LMFDB - Embedded newform 1295.2.j.a.186.5

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			186.5
Character	$\chi$	$=$	1295.186
Dual form			1295.2.j.a.926.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.597934 - 1.03565i) q^{2} +(-1.20438 + 2.08605i) q^{3} +(0.284950 - 0.493547i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.88056 q^{6} +(-1.59963 + 2.10741i) q^{7} -3.07326 q^{8} +(-1.40107 - 2.42672i) q^{9} +(-0.597934 + 1.03565i) q^{10} +(0.920878 - 1.59501i) q^{11} +(0.686376 + 1.18884i) q^{12} +2.88517 q^{13} +(3.13902 + 0.396571i) q^{14} +2.40876 q^{15} +(1.26771 + 2.19574i) q^{16} +(0.262482 - 0.454632i) q^{17} +(-1.67549 + 2.90204i) q^{18} +(2.04785 + 3.54697i) q^{19} -0.569899 q^{20} +(-2.46959 - 5.87504i) q^{21} -2.20250 q^{22} +(1.44561 + 2.50386i) q^{23} +(3.70138 - 6.41097i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.72514 - 2.98803i) q^{26} -0.476604 q^{27} +(0.584291 + 1.39000i) q^{28} -8.93230 q^{29} +(-1.44028 - 2.49464i) q^{30} +(4.46210 - 7.72858i) q^{31} +(-1.55725 + 2.69723i) q^{32} +(2.21818 + 3.84199i) q^{33} -0.627788 q^{34} +(2.62489 + 0.331618i) q^{35} -1.59694 q^{36} +(-0.500000 - 0.866025i) q^{37} +(2.44895 - 4.24171i) q^{38} +(-3.47484 + 6.01861i) q^{39} +(1.53663 + 2.66152i) q^{40} -9.13818 q^{41} +(-4.60784 + 6.07053i) q^{42} -1.08465 q^{43} +(-0.524807 - 0.908993i) q^{44} +(-1.40107 + 2.42672i) q^{45} +(1.72875 - 2.99429i) q^{46} +(-2.80970 - 4.86655i) q^{47} -6.10722 q^{48} +(-1.88235 - 6.74216i) q^{49} +1.19587 q^{50} +(0.632257 + 1.09510i) q^{51} +(0.822128 - 1.42397i) q^{52} +(-4.57531 + 7.92467i) q^{53} +(0.284978 + 0.493596i) q^{54} -1.84176 q^{55} +(4.91609 - 6.47662i) q^{56} -9.86555 q^{57} +(5.34093 + 9.25075i) q^{58} +(3.19071 - 5.52647i) q^{59} +(0.686376 - 1.18884i) q^{60} +(-4.62308 - 8.00741i) q^{61} -10.6722 q^{62} +(7.35529 + 0.929239i) q^{63} +8.79536 q^{64} +(-1.44258 - 2.49863i) q^{65} +(2.65265 - 4.59452i) q^{66} +(2.98693 - 5.17351i) q^{67} +(-0.149588 - 0.259094i) q^{68} -6.96425 q^{69} +(-1.22607 - 2.91676i) q^{70} -4.62779 q^{71} +(4.30585 + 7.45795i) q^{72} +(3.66142 - 6.34176i) q^{73} +(-0.597934 + 1.03565i) q^{74} +(-1.20438 - 2.08605i) q^{75} +2.33413 q^{76} +(1.88827 + 4.49209i) q^{77} +8.31091 q^{78} +(-3.76889 - 6.52791i) q^{79} +(1.26771 - 2.19574i) q^{80} +(4.77722 - 8.27439i) q^{81} +(5.46403 + 9.46397i) q^{82} -2.75742 q^{83} +(-3.60332 - 0.455229i) q^{84} -0.524964 q^{85} +(0.648546 + 1.12332i) q^{86} +(10.7579 - 18.6332i) q^{87} +(-2.83010 + 4.90187i) q^{88} +(0.315779 + 0.546946i) q^{89} +3.35099 q^{90} +(-4.61521 + 6.08023i) q^{91} +1.64770 q^{92} +(10.7481 + 18.6163i) q^{93} +(-3.36004 + 5.81975i) q^{94} +(2.04785 - 3.54697i) q^{95} +(-3.75104 - 6.49700i) q^{96} -11.4070 q^{97} +(-5.85701 + 5.98083i) q^{98} -5.16085 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 $

$2$	−0.597934	−	1.03565i	−0.422803	−	0.732317i	0.573409	−	0.819269i	$-0.305621\pi$
$2$	−0.597934	−	1.03565i	−0.422803	−	0.732317i	−0.996212	+	0.0869524i	$0.972287\pi$
$3$	−1.20438	+	2.08605i	−0.695350	+	1.20438i	0.274713	+	0.961526i	$0.411417\pi$
$3$	−1.20438	+	2.08605i	−0.695350	+	1.20438i	−0.970063	+	0.242855i	$0.921916\pi$
$4$	0.284950	−	0.493547i	0.142475	−	0.246774i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	2.88056			1.17598
$7$	−1.59963	+	2.10741i	−0.604604	+	0.796526i
$7$	−1.59963	+	2.10741i	−0.604604	+	0.796526i
$8$	−3.07326			−1.08656
$9$	−1.40107	−	2.42672i	−0.467023	−	0.808907i
$10$	−0.597934	+	1.03565i	−0.189083	+	0.327502i
$11$	0.920878	−	1.59501i	0.277655	−	0.480913i	−0.693146	−	0.720797i	$-0.743776\pi$
$11$	0.920878	−	1.59501i	0.277655	−	0.480913i	0.970802	+	0.239884i	$0.0771094\pi$
$12$	0.686376	+	1.18884i	0.198140	+	0.343188i
$13$	2.88517			0.800202			0.400101	−	0.916471i	$-0.368975\pi$
$13$	2.88517			0.800202			0.400101	+	0.916471i	$0.368975\pi$
$14$	3.13902	+	0.396571i	0.838938	+	0.105988i
$15$	2.40876			0.621940
$16$	1.26771	+	2.19574i	0.316927	+	0.548934i
$17$	0.262482	−	0.454632i	0.0636612	−	0.110264i	−0.832438	−	0.554118i	$-0.813056\pi$
$17$	0.262482	−	0.454632i	0.0636612	−	0.110264i	0.896099	+	0.443854i	$0.146389\pi$
$18$	−1.67549	+	2.90204i	−0.394918	+	0.684017i
$19$	2.04785	+	3.54697i	0.469808	+	0.813731i	0.999404	−	0.0345186i	$-0.0109898\pi$
$19$	2.04785	+	3.54697i	0.469808	+	0.813731i	−0.529596	+	0.848250i	$0.677656\pi$
$20$	−0.569899			−0.127433
$21$	−2.46959	−	5.87504i	−0.538909	−	1.28204i
$22$	−2.20250			−0.469574
$23$	1.44561	+	2.50386i	0.301430	+	0.522092i	0.976460	−	0.215698i	$-0.0692028\pi$
$23$	1.44561	+	2.50386i	0.301430	+	0.522092i	−0.675030	+	0.737790i	$0.735869\pi$
$24$	3.70138	−	6.41097i	0.755541	−	1.30863i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.72514	−	2.98803i	−0.338328	−	0.586001i
$27$	−0.476604			−0.0917225
$28$	0.584291	+	1.39000i	0.110421	+	0.262685i
$29$	−8.93230			−1.65869			−0.829343	−	0.558740i	$-0.811285\pi$
$29$	−8.93230			−1.65869			−0.829343	+	0.558740i	$0.811285\pi$
$30$	−1.44028	−	2.49464i	−0.262958	−	0.455457i
$31$	4.46210	−	7.72858i	0.801417	−	1.38809i	−0.117267	−	0.993100i	$-0.537413\pi$
$31$	4.46210	−	7.72858i	0.801417	−	1.38809i	0.918684	−	0.394994i	$-0.129253\pi$
$32$	−1.55725	+	2.69723i	−0.275285	+	0.476808i
$33$	2.21818	+	3.84199i	0.386135	+	0.668805i
$34$	−0.627788			−0.107665
$35$	2.62489	+	0.331618i	0.443687	+	0.0560536i
$36$	−1.59694			−0.266156
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i
$38$	2.44895	−	4.24171i	0.397273	−	0.688097i
$39$	−3.47484	+	6.01861i	−0.556420	+	0.963748i
$40$	1.53663	+	2.66152i	0.242963	+	0.420824i
$41$	−9.13818			−1.42714			−0.713572	−	0.700582i	$-0.752924\pi$
$41$	−9.13818			−1.42714			−0.713572	+	0.700582i	$0.752924\pi$
$42$	−4.60784	+	6.07053i	−0.711006	+	0.936702i
$43$	−1.08465			−0.165407			−0.0827034	−	0.996574i	$-0.526355\pi$
$43$	−1.08465			−0.165407			−0.0827034	+	0.996574i	$0.526355\pi$
$44$	−0.524807	−	0.908993i	−0.0791177	−	0.137036i
$45$	−1.40107	+	2.42672i	−0.208859	+	0.361754i
$46$	1.72875	−	2.99429i	0.254891	−	0.441484i
$47$	−2.80970	−	4.86655i	−0.409837	−	0.709859i	0.585034	−	0.811009i	$-0.301081\pi$
$47$	−2.80970	−	4.86655i	−0.409837	−	0.709859i	−0.994871	+	0.101150i	$0.967748\pi$
$48$	−6.10722			−0.881501
$49$	−1.88235	−	6.74216i	−0.268907	−	0.963166i
$50$	1.19587			0.169121
$51$	0.632257	+	1.09510i	0.0885337	+	0.153345i
$52$	0.822128	−	1.42397i	0.114009	−	0.197469i
$53$	−4.57531	+	7.92467i	−0.628467	+	1.08854i	0.359393	+	0.933186i	$0.382984\pi$
$53$	−4.57531	+	7.92467i	−0.628467	+	1.08854i	−0.987859	+	0.155350i	$0.950349\pi$
$54$	0.284978	+	0.493596i	0.0387806	+	0.0671699i
$55$	−1.84176			−0.248342
$56$	4.91609	−	6.47662i	0.656940	−	0.865475i
$57$	−9.86555			−1.30672
$58$	5.34093	+	9.25075i	0.701298	+	1.21468i
$59$	3.19071	−	5.52647i	0.415395	−	0.719485i	−0.580075	−	0.814563i	$-0.696977\pi$
$59$	3.19071	−	5.52647i	0.415395	−	0.719485i	0.995470	+	0.0950781i	$0.0303101\pi$
$60$	0.686376	−	1.18884i	0.0886107	−	0.153478i
$61$	−4.62308	−	8.00741i	−0.591925	−	1.02524i	−0.993973	−	0.109626i	$-0.965035\pi$
$61$	−4.62308	−	8.00741i	−0.591925	−	1.02524i	0.402048	−	0.915619i	$-0.368299\pi$
$62$	−10.6722			−1.35537
$63$	7.35529	+	0.929239i	0.926680	+	0.117073i
$64$	8.79536			1.09942
$65$	−1.44258	−	2.49863i	−0.178931	−	0.309917i
$66$	2.65265	−	4.59452i	0.326518	−	0.565546i
$67$	2.98693	−	5.17351i	0.364911	−	0.632044i	−0.623851	−	0.781543i	$-0.714433\pi$
$67$	2.98693	−	5.17351i	0.364911	−	0.632044i	0.988762	+	0.149499i	$0.0477661\pi$
$68$	−0.149588	−	0.259094i	−0.0181402	−	0.0314198i
$69$	−6.96425			−0.838397
$70$	−1.22607	−	2.91676i	−0.146543	−	0.348619i
$71$	−4.62779			−0.549217			−0.274609	−	0.961556i	$-0.588548\pi$
$71$	−4.62779			−0.549217			−0.274609	+	0.961556i	$0.588548\pi$
$72$	4.30585	+	7.45795i	0.507449	+	0.878928i
$73$	3.66142	−	6.34176i	0.428536	−	0.742247i	−0.568207	−	0.822886i	$-0.692363\pi$
$73$	3.66142	−	6.34176i	0.428536	−	0.742247i	0.996743	+	0.0806388i	$0.0256960\pi$
$74$	−0.597934	+	1.03565i	−0.0695084	+	0.120392i
$75$	−1.20438	−	2.08605i	−0.139070	−	0.240876i
$76$	2.33413			0.267743
$77$	1.88827	+	4.49209i	0.215188	+	0.511921i
$78$	8.31091			0.941025
$79$	−3.76889	−	6.52791i	−0.424034	−	0.734448i	0.572296	−	0.820047i	$-0.306053\pi$
$79$	−3.76889	−	6.52791i	−0.424034	−	0.734448i	−0.996330	+	0.0855993i	$0.972720\pi$
$80$	1.26771	−	2.19574i	0.141734	−	0.245491i
$81$	4.77722	−	8.27439i	0.530802	−	0.919376i
$82$	5.46403	+	9.46397i	0.603401	+	1.04512i
$83$	−2.75742			−0.302666			−0.151333	−	0.988483i	$-0.548357\pi$
$83$	−2.75742			−0.302666			−0.151333	+	0.988483i	$0.548357\pi$
$84$	−3.60332	−	0.455229i	−0.393154	−	0.0496695i
$85$	−0.524964			−0.0569403
$86$	0.648546	+	1.12332i	0.0699346	+	0.121130i
$87$	10.7579	−	18.6332i	1.15337	−	1.99769i
$88$	−2.83010	+	4.90187i	−0.301689	+	0.522541i
$89$	0.315779	+	0.546946i	0.0334725	+	0.0579761i	0.882276	−	0.470732i	$-0.156010\pi$
$89$	0.315779	+	0.546946i	0.0334725	+	0.0579761i	−0.848804	+	0.528708i	$0.822677\pi$
$90$	3.35099			0.353225
$91$	−4.61521	+	6.08023i	−0.483806	+	0.637382i
$92$	1.64770			0.171785
$93$	10.7481	+	18.6163i	1.11453	+	1.93042i
$94$	−3.36004	+	5.81975i	−0.346561	+	0.600262i
$95$	2.04785	−	3.54697i	0.210105	−	0.363912i
$96$	−3.75104	−	6.49700i	−0.382839	−	0.663097i
$97$	−11.4070			−1.15821			−0.579105	−	0.815253i	$-0.696598\pi$
$97$	−11.4070			−1.15821			−0.579105	+	0.815253i	$0.696598\pi$
$98$	−5.85701	+	5.98083i	−0.591648	+	0.604155i
$99$	−5.16085			−0.518685
$100$	0.284950	+	0.493547i	0.0284950	+	0.0493547i
$101$	4.48162	−	7.76239i	0.445938	−	0.772387i	−0.552179	−	0.833725i	$-0.686204\pi$
$101$	4.48162	−	7.76239i	0.445938	−	0.772387i	0.998117	+	0.0613386i	$0.0195370\pi$
$102$	0.756096	−	1.30960i	0.0748647	−	0.129669i
$103$	−0.131014	−	0.226922i	−0.0129092	−	0.0223593i	0.859499	−	0.511138i	$-0.170776\pi$
$103$	−0.131014	−	0.226922i	−0.0129092	−	0.0223593i	−0.872408	+	0.488779i	$0.837443\pi$
$104$	−8.86688			−0.869469
$105$	−3.85314	+	5.07625i	−0.376028	+	0.495391i
$106$	10.9429			1.06287
$107$	−7.66863	−	13.2825i	−0.741354	−	1.28406i	−0.951879	−	0.306475i	$-0.900850\pi$
$107$	−7.66863	−	13.2825i	−0.741354	−	1.28406i	0.210524	−	0.977589i	$-0.432483\pi$
$108$	−0.135808	+	0.235226i	−0.0130681	+	0.0226347i
$109$	−7.54143	+	13.0621i	−0.722338	+	1.25113i	0.237722	+	0.971333i	$0.423599\pi$
$109$	−7.54143	+	13.0621i	−0.722338	+	1.25113i	−0.960060	+	0.279793i	$0.909734\pi$
$110$	1.10125	+	1.90742i	0.105000	+	0.181865i
$111$	2.40876			0.228630
$112$	−6.65518	−	0.840789i	−0.628856	−	0.0794471i
$113$	−14.7260			−1.38531			−0.692654	−	0.721270i	$-0.743559\pi$
$113$	−14.7260			−1.38531			−0.692654	+	0.721270i	$0.743559\pi$
$114$	5.89895	+	10.2173i	0.552487	+	0.956936i
$115$	1.44561	−	2.50386i	0.134804	−	0.233487i
$116$	−2.54525	+	4.40851i	−0.236321	+	0.409320i
$117$	−4.04232	−	7.00150i	−0.373713	−	0.647289i
$118$	−7.63133			−0.702521
$119$	0.538221	+	1.28040i	0.0493387	+	0.117374i
$120$	−7.40276			−0.675776
$121$	3.80397	+	6.58867i	0.345815	+	0.598970i
$122$	−5.52860	+	9.57581i	−0.500536	+	0.866953i
$123$	11.0058	−	19.0627i	0.992364	−	1.71882i
$124$	−2.54295	−	4.40451i	−0.228363	−	0.395537i
$125$	1.00000			0.0894427
$126$	−3.43561	−	8.17315i	−0.306069	−	0.728122i
$127$	−18.0723			−1.60366			−0.801829	−	0.597554i	$-0.796139\pi$
$127$	−18.0723			−1.60366			−0.801829	+	0.597554i	$0.796139\pi$
$128$	−2.14455	−	3.71447i	−0.189553	−	0.328316i
$129$	1.30633	−	2.26262i	0.115016	−	0.199213i
$130$	−1.72514	+	2.98803i	−0.151305	+	0.262068i
$131$	−1.55954	−	2.70120i	−0.136258	−	0.236005i	0.789820	−	0.613339i	$-0.210174\pi$
$131$	−1.55954	−	2.70120i	−0.136258	−	0.236005i	−0.926077	+	0.377334i	$0.876841\pi$
$132$	2.52827			0.220058
$133$	−10.7507	−	1.35820i	−0.932206	−	0.117771i
$134$	−7.14394			−0.617142
$135$	0.238302	+	0.412751i	0.0205098	+	0.0355240i
$136$	−0.806676	+	1.39720i	−0.0691719	+	0.119809i
$137$	−2.21449	+	3.83561i	−0.189197	+	0.327699i	−0.944983	−	0.327120i	$-0.893922\pi$
$137$	−2.21449	+	3.83561i	−0.189197	+	0.327699i	0.755786	+	0.654819i	$0.227255\pi$
$138$	4.16416	+	7.21254i	0.354477	+	0.613972i
$139$	−4.46204			−0.378466			−0.189233	−	0.981932i	$-0.560600\pi$
$139$	−4.46204			−0.378466			−0.189233	+	0.981932i	$0.560600\pi$
$140$	0.911629	−	1.20101i	0.0770467	−	0.101504i
$141$	13.5358			1.13992
$142$	2.76711	+	4.79278i	0.232211	+	0.402201i
$143$	2.65689	−	4.60186i	0.222180	−	0.384827i
$144$	3.55229	−	6.15275i	0.296024	−	0.512729i
$145$	4.46615	+	7.73560i	0.370893	+	0.642406i
$146$	−8.75715			−0.724747
$147$	16.3316	+	4.19346i	1.34700	+	0.345871i
$148$	−0.569899			−0.0468454
$149$	−10.6427	−	18.4338i	−0.871887	−	1.51015i	−0.860042	−	0.510223i	$-0.829563\pi$
$149$	−10.6427	−	18.4338i	−0.871887	−	1.51015i	−0.0118456	−	0.999930i	$-0.503771\pi$
$150$	−1.44028	+	2.49464i	−0.117598	+	0.203687i
$151$	1.71337	−	2.96764i	0.139432	−	0.241503i	−0.787850	−	0.615867i	$-0.788806\pi$
$151$	1.71337	−	2.96764i	0.139432	−	0.241503i	0.927282	+	0.374364i	$0.122139\pi$
$152$	−6.29356	−	10.9008i	−0.510475	−	0.884169i
$153$	−1.47102			−0.118925
$154$	3.52319	−	4.64156i	0.283906	−	0.374028i
$155$	−8.92420			−0.716809
$156$	1.98031	+	3.43000i	0.158552	+	0.274620i
$157$	−4.25359	+	7.36744i	−0.339474	+	0.587986i	−0.984334	−	0.176315i	$-0.943582\pi$
$157$	−4.25359	+	7.36744i	−0.339474	+	0.587986i	0.644860	+	0.764301i	$0.276916\pi$
$158$	−4.50710	+	7.80653i	−0.358566	+	0.621054i
$159$	−11.0208	−	19.0886i	−0.874009	−	1.51383i
$160$	3.11450			0.246223
$161$	−7.58911	−	0.958778i	−0.598105	−	0.0755623i
$162$	−11.4258			−0.897700
$163$	3.68670	+	6.38555i	0.288765	+	0.500155i	0.973515	−	0.228622i	$-0.0734221\pi$
$163$	3.68670	+	6.38555i	0.288765	+	0.500155i	−0.684750	+	0.728778i	$0.740089\pi$
$164$	−2.60392	+	4.51012i	−0.203332	+	0.352181i
$165$	2.21818	−	3.84199i	0.172685	−	0.299099i
$166$	1.64875	+	2.85572i	0.127968	+	0.221647i
$167$	20.4447			1.58206			0.791029	−	0.611779i	$-0.209546\pi$
$167$	20.4447			1.58206			0.791029	+	0.611779i	$0.209546\pi$
$168$	7.58970	+	18.0555i	0.585558	+	1.39301i
$169$	−4.67580			−0.359677
$170$	0.313894	+	0.543680i	0.0240746	+	0.0416984i
$171$	5.73835	−	9.93911i	0.438822	−	0.760062i
$172$	−0.309069	+	0.535323i	−0.0235663	+	0.0408180i
$173$	−1.11735	−	1.93531i	−0.0849505	−	0.147139i	0.820420	−	0.571762i	$-0.193740\pi$
$173$	−1.11735	−	1.93531i	−0.0849505	−	0.147139i	−0.905370	+	0.424623i	$0.860407\pi$
$174$	−25.7300			−1.95059
$175$	−1.02525	−	2.43903i	−0.0775019	−	0.184373i
$176$	4.66962			0.351986
$177$	7.68566	+	13.3120i	0.577690	+	1.00059i
$178$	0.377630	−	0.654075i	0.0283046	−	0.0490250i
$179$	−4.25255	+	7.36563i	−0.317851	+	0.550533i	−0.980039	−	0.198804i	$-0.936294\pi$
$179$	−4.25255	+	7.36563i	−0.317851	+	0.550533i	0.662189	+	0.749337i	$0.269628\pi$
$180$	0.798468	+	1.38299i	0.0595143	+	0.103082i
$181$	17.1339			1.27355			0.636775	−	0.771050i	$-0.280268\pi$
$181$	17.1339			1.27355			0.636775	+	0.771050i	$0.280268\pi$
$182$	9.05660	+	1.14417i	0.671320	+	0.0848119i
$183$	22.2718			1.64638
$184$	−4.44273	−	7.69503i	−0.327522	−	0.567285i
$185$	−0.500000	+	0.866025i	−0.0367607	+	0.0636715i
$186$	12.8534	−	22.2627i	0.942454	−	1.63238i
$187$	−0.483428	−	0.837321i	−0.0353517	−	0.0612310i
$188$	−3.20250			−0.233566
$189$	0.762391	−	1.00440i	0.0554558	−	0.0730593i
$190$	−4.89791			−0.355332
$191$	7.09571	+	12.2901i	0.513427	+	0.889282i	0.999879	+	0.0155748i	$0.00495780\pi$
$191$	7.09571	+	12.2901i	0.513427	+	0.889282i	−0.486451	+	0.873708i	$0.661709\pi$
$192$	−10.5930	+	18.3476i	−0.764482	+	1.32412i
$193$	2.35475	−	4.07854i	0.169498	−	0.293580i	−0.768745	−	0.639555i	$-0.779119\pi$
$193$	2.35475	−	4.07854i	0.169498	−	0.293580i	0.938244	+	0.345975i	$0.112452\pi$
$194$	6.82066	+	11.8137i	0.489695	+	0.848176i
$195$	6.94969			0.497677
$196$	−3.86395	−	0.992148i	−0.275996	−	0.0708677i
$197$	−4.83669			−0.344600			−0.172300	−	0.985045i	$-0.555120\pi$
$197$	−4.83669			−0.344600			−0.172300	+	0.985045i	$0.555120\pi$
$198$	3.08585	+	5.34485i	0.219302	+	0.379842i
$199$	−2.43798	+	4.22271i	−0.172824	+	0.299340i	−0.939406	−	0.342806i	$-0.888623\pi$
$199$	−2.43798	+	4.22271i	−0.172824	+	0.299340i	0.766582	+	0.642146i	$0.221956\pi$
$200$	1.53663	−	2.66152i	0.108656	−	0.188198i
$201$	7.19479	+	12.4617i	0.507482	+	0.878984i
$202$	−10.7189			−0.754176
$203$	14.2884	−	18.8240i	1.00285	−	1.32119i
$204$	0.720645			0.0504553
$205$	4.56909	+	7.91389i	0.319119	+	0.552730i
$206$	−0.156675	+	0.271369i	−0.0109161	+	0.0189072i
$207$	4.05079	−	7.01617i	0.281549	−	0.487658i
$208$	3.65755	+	6.33507i	0.253606	+	0.439258i
$209$	7.54326			0.521778
$210$	7.56115	+	0.955246i	0.521769	+	0.0659182i
$211$	10.7161			0.737729			0.368865	−	0.929483i	$-0.379747\pi$
$211$	10.7161			0.737729			0.368865	+	0.929483i	$0.379747\pi$
$212$	2.60746	+	4.51626i	0.179081	+	0.310178i
$213$	5.57362	−	9.65379i	0.381898	−	0.661467i
$214$	−9.17067	+	15.8841i	−0.626894	+	1.08581i
$215$	0.542323	+	0.939330i	0.0369861	+	0.0640618i
$216$	1.46473			0.0996621
$217$	9.14957	+	21.7664i	0.621113	+	1.47760i
$218$	18.0371			1.22163
$219$	8.81949	+	15.2758i	0.595966	+	1.03224i
$220$	−0.524807	+	0.908993i	−0.0353825	+	0.0612843i
$221$	0.757305	−	1.31169i	0.0509418	−	0.0882339i
$222$	−1.44028	−	2.49464i	−0.0966654	−	0.167429i
$223$	9.10466			0.609693			0.304846	−	0.952402i	$-0.401395\pi$
$223$	9.10466			0.609693			0.304846	+	0.952402i	$0.401395\pi$
$224$	−3.19315	−	7.59634i	−0.213351	−	0.507552i
$225$	2.80214			0.186809
$226$	8.80519	+	15.2510i	0.585713	+	1.01448i
$227$	8.42042	−	14.5846i	0.558883	−	0.968014i	−0.438707	−	0.898630i	$-0.644563\pi$
$227$	8.42042	−	14.5846i	0.558883	−	0.968014i	0.997590	−	0.0693835i	$-0.0221032\pi$
$228$	−2.81118	+	4.86911i	−0.186175	+	0.322465i
$229$	5.68323	+	9.84364i	0.375558	+	0.650486i	0.990410	−	0.138156i	$-0.0441176\pi$
$229$	5.68323	+	9.84364i	0.375558	+	0.650486i	−0.614852	+	0.788643i	$0.710784\pi$
$230$	−3.45751			−0.227981
$231$	−11.6449	−	1.47117i	−0.766180	−	0.0967961i
$232$	27.4513			1.80226
$233$	−3.73914	−	6.47639i	−0.244959	−	0.424282i	0.717161	−	0.696908i	$-0.245441\pi$
$233$	−3.73914	−	6.47639i	−0.244959	−	0.424282i	−0.962120	+	0.272626i	$0.912108\pi$
$234$	−4.83408	+	8.37288i	−0.316014	+	0.547352i
$235$	−2.80970	+	4.86655i	−0.183285	+	0.317459i
$236$	−1.81838	−	3.14953i	−0.118367	−	0.205017i
$237$	18.1567			1.17941
$238$	1.00423	−	1.32301i	0.0650946	−	0.0857577i
$239$	28.2350			1.82637			0.913185	−	0.407546i	$-0.133615\pi$
$239$	28.2350			1.82637			0.913185	+	0.407546i	$0.133615\pi$
$240$	3.05361	+	5.28901i	0.197110	+	0.341404i
$241$	−15.1343	+	26.2134i	−0.974885	+	1.68855i	−0.294572	+	0.955629i	$0.595177\pi$
$241$	−15.1343	+	26.2134i	−0.974885	+	1.68855i	−0.680313	+	0.732921i	$0.738156\pi$
$242$	4.54905	−	7.87918i	0.292424	−	0.506493i
$243$	10.7923	+	18.6928i	0.692325	+	1.19914i
$244$	−5.26938			−0.337338
$245$	−4.89771	+	5.00124i	−0.312903	+	0.319518i
$246$	−26.3231			−1.67830
$247$	5.90838	+	10.2336i	0.375941	+	0.651149i
$248$	−13.7132	+	23.7519i	−0.870789	+	1.50825i
$249$	3.32098	−	5.75211i	0.210459	−	0.364525i
$250$	−0.597934	−	1.03565i	−0.0378167	−	0.0655004i
$251$	−29.5260			−1.86367			−0.931833	−	0.362888i	$-0.881791\pi$
$251$	−29.5260			−1.86367			−0.931833	+	0.362888i	$0.881791\pi$
$252$	2.55451	−	3.36540i	0.160919	−	0.212000i
$253$	5.32491			0.334774
$254$	10.8060	+	18.7166i	0.678032	+	1.17439i
$255$	0.632257	−	1.09510i	0.0395935	−	0.0685779i
$256$	6.23076	−	10.7920i	0.389423	−	0.674500i
$257$	−3.75320	−	6.50073i	−0.234118	−	0.405504i	0.724898	−	0.688856i	$-0.241887\pi$
$257$	−3.75320	−	6.50073i	−0.234118	−	0.405504i	−0.959016	+	0.283352i	$0.908554\pi$
$258$	−3.12439			−0.194516
$259$	2.62489	+	0.331618i	0.163103	+	0.0206057i
$260$	−1.64426			−0.101972
$261$	12.5148	+	21.6762i	0.774644	+	1.34172i
$262$	−1.86500	+	3.23028i	−0.115220	+	0.199567i
$263$	1.72151	−	2.98175i	0.106153	−	0.183863i	−0.808056	−	0.589106i	$-0.799480\pi$
$263$	1.72151	−	2.98175i	0.106153	−	0.183863i	0.914209	+	0.405244i	$0.132813\pi$
$264$	−6.81703	−	11.8074i	−0.419559	−	0.726698i
$265$	9.15062			0.562118
$266$	5.02160	+	11.9461i	0.307894	+	0.732464i
$267$	−1.52127			−0.0931005
$268$	−1.70225	−	2.94838i	−0.103981	−	0.180101i
$269$	9.89778	−	17.1435i	0.603479	−	1.04526i	−0.388811	−	0.921317i	$-0.627114\pi$
$269$	9.89778	−	17.1435i	0.603479	−	1.04526i	0.992290	−	0.123938i	$-0.0395524\pi$
$270$	0.284978	−	0.493596i	0.0173432	−	0.0300393i
$271$	−6.52979	−	11.3099i	−0.396656	−	0.687029i	0.596655	−	0.802498i	$-0.296496\pi$
$271$	−6.52979	−	11.3099i	−0.396656	−	0.687029i	−0.993311	+	0.115469i	$0.963163\pi$
$272$	1.33100			0.0807039
$273$	−7.12519	−	16.9505i	−0.431236	−	1.02589i
$274$	5.29648			0.319972
$275$	0.920878	+	1.59501i	0.0555310	+	0.0961825i
$276$	−1.98446	+	3.43718i	−0.119450	+	0.206894i
$277$	12.9892	−	22.4979i	0.780443	−	1.35177i	−0.151241	−	0.988497i	$-0.548327\pi$
$277$	12.9892	−	22.4979i	0.780443	−	1.35177i	0.931684	−	0.363270i	$-0.118340\pi$
$278$	2.66801	+	4.62112i	0.160016	+	0.277157i
$279$	−25.0068			−1.49712
$280$	−8.06696	−	1.01915i	−0.482093	−	0.0609057i
$281$	−9.29192			−0.554309			−0.277155	−	0.960825i	$-0.589391\pi$
$281$	−9.29192			−0.554309			−0.277155	+	0.960825i	$0.589391\pi$
$282$	−8.09353	−	14.0184i	−0.481963	−	0.834784i
$283$	5.17238	−	8.95883i	0.307466	−	0.532547i	−0.670341	−	0.742053i	$-0.733852\pi$
$283$	5.17238	−	8.95883i	0.307466	−	0.532547i	0.977807	+	0.209506i	$0.0671856\pi$
$284$	−1.31869	+	2.28403i	−0.0782496	+	0.135532i
$285$	4.93277	+	8.54382i	0.292192	+	0.506092i
$286$	−6.35458			−0.375754
$287$	14.6177	−	19.2579i	0.862857	−	1.13676i
$288$	8.72725			0.514258
$289$	8.36221	+	14.4838i	0.491894	+	0.851986i
$290$	5.34093	−	9.25075i	0.313630	−	0.543223i
$291$	13.7384	−	23.7957i	0.805361	−	1.39493i
$292$	−2.08664	−	3.61416i	−0.122111	−	0.211503i
$293$	−17.6437			−1.03076			−0.515378	−	0.856963i	$-0.672348\pi$
$293$	−17.6437			−1.03076			−0.515378	+	0.856963i	$0.672348\pi$
$294$	−5.42223	−	19.4212i	−0.316231	−	1.13267i
$295$	−6.38142			−0.371540
$296$	1.53663	+	2.66152i	0.0893148	+	0.154698i
$297$	−0.438894	+	0.760187i	−0.0254672	+	0.0441105i
$298$	−12.7273	+	22.0444i	−0.737274	+	1.27700i
$299$	4.17082	+	7.22407i	0.241205	+	0.417779i
$300$	−1.37275			−0.0792559
$301$	1.73503	−	2.28579i	0.100006	−	0.131751i
$302$	−4.09792			−0.235809
$303$	10.7952	+	18.6978i	0.620165	+	1.07416i
$304$	−5.19214	+	8.99305i	−0.297790	+	0.515787i
$305$	−4.62308	+	8.00741i	−0.264717	+	0.458503i
$306$	0.879574	+	1.52347i	0.0502819	+	0.0870908i
$307$	−12.2919			−0.701535			−0.350768	−	0.936463i	$-0.614079\pi$
$307$	−12.2919			−0.701535			−0.350768	+	0.936463i	$0.614079\pi$
$308$	2.75512	+	0.348071i	0.156988	+	0.0198332i
$309$	0.631162			0.0359055
$310$	5.33608	+	9.24237i	0.303069	+	0.524931i
$311$	−4.15014	+	7.18825i	−0.235333	+	0.407608i	−0.959369	−	0.282153i	$-0.908951\pi$
$311$	−4.15014	+	7.18825i	−0.235333	+	0.407608i	0.724037	+	0.689762i	$0.242285\pi$
$312$	10.6791	−	18.4967i	0.604585	−	1.04717i
$313$	−0.987751	−	1.71084i	−0.0558310	−	0.0967021i	0.836759	−	0.547571i	$-0.184447\pi$
$313$	−0.987751	−	1.71084i	−0.0558310	−	0.0967021i	−0.892590	+	0.450869i	$0.851114\pi$
$314$	10.1735			0.574122
$315$	−2.87290	−	6.83449i	−0.161870	−	0.385080i
$316$	−4.29578			−0.241656
$317$	13.3017	+	23.0392i	0.747098	+	1.29401i	0.949208	+	0.314649i	$0.101887\pi$
$317$	13.3017	+	23.0392i	0.747098	+	1.29401i	−0.202110	+	0.979363i	$0.564780\pi$
$318$	−13.1795	+	22.8275i	−0.739068	+	1.28010i
$319$	−8.22555	+	14.2471i	−0.460543	+	0.797683i
$320$	−4.39768	−	7.61701i	−0.245838	−	0.425804i
$321$	36.9438			2.06200
$322$	3.54483	+	8.43296i	0.197545	+	0.469951i
$323$	2.15009			0.119634
$324$	−2.72253	−	4.71557i	−0.151252	−	0.261976i
$325$	−1.44258	+	2.49863i	−0.0800202	+	0.138599i
$326$	4.40881	−	7.63628i	0.244181	−	0.422935i
$327$	−18.1655	−	31.4636i	−1.00456	−	1.73994i
$328$	28.0840			1.55068
$329$	14.7503	+	1.86350i	0.813211	+	0.102738i
$330$	−5.30529			−0.292047
$331$	12.7252	+	22.0407i	0.699442	+	1.21147i	0.968660	+	0.248390i	$0.0799014\pi$
$331$	12.7252	+	22.0407i	0.699442	+	1.21147i	−0.269218	+	0.963079i	$0.586765\pi$
$332$	−0.785724	+	1.36091i	−0.0431222	+	0.0746899i
$333$	−1.40107	+	2.42672i	−0.0767781	+	0.132984i
$334$	−12.2246	−	21.1736i	−0.668899	−	1.15857i
$335$	−5.97385			−0.326386
$336$	9.76930	−	12.8704i	0.532959	−	0.702138i
$337$	−21.4944			−1.17087			−0.585436	−	0.810718i	$-0.699077\pi$
$337$	−21.4944			−1.17087			−0.585436	+	0.810718i	$0.699077\pi$
$338$	2.79582	+	4.84250i	0.152073	+	0.263397i
$339$	17.7357	−	30.7192i	0.963274	−	1.66844i
$340$	−0.149588	+	0.259094i	−0.00811256	+	0.0140514i
$341$	−8.21810	−	14.2342i	−0.445035	−	0.770823i
$342$	−13.7246			−0.742142
$343$	17.2196	+	6.81810i	0.929769	+	0.368143i
$344$	3.33340			0.179725
$345$	3.48212	+	6.03121i	0.187471	+	0.324710i
$346$	−1.33620	+	2.31437i	−0.0718347	+	0.124421i
$347$	−5.19485	+	8.99774i	−0.278874	+	0.483024i	−0.971105	−	0.238652i	$-0.923295\pi$
$347$	−5.19485	+	8.99774i	−0.278874	+	0.483024i	0.692231	+	0.721676i	$0.256628\pi$
$348$	−6.13091	−	10.6191i	−0.328651	−	0.569241i
$349$	14.8759			0.796290			0.398145	−	0.917323i	$-0.369654\pi$
$349$	14.8759			0.796290			0.398145	+	0.917323i	$0.369654\pi$
$350$	−1.91295	+	2.52018i	−0.102251	+	0.134710i
$351$	−1.37508			−0.0733965
$352$	2.86807	+	4.96764i	0.152869	+	0.264776i
$353$	−10.8486	+	18.7904i	−0.577414	+	1.00011i	0.418361	+	0.908281i	$0.362605\pi$
$353$	−10.8486	+	18.7904i	−0.577414	+	1.00011i	−0.995775	+	0.0918295i	$0.970729\pi$
$354$	9.19104	−	15.9193i	0.488498	−	0.846104i
$355$	2.31389	+	4.00778i	0.122809	+	0.212711i
$356$	0.359925			0.0190760
$357$	−3.31921	−	0.419335i	−0.175671	−	0.0221936i
$358$	10.1710			0.537553
$359$	4.45770	+	7.72097i	0.235268	+	0.407497i	0.959351	−	0.282217i	$-0.0910697\pi$
$359$	4.45770	+	7.72097i	0.235268	+	0.407497i	−0.724082	+	0.689714i	$0.757736\pi$
$360$	4.30585	−	7.45795i	0.226938	−	0.393068i
$361$	1.11266	−	1.92718i	0.0585609	−	0.101430i
$362$	−10.2449	−	17.7447i	−0.538461	−	0.932642i
$363$	−18.3257			−0.961851
$364$	1.68578	+	4.01038i	0.0883588	+	0.210201i
$365$	−7.32283			−0.383295
$366$	−13.3171	−	23.0659i	−0.696095	−	1.20567i
$367$	11.3741	−	19.7005i	0.593724	−	1.02836i	−0.400002	−	0.916514i	$-0.630990\pi$
$367$	11.3741	−	19.7005i	0.593724	−	1.02836i	0.993726	−	0.111846i	$-0.0356762\pi$
$368$	−3.66522	+	6.34834i	−0.191063	+	0.330930i
$369$	12.8032	+	22.1758i	0.666509	+	1.15443i
$370$	1.19587			0.0621702
$371$	−9.38170	−	22.3186i	−0.487074	−	1.15872i
$372$	12.2507			0.635170
$373$	−7.23641	−	12.5338i	−0.374687	−	0.648977i	0.615593	−	0.788064i	$-0.288917\pi$
$373$	−7.23641	−	12.5338i	−0.374687	−	0.648977i	−0.990280	+	0.139087i	$0.955583\pi$
$374$	−0.578116	+	1.00133i	−0.0298937	+	0.0517773i
$375$	−1.20438	+	2.08605i	−0.0621940	+	0.107723i
$376$	8.63495	+	14.9562i	0.445314	+	0.771306i
$377$	−25.7712			−1.32728
$378$	−1.49607	−	0.189007i	−0.0769495	−	0.00972149i
$379$	1.90563			0.0978857			0.0489429	−	0.998802i	$-0.484415\pi$
$379$	1.90563			0.0978857			0.0489429	+	0.998802i	$0.484415\pi$
$380$	−1.16707	−	2.02142i	−0.0598692	−	0.103696i
$381$	21.7659	−	37.6997i	1.11510	−	1.93141i
$382$	8.48553	−	14.6974i	0.434158	−	0.751983i
$383$	−9.53489	−	16.5149i	−0.487210	−	0.843873i	0.512682	−	0.858579i	$-0.328652\pi$
$383$	−9.53489	−	16.5149i	−0.487210	−	0.843873i	−0.999892	+	0.0147060i	$0.995319\pi$
$384$	10.3314			0.527223
$385$	2.94613	−	3.88133i	0.150149	−	0.197811i
$386$	−5.63194			−0.286658
$387$	1.51966	+	2.63213i	0.0772488	+	0.133799i
$388$	−3.25043	+	5.62991i	−0.165016	+	0.285816i
$389$	−8.04073	+	13.9270i	−0.407681	+	0.706125i	−0.994629	−	0.103500i	$-0.966996\pi$
$389$	−8.04073	+	13.9270i	−0.407681	+	0.706125i	0.586948	+	0.809624i	$0.300329\pi$
$390$	−4.15546	−	7.19746i	−0.210420	−	0.364458i
$391$	1.51778			0.0767576
$392$	5.78495	+	20.7204i	0.292184	+	1.04654i
$393$	7.51312			0.378987
$394$	2.89202	+	5.00913i	0.145698	+	0.252357i
$395$	−3.76889	+	6.52791i	−0.189634	+	0.328455i
$396$	−1.47058	+	2.54712i	−0.0738995	+	0.127998i
$397$	−1.82700	−	3.16446i	−0.0916945	−	0.158819i	0.816530	−	0.577303i	$-0.195895\pi$
$397$	−1.82700	−	3.16446i	−0.0916945	−	0.158819i	−0.908224	+	0.418484i	$0.862562\pi$
$398$	5.83101			0.292282
$399$	15.7813	−	20.7908i	0.790051	−	1.04084i
$400$	−2.53542			−0.126771
$401$	−9.69294	−	16.7887i	−0.484042	−	0.838386i	0.515790	−	0.856715i	$-0.327499\pi$
$401$	−9.69294	−	16.7887i	−0.484042	−	0.838386i	−0.999832	+	0.0183295i	$0.994165\pi$
$402$	8.60403	−	14.9026i	0.429130	−	0.743275i
$403$	12.8739	−	22.2983i	0.641295	−	1.11076i
$404$	−2.55407	−	4.42378i	−0.127070	−	0.220091i
$405$	−9.55444			−0.474764
$406$	−28.0386	−	3.54229i	−1.39153	−	0.175801i
$407$	−1.84176			−0.0912924
$408$	−1.94309	−	3.36553i	−0.0961973	−	0.166619i
$409$	0.731144	−	1.26638i	0.0361527	−	0.0626184i	−0.847383	−	0.530982i	$-0.821823\pi$
$409$	0.731144	−	1.26638i	0.0361527	−	0.0626184i	0.883536	+	0.468364i	$0.155156\pi$
$410$	5.46403	−	9.46397i	0.269849	−	0.467392i
$411$	−5.33419	−	9.23908i	−0.263116	−	0.455730i
$412$	−0.149329			−0.00735692
$413$	6.54257	+	15.5645i	0.321939	+	0.765877i
$414$	−9.68842			−0.476160
$415$	1.37871	+	2.38799i	0.0676781	+	0.117222i
$416$	−4.49292	+	7.78197i	−0.220284	+	0.381543i
$417$	5.37400	−	9.30804i	0.263166	−	0.455817i
$418$	−4.51037	−	7.81220i	−0.220610	−	0.382107i
$419$	24.3498			1.18957			0.594784	−	0.803886i	$-0.297238\pi$
$419$	24.3498			1.18957			0.594784	+	0.803886i	$0.297238\pi$
$420$	1.40742	+	3.34818i	0.0686750	+	0.163374i
$421$	−29.2002			−1.42313			−0.711566	−	0.702620i	$-0.752014\pi$
$421$	−29.2002			−1.42313			−0.711566	+	0.702620i	$0.752014\pi$
$422$	−6.40754	−	11.0982i	−0.311914	−	0.540251i
$423$	−7.87318	+	13.6367i	−0.382807	+	0.663041i
$424$	14.0611	−	24.3546i	0.682868	−	1.18276i
$425$	0.262482	+	0.454632i	0.0127322	+	0.0220529i
$426$	−13.3306			−0.645871
$427$	24.2701	+	3.06619i	1.17451	+	0.148383i
$428$	−8.74069			−0.422497
$429$	6.39981	+	11.0848i	0.308986	+	0.535179i
$430$	0.648546	−	1.12332i	0.0312757	−	0.0541711i
$431$	13.1720	−	22.8146i	0.634473	−	1.09894i	−0.352154	−	0.935942i	$-0.614551\pi$
$431$	13.1720	−	22.8146i	0.634473	−	1.09894i	0.986627	−	0.162997i	$-0.0521160\pi$
$432$	−0.604195	−	1.04650i	−0.0290693	−	0.0503496i
$433$	36.0542			1.73265			0.866327	−	0.499478i	$-0.166475\pi$
$433$	36.0542			1.73265			0.866327	+	0.499478i	$0.166475\pi$
$434$	17.0715	−	22.4906i	0.819460	−	1.07958i
$435$	−21.5158			−1.03160
$436$	4.29786	+	7.44410i	0.205830	+	0.356508i
$437$	−5.92076	+	10.2551i	−0.283228	+	0.490566i
$438$	10.5469	−	18.2678i	0.503952	−	0.872871i
$439$	3.90807	+	6.76898i	0.186522	+	0.323066i	0.944088	−	0.329693i	$-0.106945\pi$
$439$	3.90807	+	6.76898i	0.186522	+	0.323066i	−0.757566	+	0.652758i	$0.773612\pi$
$440$	5.66019			0.269839
$441$	−13.7241	+	14.0142i	−0.653526	+	0.667342i
$442$	−1.81127			−0.0861535
$443$	12.6540	+	21.9173i	0.601208	+	1.04132i	0.992639	+	0.121115i	$0.0386468\pi$
$443$	12.6540	+	21.9173i	0.601208	+	1.04132i	−0.391431	+	0.920207i	$0.628020\pi$
$444$	0.686376	−	1.18884i	0.0325740	−	0.0564197i
$445$	0.315779	−	0.546946i	0.0149694	−	0.0259277i
$446$	−5.44399	−	9.42926i	−0.257780	−	0.446488i
$447$	51.2717			2.42507
$448$	−14.0693	+	18.5354i	−0.664714	+	0.875717i
$449$	36.7785			1.73569			0.867843	−	0.496838i	$-0.165506\pi$
$449$	36.7785			1.73569			0.867843	+	0.496838i	$0.165506\pi$
$450$	−1.67549	−	2.90204i	−0.0789835	−	0.136803i
$451$	−8.41514	+	14.5755i	−0.396254	+	0.686331i
$452$	−4.19617	+	7.26799i	−0.197371	+	0.341857i
$453$	4.12709	+	7.14833i	0.193908	+	0.335858i
$454$	−20.1394			−0.945190
$455$	7.57324	+	0.956773i	0.355039	+	0.0448542i
$456$	30.3194			1.41984
$457$	−12.8129	−	22.1926i	−0.599363	−	1.03813i	−0.992915	−	0.118824i	$-0.962087\pi$
$457$	−12.8129	−	22.1926i	−0.599363	−	1.03813i	0.393553	−	0.919302i	$-0.371246\pi$
$458$	6.79640	−	11.7717i	0.317575	−	0.550056i
$459$	−0.125100	+	0.216679i	−0.00583917	+	0.0101137i
$460$	−0.823850	−	1.42695i	−0.0384122	−	0.0665319i
$461$	−32.9731			−1.53571			−0.767856	−	0.640623i	$-0.778676\pi$
$461$	−32.9731			−1.53571			−0.767856	+	0.640623i	$0.778676\pi$
$462$	5.43927	+	12.9398i	0.253058	+	0.602012i
$463$	−39.1489			−1.81940			−0.909702	−	0.415261i	$-0.863690\pi$
$463$	−39.1489			−1.81940			−0.909702	+	0.415261i	$0.863690\pi$
$464$	−11.3235	−	19.6130i	−0.525683	−	0.910509i
$465$	10.7481	−	18.6163i	0.498433	−	0.863311i
$466$	−4.47152	+	7.74490i	−0.207139	+	0.358776i
$467$	−8.76824	−	15.1870i	−0.405746	−	0.702772i	0.588662	−	0.808379i	$-0.299655\pi$
$467$	−8.76824	−	15.1870i	−0.405746	−	0.702772i	−0.994408	+	0.105607i	$0.966321\pi$
$468$	−4.60743			−0.212978
$469$	6.12471	+	14.5704i	0.282813	+	0.672798i
$470$	6.72007			0.309974
$471$	−10.2459	−	17.7464i	−0.472106	−	0.817712i
$472$	−9.80588	+	16.9843i	−0.451352	+	0.781765i
$473$	−0.998826	+	1.73002i	−0.0459261	+	0.0795463i
$474$	−10.8565	−	18.8041i	−0.498657	−	0.863699i
$475$	−4.09569			−0.187923
$476$	0.785304	+	0.0992123i	0.0359944	+	0.00454739i
$477$	25.6413			1.17403
$478$	−16.8827	−	29.2416i	−0.772195	−	1.33748i
$479$	−2.90941	+	5.03925i	−0.132934	+	0.230249i	−0.924807	−	0.380438i	$-0.875773\pi$
$479$	−2.90941	+	5.03925i	−0.132934	+	0.230249i	0.791872	+	0.610687i	$0.209107\pi$
$480$	−3.75104	+	6.49700i	−0.171211	+	0.296546i
$481$	−1.44258	−	2.49863i	−0.0657762	−	0.113928i
$482$	36.1972			1.64874
$483$	11.1402	−	14.6765i	0.506898	−	0.667805i
$484$	4.33576			0.197080
$485$	5.70352	+	9.87879i	0.258984	+	0.448573i
$486$	12.9061	−	22.3541i	0.585435	−	1.01400i
$487$	−9.31958	+	16.1420i	−0.422311	+	0.731463i	−0.996165	−	0.0874940i	$-0.972114\pi$
$487$	−9.31958	+	16.1420i	−0.422311	+	0.731463i	0.573855	+	0.818957i	$0.305447\pi$
$488$	14.2079	+	24.6089i	0.643163	+	1.11399i
$489$	−17.7608			−0.803170
$490$	8.10806	+	2.08191i	0.366285	+	0.0940511i
$491$	17.3309			0.782134			0.391067	−	0.920362i	$-0.372106\pi$
$491$	17.3309			0.782134			0.391067	+	0.920362i	$0.372106\pi$
$492$	−6.27222	−	10.8638i	−0.282774	−	0.489778i
$493$	−2.34457	+	4.06091i	−0.105594	+	0.182894i
$494$	7.06564	−	12.2381i	0.317898	−	0.550616i
$495$	2.58043	+	4.46943i	0.115982	+	0.200886i
$496$	22.6266			1.01596
$497$	7.40276	−	9.75264i	0.332059	−	0.437466i
$498$	−7.94291			−0.355930
$499$	15.1532	+	26.2461i	0.678349	+	1.17494i	0.975478	+	0.220098i	$0.0706377\pi$
$499$	15.1532	+	26.2461i	0.678349	+	1.17494i	−0.297128	+	0.954838i	$0.596029\pi$
$500$	0.284950	−	0.493547i	0.0127433	−	0.0220721i
$501$	−24.6232	+	42.6486i	−1.10008	+	1.90540i
$502$	17.6546	+	30.5787i	0.787964	+	1.36479i
$503$	−12.9328			−0.576645			−0.288323	−	0.957533i	$-0.593098\pi$
$503$	−12.9328			−0.576645			−0.288323	+	0.957533i	$0.593098\pi$
$504$	−22.6047	−	2.85579i	−1.00689	−	0.127207i
$505$	−8.96324			−0.398859
$506$	−3.18394	−	5.51475i	−0.141544	−	0.245161i
$507$	5.63145	−	9.75395i	0.250101	−	0.433188i
$508$	−5.14969	+	8.91953i	−0.228481	+	0.395740i
$509$	−3.23052	−	5.59543i	−0.143190	−	0.248013i	0.785506	−	0.618854i	$-0.212403\pi$
$509$	−3.23052	−	5.59543i	−0.143190	−	0.248013i	−0.928696	+	0.370841i	$0.879069\pi$
$510$	−1.51219			−0.0669610
$511$	7.50776	+	17.8606i	0.332124	+	0.790106i
$512$	−23.4805			−1.03770
$513$	−0.976011	−	1.69050i	−0.0430920	−	0.0746375i
$514$	−4.48833	+	7.77401i	−0.197972	+	0.342897i
$515$	−0.131014	+	0.226922i	−0.00577315	+	0.00999940i
$516$	−0.744474	−	1.28947i	−0.0327737	−	0.0567656i
$517$	−10.3496			−0.455174
$518$	−1.22607	−	2.91676i	−0.0538704	−	0.128155i
$519$	5.38286			0.236281
$520$	4.43344	+	7.67894i	0.194419	+	0.336744i
$521$	−13.3750	+	23.1661i	−0.585969	+	1.01493i	0.408785	+	0.912631i	$0.365952\pi$
$521$	−13.3750	+	23.1661i	−0.585969	+	1.01493i	−0.994754	+	0.102297i	$0.967381\pi$
$522$	14.9660	−	25.9219i	0.655044	−	1.13457i
$523$	13.9114	+	24.0952i	0.608302	+	1.05361i	0.991520	+	0.129952i	$0.0414825\pi$
$523$	13.9114	+	24.0952i	0.608302	+	1.05361i	−0.383218	+	0.923658i	$0.625184\pi$
$524$	−1.77756			−0.0776531
$525$	6.32273	+	0.798789i	0.275947	+	0.0348620i
$526$	−4.11741			−0.179527
$527$	−2.34244	−	4.05723i	−0.102038	−	0.176736i
$528$	−5.62400	+	9.74105i	−0.244753	+	0.423925i
$529$	7.32044	−	12.6794i	0.318280	−	0.551277i
$530$	−5.47147	−	9.47686i	−0.237665	−	0.411648i
$531$	−17.8816			−0.775996
$532$	−3.73375	+	4.91897i	−0.161879	+	0.213264i
$533$	−26.3652			−1.14200
$534$	0.909622	+	1.57551i	0.0393632	+	0.0681791i
$535$	−7.66863	+	13.2825i	−0.331544	+	0.574251i
$536$	−9.17960	+	15.8995i	−0.396498	+	0.686755i
$537$	−10.2434	−	17.7421i	−0.442035	−	0.765627i
$538$	−23.6729			−1.02061
$539$	−12.4872	−	3.20635i	−0.537862	−	0.138107i
$540$	0.271616			0.0116885
$541$	−0.664784	−	1.15144i	−0.0285813	−	0.0495042i	0.851381	−	0.524548i	$-0.175766\pi$
$541$	−0.664784	−	1.15144i	−0.0285813	−	0.0495042i	−0.879962	+	0.475044i	$0.842432\pi$
$542$	−7.80877	+	13.5252i	−0.335415	+	0.580956i
$543$	−20.6357	+	35.7421i	−0.885563	+	1.53384i
$544$	0.817499	+	1.41595i	0.0350500	+	0.0607084i
$545$	15.0829			0.646079
$546$	−13.2944	+	17.5145i	−0.568948	+	0.749551i
$547$	−25.1115			−1.07369			−0.536845	−	0.843681i	$-0.680384\pi$
$547$	−25.1115			−1.07369			−0.536845	+	0.843681i	$0.680384\pi$
$548$	1.26204	+	2.18591i	0.0539116	+	0.0933776i
$549$	−12.9545	+	22.4379i	−0.552885	+	0.957625i
$550$	1.10125	−	1.90742i	0.0469574	−	0.0813326i
$551$	−18.2920	−	31.6826i	−0.779264	−	1.34972i
$552$	21.4029			0.910970
$553$	19.7858	+	2.49966i	0.841379	+	0.106297i
$554$	−31.0667			−1.31990
$555$	−1.20438	−	2.08605i	−0.0511231	−	0.0885479i
$556$	−1.27146	+	2.20223i	−0.0539218	+	0.0933953i
$557$	−19.6884	+	34.1013i	−0.834223	+	1.44492i	0.0604384	+	0.998172i	$0.480750\pi$
$557$	−19.6884	+	34.1013i	−0.834223	+	1.44492i	−0.894661	+	0.446745i	$0.852583\pi$
$558$	14.9524	+	25.8984i	0.632987	+	1.09637i
$559$	−3.12938			−0.132359
$560$	2.59945	+	6.18395i	0.109847	+	0.261320i
$561$	2.32893			0.0983273
$562$	5.55595	+	9.62319i	0.234364	+	0.405930i
$563$	−1.01036	+	1.74999i	−0.0425814	+	0.0737532i	−0.886531	−	0.462670i	$-0.846892\pi$
$563$	−1.01036	+	1.74999i	−0.0425814	+	0.0737532i	0.843949	+	0.536423i	$0.180225\pi$
$564$	3.85703	−	6.68056i	0.162410	−	0.281303i
$565$	7.36301	+	12.7531i	0.309764	+	0.536527i
$566$	−12.3710			−0.519991
$567$	9.79572	+	23.3035i	0.411382	+	0.978657i
$568$	14.2224			0.596758
$569$	−22.5846	−	39.1177i	−0.946797	−	1.63990i	−0.752112	−	0.659035i	$-0.770965\pi$
$569$	−22.5846	−	39.1177i	−0.946797	−	1.63990i	−0.194685	−	0.980866i	$-0.562368\pi$
$570$	5.89895	−	10.2173i	0.247080	−	0.427955i
$571$	−3.89308	+	6.74301i	−0.162920	+	0.282186i	−0.935915	−	0.352226i	$-0.885425\pi$
$571$	−3.89308	+	6.74301i	−0.162920	+	0.282186i	0.772994	+	0.634413i	$0.218758\pi$
$572$	−1.51416	−	2.62260i	−0.0633101	−	0.109656i
$573$	−34.1838			−1.42805
$574$	−28.6849	−	3.62394i	−1.19728	−	0.151260i
$575$	−2.89121			−0.120572
$576$	−12.3229	−	21.3439i	−0.513454	−	0.889329i
$577$	−3.53363	+	6.12042i	−0.147107	+	0.254796i	−0.930157	−	0.367162i	$-0.880329\pi$
$577$	−3.53363	+	6.12042i	−0.147107	+	0.254796i	0.783050	+	0.621958i	$0.213663\pi$
$578$	10.0001	−	17.3207i	0.415949	−	0.720445i
$579$	5.67203	+	9.82424i	0.235721	+	0.408281i
$580$	5.09051			0.211372
$581$	4.41085	−	5.81100i	0.182993	−	0.241081i
$582$	−32.8587			−1.36204
$583$	8.42660	+	14.5953i	0.348994	+	0.604475i
$584$	−11.2525	+	19.4899i	−0.465631	+	0.806497i
$585$	−4.04232	+	7.00150i	−0.167129	+	0.289477i
$586$	10.5498	+	18.2727i	0.435807	+	0.754840i
$587$	39.3373			1.62363			0.811813	−	0.583918i	$-0.198481\pi$
$587$	39.3373			1.62363			0.811813	+	0.583918i	$0.198481\pi$
$588$	6.72334	−	6.86547i	0.277266	−	0.283127i
$589$	36.5508			1.50605
$590$	3.81567	+	6.60893i	0.157089	+	0.272085i
$591$	5.82522	−	10.0896i	0.239618	−	0.415030i
$592$	1.26771	−	2.19574i	0.0521025	−	0.0902442i
$593$	0.786941	+	1.36302i	0.0323158	+	0.0559726i	0.881731	−	0.471753i	$-0.156378\pi$
$593$	0.786941	+	1.36302i	0.0323158	+	0.0559726i	−0.849415	+	0.527725i	$0.823045\pi$
$594$	1.04972			0.0430705
$595$	0.839750	−	1.10631i	0.0344264	−	0.0453545i
$596$	−12.1306			−0.496888
$597$	−5.87252	−	10.1715i	−0.240346	−	0.416292i
$598$	4.98775	−	8.63904i	0.203964	−	0.353276i
$599$	11.7156	−	20.2920i	0.478687	−	0.829111i	−0.521014	−	0.853548i	$-0.674446\pi$
$599$	11.7156	−	20.2920i	0.478687	−	0.829111i	0.999701	+	0.0244375i	$0.00777946\pi$
$600$	3.70138	+	6.41097i	0.151108	+	0.261727i
$601$	−21.6912			−0.884801			−0.442400	−	0.896818i	$-0.645873\pi$
$601$	−21.6912			−0.884801			−0.442400	+	0.896818i	$0.645873\pi$
$602$	−3.40472	−	0.430139i	−0.138766	−	0.0175312i
$603$	−16.7396			−0.681687
$604$	−0.976445	−	1.69125i	−0.0397310	−	0.0688161i
$605$	3.80397	−	6.58867i	0.154653	−	0.267867i
$606$	12.9096	−	22.3601i	0.524416	−	0.908315i
$607$	−22.8744	−	39.6196i	−0.928442	−	1.60811i	−0.785930	−	0.618315i	$-0.787816\pi$
$607$	−22.8744	−	39.6196i	−0.928442	−	1.60811i	−0.142511	−	0.989793i	$-0.545518\pi$
$608$	−12.7560			−0.517325
$609$	22.0591	+	52.4776i	0.893882	+	2.12650i
$610$	11.0572			0.447693
$611$	−8.10647	−	14.0408i	−0.327953	−	0.568031i
$612$	−0.419167	+	0.726018i	−0.0169438	+	0.0293476i
$613$	−9.58874	+	16.6082i	−0.387286	+	0.670798i	−0.992083	−	0.125581i	$-0.959921\pi$
$613$	−9.58874	+	16.6082i	−0.387286	+	0.670798i	0.604798	+	0.796379i	$0.293254\pi$
$614$	7.34974	+	12.7301i	0.296611	+	0.513746i
$615$	−22.0117			−0.887597
$616$	−5.80314	−	13.8054i	−0.233815	−	0.556234i
$617$	−12.4394			−0.500793			−0.250397	−	0.968143i	$-0.580561\pi$
$617$	−12.4394			−0.500793			−0.250397	+	0.968143i	$0.580561\pi$
$618$	−0.377393	−	0.653664i	−0.0151810	−	0.0262942i
$619$	−10.0151	+	17.3466i	−0.402540	+	0.697220i	−0.994032	−	0.109091i	$-0.965206\pi$
$619$	−10.0151	+	17.3466i	−0.402540	+	0.697220i	0.591492	+	0.806311i	$0.298539\pi$
$620$	−2.54295	+	4.40451i	−0.102127	+	0.176889i
$621$	−0.688982	−	1.19335i	−0.0276479	−	0.0478875i
$622$	9.92604			0.397998
$623$	−1.65777	−	0.209436i	−0.0664171	−	0.00839088i
$624$	−17.6204			−0.705379
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−1.18122	+	2.04593i	−0.0472111	+	0.0817719i
$627$	−9.08496	+	15.7356i	−0.362819	+	0.628420i
$628$	2.42412	+	4.19870i	0.0967329	+	0.167546i
$629$	−0.524964			−0.0209317
$630$	−5.36035	+	7.06190i	−0.213561	+	0.281353i
$631$	−20.1530			−0.802277			−0.401139	−	0.916017i	$-0.631385\pi$
$631$	−20.1530			−0.802277			−0.401139	+	0.916017i	$0.631385\pi$
$632$	11.5828	+	20.0620i	0.460739	+	0.798023i
$633$	−12.9063	+	22.3544i	−0.512980	+	0.888507i
$634$	15.9071	−	27.5519i	0.631751	−	1.09423i
$635$	9.03615	+	15.6511i	0.358589	+	0.621094i
$636$	−12.5615			−0.498097
$637$	−5.43090	−	19.4523i	−0.215180	−	0.770727i
$638$	19.6734			0.778876
$639$	6.48385	+	11.2303i	0.256497	+	0.444266i
$640$	−2.14455	+	3.71447i	−0.0847708	+	0.146827i
$641$	6.11274	−	10.5876i	0.241439	−	0.418184i	−0.719686	−	0.694300i	$-0.755714\pi$
$641$	6.11274	−	10.5876i	0.241439	−	0.418184i	0.961124	+	0.276116i	$0.0890474\pi$
$642$	−22.0900	−	38.2610i	−0.871822	−	1.51004i
$643$	3.58210			0.141264			0.0706321	−	0.997502i	$-0.477498\pi$
$643$	3.58210			0.141264			0.0706321	+	0.997502i	$0.477498\pi$
$644$	−2.63571	+	3.47238i	−0.103862	+	0.136831i
$645$	−2.61265			−0.102873
$646$	−1.28561	−	2.22675i	−0.0505817	−	0.0876102i
$647$	14.3745	−	24.8974i	0.565122	−	0.978820i	−0.431917	−	0.901914i	$-0.642163\pi$
$647$	14.3745	−	24.8974i	0.565122	−	0.978820i	0.997038	−	0.0769060i	$-0.0245041\pi$
$648$	−14.6816	+	25.4293i	−0.576749	+	0.998959i
$649$	−5.87651	−	10.1784i	−0.230673	−	0.399537i
$650$	3.45028			0.135331
$651$	−56.4253	−	7.12855i	−2.21148	−	0.279390i
$652$	4.20210			0.164567
$653$	11.9874	+	20.7628i	0.469104	+	0.812513i	0.999376	−	0.0353149i	$-0.0112434\pi$
$653$	11.9874	+	20.7628i	0.469104	+	0.812513i	−0.530272	+	0.847828i	$0.677910\pi$
$654$	−21.7236	+	37.6263i	−0.849459	+	1.47131i
$655$	−1.55954	+	2.70120i	−0.0609363	+	0.105545i
$656$	−11.5845	−	20.0650i	−0.452300	−	0.783407i
$657$	−20.5196			−0.800545
$658$	−6.88978	−	16.3904i	−0.268592	−	0.638966i
$659$	−0.772192			−0.0300803			−0.0150402	−	0.999887i	$-0.504788\pi$
$659$	−0.772192			−0.0300803			−0.0150402	+	0.999887i	$0.504788\pi$
$660$	−1.26414	−	2.18955i	−0.0492064	−	0.0852281i
$661$	1.95992	−	3.39467i	0.0762319	−	0.132037i	−0.825389	−	0.564564i	$-0.809044\pi$
$661$	1.95992	−	3.39467i	0.0762319	−	0.132037i	0.901621	+	0.432526i	$0.142378\pi$
$662$	15.2177	−	26.3578i	0.591453	−	1.02443i
$663$	1.82417	+	3.15955i	0.0708448	+	0.122707i
$664$	8.47426			0.328865
$665$	4.19912	+	9.98950i	0.162835	+	0.387376i
$666$	3.35099			0.129848
$667$	−12.9126	−	22.3653i	−0.499977	−	0.865986i
$668$	5.82570	−	10.0904i	0.225403	−	0.390410i
$669$	−10.9655	+	18.9928i	−0.423950	+	0.734303i
$670$	3.57197	+	6.18683i	0.137997	+	0.239018i
$671$	−17.0292			−0.657404
$672$	19.6921	+	2.48782i	0.759640	+	0.0959699i
$673$	−26.7340			−1.03052			−0.515261	−	0.857033i	$-0.672305\pi$
$673$	−26.7340			−1.03052			−0.515261	+	0.857033i	$0.672305\pi$
$674$	12.8522	+	22.2607i	0.495049	+	0.857450i
$675$	0.238302	−	0.412751i	0.00917225	−	0.0158868i
$676$	−1.33237	+	2.30773i	−0.0512449	+	0.0887588i
$677$	−6.64761	−	11.5140i	−0.255488	−	0.442519i	0.709540	−	0.704666i	$-0.248903\pi$
$677$	−6.64761	−	11.5140i	−0.255488	−	0.442519i	−0.965028	+	0.262147i	$0.915570\pi$
$678$	−42.4192			−1.62910
$679$	18.2471	−	24.0393i	0.700259	−	0.922544i
$680$	1.61335			0.0618692
$681$	20.2828	+	35.1308i	0.777238	+	1.34622i
$682$	−9.82776	+	17.0222i	−0.376324	+	0.651813i
$683$	−13.5534	+	23.4752i	−0.518607	+	0.898254i	0.481159	+	0.876633i	$0.340216\pi$
$683$	−13.5534	+	23.4752i	−0.518607	+	0.898254i	−0.999766	+	0.0216206i	$0.993117\pi$
$684$	−3.27028	−	5.66429i	−0.125042	−	0.216579i
$685$	4.42898			0.169223
$686$	−3.23498	−	21.9103i	−0.123512	−	0.836538i
$687$	−27.3791			−1.04458
$688$	−1.37501	−	2.38159i	−0.0524219	−	0.0907974i
$689$	−13.2005	+	22.8640i	−0.502900	+	0.871049i
$690$	4.16416	−	7.21254i	0.158527	−	0.274577i
$691$	6.38217	+	11.0542i	0.242789	+	0.420523i	0.961508	−	0.274778i	$-0.0886043\pi$
$691$	6.38217	+	11.0542i	0.242789	+	0.420523i	−0.718718	+	0.695301i	$0.755271\pi$
$692$	−1.27355			−0.0484132
$693$	8.25547	−	10.8760i	0.313599	−	0.413146i
$694$	12.4247			0.471635
$695$	2.23102	+	3.86424i	0.0846275	+	0.146579i
$696$	−33.0618	+	57.2647i	−1.25320	+	2.17061i
$697$	−2.39861	+	4.15451i	−0.0908537	+	0.157363i
$698$	−8.89482	−	15.4063i	−0.336674	−	0.583136i
$699$	18.0134			0.681330
$700$	−1.49592	−	0.188989i	−0.0565405	−	0.00714310i
$701$	33.0588			1.24861			0.624306	−	0.781180i	$-0.285382\pi$
$701$	33.0588			1.24861			0.624306	+	0.781180i	$0.285382\pi$
$702$	0.822209	+	1.42411i	0.0310323	+	0.0537495i
$703$	2.04785	−	3.54697i	0.0772360	−	0.133777i
$704$	8.09945	−	14.0287i	0.305260	−	0.528725i
$705$	−6.76791	−	11.7224i	−0.254894	−	0.441490i
$706$	25.9471			0.976530
$707$	9.18959	+	21.8616i	0.345610	+	0.822189i
$708$	8.76010			0.329225
$709$	−14.0312	−	24.3028i	−0.526953	−	0.912709i	−0.999507	−	0.0314074i	$-0.990001\pi$
$709$	−14.0312	−	24.3028i	−0.526953	−	0.912709i	0.472554	−	0.881302i	$-0.343332\pi$
$710$	2.76711	−	4.79278i	0.103848	−	0.179870i
$711$	−10.5610	+	18.2921i	−0.396067	+	0.686008i
$712$	−0.970472	−	1.68091i	−0.0363700	−	0.0629947i
$713$	25.8018			0.966283
$714$	1.55038	+	3.68828i	0.0580215	+	0.138030i
$715$	−5.31378			−0.198724
$716$	2.42352	+	4.19767i	0.0905714	+	0.156874i
$717$	−34.0057	+	58.8996i	−1.26997	+	2.19965i
$718$	5.33082	−	9.23326i	0.198945	−	0.344582i
$719$	−11.0299	−	19.1044i	−0.411346	−	0.712473i	0.583691	−	0.811976i	$-0.301608\pi$
$719$	−11.0299	−	19.1044i	−0.411346	−	0.712473i	−0.995037	+	0.0995033i	$0.968275\pi$
$720$	−7.10459			−0.264772
$721$	0.687792	+	0.0868930i	0.0256147	+	0.00323606i
$722$	−2.66118			−0.0990389
$723$	−36.4549	−	63.1418i	−1.35577	−	2.34827i
$724$	4.88229	−	8.45637i	0.181449	−	0.314278i
$725$	4.46615	−	7.73560i	0.165869	−	0.287293i
$726$	10.9576	+	18.9791i	0.406674	+	0.704379i
$727$	25.4510			0.943924			0.471962	−	0.881619i	$-0.343546\pi$
$727$	25.4510			0.943924			0.471962	+	0.881619i	$0.343546\pi$
$728$	14.1837	−	18.6861i	0.525685	−	0.692554i
$729$	−23.3288			−0.864029
$730$	4.37857	+	7.58391i	0.162058	+	0.280693i
$731$	−0.284700	+	0.493115i	−0.0105300	+	0.0182385i
$732$	6.34634	−	10.9922i	0.234568	−	0.406283i
$733$	20.0686	+	34.7598i	0.741249	+	1.28388i	0.951927	+	0.306326i	$0.0990996\pi$
$733$	20.0686	+	34.7598i	0.741249	+	1.28388i	−0.210678	+	0.977556i	$0.567567\pi$
$734$	−27.2039			−1.00411
$735$	−4.53413	−	16.2403i	−0.167244	−	0.599031i
$736$	−9.00467			−0.331917
$737$	−5.50119	−	9.52833i	−0.202639	−	0.350981i
$738$	15.3110	−	26.5194i	0.563604	−	0.976191i
$739$	9.97031	−	17.2691i	0.366764	−	0.635254i	−0.622294	−	0.782784i	$-0.713799\pi$
$739$	9.97031	−	17.2691i	0.366764	−	0.635254i	0.989058	+	0.147530i	$0.0471324\pi$
$740$	0.284950	+	0.493547i	0.0104750	+	0.0181432i
$741$	−28.4638			−1.04564
$742$	−17.5047	+	23.0612i	−0.642617	+	0.846605i
$743$	−45.7278			−1.67759			−0.838795	−	0.544447i	$-0.816740\pi$
$743$	−45.7278			−1.67759			−0.838795	+	0.544447i	$0.816740\pi$
$744$	−33.0318	−	57.2128i	−1.21101	−	2.09752i
$745$	−10.6427	+	18.4338i	−0.389920	+	0.675361i
$746$	−8.65379	+	14.9888i	−0.316838	+	0.548779i
$747$	3.86333	+	6.69148i	0.141352	+	0.244828i
$748$	−0.551010			−0.0201469
$749$	40.2586	+	5.08611i	1.47102	+	0.185842i
$750$	2.88056			0.105183
$751$	−2.62430	−	4.54543i	−0.0957622	−	0.165865i	0.814164	−	0.580635i	$-0.197196\pi$
$751$	−2.62430	−	4.54543i	−0.0957622	−	0.165865i	−0.909926	+	0.414770i	$0.863862\pi$
$752$	7.12377	−	12.3387i	0.259777	−	0.449947i
$753$	35.5606	−	61.5927i	1.29590	−	2.24456i
$754$	15.4095	+	26.6900i	0.561180	+	0.971992i
$755$	−3.42673			−0.124712
$756$	−0.278476	−	0.662479i	−0.0101281	−	0.0240941i
$757$	19.2418			0.699356			0.349678	−	0.936870i	$-0.386291\pi$
$757$	19.2418			0.699356			0.349678	+	0.936870i	$0.386291\pi$
$758$	−1.13944	−	1.97357i	−0.0413864	−	0.0716834i
$759$	−6.41322	+	11.1080i	−0.232785	+	0.403196i
$760$	−6.29356	+	10.9008i	−0.228292	+	0.395413i
$761$	8.59247	+	14.8826i	0.311477	+	0.539494i	0.978682	−	0.205380i	$-0.0658430\pi$
$761$	8.59247	+	14.8826i	0.311477	+	0.539494i	−0.667205	+	0.744874i	$0.732510\pi$
$762$	−52.0584			−1.88588
$763$	−15.4638	−	36.7875i	−0.559826	−	1.33180i
$764$	8.08768			0.292602
$765$	0.735511	+	1.27394i	0.0265924	+	0.0460595i
$766$	−11.4025	+	19.7497i	−0.411988	+	0.713584i
$767$	9.20573	−	15.9448i	0.332400	−	0.575733i
$768$	15.0084	+	25.9954i	0.541570	+	0.938027i
$769$	30.0343			1.08306			0.541532	−	0.840680i	$-0.317844\pi$
$769$	30.0343			1.08306			0.541532	+	0.840680i	$0.317844\pi$
$770$	−5.78130	−	0.730387i	−0.208344	−	0.0263213i
$771$	18.0811			0.651175
$772$	−1.34197	−	2.32436i	−0.0482985	−	0.0836555i
$773$	2.03360	−	3.52229i	0.0731434	−	0.126688i	−0.827134	−	0.562005i	$-0.810030\pi$
$773$	2.03360	−	3.52229i	0.0731434	−	0.126688i	0.900277	+	0.435317i	$0.143364\pi$
$774$	1.81732	−	3.14768i	0.0653221	−	0.113141i
$775$	4.46210	+	7.72858i	0.160283	+	0.277619i
$776$	35.0568			1.25847
$777$	−3.85314	+	5.07625i	−0.138230	+	0.182109i
$778$	19.2313			0.689476
$779$	−18.7136	−	32.4129i	−0.670483	−	1.16131i
$780$	1.98031	−	3.43000i	0.0709065	−	0.122814i
$781$	−4.26162	+	7.38135i	−0.152493	+	0.264125i
$782$	−0.907534	−	1.57190i	−0.0324534	−	0.0562109i
$783$	4.25717			0.152139
$784$	12.4177	−	12.6802i	0.443491	−	0.452866i
$785$	8.50719			0.303635
$786$	−4.49235	−	7.78098i	−0.160237	−	0.277538i
$787$	25.1838	−	43.6196i	0.897705	−	1.55487i	0.0672833	−	0.997734i	$-0.478567\pi$
$787$	25.1838	−	43.6196i	0.897705	−	1.55487i	0.830421	−	0.557136i	$-0.188100\pi$
$788$	−1.37821	+	2.38714i	−0.0490968	+	0.0850382i
$789$	4.14672	+	7.18233i	0.147627	+	0.255698i
$790$	9.01420			0.320711
$791$	23.5562	−	31.0338i	0.837563	−	1.10343i
$792$	15.8606			0.563583
$793$	−13.3384	−	23.1027i	−0.473660	−	0.820402i
$794$	−2.18485	+	3.78427i	−0.0775374	+	0.134299i
$795$	−11.0208	+	19.0886i	−0.390869	+	0.677004i
$796$	1.38940	+	2.40652i	0.0492461	+	0.0852968i
$797$	31.6341			1.12054			0.560269	−	0.828311i	$-0.310698\pi$
$797$	31.6341			1.12054			0.560269	+	0.828311i	$0.310698\pi$
$798$	−30.9681	−	3.91239i	−1.09626	−	0.138497i
$799$	−2.94999			−0.104363
$800$	−1.55725	−	2.69723i	−0.0550570	−	0.0953616i
$801$	0.884857	−	1.53262i	0.0312649	−	0.0541524i
$802$	−11.5915	+	20.0770i	−0.409309	+	0.708944i
$803$	−6.74344	−	11.6800i	−0.237971	−	0.412177i
$804$	8.20061			0.289213
$805$	2.96423	+	7.05175i	0.104475	+	0.248541i
$806$	−30.7910			−1.08457
$807$	23.8414	+	41.2945i	0.839257	+	1.45364i
$808$	−13.7732	+	23.8559i	−0.484539	+	0.839246i
$809$	−13.2132	+	22.8859i	−0.464551	+	0.804625i	−0.999181	−	0.0404606i	$-0.987117\pi$
$809$	−13.2132	+	22.8859i	−0.464551	+	0.804625i	0.534630	+	0.845086i	$0.320451\pi$
$810$	5.71292	+	9.89508i	0.200732	+	0.347678i
$811$	−0.880739			−0.0309269			−0.0154635	−	0.999880i	$-0.504922\pi$
$811$	−0.880739			−0.0309269			−0.0154635	+	0.999880i	$0.504922\pi$
$812$	−5.21906	−	12.4159i	−0.183153	−	0.435712i
$813$	31.4574			1.10326
$814$	1.10125	+	1.90742i	0.0385987	+	0.0668550i
$815$	3.68670	−	6.38555i	0.129140	−	0.223676i
$816$	−1.60303	+	2.77654i	−0.0561174	+	0.0971983i
$817$	−2.22119	−	3.84721i	−0.0777095	−	0.134597i
$818$	−1.74870			−0.0611420
$819$	21.2213	+	2.68101i	0.741531	+	0.0936821i
$820$	5.20784			0.181866
$821$	5.40459	+	9.36102i	0.188621	+	0.326702i	0.944791	−	0.327674i	$-0.106265\pi$
$821$	5.40459	+	9.36102i	0.188621	+	0.326702i	−0.756169	+	0.654376i	$0.772931\pi$
$822$	−6.37898	+	11.0487i	−0.222493	+	0.385369i
$823$	−3.96623	+	6.86971i	−0.138254	+	0.239463i	−0.926836	−	0.375467i	$-0.877482\pi$
$823$	−3.96623	+	6.86971i	−0.138254	+	0.239463i	0.788582	+	0.614930i	$0.210816\pi$
$824$	0.402639	+	0.697392i	0.0140266	+	0.0242948i
$825$	−4.43635			−0.154454
$826$	12.2073	−	16.0823i	0.424747	−	0.559576i
$827$	−8.86830			−0.308381			−0.154190	−	0.988041i	$-0.549277\pi$
$827$	−8.86830			−0.308381			−0.154190	+	0.988041i	$0.549277\pi$
$828$	−2.30854	−	3.99851i	−0.0802273	−	0.138958i
$829$	−3.76566	+	6.52232i	−0.130787	+	0.226530i	−0.923980	−	0.382440i	$-0.875084\pi$
$829$	−3.76566	+	6.52232i	−0.130787	+	0.226530i	0.793193	+	0.608970i	$0.208417\pi$
$830$	1.64875	−	2.85572i	0.0572290	−	0.0991236i
$831$	31.2878	+	54.1921i	1.08536	+	1.87990i
$832$	25.3761			0.879758
$833$	−3.55929	−	0.913919i	−0.123322	−	0.0316654i
$834$	−12.8532			−0.445070
$835$	−10.2223	−	17.7056i	−0.353759	−	0.612728i
$836$	2.14945	−	3.72296i	0.0743403	−	0.128761i
$837$	−2.12665	+	3.68347i	−0.0735079	+	0.127319i
$838$	−14.5596	−	25.2180i	−0.502953	−	0.871140i
$839$	38.6053			1.33280			0.666401	−	0.745593i	$-0.267834\pi$
$839$	38.6053			1.33280			0.666401	+	0.745593i	$0.267834\pi$
$840$	11.8417	−	15.6006i	0.408577	−	0.538273i
$841$	50.7859			1.75124
$842$	17.4598	+	30.2413i	0.601705	+	1.04218i
$843$	11.1910	−	19.3834i	0.385439	−	0.667600i
$844$	3.05356	−	5.28892i	0.105108	−	0.182052i
$845$	2.33790	+	4.04936i	0.0804262	+	0.139302i
$846$	18.8306			0.647408
$847$	−19.9700	−	2.52293i	−0.686176	−	0.0866888i
$848$	−23.2006			−0.796713
$849$	12.4590	+	21.5797i	0.427593	+	0.740613i
$850$	0.313894	−	0.543680i	0.0107665	−	0.0186481i
$851$	1.44561	−	2.50386i	0.0495548	−	0.0858313i
$852$	−3.17640	−	5.50169i	−0.108822	−	0.188485i
$853$	−11.4380			−0.391629			−0.195815	−	0.980641i	$-0.562735\pi$
$853$	−11.4380			−0.391629			−0.195815	+	0.980641i	$0.562735\pi$
$854$	−11.3364	−	26.9688i	−0.387925	−	0.922854i
$855$	−11.4767			−0.392495
$856$	23.5677	+	40.8205i	0.805527	+	1.39521i
$857$	8.67949	−	15.0333i	0.296486	−	0.513528i	−0.678844	−	0.734283i	$-0.737519\pi$
$857$	8.67949	−	15.0333i	0.296486	−	0.513528i	0.975329	+	0.220755i	$0.0708520\pi$
$858$	7.65333	−	13.2560i	0.261280	−	0.452551i
$859$	13.5200	+	23.4173i	0.461296	+	0.798987i	0.999026	−	0.0441295i	$-0.0140514\pi$
$859$	13.5200	+	23.4173i	0.461296	+	0.798987i	−0.537730	+	0.843117i	$0.680718\pi$
$860$	0.618138			0.0210783
$861$	22.5676	+	53.6871i	0.769101	+	1.82965i
$862$	−31.5039			−1.07303
$863$	−4.67783	−	8.10224i	−0.159235	−	0.275804i	0.775358	−	0.631522i	$-0.217570\pi$
$863$	−4.67783	−	8.10224i	−0.159235	−	0.275804i	−0.934593	+	0.355719i	$0.884236\pi$
$864$	0.742191	−	1.28551i	0.0252498	−	0.0437340i
$865$	−1.11735	+	1.93531i	−0.0379910	+	0.0658024i
$866$	−21.5580	−	37.3396i	−0.732572	−	1.26885i
$867$	−40.2851			−1.36816
$868$	13.3499	+	1.68657i	0.453125	+	0.0572460i
$869$	−13.8828			−0.470940
$870$	12.8650	+	22.2829i	0.436165	+	0.755460i
$871$	8.61778	−	14.9264i	0.292002	−	0.505763i
$872$	23.1768	−	40.1434i	0.784865	−	1.35943i
$873$	15.9821	+	27.6817i	0.540911	+	0.936885i
$874$	14.1609			0.478999
$875$	−1.59963	+	2.10741i	−0.0540775	+	0.0712434i
$876$	10.0524			0.339640
$877$	−12.7315	−	22.0515i	−0.429911	−	0.744628i	0.566954	−	0.823749i	$-0.308122\pi$
$877$	−12.7315	−	22.0515i	−0.429911	−	0.744628i	−0.996865	+	0.0791218i	$0.974788\pi$
$878$	4.67354	−	8.09480i	0.157724	−	0.273186i
$879$	21.2497	−	36.8056i	0.716736	−	1.24142i
$880$	−2.33481	−	4.04401i	−0.0787064	−	0.136323i
$881$	−41.3942			−1.39461			−0.697303	−	0.716776i	$-0.745617\pi$
$881$	−41.3942			−1.39461			−0.697303	+	0.716776i	$0.745617\pi$
$882$	22.7199	+	5.83380i	0.765019	+	0.196434i
$883$	−37.6354			−1.26653			−0.633265	−	0.773935i	$-0.718286\pi$
$883$	−37.6354			−1.26653			−0.633265	+	0.773935i	$0.718286\pi$
$884$	−0.431587	−	0.747531i	−0.0145159	−	0.0251422i
$885$	7.68566	−	13.3120i	0.258351	−	0.447476i
$886$	15.1325	−	26.2102i	0.508385	−	0.880549i
$887$	9.64450	+	16.7048i	0.323831	+	0.560891i	0.981275	−	0.192612i	$-0.0616959\pi$
$887$	9.64450	+	16.7048i	0.323831	+	0.560891i	−0.657444	+	0.753503i	$0.728363\pi$
$888$	−7.40276			−0.248420
$889$	28.9090	−	38.0857i	0.969578	−	1.27735i
$890$	−0.755261			−0.0253164
$891$	−8.79847	−	15.2394i	−0.294760	−	0.510539i
$892$	2.59437	−	4.49358i	0.0868659	−	0.150456i
$893$	11.5077	−	19.9319i	0.385090	−	0.666995i
$894$	−30.6571	−	53.0996i	−1.02533	−	1.77592i
$895$	8.50510			0.284294
$896$	11.2584	+	1.42234i	0.376117	+	0.0475171i
$897$	−20.0930			−0.670887
$898$	−21.9911	−	38.0898i	−0.733854	−	1.27107i
$899$	−39.8568	+	69.0340i	−1.32930	+	2.30241i
$900$	0.798468	−	1.38299i	0.0266156	−	0.0460996i
$901$	2.40187	+	4.16016i	0.0800180	+	0.138595i
$902$	20.1268			0.670149
$903$	2.67863	+	6.37233i	0.0891393	+	0.212058i
$904$	45.2569			1.50522
$905$	−8.56693	−	14.8384i	−0.284774	−	0.493244i
$906$	4.93546	−	8.54846i	0.163970	−	0.284004i
$907$	−20.4705	+	35.4560i	−0.679712	+	1.17730i	0.295355	+	0.955387i	$0.404562\pi$
$907$	−20.4705	+	35.4560i	−0.679712	+	1.17730i	−0.975067	+	0.221909i	$0.928771\pi$
$908$	−4.79879	−	8.31175i	−0.159253	−	0.275835i
$909$	−25.1162			−0.833052
$910$	−3.53741	−	8.41533i	−0.117264	−	0.278966i
$911$	−15.7726			−0.522571			−0.261285	−	0.965262i	$-0.584146\pi$
$911$	−15.7726			−0.522571			−0.261285	+	0.965262i	$0.584146\pi$
$912$	−12.5066	−	21.6621i	−0.414136	−	0.717305i
$913$	−2.53924	+	4.39810i	−0.0840367	+	0.145556i
$914$	−15.3225	+	26.5394i	−0.506825	+	0.877846i
$915$	−11.1359	−	19.2880i	−0.368142	−	0.637640i
$916$	6.47774			0.214030
$917$	8.18723	+	1.03434i	0.270366	+	0.0341570i
$918$	0.299206			0.00987527
$919$	3.14936	+	5.45486i	0.103888	+	0.179939i	0.913283	−	0.407325i	$-0.133538\pi$
$919$	3.14936	+	5.45486i	0.103888	+	0.179939i	−0.809395	+	0.587264i	$0.800205\pi$
$920$	−4.44273	+	7.69503i	−0.146472	+	0.253698i
$921$	14.8041	−	25.6415i	0.487812	−	0.844916i
$922$	19.7158	+	34.1487i	0.649304	+	1.12463i
$923$	−13.3519			−0.439485
$924$	−4.04431	+	5.32811i	−0.133048	+	0.175282i
$925$	1.00000			0.0328798
$926$	23.4085	+	40.5447i	0.769250	+	1.33238i
$927$	−0.367118	+	0.635868i	−0.0120578	+	0.0208846i
$928$	13.9098	−	24.0925i	0.456612	−	0.790875i
$929$	8.06947	+	13.9767i	0.264751	+	0.458562i	0.967498	−	0.252877i	$-0.0813770\pi$
$929$	8.06947	+	13.9767i	0.264751	+	0.458562i	−0.702747	+	0.711439i	$0.748044\pi$
$930$	−25.7067			−0.842956
$931$	20.0595	−	20.4836i	0.657424	−	0.671321i
$932$	−4.26187			−0.139602
$933$	−9.99670	−	17.3148i	−0.327277	−	0.566861i
$934$	−10.4857	+	18.1617i	−0.343101	+	0.594269i
$935$	−0.483428	+	0.837321i	−0.0158098	+	0.0273833i
$936$	12.4231	+	21.5174i	0.406062	+	0.703320i
$937$	−15.7234			−0.513660			−0.256830	−	0.966457i	$-0.582678\pi$
$937$	−15.7234			−0.513660			−0.256830	+	0.966457i	$0.582678\pi$
$938$	11.4277	−	15.0552i	0.373127	−	0.491570i
$939$	4.75852			0.155288
$940$	1.60125	+	2.77344i	0.0522269	+	0.0904597i
$941$	4.64750	−	8.04970i	0.151504	−	0.262413i	−0.780277	−	0.625435i	$-0.784922\pi$
$941$	4.64750	−	8.04970i	0.151504	−	0.262413i	0.931781	+	0.363022i	$0.118255\pi$
$942$	−12.2527	+	21.2224i	−0.399216	+	0.691462i
$943$	−13.2102	−	22.8808i	−0.430184	−	0.745100i
$944$	16.1796			0.526600
$945$	−1.25103	−	0.158050i	−0.0406961	−	0.00514138i
$946$	2.38893			0.0776707
$947$	−0.283020	−	0.490205i	−0.00919692	−	0.0159295i	0.861390	−	0.507944i	$-0.169594\pi$
$947$	−0.283020	−	0.490205i	−0.00919692	−	0.0159295i	−0.870587	+	0.492014i	$0.836261\pi$
$948$	5.17375	−	8.96121i	0.168036	−	0.291046i
$949$	10.5638	−	18.2971i	0.342916	−	0.593947i
$950$	2.44895	+	4.24171i	0.0794545	+	0.137619i
$951$	−64.0813			−2.07798
$952$	−1.65409	−	3.93501i	−0.0536095	−	0.127534i
$953$	18.1890			0.589201			0.294600	−	0.955621i	$-0.404813\pi$
$953$	18.1890			0.589201			0.294600	+	0.955621i	$0.404813\pi$
$954$	−15.3318	−	26.5555i	−0.496385	−	0.859765i
$955$	7.09571	−	12.2901i	0.229612	−	0.397699i
$956$	8.04555	−	13.9353i	0.260212	−	0.450700i
$957$	−19.8134	−	34.3178i	−0.640477	−	1.10934i
$958$	6.95855			0.224820
$959$	−4.54083	−	10.8024i	−0.146631	−	0.348828i
$960$	21.1859			0.683773
$961$	−24.3207	−	42.1246i	−0.784537	−	1.35886i
$962$	−1.72514	+	2.98803i	−0.0556208	+	0.0963380i
$963$	−21.4886	+	37.2193i	−0.692459	+	1.19937i
$964$	8.62502	+	14.9390i	0.277793	+	0.481152i
$965$	−4.70949			−0.151604
$966$	−21.8609	−	2.76182i	−0.703363	−	0.0888601i
$967$	−45.4584			−1.46184			−0.730921	−	0.682462i	$-0.760909\pi$
$967$	−45.4584			−1.46184			−0.730921	+	0.682462i	$0.760909\pi$
$968$	−11.6906	−	20.2487i	−0.375750	−	0.650818i
$969$	−2.58953	+	4.48520i	−0.0831877	+	0.144085i
$970$	6.82066	−	11.8137i	0.218998	−	0.379316i
$971$	2.84914	+	4.93485i	0.0914332	+	0.158367i	0.908114	−	0.418722i	$-0.137522\pi$
$971$	2.84914	+	4.93485i	0.0914332	+	0.158367i	−0.816681	+	0.577089i	$0.804189\pi$
$972$	12.3010			0.394555
$973$	7.13763	−	9.40335i	0.228822	−	0.301458i
$974$	22.2900			0.714217
$975$	−3.47484	−	6.01861i	−0.111284	−	0.192750i
$976$	11.7214	−	20.3021i	0.375194	−	0.649855i
$977$	−0.992149	+	1.71845i	−0.0317417	+	0.0549782i	−0.881460	−	0.472259i	$-0.843439\pi$
$977$	−0.992149	+	1.71845i	−0.0317417	+	0.0549782i	0.849718	+	0.527237i	$0.176772\pi$
$978$	10.6198	+	18.3940i	0.339583	+	0.588175i
$979$	1.16318			0.0371753
$980$	1.07275	+	3.84235i	0.0342677	+	0.122739i
$981$	42.2643			1.34939
$982$	−10.3628	−	17.9488i	−0.330689	−	0.572770i
$983$	2.18575	−	3.78583i	0.0697146	−	0.120749i	−0.829061	−	0.559158i	$-0.811124\pi$
$983$	2.18575	−	3.78583i	0.0697146	−	0.120749i	0.898776	+	0.438409i	$0.144458\pi$
$984$	−33.8238	+	58.5846i	−1.07826	+	1.86761i
$985$	2.41835	+	4.18870i	0.0770549	+	0.133463i
$986$	5.60759			0.178582
$987$	−21.6523	+	28.5255i	−0.689202	+	0.907977i
$988$	6.73436			0.214249
$989$	−1.56797	−	2.71580i	−0.0498586	−	0.0863575i
$990$	3.08585	−	5.34485i	0.0980747	−	0.169870i
$991$	4.47479	−	7.75056i	0.142146	−	0.246204i	−0.786158	−	0.618025i	$-0.787933\pi$
$991$	4.47479	−	7.75056i	0.142146	−	0.246204i	0.928305	+	0.371821i	$0.121266\pi$
$992$	13.8972	+	24.0706i	0.441236	+	0.764244i
$993$	−61.3041			−1.94543
$994$	−14.5267	−	1.83525i	−0.460759	−	0.0582105i
$995$	4.87596			0.154578
$996$	−1.89262	−	3.27812i	−0.0599701	−	0.103871i
$997$	6.36737	−	11.0286i	0.201657	−	0.349280i	−0.747406	−	0.664368i	$-0.768701\pi$
$997$	6.36737	−	11.0286i	0.201657	−	0.349280i	0.949062	+	0.315088i	$0.102034\pi$
$998$	18.1212	−	31.3868i	0.573617	−	0.993533i
$999$	0.238302	+	0.412751i	0.00753954	+	0.0130589i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1295.2.j.a.186.5	✓	38
7.2	even	3	inner	1295.2.j.a.926.5	yes	38
7.3	odd	6		9065.2.a.s.1.15		19
7.4	even	3		9065.2.a.r.1.15		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1295.2.j.a.186.5	✓	38	1.1	even	1	trivial
1295.2.j.a.926.5	yes	38	7.2	even	3	inner
9065.2.a.r.1.15		19	7.4	even	3
9065.2.a.s.1.15		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+(-0.597934 - 1.03565i) q^{2} +(-1.20438 + 2.08605i) q^{3} +(0.284950 - 0.493547i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.88056 q^{6} +(-1.59963 + 2.10741i) q^{7} -3.07326 q^{8} +(-1.40107 - 2.42672i) q^{9} +(-0.597934 + 1.03565i) q^{10} +(0.920878 - 1.59501i) q^{11} +(0.686376 + 1.18884i) q^{12} +2.88517 q^{13} +(3.13902 + 0.396571i) q^{14} +2.40876 q^{15} +(1.26771 + 2.19574i) q^{16} +(0.262482 - 0.454632i) q^{17} +(-1.67549 + 2.90204i) q^{18} +(2.04785 + 3.54697i) q^{19} -0.569899 q^{20} +(-2.46959 - 5.87504i) q^{21} -2.20250 q^{22} +(1.44561 + 2.50386i) q^{23} +(3.70138 - 6.41097i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.72514 - 2.98803i) q^{26} -0.476604 q^{27} +(0.584291 + 1.39000i) q^{28} -8.93230 q^{29} +(-1.44028 - 2.49464i) q^{30} +(4.46210 - 7.72858i) q^{31} +(-1.55725 + 2.69723i) q^{32} +(2.21818 + 3.84199i) q^{33} -0.627788 q^{34} +(2.62489 + 0.331618i) q^{35} -1.59694 q^{36} +(-0.500000 - 0.866025i) q^{37} +(2.44895 - 4.24171i) q^{38} +(-3.47484 + 6.01861i) q^{39} +(1.53663 + 2.66152i) q^{40} -9.13818 q^{41} +(-4.60784 + 6.07053i) q^{42} -1.08465 q^{43} +(-0.524807 - 0.908993i) q^{44} +(-1.40107 + 2.42672i) q^{45} +(1.72875 - 2.99429i) q^{46} +(-2.80970 - 4.86655i) q^{47} -6.10722 q^{48} +(-1.88235 - 6.74216i) q^{49} +1.19587 q^{50} +(0.632257 + 1.09510i) q^{51} +(0.822128 - 1.42397i) q^{52} +(-4.57531 + 7.92467i) q^{53} +(0.284978 + 0.493596i) q^{54} -1.84176 q^{55} +(4.91609 - 6.47662i) q^{56} -9.86555 q^{57} +(5.34093 + 9.25075i) q^{58} +(3.19071 - 5.52647i) q^{59} +(0.686376 - 1.18884i) q^{60} +(-4.62308 - 8.00741i) q^{61} -10.6722 q^{62} +(7.35529 + 0.929239i) q^{63} +8.79536 q^{64} +(-1.44258 - 2.49863i) q^{65} +(2.65265 - 4.59452i) q^{66} +(2.98693 - 5.17351i) q^{67} +(-0.149588 - 0.259094i) q^{68} -6.96425 q^{69} +(-1.22607 - 2.91676i) q^{70} -4.62779 q^{71} +(4.30585 + 7.45795i) q^{72} +(3.66142 - 6.34176i) q^{73} +(-0.597934 + 1.03565i) q^{74} +(-1.20438 - 2.08605i) q^{75} +2.33413 q^{76} +(1.88827 + 4.49209i) q^{77} +8.31091 q^{78} +(-3.76889 - 6.52791i) q^{79} +(1.26771 - 2.19574i) q^{80} +(4.77722 - 8.27439i) q^{81} +(5.46403 + 9.46397i) q^{82} -2.75742 q^{83} +(-3.60332 - 0.455229i) q^{84} -0.524964 q^{85} +(0.648546 + 1.12332i) q^{86} +(10.7579 - 18.6332i) q^{87} +(-2.83010 + 4.90187i) q^{88} +(0.315779 + 0.546946i) q^{89} +3.35099 q^{90} +(-4.61521 + 6.08023i) q^{91} +1.64770 q^{92} +(10.7481 + 18.6163i) q^{93} +(-3.36004 + 5.81975i) q^{94} +(2.04785 - 3.54697i) q^{95} +(-3.75104 - 6.49700i) q^{96} -11.4070 q^{97} +(-5.85701 + 5.98083i) q^{98} -5.16085 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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