LMFDB - Embedded newform 82.5.e.a.3.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [82,5,Mod(3,82)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(82, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([3])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("82.3"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 82 = 2 \cdot 41 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	82.e (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,-56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$8.47633697288$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			3.4
Character	$\chi$	$=$	82.3
Dual form			82.5.e.a.55.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.00000 + 2.00000i) q^{2} +(0.493125 - 1.19051i) q^{3} -8.00000i q^{4} +(-21.5675 - 21.5675i) q^{5} +(1.39477 + 3.36727i) q^{6} +(-12.4355 + 30.0219i) q^{7} +(16.0000 + 16.0000i) q^{8} +(56.1015 + 56.1015i) q^{9} +86.2700 q^{10} +(100.730 + 41.7238i) q^{11} +(-9.52408 - 3.94500i) q^{12} +(-11.1215 + 26.8496i) q^{13} +(-35.1728 - 84.9146i) q^{14} +(-36.3118 + 15.0408i) q^{15} -64.0000 q^{16} +(60.8049 + 146.796i) q^{17} -224.406 q^{18} +(186.436 + 450.098i) q^{19} +(-172.540 + 172.540i) q^{20} +(29.6091 + 29.6091i) q^{21} +(-284.908 + 118.013i) q^{22} +362.404i q^{23} +(26.9382 - 11.1582i) q^{24} +305.314i q^{25} +(-31.4563 - 75.9422i) q^{26} +(190.886 - 79.0675i) q^{27} +(240.175 + 99.4837i) q^{28} +(-0.202955 + 0.489978i) q^{29} +(42.5419 - 102.705i) q^{30} +838.268i q^{31} +(128.000 - 128.000i) q^{32} +(99.3452 - 99.3452i) q^{33} +(-415.202 - 171.982i) q^{34} +(915.698 - 379.294i) q^{35} +(448.812 - 448.812i) q^{36} -1216.27 q^{37} +(-1273.07 - 527.322i) q^{38} +(26.4805 + 26.4805i) q^{39} -690.160i q^{40} +(1249.36 - 1124.66i) q^{41} -118.436 q^{42} +(239.858 - 239.858i) q^{43} +(333.790 - 805.841i) q^{44} -2419.94i q^{45} +(-724.808 - 724.808i) q^{46} +(-434.188 - 1048.22i) q^{47} +(-31.5600 + 76.1926i) q^{48} +(951.092 + 951.092i) q^{49} +(-610.628 - 610.628i) q^{50} +204.747 q^{51} +(214.797 + 88.9718i) q^{52} +(1948.51 + 807.099i) q^{53} +(-223.637 + 539.907i) q^{54} +(-1272.62 - 3072.38i) q^{55} +(-679.317 + 281.382i) q^{56} +627.782 q^{57} +(-0.574045 - 1.38587i) q^{58} +4075.64 q^{59} +(120.327 + 290.494i) q^{60} +(-2773.66 + 2773.66i) q^{61} +(-1676.54 - 1676.54i) q^{62} +(-2381.92 + 986.623i) q^{63} +512.000i q^{64} +(818.942 - 339.217i) q^{65} +397.381i q^{66} +(-1651.38 - 3986.79i) q^{67} +(1174.37 - 486.439i) q^{68} +(431.446 + 178.711i) q^{69} +(-1072.81 + 2589.98i) q^{70} +(-1136.03 + 2742.62i) q^{71} +1795.25i q^{72} +(-3868.68 + 3868.68i) q^{73} +(2432.54 - 2432.54i) q^{74} +(363.479 + 150.558i) q^{75} +(3600.78 - 1491.49i) q^{76} +(-2505.25 + 2505.25i) q^{77} -105.922 q^{78} +(-7813.71 - 3236.55i) q^{79} +(1380.32 + 1380.32i) q^{80} +6160.26i q^{81} +(-249.405 + 4748.04i) q^{82} +10467.8 q^{83} +(236.873 - 236.873i) q^{84} +(1854.61 - 4477.43i) q^{85} +959.431i q^{86} +(0.483241 + 0.483241i) q^{87} +(944.102 + 2279.26i) q^{88} +(-4725.85 + 11409.2i) q^{89} +(4839.88 + 4839.88i) q^{90} +(-667.775 - 667.775i) q^{91} +2899.23 q^{92} +(997.967 + 413.371i) q^{93} +(2964.82 + 1228.07i) q^{94} +(5686.51 - 13728.4i) q^{95} +(-89.2652 - 215.505i) q^{96} +(-10933.1 + 4528.63i) q^{97} -3804.37 q^{98} +(3310.35 + 7991.88i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 56 q^{2} + 16 q^{3} - 16 q^{6} + 448 q^{8} + 24 q^{9} + 328 q^{11} - 64 q^{12} - 348 q^{13} + 192 q^{14} + 1036 q^{15} - 1792 q^{16} - 1832 q^{17} - 96 q^{18} - 504 q^{19} + 2004 q^{21} - 856 q^{22}+ \cdots + 11544 q^{99}+O(q^{100}) $ 28 * q - 56 * q^2 + 16 * q^3 - 16 * q^6 + 448 * q^8 + 24 * q^9 + 328 * q^11 - 64 * q^12 - 348 * q^13 + 192 * q^14 + 1036 * q^15 - 1792 * q^16 - 1832 * q^17 - 96 * q^18 - 504 * q^19 + 2004 * q^21 - 856 * q^22 + 384 * q^24 + 384 * q^26 + 964 * q^27 - 768 * q^28 - 4 * q^29 - 4456 * q^30 + 3584 * q^32 - 748 * q^33 + 3576 * q^34 - 1104 * q^35 + 192 * q^36 + 5488 * q^37 + 256 * q^38 + 1232 * q^39 - 3760 * q^41 - 8016 * q^42 + 4756 * q^43 + 800 * q^44 - 2320 * q^46 - 4240 * q^47 - 1024 * q^48 + 2088 * q^49 - 6280 * q^50 + 29792 * q^51 + 1248 * q^52 - 10492 * q^53 - 1992 * q^54 + 14840 * q^55 + 1536 * q^56 - 33512 * q^57 + 2192 * q^58 - 11376 * q^59 + 9536 * q^60 - 3360 * q^61 + 2224 * q^62 - 13912 * q^63 + 41300 * q^65 + 15440 * q^67 + 352 * q^68 - 1004 * q^69 - 6792 * q^70 - 28392 * q^71 + 4284 * q^73 - 10976 * q^74 + 23812 * q^75 + 3008 * q^76 - 16524 * q^77 - 4928 * q^78 - 22236 * q^79 + 16752 * q^82 - 4024 * q^83 + 16032 * q^84 - 16616 * q^85 - 4628 * q^87 + 3648 * q^88 - 54412 * q^89 + 18336 * q^90 + 59948 * q^91 + 9280 * q^92 - 26800 * q^93 - 3240 * q^94 - 47636 * q^95 + 1024 * q^96 + 46764 * q^97 - 8352 * q^98 + 11544 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/82\mathbb{Z}\right)^\times$.

$n$	$47$
$\chi(n)$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−2.00000	+	2.00000i	−0.500000	+	0.500000i
$2$	−2.00000	+	2.00000i	−0.500000	+	0.500000i
$3$	0.493125	−	1.19051i	0.0547917	−	0.132279i	−0.894113	−	0.447841i	$-0.852193\pi$
$3$	0.493125	−	1.19051i	0.0547917	−	0.132279i	0.948905	+	0.315562i	$0.102193\pi$
$4$		−	8.00000i		−	0.500000i
$5$	−21.5675	−	21.5675i	−0.862700	−	0.862700i	0.128951	−	0.991651i	$-0.458839\pi$
$5$	−21.5675	−	21.5675i	−0.862700	−	0.862700i	−0.991651	+	0.128951i	$0.958839\pi$
$6$	1.39477	+	3.36727i	0.0387436	+	0.0935353i
$7$	−12.4355	+	30.0219i	−0.253785	+	0.612691i	−0.998504	−	0.0546877i	$-0.982584\pi$
$7$	−12.4355	+	30.0219i	−0.253785	+	0.612691i	0.744719	+	0.667379i	$0.232584\pi$
$8$	16.0000	+	16.0000i	0.250000	+	0.250000i
$9$	56.1015	+	56.1015i	0.692611	+	0.692611i
$10$	86.2700			0.862700
$11$	100.730	+	41.7238i	0.832481	+	0.344825i	0.757884	−	0.652389i	$-0.226233\pi$
$11$	100.730	+	41.7238i	0.832481	+	0.344825i	0.0745963	+	0.997214i	$0.476233\pi$
$12$	−9.52408	−	3.94500i	−0.0661394	−	0.0273959i
$13$	−11.1215	+	26.8496i	−0.0658076	+	0.158873i	−0.953362	−	0.301830i	$-0.902403\pi$
$13$	−11.1215	+	26.8496i	−0.0658076	+	0.158873i	0.887554	+	0.460703i	$0.152403\pi$
$14$	−35.1728	−	84.9146i	−0.179453	−	0.433238i
$15$	−36.3118	+	15.0408i	−0.161386	+	0.0668482i
$16$	−64.0000			−0.250000
$17$	60.8049	+	146.796i	0.210398	+	0.507945i	0.993484	−	0.113968i	$-0.0363560\pi$
$17$	60.8049	+	146.796i	0.210398	+	0.507945i	−0.783087	+	0.621912i	$0.786356\pi$
$18$	−224.406			−0.692611
$19$	186.436	+	450.098i	0.516445	+	1.24681i	0.940074	+	0.340972i	$0.110756\pi$
$19$	186.436	+	450.098i	0.516445	+	1.24681i	−0.423629	+	0.905836i	$0.639244\pi$
$20$	−172.540	+	172.540i	−0.431350	+	0.431350i
$21$	29.6091	+	29.6091i	0.0671408	+	0.0671408i
$22$	−284.908	+	118.013i	−0.588653	+	0.243828i
$23$			362.404i			0.685074i	0.939504	+	0.342537i	$0.111286\pi$
$23$			362.404i			0.685074i	−0.939504	+	0.342537i	$0.888714\pi$
$24$	26.9382	−	11.1582i	0.0467676	−	0.0193718i
$25$			305.314i			0.488502i
$26$	−31.4563	−	75.9422i	−0.0465330	−	0.112341i
$27$	190.886	−	79.0675i	0.261846	−	0.108460i
$28$	240.175	+	99.4837i	0.306345	+	0.126892i
$29$	−0.202955	+	0.489978i	−0.000241326	+	0.000582613i	−0.924000	−	0.382392i	$-0.875100\pi$
$29$	−0.202955	+	0.489978i	−0.000241326	+	0.000582613i	0.923759	+	0.382975i	$0.125100\pi$
$30$	42.5419	−	102.705i	0.0472688	−	0.114117i
$31$			838.268i			0.872288i	0.899877	+	0.436144i	$0.143656\pi$
$31$			838.268i			0.872288i	−0.899877	+	0.436144i	$0.856344\pi$
$32$	128.000	−	128.000i	0.125000	−	0.125000i
$33$	99.3452	−	99.3452i	0.0912261	−	0.0912261i
$34$	−415.202	−	171.982i	−0.359171	−	0.148774i
$35$	915.698	−	379.294i	0.747508	−	0.309628i
$36$	448.812	−	448.812i	0.346306	−	0.346306i
$37$	−1216.27			−0.888437			−0.444218	−	0.895919i	$-0.646519\pi$
$37$	−1216.27			−0.888437			−0.444218	+	0.895919i	$0.646519\pi$
$38$	−1273.07	−	527.322i	−0.881626	−	0.365181i
$39$	26.4805	+	26.4805i	0.0174099	+	0.0174099i
$40$		−	690.160i		−	0.431350i
$41$	1249.36	−	1124.66i	0.743225	−	0.669041i
$41$	1249.36	−	1124.66i	0.743225	−	0.669041i
$42$	−118.436			−0.0671408
$43$	239.858	−	239.858i	0.129723	−	0.129723i	−0.639264	−	0.768987i	$-0.720761\pi$
$43$	239.858	−	239.858i	0.129723	−	0.129723i	0.768987	+	0.639264i	$0.220761\pi$
$44$	333.790	−	805.841i	0.172412	−	0.416240i
$45$		−	2419.94i		−	1.19503i
$46$	−724.808	−	724.808i	−0.342537	−	0.342537i
$47$	−434.188	−	1048.22i	−0.196554	−	0.474523i	0.794617	−	0.607111i	$-0.207671\pi$
$47$	−434.188	−	1048.22i	−0.196554	−	0.474523i	−0.991171	+	0.132587i	$0.957671\pi$
$48$	−31.5600	+	76.1926i	−0.0136979	+	0.0330697i
$49$	951.092	+	951.092i	0.396123	+	0.396123i
$50$	−610.628	−	610.628i	−0.244251	−	0.244251i
$51$	204.747			0.0787184
$52$	214.797	+	88.9718i	0.0794367	+	0.0329038i
$53$	1948.51	+	807.099i	0.693667	+	0.287326i	0.701527	−	0.712643i	$-0.252502\pi$
$53$	1948.51	+	807.099i	0.693667	+	0.287326i	−0.00786012	+	0.999969i	$0.502502\pi$
$54$	−223.637	+	539.907i	−0.0766929	+	0.185153i
$55$	−1272.62	−	3072.38i	−0.420701	−	1.01566i
$56$	−679.317	+	281.382i	−0.216619	+	0.0897265i
$57$	627.782			0.193223
$58$	−0.574045	−	1.38587i	−0.000170643	−	0.000411970i
$59$	4075.64			1.17083			0.585413	−	0.810735i	$-0.300932\pi$
$59$	4075.64			1.17083			0.585413	+	0.810735i	$0.300932\pi$
$60$	120.327	+	290.494i	0.0334241	+	0.0806929i
$61$	−2773.66	+	2773.66i	−0.745406	+	0.745406i	−0.973613	−	0.228207i	$-0.926714\pi$
$61$	−2773.66	+	2773.66i	−0.745406	+	0.745406i	0.228207	+	0.973613i	$0.426714\pi$
$62$	−1676.54	−	1676.54i	−0.436144	−	0.436144i
$63$	−2381.92	+	986.623i	−0.600131	+	0.248582i
$64$			512.000i			0.125000i
$65$	818.942	−	339.217i	0.193832	−	0.0802880i
$66$			397.381i			0.0912261i
$67$	−1651.38	−	3986.79i	−0.367873	−	0.888124i	−0.994098	−	0.108482i	$-0.965401\pi$
$67$	−1651.38	−	3986.79i	−0.367873	−	0.888124i	0.626225	−	0.779642i	$-0.284599\pi$
$68$	1174.37	−	486.439i	0.253972	−	0.105199i
$69$	431.446	+	178.711i	0.0906208	+	0.0375364i
$70$	−1072.81	+	2589.98i	−0.218940	+	0.528568i
$71$	−1136.03	+	2742.62i	−0.225358	+	0.544062i	−0.995602	−	0.0936874i	$-0.970135\pi$
$71$	−1136.03	+	2742.62i	−0.225358	+	0.544062i	0.770244	+	0.637750i	$0.220135\pi$
$72$			1795.25i			0.346306i
$73$	−3868.68	+	3868.68i	−0.725967	+	0.725967i	−0.969814	−	0.243847i	$-0.921591\pi$
$73$	−3868.68	+	3868.68i	−0.725967	+	0.725967i	0.243847	+	0.969814i	$0.421591\pi$
$74$	2432.54	−	2432.54i	0.444218	−	0.444218i
$75$	363.479	+	150.558i	0.0646185	+	0.0267659i
$76$	3600.78	−	1491.49i	0.623404	−	0.258222i
$77$	−2505.25	+	2505.25i	−0.422542	+	0.422542i
$78$	−105.922			−0.0174099
$79$	−7813.71	−	3236.55i	−1.25200	−	0.518594i	−0.344553	−	0.938767i	$-0.611969\pi$
$79$	−7813.71	−	3236.55i	−1.25200	−	0.518594i	−0.907444	+	0.420173i	$0.861969\pi$
$80$	1380.32	+	1380.32i	0.215675	+	0.215675i
$81$			6160.26i			0.938921i
$82$	−249.405	+	4748.04i	−0.0370918	+	0.706133i
$83$	10467.8			1.51949			0.759747	−	0.650219i	$-0.225323\pi$
$83$	10467.8			1.51949			0.759747	+	0.650219i	$0.225323\pi$
$84$	236.873	−	236.873i	0.0335704	−	0.0335704i
$85$	1854.61	−	4477.43i	0.256694	−	0.619714i
$86$			959.431i			0.129723i
$87$	0.483241	+	0.483241i	6.38448e−5	+	6.38448e-5i
$88$	944.102	+	2279.26i	0.121914	+	0.294326i
$89$	−4725.85	+	11409.2i	−0.596623	+	1.44038i	0.280379	+	0.959889i	$0.409540\pi$
$89$	−4725.85	+	11409.2i	−0.596623	+	1.44038i	−0.877002	+	0.480486i	$0.840460\pi$
$90$	4839.88	+	4839.88i	0.597516	+	0.597516i
$91$	−667.775	−	667.775i	−0.0806394	−	0.0806394i
$92$	2899.23			0.342537
$93$	997.967	+	413.371i	0.115385	+	0.0477941i
$94$	2964.82	+	1228.07i	0.335539	+	0.138985i
$95$	5686.51	−	13728.4i	0.630084	−	1.52116i
$96$	−89.2652	−	215.505i	−0.00968590	−	0.0233838i
$97$	−10933.1	+	4528.63i	−1.16198	+	0.481308i	−0.878534	−	0.477679i	$-0.841478\pi$
$97$	−10933.1	+	4528.63i	−1.16198	+	0.481308i	−0.283447	+	0.958988i	$0.591478\pi$
$98$	−3804.37			−0.396123
$99$	3310.35	+	7991.88i	0.337756	+	0.815415i
$100$	2442.51			0.244251
$101$	−311.325	−	751.605i	−0.0305191	−	0.0736796i	0.907885	−	0.419219i	$-0.137696\pi$
$101$	−311.325	−	751.605i	−0.0305191	−	0.0736796i	−0.938404	+	0.345539i	$0.887696\pi$
$102$	−409.493	+	409.493i	−0.0393592	+	0.0393592i
$103$	720.298	+	720.298i	0.0678950	+	0.0678950i	0.740239	−	0.672344i	$-0.234712\pi$
$103$	720.298	+	720.298i	0.0678950	+	0.0678950i	−0.672344	+	0.740239i	$0.734712\pi$
$104$	−607.538	+	251.650i	−0.0561703	+	0.0232665i
$105$		−	1277.19i		−	0.115845i
$106$	−5511.22	+	2282.82i	−0.490497	+	0.203170i
$107$		−	18224.3i		−	1.59178i	−0.605440	−	0.795891i	$-0.707003\pi$
$107$		−	18224.3i		−	1.59178i	0.605440	−	0.795891i	$-0.292997\pi$
$108$	−632.540	−	1527.09i	−0.0542301	−	0.130923i
$109$	3186.31	−	1319.81i	0.268186	−	0.111086i	−0.244538	−	0.969640i	$-0.578636\pi$
$109$	3186.31	−	1319.81i	0.268186	−	0.111086i	0.512724	+	0.858553i	$0.328636\pi$
$110$	8689.99	+	3599.51i	0.718181	+	0.297480i
$111$	−599.774	+	1447.98i	−0.0486790	+	0.117521i
$112$	795.869	−	1921.40i	0.0634462	−	0.153173i
$113$		−	5310.73i		−	0.415908i	−0.978139	−	0.207954i	$-0.933320\pi$
$113$		−	5310.73i		−	0.415908i	0.978139	−	0.207954i	$-0.0666804\pi$
$114$	−1255.56	+	1255.56i	−0.0966116	+	0.0966116i
$115$	7816.15	−	7816.15i	0.591013	−	0.591013i
$116$	3.91982	+	1.62364i	0.000291307	+	0.000120663i
$117$	−2130.24	+	882.373i	−0.155617	+	0.0644585i
$118$	−8151.29	+	8151.29i	−0.585413	+	0.585413i
$119$	−5163.23			−0.364609
$120$	−821.642	−	340.335i	−0.0570585	−	0.0236344i
$121$	−1947.06	−	1947.06i	−0.132987	−	0.132987i
$122$		−	11094.6i		−	0.745406i
$123$	−722.826	−	2041.97i	−0.0477775	−	0.134971i
$124$	6706.15			0.436144
$125$	−6894.83	+	6894.83i	−0.441269	+	0.441269i
$126$	2790.59	−	6737.08i	0.175774	−	0.424357i
$127$			14383.7i			0.891792i	0.895085	+	0.445896i	$0.147115\pi$
$127$			14383.7i			0.891792i	−0.895085	+	0.445896i	$0.852885\pi$
$128$	−1024.00	−	1024.00i	−0.0625000	−	0.0625000i
$129$	−167.273	−	403.833i	−0.0100519	−	0.0242674i
$130$	−959.450	+	2316.32i	−0.0567722	+	0.137060i
$131$	10563.4	+	10563.4i	0.615549	+	0.615549i	0.944386	−	0.328838i	$-0.106657\pi$
$131$	10563.4	+	10563.4i	0.615549	+	0.615549i	−0.328838	+	0.944386i	$0.606657\pi$
$132$	−794.762	−	794.762i	−0.0456130	−	0.0456130i
$133$	−15831.2			−0.894973
$134$	11276.3	+	4670.81i	0.627998	+	0.260125i
$135$	−5822.22	−	2411.64i	−0.319463	−	0.132326i
$136$	−1375.86	+	3321.62i	−0.0743868	+	0.179586i
$137$	−10087.0	−	24352.1i	−0.537427	−	1.29746i	−0.926513	−	0.376262i	$-0.877209\pi$
$137$	−10087.0	−	24352.1i	−0.537427	−	1.29746i	0.389086	−	0.921201i	$-0.372791\pi$
$138$	−1220.31	+	505.470i	−0.0640786	+	0.0265422i
$139$	4027.42			0.208448			0.104224	−	0.994554i	$-0.466764\pi$
$139$	4027.42			0.208448			0.104224	+	0.994554i	$0.466764\pi$
$140$	−3034.36	−	7325.58i	−0.154814	−	0.373754i
$141$	−1462.03			−0.0735389
$142$	−3213.18	−	7757.29i	−0.159352	−	0.384710i
$143$	−2240.54	+	2240.54i	−0.109567	+	0.109567i
$144$	−3590.50	−	3590.50i	−0.173153	−	0.173153i
$145$	14.9448	−	6.19035i	0.000710813	−	0.000294428i
$146$		−	15474.7i		−	0.725967i
$147$	1601.29	−	663.277i	0.0741031	−	0.0306945i
$148$			9730.16i			0.444218i
$149$	−8827.81	−	21312.2i	−0.397631	−	0.959967i	−0.988226	−	0.152999i	$-0.951107\pi$
$149$	−8827.81	−	21312.2i	−0.397631	−	0.959967i	0.590595	−	0.806968i	$-0.298893\pi$
$150$	−1028.07	+	425.842i	−0.0456922	+	0.0189263i
$151$	−5656.21	−	2342.88i	−0.248069	−	0.102753i	0.255185	−	0.966892i	$-0.417864\pi$
$151$	−5656.21	−	2342.88i	−0.248069	−	0.102753i	−0.503253	+	0.864139i	$0.667864\pi$
$152$	−4218.58	+	10184.5i	−0.182591	+	0.440813i
$153$	−4824.23	+	11646.7i	−0.206085	+	0.497532i
$154$		−	10021.0i		−	0.422542i
$155$	18079.4	−	18079.4i	0.752522	−	0.752522i
$156$	211.844	−	211.844i	0.00870495	−	0.00870495i
$157$	26430.0	+	10947.7i	1.07226	+	0.444143i	0.847786	−	0.530338i	$-0.177935\pi$
$157$	26430.0	+	10947.7i	1.07226	+	0.444143i	0.224470	+	0.974481i	$0.427935\pi$
$158$	22100.5	−	9154.34i	0.885296	−	0.366701i
$159$	1921.72	−	1921.72i	0.0760144	−	0.0760144i
$160$	−5521.28			−0.215675
$161$	−10880.0	−	4506.66i	−0.419739	−	0.173861i
$162$	−12320.5	−	12320.5i	−0.469460	−	0.469460i
$163$		−	5487.88i		−	0.206552i	−0.994653	−	0.103276i	$-0.967068\pi$
$163$		−	5487.88i		−	0.206552i	0.994653	−	0.103276i	$-0.0329325\pi$
$164$	−8997.27	−	9994.89i	−0.334521	−	0.371613i
$165$	−4285.25			−0.157401
$166$	−20935.6	+	20935.6i	−0.759747	+	0.759747i
$167$	18408.5	−	44442.1i	0.660064	−	1.59354i	−0.137637	−	0.990483i	$-0.543951\pi$
$167$	18408.5	−	44442.1i	0.660064	−	1.59354i	0.797701	−	0.603053i	$-0.206049\pi$
$168$			947.490i			0.0335704i
$169$	19598.5	+	19598.5i	0.686197	+	0.686197i
$170$	5245.64	+	12664.1i	0.181510	+	0.438204i
$171$	−14791.8	+	35710.5i	−0.505858	+	1.22125i
$172$	−1918.86	−	1918.86i	−0.0648615	−	0.0648615i
$173$	23706.2	+	23706.2i	0.792083	+	0.792083i	0.981832	−	0.189750i	$-0.0607677\pi$
$173$	23706.2	+	23706.2i	0.792083	+	0.792083i	−0.189750	+	0.981832i	$0.560768\pi$
$174$	−1.93296			−6.38448e−5
$175$	−9166.09	−	3796.72i	−0.299301	−	0.123974i
$176$	−6446.73	−	2670.32i	−0.208120	−	0.0862062i
$177$	2009.80	−	4852.10i	0.0641515	−	0.154876i
$178$	−13366.7	−	32270.1i	−0.421876	−	1.01850i
$179$	37901.7	−	15699.4i	1.18291	−	0.489979i	0.297472	−	0.954731i	$-0.403856\pi$
$179$	37901.7	−	15699.4i	1.18291	−	0.489979i	0.885441	+	0.464752i	$0.153856\pi$
$180$	−19359.5			−0.597516
$181$	11941.7	+	28829.8i	0.364510	+	0.880004i	0.994629	+	0.103506i	$0.0330059\pi$
$181$	11941.7	+	28829.8i	0.364510	+	0.880004i	−0.630119	+	0.776498i	$0.716994\pi$
$182$	2671.10			0.0806394
$183$	1934.31	+	4669.83i	0.0577594	+	0.139444i
$184$	−5798.47	+	5798.47i	−0.171269	+	0.171269i
$185$	26231.9	+	26231.9i	0.766454	+	0.766454i
$186$	−2822.68	+	1169.19i	−0.0815897	+	0.0337956i
$187$			17323.8i			0.495405i
$188$	−8385.77	+	3473.50i	−0.237262	+	0.0982770i
$189$			6713.99i			0.187956i
$190$	16083.9	+	38829.9i	0.445537	+	1.07562i
$191$	27107.5	−	11228.3i	0.743057	−	0.307784i	0.0211520	−	0.999776i	$-0.493267\pi$
$191$	27107.5	−	11228.3i	0.743057	−	0.307784i	0.721905	+	0.691992i	$0.243267\pi$
$192$	609.541	+	252.480i	0.0165349	+	0.00684896i
$193$	−5986.06	+	14451.6i	−0.160704	+	0.387973i	−0.983636	−	0.180166i	$-0.942337\pi$
$193$	−5986.06	+	14451.6i	−0.160704	+	0.387973i	0.822932	+	0.568139i	$0.192337\pi$
$194$	12808.9	−	30923.4i	0.340336	−	0.821645i
$195$		−	1142.23i		−	0.0300390i
$196$	7608.74	−	7608.74i	0.198062	−	0.198062i
$197$	−43937.5	+	43937.5i	−1.13215	+	1.13215i	−0.142327	+	0.989820i	$0.545459\pi$
$197$	−43937.5	+	43937.5i	−1.13215	+	1.13215i	−0.989820	+	0.142327i	$0.954541\pi$
$198$	−22604.5	−	9363.07i	−0.576585	−	0.238829i
$199$	33227.9	−	13763.4i	0.839067	−	0.347553i	0.0785813	−	0.996908i	$-0.474961\pi$
$199$	33227.9	−	13763.4i	0.839067	−	0.347553i	0.760486	+	0.649355i	$0.224961\pi$
$200$	−4885.02	+	4885.02i	−0.122126	+	0.122126i
$201$	−5560.65			−0.137636
$202$	2125.86	+	880.560i	0.0520993	+	0.0215802i
$203$	−12.1862	−	12.1862i	−0.000295717	−	0.000295717i
$204$		−	1637.97i		−	0.0393592i
$205$	−51201.7	−	2689.52i	−1.21836	−	0.0639982i
$206$	−2881.19			−0.0678950
$207$	−20331.4	+	20331.4i	−0.474490	+	0.474490i
$208$	711.775	−	1718.38i	0.0164519	−	0.0397184i
$209$			53117.2i			1.21603i
$210$	2554.37	+	2554.37i	0.0579223	+	0.0579223i
$211$	−9898.38	−	23896.8i	−0.222331	−	0.536754i	0.772875	−	0.634558i	$-0.218818\pi$
$211$	−9898.38	−	23896.8i	−0.222331	−	0.536754i	−0.995206	+	0.0978047i	$0.968818\pi$
$212$	6456.80	−	15588.1i	0.143663	−	0.346833i
$213$	2704.91	+	2704.91i	0.0596202	+	0.0596202i
$214$	36448.6	+	36448.6i	0.795891	+	0.795891i
$215$	−10346.3			−0.223824
$216$	4319.25	+	1789.09i	0.0925766	+	0.0383465i
$217$	−25166.4	−	10424.3i	−0.534443	−	0.221373i
$218$	−3733.00	+	9012.26i	−0.0785498	+	0.189636i
$219$	2697.96	+	6513.44i	0.0562531	+	0.135807i
$220$	−24579.0	+	10181.0i	−0.507831	+	0.210350i
$221$	−4617.66			−0.0945447
$222$	−1696.42	−	4095.51i	−0.0344212	−	0.0831002i
$223$	−26862.1			−0.540171			−0.270085	−	0.962836i	$-0.587052\pi$
$223$	−26862.1			−0.540171			−0.270085	+	0.962836i	$0.587052\pi$
$224$	2251.06	+	5434.54i	0.0448632	+	0.108309i
$225$	−17128.6	+	17128.6i	−0.338342	+	0.338342i
$226$	10621.5	+	10621.5i	0.207954	+	0.207954i
$227$	−4462.31	+	1848.35i	−0.0865979	+	0.0358700i	−0.425562	−	0.904929i	$-0.639924\pi$
$227$	−4462.31	+	1848.35i	−0.0865979	+	0.0358700i	0.338964	+	0.940799i	$0.389924\pi$
$228$		−	5022.26i		−	0.0966116i
$229$	72640.8	−	30088.8i	1.38519	−	0.573765i	0.439326	−	0.898328i	$-0.355217\pi$
$229$	72640.8	−	30088.8i	1.38519	−	0.573765i	0.945864	+	0.324563i	$0.105217\pi$
$230$			31264.6i			0.591013i
$231$	1747.12	+	4217.93i	0.0327416	+	0.0790452i
$232$	−11.0869	+	4.59236i	−0.000205985	+	8.53217e-5i
$233$	7222.50	+	2991.66i	0.133038	+	0.0551062i	0.448209	−	0.893929i	$-0.352062\pi$
$233$	7222.50	+	2991.66i	0.133038	+	0.0551062i	−0.315171	+	0.949035i	$0.602062\pi$
$234$	2495.73	−	6025.22i	0.0455790	−	0.110038i
$235$	−13243.2	+	31971.9i	−0.239804	+	0.578938i
$236$		−	32605.2i		−	0.585413i
$237$	−7706.28	+	7706.28i	−0.137198	+	0.137198i
$238$	10326.5	−	10326.5i	0.182304	−	0.182304i
$239$	53969.7	+	22355.0i	0.944831	+	0.391362i	0.801286	−	0.598282i	$-0.204150\pi$
$239$	53969.7	+	22355.0i	0.944831	+	0.391362i	0.143545	+	0.989644i	$0.454150\pi$
$240$	2323.96	−	962.614i	0.0403464	−	0.0167120i
$241$	41527.1	−	41527.1i	0.714986	−	0.714986i	−0.252588	−	0.967574i	$-0.581282\pi$
$241$	41527.1	−	41527.1i	0.714986	−	0.714986i	0.967574	+	0.252588i	$0.0812818\pi$
$242$	7788.25			0.132987
$243$	22795.6	+	9442.25i	0.386045	+	0.159905i
$244$	22189.3	+	22189.3i	0.372703	+	0.372703i
$245$		−	41025.4i		−	0.683471i
$246$	5529.60	+	2638.30i	0.0913742	+	0.0435967i
$247$	−14158.4			−0.232071
$248$	−13412.3	+	13412.3i	−0.218072	+	0.218072i
$249$	5161.93	−	12462.0i	0.0832557	−	0.200997i
$250$		−	27579.3i		−	0.441269i
$251$	−46476.8	−	46476.8i	−0.737715	−	0.737715i	0.234421	−	0.972135i	$-0.424681\pi$
$251$	−46476.8	−	46476.8i	−0.737715	−	0.737715i	−0.972135	+	0.234421i	$0.924681\pi$
$252$	7892.99	+	19055.4i	0.124291	+	0.300065i
$253$	−15120.9	+	36505.0i	−0.236231	+	0.570311i
$254$	−28767.4	−	28767.4i	−0.445896	−	0.445896i
$255$	−4415.87	−	4415.87i	−0.0679104	−	0.0679104i
$256$	4096.00			0.0625000
$257$	−66594.9	−	27584.5i	−1.00826	−	0.417637i	−0.183443	−	0.983030i	$-0.558724\pi$
$257$	−66594.9	−	27584.5i	−1.00826	−	0.417637i	−0.824821	+	0.565393i	$0.808724\pi$
$258$	1142.21	+	473.120i	0.0171596	+	0.00710774i
$259$	15124.9	−	36514.7i	0.225472	−	0.544337i
$260$	−2713.73	−	6551.53i	−0.0401440	−	0.0969162i
$261$	−38.8746	+	16.1024i	−0.000570670	+	0.000236379i
$262$	−42253.7			−0.615549
$263$	−32067.5	−	77417.7i	−0.463610	−	1.11925i	−0.966904	−	0.255139i	$-0.917879\pi$
$263$	−32067.5	−	77417.7i	−0.463610	−	1.11925i	0.503294	−	0.864115i	$-0.332121\pi$
$264$	3179.05			0.0456130
$265$	−24617.4	−	59431.6i	−0.350550	−	0.846303i
$266$	31662.4	−	31662.4i	0.447487	−	0.447487i
$267$	11252.3	+	11252.3i	0.157841	+	0.157841i
$268$	−31894.3	+	13211.1i	−0.444062	+	0.183937i
$269$			33231.2i			0.459241i	0.973280	+	0.229621i	$0.0737486\pi$
$269$			33231.2i			0.459241i	−0.973280	+	0.229621i	$0.926251\pi$
$270$	16467.7	−	6821.15i	0.225895	−	0.0935686i
$271$		−	119832.i		−	1.63168i	−0.578280	−	0.815838i	$-0.696276\pi$
$271$		−	119832.i		−	1.63168i	0.578280	−	0.815838i	$-0.303724\pi$
$272$	−3891.52	−	9394.95i	−0.0525994	−	0.126986i
$273$	−1124.29	+	465.696i	−0.0150853	+	0.00624852i
$274$	68878.1	+	28530.3i	0.917445	+	0.380018i
$275$	−12738.9	+	30754.3i	−0.168448	+	0.406669i
$276$	1429.69	−	3451.57i	0.0187682	−	0.0453104i
$277$		−	141072.i		−	1.83858i	−0.393582	−	0.919289i	$-0.628764\pi$
$277$		−	141072.i		−	1.83858i	0.393582	−	0.919289i	$-0.371236\pi$
$278$	−8054.83	+	8054.83i	−0.104224	+	0.104224i
$279$	−47028.1	+	47028.1i	−0.604156	+	0.604156i
$280$	20719.9	+	8582.45i	0.264284	+	0.109470i
$281$	−1701.26	+	704.684i	−0.0215456	+	0.00892446i	−0.393430	−	0.919354i	$-0.628712\pi$
$281$	−1701.26	+	704.684i	−0.0215456	+	0.00892446i	0.371885	+	0.928279i	$0.378712\pi$
$282$	2924.06	−	2924.06i	0.0367695	−	0.0367695i
$283$	9687.57			0.120960			0.0604800	−	0.998169i	$-0.480737\pi$
$283$	9687.57			0.120960			0.0604800	+	0.998169i	$0.480737\pi$
$284$	21940.9	+	9088.24i	0.272031	+	0.112679i
$285$	−13539.7	−	13539.7i	−0.166694	−	0.166694i
$286$		−	8962.14i		−	0.109567i
$287$	18228.0	+	51493.8i	0.221296	+	0.625160i
$288$	14362.0			0.173153
$289$	41206.4	−	41206.4i	0.493366	−	0.493366i
$290$	−17.5090	+	42.2704i	−0.000208192	+	0.000502620i
$291$			15249.1i			0.180077i
$292$	30949.4	+	30949.4i	0.362984	+	0.362984i
$293$	−28999.0	−	70009.9i	−0.337791	−	0.815500i	−0.997927	−	0.0643540i	$-0.979501\pi$
$293$	−28999.0	−	70009.9i	−0.337791	−	0.815500i	0.660136	−	0.751146i	$-0.270499\pi$
$294$	−1876.03	+	4529.14i	−0.0217043	+	0.0523988i
$295$	−87901.4	−	87901.4i	−1.01007	−	1.01007i
$296$	−19460.3	−	19460.3i	−0.222109	−	0.222109i
$297$	22527.0			0.255382
$298$	60280.1	+	24968.8i	0.678799	+	0.281168i
$299$	−9730.41	−	4030.47i	−0.108840	−	0.0450831i
$300$	1204.46	−	2907.83i	0.0133829	−	0.0323093i
$301$	4218.23	+	10183.7i	0.0465583	+	0.112402i
$302$	15998.2	−	6626.66i	0.175411	−	0.0726576i
$303$	−1048.32			−0.0114184
$304$	−11931.9	−	28806.2i	−0.129111	−	0.311702i
$305$	119642.			1.28612
$306$	−13645.0	−	32941.9i	−0.145724	−	0.351808i
$307$	−43421.3	+	43421.3i	−0.460708	+	0.460708i	−0.898887	−	0.438180i	$-0.855623\pi$
$307$	−43421.3	+	43421.3i	−0.460708	+	0.460708i	0.438180	+	0.898887i	$0.355623\pi$
$308$	20042.0	+	20042.0i	0.211271	+	0.211271i
$309$	1212.72	−	502.325i	0.0127012	−	0.00526099i
$310$			72317.4i			0.752522i
$311$	39481.6	−	16353.8i	0.408201	−	0.169083i	−0.169128	−	0.985594i	$-0.554095\pi$
$311$	39481.6	−	16353.8i	0.408201	−	0.169083i	0.577329	+	0.816512i	$0.304095\pi$
$312$			847.375i			0.00870495i
$313$	35637.3	+	86036.1i	0.363761	+	0.878197i	0.994743	+	0.102400i	$0.0326521\pi$
$313$	35637.3	+	86036.1i	0.363761	+	0.878197i	−0.630982	+	0.775797i	$0.717348\pi$
$314$	−74755.4	+	30964.7i	−0.758199	+	0.314056i
$315$	72651.0	+	30093.0i	0.732185	+	0.303281i
$316$	−25892.4	+	62509.7i	−0.259297	+	0.625999i
$317$	−30078.7	+	72616.4i	−0.299323	+	0.722630i	0.700635	+	0.713520i	$0.252900\pi$
$317$	−30078.7	+	72616.4i	−0.299323	+	0.722630i	−0.999958	+	0.00911047i	$0.997100\pi$
$318$			7686.88i			0.0760144i
$319$	−40.8875	+	40.8875i	−0.000401799	+	0.000401799i
$320$	11042.6	−	11042.6i	0.107837	−	0.107837i
$321$	−21696.2	−	8986.87i	−0.210559	−	0.0872164i
$322$	30773.4	−	12746.8i	0.296800	−	0.122939i
$323$	−54736.3	+	54736.3i	−0.524651	+	0.524651i
$324$	49282.1			0.469460
$325$	−8197.56	−	3395.54i	−0.0776101	−	0.0321471i
$326$	10975.8	+	10975.8i	0.103276	+	0.103276i
$327$		−	4444.17i		−	0.0415619i
$328$	37984.3	+	1995.24i	0.353067	+	0.0185459i
$329$	36868.9			0.340618
$330$	8570.51	−	8570.51i	0.0787007	−	0.0787007i
$331$	−69220.6	+	167113.i	−0.631800	+	1.52530i	0.205558	+	0.978645i	$0.434099\pi$
$331$	−69220.6	+	167113.i	−0.631800	+	1.52530i	−0.837358	+	0.546655i	$0.815901\pi$
$332$		−	83742.3i		−	0.759747i
$333$	−68234.6	−	68234.6i	−0.615341	−	0.615341i
$334$	52067.2	+	125701.i	0.466736	+	1.12680i
$335$	−50368.9	+	121601.i	−0.448820	+	1.08355i
$336$	−1894.98	−	1894.98i	−0.0167852	−	0.0167852i
$337$	−110152.	−	110152.i	−0.969913	−	0.969913i	0.0296471	−	0.999560i	$-0.490562\pi$
$337$	−110152.	−	110152.i	−0.969913	−	0.969913i	−0.999560	+	0.0296471i	$0.990562\pi$
$338$	−78393.8			−0.686197
$339$	−6322.47	−	2618.85i	−0.0550158	−	0.0227883i
$340$	−35819.5	−	14836.9i	−0.309857	−	0.128347i
$341$	−34975.7	+	84438.9i	−0.300786	+	0.726162i
$342$	−41837.5	−	101005.i	−0.357695	−	0.863553i
$343$	−112463.	+	46583.8i	−0.955922	+	0.395956i
$344$	7675.45			0.0648615
$345$	−5450.86	−	13159.5i	−0.0457960	−	0.110561i
$346$	−94825.0			−0.792083
$347$	3785.36	+	9138.68i	0.0314375	+	0.0758969i	0.938819	−	0.344412i	$-0.111922\pi$
$347$	3785.36	+	9138.68i	0.0314375	+	0.0758969i	−0.907381	+	0.420309i	$0.861922\pi$
$348$	3.86593	−	3.86593i	3.19224e−5	−	3.19224e-5i
$349$	124779.	+	124779.i	1.02445	+	1.02445i	0.999694	+	0.0247523i	$0.00787970\pi$
$349$	124779.	+	124779.i	1.02445	+	1.02445i	0.0247523	+	0.999694i	$0.492120\pi$
$350$	25925.6	−	10738.7i	0.211638	−	0.0876632i
$351$			6004.56i			0.0487379i
$352$	18234.1	−	7552.81i	0.147163	−	0.0609570i
$353$		−	42450.2i		−	0.340667i	−0.985386	−	0.170334i	$-0.945515\pi$
$353$		−	42450.2i		−	0.340667i	0.985386	−	0.170334i	$-0.0544846\pi$
$354$	5684.58	+	13723.8i	0.0453620	+	0.109514i
$355$	83652.7	−	34650.1i	0.663779	−	0.274946i
$356$	91273.7	+	37806.8i	0.720188	+	0.298312i
$357$	−2546.12	+	6146.87i	−0.0199775	+	0.0482301i
$358$	−44404.6	+	107202.i	−0.346467	+	0.836446i
$359$			52907.4i			0.410514i	0.978708	+	0.205257i	$0.0658030\pi$
$359$			52907.4i			0.410514i	−0.978708	+	0.205257i	$0.934197\pi$
$360$	38719.0	−	38719.0i	0.298758	−	0.298758i
$361$	−75678.3	+	75678.3i	−0.580707	+	0.580707i
$362$	−81543.0	−	33776.2i	−0.622257	−	0.257747i
$363$	−3278.14	+	1357.85i	−0.0248780	+	0.0103048i
$364$	−5342.20	+	5342.20i	−0.0403197	+	0.0403197i
$365$	166875.			1.25258
$366$	−13208.3	−	5471.04i	−0.0986015	−	0.0408421i
$367$	136093.	+	136093.i	1.01043	+	1.01043i	0.999945	+	0.0104826i	$0.00333678\pi$
$367$	136093.	+	136093.i	1.01043	+	1.01043i	0.0104826	+	0.999945i	$0.496663\pi$
$368$		−	23193.9i		−	0.171269i
$369$	133186.	+	6996.00i	0.978152	+	0.0513804i
$370$	−104928.			−0.766454
$371$	−48461.2	+	48461.2i	−0.352084	+	0.352084i
$372$	3306.97	−	7983.74i	0.0238971	−	0.0576926i
$373$		−	172569.i		−	1.24036i	−0.784461	−	0.620178i	$-0.787060\pi$
$373$		−	172569.i		−	1.24036i	0.784461	−	0.620178i	$-0.212940\pi$
$374$	−34647.6	−	34647.6i	−0.247702	−	0.247702i
$375$	4808.35	+	11608.4i	0.0341927	+	0.0825485i
$376$	9824.55	−	23718.6i	0.0694923	−	0.167769i
$377$	−10.8986	−	10.8986i	−7.66807e−5	−	7.66807e-5i
$378$	−13428.0	−	13428.0i	−0.0939781	−	0.0939781i
$379$	217031.			1.51092			0.755462	−	0.655193i	$-0.227413\pi$
$379$	217031.			1.51092			0.755462	+	0.655193i	$0.227413\pi$
$380$	−109828.	−	45492.1i	−0.760579	−	0.315042i
$381$	17124.0	+	7092.97i	0.117965	+	0.0488628i
$382$	−31758.4	+	76671.5i	−0.217636	+	0.525421i
$383$	−18465.5	−	44579.6i	−0.125882	−	0.303905i	0.848357	−	0.529425i	$-0.177592\pi$
$383$	−18465.5	−	44579.6i	−0.125882	−	0.303905i	−0.974239	+	0.225519i	$0.927592\pi$
$384$	−1724.04	+	714.122i	−0.0116919	+	0.00484295i
$385$	108064.			0.729054
$386$	−16931.1	−	40875.4i	−0.113635	−	0.274339i
$387$	26912.8			0.179695
$388$	36229.0	+	87464.7i	0.240654	+	0.580991i
$389$	130724.	−	130724.i	0.863887	−	0.863887i	−0.127900	−	0.991787i	$-0.540824\pi$
$389$	130724.	−	130724.i	0.863887	−	0.863887i	0.991787	+	0.127900i	$0.0408237\pi$
$390$	2284.47	+	2284.47i	0.0150195	+	0.0150195i
$391$	−53199.5	+	22036.0i	−0.347980	+	0.144138i
$392$			30435.0i			0.198062i
$393$	17785.0	−	7366.77i	0.115151	−	0.0476971i
$394$		−	175750.i		−	1.13215i
$395$	98718.0	+	238326.i	0.632707	+	1.52749i
$396$	63935.0	−	26482.8i	0.407707	−	0.168878i
$397$	70950.5	+	29388.7i	0.450168	+	0.186466i	0.596237	−	0.802809i	$-0.296662\pi$
$397$	70950.5	+	29388.7i	0.450168	+	0.186466i	−0.146069	+	0.989274i	$0.546662\pi$
$398$	−38928.9	+	93982.7i	−0.245757	+	0.593310i
$399$	−7806.76	+	18847.2i	−0.0490371	+	0.118386i
$400$		−	19540.1i		−	0.122126i
$401$	−105924.	+	105924.i	−0.658728	+	0.658728i	−0.955079	−	0.296351i	$-0.904230\pi$
$401$	−105924.	+	105924.i	−0.658728	+	0.658728i	0.296351	+	0.955079i	$0.404230\pi$
$402$	11121.3	−	11121.3i	0.0688182	−	0.0688182i
$403$	−22507.2	−	9322.78i	−0.138583	−	0.0574031i
$404$	−6012.84	+	2490.60i	−0.0368398	+	0.0152595i
$405$	132861.	−	132861.i	0.810007	−	0.810007i
$406$	48.7448			0.000295717
$407$	−122515.	−	50747.4i	−0.739606	−	0.306355i
$408$	3275.95	+	3275.95i	0.0196796	+	0.0196796i
$409$		−	168408.i		−	1.00674i	−0.864072	−	0.503369i	$-0.832094\pi$
$409$		−	168408.i		−	1.00674i	0.864072	−	0.503369i	$-0.167906\pi$
$410$	107782.	−	97024.3i	0.641180	−	0.577182i
$411$	−33965.6			−0.201074
$412$	5762.38	−	5762.38i	0.0339475	−	0.0339475i
$413$	−50682.5	+	122358.i	−0.297138	+	0.717354i
$414$		−	81325.7i		−	0.474490i
$415$	−225764.	−	225764.i	−1.31087	−	1.31087i
$416$	2013.20	+	4860.30i	0.0116332	+	0.0280851i
$417$	1986.02	−	4794.68i	0.0114212	−	0.0275732i
$418$	−106234.	−	106234.i	−0.608013	−	0.608013i
$419$	60169.4	+	60169.4i	0.342727	+	0.342727i	0.857391	−	0.514665i	$-0.172084\pi$
$419$	60169.4	+	60169.4i	0.342727	+	0.342727i	−0.514665	+	0.857391i	$0.672084\pi$
$420$	−10217.5			−0.0579223
$421$	−298611.	−	123689.i	−1.68477	−	0.697856i	−0.685237	−	0.728320i	$-0.740301\pi$
$421$	−298611.	−	123689.i	−1.68477	−	0.697856i	−0.999536	+	0.0304643i	$0.990301\pi$
$422$	67590.4	+	27996.8i	0.379542	+	0.157211i
$423$	34448.2	−	83165.4i	0.192525	−	0.464796i
$424$	18262.6	+	44089.8i	0.101585	+	0.245248i
$425$	−44818.9	+	18564.6i	−0.248132	+	0.102780i
$426$	−10819.6			−0.0596202
$427$	−48778.6	−	117762.i	−0.267531	−	0.645876i
$428$	−145794.			−0.795891
$429$	1562.52	+	3772.25i	0.00849004	+	0.0204968i
$430$	20692.5	−	20692.5i	0.111912	−	0.111912i
$431$	84324.4	+	84324.4i	0.453940	+	0.453940i	0.896660	−	0.442720i	$-0.145986\pi$
$431$	84324.4	+	84324.4i	0.453940	+	0.453940i	−0.442720	+	0.896660i	$0.645986\pi$
$432$	−12216.7	+	5060.32i	−0.0654615	+	0.0271150i
$433$		−	78259.8i		−	0.417410i	−0.977979	−	0.208705i	$-0.933075\pi$
$433$		−	78259.8i		−	0.417410i	0.977979	−	0.208705i	$-0.0669249\pi$
$434$	71181.2	−	29484.2i	0.377908	−	0.156535i
$435$		−	20.8446i		−	0.000110158i
$436$	−10558.5	−	25490.5i	−0.0555431	−	0.134093i
$437$	−163117.	+	67565.4i	−0.854156	+	0.353803i
$438$	−18422.8	−	7630.97i	−0.0960301	−	0.0397770i
$439$	43904.2	−	105994.i	0.227812	−	0.549987i	−0.768098	−	0.640332i	$-0.778797\pi$
$439$	43904.2	−	105994.i	0.227812	−	0.549987i	0.995911	+	0.0903447i	$0.0287969\pi$
$440$	28796.1	−	69519.9i	0.148740	−	0.359090i
$441$			106715.i			0.548719i
$442$	9235.32	−	9235.32i	0.0472724	−	0.0472724i
$443$	−217886.	+	217886.i	−1.11025	+	1.11025i	−0.117136	+	0.993116i	$0.537371\pi$
$443$	−217886.	+	217886.i	−1.11025	+	1.11025i	−0.993116	+	0.117136i	$0.962629\pi$
$444$	11583.9	+	4798.19i	0.0587607	+	0.0243395i
$445$	347993.	−	144143.i	1.75732	−	0.727905i
$446$	53724.3	−	53724.3i	0.270085	−	0.270085i
$447$	−29725.6			−0.148770
$448$	−15371.2	−	6366.95i	−0.0765864	−	0.0317231i
$449$	−72111.9	−	72111.9i	−0.357696	−	0.357696i	0.505267	−	0.862963i	$-0.331394\pi$
$449$	−72111.9	−	72111.9i	−0.357696	−	0.357696i	−0.862963	+	0.505267i	$0.831394\pi$
$450$		−	68514.3i		−	0.338342i
$451$	172773.	−	61158.9i	0.849422	−	0.300682i
$452$	−42485.8			−0.207954
$453$	−5578.44	+	5578.44i	−0.0271842	+	0.0271842i
$454$	5227.92	−	12621.3i	0.0253640	−	0.0612340i
$455$			28804.5i			0.139135i
$456$	10044.5	+	10044.5i	0.0483058	+	0.0483058i
$457$	46012.0	+	111083.i	0.220312	+	0.531881i	0.994932	−	0.100546i	$-0.0320589\pi$
$457$	46012.0	+	111083.i	0.220312	+	0.531881i	−0.774620	+	0.632427i	$0.782059\pi$
$458$	−85104.0	+	205459.i	−0.405713	+	0.979478i
$459$	23213.6	+	23213.6i	0.110184	+	0.110184i
$460$	−62529.2	−	62529.2i	−0.295507	−	0.295507i
$461$	−110184.			−0.518459			−0.259230	−	0.965816i	$-0.583469\pi$
$461$	−110184.			−0.518459			−0.259230	+	0.965816i	$0.583469\pi$
$462$	−11930.1	−	4941.61i	−0.0558934	−	0.0231518i
$463$	−273415.	−	113252.i	−1.27544	−	0.528306i	−0.360828	−	0.932632i	$-0.617506\pi$
$463$	−273415.	−	113252.i	−1.27544	−	0.528306i	−0.914615	+	0.404327i	$0.867506\pi$
$464$	12.9891	−	31.3586i	6.03316e−5	−	0.000145653i
$465$	−12608.3	−	30439.0i	−0.0583108	−	0.140775i
$466$	−20428.3	+	8461.69i	−0.0940721	+	0.0389659i
$467$	234667.			1.07602			0.538008	−	0.842940i	$-0.319177\pi$
$467$	234667.			1.07602			0.538008	+	0.842940i	$0.319177\pi$
$468$	7058.98	+	17041.9i	0.0322293	+	0.0778083i
$469$	140226.			0.637506
$470$	−37457.4	−	90430.1i	−0.169567	−	0.409371i
$471$	26066.6	−	26066.6i	0.117501	−	0.117501i
$472$	65210.3	+	65210.3i	0.292706	+	0.292706i
$473$	34168.7	−	14153.1i	0.152724	−	0.0632602i
$474$		−	30825.1i		−	0.137198i
$475$	−137421.	+	56921.7i	−0.609068	+	0.252284i
$476$			41305.8i			0.182304i
$477$	64034.9	+	154594.i	0.281436	+	0.679447i
$478$	−152649.	+	63229.4i	−0.668096	+	0.276735i
$479$	86520.6	+	35838.0i	0.377093	+	0.156197i	0.563176	−	0.826337i	$-0.309579\pi$
$479$	86520.6	+	35838.0i	0.377093	+	0.156197i	−0.186083	+	0.982534i	$0.559579\pi$
$480$	−2722.68	+	6573.14i	−0.0118172	+	0.0285292i
$481$	13526.7	−	32656.4i	0.0584659	−	0.141149i
$482$			166108.i			0.714986i
$483$	−10730.5	+	10730.5i	−0.0459964	+	0.0459964i
$484$	−15576.5	+	15576.5i	−0.0664935	+	0.0664935i
$485$	333470.	+	138128.i	1.41767	+	0.587216i
$486$	−64475.7	+	26706.7i	−0.272975	+	0.113070i
$487$	−24390.6	+	24390.6i	−0.102841	+	0.102841i	−0.756655	−	0.653814i	$-0.773168\pi$
$487$	−24390.6	+	24390.6i	−0.102841	+	0.102841i	0.653814	+	0.756655i	$0.273168\pi$
$488$	−88757.0			−0.372703
$489$	−6533.38	−	2706.21i	−0.0273225	−	0.0113173i
$490$	82050.7	+	82050.7i	0.341736	+	0.341736i
$491$		−	364531.i		−	1.51207i	−0.654531	−	0.756035i	$-0.727134\pi$
$491$		−	364531.i		−	1.51207i	0.654531	−	0.756035i	$-0.272866\pi$
$492$	−16335.8	+	5782.61i	−0.0674855	+	0.0238887i
$493$	−84.2675			−0.000346710
$494$	28316.8	−	28316.8i	0.116035	−	0.116035i
$495$	100969.	−	243761.i	0.412076	−	0.994840i
$496$		−	53649.2i		−	0.218072i
$497$	−68211.4	−	68211.4i	−0.276149	−	0.276149i
$498$	14600.2	+	35247.9i	0.0588706	+	0.142126i
$499$	−97664.3	+	235782.i	−0.392224	+	0.946914i	0.597230	+	0.802070i	$0.296268\pi$
$499$	−97664.3	+	235782.i	−0.392224	+	0.946914i	−0.989455	+	0.144844i	$0.953732\pi$
$500$	55158.6	+	55158.6i	0.220635	+	0.220635i
$501$	−43831.1	−	43831.1i	−0.174625	−	0.174625i
$502$	185907.			0.737715
$503$	−379793.	−	157316.i	−1.50111	−	0.621779i	−0.527406	−	0.849613i	$-0.676835\pi$
$503$	−379793.	−	157316.i	−1.50111	−	0.621779i	−0.973700	+	0.227835i	$0.926835\pi$
$504$	−53896.7	−	22324.7i	−0.212178	−	0.0878871i
$505$	−9495.74	+	22924.7i	−0.0372346	+	0.0898922i
$506$	−42768.3	−	103252.i	−0.167040	−	0.403271i
$507$	32996.7	−	13667.7i	0.128367	−	0.0531714i
$508$	115070.			0.445896
$509$	−70331.0	−	169794.i	−0.271463	−	0.655371i	0.728083	−	0.685489i	$-0.240412\pi$
$509$	−70331.0	−	169794.i	−0.271463	−	0.655371i	−0.999546	+	0.0301184i	$0.990412\pi$
$510$	17663.5			0.0679104
$511$	−68036.1	−	164254.i	−0.260554	−	0.629033i
$512$	−8192.00	+	8192.00i	−0.0312500	+	0.0312500i
$513$	71176.2	+	71176.2i	0.270458	+	0.270458i
$514$	188359.	−	78020.8i	0.712951	−	0.295314i
$515$		−	31070.1i		−	0.117146i
$516$	−3230.66	+	1338.18i	−0.0121337	+	0.00502593i
$517$		−	123703.i		−	0.462808i
$518$	42779.6	+	103279.i	0.159433	+	0.384904i
$519$	39912.7	−	16532.4i	0.148175	−	0.0613762i
$520$	18530.5	+	7675.60i	0.0685301	+	0.0283861i
$521$	−191393.	+	462063.i	−0.705098	+	1.70226i	0.00680166	+	0.999977i	$0.497835\pi$
$521$	−191393.	+	462063.i	−0.705098	+	1.70226i	−0.711900	+	0.702281i	$0.752165\pi$
$522$	45.5444	−	109.954i	0.000167145	−	0.000403524i
$523$		−	146294.i		−	0.534837i	−0.963580	−	0.267419i	$-0.913829\pi$
$523$		−	146294.i		−	0.534837i	0.963580	−	0.267419i	$-0.0861707\pi$
$524$	84507.4	−	84507.4i	0.307774	−	0.307774i
$525$	−9040.06	+	9040.06i	−0.0327984	+	0.0327984i
$526$	218970.	+	90700.4i	0.791432	+	0.327822i
$527$	−123055.	+	50970.8i	−0.443074	+	0.183527i
$528$	−6358.09	+	6358.09i	−0.0228065	+	0.0228065i
$529$	148504.			0.530673
$530$	168098.	+	69628.5i	0.598426	+	0.247876i
$531$	228650.	+	228650.i	0.810927	+	0.810927i
$532$			126649.i			0.447487i
$533$	16301.9	+	46052.7i	0.0573831	+	0.162107i
$534$	−45009.4			−0.157841
$535$	−393053.	+	393053.i	−1.37323	+	1.37323i
$536$	37366.5	−	90210.7i	0.130063	−	0.313999i
$537$		−	52864.1i		−	0.183321i
$538$	−66462.3	−	66462.3i	−0.229621	−	0.229621i
$539$	56120.5	+	135487.i	0.193172	+	0.466358i
$540$	−19293.1	+	46577.7i	−0.0661630	+	0.159732i
$541$	−173892.	−	173892.i	−0.594137	−	0.594137i	0.344610	−	0.938746i	$-0.388011\pi$
$541$	−173892.	−	173892.i	−0.594137	−	0.594137i	−0.938746	+	0.344610i	$0.888011\pi$
$542$	239664.	+	239664.i	0.815838	+	0.815838i
$543$	40210.9			0.136378
$544$	26572.9	+	11006.9i	0.0897928	+	0.0371934i
$545$	−97185.9	−	40255.7i	−0.327198	−	0.135530i
$546$	1317.19	−	3179.97i	0.00441837	−	0.0106669i
$547$	128833.	+	311029.i	0.430577	+	1.03951i	0.979102	+	0.203371i	$0.0651897\pi$
$547$	128833.	+	311029.i	0.430577	+	1.03951i	−0.548525	+	0.836134i	$0.684810\pi$
$548$	−194817.	+	80695.7i	−0.648732	+	0.268714i
$549$	−311213.			−1.03255
$550$	−36030.9	−	86986.3i	−0.119110	−	0.287558i
$551$	−258.376			−0.000851038
$552$	4043.76	+	9762.50i	0.0132711	+	0.0320393i
$553$	194334.	−	194334.i	0.635476	−	0.635476i
$554$	282145.	+	282145.i	0.919289	+	0.919289i
$555$	44165.0	−	18293.7i	0.143381	−	0.0593904i
$556$		−	32219.3i		−	0.104224i
$557$	−43355.5	+	17958.4i	−0.139744	+	0.0578840i	−0.451460	−	0.892292i	$-0.649096\pi$
$557$	−43355.5	+	17958.4i	−0.139744	+	0.0578840i	0.311715	+	0.950176i	$0.399096\pi$
$558$		−	188112.i		−	0.604156i
$559$	3772.52	+	9107.66i	0.0120728	+	0.0291463i
$560$	−58604.7	+	24274.8i	−0.186877	+	0.0774070i
$561$	20624.2	+	8542.81i	0.0655316	+	0.0271441i
$562$	1993.15	−	4811.89i	0.00631055	−	0.0152350i
$563$	−151034.	+	364628.i	−0.476493	+	1.15036i	0.484749	+	0.874653i	$0.338911\pi$
$563$	−151034.	+	364628.i	−0.476493	+	1.15036i	−0.961243	+	0.275704i	$0.911089\pi$
$564$			11696.2i			0.0367695i
$565$	−114539.	+	114539.i	−0.358804	+	0.358804i
$566$	−19375.1	+	19375.1i	−0.0604800	+	0.0604800i
$567$	−184942.	−	76605.6i	−0.575268	−	0.238284i
$568$	−62058.4	+	25705.4i	−0.192355	+	0.0796761i
$569$	293696.	−	293696.i	0.907139	−	0.907139i	−0.0889015	−	0.996040i	$-0.528336\pi$
$569$	293696.	−	293696.i	0.907139	−	0.907139i	0.996040	+	0.0889015i	$0.0283356\pi$
$570$	54158.8			0.166694
$571$	509235.	+	210932.i	1.56187	+	0.646949i	0.985414	−	0.170176i	$-0.0544335\pi$
$571$	509235.	+	210932.i	1.56187	+	0.646949i	0.576460	+	0.817125i	$0.304433\pi$
$572$	17924.3	+	17924.3i	0.0547835	+	0.0547835i
$573$		−	37808.7i		−	0.115155i
$574$	−139443.	−	66531.7i	−0.423228	−	0.201932i
$575$	−110647.			−0.334660
$576$	−28724.0	+	28724.0i	−0.0865764	+	0.0865764i
$577$	188504.	−	455090.i	0.566200	−	1.36693i	−0.338536	−	0.940954i	$-0.609932\pi$
$577$	188504.	−	455090.i	0.566200	−	1.36693i	0.904735	−	0.425974i	$-0.140068\pi$
$578$			164826.i			0.493366i
$579$	14252.9	+	14252.9i	0.0425155	+	0.0425155i
$580$	−49.5228	−	119.559i	−0.000147214	−	0.000355406i
$581$	−130172.	+	314263.i	−0.385625	+	0.930980i
$582$	−30498.3	−	30498.3i	−0.0900387	−	0.0900387i
$583$	162598.	+	162598.i	0.478387	+	0.478387i
$584$	−123798.			−0.362984
$585$	64974.4	+	26913.3i	0.189859	+	0.0786421i
$586$	198018.	+	82021.7i	0.576646	+	0.238854i
$587$	−31429.9	+	75878.5i	−0.0912151	+	0.220213i	−0.962902	−	0.269850i	$-0.913026\pi$
$587$	−31429.9	+	75878.5i	−0.0912151	+	0.220213i	0.871687	+	0.490062i	$0.163026\pi$
$588$	−5306.22	−	12810.3i	−0.0153472	−	0.0370515i
$589$	−377303.	+	156284.i	−1.08757	+	0.450488i
$590$	351606.			1.01007
$591$	30641.3	+	73974.7i	0.0877269	+	0.211791i
$592$	77841.3			0.222109
$593$	−177146.	−	427669.i	−0.503759	−	1.21618i	−0.947422	−	0.319988i	$-0.896321\pi$
$593$	−177146.	−	427669.i	−0.503759	−	1.21618i	0.443662	−	0.896194i	$-0.353679\pi$
$594$	−45053.9	+	45053.9i	−0.127691	+	0.127691i
$595$	111358.	+	111358.i	0.314548	+	0.314548i
$596$	−170498.	+	70622.5i	−0.479984	+	0.198816i
$597$		−	46345.2i		−	0.130034i
$598$	27521.8	−	11399.9i	0.0769616	−	0.0318785i
$599$		−	189056.i		−	0.526910i	−0.964672	−	0.263455i	$-0.915138\pi$
$599$		−	189056.i		−	0.526910i	0.964672	−	0.263455i	$-0.0848620\pi$
$600$	3406.74	+	8224.60i	0.00946317	+	0.0228461i
$601$	−327801.	+	135780.i	−0.907531	+	0.375912i	−0.787111	−	0.616811i	$-0.788424\pi$
$601$	−327801.	+	135780.i	−0.907531	+	0.375912i	−0.120420	+	0.992723i	$0.538424\pi$
$602$	−28803.9	−	11931.0i	−0.0794801	−	0.0329217i
$603$	131020.	−	316310.i	0.360332	−	0.869918i
$604$	−18743.0	+	45249.7i	−0.0513767	+	0.124034i
$605$			83986.5i			0.229456i
$606$	2096.63	−	2096.63i	0.00570922	−	0.00570922i
$607$	172351.	−	172351.i	0.467773	−	0.467773i	−0.433419	−	0.901192i	$-0.642693\pi$
$607$	172351.	−	172351.i	0.467773	−	0.467773i	0.901192	+	0.433419i	$0.142693\pi$
$608$	81476.4	+	33748.6i	0.220407	+	0.0912954i
$609$	−20.5171	+	8.49847i	−5.53199e−5	+	2.29143e-5i
$610$	−239283.	+	239283.i	−0.643062	+	0.643062i
$611$	32973.2			0.0883239
$612$	93173.8	+	38593.9i	0.248766	+	0.103042i
$613$	−20214.3	−	20214.3i	−0.0537944	−	0.0537944i	0.679698	−	0.733492i	$-0.262111\pi$
$613$	−20214.3	−	20214.3i	−0.0537944	−	0.0537944i	−0.733492	+	0.679698i	$0.762111\pi$
$614$		−	173685.i		−	0.460708i
$615$	−28450.7	+	59629.8i	−0.0752218	+	0.157657i
$616$	−80168.0			−0.211271
$617$	−464006.	+	464006.i	−1.21886	+	1.21886i	−0.250828	+	0.968032i	$0.580703\pi$
$617$	−464006.	+	464006.i	−1.21886	+	1.21886i	−0.968032	+	0.250828i	$0.919297\pi$
$618$	−1420.79	+	3430.09i	−0.00372008	+	0.00898107i
$619$		−	186001.i		−	0.485438i	−0.970097	−	0.242719i	$-0.921961\pi$
$619$		−	186001.i		−	0.485438i	0.970097	−	0.242719i	$-0.0780393\pi$
$620$	−144635.	−	144635.i	−0.376261	−	0.376261i
$621$	28654.4	+	69177.8i	0.0743033	+	0.179384i
$622$	−46255.6	+	111671.i	−0.119559	+	0.288642i
$623$	−283758.	−	283758.i	−0.731091	−	0.731091i
$624$	−1694.75	−	1694.75i	−0.00435248	−	0.00435248i
$625$	488230.			1.24987
$626$	−243347.	−	100798.i	−0.620979	−	0.257218i
$627$	63236.6	+	26193.5i	0.160855	+	0.0666281i
$628$	87581.4	−	211440.i	0.222071	−	0.536128i
$629$	−73955.2	−	178544.i	−0.186925	−	0.451277i
$630$	−205488.	+	85116.0i	−0.517733	+	0.214452i
$631$	−624104.			−1.56747			−0.783733	−	0.621097i	$-0.786687\pi$
$631$	−624104.			−1.56747			−0.783733	+	0.621097i	$0.786687\pi$
$632$	−73234.7	−	176804.i	−0.183351	−	0.442648i
$633$	−33330.5			−0.0831830
$634$	−85075.4	−	205390.i	−0.211653	−	0.510977i
$635$	310221.	−	310221.i	0.769349	−	0.769349i
$636$	−15373.8	−	15373.8i	−0.0380072	−	0.0380072i
$637$	−36114.0	+	14958.9i	−0.0890014	+	0.0368656i
$638$		−	163.550i		−	0.000401799i
$639$	−217598.	+	90132.0i	−0.532909	+	0.220738i
$640$			44170.2i			0.107837i
$641$	−188323.	−	454653.i	−0.458341	−	1.10653i	−0.969069	−	0.246790i	$-0.920624\pi$
$641$	−188323.	−	454653.i	−0.458341	−	1.10653i	0.510728	−	0.859742i	$-0.329376\pi$
$642$	61366.2	−	25418.7i	0.148888	−	0.0616713i
$643$	596151.	+	246934.i	1.44190	+	0.597254i	0.960258	−	0.279116i	$-0.0900413\pi$
$643$	596151.	+	246934.i	1.44190	+	0.597254i	0.481640	+	0.876369i	$0.340041\pi$
$644$	−36053.3	+	87040.4i	−0.0869307	+	0.209869i
$645$	−5102.00	+	12317.3i	−0.0122637	+	0.0296072i
$646$		−	218945.i		−	0.524651i
$647$	409185.	−	409185.i	0.977487	−	0.977487i	−0.0222652	−	0.999752i	$-0.507088\pi$
$647$	409185.	−	409185.i	0.977487	−	0.977487i	0.999752	+	0.0222652i	$0.00708782\pi$
$648$	−98564.1	+	98564.1i	−0.234730	+	0.234730i
$649$	410540.	+	170051.i	0.974690	+	0.403730i
$650$	23186.2	−	9604.04i	0.0548786	−	0.0227315i
$651$	−24820.3	+	24820.3i	−0.0585660	+	0.0585660i
$652$	−43903.0			−0.103276
$653$	−197035.	−	81614.7i	−0.462081	−	0.191400i	0.139484	−	0.990224i	$-0.455456\pi$
$653$	−197035.	−	81614.7i	−0.462081	−	0.191400i	−0.601564	+	0.798824i	$0.705456\pi$
$654$	8888.35	+	8888.35i	0.0207810	+	0.0207810i
$655$		−	455653.i		−	1.06207i
$656$	−79959.1	+	71978.2i	−0.185806	+	0.167260i
$657$	−434077.			−1.00563
$658$	−73737.8	+	73737.8i	−0.170309	+	0.170309i
$659$	263649.	−	636505.i	0.607093	−	1.46565i	−0.259054	−	0.965863i	$-0.583411\pi$
$659$	263649.	−	636505.i	0.607093	−	1.46565i	0.866147	−	0.499790i	$-0.166589\pi$
$660$			34282.0i			0.0787007i
$661$	367749.	+	367749.i	0.841684	+	0.841684i	0.989078	−	0.147394i	$-0.0470885\pi$
$661$	367749.	+	367749.i	0.841684	+	0.841684i	−0.147394	+	0.989078i	$0.547089\pi$
$662$	−195785.	−	472668.i	−0.446750	−	1.07855i
$663$	−2277.09	+	5497.37i	−0.00518027	+	0.0125063i
$664$	167485.	+	167485.i	0.379873	+	0.379873i
$665$	341439.	+	341439.i	0.772093	+	0.772093i
$666$	272938.			0.615341
$667$	−177.570	−	73.5519i	−0.000399133	−	0.000165326i
$668$	−355537.	−	147268.i	−0.796768	−	0.330032i
$669$	−13246.4	+	31979.6i	−0.0295969	+	0.0714532i
$670$	−142465.	−	343940.i	−0.317364	−	0.766184i
$671$	−395118.	+	163663.i	−0.877571	+	0.363502i
$672$	7579.92			0.0167852
$673$	96881.7	+	233893.i	0.213900	+	0.516401i	0.994016	−	0.109234i	$-0.0348398\pi$
$673$	96881.7	+	233893.i	0.213900	+	0.516401i	−0.780116	+	0.625635i	$0.784840\pi$
$674$	440608.			0.969913
$675$	24140.4	+	58280.1i	0.0529830	+	0.127912i
$676$	156788.	−	156788.i	0.343098	−	0.343098i
$677$	501624.	+	501624.i	1.09446	+	1.09446i	0.995046	+	0.0994157i	$0.0316974\pi$
$677$	501624.	+	501624.i	1.09446	+	1.09446i	0.0994157	+	0.995046i	$0.468303\pi$
$678$	17882.7	−	7407.24i	0.0389021	−	0.0161138i
$679$		−	384547.i		−	0.834084i
$680$	101313.	−	41965.1i	0.219102	−	0.0907550i
$681$			6223.89i			0.0134205i
$682$	−98926.3	−	238829.i	−0.212688	−	0.513474i
$683$	611184.	−	253161.i	1.31018	−	0.542694i	0.385242	−	0.922816i	$-0.374118\pi$
$683$	611184.	−	253161.i	1.31018	−	0.542694i	0.924936	+	0.380122i	$0.124118\pi$
$684$	285684.	+	118334.i	0.610624	+	0.252929i
$685$	−307663.	+	742764.i	−0.655683	+	1.58296i
$686$	131759.	−	318094.i	0.279983	−	0.675939i
$687$		−	101317.i		−	0.214669i
$688$	−15350.9	+	15350.9i	−0.0324307	+	0.0324307i
$689$	−43340.6	+	43340.6i	−0.0912970	+	0.0912970i
$690$	37220.8	+	15417.4i	0.0781786	+	0.0323826i
$691$	371930.	−	154058.i	0.778942	−	0.322648i	0.0424534	−	0.999098i	$-0.486483\pi$
$691$	371930.	−	154058.i	0.778942	−	0.322648i	0.736488	+	0.676450i	$0.236483\pi$
$692$	189650.	−	189650.i	0.396041	−	0.396041i
$693$	−281097.			−0.585315
$694$	−25848.1	−	10706.6i	−0.0536672	−	0.0222297i
$695$	−86861.3	−	86861.3i	−0.179828	−	0.179828i
$696$			15.4637i			3.19224e-5i
$697$	241063.	+	115017.i	0.496209	+	0.236753i
$698$	−499114.			−1.02445
$699$	7123.20	−	7123.20i	0.0145788	−	0.0145788i
$700$	−30373.7	+	73328.7i	−0.0619872	+	0.149650i
$701$		−	337213.i		−	0.686228i	−0.939294	−	0.343114i	$-0.888518\pi$
$701$		−	337213.i		−	0.686228i	0.939294	−	0.343114i	$-0.111482\pi$
$702$	−12009.1	−	12009.1i	−0.0243690	−	0.0243690i
$703$	−226757.	−	547440.i	−0.458828	−	1.10771i
$704$	−21362.6	+	51573.8i	−0.0431031	+	0.104060i
$705$	31532.3	+	31532.3i	0.0634420	+	0.0634420i
$706$	84900.4	+	84900.4i	0.170334	+	0.170334i
$707$	26436.1			0.0528881
$708$	−38816.8	−	16078.4i	−0.0774378	−	0.0320758i
$709$	−482181.	−	199726.i	−0.959219	−	0.397321i	−0.152531	−	0.988299i	$-0.548742\pi$
$709$	−482181.	−	199726.i	−0.959219	−	0.397321i	−0.806688	+	0.590977i	$0.798742\pi$
$710$	−98005.2	+	236606.i	−0.194416	+	0.469362i
$711$	−256786.	−	619936.i	−0.507963	−	1.22633i
$712$	−258161.	+	106934.i	−0.509250	+	0.210938i
$713$	−303792.			−0.597582
$714$	−7201.51	−	17386.0i	−0.0141263	−	0.0341038i
$715$	96645.5			0.189047
$716$	−125595.	−	303214.i	−0.244989	−	0.591457i
$717$	53227.6	−	53227.6i	0.103538	−	0.103538i
$718$	−105815.	−	105815.i	−0.205257	−	0.205257i
$719$	154606.	−	64040.1i	0.299068	−	0.123878i	−0.228104	−	0.973637i	$-0.573253\pi$
$719$	154606.	−	64040.1i	0.299068	−	0.123878i	0.527172	+	0.849759i	$0.323253\pi$
$720$			154876.i			0.298758i
$721$	−30581.9	+	12667.4i	−0.0588294	+	0.0243679i
$722$		−	302713.i		−	0.580707i
$723$	−28960.4	−	69916.5i	−0.0554022	−	0.133753i
$724$	230638.	−	95533.6i	0.440002	−	0.182255i
$725$	−149.597	−	61.9651i	−0.000284608	−	0.000117888i
$726$	3840.58	−	9271.99i	0.00728658	−	0.0175914i
$727$	−335302.	+	809491.i	−0.634406	+	1.53159i	0.199623	+	0.979873i	$0.436028\pi$
$727$	−335302.	+	809491.i	−0.634406	+	1.53159i	−0.834030	+	0.551720i	$0.813972\pi$
$728$		−	21368.8i		−	0.0403197i
$729$	−330351.	+	330351.i	−0.621613	+	0.621613i
$730$	−333751.	+	333751.i	−0.626292	+	0.626292i
$731$	49794.7	+	20625.6i	0.0931855	+	0.0385987i
$732$	37358.6	−	15474.4i	0.0697218	−	0.0288797i
$733$	94568.9	−	94568.9i	0.176011	−	0.176011i	−0.613603	−	0.789614i	$-0.710281\pi$
$733$	94568.9	−	94568.9i	0.176011	−	0.176011i	0.789614	+	0.613603i	$0.210281\pi$
$734$	−544374.			−1.01043
$735$	−48841.1	−	20230.7i	−0.0904088	−	0.0374486i
$736$	46387.7	+	46387.7i	0.0856343	+	0.0856343i
$737$		−	470492.i		−	0.866198i
$738$	−280364.	+	252380.i	−0.514766	+	0.463386i
$739$	−23816.4			−0.0436100			−0.0218050	−	0.999762i	$-0.506941\pi$
$739$	−23816.4			−0.0436100			−0.0218050	+	0.999762i	$0.506941\pi$
$740$	209855.	−	209855.i	0.383227	−	0.383227i
$741$	−6981.86	+	16855.7i	−0.0127155	+	0.0306980i
$742$		−	193845.i		−	0.352084i
$743$	711291.	+	711291.i	1.28846	+	1.28846i	0.935724	+	0.352732i	$0.114747\pi$
$743$	711291.	+	711291.i	1.28846	+	1.28846i	0.352732	+	0.935724i	$0.385253\pi$
$744$	9353.53	+	22581.4i	0.0168978	+	0.0407948i
$745$	−269258.	+	650045.i	−0.485127	+	1.17120i
$746$	345139.	+	345139.i	0.620178	+	0.620178i
$747$	587259.	+	587259.i	1.05242	+	1.05242i
$748$	138590.			0.247702
$749$	547127.	+	226628.i	0.975270	+	0.403970i
$750$	−32833.5	−	13600.1i	−0.0583706	−	0.0241779i
$751$	29806.4	−	71959.1i	0.0528482	−	0.127587i	−0.895250	−	0.445563i	$-0.853003\pi$
$751$	29806.4	−	71959.1i	0.0528482	−	0.127587i	0.948099	+	0.317977i	$0.103003\pi$
$752$	27788.0	+	67086.2i	0.0491385	+	0.118631i
$753$	−78249.9	+	32412.2i	−0.138005	+	0.0571634i
$754$	43.5942			7.66807e−5
$755$	71460.3	+	172520.i	0.125363	+	0.302654i
$756$	53711.9			0.0939781
$757$	140842.	+	340023.i	0.245777	+	0.593358i	0.997837	−	0.0657363i	$-0.0209396\pi$
$757$	140842.	+	340023.i	0.245777	+	0.593358i	−0.752060	+	0.659095i	$0.770940\pi$
$758$	−434061.	+	434061.i	−0.755462	+	0.755462i
$759$	36003.1	+	36003.1i	0.0624966	+	0.0624966i
$760$	310639.	−	128671.i	0.537810	−	0.222768i
$761$			722130.i			1.24694i	0.781847	+	0.623471i	$0.214278\pi$
$761$			722130.i			1.24694i	−0.781847	+	0.623471i	$0.785722\pi$
$762$	−48433.9	+	20062.0i	−0.0834140	+	0.0345512i
$763$			112072.i			0.192507i
$764$	−89826.3	−	216860.i	−0.153892	−	0.371529i
$765$	355237.	−	147144.i	0.607010	−	0.251432i
$766$	126090.	+	52228.2i	0.214894	+	0.0890118i
$767$	−45327.2	+	109429.i	−0.0770492	+	0.186013i
$768$	2019.84	−	4876.33i	0.00342448	−	0.00826743i
$769$			943264.i			1.59507i	0.603270	+	0.797537i	$0.293864\pi$
$769$			943264.i			1.59507i	−0.603270	+	0.797537i	$0.706136\pi$
$770$	−216128.	+	216128.i	−0.364527	+	0.364527i
$771$	−65679.3	+	65679.3i	−0.110489	+	0.110489i
$772$	115613.	+	47888.5i	0.193987	+	0.0803519i
$773$	358552.	−	148517.i	0.600058	−	0.248552i	−0.0619132	−	0.998082i	$-0.519720\pi$
$773$	358552.	−	148517.i	0.600058	−	0.248552i	0.661971	+	0.749529i	$0.269720\pi$
$774$	−53825.5	+	53825.5i	−0.0898476	+	0.0898476i
$775$	−255935.			−0.426114
$776$	−247387.	−	102471.i	−0.410822	−	0.170168i
$777$	−36012.6	−	36012.6i	−0.0596503	−	0.0596503i
$778$			522897.i			0.863887i
$779$	739133.	+	352657.i	1.21800	+	0.581136i
$780$	−9137.88			−0.0150195
$781$	−228865.	+	228865.i	−0.375212	+	0.375212i
$782$	62327.1	−	150471.i	0.101921	−	0.246059i
$783$			109.577i			0.000178729i
$784$	−60869.9	−	60869.9i	−0.0990309	−	0.0990309i
$785$	−333916.	−	806144.i	−0.541873	−	1.30820i
$786$	−20836.4	+	50303.5i	−0.0337270	+	0.0814241i
$787$	−649956.	−	649956.i	−1.04938	−	1.04938i	−0.998716	−	0.0506688i	$-0.983865\pi$
$787$	−649956.	−	649956.i	−1.04938	−	1.04938i	−0.0506688	−	0.998716i	$-0.516135\pi$
$788$	351500.	+	351500.i	0.566074	+	0.566074i
$789$	−107980.			−0.173456
$790$	−674089.	−	279217.i	−1.08010	−	0.447391i
$791$	159438.	+	66041.3i	0.254823	+	0.105551i
$792$	−74904.6	+	180836.i	−0.119415	+	0.288293i
$793$	−43624.5	−	105319.i	−0.0693719	−	0.167479i
$794$	−200678.	+	83123.7i	−0.318317	+	0.131851i
$795$	−82893.4			−0.131155
$796$	−110108.	−	265823.i	−0.173776	−	0.419533i
$797$	1.09925e6			1.73054			0.865268	−	0.501309i	$-0.167148\pi$
$797$	1.09925e6			1.73054			0.865268	+	0.501309i	$0.167148\pi$
$798$	−22080.8	−	53307.9i	−0.0346745	−	0.0837116i
$799$	127474.	−	127474.i	0.199677	−	0.199677i
$800$	39080.2	+	39080.2i	0.0610628	+	0.0610628i
$801$	−905201.	+	374947.i	−1.41085	+	0.584392i
$802$		−	423696.i		−	0.658728i
$803$	−551109.	+	228277.i	−0.854685	+	0.354022i
$804$			44485.2i			0.0688182i
$805$	137458.	+	331853.i	0.212118	+	0.512099i
$806$	63659.9	−	26368.8i	0.0979932	−	0.0405901i
$807$	39562.0	+	16387.1i	0.0607479	+	0.0251626i
$808$	7044.48	−	17006.9i	0.0107901	−	0.0260497i
$809$	211326.	−	510185.i	0.322891	−	0.779527i	−0.676193	−	0.736725i	$-0.736371\pi$
$809$	211326.	−	510185.i	0.322891	−	0.779527i	0.999084	−	0.0428023i	$-0.0136286\pi$
$810$			531445.i			0.810007i
$811$	9353.61	−	9353.61i	0.0142212	−	0.0142212i	−0.699960	−	0.714182i	$-0.746799\pi$
$811$	9353.61	−	9353.61i	0.0142212	−	0.0142212i	0.714182	+	0.699960i	$0.246799\pi$
$812$	−97.4896	+	97.4896i	−0.000147858	+	0.000147858i
$813$	−142661.	−	59092.2i	−0.215836	−	0.0894023i
$814$	346525.	−	143535.i	0.522981	−	0.216626i
$815$	−118360.	+	118360.i	−0.178192	+	0.178192i
$816$	−13103.8			−0.0196796
$817$	152678.	+	63241.1i	0.228734	+	0.0947448i
$818$	336816.	+	336816.i	0.503369	+	0.503369i
$819$		−	74926.3i		−	0.111703i
$820$	−21516.2	+	409613.i	−0.0319991	+	0.609181i
$821$	−511811.			−0.759318			−0.379659	−	0.925127i	$-0.623959\pi$
$821$	−511811.			−0.759318			−0.379659	+	0.925127i	$0.623959\pi$
$822$	67931.1	−	67931.1i	0.100537	−	0.100537i
$823$	367829.	−	888018.i	0.543058	−	1.31106i	−0.379496	−	0.925193i	$-0.623903\pi$
$823$	367829.	−	888018.i	0.543058	−	1.31106i	0.922555	−	0.385866i	$-0.126097\pi$
$824$			23049.5i			0.0339475i
$825$	30331.5	+	30331.5i	0.0445641	+	0.0445641i
$826$	−143352.	−	346082.i	−0.210108	−	0.507246i
$827$	−235340.	+	568161.i	−0.344100	+	0.830731i	0.653192	+	0.757192i	$0.273429\pi$
$827$	−235340.	+	568161.i	−0.344100	+	0.830731i	−0.997292	+	0.0735389i	$0.976571\pi$
$828$	162651.	+	162651.i	0.237245	+	0.237245i
$829$	−473680.	−	473680.i	−0.689248	−	0.689248i	0.272818	−	0.962066i	$-0.412044\pi$
$829$	−473680.	−	473680.i	−0.689248	−	0.689248i	−0.962066	+	0.272818i	$0.912044\pi$
$830$	903056.			1.31087
$831$	−167948.	−	69566.3i	−0.243205	−	0.100739i
$832$	−13747.0	−	5694.20i	−0.0198592	−	0.00822594i
$833$	−81785.5	+	197448.i	−0.117865	+	0.284552i
$834$	5617.32	+	13561.4i	0.00807601	+	0.0194972i
$835$	−1.35553e6	+	561479.i	−1.94418	+	0.805306i
$836$	424938.			0.608013
$837$	66279.8	+	160014.i	0.0946085	+	0.228405i
$838$	−240678.			−0.342727
$839$	17283.6	+	41726.2i	0.0245533	+	0.0592769i	0.935681	−	0.352848i	$-0.114787\pi$
$839$	17283.6	+	41726.2i	0.0245533	+	0.0592769i	−0.911127	+	0.412125i	$0.864787\pi$
$840$	20435.0	−	20435.0i	0.0289612	−	0.0289612i
$841$	500123.	+	500123.i	0.707106	+	0.707106i
$842$	844599.	−	349844.i	1.19131	−	0.493459i
$843$			2372.86i			0.00333901i
$844$	−191174.	+	79187.0i	−0.268377	+	0.111165i
$845$		−	845380.i		−	1.18396i
$846$	97434.3	+	235227.i	0.136135	+	0.328660i
$847$	82667.0	−	34241.8i	0.115230	−	0.0477298i
$848$	−124705.	−	51654.4i	−0.173417	−	0.0718316i
$849$	4777.19	−	11533.2i	0.00662761	−	0.0160005i
$850$	52508.6	−	126767.i	0.0726762	−	0.175456i
$851$		−	440781.i		−	0.608645i
$852$	21639.3	−	21639.3i	0.0298101	−	0.0298101i
$853$	−253725.	+	253725.i	−0.348710	+	0.348710i	−0.859629	−	0.510919i	$-0.829305\pi$
$853$	−253725.	+	253725.i	−0.348710	+	0.348710i	0.510919	+	0.859629i	$0.329305\pi$
$854$	333081.	+	137967.i	0.456704	+	0.189173i
$855$	1.08921e6	−	451165.i	1.48997	−	0.617167i
$856$	291589.	−	291589.i	0.397945	−	0.397945i
$857$	−576857.			−0.785429			−0.392714	−	0.919661i	$-0.628464\pi$
$857$	−576857.			−0.785429			−0.392714	+	0.919661i	$0.628464\pi$
$858$	−10669.5	−	4419.46i	−0.0144934	−	0.00600336i
$859$	537991.	+	537991.i	0.729103	+	0.729103i	0.970441	−	0.241338i	$-0.0775864\pi$
$859$	537991.	+	537991.i	0.729103	+	0.729103i	−0.241338	+	0.970441i	$0.577586\pi$
$860$			82770.1i			0.111912i
$861$	70292.5	+	3692.33i	0.0948206	+	0.00498074i
$862$	−337298.			−0.453940
$863$	550570.	−	550570.i	0.739250	−	0.739250i	−0.233183	−	0.972433i	$-0.574914\pi$
$863$	550570.	−	550570.i	0.739250	−	0.739250i	0.972433	+	0.233183i	$0.0749141\pi$
$864$	14312.7	−	34554.0i	0.0191732	−	0.0462883i
$865$		−	1.02257e6i		−	1.36666i
$866$	156520.	+	156520.i	0.208705	+	0.208705i
$867$	−28736.7	−	69376.6i	−0.0382295	−	0.0922943i
$868$	−83394.0	+	201331.i	−0.110687	+	0.267221i
$869$	−652036.	−	652036.i	−0.863439	−	0.863439i
$870$	41.6892	+	41.6892i	5.50789e−5	+	5.50789e-5i
$871$	125410.			0.165308
$872$	72098.1	+	29864.0i	0.0948180	+	0.0392749i
$873$	−867425.	−	359299.i	−1.13816	−	0.471442i
$874$	191104.	−	461365.i	0.250176	−	0.603979i
$875$	−121255.	−	292736.i	−0.158374	−	0.382349i
$876$	52107.6	−	21583.7i	0.0679036	−	0.0281266i
$877$	−116444.			−0.151397			−0.0756987	−	0.997131i	$-0.524119\pi$
$877$	−116444.			−0.151397			−0.0756987	+	0.997131i	$0.524119\pi$
$878$	124180.	+	299796.i	0.161087	+	0.388900i
$879$	−97647.6			−0.126382
$880$	81447.6	+	196632.i	0.105175	+	0.253915i
$881$	867060.	−	867060.i	1.11711	−	1.11711i	0.124950	−	0.992163i	$-0.460123\pi$
$881$	867060.	−	867060.i	1.11711	−	1.11711i	0.992163	−	0.124950i	$-0.0398771\pi$
$882$	−213431.	−	213431.i	−0.274360	−	0.274360i
$883$	270779.	−	112160.i	0.347291	−	0.143852i	−0.202218	−	0.979341i	$-0.564815\pi$
$883$	270779.	−	112160.i	0.347291	−	0.143852i	0.549509	+	0.835488i	$0.314815\pi$
$884$			36941.3i			0.0472724i
$885$	−147994.	+	61301.1i	−0.188955	+	0.0782676i
$886$		−	871544.i		−	1.11025i
$887$	−163832.	−	395525.i	−0.208234	−	0.502721i	0.784911	−	0.619608i	$-0.212708\pi$
$887$	−163832.	−	395525.i	−0.208234	−	0.502721i	−0.993145	+	0.116887i	$0.962708\pi$
$888$	−32764.1	+	13571.3i	−0.0415501	+	0.0172106i
$889$	−431826.	−	178868.i	−0.546393	−	0.226323i
$890$	−407699.	+	984273.i	−0.514707	+	1.24261i
$891$	−257029.	+	620524.i	−0.323763	+	0.781633i
$892$			214897.i			0.270085i
$893$	390854.	−	390854.i	0.490130	−	0.490130i
$894$	59451.3	−	59451.3i	0.0743851	−	0.0743851i
$895$	−1.15604e6	−	478848.i	−1.44320	−	0.597794i
$896$	43476.3	−	18008.5i	0.0541547	−	0.0224316i
$897$	−9596.63	+	9596.63i	−0.0119271	+	0.0119271i
$898$	288448.			0.357696
$899$	−410.733	−	170.131i	−0.000508206	−	0.000210506i
$900$	137029.	+	137029.i	0.169171	+	0.169171i
$901$			335109.i			0.412797i
$902$	−223229.	+	467865.i	−0.274370	+	0.575052i
$903$	14203.9			0.0174194
$904$	84971.6	−	84971.6i	0.103977	−	0.103977i
$905$	364234.	−	879339.i	0.444717	−	1.07364i
$906$		−	22313.8i		−	0.0271842i
$907$	−160335.	−	160335.i	−0.194901	−	0.194901i	0.602909	−	0.797810i	$-0.294008\pi$
$907$	−160335.	−	160335.i	−0.194901	−	0.194901i	−0.797810	+	0.602909i	$0.794008\pi$
$908$	14786.8	+	35698.4i	0.0179350	+	0.0432990i
$909$	24700.4	−	59632.0i	0.0298934	−	0.0721691i
$910$	−57608.9	−	57608.9i	−0.0695676	−	0.0695676i
$911$	351248.	+	351248.i	0.423230	+	0.423230i	0.886314	−	0.463084i	$-0.153257\pi$
$911$	351248.	+	351248.i	0.423230	+	0.423230i	−0.463084	+	0.886314i	$0.653257\pi$
$912$	−40178.1			−0.0483058
$913$	1.05442e6	+	436756.i	1.26495	+	0.523959i
$914$	−314190.	−	130142.i	−0.376097	−	0.155784i
$915$	58998.3	−	142435.i	0.0704689	−	0.170127i
$916$	−240710.	−	581126.i	−0.286882	−	0.692595i
$917$	−448495.	+	185773.i	−0.533358	+	0.220924i
$918$	−92854.4			−0.110184
$919$	110829.	+	267565.i	0.131227	+	0.316809i	0.975812	−	0.218612i	$-0.0701529\pi$
$919$	110829.	+	267565.i	0.131227	+	0.316809i	−0.844585	+	0.535421i	$0.820153\pi$
$920$	250117.			0.295507
$921$	30281.3	+	73105.6i	0.0356990	+	0.0861849i
$922$	220367.	−	220367.i	0.259230	−	0.259230i
$923$	−61003.9	−	61003.9i	−0.0716068	−	0.0716068i
$924$	33743.4	−	13977.0i	0.0395226	−	0.0163708i
$925$		−	371344.i		−	0.434003i
$926$	773336.	−	320326.i	0.901874	−	0.373569i
$927$			80819.6i			0.0940497i
$928$	36.7389	+	88.6954i	4.26609e−5	+	0.000102992i
$929$	−1.04525e6	+	432959.i	−1.21113	+	0.501666i	−0.894579	−	0.446909i	$-0.852525\pi$
$929$	−1.04525e6	+	432959.i	−1.21113	+	0.501666i	−0.316551	+	0.948576i	$0.602525\pi$
$930$	86094.6	+	35661.5i	0.0995428	+	0.0412320i
$931$	−250766.	+	605403.i	−0.289314	+	0.698466i
$932$	23933.3	−	57780.0i	0.0275531	−	0.0665190i
$933$		−	55067.8i		−	0.0632607i
$934$	−469334.	+	469334.i	−0.538008	+	0.538008i
$935$	373631.	−	373631.i	0.427385	−	0.427385i
$936$	−48201.7	−	19965.8i	−0.0550188	−	0.0227895i
$937$	−841936.	+	348741.i	−0.958959	+	0.397214i	−0.806591	−	0.591110i	$-0.798690\pi$
$937$	−841936.	+	348741.i	−0.958959	+	0.397214i	−0.152368	+	0.988324i	$0.548690\pi$
$938$	−280453.	+	280453.i	−0.318753	+	0.318753i
$939$	120000.			0.136098
$940$	255775.	+	105945.i	0.289469	+	0.119902i
$941$	−1.08780e6	−	1.08780e6i	−1.22848	−	1.22848i	−0.964538	−	0.263945i	$-0.914976\pi$
$941$	−1.08780e6	−	1.08780e6i	−1.22848	−	1.22848i	−0.263945	−	0.964538i	$-0.585024\pi$
$942$			104267.i			0.117501i
$943$	407581.	+	452774.i	0.458343	+	0.509164i
$944$	−260841.			−0.292706
$945$	144804.	−	144804.i	0.162150	−	0.162150i
$946$	−40031.1	+	96643.6i	−0.0447317	+	0.107992i
$947$		−	734280.i		−	0.818769i	−0.912362	−	0.409385i	$-0.865743\pi$
$947$		−	734280.i		−	0.818769i	0.912362	−	0.409385i	$-0.134257\pi$
$948$	61650.3	+	61650.3i	0.0685991	+	0.0685991i
$949$	−60847.1	−	146898.i	−0.0675628	−	0.163111i
$950$	160999.	−	388685.i	0.178392	−	0.430676i
$951$	71617.9	+	71617.9i	0.0791883	+	0.0791883i
$952$	−82611.6	−	82611.6i	−0.0911522	−	0.0911522i
$953$	596913.			0.657242			0.328621	−	0.944462i	$-0.393416\pi$
$953$	596913.			0.657242			0.328621	+	0.944462i	$0.393416\pi$
$954$	−437257.	−	181118.i	−0.480441	−	0.199005i
$955$	−826806.	−	342474.i	−0.906561	−	0.375510i
$956$	178840.	−	431757.i	0.195681	−	0.472415i
$957$	28.5143	+	68.8396i	3.11343e−5	+	7.51648e-5i
$958$	−244717.	+	101365.i	−0.266645	+	0.110448i
$959$	856531.			0.931335
$960$	−7700.91	−	18591.6i	−0.00835602	−	0.0201732i
$961$	220827.			0.239114
$962$	38259.3	+	92366.2i	0.0413416	+	0.0998075i
$963$	1.02241e6	−	1.02241e6i	1.10249	−	1.10249i
$964$	−332217.	−	332217.i	−0.357493	−	0.357493i
$965$	440790.	−	182581.i	0.473344	−	0.196065i
$966$		−	42921.8i		−	0.0459964i
$967$	−1.31548e6	+	544889.i	−1.40680	+	0.582714i	−0.951506	−	0.307629i	$-0.900464\pi$
$967$	−1.31548e6	+	544889.i	−1.40680	+	0.582714i	−0.455290	+	0.890343i	$0.650464\pi$
$968$		−	62306.0i		−	0.0664935i
$969$	38172.2	+	92156.0i	0.0406537	+	0.0981467i
$970$	−943197.	+	390685.i	−1.00244	+	0.415225i
$971$	−952226.	−	394425.i	−1.00995	−	0.418337i	−0.184516	−	0.982829i	$-0.559072\pi$
$971$	−952226.	−	394425.i	−1.00995	−	0.418337i	−0.825438	+	0.564493i	$0.809072\pi$
$972$	75538.0	−	182365.i	0.0799526	−	0.193023i
$973$	−50082.8	+	120911.i	−0.0529009	+	0.127714i
$974$		−	97562.5i		−	0.102841i
$975$	−8084.85	+	8084.85i	−0.00850478	+	0.00850478i
$976$	177514.	−	177514.i	0.186352	−	0.186352i
$977$	1.24237e6	+	514607.i	1.30155	+	0.539122i	0.922409	−	0.386215i	$-0.126218\pi$
$977$	1.24237e6	+	514607.i	1.30155	+	0.539122i	0.379146	+	0.925337i	$0.376218\pi$
$978$	18479.2	−	7654.33i	0.0193199	−	0.00800257i
$979$	−952071.	+	952071.i	−0.993354	+	0.993354i
$980$	−328203.			−0.341736
$981$	252801.	+	104713.i	0.262688	+	0.108809i
$982$	729063.	+	729063.i	0.756035	+	0.756035i
$983$		−	1.45219e6i		−	1.50285i	−0.659816	−	0.751427i	$-0.729366\pi$
$983$		−	1.45219e6i		−	1.50285i	0.659816	−	0.751427i	$-0.270634\pi$
$984$	21106.4	−	44236.8i	0.0217984	−	0.0456871i
$985$	1.89524e6			1.95341
$986$	168.535	−	168.535i	0.000173355	−	0.000173355i
$987$	18181.0	−	43892.8i	0.0186631	−	0.0450566i
$988$			113267.i			0.116035i
$989$	86925.5	+	86925.5i	0.0888698	+	0.0888698i
$990$	285583.	+	689459.i	0.291382	+	0.703458i
$991$	−484474.	+	1.16962e6i	−0.493313	+	1.19096i	0.459711	+	0.888069i	$0.347953\pi$
$991$	−484474.	+	1.16962e6i	−0.493313	+	1.19096i	−0.953024	+	0.302895i	$0.902047\pi$
$992$	107298.	+	107298.i	0.109036	+	0.109036i
$993$	164816.	+	164816.i	0.167148	+	0.167148i
$994$	272846.			0.276149
$995$	−1.01349e6	−	419799.i	−1.02370	−	0.424029i
$996$	−99696.1	−	41295.5i	−0.100498	−	0.0416278i
$997$	−508465.	+	1.22754e6i	−0.511530	+	1.23494i	0.431463	+	0.902131i	$0.357998\pi$
$997$	−508465.	+	1.22754e6i	−0.511530	+	1.23494i	−0.942993	+	0.332812i	$0.892002\pi$
$998$	−276236.	−	666893.i	−0.277345	−	0.669569i
$999$	−232169.	+	96167.4i	−0.232634	+	0.0963600i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.5.e.a.3.4	✓	28
41.14	odd	8	inner	82.5.e.a.55.4	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.5.e.a.3.4	✓	28	1.1	even	1	trivial
82.5.e.a.55.4	yes	28	41.14	odd	8	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:	\( N \)	\(=\)	\( 82 = 2 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	82.e (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 2.00000i) q^{2} +(0.493125 - 1.19051i) q^{3} -8.00000i q^{4} +(-21.5675 - 21.5675i) q^{5} +(1.39477 + 3.36727i) q^{6} +(-12.4355 + 30.0219i) q^{7} +(16.0000 + 16.0000i) q^{8} +(56.1015 + 56.1015i) q^{9} +86.2700 q^{10} +(100.730 + 41.7238i) q^{11} +(-9.52408 - 3.94500i) q^{12} +(-11.1215 + 26.8496i) q^{13} +(-35.1728 - 84.9146i) q^{14} +(-36.3118 + 15.0408i) q^{15} -64.0000 q^{16} +(60.8049 + 146.796i) q^{17} -224.406 q^{18} +(186.436 + 450.098i) q^{19} +(-172.540 + 172.540i) q^{20} +(29.6091 + 29.6091i) q^{21} +(-284.908 + 118.013i) q^{22} +362.404i q^{23} +(26.9382 - 11.1582i) q^{24} +305.314i q^{25} +(-31.4563 - 75.9422i) q^{26} +(190.886 - 79.0675i) q^{27} +(240.175 + 99.4837i) q^{28} +(-0.202955 + 0.489978i) q^{29} +(42.5419 - 102.705i) q^{30} +838.268i q^{31} +(128.000 - 128.000i) q^{32} +(99.3452 - 99.3452i) q^{33} +(-415.202 - 171.982i) q^{34} +(915.698 - 379.294i) q^{35} +(448.812 - 448.812i) q^{36} -1216.27 q^{37} +(-1273.07 - 527.322i) q^{38} +(26.4805 + 26.4805i) q^{39} -690.160i q^{40} +(1249.36 - 1124.66i) q^{41} -118.436 q^{42} +(239.858 - 239.858i) q^{43} +(333.790 - 805.841i) q^{44} -2419.94i q^{45} +(-724.808 - 724.808i) q^{46} +(-434.188 - 1048.22i) q^{47} +(-31.5600 + 76.1926i) q^{48} +(951.092 + 951.092i) q^{49} +(-610.628 - 610.628i) q^{50} +204.747 q^{51} +(214.797 + 88.9718i) q^{52} +(1948.51 + 807.099i) q^{53} +(-223.637 + 539.907i) q^{54} +(-1272.62 - 3072.38i) q^{55} +(-679.317 + 281.382i) q^{56} +627.782 q^{57} +(-0.574045 - 1.38587i) q^{58} +4075.64 q^{59} +(120.327 + 290.494i) q^{60} +(-2773.66 + 2773.66i) q^{61} +(-1676.54 - 1676.54i) q^{62} +(-2381.92 + 986.623i) q^{63} +512.000i q^{64} +(818.942 - 339.217i) q^{65} +397.381i q^{66} +(-1651.38 - 3986.79i) q^{67} +(1174.37 - 486.439i) q^{68} +(431.446 + 178.711i) q^{69} +(-1072.81 + 2589.98i) q^{70} +(-1136.03 + 2742.62i) q^{71} +1795.25i q^{72} +(-3868.68 + 3868.68i) q^{73} +(2432.54 - 2432.54i) q^{74} +(363.479 + 150.558i) q^{75} +(3600.78 - 1491.49i) q^{76} +(-2505.25 + 2505.25i) q^{77} -105.922 q^{78} +(-7813.71 - 3236.55i) q^{79} +(1380.32 + 1380.32i) q^{80} +6160.26i q^{81} +(-249.405 + 4748.04i) q^{82} +10467.8 q^{83} +(236.873 - 236.873i) q^{84} +(1854.61 - 4477.43i) q^{85} +959.431i q^{86} +(0.483241 + 0.483241i) q^{87} +(944.102 + 2279.26i) q^{88} +(-4725.85 + 11409.2i) q^{89} +(4839.88 + 4839.88i) q^{90} +(-667.775 - 667.775i) q^{91} +2899.23 q^{92} +(997.967 + 413.371i) q^{93} +(2964.82 + 1228.07i) q^{94} +(5686.51 - 13728.4i) q^{95} +(-89.2652 - 215.505i) q^{96} +(-10933.1 + 4528.63i) q^{97} -3804.37 q^{98} +(3310.35 + 7991.88i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 56 q^{2} + 16 q^{3} - 16 q^{6} + 448 q^{8} + 24 q^{9} + 328 q^{11} - 64 q^{12} - 348 q^{13} + 192 q^{14} + 1036 q^{15} - 1792 q^{16} - 1832 q^{17} - 96 q^{18} - 504 q^{19} + 2004 q^{21} - 856 q^{22}+ \cdots + 11544 q^{99}+O(q^{100}) \) 28 * q - 56 * q^2 + 16 * q^3 - 16 * q^6 + 448 * q^8 + 24 * q^9 + 328 * q^11 - 64 * q^12 - 348 * q^13 + 192 * q^14 + 1036 * q^15 - 1792 * q^16 - 1832 * q^17 - 96 * q^18 - 504 * q^19 + 2004 * q^21 - 856 * q^22 + 384 * q^24 + 384 * q^26 + 964 * q^27 - 768 * q^28 - 4 * q^29 - 4456 * q^30 + 3584 * q^32 - 748 * q^33 + 3576 * q^34 - 1104 * q^35 + 192 * q^36 + 5488 * q^37 + 256 * q^38 + 1232 * q^39 - 3760 * q^41 - 8016 * q^42 + 4756 * q^43 + 800 * q^44 - 2320 * q^46 - 4240 * q^47 - 1024 * q^48 + 2088 * q^49 - 6280 * q^50 + 29792 * q^51 + 1248 * q^52 - 10492 * q^53 - 1992 * q^54 + 14840 * q^55 + 1536 * q^56 - 33512 * q^57 + 2192 * q^58 - 11376 * q^59 + 9536 * q^60 - 3360 * q^61 + 2224 * q^62 - 13912 * q^63 + 41300 * q^65 + 15440 * q^67 + 352 * q^68 - 1004 * q^69 - 6792 * q^70 - 28392 * q^71 + 4284 * q^73 - 10976 * q^74 + 23812 * q^75 + 3008 * q^76 - 16524 * q^77 - 4928 * q^78 - 22236 * q^79 + 16752 * q^82 - 4024 * q^83 + 16032 * q^84 - 16616 * q^85 - 4628 * q^87 + 3648 * q^88 - 54412 * q^89 + 18336 * q^90 + 59948 * q^91 + 9280 * q^92 - 26800 * q^93 - 3240 * q^94 - 47636 * q^95 + 1024 * q^96 + 46764 * q^97 - 8352 * q^98 + 11544 * q^99

Introduction

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