Properties

Label 260.2.bk.b.193.1
Level $260$
Weight $2$
Character 260.193
Analytic conductor $2.076$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.bk (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.07611045255\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 193.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 260.193
Dual form 260.2.bk.b.97.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.133975 - 0.500000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(-0.232051 - 0.133975i) q^{7} +(2.36603 + 1.36603i) q^{9} +O(q^{10})\) \(q+(0.133975 - 0.500000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(-0.232051 - 0.133975i) q^{7} +(2.36603 + 1.36603i) q^{9} +(4.59808 + 1.23205i) q^{11} +(3.00000 + 2.00000i) q^{13} +(0.866025 + 0.767949i) q^{15} +(-2.86603 + 0.767949i) q^{17} +(-0.866025 - 3.23205i) q^{19} +(-0.0980762 + 0.0980762i) q^{21} +(-0.133975 - 0.0358984i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(2.09808 - 2.09808i) q^{27} +(-1.03590 + 0.598076i) q^{29} +(2.26795 + 2.26795i) q^{31} +(1.23205 - 2.13397i) q^{33} +(0.500000 - 0.330127i) q^{35} +(-3.23205 + 1.86603i) q^{37} +(1.40192 - 1.23205i) q^{39} +(-1.86603 + 6.96410i) q^{41} +(-2.66987 - 9.96410i) q^{43} +(-5.09808 + 3.36603i) q^{45} +7.46410i q^{47} +(-3.46410 - 6.00000i) q^{49} +1.53590i q^{51} +(-8.46410 - 8.46410i) q^{53} +(-7.06218 + 7.96410i) q^{55} -1.73205 q^{57} +(13.7942 - 3.69615i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-0.366025 - 0.633975i) q^{63} +(-7.00000 + 4.00000i) q^{65} +(-6.23205 - 10.7942i) q^{67} +(-0.0358984 + 0.0621778i) q^{69} +(2.86603 - 0.767949i) q^{71} +0.928203 q^{73} +(-2.40192 + 0.964102i) q^{75} +(-0.901924 - 0.901924i) q^{77} -11.4641i q^{79} +(3.33013 + 5.76795i) q^{81} -3.46410i q^{83} +(1.33013 - 6.50000i) q^{85} +(0.160254 + 0.598076i) q^{87} +(-0.794229 + 2.96410i) q^{89} +(-0.428203 - 0.866025i) q^{91} +(1.43782 - 0.830127i) q^{93} +(7.33013 + 1.50000i) q^{95} +(1.23205 - 2.13397i) q^{97} +(9.19615 + 9.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{3} - 4 q^{5} + 6 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{3} - 4 q^{5} + 6 q^{7} + 6 q^{9} + 8 q^{11} + 12 q^{13} - 8 q^{17} + 10 q^{21} - 4 q^{23} - 12 q^{25} - 2 q^{27} - 18 q^{29} + 16 q^{31} - 2 q^{33} + 2 q^{35} - 6 q^{37} + 16 q^{39} - 4 q^{41} - 28 q^{43} - 10 q^{45} - 20 q^{53} - 4 q^{55} + 24 q^{59} + 2 q^{61} + 2 q^{63} - 28 q^{65} - 18 q^{67} - 14 q^{69} + 8 q^{71} - 24 q^{73} - 20 q^{75} - 14 q^{77} - 4 q^{81} - 12 q^{85} - 34 q^{87} + 28 q^{89} + 26 q^{91} + 30 q^{93} + 12 q^{95} - 2 q^{97} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(e\left(\frac{7}{12}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) 0.133975 0.500000i 0.0773503 0.288675i −0.916406 0.400251i \(-0.868923\pi\)
0.993756 + 0.111576i \(0.0355897\pi\)
\(4\) 0 0
\(5\) −1.00000 + 2.00000i −0.447214 + 0.894427i
\(6\) 0 0
\(7\) −0.232051 0.133975i −0.0877070 0.0506376i 0.455505 0.890233i \(-0.349459\pi\)
−0.543212 + 0.839596i \(0.682792\pi\)
\(8\) 0 0
\(9\) 2.36603 + 1.36603i 0.788675 + 0.455342i
\(10\) 0 0
\(11\) 4.59808 + 1.23205i 1.38637 + 0.371477i 0.873432 0.486947i \(-0.161889\pi\)
0.512941 + 0.858424i \(0.328556\pi\)
\(12\) 0 0
\(13\) 3.00000 + 2.00000i 0.832050 + 0.554700i
\(14\) 0 0
\(15\) 0.866025 + 0.767949i 0.223607 + 0.198284i
\(16\) 0 0
\(17\) −2.86603 + 0.767949i −0.695113 + 0.186255i −0.589041 0.808103i \(-0.700494\pi\)
−0.106073 + 0.994358i \(0.533828\pi\)
\(18\) 0 0
\(19\) −0.866025 3.23205i −0.198680 0.741483i −0.991283 0.131746i \(-0.957942\pi\)
0.792604 0.609737i \(-0.208725\pi\)
\(20\) 0 0
\(21\) −0.0980762 + 0.0980762i −0.0214020 + 0.0214020i
\(22\) 0 0
\(23\) −0.133975 0.0358984i −0.0279356 0.00748533i 0.244824 0.969567i \(-0.421270\pi\)
−0.272760 + 0.962082i \(0.587936\pi\)
\(24\) 0 0
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) 0 0
\(27\) 2.09808 2.09808i 0.403775 0.403775i
\(28\) 0 0
\(29\) −1.03590 + 0.598076i −0.192362 + 0.111060i −0.593088 0.805138i \(-0.702091\pi\)
0.400726 + 0.916198i \(0.368758\pi\)
\(30\) 0 0
\(31\) 2.26795 + 2.26795i 0.407336 + 0.407336i 0.880808 0.473473i \(-0.157000\pi\)
−0.473473 + 0.880808i \(0.657000\pi\)
\(32\) 0 0
\(33\) 1.23205 2.13397i 0.214473 0.371477i
\(34\) 0 0
\(35\) 0.500000 0.330127i 0.0845154 0.0558017i
\(36\) 0 0
\(37\) −3.23205 + 1.86603i −0.531346 + 0.306773i −0.741564 0.670882i \(-0.765916\pi\)
0.210218 + 0.977654i \(0.432582\pi\)
\(38\) 0 0
\(39\) 1.40192 1.23205i 0.224487 0.197286i
\(40\) 0 0
\(41\) −1.86603 + 6.96410i −0.291424 + 1.08761i 0.652592 + 0.757710i \(0.273682\pi\)
−0.944016 + 0.329900i \(0.892985\pi\)
\(42\) 0 0
\(43\) −2.66987 9.96410i −0.407152 1.51951i −0.800052 0.599930i \(-0.795195\pi\)
0.392900 0.919581i \(-0.371472\pi\)
\(44\) 0 0
\(45\) −5.09808 + 3.36603i −0.759976 + 0.501777i
\(46\) 0 0
\(47\) 7.46410i 1.08875i 0.838842 + 0.544376i \(0.183233\pi\)
−0.838842 + 0.544376i \(0.816767\pi\)
\(48\) 0 0
\(49\) −3.46410 6.00000i −0.494872 0.857143i
\(50\) 0 0
\(51\) 1.53590i 0.215069i
\(52\) 0 0
\(53\) −8.46410 8.46410i −1.16263 1.16263i −0.983897 0.178737i \(-0.942799\pi\)
−0.178737 0.983897i \(-0.557201\pi\)
\(54\) 0 0
\(55\) −7.06218 + 7.96410i −0.952264 + 1.07388i
\(56\) 0 0
\(57\) −1.73205 −0.229416
\(58\) 0 0
\(59\) 13.7942 3.69615i 1.79586 0.481198i 0.802537 0.596602i \(-0.203483\pi\)
0.993319 + 0.115404i \(0.0368164\pi\)
\(60\) 0 0
\(61\) 0.500000 0.866025i 0.0640184 0.110883i −0.832240 0.554416i \(-0.812942\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) 0 0
\(63\) −0.366025 0.633975i −0.0461149 0.0798733i
\(64\) 0 0
\(65\) −7.00000 + 4.00000i −0.868243 + 0.496139i
\(66\) 0 0
\(67\) −6.23205 10.7942i −0.761366 1.31872i −0.942146 0.335201i \(-0.891196\pi\)
0.180780 0.983524i \(-0.442138\pi\)
\(68\) 0 0
\(69\) −0.0358984 + 0.0621778i −0.00432166 + 0.00748533i
\(70\) 0 0
\(71\) 2.86603 0.767949i 0.340135 0.0911388i −0.0847085 0.996406i \(-0.526996\pi\)
0.424843 + 0.905267i \(0.360329\pi\)
\(72\) 0 0
\(73\) 0.928203 0.108638 0.0543190 0.998524i \(-0.482701\pi\)
0.0543190 + 0.998524i \(0.482701\pi\)
\(74\) 0 0
\(75\) −2.40192 + 0.964102i −0.277350 + 0.111325i
\(76\) 0 0
\(77\) −0.901924 0.901924i −0.102784 0.102784i
\(78\) 0 0
\(79\) 11.4641i 1.28981i −0.764262 0.644906i \(-0.776896\pi\)
0.764262 0.644906i \(-0.223104\pi\)
\(80\) 0 0
\(81\) 3.33013 + 5.76795i 0.370014 + 0.640883i
\(82\) 0 0
\(83\) 3.46410i 0.380235i −0.981761 0.190117i \(-0.939113\pi\)
0.981761 0.190117i \(-0.0608868\pi\)
\(84\) 0 0
\(85\) 1.33013 6.50000i 0.144273 0.705024i
\(86\) 0 0
\(87\) 0.160254 + 0.598076i 0.0171810 + 0.0641205i
\(88\) 0 0
\(89\) −0.794229 + 2.96410i −0.0841881 + 0.314194i −0.995159 0.0982760i \(-0.968667\pi\)
0.910971 + 0.412470i \(0.135334\pi\)
\(90\) 0 0
\(91\) −0.428203 0.866025i −0.0448879 0.0907841i
\(92\) 0 0
\(93\) 1.43782 0.830127i 0.149095 0.0860802i
\(94\) 0 0
\(95\) 7.33013 + 1.50000i 0.752055 + 0.153897i
\(96\) 0 0
\(97\) 1.23205 2.13397i 0.125096 0.216672i −0.796675 0.604408i \(-0.793410\pi\)
0.921770 + 0.387736i \(0.126743\pi\)
\(98\) 0 0
\(99\) 9.19615 + 9.19615i 0.924248 + 0.924248i
\(100\) 0 0
\(101\) 1.50000 0.866025i 0.149256 0.0861727i −0.423512 0.905890i \(-0.639203\pi\)
0.572768 + 0.819718i \(0.305870\pi\)
\(102\) 0 0
\(103\) −10.6603 + 10.6603i −1.05039 + 1.05039i −0.0517247 + 0.998661i \(0.516472\pi\)
−0.998661 + 0.0517247i \(0.983528\pi\)
\(104\) 0 0
\(105\) −0.0980762 0.294229i −0.00957126 0.0287138i
\(106\) 0 0
\(107\) −3.59808 0.964102i −0.347839 0.0932032i 0.0806695 0.996741i \(-0.474294\pi\)
−0.428509 + 0.903538i \(0.640961\pi\)
\(108\) 0 0
\(109\) −11.3923 + 11.3923i −1.09118 + 1.09118i −0.0957826 + 0.995402i \(0.530535\pi\)
−0.995402 + 0.0957826i \(0.969465\pi\)
\(110\) 0 0
\(111\) 0.500000 + 1.86603i 0.0474579 + 0.177115i
\(112\) 0 0
\(113\) 15.5263 4.16025i 1.46059 0.391364i 0.560896 0.827886i \(-0.310457\pi\)
0.899693 + 0.436522i \(0.143790\pi\)
\(114\) 0 0
\(115\) 0.205771 0.232051i 0.0191883 0.0216388i
\(116\) 0 0
\(117\) 4.36603 + 8.83013i 0.403639 + 0.816346i
\(118\) 0 0
\(119\) 0.767949 + 0.205771i 0.0703978 + 0.0188630i
\(120\) 0 0
\(121\) 10.0981 + 5.83013i 0.918007 + 0.530012i
\(122\) 0 0
\(123\) 3.23205 + 1.86603i 0.291424 + 0.168254i
\(124\) 0 0
\(125\) 11.0000 2.00000i 0.983870 0.178885i
\(126\) 0 0
\(127\) 1.20577 4.50000i 0.106995 0.399310i −0.891569 0.452885i \(-0.850395\pi\)
0.998564 + 0.0535746i \(0.0170615\pi\)
\(128\) 0 0
\(129\) −5.33975 −0.470138
\(130\) 0 0
\(131\) −13.8564 −1.21064 −0.605320 0.795982i \(-0.706955\pi\)
−0.605320 + 0.795982i \(0.706955\pi\)
\(132\) 0 0
\(133\) −0.232051 + 0.866025i −0.0201214 + 0.0750939i
\(134\) 0 0
\(135\) 2.09808 + 6.29423i 0.180574 + 0.541721i
\(136\) 0 0
\(137\) 9.69615 + 5.59808i 0.828398 + 0.478276i 0.853304 0.521414i \(-0.174595\pi\)
−0.0249057 + 0.999690i \(0.507929\pi\)
\(138\) 0 0
\(139\) 5.42820 + 3.13397i 0.460414 + 0.265820i 0.712218 0.701958i \(-0.247691\pi\)
−0.251804 + 0.967778i \(0.581024\pi\)
\(140\) 0 0
\(141\) 3.73205 + 1.00000i 0.314295 + 0.0842152i
\(142\) 0 0
\(143\) 11.3301 + 12.8923i 0.947473 + 1.07811i
\(144\) 0 0
\(145\) −0.160254 2.66987i −0.0133084 0.221721i
\(146\) 0 0
\(147\) −3.46410 + 0.928203i −0.285714 + 0.0765569i
\(148\) 0 0
\(149\) −4.25833 15.8923i −0.348856 1.30195i −0.888042 0.459762i \(-0.847935\pi\)
0.539186 0.842187i \(-0.318732\pi\)
\(150\) 0 0
\(151\) 11.1962 11.1962i 0.911130 0.911130i −0.0852312 0.996361i \(-0.527163\pi\)
0.996361 + 0.0852312i \(0.0271629\pi\)
\(152\) 0 0
\(153\) −7.83013 2.09808i −0.633028 0.169619i
\(154\) 0 0
\(155\) −6.80385 + 2.26795i −0.546498 + 0.182166i
\(156\) 0 0
\(157\) 13.3923 13.3923i 1.06882 1.06882i 0.0713726 0.997450i \(-0.477262\pi\)
0.997450 0.0713726i \(-0.0227379\pi\)
\(158\) 0 0
\(159\) −5.36603 + 3.09808i −0.425553 + 0.245693i
\(160\) 0 0
\(161\) 0.0262794 + 0.0262794i 0.00207111 + 0.00207111i
\(162\) 0 0
\(163\) 4.23205 7.33013i 0.331480 0.574140i −0.651322 0.758801i \(-0.725785\pi\)
0.982802 + 0.184661i \(0.0591188\pi\)
\(164\) 0 0
\(165\) 3.03590 + 4.59808i 0.236344 + 0.357960i
\(166\) 0 0
\(167\) −9.23205 + 5.33013i −0.714398 + 0.412458i −0.812687 0.582700i \(-0.801996\pi\)
0.0982896 + 0.995158i \(0.468663\pi\)
\(168\) 0 0
\(169\) 5.00000 + 12.0000i 0.384615 + 0.923077i
\(170\) 0 0
\(171\) 2.36603 8.83013i 0.180934 0.675257i
\(172\) 0 0
\(173\) 3.40192 + 12.6962i 0.258643 + 0.965271i 0.966027 + 0.258441i \(0.0832087\pi\)
−0.707384 + 0.706830i \(0.750125\pi\)
\(174\) 0 0
\(175\) 0.160254 + 1.33013i 0.0121141 + 0.100548i
\(176\) 0 0
\(177\) 7.39230i 0.555640i
\(178\) 0 0
\(179\) −0.964102 1.66987i −0.0720603 0.124812i 0.827744 0.561106i \(-0.189624\pi\)
−0.899804 + 0.436294i \(0.856291\pi\)
\(180\) 0 0
\(181\) 1.07180i 0.0796660i 0.999206 + 0.0398330i \(0.0126826\pi\)
−0.999206 + 0.0398330i \(0.987317\pi\)
\(182\) 0 0
\(183\) −0.366025 0.366025i −0.0270574 0.0270574i
\(184\) 0 0
\(185\) −0.500000 8.33013i −0.0367607 0.612443i
\(186\) 0 0
\(187\) −14.1244 −1.03288
\(188\) 0 0
\(189\) −0.767949 + 0.205771i −0.0558601 + 0.0149677i
\(190\) 0 0
\(191\) −5.03590 + 8.72243i −0.364385 + 0.631133i −0.988677 0.150058i \(-0.952054\pi\)
0.624292 + 0.781191i \(0.285387\pi\)
\(192\) 0 0
\(193\) −5.16025 8.93782i −0.371443 0.643359i 0.618345 0.785907i \(-0.287804\pi\)
−0.989788 + 0.142549i \(0.954470\pi\)
\(194\) 0 0
\(195\) 1.06218 + 4.03590i 0.0760641 + 0.289017i
\(196\) 0 0
\(197\) 10.1603 + 17.5981i 0.723888 + 1.25381i 0.959430 + 0.281947i \(0.0909802\pi\)
−0.235542 + 0.971864i \(0.575686\pi\)
\(198\) 0 0
\(199\) −1.96410 + 3.40192i −0.139231 + 0.241156i −0.927206 0.374552i \(-0.877797\pi\)
0.787974 + 0.615708i \(0.211130\pi\)
\(200\) 0 0
\(201\) −6.23205 + 1.66987i −0.439575 + 0.117784i
\(202\) 0 0
\(203\) 0.320508 0.0224953
\(204\) 0 0
\(205\) −12.0622 10.6962i −0.842459 0.747052i
\(206\) 0 0
\(207\) −0.267949 0.267949i −0.0186238 0.0186238i
\(208\) 0 0
\(209\) 15.9282i 1.10178i
\(210\) 0 0
\(211\) −4.96410 8.59808i −0.341743 0.591916i 0.643014 0.765855i \(-0.277684\pi\)
−0.984756 + 0.173939i \(0.944351\pi\)
\(212\) 0 0
\(213\) 1.53590i 0.105238i
\(214\) 0 0
\(215\) 22.5981 + 4.62436i 1.54118 + 0.315378i
\(216\) 0 0
\(217\) −0.222432 0.830127i −0.0150997 0.0563527i
\(218\) 0 0
\(219\) 0.124356 0.464102i 0.00840318 0.0313611i
\(220\) 0 0
\(221\) −10.1340 3.42820i −0.681685 0.230606i
\(222\) 0 0
\(223\) −17.0885 + 9.86603i −1.14433 + 0.660678i −0.947499 0.319760i \(-0.896398\pi\)
−0.196829 + 0.980438i \(0.563064\pi\)
\(224\) 0 0
\(225\) −1.63397 13.5622i −0.108932 0.904145i
\(226\) 0 0
\(227\) 0.232051 0.401924i 0.0154018 0.0266766i −0.858222 0.513279i \(-0.828431\pi\)
0.873624 + 0.486602i \(0.161764\pi\)
\(228\) 0 0
\(229\) 10.8564 + 10.8564i 0.717412 + 0.717412i 0.968074 0.250663i \(-0.0806486\pi\)
−0.250663 + 0.968074i \(0.580649\pi\)
\(230\) 0 0
\(231\) −0.571797 + 0.330127i −0.0376215 + 0.0217208i
\(232\) 0 0
\(233\) −11.0000 + 11.0000i −0.720634 + 0.720634i −0.968734 0.248100i \(-0.920194\pi\)
0.248100 + 0.968734i \(0.420194\pi\)
\(234\) 0 0
\(235\) −14.9282 7.46410i −0.973809 0.486904i
\(236\) 0 0
\(237\) −5.73205 1.53590i −0.372337 0.0997673i
\(238\) 0 0
\(239\) −9.19615 + 9.19615i −0.594850 + 0.594850i −0.938937 0.344088i \(-0.888188\pi\)
0.344088 + 0.938937i \(0.388188\pi\)
\(240\) 0 0
\(241\) −4.93782 18.4282i −0.318073 1.18706i −0.921094 0.389340i \(-0.872703\pi\)
0.603021 0.797725i \(-0.293963\pi\)
\(242\) 0 0
\(243\) 11.9282 3.19615i 0.765195 0.205033i
\(244\) 0 0
\(245\) 15.4641 0.928203i 0.987965 0.0593007i
\(246\) 0 0
\(247\) 3.86603 11.4282i 0.245989 0.727159i
\(248\) 0 0
\(249\) −1.73205 0.464102i −0.109764 0.0294112i
\(250\) 0 0
\(251\) −23.8923 13.7942i −1.50807 0.870684i −0.999956 0.00939359i \(-0.997010\pi\)
−0.508113 0.861290i \(-0.669657\pi\)
\(252\) 0 0
\(253\) −0.571797 0.330127i −0.0359486 0.0207549i
\(254\) 0 0
\(255\) −3.07180 1.53590i −0.192363 0.0961817i
\(256\) 0 0
\(257\) −3.52628 + 13.1603i −0.219963 + 0.820914i 0.764397 + 0.644746i \(0.223037\pi\)
−0.984360 + 0.176168i \(0.943630\pi\)
\(258\) 0 0
\(259\) 1.00000 0.0621370
\(260\) 0 0
\(261\) −3.26795 −0.202281
\(262\) 0 0
\(263\) −4.79423 + 17.8923i −0.295625 + 1.10329i 0.645095 + 0.764102i \(0.276818\pi\)
−0.940720 + 0.339184i \(0.889849\pi\)
\(264\) 0 0
\(265\) 25.3923 8.46410i 1.55984 0.519946i
\(266\) 0 0
\(267\) 1.37564 + 0.794229i 0.0841881 + 0.0486060i
\(268\) 0 0
\(269\) −23.4282 13.5263i −1.42844 0.824712i −0.431445 0.902139i \(-0.641996\pi\)
−0.996998 + 0.0774275i \(0.975329\pi\)
\(270\) 0 0
\(271\) −19.7942 5.30385i −1.20241 0.322186i −0.398633 0.917111i \(-0.630515\pi\)
−0.803781 + 0.594925i \(0.797182\pi\)
\(272\) 0 0
\(273\) −0.490381 + 0.0980762i −0.0296792 + 0.00593584i
\(274\) 0 0
\(275\) −8.86603 22.0885i −0.534641 1.33198i
\(276\) 0 0
\(277\) 22.9904 6.16025i 1.38136 0.370134i 0.509744 0.860326i \(-0.329740\pi\)
0.871614 + 0.490192i \(0.163073\pi\)
\(278\) 0 0
\(279\) 2.26795 + 8.46410i 0.135779 + 0.506733i
\(280\) 0 0
\(281\) −7.39230 + 7.39230i −0.440988 + 0.440988i −0.892344 0.451356i \(-0.850940\pi\)
0.451356 + 0.892344i \(0.350940\pi\)
\(282\) 0 0
\(283\) −12.5263 3.35641i −0.744610 0.199518i −0.133484 0.991051i \(-0.542616\pi\)
−0.611126 + 0.791533i \(0.709283\pi\)
\(284\) 0 0
\(285\) 1.73205 3.46410i 0.102598 0.205196i
\(286\) 0 0
\(287\) 1.36603 1.36603i 0.0806339 0.0806339i
\(288\) 0 0
\(289\) −7.09808 + 4.09808i −0.417534 + 0.241063i
\(290\) 0 0
\(291\) −0.901924 0.901924i −0.0528717 0.0528717i
\(292\) 0 0
\(293\) 11.2321 19.4545i 0.656183 1.13654i −0.325412 0.945572i \(-0.605503\pi\)
0.981596 0.190971i \(-0.0611636\pi\)
\(294\) 0 0
\(295\) −6.40192 + 31.2846i −0.372734 + 1.82146i
\(296\) 0 0
\(297\) 12.2321 7.06218i 0.709776 0.409789i
\(298\) 0 0
\(299\) −0.330127 0.375644i −0.0190917 0.0217241i
\(300\) 0 0
\(301\) −0.715390 + 2.66987i −0.0412344 + 0.153889i
\(302\) 0 0
\(303\) −0.232051 0.866025i −0.0133310 0.0497519i
\(304\) 0 0
\(305\) 1.23205 + 1.86603i 0.0705470 + 0.106848i
\(306\) 0 0
\(307\) 30.3923i 1.73458i 0.497803 + 0.867290i \(0.334140\pi\)
−0.497803 + 0.867290i \(0.665860\pi\)
\(308\) 0 0
\(309\) 3.90192 + 6.75833i 0.221973 + 0.384468i
\(310\) 0 0
\(311\) 16.2487i 0.921380i −0.887561 0.460690i \(-0.847602\pi\)
0.887561 0.460690i \(-0.152398\pi\)
\(312\) 0 0
\(313\) 20.3205 + 20.3205i 1.14858 + 1.14858i 0.986832 + 0.161752i \(0.0517143\pi\)
0.161752 + 0.986832i \(0.448286\pi\)
\(314\) 0 0
\(315\) 1.63397 0.0980762i 0.0920640 0.00552597i
\(316\) 0 0
\(317\) −3.07180 −0.172529 −0.0862646 0.996272i \(-0.527493\pi\)
−0.0862646 + 0.996272i \(0.527493\pi\)
\(318\) 0 0
\(319\) −5.50000 + 1.47372i −0.307941 + 0.0825125i
\(320\) 0 0
\(321\) −0.964102 + 1.66987i −0.0538109 + 0.0932032i
\(322\) 0 0
\(323\) 4.96410 + 8.59808i 0.276210 + 0.478410i
\(324\) 0 0
\(325\) −1.00000 18.0000i −0.0554700 0.998460i
\(326\) 0 0
\(327\) 4.16987 + 7.22243i 0.230595 + 0.399401i
\(328\) 0 0
\(329\) 1.00000 1.73205i 0.0551318 0.0954911i
\(330\) 0 0
\(331\) 10.3301 2.76795i 0.567795 0.152140i 0.0365099 0.999333i \(-0.488376\pi\)
0.531285 + 0.847193i \(0.321709\pi\)
\(332\) 0 0
\(333\) −10.1962 −0.558746
\(334\) 0 0
\(335\) 27.8205 1.66987i 1.52000 0.0912349i
\(336\) 0 0
\(337\) −0.0717968 0.0717968i −0.00391102 0.00391102i 0.705149 0.709060i \(-0.250880\pi\)
−0.709060 + 0.705149i \(0.750880\pi\)
\(338\) 0 0
\(339\) 8.32051i 0.451908i
\(340\) 0 0
\(341\) 7.63397 + 13.2224i 0.413403 + 0.716035i
\(342\) 0 0
\(343\) 3.73205i 0.201512i
\(344\) 0 0
\(345\) −0.0884573 0.133975i −0.00476238 0.00721295i
\(346\) 0 0
\(347\) −6.66987 24.8923i −0.358058 1.33629i −0.876593 0.481233i \(-0.840189\pi\)
0.518535 0.855056i \(-0.326477\pi\)
\(348\) 0 0
\(349\) −5.47372 + 20.4282i −0.293002 + 1.09350i 0.649790 + 0.760114i \(0.274857\pi\)
−0.942792 + 0.333383i \(0.891810\pi\)
\(350\) 0 0
\(351\) 10.4904 2.09808i 0.559935 0.111987i
\(352\) 0 0
\(353\) −13.6244 + 7.86603i −0.725151 + 0.418666i −0.816646 0.577139i \(-0.804169\pi\)
0.0914944 + 0.995806i \(0.470836\pi\)
\(354\) 0 0
\(355\) −1.33013 + 6.50000i −0.0705958 + 0.344984i
\(356\) 0 0
\(357\) 0.205771 0.356406i 0.0108906 0.0188630i
\(358\) 0 0
\(359\) −7.58846 7.58846i −0.400503 0.400503i 0.477907 0.878410i \(-0.341396\pi\)
−0.878410 + 0.477907i \(0.841396\pi\)
\(360\) 0 0
\(361\) 6.75833 3.90192i 0.355702 0.205364i
\(362\) 0 0
\(363\) 4.26795 4.26795i 0.224009 0.224009i
\(364\) 0 0
\(365\) −0.928203 + 1.85641i −0.0485844 + 0.0971688i
\(366\) 0 0
\(367\) 10.7942 + 2.89230i 0.563454 + 0.150977i 0.529293 0.848439i \(-0.322457\pi\)
0.0341614 + 0.999416i \(0.489124\pi\)
\(368\) 0 0
\(369\) −13.9282 + 13.9282i −0.725073 + 0.725073i
\(370\) 0 0
\(371\) 0.830127 + 3.09808i 0.0430980 + 0.160844i
\(372\) 0 0
\(373\) 26.9904 7.23205i 1.39751 0.374461i 0.520059 0.854130i \(-0.325910\pi\)
0.877450 + 0.479669i \(0.159243\pi\)
\(374\) 0 0
\(375\) 0.473721 5.76795i 0.0244628 0.297856i
\(376\) 0 0
\(377\) −4.30385 0.277568i −0.221659 0.0142955i
\(378\) 0 0
\(379\) 23.5263 + 6.30385i 1.20846 + 0.323807i 0.806159 0.591699i \(-0.201543\pi\)
0.402305 + 0.915506i \(0.368209\pi\)
\(380\) 0 0
\(381\) −2.08846 1.20577i −0.106995 0.0617735i
\(382\) 0 0
\(383\) 0.696152 + 0.401924i 0.0355717 + 0.0205373i 0.517680 0.855574i \(-0.326796\pi\)
−0.482109 + 0.876111i \(0.660129\pi\)
\(384\) 0 0
\(385\) 2.70577 0.901924i 0.137899 0.0459663i
\(386\) 0 0
\(387\) 7.29423 27.2224i 0.370786 1.38379i
\(388\) 0 0
\(389\) −3.85641 −0.195528 −0.0977638 0.995210i \(-0.531169\pi\)
−0.0977638 + 0.995210i \(0.531169\pi\)
\(390\) 0 0
\(391\) 0.411543 0.0208126
\(392\) 0 0
\(393\) −1.85641 + 6.92820i −0.0936433 + 0.349482i
\(394\) 0 0
\(395\) 22.9282 + 11.4641i 1.15364 + 0.576822i
\(396\) 0 0
\(397\) −7.37564 4.25833i −0.370173 0.213719i 0.303361 0.952876i \(-0.401891\pi\)
−0.673534 + 0.739156i \(0.735225\pi\)
\(398\) 0 0
\(399\) 0.401924 + 0.232051i 0.0201214 + 0.0116171i
\(400\) 0 0
\(401\) 5.86603 + 1.57180i 0.292935 + 0.0784918i 0.402294 0.915511i \(-0.368213\pi\)
−0.109359 + 0.994002i \(0.534880\pi\)
\(402\) 0 0
\(403\) 2.26795 + 11.3397i 0.112975 + 0.564873i
\(404\) 0 0
\(405\) −14.8660 + 0.892305i −0.738699 + 0.0443390i
\(406\) 0 0
\(407\) −17.1603 + 4.59808i −0.850602 + 0.227918i
\(408\) 0 0
\(409\) 3.06218 + 11.4282i 0.151415 + 0.565088i 0.999386 + 0.0350453i \(0.0111575\pi\)
−0.847971 + 0.530043i \(0.822176\pi\)
\(410\) 0 0
\(411\) 4.09808 4.09808i 0.202143 0.202143i
\(412\) 0 0
\(413\) −3.69615 0.990381i −0.181876 0.0487335i
\(414\) 0 0
\(415\) 6.92820 + 3.46410i 0.340092 + 0.170046i
\(416\) 0 0
\(417\) 2.29423 2.29423i 0.112349 0.112349i
\(418\) 0 0
\(419\) 27.3564 15.7942i 1.33645 0.771599i 0.350169 0.936687i \(-0.386124\pi\)
0.986279 + 0.165088i \(0.0527908\pi\)
\(420\) 0 0
\(421\) 14.0718 + 14.0718i 0.685817 + 0.685817i 0.961305 0.275487i \(-0.0888392\pi\)
−0.275487 + 0.961305i \(0.588839\pi\)
\(422\) 0 0
\(423\) −10.1962 + 17.6603i −0.495754 + 0.858671i
\(424\) 0 0
\(425\) 11.6699 + 9.16025i 0.566072 + 0.444338i
\(426\) 0 0
\(427\) −0.232051 + 0.133975i −0.0112297 + 0.00648349i
\(428\) 0 0
\(429\) 7.96410 3.93782i 0.384510 0.190120i
\(430\) 0 0
\(431\) 8.47372 31.6244i 0.408165 1.52329i −0.389979 0.920824i \(-0.627518\pi\)
0.798143 0.602468i \(-0.205816\pi\)
\(432\) 0 0
\(433\) 2.72243 + 10.1603i 0.130832 + 0.488271i 0.999980 0.00628046i \(-0.00199914\pi\)
−0.869149 + 0.494551i \(0.835332\pi\)
\(434\) 0 0
\(435\) −1.35641 0.277568i −0.0650347 0.0133084i
\(436\) 0 0
\(437\) 0.464102i 0.0222010i
\(438\) 0 0
\(439\) 5.96410 + 10.3301i 0.284651 + 0.493030i 0.972524 0.232801i \(-0.0747889\pi\)
−0.687873 + 0.725831i \(0.741456\pi\)
\(440\) 0 0
\(441\) 18.9282i 0.901343i
\(442\) 0 0
\(443\) 27.0526 + 27.0526i 1.28531 + 1.28531i 0.937606 + 0.347700i \(0.113037\pi\)
0.347700 + 0.937606i \(0.386963\pi\)
\(444\) 0 0
\(445\) −5.13397 4.55256i −0.243374 0.215812i
\(446\) 0 0
\(447\) −8.51666 −0.402824
\(448\) 0 0
\(449\) −23.9904 + 6.42820i −1.13218 + 0.303366i −0.775801 0.630977i \(-0.782654\pi\)
−0.356375 + 0.934343i \(0.615987\pi\)
\(450\) 0 0
\(451\) −17.1603 + 29.7224i −0.808045 + 1.39957i
\(452\) 0 0
\(453\) −4.09808 7.09808i −0.192544 0.333497i
\(454\) 0 0
\(455\) 2.16025 + 0.00961894i 0.101274 + 0.000450943i
\(456\) 0 0
\(457\) 14.6962 + 25.4545i 0.687457 + 1.19071i 0.972658 + 0.232243i \(0.0746064\pi\)
−0.285201 + 0.958468i \(0.592060\pi\)
\(458\) 0 0
\(459\) −4.40192 + 7.62436i −0.205464 + 0.355874i
\(460\) 0 0
\(461\) −23.9904 + 6.42820i −1.11734 + 0.299391i −0.769808 0.638276i \(-0.779648\pi\)
−0.347535 + 0.937667i \(0.612981\pi\)
\(462\) 0 0
\(463\) −29.8564 −1.38754 −0.693772 0.720194i \(-0.744053\pi\)
−0.693772 + 0.720194i \(0.744053\pi\)
\(464\) 0 0
\(465\) 0.222432 + 3.70577i 0.0103150 + 0.171851i
\(466\) 0 0
\(467\) 20.1244 + 20.1244i 0.931244 + 0.931244i 0.997784 0.0665397i \(-0.0211959\pi\)
−0.0665397 + 0.997784i \(0.521196\pi\)
\(468\) 0 0
\(469\) 3.33975i 0.154215i
\(470\) 0 0
\(471\) −4.90192 8.49038i −0.225869 0.391216i
\(472\) 0 0
\(473\) 49.1051i 2.25786i
\(474\) 0 0
\(475\) −10.3301 + 13.1603i −0.473979 + 0.603834i
\(476\) 0 0
\(477\) −8.46410 31.5885i −0.387545 1.44634i
\(478\) 0 0
\(479\) 1.00962 3.76795i 0.0461307 0.172162i −0.939017 0.343870i \(-0.888262\pi\)
0.985148 + 0.171708i \(0.0549286\pi\)
\(480\) 0 0
\(481\) −13.4282 0.866025i −0.612273 0.0394874i
\(482\) 0 0
\(483\) 0.0166605 0.00961894i 0.000758079 0.000437677i
\(484\) 0 0
\(485\) 3.03590 + 4.59808i 0.137853 + 0.208788i
\(486\) 0 0
\(487\) 17.1603 29.7224i 0.777605 1.34685i −0.155713 0.987802i \(-0.549768\pi\)
0.933318 0.359050i \(-0.116899\pi\)
\(488\) 0 0
\(489\) −3.09808 3.09808i −0.140100 0.140100i
\(490\) 0 0
\(491\) −13.9641 + 8.06218i −0.630191 + 0.363841i −0.780826 0.624748i \(-0.785202\pi\)
0.150635 + 0.988589i \(0.451868\pi\)
\(492\) 0 0
\(493\) 2.50962 2.50962i 0.113028 0.113028i
\(494\) 0 0
\(495\) −27.5885 + 9.19615i −1.24001 + 0.413336i
\(496\) 0 0
\(497\) −0.767949 0.205771i −0.0344472 0.00923011i
\(498\) 0 0
\(499\) 3.19615 3.19615i 0.143079 0.143079i −0.631939 0.775018i \(-0.717741\pi\)
0.775018 + 0.631939i \(0.217741\pi\)
\(500\) 0 0
\(501\) 1.42820 + 5.33013i 0.0638074 + 0.238133i
\(502\) 0 0
\(503\) 15.0622 4.03590i 0.671589 0.179952i 0.0931187 0.995655i \(-0.470316\pi\)
0.578471 + 0.815703i \(0.303650\pi\)
\(504\) 0 0
\(505\) 0.232051 + 3.86603i 0.0103261 + 0.172036i
\(506\) 0 0
\(507\) 6.66987 0.892305i 0.296219 0.0396286i
\(508\) 0 0
\(509\) 8.79423 + 2.35641i 0.389797 + 0.104446i 0.448394 0.893836i \(-0.351996\pi\)
−0.0585970 + 0.998282i \(0.518663\pi\)
\(510\) 0 0
\(511\) −0.215390 0.124356i −0.00952831 0.00550117i
\(512\) 0 0
\(513\) −8.59808 4.96410i −0.379614 0.219170i
\(514\) 0 0
\(515\) −10.6603 31.9808i −0.469747 1.40924i
\(516\) 0 0
\(517\) −9.19615 + 34.3205i −0.404446 + 1.50941i
\(518\) 0 0
\(519\) 6.80385 0.298656
\(520\) 0 0
\(521\) 3.85641 0.168952 0.0844761 0.996426i \(-0.473078\pi\)
0.0844761 + 0.996426i \(0.473078\pi\)
\(522\) 0 0
\(523\) 9.06218 33.8205i 0.396261 1.47887i −0.423360 0.905962i \(-0.639149\pi\)
0.819621 0.572906i \(-0.194184\pi\)
\(524\) 0 0
\(525\) 0.686533 + 0.0980762i 0.0299628 + 0.00428040i
\(526\) 0 0
\(527\) −8.24167 4.75833i −0.359013 0.207276i
\(528\) 0 0
\(529\) −19.9019 11.4904i −0.865301 0.499582i
\(530\) 0 0
\(531\) 37.6865 + 10.0981i 1.63546 + 0.438219i
\(532\) 0 0
\(533\) −19.5263 + 17.1603i −0.845777 + 0.743293i
\(534\) 0 0
\(535\) 5.52628 6.23205i 0.238922 0.269435i
\(536\) 0 0
\(537\) −0.964102 + 0.258330i −0.0416041 + 0.0111478i
\(538\) 0 0
\(539\) −8.53590 31.8564i −0.367667 1.37215i
\(540\) 0 0
\(541\) 14.0718 14.0718i 0.604994 0.604994i −0.336640 0.941634i \(-0.609290\pi\)
0.941634 + 0.336640i \(0.109290\pi\)
\(542\) 0 0
\(543\) 0.535898 + 0.143594i 0.0229976 + 0.00616219i
\(544\) 0 0
\(545\) −11.3923 34.1769i −0.487993 1.46398i
\(546\) 0 0
\(547\) −9.19615 + 9.19615i −0.393199 + 0.393199i −0.875826 0.482627i \(-0.839683\pi\)
0.482627 + 0.875826i \(0.339683\pi\)
\(548\) 0 0
\(549\) 2.36603 1.36603i 0.100980 0.0583005i
\(550\) 0 0
\(551\) 2.83013 + 2.83013i 0.120567 + 0.120567i
\(552\) 0 0
\(553\) −1.53590 + 2.66025i −0.0653130 + 0.113126i
\(554\) 0 0
\(555\) −4.23205 0.866025i −0.179641 0.0367607i
\(556\) 0 0
\(557\) −17.7679 + 10.2583i −0.752852 + 0.434659i −0.826724 0.562608i \(-0.809798\pi\)
0.0738714 + 0.997268i \(0.476465\pi\)
\(558\) 0 0
\(559\) 11.9186 35.2321i 0.504102 1.49016i
\(560\) 0 0
\(561\) −1.89230 + 7.06218i −0.0798932 + 0.298165i
\(562\) 0 0
\(563\) −8.52628 31.8205i −0.359340 1.34107i −0.874934 0.484242i \(-0.839096\pi\)
0.515594 0.856833i \(-0.327571\pi\)
\(564\) 0 0
\(565\) −7.20577 + 35.2128i −0.303149 + 1.48141i
\(566\) 0 0
\(567\) 1.78461i 0.0749466i
\(568\) 0 0
\(569\) 1.57180 + 2.72243i 0.0658931 + 0.114130i 0.897090 0.441848i \(-0.145677\pi\)
−0.831197 + 0.555978i \(0.812344\pi\)
\(570\) 0 0
\(571\) 42.1051i 1.76204i 0.473075 + 0.881022i \(0.343144\pi\)
−0.473075 + 0.881022i \(0.656856\pi\)
\(572\) 0 0
\(573\) 3.68653 + 3.68653i 0.154007 + 0.154007i
\(574\) 0 0
\(575\) 0.258330 + 0.643594i 0.0107731 + 0.0268397i
\(576\) 0 0
\(577\) −28.9282 −1.20430 −0.602148 0.798384i \(-0.705688\pi\)
−0.602148 + 0.798384i \(0.705688\pi\)
\(578\) 0 0
\(579\) −5.16025 + 1.38269i −0.214453 + 0.0574625i
\(580\) 0 0
\(581\) −0.464102 + 0.803848i −0.0192542 + 0.0333492i
\(582\) 0 0
\(583\) −28.4904 49.3468i −1.17995 2.04374i
\(584\) 0 0
\(585\) −22.0263 0.0980762i −0.910675 0.00405495i
\(586\) 0 0
\(587\) −13.1603 22.7942i −0.543182 0.940819i −0.998719 0.0506017i \(-0.983886\pi\)
0.455537 0.890217i \(-0.349447\pi\)
\(588\) 0 0
\(589\) 5.36603 9.29423i 0.221103 0.382962i
\(590\) 0 0
\(591\) 10.1603 2.72243i 0.417937 0.111986i
\(592\) 0 0
\(593\) −7.07180 −0.290404 −0.145202 0.989402i \(-0.546383\pi\)
−0.145202 + 0.989402i \(0.546383\pi\)
\(594\) 0 0
\(595\) −1.17949 + 1.33013i −0.0483545 + 0.0545299i
\(596\) 0 0
\(597\) 1.43782 + 1.43782i 0.0588461 + 0.0588461i
\(598\) 0 0
\(599\) 5.60770i 0.229124i −0.993416 0.114562i \(-0.963454\pi\)
0.993416 0.114562i \(-0.0365465\pi\)
\(600\) 0 0
\(601\) −4.57180 7.91858i −0.186487 0.323006i 0.757589 0.652732i \(-0.226377\pi\)
−0.944077 + 0.329726i \(0.893044\pi\)
\(602\) 0 0
\(603\) 34.0526i 1.38673i
\(604\) 0 0
\(605\) −21.7583 + 14.3660i −0.884602 + 0.584062i
\(606\) 0 0
\(607\) 8.93782 + 33.3564i 0.362775 + 1.35389i 0.870412 + 0.492324i \(0.163852\pi\)
−0.507637 + 0.861571i \(0.669481\pi\)
\(608\) 0 0
\(609\) 0.0429399 0.160254i 0.00174001 0.00649382i
\(610\) 0 0
\(611\) −14.9282 + 22.3923i −0.603930 + 0.905896i
\(612\) 0 0
\(613\) −9.23205 + 5.33013i −0.372879 + 0.215282i −0.674715 0.738078i \(-0.735734\pi\)
0.301836 + 0.953360i \(0.402400\pi\)
\(614\) 0 0
\(615\) −6.96410 + 4.59808i −0.280820 + 0.185412i
\(616\) 0 0
\(617\) −16.0885 + 27.8660i −0.647697 + 1.12184i 0.335975 + 0.941871i \(0.390934\pi\)
−0.983672 + 0.179973i \(0.942399\pi\)
\(618\) 0 0
\(619\) 5.87564 + 5.87564i 0.236162 + 0.236162i 0.815259 0.579097i \(-0.196595\pi\)
−0.579097 + 0.815259i \(0.696595\pi\)
\(620\) 0 0
\(621\) −0.356406 + 0.205771i −0.0143021 + 0.00825732i
\(622\) 0 0
\(623\) 0.581416 0.581416i 0.0232939 0.0232939i
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 0 0
\(627\) −7.96410 2.13397i −0.318056 0.0852227i
\(628\) 0 0
\(629\) 7.83013 7.83013i 0.312208 0.312208i
\(630\) 0 0
\(631\) 6.20577 + 23.1603i 0.247048 + 0.921995i 0.972343 + 0.233557i \(0.0750366\pi\)
−0.725295 + 0.688438i \(0.758297\pi\)
\(632\) 0 0
\(633\) −4.96410 + 1.33013i −0.197305 + 0.0528678i
\(634\) 0 0
\(635\) 7.79423 + 6.91154i 0.309305 + 0.274276i
\(636\) 0 0
\(637\) 1.60770 24.9282i 0.0636992 0.987691i
\(638\) 0 0
\(639\) 7.83013 + 2.09808i 0.309755 + 0.0829986i
\(640\) 0 0
\(641\) 40.2846 + 23.2583i 1.59115 + 0.918649i 0.993111 + 0.117179i \(0.0373852\pi\)
0.598036 + 0.801470i \(0.295948\pi\)
\(642\) 0 0
\(643\) 35.7679 + 20.6506i 1.41055 + 0.814382i 0.995440 0.0953896i \(-0.0304097\pi\)
0.415110 + 0.909771i \(0.363743\pi\)
\(644\) 0 0
\(645\) 5.33975 10.6795i 0.210252 0.420505i
\(646\) 0 0
\(647\) −0.794229 + 2.96410i −0.0312243 + 0.116531i −0.979779 0.200082i \(-0.935879\pi\)
0.948555 + 0.316613i \(0.102546\pi\)
\(648\) 0 0
\(649\) 67.9808 2.66848
\(650\) 0 0
\(651\) −0.444864 −0.0174356
\(652\) 0 0
\(653\) 0.186533 0.696152i 0.00729962 0.0272425i −0.962180 0.272415i \(-0.912178\pi\)
0.969480 + 0.245172i \(0.0788444\pi\)
\(654\) 0 0
\(655\) 13.8564 27.7128i 0.541415 1.08283i
\(656\) 0 0
\(657\) 2.19615 + 1.26795i 0.0856801 + 0.0494674i
\(658\) 0 0
\(659\) −29.2128 16.8660i −1.13797 0.657007i −0.192043 0.981387i \(-0.561511\pi\)
−0.945927 + 0.324380i \(0.894845\pi\)
\(660\) 0 0
\(661\) −1.59808 0.428203i −0.0621580 0.0166552i 0.227606 0.973753i \(-0.426910\pi\)
−0.289764 + 0.957098i \(0.593577\pi\)
\(662\) 0 0
\(663\) −3.07180 + 4.60770i −0.119299 + 0.178948i
\(664\) 0 0
\(665\) −1.50000 1.33013i −0.0581675 0.0515801i
\(666\) 0 0
\(667\) 0.160254 0.0429399i 0.00620506 0.00166264i
\(668\) 0 0
\(669\) 2.64359 + 9.86603i 0.102207 + 0.381443i
\(670\) 0 0
\(671\) 3.36603 3.36603i 0.129944 0.129944i
\(672\) 0 0
\(673\) 26.9904 + 7.23205i 1.04040 + 0.278775i 0.738280 0.674494i \(-0.235638\pi\)
0.302122 + 0.953269i \(0.402305\pi\)
\(674\) 0 0
\(675\) −14.6865 2.09808i −0.565285 0.0807550i
\(676\) 0 0
\(677\) −10.3205 + 10.3205i −0.396649 + 0.396649i −0.877049 0.480400i \(-0.840491\pi\)
0.480400 + 0.877049i \(0.340491\pi\)
\(678\) 0 0
\(679\) −0.571797 + 0.330127i −0.0219435 + 0.0126691i
\(680\) 0 0
\(681\) −0.169873 0.169873i −0.00650955 0.00650955i
\(682\) 0 0
\(683\) −15.2321 + 26.3827i −0.582838 + 1.00951i 0.412303 + 0.911047i \(0.364725\pi\)
−0.995141 + 0.0984586i \(0.968609\pi\)
\(684\) 0 0
\(685\) −20.8923 + 13.7942i −0.798254 + 0.527050i
\(686\) 0 0
\(687\) 6.88269 3.97372i 0.262591 0.151607i
\(688\) 0 0
\(689\) −8.46410 42.3205i −0.322457 1.61228i
\(690\) 0 0
\(691\) −0.0621778 + 0.232051i −0.00236536 + 0.00882763i −0.967098 0.254403i \(-0.918121\pi\)
0.964733 + 0.263230i \(0.0847879\pi\)
\(692\) 0 0
\(693\) −0.901924 3.36603i −0.0342613 0.127865i
\(694\) 0 0
\(695\) −11.6962 + 7.72243i −0.443660 + 0.292929i
\(696\) 0 0
\(697\) 21.3923i 0.810291i
\(698\) 0 0
\(699\) 4.02628 + 6.97372i 0.152288 + 0.263770i
\(700\) 0 0
\(701\) 29.0718i 1.09803i −0.835814 0.549013i \(-0.815004\pi\)
0.835814 0.549013i \(-0.184996\pi\)
\(702\) 0 0
\(703\) 8.83013 + 8.83013i 0.333035 + 0.333035i
\(704\) 0 0
\(705\) −5.73205 + 6.46410i −0.215882 + 0.243452i
\(706\) 0 0
\(707\) −0.464102 −0.0174543
\(708\) 0 0
\(709\) −5.59808 + 1.50000i −0.210240 + 0.0563337i −0.362402 0.932022i \(-0.618043\pi\)
0.152162 + 0.988356i \(0.451377\pi\)
\(710\) 0 0
\(711\) 15.6603 27.1244i 0.587305 1.01724i
\(712\) 0 0
\(713\) −0.222432 0.385263i −0.00833014 0.0144282i
\(714\) 0 0
\(715\) −37.1147 + 9.76795i −1.38801 + 0.365301i
\(716\) 0 0
\(717\) 3.36603 + 5.83013i 0.125707 + 0.217730i
\(718\) 0 0
\(719\) −14.8923 + 25.7942i −0.555389 + 0.961962i 0.442484 + 0.896776i \(0.354097\pi\)
−0.997873 + 0.0651859i \(0.979236\pi\)
\(720\) 0 0
\(721\) 3.90192 1.04552i 0.145315 0.0389371i
\(722\) 0 0
\(723\) −9.87564 −0.367279
\(724\) 0 0
\(725\) 5.50000 + 2.34936i 0.204265 + 0.0872532i
\(726\) 0 0
\(727\) 13.5885 + 13.5885i 0.503968 + 0.503968i 0.912669 0.408701i \(-0.134018\pi\)
−0.408701 + 0.912669i \(0.634018\pi\)
\(728\) 0 0
\(729\) 13.5885i 0.503276i
\(730\) 0 0
\(731\) 15.3038 + 26.5070i 0.566033 + 0.980398i
\(732\) 0 0
\(733\) 38.6410i 1.42724i −0.700534 0.713619i \(-0.747055\pi\)
0.700534 0.713619i \(-0.252945\pi\)
\(734\) 0 0
\(735\) 1.60770 7.85641i 0.0593007 0.289788i
\(736\) 0 0
\(737\) −15.3564 57.3109i −0.565661 2.11107i
\(738\) 0 0
\(739\) −10.7417 + 40.0885i −0.395139 + 1.47468i 0.426405 + 0.904532i \(0.359780\pi\)
−0.821544 + 0.570145i \(0.806887\pi\)
\(740\) 0 0
\(741\) −5.19615 3.46410i −0.190885 0.127257i
\(742\) 0 0
\(743\) 30.4808 17.5981i 1.11823 0.645611i 0.177282 0.984160i \(-0.443270\pi\)
0.940949 + 0.338549i \(0.109936\pi\)
\(744\) 0 0
\(745\) 36.0429 + 7.37564i 1.32051 + 0.270223i
\(746\) 0 0
\(747\) 4.73205 8.19615i 0.173137 0.299882i
\(748\) 0 0
\(749\) 0.705771 + 0.705771i 0.0257883 + 0.0257883i
\(750\) 0 0
\(751\) 31.7487 18.3301i 1.15853 0.668876i 0.207576 0.978219i \(-0.433442\pi\)
0.950951 + 0.309343i \(0.100109\pi\)
\(752\) 0 0
\(753\) −10.0981 + 10.0981i −0.367994 + 0.367994i
\(754\) 0 0
\(755\) 11.1962 + 33.5885i 0.407470 + 1.22241i
\(756\) 0 0
\(757\) 16.0622 + 4.30385i 0.583790 + 0.156426i 0.538613 0.842553i \(-0.318948\pi\)
0.0451764 + 0.998979i \(0.485615\pi\)
\(758\) 0 0
\(759\) −0.241670 + 0.241670i −0.00877206 + 0.00877206i
\(760\) 0 0
\(761\) 2.66987 + 9.96410i 0.0967828 + 0.361198i 0.997284 0.0736557i \(-0.0234666\pi\)
−0.900501 + 0.434854i \(0.856800\pi\)
\(762\) 0 0
\(763\) 4.16987 1.11731i 0.150960 0.0404495i
\(764\) 0 0
\(765\) 12.0263 13.5622i 0.434811 0.490342i
\(766\) 0 0
\(767\) 48.7750 + 16.5000i 1.76116 + 0.595780i
\(768\) 0 0
\(769\) 5.33013 + 1.42820i 0.192209 + 0.0515023i 0.353639 0.935382i \(-0.384944\pi\)
−0.161430 + 0.986884i \(0.551611\pi\)
\(770\) 0 0
\(771\) 6.10770 + 3.52628i 0.219963 + 0.126996i
\(772\) 0 0
\(773\) 36.4808 + 21.0622i 1.31212 + 0.757554i 0.982447 0.186541i \(-0.0597276\pi\)
0.329675 + 0.944095i \(0.393061\pi\)
\(774\) 0 0
\(775\) 2.26795 15.8756i 0.0814671 0.570270i
\(776\) 0 0
\(777\) 0.133975 0.500000i 0.00480631 0.0179374i
\(778\) 0 0
\(779\) 24.1244 0.864345
\(780\) 0 0
\(781\) 14.1244 0.505409
\(782\) 0 0
\(783\) −0.918584 + 3.42820i −0.0328275 + 0.122514i
\(784\) 0 0
\(785\) 13.3923 + 40.1769i 0.477992 + 1.43398i
\(786\) 0 0
\(787\) −38.0885 21.9904i −1.35771 0.783872i −0.368392 0.929670i \(-0.620092\pi\)
−0.989314 + 0.145798i \(0.953425\pi\)
\(788\) 0 0
\(789\) 8.30385 + 4.79423i 0.295625 + 0.170679i
\(790\) 0 0
\(791\) −4.16025 1.11474i −0.147922