LMFDB - Embedded newform 1295.2.j.a.186.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1295,2,Mod(186,1295)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1295, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1295.186"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1295 = 5 \cdot 7 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1295.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [38] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.3406270618$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			186.12
Character	$\chi$	$=$	1295.186
Dual form			1295.2.j.a.926.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.357733 + 0.619611i) q^{2} +(0.00692605 - 0.0119963i) q^{3} +(0.744055 - 1.28874i) q^{4} +(-0.500000 - 0.866025i) q^{5} +0.00991070 q^{6} +(2.33024 - 1.25300i) q^{7} +2.49562 q^{8} +(1.49990 + 2.59791i) q^{9} +(0.357733 - 0.619611i) q^{10} +(-0.105422 + 0.182597i) q^{11} +(-0.0103067 - 0.0178518i) q^{12} +3.95119 q^{13} +(1.60997 + 0.995602i) q^{14} -0.0138521 q^{15} +(-0.595343 - 1.03117i) q^{16} +(-2.63704 + 4.56750i) q^{17} +(-1.07313 + 1.85872i) q^{18} +(0.483442 + 0.837346i) q^{19} -1.48811 q^{20} +(0.00110802 - 0.0366324i) q^{21} -0.150852 q^{22} +(0.367314 + 0.636207i) q^{23} +(0.0172848 - 0.0299381i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.41347 + 2.44820i) q^{26} +0.0831099 q^{27} +(0.119033 - 3.93537i) q^{28} +2.81857 q^{29} +(-0.00495535 - 0.00858292i) q^{30} +(3.55482 - 6.15713i) q^{31} +(2.92157 - 5.06031i) q^{32} +(0.00146032 + 0.00252935i) q^{33} -3.77343 q^{34} +(-2.25025 - 1.39154i) q^{35} +4.46404 q^{36} +(-0.500000 - 0.866025i) q^{37} +(-0.345886 + 0.599092i) q^{38} +(0.0273661 - 0.0473995i) q^{39} +(-1.24781 - 2.16127i) q^{40} -12.7537 q^{41} +(0.0230943 - 0.0124181i) q^{42} -3.80868 q^{43} +(0.156880 + 0.271724i) q^{44} +(1.49990 - 2.59791i) q^{45} +(-0.262801 + 0.455184i) q^{46} +(3.83255 + 6.63817i) q^{47} -0.0164935 q^{48} +(3.85999 - 5.83956i) q^{49} -0.715466 q^{50} +(0.0365286 + 0.0632694i) q^{51} +(2.93990 - 5.09205i) q^{52} +(3.78478 - 6.55543i) q^{53} +(0.0297311 + 0.0514958i) q^{54} +0.210845 q^{55} +(5.81539 - 3.12701i) q^{56} +0.0133934 q^{57} +(1.00830 + 1.74642i) q^{58} +(-0.959792 + 1.66241i) q^{59} +(-0.0103067 + 0.0178518i) q^{60} +(2.61415 + 4.52783i) q^{61} +5.08670 q^{62} +(6.75031 + 4.17436i) q^{63} +1.79919 q^{64} +(-1.97559 - 3.42183i) q^{65} +(-0.00104481 + 0.00180966i) q^{66} +(3.97468 - 6.88435i) q^{67} +(3.92421 + 6.79693i) q^{68} +0.0101761 q^{69} +(0.0572297 - 1.89208i) q^{70} +15.8240 q^{71} +(3.74319 + 6.48340i) q^{72} +(0.912840 - 1.58109i) q^{73} +(0.357733 - 0.619611i) q^{74} +(0.00692605 + 0.0119963i) q^{75} +1.43883 q^{76} +(-0.0168653 + 0.557587i) q^{77} +0.0391590 q^{78} +(-2.13301 - 3.69448i) q^{79} +(-0.595343 + 1.03117i) q^{80} +(-4.49914 + 7.79273i) q^{81} +(-4.56243 - 7.90236i) q^{82} -7.59105 q^{83} +(-0.0463853 - 0.0286845i) q^{84} +5.27409 q^{85} +(-1.36249 - 2.35990i) q^{86} +(0.0195216 - 0.0338124i) q^{87} +(-0.263094 + 0.455692i) q^{88} +(-8.23461 - 14.2628i) q^{89} +2.14626 q^{90} +(9.20719 - 4.95083i) q^{91} +1.09321 q^{92} +(-0.0492417 - 0.0852892i) q^{93} +(-2.74205 + 4.74938i) q^{94} +(0.483442 - 0.837346i) q^{95} +(-0.0404699 - 0.0700959i) q^{96} -4.84852 q^{97} +(4.99910 + 0.302693i) q^{98} -0.632493 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 3 q^{2} + q^{3} - 11 q^{4} - 19 q^{5} - 8 q^{6} - 18 q^{8} - 12 q^{9} + 3 q^{10} + 13 q^{11} + 4 q^{12} - 6 q^{13} - q^{14} - 2 q^{15} + 5 q^{16} + 2 q^{17} + 11 q^{18} + 12 q^{19} + 22 q^{20}+ \cdots - 142 q^{99}+O(q^{100}) $ 38 * q + 3 * q^2 + q^3 - 11 * q^4 - 19 * q^5 - 8 * q^6 - 18 * q^8 - 12 * q^9 + 3 * q^10 + 13 * q^11 + 4 * q^12 - 6 * q^13 - q^14 - 2 * q^15 + 5 * q^16 + 2 * q^17 + 11 * q^18 + 12 * q^19 + 22 * q^20 - 8 * q^21 - 20 * q^22 + 16 * q^23 - 15 * q^24 - 19 * q^25 + 3 * q^26 - 14 * q^27 + 27 * q^28 - 2 * q^29 + 4 * q^30 + 8 * q^31 + 16 * q^32 + 2 * q^33 - 28 * q^34 + 10 * q^36 - 19 * q^37 - 2 * q^38 + 45 * q^39 + 9 * q^40 - 36 * q^41 + 29 * q^42 - 74 * q^43 - q^44 - 12 * q^45 + 29 * q^46 - 2 * q^47 - 70 * q^48 + 6 * q^49 - 6 * q^50 + 43 * q^51 - 40 * q^52 + 10 * q^53 + 38 * q^54 - 26 * q^55 + 21 * q^56 + 24 * q^57 + 13 * q^58 + 28 * q^59 + 4 * q^60 - 22 * q^61 - 20 * q^62 - 27 * q^63 - 14 * q^64 + 3 * q^65 - 34 * q^66 + 61 * q^67 + 17 * q^68 - 40 * q^69 + 5 * q^70 - 34 * q^71 - 17 * q^72 - 16 * q^73 + 3 * q^74 + q^75 - 90 * q^76 + 5 * q^77 + 106 * q^78 + 63 * q^79 + 5 * q^80 + 5 * q^81 - 37 * q^82 - 48 * q^83 + 40 * q^84 - 4 * q^85 + 19 * q^86 - 32 * q^87 + 58 * q^88 + 16 * q^89 - 22 * q^90 - 11 * q^91 + 14 * q^92 + 31 * q^93 + 12 * q^95 - 40 * q^96 - 48 * q^97 + 66 * q^98 - 142 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1295\mathbb{Z}\right)^\times$.

$n$	$556$	$631$	$1037$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.357733	+	0.619611i	0.252955	+	0.438131i	0.964338	−	0.264673i	$-0.0852641\pi$
$2$	0.357733	+	0.619611i	0.252955	+	0.438131i	−0.711383	+	0.702805i	$0.751931\pi$
$3$	0.00692605	−	0.0119963i	0.00399876	−	0.00692605i	−0.864019	−	0.503459i	$-0.832060\pi$
$3$	0.00692605	−	0.0119963i	0.00399876	−	0.00692605i	0.868018	+	0.496533i	$0.165394\pi$
$4$	0.744055	−	1.28874i	0.372027	−	0.644370i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	0.00991070			0.00404603
$7$	2.33024	−	1.25300i	0.880746	−	0.473589i
$7$	2.33024	−	1.25300i	0.880746	−	0.473589i
$8$	2.49562			0.882336
$9$	1.49990	+	2.59791i	0.499968	+	0.865970i
$10$	0.357733	−	0.619611i	0.113125	−	0.195938i
$11$	−0.105422	+	0.182597i	−0.0317860	+	0.0550550i	−0.881481	−	0.472220i	$-0.843453\pi$
$11$	−0.105422	+	0.182597i	−0.0317860	+	0.0550550i	0.849695	+	0.527275i	$0.176786\pi$
$12$	−0.0103067	−	0.0178518i	−0.00297529	−	0.00515336i
$13$	3.95119			1.09586			0.547931	−	0.836524i	$-0.315416\pi$
$13$	3.95119			1.09586			0.547931	+	0.836524i	$0.315416\pi$
$14$	1.60997	+	0.995602i	0.430283	+	0.266086i
$15$	−0.0138521			−0.00357660
$16$	−0.595343	−	1.03117i	−0.148836	−	0.257791i
$17$	−2.63704	+	4.56750i	−0.639577	+	1.10778i	0.345948	+	0.938254i	$0.387557\pi$
$17$	−2.63704	+	4.56750i	−0.639577	+	1.10778i	−0.985526	+	0.169527i	$0.945776\pi$
$18$	−1.07313	+	1.85872i	−0.252939	+	0.438103i
$19$	0.483442	+	0.837346i	0.110909	+	0.192100i	0.916137	−	0.400865i	$-0.131290\pi$
$19$	0.483442	+	0.837346i	0.110909	+	0.192100i	−0.805228	+	0.592965i	$0.797957\pi$
$20$	−1.48811			−0.332751
$21$	0.00110802	−	0.0366324i	0.000241790	−	0.00799386i
$22$	−0.150852			−0.0321618
$23$	0.367314	+	0.636207i	0.0765903	+	0.132658i	0.901777	−	0.432202i	$-0.142263\pi$
$23$	0.367314	+	0.636207i	0.0765903	+	0.132658i	−0.825186	+	0.564860i	$0.808930\pi$
$24$	0.0172848	−	0.0299381i	0.00352824	−	0.00611110i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.41347	+	2.44820i	0.277204	+	0.480132i
$27$	0.0831099			0.0159945
$28$	0.119033	−	3.93537i	0.0224951	−	0.743714i
$29$	2.81857			0.523396			0.261698	−	0.965150i	$-0.415718\pi$
$29$	2.81857			0.523396			0.261698	+	0.965150i	$0.415718\pi$
$30$	−0.00495535	−	0.00858292i	−0.000904719	−	0.00156702i
$31$	3.55482	−	6.15713i	0.638465	−	1.10585i	−0.347305	−	0.937752i	$-0.612903\pi$
$31$	3.55482	−	6.15713i	0.638465	−	1.10585i	0.985770	−	0.168101i	$-0.0537635\pi$
$32$	2.92157	−	5.06031i	0.516465	−	0.894544i
$33$	0.00146032	+	0.00252935i	0.000254209	+	0.000440303i
$34$	−3.77343			−0.647138
$35$	−2.25025	−	1.39154i	−0.380361	−	0.235214i
$36$	4.46404			0.744007
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i
$38$	−0.345886	+	0.599092i	−0.0561101	+	0.0971856i
$39$	0.0273661	−	0.0473995i	0.00438208	−	0.00758999i
$40$	−1.24781	−	2.16127i	−0.197296	−	0.341727i
$41$	−12.7537			−1.99180			−0.995899	−	0.0904715i	$-0.971163\pi$
$41$	−12.7537			−1.99180			−0.995899	+	0.0904715i	$0.971163\pi$
$42$	0.0230943	−	0.0124181i	0.00356352	−	0.00191615i
$43$	−3.80868			−0.580818			−0.290409	−	0.956903i	$-0.593791\pi$
$43$	−3.80868			−0.580818			−0.290409	+	0.956903i	$0.593791\pi$
$44$	0.156880	+	0.271724i	0.0236505	+	0.0409639i
$45$	1.49990	−	2.59791i	0.223592	−	0.387274i
$46$	−0.262801	+	0.455184i	−0.0387478	+	0.0671132i
$47$	3.83255	+	6.63817i	0.559034	+	0.968276i	0.997577	+	0.0695657i	$0.0221614\pi$
$47$	3.83255	+	6.63817i	0.559034	+	0.968276i	−0.438543	+	0.898710i	$0.644505\pi$
$48$	−0.0164935			−0.00238063
$49$	3.85999	−	5.83956i	0.551427	−	0.834223i
$50$	−0.715466			−0.101182
$51$	0.0365286	+	0.0632694i	0.00511503	+	0.00885949i
$52$	2.93990	−	5.09205i	0.407691	−	0.706141i
$53$	3.78478	−	6.55543i	0.519879	−	0.900457i	−0.479854	−	0.877348i	$-0.659310\pi$
$53$	3.78478	−	6.55543i	0.519879	−	0.900457i	0.999733	−	0.0231086i	$-0.00735637\pi$
$54$	0.0297311	+	0.0514958i	0.00404590	+	0.00700770i
$55$	0.210845			0.0284303
$56$	5.81539	−	3.12701i	0.777114	−	0.417864i
$57$	0.0133934			0.00177400
$58$	1.00830	+	1.74642i	0.132396	+	0.229316i
$59$	−0.959792	+	1.66241i	−0.124954	+	0.216427i	−0.921715	−	0.387868i	$-0.873212\pi$
$59$	−0.959792	+	1.66241i	−0.124954	+	0.216427i	0.796761	+	0.604295i	$0.206545\pi$
$60$	−0.0103067	+	0.0178518i	−0.00133059	+	0.00230465i
$61$	2.61415	+	4.52783i	0.334707	+	0.579730i	0.983429	−	0.181296i	$-0.0580293\pi$
$61$	2.61415	+	4.52783i	0.334707	+	0.579730i	−0.648721	+	0.761026i	$0.724696\pi$
$62$	5.08670			0.646012
$63$	6.75031	+	4.17436i	0.850459	+	0.525921i
$64$	1.79919			0.224899
$65$	−1.97559	−	3.42183i	−0.245042	−	0.424426i
$66$	−0.00104481	+	0.00180966i	−0.000128607	+	0.000222754i
$67$	3.97468	−	6.88435i	0.485585	−	0.841058i	−0.514278	−	0.857624i	$-0.671940\pi$
$67$	3.97468	−	6.88435i	0.485585	−	0.841058i	0.999863	+	0.0165659i	$0.00527334\pi$
$68$	3.92421	+	6.79693i	0.475880	+	0.824249i
$69$	0.0101761			0.00122506
$70$	0.0572297	−	1.89208i	0.00684026	−	0.226147i
$71$	15.8240			1.87796			0.938981	−	0.343968i	$-0.111771\pi$
$71$	15.8240			1.87796			0.938981	+	0.343968i	$0.111771\pi$
$72$	3.74319	+	6.48340i	0.441140	+	0.764076i
$73$	0.912840	−	1.58109i	0.106840	−	0.185052i	−0.807649	−	0.589664i	$-0.799260\pi$
$73$	0.912840	−	1.58109i	0.106840	−	0.185052i	0.914488	+	0.404612i	$0.132593\pi$
$74$	0.357733	−	0.619611i	0.0415856	−	0.0720284i
$75$	0.00692605	+	0.0119963i	0.000799751	+	0.00138521i
$76$	1.43883			0.165045
$77$	−0.0168653	+	0.557587i	−0.00192198	+	0.0635430i
$78$	0.0391590			0.00443389
$79$	−2.13301	−	3.69448i	−0.239982	−	0.415661i	0.720727	−	0.693219i	$-0.243808\pi$
$79$	−2.13301	−	3.69448i	−0.239982	−	0.415661i	−0.960709	+	0.277558i	$0.910475\pi$
$80$	−0.595343	+	1.03117i	−0.0665614	+	0.115288i
$81$	−4.49914	+	7.79273i	−0.499904	+	0.865859i
$82$	−4.56243	−	7.90236i	−0.503836	−	0.872669i
$83$	−7.59105			−0.833226			−0.416613	−	0.909084i	$-0.636783\pi$
$83$	−7.59105			−0.833226			−0.416613	+	0.909084i	$0.636783\pi$
$84$	−0.0463853	−	0.0286845i	−0.00506105	−	0.00312973i
$85$	5.27409			0.572055
$86$	−1.36249	−	2.35990i	−0.146921	−	0.254474i
$87$	0.0195216	−	0.0338124i	0.00209293	−	0.00362507i
$88$	−0.263094	+	0.455692i	−0.0280459	+	0.0485770i
$89$	−8.23461	−	14.2628i	−0.872867	−	1.51185i	−0.859017	−	0.511947i	$-0.828925\pi$
$89$	−8.23461	−	14.2628i	−0.872867	−	1.51185i	−0.0138500	−	0.999904i	$-0.504409\pi$
$90$	2.14626			0.226236
$91$	9.20719	−	4.95083i	0.965176	−	0.518988i
$92$	1.09321			0.113975
$93$	−0.0492417	−	0.0852892i	−0.00510613	−	0.00884407i
$94$	−2.74205	+	4.74938i	−0.282821	+	0.489861i
$95$	0.483442	−	0.837346i	0.0496001	−	0.0859099i
$96$	−0.0404699	−	0.0700959i	−0.00413044	−	0.00715413i
$97$	−4.84852			−0.492293			−0.246146	−	0.969233i	$-0.579164\pi$
$97$	−4.84852			−0.492293			−0.246146	+	0.969233i	$0.579164\pi$
$98$	4.99910	+	0.302693i	0.504986	+	0.0305766i
$99$	−0.632493			−0.0635679
$100$	0.744055	+	1.28874i	0.0744055	+	0.128874i
$101$	−8.22121	+	14.2395i	−0.818041	+	1.41689i	0.0890831	+	0.996024i	$0.471606\pi$
$101$	−8.22121	+	14.2395i	−0.818041	+	1.41689i	−0.907124	+	0.420864i	$0.861727\pi$
$102$	−0.0261350	+	0.0452671i	−0.00258775	+	0.00448211i
$103$	−8.03850	−	13.9231i	−0.792057	−	1.37188i	−0.924691	−	0.380718i	$-0.875677\pi$
$103$	−8.03850	−	13.9231i	−0.792057	−	1.37188i	0.132634	−	0.991165i	$-0.457657\pi$
$104$	9.86067			0.966918
$105$	−0.0322786	+	0.0173566i	−0.00315007	+	0.00169384i
$106$	5.41576			0.526025
$107$	−0.579632	−	1.00395i	−0.0560352	−	0.0970558i	0.836647	−	0.547742i	$-0.184513\pi$
$107$	−0.579632	−	1.00395i	−0.0560352	−	0.0970558i	−0.892682	+	0.450687i	$0.851179\pi$
$108$	0.0618383	−	0.107107i	0.00595039	−	0.0103064i
$109$	−8.28363	+	14.3477i	−0.793427	+	1.37426i	0.130406	+	0.991461i	$0.458372\pi$
$109$	−8.28363	+	14.3477i	−0.793427	+	1.37426i	−0.923833	+	0.382796i	$0.874961\pi$
$110$	0.0754260	+	0.130642i	0.00719159	+	0.0124562i
$111$	−0.0138521			−0.00131478
$112$	−2.67934	−	1.65689i	−0.253174	−	0.156562i
$113$	−7.74884			−0.728949			−0.364475	−	0.931213i	$-0.618751\pi$
$113$	−7.74884			−0.728949			−0.364475	+	0.931213i	$0.618751\pi$
$114$	0.00479125	+	0.00829869i	0.000448742	+	0.000777243i
$115$	0.367314	−	0.636207i	0.0342522	−	0.0593266i
$116$	2.09717	−	3.63241i	0.194718	−	0.337261i
$117$	5.92640	+	10.2648i	0.547896	+	0.948984i
$118$	−1.37340			−0.126431
$119$	−0.421872	+	13.9476i	−0.0386729	+	1.27857i
$120$	−0.0345696			−0.00315576
$121$	5.47777	+	9.48778i	0.497979	+	0.862525i
$122$	−1.87033	+	3.23951i	−0.169332	+	0.293291i
$123$	−0.0883330	+	0.152997i	−0.00796471	+	0.0137953i
$124$	−5.28996	−	9.16248i	−0.475053	−	0.822815i
$125$	1.00000			0.0894427
$126$	−0.171678	+	5.67587i	−0.0152943	+	0.505647i
$127$	13.0860			1.16119			0.580597	−	0.814191i	$-0.302819\pi$
$127$	13.0860			1.16119			0.580597	+	0.814191i	$0.302819\pi$
$128$	−5.19951	−	9.00581i	−0.459576	−	0.796009i
$129$	−0.0263791	+	0.0456899i	−0.00232255	+	0.00402277i
$130$	1.41347	−	2.44820i	0.123969	−	0.214721i
$131$	10.3459	+	17.9197i	0.903929	+	1.56565i	0.822349	+	0.568984i	$0.192663\pi$
$131$	10.3459	+	17.9197i	0.903929	+	1.56565i	0.0815799	+	0.996667i	$0.474003\pi$
$132$	0.00434623			0.000378291
$133$	2.17573	+	1.34546i	0.188659	+	0.116666i
$134$	5.68750			0.491325
$135$	−0.0415550	−	0.0719753i	−0.00357648	−	0.00619465i
$136$	−6.58107	+	11.3987i	−0.564322	+	0.977434i
$137$	7.91104	−	13.7023i	0.675886	−	1.17067i	−0.300323	−	0.953837i	$-0.597095\pi$
$137$	7.91104	−	13.7023i	0.675886	−	1.17067i	0.976209	−	0.216831i	$-0.0695721\pi$
$138$	0.00364034	+	0.00630525i	0.000309886	+	0.000536739i
$139$	−14.9798			−1.27057			−0.635283	−	0.772279i	$-0.719117\pi$
$139$	−14.9798			−1.27057			−0.635283	+	0.772279i	$0.719117\pi$
$140$	−3.46764	+	1.86460i	−0.293069	+	0.157587i
$141$	0.106178			0.00894177
$142$	5.66076	+	9.80473i	0.475041	+	0.822794i
$143$	−0.416543	+	0.721474i	−0.0348331	+	0.0603327i
$144$	1.78592	−	3.09330i	0.148826	−	0.257775i
$145$	−1.40929	−	2.44096i	−0.117035	−	0.202710i
$146$	1.30621			0.108103
$147$	−0.0433184	−	0.0867506i	−0.00357284	−	0.00715507i
$148$	−1.48811			−0.122322
$149$	1.70855	+	2.95930i	0.139970	+	0.242435i	0.927485	−	0.373860i	$-0.121966\pi$
$149$	1.70855	+	2.95930i	0.139970	+	0.242435i	−0.787515	+	0.616296i	$0.788633\pi$
$150$	−0.00495535	+	0.00858292i	−0.000404603	+	0.000700792i
$151$	2.49223	−	4.31667i	0.202815	−	0.351286i	−0.746619	−	0.665251i	$-0.768324\pi$
$151$	2.49223	−	4.31667i	0.202815	−	0.351286i	0.949434	+	0.313966i	$0.101658\pi$
$152$	1.20649	+	2.08970i	0.0978592	+	0.169497i
$153$	−15.8213			−1.27907
$154$	−0.351521	+	0.189017i	−0.0283263	+	0.0152314i
$155$	−7.10964			−0.571060
$156$	−0.0407238	−	0.0705356i	−0.00326051	−	0.00564737i
$157$	−0.129386	+	0.224103i	−0.0103261	+	0.0178854i	−0.871142	−	0.491031i	$-0.836620\pi$
$157$	−0.129386	+	0.224103i	−0.0103261	+	0.0178854i	0.860816	+	0.508916i	$0.169954\pi$
$158$	1.52609	−	2.64327i	0.121410	−	0.210287i
$159$	−0.0524271	−	0.0908064i	−0.00415774	−	0.00720142i
$160$	−5.84314			−0.461941
$161$	1.65309	+	1.02227i	0.130282	+	0.0805660i
$162$	−6.43795			−0.505813
$163$	0.456938	+	0.791439i	0.0357901	+	0.0619903i	0.883366	−	0.468685i	$-0.155272\pi$
$163$	0.456938	+	0.791439i	0.0357901	+	0.0619903i	−0.847576	+	0.530675i	$0.821939\pi$
$164$	−9.48947	+	16.4362i	−0.741003	+	1.28346i
$165$	0.00146032	−	0.00252935i	0.000113686	−	0.000196909i
$166$	−2.71557	−	4.70350i	−0.210769	−	0.365062i
$167$	−16.0074			−1.23869			−0.619343	−	0.785120i	$-0.712601\pi$
$167$	−16.0074			−1.23869			−0.619343	+	0.785120i	$0.712601\pi$
$168$	0.00276520	−	0.0914207i	0.000213340	−	0.00705326i
$169$	2.61188			0.200914
$170$	1.88671	+	3.26789i	0.144704	+	0.250635i
$171$	−1.45023	+	2.51188i	−0.110902	+	0.192088i
$172$	−2.83386	+	4.90839i	−0.216080	+	0.374262i
$173$	−8.97904	−	15.5522i	−0.682664	−	1.18241i	−0.974165	−	0.225838i	$-0.927488\pi$
$173$	−8.97904	−	15.5522i	−0.682664	−	1.18241i	0.291501	−	0.956570i	$-0.405845\pi$
$174$	0.0279340			0.00211767
$175$	−0.0799895	+	2.64454i	−0.00604664	+	0.199909i
$176$	0.251050			0.0189236
$177$	0.0132951	+	0.0230278i	0.000999323	+	0.00173088i
$178$	5.89158	−	10.2045i	0.441593	−	0.764861i
$179$	−9.85287	+	17.0657i	−0.736438	+	1.27555i	0.217652	+	0.976027i	$0.430160\pi$
$179$	−9.85287	+	17.0657i	−0.736438	+	1.27555i	−0.954090	+	0.299521i	$0.903173\pi$
$180$	−2.23202	−	3.86597i	−0.166365	−	0.288153i
$181$	11.2099			0.833224			0.416612	−	0.909084i	$-0.363217\pi$
$181$	11.2099			0.833224			0.416612	+	0.909084i	$0.363217\pi$
$182$	6.36130	+	3.93381i	0.471531	+	0.291593i
$183$	0.0724228			0.00535365
$184$	0.916677	+	1.58773i	0.0675783	+	0.117049i
$185$	−0.500000	+	0.866025i	−0.0367607	+	0.0636715i
$186$	0.0352308	−	0.0610215i	0.00258324	−	0.00447431i
$187$	−0.556006	−	0.963031i	−0.0406592	−	0.0704238i
$188$	11.4065			0.831904
$189$	0.193666	−	0.104137i	0.0140871	−	0.00757482i
$190$	0.691772			0.0501864
$191$	5.48370	+	9.49804i	0.396786	+	0.687254i	0.993327	−	0.115328i	$-0.0367920\pi$
$191$	5.48370	+	9.49804i	0.396786	+	0.687254i	−0.596541	+	0.802583i	$0.703459\pi$
$192$	0.0124613	−	0.0215836i	0.000899316	−	0.00155766i
$193$	2.80685	−	4.86161i	0.202041	−	0.349946i	−0.747145	−	0.664661i	$-0.768576\pi$
$193$	2.80685	−	4.86161i	0.202041	−	0.349946i	0.949186	+	0.314715i	$0.101909\pi$
$194$	−1.73447	−	3.00420i	−0.124528	−	0.215689i
$195$	−0.0547322			−0.00391946
$196$	−4.65363	−	9.31948i	−0.332402	−	0.665677i
$197$	5.60002			0.398985			0.199492	−	0.979899i	$-0.436071\pi$
$197$	5.60002			0.398985			0.199492	+	0.979899i	$0.436071\pi$
$198$	−0.226263	−	0.391900i	−0.0160798	−	0.0278511i
$199$	−10.1777	+	17.6283i	−0.721478	+	1.24964i	0.238929	+	0.971037i	$0.423204\pi$
$199$	−10.1777	+	17.6283i	−0.721478	+	1.24964i	−0.960407	+	0.278599i	$0.910130\pi$
$200$	−1.24781	+	2.16127i	−0.0882336	+	0.152825i
$201$	−0.0550577	−	0.0953627i	−0.00388347	−	0.00672637i
$202$	−11.7640			−0.827711
$203$	6.56794	−	3.53167i	0.460979	−	0.247874i
$204$	0.108717			0.00761172
$205$	6.37687	+	11.0451i	0.445380	+	0.771420i
$206$	5.75127	−	9.96149i	0.400710	−	0.694050i
$207$	−1.10187	+	1.90850i	−0.0765854	+	0.132650i
$208$	−2.35231	−	4.07433i	−0.163104	−	0.282504i
$209$	−0.203862			−0.0141014
$210$	−0.0223015	−	0.0137912i	−0.00153895	−	0.000951681i
$211$	−19.5963			−1.34907			−0.674533	−	0.738245i	$-0.735655\pi$
$211$	−19.5963			−1.34907			−0.674533	+	0.738245i	$0.735655\pi$
$212$	−5.63216	−	9.75519i	−0.386818	−	0.669989i
$213$	0.109598	−	0.189829i	0.00750951	−	0.0130069i
$214$	0.414707	−	0.718294i	0.0283488	−	0.0491015i
$215$	1.90434	+	3.29841i	0.129875	+	0.224950i
$216$	0.207411			0.0141125
$217$	0.568697	−	18.8017i	0.0386056	−	1.27635i
$218$	−11.8533			−0.802807
$219$	−0.0126447	−	0.0219013i	−0.000854453	−	0.00147996i
$220$	0.156880	−	0.271724i	0.0105768	−	0.0183196i
$221$	−10.4195	+	18.0470i	−0.700888	+	1.21397i
$222$	−0.00495535	−	0.00858292i	−0.000332581	−	0.000576048i
$223$	−5.46542			−0.365992			−0.182996	−	0.983114i	$-0.558579\pi$
$223$	−5.46542			−0.365992			−0.182996	+	0.983114i	$0.558579\pi$
$224$	0.467390	−	15.4524i	0.0312288	−	1.03246i
$225$	−2.99981			−0.199987
$226$	−2.77201	−	4.80127i	−0.184392	−	0.319376i
$227$	5.32962	−	9.23117i	0.353739	−	0.612694i	−0.633162	−	0.774019i	$-0.718243\pi$
$227$	5.32962	−	9.23117i	0.353739	−	0.612694i	0.986901	+	0.161325i	$0.0515767\pi$
$228$	0.00996540	−	0.0172606i	0.000659975	−	0.00114311i
$229$	−3.08276	−	5.33950i	−0.203715	−	0.352844i	0.746008	−	0.665937i	$-0.231968\pi$
$229$	−3.08276	−	5.33950i	−0.203715	−	0.352844i	−0.949722	+	0.313093i	$0.898635\pi$
$230$	0.525601			0.0346571
$231$	0.00657215	+	0.00406420i	0.000432416	+	0.000267405i
$232$	7.03409			0.461811
$233$	−1.33450	−	2.31142i	−0.0874258	−	0.151426i	0.818997	−	0.573798i	$-0.194531\pi$
$233$	−1.33450	−	2.31142i	−0.0874258	−	0.151426i	−0.906422	+	0.422373i	$0.861197\pi$
$234$	−4.24014	+	7.34413i	−0.277186	+	0.480101i
$235$	3.83255	−	6.63817i	0.250008	−	0.433026i
$236$	1.42828	+	2.47385i	0.0929728	+	0.161034i
$237$	−0.0590933			−0.00383852
$238$	−8.79298	+	4.72810i	−0.569964	+	0.306477i
$239$	−19.9547			−1.29076			−0.645382	−	0.763860i	$-0.723302\pi$
$239$	−19.9547			−1.29076			−0.645382	+	0.763860i	$0.723302\pi$
$240$	0.00824675	+	0.0142838i	0.000532326	+	0.000922015i
$241$	12.7434	−	22.0722i	0.820872	−	1.42179i	−0.0841615	−	0.996452i	$-0.526821\pi$
$241$	12.7434	−	22.0722i	0.820872	−	1.42179i	0.905034	−	0.425340i	$-0.139846\pi$
$242$	−3.91916	+	6.78818i	−0.251933	+	0.436361i
$243$	0.186987	+	0.323872i	0.0119952	+	0.0207764i
$244$	7.78027			0.498081
$245$	−6.98720	−	0.423071i	−0.446396	−	0.0270290i
$246$	−0.126398			−0.00805887
$247$	1.91017	+	3.30851i	0.121541	+	0.210516i
$248$	8.87149	−	15.3659i	0.563340	−	0.975734i
$249$	−0.0525760	+	0.0910643i	−0.00333187	+	0.00577096i
$250$	0.357733	+	0.619611i	0.0226250	+	0.0391877i
$251$	−10.1497			−0.640641			−0.320321	−	0.947309i	$-0.603791\pi$
$251$	−10.1497			−0.640641			−0.320321	+	0.947309i	$0.603791\pi$
$252$	10.4023	−	5.59344i	0.655281	−	0.352353i
$253$	−0.154892			−0.00973800
$254$	4.68129	+	8.10823i	0.293730	+	0.508756i
$255$	0.0365286	−	0.0632694i	0.00228751	−	0.00396208i
$256$	5.51926	−	9.55964i	0.344954	−	0.597477i
$257$	6.84235	+	11.8513i	0.426814	+	0.739264i	0.996588	−	0.0825376i	$-0.0263025\pi$
$257$	6.84235	+	11.8513i	0.426814	+	0.739264i	−0.569774	+	0.821802i	$0.692969\pi$
$258$	−0.0377466			−0.00235000
$259$	−2.25025	−	1.39154i	−0.139823	−	0.0864663i
$260$	−5.87980			−0.364650
$261$	4.22759	+	7.32240i	0.261681	+	0.453245i
$262$	−7.40216	+	12.8209i	−0.457307	+	0.792079i
$263$	8.54079	−	14.7931i	0.526648	−	0.912180i	−0.472870	−	0.881132i	$-0.656782\pi$
$263$	8.54079	−	14.7931i	0.526648	−	0.912180i	0.999518	−	0.0310483i	$-0.00988455\pi$
$264$	0.00364440	+	0.00631229i	0.000224298	+	0.000388495i
$265$	−7.56955			−0.464994
$266$	−0.0553345	+	1.82942i	−0.00339278	+	0.112169i
$267$	−0.228133			−0.0139615
$268$	−5.91476	−	10.2447i	−0.361302	−	0.625793i
$269$	3.43277	−	5.94574i	0.209300	−	0.362518i	−0.742194	−	0.670185i	$-0.766215\pi$
$269$	3.43277	−	5.94574i	0.209300	−	0.362518i	0.951494	+	0.307667i	$0.0995482\pi$
$270$	0.0297311	−	0.0514958i	0.00180938	−	0.00313394i
$271$	13.7701	+	23.8506i	0.836476	+	1.44882i	0.892823	+	0.450408i	$0.148722\pi$
$271$	13.7701	+	23.8506i	0.836476	+	1.44882i	−0.0563464	+	0.998411i	$0.517945\pi$
$272$	6.27979			0.380768
$273$	0.00437800	−	0.144742i	0.000264969	−	0.00876016i
$274$	11.3202			0.683875
$275$	−0.105422	−	0.182597i	−0.00635720	−	0.0110110i
$276$	0.00757160	−	0.0131144i	0.000455757	−	0.000789394i
$277$	−10.5776	+	18.3210i	−0.635548	+	1.10080i	0.350851	+	0.936431i	$0.385892\pi$
$277$	−10.5776	+	18.3210i	−0.635548	+	1.10080i	−0.986399	+	0.164370i	$0.947441\pi$
$278$	−5.35875	−	9.28163i	−0.321396	−	0.556675i
$279$	21.3276			1.27685
$280$	−5.61576	−	3.47277i	−0.335606	−	0.207538i
$281$	0.630957			0.0376397			0.0188199	−	0.999823i	$-0.494009\pi$
$281$	0.630957			0.0376397			0.0188199	+	0.999823i	$0.494009\pi$
$282$	0.0379832	+	0.0657889i	0.00226187	+	0.00391767i
$283$	3.21211	−	5.56354i	0.190940	−	0.330718i	−0.754622	−	0.656160i	$-0.772180\pi$
$283$	3.21211	−	5.56354i	0.190940	−	0.330718i	0.945562	+	0.325442i	$0.105513\pi$
$284$	11.7739	−	20.3930i	0.698653	−	1.21010i
$285$	−0.00669669	−	0.0115990i	−0.000396678	−	0.000687066i
$286$	−0.596044			−0.0352448
$287$	−29.7192	+	15.9804i	−1.75427	+	0.943293i
$288$	17.5283			1.03286
$289$	−5.40801	−	9.36695i	−0.318118	−	0.550997i
$290$	1.00830	−	1.74642i	0.0592092	−	0.102553i
$291$	−0.0335811	+	0.0581642i	−0.00196856	+	0.00340964i
$292$	−1.35841	−	2.35283i	−0.0794947	−	0.137689i
$293$	−22.3355			−1.30485			−0.652426	−	0.757852i	$-0.726249\pi$
$293$	−22.3355			−1.30485			−0.652426	+	0.757852i	$0.726249\pi$
$294$	0.0382552	−	0.0578741i	0.00223109	−	0.00337529i
$295$	1.91958			0.111763
$296$	−1.24781	−	2.16127i	−0.0725275	−	0.125621i
$297$	−0.00876164	+	0.0151756i	−0.000508402	+	0.000880578i
$298$	−1.22241	+	2.11728i	−0.0708123	+	0.122651i
$299$	1.45133	+	2.51377i	0.0839324	+	0.145375i
$300$	0.0206134			0.00119012
$301$	−8.87511	+	4.77226i	−0.511553	+	0.275069i
$302$	3.56621			0.205212
$303$	0.113881	+	0.197248i	0.00654229	+	0.0113316i
$304$	0.575628	−	0.997017i	0.0330145	−	0.0571829i
$305$	2.61415	−	4.52783i	0.149686	−	0.259263i
$306$	−5.65978	−	9.80303i	−0.323548	−	0.560402i
$307$	6.05483			0.345568			0.172784	−	0.984960i	$-0.444724\pi$
$307$	6.05483			0.345568			0.172784	+	0.984960i	$0.444724\pi$
$308$	0.706036	+	0.436610i	0.0402301	+	0.0248782i
$309$	−0.222700			−0.0126690
$310$	−2.54335	−	4.40521i	−0.144453	−	0.250199i
$311$	−5.86602	+	10.1603i	−0.332632	+	0.576135i	−0.983027	−	0.183461i	$-0.941270\pi$
$311$	−5.86602	+	10.1603i	−0.332632	+	0.576135i	0.650395	+	0.759596i	$0.274603\pi$
$312$	0.0682955	−	0.118291i	0.00386647	−	0.00669692i
$313$	−1.52595	−	2.64302i	−0.0862518	−	0.149392i	0.819672	−	0.572833i	$-0.194156\pi$
$313$	−1.52595	−	2.64302i	−0.0862518	−	0.149392i	−0.905924	+	0.423440i	$0.860822\pi$
$314$	−0.185142			−0.0104482
$315$	0.239953	−	7.93312i	0.0135198	−	0.446981i
$316$	−6.34830			−0.357120
$317$	11.9936	+	20.7736i	0.673630	+	1.16676i	0.976867	+	0.213846i	$0.0685992\pi$
$317$	11.9936	+	20.7736i	0.673630	+	1.16676i	−0.303237	+	0.952915i	$0.598067\pi$
$318$	0.0375098	−	0.0649689i	0.00210344	−	0.00364327i
$319$	−0.297140	+	0.514662i	−0.0166367	+	0.0288156i
$320$	−0.899595	−	1.55815i	−0.0502889	−	0.0871030i
$321$	−0.0160582			−0.000896284
$322$	−0.0420426	+	1.38997i	−0.00234294	+	0.0774602i
$323$	−5.09943			−0.283740
$324$	6.69521	+	11.5964i	0.371956	+	0.644246i
$325$	−1.97559	+	3.42183i	−0.109586	+	0.189809i
$326$	−0.326923	+	0.566248i	−0.0181066	+	0.0313615i
$327$	0.114746	+	0.198745i	0.00634544	+	0.0109906i
$328$	−31.8285			−1.75743
$329$	17.2483	+	10.6663i	0.950932	+	0.588053i
$330$	0.00208962			0.000115030
$331$	10.1887	+	17.6473i	0.560021	+	0.969985i	0.997494	+	0.0707531i	$0.0225402\pi$
$331$	10.1887	+	17.6473i	0.560021	+	0.969985i	−0.437473	+	0.899232i	$0.644126\pi$
$332$	−5.64816	+	9.78289i	−0.309983	+	0.536906i
$333$	1.49990	−	2.59791i	0.0821942	−	0.142365i
$334$	−5.72636	−	9.91834i	−0.313332	−	0.542707i
$335$	−7.94937			−0.434320
$336$	−0.0384338	+	0.0206663i	−0.00209673	+	0.00112744i
$337$	−27.6151			−1.50429			−0.752146	−	0.658997i	$-0.770981\pi$
$337$	−27.6151			−1.50429			−0.752146	+	0.658997i	$0.770981\pi$
$338$	0.934354	+	1.61835i	0.0508221	+	0.0880265i
$339$	−0.0536688	+	0.0929571i	−0.00291489	+	0.00504874i
$340$	3.92421	−	6.79693i	0.212820	−	0.368615i
$341$	0.749514	+	1.29820i	0.0405885	+	0.0703013i
$342$	−2.07518			−0.112213
$343$	1.67773	−	18.4441i	0.0905890	−	0.995888i
$344$	−9.50501			−0.512476
$345$	−0.00508807	−	0.00881280i	−0.000273933	−	0.000474465i
$346$	6.42419	−	11.1270i	0.345367	−	0.598193i
$347$	−5.42049	+	9.38856i	−0.290987	+	0.504004i	−0.974043	−	0.226361i	$-0.927317\pi$
$347$	−5.42049	+	9.38856i	−0.290987	+	0.504004i	0.683056	+	0.730366i	$0.260650\pi$
$348$	−0.0290502	−	0.0503165i	−0.00155726	−	0.00269725i
$349$	−0.669951			−0.0358617			−0.0179308	−	0.999839i	$-0.505708\pi$
$349$	−0.669951			−0.0358617			−0.0179308	+	0.999839i	$0.505708\pi$
$350$	−1.66720	+	0.896477i	−0.0891157	+	0.0479187i
$351$	0.328383			0.0175278
$352$	0.615997	+	1.06694i	0.0328327	+	0.0568680i
$353$	−17.3231	+	30.0045i	−0.922016	+	1.59698i	−0.125725	+	0.992065i	$0.540126\pi$
$353$	−17.3231	+	30.0045i	−0.922016	+	1.59698i	−0.796291	+	0.604913i	$0.793208\pi$
$354$	−0.00951221	+	0.0164756i	−0.000505568	+	0.000875670i
$355$	−7.91200	−	13.7040i	−0.419925	−	0.727332i
$356$	−24.5080			−1.29892
$357$	0.164397	+	0.101662i	0.00870079	+	0.00538054i
$358$	−14.0988			−0.745143
$359$	−5.63902	−	9.76707i	−0.297616	−	0.515486i	0.677974	−	0.735086i	$-0.262858\pi$
$359$	−5.63902	−	9.76707i	−0.297616	−	0.515486i	−0.975590	+	0.219600i	$0.929525\pi$
$360$	3.74319	−	6.48340i	0.197284	−	0.341705i
$361$	9.03257	−	15.6449i	0.475398	−	0.823414i
$362$	4.01014	+	6.94577i	0.210769	+	0.365062i
$363$	0.151757			0.00796519
$364$	0.470322	−	15.5494i	0.0246516	−	0.815008i
$365$	−1.82568			−0.0955605
$366$	0.0259080	+	0.0448740i	0.00135423	+	0.00234560i
$367$	−5.89093	+	10.2034i	−0.307504	+	0.532613i	−0.977816	−	0.209467i	$-0.932827\pi$
$367$	−5.89093	+	10.2034i	−0.307504	+	0.532613i	0.670312	+	0.742080i	$0.266160\pi$
$368$	0.437356	−	0.757523i	0.0227988	−	0.0394886i
$369$	−19.1294	−	33.1330i	−0.995835	−	1.72484i
$370$	−0.715466			−0.0371953
$371$	0.605485	−	20.0180i	0.0314352	−	1.03928i
$372$	−0.146554			−0.00759848
$373$	−12.4891	−	21.6318i	−0.646663	−	1.12005i	−0.983915	−	0.178638i	$-0.942831\pi$
$373$	−12.4891	−	21.6318i	−0.646663	−	1.12005i	0.337252	−	0.941414i	$-0.390503\pi$
$374$	0.397803	−	0.689016i	0.0205699	−	0.0356282i
$375$	0.00692605	−	0.0119963i	0.000357660	−	0.000619485i
$376$	9.56459	+	16.5664i	0.493256	+	0.854344i
$377$	11.1367			0.573570
$378$	0.133805	+	0.0827444i	0.00688217	+	0.00425591i
$379$	−13.0471			−0.670186			−0.335093	−	0.942185i	$-0.608768\pi$
$379$	−13.0471			−0.670186			−0.335093	+	0.942185i	$0.608768\pi$
$380$	−0.719415	−	1.24606i	−0.0369052	−	0.0639217i
$381$	0.0906343	−	0.156983i	0.00464333	−	0.00804249i
$382$	−3.92340	+	6.79552i	−0.200738	+	0.347689i
$383$	3.68272	+	6.37866i	0.188178	+	0.325935i	0.944643	−	0.328100i	$-0.106408\pi$
$383$	3.68272	+	6.37866i	0.188178	+	0.325935i	−0.756465	+	0.654035i	$0.773075\pi$
$384$	−0.144048			−0.00735093
$385$	0.491317	−	0.264188i	0.0250398	−	0.0134643i
$386$	4.01641			0.204430
$387$	−5.71265	−	9.89460i	−0.290390	−	0.502971i
$388$	−3.60756	+	6.24848i	−0.183146	+	0.317219i
$389$	3.04341	−	5.27134i	0.154307	−	0.267268i	−0.778499	−	0.627645i	$-0.784019\pi$
$389$	3.04341	−	5.27134i	0.154307	−	0.267268i	0.932806	+	0.360378i	$0.117352\pi$
$390$	−0.0195795	−	0.0339127i	−0.000991447	−	0.00171724i
$391$	−3.87450			−0.195942
$392$	9.63308	−	14.5733i	0.486544	−	0.736064i
$393$	0.286626			0.0144584
$394$	2.00331	+	3.46983i	0.100925	+	0.174808i
$395$	−2.13301	+	3.69448i	−0.107323	+	0.185889i
$396$	−0.470609	+	0.815119i	−0.0236490	+	0.0409613i
$397$	−8.31279	−	14.3982i	−0.417207	−	0.722624i	0.578450	−	0.815718i	$-0.303658\pi$
$397$	−8.31279	−	14.3982i	−0.417207	−	0.722624i	−0.995657	+	0.0930938i	$0.970324\pi$
$398$	−14.5636			−0.730007
$399$	0.0312097	−	0.0167819i	0.00156244	−	0.000840144i
$400$	1.19069			0.0595343
$401$	8.47043	+	14.6712i	0.422993	+	0.732646i	0.996231	−	0.0867436i	$-0.0276461\pi$
$401$	8.47043	+	14.6712i	0.422993	+	0.732646i	−0.573238	+	0.819389i	$0.694313\pi$
$402$	0.0393919	−	0.0682287i	0.00196469	−	0.00340294i
$403$	14.0458	−	24.3280i	0.699669	−	1.21186i
$404$	12.2341	+	21.1900i	0.608667	+	1.05424i
$405$	8.99827			0.447128
$406$	4.53783	+	2.80618i	0.225209	+	0.139268i
$407$	0.210845			0.0104512
$408$	0.0911616	+	0.157896i	0.00451317	+	0.00781704i
$409$	−8.84062	+	15.3124i	−0.437140	+	0.757149i	−0.997468	−	0.0711220i	$-0.977342\pi$
$409$	−8.84062	+	15.3124i	−0.437140	+	0.757149i	0.560327	+	0.828271i	$0.310675\pi$
$410$	−4.56243	+	7.90236i	−0.225322	+	0.390270i
$411$	−0.109584	−	0.189806i	−0.00540540	−	0.00936243i
$412$	−23.9243			−1.17867
$413$	−0.153547	+	5.07642i	−0.00755553	+	0.249794i
$414$	−1.57670			−0.0774907
$415$	3.79553	+	6.57404i	0.186315	+	0.322707i
$416$	11.5437	−	19.9942i	0.565975	−	0.980297i
$417$	−0.103751	+	0.179701i	−0.00508068	+	0.00880000i
$418$	−0.0729282	−	0.126315i	−0.00356703	−	0.00617829i
$419$	−2.69275			−0.131550			−0.0657748	−	0.997834i	$-0.520952\pi$
$419$	−2.69275			−0.131550			−0.0657748	+	0.997834i	$0.520952\pi$
$420$	−0.00164886	+	0.0545131i	−8.04560e−5	+	0.00265997i
$421$	−21.4737			−1.04656			−0.523282	−	0.852160i	$-0.675293\pi$
$421$	−21.4737			−1.04656			−0.523282	+	0.852160i	$0.675293\pi$
$422$	−7.01024	−	12.1421i	−0.341253	−	0.591068i
$423$	−11.4969	+	19.9132i	−0.558999	+	0.968214i
$424$	9.44537	−	16.3599i	0.458708	−	0.794505i
$425$	−2.63704	−	4.56750i	−0.127915	−	0.221556i
$426$	0.156827			0.00759829
$427$	11.7649	+	7.27540i	0.569345	+	0.352081i
$428$	−1.72511			−0.0833865
$429$	0.00576999	+	0.00999392i	0.000278578	+	0.000482511i
$430$	−1.36249	+	2.35990i	−0.0657050	+	0.113804i
$431$	−8.16486	+	14.1419i	−0.393287	+	0.681194i	−0.992881	−	0.119111i	$-0.961996\pi$
$431$	−8.16486	+	14.1419i	−0.393287	+	0.681194i	0.599594	+	0.800305i	$0.295329\pi$
$432$	−0.0494789	−	0.0857000i	−0.00238056	−	0.00412325i
$433$	10.3461			0.497201			0.248601	−	0.968606i	$-0.420029\pi$
$433$	10.3461			0.497201			0.248601	+	0.968606i	$0.420029\pi$
$434$	11.8532	−	6.37363i	0.568973	−	0.305944i
$435$	−0.0390432			−0.00187198
$436$	12.3269	+	21.3509i	0.590353	+	1.02252i
$437$	−0.355150	+	0.615138i	−0.0169891	+	0.0294261i
$438$	0.00904688	−	0.0156697i	0.000432277	−	0.000748725i
$439$	6.17518	+	10.6957i	0.294725	+	0.510479i	0.974921	−	0.222551i	$-0.0714385\pi$
$439$	6.17518	+	10.6957i	0.294725	+	0.510479i	−0.680196	+	0.733031i	$0.738105\pi$
$440$	0.526188			0.0250850
$441$	20.9603	+	1.26913i	0.998108	+	0.0604349i
$442$	−14.9095			−0.709174
$443$	10.2818	+	17.8086i	0.488503	+	0.846112i	0.999913	−	0.0132254i	$-0.00420990\pi$
$443$	10.2818	+	17.8086i	0.488503	+	0.846112i	−0.511410	+	0.859337i	$0.670877\pi$
$444$	−0.0103067	+	0.0178518i	−0.000489135	+	0.000847207i
$445$	−8.23461	+	14.2628i	−0.390358	+	0.676120i
$446$	−1.95516	−	3.38644i	−0.0925795	−	0.160352i
$447$	0.0473341			0.00223883
$448$	4.19254	−	2.25438i	0.198079	−	0.106510i
$449$	8.26869			0.390224			0.195112	−	0.980781i	$-0.437493\pi$
$449$	8.26869			0.390224			0.195112	+	0.980781i	$0.437493\pi$
$450$	−1.07313	−	1.85872i	−0.0505878	−	0.0876207i
$451$	1.34453	−	2.32879i	0.0633113	−	0.109658i
$452$	−5.76556	+	9.98624i	−0.271189	+	0.469713i
$453$	−0.0345226	−	0.0597949i	−0.00162201	−	0.00280941i
$454$	7.62632			0.357921
$455$	−8.89114	−	5.49825i	−0.416823	−	0.257762i
$456$	0.0334248			0.00156526
$457$	4.89242	+	8.47392i	0.228858	+	0.396393i	0.957470	−	0.288533i	$-0.0931676\pi$
$457$	4.89242	+	8.47392i	0.228858	+	0.396393i	−0.728612	+	0.684926i	$0.759834\pi$
$458$	2.20561	−	3.82023i	0.103061	−	0.178508i
$459$	−0.219165	+	0.379604i	−0.0102297	+	0.0177184i
$460$	−0.546603	−	0.946745i	−0.0254855	−	0.0441422i
$461$	−2.82065			−0.131371			−0.0656853	−	0.997840i	$-0.520923\pi$
$461$	−2.82065			−0.131371			−0.0656853	+	0.997840i	$0.520923\pi$
$462$	−0.000167147		0.00552608i	−7.77640e−6		0.000257096i
$463$	36.2445			1.68442			0.842211	−	0.539147i	$-0.181253\pi$
$463$	36.2445			1.68442			0.842211	+	0.539147i	$0.181253\pi$
$464$	−1.67802	−	2.90641i	−0.0779001	−	0.134927i
$465$	−0.0492417	+	0.0852892i	−0.00228353	+	0.00395519i
$466$	0.954786	−	1.65374i	0.0442296	−	0.0766079i
$467$	16.2974	+	28.2279i	0.754153	+	1.30623i	0.945794	+	0.324767i	$0.105286\pi$
$467$	16.2974	+	28.2279i	0.754153	+	1.30623i	−0.191641	+	0.981465i	$0.561381\pi$
$468$	17.6383			0.815329
$469$	0.635866	−	21.0224i	0.0293616	−	0.970726i
$470$	5.48411			0.252963
$471$	0.00179227	+	0.00310430i	8.25832e−5	+	0.000143038i
$472$	−2.39528	+	4.14874i	−0.110252	+	0.190961i
$473$	0.401519	−	0.695452i	0.0184619	−	0.0319769i
$474$	−0.0211396	−	0.0366149i	−0.000970974	−	0.00168178i
$475$	−0.966884			−0.0443637
$476$	17.6609	+	10.9214i	0.809485	+	0.500583i
$477$	22.7072			1.03969
$478$	−7.13846	−	12.3642i	−0.326506	−	0.565524i
$479$	5.57842	−	9.66211i	0.254885	−	0.441473i	−0.709980	−	0.704222i	$-0.751296\pi$
$479$	5.57842	−	9.66211i	0.254885	−	0.441473i	0.964864	+	0.262749i	$0.0846292\pi$
$480$	−0.0404699	+	0.0700959i	−0.00184719	+	0.00319942i
$481$	−1.97559	−	3.42183i	−0.0900793	−	0.156022i
$482$	18.2349			0.830576
$483$	0.0237128	−	0.0127507i	0.00107897	−	0.000580176i
$484$	16.3030			0.741048
$485$	2.42426	+	4.19894i	0.110080	+	0.190664i
$486$	−0.133783	+	0.231719i	−0.00606852	+	0.0105110i
$487$	16.9639	−	29.3823i	0.768708	−	1.33144i	−0.169556	−	0.985521i	$-0.554233\pi$
$487$	16.9639	−	29.3823i	0.768708	−	1.33144i	0.938264	−	0.345921i	$-0.112433\pi$
$488$	6.52392	+	11.2998i	0.295324	+	0.511516i
$489$	0.0126591			0.000572464
$490$	−2.23741	−	4.48070i	−0.101076	−	0.202417i
$491$	−0.491585			−0.0221849			−0.0110925	−	0.999938i	$-0.503531\pi$
$491$	−0.491585			−0.0221849			−0.0110925	+	0.999938i	$0.503531\pi$
$492$	0.131449	+	0.227676i	0.00592618	+	0.0102644i
$493$	−7.43270	+	12.8738i	−0.334752	+	0.579808i
$494$	−1.36666	+	2.36713i	−0.0614890	+	0.106502i
$495$	0.316247	+	0.547755i	0.0142142	+	0.0246198i
$496$	−8.46536			−0.380106
$497$	36.8736	−	19.8274i	1.65401	−	0.889382i
$498$	−0.0752326			−0.00337125
$499$	−1.94784	−	3.37377i	−0.0871975	−	0.151030i	0.819128	−	0.573611i	$-0.194458\pi$
$499$	−1.94784	−	3.37377i	−0.0871975	−	0.151030i	−0.906325	+	0.422580i	$0.861124\pi$
$500$	0.744055	−	1.28874i	0.0332751	−	0.0576342i
$501$	−0.110868	+	0.192029i	−0.00495320	+	0.00857920i
$502$	−3.63087	−	6.28885i	−0.162054	−	0.280685i
$503$	−22.8507			−1.01886			−0.509430	−	0.860512i	$-0.670144\pi$
$503$	−22.8507			−1.01886			−0.509430	+	0.860512i	$0.670144\pi$
$504$	16.8462	+	10.4176i	0.750390	+	0.464038i
$505$	16.4424			0.731678
$506$	−0.0554101	−	0.0959730i	−0.00246328	−	0.00426652i
$507$	0.0180900	−	0.0313328i	0.000803404	−	0.00139154i
$508$	9.73670	−	16.8645i	0.431996	−	0.748239i
$509$	−16.4327	−	28.4623i	−0.728367	−	1.26157i	−0.957573	−	0.288191i	$-0.906946\pi$
$509$	−16.4327	−	28.4623i	−0.728367	−	1.26157i	0.229206	−	0.973378i	$-0.426387\pi$
$510$	0.0522699			0.00231455
$511$	0.146035	−	4.82809i	0.00646022	−	0.213582i
$512$	−12.9004			−0.570121
$513$	0.0401788	+	0.0695918i	0.00177394	+	0.00307255i
$514$	−4.89547	+	8.47920i	−0.215930	+	0.374001i
$515$	−8.03850	+	13.9231i	−0.354219	+	0.613525i
$516$	0.0392549	+	0.0679915i	0.00172810	+	0.00299316i
$517$	−1.61614			−0.0710779
$518$	0.0572297	−	1.89208i	0.00251453	−	0.0831332i
$519$	−0.248757			−0.0109192
$520$	−4.93033	−	8.53959i	−0.216209	−	0.374486i
$521$	−8.95418	+	15.5091i	−0.392290	+	0.679466i	−0.992751	−	0.120188i	$-0.961650\pi$
$521$	−8.95418	+	15.5091i	−0.392290	+	0.679466i	0.600461	+	0.799654i	$0.294984\pi$
$522$	−3.02469	+	5.23892i	−0.132387	+	0.229302i
$523$	9.20709	+	15.9471i	0.402598	+	0.697320i	0.994039	−	0.109029i	$-0.0347740\pi$
$523$	9.20709	+	15.9471i	0.402598	+	0.697320i	−0.591441	+	0.806348i	$0.701441\pi$
$524$	30.7918			1.34514
$525$	0.0311706	+	0.0192758i	0.00136040	+	0.000841265i
$526$	12.2213			0.532873
$527$	18.7484	+	32.4733i	0.816695	+	1.41456i
$528$	0.00173878	−	0.00301166i	7.56708e−5	−	0.000131066i
$529$	11.2302	−	19.4512i	0.488268	−	0.845705i
$530$	−2.70788	−	4.69018i	−0.117623	−	0.203728i
$531$	−5.75838			−0.249893
$532$	3.35281	−	1.80285i	0.145363	−	0.0781635i
$533$	−50.3924			−2.18274
$534$	−0.0816108	−	0.141354i	−0.00353164	−	0.00611699i
$535$	−0.579632	+	1.00395i	−0.0250597	+	0.0434047i
$536$	9.91931	−	17.1807i	0.428449	−	0.742095i
$537$	0.136483	+	0.236395i	0.00588967	+	0.0102012i
$538$	4.91206			0.211774
$539$	0.659355	+	1.32044i	0.0284004	+	0.0568754i
$540$	−0.123677			−0.00532219
$541$	8.53819	+	14.7886i	0.367085	+	0.635811i	0.989108	−	0.147188i	$-0.0470224\pi$
$541$	8.53819	+	14.7886i	0.367085	+	0.635811i	−0.622023	+	0.782999i	$0.713689\pi$
$542$	−9.85206	+	17.0643i	−0.423182	+	0.732973i
$543$	0.0776402	−	0.134477i	0.00333186	−	0.00577095i
$544$	15.4086	+	26.6885i	0.660639	+	1.14426i
$545$	16.5673			0.709663
$546$	0.0912497	−	0.0490662i	0.00390513	−	0.00209984i
$547$	−29.9033			−1.27857			−0.639286	−	0.768969i	$-0.720770\pi$
$547$	−29.9033			−1.27857			−0.639286	+	0.768969i	$0.720770\pi$
$548$	−11.7725	−	20.3906i	−0.502896	−	0.871041i
$549$	−7.84193	+	13.5826i	−0.334686	+	0.579692i
$550$	0.0754260	−	0.130642i	0.00321618	−	0.00557058i
$551$	1.36262	+	2.36012i	0.0580494	+	0.100545i
$552$	0.0253958			0.00108092
$553$	−9.59959	−	5.93635i	−0.408216	−	0.252439i
$554$	−15.1359			−0.643061
$555$	0.00692605	+	0.0119963i	0.000293994	+	0.000509213i
$556$	−11.1458	+	19.3050i	−0.472685	+	0.818715i
$557$	21.1997	−	36.7189i	0.898259	−	1.55583i	0.0685399	−	0.997648i	$-0.478166\pi$
$557$	21.1997	−	36.7189i	0.898259	−	1.55583i	0.829719	−	0.558181i	$-0.188501\pi$
$558$	7.62957	+	13.2148i	0.322985	+	0.559427i
$559$	−15.0488			−0.636496
$560$	−0.0952424	+	3.14882i	−0.00402473	+	0.133062i
$561$	−0.0154037			−0.000650345
$562$	0.225714	+	0.390948i	0.00952116	+	0.0164911i
$563$	7.12065	−	12.3333i	0.300100	−	0.519788i	−0.676059	−	0.736848i	$-0.736313\pi$
$563$	7.12065	−	12.3333i	0.300100	−	0.519788i	0.976158	+	0.217060i	$0.0696467\pi$
$564$	0.0790019	−	0.136835i	0.00332658	−	0.00576181i
$565$	3.87442	+	6.71069i	0.162998	+	0.282321i
$566$	4.59631			0.193197
$567$	−0.719767	+	23.7963i	−0.0302274	+	0.999351i
$568$	39.4907			1.65699
$569$	9.51091	+	16.4734i	0.398718	+	0.690600i	0.993568	−	0.113237i	$-0.0361219\pi$
$569$	9.51091	+	16.4734i	0.398718	+	0.690600i	−0.594850	+	0.803837i	$0.702789\pi$
$570$	0.00479125	−	0.00829869i	0.000200683	−	0.000347594i
$571$	−20.8079	+	36.0403i	−0.870781	+	1.50824i	−0.00959173	+	0.999954i	$0.503053\pi$
$571$	−20.8079	+	36.0403i	−0.870781	+	1.50824i	−0.861190	+	0.508284i	$0.830280\pi$
$572$	0.619861	+	1.07363i	0.0259177	+	0.0448908i
$573$	0.151921			0.00634661
$574$	−20.5332	−	12.6976i	−0.857038	−	0.529989i
$575$	−0.734628			−0.0306361
$576$	2.69861	+	4.67414i	0.112442	+	0.194756i
$577$	−8.02041	+	13.8918i	−0.333894	+	0.578321i	−0.983272	−	0.182145i	$-0.941696\pi$
$577$	−8.02041	+	13.8918i	−0.333894	+	0.578321i	0.649378	+	0.760466i	$0.275029\pi$
$578$	3.86925	−	6.70173i	0.160939	−	0.278755i
$579$	−0.0388807	−	0.0673434i	−0.00161583	−	0.00279870i
$580$	−4.19434			−0.174161
$581$	−17.6889	+	9.51157i	−0.733861	+	0.394606i
$582$	−0.0480522			−0.00199183
$583$	0.798000	+	1.38218i	0.0330498	+	0.0572439i
$584$	2.27810	−	3.94579i	0.0942686	−	0.163278i
$585$	5.92640	−	10.2648i	0.245027	−	0.424398i
$586$	−7.99013	−	13.8393i	−0.330069	−	0.571697i
$587$	35.6597			1.47183			0.735916	−	0.677073i	$-0.236752\pi$
$587$	35.6597			1.47183			0.735916	+	0.677073i	$0.236752\pi$
$588$	−0.144030	−	0.00872095i	−0.00593971	−	0.000359646i
$589$	6.87420			0.283246
$590$	0.686698	+	1.18940i	0.0282709	+	0.0489667i
$591$	0.0387860	−	0.0671793i	0.00159544	−	0.00276339i
$592$	−0.595343	+	1.03117i	−0.0244685	+	0.0423806i
$593$	−15.1309	−	26.2075i	−0.621351	−	1.07621i	−0.989234	−	0.146340i	$-0.953251\pi$
$593$	−15.1309	−	26.2075i	−0.621351	−	1.07621i	0.367883	−	0.929872i	$-0.380083\pi$
$594$	−0.0125373			−0.000514412
$595$	12.2899	−	6.60842i	0.503836	−	0.270919i
$596$	5.08503			0.208291
$597$	0.140982	+	0.244189i	0.00577003	+	0.00999398i
$598$	−1.03837	+	1.79852i	−0.0424623	+	0.0735468i
$599$	14.7305	−	25.5140i	0.601872	−	1.04247i	−0.390666	−	0.920533i	$-0.627755\pi$
$599$	14.7305	−	25.5140i	0.601872	−	1.04247i	0.992538	−	0.121940i	$-0.0389115\pi$
$600$	0.0172848	+	0.0299381i	0.000705649	+	0.00122222i
$601$	−6.17362			−0.251827			−0.125914	−	0.992041i	$-0.540186\pi$
$601$	−6.17362			−0.251827			−0.125914	+	0.992041i	$0.540186\pi$
$602$	−6.13187	−	3.79192i	−0.249916	−	0.154547i
$603$	23.8466			0.971108
$604$	−3.70871	−	6.42368i	−0.150905	−	0.261376i
$605$	5.47777	−	9.48778i	0.222703	−	0.385733i
$606$	−0.0814779	+	0.141124i	−0.00330981	+	0.00573277i
$607$	−0.791970	−	1.37173i	−0.0321451	−	0.0556769i	0.849505	−	0.527580i	$-0.176901\pi$
$607$	−0.791970	−	1.37173i	−0.0321451	−	0.0556769i	−0.881650	+	0.471903i	$0.843567\pi$
$608$	5.64964			0.229123
$609$	0.00312304	−	0.103251i	0.000126552	−	0.00418395i
$610$	3.74066			0.151455
$611$	15.1431	+	26.2286i	0.612625	+	1.06110i
$612$	−11.7719	+	20.3895i	−0.475850	+	0.824196i
$613$	−1.37117	+	2.37493i	−0.0553810	+	0.0959226i	−0.892387	−	0.451271i	$-0.850971\pi$
$613$	−1.37117	+	2.37493i	−0.0553810	+	0.0959226i	0.837006	+	0.547194i	$0.184304\pi$
$614$	2.16601	+	3.75164i	0.0874131	+	0.151404i
$615$	0.176666			0.00712386
$616$	−0.0420895	+	1.39153i	−0.00169584	+	0.0560662i
$617$	−20.0279			−0.806294			−0.403147	−	0.915135i	$-0.632084\pi$
$617$	−20.0279			−0.806294			−0.403147	+	0.915135i	$0.632084\pi$
$618$	−0.0796672	−	0.137988i	−0.00320468	−	0.00555067i
$619$	−17.2470	+	29.8727i	−0.693215	+	1.20068i	0.277564	+	0.960707i	$0.410473\pi$
$619$	−17.2470	+	29.8727i	−0.693215	+	1.20068i	−0.970779	+	0.239976i	$0.922860\pi$
$620$	−5.28996	+	9.16248i	−0.212450	+	0.367974i
$621$	0.0305274	+	0.0528751i	0.00122502	+	0.00212180i
$622$	−8.39388			−0.336564
$623$	−37.0598	−	22.9177i	−1.48477	−	0.918176i
$624$	−0.0651689			−0.00260885
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	1.09176	−	1.89099i	0.0436357	−	0.0755792i
$627$	−0.00141196	+	0.00244559i	−5.63882e−5	+	9.76673e-5i
$628$	0.192540	+	0.333490i	0.00768319	+	0.0133077i
$629$	5.27409			0.210292
$630$	5.00129	−	2.68926i	0.199256	−	0.107143i
$631$	33.8314			1.34681			0.673404	−	0.739275i	$-0.264832\pi$
$631$	33.8314			1.34681			0.673404	+	0.739275i	$0.264832\pi$
$632$	−5.32318	−	9.22002i	−0.211745	−	0.366753i
$633$	−0.135725	+	0.235083i	−0.00539458	+	0.00934369i
$634$	−8.58104	+	14.8628i	−0.340797	+	0.590277i
$635$	−6.54300	−	11.3328i	−0.259651	−	0.449729i
$636$	−0.156034			−0.00618717
$637$	15.2515	−	23.0732i	0.604288	−	0.914193i
$638$	−0.425187			−0.0168333
$639$	23.7345	+	41.1093i	0.938921	+	1.62626i
$640$	−5.19951	+	9.00581i	−0.205529	+	0.355986i
$641$	11.9424	−	20.6848i	0.471696	−	0.817001i	−0.527780	−	0.849381i	$-0.676975\pi$
$641$	11.9424	−	20.6848i	0.471696	−	0.817001i	0.999476	+	0.0323801i	$0.0103087\pi$
$642$	−0.00574456	−	0.00994987i	−0.000226720	−	0.000392690i
$643$	−5.59825			−0.220773			−0.110387	−	0.993889i	$-0.535209\pi$
$643$	−5.59825			−0.220773			−0.110387	+	0.993889i	$0.535209\pi$
$644$	2.54743	−	1.36979i	0.100383	−	0.0539771i
$645$	0.0527581			0.00207735
$646$	−1.82423	−	3.15967i	−0.0717736	−	0.124315i
$647$	15.2748	−	26.4568i	0.600515	−	1.04012i	−0.392228	−	0.919868i	$-0.628295\pi$
$647$	15.2748	−	26.4568i	0.600515	−	1.04012i	0.992743	−	0.120255i	$-0.0383712\pi$
$648$	−11.2281	+	19.4477i	−0.441083	+	0.763978i
$649$	−0.202367	−	0.350510i	−0.00794360	−	0.0137587i
$650$	−2.82694			−0.110882
$651$	−0.221612	−	0.137044i	−0.00868566	−	0.00537118i
$652$	1.35995			0.0532596
$653$	10.3089	+	17.8556i	0.403420	+	0.698744i	0.994136	−	0.108135i	$-0.0344880\pi$
$653$	10.3089	+	17.8556i	0.403420	+	0.698744i	−0.590716	+	0.806880i	$0.701155\pi$
$654$	−0.0820965	+	0.142195i	−0.00321023	+	0.00556028i
$655$	10.3459	−	17.9197i	0.404249	−	0.700180i
$656$	7.59285	+	13.1512i	0.296451	+	0.513468i
$657$	5.47669			0.213666
$658$	−0.438671	+	14.5030i	−0.0171012	+	0.565384i
$659$	2.12038			0.0825982			0.0412991	−	0.999147i	$-0.486850\pi$
$659$	2.12038			0.0825982			0.0412991	+	0.999147i	$0.486850\pi$
$660$	−0.00217311	−	0.00376394i	−8.45884e−5	−	0.000146511i
$661$	15.5231	−	26.8868i	0.603779	−	1.04578i	−0.388465	−	0.921464i	$-0.626994\pi$
$661$	15.5231	−	26.8868i	0.603779	−	1.04578i	0.992243	−	0.124312i	$-0.0396722\pi$
$662$	−7.28965	+	12.6261i	−0.283320	+	0.490725i
$663$	0.144331	+	0.249989i	0.00560536	+	0.00970878i
$664$	−18.9444			−0.735185
$665$	0.0773406	−	2.55697i	0.00299914	−	0.0991549i
$666$	2.14626			0.0831659
$667$	1.03530	+	1.79320i	0.0400870	+	0.0694328i
$668$	−11.9103	+	20.6293i	−0.460825	+	0.798173i
$669$	−0.0378538	+	0.0655646i	−0.00146351	+	0.00253488i
$670$	−2.84375	−	4.92552i	−0.109864	−	0.190289i
$671$	−1.10236			−0.0425560
$672$	−0.182134	−	0.112631i	−0.00702598	−	0.00434484i
$673$	−1.94529			−0.0749853			−0.0374926	−	0.999297i	$-0.511937\pi$
$673$	−1.94529			−0.0749853			−0.0374926	+	0.999297i	$0.511937\pi$
$674$	−9.87883	−	17.1106i	−0.380518	−	0.659077i
$675$	−0.0415550	+	0.0719753i	−0.00159945	+	0.00277033i
$676$	1.94338	−	3.36603i	0.0747453	−	0.129463i
$677$	2.16425	+	3.74860i	0.0831790	+	0.144070i	0.904614	−	0.426232i	$-0.140159\pi$
$677$	2.16425	+	3.74860i	0.0831790	+	0.144070i	−0.821435	+	0.570302i	$0.806826\pi$
$678$	−0.0767964			−0.00294935
$679$	−11.2982	+	6.07519i	−0.433585	+	0.233144i
$680$	13.1621			0.504745
$681$	−0.0738264	−	0.127871i	−0.00282903	−	0.00490003i
$682$	−0.536252	+	0.928815i	−0.0205341	+	0.0355662i
$683$	2.24213	−	3.88348i	0.0857927	−	0.148597i	−0.819936	−	0.572455i	$-0.805991\pi$
$683$	2.24213	−	3.88348i	0.0857927	−	0.148597i	0.905729	+	0.423858i	$0.139324\pi$
$684$	2.15811	+	3.73795i	0.0825172	+	0.142924i
$685$	−15.8221			−0.604531
$686$	12.0284	−	5.55852i	0.459245	−	0.212225i
$687$	−0.0854055			−0.00325842
$688$	2.26747	+	3.92737i	0.0864465	+	0.149730i
$689$	14.9544	−	25.9017i	0.569716	−	0.986777i
$690$	0.00364034	−	0.00630525i	0.000138585	−	0.000240037i
$691$	−12.7984	−	22.1675i	−0.486875	−	0.843292i	0.513012	−	0.858382i	$-0.328530\pi$
$691$	−12.7984	−	22.1675i	−0.486875	−	0.843292i	−0.999886	+	0.0150902i	$0.995196\pi$
$692$	−26.7236			−1.01588
$693$	−1.47386	+	0.792513i	−0.0559872	+	0.0301051i
$694$	−7.75635			−0.294427
$695$	7.48988	+	12.9729i	0.284107	+	0.492088i
$696$	0.0487185	−	0.0843829i	0.00184667	−	0.00319852i
$697$	33.6322	−	58.2526i	1.27391	−	2.20647i
$698$	−0.239664	−	0.415110i	−0.00907140	−	0.0157121i
$699$	−0.0369711			−0.00139838
$700$	3.34861	+	2.07077i	0.126566	+	0.0782677i
$701$	−21.7865			−0.822866			−0.411433	−	0.911440i	$-0.634972\pi$
$701$	−21.7865			−0.822866			−0.411433	+	0.911440i	$0.634972\pi$
$702$	0.117473	+	0.203470i	0.00443374	+	0.00767947i
$703$	0.483442	−	0.837346i	0.0182334	−	0.0315811i
$704$	−0.189675	+	0.328526i	−0.00714864	+	0.0123818i
$705$	−0.0530888	−	0.0919525i	−0.00199944	−	0.00346313i
$706$	−24.7882			−0.932915
$707$	−1.31522	+	43.4827i	−0.0494640	+	1.63533i
$708$	0.0395692			0.00148710
$709$	13.2287	+	22.9129i	0.496816	+	0.860511i	0.999993	−	0.00367257i	$-0.00116902\pi$
$709$	13.2287	+	22.9129i	0.496816	+	0.860511i	−0.503177	+	0.864183i	$0.667836\pi$
$710$	5.66076	−	9.80473i	0.212445	−	0.367965i
$711$	6.39862	−	11.0827i	0.239967	−	0.415635i
$712$	−20.5505	−	35.5945i	−0.770162	−	1.33396i
$713$	5.22294			0.195601
$714$	−0.00418104	+	0.138230i	−0.000156472	+	0.00517313i
$715$	0.833086			0.0311557
$716$	14.6621	+	25.3956i	0.547950	+	0.949077i
$717$	−0.138207	+	0.239382i	−0.00516145	+	0.00893989i
$718$	4.03452	−	6.98800i	0.150567	−	0.260790i
$719$	15.4575	+	26.7732i	0.576469	+	0.998473i	0.995880	+	0.0906768i	$0.0289030\pi$
$719$	15.4575	+	26.7732i	0.576469	+	0.998473i	−0.419412	+	0.907796i	$0.637764\pi$
$720$	−3.57183			−0.133114
$721$	−36.1772	−	22.3719i	−1.34731	−	0.833171i
$722$	12.9250			0.481018
$723$	−0.176522	−	0.305746i	−0.00656493	−	0.0113708i
$724$	8.34077	−	14.4466i	0.309982	−	0.536905i
$725$	−1.40929	+	2.44096i	−0.0523396	+	0.0906548i
$726$	0.0542885	+	0.0940305i	0.00201484	+	0.00348980i
$727$	27.4712			1.01885			0.509425	−	0.860515i	$-0.329858\pi$
$727$	27.4712			1.01885			0.509425	+	0.860515i	$0.329858\pi$
$728$	22.9777	−	12.3554i	0.851609	−	0.457921i
$729$	−26.9896			−0.999616
$730$	−0.653106	−	1.13121i	−0.0241725	−	0.0418680i
$731$	10.0436	−	17.3961i	0.371478	−	0.643418i
$732$	0.0538865	−	0.0933342i	0.00199170	−	0.00344973i
$733$	−12.2834	−	21.2755i	−0.453699	−	0.785830i	0.544913	−	0.838493i	$-0.316563\pi$
$733$	−12.2834	−	21.2755i	−0.453699	−	0.785830i	−0.998612	+	0.0526622i	$0.983229\pi$
$734$	−8.42952			−0.311139
$735$	−0.0534690	+	0.0808902i	−0.00197223	+	0.00298368i
$736$	4.29253			0.158225
$737$	0.838040	+	1.45153i	0.0308696	+	0.0534677i
$738$	13.6864	−	23.7056i	0.503804	−	0.872613i
$739$	−5.33188	+	9.23509i	−0.196136	+	0.339718i	−0.947272	−	0.320429i	$-0.896173\pi$
$739$	−5.33188	+	9.23509i	−0.196136	+	0.339718i	0.751136	+	0.660147i	$0.229506\pi$
$740$	0.744055	+	1.28874i	0.0273520	+	0.0473750i
$741$	0.0529197			0.00194405
$742$	12.6200	−	6.78593i	0.463294	−	0.249119i
$743$	12.9938			0.476696			0.238348	−	0.971180i	$-0.423394\pi$
$743$	12.9938			0.476696			0.238348	+	0.971180i	$0.423394\pi$
$744$	−0.122889	−	0.212849i	−0.00450532	−	0.00780344i
$745$	1.70855	−	2.95930i	0.0625965	−	0.108420i
$746$	8.93554	−	15.4768i	0.327153	−	0.566646i
$747$	−11.3858	−	19.7209i	−0.416586	−	0.721549i
$748$	−1.65480			−0.0605054
$749$	−2.60863	−	1.61317i	−0.0953173	−	0.0589439i
$750$	0.00991070			0.000361888
$751$	4.81675	+	8.34285i	0.175766	+	0.304435i	0.940426	−	0.339999i	$-0.110427\pi$
$751$	4.81675	+	8.34285i	0.175766	+	0.304435i	−0.764660	+	0.644434i	$0.777093\pi$
$752$	4.56336	−	7.90398i	0.166409	−	0.288228i
$753$	−0.0702971	+	0.121758i	−0.00256177	+	0.00443711i
$754$	3.98397	+	6.90043i	0.145087	+	0.251299i
$755$	−4.98446			−0.181403
$756$	0.00989283	−	0.327068i	0.000359799	−	0.0118953i
$757$	40.5703			1.47455			0.737276	−	0.675591i	$-0.236112\pi$
$757$	40.5703			1.47455			0.737276	+	0.675591i	$0.236112\pi$
$758$	−4.66739	−	8.08415i	−0.169527	−	0.293630i
$759$	−0.00107279	+	0.00185813i	−3.89399e−5	+	6.74458e-5i
$760$	1.20649	−	2.08970i	0.0437639	−	0.0758014i
$761$	0.0297730	+	0.0515683i	0.00107927	+	0.00186935i	0.866565	−	0.499065i	$-0.166323\pi$
$761$	0.0297730	+	0.0515683i	0.00107927	+	0.00186935i	−0.865485	+	0.500934i	$0.832990\pi$
$762$	0.129691			0.00469822
$763$	−1.32521	+	43.8128i	−0.0479757	+	1.58613i
$764$	16.3207			0.590462
$765$	7.91063	+	13.7016i	0.286009	+	0.495383i
$766$	−2.63486	+	4.56371i	−0.0952014	+	0.164894i
$767$	−3.79232	+	6.56849i	−0.136933	+	0.237174i
$768$	−0.0764533	−	0.132421i	−0.00275877	−	0.00477833i
$769$	47.2742			1.70475			0.852376	−	0.522930i	$-0.175161\pi$
$769$	47.2742			1.70475			0.852376	+	0.522930i	$0.175161\pi$
$770$	0.339454	+	0.209917i	0.0122331	+	0.00756489i
$771$	0.189562			0.00682690
$772$	−4.17690	−	7.23460i	−0.150330	−	0.260379i
$773$	−14.8494	+	25.7199i	−0.534095	+	0.925079i	0.465112	+	0.885252i	$0.346014\pi$
$773$	−14.8494	+	25.7199i	−0.534095	+	0.925079i	−0.999207	+	0.0398272i	$0.987319\pi$
$774$	4.08720	−	7.07924i	0.146911	−	0.254458i
$775$	3.55482	+	6.15713i	0.127693	+	0.221171i
$776$	−12.1001			−0.434367
$777$	−0.0322786	+	0.0173566i	−0.00115799	+	0.000622666i
$778$	4.35491			0.156131
$779$	−6.16569	−	10.6793i	−0.220909	−	0.382625i
$780$	−0.0407238	+	0.0705356i	−0.00145814	+	0.00252558i
$781$	−1.66820	+	2.88941i	−0.0596929	+	0.103391i
$782$	−1.38603	−	2.40068i	−0.0495645	−	0.0858482i
$783$	0.234251			0.00837146
$784$	−8.31957	−	0.503745i	−0.297128	−	0.0179909i
$785$	0.258772			0.00923596
$786$	0.102535	+	0.177597i	0.00365732	+	0.00633466i
$787$	22.9297	−	39.7153i	0.817354	−	1.41570i	−0.0902709	−	0.995917i	$-0.528773\pi$
$787$	22.9297	−	39.7153i	0.817354	−	1.41570i	0.907625	−	0.419782i	$-0.137893\pi$
$788$	4.16672	−	7.21697i	0.148433	−	0.257094i
$789$	−0.118308	−	0.204915i	−0.00421187	−	0.00729517i
$790$	−3.05219			−0.108592
$791$	−18.0566	+	9.70928i	−0.642019	+	0.345222i
$792$	−1.57846			−0.0560883
$793$	10.3290	+	17.8903i	0.366793	+	0.635304i
$794$	5.94752	−	10.3014i	0.211069	−	0.365583i
$795$	−0.0524271	+	0.0908064i	−0.00185940	+	0.00322057i
$796$	15.1455	+	26.2328i	0.536819	+	0.929798i
$797$	−13.2190			−0.468243			−0.234121	−	0.972207i	$-0.575221\pi$
$797$	−13.2190			−0.468243			−0.234121	+	0.972207i	$0.575221\pi$
$798$	0.0215630	+	0.0133345i	0.000763321	+	0.000472035i
$799$	−40.4264			−1.43018
$800$	2.92157	+	5.06031i	0.103293	+	0.178909i
$801$	24.7023	−	42.7856i	0.872812	−	1.51175i
$802$	−6.06030	+	10.4968i	−0.213997	+	0.370653i
$803$	0.192467	+	0.333363i	0.00679202	+	0.0117641i
$804$	−0.163864			−0.00577903
$805$	0.0587625	−	1.94276i	0.00207111	−	0.0684731i
$806$	20.0985			0.707940
$807$	−0.0475511	−	0.0823609i	−0.00167388	−	0.00289924i
$808$	−20.5170	+	35.5365i	−0.721786	+	1.25017i
$809$	6.02150	−	10.4295i	0.211705	−	0.366683i	−0.740544	−	0.672008i	$-0.765432\pi$
$809$	6.02150	−	10.4295i	0.211705	−	0.366683i	0.952248	+	0.305325i	$0.0987652\pi$
$810$	3.21898	+	5.57543i	0.113103	+	0.195901i
$811$	−10.1408			−0.356093			−0.178047	−	0.984022i	$-0.556978\pi$
$811$	−10.1408			−0.356093			−0.178047	+	0.984022i	$0.556978\pi$
$812$	0.335503	−	11.0921i	0.0117739	−	0.389257i
$813$	0.381491			0.0133795
$814$	0.0754260	+	0.130642i	0.00264368	+	0.00457899i
$815$	0.456938	−	0.791439i	0.0160058	−	0.0277229i
$816$	0.0434941	−	0.0753340i	0.00152260	−	0.00263722i
$817$	−1.84127	−	3.18918i	−0.0644180	−	0.111575i
$818$	−12.6503			−0.442308
$819$	26.6717	+	16.4937i	0.931985	+	0.576336i
$820$	18.9789			0.662773
$821$	−26.1578	−	45.3066i	−0.912912	−	1.58121i	−0.809930	−	0.586526i	$-0.800495\pi$
$821$	−26.1578	−	45.3066i	−0.912912	−	1.58121i	−0.102982	−	0.994683i	$-0.532838\pi$
$822$	0.0784039	−	0.135800i	0.00273465	−	0.00473655i
$823$	17.2011	−	29.7932i	0.599594	−	1.03853i	−0.393287	−	0.919416i	$-0.628662\pi$
$823$	17.2011	−	29.7932i	0.599594	−	1.03853i	0.992881	−	0.119112i	$-0.0380046\pi$
$824$	−20.0611	−	34.7468i	−0.698860	−	1.21046i
$825$	−0.00292064			−0.000101684
$826$	−3.20034	+	1.72086i	−0.111354	+	0.0598765i
$827$	−25.0842			−0.872264			−0.436132	−	0.899883i	$-0.643652\pi$
$827$	−25.0842			−0.872264			−0.436132	+	0.899883i	$0.643652\pi$
$828$	1.63971	+	2.84005i	0.0569837	+	0.0986987i
$829$	−1.12592	+	1.95016i	−0.0391049	+	0.0677318i	−0.884915	−	0.465752i	$-0.845784\pi$
$829$	−1.12592	+	1.95016i	−0.0391049	+	0.0677318i	0.845811	+	0.533483i	$0.179117\pi$
$830$	−2.71557	+	4.70350i	−0.0942587	+	0.163261i
$831$	0.146522	+	0.253784i	0.00508280	+	0.00880367i
$832$	7.10894			0.246458
$833$	16.4932	+	33.0297i	0.571455	+	1.14441i
$834$	−0.148460			−0.00514074
$835$	8.00368	+	13.8628i	0.276979	+	0.479741i
$836$	−0.151685	+	0.262725i	−0.00524612	+	0.00908655i
$837$	0.295441	−	0.511719i	0.0102119	−	0.0176876i
$838$	−0.963286	−	1.66846i	−0.0332762	−	0.0576360i
$839$	49.6406			1.71378			0.856891	−	0.515497i	$-0.172393\pi$
$839$	49.6406			1.71378			0.856891	+	0.515497i	$0.172393\pi$
$840$	−0.0805553	+	0.0433156i	−0.00277942	+	0.00149453i
$841$	−21.0556			−0.726057
$842$	−7.68184	−	13.3053i	−0.264734	−	0.458532i
$843$	0.00437004	−	0.00756912i	0.000150512	−	0.000260695i
$844$	−14.5807	+	25.2545i	−0.501889	+	0.869297i
$845$	−1.30594	−	2.26195i	−0.0449256	−	0.0778135i
$846$	−16.4513			−0.565607
$847$	24.6527	+	15.2451i	0.847076	+	0.523829i
$848$	−9.01297			−0.309507
$849$	−0.0444945	−	0.0770667i	−0.00152705	−	0.00264492i
$850$	1.88671	−	3.26789i	0.0647138	−	0.112088i
$851$	0.367314	−	0.636207i	0.0125914	−	0.0218089i
$852$	−0.163093	−	0.282486i	−0.00558749	−	0.00967781i
$853$	−43.8842			−1.50257			−0.751284	−	0.659979i	$-0.770565\pi$
$853$	−43.8842			−1.50257			−0.751284	+	0.659979i	$0.770565\pi$
$854$	−0.299214	+	9.89234i	−0.0102389	+	0.338509i
$855$	2.90047			0.0991939
$856$	−1.44654	−	2.50549i	−0.0494418	−	0.0856358i
$857$	−22.8744	+	39.6196i	−0.781373	+	1.35338i	0.149768	+	0.988721i	$0.452147\pi$
$857$	−22.8744	+	39.6196i	−0.781373	+	1.35338i	−0.931142	+	0.364657i	$0.881186\pi$
$858$	−0.00412823	+	0.00715031i	−0.000140936	+	0.000244107i
$859$	22.3800	+	38.7634i	0.763597	+	1.32259i	0.940985	+	0.338448i	$0.109902\pi$
$859$	22.3800	+	38.7634i	0.763597	+	1.32259i	−0.177388	+	0.984141i	$0.556765\pi$
$860$	5.66773			0.193268
$861$	−0.0141314	+	0.467200i	−0.000481597	+	0.0159221i
$862$	−11.6833			−0.397936
$863$	22.1918	+	38.4373i	0.755417	+	1.30842i	0.945167	+	0.326587i	$0.105899\pi$
$863$	22.1918	+	38.4373i	0.755417	+	1.30842i	−0.189750	+	0.981832i	$0.560768\pi$
$864$	0.242811	−	0.420562i	0.00826061	−	0.0143078i
$865$	−8.97904	+	15.5522i	−0.305296	+	0.528789i
$866$	3.70113	+	6.41055i	0.125770	+	0.217839i
$867$	−0.149825			−0.00508831
$868$	−23.8074	−	14.7224i	−0.808077	−	0.499712i
$869$	0.899466			0.0305123
$870$	−0.0139670	−	0.0241916i	−0.000473526	−	0.000820171i
$871$	15.7047	−	27.2014i	0.532134	−	0.921683i
$872$	−20.6728	+	35.8063i	−0.700069	+	1.21256i
$873$	−7.27232	−	12.5960i	−0.246131	−	0.426311i
$874$	−0.508195			−0.0171900
$875$	2.33024	−	1.25300i	0.0787763	−	0.0423591i
$876$	−0.0376335			−0.00127152
$877$	−27.6436	−	47.8801i	−0.933457	−	1.61680i	−0.777362	−	0.629053i	$-0.783443\pi$
$877$	−27.6436	−	47.8801i	−0.933457	−	1.61680i	−0.156095	−	0.987742i	$-0.549891\pi$
$878$	−4.41813	+	7.65243i	−0.149105	+	0.258257i
$879$	−0.154697	+	0.267942i	−0.00521779	+	0.00903747i
$880$	−0.125525	−	0.217415i	−0.00423144	−	0.00732907i
$881$	14.8771			0.501223			0.250612	−	0.968088i	$-0.419368\pi$
$881$	14.8771			0.501223			0.250612	+	0.968088i	$0.419368\pi$
$882$	6.71181	+	13.4412i	0.225998	+	0.452590i
$883$	−52.1314			−1.75436			−0.877180	−	0.480161i	$-0.840578\pi$
$883$	−52.1314			−1.75436			−0.877180	+	0.480161i	$0.840578\pi$
$884$	15.5053	+	26.8559i	0.521499	+	0.903263i
$885$	0.0132951	−	0.0230278i	0.000446911	−	0.000774073i
$886$	−7.35627	+	12.7414i	−0.247139	+	0.428057i
$887$	6.51951	+	11.2921i	0.218904	+	0.379152i	0.954473	−	0.298297i	$-0.0964186\pi$
$887$	6.51951	+	11.2921i	0.218904	+	0.379152i	−0.735569	+	0.677449i	$0.763085\pi$
$888$	−0.0345696			−0.00116008
$889$	30.4935	−	16.3967i	1.02272	−	0.549929i
$890$	−11.7832			−0.394973
$891$	−0.948618	−	1.64306i	−0.0317799	−	0.0550444i
$892$	−4.06657	+	7.04351i	−0.136159	+	0.235834i
$893$	−3.70563	+	6.41834i	−0.124004	+	0.214781i
$894$	0.0169330	+	0.0293287i	0.000566323	+	0.000980900i
$895$	19.7057			0.658690
$896$	−23.4003	−	14.4707i	−0.781751	−	0.483432i
$897$	0.0402078			0.00134250
$898$	2.95798	+	5.12337i	0.0987091	+	0.170969i
$899$	10.0195	−	17.3543i	0.334170	−	0.578799i
$900$	−2.23202	+	3.86597i	−0.0744007	+	0.128866i
$901$	19.9613	+	34.5739i	0.665006	+	1.15182i
$902$	1.92393			0.0640597
$903$	−0.00422010	+	0.139521i	−0.000140436	+	0.00464297i
$904$	−19.3382			−0.643178
$905$	−5.60494	−	9.70805i	−0.186315	−	0.322706i
$906$	0.0246997	−	0.0427812i	0.000820594	−	0.00142131i
$907$	21.0928	−	36.5337i	0.700374	−	1.21308i	−0.267961	−	0.963430i	$-0.586350\pi$
$907$	21.0928	−	36.5337i	0.700374	−	1.21308i	0.968335	−	0.249654i	$-0.0803167\pi$
$908$	−7.93106	−	13.7370i	−0.263201	−	0.455878i
$909$	−49.3241			−1.63598
$910$	0.226125	−	7.47596i	0.00749598	−	0.247826i
$911$	33.0226			1.09409			0.547044	−	0.837104i	$-0.315753\pi$
$911$	33.0226			1.09409			0.547044	+	0.837104i	$0.315753\pi$
$912$	−0.00797366	−	0.0138108i	−0.000264034	−	0.000457321i
$913$	0.800266	−	1.38610i	0.0264849	−	0.0458732i
$914$	−3.50036	+	6.06280i	−0.115781	+	0.200539i
$915$	−0.0362114	−	0.0627200i	−0.00119711	−	0.00207346i
$916$	−9.17498			−0.303150
$917$	46.5618	+	28.7937i	1.53761	+	0.950850i
$918$	−0.313609			−0.0103507
$919$	9.91827	+	17.1789i	0.327173	+	0.566681i	0.981950	−	0.189142i	$-0.0605705\pi$
$919$	9.91827	+	17.1789i	0.327173	+	0.566681i	−0.654776	+	0.755823i	$0.727237\pi$
$920$	0.916677	−	1.58773i	0.0302219	−	0.0523460i
$921$	0.0419361	−	0.0726354i	0.00138184	−	0.00239342i
$922$	−1.00904	−	1.74770i	−0.0332309	−	0.0575576i
$923$	62.5236			2.05799
$924$	0.0101277	−	0.00544582i	0.000333178	−	0.000179154i
$925$	1.00000			0.0328798
$926$	12.9658	+	22.4575i	0.426084	+	0.737999i
$927$	24.1140	−	41.7666i	0.792007	−	1.37180i
$928$	8.23466	−	14.2628i	0.270316	−	0.468201i
$929$	7.27055	+	12.5930i	0.238539	+	0.413162i	0.960295	−	0.278986i	$-0.0899982\pi$
$929$	7.27055	+	12.5930i	0.238539	+	0.413162i	−0.721756	+	0.692147i	$0.756665\pi$
$930$	−0.0704615			−0.00231052
$931$	6.75582	+	0.409061i	0.221413	+	0.0134064i
$932$	−3.97175			−0.130099
$933$	0.0812567	+	0.140741i	0.00266023	+	0.00460765i
$934$	−11.6602	+	20.1961i	−0.381534	+	0.660837i
$935$	−0.556006	+	0.963031i	−0.0181834	+	0.0314945i
$936$	14.7901	+	25.6171i	0.483428	+	0.837322i
$937$	26.6115			0.869361			0.434680	−	0.900585i	$-0.356861\pi$
$937$	26.6115			0.869361			0.434680	+	0.900585i	$0.356861\pi$
$938$	13.2532	−	7.12642i	0.432733	−	0.232686i
$939$	−0.0422752			−0.00137960
$940$	−5.70325	−	9.87831i	−0.186019	−	0.322195i
$941$	19.5605	−	33.8799i	0.637656	−	1.10445i	−0.348290	−	0.937387i	$-0.613238\pi$
$941$	19.5605	−	33.8799i	0.637656	−	1.10445i	0.985946	−	0.167065i	$-0.0534290\pi$
$942$	−0.00128230	+	0.00222102i	−4.17797e−5	+	7.23646e-5i
$943$	−4.68463	−	8.11401i	−0.152552	−	0.264228i
$944$	2.28562			0.0743907
$945$	−0.187018	−	0.115651i	−0.00608369	−	0.00376213i
$946$	0.574546			0.0186801
$947$	−4.08592	−	7.07702i	−0.132775	−	0.229972i	0.791971	−	0.610559i	$-0.209055\pi$
$947$	−4.08592	−	7.07702i	−0.132775	−	0.229972i	−0.924745	+	0.380587i	$0.875722\pi$
$948$	−0.0439686	+	0.0761559i	−0.00142803	+	0.00247343i
$949$	3.60680	−	6.24716i	0.117082	−	0.202792i
$950$	−0.345886	−	0.599092i	−0.0112220	−	0.0194371i
$951$	0.332274			0.0107747
$952$	−1.05283	+	34.8078i	−0.0341225	+	1.12813i
$953$	29.1012			0.942682			0.471341	−	0.881951i	$-0.343770\pi$
$953$	29.1012			0.942682			0.471341	+	0.881951i	$0.343770\pi$
$954$	8.12311	+	14.0696i	0.262996	+	0.455522i
$955$	5.48370	−	9.49804i	0.177448	−	0.307349i
$956$	−14.8474	+	25.7165i	−0.480199	+	0.831730i
$957$	0.00411602	+	0.00712915i	0.000133052	+	0.000230453i
$958$	7.98234			0.257898
$959$	1.26560	−	41.8422i	0.0408684	−	1.35115i
$960$	−0.0249226			−0.000804372
$961$	−9.77350	−	16.9282i	−0.315274	−	0.546071i
$962$	1.41347	−	2.44820i	0.0455721	−	0.0789331i
$963$	1.73879	−	3.01167i	0.0560316	−	0.0970496i
$964$	−18.9635	−	32.8458i	−0.610774	−	1.05789i
$965$	−5.61370			−0.180711
$966$	0.0163833	+	0.0101314i	0.000527125	+	0.000325972i
$967$	−1.96419			−0.0631642			−0.0315821	−	0.999501i	$-0.510055\pi$
$967$	−1.96419			−0.0631642			−0.0315821	+	0.999501i	$0.510055\pi$
$968$	13.6704	+	23.6779i	0.439385	+	0.761037i
$969$	−0.0353189	+	0.0611742i	−0.00113461	+	0.00196520i
$970$	−1.73447	+	3.00420i	−0.0556906	+	0.0964590i
$971$	6.00715	+	10.4047i	0.192779	+	0.333902i	0.946170	−	0.323670i	$-0.104917\pi$
$971$	6.00715	+	10.4047i	0.192779	+	0.333902i	−0.753391	+	0.657572i	$0.771583\pi$
$972$	0.556515			0.0178502
$973$	−34.9064	+	18.7696i	−1.11905	+	0.601726i
$974$	24.2742			0.777795
$975$	0.0273661	+	0.0473995i	0.000876417	+	0.00151800i
$976$	3.11263	−	5.39123i	0.0996328	−	0.172569i
$977$	−18.1644	+	31.4617i	−0.581131	+	1.00655i	0.414215	+	0.910179i	$0.364056\pi$
$977$	−18.1644	+	31.4617i	−0.581131	+	1.00655i	−0.995346	+	0.0963693i	$0.969277\pi$
$978$	0.00452857	+	0.00784372i	0.000144808	+	0.000250814i
$979$	3.47245			0.110980
$980$	−5.74409	+	8.68990i	−0.183488	+	0.277589i
$981$	−49.6986			−1.58675
$982$	−0.175856	−	0.304592i	−0.00561179	−	0.00971991i
$983$	12.5471	−	21.7322i	0.400190	−	0.693150i	−0.593559	−	0.804791i	$-0.702277\pi$
$983$	12.5471	−	21.7322i	0.400190	−	0.693150i	0.993749	+	0.111641i	$0.0356108\pi$
$984$	−0.220446	+	0.381823i	−0.00702755	+	0.0121721i
$985$	−2.80001	−	4.84976i	−0.0892157	−	0.154526i
$986$	−10.6357			−0.338709
$987$	0.247419	−	0.133040i	0.00787543	−	0.00423472i
$988$	5.68508			0.180867
$989$	−1.39898	−	2.42311i	−0.0444850	−	0.0770503i
$990$	−0.226263	+	0.391900i	−0.00719113	+	0.0124554i
$991$	−24.8276	+	43.0027i	−0.788674	+	1.36602i	0.138105	+	0.990418i	$0.455899\pi$
$991$	−24.8276	+	43.0027i	−0.788674	+	1.36602i	−0.926779	+	0.375607i	$0.877434\pi$
$992$	−20.7713	−	35.9770i	−0.659490	−	1.14227i
$993$	0.282269			0.00895755
$994$	25.4762	+	15.7544i	0.808056	+	0.499699i
$995$	20.3554			0.645309
$996$	0.0782388	+	0.135514i	0.00247909	+	0.00429391i
$997$	2.18691	−	3.78783i	0.0692600	−	0.119962i	−0.829316	−	0.558780i	$-0.811270\pi$
$997$	2.18691	−	3.78783i	0.0692600	−	0.119962i	0.898576	+	0.438818i	$0.144603\pi$
$998$	1.39362	−	2.41381i	0.0441141	−	0.0764079i
$999$	−0.0415550	−	0.0719753i	−0.00131474	−	0.00227720i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1295.2.j.a.186.12	✓	38
7.2	even	3	inner	1295.2.j.a.926.12	yes	38
7.3	odd	6		9065.2.a.s.1.8		19
7.4	even	3		9065.2.a.r.1.8		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1295.2.j.a.186.12	✓	38	1.1	even	1	trivial
1295.2.j.a.926.12	yes	38	7.2	even	3	inner
9065.2.a.r.1.8		19	7.4	even	3
9065.2.a.s.1.8		19	7.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1295 = 5 \cdot 7 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1295.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.357733 + 0.619611i) q^{2} +(0.00692605 - 0.0119963i) q^{3} +(0.744055 - 1.28874i) q^{4} +(-0.500000 - 0.866025i) q^{5} +0.00991070 q^{6} +(2.33024 - 1.25300i) q^{7} +2.49562 q^{8} +(1.49990 + 2.59791i) q^{9} +(0.357733 - 0.619611i) q^{10} +(-0.105422 + 0.182597i) q^{11} +(-0.0103067 - 0.0178518i) q^{12} +3.95119 q^{13} +(1.60997 + 0.995602i) q^{14} -0.0138521 q^{15} +(-0.595343 - 1.03117i) q^{16} +(-2.63704 + 4.56750i) q^{17} +(-1.07313 + 1.85872i) q^{18} +(0.483442 + 0.837346i) q^{19} -1.48811 q^{20} +(0.00110802 - 0.0366324i) q^{21} -0.150852 q^{22} +(0.367314 + 0.636207i) q^{23} +(0.0172848 - 0.0299381i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.41347 + 2.44820i) q^{26} +0.0831099 q^{27} +(0.119033 - 3.93537i) q^{28} +2.81857 q^{29} +(-0.00495535 - 0.00858292i) q^{30} +(3.55482 - 6.15713i) q^{31} +(2.92157 - 5.06031i) q^{32} +(0.00146032 + 0.00252935i) q^{33} -3.77343 q^{34} +(-2.25025 - 1.39154i) q^{35} +4.46404 q^{36} +(-0.500000 - 0.866025i) q^{37} +(-0.345886 + 0.599092i) q^{38} +(0.0273661 - 0.0473995i) q^{39} +(-1.24781 - 2.16127i) q^{40} -12.7537 q^{41} +(0.0230943 - 0.0124181i) q^{42} -3.80868 q^{43} +(0.156880 + 0.271724i) q^{44} +(1.49990 - 2.59791i) q^{45} +(-0.262801 + 0.455184i) q^{46} +(3.83255 + 6.63817i) q^{47} -0.0164935 q^{48} +(3.85999 - 5.83956i) q^{49} -0.715466 q^{50} +(0.0365286 + 0.0632694i) q^{51} +(2.93990 - 5.09205i) q^{52} +(3.78478 - 6.55543i) q^{53} +(0.0297311 + 0.0514958i) q^{54} +0.210845 q^{55} +(5.81539 - 3.12701i) q^{56} +0.0133934 q^{57} +(1.00830 + 1.74642i) q^{58} +(-0.959792 + 1.66241i) q^{59} +(-0.0103067 + 0.0178518i) q^{60} +(2.61415 + 4.52783i) q^{61} +5.08670 q^{62} +(6.75031 + 4.17436i) q^{63} +1.79919 q^{64} +(-1.97559 - 3.42183i) q^{65} +(-0.00104481 + 0.00180966i) q^{66} +(3.97468 - 6.88435i) q^{67} +(3.92421 + 6.79693i) q^{68} +0.0101761 q^{69} +(0.0572297 - 1.89208i) q^{70} +15.8240 q^{71} +(3.74319 + 6.48340i) q^{72} +(0.912840 - 1.58109i) q^{73} +(0.357733 - 0.619611i) q^{74} +(0.00692605 + 0.0119963i) q^{75} +1.43883 q^{76} +(-0.0168653 + 0.557587i) q^{77} +0.0391590 q^{78} +(-2.13301 - 3.69448i) q^{79} +(-0.595343 + 1.03117i) q^{80} +(-4.49914 + 7.79273i) q^{81} +(-4.56243 - 7.90236i) q^{82} -7.59105 q^{83} +(-0.0463853 - 0.0286845i) q^{84} +5.27409 q^{85} +(-1.36249 - 2.35990i) q^{86} +(0.0195216 - 0.0338124i) q^{87} +(-0.263094 + 0.455692i) q^{88} +(-8.23461 - 14.2628i) q^{89} +2.14626 q^{90} +(9.20719 - 4.95083i) q^{91} +1.09321 q^{92} +(-0.0492417 - 0.0852892i) q^{93} +(-2.74205 + 4.74938i) q^{94} +(0.483442 - 0.837346i) q^{95} +(-0.0404699 - 0.0700959i) q^{96} -4.84852 q^{97} +(4.99910 + 0.302693i) q^{98} -0.632493 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 3 q^{2} + q^{3} - 11 q^{4} - 19 q^{5} - 8 q^{6} - 18 q^{8} - 12 q^{9} + 3 q^{10} + 13 q^{11} + 4 q^{12} - 6 q^{13} - q^{14} - 2 q^{15} + 5 q^{16} + 2 q^{17} + 11 q^{18} + 12 q^{19} + 22 q^{20}+ \cdots - 142 q^{99}+O(q^{100}) \) 38 * q + 3 * q^2 + q^3 - 11 * q^4 - 19 * q^5 - 8 * q^6 - 18 * q^8 - 12 * q^9 + 3 * q^10 + 13 * q^11 + 4 * q^12 - 6 * q^13 - q^14 - 2 * q^15 + 5 * q^16 + 2 * q^17 + 11 * q^18 + 12 * q^19 + 22 * q^20 - 8 * q^21 - 20 * q^22 + 16 * q^23 - 15 * q^24 - 19 * q^25 + 3 * q^26 - 14 * q^27 + 27 * q^28 - 2 * q^29 + 4 * q^30 + 8 * q^31 + 16 * q^32 + 2 * q^33 - 28 * q^34 + 10 * q^36 - 19 * q^37 - 2 * q^38 + 45 * q^39 + 9 * q^40 - 36 * q^41 + 29 * q^42 - 74 * q^43 - q^44 - 12 * q^45 + 29 * q^46 - 2 * q^47 - 70 * q^48 + 6 * q^49 - 6 * q^50 + 43 * q^51 - 40 * q^52 + 10 * q^53 + 38 * q^54 - 26 * q^55 + 21 * q^56 + 24 * q^57 + 13 * q^58 + 28 * q^59 + 4 * q^60 - 22 * q^61 - 20 * q^62 - 27 * q^63 - 14 * q^64 + 3 * q^65 - 34 * q^66 + 61 * q^67 + 17 * q^68 - 40 * q^69 + 5 * q^70 - 34 * q^71 - 17 * q^72 - 16 * q^73 + 3 * q^74 + q^75 - 90 * q^76 + 5 * q^77 + 106 * q^78 + 63 * q^79 + 5 * q^80 + 5 * q^81 - 37 * q^82 - 48 * q^83 + 40 * q^84 - 4 * q^85 + 19 * q^86 - 32 * q^87 + 58 * q^88 + 16 * q^89 - 22 * q^90 - 11 * q^91 + 14 * q^92 + 31 * q^93 + 12 * q^95 - 40 * q^96 - 48 * q^97 + 66 * q^98 - 142 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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