Properties

Label 108.6.b.c.107.12
Level 108
Weight 6
Character 108.107
Analytic conductor 17.321
Analytic rank 0
Dimension 20
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 108.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.3214525398\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{50}\cdot 3^{40} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 107.12
Root \(-5.25764 + 3.03550i\) of \(x^{20} - 94 x^{18} + 5872 x^{16} - 207192 x^{14} + 5271952 x^{12} - 76648960 x^{10} + 792478720 x^{8} - 4371873792 x^{6} + 17152147456 x^{4} - 32033996800 x^{2} + 41943040000\)
Character \(\chi\) \(=\) 108.107
Dual form 108.6.b.c.107.11

$q$-expansion

\(f(q)\) \(=\) \(q+(0.821088 + 5.59695i) q^{2} +(-30.6516 + 9.19117i) q^{4} +8.15731i q^{5} +63.0026i q^{7} +(-76.6102 - 164.009i) q^{8} +O(q^{10})\) \(q+(0.821088 + 5.59695i) q^{2} +(-30.6516 + 9.19117i) q^{4} +8.15731i q^{5} +63.0026i q^{7} +(-76.6102 - 164.009i) q^{8} +(-45.6560 + 6.69787i) q^{10} -442.855 q^{11} -76.3186 q^{13} +(-352.622 + 51.7307i) q^{14} +(855.045 - 563.449i) q^{16} -643.601i q^{17} -2189.93i q^{19} +(-74.9752 - 250.035i) q^{20} +(-363.623 - 2478.64i) q^{22} -2735.75 q^{23} +3058.46 q^{25} +(-62.6643 - 427.151i) q^{26} +(-579.068 - 1931.13i) q^{28} -1503.56i q^{29} -5500.91i q^{31} +(3855.66 + 4323.00i) q^{32} +(3602.20 - 528.453i) q^{34} -513.932 q^{35} -4828.88 q^{37} +(12256.9 - 1798.12i) q^{38} +(1337.87 - 624.933i) q^{40} +10911.9i q^{41} -8358.97i q^{43} +(13574.2 - 4070.36i) q^{44} +(-2246.29 - 15311.8i) q^{46} -13956.1 q^{47} +12837.7 q^{49} +(2511.26 + 17118.0i) q^{50} +(2339.29 - 701.458i) q^{52} -22806.4i q^{53} -3612.50i q^{55} +(10333.0 - 4826.64i) q^{56} +(8415.33 - 1234.55i) q^{58} -48313.0 q^{59} +5102.35 q^{61} +(30788.3 - 4516.73i) q^{62} +(-21029.8 + 25129.5i) q^{64} -622.555i q^{65} +37352.3i q^{67} +(5915.45 + 19727.4i) q^{68} +(-421.983 - 2876.45i) q^{70} -75093.0 q^{71} -65283.5 q^{73} +(-3964.93 - 27027.0i) q^{74} +(20128.0 + 67124.8i) q^{76} -27901.0i q^{77} +73222.7i q^{79} +(4596.22 + 6974.86i) q^{80} +(-61073.3 + 8959.62i) q^{82} -65245.0 q^{83} +5250.05 q^{85} +(46784.7 - 6863.45i) q^{86} +(33927.2 + 72632.1i) q^{88} -9200.06i q^{89} -4808.27i q^{91} +(83855.2 - 25144.7i) q^{92} +(-11459.2 - 78111.5i) q^{94} +17863.9 q^{95} +125288. q^{97} +(10540.9 + 71851.8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 20q^{4} + O(q^{10}) \) \( 20q + 20q^{4} + 184q^{10} - 116q^{13} - 4168q^{16} + 696q^{22} - 15228q^{25} - 4764q^{28} - 16520q^{34} - 6452q^{37} + 1504q^{40} - 9336q^{46} - 44464q^{49} + 8236q^{52} - 58736q^{58} + 84604q^{61} - 6496q^{64} + 138696q^{70} + 85420q^{73} + 89172q^{76} + 221200q^{82} + 180320q^{85} - 85824q^{88} - 60936q^{94} - 219908q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.821088 + 5.59695i 0.145149 + 0.989410i
\(3\) 0 0
\(4\) −30.6516 + 9.19117i −0.957863 + 0.287224i
\(5\) 8.15731i 0.145922i 0.997335 + 0.0729612i \(0.0232449\pi\)
−0.997335 + 0.0729612i \(0.976755\pi\)
\(6\) 0 0
\(7\) 63.0026i 0.485974i 0.970030 + 0.242987i \(0.0781273\pi\)
−0.970030 + 0.242987i \(0.921873\pi\)
\(8\) −76.6102 164.009i −0.423215 0.906029i
\(9\) 0 0
\(10\) −45.6560 + 6.69787i −0.144377 + 0.0211805i
\(11\) −442.855 −1.10352 −0.551760 0.834003i \(-0.686043\pi\)
−0.551760 + 0.834003i \(0.686043\pi\)
\(12\) 0 0
\(13\) −76.3186 −0.125248 −0.0626242 0.998037i \(-0.519947\pi\)
−0.0626242 + 0.998037i \(0.519947\pi\)
\(14\) −352.622 + 51.7307i −0.480828 + 0.0705388i
\(15\) 0 0
\(16\) 855.045 563.449i 0.835005 0.550243i
\(17\) 643.601i 0.540125i −0.962843 0.270063i \(-0.912956\pi\)
0.962843 0.270063i \(-0.0870444\pi\)
\(18\) 0 0
\(19\) 2189.93i 1.39170i −0.718188 0.695850i \(-0.755028\pi\)
0.718188 0.695850i \(-0.244972\pi\)
\(20\) −74.9752 250.035i −0.0419124 0.139774i
\(21\) 0 0
\(22\) −363.623 2478.64i −0.160175 1.09183i
\(23\) −2735.75 −1.07834 −0.539171 0.842196i \(-0.681262\pi\)
−0.539171 + 0.842196i \(0.681262\pi\)
\(24\) 0 0
\(25\) 3058.46 0.978707
\(26\) −62.6643 427.151i −0.0181797 0.123922i
\(27\) 0 0
\(28\) −579.068 1931.13i −0.139584 0.465497i
\(29\) 1503.56i 0.331990i −0.986127 0.165995i \(-0.946916\pi\)
0.986127 0.165995i \(-0.0530836\pi\)
\(30\) 0 0
\(31\) 5500.91i 1.02809i −0.857764 0.514044i \(-0.828147\pi\)
0.857764 0.514044i \(-0.171853\pi\)
\(32\) 3855.66 + 4323.00i 0.665616 + 0.746294i
\(33\) 0 0
\(34\) 3602.20 528.453i 0.534405 0.0783988i
\(35\) −513.932 −0.0709145
\(36\) 0 0
\(37\) −4828.88 −0.579885 −0.289943 0.957044i \(-0.593636\pi\)
−0.289943 + 0.957044i \(0.593636\pi\)
\(38\) 12256.9 1798.12i 1.37696 0.202004i
\(39\) 0 0
\(40\) 1337.87 624.933i 0.132210 0.0617566i
\(41\) 10911.9i 1.01377i 0.862013 + 0.506886i \(0.169204\pi\)
−0.862013 + 0.506886i \(0.830796\pi\)
\(42\) 0 0
\(43\) 8358.97i 0.689416i −0.938710 0.344708i \(-0.887978\pi\)
0.938710 0.344708i \(-0.112022\pi\)
\(44\) 13574.2 4070.36i 1.05702 0.316957i
\(45\) 0 0
\(46\) −2246.29 15311.8i −0.156521 1.06692i
\(47\) −13956.1 −0.921551 −0.460775 0.887517i \(-0.652429\pi\)
−0.460775 + 0.887517i \(0.652429\pi\)
\(48\) 0 0
\(49\) 12837.7 0.763829
\(50\) 2511.26 + 17118.0i 0.142058 + 0.968342i
\(51\) 0 0
\(52\) 2339.29 701.458i 0.119971 0.0359744i
\(53\) 22806.4i 1.11524i −0.830098 0.557618i \(-0.811715\pi\)
0.830098 0.557618i \(-0.188285\pi\)
\(54\) 0 0
\(55\) 3612.50i 0.161028i
\(56\) 10333.0 4826.64i 0.440307 0.205672i
\(57\) 0 0
\(58\) 8415.33 1234.55i 0.328474 0.0481881i
\(59\) −48313.0 −1.80690 −0.903450 0.428694i \(-0.858974\pi\)
−0.903450 + 0.428694i \(0.858974\pi\)
\(60\) 0 0
\(61\) 5102.35 0.175568 0.0877840 0.996140i \(-0.472021\pi\)
0.0877840 + 0.996140i \(0.472021\pi\)
\(62\) 30788.3 4516.73i 1.01720 0.149226i
\(63\) 0 0
\(64\) −21029.8 + 25129.5i −0.641777 + 0.766891i
\(65\) 622.555i 0.0182765i
\(66\) 0 0
\(67\) 37352.3i 1.01655i 0.861193 + 0.508277i \(0.169717\pi\)
−0.861193 + 0.508277i \(0.830283\pi\)
\(68\) 5915.45 + 19727.4i 0.155137 + 0.517366i
\(69\) 0 0
\(70\) −421.983 2876.45i −0.0102932 0.0701635i
\(71\) −75093.0 −1.76788 −0.883942 0.467597i \(-0.845120\pi\)
−0.883942 + 0.467597i \(0.845120\pi\)
\(72\) 0 0
\(73\) −65283.5 −1.43382 −0.716912 0.697163i \(-0.754445\pi\)
−0.716912 + 0.697163i \(0.754445\pi\)
\(74\) −3964.93 27027.0i −0.0841698 0.573744i
\(75\) 0 0
\(76\) 20128.0 + 67124.8i 0.399730 + 1.33306i
\(77\) 27901.0i 0.536282i
\(78\) 0 0
\(79\) 73222.7i 1.32001i 0.751260 + 0.660006i \(0.229446\pi\)
−0.751260 + 0.660006i \(0.770554\pi\)
\(80\) 4596.22 + 6974.86i 0.0802927 + 0.121846i
\(81\) 0 0
\(82\) −61073.3 + 8959.62i −1.00304 + 0.147148i
\(83\) −65245.0 −1.03957 −0.519783 0.854299i \(-0.673987\pi\)
−0.519783 + 0.854299i \(0.673987\pi\)
\(84\) 0 0
\(85\) 5250.05 0.0788164
\(86\) 46784.7 6863.45i 0.682115 0.100068i
\(87\) 0 0
\(88\) 33927.2 + 72632.1i 0.467026 + 0.999820i
\(89\) 9200.06i 0.123116i −0.998103 0.0615581i \(-0.980393\pi\)
0.998103 0.0615581i \(-0.0196070\pi\)
\(90\) 0 0
\(91\) 4808.27i 0.0608675i
\(92\) 83855.2 25144.7i 1.03290 0.309726i
\(93\) 0 0
\(94\) −11459.2 78111.5i −0.133762 0.911791i
\(95\) 17863.9 0.203080
\(96\) 0 0
\(97\) 125288. 1.35201 0.676005 0.736897i \(-0.263710\pi\)
0.676005 + 0.736897i \(0.263710\pi\)
\(98\) 10540.9 + 71851.8i 0.110869 + 0.755740i
\(99\) 0 0
\(100\) −93746.7 + 28110.8i −0.937467 + 0.281108i
\(101\) 153747.i 1.49970i 0.661611 + 0.749848i \(0.269873\pi\)
−0.661611 + 0.749848i \(0.730127\pi\)
\(102\) 0 0
\(103\) 10978.1i 0.101961i −0.998700 0.0509807i \(-0.983765\pi\)
0.998700 0.0509807i \(-0.0162347\pi\)
\(104\) 5846.78 + 12516.9i 0.0530071 + 0.113479i
\(105\) 0 0
\(106\) 127646. 18726.1i 1.10343 0.161876i
\(107\) 92087.1 0.777570 0.388785 0.921329i \(-0.372895\pi\)
0.388785 + 0.921329i \(0.372895\pi\)
\(108\) 0 0
\(109\) −179611. −1.44800 −0.723998 0.689802i \(-0.757698\pi\)
−0.723998 + 0.689802i \(0.757698\pi\)
\(110\) 20219.0 2966.18i 0.159323 0.0233731i
\(111\) 0 0
\(112\) 35498.7 + 53870.0i 0.267404 + 0.405791i
\(113\) 214627.i 1.58120i −0.612332 0.790601i \(-0.709768\pi\)
0.612332 0.790601i \(-0.290232\pi\)
\(114\) 0 0
\(115\) 22316.3i 0.157354i
\(116\) 13819.5 + 46086.5i 0.0953556 + 0.318001i
\(117\) 0 0
\(118\) −39669.2 270405.i −0.262270 1.78776i
\(119\) 40548.5 0.262487
\(120\) 0 0
\(121\) 35069.6 0.217754
\(122\) 4189.47 + 28557.6i 0.0254835 + 0.173709i
\(123\) 0 0
\(124\) 50559.8 + 168612.i 0.295292 + 0.984768i
\(125\) 50440.4i 0.288738i
\(126\) 0 0
\(127\) 77928.5i 0.428733i −0.976753 0.214367i \(-0.931231\pi\)
0.976753 0.214367i \(-0.0687687\pi\)
\(128\) −157916. 97068.9i −0.851923 0.523667i
\(129\) 0 0
\(130\) 3484.41 511.172i 0.0180830 0.00265283i
\(131\) 191085. 0.972855 0.486428 0.873721i \(-0.338300\pi\)
0.486428 + 0.873721i \(0.338300\pi\)
\(132\) 0 0
\(133\) 137971. 0.676330
\(134\) −209059. + 30669.5i −1.00579 + 0.147552i
\(135\) 0 0
\(136\) −105556. + 49306.4i −0.489369 + 0.228589i
\(137\) 334957.i 1.52471i 0.647159 + 0.762355i \(0.275957\pi\)
−0.647159 + 0.762355i \(0.724043\pi\)
\(138\) 0 0
\(139\) 122670.i 0.538518i −0.963068 0.269259i \(-0.913221\pi\)
0.963068 0.269259i \(-0.0867787\pi\)
\(140\) 15752.8 4723.63i 0.0679264 0.0203684i
\(141\) 0 0
\(142\) −61658.0 420292.i −0.256607 1.74916i
\(143\) 33798.1 0.138214
\(144\) 0 0
\(145\) 12265.0 0.0484448
\(146\) −53603.5 365388.i −0.208119 1.41864i
\(147\) 0 0
\(148\) 148013. 44383.0i 0.555451 0.166557i
\(149\) 344978.i 1.27299i −0.771280 0.636496i \(-0.780383\pi\)
0.771280 0.636496i \(-0.219617\pi\)
\(150\) 0 0
\(151\) 208482.i 0.744093i −0.928214 0.372046i \(-0.878656\pi\)
0.928214 0.372046i \(-0.121344\pi\)
\(152\) −359167. + 167771.i −1.26092 + 0.588989i
\(153\) 0 0
\(154\) 156160. 22909.2i 0.530603 0.0778409i
\(155\) 44872.6 0.150021
\(156\) 0 0
\(157\) 229386. 0.742706 0.371353 0.928492i \(-0.378894\pi\)
0.371353 + 0.928492i \(0.378894\pi\)
\(158\) −409824. + 60122.3i −1.30603 + 0.191599i
\(159\) 0 0
\(160\) −35264.0 + 31451.8i −0.108901 + 0.0971282i
\(161\) 172359.i 0.524047i
\(162\) 0 0
\(163\) 358203.i 1.05599i −0.849247 0.527996i \(-0.822944\pi\)
0.849247 0.527996i \(-0.177056\pi\)
\(164\) −100293. 334467.i −0.291180 0.971055i
\(165\) 0 0
\(166\) −53571.8 365173.i −0.150892 1.02856i
\(167\) 323824. 0.898500 0.449250 0.893406i \(-0.351691\pi\)
0.449250 + 0.893406i \(0.351691\pi\)
\(168\) 0 0
\(169\) −365468. −0.984313
\(170\) 4310.76 + 29384.3i 0.0114401 + 0.0779817i
\(171\) 0 0
\(172\) 76828.7 + 256216.i 0.198017 + 0.660367i
\(173\) 587779.i 1.49313i 0.665310 + 0.746567i \(0.268299\pi\)
−0.665310 + 0.746567i \(0.731701\pi\)
\(174\) 0 0
\(175\) 192691.i 0.475626i
\(176\) −378661. + 249526.i −0.921444 + 0.607204i
\(177\) 0 0
\(178\) 51492.2 7554.06i 0.121812 0.0178702i
\(179\) 496110. 1.15730 0.578649 0.815577i \(-0.303580\pi\)
0.578649 + 0.815577i \(0.303580\pi\)
\(180\) 0 0
\(181\) 206785. 0.469163 0.234581 0.972096i \(-0.424628\pi\)
0.234581 + 0.972096i \(0.424628\pi\)
\(182\) 26911.6 3948.01i 0.0602229 0.00883487i
\(183\) 0 0
\(184\) 209586. + 448687.i 0.456371 + 0.977010i
\(185\) 39390.6i 0.0846182i
\(186\) 0 0
\(187\) 285022.i 0.596039i
\(188\) 427777. 128273.i 0.882720 0.264692i
\(189\) 0 0
\(190\) 14667.8 + 99983.3i 0.0294769 + 0.200929i
\(191\) 601888. 1.19380 0.596901 0.802315i \(-0.296398\pi\)
0.596901 + 0.802315i \(0.296398\pi\)
\(192\) 0 0
\(193\) −267729. −0.517372 −0.258686 0.965961i \(-0.583289\pi\)
−0.258686 + 0.965961i \(0.583289\pi\)
\(194\) 102872. + 701230.i 0.196243 + 1.33769i
\(195\) 0 0
\(196\) −393496. + 117993.i −0.731644 + 0.219390i
\(197\) 652488.i 1.19786i −0.800800 0.598931i \(-0.795592\pi\)
0.800800 0.598931i \(-0.204408\pi\)
\(198\) 0 0
\(199\) 1.08073e6i 1.93458i 0.253675 + 0.967289i \(0.418361\pi\)
−0.253675 + 0.967289i \(0.581639\pi\)
\(200\) −234309. 501614.i −0.414204 0.886737i
\(201\) 0 0
\(202\) −860513. + 126240.i −1.48381 + 0.217680i
\(203\) 94728.1 0.161339
\(204\) 0 0
\(205\) −89011.7 −0.147932
\(206\) 61444.0 9014.02i 0.100882 0.0147996i
\(207\) 0 0
\(208\) −65255.9 + 43001.6i −0.104583 + 0.0689171i
\(209\) 969820.i 1.53577i
\(210\) 0 0
\(211\) 3191.14i 0.00493447i −0.999997 0.00246723i \(-0.999215\pi\)
0.999997 0.00246723i \(-0.000785346\pi\)
\(212\) 209617. + 699053.i 0.320323 + 1.06824i
\(213\) 0 0
\(214\) 75611.6 + 515407.i 0.112864 + 0.769335i
\(215\) 68186.7 0.100601
\(216\) 0 0
\(217\) 346572. 0.499624
\(218\) −147477. 1.00527e6i −0.210175 1.43266i
\(219\) 0 0
\(220\) 33203.1 + 110729.i 0.0462511 + 0.154243i
\(221\) 49118.8i 0.0676498i
\(222\) 0 0
\(223\) 105595.i 0.142194i 0.997469 + 0.0710971i \(0.0226500\pi\)
−0.997469 + 0.0710971i \(0.977350\pi\)
\(224\) −272360. + 242917.i −0.362680 + 0.323472i
\(225\) 0 0
\(226\) 1.20125e6 176227.i 1.56446 0.229510i
\(227\) −620193. −0.798845 −0.399423 0.916767i \(-0.630789\pi\)
−0.399423 + 0.916767i \(0.630789\pi\)
\(228\) 0 0
\(229\) −867924. −1.09369 −0.546844 0.837235i \(-0.684171\pi\)
−0.546844 + 0.837235i \(0.684171\pi\)
\(230\) 124903. 18323.7i 0.155688 0.0228398i
\(231\) 0 0
\(232\) −246597. + 115188.i −0.300793 + 0.140503i
\(233\) 296205.i 0.357440i −0.983900 0.178720i \(-0.942804\pi\)
0.983900 0.178720i \(-0.0571956\pi\)
\(234\) 0 0
\(235\) 113844.i 0.134475i
\(236\) 1.48087e6 444053.i 1.73076 0.518985i
\(237\) 0 0
\(238\) 33293.9 + 226948.i 0.0380998 + 0.259707i
\(239\) −696767. −0.789028 −0.394514 0.918890i \(-0.629087\pi\)
−0.394514 + 0.918890i \(0.629087\pi\)
\(240\) 0 0
\(241\) −138720. −0.153849 −0.0769247 0.997037i \(-0.524510\pi\)
−0.0769247 + 0.997037i \(0.524510\pi\)
\(242\) 28795.2 + 196282.i 0.0316069 + 0.215448i
\(243\) 0 0
\(244\) −156395. + 46896.5i −0.168170 + 0.0504273i
\(245\) 104721.i 0.111460i
\(246\) 0 0
\(247\) 167132.i 0.174308i
\(248\) −902197. + 421426.i −0.931477 + 0.435103i
\(249\) 0 0
\(250\) −282312. + 41416.0i −0.285680 + 0.0419100i
\(251\) −730682. −0.732056 −0.366028 0.930604i \(-0.619283\pi\)
−0.366028 + 0.930604i \(0.619283\pi\)
\(252\) 0 0
\(253\) 1.21154e6 1.18997
\(254\) 436162. 63986.1i 0.424193 0.0622303i
\(255\) 0 0
\(256\) 413627. 963548.i 0.394466 0.918911i
\(257\) 1.47952e6i 1.39730i −0.715465 0.698649i \(-0.753785\pi\)
0.715465 0.698649i \(-0.246215\pi\)
\(258\) 0 0
\(259\) 304232.i 0.281809i
\(260\) 5722.01 + 19082.3i 0.00524946 + 0.0175064i
\(261\) 0 0
\(262\) 156898. + 1.06949e6i 0.141209 + 0.962552i
\(263\) −1.91797e6 −1.70983 −0.854914 0.518770i \(-0.826390\pi\)
−0.854914 + 0.518770i \(0.826390\pi\)
\(264\) 0 0
\(265\) 186039. 0.162738
\(266\) 113286. + 772216.i 0.0981688 + 0.669168i
\(267\) 0 0
\(268\) −343312. 1.14491e6i −0.291979 0.973720i
\(269\) 416360.i 0.350823i −0.984495 0.175411i \(-0.943874\pi\)
0.984495 0.175411i \(-0.0561256\pi\)
\(270\) 0 0
\(271\) 140033.i 0.115826i 0.998322 + 0.0579130i \(0.0184446\pi\)
−0.998322 + 0.0579130i \(0.981555\pi\)
\(272\) −362636. 550308.i −0.297200 0.451007i
\(273\) 0 0
\(274\) −1.87473e6 + 275029.i −1.50856 + 0.221310i
\(275\) −1.35445e6 −1.08002
\(276\) 0 0
\(277\) −1.45860e6 −1.14219 −0.571095 0.820884i \(-0.693481\pi\)
−0.571095 + 0.820884i \(0.693481\pi\)
\(278\) 686575. 100723.i 0.532815 0.0781654i
\(279\) 0 0
\(280\) 39372.4 + 84289.3i 0.0300121 + 0.0642506i
\(281\) 1.04557e6i 0.789927i 0.918697 + 0.394963i \(0.129243\pi\)
−0.918697 + 0.394963i \(0.870757\pi\)
\(282\) 0 0
\(283\) 1.18731e6i 0.881244i −0.897693 0.440622i \(-0.854758\pi\)
0.897693 0.440622i \(-0.145242\pi\)
\(284\) 2.30172e6 690193.i 1.69339 0.507779i
\(285\) 0 0
\(286\) 27751.2 + 189166.i 0.0200617 + 0.136750i
\(287\) −687477. −0.492667
\(288\) 0 0
\(289\) 1.00563e6 0.708265
\(290\) 10070.6 + 68646.5i 0.00703172 + 0.0479317i
\(291\) 0 0
\(292\) 2.00104e6 600032.i 1.37341 0.411829i
\(293\) 638803.i 0.434708i −0.976093 0.217354i \(-0.930257\pi\)
0.976093 0.217354i \(-0.0697426\pi\)
\(294\) 0 0
\(295\) 394104.i 0.263667i
\(296\) 369941. + 791978.i 0.245416 + 0.525393i
\(297\) 0 0
\(298\) 1.93082e6 283257.i 1.25951 0.184774i
\(299\) 208789. 0.135061
\(300\) 0 0
\(301\) 526637. 0.335039
\(302\) 1.16687e6 171182.i 0.736213 0.108004i
\(303\) 0 0
\(304\) −1.23391e6 1.87248e6i −0.765773 1.16208i
\(305\) 41621.4i 0.0256193i
\(306\) 0 0
\(307\) 1.84508e6i 1.11730i −0.829404 0.558650i \(-0.811320\pi\)
0.829404 0.558650i \(-0.188680\pi\)
\(308\) 256443. + 855212.i 0.154033 + 0.513685i
\(309\) 0 0
\(310\) 36844.4 + 251150.i 0.0217754 + 0.148432i
\(311\) 987920. 0.579189 0.289595 0.957149i \(-0.406479\pi\)
0.289595 + 0.957149i \(0.406479\pi\)
\(312\) 0 0
\(313\) 76622.6 0.0442075 0.0221037 0.999756i \(-0.492964\pi\)
0.0221037 + 0.999756i \(0.492964\pi\)
\(314\) 188346. + 1.28386e6i 0.107803 + 0.734841i
\(315\) 0 0
\(316\) −673002. 2.24440e6i −0.379139 1.26439i
\(317\) 1.50331e6i 0.840232i 0.907470 + 0.420116i \(0.138011\pi\)
−0.907470 + 0.420116i \(0.861989\pi\)
\(318\) 0 0
\(319\) 665858.i 0.366357i
\(320\) −204989. 171546.i −0.111907 0.0936497i
\(321\) 0 0
\(322\) 964686. 141522.i 0.518497 0.0760650i
\(323\) −1.40944e6 −0.751692
\(324\) 0 0
\(325\) −233417. −0.122581
\(326\) 2.00484e6 294116.i 1.04481 0.153276i
\(327\) 0 0
\(328\) 1.78965e6 835962.i 0.918507 0.429044i
\(329\) 879270.i 0.447850i
\(330\) 0 0
\(331\) 2.95260e6i 1.48127i −0.671906 0.740636i \(-0.734524\pi\)
0.671906 0.740636i \(-0.265476\pi\)
\(332\) 1.99986e6 599678.i 0.995761 0.298588i
\(333\) 0 0
\(334\) 265888. + 1.81243e6i 0.130417 + 0.888985i
\(335\) −304694. −0.148338
\(336\) 0 0
\(337\) 376009. 0.180353 0.0901766 0.995926i \(-0.471257\pi\)
0.0901766 + 0.995926i \(0.471257\pi\)
\(338\) −300082. 2.04551e6i −0.142872 0.973889i
\(339\) 0 0
\(340\) −160923. + 48254.1i −0.0754953 + 0.0226380i
\(341\) 2.43611e6i 1.13451i
\(342\) 0 0
\(343\) 1.86769e6i 0.857176i
\(344\) −1.37094e6 + 640382.i −0.624631 + 0.291772i
\(345\) 0 0
\(346\) −3.28977e6 + 482618.i −1.47732 + 0.216727i
\(347\) 1.46748e6 0.654255 0.327128 0.944980i \(-0.393919\pi\)
0.327128 + 0.944980i \(0.393919\pi\)
\(348\) 0 0
\(349\) 2.03644e6 0.894970 0.447485 0.894291i \(-0.352320\pi\)
0.447485 + 0.894291i \(0.352320\pi\)
\(350\) −1.07848e6 + 158216.i −0.470589 + 0.0690368i
\(351\) 0 0
\(352\) −1.70750e6 1.91446e6i −0.734520 0.823550i
\(353\) 2.68754e6i 1.14794i −0.818877 0.573969i \(-0.805403\pi\)
0.818877 0.573969i \(-0.194597\pi\)
\(354\) 0 0
\(355\) 612557.i 0.257974i
\(356\) 84559.3 + 281997.i 0.0353620 + 0.117929i
\(357\) 0 0
\(358\) 407350. + 2.77670e6i 0.167981 + 1.14504i
\(359\) 929088. 0.380470 0.190235 0.981739i \(-0.439075\pi\)
0.190235 + 0.981739i \(0.439075\pi\)
\(360\) 0 0
\(361\) −2.31968e6 −0.936827
\(362\) 169789. + 1.15737e6i 0.0680986 + 0.464194i
\(363\) 0 0
\(364\) 44193.7 + 147381.i 0.0174826 + 0.0583028i
\(365\) 532537.i 0.209227i
\(366\) 0 0
\(367\) 5.08684e6i 1.97144i 0.168398 + 0.985719i \(0.446141\pi\)
−0.168398 + 0.985719i \(0.553859\pi\)
\(368\) −2.33919e6 + 1.54145e6i −0.900421 + 0.593350i
\(369\) 0 0
\(370\) 220467. 32343.2i 0.0837221 0.0122823i
\(371\) 1.43686e6 0.541976
\(372\) 0 0
\(373\) −770228. −0.286647 −0.143323 0.989676i \(-0.545779\pi\)
−0.143323 + 0.989676i \(0.545779\pi\)
\(374\) −1.59525e6 + 234028.i −0.589726 + 0.0865145i
\(375\) 0 0
\(376\) 1.06918e6 + 2.28892e6i 0.390014 + 0.834952i
\(377\) 114750.i 0.0415812i
\(378\) 0 0
\(379\) 174443.i 0.0623815i 0.999513 + 0.0311907i \(0.00992993\pi\)
−0.999513 + 0.0311907i \(0.990070\pi\)
\(380\) −547558. + 164190.i −0.194523 + 0.0583295i
\(381\) 0 0
\(382\) 494203. + 3.36874e6i 0.173279 + 1.18116i
\(383\) −1.32370e6 −0.461096 −0.230548 0.973061i \(-0.574052\pi\)
−0.230548 + 0.973061i \(0.574052\pi\)
\(384\) 0 0
\(385\) 227597. 0.0782555
\(386\) −219829. 1.49847e6i −0.0750961 0.511893i
\(387\) 0 0
\(388\) −3.84028e6 + 1.15154e6i −1.29504 + 0.388330i
\(389\) 2.29230e6i 0.768064i −0.923320 0.384032i \(-0.874535\pi\)
0.923320 0.384032i \(-0.125465\pi\)
\(390\) 0 0
\(391\) 1.76073e6i 0.582440i
\(392\) −983496. 2.10549e6i −0.323264 0.692051i
\(393\) 0 0
\(394\) 3.65194e6 535750.i 1.18518 0.173869i
\(395\) −597300. −0.192619
\(396\) 0 0
\(397\) −5.02339e6 −1.59963 −0.799816 0.600245i \(-0.795070\pi\)
−0.799816 + 0.600245i \(0.795070\pi\)
\(398\) −6.04882e6 + 887378.i −1.91409 + 0.280803i
\(399\) 0 0
\(400\) 2.61512e6 1.72328e6i 0.817225 0.538526i
\(401\) 5.23840e6i 1.62681i 0.581696 + 0.813406i \(0.302389\pi\)
−0.581696 + 0.813406i \(0.697611\pi\)
\(402\) 0 0
\(403\) 419822.i 0.128766i
\(404\) −1.41311e6 4.71259e6i −0.430749 1.43650i
\(405\) 0 0
\(406\) 77780.1 + 530188.i 0.0234182 + 0.159630i
\(407\) 2.13849e6 0.639914
\(408\) 0 0
\(409\) 1.62846e6 0.481360 0.240680 0.970605i \(-0.422630\pi\)
0.240680 + 0.970605i \(0.422630\pi\)
\(410\) −73086.4 498193.i −0.0214722 0.146365i
\(411\) 0 0
\(412\) 100902. + 336498.i 0.0292858 + 0.0976650i
\(413\) 3.04385e6i 0.878107i
\(414\) 0 0
\(415\) 532223.i 0.151696i
\(416\) −294259. 329925.i −0.0833673 0.0934722i
\(417\) 0 0
\(418\) −5.42803e6 + 796307.i −1.51950 + 0.222915i
\(419\) 1.94936e6 0.542446 0.271223 0.962517i \(-0.412572\pi\)
0.271223 + 0.962517i \(0.412572\pi\)
\(420\) 0 0
\(421\) 3.98298e6 1.09522 0.547611 0.836733i \(-0.315537\pi\)
0.547611 + 0.836733i \(0.315537\pi\)
\(422\) 17860.7 2620.21i 0.00488221 0.000716234i
\(423\) 0 0
\(424\) −3.74045e6 + 1.74720e6i −1.01044 + 0.471985i
\(425\) 1.96843e6i 0.528624i
\(426\) 0 0
\(427\) 321461.i 0.0853215i
\(428\) −2.82262e6 + 846388.i −0.744806 + 0.223337i
\(429\) 0 0
\(430\) 55987.3 + 381637.i 0.0146022 + 0.0995359i
\(431\) 7.18163e6 1.86222 0.931108 0.364745i \(-0.118844\pi\)
0.931108 + 0.364745i \(0.118844\pi\)
\(432\) 0 0
\(433\) 150971. 0.0386966 0.0193483 0.999813i \(-0.493841\pi\)
0.0193483 + 0.999813i \(0.493841\pi\)
\(434\) 284566. + 1.93974e6i 0.0725201 + 0.494333i
\(435\) 0 0
\(436\) 5.50538e6 1.65084e6i 1.38698 0.415899i
\(437\) 5.99109e6i 1.50073i
\(438\) 0 0
\(439\) 4.22773e6i 1.04700i 0.852026 + 0.523499i \(0.175374\pi\)
−0.852026 + 0.523499i \(0.824626\pi\)
\(440\) −592482. + 276755.i −0.145896 + 0.0681496i
\(441\) 0 0
\(442\) −274915. + 40330.8i −0.0669334 + 0.00981932i
\(443\) 3.31077e6 0.801529 0.400764 0.916181i \(-0.368745\pi\)
0.400764 + 0.916181i \(0.368745\pi\)
\(444\) 0 0
\(445\) 75047.7 0.0179654
\(446\) −591010. + 86702.9i −0.140688 + 0.0206394i
\(447\) 0 0
\(448\) −1.58322e6 1.32493e6i −0.372689 0.311887i
\(449\) 5.19683e6i 1.21653i 0.793734 + 0.608265i \(0.208134\pi\)
−0.793734 + 0.608265i \(0.791866\pi\)
\(450\) 0 0
\(451\) 4.83239e6i 1.11872i
\(452\) 1.97267e6 + 6.57865e6i 0.454159 + 1.51458i
\(453\) 0 0
\(454\) −509233. 3.47119e6i −0.115952 0.790385i
\(455\) 39222.6 0.00888193
\(456\) 0 0
\(457\) −851714. −0.190767 −0.0953835 0.995441i \(-0.530408\pi\)
−0.0953835 + 0.995441i \(0.530408\pi\)
\(458\) −712642. 4.85773e6i −0.158748 1.08210i
\(459\) 0 0
\(460\) 205113. + 684032.i 0.0451959 + 0.150724i
\(461\) 8.48893e6i 1.86038i −0.367084 0.930188i \(-0.619644\pi\)
0.367084 0.930188i \(-0.380356\pi\)
\(462\) 0 0
\(463\) 5.13046e6i 1.11225i 0.831098 + 0.556127i \(0.187713\pi\)
−0.831098 + 0.556127i \(0.812287\pi\)
\(464\) −847178. 1.28561e6i −0.182675 0.277213i
\(465\) 0 0
\(466\) 1.65784e6 243211.i 0.353654 0.0518821i
\(467\) 5.02410e6 1.06602 0.533011 0.846108i \(-0.321060\pi\)
0.533011 + 0.846108i \(0.321060\pi\)
\(468\) 0 0
\(469\) −2.35329e6 −0.494019
\(470\) 637180. 93476.1i 0.133051 0.0195189i
\(471\) 0 0
\(472\) 3.70127e6 + 7.92376e6i 0.764708 + 1.63710i
\(473\) 3.70181e6i 0.760784i
\(474\) 0 0
\(475\) 6.69780e6i 1.36207i
\(476\) −1.24288e6 + 372689.i −0.251427 + 0.0753926i
\(477\) 0 0
\(478\) −572107. 3.89977e6i −0.114527 0.780672i
\(479\) 2.68540e6 0.534773 0.267387 0.963589i \(-0.413840\pi\)
0.267387 + 0.963589i \(0.413840\pi\)
\(480\) 0 0
\(481\) 368533. 0.0726297
\(482\) −113901. 776408.i −0.0223311 0.152220i
\(483\) 0 0
\(484\) −1.07494e6 + 322330.i −0.208579 + 0.0625443i
\(485\) 1.02201e6i 0.197288i
\(486\) 0 0
\(487\) 5.34008e6i 1.02029i 0.860087 + 0.510147i \(0.170409\pi\)
−0.860087 + 0.510147i \(0.829591\pi\)
\(488\) −390892. 836829.i −0.0743031 0.159070i
\(489\) 0 0
\(490\) −586117. + 85985.0i −0.110279 + 0.0161783i
\(491\) 2.63306e6 0.492898 0.246449 0.969156i \(-0.420736\pi\)
0.246449 + 0.969156i \(0.420736\pi\)
\(492\) 0 0
\(493\) −967692. −0.179316
\(494\) −935430. + 137230.i −0.172462 + 0.0253007i
\(495\) 0 0
\(496\) −3.09948e6 4.70352e6i −0.565698 0.858458i
\(497\) 4.73106e6i 0.859146i
\(498\) 0 0
\(499\) 9.98944e6i 1.79593i −0.440066 0.897966i \(-0.645045\pi\)
0.440066 0.897966i \(-0.354955\pi\)
\(500\) −463606. 1.54608e6i −0.0829324 0.276571i
\(501\) 0 0
\(502\) −599954. 4.08959e6i −0.106257 0.724303i
\(503\) −6.68072e6 −1.17734 −0.588672 0.808372i \(-0.700349\pi\)
−0.588672 + 0.808372i \(0.700349\pi\)
\(504\) 0 0
\(505\) −1.25416e6 −0.218839
\(506\) 994781. + 6.78093e6i 0.172723 + 1.17737i
\(507\) 0 0
\(508\) 716254. + 2.38864e6i 0.123142 + 0.410668i
\(509\) 5.03549e6i 0.861483i 0.902475 + 0.430742i \(0.141748\pi\)
−0.902475 + 0.430742i \(0.858252\pi\)
\(510\) 0 0
\(511\) 4.11303e6i 0.696802i
\(512\) 5.73255e6 + 1.52389e6i 0.966436 + 0.256909i
\(513\) 0 0
\(514\) 8.28081e6 1.21482e6i 1.38250 0.202817i
\(515\) 89552.0 0.0148784
\(516\) 0 0
\(517\) 6.18053e6 1.01695
\(518\) 1.70277e6 249801.i 0.278825 0.0409044i
\(519\) 0 0
\(520\) −102104. + 47694.0i −0.0165591 + 0.00773492i
\(521\) 3.01932e6i 0.487321i −0.969861 0.243661i \(-0.921652\pi\)
0.969861 0.243661i \(-0.0783483\pi\)
\(522\) 0 0
\(523\) 4.99932e6i 0.799202i −0.916689 0.399601i \(-0.869149\pi\)
0.916689 0.399601i \(-0.130851\pi\)
\(524\) −5.85706e6 + 1.75629e6i −0.931862 + 0.279427i
\(525\) 0 0
\(526\) −1.57482e6 1.07348e7i −0.248180 1.69172i
\(527\) −3.54039e6 −0.555296
\(528\) 0 0
\(529\) 1.04798e6 0.162823
\(530\) 152754. + 1.04125e6i 0.0236213 + 0.161014i
\(531\) 0 0
\(532\) −4.22904e6 + 1.26812e6i −0.647832 + 0.194258i
\(533\) 832781.i 0.126973i
\(534\) 0 0
\(535\) 751183.i 0.113465i
\(536\) 6.12611e6 2.86157e6i 0.921028 0.430222i
\(537\) 0 0
\(538\) 2.33034e6 341868.i 0.347108 0.0509217i
\(539\) −5.68523e6 −0.842900
\(540\) 0 0
\(541\) 9.44567e6 1.38752 0.693761 0.720206i \(-0.255953\pi\)
0.693761 + 0.720206i \(0.255953\pi\)
\(542\) −783755. + 114979.i −0.114599 + 0.0168121i
\(543\) 0 0
\(544\) 2.78229e6 2.48151e6i 0.403093 0.359516i
\(545\) 1.46514e6i 0.211295i
\(546\) 0 0
\(547\) 2.41771e6i 0.345491i −0.984967 0.172745i \(-0.944736\pi\)
0.984967 0.172745i \(-0.0552638\pi\)
\(548\) −3.07864e6 1.02670e7i −0.437933 1.46046i
\(549\) 0 0
\(550\) −1.11213e6 7.58080e6i −0.156764 1.06858i
\(551\) −3.29268e6 −0.462030
\(552\) 0 0
\(553\) −4.61322e6 −0.641492
\(554\) −1.19764e6 8.16373e6i −0.165788 1.13009i
\(555\) 0 0
\(556\) 1.12748e6 + 3.76002e6i 0.154675 + 0.515826i
\(557\) 6.84325e6i 0.934597i 0.884100 + 0.467298i \(0.154773\pi\)
−0.884100 + 0.467298i \(0.845227\pi\)
\(558\) 0 0
\(559\) 637945.i 0.0863483i
\(560\) −439434. + 289574.i −0.0592140 + 0.0390202i
\(561\) 0 0
\(562\) −5.85199e6 + 858504.i −0.781561 + 0.114657i
\(563\) −1.21299e7 −1.61282 −0.806411 0.591355i \(-0.798593\pi\)
−0.806411 + 0.591355i \(0.798593\pi\)
\(564\) 0 0
\(565\) 1.75077e6 0.230733
\(566\) 6.64529e6 974882.i 0.871912 0.127912i
\(567\) 0 0
\(568\) 5.75289e6 + 1.23159e7i 0.748196 + 1.60175i
\(569\) 9.32124e6i 1.20696i −0.797378 0.603480i \(-0.793780\pi\)
0.797378 0.603480i \(-0.206220\pi\)
\(570\) 0 0
\(571\) 4.70232e6i 0.603562i −0.953377 0.301781i \(-0.902419\pi\)
0.953377 0.301781i \(-0.0975811\pi\)
\(572\) −1.03597e6 + 310644.i −0.132390 + 0.0396984i
\(573\) 0 0
\(574\) −564479. 3.84777e6i −0.0715103 0.487450i
\(575\) −8.36718e6 −1.05538
\(576\) 0 0
\(577\) −2.02368e6 −0.253048 −0.126524 0.991964i \(-0.540382\pi\)
−0.126524 + 0.991964i \(0.540382\pi\)
\(578\) 825714. + 5.62848e6i 0.102804 + 0.700764i
\(579\) 0 0
\(580\) −375942. + 112730.i −0.0464035 + 0.0139145i
\(581\) 4.11060e6i 0.505202i
\(582\) 0 0
\(583\) 1.00999e7i 1.23068i
\(584\) 5.00138e6 + 1.07071e7i 0.606817 + 1.29909i
\(585\) 0 0
\(586\) 3.57534e6 524513.i 0.430104 0.0630975i
\(587\) −1.16472e7 −1.39517 −0.697586 0.716501i \(-0.745742\pi\)
−0.697586 + 0.716501i \(0.745742\pi\)
\(588\) 0 0
\(589\) −1.20466e7 −1.43079
\(590\) 2.20578e6 323594.i 0.260875 0.0382711i
\(591\) 0 0
\(592\) −4.12891e6 + 2.72082e6i −0.484207 + 0.319078i
\(593\) 1.67099e6i 0.195136i 0.995229 + 0.0975681i \(0.0311064\pi\)
−0.995229 + 0.0975681i \(0.968894\pi\)
\(594\) 0 0
\(595\) 330767.i 0.0383027i
\(596\) 3.17075e6 + 1.05741e7i 0.365634 + 1.21935i
\(597\) 0 0
\(598\) 171434. + 1.16858e6i 0.0196040 + 0.133630i
\(599\) 7.06244e6 0.804244 0.402122 0.915586i \(-0.368273\pi\)
0.402122 + 0.915586i \(0.368273\pi\)
\(600\) 0 0
\(601\) −7.79092e6 −0.879838 −0.439919 0.898038i \(-0.644993\pi\)
−0.439919 + 0.898038i \(0.644993\pi\)
\(602\) 432415. + 2.94756e6i 0.0486306 + 0.331491i
\(603\) 0 0
\(604\) 1.91620e6 + 6.39033e6i 0.213721 + 0.712739i
\(605\) 286073.i 0.0317752i
\(606\) 0 0
\(607\) 1.43345e7i 1.57911i 0.613682 + 0.789553i \(0.289688\pi\)
−0.613682 + 0.789553i \(0.710312\pi\)
\(608\) 9.46705e6 8.44361e6i 1.03862 0.926337i
\(609\) 0 0
\(610\) −232953. + 34174.8i −0.0253480 + 0.00371862i
\(611\) 1.06511e6 0.115423
\(612\) 0 0
\(613\) 13027.0 0.00140021 0.000700105 1.00000i \(-0.499777\pi\)
0.000700105 1.00000i \(0.499777\pi\)
\(614\) 1.03268e7 1.51497e6i 1.10547 0.162175i
\(615\) 0 0
\(616\) −4.57601e6 + 2.13750e6i −0.485887 + 0.226963i
\(617\) 4.07010e6i 0.430420i −0.976568 0.215210i \(-0.930956\pi\)
0.976568 0.215210i \(-0.0690436\pi\)
\(618\) 0 0
\(619\) 4.13635e6i 0.433902i 0.976183 + 0.216951i \(0.0696111\pi\)
−0.976183 + 0.216951i \(0.930389\pi\)
\(620\) −1.37542e6 + 412432.i −0.143700 + 0.0430896i
\(621\) 0 0
\(622\) 811169. + 5.52933e6i 0.0840689 + 0.573056i
\(623\) 579628. 0.0598314
\(624\) 0 0
\(625\) 9.14622e6 0.936573
\(626\) 62913.9 + 428853.i 0.00641668 + 0.0437393i
\(627\) 0 0
\(628\) −7.03104e6 + 2.10832e6i −0.711411 + 0.213323i
\(629\) 3.10787e6i 0.313211i
\(630\) 0 0
\(631\) 7.49325e6i 0.749198i 0.927187 + 0.374599i \(0.122220\pi\)
−0.927187 + 0.374599i \(0.877780\pi\)
\(632\) 1.20092e7 5.60960e6i 1.19597 0.558650i
\(633\) 0 0
\(634\) −8.41392e6 + 1.23435e6i −0.831334 + 0.121959i
\(635\) 635687. 0.0625617
\(636\) 0 0
\(637\) −979754. −0.0956684
\(638\) −3.72677e6 + 546728.i −0.362478 + 0.0531765i
\(639\) 0 0
\(640\) 791821. 1.28817e6i 0.0764148 0.124315i
\(641\) 8.26174e6i 0.794194i 0.917777 + 0.397097i \(0.129982\pi\)
−0.917777 + 0.397097i \(0.870018\pi\)
\(642\) 0 0
\(643\) 7.49878e6i 0.715259i −0.933864 0.357630i \(-0.883585\pi\)
0.933864 0.357630i \(-0.116415\pi\)
\(644\) 1.58418e6 + 5.28309e6i 0.150519 + 0.501965i
\(645\) 0 0
\(646\) −1.15727e6 7.88855e6i −0.109107 0.743731i
\(647\) −9.71856e6 −0.912728 −0.456364 0.889793i \(-0.650848\pi\)
−0.456364 + 0.889793i \(0.650848\pi\)
\(648\) 0 0
\(649\) 2.13957e7 1.99395
\(650\) −191656. 1.30642e6i −0.0177926 0.121283i
\(651\) 0 0
\(652\) 3.29231e6 + 1.09795e7i 0.303306 + 1.01150i
\(653\) 3.11570e6i 0.285939i −0.989727 0.142969i \(-0.954335\pi\)
0.989727 0.142969i \(-0.0456651\pi\)
\(654\) 0 0
\(655\) 1.55874e6i 0.141961i
\(656\) 6.14829e6 + 9.33016e6i 0.557821 + 0.846505i
\(657\) 0 0
\(658\) 4.92123e6 721958.i 0.443107 0.0650051i
\(659\) 259955. 0.0233176 0.0116588 0.999932i \(-0.496289\pi\)
0.0116588 + 0.999932i \(0.496289\pi\)
\(660\) 0 0
\(661\) −1.17173e7 −1.04310 −0.521548 0.853222i \(-0.674645\pi\)
−0.521548 + 0.853222i \(0.674645\pi\)
\(662\) 1.65256e7 2.42435e6i 1.46558 0.215005i
\(663\) 0 0
\(664\) 4.99843e6 + 1.07007e7i 0.439960 + 0.941876i
\(665\) 1.12547e6i 0.0986917i
\(666\) 0 0
\(667\) 4.11336e6i 0.357999i
\(668\) −9.92574e6 + 2.97632e6i −0.860640 + 0.258071i
\(669\) 0 0
\(670\) −250181. 1.70536e6i −0.0215311 0.146767i
\(671\) −2.25960e6 −0.193743
\(672\) 0 0
\(673\) −1.35278e7 −1.15130 −0.575652 0.817695i \(-0.695252\pi\)
−0.575652 + 0.817695i \(0.695252\pi\)
\(674\) 308737. + 2.10450e6i 0.0261781 + 0.178443i
\(675\) 0 0
\(676\) 1.12022e7 3.35908e6i 0.942837 0.282718i
\(677\) 2.52827e6i 0.212008i −0.994366 0.106004i \(-0.966194\pi\)
0.994366 0.106004i \(-0.0338056\pi\)
\(678\) 0 0
\(679\) 7.89347e6i 0.657042i
\(680\) −402207. 861055.i −0.0333563 0.0714099i
\(681\) 0 0
\(682\) −1.36348e7 + 2.00026e6i −1.12250 + 0.164674i
\(683\) 1.20227e7 0.986170 0.493085 0.869981i \(-0.335869\pi\)
0.493085 + 0.869981i \(0.335869\pi\)
\(684\) 0 0
\(685\) −2.73234e6 −0.222489
\(686\) −1.04534e7 + 1.53354e6i −0.848098 + 0.124418i
\(687\) 0 0
\(688\) −4.70985e6 7.14729e6i −0.379346 0.575666i
\(689\) 1.74055e6i 0.139682i
\(690\) 0 0
\(691\) 2.30168e7i 1.83379i −0.399129 0.916895i \(-0.630688\pi\)
0.399129 0.916895i \(-0.369312\pi\)
\(692\) −5.40238e6 1.80164e7i −0.428864 1.43022i
\(693\) 0 0
\(694\) 1.20493e6 + 8.21338e6i 0.0949646 + 0.647327i
\(695\) 1.00065e6 0.0785818
\(696\) 0 0
\(697\) 7.02291e6 0.547564
\(698\) 1.67210e6 + 1.13979e7i 0.129904 + 0.885492i
\(699\) 0 0
\(700\) −1.77105e6 5.90629e6i −0.136611 0.455585i
\(701\) 3.57908e6i 0.275091i −0.990495 0.137545i \(-0.956079\pi\)
0.990495 0.137545i \(-0.0439213\pi\)
\(702\) 0 0
\(703\) 1.05749e7i 0.807025i
\(704\) 9.31314e6 1.11287e7i 0.708214 0.846279i
\(705\) 0 0
\(706\) 1.50420e7 2.20671e6i 1.13578 0.166622i
\(707\) −9.68646e6 −0.728813
\(708\) 0 0
\(709\) −9.92822e6 −0.741747 −0.370874 0.928683i \(-0.620942\pi\)
−0.370874 + 0.928683i \(0.620942\pi\)
\(710\) 3.42845e6 502963.i 0.255242 0.0374447i
\(711\) 0 0
\(712\) −1.50889e6 + 704818.i −0.111547 + 0.0521047i
\(713\) 1.50491e7i 1.10863i
\(714\) 0 0
\(715\) 275701.i 0.0201685i
\(716\) −1.52066e7 + 4.55983e6i −1.10853 + 0.332404i
\(717\) 0 0
\(718\) 762863. + 5.20006e6i 0.0552250 + 0.376441i
\(719\) 7.53578e6 0.543633 0.271817 0.962349i \(-0.412376\pi\)
0.271817 + 0.962349i \(0.412376\pi\)
\(720\) 0 0
\(721\) 691651. 0.0495506
\(722\) −1.90466e6 1.29831e7i −0.135980 0.926905i
\(723\) 0 0
\(724\) −6.33831e6 + 1.90060e6i −0.449394 + 0.134755i
\(725\) 4.59857e6i 0.324921i
\(726\) 0 0
\(727\) 1.14512e7i 0.803553i 0.915738 + 0.401776i \(0.131607\pi\)
−0.915738 + 0.401776i \(0.868393\pi\)
\(728\) −788599. + 368363.i −0.0551477 + 0.0257601i
\(729\) 0 0
\(730\) 2.98058e6 437260.i 0.207011 0.0303691i
\(731\) −5.37984e6 −0.372371
\(732\) 0 0
\(733\) 6.93007e6 0.476407 0.238203 0.971215i \(-0.423442\pi\)
0.238203 + 0.971215i \(0.423442\pi\)
\(734\) −2.84708e7 + 4.17675e6i −1.95056 + 0.286153i
\(735\) 0 0
\(736\) −1.05481e7 1.18266e7i −0.717762 0.804761i
\(737\) 1.65417e7i 1.12179i
\(738\) 0 0
\(739\) 796923.i 0.0536791i 0.999640 + 0.0268396i \(0.00854432\pi\)
−0.999640 + 0.0268396i \(0.991456\pi\)
\(740\) 362046. + 1.20739e6i 0.0243044 + 0.0810527i
\(741\) 0 0
\(742\) 1.17979e6 + 8.04204e6i 0.0786674 + 0.536237i
\(743\) 4.25494e6 0.282762 0.141381 0.989955i \(-0.454846\pi\)
0.141381 + 0.989955i \(0.454846\pi\)
\(744\) 0 0
\(745\) 2.81409e6 0.185758
\(746\) −632425. 4.31093e6i −0.0416066 0.283611i
\(747\) 0 0
\(748\) −2.61969e6 8.73639e6i −0.171197 0.570924i
\(749\) 5.80173e6i 0.377879i
\(750\) 0 0
\(751\) 1.84503e7i 1.19372i −0.802344 0.596862i \(-0.796414\pi\)
0.802344 0.596862i \(-0.203586\pi\)
\(752\) −1.19331e7 + 7.86354e6i −0.769499 + 0.507077i
\(753\) 0 0
\(754\) −642247. + 94219.4i −0.0411409 + 0.00603548i
\(755\) 1.70066e6 0.108580
\(756\) 0 0
\(757\) 6.70750e6 0.425423 0.212712 0.977115i \(-0.431771\pi\)
0.212712 + 0.977115i \(0.431771\pi\)
\(758\) −976348. + 143233.i −0.0617208 + 0.00905462i
\(759\) 0 0
\(760\) −1.36856e6 2.92984e6i −0.0859466 0.183996i
\(761\) 1.01808e6i 0.0637268i 0.999492 + 0.0318634i \(0.0101442\pi\)
−0.999492 + 0.0318634i \(0.989856\pi\)
\(762\) 0 0
\(763\) 1.13160e7i 0.703689i
\(764\) −1.84489e7 + 5.53206e6i −1.14350 + 0.342889i
\(765\) 0 0
\(766\) −1.08687e6 7.40865e6i −0.0669277 0.456213i
\(767\) 3.68718e6 0.226311
\(768\) 0 0
\(769\) −1.26712e7 −0.772683 −0.386342 0.922356i \(-0.626261\pi\)
−0.386342 + 0.922356i \(0.626261\pi\)
\(770\) 186877. + 1.27385e6i 0.0113587 + 0.0774268i
\(771\) 0 0
\(772\) 8.20634e6 2.46075e6i 0.495572 0.148602i
\(773\) 2.04393e7i 1.23031i −0.788404 0.615157i \(-0.789092\pi\)
0.788404 0.615157i \(-0.210908\pi\)
\(774\) 0 0
\(775\) 1.68243e7i 1.00620i
\(776\) −9.59833e6 2.05483e7i −0.572192 1.22496i
\(777\) 0 0
\(778\) 1.28299e7 1.88218e6i 0.759930 0.111484i
\(779\) 2.38962e7 1.41087
\(780\) 0 0
\(781\) 3.32553e7 1.95089
\(782\) −9.85472e6 + 1.44572e6i −0.576272 + 0.0845407i
\(783\) 0 0
\(784\) 1.09768e7 7.23337e6i 0.637801 0.420291i
\(785\) 1.87117e6i 0.108377i
\(786\) 0 0