.23327i		−	0.588789i	−0.955684	−	0.294394i	$-0.904882\pi$
$79$		−	5.23327i		−	0.588789i	0.955684	−	0.294394i	$-0.0951179\pi$
$80$	−2.01353	+	3.45625i	−0.225120	+	0.386421i
$81$	8.38013	+	3.28229i	0.931125	+	0.364699i
$82$	5.83972	−	4.47191i	0.644889	−	0.493840i
$83$	4.47848			0.491577			0.245788	−	0.969324i	$-0.420953\pi$
$83$	4.47848			0.491577			0.245788	+	0.969324i	$0.420953\pi$
$84$	−3.24559	−	1.21085i	−0.354123	−	0.132114i
$85$	0.634962			0.0688713
$86$	−6.97299	+	5.33974i	−0.751917	+	0.575799i
$87$	1.68849	−	18.0395i	0.181025	−	1.93404i
$88$	−13.8799	+	5.70160i	−1.47960	+	0.607793i
$89$		−	11.3607i		−	1.20424i	−0.798407	−	0.602118i	$-0.794324\pi$
$89$		−	11.3607i		−	1.20424i	0.798407	−	0.602118i	$-0.205676\pi$
$90$	−3.78861	+	1.90957i	−0.399354	+	0.201286i
$91$			3.33407i			0.349505i
$92$	−4.40679	+	16.3187i	−0.459440	+	1.70134i
$93$	0.702843	−	7.50905i	0.0728814	−	0.778652i
$94$	11.2154	+	14.6458i	1.15678	+	1.51060i
$95$	5.08185			0.521387
$96$	−0.320181	−	9.79273i	−0.0326783	−	0.999466i
$97$	−10.9809			−1.11495			−0.557473	−	0.830195i	$-0.688229\pi$
$97$	−10.9809			−1.11495			−0.557473	+	0.830195i	$0.688229\pi$
$98$	0.859821	+	1.12281i	0.0868551	+	0.113421i
$99$	−15.6391	−	2.95350i	−1.57179	−	0.296837i
$100$	0.521414	−	1.93084i	0.0521414	−	0.193084i
$101$		−	6.49341i		−	0.646118i	−0.946379	−	0.323059i	$-0.895289\pi$
$101$		−	6.49341i		−	0.646118i	0.946379	−	0.323059i	$-0.104711\pi$
$102$	−1.31760	+	0.826426i	−0.130462	+	0.0818284i
$103$			4.45217i			0.438685i	0.975648	+	0.219342i	$0.0703912\pi$
$103$			4.45217i			0.438685i	−0.975648	+	0.219342i	$0.929609\pi$
$104$	−8.72289	+	3.58320i	−0.855350	+	0.351362i
$105$	1.72451	+	0.161413i	0.168295	+	0.0157523i
$106$	9.78778	−	7.49524i	0.950673	−	0.728002i
$107$	−1.19494			−0.115519			−0.0577594	−	0.998331i	$-0.518396\pi$
$107$	−1.19494			−0.115519			−0.0577594	+	0.998331i	$0.518396\pi$
$108$	5.37633	−	8.89354i	0.517338	−	0.855781i
$109$	1.19967			0.114908			0.0574540	−	0.998348i	$-0.481702\pi$
$109$	1.19967			0.114908			0.0574540	+	0.998348i	$0.481702\pi$
$110$	5.95672	−	4.56151i	0.567951	−	0.434923i
$111$	0.440186	+	0.0412011i	0.0417806	+	0.00391064i
$112$	−2.01353	+	3.45625i	−0.190261	+	0.326585i
$113$		−	7.18544i		−	0.675950i	−0.941155	−	0.337975i	$-0.890258\pi$
$113$		−	7.18544i		−	0.675950i	0.941155	−	0.337975i	$-0.109742\pi$
$114$	−10.5453	+	6.61421i	−0.987658	+	0.619478i
$115$		−	8.45161i		−	0.788117i
$116$	−20.1978	−	5.45432i	−1.87532	−	0.506421i
$117$	−9.82848	−	1.85614i	−0.908643	−	0.171600i
$118$	−1.56605	−	2.04506i	−0.144167	−	0.188263i
$119$	0.634962			0.0582069
$120$	1.43107	+	4.68530i	0.130638	+	0.427707i
$121$	17.1449			1.55863
$122$	1.36083	+	1.77706i	0.123203	+	0.160887i
$123$	0.839507	−	8.96915i	0.0756958	−	0.808721i
$124$	−8.40744	−	2.27040i	−0.755011	−	0.203888i
$125$			1.00000i			0.0894427i
$126$	−3.78861	+	1.90957i	−0.337516	+	0.170118i
$127$		−	6.03720i		−	0.535715i	−0.963459	−	0.267858i	$-0.913684\pi$
$127$		−	6.03720i		−	0.535715i	0.963459	−	0.267858i	$-0.0863157\pi$
$128$	−11.2065	−	1.55346i	−0.990528	−	0.137308i
$129$	−1.00242	+	10.7097i	−0.0882585	+	0.942939i
$130$	3.74353	−	2.86670i	0.328330	−	0.251427i
$131$	−6.80880			−0.594888			−0.297444	−	0.954739i	$-0.596134\pi$
$131$	−6.80880			−0.594888			−0.297444	+	0.954739i	$0.596134\pi$
$132$	−6.42377	+	17.2184i	−0.559118	+	1.49867i
$133$	5.08185			0.440652
$134$	10.5402	−	8.07139i	0.910531	−	0.697262i
$135$	−1.43590	+	4.99382i	−0.123582	+	0.429799i
$136$	0.682409	+	1.66124i	0.0585161	+	0.142451i
$137$			9.93629i			0.848915i	0.905448	+	0.424457i	$0.139535\pi$
$137$			9.93629i			0.848915i	−0.905448	+	0.424457i	$0.860465\pi$
$138$	11.0001	+	17.5379i	0.936389	+	1.49292i
$139$		−	7.44036i		−	0.631083i	−0.948912	−	0.315542i	$-0.897814\pi$
$139$		−	7.44036i		−	0.631083i	0.948912	−	0.315542i	$-0.102186\pi$
$140$	0.521414	−	1.93084i	0.0440676	−	0.163185i
$141$	22.4943	+	2.10545i	1.89436	+	0.177311i
$142$	2.31967	+	3.02918i	0.194662	+	0.254203i
$143$	17.6878			1.47913
$144$	−9.06769	−	7.85983i	−0.755641	−	0.654986i
$145$	10.4606			0.868708
$146$	7.97798	+	10.4182i	0.660263	+	0.862215i
$147$	1.72451	+	0.161413i	0.142235	+	0.0133132i
$148$	0.133092	−	0.492850i	0.0109401	−	0.0405120i
$149$		−	0.318054i		−	0.0260560i	−0.999915	−	0.0130280i	$-0.995853\pi$
$149$		−	0.318054i		−	0.0260560i	0.999915	−	0.0130280i	$-0.00414706\pi$
$150$	−1.30154	−	2.07509i	−0.106270	−	0.169430i
$151$			11.9757i			0.974571i	0.873243	+	0.487285i	$0.162013\pi$
$151$			11.9757i			0.974571i	−0.873243	+	0.487285i	$0.837987\pi$
$152$	5.46158	+	13.2956i	0.442993	+	1.07841i
$153$	−0.353495	+	1.87180i	−0.0285784	+	0.151326i
$154$	5.95672	−	4.56151i	0.480006	−	0.367577i
$155$	4.35430			0.349746
$156$	−4.03705	+	10.8210i	−0.323223	+	0.866375i
$157$	−18.4070			−1.46904			−0.734518	−	0.678589i	$-0.762592\pi$
$157$	−18.4070			−1.46904			−0.734518	+	0.678589i	$0.762592\pi$
$158$	−5.87598	+	4.49968i	−0.467468	+	0.357975i
$159$	1.40707	−	15.0329i	0.111588	−	1.19219i
$160$	5.61200	−	0.710944i	0.443668	−	0.0562051i
$161$		−	8.45161i		−	0.666080i
$162$	−3.52001	−	12.2315i	−0.276558	−	0.960997i
$163$			7.87720i			0.616990i	0.951226	+	0.308495i	$0.0998253\pi$
$163$			7.87720i			0.616990i	−0.951226	+	0.308495i	$0.900175\pi$
$164$	−10.0422	−	2.71186i	−0.784166	−	0.211761i
$165$	0.856327	−	9.14886i	0.0666650	−	0.712237i
$166$	−3.85069	−	5.02849i	−0.298871	−	0.390286i
$167$	−5.37443			−0.415886			−0.207943	−	0.978141i	$-0.566677\pi$
$167$	−5.37443			−0.415886			−0.207943	+	0.978141i	$0.566677\pi$
$168$	1.43107	+	4.68530i	0.110410	+	0.361479i
$169$	−1.88398			−0.144922
$170$	−0.545954	−	0.712943i	−0.0418728	−	0.0546802i
$171$	−2.82916	+	14.9807i	−0.216351	+	1.14561i
$172$	11.9911	+	3.23814i	0.914309	+	0.246905i
$173$		−	20.0897i		−	1.52739i	−0.645578	−	0.763694i	$-0.723384\pi$
$173$		−	20.0897i		−	1.52739i	0.645578	−	0.763694i	$-0.276616\pi$
$174$	−21.7068	+	13.6149i	−1.64559	+	1.03214i
$175$			1.00000i			0.0755929i
$176$	18.3361	+	10.6821i	1.38213	+	0.805197i
$177$	−3.14098	−	0.293993i	−0.236090	−	0.0220979i
$178$	−12.7560	+	9.76821i	−0.956101	+	0.732158i
$179$	16.4405			1.22882			0.614409	−	0.788988i	$-0.289394\pi$
$179$	16.4405			1.22882			0.614409	+	0.788988i	$0.289394\pi$
$180$	5.40161	+	2.61201i	0.402612	+	0.194687i
$181$	−8.10002			−0.602069			−0.301035	−	0.953613i	$-0.597332\pi$
$181$	−8.10002			−0.602069			−0.301035	+	0.953613i	$0.597332\pi$
$182$	3.74353	−	2.86670i	0.277489	−	0.212494i
$183$	2.72936	+	0.255467i	0.201760	+	0.0188846i
$184$	22.1119	−	9.08314i	1.63011	−	0.669618i
$185$			0.255252i			0.0187665i
$186$	−9.03557	+	5.66728i	−0.662520	+	0.415545i
$187$		−	3.36859i		−	0.246336i
$188$	6.80124	−	25.1855i	0.496031	−	1.83684i
$189$	−1.43590	+	4.99382i	−0.104446	+	0.363247i
$190$	−4.36948	−	5.70596i	−0.316996	−	0.413954i
$191$	3.44063			0.248956			0.124478	−	0.992222i	$-0.460274\pi$
$191$	3.44063			0.248956			0.124478	+	0.992222i	$0.460274\pi$
$192$	−10.7201	+	8.77950i	−0.773656	+	0.633606i
$193$	2.71718			0.195587			0.0977933	−	0.995207i	$-0.468822\pi$
$193$	2.71718			0.195587			0.0977933	+	0.995207i	$0.468822\pi$
$194$	9.44165	+	12.3295i	0.677871	+	0.885209i
$195$	0.538164	−	5.74965i	0.0385387	−	0.411741i
$196$	0.521414	−	1.93084i	0.0372439	−	0.137917i
$197$		−	13.2320i		−	0.942742i	−0.881935	−	0.471371i	$-0.843759\pi$
$197$		−	13.2320i		−	0.942742i	0.881935	−	0.471371i	$-0.156241\pi$
$198$	10.1306	+	20.0992i	0.719951	+	1.42839i
$199$			14.2223i			1.00819i	0.863648	+	0.504095i	$0.168174\pi$
$199$			14.2223i			1.00819i	−0.863648	+	0.504095i	$0.831826\pi$
$200$	−2.61629	+	1.07472i	−0.185000	+	0.0759944i
$201$	1.51523	−	16.1885i	0.106876	−	1.14185i
$202$	−7.29088	+	5.58317i	−0.512985	+	0.392831i
$203$	10.4606			0.734192
$204$	2.06083	+	0.768843i	0.144287	+	0.0538298i
$205$	5.20097			0.363252
$206$	4.99895	−	3.82807i	0.348293	−	0.266714i
$207$	24.9144	+	4.70517i	1.73167	+	0.327032i
$208$	11.5234	+	6.71325i	0.799003	+	0.465480i
$209$		−	26.9601i		−	1.86487i
$210$	−1.30154	−	2.07509i	−0.0898145	−	0.143195i
$211$			7.93976i			0.546596i	0.961929	+	0.273298i	$0.0881144\pi$
$211$			7.93976i			0.546596i	−0.961929	+	0.273298i	$0.911886\pi$
$212$	−16.8315	−	4.54527i	−1.15599	−	0.312171i
$213$	4.65248	+	0.435469i	0.318783	+	0.0298379i
$214$	1.02743	+	1.34169i	0.0702337	+	0.0917159i
$215$	−6.21029			−0.423538
$216$	−14.6085	+	1.61025i	−0.993980	+	0.109563i
$217$	4.35430			0.295589
$218$	−1.03151	−	1.34701i	−0.0698624	−	0.0912309i
$219$	16.0012	+	1.49770i	1.08126	+	0.101205i
$220$	−10.2434	−	2.76620i	−0.690612	−	0.186497i
$221$		−	2.11701i		−	0.142405i
$222$	−0.332220	−	0.529672i	−0.0222972	−	0.0355492i
$223$			15.0803i			1.00985i	0.863163	+	0.504925i	$0.168480\pi$
$223$			15.0803i			1.00985i	−0.863163	+	0.504925i	$0.831520\pi$
$224$	5.61200	−	0.710944i	0.374968	−	0.0475020i
$225$	−2.94789	−	0.556719i	−0.196526	−	0.0371146i
$226$	−8.06790	+	6.17820i	−0.536669	+	0.410968i
$227$	9.80204			0.650584			0.325292	−	0.945614i	$-0.394537\pi$
$227$	9.80204			0.650584			0.325292	+	0.945614i	$0.394537\pi$
$228$	16.4936	+	6.15335i	1.09232	+	0.407516i
$229$	7.78301			0.514316			0.257158	−	0.966369i	$-0.417214\pi$
$229$	7.78301			0.514316			0.257158	+	0.966369i	$0.417214\pi$
$230$	−9.48957	+	7.26687i	−0.625724	+	0.479164i
$231$	0.856327	−	9.14886i	0.0563422	−	0.601950i
$232$	11.2423	+	27.3680i	0.738092	+	1.79680i
$233$			11.7611i			0.770498i	0.922813	+	0.385249i	$0.125884\pi$
$233$			11.7611i			0.770498i	−0.922813	+	0.385249i	$0.874116\pi$
$234$	6.36664	+	12.6315i	0.416200	+	0.825746i
$235$			13.0438i			0.850886i
$236$	−0.949688	+	3.51677i	−0.0618194	+	0.228922i
$237$	−0.844720	+	9.02484i	−0.0548705	+	0.586227i
$238$	−0.545954	−	0.712943i	−0.0353889	−	0.0462132i
$239$	−10.5279			−0.680995			−0.340497	−	0.940245i	$-0.610595\pi$
$239$	−10.5279			−0.680995			−0.340497	+	0.940245i	$0.610595\pi$
$240$	4.03025	−	5.63535i	0.260151	−	0.363760i
$241$	12.6411			0.814284			0.407142	−	0.913365i	$-0.366525\pi$
$241$	12.6411			0.814284			0.407142	+	0.913365i	$0.366525\pi$
$242$	−14.7416	−	19.2506i	−0.947626	−	1.23747i
$243$	−13.9218	−	7.01303i	−0.893086	−	0.449886i
$244$	0.825235	−	3.05591i	0.0528303	−	0.195634i
$245$			1.00000i			0.0638877i
$246$	−10.7925	+	6.76926i	−0.688104	+	0.431592i
$247$		−	16.9432i		−	1.07807i
$248$	4.67967	+	11.3921i	0.297159	+	0.723400i
$249$	−7.72319	−	0.722886i	−0.489437	−	0.0458110i
$250$	1.12281	−	0.859821i	0.0710129	−	0.0543799i
$251$	−9.29198			−0.586504			−0.293252	−	0.956035i	$-0.594738\pi$
$251$	−9.29198			−0.586504			−0.293252	+	0.956035i	$0.594738\pi$
$252$	5.40161	+	2.61201i	0.340270	+	0.164541i
$253$	−44.8373			−2.81890
$254$	−6.77865	+	5.19092i	−0.425330	+	0.325707i
$255$	−1.09500	−	0.102491i	−0.0685716	−	0.00641826i
$256$	7.89139	+	13.9185i	0.493212	+	0.869909i
$257$			14.9631i			0.933374i	0.884423	+	0.466687i	$0.154553\pi$
$257$			14.9631i			0.933374i	−0.884423	+	0.466687i	$0.845447\pi$
$258$	12.8869	−	8.08292i	0.802305	−	0.503221i
$259$			0.255252i			0.0158606i
$260$	−6.43754	−	1.73843i	−0.399239	−	0.107813i
$261$	−5.82363	+	30.8368i	−0.360474	+	1.90875i
$262$	5.85436	+	7.64501i	0.361683	+	0.472310i
$263$	−16.4616			−1.01507			−0.507533	−	0.861632i	$-0.669442\pi$
$263$	−16.4616			−1.01507			−0.507533	+	0.861632i	$0.669442\pi$
$264$	24.8564	−	7.59209i	1.52980	−	0.467261i
$265$	8.71720			0.535493
$266$	−4.36948	−	5.70596i	−0.267910	−	0.349855i
$267$	−1.83378	+	19.5917i	−0.112225	+	1.19900i
$268$	−18.1253	−	4.89467i	−1.10718	−	0.298989i
$269$			0.885305i			0.0539780i	0.999636	+	0.0269890i	$0.00859191\pi$
$269$			0.885305i			0.0539780i	−0.999636	+	0.0269890i	$0.991408\pi$
$270$	6.84173	−	2.68155i	0.416375	−	0.163194i
$271$			20.3207i			1.23439i	0.786808	+	0.617197i	$0.211732\pi$
$271$			20.3207i			1.23439i	−0.786808	+	0.617197i	$0.788268\pi$
$272$	1.27852	−	2.19459i	0.0775214	−	0.133067i
$273$	0.538164	−	5.74965i	0.0325711	−	0.347984i
$274$	11.1566	−	8.54344i	0.673994	−	0.516128i
$275$	5.30518			0.319914
$276$	10.2336	−	27.4304i	0.615992	−	1.65112i
$277$	−30.2510			−1.81760			−0.908802	−	0.417228i	$-0.863002\pi$
$277$	−30.2510			−1.81760			−0.908802	+	0.417228i	$0.863002\pi$
$278$	−8.35413	+	6.39738i	−0.501047	+	0.383689i
$279$	−2.42412	+	12.8360i	−0.145128	+	0.768472i
$280$	−2.61629	+	1.07472i	−0.156353	+	0.0642270i
$281$		−	14.9367i		−	0.891049i	−0.895270	−	0.445525i	$-0.853017\pi$
$281$		−	14.9367i		−	0.891049i	0.895270	−	0.445525i	$-0.146983\pi$
$282$	−16.9770	−	27.0671i	−1.01097	−	1.61182i
$283$			8.58671i			0.510427i	0.966885	+	0.255214i	$0.0821458\pi$
$283$			8.58671i			0.510427i	−0.966885	+	0.255214i	$0.917854\pi$
$284$	1.40670	−	5.20911i	0.0834722	−	0.309104i
$285$	−8.76372	−	0.820279i	−0.519118	−	0.0485891i
$286$	−15.2084	−	19.8601i	−0.899291	−	1.17435i
$287$	5.20097			0.307004
$288$	−1.02852	+	16.9394i	−0.0606062	+	0.998162i
$289$	16.5968			0.976284
$290$	−8.99428	−	11.7453i	−0.528162	−	0.689709i
$291$	18.9368	+	1.77247i	1.11009	+	0.103904i
$292$	4.83802	−	17.9156i	0.283124	−	1.04843i
$293$			10.6162i			0.620205i	0.950703	+	0.310102i	$0.100363\pi$
$293$			10.6162i			0.620205i	−0.950703	+	0.310102i	$0.899637\pi$
$294$	−1.30154	−	2.07509i	−0.0759071	−	0.121022i
$295$		−	1.82137i		−	0.106044i
$296$	−0.667814	+	0.274326i	−0.0388159	+	0.0159449i
$297$	26.4931	+	7.61770i	1.53729	+	0.442024i
$298$	−0.357115	+	0.273470i	−0.0206871	+	0.0158417i
$299$	−28.1783			−1.62959
$300$	−1.21085	+	3.24559i	−0.0699084	+	0.187384i
$301$	−6.21029			−0.357955
$302$	13.4465	−	10.2970i	0.773759	−	0.592525i
$303$	−1.04812	+	11.1980i	−0.0602131	+	0.643307i
$304$	10.2325	−	17.5642i	0.586872	−	1.00737i
$305$			1.58269i			0.0906243i
$306$	2.40562	−	1.21250i	0.137520	−	0.0693142i
$307$		−	12.6754i		−	0.723425i	−0.932290	−	0.361713i	$-0.882192\pi$
$307$		−	12.6754i		−	0.723425i	0.932290	−	0.361713i	$-0.117808\pi$
$308$	−10.2434	−	2.76620i	−0.583674	−	0.157619i
$309$	0.718639	−	7.67782i	0.0408820	−	0.436776i
$310$	−3.74392	−	4.88906i	−0.212640	−	0.277680i
$311$	7.46893			0.423524			0.211762	−	0.977321i	$-0.432080\pi$
$311$	7.46893			0.423524			0.211762	+	0.977321i	$0.432080\pi$
$312$	15.6211	−	4.77129i	0.884372	−	0.270121i
$313$	3.25390			0.183921			0.0919607	−	0.995763i	$-0.470687\pi$
$313$	3.25390			0.183921			0.0919607	+	0.995763i	$0.470687\pi$
$314$	15.8267	+	20.6676i	0.893153	+	1.16634i
$315$	−2.94789	−	0.556719i	−0.166095	−	0.0313676i
$316$	10.1046	+	2.72870i	0.568427	+	0.153501i
$317$		−	19.0288i		−	1.06876i	−0.845243	−	0.534382i	$-0.820544\pi$
$317$		−	19.0288i		−	1.06876i	0.845243	−	0.534382i	$-0.179456\pi$
$318$	−18.0890	+	11.3458i	−1.01438	+	0.636238i
$319$		−	55.4956i		−	3.10715i
$320$	−5.62358	−	5.68994i	−0.314367	−	0.318077i
$321$	2.06068	+	0.192879i	0.115016	+	0.0107654i
$322$	−9.48957	+	7.26687i	−0.528833	+	0.404967i
$323$	−3.22678			−0.179543
$324$	−10.7071	+	14.4692i	−0.594838	+	0.803845i
$325$	3.33407			0.184941
$326$	8.84462	−	6.77298i	0.489858	−	0.375121i
$327$	−2.06885	−	0.193643i	−0.114408	−	0.0107085i
$328$	5.58961	+	13.6072i	0.308634	+	0.751335i
$329$			13.0438i			0.719130i
$330$	−11.0087	+	6.90489i	−0.606011	+	0.380102i
$331$		−	6.95513i		−	0.382288i	−0.981562	−	0.191144i	$-0.938780\pi$
$331$		−	6.95513i		−	0.382288i	0.981562	−	0.191144i	$-0.0612198\pi$
$332$	−2.33514	+	8.64720i	−0.128158	+	0.474577i
$333$	−0.752456	−	0.142104i	−0.0412343	−	0.00778724i
$334$	4.62105	+	6.03448i	0.252853	+	0.330192i
$335$	9.38729			0.512882
$336$	4.03025	−	5.63535i	0.219868	−	0.307433i
$337$	28.1902			1.53562			0.767810	−	0.640678i	$-0.221346\pi$
$337$	28.1902			1.53562			0.767810	+	0.640678i	$0.221346\pi$
$338$	1.61989	+	2.11536i	0.0881102	+	0.115060i
$339$	−1.15983	+	12.3914i	−0.0629931	+	0.673008i
$340$	−0.331078	+	1.22601i	−0.0179552	+	0.0664896i
$341$		−	23.1004i		−	1.25095i
$342$	19.2531	−	9.70414i	1.04109	−	0.524740i
$343$			1.00000i			0.0539949i
$344$	−6.67435	−	16.2479i	−0.359857	−	0.876029i
$345$	−1.36420	+	14.5749i	−0.0734462	+	0.784687i
$346$	−22.5569	+	17.2735i	−1.21267	+	0.928630i
$347$	−12.2776			−0.659097			−0.329549	−	0.944139i	$-0.606897\pi$
$347$	−12.2776			−0.659097			−0.329549	+	0.944139i	$0.606897\pi$
$348$	33.9509	+	12.6662i	1.81996	+	0.678982i
$349$	−7.47233			−0.399985			−0.199992	−	0.979797i	$-0.564092\pi$
$349$	−7.47233			−0.399985			−0.199992	+	0.979797i	$0.564092\pi$
$350$	1.12281	−	0.859821i	0.0600168	−	0.0459594i
$351$	16.6497	+	4.78739i	0.888697	+	0.255532i
$352$	−3.77169	−	29.7727i	−0.201032	−	1.58689i
$353$			22.9029i			1.21900i	0.792786	+	0.609500i	$0.208630\pi$
$353$			22.9029i			1.21900i	−0.792786	+	0.609500i	$0.791370\pi$
$354$	2.37058	+	3.77951i	0.125995	+	0.200879i
$355$			2.69785i			0.143187i
$356$	21.9357	+	5.92365i	1.16259	+	0.313953i
$357$	−1.09500	−	0.102491i	−0.0579536	−	0.00542442i
$358$	−14.1359	−	18.4596i	−0.747104	−	0.975618i
$359$	−29.5073			−1.55734			−0.778669	−	0.627435i	$-0.784105\pi$
$359$	−29.5073			−1.55734			−0.778669	+	0.627435i	$0.784105\pi$
$360$	−1.71163	−	8.31086i	−0.0902109	−	0.438021i
$361$	−6.82520			−0.359221
$362$	6.96457	+	9.09480i	0.366050	+	0.478012i
$363$	−29.5667	−	2.76742i	−1.55185	−	0.145252i
$364$	−6.43754	−	1.73843i	−0.337419	−	0.0911186i
$365$			9.27865i			0.485667i
$366$	−2.05992	−	3.28422i	−0.107674	−	0.171669i
$367$		−	13.4540i		−	0.702294i	−0.936320	−	0.351147i	$-0.885792\pi$
$367$		−	13.4540i		−	0.702294i	0.936320	−	0.351147i	$-0.114208\pi$
$368$	−29.2109	−	17.0176i	−1.52272	−	0.887103i
$369$	−2.89548	+	15.3319i	−0.150733	+	0.798147i
$370$	0.286600	−	0.219471i	0.0148996	−	0.0114098i
$371$	8.71720			0.452575
$372$	14.1323	+	5.27240i	0.732724	+	0.273361i
$373$	8.50833			0.440545			0.220272	−	0.975438i	$-0.429305\pi$
$373$	8.50833			0.440545			0.220272	+	0.975438i	$0.429305\pi$
$374$	−3.78229	+	2.89638i	−0.195578	+	0.149768i
$375$	0.161413	−	1.72451i	0.00833535	−	0.0890535i
$376$	−34.1264	+	14.0185i	−1.75994	+	0.722950i
$377$		−	34.8765i		−	1.79623i
$378$	6.84173	−	2.68155i	0.351901	−	0.137924i
$379$		−	5.79569i		−	0.297705i	−0.988859	−	0.148852i	$-0.952442\pi$
$379$		−	5.79569i		−	0.297705i	0.988859	−	0.148852i	$-0.0475579\pi$
$380$	−2.64975	+	9.81222i	−0.135929	+	0.503356i
$381$	−0.974486	+	10.4112i	−0.0499244	+	0.533384i
$382$	−2.95833	−	3.86319i	−0.151361	−	0.197658i
$383$	−7.49424			−0.382938			−0.191469	−	0.981499i	$-0.561325\pi$
$383$	−7.49424			−0.382938			−0.191469	+	0.981499i	$0.561325\pi$
$384$	19.0751	+	4.48785i	0.973422	+	0.229020i
$385$	5.30518			0.270377
$386$	−2.33629	−	3.05088i	−0.118914	−	0.155286i
$387$	3.45739	−	18.3073i	0.175749	−	0.930611i
$388$	5.72562	−	21.2024i	0.290674	−	1.07639i
$389$		−	8.73606i		−	0.442936i	−0.975168	−	0.221468i	$-0.928915\pi$
$389$		−	8.73606i		−	0.442936i	0.975168	−	0.221468i	$-0.0710848\pi$
$390$	−6.91850	+	4.33941i	−0.350332	+	0.219735i
$391$			5.36645i			0.271393i
$392$	−2.61629	+	1.07472i	−0.132143	+	0.0542817i
$393$	11.7419	+	1.09903i	0.592299	+	0.0554388i
$394$	−14.8571	+	11.3772i	−0.748488	+	0.573174i
$395$	−5.23327			−0.263314
$396$	13.8572	−	28.6565i	0.696349	−	1.44005i
$397$	−8.51292			−0.427251			−0.213626	−	0.976916i	$-0.568527\pi$
$397$	−8.51292			−0.427251			−0.213626	+	0.976916i	$0.568527\pi$
$398$	15.9689	−	12.2286i	0.800451	−	0.612965i
$399$	−8.76372	−	0.820279i	−0.438735	−	0.0410653i
$400$	3.45625	+	2.01353i	0.172813	+	0.100677i
$401$			19.3983i			0.968705i	0.874873	+	0.484353i	$0.160945\pi$
$401$			19.3983i			0.968705i	−0.874873	+	0.484353i	$0.839055\pi$
$402$	−19.4795	+	12.2179i	−0.971548	+	0.609373i
$403$		−	14.5175i		−	0.723170i
$404$	12.5377	+	3.38576i	0.623774	+	0.168448i
$405$	3.28229	−	8.38013i	0.163099	−	0.416412i
$406$	−8.99428	−	11.7453i	−0.446378	−	0.582911i
$407$	1.35416			0.0671232
$408$	−0.908676	−	2.97499i	−0.0449861	−	0.147284i
$409$	−8.86189			−0.438192			−0.219096	−	0.975703i	$-0.570311\pi$
$409$	−8.86189			−0.438192			−0.219096	+	0.975703i	$0.570311\pi$
$410$	−4.47191	−	5.83972i	−0.220852	−	0.288403i
$411$	1.60385	−	17.1353i	0.0791121	−	0.845221i
$412$	−8.59640	−	2.32142i	−0.423514	−	0.114368i
$413$		−	1.82137i		−	0.0896237i
$414$	−16.1389	−	32.0198i	−0.793185	−	1.57369i
$415$		−	4.47848i		−	0.219840i
$416$	−2.37034	−	18.7108i	−0.116215	−	0.917373i
$417$	−1.20097	+	12.8310i	−0.0588119	+	0.628337i
$418$	−30.2712	+	23.1809i	−1.48061	+	1.13382i
$419$	28.6628			1.40027			0.700136	−	0.714010i	$-0.253123\pi$
$419$	28.6628			1.40027			0.700136	+	0.714010i	$0.253123\pi$
$420$	−1.21085	+	3.24559i	−0.0590834	+	0.158369i
$421$	13.0039			0.633771			0.316885	−	0.948464i	$-0.397363\pi$
$421$	13.0039			0.633771			0.316885	+	0.948464i	$0.397363\pi$
$422$	8.91486	−	6.82678i	0.433969	−	0.332322i
$423$	−38.4518	−	7.26175i	−1.86959	−	0.353078i
$424$	9.36858	+	22.8067i	0.454979	+	1.10759i
$425$		−	0.634962i		−	0.0308002i
$426$	−3.51135	−	5.59829i	−0.170125	−	0.271238i
$427$			1.58269i			0.0765915i
$428$	0.623056	−	2.30722i	0.0301166	−	0.111524i
$429$	−30.5029	−	2.85506i	−1.47269	−	0.137843i
$430$	5.33974	+	6.97299i	0.257505	+	0.336268i
$431$	−13.2607			−0.638745			−0.319372	−	0.947629i	$-0.603472\pi$
$431$	−13.2607			−0.638745			−0.319372	+	0.947629i	$0.603472\pi$
$432$	14.3687	+	15.0180i	0.691313	+	0.722555i
$433$	31.8638			1.53127			0.765637	−	0.643272i	$-0.222424\pi$
$433$	31.8638			1.53127			0.765637	+	0.643272i	$0.222424\pi$
$434$	−3.74392	−	4.88906i	−0.179714	−	0.234683i
$435$	−18.0395	−	1.68849i	−0.864928	−	0.0809567i
$436$	−0.625527	+	2.31637i	−0.0299573	+	0.110934i
$437$			42.9498i			2.05457i
$438$	−12.0765	−	19.2540i	−0.577038	−	0.919994i
$439$			5.49234i			0.262135i	0.991373	+	0.131068i	$0.0418405\pi$
$439$			5.49234i			0.262135i	−0.991373	+	0.131068i	$0.958160\pi$
$440$	5.70160	+	13.8799i	0.271813	+	0.661698i
$441$	−2.94789	−	0.556719i	−0.140376	−	0.0265104i
$442$	−2.37700	+	1.82025i	−0.113062	+	0.0865804i
$443$	11.1726			0.530825			0.265412	−	0.964135i	$-0.414492\pi$
$443$	11.1726			0.530825			0.265412	+	0.964135i	$0.414492\pi$
$444$	−0.309072	+	0.828444i	−0.0146679	+	0.0393162i
$445$	−11.3607			−0.538551
$446$	16.9323	−	12.9663i	0.801768	−	0.613974i
$447$	−0.0513382	+	0.548489i	−0.00242821	+	0.0259426i
$448$	−5.62358	−	5.68994i	−0.265689	−	0.268824i
$449$		−	15.4449i		−	0.728890i	−0.931225	−	0.364445i	$-0.881259\pi$
$449$		−	15.4449i		−	0.728890i	0.931225	−	0.364445i	$-0.118741\pi$
$450$	1.90957	+	3.78861i	0.0900180	+	0.178597i
$451$		−	27.5921i		−	1.29926i
$452$	13.8739	+	3.74659i	0.652574	+	0.176225i
$453$	1.93304	−	20.6523i	0.0908223	−	0.970330i
$454$	−8.42800	−	11.0058i	−0.395546	−	0.516530i
$455$	3.33407			0.156304
$456$	−7.27249	−	23.8100i	−0.340565	−	1.11501i
$457$	−35.7005			−1.67000			−0.834999	−	0.550251i	$-0.814532\pi$
$457$	−35.7005			−1.67000			−0.834999	+	0.550251i	$0.814532\pi$
$458$	−6.69200	−	8.73886i	−0.312697	−	0.408340i
$459$	0.911741	−	3.17088i	0.0425564	−	0.148004i
$460$	16.3187	+	4.40679i	0.760862	+	0.205468i
$461$			33.2736i			1.54971i	0.632141	+	0.774854i	$0.282176\pi$
$461$			33.2736i			1.54971i	−0.632141	+	0.774854i	$0.717824\pi$
$462$	−11.0087	+	6.90489i	−0.512173	+	0.321244i
$463$		−	21.1066i		−	0.980906i	−0.871468	−	0.490453i	$-0.836831\pi$
$463$		−	21.1066i		−	0.980906i	0.871468	−	0.490453i	$-0.163169\pi$
$464$	21.0628	−	36.1546i	0.977816	−	1.67844i
$465$	−7.50905	−	0.702843i	−0.348224	−	0.0325935i
$466$	13.2056	−	10.1125i	0.611735	−	0.468452i
$467$	19.2492			0.890747			0.445373	−	0.895345i	$-0.353071\pi$
$467$	19.2492			0.890747			0.445373	+	0.895345i	$0.353071\pi$
$468$	8.70861	−	18.0094i	0.402556	−	0.832483i
$469$	9.38729			0.433465
$470$	14.6458	−	11.2154i	0.675559	−	0.517326i
$471$	31.7431	+	2.97113i	1.46264	+	0.136903i
$472$	4.76523	−	1.95747i	0.219337	−	0.0900998i
$473$			32.9467i			1.51489i
$474$	10.8595	−	6.81129i	0.498794	−	0.312853i
$475$		−	5.08185i		−	0.233171i
$476$	−0.331078	+	1.22601i	−0.0151749	+	0.0561940i
$477$	−4.85303	+	25.6974i	−0.222205	+	1.17660i
$478$	9.05214	+	11.8209i	0.414035	+	0.540675i
$479$	11.5535			0.527891			0.263946	−	0.964538i	$-0.414976\pi$
$479$	11.5535			0.527891			0.263946	+	0.964538i	$0.414976\pi$
$480$	−9.79273	+	0.320181i	−0.446975	+	0.0146142i
$481$	0.851029			0.0388036
$482$	−10.8691	−	14.1936i	−0.495073	−	0.646499i
$483$	−1.36420	+	14.5749i	−0.0620734	+	0.663181i
$484$	−8.93962	+	33.1041i	−0.406346	+	1.50473i
$485$			10.9809i			0.498619i
$486$	4.09598	+	21.6616i	0.185797	+	0.982588i
$487$			18.0727i			0.818953i	0.912321	+	0.409476i	$0.134289\pi$
$487$			18.0727i			0.818953i	−0.912321	+	0.409476i	$0.865711\pi$
$488$	−4.14076	+	1.70095i	−0.187444	+	0.0769984i
$489$	1.27149	−	13.5843i	0.0574986	−	0.614305i
$490$	1.12281	−	0.859821i	0.0507235	−	0.0388428i
$491$	−12.0038			−0.541725			−0.270863	−	0.962618i	$-0.587309\pi$
$491$	−12.0038			−0.541725			−0.270863	+	0.962618i	$0.587309\pi$
$492$	16.8802	+	6.29759i	0.761019	+	0.283917i
$493$	−6.64210			−0.299145
$494$	−19.0241	+	14.5682i	−0.855934	+	0.655453i
$495$	−2.95350	+	15.6391i	−0.132750	+	0.702925i
$496$	8.76752	−	15.0496i	0.393673	−	0.675746i
$497$			2.69785i			0.121015i
$498$	5.82890	+	9.29324i	0.261199	+	0.416440i
$499$			21.7624i			0.974219i	0.873341	+	0.487109i	$0.161949\pi$
$499$			21.7624i			0.974219i	−0.873341	+	0.487109i	$0.838051\pi$
$500$	−1.93084	−	0.521414i	−0.0863496	−	0.0233184i
$501$	9.26828	+	0.867506i	0.414076	+	0.0387573i
$502$	7.98944	+	10.4331i	0.356586	+	0.465654i
$503$	−23.8126			−1.06175			−0.530877	−	0.847449i	$-0.678137\pi$
$503$	−23.8126			−1.06175			−0.530877	+	0.847449i	$0.678137\pi$
$504$	−1.71163	−	8.31086i	−0.0762421	−	0.370195i
$505$	−6.49341			−0.288953
$506$	38.5521	+	50.3439i	1.71385	+	2.23806i
$507$	3.24895	+	0.304100i	0.144291	+	0.0135055i
$508$	11.6568	+	3.14788i	0.517189	+	0.139665i
$509$			30.4045i			1.34765i	0.738889	+	0.673827i	$0.235351\pi$
$509$			30.4045i			1.34765i	−0.738889	+	0.673827i	$0.764649\pi$
$510$	0.826426	+	1.31760i	0.0365948	+	0.0583445i
$511$			9.27865i			0.410463i
$512$	8.84273	−	20.8280i	0.390797	−	0.920477i
$513$	7.29702	−	25.3778i	0.322171	−	1.12046i
$514$	16.8008	−	12.8656i	0.741051	−	0.567478i
$515$	4.45217			0.196186
$516$	−20.1561	−	7.51972i	−0.887321	−	0.331037i
$517$	69.1999			3.04341
$518$	0.286600	−	0.219471i	0.0125925	−	0.00964302i
$519$	−3.24274	+	34.6449i	−0.142340	+	1.52074i
$520$	3.58320	+	8.72289i	0.157134	+	0.382524i
$521$		−	41.1496i		−	1.80280i	−0.432990	−	0.901399i	$-0.642542\pi$
$521$		−	41.1496i		−	1.80280i	0.432990	−	0.901399i	$-0.357458\pi$
$522$	39.6312	−	19.9753i	1.73461	−	0.874295i
$523$		−	8.44746i		−	0.369381i	−0.982797	−	0.184691i	$-0.940872\pi$
$523$		−	8.44746i		−	0.369381i	0.982797	−	0.184691i	$-0.0591283\pi$
$524$	3.55021	−	13.1467i	0.155092	−	0.574316i
$525$	0.161413	−	1.72451i	0.00704466	−	0.0752639i
$526$	14.1540	+	18.4833i	0.617145	+	0.805909i
$527$	−2.76482			−0.120437
$528$	−29.8965	−	21.3812i	−1.30108	−	0.930497i
$529$	48.4297			2.10564
$530$	−7.49524	−	9.78778i	−0.325572	−	0.425154i
$531$	5.36920	+	1.01399i	0.233003	+	0.0440035i
$532$	−2.64975	+	9.81222i	−0.114881	+	0.425414i
$533$		−	17.3404i		−	0.751096i
$534$	23.5746	−	14.7864i	1.02017	−	0.639871i
$535$			1.19494i			0.0516616i
$536$	10.0887	+	24.5599i	0.435767	+	1.06082i
$537$	−28.3518	−	2.65371i	−1.22347	−	0.114516i
$538$	0.994031	−	0.761204i	0.0428557	−	0.0328178i
$539$	5.30518			0.228510
$540$	−8.89354	−	5.37633i	−0.382717	−	0.231360i
$541$	−28.0162			−1.20451			−0.602254	−	0.798304i	$-0.705731\pi$
$541$	−28.0162			−1.20451			−0.602254	+	0.798304i	$0.705731\pi$
$542$	22.8163	−	17.4722i	0.980045	−	0.750494i
$543$	13.9686	+	1.30745i	0.599449	+	0.0561081i
$544$	−3.56341	+	0.451423i	−0.152780	+	0.0193546i
$545$		−	1.19967i		−	0.0513884i
$546$	−6.91850	+	4.33941i	−0.296084	+	0.185710i
$547$		−	32.9367i		−	1.40827i	−0.710064	−	0.704137i	$-0.751334\pi$
$547$		−	32.9367i		−	1.40827i	0.710064	−	0.704137i	$-0.248666\pi$
$548$	−19.1854	−	5.18093i	−0.819558	−	0.221318i
$549$	−4.66559	−	0.881111i	−0.199122	−	0.0376049i
$550$	−4.56151	−	5.95672i	−0.194503	−	0.253995i
$551$	−53.1594			−2.26467
$552$	−39.5983	+	12.0949i	−1.68542	+	0.514791i
$553$	−5.23327			−0.222541
$554$	26.0104	+	33.9661i	1.10508	+	1.44308i
$555$	0.0412011	−	0.440186i	0.00174889	−	0.0186848i
$556$	14.3661	+	3.87951i	0.609259	+	0.164528i
$557$			20.2282i			0.857095i	0.903519	+	0.428547i	$0.140974\pi$
$557$			20.2282i			0.857095i	−0.903519	+	0.428547i	$0.859026\pi$
$558$	16.4967	−	8.31484i	0.698363	−	0.351995i
$559$			20.7055i			0.875751i
$560$	3.45625	+	2.01353i	0.146053	+	0.0850872i
$561$	−0.543735	+	5.80918i	−0.0229565	+	0.245264i
$562$	−16.7711	+	12.8429i	−0.707447	+	0.541745i
$563$	15.9046			0.670301			0.335150	−	0.942165i	$-0.391213\pi$
$563$	15.9046			0.670301			0.335150	+	0.942165i	$0.391213\pi$
$564$	−15.7941	+	42.3349i	−0.665052	+	1.78262i
$565$	−7.18544			−0.302294
$566$	9.64126	−	7.38304i	0.405253	−	0.310332i
$567$	3.28229	−	8.38013i	0.137843	−	0.351932i
$568$	−7.05836	+	2.89944i	−0.296162	+	0.121658i
$569$			34.8398i			1.46056i	0.683149	+	0.730279i	$0.260610\pi$
$569$			34.8398i			1.46056i	−0.683149	+	0.730279i	$0.739390\pi$
$570$	6.61421	+	10.5453i	0.277039	+	0.441694i
$571$		−	34.6927i		−	1.45184i	−0.687777	−	0.725922i	$-0.741413\pi$
$571$		−	34.6927i		−	1.45184i	0.687777	−	0.725922i	$-0.258587\pi$
$572$	−9.22270	+	34.1523i	−0.385620	+	1.42798i
$573$	−5.93342	−	0.555364i	−0.247872	−	0.0232007i
$574$	−4.47191	−	5.83972i	−0.186654	−	0.243745i
$575$	−8.45161			−0.352456
$576$	19.9041	−	13.4100i	0.829336	−	0.558750i
$577$	28.0937			1.16956			0.584779	−	0.811193i	$-0.301181\pi$
$577$	28.0937			1.16956			0.584779	+	0.811193i	$0.301181\pi$
$578$	−14.2703	−	18.6351i	−0.593566	−	0.775119i
$579$	−4.68581	−	0.438589i	−0.194735	−	0.0182271i
$580$	−5.45432	+	20.1978i	−0.226478	+	0.838667i
$581$		−	4.47848i		−	0.185798i
$582$	−14.2921	−	22.7865i	−0.592426	−	0.944529i
$583$		−	46.2463i		−	1.91533i
$584$	−24.2756	+	9.97199i	−1.00453	+	0.412644i
$585$	−1.85614	+	9.82848i	−0.0767420	+	0.406357i
$586$	11.9200	−	9.12803i	0.492410	−	0.377075i
$587$	22.9647			0.947857			0.473928	−	0.880563i	$-0.342836\pi$
$587$	22.9647			0.947857			0.473928	+	0.880563i	$0.342836\pi$
$588$	−1.21085	+	3.24559i	−0.0499346	+	0.133846i
$589$	−22.1279			−0.911765
$590$	−2.04506	+	1.56605i	−0.0841936	+	0.0644734i
$591$	−2.13582	+	22.8188i	−0.0878561	+	0.938639i
$592$	0.882217	+	0.513958i	0.0362589	+	0.0211236i
$593$			46.8926i			1.92565i	0.270131	+	0.962824i	$0.412933\pi$
$593$			46.8926i			1.92565i	−0.270131	+	0.962824i	$0.587067\pi$
$594$	−14.2261	−	36.2966i	−0.583703	−	1.48927i
$595$		−	0.634962i		−	0.0260309i
$596$	0.614110	+	0.165838i	0.0251549	+	0.00679299i
$597$	2.29567	−	24.5265i	0.0939553	−	1.00380i
$598$	24.2283	+	31.6389i	0.990768	+	1.29381i
$599$	−12.7934			−0.522725			−0.261363	−	0.965241i	$-0.584172\pi$
$599$	−12.7934			−0.522725			−0.261363	+	0.965241i	$0.584172\pi$
$600$	4.68530	−	1.43107i	0.191277	−	0.0584232i
$601$	18.5764			0.757746			0.378873	−	0.925449i	$-0.376312\pi$
$601$	18.5764			0.757746			0.378873	+	0.925449i	$0.376312\pi$
$602$	5.33974	+	6.97299i	0.217632	+	0.284198i
$603$	−5.22608	+	27.6727i	−0.212823	+	1.12692i
$604$	−23.1232	−	6.24432i	−0.940868	−	0.254078i
$605$		−	17.1449i		−	0.697041i
$606$	13.4744	−	8.45141i	0.547361	−	0.343315i
$607$			36.7737i			1.49260i	0.665611	+	0.746299i	$0.268171\pi$
$607$			36.7737i			1.49260i	−0.665611	+	0.746299i	$0.731829\pi$
$608$	−28.5193	+	3.61291i	−1.15661	+	0.146523i
$609$	−18.0395	−	1.68849i	−0.730997	−	0.0684209i
$610$	1.77706	−	1.36083i	0.0719510	−	0.0550983i
$611$	43.4890			1.75938
$612$	−3.42982	−	1.65852i	−0.138642	−	0.0670419i
$613$	−7.48353			−0.302257			−0.151128	−	0.988514i	$-0.548291\pi$
$613$	−7.48353			−0.302257			−0.151128	+	0.988514i	$0.548291\pi$
$614$	−14.2321	+	10.8986i	−0.574362	+	0.439832i
$615$	−8.96915	−	0.839507i	−0.361671	−	0.0338522i
$616$	5.70160	+	13.8799i	0.229724	+	0.559237i
$617$		−	11.8571i		−	0.477351i	−0.971099	−	0.238675i	$-0.923287\pi$
$617$		−	11.8571i		−	0.477351i	0.971099	−	0.238675i	$-0.0767132\pi$
$618$	−9.23865	+	5.79466i	−0.371633	+	0.233095i
$619$			12.9076i			0.518800i	0.965770	+	0.259400i	$0.0835247\pi$
$619$			12.9076i			0.518800i	−0.965770	+	0.259400i	$0.916475\pi$
$620$	−2.27040	+	8.40744i	−0.0911813	+	0.337651i
$621$	−42.2058	−	12.1357i	−1.69366	−	0.486987i
$622$	−6.42194	−	8.38620i	−0.257496	−	0.336256i
$623$	−11.3607			−0.455158
$624$	−18.7886	−	13.4371i	−0.752147	−	0.537915i
$625$	1.00000			0.0400000
$626$	−2.79777	−	3.65352i	−0.111822	−	0.146024i
$627$	−4.35173	+	46.4931i	−0.173791	+	1.85676i
$628$	9.59766	−	35.5408i	0.382988	−	1.41823i
$629$		−	0.162075i		−	0.00646237i
$630$	1.90957	+	3.78861i	0.0760791	+	0.150942i
$631$			27.1666i			1.08148i	0.841189	+	0.540742i	$0.181856\pi$
$631$			27.1666i			1.08148i	−0.841189	+	0.540742i	$0.818144\pi$
$632$	−5.62432	−	13.6917i	−0.223723	−	0.544629i
$633$	1.28158	−	13.6922i	0.0509384	−	0.544217i
$634$	−21.3658	+	16.3614i	−0.848543	+	0.649793i
$635$	−6.03720			−0.239579
$636$	28.2924	+	10.5552i	1.12187	+	0.418541i
$637$	3.33407			0.132101
$638$	−62.3111	+	47.7163i	−2.46692	+	1.88910i
$639$	−7.95297	−	1.50194i	−0.314615	−	0.0594160i
$640$	−1.55346	+	11.2065i	−0.0614059	+	0.442978i
$641$		−	25.6216i		−	1.01199i	−0.862536	−	0.505996i	$-0.831125\pi$
$641$		−	25.6216i		−	1.01199i	0.862536	−	0.505996i	$-0.168875\pi$
$642$	−1.55525	−	2.47960i	−0.0613809	−	0.0978620i
$643$			44.1093i			1.73950i	0.493493	+	0.869750i	$0.335720\pi$
$643$			44.1093i			1.73950i	−0.493493	+	0.869750i	$0.664280\pi$
$644$	16.3187	+	4.40679i	0.643046	+	0.173652i
$645$	10.7097	+	1.00242i	0.421695	+	0.0394704i
$646$	2.77446	+	3.62307i	0.109160	+	0.142548i
$647$	−34.7259			−1.36521			−0.682607	−	0.730785i	$-0.739154\pi$
$647$	−34.7259			−1.36521			−0.682607	+	0.730785i	$0.739154\pi$
$648$	25.4524	−	0.418889i	0.999865	−	0.0164555i
$649$	−9.66269			−0.379294
$650$	−2.86670	−	3.74353i	−0.112441	−	0.146833i
$651$	−7.50905	−	0.702843i	−0.294303	−	0.0275466i
$652$	−15.2096	−	4.10728i	−0.595653	−	0.160854i
$653$		−	20.8680i		−	0.816628i	−0.912842	−	0.408314i	$-0.866117\pi$
$653$		−	20.8680i		−	0.816628i	0.912842	−	0.408314i	$-0.133883\pi$
$654$	1.56142	+	2.48943i	0.0610563	+	0.0973445i
$655$			6.80880i			0.266042i
$656$	10.4723	−	17.9759i	0.408875	−	0.701840i
$657$	−27.3525	−	5.16560i	−1.06712	−	0.201529i
$658$	14.6458	−	11.2154i	0.570952	−	0.437220i
$659$	44.9911			1.75260			0.876302	−	0.481762i	$-0.160003\pi$
$659$	44.9911			1.75260			0.876302	+	0.481762i	$0.160003\pi$
$660$	17.2184	+	6.42377i	0.670227	+	0.250045i
$661$	17.1815			0.668282			0.334141	−	0.942523i	$-0.391554\pi$
$661$	17.1815			0.668282			0.334141	+	0.942523i	$0.391554\pi$
$662$	−7.80930	+	5.98017i	−0.303517	+	0.232426i
$663$	−0.341713	+	3.65081i	−0.0132710	+	0.141786i
$664$	11.7170	−	4.81312i	0.454707	−	0.186785i
$665$		−	5.08185i		−	0.197066i
$666$	0.487422	+	0.967050i	0.0188872	+	0.0374724i
$667$			88.4092i			3.42322i
$668$	2.80231	−	10.3771i	0.108425	−	0.401504i
$669$	2.43416	−	26.0061i	0.0941099	−	1.00545i
$670$	−8.07139	−	10.5402i	−0.311825	−	0.407202i
$671$	8.39643			0.324141
$672$	−9.79273	+	0.320181i	−0.377763	+	0.0123512i
$673$	−24.6291			−0.949381			−0.474690	−	0.880153i	$-0.657440\pi$
$673$	−24.6291			−0.949381			−0.474690	+	0.880153i	$0.657440\pi$
$674$	−24.2386	−	31.6523i	−0.933635	−	1.21920i
$675$	4.99382	+	1.43590i	0.192212	+	0.0552678i
$676$	0.982334	−	3.63766i	0.0377821	−	0.139910i
$677$		−	32.7356i		−	1.25813i	−0.777353	−	0.629065i	$-0.783438\pi$
$677$		−	32.7356i		−	1.25813i	0.777353	−	0.629065i	$-0.216562\pi$
$678$	14.9104	−	9.35212i	0.572632	−	0.359166i
$679$			10.9809i			0.421410i
$680$	1.66124	−	0.682409i	0.0637058	−	0.0261692i
$681$	−16.9037	−	1.58218i	−0.647753	−	0.0606293i
$682$	−25.9374	+	19.8622i	−0.993193	+	0.760562i
$683$	9.21587			0.352635			0.176318	−	0.984333i	$-0.443581\pi$
$683$	9.21587			0.352635			0.176318	+	0.984333i	$0.443581\pi$
$684$	−27.4502	−	13.2738i	−1.04958	−	0.507537i
$685$	9.93629			0.379646
$686$	1.12281	−	0.859821i	0.0428692	−	0.0328281i
$687$	−13.4219	−	1.25628i	−0.512078	−	0.0479302i
$688$	−12.5046	+	21.4643i	−0.476734	+	0.818321i
$689$		−	29.0638i		−	1.10724i
$690$	17.5379	−	11.0001i	0.667655	−	0.418766i
$691$		−	46.3653i		−	1.76382i	−0.471419	−	0.881909i	$-0.656258\pi$
$691$		−	46.3653i		−	1.76382i	0.471419	−	0.881909i	$-0.343742\pi$
$692$	38.7898	+	10.4750i	1.47457	+	0.398201i
$693$	−2.95350	+	15.6391i	−0.112194	+	0.594080i
$694$	10.5566	+	13.7855i	0.400722	+	0.523289i
$695$	−7.44036			−0.282229
$696$	−14.9699	−	49.0112i	−0.567433	−	1.85776i
$697$	−3.30242			−0.125088
$698$	6.42487	+	8.39002i	0.243185	+	0.317567i
$699$	1.89841	−	20.2822i	0.0718043	−	0.767145i
$700$	−1.93084	−	0.521414i	−0.0729787	−	0.0197076i
$701$			20.2227i			0.763801i	0.924203	+	0.381901i	$0.124730\pi$
$701$			20.2227i			0.763801i	−0.924203	+	0.381901i	$0.875270\pi$
$702$	−8.94046	−	22.8108i	−0.337436	−	0.860939i
$703$		−	1.29715i		−	0.0489231i
$704$	−30.1862	+	29.8341i	−1.13768	+	1.12441i
$705$	2.10545	−	22.4943i	0.0792958	−	0.847183i
$706$	25.7157	−	19.6924i	0.967822	−	0.741134i
$707$	−6.49341			−0.244210
$708$	2.20540	−	5.91142i	0.0828841	−	0.222165i
$709$	21.4682			0.806254			0.403127	−	0.915144i	$-0.367923\pi$
$709$	21.4682			0.806254			0.403127	+	0.915144i	$0.367923\pi$
$710$	3.02918	−	2.31967i	0.113683	−	0.0870556i
$711$	2.91346	−	15.4271i	0.109263	−	0.578562i
$712$	−12.2097	−	29.7230i	−0.457576	−	1.11392i
$713$			36.8009i			1.37820i
$714$	0.826426	+	1.31760i	0.0309282	+	0.0493101i
$715$		−	17.6878i		−	0.661488i
$716$	−8.57230	+	31.7439i	−0.320362	+	1.18632i
$717$	18.1555	+	1.69935i	0.678031	+	0.0634633i
$718$	25.3710	+	33.1312i	0.946838	+	1.23644i
$719$	17.5562			0.654736			0.327368	−	0.944897i	$-0.393838\pi$
$719$	17.5562			0.654736			0.327368	+	0.944897i	$0.393838\pi$
$720$	−7.85983	+	9.06769i	−0.292919	+	0.337933i
$721$	4.45217			0.165807
$722$	5.86845	+	7.66342i	0.218401	+	0.285203i
$723$	−21.7997	−	2.04044i	−0.810740	−	0.0758848i
$724$	4.22346	−	15.6398i	0.156964	−	0.581249i
$725$		−	10.4606i		−	0.388498i
$726$	22.3148	+	35.5773i	0.828179	+	1.32040i
$727$		−	52.6328i		−	1.95204i	−0.217672	−	0.976022i	$-0.569846\pi$
$727$		−	52.6328i		−	1.95204i	0.217672	−	0.976022i	$-0.430154\pi$
$728$	3.58320	+	8.72289i	0.132802	+	0.323292i
$729$	22.8764	+	14.3412i	0.847274	+	0.531157i
$730$	10.4182	−	7.97798i	0.385594	−	0.295278i
$731$	3.94330			0.145848
$732$	−1.91639	+	5.13675i	−0.0708319	+	0.189860i
$733$	29.6945			1.09679			0.548397	−	0.836218i	$-0.315238\pi$
$733$	29.6945			1.09679			0.548397	+	0.836218i	$0.315238\pi$
$734$	−15.1063	+	11.5681i	−0.557585	+	0.426985i
$735$	0.161413	−	1.72451i	0.00595382	−	0.0636096i
$736$	6.00862	+	47.4304i	0.221481	+	1.74831i
$737$		−	49.8013i		−	1.83445i
$738$	19.7044	−	9.93162i	0.725331	−	0.365588i
$739$			12.2489i			0.450584i	0.974291	+	0.225292i	$0.0723335\pi$
$739$			12.2489i			0.450584i	−0.974291	+	0.225292i	$0.927666\pi$
$740$	−0.492850	−	0.133092i	−0.0181175	−	0.00489257i
$741$	−2.73487	+	29.2188i	−0.100468	+	1.07338i
$742$	−7.49524	−	9.78778i	−0.275159	−	0.359321i
$743$	19.3640			0.710395			0.355198	−	0.934791i	$-0.384414\pi$
$743$	19.3640			0.710395			0.355198	+	0.934791i	$0.384414\pi$
$744$	−6.23132	−	20.4012i	−0.228451	−	0.747945i
$745$	−0.318054			−0.0116526
$746$	−7.31565	−	9.55326i	−0.267845	−	0.349770i
$747$	13.2021	+	2.49325i	0.483038	+	0.0912233i
$748$	6.50419	+	1.75643i	0.237817	+	0.0642215i
$749$			1.19494i			0.0436620i
$750$	−2.07509	+	1.30154i	−0.0757716	+	0.0475254i
$751$			8.42612i			0.307474i	0.988112	+	0.153737i	$0.0491308\pi$
$751$			8.42612i			0.307474i	−0.988112	+	0.153737i	$0.950869\pi$
$752$	45.0828	+	26.2642i	1.64400	+	0.957755i
$753$	16.0241	+	1.49985i	0.583952	+	0.0546576i
$754$	−39.1597	+	29.9875i	−1.42611	+	1.09208i
$755$	11.9757			0.435841
$756$	−8.89354	−	5.37633i	−0.323455	−	0.195535i
$757$	−31.5748			−1.14761			−0.573804	−	0.818993i	$-0.694533\pi$
$757$	−31.5748			−1.14761			−0.573804	+	0.818993i	$0.694533\pi$
$758$	−6.50747	+	4.98326i	−0.236362	+	0.181000i
$759$	77.3226	+	7.23734i	2.80663	+	0.262699i
$760$	13.2956	−	5.46158i	0.482282	−	0.198112i
$761$		−	18.4547i		−	0.668982i	−0.942399	−	0.334491i	$-0.891436\pi$
$761$		−	18.4547i		−	0.668982i	0.942399	−	0.334491i	$-0.108564\pi$
$762$	12.5277	−	7.85764i	0.453832	−	0.284652i
$763$		−	1.19967i		−	0.0434311i
$764$	−1.79400	+	6.64330i	−0.0649045	+	0.240346i
$765$	1.87180	+	0.353495i	0.0676750	+	0.0127807i
$766$	6.44371	+	8.41463i	0.232821	+	0.304033i
$767$	−6.07257			−0.219268
$768$	−11.3622	−	25.2765i	−0.409997	−	0.912087i
$769$	5.19876			0.187472			0.0937361	−	0.995597i	$-0.470119\pi$
$769$	5.19876			0.187472			0.0937361	+	0.995597i	$0.470119\pi$
$770$	−4.56151	−	5.95672i	−0.164385	−	0.214665i
$771$	2.41525	−	25.8041i	0.0869831	−	0.929312i
$772$	−1.41677	+	5.24642i	−0.0509908	+	0.188823i
$773$			11.2632i			0.405108i	0.979271	+	0.202554i	$0.0649241\pi$
$773$			11.2632i			0.405108i	−0.979271	+	0.202554i	$0.935076\pi$
$774$	−23.5284	+	11.8590i	−0.845709	+	0.426262i
$775$		−	4.35430i		−	0.156411i
$776$	−28.7293	+	11.8015i	−1.03132	+	0.423648i
$777$	0.0412011	−	0.440186i	0.00147808	−	0.0157916i
$778$	−9.80895	+	7.51145i	−0.351668	+	0.269298i
$779$	−26.4306			−0.946973
$780$	10.8210	+	4.03705i	0.387455	+	0.144550i
$781$	14.3126			0.512145
$782$	6.02552	−	4.61419i	0.215472	−	0.165003i
$783$	15.0204	−	52.2385i	0.536786	−	1.86685i
$784$	3.45625	+	2.01353i	0.123438	+	0.0719118i
$785$			18.4070i			0.656973i
$786$	−8.86191	−	14.1289i	−0.316094	−	0.503961i
$787$		−	19.6731i		−	0.701272i	−0.936512	−	0.350636i	$-0.885965\pi$
$787$		−	19.6731i		−	0.701272i	0.936512	−	0.350636i	$-0.114035\pi$
$788$	25.5488	+	6.89936i	0.910140	+	0.245780i
$789$	28.3882	+	2.65712i	1.01065	+	0.0945960i
$790$	4.49968	+	5.87598i	0.160091	+	0.209058i
$791$	−7.18544			−0.255485
$792$	−44.0906	+	9.08051i	−1.56669	+	0.322662i
$793$	5.27678			0.187384
$794$	7.31959	+	9.55841i	0.259763	+	0.339215i
$795$	−15.0329	−	1.40707i	−0.533163	−	0.0499037i
$796$	−27.4609	−	7.41570i	−0.973325	−	0.262842i
$797$		−	24.6497i		−	0.873139i	−0.899671	−	0.436569i	$-0.856193\pi$
$797$		−	24.6497i		−	0.873139i	0.899671	−	0.436569i	$-0.143807\pi$
$798$	6.61421	+	10.5453i	0.234141	+	0.373300i
$799$		−	8.28234i		−	0.293008i
$800$	−0.710944	−	5.61200i	−0.0251357	−	0.198414i
$801$	6.32474	−	33.4902i	0.223474	−	1.18332i
$802$	21.7807	−	16.6791i	0.769102	−	0.588959i
$803$	49.2249			1.73711
$804$	30.4673	+	11.3666i	1.07450	+	0.400869i
$805$	−8.45161			−0.297880
$806$	−16.3005	+	12.4825i	−0.574160	+	0.439677i
$807$	0.142900	−	1.52672i	0.00503032	−	0.0537431i
$808$	−6.97862	−	16.9886i	−0.245507	−	0.597658i
$809$			44.9047i			1.57877i	0.613901	+	0.789383i	$0.289599\pi$
$809$			44.9047i			1.57877i	−0.613901	+	0.789383i	$0.710401\pi$
$810$	−12.2315	+	3.52001i	−0.429771	+	0.123681i
$811$		−	21.5803i		−	0.757786i	−0.925441	−	0.378893i	$-0.876305\pi$
$811$		−	21.5803i		−	0.757786i	0.925441	−	0.378893i	$-0.123695\pi$
$812$	−5.45432	+	20.1978i	−0.191409	+	0.708803i
$813$	3.28003	−	35.0433i	0.115036	−	1.22902i
$814$	−1.16434	−	1.52047i	−0.0408099	−	0.0532923i
$815$	7.87720			0.275926
$816$	−2.55905	+	3.57823i	−0.0895848	+	0.125263i
$817$	31.5598			1.10414
$818$	7.61964	+	9.95023i	0.266414	+	0.347902i
$819$	−1.85614	+	9.82848i	−0.0648588	+	0.343435i
$820$	−2.71186	+	10.0422i	−0.0947023	+	0.350690i
$821$			38.9718i			1.36013i	0.733154	+	0.680063i	$0.238048\pi$
$821$			38.9718i			1.36013i	−0.733154	+	0.680063i	$0.761952\pi$
$822$	−20.6187	+	12.9324i	−0.719160	+	0.451071i
$823$		−	9.16920i		−	0.319618i	−0.987148	−	0.159809i	$-0.948912\pi$
$823$		−	9.16920i		−	0.319618i	0.987148	−	0.159809i	$-0.0510879\pi$
$824$	4.78485	+	11.6482i	0.166688	+	0.405783i
$825$	−9.14886	−	0.856327i	−0.318522	−	0.0298135i
$826$	−2.04506	+	1.56605i	−0.0711566	+	0.0544899i
$827$	−30.5978			−1.06399			−0.531995	−	0.846747i	$-0.678558\pi$
$827$	−30.5978			−1.06399			−0.531995	+	0.846747i	$0.678558\pi$
$828$	−22.0757	+	45.6523i	−0.767182	+	1.58653i
$829$	−17.5068			−0.608037			−0.304018	−	0.952666i	$-0.598328\pi$
$829$	−17.5068			−0.608037			−0.304018	+	0.952666i	$0.598328\pi$
$830$	−5.02849	+	3.85069i	−0.174541	+	0.133659i
$831$	52.1682	+	4.88291i	1.80969	+	0.169386i
$832$	−18.9707	+	18.7494i	−0.657689	+	0.650018i
$833$		−	0.634962i		−	0.0220001i
$834$	15.4394	−	9.68390i	0.534624	−	0.335326i
$835$			5.37443i			0.185990i
$836$	52.0556	+	14.0574i	1.80038	+	0.486185i
$837$	6.25234	−	21.7446i	0.216112	−	0.751603i
$838$	−24.6449	−	32.1830i	−0.851345	−	1.11174i
$839$	10.5056			0.362694			0.181347	−	0.983419i	$-0.441954\pi$
$839$	10.5056			0.362694			0.181347	+	0.983419i	$0.441954\pi$
$840$	4.68530	−	1.43107i	0.161658	−	0.0493766i
$841$	−80.4248			−2.77327
$842$	−11.1810	−	14.6009i	−0.385323	−	0.503181i
$843$	−2.41098	+	25.7585i	−0.0830387	+	0.887171i
$844$	−15.3304	−	4.13990i	−0.527693	−	0.142501i
$845$			1.88398i			0.0648109i
$846$	24.9081	+	49.4180i	0.856358	+	1.69902i
$847$		−	17.1449i		−	0.589107i
$848$	17.5524	−	30.1289i	0.602750	−	1.03463i
$849$	1.38601	−	14.8079i	0.0475678	−	0.508206i
$850$	−0.712943	+	0.545954i	−0.0244537	+	0.0187261i
$851$	−2.15729			−0.0739510
$852$	−3.26669	+	8.75611i	−0.111915	+	0.299979i
$853$	10.3433			0.354147			0.177073	−	0.984198i	$-0.443337\pi$
$853$	10.3433			0.354147			0.177073	+	0.984198i	$0.443337\pi$
$854$	1.77706	−	1.36083i	0.0608097	−	0.0465665i
$855$	14.9807	+	2.82916i	0.512331	+	0.0967553i
$856$	−3.12630	+	1.28423i	−0.106855	+	0.0438939i
$857$		−	41.9371i		−	1.43254i	−0.697821	−	0.716272i	$-0.745847\pi$
$857$		−	41.9371i		−	1.43254i	0.697821	−	0.716272i	$-0.254153\pi$
$858$	23.0214	+	36.7039i	0.785937	+	1.25305i
$859$		−	45.7121i		−	1.55968i	−0.625981	−	0.779838i	$-0.715301\pi$
$859$		−	45.7121i		−	1.55968i	0.625981	−	0.779838i	$-0.284699\pi$
$860$	3.23814	−	11.9911i	0.110419	−	0.408892i
$861$	−8.96915	−	0.839507i	−0.305668	−	0.0286103i
$862$	11.4018	+	14.8893i	0.388348	+	0.507130i
$863$	30.1224			1.02538			0.512690	−	0.858574i	$-0.328649\pi$
$863$	30.1224			1.02538			0.512690	+	0.858574i	$0.328649\pi$
$864$	4.50794	−	29.0461i	0.153363	−	0.988170i
$865$	−20.0897			−0.683069
$866$	−27.3971	−	35.7770i	−0.930993	−	1.21575i
$867$	−28.6214	−	2.67895i	−0.972035	−	0.0909819i
$868$	−2.27040	+	8.40744i	−0.0770622	+	0.285367i
$869$			27.7634i			0.941810i
$870$	13.6149	+	21.7068i	0.461588	+	0.735928i
$871$		−	31.2979i		−	1.06049i
$872$	3.13869	−	1.28932i	0.106290	−	0.0436618i
$873$	−32.3706	−	6.11330i	−1.09558	−	0.206904i
$874$	48.2246	−	36.9292i	1.63122	−	1.24915i
$875$	1.00000			0.0338062
$876$	−11.2350	+	30.1147i	−0.379597	+	1.01748i
$877$	11.2068			0.378426			0.189213	−	0.981936i	$-0.439406\pi$
$877$	11.2068			0.378426			0.189213	+	0.981936i	$0.439406\pi$
$878$	6.16687	−	4.72243i	0.208122	−	0.159374i
$879$	1.71360	−	18.3078i	0.0577982	−	0.617506i
$880$	10.6821	−	18.3361i	0.360095	−	0.618108i
$881$		−	10.9843i		−	0.370072i	−0.982732	−	0.185036i	$-0.940760\pi$
$881$		−	10.9843i		−	0.370072i	0.982732	−	0.185036i	$-0.0592401\pi$
$882$	1.90957	+	3.78861i	0.0642985	+	0.127569i
$883$		−	18.3404i		−	0.617204i	−0.951191	−	0.308602i	$-0.900139\pi$
$883$		−	18.3404i		−	0.617204i	0.951191	−	0.308602i	$-0.0998611\pi$
$884$	4.08759	+	1.10384i	0.137481	+	0.0371261i
$885$	−0.293993	+	3.14098i	−0.00988248	+	0.105583i
$886$	−9.60641	−	12.5447i	−0.322734	−	0.421447i
$887$	27.4035			0.920119			0.460059	−	0.887888i	$-0.347828\pi$
$887$	27.4035			0.920119			0.460059	+	0.887888i	$0.347828\pi$
$888$	1.19593	−	0.365284i	0.0401329	−	0.0122581i
$889$	−6.03720			−0.202481
$890$	9.76821	+	12.7560i	0.327431	+	0.427581i
$891$	−44.4581	−	17.4132i	−1.48940	−	0.583363i
$892$	−29.1175	−	7.86307i	−0.974926	−	0.263275i
$893$		−	66.2868i		−	2.21820i
$894$	0.659991	−	0.413959i	0.0220734	−	0.0138449i
$895$		−	16.4405i		−	0.549544i
$896$	−1.55346	+	11.2065i	−0.0518975	+	0.374385i
$897$	48.5938	+	4.54835i	1.62250	+	0.151865i
$898$	−17.3417	+	13.2799i	−0.578701	+	0.443155i
$899$	−45.5488			−1.51914
$900$	2.61201	−	5.40161i	0.0870669	−	0.180054i
$901$	−5.53509			−0.184401
$902$	−30.9808	+	23.7243i	−1.03155	+	0.789932i
$903$	10.7097	+	1.00242i	0.356398	+	0.0333586i
$904$	−7.72237	−	18.7992i	−0.256842	−	0.625252i
$905$			8.10002i			0.269254i
$906$	−24.8507	+	15.5868i	−0.825610	+	0.517838i
$907$			35.6439i			1.18354i	0.806108	+	0.591768i	$0.201570\pi$
$907$			35.6439i			1.18354i	−0.806108	+	0.591768i	$0.798430\pi$
$908$	−5.11092	+	18.9261i	−0.169612	+	0.628085i
$909$	3.61501	−	19.1419i	0.119902	−	0.634896i
$910$	−2.86670	−	3.74353i	−0.0950303	−	0.124097i
$911$	7.57710			0.251041			0.125520	−	0.992091i	$-0.459940\pi$
$911$	7.57710			0.251041			0.125520	+	0.992091i	$0.459940\pi$
$912$	−20.4811	+	28.6380i	−0.678197	+	0.948298i
$913$	−23.7591			−0.786312
$914$	30.6961	+	40.0850i	1.01534	+	1.32589i
$915$	0.255467	−	2.72936i	0.00844547	−	0.0902299i
$916$	−4.05817	+	15.0277i	−0.134086	+	0.496530i
$917$			6.80880i			0.224847i
$918$	−4.34424	+	1.70268i	−0.143381	+	0.0561968i
$919$		−	31.7138i		−	1.04614i	−0.852290	−	0.523070i	$-0.824787\pi$
$919$		−	31.7138i		−	1.04614i	0.852290	−	0.523070i	$-0.175213\pi$
$920$	−9.08314	−	22.1119i	−0.299462	−	0.729006i
$921$	−2.04598	+	21.8590i	−0.0674175	+	0.720277i
$922$	37.3600	−	28.6094i	1.23039	−	0.942199i
$923$	8.99482			0.296068
$924$	17.2184	+	6.42377i	0.566445	+	0.211327i
$925$	0.255252			0.00839264
$926$	−23.6987	+	18.1479i	−0.778788	+	0.596377i
$927$	−2.47861	+	13.1245i	−0.0814081	+	0.431065i
$928$	−58.7051	+	7.43693i	−1.92709	+	0.244129i
$929$		−	5.57740i		−	0.182989i	−0.995806	−	0.0914943i	$-0.970836\pi$
$929$		−	5.57740i		−	0.182989i	0.995806	−	0.0914943i	$-0.0291643\pi$
$930$	5.66728	+	9.03557i	0.185838	+	0.296288i
$931$		−	5.08185i		−	0.166551i
$932$	−22.7088	−	6.13243i	−0.743853	−	0.200874i
$933$	−12.8803	−	1.20558i	−0.421681	−	0.0394691i
$934$	−16.5509	−	21.6132i	−0.541561	−	0.707207i
$935$	−3.36859			−0.110165
$936$	−27.7090	+	5.70670i	−0.905696	+	0.186529i
$937$	−2.78492			−0.0909793			−0.0454896	−	0.998965i	$-0.514485\pi$
$937$	−2.78492			−0.0909793			−0.0454896	+	0.998965i	$0.514485\pi$
$938$	−8.07139	−	10.5402i	−0.263540	−	0.344148i
$939$	−5.61140	−	0.525223i	−0.183121	−	0.0171400i
$940$	−25.1855	−	6.80124i	−0.821460	−	0.221832i
$941$			20.8911i			0.681031i	0.940239	+	0.340516i	$0.110602\pi$
$941$			20.8911i			0.681031i	−0.940239	+	0.340516i	$0.889398\pi$
$942$	−23.9573	−	38.1961i	−0.780572	−	1.24450i
$943$			43.9566i			1.43142i
$944$	−6.29512	−	3.66738i	−0.204889	−	0.119363i
$945$	4.99382	+	1.43590i	0.162449	+	0.0467098i
$946$	36.9930	−	28.3283i	1.20275	−	0.921032i
$947$	−18.9949			−0.617250			−0.308625	−	0.951184i	$-0.599869\pi$
$947$	−18.9949			−0.617250			−0.308625	+	0.951184i	$0.599869\pi$
$948$	−16.9850	−	6.33670i	−0.551649	−	0.205806i
$949$	30.9357			1.00421
$950$	−5.70596	+	4.36948i	−0.185126	+	0.141765i
$951$	−3.07150	+	32.8154i	−0.0996003	+	1.06411i
$952$	1.66124	−	0.682409i	0.0538412	−	0.0221170i
$953$			39.3255i			1.27388i	0.770915	+	0.636938i	$0.219799\pi$
$953$			39.3255i			1.27388i	−0.770915	+	0.636938i	$0.780201\pi$
$954$	33.0261	−	16.6461i	1.06926	−	0.538937i
$955$		−	3.44063i		−	0.111336i
$956$	5.48941	−	20.3277i	0.177540	−	0.657445i
$957$	−8.95773	+	95.7028i	−0.289562	+	3.09363i
$958$	−9.93392	−	12.9724i	−0.320950	−	0.419118i
$959$	9.93629			0.320860
$960$	8.77950	+	10.7201i	0.283357	+	0.345990i
$961$	12.0401			0.388389
$962$	−0.731733	−	0.955545i	−0.0235920	−	0.0308080i
$963$	−3.52254	−	0.665243i	−0.113512	−	0.0214372i
$964$	−6.59124	+	24.4079i	−0.212290	+	0.786124i
$965$		−	2.71718i		−	0.0874690i
$966$	17.5379	−	11.0001i	0.564271	−	0.353922i
$967$			9.05917i			0.291323i	0.989334	+	0.145662i	$0.0465311\pi$
$967$			9.05917i			0.291323i	−0.989334	+	0.145662i	$0.953469\pi$
$968$	44.8561	−	18.4261i	1.44173	−	0.592237i
$969$	5.56463	+	0.520846i	0.178762	+	0.0167320i
$970$	12.3295	−	9.44165i	0.395877	−	0.303153i
$971$	21.2643			0.682404			0.341202	−	0.939990i	$-0.389166\pi$
$971$	21.2643			0.682404			0.341202	+	0.939990i	$0.389166\pi$
$972$	20.8000	−	23.2241i	0.667162	−	0.744913i
$973$	−7.44036			−0.238527
$974$	20.2923	−	15.5393i	0.650206	−	0.497911i
$975$	−5.74965	−	0.538164i	−0.184136	−	0.0172350i
$976$	5.47016	+	3.18679i	0.175096	+	0.102007i
$977$			4.77207i			0.152672i	0.997082	+	0.0763360i	$0.0243222\pi$
$977$			4.77207i			0.152672i	−0.997082	+	0.0763360i	$0.975678\pi$
$978$	−16.3459	+	10.2525i	−0.522684	+	0.327838i
$979$			60.2708i			1.92626i
$980$	−1.93084	−	0.521414i	−0.0616783	−	0.0166560i
$981$	3.53651	+	0.667881i	0.112912	+	0.0213238i
$982$	10.3211	+	13.4780i	0.329361	+	0.430102i
$983$	20.8914			0.666332			0.333166	−	0.942868i	$-0.391883\pi$
$983$	20.8914			0.666332			0.333166	+	0.942868i	$0.391883\pi$
$984$	−7.44296	−	24.3681i	−0.237273	−	0.776827i
$985$	−13.2320			−0.421607
$986$	5.71102	+	7.45783i	0.181876	+	0.237506i
$987$	2.10545	−	22.4943i	0.0670172	−	0.716000i
$988$	32.7146	+	8.83445i	1.04079	+	0.281061i
$989$		−	52.4870i		−	1.66899i
$990$	20.0992	−	10.1306i	0.638796	−	0.321972i
$991$		−	14.5634i		−	0.462622i	−0.972880	−	0.231311i	$-0.925699\pi$
$991$		−	14.5634i		−	0.462622i	0.972880	−	0.231311i	$-0.0743014\pi$
$992$	−24.4363	+	3.09567i	−0.775855	+	0.0982875i
$993$	−1.12265	+	11.9942i	−0.0356263	+	0.380625i
$994$	3.02918	−	2.31967i	0.0960797	−	0.0735754i
$995$	14.2223			0.450876
$996$	5.42276	−	14.5353i	0.171827	−	0.460568i
$997$	27.7568			0.879067			0.439533	−	0.898226i	$-0.355144\pi$
$997$	27.7568			0.879067			0.439533	+	0.898226i	$0.355144\pi$
$998$	24.4351	−	18.7118i	0.773479	−	0.592311i
$999$	1.27468	+	0.366516i	0.0403292	+	0.0115961i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.859821 - 1.12281i) q^{2} +(-1.72451 - 0.161413i) q^{3} +(-0.521414 + 1.93084i) q^{4} -1.00000i q^{5} +(1.30154 + 2.07509i) q^{6} -1.00000i q^{7} +(2.61629 - 1.07472i) q^{8} +(2.94789 + 0.556719i) q^{9} +O(q^{10})\)	\(q+(-0.859821 - 1.12281i) q^{2} +(-1.72451 - 0.161413i) q^{3} +(-0.521414 + 1.93084i) q^{4} -1.00000i q^{5} +(1.30154 + 2.07509i) q^{6} -1.00000i q^{7} +(2.61629 - 1.07472i) q^{8} +(2.94789 + 0.556719i) q^{9} +(-1.12281 + 0.859821i) q^{10} -5.30518 q^{11} +(1.21085 - 3.24559i) q^{12} -3.33407 q^{13} +(-1.12281 + 0.859821i) q^{14} +(-0.161413 + 1.72451i) q^{15} +(-3.45625 - 2.01353i) q^{16} +0.634962i q^{17} +(-1.90957 - 3.78861i) q^{18} +5.08185i q^{19} +(1.93084 + 0.521414i) q^{20} +(-0.161413 + 1.72451i) q^{21} +(4.56151 + 5.95672i) q^{22} +8.45161 q^{23} +(-4.68530 + 1.43107i) q^{24} -1.00000 q^{25} +(2.86670 + 3.74353i) q^{26} +(-4.99382 - 1.43590i) q^{27} +(1.93084 + 0.521414i) q^{28} +10.4606i q^{29} +(2.07509 - 1.30154i) q^{30} +4.35430i q^{31} +(0.710944 + 5.61200i) q^{32} +(9.14886 + 0.856327i) q^{33} +(0.712943 - 0.545954i) q^{34} -1.00000 q^{35} +(-2.61201 + 5.40161i) q^{36} -0.255252 q^{37} +(5.70596 - 4.36948i) q^{38} +(5.74965 + 0.538164i) q^{39} +(-1.07472 - 2.61629i) q^{40} +5.20097i q^{41} +(2.07509 - 1.30154i) q^{42} -6.21029i q^{43} +(2.76620 - 10.2434i) q^{44} +(0.556719 - 2.94789i) q^{45} +(-7.26687 - 9.48957i) q^{46} -13.0438 q^{47} +(5.63535 + 4.03025i) q^{48} -1.00000 q^{49} +(0.859821 + 1.12281i) q^{50} +(0.102491 - 1.09500i) q^{51} +(1.73843 - 6.43754i) q^{52} +8.71720i q^{53} +(2.68155 + 6.84173i) q^{54} +5.30518i q^{55} +(-1.07472 - 2.61629i) q^{56} +(0.820279 - 8.76372i) q^{57} +(11.7453 - 8.99428i) q^{58} +1.82137 q^{59} +(-3.24559 - 1.21085i) q^{60} -1.58269 q^{61} +(4.88906 - 3.74392i) q^{62} +(0.556719 - 2.94789i) q^{63} +(5.68994 - 5.62358i) q^{64} +3.33407i q^{65} +(-6.90489 - 11.0087i) q^{66} +9.38729i q^{67} +(-1.22601 - 0.331078i) q^{68} +(-14.5749 - 1.36420i) q^{69} +(0.859821 + 1.12281i) q^{70} -2.69785 q^{71} +(8.31086 - 1.71163i) q^{72} -9.27865 q^{73} +(0.219471 + 0.286600i) q^{74} +(1.72451 + 0.161413i) q^{75} +(-9.81222 - 2.64975i) q^{76} +5.30518i q^{77} +(-4.33941 - 6.91850i) q^{78} -5.23327i q^{79} +(-2.01353 + 3.45625i) q^{80} +(8.38013 + 3.28229i) q^{81} +(5.83972 - 4.47191i) q^{82} +4.47848 q^{83} +(-3.24559 - 1.21085i) q^{84} +0.634962 q^{85} +(-6.97299 + 5.33974i) q^{86} +(1.68849 - 18.0395i) q^{87} +(-13.8799 + 5.70160i) q^{88} -11.3607i q^{89} +(-3.78861 + 1.90957i) q^{90} +3.33407i q^{91} +(-4.40679 + 16.3187i) q^{92} +(0.702843 - 7.50905i) q^{93} +(11.2154 + 14.6458i) q^{94} +5.08185 q^{95} +(-0.320181 - 9.79273i) q^{96} -10.9809 q^{97} +(0.859821 + 1.12281i) q^{98} +(-15.6391 - 2.95350i) 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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