Properties

Label 160.6.n.b.127.2
Level 160
Weight 6
Character 160.127
Analytic conductor 25.661
Analytic rank 0
Dimension 14
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 160.n (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.6614111701\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 4 x^{13} + 8 x^{12} - 4626 x^{11} + 149441 x^{10} - 2113414 x^{9} + 17958066 x^{8} - 97717112 x^{7} + 355171384 x^{6} - 910571904 x^{5} + 2428303248 x^{4} - 9166992192 x^{3} + 32237484304 x^{2} - 66916821408 x + 69451154208\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{31}\cdot 5^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 127.2
Root \(3.77108 - 3.77108i\) of defining polynomial
Character \(\chi\) \(=\) 160.127
Dual form 160.6.n.b.63.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-13.4331 - 13.4331i) q^{3} +(15.0352 - 53.8418i) q^{5} +(-76.4413 + 76.4413i) q^{7} +117.896i q^{9} +O(q^{10})\) \(q+(-13.4331 - 13.4331i) q^{3} +(15.0352 - 53.8418i) q^{5} +(-76.4413 + 76.4413i) q^{7} +117.896i q^{9} +622.995i q^{11} +(-293.552 + 293.552i) q^{13} +(-925.232 + 521.293i) q^{15} +(-1153.02 - 1153.02i) q^{17} +2003.44 q^{19} +2053.69 q^{21} +(1392.29 + 1392.29i) q^{23} +(-2672.88 - 1619.05i) q^{25} +(-1680.53 + 1680.53i) q^{27} -305.819i q^{29} -2108.06i q^{31} +(8368.75 - 8368.75i) q^{33} +(2966.43 + 5265.05i) q^{35} +(9903.12 + 9903.12i) q^{37} +7886.62 q^{39} +16996.0 q^{41} +(-2031.28 - 2031.28i) q^{43} +(6347.74 + 1772.59i) q^{45} +(-682.885 + 682.885i) q^{47} +5120.46i q^{49} +30977.2i q^{51} +(21092.5 - 21092.5i) q^{53} +(33543.2 + 9366.86i) q^{55} +(-26912.4 - 26912.4i) q^{57} +11617.4 q^{59} -1309.80 q^{61} +(-9012.12 - 9012.12i) q^{63} +(11391.8 + 20219.0i) q^{65} +(-39870.6 + 39870.6i) q^{67} -37405.7i q^{69} -25454.3i q^{71} +(1031.25 - 1031.25i) q^{73} +(14156.3 + 57653.9i) q^{75} +(-47622.5 - 47622.5i) q^{77} -11849.6 q^{79} +73798.3 q^{81} +(45180.7 + 45180.7i) q^{83} +(-79416.5 + 44744.7i) q^{85} +(-4108.09 + 4108.09i) q^{87} +143889. i q^{89} -44879.0i q^{91} +(-28317.8 + 28317.8i) q^{93} +(30122.1 - 107869. i) q^{95} +(-24390.9 - 24390.9i) q^{97} -73448.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 10q^{3} + 42q^{5} + 66q^{7} + O(q^{10}) \) \( 14q + 10q^{3} + 42q^{5} + 66q^{7} - 414q^{13} + 278q^{15} + 1222q^{17} + 5672q^{19} + 5924q^{21} + 2902q^{23} - 4466q^{25} - 2168q^{27} - 2444q^{33} - 2618q^{35} - 1790q^{37} - 11076q^{39} + 11644q^{41} - 3982q^{43} + 14704q^{45} - 1278q^{47} + 5882q^{53} + 65608q^{55} - 14552q^{57} - 8504q^{59} + 20564q^{61} + 19422q^{63} + 40798q^{65} + 107926q^{67} - 16418q^{73} + 66586q^{75} - 13348q^{77} - 146544q^{79} + 173806q^{81} - 36398q^{83} - 66262q^{85} + 124384q^{87} - 306620q^{93} + 173768q^{95} - 60314q^{97} - 388628q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(101\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\)

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 0
\(3\) −13.4331 13.4331i −0.861733 0.861733i 0.129806 0.991539i \(-0.458565\pi\)
−0.991539 + 0.129806i \(0.958565\pi\)
\(4\) 0 0
\(5\) 15.0352 53.8418i 0.268958 0.963152i
\(6\) 0 0
\(7\) −76.4413 + 76.4413i −0.589634 + 0.589634i −0.937532 0.347898i \(-0.886896\pi\)
0.347898 + 0.937532i \(0.386896\pi\)
\(8\) 0 0
\(9\) 117.896i 0.485169i
\(10\) 0 0
\(11\) 622.995i 1.55240i 0.630488 + 0.776199i \(0.282855\pi\)
−0.630488 + 0.776199i \(0.717145\pi\)
\(12\) 0 0
\(13\) −293.552 + 293.552i −0.481755 + 0.481755i −0.905692 0.423937i \(-0.860648\pi\)
0.423937 + 0.905692i \(0.360648\pi\)
\(14\) 0 0
\(15\) −925.232 + 521.293i −1.06175 + 0.598210i
\(16\) 0 0
\(17\) −1153.02 1153.02i −0.967640 0.967640i 0.0318524 0.999493i \(-0.489859\pi\)
−0.999493 + 0.0318524i \(0.989859\pi\)
\(18\) 0 0
\(19\) 2003.44 1.27319 0.636593 0.771200i \(-0.280343\pi\)
0.636593 + 0.771200i \(0.280343\pi\)
\(20\) 0 0
\(21\) 2053.69 1.01622
\(22\) 0 0
\(23\) 1392.29 + 1392.29i 0.548797 + 0.548797i 0.926093 0.377296i \(-0.123146\pi\)
−0.377296 + 0.926093i \(0.623146\pi\)
\(24\) 0 0
\(25\) −2672.88 1619.05i −0.855323 0.518095i
\(26\) 0 0
\(27\) −1680.53 + 1680.53i −0.443647 + 0.443647i
\(28\) 0 0
\(29\) 305.819i 0.0675257i −0.999430 0.0337629i \(-0.989251\pi\)
0.999430 0.0337629i \(-0.0107491\pi\)
\(30\) 0 0
\(31\) 2108.06i 0.393985i −0.980405 0.196992i \(-0.936883\pi\)
0.980405 0.196992i \(-0.0631174\pi\)
\(32\) 0 0
\(33\) 8368.75 8368.75i 1.33775 1.33775i
\(34\) 0 0
\(35\) 2966.43 + 5265.05i 0.409321 + 0.726494i
\(36\) 0 0
\(37\) 9903.12 + 9903.12i 1.18924 + 1.18924i 0.977279 + 0.211957i \(0.0679835\pi\)
0.211957 + 0.977279i \(0.432016\pi\)
\(38\) 0 0
\(39\) 7886.62 0.830289
\(40\) 0 0
\(41\) 16996.0 1.57902 0.789511 0.613736i \(-0.210334\pi\)
0.789511 + 0.613736i \(0.210334\pi\)
\(42\) 0 0
\(43\) −2031.28 2031.28i −0.167533 0.167533i 0.618361 0.785894i \(-0.287797\pi\)
−0.785894 + 0.618361i \(0.787797\pi\)
\(44\) 0 0
\(45\) 6347.74 + 1772.59i 0.467291 + 0.130490i
\(46\) 0 0
\(47\) −682.885 + 682.885i −0.0450924 + 0.0450924i −0.729293 0.684201i \(-0.760151\pi\)
0.684201 + 0.729293i \(0.260151\pi\)
\(48\) 0 0
\(49\) 5120.46i 0.304663i
\(50\) 0 0
\(51\) 30977.2i 1.66770i
\(52\) 0 0
\(53\) 21092.5 21092.5i 1.03143 1.03143i 0.0319374 0.999490i \(-0.489832\pi\)
0.999490 0.0319374i \(-0.0101677\pi\)
\(54\) 0 0
\(55\) 33543.2 + 9366.86i 1.49519 + 0.417530i
\(56\) 0 0
\(57\) −26912.4 26912.4i −1.09715 1.09715i
\(58\) 0 0
\(59\) 11617.4 0.434490 0.217245 0.976117i \(-0.430293\pi\)
0.217245 + 0.976117i \(0.430293\pi\)
\(60\) 0 0
\(61\) −1309.80 −0.0450694 −0.0225347 0.999746i \(-0.507174\pi\)
−0.0225347 + 0.999746i \(0.507174\pi\)
\(62\) 0 0
\(63\) −9012.12 9012.12i −0.286072 0.286072i
\(64\) 0 0
\(65\) 11391.8 + 20219.0i 0.334432 + 0.593576i
\(66\) 0 0
\(67\) −39870.6 + 39870.6i −1.08509 + 1.08509i −0.0890646 + 0.996026i \(0.528388\pi\)
−0.996026 + 0.0890646i \(0.971612\pi\)
\(68\) 0 0
\(69\) 37405.7i 0.945833i
\(70\) 0 0
\(71\) 25454.3i 0.599259i −0.954056 0.299630i \(-0.903137\pi\)
0.954056 0.299630i \(-0.0968631\pi\)
\(72\) 0 0
\(73\) 1031.25 1031.25i 0.0226495 0.0226495i −0.695691 0.718341i \(-0.744902\pi\)
0.718341 + 0.695691i \(0.244902\pi\)
\(74\) 0 0
\(75\) 14156.3 + 57653.9i 0.290601 + 1.18352i
\(76\) 0 0
\(77\) −47622.5 47622.5i −0.915347 0.915347i
\(78\) 0 0
\(79\) −11849.6 −0.213617 −0.106808 0.994280i \(-0.534063\pi\)
−0.106808 + 0.994280i \(0.534063\pi\)
\(80\) 0 0
\(81\) 73798.3 1.24978
\(82\) 0 0
\(83\) 45180.7 + 45180.7i 0.719876 + 0.719876i 0.968580 0.248703i \(-0.0800044\pi\)
−0.248703 + 0.968580i \(0.580004\pi\)
\(84\) 0 0
\(85\) −79416.5 + 44744.7i −1.19224 + 0.671730i
\(86\) 0 0
\(87\) −4108.09 + 4108.09i −0.0581892 + 0.0581892i
\(88\) 0 0
\(89\) 143889.i 1.92553i 0.270332 + 0.962767i \(0.412867\pi\)
−0.270332 + 0.962767i \(0.587133\pi\)
\(90\) 0 0
\(91\) 44879.0i 0.568119i
\(92\) 0 0
\(93\) −28317.8 + 28317.8i −0.339510 + 0.339510i
\(94\) 0 0
\(95\) 30122.1 107869.i 0.342434 1.22627i
\(96\) 0 0
\(97\) −24390.9 24390.9i −0.263207 0.263207i 0.563148 0.826356i \(-0.309590\pi\)
−0.826356 + 0.563148i \(0.809590\pi\)
\(98\) 0 0
\(99\) −73448.7 −0.753175
\(100\) 0 0
\(101\) 169993. 1.65816 0.829082 0.559127i \(-0.188864\pi\)
0.829082 + 0.559127i \(0.188864\pi\)
\(102\) 0 0
\(103\) −116026. 116026.i −1.07761 1.07761i −0.996723 0.0808914i \(-0.974223\pi\)
−0.0808914 0.996723i \(1.47422\pi\)
\(104\) 0 0
\(105\) 30877.6 110574.i 0.273319 0.978770i
\(106\) 0 0
\(107\) −68471.5 + 68471.5i −0.578163 + 0.578163i −0.934397 0.356234i \(-0.884061\pi\)
0.356234 + 0.934397i \(0.384061\pi\)
\(108\) 0 0
\(109\) 20202.8i 0.162872i 0.996679 + 0.0814360i \(0.0259506\pi\)
−0.996679 + 0.0814360i \(0.974049\pi\)
\(110\) 0 0
\(111\) 266059.i 2.04961i
\(112\) 0 0
\(113\) −79268.7 + 79268.7i −0.583990 + 0.583990i −0.935997 0.352007i \(-0.885499\pi\)
0.352007 + 0.935997i \(0.385499\pi\)
\(114\) 0 0
\(115\) 95897.1 54030.2i 0.676178 0.380971i
\(116\) 0 0
\(117\) −34608.6 34608.6i −0.233733 0.233733i
\(118\) 0 0
\(119\) 176276. 1.14111
\(120\) 0 0
\(121\) −227072. −1.40994
\(122\) 0 0
\(123\) −228309. 228309.i −1.36070 1.36070i
\(124\) 0 0
\(125\) −127360. + 119570.i −0.729050 + 0.684460i
\(126\) 0 0
\(127\) 133983. 133983.i 0.737121 0.737121i −0.234898 0.972020i \(-0.575476\pi\)
0.972020 + 0.234898i \(0.0754758\pi\)
\(128\) 0 0
\(129\) 54572.8i 0.288737i
\(130\) 0 0
\(131\) 358577.i 1.82559i 0.408414 + 0.912797i \(0.366082\pi\)
−0.408414 + 0.912797i \(0.633918\pi\)
\(132\) 0 0
\(133\) −153145. + 153145.i −0.750715 + 0.750715i
\(134\) 0 0
\(135\) 65215.8 + 115750.i 0.307977 + 0.546622i
\(136\) 0 0
\(137\) −156028. 156028.i −0.710232 0.710232i 0.256352 0.966584i \(-0.417479\pi\)
−0.966584 + 0.256352i \(0.917479\pi\)
\(138\) 0 0
\(139\) −211815. −0.929865 −0.464932 0.885346i \(-0.653921\pi\)
−0.464932 + 0.885346i \(0.653921\pi\)
\(140\) 0 0
\(141\) 18346.5 0.0777152
\(142\) 0 0
\(143\) −182881. 182881.i −0.747876 0.747876i
\(144\) 0 0
\(145\) −16465.8 4598.05i −0.0650375 0.0181616i
\(146\) 0 0
\(147\) 68783.7 68783.7i 0.262538 0.262538i
\(148\) 0 0
\(149\) 55272.1i 0.203958i 0.994787 + 0.101979i \(0.0325174\pi\)
−0.994787 + 0.101979i \(0.967483\pi\)
\(150\) 0 0
\(151\) 358721.i 1.28031i 0.768247 + 0.640154i \(0.221129\pi\)
−0.768247 + 0.640154i \(0.778871\pi\)
\(152\) 0 0
\(153\) 135936. 135936.i 0.469469 0.469469i
\(154\) 0 0
\(155\) −113502. 31695.2i −0.379467 0.105965i
\(156\) 0 0
\(157\) 355644. + 355644.i 1.15151 + 1.15151i 0.986251 + 0.165255i \(0.0528447\pi\)
0.165255 + 0.986251i \(0.447155\pi\)
\(158\) 0 0
\(159\) −566675. −1.77763
\(160\) 0 0
\(161\) −212858. −0.647179
\(162\) 0 0
\(163\) 288242. + 288242.i 0.849745 + 0.849745i 0.990101 0.140356i \(-0.0448248\pi\)
−0.140356 + 0.990101i \(0.544825\pi\)
\(164\) 0 0
\(165\) −324763. 576415.i −0.928660 1.64826i
\(166\) 0 0
\(167\) 78292.2 78292.2i 0.217234 0.217234i −0.590098 0.807332i \(-0.700911\pi\)
0.807332 + 0.590098i \(0.200911\pi\)
\(168\) 0 0
\(169\) 198947.i 0.535823i
\(170\) 0 0
\(171\) 236197.i 0.617711i
\(172\) 0 0
\(173\) −242048. + 242048.i −0.614875 + 0.614875i −0.944212 0.329337i \(-0.893175\pi\)
0.329337 + 0.944212i \(0.393175\pi\)
\(174\) 0 0
\(175\) 328081. 80556.7i 0.809814 0.198841i
\(176\) 0 0
\(177\) −156058. 156058.i −0.374414 0.374414i
\(178\) 0 0
\(179\) 28397.8 0.0662448 0.0331224 0.999451i \(-0.489455\pi\)
0.0331224 + 0.999451i \(0.489455\pi\)
\(180\) 0 0
\(181\) 637320. 1.44598 0.722988 0.690861i \(-0.242768\pi\)
0.722988 + 0.690861i \(0.242768\pi\)
\(182\) 0 0
\(183\) 17594.7 + 17594.7i 0.0388378 + 0.0388378i
\(184\) 0 0
\(185\) 682098. 384307.i 1.46527 0.825560i
\(186\) 0 0
\(187\) 718325. 718325.i 1.50216 1.50216i
\(188\) 0 0
\(189\) 256924.i 0.523179i
\(190\) 0 0
\(191\) 618423.i 1.22660i 0.789851 + 0.613299i \(0.210158\pi\)
−0.789851 + 0.613299i \(0.789842\pi\)
\(192\) 0 0
\(193\) 21641.0 21641.0i 0.0418199 0.0418199i −0.685888 0.727708i \(-0.740586\pi\)
0.727708 + 0.685888i \(0.240586\pi\)
\(194\) 0 0
\(195\) 118577. 424630.i 0.223313 0.799695i
\(196\) 0 0
\(197\) 38033.2 + 38033.2i 0.0698227 + 0.0698227i 0.741156 0.671333i \(-0.234278\pi\)
−0.671333 + 0.741156i \(0.734278\pi\)
\(198\) 0 0
\(199\) 258481. 0.462696 0.231348 0.972871i \(-0.425686\pi\)
0.231348 + 0.972871i \(0.425686\pi\)
\(200\) 0 0
\(201\) 1.07117e6 1.87012
\(202\) 0 0
\(203\) 23377.2 + 23377.2i 0.0398155 + 0.0398155i
\(204\) 0 0
\(205\) 255539. 915098.i 0.424691 1.52084i
\(206\) 0 0
\(207\) −164146. + 164146.i −0.266259 + 0.266259i
\(208\) 0 0
\(209\) 1.24813e6i 1.97649i
\(210\) 0 0
\(211\) 185768.i 0.287253i 0.989632 + 0.143626i \(0.0458764\pi\)
−0.989632 + 0.143626i \(0.954124\pi\)
\(212\) 0 0
\(213\) −341930. + 341930.i −0.516402 + 0.516402i
\(214\) 0 0
\(215\) −139909. + 78827.2i −0.206419 + 0.116300i
\(216\) 0 0
\(217\) 161143. + 161143.i 0.232307 + 0.232307i
\(218\) 0 0
\(219\) −27705.8 −0.0390356
\(220\) 0 0
\(221\) 676942. 0.932332
\(222\) 0 0
\(223\) 759885. + 759885.i 1.02326 + 1.02326i 0.999723 + 0.0235364i \(0.00749255\pi\)
0.0235364 + 0.999723i \(0.492507\pi\)
\(224\) 0 0
\(225\) 190879. 315122.i 0.251363 0.414976i
\(226\) 0 0
\(227\) 35910.4 35910.4i 0.0462547 0.0462547i −0.683601 0.729856i \(-0.739587\pi\)
0.729856 + 0.683601i \(0.239587\pi\)
\(228\) 0 0
\(229\) 1.54665e6i 1.94896i −0.224469 0.974481i \(-0.572065\pi\)
0.224469 0.974481i \(-0.427935\pi\)
\(230\) 0 0
\(231\) 1.27944e6i 1.57757i
\(232\) 0 0
\(233\) −389263. + 389263.i −0.469735 + 0.469735i −0.901829 0.432093i \(-0.857775\pi\)
0.432093 + 0.901829i \(0.357775\pi\)
\(234\) 0 0
\(235\) 26500.5 + 47035.1i 0.0313028 + 0.0555587i
\(236\) 0 0
\(237\) 159176. + 159176.i 0.184081 + 0.184081i
\(238\) 0 0
\(239\) −823778. −0.932858 −0.466429 0.884559i \(-0.654460\pi\)
−0.466429 + 0.884559i \(0.654460\pi\)
\(240\) 0 0
\(241\) −139658. −0.154890 −0.0774451 0.996997i \(-0.524676\pi\)
−0.0774451 + 0.996997i \(0.524676\pi\)
\(242\) 0 0
\(243\) −582969. 582969.i −0.633330 0.633330i
\(244\) 0 0
\(245\) 275695. + 76987.3i 0.293436 + 0.0819415i
\(246\) 0 0
\(247\) −588113. + 588113.i −0.613365 + 0.613365i
\(248\) 0 0
\(249\) 1.21383e6i 1.24068i
\(250\) 0 0
\(251\) 1.26857e6i 1.27096i 0.772118 + 0.635480i \(0.219198\pi\)
−0.772118 + 0.635480i \(0.780802\pi\)
\(252\) 0 0
\(253\) −867393. + 867393.i −0.851951 + 0.851951i
\(254\) 0 0
\(255\) 1.66787e6 + 465749.i 1.60624 + 0.448540i
\(256\) 0 0
\(257\) 79307.5 + 79307.5i 0.0749000 + 0.0749000i 0.743564 0.668664i \(-0.233134\pi\)
−0.668664 + 0.743564i \(0.733134\pi\)
\(258\) 0 0
\(259\) −1.51401e6 −1.40243
\(260\) 0 0
\(261\) 36054.8 0.0327614
\(262\) 0 0
\(263\) −750568. 750568.i −0.669115 0.669115i 0.288396 0.957511i \(-0.406878\pi\)
−0.957511 + 0.288396i \(0.906878\pi\)
\(264\) 0 0
\(265\) −818529. 1.45279e6i −0.716010 1.27083i
\(266\) 0 0
\(267\) 1.93287e6 1.93287e6i 1.65930 1.65930i
\(268\) 0 0
\(269\) 2.07912e6i 1.75186i 0.482441 + 0.875928i \(0.339750\pi\)
−0.482441 + 0.875928i \(0.660250\pi\)
\(270\) 0 0
\(271\) 826197.i 0.683377i 0.939813 + 0.341689i \(0.110999\pi\)
−0.939813 + 0.341689i \(0.889001\pi\)
\(272\) 0 0
\(273\) −602863. + 602863.i −0.489567 + 0.489567i
\(274\) 0 0
\(275\) 1.00866e6 1.66519e6i 0.804289 1.32780i
\(276\) 0 0
\(277\) −1.13631e6 1.13631e6i −0.889808 0.889808i 0.104696 0.994504i \(-0.466613\pi\)
−0.994504 + 0.104696i \(0.966613\pi\)
\(278\) 0 0
\(279\) 248532. 0.191149
\(280\) 0 0
\(281\) 812.516 0.000613856 0.000306928 1.00000i \(-0.499902\pi\)
0.000306928 1.00000i \(0.499902\pi\)
\(282\) 0 0
\(283\) 129621. + 129621.i 0.0962076 + 0.0962076i 0.753572 0.657365i \(-0.228329\pi\)
−0.657365 + 0.753572i \(0.728329\pi\)
\(284\) 0 0
\(285\) −1.85365e6 + 1.04438e6i −1.35181 + 0.761633i
\(286\) 0 0
\(287\) −1.29920e6 + 1.29920e6i −0.931046 + 0.931046i
\(288\) 0 0
\(289\) 1.23905e6i 0.872655i
\(290\) 0 0
\(291\) 655290.i 0.453629i
\(292\) 0 0
\(293\) 1.81804e6 1.81804e6i 1.23719 1.23719i 0.276039 0.961147i \(-0.410978\pi\)
0.961147 0.276039i \(-0.0890218\pi\)
\(294\) 0 0
\(295\) 174670. 625503.i 0.116860 0.418480i
\(296\) 0 0
\(297\) −1.04696e6 1.04696e6i −0.688717 0.688717i
\(298\) 0 0
\(299\) −817422. −0.528772
\(300\) 0 0
\(301\) 310548. 0.197566
\(302\) 0 0
\(303\) −2.28353e6 2.28353e6i −1.42890 1.42890i
\(304\) 0 0
\(305\) −19693.2 + 70522.2i −0.0121218 + 0.0434087i
\(306\) 0 0
\(307\) 1.39031e6 1.39031e6i 0.841907 0.841907i −0.147199 0.989107i \(-0.547026\pi\)
0.989107 + 0.147199i \(0.0470259\pi\)
\(308\) 0 0
\(309\) 3.11718e6i 1.85723i
\(310\) 0 0
\(311\) 2.77199e6i 1.62514i −0.582863 0.812570i \(-0.698068\pi\)
0.582863 0.812570i \(-0.301932\pi\)
\(312\) 0 0
\(313\) −393418. + 393418.i −0.226983 + 0.226983i −0.811431 0.584448i \(-0.801311\pi\)
0.584448 + 0.811431i \(0.301311\pi\)
\(314\) 0 0
\(315\) −620728. + 349730.i −0.352472 + 0.198590i
\(316\) 0 0
\(317\) 594016. + 594016.i 0.332009 + 0.332009i 0.853349 0.521340i \(-0.174568\pi\)
−0.521340 + 0.853349i \(0.674568\pi\)
\(318\) 0 0
\(319\) 190524. 0.104827
\(320\) 0 0
\(321\) 1.83957e6 0.996445
\(322\) 0 0
\(323\) −2.31000e6 2.31000e6i −1.23199 1.23199i
\(324\) 0 0
\(325\) 1.25990e6 309356.i 0.661652 0.162462i
\(326\) 0 0
\(327\) 271387. 271387.i 0.140352 0.140352i
\(328\) 0 0
\(329\) 104401.i 0.0531760i
\(330\) 0 0
\(331\) 2.17459e6i 1.09096i −0.838124 0.545479i \(-0.816348\pi\)
0.838124 0.545479i \(-0.183652\pi\)
\(332\) 0 0
\(333\) −1.16754e6 + 1.16754e6i −0.576980 + 0.576980i
\(334\) 0 0
\(335\) 1.54724e6 + 2.74617e6i 0.753263 + 1.33695i
\(336\) 0 0
\(337\) −603974. 603974.i −0.289696 0.289696i 0.547264 0.836960i \(-0.315669\pi\)
−0.836960 + 0.547264i \(0.815669\pi\)
\(338\) 0 0
\(339\) 2.12965e6 1.00649
\(340\) 0 0
\(341\) 1.31331e6 0.611621
\(342\) 0 0
\(343\) −1.67616e6 1.67616e6i −0.769274 0.769274i
\(344\) 0 0
\(345\) −2.01399e6 562402.i −0.910981 0.254389i
\(346\) 0 0
\(347\) −2.94638e6 + 2.94638e6i −1.31361 + 1.31361i −0.394869 + 0.918738i \(0.629210\pi\)
−0.918738 + 0.394869i \(0.870790\pi\)
\(348\) 0 0
\(349\) 1.01585e6i 0.446443i 0.974768 + 0.223221i \(0.0716573\pi\)
−0.974768 + 0.223221i \(0.928343\pi\)
\(350\) 0 0
\(351\) 986648.i 0.427459i
\(352\) 0 0
\(353\) −3.05696e6 + 3.05696e6i −1.30573 + 1.30573i −0.381259 + 0.924468i \(0.624509\pi\)
−0.924468 + 0.381259i \(0.875491\pi\)
\(354\) 0 0
\(355\) −1.37050e6 382710.i −0.577178 0.161176i
\(356\) 0 0
\(357\) −2.36794e6 2.36794e6i −0.983331 0.983331i
\(358\) 0 0
\(359\) −1.01289e6 −0.414787 −0.207393 0.978258i \(-0.566498\pi\)
−0.207393 + 0.978258i \(0.566498\pi\)
\(360\) 0 0
\(361\) 1.53767e6 0.621005
\(362\) 0 0
\(363\) 3.05028e6 + 3.05028e6i 1.21499 + 1.21499i
\(364\) 0 0
\(365\) −40019.4 71029.6i −0.0157231 0.0279066i
\(366\) 0 0
\(367\) 1.78687e6 1.78687e6i 0.692511 0.692511i −0.270272 0.962784i \(-0.587114\pi\)
0.962784 + 0.270272i \(0.0871138\pi\)
\(368\) 0 0
\(369\) 2.00377e6i 0.766092i
\(370\) 0 0
\(371\) 3.22468e6i 1.21633i
\(372\) 0 0
\(373\) 382840. 382840.i 0.142477 0.142477i −0.632270 0.774748i \(-0.717877\pi\)
0.774748 + 0.632270i \(0.217877\pi\)
\(374\) 0 0
\(375\) 3.31704e6 + 104637.i 1.21807 + 0.0384245i
\(376\) 0 0
\(377\) 89773.7 + 89773.7i 0.0325309 + 0.0325309i
\(378\) 0 0
\(379\) −2.37584e6 −0.849610 −0.424805 0.905285i \(-0.639657\pi\)
−0.424805 + 0.905285i \(0.639657\pi\)
\(380\) 0 0
\(381\) −3.59960e6 −1.27040
\(382\) 0 0
\(383\) −748285. 748285.i −0.260657 0.260657i 0.564664 0.825321i \(-0.309006\pi\)
−0.825321 + 0.564664i \(0.809006\pi\)
\(384\) 0 0
\(385\) −3.28010e6 + 1.84807e6i −1.12781 + 0.635428i
\(386\) 0 0
\(387\) 239480. 239480.i 0.0812816 0.0812816i
\(388\) 0 0
\(389\) 3.04186e6i 1.01921i −0.860407 0.509607i \(-0.829791\pi\)
0.860407 0.509607i \(-0.170209\pi\)
\(390\) 0 0
\(391\) 3.21068e6i 1.06208i
\(392\) 0 0
\(393\) 4.81680e6 4.81680e6i 1.57317 1.57317i
\(394\) 0 0
\(395\) −178161. + 638003.i −0.0574539 + 0.205745i
\(396\) 0 0
\(397\) −3.19165e6 3.19165e6i −1.01634 1.01634i −0.999864 0.0164751i \(-0.994756\pi\)
−0.0164751 0.999864i \(-0.505244\pi\)
\(398\) 0 0
\(399\) 4.11443e6 1.29383
\(400\) 0 0
\(401\) 4.27231e6 1.32679 0.663395 0.748270i \(-0.269115\pi\)
0.663395 + 0.748270i \(0.269115\pi\)
\(402\) 0 0
\(403\) 618826. + 618826.i 0.189804 + 0.189804i
\(404\) 0 0
\(405\) 1.10957e6 3.97343e6i 0.336138 1.20373i
\(406\) 0 0
\(407\) −6.16960e6 + 6.16960e6i −1.84617 + 1.84617i
\(408\) 0 0
\(409\) 4.39056e6i 1.29781i −0.760869 0.648906i \(-0.775227\pi\)
0.760869 0.648906i \(-0.224773\pi\)
\(410\) 0 0
\(411\) 4.19187e6i 1.22406i
\(412\) 0 0
\(413\) −888050. + 888050.i −0.256190 + 0.256190i
\(414\) 0 0
\(415\) 3.11191e6 1.75331e6i 0.886967 0.499734i
\(416\) 0 0
\(417\) 2.84533e6 + 2.84533e6i 0.801295 + 0.801295i
\(418\) 0 0
\(419\) −5.83290e6 −1.62312 −0.811558 0.584271i \(-0.801380\pi\)
−0.811558 + 0.584271i \(0.801380\pi\)
\(420\) 0 0
\(421\) −741629. −0.203930 −0.101965 0.994788i \(-0.532513\pi\)
−0.101965 + 0.994788i \(0.532513\pi\)
\(422\) 0 0
\(423\) −80509.4 80509.4i −0.0218774 0.0218774i
\(424\) 0 0
\(425\) 1.21509e6 + 4.94868e6i 0.326316 + 1.32897i
\(426\) 0 0
\(427\) 100123. 100123.i 0.0265745 0.0265745i
\(428\) 0 0
\(429\) 4.91333e6i 1.28894i
\(430\) 0 0
\(431\) 12397.3i 0.00321464i 0.999999 + 0.00160732i \(0.000511626\pi\)
−0.999999 + 0.00160732i \(0.999488\pi\)
\(432\) 0 0
\(433\) −203088. + 203088.i −0.0520552 + 0.0520552i −0.732655 0.680600i \(-0.761719\pi\)
0.680600 + 0.732655i \(0.261719\pi\)
\(434\) 0 0
\(435\) 159421. + 282953.i 0.0403946 + 0.0716954i
\(436\) 0 0
\(437\) 2.78938e6 + 2.78938e6i 0.698721 + 0.698721i
\(438\) 0 0
\(439\) 6.21348e6 1.53877 0.769384 0.638786i \(-0.220563\pi\)
0.769384 + 0.638786i \(0.220563\pi\)
\(440\) 0 0
\(441\) −603682. −0.147813
\(442\) 0 0
\(443\) 4.93074e6 + 4.93074e6i 1.19372 + 1.19372i 0.976015 + 0.217705i \(0.0698571\pi\)
0.217705 + 0.976015i \(0.430143\pi\)
\(444\) 0 0
\(445\) 7.74722e6 + 2.16340e6i 1.85458 + 0.517888i
\(446\) 0 0
\(447\) 742475. 742475.i 0.175757 0.175757i
\(448\) 0 0
\(449\) 3.32541e6i 0.778449i −0.921143 0.389224i \(-0.872743\pi\)
0.921143 0.389224i \(-0.127257\pi\)
\(450\) 0 0
\(451\) 1.05885e7i 2.45127i
\(452\) 0 0
\(453\) 4.81873e6 4.81873e6i 1.10328 1.10328i
\(454\) 0 0
\(455\) −2.41637e6 674765.i −0.547185 0.152800i
\(456\) 0 0
\(457\) 1.03786e6 + 1.03786e6i 0.232460 + 0.232460i 0.813719 0.581259i \(-0.197440\pi\)
−0.581259 + 0.813719i \(0.697440\pi\)
\(458\) 0 0
\(459\) 3.87537e6 0.858582
\(460\) 0 0
\(461\) 4.98358e6 1.09217 0.546083 0.837731i \(-0.316118\pi\)
0.546083 + 0.837731i \(0.316118\pi\)
\(462\) 0 0
\(463\) −867273. 867273.i −0.188020 0.188020i 0.606820 0.794839i \(-0.292445\pi\)
−0.794839 + 0.606820i \(0.792445\pi\)
\(464\) 0 0
\(465\) 1.09892e6 + 1.95045e6i 0.235686 + 0.418313i
\(466\) 0 0
\(467\) 6.21652e6 6.21652e6i 1.31903 1.31903i 0.404489 0.914543i \(-0.367449\pi\)
0.914543 0.404489i \(-0.132551\pi\)
\(468\) 0 0
\(469\) 6.09552e6i 1.27961i
\(470\) 0 0
\(471\) 9.55479e6i 1.98458i
\(472\) 0 0
\(473\) 1.26548e6 1.26548e6i 0.260077 0.260077i
\(474\) 0 0
\(475\) −5.35496e6 3.24366e6i −1.08899 0.659632i
\(476\) 0 0
\(477\) 2.48672e6 + 2.48672e6i 0.500416 + 0.500416i
\(478\) 0 0
\(479\) −5.54732e6 −1.10470 −0.552350 0.833612i \(-0.686269\pi\)
−0.552350 + 0.833612i \(0.686269\pi\)
\(480\) 0 0
\(481\) −5.81416e6 −1.14584
\(482\) 0 0
\(483\) 2.85934e6 + 2.85934e6i 0.557696 + 0.557696i
\(484\) 0 0
\(485\) −1.67997e6 + 946528.i −0.324300 + 0.182717i
\(486\) 0 0
\(487\) −45082.0 + 45082.0i −0.00861353 + 0.00861353i −0.711400 0.702787i \(-0.751939\pi\)
0.702787 + 0.711400i \(0.251939\pi\)
\(488\) 0 0
\(489\) 7.74397e6i 1.46451i
\(490\) 0 0
\(491\) 4.49346e6i 0.841157i −0.907256 0.420579i \(-0.861827\pi\)
0.907256 0.420579i \(-0.138173\pi\)
\(492\) 0 0
\(493\) −352615. + 352615.i −0.0653406 + 0.0653406i
\(494\) 0 0
\(495\) −1.10432e6 + 3.95461e6i −0.202572 + 0.725422i
\(496\) 0 0
\(497\) 1.94576e6 + 1.94576e6i 0.353344 + 0.353344i
\(498\) 0 0
\(499\) 1.35470e6 0.243552 0.121776 0.992558i \(-0.461141\pi\)
0.121776 + 0.992558i \(0.461141\pi\)
\(500\) 0 0
\(501\) −2.10341e6 −0.374395
\(502\) 0 0
\(503\) 5.30723e6 + 5.30723e6i 0.935294 + 0.935294i 0.998030 0.0627366i \(-0.0199828\pi\)
−0.0627366 + 0.998030i \(0.519983\pi\)
\(504\) 0 0
\(505\) 2.55588e6 9.15273e6i 0.445976 1.59706i
\(506\) 0 0
\(507\) 2.67248e6 2.67248e6i 0.461737 0.461737i
\(508\) 0 0
\(509\) 7.90014e6i 1.35158i 0.737096 + 0.675788i \(0.236197\pi\)
−0.737096 + 0.675788i \(0.763803\pi\)
\(510\) 0 0
\(511\) 157661.i 0.0267098i
\(512\) 0 0
\(513\) −3.36685e6 + 3.36685e6i −0.564846 + 0.564846i
\(514\) 0 0
\(515\) −7.99155e6 + 4.50259e6i −1.32774 + 0.748073i
\(516\) 0 0
\(517\) −425434. 425434.i −0.0700013 0.0700013i
\(518\) 0 0
\(519\) 6.50292e6 1.05972
\(520\) 0 0
\(521\) −90092.2 −0.0145410 −0.00727048 0.999974i \(-0.502314\pi\)
−0.00727048 + 0.999974i \(0.502314\pi\)
\(522\) 0 0
\(523\) 1.47517e6 + 1.47517e6i 0.235824 + 0.235824i 0.815118 0.579295i \(-0.196672\pi\)
−0.579295 + 0.815118i \(0.696672\pi\)
\(524\) 0 0
\(525\) −5.48926e6 3.32501e6i −0.869192 0.526496i
\(526\) 0 0
\(527\) −2.43064e6 + 2.43064e6i −0.381235 + 0.381235i
\(528\) 0 0
\(529\) 2.55937e6i 0.397644i
\(530\) 0 0
\(531\) 1.36965e6i 0.210801i
\(532\) 0 0
\(533\) −4.98922e6 + 4.98922e6i −0.760702 + 0.760702i
\(534\) 0 0
\(535\) 2.65715e6 + 4.71612e6i 0.401357 + 0.712361i
\(536\) 0 0
\(537\) −381470. 381470.i −0.0570854 0.0570854i
\(538\) 0 0
\(539\) −3.19002e6 −0.472958
\(540\) 0 0
\(541\) −1.00732e7 −1.47970 −0.739852 0.672769i \(-0.765105\pi\)
−0.739852 + 0.672769i \(0.765105\pi\)
\(542\) 0 0
\(543\) −8.56118e6 8.56118e6i −1.24605 1.24605i
\(544\) 0 0
\(545\) 1.08776e6 + 303754.i 0.156870 + 0.0438057i
\(546\) 0 0
\(547\) −1.68628e6 + 1.68628e6i −0.240969 + 0.240969i −0.817251 0.576282i \(-0.804503\pi\)
0.576282 + 0.817251i \(0.304503\pi\)
\(548\) 0 0
\(549\) 154421.i 0.0218663i
\(550\) 0 0
\(551\) 612689.i 0.0859728i
\(552\) 0 0
\(553\) 905796. 905796.i 0.125956 0.125956i
\(554\) 0 0
\(555\) −1.43251e7 4.00026e6i −1.97408 0.551259i
\(556\) 0 0
\(557\) 5.82782e6 + 5.82782e6i 0.795917 + 0.795917i 0.982449 0.186532i \(-0.0597247\pi\)
−0.186532 + 0.982449i \(0.559725\pi\)
\(558\) 0 0
\(559\) 1.19257e6 0.161420
\(560\) 0 0
\(561\) −1.92987e7 −2.58893
\(562\) 0 0
\(563\) 3.92139e6 + 3.92139e6i 0.521397 + 0.521397i 0.917993 0.396596i \(-0.129809\pi\)
−0.396596 + 0.917993i \(0.629809\pi\)
\(564\) 0 0
\(565\) 3.07615e6 + 5.45979e6i 0.405402 + 0.719540i
\(566\) 0 0
\(567\) −5.64123e6 + 5.64123e6i −0.736913 + 0.736913i
\(568\) 0 0
\(569\) 9.00329e6i 1.16579i 0.812547 + 0.582895i \(0.198080\pi\)
−0.812547 + 0.582895i \(0.801920\pi\)
\(570\) 0 0
\(571\) 1.33754e7i 1.71678i −0.512995 0.858392i \(-0.671464\pi\)
0.512995 0.858392i \(-0.328536\pi\)
\(572\) 0 0
\(573\) 8.30734e6 8.30734e6i 1.05700 1.05700i
\(574\) 0 0
\(575\) −1.46725e6 5.97563e6i −0.185070 0.753727i
\(576\) 0 0
\(577\) 5.22216e6 + 5.22216e6i 0.652996 + 0.652996i 0.953713 0.300717i \(-0.0972261\pi\)
−0.300717 + 0.953713i \(0.597226\pi\)
\(578\) 0 0
\(579\) −581410. −0.0720752
\(580\) 0 0
\(581\) −6.90734e6 −0.848928
\(582\) 0 0
\(583\) 1.31405e7 + 1.31405e7i 1.60119 + 1.60119i
\(584\) 0 0
\(585\) −2.38374e6 + 1.34304e6i −0.287984 + 0.162256i
\(586\) 0 0
\(587\) 3.91266e6 3.91266e6i 0.468680 0.468680i −0.432807 0.901487i \(-0.642477\pi\)
0.901487 + 0.432807i \(0.142477\pi\)
\(588\) 0 0
\(589\) 4.22338e6i 0.501616i
\(590\) 0 0
\(591\) 1.02181e6i 0.120337i
\(592\) 0 0
\(593\) −377034. + 377034.i −0.0440295 + 0.0440295i −0.728779 0.684749i \(-0.759912\pi\)
0.684749 + 0.728779i \(0.259912\pi\)
\(594\) 0 0
\(595\) 2.65035e6 9.49104e6i 0.306910 1.09906i
\(596\) 0 0
\(597\) −3.47220e6 3.47220e6i −0.398721 0.398721i
\(598\) 0 0
\(599\) −3.69548e6 −0.420827 −0.210413 0.977613i \(-0.567481\pi\)
−0.210413 + 0.977613i \(0.567481\pi\)
\(600\) 0 0
\(601\) −5.53615e6 −0.625204 −0.312602 0.949884i \(-0.601201\pi\)
−0.312602 + 0.949884i \(0.601201\pi\)
\(602\) 0 0
\(603\) −4.70059e6 4.70059e6i −0.526452 0.526452i
\(604\) 0 0
\(605\) −3.41408e6 + 1.22260e7i −0.379214 + 1.35798i
\(606\) 0 0
\(607\) −851040. + 851040.i −0.0937515 + 0.0937515i −0.752427 0.658676i \(-0.771117\pi\)
0.658676 + 0.752427i \(0.271117\pi\)
\(608\) 0 0
\(609\) 628056.i 0.0686207i
\(610\) 0 0
\(611\) 400924.i 0.0434470i
\(612\) 0 0
\(613\) −2.99552e6 + 2.99552e6i −0.321974 + 0.321974i −0.849524 0.527550i \(-0.823111\pi\)
0.527550 + 0.849524i \(0.323111\pi\)
\(614\) 0 0
\(615\) −1.57253e7 + 8.85992e6i −1.67653 + 0.944587i
\(616\) 0 0
\(617\) 2.10245e6 + 2.10245e6i 0.222337 + 0.222337i 0.809482 0.587145i \(-0.199748\pi\)
−0.587145 + 0.809482i \(0.699748\pi\)
\(618\) 0 0
\(619\) 4.83196e6 0.506870 0.253435 0.967352i \(-0.418440\pi\)
0.253435 + 0.967352i \(0.418440\pi\)
\(620\) 0 0
\(621\) −4.67960e6 −0.486944
\(622\) 0 0
\(623\) −1.09990e7 1.09990e7i −1.13536 1.13536i
\(624\) 0 0
\(625\) 4.52300e6 + 8.65505e6i 0.463155 + 0.886277i
\(626\) 0 0
\(627\) 1.67663e7 1.67663e7i 1.70321 1.70321i
\(628\) 0 0
\(629\) 2.28370e7i 2.30150i
\(630\) 0 0
\(631\) 1.27571e7i 1.27550i −0.770244 0.637749i \(-0.779866\pi\)
0.770244 0.637749i \(-0.220134\pi\)
\(632\) 0 0
\(633\) 2.49544e6 2.49544e6i 0.247535 0.247535i
\(634\) 0 0
\(635\) −5.19941e6 9.22832e6i −0.511705 0.908215i
\(636\) 0 0
\(637\) −1.50312e6 1.50312e6i −0.146773 0.146773i
\(638\) 0 0
\(639\) 3.00096e6 0.290742
\(640\) 0 0
\(641\) 7.64611e6 0.735014 0.367507 0.930021i \(-0.380211\pi\)
0.367507 + 0.930021i \(0.380211\pi\)
\(642\) 0 0
\(643\) −2.54976e6 2.54976e6i −0.243204 0.243204i 0.574970 0.818174i \(-0.305014\pi\)
−0.818174 + 0.574970i \(0.805014\pi\)
\(644\) 0 0
\(645\) 2.93830e6 + 820514.i 0.278098 + 0.0776581i
\(646\) 0 0
\(647\) −3.90727e6 + 3.90727e6i −0.366954 + 0.366954i −0.866365 0.499411i \(-0.833550\pi\)
0.499411 + 0.866365i \(0.333550\pi\)
\(648\) 0 0
\(649\) 7.23760e6i 0.674501i
\(650\) 0 0
\(651\) 4.32930e6i 0.400373i
\(652\) 0 0
\(653\) −4.91675e6 + 4.91675e6i −0.451227 + 0.451227i −0.895762 0.444535i \(-0.853369\pi\)
0.444535 + 0.895762i \(0.353369\pi\)
\(654\) 0 0
\(655\) 1.93064e7 + 5.39128e6i 1.75832 + 0.491008i
\(656\) 0 0
\(657\) 121581. + 121581.i 0.0109888 + 0.0109888i
\(658\) 0 0
\(659\) −1.22997e6 −0.110327 −0.0551636 0.998477i \(-0.517568\pi\)
−0.0551636 + 0.998477i \(0.517568\pi\)
\(660\) 0 0
\(661\) 2.50222e6 0.222752 0.111376 0.993778i \(-0.464474\pi\)
0.111376 + 0.993778i \(0.464474\pi\)
\(662\) 0 0
\(663\) −9.09342e6 9.09342e6i −0.803421 0.803421i
\(664\) 0 0
\(665\) 5.94306e6 + 1.05482e7i 0.521142 + 0.924963i
\(666\) 0 0
\(667\) 425790. 425790.i 0.0370579 0.0370579i
\(668\) 0 0
\(669\) 2.04152e7i 1.76355i
\(670\) 0 0
\(671\) 816001.i 0.0699656i
\(672\) 0 0
\(673\) 4.60945e6 4.60945e6i 0.392294 0.392294i −0.483210 0.875504i \(-0.660529\pi\)
0.875504 + 0.483210i \(0.160529\pi\)
\(674\) 0 0
\(675\) 7.21273e6 1.77101e6i 0.609313 0.149610i
\(676\) 0 0
\(677\) 1.03990e7 + 1.03990e7i 0.872006 + 0.872006i 0.992691 0.120685i \(-0.0385091\pi\)
−0.120685 + 0.992691i \(0.538509\pi\)
\(678\) 0 0
\(679\) 3.72894e6 0.310392
\(680\) 0 0
\(681\) −964776. −0.0797185
\(682\) 0 0
\(683\) 1.39930e7 + 1.39930e7i 1.14778 + 1.14778i 0.986988 + 0.160795i \(0.0514059\pi\)
0.160795 + 0.986988i \(0.448594\pi\)
\(684\) 0 0
\(685\) −1.07467e7 + 6.05490e6i −0.875084 + 0.493038i
\(686\) 0 0
\(687\) −2.07763e7 + 2.07763e7i −1.67949 + 1.67949i
\(688\) 0 0
\(689\) 1.23835e7i 0.993791i
\(690\) 0 0
\(691\) 9.98056e6i 0.795169i −0.917565 0.397585i \(-0.869848\pi\)
0.917565 0.397585i \(-0.130152\pi\)
\(692\) 0 0
\(693\) 5.61451e6 5.61451e6i 0.444098 0.444098i
\(694\) 0 0
\(695\) −3.18468e6 + 1.14045e7i −0.250095 + 0.895601i
\(696\) 0 0
\(697\) −1.95968e7 1.95968e7i −1.52793 1.52793i
\(698\) 0 0
\(699\) 1.04580e7 0.809573
\(700\) 0 0
\(701\) −7.67178e6 −0.589659 −0.294830 0.955550i \(-0.595263\pi\)
−0.294830 + 0.955550i \(0.595263\pi\)
\(702\) 0 0
\(703\) 1.98403e7 + 1.98403e7i 1.51412 + 1.51412i
\(704\) 0 0
\(705\) 275844. 987810.i 0.0209021 0.0748515i
\(706\) 0 0
\(707\) −1.29945e7 + 1.29945e7i −0.977710 + 0.977710i
\(708\) 0 0
\(709\) 1.61069e7i 1.20336i 0.798737 + 0.601681i \(0.205502\pi\)
−0.798737 + 0.601681i \(0.794498\pi\)
\(710\) 0 0
\(711\) 1.39702e6i 0.103640i
\(712\) 0 0
\(713\) 2.93505e6 2.93505e6i 0.216218 0.216218i
\(714\) 0 0
\(715\) −1.25963e7 + 7.09701e6i −0.921465 + 0.519171i
\(716\) 0 0
\(717\) 1.10659e7 + 1.10659e7i 0.803874 + 0.803874i
\(718\) 0 0
\(719\) 9.25776e6 0.667857 0.333929 0.942598i \(-0.391626\pi\)
0.333929 + 0.942598i \(0.391626\pi\)
\(720\) 0 0
\(721\) 1.77384e7 1.27080
\(722\) 0 0
\(723\) 1.87604e6 + 1.87604e6i 0.133474 + 0.133474i
\(724\) 0 0
\(725\) −495135. + 817418.i −0.0349847 + 0.0577563i
\(726\) 0 0
\(727\) −1.17208e7 + 1.17208e7i −0.822475 + 0.822475i −0.986462 0.163988i \(-0.947564\pi\)
0.163988 + 0.986462i \(0.447564\pi\)
\(728\) 0 0
\(729\) 2.27081e6i 0.158257i
\(730\) 0 0
\(731\) 4.68421e6i 0.324223i
\(732\) 0 0
\(733\) 5.35037e6 5.35037e6i 0.367811 0.367811i −0.498868 0.866678i \(-0.666251\pi\)
0.866678 + 0.498868i \(0.166251\pi\)
\(734\) 0 0
\(735\) −2.66926e6 4.73762e6i −0.182252 0.323476i
\(736\) 0 0
\(737\) −2.48392e7 2.48392e7i −1.68449 1.68449i
\(738\) 0 0
\(739\) −2.80515e7 −1.88949 −0.944746 0.327803i \(-0.893692\pi\)
−0.944746 + 0.327803i \(0.893692\pi\)
\(740\) 0 0
\(741\) 1.58004e7 1.05711
\(742\) 0 0
\(743\) 3.89759e6 + 3.89759e6i 0.259014 + 0.259014i 0.824653 0.565639i \(-0.191370\pi\)
−0.565639 + 0.824653i \(0.691370\pi\)
\(744\) 0 0
\(745\) 2.97595e6 + 831028.i 0.196442 + 0.0548561i
\(746\) 0 0
\(747\) −5.32663e6 + 5.32663e6i −0.349262 + 0.349262i
\(748\) 0 0
\(749\) 1.04681e7i 0.681810i
\(750\) 0 0
\(751\) 1.33082e6i 0.0861032i −0.999073 0.0430516i \(-0.986292\pi\)
0.999073 0.0430516i \(-0.0137080\pi\)
\(752\) 0 0
\(753\) 1.70409e7 1.70409e7i 1.09523 1.09523i
\(754\) 0 0
\(755\) 1.93142e7 + 5.39344e6i 1.23313 + 0.344349i
\(756\) 0 0
\(757\) −4.82595e6 4.82595e6i −0.306085 0.306085i 0.537303 0.843389i \(-0.319443\pi\)
−0.843389 + 0.537303i \(0.819443\pi\)
\(758\) 0 0
\(759\) 2.33035e7 1.46831
\(760\) 0 0
\(761\) −1.62700e7 −1.01842 −0.509210 0.860642i \(-0.670062\pi\)
−0.509210 + 0.860642i \(0.670062\pi\)
\(762\) 0 0
\(763\) −1.54433e6 1.54433e6i −0.0960349 0.0960349i
\(764\) 0 0
\(765\) −5.27523e6 9.36289e6i −0.325902 0.578437i
\(766\) 0 0
\(767\) −3.41032e6 + 3.41032e6i −0.209318 + 0.209318i
\(768\) 0 0
\(769\) 7.50924e6i 0.457910i −0.973437 0.228955i \(-0.926469\pi\)
0.973437 0.228955i \(-0.0735308\pi\)
\(770\) 0 0
\(771\) 2.13069e6i 0.129088i
\(772\) 0 0
\(773\) −2.21009e6 + 2.21009e6i −0.133034 + 0.133034i −0.770488 0.637454i \(-0.779987\pi\)
0.637454 + 0.770488i \(0.279987\pi\)
\(774\) 0 0
\(775\) −3.41305e6 + 5.63461e6i −0.204121 + 0.336984i
\(776\) 0 0
\(777\) 2.03379e7 + 2.03379e7i 1.20852 + 1.20852i
\(778\) 0 0
\(779\) 3.40505e7 2.01039
\(780\) 0 0
\(781\) 1.58579e7 0.930289
\(782\) 0 0
\(783\) 513939. + 513939.i 0.0299576 + 0.0299576i
\(784\) 0 0
\(785\) 2.44957e7 1.38013e7i 1.41878 0.799368i
\(786\) 0 0
\(787\) −6.25543e6 + 6.25543e6i −0.360015 + 0.360015i −0.863818 0.503803i \(-0.831934\pi\)
0.503803 + 0.863818i \(0.331934\pi\)
\(788\) 0 0
\(789\) 2.01649e7i 1.15320i
\(790\) 0 0
\(791\) 1.21188e7i 0.688681i
\(792\) 0 0
\(793\) 384495. 384495.i 0.0217124 0.0217124i