Properties

Label 432.2.be.b.335.2
Level $432$
Weight $2$
Character 432.335
Analytic conductor $3.450$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.be (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 335.2
Character \(\chi\) \(=\) 432.335
Dual form 432.2.be.b.383.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.35972 - 1.07292i) q^{3} +(1.16481 - 3.20030i) q^{5} +(4.32834 + 0.763203i) q^{7} +(0.697681 + 2.91775i) q^{9} +O(q^{10})\) \(q+(-1.35972 - 1.07292i) q^{3} +(1.16481 - 3.20030i) q^{5} +(4.32834 + 0.763203i) q^{7} +(0.697681 + 2.91775i) q^{9} +(-3.88970 + 1.41573i) q^{11} +(4.63966 - 3.89314i) q^{13} +(-5.01749 + 3.10176i) q^{15} +(0.945866 - 0.546096i) q^{17} +(-2.45107 - 1.41513i) q^{19} +(-5.06647 - 5.68171i) q^{21} +(-0.327067 - 1.85489i) q^{23} +(-5.05492 - 4.24158i) q^{25} +(2.18186 - 4.71588i) q^{27} +(-3.45728 + 4.12023i) q^{29} +(1.52041 - 0.268090i) q^{31} +(6.80787 + 2.24833i) q^{33} +(7.48419 - 12.9630i) q^{35} +(-2.48926 - 4.31152i) q^{37} +(-10.4857 + 0.315590i) q^{39} +(-3.29698 - 3.92918i) q^{41} +(1.43112 + 3.93198i) q^{43} +(10.1503 + 1.16584i) q^{45} +(1.51654 - 8.60072i) q^{47} +(11.5742 + 4.21266i) q^{49} +(-1.87203 - 0.272302i) q^{51} +12.1741i q^{53} +14.0973i q^{55} +(1.81445 + 4.55398i) q^{57} +(3.09392 + 1.12609i) q^{59} +(-0.463630 + 2.62938i) q^{61} +(0.792966 + 13.1615i) q^{63} +(-7.05488 - 19.3831i) q^{65} +(2.32819 + 2.77463i) q^{67} +(-1.54543 + 2.87305i) q^{69} +(-0.842160 - 1.45866i) q^{71} +(-5.58205 + 9.66839i) q^{73} +(2.32240 + 11.1909i) q^{75} +(-17.9164 + 3.15915i) q^{77} +(-6.26169 + 7.46239i) q^{79} +(-8.02648 + 4.07131i) q^{81} +(-0.240134 - 0.201496i) q^{83} +(-0.645914 - 3.66316i) q^{85} +(9.12161 - 1.89297i) q^{87} +(6.60573 + 3.81382i) q^{89} +(23.0533 - 13.3098i) q^{91} +(-2.35498 - 1.26676i) q^{93} +(-7.38387 + 6.19580i) q^{95} +(0.903887 - 0.328988i) q^{97} +(-6.84452 - 10.3614i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{13}{18}\right)\)

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
\(3\) −1.35972 1.07292i −0.785035 0.619451i
\(4\) 0 0
\(5\) 1.16481 3.20030i 0.520921 1.43122i −0.348576 0.937281i \(-0.613335\pi\)
0.869497 0.493938i \(-0.164443\pi\)
\(6\) 0 0
\(7\) 4.32834 + 0.763203i 1.63596 + 0.288464i 0.914679 0.404181i \(-0.132443\pi\)
0.721279 + 0.692645i \(0.243555\pi\)
\(8\) 0 0
\(9\) 0.697681 + 2.91775i 0.232560 + 0.972582i
\(10\) 0 0
\(11\) −3.88970 + 1.41573i −1.17279 + 0.426860i −0.853649 0.520849i \(-0.825616\pi\)
−0.319138 + 0.947708i \(0.603393\pi\)
\(12\) 0 0
\(13\) 4.63966 3.89314i 1.28681 1.07976i 0.294545 0.955638i \(-0.404832\pi\)
0.992267 0.124125i \(-0.0396124\pi\)
\(14\) 0 0
\(15\) −5.01749 + 3.10176i −1.29551 + 0.800872i
\(16\) 0 0
\(17\) 0.945866 0.546096i 0.229406 0.132448i −0.380892 0.924620i \(-0.624383\pi\)
0.610298 + 0.792172i \(0.291050\pi\)
\(18\) 0 0
\(19\) −2.45107 1.41513i −0.562314 0.324652i 0.191760 0.981442i \(-0.438581\pi\)
−0.754074 + 0.656790i \(0.771914\pi\)
\(20\) 0 0
\(21\) −5.06647 5.68171i −1.10560 1.23985i
\(22\) 0 0
\(23\) −0.327067 1.85489i −0.0681982 0.386771i −0.999733 0.0231182i \(-0.992641\pi\)
0.931535 0.363653i \(-0.118471\pi\)
\(24\) 0 0
\(25\) −5.05492 4.24158i −1.01098 0.848316i
\(26\) 0 0
\(27\) 2.18186 4.71588i 0.419899 0.907571i
\(28\) 0 0
\(29\) −3.45728 + 4.12023i −0.642001 + 0.765107i −0.984685 0.174344i \(-0.944220\pi\)
0.342684 + 0.939451i \(0.388664\pi\)
\(30\) 0 0
\(31\) 1.52041 0.268090i 0.273074 0.0481504i −0.0354340 0.999372i \(-0.511281\pi\)
0.308508 + 0.951222i \(0.400170\pi\)
\(32\) 0 0
\(33\) 6.80787 + 2.24833i 1.18510 + 0.391385i
\(34\) 0 0
\(35\) 7.48419 12.9630i 1.26506 2.19115i
\(36\) 0 0
\(37\) −2.48926 4.31152i −0.409232 0.708810i 0.585572 0.810620i \(-0.300870\pi\)
−0.994804 + 0.101810i \(0.967537\pi\)
\(38\) 0 0
\(39\) −10.4857 + 0.315590i −1.67905 + 0.0505348i
\(40\) 0 0
\(41\) −3.29698 3.92918i −0.514901 0.613635i 0.444466 0.895796i \(-0.353393\pi\)
−0.959367 + 0.282160i \(0.908949\pi\)
\(42\) 0 0
\(43\) 1.43112 + 3.93198i 0.218244 + 0.599622i 0.999704 0.0243344i \(-0.00774665\pi\)
−0.781459 + 0.623956i \(0.785524\pi\)
\(44\) 0 0
\(45\) 10.1503 + 1.16584i 1.51312 + 0.173794i
\(46\) 0 0
\(47\) 1.51654 8.60072i 0.221210 1.25454i −0.648589 0.761138i \(-0.724641\pi\)
0.869799 0.493406i \(-0.164248\pi\)
\(48\) 0 0
\(49\) 11.5742 + 4.21266i 1.65345 + 0.601808i
\(50\) 0 0
\(51\) −1.87203 0.272302i −0.262137 0.0381298i
\(52\) 0 0
\(53\) 12.1741i 1.67224i 0.548548 + 0.836119i \(0.315181\pi\)
−0.548548 + 0.836119i \(0.684819\pi\)
\(54\) 0 0
\(55\) 14.0973i 1.90088i
\(56\) 0 0
\(57\) 1.81445 + 4.55398i 0.240330 + 0.603189i
\(58\) 0 0
\(59\) 3.09392 + 1.12609i 0.402793 + 0.146605i 0.535469 0.844555i \(-0.320135\pi\)
−0.132676 + 0.991159i \(0.542357\pi\)
\(60\) 0 0
\(61\) −0.463630 + 2.62938i −0.0593618 + 0.336657i −0.999996 0.00276409i \(-0.999120\pi\)
0.940634 + 0.339421i \(0.110231\pi\)
\(62\) 0 0
\(63\) 0.792966 + 13.1615i 0.0999043 + 1.65819i
\(64\) 0 0
\(65\) −7.05488 19.3831i −0.875050 2.40418i
\(66\) 0 0
\(67\) 2.32819 + 2.77463i 0.284434 + 0.338975i 0.889277 0.457370i \(-0.151208\pi\)
−0.604843 + 0.796345i \(0.706764\pi\)
\(68\) 0 0
\(69\) −1.54543 + 2.87305i −0.186048 + 0.345874i
\(70\) 0 0
\(71\) −0.842160 1.45866i −0.0999460 0.173112i 0.811716 0.584052i \(-0.198534\pi\)
−0.911662 + 0.410941i \(0.865200\pi\)
\(72\) 0 0
\(73\) −5.58205 + 9.66839i −0.653329 + 1.13160i 0.328981 + 0.944337i \(0.393295\pi\)
−0.982310 + 0.187262i \(0.940039\pi\)
\(74\) 0 0
\(75\) 2.32240 + 11.1909i 0.268167 + 1.29221i
\(76\) 0 0
\(77\) −17.9164 + 3.15915i −2.04176 + 0.360018i
\(78\) 0 0
\(79\) −6.26169 + 7.46239i −0.704495 + 0.839584i −0.993027 0.117886i \(-0.962388\pi\)
0.288532 + 0.957470i \(0.406833\pi\)
\(80\) 0 0
\(81\) −8.02648 + 4.07131i −0.891832 + 0.452368i
\(82\) 0 0
\(83\) −0.240134 0.201496i −0.0263581 0.0221171i 0.629513 0.776990i \(-0.283254\pi\)
−0.655872 + 0.754873i \(0.727699\pi\)
\(84\) 0 0
\(85\) −0.645914 3.66316i −0.0700592 0.397325i
\(86\) 0 0
\(87\) 9.12161 1.89297i 0.977940 0.202947i
\(88\) 0 0
\(89\) 6.60573 + 3.81382i 0.700206 + 0.404264i 0.807424 0.589971i \(-0.200861\pi\)
−0.107218 + 0.994236i \(0.534194\pi\)
\(90\) 0 0
\(91\) 23.0533 13.3098i 2.41664 1.39525i
\(92\) 0 0
\(93\) −2.35498 1.26676i −0.244200 0.131357i
\(94\) 0 0
\(95\) −7.38387 + 6.19580i −0.757569 + 0.635676i
\(96\) 0 0
\(97\) 0.903887 0.328988i 0.0917758 0.0334037i −0.295724 0.955273i \(-0.595561\pi\)
0.387500 + 0.921870i \(0.373339\pi\)
\(98\) 0 0
\(99\) −6.84452 10.3614i −0.687900 1.04136i
\(100\) 0 0
\(101\) 13.8908 + 2.44933i 1.38219 + 0.243717i 0.814804 0.579736i \(-0.196844\pi\)
0.567384 + 0.823453i \(0.307955\pi\)
\(102\) 0 0
\(103\) 2.88921 7.93804i 0.284682 0.782158i −0.712106 0.702072i \(-0.752258\pi\)
0.996788 0.0800861i \(-0.0255195\pi\)
\(104\) 0 0
\(105\) −24.0847 + 9.59611i −2.35042 + 0.936485i
\(106\) 0 0
\(107\) 5.48494 0.530249 0.265125 0.964214i \(-0.414587\pi\)
0.265125 + 0.964214i \(0.414587\pi\)
\(108\) 0 0
\(109\) 7.87082 0.753888 0.376944 0.926236i \(-0.376975\pi\)
0.376944 + 0.926236i \(0.376975\pi\)
\(110\) 0 0
\(111\) −1.24123 + 8.53325i −0.117812 + 0.809940i
\(112\) 0 0
\(113\) −3.88780 + 10.6816i −0.365733 + 1.00484i 0.611233 + 0.791451i \(0.290674\pi\)
−0.976966 + 0.213393i \(0.931548\pi\)
\(114\) 0 0
\(115\) −6.31718 1.11389i −0.589080 0.103871i
\(116\) 0 0
\(117\) 14.5962 + 10.8212i 1.34942 + 1.00042i
\(118\) 0 0
\(119\) 4.51081 1.64180i 0.413505 0.150504i
\(120\) 0 0
\(121\) 4.69894 3.94288i 0.427176 0.358444i
\(122\) 0 0
\(123\) 0.267263 + 8.87999i 0.0240983 + 0.800682i
\(124\) 0 0
\(125\) −4.71532 + 2.72239i −0.421751 + 0.243498i
\(126\) 0 0
\(127\) 9.65557 + 5.57465i 0.856793 + 0.494670i 0.862937 0.505311i \(-0.168622\pi\)
−0.00614387 + 0.999981i \(0.501956\pi\)
\(128\) 0 0
\(129\) 2.27278 6.88188i 0.200107 0.605916i
\(130\) 0 0
\(131\) −1.91696 10.8716i −0.167486 0.949858i −0.946464 0.322808i \(-0.895373\pi\)
0.778979 0.627050i \(-0.215738\pi\)
\(132\) 0 0
\(133\) −9.52903 7.99580i −0.826272 0.693324i
\(134\) 0 0
\(135\) −12.5508 12.4757i −1.08020 1.07374i
\(136\) 0 0
\(137\) 7.49116 8.92762i 0.640013 0.762738i −0.344359 0.938838i \(-0.611904\pi\)
0.984372 + 0.176100i \(0.0563483\pi\)
\(138\) 0 0
\(139\) 1.75412 0.309298i 0.148782 0.0262343i −0.0987610 0.995111i \(-0.531488\pi\)
0.247543 + 0.968877i \(0.420377\pi\)
\(140\) 0 0
\(141\) −11.2900 + 10.0675i −0.950787 + 0.847832i
\(142\) 0 0
\(143\) −12.5352 + 21.7117i −1.04825 + 1.81562i
\(144\) 0 0
\(145\) 9.15888 + 15.8636i 0.760604 + 1.31740i
\(146\) 0 0
\(147\) −11.2178 18.1462i −0.925229 1.49668i
\(148\) 0 0
\(149\) 4.09859 + 4.88451i 0.335770 + 0.400155i 0.907339 0.420399i \(-0.138110\pi\)
−0.571570 + 0.820553i \(0.693665\pi\)
\(150\) 0 0
\(151\) 2.40548 + 6.60901i 0.195755 + 0.537834i 0.998270 0.0587991i \(-0.0187271\pi\)
−0.802514 + 0.596633i \(0.796505\pi\)
\(152\) 0 0
\(153\) 2.25328 + 2.37880i 0.182167 + 0.192314i
\(154\) 0 0
\(155\) 0.913032 5.17806i 0.0733365 0.415912i
\(156\) 0 0
\(157\) −18.7388 6.82035i −1.49552 0.544323i −0.540620 0.841267i \(-0.681810\pi\)
−0.954895 + 0.296944i \(0.904033\pi\)
\(158\) 0 0
\(159\) 13.0618 16.5533i 1.03587 1.31277i
\(160\) 0 0
\(161\) 8.27820i 0.652414i
\(162\) 0 0
\(163\) 8.53829i 0.668770i 0.942437 + 0.334385i \(0.108529\pi\)
−0.942437 + 0.334385i \(0.891471\pi\)
\(164\) 0 0
\(165\) 15.1253 19.1683i 1.17750 1.49225i
\(166\) 0 0
\(167\) 21.2266 + 7.72587i 1.64257 + 0.597846i 0.987485 0.157712i \(-0.0504118\pi\)
0.655082 + 0.755558i \(0.272634\pi\)
\(168\) 0 0
\(169\) 4.11251 23.3232i 0.316347 1.79409i
\(170\) 0 0
\(171\) 2.41891 8.13890i 0.184979 0.622397i
\(172\) 0 0
\(173\) 1.10479 + 3.03538i 0.0839954 + 0.230776i 0.974579 0.224044i \(-0.0719260\pi\)
−0.890584 + 0.454820i \(0.849704\pi\)
\(174\) 0 0
\(175\) −18.6422 22.2169i −1.40922 1.67944i
\(176\) 0 0
\(177\) −2.99865 4.85070i −0.225392 0.364601i
\(178\) 0 0
\(179\) 1.89356 + 3.27975i 0.141531 + 0.245140i 0.928074 0.372397i \(-0.121464\pi\)
−0.786542 + 0.617537i \(0.788131\pi\)
\(180\) 0 0
\(181\) −11.0399 + 19.1216i −0.820586 + 1.42130i 0.0846611 + 0.996410i \(0.473019\pi\)
−0.905247 + 0.424886i \(0.860314\pi\)
\(182\) 0 0
\(183\) 3.45152 3.07778i 0.255144 0.227516i
\(184\) 0 0
\(185\) −16.6977 + 2.94426i −1.22764 + 0.216466i
\(186\) 0 0
\(187\) −2.90600 + 3.46324i −0.212508 + 0.253257i
\(188\) 0 0
\(189\) 13.0430 18.7467i 0.948739 1.36362i
\(190\) 0 0
\(191\) −9.73071 8.16503i −0.704089 0.590801i 0.218844 0.975760i \(-0.429771\pi\)
−0.922934 + 0.384959i \(0.874216\pi\)
\(192\) 0 0
\(193\) −1.17091 6.64057i −0.0842841 0.477999i −0.997509 0.0705424i \(-0.977527\pi\)
0.913225 0.407456i \(-0.133584\pi\)
\(194\) 0 0
\(195\) −11.2039 + 33.9250i −0.802327 + 2.42942i
\(196\) 0 0
\(197\) 10.9892 + 6.34463i 0.782950 + 0.452036i 0.837475 0.546476i \(-0.184031\pi\)
−0.0545249 + 0.998512i \(0.517364\pi\)
\(198\) 0 0
\(199\) 2.36052 1.36285i 0.167333 0.0966097i −0.413995 0.910279i \(-0.635867\pi\)
0.581328 + 0.813670i \(0.302533\pi\)
\(200\) 0 0
\(201\) −0.188731 6.27069i −0.0133120 0.442301i
\(202\) 0 0
\(203\) −18.1088 + 15.1951i −1.27099 + 1.06649i
\(204\) 0 0
\(205\) −16.4149 + 5.97455i −1.14647 + 0.417281i
\(206\) 0 0
\(207\) 5.18391 2.24842i 0.360306 0.156276i
\(208\) 0 0
\(209\) 11.5374 + 2.03435i 0.798055 + 0.140719i
\(210\) 0 0
\(211\) −3.06103 + 8.41010i −0.210730 + 0.578975i −0.999355 0.0358983i \(-0.988571\pi\)
0.788626 + 0.614874i \(0.210793\pi\)
\(212\) 0 0
\(213\) −0.419929 + 2.88695i −0.0287731 + 0.197810i
\(214\) 0 0
\(215\) 14.2505 0.971878
\(216\) 0 0
\(217\) 6.78547 0.460628
\(218\) 0 0
\(219\) 17.9634 7.15721i 1.21386 0.483639i
\(220\) 0 0
\(221\) 2.26247 6.21609i 0.152190 0.418139i
\(222\) 0 0
\(223\) −20.0713 3.53911i −1.34407 0.236996i −0.545104 0.838368i \(-0.683510\pi\)
−0.798969 + 0.601372i \(0.794621\pi\)
\(224\) 0 0
\(225\) 8.84914 17.7082i 0.589943 1.18055i
\(226\) 0 0
\(227\) −26.8955 + 9.78916i −1.78512 + 0.649729i −0.785597 + 0.618739i \(0.787644\pi\)
−0.999520 + 0.0309904i \(0.990134\pi\)
\(228\) 0 0
\(229\) 7.21555 6.05457i 0.476817 0.400097i −0.372457 0.928050i \(-0.621485\pi\)
0.849274 + 0.527953i \(0.177040\pi\)
\(230\) 0 0
\(231\) 27.7508 + 14.9273i 1.82587 + 0.982147i
\(232\) 0 0
\(233\) 5.57469 3.21855i 0.365210 0.210854i −0.306154 0.951982i \(-0.599042\pi\)
0.671364 + 0.741128i \(0.265709\pi\)
\(234\) 0 0
\(235\) −25.7584 14.8716i −1.68029 0.970118i
\(236\) 0 0
\(237\) 16.5207 3.42847i 1.07313 0.222703i
\(238\) 0 0
\(239\) 0.774137 + 4.39035i 0.0500748 + 0.283988i 0.999555 0.0298396i \(-0.00949966\pi\)
−0.949480 + 0.313828i \(0.898389\pi\)
\(240\) 0 0
\(241\) 8.43801 + 7.08033i 0.543540 + 0.456084i 0.872746 0.488174i \(-0.162337\pi\)
−0.329207 + 0.944258i \(0.606781\pi\)
\(242\) 0 0
\(243\) 15.2820 + 3.07594i 0.980339 + 0.197322i
\(244\) 0 0
\(245\) 26.9636 32.1339i 1.72264 2.05296i
\(246\) 0 0
\(247\) −16.8814 + 2.97665i −1.07414 + 0.189400i
\(248\) 0 0
\(249\) 0.110325 + 0.531623i 0.00699159 + 0.0336902i
\(250\) 0 0
\(251\) 9.58454 16.6009i 0.604971 1.04784i −0.387085 0.922044i \(-0.626518\pi\)
0.992056 0.125796i \(-0.0401485\pi\)
\(252\) 0 0
\(253\) 3.89822 + 6.75191i 0.245079 + 0.424489i
\(254\) 0 0
\(255\) −3.05202 + 5.67389i −0.191125 + 0.355312i
\(256\) 0 0
\(257\) −1.69182 2.01624i −0.105533 0.125769i 0.710692 0.703503i \(-0.248382\pi\)
−0.816226 + 0.577733i \(0.803937\pi\)
\(258\) 0 0
\(259\) −7.48379 20.5615i −0.465020 1.27763i
\(260\) 0 0
\(261\) −14.4339 7.21286i −0.893433 0.446465i
\(262\) 0 0
\(263\) −1.32969 + 7.54107i −0.0819924 + 0.465002i 0.915973 + 0.401241i \(0.131421\pi\)
−0.997965 + 0.0637616i \(0.979690\pi\)
\(264\) 0 0
\(265\) 38.9607 + 14.1805i 2.39334 + 0.871104i
\(266\) 0 0
\(267\) −4.89002 12.2732i −0.299264 0.751105i
\(268\) 0 0
\(269\) 7.03704i 0.429056i 0.976718 + 0.214528i \(0.0688213\pi\)
−0.976718 + 0.214528i \(0.931179\pi\)
\(270\) 0 0
\(271\) 24.1189i 1.46512i −0.680704 0.732559i \(-0.738326\pi\)
0.680704 0.732559i \(-0.261674\pi\)
\(272\) 0 0
\(273\) −45.6264 6.63672i −2.76144 0.401673i
\(274\) 0 0
\(275\) 25.6670 + 9.34204i 1.54778 + 0.563346i
\(276\) 0 0
\(277\) 3.42494 19.4238i 0.205785 1.16706i −0.690416 0.723413i \(-0.742572\pi\)
0.896200 0.443650i \(-0.146317\pi\)
\(278\) 0 0
\(279\) 1.84298 + 4.24914i 0.110336 + 0.254389i
\(280\) 0 0
\(281\) 2.28394 + 6.27507i 0.136248 + 0.374339i 0.988988 0.147997i \(-0.0472827\pi\)
−0.852739 + 0.522337i \(0.825060\pi\)
\(282\) 0 0
\(283\) 10.6684 + 12.7141i 0.634172 + 0.755777i 0.983438 0.181247i \(-0.0580133\pi\)
−0.349265 + 0.937024i \(0.613569\pi\)
\(284\) 0 0
\(285\) 16.6876 0.502251i 0.988489 0.0297508i
\(286\) 0 0
\(287\) −11.2717 19.5231i −0.665345 1.15241i
\(288\) 0 0
\(289\) −7.90356 + 13.6894i −0.464915 + 0.805257i
\(290\) 0 0
\(291\) −1.58201 0.522468i −0.0927392 0.0306276i
\(292\) 0 0
\(293\) −12.2915 + 2.16732i −0.718075 + 0.126616i −0.520734 0.853719i \(-0.674342\pi\)
−0.197341 + 0.980335i \(0.563231\pi\)
\(294\) 0 0
\(295\) 7.20768 8.58978i 0.419647 0.500116i
\(296\) 0 0
\(297\) −1.81035 + 21.4323i −0.105047 + 1.24363i
\(298\) 0 0
\(299\) −8.73882 7.33274i −0.505379 0.424063i
\(300\) 0 0
\(301\) 3.19349 + 18.1112i 0.184070 + 1.04391i
\(302\) 0 0
\(303\) −16.2597 18.2342i −0.934096 1.04753i
\(304\) 0 0
\(305\) 7.87476 + 4.54650i 0.450908 + 0.260332i
\(306\) 0 0
\(307\) −23.3290 + 13.4690i −1.33145 + 0.768715i −0.985523 0.169545i \(-0.945770\pi\)
−0.345931 + 0.938260i \(0.612437\pi\)
\(308\) 0 0
\(309\) −12.4454 + 7.69362i −0.707995 + 0.437675i
\(310\) 0 0
\(311\) −17.6156 + 14.7812i −0.998888 + 0.838167i −0.986830 0.161761i \(-0.948283\pi\)
−0.0120581 + 0.999927i \(0.503838\pi\)
\(312\) 0 0
\(313\) −9.95877 + 3.62469i −0.562903 + 0.204880i −0.607770 0.794113i \(-0.707936\pi\)
0.0448672 + 0.998993i \(0.485714\pi\)
\(314\) 0 0
\(315\) 43.0443 + 12.7929i 2.42527 + 0.720800i
\(316\) 0 0
\(317\) −34.2177 6.03350i −1.92186 0.338875i −0.922919 0.384994i \(-0.874204\pi\)
−0.998936 + 0.0461189i \(0.985315\pi\)
\(318\) 0 0
\(319\) 7.61463 20.9210i 0.426337 1.17135i
\(320\) 0 0
\(321\) −7.45799 5.88491i −0.416264 0.328463i
\(322\) 0 0
\(323\) −3.09118 −0.171998
\(324\) 0 0
\(325\) −39.9662 −2.21693
\(326\) 0 0
\(327\) −10.7021 8.44477i −0.591828 0.466997i
\(328\) 0 0
\(329\) 13.1282 36.0694i 0.723780 1.98857i
\(330\) 0 0
\(331\) 5.68194 + 1.00188i 0.312308 + 0.0550682i 0.327605 0.944815i \(-0.393758\pi\)
−0.0152976 + 0.999883i \(0.504870\pi\)
\(332\) 0 0
\(333\) 10.8432 10.2711i 0.594205 0.562852i
\(334\) 0 0
\(335\) 11.5916 4.21899i 0.633316 0.230508i
\(336\) 0 0
\(337\) −5.65269 + 4.74317i −0.307922 + 0.258377i −0.783632 0.621225i \(-0.786635\pi\)
0.475711 + 0.879602i \(0.342191\pi\)
\(338\) 0 0
\(339\) 16.7469 10.3527i 0.909565 0.562284i
\(340\) 0 0
\(341\) −5.53440 + 3.19529i −0.299705 + 0.173035i
\(342\) 0 0
\(343\) 20.2379 + 11.6844i 1.09275 + 0.630897i
\(344\) 0 0
\(345\) 7.39448 + 8.29241i 0.398105 + 0.446448i
\(346\) 0 0
\(347\) 4.01371 + 22.7629i 0.215467 + 1.22198i 0.880094 + 0.474800i \(0.157480\pi\)
−0.664626 + 0.747176i \(0.731409\pi\)
\(348\) 0 0
\(349\) −21.3840 17.9433i −1.14466 0.960482i −0.145077 0.989420i \(-0.546343\pi\)
−0.999581 + 0.0289385i \(0.990787\pi\)
\(350\) 0 0
\(351\) −8.23647 30.3744i −0.439630 1.62126i
\(352\) 0 0
\(353\) −4.12725 + 4.91866i −0.219671 + 0.261794i −0.864614 0.502437i \(-0.832437\pi\)
0.644943 + 0.764231i \(0.276881\pi\)
\(354\) 0 0
\(355\) −5.64913 + 0.996094i −0.299825 + 0.0528672i
\(356\) 0 0
\(357\) −7.89496 2.60735i −0.417846 0.137996i
\(358\) 0 0
\(359\) −1.88368 + 3.26264i −0.0994170 + 0.172195i −0.911443 0.411425i \(-0.865031\pi\)
0.812026 + 0.583621i \(0.198364\pi\)
\(360\) 0 0
\(361\) −5.49484 9.51734i −0.289202 0.500913i
\(362\) 0 0
\(363\) −10.6196 + 0.319622i −0.557387 + 0.0167758i
\(364\) 0 0
\(365\) 24.4397 + 29.1261i 1.27923 + 1.52453i
\(366\) 0 0
\(367\) 6.60798 + 18.1553i 0.344934 + 0.947697i 0.983941 + 0.178496i \(0.0571233\pi\)
−0.639007 + 0.769201i \(0.720654\pi\)
\(368\) 0 0
\(369\) 9.16412 12.3611i 0.477065 0.643491i
\(370\) 0 0
\(371\) −9.29129 + 52.6935i −0.482380 + 2.73571i
\(372\) 0 0
\(373\) −0.646074 0.235152i −0.0334524 0.0121757i 0.325240 0.945632i \(-0.394555\pi\)
−0.358692 + 0.933456i \(0.616777\pi\)
\(374\) 0 0
\(375\) 9.33242 + 1.35747i 0.481924 + 0.0700996i
\(376\) 0 0
\(377\) 32.5761i 1.67776i
\(378\) 0 0
\(379\) 17.2965i 0.888463i −0.895912 0.444232i \(-0.853477\pi\)
0.895912 0.444232i \(-0.146523\pi\)
\(380\) 0 0
\(381\) −7.14772 17.9396i −0.366189 0.919075i
\(382\) 0 0
\(383\) −3.32586 1.21051i −0.169944 0.0618544i 0.255647 0.966770i \(-0.417711\pi\)
−0.425591 + 0.904916i \(0.639934\pi\)
\(384\) 0 0
\(385\) −10.7591 + 61.0177i −0.548333 + 3.10975i
\(386\) 0 0
\(387\) −10.4741 + 6.91892i −0.532426 + 0.351709i
\(388\) 0 0
\(389\) 11.5224 + 31.6576i 0.584210 + 1.60510i 0.780913 + 0.624640i \(0.214754\pi\)
−0.196703 + 0.980463i \(0.563024\pi\)
\(390\) 0 0
\(391\) −1.32231 1.57587i −0.0668720 0.0796950i
\(392\) 0 0
\(393\) −9.05786 + 16.8391i −0.456909 + 0.849421i
\(394\) 0 0
\(395\) 16.5882 + 28.7316i 0.834642 + 1.44564i
\(396\) 0 0
\(397\) 14.8687 25.7534i 0.746239 1.29252i −0.203374 0.979101i \(-0.565191\pi\)
0.949614 0.313423i \(-0.101476\pi\)
\(398\) 0 0
\(399\) 4.37795 + 21.0960i 0.219172 + 1.05612i
\(400\) 0 0
\(401\) 8.62018 1.51997i 0.430471 0.0759037i 0.0457855 0.998951i \(-0.485421\pi\)
0.384686 + 0.923048i \(0.374310\pi\)
\(402\) 0 0
\(403\) 6.01050 7.16303i 0.299404 0.356816i
\(404\) 0 0
\(405\) 3.68006 + 30.4295i 0.182863 + 1.51205i
\(406\) 0 0
\(407\) 15.7864 + 13.2464i 0.782504 + 0.656599i
\(408\) 0 0
\(409\) −3.71415 21.0640i −0.183653 1.04155i −0.927674 0.373392i \(-0.878195\pi\)
0.744021 0.668157i \(-0.232916\pi\)
\(410\) 0 0
\(411\) −19.7645 + 4.10164i −0.974911 + 0.202319i
\(412\) 0 0
\(413\) 12.5321 + 7.23540i 0.616663 + 0.356031i
\(414\) 0 0
\(415\) −0.924560 + 0.533795i −0.0453849 + 0.0262030i
\(416\) 0 0
\(417\) −2.71696 1.46147i −0.133050 0.0715684i
\(418\) 0 0
\(419\) −28.0877 + 23.5684i −1.37217 + 1.15139i −0.400165 + 0.916443i \(0.631047\pi\)
−0.972008 + 0.234947i \(0.924508\pi\)
\(420\) 0 0
\(421\) −10.5196 + 3.82881i −0.512692 + 0.186605i −0.585394 0.810749i \(-0.699060\pi\)
0.0727019 + 0.997354i \(0.476838\pi\)
\(422\) 0 0
\(423\) 26.1528 1.57568i 1.27159 0.0766122i
\(424\) 0 0
\(425\) −7.09759 1.25150i −0.344284 0.0607065i
\(426\) 0 0
\(427\) −4.01350 + 11.0270i −0.194227 + 0.533634i
\(428\) 0 0
\(429\) 40.3393 16.0725i 1.94760 0.775986i
\(430\) 0 0
\(431\) 0.802008 0.0386314 0.0193157 0.999813i \(-0.493851\pi\)
0.0193157 + 0.999813i \(0.493851\pi\)
\(432\) 0 0
\(433\) 3.12308 0.150086 0.0750428 0.997180i \(-0.476091\pi\)
0.0750428 + 0.997180i \(0.476091\pi\)
\(434\) 0 0
\(435\) 4.56692 31.3969i 0.218967 1.50537i
\(436\) 0 0
\(437\) −1.82324 + 5.00930i −0.0872172 + 0.239627i
\(438\) 0 0
\(439\) 4.04187 + 0.712690i 0.192908 + 0.0340149i 0.269267 0.963066i \(-0.413219\pi\)
−0.0763594 + 0.997080i \(0.524330\pi\)
\(440\) 0 0
\(441\) −4.21638 + 36.7096i −0.200780 + 1.74808i
\(442\) 0 0
\(443\) 32.3631 11.7792i 1.53762 0.559646i 0.572143 0.820154i \(-0.306112\pi\)
0.965472 + 0.260507i \(0.0838899\pi\)
\(444\) 0 0
\(445\) 19.8998 16.6979i 0.943343 0.791559i
\(446\) 0 0
\(447\) −0.332244 11.0390i −0.0157146 0.522128i
\(448\) 0 0
\(449\) 12.4452 7.18523i 0.587324 0.339092i −0.176715 0.984262i \(-0.556547\pi\)
0.764039 + 0.645170i \(0.223214\pi\)
\(450\) 0 0
\(451\) 18.3869 + 10.6157i 0.865806 + 0.499873i
\(452\) 0 0
\(453\) 3.82016 11.5673i 0.179487 0.543479i
\(454\) 0 0
\(455\) −15.7426 89.2810i −0.738027 4.18556i
\(456\) 0 0
\(457\) 6.63409 + 5.56666i 0.310330 + 0.260398i 0.784628 0.619967i \(-0.212854\pi\)
−0.474299 + 0.880364i \(0.657298\pi\)
\(458\) 0 0
\(459\) −0.511573 5.65209i −0.0238782 0.263817i
\(460\) 0 0
\(461\) −15.0829 + 17.9751i −0.702481 + 0.837184i −0.992805 0.119745i \(-0.961792\pi\)
0.290324 + 0.956928i \(0.406237\pi\)
\(462\) 0 0
\(463\) 30.2719 5.33776i 1.40686 0.248067i 0.581899 0.813261i \(-0.302310\pi\)
0.824958 + 0.565194i \(0.191199\pi\)
\(464\) 0 0
\(465\) −6.79712 + 6.06110i −0.315209 + 0.281077i
\(466\) 0 0
\(467\) 9.51526 16.4809i 0.440314 0.762646i −0.557399 0.830245i \(-0.688201\pi\)
0.997713 + 0.0675990i \(0.0215338\pi\)
\(468\) 0 0
\(469\) 7.95960 + 13.7864i 0.367540 + 0.636598i
\(470\) 0 0
\(471\) 18.1618 + 29.3790i 0.836850 + 1.35371i
\(472\) 0 0
\(473\) −11.1333 13.2681i −0.511909 0.610069i
\(474\) 0 0
\(475\) 6.38759 + 17.5498i 0.293083 + 0.805238i
\(476\) 0 0
\(477\) −35.5209 + 8.49362i −1.62639 + 0.388896i
\(478\) 0 0
\(479\) 2.75148 15.6044i 0.125718 0.712984i −0.855160 0.518363i \(-0.826541\pi\)
0.980879 0.194620i \(-0.0623474\pi\)
\(480\) 0 0
\(481\) −28.3347 10.3130i −1.29195 0.470232i
\(482\) 0 0
\(483\) −8.88186 + 11.2560i −0.404139 + 0.512168i
\(484\) 0 0
\(485\) 3.27592i 0.148752i
\(486\) 0 0
\(487\) 4.49577i 0.203723i 0.994799 + 0.101861i \(0.0324798\pi\)
−0.994799 + 0.101861i \(0.967520\pi\)
\(488\) 0 0
\(489\) 9.16091 11.6097i 0.414271 0.525008i
\(490\) 0 0
\(491\) 34.4443 + 12.5367i 1.55445 + 0.565773i 0.969456 0.245266i \(-0.0788753\pi\)
0.584992 + 0.811039i \(0.301097\pi\)
\(492\) 0 0
\(493\) −1.02008 + 5.78519i −0.0459423 + 0.260552i
\(494\) 0 0
\(495\) −41.1322 + 9.83539i −1.84876 + 0.442068i
\(496\) 0 0
\(497\) −2.53190 6.95633i −0.113571 0.312034i
\(498\) 0 0
\(499\) −23.9018 28.4851i −1.06999 1.27517i −0.959627 0.281275i \(-0.909243\pi\)
−0.110364 0.993891i \(-0.535202\pi\)
\(500\) 0 0
\(501\) −20.5731 33.2795i −0.919137 1.48682i
\(502\) 0 0
\(503\) 19.5952 + 33.9399i 0.873706 + 1.51330i 0.858135 + 0.513425i \(0.171623\pi\)
0.0155717 + 0.999879i \(0.495043\pi\)
\(504\) 0 0
\(505\) 24.0188 41.6018i 1.06882 1.85126i
\(506\) 0 0
\(507\) −30.6159 + 27.3007i −1.35970 + 1.21247i
\(508\) 0 0
\(509\) −13.0715 + 2.30486i −0.579385 + 0.102161i −0.455658 0.890155i \(-0.650596\pi\)
−0.123727 + 0.992316i \(0.539485\pi\)
\(510\) 0 0
\(511\) −31.5399 + 37.5878i −1.39524 + 1.66279i
\(512\) 0 0
\(513\) −12.0214 + 8.47133i −0.530760 + 0.374018i
\(514\) 0 0
\(515\) −22.0387 18.4927i −0.971143 0.814886i
\(516\) 0 0
\(517\) 6.27745 + 35.6012i 0.276082 + 1.56574i
\(518\) 0 0
\(519\) 1.75452 5.31262i 0.0770149 0.233198i
\(520\) 0 0
\(521\) −38.3054 22.1156i −1.67819 0.968903i −0.962815 0.270162i \(-0.912923\pi\)
−0.715375 0.698741i \(-0.753744\pi\)
\(522\) 0 0
\(523\) −38.8478 + 22.4288i −1.69870 + 0.980742i −0.751694 + 0.659512i \(0.770763\pi\)
−0.947001 + 0.321230i \(0.895904\pi\)
\(524\) 0 0
\(525\) 1.51120 + 50.2104i 0.0659540 + 2.19136i
\(526\) 0 0
\(527\) 1.29170 1.08387i 0.0562675 0.0472141i
\(528\) 0 0
\(529\) 18.2793 6.65312i 0.794752 0.289266i
\(530\) 0 0
\(531\) −1.12709 + 9.81291i −0.0489115 + 0.425844i
\(532\) 0 0
\(533\) −30.5937 5.39450i −1.32516 0.233662i
\(534\) 0 0
\(535\) 6.38894 17.5535i 0.276218 0.758902i
\(536\) 0 0
\(537\) 0.944193 6.49118i 0.0407449 0.280115i
\(538\) 0 0
\(539\) −50.9840 −2.19604
\(540\) 0 0
\(541\) 10.2100 0.438964 0.219482 0.975617i \(-0.429563\pi\)
0.219482 + 0.975617i \(0.429563\pi\)
\(542\) 0 0
\(543\) 35.5271 14.1551i 1.52461 0.607454i
\(544\) 0 0
\(545\) 9.16805 25.1890i 0.392716 1.07898i
\(546\) 0 0
\(547\) 41.0351 + 7.23559i 1.75453 + 0.309372i 0.956172 0.292807i \(-0.0945893\pi\)
0.798361 + 0.602178i \(0.205700\pi\)
\(548\) 0 0
\(549\) −7.99532 + 0.481711i −0.341232 + 0.0205589i
\(550\) 0 0
\(551\) 14.3047 5.20647i 0.609399 0.221803i
\(552\) 0 0
\(553\) −32.7980 + 27.5208i −1.39471 + 1.17030i
\(554\) 0 0
\(555\) 25.8632 + 13.9120i 1.09783 + 0.590530i
\(556\) 0 0
\(557\) 21.7735 12.5709i 0.922571 0.532647i 0.0381165 0.999273i \(-0.487864\pi\)
0.884454 + 0.466627i \(0.154531\pi\)
\(558\) 0 0
\(559\) 21.9477 + 12.6715i 0.928289 + 0.535948i
\(560\) 0 0
\(561\) 7.66714 1.59113i 0.323707 0.0671774i
\(562\) 0 0
\(563\) −7.04571 39.9582i −0.296941 1.68404i −0.659206 0.751962i \(-0.729108\pi\)
0.362265 0.932075i \(-0.382003\pi\)
\(564\) 0 0
\(565\) 29.6559 + 24.8843i 1.24763 + 1.04689i
\(566\) 0 0
\(567\) −37.8486 + 11.4962i −1.58949 + 0.482794i
\(568\) 0 0
\(569\) 2.01852 2.40558i 0.0846208 0.100847i −0.722073 0.691817i \(-0.756810\pi\)
0.806694 + 0.590970i \(0.201255\pi\)
\(570\) 0 0
\(571\) −8.87330 + 1.56460i −0.371336 + 0.0654765i −0.356202 0.934409i \(-0.615929\pi\)
−0.0151338 + 0.999885i \(0.504817\pi\)
\(572\) 0 0
\(573\) 4.47061 + 21.5424i 0.186762 + 0.899949i
\(574\) 0 0
\(575\) −6.21436 + 10.7636i −0.259157 + 0.448873i
\(576\) 0 0
\(577\) 0.994209 + 1.72202i 0.0413895 + 0.0716886i 0.885978 0.463727i \(-0.153488\pi\)
−0.844589 + 0.535416i \(0.820155\pi\)
\(578\) 0 0
\(579\) −5.53269 + 10.2856i −0.229931 + 0.427456i
\(580\) 0 0
\(581\) −0.885598 1.05541i −0.0367408 0.0437860i
\(582\) 0 0
\(583\) −17.2352 47.3534i −0.713811 1.96118i
\(584\) 0 0
\(585\) 51.6330 34.1076i 2.13476 1.41017i
\(586\) 0 0
\(587\) 7.64588 43.3619i 0.315579 1.78974i −0.253374 0.967369i \(-0.581540\pi\)
0.568953 0.822370i \(-0.307349\pi\)
\(588\) 0 0
\(589\) −4.10602 1.49447i −0.169186 0.0615785i
\(590\) 0 0
\(591\) −8.13499 20.4175i −0.334629 0.839863i
\(592\) 0 0
\(593\) 37.9415i 1.55807i −0.626979 0.779036i \(-0.715709\pi\)
0.626979 0.779036i \(-0.284291\pi\)
\(594\) 0 0
\(595\) 16.3483i 0.670217i
\(596\) 0 0
\(597\) −4.67188 0.679561i −0.191207 0.0278126i
\(598\) 0 0
\(599\) −33.3395 12.1346i −1.36221 0.495805i −0.445476 0.895294i \(-0.646965\pi\)
−0.916738 + 0.399489i \(0.869188\pi\)
\(600\) 0 0
\(601\) 4.82497 27.3638i 0.196815 1.11619i −0.712996 0.701168i \(-0.752662\pi\)
0.909811 0.415024i \(-0.136227\pi\)
\(602\) 0 0
\(603\) −6.47134 + 8.72888i −0.263533 + 0.355468i
\(604\) 0 0
\(605\) −7.14501 19.6308i −0.290486 0.798104i
\(606\) 0 0
\(607\) 18.0150 + 21.4694i 0.731207 + 0.871418i 0.995668 0.0929782i \(-0.0296387\pi\)
−0.264462 + 0.964396i \(0.585194\pi\)
\(608\) 0 0
\(609\) 40.9261 1.23176i 1.65841 0.0499136i
\(610\) 0 0
\(611\) −26.4476 45.8086i −1.06995 1.85322i
\(612\) 0 0
\(613\) −2.08983 + 3.61970i −0.0844076 + 0.146198i −0.905139 0.425117i \(-0.860233\pi\)
0.820731 + 0.571315i \(0.193566\pi\)
\(614\) 0 0
\(615\) 28.7300 + 9.48822i 1.15850 + 0.382602i
\(616\) 0 0
\(617\) −26.3586 + 4.64774i −1.06116 + 0.187111i −0.676870 0.736102i \(-0.736664\pi\)
−0.384288 + 0.923213i \(0.625553\pi\)
\(618\) 0 0
\(619\) 19.8689 23.6788i 0.798597 0.951731i −0.201015 0.979588i \(-0.564424\pi\)
0.999612 + 0.0278575i \(0.00886846\pi\)
\(620\) 0 0
\(621\) −9.46104 2.50470i −0.379658 0.100510i
\(622\) 0 0
\(623\) 25.6811 + 21.5490i 1.02889 + 0.863343i
\(624\) 0 0
\(625\) −2.50929 14.2309i −0.100372 0.569235i
\(626\) 0 0
\(627\) −13.5049 15.1448i −0.539333 0.604826i
\(628\) 0 0
\(629\) −4.70901 2.71875i −0.187761 0.108404i
\(630\) 0 0
\(631\) 4.48915 2.59181i 0.178710 0.103178i −0.407976 0.912993i \(-0.633765\pi\)
0.586687 + 0.809814i \(0.300432\pi\)
\(632\) 0 0
\(633\) 13.1855 8.15115i 0.524077 0.323979i
\(634\) 0 0
\(635\) 29.0875 24.4073i 1.15430 0.968575i
\(636\) 0 0
\(637\) 70.1008 25.5146i 2.77749 1.01093i
\(638\) 0 0
\(639\) 3.66845 3.47489i 0.145122 0.137465i
\(640\) 0 0
\(641\) 32.6707 + 5.76073i 1.29042 + 0.227535i 0.776397 0.630244i \(-0.217045\pi\)
0.514019 + 0.857779i \(0.328156\pi\)
\(642\) 0 0
\(643\) −7.68834 + 21.1236i −0.303199 + 0.833032i 0.690741 + 0.723102i \(0.257285\pi\)
−0.993939 + 0.109929i \(0.964938\pi\)
\(644\) 0 0
\(645\) −19.3767 15.2897i −0.762958 0.602031i
\(646\) 0 0
\(647\) 20.0311 0.787505 0.393752 0.919217i \(-0.371177\pi\)
0.393752 + 0.919217i \(0.371177\pi\)
\(648\) 0 0
\(649\) −13.6286 −0.534971
\(650\) 0 0
\(651\) −9.22635 7.28028i −0.361609 0.285337i
\(652\) 0 0
\(653\) −4.59529 + 12.6255i −0.179828 + 0.494072i −0.996553 0.0829537i \(-0.973565\pi\)
0.816726 + 0.577026i \(0.195787\pi\)
\(654\) 0 0
\(655\) −37.0254 6.52858i −1.44670 0.255093i
\(656\) 0 0
\(657\) −32.1044 9.54155i −1.25251 0.372251i
\(658\) 0 0
\(659\) −36.5498 + 13.3030i −1.42378 + 0.518213i −0.935141 0.354275i \(-0.884728\pi\)
−0.488636 + 0.872488i \(0.662505\pi\)
\(660\) 0 0
\(661\) 3.65798 3.06941i 0.142279 0.119386i −0.568871 0.822427i \(-0.692619\pi\)
0.711149 + 0.703041i \(0.248175\pi\)
\(662\) 0 0
\(663\) −9.74570 + 6.02469i −0.378492 + 0.233980i
\(664\) 0 0
\(665\) −36.6885 + 21.1821i −1.42272 + 0.821408i
\(666\) 0 0
\(667\) 8.77332 + 5.06528i 0.339704 + 0.196128i
\(668\) 0 0
\(669\) 23.4942 + 26.3471i 0.908337 + 1.01864i
\(670\) 0 0
\(671\) −1.91912 10.8839i −0.0740867 0.420167i
\(672\) 0 0
\(673\) −15.6817 13.1585i −0.604487 0.507225i 0.288397 0.957511i \(-0.406878\pi\)
−0.892884 + 0.450286i \(0.851322\pi\)
\(674\) 0 0
\(675\) −31.0319 + 14.5838i −1.19442 + 0.561332i
\(676\) 0 0
\(677\) 2.71884 3.24019i 0.104494 0.124531i −0.711263 0.702926i \(-0.751876\pi\)
0.815757 + 0.578395i \(0.196321\pi\)
\(678\) 0 0
\(679\) 4.16341 0.734122i 0.159777 0.0281730i
\(680\) 0 0
\(681\) 47.0733 + 15.5462i 1.80385 + 0.595732i
\(682\) 0 0
\(683\) 4.10080 7.10280i 0.156913 0.271781i −0.776841 0.629697i \(-0.783179\pi\)
0.933754 + 0.357916i \(0.116512\pi\)
\(684\) 0 0
\(685\) −19.8453 34.3730i −0.758248 1.31332i
\(686\) 0 0
\(687\) −16.3072 + 0.490802i −0.622159 + 0.0187253i
\(688\) 0 0
\(689\) 47.3954 + 56.4836i 1.80562 + 2.15185i
\(690\) 0 0
\(691\) 7.36741 + 20.2418i 0.280269 + 0.770034i 0.997330 + 0.0730233i \(0.0232647\pi\)
−0.717061 + 0.697011i \(0.754513\pi\)
\(692\) 0 0
\(693\) −21.7175 50.0715i −0.824980 1.90206i
\(694\) 0 0
\(695\) 1.05337 5.97398i 0.0399567 0.226606i
\(696\) 0 0
\(697\) −5.26421 1.91602i −0.199396 0.0725743i
\(698\) 0 0
\(699\) −11.0333 1.60487i −0.417316 0.0607019i
\(700\) 0 0
\(701\) 27.8257i 1.05096i −0.850806 0.525481i \(-0.823886\pi\)
0.850806 0.525481i \(-0.176114\pi\)
\(702\) 0 0
\(703\) 14.0905i 0.531432i
\(704\) 0 0
\(705\) 19.0682 + 47.8580i 0.718149 + 1.80244i
\(706\) 0 0
\(707\) 58.2548 + 21.2030i 2.19090 + 0.797422i
\(708\) 0 0
\(709\) 0.557300 3.16061i 0.0209298 0.118699i −0.972553 0.232682i \(-0.925250\pi\)
0.993483 + 0.113983i \(0.0363610\pi\)
\(710\) 0 0
\(711\) −26.1420 13.0636i −0.980402 0.489925i
\(712\) 0 0
\(713\) −0.994554 2.73251i −0.0372463 0.102333i
\(714\) 0 0
\(715\) 54.8826 + 65.4066i 2.05249 + 2.44607i
\(716\) 0 0
\(717\) 3.65789 6.80024i 0.136606 0.253960i
\(718\) 0 0
\(719\) −6.67788 11.5664i −0.249043 0.431355i 0.714218 0.699924i \(-0.246783\pi\)
−0.963260 + 0.268569i \(0.913449\pi\)
\(720\) 0 0
\(721\) 18.5638 32.1535i 0.691353 1.19746i
\(722\) 0 0
\(723\) −3.87670 18.6806i −0.144176 0.694738i
\(724\) 0 0
\(725\) 34.9526 6.16308i 1.29811 0.228891i
\(726\) 0 0
\(727\) −2.08083 + 2.47984i −0.0771737 + 0.0919720i −0.803250 0.595642i \(-0.796898\pi\)
0.726076 + 0.687614i \(0.241342\pi\)
\(728\) 0 0
\(729\) −17.4790 20.5788i −0.647369 0.762177i
\(730\) 0 0
\(731\) 3.50089 + 2.93760i 0.129485 + 0.108651i
\(732\) 0 0
\(733\) −8.17205 46.3460i −0.301842 1.71183i −0.638011 0.770027i \(-0.720243\pi\)
0.336170 0.941801i \(-0.390868\pi\)
\(734\) 0 0
\(735\) −71.1401 + 14.7634i −2.62404 + 0.544556i
\(736\) 0 0
\(737\) −12.9841 7.49637i −0.478276 0.276132i
\(738\) 0 0
\(739\) 3.41970 1.97436i 0.125796 0.0726281i −0.435782 0.900052i \(-0.643528\pi\)
0.561577 + 0.827424i \(0.310195\pi\)
\(740\) 0 0
\(741\) 26.1477 + 14.0650i 0.960561 + 0.516691i
\(742\) 0 0
\(743\) −37.8736 + 31.7797i −1.38945 + 1.16589i −0.423885 + 0.905716i \(0.639334\pi\)
−0.965563 + 0.260170i \(0.916222\pi\)
\(744\) 0 0
\(745\) 20.4060 7.42718i 0.747618 0.272111i
\(746\) 0 0
\(747\) 0.420378 0.841229i 0.0153808 0.0307790i
\(748\) 0 0
\(749\) 23.7407 + 4.18612i 0.867465 + 0.152958i
\(750\) 0 0
\(751\) −16.7877 + 46.1239i −0.612592 + 1.68308i 0.111830 + 0.993727i \(0.464329\pi\)
−0.724423 + 0.689356i \(0.757894\pi\)
\(752\) 0 0
\(753\) −30.8438 + 12.2891i −1.12401 + 0.447841i
\(754\) 0 0
\(755\) 23.9528 0.871731
\(756\) 0 0
\(757\) 23.1774 0.842397 0.421199 0.906968i \(-0.361610\pi\)
0.421199 + 0.906968i \(0.361610\pi\)
\(758\) 0 0
\(759\) 1.94378 13.3632i 0.0705548 0.485053i
\(760\) 0 0
\(761\) −2.42482 + 6.66214i −0.0878997 + 0.241502i −0.975852 0.218433i \(-0.929905\pi\)
0.887952 + 0.459936i \(0.152128\pi\)
\(762\) 0 0
\(763\) 34.0676 + 6.00703i 1.23333 + 0.217469i
\(764\) 0 0
\(765\) 10.2375 4.44033i 0.370138 0.160540i
\(766\) 0 0
\(767\) 18.7388 6.82035i 0.676618 0.246269i
\(768\) 0 0
\(769\) −34.5271 + 28.9717i −1.24508 + 1.04475i −0.247970 + 0.968768i \(0.579763\pi\)
−0.997109 + 0.0759780i \(0.975792\pi\)
\(770\) 0 0
\(771\) 0.137144 + 4.55671i 0.00493914 + 0.164106i
\(772\) 0 0
\(773\) −13.9113 + 8.03167i −0.500353 + 0.288879i −0.728859 0.684663i \(-0.759949\pi\)
0.228506 + 0.973542i \(0.426616\pi\)
\(774\) 0 0
\(775\) −8.82270 5.09379i −0.316921 0.182974i
\(776\) 0 0
\(777\) −11.8851 + 35.9875i −0.426374 + 1.29104i
\(778\) 0 0
\(779\) 2.52083 + 14.2963i 0.0903181 + 0.512219i
\(780\) 0 0
\(781\) 5.34083 + 4.48149i 0.191110 + 0.160360i
\(782\) 0 0
\(783\) 11.8872 + 25.2939i 0.424813 + 0.903929i
\(784\) 0 0
\(785\) −43.6543 + 52.0252i −1.55809 + 1.85686i
\(786\) 0 0
\(787\) 3.80955 0.671726i 0.135796 0.0239444i −0.105337 0.994437i \(-0.533592\pi\)
0.241133 + 0.970492i \(0.422481\pi\)
\(788\) 0 0
\(789\) 9.89898 8.82709i 0.352413 0.314253i
\(790\) 0 0
\(791\) −24.9800 + 43.2666i −0.888185 + 1.53838i
\(792\) 0 0
\(793\) 8.08545 + 14.0044i 0.287123 + 0.497311i
\(794\) 0 0
\(795\)