LMFDB - Embedded newform 82.5.e.b.3.2

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)

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);

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")

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			3.2
Character	$\chi$	$=$	82.3
Dual form			82.5.e.b.55.2

$q$-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} +(-4.26669 + 10.3007i) q^{3} -8.00000i q^{4} +(-14.4749 - 14.4749i) q^{5} +(12.0680 + 29.1348i) q^{6} +(18.7890 - 45.3606i) q^{7} +(-16.0000 - 16.0000i) q^{8} +(-30.6241 - 30.6241i) q^{9} -57.8996 q^{10} +(-0.277584 - 0.114979i) q^{11} +(82.4056 + 34.1335i) q^{12} +(128.763 - 310.862i) q^{13} +(-53.1433 - 128.299i) q^{14} +(210.861 - 87.3416i) q^{15} -64.0000 q^{16} +(-132.567 - 320.044i) q^{17} -122.496 q^{18} +(44.1395 + 106.562i) q^{19} +(-115.799 + 115.799i) q^{20} +(387.079 + 387.079i) q^{21} +(-0.785127 + 0.325210i) q^{22} -118.541i q^{23} +(233.078 - 96.5441i) q^{24} -205.955i q^{25} +(-364.198 - 879.251i) q^{26} +(-388.244 + 160.816i) q^{27} +(-362.885 - 150.312i) q^{28} +(-524.562 + 1266.41i) q^{29} +(247.039 - 596.406i) q^{30} +158.381i q^{31} +(-128.000 + 128.000i) q^{32} +(2.36873 - 2.36873i) q^{33} +(-905.222 - 374.955i) q^{34} +(-928.559 + 384.622i) q^{35} +(-244.993 + 244.993i) q^{36} -1200.36 q^{37} +(301.403 + 124.845i) q^{38} +(2652.70 + 2652.70i) q^{39} +463.197i q^{40} +(1197.76 - 1179.47i) q^{41} +1548.32 q^{42} +(1967.26 - 1967.26i) q^{43} +(-0.919834 + 2.22068i) q^{44} +886.560i q^{45} +(-237.083 - 237.083i) q^{46} +(945.358 + 2282.30i) q^{47} +(273.068 - 659.245i) q^{48} +(-6.79836 - 6.79836i) q^{49} +(-411.910 - 411.910i) q^{50} +3862.30 q^{51} +(-2486.90 - 1030.11i) q^{52} +(-948.973 - 393.078i) q^{53} +(-454.856 + 1098.12i) q^{54} +(2.35369 + 5.68232i) q^{55} +(-1026.39 + 425.146i) q^{56} -1285.99 q^{57} +(1483.69 + 3581.93i) q^{58} +1801.64 q^{59} +(-698.733 - 1686.89i) q^{60} +(-2698.84 + 2698.84i) q^{61} +(316.761 + 316.761i) q^{62} +(-1964.52 + 813.732i) q^{63} +512.000i q^{64} +(-6363.53 + 2635.86i) q^{65} -9.47493i q^{66} +(-1070.23 - 2583.76i) q^{67} +(-2560.35 + 1060.53i) q^{68} +(1221.06 + 505.779i) q^{69} +(-1087.87 + 2626.36i) q^{70} +(1598.94 - 3860.19i) q^{71} +979.970i q^{72} +(-832.923 + 832.923i) q^{73} +(-2400.72 + 2400.72i) q^{74} +(2121.48 + 878.746i) q^{75} +(852.497 - 353.116i) q^{76} +(-10.4311 + 10.4311i) q^{77} +10610.8 q^{78} +(-4234.05 - 1753.80i) q^{79} +(926.393 + 926.393i) q^{80} -8193.36i q^{81} +(36.5749 - 4754.45i) q^{82} +11331.9 q^{83} +(3096.64 - 3096.64i) q^{84} +(-2713.72 + 6551.49i) q^{85} -7869.05i q^{86} +(-10806.7 - 10806.7i) q^{87} +(2.60168 + 6.28102i) q^{88} +(34.9899 - 84.4732i) q^{89} +(1773.12 + 1773.12i) q^{90} +(-11681.6 - 11681.6i) q^{91} -948.332 q^{92} +(-1631.43 - 675.761i) q^{93} +(6455.31 + 2673.88i) q^{94} +(903.561 - 2181.39i) q^{95} +(-772.353 - 1864.63i) q^{96} +(12974.3 - 5374.13i) q^{97} -27.1935 q^{98} +(4.97963 + 12.0219i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 56 q^{2} + 16 q^{6} - 448 q^{8} + 24 q^{9} - 328 q^{11} + 64 q^{12} - 60 q^{13} + 192 q^{14} - 340 q^{15} - 1792 q^{16} - 136 q^{17} + 96 q^{18} + 600 q^{19} - 1580 q^{21} - 1768 q^{22} + 128 q^{24}+ \cdots - 19224 q^{99}+O(q^{100}) $ 28 * q + 56 * q^2 + 16 * q^6 - 448 * q^8 + 24 * q^9 - 328 * q^11 + 64 * q^12 - 60 * q^13 + 192 * q^14 - 340 * q^15 - 1792 * q^16 - 136 * q^17 + 96 * q^18 + 600 * q^19 - 1580 * q^21 - 1768 * q^22 + 128 * q^24 - 192 * q^26 + 2148 * q^27 + 768 * q^28 - 2564 * q^29 - 1048 * q^30 - 3584 * q^32 + 6420 * q^33 - 2040 * q^34 + 4656 * q^35 + 192 * q^36 + 7792 * q^37 + 896 * q^38 + 1232 * q^39 + 5584 * q^41 - 6320 * q^42 - 3788 * q^43 - 4448 * q^44 - 1648 * q^46 - 2000 * q^47 + 6312 * q^49 + 7048 * q^50 - 6208 * q^51 - 288 * q^52 + 1924 * q^53 + 1544 * q^54 + 17048 * q^55 + 1536 * q^56 + 11992 * q^57 + 2864 * q^58 + 11376 * q^59 - 1472 * q^60 - 9600 * q^61 - 9904 * q^62 - 13656 * q^63 - 2156 * q^65 - 22336 * q^67 - 7072 * q^68 + 17044 * q^69 + 16392 * q^70 + 2808 * q^71 + 6588 * q^73 + 15584 * q^74 + 4980 * q^75 - 1216 * q^76 + 9204 * q^77 + 4928 * q^78 - 8796 * q^79 + 5904 * q^82 - 24248 * q^83 - 12640 * q^84 - 28616 * q^85 - 55700 * q^87 - 3648 * q^88 - 4844 * q^89 + 11360 * q^90 - 53332 * q^91 - 6592 * q^92 - 44176 * q^93 + 552 * q^94 + 7628 * q^95 - 1024 * q^96 - 17844 * q^97 + 25248 * q^98 - 19224 * q^99

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.00000	−	2.00000i	0.500000	−	0.500000i
$2$	2.00000	−	2.00000i	0.500000	−	0.500000i
$3$	−4.26669	+	10.3007i	−0.474076	+	1.14452i	0.488269	+	0.872693i	$0.337628\pi$
$3$	−4.26669	+	10.3007i	−0.474076	+	1.14452i	−0.962346	+	0.271829i	$0.912372\pi$
$4$		−	8.00000i		−	0.500000i
$5$	−14.4749	−	14.4749i	−0.578996	−	0.578996i	0.355631	−	0.934627i	$-0.384266\pi$
$5$	−14.4749	−	14.4749i	−0.578996	−	0.578996i	−0.934627	+	0.355631i	$0.884266\pi$
$6$	12.0680	+	29.1348i	0.335223	+	0.809299i
$7$	18.7890	−	45.3606i	0.383449	−	0.925727i	−0.607845	−	0.794056i	$-0.707966\pi$
$7$	18.7890	−	45.3606i	0.383449	−	0.925727i	0.991293	−	0.131671i	$-0.0420344\pi$
$8$	−16.0000	−	16.0000i	−0.250000	−	0.250000i
$9$	−30.6241	−	30.6241i	−0.378075	−	0.378075i
$10$	−57.8996			−0.578996
$11$	−0.277584	−	0.114979i	−0.00229409	−	0.000950242i	0.381536	−	0.924354i	$-0.375395\pi$
$11$	−0.277584	−	0.114979i	−0.00229409	−	0.000950242i	−0.383830	+	0.923404i	$0.625395\pi$
$12$	82.4056	+	34.1335i	0.572261	+	0.237038i
$13$	128.763	−	310.862i	0.761913	−	1.83942i	0.293290	−	0.956024i	$-0.405250\pi$
$13$	128.763	−	310.862i	0.761913	−	1.83942i	0.468624	−	0.883398i	$-0.344750\pi$
$14$	−53.1433	−	128.299i	−0.271139	−	0.654588i
$15$	210.861	−	87.3416i	0.937161	−	0.388185i
$16$	−64.0000			−0.250000
$17$	−132.567	−	320.044i	−0.458708	−	1.10742i	−0.968921	−	0.247371i	$-0.920433\pi$
$17$	−132.567	−	320.044i	−0.458708	−	1.10742i	0.510213	−	0.860048i	$-0.329567\pi$
$18$	−122.496			−0.378075
$19$	44.1395	+	106.562i	0.122270	+	0.295186i	0.973149	−	0.230176i	$-0.0739301\pi$
$19$	44.1395	+	106.562i	0.122270	+	0.295186i	−0.850879	+	0.525362i	$0.823930\pi$
$20$	−115.799	+	115.799i	−0.289498	+	0.289498i
$21$	387.079	+	387.079i	0.877731	+	0.877731i
$22$	−0.785127	+	0.325210i	−0.00162216	+	0.000671922i
$23$		−	118.541i		−	0.224086i	−0.993703	−	0.112043i	$-0.964261\pi$
$23$		−	118.541i		−	0.224086i	0.993703	−	0.112043i	$-0.0357394\pi$
$24$	233.078	−	96.5441i	0.404650	−	0.167611i
$25$		−	205.955i		−	0.329528i
$26$	−364.198	−	879.251i	−0.538754	−	1.30067i
$27$	−388.244	+	160.816i	−0.532570	+	0.220598i
$28$	−362.885	−	150.312i	−0.462864	−	0.191724i
$29$	−524.562	+	1266.41i	−0.623736	+	1.50583i	0.223548	+	0.974693i	$0.428236\pi$
$29$	−524.562	+	1266.41i	−0.623736	+	1.50583i	−0.847284	+	0.531140i	$0.821764\pi$
$30$	247.039	−	596.406i	0.274488	−	0.662673i
$31$			158.381i			0.164808i	0.996599	+	0.0824041i	$0.0262598\pi$
$31$			158.381i			0.164808i	−0.996599	+	0.0824041i	$0.973740\pi$
$32$	−128.000	+	128.000i	−0.125000	+	0.125000i
$33$	2.36873	−	2.36873i	0.00217514	−	0.00217514i
$34$	−905.222	−	374.955i	−0.783064	−	0.324356i
$35$	−928.559	+	384.622i	−0.758007	+	0.313977i
$36$	−244.993	+	244.993i	−0.189037	+	0.189037i
$37$	−1200.36			−0.876814			−0.438407	−	0.898776i	$-0.644457\pi$
$37$	−1200.36			−0.876814			−0.438407	+	0.898776i	$0.644457\pi$
$38$	301.403	+	124.845i	0.208728	+	0.0864580i
$39$	2652.70	+	2652.70i	1.74405	+	1.74405i
$40$			463.197i			0.289498i
$41$	1197.76	−	1179.47i	0.712525	−	0.701646i
$41$	1197.76	−	1179.47i	0.712525	−	0.701646i
$42$	1548.32			0.877731
$43$	1967.26	−	1967.26i	1.06396	−	1.06396i	0.0661507	−	0.997810i	$-0.478928\pi$
$43$	1967.26	−	1967.26i	1.06396	−	1.06396i	0.997810	−	0.0661507i	$-0.0210718\pi$
$44$	−0.919834	+	2.22068i	−0.000475121	+	0.00114704i
$45$			886.560i			0.437808i
$46$	−237.083	−	237.083i	−0.112043	−	0.112043i
$47$	945.358	+	2282.30i	0.427958	+	1.03318i	0.979934	+	0.199321i	$0.0638738\pi$
$47$	945.358	+	2282.30i	0.427958	+	1.03318i	−0.551977	+	0.833860i	$0.686126\pi$
$48$	273.068	−	659.245i	0.118519	−	0.286130i
$49$	−6.79836	−	6.79836i	−0.00283147	−	0.00283147i
$50$	−411.910	−	411.910i	−0.164764	−	0.164764i
$51$	3862.30			1.48493
$52$	−2486.90	−	1030.11i	−0.919711	−	0.380957i
$53$	−948.973	−	393.078i	−0.337833	−	0.139935i	0.207316	−	0.978274i	$-0.433527\pi$
$53$	−948.973	−	393.078i	−0.337833	−	0.139935i	−0.545149	+	0.838339i	$0.683527\pi$
$54$	−454.856	+	1098.12i	−0.155986	+	0.376584i
$55$	2.35369	+	5.68232i	0.000778080	+	0.00187845i
$56$	−1026.39	+	425.146i	−0.327294	+	0.135570i
$57$	−1285.99			−0.395812
$58$	1483.69	+	3581.93i	0.441048	+	1.06478i
$59$	1801.64			0.517564			0.258782	−	0.965936i	$-0.416679\pi$
$59$	1801.64			0.517564			0.258782	+	0.965936i	$0.416679\pi$
$60$	−698.733	−	1686.89i	−0.194092	−	0.468581i
$61$	−2698.84	+	2698.84i	−0.725299	+	0.725299i	−0.969679	−	0.244380i	$-0.921415\pi$
$61$	−2698.84	+	2698.84i	−0.725299	+	0.725299i	0.244380	+	0.969679i	$0.421415\pi$
$62$	316.761	+	316.761i	0.0824041	+	0.0824041i
$63$	−1964.52	+	813.732i	−0.494967	+	0.205022i
$64$			512.000i			0.125000i
$65$	−6363.53	+	2635.86i	−1.50616	+	0.623873i
$66$		−	9.47493i		−	0.00217514i
$67$	−1070.23	−	2583.76i	−0.238411	−	0.575576i	0.758708	−	0.651431i	$-0.225831\pi$
$67$	−1070.23	−	2583.76i	−0.238411	−	0.575576i	−0.997119	+	0.0758557i	$0.975831\pi$
$68$	−2560.35	+	1060.53i	−0.553710	+	0.229354i
$69$	1221.06	+	505.779i	0.256471	+	0.106234i
$70$	−1087.87	+	2626.36i	−0.222015	+	0.535992i
$71$	1598.94	−	3860.19i	0.317188	−	0.765759i	−0.682213	−	0.731153i	$-0.738982\pi$
$71$	1598.94	−	3860.19i	0.317188	−	0.765759i	0.999401	−	0.0346060i	$-0.0110176\pi$
$72$			979.970i			0.189037i
$73$	−832.923	+	832.923i	−0.156300	+	0.156300i	−0.780925	−	0.624625i	$-0.785252\pi$
$73$	−832.923	+	832.923i	−0.156300	+	0.156300i	0.624625	+	0.780925i	$0.285252\pi$
$74$	−2400.72	+	2400.72i	−0.438407	+	0.438407i
$75$	2121.48	+	878.746i	0.377152	+	0.156221i
$76$	852.497	−	353.116i	0.147593	−	0.0611350i
$77$	−10.4311	+	10.4311i	−0.00175933	+	0.00175933i
$78$	10610.8			1.74405
$79$	−4234.05	−	1753.80i	−0.678425	−	0.281013i	0.0167431	−	0.999860i	$-0.494670\pi$
$79$	−4234.05	−	1753.80i	−0.678425	−	0.281013i	−0.695169	+	0.718847i	$0.744670\pi$
$80$	926.393	+	926.393i	0.144749	+	0.144749i
$81$		−	8193.36i		−	1.24880i
$82$	36.5749	−	4754.45i	0.00543946	−	0.707086i
$83$	11331.9			1.64493			0.822463	−	0.568819i	$-0.192599\pi$
$83$	11331.9			1.64493			0.822463	+	0.568819i	$0.192599\pi$
$84$	3096.64	−	3096.64i	0.438866	−	0.438866i
$85$	−2713.72	+	6551.49i	−0.375601	+	0.906781i
$86$		−	7869.05i		−	1.06396i
$87$	−10806.7	−	10806.7i	−1.42776	−	1.42776i
$88$	2.60168	+	6.28102i	0.000335961	+	0.000811082i
$89$	34.9899	−	84.4732i	0.00441736	−	0.0106645i	−0.921655	−	0.388009i	$-0.873163\pi$
$89$	34.9899	−	84.4732i	0.00441736	−	0.0106645i	0.926073	+	0.377345i	$0.123163\pi$
$90$	1773.12	+	1773.12i	0.218904	+	0.218904i
$91$	−11681.6	−	11681.6i	−1.41065	−	1.41065i
$92$	−948.332			−0.112043
$93$	−1631.43	−	675.761i	−0.188627	−	0.0781317i
$94$	6455.31	+	2673.88i	0.730569	+	0.302612i
$95$	903.561	−	2181.39i	0.100118	−	0.241705i
$96$	−772.353	−	1864.63i	−0.0838057	−	0.202325i
$97$	12974.3	−	5374.13i	1.37892	−	0.571169i	0.434731	−	0.900560i	$-0.356843\pi$
$97$	12974.3	−	5374.13i	1.37892	−	0.571169i	0.944194	+	0.329391i	$0.106843\pi$
$98$	−27.1935			−0.00283147
$99$	4.97963	+	12.0219i	0.000508074	+	0.00122660i
$100$	−1647.64			−0.164764
$101$	3642.80	+	8794.49i	0.357102	+	0.862121i	0.995705	+	0.0925842i	$0.0295127\pi$
$101$	3642.80	+	8794.49i	0.357102	+	0.862121i	−0.638603	+	0.769537i	$0.720487\pi$
$102$	7724.60	−	7724.60i	0.742464	−	0.742464i
$103$	4991.09	+	4991.09i	0.470458	+	0.470458i	0.902063	−	0.431605i	$-0.142053\pi$
$103$	4991.09	+	4991.09i	0.470458	+	0.470458i	−0.431605	+	0.902063i	$0.642053\pi$
$104$	−7034.01	+	2913.58i	−0.650334	+	0.269377i
$105$		−	11205.9i		−	1.01641i
$106$	−2684.10	+	1111.79i	−0.238884	+	0.0989490i
$107$			3387.88i			0.295911i	0.988994	+	0.147955i	$0.0472692\pi$
$107$			3387.88i			0.295911i	−0.988994	+	0.147955i	$0.952731\pi$
$108$	1286.53	+	3105.95i	0.110299	+	0.266285i
$109$	−927.031	+	383.989i	−0.0780263	+	0.0323196i	−0.421355	−	0.906896i	$-0.638445\pi$
$109$	−927.031	+	383.989i	−0.0780263	+	0.0323196i	0.343329	+	0.939215i	$0.388445\pi$
$110$	16.0720	+	6.65725i	0.00132827	+	0.000550186i
$111$	5121.56	−	12364.5i	0.415677	−	1.00353i
$112$	−1202.50	+	2903.08i	−0.0958622	+	0.231432i
$113$			10069.4i			0.788582i	0.918986	+	0.394291i	$0.129010\pi$
$113$			10069.4i			0.788582i	−0.918986	+	0.394291i	$0.870990\pi$
$114$	−2571.99	+	2571.99i	−0.197906	+	0.197906i
$115$	−1715.87	+	1715.87i	−0.129745	+	0.129745i
$116$	10131.2	+	4196.50i	0.752916	+	0.311868i
$117$	−13463.1	+	5576.61i	−0.983500	+	0.407379i
$118$	3603.28	−	3603.28i	0.258782	−	0.258782i
$119$	−17008.2			−1.20106
$120$	−4771.25	−	1976.32i	−0.331337	−	0.137244i
$121$	−10352.7	−	10352.7i	−0.707102	−	0.707102i
$122$			10795.4i			0.725299i
$123$	7038.89	+	17370.1i	0.465258	+	1.14813i
$124$	1267.05			0.0824041
$125$	−12028.0	+	12028.0i	−0.769791	+	0.769791i
$126$	−2301.58	+	5556.51i	−0.144972	+	0.349994i
$127$		−	23685.2i		−	1.46849i	−0.678886	−	0.734244i	$-0.737537\pi$
$127$		−	23685.2i		−	1.46849i	0.678886	−	0.734244i	$-0.262463\pi$
$128$	1024.00	+	1024.00i	0.0625000	+	0.0625000i
$129$	11870.5	+	28657.9i	0.713327	+	1.72212i
$130$	−7455.34	+	17998.8i	−0.441145	+	1.06502i
$131$	−12288.4	−	12288.4i	−0.716066	−	0.716066i	0.251731	−	0.967797i	$-0.419000\pi$
$131$	−12288.4	−	12288.4i	−0.716066	−	0.716066i	−0.967797	+	0.251731i	$0.919000\pi$
$132$	−18.9499	−	18.9499i	−0.00108757	−	0.00108757i
$133$	5663.06			0.320146
$134$	−7307.98	−	3027.06i	−0.406994	−	0.168582i
$135$	7947.58	+	3291.99i	0.436081	+	0.180631i
$136$	−2999.64	+	7241.77i	−0.162178	+	0.391532i
$137$	873.440	+	2108.67i	0.0465363	+	0.112349i	0.945438	−	0.325801i	$-0.105634\pi$
$137$	873.440	+	2108.67i	0.0465363	+	0.112349i	−0.898902	+	0.438150i	$0.855634\pi$
$138$	3453.68	−	1430.56i	0.181353	−	0.0751187i
$139$	20915.3			1.08251			0.541257	−	0.840857i	$-0.317949\pi$
$139$	20915.3			1.08251			0.541257	+	0.840857i	$0.317949\pi$
$140$	3076.97	+	7428.47i	0.156988	+	0.379004i
$141$	−27542.8			−1.38538
$142$	−4522.50	−	10918.3i	−0.224286	−	0.541474i
$143$	−71.4854	+	71.4854i	−0.00349579	+	0.00349579i
$144$	1959.94	+	1959.94i	0.0945187	+	0.0945187i
$145$	25924.1	−	10738.1i	1.23301	−	0.510730i
$146$			3331.69i			0.156300i
$147$	99.0344	−	41.0214i	0.00458302	−	0.00189835i
$148$			9602.87i			0.438407i
$149$	9878.08	+	23847.8i	0.444939	+	1.07418i	0.974194	+	0.225714i	$0.0724715\pi$
$149$	9878.08	+	23847.8i	0.444939	+	1.07418i	−0.529255	+	0.848463i	$0.677529\pi$
$150$	6000.45	−	2485.47i	0.266687	−	0.110465i
$151$	19647.5	+	8138.27i	0.861696	+	0.356926i	0.769371	−	0.638803i	$-0.220570\pi$
$151$	19647.5	+	8138.27i	0.861696	+	0.356926i	0.0923254	+	0.995729i	$0.470570\pi$
$152$	998.762	−	2411.23i	0.0432290	−	0.104364i
$153$	−5741.33	+	13860.8i	−0.245261	+	0.592114i
$154$			41.7243i			0.00175933i
$155$	2292.54	−	2292.54i	0.0954232	−	0.0954232i
$156$	21221.6	−	21221.6i	0.872026	−	0.872026i
$157$	36759.2	+	15226.2i	1.49131	+	0.617720i	0.971601	−	0.236625i	$-0.0760413\pi$
$157$	36759.2	+	15226.2i	1.49131	+	0.617720i	0.519706	+	0.854345i	$0.326041\pi$
$158$	−11975.7	+	4960.50i	−0.479719	+	0.198706i
$159$	8097.95	−	8097.95i	0.320317	−	0.320317i
$160$	3705.57			0.144749
$161$	−5377.12	−	2227.27i	−0.207443	−	0.0859255i
$162$	−16386.7	−	16386.7i	−0.624399	−	0.624399i
$163$			36569.6i			1.37640i	0.725521	+	0.688200i	$0.241599\pi$
$163$			36569.6i			1.37640i	−0.725521	+	0.688200i	$0.758401\pi$
$164$	−9435.74	−	9582.04i	−0.350823	−	0.356263i
$165$	−68.5743			−0.00251880
$166$	22663.8	−	22663.8i	0.822463	−	0.822463i
$167$	−15780.5	+	38097.6i	−0.565833	+	1.36604i	0.339205	+	0.940713i	$0.389842\pi$
$167$	−15780.5	+	38097.6i	−0.565833	+	1.36604i	−0.905038	+	0.425330i	$0.860158\pi$
$168$		−	12386.5i		−	0.438866i
$169$	−59859.7	−	59859.7i	−2.09585	−	2.09585i
$170$	7675.55	+	18530.4i	0.265590	+	0.641191i
$171$	1911.64	−	4615.10i	0.0653752	−	0.157830i
$172$	−15738.1	−	15738.1i	−0.531980	−	0.531980i
$173$	−42.6347	−	42.6347i	−0.00142453	−	0.00142453i	0.706394	−	0.707819i	$-0.250321\pi$
$173$	−42.6347	−	42.6347i	−0.00142453	−	0.00142453i	−0.707819	+	0.706394i	$0.750321\pi$
$174$	−43226.9			−1.42776
$175$	−9342.25	−	3869.69i	−0.305053	−	0.126357i
$176$	17.7654	+	7.35867i	0.000573522	+	0.000237560i
$177$	−7687.04	+	18558.2i	−0.245365	+	0.592364i
$178$	−98.9665	−	238.926i	−0.00312355	−	0.00754091i
$179$	49662.7	−	20570.9i	1.54997	−	0.642019i	0.566661	−	0.823951i	$-0.308235\pi$
$179$	49662.7	−	20570.9i	1.54997	−	0.642019i	0.983311	+	0.181932i	$0.0582350\pi$
$180$	7092.48			0.218904
$181$	4988.70	+	12043.8i	0.152275	+	0.367625i	0.981547	−	0.191220i	$-0.0612444\pi$
$181$	4988.70	+	12043.8i	0.152275	+	0.367625i	−0.829272	+	0.558846i	$0.811244\pi$
$182$	−46726.3			−1.41065
$183$	−16284.8	−	39315.0i	−0.486274	−	1.17397i
$184$	−1896.66	+	1896.66i	−0.0560215	+	0.0560215i
$185$	17375.1	+	17375.1i	0.507672	+	0.507672i
$186$	−4614.38	+	1911.34i	−0.133379	+	0.0552474i
$187$			104.082i			0.00297640i
$188$	18258.4	−	7562.87i	0.516590	−	0.213979i
$189$			20632.6i			0.577603i
$190$	−2555.66	−	6169.90i	−0.0707938	−	0.170911i
$191$	−25572.9	+	10592.6i	−0.700991	+	0.290360i	−0.704571	−	0.709633i	$-0.748861\pi$
$191$	−25572.9	+	10592.6i	−0.700991	+	0.290360i	0.00357960	+	0.999994i	$0.498861\pi$
$192$	−5273.96	−	2184.54i	−0.143065	−	0.0592596i
$193$	12597.0	−	30411.9i	0.338184	−	0.816448i	−0.659706	−	0.751524i	$-0.729319\pi$
$193$	12597.0	−	30411.9i	0.338184	−	0.816448i	0.997890	−	0.0649247i	$-0.0206807\pi$
$194$	15200.3	−	36696.9i	0.403878	−	0.975047i
$195$		−	76795.2i		−	2.01960i
$196$	−54.3869	+	54.3869i	−0.00141574	+	0.00141574i
$197$	−7091.81	+	7091.81i	−0.182736	+	0.182736i	−0.792547	−	0.609811i	$-0.791245\pi$
$197$	−7091.81	+	7091.81i	−0.182736	+	0.182736i	0.609811	+	0.792547i	$0.291245\pi$
$198$	34.0031	+	14.0845i	0.000867337	+	0.000359263i
$199$	54414.6	−	22539.3i	1.37407	−	0.569159i	0.431182	−	0.902265i	$-0.358097\pi$
$199$	54414.6	−	22539.3i	1.37407	−	0.569159i	0.942889	+	0.333106i	$0.108097\pi$
$200$	−3295.28	+	3295.28i	−0.0823820	+	0.0823820i
$201$	31180.9			0.771784
$202$	24874.6	+	10303.4i	0.609611	+	0.252509i
$203$	47589.0	+	47589.0i	1.15482	+	1.15482i
$204$		−	30898.4i		−	0.742464i
$205$	−34410.0	−	264.709i	−0.818799	−	0.00629884i
$206$	19964.3			0.470458
$207$	−3630.22	+	3630.22i	−0.0847213	+	0.0847213i
$208$	−8240.85	+	19895.2i	−0.190478	+	0.459855i
$209$		−	34.6551i		−	0.000793368i
$210$	−22411.7	−	22411.7i	−0.508203	−	0.508203i
$211$	−5725.54	−	13822.7i	−0.128603	−	0.310475i	0.846443	−	0.532480i	$-0.178740\pi$
$211$	−5725.54	−	13822.7i	−0.128603	−	0.310475i	−0.975046	+	0.222005i	$0.928740\pi$
$212$	−3144.62	+	7591.79i	−0.0699675	+	0.168917i
$213$	32940.5	+	32940.5i	0.726057	+	0.726057i
$214$	6775.77	+	6775.77i	0.147955	+	0.147955i
$215$	−56951.8			−1.23206
$216$	8784.95	+	3638.85i	0.188292	+	0.0779931i
$217$	7184.25	+	2975.81i	0.152567	+	0.0631955i
$218$	−1086.08	+	2622.04i	−0.0228534	+	0.0551729i
$219$	−5025.87	−	12133.5i	−0.104791	−	0.252987i
$220$	45.4585	−	18.8295i	0.000939226	−	0.000389040i
$221$	−116559.			−2.38651
$222$	−14486.0	−	34972.2i	−0.293928	−	0.709605i
$223$	46581.1			0.936699			0.468349	−	0.883543i	$-0.344849\pi$
$223$	46581.1			0.936699			0.468349	+	0.883543i	$0.344849\pi$
$224$	3401.17	+	8211.15i	0.0677848	+	0.163647i
$225$	−6307.18	+	6307.18i	−0.124586	+	0.124586i
$226$	20138.8	+	20138.8i	0.394291	+	0.394291i
$227$	18703.7	−	7747.32i	0.362974	−	0.150349i	−0.193740	−	0.981053i	$-0.562062\pi$
$227$	18703.7	−	7747.32i	0.362974	−	0.150349i	0.556714	+	0.830704i	$0.312062\pi$
$228$			10287.9i			0.197906i
$229$	−14458.9	+	5989.07i	−0.275717	+	0.114206i	−0.516258	−	0.856433i	$-0.672675\pi$
$229$	−14458.9	+	5989.07i	−0.275717	+	0.114206i	0.240541	+	0.970639i	$0.422675\pi$
$230$			6863.50i			0.129745i
$231$	−62.9411	−	151.953i	−0.00117953	−	0.00284765i
$232$	28655.5	−	11869.5i	0.532392	−	0.220524i
$233$	−56040.6	−	23212.8i	−1.03227	−	0.427578i	−0.198736	−	0.980053i	$-0.563683\pi$
$233$	−56040.6	−	23212.8i	−1.03227	−	0.427578i	−0.833530	+	0.552475i	$0.813683\pi$
$234$	−15773.0	+	38079.5i	−0.288060	+	0.695439i
$235$	19352.0	−	46720.0i	0.350422	−	0.845993i
$236$		−	14413.1i		−	0.258782i
$237$	36130.8	−	36130.8i	0.643251	−	0.643251i
$238$	−34016.4	+	34016.4i	−0.600530	+	0.600530i
$239$	−33066.2	−	13696.5i	−0.578881	−	0.239780i	0.0739781	−	0.997260i	$-0.476430\pi$
$239$	−33066.2	−	13696.5i	−0.578881	−	0.239780i	−0.652859	+	0.757480i	$0.726430\pi$
$240$	−13495.1	+	5589.86i	−0.234290	+	0.0970462i
$241$	38209.6	−	38209.6i	0.657867	−	0.657867i	−0.297008	−	0.954875i	$-0.595989\pi$
$241$	38209.6	−	38209.6i	0.657867	−	0.657867i	0.954875	+	0.297008i	$0.0959887\pi$
$242$	−41410.7			−0.707102
$243$	52949.6	+	21932.4i	0.896706	+	0.371428i
$244$	21590.7	+	21590.7i	0.362650	+	0.362650i
$245$			196.811i			0.00327882i
$246$	48818.0	+	20662.5i	0.806696	+	0.341438i
$247$	38809.7			0.636131
$248$	2534.09	−	2534.09i	0.0412020	−	0.0412020i
$249$	−48349.7	+	116726.i	−0.779821	+	1.88265i
$250$			48111.9i			0.769791i
$251$	−22080.2	−	22080.2i	−0.350474	−	0.350474i	0.509812	−	0.860286i	$-0.329715\pi$
$251$	−22080.2	−	22080.2i	−0.350474	−	0.350474i	−0.860286	+	0.509812i	$0.829715\pi$
$252$	6509.86	+	15716.2i	0.102511	+	0.247483i
$253$	−13.6298	+	32.9053i	−0.000212936	+	0.000514073i
$254$	−47370.5	−	47370.5i	−0.734244	−	0.734244i
$255$	−55906.4	−	55906.4i	−0.859767	−	0.859767i
$256$	4096.00			0.0625000
$257$	−101782.	−	42159.3i	−1.54100	−	0.638304i	−0.559340	−	0.828938i	$-0.688945\pi$
$257$	−101782.	−	42159.3i	−1.54100	−	0.638304i	−0.981661	+	0.190635i	$0.938945\pi$
$258$	81056.7	+	33574.8i	1.21773	+	0.504399i
$259$	−22553.5	+	54449.1i	−0.336213	+	0.811691i
$260$	21086.9	+	50908.3i	0.311936	+	0.753081i
$261$	54846.7	−	22718.3i	0.805137	−	0.333499i
$262$	−49153.6			−0.716066
$263$	43686.2	+	105468.i	0.631586	+	1.52478i	0.837628	+	0.546241i	$0.183942\pi$
$263$	43686.2	+	105468.i	0.631586	+	1.52478i	−0.206042	+	0.978543i	$0.566058\pi$
$264$	−75.7995			−0.00108757
$265$	8046.53	+	19426.0i	0.114582	+	0.276626i
$266$	11326.1	−	11326.1i	0.160073	−	0.160073i
$267$	720.841	+	720.841i	0.0101115	+	0.0101115i
$268$	−20670.1	+	8561.83i	−0.287788	+	0.119206i
$269$			107281.i			1.48258i	0.671182	+	0.741292i	$0.265787\pi$
$269$			107281.i			1.48258i	−0.671182	+	0.741292i	$0.734213\pi$
$270$	22479.1	−	9311.17i	0.308356	−	0.127725i
$271$			68132.8i			0.927721i	0.885908	+	0.463860i	$0.153536\pi$
$271$			68132.8i			0.927721i	−0.885908	+	0.463860i	$0.846464\pi$
$272$	8484.27	+	20482.8i	0.114677	+	0.276855i
$273$	170170.	−	70486.7i	2.28327	−	0.945763i
$274$	5964.22	+	2470.46i	0.0794425	+	0.0329061i
$275$	−23.6806	+	57.1699i	−0.000313131	+	0.000755966i
$276$	4046.24	−	9768.48i	0.0531169	−	0.128236i
$277$		−	121692.i		−	1.58600i	−0.609219	−	0.793002i	$-0.708517\pi$
$277$		−	121692.i		−	1.58600i	0.609219	−	0.793002i	$-0.291483\pi$
$278$	41830.5	−	41830.5i	0.541257	−	0.541257i
$279$	4850.26	−	4850.26i	0.0623098	−	0.0623098i
$280$	21010.9	+	8703.00i	0.267996	+	0.111008i
$281$	−57001.1	+	23610.6i	−0.721889	+	0.299016i	−0.713214	−	0.700946i	$-0.752761\pi$
$281$	−57001.1	+	23610.6i	−0.721889	+	0.299016i	−0.00867495	+	0.999962i	$0.502761\pi$
$282$	−55085.6	+	55085.6i	−0.692691	+	0.692691i
$283$	−70639.0			−0.882007			−0.441003	−	0.897505i	$-0.645377\pi$
$283$	−70639.0			−0.882007			−0.441003	+	0.897505i	$0.645377\pi$
$284$	−30881.5	−	12791.6i	−0.382880	−	0.158594i
$285$	18614.6	+	18614.6i	0.229174	+	0.229174i
$286$			285.942i			0.00349579i
$287$	−30996.8	−	76492.0i	−0.376316	−	0.928650i
$288$	7839.76			0.0945187
$289$	−25796.1	+	25796.1i	−0.308858	+	0.308858i
$290$	30371.9	−	73324.3i	0.361141	−	0.871871i
$291$			156574.i			1.84899i
$292$	6663.39	+	6663.39i	0.0781500	+	0.0781500i
$293$	23933.4	+	57780.4i	0.278785	+	0.673047i	0.999803	−	0.0198698i	$-0.00632519\pi$
$293$	23933.4	+	57780.4i	0.278785	+	0.673047i	−0.721017	+	0.692917i	$0.756325\pi$
$294$	116.026	−	280.112i	0.00134233	−	0.00324068i
$295$	−26078.6	−	26078.6i	−0.299668	−	0.299668i
$296$	19205.7	+	19205.7i	0.219204	+	0.219204i
$297$	126.261			0.00143138
$298$	67451.8	+	27939.4i	0.759558	+	0.314619i
$299$	−36850.1	−	15263.8i	−0.412189	−	0.170734i
$300$	7029.97	−	16971.8i	0.0781107	−	0.188576i
$301$	−52273.4	−	126199.i	−0.576963	−	1.39291i
$302$	55571.6	−	23018.5i	0.609311	−	0.252385i
$303$	−106132.			−1.15601
$304$	−2824.93	−	6819.98i	−0.0305675	−	0.0737965i
$305$	78130.8			0.839890
$306$	16238.9	+	39204.2i	0.173426	+	0.418688i
$307$	−28790.9	+	28790.9i	−0.305477	+	0.305477i	−0.843152	−	0.537675i	$-0.819303\pi$
$307$	−28790.9	+	28790.9i	−0.305477	+	0.305477i	0.537675	+	0.843152i	$0.319303\pi$
$308$	83.4485	+	83.4485i	0.000879665	+	0.000879665i
$309$	−72707.1	+	30116.3i	−0.761482	+	0.315416i
$310$		−	9170.17i		−	0.0954232i
$311$	138746.	−	57470.3i	1.43449	−	0.594187i	0.476037	−	0.879425i	$-0.342073\pi$
$311$	138746.	−	57470.3i	1.43449	−	0.594187i	0.958457	+	0.285238i	$0.0920728\pi$
$312$		−	84886.5i		−	0.872026i
$313$	−18559.6	−	44806.8i	−0.189444	−	0.457357i	0.800409	−	0.599454i	$-0.204616\pi$
$313$	−18559.6	−	44806.8i	−0.189444	−	0.457357i	−0.989853	+	0.142097i	$0.954616\pi$
$314$	103971.	−	43066.1i	1.05451	−	0.436794i
$315$	40214.9	+	16657.6i	0.405290	+	0.167877i
$316$	−14030.4	+	33872.4i	−0.140507	+	0.339213i
$317$	−4725.46	+	11408.3i	−0.0470246	+	0.113527i	−0.945646	−	0.325197i	$-0.894569\pi$
$317$	−4725.46	+	11408.3i	−0.0470246	+	0.113527i	0.898622	+	0.438724i	$0.144569\pi$
$318$		−	32391.8i		−	0.320317i
$319$	291.221	−	291.221i	0.00286181	−	0.00286181i
$320$	7411.14	−	7411.14i	0.0723745	−	0.0723745i
$321$	−34897.6	−	14455.0i	−0.338677	−	0.140284i
$322$	−15208.8	+	6299.68i	−0.146684	+	0.0607585i
$323$	28253.2	−	28253.2i	0.270808	−	0.270808i
$324$	−65546.9			−0.624399
$325$	−64023.6	−	26519.5i	−0.606141	−	0.251072i
$326$	73139.2	+	73139.2i	0.688200	+	0.688200i
$327$		−	11187.4i		−	0.104625i
$328$	−38035.6	−	292.599i	−0.353543	−	0.00271973i
$329$	121289.			1.12054
$330$	−137.149	+	137.149i	−0.00125940	+	0.00125940i
$331$	−59825.1	+	144430.i	−0.546043	+	1.31827i	0.374356	+	0.927285i	$0.377864\pi$
$331$	−59825.1	+	144430.i	−0.546043	+	1.31827i	−0.920399	+	0.390980i	$0.872136\pi$
$332$		−	90655.2i		−	0.822463i
$333$	36759.9	+	36759.9i	0.331502	+	0.331502i
$334$	44634.1	+	107756.i	0.400105	+	0.965938i
$335$	−21908.2	+	52891.1i	−0.195217	+	0.471295i
$336$	−24773.1	−	24773.1i	−0.219433	−	0.219433i
$337$	−111914.	−	111914.i	−0.985425	−	0.985425i	0.0144706	−	0.999895i	$-0.495394\pi$
$337$	−111914.	−	111914.i	−0.985425	−	0.985425i	−0.999895	+	0.0144706i	$0.995394\pi$
$338$	−239439.			−2.09585
$339$	−103722.	−	42963.0i	−0.902550	−	0.373848i
$340$	52411.9	+	21709.7i	0.453391	+	0.187801i
$341$	18.2105	−	43.9640i	0.000156608	−	0.000378084i
$342$	−5406.92	−	13053.5i	−0.0462272	−	0.111602i
$343$	108475.	−	44931.7i	0.922021	−	0.381913i
$344$	−62952.4			−0.531980
$345$	−10353.6	−	24995.8i	−0.0869868	−	0.210005i
$346$	−170.539			−0.00142453
$347$	61833.2	+	149279.i	0.513527	+	1.23976i	0.941818	+	0.336122i	$0.109116\pi$
$347$	61833.2	+	149279.i	0.513527	+	1.23976i	−0.428292	+	0.903640i	$0.640884\pi$
$348$	−86453.7	+	86453.7i	−0.713880	+	0.713880i
$349$	−33816.5	−	33816.5i	−0.277637	−	0.277637i	0.554528	−	0.832165i	$-0.312899\pi$
$349$	−33816.5	−	33816.5i	−0.277637	−	0.277637i	−0.832165	+	0.554528i	$0.812899\pi$
$350$	−26423.9	+	10945.1i	−0.215705	+	0.0893480i
$351$			141398.i			1.14770i
$352$	50.2482	−	20.8135i	0.000405541	−	0.000167981i
$353$		−	231128.i		−	1.85483i	−0.374038	−	0.927413i	$-0.622027\pi$
$353$		−	231128.i		−	1.85483i	0.374038	−	0.927413i	$-0.377973\pi$
$354$	21742.2	+	52490.4i	0.173499	+	0.418864i
$355$	−79020.4	+	32731.3i	−0.627022	+	0.259721i
$356$	−675.785	−	279.919i	−0.00533223	−	0.00220868i
$357$	72568.7	−	175196.i	0.569394	−	1.37464i
$358$	58183.4	−	140467.i	0.453976	−	1.09600i
$359$		−	148044.i		−	1.14869i	−0.818613	−	0.574345i	$-0.805257\pi$
$359$		−	148044.i		−	1.14869i	0.818613	−	0.574345i	$-0.194743\pi$
$360$	14185.0	−	14185.0i	0.109452	−	0.109452i
$361$	82743.7	−	82743.7i	0.634922	−	0.634922i
$362$	34064.9	+	14110.2i	0.259950	+	0.107675i
$363$	150812.	−	62468.2i	1.14451	−	0.474074i
$364$	−93452.6	+	93452.6i	−0.705324	+	0.705324i
$365$	24112.9			0.180994
$366$	−111200.	−	46060.4i	−0.830121	−	0.343847i
$367$	−91445.5	−	91445.5i	−0.678938	−	0.678938i	0.280822	−	0.959760i	$-0.409393\pi$
$367$	−91445.5	−	91445.5i	−0.678938	−	0.678938i	−0.959760	+	0.280822i	$0.909393\pi$
$368$			7586.65i			0.0560215i
$369$	−72800.2	−	560.036i	−0.534663	−	0.00411304i
$370$	69500.3			0.507672
$371$	−35660.5	+	35660.5i	−0.259083	+	0.259083i
$372$	−5406.09	+	13051.4i	−0.0390658	+	0.0943133i
$373$		−	37212.5i		−	0.267467i	−0.991017	−	0.133734i	$-0.957303\pi$
$373$		−	37212.5i		−	0.267467i	0.991017	−	0.133734i	$-0.0426967\pi$
$374$	208.163	+	208.163i	0.00148820	+	0.00148820i
$375$	−72577.0	−	175216.i	−0.516103	−	1.24598i
$376$	21391.0	−	51642.5i	0.151306	−	0.365285i
$377$	326133.	+	326133.i	2.29463	+	2.29463i
$378$	41265.1	+	41265.1i	0.288801	+	0.288801i
$379$	−230069.			−1.60169			−0.800846	−	0.598871i	$-0.795616\pi$
$379$	−230069.			−1.60169			−0.800846	+	0.598871i	$0.795616\pi$
$380$	−17451.1	−	7228.49i	−0.120853	−	0.0500588i
$381$	243974.	+	101057.i	1.68072	+	0.696175i
$382$	−29960.5	+	72331.0i	−0.205316	+	0.495676i
$383$	−38380.1	−	92657.9i	−0.261643	−	0.631662i	0.737398	−	0.675459i	$-0.236054\pi$
$383$	−38380.1	−	92657.9i	−0.261643	−	0.631662i	−0.999040	+	0.0437971i	$0.986054\pi$
$384$	−14917.0	+	6178.82i	−0.101162	+	0.0419028i
$385$	301.977			0.00203729
$386$	−35629.7	−	86017.8i	−0.239132	−	0.577316i
$387$	−120491.			−0.804513
$388$	−42993.1	−	103794.i	−0.285585	−	0.689462i
$389$	46967.1	−	46967.1i	0.310380	−	0.310380i	−0.534677	−	0.845057i	$-0.679567\pi$
$389$	46967.1	−	46967.1i	0.310380	−	0.310380i	0.845057	+	0.534677i	$0.179567\pi$
$390$	−153590.	−	153590.i	−1.00980	−	1.00980i
$391$	−37938.5	+	15714.6i	−0.248157	+	0.102790i
$392$			217.548i			0.00141574i
$393$	179010.	−	74148.4i	1.15902	−	0.480083i
$394$			28367.3i			0.182736i
$395$	35901.4	+	86673.6i	0.230100	+	0.555511i
$396$	96.1752	−	39.8371i	0.000613300	−	0.000254037i
$397$	133884.	+	55456.4i	0.849467	+	0.351861i	0.764579	−	0.644530i	$-0.222947\pi$
$397$	133884.	+	55456.4i	0.849467	+	0.351861i	0.0848875	+	0.996391i	$0.472947\pi$
$398$	63750.7	−	153908.i	0.402456	−	0.971615i
$399$	−24162.5	+	58333.5i	−0.151774	+	0.366414i
$400$			13181.1i			0.0823820i
$401$	107684.	−	107684.i	0.669674	−	0.669674i	−0.287967	−	0.957640i	$-0.592979\pi$
$401$	107684.	−	107684.i	0.669674	−	0.669674i	0.957640	+	0.287967i	$0.0929792\pi$
$402$	62361.7	−	62361.7i	0.385892	−	0.385892i
$403$	49234.6	+	20393.6i	0.303152	+	0.125570i
$404$	70355.9	−	29142.4i	0.431060	−	0.178551i
$405$	−118598.	+	118598.i	−0.723048	+	0.723048i
$406$	190356.			1.15482
$407$	333.201	+	138.016i	0.00201149	+	0.000833186i
$408$	−61796.8	−	61796.8i	−0.371232	−	0.371232i
$409$			263386.i			1.57451i	0.616626	+	0.787256i	$0.288499\pi$
$409$			263386.i			1.57451i	−0.616626	+	0.787256i	$0.711501\pi$
$410$	−69349.5	+	68290.7i	−0.412549	+	0.406250i
$411$	−25447.5			−0.150647
$412$	39928.7	−	39928.7i	0.235229	−	0.235229i
$413$	33851.0	−	81723.6i	0.198459	−	0.479124i
$414$			14520.9i			0.0847213i
$415$	−164028.	−	164028.i	−0.952405	−	0.952405i
$416$	23308.7	+	56272.1i	0.134689	+	0.325167i
$417$	−89238.9	+	215442.i	−0.513195	+	1.23896i
$418$	−69.3102	−	69.3102i	−0.000396684	−	0.000396684i
$419$	47695.9	+	47695.9i	0.271677	+	0.271677i	0.829775	−	0.558098i	$-0.188469\pi$
$419$	47695.9	+	47695.9i	0.271677	+	0.271677i	−0.558098	+	0.829775i	$0.688469\pi$
$420$	−89646.9			−0.508203
$421$	323071.	+	133820.i	1.82278	+	0.755019i	0.974104	+	0.226100i	$0.0725977\pi$
$421$	323071.	+	133820.i	1.82278	+	0.755019i	0.848673	+	0.528918i	$0.177402\pi$
$422$	−39096.4	−	16194.3i	−0.219539	−	0.0909361i
$423$	40942.5	−	98843.9i	0.228820	−	0.552420i
$424$	8894.33	+	21472.8i	0.0494745	+	0.119442i
$425$	−65914.7	+	27302.8i	−0.364926	+	0.151157i
$426$	131762.			0.726057
$427$	71712.6	+	173130.i	0.393314	+	0.949545i
$428$	27103.1			0.147955
$429$	−431.344	−	1041.36i	−0.00234374	−	0.00565828i
$430$	−113904.	+	113904.i	−0.616028	+	0.616028i
$431$	2687.04	+	2687.04i	0.0144650	+	0.0144650i	0.714302	−	0.699837i	$-0.246744\pi$
$431$	2687.04	+	2687.04i	0.0144650	+	0.0144650i	−0.699837	+	0.714302i	$0.746744\pi$
$432$	24847.6	−	10292.2i	0.133143	−	0.0551495i
$433$		−	185975.i		−	0.991925i	−0.868344	−	0.495963i	$-0.834815\pi$
$433$		−	185975.i		−	0.991925i	0.868344	−	0.495963i	$-0.165185\pi$
$434$	20320.1	−	8416.87i	0.107881	−	0.0446860i
$435$			312852.i			1.65333i
$436$	3071.91	+	7416.24i	0.0161598	+	0.0390132i
$437$	12632.0	−	5232.36i	0.0661470	−	0.0273990i
$438$	−34318.8	−	14215.3i	−0.178889	−	0.0740982i
$439$	−104366.	+	251961.i	−0.541538	+	1.30739i	0.382100	+	0.924121i	$0.375201\pi$
$439$	−104366.	+	251961.i	−0.541538	+	1.30739i	−0.923638	+	0.383266i	$0.874799\pi$
$440$	53.2580	−	128.576i	0.000275093	−	0.000664133i
$441$			416.387i			0.00214102i
$442$	−233119.	+	233119.i	−1.19325	+	1.19325i
$443$	124014.	−	124014.i	0.631920	−	0.631920i	−0.316629	−	0.948549i	$-0.602551\pi$
$443$	124014.	−	124014.i	0.631920	−	0.631920i	0.948549	+	0.316629i	$0.102551\pi$
$444$	−98916.3	−	40972.5i	−0.501767	−	0.207839i
$445$	−1729.22	+	716.264i	−0.00873231	+	0.00361704i
$446$	93162.2	−	93162.2i	0.468349	−	0.468349i
$447$	−287796.			−1.44035
$448$	23224.6	+	9619.96i	0.115716	+	0.0479311i
$449$	−203859.	−	203859.i	−1.01120	−	1.01120i	−0.999937	−	0.0112630i	$-0.996415\pi$
$449$	−203859.	−	203859.i	−1.01120	−	1.01120i	−0.0112630	−	0.999937i	$-0.503585\pi$
$450$			25228.7i			0.124586i
$451$	−468.093	+	189.685i	−0.00230133	+	0.000932566i
$452$	80555.2			0.394291
$453$	−167660.	+	167660.i	−0.817020	+	0.817020i
$454$	21912.7	−	52902.0i	0.106313	−	0.256661i
$455$			338179.i			1.63352i
$456$	20575.9	+	20575.9i	0.0989530	+	0.0989530i
$457$	43431.7	+	104853.i	0.207957	+	0.502053i	0.993101	−	0.117260i	$-0.0374111\pi$
$457$	43431.7	+	104853.i	0.207957	+	0.502053i	−0.785144	+	0.619313i	$0.787411\pi$
$458$	−16939.6	+	40895.9i	−0.0807557	+	0.194961i
$459$	102936.	+	102936.i	0.488589	+	0.488589i
$460$	13727.0	+	13727.0i	0.0648724	+	0.0648724i
$461$	114657.			0.539511			0.269756	−	0.962929i	$-0.413057\pi$
$461$	114657.			0.539511			0.269756	+	0.962929i	$0.413057\pi$
$462$	−429.789	−	178.024i	−0.00201359	−	0.000834057i
$463$	−75502.1	−	31274.0i	−0.352206	−	0.145889i	0.199564	−	0.979885i	$-0.436047\pi$
$463$	−75502.1	−	31274.0i	−0.352206	−	0.145889i	−0.551770	+	0.833996i	$0.686047\pi$
$464$	33572.0	−	81049.9i	0.155934	−	0.376458i
$465$	13833.2	+	33396.4i	0.0639761	+	0.154452i
$466$	−158507.	+	65655.7i	−0.729922	+	0.302343i
$467$	376345.			1.72565			0.862825	−	0.505503i	$-0.168693\pi$
$467$	376345.			1.72565			0.862825	+	0.505503i	$0.168693\pi$
$468$	44612.9	+	107705.i	0.203689	+	0.491750i
$469$	−137310.			−0.624245
$470$	−54735.8	−	132144.i	−0.247786	−	0.598207i
$471$	−313680.	+	313680.i	−1.41399	+	1.41399i
$472$	−28826.3	−	28826.3i	−0.129391	−	0.129391i
$473$	−772.276	+	319.887i	−0.00345184	+	0.00142980i
$474$		−	144523.i		−	0.643251i
$475$	21947.0	−	9090.75i	0.0972721	−	0.0402914i
$476$			136066.i			0.600530i
$477$	17023.8	+	41099.1i	0.0748203	+	0.180632i
$478$	−93525.5	+	38739.5i	−0.409330	+	0.169550i
$479$	−261299.	−	108234.i	−1.13885	−	0.471728i	−0.268071	−	0.963399i	$-0.586386\pi$
$479$	−261299.	−	108234.i	−1.13885	−	0.471728i	−0.870781	+	0.491671i	$0.836386\pi$
$480$	−15810.5	+	38170.0i	−0.0686221	+	0.165668i
$481$	−154562.	+	373146.i	−0.668057	+	1.61283i
$482$		−	152838.i		−	0.657867i
$483$	45885.0	−	45885.0i	0.196687	−	0.196687i
$484$	−82821.5	+	82821.5i	−0.353551	+	0.353551i
$485$	−265592.	−	110012.i	−1.12910	−	0.467687i
$486$	149764.	−	62034.3i	0.634067	−	0.262639i
$487$	100149.	−	100149.i	0.422268	−	0.422268i	−0.463716	−	0.885984i	$-0.653484\pi$
$487$	100149.	−	100149.i	0.422268	−	0.422268i	0.885984	+	0.463716i	$0.153484\pi$
$488$	86362.8			0.362650
$489$	−376692.	−	156031.i	−1.57532	−	0.652519i
$490$	393.622	+	393.622i	0.00163941	+	0.00163941i
$491$			33928.8i			0.140736i	0.997521	+	0.0703681i	$0.0224174\pi$
$491$			33928.8i			0.140736i	−0.997521	+	0.0703681i	$0.977583\pi$
$492$	138961.	−	56311.1i	0.574067	−	0.232629i
$493$	474845.			1.95370
$494$	77619.4	−	77619.4i	0.318065	−	0.318065i
$495$	101.936	−	246.095i	0.000416023	−	0.00100437i
$496$		−	10136.4i		−	0.0412020i
$497$	−145058.	−	145058.i	−0.587259	−	0.587259i
$498$	136753.	+	330152.i	0.551416	+	1.33124i
$499$	119963.	−	289617.i	0.481779	−	1.16312i	−0.476984	−	0.878912i	$-0.658270\pi$
$499$	119963.	−	289617.i	0.481779	−	1.16312i	0.958763	−	0.284206i	$-0.0917299\pi$
$500$	96223.9	+	96223.9i	0.384895	+	0.384895i
$501$	−325101.	−	325101.i	−1.29522	−	1.29522i
$502$	−88320.8			−0.350474
$503$	339650.	+	140688.i	1.34244	+	0.556059i	0.934179	−	0.356805i	$-0.116134\pi$
$503$	339650.	+	140688.i	1.34244	+	0.556059i	0.408265	+	0.912863i	$0.366134\pi$
$504$	44452.1	+	18412.7i	0.174997	+	0.0724862i
$505$	74570.2	−	180028.i	0.292404	−	0.705925i
$506$	38.5509	+	93.0702i	0.000150568	+	0.000363504i
$507$	871999.	−	361194.i	3.39234	−	1.40515i
$508$	−189482.			−0.734244
$509$	−108856.	−	262801.i	−0.420161	−	1.01436i	−0.982300	−	0.187316i	$-0.940021\pi$
$509$	−108856.	−	262801.i	−0.420161	−	1.01436i	0.562139	−	0.827043i	$-0.309979\pi$
$510$	−223625.			−0.859767
$511$	22132.1	+	53431.7i	0.0847582	+	0.204624i
$512$	8192.00	−	8192.00i	0.0312500	−	0.0312500i
$513$	−34273.8	−	34273.8i	−0.130235	−	0.130235i
$514$	−287882.	+	119245.i	−1.08965	+	0.451349i
$515$		−	144491.i		−	0.544786i
$516$	229263.	−	94963.8i	0.861062	−	0.356664i
$517$		−	742.227i		−	0.00277687i
$518$	63791.0	+	154005.i	0.237739	+	0.573952i
$519$	621.076	−	257.258i	0.00230574	−	0.000955068i
$520$	143990.	+	59642.7i	0.532509	+	0.220572i
$521$	188976.	−	456228.i	0.696194	−	1.68076i	−0.0357172	−	0.999362i	$-0.511372\pi$
$521$	188976.	−	456228.i	0.696194	−	1.68076i	0.731911	−	0.681400i	$-0.238628\pi$
$522$	64256.9	−	155130.i	0.235819	−	0.569318i
$523$			211.971i			0.000774950i	1.00000		0.000387475i	$0.000123337\pi$
$523$			211.971i			0.000774950i	−1.00000		0.000387475i	$0.999877\pi$
$524$	−98307.3	+	98307.3i	−0.358033	+	0.358033i
$525$	79721.0	−	79721.0i	0.289237	−	0.289237i
$526$	298308.	+	123563.i	1.07819	+	0.446599i
$527$	50688.8	−	20996.0i	0.182512	−	0.0755989i
$528$	−151.599	+	151.599i	−0.000543786	+	0.000543786i
$529$	265789.			0.949785
$530$	54945.1	+	22759.0i	0.195604	+	0.0810218i
$531$	−55173.6	−	55173.6i	−0.195678	−	0.195678i
$532$		−	45304.5i		−	0.160073i
$533$	−212425.	−	524209.i	−0.747741	−	1.84523i
$534$	2883.37			0.0101115
$535$	49039.3	−	49039.3i	0.171331	−	0.171331i
$536$	−24216.5	+	58463.8i	−0.0842911	+	0.203497i
$537$			599330.i			2.07834i
$538$	214563.	+	214563.i	0.741292	+	0.741292i
$539$	1.10545	+	2.66879i	3.80506e−6	+	9.18623e-6i
$540$	26336.0	−	63580.6i	0.0903154	−	0.218041i
$541$	−289889.	−	289889.i	−0.990461	−	0.990461i	0.00949387	−	0.999955i	$-0.496978\pi$
$541$	−289889.	−	289889.i	−0.990461	−	0.990461i	−0.999955	+	0.00949387i	$0.996978\pi$
$542$	136266.	+	136266.i	0.463860	+	0.463860i
$543$	−145345.			−0.492946
$544$	57934.2	+	23997.1i	0.195766	+	0.0810889i
$545$	18976.9	+	7860.47i	0.0638898	+	0.0264640i
$546$	199367.	−	481314.i	0.668755	−	1.61452i
$547$	72376.0	+	174731.i	0.241891	+	0.583977i	0.997471	−	0.0710799i	$-0.0226445\pi$
$547$	72376.0	+	174731.i	0.241891	+	0.583977i	−0.755579	+	0.655057i	$0.772645\pi$
$548$	16869.4	−	6987.52i	0.0561743	−	0.0232682i
$549$	165299.			0.548435
$550$	66.9787	+	161.701i	0.000221417	+	0.000534549i
$551$	−158105.			−0.520765
$552$	−11444.5	−	27629.4i	−0.0375593	−	0.0906763i
$553$	−159107.	+	159107.i	−0.520283	+	0.520283i
$554$	−243385.	−	243385.i	−0.793002	−	0.793002i
$555$	−253109.	+	104841.i	−0.821717	+	0.340366i
$556$		−	167322.i		−	0.541257i
$557$	−283708.	+	117516.i	−0.914452	+	0.378779i	−0.789759	−	0.613417i	$-0.789795\pi$
$557$	−283708.	+	117516.i	−0.914452	+	0.378779i	−0.124693	+	0.992195i	$0.539795\pi$
$558$		−	19401.0i		−	0.0623098i
$559$	−358236.	−	864859.i	−1.14643	−	2.76772i
$560$	59427.8	−	24615.8i	0.189502	−	0.0784942i
$561$	−1072.11	−	444.084i	−0.00340655	−	0.00141104i
$562$	−66780.9	+	161223.i	−0.211436	+	0.510453i
$563$	−83095.0	+	200609.i	−0.262155	+	0.632898i	−0.999071	−	0.0430860i	$-0.986281\pi$
$563$	−83095.0	+	200609.i	−0.262155	+	0.632898i	0.736917	+	0.675984i	$0.236281\pi$
$564$			220342.i			0.692691i
$565$	145754.	−	145754.i	0.456586	−	0.456586i
$566$	−141278.	+	141278.i	−0.441003	+	0.441003i
$567$	−371656.	−	153945.i	−1.15605	−	0.478850i
$568$	−87346.2	+	36180.0i	−0.270737	+	0.112143i
$569$	−196963.	+	196963.i	−0.608359	+	0.608359i	−0.942517	−	0.334158i	$-0.891548\pi$
$569$	−196963.	+	196963.i	−0.608359	+	0.608359i	0.334158	+	0.942517i	$0.391548\pi$
$570$	74458.5			0.229174
$571$	−419000.	−	173556.i	−1.28511	−	0.532312i	−0.367589	−	0.929988i	$-0.619817\pi$
$571$	−419000.	−	173556.i	−1.28511	−	0.532312i	−0.917526	+	0.397677i	$0.869817\pi$
$572$	571.883	+	571.883i	0.00174790	+	0.00174790i
$573$		−	308614.i		−	0.939953i
$574$	−214977.	−	90990.3i	−0.652483	−	0.276167i
$575$	−24414.2			−0.0738426
$576$	15679.5	−	15679.5i	0.0472594	−	0.0472594i
$577$	−4651.66	+	11230.1i	−0.0139719	+	0.0337312i	−0.930712	−	0.365754i	$-0.880811\pi$
$577$	−4651.66	+	11230.1i	−0.0139719	+	0.0337312i	0.916740	+	0.399485i	$0.130811\pi$
$578$			103184.i			0.308858i
$579$	259516.	+	259516.i	0.774118	+	0.774118i
$580$	−85904.8	−	207392.i	−0.255365	−	0.616506i
$581$	212915.	−	514022.i	0.630745	−	1.52275i
$582$	313148.	+	313148.i	0.924494	+	0.924494i
$583$	218.224	+	218.224i	0.000642046	+	0.000642046i
$584$	26653.5			0.0781500
$585$	275598.	+	114156.i	0.805313	+	0.333571i
$586$	163428.	+	67694.0i	0.475916	+	0.197131i
$587$	−39410.2	+	95144.6i	−0.114375	+	0.276126i	−0.970693	−	0.240323i	$-0.922747\pi$
$587$	−39410.2	+	95144.6i	−0.114375	+	0.276126i	0.856318	+	0.516450i	$0.172747\pi$
$588$	−328.171	−	792.275i	−0.000949174	−	0.00229151i
$589$	−16877.4	+	6990.84i	−0.0486491	+	0.0201511i
$590$	−104314.			−0.299668
$591$	−42792.1	−	103309.i	−0.122515	−	0.295777i
$592$	76823.0			0.219204
$593$	117382.	+	283384.i	0.333803	+	0.805872i	0.998284	+	0.0585665i	$0.0186530\pi$
$593$	117382.	+	283384.i	0.333803	+	0.805872i	−0.664480	+	0.747306i	$0.731347\pi$
$594$	252.522	−	252.522i	0.000715692	−	0.000715692i
$595$	246192.	+	246192.i	0.695408	+	0.695408i
$596$	190782.	−	79024.7i	0.537088	−	0.222469i
$597$			656676.i			1.84248i
$598$	−104228.	+	43172.5i	−0.291461	+	0.120727i
$599$			117282.i			0.326872i	0.986554	+	0.163436i	$0.0522577\pi$
$599$			117282.i			0.326872i	−0.986554	+	0.163436i	$0.947742\pi$
$600$	−19883.7	−	48003.6i	−0.0552326	−	0.133343i
$601$	−470108.	+	194725.i	−1.30151	+	0.539105i	−0.922397	−	0.386244i	$-0.873772\pi$
$601$	−470108.	+	194725.i	−1.30151	+	0.539105i	−0.379118	+	0.925348i	$0.623772\pi$
$602$	−356945.	−	147852.i	−0.984937	−	0.407974i
$603$	−46350.5	+	111900.i	−0.127473	+	0.307748i
$604$	65106.2	−	157180.i	0.178463	−	0.430848i
$605$			299708.i			0.818818i
$606$	−212264.	+	212264.i	−0.578005	+	0.578005i
$607$	−214018.	+	214018.i	−0.580862	+	0.580862i	−0.935140	−	0.354278i	$-0.884727\pi$
$607$	−214018.	+	214018.i	−0.580862	+	0.580862i	0.354278	+	0.935140i	$0.384727\pi$
$608$	−19289.8	−	7990.10i	−0.0521820	−	0.0216145i
$609$	−693247.	+	287152.i	−1.86919	+	0.774243i
$610$	156262.	−	156262.i	0.419945	−	0.419945i
$611$	831207.			2.22652
$612$	110886.	+	45930.6i	0.296057	+	0.122631i
$613$	−208178.	−	208178.i	−0.554004	−	0.554004i	0.373590	−	0.927594i	$-0.378127\pi$
$613$	−208178.	−	208178.i	−0.554004	−	0.554004i	−0.927594	+	0.373590i	$0.878127\pi$
$614$			115164.i			0.305477i
$615$	149544.	−	353318.i	0.395383	−	0.934148i
$616$	333.794			0.000879665
$617$	−23061.6	+	23061.6i	−0.0605786	+	0.0605786i	−0.736747	−	0.676168i	$-0.763639\pi$
$617$	−23061.6	+	23061.6i	−0.0605786	+	0.0605786i	0.676168	+	0.736747i	$0.263639\pi$
$618$	−85181.7	+	205647.i	−0.223033	+	0.538449i
$619$			83246.3i			0.217262i	0.994082	+	0.108631i	$0.0346467\pi$
$619$			83246.3i			0.217262i	−0.994082	+	0.108631i	$0.965353\pi$
$620$	−18340.3	−	18340.3i	−0.0477116	−	0.0477116i
$621$	19063.3	+	46023.0i	0.0494329	+	0.119342i
$622$	162551.	−	392432.i	0.420153	−	1.01434i
$623$	−3174.33	−	3174.33i	−0.00817855	−	0.00817855i
$624$	−169773.	−	169773.i	−0.436013	−	0.436013i
$625$	219486.			0.561883
$626$	−126733.	−	52494.5i	−0.323400	−	0.133957i
$627$	356.972	+	147.863i	0.000908027	+	0.000376117i
$628$	121809.	−	294074.i	0.308860	−	0.745654i
$629$	159128.	+	384168.i	0.402202	+	0.971001i
$630$	113745.	−	47114.7i	0.286584	−	0.118707i
$631$	342079.			0.859148			0.429574	−	0.903032i	$-0.358664\pi$
$631$	342079.			0.859148			0.429574	+	0.903032i	$0.358664\pi$
$632$	39684.0	+	95805.7i	0.0993531	+	0.239860i
$633$	166812.			0.416313
$634$	13365.6	+	32267.4i	0.0332514	+	0.0802760i
$635$	−342841.	+	342841.i	−0.850248	+	0.850248i
$636$	−64783.6	−	64783.6i	−0.160159	−	0.160159i
$637$	−2988.74	+	1237.97i	−0.00736561	+	0.00305093i
$638$		−	1164.88i		−	0.00286181i
$639$	−167181.	+	69248.6i	−0.409435	+	0.169594i
$640$		−	29644.6i		−	0.0723745i
$641$	121438.	+	293177.i	0.295555	+	0.713532i	0.999993	+	0.00376688i	$0.00119904\pi$
$641$	121438.	+	293177.i	0.295555	+	0.713532i	−0.704438	+	0.709765i	$0.748801\pi$
$642$	−98705.2	+	40885.0i	−0.239480	+	0.0991961i
$643$	660890.	+	273750.i	1.59848	+	0.662112i	0.991200	−	0.132376i	$-0.0422606\pi$
$643$	660890.	+	273750.i	1.59848	+	0.662112i	0.607280	+	0.794488i	$0.292261\pi$
$644$	−17818.2	+	43016.9i	−0.0429627	+	0.103721i
$645$	242996.	−	586643.i	0.584089	−	1.41012i
$646$		−	113013.i		−	0.270808i
$647$	103243.	−	103243.i	0.246633	−	0.246633i	−0.572954	−	0.819587i	$-0.694203\pi$
$647$	103243.	−	103243.i	0.246633	−	0.246633i	0.819587	+	0.572954i	$0.194203\pi$
$648$	−131094.	+	131094.i	−0.312199	+	0.312199i
$649$	−500.108	−	207.151i	−0.00118734	−	0.000491811i
$650$	−181086.	+	75008.4i	−0.428606	+	0.177535i
$651$	−61305.9	+	61305.9i	−0.144657	+	0.144657i
$652$	292557.			0.688200
$653$	239506.	+	99206.8i	0.561682	+	0.232656i	0.645415	−	0.763832i	$-0.276684\pi$
$653$	239506.	+	99206.8i	0.561682	+	0.232656i	−0.0837331	+	0.996488i	$0.526684\pi$
$654$	−22374.8	−	22374.8i	−0.0523124	−	0.0523124i
$655$			355747.i			0.829198i
$656$	−76656.3	+	75485.9i	−0.178131	+	0.175412i
$657$	51015.0			0.118186
$658$	242578.	−	242578.i	0.560272	−	0.560272i
$659$	−18220.5	+	43988.2i	−0.0419556	+	0.101290i	−0.943468	−	0.331463i	$-0.892458\pi$
$659$	−18220.5	+	43988.2i	−0.0419556	+	0.101290i	0.901513	+	0.432753i	$0.142458\pi$
$660$			548.594i			0.00125940i
$661$	301855.	+	301855.i	0.690868	+	0.690868i	0.962423	−	0.271555i	$-0.0875377\pi$
$661$	301855.	+	301855.i	0.690868	+	0.690868i	−0.271555	+	0.962423i	$0.587538\pi$
$662$	169211.	+	408511.i	0.386111	+	0.932155i
$663$	497323.	−	1.20064e6i	1.13139	−	2.73141i
$664$	−181310.	−	181310.i	−0.411231	−	0.411231i
$665$	−81972.2	−	81972.2i	−0.185363	−	0.185363i
$666$	147040.			0.331502
$667$	150122.	+	62182.4i	0.337436	+	0.139771i
$668$	304781.	+	126244.i	0.683021	+	0.282917i
$669$	−198747.	+	479818.i	−0.444067	+	1.07207i
$670$	61965.8	+	149599.i	0.138039	+	0.333256i
$671$	1059.47	−	438.845i	0.00235311	−	0.000974690i
$672$	−99092.3			−0.219433
$673$	158911.	+	383645.i	0.350852	+	0.847032i	0.996515	+	0.0834096i	$0.0265810\pi$
$673$	158911.	+	383645.i	0.350852	+	0.847032i	−0.645663	+	0.763622i	$0.723419\pi$
$674$	−447655.			−0.985425
$675$	33120.8	+	79960.8i	0.0726932	+	0.175497i
$676$	−478877.	+	478877.i	−1.04793	+	1.04793i
$677$	−533333.	−	533333.i	−1.16365	−	1.16365i	−0.983671	−	0.179977i	$-0.942398\pi$
$677$	−533333.	−	533333.i	−1.16365	−	1.16365i	−0.179977	−	0.983671i	$-0.557602\pi$
$678$	−293370.	+	121518.i	−0.638199	+	0.264351i
$679$		−	689497.i		−	1.49552i
$680$	148243.	−	61404.4i	0.320596	−	0.132795i
$681$			225716.i			0.486708i
$682$	−51.5070	−	124.349i	−0.000110738	−	0.000267346i
$683$	−355294.	+	147168.i	−0.761635	+	0.315480i	−0.729479	−	0.684003i	$-0.760237\pi$
$683$	−355294.	+	147168.i	−0.761635	+	0.315480i	−0.0321562	+	0.999483i	$0.510237\pi$
$684$	−36920.8	−	15293.1i	−0.0789148	−	0.0326876i
$685$	17879.8	−	43165.7i	0.0381050	−	0.0919937i
$686$	127086.	−	306813.i	0.270054	−	0.651967i
$687$		−	174490.i		−	0.369707i
$688$	−125905.	+	125905.i	−0.265990	+	0.265990i
$689$	−244386.	+	244386.i	−0.514799	+	0.514799i
$690$	−70698.8	−	29284.4i	−0.148496	−	0.0615090i
$691$	−324524.	+	134422.i	−0.679658	+	0.281523i	−0.695684	−	0.718348i	$-0.744898\pi$
$691$	−324524.	+	134422.i	−0.679658	+	0.281523i	0.0160262	+	0.999872i	$0.494898\pi$
$692$	−341.077	+	341.077i	−0.000712264	+	0.000712264i
$693$	638.883			0.00133032
$694$	422224.	+	174891.i	0.876645	+	0.363118i
$695$	−302746.	−	302746.i	−0.626771	−	0.626771i
$696$			345815.i			0.713880i
$697$	−536264.	−	226977.i	−1.10386	−	0.467213i
$698$	−135266.			−0.277637
$699$	478216.	−	478216.i	0.978745	−	0.978745i
$700$	−30957.5	+	74738.0i	−0.0631786	+	0.152527i
$701$			761015.i			1.54866i	0.632780	+	0.774332i	$0.281914\pi$
$701$			761015.i			1.54866i	−0.632780	+	0.774332i	$0.718086\pi$
$702$	282795.	+	282795.i	0.573849	+	0.573849i
$703$	−52983.2	−	127913.i	−0.107208	−	0.258823i
$704$	58.8694	−	142.123i	0.000118780	−	0.000286761i
$705$	398679.	+	398679.i	0.802131	+	0.802131i
$706$	−462256.	−	462256.i	−0.927413	−	0.927413i
$707$	467368.			0.935019
$708$	148465.	+	61496.3i	0.296182	+	0.122683i
$709$	317881.	+	131670.i	0.632371	+	0.261936i	0.675760	−	0.737122i	$-0.263816\pi$
$709$	317881.	+	131670.i	0.632371	+	0.261936i	−0.0433894	+	0.999058i	$0.513816\pi$
$710$	−92578.2	+	223504.i	−0.183650	+	0.443371i
$711$	75955.4	+	183373.i	0.150252	+	0.362740i
$712$	−1911.41	+	791.732i	−0.00377045	+	0.00156177i
$713$	18774.7			0.0369312
$714$	−205255.	−	495530.i	−0.402622	−	0.972017i
$715$	2069.49			0.00404810
$716$	−164568.	−	397301.i	−0.321010	−	0.774986i
$717$	282167.	−	282167.i	0.548867	−	0.548867i
$718$	−296089.	−	296089.i	−0.574345	−	0.574345i
$719$	−857497.	+	355187.i	−1.65873	+	0.687067i	−0.997979	−	0.0635420i	$-0.979760\pi$
$719$	−857497.	+	355187.i	−1.65873	+	0.687067i	−0.660747	+	0.750609i	$0.729760\pi$
$720$		−	56739.9i		−	0.109452i
$721$	320176.	−	132621.i	0.615912	−	0.255119i
$722$		−	330975.i		−	0.634922i
$723$	230557.	+	556614.i	0.441064	+	1.06482i
$724$	96350.2	−	39909.6i	0.183813	−	0.0761377i
$725$	260823.	+	108036.i	0.496214	+	0.205539i
$726$	176687.	−	426560.i	0.335221	−	0.809294i
$727$	−164611.	+	397406.i	−0.311451	+	0.751909i	0.688201	+	0.725520i	$0.258401\pi$
$727$	−164611.	+	397406.i	−0.311451	+	0.751909i	−0.999652	+	0.0263890i	$0.991599\pi$
$728$			373810.i			0.705324i
$729$	17441.4	−	17441.4i	0.0328191	−	0.0328191i
$730$	48225.9	−	48225.9i	0.0904971	−	0.0904971i
$731$	−890404.	−	368818.i	−1.66630	−	0.690203i
$732$	−314520.	+	130279.i	−0.586984	+	0.243137i
$733$	−93556.1	+	93556.1i	−0.174126	+	0.174126i	−0.788790	−	0.614663i	$-0.789292\pi$
$733$	−93556.1	+	93556.1i	−0.174126	+	0.174126i	0.614663	+	0.788790i	$0.289292\pi$
$734$	−365782.			−0.678938
$735$	−2027.29	−	839.732i	−0.00375268	−	0.00155441i
$736$	15173.3	+	15173.3i	0.0280107	+	0.0280107i
$737$			840.266i			0.00154697i
$738$	−146721.	+	144480.i	−0.269388	+	0.265275i
$739$	386573.			0.707853			0.353926	−	0.935273i	$-0.384846\pi$
$739$	386573.			0.707853			0.353926	+	0.935273i	$0.384846\pi$
$740$	139001.	−	139001.i	0.253836	−	0.253836i
$741$	−165589.	+	399767.i	−0.301575	+	0.728065i
$742$			142642.i			0.259083i
$743$	152610.	+	152610.i	0.276442	+	0.276442i	0.831687	−	0.555245i	$-0.187375\pi$
$743$	152610.	+	152610.i	0.276442	+	0.276442i	−0.555245	+	0.831687i	$0.687375\pi$
$744$	15290.7	+	36915.1i	0.0276237	+	0.0666896i
$745$	202210.	−	488178.i	0.364326	−	0.879561i
$746$	−74424.9	−	74424.9i	−0.133734	−	0.133734i
$747$	−347029.	−	347029.i	−0.621905	−	0.621905i
$748$	832.654			0.00148820
$749$	153677.	+	63654.9i	0.273933	+	0.113467i
$750$	−495586.	−	205279.i	−0.881043	−	0.364940i
$751$	109974.	−	265501.i	0.194989	−	0.470746i	−0.795899	−	0.605429i	$-0.793002\pi$
$751$	109974.	−	265501.i	0.194989	−	0.470746i	0.990889	+	0.134683i	$0.0430016\pi$
$752$	−60502.9	−	146067.i	−0.106989	−	0.258295i
$753$	321651.	−	133232.i	0.567277	−	0.234974i
$754$	1.30453e6			2.29463
$755$	−166595.	−	402196.i	−0.292260	−	0.705577i
$756$	165060.			0.288801
$757$	289864.	+	699794.i	0.505828	+	1.22118i	0.946265	+	0.323393i	$0.104824\pi$
$757$	289864.	+	699794.i	0.505828	+	1.22118i	−0.440437	+	0.897784i	$0.645176\pi$
$758$	−460137.	+	460137.i	−0.800846	+	0.800846i
$759$	−280.793	−	280.793i	−0.000487419	−	0.000487419i
$760$	−49359.2	+	20445.3i	−0.0854557	+	0.0353969i
$761$			271027.i			0.467997i	0.972237	+	0.233998i	$0.0751811\pi$
$761$			271027.i			0.467997i	−0.972237	+	0.233998i	$0.924819\pi$
$762$	690064.	−	285834.i	1.18845	−	0.492270i
$763$			49265.5i			0.0846240i
$764$	84741.0	+	204583.i	0.145180	+	0.350496i
$765$	283738.	−	117528.i	0.484837	−	0.200826i
$766$	−262076.	−	108555.i	−0.446652	−	0.185009i
$767$	231985.	−	560062.i	0.394339	−	0.952019i
$768$	−17476.4	+	42191.7i	−0.0296298	+	0.0715326i
$769$		−	475329.i		−	0.803789i	−0.915686	−	0.401894i	$-0.868352\pi$
$769$		−	475329.i		−	0.803789i	0.915686	−	0.401894i	$-0.131648\pi$
$770$	603.954	−	603.954i	0.00101864	−	0.00101864i
$771$	868541.	−	868541.i	1.46110	−	1.46110i
$772$	−243295.	−	100776.i	−0.408224	−	0.169092i
$773$	315100.	−	130519.i	0.527338	−	0.218431i	−0.103099	−	0.994671i	$-0.532876\pi$
$773$	315100.	−	130519.i	0.527338	−	0.218431i	0.630437	+	0.776240i	$0.282876\pi$
$774$	−240982.	+	240982.i	−0.402257	+	0.402257i
$775$	32619.3			0.0543089
$776$	−293575.	−	121603.i	−0.487524	−	0.201939i
$777$	−464634.	−	464634.i	−0.769607	−	0.769607i
$778$		−	187868.i		−	0.310380i
$779$	178555.	+	75574.2i	0.294237	+	0.124537i
$780$	−614362.			−1.00980
$781$	−887.684	+	887.684i	−0.00145531	+	0.00145531i
$782$	−44447.7	+	107306.i	−0.0726835	+	0.175474i
$783$		−	576032.i		−	0.939557i
$784$	435.095	+	435.095i	0.000707868	+	0.000707868i
$785$	−311689.	−	752483.i	−0.505803	−	1.22112i
$786$	209723.	−	506317.i	0.339470	−	0.819553i
$787$	11979.7	+	11979.7i	0.0193418	+	0.0193418i	0.716712	−	0.697370i	$-0.245646\pi$
$787$	11979.7	+	11979.7i	0.0193418	+	0.0193418i	−0.697370	+	0.716712i	$0.745646\pi$
$788$	56734.5	+	56734.5i	0.0913682	+	0.0913682i
$789$	−1.27279e6			−2.04457
$790$	245150.	+	101544.i	0.392805	+	0.162705i
$791$	456755.	+	189194.i	0.730012	+	0.302381i
$792$	112.676	−	272.025i	0.000179631	−	0.000433668i
$793$	491455.	+	1.18648e6i	0.781516	+	1.88675i
$794$	378680.	−	156854.i	0.600664	−	0.248803i
$795$	−234434.			−0.370925
$796$	−180314.	−	435317.i	−0.284580	−	0.687036i
$797$	−337952.			−0.532032			−0.266016	−	0.963969i	$-0.585707\pi$
$797$	−337952.			−0.532032			−0.266016	+	0.963969i	$0.585707\pi$
$798$	68341.9	+	164992.i	0.107320	+	0.259094i
$799$	605113.	−	605113.i	0.947857	−	0.947857i
$800$	26362.2	+	26362.2i	0.0411910	+	0.0411910i
$801$	−3658.45	+	1515.38i	−0.00570206	+	0.00236187i
$802$		−	430737.i		−	0.669674i
$803$	326.975	−	135.438i	0.000507089	−	0.000210043i
$804$		−	249447.i		−	0.385892i
$805$	45593.6	+	110073.i	0.0703578	+	0.169859i
$806$	139256.	−	57681.9i	0.214361	−	0.0887911i
$807$	−1.10507e6	−	457736.i	−1.69685	−	0.702859i
$808$	82427.1	−	198997.i	0.126255	−	0.304806i
$809$	−195869.	+	472871.i	−0.299274	+	0.722512i	0.700685	+	0.713471i	$0.252878\pi$
$809$	−195869.	+	472871.i	−0.299274	+	0.722512i	−0.999959	+	0.00904124i	$0.997122\pi$
$810$			474392.i			0.723048i
$811$	−769554.	+	769554.i	−1.17003	+	1.17003i	−0.187830	+	0.982202i	$0.560145\pi$
$811$	−769554.	+	769554.i	−1.17003	+	1.17003i	−0.982202	+	0.187830i	$0.939855\pi$
$812$	380712.	−	380712.i	0.577410	−	0.577410i
$813$	−701815.	−	290701.i	−1.06180	−	0.439811i
$814$	942.435	−	390.369i	0.00142234	−	0.000589151i
$815$	529341.	−	529341.i	0.796930	−	0.796930i
$816$	−247187.			−0.371232
$817$	296470.	+	122802.i	0.444157	+	0.183976i
$818$	526772.	+	526772.i	0.787256	+	0.787256i
$819$			715475.i			1.06666i
$820$	−2117.67	+	275280.i	−0.00314942	+	0.409400i
$821$	−966230.			−1.43349			−0.716744	−	0.697336i	$-0.754369\pi$
$821$	−966230.			−1.43349			−0.716744	+	0.697336i	$0.754369\pi$
$822$	−50894.9	+	50894.9i	−0.0753236	+	0.0753236i
$823$	−474929.	+	1.14658e6i	−0.701179	+	1.69280i	0.0197673	+	0.999805i	$0.493707\pi$
$823$	−474929.	+	1.14658e6i	−0.701179	+	1.69280i	−0.720946	+	0.692991i	$0.756293\pi$
$824$		−	159715.i		−	0.235229i
$825$	−487.852	−	487.852i	−0.000716771	−	0.000716771i
$826$	−95745.2	−	231149.i	−0.140332	−	0.338792i
$827$	191689.	−	462779.i	0.280277	−	0.676647i	−0.719565	−	0.694425i	$-0.755659\pi$
$827$	191689.	−	462779.i	0.280277	−	0.676647i	0.999842	+	0.0177772i	$0.00565896\pi$
$828$	29041.8	+	29041.8i	0.0423606	+	0.0423606i
$829$	−310751.	−	310751.i	−0.452172	−	0.452172i	0.443903	−	0.896075i	$-0.353593\pi$
$829$	−310751.	−	310751.i	−0.452172	−	0.452172i	−0.896075	+	0.443903i	$0.853593\pi$
$830$	−656112.			−0.952405
$831$	1.25352e6	+	519224.i	1.81522	+	0.751887i
$832$	159161.	+	65926.8i	0.229928	+	0.0952392i
$833$	−1274.54	+	3077.01i	−0.00183681	+	0.00443445i
$834$	252406.	+	609361.i	0.362883	+	0.876078i
$835$	779880.	−	323037.i	1.11855	−	0.463318i
$836$	−277.241			−0.000396684
$837$	−25470.1	−	61490.3i	−0.0363563	−	0.0877719i
$838$	190784.			0.271677
$839$	271674.	+	655879.i	0.385944	+	0.931751i	0.990790	+	0.135408i	$0.0432346\pi$
$839$	271674.	+	655879.i	0.385944	+	0.931751i	−0.604846	+	0.796342i	$0.706765\pi$
$840$	−179294.	+	179294.i	−0.254101	+	0.254101i
$841$	−828494.	−	828494.i	−1.17138	−	1.17138i
$842$	913782.	−	378501.i	1.28890	−	0.533879i
$843$		−	687890.i		−	0.967975i
$844$	−110581.	+	45804.3i	−0.155238	+	0.0643015i
$845$			1.73292e6i			2.42698i
$846$	−115803.	−	279573.i	−0.161800	−	0.390620i
$847$	−664121.	+	275088.i	−0.925722	+	0.383446i
$848$	60734.3	+	25157.0i	0.0844583	+	0.0349838i
$849$	301395.	−	727631.i	0.418139	−	1.00948i
$850$	−77223.9	+	186435.i	−0.106884	+	0.258041i
$851$			142292.i			0.196482i
$852$	263524.	−	263524.i	0.363029	−	0.363029i
$853$	754646.	−	754646.i	1.03716	−	1.03716i	0.0378761	−	0.999282i	$-0.487941\pi$
$853$	754646.	−	754646.i	1.03716	−	1.03716i	0.999282	−	0.0378761i	$-0.0120592\pi$
$854$	489684.	+	202834.i	0.671429	+	0.278115i
$855$	−94473.7	+	39132.3i	−0.129235	+	0.0535307i
$856$	54206.2	−	54206.2i	0.0739777	−	0.0739777i
$857$	6621.33			0.00901537			0.00450769	−	0.999990i	$-0.498565\pi$
$857$	6621.33			0.00901537			0.00450769	+	0.999990i	$0.498565\pi$
$858$	−2945.40	−	1220.02i	−0.00400101	−	0.00165727i
$859$	−248298.	−	248298.i	−0.336502	−	0.336502i	0.518547	−	0.855049i	$-0.326473\pi$
$859$	−248298.	−	248298.i	−0.336502	−	0.336502i	−0.855049	+	0.518547i	$0.826473\pi$
$860$			455615.i			0.616028i
$861$	920174.	+	7078.70i	1.24126	+	0.00954876i
$862$	10748.2			0.0144650
$863$	−79847.5	+	79847.5i	−0.107211	+	0.107211i	−0.758677	−	0.651466i	$-0.774154\pi$
$863$	−79847.5	+	79847.5i	−0.107211	+	0.107211i	0.651466	+	0.758677i	$0.274154\pi$
$864$	29110.8	−	70279.6i	0.0389966	−	0.0941460i
$865$			1234.26i			0.00164959i
$866$	−371950.	−	371950.i	−0.495963	−	0.495963i
$867$	−155654.	−	375782.i	−0.207072	−	0.499917i
$868$	23806.5	−	57474.0i	0.0315978	−	0.0762837i
$869$	973.657	+	973.657i	0.00128934	+	0.00128934i
$870$	625704.	+	625704.i	0.826667	+	0.826667i
$871$	−940999.			−1.24038
$872$	20976.3	+	8688.67i	0.0275865	+	0.0114267i
$873$	−561904.	−	232748.i	−0.737282	−	0.305392i
$874$	14799.3	−	35728.8i	0.0193740	−	0.0467730i
$875$	319603.	+	771591.i	0.417441	+	1.00779i
$876$	−97068.1	+	40206.9i	−0.126494	+	0.0523953i
$877$	−433842.			−0.564070			−0.282035	−	0.959404i	$-0.591009\pi$
$877$	−433842.			−0.564070			−0.282035	+	0.959404i	$0.591009\pi$
$878$	295191.	+	712653.i	0.382925	+	0.924462i
$879$	−697295.			−0.902483
$880$	−150.636	−	363.668i	−0.000194520	−	0.000469613i
$881$	140720.	−	140720.i	0.181302	−	0.181302i	−0.610621	−	0.791923i	$-0.709080\pi$
$881$	140720.	−	140720.i	0.181302	−	0.181302i	0.791923	+	0.610621i	$0.209080\pi$
$882$	832.774	+	832.774i	0.00107051	+	0.00107051i
$883$	415615.	−	172153.i	0.533052	−	0.220797i	−0.0998872	−	0.994999i	$-0.531848\pi$
$883$	415615.	−	172153.i	0.533052	−	0.220797i	0.632939	+	0.774201i	$0.281848\pi$
$884$			932475.i			1.19325i
$885$	379897.	−	157358.i	0.485041	−	0.200911i
$886$		−	496055.i		−	0.631920i
$887$	−206003.	−	497336.i	−0.261835	−	0.632125i	0.737217	−	0.675656i	$-0.236139\pi$
$887$	−206003.	−	497336.i	−0.261835	−	0.632125i	−0.999052	+	0.0435306i	$0.986139\pi$
$888$	−279777.	+	115888.i	−0.354803	+	0.146964i
$889$	−1.07438e6	−	445022.i	−1.35942	−	0.563090i
$890$	−2025.90	+	4890.96i	−0.00255763	+	0.00617467i
$891$	−942.066	+	2274.35i	−0.00118666	+	0.00286485i
$892$		−	372649.i		−	0.468349i
$893$	−201479.	+	201479.i	−0.252654	+	0.252654i
$894$	−575591.	+	575591.i	−0.720177	+	0.720177i
$895$	−1.01662e6	−	421099.i	−1.26915	−	0.525701i
$896$	65689.2	−	27209.4i	0.0818235	−	0.0338924i
$897$	314455.	−	314455.i	0.390818	−	0.390818i
$898$	−815435.			−1.01120
$899$	−200574.	−	83080.5i	−0.248174	−	0.102797i
$900$	50457.4	+	50457.4i	0.0622931	+	0.0622931i
$901$			355822.i			0.438312i
$902$	−556.815	+	1315.55i	−0.000684381	+	0.00161695i
$903$	1.52297e6			1.86774
$904$	161110.	−	161110.i	0.197146	−	0.197146i
$905$	102122.	−	246543.i	0.124687	−	0.301020i
$906$			670639.i			0.817020i
$907$	780619.	+	780619.i	0.948909	+	0.948909i	0.998757	−	0.0498477i	$-0.0158736\pi$
$907$	780619.	+	780619.i	0.948909	+	0.948909i	−0.0498477	+	0.998757i	$0.515874\pi$
$908$	−61978.6	−	149629.i	−0.0751744	−	0.181487i
$909$	157766.	−	380881.i	0.190935	−	0.460958i
$910$	676358.	+	676358.i	0.816759	+	0.816759i
$911$	565715.	+	565715.i	0.681649	+	0.681649i	0.960372	−	0.278723i	$-0.0899110\pi$
$911$	565715.	+	565715.i	0.681649	+	0.681649i	−0.278723	+	0.960372i	$0.589911\pi$
$912$	82303.6			0.0989530
$913$	−3145.56	−	1302.93i	−0.00377360	−	0.00156308i
$914$	296570.	+	122843.i	0.355005	+	0.147048i
$915$	−333360.	+	804802.i	−0.398172	+	0.961273i
$916$	47912.5	+	115671.i	0.0571029	+	0.137859i
$917$	−788297.	+	326523.i	−0.937457	+	0.388307i
$918$	411745.			0.488589
$919$	469452.	+	1.13336e6i	0.555854	+	1.34195i	0.913022	+	0.407910i	$0.133742\pi$
$919$	469452.	+	1.13336e6i	0.555854	+	1.34195i	−0.357169	+	0.934040i	$0.616258\pi$
$920$	54908.0			0.0648724
$921$	−173725.	−	419409.i	−0.204806	−	0.494445i
$922$	229315.	−	229315.i	0.269756	−	0.269756i
$923$	−994103.	−	994103.i	−1.16688	−	1.16688i
$924$	−1215.63	+	503.529i	−0.00142382	+	0.000589767i
$925$			247220.i			0.288935i
$926$	−213552.	+	88456.2i	−0.249048	+	0.103159i
$927$		−	305695.i		−	0.355737i
$928$	−94955.9	−	229244.i	−0.110262	−	0.266196i
$929$	1.15851e6	−	479870.i	1.34236	−	0.556022i	0.408202	−	0.912892i	$-0.366156\pi$
$929$	1.15851e6	−	479870.i	1.34236	−	0.556022i	0.934154	+	0.356869i	$0.116156\pi$
$930$	94459.1	+	39126.3i	0.109214	+	0.0452379i
$931$	424.372	−	1024.52i	0.000489607	−	0.00118202i
$932$	−185702.	+	448325.i	−0.213789	+	0.516133i
$933$			1.67438e6i			1.92350i
$934$	752690.	−	752690.i	0.862825	−	0.862825i
$935$	1506.57	−	1506.57i	0.00172332	−	0.00172332i
$936$	304636.	+	126184.i	0.347720	+	0.144030i
$937$	1.15631e6	−	478959.i	1.31703	−	0.545531i	0.390101	−	0.920772i	$-0.372440\pi$
$937$	1.15631e6	−	478959.i	1.31703	−	0.545531i	0.926927	+	0.375241i	$0.122440\pi$
$938$	−274619.	+	274619.i	−0.312122	+	0.312122i
$939$	540730.			0.613266
$940$	−373760.	−	154816.i	−0.422996	−	0.175211i
$941$	−316717.	−	316717.i	−0.357678	−	0.357678i	0.505279	−	0.862956i	$-0.331390\pi$
$941$	−316717.	−	316717.i	−0.357678	−	0.357678i	−0.862956	+	0.505279i	$0.831390\pi$
$942$			1.25472e6i			1.41399i
$943$	−139816.	−	141984.i	−0.157229	−	0.159667i
$944$	−115305.			−0.129391
$945$	298654.	−	298654.i	0.334430	−	0.334430i
$946$	−904.778	+	2184.33i	−0.00101102	+	0.00244082i
$947$			285798.i			0.318683i	0.987223	+	0.159342i	$0.0509371\pi$
$947$			285798.i			0.318683i	−0.987223	+	0.159342i	$0.949063\pi$
$948$	−289046.	−	289046.i	−0.321626	−	0.321626i
$949$	151674.	+	366174.i	0.168415	+	0.406589i
$950$	25712.5	−	62075.5i	0.0284903	−	0.0687817i
$951$	−97351.0	−	97351.0i	−0.107641	−	0.107641i
$952$	272131.	+	272131.i	0.300265	+	0.300265i
$953$	42402.2			0.0466877			0.0233439	−	0.999727i	$-0.492569\pi$
$953$	42402.2			0.0466877			0.0233439	+	0.999727i	$0.492569\pi$
$954$	116246.	+	48150.5i	0.127726	+	0.0529059i
$955$	523492.	+	216837.i	0.573988	+	0.237754i
$956$	−109572.	+	264530.i	−0.119890	+	0.289440i
$957$	1757.23	+	4242.32i	0.00191869	+	0.00463212i
$958$	−739067.	+	306131.i	−0.805290	+	0.333562i
$959$	112062.			0.121848
$960$	44718.9	+	107961.i	0.0485231	+	0.117145i
$961$	898437.			0.972838
$962$	437168.	+	1.05542e6i	0.472387	+	1.14044i
$963$	103751.	−	103751.i	0.111877	−	0.111877i
$964$	−305677.	−	305677.i	−0.328934	−	0.328934i
$965$	−622549.	+	257868.i	−0.668527	+	0.276913i
$966$		−	183540.i		−	0.196687i
$967$	−1.23266e6	+	510583.i	−1.31822	+	0.546026i	−0.927273	−	0.374386i	$-0.877853\pi$
$967$	−1.23266e6	+	510583.i	−1.31822	+	0.546026i	−0.390950	+	0.920412i	$0.627853\pi$
$968$			331286.i			0.353551i
$969$	170480.	+	411575.i	0.181562	+	0.438330i
$970$	−751207.	+	311160.i	−0.798392	+	0.330705i
$971$	−167569.	−	69409.3i	−0.177728	−	0.0736172i	0.292045	−	0.956405i	$-0.405664\pi$
$971$	−167569.	−	69409.3i	−0.177728	−	0.0736172i	−0.469773	+	0.882787i	$0.655664\pi$
$972$	175459.	−	423597.i	0.185714	−	0.448353i
$973$	392977.	−	948730.i	0.415089	−	1.00211i
$974$		−	400595.i		−	0.422268i
$975$	546338.	−	546338.i	0.574714	−	0.574714i
$976$	172726.	−	172726.i	0.181325	−	0.181325i
$977$	−855308.	−	354280.i	−0.896053	−	0.371157i	−0.113352	−	0.993555i	$-0.536159\pi$
$977$	−855308.	−	354280.i	−0.896053	−	0.371157i	−0.782701	+	0.622398i	$0.786159\pi$
$978$	−1.06545e6	+	441322.i	−1.11392	+	0.461401i
$979$	−19.4253	+	19.4253i	−2.02676e−5	+	2.02676e-5i
$980$	1574.49			0.00163941
$981$	40148.7	+	16630.2i	0.0417190	+	0.0172806i
$982$	67857.6	+	67857.6i	0.0703681	+	0.0703681i
$983$		−	52895.1i		−	0.0547405i	−0.999625	−	0.0273702i	$-0.991287\pi$
$983$		−	52895.1i		−	0.0547405i	0.999625	−	0.0273702i	$-0.00871330\pi$
$984$	165300.	−	390544.i	0.170719	−	0.403348i
$985$	205306.			0.211607
$986$	949690.	−	949690.i	0.976851	−	0.976851i
$987$	−517501.	+	1.24936e6i	−0.531223	+	1.28249i
$988$		−	310478.i		−	0.318065i
$989$	−233202.	−	233202.i	−0.238419	−	0.238419i
$990$	−288.319	−	696.063i	−0.000294173	−	0.000710196i
$991$	−606512.	+	1.46425e6i	−0.617578	+	1.49097i	0.236930	+	0.971527i	$0.423859\pi$
$991$	−606512.	+	1.46425e6i	−0.617578	+	1.49097i	−0.854508	+	0.519439i	$0.826141\pi$
$992$	−20272.7	−	20272.7i	−0.0206010	−	0.0206010i
$993$	−1.23248e6	−	1.23248e6i	−1.24992	−	1.24992i
$994$	−580233.			−0.587259
$995$	−1.11390e6	−	461392.i	−1.12512	−	0.466041i
$996$	933811.	+	386797.i	0.941327	+	0.389910i
$997$	−448244.	+	1.08216e6i	−0.450946	+	1.08868i	0.521018	+	0.853546i	$0.325553\pi$
$997$	−448244.	+	1.08216e6i	−0.450946	+	1.08868i	−0.971963	+	0.235133i	$0.924447\pi$
$998$	−339308.	−	819162.i	−0.340669	−	0.822448i
$999$	466032.	−	193037.i	0.466965	−	0.193423i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.5.e.b.3.2	✓	28
41.14	odd	8	inner	82.5.e.b.55.2	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.5.e.b.3.2	✓	28	1.1	even	1	trivial
82.5.e.b.55.2	yes	28	41.14	odd	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.00000 - 2.00000i) q^{2} +(-4.26669 + 10.3007i) q^{3} -8.00000i q^{4} +(-14.4749 - 14.4749i) q^{5} +(12.0680 + 29.1348i) q^{6} +(18.7890 - 45.3606i) q^{7} +(-16.0000 - 16.0000i) q^{8} +(-30.6241 - 30.6241i) q^{9} -57.8996 q^{10} +(-0.277584 - 0.114979i) q^{11} +(82.4056 + 34.1335i) q^{12} +(128.763 - 310.862i) q^{13} +(-53.1433 - 128.299i) q^{14} +(210.861 - 87.3416i) q^{15} -64.0000 q^{16} +(-132.567 - 320.044i) q^{17} -122.496 q^{18} +(44.1395 + 106.562i) q^{19} +(-115.799 + 115.799i) q^{20} +(387.079 + 387.079i) q^{21} +(-0.785127 + 0.325210i) q^{22} -118.541i q^{23} +(233.078 - 96.5441i) q^{24} -205.955i q^{25} +(-364.198 - 879.251i) q^{26} +(-388.244 + 160.816i) q^{27} +(-362.885 - 150.312i) q^{28} +(-524.562 + 1266.41i) q^{29} +(247.039 - 596.406i) q^{30} +158.381i q^{31} +(-128.000 + 128.000i) q^{32} +(2.36873 - 2.36873i) q^{33} +(-905.222 - 374.955i) q^{34} +(-928.559 + 384.622i) q^{35} +(-244.993 + 244.993i) q^{36} -1200.36 q^{37} +(301.403 + 124.845i) q^{38} +(2652.70 + 2652.70i) q^{39} +463.197i q^{40} +(1197.76 - 1179.47i) q^{41} +1548.32 q^{42} +(1967.26 - 1967.26i) q^{43} +(-0.919834 + 2.22068i) q^{44} +886.560i q^{45} +(-237.083 - 237.083i) q^{46} +(945.358 + 2282.30i) q^{47} +(273.068 - 659.245i) q^{48} +(-6.79836 - 6.79836i) q^{49} +(-411.910 - 411.910i) q^{50} +3862.30 q^{51} +(-2486.90 - 1030.11i) q^{52} +(-948.973 - 393.078i) q^{53} +(-454.856 + 1098.12i) q^{54} +(2.35369 + 5.68232i) q^{55} +(-1026.39 + 425.146i) q^{56} -1285.99 q^{57} +(1483.69 + 3581.93i) q^{58} +1801.64 q^{59} +(-698.733 - 1686.89i) q^{60} +(-2698.84 + 2698.84i) q^{61} +(316.761 + 316.761i) q^{62} +(-1964.52 + 813.732i) q^{63} +512.000i q^{64} +(-6363.53 + 2635.86i) q^{65} -9.47493i q^{66} +(-1070.23 - 2583.76i) q^{67} +(-2560.35 + 1060.53i) q^{68} +(1221.06 + 505.779i) q^{69} +(-1087.87 + 2626.36i) q^{70} +(1598.94 - 3860.19i) q^{71} +979.970i q^{72} +(-832.923 + 832.923i) q^{73} +(-2400.72 + 2400.72i) q^{74} +(2121.48 + 878.746i) q^{75} +(852.497 - 353.116i) q^{76} +(-10.4311 + 10.4311i) q^{77} +10610.8 q^{78} +(-4234.05 - 1753.80i) q^{79} +(926.393 + 926.393i) q^{80} -8193.36i q^{81} +(36.5749 - 4754.45i) q^{82} +11331.9 q^{83} +(3096.64 - 3096.64i) q^{84} +(-2713.72 + 6551.49i) q^{85} -7869.05i q^{86} +(-10806.7 - 10806.7i) q^{87} +(2.60168 + 6.28102i) q^{88} +(34.9899 - 84.4732i) q^{89} +(1773.12 + 1773.12i) q^{90} +(-11681.6 - 11681.6i) q^{91} -948.332 q^{92} +(-1631.43 - 675.761i) q^{93} +(6455.31 + 2673.88i) q^{94} +(903.561 - 2181.39i) q^{95} +(-772.353 - 1864.63i) q^{96} +(12974.3 - 5374.13i) q^{97} -27.1935 q^{98} +(4.97963 + 12.0219i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 56 q^{2} + 16 q^{6} - 448 q^{8} + 24 q^{9} - 328 q^{11} + 64 q^{12} - 60 q^{13} + 192 q^{14} - 340 q^{15} - 1792 q^{16} - 136 q^{17} + 96 q^{18} + 600 q^{19} - 1580 q^{21} - 1768 q^{22} + 128 q^{24}+ \cdots - 19224 q^{99}+O(q^{100}) \) 28 * q + 56 * q^2 + 16 * q^6 - 448 * q^8 + 24 * q^9 - 328 * q^11 + 64 * q^12 - 60 * q^13 + 192 * q^14 - 340 * q^15 - 1792 * q^16 - 136 * q^17 + 96 * q^18 + 600 * q^19 - 1580 * q^21 - 1768 * q^22 + 128 * q^24 - 192 * q^26 + 2148 * q^27 + 768 * q^28 - 2564 * q^29 - 1048 * q^30 - 3584 * q^32 + 6420 * q^33 - 2040 * q^34 + 4656 * q^35 + 192 * q^36 + 7792 * q^37 + 896 * q^38 + 1232 * q^39 + 5584 * q^41 - 6320 * q^42 - 3788 * q^43 - 4448 * q^44 - 1648 * q^46 - 2000 * q^47 + 6312 * q^49 + 7048 * q^50 - 6208 * q^51 - 288 * q^52 + 1924 * q^53 + 1544 * q^54 + 17048 * q^55 + 1536 * q^56 + 11992 * q^57 + 2864 * q^58 + 11376 * q^59 - 1472 * q^60 - 9600 * q^61 - 9904 * q^62 - 13656 * q^63 - 2156 * q^65 - 22336 * q^67 - 7072 * q^68 + 17044 * q^69 + 16392 * q^70 + 2808 * q^71 + 6588 * q^73 + 15584 * q^74 + 4980 * q^75 - 1216 * q^76 + 9204 * q^77 + 4928 * q^78 - 8796 * q^79 + 5904 * q^82 - 24248 * q^83 - 12640 * q^84 - 28616 * q^85 - 55700 * q^87 - 3648 * q^88 - 4844 * q^89 + 11360 * q^90 - 53332 * q^91 - 6592 * q^92 - 44176 * q^93 + 552 * q^94 + 7628 * q^95 - 1024 * q^96 - 17844 * q^97 + 25248 * q^98 - 19224 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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