LMFDB - Embedded newform 95.2.e.b.11.1

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			11.1
Root			$1.14257 - 1.97899i$ of defining polynomial
Character	$\chi$	$=$	95.11
Dual form			95.2.e.b.26.1

$q$-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 $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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	0.106382	+	0.994325i	$0.466073\pi$
$2$	−1.14257	+	1.97899i	−0.807920	+	1.39936i	−0.914302	+	0.405033i	$0.867260\pi$
$3$	1.25351	−	2.17114i	0.723714	−	1.25351i	−0.235787	−	0.971805i	$-0.575767\pi$
$3$	1.25351	−	2.17114i	0.723714	−	1.25351i	0.959501	−	0.281705i	$-0.0908998\pi$
$4$	−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	0.970725	+	0.240192i	$0.0772105\pi$
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	−0.277350	+	0.960769i	$0.589456\pi$
$14$	−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	−0.875482	−	0.483250i	$-0.839456\pi$
$17$	−0.0793049	+	0.137360i	−0.0192343	+	0.0333147i	0.856248	+	0.516565i	$0.172790\pi$
$18$	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	0.799287	−	0.600949i	$-0.205211\pi$
$23$	−0.579305	−	1.00339i	−0.120793	−	0.209220i	−0.920081	+	0.391729i	$0.871877\pi$
$24$	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	0.981637	−	0.190757i	$-0.0610942\pi$
$29$	1.75351	+	3.03717i	0.325619	+	0.563988i	−0.656019	+	0.754745i	$0.727761\pi$
$30$	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	−0.999576	−	0.0291332i	$-0.990725\pi$
$41$	−3.03865	+	5.26310i	−0.474558	+	0.821958i	0.525018	+	0.851091i	$0.324059\pi$
$42$	10.0457	+	17.3996i	1.55008	+	2.68482i
$43$	1.67420	−	2.89981i	0.255314	−	0.442216i	−0.709667	−	0.704537i	$-0.751155\pi$
$43$	1.67420	−	2.89981i	0.255314	−	0.442216i	0.964981	+	0.262321i	$0.0844879\pi$
$44$	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	0.732430	−	0.680842i	$-0.238386\pi$
$47$	−1.53163	−	2.65287i	−0.223412	−	0.386960i	−0.955842	+	0.293882i	$0.905053\pi$
$48$	−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	0.993028	−	0.117881i	$-0.0376100\pi$
$53$	2.87147	+	4.97353i	0.394426	+	0.683166i	−0.598602	+	0.801047i	$0.704277\pi$
$54$	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	−0.948335	−	0.317272i	$-0.897233\pi$
$59$	−1.53163	+	2.65287i	−0.199402	+	0.345374i	0.748933	+	0.662646i	$0.230567\pi$
$60$	−4.03865	+	6.99515i	−0.521388	+	0.903070i
$61$	0.436734	+	0.756445i	0.0559180	+	0.0968528i	0.892629	−	0.450791i	$-0.148858\pi$
$61$	0.436734	+	0.756445i	0.0559180	+	0.0968528i	−0.836711	+	0.547644i	$0.815525\pi$
$62$	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	0.999832	+	0.0183230i	$0.00583273\pi$
$67$	4.22188	+	7.31250i	0.515784	+	0.893365i	−0.484048	+	0.875042i	$0.660834\pi$
$68$	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	0.249634	−	0.968340i	$-0.419690\pi$
$71$	8.11796	−	14.0607i	0.963424	−	1.66870i	0.713790	−	0.700359i	$-0.246977\pi$
$72$	−4.58632	−	7.94375i	−0.540503	−	0.936179i
$73$	3.57930	−	6.19954i	0.418926	−	0.725601i	−0.576906	−	0.816811i	$-0.695740\pi$
$73$	3.57930	−	6.19954i	0.418926	−	0.725601i	0.995832	+	0.0912097i	$0.0290733\pi$
$74$	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	−0.426937	−	0.904281i	$-0.640407\pi$
$79$	5.06327	−	8.76983i	0.569662	−	0.986683i	0.996599	−	0.0824022i	$-0.0262592\pi$
$80$	−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	0.894000	−	0.448067i	$-0.147888\pi$
$89$	0.556248	+	0.963449i	0.0589621	+	0.102125i	−0.835038	+	0.550193i	$0.814554\pi$
$90$	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	−0.904203	−	0.427104i	$-0.859534\pi$
$97$	−0.809757	+	1.40254i	−0.0822184	+	0.142406i	0.821984	+	0.569510i	$0.192867\pi$
$98$	−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	−0.990800	−	0.135337i	$-0.956788\pi$
$101$	−6.15661	−	10.6636i	−0.612605	−	1.06106i	0.378194	−	0.925726i	$-0.376545\pi$
$102$	−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	0.186393	+	0.982475i	$0.440320\pi$
$109$	−7.91012	+	13.7007i	−0.757652	+	1.31229i	−0.944045	+	0.329816i	$0.893013\pi$
$110$	−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	−0.969483	−	0.245160i	$-0.921159\pi$
$127$	−7.85543	−	13.6060i	−0.697056	−	1.20734i	0.272426	−	0.962177i	$-0.412174\pi$
$128$	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	−0.496077	−	0.868279i	$-0.665227\pi$
$131$	5.76755	−	9.98968i	0.503913	−	0.872803i	0.999990	−	0.00452412i	$-0.00144008\pi$
$132$	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	0.863680	−	0.504041i	$-0.168154\pi$
$137$	−0.0546904	−	0.0947266i	−0.00467252	−	0.00809304i	−0.868352	+	0.495948i	$0.834821\pi$
$138$	3.31878	−	5.74829i	0.282513	−	0.489327i
$139$	−0.721876	−	1.25033i	−0.0612287	−	0.106051i	0.833786	−	0.552088i	$-0.186169\pi$
$139$	−0.721876	−	1.25033i	−0.0612287	−	0.106051i	−0.895015	+	0.446036i	$0.852835\pi$
$140$	−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	−0.899260	−	0.437414i	$-0.855894\pi$
$149$	−0.864447	+	1.49727i	−0.0708183	+	0.122661i	0.828442	+	0.560075i	$0.189228\pi$
$150$	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	−0.931508	−	0.363720i	$-0.881507\pi$
$157$	−1.88906	+	3.27195i	−0.150764	+	0.261130i	0.780745	+	0.624850i	$0.214840\pi$
$158$	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	0.712641	−	0.701529i	$-0.247499\pi$
$167$	−3.24649	−	5.62309i	−0.251221	−	0.435128i	−0.963862	+	0.266401i	$0.914165\pi$
$168$	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	−0.981294	−	0.192517i	$-0.938335\pi$
$173$	−4.26053	+	7.37945i	−0.323922	+	0.561049i	0.657372	+	0.753567i	$0.271668\pi$
$174$	−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	0.542836	−	0.839838i	$-0.317350\pi$
$181$	−6.13355	−	10.6236i	−0.455903	−	0.789648i	−0.998740	+	0.0501908i	$0.984017\pi$
$182$	−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	−0.623259	−	0.782016i	$-0.714192\pi$
$193$	5.07930	−	8.79761i	0.365616	−	0.633266i	0.988875	+	0.148750i	$0.0475249\pi$
$194$	−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	0.860039	−	0.510229i	$-0.170439\pi$
$199$	−0.167186	−	0.289574i	−0.0118515	−	0.0205274i	−0.871890	+	0.489701i	$0.837106\pi$
$200$	−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	−0.898817	−	0.438324i	$-0.855572\pi$
$211$	−1.01404	+	1.75636i	−0.0698092	+	0.120913i	0.829008	+	0.559237i	$0.188906\pi$
$212$	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	−0.340615	−	0.940203i	$-0.610635\pi$
$223$	9.61596	−	16.6553i	0.643932	−	1.11532i	0.984547	−	0.175120i	$-0.0560314\pi$
$224$	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	−0.0431968	+	0.999067i	$0.513754\pi$
$233$	−13.5367	+	23.4462i	−0.886815	+	1.53601i	−0.843619	+	0.536943i	$0.819579\pi$
$234$	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	0.970119	+	0.242631i	$0.0780105\pi$
$241$	10.7922	+	18.6926i	0.695184	+	1.20409i	−0.274934	+	0.961463i	$0.588656\pi$
$242$	−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	0.957623	−	0.288024i	$-0.0929982\pi$
$251$	3.63400	+	6.29426i	0.229376	+	0.397290i	−0.728248	+	0.685314i	$0.759665\pi$
$252$	−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	0.529173	−	0.848514i	$-0.322502\pi$
$257$	−7.53865	−	13.0573i	−0.470248	−	0.814494i	−0.999421	+	0.0340202i	$0.989169\pi$
$258$	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	0.367833	+	0.929892i	$0.380100\pi$
$263$	−10.0773	+	17.4544i	−0.621393	+	1.07628i	−0.989227	+	0.146393i	$0.953234\pi$
$264$	−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	−0.723920	−	0.689884i	$-0.757661\pi$
$269$	3.86245	−	6.68995i	0.235497	−	0.407894i	0.959417	+	0.281991i	$0.0909947\pi$
$270$	−0.816776	−	1.41470i	−0.0497074	−	0.0860957i
$271$	2.64257	−	4.57707i	0.160525	−	0.278037i	−0.774532	−	0.632534i	$-0.782015\pi$
$271$	2.64257	−	4.57707i	0.160525	−	0.278037i	0.935057	+	0.354497i	$0.115348\pi$
$272$	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	0.594981	−	0.803740i	$-0.297159\pi$
$281$	−6.68122	−	11.5722i	−0.398568	−	0.690341i	−0.993550	+	0.113399i	$0.963826\pi$
$282$	8.77457	−	15.1980i	0.522518	−	0.905027i
$283$	−2.04767	+	3.54667i	−0.121721	+	0.210828i	−0.920447	−	0.390868i	$-0.872175\pi$
$283$	−2.04767	+	3.54667i	−0.121721	+	0.210828i	0.798725	+	0.601696i	$0.205508\pi$
$284$	−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	0.268269	+	0.963344i	$0.413548\pi$
$307$	−12.2675	+	21.2480i	−0.700146	+	1.21269i	−0.968415	+	0.249344i	$0.919785\pi$
$308$	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	0.822435	+	0.568859i	$0.192615\pi$
$313$	15.9910	+	27.6972i	0.903864	+	1.56554i	0.0814282	+	0.996679i	$0.474052\pi$
$314$	−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	0.832921	−	0.553392i	$-0.186667\pi$
$317$	−1.11796	−	1.93636i	−0.0627907	−	0.108757i	−0.895712	+	0.444635i	$0.853333\pi$
$318$	−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	−0.932279	−	0.361740i	$-0.882183\pi$
$337$	−2.80620	+	4.86048i	−0.152863	+	0.264767i	0.779416	+	0.626507i	$0.215516\pi$
$338$	−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	−0.930101	−	0.367305i	$-0.880281\pi$
$347$	−2.73747	+	4.74144i	−0.146955	+	0.254534i	0.783146	+	0.621838i	$0.213614\pi$
$348$	−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	−0.681976	−	0.731375i	$-0.738879\pi$
$359$	5.54021	−	9.59592i	0.292401	−	0.506453i	0.974377	+	0.224921i	$0.0722125\pi$
$360$	−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	0.998974	+	0.0452932i	$0.0144222\pi$
$367$	10.3202	+	17.8752i	0.538712	+	0.933076i	−0.460262	+	0.887783i	$0.652244\pi$
$368$	−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	−0.489595	−	0.871950i	$-0.662855\pi$
$383$	9.98742	−	17.2987i	0.510333	−	0.883923i	0.999928	−	0.0119734i	$-0.00381133\pi$
$384$	−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	0.636332	−	0.771416i	$-0.280451\pi$
$389$	−6.90110	−	11.9531i	−0.349900	−	0.606044i	−0.986231	+	0.165372i	$0.947118\pi$
$390$	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	−0.580170	−	0.814495i	$-0.697014\pi$
$397$	8.27457	−	14.3320i	0.415289	−	0.719301i	0.995459	+	0.0951945i	$0.0303473\pi$
$398$	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	−0.952609	−	0.304199i	$-0.901611\pi$
$401$	−4.26253	+	7.38292i	−0.212861	+	0.368685i	0.739748	+	0.672884i	$0.234945\pi$
$402$	−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	0.972841	−	0.231474i	$-0.0743549\pi$
$409$	5.78314	+	10.0167i	0.285958	+	0.495294i	−0.686883	+	0.726768i	$0.741022\pi$
$410$	−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	−0.769266	−	0.638929i	$-0.779378\pi$
$421$	3.46135	−	5.99523i	0.168696	−	0.292190i	0.937962	+	0.346739i	$0.112711\pi$
$422$	−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	0.976805	+	0.214133i	$0.0686926\pi$
$431$	13.9894	+	24.2304i	0.673847	+	1.16714i	−0.302958	+	0.953004i	$0.597974\pi$
$432$	−0.0226132	+	0.0391672i	−0.00108798	+	0.00188443i
$433$	−3.12698	−	5.41608i	−0.150273	−	0.260280i	0.781055	−	0.624462i	$-0.214682\pi$
$433$	−3.12698	−	5.41608i	−0.150273	−	0.260280i	−0.931328	+	0.364182i	$0.881349\pi$
$434$	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	0.205942	+	0.978564i	$0.433974\pi$
$439$	−15.5988	+	27.0179i	−0.744490	+	1.28949i	−0.950433	+	0.310931i	$0.899359\pi$
$440$	−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	0.933720	+	0.358004i	$0.116543\pi$
$443$	16.3519	+	28.3223i	0.776901	+	1.34563i	−0.156819	+	0.987627i	$0.550124\pi$
$444$	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	−0.890247	−	0.455478i	$-0.849468\pi$
$461$	−1.08788	+	1.88426i	−0.0506677	+	0.0877590i	0.839579	+	0.543237i	$0.182802\pi$
$462$	−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	0.907612	+	0.419810i	$0.137903\pi$
$479$	17.8891	+	30.9848i	0.817372	+	1.41573i	−0.0902399	+	0.995920i	$0.528763\pi$
$480$	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	0.0376474	−	0.999291i	$-0.488014\pi$
$491$	19.5933	−	33.9367i	0.884235	−	1.53154i	0.846588	−	0.532249i	$-0.178653\pi$
$492$	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	−0.741800	−	0.670621i	$-0.766028\pi$
$499$	4.68824	−	8.12027i	0.209875	−	0.363513i	0.951675	+	0.307107i	$0.0993611\pi$
$500$	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	0.675509	−	0.737352i	$-0.263924\pi$
$503$	−6.74649	−	11.6853i	−0.300811	−	0.521020i	−0.976320	+	0.216332i	$0.930591\pi$
$504$	−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	−0.996594	−	0.0824703i	$-0.973719\pi$
$509$	−12.8534	−	22.2628i	−0.569718	−	0.986781i	0.426875	−	0.904310i	$-0.359614\pi$
$510$	−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	−0.890255	−	0.455462i	$-0.849474\pi$
$523$	−19.2003	−	33.2559i	−0.839570	−	1.45418i	0.0506855	−	0.998715i	$-0.483859\pi$
$524$	−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	0.970208	−	0.242272i	$-0.0778926\pi$
$541$	6.40310	+	11.0905i	0.275291	+	0.476818i	−0.694918	+	0.719089i	$0.744559\pi$
$542$	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	0.992490	−	0.122326i	$-0.0390352\pi$
$547$	9.12853	+	15.8111i	0.390308	+	0.676033i	−0.602182	+	0.798359i	$0.705702\pi$
$548$	−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	0.663835	−	0.747879i	$-0.268928\pi$
$557$	−7.45233	−	12.9078i	−0.315765	−	0.546922i	−0.979600	+	0.200958i	$0.935595\pi$
$558$	−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	0.0443559	+	0.999016i	$0.485876\pi$
$587$	−20.4242	+	35.3757i	−0.842995	+	1.46011i	−0.887351	+	0.461095i	$0.847457\pi$
$588$	−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	0.974406	−	0.224796i	$-0.0721716\pi$
$593$	7.12342	+	12.3381i	0.292524	+	0.506666i	−0.681882	+	0.731462i	$0.738838\pi$
$594$	−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	0.981276	−	0.192607i	$-0.0616941\pi$
$599$	7.92571	+	13.7277i	0.323836	+	0.560900i	−0.657440	+	0.753507i	$0.728361\pi$
$600$	−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	−0.557740	−	0.830016i	$-0.688331\pi$
$613$	10.8925	−	18.8664i	0.439945	−	0.762007i	0.997685	+	0.0680090i	$0.0216647\pi$
$614$	−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	0.871015	+	0.491256i	$0.163462\pi$
$617$	21.3855	+	37.0408i	0.860948	+	1.49121i	−0.0100671	+	0.999949i	$0.503205\pi$
$618$	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	0.991894	−	0.127071i	$-0.0405576\pi$
$631$	9.69370	+	16.7900i	0.385900	+	0.668399i	−0.605993	+	0.795470i	$0.707224\pi$
$632$	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	0.113779	+	0.993506i	$0.463704\pi$
$641$	−20.3433	+	35.2356i	−0.803512	+	1.39172i	−0.917291	+	0.398217i	$0.869629\pi$
$642$	−6.22343	−	10.7793i	−0.245619	−	0.425425i
$643$	17.0527	−	29.5361i	0.672492	−	1.16479i	−0.304703	−	0.952448i	$-0.598557\pi$
$643$	17.0527	−	29.5361i	0.672492	−	1.16479i	0.977195	−	0.212344i	$-0.0681096\pi$
$644$	−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	0.709952	−	0.704250i	$-0.248717\pi$
$659$	−6.54411	−	11.3347i	−0.254922	−	0.441539i	−0.964874	+	0.262711i	$0.915383\pi$
$660$	18.2023	−	31.5273i	0.708523	−	1.22720i
$661$	11.9714	+	20.7350i	0.465633	+	0.806500i	0.999230	−	0.0392391i	$-0.0124934\pi$
$661$	11.9714	+	20.7350i	0.465633	+	0.806500i	−0.533597	+	0.845739i	$0.679160\pi$
$662$	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	−0.888239	−	0.459381i	$-0.848071\pi$
$701$	−1.22543	+	2.12252i	−0.0462840	+	0.0801663i	0.841955	+	0.539547i	$0.181405\pi$
$702$	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	0.757139	+	0.653254i	$0.226597\pi$
$709$	25.1440	+	43.5507i	0.944304	+	1.63558i	0.187165	+	0.982329i	$0.440070\pi$
$710$	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	0.0654223	−	0.997858i	$-0.479161\pi$
$719$	24.0491	−	41.6543i	0.896881	−	1.55344i	0.831459	−	0.555586i	$-0.187506\pi$
$720$	−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	−0.668904	−	0.743349i	$-0.733236\pi$
$727$	8.33983	−	14.4450i	0.309307	−	0.535736i	0.978211	+	0.207613i	$0.0665695\pi$
$728$	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	0.00407159	+	0.999992i	$0.498704\pi$
$739$	−23.4870	+	40.6806i	−0.863982	+	1.49646i	−0.868054	+	0.496470i	$0.834629\pi$
$740$	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	0.188883	+	0.982000i	$0.439513\pi$
$743$	−20.6069	+	35.6923i	−0.755995	+	1.30942i	−0.944878	+	0.327422i	$0.893820\pi$
$744$	−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	0.806314	−	0.591487i	$-0.201459\pi$
$751$	−2.98942	−	5.17783i	−0.109086	−	0.188942i	−0.915400	+	0.402545i	$0.868126\pi$
$752$	−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	0.318880	+	0.947795i	$0.396693\pi$
$757$	−18.1968	+	31.5178i	−0.661375	+	1.14553i	−0.980255	+	0.197739i	$0.936640\pi$
$758$	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	−0.961950	−	0.273226i	$-0.911909\pi$
$769$	−19.8995	−	34.4670i	−0.717596	−	1.24291i	0.244354	−	0.969686i	$-0.421424\pi$
$770$	−18.0597	−	31.2803i	−0.650827	−	1.12726i
$771$	−37.7991			−1.36130
$772$	−32.7298			−1.17797
$773$	−22.4874

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

Varieties

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Representations

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Database

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