Properties

Label 405.2.r.a.197.9
Level $405$
Weight $2$
Character 405.197
Analytic conductor $3.234$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.r (of order \(36\), degree \(12\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(16\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 197.9
Character \(\chi\) \(=\) 405.197
Dual form 405.2.r.a.368.9

$q$-expansion

\(f(q)\) \(=\) \(q+(0.576956 - 0.0504771i) q^{2} +(-1.63929 + 0.289050i) q^{4} +(-2.18512 + 0.474625i) q^{5} +(2.78018 - 1.94671i) q^{7} +(-2.05006 + 0.549311i) q^{8} +O(q^{10})\) \(q+(0.576956 - 0.0504771i) q^{2} +(-1.63929 + 0.289050i) q^{4} +(-2.18512 + 0.474625i) q^{5} +(2.78018 - 1.94671i) q^{7} +(-2.05006 + 0.549311i) q^{8} +(-1.23676 + 0.384136i) q^{10} +(-1.55726 - 4.27854i) q^{11} +(0.357151 - 4.08225i) q^{13} +(1.50578 - 1.26350i) q^{14} +(1.97331 - 0.718227i) q^{16} +(-0.284890 - 0.0763360i) q^{17} +(-4.26213 - 2.46074i) q^{19} +(3.44484 - 1.40965i) q^{20} +(-1.11444 - 2.38992i) q^{22} +(-0.869642 + 1.24198i) q^{23} +(4.54946 - 2.07422i) q^{25} -2.37331i q^{26} +(-3.99482 + 3.99482i) q^{28} +(-5.57542 - 4.67834i) q^{29} +(0.591015 + 3.35181i) q^{31} +(4.94931 - 2.30790i) q^{32} +(-0.168222 - 0.0296621i) q^{34} +(-5.15107 + 5.57332i) q^{35} +(1.28961 - 4.81289i) q^{37} +(-2.58327 - 1.20460i) q^{38} +(4.21889 - 2.17331i) q^{40} +(2.42980 + 2.89573i) q^{41} +(-4.02865 + 8.63947i) q^{43} +(3.78950 + 6.56361i) q^{44} +(-0.439054 + 0.760463i) q^{46} +(-1.09911 - 1.56969i) q^{47} +(1.54562 - 4.24655i) q^{49} +(2.52014 - 1.42638i) q^{50} +(0.594504 + 6.79521i) q^{52} +(1.39575 + 1.39575i) q^{53} +(5.43349 + 8.60998i) q^{55} +(-4.63018 + 5.51804i) q^{56} +(-3.45292 - 2.41776i) q^{58} +(9.34637 + 3.40180i) q^{59} +(-0.249603 + 1.41557i) q^{61} +(0.510179 + 1.90402i) q^{62} +(-0.898191 + 0.518571i) q^{64} +(1.15712 + 9.08971i) q^{65} +(-9.46116 - 0.827744i) q^{67} +(0.489081 + 0.0427890i) q^{68} +(-2.69061 + 3.47557i) q^{70} +(-0.728237 + 0.420448i) q^{71} +(0.166069 + 0.619776i) q^{73} +(0.501107 - 2.84192i) q^{74} +(7.69812 + 2.80189i) q^{76} +(-12.6585 - 8.86359i) q^{77} +(9.56341 - 11.3972i) q^{79} +(-3.97103 + 2.50599i) q^{80} +(1.54806 + 1.54806i) q^{82} +(-0.830405 - 9.49158i) q^{83} +(0.658748 + 0.0315873i) q^{85} +(-1.88826 + 5.18795i) q^{86} +(5.54271 + 7.91582i) q^{88} +(6.19767 - 10.7347i) q^{89} +(-6.95400 - 12.0447i) q^{91} +(1.06660 - 2.28733i) q^{92} +(-0.713371 - 0.850162i) q^{94} +(10.4812 + 3.35409i) q^{95} +(-4.11255 - 1.91772i) q^{97} +(0.677399 - 2.52809i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{13}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.576956 0.0504771i 0.407969 0.0356927i 0.118676 0.992933i \(-0.462135\pi\)
0.289294 + 0.957240i \(0.406580\pi\)
\(3\) 0 0
\(4\) −1.63929 + 0.289050i −0.819643 + 0.144525i
\(5\) −2.18512 + 0.474625i −0.977214 + 0.212259i
\(6\) 0 0
\(7\) 2.78018 1.94671i 1.05081 0.735785i 0.0853543 0.996351i \(-0.472798\pi\)
0.965456 + 0.260565i \(0.0839089\pi\)
\(8\) −2.05006 + 0.549311i −0.724804 + 0.194211i
\(9\) 0 0
\(10\) −1.23676 + 0.384136i −0.391097 + 0.121474i
\(11\) −1.55726 4.27854i −0.469531 1.29003i −0.918125 0.396291i \(-0.870297\pi\)
0.448594 0.893736i \(-0.351925\pi\)
\(12\) 0 0
\(13\) 0.357151 4.08225i 0.0990558 1.13221i −0.770184 0.637822i \(-0.779835\pi\)
0.869239 0.494391i \(-0.164609\pi\)
\(14\) 1.50578 1.26350i 0.402436 0.337684i
\(15\) 0 0
\(16\) 1.97331 0.718227i 0.493328 0.179557i
\(17\) −0.284890 0.0763360i −0.0690959 0.0185142i 0.224105 0.974565i \(-0.428054\pi\)
−0.293201 + 0.956051i \(0.594721\pi\)
\(18\) 0 0
\(19\) −4.26213 2.46074i −0.977799 0.564532i −0.0761939 0.997093i \(-0.524277\pi\)
−0.901605 + 0.432561i \(0.857610\pi\)
\(20\) 3.44484 1.40965i 0.770289 0.315208i
\(21\) 0 0
\(22\) −1.11444 2.38992i −0.237599 0.509533i
\(23\) −0.869642 + 1.24198i −0.181333 + 0.258970i −0.899520 0.436880i \(-0.856083\pi\)
0.718187 + 0.695850i \(0.244972\pi\)
\(24\) 0 0
\(25\) 4.54946 2.07422i 0.909893 0.414844i
\(26\) 2.37331i 0.465444i
\(27\) 0 0
\(28\) −3.99482 + 3.99482i −0.754950 + 0.754950i
\(29\) −5.57542 4.67834i −1.03533 0.868745i −0.0438548 0.999038i \(-0.513964\pi\)
−0.991476 + 0.130293i \(0.958408\pi\)
\(30\) 0 0
\(31\) 0.591015 + 3.35181i 0.106149 + 0.602003i 0.990755 + 0.135663i \(0.0433165\pi\)
−0.884606 + 0.466340i \(0.845572\pi\)
\(32\) 4.94931 2.30790i 0.874922 0.407983i
\(33\) 0 0
\(34\) −0.168222 0.0296621i −0.0288498 0.00508701i
\(35\) −5.15107 + 5.57332i −0.870690 + 0.942063i
\(36\) 0 0
\(37\) 1.28961 4.81289i 0.212011 0.791234i −0.775187 0.631732i \(-0.782344\pi\)
0.987198 0.159502i \(-0.0509890\pi\)
\(38\) −2.58327 1.20460i −0.419062 0.195412i
\(39\) 0 0
\(40\) 4.21889 2.17331i 0.667066 0.343631i
\(41\) 2.42980 + 2.89573i 0.379472 + 0.452237i 0.921647 0.388028i \(-0.126844\pi\)
−0.542176 + 0.840265i \(0.682399\pi\)
\(42\) 0 0
\(43\) −4.02865 + 8.63947i −0.614364 + 1.31751i 0.315263 + 0.949004i \(0.397907\pi\)
−0.929627 + 0.368503i \(0.879871\pi\)
\(44\) 3.78950 + 6.56361i 0.571289 + 0.989502i
\(45\) 0 0
\(46\) −0.439054 + 0.760463i −0.0647349 + 0.112124i
\(47\) −1.09911 1.56969i −0.160322 0.228963i 0.730952 0.682429i \(-0.239076\pi\)
−0.891274 + 0.453466i \(0.850187\pi\)
\(48\) 0 0
\(49\) 1.54562 4.24655i 0.220802 0.606650i
\(50\) 2.52014 1.42638i 0.356401 0.201720i
\(51\) 0 0
\(52\) 0.594504 + 6.79521i 0.0824429 + 0.942327i
\(53\) 1.39575 + 1.39575i 0.191721 + 0.191721i 0.796439 0.604719i \(-0.206714\pi\)
−0.604719 + 0.796439i \(0.706714\pi\)
\(54\) 0 0
\(55\) 5.43349 + 8.60998i 0.732652 + 1.16097i
\(56\) −4.63018 + 5.51804i −0.618734 + 0.737379i
\(57\) 0 0
\(58\) −3.45292 2.41776i −0.453391 0.317468i
\(59\) 9.34637 + 3.40180i 1.21679 + 0.442877i 0.869055 0.494715i \(-0.164728\pi\)
0.347738 + 0.937592i \(0.386950\pi\)
\(60\) 0 0
\(61\) −0.249603 + 1.41557i −0.0319584 + 0.181245i −0.996609 0.0822889i \(-0.973777\pi\)
0.964650 + 0.263534i \(0.0848881\pi\)
\(62\) 0.510179 + 1.90402i 0.0647928 + 0.241810i
\(63\) 0 0
\(64\) −0.898191 + 0.518571i −0.112274 + 0.0648214i
\(65\) 1.15712 + 9.08971i 0.143523 + 1.12744i
\(66\) 0 0
\(67\) −9.46116 0.827744i −1.15586 0.101125i −0.506943 0.861980i \(-0.669224\pi\)
−0.648922 + 0.760855i \(0.724780\pi\)
\(68\) 0.489081 + 0.0427890i 0.0593097 + 0.00518893i
\(69\) 0 0
\(70\) −2.69061 + 3.47557i −0.321590 + 0.415410i
\(71\) −0.728237 + 0.420448i −0.0864258 + 0.0498980i −0.542590 0.839998i \(-0.682556\pi\)
0.456164 + 0.889896i \(0.349223\pi\)
\(72\) 0 0
\(73\) 0.166069 + 0.619776i 0.0194369 + 0.0725393i 0.974963 0.222367i \(-0.0713783\pi\)
−0.955526 + 0.294906i \(0.904712\pi\)
\(74\) 0.501107 2.84192i 0.0582526 0.330367i
\(75\) 0 0
\(76\) 7.69812 + 2.80189i 0.883035 + 0.321398i
\(77\) −12.6585 8.86359i −1.44257 1.01010i
\(78\) 0 0
\(79\) 9.56341 11.3972i 1.07597 1.28229i 0.118748 0.992924i \(-0.462112\pi\)
0.957219 0.289364i \(-0.0934436\pi\)
\(80\) −3.97103 + 2.50599i −0.443974 + 0.280178i
\(81\) 0 0
\(82\) 1.54806 + 1.54806i 0.170954 + 0.170954i
\(83\) −0.830405 9.49158i −0.0911488 1.04184i −0.894720 0.446627i \(-0.852625\pi\)
0.803571 0.595209i \(-0.202931\pi\)
\(84\) 0 0
\(85\) 0.658748 + 0.0315873i 0.0714513 + 0.00342612i
\(86\) −1.88826 + 5.18795i −0.203616 + 0.559431i
\(87\) 0 0
\(88\) 5.54271 + 7.91582i 0.590855 + 0.843829i
\(89\) 6.19767 10.7347i 0.656952 1.13787i −0.324448 0.945903i \(-0.605179\pi\)
0.981401 0.191971i \(-0.0614880\pi\)
\(90\) 0 0
\(91\) −6.95400 12.0447i −0.728977 1.26263i
\(92\) 1.06660 2.28733i 0.111200 0.238470i
\(93\) 0 0
\(94\) −0.713371 0.850162i −0.0735786 0.0876876i
\(95\) 10.4812 + 3.35409i 1.07534 + 0.344123i
\(96\) 0 0
\(97\) −4.11255 1.91772i −0.417567 0.194715i 0.202468 0.979289i \(-0.435104\pi\)
−0.620035 + 0.784574i \(0.712882\pi\)
\(98\) 0.677399 2.52809i 0.0684277 0.255376i
\(99\) 0 0
\(100\) −6.85831 + 4.71526i −0.685831 + 0.471526i
\(101\) 8.64670 + 1.52465i 0.860378 + 0.151708i 0.586394 0.810026i \(-0.300547\pi\)
0.273985 + 0.961734i \(0.411658\pi\)
\(102\) 0 0
\(103\) −2.78831 + 1.30021i −0.274741 + 0.128114i −0.555106 0.831780i \(-0.687322\pi\)
0.280365 + 0.959893i \(0.409544\pi\)
\(104\) 1.51025 + 8.56503i 0.148092 + 0.839871i
\(105\) 0 0
\(106\) 0.875738 + 0.734831i 0.0850592 + 0.0713731i
\(107\) 0.840083 0.840083i 0.0812138 0.0812138i −0.665333 0.746547i \(-0.731710\pi\)
0.746547 + 0.665333i \(0.231710\pi\)
\(108\) 0 0
\(109\) 15.3404i 1.46935i 0.678422 + 0.734673i \(0.262664\pi\)
−0.678422 + 0.734673i \(0.737336\pi\)
\(110\) 3.56949 + 4.69331i 0.340338 + 0.447490i
\(111\) 0 0
\(112\) 4.08799 5.83826i 0.386279 0.551664i
\(113\) −1.57466 3.37688i −0.148132 0.317670i 0.818215 0.574912i \(-0.194964\pi\)
−0.966347 + 0.257242i \(0.917186\pi\)
\(114\) 0 0
\(115\) 1.31080 3.12662i 0.122232 0.291559i
\(116\) 10.4920 + 6.05755i 0.974156 + 0.562429i
\(117\) 0 0
\(118\) 5.56415 + 1.49091i 0.512222 + 0.137249i
\(119\) −0.940649 + 0.342368i −0.0862292 + 0.0313849i
\(120\) 0 0
\(121\) −7.45432 + 6.25492i −0.677665 + 0.568629i
\(122\) −0.0725561 + 0.829320i −0.00656892 + 0.0750831i
\(123\) 0 0
\(124\) −1.93768 5.32374i −0.174009 0.478086i
\(125\) −8.95663 + 6.69170i −0.801105 + 0.598523i
\(126\) 0 0
\(127\) −17.0553 + 4.56996i −1.51342 + 0.405518i −0.917568 0.397579i \(-0.869850\pi\)
−0.595847 + 0.803098i \(0.703184\pi\)
\(128\) −9.43875 + 6.60908i −0.834275 + 0.584166i
\(129\) 0 0
\(130\) 1.12643 + 5.18595i 0.0987945 + 0.454838i
\(131\) 4.36693 0.770008i 0.381540 0.0672759i 0.0204113 0.999792i \(-0.493502\pi\)
0.361129 + 0.932516i \(0.382391\pi\)
\(132\) 0 0
\(133\) −16.6398 + 1.45580i −1.44286 + 0.126234i
\(134\) −5.50045 −0.475167
\(135\) 0 0
\(136\) 0.625972 0.0536767
\(137\) 17.1191 1.49772i 1.46258 0.127959i 0.672107 0.740454i \(-0.265390\pi\)
0.790474 + 0.612495i \(0.209834\pi\)
\(138\) 0 0
\(139\) 3.49278 0.615871i 0.296254 0.0522375i −0.0235459 0.999723i \(-0.507496\pi\)
0.319799 + 0.947485i \(0.396384\pi\)
\(140\) 6.83310 10.6252i 0.577503 0.897992i
\(141\) 0 0
\(142\) −0.398938 + 0.279339i −0.0334781 + 0.0234416i
\(143\) −18.0222 + 4.82905i −1.50710 + 0.403825i
\(144\) 0 0
\(145\) 14.4034 + 7.57647i 1.19614 + 0.629192i
\(146\) 0.127099 + 0.349201i 0.0105188 + 0.0289001i
\(147\) 0 0
\(148\) −0.722872 + 8.26246i −0.0594197 + 0.679170i
\(149\) 2.74544 2.30369i 0.224915 0.188726i −0.523366 0.852108i \(-0.675324\pi\)
0.748281 + 0.663382i \(0.230880\pi\)
\(150\) 0 0
\(151\) 18.4206 6.70454i 1.49904 0.545607i 0.543231 0.839583i \(-0.317201\pi\)
0.955813 + 0.293976i \(0.0949785\pi\)
\(152\) 10.0893 + 2.70342i 0.818351 + 0.219276i
\(153\) 0 0
\(154\) −7.75081 4.47493i −0.624578 0.360600i
\(155\) −2.88229 7.04359i −0.231511 0.565755i
\(156\) 0 0
\(157\) 0.239187 + 0.512939i 0.0190892 + 0.0409370i 0.915621 0.402042i \(-0.131699\pi\)
−0.896532 + 0.442979i \(0.853922\pi\)
\(158\) 4.94237 7.05843i 0.393193 0.561538i
\(159\) 0 0
\(160\) −9.71943 + 7.39209i −0.768388 + 0.584396i
\(161\) 5.14586i 0.405551i
\(162\) 0 0
\(163\) 3.48997 3.48997i 0.273355 0.273355i −0.557094 0.830449i \(-0.688084\pi\)
0.830449 + 0.557094i \(0.188084\pi\)
\(164\) −4.82015 4.04459i −0.376391 0.315829i
\(165\) 0 0
\(166\) −0.958215 5.43431i −0.0743719 0.421784i
\(167\) −13.2832 + 6.19404i −1.02788 + 0.479309i −0.862039 0.506843i \(-0.830812\pi\)
−0.165844 + 0.986152i \(0.553035\pi\)
\(168\) 0 0
\(169\) −3.73474 0.658535i −0.287288 0.0506566i
\(170\) 0.381663 0.0150272i 0.0292722 0.00115253i
\(171\) 0 0
\(172\) 4.10687 15.3270i 0.313146 1.16868i
\(173\) 8.49331 + 3.96050i 0.645735 + 0.301111i 0.717759 0.696292i \(-0.245168\pi\)
−0.0720241 + 0.997403i \(0.522946\pi\)
\(174\) 0 0
\(175\) 8.61045 14.6232i 0.650889 1.10541i
\(176\) −6.14592 7.32442i −0.463266 0.552099i
\(177\) 0 0
\(178\) 3.03393 6.50628i 0.227403 0.487666i
\(179\) −10.1322 17.5496i −0.757320 1.31172i −0.944213 0.329336i \(-0.893175\pi\)
0.186893 0.982380i \(-0.440158\pi\)
\(180\) 0 0
\(181\) 5.71685 9.90188i 0.424930 0.736001i −0.571484 0.820613i \(-0.693632\pi\)
0.996414 + 0.0846126i \(0.0269653\pi\)
\(182\) −4.62013 6.59823i −0.342467 0.489094i
\(183\) 0 0
\(184\) 1.10058 3.02383i 0.0811361 0.222920i
\(185\) −0.533632 + 11.1288i −0.0392334 + 0.818206i
\(186\) 0 0
\(187\) 0.117041 + 1.33779i 0.00855889 + 0.0978286i
\(188\) 2.25547 + 2.25547i 0.164497 + 0.164497i
\(189\) 0 0
\(190\) 6.21648 + 1.40610i 0.450991 + 0.102010i
\(191\) 3.38340 4.03218i 0.244814 0.291758i −0.629619 0.776904i \(-0.716789\pi\)
0.874433 + 0.485146i \(0.161233\pi\)
\(192\) 0 0
\(193\) 8.91213 + 6.24034i 0.641509 + 0.449189i 0.848530 0.529147i \(-0.177488\pi\)
−0.207021 + 0.978336i \(0.566377\pi\)
\(194\) −2.46956 0.898848i −0.177304 0.0645335i
\(195\) 0 0
\(196\) −1.30624 + 7.40806i −0.0933030 + 0.529147i
\(197\) −2.41739 9.02182i −0.172232 0.642778i −0.997007 0.0773166i \(-0.975365\pi\)
0.824775 0.565461i \(-0.191302\pi\)
\(198\) 0 0
\(199\) 10.1326 5.85008i 0.718284 0.414701i −0.0958368 0.995397i \(-0.530553\pi\)
0.814121 + 0.580696i \(0.197219\pi\)
\(200\) −8.18726 + 6.75133i −0.578927 + 0.477391i
\(201\) 0 0
\(202\) 5.06572 + 0.443193i 0.356423 + 0.0311830i
\(203\) −24.6080 2.15293i −1.72715 0.151106i
\(204\) 0 0
\(205\) −6.68379 5.17426i −0.466816 0.361386i
\(206\) −1.54310 + 0.890911i −0.107513 + 0.0620727i
\(207\) 0 0
\(208\) −2.22721 8.31207i −0.154429 0.576339i
\(209\) −3.89112 + 22.0677i −0.269155 + 1.52645i
\(210\) 0 0
\(211\) −13.7093 4.98977i −0.943786 0.343510i −0.176126 0.984368i \(-0.556357\pi\)
−0.767660 + 0.640858i \(0.778579\pi\)
\(212\) −2.69147 1.88459i −0.184851 0.129434i
\(213\) 0 0
\(214\) 0.442286 0.527096i 0.0302340 0.0360315i
\(215\) 4.70257 20.7903i 0.320712 1.41789i
\(216\) 0 0
\(217\) 8.16812 + 8.16812i 0.554488 + 0.554488i
\(218\) 0.774340 + 8.85074i 0.0524449 + 0.599448i
\(219\) 0 0
\(220\) −11.3958 12.5437i −0.768302 0.845694i
\(221\) −0.413372 + 1.13573i −0.0278064 + 0.0763974i
\(222\) 0 0
\(223\) −11.8646 16.9444i −0.794514 1.13468i −0.988132 0.153607i \(-0.950911\pi\)
0.193618 0.981077i \(-0.437978\pi\)
\(224\) 9.26718 16.0512i 0.619190 1.07247i
\(225\) 0 0
\(226\) −1.07897 1.86883i −0.0717718 0.124312i
\(227\) 4.17394 8.95104i 0.277034 0.594101i −0.717728 0.696324i \(-0.754818\pi\)
0.994762 + 0.102223i \(0.0325954\pi\)
\(228\) 0 0
\(229\) 17.3346 + 20.6585i 1.14550 + 1.36515i 0.920475 + 0.390800i \(0.127802\pi\)
0.225024 + 0.974353i \(0.427754\pi\)
\(230\) 0.598449 1.87009i 0.0394605 0.123310i
\(231\) 0 0
\(232\) 13.9998 + 6.52821i 0.919131 + 0.428598i
\(233\) 1.67108 6.23657i 0.109476 0.408571i −0.889338 0.457250i \(-0.848834\pi\)
0.998814 + 0.0486789i \(0.0155011\pi\)
\(234\) 0 0
\(235\) 3.14669 + 2.90829i 0.205268 + 0.189716i
\(236\) −16.3047 2.87495i −1.06134 0.187143i
\(237\) 0 0
\(238\) −0.525432 + 0.245013i −0.0340587 + 0.0158818i
\(239\) 2.94647 + 16.7103i 0.190591 + 1.08090i 0.918558 + 0.395286i \(0.129354\pi\)
−0.727967 + 0.685612i \(0.759535\pi\)
\(240\) 0 0
\(241\) −3.88280 3.25805i −0.250113 0.209870i 0.509108 0.860703i \(-0.329975\pi\)
−0.759221 + 0.650833i \(0.774420\pi\)
\(242\) −3.98508 + 3.98508i −0.256171 + 0.256171i
\(243\) 0 0
\(244\) 2.39267i 0.153175i
\(245\) −1.36184 + 10.0128i −0.0870045 + 0.639693i
\(246\) 0 0
\(247\) −11.5676 + 16.5202i −0.736028 + 1.05116i
\(248\) −3.05280 6.54675i −0.193853 0.415719i
\(249\) 0 0
\(250\) −4.82980 + 4.31292i −0.305464 + 0.272773i
\(251\) 7.62764 + 4.40382i 0.481452 + 0.277967i 0.721022 0.692913i \(-0.243673\pi\)
−0.239569 + 0.970879i \(0.577006\pi\)
\(252\) 0 0
\(253\) 6.66810 + 1.78671i 0.419220 + 0.112330i
\(254\) −9.60949 + 3.49757i −0.602953 + 0.219457i
\(255\) 0 0
\(256\) −3.52314 + 2.95627i −0.220196 + 0.184767i
\(257\) −2.26790 + 25.9222i −0.141468 + 1.61698i 0.511286 + 0.859411i \(0.329169\pi\)
−0.652753 + 0.757571i \(0.726386\pi\)
\(258\) 0 0
\(259\) −5.78393 15.8912i −0.359396 0.987432i
\(260\) −4.52424 14.5662i −0.280581 0.903355i
\(261\) 0 0
\(262\) 2.48066 0.664690i 0.153256 0.0410647i
\(263\) 4.72837 3.31084i 0.291564 0.204155i −0.418638 0.908153i \(-0.637493\pi\)
0.710202 + 0.703998i \(0.248604\pi\)
\(264\) 0 0
\(265\) −3.71232 2.38741i −0.228046 0.146658i
\(266\) −9.52696 + 1.67986i −0.584136 + 0.102999i
\(267\) 0 0
\(268\) 15.7488 1.37784i 0.962011 0.0841651i
\(269\) 21.3254 1.30023 0.650116 0.759835i \(-0.274720\pi\)
0.650116 + 0.759835i \(0.274720\pi\)
\(270\) 0 0
\(271\) 13.8664 0.842325 0.421162 0.906985i \(-0.361622\pi\)
0.421162 + 0.906985i \(0.361622\pi\)
\(272\) −0.617003 + 0.0539808i −0.0374113 + 0.00327306i
\(273\) 0 0
\(274\) 9.80135 1.72824i 0.592121 0.104407i
\(275\) −15.9593 16.2349i −0.962383 0.979004i
\(276\) 0 0
\(277\) −3.39790 + 2.37923i −0.204160 + 0.142954i −0.671185 0.741290i \(-0.734215\pi\)
0.467025 + 0.884244i \(0.345326\pi\)
\(278\) 1.98409 0.531636i 0.118998 0.0318854i
\(279\) 0 0
\(280\) 7.49849 14.2552i 0.448121 0.851908i
\(281\) −4.59659 12.6290i −0.274210 0.753385i −0.997991 0.0633553i \(-0.979820\pi\)
0.723781 0.690029i \(-0.242402\pi\)
\(282\) 0 0
\(283\) 1.01502 11.6017i 0.0603367 0.689651i −0.904443 0.426594i \(-0.859713\pi\)
0.964780 0.263058i \(-0.0847310\pi\)
\(284\) 1.07226 0.899731i 0.0636268 0.0533892i
\(285\) 0 0
\(286\) −10.1543 + 3.69586i −0.600435 + 0.218541i
\(287\) 12.3924 + 3.32054i 0.731502 + 0.196005i
\(288\) 0 0
\(289\) −14.6471 8.45651i −0.861594 0.497441i
\(290\) 8.69257 + 3.64425i 0.510445 + 0.213998i
\(291\) 0 0
\(292\) −0.451380 0.967988i −0.0264150 0.0566472i
\(293\) 15.1248 21.6004i 0.883598 1.26191i −0.0806060 0.996746i \(-0.525686\pi\)
0.964204 0.265162i \(-0.0854256\pi\)
\(294\) 0 0
\(295\) −22.0375 2.99731i −1.28307 0.174510i
\(296\) 10.5751i 0.614665i
\(297\) 0 0
\(298\) 1.46771 1.46771i 0.0850222 0.0850222i
\(299\) 4.75947 + 3.99367i 0.275248 + 0.230960i
\(300\) 0 0
\(301\) 5.61812 + 31.8619i 0.323823 + 1.83649i
\(302\) 10.2894 4.79804i 0.592090 0.276096i
\(303\) 0 0
\(304\) −10.1779 1.79463i −0.583741 0.102929i
\(305\) −0.126452 3.21165i −0.00724063 0.183899i
\(306\) 0 0
\(307\) 4.69578 17.5249i 0.268003 1.00020i −0.692384 0.721529i \(-0.743440\pi\)
0.960387 0.278670i \(-0.0898936\pi\)
\(308\) 23.3129 + 10.8710i 1.32838 + 0.619433i
\(309\) 0 0
\(310\) −2.01849 3.91835i −0.114643 0.222547i
\(311\) −11.0997 13.2281i −0.629405 0.750095i 0.353252 0.935528i \(-0.385076\pi\)
−0.982657 + 0.185433i \(0.940631\pi\)
\(312\) 0 0
\(313\) −6.31743 + 13.5478i −0.357082 + 0.765766i −1.00000 0.000169586i \(-0.999946\pi\)
0.642918 + 0.765935i \(0.277724\pi\)
\(314\) 0.163892 + 0.283870i 0.00924897 + 0.0160197i
\(315\) 0 0
\(316\) −12.3828 + 21.4476i −0.696586 + 1.20652i
\(317\) 8.90361 + 12.7157i 0.500077 + 0.714183i 0.987260 0.159116i \(-0.0508645\pi\)
−0.487183 + 0.873300i \(0.661976\pi\)
\(318\) 0 0
\(319\) −11.3340 + 31.1400i −0.634585 + 1.74351i
\(320\) 1.71653 1.55944i 0.0959567 0.0871754i
\(321\) 0 0
\(322\) 0.259748 + 2.96894i 0.0144752 + 0.165452i
\(323\) 1.02639 + 1.02639i 0.0571100 + 0.0571100i
\(324\) 0 0
\(325\) −6.84264 19.3129i −0.379562 1.07129i
\(326\) 1.83739 2.18972i 0.101764 0.121277i
\(327\) 0 0
\(328\) −6.57189 4.60169i −0.362872 0.254086i
\(329\) −6.11145 2.22439i −0.336935 0.122634i
\(330\) 0 0
\(331\) 0.733175 4.15804i 0.0402990 0.228547i −0.958006 0.286749i \(-0.907426\pi\)
0.998305 + 0.0582018i \(0.0185367\pi\)
\(332\) 4.10481 + 15.3194i 0.225281 + 0.840760i
\(333\) 0 0
\(334\) −7.35114 + 4.24418i −0.402237 + 0.232231i
\(335\) 21.0666 2.68178i 1.15099 0.146521i
\(336\) 0 0
\(337\) −4.83165 0.422715i −0.263197 0.0230267i −0.0452064 0.998978i \(-0.514395\pi\)
−0.217990 + 0.975951i \(0.569950\pi\)
\(338\) −2.18802 0.191427i −0.119013 0.0104123i
\(339\) 0 0
\(340\) −1.08901 + 0.138631i −0.0590597 + 0.00751830i
\(341\) 13.4205 7.74832i 0.726760 0.419595i
\(342\) 0 0
\(343\) 2.17930 + 8.13327i 0.117671 + 0.439155i
\(344\) 3.51321 19.9244i 0.189419 1.07425i
\(345\) 0 0
\(346\) 5.10018 + 1.85631i 0.274187 + 0.0997961i
\(347\) −15.3139 10.7229i −0.822092 0.575635i 0.0850901 0.996373i \(-0.472882\pi\)
−0.907182 + 0.420738i \(0.861771\pi\)
\(348\) 0 0
\(349\) −5.80311 + 6.91588i −0.310634 + 0.370199i −0.898662 0.438641i \(-0.855460\pi\)
0.588029 + 0.808840i \(0.299904\pi\)
\(350\) 4.22971 8.87156i 0.226088 0.474205i
\(351\) 0 0
\(352\) −17.5818 17.5818i −0.937112 0.937112i
\(353\) 3.00095 + 34.3010i 0.159724 + 1.82566i 0.478794 + 0.877927i \(0.341074\pi\)
−0.319069 + 0.947731i \(0.603370\pi\)
\(354\) 0 0
\(355\) 1.39173 1.26437i 0.0738652 0.0671056i
\(356\) −7.05689 + 19.3887i −0.374015 + 1.02760i
\(357\) 0 0
\(358\) −6.73171 9.61388i −0.355782 0.508109i
\(359\) −2.43212 + 4.21256i −0.128363 + 0.222330i −0.923042 0.384698i \(-0.874305\pi\)
0.794680 + 0.607029i \(0.207639\pi\)
\(360\) 0 0
\(361\) 2.61048 + 4.52148i 0.137394 + 0.237973i
\(362\) 2.79855 6.00152i 0.147089 0.315433i
\(363\) 0 0
\(364\) 14.8811 + 17.7346i 0.779982 + 0.929546i
\(365\) −0.657040 1.27546i −0.0343910 0.0667608i
\(366\) 0 0
\(367\) 16.1484 + 7.53013i 0.842941 + 0.393070i 0.795610 0.605810i \(-0.207151\pi\)
0.0473310 + 0.998879i \(0.484928\pi\)
\(368\) −0.824053 + 3.07541i −0.0429568 + 0.160317i
\(369\) 0 0
\(370\) 0.253868 + 6.44777i 0.0131980 + 0.335203i
\(371\) 6.59754 + 1.16332i 0.342527 + 0.0603968i
\(372\) 0 0
\(373\) 1.45346 0.677762i 0.0752575 0.0350932i −0.384625 0.923073i \(-0.625669\pi\)
0.459883 + 0.887980i \(0.347891\pi\)
\(374\) 0.135055 + 0.765936i 0.00698353 + 0.0396056i
\(375\) 0 0
\(376\) 3.11548 + 2.61420i 0.160669 + 0.134817i
\(377\) −21.0894 + 21.0894i −1.08616 + 1.08616i
\(378\) 0 0
\(379\) 16.2538i 0.834901i 0.908700 + 0.417451i \(0.137076\pi\)
−0.908700 + 0.417451i \(0.862924\pi\)
\(380\) −18.1511 2.46873i −0.931133 0.126643i
\(381\) 0 0
\(382\) 1.74854 2.49717i 0.0894631 0.127767i
\(383\) 14.0616 + 30.1551i 0.718512 + 1.54085i 0.836578 + 0.547848i \(0.184553\pi\)
−0.118066 + 0.993006i \(0.537669\pi\)
\(384\) 0 0
\(385\) 31.8672 + 13.3599i 1.62410 + 0.680885i
\(386\) 5.45690 + 3.15054i 0.277749 + 0.160358i
\(387\) 0 0
\(388\) 7.29597 + 1.95495i 0.370397 + 0.0992475i
\(389\) −11.1086 + 4.04319i −0.563227 + 0.204998i −0.607914 0.794003i \(-0.707993\pi\)
0.0446865 + 0.999001i \(0.485771\pi\)
\(390\) 0 0
\(391\) 0.342560 0.287442i 0.0173240 0.0145366i
\(392\) −0.835926 + 9.55468i −0.0422207 + 0.482584i
\(393\) 0 0
\(394\) −1.85012 5.08317i −0.0932078 0.256086i
\(395\) −15.4878 + 29.4433i −0.779273 + 1.48145i
\(396\) 0 0
\(397\) 12.4793 3.34381i 0.626317 0.167821i 0.0683192 0.997664i \(-0.478236\pi\)
0.557998 + 0.829842i \(0.311570\pi\)
\(398\) 5.55079 3.88671i 0.278236 0.194823i
\(399\) 0 0
\(400\) 7.48775 7.36063i 0.374387 0.368031i
\(401\) 7.99873 1.41039i 0.399437 0.0704316i 0.0296788 0.999559i \(-0.490552\pi\)
0.369758 + 0.929128i \(0.379440\pi\)
\(402\) 0 0
\(403\) 13.8940 1.21557i 0.692111 0.0605519i
\(404\) −14.6151 −0.727129
\(405\) 0 0
\(406\) −14.3064 −0.710016
\(407\) −22.6004 + 1.97728i −1.12026 + 0.0980100i
\(408\) 0 0
\(409\) 21.0475 3.71124i 1.04073 0.183509i 0.372938 0.927856i \(-0.378350\pi\)
0.667793 + 0.744347i \(0.267239\pi\)
\(410\) −4.11743 2.64794i −0.203346 0.130772i
\(411\) 0 0
\(412\) 4.19501 2.93738i 0.206673 0.144714i
\(413\) 32.6069 8.73700i 1.60448 0.429919i
\(414\) 0 0
\(415\) 6.31947 + 20.3461i 0.310210 + 0.998749i
\(416\) −7.65378 21.0286i −0.375258 1.03101i
\(417\) 0 0
\(418\) −1.13110 + 12.9285i −0.0553237 + 0.632353i
\(419\) 2.15215 1.80587i 0.105139 0.0882223i −0.588703 0.808350i \(-0.700361\pi\)
0.693842 + 0.720127i \(0.255917\pi\)
\(420\) 0 0
\(421\) −4.87917 + 1.77587i −0.237796 + 0.0865507i −0.458169 0.888865i \(-0.651495\pi\)
0.220373 + 0.975416i \(0.429272\pi\)
\(422\) −8.16152 2.18687i −0.397297 0.106455i
\(423\) 0 0
\(424\) −3.62806 2.09466i −0.176194 0.101726i
\(425\) −1.45443 + 0.243636i −0.0705504 + 0.0118181i
\(426\) 0 0
\(427\) 2.06175 + 4.42144i 0.0997752 + 0.213969i
\(428\) −1.13431 + 1.61996i −0.0548289 + 0.0783038i
\(429\) 0 0
\(430\) 1.66374 12.2325i 0.0802325 0.589903i
\(431\) 12.2810i 0.591553i −0.955257 0.295776i \(-0.904422\pi\)
0.955257 0.295776i \(-0.0955783\pi\)
\(432\) 0 0
\(433\) 10.5318 10.5318i 0.506127 0.506127i −0.407209 0.913335i \(-0.633498\pi\)
0.913335 + 0.407209i \(0.133498\pi\)
\(434\) 5.12495 + 4.30034i 0.246005 + 0.206423i
\(435\) 0 0
\(436\) −4.43415 25.1473i −0.212357 1.20434i
\(437\) 6.76271 3.15350i 0.323504 0.150852i
\(438\) 0 0
\(439\) −0.587913 0.103665i −0.0280596 0.00494766i 0.159601 0.987182i \(-0.448979\pi\)
−0.187660 + 0.982234i \(0.560090\pi\)
\(440\) −15.8685 14.6663i −0.756502 0.699187i
\(441\) 0 0
\(442\) −0.181169 + 0.676131i −0.00861732 + 0.0321603i
\(443\) −20.1220 9.38303i −0.956024 0.445801i −0.118956 0.992900i \(-0.537955\pi\)
−0.837068 + 0.547098i \(0.815732\pi\)
\(444\) 0 0
\(445\) −8.44769 + 26.3981i −0.400459 + 1.25139i
\(446\) −7.70067 9.17730i −0.364637 0.434558i
\(447\) 0 0
\(448\) −1.48763 + 3.19024i −0.0702840 + 0.150724i
\(449\) 2.87636 + 4.98200i 0.135744 + 0.235115i 0.925881 0.377814i \(-0.123324\pi\)
−0.790137 + 0.612930i \(0.789991\pi\)
\(450\) 0 0
\(451\) 8.60564 14.9054i 0.405224 0.701868i
\(452\) 3.55741 + 5.08051i 0.167327 + 0.238967i
\(453\) 0 0
\(454\) 1.95636 5.37504i 0.0918163 0.252263i
\(455\) 20.9120 + 23.0185i 0.980370 + 1.07912i
\(456\) 0 0
\(457\) 2.29810 + 26.2674i 0.107501 + 1.22874i 0.837941 + 0.545761i \(0.183759\pi\)
−0.730440 + 0.682977i \(0.760685\pi\)
\(458\) 11.0441 + 11.0441i 0.516055 + 0.516055i
\(459\) 0 0
\(460\) −1.24502 + 5.50431i −0.0580493 + 0.256640i
\(461\) 21.8021 25.9827i 1.01542 1.21013i 0.0379057 0.999281i \(-0.487931\pi\)
0.977518 0.210853i \(-0.0676242\pi\)
\(462\) 0 0
\(463\) −14.3797 10.0688i −0.668283 0.467937i 0.189546 0.981872i \(-0.439298\pi\)
−0.857829 + 0.513935i \(0.828187\pi\)
\(464\) −14.3622 5.22740i −0.666746 0.242676i
\(465\) 0 0
\(466\) 0.649338 3.68258i 0.0300800 0.170592i
\(467\) −1.95125 7.28218i −0.0902933 0.336979i 0.905971 0.423341i \(-0.139143\pi\)
−0.996264 + 0.0863616i \(0.972476\pi\)
\(468\) 0 0
\(469\) −27.9151 + 16.1168i −1.28900 + 0.744205i
\(470\) 1.96231 + 1.51912i 0.0905144 + 0.0700718i
\(471\) 0 0
\(472\) −21.0292 1.83982i −0.967948 0.0846845i
\(473\) 43.2379 + 3.78283i 1.98808 + 0.173935i
\(474\) 0 0
\(475\) −24.4945 2.35446i −1.12388 0.108030i
\(476\) 1.44303 0.833134i 0.0661412 0.0381867i
\(477\) 0 0
\(478\) 2.54347 + 9.49236i 0.116336 + 0.434171i
\(479\) −2.36842 + 13.4320i −0.108216 + 0.613722i 0.881671 + 0.471864i \(0.156419\pi\)
−0.989887 + 0.141858i \(0.954692\pi\)
\(480\) 0 0
\(481\) −19.1869 6.98344i −0.874845 0.318418i
\(482\) −2.40466 1.68376i −0.109529 0.0766932i
\(483\) 0 0
\(484\) 10.4118 12.4083i 0.473262 0.564012i
\(485\) 9.89660 + 2.23851i 0.449382 + 0.101646i
\(486\) 0 0
\(487\) 17.1622 + 17.1622i 0.777696 + 0.777696i 0.979439 0.201743i \(-0.0646605\pi\)
−0.201743 + 0.979439i \(0.564661\pi\)
\(488\) −0.265887 3.03910i −0.0120361 0.137574i
\(489\) 0 0
\(490\) −0.280303 + 5.84568i −0.0126628 + 0.264081i
\(491\) −12.1283 + 33.3223i −0.547344 + 1.50382i 0.289938 + 0.957046i \(0.406365\pi\)
−0.837282 + 0.546771i \(0.815857\pi\)
\(492\) 0 0
\(493\) 1.23126 + 1.75842i 0.0554530 + 0.0791951i
\(494\) −5.84009 + 10.1153i −0.262758 + 0.455111i
\(495\) 0 0
\(496\) 3.57362 + 6.18969i 0.160460 + 0.277925i
\(497\) −1.20614 + 2.58658i −0.0541030 + 0.116024i
\(498\) 0 0
\(499\) −25.8228 30.7744i −1.15599 1.37765i −0.913171 0.407578i \(-0.866374\pi\)
−0.242815 0.970073i \(-0.578071\pi\)
\(500\) 12.7482 13.5585i 0.570118 0.606355i
\(501\) 0 0
\(502\) 4.62310 + 2.15579i 0.206339 + 0.0962176i
\(503\) 1.01183 3.77620i 0.0451153 0.168372i −0.939693 0.342020i \(-0.888889\pi\)
0.984808 + 0.173648i \(0.0555555\pi\)
\(504\) 0 0
\(505\) −19.6177 + 0.772406i −0.872975 + 0.0343716i
\(506\) 3.93739 + 0.694268i 0.175038 + 0.0308640i
\(507\) 0 0
\(508\) 26.6376 12.4213i 1.18185 0.551107i
\(509\) 4.88932 + 27.7287i 0.216715 + 1.22905i 0.877905 + 0.478835i \(0.158941\pi\)
−0.661190 + 0.750219i \(0.729948\pi\)
\(510\) 0 0
\(511\) 1.66822 + 1.39980i 0.0737978 + 0.0619237i
\(512\) 14.4119 14.4119i 0.636923 0.636923i
\(513\) 0 0
\(514\) 15.0704i 0.664728i
\(515\) 5.47567 4.16451i 0.241287 0.183510i
\(516\) 0 0
\(517\) −5.00438 + 7.14699i −0.220092 + 0.314324i
\(518\) −4.13921 8.87657i −0.181867 0.390014i
\(519\) 0 0
\(520\) −7.36524 17.9988i −0.322987 0.789299i
\(521\) −20.7682 11.9905i −0.909872 0.525315i −0.0294818 0.999565i \(-0.509386\pi\)
−0.880390 + 0.474251i \(0.842719\pi\)
\(522\) 0 0
\(523\) −8.27760 2.21798i −0.361954 0.0969853i 0.0732586 0.997313i \(-0.476660\pi\)
−0.435213 + 0.900328i \(0.643327\pi\)
\(524\) −6.93607 + 2.52452i −0.303004 + 0.110284i
\(525\) 0 0
\(526\) 2.56094 2.14888i 0.111662 0.0936957i
\(527\) 0.0874898 1.00001i 0.00381111 0.0435612i
\(528\) 0 0
\(529\) 7.08023 + 19.4528i 0.307836 + 0.845773i
\(530\) −2.26236 1.19004i −0.0982705 0.0516922i
\(531\) 0 0
\(532\) 26.8566 7.19621i 1.16438 0.311995i
\(533\) 12.6889 8.88487i 0.549618 0.384846i
\(534\) 0 0
\(535\) −1.43695 + 2.23440i −0.0621249 + 0.0966016i
\(536\) 19.8506 3.50020i 0.857415 0.151185i
\(537\) 0 0
\(538\) 12.3038 1.07644i 0.530455 0.0464088i
\(539\) −20.5759 −0.886268
\(540\) 0 0
\(541\) −24.1490 −1.03825 −0.519123 0.854700i \(-0.673741\pi\)
−0.519123 + 0.854700i \(0.673741\pi\)
\(542\) 8.00031 0.699936i 0.343643 0.0300648i
\(543\) 0 0
\(544\) −1.58618 + 0.279687i −0.0680070 + 0.0119915i
\(545\) −7.28094 33.5206i −0.311881 1.43586i
\(546\) 0 0
\(547\) −8.43453 + 5.90592i −0.360634 + 0.252519i −0.739825 0.672800i \(-0.765092\pi\)
0.379190 + 0.925319i \(0.376203\pi\)
\(548\) −27.6301 + 7.40347i −1.18030 + 0.316261i
\(549\) 0 0
\(550\) −10.0273 8.56127i −0.427566 0.365054i
\(551\) 12.2510 + 33.6593i 0.521910 + 1.43394i
\(552\) 0 0
\(553\) 4.40099 50.3035i 0.187149 2.13912i
\(554\) −1.84034 + 1.54423i −0.0781886 + 0.0656080i
\(555\) 0 0
\(556\) −5.54764 + 2.01918i −0.235272 + 0.0856322i
\(557\) −0.0136213 0.00364981i −0.000577152 0.000154647i 0.258530 0.966003i \(-0.416762\pi\)
−0.259108 + 0.965848i \(0.583428\pi\)
\(558\) 0 0
\(559\) 33.8297 + 19.5316i 1.43084 + 0.826098i
\(560\) −6.16176 + 14.6975i −0.260382 + 0.621084i
\(561\) 0 0
\(562\) −3.28951 7.05437i −0.138759 0.297571i
\(563\) 8.54312 12.2008i 0.360050 0.514204i −0.597734 0.801695i \(-0.703932\pi\)
0.957783 + 0.287490i \(0.0928210\pi\)
\(564\) 0 0
\(565\) 5.04357 + 6.63150i 0.212185 + 0.278989i
\(566\) 6.74492i 0.283510i
\(567\) 0 0
\(568\) 1.26197 1.26197i 0.0529511 0.0529511i
\(569\) −21.1007 17.7056i −0.884589 0.742258i 0.0825286 0.996589i \(-0.473700\pi\)
−0.967117 + 0.254331i \(0.918145\pi\)
\(570\) 0 0
\(571\) −3.36410 19.0788i −0.140783 0.798421i −0.970657 0.240470i \(-0.922699\pi\)
0.829873 0.557952i \(-0.188413\pi\)
\(572\) 28.1478 13.1255i 1.17692 0.548805i
\(573\) 0 0
\(574\) 7.31750 + 1.29027i 0.305426 + 0.0538549i
\(575\) −1.38027 + 7.45416i −0.0575613 + 0.310860i
\(576\) 0 0
\(577\) −6.81468 + 25.4327i −0.283699 + 1.05878i 0.666086 + 0.745875i \(0.267968\pi\)
−0.949785 + 0.312904i \(0.898698\pi\)
\(578\) −8.87759 4.13969i −0.369259 0.172188i
\(579\) 0 0
\(580\) −25.8013 8.25670i −1.07134 0.342841i
\(581\) −20.7860 24.7718i −0.862348 1.02771i
\(582\) 0 0
\(583\) 3.79821 8.14529i 0.157306 0.337344i
\(584\) −0.680899 1.17935i −0.0281758 0.0488020i
\(585\) 0 0
\(586\) 7.63599 13.2259i 0.315440 0.546358i
\(587\) −11.8655 16.9456i −0.489740 0.699421i 0.495882 0.868390i \(-0.334845\pi\)
−0.985621 + 0.168969i \(0.945956\pi\)
\(588\) 0 0
\(589\) 5.72896 15.7402i 0.236058 0.648563i
\(590\) −12.8659 0.616929i −0.529683 0.0253985i
\(591\) 0 0
\(592\) −0.911944 10.4236i −0.0374807 0.428406i
\(593\) −25.1558 25.1558i −1.03302 1.03302i −0.999436 0.0335886i \(-0.989306\pi\)
−0.0335886 0.999436i \(-0.510694\pi\)
\(594\) 0 0
\(595\) 1.89293 1.19457i 0.0776026 0.0489726i
\(596\) −3.83467 + 4.56998i −0.157074 + 0.187194i
\(597\) 0 0
\(598\) 2.94760 + 2.06393i 0.120536 + 0.0844003i
\(599\) 22.0669 + 8.03169i 0.901629 + 0.328166i 0.750905 0.660410i \(-0.229617\pi\)
0.150723 + 0.988576i \(0.451840\pi\)
\(600\) 0 0
\(601\) −0.359287 + 2.03762i −0.0146556 + 0.0831161i −0.991258 0.131935i \(-0.957881\pi\)
0.976603 + 0.215052i \(0.0689920\pi\)
\(602\) 4.84970 + 18.0993i 0.197659 + 0.737674i
\(603\) 0 0
\(604\) −28.2586 + 16.3151i −1.14983 + 0.663853i
\(605\) 13.3198 17.2057i 0.541527 0.699512i
\(606\) 0 0
\(607\) 27.2557 + 2.38456i 1.10627 + 0.0967864i 0.625623 0.780126i \(-0.284845\pi\)
0.480651 + 0.876912i \(0.340401\pi\)
\(608\) −26.7737 2.34240i −1.08582 0.0949967i
\(609\) 0 0
\(610\) −0.235072 1.84660i −0.00951779 0.0747665i
\(611\) −6.80042 + 3.92623i −0.275116 + 0.158838i
\(612\) 0 0
\(613\) −2.44513 9.12534i −0.0987578 0.368569i 0.898805 0.438350i \(-0.144437\pi\)
−0.997562 + 0.0697805i \(0.977770\pi\)
\(614\) 1.82465 10.3481i 0.0736370 0.417616i
\(615\) 0 0
\(616\) 30.8195 + 11.2174i 1.24175 + 0.451962i
\(617\) −26.3513 18.4514i −1.06086 0.742826i −0.0933483 0.995634i \(-0.529757\pi\)
−0.967516 + 0.252808i \(0.918646\pi\)
\(618\) 0 0
\(619\) 19.6122 23.3729i 0.788279 0.939435i −0.210996 0.977487i \(-0.567671\pi\)
0.999276 + 0.0380520i \(0.0121153\pi\)
\(620\) 6.76084 + 10.7133i 0.271522 + 0.430257i
\(621\) 0 0
\(622\) −7.07174 7.07174i −0.283551 0.283551i
\(623\) −3.66660 41.9094i −0.146899 1.67907i
\(624\) 0 0
\(625\) 16.3952 18.8732i 0.655809 0.754927i
\(626\) −2.96103 + 8.13536i −0.118346 + 0.325154i
\(627\) 0 0
\(628\) −0.540361 0.771716i −0.0215628 0.0307948i
\(629\) −0.734793 + 1.27270i −0.0292981 + 0.0507459i
\(630\) 0 0
\(631\) −13.5982 23.5528i −0.541338 0.937624i −0.998828 0.0484094i \(-0.984585\pi\)
0.457490 0.889215i \(-0.348749\pi\)
\(632\) −13.3449 + 28.6182i −0.530832 + 1.13837i
\(633\) 0 0
\(634\) 5.77884 + 6.88695i 0.229507 + 0.273516i
\(635\) 35.0988 18.0808i 1.39286 0.717513i
\(636\) 0 0
\(637\) −16.7835 7.82626i −0.664985 0.310088i
\(638\) −4.96739 + 18.5385i −0.196661 + 0.733948i
\(639\) 0 0
\(640\) 17.4879 18.9215i 0.691271 0.747937i
\(641\) −47.3771 8.35386i −1.87128 0.329957i −0.881459 0.472261i \(-0.843438\pi\)
−0.989823 + 0.142304i \(0.954549\pi\)
\(642\) 0 0
\(643\) 1.29754 0.605053i 0.0511700 0.0238610i −0.396865 0.917877i \(-0.629902\pi\)
0.448035 + 0.894016i \(0.352124\pi\)
\(644\) −1.48741 8.43554i −0.0586123 0.332407i
\(645\) 0 0
\(646\) 0.643993 + 0.540374i 0.0253376 + 0.0212607i
\(647\) 3.76082 3.76082i 0.147853 0.147853i −0.629305 0.777158i \(-0.716660\pi\)
0.777158 + 0.629305i \(0.216660\pi\)
\(648\) 0 0
\(649\) 45.2862i 1.77764i
\(650\) −4.92276 10.7973i −0.193087 0.423504i
\(651\) 0 0
\(652\) −4.71228 + 6.72983i −0.184547 + 0.263561i
\(653\) 14.6726 + 31.4655i 0.574184 + 1.23134i 0.952181 + 0.305535i \(0.0988353\pi\)
−0.377997 + 0.925807i \(0.623387\pi\)
\(654\) 0 0
\(655\) −9.17678 + 3.75521i −0.358567 + 0.146728i
\(656\) 6.87455 + 3.96902i 0.268406 + 0.154964i
\(657\) 0 0
\(658\) −3.63832 0.974884i −0.141836 0.0380049i
\(659\) −29.5525 + 10.7562i −1.15120 + 0.419003i −0.845946 0.533268i \(-0.820964\pi\)
−0.305254 + 0.952271i \(0.598742\pi\)
\(660\) 0 0
\(661\) 18.2275 15.2947i 0.708967 0.594894i −0.215342 0.976539i \(-0.569087\pi\)
0.924309 + 0.381645i \(0.124642\pi\)
\(662\) 0.213124 2.43602i 0.00828329 0.0946785i
\(663\) 0 0
\(664\) 6.91620 + 19.0021i 0.268401 + 0.737425i
\(665\) 35.6690 11.0788i 1.38318 0.429616i
\(666\) 0 0
\(667\) 10.6590 2.85607i 0.412719 0.110588i
\(668\) 19.9845 13.9933i 0.773224 0.541417i
\(669\) 0 0
\(670\) 12.0191 2.61065i 0.464340 0.100858i
\(671\) 6.44526 1.13647i 0.248816 0.0438730i
\(672\) 0 0
\(673\) −1.83430 + 0.160481i −0.0707073 + 0.00618608i −0.122454 0.992474i \(-0.539077\pi\)
0.0517472 + 0.998660i \(0.483521\pi\)
\(674\) −2.80899 −0.108198
\(675\) 0 0
\(676\) 6.31265 0.242794
\(677\) −11.1662 + 0.976915i −0.429151 + 0.0375459i −0.299686 0.954038i \(-0.596882\pi\)
−0.129466 + 0.991584i \(0.541326\pi\)
\(678\) 0 0
\(679\) −15.1669 + 2.67433i −0.582052 + 0.102631i
\(680\) −1.36782 + 0.297102i −0.0524536 + 0.0113933i
\(681\) 0 0
\(682\) 7.35191 5.14787i 0.281519 0.197122i
\(683\) −31.7505 + 8.50752i −1.21490 + 0.325531i −0.808682 0.588246i \(-0.799819\pi\)
−0.406216 + 0.913777i \(0.633152\pi\)
\(684\) 0 0
\(685\) −36.6963 + 11.3978i −1.40209 + 0.435489i
\(686\) 1.66791 + 4.58253i 0.0636809 + 0.174962i
\(687\) 0 0
\(688\) −1.74469 + 19.9419i −0.0665155 + 0.760276i
\(689\) 6.19628 5.19930i 0.236060 0.198078i
\(690\) 0 0
\(691\) 35.2185 12.8185i 1.33977 0.487638i 0.430033 0.902813i \(-0.358502\pi\)
0.909742 + 0.415175i \(0.136280\pi\)
\(692\) −15.0677 4.03739i −0.572790 0.153479i
\(693\) 0 0
\(694\) −9.37669 5.41364i −0.355934 0.205499i
\(695\) −7.33982 + 3.00351i −0.278415 + 0.113930i
\(696\) 0 0
\(697\) −0.471178 1.01044i −0.0178471 0.0382733i
\(698\) −2.99905 + 4.28308i −0.113516 + 0.162117i
\(699\) 0 0
\(700\) −9.88815 + 26.4604i −0.373737 + 1.00011i
\(701\) 8.75525i 0.330681i 0.986237 + 0.165341i \(0.0528724\pi\)
−0.986237 + 0.165341i \(0.947128\pi\)
\(702\) 0 0
\(703\) −17.3398 + 17.3398i −0.653981 + 0.653981i
\(704\) 3.61744 + 3.03539i 0.136337 + 0.114401i
\(705\) 0 0
\(706\) 3.46283 + 19.6387i 0.130325 + 0.739112i
\(707\) 27.0074 12.5938i 1.01572 0.473638i
\(708\) 0 0
\(709\) 7.84342 + 1.38301i 0.294566 + 0.0519399i 0.318978 0.947762i \(-0.396660\pi\)
−0.0244124 + 0.999702i \(0.507771\pi\)
\(710\) 0.739144 0.799734i 0.0277396 0.0300135i
\(711\) 0 0
\(712\) −6.80890 + 25.4112i −0.255174 + 0.952323i
\(713\) −4.67685 2.18085i −0.175149 0.0816735i
\(714\) 0 0
\(715\) 37.0887 19.1058i 1.38704 0.714517i
\(716\) 21.6823 + 25.8400i 0.810307 + 0.965687i
\(717\) 0 0
\(718\) −1.19059 + 2.55323i −0.0444324 + 0.0952856i
\(719\) 4.35425 + 7.54179i 0.162386 + 0.281261i 0.935724 0.352733i \(-0.114748\pi\)
−0.773338 + 0.633994i \(0.781414\pi\)
\(720\) 0 0
\(721\) −5.22089 + 9.04285i −0.194436 + 0.336773i
\(722\) 1.73436 + 2.47693i 0.0645463 + 0.0921816i
\(723\) 0 0
\(724\) −6.50941 + 17.8845i −0.241920 + 0.664671i
\(725\) −35.0691 9.71927i −1.30243 0.360965i
\(726\) 0 0
\(727\) −3.05305 34.8965i −0.113231 1.29424i −0.814005 0.580857i \(-0.802717\pi\)
0.700774 0.713383i \(-0.252838\pi\)
\(728\) 20.8724 + 20.8724i 0.773581 + 0.773581i
\(729\) 0 0
\(730\) −0.443465 0.702720i −0.0164134 0.0260088i
\(731\) 1.80722 2.15377i 0.0668426 0.0796599i
\(732\) 0 0
\(733\) 15.4172 + 10.7952i 0.569447 + 0.398731i 0.822537 0.568711i \(-0.192558\pi\)
−0.253090 + 0.967443i \(0.581447\pi\)
\(734\) 9.69703 + 3.52943i 0.357924 + 0.130274i
\(735\) 0 0
\(736\) −1.43777 + 8.15398i −0.0529968 + 0.300560i
\(737\) 11.1919 + 41.7689i 0.412261 + 1.53858i
\(738\) 0 0
\(739\) 9.05915 5.23030i 0.333246 0.192400i −0.324035 0.946045i \(-0.605040\pi\)
0.657281 + 0.753645i \(0.271706\pi\)
\(740\) −2.34201 18.3975i −0.0860940 0.676307i
\(741\) 0 0
\(742\) 3.86521 + 0.338162i 0.141896 + 0.0124143i
\(743\) −26.5503 2.32285i −0.974035 0.0852170i −0.410987 0.911641i \(-0.634816\pi\)
−0.563048 + 0.826424i \(0.690371\pi\)
\(744\) 0 0
\(745\) −4.90570 + 6.33689i −0.179731 + 0.232166i
\(746\) 0.804373 0.464405i 0.0294502 0.0170031i
\(747\) 0 0
\(748\) −0.578551 2.15918i −0.0211539 0.0789475i
\(749\) 0.700190 3.97098i 0.0255844 0.145096i
\(750\) 0 0
\(751\) −33.4699 12.1820i −1.22133 0.444529i −0.350712 0.936483i \(-0.614061\pi\)
−0.870621 + 0.491954i \(0.836283\pi\)
\(752\) −3.29628 2.30808i −0.120203 0.0841670i
\(753\) 0 0
\(754\) −11.1031 + 13.2322i −0.404352 + 0.481888i
\(755\) −37.0689 + 23.3930i −1.34908 + 0.851360i
\(756\) 0 0
\(757\) −23.2266 23.2266i −0.844185 0.844185i 0.145215 0.989400i \(-0.453613\pi\)
−0.989400 + 0.145215i \(0.953613\pi\)
\(758\) 0.820445 + 9.37772i 0.0297999 + 0.340614i
\(759\) 0 0
\(760\) −23.3294 1.11866i −0.846247 0.0405780i
\(761\) 11.0481 30.3545i 0.400494 1.10035i −0.561547 0.827445i \(-0.689794\pi\)
0.962041 0.272904i \(-0.0879842\pi\)
\(762\) 0 0
\(763\) 29.8633 + 42.6492i 1.08112 + 1.54400i
\(764\) −4.38086 + 7.58787i −0.158494 + 0.274519i
\(765\) 0 0
\(766\) 9.63504 + 16.6884i 0.348128 + 0.602976i
\(767\) 17.2251 36.9393i 0.621961 1.33380i
\(768\) 0 0
\(769\) −24.2180 28.8618i −0.873322 1.04078i −0.998814 0.0486900i \(-0.984495\pi\)
0.125492 0.992095i \(-0.459949\pi\)
\(770\) 19.0603 + 6.09952i 0.686887 + 0.219812i
\(771\) 0 0
\(772\) −16.4133 7.65364i −0.590727 0.275461i
\(773\) −1.80797 + 6.74744i −0.0650282 + 0.242689i −0.990788 0.135424i \(-0.956760\pi\)
0.925759 + 0.378113i \(0.123427\pi\)
\(774\) 0 0
\(775\) 9.64119 + 14.0231i 0.346322 + 0.503723i
\(776\) 9.48439 + 1.67235i 0.340470 + 0.0600340i
\(777\) 0 0
\(778\) −6.20507 + 2.89347i −0.222463 + 0.103736i
\(779\) −3.23050 18.3211i −0.115745 0.656421i
\(780\) 0 0
\(781\) 2.93295 + 2.46104i 0.104949 + 0.0880630i
\(782\) 0.183133 0.183133i 0.00654881 0.00654881i
\(783\) 0 0
\(784\) 9.48986i 0.338924i
\(785\) −0.766105 1.00731i −0.0273435 0.0359523i
\(786\) 0 0