LMFDB - Embedded newform 95.2.e.b.26.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [95,2,Mod(11,95)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(95, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("95.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	95.e (of order $3$, 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:	$0.758578819202$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.3518667.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 7x^{4} - 8x^{3} + 43x^{2} - 42x + 49 $ x^6 - x^5 + 7x^4 - 8x^3 + 43x^2 - 42x + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			26.1
Root			$1.14257 + 1.97899i$ of defining polynomial
Character	$\chi$	$=$	95.26
Dual form			95.2.e.b.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.14257 - 1.97899i) q^{2} +(1.25351 + 2.17114i) q^{3} +(-1.61094 + 2.79023i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.86445 - 4.96137i) q^{6} +3.50702 q^{7} +2.79216 q^{8} +(-1.64257 + 2.84502i) q^{9} +(1.14257 - 1.97899i) q^{10} -4.50702 q^{11} -8.07730 q^{12} +(2.50000 - 4.33013i) q^{13} +(-4.00702 - 6.94036i) q^{14} +(-1.25351 + 2.17114i) q^{15} +(0.0316332 + 0.0547902i) q^{16} +(-0.0793049 - 0.137360i) q^{17} +7.50702 q^{18} +(-4.26053 - 0.920816i) q^{19} -3.22188 q^{20} +(4.39608 + 7.61423i) q^{21} +(5.14959 + 8.91935i) q^{22} +(-0.579305 + 1.00339i) q^{23} +(3.50000 + 6.06218i) q^{24} +(-0.500000 + 0.866025i) q^{25} -11.4257 q^{26} -0.714858 q^{27} +(-5.64959 + 9.78538i) q^{28} +(1.75351 - 3.03717i) q^{29} +5.72889 q^{30} -2.28514 q^{31} +(2.86445 - 4.96137i) q^{32} +(-5.64959 - 9.78538i) q^{33} +(-0.181223 + 0.313888i) q^{34} +(1.75351 + 3.03717i) q^{35} +(-5.29216 - 9.16629i) q^{36} -10.9648 q^{37} +(3.04567 + 9.48365i) q^{38} +12.5351 q^{39} +(1.39608 + 2.41808i) q^{40} +(-3.03865 - 5.26310i) q^{41} +(10.0457 - 17.3996i) q^{42} +(1.67420 + 2.89981i) q^{43} +(7.26053 - 12.5756i) q^{44} -3.28514 q^{45} +2.64759 q^{46} +(-1.53163 + 2.65287i) q^{47} +(-0.0793049 + 0.137360i) q^{48} +5.29918 q^{49} +2.28514 q^{50} +(0.198819 - 0.344364i) q^{51} +(8.05469 + 13.9511i) q^{52} +(2.87147 - 4.97353i) q^{53} +(0.816776 + 1.41470i) q^{54} +(-2.25351 - 3.90319i) q^{55} +9.79216 q^{56} +(-3.34139 - 10.4045i) q^{57} -8.01404 q^{58} +(-1.53163 - 2.65287i) q^{59} +(-4.03865 - 6.99515i) q^{60} +(0.436734 - 0.756445i) q^{61} +(2.61094 + 4.52228i) q^{62} +(-5.76053 + 9.97753i) q^{63} -12.9648 q^{64} +5.00000 q^{65} +(-12.9101 + 22.3610i) q^{66} +(4.22188 - 7.31250i) q^{67} +0.511021 q^{68} -2.90466 q^{69} +(4.00702 - 6.94036i) q^{70} +(8.11796 + 14.0607i) q^{71} +(-4.58632 + 7.94375i) q^{72} +(3.57930 + 6.19954i) q^{73} +(12.5281 + 21.6993i) q^{74} -2.50702 q^{75} +(9.43273 - 10.4045i) q^{76} -15.8062 q^{77} +(-14.3222 - 24.8068i) q^{78} +(5.06327 + 8.76983i) q^{79} +(-0.0316332 + 0.0547902i) q^{80} +(4.03163 + 6.98299i) q^{81} +(-6.94375 + 12.0269i) q^{82} +4.85543 q^{83} -28.3273 q^{84} +(0.0793049 - 0.137360i) q^{85} +(3.82580 - 6.62647i) q^{86} +8.79216 q^{87} -12.5843 q^{88} +(0.556248 - 0.963449i) q^{89} +(3.75351 + 6.50127i) q^{90} +(8.76755 - 15.1858i) q^{91} +(-1.86645 - 3.23278i) q^{92} +(-2.86445 - 4.96137i) q^{93} +7.00000 q^{94} +(-1.33281 - 4.15013i) q^{95} +14.3624 q^{96} +(-0.809757 - 1.40254i) q^{97} +(-6.05469 - 10.4870i) q^{98} +(7.40310 - 12.8225i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - q^{3} - 7 q^{4} + 3 q^{5} + 6 q^{6} + 4 q^{7} - 12 q^{8} - 4 q^{9} + q^{10} - 10 q^{11} - 8 q^{12} + 15 q^{13} - 7 q^{14} + q^{15} - 3 q^{16} - q^{17} + 28 q^{18} - 14 q^{20} + 12 q^{21}+ \cdots + 13 q^{99}+O(q^{100}) $ 6 * q - q^2 - q^3 - 7 * q^4 + 3 * q^5 + 6 * q^6 + 4 * q^7 - 12 * q^8 - 4 * q^9 + q^10 - 10 * q^11 - 8 * q^12 + 15 * q^13 - 7 * q^14 + q^15 - 3 * q^16 - q^17 + 28 * q^18 - 14 * q^20 + 12 * q^21 + 8 * q^22 - 4 * q^23 + 21 * q^24 - 3 * q^25 - 10 * q^26 - 16 * q^27 - 11 * q^28 + 2 * q^29 + 12 * q^30 - 2 * q^31 + 6 * q^32 - 11 * q^33 + 25 * q^34 + 2 * q^35 - 3 * q^36 - 4 * q^37 - 19 * q^38 - 10 * q^39 - 6 * q^40 + 2 * q^41 + 23 * q^42 + q^43 + 18 * q^44 - 8 * q^45 - 48 * q^46 - 6 * q^47 - q^48 - 14 * q^49 + 2 * q^50 + 6 * q^51 + 35 * q^52 - 11 * q^53 - 10 * q^54 - 5 * q^55 + 30 * q^56 - 19 * q^57 - 14 * q^58 - 6 * q^59 - 4 * q^60 + 9 * q^61 + 13 * q^62 - 9 * q^63 - 16 * q^64 + 30 * q^65 - 29 * q^66 + 20 * q^67 + 68 * q^68 - 10 * q^69 + 7 * q^70 + 29 * q^71 - 11 * q^72 + 22 * q^73 + 7 * q^74 + 2 * q^75 - 19 * q^76 - 32 * q^77 - 30 * q^78 + 24 * q^79 + 3 * q^80 + 21 * q^81 - 31 * q^82 - 6 * q^83 - 56 * q^84 + q^85 + 32 * q^86 + 24 * q^87 - 18 * q^88 + 14 * q^89 + 14 * q^90 + 10 * q^91 - 41 * q^92 - 6 * q^93 + 42 * q^94 + 34 * q^96 - 7 * q^97 - 23 * q^98 + 13 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.14257	−	1.97899i	−0.807920	−	1.39936i	−0.914302	−	0.405033i	$-0.867260\pi$
$2$	−1.14257	−	1.97899i	−0.807920	−	1.39936i	0.106382	−	0.994325i	$-0.466073\pi$
$3$	1.25351	+	2.17114i	0.723714	+	1.25351i	0.959501	+	0.281705i	$0.0908998\pi$
$3$	1.25351	+	2.17114i	0.723714	+	1.25351i	−0.235787	+	0.971805i	$0.575767\pi$
$4$	−1.61094	+	2.79023i	−0.805469	+	1.39511i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	2.86445	−	4.96137i	1.16941	−	2.02547i
$7$	3.50702			1.32553			0.662764	−	0.748828i	$-0.269383\pi$
$7$	3.50702			1.32553			0.662764	+	0.748828i	$0.269383\pi$
$8$	2.79216			0.987178
$9$	−1.64257	+	2.84502i	−0.547524	+	0.948339i
$10$	1.14257	−	1.97899i	0.361313	−	0.625812i
$11$	−4.50702			−1.35892			−0.679459	−	0.733714i	$-0.737785\pi$
$11$	−4.50702			−1.35892			−0.679459	+	0.733714i	$0.737785\pi$
$12$	−8.07730			−2.33172
$13$	2.50000	−	4.33013i	0.693375	−	1.20096i	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	2.50000	−	4.33013i	0.693375	−	1.20096i	0.970725	−	0.240192i	$-0.0772105\pi$
$14$	−4.00702	−	6.94036i	−1.07092	−	1.85489i
$15$	−1.25351	+	2.17114i	−0.323655	+	0.560586i
$16$	0.0316332	+	0.0547902i	0.00790829	+	0.0136976i
$17$	−0.0793049	−	0.137360i	−0.0192343	−	0.0333147i	0.856248	−	0.516565i	$-0.172790\pi$
$17$	−0.0793049	−	0.137360i	−0.0192343	−	0.0333147i	−0.875482	+	0.483250i	$0.839456\pi$
$18$	7.50702			1.76942
$19$	−4.26053	−	0.920816i	−0.977432	−	0.211250i
$19$	−4.26053	−	0.920816i	−0.977432	−	0.211250i
$20$	−3.22188			−0.720433
$21$	4.39608	+	7.61423i	0.959303	+	1.66156i
$22$	5.14959	+	8.91935i	1.09790	+	1.90161i
$23$	−0.579305	+	1.00339i	−0.120793	+	0.209220i	−0.920081	−	0.391729i	$-0.871877\pi$
$23$	−0.579305	+	1.00339i	−0.120793	+	0.209220i	0.799287	+	0.600949i	$0.205211\pi$
$24$	3.50000	+	6.06218i	0.714435	+	1.23744i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−11.4257			−2.24077
$27$	−0.714858			−0.137574
$28$	−5.64959	+	9.78538i	−1.06767	+	1.84926i
$29$	1.75351	−	3.03717i	0.325619	−	0.563988i	−0.656019	−	0.754745i	$-0.727761\pi$
$29$	1.75351	−	3.03717i	0.325619	−	0.563988i	0.981637	+	0.190757i	$0.0610942\pi$
$30$	5.72889			1.04595
$31$	−2.28514			−0.410424			−0.205212	−	0.978718i	$-0.565788\pi$
$31$	−2.28514			−0.410424			−0.205212	+	0.978718i	$0.565788\pi$
$32$	2.86445	−	4.96137i	0.506368	−	0.877054i
$33$	−5.64959	−	9.78538i	−0.983467	−	1.70342i
$34$	−0.181223	+	0.313888i	−0.0310795	+	0.0538313i
$35$	1.75351	+	3.03717i	0.296397	+	0.513375i
$36$	−5.29216	−	9.16629i	−0.882027	−	1.52772i
$37$	−10.9648			−1.80260			−0.901302	−	0.433192i	$-0.857387\pi$
$37$	−10.9648			−1.80260			−0.901302	+	0.433192i	$0.857387\pi$
$38$	3.04567	+	9.48365i	0.494073	+	1.53845i
$39$	12.5351			2.00722
$40$	1.39608	+	2.41808i	0.220740	+	0.382332i
$41$	−3.03865	−	5.26310i	−0.474558	−	0.821958i	0.525018	−	0.851091i	$-0.324059\pi$
$41$	−3.03865	−	5.26310i	−0.474558	−	0.821958i	−0.999576	+	0.0291332i	$0.990725\pi$
$42$	10.0457	−	17.3996i	1.55008	−	2.68482i
$43$	1.67420	+	2.89981i	0.255314	+	0.442216i	0.964981	−	0.262321i	$-0.0844879\pi$
$43$	1.67420	+	2.89981i	0.255314	+	0.442216i	−0.709667	+	0.704537i	$0.751155\pi$
$44$	7.26053	−	12.5756i	1.09457	−	1.89584i
$45$	−3.28514			−0.489720
$46$	2.64759			0.390366
$47$	−1.53163	+	2.65287i	−0.223412	+	0.386960i	−0.955842	−	0.293882i	$-0.905053\pi$
$47$	−1.53163	+	2.65287i	−0.223412	+	0.386960i	0.732430	+	0.680842i	$0.238386\pi$
$48$	−0.0793049	+	0.137360i	−0.0114467	+	0.0198262i
$49$	5.29918			0.757026
$50$	2.28514			0.323168
$51$	0.198819	−	0.344364i	0.0278402	−	0.0482207i
$52$	8.05469	+	13.9511i	1.11698	+	1.93467i
$53$	2.87147	−	4.97353i	0.394426	−	0.683166i	−0.598602	−	0.801047i	$-0.704277\pi$
$53$	2.87147	−	4.97353i	0.394426	−	0.683166i	0.993028	+	0.117881i	$0.0376100\pi$
$54$	0.816776	+	1.41470i	0.111149	+	0.192516i
$55$	−2.25351	−	3.90319i	−0.303863	−	0.526306i
$56$	9.79216			1.30853
$57$	−3.34139	−	10.4045i	−0.442578	−	1.37810i
$58$	−8.01404			−1.05229
$59$	−1.53163	−	2.65287i	−0.199402	−	0.345374i	0.748933	−	0.662646i	$-0.230567\pi$
$59$	−1.53163	−	2.65287i	−0.199402	−	0.345374i	−0.948335	+	0.317272i	$0.897233\pi$
$60$	−4.03865	−	6.99515i	−0.521388	−	0.903070i
$61$	0.436734	−	0.756445i	0.0559180	−	0.0968528i	−0.836711	−	0.547644i	$-0.815525\pi$
$61$	0.436734	−	0.756445i	0.0559180	−	0.0968528i	0.892629	+	0.450791i	$0.148858\pi$
$62$	2.61094	+	4.52228i	0.331589	+	0.574330i
$63$	−5.76053	+	9.97753i	−0.725758	+	1.25705i
$64$	−12.9648			−1.62060
$65$	5.00000			0.620174
$66$	−12.9101	+	22.3610i	−1.58913	+	2.75245i
$67$	4.22188	−	7.31250i	0.515784	−	0.893365i	−0.484048	−	0.875042i	$-0.660834\pi$
$67$	4.22188	−	7.31250i	0.515784	−	0.893365i	0.999832	−	0.0183230i	$-0.00583273\pi$
$68$	0.511021			0.0619704
$69$	−2.90466			−0.349680
$70$	4.00702	−	6.94036i	0.478930	−	0.829532i
$71$	8.11796	+	14.0607i	0.963424	+	1.66870i	0.713790	+	0.700359i	$0.246977\pi$
$71$	8.11796	+	14.0607i	0.963424	+	1.66870i	0.249634	+	0.968340i	$0.419690\pi$
$72$	−4.58632	+	7.94375i	−0.540503	+	0.936179i
$73$	3.57930	+	6.19954i	0.418926	+	0.725601i	0.995832	−	0.0912097i	$-0.0290733\pi$
$73$	3.57930	+	6.19954i	0.418926	+	0.725601i	−0.576906	+	0.816811i	$0.695740\pi$
$74$	12.5281	+	21.6993i	1.45636	+	2.52249i
$75$	−2.50702			−0.289486
$76$	9.43273	−	10.4045i	1.08201	−	1.19347i
$77$	−15.8062			−1.80128
$78$	−14.3222	−	24.8068i	−1.62167	−	2.80882i
$79$	5.06327	+	8.76983i	0.569662	+	0.986683i	0.996599	+	0.0824022i	$0.0262592\pi$
$79$	5.06327	+	8.76983i	0.569662	+	0.986683i	−0.426937	+	0.904281i	$0.640407\pi$
$80$	−0.0316332	+	0.0547902i	−0.00353669	+	0.00612574i
$81$	4.03163	+	6.98299i	0.447959	+	0.775888i
$82$	−6.94375	+	12.0269i	−0.766809	+	1.32815i
$83$	4.85543			0.532952			0.266476	−	0.963841i	$-0.414141\pi$
$83$	4.85543			0.532952			0.266476	+	0.963841i	$0.414141\pi$
$84$	−28.3273			−3.09076
$85$	0.0793049	−	0.137360i	0.00860183	−	0.0148988i
$86$	3.82580	−	6.62647i	0.412546	−	0.714551i
$87$	8.79216			0.942619
$88$	−12.5843			−1.34149
$89$	0.556248	−	0.963449i	0.0589621	−	0.102125i	−0.835038	−	0.550193i	$-0.814554\pi$
$89$	0.556248	−	0.963449i	0.0589621	−	0.102125i	0.894000	+	0.448067i	$0.147888\pi$
$90$	3.75351	+	6.50127i	0.395655	+	0.685294i
$91$	8.76755	−	15.1858i	0.919089	−	1.59191i
$92$	−1.86645	−	3.23278i	−0.194591	−	0.337041i
$93$	−2.86445	−	4.96137i	−0.297029	−	0.514470i
$94$	7.00000			0.721995
$95$	−1.33281	−	4.15013i	−0.136744	−	0.425795i
$96$	14.3624			1.46586
$97$	−0.809757	−	1.40254i	−0.0822184	−	0.142406i	0.821984	−	0.569510i	$-0.192867\pi$
$97$	−0.809757	−	1.40254i	−0.0822184	−	0.142406i	−0.904203	+	0.427104i	$0.859534\pi$
$98$	−6.05469	−	10.4870i	−0.611616	−	1.05935i
$99$	7.40310	−	12.8225i	0.744039	−	1.28871i
$100$	−1.61094	−	2.79023i	−0.161094	−	0.279023i
$101$	−6.15661	+	10.6636i	−0.612605	+	1.06106i	0.378194	+	0.925726i	$0.376545\pi$
$101$	−6.15661	+	10.6636i	−0.612605	+	1.06106i	−0.990800	+	0.135337i	$0.956788\pi$
$102$	−0.908659			−0.0899707
$103$	10.6164			1.04606			0.523032	−	0.852313i	$-0.324801\pi$
$103$	10.6164			1.04606			0.523032	+	0.852313i	$0.324801\pi$
$104$	6.98040	−	12.0904i	0.684485	−	1.18556i
$105$	−4.39608	+	7.61423i	−0.429014	+	0.743073i
$106$	−13.1234			−1.27466
$107$	−2.17265			−0.210038			−0.105019	−	0.994470i	$-0.533490\pi$
$107$	−2.17265			−0.210038			−0.105019	+	0.994470i	$0.533490\pi$
$108$	1.15159	−	1.99461i	0.110812	−	0.191932i
$109$	−7.91012	−	13.7007i	−0.757652	−	1.31229i	−0.944045	−	0.329816i	$-0.893013\pi$
$109$	−7.91012	−	13.7007i	−0.757652	−	1.31229i	0.186393	−	0.982475i	$-0.440320\pi$
$110$	−5.14959	+	8.91935i	−0.490994	+	0.850427i
$111$	−13.7445	−	23.8062i	−1.30457	−	2.25958i
$112$	0.110938	+	0.192150i	0.0104827	+	0.0181565i
$113$	9.83828			0.925507			0.462754	−	0.886487i	$-0.346861\pi$
$113$	9.83828			0.925507			0.462754	+	0.886487i	$0.346861\pi$
$114$	−16.7726	+	18.5004i	−1.57089	+	1.73272i
$115$	−1.15861			−0.108041
$116$	5.64959	+	9.78538i	0.524551	+	0.908549i
$117$	8.21286	+	14.2251i	0.759279	+	1.31511i
$118$	−3.50000	+	6.06218i	−0.322201	+	0.558069i
$119$	−0.278124	−	0.481725i	−0.0254956	−	0.0441596i
$120$	−3.50000	+	6.06218i	−0.319505	+	0.553399i
$121$	9.31322			0.846656
$122$	−1.99600			−0.180709
$123$	7.61796	−	13.1947i	0.686888	−	1.18972i
$124$	3.68122	−	6.37607i	0.330584	−	0.572588i
$125$	−1.00000			−0.0894427
$126$	26.3273			2.34542
$127$	−7.85543	+	13.6060i	−0.697056	+	1.20734i	0.272426	+	0.962177i	$0.412174\pi$
$127$	−7.85543	+	13.6060i	−0.697056	+	1.20734i	−0.969483	+	0.245160i	$0.921159\pi$
$128$	9.08432	+	15.7345i	0.802948	+	1.39075i
$129$	−4.19726	+	7.26987i	−0.369548	+	0.640076i
$130$	−5.71286	−	9.89496i	−0.501051	−	0.867845i
$131$	5.76755	+	9.98968i	0.503913	+	0.872803i	0.999990	+	0.00452412i	$0.00144008\pi$
$131$	5.76755	+	9.98968i	0.503913	+	0.872803i	−0.496077	+	0.868279i	$0.665227\pi$
$132$	36.4046			3.16861
$133$	−14.9418	−	3.22932i	−1.29561	−	0.280017i
$134$	−19.2952			−1.66685
$135$	−0.357429	−	0.619085i	−0.0307626	−	0.0532823i
$136$	−0.221432	−	0.383532i	−0.0189876	−	0.0328876i
$137$	−0.0546904	+	0.0947266i	−0.00467252	+	0.00809304i	−0.868352	−	0.495948i	$-0.834821\pi$
$137$	−0.0546904	+	0.0947266i	−0.00467252	+	0.00809304i	0.863680	+	0.504041i	$0.168154\pi$
$138$	3.31878	+	5.74829i	0.282513	+	0.489327i
$139$	−0.721876	+	1.25033i	−0.0612287	+	0.106051i	−0.895015	−	0.446036i	$-0.852835\pi$
$139$	−0.721876	+	1.25033i	−0.0612287	+	0.106051i	0.833786	+	0.552088i	$0.186169\pi$
$140$	−11.2992			−0.954955
$141$	−7.67967			−0.646745
$142$	18.5507	−	32.1307i	1.55674	−	2.69635i
$143$	−11.2675	+	19.5160i	−0.942240	+	1.63201i
$144$	−0.207839			−0.0173199
$145$	3.50702			0.291242
$146$	8.17922	−	14.1668i	0.676917	−	1.17245i
$147$	6.64257	+	11.5053i	0.547870	+	0.948939i
$148$	17.6636	−	30.5943i	1.45194	−	2.51484i
$149$	−0.864447	−	1.49727i	−0.0708183	−	0.122661i	0.828442	−	0.560075i	$-0.189228\pi$
$149$	−0.864447	−	1.49727i	−0.0708183	−	0.122661i	−0.899260	+	0.437414i	$0.855894\pi$
$150$	2.86445	+	4.96137i	0.233881	+	0.405094i
$151$	−20.1406			−1.63902			−0.819508	−	0.573068i	$-0.805753\pi$
$151$	−20.1406			−1.63902			−0.819508	+	0.573068i	$0.805753\pi$
$152$	−11.8961	−	2.57107i	−0.964900	−	0.208541i
$153$	0.521056			0.0421249
$154$	18.0597	+	31.2803i	1.45529	+	2.52064i
$155$	−1.14257	−	1.97899i	−0.0917735	−	0.158956i
$156$	−20.1933	+	34.9758i	−1.61675	+	2.80030i
$157$	−1.88906	−	3.27195i	−0.150764	−	0.261130i	0.780745	−	0.624850i	$-0.214840\pi$
$157$	−1.88906	−	3.27195i	−0.150764	−	0.261130i	−0.931508	+	0.363720i	$0.881507\pi$
$158$	11.5703	−	20.0403i	0.920482	−	1.59432i
$159$	14.3976			1.14181
$160$	5.72889			0.452909
$161$	−2.03163	+	3.51889i	−0.160115	+	0.277328i
$162$	9.21286	−	15.9571i	0.723830	−	1.25371i
$163$	−1.61640			−0.126606			−0.0633031	−	0.997994i	$-0.520163\pi$
$163$	−1.61640			−0.126606			−0.0633031	+	0.997994i	$0.520163\pi$
$164$	19.5803			1.52897
$165$	5.64959	−	9.78538i	0.439820	−	0.761791i
$166$	−5.54767	−	9.60885i	−0.430583	−	0.745791i
$167$	−3.24649	+	5.62309i	−0.251221	+	0.435128i	−0.963862	−	0.266401i	$-0.914165\pi$
$167$	−3.24649	+	5.62309i	−0.251221	+	0.435128i	0.712641	+	0.701529i	$0.247499\pi$
$168$	12.2746	+	21.2602i	0.947003	+	1.64026i
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$	−0.362446			−0.0277983
$171$	9.61796	−	10.6088i	0.735504	−	0.811273i
$172$	−10.7882			−0.822589
$173$	−4.26053	−	7.37945i	−0.323922	−	0.561049i	0.657372	−	0.753567i	$-0.271668\pi$
$173$	−4.26053	−	7.37945i	−0.323922	−	0.561049i	−0.981294	+	0.192517i	$0.938335\pi$
$174$	−10.0457	−	17.3996i	−0.761560	−	1.31906i
$175$	−1.75351	+	3.03717i	−0.132553	+	0.229588i
$176$	−0.142571	−	0.246941i	−0.0107467	−	0.0186139i
$177$	3.83983	−	6.65079i	0.288620	−	0.499904i
$178$	−2.54221			−0.190547
$179$	−10.2711			−0.767698			−0.383849	−	0.923396i	$-0.625402\pi$
$179$	−10.2711			−0.767698			−0.383849	+	0.923396i	$0.625402\pi$
$180$	5.29216	−	9.16629i	0.394454	−	0.683215i
$181$	−6.13355	+	10.6236i	−0.455903	+	0.789648i	−0.998740	−	0.0501908i	$-0.984017\pi$
$181$	−6.13355	+	10.6236i	−0.455903	+	0.789648i	0.542836	+	0.839838i	$0.317350\pi$
$182$	−40.0702			−2.97020
$183$	2.18980			0.161875
$184$	−1.61751	+	2.80161i	−0.119245	+	0.206538i
$185$	−5.48240	−	9.49580i	−0.403074	−	0.698145i
$186$	−6.54567	+	11.3374i	−0.479952	+	0.831301i
$187$	0.357429	+	0.619085i	0.0261378	+	0.0452720i
$188$	−4.93473	−	8.54721i	−0.359902	−	0.623369i
$189$	−2.50702			−0.182359
$190$	−6.69024	+	7.37945i	−0.485361	+	0.535362i
$191$	5.71085			0.413223			0.206611	−	0.978423i	$-0.433756\pi$
$191$	5.71085			0.413223			0.206611	+	0.978423i	$0.433756\pi$
$192$	−16.2515	−	28.1484i	−1.17285	−	2.03144i
$193$	5.07930	+	8.79761i	0.365616	+	0.633266i	0.988875	−	0.148750i	$-0.0475249\pi$
$193$	5.07930	+	8.79761i	0.365616	+	0.633266i	−0.623259	+	0.782016i	$0.714192\pi$
$194$	−1.85041	+	3.20500i	−0.132852	+	0.230106i
$195$	6.26755	+	10.8557i	0.448828	+	0.777393i
$196$	−8.53665	+	14.7859i	−0.609761	+	1.05614i
$197$	16.2038			1.15448			0.577238	−	0.816576i	$-0.304131\pi$
$197$	16.2038			1.15448			0.577238	+	0.816576i	$0.304131\pi$
$198$	−33.8343			−2.40450
$199$	−0.167186	+	0.289574i	−0.0118515	+	0.0205274i	−0.871890	−	0.489701i	$-0.837106\pi$
$199$	−0.167186	+	0.289574i	−0.0118515	+	0.0205274i	0.860039	+	0.510229i	$0.170439\pi$
$200$	−1.39608	+	2.41808i	−0.0987178	+	0.170984i
$201$	21.1686			1.49312
$202$	28.1375			1.97974
$203$	6.14959	−	10.6514i	0.431617	−	0.747582i
$204$	0.640570	+	1.10950i	0.0448489	+	0.0776805i
$205$	3.03865	−	5.26310i	0.212229	−	0.367591i
$206$	−12.1300	−	21.0098i	−0.845137	−	1.46382i
$207$	−1.90310	−	3.29626i	−0.132275	−	0.229106i
$208$	0.316332			0.0219336
$209$	19.2023	+	4.15013i	1.32825	+	0.287071i
$210$	20.0913			1.38643
$211$	−1.01404	−	1.75636i	−0.0698092	−	0.120913i	0.829008	−	0.559237i	$-0.188906\pi$
$211$	−1.01404	−	1.75636i	−0.0698092	−	0.120913i	−0.898817	+	0.438324i	$0.855572\pi$
$212$	9.25151	+	16.0241i	0.635396	+	1.10054i
$213$	−20.3519	+	35.2505i	−1.39449	+	2.41532i
$214$	2.48240	+	4.29965i	0.169694	+	0.293918i
$215$	−1.67420	+	2.89981i	−0.114180	+	0.197765i
$216$	−1.99600			−0.135810
$217$	−8.01404			−0.544028
$218$	−18.0757	+	31.3081i	−1.22424	+	2.12045i
$219$	−8.97338	+	15.5424i	−0.606365	+	1.05026i
$220$	14.5211			0.979009
$221$	−0.793049			−0.0533463
$222$	−31.4081	+	54.4005i	−2.10797	+	3.65112i
$223$	9.61596	+	16.6553i	0.643932	+	1.11532i	0.984547	+	0.175120i	$0.0560314\pi$
$223$	9.61596	+	16.6553i	0.643932	+	1.11532i	−0.340615	+	0.940203i	$0.610635\pi$
$224$	10.0457	−	17.3996i	0.671205	−	1.16256i
$225$	−1.64257	−	2.84502i	−0.109505	−	0.189668i
$226$	−11.2409	−	19.4699i	−0.747736	−	1.29512i
$227$	4.00000			0.265489			0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000			0.265489			0.132745	+	0.991150i	$0.457621\pi$
$228$	34.4136	+	7.43771i	2.27909	+	0.492574i
$229$	−12.9788			−0.857666			−0.428833	−	0.903384i	$-0.641075\pi$
$229$	−12.9788			−0.857666			−0.428833	+	0.903384i	$0.641075\pi$
$230$	1.32379	+	2.29288i	0.0872884	+	0.151188i
$231$	−19.8132	−	34.3175i	−1.30361	−	2.25793i
$232$	4.89608	−	8.48026i	0.321443	−	0.556756i
$233$	−13.5367	−	23.4462i	−0.886815	−	1.53601i	−0.843619	−	0.536943i	$-0.819579\pi$
$233$	−13.5367	−	23.4462i	−0.886815	−	1.53601i	−0.0431968	−	0.999067i	$-0.513754\pi$
$234$	18.7675	−	32.5063i	1.22687	−	2.12501i
$235$	−3.06327			−0.199825
$236$	9.86946			0.642447
$237$	−12.6937	+	21.9861i	−0.824545	+	1.42815i
$238$	−0.635553	+	1.10081i	−0.0411968	+	0.0713549i
$239$	20.0602			1.29758			0.648792	−	0.760966i	$-0.275275\pi$
$239$	20.0602			1.29758			0.648792	+	0.760966i	$0.275275\pi$
$240$	−0.158610			−0.0102382
$241$	10.7922	−	18.6926i	0.695184	−	1.20409i	−0.274934	−	0.961463i	$-0.588656\pi$
$241$	10.7922	−	18.6926i	0.695184	−	1.20409i	0.970119	−	0.242631i	$-0.0780105\pi$
$242$	−10.6410	−	18.4308i	−0.684030	−	1.18478i
$243$	−11.1797	+	19.3637i	−0.717176	+	1.24219i
$244$	1.40710	+	2.43717i	0.0900805	+	0.156024i
$245$	2.64959	+	4.58922i	0.169276	+	0.293195i
$246$	−34.8162			−2.21980
$247$	−14.6386	+	16.1466i	−0.931430	+	1.02738i
$248$	−6.38049			−0.405161
$249$	6.08632	+	10.5418i	0.385705	+	0.668061i
$250$	1.14257	+	1.97899i	0.0722626	+	0.125162i
$251$	3.63400	−	6.29426i	0.229376	−	0.397290i	−0.728248	−	0.685314i	$-0.759665\pi$
$251$	3.63400	−	6.29426i	0.229376	−	0.397290i	0.957623	+	0.288024i	$0.0929982\pi$
$252$	−18.5597	−	32.1464i	−1.16915	−	2.02503i
$253$	2.61094	−	4.52228i	0.164148	−	0.284313i
$254$	35.9015			2.25266
$255$	0.397638			0.0249010
$256$	7.79416	−	13.4999i	0.487135	−	0.843743i
$257$	−7.53865	+	13.0573i	−0.470248	+	0.814494i	−0.999421	−	0.0340202i	$-0.989169\pi$
$257$	−7.53865	+	13.0573i	−0.470248	+	0.814494i	0.529173	+	0.848514i	$0.322502\pi$
$258$	19.1827			1.19426
$259$	−38.4538			−2.38940
$260$	−8.05469	+	13.9511i	−0.499531	+	0.865213i
$261$	5.76053	+	9.97753i	0.356568	+	0.617593i
$262$	13.1797	−	22.8279i	0.814242	−	1.41031i
$263$	−10.0773	−	17.4544i	−0.621393	−	1.07628i	−0.989227	−	0.146393i	$-0.953234\pi$
$263$	−10.0773	−	17.4544i	−0.621393	−	1.07628i	0.367833	−	0.929892i	$-0.380100\pi$
$264$	−15.7746	−	27.3223i	−0.970857	−	1.68157i
$265$	5.74293			0.352786
$266$	10.6812	+	33.2593i	0.654908	+	2.03926i
$267$	2.78905			0.170687
$268$	13.6024	+	23.5600i	0.830897	+	1.43915i
$269$	3.86245	+	6.68995i	0.235497	+	0.407894i	0.959417	−	0.281991i	$-0.0909947\pi$
$269$	3.86245	+	6.68995i	0.235497	+	0.407894i	−0.723920	+	0.689884i	$0.757661\pi$
$270$	−0.816776	+	1.41470i	−0.0497074	+	0.0860957i
$271$	2.64257	+	4.57707i	0.160525	+	0.278037i	0.935057	−	0.354497i	$-0.115348\pi$
$271$	2.64257	+	4.57707i	0.160525	+	0.278037i	−0.774532	+	0.632534i	$0.782015\pi$
$272$	0.00501733	−	0.00869027i	0.000304220	−	0.000526925i
$273$	43.9608			2.66063
$274$	0.249951			0.0151001
$275$	2.25351	−	3.90319i	0.135892	−	0.235371i
$276$	4.67922	−	8.10465i	0.281656	−	0.487843i
$277$	30.6264			1.84016			0.920082	−	0.391726i	$-0.128122\pi$
$277$	30.6264			1.84016			0.920082	+	0.391726i	$0.128122\pi$
$278$	3.29918			0.197872
$279$	3.75351	−	6.50127i	0.224717	−	0.389221i
$280$	4.89608	+	8.48026i	0.292597	+	0.506792i
$281$	−6.68122	+	11.5722i	−0.398568	+	0.690341i	−0.993550	−	0.113399i	$-0.963826\pi$
$281$	−6.68122	+	11.5722i	−0.398568	+	0.690341i	0.594981	+	0.803740i	$0.297159\pi$
$282$	8.77457	+	15.1980i	0.522518	+	0.905027i
$283$	−2.04767	−	3.54667i	−0.121721	−	0.210828i	0.798725	−	0.601696i	$-0.205508\pi$
$283$	−2.04767	−	3.54667i	−0.121721	−	0.210828i	−0.920447	+	0.390868i	$0.872175\pi$
$284$	−52.3101			−3.10403
$285$	7.33983	−	8.09596i	0.434774	−	0.479563i
$286$	51.4959			3.04502
$287$	−10.6566	−	18.4578i	−0.629040	−	1.08953i
$288$	9.41012	+	16.2988i	0.554497	+	0.960416i
$289$	8.48742	−	14.7006i	0.499260	−	0.864744i
$290$	−4.00702	−	6.94036i	−0.235300	−	0.407552i
$291$	2.03008	−	3.51619i	0.119005	−	0.206123i
$292$	−23.0642			−1.34973
$293$	12.1726			0.711134			0.355567	−	0.934651i	$-0.384288\pi$
$293$	12.1726			0.711134			0.355567	+	0.934651i	$0.384288\pi$
$294$	15.1792	−	26.2912i	0.885270	−	1.53333i
$295$	1.53163	−	2.65287i	0.0891751	−	0.154456i
$296$	−30.6155			−1.77949
$297$	3.22188			0.186952
$298$	−1.97539	+	3.42147i	−0.114431	+	0.198200i
$299$	2.89652	+	5.01693i	0.167510	+	0.290136i
$300$	4.03865	−	6.99515i	0.233172	−	0.403865i
$301$	5.87147	+	10.1697i	0.338426	+	0.586170i
$302$	23.0120	+	39.8580i	1.32419	+	2.29357i
$303$	−30.8695			−1.77340
$304$	−0.0843223	−	0.262564i	−0.00483621	−	0.0150591i
$305$	0.873467			0.0500146
$306$	−0.595344	−	1.03117i	−0.0340335	−	0.0589478i
$307$	−12.2675	−	21.2480i	−0.700146	−	1.21269i	−0.968415	−	0.249344i	$-0.919785\pi$
$307$	−12.2675	−	21.2480i	−0.700146	−	1.21269i	0.268269	−	0.963344i	$-0.413548\pi$
$308$	25.4628	−	44.1029i	1.45088	−	2.51299i
$309$	13.3078	+	23.0497i	0.757052	+	1.31125i
$310$	−2.61094	+	4.52228i	−0.148291	+	0.256848i
$311$	−10.2038			−0.578606			−0.289303	−	0.957238i	$-0.593424\pi$
$311$	−10.2038			−0.578606			−0.289303	+	0.957238i	$0.593424\pi$
$312$	35.0000			1.98148
$313$	15.9910	−	27.6972i	0.903864	−	1.56554i	0.0814282	−	0.996679i	$-0.474052\pi$
$313$	15.9910	−	27.6972i	0.903864	−	1.56554i	0.822435	−	0.568859i	$-0.192615\pi$
$314$	−4.31678	+	7.47687i	−0.243610	+	0.421944i
$315$	−11.5211			−0.649138
$316$	−32.6264			−1.83538
$317$	−1.11796	+	1.93636i	−0.0627907	+	0.108757i	−0.895712	−	0.444635i	$-0.853333\pi$
$317$	−1.11796	+	1.93636i	−0.0627907	+	0.108757i	0.832921	+	0.553392i	$0.186667\pi$
$318$	−16.4503	−	28.4928i	−0.922489	−	1.59780i
$319$	−7.90310	+	13.6886i	−0.442489	+	0.766413i
$320$	−6.48240	−	11.2279i	−0.362377	−	0.627656i
$321$	−2.72343	−	4.71713i	−0.152007	−	0.263284i
$322$	9.28514			0.517441
$323$	0.211397	+	0.658252i	0.0117625	+	0.0366261i
$324$	−25.9788			−1.44327
$325$	2.50000	+	4.33013i	0.138675	+	0.240192i
$326$	1.84685	+	3.19884i	0.102288	+	0.177167i
$327$	19.8308	−	34.3480i	1.09665	−	1.89945i
$328$	−8.48441	−	14.6954i	−0.468473	−	0.811419i
$329$	−5.37147	+	9.30365i	−0.296139	+	0.512927i
$330$	−25.8202			−1.42136
$331$	−10.0913			−0.554670			−0.277335	−	0.960773i	$-0.589451\pi$
$331$	−10.0913			−0.554670			−0.277335	+	0.960773i	$0.589451\pi$
$332$	−7.82179	+	13.5477i	−0.429277	+	0.743529i
$333$	18.0105	−	31.1951i	0.986968	−	1.70948i
$334$	14.8374			0.811866
$335$	8.44375			0.461331
$336$	−0.278124	+	0.481725i	−0.0151729	+	0.0262802i
$337$	−2.80620	−	4.86048i	−0.152863	−	0.264767i	0.779416	−	0.626507i	$-0.215516\pi$
$337$	−2.80620	−	4.86048i	−0.152863	−	0.264767i	−0.932279	+	0.361740i	$0.882183\pi$
$338$	−13.7109	+	23.7479i	−0.745772	+	1.29172i
$339$	12.3324	+	21.3603i	0.669802	+	1.16013i
$340$	0.255511	+	0.442557i	0.0138570	+	0.0240010i
$341$	10.2992			0.557732
$342$	−31.9839	−	6.91258i	−1.72949	−	0.373790i
$343$	−5.96481			−0.322069
$344$	4.67465	+	8.09673i	0.252040	+	0.436546i
$345$	−1.45233	−	2.51551i	−0.0781907	−	0.135430i
$346$	−9.73591	+	16.8631i	−0.523406	+	0.906566i
$347$	−2.73747	−	4.74144i	−0.146955	−	0.254534i	0.783146	−	0.621838i	$-0.213614\pi$
$347$	−2.73747	−	4.74144i	−0.146955	−	0.254534i	−0.930101	+	0.367305i	$0.880281\pi$
$348$	−14.1636	+	24.5321i	−0.759250	+	1.31506i
$349$	−18.8202			−1.00742			−0.503712	−	0.863872i	$-0.668033\pi$
$349$	−18.8202			−1.00742			−0.503712	+	0.863872i	$0.668033\pi$
$350$	8.01404			0.428368
$351$	−1.78714	+	3.09542i	−0.0953907	+	0.165222i
$352$	−12.9101	+	22.3610i	−0.688112	+	1.19184i
$353$	−12.7008			−0.675996			−0.337998	−	0.941147i	$-0.609750\pi$
$353$	−12.7008			−0.675996			−0.337998	+	0.941147i	$0.609750\pi$
$354$	−17.5491			−0.932726
$355$	−8.11796	+	14.0607i	−0.430856	+	0.746265i
$356$	1.79216	+	3.10411i	0.0949843	+	0.164518i
$357$	0.697262	−	1.20769i	0.0369030	−	0.0639179i
$358$	11.7355	+	20.3264i	0.620239	+	1.07429i
$359$	5.54021	+	9.59592i	0.292401	+	0.506453i	0.974377	−	0.224921i	$-0.0722125\pi$
$359$	5.54021	+	9.59592i	0.292401	+	0.506453i	−0.681976	+	0.731375i	$0.738879\pi$
$360$	−9.17265			−0.483441
$361$	17.3042	+	7.84632i	0.910747	+	0.412964i
$362$	28.0321			1.47333
$363$	11.6742	+	20.2203i	0.612737	+	1.06129i
$364$	28.2479	+	48.9269i	1.48059	+	2.56447i
$365$	−3.57930	+	6.19954i	−0.187349	+	0.324499i
$366$	−2.50200	−	4.33359i	−0.130782	−	0.226521i
$367$	10.3202	−	17.8752i	0.538712	−	0.933076i	−0.460262	−	0.887783i	$-0.652244\pi$
$367$	10.3202	−	17.8752i	0.538712	−	0.933076i	0.998974	−	0.0452932i	$-0.0144222\pi$
$368$	−0.0733010			−0.00382108
$369$	19.9648			1.03933
$370$	−12.5281	+	21.6993i	−0.651304	+	1.12809i
$371$	10.0703	−	17.4422i	0.522823	−	0.905556i
$372$	18.4578			0.956992
$373$	4.55313			0.235752			0.117876	−	0.993028i	$-0.462391\pi$
$373$	4.55313			0.235752			0.117876	+	0.993028i	$0.462391\pi$
$374$	0.816776	−	1.41470i	0.0422345	−	0.0731522i
$375$	−1.25351	−	2.17114i	−0.0647309	−	0.112117i
$376$	−4.27657	+	7.40723i	−0.220547	+	0.381999i
$377$	−8.76755	−	15.1858i	−0.451552	−	0.782110i
$378$	2.86445	+	4.96137i	0.147331	+	0.255185i
$379$	−19.9187			−1.02315			−0.511577	−	0.859237i	$-0.670939\pi$
$379$	−19.9187			−1.02315			−0.511577	+	0.859237i	$0.670939\pi$
$380$	13.7269	+	2.96675i	0.704175	+	0.152191i
$381$	−39.3874			−2.01788
$382$	−6.52506	−	11.3017i	−0.333851	−	0.578247i
$383$	9.98742	+	17.2987i	0.510333	+	0.883923i	0.999928	+	0.0119734i	$0.00381133\pi$
$383$	9.98742	+	17.2987i	0.510333	+	0.883923i	−0.489595	+	0.871950i	$0.662855\pi$
$384$	−22.7746	+	39.4467i	−1.16221	+	2.01301i
$385$	−7.90310	−	13.6886i	−0.402779	−	0.697634i
$386$	11.6069	−	20.1038i	0.590777	−	1.02326i
$387$	−11.0000			−0.559161
$388$	5.21787			0.264897
$389$	−6.90110	+	11.9531i	−0.349900	+	0.606044i	−0.986231	−	0.165372i	$-0.947118\pi$
$389$	−6.90110	+	11.9531i	−0.349900	+	0.606044i	0.636332	+	0.771416i	$0.280451\pi$
$390$	14.3222	−	24.8068i	0.725235	−	1.25614i
$391$	0.183767			0.00929349
$392$	14.7962			0.747319
$393$	−14.4593	+	25.0443i	−0.729378	+	1.26332i
$394$	−18.5140	−	32.0673i	−0.932724	−	1.61552i
$395$	−5.06327	+	8.76983i	−0.254761	+	0.441258i
$396$	23.8519	+	41.3126i	1.19860	+	2.07604i
$397$	8.27457	+	14.3320i	0.415289	+	0.719301i	0.995459	−	0.0951945i	$-0.0303473\pi$
$397$	8.27457	+	14.3320i	0.415289	+	0.719301i	−0.580170	+	0.814495i	$0.697014\pi$
$398$	0.764087			0.0383002
$399$	−11.7183	−	36.4886i	−0.586650	−	1.82672i
$400$	−0.0632663			−0.00316332
$401$	−4.26253	−	7.38292i	−0.212861	−	0.368685i	0.739748	−	0.672884i	$-0.234945\pi$
$401$	−4.26253	−	7.38292i	−0.212861	−	0.368685i	−0.952609	+	0.304199i	$0.901611\pi$
$402$	−24.1867	−	41.8926i	−1.20632	−	2.08941i
$403$	−5.71286	+	9.89496i	−0.284578	+	0.492903i
$404$	−19.8358	−	34.3567i	−0.986869	−	1.70931i
$405$	−4.03163	+	6.98299i	−0.200333	+	0.346988i
$406$	−28.1054			−1.39485
$407$	49.4186			2.44959
$408$	0.555134	−	0.961521i	0.0274833	−	0.0476024i
$409$	5.78314	−	10.0167i	0.285958	−	0.495294i	−0.686883	−	0.726768i	$-0.741022\pi$
$409$	5.78314	−	10.0167i	0.285958	−	0.495294i	0.972841	+	0.231474i	$0.0743549\pi$
$410$	−13.8875			−0.685855
$411$	−0.274220			−0.0135263
$412$	−17.1024	+	29.6222i	−0.842573	+	1.45938i
$413$	−5.37147	−	9.30365i	−0.264313	−	0.457803i
$414$	−4.34885	+	7.53243i	−0.213734	+	0.370199i
$415$	2.42771	+	4.20492i	0.119172	+	0.206412i
$416$	−14.3222	−	24.8068i	−0.702205	−	1.21626i
$417$	−3.61951			−0.177248
$418$	−13.7269	−	42.7430i	−0.671404	−	2.09063i
$419$	−21.7149			−1.06084			−0.530420	−	0.847735i	$-0.677966\pi$
$419$	−21.7149			−1.06084			−0.530420	+	0.847735i	$0.677966\pi$
$420$	−14.1636	−	24.5321i	−0.691114	−	1.19704i
$421$	3.46135	+	5.99523i	0.168696	+	0.292190i	0.937962	−	0.346739i	$-0.112711\pi$
$421$	3.46135	+	5.99523i	0.168696	+	0.292190i	−0.769266	+	0.638929i	$0.779378\pi$
$422$	−2.31722	+	4.01354i	−0.112800	+	0.195376i
$423$	−5.03163	−	8.71504i	−0.244646	−	0.423740i
$424$	8.01760	−	13.8869i	0.389369	−	0.674407i
$425$	0.158610			0.00769371
$426$	93.0138			4.50654
$427$	1.53163	−	2.65287i	0.0741209	−	0.128381i
$428$	3.50000	−	6.06218i	0.169179	−	0.293026i
$429$	−56.4959			−2.72765
$430$	7.65159			0.368992
$431$	13.9894	−	24.2304i	0.673847	−	1.16714i	−0.302958	−	0.953004i	$-0.597974\pi$
$431$	13.9894	−	24.2304i	0.673847	−	1.16714i	0.976805	−	0.214133i	$-0.0686926\pi$
$432$	−0.0226132	−	0.0391672i	−0.00108798	−	0.00188443i
$433$	−3.12698	+	5.41608i	−0.150273	+	0.260280i	−0.931328	−	0.364182i	$-0.881349\pi$
$433$	−3.12698	+	5.41608i	−0.150273	+	0.260280i	0.781055	+	0.624462i	$0.214682\pi$
$434$	9.15661	+	15.8597i	0.439531	+	0.761290i
$435$	4.39608	+	7.61423i	0.210776	+	0.365075i
$436$	50.9708			2.44106
$437$	3.39208	−	3.74152i	0.162265	−	0.178981i
$438$	41.0109			1.95958
$439$	−15.5988	−	27.0179i	−0.744490	−	1.28949i	−0.950433	−	0.310931i	$-0.899359\pi$
$439$	−15.5988	−	27.0179i	−0.744490	−	1.28949i	0.205942	−	0.978564i	$-0.433974\pi$
$440$	−6.29216	−	10.8983i	−0.299967	−	0.519558i
$441$	−8.70428	+	15.0763i	−0.414490	+	0.717917i
$442$	0.906115	+	1.56944i	0.0430995	+	0.0746505i
$443$	16.3519	−	28.3223i	0.776901	−	1.34563i	−0.156819	−	0.987627i	$-0.550124\pi$
$443$	16.3519	−	28.3223i	0.776901	−	1.34563i	0.933720	−	0.358004i	$-0.116543\pi$
$444$	88.5661			4.20316
$445$	1.11250			0.0527373
$446$	21.9738	−	38.0598i	1.04049	−	1.80218i
$447$	2.16719	−	3.75368i	0.102504	−	0.177543i
$448$	−45.4678			−2.14815
$449$	25.6304			1.20958			0.604788	−	0.796387i	$-0.293258\pi$
$449$	25.6304			1.20958			0.604788	+	0.796387i	$0.293258\pi$
$450$	−3.75351	+	6.50127i	−0.176942	+	0.306473i
$451$	13.6953	+	23.7209i	0.644885	+	1.11697i
$452$	−15.8489	+	27.4510i	−0.745467	+	1.29119i
$453$	−25.2464	−	43.7280i	−1.18618	−	2.05452i
$454$	−4.57028	−	7.91597i	−0.214494	−	0.371515i
$455$	17.5351			0.822058
$456$	−9.32970	−	29.0509i	−0.436903	−	1.36043i
$457$	33.1646			1.55138			0.775688	−	0.631116i	$-0.217403\pi$
$457$	33.1646			1.55138			0.775688	+	0.631116i	$0.217403\pi$
$458$	14.8293	+	25.6850i	0.692926	+	1.20018i
$459$	0.0566917	+	0.0981929i	0.00264614	+	0.00458325i
$460$	1.86645	−	3.23278i	0.0870236	−	0.150729i
$461$	−1.08788	−	1.88426i	−0.0506677	−	0.0877590i	0.839579	−	0.543237i	$-0.182802\pi$
$461$	−1.08788	−	1.88426i	−0.0506677	−	0.0877590i	−0.890247	+	0.455478i	$0.849468\pi$
$462$	−45.2760	+	78.4204i	−2.10643	+	3.64845i
$463$	−6.20072			−0.288172			−0.144086	−	0.989565i	$-0.546024\pi$
$463$	−6.20072			−0.288172			−0.144086	+	0.989565i	$0.546024\pi$
$464$	0.221876			0.0103003
$465$	2.86445	−	4.96137i	0.132836	−	0.230078i
$466$	−30.9332	+	53.5778i	−1.43295	+	2.48195i
$467$	−17.1546			−0.793821			−0.396910	−	0.917857i	$-0.629918\pi$
$467$	−17.1546			−0.793821			−0.396910	+	0.917857i	$0.629918\pi$
$468$	−52.9216			−2.44630
$469$	14.8062	−	25.6451i	0.683687	−	1.18418i
$470$	3.50000	+	6.06218i	0.161443	+	0.279627i
$471$	4.73591	−	8.20284i	0.218219	−	0.377967i
$472$	−4.27657	−	7.40723i	−0.196845	−	0.340945i
$473$	−7.54567	−	13.0695i	−0.346950	−	0.600936i
$474$	58.0138			2.66466
$475$	2.92771	−	3.22932i	0.134333	−	0.148171i
$476$	1.79216			0.0821436
$477$	9.43318	+	16.3387i	0.431915	+	0.748099i
$478$	−22.9202	−	39.6989i	−1.04834	−	1.81578i
$479$	17.8891	−	30.9848i	0.817372	−	1.41573i	−0.0902399	−	0.995920i	$-0.528763\pi$
$479$	17.8891	−	30.9848i	0.817372	−	1.41573i	0.907612	−	0.419810i	$-0.137903\pi$
$480$	7.18122	+	12.4382i	0.327776	+	0.567726i
$481$	−27.4120	+	47.4790i	−1.24988	+	2.16486i
$482$	−49.3233			−2.24661
$483$	−10.1867			−0.463510
$484$	−15.0030	+	25.9860i	−0.681955	+	1.18118i
$485$	0.809757	−	1.40254i	0.0367692	−	0.0636861i
$486$	51.0943			2.31768
$487$	−23.7149			−1.07462			−0.537311	−	0.843384i	$-0.680560\pi$
$487$	−23.7149			−1.07462			−0.537311	+	0.843384i	$0.680560\pi$
$488$	1.21943	−	2.11212i	0.0552010	−	0.0956110i
$489$	−2.02617	−	3.50943i	−0.0916267	−	0.158702i
$490$	6.05469	−	10.4870i	0.273523	−	0.473756i
$491$	19.5933	+	33.9367i	0.884235	+	1.53154i	0.846588	+	0.532249i	$0.178653\pi$
$491$	19.5933	+	33.9367i	0.884235	+	1.53154i	0.0376474	+	0.999291i	$0.488014\pi$
$492$	24.5441	+	42.5117i	1.10653	+	1.91657i
$493$	−0.556248			−0.0250521
$494$	48.6796	+	10.5210i	2.19020	+	0.473361i
$495$	14.8062			0.665489
$496$	−0.0722863	−	0.125204i	−0.00324575	−	0.00562180i
$497$	28.4698	+	49.3112i	1.27705	+	2.21191i
$498$	13.9081	−	24.0896i	0.623238	−	1.07948i
$499$	4.68824	+	8.12027i	0.209875	+	0.363513i	0.951675	−	0.307107i	$-0.0993611\pi$
$499$	4.68824	+	8.12027i	0.209875	+	0.363513i	−0.741800	+	0.670621i	$0.766028\pi$
$500$	1.61094	−	2.79023i	0.0720433	−	0.124783i
$501$	−16.2780			−0.727249
$502$	−16.6084			−0.741269
$503$	−6.74649	+	11.6853i	−0.300811	+	0.521020i	−0.976320	−	0.216332i	$-0.930591\pi$
$503$	−6.74649	+	11.6853i	−0.300811	+	0.521020i	0.675509	+	0.737352i	$0.263924\pi$
$504$	−16.0843	+	27.8589i	−0.716453	+	1.24093i
$505$	−12.3132			−0.547931
$506$	−11.9327			−0.530475
$507$	15.0421	−	26.0537i	0.668044	−	1.15709i
$508$	−25.3092	−	43.8368i	−1.12291	−	1.94495i
$509$	−12.8534	+	22.2628i	−0.569718	+	0.986781i	0.426875	+	0.904310i	$0.359614\pi$
$509$	−12.8534	+	22.2628i	−0.569718	+	0.986781i	−0.996594	+	0.0824703i	$0.973719\pi$
$510$	−0.454330	−	0.786922i	−0.0201181	−	0.0348455i
$511$	12.5527	+	21.7419i	0.555298	+	0.961805i
$512$	0.715746			0.0316318
$513$	3.04567	+	0.658252i	0.134470	+	0.0290625i
$514$	34.4538			1.51969
$515$	5.30820	+	9.19407i	0.233907	+	0.405139i
$516$	−13.5231	−	23.4226i	−0.595319	−	1.03112i
$517$	6.90310	−	11.9565i	0.303598	−	0.525847i
$518$	43.9362	+	76.0997i	1.93045	+	3.34363i
$519$	10.6812	−	18.5004i	0.468854	−	0.812078i
$520$	13.9608			0.612222
$521$	−37.7358			−1.65324			−0.826618	−	0.562763i	$-0.809738\pi$
$521$	−37.7358			−1.65324			−0.826618	+	0.562763i	$0.809738\pi$
$522$	13.1636	−	22.8001i	0.576156	−	0.997932i
$523$	−19.2003	+	33.2559i	−0.839570	+	1.45418i	0.0506855	+	0.998715i	$0.483859\pi$
$523$	−19.2003	+	33.2559i	−0.839570	+	1.45418i	−0.890255	+	0.455462i	$0.849474\pi$
$524$	−37.1646			−1.62354
$525$	−8.79216			−0.383721
$526$	−23.0281	+	39.8858i	−1.00407	+	1.73910i
$527$	0.181223	+	0.313888i	0.00789420	+	0.0136732i
$528$	0.357429	−	0.619085i	0.0155551	−	0.0269422i
$529$	10.8288	+	18.7561i	0.470818	+	0.815481i
$530$	−6.56171	−	11.3652i	−0.285022	−	0.493673i
$531$	10.0633			0.436709
$532$	33.0808	−	36.4886i	1.43423	−	1.58198i
$533$	−30.3865			−1.31619
$534$	−3.18668	−	5.51950i	−0.137901	−	0.238852i
$535$	−1.08632	−	1.88157i	−0.0469659	−	0.0813473i
$536$	11.7882	−	20.4177i	0.509171	−	0.881910i
$537$	−12.8749	−	22.3000i	−0.555594	−	0.962317i
$538$	8.82624	−	15.2875i	0.380526	−	0.659091i
$539$	−23.8835			−1.02874
$540$	2.30318			0.0991132
$541$	6.40310	−	11.0905i	0.275291	−	0.476818i	−0.694918	−	0.719089i	$-0.744559\pi$
$541$	6.40310	−	11.0905i	0.275291	−	0.476818i	0.970208	+	0.242272i	$0.0778926\pi$
$542$	6.03865	−	10.4593i	0.259382	−	0.449263i
$543$	−30.7539			−1.31977
$544$	−0.908659			−0.0389584
$545$	7.91012	−	13.7007i	0.338832	−	0.586875i
$546$	−50.2284	−	86.9981i	−2.14958	−	3.72317i
$547$	9.12853	−	15.8111i	0.390308	−	0.676033i	−0.602182	−	0.798359i	$-0.705702\pi$
$547$	9.12853	−	15.8111i	0.390308	−	0.676033i	0.992490	+	0.122326i	$0.0390352\pi$
$548$	−0.176206	−	0.305197i	−0.00752714	−	0.0130374i
$549$	1.43473	+	2.48503i	0.0612329	+	0.106058i
$550$	−10.2992			−0.439159
$551$	−10.2675	+	11.3253i	−0.437412	+	0.482473i
$552$	−8.11027			−0.345196
$553$	17.7570	+	30.7560i	0.755103	+	1.30788i
$554$	−34.9929	−	60.6095i	−1.48671	−	2.57505i
$555$	13.7445	−	23.8062i	0.583421	−	1.01051i
$556$	−2.32580	−	4.02840i	−0.0986357	−	0.170842i
$557$	−7.45233	+	12.9078i	−0.315765	+	0.546922i	−0.979600	−	0.200958i	$-0.935595\pi$
$557$	−7.45233	+	12.9078i	−0.315765	+	0.546922i	0.663835	+	0.747879i	$0.268928\pi$
$558$	−17.1546			−0.726212
$559$	16.7420			0.708113
$560$	−0.110938	+	0.192150i	−0.00468799	+	0.00811984i
$561$	−0.896081	+	1.55206i	−0.0378326	+	0.0655279i
$562$	30.5351			1.28805
$563$	45.7810			1.92944			0.964720	−	0.263276i	$-0.0848031\pi$
$563$	45.7810			1.92944			0.964720	+	0.263276i	$0.0848031\pi$
$564$	12.3715	−	21.4280i	0.520933	−	0.902282i
$565$	4.91914	+	8.52020i	0.206950	+	0.358447i
$566$	−4.67922	+	8.10465i	−0.196682	+	0.340664i
$567$	14.1390	+	24.4895i	0.593783	+	1.02846i
$568$	22.6666	+	39.2598i	0.951071	+	1.64730i
$569$	0.379598			0.0159136			0.00795679	−	0.999968i	$-0.497467\pi$
$569$	0.379598			0.0159136			0.00795679	+	0.999968i	$0.497467\pi$
$570$	−24.4081	−	5.27526i	−1.02234	−	0.220956i
$571$	−15.8514			−0.663361			−0.331681	−	0.943392i	$-0.607616\pi$
$571$	−15.8514			−0.663361			−0.331681	+	0.943392i	$0.607616\pi$
$572$	−36.3026	−	62.8780i	−1.51789	−	2.62906i
$573$	7.15861	+	12.3991i	0.299055	+	0.517979i
$574$	−24.3519	+	42.1787i	−1.01643	+	1.76050i
$575$	−0.579305	−	1.00339i	−0.0241587	−	0.0418441i
$576$	21.2956	−	36.8851i	0.887318	−	1.53688i
$577$	−19.2350			−0.800765			−0.400382	−	0.916348i	$-0.631123\pi$
$577$	−19.2350			−0.800765			−0.400382	+	0.916348i	$0.631123\pi$
$578$	−38.7899			−1.61345
$579$	−12.7339	+	22.0558i	−0.529203	+	0.916607i
$580$	−5.64959	+	9.78538i	−0.234586	+	0.406316i
$581$	17.0281			0.706444
$582$	−9.27803			−0.384587
$583$	−12.9418	+	22.4158i	−0.535993	+	0.928366i
$584$	9.99400	+	17.3101i	0.413554	+	0.716297i
$585$	−8.21286	+	14.2251i	−0.339560	+	0.588135i
$586$	−13.9081	−	24.0896i	−0.574539	−	0.995131i
$587$	−20.4242	−	35.3757i	−0.842995	−	1.46011i	−0.887351	−	0.461095i	$-0.847457\pi$
$587$	−20.4242	−	35.3757i	−0.842995	−	1.46011i	0.0443559	−	0.999016i	$-0.485876\pi$
$588$	−42.8031			−1.76517
$589$	9.73591	+	2.10419i	0.401161	+	0.0867018i
$590$	−7.00000			−0.288185
$591$	20.3117	+	35.1808i	0.835510	+	1.44715i
$592$	−0.346852	−	0.600764i	−0.0142555	−	0.0246913i
$593$	7.12342	−	12.3381i	0.292524	−	0.506666i	−0.681882	−	0.731462i	$-0.738838\pi$
$593$	7.12342	−	12.3381i	0.292524	−	0.506666i	0.974406	+	0.224796i	$0.0721716\pi$
$594$	−3.68122	−	6.37607i	−0.151042	−	0.261613i
$595$	0.278124	−	0.481725i	0.0114020	−	0.0197488i
$596$	5.57028			0.228168
$597$	−0.838276			−0.0343083
$598$	6.61897	−	11.4644i	0.270670	−	0.468814i
$599$	7.92571	−	13.7277i	0.323836	−	0.560900i	−0.657440	−	0.753507i	$-0.728361\pi$
$599$	7.92571	−	13.7277i	0.323836	−	0.560900i	0.981276	+	0.192607i	$0.0616941\pi$
$600$	−7.00000			−0.285774
$601$	16.4718			0.671900			0.335950	−	0.941880i	$-0.390943\pi$
$601$	16.4718			0.671900			0.335950	+	0.941880i	$0.390943\pi$
$602$	13.4171	−	23.2392i	0.546842	−	0.947158i
$603$	13.8695	+	24.0226i	0.564808	+	0.978277i
$604$	32.4452	−	56.1968i	1.32018	−	2.28661i
$605$	4.65661	+	8.06548i	0.189318	+	0.327908i
$606$	35.2706	+	61.0904i	1.43277	+	2.48163i
$607$	−10.3914			−0.421774			−0.210887	−	0.977510i	$-0.567635\pi$
$607$	−10.3914			−0.421774			−0.210887	+	0.977510i	$0.567635\pi$
$608$	−16.7726	+	18.5004i	−0.680217	+	0.750291i
$609$	30.8343			1.24947
$610$	−0.997999	−	1.72858i	−0.0404078	−	0.0699883i
$611$	7.65817	+	13.2643i	0.309816	+	0.536617i
$612$	−0.839389	+	1.45386i	−0.0339303	+	0.0587690i
$613$	10.8925	+	18.8664i	0.439945	+	0.762007i	0.997685	−	0.0680090i	$-0.0216647\pi$
$613$	10.8925	+	18.8664i	0.439945	+	0.762007i	−0.557740	+	0.830016i	$0.688331\pi$
$614$	−28.0331	+	48.5547i	−1.13132	+	1.95951i
$615$	15.2359			0.614371
$616$	−44.1335			−1.77819
$617$	21.3855	−	37.0408i	0.860948	−	1.49121i	−0.0100671	−	0.999949i	$-0.503205\pi$
$617$	21.3855	−	37.0408i	0.860948	−	1.49121i	0.871015	−	0.491256i	$-0.163462\pi$
$618$	30.4101	−	52.6719i	1.22327	−	2.11877i
$619$	28.7882			1.15709			0.578547	−	0.815649i	$-0.303620\pi$
$619$	28.7882			1.15709			0.578547	+	0.815649i	$0.303620\pi$
$620$	7.36245			0.295683
$621$	0.414120	−	0.717278i	0.0166181	−	0.0287834i
$622$	11.6586	+	20.1933i	0.467468	+	0.809678i
$623$	1.95077	−	3.37883i	0.0781560	−	0.135370i
$624$	0.396525	+	0.686801i	0.0158737	+	0.0274940i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−73.0833			−2.92100
$627$	15.0597	+	46.8931i	0.601427	+	1.87273i
$628$	12.1726			0.485742
$629$	0.869563	+	1.50613i	0.0346718	+	0.0600532i
$630$	13.1636	+	22.8001i	0.524451	+	0.908377i
$631$	9.69370	−	16.7900i	0.385900	−	0.668399i	−0.605993	−	0.795470i	$-0.707224\pi$
$631$	9.69370	−	16.7900i	0.385900	−	0.668399i	0.991894	+	0.127071i	$0.0405576\pi$
$632$	14.1375	+	24.4868i	0.562358	+	0.974032i
$633$	2.54221	−	4.40324i	0.101044	−	0.175013i
$634$	5.10938			0.202919
$635$	−15.7109			−0.623466
$636$	−23.1937	+	40.1727i	−0.919690	+	1.59295i
$637$	13.2479	−	22.9461i	0.524903	−	0.909158i
$638$	36.1194			1.42998
$639$	−53.3373			−2.10999
$640$	−9.08432	+	15.7345i	−0.359089	+	0.621961i
$641$	−20.3433	−	35.2356i	−0.803512	−	1.39172i	−0.917291	−	0.398217i	$-0.869629\pi$
$641$	−20.3433	−	35.2356i	−0.803512	−	1.39172i	0.113779	−	0.993506i	$-0.463704\pi$
$642$	−6.22343	+	10.7793i	−0.245619	+	0.425425i
$643$	17.0527	+	29.5361i	0.672492	+	1.16479i	0.977195	+	0.212344i	$0.0681096\pi$
$643$	17.0527	+	29.5361i	0.672492	+	1.16479i	−0.304703	+	0.952448i	$0.598557\pi$
$644$	−6.54567	−	11.3374i	−0.257936	−	0.446757i
$645$	−8.39452			−0.330534
$646$	1.06114	−	1.17045i	0.0417499	−	0.0460509i
$647$	−48.0029			−1.88719			−0.943595	−	0.331103i	$-0.892579\pi$
$647$	−48.0029			−1.88719			−0.943595	+	0.331103i	$0.892579\pi$
$648$	11.2570	+	19.4976i	0.442216	+	0.765940i
$649$	6.90310	+	11.9565i	0.270970	+	0.469334i
$650$	5.71286	−	9.89496i	0.224077	−	0.388112i
$651$	−10.0457	−	17.3996i	−0.393721	−	0.681945i
$652$	2.60392	−	4.51012i	0.101977	−	0.176630i
$653$	3.90866			0.152958			0.0764788	−	0.997071i	$-0.475632\pi$
$653$	3.90866			0.152958			0.0764788	+	0.997071i	$0.475632\pi$
$654$	−90.6325			−3.54401
$655$	−5.76755	+	9.98968i	−0.225357	+	0.390329i
$656$	0.192244	−	0.332977i	0.00750588	−	0.0130006i
$657$	−23.5171			−0.917488
$658$	24.5491			0.957025
$659$	−6.54411	+	11.3347i	−0.254922	+	0.441539i	−0.964874	−	0.262711i	$-0.915383\pi$
$659$	−6.54411	+	11.3347i	−0.254922	+	0.441539i	0.709952	+	0.704250i	$0.248717\pi$
$660$	18.2023	+	31.5273i	0.708523	+	1.22720i
$661$	11.9714	−	20.7350i	0.465633	−	0.806500i	−0.533597	−	0.845739i	$-0.679160\pi$
$661$	11.9714	−	20.7350i	0.465633	−	0.806500i	0.999230	+	0.0392391i	$0.0124934\pi$
$662$	11.5301	+	19.9707i	0.448129	+	0.776182i
$663$	−0.994095	−	1.72182i	−0.0386074	−	0.0668700i
$664$	13.5571			0.526119
$665$	−4.67420	−	14.5546i	−0.181258	−	0.564403i
$666$	−82.3130			−3.18956
$667$	2.03163	+	3.51889i	0.0786652	+	0.136252i
$668$	−10.4598	−	18.1169i	−0.404701	−	0.700963i
$669$	−24.1074	+	41.7552i	−0.932045	+	1.61435i
$670$	−9.64759	−	16.7101i	−0.372719	−	0.645568i
$671$	−1.96837	+	3.40931i	−0.0759880	+	0.131615i
$672$	50.3694			1.94304
$673$	−11.3304			−0.436754			−0.218377	−	0.975865i	$-0.570076\pi$
$673$	−11.3304			−0.436754			−0.218377	+	0.975865i	$0.570076\pi$
$674$	−6.41256	+	11.1069i	−0.247003	+	0.427821i
$675$	0.357429	−	0.619085i	0.0137574	−	0.0238286i
$676$	38.6625			1.48702
$677$	8.90466			0.342234			0.171117	−	0.985251i	$-0.445262\pi$
$677$	8.90466			0.342234			0.171117	+	0.985251i	$0.445262\pi$
$678$	28.1812	−	48.8113i	1.08229	−	1.87459i
$679$	−2.83983	−	4.91873i	−0.108983	−	0.188764i
$680$	0.221432	−	0.383532i	0.00849153	−	0.0147078i
$681$	5.01404	+	8.68457i	0.192138	+	0.332793i
$682$	−11.7675	−	20.3820i	−0.450603	−	0.780467i
$683$	−26.6977			−1.02156			−0.510780	−	0.859712i	$-0.670643\pi$
$683$	−26.6977			−1.02156			−0.510780	+	0.859712i	$0.670643\pi$
$684$	14.1069	+	43.9263i	0.539392	+	1.67957i
$685$	−0.109381			−0.00417923
$686$	6.81522	+	11.8043i	0.260206	+	0.450690i
$687$	−16.2691	−	28.1789i	−0.620705	−	1.07509i
$688$	−0.105921	+	0.183460i	−0.00403819	+	0.00699435i
$689$	−14.3573	−	24.8676i	−0.546971	−	0.947381i
$690$	−3.31878	+	5.74829i	−0.126344	+	0.218834i
$691$	35.9708			1.36840			0.684198	−	0.729297i	$-0.260153\pi$
$691$	35.9708			1.36840			0.684198	+	0.729297i	$0.260153\pi$
$692$	27.4538			1.04364
$693$	25.9628	−	44.9689i	0.986245	−	1.70823i
$694$	−6.25551	+	10.8349i	−0.237456	+	0.411286i
$695$	−1.44375			−0.0547646
$696$	24.5491			0.930532
$697$	−0.481960	+	0.834779i	−0.0182555	+	0.0316195i
$698$	21.5035	+	37.2451i	0.813918	+	1.40975i
$699$	33.9366	−	58.7800i	1.28360	−	2.22326i
$700$	−5.64959	−	9.78538i	−0.213534	−	0.369852i
$701$	−1.22543	−	2.12252i	−0.0462840	−	0.0801663i	0.841955	−	0.539547i	$-0.181405\pi$
$701$	−1.22543	−	2.12252i	−0.0462840	−	0.0801663i	−0.888239	+	0.459381i	$0.848071\pi$
$702$	8.16776			0.308272
$703$	46.7159	+	10.0966i	1.76192	+	0.380799i
$704$	58.4326			2.20226
$705$	−3.83983	−	6.65079i	−0.144616	−	0.250483i
$706$	14.5116	+	25.1348i	0.546151	+	0.945961i
$707$	−21.5913	+	37.3973i	−0.812026	+	1.40647i
$708$	12.3715	+	21.4280i	0.464948	+	0.805314i
$709$	25.1440	−	43.5507i	0.944304	−	1.63558i	0.187165	−	0.982329i	$-0.440070\pi$
$709$	25.1440	−	43.5507i	0.944304	−	1.63558i	0.757139	−	0.653254i	$-0.226597\pi$
$710$	37.1014			1.39239
$711$	−33.2671			−1.24761
$712$	1.55313	−	2.69011i	0.0582061	−	0.100816i
$713$	1.32379	−	2.29288i	0.0495765	−	0.0858690i
$714$	−3.18668			−0.119259
$715$	−22.5351			−0.842765
$716$	16.5461	−	28.6587i	0.618357	−	1.07103i
$717$	25.1456	+	43.5534i	0.939079	+	1.62653i
$718$	12.6602	−	21.9281i	0.472473	−	0.818348i
$719$	24.0491	+	41.6543i	0.896881	+	1.55344i	0.831459	+	0.555586i	$0.187506\pi$
$719$	24.0491	+	41.6543i	0.896881	+	1.55344i	0.0654223	+	0.997858i	$0.479161\pi$
$720$	−0.103919	−	0.179994i	−0.00387285	−	0.00670797i
$721$	37.2319			1.38659
$722$	−4.24347	−	43.2098i	−0.157926	−	1.60810i
$723$	54.1123			2.01246
$724$	−19.7615	−	34.2280i	−0.734432	−	1.27207i
$725$	1.75351	+	3.03717i	0.0651237	+	0.112798i
$726$	26.6772	−	46.2063i	0.990085	−	1.71488i
$727$	8.33983	+	14.4450i	0.309307	+	0.535736i	0.978211	−	0.207613i	$-0.0665695\pi$
$727$	8.33983	+	14.4450i	0.309307	+	0.535736i	−0.668904	+	0.743349i	$0.733236\pi$
$728$	24.4804	−	42.4013i	0.907304	−	1.57150i
$729$	−31.8655			−1.18020
$730$	16.3584			0.605453
$731$	0.265545	−	0.459938i	0.00982155	−	0.0170114i
$732$	−3.52763	+	6.11004i	−0.130385	+	0.225833i
$733$	−4.13365			−0.152680			−0.0763399	−	0.997082i	$-0.524323\pi$
$733$	−4.13365			−0.152680			−0.0763399	+	0.997082i	$0.524323\pi$
$734$	−47.1664			−1.74094
$735$	−6.64257	+	11.5053i	−0.245015	+	0.424378i
$736$	3.31878	+	5.74829i	0.122332	+	0.211885i
$737$	−19.0281	+	32.9576i	−0.700908	+	1.21401i
$738$	−22.8112	−	39.5102i	−0.839692	−	1.45439i
$739$	−23.4870	−	40.6806i	−0.863982	−	1.49646i	−0.868054	−	0.496470i	$-0.834629\pi$
$739$	−23.4870	−	40.6806i	−0.863982	−	1.49646i	0.00407159	−	0.999992i	$-0.498704\pi$
$740$	35.3273			1.29866
$741$	−53.4061	−	11.5425i	−1.96192	−	0.424025i
$742$	−46.0241			−1.68960
$743$	−20.6069	−	35.6923i	−0.755995	−	1.30942i	−0.944878	−	0.327422i	$-0.893820\pi$
$743$	−20.6069	−	35.6923i	−0.755995	−	1.30942i	0.188883	−	0.982000i	$-0.439513\pi$
$744$	−7.99800	−	13.8529i	−0.293221	−	0.507873i
$745$	0.864447	−	1.49727i	0.0316709	−	0.0548556i
$746$	−5.20228	−	9.01061i	−0.190469	−	0.329902i
$747$	−7.97539	+	13.8138i	−0.291804	+	0.505420i
$748$	−2.30318			−0.0842127
$749$	−7.61951			−0.278411
$750$	−2.86445	+	4.96137i	−0.104595	+	0.181164i
$751$	−2.98942	+	5.17783i	−0.109086	+	0.188942i	−0.915400	−	0.402545i	$-0.868126\pi$
$751$	−2.98942	+	5.17783i	−0.109086	+	0.188942i	0.806314	+	0.591487i	$0.201459\pi$
$752$	−0.193802			−0.00706722
$753$	18.2210			0.664010
$754$	−20.0351	+	34.7018i	−0.729635	+	1.26376i
$755$	−10.0703	−	17.4422i	−0.366495	−	0.634788i
$756$	4.03865	−	6.99515i	0.146884	−	0.254411i
$757$	−18.1968	−	31.5178i	−0.661375	−	1.14553i	−0.980255	−	0.197739i	$-0.936640\pi$
$757$	−18.1968	−	31.5178i	−0.661375	−	1.14553i	0.318880	−	0.947795i	$-0.396693\pi$
$758$	22.7585	+	39.4189i	0.826627	+	1.43176i
$759$	13.0913			0.475186
$760$	−3.72143	−	11.5878i	−0.134991	−	0.420335i
$761$	−2.71397			−0.0983813			−0.0491907	−	0.998789i	$-0.515664\pi$
$761$	−2.71397			−0.0983813			−0.0491907	+	0.998789i	$0.515664\pi$
$762$	45.0029	+	77.9473i	1.63028	+	2.82373i
$763$	−27.7409	−	48.0487i	−1.00429	−	1.73948i
$764$	−9.19983	+	15.9346i	−0.332838	+	0.576493i
$765$	0.260528	+	0.451248i	0.00941941	+	0.0163149i
$766$	22.8227	−	39.5300i	0.824617	−	1.42828i
$767$	−15.3163			−0.553041
$768$	39.0802			1.41019
$769$	−19.8995	+	34.4670i	−0.717596	+	1.24291i	0.244354	+	0.969686i	$0.421424\pi$
$769$	−19.8995	+	34.4670i	−0.717596	+	1.24291i	−0.961950	+	0.273226i	$0.911909\pi$
$770$	−18.0597	+	31.2803i	−0.650827	+	1.12726i
$771$	−37.7991			−1.36130
$772$	−32.7298			−1.17797
$773$	−22.4874	+	38.9494i	−0.808816	+	1.40091i	0.104868	+	0.994486i	$0.466558\pi$
$773$	−22.4874	+	38.9494i	−0.808816	+	1.40091i	−0.913684	+	0.406425i	$0.866775\pi$
$774$	12.5683	+	21.7689i	0.451758	+	0.782467i
$775$	1.14257	−	1.97899i	0.0410424	−	0.0710875i
$776$	−2.26097	−	3.91612i	−0.0811642	−	0.140580i
$777$	−48.2022	−	83.4886i	−1.72924	−	2.99514i
$778$	31.5400			1.13076
$779$	8.09992	+	25.2216i	0.290210	+	0.903658i
$780$	−40.3865			−1.44607
$781$	−36.5878	−	63.3719i	−1.30921	−	2.26762i
$782$	−0.209967	−	0.363673i	−0.00750840	−	0.0130049i
$783$	−1.25351	+	2.17114i	−0.0447968	+	0.0775903i
$784$	0.167630	+	0.290343i	0.00598678	+	0.0103694i
$785$	1.88906	−	3.27195i	0.0674235	−	0.116781i
$786$	66.0833			2.35711
$787$	−17.7149			−0.631466			−0.315733	−	0.948848i	$-0.602250\pi$
$787$	−17.7149			−0.631466			−0.315733	+	0.948848i	$0.602250\pi$
$788$	−26.1034	+	45.2124i	−0.929894	+	1.61062i
$789$	25.2640	−	43.7585i	0.899422	−	1.55784i
$790$	23.1406			0.823305
$791$	34.5030			1.22679
$792$	20.6706	−	35.8026i	0.734499	−	1.27219i
$793$	−2.18367	−	3.78222i	−0.0775443	−	0.134311i
$794$	18.9086	−	32.7506i	0.671040	−	1.16227i
$795$	7.19882	+	12.4687i	0.255316	+	0.442220i
$796$	−0.538652	−	0.932972i	−0.0190920	−	0.0330683i
$797$	25.4930			0.903008			0.451504	−	0.892269i	$-0.350888\pi$
$797$	25.4930			0.903008			0.451504	+	0.892269i	$0.350888\pi$
$798$	−58.8217	+	64.8813i	−2.08227	+	2.29677i
$799$	0.485864			0.0171886
$800$	2.86445	+	4.96137i	0.101274	+	0.175411i
$801$	1.82735	+	3.16507i	0.0645663	+	0.111832i
$802$	−9.74049	+	16.8710i	−0.343949	+	0.595736i
$803$	−16.1320	−	27.9414i	−0.569286	−	0.986032i
$804$	−34.1014	+	59.0653i	−1.20266	+	2.08307i
$805$	−4.06327			−0.143211
$806$	26.1094			0.919664
$807$	−9.68322	+	16.7718i	−0.340866	+	0.590397i
$808$	−17.1902	+	29.7744i	−0.604751	+	1.04746i
$809$	−20.4678			−0.719610			−0.359805	−	0.933027i	$-0.617157\pi$
$809$	−20.4678			−0.719610			−0.359805	+	0.933027i	$0.617157\pi$
$810$	18.4257			0.647414
$811$	11.4508	−	19.8333i	0.402091	−	0.696442i	−0.591887	−	0.806021i	$-0.701617\pi$
$811$	11.4508	−	19.8333i	0.402091	−	0.696442i	0.993978	+	0.109579i	$0.0349502\pi$
$812$	19.8132	+	34.3175i	0.695308	+	1.20431i
$813$	−6.62498	+	11.4748i	−0.232348	+	0.402439i
$814$	−56.4643	−	97.7990i	−1.97907	−	3.42785i
$815$	−0.808200	−	1.39984i	−0.0283100	−	0.0490344i
$816$	0.0251571			0.000880674
$817$	−4.46281	−	13.8963i	−0.156134	−	0.486171i
$818$	−26.4306			−0.924124
$819$	28.8026	+	49.8876i	1.00645	+	1.74322i
$820$	9.79016	+	16.9571i	0.341887	+	0.592166i
$821$	−15.3609	+	26.6058i	−0.536099	+	0.928550i	0.463011	+	0.886353i	$0.346769\pi$
$821$	−15.3609	+	26.6058i	−0.536099	+	0.928550i	−0.999109	+	0.0421975i	$0.986564\pi$
$822$	0.313316	+	0.542679i	0.0109281	+	0.0189281i
$823$	−2.09846	+	3.63464i	−0.0731476	+	0.126695i	−0.900279	−	0.435313i	$-0.856638\pi$
$823$	−2.09846	+	3.63464i	−0.0731476	+	0.126695i	0.827132	+	0.562008i	$0.189971\pi$
$824$	29.6427			1.03265
$825$	11.2992			0.393387
$826$	−12.2746	+	21.2602i	−0.427087	+	0.739736i
$827$	10.6652	−	18.4726i	0.370865	−	0.642357i	−0.618834	−	0.785522i	$-0.712395\pi$
$827$	10.6652	−	18.4726i	0.370865	−	0.642357i	0.989699	+	0.143165i	$0.0457280\pi$
$828$	12.2631			0.426172
$829$	34.0390			1.18222			0.591112	−	0.806590i	$-0.298689\pi$
$829$	34.0390			1.18222			0.591112	+	0.806590i	$0.298689\pi$
$830$	5.54767	−	9.60885i	0.192562	−	0.333528i
$831$	38.3905	+	66.4943i	1.33175	+	2.30666i
$832$	−32.4120	+	56.1393i	−1.12368	+	1.94628i
$833$	−0.420251	−	0.727896i	−0.0145608	−	0.0252201i
$834$	4.13555	+	7.16299i	0.143202	+	0.248034i
$835$	−6.49298			−0.224699
$836$	−42.5135	+	46.8931i	−1.47036	+	1.62183i
$837$	1.63355			0.0564638
$838$	24.8108	+	42.9735i	0.857074	+	1.48450i
$839$	−5.20584	−	9.01678i	−0.179725	−	0.311294i	0.762061	−	0.647505i	$-0.224188\pi$
$839$	−5.20584	−	9.01678i	−0.179725	−	0.311294i	−0.941786	+	0.336212i	$0.890854\pi$
$840$	−12.2746	+	21.2602i	−0.423513	+	0.733546i
$841$	8.35041	+	14.4633i	0.287945	+	0.498736i
$842$	7.90967	−	13.7000i	0.272585	−	0.472132i
$843$	−33.4999			−1.15380
$844$	6.53421			0.224917
$845$	6.00000	−	10.3923i	0.206406	−	0.357506i
$846$	−11.4980	+	19.9151i	−0.395309	+	0.684696i
$847$	32.6616			1.12227
$848$	0.363334			0.0124769
$849$	5.13355	−	8.89157i	0.176183	−	0.305158i
$850$	−0.181223	−	0.313888i	−0.00621590	−	0.0107663i
$851$	6.35197	−	11.0019i	0.217743	−	0.377141i
$852$	−65.5712	−	113.573i	−2.24643	−	3.89093i
$853$	6.56527	+	11.3714i	0.224790	+	0.389349i	0.956257	−	0.292529i	$-0.0944969\pi$
$853$	6.56527	+	11.3714i	0.224790	+	0.389349i	−0.731466	+	0.681878i	$0.761164\pi$
$854$	−7.00000			−0.239535
$855$	13.9964	+	3.02501i	0.478668	+	0.103453i
$856$	−6.06638			−0.207345
$857$	21.6230	+	37.4521i	0.738627	+	1.27934i	0.953114	+	0.302612i	$0.0978587\pi$
$857$	21.6230	+	37.4521i	0.738627	+	1.27934i	−0.214487	+	0.976727i	$0.568808\pi$
$858$	64.5506	+	111.805i	2.20372	+	3.81696i
$859$	−15.7344	+	27.2527i	−0.536849	+	0.929850i	0.462222	+	0.886764i	$0.347052\pi$
$859$	−15.7344	+	27.2527i	−0.536849	+	0.929850i	−0.999071	+	0.0430861i	$0.986281\pi$
$860$	−5.39408	−	9.34282i	−0.183937	−	0.318587i
$861$	26.7163	−	46.2740i	0.910490	−	1.57701i
$862$	−63.9356			−2.17766
$863$	−23.7842			−0.809622			−0.404811	−	0.914400i	$-0.632663\pi$
$863$	−23.7842			−0.809622			−0.404811	+	0.914400i	$0.632663\pi$
$864$	−2.04767	+	3.54667i	−0.0696632	+	0.120660i
$865$	4.26053	−	7.37945i	0.144862	−	0.250909i
$866$	14.2912			0.485634
$867$	42.5562			1.44529
$868$	12.9101	−	22.3610i	0.438198	−	0.758981i
$869$	−22.8202	−	39.5258i	−0.774123	−	1.34082i
$870$	10.0457	−	17.3996i	0.340580	−	0.589902i
$871$	−21.1094	−	36.5625i	−0.715264	−	1.23887i
$872$	−22.0863	−	38.2546i	−0.747937	−	1.29547i
$873$	5.32033			0.180066
$874$	−11.2801	−	2.43794i	−0.381556	−	0.0824646i
$875$	−3.50702			−0.118559
$876$	−28.9111	−	50.0756i	−0.976817	−	1.69190i
$877$	19.0848	+	33.0558i	0.644447	+	1.11621i	0.984429	+	0.175783i	$0.0562456\pi$
$877$	19.0848	+	33.0558i	0.644447	+	1.11621i	−0.339982	+	0.940432i	$0.610421\pi$
$878$	−35.6455	+	61.7398i	−1.20298	+	2.08362i
$879$	15.2585	+	26.4285i	0.514657	+	0.891413i
$880$	0.142571	−	0.246941i	0.00480608	−	0.00832437i
$881$	5.49209			0.185033			0.0925167	−	0.995711i	$-0.470509\pi$
$881$	5.49209			0.185033			0.0925167	+	0.995711i	$0.470509\pi$
$882$	39.7810			1.33950
$883$	17.1491	−	29.7032i	0.577115	−	0.999592i	−0.418694	−	0.908128i	$-0.637512\pi$
$883$	17.1491	−	29.7032i	0.577115	−	0.999592i	0.995808	−	0.0914644i	$-0.0291548\pi$
$884$	1.27755	−	2.21279i	0.0429688	−	0.0744241i
$885$	7.67967			0.258149
$886$	−74.7327			−2.51069
$887$	18.7585	−	32.4907i	0.629850	−	1.09093i	−0.357732	−	0.933824i	$-0.616450\pi$
$887$	18.7585	−	32.4907i	0.629850	−	1.09093i	0.987582	−	0.157107i	$-0.0502169\pi$
$888$	−38.3768	−	66.4706i	−1.28784	−	2.23061i
$889$	−27.5491	+	47.7165i	−0.923968	+	1.60036i
$890$	−1.27111	−	2.20162i	−0.0426075	−	0.0737984i
$891$	−18.1706	−	31.4725i	−0.608740	−	1.05437i
$892$	−61.9628			−2.07467
$893$	8.96837	−	9.89226i	0.300115	−	0.331032i
$894$	−9.90466			−0.331261
$895$	−5.13555	−	8.89504i	−0.171663	−	0.297328i
$896$	31.8589	+	55.1812i	1.06433	+	1.84347i
$897$	−7.26164	+	12.5775i	−0.242459	+	0.419952i
$898$	−29.2846	−	50.7224i	−0.977240	−	1.69263i
$899$	−4.00702	+	6.94036i	−0.133642	+	0.231474i
$900$	10.5843			0.352811
$901$	−0.910886			−0.0303460
$902$	31.2956	−	54.2056i	1.04203	−	1.80485i
$903$	−14.7199	+	25.4956i	−0.489847	+	0.848439i
$904$	27.4701			0.913640
$905$	−12.2671			−0.407772
$906$	−57.6916	+	99.9248i	−1.91668	+	3.31978i
$907$	11.1265	+	19.2717i	0.369450	+	0.639907i	0.989480	−	0.144672i	$-0.0462126\pi$
$907$	11.1265	+	19.2717i	0.369450	+	0.639907i	−0.620029	+	0.784579i	$0.712879\pi$
$908$	−6.44375	+	11.1609i	−0.213843	+	0.370388i
$909$	−20.2253	−	35.0313i	−0.670832	−	1.16192i
$910$	−20.0351	−	34.7018i	−0.664157	−	1.15035i
$911$	10.0421			0.332710			0.166355	−	0.986066i	$-0.446800\pi$
$911$	10.0421			0.332710			0.166355	+	0.986066i	$0.446800\pi$
$912$	0.464364	−	0.512202i	0.0153766	−	0.0169607i
$913$	−21.8835			−0.724238
$914$	−37.8930	−	65.6325i	−1.25339	−	2.17093i
$915$	1.09490	+	1.89642i	0.0361963	+	0.0626938i
$916$	20.9081	−	36.2139i	0.690824	−	1.19654i
$917$	20.2269	+	35.0340i	0.667951	+	1.15692i
$918$	0.129549	−	0.224385i	0.00427574	−	0.00740580i
$919$	6.06104			0.199935			0.0999676	−	0.994991i	$-0.468126\pi$
$919$	6.06104			0.199935			0.0999676	+	0.994991i	$0.468126\pi$
$920$	−3.23503			−0.106656
$921$	30.7550	−	53.2692i	1.01341	−	1.75528i
$922$	−2.48596	+	4.30581i	−0.0818708	+	0.141804i
$923$	81.1796			2.67206
$924$	127.671			4.20008
$925$	5.48240	−	9.49580i	0.180260	−	0.312220i
$926$	7.08477	+	12.2712i	0.232820	+	0.403256i
$927$	−17.4382	+	30.2038i	−0.572745	+	0.992024i
$928$	−10.0457	−	17.3996i	−0.329765	−	0.571170i
$929$	25.9382	+	44.9263i	0.851004	+	1.47398i	0.880303	+	0.474412i	$0.157339\pi$
$929$	25.9382	+	44.9263i	0.851004	+	1.47398i	−0.0292983	+	0.999571i	$0.509327\pi$
$930$	−13.0913			−0.429282
$931$	−22.5773	−	4.87957i	−0.739941	−	0.159921i
$932$	87.2268			2.85721
$933$	−12.7906	−	22.1540i	−0.418746	−	0.725289i
$934$	19.6004	+	33.9488i	0.641343	+	1.11084i
$935$	−0.357429	+	0.619085i	−0.0116892	+	0.0202462i
$936$	22.9316	+	39.7187i	0.749543	+	1.29825i
$937$	−12.5999	+	21.8237i	−0.411621	+	0.712949i	−0.995067	−	0.0992029i	$-0.968371\pi$
$937$	−12.5999	+	21.8237i	−0.411621	+	0.712949i	0.583446	+	0.812152i	$0.301704\pi$
$938$	−67.6685			−2.20946
$939$	80.1794			2.61655
$940$	4.93473	−	8.54721i	0.160953	−	0.278779i
$941$	0.967923	−	1.67649i	0.0315534	−	0.0546521i	−0.849817	−	0.527077i	$-0.823288\pi$
$941$	0.967923	−	1.67649i	0.0315534	−	0.0546521i	0.881371	+	0.472425i	$0.156621\pi$
$942$	−21.6445			−0.705215
$943$	7.04122			0.229294
$944$	0.0969008	−	0.167837i	0.00315385	−	0.00546263i
$945$	−1.25351	−	2.17114i	−0.0407767	−	0.0706272i
$946$	−17.2429	+	29.8656i	−0.560616	+	0.971016i
$947$	−15.6812	−	27.1607i	−0.509571	−	0.882603i	−0.999939	−	0.0110875i	$-0.996471\pi$
$947$	−15.6812	−	27.1607i	−0.509571	−	0.882603i	0.490367	−	0.871516i	$-0.336863\pi$
$948$	−40.8975	−	70.8366i	−1.32829	−	2.30067i
$949$	35.7930			1.16189
$950$	−9.73591	−	2.10419i	−0.315875	−	0.0682691i
$951$	−5.60548			−0.181770
$952$	−0.776567	−	1.34505i	−0.0251687	−	0.0435934i
$953$	−26.4542	−	45.8201i	−0.856937	−	1.48426i	−0.874837	−	0.484418i	$-0.839031\pi$
$953$	−26.4542	−	45.8201i	−0.856937	−	1.48426i	0.0179001	−	0.999840i	$-0.494302\pi$
$954$	21.5561	−	37.3363i	0.697906	−	1.20881i
$955$	2.85543	+	4.94575i	0.0923995	+	0.160041i
$956$	−32.3157	+	55.9724i	−1.04516	+	1.81028i
$957$	−39.6264			−1.28094
$958$	−81.7581			−2.64148
$959$	−0.191800	+	0.332208i	−0.00619355	+	0.0107275i
$960$	16.2515	−	28.1484i	0.524515	−	0.908487i
$961$	−25.7781			−0.831552
$962$	125.281			4.03921
$963$	3.56873	−	6.18122i	0.115001	−	0.199187i
$964$	34.7710	+	60.2252i	1.11990	+	1.93972i
$965$	−5.07930	+	8.79761i	−0.163509	+	0.283205i
$966$	11.6390	+	20.1594i	0.374479	+	0.648617i
$967$	30.0140	+	51.9858i	0.965186	+	1.67175i	0.709113	+	0.705094i	$0.249095\pi$
$967$	30.0140	+	51.9858i	0.965186	+	1.67175i	0.256073	+	0.966657i	$0.417571\pi$
$968$	26.0040			0.835800
$969$	−1.16417	+	1.28410i	−0.0373985	+	0.0412512i
$970$	−3.70082			−0.118826
$971$	−0.875025	−	1.51559i	−0.0280809	−	0.0486375i	0.851643	−	0.524122i	$-0.175606\pi$
$971$	−0.875025	−	1.51559i	−0.0280809	−	0.0486375i	−0.879724	+	0.475484i	$0.842273\pi$
$972$	−36.0195	−	62.3876i	−1.15533	−	2.00108i
$973$	−2.53163	+	4.38492i	−0.0811604	+	0.140574i
$974$	27.0959	+	46.9315i	0.868209	+	1.50378i
$975$	−6.26755	+	10.8557i	−0.200722	+	0.347661i
$976$	0.0552611			0.00176886
$977$	5.47583			0.175187			0.0875937	−	0.996156i	$-0.472082\pi$
$977$	5.47583			0.175187			0.0875937	+	0.996156i	$0.472082\pi$
$978$	−4.63009	+	8.01955i	−0.148054	+	0.256437i
$979$	−2.50702	+	4.34228i	−0.0801247	+	0.138780i
$980$	−17.0733			−0.545387
$981$	51.9717			1.65933
$982$	44.7736	−	77.5501i	1.42878	−	2.47472i
$983$	−2.52963	−	4.38145i	−0.0806827	−	0.139747i	0.822861	−	0.568243i	$-0.192377\pi$
$983$	−2.52963	−	4.38145i	−0.0806827	−	0.139747i	−0.903543	+	0.428497i	$0.859043\pi$
$984$	21.2706	−	36.8417i	0.678081	−	1.17447i
$985$	8.10192	+	14.0329i	0.258149	+	0.447126i
$986$	0.635553	+	1.10081i	0.0202401	+	0.0350569i
$987$	−26.9327			−0.857278
$988$	−21.4708	−	66.8561i	−0.683078	−	2.12698i
$989$	−3.87950			−0.123361
$990$	−16.9171	−	29.3013i	−0.537662	−	0.931258i
$991$	−0.0492290	−	0.0852672i	−0.00156381	−	0.00270860i	0.865242	−	0.501354i	$-0.167164\pi$
$991$	−0.0492290	−	0.0852672i	−0.00156381	−	0.00270860i	−0.866806	+	0.498645i	$0.833831\pi$
$992$	−6.54567	+	11.3374i	−0.207825	+	0.359964i
$993$	−12.6496	−	21.9097i	−0.401423	−	0.695284i
$994$	65.0576	−	112.683i	2.06350	−	3.57409i
$995$	−0.334372			−0.0106003
$996$	−39.2188			−1.24269
$997$	−9.17967	+	15.8996i	−0.290723	+	0.503547i	−0.973981	−	0.226630i	$-0.927229\pi$
$997$	−9.17967	+	15.8996i	−0.290723	+	0.503547i	0.683258	+	0.730177i	$0.260562\pi$
$998$	10.7133	−	18.5560i	0.339124	−	0.587379i
$999$	7.83828			0.247992

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.2.e.b.26.1	yes	6
3.2	odd	2		855.2.k.g.406.3		6
4.3	odd	2		1520.2.q.j.881.1		6
5.2	odd	4		475.2.j.b.349.5		12
5.3	odd	4		475.2.j.b.349.2		12
5.4	even	2		475.2.e.d.26.3		6
19.7	even	3		1805.2.a.h.1.3		3
19.11	even	3	inner	95.2.e.b.11.1	✓	6
19.12	odd	6		1805.2.a.g.1.1		3
57.11	odd	6		855.2.k.g.676.3		6
76.11	odd	6		1520.2.q.j.961.1		6
95.49	even	6		475.2.e.d.201.3		6
95.64	even	6		9025.2.a.z.1.1		3
95.68	odd	12		475.2.j.b.49.5		12
95.69	odd	6		9025.2.a.ba.1.3		3
95.87	odd	12		475.2.j.b.49.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.b.11.1	✓	6	19.11	even	3	inner
95.2.e.b.26.1	yes	6	1.1	even	1	trivial
475.2.e.d.26.3		6	5.4	even	2
475.2.e.d.201.3		6	95.49	even	6
475.2.j.b.49.2		12	95.87	odd	12
475.2.j.b.49.5		12	95.68	odd	12
475.2.j.b.349.2		12	5.3	odd	4
475.2.j.b.349.5		12	5.2	odd	4
855.2.k.g.406.3		6	3.2	odd	2
855.2.k.g.676.3		6	57.11	odd	6
1520.2.q.j.881.1		6	4.3	odd	2
1520.2.q.j.961.1		6	76.11	odd	6
1805.2.a.g.1.1		3	19.12	odd	6
1805.2.a.h.1.3		3	19.7	even	3
9025.2.a.z.1.1		3	95.64	even	6
9025.2.a.ba.1.3		3	95.69	odd	6

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:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14257 - 1.97899i) q^{2} +(1.25351 + 2.17114i) q^{3} +(-1.61094 + 2.79023i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.86445 - 4.96137i) q^{6} +3.50702 q^{7} +2.79216 q^{8} +(-1.64257 + 2.84502i) q^{9} +(1.14257 - 1.97899i) q^{10} -4.50702 q^{11} -8.07730 q^{12} +(2.50000 - 4.33013i) q^{13} +(-4.00702 - 6.94036i) q^{14} +(-1.25351 + 2.17114i) q^{15} +(0.0316332 + 0.0547902i) q^{16} +(-0.0793049 - 0.137360i) q^{17} +7.50702 q^{18} +(-4.26053 - 0.920816i) q^{19} -3.22188 q^{20} +(4.39608 + 7.61423i) q^{21} +(5.14959 + 8.91935i) q^{22} +(-0.579305 + 1.00339i) q^{23} +(3.50000 + 6.06218i) q^{24} +(-0.500000 + 0.866025i) q^{25} -11.4257 q^{26} -0.714858 q^{27} +(-5.64959 + 9.78538i) q^{28} +(1.75351 - 3.03717i) q^{29} +5.72889 q^{30} -2.28514 q^{31} +(2.86445 - 4.96137i) q^{32} +(-5.64959 - 9.78538i) q^{33} +(-0.181223 + 0.313888i) q^{34} +(1.75351 + 3.03717i) q^{35} +(-5.29216 - 9.16629i) q^{36} -10.9648 q^{37} +(3.04567 + 9.48365i) q^{38} +12.5351 q^{39} +(1.39608 + 2.41808i) q^{40} +(-3.03865 - 5.26310i) q^{41} +(10.0457 - 17.3996i) q^{42} +(1.67420 + 2.89981i) q^{43} +(7.26053 - 12.5756i) q^{44} -3.28514 q^{45} +2.64759 q^{46} +(-1.53163 + 2.65287i) q^{47} +(-0.0793049 + 0.137360i) q^{48} +5.29918 q^{49} +2.28514 q^{50} +(0.198819 - 0.344364i) q^{51} +(8.05469 + 13.9511i) q^{52} +(2.87147 - 4.97353i) q^{53} +(0.816776 + 1.41470i) q^{54} +(-2.25351 - 3.90319i) q^{55} +9.79216 q^{56} +(-3.34139 - 10.4045i) q^{57} -8.01404 q^{58} +(-1.53163 - 2.65287i) q^{59} +(-4.03865 - 6.99515i) q^{60} +(0.436734 - 0.756445i) q^{61} +(2.61094 + 4.52228i) q^{62} +(-5.76053 + 9.97753i) q^{63} -12.9648 q^{64} +5.00000 q^{65} +(-12.9101 + 22.3610i) q^{66} +(4.22188 - 7.31250i) q^{67} +0.511021 q^{68} -2.90466 q^{69} +(4.00702 - 6.94036i) q^{70} +(8.11796 + 14.0607i) q^{71} +(-4.58632 + 7.94375i) q^{72} +(3.57930 + 6.19954i) q^{73} +(12.5281 + 21.6993i) q^{74} -2.50702 q^{75} +(9.43273 - 10.4045i) q^{76} -15.8062 q^{77} +(-14.3222 - 24.8068i) q^{78} +(5.06327 + 8.76983i) q^{79} +(-0.0316332 + 0.0547902i) q^{80} +(4.03163 + 6.98299i) q^{81} +(-6.94375 + 12.0269i) q^{82} +4.85543 q^{83} -28.3273 q^{84} +(0.0793049 - 0.137360i) q^{85} +(3.82580 - 6.62647i) q^{86} +8.79216 q^{87} -12.5843 q^{88} +(0.556248 - 0.963449i) q^{89} +(3.75351 + 6.50127i) q^{90} +(8.76755 - 15.1858i) q^{91} +(-1.86645 - 3.23278i) q^{92} +(-2.86445 - 4.96137i) q^{93} +7.00000 q^{94} +(-1.33281 - 4.15013i) q^{95} +14.3624 q^{96} +(-0.809757 - 1.40254i) q^{97} +(-6.05469 - 10.4870i) q^{98} +(7.40310 - 12.8225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - q^{3} - 7 q^{4} + 3 q^{5} + 6 q^{6} + 4 q^{7} - 12 q^{8} - 4 q^{9} + q^{10} - 10 q^{11} - 8 q^{12} + 15 q^{13} - 7 q^{14} + q^{15} - 3 q^{16} - q^{17} + 28 q^{18} - 14 q^{20} + 12 q^{21}+ \cdots + 13 q^{99}+O(q^{100}) \) 6 * q - q^2 - q^3 - 7 * q^4 + 3 * q^5 + 6 * q^6 + 4 * q^7 - 12 * q^8 - 4 * q^9 + q^10 - 10 * q^11 - 8 * q^12 + 15 * q^13 - 7 * q^14 + q^15 - 3 * q^16 - q^17 + 28 * q^18 - 14 * q^20 + 12 * q^21 + 8 * q^22 - 4 * q^23 + 21 * q^24 - 3 * q^25 - 10 * q^26 - 16 * q^27 - 11 * q^28 + 2 * q^29 + 12 * q^30 - 2 * q^31 + 6 * q^32 - 11 * q^33 + 25 * q^34 + 2 * q^35 - 3 * q^36 - 4 * q^37 - 19 * q^38 - 10 * q^39 - 6 * q^40 + 2 * q^41 + 23 * q^42 + q^43 + 18 * q^44 - 8 * q^45 - 48 * q^46 - 6 * q^47 - q^48 - 14 * q^49 + 2 * q^50 + 6 * q^51 + 35 * q^52 - 11 * q^53 - 10 * q^54 - 5 * q^55 + 30 * q^56 - 19 * q^57 - 14 * q^58 - 6 * q^59 - 4 * q^60 + 9 * q^61 + 13 * q^62 - 9 * q^63 - 16 * q^64 + 30 * q^65 - 29 * q^66 + 20 * q^67 + 68 * q^68 - 10 * q^69 + 7 * q^70 + 29 * q^71 - 11 * q^72 + 22 * q^73 + 7 * q^74 + 2 * q^75 - 19 * q^76 - 32 * q^77 - 30 * q^78 + 24 * q^79 + 3 * q^80 + 21 * q^81 - 31 * q^82 - 6 * q^83 - 56 * q^84 + q^85 + 32 * q^86 + 24 * q^87 - 18 * q^88 + 14 * q^89 + 14 * q^90 + 10 * q^91 - 41 * q^92 - 6 * q^93 + 42 * q^94 + 34 * q^96 - 7 * q^97 - 23 * q^98 + 13 * q^99

Introduction

L-functions

Modular forms

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Database

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