Properties

Label 324.5.d.f.163.5
Level 324
Weight 5
Character 324.163
Analytic conductor 33.492
Analytic rank 0
Dimension 22
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 324.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(33.4918680392\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 163.5
Character \(\chi\) \(=\) 324.163
Dual form 324.5.d.f.163.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.19553 - 2.40595i) q^{2} +(4.42285 + 15.3766i) q^{4} -2.03090 q^{5} -23.1347i q^{7} +(22.8618 - 59.7774i) q^{8} +O(q^{10})\) \(q+(-3.19553 - 2.40595i) q^{2} +(4.42285 + 15.3766i) q^{4} -2.03090 q^{5} -23.1347i q^{7} +(22.8618 - 59.7774i) q^{8} +(6.48981 + 4.88624i) q^{10} -4.99936i q^{11} +275.648 q^{13} +(-55.6608 + 73.9276i) q^{14} +(-216.877 + 136.016i) q^{16} -266.009 q^{17} +367.194i q^{19} +(-8.98238 - 31.2283i) q^{20} +(-12.0282 + 15.9756i) q^{22} -628.704i q^{23} -620.875 q^{25} +(-880.842 - 663.194i) q^{26} +(355.732 - 102.321i) q^{28} +638.962 q^{29} +1375.47i q^{31} +(1020.28 + 87.1493i) q^{32} +(850.041 + 640.004i) q^{34} +46.9843i q^{35} +1466.19 q^{37} +(883.449 - 1173.38i) q^{38} +(-46.4301 + 121.402i) q^{40} -1186.04 q^{41} -1651.61i q^{43} +(76.8730 - 22.1114i) q^{44} +(-1512.63 + 2009.04i) q^{46} -355.491i q^{47} +1865.79 q^{49} +(1984.03 + 1493.79i) q^{50} +(1219.15 + 4238.52i) q^{52} +5297.49 q^{53} +10.1532i q^{55} +(-1382.93 - 528.900i) q^{56} +(-2041.82 - 1537.31i) q^{58} -6031.37i q^{59} +1666.73 q^{61} +(3309.31 - 4395.36i) q^{62} +(-3050.68 - 2733.24i) q^{64} -559.815 q^{65} -2203.58i q^{67} +(-1176.52 - 4090.31i) q^{68} +(113.042 - 150.140i) q^{70} -524.299i q^{71} -1492.29 q^{73} +(-4685.25 - 3527.57i) q^{74} +(-5646.18 + 1624.04i) q^{76} -115.659 q^{77} -5136.51i q^{79} +(440.456 - 276.236i) q^{80} +(3790.02 + 2853.54i) q^{82} -7988.66i q^{83} +540.239 q^{85} +(-3973.68 + 5277.77i) q^{86} +(-298.849 - 114.294i) q^{88} -8860.17 q^{89} -6377.03i q^{91} +(9667.30 - 2780.66i) q^{92} +(-855.292 + 1135.98i) q^{94} -745.735i q^{95} +6818.67 q^{97} +(-5962.18 - 4488.98i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + q^{2} + q^{4} + 2q^{5} + 61q^{8} + O(q^{10}) \) \( 22q + q^{2} + q^{4} + 2q^{5} + 61q^{8} + 14q^{10} + 2q^{13} - 252q^{14} + q^{16} - 28q^{17} + 140q^{20} + 33q^{22} + 1752q^{25} + 548q^{26} - 258q^{28} - 526q^{29} + 121q^{32} - 385q^{34} - 4q^{37} - 1395q^{38} + 2276q^{40} + 2762q^{41} + 3357q^{44} + 1788q^{46} - 3428q^{49} - 6375q^{50} - 1438q^{52} - 5044q^{53} + 7506q^{56} + 4064q^{58} + 2q^{61} - 9162q^{62} + 4513q^{64} + 2014q^{65} + 11405q^{68} - 3666q^{70} - 1708q^{73} - 14620q^{74} - 1581q^{76} + 3942q^{77} + 22760q^{80} - 4243q^{82} + 1252q^{85} - 22113q^{86} - 1995q^{88} + 6524q^{89} + 30294q^{92} - 7524q^{94} - 5638q^{97} - 46469q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.19553 2.40595i −0.798883 0.601486i
\(3\) 0 0
\(4\) 4.42285 + 15.3766i 0.276428 + 0.961035i
\(5\) −2.03090 −0.0812361 −0.0406181 0.999175i \(-0.512933\pi\)
−0.0406181 + 0.999175i \(0.512933\pi\)
\(6\) 0 0
\(7\) 23.1347i 0.472136i −0.971737 0.236068i \(-0.924141\pi\)
0.971737 0.236068i \(-0.0758589\pi\)
\(8\) 22.8618 59.7774i 0.357216 0.934022i
\(9\) 0 0
\(10\) 6.48981 + 4.88624i 0.0648981 + 0.0488624i
\(11\) 4.99936i 0.0413171i −0.999787 0.0206585i \(-0.993424\pi\)
0.999787 0.0206585i \(-0.00657628\pi\)
\(12\) 0 0
\(13\) 275.648 1.63105 0.815527 0.578719i \(-0.196447\pi\)
0.815527 + 0.578719i \(0.196447\pi\)
\(14\) −55.6608 + 73.9276i −0.283984 + 0.377182i
\(15\) 0 0
\(16\) −216.877 + 136.016i −0.847175 + 0.531314i
\(17\) −266.009 −0.920447 −0.460224 0.887803i \(-0.652231\pi\)
−0.460224 + 0.887803i \(0.652231\pi\)
\(18\) 0 0
\(19\) 367.194i 1.01716i 0.861015 + 0.508579i \(0.169829\pi\)
−0.861015 + 0.508579i \(0.830171\pi\)
\(20\) −8.98238 31.2283i −0.0224559 0.0780707i
\(21\) 0 0
\(22\) −12.0282 + 15.9756i −0.0248516 + 0.0330075i
\(23\) 628.704i 1.18848i −0.804289 0.594238i \(-0.797454\pi\)
0.804289 0.594238i \(-0.202546\pi\)
\(24\) 0 0
\(25\) −620.875 −0.993401
\(26\) −880.842 663.194i −1.30302 0.981057i
\(27\) 0 0
\(28\) 355.732 102.321i 0.453739 0.130512i
\(29\) 638.962 0.759764 0.379882 0.925035i \(-0.375965\pi\)
0.379882 + 0.925035i \(0.375965\pi\)
\(30\) 0 0
\(31\) 1375.47i 1.43129i 0.698464 + 0.715645i \(0.253867\pi\)
−0.698464 + 0.715645i \(0.746133\pi\)
\(32\) 1020.28 + 87.1493i 0.996372 + 0.0851067i
\(33\) 0 0
\(34\) 850.041 + 640.004i 0.735330 + 0.553637i
\(35\) 46.9843i 0.0383545i
\(36\) 0 0
\(37\) 1466.19 1.07099 0.535496 0.844538i \(-0.320125\pi\)
0.535496 + 0.844538i \(0.320125\pi\)
\(38\) 883.449 1173.38i 0.611807 0.812590i
\(39\) 0 0
\(40\) −46.4301 + 121.402i −0.0290188 + 0.0758763i
\(41\) −1186.04 −0.705555 −0.352777 0.935707i \(-0.614763\pi\)
−0.352777 + 0.935707i \(0.614763\pi\)
\(42\) 0 0
\(43\) 1651.61i 0.893244i −0.894723 0.446622i \(-0.852627\pi\)
0.894723 0.446622i \(-0.147373\pi\)
\(44\) 76.8730 22.1114i 0.0397071 0.0114212i
\(45\) 0 0
\(46\) −1512.63 + 2009.04i −0.714852 + 0.949453i
\(47\) 355.491i 0.160928i −0.996757 0.0804642i \(-0.974360\pi\)
0.996757 0.0804642i \(-0.0256403\pi\)
\(48\) 0 0
\(49\) 1865.79 0.777087
\(50\) 1984.03 + 1493.79i 0.793611 + 0.597517i
\(51\) 0 0
\(52\) 1219.15 + 4238.52i 0.450869 + 1.56750i
\(53\) 5297.49 1.88590 0.942950 0.332934i \(-0.108039\pi\)
0.942950 + 0.332934i \(0.108039\pi\)
\(54\) 0 0
\(55\) 10.1532i 0.00335644i
\(56\) −1382.93 528.900i −0.440986 0.168654i
\(57\) 0 0
\(58\) −2041.82 1537.31i −0.606963 0.456988i
\(59\) 6031.37i 1.73265i −0.499478 0.866327i \(-0.666475\pi\)
0.499478 0.866327i \(-0.333525\pi\)
\(60\) 0 0
\(61\) 1666.73 0.447925 0.223962 0.974598i \(-0.428101\pi\)
0.223962 + 0.974598i \(0.428101\pi\)
\(62\) 3309.31 4395.36i 0.860902 1.14343i
\(63\) 0 0
\(64\) −3050.68 2733.24i −0.744794 0.667295i
\(65\) −559.815 −0.132500
\(66\) 0 0
\(67\) 2203.58i 0.490885i −0.969411 0.245443i \(-0.921067\pi\)
0.969411 0.245443i \(-0.0789333\pi\)
\(68\) −1176.52 4090.31i −0.254437 0.884582i
\(69\) 0 0
\(70\) 113.042 150.140i 0.0230697 0.0306408i
\(71\) 524.299i 0.104007i −0.998647 0.0520035i \(-0.983439\pi\)
0.998647 0.0520035i \(-0.0165607\pi\)
\(72\) 0 0
\(73\) −1492.29 −0.280032 −0.140016 0.990149i \(-0.544715\pi\)
−0.140016 + 0.990149i \(0.544715\pi\)
\(74\) −4685.25 3527.57i −0.855597 0.644187i
\(75\) 0 0
\(76\) −5646.18 + 1624.04i −0.977524 + 0.281171i
\(77\) −115.659 −0.0195073
\(78\) 0 0
\(79\) 5136.51i 0.823027i −0.911404 0.411513i \(-0.865000\pi\)
0.911404 0.411513i \(-0.135000\pi\)
\(80\) 440.456 276.236i 0.0688212 0.0431619i
\(81\) 0 0
\(82\) 3790.02 + 2853.54i 0.563656 + 0.424382i
\(83\) 7988.66i 1.15963i −0.814750 0.579813i \(-0.803126\pi\)
0.814750 0.579813i \(-0.196874\pi\)
\(84\) 0 0
\(85\) 540.239 0.0747736
\(86\) −3973.68 + 5277.77i −0.537274 + 0.713597i
\(87\) 0 0
\(88\) −298.849 114.294i −0.0385910 0.0147591i
\(89\) −8860.17 −1.11857 −0.559283 0.828977i \(-0.688924\pi\)
−0.559283 + 0.828977i \(0.688924\pi\)
\(90\) 0 0
\(91\) 6377.03i 0.770080i
\(92\) 9667.30 2780.66i 1.14217 0.328528i
\(93\) 0 0
\(94\) −855.292 + 1135.98i −0.0967963 + 0.128563i
\(95\) 745.735i 0.0826300i
\(96\) 0 0
\(97\) 6818.67 0.724696 0.362348 0.932043i \(-0.381975\pi\)
0.362348 + 0.932043i \(0.381975\pi\)
\(98\) −5962.18 4488.98i −0.620802 0.467408i
\(99\) 0 0
\(100\) −2746.04 9546.92i −0.274604 0.954692i
\(101\) 3091.05 0.303015 0.151507 0.988456i \(-0.451587\pi\)
0.151507 + 0.988456i \(0.451587\pi\)
\(102\) 0 0
\(103\) 10865.0i 1.02413i −0.858947 0.512065i \(-0.828881\pi\)
0.858947 0.512065i \(-0.171119\pi\)
\(104\) 6301.81 16477.5i 0.582638 1.52344i
\(105\) 0 0
\(106\) −16928.3 12745.5i −1.50661 1.13434i
\(107\) 14106.5i 1.23212i −0.787699 0.616060i \(-0.788728\pi\)
0.787699 0.616060i \(-0.211272\pi\)
\(108\) 0 0
\(109\) 16328.3 1.37432 0.687160 0.726506i \(-0.258857\pi\)
0.687160 + 0.726506i \(0.258857\pi\)
\(110\) 24.4281 32.4449i 0.00201885 0.00268140i
\(111\) 0 0
\(112\) 3146.69 + 5017.38i 0.250853 + 0.399982i
\(113\) 11822.9 0.925905 0.462952 0.886383i \(-0.346790\pi\)
0.462952 + 0.886383i \(0.346790\pi\)
\(114\) 0 0
\(115\) 1276.84i 0.0965472i
\(116\) 2826.03 + 9825.03i 0.210020 + 0.730160i
\(117\) 0 0
\(118\) −14511.1 + 19273.4i −1.04217 + 1.38419i
\(119\) 6154.04i 0.434577i
\(120\) 0 0
\(121\) 14616.0 0.998293
\(122\) −5326.08 4010.06i −0.357839 0.269421i
\(123\) 0 0
\(124\) −21150.0 + 6083.50i −1.37552 + 0.395649i
\(125\) 2530.25 0.161936
\(126\) 0 0
\(127\) 20979.9i 1.30076i −0.759609 0.650379i \(-0.774610\pi\)
0.759609 0.650379i \(-0.225390\pi\)
\(128\) 3172.51 + 16073.9i 0.193635 + 0.981074i
\(129\) 0 0
\(130\) 1788.91 + 1346.88i 0.105852 + 0.0796972i
\(131\) 28548.7i 1.66358i 0.555092 + 0.831789i \(0.312683\pi\)
−0.555092 + 0.831789i \(0.687317\pi\)
\(132\) 0 0
\(133\) 8494.92 0.480237
\(134\) −5301.70 + 7041.62i −0.295261 + 0.392160i
\(135\) 0 0
\(136\) −6081.45 + 15901.3i −0.328798 + 0.859718i
\(137\) −618.873 −0.0329731 −0.0164866 0.999864i \(-0.505248\pi\)
−0.0164866 + 0.999864i \(0.505248\pi\)
\(138\) 0 0
\(139\) 19422.0i 1.00523i −0.864511 0.502613i \(-0.832372\pi\)
0.864511 0.502613i \(-0.167628\pi\)
\(140\) −722.456 + 207.804i −0.0368600 + 0.0106023i
\(141\) 0 0
\(142\) −1261.44 + 1675.41i −0.0625588 + 0.0830894i
\(143\) 1378.07i 0.0673903i
\(144\) 0 0
\(145\) −1297.67 −0.0617203
\(146\) 4768.67 + 3590.38i 0.223713 + 0.168436i
\(147\) 0 0
\(148\) 6484.72 + 22544.9i 0.296052 + 1.02926i
\(149\) 619.281 0.0278943 0.0139471 0.999903i \(-0.495560\pi\)
0.0139471 + 0.999903i \(0.495560\pi\)
\(150\) 0 0
\(151\) 4339.46i 0.190319i 0.995462 + 0.0951593i \(0.0303361\pi\)
−0.995462 + 0.0951593i \(0.969664\pi\)
\(152\) 21949.9 + 8394.72i 0.950048 + 0.363345i
\(153\) 0 0
\(154\) 369.591 + 278.268i 0.0155840 + 0.0117334i
\(155\) 2793.45i 0.116272i
\(156\) 0 0
\(157\) −6207.76 −0.251846 −0.125923 0.992040i \(-0.540189\pi\)
−0.125923 + 0.992040i \(0.540189\pi\)
\(158\) −12358.2 + 16413.9i −0.495039 + 0.657502i
\(159\) 0 0
\(160\) −2072.10 176.992i −0.0809414 0.00691374i
\(161\) −14544.9 −0.561123
\(162\) 0 0
\(163\) 15857.0i 0.596824i 0.954437 + 0.298412i \(0.0964569\pi\)
−0.954437 + 0.298412i \(0.903543\pi\)
\(164\) −5245.66 18237.2i −0.195035 0.678063i
\(165\) 0 0
\(166\) −19220.3 + 25528.0i −0.697499 + 0.926406i
\(167\) 418.996i 0.0150237i −0.999972 0.00751186i \(-0.997609\pi\)
0.999972 0.00751186i \(-0.00239112\pi\)
\(168\) 0 0
\(169\) 47420.9 1.66034
\(170\) −1726.35 1299.79i −0.0597353 0.0449753i
\(171\) 0 0
\(172\) 25396.0 7304.81i 0.858438 0.246918i
\(173\) −19200.8 −0.641545 −0.320772 0.947156i \(-0.603942\pi\)
−0.320772 + 0.947156i \(0.603942\pi\)
\(174\) 0 0
\(175\) 14363.8i 0.469021i
\(176\) 679.995 + 1084.25i 0.0219523 + 0.0350028i
\(177\) 0 0
\(178\) 28312.9 + 21317.1i 0.893604 + 0.672803i
\(179\) 49821.7i 1.55494i 0.628922 + 0.777468i \(0.283496\pi\)
−0.628922 + 0.777468i \(0.716504\pi\)
\(180\) 0 0
\(181\) 13970.7 0.426443 0.213222 0.977004i \(-0.431604\pi\)
0.213222 + 0.977004i \(0.431604\pi\)
\(182\) −15342.8 + 20378.0i −0.463193 + 0.615204i
\(183\) 0 0
\(184\) −37582.3 14373.3i −1.11006 0.424542i
\(185\) −2977.68 −0.0870031
\(186\) 0 0
\(187\) 1329.88i 0.0380302i
\(188\) 5466.22 1572.28i 0.154658 0.0444851i
\(189\) 0 0
\(190\) −1794.20 + 2383.02i −0.0497008 + 0.0660117i
\(191\) 31170.9i 0.854442i 0.904147 + 0.427221i \(0.140507\pi\)
−0.904147 + 0.427221i \(0.859493\pi\)
\(192\) 0 0
\(193\) 26996.3 0.724753 0.362377 0.932032i \(-0.381965\pi\)
0.362377 + 0.932032i \(0.381965\pi\)
\(194\) −21789.3 16405.3i −0.578948 0.435895i
\(195\) 0 0
\(196\) 8252.09 + 28689.4i 0.214809 + 0.746808i
\(197\) 10416.4 0.268402 0.134201 0.990954i \(-0.457153\pi\)
0.134201 + 0.990954i \(0.457153\pi\)
\(198\) 0 0
\(199\) 8438.68i 0.213093i −0.994308 0.106546i \(-0.966021\pi\)
0.994308 0.106546i \(-0.0339793\pi\)
\(200\) −14194.3 + 37114.3i −0.354858 + 0.927858i
\(201\) 0 0
\(202\) −9877.56 7436.91i −0.242073 0.182259i
\(203\) 14782.2i 0.358712i
\(204\) 0 0
\(205\) 2408.73 0.0573165
\(206\) −26140.6 + 34719.4i −0.616000 + 0.818159i
\(207\) 0 0
\(208\) −59781.7 + 37492.7i −1.38179 + 0.866602i
\(209\) 1835.74 0.0420260
\(210\) 0 0
\(211\) 22945.7i 0.515390i −0.966226 0.257695i \(-0.917037\pi\)
0.966226 0.257695i \(-0.0829630\pi\)
\(212\) 23430.0 + 81457.2i 0.521316 + 1.81242i
\(213\) 0 0
\(214\) −33939.6 + 45077.9i −0.741104 + 0.984320i
\(215\) 3354.25i 0.0725637i
\(216\) 0 0
\(217\) 31821.1 0.675764
\(218\) −52177.6 39285.0i −1.09792 0.826635i
\(219\) 0 0
\(220\) −156.122 + 44.9062i −0.00322565 + 0.000927813i
\(221\) −73325.0 −1.50130
\(222\) 0 0
\(223\) 64260.3i 1.29221i −0.763249 0.646105i \(-0.776397\pi\)
0.763249 0.646105i \(-0.223603\pi\)
\(224\) 2016.17 23604.0i 0.0401820 0.470423i
\(225\) 0 0
\(226\) −37780.4 28445.2i −0.739690 0.556919i
\(227\) 6705.37i 0.130128i −0.997881 0.0650641i \(-0.979275\pi\)
0.997881 0.0650641i \(-0.0207252\pi\)
\(228\) 0 0
\(229\) 35550.3 0.677910 0.338955 0.940803i \(-0.389927\pi\)
0.338955 + 0.940803i \(0.389927\pi\)
\(230\) 3072.00 4080.17i 0.0580718 0.0771299i
\(231\) 0 0
\(232\) 14607.8 38195.5i 0.271400 0.709637i
\(233\) 62439.9 1.15014 0.575070 0.818105i \(-0.304975\pi\)
0.575070 + 0.818105i \(0.304975\pi\)
\(234\) 0 0
\(235\) 721.967i 0.0130732i
\(236\) 92741.6 26675.8i 1.66514 0.478954i
\(237\) 0 0
\(238\) 14806.3 19665.4i 0.261392 0.347176i
\(239\) 3753.45i 0.0657106i −0.999460 0.0328553i \(-0.989540\pi\)
0.999460 0.0328553i \(-0.0104600\pi\)
\(240\) 0 0
\(241\) −89665.2 −1.54380 −0.771898 0.635747i \(-0.780692\pi\)
−0.771898 + 0.635747i \(0.780692\pi\)
\(242\) −46705.9 35165.3i −0.797519 0.600460i
\(243\) 0 0
\(244\) 7371.68 + 25628.5i 0.123819 + 0.430471i
\(245\) −3789.23 −0.0631275
\(246\) 0 0
\(247\) 101216.i 1.65904i
\(248\) 82222.1 + 31445.7i 1.33686 + 0.511279i
\(249\) 0 0
\(250\) −8085.50 6087.65i −0.129368 0.0974024i
\(251\) 9246.49i 0.146767i 0.997304 + 0.0733836i \(0.0233798\pi\)
−0.997304 + 0.0733836i \(0.976620\pi\)
\(252\) 0 0
\(253\) −3143.12 −0.0491043
\(254\) −50476.6 + 67042.1i −0.782389 + 1.03915i
\(255\) 0 0
\(256\) 28535.1 58997.6i 0.435411 0.900232i
\(257\) 15249.7 0.230885 0.115442 0.993314i \(-0.463171\pi\)
0.115442 + 0.993314i \(0.463171\pi\)
\(258\) 0 0
\(259\) 33919.8i 0.505654i
\(260\) −2475.97 8608.02i −0.0366268 0.127338i
\(261\) 0 0
\(262\) 68686.5 91228.1i 1.00062 1.32900i
\(263\) 103320.i 1.49374i 0.664971 + 0.746869i \(0.268444\pi\)
−0.664971 + 0.746869i \(0.731556\pi\)
\(264\) 0 0
\(265\) −10758.7 −0.153203
\(266\) −27145.8 20438.3i −0.383653 0.288856i
\(267\) 0 0
\(268\) 33883.5 9746.12i 0.471758 0.135694i
\(269\) −86017.8 −1.18873 −0.594366 0.804195i \(-0.702597\pi\)
−0.594366 + 0.804195i \(0.702597\pi\)
\(270\) 0 0
\(271\) 15629.0i 0.212810i −0.994323 0.106405i \(-0.966066\pi\)
0.994323 0.106405i \(-0.0339340\pi\)
\(272\) 57691.3 36181.6i 0.779780 0.489046i
\(273\) 0 0
\(274\) 1977.63 + 1488.97i 0.0263417 + 0.0198329i
\(275\) 3103.98i 0.0410444i
\(276\) 0 0
\(277\) −56614.6 −0.737851 −0.368926 0.929459i \(-0.620274\pi\)
−0.368926 + 0.929459i \(0.620274\pi\)
\(278\) −46728.2 + 62063.6i −0.604630 + 0.803059i
\(279\) 0 0
\(280\) 2808.60 + 1074.15i 0.0358240 + 0.0137008i
\(281\) 111067. 1.40661 0.703303 0.710890i \(-0.251708\pi\)
0.703303 + 0.710890i \(0.251708\pi\)
\(282\) 0 0
\(283\) 91197.8i 1.13871i −0.822093 0.569353i \(-0.807194\pi\)
0.822093 0.569353i \(-0.192806\pi\)
\(284\) 8061.91 2318.90i 0.0999543 0.0287504i
\(285\) 0 0
\(286\) −3315.55 + 4403.65i −0.0405344 + 0.0538370i
\(287\) 27438.6i 0.333118i
\(288\) 0 0
\(289\) −12760.0 −0.152776
\(290\) 4146.74 + 3122.12i 0.0493073 + 0.0371239i
\(291\) 0 0
\(292\) −6600.19 22946.3i −0.0774088 0.269121i
\(293\) 83015.0 0.966988 0.483494 0.875348i \(-0.339367\pi\)
0.483494 + 0.875348i \(0.339367\pi\)
\(294\) 0 0
\(295\) 12249.1i 0.140754i
\(296\) 33519.7 87644.8i 0.382575 1.00033i
\(297\) 0 0
\(298\) −1978.93 1489.96i −0.0222843 0.0167780i
\(299\) 173301.i 1.93847i
\(300\) 0 0
\(301\) −38209.4 −0.421733
\(302\) 10440.5 13866.9i 0.114474 0.152042i
\(303\) 0 0
\(304\) −49944.4 79635.9i −0.540430 0.861711i
\(305\) −3384.96 −0.0363876
\(306\) 0 0
\(307\) 65201.8i 0.691803i 0.938271 + 0.345902i \(0.112427\pi\)
−0.938271 + 0.345902i \(0.887573\pi\)
\(308\) −511.541 1778.43i −0.00539236 0.0187472i
\(309\) 0 0
\(310\) −6720.88 + 8926.55i −0.0699363 + 0.0928881i
\(311\) 133699.i 1.38231i −0.722705 0.691156i \(-0.757102\pi\)
0.722705 0.691156i \(-0.242898\pi\)
\(312\) 0 0
\(313\) 11240.1 0.114731 0.0573655 0.998353i \(-0.481730\pi\)
0.0573655 + 0.998353i \(0.481730\pi\)
\(314\) 19837.1 + 14935.5i 0.201196 + 0.151482i
\(315\) 0 0
\(316\) 78981.8 22718.0i 0.790957 0.227508i
\(317\) −39206.2 −0.390154 −0.195077 0.980788i \(-0.562496\pi\)
−0.195077 + 0.980788i \(0.562496\pi\)
\(318\) 0 0
\(319\) 3194.40i 0.0313912i
\(320\) 6195.63 + 5550.94i 0.0605042 + 0.0542084i
\(321\) 0 0
\(322\) 46478.6 + 34994.1i 0.448271 + 0.337508i
\(323\) 97677.0i 0.936240i
\(324\) 0 0
\(325\) −171143. −1.62029
\(326\) 38151.1 50671.6i 0.358981 0.476792i
\(327\) 0 0
\(328\) −27115.0 + 70898.2i −0.252035 + 0.659004i
\(329\) −8224.17 −0.0759801
\(330\) 0 0
\(331\) 74751.4i 0.682281i 0.940012 + 0.341141i \(0.110813\pi\)
−0.940012 + 0.341141i \(0.889187\pi\)
\(332\) 122838. 35332.7i 1.11444 0.320553i
\(333\) 0 0
\(334\) −1008.08 + 1338.92i −0.00903656 + 0.0120022i
\(335\) 4475.27i 0.0398776i
\(336\) 0 0
\(337\) −141818. −1.24874 −0.624370 0.781129i \(-0.714644\pi\)
−0.624370 + 0.781129i \(0.714644\pi\)
\(338\) −151535. 114092.i −1.32642 0.998670i
\(339\) 0 0
\(340\) 2389.40 + 8307.01i 0.0206695 + 0.0718600i
\(341\) 6876.48 0.0591367
\(342\) 0 0
\(343\) 98710.7i 0.839027i
\(344\) −98728.8 37758.7i −0.834309 0.319081i
\(345\) 0 0
\(346\) 61356.7 + 46196.1i 0.512519 + 0.385880i
\(347\) 183029.i 1.52006i 0.649886 + 0.760032i \(0.274817\pi\)
−0.649886 + 0.760032i \(0.725183\pi\)
\(348\) 0 0
\(349\) 134558. 1.10474 0.552368 0.833600i \(-0.313724\pi\)
0.552368 + 0.833600i \(0.313724\pi\)
\(350\) 34558.4 45899.8i 0.282110 0.374693i
\(351\) 0 0
\(352\) 435.691 5100.77i 0.00351636 0.0411671i
\(353\) −200278. −1.60725 −0.803626 0.595135i \(-0.797099\pi\)
−0.803626 + 0.595135i \(0.797099\pi\)
\(354\) 0 0
\(355\) 1064.80i 0.00844912i
\(356\) −39187.2 136239.i −0.309203 1.07498i
\(357\) 0 0
\(358\) 119868. 159207.i 0.935273 1.24221i
\(359\) 161179.i 1.25060i −0.780385 0.625300i \(-0.784977\pi\)
0.780385 0.625300i \(-0.215023\pi\)
\(360\) 0 0
\(361\) −4510.46 −0.0346104
\(362\) −44643.8 33612.8i −0.340678 0.256500i
\(363\) 0 0
\(364\) 98056.8 28204.6i 0.740073 0.212872i
\(365\) 3030.70 0.0227487
\(366\) 0 0
\(367\) 199565.i 1.48167i 0.671686 + 0.740836i \(0.265571\pi\)
−0.671686 + 0.740836i \(0.734429\pi\)
\(368\) 85514.0 + 136351.i 0.631454 + 1.00685i
\(369\) 0 0
\(370\) 9515.28 + 7164.14i 0.0695053 + 0.0523312i
\(371\) 122556.i 0.890402i
\(372\) 0 0
\(373\) −5788.69 −0.0416066 −0.0208033 0.999784i \(-0.506622\pi\)
−0.0208033 + 0.999784i \(0.506622\pi\)
\(374\) 3199.61 4249.67i 0.0228746 0.0303817i
\(375\) 0 0
\(376\) −21250.3 8127.16i −0.150311 0.0574861i
\(377\) 176129. 1.23922
\(378\) 0 0
\(379\) 217930.i 1.51719i 0.651565 + 0.758593i \(0.274113\pi\)
−0.651565 + 0.758593i \(0.725887\pi\)
\(380\) 11466.8 3298.27i 0.0794102 0.0228412i
\(381\) 0 0
\(382\) 74995.5 99607.6i 0.513935 0.682599i
\(383\) 69498.2i 0.473780i −0.971537 0.236890i \(-0.923872\pi\)
0.971537 0.236890i \(-0.0761280\pi\)
\(384\) 0 0
\(385\) 234.891 0.00158470
\(386\) −86267.6 64951.7i −0.578993 0.435929i
\(387\) 0 0
\(388\) 30157.9 + 104848.i 0.200326 + 0.696458i
\(389\) 57466.0 0.379762 0.189881 0.981807i \(-0.439190\pi\)
0.189881 + 0.981807i \(0.439190\pi\)
\(390\) 0 0
\(391\) 167241.i 1.09393i
\(392\) 42655.2 111532.i 0.277588 0.725817i
\(393\) 0 0
\(394\) −33286.0 25061.4i −0.214422 0.161440i
\(395\) 10431.7i 0.0668595i
\(396\) 0 0
\(397\) 13255.8 0.0841056 0.0420528 0.999115i \(-0.486610\pi\)
0.0420528 + 0.999115i \(0.486610\pi\)
\(398\) −20303.0 + 26966.1i −0.128172 + 0.170236i
\(399\) 0 0
\(400\) 134653. 84449.2i 0.841584 0.527808i
\(401\) −5375.31 −0.0334283 −0.0167142 0.999860i \(-0.505321\pi\)
−0.0167142 + 0.999860i \(0.505321\pi\)
\(402\) 0 0
\(403\) 379146.i 2.33451i
\(404\) 13671.3 + 47529.7i 0.0837618 + 0.291208i
\(405\) 0 0
\(406\) −35565.1 + 47236.9i −0.215761 + 0.286569i
\(407\) 7330.00i 0.0442502i
\(408\) 0 0
\(409\) −240693. −1.43885 −0.719427 0.694568i \(-0.755596\pi\)
−0.719427 + 0.694568i \(0.755596\pi\)
\(410\) −7697.16 5795.27i −0.0457892 0.0344751i
\(411\) 0 0
\(412\) 167066. 48054.2i 0.984224 0.283098i
\(413\) −139534. −0.818049
\(414\) 0 0
\(415\) 16224.2i 0.0942035i
\(416\) 281240. + 24022.5i 1.62514 + 0.138814i
\(417\) 0 0
\(418\) −5866.15 4416.68i −0.0335738 0.0252781i
\(419\) 35414.2i 0.201720i 0.994901 + 0.100860i \(0.0321595\pi\)
−0.994901 + 0.100860i \(0.967841\pi\)
\(420\) 0 0
\(421\) −165096. −0.931477 −0.465739 0.884922i \(-0.654211\pi\)
−0.465739 + 0.884922i \(0.654211\pi\)
\(422\) −55206.1 + 73323.7i −0.310000 + 0.411737i
\(423\) 0 0
\(424\) 121110. 316670.i 0.673673 1.76147i
\(425\) 165159. 0.914373
\(426\) 0 0
\(427\) 38559.2i 0.211481i
\(428\) 216910. 62391.1i 1.18411 0.340593i
\(429\) 0 0
\(430\) 8070.16 10718.6i 0.0436461 0.0579699i
\(431\) 161673.i 0.870327i −0.900351 0.435163i \(-0.856691\pi\)
0.900351 0.435163i \(-0.143309\pi\)
\(432\) 0 0
\(433\) −61835.3 −0.329808 −0.164904 0.986310i \(-0.552731\pi\)
−0.164904 + 0.986310i \(0.552731\pi\)
\(434\) −101685. 76559.8i −0.539857 0.406463i
\(435\) 0 0
\(436\) 72217.6 + 251073.i 0.379901 + 1.32077i
\(437\) 230856. 1.20887
\(438\) 0 0
\(439\) 309484.i 1.60587i −0.596069 0.802933i \(-0.703272\pi\)
0.596069 0.802933i \(-0.296728\pi\)
\(440\) 606.933 + 232.121i 0.00313499 + 0.00119897i
\(441\) 0 0
\(442\) 234312. + 176416.i 1.19936 + 0.903011i
\(443\) 46898.7i 0.238976i 0.992836 + 0.119488i \(0.0381252\pi\)
−0.992836 + 0.119488i \(0.961875\pi\)
\(444\) 0 0
\(445\) 17994.1 0.0908680
\(446\) −154607. + 205346.i −0.777246 + 1.03232i
\(447\) 0 0
\(448\) −63232.6 + 70576.4i −0.315054 + 0.351644i
\(449\) −124857. −0.619328 −0.309664 0.950846i \(-0.600217\pi\)
−0.309664 + 0.950846i \(0.600217\pi\)
\(450\) 0 0
\(451\) 5929.43i 0.0291514i
\(452\) 52290.8 + 181795.i 0.255946 + 0.889827i
\(453\) 0 0
\(454\) −16132.8 + 21427.2i −0.0782703 + 0.103957i
\(455\) 12951.1i 0.0625583i
\(456\) 0 0
\(457\) −125497. −0.600898 −0.300449 0.953798i \(-0.597137\pi\)
−0.300449 + 0.953798i \(0.597137\pi\)
\(458\) −113602. 85532.1i −0.541571 0.407754i
\(459\) 0 0
\(460\) −19633.3 + 5647.25i −0.0927852 + 0.0266883i
\(461\) 103295. 0.486045 0.243022 0.970021i \(-0.421861\pi\)
0.243022 + 0.970021i \(0.421861\pi\)
\(462\) 0 0
\(463\) 320504.i 1.49510i 0.664204 + 0.747552i \(0.268771\pi\)
−0.664204 + 0.747552i \(0.731229\pi\)
\(464\) −138576. + 86909.3i −0.643654 + 0.403673i
\(465\) 0 0
\(466\) −199529. 150227.i −0.918827 0.691793i
\(467\) 427381.i 1.95967i 0.199820 + 0.979833i \(0.435964\pi\)
−0.199820 + 0.979833i \(0.564036\pi\)
\(468\) 0 0
\(469\) −50979.2 −0.231765
\(470\) 1737.01 2307.07i 0.00786335 0.0104440i
\(471\) 0 0
\(472\) −360539. 137888.i −1.61834 0.618931i
\(473\) −8256.99 −0.0369062
\(474\) 0 0
\(475\) 227982.i 1.01045i
\(476\) −94627.9 + 27218.4i −0.417643 + 0.120129i
\(477\) 0 0
\(478\) −9030.61 + 11994.3i −0.0395240 + 0.0524951i
\(479\) 192061.i 0.837082i 0.908198 + 0.418541i \(0.137458\pi\)
−0.908198 + 0.418541i \(0.862542\pi\)
\(480\) 0 0
\(481\) 404152. 1.74684
\(482\) 286528. + 215730.i 1.23331 + 0.928572i
\(483\) 0 0
\(484\) 64644.4 + 224744.i 0.275956 + 0.959394i
\(485\) −13848.1 −0.0588715
\(486\) 0 0
\(487\) 52885.1i 0.222985i 0.993765 + 0.111492i \(0.0355631\pi\)
−0.993765 + 0.111492i \(0.964437\pi\)
\(488\) 38104.4 99632.6i 0.160006 0.418371i
\(489\) 0 0
\(490\) 12108.6 + 9116.68i 0.0504315 + 0.0379704i
\(491\) 7354.16i 0.0305049i 0.999884 + 0.0152525i \(0.00485520\pi\)
−0.999884 + 0.0152525i \(0.995145\pi\)
\(492\) 0 0
\(493\) −169970. −0.699323
\(494\) 243521. 323440.i 0.997890 1.32538i
\(495\) 0 0
\(496\) −187086. 298308.i −0.760465 1.21255i
\(497\) −12129.5 −0.0491055
\(498\) 0 0
\(499\) 415048.i 1.66685i −0.552632 0.833426i \(-0.686376\pi\)
0.552632 0.833426i \(-0.313624\pi\)
\(500\) 11190.9 + 38906.6i 0.0447637 + 0.155626i
\(501\) 0 0
\(502\) 22246.5 29547.4i 0.0882785 0.117250i
\(503\) 53242.3i 0.210436i 0.994449 + 0.105218i \(0.0335541\pi\)
−0.994449 + 0.105218i \(0.966446\pi\)
\(504\) 0 0
\(505\) −6277.63 −0.0246157
\(506\) 10043.9 + 7562.17i 0.0392286 + 0.0295356i
\(507\) 0 0
\(508\) 322599. 92791.1i 1.25007 0.359566i
\(509\) −497261. −1.91932 −0.959662 0.281155i \(-0.909283\pi\)
−0.959662 + 0.281155i \(0.909283\pi\)
\(510\) 0 0
\(511\) 34523.7i 0.132214i
\(512\) −233130. + 119875.i −0.889320 + 0.457286i
\(513\) 0 0
\(514\) −48730.9 36689.9i −0.184450 0.138874i
\(515\) 22065.7i 0.0831963i
\(516\) 0 0
\(517\) −1777.23 −0.00664909
\(518\) −81609.1 + 108392.i −0.304144 + 0.403958i
\(519\) 0 0
\(520\) −12798.4 + 33464.3i −0.0473312 + 0.123758i
\(521\) −58965.8 −0.217233 −0.108616 0.994084i \(-0.534642\pi\)
−0.108616 + 0.994084i \(0.534642\pi\)
\(522\) 0 0
\(523\) 117488.i 0.429527i 0.976666 + 0.214763i \(0.0688980\pi\)
−0.976666 + 0.214763i \(0.931102\pi\)
\(524\) −438980. + 126266.i −1.59876 + 0.459859i
\(525\) 0 0
\(526\) 248583. 330163.i 0.898463 1.19332i
\(527\) 365888.i 1.31743i
\(528\) 0 0
\(529\) −115428. −0.412475
\(530\) 34379.8 + 25884.8i 0.122391 + 0.0921497i
\(531\) 0 0
\(532\) 37571.7 + 130623.i 0.132751 + 0.461525i
\(533\) −326929. −1.15080
\(534\) 0 0
\(535\) 28649.0i 0.100093i
\(536\) −131725. 50377.9i −0.458498 0.175352i
\(537\) 0 0
\(538\) 274873. + 206954.i 0.949658 + 0.715006i
\(539\) 9327.75i 0.0321070i
\(540\) 0 0
\(541\) −16461.8 −0.0562448 −0.0281224 0.999604i \(-0.508953\pi\)
−0.0281224 + 0.999604i \(0.508953\pi\)
\(542\) −37602.5 + 49943.0i −0.128002 + 0.170011i
\(543\) 0 0
\(544\) −271405. 23182.5i −0.917108 0.0783363i
\(545\) −33161.2 −0.111644
\(546\) 0 0
\(547\) 389586.i 1.30205i −0.759056 0.651026i \(-0.774339\pi\)
0.759056 0.651026i \(-0.225661\pi\)
\(548\) −2737.18 9516.13i −0.00911470 0.0316883i
\(549\) 0 0
\(550\) 7468.01 9918.87i 0.0246876 0.0327897i
\(551\) 234623.i 0.772801i
\(552\) 0 0
\(553\) −118831. −0.388581
\(554\) 180914. + 136212.i 0.589457 + 0.443807i
\(555\) 0 0
\(556\) 298643. 85900.5i 0.966058 0.277873i
\(557\) 434133. 1.39931 0.699653 0.714483i \(-0.253338\pi\)
0.699653 + 0.714483i \(0.253338\pi\)
\(558\) 0 0
\(559\) 455263.i 1.45693i
\(560\) −6390.63 10189.8i −0.0203783 0.0324930i
\(561\) 0 0
\(562\) −354918. 267221.i −1.12371 0.846054i
\(563\) 222254.i 0.701185i 0.936528 + 0.350592i \(0.114020\pi\)
−0.936528 + 0.350592i \(0.885980\pi\)
\(564\) 0 0
\(565\) −24011.1 −0.0752169
\(566\) −219417. + 291425.i −0.684916 + 0.909692i
\(567\) 0 0
\(568\) −31341.2 11986.4i −0.0971448 0.0371529i
\(569\) 3925.12 0.0121235 0.00606175 0.999982i \(-0.498070\pi\)
0.00606175 + 0.999982i \(0.498070\pi\)
\(570\) 0 0
\(571\) 382845.i 1.17422i 0.809505 + 0.587112i \(0.199735\pi\)
−0.809505 + 0.587112i \(0.800265\pi\)
\(572\) 21189.9 6094.97i 0.0647645 0.0186286i
\(573\) 0 0
\(574\) 66015.8 87680.9i 0.200366 0.266122i
\(575\) 390347.i 1.18063i
\(576\) 0 0
\(577\) 18219.2 0.0547239 0.0273620 0.999626i \(-0.491289\pi\)
0.0273620 + 0.999626i \(0.491289\pi\)
\(578\) 40775.1 + 30700.0i 0.122051 + 0.0918930i
\(579\) 0 0
\(580\) −5739.40 19953.7i −0.0170612 0.0593154i
\(581\) −184815. −0.547502
\(582\) 0 0
\(583\) 26484.1i 0.0779198i
\(584\) −34116.5 + 89205.4i −0.100032 + 0.261556i
\(585\) 0 0
\(586\) −265277. 199730.i −0.772510 0.581630i
\(587\) 52925.7i 0.153600i −0.997047 0.0767998i \(-0.975530\pi\)
0.997047 0.0767998i \(-0.0244702\pi\)
\(588\) 0 0
\(589\) −505065. −1.45585
\(590\) 29470.7 39142.4i 0.0846616 0.112446i
\(591\) 0 0
\(592\) −317982. + 199425.i −0.907317 + 0.569032i
\(593\) 216280. 0.615046 0.307523 0.951541i \(-0.400500\pi\)
0.307523 + 0.951541i \(0.400500\pi\)
\(594\) 0 0
\(595\) 12498.3i 0.0353033i
\(596\) 2738.99 + 9522.41i 0.00771077 + 0.0268074i
\(597\) 0 0
\(598\) −416953. + 553789.i −1.16596 + 1.54861i
\(599\) 300397.i 0.837223i 0.908165 + 0.418612i \(0.137483\pi\)
−0.908165 + 0.418612i \(0.862517\pi\)
\(600\) 0 0
\(601\) 510971. 1.41464 0.707322 0.706892i \(-0.249903\pi\)
0.707322 + 0.706892i \(0.249903\pi\)
\(602\) 122099. + 91929.8i 0.336915 + 0.253667i
\(603\) 0 0
\(604\) −66725.9 + 19192.8i −0.182903 + 0.0526094i
\(605\) −29683.7 −0.0810974
\(606\) 0 0
\(607\) 178075.i 0.483310i −0.970362 0.241655i \(-0.922310\pi\)
0.970362 0.241655i \(-0.0776902\pi\)
\(608\) −32000.7 + 374642.i −0.0865670 + 1.01347i
\(609\) 0 0
\(610\) 10816.8 + 8144.03i 0.0290695 + 0.0218867i
\(611\) 97990.4i 0.262483i
\(612\) 0 0
\(613\) 570495. 1.51821 0.759103 0.650970i \(-0.225638\pi\)
0.759103 + 0.650970i \(0.225638\pi\)
\(614\) 156872. 208354.i 0.416110 0.552670i
\(615\) 0 0
\(616\) −2644.17 + 6913.77i −0.00696831 + 0.0182202i
\(617\) 215902. 0.567134 0.283567 0.958952i \(-0.408482\pi\)
0.283567 + 0.958952i \(0.408482\pi\)
\(618\) 0 0
\(619\) 182810.i 0.477110i 0.971129 + 0.238555i \(0.0766737\pi\)
−0.971129 + 0.238555i \(0.923326\pi\)
\(620\) 42953.6 12355.0i 0.111742 0.0321410i
\(621\) 0 0
\(622\) −321672. + 427238.i −0.831442 + 1.10431i
\(623\) 204977.i 0.528116i
\(624\) 0 0
\(625\) 382908. 0.980246
\(626\) −35918.0 27043.0i −0.0916566 0.0690091i
\(627\) 0 0
\(628\) −27456.0 95454.0i −0.0696174 0.242033i
\(629\) −390019. −0.985791
\(630\) 0 0
\(631\) 153307.i 0.385037i 0.981293 + 0.192518i \(0.0616655\pi\)
−0.981293 + 0.192518i \(0.938335\pi\)
\(632\) −307047. 117430.i −0.768725 0.293998i
\(633\) 0 0
\(634\) 125285. + 94328.0i 0.311687 + 0.234672i
\(635\) 42608.2i 0.105669i
\(636\) 0 0
\(637\) 514301. 1.26747
\(638\) −7685.56 + 10207.8i −0.0188814 + 0.0250779i
\(639\) 0 0
\(640\) −6443.06 32644.5i −0.0157301 0.0796986i
\(641\) 393252. 0.957095 0.478547 0.878062i \(-0.341163\pi\)
0.478547 + 0.878062i \(0.341163\pi\)
\(642\) 0 0
\(643\) 444526.i 1.07517i −0.843211 0.537583i \(-0.819338\pi\)
0.843211 0.537583i \(-0.180662\pi\)
\(644\) −64329.7 223650.i −0.155110 0.539258i
\(645\) 0 0
\(646\) −235006. + 312130.i −0.563136 + 0.747947i
\(647\) 152505.i 0.364314i 0.983269 + 0.182157i \(0.0583079\pi\)
−0.983269 + 0.182157i \(0.941692\pi\)
\(648\) 0 0
\(649\) −30153.0 −0.0715881
\(650\) 546893. + 411761.i 1.29442 + 0.974583i
\(651\) 0 0
\(652\) −243826. + 70133.1i −0.573568 + 0.164979i
\(653\) −299234. −0.701753 −0.350876 0.936422i \(-0.614116\pi\)
−0.350876 + 0.936422i \(0.614116\pi\)
\(654\) 0 0
\(655\) 57979.5i 0.135143i
\(656\) 257224. 161321.i 0.597728 0.374871i
\(657\) 0 0
\(658\) 26280.6 + 19786.9i 0.0606992 + 0.0457010i
\(659\) 417069.i 0.960367i −0.877168 0.480183i \(-0.840570\pi\)
0.877168 0.480183i \(-0.159430\pi\)
\(660\) 0 0
\(661\) 759550. 1.73842 0.869208 0.494447i \(-0.164629\pi\)
0.869208 + 0.494447i \(0.164629\pi\)
\(662\) 179848. 238870.i 0.410383 0.545063i
\(663\) 0 0
\(664\) −477542. 182635.i −1.08312 0.414237i
\(665\) −17252.3 −0.0390126
\(666\) 0 0
\(667\) 401718.i 0.902962i
\(668\) 6442.72 1853.16i 0.0144383 0.00415298i
\(669\) 0 0
\(670\) 10767.2 14300.9i 0.0239858 0.0318575i
\(671\) 8332.58i 0.0185069i
\(672\) 0 0
\(673\) −37672.0 −0.0831742 −0.0415871 0.999135i \(-0.513241\pi\)
−0.0415871 + 0.999135i \(0.513241\pi\)
\(674\) 453184. + 341207.i 0.997597 + 0.751100i
\(675\) 0 0
\(676\) 209735. + 729170.i 0.458964 + 1.59564i
\(677\) −694020. −1.51424 −0.757120 0.653276i \(-0.773394\pi\)
−0.757120 + 0.653276i \(0.773394\pi\)
\(678\) 0 0
\(679\) 157748.i 0.342156i
\(680\) 12350.8 32294.1i 0.0267103 0.0698402i
\(681\) 0 0
\(682\) −21974.0 16544.4i −0.0472433 0.0355699i
\(683\) 357197.i 0.765714i −0.923808 0.382857i \(-0.874940\pi\)
0.923808 0.382857i \(-0.125060\pi\)
\(684\) 0 0
\(685\) 1256.87 0.00267861
\(686\) −237493. + 315433.i −0.504664 + 0.670285i
\(687\) 0 0
\(688\) 224646. + 358195.i 0.474593 + 0.756734i
\(689\) 1.46024e6 3.07601
\(690\) 0 0
\(691\) 443952.i 0.929778i 0.885369 + 0.464889i \(0.153906\pi\)
−0.885369 + 0.464889i \(0.846094\pi\)
\(692\) −84922.2 295242.i −0.177341 0.616547i
\(693\) 0 0
\(694\) 440359. 584876.i 0.914297 1.21435i
\(695\) 39444.2i 0.0816607i
\(696\) 0 0
\(697\) 315497. 0.649426
\(698\) −429984. 323739.i −0.882555 0.664484i
\(699\) 0 0
\(700\) −220865. + 63528.7i −0.450745 + 0.129650i
\(701\) −483771. −0.984474 −0.492237 0.870461i \(-0.663821\pi\)
−0.492237 + 0.870461i \(0.663821\pi\)
\(702\) 0 0
\(703\) 538375.i 1.08937i
\(704\) −13664.5 + 15251.4i −0.0275706 + 0.0307727i
\(705\) 0 0
\(706\) 639995. + 481858.i 1.28401 + 0.966740i
\(707\) 71510.5i 0.143064i
\(708\) 0 0
\(709\) 158339. 0.314989 0.157494 0.987520i \(-0.449658\pi\)
0.157494 + 0.987520i \(0.449658\pi\)
\(710\) 2561.85 3402.60i 0.00508203 0.00674986i
\(711\) 0 0
\(712\) −202559. + 529638.i −0.399569 + 1.04477i
\(713\) 864764. 1.70105
\(714\) 0 0
\(715\) 2798.72i 0.00547453i
\(716\) −766087. + 220354.i −1.49435 + 0.429828i
\(717\) 0 0
\(718\) −387787. + 515051.i −0.752219 + 0.999083i
\(719\) 781622.i 1.51196i −0.654597 0.755978i \(-0.727162\pi\)
0.654597 0.755978i \(-0.272838\pi\)
\(720\) 0 0
\(721\) −251358. −0.483529
\(722\) 14413.3 + 10851.9i 0.0276496 + 0.0208177i
\(723\) 0 0
\(724\) 61790.3 + 214821.i 0.117881 + 0.409827i
\(725\) −396716. −0.754751
\(726\) 0 0
\(727\) 59571.1i 0.112711i 0.998411 + 0.0563556i \(0.0179480\pi\)
−0.998411 + 0.0563556i \(0.982052\pi\)
\(728\) −381202. 145790.i −0.719271 0.275085i
\(729\) 0 0
\(730\) −9684.71 7291.71i −0.0181736 0.0136831i
\(731\) 439343.i 0.822184i
\(732\) 0 0
\(733\) −213845. −0.398008 −0.199004 0.979999i \(-0.563771\pi\)
−0.199004 + 0.979999i \(0.563771\pi\)
\(734\) 480143. 637716.i 0.891206 1.18368i
\(735\) 0 0
\(736\) 54791.1 641457.i 0.101147 1.18416i
\(737\) −11016.5 −0.0202819
\(738\) 0 0
\(739\) 218903.i 0.400832i −0.979711 0.200416i \(-0.935771\pi\)
0.979711 0.200416i \(-0.0642294\pi\)
\(740\) −13169.8 45786.5i −0.0240501 0.0836130i
\(741\) 0 0
\(742\) −294863. + 391631.i −0.535565 + 0.711327i
\(743\) 498238.i 0.902525i 0.892391 + 0.451263i \(0.149026\pi\)
−0.892391 + 0.451263i \(0.850974\pi\)
\(744\) 0 0
\(745\) −1257.70 −0.00226602
\(746\) 18497.9 + 13927.3i 0.0332388 + 0.0250258i
\(747\) 0 0
\(748\) −20448.9 + 5881.85i −0.0365483 + 0.0105126i
\(749\) −326350. −0.581729
\(750\) 0 0
\(751\) 617010.i 1.09399i −0.837137 0.546994i \(-0.815772\pi\)
0.837137 0.546994i \(-0.184228\pi\)
\(752\) 48352.6 + 77097.7i 0.0855035 + 0.136335i
\(753\) 0 0
\(754\) −562825. 423756.i −0.989989 0.745372i
\(755\) 8813.01i 0.0154607i
\(756\) 0 0
\(757\) 483106. 0.843045 0.421523 0.906818i \(-0.361496\pi\)
0.421523 + 0.906818i \(0.361496\pi\)
\(758\) 524328. 696403.i 0.912567 1.21205i
\(759\) 0 0
\(760\) −44578.1 17048.9i −0.0771782 0.0295167i
\(761\) −137695. −0.237765 −0.118882 0.992908i \(-0.537931\pi\)
−0.118882 + 0.992908i \(0.537931\pi\)
\(762\) 0 0
\(763\) 377750.i 0.648866i
\(764\) −479301. + 137864.i −0.821148 + 0.236192i
\(765\) 0 0
\(766\) −167209. + 222084.i −0.284972 + 0.378494i
\(767\) 1.66254e6i 2.82605i
\(768\) 0 0
\(769\) −346769. −0.586392 −0.293196 0.956052i \(-0.594719\pi\)
−0.293196 + 0.956052i \(0.594719\pi\)
\(770\) −750.603 565.136i −0.00126599 0.000953173i
\(771\) 0 0
\(772\) 119401. + 415110.i 0.200342 + 0.696513i
\(773\) −456941. −0.764717 −0.382358 0.924014i \(-0.624888\pi\)
−0.382358 + 0.924014i \(0.624888\pi\)
\(774\) 0 0
\(775\) 853996.i 1.42185i
\(776\) 155887. 407602.i 0.258873 0.676882i
\(777\) 0 0
\(778\) −183634. 138260.i −0.303386 0.228422i
\(779\) 435506.i 0.717661i
\(780\) 0 0
\(781\) −2621.16 −0.00429726
\(782\) 402373. 534424.i 0.657984 0.873922i
\(783\) 0 0
\(784\) −404646. + 253777.i −0.658329 + 0.412877i
\(785\) 12607.4 0.0204590
\(786\) 0 0