LMFDB - Embedded newform 276.2.c.b.47.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(47,276)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("276.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.c (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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.11
Character	$\chi$	$=$	276.47
Dual form			276.2.c.b.47.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.133777 - 1.40787i) q^{2} +(1.73013 + 0.0815319i) q^{3} +(-1.96421 + 0.376681i) q^{4} +3.66772i q^{5} +(-0.116665 - 2.44671i) q^{6} +2.47568i q^{7} +(0.793084 + 2.71496i) q^{8} +(2.98671 + 0.282122i) q^{9} +O(q^{10})$	\(q+(-0.133777 - 1.40787i) q^{2} +(1.73013 + 0.0815319i) q^{3} +(-1.96421 + 0.376681i) q^{4} +3.66772i q^{5} +(-0.116665 - 2.44671i) q^{6} +2.47568i q^{7} +(0.793084 + 2.71496i) q^{8} +(2.98671 + 0.282122i) q^{9} +(5.16368 - 0.490656i) q^{10} -4.16174 q^{11} +(-3.42905 + 0.491562i) q^{12} +3.10670 q^{13} +(3.48544 - 0.331189i) q^{14} +(-0.299036 + 6.34564i) q^{15} +(3.71622 - 1.47976i) q^{16} +0.828110i q^{17} +(-0.00236062 - 4.24264i) q^{18} -7.27826i q^{19} +(-1.38156 - 7.20417i) q^{20} +(-0.201847 + 4.28326i) q^{21} +(0.556745 + 5.85920i) q^{22} -1.00000 q^{23} +(1.15078 + 4.76190i) q^{24} -8.45218 q^{25} +(-0.415605 - 4.37384i) q^{26} +(5.14439 + 0.731619i) q^{27} +(-0.932543 - 4.86276i) q^{28} -2.16641i q^{29} +(8.97385 - 0.427894i) q^{30} -6.69235i q^{31} +(-2.58046 - 5.03401i) q^{32} +(-7.20036 - 0.339315i) q^{33} +(1.16587 - 0.110782i) q^{34} -9.08011 q^{35} +(-5.97278 + 0.570890i) q^{36} +9.22086 q^{37} +(-10.2469 + 0.973661i) q^{38} +(5.37501 + 0.253295i) q^{39} +(-9.95772 + 2.90881i) q^{40} -1.93801i q^{41} +(6.05728 - 0.288825i) q^{42} +1.56665i q^{43} +(8.17453 - 1.56765i) q^{44} +(-1.03474 + 10.9544i) q^{45} +(0.133777 + 1.40787i) q^{46} +5.50579 q^{47} +(6.55020 - 2.25719i) q^{48} +0.870994 q^{49} +(1.13070 + 11.8996i) q^{50} +(-0.0675173 + 1.43274i) q^{51} +(-6.10221 + 1.17024i) q^{52} +5.10659i q^{53} +(0.341826 - 7.34051i) q^{54} -15.2641i q^{55} +(-6.72138 + 1.96342i) q^{56} +(0.593410 - 12.5923i) q^{57} +(-3.05003 + 0.289815i) q^{58} +10.1813 q^{59} +(-1.80291 - 12.5768i) q^{60} +0.476260 q^{61} +(-9.42198 + 0.895281i) q^{62} +(-0.698443 + 7.39413i) q^{63} +(-6.74204 + 4.30639i) q^{64} +11.3945i q^{65} +(0.485529 + 10.1826i) q^{66} +9.83504i q^{67} +(-0.311933 - 1.62658i) q^{68} +(-1.73013 - 0.0815319i) q^{69} +(1.21471 + 12.7836i) q^{70} -10.8065 q^{71} +(1.60276 + 8.33254i) q^{72} -6.39338 q^{73} +(-1.23354 - 12.9818i) q^{74} +(-14.6234 - 0.689122i) q^{75} +(2.74158 + 14.2960i) q^{76} -10.3032i q^{77} +(-0.362443 - 7.60120i) q^{78} -1.28577i q^{79} +(5.42735 + 13.6301i) q^{80} +(8.84081 + 1.68523i) q^{81} +(-2.72847 + 0.259260i) q^{82} -11.2123 q^{83} +(-1.21695 - 8.48923i) q^{84} -3.03728 q^{85} +(2.20564 - 0.209581i) q^{86} +(0.176631 - 3.74817i) q^{87} +(-3.30061 - 11.2990i) q^{88} -6.94514i q^{89} +(15.5608 - 0.00865809i) q^{90} +7.69122i q^{91} +(1.96421 - 0.376681i) q^{92} +(0.545640 - 11.5786i) q^{93} +(-0.736547 - 7.75145i) q^{94} +26.6946 q^{95} +(-4.05409 - 8.91988i) q^{96} -10.7186 q^{97} +(-0.116519 - 1.22625i) q^{98} +(-12.4299 - 1.17412i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 9 q^{8} - 2 q^{9}+O(q^{10}) $ 22 * q + 9 * q^8 - 2 * q^9	$ 22 q + 9 q^{8} - 2 q^{9} + 4 q^{10} - 7 q^{12} - 4 q^{13} - 12 q^{14} + 4 q^{16} + 13 q^{18} + 14 q^{20} + 2 q^{22} - 22 q^{23} - 30 q^{24} - 18 q^{25} - 27 q^{26} - 12 q^{27} + 6 q^{28} + 34 q^{30} + 20 q^{32} - 8 q^{33} - 6 q^{34} + 8 q^{35} - 36 q^{36} - 4 q^{37} - 22 q^{38} + 24 q^{39} - 4 q^{40} + 26 q^{42} + 56 q^{44} - 8 q^{47} - 22 q^{48} - 14 q^{49} - 20 q^{50} - 16 q^{51} - 19 q^{52} + 22 q^{54} + 18 q^{56} + 12 q^{57} + 3 q^{58} + 72 q^{59} - 28 q^{60} + 12 q^{61} - 63 q^{62} + 20 q^{63} + 3 q^{64} + 60 q^{66} + 20 q^{68} - 40 q^{71} - 36 q^{72} - 4 q^{73} - 28 q^{74} - 48 q^{75} + 26 q^{76} + 11 q^{78} + 84 q^{80} + 10 q^{81} - 29 q^{82} + 8 q^{83} - 38 q^{84} + 8 q^{85} - 28 q^{86} + 48 q^{87} - 30 q^{88} + 84 q^{90} + 12 q^{93} - 13 q^{94} - 32 q^{95} - 45 q^{96} - 4 q^{97} - 64 q^{98} - 20 q^{99}+O(q^{100}) $ 22 * q + 9 * q^8 - 2 * q^9 + 4 * q^10 - 7 * q^12 - 4 * q^13 - 12 * q^14 + 4 * q^16 + 13 * q^18 + 14 * q^20 + 2 * q^22 - 22 * q^23 - 30 * q^24 - 18 * q^25 - 27 * q^26 - 12 * q^27 + 6 * q^28 + 34 * q^30 + 20 * q^32 - 8 * q^33 - 6 * q^34 + 8 * q^35 - 36 * q^36 - 4 * q^37 - 22 * q^38 + 24 * q^39 - 4 * q^40 + 26 * q^42 + 56 * q^44 - 8 * q^47 - 22 * q^48 - 14 * q^49 - 20 * q^50 - 16 * q^51 - 19 * q^52 + 22 * q^54 + 18 * q^56 + 12 * q^57 + 3 * q^58 + 72 * q^59 - 28 * q^60 + 12 * q^61 - 63 * q^62 + 20 * q^63 + 3 * q^64 + 60 * q^66 + 20 * q^68 - 40 * q^71 - 36 * q^72 - 4 * q^73 - 28 * q^74 - 48 * q^75 + 26 * q^76 + 11 * q^78 + 84 * q^80 + 10 * q^81 - 29 * q^82 + 8 * q^83 - 38 * q^84 + 8 * q^85 - 28 * q^86 + 48 * q^87 - 30 * q^88 + 84 * q^90 + 12 * q^93 - 13 * q^94 - 32 * q^95 - 45 * q^96 - 4 * q^97 - 64 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−0.133777	−	1.40787i	−0.0945944	−	0.995516i
$2$	−0.133777	−	1.40787i	−0.0945944	−	0.995516i
$3$	1.73013	+	0.0815319i	0.998891	+	0.0470724i
$3$	1.73013	+	0.0815319i	0.998891	+	0.0470724i
$4$	−1.96421	+	0.376681i	−0.982104	+	0.188341i
$5$			3.66772i			1.64025i	0.572181	+	0.820127i	$0.306097\pi$
$5$			3.66772i			1.64025i	−0.572181	+	0.820127i	$0.693903\pi$
$6$	−0.116665	−	2.44671i	−0.0476282	−	0.998865i
$7$			2.47568i			0.935720i	0.883803	+	0.467860i	$0.154975\pi$
$7$			2.47568i			0.935720i	−0.883803	+	0.467860i	$0.845025\pi$
$8$	0.793084	+	2.71496i	0.280398	+	0.959884i
$9$	2.98671	+	0.282122i	0.995568	+	0.0940405i
$10$	5.16368	−	0.490656i	1.63290	−	0.155159i
$11$	−4.16174			−1.25481			−0.627407	−	0.778692i	$-0.715884\pi$
$11$	−4.16174			−1.25481			−0.627407	+	0.778692i	$0.715884\pi$
$12$	−3.42905	+	0.491562i	−0.989881	+	0.141902i
$13$	3.10670			0.861645			0.430822	−	0.902437i	$-0.358224\pi$
$13$	3.10670			0.861645			0.430822	+	0.902437i	$0.358224\pi$
$14$	3.48544	−	0.331189i	0.931524	−	0.0885139i
$15$	−0.299036	+	6.34564i	−0.0772108	+	1.63844i
$16$	3.71622	−	1.47976i	0.929056	−	0.369940i
$17$			0.828110i			0.200846i	0.994945	+	0.100423i	$0.0320196\pi$
$17$			0.828110i			0.200846i	−0.994945	+	0.100423i	$0.967980\pi$
$18$	−0.00236062	−	4.24264i	−0.000556403	−	1.00000i
$19$		−	7.27826i		−	1.66975i	−0.550442	−	0.834873i	$-0.685541\pi$
$19$		−	7.27826i		−	1.66975i	0.550442	−	0.834873i	$-0.314459\pi$
$20$	−1.38156	−	7.20417i	−0.308926	−	1.61090i
$21$	−0.201847	+	4.28326i	−0.0440466	+	0.934683i
$22$	0.556745	+	5.85920i	0.118698	+	1.24919i
$23$	−1.00000			−0.208514
$23$	−1.00000			−0.208514
$24$	1.15078	+	4.76190i	0.234903	+	0.972019i
$25$	−8.45218			−1.69044
$26$	−0.415605	−	4.37384i	−0.0815068	−	0.857781i
$27$	5.14439	+	0.731619i	0.990038	+	0.140800i
$28$	−0.932543	−	4.86276i	−0.176234	−	0.918974i
$29$		−	2.16641i		−	0.402292i	−0.979561	−	0.201146i	$-0.935533\pi$
$29$		−	2.16641i		−	0.402292i	0.979561	−	0.201146i	$-0.0644666\pi$
$30$	8.97385	−	0.427894i	1.63839	−	0.0781224i
$31$		−	6.69235i		−	1.20198i	−0.799256	−	0.600991i	$-0.794773\pi$
$31$		−	6.69235i		−	1.20198i	0.799256	−	0.600991i	$-0.205227\pi$
$32$	−2.58046	−	5.03401i	−0.456165	−	0.889895i
$33$	−7.20036	−	0.339315i	−1.25342	−	0.0590671i
$34$	1.16587	−	0.110782i	0.199945	−	0.0189989i
$35$	−9.08011			−1.53482
$36$	−5.97278	+	0.570890i	−0.995463	+	0.0951483i
$37$	9.22086			1.51590			0.757950	−	0.652312i	$-0.226201\pi$
$37$	9.22086			1.51590			0.757950	+	0.652312i	$0.226201\pi$
$38$	−10.2469	+	0.973661i	−1.66226	+	0.157949i
$39$	5.37501	+	0.253295i	0.860690	+	0.0405597i
$40$	−9.95772	+	2.90881i	−1.57445	+	0.459923i
$41$		−	1.93801i		−	0.302666i	−0.988483	−	0.151333i	$-0.951643\pi$
$41$		−	1.93801i		−	0.302666i	0.988483	−	0.151333i	$-0.0483566\pi$
$42$	6.05728	−	0.288825i	0.934658	−	0.0445667i
$43$			1.56665i			0.238912i	0.992840	+	0.119456i	$0.0381150\pi$
$43$			1.56665i			0.238912i	−0.992840	+	0.119456i	$0.961885\pi$
$44$	8.17453	−	1.56765i	1.23236	−	0.236332i
$45$	−1.03474	+	10.9544i	−0.154250	+	1.63299i
$46$	0.133777	+	1.40787i	0.0197243	+	0.207579i
$47$	5.50579			0.803103			0.401551	−	0.915837i	$-0.368471\pi$
$47$	5.50579			0.803103			0.401551	+	0.915837i	$0.368471\pi$
$48$	6.55020	−	2.25719i	0.945440	−	0.325797i
$49$	0.870994			0.124428
$50$	1.13070	+	11.8996i	0.159906	+	1.68286i
$51$	−0.0675173	+	1.43274i	−0.00945432	+	0.200623i
$52$	−6.10221	+	1.17024i	−0.846225	+	0.162283i
$53$			5.10659i			0.701444i	0.936480	+	0.350722i	$0.114064\pi$
$53$			5.10659i			0.701444i	−0.936480	+	0.350722i	$0.885936\pi$
$54$	0.341826	−	7.34051i	0.0465166	−	0.998918i
$55$		−	15.2641i		−	2.05821i
$56$	−6.72138	+	1.96342i	−0.898183	+	0.262374i
$57$	0.593410	−	12.5923i	0.0785990	−	1.66790i
$58$	−3.05003	+	0.289815i	−0.400488	+	0.0380546i
$59$	10.1813			1.32549			0.662745	−	0.748845i	$-0.269391\pi$
$59$	10.1813			1.32549			0.662745	+	0.748845i	$0.269391\pi$
$60$	−1.80291	−	12.5768i	−0.232755	−	1.62366i
$61$	0.476260			0.0609789			0.0304894	−	0.999535i	$-0.490293\pi$
$61$	0.476260			0.0609789			0.0304894	+	0.999535i	$0.490293\pi$
$62$	−9.42198	+	0.895281i	−1.19659	+	0.113701i
$63$	−0.698443	+	7.39413i	−0.0879956	+	0.931573i
$64$	−6.74204	+	4.30639i	−0.842754	+	0.538298i
$65$			11.3945i			1.41332i
$66$	0.485529	+	10.1826i	0.0597645	+	1.25339i
$67$			9.83504i			1.20154i	0.799421	+	0.600771i	$0.205140\pi$
$67$			9.83504i			1.20154i	−0.799421	+	0.600771i	$0.794860\pi$
$68$	−0.311933	−	1.62658i	−0.0378275	−	0.197252i
$69$	−1.73013	−	0.0815319i	−0.208283	−	0.00981528i
$70$	1.21471	+	12.7836i	0.145185	+	1.52794i
$71$	−10.8065			−1.28250			−0.641249	−	0.767333i	$-0.721583\pi$
$71$	−10.8065			−1.28250			−0.641249	+	0.767333i	$0.721583\pi$
$72$	1.60276	+	8.33254i	0.188887	+	0.981999i
$73$	−6.39338			−0.748289			−0.374144	−	0.927370i	$-0.622064\pi$
$73$	−6.39338			−0.748289			−0.374144	+	0.927370i	$0.622064\pi$
$74$	−1.23354	−	12.9818i	−0.143396	−	1.50910i
$75$	−14.6234	−	0.689122i	−1.68856	−	0.0795729i
$76$	2.74158	+	14.2960i	0.314481	+	1.63986i
$77$		−	10.3032i		−	1.17415i
$78$	−0.362443	−	7.60120i	−0.0410386	−	0.860667i
$79$		−	1.28577i		−	0.144661i	−0.997381	−	0.0723304i	$-0.976956\pi$
$79$		−	1.28577i		−	0.144661i	0.997381	−	0.0723304i	$-0.0230436\pi$
$80$	5.42735	+	13.6301i	0.606796	+	1.52389i
$81$	8.84081	+	1.68523i	0.982313	+	0.187248i
$82$	−2.72847	+	0.259260i	−0.301309	+	0.0286305i
$83$	−11.2123			−1.23071			−0.615353	−	0.788252i	$-0.710986\pi$
$83$	−11.2123			−1.23071			−0.615353	+	0.788252i	$0.710986\pi$
$84$	−1.21695	−	8.48923i	−0.132780	−	0.926251i
$85$	−3.03728			−0.329439
$86$	2.20564	−	0.209581i	0.237841	−	0.0225997i
$87$	0.176631	−	3.74817i	0.0189369	−	0.401846i
$88$	−3.30061	−	11.2990i	−0.351847	−	1.20448i
$89$		−	6.94514i		−	0.736184i	−0.929789	−	0.368092i	$-0.880011\pi$
$89$		−	6.94514i		−	0.736184i	0.929789	−	0.368092i	$-0.119989\pi$
$90$	15.5608	−	0.00865809i	1.64025	−	0.000912643i
$91$			7.69122i			0.806258i
$92$	1.96421	−	0.376681i	0.204783	−	0.0392717i
$93$	0.545640	−	11.5786i	0.0565802	−	1.20065i
$94$	−0.736547	−	7.75145i	−0.0759690	−	0.799501i
$95$	26.6946			2.73881
$96$	−4.05409	−	8.91988i	−0.413769	−	0.910382i
$97$	−10.7186			−1.08831			−0.544155	−	0.838985i	$-0.683150\pi$
$97$	−10.7186			−1.08831			−0.544155	+	0.838985i	$0.683150\pi$
$98$	−0.116519	−	1.22625i	−0.0117702	−	0.123870i
$99$	−12.4299	−	1.17412i	−1.24925	−	0.118003i
$100$	16.6018	−	3.18378i	1.66018	−	0.318378i
$101$			3.97056i			0.395085i	0.980294	+	0.197543i	$0.0632961\pi$
$101$			3.97056i			0.395085i	−0.980294	+	0.197543i	$0.936704\pi$
$102$	2.02614	−	0.0966113i	0.200618	−	0.00956594i
$103$			11.3182i			1.11521i	0.830106	+	0.557606i	$0.188280\pi$
$103$			11.3182i			1.11521i	−0.830106	+	0.557606i	$0.811720\pi$
$104$	2.46388	+	8.43458i	0.241603	+	0.827079i
$105$	−15.7098	−	0.740319i	−1.53312	−	0.0722477i
$106$	7.18943	−	0.683143i	0.698299	−	0.0663527i
$107$	7.77125			0.751275			0.375637	−	0.926767i	$-0.377424\pi$
$107$	7.77125			0.751275			0.375637	+	0.926767i	$0.377424\pi$
$108$	−10.3802	+	0.500743i	−0.998838	+	0.0481840i
$109$	−8.95574			−0.857804			−0.428902	−	0.903351i	$-0.641099\pi$
$109$	−8.95574			−0.857804			−0.428902	+	0.903351i	$0.641099\pi$
$110$	−21.4899	+	2.04198i	−2.04898	+	0.194696i
$111$	15.9533	+	0.751794i	1.51422	+	0.0713571i
$112$	3.66342	+	9.20019i	0.346160	+	0.869336i
$113$		−	8.01436i		−	0.753928i	−0.926228	−	0.376964i	$-0.876968\pi$
$113$		−	8.01436i		−	0.753928i	0.926228	−	0.376964i	$-0.123032\pi$
$114$	−17.8078	+	0.849116i	−1.66785	+	0.0795270i
$115$		−	3.66772i		−	0.342017i
$116$	0.816046	+	4.25528i	0.0757679	+	0.395093i
$117$	9.27881	+	0.876468i	0.857826	+	0.0810295i
$118$	−1.36202	−	14.3340i	−0.125384	−	1.31955i
$119$	−2.05014			−0.187936
$120$	−17.4653	+	4.22075i	−1.59436	+	0.385300i
$121$	6.32012			0.574556
$122$	−0.0637125	−	0.670513i	−0.00576826	−	0.0607054i
$123$	0.158009	−	3.35301i	0.0142472	−	0.302330i
$124$	2.52088	+	13.1452i	0.226382	+	1.18047i
$125$		−	12.6616i		−	1.13249i
$126$	10.5034	−	0.00584414i	0.935720	−	0.000520638i
$127$		−	10.8069i		−	0.958958i	−0.877553	−	0.479479i	$-0.840826\pi$
$127$		−	10.8069i		−	0.958958i	0.877553	−	0.479479i	$-0.159174\pi$
$128$	6.96477	+	8.91583i	0.615604	+	0.788055i
$129$	−0.127732	+	2.71051i	−0.0112462	+	0.238647i
$130$	16.0420	−	1.52432i	1.40698	−	0.133692i
$131$	1.68608			0.147314			0.0736568	−	0.997284i	$-0.476533\pi$
$131$	1.68608			0.147314			0.0736568	+	0.997284i	$0.476533\pi$
$132$	14.2708	−	2.04576i	1.24212	−	0.178060i
$133$	18.0187			1.56242
$134$	13.8465	−	1.31570i	1.19615	−	0.113659i
$135$	−2.68337	+	18.8682i	−0.230948	+	1.62391i
$136$	−2.24829	+	0.656761i	−0.192789	+	0.0563168i
$137$		−	15.8032i		−	1.35016i	−0.737745	−	0.675079i	$-0.764109\pi$
$137$		−	15.8032i		−	1.35016i	0.737745	−	0.675079i	$-0.235891\pi$
$138$	0.116665	+	2.44671i	0.00993117	+	0.208278i
$139$		−	4.52695i		−	0.383971i	−0.981398	−	0.191985i	$-0.938507\pi$
$139$		−	4.52695i		−	0.383971i	0.981398	−	0.191985i	$-0.0614927\pi$
$140$	17.8352	−	3.42031i	1.50735	−	0.289069i
$141$	9.52574	+	0.448898i	0.802212	+	0.0378040i
$142$	1.44566	+	15.2142i	0.121317	+	1.27675i
$143$	−12.9293			−1.08120
$144$	11.5167	−	3.37118i	0.959728	−	0.280932i
$145$	7.94579			0.659862
$146$	0.855286	+	9.00107i	0.0707840	+	0.744934i
$147$	1.50693	+	0.0710137i	0.124290	+	0.00585712i
$148$	−18.1117	+	3.47332i	−1.48877	+	0.285506i
$149$			2.01682i			0.165224i	0.996582	+	0.0826121i	$0.0263263\pi$
$149$			2.01682i			0.165224i	−0.996582	+	0.0826121i	$0.973674\pi$
$150$	0.986072	+	20.6800i	0.0805124	+	1.68852i
$151$		−	3.38240i		−	0.275256i	−0.990484	−	0.137628i	$-0.956052\pi$
$151$		−	3.38240i		−	0.275256i	0.990484	−	0.137628i	$-0.0439479\pi$
$152$	19.7602	−	5.77227i	1.60276	−	0.468193i
$153$	−0.233628	+	2.47332i	−0.0188877	+	0.199956i
$154$	−14.5055	+	1.37832i	−1.16889	+	0.111068i
$155$	24.5457			1.97156
$156$	−10.6530	+	1.52714i	−0.852926	+	0.122269i
$157$	18.7654			1.49765			0.748823	−	0.662770i	$-0.230619\pi$
$157$	18.7654			1.49765			0.748823	+	0.662770i	$0.230619\pi$
$158$	−1.81020	+	0.172006i	−0.144012	+	0.0136841i
$159$	−0.416350	+	8.83507i	−0.0330187	+	0.700667i
$160$	18.4633	−	9.46439i	1.45966	−	0.748226i
$161$		−	2.47568i		−	0.195111i
$162$	1.18989	−	12.6722i	0.0934866	−	0.995621i
$163$			3.10722i			0.243376i	0.992568	+	0.121688i	$0.0388307\pi$
$163$			3.10722i			0.243376i	−0.992568	+	0.121688i	$0.961169\pi$
$164$	0.730011	+	3.80665i	0.0570042	+	0.297249i
$165$	1.24451	−	26.4089i	0.0968851	−	2.05593i
$166$	1.49994	+	15.7854i	0.116418	+	1.22519i
$167$	−16.8213			−1.30167			−0.650837	−	0.759218i	$-0.725582\pi$
$167$	−16.8213			−1.30167			−0.650837	+	0.759218i	$0.725582\pi$
$168$	−11.7890	+	2.84897i	−0.909538	+	0.219803i
$169$	−3.34839			−0.257568
$170$	0.406317	+	4.27610i	0.0311631	+	0.327962i
$171$	2.05335	−	21.7380i	0.157024	−	1.66235i
$172$	−0.590127	−	3.07723i	−0.0449968	−	0.234636i
$173$		−	25.5907i		−	1.94563i	−0.231594	−	0.972813i	$-0.574394\pi$
$173$		−	25.5907i		−	1.94563i	0.231594	−	0.972813i	$-0.425606\pi$
$174$	−5.30058	+	0.252744i	−0.401836	+	0.0191605i
$175$		−	20.9249i		−	1.58177i
$176$	−15.4660	+	6.15838i	−1.16579	+	0.464205i
$177$	17.6150	+	0.830099i	1.32402	+	0.0623941i
$178$	−9.77787	+	0.929098i	−0.732883	+	0.0696389i
$179$	−5.32078			−0.397693			−0.198847	−	0.980031i	$-0.563720\pi$
$179$	−5.32078			−0.397693			−0.198847	+	0.980031i	$0.563720\pi$
$180$	−2.09387	−	21.9065i	−0.156067	−	1.63281i
$181$	0.0826236			0.00614137			0.00307068	−	0.999995i	$-0.499023\pi$
$181$	0.0826236			0.00614137			0.00307068	+	0.999995i	$0.499023\pi$
$182$	10.8282	−	1.02891i	0.802643	−	0.0762676i
$183$	0.823992	+	0.0388304i	0.0609113	+	0.00287042i
$184$	−0.793084	−	2.71496i	−0.0584669	−	0.200150i
$185$			33.8196i			2.48646i
$186$	−16.3742	+	0.780762i	−1.20062	+	0.0572483i
$187$		−	3.44638i		−	0.252024i
$188$	−10.8145	+	2.07393i	−0.788730	+	0.151257i
$189$	−1.81126	+	12.7359i	−0.131749	+	0.926399i
$190$	−3.57112	−	37.5826i	−0.259076	−	2.72653i
$191$	−13.7386			−0.994091			−0.497046	−	0.867724i	$-0.665582\pi$
$191$	−13.7386			−0.994091			−0.497046	+	0.867724i	$0.665582\pi$
$192$	−12.0157	+	6.90092i	−0.867159	+	0.498031i
$193$	−24.9556			−1.79634			−0.898171	−	0.439646i	$-0.855104\pi$
$193$	−24.9556			−1.79634			−0.898171	+	0.439646i	$0.855104\pi$
$194$	1.43390	+	15.0904i	0.102948	+	1.08343i
$195$	−0.929017	+	19.7140i	−0.0665283	+	1.41175i
$196$	−1.71081	+	0.328087i	−0.122201	+	0.0234348i
$197$			14.6618i			1.04461i	0.852760	+	0.522303i	$0.174927\pi$
$197$			14.6618i			1.04461i	−0.852760	+	0.522303i	$0.825073\pi$
$198$	0.00982429	+	17.6568i	0.000698182	+	1.25481i
$199$		−	3.68209i		−	0.261016i	−0.991447	−	0.130508i	$-0.958339\pi$
$199$		−	3.68209i		−	0.261016i	0.991447	−	0.130508i	$-0.0416609\pi$
$200$	−6.70329	−	22.9473i	−0.473994	−	1.62262i
$201$	−0.801869	+	17.0159i	−0.0565595	+	1.20021i
$202$	5.59003	−	0.531168i	0.393313	−	0.0373728i
$203$	5.36334			0.376433
$204$	−0.407067	−	2.83963i	−0.0285004	−	0.198814i
$205$	7.10807			0.496449
$206$	15.9345	−	1.51411i	1.11021	−	0.105493i
$207$	−2.98671	−	0.282122i	−0.207590	−	0.0196088i
$208$	11.5452	−	4.59718i	0.800516	−	0.318757i
$209$			30.2902i			2.09522i
$210$	1.05933	+	22.2164i	0.0731007	+	1.53308i
$211$			0.668043i			0.0459900i	0.999736	+	0.0229950i	$0.00732018\pi$
$211$			0.668043i			0.0459900i	−0.999736	+	0.0229950i	$0.992680\pi$
$212$	−1.92356	−	10.0304i	−0.132110	−	0.688891i
$213$	−18.6967	−	0.881076i	−1.28108	−	0.0603703i
$214$	−1.03961	−	10.9409i	−0.0710664	−	0.747906i
$215$	−5.74604			−0.391876
$216$	2.09362	+	14.5471i	0.142452	+	0.989802i
$217$	16.5681			1.12472
$218$	1.19807	+	12.6085i	0.0811435	+	0.853957i
$219$	−11.0614	−	0.521264i	−0.747459	−	0.0352238i
$220$	5.74970	+	29.9819i	0.387645	+	2.02138i
$221$			2.57269i			0.173058i
$222$	−1.07575	−	22.5608i	−0.0721996	−	1.51418i
$223$			11.7329i			0.785693i	0.919604	+	0.392847i	$0.128510\pi$
$223$			11.7329i			0.785693i	−0.919604	+	0.392847i	$0.871490\pi$
$224$	12.4626	−	6.38839i	0.832693	−	0.426842i
$225$	−25.2442	−	2.38454i	−1.68294	−	0.158969i
$226$	−11.2832	+	1.07214i	−0.750547	+	0.0713174i
$227$	−1.90471			−0.126420			−0.0632101	−	0.998000i	$-0.520134\pi$
$227$	−1.90471			−0.126420			−0.0632101	+	0.998000i	$0.520134\pi$
$228$	3.57771	+	24.9575i	0.236940	+	1.65285i
$229$	−6.82029			−0.450698			−0.225349	−	0.974278i	$-0.572352\pi$
$229$	−6.82029			−0.450698			−0.225349	+	0.974278i	$0.572352\pi$
$230$	−5.16368	+	0.490656i	−0.340483	+	0.0323529i
$231$	0.840036	−	17.8258i	0.0552703	−	1.17285i
$232$	5.88172	−	1.71815i	0.386154	−	0.112802i
$233$		−	19.2856i		−	1.26344i	−0.775195	−	0.631722i	$-0.782348\pi$
$233$		−	19.2856i		−	1.26344i	0.775195	−	0.631722i	$-0.217652\pi$
$234$	−0.00733374	−	13.1806i	−0.000479422	−	0.861645i
$235$			20.1937i			1.31729i
$236$	−19.9982	+	3.83510i	−1.30177	+	0.249644i
$237$	0.104831	−	2.22456i	0.00680953	−	0.144500i
$238$	0.274261	+	2.88633i	0.0177777	+	0.187093i
$239$	2.37187			0.153423			0.0767117	−	0.997053i	$-0.475558\pi$
$239$	2.37187			0.153423			0.0767117	+	0.997053i	$0.475558\pi$
$240$	8.27873	+	24.0243i	0.534390	+	1.55076i
$241$	−24.2098			−1.55949			−0.779745	−	0.626097i	$-0.784651\pi$
$241$	−24.2098			−1.55949			−0.779745	+	0.626097i	$0.784651\pi$
$242$	−0.845485	−	8.89792i	−0.0543498	−	0.571980i
$243$	15.1584	+	3.63647i	0.972410	+	0.233280i
$244$	−0.935474	+	0.179398i	−0.0598876	+	0.0114848i
$245$			3.19456i			0.204093i
$246$	−4.74174	+	0.226097i	−0.302322	+	0.0144154i
$247$		−	22.6114i		−	1.43873i
$248$	18.1695	−	5.30760i	1.15376	−	0.337033i
$249$	−19.3987	−	0.914156i	−1.22934	−	0.0579323i
$250$	−17.8260	+	1.69383i	−1.12741	+	0.107127i
$251$	6.18421			0.390344			0.195172	−	0.980769i	$-0.437474\pi$
$251$	6.18421			0.390344			0.195172	+	0.980769i	$0.437474\pi$
$252$	−1.41334	−	14.7867i	−0.0890322	−	0.931475i
$253$	4.16174			0.261647
$254$	−15.2147	+	1.44571i	−0.954658	+	0.0907121i
$255$	−5.25488	−	0.247635i	−0.329074	−	0.0155075i
$256$	11.6206	−	10.9982i	0.726289	−	0.687390i
$257$			13.7066i			0.854996i	0.904016	+	0.427498i	$0.140605\pi$
$257$			13.7066i			0.854996i	−0.904016	+	0.427498i	$0.859395\pi$
$258$	3.83314	−	0.182773i	0.238641	−	0.0113789i
$259$			22.8279i			1.41846i
$260$	−4.29210	−	22.3812i	−0.266185	−	1.38802i
$261$	0.611191	−	6.47043i	0.0378318	−	0.400509i
$262$	−0.225558	−	2.37379i	−0.0139350	−	0.146653i
$263$	14.4951			0.893804			0.446902	−	0.894583i	$-0.352527\pi$
$263$	14.4951			0.893804			0.446902	+	0.894583i	$0.352527\pi$
$264$	−4.78927	−	19.8178i	−0.294759	−	1.21970i
$265$	−18.7295			−1.15055
$266$	−2.41048	−	25.3680i	−0.147796	−	1.55541i
$267$	0.566250	−	12.0160i	0.0346540	−	0.735368i
$268$	−3.70467	−	19.3181i	−0.226299	−	1.18004i
$269$			10.3377i			0.630301i	0.949042	+	0.315151i	$0.102055\pi$
$269$			10.3377i			0.630301i	−0.949042	+	0.315151i	$0.897945\pi$
$270$	26.9230	+	1.25372i	1.63848	+	0.0762991i
$271$			24.9252i			1.51410i	0.653358	+	0.757049i	$0.273360\pi$
$271$			24.9252i			1.51410i	−0.653358	+	0.757049i	$0.726640\pi$
$272$	1.22540	+	3.07744i	0.0743010	+	0.186597i
$273$	−0.627079	+	13.3068i	−0.0379526	+	0.805365i
$274$	−22.2489	+	2.11410i	−1.34410	+	0.127717i
$275$	35.1758			2.12118
$276$	3.42905	−	0.491562i	0.206404	−	0.0295886i
$277$	4.27366			0.256780			0.128390	−	0.991724i	$-0.459019\pi$
$277$	4.27366			0.256780			0.128390	+	0.991724i	$0.459019\pi$
$278$	−6.37337	+	0.605601i	−0.382249	+	0.0363215i
$279$	1.88806	−	19.9881i	0.113035	−	1.19666i
$280$	−7.20129	−	24.6522i	−0.430360	−	1.47325i
$281$		−	16.0154i		−	0.955399i	−0.878523	−	0.477699i	$-0.841471\pi$
$281$		−	16.0154i		−	0.955399i	0.878523	−	0.477699i	$-0.158529\pi$
$282$	−0.642332	−	13.4711i	−0.0382503	−	0.802191i
$283$		−	26.3731i		−	1.56772i	−0.620940	−	0.783858i	$-0.713249\pi$
$283$		−	26.3731i		−	1.56772i	0.620940	−	0.783858i	$-0.286751\pi$
$284$	21.2262	−	4.07061i	1.25955	−	0.241546i
$285$	46.1852	+	2.17646i	2.73577	+	0.128922i
$286$	1.72964	+	18.2028i	0.102276	+	1.07636i
$287$	4.79789			0.283211
$288$	−6.28686	−	15.7631i	−0.370457	−	0.928850i
$289$	16.3142			0.959661
$290$	−1.06296	−	11.1867i	−0.0624193	−	0.656903i
$291$	−18.5446	−	0.873908i	−1.08710	−	0.0512294i
$292$	12.5579	−	2.40827i	0.734897	−	0.140933i
$293$		−	4.58862i		−	0.268070i	−0.990977	−	0.134035i	$-0.957207\pi$
$293$		−	4.58862i		−	0.268070i	0.990977	−	0.134035i	$-0.0427935\pi$
$294$	−0.101614	−	2.13107i	−0.00592627	−	0.124286i
$295$			37.3421i			2.17414i
$296$	7.31292	+	25.0343i	0.425055	+	1.45509i
$297$	−21.4096	−	3.04481i	−1.24231	−	0.176678i
$298$	2.83942	−	0.269803i	0.164483	−	0.0156293i
$299$	−3.10670			−0.179665
$300$	28.9829	−	4.15477i	1.67333	−	0.239876i
$301$	−3.87853			−0.223555
$302$	−4.76199	+	0.452487i	−0.274022	+	0.0260377i
$303$	−0.323727	+	6.86958i	−0.0185976	+	0.394647i
$304$	−10.7701	−	27.0476i	−0.617706	−	1.55129i
$305$			1.74679i			0.100021i
$306$	3.51337	−	0.00195485i	0.200846	−	0.000111751i
$307$			16.6930i			0.952721i	0.879250	+	0.476361i	$0.158044\pi$
$307$			16.6930i			0.952721i	−0.879250	+	0.476361i	$0.841956\pi$
$308$	3.88101	+	20.2375i	0.221141	+	1.15314i
$309$	−0.922790	+	19.5819i	−0.0524957	+	1.11397i
$310$	−3.28364	−	34.5572i	−0.186498	−	1.96272i
$311$	−18.9496			−1.07453			−0.537265	−	0.843413i	$-0.680543\pi$
$311$	−18.9496			−1.07453			−0.537265	+	0.843413i	$0.680543\pi$
$312$	3.57514	+	14.7938i	0.202403	+	0.837535i
$313$	−3.23051			−0.182599			−0.0912995	−	0.995823i	$-0.529102\pi$
$313$	−3.23051			−0.182599			−0.0912995	+	0.995823i	$0.529102\pi$
$314$	−2.51038	−	26.4193i	−0.141669	−	1.49093i
$315$	−27.1196	−	2.56170i	−1.52802	−	0.144335i
$316$	0.484326	+	2.52552i	0.0272455	+	0.142072i
$317$			11.1939i			0.628713i	0.949305	+	0.314356i	$0.101789\pi$
$317$			11.1939i			0.628713i	−0.949305	+	0.314356i	$0.898211\pi$
$318$	12.4943	−	0.595759i	0.700648	−	0.0334085i
$319$			9.01605i			0.504802i
$320$	−15.7946	−	24.7279i	−0.882946	−	1.38233i
$321$	13.4453	+	0.633604i	0.750442	+	0.0353643i
$322$	−3.48544	+	0.331189i	−0.194236	+	0.0184564i
$323$	6.02719			0.335362
$324$	−18.0000	+	0.0200305i	−0.999999	+	0.00111281i
$325$	−26.2584			−1.45656
$326$	4.37456	−	0.415673i	0.242285	−	0.0230220i
$327$	−15.4946	−	0.730178i	−0.856853	−	0.0403789i
$328$	5.26162	−	1.53700i	0.290524	−	0.0848668i
$329$			13.6306i			0.751479i
$330$	−37.3469	+	1.78079i	−2.05588	+	0.0980290i
$331$		−	13.0087i		−	0.715020i	−0.933909	−	0.357510i	$-0.883626\pi$
$331$		−	13.0087i		−	0.715020i	0.933909	−	0.357510i	$-0.116374\pi$
$332$	22.0232	−	4.22345i	1.20868	−	0.231792i
$333$	27.5400	+	2.60140i	1.50918	+	0.142556i
$334$	2.25030	+	23.6823i	0.123131	+	1.29584i
$335$	−36.0722			−1.97083
$336$	5.58808	+	16.2162i	0.304855	+	0.884667i
$337$	17.6528			0.961610			0.480805	−	0.876828i	$-0.340345\pi$
$337$	17.6528			0.961610			0.480805	+	0.876828i	$0.340345\pi$
$338$	0.447936	+	4.71410i	0.0243645	+	0.256413i
$339$	0.653426	−	13.8659i	0.0354892	−	0.753092i
$340$	5.96584	−	1.14408i	0.323543	−	0.0620467i
$341$			27.8519i			1.50826i
$342$	−30.8790	+	0.0171812i	−1.66975	+	0.000929052i
$343$			19.4861i			1.05215i
$344$	−4.25340	+	1.24249i	−0.229328	+	0.0669903i
$345$	0.299036	−	6.34564i	0.0160996	−	0.341638i
$346$	−36.0284	+	3.42344i	−1.93690	+	0.184045i
$347$	24.6520			1.32339			0.661694	−	0.749774i	$-0.269838\pi$
$347$	24.6520			1.32339			0.661694	+	0.749774i	$0.269838\pi$
$348$	1.06492	+	7.42872i	0.0570860	+	0.398221i
$349$	5.11651			0.273881			0.136940	−	0.990579i	$-0.456273\pi$
$349$	5.11651			0.273881			0.136940	+	0.990579i	$0.456273\pi$
$350$	−29.4596	+	2.79927i	−1.57468	+	0.149627i
$351$	15.9821	+	2.27292i	0.853061	+	0.121320i
$352$	10.7392	+	20.9503i	0.572401	+	1.11665i
$353$			0.765404i			0.0407384i	0.999793	+	0.0203692i	$0.00648416\pi$
$353$			0.765404i			0.0407384i	−0.999793	+	0.0203692i	$0.993516\pi$
$354$	−1.18780	−	24.9107i	−0.0631308	−	1.32399i
$355$		−	39.6353i		−	2.10362i
$356$	2.61610	+	13.6417i	0.138653	+	0.723009i
$357$	−3.54701	−	0.167151i	−0.187727	−	0.00884659i
$358$	0.711796	+	7.49097i	0.0376196	+	0.395910i
$359$	32.4019			1.71011			0.855053	−	0.518540i	$-0.173524\pi$
$359$	32.4019			1.71011			0.855053	+	0.518540i	$0.173524\pi$
$360$	−30.5614	+	5.87847i	−1.61073	+	0.309823i
$361$	−33.9730			−1.78805
$362$	−0.0110531	−	0.116323i	−0.000580939	−	0.00611383i
$363$	10.9346	+	0.515291i	0.573919	+	0.0270458i
$364$	−2.89714	−	15.1071i	−0.151851	−	0.791829i
$365$		−	23.4491i		−	1.22738i
$366$	−0.0555628	−	1.16527i	−0.00290431	−	0.0609097i
$367$			6.64746i			0.346994i	0.984834	+	0.173497i	$0.0555068\pi$
$367$			6.64746i			0.346994i	−0.984834	+	0.173497i	$0.944493\pi$
$368$	−3.71622	+	1.47976i	−0.193722	+	0.0771378i
$369$	0.546754	−	5.78826i	0.0284629	−	0.301325i
$370$	47.6136	−	4.52427i	2.47531	−	0.235206i
$371$	−12.6423			−0.656355
$372$	3.28971	+	22.9484i	0.170563	+	1.18982i
$373$	18.4608			0.955863			0.477932	−	0.878397i	$-0.341387\pi$
$373$	18.4608			0.955863			0.477932	+	0.878397i	$0.341387\pi$
$374$	−4.85206	+	0.461046i	−0.250894	+	0.0238401i
$375$	1.03233	−	21.9063i	0.0533091	−	1.13124i
$376$	4.36656	+	14.9480i	0.225188	+	0.770885i
$377$		−	6.73040i		−	0.346633i
$378$	18.1728	+	0.846253i	0.934707	+	0.0435266i
$379$			29.7699i			1.52918i	0.644518	+	0.764590i	$0.277058\pi$
$379$			29.7699i			1.52918i	−0.644518	+	0.764590i	$0.722942\pi$
$380$	−52.4338	+	10.0554i	−2.68980	+	0.515829i
$381$	0.881107	−	18.6974i	0.0451405	−	0.957895i
$382$	1.83791	+	19.3422i	0.0940355	+	0.989634i
$383$	−23.2434			−1.18768			−0.593841	−	0.804583i	$-0.702389\pi$
$383$	−23.2434			−1.18768			−0.593841	+	0.804583i	$0.702389\pi$
$384$	11.3230	+	15.9934i	0.577826	+	0.816160i
$385$	37.7891			1.92591
$386$	3.33848	+	35.1343i	0.169924	+	1.78829i
$387$	−0.441986	+	4.67912i	−0.0224674	+	0.237853i
$388$	21.0536	−	4.03750i	1.06883	−	0.204973i
$389$		−	4.28977i		−	0.217500i	−0.994069	−	0.108750i	$-0.965315\pi$
$389$		−	4.28977i		−	0.217500i	0.994069	−	0.108750i	$-0.0346848\pi$
$390$	27.8791	−	1.32934i	1.41171	−	0.0673138i
$391$		−	0.828110i		−	0.0418793i
$392$	0.690771	+	2.36472i	0.0348892	+	0.119436i
$393$	2.91714	+	0.137469i	0.147150	+	0.00693441i
$394$	20.6419	−	1.96140i	1.03992	−	0.0988140i
$395$	4.71586			0.237280
$396$	24.8572	−	2.37590i	1.24912	−	0.119393i
$397$	25.1177			1.26062			0.630311	−	0.776342i	$-0.282927\pi$
$397$	25.1177			1.26062			0.630311	+	0.776342i	$0.282927\pi$
$398$	−5.18391	+	0.492578i	−0.259846	+	0.0246907i
$399$	31.1746	+	1.46909i	1.56068	+	0.0735467i
$400$	−31.4102	+	12.5072i	−1.57051	+	0.625360i
$401$		−	30.6661i		−	1.53139i	−0.643202	−	0.765697i	$-0.722394\pi$
$401$		−	30.6661i		−	1.53139i	0.643202	−	0.765697i	$-0.277606\pi$
$402$	24.0635	−	1.14740i	1.20018	−	0.0572273i
$403$		−	20.7912i		−	1.03568i
$404$	−1.49563	−	7.79900i	−0.0744105	−	0.388015i
$405$	−6.18095	+	32.4256i	−0.307134	+	1.61124i
$406$	−0.717491	−	7.55090i	−0.0356085	−	0.374745i
$407$	−38.3749			−1.90217
$408$	−3.94338	+	0.952975i	−0.195226	+	0.0471793i
$409$	1.21156			0.0599077			0.0299539	−	0.999551i	$-0.490464\pi$
$409$	1.21156			0.0599077			0.0299539	+	0.999551i	$0.490464\pi$
$410$	−0.950894	−	10.0073i	−0.0469613	−	0.494223i
$411$	1.28846	−	27.3416i	0.0635553	−	1.34866i
$412$	−4.26334	−	22.2312i	−0.210039	−	1.09525i
$413$			25.2056i			1.24029i
$414$	0.00236062	+	4.24264i	0.000116018	+	0.208514i
$415$		−	41.1234i		−	2.01867i
$416$	−8.01672	−	15.6392i	−0.393052	−	0.766774i
$417$	0.369091	−	7.83222i	0.0180744	−	0.383545i
$418$	42.6448	−	4.05213i	2.08582	−	0.198196i
$419$	−19.3027			−0.942998			−0.471499	−	0.881867i	$-0.656287\pi$
$419$	−19.3027			−0.942998			−0.471499	+	0.881867i	$0.656287\pi$
$420$	31.1361	−	4.46344i	1.51929	−	0.217794i
$421$	−24.0720			−1.17320			−0.586598	−	0.809878i	$-0.699533\pi$
$421$	−24.0720			−1.17320			−0.586598	+	0.809878i	$0.699533\pi$
$422$	0.940519	−	0.0893686i	0.0457837	−	0.00435040i
$423$	16.4442	+	1.55330i	0.799543	+	0.0755242i
$424$	−13.8642	+	4.04996i	−0.673305	+	0.196683i
$425$		−	6.99933i		−	0.339517i
$426$	1.26074	+	26.4404i	0.0610831	+	1.28104i
$427$			1.17907i			0.0570592i
$428$	−15.2643	+	2.92728i	−0.737830	+	0.141495i
$429$	−22.3694	−	1.05415i	−1.08000	−	0.0508949i
$430$	0.768686	+	8.08968i	0.0370693	+	0.390119i
$431$	13.3722			0.644116			0.322058	−	0.946720i	$-0.395625\pi$
$431$	13.3722			0.644116			0.322058	+	0.946720i	$0.395625\pi$
$432$	20.2003	−	4.89360i	0.971888	−	0.235443i
$433$	−15.2991			−0.735230			−0.367615	−	0.929978i	$-0.619825\pi$
$433$	−15.2991			−0.735230			−0.367615	+	0.929978i	$0.619825\pi$
$434$	−2.21643	−	23.3258i	−0.106392	−	1.11968i
$435$	13.7473	+	0.647835i	0.659130	+	0.0310613i
$436$	17.5909	−	3.37346i	0.842452	−	0.161559i
$437$			7.27826i			0.348166i
$438$	0.745883	+	15.6428i	0.0356397	+	0.747440i
$439$			30.1536i			1.43915i	0.694414	+	0.719576i	$0.255664\pi$
$439$			30.1536i			1.43915i	−0.694414	+	0.719576i	$0.744336\pi$
$440$	41.4415	−	12.1057i	1.97565	−	0.577118i
$441$	2.60140	+	0.245726i	0.123876	+	0.0117012i
$442$	3.62202	−	0.344166i	0.172282	−	0.0163703i
$443$	−8.44007			−0.401000			−0.200500	−	0.979694i	$-0.564257\pi$
$443$	−8.44007			−0.401000			−0.200500	+	0.979694i	$0.564257\pi$
$444$	−31.6188	+	4.53263i	−1.50056	+	0.215109i
$445$	25.4728			1.20753
$446$	16.5184	−	1.56959i	0.782170	−	0.0743222i
$447$	−0.164435	+	3.48936i	−0.00777751	+	0.165041i
$448$	−10.6612	−	16.6911i	−0.503696	−	0.788582i
$449$			20.2514i			0.955720i	0.878436	+	0.477860i	$0.158587\pi$
$449$			20.2514i			0.955720i	−0.878436	+	0.477860i	$0.841413\pi$
$450$	0.0199524	+	35.8596i	0.000940564	+	1.69044i
$451$			8.06549i			0.379789i
$452$	3.01886	+	15.7419i	0.141995	+	0.740436i
$453$	0.275774	−	5.85200i	0.0129570	−	0.274951i
$454$	0.254806	+	2.68159i	0.0119586	+	0.125853i
$455$	−28.2092			−1.32247
$456$	34.6583	−	8.37569i	1.62303	−	0.392228i
$457$	−17.4269			−0.815194			−0.407597	−	0.913162i	$-0.633633\pi$
$457$	−17.4269			−0.815194			−0.407597	+	0.913162i	$0.633633\pi$
$458$	0.912397	+	9.60210i	0.0426335	+	0.448677i
$459$	−0.605861	+	4.26012i	−0.0282791	+	0.198845i
$460$	1.38156	+	7.20417i	0.0644156	+	0.335896i
$461$		−	18.0717i		−	0.841681i	−0.907135	−	0.420840i	$-0.861735\pi$
$461$		−	18.0717i		−	0.841681i	0.907135	−	0.420840i	$-0.138265\pi$
$462$	−25.2088	+	1.20202i	−1.17282	+	0.0559229i
$463$			24.7814i			1.15169i	0.817558	+	0.575846i	$0.195327\pi$
$463$			24.7814i			1.15169i	−0.817558	+	0.575846i	$0.804673\pi$
$464$	−3.20577	−	8.05086i	−0.148824	−	0.373752i
$465$	42.4672	+	2.00126i	1.96937	+	0.0928060i
$466$	−27.1517	+	2.57997i	−1.25778	+	0.119515i
$467$	16.9348			0.783648			0.391824	−	0.920040i	$-0.371844\pi$
$467$	16.9348			0.783648			0.391824	+	0.920040i	$0.371844\pi$
$468$	−18.5557	+	1.77359i	−0.857736	+	0.0819841i
$469$	−24.3484			−1.12431
$470$	28.4302	−	2.70145i	1.31139	−	0.124609i
$471$	32.4667	+	1.52998i	1.49599	+	0.0704978i
$472$	8.07462	+	27.6418i	0.371664	+	1.27232i
$473$		−	6.52000i		−	0.299790i
$474$	−3.14591	+	0.150004i	−0.144497	+	0.00688993i
$475$			61.5171i			2.82260i
$476$	4.02689	−	0.772248i	0.184572	−	0.0353959i
$477$	−1.44068	+	15.2519i	−0.0659642	+	0.698336i
$478$	−0.317301	−	3.33929i	−0.0145130	−	0.152735i
$479$	−2.86800			−0.131042			−0.0655210	−	0.997851i	$-0.520871\pi$
$479$	−2.86800			−0.131042			−0.0655210	+	0.997851i	$0.520871\pi$
$480$	32.7156	−	14.8693i	1.49326	−	0.678687i
$481$	28.6465			1.30617
$482$	3.23871	+	34.0843i	0.147519	+	1.55250i
$483$	0.201847	−	4.28326i	0.00918436	−	0.194895i
$484$	−12.4140	+	2.38067i	−0.564274	+	0.108212i
$485$		−	39.3129i		−	1.78511i
$486$	3.09185	−	21.8275i	0.140249	−	0.990116i
$487$			26.4510i			1.19861i	0.800521	+	0.599305i	$0.204556\pi$
$487$			26.4510i			1.19861i	−0.800521	+	0.599305i	$0.795444\pi$
$488$	0.377714	+	1.29303i	0.0170983	+	0.0585326i
$489$	−0.253337	+	5.37589i	−0.0114563	+	0.243106i
$490$	4.49754	−	0.427358i	0.203178	−	0.0193061i
$491$	−7.16588			−0.323392			−0.161696	−	0.986841i	$-0.551696\pi$
$491$	−7.16588			−0.323392			−0.161696	+	0.986841i	$0.551696\pi$
$492$	0.952651	+	6.64552i	0.0429488	+	0.299603i
$493$	1.79403			0.0807988
$494$	−31.8339	+	3.02488i	−1.43228	+	0.136096i
$495$	4.30634	−	45.5894i	0.193555	−	2.04909i
$496$	−9.90307	−	24.8703i	−0.444661	−	1.11671i
$497$		−	26.7535i		−	1.20006i
$498$	1.30808	+	27.4331i	0.0586163	+	1.22931i
$499$		−	41.0689i		−	1.83849i	−0.393680	−	0.919247i	$-0.628798\pi$
$499$		−	41.0689i		−	1.83849i	0.393680	−	0.919247i	$-0.371202\pi$
$500$	4.76940	+	24.8701i	0.213294	+	1.11222i
$501$	−29.1031	−	1.37147i	−1.30023	−	0.0612730i
$502$	−0.827303	−	8.70657i	−0.0369243	−	0.388593i
$503$	7.80983			0.348223			0.174112	−	0.984726i	$-0.444295\pi$
$503$	7.80983			0.348223			0.174112	+	0.984726i	$0.444295\pi$
$504$	−20.6287	+	3.96792i	−0.918876	+	0.176745i
$505$	−14.5629			−0.648040
$506$	−0.556745	−	5.85920i	−0.0247503	−	0.260473i
$507$	−5.79315	−	0.273000i	−0.257283	−	0.0121244i
$508$	4.07076	+	21.2270i	0.180611	+	0.941796i
$509$			32.6664i			1.44791i	0.689845	+	0.723957i	$0.257679\pi$
$509$			32.6664i			1.44791i	−0.689845	+	0.723957i	$0.742321\pi$
$510$	0.354343	+	7.43133i	0.0156906	+	0.329065i
$511$		−	15.8280i		−	0.700189i
$512$	−17.0387	−	14.8890i	−0.753010	−	0.658009i
$513$	5.32491	−	37.4422i	0.235100	−	1.65311i
$514$	19.2972	−	1.83363i	0.851162	−	0.0808779i
$515$	−41.5118			−1.82923
$516$	−0.770106	−	5.37212i	−0.0339020	−	0.236494i
$517$	−22.9137			−1.00774
$518$	32.1388	−	3.05385i	1.41210	−	0.134178i
$519$	2.08646	−	44.2753i	0.0915853	−	1.94347i
$520$	−30.9357	+	9.03682i	−1.35662	+	0.396291i
$521$		−	19.8083i		−	0.867816i	−0.900957	−	0.433908i	$-0.857134\pi$
$521$		−	19.8083i		−	0.867816i	0.900957	−	0.433908i	$-0.142866\pi$
$522$	−9.19130	+	0.00511407i	−0.402292	+	0.000223837i
$523$			25.3095i			1.10671i	0.832947	+	0.553353i	$0.186652\pi$
$523$			25.3095i			1.10671i	−0.832947	+	0.553353i	$0.813348\pi$
$524$	−3.31181	+	0.635115i	−0.144677	+	0.0277451i
$525$	1.70605	−	36.2028i	0.0744580	−	1.58002i
$526$	−1.93910	−	20.4072i	−0.0845489	−	0.889796i
$527$	5.54200			0.241413
$528$	−27.2603	+	9.39384i	−1.18635	+	0.408814i
$529$	1.00000			0.0434783
$530$	2.50558	+	26.3688i	0.108835	+	1.14539i
$531$	30.4085	+	2.87236i	1.31962	+	0.124650i
$532$	−35.3924	+	6.78729i	−1.53445	+	0.294266i
$533$		−	6.02082i		−	0.260790i
$534$	−16.9927	+	0.810254i	−0.735348	+	0.0350631i
$535$			28.5028i			1.23228i
$536$	−26.7018	+	7.80001i	−1.15334	+	0.336909i
$537$	−9.20564	−	0.433813i	−0.397253	−	0.0187204i
$538$	14.5542	−	1.38295i	0.627475	−	0.0596230i
$539$	−3.62485			−0.156134
$540$	−1.83658	−	38.0718i	−0.0790340	−	1.63835i
$541$	19.4100			0.834500			0.417250	−	0.908792i	$-0.362994\pi$
$541$	19.4100			0.834500			0.417250	+	0.908792i	$0.362994\pi$
$542$	35.0915	−	3.33441i	1.50731	−	0.143225i
$543$	0.142950	+	0.00673646i	0.00613456	+	0.000289089i
$544$	4.16871	−	2.13690i	0.178732	−	0.0916189i
$545$		−	32.8471i		−	1.40702i
$546$	18.8182	−	0.897294i	0.805343	−	0.0384007i
$547$		−	28.9039i		−	1.23584i	−0.786240	−	0.617922i	$-0.787975\pi$
$547$		−	28.9039i		−	1.23584i	0.786240	−	0.617922i	$-0.212025\pi$
$548$	5.95277	+	31.0408i	0.254290	+	1.32600i
$549$	1.42245	+	0.134363i	0.0607086	+	0.00573448i
$550$	−4.70570	−	49.5230i	−0.200652	−	2.11167i
$551$	−15.7677			−0.671726
$552$	−1.15078	−	4.76190i	−0.0489806	−	0.202680i
$553$	3.18317			0.135362
$554$	−0.571717	−	6.01677i	−0.0242899	−	0.255628i
$555$	−2.75737	+	58.5123i	−0.117044	+	2.48371i
$556$	1.70522	+	8.89187i	0.0723173	+	0.377099i
$557$			14.2100i			0.602097i	0.953609	+	0.301049i	$0.0973367\pi$
$557$			14.2100i			0.602097i	−0.953609	+	0.301049i	$0.902663\pi$
$558$	−28.3932	+	0.0157981i	−1.20198	+	0.000668787i
$559$			4.86712i			0.205857i
$560$	−33.7437	+	13.4364i	−1.42593	+	0.567791i
$561$	0.280990	−	5.96269i	0.0118634	−	0.251745i
$562$	−22.5476	+	2.14249i	−0.951114	+	0.0903754i
$563$	37.0076			1.55969			0.779843	−	0.625975i	$-0.215299\pi$
$563$	37.0076			1.55969			0.779843	+	0.625975i	$0.215299\pi$
$564$	−18.8796	+	2.70644i	−0.794976	+	0.113962i
$565$	29.3945			1.23663
$566$	−37.1299	+	3.52810i	−1.56069	+	0.148297i
$567$	−4.17209	+	21.8871i	−0.175211	+	0.919170i
$568$	−8.57048	−	29.3393i	−0.359609	−	1.23105i
$569$		−	29.2477i		−	1.22613i	−0.790033	−	0.613064i	$-0.789937\pi$
$569$		−	29.2477i		−	1.22613i	0.790033	−	0.613064i	$-0.210063\pi$
$570$	−3.11432	−	65.3140i	−0.130445	−	2.73570i
$571$		−	15.4959i		−	0.648484i	−0.945974	−	0.324242i	$-0.894891\pi$
$571$		−	15.4959i		−	0.648484i	0.945974	−	0.324242i	$-0.105109\pi$
$572$	25.3959	−	4.87023i	1.06185	−	0.203634i
$573$	−23.7696	−	1.12013i	−0.992989	−	0.0467943i
$574$	−0.641846	−	6.75482i	−0.0267901	−	0.281941i
$575$	8.45218			0.352480
$576$	−21.3514	+	10.9598i	−0.889642	+	0.456660i
$577$	30.1575			1.25547			0.627736	−	0.778426i	$-0.283982\pi$
$577$	30.1575			1.25547			0.627736	+	0.778426i	$0.283982\pi$
$578$	−2.18246	−	22.9684i	−0.0907786	−	0.955358i
$579$	−43.1764	−	2.03468i	−1.79435	−	0.0845582i
$580$	−15.6072	+	2.99303i	−0.648053	+	0.124279i
$581$		−	27.7580i		−	1.15160i
$582$	1.25048	+	26.2253i	0.0518343	+	1.08707i
$583$		−	21.2523i		−	0.880181i
$584$	−5.07049	−	17.3578i	−0.209818	−	0.718271i
$585$	−3.21464	+	34.0321i	−0.132909	+	1.40705i
$586$	−6.46019	+	0.613851i	−0.266868	+	0.0253579i
$587$	21.1729			0.873900			0.436950	−	0.899486i	$-0.356059\pi$
$587$	21.1729			0.873900			0.436950	+	0.899486i	$0.356059\pi$
$588$	−2.98668	+	0.428148i	−0.123169	+	0.0176565i
$589$	−48.7087			−2.00701
$590$	52.5729	−	4.99551i	2.16439	−	0.205662i
$591$	−1.19540	+	25.3668i	−0.0491722	+	1.04345i
$592$	34.2668	−	13.6447i	1.40836	−	0.560792i
$593$		−	38.9325i		−	1.59877i	−0.600821	−	0.799383i	$-0.705160\pi$
$593$		−	38.9325i		−	1.59877i	0.600821	−	0.799383i	$-0.294840\pi$
$594$	−1.42259	+	30.5493i	−0.0583697	+	1.25345i
$595$		−	7.51933i		−	0.308263i
$596$	−0.759698	−	3.96145i	−0.0311184	−	0.162267i
$597$	0.300207	−	6.37049i	0.0122867	−	0.260727i
$598$	0.415605	+	4.37384i	0.0169953	+	0.178860i
$599$	−27.2917			−1.11511			−0.557555	−	0.830140i	$-0.688260\pi$
$599$	−27.2917			−1.11511			−0.557555	+	0.830140i	$0.688260\pi$
$600$	−9.72663	−	40.2484i	−0.397088	−	1.64314i
$601$	19.3521			0.789389			0.394694	−	0.918812i	$-0.370850\pi$
$601$	19.3521			0.789389			0.394694	+	0.918812i	$0.370850\pi$
$602$	0.518857	+	5.46047i	0.0211470	+	0.222552i
$603$	−2.77468	+	29.3744i	−0.112994	+	1.19622i
$604$	1.27409	+	6.64374i	0.0518419	+	0.270330i
$605$			23.1804i			0.942419i
$606$	9.71480	−	0.463224i	0.394637	−	0.0188172i
$607$		−	41.1859i		−	1.67168i	−0.548971	−	0.835841i	$-0.684980\pi$
$607$		−	41.1859i		−	1.67168i	0.548971	−	0.835841i	$-0.315020\pi$
$608$	−36.6388	+	18.7812i	−1.48590	+	0.761679i
$609$	9.27929	+	0.437283i	0.376016	+	0.0177196i
$610$	2.45926	−	0.233680i	0.0995724	−	0.00946142i
$611$	17.1049			0.691989
$612$	−0.472760	−	4.94612i	−0.0191102	−	0.199935i
$613$	−23.6145			−0.953783			−0.476891	−	0.878962i	$-0.658236\pi$
$613$	−23.6145			−0.953783			−0.476891	+	0.878962i	$0.658236\pi$
$614$	23.5016	−	2.23314i	0.948449	−	0.0901221i
$615$	12.2979	+	0.579534i	0.495899	+	0.0233691i
$616$	27.9727	−	8.17127i	1.12705	−	0.329230i
$617$			13.1173i			0.528085i	0.964511	+	0.264042i	$0.0850558\pi$
$617$			13.1173i			0.528085i	−0.964511	+	0.264042i	$0.914944\pi$
$618$	27.6922	−	1.32043i	1.11395	−	0.0531155i
$619$		−	2.15938i		−	0.0867927i	−0.999058	−	0.0433963i	$-0.986182\pi$
$619$		−	2.15938i		−	0.0867927i	0.999058	−	0.0433963i	$-0.0138178\pi$
$620$	−48.2128	+	9.24590i	−1.93627	+	0.371324i
$621$	−5.14439	−	0.731619i	−0.206437	−	0.0293588i
$622$	2.53501	+	26.6785i	0.101645	+	1.06971i
$623$	17.1940			0.688862
$624$	20.3495	−	7.01241i	0.814633	−	0.280721i
$625$	4.17843			0.167137
$626$	0.432166	+	4.54814i	0.0172728	+	0.181780i
$627$	−2.46962	+	52.4061i	−0.0986271	+	2.09290i
$628$	−36.8592	+	7.06859i	−1.47084	+	0.282067i
$629$			7.63589i			0.304463i
$630$	0.0214347	+	38.5237i	0.000853978	+	1.53482i
$631$		−	4.57319i		−	0.182056i	−0.995848	−	0.0910280i	$-0.970985\pi$
$631$		−	4.57319i		−	0.182056i	0.995848	−	0.0910280i	$-0.0290153\pi$
$632$	3.49082	−	1.01973i	0.138858	−	0.0405625i
$633$	−0.0544668	+	1.15580i	−0.00216486	+	0.0459390i
$634$	15.7596	−	1.49749i	0.625894	−	0.0594727i
$635$	39.6367			1.57294
$636$	−2.51021	−	17.5107i	−0.0995361	−	0.694346i
$637$	2.70592			0.107212
$638$	12.6934	−	1.20614i	0.502538	−	0.0477514i
$639$	−32.2759	−	3.04875i	−1.27681	−	0.120607i
$640$	−32.7008	+	25.5448i	−1.29261	+	1.00975i
$641$			25.1560i			0.993603i	0.867864	+	0.496802i	$0.165492\pi$
$641$			25.1560i			0.993603i	−0.867864	+	0.496802i	$0.834508\pi$
$642$	−0.906631	−	19.0140i	−0.0357819	−	0.750422i
$643$		−	10.7983i		−	0.425843i	−0.977069	−	0.212921i	$-0.931702\pi$
$643$		−	10.7983i		−	0.425843i	0.977069	−	0.212921i	$-0.0682978\pi$
$644$	0.932543	+	4.86276i	0.0367473	+	0.191619i
$645$	−9.94139	−	0.468485i	−0.391442	−	0.0184466i
$646$	−0.806298	−	8.48552i	−0.0317234	−	0.333858i
$647$	−5.06981			−0.199315			−0.0996574	−	0.995022i	$-0.531775\pi$
$647$	−5.06981			−0.199315			−0.0996574	+	0.995022i	$0.531775\pi$
$648$	2.43618	+	25.3390i	0.0957022	+	0.995410i
$649$	−42.3719			−1.66324
$650$	3.51277	+	36.9685i	0.137782	+	1.45002i
$651$	28.6651	+	1.35083i	1.12347	+	0.0529433i
$652$	−1.17043	−	6.10322i	−0.0458376	−	0.239020i
$653$			19.1055i			0.747657i	0.927498	+	0.373828i	$0.121955\pi$
$653$			19.1055i			0.747657i	−0.927498	+	0.373828i	$0.878045\pi$
$654$	1.04482	+	21.9121i	0.0408557	+	0.856830i
$655$			6.18408i			0.241632i
$656$	−2.86778	−	7.20207i	−0.111968	−	0.281193i
$657$	−19.0952	−	1.80371i	−0.744973	−	0.0703695i
$658$	19.1901	−	1.82346i	0.748110	−	0.0710858i
$659$	−12.6073			−0.491110			−0.245555	−	0.969383i	$-0.578970\pi$
$659$	−12.6073			−0.491110			−0.245555	+	0.969383i	$0.578970\pi$
$660$	7.50326	+	52.3414i	0.292064	+	2.03739i
$661$	−37.4136			−1.45522			−0.727611	−	0.685990i	$-0.759369\pi$
$661$	−37.4136			−1.45522			−0.727611	+	0.685990i	$0.759369\pi$
$662$	−18.3145	+	1.74026i	−0.711814	+	0.0676369i
$663$	−0.209756	+	4.45109i	−0.00814626	+	0.172866i
$664$	−8.89226	−	30.4409i	−0.345087	−	1.18133i
$665$			66.0874i			2.56276i
$666$	−0.0217669	−	39.1208i	−0.000843452	−	1.51590i
$667$			2.16641i			0.0838837i
$668$	33.0406	−	6.33628i	1.27838	−	0.245158i
$669$	−0.956605	+	20.2995i	−0.0369845	+	0.784822i
$670$	4.82562	+	50.7850i	0.186430	+	1.96200i
$671$	−1.98207			−0.0765171
$672$	22.0828	−	10.0367i	0.851863	−	0.387172i
$673$	−30.1281			−1.16135			−0.580677	−	0.814134i	$-0.697212\pi$
$673$	−30.1281			−1.16135			−0.580677	+	0.814134i	$0.697212\pi$
$674$	−2.36154	−	24.8529i	−0.0909629	−	0.957298i
$675$	−43.4813	−	6.18377i	−1.67360	−	0.238014i
$676$	6.57693	−	1.26127i	0.252959	−	0.0485105i
$677$			3.25787i			0.125210i	0.998038	+	0.0626051i	$0.0199409\pi$
$677$			3.25787i			0.125210i	−0.998038	+	0.0626051i	$0.980059\pi$
$678$	−19.6088	+	0.934994i	−0.753072	+	0.0359082i
$679$		−	26.5359i		−	1.01835i
$680$	−2.40881	−	8.24609i	−0.0923738	−	0.316223i
$681$	−3.29540	−	0.155295i	−0.126280	−	0.00595090i
$682$	39.2119	−	3.72593i	1.50150	−	0.142673i
$683$	−5.01344			−0.191834			−0.0959170	−	0.995389i	$-0.530578\pi$
$683$	−5.01344			−0.191834			−0.0959170	+	0.995389i	$0.530578\pi$
$684$	4.15508	+	43.4714i	0.158874	+	1.66217i
$685$	57.9617			2.21460
$686$	27.4339	−	2.60678i	1.04743	−	0.0995275i
$687$	−11.8000	−	0.556071i	−0.450198	−	0.0212154i
$688$	2.31827	+	5.82202i	0.0883831	+	0.221962i
$689$			15.8647i			0.604396i
$690$	−8.97385	+	0.427894i	−0.341629	+	0.0162896i
$691$		−	11.6999i		−	0.445084i	−0.974923	−	0.222542i	$-0.928565\pi$
$691$		−	11.6999i		−	0.445084i	0.974923	−	0.222542i	$-0.0714354\pi$
$692$	9.63953	+	50.2655i	0.366440	+	1.91081i
$693$	2.90674	−	30.7725i	0.110418	−	1.16895i
$694$	−3.29786	−	34.7068i	−0.125185	−	1.31745i
$695$	16.6036			0.629810
$696$	10.3162	−	2.49307i	0.391036	−	0.0944995i
$697$	1.60488			0.0607893
$698$	−0.684470	−	7.20339i	−0.0259076	−	0.272652i
$699$	1.57239	−	33.3667i	0.0594734	−	1.26204i
$700$	7.88202	+	41.1009i	0.297912	+	1.55347i
$701$			5.21596i			0.197004i	0.995137	+	0.0985021i	$0.0314051\pi$
$701$			5.21596i			0.197004i	−0.995137	+	0.0985021i	$0.968595\pi$
$702$	1.06195	−	22.8048i	0.0400808	−	0.860712i
$703$		−	67.1118i		−	2.53117i
$704$	28.0586	−	17.9221i	1.05750	−	0.675464i
$705$	−1.64643	+	34.9378i	−0.0620082	+	1.31583i
$706$	1.07759	−	0.102393i	0.0405557	−	0.00385362i
$707$	−9.82984			−0.369689
$708$	−34.9121	+	5.00473i	−1.31208	+	0.188089i
$709$	19.5690			0.734930			0.367465	−	0.930037i	$-0.380226\pi$
$709$	19.5690			0.734930			0.367465	+	0.930037i	$0.380226\pi$
$710$	−55.8014	+	5.30228i	−2.09419	+	0.198991i
$711$	0.362744	−	3.84022i	0.0136040	−	0.144020i
$712$	18.8558	−	5.50808i	0.706651	−	0.206424i
$713$			6.69235i			0.250631i
$714$	0.239179	+	5.01609i	0.00895104	+	0.187722i
$715$		−	47.4211i		−	1.77345i
$716$	10.4511	−	2.00424i	0.390576	−	0.0749018i
$717$	4.10364	+	0.193383i	0.153253	+	0.00722201i
$718$	−4.33462	−	45.6177i	−0.161767	−	1.70244i
$719$	39.4330			1.47060			0.735301	−	0.677740i	$-0.237041\pi$
$719$	39.4330			1.47060			0.735301	+	0.677740i	$0.237041\pi$
$720$	12.3645	+	42.2402i	0.460799	+	1.57420i
$721$	−28.0202			−1.04353
$722$	4.54480	+	47.8296i	0.169140	+	1.78004i
$723$	−41.8861	−	1.97387i	−1.55776	−	0.0734090i
$724$	−0.162290	+	0.0311228i	−0.00603146	+	0.00115667i
$725$			18.3109i			0.680049i
$726$	−0.737336	−	15.4635i	−0.0273651	−	0.573904i
$727$			5.06434i			0.187826i	0.995580	+	0.0939129i	$0.0299375\pi$
$727$			5.06434i			0.187826i	−0.995580	+	0.0939129i	$0.970062\pi$
$728$	−20.8814	+	6.09978i	−0.773915	+	0.226073i
$729$	25.9295	+	7.52746i	0.960351	+	0.278795i
$730$	−33.0134	+	3.13695i	−1.22188	+	0.116104i
$731$	−1.29736			−0.0479845
$732$	−1.63312	+	0.234111i	−0.0603618	+	0.00865301i
$733$	−15.8662			−0.586032			−0.293016	−	0.956108i	$-0.594659\pi$
$733$	−15.8662			−0.586032			−0.293016	+	0.956108i	$0.594659\pi$
$734$	9.35877	−	0.889275i	0.345438	−	0.0328237i
$735$	−0.260459	+	5.52701i	−0.00960716	+	0.203867i
$736$	2.58046	+	5.03401i	0.0951169	+	0.185556i
$737$		−	40.9309i		−	1.50771i
$738$	−8.22227	+	0.00457490i	−0.302666	+	0.000168404i
$739$			1.82146i			0.0670034i	0.999439	+	0.0335017i	$0.0106659\pi$
$739$			1.82146i			0.0670034i	−0.999439	+	0.0335017i	$0.989334\pi$
$740$	−12.7392	−	66.4286i	−0.468302	−	2.44196i
$741$	1.84355	−	39.1207i	0.0677244	−	1.43713i
$742$	1.69125	+	17.7987i	0.0620876	+	0.653412i
$743$	5.16081			0.189332			0.0946658	−	0.995509i	$-0.469822\pi$
$743$	5.16081			0.189332			0.0946658	+	0.995509i	$0.469822\pi$
$744$	31.8683	−	7.70145i	1.16835	−	0.282349i
$745$	−7.39713			−0.271010
$746$	−2.46962	−	25.9904i	−0.0904194	−	0.951577i
$747$	−33.4877	−	3.16322i	−1.22525	−	0.115736i
$748$	1.29819	+	6.76941i	0.0474664	+	0.247514i
$749$			19.2391i			0.702983i
$750$	−30.9793	+	1.47717i	−1.13121	+	0.0539385i
$751$			41.2866i			1.50657i	0.657695	+	0.753284i	$0.271532\pi$
$751$			41.2866i			1.50657i	−0.657695	+	0.753284i	$0.728468\pi$
$752$	20.4608	−	8.14725i	0.746127	−	0.297100i
$753$	10.6995	+	0.504210i	0.389911	+	0.0183744i
$754$	−9.47554	+	0.900370i	−0.345079	+	0.0327896i
$755$	12.4057			0.451490
$756$	−1.23968	−	25.6982i	−0.0450867	−	0.934633i
$757$	−5.63182			−0.204692			−0.102346	−	0.994749i	$-0.532635\pi$
$757$	−5.63182			−0.204692			−0.102346	+	0.994749i	$0.532635\pi$
$758$	41.9123	−	3.98253i	1.52232	−	0.144652i
$759$	7.20036	+	0.339315i	0.261357	+	0.0123163i
$760$	21.1711	+	72.4749i	0.767955	+	2.62894i
$761$		−	32.6309i		−	1.18287i	−0.806353	−	0.591435i	$-0.798562\pi$
$761$		−	32.6309i		−	1.18287i	0.806353	−	0.591435i	$-0.201438\pi$
$762$	−26.4414	+	1.26079i	−0.957870	+	0.0456735i
$763$		−	22.1716i		−	0.802664i
$764$	26.9855	−	5.17508i	0.976301	−	0.187228i
$765$	−9.07145	−	0.856881i	−0.327979	−	0.0309806i
$766$	3.10942	+	32.7237i	0.112348	+	1.18236i
$767$	31.6303			1.14210
$768$	21.0019	−	18.0809i	0.757841	−	0.652439i
$769$	37.3376			1.34643			0.673214	−	0.739448i	$-0.264913\pi$
$769$	37.3376			1.34643			0.673214	+	0.739448i	$0.264913\pi$
$770$	−5.05531	−	53.2022i	−0.182181	−	1.91728i
$771$	−1.11753	+	23.7143i	−0.0402468	+	0.854048i
$772$	49.0179	−	9.40030i	1.76419	−	0.338324i
$773$		−	45.9941i		−	1.65429i	−0.561986	−	0.827147i	$-0.689963\pi$
$773$		−	45.9941i		−	1.65429i	0.561986	−	0.827147i	$-0.310037\pi$
$774$	6.64673	−	0.00369826i	0.238912	−	0.000132931i
$775$			56.5650i			2.03187i
$776$	−8.50076	−	29.1006i	−0.305159	−	1.04465i
$777$	−1.86120	+	39.4953i	−0.0667703	+	1.41689i
$778$	−6.03945	+	0.573871i	−0.216525	+	0.0205743i
$779$	−14.1053			−0.505375
$780$	−5.60112	−	39.0724i	−0.200552	−	1.39902i
$781$	44.9740			1.60930
$782$	−1.16587	+	0.110782i	−0.0416915	+	0.00396155i
$783$	1.58499	−	11.1449i	0.0566428	−	0.398285i
$784$	3.23681	−	1.28886i	0.115600	−	0.0460308i
$785$			68.8264i			2.45652i
$786$	−0.196706	−	4.12535i	−0.00701629	−	0.147146i
$787$			24.3259i			0.867124i	0.901124	+	0.433562i	$0.142744\pi$
$787$			24.3259i			0.867124i	−0.901124	+	0.433562i	$0.857256\pi$
$788$	−5.52280	−	28.7987i	−0.196742	−	1.02591i
$789$	25.0784	+	1.18181i	0.892813	+	0.0420735i
$790$	−0.630872	−	6.63932i	−0.0224454	−	0.236217i
$791$	19.8410			0.705466
$792$	−6.67027	−	34.6779i	−0.237018	−	1.23223i
$793$	1.47960			0.0525421
$794$	−3.36017	−	35.3625i	−0.119248	−	1.25497i
$795$	−32.4046	−	1.52705i	−1.14927	−	0.0541591i
$796$	1.38697	+	7.23238i	0.0491599	+	0.256345i
$797$		−	31.5546i		−	1.11772i	−0.829262	−	0.558860i	$-0.811239\pi$
$797$		−	31.5546i		−	1.11772i	0.829262	−	0.558860i	$-0.188761\pi$
$798$	−2.10214	−	44.0864i	−0.0744151	−	1.56064i
$799$			4.55940i			0.161300i
$800$	21.8105	+	42.5483i	0.771117	+	1.50431i
$801$	1.95937	−	20.7431i	0.0692311	−	0.732921i
$802$	−43.1740	+	4.10242i	−1.52453	+	0.144861i
$803$	26.6076			0.938963
$804$	−4.83453	−	33.7248i	−0.170501	−	1.18938i
$805$	9.08011			0.320032
$806$	−29.2713	+	2.78137i	−1.03104	+	0.0979697i
$807$	−0.842853	+	17.8856i	−0.0296698	+	0.629603i
$808$	−10.7799	+	3.14898i	−0.379236	+	0.110781i
$809$			50.8738i			1.78863i	0.447440	+	0.894314i	$0.352336\pi$
$809$			50.8738i			1.78863i	−0.447440	+	0.894314i	$0.647664\pi$
$810$	46.4780	+	4.36418i	1.63307	+	0.153342i
$811$			45.5412i			1.59917i	0.600554	+	0.799584i	$0.294947\pi$
$811$			45.5412i			1.59917i	−0.600554	+	0.799584i	$0.705053\pi$
$812$	−10.5347	+	2.02027i	−0.369696	+	0.0708976i
$813$	−2.03220	+	43.1239i	−0.0712723	+	1.51242i
$814$	5.13367	+	54.0269i	0.179935	+	1.89364i
$815$	−11.3964			−0.399199
$816$	1.86920	+	5.42428i	0.0654350	+	0.189888i
$817$	11.4025			0.398922
$818$	−0.162078	−	1.70572i	−0.00566694	−	0.0596391i
$819$	−2.16986	+	22.9714i	−0.0758210	+	0.802685i
$820$	−13.9617	+	2.67748i	−0.487565	+	0.0935015i
$821$			14.4084i			0.502858i	0.967876	+	0.251429i	$0.0809005\pi$
$821$			14.4084i			0.502858i	−0.967876	+	0.251429i	$0.919099\pi$
$822$	−38.6658	+	1.84368i	−1.34863	+	0.0643056i
$823$		−	31.0254i		−	1.08148i	−0.841191	−	0.540738i	$-0.818145\pi$
$823$		−	31.0254i		−	1.08148i	0.841191	−	0.540738i	$-0.181855\pi$
$824$	−30.7284	+	8.97625i	−1.07047	+	0.312702i
$825$	60.8588	+	2.86795i	2.11883	+	0.0998492i
$826$	35.4863	−	3.37193i	1.23473	−	0.117324i
$827$	−39.2574			−1.36511			−0.682556	−	0.730833i	$-0.739132\pi$
$827$	−39.2574			−1.36511			−0.682556	+	0.730833i	$0.739132\pi$
$828$	5.97278	−	0.570890i	0.207568	−	0.0198398i
$829$	−10.1123			−0.351213			−0.175607	−	0.984460i	$-0.556189\pi$
$829$	−10.1123			−0.351213			−0.175607	+	0.984460i	$0.556189\pi$
$830$	−57.8966	+	5.50136i	−2.00962	+	0.190955i
$831$	7.39400	+	0.348440i	0.256495	+	0.0120872i
$832$	−20.9455	+	13.3787i	−0.726155	+	0.463822i
$833$			0.721279i			0.0249908i
$834$	−11.0761	+	0.528136i	−0.383535	+	0.0182879i
$835$		−	61.6960i		−	2.13508i
$836$	−11.4098	−	59.4963i	−0.394615	−	2.05772i
$837$	4.89625	−	34.4281i	0.169239	−	1.19001i
$838$	2.58225	+	27.1757i	0.0892024	+	0.938770i
$839$	−26.1573			−0.903050			−0.451525	−	0.892258i	$-0.649120\pi$
$839$	−26.1573			−0.903050			−0.451525	+	0.892258i	$0.649120\pi$
$840$	−10.4492	−	43.2386i	−0.360533	−	1.49187i
$841$	24.3067			0.838161
$842$	3.22027	+	33.8902i	0.110978	+	1.16793i
$843$	1.30577	−	27.7087i	0.0449729	−	0.954340i
$844$	−0.251639	−	1.31217i	−0.00866177	−	0.0451669i
$845$		−	12.2809i		−	0.422477i
$846$	−0.0129971	−	23.3591i	−0.000446849	−	0.803102i
$847$			15.6466i			0.537624i
$848$	7.55653	+	18.9772i	0.259492	+	0.651681i
$849$	2.15025	−	45.6289i	0.0737962	−	1.56598i
$850$	−9.85416	+	0.936348i	−0.337995	+	0.0321165i
$851$	−9.22086			−0.316087
$852$	37.0561	−	5.31207i	1.26952	−	0.181989i
$853$	−11.8425			−0.405479			−0.202740	−	0.979233i	$-0.564985\pi$
$853$	−11.8425			−0.405479			−0.202740	+	0.979233i	$0.564985\pi$
$854$	1.65998	−	0.157732i	0.0568033	−	0.00539748i
$855$	79.7289	+	7.53113i	2.72667	+	0.257559i
$856$	6.16325	+	21.0986i	0.210656	+	0.721137i
$857$			52.9110i			1.80741i	0.428160	+	0.903703i	$0.359162\pi$
$857$			52.9110i			1.80741i	−0.428160	+	0.903703i	$0.640838\pi$
$858$	1.50840	+	31.6343i	0.0514958	+	1.07998i
$859$			42.0640i			1.43521i	0.696453	+	0.717603i	$0.254761\pi$
$859$			42.0640i			1.43521i	−0.696453	+	0.717603i	$0.745239\pi$
$860$	11.2864	−	2.16442i	0.384863	−	0.0738062i
$861$	8.30098	+	0.391181i	0.282897	+	0.0133314i
$862$	−1.78889	−	18.8263i	−0.0609298	−	0.641228i
$863$	−0.0143641			−0.000488961			−0.000244481	−	1.00000i	$-0.500078\pi$
$863$	−0.0143641			−0.000488961			−0.000244481		1.00000i	$0.500078\pi$
$864$	−9.59189	−	27.7848i	−0.326323	−	0.945258i
$865$	93.8596			3.19132
$866$	2.04667	+	21.5392i	0.0695486	+	0.731933i
$867$	28.2258	+	1.33013i	0.958597	+	0.0451736i
$868$	−32.5433	+	6.24091i	−1.10459	+	0.211830i
$869$			5.35106i			0.181522i
$870$	−0.926994	−	19.4410i	−0.0314280	−	0.659113i
$871$			30.5546i			1.03530i
$872$	−7.10265	−	24.3145i	−0.240526	−	0.823392i
$873$	−32.0133	−	3.02395i	−1.08349	−	0.102345i
$874$	10.2469	−	0.973661i	0.346605	−	0.0329346i
$875$	31.3462			1.05969
$876$	21.9232	−	3.14274i	0.740717	−	0.106183i
$877$	−42.0683			−1.42055			−0.710273	−	0.703926i	$-0.751428\pi$
$877$	−42.0683			−1.42055			−0.710273	+	0.703926i	$0.751428\pi$
$878$	42.4524	−	4.03385i	1.43270	−	0.136136i
$879$	0.374119	−	7.93891i	0.0126187	−	0.267773i
$880$	−22.5872	−	56.7249i	−0.761415	−	1.91219i
$881$			16.5872i			0.558838i	0.960169	+	0.279419i	$0.0901418\pi$
$881$			16.5872i			0.558838i	−0.960169	+	0.279419i	$0.909858\pi$
$882$	−0.00205608	−	3.69531i	−6.92320e−5	−	0.124428i
$883$			31.5376i			1.06133i	0.847583	+	0.530663i	$0.178057\pi$
$883$			31.5376i			1.06133i	−0.847583	+	0.530663i	$0.821943\pi$
$884$	−0.969084	−	5.05330i	−0.0325938	−	0.169961i
$885$	−3.04457	+	64.6068i	−0.102342	+	2.17173i
$886$	1.12909	+	11.8825i	0.0379324	+	0.399202i
$887$	24.6576			0.827920			0.413960	−	0.910295i	$-0.364145\pi$
$887$	24.6576			0.827920			0.413960	+	0.910295i	$0.364145\pi$
$888$	10.6112	+	43.9088i	0.356089	+	1.47348i
$889$	26.7545			0.897316
$890$	−3.40767	−	35.8625i	−0.114225	−	1.20211i
$891$	−36.7932	−	7.01349i	−1.23262	−	0.234961i
$892$	−4.41956	−	23.0459i	−0.147978	−	0.771632i
$893$		−	40.0726i		−	1.34098i
$894$	4.93457	−	0.235292i	0.165037	−	0.00786934i
$895$		−	19.5151i		−	0.652319i
$896$	−22.0728	+	17.2426i	−0.737399	+	0.576033i
$897$	−5.37501	−	0.253295i	−0.179466	−	0.00845729i
$898$	28.5113	−	2.70916i	0.951435	−	0.0904058i
$899$	−14.4984			−0.483548
$900$	50.4830	−	4.82526i	1.68277	−	0.160842i
$901$	−4.22882			−0.140882
$902$	11.3552	−	1.07898i	0.378086	−	0.0359259i
$903$	−6.71036	−	0.316224i	−0.223307	−	0.0105233i
$904$	21.7587	−	6.35606i	0.723683	−	0.211400i
$905$			0.303040i			0.0100734i
$906$	−8.27576	+	0.394608i	−0.274944	+	0.0131100i
$907$		−	49.8621i		−	1.65564i	−0.560990	−	0.827822i	$-0.689579\pi$
$907$		−	49.8621i		−	1.65564i	0.560990	−	0.827822i	$-0.310421\pi$
$908$	3.74125	−	0.717469i	0.124158	−	0.0238100i
$909$	−1.12018	+	11.8589i	−0.0371540	+	0.393334i
$910$	3.77374	+	39.7150i	0.125098	+	1.31654i
$911$	−54.2690			−1.79801			−0.899005	−	0.437938i	$-0.855709\pi$
$911$	−54.2690			−1.79801			−0.899005	+	0.437938i	$0.855709\pi$
$912$	−16.4284	−	47.6740i	−0.543998	−	1.57864i
$913$	46.6626			1.54431
$914$	2.33131	+	24.5348i	0.0771128	+	0.811539i
$915$	−0.142419	+	3.02217i	−0.00470823	+	0.0999100i
$916$	13.3965	−	2.56908i	0.442632	−	0.0848847i
$917$			4.17420i			0.137844i
$918$	6.07875	+	0.283070i	0.200629	+	0.00934269i
$919$			8.33364i			0.274901i	0.990509	+	0.137451i	$0.0438909\pi$
$919$			8.33364i			0.274901i	−0.990509	+	0.137451i	$0.956109\pi$
$920$	9.95772	−	2.90881i	0.328296	−	0.0959007i
$921$	−1.36101	+	28.8811i	−0.0448469	+	0.951665i
$922$	−25.4426	+	2.41757i	−0.837907	+	0.0796183i
$923$	−33.5727			−1.10506
$924$	5.06464	+	35.3300i	0.166614	+	1.16227i
$925$	−77.9364			−2.56253
$926$	34.8891	−	3.31518i	1.14653	−	0.108944i
$927$	−3.19310	+	33.8040i	−0.104875	+	1.11027i
$928$	−10.9057	+	5.59033i	−0.357998	+	0.183511i
$929$			37.3861i			1.22660i	0.789851	+	0.613299i	$0.210158\pi$
$929$			37.3861i			1.22660i	−0.789851	+	0.613299i	$0.789842\pi$
$930$	−2.86362	−	60.0562i	−0.0939017	−	1.96932i
$931$		−	6.33932i		−	0.207763i
$932$	7.26453	+	37.8810i	0.237958	+	1.24083i
$933$	−32.7852	−	1.54499i	−1.07334	−	0.0505808i
$934$	−2.26548	−	23.8420i	−0.0741287	−	0.780134i
$935$	12.6404			0.413384
$936$	4.97930	+	25.8867i	0.162753	+	0.846134i
$937$	−0.298557			−0.00975343			−0.00487672	−	0.999988i	$-0.501552\pi$
$937$	−0.298557			−0.00975343			−0.00487672	+	0.999988i	$0.501552\pi$
$938$	3.25725	+	34.2795i	0.106353	+	1.11927i
$939$	−5.58920	−	0.263389i	−0.182397	−	0.00859538i
$940$	−7.60659	−	39.6646i	−0.248100	−	1.29372i
$941$		−	1.07089i		−	0.0349100i	−0.999848	−	0.0174550i	$-0.994444\pi$
$941$		−	1.07089i		−	0.0349100i	0.999848	−	0.0174550i	$-0.00555638\pi$
$942$	−2.18927	−	45.9136i	−0.0713302	−	1.49595i
$943$			1.93801i			0.0631102i
$944$	37.8359	−	15.0659i	1.23145	−	0.490352i
$945$	−46.7116	−	6.64318i	−1.51953	−	0.216103i
$946$	−9.17932	+	0.872224i	−0.298446	+	0.0283585i
$947$	−15.0897			−0.490348			−0.245174	−	0.969479i	$-0.578845\pi$
$947$	−15.0897			−0.490348			−0.245174	+	0.969479i	$0.578845\pi$
$948$	0.632037	+	4.40898i	0.0205276	+	0.143197i
$949$	−19.8624			−0.644759
$950$	86.6082	−	8.22956i	2.80994	−	0.267002i
$951$	−0.912661	+	19.3669i	−0.0295950	+	0.628016i
$952$	−1.62593	−	5.56604i	−0.0526967	−	0.180397i
$953$		−	15.3045i		−	0.495763i	−0.968790	−	0.247881i	$-0.920266\pi$
$953$		−	15.3045i		−	0.495763i	0.968790	−	0.247881i	$-0.0797343\pi$
$954$	21.6654	−	0.0120547i	0.701444	−	0.000390286i
$955$		−	50.3894i		−	1.63056i
$956$	−4.65884	+	0.893437i	−0.150678	+	0.0288958i
$957$	−0.735095	+	15.5989i	−0.0237622	+	0.504242i
$958$	0.383671	+	4.03777i	0.0123958	+	0.130454i
$959$	39.1237			1.26337
$960$	−25.3106	−	44.0703i	−0.816898	−	1.42236i
$961$	−13.7876			−0.444761
$962$	−3.83223	−	40.3306i	−0.123556	−	1.30031i
$963$	23.2104	+	2.19244i	0.747945	+	0.0706503i
$964$	47.5531	−	9.11937i	1.53158	−	0.293715i
$965$		−	91.5301i		−	2.94646i
$966$	−6.05728	+	0.288825i	−0.194890	+	0.00929280i
$967$		−	47.7186i		−	1.53453i	−0.641332	−	0.767263i	$-0.721618\pi$
$967$		−	47.7186i		−	1.53453i	0.641332	−	0.767263i	$-0.278382\pi$
$968$	5.01239	+	17.1589i	0.161104	+	0.551507i
$969$	10.4278	+	0.491408i	0.334990	+	0.0157863i
$970$	−55.3475	+	5.25915i	−1.77710	+	0.168861i
$971$	29.2263			0.937917			0.468958	−	0.883220i	$-0.344629\pi$
$971$	29.2263			0.937917			0.468958	+	0.883220i	$0.344629\pi$
$972$	−31.1440	−	1.43292i	−0.998943	−	0.0459608i
$973$	11.2073			0.359289
$974$	37.2397	−	3.53853i	1.19324	−	0.113382i
$975$	−45.4305	−	2.14090i	−1.45494	−	0.0685636i
$976$	1.76989	−	0.704751i	0.0566528	−	0.0225585i
$977$		−	0.806440i		−	0.0258003i	−0.999917	−	0.0129001i	$-0.995894\pi$
$977$		−	0.806440i		−	0.0258003i	0.999917	−	0.0129001i	$-0.00410636\pi$
$978$	7.60246	−	0.362503i	0.243100	−	0.0115916i
$979$			28.9039i			0.923773i
$980$	−1.20333	−	6.27478i	−0.0384390	−	0.200441i
$981$	−26.7481	−	2.52661i	−0.854002	−	0.0806683i
$982$	0.958628	+	10.0886i	0.0305911	+	0.321942i
$983$	−45.8278			−1.46168			−0.730839	−	0.682549i	$-0.760871\pi$
$983$	−45.8278			−1.46168			−0.730839	+	0.682549i	$0.760871\pi$
$984$	9.22860	−	2.23023i	0.294197	−	0.0710970i
$985$	−53.7752			−1.71342
$986$	−0.239999	−	2.52576i	−0.00764312	−	0.0804365i
$987$	−1.11133	+	23.5827i	−0.0353740	+	0.750646i
$988$	8.51728	+	44.4135i	0.270971	+	1.41298i
$989$		−	1.56665i		−	0.0498166i
$990$	−64.7602	+	0.0360328i	−2.05821	+	0.00114520i
$991$			34.9430i			1.11000i	0.831850	+	0.555000i	$0.187282\pi$
$991$			34.9430i			1.11000i	−0.831850	+	0.555000i	$0.812718\pi$
$992$	−33.6894	+	17.2693i	−1.06964	+	0.548302i
$993$	1.06062	−	22.5067i	0.0336577	−	0.714228i
$994$	−37.6655	+	3.57900i	−1.19468	+	0.113519i
$995$	13.5049			0.428133
$996$	38.4474	−	5.51152i	1.21825	−	0.174639i
$997$	−27.7723			−0.879558			−0.439779	−	0.898106i	$-0.644943\pi$
$997$	−27.7723			−0.879558			−0.439779	+	0.898106i	$0.644943\pi$
$998$	−57.8197	+	5.49406i	−1.83025	+	0.173911i
$999$	47.4357	+	6.74616i	1.50080	+	0.213439i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.c.b.47.11	yes	22
3.2	odd	2		276.2.c.a.47.12	yes	22
4.3	odd	2		276.2.c.a.47.11	✓	22
12.11	even	2	inner	276.2.c.b.47.12	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.c.a.47.11	✓	22	4.3	odd	2
276.2.c.a.47.12	yes	22	3.2	odd	2
276.2.c.b.47.11	yes	22	1.1	even	1	trivial
276.2.c.b.47.12	yes	22	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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.133777 - 1.40787i) q^{2} +(1.73013 + 0.0815319i) q^{3} +(-1.96421 + 0.376681i) q^{4} +3.66772i q^{5} +(-0.116665 - 2.44671i) q^{6} +2.47568i q^{7} +(0.793084 + 2.71496i) q^{8} +(2.98671 + 0.282122i) q^{9} +O(q^{10})\)	\(q+(-0.133777 - 1.40787i) q^{2} +(1.73013 + 0.0815319i) q^{3} +(-1.96421 + 0.376681i) q^{4} +3.66772i q^{5} +(-0.116665 - 2.44671i) q^{6} +2.47568i q^{7} +(0.793084 + 2.71496i) q^{8} +(2.98671 + 0.282122i) q^{9} +(5.16368 - 0.490656i) q^{10} -4.16174 q^{11} +(-3.42905 + 0.491562i) q^{12} +3.10670 q^{13} +(3.48544 - 0.331189i) q^{14} +(-0.299036 + 6.34564i) q^{15} +(3.71622 - 1.47976i) q^{16} +0.828110i q^{17} +(-0.00236062 - 4.24264i) q^{18} -7.27826i q^{19} +(-1.38156 - 7.20417i) q^{20} +(-0.201847 + 4.28326i) q^{21} +(0.556745 + 5.85920i) q^{22} -1.00000 q^{23} +(1.15078 + 4.76190i) q^{24} -8.45218 q^{25} +(-0.415605 - 4.37384i) q^{26} +(5.14439 + 0.731619i) q^{27} +(-0.932543 - 4.86276i) q^{28} -2.16641i q^{29} +(8.97385 - 0.427894i) q^{30} -6.69235i q^{31} +(-2.58046 - 5.03401i) q^{32} +(-7.20036 - 0.339315i) q^{33} +(1.16587 - 0.110782i) q^{34} -9.08011 q^{35} +(-5.97278 + 0.570890i) q^{36} +9.22086 q^{37} +(-10.2469 + 0.973661i) q^{38} +(5.37501 + 0.253295i) q^{39} +(-9.95772 + 2.90881i) q^{40} -1.93801i q^{41} +(6.05728 - 0.288825i) q^{42} +1.56665i q^{43} +(8.17453 - 1.56765i) q^{44} +(-1.03474 + 10.9544i) q^{45} +(0.133777 + 1.40787i) q^{46} +5.50579 q^{47} +(6.55020 - 2.25719i) q^{48} +0.870994 q^{49} +(1.13070 + 11.8996i) q^{50} +(-0.0675173 + 1.43274i) q^{51} +(-6.10221 + 1.17024i) q^{52} +5.10659i q^{53} +(0.341826 - 7.34051i) q^{54} -15.2641i q^{55} +(-6.72138 + 1.96342i) q^{56} +(0.593410 - 12.5923i) q^{57} +(-3.05003 + 0.289815i) q^{58} +10.1813 q^{59} +(-1.80291 - 12.5768i) q^{60} +0.476260 q^{61} +(-9.42198 + 0.895281i) q^{62} +(-0.698443 + 7.39413i) q^{63} +(-6.74204 + 4.30639i) q^{64} +11.3945i q^{65} +(0.485529 + 10.1826i) q^{66} +9.83504i q^{67} +(-0.311933 - 1.62658i) q^{68} +(-1.73013 - 0.0815319i) q^{69} +(1.21471 + 12.7836i) q^{70} -10.8065 q^{71} +(1.60276 + 8.33254i) q^{72} -6.39338 q^{73} +(-1.23354 - 12.9818i) q^{74} +(-14.6234 - 0.689122i) q^{75} +(2.74158 + 14.2960i) q^{76} -10.3032i q^{77} +(-0.362443 - 7.60120i) q^{78} -1.28577i q^{79} +(5.42735 + 13.6301i) q^{80} +(8.84081 + 1.68523i) q^{81} +(-2.72847 + 0.259260i) q^{82} -11.2123 q^{83} +(-1.21695 - 8.48923i) q^{84} -3.03728 q^{85} +(2.20564 - 0.209581i) q^{86} +(0.176631 - 3.74817i) q^{87} +(-3.30061 - 11.2990i) q^{88} -6.94514i q^{89} +(15.5608 - 0.00865809i) q^{90} +7.69122i q^{91} +(1.96421 - 0.376681i) q^{92} +(0.545640 - 11.5786i) q^{93} +(-0.736547 - 7.75145i) q^{94} +26.6946 q^{95} +(-4.05409 - 8.91988i) q^{96} -10.7186 q^{97} +(-0.116519 - 1.22625i) q^{98} +(-12.4299 - 1.17412i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 9 q^{8} - 2 q^{9}+O(q^{10}) \) 22 * q + 9 * q^8 - 2 * q^9	\( 22 q + 9 q^{8} - 2 q^{9} + 4 q^{10} - 7 q^{12} - 4 q^{13} - 12 q^{14} + 4 q^{16} + 13 q^{18} + 14 q^{20} + 2 q^{22} - 22 q^{23} - 30 q^{24} - 18 q^{25} - 27 q^{26} - 12 q^{27} + 6 q^{28} + 34 q^{30} + 20 q^{32} - 8 q^{33} - 6 q^{34} + 8 q^{35} - 36 q^{36} - 4 q^{37} - 22 q^{38} + 24 q^{39} - 4 q^{40} + 26 q^{42} + 56 q^{44} - 8 q^{47} - 22 q^{48} - 14 q^{49} - 20 q^{50} - 16 q^{51} - 19 q^{52} + 22 q^{54} + 18 q^{56} + 12 q^{57} + 3 q^{58} + 72 q^{59} - 28 q^{60} + 12 q^{61} - 63 q^{62} + 20 q^{63} + 3 q^{64} + 60 q^{66} + 20 q^{68} - 40 q^{71} - 36 q^{72} - 4 q^{73} - 28 q^{74} - 48 q^{75} + 26 q^{76} + 11 q^{78} + 84 q^{80} + 10 q^{81} - 29 q^{82} + 8 q^{83} - 38 q^{84} + 8 q^{85} - 28 q^{86} + 48 q^{87} - 30 q^{88} + 84 q^{90} + 12 q^{93} - 13 q^{94} - 32 q^{95} - 45 q^{96} - 4 q^{97} - 64 q^{98} - 20 q^{99}+O(q^{100}) \) 22 * q + 9 * q^8 - 2 * q^9 + 4 * q^10 - 7 * q^12 - 4 * q^13 - 12 * q^14 + 4 * q^16 + 13 * q^18 + 14 * q^20 + 2 * q^22 - 22 * q^23 - 30 * q^24 - 18 * q^25 - 27 * q^26 - 12 * q^27 + 6 * q^28 + 34 * q^30 + 20 * q^32 - 8 * q^33 - 6 * q^34 + 8 * q^35 - 36 * q^36 - 4 * q^37 - 22 * q^38 + 24 * q^39 - 4 * q^40 + 26 * q^42 + 56 * q^44 - 8 * q^47 - 22 * q^48 - 14 * q^49 - 20 * q^50 - 16 * q^51 - 19 * q^52 + 22 * q^54 + 18 * q^56 + 12 * q^57 + 3 * q^58 + 72 * q^59 - 28 * q^60 + 12 * q^61 - 63 * q^62 + 20 * q^63 + 3 * q^64 + 60 * q^66 + 20 * q^68 - 40 * q^71 - 36 * q^72 - 4 * q^73 - 28 * q^74 - 48 * q^75 + 26 * q^76 + 11 * q^78 + 84 * q^80 + 10 * q^81 - 29 * q^82 + 8 * q^83 - 38 * q^84 + 8 * q^85 - 28 * q^86 + 48 * q^87 - 30 * q^88 + 84 * q^90 + 12 * q^93 - 13 * q^94 - 32 * q^95 - 45 * q^96 - 4 * q^97 - 64 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more