Properties

Label 315.3.ca.b.37.2
Level 315
Weight 3
Character 315.37
Analytic conductor 8.583
Analytic rank 0
Dimension 64
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 315.ca (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.58312832735\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 37.2
Character \(\chi\) \(=\) 315.37
Dual form 315.3.ca.b.298.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.41166 + 0.914152i) q^{2} +(7.33966 - 4.23756i) q^{4} +(4.98672 - 0.364163i) q^{5} +(-6.35750 - 2.92953i) q^{7} +(-11.1766 + 11.1766i) q^{8} +O(q^{10})\) \(q+(-3.41166 + 0.914152i) q^{2} +(7.33966 - 4.23756i) q^{4} +(4.98672 - 0.364163i) q^{5} +(-6.35750 - 2.92953i) q^{7} +(-11.1766 + 11.1766i) q^{8} +(-16.6801 + 5.80102i) q^{10} +(-8.72135 - 15.1058i) q^{11} +(-8.72144 + 8.72144i) q^{13} +(24.3677 + 4.18286i) q^{14} +(10.9636 - 18.9894i) q^{16} +(-3.02215 + 11.2788i) q^{17} +(-3.12903 - 1.80655i) q^{19} +(35.0577 - 23.8044i) q^{20} +(43.5633 + 43.5633i) q^{22} +(6.21349 + 23.1890i) q^{23} +(24.7348 - 3.63196i) q^{25} +(21.7819 - 37.7273i) q^{26} +(-59.0760 + 5.43848i) q^{28} +46.5831i q^{29} +(-1.10507 - 1.91403i) q^{31} +(-3.68097 + 13.7376i) q^{32} -41.2423i q^{34} +(-32.7699 - 12.2936i) q^{35} +(-29.3791 + 7.87211i) q^{37} +(12.3266 + 3.30292i) q^{38} +(-51.6647 + 59.8049i) q^{40} -29.9435 q^{41} +(-19.6771 + 19.6771i) q^{43} +(-128.024 - 73.9145i) q^{44} +(-42.3966 - 73.4331i) q^{46} +(-79.1503 + 21.2083i) q^{47} +(31.8357 + 37.2490i) q^{49} +(-81.0665 + 35.0024i) q^{50} +(-27.0549 + 100.970i) q^{52} +(-1.63190 - 0.437265i) q^{53} +(-48.9919 - 72.1526i) q^{55} +(103.798 - 38.3132i) q^{56} +(-42.5841 - 158.926i) q^{58} +(76.5567 - 44.2000i) q^{59} +(-23.4309 + 40.5836i) q^{61} +(5.51984 + 5.51984i) q^{62} +37.4755i q^{64} +(-40.3154 + 46.6674i) q^{65} +(3.01836 - 11.2647i) q^{67} +(25.6131 + 95.5894i) q^{68} +(123.038 + 11.9849i) q^{70} -67.1402 q^{71} +(-17.6525 - 4.72997i) q^{73} +(93.0353 - 53.7140i) q^{74} -30.6214 q^{76} +(11.1930 + 121.585i) q^{77} +(19.4021 + 11.2018i) q^{79} +(47.7569 - 98.6876i) q^{80} +(102.157 - 27.3729i) q^{82} +(-52.4430 + 52.4430i) q^{83} +(-10.9633 + 57.3450i) q^{85} +(49.1438 - 85.1196i) q^{86} +(266.308 + 71.3570i) q^{88} +(-44.2757 - 25.5626i) q^{89} +(80.9964 - 29.8968i) q^{91} +(143.870 + 143.870i) q^{92} +(250.647 - 144.711i) q^{94} +(-16.2615 - 7.86926i) q^{95} +(9.15031 + 9.15031i) q^{97} +(-142.664 - 97.9785i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} + O(q^{10}) \) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} - 16q^{10} - 16q^{11} + 80q^{16} - 56q^{17} - 96q^{22} - 72q^{23} - 4q^{25} + 288q^{26} - 380q^{28} - 136q^{31} + 48q^{32} - 76q^{35} - 28q^{37} + 68q^{38} + 164q^{40} - 128q^{41} + 344q^{43} + 240q^{46} - 412q^{47} + 72q^{50} + 388q^{52} + 40q^{53} - 8q^{55} + 864q^{56} + 56q^{58} - 216q^{61} + 912q^{62} - 20q^{65} - 368q^{67} + 492q^{68} + 416q^{70} - 784q^{71} - 316q^{73} - 32q^{76} - 844q^{77} - 908q^{80} + 556q^{82} - 1408q^{83} - 536q^{85} - 1024q^{86} + 372q^{88} - 1064q^{91} + 1704q^{92} - 260q^{95} + 352q^{97} - 272q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.41166 + 0.914152i −1.70583 + 0.457076i −0.974397 0.224836i \(-0.927815\pi\)
−0.731435 + 0.681912i \(0.761149\pi\)
\(3\) 0 0
\(4\) 7.33966 4.23756i 1.83492 1.05939i
\(5\) 4.98672 0.364163i 0.997344 0.0728326i
\(6\) 0 0
\(7\) −6.35750 2.92953i −0.908215 0.418505i
\(8\) −11.1766 + 11.1766i −1.39708 + 1.39708i
\(9\) 0 0
\(10\) −16.6801 + 5.80102i −1.66801 + 0.580102i
\(11\) −8.72135 15.1058i −0.792850 1.37326i −0.924195 0.381920i \(-0.875263\pi\)
0.131345 0.991337i \(-0.458070\pi\)
\(12\) 0 0
\(13\) −8.72144 + 8.72144i −0.670880 + 0.670880i −0.957919 0.287039i \(-0.907329\pi\)
0.287039 + 0.957919i \(0.407329\pi\)
\(14\) 24.3677 + 4.18286i 1.74055 + 0.298776i
\(15\) 0 0
\(16\) 10.9636 18.9894i 0.685222 1.18684i
\(17\) −3.02215 + 11.2788i −0.177774 + 0.663461i 0.818289 + 0.574807i \(0.194923\pi\)
−0.996063 + 0.0886535i \(0.971744\pi\)
\(18\) 0 0
\(19\) −3.12903 1.80655i −0.164686 0.0950814i 0.415392 0.909643i \(-0.363644\pi\)
−0.580078 + 0.814561i \(0.696978\pi\)
\(20\) 35.0577 23.8044i 1.75288 1.19022i
\(21\) 0 0
\(22\) 43.5633 + 43.5633i 1.98015 + 1.98015i
\(23\) 6.21349 + 23.1890i 0.270152 + 1.00822i 0.959021 + 0.283334i \(0.0914406\pi\)
−0.688870 + 0.724885i \(0.741893\pi\)
\(24\) 0 0
\(25\) 24.7348 3.63196i 0.989391 0.145278i
\(26\) 21.7819 37.7273i 0.837765 1.45105i
\(27\) 0 0
\(28\) −59.0760 + 5.43848i −2.10986 + 0.194231i
\(29\) 46.5831i 1.60631i 0.595767 + 0.803157i \(0.296848\pi\)
−0.595767 + 0.803157i \(0.703152\pi\)
\(30\) 0 0
\(31\) −1.10507 1.91403i −0.0356474 0.0617430i 0.847651 0.530554i \(-0.178016\pi\)
−0.883299 + 0.468811i \(0.844683\pi\)
\(32\) −3.68097 + 13.7376i −0.115030 + 0.429300i
\(33\) 0 0
\(34\) 41.2423i 1.21301i
\(35\) −32.7699 12.2936i −0.936283 0.351246i
\(36\) 0 0
\(37\) −29.3791 + 7.87211i −0.794030 + 0.212760i −0.632961 0.774183i \(-0.718161\pi\)
−0.161069 + 0.986943i \(0.551494\pi\)
\(38\) 12.3266 + 3.30292i 0.324386 + 0.0869188i
\(39\) 0 0
\(40\) −51.6647 + 59.8049i −1.29162 + 1.49512i
\(41\) −29.9435 −0.730329 −0.365165 0.930943i \(-0.618987\pi\)
−0.365165 + 0.930943i \(0.618987\pi\)
\(42\) 0 0
\(43\) −19.6771 + 19.6771i −0.457608 + 0.457608i −0.897869 0.440262i \(-0.854886\pi\)
0.440262 + 0.897869i \(0.354886\pi\)
\(44\) −128.024 73.9145i −2.90963 1.67987i
\(45\) 0 0
\(46\) −42.3966 73.4331i −0.921666 1.59637i
\(47\) −79.1503 + 21.2083i −1.68405 + 0.451240i −0.968844 0.247674i \(-0.920334\pi\)
−0.715206 + 0.698913i \(0.753667\pi\)
\(48\) 0 0
\(49\) 31.8357 + 37.2490i 0.649707 + 0.760185i
\(50\) −81.0665 + 35.0024i −1.62133 + 0.700047i
\(51\) 0 0
\(52\) −27.0549 + 100.970i −0.520286 + 1.94173i
\(53\) −1.63190 0.437265i −0.0307905 0.00825028i 0.243391 0.969928i \(-0.421740\pi\)
−0.274181 + 0.961678i \(0.588407\pi\)
\(54\) 0 0
\(55\) −48.9919 72.1526i −0.890763 1.31186i
\(56\) 103.798 38.3132i 1.85353 0.684164i
\(57\) 0 0
\(58\) −42.5841 158.926i −0.734208 2.74010i
\(59\) 76.5567 44.2000i 1.29757 0.749153i 0.317587 0.948229i \(-0.397127\pi\)
0.979984 + 0.199076i \(0.0637941\pi\)
\(60\) 0 0
\(61\) −23.4309 + 40.5836i −0.384114 + 0.665305i −0.991646 0.128990i \(-0.958826\pi\)
0.607532 + 0.794295i \(0.292160\pi\)
\(62\) 5.51984 + 5.51984i 0.0890296 + 0.0890296i
\(63\) 0 0
\(64\) 37.4755i 0.585554i
\(65\) −40.3154 + 46.6674i −0.620236 + 0.717960i
\(66\) 0 0
\(67\) 3.01836 11.2647i 0.0450501 0.168129i −0.939736 0.341902i \(-0.888929\pi\)
0.984786 + 0.173772i \(0.0555957\pi\)
\(68\) 25.6131 + 95.5894i 0.376663 + 1.40573i
\(69\) 0 0
\(70\) 123.038 + 11.9849i 1.75769 + 0.171213i
\(71\) −67.1402 −0.945636 −0.472818 0.881160i \(-0.656763\pi\)
−0.472818 + 0.881160i \(0.656763\pi\)
\(72\) 0 0
\(73\) −17.6525 4.72997i −0.241815 0.0647941i 0.135876 0.990726i \(-0.456615\pi\)
−0.377691 + 0.925932i \(0.623282\pi\)
\(74\) 93.0353 53.7140i 1.25723 0.725865i
\(75\) 0 0
\(76\) −30.6214 −0.402913
\(77\) 11.1930 + 121.585i 0.145363 + 1.57902i
\(78\) 0 0
\(79\) 19.4021 + 11.2018i 0.245596 + 0.141795i 0.617746 0.786378i \(-0.288046\pi\)
−0.372150 + 0.928173i \(0.621379\pi\)
\(80\) 47.7569 98.6876i 0.596962 1.23359i
\(81\) 0 0
\(82\) 102.157 27.3729i 1.24582 0.333816i
\(83\) −52.4430 + 52.4430i −0.631844 + 0.631844i −0.948530 0.316686i \(-0.897430\pi\)
0.316686 + 0.948530i \(0.397430\pi\)
\(84\) 0 0
\(85\) −10.9633 + 57.3450i −0.128980 + 0.674647i
\(86\) 49.1438 85.1196i 0.571440 0.989763i
\(87\) 0 0
\(88\) 266.308 + 71.3570i 3.02623 + 0.810875i
\(89\) −44.2757 25.5626i −0.497480 0.287220i 0.230192 0.973145i \(-0.426065\pi\)
−0.727672 + 0.685925i \(0.759398\pi\)
\(90\) 0 0
\(91\) 80.9964 29.8968i 0.890070 0.328536i
\(92\) 143.870 + 143.870i 1.56380 + 1.56380i
\(93\) 0 0
\(94\) 250.647 144.711i 2.66645 1.53948i
\(95\) −16.2615 7.86926i −0.171173 0.0828343i
\(96\) 0 0
\(97\) 9.15031 + 9.15031i 0.0943331 + 0.0943331i 0.752698 0.658365i \(-0.228752\pi\)
−0.658365 + 0.752698i \(0.728752\pi\)
\(98\) −142.664 97.9785i −1.45575 0.999781i
\(99\) 0 0
\(100\) 166.154 131.472i 1.66154 1.31472i
\(101\) −42.1642 73.0305i −0.417467 0.723074i 0.578217 0.815883i \(-0.303749\pi\)
−0.995684 + 0.0928089i \(0.970415\pi\)
\(102\) 0 0
\(103\) −30.3411 113.235i −0.294574 1.09937i −0.941555 0.336859i \(-0.890635\pi\)
0.646981 0.762506i \(-0.276031\pi\)
\(104\) 194.953i 1.87455i
\(105\) 0 0
\(106\) 5.96720 0.0562944
\(107\) 138.045 36.9890i 1.29014 0.345691i 0.452425 0.891802i \(-0.350559\pi\)
0.837713 + 0.546111i \(0.183892\pi\)
\(108\) 0 0
\(109\) −140.724 + 81.2472i −1.29105 + 0.745387i −0.978840 0.204627i \(-0.934402\pi\)
−0.312208 + 0.950014i \(0.601069\pi\)
\(110\) 233.102 + 201.374i 2.11911 + 1.83067i
\(111\) 0 0
\(112\) −125.331 + 88.6073i −1.11903 + 0.791136i
\(113\) 3.09464 3.09464i 0.0273862 0.0273862i −0.693281 0.720667i \(-0.743836\pi\)
0.720667 + 0.693281i \(0.243836\pi\)
\(114\) 0 0
\(115\) 39.4295 + 113.375i 0.342865 + 0.985866i
\(116\) 197.399 + 341.904i 1.70171 + 2.94745i
\(117\) 0 0
\(118\) −220.780 + 220.780i −1.87102 + 1.87102i
\(119\) 52.2551 62.8517i 0.439118 0.528166i
\(120\) 0 0
\(121\) −91.6240 + 158.697i −0.757223 + 1.31155i
\(122\) 42.8389 159.877i 0.351139 1.31047i
\(123\) 0 0
\(124\) −16.2217 9.36558i −0.130820 0.0755289i
\(125\) 122.023 27.1191i 0.976182 0.216953i
\(126\) 0 0
\(127\) −117.674 117.674i −0.926571 0.926571i 0.0709120 0.997483i \(-0.477409\pi\)
−0.997483 + 0.0709120i \(0.977409\pi\)
\(128\) −48.9822 182.804i −0.382673 1.42816i
\(129\) 0 0
\(130\) 94.8813 196.068i 0.729856 1.50821i
\(131\) −81.6255 + 141.379i −0.623095 + 1.07923i 0.365811 + 0.930689i \(0.380792\pi\)
−0.988906 + 0.148543i \(0.952542\pi\)
\(132\) 0 0
\(133\) 14.6005 + 20.6517i 0.109778 + 0.155276i
\(134\) 41.1905i 0.307392i
\(135\) 0 0
\(136\) −92.2820 159.837i −0.678544 1.17527i
\(137\) 38.2623 142.797i 0.279287 1.04231i −0.673627 0.739072i \(-0.735265\pi\)
0.952914 0.303241i \(-0.0980688\pi\)
\(138\) 0 0
\(139\) 101.553i 0.730596i −0.930891 0.365298i \(-0.880967\pi\)
0.930891 0.365298i \(-0.119033\pi\)
\(140\) −292.615 + 48.6335i −2.09011 + 0.347382i
\(141\) 0 0
\(142\) 229.060 61.3763i 1.61310 0.432228i
\(143\) 207.807 + 55.6818i 1.45320 + 0.389383i
\(144\) 0 0
\(145\) 16.9639 + 232.297i 0.116992 + 1.60205i
\(146\) 64.5483 0.442112
\(147\) 0 0
\(148\) −182.274 + 182.274i −1.23158 + 1.23158i
\(149\) −91.7653 52.9807i −0.615874 0.355575i 0.159387 0.987216i \(-0.449048\pi\)
−0.775261 + 0.631641i \(0.782382\pi\)
\(150\) 0 0
\(151\) 80.5845 + 139.576i 0.533672 + 0.924347i 0.999226 + 0.0393279i \(0.0125217\pi\)
−0.465554 + 0.885019i \(0.654145\pi\)
\(152\) 55.1632 14.7809i 0.362916 0.0972429i
\(153\) 0 0
\(154\) −149.334 404.574i −0.969699 2.62711i
\(155\) −6.20769 9.14233i −0.0400496 0.0589828i
\(156\) 0 0
\(157\) −35.5563 + 132.698i −0.226473 + 0.845210i 0.755336 + 0.655338i \(0.227474\pi\)
−0.981809 + 0.189872i \(0.939193\pi\)
\(158\) −76.4335 20.4803i −0.483756 0.129622i
\(159\) 0 0
\(160\) −13.3533 + 69.8460i −0.0834579 + 0.436537i
\(161\) 28.4309 165.627i 0.176589 1.02874i
\(162\) 0 0
\(163\) −48.8824 182.431i −0.299892 1.11921i −0.937254 0.348647i \(-0.886641\pi\)
0.637362 0.770564i \(-0.280025\pi\)
\(164\) −219.775 + 126.887i −1.34009 + 0.773703i
\(165\) 0 0
\(166\) 130.977 226.859i 0.789018 1.36662i
\(167\) 114.153 + 114.153i 0.683552 + 0.683552i 0.960799 0.277247i \(-0.0894220\pi\)
−0.277247 + 0.960799i \(0.589422\pi\)
\(168\) 0 0
\(169\) 16.8729i 0.0998396i
\(170\) −15.0189 205.664i −0.0883466 1.20979i
\(171\) 0 0
\(172\) −61.0406 + 227.807i −0.354887 + 1.32446i
\(173\) −53.9511 201.348i −0.311856 1.16386i −0.926881 0.375355i \(-0.877521\pi\)
0.615025 0.788508i \(-0.289146\pi\)
\(174\) 0 0
\(175\) −167.891 49.3712i −0.959379 0.282121i
\(176\) −382.468 −2.17312
\(177\) 0 0
\(178\) 174.422 + 46.7362i 0.979899 + 0.262563i
\(179\) 102.967 59.4481i 0.575235 0.332112i −0.184002 0.982926i \(-0.558905\pi\)
0.759238 + 0.650814i \(0.225572\pi\)
\(180\) 0 0
\(181\) −2.13381 −0.0117890 −0.00589449 0.999983i \(-0.501876\pi\)
−0.00589449 + 0.999983i \(0.501876\pi\)
\(182\) −249.002 + 176.041i −1.36814 + 0.967257i
\(183\) 0 0
\(184\) −328.622 189.730i −1.78599 1.03114i
\(185\) −143.639 + 49.9548i −0.776426 + 0.270026i
\(186\) 0 0
\(187\) 196.733 52.7146i 1.05205 0.281896i
\(188\) −491.066 + 491.066i −2.61205 + 2.61205i
\(189\) 0 0
\(190\) 62.6724 + 11.9818i 0.329855 + 0.0630621i
\(191\) −85.4671 + 148.033i −0.447472 + 0.775044i −0.998221 0.0596272i \(-0.981009\pi\)
0.550749 + 0.834671i \(0.314342\pi\)
\(192\) 0 0
\(193\) 80.0626 + 21.4527i 0.414832 + 0.111154i 0.460197 0.887817i \(-0.347779\pi\)
−0.0453656 + 0.998970i \(0.514445\pi\)
\(194\) −39.5825 22.8530i −0.204034 0.117799i
\(195\) 0 0
\(196\) 391.508 + 138.490i 1.99749 + 0.706582i
\(197\) −32.0391 32.0391i −0.162635 0.162635i 0.621098 0.783733i \(-0.286687\pi\)
−0.783733 + 0.621098i \(0.786687\pi\)
\(198\) 0 0
\(199\) 22.0307 12.7194i 0.110707 0.0639167i −0.443624 0.896213i \(-0.646307\pi\)
0.554331 + 0.832296i \(0.312974\pi\)
\(200\) −235.859 + 317.045i −1.17929 + 1.58522i
\(201\) 0 0
\(202\) 210.611 + 210.611i 1.04263 + 1.04263i
\(203\) 136.467 296.152i 0.672250 1.45888i
\(204\) 0 0
\(205\) −149.320 + 10.9043i −0.728390 + 0.0531918i
\(206\) 207.027 + 358.582i 1.00499 + 1.74069i
\(207\) 0 0
\(208\) 69.9973 + 261.233i 0.336525 + 1.25593i
\(209\) 63.0221i 0.301541i
\(210\) 0 0
\(211\) 139.996 0.663487 0.331744 0.943370i \(-0.392363\pi\)
0.331744 + 0.943370i \(0.392363\pi\)
\(212\) −13.8305 + 3.70587i −0.0652382 + 0.0174805i
\(213\) 0 0
\(214\) −437.148 + 252.388i −2.04275 + 1.17938i
\(215\) −90.9587 + 105.290i −0.423064 + 0.489721i
\(216\) 0 0
\(217\) 1.41824 + 15.4058i 0.00653568 + 0.0709945i
\(218\) 405.831 405.831i 1.86161 1.86161i
\(219\) 0 0
\(220\) −665.335 321.969i −3.02425 1.46350i
\(221\) −72.0102 124.725i −0.325838 0.564368i
\(222\) 0 0
\(223\) 132.643 132.643i 0.594809 0.594809i −0.344117 0.938927i \(-0.611822\pi\)
0.938927 + 0.344117i \(0.111822\pi\)
\(224\) 63.6465 76.5532i 0.284136 0.341755i
\(225\) 0 0
\(226\) −7.72888 + 13.3868i −0.0341986 + 0.0592337i
\(227\) −63.5422 + 237.143i −0.279922 + 1.04468i 0.672549 + 0.740052i \(0.265199\pi\)
−0.952471 + 0.304629i \(0.901467\pi\)
\(228\) 0 0
\(229\) 217.561 + 125.609i 0.950047 + 0.548510i 0.893096 0.449867i \(-0.148529\pi\)
0.0569516 + 0.998377i \(0.481862\pi\)
\(230\) −238.162 350.751i −1.03549 1.52501i
\(231\) 0 0
\(232\) −520.643 520.643i −2.24415 2.24415i
\(233\) 76.4808 + 285.430i 0.328244 + 1.22502i 0.911010 + 0.412383i \(0.135304\pi\)
−0.582767 + 0.812640i \(0.698030\pi\)
\(234\) 0 0
\(235\) −386.977 + 134.583i −1.64671 + 0.572695i
\(236\) 374.600 648.827i 1.58729 2.74927i
\(237\) 0 0
\(238\) −120.821 + 262.198i −0.507650 + 1.10167i
\(239\) 100.831i 0.421885i 0.977498 + 0.210943i \(0.0676533\pi\)
−0.977498 + 0.210943i \(0.932347\pi\)
\(240\) 0 0
\(241\) −179.672 311.201i −0.745527 1.29129i −0.949948 0.312408i \(-0.898865\pi\)
0.204421 0.978883i \(-0.434469\pi\)
\(242\) 167.517 625.181i 0.692217 2.58339i
\(243\) 0 0
\(244\) 397.160i 1.62770i
\(245\) 172.320 + 174.157i 0.703348 + 0.710846i
\(246\) 0 0
\(247\) 43.0453 11.5340i 0.174273 0.0466962i
\(248\) 33.7434 + 9.04153i 0.136062 + 0.0364578i
\(249\) 0 0
\(250\) −391.510 + 204.068i −1.56604 + 0.816274i
\(251\) −17.4715 −0.0696075 −0.0348038 0.999394i \(-0.511081\pi\)
−0.0348038 + 0.999394i \(0.511081\pi\)
\(252\) 0 0
\(253\) 296.100 296.100i 1.17035 1.17035i
\(254\) 509.038 + 293.893i 2.00409 + 1.15706i
\(255\) 0 0
\(256\) 259.270 + 449.070i 1.01278 + 1.75418i
\(257\) −77.1706 + 20.6778i −0.300275 + 0.0804583i −0.405811 0.913957i \(-0.633011\pi\)
0.105536 + 0.994415i \(0.466344\pi\)
\(258\) 0 0
\(259\) 209.839 + 36.0202i 0.810191 + 0.139074i
\(260\) −98.1454 + 513.362i −0.377482 + 1.97447i
\(261\) 0 0
\(262\) 149.236 556.957i 0.569604 2.12579i
\(263\) −167.452 44.8686i −0.636699 0.170603i −0.0739911 0.997259i \(-0.523574\pi\)
−0.562708 + 0.826656i \(0.690240\pi\)
\(264\) 0 0
\(265\) −8.29704 1.58624i −0.0313096 0.00598582i
\(266\) −68.6907 57.1096i −0.258236 0.214698i
\(267\) 0 0
\(268\) −25.5809 95.4694i −0.0954513 0.356229i
\(269\) 160.485 92.6559i 0.596597 0.344446i −0.171104 0.985253i \(-0.554734\pi\)
0.767702 + 0.640807i \(0.221400\pi\)
\(270\) 0 0
\(271\) −182.223 + 315.620i −0.672410 + 1.16465i 0.304808 + 0.952414i \(0.401408\pi\)
−0.977219 + 0.212235i \(0.931926\pi\)
\(272\) 181.045 + 181.045i 0.665607 + 0.665607i
\(273\) 0 0
\(274\) 522.152i 1.90567i
\(275\) −270.584 341.964i −0.983943 1.24350i
\(276\) 0 0
\(277\) 125.143 467.038i 0.451778 1.68606i −0.245613 0.969368i \(-0.578989\pi\)
0.697391 0.716691i \(-0.254344\pi\)
\(278\) 92.8347 + 346.464i 0.333938 + 1.24627i
\(279\) 0 0
\(280\) 503.659 228.856i 1.79878 0.817345i
\(281\) 472.914 1.68297 0.841484 0.540282i \(-0.181682\pi\)
0.841484 + 0.540282i \(0.181682\pi\)
\(282\) 0 0
\(283\) −239.837 64.2640i −0.847479 0.227081i −0.191154 0.981560i \(-0.561223\pi\)
−0.656324 + 0.754479i \(0.727890\pi\)
\(284\) −492.786 + 284.510i −1.73516 + 1.00180i
\(285\) 0 0
\(286\) −759.870 −2.65689
\(287\) 190.366 + 87.7205i 0.663296 + 0.305646i
\(288\) 0 0
\(289\) 132.203 + 76.3272i 0.457449 + 0.264108i
\(290\) −270.230 777.011i −0.931827 2.67935i
\(291\) 0 0
\(292\) −149.607 + 40.0871i −0.512353 + 0.137284i
\(293\) −61.1515 + 61.1515i −0.208708 + 0.208708i −0.803718 0.595010i \(-0.797148\pi\)
0.595010 + 0.803718i \(0.297148\pi\)
\(294\) 0 0
\(295\) 365.671 248.292i 1.23956 0.841669i
\(296\) 240.376 416.344i 0.812082 1.40657i
\(297\) 0 0
\(298\) 361.505 + 96.8649i 1.21310 + 0.325050i
\(299\) −256.433 148.051i −0.857634 0.495155i
\(300\) 0 0
\(301\) 182.742 67.4526i 0.607117 0.224095i
\(302\) −402.521 402.521i −1.33285 1.33285i
\(303\) 0 0
\(304\) −68.6106 + 39.6123i −0.225693 + 0.130304i
\(305\) −102.065 + 210.912i −0.334638 + 0.691514i
\(306\) 0 0
\(307\) −36.7448 36.7448i −0.119690 0.119690i 0.644725 0.764415i \(-0.276972\pi\)
−0.764415 + 0.644725i \(0.776972\pi\)
\(308\) 597.375 + 844.961i 1.93953 + 2.74338i
\(309\) 0 0
\(310\) 29.5360 + 25.5158i 0.0952775 + 0.0823089i
\(311\) 44.4761 + 77.0348i 0.143010 + 0.247700i 0.928629 0.371010i \(-0.120989\pi\)
−0.785619 + 0.618711i \(0.787655\pi\)
\(312\) 0 0
\(313\) 47.5609 + 177.500i 0.151952 + 0.567092i 0.999347 + 0.0361293i \(0.0115028\pi\)
−0.847395 + 0.530962i \(0.821831\pi\)
\(314\) 485.224i 1.54530i
\(315\) 0 0
\(316\) 189.873 0.600864
\(317\) 356.038 95.4002i 1.12315 0.300947i 0.350992 0.936378i \(-0.385844\pi\)
0.772157 + 0.635431i \(0.219178\pi\)
\(318\) 0 0
\(319\) 703.676 406.268i 2.20588 1.27357i
\(320\) 13.6472 + 186.880i 0.0426475 + 0.583999i
\(321\) 0 0
\(322\) 54.4118 + 591.054i 0.168981 + 1.83557i
\(323\) 29.8321 29.8321i 0.0923596 0.0923596i
\(324\) 0 0
\(325\) −184.047 + 247.399i −0.566298 + 0.761227i
\(326\) 333.540 + 577.709i 1.02313 + 1.77211i
\(327\) 0 0
\(328\) 334.668 334.668i 1.02033 1.02033i
\(329\) 565.329 + 97.0420i 1.71832 + 0.294961i
\(330\) 0 0
\(331\) 224.992 389.697i 0.679734 1.17733i −0.295327 0.955396i \(-0.595429\pi\)
0.975061 0.221937i \(-0.0712381\pi\)
\(332\) −162.684 + 607.145i −0.490012 + 1.82875i
\(333\) 0 0
\(334\) −493.805 285.099i −1.47846 0.853589i
\(335\) 10.9495 57.2729i 0.0326852 0.170964i
\(336\) 0 0
\(337\) −9.37231 9.37231i −0.0278110 0.0278110i 0.693065 0.720876i \(-0.256260\pi\)
−0.720876 + 0.693065i \(0.756260\pi\)
\(338\) −15.4244 57.5646i −0.0456343 0.170309i
\(339\) 0 0
\(340\) 162.536 + 467.350i 0.478046 + 1.37456i
\(341\) −19.2754 + 33.3859i −0.0565260 + 0.0979060i
\(342\) 0 0
\(343\) −93.2729 330.074i −0.271933 0.962316i
\(344\) 439.849i 1.27863i
\(345\) 0 0
\(346\) 368.126 + 637.613i 1.06395 + 1.84281i
\(347\) 101.459 378.650i 0.292389 1.09121i −0.650880 0.759180i \(-0.725600\pi\)
0.943269 0.332029i \(-0.107733\pi\)
\(348\) 0 0
\(349\) 480.726i 1.37744i 0.725028 + 0.688720i \(0.241827\pi\)
−0.725028 + 0.688720i \(0.758173\pi\)
\(350\) 617.921 + 14.9596i 1.76549 + 0.0427416i
\(351\) 0 0
\(352\) 239.621 64.2062i 0.680741 0.182404i
\(353\) −535.395 143.459i −1.51670 0.406398i −0.598045 0.801462i \(-0.704056\pi\)
−0.918654 + 0.395064i \(0.870722\pi\)
\(354\) 0 0
\(355\) −334.809 + 24.4500i −0.943125 + 0.0688732i
\(356\) −433.292 −1.21711
\(357\) 0 0
\(358\) −296.944 + 296.944i −0.829454 + 0.829454i
\(359\) 87.7247 + 50.6479i 0.244359 + 0.141080i 0.617178 0.786823i \(-0.288276\pi\)
−0.372820 + 0.927904i \(0.621609\pi\)
\(360\) 0 0
\(361\) −173.973 301.330i −0.481919 0.834708i
\(362\) 7.27983 1.95062i 0.0201100 0.00538846i
\(363\) 0 0
\(364\) 467.797 562.659i 1.28516 1.54577i
\(365\) −89.7506 17.1587i −0.245892 0.0470100i
\(366\) 0 0
\(367\) −78.8661 + 294.332i −0.214894 + 0.801996i 0.771310 + 0.636460i \(0.219602\pi\)
−0.986204 + 0.165536i \(0.947065\pi\)
\(368\) 508.469 + 136.244i 1.38171 + 0.370228i
\(369\) 0 0
\(370\) 444.381 301.737i 1.20103 0.815505i
\(371\) 9.09379 + 7.56061i 0.0245116 + 0.0203790i
\(372\) 0 0
\(373\) 27.7530 + 103.576i 0.0744048 + 0.277682i 0.993098 0.117290i \(-0.0374208\pi\)
−0.918693 + 0.394973i \(0.870754\pi\)
\(374\) −622.999 + 359.689i −1.66577 + 0.961734i
\(375\) 0 0
\(376\) 647.598 1121.67i 1.72234 2.98317i
\(377\) −406.272 406.272i −1.07764 1.07764i
\(378\) 0 0
\(379\) 0 5.00789e-5i 0 1.32134e-7i 1.00000 6.60672e-8i \(2.10298e-8\pi\)
−1.00000 6.60672e-8i \(1.00000\pi\)
\(380\) −152.700 + 11.1512i −0.401843 + 0.0293452i
\(381\) 0 0
\(382\) 156.260 583.170i 0.409057 1.52662i
\(383\) −48.7638 181.989i −0.127321 0.475167i 0.872591 0.488451i \(-0.162438\pi\)
−0.999912 + 0.0132843i \(0.995771\pi\)
\(384\) 0 0
\(385\) 100.093 + 602.234i 0.259982 + 1.56424i
\(386\) −292.757 −0.758439
\(387\) 0 0
\(388\) 105.935 + 28.3852i 0.273029 + 0.0731578i
\(389\) −182.547 + 105.394i −0.469273 + 0.270935i −0.715935 0.698166i \(-0.754000\pi\)
0.246662 + 0.969102i \(0.420666\pi\)
\(390\) 0 0
\(391\) −280.324 −0.716940
\(392\) −772.135 60.5035i −1.96973 0.154346i
\(393\) 0 0
\(394\) 138.595 + 80.0181i 0.351765 + 0.203092i
\(395\) 100.832 + 48.7947i 0.255271 + 0.123531i
\(396\) 0 0
\(397\) −242.295 + 64.9229i −0.610316 + 0.163534i −0.550722 0.834689i \(-0.685647\pi\)
−0.0595944 + 0.998223i \(0.518981\pi\)
\(398\) −63.5338 + 63.5338i −0.159633 + 0.159633i
\(399\) 0 0
\(400\) 202.212 509.519i 0.505530 1.27380i
\(401\) −172.876 + 299.430i −0.431113 + 0.746709i −0.996969 0.0777947i \(-0.975212\pi\)
0.565857 + 0.824503i \(0.308545\pi\)
\(402\) 0 0
\(403\) 26.3309 + 7.05535i 0.0653373 + 0.0175071i
\(404\) −618.942 357.346i −1.53203 0.884520i
\(405\) 0 0
\(406\) −194.851 + 1135.12i −0.479928 + 2.79587i
\(407\) 375.141 + 375.141i 0.921721 + 0.921721i
\(408\) 0 0
\(409\) −98.4923 + 56.8646i −0.240812 + 0.139033i −0.615550 0.788098i \(-0.711066\pi\)
0.374738 + 0.927131i \(0.377733\pi\)
\(410\) 499.461 173.703i 1.21820 0.423666i
\(411\) 0 0
\(412\) −702.532 702.532i −1.70518 1.70518i
\(413\) −616.195 + 56.7263i −1.49200 + 0.137352i
\(414\) 0 0
\(415\) −242.421 + 280.617i −0.584147 + 0.676185i
\(416\) −87.7081 151.915i −0.210837 0.365180i
\(417\) 0 0
\(418\) −57.6118 215.010i −0.137827 0.514378i
\(419\) 220.394i 0.526000i 0.964796 + 0.263000i \(0.0847120\pi\)
−0.964796 + 0.263000i \(0.915288\pi\)
\(420\) 0 0
\(421\) −611.981 −1.45364 −0.726818 0.686830i \(-0.759002\pi\)
−0.726818 + 0.686830i \(0.759002\pi\)
\(422\) −477.618 + 127.977i −1.13180 + 0.303264i
\(423\) 0 0
\(424\) 23.1263 13.3520i 0.0545431 0.0314905i
\(425\) −33.7880 + 289.956i −0.0795012 + 0.682249i
\(426\) 0 0
\(427\) 267.853 189.368i 0.627291 0.443486i
\(428\) 856.459 856.459i 2.00107 2.00107i
\(429\) 0 0
\(430\) 214.069 442.364i 0.497835 1.02875i
\(431\) −362.392 627.681i −0.840816 1.45634i −0.889206 0.457508i \(-0.848742\pi\)
0.0483893 0.998829i \(-0.484591\pi\)
\(432\) 0 0
\(433\) −152.433 + 152.433i −0.352038 + 0.352038i −0.860867 0.508829i \(-0.830078\pi\)
0.508829 + 0.860867i \(0.330078\pi\)
\(434\) −18.9218 51.2629i −0.0435987 0.118117i
\(435\) 0 0
\(436\) −688.579 + 1192.65i −1.57931 + 2.73545i
\(437\) 22.4499 83.7842i 0.0513728 0.191726i
\(438\) 0 0
\(439\) −719.426 415.361i −1.63878 0.946152i −0.981253 0.192723i \(-0.938268\pi\)
−0.657530 0.753428i \(-0.728399\pi\)
\(440\) 1353.99 + 258.858i 3.07725 + 0.588313i
\(441\) 0 0
\(442\) 359.692 + 359.692i 0.813783 + 0.813783i
\(443\) 86.1258 + 321.426i 0.194415 + 0.725566i 0.992418 + 0.122912i \(0.0392234\pi\)
−0.798003 + 0.602654i \(0.794110\pi\)
\(444\) 0 0
\(445\) −230.100 111.350i −0.517078 0.250225i
\(446\) −331.276 + 573.787i −0.742771 + 1.28652i
\(447\) 0 0
\(448\) 109.786 238.250i 0.245057 0.531809i
\(449\) 20.5616i 0.0457943i −0.999738 0.0228971i \(-0.992711\pi\)
0.999738 0.0228971i \(-0.00728902\pi\)
\(450\) 0 0
\(451\) 261.148 + 452.321i 0.579042 + 1.00293i
\(452\) 9.59989 35.8273i 0.0212387 0.0792639i
\(453\) 0 0
\(454\) 867.138i 1.91000i
\(455\) 393.019 178.583i 0.863778 0.392490i
\(456\) 0 0
\(457\) 521.445 139.721i 1.14102 0.305734i 0.361657 0.932311i \(-0.382211\pi\)
0.779360 + 0.626577i \(0.215545\pi\)
\(458\) −857.070 229.651i −1.87133 0.501422i
\(459\) 0 0
\(460\) 769.831 + 665.047i 1.67355 + 1.44575i
\(461\) −650.544 −1.41116 −0.705579 0.708632i \(-0.749313\pi\)
−0.705579 + 0.708632i \(0.749313\pi\)
\(462\) 0 0
\(463\) 229.971 229.971i 0.496697 0.496697i −0.413711 0.910408i \(-0.635768\pi\)
0.910408 + 0.413711i \(0.135768\pi\)
\(464\) 884.587 + 510.717i 1.90644 + 1.10068i
\(465\) 0 0
\(466\) −521.854 903.877i −1.11986 1.93965i
\(467\) −564.037 + 151.133i −1.20779 + 0.323626i −0.805894 0.592060i \(-0.798315\pi\)
−0.401895 + 0.915686i \(0.631648\pi\)
\(468\) 0 0
\(469\) −52.1895 + 62.7728i −0.111278 + 0.133844i
\(470\) 1197.21 812.909i 2.54725 1.72959i
\(471\) 0 0
\(472\) −361.639 + 1349.66i −0.766184 + 2.85944i
\(473\) 468.851 + 125.628i 0.991228 + 0.265599i
\(474\) 0 0
\(475\) −83.9571 33.3200i −0.176752 0.0701473i
\(476\) 117.197 682.744i 0.246212 1.43434i
\(477\) 0 0
\(478\) −92.1745 344.000i −0.192834 0.719665i
\(479\) −255.740 + 147.651i −0.533904 + 0.308249i −0.742605 0.669730i \(-0.766410\pi\)
0.208701 + 0.977980i \(0.433076\pi\)
\(480\) 0 0
\(481\) 187.572 324.885i 0.389963 0.675436i
\(482\) 897.465 + 897.465i 1.86196 + 1.86196i
\(483\) 0 0
\(484\) 1553.05i 3.20878i
\(485\) 48.9622 + 42.2978i 0.100953 + 0.0872120i
\(486\) 0 0
\(487\) −8.56814 + 31.9767i −0.0175937 + 0.0656606i −0.974165 0.225839i \(-0.927488\pi\)
0.956571 + 0.291500i \(0.0941543\pi\)
\(488\) −191.709 715.468i −0.392846 1.46612i
\(489\) 0 0
\(490\) −747.105 436.639i −1.52470 0.891099i
\(491\) −602.433 −1.22695 −0.613476 0.789713i \(-0.710229\pi\)
−0.613476 + 0.789713i \(0.710229\pi\)
\(492\) 0 0
\(493\) −525.403 140.781i −1.06573 0.285561i
\(494\) −136.312 + 78.7000i −0.275936 + 0.159312i
\(495\) 0 0
\(496\) −48.4619 −0.0977055
\(497\) 426.844 + 196.689i 0.858841 + 0.395754i
\(498\) 0 0
\(499\) 712.187 + 411.181i 1.42723 + 0.824010i 0.996901 0.0786631i \(-0.0250651\pi\)
0.430326 + 0.902673i \(0.358398\pi\)
\(500\) 780.688 716.123i 1.56138 1.43225i
\(501\) 0 0
\(502\) 59.6068 15.9716i 0.118739 0.0318159i
\(503\) 494.995 494.995i 0.984086 0.984086i −0.0157893 0.999875i \(-0.505026\pi\)
0.999875 + 0.0157893i \(0.00502609\pi\)
\(504\) 0 0
\(505\) −236.856 348.828i −0.469022 0.690749i
\(506\) −739.512 + 1280.87i −1.46149 + 2.53137i
\(507\) 0 0
\(508\) −1362.34 365.039i −2.68178 0.718580i
\(509\) 503.114 + 290.473i 0.988437 + 0.570674i 0.904807 0.425823i \(-0.140015\pi\)
0.0836299 + 0.996497i \(0.473349\pi\)
\(510\) 0 0
\(511\) 98.3692 + 81.7844i 0.192503 + 0.160048i
\(512\) −759.774 759.774i −1.48393 1.48393i
\(513\) 0 0
\(514\) 244.377 141.091i 0.475442 0.274497i
\(515\) −192.539 553.621i −0.373861 1.07499i
\(516\) 0 0
\(517\) 1010.67 + 1010.67i 1.95487 + 1.95487i
\(518\) −748.829 + 68.9365i −1.44562 + 0.133082i
\(519\) 0 0
\(520\) −70.9947 972.176i −0.136528 1.86957i
\(521\) 274.035 + 474.643i 0.525979 + 0.911023i 0.999542 + 0.0302629i \(0.00963445\pi\)
−0.473563 + 0.880760i \(0.657032\pi\)
\(522\) 0 0
\(523\) 60.8889 + 227.240i 0.116422 + 0.434494i 0.999389 0.0349409i \(-0.0111243\pi\)
−0.882967 + 0.469435i \(0.844458\pi\)
\(524\) 1383.57i 2.64040i
\(525\) 0 0
\(526\) 612.306 1.16408
\(527\) 24.9278 6.67937i 0.0473013 0.0126743i
\(528\) 0 0
\(529\) −40.9971 + 23.6697i −0.0774992 + 0.0447442i
\(530\) 29.7568 2.17304i 0.0561449 0.00410007i
\(531\) 0 0
\(532\) 194.675 + 89.7064i 0.365931 + 0.168621i
\(533\) 261.151 261.151i 0.489964 0.489964i
\(534\) 0 0
\(535\) 674.921 234.725i 1.26153 0.438737i
\(536\) 92.1661 + 159.636i 0.171952 + 0.297829i
\(537\) 0 0
\(538\) −462.818 + 462.818i −0.860256 + 0.860256i
\(539\) 285.028 805.766i 0.528808 1.49493i
\(540\) 0 0
\(541\) 261.735 453.339i 0.483799 0.837965i −0.516028 0.856572i \(-0.672590\pi\)
0.999827 + 0.0186072i \(0.00592319\pi\)
\(542\) 333.159 1243.37i 0.614685 2.29404i
\(543\) 0 0
\(544\) −143.819 83.0342i −0.264374 0.152636i
\(545\) −672.165 + 456.404i −1.23333 + 0.837438i
\(546\) 0 0
\(547\) −201.681 201.681i −0.368703 0.368703i 0.498301 0.867004i \(-0.333958\pi\)
−0.867004 + 0.498301i \(0.833958\pi\)
\(548\) −324.277 1210.22i −0.591747 2.20843i
\(549\) 0 0
\(550\) 1235.75 + 919.309i 2.24682 + 1.67147i
\(551\) 84.1545 145.760i 0.152731 0.264537i
\(552\) 0 0
\(553\) −90.5327 128.054i −0.163712 0.231563i
\(554\) 1707.78i 3.08263i
\(555\) 0 0
\(556\) −430.336 745.364i −0.773985 1.34058i
\(557\) −178.472 + 666.065i −0.320416 + 1.19581i 0.598425 + 0.801179i \(0.295793\pi\)
−0.918841 + 0.394629i \(0.870873\pi\)
\(558\) 0 0
\(559\) 343.226i 0.614000i
\(560\) −592.723 + 487.501i −1.05843 + 0.870537i
\(561\) 0 0
\(562\) −1613.42 + 432.315i −2.87086 + 0.769244i
\(563\) 739.166 + 198.059i 1.31291 + 0.351792i 0.846315 0.532682i \(-0.178816\pi\)
0.466590 + 0.884474i \(0.345483\pi\)
\(564\) 0 0
\(565\) 14.3051 16.5590i 0.0253188 0.0293080i
\(566\) 876.988 1.54945
\(567\) 0 0
\(568\) 750.402 750.402i 1.32113 1.32113i
\(569\) 116.121 + 67.0425i 0.204079 + 0.117825i 0.598557 0.801080i \(-0.295741\pi\)
−0.394478 + 0.918906i \(0.629074\pi\)
\(570\) 0 0
\(571\) −286.520 496.267i −0.501786 0.869119i −0.999998 0.00206333i \(-0.999343\pi\)
0.498212 0.867055i \(-0.333990\pi\)
\(572\) 1761.19 471.910i 3.07901 0.825017i
\(573\) 0 0
\(574\) −729.654 125.249i −1.27117 0.218205i
\(575\) 237.911 + 551.009i 0.413758 + 0.958276i
\(576\) 0 0
\(577\) −178.653 + 666.742i −0.309624 + 1.15553i 0.619268 + 0.785180i \(0.287430\pi\)
−0.928891 + 0.370352i \(0.879237\pi\)
\(578\) −520.805 139.549i −0.901048 0.241435i
\(579\) 0 0
\(580\) 1108.88 + 1633.10i 1.91186 + 2.81568i
\(581\) 487.040 179.773i 0.838280 0.309420i
\(582\) 0 0
\(583\) 7.62709 + 28.4647i 0.0130825 + 0.0488245i
\(584\) 250.161 144.430i 0.428358 0.247312i
\(585\) 0 0
\(586\) 152.726 264.530i 0.260625 0.451416i
\(587\) −688.633 688.633i −1.17314 1.17314i −0.981457 0.191682i \(-0.938606\pi\)
−0.191682 0.981457i \(-0.561394\pi\)
\(588\) 0 0
\(589\) 7.98542i 0.0135576i
\(590\) −1020.57 + 1181.37i −1.72978 + 2.00232i
\(591\) 0 0
\(592\) −172.613 + 644.199i −0.291576 + 1.08817i
\(593\) 100.681 + 375.748i 0.169783 + 0.633640i 0.997382 + 0.0723188i \(0.0230399\pi\)
−0.827598 + 0.561321i \(0.810293\pi\)
\(594\) 0 0
\(595\) 237.693 332.453i 0.399484 0.558745i
\(596\) −898.035 −1.50677
\(597\) 0 0
\(598\) 1010.20 + 270.683i 1.68930 + 0.452647i
\(599\) −223.139 + 128.830i −0.372520 + 0.215074i −0.674559 0.738221i \(-0.735666\pi\)
0.302039 + 0.953296i \(0.402333\pi\)
\(600\) 0 0
\(601\) 91.8404 0.152813 0.0764064 0.997077i \(-0.475655\pi\)
0.0764064 + 0.997077i \(0.475655\pi\)
\(602\) −561.793 + 397.180i −0.933211 + 0.659767i
\(603\) 0 0
\(604\) 1182.93 + 682.963i 1.95849 + 1.13073i
\(605\) −399.112 + 824.746i −0.659689 + 1.36322i
\(606\) 0 0
\(607\) 759.412 203.484i 1.25109 0.335229i 0.428333 0.903621i \(-0.359101\pi\)
0.822757 + 0.568393i \(0.192435\pi\)
\(608\) 36.3355 36.3355i 0.0597623 0.0597623i
\(609\) 0 0
\(610\) 155.404 812.862i 0.254761 1.33256i
\(611\) 505.338 875.272i 0.827068 1.43252i
\(612\) 0 0
\(613\) 407.928 + 109.304i 0.665461 + 0.178310i 0.575709 0.817654i \(-0.304726\pi\)
0.0897518 + 0.995964i \(0.471393\pi\)
\(614\) 158.951 + 91.7706i 0.258878 + 0.149464i
\(615\) 0 0
\(616\) −1484.01 1233.81i −2.40911 2.00294i
\(617\) −174.640 174.640i −0.283047 0.283047i 0.551276 0.834323i \(-0.314141\pi\)
−0.834323 + 0.551276i \(0.814141\pi\)
\(618\) 0 0
\(619\) 408.198 235.673i 0.659448 0.380732i −0.132619 0.991167i \(-0.542339\pi\)
0.792066 + 0.610435i \(0.209005\pi\)
\(620\) −84.3035 40.7962i −0.135973 0.0658003i
\(621\) 0 0
\(622\) −222.159 222.159i −0.357169 0.357169i
\(623\) 206.597 + 292.222i 0.331616 + 0.469056i
\(624\) 0 0
\(625\) 598.618 179.671i 0.957788 0.287474i
\(626\) −324.524 562.091i −0.518408 0.897909i
\(627\) 0 0
\(628\) 301.344 + 1124.63i 0.479847 + 1.79081i
\(629\) 355.153i 0.564631i
\(630\) 0 0
\(631\) −670.413 −1.06246 −0.531230 0.847227i \(-0.678270\pi\)
−0.531230 + 0.847227i \(0.678270\pi\)
\(632\) −342.049 + 91.6516i −0.541216 + 0.145018i
\(633\) 0 0
\(634\) −1127.47 + 650.947i −1.77835 + 1.02673i
\(635\) −629.662 543.957i −0.991594 0.856625i
\(636\) 0 0
\(637\) −602.518 47.2125i −0.945868 0.0741170i
\(638\) −2029.32 + 2029.32i −3.18075 + 3.18075i
\(639\) 0 0
\(640\) −310.831 893.755i −0.485673 1.39649i
\(641\) −617.665 1069.83i −0.963596 1.66900i −0.713341 0.700818i \(-0.752819\pi\)
−0.250256 0.968180i \(-0.580515\pi\)
\(642\) 0 0
\(643\) −504.796 + 504.796i −0.785064 + 0.785064i −0.980680 0.195617i \(-0.937329\pi\)
0.195617 + 0.980680i \(0.437329\pi\)
\(644\) −493.181 1336.12i −0.765809 2.07473i
\(645\) 0 0
\(646\) −74.5061 + 129.048i −0.115334 + 0.199765i
\(647\) −27.8251 + 103.845i −0.0430064 + 0.160502i −0.984090 0.177673i \(-0.943143\pi\)
0.941083 + 0.338175i \(0.109810\pi\)
\(648\) 0 0
\(649\) −1335.36 770.968i −2.05756 1.18793i
\(650\) 401.746 1012.29i 0.618071 1.55737i
\(651\) 0 0
\(652\) −1131.84 1131.84i −1.73596 1.73596i
\(653\) −79.6877 297.399i −0.122033 0.455434i 0.877683 0.479241i \(-0.159088\pi\)
−0.999717 + 0.0238067i \(0.992421\pi\)
\(654\) 0 0
\(655\) −355.558 + 734.745i −0.542837 + 1.12175i
\(656\) −328.287 + 568.610i −0.500438 + 0.866784i
\(657\) 0 0
\(658\) −2017.42 + 185.722i −3.06599 + 0.282252i
\(659\) 590.013i 0.895315i −0.894205 0.447658i \(-0.852258\pi\)
0.894205 0.447658i \(-0.147742\pi\)
\(660\) 0 0
\(661\) −1.19346 2.06714i −0.00180554 0.00312729i 0.865121 0.501563i \(-0.167241\pi\)
−0.866927 + 0.498436i \(0.833908\pi\)
\(662\) −411.354 + 1535.19i −0.621380 + 2.31902i
\(663\) 0 0
\(664\) 1172.27i 1.76547i
\(665\) 80.3291 + 97.6674i 0.120796 + 0.146868i
\(666\) 0 0
\(667\) −1080.22 + 289.444i −1.61952 + 0.433948i
\(668\) 1321.58 + 354.115i 1.97841 + 0.530113i
\(669\) 0 0
\(670\) 15.0001 + 205.405i 0.0223882 + 0.306575i
\(671\) 817.398 1.21818
\(672\) 0 0
\(673\) −50.3354 + 50.3354i −0.0747925 + 0.0747925i −0.743513 0.668721i \(-0.766842\pi\)
0.668721 + 0.743513i \(0.266842\pi\)
\(674\) 40.5429 + 23.4075i 0.0601527 + 0.0347292i
\(675\) 0 0
\(676\) 71.4998 + 123.841i 0.105769 + 0.183197i
\(677\) 500.800 134.189i 0.739734 0.198211i 0.130774 0.991412i \(-0.458254\pi\)
0.608960 + 0.793201i \(0.291587\pi\)
\(678\) 0 0
\(679\) −31.3670 84.9793i −0.0461958 0.125154i
\(680\) −518.391 763.457i −0.762340 1.12273i
\(681\) 0 0
\(682\) 35.2413 131.522i 0.0516734 0.192848i
\(683\) 97.0866 + 26.0143i 0.142147 + 0.0380883i 0.329191 0.944263i \(-0.393224\pi\)
−0.187044 + 0.982352i \(0.559891\pi\)
\(684\) 0 0
\(685\) 138.802 726.022i 0.202631 1.05989i
\(686\) 619.954 + 1040.84i 0.903723 + 1.51726i
\(687\) 0 0
\(688\) 157.926 + 589.389i 0.229544 + 0.856670i
\(689\) 18.0461 10.4189i 0.0261917 0.0151218i
\(690\) 0 0
\(691\) 0.723424 1.25301i 0.00104692 0.00181332i −0.865501 0.500906i \(-0.833000\pi\)
0.866548 + 0.499093i \(0.166333\pi\)
\(692\) −1249.21 1249.21i −1.80521 1.80521i
\(693\) 0 0
\(694\) 1384.57i 1.99506i
\(695\) −36.9818 506.416i −0.0532112 0.728655i
\(696\) 0 0
\(697\) 90.4939 337.728i 0.129833 0.484545i
\(698\) −439.457 1640.08i −0.629595 2.34968i
\(699\) 0 0
\(700\) −1441.48 + 349.081i −2.05926 + 0.498687i
\(701\) 230.081 0.328218 0.164109 0.986442i \(-0.447525\pi\)
0.164109 + 0.986442i \(0.447525\pi\)
\(702\) 0 0
\(703\) 106.149 + 28.4427i 0.150995 + 0.0404590i
\(704\) 566.098 326.837i 0.804117 0.464257i
\(705\) 0 0
\(706\) 1957.73 2.77299
\(707\) 54.1135 + 587.813i 0.0765396 + 0.831419i
\(708\) 0 0
\(709\) 383.431 + 221.374i 0.540805 + 0.312234i 0.745405 0.666612i \(-0.232256\pi\)
−0.204600 + 0.978846i \(0.565589\pi\)
\(710\) 1119.91 389.482i 1.57733 0.548566i
\(711\) 0 0
\(712\) 780.559 209.150i 1.09629 0.293750i
\(713\) 37.5183 37.5183i 0.0526203 0.0526203i
\(714\) 0 0
\(715\) 1056.55 + 201.994i 1.47770 + 0.282509i
\(716\) 503.829 872.658i 0.703672 1.21880i
\(717\) 0 0
\(718\) −345.587 92.5998i −0.481319 0.128969i
\(719\) 446.525 + 257.801i 0.621036 + 0.358555i 0.777272 0.629164i \(-0.216603\pi\)
−0.156236 + 0.987720i \(0.549936\pi\)
\(720\) 0 0
\(721\) −138.831 + 808.775i −0.192553 + 1.12174i
\(722\) 868.998 + 868.998i 1.20360 + 1.20360i
\(723\) 0 0
\(724\) −15.6614 + 9.04213i −0.0216318 + 0.0124891i
\(725\) 169.188 + 1152.22i 0.233363 + 1.58927i
\(726\) 0 0
\(727\) −829.146 829.146i −1.14050 1.14050i −0.988358 0.152145i \(-0.951382\pi\)
−0.152145 0.988358i \(-0.548618\pi\)
\(728\) −571.121 + 1239.41i −0.784507 + 1.70249i
\(729\) 0 0
\(730\) 321.884 23.5061i 0.440937 0.0322001i
\(731\) −162.468 281.402i −0.222254 0.384956i
\(732\) 0 0
\(733\) 266.886 + 996.034i 0.364102 + 1.35885i 0.868635 + 0.495453i \(0.164998\pi\)
−0.504533 + 0.863392i \(0.668335\pi\)
\(734\) 1076.26i 1.46629i
\(735\) 0 0
\(736\) −341.433 −0.463904
\(737\) −196.486 + 52.6484i −0.266603 + 0.0714360i
\(738\) 0 0
\(739\) −287.660 + 166.081i −0.389256 + 0.224737i −0.681838 0.731503i \(-0.738819\pi\)
0.292582 + 0.956241i \(0.405486\pi\)
\(740\) −842.574 + 975.329i −1.13861 + 1.31801i
\(741\) 0 0
\(742\) −37.9365 17.4811i −0.0511274 0.0235595i
\(743\) 764.980 764.980i 1.02958 1.02958i 0.0300340 0.999549i \(-0.490438\pi\)
0.999549 0.0300340i \(-0.00956155\pi\)
\(744\) 0 0
\(745\) −476.902 230.783i −0.640136 0.309775i
\(746\) −189.368 327.994i −0.253844 0.439671i
\(747\) 0 0
\(748\) 1220.58 1220.58i 1.63179 1.63179i
\(749\) −985.980 169.249i −1.31640 0.225967i
\(750\) 0 0
\(751\) −66.3561 + 114.932i −0.0883570 + 0.153039i −0.906817 0.421525i \(-0.861495\pi\)
0.818460 + 0.574564i \(0.194828\pi\)
\(752\) −465.036 + 1735.54i −0.618399 + 2.30790i
\(753\) 0 0
\(754\) 1757.46 + 1014.67i 2.33084 + 1.34571i
\(755\) 452.681 + 666.683i 0.599577 + 0.883024i
\(756\) 0 0
\(757\) 705.876 + 705.876i 0.932465 + 0.932465i 0.997859 0.0653945i \(-0.0208306\pi\)
−0.0653945 + 0.997859i \(0.520831\pi\)
\(758\) −4.57797e−5 0 0.000170852i −6.03954e−8 0 2.25399e-7i
\(759\) 0 0
\(760\) 269.701 93.7968i 0.354869 0.123417i
\(761\) 21.9538 38.0250i 0.0288486 0.0499672i −0.851241 0.524776i \(-0.824149\pi\)
0.880089 + 0.474808i \(0.157483\pi\)
\(762\) 0 0
\(763\) 1132.67 104.273i 1.48450 0.136661i
\(764\) 1448.69i 1.89619i
\(765\) 0 0
\(766\) 332.731 + 576.308i 0.434375 + 0.752360i
\(767\) −282.197 + 1053.17i −0.367923 + 1.37311i
\(768\) 0 0
\(769\) 317.954i 0.413464i 0.978398 + 0.206732i \(0.0662829\pi\)
−0.978398 + 0.206732i \(0.933717\pi\)
\(770\) −892.017 1963.12i −1.15846 2.54950i
\(771\) 0 0
\(772\) 678.539 181.814i 0.878937 0.235510i
\(773\) 681.538 + 182.617i 0.881679 + 0.236245i 0.671131 0.741339i \(-0.265809\pi\)
0.210547 + 0.977584i \(0.432475\pi\)
\(774\) 0 0
\(775\) −34.2853 43.3296i −0.0442391 0.0559092i