LMFDB - Embedded newform 82.5.e.a.27.2

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			27.2
Character	$\chi$	$=$	82.27
Dual form			82.5.e.a.79.2

$q$-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} +(-9.30077 + 3.85250i) q^{3} +8.00000i q^{4} +(16.4694 - 16.4694i) q^{5} +(26.3065 + 10.8965i) q^{6} +(32.0596 - 13.2795i) q^{7} +(16.0000 - 16.0000i) q^{8} +(14.3868 - 14.3868i) q^{9} -65.8775 q^{10} +(-5.87737 - 14.1892i) q^{11} +(-30.8200 - 74.4061i) q^{12} +(-235.301 + 97.4650i) q^{13} +(-90.6783 - 37.5602i) q^{14} +(-89.7295 + 216.626i) q^{15} -64.0000 q^{16} +(-147.922 - 61.2715i) q^{17} -57.5473 q^{18} +(-411.810 - 170.577i) q^{19} +(131.755 + 131.755i) q^{20} +(-247.020 + 247.020i) q^{21} +(-16.6237 + 40.1332i) q^{22} +365.346i q^{23} +(-87.1722 + 210.452i) q^{24} +82.5189i q^{25} +(665.532 + 275.673i) q^{26} +(233.670 - 564.128i) q^{27} +(106.236 + 256.477i) q^{28} +(-1104.65 + 457.563i) q^{29} +(612.712 - 253.793i) q^{30} -403.087i q^{31} +(128.000 + 128.000i) q^{32} +(109.328 + 109.328i) q^{33} +(173.302 + 418.388i) q^{34} +(309.297 - 746.708i) q^{35} +(115.095 + 115.095i) q^{36} -812.654 q^{37} +(482.466 + 1164.78i) q^{38} +(1813.00 - 1813.00i) q^{39} -527.020i q^{40} +(-1241.95 - 1132.83i) q^{41} +988.079 q^{42} +(-1115.69 - 1115.69i) q^{43} +(113.514 - 47.0190i) q^{44} -473.885i q^{45} +(730.692 - 730.692i) q^{46} +(778.576 + 322.497i) q^{47} +(595.249 - 246.560i) q^{48} +(-846.290 + 846.290i) q^{49} +(165.038 - 165.038i) q^{50} +1611.84 q^{51} +(-779.720 - 1882.41i) q^{52} +(1249.30 + 3016.08i) q^{53} +(-1595.60 + 660.917i) q^{54} +(-330.485 - 136.891i) q^{55} +(300.482 - 725.427i) q^{56} +4487.30 q^{57} +(3124.43 + 1294.18i) q^{58} +3924.10 q^{59} +(-1733.01 - 717.836i) q^{60} +(-1974.07 - 1974.07i) q^{61} +(-806.175 + 806.175i) q^{62} +(270.186 - 652.287i) q^{63} -512.000i q^{64} +(-2270.08 + 5480.45i) q^{65} -437.312i q^{66} +(-505.311 - 209.307i) q^{67} +(490.172 - 1183.38i) q^{68} +(-1407.50 - 3398.00i) q^{69} +(-2112.01 + 874.823i) q^{70} +(-2263.56 + 937.597i) q^{71} -460.379i q^{72} +(3594.91 + 3594.91i) q^{73} +(1625.31 + 1625.31i) q^{74} +(-317.904 - 767.489i) q^{75} +(1364.62 - 3294.48i) q^{76} +(-376.853 - 376.853i) q^{77} -7251.99 q^{78} +(-1513.57 - 3654.07i) q^{79} +(-1054.04 + 1054.04i) q^{80} +7795.07i q^{81} +(218.239 + 4749.57i) q^{82} -2912.02 q^{83} +(-1976.16 - 1976.16i) q^{84} +(-3445.30 + 1427.09i) q^{85} +4462.74i q^{86} +(8511.37 - 8511.37i) q^{87} +(-321.066 - 132.990i) q^{88} +(-8969.63 + 3715.34i) q^{89} +(-947.769 + 947.769i) q^{90} +(-6249.38 + 6249.38i) q^{91} -2922.77 q^{92} +(1552.90 + 3749.02i) q^{93} +(-912.158 - 2202.14i) q^{94} +(-9591.57 + 3972.96i) q^{95} +(-1683.62 - 697.378i) q^{96} +(5372.96 - 12971.5i) q^{97} +3385.16 q^{98} +(-288.695 - 119.581i) 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
$3$	−9.30077	+	3.85250i	−1.03342	+	0.428056i	−0.833945	−	0.551847i	$-0.813923\pi$
$3$	−9.30077	+	3.85250i	−1.03342	+	0.428056i	−0.199473	+	0.979903i	$0.563923\pi$
$4$			8.00000i			0.500000i
$5$	16.4694	−	16.4694i	0.658775	−	0.658775i	−0.296315	−	0.955090i	$-0.595758\pi$
$5$	16.4694	−	16.4694i	0.658775	−	0.658775i	0.955090	+	0.296315i	$0.0957578\pi$
$6$	26.3065	+	10.8965i	0.730737	+	0.302681i
$7$	32.0596	−	13.2795i	0.654278	−	0.271011i	−0.0307504	−	0.999527i	$-0.509790\pi$
$7$	32.0596	−	13.2795i	0.654278	−	0.271011i	0.685029	+	0.728516i	$0.259790\pi$
$8$	16.0000	−	16.0000i	0.250000	−	0.250000i
$9$	14.3868	−	14.3868i	0.177615	−	0.177615i
$10$	−65.8775			−0.658775
$11$	−5.87737	−	14.1892i	−0.0485733	−	0.117266i	0.897730	−	0.440545i	$-0.145215\pi$
$11$	−5.87737	−	14.1892i	−0.0485733	−	0.117266i	−0.946304	+	0.323279i	$0.895215\pi$
$12$	−30.8200	−	74.4061i	−0.214028	−	0.516709i
$13$	−235.301	+	97.4650i	−1.39231	+	0.576716i	−0.947745	−	0.319029i	$-0.896643\pi$
$13$	−235.301	+	97.4650i	−1.39231	+	0.576716i	−0.444570	+	0.895744i	$0.646643\pi$
$14$	−90.6783	−	37.5602i	−0.462644	−	0.191634i
$15$	−89.7295	+	216.626i	−0.398798	+	0.962783i
$16$	−64.0000			−0.250000
$17$	−147.922	−	61.2715i	−0.511842	−	0.212012i	0.111787	−	0.993732i	$-0.464343\pi$
$17$	−147.922	−	61.2715i	−0.511842	−	0.212012i	−0.623629	+	0.781720i	$0.714343\pi$
$18$	−57.5473			−0.177615
$19$	−411.810	−	170.577i	−1.14075	−	0.472514i	−0.269328	−	0.963049i	$-0.586801\pi$
$19$	−411.810	−	170.577i	−1.14075	−	0.472514i	−0.871422	+	0.490535i	$0.836801\pi$
$20$	131.755	+	131.755i	0.329388	+	0.329388i
$21$	−247.020	+	247.020i	−0.560135	+	0.560135i
$22$	−16.6237	+	40.1332i	−0.0343465	+	0.0829198i
$23$			365.346i			0.690636i	0.938486	+	0.345318i	$0.112229\pi$
$23$			365.346i			0.690636i	−0.938486	+	0.345318i	$0.887771\pi$
$24$	−87.1722	+	210.452i	−0.151341	+	0.365369i
$25$			82.5189i			0.132030i
$26$	665.532	+	275.673i	0.984515	+	0.407800i
$27$	233.670	−	564.128i	0.320534	−	0.773838i
$28$	106.236	+	256.477i	0.135505	+	0.327139i
$29$	−1104.65	+	457.563i	−1.31350	+	0.544070i	−0.925904	−	0.377759i	$-0.876695\pi$
$29$	−1104.65	+	457.563i	−1.31350	+	0.544070i	−0.387597	+	0.921829i	$0.626695\pi$
$30$	612.712	−	253.793i	0.680791	−	0.281993i
$31$		−	403.087i		−	0.419446i	−0.977761	−	0.209723i	$-0.932744\pi$
$31$		−	403.087i		−	0.419446i	0.977761	−	0.209723i	$-0.0672562\pi$
$32$	128.000	+	128.000i	0.125000	+	0.125000i
$33$	109.328	+	109.328i	0.100393	+	0.100393i
$34$	173.302	+	418.388i	0.149915	+	0.361927i
$35$	309.297	−	746.708i	0.252487	−	0.609558i
$36$	115.095	+	115.095i	0.0888076	+	0.0888076i
$37$	−812.654			−0.593611			−0.296806	−	0.954938i	$-0.595921\pi$
$37$	−812.654			−0.593611			−0.296806	+	0.954938i	$0.595921\pi$
$38$	482.466	+	1164.78i	0.334118	+	0.806631i
$39$	1813.00	−	1813.00i	1.19198	−	1.19198i
$40$		−	527.020i		−	0.329388i
$41$	−1241.95	−	1132.83i	−0.738818	−	0.673905i
$41$	−1241.95	−	1132.83i	−0.738818	−	0.673905i
$42$	988.079			0.560135
$43$	−1115.69	−	1115.69i	−0.603400	−	0.603400i	0.337813	−	0.941213i	$-0.390313\pi$
$43$	−1115.69	−	1115.69i	−0.603400	−	0.603400i	−0.941213	+	0.337813i	$0.890313\pi$
$44$	113.514	−	47.0190i	0.0586332	−	0.0242867i
$45$		−	473.885i		−	0.234017i
$46$	730.692	−	730.692i	0.345318	−	0.345318i
$47$	778.576	+	322.497i	0.352456	+	0.145992i	0.551885	−	0.833920i	$-0.313909\pi$
$47$	778.576	+	322.497i	0.352456	+	0.145992i	−0.199429	+	0.979912i	$0.563909\pi$
$48$	595.249	−	246.560i	0.258355	−	0.107014i
$49$	−846.290	+	846.290i	−0.352474	+	0.352474i
$50$	165.038	−	165.038i	0.0660151	−	0.0660151i
$51$	1611.84			0.619701
$52$	−779.720	−	1882.41i	−0.288358	−	0.696157i
$53$	1249.30	+	3016.08i	0.444750	+	1.07372i	0.974262	+	0.225419i	$0.0723750\pi$
$53$	1249.30	+	3016.08i	0.444750	+	1.07372i	−0.529512	+	0.848302i	$0.677625\pi$
$54$	−1595.60	+	660.917i	−0.547186	+	0.226652i
$55$	−330.485	−	136.891i	−0.109251	−	0.0452533i
$56$	300.482	−	725.427i	0.0958168	−	0.231322i
$57$	4487.30			1.38113
$58$	3124.43	+	1294.18i	0.928785	+	0.384715i
$59$	3924.10			1.12729			0.563645	−	0.826017i	$-0.309399\pi$
$59$	3924.10			1.12729			0.563645	+	0.826017i	$0.309399\pi$
$60$	−1733.01	−	717.836i	−0.481392	−	0.199399i
$61$	−1974.07	−	1974.07i	−0.530522	−	0.530522i	0.390205	−	0.920728i	$-0.372404\pi$
$61$	−1974.07	−	1974.07i	−0.530522	−	0.530522i	−0.920728	+	0.390205i	$0.872404\pi$
$62$	−806.175	+	806.175i	−0.209723	+	0.209723i
$63$	270.186	−	652.287i	0.0680741	−	0.164345i
$64$		−	512.000i		−	0.125000i
$65$	−2270.08	+	5480.45i	−0.537297	+	1.29715i
$66$		−	437.312i		−	0.100393i
$67$	−505.311	−	209.307i	−0.112566	−	0.0466266i	0.325689	−	0.945477i	$-0.394404\pi$
$67$	−505.311	−	209.307i	−0.112566	−	0.0466266i	−0.438256	+	0.898850i	$0.644404\pi$
$68$	490.172	−	1183.38i	0.106006	−	0.255921i
$69$	−1407.50	−	3398.00i	−0.295631	−	0.713716i
$70$	−2112.01	+	874.823i	−0.431022	+	0.178535i
$71$	−2263.56	+	937.597i	−0.449030	+	0.185994i	−0.595727	−	0.803187i	$-0.703136\pi$
$71$	−2263.56	+	937.597i	−0.449030	+	0.185994i	0.146697	+	0.989182i	$0.453136\pi$
$72$		−	460.379i		−	0.0888076i
$73$	3594.91	+	3594.91i	0.674594	+	0.674594i	0.958772	−	0.284178i	$-0.0917206\pi$
$73$	3594.91	+	3594.91i	0.674594	+	0.674594i	−0.284178	+	0.958772i	$0.591721\pi$
$74$	1625.31	+	1625.31i	0.296806	+	0.296806i
$75$	−317.904	−	767.489i	−0.0565163	−	0.136442i
$76$	1364.62	−	3294.48i	0.236257	−	0.570375i
$77$	−376.853	−	376.853i	−0.0635609	−	0.0635609i
$78$	−7251.99			−1.19198
$79$	−1513.57	−	3654.07i	−0.242520	−	0.585494i	0.755012	−	0.655711i	$-0.227631\pi$
$79$	−1513.57	−	3654.07i	−0.242520	−	0.585494i	−0.997532	+	0.0702166i	$0.977631\pi$
$80$	−1054.04	+	1054.04i	−0.164694	+	0.164694i
$81$			7795.07i			1.18809i
$82$	218.239	+	4749.57i	0.0324568	+	0.706361i
$83$	−2912.02			−0.422706			−0.211353	−	0.977410i	$-0.567787\pi$
$83$	−2912.02			−0.422706			−0.211353	+	0.977410i	$0.567787\pi$
$84$	−1976.16	−	1976.16i	−0.280068	−	0.280068i
$85$	−3445.30	+	1427.09i	−0.476857	+	0.197521i
$86$			4462.74i			0.603400i
$87$	8511.37	−	8511.37i	1.12450	−	1.12450i
$88$	−321.066	−	132.990i	−0.0414599	−	0.0171733i
$89$	−8969.63	+	3715.34i	−1.13239	+	0.469050i	−0.868591	−	0.495529i	$-0.834974\pi$
$89$	−8969.63	+	3715.34i	−1.13239	+	0.469050i	−0.263795	+	0.964579i	$0.584974\pi$
$90$	−947.769	+	947.769i	−0.117009	+	0.117009i
$91$	−6249.38	+	6249.38i	−0.754665	+	0.754665i
$92$	−2922.77			−0.345318
$93$	1552.90	+	3749.02i	0.179546	+	0.433463i
$94$	−912.158	−	2202.14i	−0.103232	−	0.249224i
$95$	−9591.57	+	3972.96i	−1.06278	+	0.440217i
$96$	−1683.62	−	697.378i	−0.182684	−	0.0756703i
$97$	5372.96	−	12971.5i	0.571044	−	1.37862i	−0.329623	−	0.944113i	$-0.606922\pi$
$97$	5372.96	−	12971.5i	0.571044	−	1.37862i	0.900667	−	0.434510i	$-0.143078\pi$
$98$	3385.16			0.352474
$99$	−288.695	−	119.581i	−0.0294557	−	0.0122009i
$100$	−660.151			−0.0660151
$101$	−3120.24	−	1292.44i	−0.305876	−	0.126698i	0.224466	−	0.974482i	$-0.427936\pi$
$101$	−3120.24	−	1292.44i	−0.305876	−	0.126698i	−0.530341	+	0.847784i	$0.677936\pi$
$102$	−3223.68	−	3223.68i	−0.309850	−	0.309850i
$103$	4663.44	−	4663.44i	0.439574	−	0.439574i	−0.452295	−	0.891869i	$-0.649394\pi$
$103$	4663.44	−	4663.44i	0.439574	−	0.439574i	0.891869	+	0.452295i	$0.149394\pi$
$104$	−2205.38	+	5324.26i	−0.203900	+	0.492258i
$105$			8136.52i			0.738007i
$106$	3533.56	−	8530.77i	0.314486	−	0.759235i
$107$		−	1049.18i		−	0.0916396i	−0.998950	−	0.0458198i	$-0.985410\pi$
$107$		−	1049.18i		−	0.0916396i	0.998950	−	0.0458198i	$-0.0145900\pi$
$108$	4513.03	+	1869.36i	0.386919	+	0.160267i
$109$	7271.39	−	17554.7i	0.612019	−	1.47754i	−0.248761	−	0.968565i	$-0.580023\pi$
$109$	7271.39	−	17554.7i	0.612019	−	1.47754i	0.860779	−	0.508979i	$-0.169977\pi$
$110$	387.187	+	934.751i	0.0319989	+	0.0772522i
$111$	7558.30	−	3130.75i	0.613449	−	0.254099i
$112$	−2051.82	+	849.890i	−0.163570	+	0.0677527i
$113$			11705.0i			0.916674i	0.888779	+	0.458337i	$0.151555\pi$
$113$			11705.0i			0.916674i	−0.888779	+	0.458337i	$0.848445\pi$
$114$	−8974.61	−	8974.61i	−0.690567	−	0.690567i
$115$	6017.03	+	6017.03i	0.454974	+	0.454974i
$116$	−3660.50	−	8837.23i	−0.272035	−	0.656750i
$117$	−1983.03	+	4787.45i	−0.144863	+	0.349730i
$118$	−7848.20	−	7848.20i	−0.563645	−	0.563645i
$119$	−5556.00			−0.392345
$120$	2030.35	+	4901.69i	0.140996	+	0.340395i
$121$	10186.0	−	10186.0i	0.695715	−	0.695715i
$122$			7896.30i			0.530522i
$123$	15915.4	+	5751.59i	1.05198	+	0.380170i
$124$	3224.70			0.209723
$125$	11652.4	+	11652.4i	0.745754	+	0.745754i
$126$	−1844.95	+	764.202i	−0.116210	+	0.0481357i
$127$			8051.29i			0.499181i	0.968352	+	0.249590i	$0.0802960\pi$
$127$			8051.29i			0.499181i	−0.968352	+	0.249590i	$0.919704\pi$
$128$	−1024.00	+	1024.00i	−0.0625000	+	0.0625000i
$129$	14674.9	+	6078.55i	0.881853	+	0.365276i
$130$	15501.1	−	6420.75i	0.917223	−	0.379926i
$131$	1474.24	−	1474.24i	0.0859062	−	0.0859062i	−0.662848	−	0.748754i	$-0.730652\pi$
$131$	1474.24	−	1474.24i	0.0859062	−	0.0859062i	0.748754	+	0.662848i	$0.230652\pi$
$132$	−874.625	+	874.625i	−0.0501966	+	0.0501966i
$133$	−15467.7			−0.874424
$134$	592.009	+	1429.24i	0.0329700	+	0.0795965i
$135$	−5442.45	−	13139.2i	−0.298626	−	0.720946i
$136$	−3347.10	+	1386.42i	−0.180964	+	0.0749576i
$137$	20590.2	+	8528.73i	1.09703	+	0.454405i	0.856453	−	0.516225i	$-0.172663\pi$
$137$	20590.2	+	8528.73i	1.09703	+	0.454405i	0.240578	+	0.970630i	$0.422663\pi$
$138$	−3981.00	+	9611.00i	−0.209042	+	0.504673i
$139$	13905.1			0.719690			0.359845	−	0.933012i	$-0.382830\pi$
$139$	13905.1			0.719690			0.359845	+	0.933012i	$0.382830\pi$
$140$	5973.66	+	2474.37i	0.304779	+	0.126243i
$141$	−8483.77			−0.426727
$142$	6402.31	+	2651.93i	0.317512	+	0.131518i
$143$	2765.91	+	2765.91i	0.135259	+	0.135259i
$144$	−920.757	+	920.757i	−0.0444038	+	0.0444038i
$145$	−10657.2	+	25728.7i	−0.506882	+	1.22372i
$146$		−	14379.6i		−	0.674594i
$147$	4610.81	−	11131.5i	0.213374	−	0.515132i
$148$		−	6501.23i		−	0.296806i
$149$	−24272.9	−	10054.2i	−1.09332	−	0.452870i	−0.238160	−	0.971226i	$-0.576544\pi$
$149$	−24272.9	−	10054.2i	−1.09332	−	0.452870i	−0.855165	+	0.518356i	$0.826544\pi$
$150$	−899.169	+	2170.79i	−0.0399631	+	0.0964794i
$151$	−14763.1	−	35641.2i	−0.647475	−	1.56314i	−0.816382	−	0.577512i	$-0.804024\pi$
$151$	−14763.1	−	35641.2i	−0.647475	−	1.56314i	0.168907	−	0.985632i	$-0.445976\pi$
$152$	−9318.21	+	3859.73i	−0.403316	+	0.167059i
$153$	−3009.64	+	1246.63i	−0.128568	+	0.0532544i
$154$			1507.41i			0.0635609i
$155$	−6638.60	−	6638.60i	−0.276321	−	0.276321i
$156$	14504.0	+	14504.0i	0.595989	+	0.595989i
$157$	−6393.24	−	15434.7i	−0.259371	−	0.626178i	0.739526	−	0.673128i	$-0.235050\pi$
$157$	−6393.24	−	15434.7i	−0.259371	−	0.626178i	−0.998897	+	0.0469503i	$0.985050\pi$
$158$	−4281.01	+	10335.3i	−0.171487	+	0.414007i
$159$	−23238.9	−	23238.9i	−0.919225	−	0.919225i
$160$	4216.16			0.164694
$161$	4851.63	+	11712.9i	0.187170	+	0.451868i
$162$	15590.1	−	15590.1i	0.594046	−	0.594046i
$163$			23630.5i			0.889400i	0.895679	+	0.444700i	$0.146690\pi$
$163$			23630.5i			0.889400i	−0.895679	+	0.444700i	$0.853310\pi$
$164$	9062.67	−	9935.63i	0.336952	−	0.369409i
$165$	3601.13			0.132273
$166$	5824.05	+	5824.05i	0.211353	+	0.211353i
$167$	45618.4	−	18895.8i	1.63571	−	0.677535i	0.639860	−	0.768492i	$-0.278993\pi$
$167$	45618.4	−	18895.8i	1.63571	−	0.677535i	0.995855	+	0.0909568i	$0.0289925\pi$
$168$			7904.63i			0.280068i
$169$	25671.6	−	25671.6i	0.898833	−	0.898833i
$170$	9744.77	+	4036.41i	0.337189	+	0.139668i
$171$	−8378.72	+	3470.58i	−0.286540	+	0.118689i
$172$	8925.49	−	8925.49i	0.301700	−	0.301700i
$173$	−32628.3	+	32628.3i	−1.09019	+	1.09019i	−0.0946842	+	0.995507i	$0.530184\pi$
$173$	−32628.3	+	32628.3i	−1.09019	+	1.09019i	−0.995507	+	0.0946842i	$0.969816\pi$
$174$	−34045.5			−1.12450
$175$	1095.81	+	2645.53i	0.0357816	+	0.0863845i
$176$	376.152	+	908.111i	0.0121433	+	0.0293166i
$177$	−36497.1	+	15117.6i	−1.16496	+	0.482543i
$178$	25369.9	+	10508.6i	0.800718	+	0.331668i
$179$	15597.4	−	37655.4i	0.486795	−	1.17523i	−0.469529	−	0.882917i	$-0.655576\pi$
$179$	15597.4	−	37655.4i	0.486795	−	1.17523i	0.956324	−	0.292309i	$-0.0944237\pi$
$180$	3791.08			0.117009
$181$	−21355.5	−	8845.76i	−0.651859	−	0.270009i	0.0321494	−	0.999483i	$-0.489765\pi$
$181$	−21355.5	−	8845.76i	−0.651859	−	0.270009i	−0.684008	+	0.729474i	$0.739765\pi$
$182$	24997.5			0.754665
$183$	25965.5	+	10755.3i	0.775345	+	0.321158i
$184$	5845.54	+	5845.54i	0.172659	+	0.172659i
$185$	−13383.9	+	13383.9i	−0.391056	+	0.391056i
$186$	4392.25	−	10603.8i	0.126958	−	0.306505i
$187$			2459.02i			0.0703200i
$188$	−2579.97	+	6228.60i	−0.0729961	+	0.176228i
$189$		−	21188.8i		−	0.593174i
$190$	27129.1	+	11237.2i	0.751497	+	0.311280i
$191$	−2817.98	+	6803.21i	−0.0772451	+	0.186486i	−0.957785	−	0.287486i	$-0.907180\pi$
$191$	−2817.98	+	6803.21i	−0.0772451	+	0.186486i	0.880540	+	0.473973i	$0.157180\pi$
$192$	1972.48	+	4761.99i	0.0535070	+	0.129177i
$193$	−43060.4	+	17836.2i	−1.15601	+	0.478837i	−0.876546	−	0.481319i	$-0.840158\pi$
$193$	−43060.4	+	17836.2i	−1.15601	+	0.478837i	−0.279468	+	0.960155i	$0.590158\pi$
$194$	−36688.8	+	15197.0i	−0.974833	+	0.403789i
$195$		−	59717.9i		−	1.57049i
$196$	−6770.32	−	6770.32i	−0.176237	−	0.176237i
$197$	24073.3	+	24073.3i	0.620301	+	0.620301i	0.945608	−	0.325307i	$-0.105468\pi$
$197$	24073.3	+	24073.3i	0.620301	+	0.620301i	−0.325307	+	0.945608i	$0.605468\pi$
$198$	338.227	+	816.552i	0.00862736	+	0.0208283i
$199$	−16695.3	+	40306.0i	−0.421588	+	1.01780i	0.560291	+	0.828296i	$0.310689\pi$
$199$	−16695.3	+	40306.0i	−0.421588	+	1.01780i	−0.981879	+	0.189508i	$0.939311\pi$
$200$	1320.30	+	1320.30i	0.0330076	+	0.0330076i
$201$	5506.13			0.136287
$202$	3655.58	+	8825.36i	0.0895889	+	0.216287i
$203$	−29338.6	+	29338.6i	−0.711946	+	0.711946i
$204$			12894.7i			0.309850i
$205$	−39111.3	+	1797.13i	−0.930667	+	0.0427635i
$206$	−18653.8			−0.439574
$207$	5256.17	+	5256.17i	0.122667	+	0.122667i
$208$	15059.3	−	6237.76i	0.348079	−	0.144179i
$209$			6845.82i			0.156723i
$210$	16273.0	−	16273.0i	0.369003	−	0.369003i
$211$	−63612.5	−	26349.1i	−1.42882	−	0.591836i	−0.471759	−	0.881727i	$-0.656381\pi$
$211$	−63612.5	−	26349.1i	−1.42882	−	0.591836i	−0.957060	+	0.289891i	$0.906381\pi$
$212$	−24128.7	+	9994.42i	−0.536861	+	0.222375i
$213$	17440.7	−	17440.7i	0.384420	−	0.384420i
$214$	−2098.36	+	2098.36i	−0.0458198	+	0.0458198i
$215$	−36749.3			−0.795010
$216$	−5287.34	−	12764.8i	−0.113326	−	0.273593i
$217$	−5352.81	−	12922.8i	−0.113674	−	0.274434i
$218$	−49652.2	+	20566.6i	−1.04478	+	0.432763i
$219$	−47284.8	−	19586.0i	−0.985902	−	0.408374i
$220$	1095.13	−	2643.88i	0.0226266	−	0.0546255i
$221$	40778.2			0.834917
$222$	−21378.1	−	8855.10i	−0.433774	−	0.179675i
$223$	11086.4			0.222937			0.111468	−	0.993768i	$-0.464445\pi$
$223$	11086.4			0.222937			0.111468	+	0.993768i	$0.464445\pi$
$224$	5803.41	+	2403.85i	0.115661	+	0.0479084i
$225$	1187.19	+	1187.19i	0.0234506	+	0.0234506i
$226$	23410.0	−	23410.0i	0.458337	−	0.458337i
$227$	−32595.9	+	78693.5i	−0.632574	+	1.52717i	0.203801	+	0.979012i	$0.434670\pi$
$227$	−32595.9	+	78693.5i	−0.632574	+	1.52717i	−0.836375	+	0.548157i	$0.815330\pi$
$228$			35898.4i			0.690567i
$229$	−15022.6	+	36267.7i	−0.286467	+	0.691591i	−0.999959	−	0.00907170i	$-0.997112\pi$
$229$	−15022.6	+	36267.7i	−0.286467	+	0.691591i	0.713492	+	0.700663i	$0.247112\pi$
$230$		−	24068.1i		−	0.454974i
$231$	4956.85	+	2053.19i	0.0928927	+	0.0384774i
$232$	−10353.5	+	24995.5i	−0.192358	+	0.464393i
$233$	−13156.3	−	31762.2i	−0.242339	−	0.585058i	0.755175	−	0.655523i	$-0.227552\pi$
$233$	−13156.3	−	31762.2i	−0.242339	−	0.585058i	−0.997514	+	0.0704651i	$0.977552\pi$
$234$	13541.0	−	5608.85i	0.247296	−	0.102433i
$235$	18134.0	−	7511.34i	0.328365	−	0.136013i
$236$			31392.8i			0.563645i
$237$	28154.6	+	28154.6i	0.501249	+	0.501249i
$238$	11112.0	+	11112.0i	0.196172	+	0.196172i
$239$	393.618	+	950.277i	0.00689094	+	0.0166362i	0.927288	−	0.374350i	$-0.122134\pi$
$239$	393.618	+	950.277i	0.00689094	+	0.0166362i	−0.920397	+	0.390986i	$0.872134\pi$
$240$	5742.69	−	13864.1i	0.0996995	−	0.240696i
$241$	43179.9	+	43179.9i	0.743443	+	0.743443i	0.973239	−	0.229796i	$-0.0738060\pi$
$241$	43179.9	+	43179.9i	0.743443	+	0.743443i	−0.229796	+	0.973239i	$0.573806\pi$
$242$	−40743.8			−0.695715
$243$	−11103.3	−	26805.7i	−0.188035	−	0.453957i
$244$	15792.6	−	15792.6i	0.265261	−	0.265261i
$245$			27875.7i			0.464402i
$246$	−20327.5	−	43333.9i	−0.335904	−	0.716074i
$247$	113525.			1.86079
$248$	−6449.40	−	6449.40i	−0.104861	−	0.104861i
$249$	27084.1	−	11218.6i	0.436833	−	0.180942i
$250$		−	46609.6i		−	0.745754i
$251$	83103.4	−	83103.4i	1.31908	−	1.31908i	0.404576	−	0.914504i	$-0.367419\pi$
$251$	83103.4	−	83103.4i	1.31908	−	1.31908i	0.914504	−	0.404576i	$-0.132581\pi$
$252$	5218.30	+	2161.49i	0.0821727	+	0.0340370i
$253$	5183.98	−	2147.28i	0.0809883	−	0.0335465i
$254$	16102.6	−	16102.6i	0.249590	−	0.249590i
$255$	26546.0	−	26546.0i	0.408243	−	0.408243i
$256$	4096.00			0.0625000
$257$	12386.9	+	29904.6i	0.187541	+	0.452764i	0.989485	−	0.144635i	$-0.0462008\pi$
$257$	12386.9	+	29904.6i	0.187541	+	0.452764i	−0.801944	+	0.597399i	$0.796201\pi$
$258$	−17192.7	−	41507.0i	−0.258289	−	0.623565i
$259$	−26053.4	+	10791.7i	−0.388387	+	0.160875i
$260$	−43843.6	−	18160.6i	−0.648574	−	0.268648i
$261$	−9309.60	+	22475.4i	−0.136663	+	0.329933i
$262$	−5896.95			−0.0859062
$263$	113058.	+	46830.3i	1.63452	+	0.677042i	0.995728	−	0.0923348i	$-0.0294330\pi$
$263$	113058.	+	46830.3i	1.63452	+	0.677042i	0.638795	+	0.769377i	$0.279433\pi$
$264$	3498.50			0.0501966
$265$	70248.3	+	29097.8i	1.00033	+	0.414351i
$266$	30935.4	+	30935.4i	0.437212	+	0.437212i
$267$	69111.1	−	69111.1i	0.969449	−	0.969449i
$268$	1674.45	−	4042.49i	0.0233133	−	0.0562832i
$269$		−	71146.7i		−	0.983219i	−0.870816	−	0.491610i	$-0.836409\pi$
$269$		−	71146.7i		−	0.983219i	0.870816	−	0.491610i	$-0.163591\pi$
$270$	−15393.6	+	37163.4i	−0.211160	+	0.509786i
$271$			99892.1i			1.36017i	0.733134	+	0.680084i	$0.238057\pi$
$271$			99892.1i			1.36017i	−0.733134	+	0.680084i	$0.761943\pi$
$272$	9467.04	+	3921.38i	0.127961	+	0.0530030i
$273$	34048.3	−	82199.8i	0.456846	−	1.10292i
$274$	−24122.9	−	58237.8i	−0.321313	−	0.775718i
$275$	1170.88	−	484.994i	0.0154827	−	0.00641315i
$276$	27184.0	−	11260.0i	0.356858	−	0.147815i
$277$		−	22930.3i		−	0.298848i	−0.988773	−	0.149424i	$-0.952258\pi$
$277$		−	22930.3i		−	0.298848i	0.988773	−	0.149424i	$-0.0477420\pi$
$278$	−27810.3	−	27810.3i	−0.359845	−	0.359845i
$279$	−5799.15	−	5799.15i	−0.0745000	−	0.0745000i
$280$	−6998.58	−	16896.1i	−0.0892676	−	0.215511i
$281$	−41586.2	+	100398.i	−0.526667	+	1.27149i	0.407027	+	0.913416i	$0.366565\pi$
$281$	−41586.2	+	100398.i	−0.526667	+	1.27149i	−0.933694	+	0.358071i	$0.883435\pi$
$282$	16967.5	+	16967.5i	0.213364	+	0.213364i
$283$	27902.4			0.348392			0.174196	−	0.984711i	$-0.444267\pi$
$283$	27902.4			0.348392			0.174196	+	0.984711i	$0.444267\pi$
$284$	−7500.78	−	18108.5i	−0.0929971	−	0.224515i
$285$	73903.1	−	73903.1i	0.909857	−	0.909857i
$286$		−	11063.6i		−	0.135259i
$287$	−54860.1	−	19825.7i	−0.666028	−	0.240693i
$288$	3683.03			0.0444038
$289$	−40931.4	−	40931.4i	−0.490073	−	0.490073i
$290$	72771.9	−	30143.1i	0.865302	−	0.358420i
$291$			141344.i			1.66913i
$292$	−28759.3	+	28759.3i	−0.337297	+	0.337297i
$293$	−128674.	−	53298.4i	−1.49884	−	0.620839i	−0.525619	−	0.850720i	$-0.676166\pi$
$293$	−128674.	−	53298.4i	−1.49884	−	0.620839i	−0.973219	+	0.229881i	$0.926166\pi$
$294$	−31484.6	+	13041.3i	−0.364253	+	0.150879i
$295$	64627.5	−	64627.5i	0.742631	−	0.742631i
$296$	−13002.5	+	13002.5i	−0.148403	+	0.148403i
$297$	−9377.91			−0.106315
$298$	28437.5	+	68654.1i	0.320227	+	0.773097i
$299$	−35608.4	−	85966.4i	−0.398300	−	0.961582i
$300$	6139.91	−	2543.23i	0.0682212	−	0.0282582i
$301$	−50584.3	−	20952.7i	−0.558319	−	0.231263i
$302$	−41756.3	+	100809.i	−0.457834	+	1.10531i
$303$	33999.7			0.370331
$304$	26355.9	+	10917.0i	0.285187	+	0.118128i
$305$	−65023.6			−0.698990
$306$	8512.54	+	3526.01i	0.0909110	+	0.0376566i
$307$	−121053.	−	121053.i	−1.28440	−	1.28440i	−0.938140	−	0.346255i	$-0.887453\pi$
$307$	−121053.	−	121053.i	−1.28440	−	1.28440i	−0.346255	−	0.938140i	$-0.612547\pi$
$308$	3014.82	−	3014.82i	0.0317805	−	0.0317805i
$309$	−25407.7	+	61339.5i	−0.266102	+	0.642426i
$310$			26554.4i			0.276321i
$311$	2902.19	−	7006.51i	0.0300058	−	0.0724405i	−0.908166	−	0.418609i	$-0.862518\pi$
$311$	2902.19	−	7006.51i	0.0300058	−	0.0724405i	0.938172	+	0.346169i	$0.112518\pi$
$312$		−	58015.9i		−	0.595989i
$313$	148199.	+	61386.2i	1.51272	+	0.626588i	0.976116	−	0.217249i	$-0.0697082\pi$
$313$	148199.	+	61386.2i	1.51272	+	0.626588i	0.536601	+	0.843836i	$0.319708\pi$
$314$	−18082.8	+	43655.8i	−0.183403	+	0.442775i
$315$	−6292.96	−	15192.6i	−0.0634212	−	0.153112i
$316$	29232.6	−	12108.5i	0.292747	−	0.121260i
$317$	62663.6	−	25956.1i	0.623587	−	0.258298i	−0.0484387	−	0.998826i	$-0.515425\pi$
$317$	62663.6	−	25956.1i	0.623587	−	0.258298i	0.672025	+	0.740528i	$0.265425\pi$
$318$			92955.8i			0.919225i
$319$	12984.9	+	12984.9i	0.127602	+	0.127602i
$320$	−8432.32	−	8432.32i	−0.0823469	−	0.0823469i
$321$	4041.98	+	9758.19i	0.0392269	+	0.0947020i
$322$	13722.5	−	33129.0i	0.132349	−	0.319519i
$323$	50464.5	+	50464.5i	0.483705	+	0.483705i
$324$	−62360.5			−0.594046
$325$	−8042.70	−	19416.8i	−0.0761439	−	0.183828i
$326$	47261.0	−	47261.0i	0.444700	−	0.444700i
$327$			191285.i			1.78890i
$328$	−37996.6	+	1745.92i	−0.353181	+	0.0162284i
$329$	29243.4			0.270170
$330$	−7202.27	−	7202.27i	−0.0661365	−	0.0661365i
$331$	−163321.	+	67650.0i	−1.49069	+	0.617464i	−0.971467	−	0.237175i	$-0.923779\pi$
$331$	−163321.	+	67650.0i	−1.49069	+	0.617464i	−0.519223	+	0.854639i	$0.673779\pi$
$332$		−	23296.2i		−	0.211353i
$333$	−11691.5	+	11691.5i	−0.105434	+	0.105434i
$334$	−129028.	−	53445.3i	−1.15662	−	0.479090i
$335$	−11769.3	+	4875.01i	−0.104872	+	0.0434396i
$336$	15809.3	−	15809.3i	0.140034	−	0.140034i
$337$	−60666.6	+	60666.6i	−0.534183	+	0.534183i	−0.921814	−	0.387632i	$-0.873293\pi$
$337$	−60666.6	+	60666.6i	−0.534183	+	0.534183i	0.387632	+	0.921814i	$0.373293\pi$
$338$	−102686.			−0.898833
$339$	−45093.6	−	108866.i	−0.392388	−	0.947308i
$340$	−11416.7	−	27562.4i	−0.0987604	−	0.238429i
$341$	−5719.50	+	2369.09i	−0.0491869	+	0.0203739i
$342$	23698.6	+	9816.28i	0.202614	+	0.0839256i
$343$	−47777.6	+	115345.i	−0.406103	+	0.980418i
$344$	−35702.0			−0.301700
$345$	−79143.6	−	32782.3i	−0.664932	−	0.275424i
$346$	130513.			1.09019
$347$	94460.3	+	39126.7i	0.784495	+	0.324949i	0.738728	−	0.674003i	$-0.235427\pi$
$347$	94460.3	+	39126.7i	0.784495	+	0.324949i	0.0457673	+	0.998952i	$0.485427\pi$
$348$	68090.9	+	68090.9i	0.562252	+	0.562252i
$349$	−18659.2	+	18659.2i	−0.153194	+	0.153194i	−0.779543	−	0.626349i	$-0.784549\pi$
$349$	−18659.2	+	18659.2i	−0.153194	+	0.153194i	0.626349	+	0.779543i	$0.284549\pi$
$350$	3099.43	−	7482.67i	0.0253014	−	0.0610831i
$351$			155515.i			1.26228i
$352$	1063.92	−	2568.52i	0.00858663	−	0.0207300i
$353$		−	169620.i		−	1.36122i	−0.732648	−	0.680608i	$-0.761716\pi$
$353$		−	169620.i		−	1.36122i	0.732648	−	0.680608i	$-0.238284\pi$
$354$	103229.	+	42759.0i	0.823753	+	0.341210i
$355$	−21837.8	+	52721.1i	−0.173281	+	0.418338i
$356$	−29722.7	−	71757.0i	−0.234525	−	0.566193i
$357$	51675.0	−	21404.5i	0.405457	−	0.167946i
$358$	−106506.	+	44116.1i	−0.831011	+	0.344216i
$359$		−	80582.0i		−	0.625243i	−0.949878	−	0.312622i	$-0.898793\pi$
$359$		−	80582.0i		−	0.625243i	0.949878	−	0.312622i	$-0.101207\pi$
$360$	−7582.15	−	7582.15i	−0.0585043	−	0.0585043i
$361$	48340.3	+	48340.3i	0.370933	+	0.370933i
$362$	25019.6	+	60402.6i	0.190925	+	0.460934i
$363$	−55495.8	+	133979.i	−0.421160	+	1.01677i
$364$	−49995.0	−	49995.0i	−0.377332	−	0.377332i
$365$	118412.			0.888811
$366$	−30420.5	−	73441.6i	−0.227093	−	0.548252i
$367$	−111137.	+	111137.i	−0.825137	+	0.825137i	−0.986840	−	0.161702i	$-0.948302\pi$
$367$	−111137.	+	111137.i	−0.825137	+	0.825137i	0.161702	+	0.986840i	$0.448302\pi$
$368$		−	23382.2i		−	0.172659i
$369$	−34165.7	+	1569.89i	−0.250921	+	0.0115296i
$370$	53535.6			0.391056
$371$	80104.3	+	80104.3i	0.581980	+	0.581980i
$372$	−29992.2	+	12423.2i	−0.216732	+	0.0897731i
$373$		−	58165.5i		−	0.418069i	−0.977908	−	0.209034i	$-0.932968\pi$
$373$		−	58165.5i		−	0.418069i	0.977908	−	0.209034i	$-0.0670320\pi$
$374$	4918.04	−	4918.04i	0.0351600	−	0.0351600i
$375$	−153267.	−	63485.3i	−1.08990	−	0.451451i
$376$	17617.2	−	7297.26i	0.124612	−	0.0516160i
$377$	215330.	−	215330.i	1.51503	−	1.51503i
$378$	−42377.5	+	42377.5i	−0.296587	+	0.296587i
$379$	−239659.			−1.66846			−0.834231	−	0.551416i	$-0.814088\pi$
$379$	−239659.			−1.66846			−0.834231	+	0.551416i	$0.814088\pi$
$380$	−31783.7	−	76732.6i	−0.220108	−	0.531389i
$381$	−31017.6	−	74883.1i	−0.213677	−	0.515863i
$382$	19242.4	−	7970.45i	0.131866	−	0.0546206i
$383$	54515.8	+	22581.2i	0.371642	+	0.153939i	0.560684	−	0.828030i	$-0.310538\pi$
$383$	54515.8	+	22581.2i	0.371642	+	0.153939i	−0.189042	+	0.981969i	$0.560538\pi$
$384$	5579.02	−	13468.9i	0.0378352	−	0.0913422i
$385$	−12413.1			−0.0837447
$386$	121793.	+	50448.3i	0.817425	+	0.338589i
$387$	−32102.4			−0.214346
$388$	103772.	+	42983.6i	0.689311	+	0.285522i
$389$	−152980.	−	152980.i	−1.01096	−	1.01096i	−0.999939	−	0.0110244i	$-0.996491\pi$
$389$	−152980.	−	152980.i	−1.01096	−	1.01096i	−0.0110244	−	0.999939i	$-0.503509\pi$
$390$	−119436.	+	119436.i	−0.785245	+	0.785245i
$391$	22385.3	−	54042.9i	0.146423	−	0.353497i
$392$			27081.3i			0.176237i
$393$	−8032.03	+	19391.0i	−0.0520044	+	0.125550i
$394$		−	96293.1i		−	0.620301i
$395$	−85107.7	−	35252.8i	−0.545475	−	0.225943i
$396$	956.651	−	2309.56i	0.00610047	−	0.0147278i
$397$	−51120.8	−	123417.i	−0.324352	−	0.783055i	−0.998991	−	0.0449076i	$-0.985701\pi$
$397$	−51120.8	−	123417.i	−0.324352	−	0.783055i	0.674639	−	0.738148i	$-0.264299\pi$
$398$	114003.	−	47221.4i	0.719696	−	0.298108i
$399$	143861.	−	59589.3i	0.903646	−	0.374302i
$400$		−	5281.21i		−	0.0330076i
$401$	44613.6	+	44613.6i	0.277446	+	0.277446i	0.832089	−	0.554643i	$-0.187145\pi$
$401$	44613.6	+	44613.6i	0.277446	+	0.277446i	−0.554643	+	0.832089i	$0.687145\pi$
$402$	−11012.3	−	11012.3i	−0.0681435	−	0.0681435i
$403$	39286.9	+	94847.0i	0.241901	+	0.584001i
$404$	10339.6	−	24961.9i	0.0633489	−	0.152938i
$405$	128380.	+	128380.i	0.782685	+	0.782685i
$406$	117354.			0.711946
$407$	4776.27	+	11530.9i	0.0288337	+	0.0696106i
$408$	25789.5	−	25789.5i	0.154925	−	0.154925i
$409$		−	225512.i		−	1.34810i	−0.738684	−	0.674052i	$-0.764552\pi$
$409$		−	225512.i		−	1.34810i	0.738684	−	0.674052i	$-0.235448\pi$
$410$	81816.8	+	74628.3i	0.486715	+	0.443952i
$411$	−224361.			−1.32820
$412$	37307.5	+	37307.5i	0.219787	+	0.219787i
$413$	125805.	−	52110.2i	0.737562	−	0.305508i
$414$		−	21024.7i		−	0.122667i
$415$	−47959.2	+	47959.2i	−0.278469	+	0.278469i
$416$	−42594.1	−	17643.0i	−0.246129	−	0.101950i
$417$	−129328.	+	53569.6i	−0.743741	+	0.308068i
$418$	13691.6	−	13691.6i	0.0783615	−	0.0783615i
$419$	−9265.49	+	9265.49i	−0.0527765	+	0.0527765i	−0.733002	−	0.680226i	$-0.761882\pi$
$419$	−9265.49	+	9265.49i	−0.0527765	+	0.0527765i	0.680226	+	0.733002i	$0.261882\pi$
$420$	−65092.2			−0.369003
$421$	9016.59	+	21768.0i	0.0508719	+	0.122816i	0.947272	−	0.320429i	$-0.103827\pi$
$421$	9016.59	+	21768.0i	0.0508719	+	0.122816i	−0.896401	+	0.443245i	$0.853827\pi$
$422$	74526.6	+	179923.i	0.418491	+	1.01033i
$423$	15840.9	−	6561.53i	0.0885320	−	0.0366712i
$424$	68246.2	+	28268.5i	0.379618	+	0.157243i
$425$	5056.06	−	12206.4i	0.0279920	−	0.0675787i
$426$	−69763.0			−0.384420
$427$	−89502.9	−	37073.3i	−0.490887	−	0.203332i
$428$	8393.45			0.0458198
$429$	−36380.7	−	15069.4i	−0.197677	−	0.0818806i
$430$	73498.7	+	73498.7i	0.397505	+	0.397505i
$431$	−210321.	+	210321.i	−1.13221	+	1.13221i	−0.142404	+	0.989809i	$0.545483\pi$
$431$	−210321.	+	210321.i	−1.13221	+	1.13221i	−0.989809	+	0.142404i	$0.954517\pi$
$432$	−14954.9	+	36104.2i	−0.0801336	+	0.193460i
$433$		−	182278.i		−	0.972207i	−0.873901	−	0.486104i	$-0.838418\pi$
$433$		−	182278.i		−	0.972207i	0.873901	−	0.486104i	$-0.161582\pi$
$434$	−15140.0	+	36551.3i	−0.0803799	+	0.194054i
$435$		−	280354.i		−	1.48159i
$436$	140438.	+	58171.1i	0.738772	+	0.306009i
$437$	62319.8	−	150453.i	0.326335	−	0.787842i
$438$	55397.6	+	133742.i	0.288764	+	0.697138i
$439$	200957.	−	83239.0i	1.04273	−	0.431915i	0.205441	−	0.978669i	$-0.434137\pi$
$439$	200957.	−	83239.0i	1.04273	−	0.431915i	0.837293	+	0.546755i	$0.184137\pi$
$440$	−7478.01	+	3097.49i	−0.0386261	+	0.0159995i
$441$			24350.9i			0.125209i
$442$	−81556.3	−	81556.3i	−0.417458	−	0.417458i
$443$	−88160.0	−	88160.0i	−0.449225	−	0.449225i	0.445872	−	0.895097i	$-0.352894\pi$
$443$	−88160.0	−	88160.0i	−0.449225	−	0.449225i	−0.895097	+	0.445872i	$0.852894\pi$
$444$	25046.0	+	60466.4i	0.127049	+	0.306724i
$445$	−86534.9	+	208914.i	−0.436990	+	1.05499i
$446$	−22172.9	−	22172.9i	−0.111468	−	0.111468i
$447$	264490.			1.32372
$448$	−6799.12	−	16414.5i	−0.0338764	−	0.0817848i
$449$	92873.4	−	92873.4i	0.460679	−	0.460679i	−0.438199	−	0.898878i	$-0.644383\pi$
$449$	92873.4	−	92873.4i	0.460679	−	0.460679i	0.898878	+	0.438199i	$0.144383\pi$
$450$		−	4748.74i		−	0.0234506i
$451$	−8774.62	+	24280.4i	−0.0431395	+	0.119372i
$452$	−93640.1			−0.458337
$453$	274616.	+	274616.i	1.33823	+	1.33823i
$454$	222579.	−	92195.2i	1.07987	−	0.447298i
$455$			205847.i			0.994309i
$456$	71796.9	−	71796.9i	0.345283	−	0.345283i
$457$	−232098.	−	96138.3i	−1.11132	−	0.460324i	−0.249929	−	0.968264i	$-0.580407\pi$
$457$	−232098.	−	96138.3i	−1.11132	−	0.460324i	−0.861393	+	0.507940i	$0.830407\pi$
$458$	102581.	−	42490.3i	0.489029	−	0.202562i
$459$	−69130.0	+	69130.0i	−0.328126	+	0.328126i
$460$	−48136.2	+	48136.2i	−0.227487	+	0.227487i
$461$	371823.			1.74958			0.874792	−	0.484499i	$-0.160998\pi$
$461$	371823.			1.74958			0.874792	+	0.484499i	$0.160998\pi$
$462$	−5807.31	−	14020.1i	−0.0272076	−	0.0656850i
$463$	−20491.4	−	49470.5i	−0.0955892	−	0.230773i	0.868851	−	0.495073i	$-0.164859\pi$
$463$	−20491.4	−	49470.5i	−0.0955892	−	0.230773i	−0.964440	+	0.264301i	$0.914859\pi$
$464$	70697.9	−	29284.0i	0.328375	−	0.136017i
$465$	87319.3	+	36168.8i	0.403835	+	0.167274i
$466$	−37211.7	+	89837.0i	−0.171359	+	0.413698i
$467$	287868.			1.31996			0.659978	−	0.751285i	$-0.270566\pi$
$467$	287868.			1.31996			0.659978	+	0.751285i	$0.270566\pi$
$468$	−38299.6	−	15864.2i	−0.174865	−	0.0724314i
$469$	−18979.6			−0.0862861
$470$	−51290.6	−	21245.3i	−0.232189	−	0.0961760i
$471$	118924.	+	118924.i	0.536078	+	0.536078i
$472$	62785.6	−	62785.6i	0.281823	−	0.281823i
$473$	−9273.43	+	22388.0i	−0.0414494	+	0.100068i
$474$		−	112619.i		−	0.501249i
$475$	14075.9	−	33982.1i	0.0623861	−	0.150613i
$476$		−	44448.0i		−	0.196172i
$477$	61365.4	+	25418.4i	0.269704	+	0.111715i
$478$	1113.32	−	2687.79i	0.00487263	−	0.0117636i
$479$	54768.1	+	132222.i	0.238702	+	0.576278i	0.997149	−	0.0754567i	$-0.0240415\pi$
$479$	54768.1	+	132222.i	0.238702	+	0.576278i	−0.758447	+	0.651735i	$0.774041\pi$
$480$	−39213.5	+	16242.8i	−0.170198	+	0.0704982i
$481$	191218.	−	79205.2i	0.826494	−	0.342345i
$482$		−	172720.i		−	0.743443i
$483$	−90247.7	−	90247.7i	−0.386849	−	0.386849i
$484$	81487.7	+	81487.7i	0.347857	+	0.347857i
$485$	−125143.	−	302121.i	−0.532013	−	1.28439i
$486$	−31404.9	+	75818.1i	−0.132961	+	0.320996i
$487$	171077.	+	171077.i	0.721330	+	0.721330i	0.968876	−	0.247546i	$-0.0796242\pi$
$487$	171077.	+	171077.i	0.721330	+	0.721330i	−0.247546	+	0.968876i	$0.579624\pi$
$488$	−63170.4			−0.265261
$489$	−91036.5	−	219782.i	−0.380713	−	0.919123i
$490$	55751.5	−	55751.5i	0.232201	−	0.232201i
$491$			78673.3i			0.326336i	0.986598	+	0.163168i	$0.0521712\pi$
$491$			78673.3i			0.326336i	−0.986598	+	0.163168i	$0.947829\pi$
$492$	−46012.7	+	127323.i	−0.190085	+	0.525989i
$493$	191439.			0.787655
$494$	−227050.	−	227050.i	−0.930394	−	0.930394i
$495$	−6724.06	+	2785.20i	−0.0274423	+	0.0113670i
$496$			25797.6i			0.104861i
$497$	−60118.0	+	60118.0i	−0.243384	+	0.243384i
$498$	−76605.3	−	31731.0i	−0.308887	−	0.127945i
$499$	−356004.	+	147462.i	−1.42973	+	0.592214i	−0.957285	−	0.289146i	$-0.906629\pi$
$499$	−356004.	+	147462.i	−1.42973	+	0.592214i	−0.472445	+	0.881360i	$0.656629\pi$
$500$	−93219.2	+	93219.2i	−0.372877	+	0.372877i
$501$	−351490.	+	351490.i	−1.40035	+	1.40035i
$502$	−332414.			−1.31908
$503$	−179542.	−	433453.i	−0.709627	−	1.71319i	−0.700930	−	0.713230i	$-0.747231\pi$
$503$	−179542.	−	433453.i	−0.709627	−	1.71319i	−0.00869749	−	0.999962i	$-0.502769\pi$
$504$	−6113.61	−	14759.6i	−0.0240678	−	0.0581049i
$505$	−72674.1	+	30102.6i	−0.284969	+	0.118038i
$506$	−14662.5	−	6073.41i	−0.0572674	−	0.0237209i
$507$	−139865.	+	337665.i	−0.544120	+	1.31362i
$508$	−64410.3			−0.249590
$509$	−175379.	−	72644.4i	−0.676928	−	0.280393i	0.0176141	−	0.999845i	$-0.494393\pi$
$509$	−175379.	−	72644.4i	−0.676928	−	0.280393i	−0.694542	+	0.719452i	$0.744393\pi$
$510$	−106184.			−0.408243
$511$	162990.	+	67512.7i	0.624194	+	0.258550i
$512$	−8192.00	−	8192.00i	−0.0312500	−	0.0312500i
$513$	−192455.	+	192455.i	−0.731299	+	0.731299i
$514$	35035.5	−	84583.1i	0.132612	−	0.320153i
$515$		−	153608.i		−	0.579161i
$516$	−48628.4	+	117399.i	−0.182638	+	0.440927i
$517$		−	12942.8i		−	0.0484226i
$518$	73690.1	+	30523.4i	0.274631	+	0.113756i
$519$	177768.	−	429169.i	0.659961	−	1.59329i
$520$	51366.0	+	124008.i	0.189963	+	0.458611i
$521$	−200876.	+	83205.4i	−0.740034	+	0.306532i	−0.720668	−	0.693280i	$-0.756165\pi$
$521$	−200876.	+	83205.4i	−0.740034	+	0.306532i	−0.0193662	+	0.999812i	$0.506165\pi$
$522$	63569.9	−	26331.5i	0.233298	−	0.0966351i
$523$			69748.1i			0.254993i	0.991839	+	0.127497i	$0.0406942\pi$
$523$			69748.1i			0.254993i	−0.991839	+	0.127497i	$0.959306\pi$
$524$	11793.9	+	11793.9i	0.0429531	+	0.0429531i
$525$	−20383.8	−	20383.8i	−0.0739548	−	0.0739548i
$526$	−132456.	−	319777.i	−0.478741	−	1.15578i
$527$	−24697.8	+	59625.7i	−0.0889276	+	0.214690i
$528$	−6997.00	−	6997.00i	−0.0250983	−	0.0250983i
$529$	146363.			0.523023
$530$	−82300.9	−	198692.i	−0.292990	−	0.707341i
$531$	56455.3	−	56455.3i	0.200224	−	0.200224i
$532$		−	123741.i		−	0.437212i
$533$	402645.	+	145510.i	1.41732	+	0.512199i
$534$	−276444.			−0.969449
$535$	−17279.4	−	17279.4i	−0.0603699	−	0.0603699i
$536$	−11433.9	+	4736.07i	−0.0397983	+	0.0164850i
$537$			410313.i			1.42288i
$538$	−142293.	+	142293.i	−0.491610	+	0.491610i
$539$	16982.2	+	7034.24i	0.0584541	+	0.0242125i
$540$	105114.	−	43539.6i	0.360473	−	0.149313i
$541$	−215680.	+	215680.i	−0.736911	+	0.736911i	−0.971979	−	0.235068i	$-0.924469\pi$
$541$	−215680.	+	215680.i	−0.736911	+	0.736911i	0.235068	+	0.971979i	$0.424469\pi$
$542$	199784.	−	199784.i	0.680084	−	0.680084i
$543$	232701.			0.789222
$544$	−11091.3	−	26776.8i	−0.0374788	−	0.0904818i
$545$	−169360.	−	408870.i	−0.570186	−	1.37655i
$546$	−232496.	+	96303.0i	−0.779885	+	0.323039i
$547$	−87008.1	−	36039.9i	−0.290794	−	0.120451i	0.232518	−	0.972592i	$-0.425304\pi$
$547$	−87008.1	−	36039.9i	−0.290794	−	0.120451i	−0.523312	+	0.852141i	$0.675304\pi$
$548$	−68229.8	+	164721.i	−0.227203	+	0.548515i
$549$	−56801.4			−0.188458
$550$	−3311.75	−	1371.77i	−0.0109479	−	0.00453478i
$551$	532958.			1.75546
$552$	−76888.0	−	31848.0i	−0.252337	−	0.104521i
$553$	−97048.7	−	97048.7i	−0.317351	−	0.317351i
$554$	−45860.6	+	45860.6i	−0.149424	+	0.149424i
$555$	72919.0	−	176042.i	0.236731	−	0.571519i
$556$			111241.i			0.359845i
$557$	−206478.	+	498482.i	−0.665524	+	1.60672i	0.123492	+	0.992346i	$0.460591\pi$
$557$	−206478.	+	498482.i	−0.665524	+	1.60672i	−0.789017	+	0.614372i	$0.789409\pi$
$558$			23196.6i			0.0745000i
$559$	371263.	+	153782.i	1.18811	+	0.492132i
$560$	−19795.0	+	47789.3i	−0.0631217	+	0.152389i
$561$	−9473.39	−	22870.8i	−0.0301009	−	0.0726700i
$562$	283968.	−	117623.i	0.899077	−	0.372410i
$563$	232883.	−	96463.3i	0.734718	−	0.304330i	0.0162291	−	0.999868i	$-0.494834\pi$
$563$	232883.	−	96463.3i	0.734718	−	0.304330i	0.718489	+	0.695538i	$0.244834\pi$
$564$		−	67870.2i		−	0.213364i
$565$	192774.	+	192774.i	0.603882	+	0.603882i
$566$	−55804.8	−	55804.8i	−0.174196	−	0.174196i
$567$	103515.	+	249907.i	0.321986	+	0.777342i
$568$	−21215.4	+	51218.5i	−0.0657589	+	0.158756i
$569$	145464.	+	145464.i	0.449294	+	0.449294i	0.895120	−	0.445826i	$-0.147090\pi$
$569$	145464.	+	145464.i	0.449294	+	0.449294i	−0.445826	+	0.895120i	$0.647090\pi$
$570$	−295612.			−0.909857
$571$	−238879.	−	576705.i	−0.732665	−	1.76881i	−0.633505	−	0.773738i	$-0.718384\pi$
$571$	−238879.	−	576705.i	−0.732665	−	1.76881i	−0.0991600	−	0.995072i	$-0.531616\pi$
$572$	−22127.2	+	22127.2i	−0.0676293	+	0.0676293i
$573$		−	74131.3i		−	0.225784i
$574$	70068.8	+	149371.i	0.212667	+	0.453361i
$575$	−30148.0			−0.0911848
$576$	−7366.06	−	7366.06i	−0.0222019	−	0.0222019i
$577$	−478297.	+	198117.i	−1.43663	+	0.595073i	−0.958980	−	0.283475i	$-0.908513\pi$
$577$	−478297.	+	198117.i	−1.43663	+	0.595073i	−0.477654	+	0.878548i	$0.658513\pi$
$578$			163726.i			0.490073i
$579$	331780.	−	331780.i	0.989677	−	0.989677i
$580$	−205830.	−	85257.6i	−0.611861	−	0.253441i
$581$	−93358.4	+	38670.3i	−0.276568	+	0.114558i
$582$	282688.	−	282688.i	0.834567	−	0.834567i
$583$	35453.3	−	35453.3i	0.104308	−	0.104308i
$584$	115037.			0.337297
$585$	46187.1	+	111506.i	0.134961	+	0.325825i
$586$	150751.	+	363944.i	0.438999	+	1.05984i
$587$	−244086.	+	101104.i	−0.708381	+	0.293421i	−0.707634	−	0.706579i	$-0.750238\pi$
$587$	−244086.	+	101104.i	−0.708381	+	0.293421i	−0.000746370		1.00000i	$0.500238\pi$
$588$	89051.8	+	36886.5i	0.257566	+	0.106687i
$589$	−68757.6	+	165996.i	−0.198194	+	0.478482i
$590$	−258510.			−0.742631
$591$	−316642.	−	131157.i	−0.906554	−	0.375507i
$592$	52009.8			0.148403
$593$	−96830.3	−	40108.4i	−0.275361	−	0.114058i	0.240730	−	0.970592i	$-0.422613\pi$
$593$	−96830.3	−	40108.4i	−0.275361	−	0.114058i	−0.516091	+	0.856534i	$0.672613\pi$
$594$	18755.8	+	18755.8i	0.0531573	+	0.0531573i
$595$	−91503.8	+	91503.8i	−0.258467	+	0.258467i
$596$	80433.3	−	194183.i	0.226435	−	0.546662i
$597$		−	439196.i		−	1.23228i
$598$	−100716.	+	243150.i	−0.281641	+	0.679941i
$599$			35568.7i			0.0991321i	0.998771	+	0.0495660i	$0.0157838\pi$
$599$			35568.7i			0.0991321i	−0.998771	+	0.0495660i	$0.984216\pi$
$600$	−17366.3	−	7193.35i	−0.0482397	−	0.0199815i
$601$	−271918.	+	656467.i	−0.752815	+	1.81746i	−0.209776	+	0.977750i	$0.567273\pi$
$601$	−271918.	+	656467.i	−0.752815	+	1.81746i	−0.543040	+	0.839707i	$0.682727\pi$
$602$	59263.2	+	143074.i	0.163528	+	0.394791i
$603$	−10281.1	+	4258.56i	−0.0282751	+	0.0117119i
$604$	285130.	−	118105.i	0.781572	−	0.323738i
$605$		−	335513.i		−	0.916639i
$606$	−67999.5	−	67999.5i	−0.185166	−	0.185166i
$607$	−160034.	−	160034.i	−0.434346	−	0.434346i	0.455758	−	0.890104i	$-0.349368\pi$
$607$	−160034.	−	160034.i	−0.434346	−	0.434346i	−0.890104	+	0.455758i	$0.849368\pi$
$608$	−30877.8	−	74545.7i	−0.0835294	−	0.201658i
$609$	159844.	−	385898.i	0.430985	−	1.04049i
$610$	130047.	+	130047.i	0.349495	+	0.349495i
$611$	−214632.			−0.574926
$612$	−9973.07	−	24077.1i	−0.0266272	−	0.0642838i
$613$	−330551.	+	330551.i	−0.879665	+	0.879665i	−0.993500	−	0.113835i	$-0.963687\pi$
$613$	−330551.	+	330551.i	−0.879665	+	0.879665i	0.113835	+	0.993500i	$0.463687\pi$
$614$			484212.i			1.28440i
$615$	356841.	−	167391.i	0.943463	−	0.442570i
$616$	−12059.3			−0.0317805
$617$	−415322.	−	415322.i	−1.09098	−	1.09098i	−0.995425	−	0.0955504i	$-0.969539\pi$
$617$	−415322.	−	415322.i	−1.09098	−	1.09098i	−0.0955504	−	0.995425i	$-0.530461\pi$
$618$	173494.	−	71863.7i	0.454264	−	0.188162i
$619$			618960.i			1.61540i	0.589591	+	0.807702i	$0.299289\pi$
$619$			618960.i			1.61540i	−0.589591	+	0.807702i	$0.700711\pi$
$620$	53108.8	−	53108.8i	0.138160	−	0.138160i
$621$	206102.	+	85370.3i	0.534440	+	0.221372i
$622$	−19817.4	+	8208.64i	−0.0512231	+	0.0212173i
$623$	−238225.	+	238225.i	−0.613778	+	0.613778i
$624$	−116032.	+	116032.i	−0.297994	+	0.297994i
$625$	332241.			0.850538
$626$	−173626.	−	419171.i	−0.443064	−	1.06965i
$627$	−26373.5	−	63671.4i	−0.0670862	−	0.161961i
$628$	123477.	−	51146.0i	0.313089	−	0.129686i
$629$	120210.	+	49792.5i	0.303835	+	0.125853i
$630$	−17799.2	+	42971.1i	−0.0448455	+	0.108267i
$631$	186227.			0.467718			0.233859	−	0.972270i	$-0.424865\pi$
$631$	186227.			0.467718			0.233859	+	0.972270i	$0.424865\pi$
$632$	−82682.1	−	34248.1i	−0.207003	−	0.0857436i
$633$	693155.			1.72991
$634$	−177239.	−	73415.0i	−0.440942	−	0.182644i
$635$	132600.	+	132600.i	0.328848	+	0.328848i
$636$	185912.	−	185912.i	0.459613	−	0.459613i
$637$	116649.	−	281617.i	0.287477	−	0.694032i
$638$		−	51939.7i		−	0.127602i
$639$	−19076.4	+	46054.5i	−0.0467191	+	0.112790i
$640$			33729.3i			0.0823469i
$641$	250524.	+	103770.i	0.609723	+	0.252556i	0.666110	−	0.745853i	$-0.267958\pi$
$641$	250524.	+	103770.i	0.609723	+	0.252556i	−0.0563870	+	0.998409i	$0.517958\pi$
$642$	11432.4	−	27600.3i	0.0277376	−	0.0669645i
$643$	−65101.4	−	157169.i	−0.157459	−	0.380140i	0.825387	−	0.564568i	$-0.190957\pi$
$643$	−65101.4	−	157169.i	−0.157459	−	0.380140i	−0.982846	+	0.184427i	$0.940957\pi$
$644$	−93702.9	+	38813.0i	−0.225934	+	0.0935849i
$645$	341797.	−	141577.i	0.821578	−	0.340309i
$646$		−	201858.i		−	0.483705i
$647$	−261444.	−	261444.i	−0.624554	−	0.624554i	0.322139	−	0.946693i	$-0.395598\pi$
$647$	−261444.	−	261444.i	−0.624554	−	0.624554i	−0.946693	+	0.322139i	$0.895598\pi$
$648$	124721.	+	124721.i	0.297023	+	0.297023i
$649$	−23063.4	−	55679.9i	−0.0547562	−	0.132193i
$650$	−22748.2	+	54919.0i	−0.0538419	+	0.129986i
$651$	99570.5	+	99570.5i	0.234946	+	0.234946i
$652$	−189044.			−0.444700
$653$	79412.3	+	191718.i	0.186235	+	0.449611i	0.989229	−	0.146376i	$-0.0467609\pi$
$653$	79412.3	+	191718.i	0.186235	+	0.449611i	−0.802994	+	0.595987i	$0.796761\pi$
$654$	382570.	−	382570.i	0.894450	−	0.894450i
$655$		−	48559.5i		−	0.113186i
$656$	79485.0	+	72501.4i	0.184705	+	0.168476i
$657$	103439.			0.239636
$658$	−58486.9	−	58486.9i	−0.135085	−	0.135085i
$659$	9159.10	−	3793.82i	0.0210903	−	0.00873587i	−0.372113	−	0.928187i	$-0.621367\pi$
$659$	9159.10	−	3793.82i	0.0210903	−	0.00873587i	0.393204	+	0.919451i	$0.371367\pi$
$660$			28809.1i			0.0661365i
$661$	91881.2	−	91881.2i	0.210293	−	0.210293i	−0.594099	−	0.804392i	$-0.702491\pi$
$661$	91881.2	−	91881.2i	0.210293	−	0.210293i	0.804392	+	0.594099i	$0.202491\pi$
$662$	461943.	+	191343.i	1.05408	+	0.436613i
$663$	−379268.	+	157098.i	−0.862818	+	0.357391i
$664$	−46592.4	+	46592.4i	−0.105677	+	0.105677i
$665$	−254743.	+	254743.i	−0.576049	+	0.576049i
$666$	46766.0			0.105434
$667$	−167169.	−	403581.i	−0.375754	−	0.907150i
$668$	151166.	+	364947.i	0.338768	+	0.817857i
$669$	−103112.	+	42710.5i	−0.230387	+	0.0954295i
$670$	33288.6	+	13788.6i	0.0741560	+	0.0307164i
$671$	−16408.2	+	39613.0i	−0.0364432	+	0.0879817i
$672$	−63237.0			−0.140034
$673$	151124.	+	62597.6i	0.333659	+	0.138206i	0.543222	−	0.839589i	$-0.317204\pi$
$673$	151124.	+	62597.6i	0.333659	+	0.138206i	−0.209563	+	0.977795i	$0.567204\pi$
$674$	242666.			0.534183
$675$	46551.2	+	19282.2i	0.102170	+	0.0423202i
$676$	205373.	+	205373.i	0.449416	+	0.449416i
$677$	−31493.5	+	31493.5i	−0.0687138	+	0.0687138i	−0.740629	−	0.671915i	$-0.765472\pi$
$677$	−31493.5	+	31493.5i	−0.0687138	+	0.0687138i	0.671915	+	0.740629i	$0.265472\pi$
$678$	−127544.	+	307918.i	−0.277460	+	0.669848i
$679$		−	487211.i		−	1.05676i
$680$	−32291.3	+	77958.1i	−0.0698342	+	0.168595i
$681$		−	857486.i		−	1.84898i
$682$	16177.2	+	6700.81i	0.0347804	+	0.0144065i
$683$	−152631.	+	368484.i	−0.327191	+	0.789909i	0.671608	+	0.740907i	$0.265604\pi$
$683$	−152631.	+	368484.i	−0.327191	+	0.789909i	−0.998799	+	0.0490019i	$0.984396\pi$
$684$	−27764.6	−	67029.7i	−0.0593444	−	0.143270i
$685$	479570.	−	198645.i	1.02205	−	0.423346i
$686$	326246.	−	135135.i	0.693260	−	0.287158i
$687$		−	395192.i		−	0.837327i
$688$	71403.9	+	71403.9i	0.150850	+	0.150850i
$689$	−587925.	−	587925.i	−1.23846	−	1.23846i
$690$	92722.5	+	223852.i	0.194754	+	0.470178i
$691$	168918.	−	407803.i	0.353768	−	0.854073i	−0.642380	−	0.766387i	$-0.722053\pi$
$691$	168918.	−	407803.i	0.353768	−	0.854073i	0.996148	−	0.0876861i	$-0.0279472\pi$
$692$	−261027.	−	261027.i	−0.545096	−	0.545096i
$693$	−10843.4			−0.0225788
$694$	−110667.	−	267174.i	−0.229773	−	0.554722i
$695$	229009.	−	229009.i	0.474114	−	0.474114i
$696$		−	272364.i		−	0.562252i
$697$	114302.	+	243668.i	0.235283	+	0.501571i
$698$	74636.9			0.153194
$699$	244728.	+	244728.i	0.500875	+	0.500875i
$700$	−21164.2	+	8766.50i	−0.0431922	+	0.0178908i
$701$			386197.i			0.785909i	0.919558	+	0.392955i	$0.128547\pi$
$701$			386197.i			0.785909i	−0.919558	+	0.392955i	$0.871453\pi$
$702$	311029.	−	311029.i	0.631142	−	0.631142i
$703$	334659.	+	138620.i	0.677161	+	0.280489i
$704$	−7264.89	+	3009.21i	−0.0146583	+	0.00607166i
$705$	−139722.	+	139722.i	−0.281118	+	0.281118i
$706$	−339239.	+	339239.i	−0.680608	+	0.680608i
$707$	−117197.			−0.234464
$708$	−120941.	−	291977.i	−0.241272	−	0.582481i
$709$	187295.	+	452170.i	0.372592	+	0.899517i	0.993310	+	0.115482i	$0.0368414\pi$
$709$	187295.	+	452170.i	0.372592	+	0.899517i	−0.620718	+	0.784034i	$0.713159\pi$
$710$	149118.	−	61766.6i	0.295810	−	0.122528i
$711$	−74345.9	−	30795.1i	−0.147068	−	0.0609175i
$712$	−84068.6	+	202960.i	−0.165834	+	0.400359i
$713$	147266.			0.289684
$714$	−146159.	−	60541.1i	−0.286701	−	0.118755i
$715$	91105.5			0.178210
$716$	301243.	+	124779.i	0.587613	+	0.243397i
$717$	−7321.89	−	7321.89i	−0.0142425	−	0.0142425i
$718$	−161164.	+	161164.i	−0.312622	+	0.312622i
$719$	−206115.	+	497607.i	−0.398706	+	0.962561i	0.589268	+	0.807938i	$0.299416\pi$
$719$	−206115.	+	497607.i	−0.398706	+	0.962561i	−0.987973	+	0.154623i	$0.950584\pi$
$720$			30328.6i			0.0585043i
$721$	87579.9	−	211437.i	0.168474	−	0.406733i
$722$		−	193361.i		−	0.370933i
$723$	−567957.	−	235255.i	−1.08652	−	0.450052i
$724$	70766.1	−	170844.i	0.135004	−	0.325929i
$725$	−37757.6	−	91154.8i	−0.0718337	−	0.173422i
$726$	378949.	−	156966.i	0.718965	−	0.297805i
$727$	806075.	−	333887.i	1.52513	−	0.631729i	0.546518	−	0.837447i	$-0.315953\pi$
$727$	806075.	−	333887.i	1.52513	−	0.631729i	0.978611	+	0.205718i	$0.0659530\pi$
$728$			199980.i			0.377332i
$729$	−239929.	−	239929.i	−0.451469	−	0.451469i
$730$	−236824.	−	236824.i	−0.444406	−	0.444406i
$731$	96675.3	+	233395.i	0.180918	+	0.436774i
$732$	−86042.2	+	207724.i	−0.160579	+	0.387673i
$733$	534489.	+	534489.i	0.994788	+	0.994788i	0.999986	−	0.00519823i	$-0.00165466\pi$
$733$	534489.	+	534489.i	0.994788	+	0.994788i	−0.00519823	+	0.999986i	$0.501655\pi$
$734$	444548.			0.825137
$735$	−107391.	−	259266.i	−0.198790	−	0.479922i
$736$	−46764.3	+	46764.3i	−0.0863294	+	0.0863294i
$737$			8400.15i			0.0154651i
$738$	71471.1	+	65191.6i	0.131225	+	0.119696i
$739$	−175001.			−0.320444			−0.160222	−	0.987081i	$-0.551221\pi$
$739$	−175001.			−0.320444			−0.160222	+	0.987081i	$0.551221\pi$
$740$	−107071.	−	107071.i	−0.195528	−	0.195528i
$741$	−1.05587e6	+	437355.i	−1.92297	+	0.796521i
$742$		−	320417.i		−	0.581980i
$743$	311478.	−	311478.i	0.564222	−	0.564222i	−0.366282	−	0.930504i	$-0.619369\pi$
$743$	311478.	−	311478.i	0.564222	−	0.564222i	0.930504	+	0.366282i	$0.119369\pi$
$744$	84830.7	+	35138.0i	0.153252	+	0.0634792i
$745$	−565346.	+	234174.i	−1.01860	+	0.421916i
$746$	−116331.	+	116331.i	−0.209034	+	0.209034i
$747$	−41894.8	+	41894.8i	−0.0750791	+	0.0750791i
$748$	−19672.2			−0.0351600
$749$	−13932.6	−	33636.4i	−0.0248353	−	0.0599578i
$750$	179564.	+	433505.i	0.319224	+	0.770676i
$751$	151970.	−	62948.0i	0.269450	−	0.111610i	−0.243868	−	0.969808i	$-0.578416\pi$
$751$	151970.	−	62948.0i	0.269450	−	0.111610i	0.513318	+	0.858199i	$0.328416\pi$
$752$	−49828.8	−	20639.8i	−0.0881140	−	0.0364980i
$753$	−452769.	+	1.09308e6i	−0.798522	+	1.92780i
$754$	−861320.			−1.51503
$755$	−830128.	−	343850.i	−1.45630	−	0.603220i
$756$	169510.			0.296587
$757$	−63665.9	−	26371.3i	−0.111100	−	0.0460192i	0.326441	−	0.945218i	$-0.394151\pi$
$757$	−63665.9	−	26371.3i	−0.111100	−	0.0460192i	−0.437541	+	0.899198i	$0.644151\pi$
$758$	479319.	+	479319.i	0.834231	+	0.834231i
$759$	−39942.6	+	39942.6i	−0.0693351	+	0.0693351i
$760$	−89897.8	+	217032.i	−0.155640	+	0.375749i
$761$			412106.i			0.711606i	0.934561	+	0.355803i	$0.115793\pi$
$761$			412106.i			0.711606i	−0.934561	+	0.355803i	$0.884207\pi$
$762$	−87731.1	+	211802.i	−0.151093	+	0.364770i
$763$		−	659358.i		−	1.13259i
$764$	−54425.6	−	22543.8i	−0.0932431	−	0.0386226i
$765$	−29035.6	+	70098.2i	−0.0496144	+	0.119780i
$766$	−63869.2	−	154194.i	−0.108851	−	0.262790i
$767$	−923345.	+	382462.i	−1.56954	+	0.650126i
$768$	−38095.9	+	15779.9i	−0.0645887	+	0.0267535i
$769$		−	528617.i		−	0.893899i	−0.894559	−	0.446949i	$-0.852510\pi$
$769$		−	528617.i		−	0.893899i	0.894559	−	0.446949i	$-0.147490\pi$
$770$	24826.1	+	24826.1i	0.0418724	+	0.0418724i
$771$	−230415.	−	230415.i	−0.387617	−	0.387617i
$772$	−142689.	−	344483.i	−0.239418	−	0.578007i
$773$	−130147.	+	314202.i	−0.217808	+	0.525836i	−0.994583	−	0.103943i	$-0.966854\pi$
$773$	−130147.	+	314202.i	−0.217808	+	0.525836i	0.776775	+	0.629778i	$0.216854\pi$
$774$	64204.8	+	64204.8i	0.107173	+	0.107173i
$775$	33262.3			0.0553795
$776$	−121576.	−	293511.i	−0.201895	−	0.487417i
$777$	200741.	−	200741.i	0.332503	−	0.332503i
$778$			611920.i			1.01096i
$779$	318214.	+	678362.i	0.524377	+	1.11786i
$780$	477743.			0.785245
$781$	26607.6	+	26607.6i	0.0436217	+	0.0436217i
$782$	−152856.	+	63315.2i	−0.249960	+	0.103537i
$783$			730085.i			1.19083i
$784$	54162.5	−	54162.5i	0.0881185	−	0.0881185i
$785$	−359492.	−	148906.i	−0.583378	−	0.241643i
$786$	54846.1	−	22718.0i	0.0887771	−	0.0367727i
$787$	231710.	−	231710.i	0.374107	−	0.374107i	−0.494863	−	0.868971i	$-0.664782\pi$
$787$	231710.	−	231710.i	0.374107	−	0.374107i	0.868971	+	0.494863i	$0.164782\pi$
$788$	−192586.	+	192586.i	−0.310151	+	0.310151i
$789$	−1.23194e6			−1.97896
$790$	99709.9	+	240721.i	0.159766	+	0.385709i
$791$	155437.	+	375258.i	0.248429	+	0.599760i
$792$	−6532.42	+	2705.82i	−0.0104141	+	0.00431368i
$793$	656905.	+	272099.i	1.04461	+	0.432694i
$794$	−144592.	+	349075.i	−0.229352	+	0.553704i
$795$	−765462.			−1.21113
$796$	−322448.	−	133562.i	−0.508902	−	0.210794i
$797$	−396537.			−0.624262			−0.312131	−	0.950039i	$-0.601043\pi$
$797$	−396537.			−0.624262			−0.312131	+	0.950039i	$0.601043\pi$
$798$	−406901.	−	168544.i	−0.638974	−	0.264672i
$799$	−95409.0	−	95409.0i	−0.149450	−	0.149450i
$800$	−10562.4	+	10562.4i	−0.0165038	+	0.0165038i
$801$	−75592.6	+	182497.i	−0.117819	+	0.284439i
$802$		−	178454.i		−	0.277446i
$803$	29880.4	−	72137.6i	0.0463399	−	0.111874i
$804$			44049.1i			0.0681435i
$805$	272807.	+	113000.i	0.420982	+	0.174376i
$806$	111120.	−	268268.i	0.171050	−	0.412951i
$807$	274093.	+	661719.i	0.420873	+	1.01608i
$808$	−70602.9	+	29244.7i	−0.108143	+	0.0447944i
$809$	−97651.4	+	40448.5i	−0.149204	+	0.0618024i	−0.456036	−	0.889961i	$-0.650731\pi$
$809$	−97651.4	+	40448.5i	−0.149204	+	0.0618024i	0.306832	+	0.951764i	$0.400731\pi$
$810$		−	513520.i		−	0.782685i
$811$	−760482.	−	760482.i	−1.15624	−	1.15624i	−0.985278	−	0.170960i	$-0.945313\pi$
$811$	−760482.	−	760482.i	−1.15624	−	1.15624i	−0.170960	−	0.985278i	$-0.554687\pi$
$812$	−234709.	−	234709.i	−0.355973	−	0.355973i
$813$	−384835.	−	929073.i	−0.582228	−	1.40562i
$814$	13509.3	−	32614.4i	0.0203885	−	0.0492221i
$815$	389179.	+	389179.i	0.585915	+	0.585915i
$816$	−103158.			−0.154925
$817$	269140.	+	649762.i	0.403213	+	0.973443i
$818$	−451024.	+	451024.i	−0.674052	+	0.674052i
$819$			179818.i			0.268080i
$820$	−14377.1	−	312890.i	−0.0213817	−	0.465333i
$821$	706209.			1.04772			0.523862	−	0.851803i	$-0.324491\pi$
$821$	706209.			1.04772			0.523862	+	0.851803i	$0.324491\pi$
$822$	448723.	+	448723.i	0.664101	+	0.664101i
$823$	−178700.	+	74019.9i	−0.263830	+	0.109282i	−0.510678	−	0.859772i	$-0.670605\pi$
$823$	−178700.	+	74019.9i	−0.263830	+	0.109282i	0.246847	+	0.969054i	$0.420605\pi$
$824$		−	149230.i		−	0.219787i
$825$	−9021.64	+	9021.64i	−0.0132549	+	0.0132549i
$826$	−355831.	−	147390.i	−0.521535	−	0.216027i
$827$	−889883.	+	368602.i	−1.30113	+	0.538947i	−0.922285	−	0.386511i	$-0.873680\pi$
$827$	−889883.	+	368602.i	−1.30113	+	0.538947i	−0.378849	+	0.925458i	$0.623680\pi$
$828$	−42049.4	+	42049.4i	−0.0613337	+	0.0613337i
$829$	955108.	−	955108.i	1.38977	−	1.38977i	0.563989	−	0.825782i	$-0.309266\pi$
$829$	955108.	−	955108.i	1.38977	−	1.38977i	0.825782	−	0.563989i	$-0.190734\pi$
$830$	191837.			0.278469
$831$	88339.2	+	213270.i	0.127924	+	0.308835i
$832$	49902.1	+	120474.i	0.0720895	+	0.174039i
$833$	177039.	−	73331.8i	0.255140	−	0.105682i
$834$	365796.	+	151518.i	0.525904	+	0.217837i
$835$	440106.	−	1.06251e6i	0.631225	−	1.52391i
$836$	−54766.6			−0.0783615
$837$	−227393.	−	94189.3i	−0.324583	−	0.134447i
$838$	37062.0			0.0527765
$839$	307967.	+	127564.i	0.437502	+	0.181219i	0.590553	−	0.806999i	$-0.298910\pi$
$839$	307967.	+	127564.i	0.437502	+	0.181219i	−0.153051	+	0.988218i	$0.548910\pi$
$840$	130184.	+	130184.i	0.184502	+	0.184502i
$841$	510774.	−	510774.i	0.722165	−	0.722165i
$842$	25502.8	−	61569.1i	0.0359719	−	0.0868438i
$843$		−	1.09399e6i		−	1.53942i
$844$	210793.	−	508900.i	0.295918	−	0.714410i
$845$		−	845590.i		−	1.18426i
$846$	−44804.9	−	18558.8i	−0.0626016	−	0.0259304i
$847$	191293.	−	461823.i	0.266645	−	0.643737i
$848$	−79955.3	−	193029.i	−0.111187	−	0.268430i
$849$	−259514.	+	107494.i	−0.360035	+	0.149131i
$850$	−34524.9	+	14300.7i	−0.0477853	+	0.0197933i
$851$		−	296900.i		−	0.409969i
$852$	139526.	+	139526.i	0.192210	+	0.192210i
$853$	39535.0	+	39535.0i	0.0543354	+	0.0543354i	0.733752	−	0.679417i	$-0.237767\pi$
$853$	39535.0	+	39535.0i	0.0543354	+	0.0543354i	−0.679417	+	0.733752i	$0.737767\pi$
$854$	104859.	+	253152.i	0.143777	+	0.347109i
$855$	−80834.0	+	195151.i	−0.110576	+	0.266955i
$856$	−16786.9	−	16786.9i	−0.0229099	−	0.0229099i
$857$	795574.			1.08323			0.541613	−	0.840628i	$-0.317814\pi$
$857$	795574.			1.08323			0.541613	+	0.840628i	$0.317814\pi$
$858$	42622.6	+	102900.i	0.0578983	+	0.139779i
$859$	41372.1	−	41372.1i	0.0560688	−	0.0560688i	−0.678516	−	0.734585i	$-0.737377\pi$
$859$	41372.1	−	41372.1i	0.0560688	−	0.0560688i	0.734585	+	0.678516i	$0.237377\pi$
$860$		−	293995.i		−	0.397505i
$861$	586619.	−	26954.7i	0.791316	−	0.0363604i
$862$	841284.			1.13221
$863$	618258.	+	618258.i	0.830134	+	0.830134i	0.987535	−	0.157401i	$-0.0503116\pi$
$863$	618258.	+	618258.i	0.830134	+	0.830134i	−0.157401	+	0.987535i	$0.550312\pi$
$864$	102118.	−	42298.7i	0.136797	−	0.0566630i
$865$			1.07474e6i			1.43638i
$866$	−364556.	+	364556.i	−0.486104	+	0.486104i
$867$	538382.	+	223005.i	0.716230	+	0.296672i
$868$	103383.	−	42822.5i	0.137217	−	0.0568372i
$869$	−42952.6	+	42952.6i	−0.0568788	+	0.0568788i
$870$	−560708.	+	560708.i	−0.740795	+	0.740795i
$871$	139300.			0.183618
$872$	−164533.	−	397217.i	−0.216381	−	0.522391i
$873$	−109318.	−	263918.i	−0.143438	−	0.346291i
$874$	−425546.	+	176267.i	−0.557088	+	0.230754i
$875$	528310.	+	218833.i	0.690038	+	0.285823i
$876$	156688.	−	378279.i	0.204187	−	0.492951i
$877$	−1.31577e6			−1.71073			−0.855367	−	0.518023i	$-0.826668\pi$
$877$	−1.31577e6			−1.71073			−0.855367	+	0.518023i	$0.826668\pi$
$878$	−568392.	−	235435.i	−0.737324	−	0.305410i
$879$	1.40210e6			1.81468
$880$	21151.0	+	8761.03i	0.0273128	+	0.0113133i
$881$	393077.	+	393077.i	0.506438	+	0.506438i	0.913431	−	0.406993i	$-0.133423\pi$
$881$	393077.	+	393077.i	0.506438	+	0.506438i	−0.406993	+	0.913431i	$0.633423\pi$
$882$	48701.7	−	48701.7i	0.0626047	−	0.0626047i
$883$	409671.	−	989034.i	0.525429	−	1.26850i	−0.409060	−	0.912507i	$-0.634144\pi$
$883$	409671.	−	989034.i	0.525429	−	1.26850i	0.934490	−	0.355991i	$-0.115856\pi$
$884$			326225.i			0.417458i
$885$	−352107.	+	850063.i	−0.449561	+	1.08534i
$886$			352640.i			0.449225i
$887$	781522.	+	323717.i	0.993331	+	0.411451i	0.819347	−	0.573297i	$-0.194336\pi$
$887$	781522.	+	323717.i	0.993331	+	0.411451i	0.173984	+	0.984749i	$0.444336\pi$
$888$	70840.8	−	171025.i	0.0898375	−	0.216887i
$889$	106917.	+	258121.i	0.135283	+	0.326603i
$890$	590897.	−	244758.i	0.745988	−	0.308998i
$891$	110606.	−	45814.5i	0.139323	−	0.0577095i
$892$			88691.5i			0.111468i
$893$	−265615.	−	265615.i	−0.333081	−	0.333081i
$894$	−528981.	−	528981.i	−0.661858	−	0.661858i
$895$	−363282.	−	877041.i	−0.453522	−	1.09490i
$896$	−19230.8	+	46427.3i	−0.0239542	+	0.0578306i
$897$	662372.	+	662372.i	0.823222	+	0.823222i
$898$	−371494.			−0.460679
$899$	184438.	+	445272.i	0.228208	+	0.550942i
$900$	−9497.48	+	9497.48i	−0.0117253	+	0.0117253i
$901$		−	522693.i		−	0.643868i
$902$	66110.1	−	31011.7i	0.0812559	−	0.0381164i
$903$	551193.			0.675971
$904$	187280.	+	187280.i	0.229168	+	0.229168i
$905$	−497397.	+	206029.i	−0.607304	+	0.251553i
$906$		−	1.09846e6i		−	1.33823i
$907$	−668762.	+	668762.i	−0.812937	+	0.812937i	−0.985073	−	0.172136i	$-0.944933\pi$
$907$	−668762.	+	668762.i	−0.812937	+	0.812937i	0.172136	+	0.985073i	$0.444933\pi$
$908$	−629548.	−	260767.i	−0.763585	−	0.316287i
$909$	−63484.5	+	26296.1i	−0.0768316	+	0.0318247i
$910$	411694.	−	411694.i	0.497155	−	0.497155i
$911$	11574.3	−	11574.3i	0.0139463	−	0.0139463i	−0.700099	−	0.714046i	$-0.746861\pi$
$911$	11574.3	−	11574.3i	0.0139463	−	0.0139463i	0.714046	+	0.700099i	$0.246861\pi$
$912$	−287187.			−0.345283
$913$	17115.1	+	41319.4i	0.0205323	+	0.0495692i
$914$	271920.	+	656473.i	0.325498	+	0.785823i
$915$	604769.	−	250504.i	0.722349	−	0.299207i
$916$	−290142.	−	120181.i	−0.345796	−	0.143233i
$917$	27686.3	−	66840.7i	0.0329250	−	0.0794881i
$918$	276520.			0.328126
$919$	949699.	+	393378.i	1.12449	+	0.465778i	0.865904	−	0.500210i	$-0.166744\pi$
$919$	949699.	+	393378.i	1.12449	+	0.465778i	0.258584	+	0.965989i	$0.416744\pi$
$920$	192545.			0.227487
$921$	1.59224e6	+	659529.i	1.87711	+	0.777525i
$922$	−743647.	−	743647.i	−0.874792	−	0.874792i
$923$	441235.	−	441235.i	0.517925	−	0.517925i
$924$	−16425.5	+	39654.8i	−0.0192387	+	0.0464463i
$925$		−	67059.3i		−	0.0783746i
$926$	−57958.3	+	139924.i	−0.0675918	+	0.163181i
$927$		−	134184.i		−	0.156150i
$928$	−199964.	−	82827.7i	−0.232196	−	0.0961789i
$929$	−166826.	+	402754.i	−0.193301	+	0.466669i	−0.990579	−	0.136943i	$-0.956272\pi$
$929$	−166826.	+	402754.i	−0.193301	+	0.466669i	0.797278	+	0.603612i	$0.206272\pi$
$930$	−102301.	−	246976.i	−0.118281	−	0.285555i
$931$	492869.	−	204153.i	0.568633	−	0.235535i
$932$	254098.	−	105251.i	0.292529	−	0.121169i
$933$			76346.7i			0.0877055i
$934$	−575736.	−	575736.i	−0.659978	−	0.659978i
$935$	40498.6	+	40498.6i	0.0463251	+	0.0463251i
$936$	44870.8	+	108328.i	0.0512167	+	0.123648i
$937$	−252237.	+	608953.i	−0.287296	+	0.693593i	−0.999969	−	0.00790304i	$-0.997484\pi$
$937$	−252237.	+	608953.i	−0.287296	+	0.693593i	0.712673	+	0.701496i	$0.247484\pi$
$938$	37959.2	+	37959.2i	0.0431431	+	0.0431431i
$939$	−1.61486e6			−1.83148
$940$	60090.7	+	145072.i	0.0680067	+	0.164183i
$941$	128731.	−	128731.i	0.145380	−	0.145380i	−0.630671	−	0.776051i	$-0.717220\pi$
$941$	128731.	−	128731.i	0.145380	−	0.145380i	0.776051	+	0.630671i	$0.217220\pi$
$942$		−	475697.i		−	0.536078i
$943$	413877.	−	453743.i	0.465423	−	0.510254i
$944$	−251142.			−0.281823
$945$	−348966.	−	348966.i	−0.390768	−	0.390768i
$946$	63322.9	−	26229.2i	0.0707585	−	0.0293091i
$947$			369245.i			0.411732i	0.978580	+	0.205866i	$0.0660012\pi$
$947$			369245.i			0.411732i	−0.978580	+	0.205866i	$0.933999\pi$
$948$	−225237.	+	225237.i	−0.250624	+	0.250624i
$949$	−1.19626e6	−	495509.i	−1.32830	−	0.550198i
$950$	−96116.0	+	39812.6i	−0.106500	+	0.0441136i
$951$	−482824.	+	482824.i	−0.533860	+	0.533860i
$952$	−88895.9	+	88895.9i	−0.0980862	+	0.0980862i
$953$	−843281.			−0.928510			−0.464255	−	0.885702i	$-0.653678\pi$
$953$	−843281.			−0.928510			−0.464255	+	0.885702i	$0.653678\pi$
$954$	−71894.0	−	173568.i	−0.0789943	−	0.190709i
$955$	65634.2	+	158455.i	0.0719654	+	0.173740i
$956$	−7602.22	+	3148.94i	−0.00831811	+	0.00344547i
$957$	−170794.	−	70745.3i	−0.186487	−	0.0772456i
$958$	154908.	−	373980.i	0.168788	−	0.407490i
$959$	773371.			0.840912
$960$	110913.	+	45941.5i	0.120348	+	0.0498497i
$961$	761042.			0.824065
$962$	−540847.	−	224026.i	−0.584419	−	0.242074i
$963$	−15094.4	−	15094.4i	−0.0162766	−	0.0162766i
$964$	−345439.	+	345439.i	−0.371721	+	0.371721i
$965$	−415426.	+	1.00293e6i	−0.446108	+	1.07700i
$966$			360991.i			0.386849i
$967$	−174681.	+	421716.i	−0.186806	+	0.450991i	−0.989341	−	0.145614i	$-0.953484\pi$
$967$	−174681.	+	421716.i	−0.186806	+	0.450991i	0.802535	+	0.596605i	$0.203484\pi$
$968$		−	325951.i		−	0.347857i
$969$	−663773.	−	274944.i	−0.706923	−	0.292817i
$970$	−353957.	+	854528.i	−0.376190	+	0.908203i
$971$	−152550.	−	368288.i	−0.161798	−	0.390615i	0.822100	−	0.569342i	$-0.192802\pi$
$971$	−152550.	−	368288.i	−0.161798	−	0.390615i	−0.983899	+	0.178727i	$0.942802\pi$
$972$	214446.	−	88826.4i	0.226979	−	0.0940177i
$973$	445793.	−	184654.i	0.470877	−	0.195044i
$974$		−	684308.i		−	0.721330i
$975$	149607.	+	149607.i	0.157377	+	0.157377i
$976$	126341.	+	126341.i	0.132631	+	0.132631i
$977$	−122273.	−	295192.i	−0.128097	−	0.309255i	0.846799	−	0.531913i	$-0.178527\pi$
$977$	−122273.	−	295192.i	−0.128097	−	0.309255i	−0.974897	+	0.222658i	$0.928527\pi$
$978$	−257490.	+	621636.i	−0.269205	+	0.649918i
$979$	105436.	+	105436.i	0.110007	+	0.110007i
$980$	−223006.			−0.232201
$981$	−147944.	−	357169.i	−0.153730	−	0.371138i
$982$	157347.	−	157347.i	0.163168	−	0.163168i
$983$		−	403423.i		−	0.417497i	−0.977969	−	0.208748i	$-0.933061\pi$
$983$		−	403423.i		−	0.417497i	0.977969	−	0.208748i	$-0.0669390\pi$
$984$	346671.	−	162620.i	0.358037	−	0.167952i
$985$	792944.			0.817278
$986$	−382877.	−	382877.i	−0.393827	−	0.393827i
$987$	−271986.	+	112660.i	−0.279198	+	0.115648i
$988$			908199.i			0.930394i
$989$	407612.	−	407612.i	0.416729	−	0.416729i
$990$	19018.5	+	7877.72i	0.0194047	+	0.00803767i
$991$	−1.71800e6	+	711618.i	−1.74934	+	0.724602i	−0.751447	+	0.659794i	$0.770644\pi$
$991$	−1.71800e6	+	711618.i	−1.74934	+	0.724602i	−0.997898	+	0.0648083i	$0.979356\pi$
$992$	51595.2	−	51595.2i	0.0524307	−	0.0524307i
$993$	1.25839e6	−	1.25839e6i	1.27620	−	1.27620i
$994$	240472.			0.243384
$995$	388854.	+	938777.i	0.392772	+	0.948235i
$996$	89748.7	+	216673.i	0.0904710	+	0.218416i
$997$	−300141.	+	124323.i	−0.301950	+	0.125072i	−0.528514	−	0.848924i	$-0.677251\pi$
$997$	−300141.	+	124323.i	−0.301950	+	0.125072i	0.226564	+	0.973996i	$0.427251\pi$
$998$	1.00693e6	+	417085.i	1.01097	+	0.418758i
$999$	−189892.	+	458441.i	−0.190273	+	0.459359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.5.e.a.27.2	✓	28
41.38	odd	8	inner	82.5.e.a.79.2	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.5.e.a.27.2	✓	28	1.1	even	1	trivial
82.5.e.a.79.2	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} +(-9.30077 + 3.85250i) q^{3} +8.00000i q^{4} +(16.4694 - 16.4694i) q^{5} +(26.3065 + 10.8965i) q^{6} +(32.0596 - 13.2795i) q^{7} +(16.0000 - 16.0000i) q^{8} +(14.3868 - 14.3868i) q^{9} -65.8775 q^{10} +(-5.87737 - 14.1892i) q^{11} +(-30.8200 - 74.4061i) q^{12} +(-235.301 + 97.4650i) q^{13} +(-90.6783 - 37.5602i) q^{14} +(-89.7295 + 216.626i) q^{15} -64.0000 q^{16} +(-147.922 - 61.2715i) q^{17} -57.5473 q^{18} +(-411.810 - 170.577i) q^{19} +(131.755 + 131.755i) q^{20} +(-247.020 + 247.020i) q^{21} +(-16.6237 + 40.1332i) q^{22} +365.346i q^{23} +(-87.1722 + 210.452i) q^{24} +82.5189i q^{25} +(665.532 + 275.673i) q^{26} +(233.670 - 564.128i) q^{27} +(106.236 + 256.477i) q^{28} +(-1104.65 + 457.563i) q^{29} +(612.712 - 253.793i) q^{30} -403.087i q^{31} +(128.000 + 128.000i) q^{32} +(109.328 + 109.328i) q^{33} +(173.302 + 418.388i) q^{34} +(309.297 - 746.708i) q^{35} +(115.095 + 115.095i) q^{36} -812.654 q^{37} +(482.466 + 1164.78i) q^{38} +(1813.00 - 1813.00i) q^{39} -527.020i q^{40} +(-1241.95 - 1132.83i) q^{41} +988.079 q^{42} +(-1115.69 - 1115.69i) q^{43} +(113.514 - 47.0190i) q^{44} -473.885i q^{45} +(730.692 - 730.692i) q^{46} +(778.576 + 322.497i) q^{47} +(595.249 - 246.560i) q^{48} +(-846.290 + 846.290i) q^{49} +(165.038 - 165.038i) q^{50} +1611.84 q^{51} +(-779.720 - 1882.41i) q^{52} +(1249.30 + 3016.08i) q^{53} +(-1595.60 + 660.917i) q^{54} +(-330.485 - 136.891i) q^{55} +(300.482 - 725.427i) q^{56} +4487.30 q^{57} +(3124.43 + 1294.18i) q^{58} +3924.10 q^{59} +(-1733.01 - 717.836i) q^{60} +(-1974.07 - 1974.07i) q^{61} +(-806.175 + 806.175i) q^{62} +(270.186 - 652.287i) q^{63} -512.000i q^{64} +(-2270.08 + 5480.45i) q^{65} -437.312i q^{66} +(-505.311 - 209.307i) q^{67} +(490.172 - 1183.38i) q^{68} +(-1407.50 - 3398.00i) q^{69} +(-2112.01 + 874.823i) q^{70} +(-2263.56 + 937.597i) q^{71} -460.379i q^{72} +(3594.91 + 3594.91i) q^{73} +(1625.31 + 1625.31i) q^{74} +(-317.904 - 767.489i) q^{75} +(1364.62 - 3294.48i) q^{76} +(-376.853 - 376.853i) q^{77} -7251.99 q^{78} +(-1513.57 - 3654.07i) q^{79} +(-1054.04 + 1054.04i) q^{80} +7795.07i q^{81} +(218.239 + 4749.57i) q^{82} -2912.02 q^{83} +(-1976.16 - 1976.16i) q^{84} +(-3445.30 + 1427.09i) q^{85} +4462.74i q^{86} +(8511.37 - 8511.37i) q^{87} +(-321.066 - 132.990i) q^{88} +(-8969.63 + 3715.34i) q^{89} +(-947.769 + 947.769i) q^{90} +(-6249.38 + 6249.38i) q^{91} -2922.77 q^{92} +(1552.90 + 3749.02i) q^{93} +(-912.158 - 2202.14i) q^{94} +(-9591.57 + 3972.96i) q^{95} +(-1683.62 - 697.378i) q^{96} +(5372.96 - 12971.5i) q^{97} +3385.16 q^{98} +(-288.695 - 119.581i) 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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