LMFDB - Embedded newform 95.5.n.a.21.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [95,5,Mod(21,95)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("95.21"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(95, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	95.n (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$9.82014649297$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			21.16
Character	$\chi$	$=$	95.21
Dual form			95.5.n.a.86.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.17727 + 0.383911i) q^{2} +(5.55356 - 6.61847i) q^{3} +(-10.4420 - 3.80057i) q^{4} +(10.5061 - 3.82390i) q^{5} +(14.6325 - 12.2781i) q^{6} +(-21.8707 - 37.8811i) q^{7} +(-51.9104 - 29.9705i) q^{8} +(1.10333 + 6.25730i) q^{9} +(24.3426 - 4.29225i) q^{10} +(28.2835 - 48.9884i) q^{11} +(-83.1441 + 48.0033i) q^{12} +(-138.547 - 165.114i) q^{13} +(-33.0753 - 90.8737i) q^{14} +(33.0378 - 90.7705i) q^{15} +(34.6813 + 29.1011i) q^{16} +(-22.6036 + 128.192i) q^{17} +14.0474i q^{18} +(-19.8808 - 360.452i) q^{19} -124.237 q^{20} +(-372.175 - 65.6245i) q^{21} +(80.3879 - 95.8025i) q^{22} +(-102.430 - 37.2815i) q^{23} +(-486.646 + 177.125i) q^{24} +(95.7556 - 80.3485i) q^{25} +(-238.265 - 412.687i) q^{26} +(653.606 + 377.360i) q^{27} +(84.4033 + 478.675i) q^{28} +(162.596 - 28.6700i) q^{29} +(106.780 - 184.948i) q^{30} +(991.881 - 572.663i) q^{31} +(680.807 + 811.354i) q^{32} +(-167.155 - 459.254i) q^{33} +(-98.4283 + 270.430i) q^{34} +(-374.629 - 314.351i) q^{35} +(12.2603 - 69.5319i) q^{36} -704.475i q^{37} +(95.0956 - 792.433i) q^{38} -1862.23 q^{39} +(-659.979 - 116.372i) q^{40} +(695.611 - 828.997i) q^{41} +(-785.131 - 285.764i) q^{42} +(903.402 - 328.811i) q^{43} +(-481.520 + 404.043i) q^{44} +(35.5190 + 61.5207i) q^{45} +(-208.705 - 120.496i) q^{46} +(581.984 + 3300.60i) q^{47} +(385.209 - 67.9228i) q^{48} +(243.847 - 422.356i) q^{49} +(239.332 - 138.178i) q^{50} +(722.902 + 861.521i) q^{51} +(819.178 + 2250.67i) q^{52} +(-1350.30 + 3709.93i) q^{53} +(1278.20 + 1072.54i) q^{54} +(109.822 - 622.830i) q^{55} +2621.90i q^{56} +(-2496.05 - 1870.21i) q^{57} +365.021 q^{58} +(342.338 + 60.3635i) q^{59} +(-689.959 + 822.261i) q^{60} +(4444.89 + 1617.81i) q^{61} +(2379.44 - 866.046i) q^{62} +(212.903 - 178.647i) q^{63} +(808.625 + 1400.58i) q^{64} +(-2086.97 - 1204.91i) q^{65} +(-187.628 - 1064.09i) q^{66} +(-21.4080 + 3.77481i) q^{67} +(723.228 - 1252.67i) q^{68} +(-815.597 + 470.885i) q^{69} +(-694.984 - 828.250i) q^{70} +(2408.31 + 6616.78i) q^{71} +(130.260 - 357.886i) q^{72} +(-2816.76 - 2363.54i) q^{73} +(270.456 - 1533.83i) q^{74} -1079.98i q^{75} +(-1162.33 + 3839.39i) q^{76} -2474.32 q^{77} +(-4054.57 - 714.930i) q^{78} +(4968.12 - 5920.78i) q^{79} +(475.644 + 173.120i) q^{80} +(5643.76 - 2054.16i) q^{81} +(1832.79 - 1537.89i) q^{82} +(-2978.89 - 5159.59i) q^{83} +(3636.83 + 2099.73i) q^{84} +(252.716 + 1433.23i) q^{85} +(2093.18 - 369.084i) q^{86} +(713.233 - 1235.36i) q^{87} +(-2936.41 + 1695.34i) q^{88} +(-6671.58 - 7950.87i) q^{89} +(53.7158 + 147.583i) q^{90} +(-3224.58 + 8859.47i) q^{91} +(927.881 + 778.585i) q^{92} +(1718.32 - 9745.06i) q^{93} +7409.71i q^{94} +(-1587.20 - 3710.92i) q^{95} +9150.83 q^{96} +(-6459.56 - 1138.99i) q^{97} +(693.068 - 825.966i) q^{98} +(337.741 + 122.928i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q + 24 q^{3} + 42 q^{4} + 42 q^{6} - 504 q^{9} - 150 q^{10} - 1728 q^{12} - 1122 q^{13} + 576 q^{14} + 2058 q^{16} + 1260 q^{17} + 900 q^{19} + 1026 q^{21} - 4608 q^{22} - 1260 q^{23} - 4032 q^{24}+ \cdots + 28038 q^{99}+O(q^{100}) $ 156 * q + 24 * q^3 + 42 * q^4 + 42 * q^6 - 504 * q^9 - 150 * q^10 - 1728 * q^12 - 1122 * q^13 + 576 * q^14 + 2058 * q^16 + 1260 * q^17 + 900 * q^19 + 1026 * q^21 - 4608 * q^22 - 1260 * q^23 - 4032 * q^24 + 3672 * q^26 - 2448 * q^27 + 4992 * q^28 + 1494 * q^29 - 4200 * q^30 + 5616 * q^31 + 11700 * q^32 + 2430 * q^33 + 15300 * q^34 + 1800 * q^35 + 13392 * q^36 + 9414 * q^38 - 12504 * q^39 - 2400 * q^40 - 15120 * q^41 - 36834 * q^42 + 5586 * q^43 - 61398 * q^44 - 8910 * q^46 + 3870 * q^47 + 57462 * q^48 - 16014 * q^49 + 25116 * q^51 + 6642 * q^52 + 21312 * q^53 - 14226 * q^54 - 8166 * q^57 - 10752 * q^58 - 16686 * q^59 - 18900 * q^60 - 58092 * q^61 - 6120 * q^62 - 60702 * q^63 + 33132 * q^64 + 16200 * q^65 + 41916 * q^66 + 41406 * q^67 + 9630 * q^68 + 65826 * q^69 + 41400 * q^70 + 28296 * q^71 + 76524 * q^72 + 2790 * q^73 - 32004 * q^74 + 5580 * q^76 - 5508 * q^77 - 22620 * q^78 + 5334 * q^79 - 32400 * q^80 - 55848 * q^81 - 68154 * q^82 - 8280 * q^83 - 84564 * q^84 - 33600 * q^85 + 20178 * q^86 - 28968 * q^87 - 13104 * q^88 - 13212 * q^89 - 28650 * q^90 + 122592 * q^91 + 57708 * q^92 + 93744 * q^93 - 211236 * q^96 + 18966 * q^97 + 13968 * q^98 + 28038 * q^99

Character values

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

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$1$

Coefficient data

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

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

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

$2$	2.17727	+	0.383911i	0.544317	+	0.0959777i	0.439044	−	0.898466i	$-0.355317\pi$
$2$	2.17727	+	0.383911i	0.544317	+	0.0959777i	0.105273	+	0.994443i	$0.466428\pi$
$3$	5.55356	−	6.61847i	0.617062	−	0.735386i	−0.363500	−	0.931594i	$-0.618418\pi$
$3$	5.55356	−	6.61847i	0.617062	−	0.735386i	0.980562	+	0.196208i	$0.0628629\pi$
$4$	−10.4420	−	3.80057i	−0.652624	−	0.237536i
$5$	10.5061	−	3.82390i	0.420243	−	0.152956i
$5$	10.5061	−	3.82390i	0.420243	−	0.152956i
$6$	14.6325	−	12.2781i	0.406458	−	0.341059i
$7$	−21.8707	−	37.8811i	−0.446340	−	0.773084i	0.551804	−	0.833974i	$-0.313940\pi$
$7$	−21.8707	−	37.8811i	−0.446340	−	0.773084i	−0.998145	+	0.0608896i	$0.980606\pi$
$8$	−51.9104	−	29.9705i	−0.811100	−	0.468289i
$9$	1.10333	+	6.25730i	0.0136214	+	0.0772506i
$10$	24.3426	−	4.29225i	0.243426	−	0.0429225i
$11$	28.2835	−	48.9884i	0.233748	−	0.404863i	−0.725160	−	0.688580i	$-0.758234\pi$
$11$	28.2835	−	48.9884i	0.233748	−	0.404863i	0.958908	+	0.283717i	$0.0915677\pi$
$12$	−83.1441	+	48.0033i	−0.577390	+	0.333356i
$13$	−138.547	−	165.114i	−0.819805	−	0.977005i	0.180173	−	0.983635i	$-0.442334\pi$
$13$	−138.547	−	165.114i	−0.819805	−	0.977005i	−0.999978	+	0.00662956i	$0.997890\pi$
$14$	−33.0753	−	90.8737i	−0.168752	−	0.463641i
$15$	33.0378	−	90.7705i	0.146834	−	0.403424i
$16$	34.6813	+	29.1011i	0.135474	+	0.113676i
$17$	−22.6036	+	128.192i	−0.0782133	+	0.443570i	0.920402	+	0.390972i	$0.127861\pi$
$17$	−22.6036	+	128.192i	−0.0782133	+	0.443570i	−0.998616	+	0.0525975i	$0.983250\pi$
$18$			14.0474i			0.0433561i
$19$	−19.8808	−	360.452i	−0.0550715	−	0.998482i
$19$	−19.8808	−	360.452i	−0.0550715	−	0.998482i
$20$	−124.237			−0.310593
$21$	−372.175	−	65.6245i	−0.843935	−	0.148808i
$22$	80.3879	−	95.8025i	0.166091	−	0.197939i
$23$	−102.430	−	37.2815i	−0.193629	−	0.0704754i	0.243385	−	0.969930i	$-0.421742\pi$
$23$	−102.430	−	37.2815i	−0.193629	−	0.0704754i	−0.437015	+	0.899454i	$0.643964\pi$
$24$	−486.646	+	177.125i	−0.844872	+	0.307508i
$25$	95.7556	−	80.3485i	0.153209	−	0.128558i
$26$	−238.265	−	412.687i	−0.352463	−	0.610483i
$27$	653.606	+	377.360i	0.896580	+	0.517640i
$28$	84.4033	+	478.675i	0.107657	+	0.610555i
$29$	162.596	−	28.6700i	0.193336	−	0.0340904i	−0.0761415	−	0.997097i	$-0.524260\pi$
$29$	162.596	−	28.6700i	0.193336	−	0.0340904i	0.269478	+	0.963007i	$0.413149\pi$
$30$	106.780	−	184.948i	0.118644	−	0.205498i
$31$	991.881	−	572.663i	1.03213	−	0.595903i	0.114539	−	0.993419i	$-0.463461\pi$
$31$	991.881	−	572.663i	1.03213	−	0.595903i	0.917595	+	0.397516i	$0.130128\pi$
$32$	680.807	+	811.354i	0.664851	+	0.792338i
$33$	−167.155	−	459.254i	−0.153494	−	0.421720i
$34$	−98.4283	+	270.430i	−0.0851456	+	0.233936i
$35$	−374.629	−	314.351i	−0.305819	−	0.256613i
$36$	12.2603	−	69.5319i	0.00946014	−	0.0536511i
$37$		−	704.475i		−	0.514591i	−0.966333	−	0.257295i	$-0.917169\pi$
$37$		−	704.475i		−	0.514591i	0.966333	−	0.257295i	$-0.0828314\pi$
$38$	95.0956	−	792.433i	0.0658557	−	0.548776i
$39$	−1862.23			−1.22435
$40$	−659.979	−	116.372i	−0.412487	−	0.0727326i
$41$	695.611	−	828.997i	0.413808	−	0.493157i	−0.518371	−	0.855156i	$-0.673461\pi$
$41$	695.611	−	828.997i	0.413808	−	0.493157i	0.932178	+	0.361999i	$0.117906\pi$
$42$	−785.131	−	285.764i	−0.445085	−	0.161998i
$43$	903.402	−	328.811i	0.488589	−	0.177832i	−0.0859655	−	0.996298i	$-0.527397\pi$
$43$	903.402	−	328.811i	0.488589	−	0.177832i	0.574555	+	0.818466i	$0.305175\pi$
$44$	−481.520	+	404.043i	−0.248719	+	0.208700i
$45$	35.5190	+	61.5207i	0.0175402	+	0.0303806i
$46$	−208.705	−	120.496i	−0.0986317	−	0.0569450i
$47$	581.984	+	3300.60i	0.263461	+	1.49416i	0.773383	+	0.633939i	$0.218563\pi$
$47$	581.984	+	3300.60i	0.263461	+	1.49416i	−0.509923	+	0.860220i	$0.670326\pi$
$48$	385.209	−	67.9228i	0.167192	−	0.0294804i
$49$	243.847	−	422.356i	0.101561	−	0.175908i
$50$	239.332	−	138.178i	0.0957328	−	0.0552714i
$51$	722.902	+	861.521i	0.277932	+	0.331227i
$52$	819.178	+	2250.67i	0.302951	+	0.832350i
$53$	−1350.30	+	3709.93i	−0.480706	+	1.32073i	0.428183	+	0.903692i	$0.359154\pi$
$53$	−1350.30	+	3709.93i	−0.480706	+	1.32073i	−0.908889	+	0.417038i	$0.863068\pi$
$54$	1278.20	+	1072.54i	0.438341	+	0.367812i
$55$	109.822	−	622.830i	0.0363047	−	0.205894i
$56$			2621.90i			0.836064i
$57$	−2496.05	−	1870.21i	−0.768252	−	0.575627i
$58$	365.021			0.108508
$59$	342.338	+	60.3635i	0.0983448	+	0.0173408i	0.222604	−	0.974909i	$-0.428544\pi$
$59$	342.338	+	60.3635i	0.0983448	+	0.0173408i	−0.124259	+	0.992250i	$0.539655\pi$
$60$	−689.959	+	822.261i	−0.191655	+	0.228406i
$61$	4444.89	+	1617.81i	1.19454	+	0.434778i	0.861316	−	0.508069i	$-0.169641\pi$
$61$	4444.89	+	1617.81i	1.19454	+	0.434778i	0.333226	+	0.942847i	$0.391863\pi$
$62$	2379.44	−	866.046i	0.619001	−	0.225298i
$63$	212.903	−	178.647i	0.0536414	−	0.0450105i
$64$	808.625	+	1400.58i	0.197418	+	0.341938i
$65$	−2086.97	−	1204.91i	−0.493956	−	0.285186i
$66$	−187.628	−	1064.09i	−0.0430734	−	0.244281i
$67$	−21.4080	+	3.77481i	−0.00476899	+	0.000840901i	−0.176032	−	0.984384i	$-0.556326\pi$
$67$	−21.4080	+	3.77481i	−0.00476899	+	0.000840901i	0.171263	+	0.985225i	$0.445215\pi$
$68$	723.228	−	1252.67i	0.156407	−	0.270906i
$69$	−815.597	+	470.885i	−0.171308	+	0.0989047i
$70$	−694.984	−	828.250i	−0.141833	−	0.169031i
$71$	2408.31	+	6616.78i	0.477745	+	1.31259i	0.911403	+	0.411515i	$0.135000\pi$
$71$	2408.31	+	6616.78i	0.477745	+	1.31259i	−0.433658	+	0.901077i	$0.642778\pi$
$72$	130.260	−	357.886i	0.0251273	−	0.0690367i
$73$	−2816.76	−	2363.54i	−0.528572	−	0.443525i	0.339036	−	0.940773i	$-0.389899\pi$
$73$	−2816.76	−	2363.54i	−0.528572	−	0.443525i	−0.867608	+	0.497249i	$0.834344\pi$
$74$	270.456	−	1533.83i	0.0493893	−	0.280100i
$75$		−	1079.98i		−	0.191996i
$76$	−1162.33	+	3839.39i	−0.201234	+	0.664715i
$77$	−2474.32			−0.417324
$78$	−4054.57	−	714.930i	−0.666432	−	0.117510i
$79$	4968.12	−	5920.78i	0.796046	−	0.948690i	−0.203493	−	0.979076i	$-0.565229\pi$
$79$	4968.12	−	5920.78i	0.796046	−	0.948690i	0.999538	+	0.0303862i	$0.00967373\pi$
$80$	475.644	+	173.120i	0.0743194	+	0.0270501i
$81$	5643.76	−	2054.16i	0.860199	−	0.313087i
$82$	1832.79	−	1537.89i	0.272575	−	0.228717i
$83$	−2978.89	−	5159.59i	−0.432413	−	0.748961i	0.564668	−	0.825318i	$-0.309004\pi$
$83$	−2978.89	−	5159.59i	−0.432413	−	0.748961i	−0.997081	+	0.0763573i	$0.975671\pi$
$84$	3636.83	+	2099.73i	0.515424	+	0.297580i
$85$	252.716	+	1433.23i	0.0349781	+	0.198370i
$86$	2093.18	−	369.084i	0.283015	−	0.0499032i
$87$	713.233	−	1235.36i	0.0942308	−	0.163213i
$88$	−2936.41	+	1695.34i	−0.379186	+	0.218923i
$89$	−6671.58	−	7950.87i	−0.842264	−	1.00377i	−0.999868	−	0.0162691i	$-0.994821\pi$
$89$	−6671.58	−	7950.87i	−0.842264	−	1.00377i	0.157603	−	0.987503i	$-0.449623\pi$
$90$	53.7158	+	147.583i	0.00663158	+	0.0182201i
$91$	−3224.58	+	8859.47i	−0.389395	+	1.06985i
$92$	927.881	+	778.585i	0.109627	+	0.0919878i
$93$	1718.32	−	9745.06i	0.198672	−	1.12673i
$94$			7409.71i			0.838582i
$95$	−1587.20	−	3710.92i	−0.175867	−	0.411182i
$96$	9150.83			0.992928
$97$	−6459.56	−	1138.99i	−0.686530	−	0.121054i	−0.180507	−	0.983574i	$-0.557774\pi$
$97$	−6459.56	−	1138.99i	−0.686530	−	0.121054i	−0.506023	+	0.862520i	$0.668885\pi$
$98$	693.068	−	825.966i	0.0721645	−	0.0860023i
$99$	337.741	+	122.928i	0.0344599	+	0.0125424i
$100$	−1305.25	+	475.071i	−0.130525	+	0.0475071i
$101$	−4932.79	+	4139.10i	−0.483560	+	0.405755i	−0.851712	−	0.524011i	$-0.824435\pi$
$101$	−4932.79	+	4139.10i	−0.483560	+	0.405755i	0.368152	+	0.929766i	$0.379991\pi$
$102$	1243.20	+	2153.29i	0.119493	+	0.206968i
$103$	−13584.6	−	7843.07i	−1.28048	−	0.739284i	−0.303543	−	0.952818i	$-0.598169\pi$
$103$	−13584.6	−	7843.07i	−1.28048	−	0.739284i	−0.976936	+	0.213533i	$0.931503\pi$
$104$	2243.49	+	12723.4i	0.207423	+	1.17635i
$105$	−4161.04	+	733.704i	−0.377419	+	0.0665492i
$106$	−4364.26	+	7559.11i	−0.388417	+	0.672758i
$107$	14968.5	−	8642.08i	1.30741	−	0.754833i	0.325746	−	0.945457i	$-0.394385\pi$
$107$	14968.5	−	8642.08i	1.30741	−	0.754833i	0.981663	+	0.190625i	$0.0610513\pi$
$108$	−5390.76	−	6424.46i	−0.462171	−	0.550794i
$109$	−3462.81	−	9513.99i	−0.291458	−	0.800773i	−0.995854	−	0.0909663i	$-0.971004\pi$
$109$	−3462.81	−	9513.99i	−0.291458	−	0.800773i	0.704396	−	0.709807i	$-0.251218\pi$
$110$	478.222	−	1313.90i	0.0395225	−	0.108587i
$111$	−4662.55	−	3912.34i	−0.378423	−	0.317535i
$112$	343.878	−	1950.23i	0.0274137	−	0.155471i
$113$		−	4865.82i		−	0.381065i	−0.981681	−	0.190532i	$-0.938979\pi$
$113$		−	4865.82i		−	0.381065i	0.981681	−	0.190532i	$-0.0610214\pi$
$114$	−4716.58	−	5030.21i	−0.362925	−	0.387058i
$115$	−1218.70			−0.0921511
$116$	−1806.78	−	318.585i	−0.134273	−	0.0236760i
$117$	880.304	−	1049.11i	0.0643074	−	0.0766385i
$118$	722.187	+	262.855i	0.0518664	+	0.0188778i
$119$	5350.40	−	1947.39i	0.377826	−	0.137518i
$120$	−4435.44	+	3721.77i	−0.308016	+	0.258456i
$121$	5720.59	+	9908.35i	0.390724	+	0.676754i
$122$	9056.62	+	5228.84i	0.608480	+	0.351306i
$123$	−1623.58	−	9207.76i	−0.107316	−	0.608617i
$124$	−12533.7	+	2210.02i	−0.815144	+	0.143732i
$125$	698.771	−	1210.31i	0.0447214	−	0.0774597i
$126$	532.131	−	307.226i	0.0335179	−	0.0193516i
$127$	−2775.47	−	3307.67i	−0.172079	−	0.205076i	0.673111	−	0.739541i	$-0.264957\pi$
$127$	−2775.47	−	3307.67i	−0.172079	−	0.205076i	−0.845190	+	0.534465i	$0.820513\pi$
$128$	−4573.10	−	12564.5i	−0.279120	−	0.766876i
$129$	2840.86	−	7805.21i	0.170715	−	0.469035i
$130$	−4081.30	−	3424.62i	−0.241497	−	0.202640i
$131$	3913.79	−	22196.2i	0.228063	−	1.29341i	−0.628680	−	0.777664i	$-0.716404\pi$
$131$	3913.79	−	22196.2i	0.228063	−	1.29341i	0.856742	−	0.515744i	$-0.172485\pi$
$132$			5430.80i			0.311685i
$133$	−13219.5	+	8636.44i	−0.747330	+	0.488238i
$134$	−48.0601			−0.00267655
$135$	8309.83	+	1465.25i	0.455958	+	0.0803977i
$136$	5015.33	−	5977.04i	0.271157	−	0.323153i
$137$	−1014.33	−	369.185i	−0.0540427	−	0.0196699i	0.314857	−	0.949139i	$-0.398043\pi$
$137$	−1014.33	−	369.185i	−0.0540427	−	0.0196699i	−0.368900	+	0.929469i	$0.620266\pi$
$138$	−1956.55	+	712.126i	−0.102738	+	0.0373937i
$139$	4629.48	−	3884.60i	0.239609	−	0.201056i	−0.515074	−	0.857146i	$-0.672235\pi$
$139$	4629.48	−	3884.60i	0.239609	−	0.201056i	0.754682	+	0.656090i	$0.227791\pi$
$140$	2717.15	+	4706.25i	0.138630	+	0.240115i
$141$	25077.0	+	14478.2i	1.26135	+	0.728243i
$142$	2703.28	+	15331.1i	0.134065	+	0.760319i
$143$	−12007.3	+	2117.20i	−0.587181	+	0.103536i
$144$	−143.829	+	249.119i	−0.00693621	+	0.0120139i
$145$	1598.61	−	922.960i	0.0760339	−	0.0438982i
$146$	−5225.45	−	6227.45i	−0.245142	−	0.292149i
$147$	−1441.13	−	3959.47i	−0.0666912	−	0.183233i
$148$	−2677.41	+	7356.11i	−0.122234	+	0.335834i
$149$	24025.6	+	20159.9i	1.08219	+	0.908062i	0.996101	−	0.0882256i	$-0.0281197\pi$
$149$	24025.6	+	20159.9i	1.08219	+	0.908062i	0.0860857	+	0.996288i	$0.472564\pi$
$150$	414.614	−	2351.39i	0.0184273	−	0.104506i
$151$			12355.4i			0.541880i	0.962596	+	0.270940i	$0.0873346\pi$
$151$			12355.4i			0.541880i	−0.962596	+	0.270940i	$0.912665\pi$
$152$	−9770.90	+	19307.0i	−0.422910	+	0.835658i
$153$	−827.073			−0.0353314
$154$	−5387.24	−	949.917i	−0.227157	−	0.0400538i
$155$	8230.98	−	9809.30i	0.342601	−	0.408296i
$156$	19445.4	+	7077.54i	0.799037	+	0.290826i
$157$	17116.9	−	6230.03i	0.694425	−	0.252750i	0.0293962	−	0.999568i	$-0.490642\pi$
$157$	17116.9	−	6230.03i	0.694425	−	0.252750i	0.665029	+	0.746818i	$0.268419\pi$
$158$	13090.0	−	10983.8i	0.524354	−	0.439985i
$159$	17055.1	+	29540.3i	0.674620	+	1.16848i
$160$	10255.2	+	5920.82i	0.400592	+	0.231282i
$161$	827.949	+	4695.53i	0.0319413	+	0.181148i
$162$	13076.6	−	2305.76i	0.498270	−	0.0878584i
$163$	−23093.1	+	39998.5i	−0.869176	+	1.50546i	−0.00633681	+	0.999980i	$0.502017\pi$
$163$	−23093.1	+	39998.5i	−0.869176	+	1.50546i	−0.862840	+	0.505478i	$0.831316\pi$
$164$	−10414.2	+	6012.65i	−0.387203	+	0.223552i
$165$	−3512.28	−	4185.77i	−0.129009	−	0.153747i
$166$	−4505.02	−	12377.4i	−0.163486	−	0.449174i
$167$	−13856.2	+	38069.6i	−0.496833	+	1.36504i	0.397485	+	0.917608i	$0.369883\pi$
$167$	−13856.2	+	38069.6i	−0.496833	+	1.36504i	−0.894319	+	0.447430i	$0.852339\pi$
$168$	17353.0	+	14560.9i	0.614830	+	0.515904i
$169$	−3107.76	+	17625.0i	−0.108811	+	0.617100i
$170$			3217.54i			0.111333i
$171$	2233.52	−	522.098i	0.0763832	−	0.0178550i
$172$	−10683.0			−0.361106
$173$	−23889.6	−	4212.38i	−0.798208	−	0.140746i	−0.240355	−	0.970685i	$-0.577264\pi$
$173$	−23889.6	−	4212.38i	−0.798208	−	0.140746i	−0.557854	+	0.829939i	$0.688375\pi$
$174$	2027.17	−	2415.88i	0.0669562	−	0.0797953i
$175$	−5137.93	−	1870.05i	−0.167769	−	0.0610629i
$176$	2406.52	−	875.903i	0.0776900	−	0.0282768i
$177$	2300.71	−	1930.52i	0.0734370	−	0.0616210i
$178$	−11473.4	−	19872.5i	−0.362119	−	0.627208i
$179$	44649.2	+	25778.2i	1.39350	+	0.804538i	0.993701	−	0.112064i	$-0.0357463\pi$
$179$	44649.2	+	25778.2i	1.39350	+	0.804538i	0.399800	+	0.916602i	$0.369080\pi$
$180$	−137.075	−	777.390i	−0.00423070	−	0.0239935i
$181$	−40704.0	+	7177.22i	−1.24245	+	0.219078i	−0.755967	−	0.654610i	$-0.772833\pi$
$181$	−40704.0	+	7177.22i	−1.24245	+	0.219078i	−0.486487	+	0.873688i	$0.661722\pi$
$182$	−10422.0	+	18051.5i	−0.314637	+	0.544967i
$183$	35392.4	−	20433.8i	1.05684	−	0.610164i
$184$	4199.84	+	5005.17i	0.124050	+	0.147837i
$185$	−2693.84	−	7401.27i	−0.0787098	−	0.216253i
$186$	7482.46	−	20557.9i	0.216281	−	0.594228i
$187$	5640.60	+	4733.02i	0.161303	+	0.135349i
$188$	6467.08	−	36676.6i	0.182975	−	1.03770i
$189$		−	33012.5i		−	0.924175i
$190$	−2031.10	−	8689.00i	−0.0562632	−	0.240693i
$191$	−3197.46			−0.0876471			−0.0438236	−	0.999039i	$-0.513954\pi$
$191$	−3197.46			−0.0876471			−0.0438236	+	0.999039i	$0.513954\pi$
$192$	13760.4	+	2426.34i	0.373276	+	0.0658186i
$193$	−14240.9	+	16971.6i	−0.382315	+	0.455626i	−0.922544	−	0.385893i	$-0.873893\pi$
$193$	−14240.9	+	16971.6i	−0.382315	+	0.455626i	0.540228	+	0.841518i	$0.318338\pi$
$194$	−13626.9	−	4959.79i	−0.362071	−	0.131783i
$195$	−19564.7	+	7120.99i	−0.514523	+	0.187271i
$196$	−4151.44	+	3483.47i	−0.108065	+	0.0906777i
$197$	−7296.37	−	12637.7i	−0.188007	−	0.325638i	0.756579	−	0.653903i	$-0.226869\pi$
$197$	−7296.37	−	12637.7i	−0.188007	−	0.325638i	−0.944586	+	0.328265i	$0.893536\pi$
$198$	688.159	+	397.309i	0.0175533	+	0.0101344i
$199$	−732.695	−	4155.32i	−0.0185019	−	0.104930i	0.974158	−	0.225866i	$-0.0725213\pi$
$199$	−732.695	−	4155.32i	−0.0185019	−	0.104930i	−0.992660	+	0.120937i	$0.961410\pi$
$200$	−7378.79	+	1301.08i	−0.184470	+	0.0325270i
$201$	−93.9070	+	162.652i	−0.00232437	+	0.00402593i
$202$	−12329.1	+	7118.18i	−0.302153	+	0.174448i
$203$	−4642.13	−	5532.28i	−0.112648	−	0.134249i
$204$	−4274.26	−	11743.4i	−0.102707	−	0.282185i
$205$	4138.14	−	11369.5i	0.0984686	−	0.270540i
$206$	−26566.2	−	22291.7i	−0.626031	−	0.525302i
$207$	120.267	−	682.069i	0.00280677	−	0.0159180i
$208$		−	9758.24i		−	0.225551i
$209$	−18220.3	−	9220.91i	−0.417122	−	0.211097i
$210$	−9341.38			−0.211823
$211$	−13963.4	−	2462.12i	−0.313636	−	0.0553024i	0.0146146	−	0.999893i	$-0.495348\pi$
$211$	−13963.4	−	2462.12i	−0.313636	−	0.0553024i	−0.328250	+	0.944591i	$0.606459\pi$
$212$	28199.7	−	33607.1i	0.627441	−	0.747755i
$213$	57167.7	+	20807.3i	1.26006	+	0.458624i
$214$	35908.3	−	13069.5i	0.784092	−	0.285386i
$215$	8233.87	−	6909.04i	0.178126	−	0.149465i
$216$	−22619.3	−	39177.8i	−0.484810	−	0.839716i
$217$	−43386.2	−	25049.0i	−0.921366	−	0.531951i
$218$	−3886.93	−	22043.9i	−0.0817888	−	0.463848i
$219$	−31286.1	+	5516.58i	−0.652324	+	0.115022i
$220$	−3513.86	+	6086.19i	−0.0726005	+	0.125748i
$221$	24297.9	−	14028.4i	0.497490	−	0.287226i
$222$	−8649.62	−	10308.2i	−0.175506	−	0.209159i
$223$	31541.6	+	86659.8i	0.634269	+	1.74264i	0.669020	+	0.743244i	$0.266714\pi$
$223$	31541.6	+	86659.8i	0.634269	+	1.74264i	−0.0347510	+	0.999396i	$0.511064\pi$
$224$	15845.3	−	43534.6i	0.315794	−	0.867638i
$225$	608.414	+	510.520i	0.0120181	+	0.0100843i
$226$	1868.04	−	10594.2i	0.0365737	−	0.207420i
$227$		−	45207.0i		−	0.877311i	−0.898655	−	0.438656i	$-0.855455\pi$
$227$		−	45207.0i		−	0.877311i	0.898655	−	0.438656i	$-0.144545\pi$
$228$	18955.9	+	29015.1i	0.364648	+	0.558155i
$229$	−62196.7			−1.18603			−0.593016	−	0.805191i	$-0.702063\pi$
$229$	−62196.7			−1.18603			−0.593016	+	0.805191i	$0.702063\pi$
$230$	−2653.43	−	467.872i	−0.0501594	−	0.00884446i
$231$	−13741.3	+	16376.2i	−0.257515	+	0.306894i
$232$	−9299.66	−	3384.80i	−0.172779	−	0.0628864i
$233$	60185.3	−	21905.6i	1.10861	−	0.403501i	0.278126	−	0.960545i	$-0.410287\pi$
$233$	60185.3	−	21905.6i	1.10861	−	0.403501i	0.830483	+	0.557044i	$0.188065\pi$
$234$	2319.42	−	1946.22i	0.0423592	−	0.0355436i
$235$	18735.5	+	32450.9i	0.339258	+	0.587612i
$236$	−3345.27	−	1931.39i	−0.0600631	−	0.0346774i
$237$	−11595.7	−	65762.7i	−0.206444	−	1.17080i
$238$	12396.9	−	2185.90i	0.218856	−	0.0385902i
$239$	−24211.9	+	41936.2i	−0.423870	+	0.734164i	−0.996314	−	0.0857795i	$-0.972662\pi$
$239$	−24211.9	+	41936.2i	−0.423870	+	0.734164i	0.572444	+	0.819944i	$0.305995\pi$
$240$	3787.31	−	2186.61i	0.0657519	−	0.0379619i
$241$	30373.7	+	36198.0i	0.522954	+	0.623233i	0.961277	−	0.275585i	$-0.0888716\pi$
$241$	30373.7	+	36198.0i	0.522954	+	0.623233i	−0.438322	+	0.898818i	$0.644427\pi$
$242$	8651.32	+	23769.3i	0.147724	+	0.405869i
$243$	−3160.92	+	8684.56i	−0.0535305	+	0.147074i
$244$	−40264.9	−	33786.2i	−0.676311	−	0.567493i
$245$	946.833	−	5369.75i	0.0157740	−	0.0894586i
$246$		−	20671.1i		−	0.341580i
$247$	−56761.2	+	53222.2i	−0.930375	+	0.872366i
$248$	−68651.9			−1.11622
$249$	−50692.1	−	8938.38i	−0.817601	−	0.144165i
$250$	1986.06	−	2366.90i	0.0317770	−	0.0378703i
$251$	59907.9	+	21804.7i	0.950904	+	0.346101i	0.770463	−	0.637485i	$-0.220025\pi$
$251$	59907.9	+	21804.7i	0.950904	+	0.346101i	0.180441	+	0.983586i	$0.442248\pi$
$252$	−2902.09	+	1056.27i	−0.0456993	+	0.0166332i
$253$	−4723.44	+	3963.44i	−0.0737934	+	0.0619200i
$254$	−4773.08	−	8267.21i	−0.0739828	−	0.128142i
$255$	10889.2	+	6286.91i	0.167462	+	0.0966845i
$256$	−9626.54	−	54594.8i	−0.146889	−	0.833051i
$257$	21900.4	−	3861.62i	0.331577	−	0.0584661i	−0.00538113	−	0.999986i	$-0.501713\pi$
$257$	21900.4	−	3861.62i	0.331577	−	0.0584661i	0.336959	+	0.941519i	$0.390602\pi$
$258$	9181.82	−	15903.4i	0.137940	−	0.238919i
$259$	−26686.3	+	15407.3i	−0.397822	+	0.229683i
$260$	17212.7	+	20513.3i	0.254626	+	0.303451i
$261$	358.794	+	985.777i	0.00526700	+	0.0144710i
$262$	17042.7	−	46824.5i	0.248277	−	0.682135i
$263$	44146.6	+	37043.4i	0.638242	+	0.535549i	0.903478	−	0.428635i	$-0.141005\pi$
$263$	44146.6	+	37043.4i	0.638242	+	0.535549i	−0.265236	+	0.964184i	$0.585450\pi$
$264$	−5086.99	+	28849.7i	−0.0729882	+	0.413937i
$265$			44140.3i			0.628555i
$266$	−32098.0	+	13728.7i	−0.453644	+	0.194029i
$267$	−89673.6			−1.25789
$268$	237.888	+	41.9461i	0.00331210	+	0.000584012i
$269$	76697.8	−	91404.9i	1.05993	−	1.26318i	0.0964709	−	0.995336i	$-0.469245\pi$
$269$	76697.8	−	91404.9i	1.05993	−	1.26318i	0.963462	−	0.267844i	$-0.0863110\pi$
$270$	17530.2	+	6380.47i	0.240469	+	0.0875236i
$271$	−83761.7	+	30486.8i	−1.14053	+	0.415119i	−0.842105	−	0.539313i	$-0.818684\pi$
$271$	−83761.7	+	30486.8i	−1.14053	+	0.415119i	−0.298426	+	0.954433i	$0.596462\pi$
$272$	−4514.44	+	3788.06i	−0.0610191	+	0.0512011i
$273$	40728.2	+	70543.4i	0.546475	+	0.946522i
$274$	−2066.73	−	1193.23i	−0.0275285	−	0.0158936i
$275$	−1227.84	−	6963.45i	−0.0162360	−	0.0920787i
$276$	10306.1	−	1817.24i	0.135293	−	0.0238558i
$277$	55348.2	−	95866.0i	0.721347	−	1.24941i	−0.239113	−	0.970992i	$-0.576857\pi$
$277$	55348.2	−	95866.0i	0.721347	−	1.24941i	0.960460	−	0.278418i	$-0.0898101\pi$
$278$	11571.0	−	6680.50i	0.149720	−	0.0864409i
$279$	4677.70	+	5574.66i	0.0600929	+	0.0716160i
$280$	10025.9	+	27545.9i	0.127881	+	0.351350i
$281$	−285.128	+	783.383i	−0.00361100	+	0.00992114i	−0.941485	−	0.337055i	$-0.890569\pi$
$281$	−285.128	+	783.383i	−0.00361100	+	0.00992114i	0.937874	+	0.346976i	$0.112791\pi$
$282$	49041.0	+	41150.2i	0.616681	+	0.517457i
$283$	−3717.47	+	21082.8i	−0.0464168	+	0.263242i	−0.999181	−	0.0404690i	$-0.987115\pi$
$283$	−3717.47	+	21082.8i	−0.0464168	+	0.263242i	0.952764	+	0.303712i	$0.0982259\pi$
$284$		−	78245.2i		−	0.970110i
$285$	−33375.2	−	10103.9i	−0.410898	−	0.124394i
$286$	−26955.8			−0.329550
$287$	−46616.8	−	8219.80i	−0.565951	−	0.0997924i
$288$	−4325.73	+	5155.20i	−0.0521524	+	0.0621528i
$289$	62561.9	+	22770.7i	0.749056	+	0.272634i
$290$	3834.94	−	1395.80i	0.0455998	−	0.0165970i
$291$	−43412.0	+	36427.0i	−0.512653	+	0.430167i
$292$	20429.8	+	35385.4i	0.239606	+	0.415010i
$293$	95861.0	+	55345.4i	1.11662	+	0.644683i	0.940537	−	0.339692i	$-0.110323\pi$
$293$	95861.0	+	55345.4i	1.11662	+	0.644683i	0.176087	+	0.984375i	$0.443656\pi$
$294$	−1617.64	−	9174.10i	−0.0187149	−	0.106137i
$295$	3827.46	−	674.884i	0.0439811	−	0.00775506i
$296$	−21113.5	+	36569.6i	−0.240977	+	0.417385i
$297$	36972.5	−	21346.1i	0.419147	−	0.241995i
$298$	44570.6	+	53117.1i	0.501898	+	0.598139i
$299$	8035.68	+	22077.9i	0.0898836	+	0.246953i
$300$	−4104.52	+	11277.1i	−0.0456058	+	0.125301i
$301$	−32213.7	−	27030.5i	−0.355556	−	0.298347i
$302$	−4743.38	+	26901.0i	−0.0520084	+	0.294954i
$303$			55634.3i			0.605979i
$304$	9800.05	−	13079.5i	0.106043	−	0.141529i
$305$	52884.7			0.568500
$306$	−1800.76	−	317.522i	−0.0192315	−	0.00339103i
$307$	64199.7	−	76510.2i	0.681171	−	0.811788i	−0.309087	−	0.951034i	$-0.600023\pi$
$307$	64199.7	−	76510.2i	0.681171	−	0.811788i	0.990258	+	0.139245i	$0.0444677\pi$
$308$	25836.8	+	9403.81i	0.272356	+	0.0991294i
$309$	−127352.	+	46352.3i	−1.33379	+	0.485461i
$310$	21686.9	−	18197.5i	0.225671	−	0.189360i
$311$	−19464.5	−	33713.5i	−0.201244	−	0.348564i	0.747686	−	0.664053i	$-0.231165\pi$
$311$	−19464.5	−	33713.5i	−0.201244	−	0.348564i	−0.948929	+	0.315488i	$0.897832\pi$
$312$	96669.1	+	55811.9i	0.993067	+	0.573348i
$313$	−26038.8	−	147674.i	−0.265786	−	1.50735i	−0.766786	−	0.641903i	$-0.778145\pi$
$313$	−26038.8	−	147674.i	−0.265786	−	1.50735i	0.501000	−	0.865447i	$-0.332966\pi$
$314$	39659.8	−	6993.09i	0.402245	−	0.0709267i
$315$	1553.65	−	2691.00i	0.0156578	−	0.0271201i
$316$	−74379.3	+	42942.9i	−0.744866	+	0.430049i
$317$	16059.1	+	19138.5i	0.159810	+	0.190454i	0.840007	−	0.542575i	$-0.182551\pi$
$317$	16059.1	+	19138.5i	0.159810	+	0.190454i	−0.680198	+	0.733029i	$0.738106\pi$
$318$	25792.6	+	70864.7i	0.255059	+	0.700770i
$319$	3194.28	−	8776.20i	0.0313900	−	0.0862432i
$320$	13851.2	+	11622.5i	0.135265	+	0.113501i
$321$	25931.2	−	147063.i	0.251659	−	1.42723i
$322$			10541.3i			0.101667i
$323$	46656.3	+	5598.98i	0.447204	+	0.0536665i
$324$	−66739.1			−0.635755
$325$	−26533.3	−	4678.54i	−0.251203	−	0.0442938i
$326$	−65635.8	+	78221.7i	−0.617598	+	0.736024i
$327$	−82198.9	−	29918.0i	−0.768725	−	0.279793i
$328$	−60954.9	+	22185.8i	−0.566579	+	0.206218i
$329$	112302.	−	94232.5i	1.03752	−	0.870580i
$330$	−6040.21	−	10461.9i	−0.0554656	−	0.0960693i
$331$	160838.	+	92859.7i	1.46802	+	0.847562i	0.999358	−	0.0358157i	$-0.0114029\pi$
$331$	160838.	+	92859.7i	1.46802	+	0.847562i	0.468662	+	0.883378i	$0.344736\pi$
$332$	11496.1	+	65197.9i	0.104298	+	0.591503i
$333$	4408.11	−	777.269i	0.0397525	−	0.00700943i
$334$	−44783.9	+	77568.0i	−0.401448	+	0.695328i
$335$	−210.480	+	121.520i	−0.00187551	+	0.00108283i
$336$	−10997.8	−	13106.6i	−0.0974151	−	0.116095i
$337$	1062.15	+	2918.24i	0.00935248	+	0.0256957i	0.944281	−	0.329140i	$-0.106759\pi$
$337$	1062.15	+	2918.24i	0.00935248	+	0.0256957i	−0.934929	+	0.354836i	$0.884537\pi$
$338$	−13532.8	+	37181.2i	−0.118456	+	0.325454i
$339$	−32204.3	−	27022.6i	−0.280230	−	0.235141i
$340$	2808.22	−	15926.2i	0.0242925	−	0.137770i
$341$		−	64787.6i		−	0.557164i
$342$	5063.41	−	279.274i	0.0432903	−	0.00238769i
$343$	−126355.			−1.07400
$344$	−56750.6	−	10006.7i	−0.479571	−	0.0845614i
$345$	−6768.11	+	8065.92i	−0.0568630	+	0.0677666i
$346$	−50396.8	−	18342.9i	−0.420970	−	0.153220i
$347$	−119907.	+	43642.6i	−0.995831	+	0.362453i	−0.787975	−	0.615707i	$-0.788871\pi$
$347$	−119907.	+	43642.6i	−0.995831	+	0.362453i	−0.207855	+	0.978160i	$0.566648\pi$
$348$	−12142.6	+	10188.9i	−0.100266	+	0.0841332i
$349$	115982.	+	200886.i	0.952223	+	1.64930i	0.740598	+	0.671948i	$0.234542\pi$
$349$	115982.	+	200886.i	0.952223	+	1.64930i	0.211625	+	0.977351i	$0.432124\pi$
$350$	−10468.7	−	6044.11i	−0.0854588	−	0.0493397i
$351$	−28247.9	−	160202.i	−0.229283	−	1.30033i
$352$	59002.6	−	10403.7i	0.476196	−	0.0839662i
$353$	17018.9	−	29477.6i	0.136579	−	0.236561i	−0.789621	−	0.613595i	$-0.789723\pi$
$353$	17018.9	−	29477.6i	0.136579	−	0.236561i	0.926199	+	0.377034i	$0.123056\pi$
$354$	5750.40	−	3320.00i	0.0458872	−	0.0264930i
$355$	50603.8	+	60307.3i	0.401538	+	0.478534i
$356$	39446.6	+	108379.i	0.311250	+	0.855153i
$357$	16825.0	−	46226.4i	0.132014	−	0.362705i
$358$	87316.6	+	73267.3i	0.681288	+	0.571669i
$359$	−18326.0	+	103932.i	−0.142193	+	0.806416i	0.827385	+	0.561635i	$0.189827\pi$
$359$	−18326.0	+	103932.i	−0.142193	+	0.806416i	−0.969578	+	0.244782i	$0.921284\pi$
$360$		−	4258.08i		−	0.0328556i
$361$	−129531.	+	14332.2i	−0.993934	+	0.109976i
$362$	−91378.9			−0.697315
$363$	97347.8	+	17165.0i	0.738776	+	0.130266i
$364$	67342.1	−	80255.1i	0.508257	−	0.605717i
$365$	−38631.1	−	14060.6i	−0.289969	−	0.105540i
$366$	84903.4	−	30902.3i	0.633815	−	0.230690i
$367$	−117445.	+	98547.7i	−0.871969	+	0.731669i	−0.964512	−	0.264040i	$-0.914945\pi$
$367$	−117445.	+	98547.7i	−0.871969	+	0.731669i	0.0925429	+	0.995709i	$0.470500\pi$
$368$	−2467.48	−	4273.79i	−0.0182204	−	0.0315586i
$369$	5954.77	+	3437.99i	0.0437333	+	0.0252494i
$370$	−3023.79	−	17148.7i	−0.0220875	−	0.125265i
$371$	170068.	−	29987.6i	1.23559	−	0.217869i
$372$	−54979.4	+	95227.1i	−0.397296	+	0.688137i
$373$	150823.	−	87077.8i	1.08405	−	0.625878i	0.152065	−	0.988370i	$-0.451408\pi$
$373$	150823.	−	87077.8i	1.08405	−	0.625878i	0.931987	+	0.362493i	$0.118074\pi$
$374$	10464.0	+	12470.5i	0.0748093	+	0.0891543i
$375$	−4129.72	−	11346.3i	−0.0293669	−	0.0806849i
$376$	68709.4	−	188778.i	0.486005	−	1.33529i
$377$	−27261.0	−	22874.7i	−0.191804	−	0.160943i
$378$	12673.8	−	71876.9i	0.0887002	−	0.503044i
$379$			226868.i			1.57941i	0.613488	+	0.789704i	$0.289766\pi$
$379$			226868.i			1.57941i	−0.613488	+	0.789704i	$0.710234\pi$
$380$	2469.94	+	44781.6i	0.0171048	+	0.310122i
$381$	−37305.4			−0.256993
$382$	−6961.71	−	1227.54i	−0.0477078	−	0.00841217i
$383$	−34543.0	+	41166.8i	−0.235485	+	0.280640i	−0.870826	−	0.491592i	$-0.836415\pi$
$383$	−34543.0	+	41166.8i	−0.235485	+	0.280640i	0.635341	+	0.772232i	$0.280860\pi$
$384$	−108555.	−	39510.7i	−0.736184	−	0.267949i
$385$	−25995.4	+	9461.54i	−0.175378	+	0.0638323i
$386$	−37521.7	+	31484.5i	−0.251830	+	0.211311i
$387$	3054.22	+	5290.06i	0.0203929	+	0.0353215i
$388$	63121.8	+	36443.4i	0.419291	+	0.242078i
$389$	−30564.1	−	173337.i	−0.201982	−	1.14549i	−0.902119	−	0.431487i	$-0.857989\pi$
$389$	−30564.1	−	173337.i	−0.201982	−	1.14549i	0.700138	−	0.714008i	$-0.253122\pi$
$390$	−45331.5	+	7993.17i	−0.298037	+	0.0525520i
$391$	7094.46	−	12288.0i	0.0464051	−	0.0803761i
$392$	−25316.4	+	14616.4i	−0.164752	+	0.0951195i
$393$	−125169.	−	149171.i	−0.810426	−	0.965828i
$394$	−11034.4	−	30316.8i	−0.0710814	−	0.195295i
$395$	29555.0	−	81201.8i	0.189425	−	0.520441i
$396$	−3059.49	−	2567.22i	−0.0195101	−	0.0163709i
$397$	34535.7	−	195862.i	0.219123	−	1.24271i	−0.654485	−	0.756075i	$-0.727115\pi$
$397$	34535.7	−	195862.i	0.219123	−	1.24271i	0.873608	−	0.486631i	$-0.161774\pi$
$398$		−	9328.52i		−	0.0588907i
$399$	−16255.4	+	135456.i	−0.102106	+	0.850849i
$400$	5659.16			0.0353697
$401$	−145827.	−	25713.2i	−0.906878	−	0.159907i	−0.299292	−	0.954161i	$-0.596751\pi$
$401$	−145827.	−	25713.2i	−0.906878	−	0.159907i	−0.607585	+	0.794254i	$0.707862\pi$
$402$	−266.904	+	318.084i	−0.00165160	+	0.00196829i
$403$	−231977.	−	84432.7i	−1.42835	−	0.519877i
$404$	67239.1	−	24473.0i	0.411964	−	0.149943i
$405$	51438.9	−	43162.4i	0.313604	−	0.263145i
$406$	−7983.25	−	13827.4i	−0.0484315	−	0.0838858i
$407$	−34511.1	−	19925.0i	−0.208339	−	0.120285i
$408$	−11705.9	−	66387.6i	−0.0703211	−	0.398811i
$409$	269437.	−	47509.1i	1.61069	−	0.284008i	0.705400	−	0.708809i	$-0.250767\pi$
$409$	269437.	−	47509.1i	1.61069	−	0.284008i	0.905287	+	0.424801i	$0.139656\pi$
$410$	13374.7	−	23165.7i	0.0795640	−	0.137809i
$411$	−8076.57	+	4663.01i	−0.0478127	+	0.0276047i
$412$	112042.	+	133526.i	0.660064	+	0.786634i
$413$	−5200.53	−	14288.3i	−0.0304893	−	0.0837687i
$414$	523.707	−	1438.87i	0.00305554	−	0.00839503i
$415$	−51026.3	−	42816.1i	−0.296277	−	0.248606i
$416$	39642.1	−	224821.i	0.229071	−	1.29913i
$417$		−	52213.5i		−	0.300269i
$418$	−36130.4	−	27071.4i	−0.206786	−	0.154938i
$419$	112319.			0.639771			0.319885	−	0.947456i	$-0.396356\pi$
$419$	112319.			0.639771			0.319885	+	0.947456i	$0.396356\pi$
$420$	46238.0	+	8153.01i	0.262120	+	0.0462189i
$421$	9280.50	−	11060.1i	0.0523609	−	0.0624013i	−0.739228	−	0.673455i	$-0.764810\pi$
$421$	9280.50	−	11060.1i	0.0523609	−	0.0624013i	0.791589	+	0.611054i	$0.209254\pi$
$422$	−29456.8	−	10721.4i	−0.165409	−	0.0602041i
$423$	−20010.7	+	7283.30i	−0.111836	+	0.0407050i
$424$	181283.	−	152115.i	1.00838	−	0.846135i
$425$	8135.58	+	14091.2i	0.0450412	+	0.0780137i
$426$	116481.	+	67250.4i	0.641854	+	0.370574i
$427$	−35928.4	−	203760.i	−0.197052	−	1.11754i
$428$	−189146.	+	33351.5i	−1.03255	+	0.182066i
$429$	−52670.4	+	91227.8i	−0.286188	+	0.495693i
$430$	20579.8	−	11881.7i	0.111302	−	0.0642604i
$431$	−107114.	−	127654.i	−0.576625	−	0.687195i	0.396352	−	0.918099i	$-0.370276\pi$
$431$	−107114.	−	127654.i	−0.576625	−	0.687195i	−0.972977	+	0.230904i	$0.925832\pi$
$432$	11686.4	+	32108.0i	0.0626198	+	0.172046i
$433$	16370.5	−	44977.6i	0.0873146	−	0.239895i	−0.888349	−	0.459170i	$-0.848147\pi$
$433$	16370.5	−	44977.6i	0.0873146	−	0.239895i	0.975663	+	0.219275i	$0.0703692\pi$
$434$	−84846.8	−	71194.9i	−0.450460	−	0.377981i
$435$	2769.41	−	15706.1i	0.0146355	−	0.0830022i
$436$			112505.i			0.591835i
$437$	−11401.8	+	37662.3i	−0.0597049	+	0.197217i
$438$	−70236.1			−0.366110
$439$	−189090.	−	33341.7i	−0.981159	−	0.173005i	−0.340011	−	0.940422i	$-0.610431\pi$
$439$	−189090.	−	33341.7i	−0.981159	−	0.173005i	−0.641149	+	0.767417i	$0.721542\pi$
$440$	−24367.4	+	29039.9i	−0.125865	+	0.150000i
$441$	2911.85	+	1059.83i	0.0149724	+	0.00544951i
$442$	58288.6	−	21215.3i	0.298359	−	0.108594i
$443$	−108219.	+	90806.5i	−0.551437	+	0.462711i	−0.875427	−	0.483350i	$-0.839420\pi$
$443$	−108219.	+	90806.5i	−0.551437	+	0.462711i	0.323990	+	0.946060i	$0.394976\pi$
$444$	33817.1	+	58572.9i	0.171542	+	0.297119i
$445$	−100495.	−	58021.1i	−0.507489	−	0.292999i
$446$	35404.8	+	200791.i	0.177989	+	1.00942i
$447$	266855.	−	47053.8i	1.33555	−	0.235494i
$448$	35370.3	−	61263.2i	0.176231	−	0.305242i
$449$	−114311.	+	65997.7i	−0.567018	+	0.327368i	−0.755957	−	0.654621i	$-0.772828\pi$
$449$	−114311.	+	65997.7i	−0.567018	+	0.327368i	0.188939	+	0.981989i	$0.439495\pi$
$450$	1128.69	+	1345.12i	0.00557376	+	0.00664254i
$451$	−20937.0	−	57523.8i	−0.102934	−	0.282810i
$452$	−18492.9	+	50808.8i	−0.0905165	+	0.248692i
$453$	81774.0	+	68616.5i	0.398491	+	0.334374i
$454$	17355.4	−	98427.6i	0.0842023	−	0.477535i
$455$			105409.i			0.509160i
$456$	73519.9	+	171891.i	0.353570	+	0.826655i
$457$	−214849.			−1.02873			−0.514365	−	0.857571i	$-0.671972\pi$
$457$	−214849.			−1.02873			−0.514365	+	0.857571i	$0.671972\pi$
$458$	−135419.	−	23878.0i	−0.645577	−	0.113833i
$459$	−63148.3	+	75257.2i	−0.299734	+	0.357209i
$460$	12725.6	+	4631.75i	0.0601400	+	0.0218892i
$461$	−153096.	+	55722.2i	−0.720379	+	0.262196i	−0.676087	−	0.736822i	$-0.736325\pi$
$461$	−153096.	+	55722.2i	−0.720379	+	0.262196i	−0.0442921	+	0.999019i	$0.514103\pi$
$462$	−36205.4	+	30379.9i	−0.169625	+	0.142332i
$463$	−33417.1	−	57880.2i	−0.155886	−	0.270003i	0.777495	−	0.628889i	$-0.216490\pi$
$463$	−33417.1	−	57880.2i	−0.155886	−	0.270003i	−0.933381	+	0.358886i	$0.883157\pi$
$464$	6473.36	+	3737.40i	0.0300673	+	0.0173593i
$465$	−19211.4	−	108953.i	−0.0888489	−	0.503887i
$466$	139449.	−	24588.7i	0.642161	−	0.113230i
$467$	−198186.	+	343268.i	−0.908738	+	1.57398i	−0.0929185	+	0.995674i	$0.529620\pi$
$467$	−198186.	+	343268.i	−0.908738	+	1.57398i	−0.815820	+	0.578307i	$0.803714\pi$
$468$	−13179.3	+	7609.08i	−0.0601729	+	0.0347408i
$469$	611.201	+	728.401i	0.00277868	+	0.00331150i
$470$	28334.0	+	77847.0i	0.128266	+	0.352408i
$471$	53826.3	−	147886.i	0.242634	−	0.666632i
$472$	−15961.8	−	13393.5i	−0.0716469	−	0.0601189i
$473$	9443.40	−	53556.2i	0.0422091	−	0.239380i
$474$		−	147635.i		−	0.657101i
$475$	−30865.5	−	32917.9i	−0.136800	−	0.145897i
$476$	−63269.9			−0.279244
$477$	−24704.0	−	4355.98i	−0.108575	−	0.0191447i
$478$	−68815.4	+	82011.1i	−0.301183	+	0.358936i
$479$	163307.	+	59439.1i	0.711762	+	0.259060i	0.672425	−	0.740166i	$-0.265253\pi$
$479$	163307.	+	59439.1i	0.711762	+	0.259060i	0.0393378	+	0.999226i	$0.487475\pi$
$480$	96139.3	−	34991.9i	0.417271	−	0.151874i
$481$	−116319.	+	97602.9i	−0.502758	+	0.421864i
$482$	52234.9	+	90473.5i	0.224836	+	0.389428i
$483$	35675.3	+	20597.2i	0.152923	+	0.0882903i
$484$	−22076.9	−	125204.i	−0.0942426	−	0.534476i
$485$	−72220.1	+	12734.4i	−0.307026	+	0.0541369i
$486$	−10216.3	+	17695.1i	−0.0432533	+	0.0749170i
$487$	317146.	−	183104.i	1.33721	−	0.772041i	0.350820	−	0.936443i	$-0.385903\pi$
$487$	317146.	−	183104.i	1.33721	−	0.772041i	0.986393	+	0.164402i	$0.0525695\pi$
$488$	−182250.	−	217197.i	−0.765291	−	0.912039i
$489$	136480.	+	374975.i	0.570757	+	1.56814i
$490$	4123.01	−	11327.9i	0.0171721	−	0.0471799i
$491$	262503.	+	220266.i	1.08886	+	0.913661i	0.996626	−	0.0820770i	$-0.0261553\pi$
$491$	262503.	+	220266.i	1.08886	+	0.913661i	0.0922322	+	0.995738i	$0.470600\pi$
$492$	−18041.4	+	102318.i	−0.0745315	+	0.422689i
$493$			21491.5i			0.0884244i
$494$	−144017.	+	94087.6i	−0.590146	+	0.385548i
$495$	4018.40			0.0164000
$496$	51064.9	+	9004.11i	0.207567	+	0.0365997i
$497$	197980.	−	235943.i	0.801508	−	0.955200i
$498$	−106939.	−	38922.5i	−0.431197	−	0.156943i
$499$	377528.	−	137409.i	1.51617	−	0.551841i	0.555982	−	0.831194i	$-0.312342\pi$
$499$	377528.	−	137409.i	1.51617	−	0.551841i	0.960188	+	0.279353i	$0.0901201\pi$
$500$	−11896.4	+	9982.28i	−0.0475857	+	0.0399291i
$501$	175011.	+	303128.i	0.697253	+	1.20768i
$502$	122064.	+	70473.9i	0.484375	+	0.279654i
$503$	−19432.7	−	110208.i	−0.0768062	−	0.435590i	−0.998826	−	0.0484465i	$-0.984573\pi$
$503$	−19432.7	−	110208.i	−0.0768062	−	0.435590i	0.922020	−	0.387143i	$-0.126538\pi$
$504$	−16406.0	+	2892.82i	−0.0645865	+	0.0113883i
$505$	−35996.8	+	62348.3i	−0.141150	+	0.244479i
$506$	−11805.8	+	6816.08i	−0.0461099	+	0.0266216i
$507$	99391.3	+	118450.i	0.386663	+	0.460807i
$508$	16410.3	+	45087.0i	0.0635901	+	0.174712i
$509$	56997.5	−	156599.i	0.219999	−	0.604441i	−0.779767	−	0.626069i	$-0.784663\pi$
$509$	56997.5	−	156599.i	0.219999	−	0.604441i	0.999766	+	0.0216279i	$0.00688492\pi$
$510$	21295.2	+	17868.8i	0.0818730	+	0.0686996i
$511$	−27929.2	+	158394.i	−0.106959	+	0.606594i
$512$			91370.6i			0.348551i
$513$	123026.	−	243096.i	0.467479	−	0.923726i
$514$	49165.4			0.186095
$515$	−172712.	−	30453.8i	−0.651190	−	0.114822i
$516$	−59328.5	+	70704.9i	−0.222825	+	0.265552i
$517$	178152.	+	64841.9i	0.666513	+	0.242591i
$518$	−64018.2	+	23300.7i	−0.238586	+	0.0868381i
$519$	−160552.	+	134719.i	−0.596046	+	0.500142i
$520$	72223.5	+	125095.i	0.267099	+	0.462628i
$521$	357612.	+	206467.i	1.31746	+	0.760634i	0.983319	−	0.181889i	$-0.0582213\pi$
$521$	357612.	+	206467.i	1.31746	+	0.760634i	0.334139	+	0.942524i	$0.391555\pi$
$522$	402.739	+	2284.04i	0.00147803	+	0.00838231i
$523$	219151.	−	38642.2i	0.801197	−	0.141273i	0.241966	−	0.970285i	$-0.422208\pi$
$523$	219151.	−	38642.2i	0.801197	−	0.141273i	0.559231	+	0.829012i	$0.311097\pi$
$524$	−125226.	+	216898.i	−0.456070	+	0.789936i
$525$	−40910.7	+	23619.8i	−0.148429	+	0.0856954i
$526$	81897.5	+	97601.6i	0.296005	+	0.352765i
$527$	50990.5	+	140095.i	0.183598	+	0.504431i
$528$	7567.63	−	20791.9i	0.0271451	−	0.0745807i
$529$	−205269.	−	172241.i	−0.733519	−	0.615495i
$530$	−16945.9	+	96105.1i	−0.0603273	+	0.342133i
$531$			2208.71i			0.00783340i
$532$	170861.	−	39939.8i	0.603699	−	0.141118i
$533$	−233254.			−0.821059
$534$	−195243.	−	34426.7i	−0.684690	−	0.120729i
$535$	124214.	−	148033.i	0.433974	−	0.517190i
$536$	1224.43	+	445.656i	0.00426191	+	0.00155121i
$537$	418574.	−	152348.i	1.45152	−	0.528311i
$538$	202083.	−	169568.i	0.698176	−	0.585840i
$539$	−13793.7	−	23891.4i	−0.0474792	−	0.0822364i
$540$	−81202.3	−	46882.2i	−0.278472	−	0.160776i
$541$	60031.1	+	340454.i	0.205108	+	1.16322i	0.897270	+	0.441482i	$0.145547\pi$
$541$	60031.1	+	340454.i	0.205108	+	1.16322i	−0.692162	+	0.721742i	$0.743342\pi$
$542$	−194076.	+	34220.8i	−0.660652	+	0.116491i
$543$	−178550.	+	309257.i	−0.605564	+	1.04887i
$544$	−119398.	+	68934.2i	−0.403457	+	0.232936i
$545$	−72761.1	−	86713.3i	−0.244966	−	0.291939i
$546$	61593.9	+	169228.i	0.206610	+	0.567657i
$547$	79959.2	−	219686.i	0.267235	−	0.734223i	−0.731398	−	0.681951i	$-0.761132\pi$
$547$	79959.2	−	219686.i	0.267235	−	0.734223i	0.998633	−	0.0522718i	$-0.0166462\pi$
$548$	9188.48	+	7710.05i	0.0305972	+	0.0256741i
$549$	−5218.92	+	29598.0i	−0.0173155	+	0.0982013i
$550$		−	15632.7i		−	0.0516782i
$551$	−13566.7	−	58038.0i	−0.0446860	−	0.191165i
$552$	56450.6			0.185264
$553$	−332942.	−	58706.6i	−1.08872	−	0.191972i
$554$	157312.	−	187477.i	0.512557	−	0.610841i
$555$	−63945.5	−	23274.3i	−0.207599	−	0.0755597i
$556$	−63104.7	+	22968.2i	−0.204132	+	0.0742981i
$557$	−347433.	+	291531.i	−1.11985	+	0.939669i	−0.998597	−	0.0529526i	$-0.983137\pi$
$557$	−347433.	+	291531.i	−1.11985	+	0.939669i	−0.121256	+	0.992621i	$0.538692\pi$
$558$	8044.42	+	13933.3i	0.0258361	+	0.0447494i
$559$	−179455.	−	103608.i	−0.574291	−	0.331567i
$560$	−3844.67	−	21804.2i	−0.0122598	−	0.0695287i
$561$	62650.8	−	11047.0i	0.199068	−	0.0351010i
$562$	−921.549	+	1596.17i	−0.00291774	+	0.00505367i
$563$	331024.	−	191117.i	1.04434	−	0.602951i	0.123281	−	0.992372i	$-0.460658\pi$
$563$	331024.	−	191117.i	1.04434	−	0.602951i	0.921060	+	0.389421i	$0.127325\pi$
$564$	−206828.	−	246488.i	−0.650206	−	0.774886i
$565$	−18606.4	−	51120.7i	−0.0582862	−	0.160140i
$566$	−16187.9	+	44475.8i	−0.0505308	+	0.138832i
$567$	−201247.	−	168866.i	−0.625984	−	0.525263i
$568$	73291.7	−	415658.i	0.227174	−	1.28837i
$569$			214680.i			0.663083i	0.943441	+	0.331541i	$0.107569\pi$
$569$			214680.i			0.663083i	−0.943441	+	0.331541i	$0.892431\pi$
$570$	−68787.8	−	34812.1i	−0.211720	−	0.107147i
$571$	404837.			1.24167			0.620837	−	0.783940i	$-0.286793\pi$
$571$	404837.			1.24167			0.620837	+	0.783940i	$0.286793\pi$
$572$	133426.	+	23526.6i	0.407802	+	0.0719064i
$573$	−17757.3	+	21162.3i	−0.0540837	+	0.0644545i
$574$	−98341.6	−	35793.4i	−0.298479	−	0.108637i
$575$	−12803.8	+	4660.18i	−0.0387259	+	0.0140951i
$576$	−7871.66	+	6605.11i	−0.0237258	+	0.0199083i
$577$	−228407.	−	395613.i	−0.686053	−	1.18828i	−0.973105	−	0.230364i	$-0.926008\pi$
$577$	−228407.	−	395613.i	−0.686053	−	1.18828i	0.287051	−	0.957915i	$-0.407325\pi$
$578$	127472.	+	73596.0i	0.381557	+	0.220292i
$579$	33238.6	+	188505.i	0.0991484	+	0.562298i
$580$	−20200.5	+	3561.89i	−0.0600489	+	0.0105882i
$581$	−130301.	+	225688.i	−0.386007	+	0.668583i
$582$	−108504.	+	62644.9i	−0.320332	+	0.184944i
$583$	143552.	+	171079.i	0.422351	+	0.503338i
$584$	75382.7	+	207112.i	0.221027	+	0.607267i
$585$	5236.87	−	14388.2i	0.0153024	−	0.0420430i
$586$	187467.	+	157304.i	0.545922	+	0.458083i
$587$	−57828.8	+	327963.i	−0.167829	+	0.951807i	0.778270	+	0.627930i	$0.216098\pi$
$587$	−57828.8	+	327963.i	−0.167829	+	0.951807i	−0.946099	+	0.323877i	$0.895014\pi$
$588$			46821.9i			0.135424i
$589$	−226137.	−	346141.i	−0.651840	−	0.997751i
$590$	8592.49			0.0246840
$591$	−124163.	−	21893.3i	−0.355482	−	0.0626810i
$592$	20501.0	−	24432.1i	0.0584967	−	0.0697136i
$593$	−198025.	−	72075.1i	−0.563132	−	0.204963i	0.0447396	−	0.998999i	$-0.485754\pi$
$593$	−198025.	−	72075.1i	−0.563132	−	0.204963i	−0.607871	+	0.794035i	$0.707976\pi$
$594$	88694.1	−	32282.0i	0.251375	−	0.0914929i
$595$	48765.1	−	40918.8i	0.137745	−	0.115582i
$596$	−174256.	−	301820.i	−0.490563	−	0.849681i
$597$	−31570.9	−	18227.5i	−0.0885806	−	0.0511420i
$598$	9019.89	+	51154.4i	0.0252231	+	0.143048i
$599$	49658.5	−	8756.14i	0.138401	−	0.0244039i	−0.104018	−	0.994575i	$-0.533170\pi$
$599$	49658.5	−	8756.14i	0.138401	−	0.0244039i	0.242420	+	0.970171i	$0.422059\pi$
$600$	−32367.4	+	56061.9i	−0.0899094	+	0.155728i
$601$	−104.443	+	60.3002i	−0.000289155	+	0.000166944i	−0.500145	−	0.865942i	$-0.666720\pi$
$601$	−104.443	+	60.3002i	−0.000289155	+	0.000166944i	0.499855	+	0.866109i	$0.333386\pi$
$602$	−59760.6	−	71219.9i	−0.164900	−	0.196521i
$603$	−47.2402	−	129.791i	−0.000129920	−	0.000356953i
$604$	46957.6	−	129015.i	0.128716	−	0.353644i
$605$	97989.5	+	82223.0i	0.267713	+	0.224638i
$606$	−21358.6	+	121131.i	−0.0581605	+	0.329844i
$607$		−	84755.5i		−	0.230033i	−0.993364	−	0.115017i	$-0.963308\pi$
$607$		−	84755.5i		−	0.230033i	0.993364	−	0.115017i	$-0.0366921\pi$
$608$	278919.	−	261529.i	0.754521	−	0.707477i
$609$	−62395.5			−0.168236
$610$	115144.	+	20303.0i	0.309444	+	0.0545633i
$611$	464342.	−	553382.i	1.24382	−	1.48232i
$612$	8636.28	+	3143.35i	0.0230581	+	0.00839246i
$613$	−367487.	+	133754.i	−0.977961	+	0.355949i	−0.781047	−	0.624472i	$-0.785314\pi$
$613$	−367487.	+	133754.i	−0.977961	+	0.355949i	−0.196914	+	0.980421i	$0.563092\pi$
$614$	169153.	−	141936.i	0.448686	−	0.376493i
$615$	−52267.0	−	90529.1i	−0.138190	−	0.239353i
$616$	128443.	+	74156.4i	0.338492	+	0.195428i
$617$	32568.2	+	184703.i	0.0855507	+	0.485182i	0.997236	+	0.0742937i	$0.0236702\pi$
$617$	32568.2	+	184703.i	0.0855507	+	0.485182i	−0.911686	+	0.410888i	$0.865219\pi$
$618$	−295074.	+	52029.6i	−0.772600	+	0.136230i
$619$	56753.5	−	98299.9i	0.148119	−	0.256550i	−0.782413	−	0.622760i	$-0.786011\pi$
$619$	56753.5	−	98299.9i	0.148119	−	0.256550i	0.930532	+	0.366210i	$0.119345\pi$
$620$	−123229.	+	71146.1i	−0.320574	+	0.185084i
$621$	−52880.4	−	63020.4i	−0.137123	−	0.163417i
$622$	−29436.4	−	80875.9i	−0.0760859	−	0.209044i
$623$	−155276.	+	426618.i	−0.400063	+	1.09916i
$624$	−64584.6	−	54192.9i	−0.165867	−	0.139179i
$625$	2713.25	−	15387.6i	0.00694593	−	0.0393923i
$626$		−	331521.i		−	0.845985i
$627$	−162216.	+	69381.6i	−0.412627	+	0.176486i
$628$	−202412.			−0.513235
$629$	90307.8	+	15923.7i	0.228257	+	0.0402479i
$630$	4415.81	−	5262.55i	0.0111257	−	0.0132591i
$631$	−237805.	−	86554.1i	−0.597259	−	0.217385i	0.0256599	−	0.999671i	$-0.491831\pi$
$631$	−237805.	−	86554.1i	−0.597259	−	0.217385i	−0.622919	+	0.782286i	$0.714054\pi$
$632$	−435346.	+	158453.i	−1.08993	+	0.396703i
$633$	−93841.9	+	78742.7i	−0.234201	+	0.196518i
$634$	27617.5	+	47834.9i	0.0687077	+	0.119005i
$635$	−41807.5	−	24137.6i	−0.103683	−	0.0598613i
$636$	−65819.0	−	373278.i	−0.162718	−	0.922822i
$637$	−103521.	+	18253.6i	−0.255123	+	0.0449851i
$638$	10324.1	−	17881.8i	0.0253635	−	0.0439309i
$639$	−38746.0	+	22370.0i	−0.0948910	+	0.0547853i
$640$	−96090.8	−	114517.i	−0.234597	−	0.279581i
$641$	−203195.	−	558273.i	−0.494534	−	1.35872i	−0.896491	−	0.443063i	$-0.853892\pi$
$641$	−203195.	−	558273.i	−0.494534	−	1.35872i	0.401957	−	0.915659i	$-0.368330\pi$
$642$	112918.	−	310240.i	0.273964	−	0.752711i
$643$	389826.	+	327103.i	0.942864	+	0.791157i	0.978081	−	0.208223i	$-0.0667678\pi$
$643$	389826.	+	327103.i	0.942864	+	0.791157i	−0.0352171	+	0.999380i	$0.511212\pi$
$644$	9200.27	−	52177.4i	0.0221834	−	0.125809i
$645$		−	92865.4i		−	0.223221i
$646$	99433.8	+	30102.3i	0.238270	+	0.0721332i
$647$	−140289.			−0.335131			−0.167566	−	0.985861i	$-0.553591\pi$
$647$	−140289.			−0.335131			−0.167566	+	0.985861i	$0.553591\pi$
$648$	−354534.	−	62514.0i	−0.844322	−	0.148877i
$649$	12639.6	−	15063.3i	0.0300085	−	0.0357628i
$650$	−55973.9	−	20372.8i	−0.132483	−	0.0482197i
$651$	−406734.	+	148039.i	−0.959729	+	0.349313i
$652$	393155.	−	329896.i	0.924845	−	0.776037i
$653$	−153552.	−	265960.i	−0.360105	−	0.623720i	0.627873	−	0.778316i	$-0.283926\pi$
$653$	−153552.	−	265960.i	−0.360105	−	0.623720i	−0.987978	+	0.154596i	$0.950592\pi$
$654$	−167483.	−	96696.5i	−0.391576	−	0.226076i
$655$	−43757.5	−	248161.i	−0.101993	−	0.578430i
$656$	48249.4	−	8507.67i	0.112120	−	0.0197698i
$657$	11681.6	−	20233.1i	0.0270627	−	0.0468739i
$658$	280688.	−	162055.i	0.648294	−	0.374293i
$659$	−98380.4	−	117245.i	−0.226536	−	0.269975i	0.640789	−	0.767717i	$-0.278607\pi$
$659$	−98380.4	−	117245.i	−0.226536	−	0.269975i	−0.867325	+	0.497742i	$0.834163\pi$
$660$	20766.8	+	57056.4i	0.0476741	+	0.130984i
$661$	−240232.	+	660032.i	−0.549829	+	1.51064i	0.284112	+	0.958791i	$0.408301\pi$
$661$	−240232.	+	660032.i	−0.549829	+	1.51064i	−0.833942	+	0.551853i	$0.813921\pi$
$662$	314537.	+	263928.i	0.717721	+	0.602239i
$663$	42093.2	−	238722.i	0.0957602	−	0.543083i
$664$			357115.i			0.809976i
$665$	−105861.	+	141285.i	−0.239382	+	0.319487i
$666$	9896.03			0.0223107
$667$	−17723.5	−	3125.14i	−0.0398381	−	0.00702454i
$668$	289372.	−	344860.i	0.648491	−	0.772841i
$669$	748723.	+	272513.i	1.67290	+	0.608884i
$670$	−504.923	+	183.777i	−0.00112480	+	0.000409394i
$671$	204971.	−	171991.i	0.455247	−	0.381998i
$672$	−200135.	−	346644.i	−0.443184	−	0.767617i
$673$	498921.	+	288052.i	1.10154	+	0.635977i	0.936626	−	0.350330i	$-0.113931\pi$
$673$	498921.	+	288052.i	1.10154	+	0.635977i	0.164918	+	0.986307i	$0.447264\pi$
$674$	1192.24	+	6761.55i	0.00262449	+	0.0148842i
$675$	92906.7	−	16382.0i	0.203911	−	0.0359549i
$676$	99436.1	−	172228.i	0.217596	−	0.376887i
$677$	46492.3	−	26842.3i	0.101439	−	0.0585656i	−0.448422	−	0.893822i	$-0.648014\pi$
$677$	46492.3	−	26842.3i	0.101439	−	0.0585656i	0.549861	+	0.835256i	$0.314681\pi$
$678$	−59743.0	−	71198.9i	−0.129965	−	0.154887i
$679$	98128.6	+	269606.i	0.212841	+	0.584777i
$680$	29835.9	−	81973.4i	0.0645239	−	0.177278i
$681$	−299201.	−	251060.i	−0.645162	−	0.541355i
$682$	24872.7	−	141060.i	0.0534753	−	0.303274i
$683$			213157.i			0.456938i	0.973551	+	0.228469i	$0.0733720\pi$
$683$			213157.i			0.456938i	−0.973551	+	0.228469i	$0.926628\pi$
$684$	−25306.7	−	3036.92i	−0.0540907	−	0.00649113i
$685$	−12068.3			−0.0257197
$686$	−275109.	−	48509.2i	−0.584598	−	0.103080i
$687$	−345413.	+	411647.i	−0.731855	+	0.872191i
$688$	40899.9	+	14886.4i	0.0864063	+	0.0314493i
$689$	799642.	−	291046.i	1.68445	−	0.613088i
$690$	−17832.6	+	14963.3i	−0.0374555	+	0.0314289i
$691$	−387157.	−	670576.i	−0.810832	−	1.40440i	−0.912282	−	0.409562i	$-0.865681\pi$
$691$	−387157.	−	670576.i	−0.810832	−	1.40440i	0.101450	−	0.994841i	$-0.467652\pi$
$692$	233445.	+	134780.i	0.487498	+	0.281457i
$693$	−2729.99	−	15482.5i	−0.00568453	−	0.0322385i
$694$	−277824.	+	48987.9i	−0.576835	+	0.101711i
$695$	33783.4	−	58514.6i	0.0699414	−	0.121142i
$696$	−74048.4	+	42751.9i	−0.152861	+	0.0882545i
$697$	90547.1	+	107910.i	0.186384	+	0.222124i
$698$	175401.	+	481910.i	0.360015	+	0.989133i
$699$	189260.	−	519989.i	0.387352	−	1.06424i
$700$	46542.9	+	39054.1i	0.0949855	+	0.0797023i
$701$	55722.4	−	316017.i	0.113395	−	0.643095i	−0.874137	−	0.485679i	$-0.838573\pi$
$701$	55722.4	−	316017.i	0.113395	−	0.643095i	0.987532	−	0.157416i	$-0.0503163\pi$
$702$		−	359646.i		−	0.729796i
$703$	−253930.	+	14005.5i	−0.513810	+	0.0283393i
$704$	91482.9			0.184584
$705$	318824.	+	56217.3i	0.641465	+	0.113108i
$706$	48371.5	−	57646.9i	0.0970465	−	0.115656i
$707$	264677.	+	96334.7i	0.529515	+	0.192728i
$708$	−31361.0	+	11414.5i	−0.0625639	+	0.0227714i
$709$	−676278.	+	567464.i	−1.34534	+	1.12888i	−0.365123	+	0.930959i	$0.618973\pi$
$709$	−676278.	+	567464.i	−1.34534	+	1.12888i	−0.980219	+	0.197916i	$0.936583\pi$
$710$	87025.4	+	150732.i	0.172635	+	0.299013i
$711$	42529.5	+	24554.4i	0.0841301	+	0.0485725i
$712$	108033.	+	612683.i	0.213106	+	1.20858i
$713$	−122948.	+	21679.1i	−0.241848	+	0.0426444i
$714$	54379.4	−	94187.9i	0.106669	−	0.184756i
$715$	−118053.	+	68158.1i	−0.230922	+	0.133323i
$716$	−368254.	−	438868.i	−0.718325	−	0.856067i
$717$	143091.	+	393141.i	0.278340	+	0.764733i
$718$	−79801.1	+	219252.i	−0.154796	+	0.425299i
$719$	−369612.	−	310141.i	−0.714970	−	0.599931i	0.211019	−	0.977482i	$-0.432322\pi$
$719$	−369612.	−	310141.i	−0.714970	−	0.599931i	−0.925989	+	0.377551i	$0.876766\pi$
$720$	−558.473	+	3167.26i	−0.00107730	+	0.00610968i
$721$			686133.i			1.31989i
$722$	−287525.	−	18523.2i	−0.551570	−	0.0355338i
$723$	408258.			0.781012
$724$	452308.	+	79754.1i	0.862893	+	0.152151i
$725$	13265.9	−	15809.6i	0.0252382	−	0.0300778i
$726$	205362.	+	74745.7i	0.389625	+	0.141812i
$727$	−302573.	+	110128.i	−0.572481	+	0.208366i	−0.612007	−	0.790852i	$-0.709638\pi$
$727$	−302573.	+	110128.i	−0.572481	+	0.208366i	0.0395255	+	0.999219i	$0.487415\pi$
$728$	432912.	−	363256.i	0.816839	−	0.685410i
$729$	283166.	+	490458.i	0.532827	+	0.922883i
$730$	−78712.2	−	45444.5i	−0.147705	−	0.0852777i
$731$	21730.7	+	123241.i	0.0406667	+	0.230632i
$732$	−447226.	+	78858.1i	−0.834652	+	0.147172i
$733$	−301320.	+	521902.i	−0.560816	+	0.971361i	0.436610	+	0.899651i	$0.356179\pi$
$733$	−301320.	+	521902.i	−0.560816	+	0.971361i	−0.997426	+	0.0717103i	$0.977154\pi$
$734$	−293542.	+	169476.i	−0.544851	+	0.314570i
$735$	−30281.3	−	36087.8i	−0.0560531	−	0.0668015i
$736$	−39486.6	−	108489.i	−0.0728944	−	0.200276i
$737$	−420.571	+	1155.51i	−0.000774291	+	0.00212735i
$738$	11645.2	+	9771.52i	0.0213814	+	0.0179411i
$739$	−110625.	+	627386.i	−0.202565	+	1.14880i	0.698661	+	0.715453i	$0.253780\pi$
$739$	−110625.	+	627386.i	−0.202565	+	1.14880i	−0.901226	+	0.433350i	$0.857331\pi$
$740$			87522.1i			0.159828i
$741$	37022.7	+	671245.i	0.0674266	+	1.22249i
$742$	381797.			0.693465
$743$	687799.	+	121278.i	1.24590	+	0.219686i	0.757444	−	0.652901i	$-0.226448\pi$
$743$	687799.	+	121278.i	1.24590	+	0.219686i	0.488459	+	0.872587i	$0.337559\pi$
$744$	−381262.	+	454371.i	−0.688776	+	0.820852i
$745$	329505.	+	119930.i	0.593675	+	0.216080i
$746$	361812.	−	131689.i	0.650138	−	0.236631i
$747$	28998.4	−	24332.6i	0.0519676	−	0.0436060i
$748$	−40910.8	−	70859.6i	−0.0731198	−	0.126647i
$749$	−654743.	−	378016.i	−1.16710	−	0.673825i
$750$	−4635.53	−	26289.4i	−0.00824094	−	0.0467367i
$751$	204675.	−	36089.8i	0.362899	−	0.0639889i	0.0107743	−	0.999942i	$-0.496570\pi$
$751$	204675.	−	36089.8i	0.362899	−	0.0639889i	0.352125	+	0.935953i	$0.385459\pi$
$752$	−75867.0	+	131405.i	−0.134158	+	0.232369i
$753$	477016.	−	275405.i	0.841284	−	0.485715i
$754$	−50572.6	−	60270.0i	−0.0889554	−	0.106013i
$755$	47245.9	+	129807.i	0.0828839	+	0.227722i
$756$	−125466.	+	344715.i	−0.219524	+	0.603139i
$757$	−2412.06	−	2023.95i	−0.00420916	−	0.00353191i	0.640681	−	0.767808i	$-0.278652\pi$
$757$	−2412.06	−	2023.95i	−0.00420916	−	0.00353191i	−0.644890	+	0.764276i	$0.723097\pi$
$758$	−87097.0	+	493952.i	−0.151588	+	0.859698i
$759$			53273.1i			0.0924750i
$760$	−28825.7	+	240204.i	−0.0499059	+	0.415866i
$761$	411386.			0.710363			0.355182	−	0.934797i	$-0.384419\pi$
$761$	411386.			0.710363			0.355182	+	0.934797i	$0.384419\pi$
$762$	−81223.9	−	14322.0i	−0.139886	−	0.0246656i
$763$	−284666.	+	339252.i	−0.488976	+	0.582739i
$764$	33387.8	+	12152.2i	0.0572006	+	0.0208193i
$765$	−8689.29	+	3162.64i	−0.0148478	+	0.00540415i
$766$	−91013.8	+	76369.6i	−0.155114	+	0.130156i
$767$	−37463.1	−	64888.0i	−0.0636814	−	0.110299i
$768$	−414796.	−	239482.i	−0.703253	−	0.406024i
$769$	47114.0	+	267197.i	0.0796704	+	0.451833i	0.998380	+	0.0568994i	$0.0181214\pi$
$769$	47114.0	+	267197.i	0.0796704	+	0.451833i	−0.918709	+	0.394934i	$0.870767\pi$
$770$	−60231.2	+	10620.4i	−0.101587	+	0.0179126i
$771$	96066.9	−	166393.i	0.161609	−	0.279915i
$772$	213204.	−	123094.i	0.357735	−	0.206539i
$773$	471716.	+	562169.i	0.789444	+	0.940823i	0.999319	−	0.0369057i	$-0.0117501\pi$
$773$	471716.	+	562169.i	0.789444	+	0.940823i	−0.209875	+	0.977728i	$0.567306\pi$
$774$	4618.94	+	12690.4i	0.00771010	+	0.0211833i
$775$	48965.6	−	134532.i	0.0815244	−	0.223986i
$776$	301182.	+	252722.i	0.500156	+	0.419681i
$777$	−46230.8	+	262188.i	−0.0765755	+	0.434281i
$778$		−	389136.i		−	0.642898i
$779$	−312643.	−	234253.i	−0.515198	−	0.386021i
$780$	231359.			0.380274
$781$	392261.	+	69166.2i	0.643092	+	0.113394i
$782$	20164.0	−	24030.6i	0.0329734	−	0.0392962i
$783$	117093.	+	42618.2i	0.190988	+	0.0695139i
$784$	20748.0	−	7551.64i	0.0337554	−	0.0122860i
$785$	156008.	−	130906.i	0.253168	−	0.212433i
$786$	−215259.	−	372839.i	−0.348430	−	0.603499i
$787$	159902.	+	92319.5i	0.258169	+	0.149054i	0.623499	−	0.781824i	$-0.285710\pi$
$787$	159902.	+	92319.5i	0.258169	+	0.149054i	−0.365330	+	0.930878i	$0.619044\pi$
$788$	28158.1	+	159693.i	0.0453473	+	0.257177i
$789$	490341.	−	86460.4i	0.787670	−	0.138887i
$790$	95523.4	−	165451.i	0.153058	−	0.265104i
$791$	−184323.	+	106419.i	−0.294595	+	0.170085i
$792$	−13848.1	−	16503.5i	−0.0220770	−	0.0263103i
$793$	−348704.	−	958056.i	−0.554511	−	1.52351i
$794$	150387.	−	413184.i	0.238544	−	0.655395i
$795$	292141.	+	245136.i	0.462230	+	0.387857i
$796$	−8141.79	+	46174.4i	−0.0128497	+	0.0728744i
$797$		−	400968.i		−	0.631239i	−0.948886	−	0.315619i	$-0.897788\pi$
$797$		−	400968.i		−	0.631239i	0.948886	−	0.315619i	$-0.102212\pi$
$798$	−87395.3	+	288683.i	−0.137240	+	0.453331i
$799$	−436264.			−0.683370
$800$	130382.	+	22989.9i	0.203722	+	0.0359217i
$801$	42390.0	−	50518.5i	0.0660692	−	0.0787382i
$802$	−307632.	−	111969.i	−0.478281	−	0.174080i
$803$	−195454.	+	71139.5i	−0.303119	+	0.110326i
$804$	1598.74	−	1341.51i	0.00247324	−	0.00207530i
$805$	26653.8	+	46165.7i	0.0411308	+	0.0712406i
$806$	−472661.	−	272891.i	−0.727578	−	0.420067i
$807$	−179015.	−	1.01524e6i	−0.274880	−	1.55892i
$808$	380114.	−	67024.4i	0.582226	−	0.102662i
$809$	374514.	−	648677.i	0.572230	−	0.991132i	−0.424106	−	0.905612i	$-0.639412\pi$
$809$	374514.	−	648677.i	0.572230	−	0.991132i	0.996336	−	0.0855195i	$-0.0272550\pi$
$810$	128567.	−	74228.1i	0.195956	−	0.113135i
$811$	−458082.	−	545921.i	−0.696469	−	0.830020i	0.295653	−	0.955295i	$-0.404463\pi$
$811$	−458082.	−	545921.i	−0.696469	−	0.830020i	−0.992122	+	0.125276i	$0.960018\pi$
$812$	27447.2	+	75410.7i	0.0416281	+	0.114372i
$813$	−263400.	+	723685.i	−0.398505	+	1.09488i
$814$	−67490.5	−	56631.3i	−0.101858	−	0.0854688i
$815$	−89668.2	+	508534.i	−0.134997	+	0.765604i
$816$			50915.9i			0.0764669i
$817$	−136481.	−	319096.i	−0.204469	−	0.478054i
$818$	604876.			0.903982
$819$	−58994.1	−	10402.3i	−0.0879510	−	0.0155081i
$820$	−86420.8	+	102992.i	−0.128526	+	0.153171i
$821$	−1.00699e6	−	366516.i	−1.49397	−	0.543759i	−0.539476	−	0.842001i	$-0.681378\pi$
$821$	−1.00699e6	−	366516.i	−1.49397	−	0.543759i	−0.954490	+	0.298242i	$0.903600\pi$
$822$	−19375.0	+	7051.93i	−0.0286747	+	0.0104367i
$823$	−202044.	+	169535.i	−0.298295	+	0.250299i	−0.779634	−	0.626235i	$-0.784595\pi$
$823$	−202044.	+	169535.i	−0.298295	+	0.250299i	0.481339	+	0.876534i	$0.340150\pi$
$824$	470121.	+	814274.i	0.692397	+	1.19927i
$825$	−52906.3	−	30545.5i	−0.0777319	−	0.0448786i
$826$	−5837.49	−	33106.1i	−0.00855591	−	0.0485230i
$827$	−793335.	+	139886.i	−1.15997	+	0.204533i	−0.720323	−	0.693639i	$-0.756006\pi$
$827$	−793335.	+	139886.i	−1.15997	+	0.204533i	−0.439644	+	0.898172i	$0.644895\pi$
$828$	−3848.08	+	6665.07i	−0.00561285	+	0.00972173i
$829$	−115960.	+	66949.7i	−0.168733	+	0.0974181i	−0.581988	−	0.813197i	$-0.697725\pi$
$829$	−115960.	+	66949.7i	−0.168733	+	0.0974181i	0.413255	+	0.910615i	$0.364392\pi$
$830$	−94660.2	−	112812.i	−0.137408	−	0.163756i
$831$	−327107.	−	898718.i	−0.473682	−	1.30143i
$832$	119223.	−	327561.i	0.172231	−	0.473201i
$833$	48630.7	+	40806.0i	0.0700842	+	0.0588076i
$834$	20045.3	−	113683.i	0.0288191	−	0.163441i
$835$			452947.i			0.649642i
$836$	155211.	+	165532.i	0.222080	+	0.236848i
$837$	864400.			1.23385
$838$	244548.	+	43120.4i	0.348238	+	0.0614037i
$839$	713627.	−	850468.i	1.01379	−	1.20819i	0.0358364	−	0.999358i	$-0.488590\pi$
$839$	713627.	−	850468.i	1.01379	−	1.20819i	0.977952	−	0.208829i	$-0.0669651\pi$
$840$	237991.	+	86621.6i	0.337289	+	0.122763i
$841$	−639011.	+	232581.i	−0.903476	+	0.328838i
$842$	24452.2	−	20517.8i	0.0344901	−	0.0289406i
$843$	3601.32	+	6237.68i	0.00506766	+	0.00877744i
$844$	136448.	+	78778.2i	0.191550	+	0.110591i
$845$	34745.8	+	197053.i	0.0486619	+	0.275975i
$846$	−46364.8	+	8175.36i	−0.0647809	+	0.0114226i
$847$	250226.	−	433405.i	0.348792	−	0.604125i
$848$	−154793.	+	89370.0i	−0.215259	+	0.124280i
$849$	118891.	+	141689.i	0.164943	+	0.196571i
$850$	12303.5	+	33803.7i	0.0170291	+	0.0467871i
$851$	−26263.9	+	72159.4i	−0.0362660	+	0.0996400i
$852$	−517864.	−	434539.i	−0.713405	−	0.598618i
$853$	163228.	−	925713.i	0.224335	−	1.27227i	−0.639617	−	0.768693i	$-0.720907\pi$
$853$	163228.	−	925713.i	0.224335	−	1.27227i	0.863952	−	0.503574i	$-0.167982\pi$
$854$		−	457433.i		−	0.627208i
$855$	21469.1	−	14026.0i	0.0293685	−	0.0191867i
$856$	−1.03603e6			−1.41392
$857$	556305.	+	98091.6i	0.757446	+	0.133558i	0.539017	−	0.842295i	$-0.318796\pi$
$857$	556305.	+	98091.6i	0.757446	+	0.133558i	0.218429	+	0.975853i	$0.429907\pi$
$858$	−149701.	+	178406.i	−0.203352	+	0.242346i
$859$	−727197.	−	264678.i	−0.985520	−	0.358700i	−0.201536	−	0.979481i	$-0.564593\pi$
$859$	−727197.	−	264678.i	−0.985520	−	0.358700i	−0.783984	+	0.620781i	$0.786816\pi$
$860$	−112236.	+	40850.6i	−0.151753	+	0.0552334i
$861$	−313292.	+	262883.i	−0.422613	+	0.354614i
$862$	−184209.	−	319059.i	−0.247911	−	0.429395i
$863$	−19602.4	−	11317.5i	−0.0263202	−	0.0151959i	0.486782	−	0.873523i	$-0.338171\pi$
$863$	−19602.4	−	11317.5i	−0.0263202	−	0.0151959i	−0.513102	+	0.858327i	$0.671504\pi$
$864$	138807.	+	787216.i	0.185945	+	1.05455i
$865$	−267094.	+	47095.8i	−0.356970	+	0.0629434i
$866$	52910.4	−	91643.5i	0.0705513	−	0.122199i
$867$	498148.	−	287606.i	0.662705	−	0.382613i
$868$	357837.	+	426454.i	0.474948	+	0.566021i
$869$	−149534.	−	410841.i	−0.198016	−	0.544044i
$870$	12059.5	−	33133.1i	0.0159327	−	0.0437748i
$871$	3589.29	+	3011.77i	0.00473120	+	0.00396995i
$872$	−105383.	+	597657.i	−0.138592	+	0.785993i
$873$		−	41676.1i		−	0.0546838i
$874$	−39283.7	+	77623.6i	−0.0514268	+	0.101618i
$875$	−61130.4			−0.0798438
$876$	347655.	+	61301.0i	0.453044	+	0.0798839i
$877$	−283421.	+	337768.i	−0.368497	+	0.439157i	−0.918148	−	0.396237i	$-0.870316\pi$
$877$	−283421.	+	337768.i	−0.368497	+	0.439157i	0.549652	+	0.835394i	$0.314760\pi$
$878$	−398899.	−	145187.i	−0.517457	−	0.188339i
$879$	898672.	−	327090.i	1.16312	−	0.423340i
$880$	21933.8	−	18404.6i	0.0283236	−	0.0237663i
$881$	505942.	+	876318.i	0.651852	+	1.12904i	0.982673	+	0.185348i	$0.0593411\pi$
$881$	505942.	+	876318.i	0.651852	+	1.12904i	−0.330821	+	0.943694i	$0.607326\pi$
$882$	5933.00	+	3425.42i	0.00762670	+	0.00440328i
$883$	155122.	+	879741.i	0.198954	+	1.12832i	0.906675	+	0.421831i	$0.138612\pi$
$883$	155122.	+	879741.i	0.198954	+	1.12832i	−0.707721	+	0.706492i	$0.750276\pi$
$884$	−307034.	+	54138.4i	−0.392900	+	0.0692789i
$885$	16789.3	−	29079.9i	0.0214361	−	0.0371284i
$886$	−270483.	+	156164.i	−0.344566	+	0.198935i
$887$	816332.	+	972867.i	1.03758	+	1.23653i	0.971082	+	0.238747i	$0.0767367\pi$
$887$	816332.	+	972867.i	1.03758	+	1.23653i	0.0664934	+	0.997787i	$0.478819\pi$
$888$	124780.	+	342830.i	0.158241	+	0.434763i
$889$	−64597.0	+	177479.i	−0.0817351	+	0.224565i
$890$	−196531.	−	164909.i	−0.248113	−	0.208192i
$891$	58995.1	−	334578.i	0.0743123	−	0.421446i
$892$		−	1.02478e6i		−	1.28795i
$893$	1.17814e6	−	275396.i	1.47738	−	0.345346i
$894$	599080.			0.749565
$895$	567661.	+	100094.i	0.708668	+	0.124957i
$896$	−375940.	+	448028.i	−0.468277	+	0.558071i
$897$	190748.	+	69426.7i	0.237070	+	0.0862863i
$898$	−274224.	+	99809.2i	−0.340057	+	0.123771i
$899$	144857.	−	121550.i	0.179234	−	0.150396i
$900$	−4412.78	−	7643.16i	−0.00544788	−	0.00943600i
$901$	−445060.	−	256956.i	−0.548238	−	0.316525i
$902$	−23501.3	−	133283.i	−0.0288855	−	0.163818i
$903$	−357802.	+	63090.1i	−0.438800	+	0.0773723i
$904$	−145831.	+	252586.i	−0.178448	+	0.309082i
$905$	−400195.	+	231053.i	−0.488623	+	0.282107i
$906$	151701.	+	180790.i	0.184813	+	0.220251i
$907$	−262181.	−	720337.i	−0.318704	−	0.875631i	−0.990820	−	0.135186i	$-0.956837\pi$
$907$	−262181.	−	720337.i	−0.318704	−	0.875631i	0.672116	−	0.740445i	$-0.265385\pi$
$908$	−171812.	+	472050.i	−0.208393	+	0.572554i
$909$	−31342.1	−	26299.2i	−0.0379315	−	0.0318283i
$910$	−40467.6	+	229503.i	−0.0488680	+	0.277144i
$911$		−	13136.3i		−	0.0158284i	−0.999969	−	0.00791420i	$-0.997481\pi$
$911$		−	13136.3i		−	0.0158284i	0.999969	−	0.00791420i	$-0.00251919\pi$
$912$	−32141.2	−	137499.i	−0.0386431	−	0.165314i
$913$	−337014.			−0.404302
$914$	−467784.	−	82483.0i	−0.559955	−	0.0987352i
$915$	293698.	−	350016.i	0.350800	−	0.418067i
$916$	649457.	+	236383.i	0.774033	+	0.281725i
$917$	−926414.	+	337187.i	−1.10171	+	0.400989i
$918$	−166383.	+	139612.i	−0.197434	+	0.165667i
$919$	74636.0	+	129273.i	0.0883725	+	0.153066i	0.906823	−	0.421511i	$-0.138500\pi$
$919$	74636.0	+	129273.i	0.0883725	+	0.153066i	−0.818451	+	0.574577i	$0.805167\pi$
$920$	63263.1	+	36525.0i	0.0747438	+	0.0431533i
$921$	−149844.	−	849808.i	−0.176653	−	1.00185i
$922$	−354722.	+	62547.1i	−0.417279	+	0.0735776i
$923$	758858.	−	1.31438e6i	0.890753	−	1.54283i
$924$	205725.	−	118775.i	0.240959	−	0.139118i
$925$	−56603.5	−	67457.4i	−0.0661545	−	0.0788399i
$926$	−50537.2	−	138850.i	−0.0589371	−	0.161928i
$927$	34088.1	−	93656.3i	0.0396683	−	0.108988i
$928$	133958.	+	112404.i	0.155551	+	0.130523i
$929$	191607.	−	1.08666e6i	0.222014	−	1.25910i	−0.646299	−	0.763084i	$-0.723684\pi$
$929$	191607.	−	1.08666e6i	0.222014	−	1.25910i	0.868313	−	0.496017i	$-0.165205\pi$
$930$		−	244595.i		−	0.282802i
$931$	−157087.	−	79498.5i	−0.181234	−	0.0917191i
$932$	−711707.			−0.819350
$933$	−331229.	−	58404.6i	−0.380509	−	0.0670940i
$934$	−563287.	+	671300.i	−0.645708	+	0.769525i
$935$	77359.2	+	28156.4i	0.0884889	+	0.0322073i
$936$	−77139.1	+	28076.3i	−0.0880487	+	0.0320471i
$937$	175414.	−	147190.i	0.199796	−	0.167649i	−0.537401	−	0.843327i	$-0.680594\pi$
$937$	175414.	−	147190.i	0.199796	−	0.167649i	0.737196	+	0.675679i	$0.236149\pi$
$938$	1051.11	+	1820.57i	0.00119465	+	0.00206920i
$939$	−1.12198e6	−	647776.i	−1.27249	−	0.734673i
$940$	−72304.2	−	410057.i	−0.0818291	−	0.464076i
$941$	−87209.2	+	15377.3i	−0.0984879	+	0.0173661i	−0.222675	−	0.974893i	$-0.571479\pi$
$941$	−87209.2	+	15377.3i	−0.0984879	+	0.0173661i	0.124187	+	0.992259i	$0.460368\pi$
$942$	173969.	−	301324.i	0.196052	−	0.339572i
$943$	−102158.	+	58980.8i	−0.114881	+	0.0663265i
$944$	10116.1	+	12055.9i	0.0113519	+	0.0135287i
$945$	−126236.	−	346832.i	−0.141358	−	0.388378i
$946$	41121.6	−	112981.i	0.0459502	−	0.126247i
$947$	−1.28458e6	−	1.07789e6i	−1.43239	−	1.20192i	−0.944284	−	0.329133i	$-0.893244\pi$
$947$	−1.28458e6	−	1.07789e6i	−1.43239	−	1.20192i	−0.488106	−	0.872784i	$-0.662312\pi$
$948$	−128853.	+	730764.i	−0.143377	+	0.813130i
$949$			792548.i			0.880022i
$950$	−54564.8	−	83520.6i	−0.0604596	−	0.0925436i
$951$	215853.			0.238669
$952$	−336105.	−	59264.5i	−0.370853	−	0.0653914i
$953$	−433706.	+	516871.i	−0.477540	+	0.569110i	−0.950003	−	0.312240i	$-0.898921\pi$
$953$	−433706.	+	516871.i	−0.477540	+	0.569110i	0.472463	+	0.881350i	$0.343365\pi$
$954$	−52114.8	−	18968.2i	−0.0572617	−	0.0208416i
$955$	−33592.7	+	12226.8i	−0.0368331	+	0.0134062i
$956$	412201.	−	345878.i	0.451018	−	0.378449i
$957$	−40345.4	−	69880.3i	−0.0440525	−	0.0763012i
$958$	332745.	+	192110.i	0.362560	+	0.209324i
$959$	8198.89	+	46498.2i	0.00891492	+	0.0505590i
$960$	153846.	−	27127.3i	0.166934	−	0.0294350i
$961$	194125.	−	336235.i	0.210201	−	0.364079i
$962$	−290727.	+	167852.i	−0.314149	+	0.181374i
$963$	70591.3	+	84127.4i	0.0761200	+	0.0907163i
$964$	−179589.	−	493416.i	−0.193252	−	0.530957i
$965$	−84717.9	+	232761.i	−0.0909747	+	0.249951i
$966$	69767.2	+	58541.6i	0.0747648	+	0.0627351i
$967$	−178814.	+	1.01410e6i	−0.191227	+	1.08450i	0.726464	+	0.687204i	$0.241162\pi$
$967$	−178814.	+	1.01410e6i	−0.191227	+	1.08450i	−0.917691	+	0.397296i	$0.869949\pi$
$968$		−	685795.i		−	0.731886i
$969$	296165.	−	277699.i	0.315418	−	0.295752i
$970$	−162131.			−0.172315
$971$	1.08633e6	+	191549.i	1.15219	+	0.203162i	0.716931	−	0.697144i	$-0.245546\pi$
$971$	1.08633e6	+	191549.i	1.15219	+	0.203162i	0.435258	+	0.900306i	$0.356657\pi$
$972$	66012.6	−	78670.7i	0.0698705	−	0.0832685i
$973$	−248403.	−	90411.2i	−0.262380	−	0.0954985i
$974$	760806.	−	276911.i	0.801966	−	0.291892i
$975$	−178319.	+	149627.i	−0.187581	+	0.157399i
$976$	107075.	+	185459.i	0.112405	+	0.194692i
$977$	−1.01601e6	−	586593.i	−1.06441	−	0.614537i	−0.137760	−	0.990466i	$-0.543990\pi$
$977$	−1.01601e6	−	586593.i	−1.06441	−	0.614537i	−0.926648	+	0.375929i	$0.877324\pi$
$978$	153196.	+	868817.i	0.160166	+	0.908345i
$979$	−578196.	+	101952.i	−0.603268	+	0.106372i
$980$	−30294.9	+	52472.4i	−0.0315441	+	0.0546359i
$981$	55711.2	−	32164.9i	0.0578901	−	0.0334229i
$982$	486976.	+	580356.i	0.504993	+	0.601827i
$983$	−499454.	−	1.37224e6i	−0.516879	−	1.42011i	−0.873941	−	0.486032i	$-0.838444\pi$
$983$	−499454.	−	1.37224e6i	−0.516879	−	1.42011i	0.357063	−	0.934080i	$-0.383778\pi$
$984$	−191681.	+	526638.i	−0.197965	+	0.543904i
$985$	−124982.	−	104872.i	−0.128817	−	0.108090i
$986$	−8250.81	+	46792.6i	−0.00848677	+	0.0481309i
$987$		−	1.26659e6i		−	1.30018i
$988$	794974.	−	340020.i	0.814403	−	0.348330i
$989$	−104794.			−0.107138
$990$	8749.13	+	1542.71i	0.00892677	+	0.00157403i
$991$	170366.	−	203034.i	0.173475	−	0.206739i	−0.672301	−	0.740278i	$-0.734694\pi$
$991$	170366.	−	203034.i	0.173475	−	0.206739i	0.845775	+	0.533539i	$0.179138\pi$
$992$	1.13991e6	+	414894.i	1.15837	+	0.421613i
$993$	1.50781e6	−	548798.i	1.52914	−	0.556563i
$994$	521635.	−	437704.i	0.527952	−	0.443004i
$995$	−23587.3	−	40854.4i	−0.0238249	−	0.0412660i
$996$	495355.	+	285993.i	0.499341	+	0.288295i
$997$	233747.	+	1.32565e6i	0.235156	+	1.33364i	0.842284	+	0.539034i	$0.181210\pi$
$997$	233747.	+	1.32565e6i	0.235156	+	1.33364i	−0.607128	+	0.794604i	$0.707678\pi$
$998$	874732.	−	154239.i	0.878241	−	0.154858i
$999$	265841.	−	460449.i	0.266373	−	0.461372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.5.n.a.21.16	✓	156
19.10	odd	18	inner	95.5.n.a.86.16	yes	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.5.n.a.21.16	✓	156	1.1	even	1	trivial
95.5.n.a.86.16	yes	156	19.10	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	95.n (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.17727 + 0.383911i) q^{2} +(5.55356 - 6.61847i) q^{3} +(-10.4420 - 3.80057i) q^{4} +(10.5061 - 3.82390i) q^{5} +(14.6325 - 12.2781i) q^{6} +(-21.8707 - 37.8811i) q^{7} +(-51.9104 - 29.9705i) q^{8} +(1.10333 + 6.25730i) q^{9} +(24.3426 - 4.29225i) q^{10} +(28.2835 - 48.9884i) q^{11} +(-83.1441 + 48.0033i) q^{12} +(-138.547 - 165.114i) q^{13} +(-33.0753 - 90.8737i) q^{14} +(33.0378 - 90.7705i) q^{15} +(34.6813 + 29.1011i) q^{16} +(-22.6036 + 128.192i) q^{17} +14.0474i q^{18} +(-19.8808 - 360.452i) q^{19} -124.237 q^{20} +(-372.175 - 65.6245i) q^{21} +(80.3879 - 95.8025i) q^{22} +(-102.430 - 37.2815i) q^{23} +(-486.646 + 177.125i) q^{24} +(95.7556 - 80.3485i) q^{25} +(-238.265 - 412.687i) q^{26} +(653.606 + 377.360i) q^{27} +(84.4033 + 478.675i) q^{28} +(162.596 - 28.6700i) q^{29} +(106.780 - 184.948i) q^{30} +(991.881 - 572.663i) q^{31} +(680.807 + 811.354i) q^{32} +(-167.155 - 459.254i) q^{33} +(-98.4283 + 270.430i) q^{34} +(-374.629 - 314.351i) q^{35} +(12.2603 - 69.5319i) q^{36} -704.475i q^{37} +(95.0956 - 792.433i) q^{38} -1862.23 q^{39} +(-659.979 - 116.372i) q^{40} +(695.611 - 828.997i) q^{41} +(-785.131 - 285.764i) q^{42} +(903.402 - 328.811i) q^{43} +(-481.520 + 404.043i) q^{44} +(35.5190 + 61.5207i) q^{45} +(-208.705 - 120.496i) q^{46} +(581.984 + 3300.60i) q^{47} +(385.209 - 67.9228i) q^{48} +(243.847 - 422.356i) q^{49} +(239.332 - 138.178i) q^{50} +(722.902 + 861.521i) q^{51} +(819.178 + 2250.67i) q^{52} +(-1350.30 + 3709.93i) q^{53} +(1278.20 + 1072.54i) q^{54} +(109.822 - 622.830i) q^{55} +2621.90i q^{56} +(-2496.05 - 1870.21i) q^{57} +365.021 q^{58} +(342.338 + 60.3635i) q^{59} +(-689.959 + 822.261i) q^{60} +(4444.89 + 1617.81i) q^{61} +(2379.44 - 866.046i) q^{62} +(212.903 - 178.647i) q^{63} +(808.625 + 1400.58i) q^{64} +(-2086.97 - 1204.91i) q^{65} +(-187.628 - 1064.09i) q^{66} +(-21.4080 + 3.77481i) q^{67} +(723.228 - 1252.67i) q^{68} +(-815.597 + 470.885i) q^{69} +(-694.984 - 828.250i) q^{70} +(2408.31 + 6616.78i) q^{71} +(130.260 - 357.886i) q^{72} +(-2816.76 - 2363.54i) q^{73} +(270.456 - 1533.83i) q^{74} -1079.98i q^{75} +(-1162.33 + 3839.39i) q^{76} -2474.32 q^{77} +(-4054.57 - 714.930i) q^{78} +(4968.12 - 5920.78i) q^{79} +(475.644 + 173.120i) q^{80} +(5643.76 - 2054.16i) q^{81} +(1832.79 - 1537.89i) q^{82} +(-2978.89 - 5159.59i) q^{83} +(3636.83 + 2099.73i) q^{84} +(252.716 + 1433.23i) q^{85} +(2093.18 - 369.084i) q^{86} +(713.233 - 1235.36i) q^{87} +(-2936.41 + 1695.34i) q^{88} +(-6671.58 - 7950.87i) q^{89} +(53.7158 + 147.583i) q^{90} +(-3224.58 + 8859.47i) q^{91} +(927.881 + 778.585i) q^{92} +(1718.32 - 9745.06i) q^{93} +7409.71i q^{94} +(-1587.20 - 3710.92i) q^{95} +9150.83 q^{96} +(-6459.56 - 1138.99i) q^{97} +(693.068 - 825.966i) q^{98} +(337.741 + 122.928i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q + 24 q^{3} + 42 q^{4} + 42 q^{6} - 504 q^{9} - 150 q^{10} - 1728 q^{12} - 1122 q^{13} + 576 q^{14} + 2058 q^{16} + 1260 q^{17} + 900 q^{19} + 1026 q^{21} - 4608 q^{22} - 1260 q^{23} - 4032 q^{24}+ \cdots + 28038 q^{99}+O(q^{100}) \) 156 * q + 24 * q^3 + 42 * q^4 + 42 * q^6 - 504 * q^9 - 150 * q^10 - 1728 * q^12 - 1122 * q^13 + 576 * q^14 + 2058 * q^16 + 1260 * q^17 + 900 * q^19 + 1026 * q^21 - 4608 * q^22 - 1260 * q^23 - 4032 * q^24 + 3672 * q^26 - 2448 * q^27 + 4992 * q^28 + 1494 * q^29 - 4200 * q^30 + 5616 * q^31 + 11700 * q^32 + 2430 * q^33 + 15300 * q^34 + 1800 * q^35 + 13392 * q^36 + 9414 * q^38 - 12504 * q^39 - 2400 * q^40 - 15120 * q^41 - 36834 * q^42 + 5586 * q^43 - 61398 * q^44 - 8910 * q^46 + 3870 * q^47 + 57462 * q^48 - 16014 * q^49 + 25116 * q^51 + 6642 * q^52 + 21312 * q^53 - 14226 * q^54 - 8166 * q^57 - 10752 * q^58 - 16686 * q^59 - 18900 * q^60 - 58092 * q^61 - 6120 * q^62 - 60702 * q^63 + 33132 * q^64 + 16200 * q^65 + 41916 * q^66 + 41406 * q^67 + 9630 * q^68 + 65826 * q^69 + 41400 * q^70 + 28296 * q^71 + 76524 * q^72 + 2790 * q^73 - 32004 * q^74 + 5580 * q^76 - 5508 * q^77 - 22620 * q^78 + 5334 * q^79 - 32400 * q^80 - 55848 * q^81 - 68154 * q^82 - 8280 * q^83 - 84564 * q^84 - 33600 * q^85 + 20178 * q^86 - 28968 * q^87 - 13104 * q^88 - 13212 * q^89 - 28650 * q^90 + 122592 * q^91 + 57708 * q^92 + 93744 * q^93 - 211236 * q^96 + 18966 * q^97 + 13968 * q^98 + 28038 * q^99

Introduction

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