LMFDB - Embedded newform 82.5.e.a.79.4

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			79.4
Character	$\chi$	$=$	82.79
Dual form			82.5.e.a.27.4

$q$-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} +(2.35294 + 0.974620i) q^{3} -8.00000i q^{4} +(-5.07070 - 5.07070i) q^{5} +(-6.65512 + 2.75664i) q^{6} +(13.7461 + 5.69383i) q^{7} +(16.0000 + 16.0000i) q^{8} +(-52.6892 - 52.6892i) q^{9} +20.2828 q^{10} +(53.0777 - 128.141i) q^{11} +(7.79696 - 18.8235i) q^{12} +(-78.5882 - 32.5523i) q^{13} +(-38.8799 + 16.1046i) q^{14} +(-6.98906 - 16.8731i) q^{15} -64.0000 q^{16} +(187.679 - 77.7393i) q^{17} +210.757 q^{18} +(542.264 - 224.613i) q^{19} +(-40.5656 + 40.5656i) q^{20} +(26.7945 + 26.7945i) q^{21} +(150.127 + 362.437i) q^{22} -173.542i q^{23} +(22.0531 + 53.2410i) q^{24} -573.576i q^{25} +(222.281 - 92.0718i) q^{26} +(-151.567 - 365.915i) q^{27} +(45.5506 - 109.969i) q^{28} +(745.358 + 308.738i) q^{29} +(47.7243 + 19.7680i) q^{30} -515.419i q^{31} +(128.000 - 128.000i) q^{32} +(249.778 - 249.778i) q^{33} +(-219.880 + 530.837i) q^{34} +(-40.8308 - 98.5742i) q^{35} +(-421.514 + 421.514i) q^{36} -2589.50 q^{37} +(-635.302 + 1533.75i) q^{38} +(-153.187 - 153.187i) q^{39} -162.263i q^{40} +(1513.96 + 730.543i) q^{41} -107.178 q^{42} +(-949.343 + 949.343i) q^{43} +(-1025.13 - 424.622i) q^{44} +534.343i q^{45} +(347.083 + 347.083i) q^{46} +(-1905.22 + 789.168i) q^{47} +(-150.588 - 62.3757i) q^{48} +(-1541.23 - 1541.23i) q^{49} +(1147.15 + 1147.15i) q^{50} +517.365 q^{51} +(-260.418 + 628.706i) q^{52} +(-448.434 + 1082.62i) q^{53} +(1034.96 + 428.696i) q^{54} +(-918.907 + 380.624i) q^{55} +(128.837 + 311.039i) q^{56} +1494.83 q^{57} +(-2108.19 + 873.242i) q^{58} -3218.73 q^{59} +(-134.985 + 55.9125i) q^{60} +(1487.25 - 1487.25i) q^{61} +(1030.84 + 1030.84i) q^{62} +(-424.269 - 1024.28i) q^{63} +512.000i q^{64} +(233.434 + 563.561i) q^{65} +999.110i q^{66} +(1628.28 - 674.457i) q^{67} +(-621.915 - 1501.43i) q^{68} +(169.137 - 408.333i) q^{69} +(278.810 + 115.487i) q^{70} +(4660.25 + 1930.34i) q^{71} -1686.05i q^{72} +(1842.45 - 1842.45i) q^{73} +(5178.99 - 5178.99i) q^{74} +(559.018 - 1349.59i) q^{75} +(-1796.91 - 4338.11i) q^{76} +(1459.23 - 1459.23i) q^{77} +612.749 q^{78} +(-782.127 + 1888.22i) q^{79} +(324.525 + 324.525i) q^{80} +5026.92i q^{81} +(-4489.00 + 1566.83i) q^{82} +2507.82 q^{83} +(214.356 - 214.356i) q^{84} +(-1345.86 - 557.473i) q^{85} -3797.37i q^{86} +(1452.88 + 1452.88i) q^{87} +(2899.50 - 1201.01i) q^{88} +(6721.19 + 2784.01i) q^{89} +(-1068.69 - 1068.69i) q^{90} +(-894.936 - 894.936i) q^{91} -1388.33 q^{92} +(502.338 - 1212.75i) q^{93} +(2232.11 - 5388.78i) q^{94} +(-3888.61 - 1610.71i) q^{95} +(425.928 - 176.425i) q^{96} +(1151.88 + 2780.89i) q^{97} +6164.91 q^{98} +(-9548.27 + 3955.02i) 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 $\left(\mathbb{Z}/82\mathbb{Z}\right)^\times$.

$n$	$47$
$\chi(n)$	$e\left(\frac{7}{8}\right)$

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
$3$	2.35294	+	0.974620i	0.261438	+	0.108291i	0.509552	−	0.860440i	$-0.329811\pi$
$3$	2.35294	+	0.974620i	0.261438	+	0.108291i	−0.248115	+	0.968731i	$0.579811\pi$
$4$		−	8.00000i		−	0.500000i
$5$	−5.07070	−	5.07070i	−0.202828	−	0.202828i	0.598382	−	0.801211i	$-0.295810\pi$
$5$	−5.07070	−	5.07070i	−0.202828	−	0.202828i	−0.801211	+	0.598382i	$0.795810\pi$
$6$	−6.65512	+	2.75664i	−0.184864	+	0.0765734i
$7$	13.7461	+	5.69383i	0.280533	+	0.116201i	0.518514	−	0.855069i	$-0.326486\pi$
$7$	13.7461	+	5.69383i	0.280533	+	0.116201i	−0.237981	+	0.971270i	$0.576486\pi$
$8$	16.0000	+	16.0000i	0.250000	+	0.250000i
$9$	−52.6892	−	52.6892i	−0.650484	−	0.650484i
$10$	20.2828			0.202828
$11$	53.0777	−	128.141i	0.438659	−	1.05902i	−0.537753	−	0.843102i	$-0.680727\pi$
$11$	53.0777	−	128.141i	0.438659	−	1.05902i	0.976412	−	0.215914i	$-0.0692732\pi$
$12$	7.79696	−	18.8235i	0.0541455	−	0.130719i
$13$	−78.5882	−	32.5523i	−0.465019	−	0.192617i	0.137857	−	0.990452i	$-0.455979\pi$
$13$	−78.5882	−	32.5523i	−0.465019	−	0.192617i	−0.602876	+	0.797835i	$0.705979\pi$
$14$	−38.8799	+	16.1046i	−0.198367	+	0.0821662i
$15$	−6.98906	−	16.8731i	−0.0310625	−	0.0749914i
$16$	−64.0000			−0.250000
$17$	187.679	−	77.7393i	0.649409	−	0.268994i	−0.0335649	−	0.999437i	$-0.510686\pi$
$17$	187.679	−	77.7393i	0.649409	−	0.268994i	0.682974	+	0.730442i	$0.260686\pi$
$18$	210.757			0.650484
$19$	542.264	−	224.613i	1.50212	−	0.622197i	0.528204	−	0.849118i	$-0.322866\pi$
$19$	542.264	−	224.613i	1.50212	−	0.622197i	0.973913	+	0.226920i	$0.0728657\pi$
$20$	−40.5656	+	40.5656i	−0.101414	+	0.101414i
$21$	26.7945	+	26.7945i	0.0607585	+	0.0607585i
$22$	150.127	+	362.437i	0.310179	+	0.748838i
$23$		−	173.542i		−	0.328056i	−0.986456	−	0.164028i	$-0.947551\pi$
$23$		−	173.542i		−	0.328056i	0.986456	−	0.164028i	$-0.0524488\pi$
$24$	22.0531	+	53.2410i	0.0382867	+	0.0924322i
$25$		−	573.576i		−	0.917721i
$26$	222.281	−	92.0718i	0.328818	−	0.136201i
$27$	−151.567	−	365.915i	−0.207911	−	0.501941i
$28$	45.5506	−	109.969i	0.0581003	−	0.140267i
$29$	745.358	+	308.738i	0.886276	+	0.367108i	0.778928	−	0.627114i	$-0.215764\pi$
$29$	745.358	+	308.738i	0.886276	+	0.367108i	0.107349	+	0.994221i	$0.465764\pi$
$30$	47.7243	+	19.7680i	0.0530270	+	0.0219645i
$31$		−	515.419i		−	0.536337i	−0.963372	−	0.268168i	$-0.913582\pi$
$31$		−	515.419i		−	0.536337i	0.963372	−	0.268168i	$-0.0864183\pi$
$32$	128.000	−	128.000i	0.125000	−	0.125000i
$33$	249.778	−	249.778i	0.229364	−	0.229364i
$34$	−219.880	+	530.837i	−0.190208	+	0.459202i
$35$	−40.8308	−	98.5742i	−0.0333312	−	0.0804688i
$36$	−421.514	+	421.514i	−0.325242	+	0.325242i
$37$	−2589.50			−1.89152			−0.945762	−	0.324861i	$-0.894682\pi$
$37$	−2589.50			−1.89152			−0.945762	+	0.324861i	$0.894682\pi$
$38$	−635.302	+	1533.75i	−0.439960	+	1.06216i
$39$	−153.187	−	153.187i	−0.100715	−	0.100715i
$40$		−	162.263i		−	0.101414i
$41$	1513.96	+	730.543i	0.900629	+	0.434588i
$41$	1513.96	+	730.543i	0.900629	+	0.434588i
$42$	−107.178			−0.0607585
$43$	−949.343	+	949.343i	−0.513436	+	0.513436i	−0.915577	−	0.402142i	$-0.868266\pi$
$43$	−949.343	+	949.343i	−0.513436	+	0.513436i	0.402142	+	0.915577i	$0.368266\pi$
$44$	−1025.13	−	424.622i	−0.529508	−	0.219330i
$45$			534.343i			0.263873i
$46$	347.083	+	347.083i	0.164028	+	0.164028i
$47$	−1905.22	+	789.168i	−0.862481	+	0.357251i	−0.769677	−	0.638433i	$-0.779583\pi$
$47$	−1905.22	+	789.168i	−0.862481	+	0.357251i	−0.0928038	+	0.995684i	$0.529583\pi$
$48$	−150.588	−	62.3757i	−0.0653595	−	0.0270728i
$49$	−1541.23	−	1541.23i	−0.641911	−	0.641911i
$50$	1147.15	+	1147.15i	0.458861	+	0.458861i
$51$	517.365			0.198910
$52$	−260.418	+	628.706i	−0.0963086	+	0.232509i
$53$	−448.434	+	1082.62i	−0.159642	+	0.385410i	−0.983380	−	0.181561i	$-0.941885\pi$
$53$	−448.434	+	1082.62i	−0.159642	+	0.385410i	0.823738	+	0.566971i	$0.191885\pi$
$54$	1034.96	+	428.696i	0.354926	+	0.147015i
$55$	−918.907	+	380.624i	−0.303771	+	0.125826i
$56$	128.837	+	311.039i	0.0410831	+	0.0991834i
$57$	1494.83			0.460089
$58$	−2108.19	+	873.242i	−0.626692	+	0.259584i
$59$	−3218.73			−0.924656			−0.462328	−	0.886709i	$-0.652986\pi$
$59$	−3218.73			−0.924656			−0.462328	+	0.886709i	$0.652986\pi$
$60$	−134.985	+	55.9125i	−0.0374957	+	0.0155312i
$61$	1487.25	−	1487.25i	0.399692	−	0.399692i	−0.478432	−	0.878124i	$-0.658795\pi$
$61$	1487.25	−	1487.25i	0.399692	−	0.399692i	0.878124	+	0.478432i	$0.158795\pi$
$62$	1030.84	+	1030.84i	0.268168	+	0.268168i
$63$	−424.269	−	1024.28i	−0.106896	−	0.258069i
$64$			512.000i			0.125000i
$65$	233.434	+	563.561i	0.0552508	+	0.133387i
$66$			999.110i			0.229364i
$67$	1628.28	−	674.457i	0.362727	−	0.150247i	−0.193874	−	0.981026i	$-0.562105\pi$
$67$	1628.28	−	674.457i	0.362727	−	0.150247i	0.556601	+	0.830780i	$0.312105\pi$
$68$	−621.915	−	1501.43i	−0.134497	−	0.324705i
$69$	169.137	−	408.333i	0.0355256	−	0.0857663i
$70$	278.810	+	115.487i	0.0569000	+	0.0235688i
$71$	4660.25	+	1930.34i	0.924469	+	0.382928i	0.793578	−	0.608469i	$-0.208216\pi$
$71$	4660.25	+	1930.34i	0.924469	+	0.382928i	0.130892	+	0.991397i	$0.458216\pi$
$72$		−	1686.05i		−	0.325242i
$73$	1842.45	−	1842.45i	0.345739	−	0.345739i	−0.512780	−	0.858520i	$-0.671384\pi$
$73$	1842.45	−	1842.45i	0.345739	−	0.345739i	0.858520	+	0.512780i	$0.171384\pi$
$74$	5178.99	−	5178.99i	0.945762	−	0.945762i
$75$	559.018	−	1349.59i	0.0993811	−	0.239927i
$76$	−1796.91	−	4338.11i	−0.311099	−	0.751058i
$77$	1459.23	−	1459.23i	0.246117	−	0.246117i
$78$	612.749			0.100715
$79$	−782.127	+	1888.22i	−0.125321	+	0.302551i	−0.974071	−	0.226243i	$-0.927356\pi$
$79$	−782.127	+	1888.22i	−0.125321	+	0.302551i	0.848750	+	0.528794i	$0.177356\pi$
$80$	324.525	+	324.525i	0.0507070	+	0.0507070i
$81$			5026.92i			0.766182i
$82$	−4489.00	+	1566.83i	−0.667609	+	0.233020i
$83$	2507.82			0.364032			0.182016	−	0.983296i	$-0.441738\pi$
$83$	2507.82			0.364032			0.182016	+	0.983296i	$0.441738\pi$
$84$	214.356	−	214.356i	0.0303792	−	0.0303792i
$85$	−1345.86	−	557.473i	−0.186278	−	0.0771589i
$86$		−	3797.37i		−	0.513436i
$87$	1452.88	+	1452.88i	0.191952	+	0.191952i
$88$	2899.50	−	1201.01i	0.374419	−	0.155089i
$89$	6721.19	+	2784.01i	0.848528	+	0.351472i	0.764210	−	0.644967i	$-0.223129\pi$
$89$	6721.19	+	2784.01i	0.848528	+	0.351472i	0.0843174	+	0.996439i	$0.473129\pi$
$90$	−1068.69	−	1068.69i	−0.131936	−	0.131936i
$91$	−894.936	−	894.936i	−0.108071	−	0.108071i
$92$	−1388.33			−0.164028
$93$	502.338	−	1212.75i	0.0580805	−	0.140219i
$94$	2232.11	−	5388.78i	0.252615	−	0.609866i
$95$	−3888.61	−	1610.71i	−0.430871	−	0.178473i
$96$	425.928	−	176.425i	0.0462161	−	0.0191433i
$97$	1151.88	+	2780.89i	0.122423	+	0.295556i	0.973196	−	0.229978i	$-0.0738654\pi$
$97$	1151.88	+	2780.89i	0.122423	+	0.295556i	−0.850772	+	0.525534i	$0.823865\pi$
$98$	6164.91			0.641911
$99$	−9548.27	+	3955.02i	−0.974214	+	0.403533i
$100$	−4588.61			−0.458861
$101$	15687.2	−	6497.85i	1.53781	−	0.636982i	0.556749	−	0.830681i	$-0.312049\pi$
$101$	15687.2	−	6497.85i	1.53781	−	0.636982i	0.981061	+	0.193699i	$0.0620486\pi$
$102$	−1034.73	+	1034.73i	−0.0994549	+	0.0994549i
$103$	−13197.4	−	13197.4i	−1.24398	−	1.24398i	−0.958334	−	0.285650i	$-0.907790\pi$
$103$	−13197.4	−	13197.4i	−1.24398	−	1.24398i	−0.285650	−	0.958334i	$-0.592210\pi$
$104$	−736.574	−	1778.25i	−0.0681004	−	0.164409i
$105$		−	271.734i		−	0.0246471i
$106$	−1268.36	−	3062.10i	−0.112884	−	0.272526i
$107$			9357.92i			0.817357i	0.912678	+	0.408679i	$0.134010\pi$
$107$			9357.92i			0.817357i	−0.912678	+	0.408679i	$0.865990\pi$
$108$	−2927.32	+	1212.53i	−0.250970	+	0.103955i
$109$	2230.45	+	5384.78i	0.187733	+	0.453226i	0.989522	−	0.144380i	$-0.0461187\pi$
$109$	2230.45	+	5384.78i	0.187733	+	0.453226i	−0.801790	+	0.597606i	$0.796119\pi$
$110$	1076.57	−	2599.06i	0.0889724	−	0.214798i
$111$	−6092.93	−	2523.77i	−0.494516	−	0.204835i
$112$	−879.752	−	364.405i	−0.0701333	−	0.0290501i
$113$			3672.92i			0.287643i	0.989604	+	0.143822i	$0.0459392\pi$
$113$			3672.92i			0.287643i	−0.989604	+	0.143822i	$0.954061\pi$
$114$	−2989.66	+	2989.66i	−0.230044	+	0.230044i
$115$	−879.979	+	879.979i	−0.0665390	+	0.0665390i
$116$	2469.90	−	5962.87i	0.183554	−	0.443138i
$117$	2425.60	+	5855.90i	0.177193	+	0.427782i
$118$	6437.45	−	6437.45i	0.462328	−	0.462328i
$119$	3022.50			0.213438
$120$	158.144	−	381.794i	0.0109822	−	0.0265135i
$121$	−3250.12	−	3250.12i	−0.221988	−	0.221988i
$122$			5949.01i			0.399692i
$123$	2850.25	+	3194.46i	0.188396	+	0.211148i
$124$	−4123.36			−0.268168
$125$	−6077.62	+	6077.62i	−0.388968	+	0.388968i
$126$	2897.09	+	1200.01i	0.182482	+	0.0755866i
$127$			15373.4i			0.953154i	0.879133	+	0.476577i	$0.158123\pi$
$127$			15373.4i			0.953154i	−0.879133	+	0.476577i	$0.841877\pi$
$128$	−1024.00	−	1024.00i	−0.0625000	−	0.0625000i
$129$	−3159.00	+	1308.50i	−0.189832	+	0.0786310i
$130$	−1593.99	−	660.252i	−0.0943189	−	0.0390682i
$131$	−918.031	−	918.031i	−0.0534952	−	0.0534952i	0.679853	−	0.733348i	$-0.262044\pi$
$131$	−918.031	−	918.031i	−0.0534952	−	0.0534952i	−0.733348	+	0.679853i	$0.762044\pi$
$132$	−1998.22	−	1998.22i	−0.114682	−	0.114682i
$133$	8732.94			0.493693
$134$	−1907.65	+	4605.48i	−0.106240	+	0.256487i
$135$	−1086.89	+	2624.00i	−0.0596376	+	0.143978i
$136$	4246.70	+	1759.04i	0.229601	+	0.0951038i
$137$	24438.5	−	10122.7i	1.30207	−	0.539333i	0.379506	−	0.925189i	$-0.376094\pi$
$137$	24438.5	−	10122.7i	1.30207	−	0.539333i	0.922559	+	0.385856i	$0.126094\pi$
$138$	478.392	+	1154.94i	0.0251204	+	0.0606459i
$139$	−22878.6			−1.18413			−0.592064	−	0.805891i	$-0.701687\pi$
$139$	−22878.6			−1.18413			−0.592064	+	0.805891i	$0.701687\pi$
$140$	−788.594	+	326.646i	−0.0402344	+	0.0166656i
$141$	−5252.01			−0.264172
$142$	−13181.2	+	5459.82i	−0.653699	+	0.270771i
$143$	−8342.57	+	8342.57i	−0.407970	+	0.407970i
$144$	3372.11	+	3372.11i	0.162621	+	0.162621i
$145$	−2213.97	−	5345.01i	−0.105302	−	0.254222i
$146$			7369.78i			0.345739i
$147$	−2124.31	−	5128.53i	−0.0983065	−	0.237333i
$148$			20716.0i			0.945762i
$149$	25818.9	−	10694.5i	1.16296	−	0.481714i	0.284100	−	0.958795i	$-0.408305\pi$
$149$	25818.9	−	10694.5i	1.16296	−	0.481714i	0.878859	+	0.477081i	$0.158305\pi$
$150$	1581.14	+	3817.22i	0.0702730	+	0.169654i
$151$	−9547.20	+	23049.0i	−0.418718	+	1.01088i	0.564001	+	0.825774i	$0.309261\pi$
$151$	−9547.20	+	23049.0i	−0.418718	+	1.01088i	−0.982719	+	0.185102i	$0.940739\pi$
$152$	12270.0	+	5082.42i	0.531079	+	0.219980i
$153$	−13984.7	−	5792.65i	−0.597407	−	0.247454i
$154$			5836.90i			0.246117i
$155$	−2613.54	+	2613.54i	−0.108784	+	0.108784i
$156$	−1225.50	+	1225.50i	−0.0503574	+	0.0503574i
$157$	−7927.08	+	19137.7i	−0.321599	+	0.776408i	0.677563	+	0.735465i	$0.263036\pi$
$157$	−7927.08	+	19137.7i	−0.321599	+	0.776408i	−0.999161	+	0.0409428i	$0.986964\pi$
$158$	−2212.19	−	5340.70i	−0.0886152	−	0.213936i
$159$	−2110.28	+	2110.28i	−0.0834729	+	0.0834729i
$160$	−1298.10			−0.0507070
$161$	988.117	−	2385.52i	0.0381203	−	0.0920306i
$162$	−10053.8	−	10053.8i	−0.383091	−	0.383091i
$163$		−	23490.4i		−	0.884127i	−0.896984	−	0.442064i	$-0.854247\pi$
$163$		−	23490.4i		−	0.884127i	0.896984	−	0.442064i	$-0.145753\pi$
$164$	5844.34	−	12111.7i	0.217294	−	0.450315i
$165$	−2533.10			−0.0930430
$166$	−5015.64	+	5015.64i	−0.182016	+	0.182016i
$167$	15812.8	+	6549.86i	0.566989	+	0.234854i	0.647716	−	0.761882i	$-0.275724\pi$
$167$	15812.8	+	6549.86i	0.566989	+	0.234854i	−0.0807273	+	0.996736i	$0.525724\pi$
$168$			857.423i			0.0303792i
$169$	−15079.2	−	15079.2i	−0.527966	−	0.527966i
$170$	3806.67	−	1576.77i	0.131719	−	0.0545596i
$171$	−40406.2	−	16736.8i	−1.38183	−	0.572374i
$172$	7594.74	+	7594.74i	0.256718	+	0.256718i
$173$	9126.33	+	9126.33i	0.304933	+	0.304933i	0.842940	−	0.538007i	$-0.180823\pi$
$173$	9126.33	+	9126.33i	0.304933	+	0.304933i	−0.538007	+	0.842940i	$0.680823\pi$
$174$	−5811.53			−0.191952
$175$	3265.84	−	7884.44i	0.106640	−	0.257451i
$176$	−3396.98	+	8201.02i	−0.109665	+	0.264754i
$177$	−7573.47	−	3137.04i	−0.241740	−	0.100132i
$178$	−19010.4	+	7874.36i	−0.600000	+	0.248528i
$179$	−21460.9	−	51811.2i	−0.669796	−	1.61703i	−0.781952	−	0.623339i	$-0.785776\pi$
$179$	−21460.9	−	51811.2i	−0.669796	−	1.61703i	0.112156	−	0.993691i	$-0.464224\pi$
$180$	4274.74			0.131936
$181$	40958.4	−	16965.5i	1.25022	−	0.517857i	0.343324	−	0.939217i	$-0.388447\pi$
$181$	40958.4	−	16965.5i	1.25022	−	0.517857i	0.906893	+	0.421360i	$0.138447\pi$
$182$	3579.74			0.108071
$183$	4948.93	−	2049.91i	0.147778	−	0.0612115i
$184$	2776.67	−	2776.67i	0.0820140	−	0.0820140i
$185$	13130.6	+	13130.6i	0.383654	+	0.383654i
$186$	1420.83	+	3430.18i	0.0410691	+	0.0991496i
$187$		−	28175.6i		−	0.805732i
$188$	6313.35	+	15241.8i	0.178626	+	0.431241i
$189$		−	5892.90i		−	0.164970i
$190$	10998.6	−	4555.79i	0.304672	−	0.126199i
$191$	11144.8	+	26906.0i	0.305497	+	0.737535i	0.999840	+	0.0178908i	$0.00569511\pi$
$191$	11144.8	+	26906.0i	0.305497	+	0.737535i	−0.694343	+	0.719644i	$0.744305\pi$
$192$	−499.005	+	1204.71i	−0.0135364	+	0.0326797i
$193$	52611.8	+	21792.5i	1.41243	+	0.585050i	0.952948	−	0.303135i	$-0.0980332\pi$
$193$	52611.8	+	21792.5i	1.41243	+	0.585050i	0.459487	+	0.888184i	$0.348033\pi$
$194$	−7865.54	−	3258.01i	−0.208990	−	0.0865664i
$195$			1553.53i			0.0408556i
$196$	−12329.8	+	12329.8i	−0.320955	+	0.320955i
$197$	4367.77	−	4367.77i	0.112545	−	0.112545i	−0.648591	−	0.761137i	$-0.724642\pi$
$197$	4367.77	−	4367.77i	0.112545	−	0.112545i	0.761137	+	0.648591i	$0.224642\pi$
$198$	11186.5	−	27006.6i	0.285341	−	0.688873i
$199$	−13216.6	−	31907.6i	−0.333743	−	0.805728i	−0.998289	−	0.0584799i	$-0.981375\pi$
$199$	−13216.6	−	31907.6i	−0.333743	−	0.805728i	0.664545	−	0.747248i	$-0.268625\pi$
$200$	9177.21	−	9177.21i	0.229430	−	0.229430i
$201$	4488.59			0.111101
$202$	−18378.7	+	44370.1i	−0.450414	+	1.08740i
$203$	8487.88	+	8487.88i	0.205972	+	0.205972i
$204$		−	4138.92i		−	0.0994549i
$205$	−3972.46	−	11381.2i	−0.0945262	−	0.270820i
$206$	52789.7			1.24398
$207$	−9143.77	+	9143.77i	−0.213395	+	0.213395i
$208$	5029.65	+	2083.35i	0.116255	+	0.0481543i
$209$		−	81408.2i		−	1.86370i
$210$	543.468	+	543.468i	0.0123235	+	0.0123235i
$211$	27855.9	−	11538.3i	0.625680	−	0.259165i	−0.0472365	−	0.998884i	$-0.515041\pi$
$211$	27855.9	−	11538.3i	0.625680	−	0.259165i	0.672916	+	0.739719i	$0.265041\pi$
$212$	8660.93	+	3587.47i	0.192705	+	0.0798210i
$213$	9083.94	+	9083.94i	0.200224	+	0.200224i
$214$	−18715.8	−	18715.8i	−0.408679	−	0.408679i
$215$	9627.67			0.208278
$216$	3429.57	−	8279.70i	0.0735075	−	0.177463i
$217$	2934.71	−	7085.02i	0.0623226	−	0.150460i
$218$	−15230.5	−	6308.67i	−0.320479	−	0.132747i
$219$	6130.85	−	2539.48i	0.127830	−	0.0529489i
$220$	3044.99	+	7351.25i	0.0629130	+	0.151885i
$221$	−17280.0			−0.353801
$222$	17233.4	−	7138.31i	0.349675	−	0.144840i
$223$	10564.8			0.212447			0.106223	−	0.994342i	$-0.466124\pi$
$223$	10564.8			0.212447			0.106223	+	0.994342i	$0.466124\pi$
$224$	2488.31	−	1030.69i	0.0495917	−	0.0205416i
$225$	−30221.3	+	30221.3i	−0.596963	+	0.596963i
$226$	−7345.84	−	7345.84i	−0.143822	−	0.143822i
$227$	14806.9	+	35747.0i	0.287351	+	0.693726i	0.999969	−	0.00782574i	$-0.00249104\pi$
$227$	14806.9	+	35747.0i	0.287351	+	0.693726i	−0.712619	+	0.701551i	$0.752491\pi$
$228$		−	11958.6i		−	0.230044i
$229$	3960.21	+	9560.79i	0.0755174	+	0.182315i	0.957130	−	0.289659i	$-0.0935417\pi$
$229$	3960.21	+	9560.79i	0.0755174	+	0.182315i	−0.881613	+	0.471974i	$0.843542\pi$
$230$		−	3519.92i		−	0.0665390i
$231$	4855.66	−	2011.28i	0.0909965	−	0.0376920i
$232$	6985.93	+	16865.5i	0.129792	+	0.313346i
$233$	−7614.80	+	18383.8i	−0.140264	+	0.338628i	−0.978365	−	0.206888i	$-0.933666\pi$
$233$	−7614.80	+	18383.8i	−0.140264	+	0.338628i	0.838100	+	0.545516i	$0.183666\pi$
$234$	−16563.0	−	6860.62i	−0.302487	−	0.125294i
$235$	13662.5	+	5659.17i	0.247396	+	0.102475i
$236$			25749.8i			0.462328i
$237$	−3680.60	+	3680.60i	−0.0655272	+	0.0655272i
$238$	−6044.99	+	6044.99i	−0.106719	+	0.106719i
$239$	10001.9	−	24146.7i	0.175100	−	0.422730i	−0.811826	−	0.583899i	$-0.801526\pi$
$239$	10001.9	−	24146.7i	0.175100	−	0.422730i	0.986927	+	0.161169i	$0.0515265\pi$
$240$	447.300	+	1079.88i	0.00776562	+	0.0187479i
$241$	32115.8	−	32115.8i	0.552948	−	0.552948i	−0.374342	−	0.927291i	$-0.622131\pi$
$241$	32115.8	−	32115.8i	0.552948	−	0.552948i	0.927291	+	0.374342i	$0.122131\pi$
$242$	13000.5			0.221988
$243$	−17176.3	+	41467.1i	−0.290881	+	0.702250i
$244$	−11898.0	−	11898.0i	−0.199846	−	0.199846i
$245$			15630.2i			0.260395i
$246$	−12089.4	−	688.415i	−0.199772	−	0.0113757i
$247$	−49927.2			−0.818359
$248$	8246.71	−	8246.71i	0.134084	−	0.134084i
$249$	5900.75	+	2444.17i	0.0951719	+	0.0394215i
$250$		−	24310.5i		−	0.388968i
$251$	27106.7	+	27106.7i	0.430259	+	0.430259i	0.888716	−	0.458457i	$-0.151598\pi$
$251$	27106.7	+	27106.7i	0.430259	+	0.430259i	−0.458457	+	0.888716i	$0.651598\pi$
$252$	−8194.20	+	3394.15i	−0.129034	+	0.0534478i
$253$	−22237.8	−	9211.20i	−0.347417	−	0.143905i
$254$	−30746.8	−	30746.8i	−0.476577	−	0.476577i
$255$	−2623.40	−	2623.40i	−0.0403445	−	0.0403445i
$256$	4096.00			0.0625000
$257$	−28435.3	+	68648.8i	−0.430518	+	1.03936i	0.548603	+	0.836083i	$0.315160\pi$
$257$	−28435.3	+	68648.8i	−0.430518	+	1.03936i	−0.979121	+	0.203279i	$0.934840\pi$
$258$	3700.99	−	8934.99i	0.0556005	−	0.134232i
$259$	−35595.5	−	14744.1i	−0.530635	−	0.219796i
$260$	4508.49	−	1867.48i	0.0666936	−	0.0276254i
$261$	−23005.2	−	55539.5i	−0.337711	−	0.815306i
$262$	3672.13			0.0534952
$263$	−44273.1	+	18338.5i	−0.640071	+	0.265126i	−0.679025	−	0.734115i	$-0.737597\pi$
$263$	−44273.1	+	18338.5i	−0.640071	+	0.265126i	0.0389543	+	0.999241i	$0.487597\pi$
$264$	7992.88			0.114682
$265$	7763.50	−	3215.75i	0.110552	−	0.0457921i
$266$	−17465.9	+	17465.9i	−0.246847	+	0.246847i
$267$	13101.2	+	13101.2i	0.183776	+	0.183776i
$268$	−5395.65	−	13026.3i	−0.0751233	−	0.181364i
$269$			16255.9i			0.224651i	0.993671	+	0.112325i	$0.0358299\pi$
$269$			16255.9i			0.224651i	−0.993671	+	0.112325i	$0.964170\pi$
$270$	−3074.20	−	7421.78i	−0.0421701	−	0.101808i
$271$			128825.i			1.75413i	0.480374	+	0.877064i	$0.340501\pi$
$271$			128825.i			1.75413i	−0.480374	+	0.877064i	$0.659499\pi$
$272$	−12011.5	+	4975.32i	−0.162352	+	0.0672486i
$273$	−1233.51	−	2977.95i	−0.0165507	−	0.0399570i
$274$	−28631.4	+	69122.4i	−0.381366	+	0.920699i
$275$	−73498.6	−	30444.1i	−0.971882	−	0.402567i
$276$	−3266.67	−	1353.10i	−0.0428831	−	0.0177628i
$277$			126491.i			1.64854i	0.566197	+	0.824270i	$0.308414\pi$
$277$			126491.i			1.64854i	−0.566197	+	0.824270i	$0.691586\pi$
$278$	45757.1	−	45757.1i	0.592064	−	0.592064i
$279$	−27157.0	+	27157.0i	−0.348878	+	0.348878i
$280$	923.895	−	2230.48i	0.0117844	−	0.0284500i
$281$	1927.90	+	4654.37i	0.0244159	+	0.0589452i	0.935617	−	0.353016i	$-0.114844\pi$
$281$	1927.90	+	4654.37i	0.0244159	+	0.0589452i	−0.911201	+	0.411961i	$0.864844\pi$
$282$	10504.0	−	10504.0i	0.132086	−	0.132086i
$283$	3380.48			0.0422091			0.0211045	−	0.999777i	$-0.493282\pi$
$283$	3380.48			0.0422091			0.0211045	+	0.999777i	$0.493282\pi$
$284$	15442.7	−	37282.0i	0.191464	−	0.462235i
$285$	−7579.83	−	7579.83i	−0.0933189	−	0.0933189i
$286$		−	33370.3i		−	0.407970i
$287$	16651.5	+	18662.3i	0.202157	+	0.226570i
$288$	−13488.4			−0.162621
$289$	−29878.1	+	29878.1i	−0.357732	+	0.357732i
$290$	15118.0	+	6262.07i	0.179762	+	0.0744598i
$291$			7665.91i			0.0905270i
$292$	−14739.6	−	14739.6i	−0.172870	−	0.172870i
$293$	−75286.8	+	31184.8i	−0.876967	+	0.363252i	−0.775320	−	0.631569i	$-0.782411\pi$
$293$	−75286.8	+	31184.8i	−0.876967	+	0.363252i	−0.101647	+	0.994820i	$0.532411\pi$
$294$	14505.7	+	6008.44i	0.167820	+	0.0695132i
$295$	16321.2	+	16321.2i	0.187546	+	0.187546i
$296$	−41431.9	−	41431.9i	−0.472881	−	0.472881i
$297$	−54933.5			−0.622765
$298$	−30248.7	+	73026.8i	−0.340623	+	0.822336i
$299$	−5649.18	+	13638.3i	−0.0631892	+	0.152552i
$300$	−10796.7	−	4472.15i	−0.119964	−	0.0496905i
$301$	−18455.2	+	7644.38i	−0.203697	+	0.0843741i
$302$	−27003.6	−	65192.4i	−0.296079	−	0.714797i
$303$	43244.0			0.471021
$304$	−34704.9	+	14375.2i	−0.375529	+	0.155549i
$305$	−15082.8			−0.162138
$306$	39554.7	−	16384.1i	0.422430	−	0.174976i
$307$	104108.	−	104108.i	1.10461	−	1.10461i	0.110761	−	0.993847i	$-0.464671\pi$
$307$	104108.	−	104108.i	1.10461	−	1.10461i	0.993847	−	0.110761i	$-0.0353289\pi$
$308$	−11673.8	−	11673.8i	−0.123058	−	0.123058i
$309$	−18190.3	−	43915.2i	−0.190512	−	0.459937i
$310$		−	10454.2i		−	0.108784i
$311$	17495.0	+	42236.6i	0.180881	+	0.436685i	0.988149	−	0.153501i	$-0.0490547\pi$
$311$	17495.0	+	42236.6i	0.180881	+	0.436685i	−0.807268	+	0.590185i	$0.799055\pi$
$312$		−	4901.99i		−	0.0503574i
$313$	101970.	−	42237.2i	1.04084	−	0.431128i	0.204224	−	0.978924i	$-0.434533\pi$
$313$	101970.	−	42237.2i	1.04084	−	0.431128i	0.836612	+	0.547796i	$0.184533\pi$
$314$	−22421.2	−	54129.5i	−0.227405	−	0.549003i
$315$	−3042.46	+	7345.14i	−0.0306622	+	0.0740251i
$316$	15105.8	+	6257.01i	0.151276	+	0.0626604i
$317$	24685.9	+	10225.2i	0.245658	+	0.101755i	0.502115	−	0.864801i	$-0.332555\pi$
$317$	24685.9	+	10225.2i	0.245658	+	0.101755i	−0.256457	+	0.966556i	$0.582555\pi$
$318$		−	8441.11i		−	0.0834729i
$319$	79123.9	−	79123.9i	0.777546	−	0.777546i
$320$	2596.20	−	2596.20i	0.0253535	−	0.0253535i
$321$	−9120.42	+	22018.6i	−0.0885125	+	0.213688i
$322$	2794.82	+	6747.28i	0.0269551	+	0.0650755i
$323$	84310.5	−	84310.5i	0.808122	−	0.808122i
$324$	40215.4			0.383091
$325$	−18671.2	+	45076.3i	−0.176769	+	0.426758i
$326$	46980.8	+	46980.8i	0.442064	+	0.442064i
$327$			14843.9i			0.138820i
$328$	12534.6	+	35912.0i	0.116510	+	0.333804i
$329$	−30682.8			−0.283467
$330$	5066.19	−	5066.19i	0.0465215	−	0.0465215i
$331$	72308.3	+	29951.1i	0.659982	+	0.273374i	0.687431	−	0.726250i	$-0.258738\pi$
$331$	72308.3	+	29951.1i	0.659982	+	0.273374i	−0.0274488	+	0.999623i	$0.508738\pi$
$332$		−	20062.6i		−	0.182016i
$333$	136438.	+	136438.i	1.23041	+	1.23041i
$334$	−44725.2	+	18525.8i	−0.400922	+	0.166067i
$335$	−11676.5	−	4836.57i	−0.104046	−	0.0430971i
$336$	−1714.85	−	1714.85i	−0.0151896	−	0.0151896i
$337$	−76119.4	−	76119.4i	−0.670248	−	0.670248i	0.287525	−	0.957773i	$-0.407168\pi$
$337$	−76119.4	−	76119.4i	−0.670248	−	0.670248i	−0.957773	+	0.287525i	$0.907168\pi$
$338$	60316.9			0.527966
$339$	−3579.70	+	8642.16i	−0.0311492	+	0.0752009i
$340$	−4459.79	+	10766.9i	−0.0385795	+	0.0931391i
$341$	−66046.4	−	27357.3i	−0.567989	−	0.235269i
$342$	114286.	−	47338.8i	0.977103	−	0.404729i
$343$	−26081.3	−	62965.8i	−0.221687	−	0.535201i
$344$	−30379.0			−0.256718
$345$	−2928.18	+	1212.89i	−0.0246014	+	0.0101902i
$346$	−36505.3			−0.304933
$347$	157211.	−	65119.1i	1.30564	−	0.540816i	0.382034	−	0.924148i	$-0.375224\pi$
$347$	157211.	−	65119.1i	1.30564	−	0.540816i	0.923610	+	0.383333i	$0.125224\pi$
$348$	11623.1	−	11623.1i	0.0959758	−	0.0959758i
$349$	−83262.6	−	83262.6i	−0.683595	−	0.683595i	0.277213	−	0.960808i	$-0.410589\pi$
$349$	−83262.6	−	83262.6i	−0.683595	−	0.683595i	−0.960808	+	0.277213i	$0.910589\pi$
$350$	9237.20	+	22300.6i	0.0754057	+	0.182045i
$351$			33690.4i			0.273459i
$352$	−9608.10	−	23196.0i	−0.0775447	−	0.187209i
$353$			107134.i			0.859760i	0.902886	+	0.429880i	$0.141444\pi$
$353$			107134.i			0.859760i	−0.902886	+	0.429880i	$0.858556\pi$
$354$	21421.0	−	8872.88i	0.170936	−	0.0708040i
$355$	−13842.6	−	33418.9i	−0.109840	−	0.265177i
$356$	22272.1	−	53769.5i	0.175736	−	0.424264i
$357$	7111.76	+	2945.79i	0.0558008	+	0.0231134i
$358$	146544.	+	60700.6i	1.14341	+	0.473617i
$359$		−	155196.i		−	1.20418i	−0.798428	−	0.602090i	$-0.794335\pi$
$359$		−	155196.i		−	1.20418i	0.798428	−	0.602090i	$-0.205665\pi$
$360$	−8549.48	+	8549.48i	−0.0659682	+	0.0659682i
$361$	151449.	−	151449.i	1.16212	−	1.16212i
$362$	−47985.7	+	115848.i	−0.366180	+	0.884037i
$363$	−4479.71	−	10815.0i	−0.0339967	−	0.0820752i
$364$	−7159.48	+	7159.48i	−0.0540355	+	0.0540355i
$365$	−18685.0			−0.140251
$366$	−5798.03	+	13997.7i	−0.0432831	+	0.104495i
$367$	52520.5	+	52520.5i	0.389939	+	0.389939i	0.874666	−	0.484727i	$-0.161081\pi$
$367$	52520.5	+	52520.5i	0.389939	+	0.389939i	−0.484727	+	0.874666i	$0.661081\pi$
$368$			11106.7i			0.0820140i
$369$	−41277.5	−	118261.i	−0.303152	−	0.868538i
$370$	−52522.3			−0.383654
$371$	−12328.5	+	12328.5i	−0.0895697	+	0.0895697i
$372$	−9702.01	−	4018.70i	−0.0701093	−	0.0290402i
$373$		−	198128.i		−	1.42406i	−0.702148	−	0.712031i	$-0.747776\pi$
$373$		−	198128.i		−	1.42406i	0.702148	−	0.712031i	$-0.252224\pi$
$374$	56351.3	+	56351.3i	0.402866	+	0.402866i
$375$	−20223.7	+	8376.92i	−0.143813	+	0.0595692i
$376$	−43110.2	−	17856.8i	−0.304933	−	0.126307i
$377$	−48526.3	−	48526.3i	−0.341424	−	0.341424i
$378$	11785.8	+	11785.8i	0.0824851	+	0.0824851i
$379$	−94644.2			−0.658894			−0.329447	−	0.944174i	$-0.606862\pi$
$379$	−94644.2			−0.658894			−0.329447	+	0.944174i	$0.606862\pi$
$380$	−12885.7	+	31108.9i	−0.0892363	+	0.215435i
$381$	−14983.2	+	36172.7i	−0.103218	+	0.249190i
$382$	−76101.7	−	31522.4i	−0.521516	−	0.216019i
$383$	−13979.9	+	5790.68i	−0.0953032	+	0.0394759i	−0.429826	−	0.902912i	$-0.641425\pi$
$383$	−13979.9	+	5790.68i	−0.0953032	+	0.0394759i	0.334522	+	0.942388i	$0.391425\pi$
$384$	−1411.40	−	3407.42i	−0.00957167	−	0.0231081i
$385$	−14798.6			−0.0998388
$386$	−148809.	+	61638.5i	−0.998742	+	0.413693i
$387$	100040.			0.667963
$388$	22247.1	−	9215.05i	0.147778	−	0.0612117i
$389$	4811.69	−	4811.69i	0.0317979	−	0.0317979i	−0.691029	−	0.722827i	$-0.742842\pi$
$389$	4811.69	−	4811.69i	0.0317979	−	0.0317979i	0.722827	+	0.691029i	$0.242842\pi$
$390$	−3107.07	−	3107.07i	−0.0204278	−	0.0204278i
$391$	−13491.0	−	32570.2i	−0.0882452	−	0.213043i
$392$		−	49319.3i		−	0.320955i
$393$	−1265.34	−	3054.80i	−0.00819262	−	0.0197787i
$394$			17471.1i			0.112545i
$395$	13540.5	−	5608.68i	0.0867845	−	0.0359473i
$396$	31640.2	+	76386.2i	0.201766	+	0.487107i
$397$	63257.9	−	152718.i	0.401360	−	0.968969i	−0.585976	−	0.810328i	$-0.699289\pi$
$397$	63257.9	−	152718.i	0.401360	−	0.968969i	0.987336	−	0.158641i	$-0.0507111\pi$
$398$	90248.4	+	37382.1i	0.569736	+	0.235992i
$399$	20548.1	+	8511.29i	0.129070	+	0.0534626i
$400$			36708.9i			0.229430i
$401$	−225798.	+	225798.i	−1.40421	+	1.40421i	−0.618152	+	0.786058i	$0.712119\pi$
$401$	−225798.	+	225798.i	−1.40421	+	1.40421i	−0.786058	+	0.618152i	$0.787881\pi$
$402$	−8977.18	+	8977.18i	−0.0555505	+	0.0555505i
$403$	−16778.1	+	40505.9i	−0.103308	+	0.249407i
$404$	−51982.8	−	125498.i	−0.318491	−	0.768905i
$405$	25490.0	−	25490.0i	0.155403	−	0.155403i
$406$	−33951.5			−0.205972
$407$	−137445.	+	331821.i	−0.829734	+	2.00315i
$408$	8277.83	+	8277.83i	0.0497275	+	0.0497275i
$409$		−	370.596i		−	0.00221541i	−0.999999	−	0.00110770i	$-0.999647\pi$
$409$		−	370.596i		−	0.00221541i	0.999999	−	0.00110770i	$-0.000352593\pi$
$410$	30707.3	+	14817.5i	0.182673	+	0.0881468i
$411$	67368.1			0.398814
$412$	−105579.	+	105579.i	−0.621992	+	0.621992i
$413$	−44245.0	−	18326.9i	−0.259397	−	0.107446i
$414$		−	36575.1i		−	0.213395i
$415$	−12716.4	−	12716.4i	−0.0738360	−	0.0738360i
$416$	−14226.0	+	5892.60i	−0.0822045	+	0.0340502i
$417$	−53831.9	−	22297.9i	−0.309576	−	0.128231i
$418$	162816.	+	162816.i	0.931850	+	0.931850i
$419$	−235779.	−	235779.i	−1.34300	−	1.34300i	−0.893054	−	0.449949i	$-0.851442\pi$
$419$	−235779.	−	235779.i	−1.34300	−	1.34300i	−0.449949	−	0.893054i	$-0.648558\pi$
$420$	−2173.87			−0.0123235
$421$	3822.86	−	9229.19i	0.0215687	−	0.0520714i	−0.912728	−	0.408567i	$-0.866029\pi$
$421$	3822.86	−	9229.19i	0.0215687	−	0.0520714i	0.934297	+	0.356496i	$0.116029\pi$
$422$	−32635.2	+	78788.3i	−0.183257	+	0.442422i
$423$	141965.	+	58803.9i	0.793417	+	0.328644i
$424$	−24496.8	+	10146.9i	−0.136263	+	0.0564420i
$425$	−44589.4	−	107648.i	−0.246862	−	0.595977i
$426$	−36335.8			−0.200224
$427$	28912.1	−	11975.8i	0.158571	−	0.0656824i
$428$	74863.4			0.408679
$429$	−27760.4	+	11498.7i	−0.150838	+	0.0624792i
$430$	−19255.3	+	19255.3i	−0.104139	+	0.104139i
$431$	14110.7	+	14110.7i	0.0759617	+	0.0759617i	0.744067	−	0.668105i	$-0.232894\pi$
$431$	14110.7	+	14110.7i	0.0759617	+	0.0759617i	−0.668105	+	0.744067i	$0.732894\pi$
$432$	9700.28	+	23418.5i	0.0519777	+	0.125485i
$433$			211091.i			1.12589i	0.826496	+	0.562943i	$0.190331\pi$
$433$			211091.i			1.12589i	−0.826496	+	0.562943i	$0.809669\pi$
$434$	8300.61	+	20039.5i	0.0440687	+	0.106391i
$435$		−	14734.3i		−	0.0778664i
$436$	43078.3	−	17843.6i	0.226613	−	0.0938663i
$437$	−38979.8	−	94105.5i	−0.204116	−	0.492779i
$438$	−7182.73	+	17340.7i	−0.0374405	+	0.0903894i
$439$	316337.	+	131031.i	1.64142	+	0.679900i	0.996441	−	0.0842965i	$-0.0268643\pi$
$439$	316337.	+	131031.i	1.64142	+	0.679900i	0.644983	+	0.764197i	$0.276864\pi$
$440$	−20792.5	−	8612.53i	−0.107399	−	0.0444862i
$441$			162412.i			0.835105i
$442$	34560.0	−	34560.0i	0.176900	−	0.176900i
$443$	−35826.7	+	35826.7i	−0.182557	+	0.182557i	−0.792469	−	0.609912i	$-0.791205\pi$
$443$	−35826.7	+	35826.7i	−0.182557	+	0.182557i	0.609912	+	0.792469i	$0.291205\pi$
$444$	−20190.2	+	48743.4i	−0.102418	+	0.247258i
$445$	−19964.3	−	48198.0i	−0.100817	−	0.243394i
$446$	−21129.5	+	21129.5i	−0.106223	+	0.106223i
$447$	71173.3			0.356207
$448$	−2915.24	+	7038.01i	−0.0145251	+	0.0350666i
$449$	−20386.6	−	20386.6i	−0.101123	−	0.101123i	0.654735	−	0.755858i	$-0.272780\pi$
$449$	−20386.6	−	20386.6i	−0.101123	−	0.101123i	−0.755858	+	0.654735i	$0.772780\pi$
$450$		−	120885.i		−	0.596963i
$451$	173970.	−	155224.i	0.855305	−	0.763145i
$452$	29383.4			0.143822
$453$	−44928.0	+	44928.0i	−0.218938	+	0.218938i
$454$	−101108.	−	41880.2i	−0.490538	−	0.203188i
$455$			9075.91i			0.0438397i
$456$	23917.2	+	23917.2i	0.115022	+	0.115022i
$457$	−234286.	+	97044.6i	−1.12180	+	0.464664i	−0.864985	−	0.501797i	$-0.832672\pi$
$457$	−234286.	+	97044.6i	−1.12180	+	0.464664i	−0.256813	+	0.966461i	$0.582672\pi$
$458$	−27042.0	−	11201.2i	−0.128916	−	0.0533989i
$459$	−56891.9	−	56891.9i	−0.270038	−	0.270038i
$460$	7039.83	+	7039.83i	0.0332695	+	0.0332695i
$461$	−246762.			−1.16112			−0.580558	−	0.814219i	$-0.697166\pi$
$461$	−246762.			−1.16112			−0.580558	+	0.814219i	$0.697166\pi$
$462$	−5688.76	+	13733.9i	−0.0266522	+	0.0643442i
$463$	−99582.4	+	240413.i	−0.464537	+	1.12149i	0.501978	+	0.864881i	$0.332606\pi$
$463$	−99582.4	+	240413.i	−0.464537	+	1.12149i	−0.966515	+	0.256611i	$0.917394\pi$
$464$	−47702.9	−	19759.2i	−0.221569	−	0.0917769i
$465$	−8696.71	+	3602.30i	−0.0402207	+	0.0166599i
$466$	−21537.9	−	51997.1i	−0.0991818	−	0.239446i
$467$	347771.			1.59463			0.797314	−	0.603564i	$-0.206253\pi$
$467$	347771.			1.59463			0.797314	+	0.603564i	$0.206253\pi$
$468$	46847.2	−	19404.8i	0.213891	−	0.0885965i
$469$	26222.8			0.119216
$470$	−38643.3	+	16006.6i	−0.174935	+	0.0724607i
$471$	−37303.9	+	37303.9i	−0.168156	+	0.168156i
$472$	−51499.6	−	51499.6i	−0.231164	−	0.231164i
$473$	71260.8	+	172039.i	0.318514	+	0.768960i
$474$		−	14722.4i		−	0.0655272i
$475$	−128833.	−	311030.i	−0.571004	−	1.37852i
$476$		−	24180.0i		−	0.106719i
$477$	80669.8	−	33414.5i	0.354547	−	0.146858i
$478$	28289.7	+	68297.3i	0.123815	+	0.298915i
$479$	−122184.	+	294977.i	−0.532527	+	1.28563i	0.397317	+	0.917681i	$0.369941\pi$
$479$	−122184.	+	294977.i	−0.532527	+	1.28563i	−0.929844	+	0.367953i	$0.880059\pi$
$480$	−3054.35	−	1265.15i	−0.0132567	−	0.00549112i
$481$	203504.	+	84294.0i	0.879594	+	0.364340i
$482$			128463.i			0.552948i
$483$	4649.96	−	4649.96i	0.0199322	−	0.0199322i
$484$	−26001.0	+	26001.0i	−0.110994	+	0.110994i
$485$	8260.21	−	19941.9i	0.0351162	−	0.0847781i
$486$	−48581.8	−	117287.i	−0.205684	−	0.496565i
$487$	159694.	−	159694.i	0.673336	−	0.673336i	−0.285148	−	0.958484i	$-0.592043\pi$
$487$	159694.	−	159694.i	0.673336	−	0.673336i	0.958484	+	0.285148i	$0.0920427\pi$
$488$	47592.1			0.199846
$489$	22894.2	−	55271.5i	0.0957431	−	0.231144i
$490$	−31260.4	−	31260.4i	−0.130198	−	0.130198i
$491$		−	366656.i		−	1.52088i	−0.649407	−	0.760441i	$-0.724983\pi$
$491$		−	366656.i		−	1.52088i	0.649407	−	0.760441i	$-0.275017\pi$
$492$	25555.7	−	22802.0i	0.105574	−	0.0941982i
$493$	163889.			0.674306
$494$	99854.5	−	99854.5i	0.409179	−	0.409179i
$495$	68471.2	+	28361.7i	0.279446	+	0.115750i
$496$			32986.8i			0.134084i
$497$	53069.3	+	53069.3i	0.214848	+	0.214848i
$498$	−16689.8	+	6913.16i	−0.0672967	+	0.0278752i
$499$	−452358.	−	187373.i	−1.81669	−	0.752498i	−0.978227	−	0.207540i	$-0.933454\pi$
$499$	−452358.	−	187373.i	−1.81669	−	0.752498i	−0.838463	−	0.544958i	$-0.816546\pi$
$500$	48621.0	+	48621.0i	0.194484	+	0.194484i
$501$	30822.8	+	30822.8i	0.122800	+	0.122800i
$502$	−108427.			−0.430259
$503$	−134752.	+	325321.i	−0.532599	+	1.28581i	0.397198	+	0.917733i	$0.369983\pi$
$503$	−134752.	+	325321.i	−0.532599	+	1.28581i	−0.929796	+	0.368074i	$0.880017\pi$
$504$	9600.11	−	23176.7i	0.0377933	−	0.0912411i
$505$	−112494.	−	46596.5i	−0.441109	−	0.182713i
$506$	62898.0	−	26053.2i	0.245661	−	0.101756i
$507$	−20784.0	−	50177.0i	−0.0808562	−	0.195204i
$508$	122987.			0.476577
$509$	−174959.	+	72470.3i	−0.675305	+	0.279720i	−0.693863	−	0.720107i	$-0.744093\pi$
$509$	−174959.	+	72470.3i	−0.675305	+	0.279720i	0.0185577	+	0.999828i	$0.494093\pi$
$510$	10493.6			0.0403445
$511$	35817.0	−	14835.9i	0.137166	−	0.0568162i
$512$	−8192.00	+	8192.00i	−0.0312500	+	0.0312500i
$513$	−164379.	−	164379.i	−0.624612	−	0.624612i
$514$	−80427.1	−	194168.i	−0.304422	−	0.734940i
$515$			133841.i			0.504630i
$516$	10468.0	+	25272.0i	0.0393155	+	0.0949160i
$517$			286024.i			1.07009i
$518$	100679.	−	41702.7i	0.375215	−	0.155419i
$519$	12579.0	+	30368.4i	0.0466994	+	0.112742i
$520$	−5282.02	+	12751.9i	−0.0195341	+	0.0471595i
$521$	8969.80	+	3715.41i	0.0330451	+	0.0136877i	0.399145	−	0.916888i	$-0.369307\pi$
$521$	8969.80	+	3715.41i	0.0330451	+	0.0136877i	−0.366100	+	0.930576i	$0.619307\pi$
$522$	157089.	+	65068.5i	0.576508	+	0.238798i
$523$		−	29891.9i		−	0.109282i	−0.998506	−	0.0546412i	$-0.982598\pi$
$523$		−	29891.9i		−	0.109282i	0.998506	−	0.0546412i	$-0.0174015\pi$
$524$	−7344.25	+	7344.25i	−0.0267476	+	0.0267476i
$525$	15368.7	−	15368.7i	0.0557593	−	0.0557593i
$526$	51869.1	−	125223.i	0.187472	−	0.452598i
$527$	−40068.4	−	96733.6i	−0.144271	−	0.348302i
$528$	−15985.8	+	15985.8i	−0.0573410	+	0.0573410i
$529$	249724.			0.892379
$530$	−9095.51	+	21958.5i	−0.0323799	+	0.0781720i
$531$	169592.	+	169592.i	0.601474	+	0.601474i
$532$		−	69863.5i		−	0.246847i
$533$	−95198.4	−	106695.i	−0.335100	−	0.375568i
$534$	−52404.8			−0.183776
$535$	47451.3	−	47451.3i	0.165783	−	0.165783i
$536$	36843.8	+	15261.2i	0.128243	+	0.0531202i
$537$		−	142825.i		−	0.495286i
$538$	−32511.9	−	32511.9i	−0.112325	−	0.112325i
$539$	−279299.	+	115690.i	−0.961374	+	0.398214i
$540$	20992.0	+	8695.16i	0.0719889	+	0.0298188i
$541$	331959.	+	331959.i	1.13420	+	1.13420i	0.989471	+	0.144728i	$0.0462308\pi$
$541$	331959.	+	331959.i	1.13420	+	1.13420i	0.144728	+	0.989471i	$0.453769\pi$
$542$	−257650.	−	257650.i	−0.877064	−	0.877064i
$543$	112907.			0.382933
$544$	14072.3	−	33973.6i	0.0475519	−	0.114800i
$545$	15994.7	−	38614.6i	0.0538496	−	0.130005i
$546$	8422.92	+	3488.89i	0.0282538	+	0.0117031i
$547$	218201.	−	90381.9i	0.729260	−	0.302069i	0.0130121	−	0.999915i	$-0.495858\pi$
$547$	218201.	−	90381.9i	0.729260	−	0.302069i	0.716248	+	0.697846i	$0.245858\pi$
$548$	−80982.0	−	195508.i	−0.269667	−	0.651033i
$549$	−156724.			−0.519986
$550$	207885.	−	86109.0i	0.687224	−	0.284658i
$551$	473528.			1.55970
$552$	9239.53	−	3827.14i	0.0303230	−	0.0125602i
$553$	−21502.4	+	21502.4i	−0.0703132	+	0.0703132i
$554$	−252982.	−	252982.i	−0.824270	−	0.824270i
$555$	18098.1	+	43692.8i	0.0587554	+	0.141848i
$556$			183028.i			0.592064i
$557$	−140596.	−	339429.i	−0.453172	−	1.09405i	−0.971109	−	0.238636i	$-0.923300\pi$
$557$	−140596.	−	339429.i	−0.453172	−	1.09405i	0.517937	−	0.855419i	$-0.326700\pi$
$558$		−	108628.i		−	0.348878i
$559$	105510.	−	43703.8i	0.337654	−	0.139861i
$560$	2613.17	+	6308.75i	0.00833281	+	0.0201172i
$561$	27460.5	−	66295.6i	0.0872536	−	0.210649i
$562$	−13164.5	−	5452.93i	−0.0416805	−	0.0172646i
$563$	144950.	+	60040.3i	0.457300	+	0.189420i	0.599429	−	0.800428i	$-0.295395\pi$
$563$	144950.	+	60040.3i	0.457300	+	0.189420i	−0.142128	+	0.989848i	$0.545395\pi$
$564$			42016.1i			0.132086i
$565$	18624.3	−	18624.3i	0.0583422	−	0.0583422i
$566$	−6760.96	+	6760.96i	−0.0211045	+	0.0211045i
$567$	−28622.4	+	69100.7i	−0.0890308	+	0.214939i
$568$	43678.6	+	105449.i	0.135385	+	0.326849i
$569$	123486.	−	123486.i	0.381412	−	0.381412i	−0.490199	−	0.871611i	$-0.663076\pi$
$569$	123486.	−	123486.i	0.381412	−	0.381412i	0.871611	+	0.490199i	$0.163076\pi$
$570$	30319.3			0.0933189
$571$	63652.6	−	153671.i	0.195229	−	0.471324i	−0.795703	−	0.605686i	$-0.792899\pi$
$571$	63652.6	−	153671.i	0.195229	−	0.471324i	0.990932	+	0.134362i	$0.0428986\pi$
$572$	66740.5	+	66740.5i	0.203985	+	0.203985i
$573$			74170.2i			0.225902i
$574$	−70627.6	−	4021.79i	−0.214363	−	0.0122066i
$575$	−99539.3			−0.301064
$576$	26976.9	−	26976.9i	0.0813105	−	0.0813105i
$577$	−90397.4	−	37443.8i	−0.271522	−	0.112468i	0.242768	−	0.970084i	$-0.421945\pi$
$577$	−90397.4	−	37443.8i	−0.271522	−	0.112468i	−0.514290	+	0.857616i	$0.671945\pi$
$578$		−	119513.i		−	0.357732i
$579$	102553.	+	102553.i	0.305908	+	0.305908i
$580$	−42760.1	+	17711.8i	−0.127111	+	0.0526510i
$581$	34472.8	+	14279.1i	0.102123	+	0.0423008i
$582$	−15331.8	−	15331.8i	−0.0452635	−	0.0452635i
$583$	114926.	+	114926.i	0.338127	+	0.338127i
$584$	58958.2			0.172870
$585$	17394.1	−	41993.0i	0.0508265	−	0.122706i
$586$	88203.9	−	212943.i	0.256858	−	0.620110i
$587$	−626009.	−	259301.i	−1.81679	−	0.752539i	−0.978166	−	0.207827i	$-0.933361\pi$
$587$	−626009.	−	259301.i	−1.81679	−	0.752539i	−0.838623	−	0.544712i	$-0.816639\pi$
$588$	−41028.2	+	16994.4i	−0.118666	+	0.0491533i
$589$	−115770.	−	279494.i	−0.333707	−	0.805640i
$590$	−65284.9			−0.187546
$591$	14534.0	−	6020.18i	0.0416112	−	0.0172359i
$592$	165728.			0.472881
$593$	250483.	−	103754.i	0.712311	−	0.295049i	0.00305033	−	0.999995i	$-0.499029\pi$
$593$	250483.	−	103754.i	0.712311	−	0.295049i	0.709260	+	0.704947i	$0.249029\pi$
$594$	109867.	−	109867.i	0.311383	−	0.311383i
$595$	−15326.2	−	15326.2i	−0.0432913	−	0.0432913i
$596$	−85556.2	−	206551.i	−0.240857	−	0.581480i
$597$		−	87957.9i		−	0.246789i
$598$	−15978.3	−	38575.0i	−0.0446815	−	0.107871i
$599$			616845.i			1.71918i	0.510981	+	0.859592i	$0.329282\pi$
$599$			616845.i			1.71918i	−0.510981	+	0.859592i	$0.670718\pi$
$600$	30537.7	−	12649.1i	0.0848270	−	0.0351365i
$601$	202450.	+	488756.i	0.560490	+	1.35314i	0.909375	+	0.415977i	$0.136560\pi$
$601$	202450.	+	488756.i	0.560490	+	1.35314i	−0.348885	+	0.937166i	$0.613440\pi$
$602$	21621.6	−	52199.1i	0.0596615	−	0.144036i
$603$	−121329.	−	50256.3i	−0.333681	−	0.138215i
$604$	184392.	+	76377.6i	0.505438	+	0.209359i
$605$			32960.8i			0.0900507i
$606$	−86488.0	+	86488.0i	−0.235511	+	0.235511i
$607$	−435844.	+	435844.i	−1.18291	+	1.18291i	−0.203929	+	0.978986i	$0.565371\pi$
$607$	−435844.	+	435844.i	−1.18291	+	1.18291i	−0.978986	+	0.203929i	$0.934629\pi$
$608$	40659.3	−	98160.3i	0.109990	−	0.265539i
$609$	11699.0	+	28243.9i	0.0315439	+	0.0761537i
$610$	30165.7	−	30165.7i	0.0810688	−	0.0810688i
$611$	175417.			0.469883
$612$	−46341.2	+	111878.i	−0.123727	+	0.298703i
$613$	337245.	+	337245.i	0.897479	+	0.897479i	0.995213	−	0.0977333i	$-0.0311592\pi$
$613$	337245.	+	337245.i	0.897479	+	0.897479i	−0.0977333	+	0.995213i	$0.531159\pi$
$614$			416433.i			1.10461i
$615$	1745.37	−	30650.9i	0.00461464	−	0.0810389i
$616$	46695.2			0.123058
$617$	454106.	−	454106.i	1.19285	−	1.19285i	0.216591	−	0.976262i	$-0.430506\pi$
$617$	454106.	−	454106.i	1.19285	−	1.19285i	0.976262	−	0.216591i	$-0.0694939\pi$
$618$	124211.	+	51449.9i	0.325225	+	0.134712i
$619$		−	383999.i		−	1.00219i	−0.865393	−	0.501094i	$-0.832931\pi$
$619$		−	383999.i		−	1.00219i	0.865393	−	0.501094i	$-0.167069\pi$
$620$	20908.3	+	20908.3i	0.0543921	+	0.0543921i
$621$	−63501.5	+	26303.2i	−0.164665	+	0.0682064i
$622$	−119463.	−	49483.2i	−0.308783	−	0.127902i
$623$	76538.6	+	76538.6i	0.197199	+	0.197199i
$624$	9803.98	+	9803.98i	0.0251787	+	0.0251787i
$625$	−296849.			−0.759934
$626$	−119465.	+	288414.i	−0.304854	+	0.735982i
$627$	79342.1	−	191549.i	0.201822	−	0.487241i
$628$	153101.	+	63416.7i	0.388204	+	0.160799i
$629$	−485995.	+	201306.i	−1.22837	+	0.508809i
$630$	−8605.37	−	20775.2i	−0.0216814	−	0.0523436i
$631$	−354439.			−0.890189			−0.445095	−	0.895484i	$-0.646830\pi$
$631$	−354439.			−0.890189			−0.445095	+	0.895484i	$0.646830\pi$
$632$	−42725.6	+	17697.5i	−0.106968	+	0.0443076i
$633$	76788.7			0.191642
$634$	−69822.3	+	28921.3i	−0.173706	+	0.0719515i
$635$	77954.0	−	77954.0i	0.193326	−	0.193326i
$636$	16882.2	+	16882.2i	0.0417364	+	0.0417364i
$637$	70951.8	+	171293.i	0.174858	+	0.422144i
$638$			316495.i			0.777546i
$639$	−143837.	−	347253.i	−0.352264	−	0.850441i
$640$			10384.8i			0.0253535i
$641$	514080.	−	212939.i	1.25117	−	0.518250i	0.343979	−	0.938977i	$-0.388225\pi$
$641$	514080.	−	212939.i	1.25117	−	0.518250i	0.907187	+	0.420727i	$0.138225\pi$
$642$	−25796.4	−	62278.1i	−0.0625878	−	0.151100i
$643$	−131256.	+	316879.i	−0.317465	+	0.766429i	0.681922	+	0.731425i	$0.261144\pi$
$643$	−131256.	+	316879.i	−0.317465	+	0.766429i	−0.999387	+	0.0350039i	$0.988856\pi$
$644$	−19084.2	−	7904.93i	−0.0460153	−	0.0190602i
$645$	22653.3	+	9383.32i	0.0544519	+	0.0225547i
$646$			337242.i			0.808122i
$647$	−252234.	+	252234.i	−0.602553	+	0.602553i	−0.940989	−	0.338436i	$-0.890102\pi$
$647$	−252234.	+	252234.i	−0.602553	+	0.602553i	0.338436	+	0.940989i	$0.390102\pi$
$648$	−80430.7	+	80430.7i	−0.191546	+	0.191546i
$649$	−170843.	+	412451.i	−0.405609	+	0.979226i
$650$	−52810.2	−	127495.i	−0.124994	−	0.301763i
$651$	13810.4	−	13810.4i	0.0325870	−	0.0325870i
$652$	−187923.			−0.442064
$653$	−50967.6	+	123047.i	−0.119527	+	0.288565i	−0.972307	−	0.233706i	$-0.924915\pi$
$653$	−50967.6	+	123047.i	−0.119527	+	0.288565i	0.852780	+	0.522270i	$0.174915\pi$
$654$	−29687.8	−	29687.8i	−0.0694102	−	0.0694102i
$655$			9310.13i			0.0217007i
$656$	−96893.3	−	46754.8i	−0.225157	−	0.108647i
$657$	−194154.			−0.449796
$658$	61365.6	−	61365.6i	0.141734	−	0.141734i
$659$	−275039.	−	113925.i	−0.633321	−	0.262330i	0.0428422	−	0.999082i	$-0.486359\pi$
$659$	−275039.	−	113925.i	−0.633321	−	0.262330i	−0.676164	+	0.736752i	$0.736359\pi$
$660$			20264.8i			0.0465215i
$661$	72997.5	+	72997.5i	0.167072	+	0.167072i	0.785691	−	0.618619i	$-0.212307\pi$
$661$	72997.5	+	72997.5i	0.167072	+	0.167072i	−0.618619	+	0.785691i	$0.712307\pi$
$662$	−204519.	+	84714.5i	−0.466678	+	0.193304i
$663$	−40658.8	−	16841.4i	−0.0924969	−	0.0383135i
$664$	40125.1	+	40125.1i	0.0910081	+	0.0910081i
$665$	−44282.1	−	44282.1i	−0.100135	−	0.100135i
$666$	−545754.			−1.23041
$667$	53578.8	−	129351.i	0.120432	−	0.290748i
$668$	52398.9	−	126502.i	0.117427	−	0.283494i
$669$	24858.2	+	10296.6i	0.0555416	+	0.0230061i
$670$	33026.2	−	13679.9i	0.0735713	−	0.0304742i
$671$	−111638.	−	269518.i	−0.247952	−	0.598609i
$672$	6859.39			0.0151896
$673$	−255332.	+	105762.i	−0.563735	+	0.233507i	−0.646306	−	0.763078i	$-0.723687\pi$
$673$	−255332.	+	105762.i	−0.563735	+	0.233507i	0.0825707	+	0.996585i	$0.473687\pi$
$674$	304478.			0.670248
$675$	−209880.	+	86935.1i	−0.460642	+	0.190804i
$676$	−120634.	+	120634.i	−0.263983	+	0.263983i
$677$	466263.	+	466263.i	1.01731	+	1.01731i	0.999848	+	0.0174625i	$0.00555877\pi$
$677$	466263.	+	466263.i	1.01731	+	1.01731i	0.0174625	+	0.999848i	$0.494441\pi$
$678$	−10124.9	−	24443.7i	−0.0220258	−	0.0531751i
$679$			44785.0i			0.0971390i
$680$	−12614.2	−	30453.3i	−0.0272798	−	0.0658593i
$681$			98541.6i			0.212484i
$682$	186807.	−	77378.1i	0.401629	−	0.166360i
$683$	−154958.	−	374102.i	−0.332179	−	0.801952i	−0.998419	−	0.0562138i	$-0.982097\pi$
$683$	−154958.	−	374102.i	−0.332179	−	0.801952i	0.666240	−	0.745738i	$-0.267903\pi$
$684$	−133894.	+	323249.i	−0.286187	+	0.690916i
$685$	−175250.	−	72590.8i	−0.373488	−	0.154704i
$686$	178094.	+	73769.0i	0.378444	+	0.156757i
$687$			26355.7i			0.0558419i
$688$	60757.9	−	60757.9i	0.128359	−	0.128359i
$689$	70483.3	−	70483.3i	0.148473	−	0.148473i
$690$	3430.58	−	8282.15i	0.00720559	−	0.0173958i
$691$	−214679.	−	518281.i	−0.449607	−	1.08545i	−0.972469	−	0.233031i	$-0.925136\pi$
$691$	−214679.	−	518281.i	−0.449607	−	1.08545i	0.522862	−	0.852417i	$-0.324864\pi$
$692$	73010.6	−	73010.6i	0.152466	−	0.152466i
$693$	−153771.			−0.320190
$694$	−184185.	+	444661.i	−0.382414	+	0.923230i
$695$	116010.	+	116010.i	0.240175	+	0.240175i
$696$			46492.2i			0.0959758i
$697$	340931.	+	19413.8i	0.701779	+	0.0399618i
$698$	333050.			0.683595
$699$	−35834.4	+	35834.4i	−0.0733408	+	0.0733408i
$700$	−63075.5	−	26126.7i	−0.128726	−	0.0533199i
$701$		−	620688.i		−	1.26310i	−0.775336	−	0.631549i	$-0.782419\pi$
$701$		−	620688.i		−	1.26310i	0.775336	−	0.631549i	$-0.217581\pi$
$702$	−67380.9	−	67380.9i	−0.136730	−	0.136730i
$703$	−1.40419e6	+	581635.i	−2.84129	+	1.17690i
$704$	65608.2	+	27175.8i	0.132377	+	0.0548324i
$705$	26631.4	+	26631.4i	0.0535816	+	0.0535816i
$706$	−214268.	−	214268.i	−0.429880	−	0.429880i
$707$	252636.			0.505424
$708$	−25096.3	+	60587.8i	−0.0500660	+	0.120870i
$709$	4017.98	−	9700.25i	0.00799310	−	0.0192970i	−0.919833	−	0.392311i	$-0.871676\pi$
$709$	4017.98	−	9700.25i	0.00799310	−	0.0192970i	0.927826	+	0.373014i	$0.121676\pi$
$710$	94523.0	+	39152.7i	0.187508	+	0.0776685i
$711$	140699.	−	58279.2i	0.278324	−	0.115285i
$712$	62994.9	+	152083.i	0.124264	+	0.300000i
$713$	−89446.8			−0.175949
$714$	−20115.1	+	8331.94i	−0.0394571	+	0.0163437i
$715$	84605.4			0.165495
$716$	−414490.	+	171687.i	−0.808515	+	0.334898i
$717$	47067.8	−	47067.8i	0.0915557	−	0.0915557i
$718$	310392.	+	310392.i	0.602090	+	0.602090i
$719$	−197047.	−	475713.i	−0.381164	−	0.920211i	−0.991741	−	0.128255i	$-0.959063\pi$
$719$	−197047.	−	475713.i	−0.381164	−	0.920211i	0.610577	−	0.791957i	$-0.290937\pi$
$720$		−	34197.9i		−	0.0659682i
$721$	−106270.	−	256557.i	−0.204427	−	0.493530i
$722$			605794.i			1.16212i
$723$	106867.	−	44265.9i	0.204441	−	0.0846822i
$724$	−135724.	−	327667.i	−0.258928	−	0.625108i
$725$	177084.	−	427520.i	0.336903	−	0.813355i
$726$	30589.3	+	12670.5i	0.0580359	+	0.0240393i
$727$	16331.8	+	6764.87i	0.0309005	+	0.0127994i	0.398080	−	0.917351i	$-0.369677\pi$
$727$	16331.8	+	6764.87i	0.0309005	+	0.0127994i	−0.367180	+	0.930150i	$0.619677\pi$
$728$		−	28637.9i		−	0.0540355i
$729$	207091.	−	207091.i	0.389678	−	0.389678i
$730$	37370.0	−	37370.0i	0.0701257	−	0.0701257i
$731$	−104371.	+	251973.i	−0.195319	+	0.471541i
$732$	−16399.3	−	39591.4i	−0.0306058	−	0.0738888i
$733$	634409.	−	634409.i	1.18076	−	1.18076i	0.201211	−	0.979548i	$-0.435512\pi$
$733$	634409.	−	634409.i	1.18076	−	1.18076i	0.979548	−	0.201211i	$-0.0644876\pi$
$734$	−210082.			−0.389939
$735$	−15233.5	+	36777.0i	−0.0281985	+	0.0680771i
$736$	−22213.3	−	22213.3i	−0.0410070	−	0.0410070i
$737$		−	244448.i		−	0.450041i
$738$	319077.	+	153967.i	0.585845	+	0.282693i
$739$	276682.			0.506631			0.253315	−	0.967384i	$-0.418479\pi$
$739$	276682.			0.506631			0.253315	+	0.967384i	$0.418479\pi$
$740$	105045.	−	105045.i	0.191827	−	0.191827i
$741$	−117476.	−	48660.1i	−0.213950	−	0.0886210i
$742$		−	49313.8i		−	0.0895697i
$743$	166251.	+	166251.i	0.301152	+	0.301152i	0.841465	−	0.540312i	$-0.181694\pi$
$743$	166251.	+	166251.i	0.301152	+	0.301152i	−0.540312	+	0.841465i	$0.681694\pi$
$744$	27441.4	−	11366.6i	0.0495748	−	0.0205345i
$745$	−185149.	−	76691.0i	−0.333586	−	0.138176i
$746$	396257.	+	396257.i	0.712031	+	0.712031i
$747$	−132135.	−	132135.i	−0.236797	−	0.236797i
$748$	−225405.			−0.402866
$749$	−53282.4	+	128635.i	−0.0949774	+	0.229296i
$750$	23693.5	−	57201.2i	0.0421218	−	0.101691i
$751$	621021.	+	257235.i	1.10110	+	0.456090i	0.857864	−	0.513877i	$-0.171791\pi$
$751$	621021.	+	257235.i	1.10110	+	0.456090i	0.243235	+	0.969967i	$0.421791\pi$
$752$	121934.	−	50506.8i	0.215620	−	0.0893129i
$753$	37361.8	+	90199.3i	0.0658927	+	0.159079i
$754$	194105.			0.341424
$755$	165286.	−	68463.5i	0.289962	−	0.120106i
$756$	−47143.2			−0.0824851
$757$	1.04458e6	−	432679.i	1.82285	−	0.755047i	0.848792	−	0.528726i	$-0.177330\pi$
$757$	1.04458e6	−	432679.i	1.82285	−	0.755047i	0.974053	−	0.226321i	$-0.0726698\pi$
$758$	189288.	−	189288.i	0.329447	−	0.329447i
$759$	−43346.8	−	43346.8i	−0.0752443	−	0.0752443i
$760$	−36446.3	−	87989.2i	−0.0630996	−	0.152336i
$761$			633874.i			1.09455i	0.836954	+	0.547273i	$0.184334\pi$
$761$			633874.i			1.09455i	−0.836954	+	0.547273i	$0.815666\pi$
$762$	−42379.0	−	102312.i	−0.0729862	−	0.176204i
$763$			86719.7i			0.148960i
$764$	215248.	−	89158.7i	0.368768	−	0.152749i
$765$	41539.4	+	100285.i	0.0709803	+	0.171362i
$766$	16378.5	−	39541.2i	0.0279137	−	0.0673895i
$767$	252954.	+	104777.i	0.429983	+	0.178105i
$768$	9637.64	+	3992.04i	0.0163399	+	0.00676819i
$769$		−	185778.i		−	0.314154i	−0.987586	−	0.157077i	$-0.949793\pi$
$769$		−	185778.i		−	0.314154i	0.987586	−	0.157077i	$-0.0502070\pi$
$770$	29597.2	−	29597.2i	0.0499194	−	0.0499194i
$771$	−133813.	+	133813.i	−0.225107	+	0.225107i
$772$	174340.	−	420894.i	0.292525	−	0.706217i
$773$	−109646.	−	264708.i	−0.183498	−	0.443004i	0.805185	−	0.593024i	$-0.202066\pi$
$773$	−109646.	−	264708.i	−0.183498	−	0.443004i	−0.988683	+	0.150020i	$0.952066\pi$
$774$	−200080.	+	200080.i	−0.333982	+	0.333982i
$775$	−295632.			−0.492208
$776$	−26064.1	+	62924.3i	−0.0432832	+	0.104495i
$777$	−69384.2	−	69384.2i	−0.114926	−	0.114926i
$778$			19246.7i			0.0317979i
$779$	985055.	+	56092.5i	1.62325	+	0.0924337i
$780$	12428.3			0.0204278
$781$	494711.	−	494711.i	0.811054	−	0.811054i
$782$	92122.4	+	38158.4i	0.150644	+	0.0623988i
$783$		−	319532.i		−	0.521184i
$784$	98638.5	+	98638.5i	0.160478	+	0.160478i
$785$	137237.	−	56845.6i	0.222707	−	0.0922481i
$786$	8640.29	+	3578.93i	0.0139857	+	0.00579306i
$787$	−684852.	−	684852.i	−1.10573	−	1.10573i	−0.993706	−	0.112020i	$-0.964268\pi$
$787$	−684852.	−	684852.i	−1.10573	−	1.10573i	−0.112020	−	0.993706i	$-0.535732\pi$
$788$	−34942.1	−	34942.1i	−0.0562726	−	0.0562726i
$789$	−122045.			−0.196050
$790$	−15863.7	+	38298.4i	−0.0254186	+	0.0613659i
$791$	−20913.0	+	50488.4i	−0.0334243	+	0.0806935i
$792$	−216053.	−	89492.0i	−0.344437	−	0.142670i
$793$	−165294.	+	68467.1i	−0.262852	+	0.108877i
$794$	178920.	+	431952.i	0.283804	+	0.685164i
$795$	21401.2			0.0338613
$796$	−255261.	+	105733.i	−0.402864	+	0.166872i
$797$	774229.			1.21886			0.609429	−	0.792841i	$-0.291399\pi$
$797$	774229.			1.21886			0.609429	+	0.792841i	$0.291399\pi$
$798$	−58118.8	+	24073.6i	−0.0912663	+	0.0378037i
$799$	−296221.	+	296221.i	−0.464005	+	0.464005i
$800$	−73417.7	−	73417.7i	−0.114715	−	0.114715i
$801$	−207447.	−	500821.i	−0.323327	−	0.780580i
$802$		−	903194.i		−	1.40421i
$803$	−138300.	−	333886.i	−0.214482	−	0.517805i
$804$		−	35908.7i		−	0.0555505i
$805$	−17106.7	+	7085.84i	−0.0263983	+	0.0109345i
$806$	−47455.6	−	114568.i	−0.0730495	−	0.176357i
$807$	−15843.4	+	38249.3i	−0.0243277	+	0.0587322i
$808$	354961.	+	147030.i	0.543698	+	0.225207i
$809$	1.19171e6	+	493623.i	1.82085	+	0.754220i	0.975499	+	0.220006i	$0.0706076\pi$
$809$	1.19171e6	+	493623.i	1.82085	+	0.754220i	0.845349	+	0.534214i	$0.179392\pi$
$810$			101960.i			0.155403i
$811$	−691257.	+	691257.i	−1.05099	+	1.05099i	−0.0523603	+	0.998628i	$0.516674\pi$
$811$	−691257.	+	691257.i	−1.05099	+	1.05099i	−0.998628	+	0.0523603i	$0.983326\pi$
$812$	67903.1	−	67903.1i	0.102986	−	0.102986i
$813$	−125555.	+	303117.i	−0.189956	+	0.458595i
$814$	−388752.	−	938530.i	−0.586710	−	1.41644i
$815$	−119113.	+	119113.i	−0.179326	+	0.179326i
$816$	−33111.3			−0.0497275
$817$	−301560.	+	728029.i	−0.451782	+	1.09070i
$818$	741.192	+	741.192i	0.00110770	+	0.00110770i
$819$			94306.9i			0.140597i
$820$	−91049.6	+	31779.7i	−0.135410	+	0.0472631i
$821$	1.13663e6			1.68630			0.843149	−	0.537679i	$-0.180699\pi$
$821$	1.13663e6			1.68630			0.843149	+	0.537679i	$0.180699\pi$
$822$	−134736.	+	134736.i	−0.199407	+	0.199407i
$823$	−390258.	−	161650.i	−0.576173	−	0.238659i	0.0755166	−	0.997145i	$-0.475939\pi$
$823$	−390258.	−	161650.i	−0.576173	−	0.238659i	−0.651689	+	0.758486i	$0.725939\pi$
$824$		−	422318.i		−	0.621992i
$825$	−143266.	−	143266.i	−0.210492	−	0.210492i
$826$	125144.	−	51836.2i	0.183421	−	0.0759755i
$827$	−412713.	−	170951.i	−0.603444	−	0.249955i	0.0599787	−	0.998200i	$-0.480897\pi$
$827$	−412713.	−	170951.i	−0.603444	−	0.249955i	−0.663422	+	0.748245i	$0.730897\pi$
$828$	73150.2	+	73150.2i	0.106698	+	0.106698i
$829$	93594.6	+	93594.6i	0.136189	+	0.136189i	0.771915	−	0.635726i	$-0.219299\pi$
$829$	93594.6	+	93594.6i	0.136189	+	0.136189i	−0.635726	+	0.771915i	$0.719299\pi$
$830$	50865.6			0.0738360
$831$	−123280.	+	297625.i	−0.178522	+	0.430991i
$832$	16666.8	−	40237.2i	0.0240771	−	0.0581274i
$833$	−409071.	−	169443.i	−0.589533	−	0.244193i
$834$	152260.	−	63068.0i	0.218903	−	0.0906727i
$835$	−46969.4	−	113394.i	−0.0673662	−	0.162636i
$836$	−651266.			−0.931850
$837$	−188600.	+	78120.5i	−0.269209	+	0.111510i
$838$	943116.			1.34300
$839$	695398.	−	288043.i	0.987892	−	0.409198i	0.170549	−	0.985349i	$-0.445446\pi$
$839$	695398.	−	288043.i	0.987892	−	0.409198i	0.817343	+	0.576151i	$0.195446\pi$
$840$	4347.74	−	4347.74i	0.00616176	−	0.00616176i
$841$	−39883.1	−	39883.1i	−0.0563893	−	0.0563893i
$842$	10812.7	+	26104.1i	0.0152514	+	0.0368200i
$843$			12830.4i			0.0180545i
$844$	−92306.3	−	222847.i	−0.129583	−	0.312840i
$845$			152925.i			0.214173i
$846$	−401538.	+	166323.i	−0.561030	+	0.232386i
$847$	−26170.9	−	63182.1i	−0.0364798	−	0.0880699i
$848$	28699.8	−	69287.4i	0.0399105	−	0.0963524i
$849$	7954.07	+	3294.68i	0.0110350	+	0.00457087i
$850$	304476.	+	126118.i	0.421419	+	0.174558i
$851$			449385.i			0.620526i
$852$	72671.6	−	72671.6i	0.100112	−	0.100112i
$853$	−852861.	+	852861.i	−1.17214	+	1.17214i	−0.190444	+	0.981698i	$0.560993\pi$
$853$	−852861.	+	852861.i	−1.17214	+	1.17214i	−0.981698	+	0.190444i	$0.939007\pi$
$854$	−33872.7	+	81775.9i	−0.0464444	+	0.112127i
$855$	120020.	+	289755.i	0.164181	+	0.396368i
$856$	−149727.	+	149727.i	−0.204339	+	0.204339i
$857$	−366582.			−0.499125			−0.249563	−	0.968359i	$-0.580287\pi$
$857$	−366582.			−0.499125			−0.249563	+	0.968359i	$0.580287\pi$
$858$	32523.3	−	78518.3i	0.0441795	−	0.106659i
$859$	−301296.	−	301296.i	−0.408326	−	0.408326i	0.472829	−	0.881154i	$-0.343233\pi$
$859$	−301296.	−	301296.i	−0.408326	−	0.408326i	−0.881154	+	0.472829i	$0.843233\pi$
$860$		−	77021.4i		−	0.104139i
$861$	20991.2	+	60140.2i	0.0283159	+	0.0811258i
$862$	−56442.8			−0.0759617
$863$	623355.	−	623355.i	0.836978	−	0.836978i	−0.151482	−	0.988460i	$-0.548405\pi$
$863$	623355.	−	623355.i	0.836978	−	0.836978i	0.988460	+	0.151482i	$0.0484045\pi$
$864$	−66237.6	−	27436.5i	−0.0887314	−	0.0367537i
$865$		−	92553.9i		−	0.123698i
$866$	−422183.	−	422183.i	−0.562943	−	0.562943i
$867$	−99421.3	+	41181.6i	−0.132264	+	0.0547855i
$868$	−56680.1	−	23477.7i	−0.0752301	−	0.0311613i
$869$	200445.	+	200445.i	0.265434	+	0.265434i
$870$	29468.5	+	29468.5i	0.0389332	+	0.0389332i
$871$	−149919.			−0.197615
$872$	−50469.3	+	121844.i	−0.0663735	+	0.160240i
$873$	85831.1	−	207215.i	0.112620	−	0.271889i
$874$	266170.	+	110251.i	0.348447	+	0.144332i
$875$	−118149.	+	48938.8i	−0.154317	+	0.0639201i
$876$	−20315.8	−	49046.8i	−0.0264744	−	0.0639149i
$877$	−1.04067e6			−1.35305			−0.676526	−	0.736419i	$-0.736515\pi$
$877$	−1.04067e6			−1.35305			−0.676526	+	0.736419i	$0.736515\pi$
$878$	−894736.	+	370612.i	−1.16066	+	0.480762i
$879$	−207539.			−0.268609
$880$	58810.0	−	24359.9i	0.0759427	−	0.0314565i
$881$	−282546.	+	282546.i	−0.364030	+	0.364030i	−0.865294	−	0.501264i	$-0.832868\pi$
$881$	−282546.	+	282546.i	−0.364030	+	0.364030i	0.501264	+	0.865294i	$0.332868\pi$
$882$	−324824.	−	324824.i	−0.417553	−	0.417553i
$883$	−206383.	−	498254.i	−0.264700	−	0.639042i	0.734518	−	0.678589i	$-0.237408\pi$
$883$	−206383.	−	498254.i	−0.264700	−	0.639042i	−0.999218	+	0.0395475i	$0.987408\pi$
$884$			138240.i			0.176900i
$885$	22495.9	+	54309.8i	0.0287221	+	0.0693413i
$886$		−	143307.i		−	0.182557i
$887$	42967.7	−	17797.8i	0.0546129	−	0.0226214i	−0.355210	−	0.934787i	$-0.615591\pi$
$887$	42967.7	−	17797.8i	0.0546129	−	0.0226214i	0.409823	+	0.912165i	$0.365591\pi$
$888$	−57106.5	−	137867.i	−0.0724202	−	0.174838i
$889$	−87533.6	+	211325.i	−0.110757	+	0.267391i
$890$	136325.	+	56467.5i	0.172105	+	0.0712883i
$891$	644155.	+	266818.i	0.811400	+	0.336093i
$892$		−	84518.0i		−	0.106223i
$893$	−855876.	+	855876.i	−1.07327	+	1.07327i
$894$	−142347.	+	142347.i	−0.178103	+	0.178103i
$895$	−153898.	+	371542.i	−0.192126	+	0.463833i
$896$	−8245.54	−	19906.5i	−0.0102708	−	0.0247959i
$897$	−26584.4	+	26584.4i	−0.0330401	+	0.0330401i
$898$	81546.4			0.101123
$899$	159129.	−	384172.i	0.196893	−	0.475342i
$900$	241770.	+	241770.i	0.298482	+	0.298482i
$901$			238046.i			0.293232i
$902$	−37491.0	+	658389.i	−0.0460802	+	0.809225i
$903$	−50874.3			−0.0623911
$904$	−58766.7	+	58766.7i	−0.0719109	+	0.0719109i
$905$	−293715.	−	121661.i	−0.358615	−	0.148543i
$906$		−	179712.i		−	0.218938i
$907$	1.15094e6	+	1.15094e6i	1.39906	+	1.39906i	0.802767	+	0.596292i	$0.203360\pi$
$907$	1.15094e6	+	1.15094e6i	1.39906	+	1.39906i	0.596292	+	0.802767i	$0.296640\pi$
$908$	285976.	−	118455.i	0.346863	−	0.143675i
$909$	−1.16891e6	−	484179.i	−1.41467	−	0.585974i
$910$	−18151.8	−	18151.8i	−0.0219198	−	0.0219198i
$911$	1.06072e6	+	1.06072e6i	1.27810	+	1.27810i	0.941730	+	0.336369i	$0.109199\pi$
$911$	1.06072e6	+	1.06072e6i	1.27810	+	1.27810i	0.336369	+	0.941730i	$0.390801\pi$
$912$	−95669.0			−0.115022
$913$	133109.	−	321355.i	0.159686	−	0.385516i
$914$	274484.	−	662662.i	0.328567	−	0.793231i
$915$	−35489.0	−	14700.0i	−0.0423889	−	0.0175581i
$916$	76486.3	−	31681.7i	0.0911576	−	0.0377587i
$917$	−7392.25	−	17846.5i	−0.00879100	−	0.0212233i
$918$	227568.			0.270038
$919$	−565618.	+	234287.i	−0.669719	+	0.277407i	−0.691522	−	0.722356i	$-0.743059\pi$
$919$	−565618.	+	234287.i	−0.669719	+	0.277407i	0.0218029	+	0.999762i	$0.493059\pi$
$920$	−28159.3			−0.0332695
$921$	346426.	−	143495.i	0.408406	−	0.169167i
$922$	493523.	−	493523.i	0.580558	−	0.580558i
$923$	−303404.	−	303404.i	−0.356137	−	0.356137i
$924$	−16090.2	−	38845.3i	−0.0188460	−	0.0454982i
$925$			1.48527e6i			1.73589i
$926$	−281661.	−	679991.i	−0.328477	−	0.793015i
$927$			1.39072e6i			1.61838i
$928$	134924.	−	55887.5i	0.156673	−	0.0648961i
$929$	444454.	+	1.07301e6i	0.514986	+	1.24329i	0.940950	+	0.338546i	$0.109935\pi$
$929$	444454.	+	1.07301e6i	0.514986	+	1.24329i	−0.425964	+	0.904740i	$0.640065\pi$
$930$	10188.8	−	24598.0i	0.0117804	−	0.0284403i
$931$	−1.18193e6	−	489572.i	−1.36362	−	0.564830i
$932$	147070.	+	60918.4i	0.169314	+	0.0701321i
$933$			116431.i			0.133754i
$934$	−695542.	+	695542.i	−0.797314	+	0.797314i
$935$	−142870.	+	142870.i	−0.163425	+	0.163425i
$936$	−54885.0	+	132504.i	−0.0626472	+	0.151244i
$937$	−74880.2	−	180777.i	−0.0852880	−	0.205903i	0.875481	−	0.483252i	$-0.160544\pi$
$937$	−74880.2	−	180777.i	−0.0852880	−	0.205903i	−0.960769	+	0.277348i	$0.910544\pi$
$938$	−52445.6	+	52445.6i	−0.0596078	+	0.0596078i
$939$	281094.			0.318801
$940$	45273.4	−	109300.i	0.0512374	−	0.123698i
$941$	−221779.	−	221779.i	−0.250462	−	0.250462i	0.570698	−	0.821160i	$-0.306673\pi$
$941$	−221779.	−	221779.i	−0.250462	−	0.250462i	−0.821160	+	0.570698i	$0.806673\pi$
$942$		−	149216.i		−	0.168156i
$943$	126780.	−	262735.i	0.142569	−	0.295457i
$944$	205999.			0.231164
$945$	−29881.2	+	29881.2i	−0.0334606	+	0.0334606i
$946$	−486599.	−	201556.i	−0.543737	−	0.225223i
$947$			701690.i			0.782430i	0.920299	+	0.391215i	$0.127945\pi$
$947$			701690.i			0.782430i	−0.920299	+	0.391215i	$0.872055\pi$
$948$	29444.8	+	29444.8i	0.0327636	+	0.0327636i
$949$	−204770.	+	84818.6i	−0.227371	+	0.0941800i
$950$	879725.	+	364394.i	0.974764	+	0.403761i
$951$	48118.8	+	48118.8i	0.0532051	+	0.0532051i
$952$	48359.9	+	48359.9i	0.0533595	+	0.0533595i
$953$	−709604.			−0.781323			−0.390661	−	0.920534i	$-0.627754\pi$
$953$	−709604.			−0.781323			−0.390661	+	0.920534i	$0.627754\pi$
$954$	−94510.6	+	228169.i	−0.103845	+	0.250703i
$955$	79920.3	−	192945.i	0.0876295	−	0.211556i
$956$	−193174.	−	80015.3i	−0.211365	−	0.0875502i
$957$	263289.	−	109058.i	0.287481	−	0.119079i
$958$	−345587.	−	834322.i	−0.376554	−	0.909081i
$959$	393571.			0.427943
$960$	8639.01	−	3578.40i	0.00937393	−	0.00388281i
$961$	657864.			0.712343
$962$	−575596.	+	238420.i	−0.621967	+	0.257627i
$963$	493062.	−	493062.i	0.531678	−	0.531678i
$964$	−256926.	−	256926.i	−0.276474	−	0.276474i
$965$	−156275.	−	377282.i	−0.167817	−	0.405146i
$966$			18599.8i			0.0199322i
$967$	−495316.	−	1.19580e6i	−0.529700	−	1.27881i	−0.931720	−	0.363178i	$-0.881692\pi$
$967$	−495316.	−	1.19580e6i	−0.529700	−	1.27881i	0.402020	−	0.915631i	$-0.368308\pi$
$968$		−	104004.i		−	0.110994i
$969$	280548.	−	116207.i	0.298786	−	0.123761i
$970$	23363.4	+	56404.3i	0.0248309	+	0.0599471i
$971$	372378.	−	899000.i	0.394953	−	0.953501i	−0.593891	−	0.804546i	$-0.702409\pi$
$971$	372378.	−	899000.i	0.394953	−	0.953501i	0.988844	−	0.148955i	$-0.0475911\pi$
$972$	331737.	+	137410.i	0.351125	+	0.145441i
$973$	−314491.	−	130267.i	−0.332187	−	0.137596i
$974$			638777.i			0.673336i
$975$	−87864.5	+	87864.5i	−0.0924282	+	0.0924282i
$976$	−95184.2	+	95184.2i	−0.0999230	+	0.0999230i
$977$	308735.	−	745352.i	0.323442	−	0.780859i	−0.675607	−	0.737262i	$-0.736118\pi$
$977$	308735.	−	745352.i	0.323442	−	0.780859i	0.999049	−	0.0435968i	$-0.0138817\pi$
$978$	64754.6	+	156331.i	0.0677006	+	0.163444i
$979$	713491.	−	713491.i	0.744428	−	0.744428i
$980$	125042.			0.130198
$981$	166199.	−	401241.i	0.172700	−	0.416934i
$982$	733311.	+	733311.i	0.760441	+	0.760441i
$983$		−	916720.i		−	0.948701i	−0.880336	−	0.474351i	$-0.842683\pi$
$983$		−	916720.i		−	0.948701i	0.880336	−	0.474351i	$-0.157317\pi$
$984$	−5507.32	+	96715.3i	−0.00568787	+	0.0998861i
$985$	−44295.3			−0.0456547
$986$	−327779.	+	327779.i	−0.337153	+	0.337153i
$987$	−72194.8	−	29904.0i	−0.0741091	−	0.0306970i
$988$			399418.i			0.409179i
$989$	164751.	+	164751.i	0.168436	+	0.168436i
$990$	−193666.	+	80219.0i	−0.197598	+	0.0818478i
$991$	254160.	+	105276.i	0.258797	+	0.107197i	0.508310	−	0.861174i	$-0.330270\pi$
$991$	254160.	+	105276.i	0.258797	+	0.107197i	−0.249513	+	0.968371i	$0.580270\pi$
$992$	−65973.7	−	65973.7i	−0.0670421	−	0.0670421i
$993$	140946.	+	140946.i	0.142940	+	0.142940i
$994$	−212277.			−0.214848
$995$	−94776.8	+	228812.i	−0.0957318	+	0.231117i
$996$	19553.4	−	47206.0i	0.0197107	−	0.0475859i
$997$	452330.	+	187361.i	0.455057	+	0.188491i	0.598425	−	0.801179i	$-0.295793\pi$
$997$	452330.	+	187361.i	0.455057	+	0.188491i	−0.143368	+	0.989669i	$0.545793\pi$
$998$	1.27946e6	−	529970.i	1.28459	−	0.532096i
$999$	392482.	+	947534.i	0.393268	+	0.949432i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.5.e.a.79.4	yes	28
41.27	odd	8	inner	82.5.e.a.27.4	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.5.e.a.27.4	✓	28	41.27	odd	8	inner
82.5.e.a.79.4	yes	28	1.1	even	1	trivial

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} +(2.35294 + 0.974620i) q^{3} -8.00000i q^{4} +(-5.07070 - 5.07070i) q^{5} +(-6.65512 + 2.75664i) q^{6} +(13.7461 + 5.69383i) q^{7} +(16.0000 + 16.0000i) q^{8} +(-52.6892 - 52.6892i) q^{9} +20.2828 q^{10} +(53.0777 - 128.141i) q^{11} +(7.79696 - 18.8235i) q^{12} +(-78.5882 - 32.5523i) q^{13} +(-38.8799 + 16.1046i) q^{14} +(-6.98906 - 16.8731i) q^{15} -64.0000 q^{16} +(187.679 - 77.7393i) q^{17} +210.757 q^{18} +(542.264 - 224.613i) q^{19} +(-40.5656 + 40.5656i) q^{20} +(26.7945 + 26.7945i) q^{21} +(150.127 + 362.437i) q^{22} -173.542i q^{23} +(22.0531 + 53.2410i) q^{24} -573.576i q^{25} +(222.281 - 92.0718i) q^{26} +(-151.567 - 365.915i) q^{27} +(45.5506 - 109.969i) q^{28} +(745.358 + 308.738i) q^{29} +(47.7243 + 19.7680i) q^{30} -515.419i q^{31} +(128.000 - 128.000i) q^{32} +(249.778 - 249.778i) q^{33} +(-219.880 + 530.837i) q^{34} +(-40.8308 - 98.5742i) q^{35} +(-421.514 + 421.514i) q^{36} -2589.50 q^{37} +(-635.302 + 1533.75i) q^{38} +(-153.187 - 153.187i) q^{39} -162.263i q^{40} +(1513.96 + 730.543i) q^{41} -107.178 q^{42} +(-949.343 + 949.343i) q^{43} +(-1025.13 - 424.622i) q^{44} +534.343i q^{45} +(347.083 + 347.083i) q^{46} +(-1905.22 + 789.168i) q^{47} +(-150.588 - 62.3757i) q^{48} +(-1541.23 - 1541.23i) q^{49} +(1147.15 + 1147.15i) q^{50} +517.365 q^{51} +(-260.418 + 628.706i) q^{52} +(-448.434 + 1082.62i) q^{53} +(1034.96 + 428.696i) q^{54} +(-918.907 + 380.624i) q^{55} +(128.837 + 311.039i) q^{56} +1494.83 q^{57} +(-2108.19 + 873.242i) q^{58} -3218.73 q^{59} +(-134.985 + 55.9125i) q^{60} +(1487.25 - 1487.25i) q^{61} +(1030.84 + 1030.84i) q^{62} +(-424.269 - 1024.28i) q^{63} +512.000i q^{64} +(233.434 + 563.561i) q^{65} +999.110i q^{66} +(1628.28 - 674.457i) q^{67} +(-621.915 - 1501.43i) q^{68} +(169.137 - 408.333i) q^{69} +(278.810 + 115.487i) q^{70} +(4660.25 + 1930.34i) q^{71} -1686.05i q^{72} +(1842.45 - 1842.45i) q^{73} +(5178.99 - 5178.99i) q^{74} +(559.018 - 1349.59i) q^{75} +(-1796.91 - 4338.11i) q^{76} +(1459.23 - 1459.23i) q^{77} +612.749 q^{78} +(-782.127 + 1888.22i) q^{79} +(324.525 + 324.525i) q^{80} +5026.92i q^{81} +(-4489.00 + 1566.83i) q^{82} +2507.82 q^{83} +(214.356 - 214.356i) q^{84} +(-1345.86 - 557.473i) q^{85} -3797.37i q^{86} +(1452.88 + 1452.88i) q^{87} +(2899.50 - 1201.01i) q^{88} +(6721.19 + 2784.01i) q^{89} +(-1068.69 - 1068.69i) q^{90} +(-894.936 - 894.936i) q^{91} -1388.33 q^{92} +(502.338 - 1212.75i) q^{93} +(2232.11 - 5388.78i) q^{94} +(-3888.61 - 1610.71i) q^{95} +(425.928 - 176.425i) q^{96} +(1151.88 + 2780.89i) q^{97} +6164.91 q^{98} +(-9548.27 + 3955.02i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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