Properties

Label 300.2.o.a.109.4
Level $300$
Weight $2$
Character 300.109
Analytic conductor $2.396$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.o (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 109.4
Character \(\chi\) \(=\) 300.109
Dual form 300.2.o.a.289.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.951057 - 0.309017i) q^{3} +(-1.98828 - 1.02311i) q^{5} -3.54704i q^{7} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(0.951057 - 0.309017i) q^{3} +(-1.98828 - 1.02311i) q^{5} -3.54704i q^{7} +(0.809017 - 0.587785i) q^{9} +(1.78482 + 1.29675i) q^{11} +(-4.21895 - 5.80689i) q^{13} +(-2.20712 - 0.358624i) q^{15} +(6.05378 + 1.96699i) q^{17} +(0.715151 - 2.20101i) q^{19} +(-1.09610 - 3.37344i) q^{21} +(-1.27899 + 1.76038i) q^{23} +(2.90649 + 4.06845i) q^{25} +(0.587785 - 0.809017i) q^{27} +(-0.262008 - 0.806379i) q^{29} +(-1.32905 + 4.09040i) q^{31} +(2.09819 + 0.681742i) q^{33} +(-3.62901 + 7.05250i) q^{35} +(4.24968 + 5.84918i) q^{37} +(-5.80689 - 4.21895i) q^{39} +(1.08778 - 0.790317i) q^{41} -8.18973i q^{43} +(-2.20992 + 0.340966i) q^{45} +(-5.75820 + 1.87095i) q^{47} -5.58150 q^{49} +6.36532 q^{51} +(11.3730 - 3.69530i) q^{53} +(-2.22201 - 4.40437i) q^{55} -2.31428i q^{57} +(-10.0896 + 7.33050i) q^{59} +(5.59873 + 4.06772i) q^{61} +(-2.08490 - 2.86962i) q^{63} +(2.44736 + 15.8622i) q^{65} +(4.50239 + 1.46291i) q^{67} +(-0.672404 + 2.06945i) q^{69} +(4.25799 + 13.1047i) q^{71} +(-0.640196 + 0.881155i) q^{73} +(4.02146 + 2.97117i) q^{75} +(4.59963 - 6.33085i) q^{77} +(1.80542 + 5.55650i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-11.9145 - 3.87127i) q^{83} +(-10.0241 - 10.1046i) q^{85} +(-0.498370 - 0.685947i) q^{87} +(-5.68424 - 4.12984i) q^{89} +(-20.5973 + 14.9648i) q^{91} +4.30090i q^{93} +(-3.67379 + 3.64454i) q^{95} +(17.2564 - 5.60695i) q^{97} +2.20616 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 2q^{5} + 6q^{9} + O(q^{10}) \) \( 24q - 2q^{5} + 6q^{9} - 6q^{11} + 4q^{15} + 10q^{17} + 10q^{19} - 4q^{21} + 40q^{23} - 4q^{25} + 4q^{29} + 6q^{31} + 10q^{33} - 6q^{35} - 10q^{41} + 2q^{45} - 40q^{47} - 56q^{49} + 16q^{51} - 60q^{53} - 62q^{55} - 36q^{59} - 12q^{61} - 10q^{63} + 20q^{67} + 4q^{69} + 40q^{71} + 60q^{73} + 8q^{75} - 40q^{77} + 8q^{79} - 6q^{81} - 50q^{83} + 34q^{85} - 20q^{87} - 30q^{91} - 60q^{95} - 40q^{97} - 4q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\)

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
\(3\) 0.951057 0.309017i 0.549093 0.178411i
\(4\) 0 0
\(5\) −1.98828 1.02311i −0.889185 0.457549i
\(6\) 0 0
\(7\) 3.54704i 1.34066i −0.742065 0.670328i \(-0.766154\pi\)
0.742065 0.670328i \(-0.233846\pi\)
\(8\) 0 0
\(9\) 0.809017 0.587785i 0.269672 0.195928i
\(10\) 0 0
\(11\) 1.78482 + 1.29675i 0.538145 + 0.390985i 0.823396 0.567468i \(-0.192077\pi\)
−0.285251 + 0.958453i \(0.592077\pi\)
\(12\) 0 0
\(13\) −4.21895 5.80689i −1.17013 1.61054i −0.662827 0.748773i \(-0.730643\pi\)
−0.507301 0.861769i \(-0.669357\pi\)
\(14\) 0 0
\(15\) −2.20712 0.358624i −0.569877 0.0925964i
\(16\) 0 0
\(17\) 6.05378 + 1.96699i 1.46826 + 0.477066i 0.930581 0.366086i \(-0.119302\pi\)
0.537676 + 0.843151i \(0.319302\pi\)
\(18\) 0 0
\(19\) 0.715151 2.20101i 0.164067 0.504946i −0.834899 0.550402i \(-0.814474\pi\)
0.998966 + 0.0454566i \(0.0144743\pi\)
\(20\) 0 0
\(21\) −1.09610 3.37344i −0.239188 0.736144i
\(22\) 0 0
\(23\) −1.27899 + 1.76038i −0.266687 + 0.367064i −0.921268 0.388929i \(-0.872845\pi\)
0.654580 + 0.755992i \(0.272845\pi\)
\(24\) 0 0
\(25\) 2.90649 + 4.06845i 0.581298 + 0.813691i
\(26\) 0 0
\(27\) 0.587785 0.809017i 0.113119 0.155695i
\(28\) 0 0
\(29\) −0.262008 0.806379i −0.0486538 0.149741i 0.923778 0.382928i \(-0.125084\pi\)
−0.972432 + 0.233188i \(0.925084\pi\)
\(30\) 0 0
\(31\) −1.32905 + 4.09040i −0.238705 + 0.734657i 0.757904 + 0.652367i \(0.226224\pi\)
−0.996608 + 0.0822910i \(0.973776\pi\)
\(32\) 0 0
\(33\) 2.09819 + 0.681742i 0.365248 + 0.118676i
\(34\) 0 0
\(35\) −3.62901 + 7.05250i −0.613415 + 1.19209i
\(36\) 0 0
\(37\) 4.24968 + 5.84918i 0.698643 + 0.961599i 0.999967 + 0.00807756i \(0.00257119\pi\)
−0.301325 + 0.953522i \(0.597429\pi\)
\(38\) 0 0
\(39\) −5.80689 4.21895i −0.929847 0.675573i
\(40\) 0 0
\(41\) 1.08778 0.790317i 0.169882 0.123427i −0.499595 0.866259i \(-0.666518\pi\)
0.669478 + 0.742832i \(0.266518\pi\)
\(42\) 0 0
\(43\) 8.18973i 1.24892i −0.781056 0.624461i \(-0.785319\pi\)
0.781056 0.624461i \(-0.214681\pi\)
\(44\) 0 0
\(45\) −2.20992 + 0.340966i −0.329435 + 0.0508283i
\(46\) 0 0
\(47\) −5.75820 + 1.87095i −0.839920 + 0.272907i −0.697218 0.716859i \(-0.745579\pi\)
−0.142702 + 0.989766i \(0.545579\pi\)
\(48\) 0 0
\(49\) −5.58150 −0.797357
\(50\) 0 0
\(51\) 6.36532 0.891323
\(52\) 0 0
\(53\) 11.3730 3.69530i 1.56220 0.507589i 0.604805 0.796374i \(-0.293251\pi\)
0.957394 + 0.288785i \(0.0932512\pi\)
\(54\) 0 0
\(55\) −2.22201 4.40437i −0.299615 0.593886i
\(56\) 0 0
\(57\) 2.31428i 0.306533i
\(58\) 0 0
\(59\) −10.0896 + 7.33050i −1.31355 + 0.954350i −0.313561 + 0.949568i \(0.601522\pi\)
−0.999989 + 0.00478202i \(0.998478\pi\)
\(60\) 0 0
\(61\) 5.59873 + 4.06772i 0.716844 + 0.520818i 0.885374 0.464879i \(-0.153902\pi\)
−0.168530 + 0.985696i \(0.553902\pi\)
\(62\) 0 0
\(63\) −2.08490 2.86962i −0.262672 0.361538i
\(64\) 0 0
\(65\) 2.44736 + 15.8622i 0.303558 + 1.96746i
\(66\) 0 0
\(67\) 4.50239 + 1.46291i 0.550054 + 0.178723i 0.570841 0.821060i \(-0.306617\pi\)
−0.0207870 + 0.999784i \(0.506617\pi\)
\(68\) 0 0
\(69\) −0.672404 + 2.06945i −0.0809479 + 0.249132i
\(70\) 0 0
\(71\) 4.25799 + 13.1047i 0.505330 + 1.55525i 0.800214 + 0.599714i \(0.204719\pi\)
−0.294884 + 0.955533i \(0.595281\pi\)
\(72\) 0 0
\(73\) −0.640196 + 0.881155i −0.0749293 + 0.103131i −0.844837 0.535024i \(-0.820302\pi\)
0.769907 + 0.638156i \(0.220302\pi\)
\(74\) 0 0
\(75\) 4.02146 + 2.97117i 0.464358 + 0.343082i
\(76\) 0 0
\(77\) 4.59963 6.33085i 0.524176 0.721467i
\(78\) 0 0
\(79\) 1.80542 + 5.55650i 0.203125 + 0.625156i 0.999785 + 0.0207276i \(0.00659828\pi\)
−0.796660 + 0.604428i \(0.793402\pi\)
\(80\) 0 0
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 0 0
\(83\) −11.9145 3.87127i −1.30779 0.424927i −0.429505 0.903064i \(-0.641312\pi\)
−0.878285 + 0.478137i \(0.841312\pi\)
\(84\) 0 0
\(85\) −10.0241 10.1046i −1.08727 1.09600i
\(86\) 0 0
\(87\) −0.498370 0.685947i −0.0534308 0.0735412i
\(88\) 0 0
\(89\) −5.68424 4.12984i −0.602528 0.437762i 0.244247 0.969713i \(-0.421459\pi\)
−0.846775 + 0.531951i \(0.821459\pi\)
\(90\) 0 0
\(91\) −20.5973 + 14.9648i −2.15918 + 1.56874i
\(92\) 0 0
\(93\) 4.30090i 0.445983i
\(94\) 0 0
\(95\) −3.67379 + 3.64454i −0.376923 + 0.373921i
\(96\) 0 0
\(97\) 17.2564 5.60695i 1.75212 0.569299i 0.755787 0.654818i \(-0.227255\pi\)
0.996337 + 0.0855183i \(0.0272546\pi\)
\(98\) 0 0
\(99\) 2.20616 0.221728
\(100\) 0 0
\(101\) 5.97473 0.594508 0.297254 0.954798i \(-0.403929\pi\)
0.297254 + 0.954798i \(0.403929\pi\)
\(102\) 0 0
\(103\) −0.437076 + 0.142014i −0.0430663 + 0.0139931i −0.330471 0.943816i \(-0.607208\pi\)
0.287405 + 0.957809i \(0.407208\pi\)
\(104\) 0 0
\(105\) −1.27205 + 7.82875i −0.124140 + 0.764008i
\(106\) 0 0
\(107\) 2.47862i 0.239617i 0.992797 + 0.119809i \(0.0382281\pi\)
−0.992797 + 0.119809i \(0.961772\pi\)
\(108\) 0 0
\(109\) −2.70314 + 1.96394i −0.258914 + 0.188112i −0.709668 0.704536i \(-0.751155\pi\)
0.450754 + 0.892648i \(0.351155\pi\)
\(110\) 0 0
\(111\) 5.84918 + 4.24968i 0.555180 + 0.403362i
\(112\) 0 0
\(113\) 10.3438 + 14.2370i 0.973059 + 1.33930i 0.940486 + 0.339832i \(0.110370\pi\)
0.0325728 + 0.999469i \(0.489630\pi\)
\(114\) 0 0
\(115\) 4.34404 2.19157i 0.405084 0.204365i
\(116\) 0 0
\(117\) −6.82641 2.21804i −0.631102 0.205057i
\(118\) 0 0
\(119\) 6.97700 21.4730i 0.639581 1.96843i
\(120\) 0 0
\(121\) −1.89515 5.83267i −0.172286 0.530243i
\(122\) 0 0
\(123\) 0.790317 1.08778i 0.0712605 0.0980816i
\(124\) 0 0
\(125\) −1.61643 11.0629i −0.144578 0.989493i
\(126\) 0 0
\(127\) 7.29555 10.0415i 0.647376 0.891036i −0.351606 0.936148i \(-0.614364\pi\)
0.998982 + 0.0451118i \(0.0143644\pi\)
\(128\) 0 0
\(129\) −2.53077 7.78890i −0.222822 0.685774i
\(130\) 0 0
\(131\) 4.88963 15.0487i 0.427209 1.31481i −0.473654 0.880711i \(-0.657065\pi\)
0.900863 0.434104i \(-0.142935\pi\)
\(132\) 0 0
\(133\) −7.80706 2.53667i −0.676958 0.219957i
\(134\) 0 0
\(135\) −1.99639 + 1.00718i −0.171822 + 0.0866843i
\(136\) 0 0
\(137\) −4.34663 5.98262i −0.371358 0.511130i 0.581912 0.813252i \(-0.302305\pi\)
−0.953269 + 0.302122i \(0.902305\pi\)
\(138\) 0 0
\(139\) 3.18667 + 2.31525i 0.270290 + 0.196377i 0.714671 0.699461i \(-0.246576\pi\)
−0.444381 + 0.895838i \(0.646576\pi\)
\(140\) 0 0
\(141\) −4.89822 + 3.55876i −0.412504 + 0.299702i
\(142\) 0 0
\(143\) 15.8352i 1.32421i
\(144\) 0 0
\(145\) −0.304069 + 1.87137i −0.0252516 + 0.155409i
\(146\) 0 0
\(147\) −5.30832 + 1.72478i −0.437823 + 0.142257i
\(148\) 0 0
\(149\) −3.92892 −0.321870 −0.160935 0.986965i \(-0.551451\pi\)
−0.160935 + 0.986965i \(0.551451\pi\)
\(150\) 0 0
\(151\) 7.93418 0.645674 0.322837 0.946455i \(-0.395363\pi\)
0.322837 + 0.946455i \(0.395363\pi\)
\(152\) 0 0
\(153\) 6.05378 1.96699i 0.489419 0.159022i
\(154\) 0 0
\(155\) 6.82745 6.77308i 0.548394 0.544027i
\(156\) 0 0
\(157\) 6.09738i 0.486624i −0.969948 0.243312i \(-0.921766\pi\)
0.969948 0.243312i \(-0.0782339\pi\)
\(158\) 0 0
\(159\) 9.67443 7.02889i 0.767232 0.557427i
\(160\) 0 0
\(161\) 6.24413 + 4.53662i 0.492106 + 0.357536i
\(162\) 0 0
\(163\) −0.00150257 0.00206811i −0.000117690 0.000161987i 0.808958 0.587866i \(-0.200032\pi\)
−0.809076 + 0.587704i \(0.800032\pi\)
\(164\) 0 0
\(165\) −3.47428 3.50217i −0.270472 0.272644i
\(166\) 0 0
\(167\) −9.60630 3.12128i −0.743358 0.241532i −0.0872372 0.996188i \(-0.527804\pi\)
−0.656121 + 0.754656i \(0.727804\pi\)
\(168\) 0 0
\(169\) −11.9032 + 36.6343i −0.915631 + 2.81802i
\(170\) 0 0
\(171\) −0.715151 2.20101i −0.0546889 0.168315i
\(172\) 0 0
\(173\) 3.63244 4.99963i 0.276169 0.380115i −0.648291 0.761393i \(-0.724516\pi\)
0.924460 + 0.381278i \(0.124516\pi\)
\(174\) 0 0
\(175\) 14.4310 10.3094i 1.09088 0.779321i
\(176\) 0 0
\(177\) −7.33050 + 10.0896i −0.550994 + 0.758378i
\(178\) 0 0
\(179\) −4.45991 13.7262i −0.333349 1.02594i −0.967530 0.252758i \(-0.918662\pi\)
0.634181 0.773185i \(-0.281338\pi\)
\(180\) 0 0
\(181\) 2.08366 6.41283i 0.154877 0.476662i −0.843272 0.537488i \(-0.819373\pi\)
0.998148 + 0.0608258i \(0.0193734\pi\)
\(182\) 0 0
\(183\) 6.58170 + 2.13853i 0.486534 + 0.158084i
\(184\) 0 0
\(185\) −2.46518 15.9777i −0.181244 1.17470i
\(186\) 0 0
\(187\) 8.25424 + 11.3610i 0.603610 + 0.830798i
\(188\) 0 0
\(189\) −2.86962 2.08490i −0.208734 0.151654i
\(190\) 0 0
\(191\) −12.4512 + 9.04634i −0.900938 + 0.654570i −0.938707 0.344717i \(-0.887975\pi\)
0.0377687 + 0.999287i \(0.487975\pi\)
\(192\) 0 0
\(193\) 16.3875i 1.17960i −0.807550 0.589799i \(-0.799207\pi\)
0.807550 0.589799i \(-0.200793\pi\)
\(194\) 0 0
\(195\) 7.22926 + 14.3295i 0.517698 + 1.02616i
\(196\) 0 0
\(197\) −9.36824 + 3.04392i −0.667459 + 0.216871i −0.623097 0.782145i \(-0.714126\pi\)
−0.0443625 + 0.999015i \(0.514126\pi\)
\(198\) 0 0
\(199\) 4.96275 0.351800 0.175900 0.984408i \(-0.443716\pi\)
0.175900 + 0.984408i \(0.443716\pi\)
\(200\) 0 0
\(201\) 4.73409 0.333917
\(202\) 0 0
\(203\) −2.86026 + 0.929355i −0.200751 + 0.0652279i
\(204\) 0 0
\(205\) −2.97139 + 0.458452i −0.207531 + 0.0320197i
\(206\) 0 0
\(207\) 2.17594i 0.151239i
\(208\) 0 0
\(209\) 4.13058 3.00104i 0.285718 0.207586i
\(210\) 0 0
\(211\) −2.83140 2.05713i −0.194921 0.141619i 0.486044 0.873934i \(-0.338440\pi\)
−0.680965 + 0.732316i \(0.738440\pi\)
\(212\) 0 0
\(213\) 8.09918 + 11.1476i 0.554947 + 0.763818i
\(214\) 0 0
\(215\) −8.37900 + 16.2835i −0.571443 + 1.11052i
\(216\) 0 0
\(217\) 14.5088 + 4.71420i 0.984923 + 0.320021i
\(218\) 0 0
\(219\) −0.336571 + 1.03586i −0.0227434 + 0.0699969i
\(220\) 0 0
\(221\) −14.1185 43.4523i −0.949714 2.92292i
\(222\) 0 0
\(223\) −13.5653 + 18.6710i −0.908397 + 1.25030i 0.0593138 + 0.998239i \(0.481109\pi\)
−0.967711 + 0.252062i \(0.918891\pi\)
\(224\) 0 0
\(225\) 4.74278 + 1.58305i 0.316185 + 0.105537i
\(226\) 0 0
\(227\) −3.43889 + 4.73323i −0.228247 + 0.314155i −0.907745 0.419522i \(-0.862198\pi\)
0.679498 + 0.733677i \(0.262198\pi\)
\(228\) 0 0
\(229\) 1.97484 + 6.07793i 0.130501 + 0.401641i 0.994863 0.101229i \(-0.0322775\pi\)
−0.864362 + 0.502870i \(0.832277\pi\)
\(230\) 0 0
\(231\) 2.41817 7.44236i 0.159104 0.489671i
\(232\) 0 0
\(233\) −4.32076 1.40390i −0.283062 0.0919725i 0.164045 0.986453i \(-0.447546\pi\)
−0.447107 + 0.894480i \(0.647546\pi\)
\(234\) 0 0
\(235\) 13.3631 + 2.17130i 0.871712 + 0.141640i
\(236\) 0 0
\(237\) 3.43411 + 4.72664i 0.223069 + 0.307029i
\(238\) 0 0
\(239\) 18.6407 + 13.5432i 1.20576 + 0.876040i 0.994839 0.101463i \(-0.0323522\pi\)
0.210926 + 0.977502i \(0.432352\pi\)
\(240\) 0 0
\(241\) −13.3064 + 9.66766i −0.857140 + 0.622749i −0.927105 0.374801i \(-0.877711\pi\)
0.0699655 + 0.997549i \(0.477711\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) 11.0976 + 5.71049i 0.708997 + 0.364830i
\(246\) 0 0
\(247\) −15.7982 + 5.13315i −1.00522 + 0.326614i
\(248\) 0 0
\(249\) −12.5277 −0.793910
\(250\) 0 0
\(251\) 4.66327 0.294343 0.147171 0.989111i \(-0.452983\pi\)
0.147171 + 0.989111i \(0.452983\pi\)
\(252\) 0 0
\(253\) −4.56554 + 1.48343i −0.287033 + 0.0932627i
\(254\) 0 0
\(255\) −12.6560 6.51243i −0.792551 0.407824i
\(256\) 0 0
\(257\) 5.78734i 0.361004i −0.983575 0.180502i \(-0.942228\pi\)
0.983575 0.180502i \(-0.0577723\pi\)
\(258\) 0 0
\(259\) 20.7473 15.0738i 1.28917 0.936639i
\(260\) 0 0
\(261\) −0.685947 0.498370i −0.0424591 0.0308483i
\(262\) 0 0
\(263\) 13.4896 + 18.5668i 0.831803 + 1.14488i 0.987585 + 0.157087i \(0.0502105\pi\)
−0.155781 + 0.987792i \(0.549790\pi\)
\(264\) 0 0
\(265\) −26.3933 4.28852i −1.62133 0.263442i
\(266\) 0 0
\(267\) −6.68222 2.17119i −0.408945 0.132874i
\(268\) 0 0
\(269\) 1.39366 4.28923i 0.0849727 0.261519i −0.899538 0.436842i \(-0.856097\pi\)
0.984511 + 0.175323i \(0.0560969\pi\)
\(270\) 0 0
\(271\) −3.06895 9.44525i −0.186425 0.573758i 0.813545 0.581502i \(-0.197535\pi\)
−0.999970 + 0.00774433i \(0.997535\pi\)
\(272\) 0 0
\(273\) −14.9648 + 20.5973i −0.905711 + 1.24660i
\(274\) 0 0
\(275\) −0.0881931 + 11.0305i −0.00531824 + 0.665163i
\(276\) 0 0
\(277\) −13.5280 + 18.6197i −0.812821 + 1.11875i 0.178061 + 0.984019i \(0.443017\pi\)
−0.990882 + 0.134732i \(0.956983\pi\)
\(278\) 0 0
\(279\) 1.32905 + 4.09040i 0.0795682 + 0.244886i
\(280\) 0 0
\(281\) 0.226820 0.698080i 0.0135309 0.0416439i −0.944063 0.329765i \(-0.893031\pi\)
0.957594 + 0.288121i \(0.0930305\pi\)
\(282\) 0 0
\(283\) −20.4402 6.64144i −1.21505 0.394793i −0.369771 0.929123i \(-0.620564\pi\)
−0.845276 + 0.534330i \(0.820564\pi\)
\(284\) 0 0
\(285\) −2.36776 + 4.60142i −0.140254 + 0.272565i
\(286\) 0 0
\(287\) −2.80329 3.85839i −0.165473 0.227754i
\(288\) 0 0
\(289\) 19.0259 + 13.8231i 1.11917 + 0.813126i
\(290\) 0 0
\(291\) 14.6792 10.6651i 0.860509 0.625196i
\(292\) 0 0
\(293\) 26.5961i 1.55376i 0.629649 + 0.776880i \(0.283199\pi\)
−0.629649 + 0.776880i \(0.716801\pi\)
\(294\) 0 0
\(295\) 27.5608 4.25233i 1.60465 0.247580i
\(296\) 0 0
\(297\) 2.09819 0.681742i 0.121749 0.0395587i
\(298\) 0 0
\(299\) 15.6183 0.903230
\(300\) 0 0
\(301\) −29.0493 −1.67437
\(302\) 0 0
\(303\) 5.68231 1.84629i 0.326440 0.106067i
\(304\) 0 0
\(305\) −6.97011 13.8159i −0.399107 0.791094i
\(306\) 0 0
\(307\) 12.1736i 0.694785i 0.937720 + 0.347393i \(0.112933\pi\)
−0.937720 + 0.347393i \(0.887067\pi\)
\(308\) 0 0
\(309\) −0.371799 + 0.270128i −0.0211509 + 0.0153670i
\(310\) 0 0
\(311\) 20.0330 + 14.5548i 1.13597 + 0.825327i 0.986552 0.163447i \(-0.0522614\pi\)
0.149414 + 0.988775i \(0.452261\pi\)
\(312\) 0 0
\(313\) 8.72589 + 12.0102i 0.493216 + 0.678854i 0.980977 0.194123i \(-0.0621862\pi\)
−0.487761 + 0.872977i \(0.662186\pi\)
\(314\) 0 0
\(315\) 1.20942 + 7.83867i 0.0681432 + 0.441659i
\(316\) 0 0
\(317\) 1.84725 + 0.600207i 0.103752 + 0.0337110i 0.360433 0.932785i \(-0.382629\pi\)
−0.256681 + 0.966496i \(0.582629\pi\)
\(318\) 0 0
\(319\) 0.578034 1.77901i 0.0323637 0.0996052i
\(320\) 0 0
\(321\) 0.765935 + 2.35731i 0.0427503 + 0.131572i
\(322\) 0 0
\(323\) 8.65873 11.9177i 0.481785 0.663120i
\(324\) 0 0
\(325\) 11.3627 34.0423i 0.630290 1.88833i
\(326\) 0 0
\(327\) −1.96394 + 2.70314i −0.108606 + 0.149484i
\(328\) 0 0
\(329\) 6.63635 + 20.4246i 0.365874 + 1.12604i
\(330\) 0 0
\(331\) −8.56924 + 26.3734i −0.471008 + 1.44961i 0.380258 + 0.924880i \(0.375835\pi\)
−0.851266 + 0.524734i \(0.824165\pi\)
\(332\) 0 0
\(333\) 6.87612 + 2.23419i 0.376809 + 0.122433i
\(334\) 0 0
\(335\) −7.45527 7.51512i −0.407325 0.410595i
\(336\) 0 0
\(337\) −6.40119 8.81048i −0.348695 0.479937i 0.598261 0.801301i \(-0.295859\pi\)
−0.946956 + 0.321364i \(0.895859\pi\)
\(338\) 0 0
\(339\) 14.2370 + 10.3438i 0.773246 + 0.561796i
\(340\) 0 0
\(341\) −7.67636 + 5.57720i −0.415698 + 0.302022i
\(342\) 0 0
\(343\) 5.03148i 0.271675i
\(344\) 0 0
\(345\) 3.45420 3.42669i 0.185968 0.184487i
\(346\) 0 0
\(347\) −21.7353 + 7.06224i −1.16681 + 0.379121i −0.827453 0.561536i \(-0.810211\pi\)
−0.339361 + 0.940656i \(0.610211\pi\)
\(348\) 0 0
\(349\) 28.8539 1.54451 0.772256 0.635311i \(-0.219128\pi\)
0.772256 + 0.635311i \(0.219128\pi\)
\(350\) 0 0
\(351\) −7.17771 −0.383118
\(352\) 0 0
\(353\) −25.9079 + 8.41799i −1.37894 + 0.448045i −0.902321 0.431065i \(-0.858138\pi\)
−0.476619 + 0.879110i \(0.658138\pi\)
\(354\) 0 0
\(355\) 4.94153 30.4123i 0.262269 1.61412i
\(356\) 0 0
\(357\) 22.5781i 1.19496i
\(358\) 0 0
\(359\) −19.3648 + 14.0694i −1.02204 + 0.742553i −0.966699 0.255915i \(-0.917623\pi\)
−0.0553373 + 0.998468i \(0.517623\pi\)
\(360\) 0 0
\(361\) 11.0383 + 8.01981i 0.580965 + 0.422096i
\(362\) 0 0
\(363\) −3.60479 4.96157i −0.189202 0.260415i
\(364\) 0 0
\(365\) 2.17441 1.09699i 0.113814 0.0574190i
\(366\) 0 0
\(367\) −6.38465 2.07450i −0.333276 0.108288i 0.137599 0.990488i \(-0.456062\pi\)
−0.470875 + 0.882200i \(0.656062\pi\)
\(368\) 0 0
\(369\) 0.415494 1.27876i 0.0216298 0.0665696i
\(370\) 0 0
\(371\) −13.1074 40.3404i −0.680502 2.09437i
\(372\) 0 0
\(373\) −7.99923 + 11.0100i −0.414184 + 0.570076i −0.964233 0.265057i \(-0.914609\pi\)
0.550048 + 0.835133i \(0.314609\pi\)
\(374\) 0 0
\(375\) −4.95594 10.0219i −0.255923 0.517529i
\(376\) 0 0
\(377\) −3.57715 + 4.92353i −0.184233 + 0.253575i
\(378\) 0 0
\(379\) −0.137272 0.422481i −0.00705120 0.0217014i 0.947469 0.319848i \(-0.103632\pi\)
−0.954520 + 0.298146i \(0.903632\pi\)
\(380\) 0 0
\(381\) 3.83550 11.8045i 0.196499 0.604760i
\(382\) 0 0
\(383\) −9.72980 3.16140i −0.497170 0.161540i 0.0496897 0.998765i \(-0.484177\pi\)
−0.546859 + 0.837224i \(0.684177\pi\)
\(384\) 0 0
\(385\) −15.6225 + 7.88155i −0.796196 + 0.401681i
\(386\) 0 0
\(387\) −4.81380 6.62563i −0.244699 0.336800i
\(388\) 0 0
\(389\) −19.5834 14.2282i −0.992919 0.721398i −0.0323607 0.999476i \(-0.510303\pi\)
−0.960558 + 0.278078i \(0.910303\pi\)
\(390\) 0 0
\(391\) −11.2054 + 8.14117i −0.566679 + 0.411717i
\(392\) 0 0
\(393\) 15.8232i 0.798174i
\(394\) 0 0
\(395\) 2.09525 12.8950i 0.105423 0.648818i
\(396\) 0 0
\(397\) −2.58871 + 0.841124i −0.129924 + 0.0422148i −0.373257 0.927728i \(-0.621759\pi\)
0.243333 + 0.969943i \(0.421759\pi\)
\(398\) 0 0
\(399\) −8.20883 −0.410956
\(400\) 0 0
\(401\) 31.3538 1.56573 0.782867 0.622189i \(-0.213756\pi\)
0.782867 + 0.622189i \(0.213756\pi\)
\(402\) 0 0
\(403\) 29.3597 9.53955i 1.46251 0.475199i
\(404\) 0 0
\(405\) −1.58745 + 1.57481i −0.0788809 + 0.0782527i
\(406\) 0 0
\(407\) 15.9505i 0.790639i
\(408\) 0 0
\(409\) 2.68805 1.95298i 0.132916 0.0965688i −0.519341 0.854567i \(-0.673823\pi\)
0.652256 + 0.757998i \(0.273823\pi\)
\(410\) 0 0
\(411\) −5.98262 4.34663i −0.295101 0.214404i
\(412\) 0 0
\(413\) 26.0016 + 35.7881i 1.27945 + 1.76102i
\(414\) 0 0
\(415\) 19.7287 + 19.8870i 0.968442 + 0.976216i
\(416\) 0 0
\(417\) 3.74615 + 1.21720i 0.183450 + 0.0596065i
\(418\) 0 0
\(419\) 3.41347 10.5056i 0.166759 0.513231i −0.832403 0.554171i \(-0.813035\pi\)
0.999162 + 0.0409399i \(0.0130352\pi\)
\(420\) 0 0
\(421\) −7.56044 23.2686i −0.368473 1.13404i −0.947777 0.318932i \(-0.896676\pi\)
0.579304 0.815111i \(-0.303324\pi\)
\(422\) 0 0
\(423\) −3.55876 + 4.89822i −0.173033 + 0.238160i
\(424\) 0 0
\(425\) 9.59264 + 30.3466i 0.465312 + 1.47202i
\(426\) 0 0
\(427\) 14.4284 19.8589i 0.698237 0.961041i
\(428\) 0 0
\(429\) −4.89335 15.0602i −0.236253 0.727113i
\(430\) 0 0
\(431\) 0.354621 1.09141i 0.0170815 0.0525715i −0.942152 0.335185i \(-0.891201\pi\)
0.959234 + 0.282613i \(0.0912013\pi\)
\(432\) 0 0
\(433\) −5.56802 1.80916i −0.267582 0.0869427i 0.172153 0.985070i \(-0.444928\pi\)
−0.439735 + 0.898128i \(0.644928\pi\)
\(434\) 0 0
\(435\) 0.289098 + 1.87374i 0.0138612 + 0.0898390i
\(436\) 0 0
\(437\) 2.95993 + 4.07400i 0.141593 + 0.194886i
\(438\) 0 0
\(439\) −16.4473 11.9497i −0.784988 0.570328i 0.121484 0.992593i \(-0.461235\pi\)
−0.906472 + 0.422266i \(0.861235\pi\)
\(440\) 0 0
\(441\) −4.51553 + 3.28072i −0.215025 + 0.156225i
\(442\) 0 0
\(443\) 17.5912i 0.835783i 0.908497 + 0.417891i \(0.137231\pi\)
−0.908497 + 0.417891i \(0.862769\pi\)
\(444\) 0 0
\(445\) 7.07656 + 14.0269i 0.335461 + 0.664937i
\(446\) 0 0
\(447\) −3.73662 + 1.21410i −0.176736 + 0.0574251i
\(448\) 0 0
\(449\) 2.83956 0.134007 0.0670037 0.997753i \(-0.478656\pi\)
0.0670037 + 0.997753i \(0.478656\pi\)
\(450\) 0 0
\(451\) 2.96634 0.139679
\(452\) 0 0
\(453\) 7.54585 2.45180i 0.354535 0.115195i
\(454\) 0 0
\(455\) 56.2637 8.68088i 2.63768 0.406966i
\(456\) 0 0
\(457\) 8.12004i 0.379840i 0.981800 + 0.189920i \(0.0608228\pi\)
−0.981800 + 0.189920i \(0.939177\pi\)
\(458\) 0 0
\(459\) 5.14965 3.74144i 0.240365 0.174636i
\(460\) 0 0
\(461\) −14.5629 10.5806i −0.678261 0.492786i 0.194519 0.980899i \(-0.437685\pi\)
−0.872780 + 0.488113i \(0.837685\pi\)
\(462\) 0 0
\(463\) −16.8529 23.1960i −0.783219 1.07801i −0.994919 0.100674i \(-0.967900\pi\)
0.211700 0.977335i \(-0.432100\pi\)
\(464\) 0 0
\(465\) 4.40030 8.55138i 0.204059 0.396561i
\(466\) 0 0
\(467\) −19.0638 6.19421i −0.882169 0.286634i −0.167311 0.985904i \(-0.553509\pi\)
−0.714858 + 0.699270i \(0.753509\pi\)
\(468\) 0 0
\(469\) 5.18902 15.9702i 0.239607 0.737433i
\(470\) 0 0
\(471\) −1.88419 5.79896i −0.0868191 0.267202i
\(472\) 0 0
\(473\) 10.6200 14.6172i 0.488310 0.672101i
\(474\) 0 0
\(475\) 11.0333 3.48765i 0.506241 0.160024i
\(476\) 0 0
\(477\) 7.02889 9.67443i 0.321831 0.442962i
\(478\) 0 0
\(479\) 4.78232 + 14.7185i 0.218510 + 0.672505i 0.998886 + 0.0471937i \(0.0150278\pi\)
−0.780376 + 0.625311i \(0.784972\pi\)
\(480\) 0 0
\(481\) 16.0364 49.3548i 0.731195 2.25039i
\(482\) 0 0
\(483\) 7.34041 + 2.38504i 0.334000 + 0.108523i
\(484\) 0 0
\(485\) −40.0471 6.50704i −1.81844 0.295470i
\(486\) 0 0
\(487\) −22.0222 30.3110i −0.997923 1.37352i −0.926591 0.376070i \(-0.877275\pi\)
−0.0713312 0.997453i \(-0.522725\pi\)
\(488\) 0 0
\(489\) −0.00206811 0.00150257i −9.35232e−5 6.79486e-5i
\(490\) 0 0
\(491\) −32.3517 + 23.5049i −1.46001 + 1.06076i −0.476651 + 0.879093i \(0.658149\pi\)
−0.983360 + 0.181667i \(0.941851\pi\)
\(492\) 0 0
\(493\) 5.39701i 0.243069i
\(494\) 0 0
\(495\) −4.38647 2.25715i −0.197157 0.101451i
\(496\) 0 0
\(497\) 46.4831 15.1033i 2.08505 0.677474i
\(498\) 0 0
\(499\) −28.3040 −1.26706 −0.633530 0.773718i \(-0.718395\pi\)
−0.633530 + 0.773718i \(0.718395\pi\)
\(500\) 0 0
\(501\) −10.1007 −0.451264
\(502\) 0 0
\(503\) 31.0839 10.0998i 1.38596 0.450327i 0.481338 0.876535i \(-0.340151\pi\)
0.904625 + 0.426208i \(0.140151\pi\)
\(504\) 0 0
\(505\) −11.8794 6.11281i −0.528627 0.272016i
\(506\) 0 0
\(507\) 38.5196i 1.71071i
\(508\) 0 0
\(509\) 13.8620 10.0713i 0.614422 0.446404i −0.236547 0.971620i \(-0.576016\pi\)
0.850969 + 0.525217i \(0.176016\pi\)
\(510\) 0 0
\(511\) 3.12549 + 2.27080i 0.138264 + 0.100454i
\(512\) 0 0
\(513\) −1.36030 1.87229i −0.0600586 0.0826636i
\(514\) 0 0
\(515\) 1.01432 + 0.164812i 0.0446964 + 0.00726250i
\(516\) 0 0
\(517\) −12.7035 4.12763i −0.558701 0.181533i
\(518\) 0 0
\(519\) 1.90969 5.87741i 0.0838260 0.257990i
\(520\) 0 0
\(521\) 6.22259 + 19.1512i 0.272617 + 0.839028i 0.989840 + 0.142185i \(0.0454128\pi\)
−0.717223 + 0.696843i \(0.754587\pi\)
\(522\) 0 0
\(523\) −16.4036 + 22.5777i −0.717281 + 0.987253i 0.282329 + 0.959318i \(0.408893\pi\)
−0.999610 + 0.0279349i \(0.991107\pi\)
\(524\) 0 0
\(525\) 10.5389 14.2643i 0.459954 0.622544i
\(526\) 0 0
\(527\) −16.0916 + 22.1482i −0.700960 + 0.964789i
\(528\) 0 0
\(529\) 5.64428 + 17.3713i 0.245403 + 0.755274i
\(530\) 0 0
\(531\) −3.85387 + 11.8610i −0.167244 + 0.514724i
\(532\) 0 0
\(533\) −9.17857 2.98230i −0.397568 0.129178i
\(534\) 0 0
\(535\) 2.53590 4.92818i 0.109636 0.213064i
\(536\) 0 0
\(537\) −8.48325 11.6762i −0.366079 0.503865i
\(538\) 0 0
\(539\) −9.96200 7.23781i −0.429094 0.311755i
\(540\) 0 0
\(541\) 9.00089 6.53953i 0.386979 0.281156i −0.377238 0.926116i \(-0.623126\pi\)
0.764216 + 0.644960i \(0.223126\pi\)
\(542\) 0 0
\(543\) 6.74285i 0.289363i
\(544\) 0 0
\(545\) 7.38392 1.13926i 0.316292 0.0488004i
\(546\) 0 0
\(547\) 26.4684 8.60009i 1.13171 0.367713i 0.317482 0.948264i \(-0.397163\pi\)
0.814224 + 0.580551i \(0.197163\pi\)
\(548\) 0 0
\(549\) 6.92041 0.295356
\(550\) 0 0
\(551\) −1.96222 −0.0835935
\(552\) 0 0
\(553\) 19.7091 6.40389i 0.838118 0.272321i
\(554\) 0 0
\(555\) −7.28190 14.4339i −0.309099 0.612685i
\(556\) 0 0
\(557\) 6.36580i 0.269728i 0.990864 + 0.134864i \(0.0430597\pi\)
−0.990864 + 0.134864i \(0.956940\pi\)
\(558\) 0 0
\(559\) −47.5569 + 34.5521i −2.01144 + 1.46140i
\(560\) 0 0
\(561\) 11.3610 + 8.25424i 0.479661 + 0.348494i
\(562\) 0 0
\(563\) −10.0676 13.8569i −0.424301 0.584000i 0.542333 0.840164i \(-0.317541\pi\)
−0.966633 + 0.256164i \(0.917541\pi\)
\(564\) 0 0
\(565\) −6.00028 38.8898i −0.252434 1.63611i
\(566\) 0 0
\(567\) −3.37344 1.09610i −0.141671 0.0460317i
\(568\) 0 0
\(569\) −4.75461 + 14.6332i −0.199324 + 0.613455i 0.800575 + 0.599232i \(0.204527\pi\)
−0.999899 + 0.0142229i \(0.995473\pi\)
\(570\) 0 0
\(571\) 2.63760 + 8.11770i 0.110380 + 0.339715i 0.990955 0.134191i \(-0.0428435\pi\)
−0.880575 + 0.473906i \(0.842844\pi\)
\(572\) 0 0
\(573\) −9.04634 + 12.4512i −0.377916 + 0.520157i
\(574\) 0 0
\(575\) −10.8794 0.0869850i −0.453701 0.00362752i
\(576\) 0 0
\(577\) 1.35494 1.86491i 0.0564068 0.0776374i −0.779882 0.625927i \(-0.784721\pi\)
0.836289 + 0.548290i \(0.184721\pi\)
\(578\) 0 0
\(579\) −5.06402 15.5854i −0.210453 0.647709i
\(580\) 0 0
\(581\) −13.7315 + 42.2614i −0.569681 + 1.75330i
\(582\) 0 0
\(583\) 25.0907 + 8.15245i 1.03915 + 0.337640i
\(584\) 0 0
\(585\) 11.3035 + 11.3942i 0.467342 + 0.471094i
\(586\) 0 0
\(587\) 0.540303 + 0.743663i 0.0223007 + 0.0306943i 0.820022 0.572332i \(-0.193961\pi\)
−0.797721 + 0.603027i \(0.793961\pi\)
\(588\) 0 0
\(589\) 8.05253 + 5.85051i 0.331799 + 0.241066i
\(590\) 0 0
\(591\) −7.96910 + 5.78989i −0.327805 + 0.238164i
\(592\) 0 0
\(593\) 25.5925i 1.05096i −0.850807 0.525478i \(-0.823886\pi\)
0.850807 0.525478i \(-0.176114\pi\)
\(594\) 0 0
\(595\) −35.8415 + 35.5560i −1.46936 + 1.45766i
\(596\) 0 0
\(597\) 4.71985 1.53357i 0.193171 0.0627650i
\(598\) 0 0
\(599\) 37.0204 1.51261 0.756307 0.654217i \(-0.227002\pi\)
0.756307 + 0.654217i \(0.227002\pi\)
\(600\) 0 0
\(601\) 33.4191 1.36319 0.681597 0.731728i \(-0.261286\pi\)
0.681597 + 0.731728i \(0.261286\pi\)
\(602\) 0 0
\(603\) 4.50239 1.46291i 0.183351 0.0595745i
\(604\) 0 0
\(605\) −2.19938 + 13.5359i −0.0894176 + 0.550313i
\(606\) 0 0
\(607\) 4.34502i 0.176359i −0.996105 0.0881795i \(-0.971895\pi\)
0.996105 0.0881795i \(-0.0281049\pi\)
\(608\) 0 0
\(609\) −2.43308 + 1.76774i −0.0985935 + 0.0716323i
\(610\) 0 0
\(611\) 35.1580 + 25.5438i 1.42234 + 1.03339i
\(612\) 0 0
\(613\) −2.32761 3.20367i −0.0940111 0.129395i 0.759420 0.650600i \(-0.225483\pi\)
−0.853431 + 0.521205i \(0.825483\pi\)
\(614\) 0 0
\(615\) −2.68429 + 1.35422i −0.108241 + 0.0546075i
\(616\) 0 0
\(617\) −19.2721 6.26189i −0.775866 0.252094i −0.105792 0.994388i \(-0.533738\pi\)
−0.670074 + 0.742294i \(0.733738\pi\)
\(618\) 0 0
\(619\) 4.65930 14.3398i 0.187273 0.576367i −0.812707 0.582672i \(-0.802007\pi\)
0.999980 + 0.00630532i \(0.00200706\pi\)
\(620\) 0 0
\(621\) 0.672404 + 2.06945i 0.0269826 + 0.0830440i
\(622\) 0 0
\(623\) −14.6487 + 20.1622i −0.586888 + 0.807782i
\(624\) 0 0
\(625\) −8.10462 + 23.6498i −0.324185 + 0.945994i
\(626\) 0 0
\(627\) 3.00104 4.13058i 0.119850 0.164959i
\(628\) 0 0
\(629\) 14.2213 + 43.7687i 0.567041 + 1.74517i
\(630\) 0 0
\(631\) −0.755761 + 2.32599i −0.0300864 + 0.0925963i −0.964972 0.262352i \(-0.915502\pi\)
0.934886 + 0.354949i \(0.115502\pi\)
\(632\) 0 0
\(633\) −3.32851 1.08150i −0.132296 0.0429857i
\(634\) 0 0
\(635\) −24.7791 + 12.5011i −0.983329 + 0.496090i
\(636\) 0 0
\(637\) 23.5481 + 32.4112i 0.933009 + 1.28418i
\(638\) 0 0
\(639\) 11.1476 + 8.09918i 0.440991 + 0.320399i
\(640\) 0 0
\(641\) −10.8353 + 7.87228i −0.427967 + 0.310936i −0.780836 0.624737i \(-0.785206\pi\)
0.352868 + 0.935673i \(0.385206\pi\)
\(642\) 0 0
\(643\) 35.4836i 1.39934i 0.714467 + 0.699669i \(0.246669\pi\)
−0.714467 + 0.699669i \(0.753331\pi\)
\(644\) 0 0
\(645\) −2.93704 + 18.0757i −0.115646 + 0.711731i
\(646\) 0 0
\(647\) 21.2886 6.91707i 0.836940 0.271938i 0.140974 0.990013i \(-0.454977\pi\)
0.695966 + 0.718075i \(0.254977\pi\)
\(648\) 0 0
\(649\) −27.5140 −1.08002
\(650\) 0 0
\(651\) 15.2555 0.597909
\(652\) 0 0
\(653\) −18.0021 + 5.84923i −0.704476 + 0.228898i −0.639279 0.768974i \(-0.720767\pi\)
−0.0651961 + 0.997872i \(0.520767\pi\)
\(654\) 0 0
\(655\) −25.1185 + 24.9184i −0.981460 + 0.973644i
\(656\) 0 0
\(657\) 1.08917i 0.0424925i
\(658\) 0 0
\(659\) 4.58371 3.33026i 0.178556 0.129729i −0.494917 0.868940i \(-0.664802\pi\)
0.673473 + 0.739212i \(0.264802\pi\)
\(660\) 0 0
\(661\) 20.4225 + 14.8378i 0.794342 + 0.577123i 0.909249 0.416253i \(-0.136657\pi\)
−0.114907 + 0.993376i \(0.536657\pi\)
\(662\) 0 0
\(663\) −26.8550 36.9627i −1.04296 1.43551i
\(664\) 0 0
\(665\) 12.9273 + 13.0311i 0.501300 + 0.505324i
\(666\) 0 0
\(667\) 1.75464 + 0.570116i 0.0679398 + 0.0220750i
\(668\) 0 0
\(669\) −7.13168 + 21.9491i −0.275727 + 0.848600i
\(670\) 0 0
\(671\) 4.71794 + 14.5203i 0.182134 + 0.560551i
\(672\) 0 0
\(673\) −7.74044 + 10.6538i −0.298372 + 0.410674i −0.931711 0.363201i \(-0.881684\pi\)
0.633339 + 0.773875i \(0.281684\pi\)
\(674\) 0 0
\(675\) 4.99984 + 0.0399757i 0.192444 + 0.00153867i
\(676\) 0 0
\(677\) 15.8487 21.8139i 0.609115 0.838375i −0.387389 0.921916i \(-0.626623\pi\)
0.996504 + 0.0835409i \(0.0266229\pi\)
\(678\) 0 0
\(679\) −19.8881 61.2092i −0.763234 2.34899i
\(680\) 0 0
\(681\) −1.80793 + 5.56424i −0.0692801 + 0.213222i
\(682\) 0 0
\(683\) −49.2454 16.0008i −1.88432 0.612254i −0.984326 0.176356i \(-0.943569\pi\)
−0.899996 0.435897i \(-0.856431\pi\)
\(684\) 0 0
\(685\) 2.52142 + 16.3422i 0.0963386 + 0.624403i
\(686\) 0 0
\(687\) 3.75637 + 5.17019i 0.143314 + 0.197255i
\(688\) 0 0
\(689\) −69.4403 50.4513i −2.64546 1.92204i
\(690\) 0 0
\(691\) 3.00647 2.18432i 0.114371 0.0830956i −0.529129 0.848541i \(-0.677481\pi\)
0.643501 + 0.765446i \(0.277481\pi\)
\(692\) 0 0
\(693\) 7.82536i 0.297261i
\(694\) 0 0
\(695\) −3.96722 7.86367i −0.150485 0.298286i
\(696\) 0 0
\(697\) 8.13972 2.64475i 0.308314 0.100177i
\(698\) 0 0
\(699\) −4.54311 −0.171836
\(700\) 0 0
\(701\) −28.4299 −1.07378 −0.536890 0.843652i \(-0.680401\pi\)
−0.536890 + 0.843652i \(0.680401\pi\)
\(702\) 0 0
\(703\) 15.9132 5.17053i 0.600180 0.195010i
\(704\) 0 0
\(705\) 13.3800 2.06439i 0.503921 0.0777495i
\(706\) 0 0
\(707\) 21.1926i 0.797030i
\(708\) 0 0
\(709\) 33.1126 24.0577i 1.24357 0.903507i 0.245740 0.969336i \(-0.420969\pi\)
0.997831 + 0.0658288i \(0.0209691\pi\)
\(710\) 0 0
\(711\) 4.72664 + 3.43411i 0.177263 + 0.128789i
\(712\) 0 0
\(713\) −5.50080 7.57120i −0.206007 0.283544i
\(714\) 0 0
\(715\) −16.2012 + 31.4848i −0.605890 + 1.17746i
\(716\) 0 0
\(717\) 21.9134 + 7.12010i 0.818372 + 0.265905i
\(718\) 0 0
\(719\) −1.46368 + 4.50475i −0.0545861 + 0.167999i −0.974633 0.223810i \(-0.928151\pi\)
0.920047 + 0.391809i \(0.128151\pi\)
\(720\) 0 0
\(721\) 0.503731 + 1.55032i 0.0187599 + 0.0577371i
\(722\) 0 0
\(723\) −9.66766 + 13.3064i −0.359544 + 0.494870i
\(724\) 0 0
\(725\) 2.51919 3.40970i 0.0935604 0.126633i
\(726\) 0 0
\(727\) −3.27447 + 4.50692i −0.121443 + 0.167153i −0.865410 0.501064i \(-0.832942\pi\)
0.743967 + 0.668217i \(0.232942\pi\)
\(728\) 0 0
\(729\) −0.309017 0.951057i −0.0114451 0.0352243i
\(730\) 0 0
\(731\) 16.1091 49.5788i 0.595818 1.83374i
\(732\) 0 0
\(733\) 28.8738 + 9.38166i 1.06648 + 0.346520i 0.789115 0.614246i \(-0.210540\pi\)
0.277363 + 0.960765i \(0.410540\pi\)
\(734\) 0 0
\(735\) 12.3190 + 2.00166i 0.454395 + 0.0738323i
\(736\) 0 0
\(737\) 6.13894 + 8.44952i 0.226131 + 0.311242i
\(738\) 0 0
\(739\) 39.6127 + 28.7803i 1.45718 + 1.05870i 0.984087 + 0.177686i \(0.0568611\pi\)
0.473089 + 0.881015i \(0.343139\pi\)
\(740\) 0 0
\(741\) −13.4388 + 9.76383i −0.493685 + 0.358683i
\(742\) 0 0
\(743\) 45.5953i 1.67273i −0.548174 0.836364i \(-0.684677\pi\)
0.548174 0.836364i \(-0.315323\pi\)
\(744\) 0 0
\(745\) 7.81178 + 4.01972i 0.286201 + 0.147271i
\(746\) 0 0
\(747\) −11.9145 + 3.87127i −0.435930 + 0.141642i
\(748\) 0 0
\(749\) 8.79176 0.321244
\(750\) 0 0
\(751\) −27.9100 −1.01845 −0.509225 0.860633i \(-0.670068\pi\)
−0.509225 + 0.860633i \(0.670068\pi\)
\(752\) 0 0
\(753\) 4.43503 1.44103i 0.161621 0.0525140i
\(754\) 0 0
\(755\) −15.7753 8.11754i −0.574123 0.295427i
\(756\) 0 0
\(757\) 27.6680i 1.00561i 0.864400 + 0.502804i \(0.167698\pi\)
−0.864400 + 0.502804i \(0.832302\pi\)
\(758\) 0 0
\(759\) −3.88368 + 2.82166i −0.140969 + 0.102420i
\(760\) 0 0
\(761\) 9.80362 + 7.12275i 0.355381 + 0.258199i 0.751123 0.660162i \(-0.229513\pi\)
−0.395742 + 0.918362i \(0.629513\pi\)
\(762\) 0 0
\(763\) 6.96619 + 9.58814i 0.252193 + 0.347114i
\(764\) 0 0
\(765\) −14.0490 2.28276i −0.507944 0.0825333i
\(766\) 0 0
\(767\) 85.1349 + 27.6620i 3.07404 + 0.998817i
\(768\) 0 0
\(769\) 3.13398 9.64540i 0.113014 0.347822i −0.878513 0.477718i \(-0.841464\pi\)
0.991528 + 0.129896i \(0.0414642\pi\)
\(770\) 0 0
\(771\) −1.78839 5.50409i −0.0644071 0.198225i
\(772\) 0 0
\(773\) 29.4908 40.5906i 1.06071 1.45994i 0.181569 0.983378i \(-0.441882\pi\)
0.879140 0.476563i \(-0.158118\pi\)
\(774\) 0 0
\(775\) −20.5045 + 6.48153i −0.736542 + 0.232823i
\(776\) 0 0
\(777\) 15.0738 20.7473i 0.540769 0.744304i
\(778\) 0 0
\(779\) −0.961568 2.95940i −0.0344518 0.106032i
\(780\) 0 0
\(781\) −9.39383 + 28.9112i −0.336138 + 1.03453i
\(782\) 0 0
\(783\) −0.806379 0.262008i −0.0288176 0.00936342i
\(784\) 0 0
\(785\) −6.23829 + 12.1233i −0.222654 + 0.432699i
\(786\) 0 0
\(787\) −9.08606 12.5059i −0.323883 0.445787i 0.615765 0.787930i \(-0.288847\pi\)
−0.939648 + 0.342143i \(0.888847\pi\)
\(788\) 0 0
\(789\) 18.5668 + 13.4896i 0.660996 + 0.480242i
\(790\) 0 0
\(791\) 50.4991 36.6897i 1.79554 1.30454i
\(792\) 0 0
\(793\) 49.6727i 1.76393i
\(794\) 0 0
\(795\) −26.4268 + 4.07736i −0.937261 + 0.144609i
\(796\) 0 0
\(797\) −5.45087 + 1.77110i −0.193080 + 0.0627354i −0.403961