LMFDB - Embedded newform 82.5.h.b.53.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [82,5,Mod(7,82)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(82, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([39])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("82.7"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 82 = 2 \cdot 41 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	82.h (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [112,56] 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:	$112$
Relative dimension:	$7$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			53.4
Character	$\chi$	$=$	82.53
Dual form			82.5.h.b.65.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.442463 - 2.79360i) q^{2} +(3.13167 + 1.29718i) q^{3} +(-7.60845 - 2.47214i) q^{4} +(-14.2891 + 7.28065i) q^{5} +(5.00946 - 8.17469i) q^{6} +(-7.78628 - 12.7060i) q^{7} +(-10.2726 + 20.1612i) q^{8} +(-49.1510 - 49.1510i) q^{9} +(14.0169 + 43.1395i) q^{10} +(-163.385 - 12.8587i) q^{11} +(-20.6204 - 17.6114i) q^{12} +(-75.4321 + 18.1097i) q^{13} +(-38.9408 + 16.1298i) q^{14} +(-54.1930 + 4.26508i) q^{15} +(51.7771 + 37.6183i) q^{16} +(-17.6671 - 20.6855i) q^{17} +(-159.056 + 115.561i) q^{18} +(73.4465 + 17.6329i) q^{19} +(126.717 - 20.0699i) q^{20} +(-7.90201 - 49.8914i) q^{21} +(-108.214 + 450.744i) q^{22} +(-73.6910 - 101.427i) q^{23} +(-58.3232 + 49.8127i) q^{24} +(-216.196 + 297.568i) q^{25} +(17.2152 + 218.740i) q^{26} +(-195.239 - 471.348i) q^{27} +(27.8304 + 115.922i) q^{28} +(-389.016 + 455.479i) q^{29} +(-12.0635 + 153.281i) q^{30} +(293.618 - 95.4021i) q^{31} +(128.000 - 128.000i) q^{32} +(-494.988 - 252.209i) q^{33} +(-65.6042 + 40.2023i) q^{34} +(203.767 + 124.869i) q^{35} +(252.455 + 495.471i) q^{36} +(124.318 - 382.611i) q^{37} +(81.7568 - 197.378i) q^{38} +(-259.720 - 41.1356i) q^{39} -362.876i q^{40} +(1473.73 - 808.633i) q^{41} -142.873 q^{42} +(265.630 - 1677.12i) q^{43} +(1211.32 + 501.745i) q^{44} +(1060.17 + 344.471i) q^{45} +(-315.952 + 160.986i) q^{46} +(955.233 - 1558.80i) q^{47} +(113.351 + 184.972i) q^{48} +(989.214 - 1941.44i) q^{49} +(735.628 + 735.628i) q^{50} +(-28.4947 - 87.6976i) q^{51} +(618.691 + 48.6921i) q^{52} +(-2022.34 - 1727.24i) q^{53} +(-1403.14 + 336.865i) q^{54} +(2428.24 - 1005.81i) q^{55} +(336.154 - 26.4559i) q^{56} +(207.137 + 150.494i) q^{57} +(1100.30 + 1288.29i) q^{58} +(-2011.37 + 1461.34i) q^{59} +(422.869 + 101.522i) q^{60} +(678.674 - 107.491i) q^{61} +(-136.601 - 862.463i) q^{62} +(-241.812 + 1007.22i) q^{63} +(-300.946 - 414.217i) q^{64} +(946.006 - 807.966i) q^{65} +(-923.587 + 1271.21i) q^{66} +(209.683 + 2664.28i) q^{67} +(83.2818 + 201.060i) q^{68} +(-99.2068 - 413.226i) q^{69} +(438.993 - 513.995i) q^{70} +(-717.385 + 9115.25i) q^{71} +(1495.85 - 486.032i) q^{72} +(1210.17 - 1210.17i) q^{73} +(-1013.86 - 516.586i) q^{74} +(-1063.05 + 651.439i) q^{75} +(-515.223 - 315.729i) q^{76} +(1108.78 + 2176.10i) q^{77} +(-229.833 + 707.354i) q^{78} +(585.223 - 1412.85i) q^{79} +(-1013.73 - 160.560i) q^{80} +3900.94i q^{81} +(-1606.93 - 4474.80i) q^{82} -11432.2 q^{83} +(-63.2161 + 399.131i) q^{84} +(403.051 + 166.949i) q^{85} +(-4567.69 - 1484.13i) q^{86} +(-1809.11 + 921.787i) q^{87} +(1937.64 - 3161.94i) q^{88} +(-2454.86 - 4005.97i) q^{89} +(1431.40 - 2809.29i) q^{90} +(817.438 + 817.438i) q^{91} +(309.933 + 953.876i) q^{92} +(1043.27 + 82.1069i) q^{93} +(-3932.01 - 3358.25i) q^{94} +(-1177.86 + 282.780i) q^{95} +(566.893 - 234.815i) q^{96} +(-3294.70 + 259.299i) q^{97} +(-4985.93 - 3622.49i) q^{98} +(7398.52 + 8662.56i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 56 q^{2} - 16 q^{3} + 16 q^{6} - 448 q^{8} - 24 q^{9} + 512 q^{11} - 576 q^{12} + 348 q^{13} - 192 q^{14} - 1036 q^{15} + 1792 q^{16} + 552 q^{17} + 416 q^{18} + 504 q^{19} + 876 q^{21} + 16 q^{22}+ \cdots + 36896 q^{99}+O(q^{100}) $ 112 * q + 56 * q^2 - 16 * q^3 + 16 * q^6 - 448 * q^8 - 24 * q^9 + 512 * q^11 - 576 * q^12 + 348 * q^13 - 192 * q^14 - 1036 * q^15 + 1792 * q^16 + 552 * q^17 + 416 * q^18 + 504 * q^19 + 876 * q^21 + 16 * q^22 + 800 * q^23 - 384 * q^24 - 3360 * q^25 + 1656 * q^26 - 964 * q^27 + 768 * q^28 + 4 * q^29 - 3544 * q^30 + 1380 * q^31 + 14336 * q^32 - 7392 * q^33 + 4224 * q^34 + 2264 * q^35 + 2048 * q^36 + 6212 * q^37 + 2624 * q^38 + 4928 * q^39 - 7460 * q^41 + 5056 * q^42 - 19816 * q^43 - 6560 * q^44 - 26000 * q^45 - 4400 * q^46 - 14660 * q^47 - 1536 * q^48 - 17808 * q^49 - 28720 * q^50 + 17948 * q^51 + 1152 * q^52 + 19032 * q^53 + 20152 * q^54 + 3160 * q^55 - 1536 * q^56 + 23432 * q^57 - 6752 * q^58 + 25136 * q^59 - 9536 * q^60 + 10080 * q^61 + 10496 * q^62 - 968 * q^63 - 57460 * q^65 - 2480 * q^66 + 280 * q^67 + 1568 * q^68 - 1876 * q^69 + 6792 * q^70 + 49672 * q^71 + 4480 * q^72 + 16196 * q^73 - 30984 * q^74 + 58748 * q^75 + 13312 * q^76 + 6444 * q^77 + 4928 * q^78 + 34556 * q^79 + 6888 * q^82 + 17304 * q^83 + 7008 * q^84 - 104144 * q^85 + 30800 * q^86 - 28492 * q^87 - 3648 * q^88 + 26732 * q^89 - 70336 * q^90 - 132748 * q^91 + 4160 * q^92 + 35360 * q^93 - 11160 * q^94 - 5644 * q^95 - 1024 * q^96 + 14036 * q^97 - 6528 * q^98 + 36896 * q^99

Character values

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

$n$	$47$
$\chi(n)$	$e\left(\frac{27}{40}\right)$

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 $

$2$	0.442463	−	2.79360i	0.110616	−	0.698401i
$2$	0.442463	−	2.79360i	0.110616	−	0.698401i
$3$	3.13167	+	1.29718i	0.347963	+	0.144131i	0.549818	−	0.835284i	$-0.314697\pi$
$3$	3.13167	+	1.29718i	0.347963	+	0.144131i	−0.201855	+	0.979415i	$0.564697\pi$
$4$	−7.60845	−	2.47214i	−0.475528	−	0.154508i
$5$	−14.2891	+	7.28065i	−0.571563	+	0.291226i	−0.715787	−	0.698319i	$-0.753932\pi$
$5$	−14.2891	+	7.28065i	−0.571563	+	0.291226i	0.144223	+	0.989545i	$0.453932\pi$
$6$	5.00946	−	8.17469i	0.139152	−	0.227075i
$7$	−7.78628	−	12.7060i	−0.158904	−	0.259307i	0.763273	−	0.646076i	$-0.223591\pi$
$7$	−7.78628	−	12.7060i	−0.158904	−	0.259307i	−0.922177	+	0.386769i	$0.873591\pi$
$8$	−10.2726	+	20.1612i	−0.160510	+	0.315018i
$9$	−49.1510	−	49.1510i	−0.606802	−	0.606802i
$10$	14.0169	+	43.1395i	0.140169	+	0.431395i
$11$	−163.385	−	12.8587i	−1.35029	−	0.106270i	−0.617418	−	0.786636i	$-0.711821\pi$
$11$	−163.385	−	12.8587i	−1.35029	−	0.106270i	−0.732873	+	0.680365i	$0.761821\pi$
$12$	−20.6204	−	17.6114i	−0.143197	−	0.122302i
$13$	−75.4321	+	18.1097i	−0.446344	+	0.107158i	−0.450386	−	0.892834i	$-0.648714\pi$
$13$	−75.4321	+	18.1097i	−0.446344	+	0.107158i	0.00404161	+	0.999992i	$0.498714\pi$
$14$	−38.9408	+	16.1298i	−0.198678	+	0.0822950i
$15$	−54.1930	+	4.26508i	−0.240858	+	0.0189559i
$16$	51.7771	+	37.6183i	0.202254	+	0.146946i
$17$	−17.6671	−	20.6855i	−0.0611318	−	0.0715761i	0.728997	−	0.684516i	$-0.239987\pi$
$17$	−17.6671	−	20.6855i	−0.0611318	−	0.0715761i	−0.790129	+	0.612940i	$0.789987\pi$
$18$	−159.056	+	115.561i	−0.490913	+	0.356669i
$19$	73.4465	+	17.6329i	0.203453	+	0.0488447i	0.333891	−	0.942612i	$-0.391638\pi$
$19$	73.4465	+	17.6329i	0.203453	+	0.0488447i	−0.130438	+	0.991456i	$0.541638\pi$
$20$	126.717	−	20.0699i	0.316791	−	0.0501748i
$21$	−7.90201	−	49.8914i	−0.0179184	−	0.113132i
$22$	−108.214	+	450.744i	−0.223583	+	0.931289i
$23$	−73.6910	−	101.427i	−0.139302	−	0.191733i	0.733666	−	0.679511i	$-0.237808\pi$
$23$	−73.6910	−	101.427i	−0.139302	−	0.191733i	−0.872968	+	0.487777i	$0.837808\pi$
$24$	−58.3232	+	49.8127i	−0.101256	+	0.0864804i
$25$	−216.196	+	297.568i	−0.345913	+	0.476109i
$26$	17.2152	+	218.740i	0.0254663	+	0.323581i
$27$	−195.239	−	471.348i	−0.267817	−	0.646567i
$28$	27.8304	+	115.922i	0.0354980	+	0.147860i
$29$	−389.016	+	455.479i	−0.462564	+	0.541592i	−0.941836	−	0.336074i	$-0.890901\pi$
$29$	−389.016	+	455.479i	−0.462564	+	0.541592i	0.479272	+	0.877666i	$0.340901\pi$
$30$	−12.0635	+	153.281i	−0.0134039	+	0.170312i
$31$	293.618	−	95.4021i	0.305533	−	0.0992738i	−0.152238	−	0.988344i	$-0.548648\pi$
$31$	293.618	−	95.4021i	0.305533	−	0.0992738i	0.457771	+	0.889070i	$0.348648\pi$
$32$	128.000	−	128.000i	0.125000	−	0.125000i
$33$	−494.988	−	252.209i	−0.454535	−	0.231597i
$34$	−65.6042	+	40.2023i	−0.0567510	+	0.0347771i
$35$	203.767	+	124.869i	0.166341	+	0.101934i
$36$	252.455	+	495.471i	0.194795	+	0.382308i
$37$	124.318	−	382.611i	0.0908093	−	0.279482i	−0.895330	−	0.445404i	$-0.853060\pi$
$37$	124.318	−	382.611i	0.0908093	−	0.279482i	0.986139	+	0.165922i	$0.0530600\pi$
$38$	81.7568	−	197.378i	0.0566183	−	0.136689i
$39$	−259.720	−	41.1356i	−0.170756	−	0.0270451i
$40$		−	362.876i		−	0.226798i
$41$	1473.73	−	808.633i	0.876697	−	0.481043i
$41$	1473.73	−	808.633i	0.876697	−	0.481043i
$42$	−142.873			−0.0809938
$43$	265.630	−	1677.12i	0.143662	−	0.907044i	−0.805578	−	0.592490i	$-0.798145\pi$
$43$	265.630	−	1677.12i	0.143662	−	0.907044i	0.949240	−	0.314554i	$-0.101855\pi$
$44$	1211.32	+	501.745i	0.625682	+	0.259166i
$45$	1060.17	+	344.471i	0.523543	+	0.170109i
$46$	−315.952	+	160.986i	−0.149316	+	0.0760802i
$47$	955.233	−	1558.80i	0.432428	−	0.705658i	−0.559999	−	0.828493i	$-0.689199\pi$
$47$	955.233	−	1558.80i	0.432428	−	0.705658i	0.992427	+	0.122835i	$0.0391987\pi$
$48$	113.351	+	184.972i	0.0491975	+	0.0802831i
$49$	989.214	−	1941.44i	0.412001	−	0.808597i
$50$	735.628	+	735.628i	0.294251	+	0.294251i
$51$	−28.4947	−	87.6976i	−0.0109553	−	0.0337169i
$52$	618.691	+	48.6921i	0.228806	+	0.0180074i
$53$	−2022.34	−	1727.24i	−0.719949	−	0.614895i	0.212091	−	0.977250i	$-0.431973\pi$
$53$	−2022.34	−	1727.24i	−0.719949	−	0.614895i	−0.932040	+	0.362355i	$0.881973\pi$
$54$	−1403.14	+	336.865i	−0.481188	+	0.115523i
$55$	2428.24	−	1005.81i	0.802726	−	0.332500i
$56$	336.154	−	26.4559i	0.107192	−	0.00843620i
$57$	207.137	+	150.494i	0.0637541	+	0.0463201i
$58$	1100.30	+	1288.29i	0.327082	+	0.382964i
$59$	−2011.37	+	1461.34i	−0.577813	+	0.419805i	−0.837935	−	0.545770i	$-0.816237\pi$
$59$	−2011.37	+	1461.34i	−0.577813	+	0.419805i	0.260122	+	0.965576i	$0.416237\pi$
$60$	422.869	+	101.522i	0.117464	+	0.0282005i
$61$	678.674	−	107.491i	0.182390	−	0.0288878i	−0.0645711	−	0.997913i	$-0.520568\pi$
$61$	678.674	−	107.491i	0.182390	−	0.0288878i	0.246961	+	0.969025i	$0.420568\pi$
$62$	−136.601	−	862.463i	−0.0355361	−	0.224366i
$63$	−241.812	+	1007.22i	−0.0609251	+	0.253771i
$64$	−300.946	−	414.217i	−0.0734732	−	0.101127i
$65$	946.006	−	807.966i	0.223907	−	0.191235i
$66$	−923.587	+	1271.21i	−0.212026	+	0.291829i
$67$	209.683	+	2664.28i	0.0467105	+	0.593513i	0.975080	+	0.221854i	$0.0712109\pi$
$67$	209.683	+	2664.28i	0.0467105	+	0.593513i	−0.928369	+	0.371659i	$0.878789\pi$
$68$	83.2818	+	201.060i	0.0180108	+	0.0434819i
$69$	−99.2068	−	413.226i	−0.0208374	−	0.0867940i
$70$	438.993	−	513.995i	0.0895904	−	0.104897i
$71$	−717.385	+	9115.25i	−0.142310	+	1.80822i	0.348878	+	0.937168i	$0.386563\pi$
$71$	−717.385	+	9115.25i	−0.142310	+	1.80822i	−0.491188	+	0.871053i	$0.663437\pi$
$72$	1495.85	−	486.032i	0.288552	−	0.0937561i
$73$	1210.17	−	1210.17i	0.227091	−	0.227091i	−0.584385	−	0.811476i	$-0.698664\pi$
$73$	1210.17	−	1210.17i	0.227091	−	0.227091i	0.811476	+	0.584385i	$0.198664\pi$
$74$	−1013.86	−	516.586i	−0.185146	−	0.0943365i
$75$	−1063.05	+	651.439i	−0.188987	+	0.115811i
$76$	−515.223	−	315.729i	−0.0892007	−	0.0546622i
$77$	1108.78	+	2176.10i	0.187009	+	0.367027i
$78$	−229.833	+	707.354i	−0.0377767	+	0.116265i
$79$	585.223	−	1412.85i	0.0937707	−	0.226383i	−0.870034	−	0.492992i	$-0.835903\pi$
$79$	585.223	−	1412.85i	0.0937707	−	0.226383i	0.963805	+	0.266609i	$0.0859033\pi$
$80$	−1013.73	−	160.560i	−0.158396	−	0.0250874i
$81$			3900.94i			0.594565i
$82$	−1606.93	−	4474.80i	−0.238984	−	0.665497i
$83$	−11432.2			−1.65949			−0.829743	−	0.558146i	$-0.811513\pi$
$83$	−11432.2			−1.65949			−0.829743	+	0.558146i	$0.811513\pi$
$84$	−63.2161	+	399.131i	−0.00895920	+	0.0565662i
$85$	403.051	+	166.949i	0.0557855	+	0.0231071i
$86$	−4567.69	−	1484.13i	−0.617589	−	0.200667i
$87$	−1809.11	+	921.787i	−0.239015	+	0.121784i
$88$	1937.64	−	3161.94i	0.250212	−	0.408309i
$89$	−2454.86	−	4005.97i	−0.309918	−	0.505741i	0.659321	−	0.751862i	$-0.270844\pi$
$89$	−2454.86	−	4005.97i	−0.309918	−	0.505741i	−0.969239	+	0.246121i	$0.920844\pi$
$90$	1431.40	−	2809.29i	0.176717	−	0.346826i
$91$	817.438	+	817.438i	0.0987124	+	0.0987124i
$92$	309.933	+	953.876i	0.0366178	+	0.112698i
$93$	1043.27	+	82.1069i	0.120623	+	0.00949322i
$94$	−3932.01	−	3358.25i	−0.444999	−	0.380065i
$95$	−1177.86	+	282.780i	−0.130511	+	0.0313329i
$96$	566.893	−	234.815i	0.0615118	−	0.0254790i
$97$	−3294.70	+	259.299i	−0.350165	+	0.0275586i	−0.252322	−	0.967643i	$-0.581194\pi$
$97$	−3294.70	+	259.299i	−0.350165	+	0.0275586i	−0.0978428	+	0.995202i	$0.531194\pi$
$98$	−4985.93	−	3622.49i	−0.519151	−	0.377185i
$99$	7398.52	+	8662.56i	0.754874	+	0.883844i
$100$	2380.54	−	1729.57i	0.238054	−	0.172957i
$101$	−5657.63	−	1358.28i	−0.554615	−	0.133151i	−0.0535569	−	0.998565i	$-0.517056\pi$
$101$	−5657.63	−	1358.28i	−0.554615	−	0.133151i	−0.501058	+	0.865413i	$0.667056\pi$
$102$	−257.600	+	40.7999i	−0.0247597	+	0.00392155i
$103$	1253.81	+	7916.23i	0.118183	+	0.746180i	0.973604	+	0.228246i	$0.0732989\pi$
$103$	1253.81	+	7916.23i	0.118183	+	0.746180i	−0.855420	+	0.517935i	$0.826701\pi$
$104$	409.775	−	1706.83i	0.0378860	−	0.157806i
$105$	476.154	+	655.370i	0.0431886	+	0.0594440i
$106$	−5720.03	+	4885.37i	−0.509081	+	0.434796i
$107$	−3766.64	+	5184.34i	−0.328993	+	0.452821i	−0.941186	−	0.337888i	$-0.890288\pi$
$107$	−3766.64	+	5184.34i	−0.328993	+	0.452821i	0.612193	+	0.790708i	$0.290288\pi$
$108$	320.228	+	4068.88i	0.0274544	+	0.348841i
$109$	−5200.79	−	12555.8i	−0.437740	−	1.05680i	−0.976727	−	0.214484i	$-0.931193\pi$
$109$	−5200.79	−	12555.8i	−0.437740	−	1.05680i	0.538987	−	0.842314i	$-0.318807\pi$
$110$	−1735.43	−	7228.59i	−0.143424	−	0.597404i
$111$	885.638	−	1036.95i	0.0718804	−	0.0841611i
$112$	74.8287	−	950.788i	0.00596530	−	0.0757963i
$113$	−3407.20	+	1107.07i	−0.266834	+	0.0866996i	−0.439378	−	0.898302i	$-0.644801\pi$
$113$	−3407.20	+	1107.07i	−0.266834	+	0.0866996i	0.172544	+	0.985002i	$0.444801\pi$
$114$	512.071	−	512.071i	0.0394022	−	0.0394022i
$115$	1791.43	+	912.780i	0.135458	+	0.0690193i
$116$	4085.82	−	2503.79i	0.303643	−	0.186072i
$117$	4597.67	+	2817.46i	0.335866	+	0.205819i
$118$	3192.46	+	6265.55i	0.229277	+	0.449982i
$119$	−125.270	+	385.542i	−0.00884614	+	0.0272256i
$120$	470.716	−	1136.41i	0.0326886	−	0.0789173i
$121$	12068.6	+	1911.48i	0.824304	+	0.130557i
$122$		−	1943.51i		−	0.130577i
$123$	5664.17	−	620.683i	0.374392	−	0.0410260i
$124$	−2469.82			−0.160628
$125$	2490.71	−	15725.8i	0.159406	−	1.00645i
$126$	2706.77	+	1121.18i	0.170495	+	0.0706212i
$127$	6637.79	+	2156.75i	0.411544	+	0.133719i	0.507469	−	0.861670i	$-0.330581\pi$
$127$	6637.79	+	2156.75i	0.411544	+	0.133719i	−0.0959256	+	0.995389i	$0.530581\pi$
$128$	−1290.32	+	657.448i	−0.0787546	+	0.0401275i
$129$	3007.40	−	4907.63i	0.180722	−	0.294912i
$130$	−1838.56	−	3000.26i	−0.108791	−	0.177530i
$131$	−9773.89	+	19182.3i	−0.569541	+	1.11779i	0.409154	+	0.912465i	$0.365824\pi$
$131$	−9773.89	+	19182.3i	−0.569541	+	1.11779i	−0.978695	+	0.205321i	$0.934176\pi$
$132$	3142.60	+	3142.60i	0.180360	+	0.180360i
$133$	−347.830	−	1070.51i	−0.0196636	−	0.0605184i
$134$	7535.72	+	593.074i	0.419677	+	0.0330293i
$135$	6221.50	+	5313.66i	0.341372	+	0.291559i
$136$	598.532	−	143.695i	0.0323601	−	0.00776896i
$137$	−6101.49	+	2527.32i	−0.325083	+	0.134654i	−0.539256	−	0.842142i	$-0.681294\pi$
$137$	−6101.49	+	2527.32i	−0.325083	+	0.134654i	0.214173	+	0.976796i	$0.431294\pi$
$138$	−1198.29	+	94.3071i	−0.0629220	+	0.00495207i
$139$	13468.8	+	9785.69i	0.697109	+	0.506479i	0.878989	−	0.476841i	$-0.158218\pi$
$139$	13468.8	+	9785.69i	0.697109	+	0.506479i	−0.181880	+	0.983321i	$0.558218\pi$
$140$	−1241.66	−	1453.80i	−0.0633500	−	0.0741733i
$141$	5013.52	−	3642.53i	0.252176	−	0.183217i
$142$	25147.0	+	6037.25i	1.24712	+	0.299408i
$143$	12557.4	−	1988.89i	0.614082	−	0.0972610i
$144$	−695.920	−	4393.87i	−0.0335610	−	0.211896i
$145$	2242.50	−	9340.67i	0.106659	−	0.444265i
$146$	−2845.28	−	3916.19i	−0.133481	−	0.183720i
$147$	5616.29	−	4796.76i	0.259905	−	0.221980i
$148$	−1891.73	+	2603.75i	−0.0863647	+	0.118871i
$149$	−1944.83	−	24711.4i	−0.0876010	−	1.11308i	−0.870910	−	0.491443i	$-0.836470\pi$
$149$	−1944.83	−	24711.4i	−0.0876010	−	1.11308i	0.783309	−	0.621633i	$-0.213530\pi$
$150$	1349.50	+	3257.99i	0.0599779	+	0.144799i
$151$	−1499.75	−	6246.89i	−0.0657755	−	0.273975i	0.929784	−	0.368104i	$-0.119993\pi$
$151$	−1499.75	−	6246.89i	−0.0657755	−	0.273975i	−0.995560	+	0.0941299i	$0.969993\pi$
$152$	−1109.99	+	1299.63i	−0.0480432	+	0.0562513i
$153$	−148.358	+	1885.07i	−0.00633765	+	0.0805274i
$154$	6569.76	−	2134.64i	0.277018	−	0.0900086i
$155$	−3500.94	+	3500.94i	−0.145721	+	0.145721i
$156$	1874.37	+	955.042i	0.0770207	+	0.0392440i
$157$	36881.6	−	22601.1i	1.49627	−	0.916916i	0.497494	−	0.867468i	$-0.334254\pi$
$157$	36881.6	−	22601.1i	1.49627	−	0.916916i	0.998777	−	0.0494479i	$-0.0157462\pi$
$158$	−3688.01	−	2260.02i	−0.147733	−	0.0905311i
$159$	−4092.75	−	8032.48i	−0.161890	−	0.317728i
$160$	−897.079	+	2760.93i	−0.0350422	+	0.107849i
$161$	−714.957	+	1726.06i	−0.0275822	+	0.0665892i
$162$	10897.7	+	1726.02i	0.415245	+	0.0657684i
$163$			19049.6i			0.716984i	0.933533	+	0.358492i	$0.116709\pi$
$163$			19049.6i			0.716984i	−0.933533	+	0.358492i	$0.883291\pi$
$164$	−13211.8	+	2509.19i	−0.491219	+	0.0932925i
$165$	8909.18			0.327243
$166$	−5058.33	+	31937.0i	−0.183566	+	1.15899i
$167$	−15244.6	−	6314.53i	−0.546618	−	0.226417i	0.0922460	−	0.995736i	$-0.470595\pi$
$167$	−15244.6	−	6314.53i	−0.546618	−	0.226417i	−0.638864	+	0.769320i	$0.720595\pi$
$168$	1087.04	+	353.202i	0.0385148	+	0.0125142i
$169$	−20086.0	+	10234.3i	−0.703266	+	0.358332i
$170$	644.725	−	1052.09i	0.0223088	−	0.0364047i
$171$	−2743.29	−	4476.64i	−0.0938165	−	0.153095i
$172$	−6167.11	+	12103.6i	−0.208461	+	0.409128i
$173$	−33283.9	−	33283.9i	−1.11210	−	1.11210i	−0.992867	−	0.119228i	$-0.961958\pi$
$173$	−33283.9	−	33283.9i	−1.11210	−	1.11210i	−0.119228	−	0.992867i	$-0.538042\pi$
$174$	1774.64	+	5461.79i	0.0586155	+	0.180400i
$175$	5464.27	+	430.047i	0.178425	+	0.0140424i
$176$	−7975.89	−	6812.05i	−0.257486	−	0.219914i
$177$	−8194.56	+	1967.34i	−0.261565	+	0.0627961i
$178$	−12277.3	+	5085.42i	−0.387492	+	0.160504i
$179$	−47049.7	+	3702.89i	−1.46842	+	0.115567i	−0.787284	−	0.616590i	$-0.788514\pi$
$179$	−47049.7	+	3702.89i	−1.46842	+	0.115567i	−0.681136	+	0.732157i	$0.738514\pi$
$180$	−7214.70	−	5241.79i	−0.222676	−	0.161784i
$181$	−2440.40	−	2857.34i	−0.0744909	−	0.0872177i	0.721909	−	0.691988i	$-0.243265\pi$
$181$	−2440.40	−	2857.34i	−0.0744909	−	0.0872177i	−0.796400	+	0.604770i	$0.793265\pi$
$182$	2645.28	−	1921.91i	0.0798600	−	0.0580217i
$183$	2264.82	+	543.735i	0.0676287	+	0.0162362i
$184$	2801.89	−	443.775i	0.0827589	−	0.0131077i
$185$	1009.27	+	6372.28i	0.0294893	+	0.186188i
$186$	690.982	−	2878.15i	0.0199729	−	0.0831930i
$187$	2620.55	+	3606.88i	0.0749393	+	0.103145i
$188$	−11121.4	+	9498.58i	−0.314662	+	0.268746i
$189$	−4468.78	+	6150.75i	−0.125102	+	0.172189i
$190$	268.814	+	3415.60i	0.00744636	+	0.0946150i
$191$	−12599.3	−	30417.4i	−0.345366	−	0.833787i	−0.997154	−	0.0753862i	$-0.975981\pi$
$191$	−12599.3	−	30417.4i	−0.345366	−	0.833787i	0.651789	−	0.758401i	$-0.274019\pi$
$192$	−405.150	−	1687.57i	−0.0109904	−	0.0457783i
$193$	26724.9	−	31290.8i	0.717466	−	0.840045i	−0.275143	−	0.961403i	$-0.588725\pi$
$193$	26724.9	−	31290.8i	0.717466	−	0.840045i	0.992609	+	0.121358i	$0.0387250\pi$
$194$	−733.407	+	9318.82i	−0.0194868	+	0.247604i
$195$	4010.66	−	1303.14i	0.105474	−	0.0342706i
$196$	−12325.9	+	12325.9i	−0.320853	+	0.320853i
$197$	−2279.95	−	1161.69i	−0.0587481	−	0.0299336i	0.424370	−	0.905489i	$-0.360496\pi$
$197$	−2279.95	−	1161.69i	−0.0587481	−	0.0299336i	−0.483118	+	0.875555i	$0.660496\pi$
$198$	27473.3	−	16835.7i	0.700779	−	0.429438i
$199$	−20481.1	−	12550.8i	−0.517187	−	0.316932i	0.239295	−	0.970947i	$-0.423084\pi$
$199$	−20481.1	−	12550.8i	−0.517187	−	0.316932i	−0.756482	+	0.654014i	$0.773084\pi$
$200$	−3778.42	−	7415.56i	−0.0944605	−	0.185389i
$201$	−2799.39	+	8615.64i	−0.0692902	+	0.213253i
$202$	−6297.78	+	15204.2i	−0.154342	+	0.372615i
$203$	8816.33	+	1396.37i	0.213942	+	0.0338850i
$204$			737.685i			0.0177260i
$205$	−15170.8	+	22284.3i	−0.360996	+	0.530264i
$206$	22669.6			0.534206
$207$	−1363.25	+	8607.22i	−0.0318152	+	0.200873i
$208$	−4586.91	−	1899.96i	−0.106021	−	0.0439155i
$209$	−11773.3	−	3825.39i	−0.269530	−	0.0875755i
$210$	2041.53	−	1040.21i	0.0462931	−	0.0235875i
$211$	−31057.8	+	50681.7i	−0.697598	+	1.13838i	0.286039	+	0.958218i	$0.407661\pi$
$211$	−31057.8	+	50681.7i	−0.697598	+	1.13838i	−0.983638	+	0.180159i	$0.942339\pi$
$212$	11116.9	+	18141.1i	0.247350	+	0.403638i
$213$	−14070.7	+	27615.4i	−0.310140	+	0.608683i
$214$	12816.4	+	12816.4i	0.279858	+	0.279858i
$215$	8414.94	+	25898.5i	0.182043	+	0.560271i
$216$	11508.5	+	905.741i	0.246668	+	0.0194132i
$217$	−3498.37	−	2987.89i	−0.0742928	−	0.0634520i
$218$	−37377.1	+	8973.46i	−0.786490	+	0.188820i
$219$	5359.65	−	2220.04i	0.111750	−	0.0462885i
$220$	−20961.7	+	1649.72i	−0.433093	+	0.0340851i
$221$	1707.27	+	1240.41i	0.0349557	+	0.0253968i
$222$	−2504.96	−	2932.93i	−0.0508271	−	0.0595109i
$223$	10769.6	−	7824.55i	0.216565	−	0.157344i	−0.474214	−	0.880410i	$-0.657268\pi$
$223$	10769.6	−	7824.55i	0.216565	−	0.157344i	0.690779	+	0.723066i	$0.257268\pi$
$224$	−2623.02	−	629.731i	−0.0522763	−	0.0125504i
$225$	25252.0	−	3999.52i	0.498804	−	0.0790029i
$226$	1585.14	+	10008.2i	0.0310350	+	0.195947i
$227$	764.303	−	3183.55i	0.0148325	−	0.0617817i	−0.964463	−	0.264218i	$-0.914886\pi$
$227$	764.303	−	3183.55i	0.0148325	−	0.0617817i	0.979295	+	0.202437i	$0.0648860\pi$
$228$	−1203.95	−	1657.10i	−0.0231600	−	0.0318770i
$229$	17964.0	−	15342.7i	0.342556	−	0.292571i	−0.461480	−	0.887150i	$-0.652682\pi$
$229$	17964.0	−	15342.7i	0.342556	−	0.292571i	0.804037	+	0.594580i	$0.202682\pi$
$230$	3342.59	−	4600.68i	0.0631869	−	0.0869694i
$231$	649.534	+	8253.12i	0.0121725	+	0.154666i
$232$	−5186.78	−	12522.0i	−0.0963655	−	0.232647i
$233$	−9403.94	−	39170.2i	−0.173220	−	0.721513i	−0.989582	−	0.143972i	$-0.954012\pi$
$233$	−9403.94	−	39170.2i	−0.173220	−	0.721513i	0.816362	−	0.577541i	$-0.195988\pi$
$234$	9905.16	−	11597.5i	0.180896	−	0.211802i
$235$	−2300.33	+	29228.5i	−0.0416539	+	0.529262i
$236$	18916.0	−	6146.19i	0.339630	−	0.110352i
$237$	3665.45	−	3665.45i	0.0652576	−	0.0652576i
$238$	1021.62	+	520.544i	0.0180359	+	0.00918974i
$239$	36507.5	−	22371.8i	0.639126	−	0.391657i	−0.164850	−	0.986319i	$-0.552714\pi$
$239$	36507.5	−	22371.8i	0.639126	−	0.391657i	0.803976	+	0.594662i	$0.202714\pi$
$240$	−2966.40	−	1817.81i	−0.0515000	−	0.0315593i
$241$	−6960.48	−	13660.7i	−0.119841	−	0.235201i	0.823291	−	0.567619i	$-0.192135\pi$
$241$	−6960.48	−	13660.7i	−0.119841	−	0.235201i	−0.943132	+	0.332418i	$0.892135\pi$
$242$	10679.9	−	32869.2i	0.182362	−	0.561253i
$243$	−20874.5	+	50395.6i	−0.353512	+	0.853454i
$244$	−5429.39	−	859.931i	−0.0911951	−	0.0144439i
$245$			34943.5i			0.582150i
$246$	772.247	−	16098.1i	0.0127610	−	0.266014i
$247$	−5859.55			−0.0960441
$248$	−1092.81	+	6899.71i	−0.0177681	+	0.112183i
$249$	−35801.9	−	14829.6i	−0.577440	−	0.239184i
$250$	−42829.5	−	13916.1i	−0.685272	−	0.222658i
$251$	43005.8	−	21912.5i	0.682621	−	0.347813i	−0.0780509	−	0.996949i	$-0.524870\pi$
$251$	43005.8	−	21912.5i	0.682621	−	0.347813i	0.760672	+	0.649137i	$0.224870\pi$
$252$	4329.79	−	7065.58i	0.0681814	−	0.111262i
$253$	10735.8	+	17519.2i	0.167723	+	0.273699i
$254$	8962.08	−	17589.1i	0.138912	−	0.272631i
$255$	1045.66	+	1045.66i	0.0160809	+	0.0160809i
$256$	1265.73	+	3895.53i	0.0193136	+	0.0594410i
$257$	−808.849	−	63.6578i	−0.0122462	−	0.000963797i	0.0723345	−	0.997380i	$-0.476955\pi$
$257$	−808.849	−	63.6578i	−0.0122462	−	0.000963797i	−0.0845807	+	0.996417i	$0.526955\pi$
$258$	−12379.3	−	10572.9i	−0.185976	−	0.158839i
$259$	−5829.45	+	1399.53i	−0.0869016	+	0.0208632i
$260$	−9195.05	+	3808.71i	−0.136021	+	0.0563419i
$261$	41507.8	−	3266.73i	0.609324	−	0.0479548i
$262$	49263.3	+	35791.9i	0.717663	+	0.521413i
$263$	32936.0	+	38563.1i	0.476168	+	0.557521i	0.945551	−	0.325474i	$-0.105524\pi$
$263$	32936.0	+	38563.1i	0.476168	+	0.557521i	−0.469384	+	0.882994i	$0.655524\pi$
$264$	10169.7	−	7388.70i	0.145915	−	0.106013i
$265$	41472.8	+	9956.74i	0.590570	+	0.141783i
$266$	−3144.48	+	498.037i	−0.0444412	+	0.00703880i
$267$	−2491.35	−	15729.8i	−0.0349472	−	0.220648i
$268$	4991.10	−	20789.4i	0.0694907	−	0.289449i
$269$	−37412.7	−	51494.1i	−0.517028	−	0.711628i	0.468057	−	0.883699i	$-0.344954\pi$
$269$	−37412.7	−	51494.1i	−0.517028	−	0.711628i	−0.985085	+	0.172070i	$0.944954\pi$
$270$	17597.1	−	15029.3i	0.241386	−	0.206163i
$271$	9576.69	−	13181.2i	0.130400	−	0.179480i	−0.738825	−	0.673898i	$-0.764619\pi$
$271$	9576.69	−	13181.2i	0.130400	−	0.179480i	0.869224	+	0.494418i	$0.164619\pi$
$272$	−136.598	−	1735.64i	−0.00184632	−	0.0234597i
$273$	1499.58	+	3620.31i	0.0201208	+	0.0485758i
$274$	4360.64	+	18163.4i	0.0580830	+	0.241933i
$275$	39149.5	−	45838.2i	0.517679	−	0.606125i
$276$	−266.741	+	3389.26i	−0.00350164	+	0.0444925i
$277$	108047.	−	35106.5i	1.40816	−	0.457539i	0.496339	−	0.868129i	$-0.334677\pi$
$277$	108047.	−	35106.5i	1.40816	−	0.457539i	0.911820	+	0.410590i	$0.134677\pi$
$278$	33296.8	−	33296.8i	0.430837	−	0.430837i
$279$	−19120.7	−	9742.48i	−0.245638	−	0.125159i
$280$	−4610.72	+	2825.46i	−0.0588103	+	0.0360390i
$281$	41683.4	+	25543.6i	0.527899	+	0.323497i	0.760782	−	0.649008i	$-0.224816\pi$
$281$	41683.4	+	25543.6i	0.527899	+	0.323497i	−0.232883	+	0.972505i	$0.574816\pi$
$282$	−7957.50	−	15617.5i	−0.100064	−	0.196387i
$283$	−5330.42	+	16405.3i	−0.0665562	+	0.204839i	−0.978804	−	0.204800i	$-0.934345\pi$
$283$	−5330.42	+	16405.3i	−0.0665562	+	0.204839i	0.912248	+	0.409639i	$0.134345\pi$
$284$	27992.3	−	67579.4i	0.347058	−	0.837872i
$285$	−4055.49	−	642.327i	−0.0499291	−	0.00790800i
$286$		−	35960.3i		−	0.439634i
$287$	−21749.4	−	12429.0i	−0.264048	−	0.150894i
$288$	−12582.6			−0.151701
$289$	12949.8	−	81761.8i	0.155048	−	0.978937i
$290$	−25101.9	−	10397.6i	−0.298477	−	0.123633i
$291$	−10654.3	−	3461.78i	−0.125817	−	0.0408803i
$292$	−12199.2	+	6215.80i	−0.143076	+	0.0729007i
$293$	−80634.8	+	131584.i	−0.939263	+	1.53274i	−0.0959017	+	0.995391i	$0.530573\pi$
$293$	−80634.8	+	131584.i	−0.939263	+	1.53274i	−0.843361	+	0.537347i	$0.819427\pi$
$294$	−10915.3	−	17812.1i	−0.126281	−	0.206073i
$295$	18101.0	−	35525.3i	0.207998	−	0.408220i
$296$	6436.82	+	6436.82i	0.0734662	+	0.0734662i
$297$	25838.2	+	79521.7i	0.292920	+	0.901515i
$298$	−69894.4	−	5500.81i	−0.787063	−	0.0619432i
$299$	7395.48	+	6316.33i	0.0827225	+	0.0706517i
$300$	9698.63	−	2328.44i	0.107763	−	0.0258715i
$301$	−23377.9	+	9683.44i	−0.258031	+	0.106880i
$302$	−18114.9	+	1425.68i	−0.198620	+	0.0156317i
$303$	−15955.9	−	11592.6i	−0.173795	−	0.126269i
$304$	3139.52	+	3675.91i	0.0339717	+	0.0397757i
$305$	−8915.03	+	6477.15i	−0.0958347	+	0.0696280i
$306$	5200.49	+	1248.53i	0.0555394	+	0.0133338i
$307$	100446.	−	15909.1i	1.06575	−	0.168799i	0.401163	−	0.916007i	$-0.368606\pi$
$307$	100446.	−	15909.1i	1.06575	−	0.168799i	0.664590	+	0.747208i	$0.268606\pi$
$308$	−3056.47	−	19297.8i	−0.0322195	−	0.203426i
$309$	−6342.26	+	26417.4i	−0.0664243	+	0.276677i
$310$	8231.20	+	11329.3i	0.0856524	+	0.117890i
$311$	−51303.4	+	43817.3i	−0.530427	+	0.453027i	−0.873879	−	0.486143i	$-0.838404\pi$
$311$	−51303.4	+	43817.3i	−0.530427	+	0.453027i	0.343453	+	0.939170i	$0.388404\pi$
$312$	3497.35	−	4813.69i	0.0359278	−	0.0494503i
$313$	10912.6	+	138658.i	0.111388	+	1.41532i	0.757876	+	0.652399i	$0.226237\pi$
$313$	10912.6	+	138658.i	0.111388	+	1.41532i	−0.646488	+	0.762924i	$0.723763\pi$
$314$	−46819.7	−	113033.i	−0.474864	−	1.14642i
$315$	−3877.94	−	16152.8i	−0.0390822	−	0.162789i
$316$	−7945.41	+	9302.88i	−0.0795687	+	0.0931629i
$317$	−14366.6	+	182545.i	−0.142967	+	1.81657i	0.339447	+	0.940625i	$0.389760\pi$
$317$	−14366.6	+	182545.i	−0.142967	+	1.81657i	−0.482414	+	0.875943i	$0.660240\pi$
$318$	−24250.5	+	7879.45i	−0.239809	+	0.0779187i
$319$	69416.3	−	69416.3i	0.682151	−	0.682151i
$320$	7316.01	+	3727.69i	0.0714454	+	0.0364033i
$321$	−18520.9	+	11349.6i	−0.179743	+	0.110147i
$322$	4505.59	+	2761.03i	0.0434550	+	0.0266292i
$323$	−932.839	−	1830.80i	−0.00894132	−	0.0175483i
$324$	9643.66	−	29680.1i	0.0918654	−	0.282733i
$325$	10919.3	−	26361.4i	0.103378	−	0.249575i
$326$	53216.9	+	8428.73i	0.500743	+	0.0793098i
$327$		−	46067.0i		−	0.430819i
$328$	1163.94	+	38018.9i	0.0108189	+	0.353388i
$329$	−27243.9			−0.251696
$330$	3941.99	−	24888.7i	0.0361982	−	0.228547i
$331$	−71714.5	−	29705.1i	−0.654562	−	0.271129i	0.0305862	−	0.999532i	$-0.490263\pi$
$331$	−71714.5	−	29705.1i	−0.654562	−	0.271129i	−0.685148	+	0.728404i	$0.740263\pi$
$332$	86981.3	+	28262.0i	0.789133	+	0.256405i
$333$	−24916.1	+	12695.4i	−0.224694	+	0.114487i
$334$	−24385.5	+	39793.5i	−0.218594	+	0.356713i
$335$	−22393.9	−	36543.5i	−0.199545	−	0.325627i
$336$	1467.68	−	2880.49i	0.0130003	−	0.0255145i
$337$	90622.0	+	90622.0i	0.797946	+	0.797946i	0.982771	−	0.184825i	$-0.0591718\pi$
$337$	90622.0	+	90622.0i	0.797946	+	0.797946i	−0.184825	+	0.982771i	$0.559172\pi$
$338$	19703.3	+	60640.6i	0.172467	+	0.530799i
$339$	−12106.3	−	952.786i	−0.105345	−	0.00829079i
$340$	−2653.87	−	2266.62i	−0.0229574	−	0.0196074i
$341$	−49199.5	+	11811.8i	−0.423109	+	0.101579i
$342$	−13719.8	+	5682.92i	−0.117299	+	0.0485869i
$343$	−68039.8	+	5354.84i	−0.578328	+	0.0455154i
$344$	31084.1	+	22583.9i	0.262676	+	0.190846i
$345$	4426.13	+	5182.33i	0.0371866	+	0.0435399i
$346$	−107709.	+	78255.1i	−0.899704	+	0.653673i
$347$	−75998.9	−	18245.7i	−0.631173	−	0.151531i	−0.0947779	−	0.995498i	$-0.530214\pi$
$347$	−75998.9	−	18245.7i	−0.631173	−	0.151531i	−0.536395	+	0.843967i	$0.680214\pi$
$348$	16043.3	−	2541.01i	0.132475	−	0.0209820i
$349$	−29363.2	−	185392.i	−0.241075	−	1.52209i	−0.750092	−	0.661333i	$-0.769991\pi$
$349$	−29363.2	−	185392.i	−0.241075	−	1.52209i	0.509017	−	0.860757i	$-0.330009\pi$
$350$	3619.12	−	15074.7i	0.0295439	−	0.123059i
$351$	23263.2	+	32019.1i	0.188823	+	0.259893i
$352$	−22559.2	+	19267.4i	−0.182070	+	0.155503i
$353$	−100996.	+	139009.i	−0.810500	+	1.11556i	0.180745	+	0.983530i	$0.442149\pi$
$353$	−100996.	+	139009.i	−0.810500	+	1.11556i	−0.991246	+	0.132028i	$0.957851\pi$
$354$	1870.17	+	23762.8i	0.0149237	+	0.189623i
$355$	−56114.2	−	135472.i	−0.445262	−	1.07496i
$356$	8774.40	+	36548.0i	0.0692337	+	0.288379i
$357$	−892.422	+	1044.89i	−0.00700219	+	0.00819851i
$358$	−10473.3	+	133077.i	−0.0817183	+	1.03833i
$359$	123444.	−	40109.4i	0.957814	−	0.311213i	0.211927	−	0.977285i	$-0.432026\pi$
$359$	123444.	−	40109.4i	0.957814	−	0.311213i	0.745887	+	0.666073i	$0.232026\pi$
$360$	−17835.7	+	17835.7i	−0.137621	+	0.137621i
$361$	−111033.	−	56574.3i	−0.851999	−	0.434115i
$362$	−9062.06	+	5553.24i	−0.0691528	+	0.0423769i
$363$	35315.4	+	21641.3i	0.268010	+	0.164237i
$364$	−4198.62	−	8240.25i	−0.0316886	−	0.0621925i
$365$	−8481.38	+	26103.0i	−0.0636621	+	0.195932i
$366$	2521.08	−	6086.43i	0.0188202	−	0.0454360i
$367$	−115858.	−	18350.2i	−0.860193	−	0.136241i	−0.289273	−	0.957247i	$-0.593413\pi$
$367$	−115858.	−	18350.2i	−0.860193	−	0.136241i	−0.570920	+	0.821006i	$0.693413\pi$
$368$		−	8023.72i		−	0.0592489i
$369$	−112180.	−	32690.0i	−0.823880	−	0.240084i
$370$	18248.2			0.133296
$371$	−6199.91	+	39144.7i	−0.0450441	+	0.284397i
$372$	−7734.67	−	3203.80i	−0.0558928	−	0.0231516i
$373$	18257.1	+	5932.09i	0.131224	+	0.0426373i	0.373893	−	0.927472i	$-0.378023\pi$
$373$	18257.1	+	5932.09i	0.131224	+	0.0426373i	−0.242669	+	0.970109i	$0.578023\pi$
$374$	11235.7	−	5724.87i	0.0803261	−	0.0409282i
$375$	28199.2	−	46017.0i	0.200528	−	0.327232i
$376$	21614.4	+	35271.6i	0.152886	+	0.249488i
$377$	21095.7	−	41402.7i	0.148427	−	0.291304i
$378$	15205.5	+	15205.5i	0.106418	+	0.106418i
$379$	−11119.7	−	34223.0i	−0.0774134	−	0.238254i	0.904860	−	0.425710i	$-0.139976\pi$
$379$	−11119.7	−	34223.0i	−0.0774134	−	0.238254i	−0.982273	+	0.187456i	$0.939976\pi$
$380$	9660.78	+	760.320i	0.0669029	+	0.00526537i
$381$	17989.7	+	15364.6i	0.123929	+	0.105845i
$382$	−90548.9	+	21738.9i	−0.620521	+	0.148974i
$383$	120641.	−	49971.2i	0.822429	−	0.340661i	0.0685278	−	0.997649i	$-0.478170\pi$
$383$	120641.	−	49971.2i	0.822429	−	0.340661i	0.753901	+	0.656988i	$0.228170\pi$
$384$	−4893.67	+	385.140i	−0.0331873	+	0.00261190i
$385$	−31686.9	−	23021.9i	−0.213776	−	0.155317i
$386$	−75589.4	−	88503.9i	−0.507325	−	0.594002i
$387$	−95488.2	+	69376.3i	−0.637570	+	0.463222i
$388$	25708.6	+	6172.09i	0.170771	+	0.0409986i
$389$	−20793.5	+	3293.36i	−0.137413	+	0.0217641i	−0.224762	−	0.974414i	$-0.572160\pi$
$389$	−20793.5	+	3293.36i	−0.137413	+	0.0217641i	0.0873490	+	0.996178i	$0.472160\pi$
$390$	−1865.89	−	11780.8i	−0.0122675	−	0.0774542i
$391$	−796.162	+	3316.25i	−0.00520772	+	0.0216917i
$392$	28979.9	+	39887.4i	0.188593	+	0.259576i
$393$	−55491.5	+	47394.3i	−0.359287	+	0.306860i
$394$	−4254.11	+	5855.28i	−0.0274041	+	0.0377186i
$395$	1924.19	+	24449.2i	0.0123326	+	0.156701i
$396$	−34876.3	−	84198.8i	−0.222403	−	0.536927i
$397$	−50706.3	−	211207.i	−0.321722	−	1.34007i	−0.865529	−	0.500859i	$-0.833017\pi$
$397$	−50706.3	−	211207.i	−0.321722	−	1.34007i	0.543806	−	0.839211i	$-0.316983\pi$
$398$	−44124.2	+	51662.8i	−0.278555	+	0.326146i
$399$	299.356	−	3803.68i	0.00188037	−	0.0238923i
$400$	−22388.0	+	7274.29i	−0.139925	+	0.0454643i
$401$	164594.	−	164594.i	1.02359	−	1.02359i	0.0238746	−	0.999715i	$-0.492400\pi$
$401$	164594.	−	164594.i	1.02359	−	1.02359i	0.999715	−	0.0238746i	$-0.00760025\pi$
$402$	22830.1	+	11632.5i	0.141272	+	0.0719815i
$403$	−20420.5	+	12513.7i	−0.125735	+	0.0770505i
$404$	39688.0	+	24320.8i	0.243162	+	0.149010i
$405$	−28401.4	−	55740.9i	−0.173153	−	0.339832i
$406$	7801.81	−	24011.5i	0.0473307	−	0.145669i
$407$	−25231.6	+	60914.4i	−0.152320	+	0.367732i
$408$	2060.80	+	326.399i	0.0123799	+	0.00196078i
$409$		−	57074.7i		−	0.341190i	−0.985341	−	0.170595i	$-0.945431\pi$
$409$		−	57074.7i		−	0.341190i	0.985341	−	0.170595i	$-0.0545690\pi$
$410$	55541.1	+	52241.3i	0.330405	+	0.310775i
$411$	−22386.2			−0.132525
$412$	10030.5	−	63329.8i	0.0590917	−	0.373090i
$413$	34228.9	+	14178.1i	0.200675	+	0.0831223i
$414$	23442.0	+	7616.76i	0.136771	+	0.0444395i
$415$	163356.	−	83233.9i	0.948502	−	0.483286i
$416$	−7337.28	+	11973.4i	−0.0423983	+	0.0691877i
$417$	29486.2	+	48117.1i	0.169569	+	0.276711i
$418$	−15895.9	+	31197.4i	−0.0909771	+	0.178553i
$419$	122002.	+	122002.i	0.694925	+	0.694925i	0.963311	−	0.268386i	$-0.0864904\pi$
$419$	122002.	+	122002.i	0.694925	+	0.694925i	−0.268386	+	0.963311i	$0.586490\pi$
$420$	−2002.63	−	6163.47i	−0.0113528	−	0.0349403i
$421$	137637.	+	10832.3i	0.776554	+	0.0611161i	0.460540	−	0.887639i	$-0.347656\pi$
$421$	137637.	+	10832.3i	0.776554	+	0.0611161i	0.316013	+	0.948755i	$0.397656\pi$
$422$	127843.	+	109188.i	0.717878	+	0.613126i
$423$	−123567.	+	29665.8i	−0.690593	+	0.165797i
$424$	55597.9	−	23029.4i	0.309262	−	0.128101i
$425$	9974.89	−	785.041i	0.0552243	−	0.00434625i
$426$	70920.6	+	51526.8i	0.390799	+	0.283932i
$427$	−6650.14	−	7786.31i	−0.0364733	−	0.0427047i
$428$	41474.7	−	30133.2i	0.226410	−	0.164497i
$429$	41905.5	+	10060.6i	0.227696	+	0.0546651i
$430$	76073.6	−	12048.9i	0.411431	−	0.0651642i
$431$	−52809.1	−	333424.i	−0.284285	−	1.79491i	−0.554581	−	0.832130i	$-0.687121\pi$
$431$	−52809.1	−	333424.i	−0.284285	−	1.79491i	0.270295	−	0.962777i	$-0.412879\pi$
$432$	7622.39	−	31749.5i	0.0408436	−	0.170126i
$433$	1350.16	+	1858.34i	0.00720127	+	0.00991170i	0.812602	−	0.582818i	$-0.198050\pi$
$433$	1350.16	+	1858.34i	0.00720127	+	0.00991170i	−0.805401	+	0.592730i	$0.798050\pi$
$434$	−9894.89	+	8451.03i	−0.0525329	+	0.0448674i
$435$	19139.3	−	26343.0i	0.101146	−	0.139215i
$436$	8530.27	+	108387.i	0.0448735	+	0.570172i
$437$	−3623.89	−	8748.84i	−0.0189763	−	0.0458129i
$438$	−3830.46	−	15955.0i	−0.0199666	−	0.0831667i
$439$	206198.	−	241427.i	1.06993	−	1.25273i	0.103820	−	0.994596i	$-0.466893\pi$
$439$	206198.	−	241427.i	1.06993	−	1.25273i	0.966110	−	0.258131i	$-0.0831067\pi$
$440$	−4666.11	+	59288.6i	−0.0241018	+	0.306243i
$441$	−144045.	+	46802.9i	−0.740661	+	0.240655i
$442$	4220.61	−	4220.61i	0.0216038	−	0.0216038i
$443$	260098.	+	132526.i	1.32535	+	0.675297i	0.966154	−	0.257967i	$-0.0830524\pi$
$443$	260098.	+	132526.i	1.32535	+	0.675297i	0.359192	+	0.933264i	$0.383052\pi$
$444$	−9301.81	+	5700.16i	−0.0471848	+	0.0289149i
$445$	64243.8	+	39368.7i	0.324423	+	0.198807i
$446$	−17093.5	−	33548.0i	−0.0859335	−	0.168654i
$447$	25964.6	−	79910.7i	0.129947	−	0.399936i
$448$	−2919.81	+	7049.04i	−0.0145478	+	0.0351216i
$449$	285155.	+	45164.1i	1.41445	+	0.224027i	0.816426	−	0.577450i	$-0.195952\pi$
$449$	285155.	+	45164.1i	1.41445	+	0.224027i	0.598026	+	0.801477i	$0.295952\pi$
$450$		−	72313.7i		−	0.357105i
$451$	−251183.	+	113169.i	−1.23492	+	0.556381i
$452$	28660.4			0.140283
$453$	3406.64	−	21508.6i	0.0166008	−	0.104813i
$454$	−8555.41	−	3543.76i	−0.0415077	−	0.0171931i
$455$	−17631.9	−	5728.96i	−0.0851681	−	0.0276728i
$456$	−5161.98	+	2630.16i	−0.0248248	+	0.0126489i
$457$	−74604.5	+	121743.i	−0.357217	+	0.582926i	−0.979886	−	0.199560i	$-0.936049\pi$
$457$	−74604.5	+	121743.i	−0.357217	+	0.582926i	0.622668	+	0.782486i	$0.286049\pi$
$458$	−34913.0	−	56972.9i	−0.166440	−	0.271605i
$459$	−6300.76	+	12365.9i	−0.0299067	+	0.0586951i
$460$	−11373.5	−	11373.5i	−0.0537500	−	0.0537500i
$461$	76621.2	+	235816.i	0.360535	+	1.10961i	0.952730	+	0.303817i	$0.0982612\pi$
$461$	76621.2	+	235816.i	0.360535	+	1.10961i	−0.592196	+	0.805794i	$0.701739\pi$
$462$	23343.3	+	1837.16i	0.109365	+	0.00860723i
$463$	34849.2	+	29764.0i	0.162567	+	0.138845i	0.727010	−	0.686627i	$-0.240909\pi$
$463$	34849.2	+	29764.0i	0.162567	+	0.138845i	−0.564444	+	0.825472i	$0.690909\pi$
$464$	−37276.4	+	8949.28i	−0.173140	+	0.0415673i
$465$	−15505.1	+	6422.43i	−0.0717083	+	0.0297025i
$466$	−113587.	+	8939.49i	−0.523067	+	0.0411662i
$467$	14264.1	+	10363.5i	0.0654052	+	0.0475196i	0.620007	−	0.784596i	$-0.287130\pi$
$467$	14264.1	+	10363.5i	0.0654052	+	0.0475196i	−0.554602	+	0.832116i	$0.687130\pi$
$468$	−28016.0	−	32802.5i	−0.127913	−	0.149767i
$469$	32219.8	−	23409.1i	0.146480	−	0.106424i
$470$	80635.1	+	19358.8i	0.365030	+	0.0876359i
$471$	144819.	−	22937.0i	0.652803	−	0.103394i
$472$	−8800.37	−	55563.3i	−0.0395018	−	0.249404i
$473$	−64965.7	+	270602.i	−0.290377	+	1.20951i
$474$	−8617.99	−	11861.7i	−0.0383574	−	0.0527945i
$475$	−21125.8	+	18043.1i	−0.0936324	+	0.0799696i
$476$	1906.22	−	2623.69i	0.00841318	−	0.0115797i
$477$	14504.4	+	184295.i	0.0637473	+	0.809986i
$478$	−46344.8	−	111886.i	−0.202836	−	0.489690i
$479$	−38000.8	−	158285.i	−0.165623	−	0.689871i	−0.991945	−	0.126672i	$-0.959570\pi$
$479$	−38000.8	−	158285.i	−0.165623	−	0.689871i	0.826321	−	0.563199i	$-0.190430\pi$
$480$	−6390.78	+	7482.64i	−0.0277377	+	0.0324767i
$481$	−2448.61	+	31112.5i	−0.0105835	+	0.134476i
$482$	−41242.4	+	13400.5i	−0.177521	+	0.0576800i
$483$	−4478.02	+	4478.02i	−0.0191952	+	0.0191952i
$484$	−87098.1	−	44378.7i	−0.371807	−	0.189445i
$485$	45190.4	−	27692.7i	0.192116	−	0.117729i
$486$	131549.	+	80613.4i	0.556949	+	0.341299i
$487$	−184083.	−	361283.i	−0.776167	−	1.52331i	−0.850438	−	0.526076i	$-0.823663\pi$
$487$	−184083.	−	361283.i	−0.776167	−	1.52331i	0.0742702	−	0.997238i	$-0.476337\pi$
$488$	−4804.62	+	14787.1i	−0.0201753	+	0.0620931i
$489$	−24710.7	+	59656.9i	−0.103340	+	0.249484i
$490$	97618.4	+	15461.2i	0.406574	+	0.0643950i
$491$			182075.i			0.755246i	0.925959	+	0.377623i	$0.123258\pi$
$491$			182075.i			0.755246i	−0.925959	+	0.377623i	$0.876742\pi$
$492$	−44630.0	−	9280.17i	−0.184373	−	0.0383377i
$493$	16294.6			0.0670424
$494$	−2592.64	+	16369.3i	−0.0106240	+	0.0670773i
$495$	−168787.	−	69914.0i	−0.688857	−	0.285334i
$496$	18791.5	+	6105.74i	0.0763833	+	0.0248185i
$497$	121405.	−	61858.7i	0.491498	−	0.250431i
$498$	−57269.1	+	93454.7i	−0.230920	+	0.376827i
$499$	−10612.4	−	17317.8i	−0.0426198	−	0.0695492i	0.830621	−	0.556838i	$-0.187986\pi$
$499$	−10612.4	−	17317.8i	−0.0426198	−	0.0695492i	−0.873241	+	0.487289i	$0.837986\pi$
$500$	−57826.7	+	113491.i	−0.231307	+	0.453965i
$501$	−39550.1	−	39550.1i	−0.157569	−	0.157569i
$502$	−42186.5	−	129837.i	−0.167404	−	0.515217i
$503$	343286.	+	27017.2i	1.35681	+	0.106783i	0.735897	−	0.677094i	$-0.236761\pi$
$503$	343286.	+	27017.2i	1.35681	+	0.106783i	0.620916	+	0.783877i	$0.286761\pi$
$504$	−17822.7	−	15222.0i	−0.0701635	−	0.0599253i
$505$	90731.5	−	21782.7i	0.355775	−	0.0854140i
$506$	53692.0	−	22240.0i	0.209705	−	0.0868626i
$507$	−76178.4	+	5995.37i	−0.296358	+	0.0233239i
$508$	−45171.5	−	32819.0i	−0.175040	−	0.127174i
$509$	−139366.	−	163177.i	−0.537925	−	0.629829i	0.423169	−	0.906051i	$-0.360918\pi$
$509$	−139366.	−	163177.i	−0.537925	−	0.629829i	−0.961094	+	0.276222i	$0.910918\pi$
$510$	3383.82	−	2458.49i	0.0130097	−	0.00945210i
$511$	−24799.2	−	5953.75i	−0.0949719	−	0.0228007i
$512$	11442.6	−	1812.33i	0.0436501	−	0.00691349i
$513$	−6028.34	−	38061.4i	−0.0229067	−	0.144627i
$514$	−535.721	+	2231.44i	−0.00202774	+	0.00844615i
$515$	−75551.1	−	103987.i	−0.284856	−	0.392071i
$516$	−35014.0	+	29904.8i	−0.131505	+	0.112316i
$517$	−176115.	+	242401.i	−0.658893	+	0.906889i
$518$	1330.41	+	16904.4i	0.00495821	+	0.0630000i
$519$	−61059.0	−	147409.i	−0.226681	−	0.547256i
$520$	6571.56	+	27372.5i	0.0243031	+	0.101230i
$521$	−2734.35	+	3201.51i	−0.0100735	+	0.0117945i	−0.765420	−	0.643531i	$-0.777469\pi$
$521$	−2734.35	+	3201.51i	−0.0100735	+	0.0117945i	0.755346	+	0.655326i	$0.227469\pi$
$522$	9239.71	−	117402.i	0.0339092	−	0.430857i
$523$	−311430.	+	101190.i	−1.13856	+	0.369941i	−0.816823	−	0.576888i	$-0.804267\pi$
$523$	−311430.	+	101190.i	−1.13856	+	0.369941i	−0.321738	+	0.946829i	$0.604267\pi$
$524$	121786.	−	121786.i	0.443540	−	0.443540i
$525$	16554.4	+	8434.91i	0.0600615	+	0.0306028i
$526$	122303.	−	74947.5i	0.442045	−	0.270885i
$527$	−7160.81	−	4388.15i	−0.0257834	−	0.0158001i
$528$	−16141.4	−	31679.3i	−0.0578993	−	0.113634i
$529$	81618.6	−	251196.i	0.291660	−	0.897639i
$530$	46165.4	−	111453.i	0.164348	−	0.396771i
$531$	170687.	+	27034.2i	0.605357	+	0.0958791i
$532$			9004.80i			0.0318164i
$533$	−96522.4	+	87685.7i	−0.339761	+	0.308656i
$534$	−45045.1			−0.157967
$535$	16076.5	−	101503.i	0.0561674	−	0.354627i
$536$	−55869.0	−	23141.7i	−0.194465	−	0.0805501i
$537$	−152147.	−	49435.7i	−0.527613	−	0.171432i
$538$	−160408.	+	81731.9i	−0.554193	+	0.282376i
$539$	−186587.	+	304483.i	−0.642250	+	1.04806i
$540$	−34199.9	−	55809.1i	−0.117284	−	0.191389i
$541$	−212100.	+	416270.i	−0.724681	+	1.42227i	0.174486	+	0.984660i	$0.444174\pi$
$541$	−212100.	+	416270.i	−0.724681	+	1.42227i	−0.899167	+	0.437606i	$0.855826\pi$
$542$	−32585.7	−	32585.7i	−0.110925	−	0.110925i
$543$	−3936.04	−	12113.9i	−0.0133493	−	0.0410850i
$544$	−4909.13	−	386.357i	−0.0165885	−	0.00130554i
$545$	165729.	+	141546.i	0.557963	+	0.476546i
$546$	10777.2	−	2587.38i	0.0361511	−	0.00867911i
$547$	−21750.5	+	9009.33i	−0.0726932	+	0.0301105i	−0.418734	−	0.908109i	$-0.637526\pi$
$547$	−21750.5	+	9009.33i	−0.0726932	+	0.0301105i	0.346041	+	0.938220i	$0.387526\pi$
$548$	52670.7	−	4145.28i	0.175391	−	0.0138036i
$549$	−38640.8	−	28074.2i	−0.128204	−	0.0931456i
$550$	−110732.	−	129650.i	−0.366055	−	0.428595i
$551$	−36603.3	+	26593.8i	−0.120564	+	0.0875947i
$552$	9350.24	+	2244.79i	0.0306863	+	0.00736713i
$553$	−22508.5	+	3565.00i	−0.0736031	+	0.0116576i
$554$	−50266.9	−	317373.i	−0.163781	−	1.03407i
$555$	−5105.29	+	21265.1i	−0.0165743	+	0.0690369i
$556$	−78285.5	−	107751.i	−0.253240	−	0.348555i
$557$	−98655.5	+	84259.8i	−0.317988	+	0.271588i	−0.794087	−	0.607804i	$-0.792051\pi$
$557$	−98655.5	+	84259.8i	−0.317988	+	0.271588i	0.476099	+	0.879392i	$0.342051\pi$
$558$	−35676.9	+	49105.0i	−0.114582	+	0.157709i
$559$	10335.1	+	131320.i	0.0330742	+	0.420248i
$560$	5853.13	+	14130.7i	0.0186643	+	0.0450596i
$561$	3527.93	+	14694.9i	0.0112097	+	0.0466918i
$562$	89802.2	−	105145.i	0.284325	−	0.332901i
$563$	−38160.0	+	484869.i	−0.120390	+	1.52970i	0.579215	+	0.815175i	$0.303359\pi$
$563$	−38160.0	+	484869.i	−0.120390	+	1.52970i	−0.699606	+	0.714529i	$0.746641\pi$
$564$	−47149.9	+	15319.9i	−0.148225	+	0.0481614i
$565$	40625.6	−	40625.6i	0.127263	−	0.127263i
$566$	43471.5	+	22149.8i	0.135698	+	0.0691413i
$567$	49565.6	−	30373.8i	0.154175	−	0.0944786i
$568$	−176405.	−	108101.i	−0.546781	−	0.335068i
$569$	−104836.	−	205752.i	−0.323807	−	0.635507i	0.670518	−	0.741893i	$-0.266072\pi$
$569$	−104836.	−	205752.i	−0.323807	−	0.635507i	−0.994325	+	0.106386i	$0.966072\pi$
$570$	−3588.81	+	11045.2i	−0.0110459	+	0.0339958i
$571$	−175811.	+	424446.i	−0.539230	+	1.30182i	0.386031	+	0.922486i	$0.373846\pi$
$571$	−175811.	+	424446.i	−0.539230	+	1.30182i	−0.925261	+	0.379331i	$0.876154\pi$
$572$	−100459.	−	15911.1i	−0.307041	−	0.0486305i
$573$		−	111601.i		−	0.339905i
$574$	−44345.0	+	55259.8i	−0.134593	+	0.167720i
$575$	46113.1			0.139472
$576$	−5567.36	+	35150.9i	−0.0167805	+	0.105948i
$577$	−483486.	−	200266.i	−1.45222	−	0.601529i	−0.489493	−	0.872007i	$-0.662818\pi$
$577$	−483486.	−	200266.i	−1.45222	−	0.601529i	−0.962726	+	0.270478i	$0.912818\pi$
$578$	−222680.	−	72353.2i	−0.666540	−	0.216572i
$579$	124283.	−	63325.6i	0.370729	−	0.188896i
$580$	−40153.3	+	65524.3i	−0.119362	+	0.194781i
$581$	89014.3	+	145258.i	0.263698	+	0.430317i
$582$	−14385.0	+	28232.1i	−0.0424681	+	0.0833484i
$583$	308210.	+	308210.i	0.906796	+	0.906796i
$584$	11966.8	+	36830.0i	0.0350875	+	0.107988i
$585$	−86209.4	−	6784.83i	−0.251909	−	0.0198256i
$586$	331916.	+	283483.i	0.966568	+	0.825527i
$587$	−539593.	+	129545.i	−1.56599	+	0.375962i	−0.921416	−	0.388577i	$-0.872967\pi$
$587$	−539593.	+	129545.i	−1.56599	+	0.375962i	−0.644578	+	0.764539i	$0.722967\pi$
$588$	−54589.5	+	22611.7i	−0.157890	+	0.0654002i
$589$	23247.4	−	1829.61i	0.0670106	−	0.00527385i
$590$	−91234.6	−	66285.8i	−0.262093	−	0.190422i
$591$	−5633.13	−	6595.55i	−0.0161278	−	0.0188832i
$592$	20830.0	−	15133.9i	0.0594354	−	0.0431824i
$593$	425465.	+	102145.i	1.20991	+	0.290474i	0.787721	−	0.616032i	$-0.211261\pi$
$593$	425465.	+	102145.i	1.20991	+	0.290474i	0.422192	+	0.906507i	$0.361261\pi$
$594$	233585.	−	36996.2i	0.662021	−	0.104854i
$595$	−1017.00	−	6421.09i	−0.00287268	−	0.0181374i
$596$	−46292.8	+	192823.i	−0.130323	+	0.542834i
$597$	−47859.4	−	65872.8i	−0.134282	−	0.184824i
$598$	20917.6	−	17865.3i	0.0584937	−	0.0499583i
$599$	327084.	−	450193.i	0.911603	−	1.25471i	−0.0550129	−	0.998486i	$-0.517520\pi$
$599$	327084.	−	450193.i	0.911603	−	1.25471i	0.966616	−	0.256229i	$-0.0824800\pi$
$600$	−2213.44	−	28124.4i	−0.00614844	−	0.0781233i
$601$	−12577.1	−	30363.7i	−0.0348201	−	0.0840632i	0.905513	−	0.424319i	$-0.139486\pi$
$601$	−12577.1	−	30363.7i	−0.0348201	−	0.0840632i	−0.940333	+	0.340256i	$0.889486\pi$
$602$	16707.8	+	69593.1i	0.0461028	+	0.192032i
$603$	120646.	−	141258.i	0.331801	−	0.388489i
$604$	−4032.42	+	51236.8i	−0.0110533	+	0.140446i
$605$	−186367.	+	60554.2i	−0.509163	+	0.165437i
$606$	−39445.2	+	39445.2i	−0.107411	+	0.107411i
$607$	305371.	+	155594.i	0.828802	+	0.422295i	0.816301	−	0.577626i	$-0.196021\pi$
$607$	305371.	+	155594.i	0.828802	+	0.422295i	0.0125003	+	0.999922i	$0.496021\pi$
$608$	11658.2	−	7144.13i	0.0315372	−	0.0193260i
$609$	25798.5	+	15809.3i	0.0695600	+	0.0426264i
$610$	14150.0	+	27771.0i	0.0380274	+	0.0746330i
$611$	−43826.0	+	134882.i	−0.117395	+	0.361304i
$612$	5788.92	−	13975.7i	0.0154559	−	0.0373139i
$613$	696921.	+	110381.i	1.85465	+	0.293748i	0.981176	−	0.193118i	$-0.0618600\pi$
$613$	696921.	+	110381.i	1.85465	+	0.293748i	0.873477	+	0.486866i	$0.161860\pi$
$614$		−	287646.i		−	0.762995i
$615$	−76416.9	+	50107.9i	−0.202041	+	0.132482i
$616$	−55262.8			−0.145637
$617$	106060.	−	669638.i	0.278601	−	1.75902i	−0.310137	−	0.950692i	$-0.600375\pi$
$617$	106060.	−	669638.i	0.278601	−	1.75902i	0.588738	−	0.808324i	$-0.299625\pi$
$618$	70993.6	+	29406.5i	0.185884	+	0.0769957i
$619$	420396.	+	136595.i	1.09718	+	0.356495i	0.801016	−	0.598643i	$-0.204293\pi$
$619$	420396.	+	136595.i	1.09718	+	0.356495i	0.296162	+	0.955138i	$0.404293\pi$
$620$	35291.5	−	17981.9i	0.0918093	−	0.0467792i
$621$	−33420.0	+	54536.5i	−0.0866610	+	0.141418i
$622$	99708.2	+	162709.i	0.257721	+	0.420563i
$623$	−31785.8	+	62383.2i	−0.0818950	+	0.160728i
$624$	−11900.1	−	11900.1i	−0.0305620	−	0.0305620i
$625$	7865.72	+	24208.2i	0.0201362	+	0.0619730i
$626$	392183.	+	30865.5i	1.00078	+	0.0787634i
$627$	−31908.0	−	27252.0i	−0.0811641	−	0.0693207i
$628$	−336484.	+	80782.8i	−0.853190	+	0.204833i
$629$	−10110.8	+	4188.05i	−0.0255556	+	0.0105855i
$630$	−46840.3	+	3686.41i	−0.118015	+	0.00928801i
$631$	−263127.	−	191173.i	−0.660856	−	0.480140i	0.206096	−	0.978532i	$-0.433924\pi$
$631$	−263127.	−	191173.i	−0.660856	−	0.480140i	−0.866952	+	0.498392i	$0.833924\pi$
$632$	22473.0	+	26312.5i	0.0562635	+	0.0658762i
$633$	−163006.	+	118431.i	−0.406814	+	0.295568i
$634$	503602.	+	120904.i	1.25288	+	0.300790i
$635$	−110550.	+	17509.5i	−0.274166	+	0.0434236i
$636$	11282.1	+	71232.6i	0.0278918	+	0.176102i
$637$	−39459.7	+	164361.i	−0.0972467	+	0.405061i
$638$	−163208.	−	224636.i	−0.400958	−	0.551871i
$639$	483283.	−	412763.i	1.18359	−	1.01088i
$640$	13650.8	−	18788.7i	0.0333271	−	0.0458708i
$641$	−39565.1	−	502722.i	−0.0962934	−	1.22352i	−0.835288	−	0.549812i	$-0.814699\pi$
$641$	−39565.1	−	502722.i	−0.0962934	−	1.22352i	0.738995	−	0.673711i	$-0.235301\pi$
$642$	23511.6	+	56761.9i	0.0570442	+	0.137717i
$643$	178739.	+	744500.i	0.432311	+	1.80071i	0.583399	+	0.812185i	$0.301722\pi$
$643$	178739.	+	744500.i	0.432311	+	1.80071i	−0.151088	+	0.988520i	$0.548278\pi$
$644$	9706.77	−	11365.2i	0.0234047	−	0.0274034i
$645$	−7242.24	+	92021.3i	−0.0174082	+	0.221192i
$646$	−5527.28	+	1795.92i	−0.0132448	+	0.00430351i
$647$	78178.9	−	78178.9i	0.186759	−	0.186759i	−0.607535	−	0.794293i	$-0.707841\pi$
$647$	78178.9	−	78178.9i	0.186759	−	0.186759i	0.794293	+	0.607535i	$0.207841\pi$
$648$	−78647.6	−	40073.0i	−0.187299	−	0.0954336i
$649$	347418.	−	212898.i	0.824828	−	0.505455i
$650$	−68812.0	−	42168.0i	−0.162869	−	0.0998060i
$651$	−7079.91	−	13895.1i	−0.0167057	−	0.0327869i
$652$	47093.1	−	144938.i	0.110780	−	0.340946i
$653$	109422.	−	264168.i	0.256613	−	0.619518i	−0.742098	−	0.670292i	$-0.766169\pi$
$653$	109422.	−	264168.i	0.256613	−	0.619518i	0.998710	+	0.0507743i	$0.0161689\pi$
$654$	−128693.	−	20383.0i	−0.300884	−	0.0476554i
$655$		−	345258.i		−	0.804751i
$656$	106725.	+	13570.4i	0.248003	+	0.0315344i
$657$	−118962.			−0.275599
$658$	−12054.4	+	76108.6i	−0.0278416	+	0.175785i
$659$	−378897.	−	156944.i	−0.872470	−	0.361389i	−0.0988982	−	0.995098i	$-0.531532\pi$
$659$	−378897.	−	156944.i	−0.872470	−	0.361389i	−0.773572	+	0.633709i	$0.781532\pi$
$660$	−67785.1	−	22024.7i	−0.155613	−	0.0505618i
$661$	228829.	−	116594.i	0.523731	−	0.266854i	−0.172075	−	0.985084i	$-0.555047\pi$
$661$	228829.	−	116594.i	0.523731	−	0.266854i	0.695806	+	0.718230i	$0.255047\pi$
$662$	−114715.	+	187198.i	−0.261761	+	0.427156i
$663$	3737.59	+	6099.19i	0.00850284	+	0.0138754i
$664$	117439.	−	230487.i	0.266364	−	0.522769i
$665$	12764.2	+	12764.2i	0.0288635	+	0.0288635i
$666$	24441.4	+	75222.8i	0.0551033	+	0.169590i
$667$	74864.8	+	5891.99i	0.168278	+	0.0132437i
$668$	100378.	+	85730.6i	0.224949	+	0.192125i
$669$	43876.6	−	10533.8i	0.0980348	−	0.0235361i
$670$	−111997.	+	46390.5i	−0.249491	+	0.103343i
$671$	−112267.	+	8835.64i	−0.249350	+	0.0196243i
$672$	−7397.55	−	5374.64i	−0.0163813	−	0.0119017i
$673$	15850.2	+	18558.2i	0.0349950	+	0.0409738i	0.777627	−	0.628725i	$-0.216423\pi$
$673$	15850.2	+	18558.2i	0.0349950	+	0.0409738i	−0.742632	+	0.669699i	$0.766423\pi$
$674$	293259.	−	213065.i	0.645552	−	0.469021i
$675$	182468.	+	43806.6i	0.400478	+	0.0961462i
$676$	178124.	−	28212.1i	0.389788	−	0.0617364i
$677$	−82998.4	−	524031.i	−0.181089	−	1.14335i	−0.895973	−	0.444108i	$-0.853521\pi$
$677$	−82998.4	−	524031.i	−0.181089	−	1.14335i	0.714884	−	0.699243i	$-0.246479\pi$
$678$	−8018.30	+	33398.6i	−0.0174431	+	0.0726556i
$679$	28948.1	+	39843.7i	0.0627886	+	0.0864211i
$680$	−7506.28	+	6410.97i	−0.0162333	+	0.0138645i
$681$	6523.18	−	8978.39i	0.0140658	−	0.0193600i
$682$	11228.4	+	142670.i	0.0241406	+	0.306736i
$683$	−198143.	−	478359.i	−0.424754	−	1.02545i	−0.980926	−	0.194379i	$-0.937731\pi$
$683$	−198143.	−	478359.i	−0.424754	−	1.02545i	0.556173	−	0.831067i	$-0.312269\pi$
$684$	9805.32	+	40842.1i	0.0209580	+	0.0872963i
$685$	68784.1	−	80535.9i	0.146591	−	0.171636i
$686$	−15145.8	+	192445.i	−0.0321843	+	0.408940i
$687$	76159.6	−	24745.7i	0.161366	−	0.0524309i
$688$	76844.0	−	76844.0i	0.162343	−	0.162343i
$689$	183829.	+	93665.5i	0.387236	+	0.197307i
$690$	16435.8	−	10071.9i	0.0345217	−	0.0211549i
$691$	−154636.	−	94761.3i	−0.323859	−	0.198461i	0.351060	−	0.936353i	$-0.385821\pi$
$691$	−154636.	−	94761.3i	−0.323859	−	0.198461i	−0.674919	+	0.737892i	$0.735821\pi$
$692$	170957.	+	335521.i	0.357005	+	0.700661i
$693$	52459.9	−	161455.i	0.109235	−	0.336190i
$694$	−84598.0	+	204238.i	−0.175647	+	0.424050i
$695$	−263704.	−	41766.6i	−0.545942	−	0.0864687i
$696$		−	45942.9i		−	0.0948419i
$697$	−42763.5	−	16198.6i	−0.0880253	−	0.0333436i
$698$	−530904.			−1.08970
$699$	21360.8	−	134867.i	0.0437183	−	0.276027i
$700$	−40511.5	−	16780.4i	−0.0826765	−	0.0342457i
$701$	82391.7	+	26770.7i	0.167667	+	0.0544783i	0.391648	−	0.920115i	$-0.371905\pi$
$701$	82391.7	+	26770.7i	0.167667	+	0.0544783i	−0.223981	+	0.974594i	$0.571905\pi$
$702$	99741.7	−	50820.9i	0.202396	−	0.103126i
$703$	15877.3	−	25909.4i	0.0321266	−	0.0524259i
$704$	43843.8	+	71546.6i	0.0884633	+	0.144359i
$705$	−45118.5	+	88550.1i	−0.0907772	+	0.178160i
$706$	343648.	+	343648.i	0.689453	+	0.689453i
$707$	26793.5	+	82462.1i	0.0536033	+	0.164974i
$708$	67211.4	+	5289.65i	0.134084	+	0.0105526i
$709$	−633380.	−	540957.i	−1.26000	−	1.07614i	−0.993679	−	0.112261i	$-0.964191\pi$
$709$	−633380.	−	540957.i	−1.26000	−	1.07614i	−0.266324	−	0.963883i	$-0.585809\pi$
$710$	−403282.	+	96819.5i	−0.800005	+	0.192064i
$711$	−98207.4	+	40678.8i	−0.194270	+	0.0804692i
$712$	105983.	−	8341.04i	0.209063	−	0.0164536i
$713$	−31313.3	−	22750.5i	−0.0615956	−	0.0447519i
$714$	2524.15	+	2955.40i	0.00495130	+	0.00579722i
$715$	−164953.	+	119845.i	−0.322662	+	0.234428i
$716$	367129.	+	88139.9i	0.716131	+	0.171928i
$717$	143350.	−	22704.4i	0.278842	−	0.0441643i
$718$	−57430.3	−	362601.i	−0.111402	−	0.703363i
$719$	−187396.	+	780559.i	−0.362495	+	1.50990i	0.431578	+	0.902076i	$0.357957\pi$
$719$	−187396.	+	780559.i	−0.362495	+	1.50990i	−0.794073	+	0.607823i	$0.792043\pi$
$720$	41934.3	+	57717.6i	0.0808918	+	0.111338i
$721$	90821.5	−	77568.9i	0.174710	−	0.149217i
$722$	−207175.	+	285151.i	−0.397431	+	0.547017i
$723$	−4077.52	−	51809.8i	−0.00780045	−	0.0991141i
$724$	11503.9	+	27772.9i	0.0219467	+	0.0529839i
$725$	−51432.4	−	214231.i	−0.0978500	−	0.407574i
$726$	76083.1	−	89081.8i	0.144349	−	0.169011i
$727$	−52205.2	+	663331.i	−0.0987746	+	1.25505i	0.725246	+	0.688490i	$0.241726\pi$
$727$	−52205.2	+	663331.i	−0.0987746	+	1.25505i	−0.824020	+	0.566560i	$0.808274\pi$
$728$	−24877.7	+	8083.27i	−0.0469406	+	0.0152519i
$729$	92684.7	−	92684.7i	0.174403	−	0.174403i
$730$	69168.8	+	35243.3i	0.129797	+	0.0661348i
$731$	−39385.1	+	24135.2i	−0.0737050	+	0.0451665i
$732$	−15887.6	−	9735.92i	−0.0296507	−	0.0181700i
$733$	−206500.	−	405279.i	−0.384337	−	0.754304i	0.615079	−	0.788465i	$-0.289124\pi$
$733$	−206500.	−	405279.i	−0.384337	−	0.754304i	−0.999416	+	0.0341612i	$0.989124\pi$
$734$	−102526.	+	315543.i	−0.190302	+	0.585689i
$735$	−45328.1	+	109432.i	−0.0839059	+	0.202567i
$736$	−22415.1	−	3550.20i	−0.0413795	−	0.00655386i
$737$		−	438000.i		−	0.806379i
$738$	−140959.	+	298923.i	−0.258809	+	0.548841i
$739$	−580944.			−1.06376			−0.531882	−	0.846819i	$-0.678515\pi$
$739$	−580944.			−1.06376			−0.531882	+	0.846819i	$0.678515\pi$
$740$	8074.16	−	50978.2i	0.0147446	−	0.0930939i
$741$	−18350.2	−	7600.90i	−0.0334198	−	0.0138429i
$742$	106612.	+	34640.2i	0.193641	+	0.0629176i
$743$	361896.	−	184395.i	0.655550	−	0.334019i	−0.0943805	−	0.995536i	$-0.530087\pi$
$743$	361896.	−	184395.i	0.655550	−	0.334019i	0.749930	+	0.661517i	$0.230087\pi$
$744$	−12372.5	+	20190.0i	−0.0223517	+	0.0364747i
$745$	207705.	+	338944.i	0.374226	+	0.610682i
$746$	24650.0	−	48378.4i	0.0442934	−	0.0869308i
$747$	561904.	+	561904.i	1.00698	+	1.00698i
$748$	−11021.6	−	33921.1i	−0.0196990	−	0.0606272i
$749$	95200.6	+	7492.45i	0.169698	+	0.0133555i
$750$	−116076.	−	99138.3i	−0.206357	−	0.176246i
$751$	−695087.	+	166876.i	−1.23242	+	0.295878i	−0.796795	−	0.604250i	$-0.793473\pi$
$751$	−695087.	+	166876.i	−1.23242	+	0.295878i	−0.435626	+	0.900128i	$0.643473\pi$
$752$	108098.	−	44775.8i	0.191154	−	0.0791786i
$753$	163104.	−	12836.6i	0.287658	−	0.0226391i
$754$	−106329.	−	77252.3i	−0.187029	−	0.135884i
$755$	66911.5	+	78343.3i	0.117383	+	0.137438i
$756$	49206.0	−	35750.3i	0.0860944	−	0.0625512i
$757$	469586.	+	112738.i	0.819452	+	0.196733i	0.621435	−	0.783466i	$-0.286550\pi$
$757$	469586.	+	112738.i	0.819452	+	0.196733i	0.198017	+	0.980199i	$0.436550\pi$
$758$	−100526.	+	15921.7i	−0.174960	+	0.0277109i
$759$	10895.4	+	68790.7i	0.0189129	+	0.119412i
$760$	6398.58	−	26652.0i	0.0110779	−	0.0461426i
$761$	−585369.	−	805692.i	−1.01079	−	1.39123i	−0.918465	−	0.395503i	$-0.870570\pi$
$761$	−585369.	−	805692.i	−1.01079	−	1.39123i	−0.0923244	−	0.995729i	$-0.529430\pi$
$762$	50882.5	−	43457.7i	0.0876311	−	0.0748440i
$763$	−119040.	+	163845.i	−0.204477	+	0.281438i
$764$	20665.2	+	262576.i	0.0354041	+	0.449851i
$765$	−11604.6	−	28016.0i	−0.0198293	−	0.0478722i
$766$	−86220.5	−	359134.i	−0.146944	−	0.612068i
$767$	125257.	−	146657.i	0.212918	−	0.249295i
$768$	−1089.34	+	13841.4i	−0.00184689	+	0.0234670i
$769$	−301311.	+	97902.0i	−0.509522	+	0.165554i	−0.552485	−	0.833523i	$-0.686320\pi$
$769$	−301311.	+	97902.0i	−0.509522	+	0.165554i	0.0429629	+	0.999077i	$0.486320\pi$
$770$	−78334.3	+	78334.3i	−0.132121	+	0.132121i
$771$	−2450.47	−	1248.58i	−0.00412231	−	0.00210042i
$772$	−280690.	+	172007.i	−0.470970	+	0.288611i
$773$	75139.6	+	46045.6i	0.125751	+	0.0770601i	0.583951	−	0.811789i	$-0.301506\pi$
$773$	75139.6	+	46045.6i	0.125751	+	0.0770601i	−0.458201	+	0.888849i	$0.651506\pi$
$774$	151560.	+	297453.i	0.252989	+	0.496519i
$775$	−35090.2	+	107997.i	−0.0584229	+	0.179807i
$776$	28617.5	−	69088.7i	0.0475235	−	0.114732i
$777$	−20071.3	−	3178.99i	−0.0332456	−	0.00526559i
$778$			59546.0i			0.0983769i
$779$	122499.	−	33405.1i	0.201863	−	0.0550476i
$780$	−33736.4			−0.0554511
$781$	234420.	−	1.48007e6i	0.384320	−	2.42650i
$782$	8912.03	+	3691.48i	0.0145735	+	0.00603653i
$783$	290640.	+	94434.6i	0.474058	+	0.154031i
$784$	124252.	−	63309.7i	0.202149	−	0.103000i
$785$	−362453.	+	591470.i	−0.588184	+	0.959828i
$786$	107848.	+	175992.i	0.174569	+	0.284870i
$787$	−435768.	+	855244.i	−0.703568	+	1.38083i	0.211438	+	0.977391i	$0.432185\pi$
$787$	−435768.	+	855244.i	−0.703568	+	1.38083i	−0.915007	+	0.403439i	$0.867815\pi$
$788$	14475.0	+	14475.0i	0.0233114	+	0.0233114i
$789$	53121.4	+	163491.i	0.0853328	+	0.262627i
$790$	69152.8	+	5442.44i	0.110804	+	0.00872046i
$791$	40595.9	+	34672.1i	0.0648827	+	0.0554151i
$792$	−250650.	+	60175.7i	−0.399592	+	0.0959335i
$793$	−49247.2	+	20398.9i	−0.0783133	+	0.0324384i
$794$	−612465.	+	48202.0i	−0.971494	+	0.0764582i
$795$	116963.	+	84978.9i	0.185061	+	0.134455i
$796$	124802.	+	146125.i	0.196968	+	0.230620i
$797$	−541241.	+	393235.i	−0.852067	+	0.619063i	−0.925715	−	0.378221i	$-0.876536\pi$
$797$	−541241.	+	393235.i	−0.852067	+	0.619063i	0.0736479	+	0.997284i	$0.476536\pi$
$798$	−10493.5	−	2519.27i	−0.0164784	−	0.00395612i
$799$	−49120.7	+	7779.96i	−0.0769433	+	0.0121866i
$800$	10415.6	+	65761.7i	0.0162744	+	0.102753i
$801$	−76238.5	+	317556.i	−0.118825	+	0.494944i
$802$	−386984.	−	532638.i	−0.601651	−	0.828101i
$803$	−213285.	+	182162.i	−0.330772	+	0.282506i
$804$	42598.1	−	58631.2i	0.0658989	−	0.0907020i
$805$	−2350.75	−	29869.2i	−0.00362757	−	0.0460926i
$806$	25923.0	+	62583.7i	0.0399039	+	0.0963365i
$807$	−50367.0	−	209794.i	−0.0773391	−	0.322140i
$808$	85503.2	−	100111.i	0.130966	−	0.153342i
$809$	−21038.8	+	267323.i	−0.0321457	+	0.408450i	0.959702	+	0.281020i	$0.0906728\pi$
$809$	−21038.8	+	267323.i	−0.0321457	+	0.408450i	−0.991848	+	0.127430i	$0.959327\pi$
$810$	−168285.	+	54679.0i	−0.256492	+	0.0833394i
$811$	−418134.	+	418134.i	−0.635732	+	0.635732i	−0.949500	−	0.313768i	$-0.898409\pi$
$811$	−418134.	+	418134.i	−0.635732	+	0.635732i	0.313768	+	0.949500i	$0.398409\pi$
$812$	−63626.6	−	32419.4i	−0.0964998	−	0.0491691i
$813$	47089.4	−	28856.4i	0.0712430	−	0.0436578i
$814$	159007.	+	97439.5i	0.239975	+	0.147057i
$815$	−138693.	−	272201.i	−0.208805	−	0.409802i
$816$	1823.66	−	5612.64i	0.00273882	−	0.00842922i
$817$	49082.2	−	118495.i	0.0735327	−	0.177524i
$818$	−159444.	−	25253.5i	−0.238288	−	0.0377411i
$819$		−	80355.7i		−	0.119798i
$820$	170517.	−	132045.i	0.253594	−	0.196378i
$821$	−754679.			−1.11963			−0.559817	−	0.828616i	$-0.689129\pi$
$821$	−754679.			−1.11963			−0.559817	+	0.828616i	$0.689129\pi$
$822$	−9905.09	+	62538.3i	−0.0146593	+	0.0925555i
$823$	121991.	+	50530.4i	0.180106	+	0.0746024i	0.470914	−	0.882179i	$-0.343924\pi$
$823$	121991.	+	50530.4i	0.180106	+	0.0746024i	−0.290808	+	0.956781i	$0.593924\pi$
$824$	−172480.	−	56042.3i	−0.254030	−	0.0825394i
$825$	182064.	−	92766.1i	0.267495	−	0.136295i
$826$	54753.0	−	89348.8i	0.0802506	−	0.130957i
$827$	−2891.94	−	4719.22i	−0.00422842	−	0.00690016i	0.850519	−	0.525944i	$-0.176288\pi$
$827$	−2891.94	−	4719.22i	−0.00422842	−	0.00690016i	−0.854747	+	0.519044i	$0.826288\pi$
$828$	31650.4	−	62117.5i	0.0461656	−	0.0906052i
$829$	734240.	+	734240.i	1.06839	+	1.06839i	0.997483	+	0.0709043i	$0.0225885\pi$
$829$	734240.	+	734240.i	1.06839	+	1.06839i	0.0709043	+	0.997483i	$0.477412\pi$
$830$	−160244.	−	493179.i	−0.232608	−	0.715894i
$831$	383906.	+	30214.0i	0.555933	+	0.0437529i
$832$	30202.3	+	25795.2i	0.0436309	+	0.0372643i
$833$	−57636.2	+	13837.2i	−0.0830626	+	0.0199416i
$834$	147467.	−	61082.7i	0.212013	−	0.0878185i
$835$	263806.	−	20762.0i	0.378365	−	0.0297780i
$836$	80119.9	+	58210.5i	0.114638	+	0.0832893i
$837$	−102293.	−	119770.i	−0.146014	−	0.170961i
$838$	394806.	−	286843.i	0.562206	−	0.408467i
$839$	279842.	+	67184.0i	0.397547	+	0.0954426i	0.427289	−	0.904115i	$-0.359469\pi$
$839$	279842.	+	67184.0i	0.397547	+	0.0954426i	−0.0297422	+	0.999558i	$0.509469\pi$
$840$	−18104.4	+	2867.45i	−0.0256581	+	0.00406385i
$841$	54515.3	+	344196.i	0.0770772	+	0.486646i
$842$	91160.5	−	379711.i	0.128583	−	0.535586i
$843$	97404.1	+	134065.i	0.137064	+	0.188652i
$844$	361594.	−	308830.i	0.507617	−	0.433546i
$845$	212498.	−	292478.i	0.297606	−	0.409619i
$846$	28200.7	+	358324.i	0.0394020	+	0.500650i
$847$	−69682.3	−	168228.i	−0.0971305	−	0.234494i
$848$	−39735.0	−	165508.i	−0.0552563	−	0.230159i
$849$	−37973.8	+	44461.6i	−0.0526828	+	0.0616836i
$850$	2220.43	−	28213.2i	0.00307326	−	0.0390495i
$851$	−47968.2	+	15585.8i	−0.0662360	+	0.0215214i
$852$	175325.	−	175325.i	0.241527	−	0.241527i
$853$	−447422.	−	227973.i	−0.614921	−	0.313318i	0.118644	−	0.992937i	$-0.462145\pi$
$853$	−447422.	−	227973.i	−0.614921	−	0.313318i	−0.733565	+	0.679619i	$0.762145\pi$
$854$	−24694.3	+	15132.7i	−0.0338595	+	0.0207492i
$855$	71792.0	+	43994.2i	0.0982073	+	0.0601815i
$856$	−65829.1	−	129197.i	−0.0898401	−	0.176321i
$857$	−275042.	+	846492.i	−0.374487	+	1.15255i	0.569337	+	0.822104i	$0.307200\pi$
$857$	−275042.	+	846492.i	−0.374487	+	1.15255i	−0.943824	+	0.330449i	$0.892800\pi$
$858$	46647.0	−	112616.i	0.0633650	−	0.152977i
$859$	309485.	+	49017.6i	0.419424	+	0.0664302i	0.362579	−	0.931953i	$-0.381896\pi$
$859$	309485.	+	49017.6i	0.419424	+	0.0664302i	0.0568442	+	0.998383i	$0.481896\pi$
$860$		−	217851.i		−	0.294552i
$861$	−51989.2	−	67136.4i	−0.0701305	−	0.0905632i
$862$	−954820.			−1.28501
$863$	154031.	−	972514.i	0.206817	−	1.30579i	−0.637709	−	0.770278i	$-0.720118\pi$
$863$	154031.	−	972514.i	0.206817	−	1.30579i	0.844526	−	0.535515i	$-0.179882\pi$
$864$	−85323.0	−	35342.0i	−0.114298	−	0.0473438i
$865$	717925.	+	233268.i	0.959504	+	0.311762i
$866$	5788.85	−	2949.57i	0.00771892	−	0.00393299i
$867$	146614.	−	239253.i	0.195046	−	0.318287i
$868$	19230.7	+	31381.7i	0.0255244	+	0.0416521i
$869$	−113784.	+	223314.i	−0.150675	+	0.295717i
$870$	−65123.4	−	65123.4i	−0.0860397	−	0.0860397i
$871$	−64066.1	−	197175.i	−0.0844485	−	0.259906i
$872$	306566.	+	24127.3i	0.403172	+	0.0317304i
$873$	174682.	+	149193.i	0.229203	+	0.195758i
$874$	−26044.2	+	6252.67i	−0.0340949	+	0.00818545i
$875$	−219206.	+	90797.9i	−0.286309	+	0.118593i
$876$	−46266.9	+	3641.28i	−0.0602923	+	0.00474511i
$877$	−54236.7	−	39405.3i	−0.0705171	−	0.0512337i	0.551968	−	0.833865i	$-0.313877\pi$
$877$	−54236.7	−	39405.3i	−0.0705171	−	0.0512337i	−0.622485	+	0.782631i	$0.713877\pi$
$878$	−583216.	−	682858.i	−0.756555	−	0.885812i
$879$	−423210.	+	307480.i	−0.547744	+	0.397960i
$880$	163564.	+	39268.3i	0.211214	+	0.0507081i
$881$	−1.01214e6	+	160307.i	−1.30403	+	0.206538i	−0.769518	−	0.638625i	$-0.779504\pi$
$881$	−1.01214e6	+	160307.i	−1.30403	+	0.206538i	−0.534510	+	0.845162i	$0.679504\pi$
$882$	67014.4	+	423112.i	0.0861451	+	0.543899i
$883$	−184735.	+	769478.i	−0.236935	+	0.986903i	0.719392	+	0.694604i	$0.244420\pi$
$883$	−184735.	+	769478.i	−0.236935	+	0.986903i	−0.956327	+	0.292299i	$0.905580\pi$
$884$	−9923.26	−	13658.2i	−0.0126984	−	0.0174779i
$885$	102769.	−	87773.2i	0.131213	−	0.112066i
$886$	485310.	−	667972.i	0.618233	−	0.850924i
$887$	−70156.5	−	891422.i	−0.0891703	−	1.13302i	−0.864898	−	0.501948i	$-0.832617\pi$
$887$	−70156.5	−	891422.i	−0.0891703	−	1.13302i	0.775727	−	0.631068i	$-0.217383\pi$
$888$	11808.3	+	28507.7i	0.0149748	+	0.0361523i
$889$	−24279.9	−	101133.i	−0.0307216	−	0.127965i
$890$	138406.	−	162053.i	0.174733	−	0.204586i
$891$	50161.0	−	637356.i	0.0631846	−	0.802836i
$892$	−101283.	+	32908.9i	−0.127294	+	0.0413602i
$893$	97644.7	−	97644.7i	0.122446	−	0.122446i
$894$	−211751.	−	107892.i	−0.264941	−	0.134994i
$895$	645337.	−	395463.i	0.805639	−	0.493696i
$896$	18400.3	+	11275.7i	0.0229197	+	0.0140452i
$897$	14966.8	+	29373.9i	0.0186013	+	0.0365071i
$898$	252341.	−	776627.i	0.312922	−	0.963074i
$899$	−70768.2	+	170850.i	−0.0875627	+	0.211395i
$900$	−202016.	−	31996.2i	−0.249402	−	0.0395014i
$901$			72348.4i			0.0891208i
$902$	205009.	+	751780.i	0.251976	+	0.924012i
$903$	−85773.0			−0.105190
$904$	12681.2	−	80065.7i	0.0155175	−	0.0979737i
$905$	55674.3	+	23061.1i	0.0679764	+	0.0281567i
$906$	−58579.3	−	19033.6i	−0.0713655	−	0.0231880i
$907$	879630.	−	448194.i	1.06927	−	0.544818i	0.171451	−	0.985193i	$-0.445154\pi$
$907$	879630.	−	448194.i	1.06927	−	0.544818i	0.897814	+	0.440375i	$0.145154\pi$
$908$	−13685.3	+	22332.4i	−0.0165991	+	0.0270872i
$909$	211317.	+	344839.i	0.255745	+	0.417338i
$910$	−23805.9	+	46721.8i	−0.0287476	+	0.0564204i
$911$	895239.	+	895239.i	1.07870	+	1.07870i	0.996626	+	0.0820780i	$0.0261556\pi$
$911$	895239.	+	895239.i	1.07870	+	1.07870i	0.0820780	+	0.996626i	$0.473844\pi$
$912$	5063.64	+	15584.3i	0.00608797	+	0.0187369i
$913$	1.86785e6	+	147003.i	2.24079	+	0.176354i
$914$	307093.	+	262282.i	0.367602	+	0.313962i
$915$	−36320.9	+	8719.89i	−0.0433825	+	0.0104152i
$916$	−174607.	+	72324.8i	−0.208100	+	0.0861978i
$917$	319834.	−	25171.5i	0.380352	−	0.0299344i
$918$	31757.7	+	23073.3i	0.0376846	+	0.0273795i
$919$	−311749.	−	365011.i	−0.369126	−	0.432191i	0.544491	−	0.838767i	$-0.316723\pi$
$919$	−311749.	−	365011.i	−0.369126	−	0.432191i	−0.913617	+	0.406576i	$0.866723\pi$
$920$	−36805.4	+	26740.7i	−0.0434847	+	0.0315935i
$921$	335201.	+	80474.7i	0.395172	+	0.0948725i
$922$	692678.	−	109709.i	0.814834	−	0.129057i
$923$	−110960.	−	700574.i	−0.130246	−	0.822339i
$924$	15460.9	−	64399.2i	0.0181088	−	0.0754287i
$925$	86975.8	+	119712.i	0.101652	+	0.139912i
$926$	98568.5	−	84185.4i	0.114952	−	0.0981782i
$927$	327464.	−	450716.i	0.381070	−	0.524498i
$928$	8507.29	+	108095.i	0.00987860	+	0.125519i
$929$	−224752.	−	542599.i	−0.260418	−	0.628706i	0.738546	−	0.674203i	$-0.235513\pi$
$929$	−224752.	−	542599.i	−0.260418	−	0.628706i	−0.998964	+	0.0454973i	$0.985513\pi$
$930$	11081.3	+	46156.9i	0.0128122	+	0.0533667i
$931$	106888.	−	125149.i	0.123318	−	0.144387i
$932$	−25284.7	+	321273.i	−0.0291089	+	0.369864i
$933$	−217504.	+	70671.4i	−0.249864	+	0.0811859i
$934$	35262.9	−	35262.9i	0.0404226	−	0.0404226i
$935$	−63705.7	−	32459.7i	−0.0728711	−	0.0371297i
$936$	−104033.	+	63751.8i	−0.118747	+	0.0727680i
$937$	−464093.	−	284396.i	−0.528598	−	0.323925i	0.232463	−	0.972605i	$-0.425321\pi$
$937$	−464093.	−	284396.i	−0.528598	−	0.323925i	−0.761061	+	0.648680i	$0.775321\pi$
$938$	−51139.6	−	100367.i	−0.0581235	−	0.114074i
$939$	−145689.	+	448386.i	−0.165233	+	0.508535i
$940$	89758.9	−	216697.i	0.101583	−	0.245243i
$941$	1.19051e6	+	188558.i	1.34448	+	0.212944i	0.786848	−	0.617146i	$-0.211711\pi$
$941$	1.19051e6	+	188558.i	1.34448	+	0.212944i	0.557629	+	0.830091i	$0.311711\pi$
$942$		−	414714.i		−	0.467356i
$943$	−190618.	−	89886.7i	−0.214358	−	0.101082i
$944$	−159116.			−0.178554
$945$	19073.3	−	120424.i	0.0213581	−	0.134850i
$946$	727209.	+	301220.i	0.812600	+	0.336590i
$947$	459661.	+	149353.i	0.512551	+	0.166538i	0.553862	−	0.832608i	$-0.313153\pi$
$947$	459661.	+	149353.i	0.512551	+	0.166538i	−0.0413109	+	0.999146i	$0.513153\pi$
$948$	−36949.9	+	18826.9i	−0.0411147	+	0.0209490i
$949$	−69369.8	+	113201.i	−0.0770262	+	0.125695i
$950$	41058.0	+	67000.6i	0.0454936	+	0.0742389i
$951$	−281785.	+	553035.i	−0.311571	+	0.611493i
$952$	−6486.12	−	6486.12i	−0.00715668	−	0.00715668i
$953$	246234.	+	757831.i	0.271121	+	0.834424i	0.990220	+	0.139516i	$0.0445548\pi$
$953$	246234.	+	757831.i	0.271121	+	0.834424i	−0.719099	+	0.694908i	$0.755445\pi$
$954$	521266.	+	41024.5i	0.572747	+	0.0450761i
$955$	401491.	+	342906.i	0.440219	+	0.375983i
$956$	−333072.	+	79963.5i	−0.364437	+	0.0874935i
$957$	307434.	−	127344.i	0.335682	−	0.139044i
$958$	−458999.	+	36124.0i	−0.500128	+	0.0393609i
$959$	79620.1	+	57847.4i	0.0865736	+	0.0628994i
$960$	18075.8	+	21164.1i	0.0196135	+	0.0229645i
$961$	−670034.	+	486809.i	−0.725522	+	0.527122i
$962$	85832.7	+	20606.6i	0.0927476	+	0.0222667i
$963$	439950.	−	69681.2i	0.474406	−	0.0751386i
$964$	19187.3	+	121144.i	0.0206472	+	0.130361i
$965$	−154057.	+	641692.i	−0.165434	+	0.689084i
$966$	10528.5	+	14491.2i	0.0112826	+	0.0155292i
$967$	−1.24443e6	+	1.06285e6i	−1.33082	+	1.13663i	−0.351081	+	0.936345i	$0.614186\pi$
$967$	−1.24443e6	+	1.06285e6i	−1.33082	+	1.13663i	−0.979738	+	0.200282i	$0.935814\pi$
$968$	−162514.	+	223682.i	−0.173437	+	0.238715i
$969$	−546.467	−	6943.52i	−0.000581991	−	0.00739490i
$970$	−57367.4	−	138497.i	−0.0609708	−	0.147196i
$971$	−341264.	−	1.42147e6i	−0.361953	−	1.50764i	−0.795189	−	0.606361i	$-0.792628\pi$
$971$	−341264.	−	1.42147e6i	−0.361953	−	1.50764i	0.433236	−	0.901280i	$-0.357372\pi$
$972$	283408.	−	331828.i	0.299971	−	0.351221i
$973$	19465.3	−	247330.i	0.0205606	−	0.261247i
$974$	−1.09073e6	+	354400.i	−1.14974	+	0.373573i
$975$	68391.0	−	68391.0i	0.0719432	−	0.0719432i
$976$	39183.4	+	19964.9i	0.0411342	+	0.0209589i
$977$	389823.	−	238884.i	0.408393	−	0.250264i	−0.303097	−	0.952960i	$-0.598021\pi$
$977$	389823.	−	238884.i	0.408393	−	0.250264i	0.711490	+	0.702696i	$0.248021\pi$
$978$	155724.	+	95427.9i	0.162809	+	0.0997695i
$979$	349577.	+	686083.i	0.364735	+	0.715832i
$980$	86385.2	−	265866.i	0.0899471	−	0.276829i
$981$	−361507.	+	872754.i	−0.375646	+	0.906889i
$982$	508647.	+	80561.7i	0.527465	+	0.0835422i
$983$		−	218928.i		−	0.226566i	−0.993563	−	0.113283i	$-0.963863\pi$
$983$		−	218928.i		−	0.226566i	0.993563	−	0.113283i	$-0.0361367\pi$
$984$	−45672.3	+	120572.i	−0.0471696	+	0.124525i
$985$	41036.3			0.0422957
$986$	7209.76	−	45520.7i	0.00741596	−	0.0468225i
$987$	−85318.8	−	35340.2i	−0.0875811	−	0.0362773i
$988$	44582.1	+	14485.6i	0.0456717	+	0.0148396i
$989$	−189680.	+	96646.8i	−0.193923	+	0.0988087i
$990$	−269994.	+	440590.i	−0.275476	+	0.449536i
$991$	−531238.	−	866901.i	−0.540930	−	0.882718i	0.459053	−	0.888409i	$-0.348189\pi$
$991$	−531238.	−	866901.i	−0.540930	−	0.882718i	−0.999984	+	0.00569040i	$0.998189\pi$
$992$	25371.6	−	49794.5i	0.0257824	−	0.0506009i
$993$	−186053.	−	186053.i	−0.188686	−	0.188686i
$994$	−119092.	−	366526.i	−0.120534	−	0.370965i
$995$	384035.	+	30224.2i	0.387904	+	0.0305287i
$996$	235736.	+	201338.i	0.237633	+	0.202958i
$997$	−889931.	+	213654.i	−0.895295	+	0.214941i	−0.654884	−	0.755730i	$-0.727282\pi$
$997$	−889931.	+	213654.i	−0.895295	+	0.214941i	−0.240412	+	0.970671i	$0.577282\pi$
$998$	−53074.7	+	21984.3i	−0.0532876	+	0.0220725i
$999$	−204614.	+	16103.5i	−0.205024	+	0.0161358i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.5.h.b.53.4	✓	112
41.24	odd	40	inner	82.5.h.b.65.4	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.5.h.b.53.4	✓	112	1.1	even	1	trivial
82.5.h.b.65.4	yes	112	41.24	odd	40	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.h (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.442463 - 2.79360i) q^{2} +(3.13167 + 1.29718i) q^{3} +(-7.60845 - 2.47214i) q^{4} +(-14.2891 + 7.28065i) q^{5} +(5.00946 - 8.17469i) q^{6} +(-7.78628 - 12.7060i) q^{7} +(-10.2726 + 20.1612i) q^{8} +(-49.1510 - 49.1510i) q^{9} +(14.0169 + 43.1395i) q^{10} +(-163.385 - 12.8587i) q^{11} +(-20.6204 - 17.6114i) q^{12} +(-75.4321 + 18.1097i) q^{13} +(-38.9408 + 16.1298i) q^{14} +(-54.1930 + 4.26508i) q^{15} +(51.7771 + 37.6183i) q^{16} +(-17.6671 - 20.6855i) q^{17} +(-159.056 + 115.561i) q^{18} +(73.4465 + 17.6329i) q^{19} +(126.717 - 20.0699i) q^{20} +(-7.90201 - 49.8914i) q^{21} +(-108.214 + 450.744i) q^{22} +(-73.6910 - 101.427i) q^{23} +(-58.3232 + 49.8127i) q^{24} +(-216.196 + 297.568i) q^{25} +(17.2152 + 218.740i) q^{26} +(-195.239 - 471.348i) q^{27} +(27.8304 + 115.922i) q^{28} +(-389.016 + 455.479i) q^{29} +(-12.0635 + 153.281i) q^{30} +(293.618 - 95.4021i) q^{31} +(128.000 - 128.000i) q^{32} +(-494.988 - 252.209i) q^{33} +(-65.6042 + 40.2023i) q^{34} +(203.767 + 124.869i) q^{35} +(252.455 + 495.471i) q^{36} +(124.318 - 382.611i) q^{37} +(81.7568 - 197.378i) q^{38} +(-259.720 - 41.1356i) q^{39} -362.876i q^{40} +(1473.73 - 808.633i) q^{41} -142.873 q^{42} +(265.630 - 1677.12i) q^{43} +(1211.32 + 501.745i) q^{44} +(1060.17 + 344.471i) q^{45} +(-315.952 + 160.986i) q^{46} +(955.233 - 1558.80i) q^{47} +(113.351 + 184.972i) q^{48} +(989.214 - 1941.44i) q^{49} +(735.628 + 735.628i) q^{50} +(-28.4947 - 87.6976i) q^{51} +(618.691 + 48.6921i) q^{52} +(-2022.34 - 1727.24i) q^{53} +(-1403.14 + 336.865i) q^{54} +(2428.24 - 1005.81i) q^{55} +(336.154 - 26.4559i) q^{56} +(207.137 + 150.494i) q^{57} +(1100.30 + 1288.29i) q^{58} +(-2011.37 + 1461.34i) q^{59} +(422.869 + 101.522i) q^{60} +(678.674 - 107.491i) q^{61} +(-136.601 - 862.463i) q^{62} +(-241.812 + 1007.22i) q^{63} +(-300.946 - 414.217i) q^{64} +(946.006 - 807.966i) q^{65} +(-923.587 + 1271.21i) q^{66} +(209.683 + 2664.28i) q^{67} +(83.2818 + 201.060i) q^{68} +(-99.2068 - 413.226i) q^{69} +(438.993 - 513.995i) q^{70} +(-717.385 + 9115.25i) q^{71} +(1495.85 - 486.032i) q^{72} +(1210.17 - 1210.17i) q^{73} +(-1013.86 - 516.586i) q^{74} +(-1063.05 + 651.439i) q^{75} +(-515.223 - 315.729i) q^{76} +(1108.78 + 2176.10i) q^{77} +(-229.833 + 707.354i) q^{78} +(585.223 - 1412.85i) q^{79} +(-1013.73 - 160.560i) q^{80} +3900.94i q^{81} +(-1606.93 - 4474.80i) q^{82} -11432.2 q^{83} +(-63.2161 + 399.131i) q^{84} +(403.051 + 166.949i) q^{85} +(-4567.69 - 1484.13i) q^{86} +(-1809.11 + 921.787i) q^{87} +(1937.64 - 3161.94i) q^{88} +(-2454.86 - 4005.97i) q^{89} +(1431.40 - 2809.29i) q^{90} +(817.438 + 817.438i) q^{91} +(309.933 + 953.876i) q^{92} +(1043.27 + 82.1069i) q^{93} +(-3932.01 - 3358.25i) q^{94} +(-1177.86 + 282.780i) q^{95} +(566.893 - 234.815i) q^{96} +(-3294.70 + 259.299i) q^{97} +(-4985.93 - 3622.49i) q^{98} +(7398.52 + 8662.56i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 56 q^{2} - 16 q^{3} + 16 q^{6} - 448 q^{8} - 24 q^{9} + 512 q^{11} - 576 q^{12} + 348 q^{13} - 192 q^{14} - 1036 q^{15} + 1792 q^{16} + 552 q^{17} + 416 q^{18} + 504 q^{19} + 876 q^{21} + 16 q^{22}+ \cdots + 36896 q^{99}+O(q^{100}) \) 112 * q + 56 * q^2 - 16 * q^3 + 16 * q^6 - 448 * q^8 - 24 * q^9 + 512 * q^11 - 576 * q^12 + 348 * q^13 - 192 * q^14 - 1036 * q^15 + 1792 * q^16 + 552 * q^17 + 416 * q^18 + 504 * q^19 + 876 * q^21 + 16 * q^22 + 800 * q^23 - 384 * q^24 - 3360 * q^25 + 1656 * q^26 - 964 * q^27 + 768 * q^28 + 4 * q^29 - 3544 * q^30 + 1380 * q^31 + 14336 * q^32 - 7392 * q^33 + 4224 * q^34 + 2264 * q^35 + 2048 * q^36 + 6212 * q^37 + 2624 * q^38 + 4928 * q^39 - 7460 * q^41 + 5056 * q^42 - 19816 * q^43 - 6560 * q^44 - 26000 * q^45 - 4400 * q^46 - 14660 * q^47 - 1536 * q^48 - 17808 * q^49 - 28720 * q^50 + 17948 * q^51 + 1152 * q^52 + 19032 * q^53 + 20152 * q^54 + 3160 * q^55 - 1536 * q^56 + 23432 * q^57 - 6752 * q^58 + 25136 * q^59 - 9536 * q^60 + 10080 * q^61 + 10496 * q^62 - 968 * q^63 - 57460 * q^65 - 2480 * q^66 + 280 * q^67 + 1568 * q^68 - 1876 * q^69 + 6792 * q^70 + 49672 * q^71 + 4480 * q^72 + 16196 * q^73 - 30984 * q^74 + 58748 * q^75 + 13312 * q^76 + 6444 * q^77 + 4928 * q^78 + 34556 * q^79 + 6888 * q^82 + 17304 * q^83 + 7008 * q^84 - 104144 * q^85 + 30800 * q^86 - 28492 * q^87 - 3648 * q^88 + 26732 * q^89 - 70336 * q^90 - 132748 * q^91 + 4160 * q^92 + 35360 * q^93 - 11160 * q^94 - 5644 * q^95 - 1024 * q^96 + 14036 * q^97 - 6528 * q^98 + 36896 * q^99

Introduction

L-functions

Modular forms

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Database

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