LMFDB - Embedded newform 82.5.e.a.27.4

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			27.4
Character	$\chi$	$=$	82.27
Dual form			82.5.e.a.79.4

$q$-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 $\left(\mathbb{Z}/82\mathbb{Z}\right)^\times$.

$n$	$47$
$\chi(n)$	$e\left(\frac{1}{8}\right)$

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	−0.248115	−	0.968731i	$-0.579811\pi$
$3$	2.35294	−	0.974620i	0.261438	−	0.108291i	0.509552	+	0.860440i	$0.329811\pi$
$4$			8.00000i			0.500000i
$5$	−5.07070	+	5.07070i	−0.202828	+	0.202828i	−0.801211	−	0.598382i	$-0.795810\pi$
$5$	−5.07070	+	5.07070i	−0.202828	+	0.202828i	0.598382	+	0.801211i	$0.295810\pi$
$6$	−6.65512	−	2.75664i	−0.184864	−	0.0765734i
$7$	13.7461	−	5.69383i	0.280533	−	0.116201i	−0.237981	−	0.971270i	$-0.576486\pi$
$7$	13.7461	−	5.69383i	0.280533	−	0.116201i	0.518514	+	0.855069i	$0.326486\pi$
$8$	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	0.976412	+	0.215914i	$0.0692732\pi$
$11$	53.0777	+	128.141i	0.438659	+	1.05902i	−0.537753	+	0.843102i	$0.680727\pi$
$12$	7.79696	+	18.8235i	0.0541455	+	0.130719i
$13$	−78.5882	+	32.5523i	−0.465019	+	0.192617i	−0.602876	−	0.797835i	$-0.705979\pi$
$13$	−78.5882	+	32.5523i	−0.465019	+	0.192617i	0.137857	+	0.990452i	$0.455979\pi$
$14$	−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	0.682974	−	0.730442i	$-0.260686\pi$
$17$	187.679	+	77.7393i	0.649409	+	0.268994i	−0.0335649	+	0.999437i	$0.510686\pi$
$18$	210.757			0.650484
$19$	542.264	+	224.613i	1.50212	+	0.622197i	0.973913	−	0.226920i	$-0.0728657\pi$
$19$	542.264	+	224.613i	1.50212	+	0.622197i	0.528204	+	0.849118i	$0.322866\pi$
$20$	−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	$0.0524488\pi$
$23$			173.542i			0.328056i	−0.986456	+	0.164028i	$0.947551\pi$
$24$	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	0.107349	−	0.994221i	$-0.465764\pi$
$29$	745.358	−	308.738i	0.886276	−	0.367108i	0.778928	+	0.627114i	$0.215764\pi$
$30$	47.7243	−	19.7680i	0.0530270	−	0.0219645i
$31$			515.419i			0.536337i	0.963372	+	0.268168i	$0.0864183\pi$
$31$			515.419i			0.536337i	−0.963372	+	0.268168i	$0.913582\pi$
$32$	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	0.402142	−	0.915577i	$-0.368266\pi$
$43$	−949.343	−	949.343i	−0.513436	−	0.513436i	−0.915577	+	0.402142i	$0.868266\pi$
$44$	−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	−0.0928038	−	0.995684i	$-0.529583\pi$
$47$	−1905.22	−	789.168i	−0.862481	−	0.357251i	−0.769677	+	0.638433i	$0.779583\pi$
$48$	−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	0.823738	−	0.566971i	$-0.191885\pi$
$53$	−448.434	−	1082.62i	−0.159642	−	0.385410i	−0.983380	+	0.181561i	$0.941885\pi$
$54$	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	0.878124	−	0.478432i	$-0.158795\pi$
$61$	1487.25	+	1487.25i	0.399692	+	0.399692i	−0.478432	+	0.878124i	$0.658795\pi$
$62$	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	0.556601	−	0.830780i	$-0.312105\pi$
$67$	1628.28	+	674.457i	0.362727	+	0.150247i	−0.193874	+	0.981026i	$0.562105\pi$
$68$	−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	0.130892	−	0.991397i	$-0.458216\pi$
$71$	4660.25	−	1930.34i	0.924469	−	0.382928i	0.793578	+	0.608469i	$0.208216\pi$
$72$			1686.05i			0.325242i
$73$	1842.45	+	1842.45i	0.345739	+	0.345739i	0.858520	−	0.512780i	$-0.171384\pi$
$73$	1842.45	+	1842.45i	0.345739	+	0.345739i	−0.512780	+	0.858520i	$0.671384\pi$
$74$	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	0.848750	−	0.528794i	$-0.177356\pi$
$79$	−782.127	−	1888.22i	−0.125321	−	0.302551i	−0.974071	+	0.226243i	$0.927356\pi$
$80$	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	0.0843174	−	0.996439i	$-0.473129\pi$
$89$	6721.19	−	2784.01i	0.848528	−	0.351472i	0.764210	+	0.644967i	$0.223129\pi$
$90$	−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	−0.850772	−	0.525534i	$-0.823865\pi$
$97$	1151.88	−	2780.89i	0.122423	−	0.295556i	0.973196	+	0.229978i	$0.0738654\pi$
$98$	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	0.981061	−	0.193699i	$-0.0620486\pi$
$101$	15687.2	+	6497.85i	1.53781	+	0.636982i	0.556749	+	0.830681i	$0.312049\pi$
$102$	−1034.73	−	1034.73i	−0.0994549	−	0.0994549i
$103$	−13197.4	+	13197.4i	−1.24398	+	1.24398i	−0.285650	+	0.958334i	$0.592210\pi$
$103$	−13197.4	+	13197.4i	−1.24398	+	1.24398i	−0.958334	+	0.285650i	$0.907790\pi$
$104$	−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	$-0.865990\pi$
$107$		−	9357.92i		−	0.817357i	0.912678	−	0.408679i	$-0.134010\pi$
$108$	−2927.32	−	1212.53i	−0.250970	−	0.103955i
$109$	2230.45	−	5384.78i	0.187733	−	0.453226i	−0.801790	−	0.597606i	$-0.796119\pi$
$109$	2230.45	−	5384.78i	0.187733	−	0.453226i	0.989522	+	0.144380i	$0.0461187\pi$
$110$	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	$-0.954061\pi$
$113$		−	3672.92i		−	0.287643i	0.989604	−	0.143822i	$-0.0459392\pi$
$114$	−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	$-0.841877\pi$
$127$		−	15373.4i		−	0.953154i	0.879133	−	0.476577i	$-0.158123\pi$
$128$	−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	−0.733348	−	0.679853i	$-0.762044\pi$
$131$	−918.031	+	918.031i	−0.0534952	+	0.0534952i	0.679853	+	0.733348i	$0.262044\pi$
$132$	−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	0.922559	−	0.385856i	$-0.126094\pi$
$137$	24438.5	+	10122.7i	1.30207	+	0.539333i	0.379506	+	0.925189i	$0.376094\pi$
$138$	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	0.878859	−	0.477081i	$-0.158305\pi$
$149$	25818.9	+	10694.5i	1.16296	+	0.481714i	0.284100	+	0.958795i	$0.408305\pi$
$150$	1581.14	−	3817.22i	0.0702730	−	0.169654i
$151$	−9547.20	−	23049.0i	−0.418718	−	1.01088i	−0.982719	−	0.185102i	$-0.940739\pi$
$151$	−9547.20	−	23049.0i	−0.418718	−	1.01088i	0.564001	−	0.825774i	$-0.309261\pi$
$152$	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	−0.999161	−	0.0409428i	$-0.986964\pi$
$157$	−7927.08	−	19137.7i	−0.321599	−	0.776408i	0.677563	−	0.735465i	$-0.263036\pi$
$158$	−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	$0.145753\pi$
$163$			23490.4i			0.884127i	−0.896984	+	0.442064i	$0.854247\pi$
$164$	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	−0.0807273	−	0.996736i	$-0.525724\pi$
$167$	15812.8	−	6549.86i	0.566989	−	0.234854i	0.647716	+	0.761882i	$0.275724\pi$
$168$		−	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	−0.538007	−	0.842940i	$-0.680823\pi$
$173$	9126.33	−	9126.33i	0.304933	−	0.304933i	0.842940	+	0.538007i	$0.180823\pi$
$174$	−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	0.112156	+	0.993691i	$0.464224\pi$
$179$	−21460.9	+	51811.2i	−0.669796	+	1.61703i	−0.781952	+	0.623339i	$0.785776\pi$
$180$	4274.74			0.131936
$181$	40958.4	+	16965.5i	1.25022	+	0.517857i	0.906893	−	0.421360i	$-0.138447\pi$
$181$	40958.4	+	16965.5i	1.25022	+	0.517857i	0.343324	+	0.939217i	$0.388447\pi$
$182$	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	−0.694343	−	0.719644i	$-0.744305\pi$
$191$	11144.8	−	26906.0i	0.305497	−	0.737535i	0.999840	−	0.0178908i	$-0.00569511\pi$
$192$	−499.005	−	1204.71i	−0.0135364	−	0.0326797i
$193$	52611.8	−	21792.5i	1.41243	−	0.585050i	0.459487	−	0.888184i	$-0.348033\pi$
$193$	52611.8	−	21792.5i	1.41243	−	0.585050i	0.952948	+	0.303135i	$0.0980332\pi$
$194$	−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	0.761137	−	0.648591i	$-0.224642\pi$
$197$	4367.77	+	4367.77i	0.112545	+	0.112545i	−0.648591	+	0.761137i	$0.724642\pi$
$198$	11186.5	+	27006.6i	0.285341	+	0.688873i
$199$	−13216.6	+	31907.6i	−0.333743	+	0.805728i	0.664545	+	0.747248i	$0.268625\pi$
$199$	−13216.6	+	31907.6i	−0.333743	+	0.805728i	−0.998289	+	0.0584799i	$0.981375\pi$
$200$	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	0.672916	−	0.739719i	$-0.265041\pi$
$211$	27855.9	+	11538.3i	0.625680	+	0.259165i	−0.0472365	+	0.998884i	$0.515041\pi$
$212$	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	−0.712619	−	0.701551i	$-0.752491\pi$
$227$	14806.9	−	35747.0i	0.287351	−	0.693726i	0.999969	+	0.00782574i	$0.00249104\pi$
$228$			11958.6i			0.230044i
$229$	3960.21	−	9560.79i	0.0755174	−	0.182315i	−0.881613	−	0.471974i	$-0.843542\pi$
$229$	3960.21	−	9560.79i	0.0755174	−	0.182315i	0.957130	+	0.289659i	$0.0935417\pi$
$230$			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	0.838100	−	0.545516i	$-0.183666\pi$
$233$	−7614.80	−	18383.8i	−0.140264	−	0.338628i	−0.978365	+	0.206888i	$0.933666\pi$
$234$	−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	0.986927	−	0.161169i	$-0.0515265\pi$
$239$	10001.9	+	24146.7i	0.175100	+	0.422730i	−0.811826	+	0.583899i	$0.801526\pi$
$240$	447.300	−	1079.88i	0.00776562	−	0.0187479i
$241$	32115.8	+	32115.8i	0.552948	+	0.552948i	0.927291	−	0.374342i	$-0.122131\pi$
$241$	32115.8	+	32115.8i	0.552948	+	0.552948i	−0.374342	+	0.927291i	$0.622131\pi$
$242$	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	−0.458457	−	0.888716i	$-0.651598\pi$
$251$	27106.7	−	27106.7i	0.430259	−	0.430259i	0.888716	+	0.458457i	$0.151598\pi$
$252$	−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	−0.979121	−	0.203279i	$-0.934840\pi$
$257$	−28435.3	−	68648.8i	−0.430518	−	1.03936i	0.548603	−	0.836083i	$-0.315160\pi$
$258$	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	0.0389543	−	0.999241i	$-0.487597\pi$
$263$	−44273.1	−	18338.5i	−0.640071	−	0.265126i	−0.679025	+	0.734115i	$0.737597\pi$
$264$	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	$-0.964170\pi$
$269$		−	16255.9i		−	0.224651i	0.993671	−	0.112325i	$-0.0358299\pi$
$270$	−3074.20	+	7421.78i	−0.0421701	+	0.101808i
$271$		−	128825.i		−	1.75413i	−0.480374	−	0.877064i	$-0.659499\pi$
$271$		−	128825.i		−	1.75413i	0.480374	−	0.877064i	$-0.340501\pi$
$272$	−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	$-0.691586\pi$
$277$		−	126491.i		−	1.64854i	0.566197	−	0.824270i	$-0.308414\pi$
$278$	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	−0.911201	−	0.411961i	$-0.864844\pi$
$281$	1927.90	−	4654.37i	0.0244159	−	0.0589452i	0.935617	+	0.353016i	$0.114844\pi$
$282$	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	−0.101647	−	0.994820i	$-0.532411\pi$
$293$	−75286.8	−	31184.8i	−0.876967	−	0.363252i	−0.775320	+	0.631569i	$0.782411\pi$
$294$	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	0.993847	+	0.110761i	$0.0353289\pi$
$307$	104108.	+	104108.i	1.10461	+	1.10461i	0.110761	+	0.993847i	$0.464671\pi$
$308$	−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	−0.807268	−	0.590185i	$-0.799055\pi$
$311$	17495.0	−	42236.6i	0.180881	−	0.436685i	0.988149	+	0.153501i	$0.0490547\pi$
$312$			4901.99i			0.0503574i
$313$	101970.	+	42237.2i	1.04084	+	0.431128i	0.836612	−	0.547796i	$-0.184533\pi$
$313$	101970.	+	42237.2i	1.04084	+	0.431128i	0.204224	+	0.978924i	$0.434533\pi$
$314$	−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	−0.256457	−	0.966556i	$-0.582555\pi$
$317$	24685.9	−	10225.2i	0.245658	−	0.101755i	0.502115	+	0.864801i	$0.332555\pi$
$318$			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	−0.0274488	−	0.999623i	$-0.508738\pi$
$331$	72308.3	−	29951.1i	0.659982	−	0.273374i	0.687431	+	0.726250i	$0.258738\pi$
$332$			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	−0.957773	−	0.287525i	$-0.907168\pi$
$337$	−76119.4	+	76119.4i	−0.670248	+	0.670248i	0.287525	+	0.957773i	$0.407168\pi$
$338$	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	0.923610	−	0.383333i	$-0.125224\pi$
$347$	157211.	+	65119.1i	1.30564	+	0.540816i	0.382034	+	0.924148i	$0.375224\pi$
$348$	11623.1	+	11623.1i	0.0959758	+	0.0959758i
$349$	−83262.6	+	83262.6i	−0.683595	+	0.683595i	−0.960808	−	0.277213i	$-0.910589\pi$
$349$	−83262.6	+	83262.6i	−0.683595	+	0.683595i	0.277213	+	0.960808i	$0.410589\pi$
$350$	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	$-0.858556\pi$
$353$		−	107134.i		−	0.859760i	0.902886	−	0.429880i	$-0.141444\pi$
$354$	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	$0.205665\pi$
$359$			155196.i			1.20418i	−0.798428	+	0.602090i	$0.794335\pi$
$360$	−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	−0.484727	−	0.874666i	$-0.661081\pi$
$367$	52520.5	−	52520.5i	0.389939	−	0.389939i	0.874666	+	0.484727i	$0.161081\pi$
$368$		−	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	$0.252224\pi$
$373$			198128.i			1.42406i	−0.702148	+	0.712031i	$0.747776\pi$
$374$	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	0.334522	−	0.942388i	$-0.391425\pi$
$383$	−13979.9	−	5790.68i	−0.0953032	−	0.0394759i	−0.429826	+	0.902912i	$0.641425\pi$
$384$	−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	0.722827	−	0.691029i	$-0.242842\pi$
$389$	4811.69	+	4811.69i	0.0317979	+	0.0317979i	−0.691029	+	0.722827i	$0.742842\pi$
$390$	−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	0.987336	+	0.158641i	$0.0507111\pi$
$397$	63257.9	+	152718.i	0.401360	+	0.968969i	−0.585976	+	0.810328i	$0.699289\pi$
$398$	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	−0.786058	−	0.618152i	$-0.787881\pi$
$401$	−225798.	−	225798.i	−1.40421	−	1.40421i	−0.618152	−	0.786058i	$-0.712119\pi$
$402$	−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	$0.000352593\pi$
$409$			370.596i			0.00221541i	−0.999999	+	0.00110770i	$0.999647\pi$
$410$	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	−0.449949	+	0.893054i	$0.648558\pi$
$419$	−235779.	+	235779.i	−1.34300	+	1.34300i	−0.893054	+	0.449949i	$0.851442\pi$
$420$	−2173.87			−0.0123235
$421$	3822.86	+	9229.19i	0.0215687	+	0.0520714i	0.934297	−	0.356496i	$-0.116029\pi$
$421$	3822.86	+	9229.19i	0.0215687	+	0.0520714i	−0.912728	+	0.408567i	$0.866029\pi$
$422$	−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	−0.668105	−	0.744067i	$-0.732894\pi$
$431$	14110.7	−	14110.7i	0.0759617	−	0.0759617i	0.744067	+	0.668105i	$0.232894\pi$
$432$	9700.28	−	23418.5i	0.0519777	−	0.125485i
$433$		−	211091.i		−	1.12589i	−0.826496	−	0.562943i	$-0.809669\pi$
$433$		−	211091.i		−	1.12589i	0.826496	−	0.562943i	$-0.190331\pi$
$434$	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	0.644983	−	0.764197i	$-0.276864\pi$
$439$	316337.	−	131031.i	1.64142	−	0.679900i	0.996441	+	0.0842965i	$0.0268643\pi$
$440$	−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	0.609912	−	0.792469i	$-0.291205\pi$
$443$	−35826.7	−	35826.7i	−0.182557	−	0.182557i	−0.792469	+	0.609912i	$0.791205\pi$
$444$	−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	−0.755858	−	0.654735i	$-0.772780\pi$
$449$	−20386.6	+	20386.6i	−0.101123	+	0.101123i	0.654735	+	0.755858i	$0.272780\pi$
$450$			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	−0.256813	−	0.966461i	$-0.582672\pi$
$457$	−234286.	−	97044.6i	−1.12180	−	0.464664i	−0.864985	+	0.501797i	$0.832672\pi$
$458$	−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	−0.966515	−	0.256611i	$-0.917394\pi$
$463$	−99582.4	−	240413.i	−0.464537	−	1.12149i	0.501978	−	0.864881i	$-0.332606\pi$
$464$	−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	−0.929844	−	0.367953i	$-0.880059\pi$
$479$	−122184.	−	294977.i	−0.532527	−	1.28563i	0.397317	−	0.917681i	$-0.369941\pi$
$480$	−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	0.958484	−	0.285148i	$-0.0920427\pi$
$487$	159694.	+	159694.i	0.673336	+	0.673336i	−0.285148	+	0.958484i	$0.592043\pi$
$488$	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	$0.275017\pi$
$491$			366656.i			1.52088i	−0.649407	+	0.760441i	$0.724983\pi$
$492$	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	−0.838463	+	0.544958i	$0.816546\pi$
$499$	−452358.	+	187373.i	−1.81669	+	0.752498i	−0.978227	+	0.207540i	$0.933454\pi$
$500$	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	−0.929796	−	0.368074i	$-0.880017\pi$
$503$	−134752.	−	325321.i	−0.532599	−	1.28581i	0.397198	−	0.917733i	$-0.369983\pi$
$504$	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	0.0185577	−	0.999828i	$-0.494093\pi$
$509$	−174959.	−	72470.3i	−0.675305	−	0.279720i	−0.693863	+	0.720107i	$0.744093\pi$
$510$	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	−0.366100	−	0.930576i	$-0.619307\pi$
$521$	8969.80	−	3715.41i	0.0330451	−	0.0136877i	0.399145	+	0.916888i	$0.369307\pi$
$522$	157089.	−	65068.5i	0.576508	−	0.238798i
$523$			29891.9i			0.109282i	0.998506	+	0.0546412i	$0.0174015\pi$
$523$			29891.9i			0.109282i	−0.998506	+	0.0546412i	$0.982598\pi$
$524$	−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	0.144728	−	0.989471i	$-0.453769\pi$
$541$	331959.	−	331959.i	1.13420	−	1.13420i	0.989471	−	0.144728i	$-0.0462308\pi$
$542$	−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	0.716248	−	0.697846i	$-0.245858\pi$
$547$	218201.	+	90381.9i	0.729260	+	0.302069i	0.0130121	+	0.999915i	$0.495858\pi$
$548$	−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	0.517937	+	0.855419i	$0.326700\pi$
$557$	−140596.	+	339429.i	−0.453172	+	1.09405i	−0.971109	+	0.238636i	$0.923300\pi$
$558$			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	−0.142128	−	0.989848i	$-0.545395\pi$
$563$	144950.	−	60040.3i	0.457300	−	0.189420i	0.599429	+	0.800428i	$0.295395\pi$
$564$		−	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	0.871611	−	0.490199i	$-0.163076\pi$
$569$	123486.	+	123486.i	0.381412	+	0.381412i	−0.490199	+	0.871611i	$0.663076\pi$
$570$	30319.3			0.0933189
$571$	63652.6	+	153671.i	0.195229	+	0.471324i	0.990932	−	0.134362i	$-0.0428986\pi$
$571$	63652.6	+	153671.i	0.195229	+	0.471324i	−0.795703	+	0.605686i	$0.792899\pi$
$572$	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	−0.514290	−	0.857616i	$-0.671945\pi$
$577$	−90397.4	+	37443.8i	−0.271522	+	0.112468i	0.242768	+	0.970084i	$0.421945\pi$
$578$			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	−0.838623	+	0.544712i	$0.816639\pi$
$587$	−626009.	+	259301.i	−1.81679	+	0.752539i	−0.978166	+	0.207827i	$0.933361\pi$
$588$	−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	0.709260	−	0.704947i	$-0.249029\pi$
$593$	250483.	+	103754.i	0.712311	+	0.295049i	0.00305033	+	0.999995i	$0.499029\pi$
$594$	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	$-0.670718\pi$
$599$		−	616845.i		−	1.71918i	0.510981	−	0.859592i	$-0.329282\pi$
$600$	30537.7	+	12649.1i	0.0848270	+	0.0351365i
$601$	202450.	−	488756.i	0.560490	−	1.35314i	−0.348885	−	0.937166i	$-0.613440\pi$
$601$	202450.	−	488756.i	0.560490	−	1.35314i	0.909375	−	0.415977i	$-0.136560\pi$
$602$	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	−0.978986	−	0.203929i	$-0.934629\pi$
$607$	−435844.	−	435844.i	−1.18291	−	1.18291i	−0.203929	−	0.978986i	$-0.565371\pi$
$608$	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	−0.0977333	−	0.995213i	$-0.531159\pi$
$613$	337245.	−	337245.i	0.897479	−	0.897479i	0.995213	+	0.0977333i	$0.0311592\pi$
$614$		−	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	0.976262	+	0.216591i	$0.0694939\pi$
$617$	454106.	+	454106.i	1.19285	+	1.19285i	0.216591	+	0.976262i	$0.430506\pi$
$618$	124211.	−	51449.9i	0.325225	−	0.134712i
$619$			383999.i			1.00219i	0.865393	+	0.501094i	$0.167069\pi$
$619$			383999.i			1.00219i	−0.865393	+	0.501094i	$0.832931\pi$
$620$	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	0.907187	−	0.420727i	$-0.138225\pi$
$641$	514080.	+	212939.i	1.25117	+	0.518250i	0.343979	+	0.938977i	$0.388225\pi$
$642$	−25796.4	+	62278.1i	−0.0625878	+	0.151100i
$643$	−131256.	−	316879.i	−0.317465	−	0.766429i	−0.999387	−	0.0350039i	$-0.988856\pi$
$643$	−131256.	−	316879.i	−0.317465	−	0.766429i	0.681922	−	0.731425i	$-0.261144\pi$
$644$	−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	0.338436	−	0.940989i	$-0.390102\pi$
$647$	−252234.	−	252234.i	−0.602553	−	0.602553i	−0.940989	+	0.338436i	$0.890102\pi$
$648$	−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	0.852780	−	0.522270i	$-0.174915\pi$
$653$	−50967.6	−	123047.i	−0.119527	−	0.288565i	−0.972307	+	0.233706i	$0.924915\pi$
$654$	−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	−0.676164	−	0.736752i	$-0.736359\pi$
$659$	−275039.	+	113925.i	−0.633321	+	0.262330i	0.0428422	+	0.999082i	$0.486359\pi$
$660$		−	20264.8i		−	0.0465215i
$661$	72997.5	−	72997.5i	0.167072	−	0.167072i	−0.618619	−	0.785691i	$-0.712307\pi$
$661$	72997.5	−	72997.5i	0.167072	−	0.167072i	0.785691	+	0.618619i	$0.212307\pi$
$662$	−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	0.0825707	−	0.996585i	$-0.473687\pi$
$673$	−255332.	−	105762.i	−0.563735	−	0.233507i	−0.646306	+	0.763078i	$0.723687\pi$
$674$	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	0.0174625	−	0.999848i	$-0.494441\pi$
$677$	466263.	−	466263.i	1.01731	−	1.01731i	0.999848	−	0.0174625i	$-0.00555877\pi$
$678$	−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	0.666240	+	0.745738i	$0.267903\pi$
$683$	−154958.	+	374102.i	−0.332179	+	0.801952i	−0.998419	+	0.0562138i	$0.982097\pi$
$684$	−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	0.522862	+	0.852417i	$0.324864\pi$
$691$	−214679.	+	518281.i	−0.449607	+	1.08545i	−0.972469	+	0.233031i	$0.925136\pi$
$692$	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	$0.217581\pi$
$701$			620688.i			1.26310i	−0.775336	+	0.631549i	$0.782419\pi$
$702$	−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	0.927826	−	0.373014i	$-0.121676\pi$
$709$	4017.98	+	9700.25i	0.00799310	+	0.0192970i	−0.919833	+	0.392311i	$0.871676\pi$
$710$	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	0.610577	+	0.791957i	$0.290937\pi$
$719$	−197047.	+	475713.i	−0.381164	+	0.920211i	−0.991741	+	0.128255i	$0.959063\pi$
$720$			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	−0.367180	−	0.930150i	$-0.619677\pi$
$727$	16331.8	−	6764.87i	0.0309005	−	0.0127994i	0.398080	+	0.917351i	$0.369677\pi$
$728$			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	0.979548	+	0.201211i	$0.0644876\pi$
$733$	634409.	+	634409.i	1.18076	+	1.18076i	0.201211	+	0.979548i	$0.435512\pi$
$734$	−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	−0.540312	−	0.841465i	$-0.681694\pi$
$743$	166251.	−	166251.i	0.301152	−	0.301152i	0.841465	+	0.540312i	$0.181694\pi$
$744$	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	0.243235	−	0.969967i	$-0.421791\pi$
$751$	621021.	−	257235.i	1.10110	−	0.456090i	0.857864	+	0.513877i	$0.171791\pi$
$752$	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	0.974053	+	0.226321i	$0.0726698\pi$
$757$	1.04458e6	+	432679.i	1.82285	+	0.755047i	0.848792	+	0.528726i	$0.177330\pi$
$758$	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	$-0.815666\pi$
$761$		−	633874.i		−	1.09455i	0.836954	−	0.547273i	$-0.184334\pi$
$762$	−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	$0.0502070\pi$
$769$			185778.i			0.314154i	−0.987586	+	0.157077i	$0.949793\pi$
$770$	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	−0.988683	−	0.150020i	$-0.952066\pi$
$773$	−109646.	+	264708.i	−0.183498	+	0.443004i	0.805185	+	0.593024i	$0.202066\pi$
$774$	−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	−0.112020	+	0.993706i	$0.535732\pi$
$787$	−684852.	+	684852.i	−1.10573	+	1.10573i	−0.993706	+	0.112020i	$0.964268\pi$
$788$	−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	0.845349	−	0.534214i	$-0.179392\pi$
$809$	1.19171e6	−	493623.i	1.82085	−	0.754220i	0.975499	−	0.220006i	$-0.0706076\pi$
$810$		−	101960.i		−	0.155403i
$811$	−691257.	−	691257.i	−1.05099	−	1.05099i	−0.998628	−	0.0523603i	$-0.983326\pi$
$811$	−691257.	−	691257.i	−1.05099	−	1.05099i	−0.0523603	−	0.998628i	$-0.516674\pi$
$812$	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	−0.651689	−	0.758486i	$-0.725939\pi$
$823$	−390258.	+	161650.i	−0.576173	+	0.238659i	0.0755166	+	0.997145i	$0.475939\pi$
$824$			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	−0.663422	−	0.748245i	$-0.730897\pi$
$827$	−412713.	+	170951.i	−0.603444	+	0.249955i	0.0599787	+	0.998200i	$0.480897\pi$
$828$	73150.2	−	73150.2i	0.106698	−	0.106698i
$829$	93594.6	−	93594.6i	0.136189	−	0.136189i	−0.635726	−	0.771915i	$-0.719299\pi$
$829$	93594.6	−	93594.6i	0.136189	−	0.136189i	0.771915	+	0.635726i	$0.219299\pi$
$830$	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	0.817343	−	0.576151i	$-0.195446\pi$
$839$	695398.	+	288043.i	0.987892	+	0.409198i	0.170549	+	0.985349i	$0.445446\pi$
$840$	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	−0.981698	−	0.190444i	$-0.939007\pi$
$853$	−852861.	−	852861.i	−1.17214	−	1.17214i	−0.190444	−	0.981698i	$-0.560993\pi$
$854$	−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	−0.881154	−	0.472829i	$-0.843233\pi$
$859$	−301296.	+	301296.i	−0.408326	+	0.408326i	0.472829	+	0.881154i	$0.343233\pi$
$860$			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	0.988460	−	0.151482i	$-0.0484045\pi$
$863$	623355.	+	623355.i	0.836978	+	0.836978i	−0.151482	+	0.988460i	$0.548405\pi$
$864$	−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	0.501264	−	0.865294i	$-0.332868\pi$
$881$	−282546.	−	282546.i	−0.364030	−	0.364030i	−0.865294	+	0.501264i	$0.832868\pi$
$882$	−324824.	+	324824.i	−0.417553	+	0.417553i
$883$	−206383.	+	498254.i	−0.264700	+	0.639042i	−0.999218	−	0.0395475i	$-0.987408\pi$
$883$	−206383.	+	498254.i	−0.264700	+	0.639042i	0.734518	+	0.678589i	$0.237408\pi$
$884$		−	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	0.409823	−	0.912165i	$-0.365591\pi$
$887$	42967.7	+	17797.8i	0.0546129	+	0.0226214i	−0.355210	+	0.934787i	$0.615591\pi$
$888$	−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	0.596292	−	0.802767i	$-0.296640\pi$
$907$	1.15094e6	−	1.15094e6i	1.39906	−	1.39906i	0.802767	−	0.596292i	$-0.203360\pi$
$908$	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	0.336369	−	0.941730i	$-0.390801\pi$
$911$	1.06072e6	−	1.06072e6i	1.27810	−	1.27810i	0.941730	−	0.336369i	$-0.109199\pi$
$912$	−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	0.0218029	−	0.999762i	$-0.493059\pi$
$919$	−565618.	−	234287.i	−0.669719	−	0.277407i	−0.691522	+	0.722356i	$0.743059\pi$
$920$	−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	−0.425964	−	0.904740i	$-0.640065\pi$
$929$	444454.	−	1.07301e6i	0.514986	−	1.24329i	0.940950	−	0.338546i	$-0.109935\pi$
$930$	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	−0.960769	−	0.277348i	$-0.910544\pi$
$937$	−74880.2	+	180777.i	−0.0852880	+	0.205903i	0.875481	+	0.483252i	$0.160544\pi$
$938$	−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	−0.821160	−	0.570698i	$-0.806673\pi$
$941$	−221779.	+	221779.i	−0.250462	+	0.250462i	0.570698	+	0.821160i	$0.306673\pi$
$942$			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	$-0.872055\pi$
$947$		−	701690.i		−	0.782430i	0.920299	−	0.391215i	$-0.127945\pi$
$948$	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	0.402020	+	0.915631i	$0.368308\pi$
$967$	−495316.	+	1.19580e6i	−0.529700	+	1.27881i	−0.931720	+	0.363178i	$0.881692\pi$
$968$			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	0.988844	+	0.148955i	$0.0475911\pi$
$971$	372378.	+	899000.i	0.394953	+	0.953501i	−0.593891	+	0.804546i	$0.702409\pi$
$972$	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	0.999049	+	0.0435968i	$0.0138817\pi$
$977$	308735.	+	745352.i	0.323442	+	0.780859i	−0.675607	+	0.737262i	$0.736118\pi$
$978$	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	$0.157317\pi$
$983$			916720.i			0.948701i	−0.880336	+	0.474351i	$0.842683\pi$
$984$	−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	−0.249513	−	0.968371i	$-0.580270\pi$
$991$	254160.	−	105276.i	0.258797	−	0.107197i	0.508310	+	0.861174i	$0.330270\pi$
$992$	−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	−0.143368	−	0.989669i	$-0.545793\pi$
$997$	452330.	−	187361.i	0.455057	−	0.188491i	0.598425	+	0.801179i	$0.295793\pi$
$998$	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.27.4	✓	28
41.38	odd	8	inner	82.5.e.a.79.4	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.5.e.a.27.4	✓	28	1.1	even	1	trivial
82.5.e.a.79.4	yes	28	41.38	odd	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.00000 - 2.00000i) q^{2} +(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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