Properties

Label 177.6.d.b.176.20
Level $177$
Weight $6$
Character 177.176
Analytic conductor $28.388$
Analytic rank $0$
Dimension $92$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 177.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.3879361069\)
Analytic rank: \(0\)
Dimension: \(92\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 176.20
Character \(\chi\) \(=\) 177.176
Dual form 177.6.d.b.176.19

$q$-expansion

\(f(q)\) \(=\) \(q-7.43533 q^{2} +(-12.1962 + 9.70834i) q^{3} +23.2842 q^{4} -26.1059i q^{5} +(90.6831 - 72.1847i) q^{6} +171.796 q^{7} +64.8050 q^{8} +(54.4964 - 236.810i) q^{9} +O(q^{10})\) \(q-7.43533 q^{2} +(-12.1962 + 9.70834i) q^{3} +23.2842 q^{4} -26.1059i q^{5} +(90.6831 - 72.1847i) q^{6} +171.796 q^{7} +64.8050 q^{8} +(54.4964 - 236.810i) q^{9} +194.106i q^{10} +440.416 q^{11} +(-283.979 + 226.051i) q^{12} +280.019i q^{13} -1277.36 q^{14} +(253.445 + 318.393i) q^{15} -1226.94 q^{16} -1401.23i q^{17} +(-405.199 + 1760.76i) q^{18} +616.070 q^{19} -607.854i q^{20} +(-2095.26 + 1667.85i) q^{21} -3274.64 q^{22} -4168.15 q^{23} +(-790.378 + 629.149i) q^{24} +2443.48 q^{25} -2082.04i q^{26} +(1634.38 + 3417.26i) q^{27} +4000.13 q^{28} -6604.87i q^{29} +(-1884.44 - 2367.36i) q^{30} +5981.69i q^{31} +7048.95 q^{32} +(-5371.42 + 4275.71i) q^{33} +10418.6i q^{34} -4484.88i q^{35} +(1268.90 - 5513.93i) q^{36} +2032.97i q^{37} -4580.68 q^{38} +(-2718.52 - 3415.18i) q^{39} -1691.79i q^{40} -1979.58i q^{41} +(15579.0 - 12401.0i) q^{42} +2469.75i q^{43} +10254.7 q^{44} +(-6182.14 - 1422.68i) q^{45} +30991.6 q^{46} +4981.17 q^{47} +(14964.1 - 11911.6i) q^{48} +12706.9 q^{49} -18168.1 q^{50} +(13603.6 + 17089.7i) q^{51} +6520.02i q^{52} -36193.5i q^{53} +(-12152.2 - 25408.5i) q^{54} -11497.4i q^{55} +11133.2 q^{56} +(-7513.73 + 5981.01i) q^{57} +49109.4i q^{58} +(3990.97 + 26438.5i) q^{59} +(5901.25 + 7413.53i) q^{60} -76.2899i q^{61} -44475.8i q^{62} +(9362.26 - 40683.1i) q^{63} -13149.2 q^{64} +7310.15 q^{65} +(39938.3 - 31791.3i) q^{66} -43781.8i q^{67} -32626.4i q^{68} +(50835.7 - 40465.8i) q^{69} +33346.6i q^{70} +5732.24i q^{71} +(3531.64 - 15346.5i) q^{72} -79764.2i q^{73} -15115.8i q^{74} +(-29801.3 + 23722.2i) q^{75} +14344.7 q^{76} +75661.7 q^{77} +(20213.1 + 25393.0i) q^{78} -52467.3 q^{79} +32030.4i q^{80} +(-53109.3 - 25810.6i) q^{81} +14718.8i q^{82} -12824.6 q^{83} +(-48786.5 + 38834.6i) q^{84} -36580.2 q^{85} -18363.4i q^{86} +(64122.3 + 80554.5i) q^{87} +28541.2 q^{88} +91752.4 q^{89} +(45966.3 + 10578.1i) q^{90} +48106.2i q^{91} -97051.9 q^{92} +(-58072.2 - 72954.1i) q^{93} -37036.7 q^{94} -16083.0i q^{95} +(-85970.7 + 68433.6i) q^{96} +124010. i q^{97} -94479.7 q^{98} +(24001.1 - 104295. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 92q + 22q^{3} + 1724q^{4} - 80q^{7} + 2q^{9} + O(q^{10}) \) \( 92q + 22q^{3} + 1724q^{4} - 80q^{7} + 2q^{9} - 1244q^{12} + 1116q^{15} + 14724q^{16} + 1784q^{19} + 6388q^{21} - 8140q^{22} - 48208q^{25} - 6458q^{27} - 19092q^{28} - 20832q^{36} - 134984q^{45} + 51180q^{46} + 61720q^{48} + 174556q^{49} + 8332q^{51} + 236784q^{57} + 375208q^{60} - 429890q^{63} + 561472q^{64} - 11596q^{66} + 169948q^{75} + 111488q^{76} + 356264q^{78} + 180260q^{79} + 79554q^{81} + 269308q^{84} + 111028q^{85} - 318764q^{87} - 1242976q^{88} - 513608q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(-1\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.43533 −1.31439 −0.657197 0.753719i \(-0.728258\pi\)
−0.657197 + 0.753719i \(0.728258\pi\)
\(3\) −12.1962 + 9.70834i −0.782389 + 0.622790i
\(4\) 23.2842 0.727631
\(5\) 26.1059i 0.466996i −0.972357 0.233498i \(-0.924983\pi\)
0.972357 0.233498i \(-0.0750172\pi\)
\(6\) 90.6831 72.1847i 1.02837 0.818591i
\(7\) 171.796 1.32516 0.662579 0.748992i \(-0.269462\pi\)
0.662579 + 0.748992i \(0.269462\pi\)
\(8\) 64.8050 0.358001
\(9\) 54.4964 236.810i 0.224265 0.974528i
\(10\) 194.106i 0.613816i
\(11\) 440.416 1.09744 0.548721 0.836006i \(-0.315115\pi\)
0.548721 + 0.836006i \(0.315115\pi\)
\(12\) −283.979 + 226.051i −0.569290 + 0.453161i
\(13\) 280.019i 0.459547i 0.973244 + 0.229773i \(0.0737985\pi\)
−0.973244 + 0.229773i \(0.926201\pi\)
\(14\) −1277.36 −1.74178
\(15\) 253.445 + 318.393i 0.290840 + 0.365372i
\(16\) −1226.94 −1.19818
\(17\) 1401.23i 1.17594i −0.808882 0.587971i \(-0.799927\pi\)
0.808882 0.587971i \(-0.200073\pi\)
\(18\) −405.199 + 1760.76i −0.294772 + 1.28091i
\(19\) 616.070 0.391513 0.195756 0.980653i \(-0.437284\pi\)
0.195756 + 0.980653i \(0.437284\pi\)
\(20\) 607.854i 0.339800i
\(21\) −2095.26 + 1667.85i −1.03679 + 0.825296i
\(22\) −3274.64 −1.44247
\(23\) −4168.15 −1.64295 −0.821473 0.570247i \(-0.806848\pi\)
−0.821473 + 0.570247i \(0.806848\pi\)
\(24\) −790.378 + 629.149i −0.280096 + 0.222959i
\(25\) 2443.48 0.781915
\(26\) 2082.04i 0.604026i
\(27\) 1634.38 + 3417.26i 0.431464 + 0.902130i
\(28\) 4000.13 0.964226
\(29\) 6604.87i 1.45837i −0.684314 0.729187i \(-0.739898\pi\)
0.684314 0.729187i \(-0.260102\pi\)
\(30\) −1884.44 2367.36i −0.382279 0.480243i
\(31\) 5981.69i 1.11794i 0.829187 + 0.558971i \(0.188804\pi\)
−0.829187 + 0.558971i \(0.811196\pi\)
\(32\) 7048.95 1.21689
\(33\) −5371.42 + 4275.71i −0.858626 + 0.683476i
\(34\) 10418.6i 1.54565i
\(35\) 4484.88i 0.618844i
\(36\) 1268.90 5513.93i 0.163182 0.709096i
\(37\) 2032.97i 0.244133i 0.992522 + 0.122067i \(0.0389522\pi\)
−0.992522 + 0.122067i \(0.961048\pi\)
\(38\) −4580.68 −0.514602
\(39\) −2718.52 3415.18i −0.286201 0.359544i
\(40\) 1691.79i 0.167185i
\(41\) 1979.58i 0.183913i −0.995763 0.0919567i \(-0.970688\pi\)
0.995763 0.0919567i \(-0.0293121\pi\)
\(42\) 15579.0 12401.0i 1.36275 1.08476i
\(43\) 2469.75i 0.203695i 0.994800 + 0.101848i \(0.0324755\pi\)
−0.994800 + 0.101848i \(0.967525\pi\)
\(44\) 10254.7 0.798532
\(45\) −6182.14 1422.68i −0.455101 0.104731i
\(46\) 30991.6 2.15948
\(47\) 4981.17 0.328917 0.164459 0.986384i \(-0.447412\pi\)
0.164459 + 0.986384i \(0.447412\pi\)
\(48\) 14964.1 11911.6i 0.937446 0.746217i
\(49\) 12706.9 0.756046
\(50\) −18168.1 −1.02774
\(51\) 13603.6 + 17089.7i 0.732365 + 0.920044i
\(52\) 6520.02i 0.334380i
\(53\) 36193.5i 1.76987i −0.465717 0.884934i \(-0.654204\pi\)
0.465717 0.884934i \(-0.345796\pi\)
\(54\) −12152.2 25408.5i −0.567114 1.18575i
\(55\) 11497.4i 0.512501i
\(56\) 11133.2 0.474408
\(57\) −7513.73 + 5981.01i −0.306315 + 0.243830i
\(58\) 49109.4i 1.91688i
\(59\) 3990.97 + 26438.5i 0.149262 + 0.988798i
\(60\) 5901.25 + 7413.53i 0.211624 + 0.265856i
\(61\) 76.2899i 0.00262508i −0.999999 0.00131254i \(-0.999582\pi\)
0.999999 0.00131254i \(-0.000417794\pi\)
\(62\) 44475.8i 1.46942i
\(63\) 9362.26 40683.1i 0.297187 1.29140i
\(64\) −13149.2 −0.401282
\(65\) 7310.15 0.214607
\(66\) 39938.3 31791.3i 1.12857 0.898356i
\(67\) 43781.8i 1.19154i −0.803157 0.595768i \(-0.796848\pi\)
0.803157 0.595768i \(-0.203152\pi\)
\(68\) 32626.4i 0.855652i
\(69\) 50835.7 40465.8i 1.28542 1.02321i
\(70\) 33346.6i 0.813404i
\(71\) 5732.24i 0.134952i 0.997721 + 0.0674759i \(0.0214946\pi\)
−0.997721 + 0.0674759i \(0.978505\pi\)
\(72\) 3531.64 15346.5i 0.0802870 0.348882i
\(73\) 79764.2i 1.75187i −0.482432 0.875933i \(-0.660247\pi\)
0.482432 0.875933i \(-0.339753\pi\)
\(74\) 15115.8i 0.320887i
\(75\) −29801.3 + 23722.2i −0.611762 + 0.486969i
\(76\) 14344.7 0.284877
\(77\) 75661.7 1.45428
\(78\) 20213.1 + 25393.0i 0.376181 + 0.472583i
\(79\) −52467.3 −0.945847 −0.472924 0.881103i \(-0.656801\pi\)
−0.472924 + 0.881103i \(0.656801\pi\)
\(80\) 32030.4i 0.559547i
\(81\) −53109.3 25810.6i −0.899410 0.437105i
\(82\) 14718.8i 0.241735i
\(83\) −12824.6 −0.204338 −0.102169 0.994767i \(-0.532578\pi\)
−0.102169 + 0.994767i \(0.532578\pi\)
\(84\) −48786.5 + 38834.6i −0.754400 + 0.600510i
\(85\) −36580.2 −0.549160
\(86\) 18363.4i 0.267736i
\(87\) 64122.3 + 80554.5i 0.908261 + 1.14102i
\(88\) 28541.2 0.392885
\(89\) 91752.4 1.22784 0.613921 0.789367i \(-0.289591\pi\)
0.613921 + 0.789367i \(0.289591\pi\)
\(90\) 45966.3 + 10578.1i 0.598181 + 0.137658i
\(91\) 48106.2i 0.608973i
\(92\) −97051.9 −1.19546
\(93\) −58072.2 72954.1i −0.696244 0.874666i
\(94\) −37036.7 −0.432327
\(95\) 16083.0i 0.182835i
\(96\) −85970.7 + 68433.6i −0.952078 + 0.757864i
\(97\) 124010.i 1.33822i 0.743163 + 0.669111i \(0.233325\pi\)
−0.743163 + 0.669111i \(0.766675\pi\)
\(98\) −94479.7 −0.993742
\(99\) 24001.1 104295.i 0.246118 1.06949i
\(100\) 56894.5 0.568945
\(101\) 25569.9 0.249417 0.124709 0.992193i \(-0.460200\pi\)
0.124709 + 0.992193i \(0.460200\pi\)
\(102\) −101147. 127068.i −0.962616 1.20930i
\(103\) 144114.i 1.33848i 0.743045 + 0.669242i \(0.233381\pi\)
−0.743045 + 0.669242i \(0.766619\pi\)
\(104\) 18146.7i 0.164518i
\(105\) 43540.8 + 54698.7i 0.385410 + 0.484177i
\(106\) 269111.i 2.32630i
\(107\) 65308.3i 0.551453i 0.961236 + 0.275727i \(0.0889184\pi\)
−0.961236 + 0.275727i \(0.911082\pi\)
\(108\) 38055.3 + 79568.2i 0.313946 + 0.656417i
\(109\) 113518.i 0.915166i −0.889167 0.457583i \(-0.848715\pi\)
0.889167 0.457583i \(-0.151285\pi\)
\(110\) 85487.3i 0.673628i
\(111\) −19736.8 24794.6i −0.152044 0.191007i
\(112\) −210783. −1.58778
\(113\) −103901. −0.765464 −0.382732 0.923859i \(-0.625017\pi\)
−0.382732 + 0.923859i \(0.625017\pi\)
\(114\) 55867.1 44470.8i 0.402619 0.320489i
\(115\) 108813.i 0.767249i
\(116\) 153789.i 1.06116i
\(117\) 66311.5 + 15260.1i 0.447841 + 0.103060i
\(118\) −29674.2 196579.i −0.196189 1.29967i
\(119\) 240725.i 1.55831i
\(120\) 16424.5 + 20633.5i 0.104121 + 0.130804i
\(121\) 32915.4 0.204379
\(122\) 567.241i 0.00345039i
\(123\) 19218.4 + 24143.4i 0.114539 + 0.143892i
\(124\) 139279.i 0.813449i
\(125\) 145370.i 0.832147i
\(126\) −69611.5 + 302492.i −0.390620 + 1.69741i
\(127\) 239071. 1.31528 0.657639 0.753333i \(-0.271555\pi\)
0.657639 + 0.753333i \(0.271555\pi\)
\(128\) −127798. −0.689443
\(129\) −23977.1 30121.6i −0.126860 0.159369i
\(130\) −54353.4 −0.282077
\(131\) −29466.1 −0.150019 −0.0750093 0.997183i \(-0.523899\pi\)
−0.0750093 + 0.997183i \(0.523899\pi\)
\(132\) −125069. + 99556.3i −0.624763 + 0.497318i
\(133\) 105838. 0.518817
\(134\) 325532.i 1.56615i
\(135\) 89210.6 42667.0i 0.421291 0.201492i
\(136\) 90806.6i 0.420988i
\(137\) 320384.i 1.45837i −0.684314 0.729187i \(-0.739898\pi\)
0.684314 0.729187i \(-0.260102\pi\)
\(138\) −377980. + 300877.i −1.68955 + 1.34490i
\(139\) 46413.4 0.203754 0.101877 0.994797i \(-0.467515\pi\)
0.101877 + 0.994797i \(0.467515\pi\)
\(140\) 104427.i 0.450290i
\(141\) −60751.5 + 48358.9i −0.257341 + 0.204846i
\(142\) 42621.1i 0.177380i
\(143\) 123325.i 0.504326i
\(144\) −66863.9 + 290552.i −0.268711 + 1.16766i
\(145\) −172426. −0.681055
\(146\) 593074.i 2.30264i
\(147\) −154976. + 123362.i −0.591522 + 0.470858i
\(148\) 47336.1i 0.177639i
\(149\) 436747. 1.61163 0.805814 0.592169i \(-0.201728\pi\)
0.805814 + 0.592169i \(0.201728\pi\)
\(150\) 221583. 176382.i 0.804095 0.640069i
\(151\) 440574.i 1.57245i −0.617942 0.786224i \(-0.712033\pi\)
0.617942 0.786224i \(-0.287967\pi\)
\(152\) 39924.4 0.140162
\(153\) −331825. 76361.8i −1.14599 0.263723i
\(154\) −562570. −1.91150
\(155\) 156157. 0.522075
\(156\) −63298.6 79519.7i −0.208249 0.261616i
\(157\) 254134.i 0.822836i −0.911447 0.411418i \(-0.865034\pi\)
0.911447 0.411418i \(-0.134966\pi\)
\(158\) 390112. 1.24322
\(159\) 351379. + 441424.i 1.10226 + 1.38472i
\(160\) 184019.i 0.568280i
\(161\) −716071. −2.17717
\(162\) 394885. + 191911.i 1.18218 + 0.574528i
\(163\) −375888. −1.10813 −0.554063 0.832475i \(-0.686923\pi\)
−0.554063 + 0.832475i \(0.686923\pi\)
\(164\) 46092.9i 0.133821i
\(165\) 111621. + 140226.i 0.319180 + 0.400975i
\(166\) 95355.3 0.268580
\(167\) 154944.i 0.429916i −0.976623 0.214958i \(-0.931039\pi\)
0.976623 0.214958i \(-0.0689614\pi\)
\(168\) −135784. + 108085.i −0.371171 + 0.295456i
\(169\) 292882. 0.788817
\(170\) 271986. 0.721813
\(171\) 33573.6 145892.i 0.0878026 0.381540i
\(172\) 57506.0i 0.148215i
\(173\) −262409. −0.666597 −0.333298 0.942821i \(-0.608162\pi\)
−0.333298 + 0.942821i \(0.608162\pi\)
\(174\) −476771. 598950.i −1.19381 1.49974i
\(175\) 419781. 1.03616
\(176\) −540365. −1.31494
\(177\) −305349. 283705.i −0.732594 0.680666i
\(178\) −682210. −1.61387
\(179\) 261369. 0.609708 0.304854 0.952399i \(-0.401392\pi\)
0.304854 + 0.952399i \(0.401392\pi\)
\(180\) −143946. 33125.8i −0.331145 0.0762054i
\(181\) 134751. 0.305729 0.152865 0.988247i \(-0.451150\pi\)
0.152865 + 0.988247i \(0.451150\pi\)
\(182\) 357686.i 0.800430i
\(183\) 740.648 + 930.450i 0.00163487 + 0.00205383i
\(184\) −270117. −0.588176
\(185\) 53072.5 0.114009
\(186\) 431786. + 542438.i 0.915138 + 1.14966i
\(187\) 617123.i 1.29053i
\(188\) 115982. 0.239330
\(189\) 280781. + 587072.i 0.571758 + 1.19547i
\(190\) 119583.i 0.240317i
\(191\) 848340. 1.68262 0.841311 0.540552i \(-0.181785\pi\)
0.841311 + 0.540552i \(0.181785\pi\)
\(192\) 160371. 127657.i 0.313958 0.249914i
\(193\) 880120. 1.70078 0.850391 0.526152i \(-0.176366\pi\)
0.850391 + 0.526152i \(0.176366\pi\)
\(194\) 922057.i 1.75895i
\(195\) −89156.3 + 70969.4i −0.167906 + 0.133655i
\(196\) 295869. 0.550122
\(197\) 100950.i 0.185329i −0.995697 0.0926643i \(-0.970462\pi\)
0.995697 0.0926643i \(-0.0295383\pi\)
\(198\) −178456. + 775469.i −0.323496 + 1.40573i
\(199\) 321301. 0.575148 0.287574 0.957758i \(-0.407151\pi\)
0.287574 + 0.957758i \(0.407151\pi\)
\(200\) 158350. 0.279926
\(201\) 425049. + 533974.i 0.742076 + 0.932244i
\(202\) −190121. −0.327832
\(203\) 1.13469e6i 1.93258i
\(204\) 316748. + 397919.i 0.532891 + 0.669452i
\(205\) −51678.7 −0.0858868
\(206\) 1.07154e6i 1.75929i
\(207\) −227149. + 987060.i −0.368455 + 1.60110i
\(208\) 343567.i 0.550622i
\(209\) 271327. 0.429663
\(210\) −323740. 406703.i −0.506580 0.636398i
\(211\) 1.10823e6i 1.71366i −0.515603 0.856828i \(-0.672432\pi\)
0.515603 0.856828i \(-0.327568\pi\)
\(212\) 842735.i 1.28781i
\(213\) −55650.6 69911.8i −0.0840467 0.105585i
\(214\) 485589.i 0.724827i
\(215\) 64474.9 0.0951250
\(216\) 105916. + 221456.i 0.154464 + 0.322963i
\(217\) 1.02763e6i 1.48145i
\(218\) 844047.i 1.20289i
\(219\) 774378. + 972823.i 1.09105 + 1.37064i
\(220\) 267709.i 0.372911i
\(221\) 392371. 0.540401
\(222\) 146749. + 184356.i 0.199845 + 0.251059i
\(223\) 890367. 1.19897 0.599483 0.800387i \(-0.295373\pi\)
0.599483 + 0.800387i \(0.295373\pi\)
\(224\) 1.21098e6 1.61257
\(225\) 133161. 578642.i 0.175356 0.761998i
\(226\) 772540. 1.00612
\(227\) −1.50924e6 −1.94398 −0.971991 0.235017i \(-0.924485\pi\)
−0.971991 + 0.235017i \(0.924485\pi\)
\(228\) −174951. + 139263.i −0.222884 + 0.177418i
\(229\) 667818.i 0.841530i −0.907170 0.420765i \(-0.861762\pi\)
0.907170 0.420765i \(-0.138238\pi\)
\(230\) 809062.i 1.00847i
\(231\) −922788. + 734550.i −1.13782 + 0.905714i
\(232\) 428029.i 0.522099i
\(233\) −982501. −1.18561 −0.592807 0.805345i \(-0.701980\pi\)
−0.592807 + 0.805345i \(0.701980\pi\)
\(234\) −493048. 113464.i −0.588640 0.135462i
\(235\) 130038.i 0.153603i
\(236\) 92926.6 + 615600.i 0.108608 + 0.719479i
\(237\) 639904. 509370.i 0.740020 0.589064i
\(238\) 1.78987e6i 2.04823i
\(239\) 152933.i 0.173183i 0.996244 + 0.0865917i \(0.0275976\pi\)
−0.996244 + 0.0865917i \(0.972402\pi\)
\(240\) −310961. 390650.i −0.348480 0.437784i
\(241\) 139801. 0.155048 0.0775241 0.996990i \(-0.475299\pi\)
0.0775241 + 0.996990i \(0.475299\pi\)
\(242\) −244737. −0.268634
\(243\) 898312. 200810.i 0.975914 0.218158i
\(244\) 1776.35i 0.00191009i
\(245\) 331724.i 0.353070i
\(246\) −142895. 179514.i −0.150550 0.189131i
\(247\) 172512.i 0.179919i
\(248\) 387644.i 0.400224i
\(249\) 156412. 124506.i 0.159872 0.127260i
\(250\) 1.08088e6i 1.09377i
\(251\) 787440.i 0.788920i −0.918913 0.394460i \(-0.870932\pi\)
0.918913 0.394460i \(-0.129068\pi\)
\(252\) 217993. 947272.i 0.216242 0.939665i
\(253\) −1.83572e6 −1.80304
\(254\) −1.77757e6 −1.72879
\(255\) 446141. 355133.i 0.429657 0.342012i
\(256\) 1.37099e6 1.30748
\(257\) 381321.i 0.360129i 0.983655 + 0.180064i \(0.0576306\pi\)
−0.983655 + 0.180064i \(0.942369\pi\)
\(258\) 178278. + 223964.i 0.166743 + 0.209474i
\(259\) 349256.i 0.323515i
\(260\) 170211. 0.156154
\(261\) −1.56410e6 359942.i −1.42123 0.327062i
\(262\) 219090. 0.197183
\(263\) 234006.i 0.208611i −0.994545 0.104306i \(-0.966738\pi\)
0.994545 0.104306i \(-0.0332620\pi\)
\(264\) −348095. + 277087.i −0.307389 + 0.244685i
\(265\) −944862. −0.826521
\(266\) −786943. −0.681929
\(267\) −1.11903e6 + 890763.i −0.960650 + 0.764688i
\(268\) 1.01942e6i 0.866997i
\(269\) −275892. −0.232466 −0.116233 0.993222i \(-0.537082\pi\)
−0.116233 + 0.993222i \(0.537082\pi\)
\(270\) −663311. + 317243.i −0.553742 + 0.264840i
\(271\) 2.13938e6 1.76956 0.884779 0.466012i \(-0.154310\pi\)
0.884779 + 0.466012i \(0.154310\pi\)
\(272\) 1.71922e6i 1.40900i
\(273\) −467031. 586715.i −0.379262 0.476453i
\(274\) 2.38216e6i 1.91688i
\(275\) 1.07615e6 0.858106
\(276\) 1.18367e6 942212.i 0.935313 0.744519i
\(277\) −1.60167e6 −1.25422 −0.627109 0.778931i \(-0.715762\pi\)
−0.627109 + 0.778931i \(0.715762\pi\)
\(278\) −345099. −0.267813
\(279\) 1.41653e6 + 325980.i 1.08947 + 0.250715i
\(280\) 290643.i 0.221546i
\(281\) 255652.i 0.193145i 0.995326 + 0.0965724i \(0.0307879\pi\)
−0.995326 + 0.0965724i \(0.969212\pi\)
\(282\) 451708. 359564.i 0.338248 0.269249i
\(283\) 2.43336e6i 1.80609i 0.429541 + 0.903047i \(0.358675\pi\)
−0.429541 + 0.903047i \(0.641325\pi\)
\(284\) 133471.i 0.0981951i
\(285\) 156140. + 196153.i 0.113868 + 0.143048i
\(286\) 916963.i 0.662883i
\(287\) 340084.i 0.243715i
\(288\) 384142. 1.66926e6i 0.272905 1.18589i
\(289\) −543579. −0.382841
\(290\) 1.28204e6 0.895175
\(291\) −1.20393e6 1.51246e6i −0.833431 1.04701i
\(292\) 1.85724e6i 1.27471i
\(293\) 858924.i 0.584501i 0.956342 + 0.292251i \(0.0944042\pi\)
−0.956342 + 0.292251i \(0.905596\pi\)
\(294\) 1.15230e6 917241.i 0.777492 0.618892i
\(295\) 690201. 104188.i 0.461764 0.0697047i
\(296\) 131747.i 0.0873999i
\(297\) 719809. + 1.50502e6i 0.473507 + 0.990035i
\(298\) −3.24736e6 −2.11831
\(299\) 1.16716e6i 0.755011i
\(300\) −693899. + 552351.i −0.445136 + 0.354333i
\(301\) 424293.i 0.269929i
\(302\) 3.27581e6i 2.06682i
\(303\) −311857. + 248242.i −0.195141 + 0.155335i
\(304\) −755881. −0.469105
\(305\) −1991.61 −0.00122590
\(306\) 2.46723e6 + 567775.i 1.50628 + 0.346635i
\(307\) 239480. 0.145019 0.0725094 0.997368i \(-0.476899\pi\)
0.0725094 + 0.997368i \(0.476899\pi\)
\(308\) 1.76172e6 1.05818
\(309\) −1.39911e6 1.75765e6i −0.833594 1.04721i
\(310\) −1.16108e6 −0.686212
\(311\) 2.91324e6i 1.70795i −0.520312 0.853976i \(-0.674184\pi\)
0.520312 0.853976i \(-0.325816\pi\)
\(312\) −176174. 221321.i −0.102460 0.128717i
\(313\) 1.30732e6i 0.754261i −0.926160 0.377130i \(-0.876911\pi\)
0.926160 0.377130i \(-0.123089\pi\)
\(314\) 1.88957e6i 1.08153i
\(315\) −1.06207e6 244410.i −0.603081 0.138785i
\(316\) −1.22166e6 −0.688227
\(317\) 2.26014e6i 1.26324i 0.775277 + 0.631622i \(0.217610\pi\)
−0.775277 + 0.631622i \(0.782390\pi\)
\(318\) −2.61262e6 3.28214e6i −1.44880 1.82007i
\(319\) 2.90889e6i 1.60048i
\(320\) 343271.i 0.187397i
\(321\) −634035. 796515.i −0.343440 0.431451i
\(322\) 5.32423e6 2.86165
\(323\) 863254.i 0.460397i
\(324\) −1.23661e6 600979.i −0.654438 0.318051i
\(325\) 684223.i 0.359327i
\(326\) 2.79485e6 1.45651
\(327\) 1.10207e6 + 1.38450e6i 0.569956 + 0.716016i
\(328\) 128287.i 0.0658411i
\(329\) 855745. 0.435868
\(330\) −829940. 1.04262e6i −0.419529 0.527039i
\(331\) 967839. 0.485549 0.242775 0.970083i \(-0.421942\pi\)
0.242775 + 0.970083i \(0.421942\pi\)
\(332\) −298611. −0.148683
\(333\) 481429. + 110790.i 0.237915 + 0.0547506i
\(334\) 1.15206e6i 0.565078i
\(335\) −1.14296e6 −0.556442
\(336\) 2.57077e6 2.04636e6i 1.24227 0.988856i
\(337\) 3.29932e6i 1.58252i 0.611479 + 0.791261i \(0.290575\pi\)
−0.611479 + 0.791261i \(0.709425\pi\)
\(338\) −2.17768e6 −1.03682
\(339\) 1.26720e6 1.00871e6i 0.598891 0.476723i
\(340\) −851741. −0.399586
\(341\) 2.63443e6i 1.22688i
\(342\) −249631. + 1.08475e6i −0.115407 + 0.501494i
\(343\) −704388. −0.323278
\(344\) 160052.i 0.0729231i
\(345\) −1.05639e6 1.32711e6i −0.477835 0.600287i
\(346\) 1.95110e6 0.876171
\(347\) −378954. −0.168952 −0.0844760 0.996426i \(-0.526922\pi\)
−0.0844760 + 0.996426i \(0.526922\pi\)
\(348\) 1.49303e6 + 1.87565e6i 0.660879 + 0.830238i
\(349\) 1.47081e6i 0.646388i −0.946333 0.323194i \(-0.895243\pi\)
0.946333 0.323194i \(-0.104757\pi\)
\(350\) −3.12121e6 −1.36192
\(351\) −956901. + 457659.i −0.414571 + 0.198278i
\(352\) 3.10447e6 1.33546
\(353\) 877815. 0.374944 0.187472 0.982270i \(-0.439971\pi\)
0.187472 + 0.982270i \(0.439971\pi\)
\(354\) 2.27037e6 + 2.10944e6i 0.962917 + 0.894662i
\(355\) 149645. 0.0630220
\(356\) 2.13638e6 0.893415
\(357\) 2.33704e6 + 2.93594e6i 0.970500 + 1.21920i
\(358\) −1.94337e6 −0.801396
\(359\) 3.25620e6i 1.33344i 0.745306 + 0.666722i \(0.232303\pi\)
−0.745306 + 0.666722i \(0.767697\pi\)
\(360\) −400634. 92196.6i −0.162926 0.0374937i
\(361\) −2.09656e6 −0.846718
\(362\) −1.00192e6 −0.401849
\(363\) −401444. + 319554.i −0.159904 + 0.127285i
\(364\) 1.12011e6i 0.443107i
\(365\) −2.08231e6 −0.818115
\(366\) −5506.96 6918.20i −0.00214887 0.00269955i
\(367\) 3.59027e6i 1.39143i −0.718316 0.695717i \(-0.755087\pi\)
0.718316 0.695717i \(-0.244913\pi\)
\(368\) 5.11407e6 1.96855
\(369\) −468785. 107880.i −0.179229 0.0412454i
\(370\) −394612. −0.149853
\(371\) 6.21790e6i 2.34536i
\(372\) −1.35216e6 1.69868e6i −0.506608 0.636434i
\(373\) −1.15069e6 −0.428238 −0.214119 0.976808i \(-0.568688\pi\)
−0.214119 + 0.976808i \(0.568688\pi\)
\(374\) 4.58851e6i 1.69626i
\(375\) 1.41130e6 + 1.77297e6i 0.518253 + 0.651063i
\(376\) 322805. 0.117753
\(377\) 1.84949e6 0.670192
\(378\) −2.08770e6 4.36508e6i −0.751515 1.57131i
\(379\) −238627. −0.0853338 −0.0426669 0.999089i \(-0.513585\pi\)
−0.0426669 + 0.999089i \(0.513585\pi\)
\(380\) 374480.i 0.133036i
\(381\) −2.91577e6 + 2.32098e6i −1.02906 + 0.819142i
\(382\) −6.30769e6 −2.21163
\(383\) 1.38488e6i 0.482410i −0.970474 0.241205i \(-0.922457\pi\)
0.970474 0.241205i \(-0.0775427\pi\)
\(384\) 1.55865e6 1.24070e6i 0.539413 0.429378i
\(385\) 1.97521e6i 0.679145i
\(386\) −6.54398e6 −2.23550
\(387\) 584862. + 134592.i 0.198507 + 0.0456818i
\(388\) 2.88747e6i 0.973731i
\(389\) 1.44787e6i 0.485126i 0.970136 + 0.242563i \(0.0779880\pi\)
−0.970136 + 0.242563i \(0.922012\pi\)
\(390\) 662907. 527681.i 0.220694 0.175675i
\(391\) 5.84052e6i 1.93201i
\(392\) 823469. 0.270665
\(393\) 359376. 286067.i 0.117373 0.0934300i
\(394\) 750599.i 0.243595i
\(395\) 1.36970e6i 0.441707i
\(396\) 558846. 2.42843e6i 0.179083 0.778192i
\(397\) 856129.i 0.272623i 0.990666 + 0.136312i \(0.0435248\pi\)
−0.990666 + 0.136312i \(0.956475\pi\)
\(398\) −2.38898e6 −0.755971
\(399\) −1.29083e6 + 1.02751e6i −0.405916 + 0.323114i
\(400\) −2.99801e6 −0.936878
\(401\) −1.07592e6 −0.334133 −0.167066 0.985946i \(-0.553429\pi\)
−0.167066 + 0.985946i \(0.553429\pi\)
\(402\) −3.16038e6 3.97027e6i −0.975380 1.22534i
\(403\) −1.67499e6 −0.513747
\(404\) 595375. 0.181484
\(405\) −673809. + 1.38646e6i −0.204126 + 0.420021i
\(406\) 8.43680e6i 2.54017i
\(407\) 895354.i 0.267922i
\(408\) 881581. + 1.10750e6i 0.262187 + 0.329377i
\(409\) 473425.i 0.139940i −0.997549 0.0699702i \(-0.977710\pi\)
0.997549 0.0699702i \(-0.0222904\pi\)
\(410\) 384248. 0.112889
\(411\) 3.11039e6 + 3.90748e6i 0.908261 + 1.14102i
\(412\) 3.35557e6i 0.973921i
\(413\) 685633. + 4.54204e6i 0.197796 + 1.31031i
\(414\) 1.68893e6 7.33912e6i 0.484295 2.10447i
\(415\) 334798.i 0.0954250i
\(416\) 1.97384e6i 0.559216i
\(417\) −566069. + 450597.i −0.159415 + 0.126896i
\(418\) −2.01741e6 −0.564746
\(419\) −2.63755e6 −0.733949 −0.366975 0.930231i \(-0.619606\pi\)
−0.366975 + 0.930231i \(0.619606\pi\)
\(420\) 1.01381e6 + 1.27361e6i 0.280436 + 0.352302i
\(421\) 224103.i 0.0616231i −0.999525 0.0308115i \(-0.990191\pi\)
0.999525 0.0308115i \(-0.00980917\pi\)
\(422\) 8.24006e6i 2.25242i
\(423\) 271456. 1.17959e6i 0.0737646 0.320539i
\(424\) 2.34552e6i 0.633614i
\(425\) 3.42387e6i 0.919487i
\(426\) 413780. + 519818.i 0.110470 + 0.138780i
\(427\) 13106.3i 0.00347865i
\(428\) 1.52065e6i 0.401254i
\(429\) −1.19728e6 1.50410e6i −0.314089 0.394579i
\(430\) −479392. −0.125032
\(431\) 5.10289e6 1.32319 0.661596 0.749860i \(-0.269879\pi\)
0.661596 + 0.749860i \(0.269879\pi\)
\(432\) −2.00529e6 4.19278e6i −0.516973 1.08092i
\(433\) 5.37069e6 1.37661 0.688304 0.725422i \(-0.258355\pi\)
0.688304 + 0.725422i \(0.258355\pi\)
\(434\) 7.64077e6i 1.94721i
\(435\) 2.10295e6 1.67397e6i 0.532850 0.424154i
\(436\) 2.64318e6i 0.665903i
\(437\) −2.56787e6 −0.643235
\(438\) −5.75776e6 7.23327e6i −1.43406 1.80156i
\(439\) 919173. 0.227634 0.113817 0.993502i \(-0.463692\pi\)
0.113817 + 0.993502i \(0.463692\pi\)
\(440\) 745092.i 0.183476i
\(441\) 692478. 3.00912e6i 0.169555 0.736788i
\(442\) −2.91741e6 −0.710299
\(443\) 865376. 0.209505 0.104753 0.994498i \(-0.466595\pi\)
0.104753 + 0.994498i \(0.466595\pi\)
\(444\) −459555. 577322.i −0.110632 0.138983i
\(445\) 2.39528e6i 0.573397i
\(446\) −6.62018e6 −1.57591
\(447\) −5.32667e6 + 4.24009e6i −1.26092 + 1.00371i
\(448\) −2.25898e6 −0.531762
\(449\) 254593.i 0.0595980i −0.999556 0.0297990i \(-0.990513\pi\)
0.999556 0.0297990i \(-0.00948671\pi\)
\(450\) −990097. + 4.30240e6i −0.230487 + 1.00157i
\(451\) 871839.i 0.201834i
\(452\) −2.41926e6 −0.556975
\(453\) 4.27724e6 + 5.37334e6i 0.979305 + 1.23027i
\(454\) 1.12217e7 2.55516
\(455\) 1.25585e6 0.284388
\(456\) −486928. + 387600.i −0.109661 + 0.0872914i
\(457\) 5.19163e6i 1.16282i −0.813610 0.581411i \(-0.802501\pi\)
0.813610 0.581411i \(-0.197499\pi\)
\(458\) 4.96545e6i 1.10610i
\(459\) 4.78836e6 2.29014e6i 1.06085 0.507377i
\(460\) 2.53362e6i 0.558274i
\(461\) 6.10693e6i 1.33835i −0.743104 0.669176i \(-0.766647\pi\)
0.743104 0.669176i \(-0.233353\pi\)
\(462\) 6.86124e6 5.46162e6i 1.49554 1.19046i
\(463\) 1.24942e6i 0.270866i 0.990786 + 0.135433i \(0.0432426\pi\)
−0.990786 + 0.135433i \(0.956757\pi\)
\(464\) 8.10378e6i 1.74740i
\(465\) −1.90453e6 + 1.51603e6i −0.408465 + 0.325143i
\(466\) 7.30522e6 1.55836
\(467\) 851634. 0.180701 0.0903506 0.995910i \(-0.471201\pi\)
0.0903506 + 0.995910i \(0.471201\pi\)
\(468\) 1.54401e6 + 355318.i 0.325863 + 0.0749898i
\(469\) 7.52154e6i 1.57897i
\(470\) 966874.i 0.201895i
\(471\) 2.46722e6 + 3.09948e6i 0.512454 + 0.643778i
\(472\) 258635. + 1.71335e6i 0.0534359 + 0.353990i
\(473\) 1.08772e6i 0.223544i
\(474\) −4.75790e6 + 3.78734e6i −0.972678 + 0.774262i
\(475\) 1.50536e6 0.306130
\(476\) 5.60509e6i 1.13387i
\(477\) −8.57099e6 1.97241e6i −1.72479 0.396919i
\(478\) 1.13711e6i 0.227631i
\(479\) 5.59727e6i 1.11465i −0.830295 0.557324i \(-0.811828\pi\)
0.830295 0.557324i \(-0.188172\pi\)
\(480\) 1.78652e6 + 2.24434e6i 0.353919 + 0.444616i
\(481\) −569272. −0.112191
\(482\) −1.03947e6 −0.203794
\(483\) 8.73337e6 6.95186e6i 1.70339 1.35592i
\(484\) 766408. 0.148712
\(485\) 3.23739e6 0.624944
\(486\) −6.67925e6 + 1.49309e6i −1.28273 + 0.286745i
\(487\) −2.75944e6 −0.527229 −0.263614 0.964628i \(-0.584915\pi\)
−0.263614 + 0.964628i \(0.584915\pi\)
\(488\) 4943.97i 0.000939780i
\(489\) 4.58441e6 3.64924e6i 0.866985 0.690130i
\(490\) 2.46648e6i 0.464073i
\(491\) 8.15857e6i 1.52725i 0.645659 + 0.763626i \(0.276583\pi\)
−0.645659 + 0.763626i \(0.723417\pi\)
\(492\) 447485. + 562160.i 0.0833424 + 0.104700i
\(493\) −9.25492e6 −1.71496
\(494\) 1.28268e6i 0.236484i
\(495\) −2.72271e6 626569.i −0.499447 0.114936i
\(496\) 7.33918e6i 1.33950i
\(497\) 984777.i 0.178833i
\(498\) −1.16298e6 + 925741.i −0.210134 + 0.167269i
\(499\) 5.01897e6 0.902326 0.451163 0.892442i \(-0.351009\pi\)
0.451163 + 0.892442i \(0.351009\pi\)
\(500\) 3.38482e6i 0.605496i
\(501\) 1.50425e6 + 1.88973e6i 0.267747 + 0.336361i
\(502\) 5.85488e6i 1.03695i
\(503\) −8.21342e6 −1.44745 −0.723726 0.690087i \(-0.757572\pi\)
−0.723726 + 0.690087i \(0.757572\pi\)
\(504\) 606722. 2.63647e6i 0.106393 0.462324i
\(505\) 667525.i 0.116477i
\(506\) 1.36492e7 2.36990
\(507\) −3.57206e6 + 2.84340e6i −0.617161 + 0.491267i
\(508\) 5.56657e6 0.957036
\(509\) 7.69651e6 1.31674 0.658369 0.752695i \(-0.271247\pi\)
0.658369 + 0.752695i \(0.271247\pi\)
\(510\) −3.31721e6 + 2.64053e6i −0.564738 + 0.449538i
\(511\) 1.37032e7i 2.32150i
\(512\) −6.10426e6 −1.02910
\(513\) 1.00689e6 + 2.10527e6i 0.168924 + 0.353196i
\(514\) 2.83525e6i 0.473351i
\(515\) 3.76222e6 0.625066
\(516\) −558288. 701357.i −0.0923069 0.115962i
\(517\) 2.19379e6 0.360968
\(518\) 2.59684e6i 0.425227i
\(519\) 3.20040e6 2.54755e6i 0.521538 0.415150i
\(520\) 473735. 0.0768293
\(521\) 131488.i 0.0212222i 0.999944 + 0.0106111i \(0.00337768\pi\)
−0.999944 + 0.0106111i \(0.996622\pi\)
\(522\) 1.16296e7 + 2.67629e6i 1.86805 + 0.429889i
\(523\) 9.59429e6 1.53376 0.766882 0.641788i \(-0.221807\pi\)
0.766882 + 0.641788i \(0.221807\pi\)
\(524\) −686095. −0.109158
\(525\) −5.11974e6 + 4.07537e6i −0.810681 + 0.645311i
\(526\) 1.73991e6i 0.274197i
\(527\) 8.38170e6 1.31464
\(528\) 6.59041e6 5.24604e6i 1.02879 0.818930i
\(529\) 1.09371e7 1.69927
\(530\) 7.02537e6 1.08637
\(531\) 6.47841e6 + 495701.i 0.997085 + 0.0762928i
\(532\) 2.46436e6 0.377507
\(533\) 554321. 0.0845169
\(534\) 8.32039e6 6.62312e6i 1.26267 1.00510i
\(535\) 1.70493e6 0.257526
\(536\) 2.83728e6i 0.426570i
\(537\) −3.18772e6 + 2.53746e6i −0.477029 + 0.379720i
\(538\) 2.05135e6 0.305552
\(539\) 5.59631e6 0.829716
\(540\) 2.07720e6 993466.i 0.306544 0.146612i
\(541\) 4.10361e6i 0.602799i −0.953498 0.301400i \(-0.902546\pi\)
0.953498 0.301400i \(-0.0974538\pi\)
\(542\) −1.59070e7 −2.32589
\(543\) −1.64346e6 + 1.30821e6i −0.239199 + 0.190405i
\(544\) 9.87718e6i 1.43099i
\(545\) −2.96350e6 −0.427379
\(546\) 3.47253e6 + 4.36242e6i 0.498500 + 0.626247i
\(547\) −4.10117e6 −0.586057 −0.293028 0.956104i \(-0.594663\pi\)
−0.293028 + 0.956104i \(0.594663\pi\)
\(548\) 7.45987e6i 1.06116i
\(549\) −18066.2 4157.52i −0.00255821 0.000588713i
\(550\) −8.00153e6 −1.12789
\(551\) 4.06906e6i 0.570972i
\(552\) 3.29441e6 2.62239e6i 0.460182 0.366310i
\(553\) −9.01367e6 −1.25340
\(554\) 1.19089e7 1.64854
\(555\) −647285. + 515246.i −0.0891996 + 0.0710038i
\(556\) 1.08070e6 0.148258
\(557\) 8.40721e6i 1.14819i 0.818788 + 0.574095i \(0.194646\pi\)
−0.818788 + 0.574095i \(0.805354\pi\)
\(558\) −1.05323e7 2.42377e6i −1.43199 0.329539i
\(559\) −691577. −0.0936076
\(560\) 5.50269e6i 0.741489i
\(561\) 5.99124e6 + 7.52658e6i 0.803728 + 1.00970i
\(562\) 1.90086e6i 0.253868i
\(563\) −571838. −0.0760329 −0.0380165 0.999277i \(-0.512104\pi\)
−0.0380165 + 0.999277i \(0.512104\pi\)
\(564\) −1.41455e6 + 1.12600e6i −0.187249 + 0.149052i
\(565\) 2.71243e6i 0.357469i
\(566\) 1.80929e7i 2.37392i
\(567\) −9.12396e6 4.43416e6i −1.19186 0.579234i
\(568\) 371478.i 0.0483129i
\(569\) −1.04132e7 −1.34836 −0.674178 0.738569i \(-0.735502\pi\)
−0.674178 + 0.738569i \(0.735502\pi\)
\(570\) −1.16095e6 1.45846e6i −0.149667 0.188021i
\(571\) 1.52434e7i 1.95655i 0.207307 + 0.978276i \(0.433530\pi\)
−0.207307 + 0.978276i \(0.566470\pi\)
\(572\) 2.87152e6i 0.366963i
\(573\) −1.03466e7 + 8.23597e6i −1.31646 + 1.04792i
\(574\) 2.52864e6i 0.320337i
\(575\) −1.01848e7 −1.28464
\(576\) −716584. + 3.11387e6i −0.0899934 + 0.391060i
\(577\) 5.95811e6 0.745022 0.372511 0.928028i \(-0.378497\pi\)
0.372511 + 0.928028i \(0.378497\pi\)
\(578\) 4.04169e6 0.503203
\(579\) −1.07341e7 + 8.54450e6i −1.33067 + 1.05923i
\(580\) −4.01479e6 −0.495557
\(581\) −2.20322e6 −0.270780
\(582\) 8.95164e6 + 1.12456e7i 1.09546 + 1.37618i
\(583\) 1.59402e7i 1.94233i
\(584\) 5.16912e6i 0.627169i
\(585\) 398377. 1.73112e6i 0.0481287 0.209140i
\(586\) 6.38638e6i 0.768265i
\(587\) −1.27267e7 −1.52448 −0.762240 0.647295i \(-0.775900\pi\)
−0.762240 + 0.647295i \(0.775900\pi\)
\(588\) −3.60849e6 + 2.87239e6i −0.430409 + 0.342610i
\(589\) 3.68514e6i 0.437689i
\(590\) −5.13187e6 + 774671.i −0.606940 + 0.0916194i
\(591\) 980060. + 1.23121e6i 0.115421 + 0.144999i
\(592\) 2.49434e6i 0.292517i
\(593\) 1.95292e6i 0.228059i 0.993477 + 0.114030i \(0.0363758\pi\)
−0.993477 + 0.114030i \(0.963624\pi\)
\(594\) −5.35202e6 1.11903e7i −0.622374 1.30130i
\(595\) −6.28434e6 −0.727725
\(596\) 1.01693e7 1.17267
\(597\) −3.91867e6 + 3.11930e6i −0.449990 + 0.358197i
\(598\) 8.67824e6i 0.992382i
\(599\) 1.05042e7i 1.19618i −0.801429 0.598091i \(-0.795926\pi\)
0.801429 0.598091i \(-0.204074\pi\)
\(600\) −1.93128e6 + 1.53732e6i −0.219011 + 0.174335i
\(601\) 1.08997e6i 0.123091i −0.998104 0.0615457i \(-0.980397\pi\)
0.998104 0.0615457i \(-0.0196030\pi\)
\(602\) 3.15476e6i 0.354793i
\(603\) −1.03680e7 2.38595e6i −1.16118 0.267220i
\(604\) 1.02584e7i 1.14416i
\(605\) 859285.i 0.0954440i
\(606\) 2.31876e6 1.84576e6i 0.256492 0.204171i
\(607\) −1.03785e7 −1.14330 −0.571652 0.820496i \(-0.693697\pi\)
−0.571652 + 0.820496i \(0.693697\pi\)
\(608\) 4.34265e6 0.476426
\(609\) 1.10160e7 + 1.38389e7i 1.20359 + 1.51203i
\(610\) 14808.3 0.00161132
\(611\) 1.39482e6i 0.151153i
\(612\) −7.72627e6 1.77802e6i −0.833857 0.191893i
\(613\) 4.22332e6i 0.453945i 0.973901 + 0.226972i \(0.0728827\pi\)
−0.973901 + 0.226972i \(0.927117\pi\)
\(614\) −1.78062e6 −0.190612
\(615\) 630285. 501714.i 0.0671969 0.0534895i
\(616\) 4.90326e6 0.520635
\(617\) 183600.i 0.0194160i −0.999953 0.00970802i \(-0.996910\pi\)
0.999953 0.00970802i \(-0.00309021\pi\)
\(618\) 1.04028e7 + 1.30687e7i 1.09567 + 1.37645i
\(619\) −1.53577e7 −1.61102 −0.805510 0.592583i \(-0.798108\pi\)
−0.805510 + 0.592583i \(0.798108\pi\)
\(620\) 3.63599e6 0.379877
\(621\) −6.81235e6 1.42437e7i −0.708872 1.48215i
\(622\) 2.16609e7i 2.24492i
\(623\) 1.57627e7 1.62709
\(624\) 3.33547e6 + 4.19023e6i 0.342922 + 0.430801i
\(625\) 3.84087e6 0.393306
\(626\) 9.72037e6i 0.991395i
\(627\) −3.30917e6 + 2.63414e6i −0.336163 + 0.267590i
\(628\) 5.91730e6i 0.598721i
\(629\) 2.84865e6 0.287087
\(630\) 7.89682e6 + 1.81727e6i 0.792685 + 0.182418i
\(631\) −8.11179e6 −0.811042 −0.405521 0.914086i \(-0.632910\pi\)
−0.405521 + 0.914086i \(0.632910\pi\)
\(632\) −3.40015e6 −0.338614
\(633\) 1.07591e7 + 1.35162e7i 1.06725 + 1.34075i
\(634\) 1.68049e7i 1.66040i
\(635\) 6.24115e6i 0.614229i
\(636\) 8.18156e6 + 1.02782e7i 0.802035 + 1.00757i
\(637\) 3.55817e6i 0.347438i
\(638\) 2.16286e7i 2.10366i
\(639\) 1.35745e6 + 312387.i 0.131514 + 0.0302650i
\(640\) 3.33627e6i 0.321967i
\(641\) 1.44500e7i 1.38907i 0.719461 + 0.694533i \(0.244389\pi\)
−0.719461 + 0.694533i \(0.755611\pi\)
\(642\) 4.71426e6 + 5.92235e6i 0.451415 + 0.567096i
\(643\) −1.17789e7 −1.12352 −0.561758 0.827302i \(-0.689875\pi\)
−0.561758 + 0.827302i \(0.689875\pi\)
\(644\) −1.66731e7 −1.58417
\(645\) −786351. + 625944.i −0.0744247 + 0.0592429i
\(646\) 6.41858e6i 0.605142i
\(647\) 8.19790e6i 0.769914i −0.922935 0.384957i \(-0.874216\pi\)
0.922935 0.384957i \(-0.125784\pi\)
\(648\) −3.44175e6 1.67266e6i −0.321990 0.156484i
\(649\) 1.75769e6 + 1.16440e7i 0.163806 + 1.08515i
\(650\) 5.08743e6i 0.472296i
\(651\) −9.97658e6 1.25332e7i −0.922633 1.15907i
\(652\) −8.75223e6 −0.806306
\(653\) 1.14233e7i 1.04836i 0.851608 + 0.524180i \(0.175628\pi\)
−0.851608 + 0.524180i \(0.824372\pi\)
\(654\) −8.19429e6 1.02942e7i −0.749147 0.941127i
\(655\) 769239.i 0.0700580i
\(656\) 2.42883e6i 0.220362i
\(657\) −1.88890e7 4.34686e6i −1.70724 0.392882i
\(658\) −6.36275e6 −0.572902
\(659\) 232316. 0.0208385 0.0104192 0.999946i \(-0.496683\pi\)
0.0104192 + 0.999946i \(0.496683\pi\)
\(660\) 2.59900e6 + 3.26504e6i 0.232245 + 0.291762i
\(661\) 5.99123e6 0.533350 0.266675 0.963787i \(-0.414075\pi\)
0.266675 + 0.963787i \(0.414075\pi\)
\(662\) −7.19620e6 −0.638203
\(663\) −4.78545e6 + 3.80927e6i −0.422804 + 0.336556i
\(664\) −831100. −0.0731531
\(665\) 2.76300e6i 0.242285i
\(666\) −3.57958e6 823758.i −0.312714 0.0719638i
\(667\) 2.75301e7i 2.39603i
\(668\) 3.60774e6i 0.312820i
\(669\) −1.08591e7 + 8.64399e6i −0.938058 + 0.746705i
\(670\) 8.49831e6 0.731384
\(671\) 33599.3i 0.00288087i
\(672\) −1.47694e7 + 1.17566e7i −1.26165 + 1.00429i
\(673\) 7.42847e6i 0.632211i −0.948724 0.316105i \(-0.897625\pi\)
0.948724 0.316105i \(-0.102375\pi\)
\(674\) 2.45315e7i 2.08006i
\(675\) 3.99359e6 + 8.35003e6i 0.337368 + 0.705389i
\(676\) 6.81952e6 0.573967
\(677\) 1.71931e6i 0.144173i 0.997398 + 0.0720863i \(0.0229657\pi\)
−0.997398 + 0.0720863i \(0.977034\pi\)
\(678\) −9.42209e6 + 7.50008e6i −0.787178 + 0.626602i
\(679\) 2.13045e7i 1.77336i
\(680\) −2.37058e6 −0.196600
\(681\) 1.84070e7 1.46522e7i 1.52095 1.21069i
\(682\) 1.95879e7i 1.61260i
\(683\) 5.36526e6 0.440087 0.220044 0.975490i \(-0.429380\pi\)
0.220044 + 0.975490i \(0.429380\pi\)
\(684\) 781733. 3.39697e6i 0.0638879 0.277620i
\(685\) −8.36389e6 −0.681055
\(686\) 5.23736e6 0.424915
\(687\) 6.48340e6 + 8.14487e6i 0.524097 + 0.658404i
\(688\) 3.03023e6i 0.244065i
\(689\) 1.01349e7 0.813337
\(690\) 7.85464e6 + 9.86751e6i 0.628064 + 0.789014i
\(691\) 4.91758e6i 0.391793i −0.980625 0.195896i \(-0.937238\pi\)
0.980625 0.195896i \(-0.0627616\pi\)
\(692\) −6.10998e6 −0.485036
\(693\) 4.12329e6 1.79175e7i 0.326145 1.41724i
\(694\) 2.81765e6 0.222069
\(695\) 1.21166e6i 0.0951524i
\(696\) 4.15545e6 + 5.22034e6i 0.325158 + 0.408485i
\(697\) −2.77384e6 −0.216272
\(698\) 1.09360e7i 0.849608i
\(699\) 1.19828e7 9.53845e6i 0.927611 0.738388i
\(700\) 9.77425e6 0.753943
\(701\) −1.87262e7 −1.43931 −0.719656 0.694331i \(-0.755700\pi\)
−0.719656 + 0.694331i \(0.755700\pi\)
\(702\) 7.11487e6 3.40285e6i 0.544910 0.260615i
\(703\) 1.25245e6i 0.0955813i
\(704\) −5.79112e6 −0.440383
\(705\) 1.26245e6 + 1.58597e6i 0.0956624 + 0.120177i
\(706\) −6.52685e6 −0.492824
\(707\) 4.39281e6 0.330517
\(708\) −7.10980e6 6.60584e6i −0.533058 0.495273i
\(709\) 3.13769e6 0.234420 0.117210 0.993107i \(-0.462605\pi\)
0.117210 + 0.993107i \(0.462605\pi\)
\(710\) −1.11266e6 −0.0828357
\(711\) −2.85928e6 + 1.24248e7i −0.212120 + 0.921755i
\(712\) 5.94602e6 0.439568
\(713\) 2.49326e7i 1.83672i
\(714\) −1.73767e7 2.18297e7i −1.27562 1.60252i
\(715\) 3.21951e6 0.235518
\(716\) 6.08576e6 0.443642
\(717\) −1.48473e6 1.86521e6i −0.107857 0.135497i
\(718\) 2.42109e7i 1.75267i
\(719\) −1.22765e7 −0.885633 −0.442816 0.896612i \(-0.646021\pi\)
−0.442816 + 0.896612i \(0.646021\pi\)
\(720\) 7.58512e6 + 1.74554e6i 0.545295 + 0.125487i
\(721\) 2.47582e7i 1.77370i
\(722\) 1.55886e7 1.11292
\(723\) −1.70504e6 + 1.35723e6i −0.121308 + 0.0965625i
\(724\) 3.13758e6 0.222458
\(725\) 1.61389e7i 1.14032i
\(726\) 2.98487e6 2.37599e6i 0.210176 0.167303i
\(727\) 2.24682e7 1.57664 0.788318 0.615268i \(-0.210952\pi\)
0.788318 + 0.615268i \(0.210952\pi\)
\(728\) 3.11753e6i 0.218013i
\(729\) −9.00649e6 + 1.11702e7i −0.627678 + 0.778473i
\(730\) 1.54827e7 1.07532
\(731\) 3.46068e6 0.239534
\(732\) 17245.4 + 21664.8i 0.00118958 + 0.00149443i
\(733\) −1.67016e7 −1.14815 −0.574076 0.818802i \(-0.694638\pi\)
−0.574076 + 0.818802i \(0.694638\pi\)
\(734\) 2.66949e7i 1.82889i
\(735\) 3.22048e6 + 4.04578e6i 0.219889 + 0.276238i
\(736\) −2.93811e7 −1.99928
\(737\) 1.92822e7i 1.30764i
\(738\) 3.48557e6 + 802124.i 0.235577 + 0.0542126i
\(739\) 9.90722e6i 0.667330i −0.942692 0.333665i \(-0.891715\pi\)
0.942692 0.333665i \(-0.108285\pi\)
\(740\) 1.23575e6 0.0829566
\(741\) −1.67480e6 2.10399e6i −0.112051 0.140766i
\(742\) 4.62321e7i 3.08272i
\(743\) 9.99364e6i 0.664128i −0.943257 0.332064i \(-0.892255\pi\)
0.943257 0.332064i \(-0.107745\pi\)
\(744\) −3.76337e6 4.72779e6i −0.249256 0.313131i
\(745\) 1.14017e7i 0.752623i
\(746\) 8.55573e6 0.562873
\(747\) −698895. + 3.03700e6i −0.0458258 + 0.199133i
\(748\) 1.43692e7i 0.939028i
\(749\) 1.12197e7i 0.730763i
\(750\) −1.04935e7 1.31826e7i −0.681188 0.855753i
\(751\) 8.95464e6i 0.579360i 0.957124 + 0.289680i \(0.0935489\pi\)
−0.957124 + 0.289680i \(0.906451\pi\)
\(752\) −6.11160e6 −0.394103
\(753\) 7.64473e6 + 9.60380e6i 0.491332 + 0.617242i
\(754\) −1.37516e7 −0.880896
\(755\) −1.15016e7 −0.734327
\(756\) 6.53774e6 + 1.36695e7i 0.416029 + 0.869857i
\(757\) −3.54920e6 −0.225108 −0.112554 0.993646i \(-0.535903\pi\)
−0.112554 + 0.993646i \(0.535903\pi\)
\(758\) 1.77427e6 0.112162
\(759\) 2.23889e7 1.78218e7i 1.41068 1.12291i
\(760\) 1.04226e6i 0.0654550i
\(761\) 1.57471e7i 0.985687i 0.870118 + 0.492843i \(0.164042\pi\)
−0.870118 + 0.492843i \(0.835958\pi\)
\(762\) 2.16797e7 1.72573e7i 1.35259 1.07667i
\(763\) 1.95020e7i 1.21274i
\(764\) 1.97529e7 1.22433
\(765\) −1.99349e6 + 8.66258e6i −0.123157 + 0.535172i
\(766\) 1.02971e7i 0.634077i
\(767\) −7.40331e6 + 1.11755e6i −0.454399 + 0.0685928i
\(768\) −1.67210e7 + 1.33101e7i −1.02296 + 0.814286i
\(769\) 3.46575e6i 0.211340i −0.994401 0.105670i \(-0.966301\pi\)
0.994401 0.105670i \(-0.0336987\pi\)
\(770\) 1.46864e7i 0.892664i
\(771\) −3.70199e6 4.65068e6i −0.224285 0.281761i
\(772\) 2.04929e7 1.23754
\(773\) 1.93604e7 1.16537 0.582687 0.812697i \(-0.302001\pi\)
0.582687 + 0.812697i \(0.302001\pi\)
\(774\) −4.34864e6 1.00074e6i −0.260916 0.0600438i
\(775\) 1.46162e7i 0.874136i
\(776\) 8.03649e6i 0.479084i
\(777\) −3.39070e6 4.25961e6i −0.201482 0.253115i
\(778\) 1.07654e7i 0.637646i
\(779\) 1.21956e6i 0.0720045i