Properties

Label 300.5.c.c.151.3
Level $300$
Weight $5$
Character 300.151
Analytic conductor $31.011$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 300.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(31.0109889252\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{15} + 20 x^{14} - 108 x^{13} + 492 x^{12} - 2160 x^{11} + 7360 x^{10} - 39552 x^{9} + 234752 x^{8} - 632832 x^{7} + 1884160 x^{6} - 8847360 x^{5} + 32243712 x^{4} - 113246208 x^{3} + 335544320 x^{2} - 1610612736 x + 4294967296\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{32}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 151.3
Root \(-3.55818 - 1.82740i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.5.c.c.151.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.36166 - 2.16777i) q^{2} -5.19615i q^{3} +(6.60152 + 14.5746i) q^{4} +(-11.2641 + 17.4677i) q^{6} -36.6738i q^{7} +(9.40241 - 63.3056i) q^{8} -27.0000 q^{9} +O(q^{10})\) \(q+(-3.36166 - 2.16777i) q^{2} -5.19615i q^{3} +(6.60152 + 14.5746i) q^{4} +(-11.2641 + 17.4677i) q^{6} -36.6738i q^{7} +(9.40241 - 63.3056i) q^{8} -27.0000 q^{9} -56.2282i q^{11} +(75.7320 - 34.3025i) q^{12} +219.043 q^{13} +(-79.5004 + 123.285i) q^{14} +(-168.840 + 192.430i) q^{16} +54.4527 q^{17} +(90.7648 + 58.5299i) q^{18} +155.937i q^{19} -190.562 q^{21} +(-121.890 + 189.020i) q^{22} -322.708i q^{23} +(-328.945 - 48.8564i) q^{24} +(-736.347 - 474.834i) q^{26} +140.296i q^{27} +(534.506 - 242.103i) q^{28} +989.618 q^{29} -847.804i q^{31} +(984.726 - 280.876i) q^{32} -292.171 q^{33} +(-183.051 - 118.041i) q^{34} +(-178.241 - 393.515i) q^{36} +1837.88 q^{37} +(338.035 - 524.206i) q^{38} -1138.18i q^{39} -2470.86 q^{41} +(640.606 + 413.096i) q^{42} -171.009i q^{43} +(819.506 - 371.192i) q^{44} +(-699.557 + 1084.83i) q^{46} -3346.60i q^{47} +(999.893 + 877.317i) q^{48} +1056.04 q^{49} -282.944i q^{51} +(1446.01 + 3192.46i) q^{52} -2748.29 q^{53} +(304.130 - 471.628i) q^{54} +(-2321.65 - 344.822i) q^{56} +810.271 q^{57} +(-3326.76 - 2145.27i) q^{58} -1780.57i q^{59} -5039.83 q^{61} +(-1837.85 + 2850.03i) q^{62} +990.191i q^{63} +(-3919.19 - 1190.45i) q^{64} +(982.178 + 633.359i) q^{66} +4015.61i q^{67} +(359.470 + 793.628i) q^{68} -1676.84 q^{69} -5381.54i q^{71} +(-253.865 + 1709.25i) q^{72} -6555.14 q^{73} +(-6178.33 - 3984.11i) q^{74} +(-2272.72 + 1029.42i) q^{76} -2062.10 q^{77} +(-2467.31 + 3826.17i) q^{78} +11497.9i q^{79} +729.000 q^{81} +(8306.20 + 5356.27i) q^{82} -8231.85i q^{83} +(-1258.00 - 2777.38i) q^{84} +(-370.709 + 574.874i) q^{86} -5142.21i q^{87} +(-3559.56 - 528.681i) q^{88} -5360.84 q^{89} -8033.11i q^{91} +(4703.34 - 2130.36i) q^{92} -4405.32 q^{93} +(-7254.66 + 11250.1i) q^{94} +(-1459.48 - 5116.78i) q^{96} -12933.5 q^{97} +(-3550.03 - 2289.25i) q^{98} +1518.16i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 6q^{2} + 8q^{4} + 18q^{6} - 180q^{8} - 432q^{9} + O(q^{10}) \) \( 16q + 6q^{2} + 8q^{4} + 18q^{6} - 180q^{8} - 432q^{9} + 176q^{13} + 78q^{14} - 376q^{16} - 162q^{18} - 144q^{21} - 788q^{22} + 108q^{24} + 678q^{26} + 3368q^{28} + 1728q^{29} + 2016q^{32} - 2932q^{34} - 216q^{36} - 1568q^{37} - 6990q^{38} + 1248q^{41} + 162q^{42} + 8088q^{44} + 5956q^{46} + 2088q^{48} - 10720q^{49} + 3128q^{52} - 288q^{53} - 486q^{54} - 10236q^{56} + 5616q^{57} - 16164q^{58} - 3760q^{61} - 12714q^{62} + 10544q^{64} + 8100q^{66} + 26136q^{68} + 9792q^{69} + 4860q^{72} + 11040q^{73} - 17004q^{74} - 28344q^{76} + 768q^{77} - 16830q^{78} + 11664q^{81} - 21280q^{82} + 15120q^{84} + 24414q^{86} + 52840q^{88} - 768q^{89} + 23736q^{92} - 9936q^{93} - 45156q^{94} - 11088q^{96} + 7248q^{97} - 58140q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.36166 2.16777i −0.840415 0.541943i
\(3\) 5.19615i 0.577350i
\(4\) 6.60152 + 14.5746i 0.412595 + 0.910915i
\(5\) 0 0
\(6\) −11.2641 + 17.4677i −0.312891 + 0.485214i
\(7\) 36.6738i 0.748444i −0.927339 0.374222i \(-0.877910\pi\)
0.927339 0.374222i \(-0.122090\pi\)
\(8\) 9.40241 63.3056i 0.146913 0.989149i
\(9\) −27.0000 −0.333333
\(10\) 0 0
\(11\) 56.2282i 0.464696i −0.972633 0.232348i \(-0.925359\pi\)
0.972633 0.232348i \(-0.0746409\pi\)
\(12\) 75.7320 34.3025i 0.525917 0.238212i
\(13\) 219.043 1.29611 0.648055 0.761594i \(-0.275583\pi\)
0.648055 + 0.761594i \(0.275583\pi\)
\(14\) −79.5004 + 123.285i −0.405614 + 0.629004i
\(15\) 0 0
\(16\) −168.840 + 192.430i −0.659530 + 0.751678i
\(17\) 54.4527 0.188418 0.0942088 0.995552i \(-0.469968\pi\)
0.0942088 + 0.995552i \(0.469968\pi\)
\(18\) 90.7648 + 58.5299i 0.280138 + 0.180648i
\(19\) 155.937i 0.431957i 0.976398 + 0.215979i \(0.0692942\pi\)
−0.976398 + 0.215979i \(0.930706\pi\)
\(20\) 0 0
\(21\) −190.562 −0.432114
\(22\) −121.890 + 189.020i −0.251839 + 0.390538i
\(23\) 322.708i 0.610033i −0.952347 0.305017i \(-0.901338\pi\)
0.952347 0.305017i \(-0.0986620\pi\)
\(24\) −328.945 48.8564i −0.571086 0.0848201i
\(25\) 0 0
\(26\) −736.347 474.834i −1.08927 0.702418i
\(27\) 140.296i 0.192450i
\(28\) 534.506 242.103i 0.681768 0.308804i
\(29\) 989.618 1.17672 0.588358 0.808601i \(-0.299775\pi\)
0.588358 + 0.808601i \(0.299775\pi\)
\(30\) 0 0
\(31\) 847.804i 0.882210i −0.897456 0.441105i \(-0.854587\pi\)
0.897456 0.441105i \(-0.145413\pi\)
\(32\) 984.726 280.876i 0.961646 0.274293i
\(33\) −292.171 −0.268292
\(34\) −183.051 118.041i −0.158349 0.102112i
\(35\) 0 0
\(36\) −178.241 393.515i −0.137532 0.303638i
\(37\) 1837.88 1.34250 0.671249 0.741232i \(-0.265758\pi\)
0.671249 + 0.741232i \(0.265758\pi\)
\(38\) 338.035 524.206i 0.234096 0.363024i
\(39\) 1138.18i 0.748309i
\(40\) 0 0
\(41\) −2470.86 −1.46988 −0.734939 0.678134i \(-0.762789\pi\)
−0.734939 + 0.678134i \(0.762789\pi\)
\(42\) 640.606 + 413.096i 0.363155 + 0.234181i
\(43\) 171.009i 0.0924873i −0.998930 0.0462436i \(-0.985275\pi\)
0.998930 0.0462436i \(-0.0147251\pi\)
\(44\) 819.506 371.192i 0.423299 0.191731i
\(45\) 0 0
\(46\) −699.557 + 1084.83i −0.330603 + 0.512681i
\(47\) 3346.60i 1.51498i −0.652845 0.757492i \(-0.726425\pi\)
0.652845 0.757492i \(-0.273575\pi\)
\(48\) 999.893 + 877.317i 0.433981 + 0.380780i
\(49\) 1056.04 0.439832
\(50\) 0 0
\(51\) 282.944i 0.108783i
\(52\) 1446.01 + 3192.46i 0.534769 + 1.18065i
\(53\) −2748.29 −0.978386 −0.489193 0.872176i \(-0.662709\pi\)
−0.489193 + 0.872176i \(0.662709\pi\)
\(54\) 304.130 471.628i 0.104297 0.161738i
\(55\) 0 0
\(56\) −2321.65 344.822i −0.740323 0.109956i
\(57\) 810.271 0.249391
\(58\) −3326.76 2145.27i −0.988930 0.637713i
\(59\) 1780.57i 0.511511i −0.966742 0.255755i \(-0.917676\pi\)
0.966742 0.255755i \(-0.0823242\pi\)
\(60\) 0 0
\(61\) −5039.83 −1.35443 −0.677214 0.735786i \(-0.736813\pi\)
−0.677214 + 0.735786i \(0.736813\pi\)
\(62\) −1837.85 + 2850.03i −0.478108 + 0.741422i
\(63\) 990.191i 0.249481i
\(64\) −3919.19 1190.45i −0.956833 0.290637i
\(65\) 0 0
\(66\) 982.178 + 633.359i 0.225477 + 0.145399i
\(67\) 4015.61i 0.894543i 0.894398 + 0.447272i \(0.147604\pi\)
−0.894398 + 0.447272i \(0.852396\pi\)
\(68\) 359.470 + 793.628i 0.0777402 + 0.171632i
\(69\) −1676.84 −0.352203
\(70\) 0 0
\(71\) 5381.54i 1.06755i −0.845625 0.533777i \(-0.820772\pi\)
0.845625 0.533777i \(-0.179228\pi\)
\(72\) −253.865 + 1709.25i −0.0489709 + 0.329716i
\(73\) −6555.14 −1.23009 −0.615044 0.788493i \(-0.710862\pi\)
−0.615044 + 0.788493i \(0.710862\pi\)
\(74\) −6178.33 3984.11i −1.12826 0.727558i
\(75\) 0 0
\(76\) −2272.72 + 1029.42i −0.393476 + 0.178224i
\(77\) −2062.10 −0.347799
\(78\) −2467.31 + 3826.17i −0.405541 + 0.628890i
\(79\) 11497.9i 1.84232i 0.389188 + 0.921158i \(0.372756\pi\)
−0.389188 + 0.921158i \(0.627244\pi\)
\(80\) 0 0
\(81\) 729.000 0.111111
\(82\) 8306.20 + 5356.27i 1.23531 + 0.796590i
\(83\) 8231.85i 1.19493i −0.801896 0.597463i \(-0.796175\pi\)
0.801896 0.597463i \(-0.203825\pi\)
\(84\) −1258.00 2777.38i −0.178288 0.393619i
\(85\) 0 0
\(86\) −370.709 + 574.874i −0.0501229 + 0.0777277i
\(87\) 5142.21i 0.679377i
\(88\) −3559.56 528.681i −0.459654 0.0682698i
\(89\) −5360.84 −0.676788 −0.338394 0.941005i \(-0.609884\pi\)
−0.338394 + 0.941005i \(0.609884\pi\)
\(90\) 0 0
\(91\) 8033.11i 0.970065i
\(92\) 4703.34 2130.36i 0.555688 0.251697i
\(93\) −4405.32 −0.509344
\(94\) −7254.66 + 11250.1i −0.821035 + 1.27321i
\(95\) 0 0
\(96\) −1459.48 5116.78i −0.158363 0.555207i
\(97\) −12933.5 −1.37459 −0.687295 0.726379i \(-0.741202\pi\)
−0.687295 + 0.726379i \(0.741202\pi\)
\(98\) −3550.03 2289.25i −0.369641 0.238364i
\(99\) 1518.16i 0.154899i
\(100\) 0 0
\(101\) −10633.8 −1.04243 −0.521216 0.853425i \(-0.674521\pi\)
−0.521216 + 0.853425i \(0.674521\pi\)
\(102\) −613.359 + 951.163i −0.0589542 + 0.0914228i
\(103\) 10524.5i 0.992031i −0.868314 0.496016i \(-0.834796\pi\)
0.868314 0.496016i \(-0.165204\pi\)
\(104\) 2059.53 13866.6i 0.190415 1.28205i
\(105\) 0 0
\(106\) 9238.81 + 5957.66i 0.822250 + 0.530230i
\(107\) 16409.2i 1.43324i −0.697462 0.716621i \(-0.745688\pi\)
0.697462 0.716621i \(-0.254312\pi\)
\(108\) −2044.76 + 926.168i −0.175306 + 0.0794040i
\(109\) 2190.64 0.184382 0.0921908 0.995741i \(-0.470613\pi\)
0.0921908 + 0.995741i \(0.470613\pi\)
\(110\) 0 0
\(111\) 9549.91i 0.775092i
\(112\) 7057.11 + 6191.99i 0.562589 + 0.493622i
\(113\) −235.041 −0.0184072 −0.00920358 0.999958i \(-0.502930\pi\)
−0.00920358 + 0.999958i \(0.502930\pi\)
\(114\) −2723.85 1756.48i −0.209592 0.135156i
\(115\) 0 0
\(116\) 6532.99 + 14423.3i 0.485507 + 1.07189i
\(117\) −5914.15 −0.432037
\(118\) −3859.87 + 5985.67i −0.277210 + 0.429881i
\(119\) 1996.98i 0.141020i
\(120\) 0 0
\(121\) 11479.4 0.784057
\(122\) 16942.2 + 10925.2i 1.13828 + 0.734023i
\(123\) 12839.0i 0.848634i
\(124\) 12356.4 5596.79i 0.803618 0.363996i
\(125\) 0 0
\(126\) 2146.51 3328.69i 0.135205 0.209668i
\(127\) 18937.2i 1.17411i −0.809548 0.587054i \(-0.800288\pi\)
0.809548 0.587054i \(-0.199712\pi\)
\(128\) 10594.4 + 12497.8i 0.646628 + 0.762805i
\(129\) −888.589 −0.0533976
\(130\) 0 0
\(131\) 8486.92i 0.494547i 0.968946 + 0.247273i \(0.0795346\pi\)
−0.968946 + 0.247273i \(0.920465\pi\)
\(132\) −1928.77 4258.28i −0.110696 0.244392i
\(133\) 5718.78 0.323296
\(134\) 8704.92 13499.1i 0.484792 0.751788i
\(135\) 0 0
\(136\) 511.986 3447.16i 0.0276809 0.186373i
\(137\) 307.323 0.0163740 0.00818699 0.999966i \(-0.497394\pi\)
0.00818699 + 0.999966i \(0.497394\pi\)
\(138\) 5636.96 + 3635.00i 0.295997 + 0.190874i
\(139\) 33154.2i 1.71597i 0.513677 + 0.857984i \(0.328283\pi\)
−0.513677 + 0.857984i \(0.671717\pi\)
\(140\) 0 0
\(141\) −17389.4 −0.874676
\(142\) −11666.0 + 18090.9i −0.578554 + 0.897189i
\(143\) 12316.4i 0.602297i
\(144\) 4558.67 5195.60i 0.219843 0.250559i
\(145\) 0 0
\(146\) 22036.2 + 14210.1i 1.03378 + 0.666638i
\(147\) 5487.32i 0.253937i
\(148\) 12132.8 + 26786.4i 0.553908 + 1.22290i
\(149\) 33856.8 1.52501 0.762506 0.646981i \(-0.223969\pi\)
0.762506 + 0.646981i \(0.223969\pi\)
\(150\) 0 0
\(151\) 12036.5i 0.527894i −0.964537 0.263947i \(-0.914976\pi\)
0.964537 0.263947i \(-0.0850244\pi\)
\(152\) 9871.66 + 1466.18i 0.427270 + 0.0634600i
\(153\) −1470.22 −0.0628058
\(154\) 6932.08 + 4470.17i 0.292296 + 0.188487i
\(155\) 0 0
\(156\) 16588.5 7513.71i 0.681646 0.308749i
\(157\) −29036.3 −1.17799 −0.588995 0.808137i \(-0.700476\pi\)
−0.588995 + 0.808137i \(0.700476\pi\)
\(158\) 24924.8 38652.0i 0.998431 1.54831i
\(159\) 14280.5i 0.564871i
\(160\) 0 0
\(161\) −11834.9 −0.456576
\(162\) −2450.65 1580.31i −0.0933795 0.0602159i
\(163\) 14158.1i 0.532879i −0.963852 0.266439i \(-0.914153\pi\)
0.963852 0.266439i \(-0.0858472\pi\)
\(164\) −16311.5 36011.9i −0.606464 1.33893i
\(165\) 0 0
\(166\) −17844.8 + 27672.7i −0.647582 + 1.00423i
\(167\) 24992.4i 0.896139i −0.893999 0.448069i \(-0.852112\pi\)
0.893999 0.448069i \(-0.147888\pi\)
\(168\) −1791.75 + 12063.7i −0.0634831 + 0.427426i
\(169\) 19418.6 0.679900
\(170\) 0 0
\(171\) 4210.29i 0.143986i
\(172\) 2492.39 1128.92i 0.0842480 0.0381598i
\(173\) 49606.1 1.65746 0.828730 0.559648i \(-0.189064\pi\)
0.828730 + 0.559648i \(0.189064\pi\)
\(174\) −11147.1 + 17286.4i −0.368184 + 0.570959i
\(175\) 0 0
\(176\) 10820.0 + 9493.56i 0.349302 + 0.306481i
\(177\) −9252.11 −0.295321
\(178\) 18021.3 + 11621.1i 0.568783 + 0.366780i
\(179\) 6175.50i 0.192737i −0.995346 0.0963687i \(-0.969277\pi\)
0.995346 0.0963687i \(-0.0307228\pi\)
\(180\) 0 0
\(181\) 24421.3 0.745437 0.372719 0.927944i \(-0.378426\pi\)
0.372719 + 0.927944i \(0.378426\pi\)
\(182\) −17414.0 + 27004.6i −0.525720 + 0.815258i
\(183\) 26187.7i 0.781980i
\(184\) −20429.2 3034.23i −0.603414 0.0896216i
\(185\) 0 0
\(186\) 14809.2 + 9549.73i 0.428060 + 0.276036i
\(187\) 3061.78i 0.0875569i
\(188\) 48775.4 22092.6i 1.38002 0.625075i
\(189\) 5145.19 0.144038
\(190\) 0 0
\(191\) 47105.7i 1.29124i 0.763659 + 0.645620i \(0.223401\pi\)
−0.763659 + 0.645620i \(0.776599\pi\)
\(192\) −6185.76 + 20364.7i −0.167799 + 0.552428i
\(193\) 18873.5 0.506686 0.253343 0.967377i \(-0.418470\pi\)
0.253343 + 0.967377i \(0.418470\pi\)
\(194\) 43478.1 + 28036.9i 1.15523 + 0.744950i
\(195\) 0 0
\(196\) 6971.44 + 15391.3i 0.181472 + 0.400649i
\(197\) −35212.2 −0.907319 −0.453660 0.891175i \(-0.649882\pi\)
−0.453660 + 0.891175i \(0.649882\pi\)
\(198\) 3291.03 5103.55i 0.0839463 0.130179i
\(199\) 31238.6i 0.788834i −0.918932 0.394417i \(-0.870947\pi\)
0.918932 0.394417i \(-0.129053\pi\)
\(200\) 0 0
\(201\) 20865.7 0.516465
\(202\) 35747.4 + 23051.7i 0.876075 + 0.564938i
\(203\) 36293.0i 0.880706i
\(204\) 4123.81 1867.86i 0.0990919 0.0448833i
\(205\) 0 0
\(206\) −22814.6 + 35379.7i −0.537624 + 0.833718i
\(207\) 8713.11i 0.203344i
\(208\) −36983.1 + 42150.3i −0.854824 + 0.974257i
\(209\) 8768.04 0.200729
\(210\) 0 0
\(211\) 59099.8i 1.32746i −0.747973 0.663730i \(-0.768973\pi\)
0.747973 0.663730i \(-0.231027\pi\)
\(212\) −18142.9 40055.3i −0.403677 0.891226i
\(213\) −27963.3 −0.616353
\(214\) −35571.4 + 55162.1i −0.776736 + 1.20452i
\(215\) 0 0
\(216\) 8881.52 + 1319.12i 0.190362 + 0.0282734i
\(217\) −31092.1 −0.660285
\(218\) −7364.18 4748.80i −0.154957 0.0999243i
\(219\) 34061.5i 0.710192i
\(220\) 0 0
\(221\) 11927.4 0.244210
\(222\) −20702.0 + 32103.5i −0.420056 + 0.651399i
\(223\) 63431.3i 1.27554i 0.770227 + 0.637769i \(0.220143\pi\)
−0.770227 + 0.637769i \(0.779857\pi\)
\(224\) −10300.8 36113.6i −0.205293 0.719738i
\(225\) 0 0
\(226\) 790.128 + 509.515i 0.0154697 + 0.00997563i
\(227\) 81211.1i 1.57603i −0.615658 0.788013i \(-0.711110\pi\)
0.615658 0.788013i \(-0.288890\pi\)
\(228\) 5349.02 + 11809.4i 0.102897 + 0.227174i
\(229\) 37312.5 0.711513 0.355757 0.934579i \(-0.384223\pi\)
0.355757 + 0.934579i \(0.384223\pi\)
\(230\) 0 0
\(231\) 10715.0i 0.200802i
\(232\) 9304.80 62648.3i 0.172875 1.16395i
\(233\) −59419.3 −1.09450 −0.547250 0.836969i \(-0.684325\pi\)
−0.547250 + 0.836969i \(0.684325\pi\)
\(234\) 19881.4 + 12820.5i 0.363090 + 0.234139i
\(235\) 0 0
\(236\) 25951.1 11754.5i 0.465943 0.211047i
\(237\) 59744.8 1.06366
\(238\) −4329.01 + 6713.18i −0.0764248 + 0.118515i
\(239\) 15215.1i 0.266365i 0.991092 + 0.133183i \(0.0425197\pi\)
−0.991092 + 0.133183i \(0.957480\pi\)
\(240\) 0 0
\(241\) 113924. 1.96146 0.980732 0.195356i \(-0.0625862\pi\)
0.980732 + 0.195356i \(0.0625862\pi\)
\(242\) −38589.8 24884.7i −0.658934 0.424915i
\(243\) 3788.00i 0.0641500i
\(244\) −33270.5 73453.6i −0.558831 1.23377i
\(245\) 0 0
\(246\) 27832.0 43160.3i 0.459911 0.713205i
\(247\) 34156.8i 0.559864i
\(248\) −53670.7 7971.40i −0.872637 0.129608i
\(249\) −42773.9 −0.689891
\(250\) 0 0
\(251\) 6177.27i 0.0980504i −0.998798 0.0490252i \(-0.984389\pi\)
0.998798 0.0490252i \(-0.0156115\pi\)
\(252\) −14431.7 + 6536.77i −0.227256 + 0.102935i
\(253\) −18145.3 −0.283480
\(254\) −41051.5 + 63660.4i −0.636300 + 0.986739i
\(255\) 0 0
\(256\) −8522.24 64979.5i −0.130039 0.991509i
\(257\) 104659. 1.58457 0.792286 0.610150i \(-0.208891\pi\)
0.792286 + 0.610150i \(0.208891\pi\)
\(258\) 2987.13 + 1926.26i 0.0448761 + 0.0289384i
\(259\) 67402.0i 1.00478i
\(260\) 0 0
\(261\) −26719.7 −0.392239
\(262\) 18397.7 28530.1i 0.268016 0.415625i
\(263\) 74062.0i 1.07074i −0.844618 0.535370i \(-0.820172\pi\)
0.844618 0.535370i \(-0.179828\pi\)
\(264\) −2747.11 + 18496.0i −0.0394156 + 0.265381i
\(265\) 0 0
\(266\) −19224.6 12397.0i −0.271703 0.175208i
\(267\) 27855.7i 0.390744i
\(268\) −58526.0 + 26509.1i −0.814853 + 0.369084i
\(269\) −21868.5 −0.302213 −0.151107 0.988517i \(-0.548284\pi\)
−0.151107 + 0.988517i \(0.548284\pi\)
\(270\) 0 0
\(271\) 40797.1i 0.555508i −0.960652 0.277754i \(-0.910410\pi\)
0.960652 0.277754i \(-0.0895900\pi\)
\(272\) −9193.78 + 10478.3i −0.124267 + 0.141629i
\(273\) −41741.3 −0.560068
\(274\) −1033.12 666.207i −0.0137609 0.00887376i
\(275\) 0 0
\(276\) −11069.7 24439.3i −0.145317 0.320827i
\(277\) −43989.6 −0.573311 −0.286655 0.958034i \(-0.592544\pi\)
−0.286655 + 0.958034i \(0.592544\pi\)
\(278\) 71870.8 111453.i 0.929957 1.44213i
\(279\) 22890.7i 0.294070i
\(280\) 0 0
\(281\) −135950. −1.72174 −0.860869 0.508827i \(-0.830079\pi\)
−0.860869 + 0.508827i \(0.830079\pi\)
\(282\) 58457.4 + 37696.3i 0.735091 + 0.474025i
\(283\) 78066.1i 0.974742i 0.873195 + 0.487371i \(0.162044\pi\)
−0.873195 + 0.487371i \(0.837956\pi\)
\(284\) 78434.0 35526.4i 0.972451 0.440468i
\(285\) 0 0
\(286\) −26699.1 + 41403.5i −0.326411 + 0.506180i
\(287\) 90615.8i 1.10012i
\(288\) −26587.6 + 7583.66i −0.320549 + 0.0914311i
\(289\) −80555.9 −0.964499
\(290\) 0 0
\(291\) 67204.5i 0.793620i
\(292\) −43273.9 95538.7i −0.507528 1.12050i
\(293\) −61325.1 −0.714337 −0.357169 0.934040i \(-0.616258\pi\)
−0.357169 + 0.934040i \(0.616258\pi\)
\(294\) −11895.3 + 18446.5i −0.137619 + 0.213412i
\(295\) 0 0
\(296\) 17280.5 116348.i 0.197230 1.32793i
\(297\) 7888.60 0.0894308
\(298\) −113815. 73393.8i −1.28164 0.826470i
\(299\) 70686.7i 0.790670i
\(300\) 0 0
\(301\) −6271.54 −0.0692215
\(302\) −26092.4 + 40462.7i −0.286088 + 0.443650i
\(303\) 55255.0i 0.601848i
\(304\) −30006.8 26328.3i −0.324693 0.284889i
\(305\) 0 0
\(306\) 4942.39 + 3187.11i 0.0527830 + 0.0340372i
\(307\) 126561.i 1.34283i 0.741080 + 0.671417i \(0.234314\pi\)
−0.741080 + 0.671417i \(0.765686\pi\)
\(308\) −13613.0 30054.4i −0.143500 0.316815i
\(309\) −54686.7 −0.572749
\(310\) 0 0
\(311\) 147924.i 1.52939i 0.644395 + 0.764693i \(0.277109\pi\)
−0.644395 + 0.764693i \(0.722891\pi\)
\(312\) −72053.0 10701.6i −0.740190 0.109936i
\(313\) 154062. 1.57256 0.786278 0.617872i \(-0.212005\pi\)
0.786278 + 0.617872i \(0.212005\pi\)
\(314\) 97610.1 + 62944.0i 0.990001 + 0.638404i
\(315\) 0 0
\(316\) −167578. + 75903.6i −1.67819 + 0.760131i
\(317\) 40362.8 0.401664 0.200832 0.979626i \(-0.435635\pi\)
0.200832 + 0.979626i \(0.435635\pi\)
\(318\) 30956.9 48006.2i 0.306128 0.474727i
\(319\) 55644.5i 0.546815i
\(320\) 0 0
\(321\) −85264.7 −0.827483
\(322\) 39784.9 + 25655.4i 0.383713 + 0.247438i
\(323\) 8491.16i 0.0813883i
\(324\) 4812.51 + 10624.9i 0.0458439 + 0.101213i
\(325\) 0 0
\(326\) −30691.5 + 47594.6i −0.288790 + 0.447840i
\(327\) 11382.9i 0.106453i
\(328\) −23232.1 + 156419.i −0.215944 + 1.45393i
\(329\) −122732. −1.13388
\(330\) 0 0
\(331\) 103314.i 0.942982i −0.881871 0.471491i \(-0.843716\pi\)
0.881871 0.471491i \(-0.156284\pi\)
\(332\) 119976. 54342.7i 1.08848 0.493021i
\(333\) −49622.8 −0.447499
\(334\) −54177.9 + 84016.0i −0.485656 + 0.753129i
\(335\) 0 0
\(336\) 32174.5 36669.8i 0.284993 0.324811i
\(337\) 132569. 1.16730 0.583649 0.812006i \(-0.301625\pi\)
0.583649 + 0.812006i \(0.301625\pi\)
\(338\) −65278.8 42095.2i −0.571398 0.368467i
\(339\) 1221.31i 0.0106274i
\(340\) 0 0
\(341\) −47670.5 −0.409960
\(342\) −9126.95 + 14153.6i −0.0780321 + 0.121008i
\(343\) 126782.i 1.07763i
\(344\) −10825.8 1607.90i −0.0914837 0.0135876i
\(345\) 0 0
\(346\) −166759. 107535.i −1.39295 0.898249i
\(347\) 235031.i 1.95194i 0.217916 + 0.975968i \(0.430074\pi\)
−0.217916 + 0.975968i \(0.569926\pi\)
\(348\) 74945.8 33946.4i 0.618855 0.280308i
\(349\) −10835.2 −0.0889583 −0.0444791 0.999010i \(-0.514163\pi\)
−0.0444791 + 0.999010i \(0.514163\pi\)
\(350\) 0 0
\(351\) 30730.8i 0.249436i
\(352\) −15793.2 55369.4i −0.127463 0.446873i
\(353\) 87770.7 0.704369 0.352184 0.935931i \(-0.385439\pi\)
0.352184 + 0.935931i \(0.385439\pi\)
\(354\) 31102.5 + 20056.5i 0.248192 + 0.160047i
\(355\) 0 0
\(356\) −35389.7 78132.2i −0.279239 0.616496i
\(357\) −10376.6 −0.0814179
\(358\) −13387.1 + 20759.9i −0.104453 + 0.161979i
\(359\) 32404.1i 0.251427i 0.992067 + 0.125713i \(0.0401219\pi\)
−0.992067 + 0.125713i \(0.959878\pi\)
\(360\) 0 0
\(361\) 106005. 0.813413
\(362\) −82096.0 52939.8i −0.626477 0.403985i
\(363\) 59648.6i 0.452676i
\(364\) 117080. 53030.8i 0.883647 0.400244i
\(365\) 0 0
\(366\) 56769.0 88034.2i 0.423789 0.657187i
\(367\) 98110.7i 0.728424i 0.931316 + 0.364212i \(0.118662\pi\)
−0.931316 + 0.364212i \(0.881338\pi\)
\(368\) 62098.5 + 54485.9i 0.458548 + 0.402336i
\(369\) 66713.3 0.489959
\(370\) 0 0
\(371\) 100790.i 0.732267i
\(372\) −29081.8 64205.9i −0.210153 0.463969i
\(373\) 113856. 0.818345 0.409172 0.912457i \(-0.365817\pi\)
0.409172 + 0.912457i \(0.365817\pi\)
\(374\) −6637.24 + 10292.7i −0.0474509 + 0.0735841i
\(375\) 0 0
\(376\) −211858. 31466.1i −1.49854 0.222570i
\(377\) 216768. 1.52515
\(378\) −17296.4 11153.6i −0.121052 0.0780605i
\(379\) 97914.7i 0.681663i −0.940124 0.340831i \(-0.889292\pi\)
0.940124 0.340831i \(-0.110708\pi\)
\(380\) 0 0
\(381\) −98400.6 −0.677872
\(382\) 102114. 158353.i 0.699778 1.08518i
\(383\) 199529.i 1.36022i 0.733112 + 0.680108i \(0.238067\pi\)
−0.733112 + 0.680108i \(0.761933\pi\)
\(384\) 64940.5 55049.9i 0.440406 0.373331i
\(385\) 0 0
\(386\) −63446.4 40913.5i −0.425826 0.274595i
\(387\) 4617.24i 0.0308291i
\(388\) −85380.9 188501.i −0.567149 1.25213i
\(389\) −28806.1 −0.190364 −0.0951820 0.995460i \(-0.530343\pi\)
−0.0951820 + 0.995460i \(0.530343\pi\)
\(390\) 0 0
\(391\) 17572.3i 0.114941i
\(392\) 9929.29 66852.9i 0.0646169 0.435059i
\(393\) 44099.3 0.285527
\(394\) 118371. + 76332.0i 0.762525 + 0.491716i
\(395\) 0 0
\(396\) −22126.7 + 10022.2i −0.141100 + 0.0639105i
\(397\) −108324. −0.687293 −0.343646 0.939099i \(-0.611662\pi\)
−0.343646 + 0.939099i \(0.611662\pi\)
\(398\) −67718.2 + 105014.i −0.427503 + 0.662948i
\(399\) 29715.7i 0.186655i
\(400\) 0 0
\(401\) 23481.5 0.146028 0.0730141 0.997331i \(-0.476738\pi\)
0.0730141 + 0.997331i \(0.476738\pi\)
\(402\) −70143.4 45232.1i −0.434045 0.279895i
\(403\) 185705.i 1.14344i
\(404\) −70199.5 154984.i −0.430102 0.949566i
\(405\) 0 0
\(406\) −78675.0 + 122005.i −0.477293 + 0.740159i
\(407\) 103341.i 0.623854i
\(408\) −17912.0 2660.36i −0.107603 0.0159816i
\(409\) 129856. 0.776272 0.388136 0.921602i \(-0.373119\pi\)
0.388136 + 0.921602i \(0.373119\pi\)
\(410\) 0 0
\(411\) 1596.90i 0.00945352i
\(412\) 153390. 69477.4i 0.903655 0.409307i
\(413\) −65300.2 −0.382837
\(414\) 18888.0 29290.5i 0.110201 0.170894i
\(415\) 0 0
\(416\) 215697. 61523.9i 1.24640 0.355514i
\(417\) 172274. 0.990714
\(418\) −29475.2 19007.1i −0.168696 0.108784i
\(419\) 193614.i 1.10283i −0.834230 0.551416i \(-0.814088\pi\)
0.834230 0.551416i \(-0.185912\pi\)
\(420\) 0 0
\(421\) 185577. 1.04703 0.523515 0.852016i \(-0.324620\pi\)
0.523515 + 0.852016i \(0.324620\pi\)
\(422\) −128115. + 198674.i −0.719407 + 1.11562i
\(423\) 90358.1i 0.504994i
\(424\) −25840.5 + 173982.i −0.143737 + 0.967770i
\(425\) 0 0
\(426\) 94003.2 + 60618.1i 0.517992 + 0.334028i
\(427\) 184829.i 1.01371i
\(428\) 239158. 108326.i 1.30556 0.591349i
\(429\) −63997.8 −0.347736
\(430\) 0 0
\(431\) 37823.7i 0.203615i −0.994804 0.101808i \(-0.967537\pi\)
0.994804 0.101808i \(-0.0324626\pi\)
\(432\) −26997.1 23687.6i −0.144660 0.126927i
\(433\) −13758.6 −0.0733834 −0.0366917 0.999327i \(-0.511682\pi\)
−0.0366917 + 0.999327i \(0.511682\pi\)
\(434\) 104521. + 67400.7i 0.554913 + 0.357837i
\(435\) 0 0
\(436\) 14461.5 + 31927.7i 0.0760749 + 0.167956i
\(437\) 50321.9 0.263508
\(438\) 73837.6 114503.i 0.384884 0.596856i
\(439\) 100071.i 0.519252i −0.965709 0.259626i \(-0.916401\pi\)
0.965709 0.259626i \(-0.0835993\pi\)
\(440\) 0 0
\(441\) −28513.0 −0.146611
\(442\) −40096.0 25856.0i −0.205238 0.132348i
\(443\) 314053.i 1.60028i 0.599815 + 0.800139i \(0.295241\pi\)
−0.599815 + 0.800139i \(0.704759\pi\)
\(444\) 139186. 63043.9i 0.706042 0.319799i
\(445\) 0 0
\(446\) 137505. 213234.i 0.691270 1.07198i
\(447\) 175925.i 0.880466i
\(448\) −43658.3 + 143731.i −0.217526 + 0.716136i
\(449\) −104489. −0.518294 −0.259147 0.965838i \(-0.583441\pi\)
−0.259147 + 0.965838i \(0.583441\pi\)
\(450\) 0 0
\(451\) 138932.i 0.683046i
\(452\) −1551.63 3425.64i −0.00759470 0.0167673i
\(453\) −62543.5 −0.304780
\(454\) −176047. + 273004.i −0.854117 + 1.32452i
\(455\) 0 0
\(456\) 7618.50 51294.6i 0.0366387 0.246685i
\(457\) −227716. −1.09034 −0.545169 0.838326i \(-0.683535\pi\)
−0.545169 + 0.838326i \(0.683535\pi\)
\(458\) −125432. 80885.0i −0.597967 0.385600i
\(459\) 7639.50i 0.0362610i
\(460\) 0 0
\(461\) 39587.7 0.186276 0.0931382 0.995653i \(-0.470310\pi\)
0.0931382 + 0.995653i \(0.470310\pi\)
\(462\) 23227.7 36020.2i 0.108823 0.168757i
\(463\) 68330.8i 0.318753i −0.987218 0.159377i \(-0.949052\pi\)
0.987218 0.159377i \(-0.0509484\pi\)
\(464\) −167087. + 190432.i −0.776080 + 0.884511i
\(465\) 0 0
\(466\) 199748. + 128808.i 0.919834 + 0.593157i
\(467\) 51291.7i 0.235187i −0.993062 0.117594i \(-0.962482\pi\)
0.993062 0.117594i \(-0.0375180\pi\)
\(468\) −39042.4 86196.5i −0.178256 0.393548i
\(469\) 147267. 0.669516
\(470\) 0 0
\(471\) 150877.i 0.680113i
\(472\) −112720. 16741.6i −0.505961 0.0751474i
\(473\) −9615.53 −0.0429785
\(474\) −200842. 129513.i −0.893918 0.576444i
\(475\) 0 0
\(476\) 29105.3 13183.1i 0.128457 0.0581841i
\(477\) 74203.7 0.326129
\(478\) 32982.8 51147.9i 0.144355 0.223858i
\(479\) 420785.i 1.83396i 0.398935 + 0.916979i \(0.369380\pi\)
−0.398935 + 0.916979i \(0.630620\pi\)
\(480\) 0 0
\(481\) 402574. 1.74003
\(482\) −382973. 246961.i −1.64844 1.06300i
\(483\) 61495.9i 0.263604i
\(484\) 75781.4 + 167308.i 0.323498 + 0.714209i
\(485\) 0 0
\(486\) −8211.51 + 12734.0i −0.0347657 + 0.0539127i
\(487\) 62163.7i 0.262107i −0.991375 0.131054i \(-0.958164\pi\)
0.991375 0.131054i \(-0.0418360\pi\)
\(488\) −47386.5 + 319049.i −0.198983 + 1.33973i
\(489\) −73567.4 −0.307658
\(490\) 0 0
\(491\) 244825.i 1.01553i −0.861496 0.507764i \(-0.830472\pi\)
0.861496 0.507764i \(-0.169528\pi\)
\(492\) −187123. + 84756.8i −0.773033 + 0.350142i
\(493\) 53887.3 0.221714
\(494\) 74044.1 114823.i 0.303415 0.470518i
\(495\) 0 0
\(496\) 163142. + 143143.i 0.663138 + 0.581844i
\(497\) −197361. −0.799005
\(498\) 143791. + 92724.2i 0.579795 + 0.373882i
\(499\) 248564.i 0.998245i 0.866532 + 0.499122i \(0.166344\pi\)
−0.866532 + 0.499122i \(0.833656\pi\)
\(500\) 0 0
\(501\) −129864. −0.517386
\(502\) −13390.9 + 20765.9i −0.0531377 + 0.0824030i
\(503\) 222640.i 0.879970i 0.898005 + 0.439985i \(0.145016\pi\)
−0.898005 + 0.439985i \(0.854984\pi\)
\(504\) 62684.6 + 9310.19i 0.246774 + 0.0366520i
\(505\) 0 0
\(506\) 60998.3 + 39334.8i 0.238241 + 0.153630i
\(507\) 100902.i 0.392541i
\(508\) 276003. 125014.i 1.06951 0.484431i
\(509\) −119110. −0.459741 −0.229870 0.973221i \(-0.573830\pi\)
−0.229870 + 0.973221i \(0.573830\pi\)
\(510\) 0 0
\(511\) 240402.i 0.920652i
\(512\) −112212. + 236913.i −0.428055 + 0.903753i
\(513\) −21877.3 −0.0831302
\(514\) −351829. 226878.i −1.33170 0.858748i
\(515\) 0 0
\(516\) −5866.04 12950.9i −0.0220316 0.0486406i
\(517\) −188173. −0.704007
\(518\) −146112. + 226583.i −0.544536 + 0.844436i
\(519\) 257761.i 0.956935i
\(520\) 0 0
\(521\) 191412. 0.705170 0.352585 0.935780i \(-0.385303\pi\)
0.352585 + 0.935780i \(0.385303\pi\)
\(522\) 89822.5 + 57922.2i 0.329643 + 0.212571i
\(523\) 393137.i 1.43728i −0.695383 0.718639i \(-0.744765\pi\)
0.695383 0.718639i \(-0.255235\pi\)
\(524\) −123694. + 56026.6i −0.450490 + 0.204048i
\(525\) 0 0
\(526\) −160550. + 248971.i −0.580280 + 0.899866i
\(527\) 46165.2i 0.166224i
\(528\) 49330.0 56222.2i 0.176947 0.201669i
\(529\) 175701. 0.627859
\(530\) 0 0
\(531\) 48075.4i 0.170504i
\(532\) 37752.7 + 83349.1i 0.133390 + 0.294495i
\(533\) −541224. −1.90512
\(534\) 60384.9 93641.5i 0.211761 0.328387i
\(535\) 0 0
\(536\) 254210. + 37756.4i 0.884837 + 0.131420i
\(537\) −32088.8 −0.111277
\(538\) 73514.3 + 47405.8i 0.253985 + 0.163782i
\(539\) 59379.0i 0.204388i
\(540\) 0 0
\(541\) 466336. 1.59333 0.796663 0.604423i \(-0.206596\pi\)
0.796663 + 0.604423i \(0.206596\pi\)
\(542\) −88438.8 + 137146.i −0.301054 + 0.466858i
\(543\) 126897.i 0.430378i
\(544\) 53620.9 15294.5i 0.181191 0.0516817i
\(545\) 0 0
\(546\) 140320. + 90485.6i 0.470689 + 0.303525i
\(547\) 188282.i 0.629265i 0.949214 + 0.314632i \(0.101881\pi\)
−0.949214 + 0.314632i \(0.898119\pi\)
\(548\) 2028.80 + 4479.12i 0.00675582 + 0.0149153i
\(549\) 136075. 0.451476
\(550\) 0 0
\(551\) 154318.i 0.508291i
\(552\) −15766.3 + 106153.i −0.0517431 + 0.348381i
\(553\) 421671. 1.37887
\(554\) 147878. + 95359.4i 0.481819 + 0.310702i
\(555\) 0 0
\(556\) −483210. + 218868.i −1.56310 + 0.708000i
\(557\) −267269. −0.861466 −0.430733 0.902479i \(-0.641745\pi\)
−0.430733 + 0.902479i \(0.641745\pi\)
\(558\) 49621.8 76950.8i 0.159369 0.247141i
\(559\) 37458.2i 0.119874i
\(560\) 0 0
\(561\) −15909.5 −0.0505510
\(562\) 457018. + 294709.i 1.44697 + 0.933084i
\(563\) 41516.3i 0.130979i 0.997853 + 0.0654896i \(0.0208609\pi\)
−0.997853 + 0.0654896i \(0.979139\pi\)
\(564\) −114797. 253445.i −0.360887 0.796755i
\(565\) 0 0
\(566\) 169230. 262432.i 0.528255 0.819188i
\(567\) 26735.2i 0.0831604i
\(568\) −340682. 50599.5i −1.05597 0.156837i
\(569\) 432092. 1.33460 0.667301 0.744788i \(-0.267450\pi\)
0.667301 + 0.744788i \(0.267450\pi\)
\(570\) 0 0
\(571\) 568904.i 1.74488i −0.488717 0.872442i \(-0.662535\pi\)
0.488717 0.872442i \(-0.337465\pi\)
\(572\) 179507. 81306.8i 0.548641 0.248505i
\(573\) 244768. 0.745497
\(574\) 196435. 304620.i 0.596203 0.924558i
\(575\) 0 0
\(576\) 105818. + 32142.2i 0.318944 + 0.0968791i
\(577\) −81702.4 −0.245405 −0.122702 0.992444i \(-0.539156\pi\)
−0.122702 + 0.992444i \(0.539156\pi\)
\(578\) 270802. + 174627.i 0.810579 + 0.522704i
\(579\) 98069.8i 0.292535i
\(580\) 0 0
\(581\) −301893. −0.894335
\(582\) 145684. 225919.i 0.430097 0.666970i
\(583\) 154531.i 0.454652i
\(584\) −61634.1 + 414977.i −0.180716 + 1.21674i
\(585\) 0 0
\(586\) 206154. + 132939.i 0.600340 + 0.387130i
\(587\) 435087.i 1.26270i −0.775498 0.631350i \(-0.782501\pi\)
0.775498 0.631350i \(-0.217499\pi\)
\(588\) 79975.7 36224.7i 0.231315 0.104773i
\(589\) 132204. 0.381077
\(590\) 0 0
\(591\) 182968.i 0.523841i
\(592\) −310307. + 353662.i −0.885419 + 1.00913i
\(593\) −13910.0 −0.0395566 −0.0197783 0.999804i \(-0.506296\pi\)
−0.0197783 + 0.999804i \(0.506296\pi\)
\(594\) −26518.8 17100.7i −0.0751590 0.0484664i
\(595\) 0 0
\(596\) 223506. + 493450.i 0.629212 + 1.38916i
\(597\) −162321. −0.455434
\(598\) −153233. + 237625.i −0.428498 + 0.664491i
\(599\) 252321.i 0.703233i 0.936144 + 0.351616i \(0.114368\pi\)
−0.936144 + 0.351616i \(0.885632\pi\)
\(600\) 0 0
\(601\) −546279. −1.51240 −0.756198 0.654342i \(-0.772945\pi\)
−0.756198 + 0.654342i \(0.772945\pi\)
\(602\) 21082.8 + 13595.3i 0.0581748 + 0.0375141i
\(603\) 108421.i 0.298181i
\(604\) 175428. 79459.3i 0.480866 0.217806i
\(605\) 0 0
\(606\) 119780. 185749.i 0.326167 0.505802i
\(607\) 538337.i 1.46109i −0.682865 0.730544i \(-0.739266\pi\)
0.682865 0.730544i \(-0.260734\pi\)
\(608\) 43798.9 + 153555.i 0.118483 + 0.415390i
\(609\) −188584. −0.508476
\(610\) 0 0
\(611\) 733047.i 1.96358i
\(612\) −9705.70 21427.9i −0.0259134 0.0572107i
\(613\) 238346. 0.634289 0.317144 0.948377i \(-0.397276\pi\)
0.317144 + 0.948377i \(0.397276\pi\)
\(614\) 274355. 425454.i 0.727739 1.12854i
\(615\) 0 0
\(616\) −19388.7 + 130542.i −0.0510961 + 0.344025i
\(617\) −233463. −0.613264 −0.306632 0.951828i \(-0.599202\pi\)
−0.306632 + 0.951828i \(0.599202\pi\)
\(618\) 183838. + 118548.i 0.481347 + 0.310398i
\(619\) 18530.9i 0.0483633i 0.999708 + 0.0241816i \(0.00769800\pi\)
−0.999708 + 0.0241816i \(0.992302\pi\)
\(620\) 0 0
\(621\) 45274.6 0.117401
\(622\) 320665. 497269.i 0.828840 1.28532i
\(623\) 196602.i 0.506538i
\(624\) 219019. + 192170.i 0.562487 + 0.493533i
\(625\) 0 0
\(626\) −517904. 333971.i −1.32160 0.852237i
\(627\) 45560.1i 0.115891i
\(628\) −191684. 423193.i −0.486033 1.07305i
\(629\) 100077. 0.252950
\(630\) 0 0
\(631\) 2833.16i 0.00711560i 0.999994 + 0.00355780i \(0.00113249\pi\)
−0.999994 + 0.00355780i \(0.998868\pi\)
\(632\) 727881. + 108108.i 1.82233 + 0.270660i
\(633\) −307092. −0.766409
\(634\) −135686. 87497.5i −0.337565 0.217679i
\(635\) 0 0
\(636\) −208133. + 94273.1i −0.514550 + 0.233063i
\(637\) 231317. 0.570070
\(638\) −120625. + 187058.i −0.296343 + 0.459552i
\(639\) 145302.i 0.355852i
\(640\) 0 0
\(641\) −14308.7 −0.0348244 −0.0174122 0.999848i \(-0.505543\pi\)
−0.0174122 + 0.999848i \(0.505543\pi\)
\(642\) 286631. + 184834.i 0.695429 + 0.448449i
\(643\) 436544.i 1.05586i −0.849288 0.527930i \(-0.822968\pi\)
0.849288 0.527930i \(-0.177032\pi\)
\(644\) −78128.4 172489.i −0.188381 0.415901i
\(645\) 0 0
\(646\) 18406.9 28544.4i 0.0441079 0.0684000i
\(647\) 104345.i 0.249266i −0.992203 0.124633i \(-0.960225\pi\)
0.992203 0.124633i \(-0.0397753\pi\)
\(648\) 6854.36 46149.8i 0.0163236 0.109905i
\(649\) −100118. −0.237697
\(650\) 0 0
\(651\) 161560.i 0.381216i
\(652\) 206349. 93464.8i 0.485407 0.219863i
\(653\) 382198. 0.896317 0.448159 0.893954i \(-0.352080\pi\)
0.448159 + 0.893954i \(0.352080\pi\)
\(654\) −24675.5 + 38265.4i −0.0576913 + 0.0894645i
\(655\) 0 0
\(656\) 417180. 475467.i 0.969429 1.10487i
\(657\) 176989. 0.410029
\(658\) 412584. + 266056.i 0.952930 + 0.614498i
\(659\) 663093.i 1.52688i 0.645881 + 0.763438i \(0.276490\pi\)
−0.645881 + 0.763438i \(0.723510\pi\)
\(660\) 0 0
\(661\) −510788. −1.16906 −0.584531 0.811371i \(-0.698721\pi\)
−0.584531 + 0.811371i \(0.698721\pi\)
\(662\) −223961. + 347307.i −0.511043 + 0.792496i
\(663\) 61976.8i 0.140995i
\(664\) −521122. 77399.2i −1.18196 0.175550i
\(665\) 0 0
\(666\) 166815. + 107571.i 0.376085 + 0.242519i
\(667\) 319357.i 0.717836i
\(668\) 364255. 164988.i 0.816306 0.369743i
\(669\) 329599. 0.736433
\(670\) 0 0
\(671\) 283381.i 0.629398i
\(672\) −187652. + 53524.5i −0.415541 + 0.118526i
\(673\) −367929. −0.812332 −0.406166 0.913799i \(-0.633134\pi\)
−0.406166 + 0.913799i \(0.633134\pi\)
\(674\) −445651. 287379.i −0.981014 0.632609i
\(675\) 0 0
\(676\) 128193. + 283019.i 0.280524 + 0.619331i
\(677\) 87657.7 0.191255 0.0956275 0.995417i \(-0.469514\pi\)
0.0956275 + 0.995417i \(0.469514\pi\)
\(678\) 2647.52 4105.63i 0.00575943 0.00893141i
\(679\) 474321.i 1.02880i
\(680\) 0 0
\(681\) −421985. −0.909919
\(682\) 160252. + 103339.i 0.344536 + 0.222175i
\(683\) 694219.i 1.48818i −0.668080 0.744090i \(-0.732884\pi\)
0.668080 0.744090i \(-0.267116\pi\)
\(684\) 61363.4 27794.3i 0.131159 0.0594078i
\(685\) 0 0
\(686\) −274836. + 426200.i −0.584016 + 0.905659i
\(687\) 193881.i 0.410793i
\(688\) 32907.2 + 28873.1i 0.0695206 + 0.0609982i
\(689\) −601992. −1.26810
\(690\) 0 0
\(691\) 538950.i 1.12874i −0.825523 0.564368i \(-0.809120\pi\)
0.825523 0.564368i \(-0.190880\pi\)
\(692\) 327476. + 722991.i 0.683860 + 1.50980i
\(693\) 55676.7 0.115933
\(694\) 509493. 790093.i 1.05784 1.64044i
\(695\) 0 0
\(696\) −325530. 48349.2i −0.672006 0.0998092i
\(697\) −134545. −0.276951
\(698\) 36424.3 + 23488.3i 0.0747619 + 0.0482103i
\(699\) 308752.i 0.631910i
\(700\) 0 0
\(701\) −741852. −1.50967 −0.754834 0.655916i \(-0.772283\pi\)
−0.754834 + 0.655916i \(0.772283\pi\)
\(702\) 66617.4 103307.i 0.135180 0.209630i
\(703\) 286593.i 0.579902i
\(704\) −66936.9 + 220369.i −0.135058 + 0.444637i
\(705\) 0 0
\(706\) −295055. 190267.i −0.591962 0.381728i
\(707\) 389983.i 0.780201i
\(708\) −61078.0 134846.i −0.121848 0.269012i
\(709\) 199695. 0.397260 0.198630 0.980075i \(-0.436351\pi\)
0.198630 + 0.980075i \(0.436351\pi\)
\(710\) 0 0
\(711\) 310443.i 0.614106i
\(712\) −50404.8 + 339371.i −0.0994287 + 0.669444i
\(713\) −273593. −0.538177
\(714\) 34882.7 + 22494.2i 0.0684248 + 0.0441239i
\(715\) 0 0
\(716\) 90005.6 40767.7i 0.175567 0.0795225i
\(717\) 79059.8 0.153786
\(718\) 70244.8 108932.i 0.136259 0.211303i
\(719\) 142037.i 0.274755i −0.990519 0.137377i \(-0.956133\pi\)
0.990519 0.137377i \(-0.0438673\pi\)
\(720\) 0 0
\(721\) −385971. −0.742480
\(722\) −356352. 229794.i −0.683604 0.440824i
\(723\) 591966.i 1.13245i
\(724\) 161218. + 355931.i 0.307564 + 0.679030i
\(725\) 0 0
\(726\) −129305. + 200518.i −0.245325 + 0.380436i
\(727\) 85013.5i 0.160849i −0.996761 0.0804247i \(-0.974372\pi\)
0.996761 0.0804247i \(-0.0256276\pi\)
\(728\) −508541. 75530.6i −0.959540 0.142515i
\(729\) −19683.0 −0.0370370
\(730\) 0 0
\(731\) 9311.89i 0.0174262i
\(732\) −381676. + 172879.i −0.712317 + 0.322641i
\(733\) −3612.19 −0.00672300 −0.00336150 0.999994i \(-0.501070\pi\)
−0.00336150 + 0.999994i \(0.501070\pi\)
\(734\) 212682. 329815.i 0.394764 0.612179i
\(735\) 0 0
\(736\) −90641.0 317778.i −0.167328 0.586636i
\(737\) 225790. 0.415691
\(738\) −224267. 144619.i −0.411769 0.265530i
\(739\) 644842.i 1.18077i −0.807123 0.590384i \(-0.798976\pi\)
0.807123 0.590384i \(-0.201024\pi\)
\(740\) 0 0
\(741\) 177484. 0.323238
\(742\) 218490. 338822.i 0.396847 0.615408i
\(743\) 78321.7i 0.141875i −0.997481 0.0709373i \(-0.977401\pi\)
0.997481 0.0709373i \(-0.0225990\pi\)
\(744\) −41420.6 + 278881.i −0.0748291 + 0.503817i
\(745\) 0 0
\(746\) −382744. 246813.i −0.687750 0.443496i
\(747\) 222260.i 0.398309i
\(748\) 44624.3 20212.4i 0.0797569 0.0361256i
\(749\) −601787. −1.07270
\(750\) 0 0
\(751\) 72594.7i 0.128714i 0.997927 + 0.0643569i \(0.0204996\pi\)
−0.997927 + 0.0643569i \(0.979500\pi\)
\(752\) 643984. + 565039.i 1.13878 + 0.999177i
\(753\) −32098.1 −0.0566094
\(754\) −728702. 469905.i −1.28176 0.826546i
\(755\) 0 0
\(756\) 33966.1 + 74989.2i 0.0594294 + 0.131206i
\(757\) −627366. −1.09479 −0.547393 0.836876i \(-0.684380\pi\)
−0.547393 + 0.836876i \(0.684380\pi\)
\(758\) −212257. + 329156.i −0.369422 + 0.572880i
\(759\) 94285.6i 0.163667i
\(760\) 0 0
\(761\) 95973.0 0.165722 0.0828609 0.996561i \(-0.473594\pi\)
0.0828609 + 0.996561i \(0.473594\pi\)
\(762\) 330789. + 213310.i 0.569694 + 0.367368i
\(763\) 80338.9i 0.137999i
\(764\) −686548. + 310969.i −1.17621 + 0.532759i
\(765\) 0 0
\(766\) 432533. 670748.i 0.737160 1.14315i
\(767\) 390020.i 0.662974i
\(768\) −337644. + 44282.9i −0.572448 + 0.0750781i
\(769\) −309887. −0.524023 −0.262011 0.965065i \(-0.584386\pi\)
−0.262011 + 0.965065i \(0.584386\pi\)
\(770\) 0 0
\(771\) 543826.i 0.914853i
\(772\) 124594. + 275075.i 0.209056 + 0.461547i
\(773\) −377481. −0.631737 −0.315869 0.948803i \(-0.602296\pi\)
−0.315869 + 0.948803i \(0.602296\pi\)
\(774\) 10009.1 15521.6i 0.0167076 0.0259092i
\(775\) 0 0
\(776\) −121606. + 818763.i −0.201945 + 1.35967i
\(777\) −350231. −0.580113
\(778\) 96836.2 + 62445.0i 0.159985 + 0.103166i
\(779\) 385298.i 0.634924i
\(780\) 0 0
\(781\) −302595. −0.496089
\(782\) −38092.7 + 59072.1i −0.0622915 + 0.0965981i
\(783\) 138840.i