LMFDB - Embedded newform 510.2.l.g.137.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [510,2,Mod(137,510)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(510, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 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("510.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.l (of order $4$, degree $2$, 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:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			137.12
Character	$\chi$	$=$	510.137
Dual form			510.2.l.g.443.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.759217 - 1.55679i) q^{3} -1.00000i q^{4} +(-0.738113 - 2.11073i) q^{5} +(-0.563968 - 1.63766i) q^{6} +(-1.28132 - 1.28132i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.84718 - 2.36388i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.759217 - 1.55679i) q^{3} -1.00000i q^{4} +(-0.738113 - 2.11073i) q^{5} +(-0.563968 - 1.63766i) q^{6} +(-1.28132 - 1.28132i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.84718 - 2.36388i) q^{9} +(-2.01444 - 0.970588i) q^{10} +6.49808i q^{11} +(-1.55679 - 0.759217i) q^{12} +(3.68142 - 3.68142i) q^{13} -1.81207 q^{14} +(-3.84635 - 0.453418i) q^{15} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} +(-2.97767 - 0.365364i) q^{18} +3.69058i q^{19} +(-2.11073 + 0.738113i) q^{20} +(-2.96755 + 1.02195i) q^{21} +(4.59483 + 4.59483i) q^{22} +(-5.32876 - 5.32876i) q^{23} +(-1.63766 + 0.563968i) q^{24} +(-3.91038 + 3.11592i) q^{25} -5.20631i q^{26} +(-5.08247 + 1.08097i) q^{27} +(-1.28132 + 1.28132i) q^{28} +5.82957 q^{29} +(-3.04040 + 2.39917i) q^{30} +8.83803 q^{31} +(-0.707107 + 0.707107i) q^{32} +(10.1161 + 4.93345i) q^{33} -1.00000i q^{34} +(-1.75877 + 3.65029i) q^{35} +(-2.36388 + 1.84718i) q^{36} +(0.321811 + 0.321811i) q^{37} +(2.60964 + 2.60964i) q^{38} +(-2.93619 - 8.52618i) q^{39} +(-0.970588 + 2.01444i) q^{40} -5.74285i q^{41} +(-1.37575 + 2.82100i) q^{42} +(3.47671 - 3.47671i) q^{43} +6.49808 q^{44} +(-3.62609 + 5.64371i) q^{45} -7.53601 q^{46} +(2.21244 - 2.21244i) q^{47} +(-0.759217 + 1.55679i) q^{48} -3.71642i q^{49} +(-0.561767 + 4.96834i) q^{50} +(-0.563968 - 1.63766i) q^{51} +(-3.68142 - 3.68142i) q^{52} +(-2.73273 - 2.73273i) q^{53} +(-2.82949 + 4.35821i) q^{54} +(13.7157 - 4.79632i) q^{55} +1.81207i q^{56} +(5.74546 + 2.80196i) q^{57} +(4.12213 - 4.12213i) q^{58} +8.30098 q^{59} +(-0.453418 + 3.84635i) q^{60} -11.1278 q^{61} +(6.24943 - 6.24943i) q^{62} +(-0.662064 + 5.39573i) q^{63} +1.00000i q^{64} +(-10.4878 - 5.05318i) q^{65} +(10.6417 - 3.66470i) q^{66} +(1.83091 + 1.83091i) q^{67} +(-0.707107 - 0.707107i) q^{68} +(-12.3414 + 4.25007i) q^{69} +(1.33751 + 3.82479i) q^{70} +4.09434i q^{71} +(-0.365364 + 2.97767i) q^{72} +(-4.36323 + 4.36323i) q^{73} +0.455109 q^{74} +(1.88200 + 8.45329i) q^{75} +3.69058 q^{76} +(8.32614 - 8.32614i) q^{77} +(-8.10512 - 3.95272i) q^{78} +6.14323i q^{79} +(0.738113 + 2.11073i) q^{80} +(-2.17587 + 8.73302i) q^{81} +(-4.06081 - 4.06081i) q^{82} +(1.86990 + 1.86990i) q^{83} +(1.02195 + 2.96755i) q^{84} +(-2.01444 - 0.970588i) q^{85} -4.91680i q^{86} +(4.42591 - 9.07541i) q^{87} +(4.59483 - 4.59483i) q^{88} +7.94509 q^{89} +(1.42667 + 6.55474i) q^{90} -9.43417 q^{91} +(-5.32876 + 5.32876i) q^{92} +(6.70999 - 13.7589i) q^{93} -3.12886i q^{94} +(7.78983 - 2.72407i) q^{95} +(0.563968 + 1.63766i) q^{96} +(9.26552 + 9.26552i) q^{97} +(-2.62790 - 2.62790i) q^{98} +(15.3607 - 12.0031i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{7}+O(q^{10}) $ 28 * q + 4 * q^7	$ 28 q + 4 q^{7} - 12 q^{10} - 8 q^{13} + 8 q^{15} - 28 q^{16} - 16 q^{18} + 48 q^{21} + 20 q^{22} + 40 q^{25} - 36 q^{27} + 4 q^{28} - 12 q^{30} + 16 q^{31} + 8 q^{33} + 8 q^{37} - 8 q^{40} - 48 q^{42} + 48 q^{43} + 36 q^{45} - 64 q^{46} + 8 q^{52} - 36 q^{55} - 32 q^{57} + 20 q^{58} + 12 q^{60} - 16 q^{61} - 56 q^{63} + 32 q^{66} + 112 q^{67} - 28 q^{70} + 16 q^{72} + 12 q^{73} + 16 q^{75} - 8 q^{76} - 32 q^{78} - 48 q^{81} + 24 q^{82} - 12 q^{85} - 44 q^{87} + 20 q^{88} - 20 q^{90} - 80 q^{91} + 28 q^{93} + 60 q^{97}+O(q^{100}) $ 28 * q + 4 * q^7 - 12 * q^10 - 8 * q^13 + 8 * q^15 - 28 * q^16 - 16 * q^18 + 48 * q^21 + 20 * q^22 + 40 * q^25 - 36 * q^27 + 4 * q^28 - 12 * q^30 + 16 * q^31 + 8 * q^33 + 8 * q^37 - 8 * q^40 - 48 * q^42 + 48 * q^43 + 36 * q^45 - 64 * q^46 + 8 * q^52 - 36 * q^55 - 32 * q^57 + 20 * q^58 + 12 * q^60 - 16 * q^61 - 56 * q^63 + 32 * q^66 + 112 * q^67 - 28 * q^70 + 16 * q^72 + 12 * q^73 + 16 * q^75 - 8 * q^76 - 32 * q^78 - 48 * q^81 + 24 * q^82 - 12 * q^85 - 44 * q^87 + 20 * q^88 - 20 * q^90 - 80 * q^91 + 28 * q^93 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	0.759217	−	1.55679i	0.438334	−	0.898812i
$3$	0.759217	−	1.55679i	0.438334	−	0.898812i
$4$		−	1.00000i		−	0.500000i
$5$	−0.738113	−	2.11073i	−0.330094	−	0.943948i
$5$	−0.738113	−	2.11073i	−0.330094	−	0.943948i
$6$	−0.563968	−	1.63766i	−0.230239	−	0.668573i
$7$	−1.28132	−	1.28132i	−0.484295	−	0.484295i	0.422205	−	0.906500i	$-0.361256\pi$
$7$	−1.28132	−	1.28132i	−0.484295	−	0.484295i	−0.906500	+	0.422205i	$0.861256\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.84718	−	2.36388i	−0.615726	−	0.787960i
$10$	−2.01444	−	0.970588i	−0.637021	−	0.306927i
$11$			6.49808i			1.95924i	0.200852	+	0.979622i	$0.435629\pi$
$11$			6.49808i			1.95924i	−0.200852	+	0.979622i	$0.564371\pi$
$12$	−1.55679	−	0.759217i	−0.449406	−	0.219167i
$13$	3.68142	−	3.68142i	1.02104	−	1.02104i	0.0212670	−	0.999774i	$-0.493230\pi$
$13$	3.68142	−	3.68142i	1.02104	−	1.02104i	0.999774	−	0.0212670i	$-0.00677001\pi$
$14$	−1.81207			−0.484295
$15$	−3.84635	−	0.453418i	−0.993123	−	0.117072i
$16$	−1.00000			−0.250000
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i
$18$	−2.97767	−	0.365364i	−0.701843	−	0.0861171i
$19$			3.69058i			0.846678i	0.905971	+	0.423339i	$0.139142\pi$
$19$			3.69058i			0.846678i	−0.905971	+	0.423339i	$0.860858\pi$
$20$	−2.11073	+	0.738113i	−0.471974	+	0.165047i
$21$	−2.96755	+	1.02195i	−0.647573	+	0.223007i
$22$	4.59483	+	4.59483i	0.979622	+	0.979622i
$23$	−5.32876	−	5.32876i	−1.11112	−	1.11112i	−0.992999	−	0.118125i	$-0.962312\pi$
$23$	−5.32876	−	5.32876i	−1.11112	−	1.11112i	−0.118125	−	0.992999i	$-0.537688\pi$
$24$	−1.63766	+	0.563968i	−0.334287	+	0.115119i
$25$	−3.91038	+	3.11592i	−0.782075	+	0.623184i
$26$		−	5.20631i		−	1.02104i
$27$	−5.08247	+	1.08097i	−0.978122	+	0.208032i
$28$	−1.28132	+	1.28132i	−0.242148	+	0.242148i
$29$	5.82957			1.08252			0.541262	−	0.840854i	$-0.317947\pi$
$29$	5.82957			1.08252			0.541262	+	0.840854i	$0.317947\pi$
$30$	−3.04040	+	2.39917i	−0.555098	+	0.438026i
$31$	8.83803			1.58736			0.793679	−	0.608337i	$-0.208163\pi$
$31$	8.83803			1.58736			0.793679	+	0.608337i	$0.208163\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	10.1161	+	4.93345i	1.76099	+	0.858804i
$34$		−	1.00000i		−	0.171499i
$35$	−1.75877	+	3.65029i	−0.297286	+	0.617012i
$36$	−2.36388	+	1.84718i	−0.393980	+	0.307863i
$37$	0.321811	+	0.321811i	0.0529054	+	0.0529054i	0.733065	−	0.680159i	$-0.238089\pi$
$37$	0.321811	+	0.321811i	0.0529054	+	0.0529054i	−0.680159	+	0.733065i	$0.738089\pi$
$38$	2.60964	+	2.60964i	0.423339	+	0.423339i
$39$	−2.93619	−	8.52618i	−0.470167	−	1.36528i
$40$	−0.970588	+	2.01444i	−0.153463	+	0.318511i
$41$		−	5.74285i		−	0.896883i	−0.893812	−	0.448441i	$-0.851979\pi$
$41$		−	5.74285i		−	0.896883i	0.893812	−	0.448441i	$-0.148021\pi$
$42$	−1.37575	+	2.82100i	−0.212283	+	0.435290i
$43$	3.47671	−	3.47671i	0.530193	−	0.530193i	−0.390437	−	0.920630i	$-0.627676\pi$
$43$	3.47671	−	3.47671i	0.530193	−	0.530193i	0.920630	+	0.390437i	$0.127676\pi$
$44$	6.49808			0.979622
$45$	−3.62609	+	5.64371i	−0.540546	+	0.841315i
$46$	−7.53601			−1.11112
$47$	2.21244	−	2.21244i	0.322717	−	0.322717i	−0.527092	−	0.849809i	$-0.676718\pi$
$47$	2.21244	−	2.21244i	0.322717	−	0.322717i	0.849809	+	0.527092i	$0.176718\pi$
$48$	−0.759217	+	1.55679i	−0.109584	+	0.224703i
$49$		−	3.71642i		−	0.530917i
$50$	−0.561767	+	4.96834i	−0.0794459	+	0.702630i
$51$	−0.563968	−	1.63766i	−0.0789713	−	0.229319i
$52$	−3.68142	−	3.68142i	−0.510520	−	0.510520i
$53$	−2.73273	−	2.73273i	−0.375370	−	0.375370i	0.494059	−	0.869429i	$-0.335513\pi$
$53$	−2.73273	−	2.73273i	−0.375370	−	0.375370i	−0.869429	+	0.494059i	$0.835513\pi$
$54$	−2.82949	+	4.35821i	−0.385045	+	0.593077i
$55$	13.7157	−	4.79632i	1.84942	−	0.646735i
$56$			1.81207i			0.242148i
$57$	5.74546	+	2.80196i	0.761004	+	0.371128i
$58$	4.12213	−	4.12213i	0.541262	−	0.541262i
$59$	8.30098			1.08070			0.540348	−	0.841442i	$-0.318293\pi$
$59$	8.30098			1.08070			0.540348	+	0.841442i	$0.318293\pi$
$60$	−0.453418	+	3.84635i	−0.0585360	+	0.496562i
$61$	−11.1278			−1.42477			−0.712383	−	0.701791i	$-0.752384\pi$
$61$	−11.1278			−1.42477			−0.712383	+	0.701791i	$0.752384\pi$
$62$	6.24943	−	6.24943i	0.793679	−	0.793679i
$63$	−0.662064	+	5.39573i	−0.0834122	+	0.679798i
$64$			1.00000i			0.125000i
$65$	−10.4878	−	5.05318i	−1.30085	−	0.626770i
$66$	10.6417	−	3.66470i	1.30990	−	0.451094i
$67$	1.83091	+	1.83091i	0.223681	+	0.223681i	0.810047	−	0.586366i	$-0.199442\pi$
$67$	1.83091	+	1.83091i	0.223681	+	0.223681i	−0.586366	+	0.810047i	$0.699442\pi$
$68$	−0.707107	−	0.707107i	−0.0857493	−	0.0857493i
$69$	−12.3414	+	4.25007i	−1.48574	+	0.511648i
$70$	1.33751	+	3.82479i	0.159863	+	0.457149i
$71$			4.09434i			0.485909i	0.970038	+	0.242954i	$0.0781165\pi$
$71$			4.09434i			0.485909i	−0.970038	+	0.242954i	$0.921883\pi$
$72$	−0.365364	+	2.97767i	−0.0430586	+	0.350922i
$73$	−4.36323	+	4.36323i	−0.510678	+	0.510678i	−0.914734	−	0.404056i	$-0.867600\pi$
$73$	−4.36323	+	4.36323i	−0.510678	+	0.510678i	0.404056	+	0.914734i	$0.367600\pi$
$74$	0.455109			0.0529054
$75$	1.88200	+	8.45329i	0.217314	+	0.976102i
$76$	3.69058			0.423339
$77$	8.32614	−	8.32614i	0.948852	−	0.948852i
$78$	−8.10512	−	3.95272i	−0.917724	−	0.447557i
$79$			6.14323i			0.691167i	0.938388	+	0.345584i	$0.112319\pi$
$79$			6.14323i			0.691167i	−0.938388	+	0.345584i	$0.887681\pi$
$80$	0.738113	+	2.11073i	0.0825236	+	0.235987i
$81$	−2.17587	+	8.73302i	−0.241763	+	0.970335i
$82$	−4.06081	−	4.06081i	−0.448441	−	0.448441i
$83$	1.86990	+	1.86990i	0.205248	+	0.205248i	0.802244	−	0.596996i	$-0.203639\pi$
$83$	1.86990	+	1.86990i	0.205248	+	0.205248i	−0.596996	+	0.802244i	$0.703639\pi$
$84$	1.02195	+	2.96755i	0.111504	+	0.323787i
$85$	−2.01444	−	0.970588i	−0.218496	−	0.105275i
$86$		−	4.91680i		−	0.530193i
$87$	4.42591	−	9.07541i	0.474508	−	0.972986i
$88$	4.59483	−	4.59483i	0.489811	−	0.489811i
$89$	7.94509			0.842178			0.421089	−	0.907019i	$-0.361648\pi$
$89$	7.94509			0.842178			0.421089	+	0.907019i	$0.361648\pi$
$90$	1.42667	+	6.55474i	0.150384	+	0.690930i
$91$	−9.43417			−0.988970
$92$	−5.32876	+	5.32876i	−0.555562	+	0.555562i
$93$	6.70999	−	13.7589i	0.695793	−	1.42674i
$94$		−	3.12886i		−	0.322717i
$95$	7.78983	−	2.72407i	0.799220	−	0.279484i
$96$	0.563968	+	1.63766i	0.0575597	+	0.167143i
$97$	9.26552	+	9.26552i	0.940771	+	0.940771i	0.998341	−	0.0575706i	$-0.0183354\pi$
$97$	9.26552	+	9.26552i	0.940771	+	0.940771i	−0.0575706	+	0.998341i	$0.518335\pi$
$98$	−2.62790	−	2.62790i	−0.265458	−	0.265458i
$99$	15.3607	−	12.0031i	1.54381	−	1.20636i
$100$	3.11592	+	3.91038i	0.311592	+	0.391038i
$101$			2.51702i			0.250453i	0.992128	+	0.125226i	$0.0399657\pi$
$101$			2.51702i			0.250453i	−0.992128	+	0.125226i	$0.960034\pi$
$102$	−1.55679	−	0.759217i	−0.154145	−	0.0751737i
$103$	10.0675	−	10.0675i	0.991976	−	0.991976i	−0.00799239	−	0.999968i	$-0.502544\pi$
$103$	10.0675	−	10.0675i	0.991976	−	0.991976i	0.999968	+	0.00799239i	$0.00254408\pi$
$104$	−5.20631			−0.510520
$105$	4.34745	+	5.50940i	0.424267	+	0.537662i
$106$	−3.86467			−0.375370
$107$	−1.47204	+	1.47204i	−0.142308	+	0.142308i	−0.774672	−	0.632364i	$-0.782085\pi$
$107$	−1.47204	+	1.47204i	−0.142308	+	0.142308i	0.632364	+	0.774672i	$0.282085\pi$
$108$	1.08097	+	5.08247i	0.104016	+	0.489061i
$109$			0.539843i			0.0517076i	0.999666	+	0.0258538i	$0.00823043\pi$
$109$			0.539843i			0.0517076i	−0.999666	+	0.0258538i	$0.991770\pi$
$110$	6.30695	−	13.0900i	0.601344	−	1.24808i
$111$	0.745316	−	0.256667i	0.0707423	−	0.0243618i
$112$	1.28132	+	1.28132i	0.121074	+	0.121074i
$113$	0.595666	+	0.595666i	0.0560355	+	0.0560355i	0.734569	−	0.678534i	$-0.237384\pi$
$113$	0.595666	+	0.595666i	0.0560355	+	0.0560355i	−0.678534	+	0.734569i	$0.737384\pi$
$114$	6.04393	−	2.08137i	0.566066	−	0.194938i
$115$	−7.31436	+	15.1808i	−0.682067	+	1.41562i
$116$		−	5.82957i		−	0.541262i
$117$	−15.5027	−	1.90220i	−1.43322	−	0.175858i
$118$	5.86968	−	5.86968i	0.540348	−	0.540348i
$119$	−1.81207			−0.166112
$120$	2.39917	+	3.04040i	0.219013	+	0.277549i
$121$	−31.2250			−2.83863
$122$	−7.86853	+	7.86853i	−0.712383	+	0.712383i
$123$	−8.94040	−	4.36007i	−0.806129	−	0.393134i
$124$		−	8.83803i		−	0.793679i
$125$	9.46317	+	5.95386i	0.846412	+	0.532529i
$126$	3.34721	+	4.28351i	0.298193	+	0.381605i
$127$	9.28606	+	9.28606i	0.824004	+	0.824004i	0.986680	−	0.162675i	$-0.0520123\pi$
$127$	9.28606	+	9.28606i	0.824004	+	0.824004i	−0.162675	+	0.986680i	$0.552012\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−2.77292	−	8.05207i	−0.244142	−	0.708945i
$130$	−10.9891	+	3.84284i	−0.963809	+	0.337040i
$131$		−	2.43636i		−	0.212866i	−0.994320	−	0.106433i	$-0.966057\pi$
$131$		−	2.43636i		−	0.212866i	0.994320	−	0.106433i	$-0.0339430\pi$
$132$	4.93345	−	10.1161i	0.429402	−	0.880496i
$133$	4.72884	−	4.72884i	0.410042	−	0.410042i
$134$	2.58929			0.223681
$135$	6.03307	+	9.92986i	0.519244	+	0.854626i
$136$	−1.00000			−0.0857493
$137$	11.2010	−	11.2010i	0.956963	−	0.956963i	−0.0421487	−	0.999111i	$-0.513420\pi$
$137$	11.2010	−	11.2010i	0.956963	−	0.956963i	0.999111	+	0.0421487i	$0.0134203\pi$
$138$	−5.72147	+	11.7320i	−0.487044	+	0.998691i
$139$			14.3172i			1.21437i	0.794562	+	0.607183i	$0.207701\pi$
$139$			14.3172i			1.21437i	−0.794562	+	0.607183i	$0.792299\pi$
$140$	3.65029	+	1.75877i	0.308506	+	0.148643i
$141$	−1.76457	−	5.12401i	−0.148604	−	0.431520i
$142$	2.89513	+	2.89513i	0.242954	+	0.242954i
$143$	23.9221	+	23.9221i	2.00047	+	2.00047i
$144$	1.84718	+	2.36388i	0.153932	+	0.196990i
$145$	−4.30288	−	12.3047i	−0.357335	−	1.02185i
$146$			6.17054i			0.510678i
$147$	−5.78567	−	2.82157i	−0.477194	−	0.232719i
$148$	0.321811	−	0.321811i	0.0264527	−	0.0264527i
$149$	16.0846			1.31771			0.658853	−	0.752272i	$-0.271042\pi$
$149$	16.0846			1.31771			0.658853	+	0.752272i	$0.271042\pi$
$150$	7.30815	+	4.64660i	0.596708	+	0.379394i
$151$	−15.7917			−1.28511			−0.642556	−	0.766238i	$-0.722126\pi$
$151$	−15.7917			−1.28511			−0.642556	+	0.766238i	$0.722126\pi$
$152$	2.60964	−	2.60964i	0.211670	−	0.211670i
$153$	−2.97767	−	0.365364i	−0.240730	−	0.0295379i
$154$		−	11.7749i		−	0.948852i
$155$	−6.52347	−	18.6547i	−0.523978	−	1.49838i
$156$	−8.52618	+	2.93619i	−0.682641	+	0.235083i
$157$	14.3701	+	14.3701i	1.14686	+	1.14686i	0.987168	+	0.159688i	$0.0510488\pi$
$157$	14.3701	+	14.3701i	1.14686	+	1.14686i	0.159688	+	0.987168i	$0.448951\pi$
$158$	4.34392	+	4.34392i	0.345584	+	0.345584i
$159$	−6.32903	+	2.17955i	−0.501925	+	0.172849i
$160$	2.01444	+	0.970588i	0.159255	+	0.0767317i
$161$			13.6557i			1.07622i
$162$	4.63661	+	7.71375i	0.364286	+	0.606049i
$163$	−2.93966	+	2.93966i	−0.230252	+	0.230252i	−0.812798	−	0.582546i	$-0.802057\pi$
$163$	−2.93966	+	2.93966i	−0.230252	+	0.230252i	0.582546	+	0.812798i	$0.302057\pi$
$164$	−5.74285			−0.448441
$165$	2.94634	−	24.9939i	0.229373	−	1.94577i
$166$	2.64443			0.205248
$167$	−14.5022	+	14.5022i	−1.12221	+	1.12221i	−0.130806	+	0.991408i	$0.541757\pi$
$167$	−14.5022	+	14.5022i	−1.12221	+	1.12221i	−0.991408	+	0.130806i	$0.958243\pi$
$168$	2.82100	+	1.37575i	0.217645	+	0.106142i
$169$		−	14.1056i		−	1.08505i
$170$	−2.11073	+	0.738113i	−0.161886	+	0.0566107i
$171$	8.72410	−	6.81717i	0.667149	−	0.521322i
$172$	−3.47671	−	3.47671i	−0.265096	−	0.265096i
$173$	−5.79516	−	5.79516i	−0.440598	−	0.440598i	0.451615	−	0.892213i	$-0.350848\pi$
$173$	−5.79516	−	5.79516i	−0.440598	−	0.440598i	−0.892213	+	0.451615i	$0.850848\pi$
$174$	−3.28769	−	9.54687i	−0.249239	−	0.723747i
$175$	9.00296	+	1.01796i	0.680560	+	0.0769505i
$176$		−	6.49808i		−	0.489811i
$177$	6.30225	−	12.9229i	0.473706	−	0.971342i
$178$	5.61803	−	5.61803i	0.421089	−	0.421089i
$179$	3.27890			0.245076			0.122538	−	0.992464i	$-0.460897\pi$
$179$	3.27890			0.245076			0.122538	+	0.992464i	$0.460897\pi$
$180$	5.64371	+	3.62609i	0.420657	+	0.270273i
$181$	3.17612			0.236079			0.118039	−	0.993009i	$-0.462339\pi$
$181$	3.17612			0.236079			0.118039	+	0.993009i	$0.462339\pi$
$182$	−6.67097	+	6.67097i	−0.494485	+	0.494485i
$183$	−8.44841	+	17.3236i	−0.624524	+	1.28060i
$184$			7.53601i			0.555562i
$185$	0.441724	−	0.916790i	0.0324762	−	0.0674037i
$186$	−4.98436	−	14.4737i	−0.365471	−	1.06126i
$187$	4.59483	+	4.59483i	0.336007	+	0.336007i
$188$	−2.21244	−	2.21244i	−0.161358	−	0.161358i
$189$	7.89736	+	5.12723i	0.574449	+	0.372951i
$190$	3.58204	−	7.43445i	0.259868	−	0.539352i
$191$		−	2.99609i		−	0.216790i	−0.994108	−	0.108395i	$-0.965429\pi$
$191$		−	2.99609i		−	0.216790i	0.994108	−	0.108395i	$-0.0345711\pi$
$192$	1.55679	+	0.759217i	0.112351	+	0.0547918i
$193$	−18.0972	+	18.0972i	−1.30267	+	1.30267i	−0.376081	+	0.926587i	$0.622728\pi$
$193$	−18.0972	+	18.0972i	−1.30267	+	1.30267i	−0.926587	+	0.376081i	$0.877272\pi$
$194$	13.1034			0.940771
$195$	−15.8292	+	12.4908i	−1.13355	+	0.894484i
$196$	−3.71642			−0.265458
$197$	−2.19929	+	2.19929i	−0.156693	+	0.156693i	−0.781100	−	0.624406i	$-0.785341\pi$
$197$	−2.19929	+	2.19929i	−0.156693	+	0.156693i	0.624406	+	0.781100i	$0.285341\pi$
$198$	2.37416	−	19.3491i	0.168724	−	1.37508i
$199$		−	3.05251i		−	0.216386i	−0.994130	−	0.108193i	$-0.965493\pi$
$199$		−	3.05251i		−	0.216386i	0.994130	−	0.108193i	$-0.0345065\pi$
$200$	4.96834	+	0.561767i	0.351315	+	0.0397229i
$201$	4.24039	−	1.46028i	0.299094	−	0.103000i
$202$	1.77980	+	1.77980i	0.125226	+	0.125226i
$203$	−7.46957	−	7.46957i	−0.524261	−	0.524261i
$204$	−1.63766	+	0.563968i	−0.114659	+	0.0394856i
$205$	−12.1216	+	4.23887i	−0.846610	+	0.296056i
$206$		−	14.2375i		−	0.991976i
$207$	−2.75339	+	22.4397i	−0.191374	+	1.55967i
$208$	−3.68142	+	3.68142i	−0.255260	+	0.255260i
$209$	−23.9817			−1.65885
$210$	6.96984	+	0.821624i	0.480965	+	0.0566974i
$211$	4.12951			0.284288			0.142144	−	0.989846i	$-0.454600\pi$
$211$	4.12951			0.284288			0.142144	+	0.989846i	$0.454600\pi$
$212$	−2.73273	+	2.73273i	−0.187685	+	0.187685i
$213$	6.37402	+	3.10849i	0.436740	+	0.212990i
$214$			2.08178i			0.142308i
$215$	−9.90460	−	4.77219i	−0.675488	−	0.325461i
$216$	4.35821	+	2.82949i	0.296538	+	0.192523i
$217$	−11.3244	−	11.3244i	−0.768749	−	0.768749i
$218$	0.381727	+	0.381727i	0.0258538	+	0.0258538i
$219$	3.47999	+	10.1053i	0.235156	+	0.682851i
$220$	−4.79632	−	13.7157i	−0.323368	−	0.924712i
$221$		−	5.20631i		−	0.350214i
$222$	0.345527	−	0.708509i	0.0231902	−	0.0475520i
$223$	−8.15006	+	8.15006i	−0.545768	+	0.545768i	−0.925214	−	0.379446i	$-0.876115\pi$
$223$	−8.15006	+	8.15006i	−0.545768	+	0.545768i	0.379446	+	0.925214i	$0.376115\pi$
$224$	1.81207			0.121074
$225$	14.5888	+	3.48801i	0.972588	+	0.232534i
$226$	0.842399			0.0560355
$227$	−0.935113	+	0.935113i	−0.0620656	+	0.0620656i	−0.737458	−	0.675393i	$-0.763974\pi$
$227$	−0.935113	+	0.935113i	−0.0620656	+	0.0620656i	0.675393	+	0.737458i	$0.263974\pi$
$228$	2.80196	−	5.74546i	0.185564	−	0.380502i
$229$			3.24836i			0.214658i	0.994224	+	0.107329i	$0.0342297\pi$
$229$			3.24836i			0.214658i	−0.994224	+	0.107329i	$0.965770\pi$
$230$	5.56243	+	15.9065i	0.366776	+	1.04884i
$231$	−6.64069	−	19.2834i	−0.436925	−	1.26875i
$232$	−4.12213	−	4.12213i	−0.270631	−	0.270631i
$233$	−4.21980	−	4.21980i	−0.276448	−	0.276448i	0.555241	−	0.831689i	$-0.312626\pi$
$233$	−4.21980	−	4.21980i	−0.276448	−	0.276448i	−0.831689	+	0.555241i	$0.812626\pi$
$234$	−12.3071	+	9.61698i	−0.804540	+	0.628681i
$235$	−6.30289	−	3.03683i	−0.411155	−	0.198101i
$236$		−	8.30098i		−	0.540348i
$237$	9.56371	+	4.66405i	0.621229	+	0.302962i
$238$	−1.28132	+	1.28132i	−0.0830559	+	0.0830559i
$239$	−18.6750			−1.20798			−0.603992	−	0.796991i	$-0.706424\pi$
$239$	−18.6750			−1.20798			−0.603992	+	0.796991i	$0.706424\pi$
$240$	3.84635	+	0.453418i	0.248281	+	0.0292680i
$241$	−7.33380			−0.472411			−0.236206	−	0.971703i	$-0.575904\pi$
$241$	−7.33380			−0.472411			−0.236206	+	0.971703i	$0.575904\pi$
$242$	−22.0794	+	22.0794i	−1.41932	+	1.41932i
$243$	11.9435	+	10.0176i	0.766176	+	0.642631i
$244$			11.1278i			0.712383i
$245$	−7.84436	+	2.74314i	−0.501158	+	0.175253i
$246$	−9.40485	+	3.23878i	−0.599632	+	0.206497i
$247$	13.5866	+	13.5866i	0.864493	+	0.864493i
$248$	−6.24943	−	6.24943i	−0.396839	−	0.396839i
$249$	4.33069	−	1.49137i	0.274446	−	0.0945120i
$250$	10.9015	−	2.48146i	0.689470	−	0.156941i
$251$		−	9.88473i		−	0.623919i	−0.950095	−	0.311959i	$-0.899015\pi$
$251$		−	9.88473i		−	0.623919i	0.950095	−	0.311959i	$-0.100985\pi$
$252$	5.39573	+	0.662064i	0.339899	+	0.0417061i
$253$	34.6267	−	34.6267i	2.17696	−	2.17696i
$254$	13.1325			0.824004
$255$	−3.04040	+	2.39917i	−0.190397	+	0.150242i
$256$	1.00000			0.0625000
$257$	−17.0277	+	17.0277i	−1.06216	+	1.06216i	−0.0642262	+	0.997935i	$0.520458\pi$
$257$	−17.0277	+	17.0277i	−1.06216	+	1.06216i	−0.997935	+	0.0642262i	$0.979542\pi$
$258$	−7.65442	−	3.73292i	−0.476544	−	0.232402i
$259$		−	0.824688i		−	0.0512436i
$260$	−5.05318	+	10.4878i	−0.313385	+	0.650425i
$261$	−10.7683	−	13.7804i	−0.666538	−	0.852986i
$262$	−1.72277	−	1.72277i	−0.106433	−	0.106433i
$263$	7.82956	+	7.82956i	0.482792	+	0.482792i	0.906022	−	0.423230i	$-0.139104\pi$
$263$	7.82956	+	7.82956i	0.482792	+	0.482792i	−0.423230	+	0.906022i	$0.639104\pi$
$264$	−3.66470	−	10.6417i	−0.225547	−	0.654949i
$265$	−3.75100	+	7.78514i	−0.230422	+	0.478237i
$266$		−	6.68758i		−	0.410042i
$267$	6.03205	−	12.3688i	0.369155	−	0.756960i
$268$	1.83091	−	1.83091i	0.111840	−	0.111840i
$269$	−13.3600			−0.814575			−0.407287	−	0.913300i	$-0.633525\pi$
$269$	−13.3600			−0.814575			−0.407287	+	0.913300i	$0.633525\pi$
$270$	11.2875	+	2.75545i	0.686935	+	0.167691i
$271$	24.9500			1.51560			0.757802	−	0.652485i	$-0.226273\pi$
$271$	24.9500			1.51560			0.757802	+	0.652485i	$0.226273\pi$
$272$	−0.707107	+	0.707107i	−0.0428746	+	0.0428746i
$273$	−7.16259	+	14.6870i	−0.433500	+	0.888898i
$274$		−	15.8406i		−	0.956963i
$275$	−20.2475	−	25.4099i	−1.22097	−	1.53228i
$276$	4.25007	+	12.3414i	0.255824	+	0.742868i
$277$	−9.08452	−	9.08452i	−0.545836	−	0.545836i	0.379398	−	0.925234i	$-0.376131\pi$
$277$	−9.08452	−	9.08452i	−0.545836	−	0.545836i	−0.925234	+	0.379398i	$0.876131\pi$
$278$	10.1238	+	10.1238i	0.607183	+	0.607183i
$279$	−16.3254	−	20.8921i	−0.977377	−	1.25077i
$280$	3.82479	−	1.33751i	0.228575	−	0.0799315i
$281$			9.55817i			0.570193i	0.958499	+	0.285096i	$0.0920256\pi$
$281$			9.55817i			0.570193i	−0.958499	+	0.285096i	$0.907974\pi$
$282$	−4.87097	−	2.37548i	−0.290062	−	0.141458i
$283$	−0.229619	+	0.229619i	−0.0136494	+	0.0136494i	−0.713899	−	0.700249i	$-0.753072\pi$
$283$	−0.229619	+	0.229619i	−0.0136494	+	0.0136494i	0.700249	+	0.713899i	$0.253072\pi$
$284$	4.09434			0.242954
$285$	1.67338	−	14.1953i	0.0991223	−	0.840856i
$286$	33.8310			2.00047
$287$	−7.35845	+	7.35845i	−0.434356	+	0.434356i
$288$	2.97767	+	0.365364i	0.175461	+	0.0215293i
$289$		−	1.00000i		−	0.0588235i
$290$	−11.7433	−	5.65811i	−0.689591	−	0.332256i
$291$	21.4590	−	7.38991i	1.25795	−	0.433204i
$292$	4.36323	+	4.36323i	0.255339	+	0.255339i
$293$	−5.91163	−	5.91163i	−0.345361	−	0.345361i	0.513017	−	0.858378i	$-0.328528\pi$
$293$	−5.91163	−	5.91163i	−0.345361	−	0.345361i	−0.858378	+	0.513017i	$0.828528\pi$
$294$	−6.08624	+	2.09594i	−0.354957	+	0.122238i
$295$	−6.12707	−	17.5211i	−0.356732	−	1.02012i
$296$		−	0.455109i		−	0.0264527i
$297$	−7.02419	−	33.0263i	−0.407585	−	1.91638i
$298$	11.3736	−	11.3736i	0.658853	−	0.658853i
$299$	−39.2348			−2.26901
$300$	8.45329	−	1.88200i	0.488051	−	0.108657i
$301$	−8.90958			−0.513539
$302$	−11.1664	+	11.1664i	−0.642556	+	0.642556i
$303$	3.91847	+	1.91096i	0.225110	+	0.109782i
$304$		−	3.69058i		−	0.211670i
$305$	8.21357	+	23.4878i	0.470307	+	1.34491i
$306$	−2.36388	+	1.84718i	−0.135134	+	0.105596i
$307$	−15.1291	−	15.1291i	−0.863461	−	0.863461i	0.128278	−	0.991738i	$-0.459055\pi$
$307$	−15.1291	−	15.1291i	−0.863461	−	0.863461i	−0.991738	+	0.128278i	$0.959055\pi$
$308$	−8.32614	−	8.32614i	−0.474426	−	0.474426i
$309$	−8.02951	−	23.3163i	−0.456783	−	1.32642i
$310$	−17.8037	−	8.57808i	−1.01118	−	0.487202i
$311$			5.15391i			0.292251i	0.989266	+	0.146126i	$0.0466804\pi$
$311$			5.15391i			0.292251i	−0.989266	+	0.146126i	$0.953320\pi$
$312$	−3.95272	+	8.10512i	−0.223779	+	0.458862i
$313$	−7.31819	+	7.31819i	−0.413648	+	0.413648i	−0.883007	−	0.469359i	$-0.844485\pi$
$313$	−7.31819	+	7.31819i	−0.413648	+	0.413648i	0.469359	+	0.883007i	$0.344485\pi$
$314$	20.3223			1.14686
$315$	11.8776	−	2.58522i	0.669228	−	0.145661i
$316$	6.14323			0.345584
$317$	10.9391	−	10.9391i	0.614403	−	0.614403i	−0.329687	−	0.944090i	$-0.606943\pi$
$317$	10.9391	−	10.9391i	0.614403	−	0.614403i	0.944090	+	0.329687i	$0.106943\pi$
$318$	−2.93412	+	6.01647i	−0.164538	+	0.337387i
$319$			37.8810i			2.12093i
$320$	2.11073	−	0.738113i	0.117993	−	0.0412618i
$321$	1.17406	+	3.40926i	0.0655296	+	0.190286i
$322$	9.65607	+	9.65607i	0.538112	+	0.538112i
$323$	2.60964	+	2.60964i	0.145204	+	0.145204i
$324$	8.73302	+	2.17587i	0.485168	+	0.120881i
$325$	−2.92473	+	25.8667i	−0.162235	+	1.43483i
$326$			4.15730i			0.230252i
$327$	0.840421	+	0.409858i	0.0464754	+	0.0226652i
$328$	−4.06081	+	4.06081i	−0.224221	+	0.224221i
$329$	−5.66970			−0.312581
$330$	−15.5900	−	19.7567i	−0.858199	−	1.08757i
$331$	−2.04286			−0.112286			−0.0561428	−	0.998423i	$-0.517880\pi$
$331$	−2.04286			−0.112286			−0.0561428	+	0.998423i	$0.517880\pi$
$332$	1.86990	−	1.86990i	0.102624	−	0.102624i
$333$	0.166281	−	1.35516i	0.00911212	−	0.0742626i
$334$			20.5092i			1.12221i
$335$	2.51314	−	5.21597i	0.137307	−	0.284979i
$336$	2.96755	−	1.02195i	0.161893	−	0.0557518i
$337$	−10.2776	−	10.2776i	−0.559857	−	0.559857i	0.369410	−	0.929267i	$-0.379560\pi$
$337$	−10.2776	−	10.2776i	−0.559857	−	0.559857i	−0.929267	+	0.369410i	$0.879560\pi$
$338$	−9.97419	−	9.97419i	−0.542524	−	0.542524i
$339$	1.37957	−	0.475086i	0.0749277	−	0.0258031i
$340$	−0.970588	+	2.01444i	−0.0526375	+	0.109248i
$341$			57.4302i			3.11002i
$342$	1.34841	−	10.9893i	0.0729135	−	0.594235i
$343$	−13.7312	+	13.7312i	−0.741415	+	0.741415i
$344$	−4.91680			−0.265096
$345$	18.0801	+	22.9124i	0.973402	+	1.23356i
$346$	−8.19559			−0.440598
$347$	12.5864	−	12.5864i	0.675672	−	0.675672i	−0.283346	−	0.959018i	$-0.591444\pi$
$347$	12.5864	−	12.5864i	0.675672	−	0.675672i	0.959018	+	0.283346i	$0.0914445\pi$
$348$	−9.07541	−	4.42591i	−0.486493	−	0.237254i
$349$		−	35.1750i		−	1.88287i	−0.337191	−	0.941436i	$-0.609477\pi$
$349$		−	35.1750i		−	1.88287i	0.337191	−	0.941436i	$-0.390523\pi$
$350$	7.08586	−	5.64625i	0.378755	−	0.301805i
$351$	−14.7312	+	22.6902i	−0.786294	+	1.21111i
$352$	−4.59483	−	4.59483i	−0.244905	−	0.244905i
$353$	−15.3680	−	15.3680i	−0.817959	−	0.817959i	0.167853	−	0.985812i	$-0.446316\pi$
$353$	−15.3680	−	15.3680i	−0.817959	−	0.817959i	−0.985812	+	0.167853i	$0.946316\pi$
$354$	−4.68149	−	13.5942i	−0.248818	−	0.722524i
$355$	8.64205	−	3.02209i	0.458672	−	0.160396i
$356$		−	7.94509i		−	0.421089i
$357$	−1.37575	+	2.82100i	−0.0728125	+	0.149303i
$358$	2.31853	−	2.31853i	0.122538	−	0.122538i
$359$	23.0689			1.21753			0.608766	−	0.793350i	$-0.291665\pi$
$359$	23.0689			1.21753			0.608766	+	0.793350i	$0.291665\pi$
$360$	6.55474	−	1.42667i	0.345465	−	0.0751922i
$361$	5.37959			0.283136
$362$	2.24585	−	2.24585i	0.118039	−	0.118039i
$363$	−23.7065	+	48.6107i	−1.24427	+	2.55140i
$364$			9.43417i			0.494485i
$365$	12.4302	+	5.98905i	0.650625	+	0.313481i
$366$	6.27571	+	18.2236i	0.328037	+	0.952561i
$367$	20.8900	+	20.8900i	1.09045	+	1.09045i	0.995480	+	0.0949673i	$0.0302747\pi$
$367$	20.8900	+	20.8900i	1.09045	+	1.09045i	0.0949673	+	0.995480i	$0.469725\pi$
$368$	5.32876	+	5.32876i	0.277781	+	0.277781i
$369$	−13.5754	+	10.6081i	−0.706708	+	0.552234i
$370$	−0.335922	−	0.960614i	−0.0174638	−	0.0499399i
$371$			7.00304i			0.363580i
$372$	−13.7589	−	6.70999i	−0.713368	−	0.347897i
$373$	−3.69848	+	3.69848i	−0.191500	+	0.191500i	−0.796344	−	0.604844i	$-0.793236\pi$
$373$	−3.69848	+	3.69848i	−0.191500	+	0.191500i	0.604844	+	0.796344i	$0.293236\pi$
$374$	6.49808			0.336007
$375$	16.4535	−	10.2119i	0.849655	−	0.527339i
$376$	−3.12886			−0.161358
$377$	21.4611	−	21.4611i	1.10530	−	1.10530i
$378$	9.20978	−	1.95878i	0.473700	−	0.100749i
$379$			5.61661i			0.288506i	0.989541	+	0.144253i	$0.0460779\pi$
$379$			5.61661i			0.288506i	−0.989541	+	0.144253i	$0.953922\pi$
$380$	−2.72407	−	7.78983i	−0.139742	−	0.399610i
$381$	21.5066	−	7.40629i	1.10181	−	0.379436i
$382$	−2.11856	−	2.11856i	−0.108395	−	0.108395i
$383$	1.33891	+	1.33891i	0.0684149	+	0.0684149i	0.740486	−	0.672071i	$-0.234595\pi$
$383$	1.33891	+	1.33891i	0.0684149	+	0.0684149i	−0.672071	+	0.740486i	$0.734595\pi$
$384$	1.63766	−	0.563968i	0.0835716	−	0.0287799i
$385$	−23.7199	−	11.4286i	−1.20888	−	0.582456i
$386$			25.5934i			1.30267i
$387$	−14.6406	−	1.79642i	−0.744224	−	0.0913174i
$388$	9.26552	−	9.26552i	0.470385	−	0.470385i
$389$	3.22857			0.163695			0.0818475	−	0.996645i	$-0.473918\pi$
$389$	3.22857			0.163695			0.0818475	+	0.996645i	$0.473918\pi$
$390$	−2.36063	+	20.0253i	−0.119535	+	1.01402i
$391$	−7.53601			−0.381112
$392$	−2.62790	+	2.62790i	−0.132729	+	0.132729i
$393$	−3.79290	−	1.84973i	−0.191326	−	0.0933065i
$394$			3.11027i			0.156693i
$395$	12.9667	−	4.53440i	0.652426	−	0.228150i
$396$	−12.0031	−	15.3607i	−0.603179	−	0.771903i
$397$	−13.5989	−	13.5989i	−0.682508	−	0.682508i	0.278057	−	0.960565i	$-0.410310\pi$
$397$	−13.5989	−	13.5989i	−0.682508	−	0.682508i	−0.960565	+	0.278057i	$0.910310\pi$
$398$	−2.15845	−	2.15845i	−0.108193	−	0.108193i
$399$	−3.77158	−	10.9520i	−0.188815	−	0.548286i
$400$	3.91038	−	3.11592i	0.195519	−	0.155796i
$401$		−	27.4995i		−	1.37326i	−0.727007	−	0.686630i	$-0.759089\pi$
$401$		−	27.4995i		−	1.37326i	0.727007	−	0.686630i	$-0.240911\pi$
$402$	1.96584	−	4.03098i	0.0980470	−	0.201047i
$403$	32.5365	−	32.5365i	1.62076	−	1.62076i
$404$	2.51702			0.125226
$405$	20.0391	−	1.85329i	0.995751	−	0.0920906i
$406$	−10.5636			−0.524261
$407$	−2.09115	+	2.09115i	−0.103655	+	0.103655i
$408$	−0.759217	+	1.55679i	−0.0375869	+	0.0770725i
$409$		−	10.1786i		−	0.503300i	−0.967818	−	0.251650i	$-0.919027\pi$
$409$		−	10.1786i		−	0.503300i	0.967818	−	0.251650i	$-0.0809731\pi$
$410$	−5.57394	+	11.5686i	−0.275277	+	0.571333i
$411$	−8.93356	−	25.9415i	−0.440660	−	1.27960i
$412$	−10.0675	−	10.0675i	−0.495988	−	0.495988i
$413$	−10.6363	−	10.6363i	−0.523376	−	0.523376i
$414$	13.9203	+	17.8142i	0.684148	+	0.875521i
$415$	2.56665	−	5.32705i	0.125992	−	0.261494i
$416$			5.20631i			0.255260i
$417$	22.2888	+	10.8698i	1.09149	+	0.532298i
$418$	−16.9576	+	16.9576i	−0.829424	+	0.829424i
$419$	−23.5704			−1.15149			−0.575746	−	0.817629i	$-0.695288\pi$
$419$	−23.5704			−1.15149			−0.575746	+	0.817629i	$0.695288\pi$
$420$	5.50940	−	4.34745i	0.268831	−	0.212134i
$421$	12.7315			0.620498			0.310249	−	0.950655i	$-0.399588\pi$
$421$	12.7315			0.620498			0.310249	+	0.950655i	$0.399588\pi$
$422$	2.92001	−	2.92001i	0.142144	−	0.142144i
$423$	−9.31670	−	1.14317i	−0.452993	−	0.0555829i
$424$			3.86467i			0.187685i
$425$	−0.561767	+	4.96834i	−0.0272497	+	0.241000i
$426$	6.70515	−	2.30907i	0.324865	−	0.111875i
$427$	14.2583	+	14.2583i	0.690008	+	0.690008i
$428$	1.47204	+	1.47204i	0.0711539	+	0.0711539i
$429$	55.4037	−	19.0796i	2.67492	−	0.921171i
$430$	−10.3781	+	3.62916i	−0.500474	+	0.175014i
$431$			1.82801i			0.0880521i	0.999030	+	0.0440260i	$0.0140185\pi$
$431$			1.82801i			0.0880521i	−0.999030	+	0.0440260i	$0.985982\pi$
$432$	5.08247	−	1.08097i	0.244531	−	0.0520080i
$433$	−0.830323	+	0.830323i	−0.0399028	+	0.0399028i	−0.726777	−	0.686874i	$-0.758982\pi$
$433$	−0.830323	+	0.830323i	−0.0399028	+	0.0399028i	0.686874	+	0.726777i	$0.258982\pi$
$434$	−16.0151			−0.768749
$435$	−22.4226	−	2.64323i	−1.07508	−	0.126733i
$436$	0.539843			0.0258538
$437$	19.6662	−	19.6662i	0.940764	−	0.940764i
$438$	9.60623	+	4.68478i	0.459003	+	0.223848i
$439$			17.5478i			0.837513i	0.908099	+	0.418756i	$0.137534\pi$
$439$			17.5478i			0.837513i	−0.908099	+	0.418756i	$0.862466\pi$
$440$	−13.0900	−	6.30695i	−0.624040	−	0.300672i
$441$	−8.78516	+	6.86488i	−0.418341	+	0.326899i
$442$	−3.68142	−	3.68142i	−0.175107	−	0.175107i
$443$	5.89316	+	5.89316i	0.279993	+	0.279993i	0.833106	−	0.553113i	$-0.186560\pi$
$443$	5.89316	+	5.89316i	0.279993	+	0.279993i	−0.553113	+	0.833106i	$0.686560\pi$
$444$	−0.256667	−	0.745316i	−0.0121809	−	0.0353711i
$445$	−5.86438	−	16.7700i	−0.277998	−	0.794972i
$446$			11.5259i			0.545768i
$447$	12.2117	−	25.0404i	0.577596	−	1.18437i
$448$	1.28132	−	1.28132i	0.0605369	−	0.0605369i
$449$	−24.7722			−1.16907			−0.584537	−	0.811367i	$-0.698724\pi$
$449$	−24.7722			−1.16907			−0.584537	+	0.811367i	$0.698724\pi$
$450$	12.7823	−	7.84946i	0.602561	−	0.370027i
$451$	37.3175			1.75721
$452$	0.595666	−	0.595666i	0.0280178	−	0.0280178i
$453$	−11.9894	+	24.5844i	−0.563309	+	1.15507i
$454$			1.32245i			0.0620656i
$455$	6.96349	+	19.9130i	0.326453	+	0.933536i
$456$	−2.08137	−	6.04393i	−0.0974691	−	0.283033i
$457$	17.4510	+	17.4510i	0.816322	+	0.816322i	0.985573	−	0.169251i	$-0.0541348\pi$
$457$	17.4510	+	17.4510i	0.816322	+	0.816322i	−0.169251	+	0.985573i	$0.554135\pi$
$458$	2.29694	+	2.29694i	0.107329	+	0.107329i
$459$	−2.82949	+	4.35821i	−0.132069	+	0.203424i
$460$	15.1808	+	7.31436i	0.707809	+	0.341034i
$461$			21.0958i			0.982527i	0.871011	+	0.491264i	$0.163465\pi$
$461$			21.0958i			0.982527i	−0.871011	+	0.491264i	$0.836535\pi$
$462$	−18.3311	−	8.93974i	−0.852840	−	0.415914i
$463$	3.49416	−	3.49416i	0.162388	−	0.162388i	−0.621236	−	0.783624i	$-0.713369\pi$
$463$	3.49416	−	3.49416i	0.162388	−	0.162388i	0.783624	+	0.621236i	$0.213369\pi$
$464$	−5.82957			−0.270631
$465$	−33.9942	−	4.00732i	−1.57644	−	0.185835i
$466$	−5.96770			−0.276448
$467$	−15.2682	+	15.2682i	−0.706527	+	0.706527i	−0.965803	−	0.259276i	$-0.916516\pi$
$467$	−15.2682	+	15.2682i	−0.706527	+	0.706527i	0.259276	+	0.965803i	$0.416516\pi$
$468$	−1.90220	+	15.5027i	−0.0879291	+	0.716611i
$469$		−	4.69197i		−	0.216655i
$470$	−6.60418	+	2.30945i	−0.304628	+	0.106527i
$471$	33.2811	−	11.4611i	1.53351	−	0.528101i
$472$	−5.86968	−	5.86968i	−0.270174	−	0.270174i
$473$	22.5919	+	22.5919i	1.03878	+	1.03878i
$474$	10.0605	−	3.46458i	0.462096	−	0.159134i
$475$	−11.4996	−	14.4316i	−0.527636	−	0.662166i
$476$			1.81207i			0.0830559i
$477$	−1.41201	+	11.5077i	−0.0646516	+	0.526902i
$478$	−13.2052	+	13.2052i	−0.603992	+	0.603992i
$479$	15.2872			0.698488			0.349244	−	0.937032i	$-0.386438\pi$
$479$	15.2872			0.698488			0.349244	+	0.937032i	$0.386438\pi$
$480$	3.04040	−	2.39917i	0.138774	−	0.109506i
$481$	2.36944			0.108037
$482$	−5.18578	+	5.18578i	−0.236206	+	0.236206i
$483$	21.2591	+	10.3677i	0.967323	+	0.471746i
$484$			31.2250i			1.41932i
$485$	12.7180	−	26.3960i	0.577496	−	1.19858i
$486$	15.5289	−	1.36180i	0.704403	−	0.0617727i
$487$	15.8219	+	15.8219i	0.716961	+	0.716961i	0.967982	−	0.251021i	$-0.0807663\pi$
$487$	15.8219	+	15.8219i	0.716961	+	0.716961i	−0.251021	+	0.967982i	$0.580766\pi$
$488$	7.86853	+	7.86853i	0.356192	+	0.356192i
$489$	2.34458	+	6.80826i	0.106026	+	0.307880i
$490$	−3.60711	+	7.48649i	−0.162953	+	0.338205i
$491$			30.0697i			1.35703i	0.734588	+	0.678514i	$0.237376\pi$
$491$			30.0697i			1.35703i	−0.734588	+	0.678514i	$0.762624\pi$
$492$	−4.36007	+	8.94040i	−0.196567	+	0.403064i
$493$	4.12213	−	4.12213i	0.185651	−	0.185651i
$494$	19.2143			0.864493
$495$	−36.6732	−	23.5626i	−1.64834	−	1.05906i
$496$	−8.83803			−0.396839
$497$	5.24618	−	5.24618i	0.235323	−	0.235323i
$498$	2.00770	−	4.11682i	0.0899672	−	0.184479i
$499$			7.40716i			0.331590i	0.986160	+	0.165795i	$0.0530190\pi$
$499$			7.40716i			0.331590i	−0.986160	+	0.165795i	$0.946981\pi$
$500$	5.95386	−	9.46317i	0.266265	−	0.423206i
$501$	11.5665	+	33.5872i	0.516755	+	1.50056i
$502$	−6.98956	−	6.98956i	−0.311959	−	0.311959i
$503$	3.66020	+	3.66020i	0.163200	+	0.163200i	0.783983	−	0.620782i	$-0.213185\pi$
$503$	3.66020	+	3.66020i	0.163200	+	0.163200i	−0.620782	+	0.783983i	$0.713185\pi$
$504$	4.28351	−	3.34721i	0.190803	−	0.149097i
$505$	5.31275	−	1.85785i	0.236414	−	0.0826730i
$506$		−	48.9695i		−	2.17696i
$507$	−21.9595	−	10.7092i	−0.975255	−	0.475614i
$508$	9.28606	−	9.28606i	0.412002	−	0.412002i
$509$	30.3898			1.34701			0.673503	−	0.739185i	$-0.264789\pi$
$509$	30.3898			1.34701			0.673503	+	0.739185i	$0.264789\pi$
$510$	−0.453418	+	3.84635i	−0.0200777	+	0.170319i
$511$	11.1814			0.494637
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−3.98939	−	18.7573i	−0.176136	−	0.828154i
$514$			24.0809i			1.06216i
$515$	−28.6806	−	13.8188i	−1.26382	−	0.608928i
$516$	−8.05207	+	2.77292i	−0.354473	+	0.122071i
$517$	14.3766	+	14.3766i	0.632281	+	0.632281i
$518$	−0.583143	−	0.583143i	−0.0256218	−	0.0256218i
$519$	−13.4216	+	4.62205i	−0.589143	+	0.202885i
$520$	3.84284	+	10.9891i	0.168520	+	0.481905i
$521$		−	2.86672i		−	0.125593i	−0.998026	−	0.0627965i	$-0.979998\pi$
$521$		−	2.86672i		−	0.125593i	0.998026	−	0.0627965i	$-0.0200019\pi$
$522$	−17.3585	−	2.12992i	−0.759762	−	0.0932239i
$523$	2.08882	−	2.08882i	0.0913378	−	0.0913378i	−0.659962	−	0.751299i	$-0.729427\pi$
$523$	2.08882	−	2.08882i	0.0913378	−	0.0913378i	0.751299	+	0.659962i	$0.229427\pi$
$524$	−2.43636			−0.106433
$525$	8.41995	−	13.2429i	0.367477	−	0.577966i
$526$	11.0727			0.482792
$527$	6.24943	−	6.24943i	0.272229	−	0.272229i
$528$	−10.1161	−	4.93345i	−0.440248	−	0.214701i
$529$			33.7914i			1.46919i
$530$	2.85257	+	8.15728i	0.123908	+	0.354330i
$531$	−15.3334	−	19.6225i	−0.665413	−	0.851545i
$532$	−4.72884	−	4.72884i	−0.205021	−	0.205021i
$533$	−21.1418	−	21.1418i	−0.915754	−	0.915754i
$534$	−4.48077	−	13.0114i	−0.193902	−	0.563058i
$535$	4.19362	+	2.02055i	0.181306	+	0.0873562i
$536$		−	2.58929i		−	0.111840i
$537$	2.48939	−	5.10455i	0.107425	−	0.220277i
$538$	−9.44696	+	9.44696i	−0.407287	+	0.407287i
$539$	24.1495			1.04019
$540$	9.92986	−	6.03307i	0.427313	−	0.259622i
$541$	24.7247			1.06300			0.531499	−	0.847059i	$-0.321629\pi$
$541$	24.7247			1.06300			0.531499	+	0.847059i	$0.321629\pi$
$542$	17.6423	−	17.6423i	0.757802	−	0.757802i
$543$	2.41136	−	4.94454i	0.103481	−	0.212191i
$544$			1.00000i			0.0428746i
$545$	1.13946	−	0.398465i	0.0488092	−	0.0170684i
$546$	5.32057	+	15.4500i	0.227699	+	0.661199i
$547$	−28.6480	−	28.6480i	−1.22490	−	1.22490i	−0.965869	−	0.259029i	$-0.916597\pi$
$547$	−28.6480	−	28.6480i	−1.22490	−	1.22490i	−0.259029	−	0.965869i	$-0.583403\pi$
$548$	−11.2010	−	11.2010i	−0.478481	−	0.478481i
$549$	20.5550	+	26.3048i	0.877266	+	1.12266i
$550$	−32.2847	−	3.65040i	−1.37662	−	0.155654i
$551$			21.5145i			0.916550i
$552$	11.7320	+	5.72147i	0.499346	+	0.243522i
$553$	7.87147	−	7.87147i	0.334729	−	0.334729i
$554$	−12.8474			−0.545836
$555$	−1.09188	−	1.38371i	−0.0463478	−	0.0587353i
$556$	14.3172			0.607183
$557$	−8.74085	+	8.74085i	−0.370362	+	0.370362i	−0.867609	−	0.497247i	$-0.834344\pi$
$557$	−8.74085	+	8.74085i	−0.370362	+	0.370362i	0.497247	+	0.867609i	$0.334344\pi$
$558$	−26.3167	−	3.22910i	−1.11408	−	0.136699i
$559$		−	25.5984i		−	1.08270i
$560$	1.75877	−	3.65029i	0.0743216	−	0.154253i
$561$	10.6417	−	3.66470i	0.449291	−	0.154724i
$562$	6.75865	+	6.75865i	0.285096	+	0.285096i
$563$	24.3107	+	24.3107i	1.02458	+	1.02458i	0.999690	+	0.0248847i	$0.00792187\pi$
$563$	24.3107	+	24.3107i	1.02458	+	1.02458i	0.0248847	+	0.999690i	$0.492078\pi$
$564$	−5.12401	+	1.76457i	−0.215760	+	0.0743020i
$565$	0.817622	−	1.69696i	0.0343976	−	0.0713917i
$566$			0.324730i			0.0136494i
$567$	13.9778	−	8.40184i	0.587013	−	0.352844i
$568$	2.89513	−	2.89513i	0.121477	−	0.121477i
$569$	4.68960			0.196598			0.0982992	−	0.995157i	$-0.468660\pi$
$569$	4.68960			0.196598			0.0982992	+	0.995157i	$0.468660\pi$
$570$	−8.85432	−	11.2208i	−0.370867	−	0.469989i
$571$	33.2162			1.39005			0.695027	−	0.718984i	$-0.255393\pi$
$571$	33.2162			1.39005			0.695027	+	0.718984i	$0.255393\pi$
$572$	23.9221	−	23.9221i	1.00023	−	1.00023i
$573$	−4.66428	−	2.27469i	−0.194853	−	0.0950263i
$574$			10.4064i			0.434356i
$575$	37.4415	+	4.23348i	1.56142	+	0.176548i
$576$	2.36388	−	1.84718i	0.0984950	−	0.0769658i
$577$	−9.66775	−	9.66775i	−0.402474	−	0.402474i	0.476630	−	0.879104i	$-0.341858\pi$
$577$	−9.66775	−	9.66775i	−0.402474	−	0.402474i	−0.879104	+	0.476630i	$0.841858\pi$
$578$	−0.707107	−	0.707107i	−0.0294118	−	0.0294118i
$579$	14.4338	+	41.9133i	0.599849	+	1.74186i
$580$	−12.3047	+	4.30288i	−0.510923	+	0.178668i
$581$		−	4.79189i		−	0.198801i
$582$	9.94834	−	20.3992i	0.412372	−	0.845576i
$583$	17.7575	−	17.7575i	0.735441	−	0.735441i
$584$	6.17054			0.255339
$585$	7.42769	+	34.1260i	0.307097	+	1.41094i
$586$	−8.36031			−0.345361
$587$	12.2501	−	12.2501i	0.505616	−	0.505616i	−0.407561	−	0.913178i	$-0.633621\pi$
$587$	12.2501	−	12.2501i	0.505616	−	0.505616i	0.913178	+	0.407561i	$0.133621\pi$
$588$	−2.82157	+	5.78567i	−0.116359	+	0.238597i
$589$			32.6175i			1.34398i
$590$	−16.7218	−	8.05683i	−0.688426	−	0.331695i
$591$	1.75409	+	5.09357i	0.0721537	+	0.209522i
$592$	−0.321811	−	0.321811i	−0.0132263	−	0.0132263i
$593$	8.26080	+	8.26080i	0.339230	+	0.339230i	0.856078	−	0.516847i	$-0.172895\pi$
$593$	8.26080	+	8.26080i	0.339230	+	0.339230i	−0.516847	+	0.856078i	$0.672895\pi$
$594$	−28.3200	−	18.3863i	−1.16198	−	0.754397i
$595$	1.33751	+	3.82479i	0.0548326	+	0.156801i
$596$		−	16.0846i		−	0.658853i
$597$	−4.75211	−	2.31752i	−0.194491	−	0.0948496i
$598$	−27.7432	+	27.7432i	−1.13450	+	1.13450i
$599$	−43.7205			−1.78637			−0.893186	−	0.449687i	$-0.851536\pi$
$599$	−43.7205			−1.78637			−0.893186	+	0.449687i	$0.851536\pi$
$600$	4.64660	−	7.30815i	0.189697	−	0.298354i
$601$	11.0485			0.450679			0.225339	−	0.974280i	$-0.427651\pi$
$601$	11.0485			0.450679			0.225339	+	0.974280i	$0.427651\pi$
$602$	−6.30002	+	6.30002i	−0.256770	+	0.256770i
$603$	0.946035	−	7.71006i	0.0385255	−	0.313978i
$604$			15.7917i			0.642556i
$605$	23.0476	+	65.9076i	0.937017	+	2.67952i
$606$	4.12203	−	1.41952i	0.167446	−	0.0576640i
$607$	−18.0435	−	18.0435i	−0.732363	−	0.732363i	0.238724	−	0.971087i	$-0.423271\pi$
$607$	−18.0435	−	18.0435i	−0.732363	−	0.732363i	−0.971087	+	0.238724i	$0.923271\pi$
$608$	−2.60964	−	2.60964i	−0.105835	−	0.105835i
$609$	−17.2996	+	5.95751i	−0.701014	+	0.241411i
$610$	22.4162	+	10.8005i	0.907607	+	0.437299i
$611$		−	16.2898i		−	0.659014i
$612$	−0.365364	+	2.97767i	−0.0147690	+	0.120365i
$613$	9.22703	−	9.22703i	0.372676	−	0.372676i	−0.495775	−	0.868451i	$-0.665116\pi$
$613$	9.22703	−	9.22703i	0.372676	−	0.372676i	0.868451	+	0.495775i	$0.165116\pi$
$614$	−21.3957			−0.863461
$615$	−2.60391	+	22.0890i	−0.105000	+	0.890715i
$616$	−11.7749			−0.474426
$617$	11.0633	−	11.0633i	0.445393	−	0.445393i	−0.448426	−	0.893820i	$-0.648015\pi$
$617$	11.0633	−	11.0633i	0.445393	−	0.445393i	0.893820	+	0.448426i	$0.148015\pi$
$618$	−22.1648	−	10.8094i	−0.891600	−	0.434817i
$619$		−	10.7472i		−	0.431966i	−0.976397	−	0.215983i	$-0.930704\pi$
$619$		−	10.7472i		−	0.431966i	0.976397	−	0.215983i	$-0.0692955\pi$
$620$	−18.6547	+	6.52347i	−0.749191	+	0.261989i
$621$	32.8435	+	21.3231i	1.31796	+	0.855666i
$622$	3.64436	+	3.64436i	0.146126	+	0.146126i
$623$	−10.1802	−	10.1802i	−0.407863	−	0.407863i
$624$	2.93619	+	8.52618i	0.117542	+	0.341320i
$625$	5.58210	−	24.3688i	0.223284	−	0.974753i
$626$			10.3495i			0.413648i
$627$	−18.2073	+	37.3344i	−0.727130	+	1.49099i
$628$	14.3701	−	14.3701i	0.573428	−	0.573428i
$629$	0.455109			0.0181464
$630$	6.57072	−	10.2268i	0.261784	−	0.407445i
$631$	−46.0274			−1.83232			−0.916161	−	0.400810i	$-0.868729\pi$
$631$	−46.0274			−1.83232			−0.916161	+	0.400810i	$0.868729\pi$
$632$	4.34392	−	4.34392i	0.172792	−	0.172792i
$633$	3.13520	−	6.42878i	0.124613	−	0.255521i
$634$		−	15.4703i		−	0.614403i
$635$	12.7462	−	26.4545i	0.505818	−	1.04982i
$636$	2.17955	+	6.32903i	0.0864247	+	0.250962i
$637$	−13.6817	−	13.6817i	−0.542087	−	0.542087i
$638$	26.7859	+	26.7859i	1.06046	+	1.06046i
$639$	9.67853	−	7.56297i	0.382877	−	0.299187i
$640$	0.970588	−	2.01444i	0.0383659	−	0.0796276i
$641$			26.9523i			1.06455i	0.846571	+	0.532275i	$0.178663\pi$
$641$			26.9523i			1.06455i	−0.846571	+	0.532275i	$0.821337\pi$
$642$	3.24090	+	1.58053i	0.127908	+	0.0623784i
$643$	−16.2541	+	16.2541i	−0.640998	+	0.640998i	−0.950801	−	0.309803i	$-0.899737\pi$
$643$	−16.2541	+	16.2541i	−0.640998	+	0.640998i	0.309803	+	0.950801i	$0.399737\pi$
$644$	13.6557			0.538112
$645$	−14.9490	+	11.7962i	−0.588618	+	0.464476i
$646$	3.69058			0.145204
$647$	−24.5465	+	24.5465i	−0.965021	+	0.965021i	−0.999409	−	0.0343878i	$-0.989052\pi$
$647$	−24.5465	+	24.5465i	−0.965021	+	0.965021i	0.0343878	+	0.999409i	$0.489052\pi$
$648$	7.71375	−	4.63661i	0.303025	−	0.182143i
$649$			53.9404i			2.11735i
$650$	16.2224	+	20.3586i	0.636296	+	0.798531i
$651$	−26.2273	+	9.03200i	−1.02793	+	0.353992i
$652$	2.93966	+	2.93966i	0.115126	+	0.115126i
$653$	−11.0523	−	11.0523i	−0.432511	−	0.432511i	0.456971	−	0.889482i	$-0.348934\pi$
$653$	−11.0523	−	11.0523i	−0.432511	−	0.432511i	−0.889482	+	0.456971i	$0.848934\pi$
$654$	0.884081	−	0.304454i	0.0345703	−	0.0119051i
$655$	−5.14251	+	1.79831i	−0.200934	+	0.0702658i
$656$			5.74285i			0.224221i
$657$	18.3738	+	2.25449i	0.716831	+	0.0879562i
$658$	−4.00908	+	4.00908i	−0.156290	+	0.156290i
$659$	−5.66672			−0.220744			−0.110372	−	0.993890i	$-0.535204\pi$
$659$	−5.66672			−0.220744			−0.110372	+	0.993890i	$0.535204\pi$
$660$	−24.9939	−	2.94634i	−0.972885	−	0.114686i
$661$	−13.9792			−0.543726			−0.271863	−	0.962336i	$-0.587640\pi$
$661$	−13.9792			−0.543726			−0.271863	+	0.962336i	$0.587640\pi$
$662$	−1.44452	+	1.44452i	−0.0561428	+	0.0561428i
$663$	−8.10512	−	3.95272i	−0.314777	−	0.153511i
$664$		−	2.64443i		−	0.102624i
$665$	−13.4717	−	6.49089i	−0.522411	−	0.251706i
$666$	−0.840668	−	1.07582i	−0.0325752	−	0.0416873i
$667$	−31.0644	−	31.0644i	−1.20282	−	1.20282i
$668$	14.5022	+	14.5022i	0.561107	+	0.561107i
$669$	6.50025	+	18.8756i	0.251314	+	0.729772i
$670$	−1.91119	−	5.46530i	−0.0738358	−	0.211143i
$671$		−	72.3092i		−	2.79146i
$672$	1.37575	−	2.82100i	0.0530708	−	0.108823i
$673$	−1.19595	+	1.19595i	−0.0461005	+	0.0461005i	−0.729781	−	0.683681i	$-0.760378\pi$
$673$	−1.19595	+	1.19595i	−0.0461005	+	0.0461005i	0.683681	+	0.729781i	$0.260378\pi$
$674$	−14.5347			−0.559857
$675$	16.5062	−	20.0635i	0.635323	−	0.772246i
$676$	−14.1056			−0.542524
$677$	2.57786	−	2.57786i	0.0990753	−	0.0990753i	−0.655832	−	0.754907i	$-0.727682\pi$
$677$	2.57786	−	2.57786i	0.0990753	−	0.0990753i	0.754907	+	0.655832i	$0.227682\pi$
$678$	0.639564	−	1.31144i	0.0245623	−	0.0503654i
$679$		−	23.7443i		−	0.911221i
$680$	0.738113	+	2.11073i	0.0283054	+	0.0809429i
$681$	0.745819	+	2.16573i	0.0285798	+	0.0829908i
$682$	40.6093	+	40.6093i	1.55501	+	1.55501i
$683$	20.4838	+	20.4838i	0.783790	+	0.783790i	0.980468	−	0.196678i	$-0.0630153\pi$
$683$	20.4838	+	20.4838i	0.783790	+	0.783790i	−0.196678	+	0.980468i	$0.563015\pi$
$684$	−6.81717	−	8.72410i	−0.260661	−	0.333574i
$685$	−31.9098	−	15.3746i	−1.21921	−	0.587435i
$686$			19.4189i			0.741415i
$687$	5.05701	+	2.46621i	0.192937	+	0.0940918i
$688$	−3.47671	+	3.47671i	−0.132548	+	0.132548i
$689$	−20.1207			−0.766536
$690$	28.9861	+	3.41696i	1.10348	+	0.130082i
$691$	−35.8550			−1.36399			−0.681994	−	0.731358i	$-0.738887\pi$
$691$	−35.8550			−1.36399			−0.681994	+	0.731358i	$0.738887\pi$
$692$	−5.79516	+	5.79516i	−0.220299	+	0.220299i
$693$	−35.0619	−	4.30214i	−1.33189	−	0.163425i
$694$		−	17.7998i		−	0.675672i
$695$	30.2197	−	10.5677i	1.14630	−	0.400855i
$696$	−9.54687	+	3.28769i	−0.361873	+	0.124620i
$697$	−4.06081	−	4.06081i	−0.153814	−	0.153814i
$698$	−24.8725	−	24.8725i	−0.941436	−	0.941436i
$699$	−9.77308	+	3.36559i	−0.369652	+	0.127298i
$700$	1.01796	−	9.00296i	0.0384752	−	0.340280i
$701$		−	23.4780i		−	0.886753i	−0.896336	−	0.443376i	$-0.853781\pi$
$701$		−	23.4780i		−	0.886753i	0.896336	−	0.443376i	$-0.146219\pi$
$702$	5.62784	+	26.4609i	0.212409	+	0.998703i
$703$	−1.18767	+	1.18767i	−0.0447938	+	0.0447938i
$704$	−6.49808			−0.244905
$705$	−9.51296	+	7.50665i	−0.358279	+	0.282717i
$706$	−21.7337			−0.817959
$707$	3.22512	−	3.22512i	0.121293	−	0.121293i
$708$	−12.9229	−	6.30225i	−0.485671	−	0.236853i
$709$			10.0107i			0.375960i	0.982173	+	0.187980i	$0.0601939\pi$
$709$			10.0107i			0.375960i	−0.982173	+	0.187980i	$0.939806\pi$
$710$	3.97392	−	8.24779i	0.149138	−	0.309534i
$711$	14.5219	−	11.3476i	0.544612	−	0.425570i
$712$	−5.61803	−	5.61803i	−0.210544	−	0.210544i
$713$	−47.0958	−	47.0958i	−1.76375	−	1.76375i
$714$	1.02195	+	2.96755i	0.0382454	+	0.111058i
$715$	32.8359	−	68.1504i	1.22799	−	2.54868i
$716$		−	3.27890i		−	0.122538i
$717$	−14.1784	+	29.0730i	−0.529501	+	1.08575i
$718$	16.3122	−	16.3122i	0.608766	−	0.608766i
$719$	15.5803			0.581046			0.290523	−	0.956868i	$-0.406171\pi$
$719$	15.5803			0.581046			0.290523	+	0.956868i	$0.406171\pi$
$720$	3.62609	−	5.64371i	0.135136	−	0.210329i
$721$	−25.7993			−0.960818
$722$	3.80394	−	3.80394i	0.141568	−	0.141568i
$723$	−5.56794	+	11.4172i	−0.207074	+	0.424609i
$724$		−	3.17612i		−	0.118039i
$725$	−22.7958	+	18.1645i	−0.846616	+	0.674612i
$726$	17.6099	+	51.1360i	0.653564	+	1.89783i
$727$	−23.9979	−	23.9979i	−0.890031	−	0.890031i	0.104494	−	0.994525i	$-0.466678\pi$
$727$	−23.9979	−	23.9979i	−0.890031	−	0.890031i	−0.994525	+	0.104494i	$0.966678\pi$
$728$	6.67097	+	6.67097i	0.247243	+	0.247243i
$729$	24.6630	−	10.9880i	0.913445	−	0.406961i
$730$	13.0244	−	4.55456i	0.482053	−	0.168572i
$731$		−	4.91680i		−	0.181855i
$732$	17.3236	+	8.44841i	0.640299	+	0.312262i
$733$	17.9045	−	17.9045i	0.661319	−	0.661319i	−0.294372	−	0.955691i	$-0.595110\pi$
$733$	17.9045	−	17.9045i	0.661319	−	0.661319i	0.955691	+	0.294372i	$0.0951105\pi$
$734$	29.5429			1.09045
$735$	−1.68509	+	14.2946i	−0.0621555	+	0.527266i
$736$	7.53601			0.277781
$737$	−11.8974	+	11.8974i	−0.438245	+	0.438245i
$738$	−2.09823	+	17.1003i	−0.0772370	+	0.629471i
$739$		−	32.1498i		−	1.18265i	−0.806433	−	0.591325i	$-0.798605\pi$
$739$		−	32.1498i		−	1.18265i	0.806433	−	0.591325i	$-0.201395\pi$
$740$	−0.916790	−	0.441724i	−0.0337019	−	0.0162381i
$741$	31.4666	−	10.8363i	1.15595	−	0.398080i
$742$	4.95190	+	4.95190i	0.181790	+	0.181790i
$743$	−7.34355	−	7.34355i	−0.269409	−	0.269409i	0.559453	−	0.828862i	$-0.311011\pi$
$743$	−7.34355	−	7.34355i	−0.269409	−	0.269409i	−0.828862	+	0.559453i	$0.811011\pi$
$744$	−14.4737	+	4.98436i	−0.530632	+	0.182736i
$745$	−11.8723	−	33.9504i	−0.434967	−	1.24385i
$746$			5.23045i			0.191500i
$747$	0.966181	−	7.87424i	0.0353507	−	0.288104i
$748$	4.59483	−	4.59483i	0.168004	−	0.168004i
$749$	3.77233			0.137838
$750$	4.41349	−	18.8553i	0.161158	−	0.688497i
$751$	32.5184			1.18661			0.593306	−	0.804977i	$-0.297822\pi$
$751$	32.5184			1.18661			0.593306	+	0.804977i	$0.297822\pi$
$752$	−2.21244	+	2.21244i	−0.0806792	+	0.0806792i
$753$	−15.3884	−	7.50466i	−0.560786	−	0.273485i
$754$		−	30.3505i		−	1.10530i
$755$	11.6561	+	33.3321i	0.424208	+	1.21308i
$756$	5.12723	−	7.89736i	0.186475	−	0.287224i
$757$	2.53775	+	2.53775i	0.0922362	+	0.0922362i	0.751719	−	0.659483i	$-0.229225\pi$
$757$	2.53775	+	2.53775i	0.0922362	+	0.0922362i	−0.659483	+	0.751719i	$0.729225\pi$
$758$	3.97154	+	3.97154i	0.144253	+	0.144253i
$759$	−27.6172	−	80.1956i	−1.00244	−	2.91092i
$760$	−7.43445	−	3.58204i	−0.269676	−	0.129934i
$761$			29.9525i			1.08578i	0.839805	+	0.542889i	$0.182670\pi$
$761$			29.9525i			1.08578i	−0.839805	+	0.542889i	$0.817330\pi$
$762$	9.97040	−	20.4445i	0.361189	−	0.740625i
$763$	0.691714	−	0.691714i	0.0250417	−	0.0250417i
$764$	−2.99609			−0.108395
$765$	1.42667	+	6.55474i	0.0515814	+	0.236987i
$766$	1.89350			0.0684149
$767$	30.5594	−	30.5594i	1.10343	−	1.10343i
$768$	0.759217	−	1.55679i	0.0273959	−	0.0561757i
$769$			43.2504i			1.55965i	0.625997	+	0.779825i	$0.284692\pi$
$769$			43.2504i			1.55965i	−0.625997	+	0.779825i	$0.715308\pi$
$770$	−24.8537	+	8.69124i	−0.895667	+	0.313211i
$771$	13.5808	+	39.4363i	0.489102	+	1.42027i
$772$	18.0972	+	18.0972i	0.651334	+	0.651334i
$773$	−13.8584	−	13.8584i	−0.498453	−	0.498453i	0.412503	−	0.910956i	$-0.364655\pi$
$773$	−13.8584	−	13.8584i	−0.498453	−	0.498453i	−0.910956	+	0.412503i	$0.864655\pi$
$774$	−11.6227	+	9.08221i	−0.417771	+	0.326453i
$775$	−34.5600	+	27.5386i	−1.24143	+	0.989215i
$776$		−	13.1034i		−	0.470385i
$777$	−1.28387	−	0.626118i	−0.0460584	−	0.0224618i
$778$	2.28294	−	2.28294i	0.0818475	−	0.0818475i
$779$	21.1945			0.759371
$780$	12.4908	+	15.8292i	0.447242	+	0.566777i
$781$	−26.6053			−0.952013
$782$	−5.32876	+	5.32876i	−0.190556	+	0.190556i
$783$	−29.6286	+	6.30157i	−1.05884	+	0.225200i
$784$			3.71642i			0.132729i
$785$	19.7246	−	40.9381i	0.704001	−	1.46114i
$786$	−3.98994	+	1.37403i	−0.142316	+	0.0490100i
$787$	−5.13983	−	5.13983i	−0.183215	−	0.183215i	0.609540	−	0.792755i	$-0.291354\pi$
$787$	−5.13983	−	5.13983i	−0.183215	−	0.183215i	−0.792755	+	0.609540i	$0.791354\pi$
$788$	2.19929	+	2.19929i	0.0783465	+	0.0783465i
$789$	18.1333	−	6.24463i	0.645563	−	0.222315i
$790$	5.96254	−	12.3752i	0.212138	−	0.440288i
$791$		−	1.52648i		−	0.0542755i
$792$	−19.3491	−	2.37416i	−0.687541	−	0.0843622i
$793$	−40.9660	+	40.9660i	−1.45475	+	1.45475i
$794$	−19.2317			−0.682508
$795$	9.27198	+	11.7501i	0.328843	+	0.416734i
$796$	−3.05251			−0.108193
$797$	−36.7267	+	36.7267i	−1.30093	+	1.30093i	−0.373159	+	0.927767i	$0.621725\pi$
$797$	−36.7267	+	36.7267i	−1.30093	+	1.30093i	−0.927767	+	0.373159i	$0.878275\pi$
$798$	−10.4111	−	5.07733i	−0.368551	−	0.179736i
$799$		−	3.12886i		−	0.110691i
$800$	0.561767	−	4.96834i	0.0198615	−	0.175657i
$801$	−14.6760	−	18.7812i	−0.518551	−	0.663603i
$802$	−19.4451	−	19.4451i	−0.686630	−	0.686630i
$803$	−28.3526	−	28.3526i	−1.00054	−	1.00054i
$804$	−1.46028	−	4.24039i	−0.0515000	−	0.149547i
$805$	28.8236	−	10.0795i	1.01590	−	0.355255i
$806$		−	46.0135i		−	1.62076i
$807$	−10.1432	+	20.7987i	−0.357056	+	0.732149i
$808$	1.77980	−	1.77980i	0.0626132	−	0.0626132i
$809$	−1.52541			−0.0536305			−0.0268153	−	0.999640i	$-0.508537\pi$
$809$	−1.52541			−0.0536305			−0.0268153	+	0.999640i	$0.508537\pi$
$810$	12.8593	−	15.4803i	0.451830	−	0.543921i
$811$	42.9829			1.50933			0.754667	−	0.656107i	$-0.227798\pi$
$811$	42.9829			1.50933			0.754667	+	0.656107i	$0.227798\pi$
$812$	−7.46957	+	7.46957i	−0.262131	+	0.262131i
$813$	18.9425	−	38.8418i	0.664341	−	1.36224i
$814$			2.95733i			0.103655i
$815$	8.37462	+	4.03503i	0.293350	+	0.141341i
$816$	0.563968	+	1.63766i	0.0197428	+	0.0573297i
$817$	12.8311	+	12.8311i	0.448903	+	0.448903i
$818$	−7.19736	−	7.19736i	−0.251650	−	0.251650i
$819$	17.4266	+	22.3013i	0.608935	+	0.779269i
$820$	4.23887	+	12.1216i	0.148028	+	0.423305i
$821$		−	17.0867i		−	0.596331i	−0.954514	−	0.298166i	$-0.903625\pi$
$821$		−	17.0867i		−	0.596331i	0.954514	−	0.298166i	$-0.0963748\pi$
$822$	−24.6604	−	12.0264i	−0.860130	−	0.419470i
$823$	−22.2865	+	22.2865i	−0.776858	+	0.776858i	−0.979295	−	0.202438i	$-0.935114\pi$
$823$	−22.2865	+	22.2865i	−0.776858	+	0.776858i	0.202438	+	0.979295i	$0.435114\pi$
$824$	−14.2375			−0.495988
$825$	−54.9301	+	12.2294i	−1.91242	+	0.425772i
$826$	−15.0419			−0.523376
$827$	22.1828	−	22.1828i	0.771372	−	0.771372i	−0.206974	−	0.978346i	$-0.566362\pi$
$827$	22.1828	−	22.1828i	0.771372	−	0.771372i	0.978346	+	0.206974i	$0.0663617\pi$
$828$	22.4397	+	2.75339i	0.779835	+	0.0956868i
$829$		−	33.6590i		−	1.16902i	−0.811385	−	0.584512i	$-0.801286\pi$
$829$		−	33.6590i		−	1.16902i	0.811385	−	0.584512i	$-0.198714\pi$
$830$	−1.95189	−	5.58169i	−0.0677511	−	0.193743i
$831$	−21.0398	+	7.24555i	−0.729862	+	0.251345i
$832$	3.68142	+	3.68142i	0.127630	+	0.127630i
$833$	−2.62790	−	2.62790i	−0.0910514	−	0.0910514i
$834$	23.4467	−	8.07442i	0.811893	−	0.279594i
$835$	41.3145	+	19.9060i	1.42975	+	0.688875i
$836$			23.9817i			0.829424i
$837$	−44.9190	+	9.55360i	−1.55263	+	0.330221i
$838$	−16.6668	+	16.6668i	−0.575746	+	0.575746i
$839$	−8.84920			−0.305508			−0.152754	−	0.988264i	$-0.548814\pi$
$839$	−8.84920			−0.305508			−0.152754	+	0.988264i	$0.548814\pi$
$840$	0.821624	−	6.96984i	0.0283487	−	0.240482i
$841$	4.98391			0.171859
$842$	9.00256	−	9.00256i	0.310249	−	0.310249i
$843$	14.8801	+	7.25673i	0.512496	+	0.249935i
$844$		−	4.12951i		−	0.142144i
$845$	−29.7732	+	10.4116i	−1.02423	+	0.358168i
$846$	−7.39625	+	5.77956i	−0.254288	+	0.198705i
$847$	40.0093	+	40.0093i	1.37474	+	1.37474i
$848$	2.73273	+	2.73273i	0.0938425	+	0.0938425i
$849$	0.183137	+	0.531798i	0.00628525	+	0.0182513i
$850$	3.11592	+	3.91038i	0.106875	+	0.134125i
$851$		−	3.42971i		−	0.117569i
$852$	3.10849	−	6.37402i	0.106495	−	0.218370i
$853$	−13.2125	+	13.2125i	−0.452387	+	0.452387i	−0.896146	−	0.443759i	$-0.853645\pi$
$853$	−13.2125	+	13.2125i	−0.452387	+	0.452387i	0.443759	+	0.896146i	$0.353645\pi$
$854$	20.1643			0.690008
$855$	−20.8286	−	13.3824i	−0.712323	−	0.457668i
$856$	2.08178			0.0711539
$857$	−8.31831	+	8.31831i	−0.284148	+	0.284148i	−0.834761	−	0.550613i	$-0.814394\pi$
$857$	−8.31831	+	8.31831i	−0.284148	+	0.284148i	0.550613	+	0.834761i	$0.314394\pi$
$858$	25.6851	−	52.6677i	0.876874	−	1.79804i
$859$		−	46.0675i		−	1.57180i	−0.618352	−	0.785901i	$-0.712199\pi$
$859$		−	46.0675i		−	1.57180i	0.618352	−	0.785901i	$-0.287801\pi$
$860$	−4.77219	+	9.90460i	−0.162730	+	0.337744i
$861$	5.86889	+	17.0422i	0.200011	+	0.580797i
$862$	1.29260	+	1.29260i	0.0440260	+	0.0440260i
$863$	−14.1932	−	14.1932i	−0.483142	−	0.483142i	0.422991	−	0.906134i	$-0.360980\pi$
$863$	−14.1932	−	14.1932i	−0.483142	−	0.483142i	−0.906134	+	0.422991i	$0.860980\pi$
$864$	2.82949	−	4.35821i	0.0962613	−	0.148269i
$865$	−7.95454	+	16.5095i	−0.270462	+	0.561340i
$866$			1.17425i			0.0399028i
$867$	−1.55679	−	0.759217i	−0.0528713	−	0.0257844i
$868$	−11.3244	+	11.3244i	−0.384375	+	0.384375i
$869$	−39.9192			−1.35416
$870$	−17.7242	+	13.9861i	−0.600907	+	0.474173i
$871$	13.4807			0.456775
$872$	0.381727	−	0.381727i	0.0129269	−	0.0129269i
$873$	4.78752	−	39.0176i	0.162033	−	1.32055i
$874$		−	27.8123i		−	0.940764i
$875$	−4.49657	−	19.7542i	−0.152012	−	0.667814i
$876$	10.1053	−	3.47999i	0.341425	−	0.117578i
$877$	12.9910	+	12.9910i	0.438675	+	0.438675i	0.891566	−	0.452891i	$-0.149607\pi$
$877$	12.9910	+	12.9910i	0.438675	+	0.438675i	−0.452891	+	0.891566i	$0.649607\pi$
$878$	12.4082	+	12.4082i	0.418756	+	0.418756i
$879$	−13.6914	+	4.71494i	−0.461798	+	0.159031i
$880$	−13.7157	+	4.79632i	−0.462356	+	0.161684i
$881$		−	28.3494i		−	0.955115i	−0.878601	−	0.477557i	$-0.841522\pi$
$881$		−	28.3494i		−	0.955115i	0.878601	−	0.477557i	$-0.158478\pi$
$882$	−1.35784	+	11.0663i	−0.0457210	+	0.372620i
$883$	5.28177	−	5.28177i	0.177746	−	0.177746i	−0.612627	−	0.790372i	$-0.709887\pi$
$883$	5.28177	−	5.28177i	0.177746	−	0.177746i	0.790372	+	0.612627i	$0.209887\pi$
$884$	−5.20631			−0.175107
$885$	−31.9285	−	3.76382i	−1.07326	−	0.126519i
$886$	8.33419			0.279993
$887$	20.3751	−	20.3751i	0.684130	−	0.684130i	−0.276798	−	0.960928i	$-0.589273\pi$
$887$	20.3751	−	20.3751i	0.684130	−	0.684130i	0.960928	+	0.276798i	$0.0892732\pi$
$888$	−0.708509	−	0.345527i	−0.0237760	−	0.0115951i
$889$		−	23.7969i		−	0.798122i
$890$	−16.0049	−	7.71141i	−0.536485	−	0.258487i
$891$	−56.7478	−	14.1389i	−1.90112	−	0.473672i
$892$	8.15006	+	8.15006i	0.272884	+	0.272884i
$893$	8.16518	+	8.16518i	0.273237	+	0.273237i
$894$	−9.07122	−	26.3412i	−0.303387	−	0.880982i
$895$	−2.42020	−	6.92087i	−0.0808983	−	0.231339i
$896$		−	1.81207i		−	0.0605369i
$897$	−29.7877	+	61.0802i	−0.994583	+	2.03941i
$898$	−17.5166	+	17.5166i	−0.584537	+	0.584537i
$899$	51.5219			1.71835
$900$	3.48801	−	14.5888i	0.116267	−	0.486294i
$901$	−3.86467			−0.128751
$902$	26.3874	−	26.3874i	0.878606	−	0.878606i
$903$	−6.76430	+	13.8703i	−0.225102	+	0.461575i
$904$		−	0.842399i		−	0.0280178i
$905$	−2.34433	−	6.70393i	−0.0779283	−	0.222846i
$906$	8.90602	+	25.8615i	0.295883	+	0.859192i
$907$	−16.2795	−	16.2795i	−0.540551	−	0.540551i	0.383139	−	0.923691i	$-0.374843\pi$
$907$	−16.2795	−	16.2795i	−0.540551	−	0.540551i	−0.923691	+	0.383139i	$0.874843\pi$
$908$	0.935113	+	0.935113i	0.0310328	+	0.0310328i
$909$	5.94993	−	4.64938i	0.197347	−	0.154210i
$910$	19.0046	+	9.15669i	0.629995	+	0.303541i
$911$		−	22.2450i		−	0.737011i	−0.929626	−	0.368505i	$-0.879870\pi$
$911$		−	22.2450i		−	0.737011i	0.929626	−	0.368505i	$-0.120130\pi$
$912$	−5.74546	−	2.80196i	−0.190251	−	0.0927820i
$913$	−12.1507	+	12.1507i	−0.402130	+	0.402130i
$914$	24.6794			0.816322
$915$	42.8014	+	5.04554i	1.41497	+	0.166800i
$916$	3.24836			0.107329
$917$	−3.12177	+	3.12177i	−0.103090	+	0.103090i
$918$	1.08097	+	5.08247i	0.0356772	+	0.167747i
$919$		−	11.5245i		−	0.380160i	−0.981769	−	0.190080i	$-0.939125\pi$
$919$		−	11.5245i		−	0.380160i	0.981769	−	0.190080i	$-0.0608747\pi$
$920$	15.9065	−	5.56243i	0.524422	−	0.183388i
$921$	−35.0390	+	12.0665i	−1.15457	+	0.397604i
$922$	14.9169	+	14.9169i	0.491264	+	0.491264i
$923$	15.0730	+	15.0730i	0.496133	+	0.496133i
$924$	−19.2834	+	6.64069i	−0.634377	+	0.218463i
$925$	−2.26114	−	0.255665i	−0.0743458	−	0.00840623i
$926$		−	4.94149i		−	0.162388i
$927$	−42.3946	−	5.20188i	−1.39242	−	0.170852i
$928$	−4.12213	+	4.12213i	−0.135316	+	0.135316i
$929$	43.7020			1.43382			0.716908	−	0.697167i	$-0.245557\pi$
$929$	43.7020			1.43382			0.716908	+	0.697167i	$0.245557\pi$
$930$	−26.8711	+	21.2039i	−0.881138	+	0.695303i
$931$	13.7157			0.449515
$932$	−4.21980	+	4.21980i	−0.138224	+	0.138224i
$933$	8.02354	+	3.91293i	0.262679	+	0.128104i
$934$			21.5925i			0.706527i
$935$	6.30695	−	13.0900i	0.206259	−	0.428088i
$936$	9.61698	+	12.3071i	0.314341	+	0.402270i
$937$	−5.07640	−	5.07640i	−0.165839	−	0.165839i	0.619309	−	0.785148i	$-0.287413\pi$
$937$	−5.07640	−	5.07640i	−0.165839	−	0.165839i	−0.785148	+	0.619309i	$0.787413\pi$
$938$	−3.31773	−	3.31773i	−0.108328	−	0.108328i
$939$	5.83677	+	16.9490i	0.190476	+	0.553108i
$940$	−3.03683	+	6.30289i	−0.0990505	+	0.205578i
$941$		−	24.1628i		−	0.787686i	−0.919178	−	0.393843i	$-0.871145\pi$
$941$		−	24.1628i		−	0.787686i	0.919178	−	0.393843i	$-0.128855\pi$
$942$	15.4291	−	31.6376i	0.502706	−	1.03081i
$943$	−30.6023	+	30.6023i	−0.996548	+	0.996548i
$944$	−8.30098			−0.270174
$945$	4.99305	−	20.4537i	0.162424	−	0.665358i
$946$	31.9498			1.03878
$947$	−2.56616	+	2.56616i	−0.0833889	+	0.0833889i	−0.747571	−	0.664182i	$-0.768780\pi$
$947$	−2.56616	+	2.56616i	−0.0833889	+	0.0833889i	0.664182	+	0.747571i	$0.268780\pi$
$948$	4.66405	−	9.56371i	0.151481	−	0.310615i
$949$			32.1257i			1.04285i
$950$	−18.3361	−	2.07325i	−0.594901	−	0.0672651i
$951$	−8.72474	−	25.3351i	−0.282919	−	0.821547i
$952$	1.28132	+	1.28132i	0.0415280	+	0.0415280i
$953$	26.7418	+	26.7418i	0.866252	+	0.866252i	0.992055	−	0.125803i	$-0.0401509\pi$
$953$	26.7418	+	26.7418i	0.866252	+	0.866252i	−0.125803	+	0.992055i	$0.540151\pi$
$954$	7.13873	+	9.13562i	0.231125	+	0.295777i
$955$	−6.32395	+	2.21146i	−0.204638	+	0.0715610i
$956$			18.6750i			0.603992i
$957$	58.9727	+	28.7599i	1.90632	+	0.929676i
$958$	10.8097	−	10.8097i	0.349244	−	0.349244i
$959$	−28.7041			−0.926905
$960$	0.453418	−	3.84635i	0.0146340	−	0.124140i
$961$	47.1108			1.51970
$962$	1.67545	−	1.67545i	0.0540186	−	0.0540186i
$963$	6.19886	+	0.760609i	0.199756	+	0.0245103i
$964$			7.33380i			0.236206i
$965$	51.5562	+	24.8406i	1.65965	+	0.799647i
$966$	22.3635	−	7.70140i	0.719534	−	0.247788i
$967$	−8.15916	−	8.15916i	−0.262381	−	0.262381i	0.563640	−	0.826021i	$-0.309401\pi$
$967$	−8.15916	−	8.15916i	−0.262381	−	0.262381i	−0.826021	+	0.563640i	$0.809401\pi$
$968$	22.0794	+	22.0794i	0.709659	+	0.709659i
$969$	6.04393	−	2.08137i	0.194159	−	0.0668632i
$970$	−9.67181	−	27.6578i	−0.310543	−	0.888039i
$971$			54.0041i			1.73307i	0.499112	+	0.866537i	$0.333660\pi$
$971$			54.0041i			1.73307i	−0.499112	+	0.866537i	$0.666340\pi$
$972$	10.0176	−	11.9435i	0.321315	−	0.383088i
$973$	18.3449	−	18.3449i	0.588112	−	0.588112i
$974$	22.3756			0.716961
$975$	38.0485	+	24.1916i	1.21853	+	0.774753i
$976$	11.1278			0.356192
$977$	−0.724617	+	0.724617i	−0.0231825	+	0.0231825i	−0.718603	−	0.695421i	$-0.755218\pi$
$977$	−0.724617	+	0.724617i	−0.0231825	+	0.0231825i	0.695421	+	0.718603i	$0.255218\pi$
$978$	6.47204	+	3.15630i	0.206953	+	0.100927i
$979$			51.6278i			1.65003i
$980$	2.74314	+	7.84436i	0.0876263	+	0.250579i
$981$	1.27612	−	0.997186i	0.0407435	−	0.0318377i
$982$	21.2625	+	21.2625i	0.678514	+	0.678514i
$983$	−31.7083	−	31.7083i	−1.01134	−	1.01134i	−0.999935	−	0.0114026i	$-0.996370\pi$
$983$	−31.7083	−	31.7083i	−1.01134	−	1.01134i	−0.0114026	−	0.999935i	$-0.503630\pi$
$984$	3.23878	+	9.40485i	0.103249	+	0.299816i
$985$	6.26544	+	3.01879i	0.199634	+	0.0961866i
$986$		−	5.82957i		−	0.185651i
$987$	−4.30453	+	8.82652i	−0.137015	+	0.280951i
$988$	13.5866	−	13.5866i	0.432246	−	0.432246i
$989$	−37.0531			−1.17822
$990$	−42.5932	+	9.27062i	−1.35370	+	0.294640i
$991$	2.78104			0.0883425			0.0441713	−	0.999024i	$-0.485935\pi$
$991$	2.78104			0.0883425			0.0441713	+	0.999024i	$0.485935\pi$
$992$	−6.24943	+	6.24943i	−0.198420	+	0.198420i
$993$	−1.55097	+	3.18029i	−0.0492186	+	0.100924i
$994$		−	7.41921i		−	0.235323i
$995$	−6.44302	+	2.25310i	−0.204258	+	0.0714279i
$996$	−1.49137	−	4.33069i	−0.0472560	−	0.137223i
$997$	13.8822	+	13.8822i	0.439654	+	0.439654i	0.891896	−	0.452241i	$-0.149375\pi$
$997$	13.8822	+	13.8822i	0.439654	+	0.439654i	−0.452241	+	0.891896i	$0.649375\pi$
$998$	5.23765	+	5.23765i	0.165795	+	0.165795i
$999$	−1.98346	−	1.28773i	−0.0627539	−	0.0407419i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.l.g.137.12	yes	28
3.2	odd	2	inner	510.2.l.g.137.7	✓	28
5.3	odd	4	inner	510.2.l.g.443.7	yes	28
15.8	even	4	inner	510.2.l.g.443.12	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.l.g.137.7	✓	28	3.2	odd	2	inner
510.2.l.g.137.12	yes	28	1.1	even	1	trivial
510.2.l.g.443.7	yes	28	5.3	odd	4	inner
510.2.l.g.443.12	yes	28	15.8	even	4	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:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.759217 - 1.55679i) q^{3} -1.00000i q^{4} +(-0.738113 - 2.11073i) q^{5} +(-0.563968 - 1.63766i) q^{6} +(-1.28132 - 1.28132i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.84718 - 2.36388i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.759217 - 1.55679i) q^{3} -1.00000i q^{4} +(-0.738113 - 2.11073i) q^{5} +(-0.563968 - 1.63766i) q^{6} +(-1.28132 - 1.28132i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.84718 - 2.36388i) q^{9} +(-2.01444 - 0.970588i) q^{10} +6.49808i q^{11} +(-1.55679 - 0.759217i) q^{12} +(3.68142 - 3.68142i) q^{13} -1.81207 q^{14} +(-3.84635 - 0.453418i) q^{15} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} +(-2.97767 - 0.365364i) q^{18} +3.69058i q^{19} +(-2.11073 + 0.738113i) q^{20} +(-2.96755 + 1.02195i) q^{21} +(4.59483 + 4.59483i) q^{22} +(-5.32876 - 5.32876i) q^{23} +(-1.63766 + 0.563968i) q^{24} +(-3.91038 + 3.11592i) q^{25} -5.20631i q^{26} +(-5.08247 + 1.08097i) q^{27} +(-1.28132 + 1.28132i) q^{28} +5.82957 q^{29} +(-3.04040 + 2.39917i) q^{30} +8.83803 q^{31} +(-0.707107 + 0.707107i) q^{32} +(10.1161 + 4.93345i) q^{33} -1.00000i q^{34} +(-1.75877 + 3.65029i) q^{35} +(-2.36388 + 1.84718i) q^{36} +(0.321811 + 0.321811i) q^{37} +(2.60964 + 2.60964i) q^{38} +(-2.93619 - 8.52618i) q^{39} +(-0.970588 + 2.01444i) q^{40} -5.74285i q^{41} +(-1.37575 + 2.82100i) q^{42} +(3.47671 - 3.47671i) q^{43} +6.49808 q^{44} +(-3.62609 + 5.64371i) q^{45} -7.53601 q^{46} +(2.21244 - 2.21244i) q^{47} +(-0.759217 + 1.55679i) q^{48} -3.71642i q^{49} +(-0.561767 + 4.96834i) q^{50} +(-0.563968 - 1.63766i) q^{51} +(-3.68142 - 3.68142i) q^{52} +(-2.73273 - 2.73273i) q^{53} +(-2.82949 + 4.35821i) q^{54} +(13.7157 - 4.79632i) q^{55} +1.81207i q^{56} +(5.74546 + 2.80196i) q^{57} +(4.12213 - 4.12213i) q^{58} +8.30098 q^{59} +(-0.453418 + 3.84635i) q^{60} -11.1278 q^{61} +(6.24943 - 6.24943i) q^{62} +(-0.662064 + 5.39573i) q^{63} +1.00000i q^{64} +(-10.4878 - 5.05318i) q^{65} +(10.6417 - 3.66470i) q^{66} +(1.83091 + 1.83091i) q^{67} +(-0.707107 - 0.707107i) q^{68} +(-12.3414 + 4.25007i) q^{69} +(1.33751 + 3.82479i) q^{70} +4.09434i q^{71} +(-0.365364 + 2.97767i) q^{72} +(-4.36323 + 4.36323i) q^{73} +0.455109 q^{74} +(1.88200 + 8.45329i) q^{75} +3.69058 q^{76} +(8.32614 - 8.32614i) q^{77} +(-8.10512 - 3.95272i) q^{78} +6.14323i q^{79} +(0.738113 + 2.11073i) q^{80} +(-2.17587 + 8.73302i) q^{81} +(-4.06081 - 4.06081i) q^{82} +(1.86990 + 1.86990i) q^{83} +(1.02195 + 2.96755i) q^{84} +(-2.01444 - 0.970588i) q^{85} -4.91680i q^{86} +(4.42591 - 9.07541i) q^{87} +(4.59483 - 4.59483i) q^{88} +7.94509 q^{89} +(1.42667 + 6.55474i) q^{90} -9.43417 q^{91} +(-5.32876 + 5.32876i) q^{92} +(6.70999 - 13.7589i) q^{93} -3.12886i q^{94} +(7.78983 - 2.72407i) q^{95} +(0.563968 + 1.63766i) q^{96} +(9.26552 + 9.26552i) q^{97} +(-2.62790 - 2.62790i) q^{98} +(15.3607 - 12.0031i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{7}+O(q^{10}) \) 28 * q + 4 * q^7	\( 28 q + 4 q^{7} - 12 q^{10} - 8 q^{13} + 8 q^{15} - 28 q^{16} - 16 q^{18} + 48 q^{21} + 20 q^{22} + 40 q^{25} - 36 q^{27} + 4 q^{28} - 12 q^{30} + 16 q^{31} + 8 q^{33} + 8 q^{37} - 8 q^{40} - 48 q^{42} + 48 q^{43} + 36 q^{45} - 64 q^{46} + 8 q^{52} - 36 q^{55} - 32 q^{57} + 20 q^{58} + 12 q^{60} - 16 q^{61} - 56 q^{63} + 32 q^{66} + 112 q^{67} - 28 q^{70} + 16 q^{72} + 12 q^{73} + 16 q^{75} - 8 q^{76} - 32 q^{78} - 48 q^{81} + 24 q^{82} - 12 q^{85} - 44 q^{87} + 20 q^{88} - 20 q^{90} - 80 q^{91} + 28 q^{93} + 60 q^{97}+O(q^{100}) \) 28 * q + 4 * q^7 - 12 * q^10 - 8 * q^13 + 8 * q^15 - 28 * q^16 - 16 * q^18 + 48 * q^21 + 20 * q^22 + 40 * q^25 - 36 * q^27 + 4 * q^28 - 12 * q^30 + 16 * q^31 + 8 * q^33 + 8 * q^37 - 8 * q^40 - 48 * q^42 + 48 * q^43 + 36 * q^45 - 64 * q^46 + 8 * q^52 - 36 * q^55 - 32 * q^57 + 20 * q^58 + 12 * q^60 - 16 * q^61 - 56 * q^63 + 32 * q^66 + 112 * q^67 - 28 * q^70 + 16 * q^72 + 12 * q^73 + 16 * q^75 - 8 * q^76 - 32 * q^78 - 48 * q^81 + 24 * q^82 - 12 * q^85 - 44 * q^87 + 20 * q^88 - 20 * q^90 - 80 * q^91 + 28 * q^93 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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