Properties

Label 405.2.r.a.368.9
Level $405$
Weight $2$
Character 405.368
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 368.9
Character \(\chi\) \(=\) 405.368
Dual form 405.2.r.a.197.9

$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{18}\right)\)

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 0.289294 0.957240i \(-0.406580\pi\)
0.118676 + 0.992933i \(0.462135\pi\)
\(3\) 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 0.965456 0.260565i \(-0.0839089\pi\)
0.0853543 + 0.996351i \(0.472798\pi\)
\(8\) −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 0.448594 + 0.893736i \(0.351925\pi\)
−0.918125 + 0.396291i \(0.870297\pi\)
\(12\) 0 0
\(13\) 0.357151 + 4.08225i 0.0990558 + 1.13221i 0.869239 + 0.494391i \(0.164609\pi\)
−0.770184 + 0.637822i \(0.779835\pi\)
\(14\) 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 −0.293201 0.956051i \(-0.594721\pi\)
0.224105 + 0.974565i \(0.428054\pi\)
\(18\) 0 0
\(19\) −4.26213 + 2.46074i −0.977799 + 0.564532i −0.901605 0.432561i \(-0.857610\pi\)
−0.0761939 + 0.997093i \(0.524277\pi\)
\(20\) 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 0.718187 0.695850i \(-0.244972\pi\)
−0.899520 + 0.436880i \(0.856083\pi\)
\(24\) 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 −0.991476 0.130293i \(-0.958408\pi\)
−0.0438548 + 0.999038i \(0.513964\pi\)
\(30\) 0 0
\(31\) 0.591015 3.35181i 0.106149 0.602003i −0.884606 0.466340i \(-0.845572\pi\)
0.990755 0.135663i \(-0.0433165\pi\)
\(32\) 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 0.987198 + 0.159502i \(0.0509890\pi\)
−0.775187 + 0.631732i \(0.782344\pi\)
\(38\) −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 −0.542176 0.840265i \(-0.682399\pi\)
0.921647 + 0.388028i \(0.126844\pi\)
\(42\) 0 0
\(43\) −4.02865 8.63947i −0.614364 1.31751i −0.929627 0.368503i \(-0.879871\pi\)
0.315263 0.949004i \(-0.397907\pi\)
\(44\) 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 −0.891274 0.453466i \(-0.850187\pi\)
0.730952 + 0.682429i \(0.239076\pi\)
\(48\) 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 −0.604719 0.796439i \(-0.706714\pi\)
0.796439 + 0.604719i \(0.206714\pi\)
\(54\) 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 0.347738 0.937592i \(-0.386950\pi\)
0.869055 + 0.494715i \(0.164728\pi\)
\(60\) 0 0
\(61\) −0.249603 1.41557i −0.0319584 0.181245i 0.964650 0.263534i \(-0.0848881\pi\)
−0.996609 + 0.0822889i \(0.973777\pi\)
\(62\) 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 −0.648922 0.760855i \(-0.724780\pi\)
−0.506943 + 0.861980i \(0.669224\pi\)
\(68\) 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 0.456164 0.889896i \(-0.349223\pi\)
−0.542590 + 0.839998i \(0.682556\pi\)
\(72\) 0 0
\(73\) 0.166069 0.619776i 0.0194369 0.0725393i −0.955526 0.294906i \(-0.904712\pi\)
0.974963 + 0.222367i \(0.0713783\pi\)
\(74\) 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 0.957219 + 0.289364i \(0.0934436\pi\)
0.118748 + 0.992924i \(0.462112\pi\)
\(80\) −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 0.803571 + 0.595209i \(0.202931\pi\)
−0.894720 + 0.446627i \(0.852625\pi\)
\(84\) 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 0.981401 + 0.191971i \(0.0614880\pi\)
−0.324448 + 0.945903i \(0.605179\pi\)
\(90\) 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 −0.620035 0.784574i \(-0.712882\pi\)
0.202468 + 0.979289i \(0.435104\pi\)
\(98\) 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 0.273985 0.961734i \(-0.411658\pi\)
0.586394 + 0.810026i \(0.300547\pi\)
\(102\) 0 0
\(103\) −2.78831 1.30021i −0.274741 0.128114i 0.280365 0.959893i \(-0.409544\pi\)
−0.555106 + 0.831780i \(0.687322\pi\)
\(104\) 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 0.746547 0.665333i \(-0.231710\pi\)
−0.665333 + 0.746547i \(0.731710\pi\)
\(108\) 0 0
\(109\) 15.3404i 1.46935i −0.678422 0.734673i \(-0.737336\pi\)
0.678422 0.734673i \(-0.262664\pi\)
\(110\) 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 −0.966347 0.257242i \(-0.917186\pi\)
0.818215 + 0.574912i \(0.194964\pi\)
\(114\) 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 −0.595847 0.803098i \(-0.703184\pi\)
−0.917568 + 0.397579i \(0.869850\pi\)
\(128\) −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 0.361129 0.932516i \(-0.382391\pi\)
0.0204113 + 0.999792i \(0.493502\pi\)
\(132\) 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 0.790474 0.612495i \(-0.209834\pi\)
0.672107 + 0.740454i \(0.265390\pi\)
\(138\) 0 0
\(139\) 3.49278 + 0.615871i 0.296254 + 0.0522375i 0.319799 0.947485i \(-0.396384\pi\)
−0.0235459 + 0.999723i \(0.507496\pi\)
\(140\) 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 0.748281 0.663382i \(-0.230880\pi\)
−0.523366 + 0.852108i \(0.675324\pi\)
\(150\) 0 0
\(151\) 18.4206 + 6.70454i 1.49904 + 0.545607i 0.955813 0.293976i \(-0.0949785\pi\)
0.543231 + 0.839583i \(0.317201\pi\)
\(152\) 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 −0.896532 0.442979i \(-0.853922\pi\)
0.915621 + 0.402042i \(0.131699\pi\)
\(158\) 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 0.830449 0.557094i \(-0.188084\pi\)
−0.557094 + 0.830449i \(0.688084\pi\)
\(164\) −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 −0.165844 0.986152i \(-0.553035\pi\)
−0.862039 + 0.506843i \(0.830812\pi\)
\(168\) 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 −0.0720241 0.997403i \(-0.522946\pi\)
0.717759 + 0.696292i \(0.245168\pi\)
\(174\) 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 0.186893 + 0.982380i \(0.440158\pi\)
−0.944213 + 0.329336i \(0.893175\pi\)
\(180\) 0 0
\(181\) 5.71685 + 9.90188i 0.424930 + 0.736001i 0.996414 0.0846126i \(-0.0269653\pi\)
−0.571484 + 0.820613i \(0.693632\pi\)
\(182\) −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 0.874433 0.485146i \(-0.161233\pi\)
−0.629619 + 0.776904i \(0.716789\pi\)
\(192\) 0 0
\(193\) 8.91213 6.24034i 0.641509 0.449189i −0.207021 0.978336i \(-0.566377\pi\)
0.848530 + 0.529147i \(0.177488\pi\)
\(194\) −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 0.824775 + 0.565461i \(0.191302\pi\)
−0.997007 + 0.0773166i \(0.975365\pi\)
\(198\) 0 0
\(199\) 10.1326 + 5.85008i 0.718284 + 0.414701i 0.814121 0.580696i \(-0.197219\pi\)
−0.0958368 + 0.995397i \(0.530553\pi\)
\(200\) −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 −0.767660 0.640858i \(-0.778579\pi\)
−0.176126 + 0.984368i \(0.556357\pi\)
\(212\) −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 0.193618 + 0.981077i \(0.437978\pi\)
−0.988132 + 0.153607i \(0.950911\pi\)
\(224\) 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 0.994762 0.102223i \(-0.0325954\pi\)
−0.717728 + 0.696324i \(0.754818\pi\)
\(228\) 0 0
\(229\) 17.3346 20.6585i 1.14550 1.36515i 0.225024 0.974353i \(-0.427754\pi\)
0.920475 0.390800i \(-0.127802\pi\)
\(230\) 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 0.998814 0.0486789i \(-0.0155011\pi\)
−0.889338 + 0.457250i \(0.848834\pi\)
\(234\) 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 −0.727967 0.685612i \(-0.759535\pi\)
0.918558 0.395286i \(-0.129354\pi\)
\(240\) 0 0
\(241\) −3.88280 + 3.25805i −0.250113 + 0.209870i −0.759221 0.650833i \(-0.774420\pi\)
0.509108 + 0.860703i \(0.329975\pi\)
\(242\) −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 −0.239569 0.970879i \(-0.577006\pi\)
0.721022 + 0.692913i \(0.243673\pi\)
\(252\) 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 −0.652753 0.757571i \(-0.726386\pi\)
0.511286 0.859411i \(-0.329169\pi\)
\(258\) 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 0.710202 0.703998i \(-0.248604\pi\)
−0.418638 + 0.908153i \(0.637493\pi\)
\(264\) 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 0.467025 0.884244i \(-0.345326\pi\)
−0.671185 + 0.741290i \(0.734215\pi\)
\(278\) 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 0.723781 + 0.690029i \(0.242402\pi\)
−0.997991 + 0.0633553i \(0.979820\pi\)
\(282\) 0 0
\(283\) 1.01502 + 11.6017i 0.0603367 + 0.689651i 0.964780 + 0.263058i \(0.0847310\pi\)
−0.904443 + 0.426594i \(0.859713\pi\)
\(284\) 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 0.964204 + 0.265162i \(0.0854256\pi\)
−0.0806060 + 0.996746i \(0.525686\pi\)
\(294\) 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 0.960387 + 0.278670i \(0.0898936\pi\)
−0.692384 + 0.721529i \(0.743440\pi\)
\(308\) 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 −0.982657 0.185433i \(-0.940631\pi\)
0.353252 + 0.935528i \(0.385076\pi\)
\(312\) 0 0
\(313\) −6.31743 13.5478i −0.357082 0.765766i 0.642918 0.765935i \(-0.277724\pi\)
−1.00000 0.000169586i \(0.999946\pi\)
\(314\) 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 −0.487183 0.873300i \(-0.661976\pi\)
0.987260 + 0.159116i \(0.0508645\pi\)
\(318\) 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 0.998305 0.0582018i \(-0.0185367\pi\)
−0.958006 + 0.286749i \(0.907426\pi\)
\(332\) 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 −0.217990 0.975951i \(-0.569950\pi\)
−0.0452064 + 0.998978i \(0.514395\pi\)
\(338\) −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 −0.907182 0.420738i \(-0.861771\pi\)
0.0850901 + 0.996373i \(0.472882\pi\)
\(348\) 0 0
\(349\) −5.80311 6.91588i −0.310634 0.370199i 0.588029 0.808840i \(-0.299904\pi\)
−0.898662 + 0.438641i \(0.855460\pi\)
\(350\) 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 −0.319069 0.947731i \(-0.603370\pi\)
0.478794 0.877927i \(-0.341074\pi\)
\(354\) 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 0.794680 0.607029i \(-0.207639\pi\)
−0.923042 + 0.384698i \(0.874305\pi\)
\(360\) 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 0.0473310 0.998879i \(-0.484928\pi\)
0.795610 + 0.605810i \(0.207151\pi\)
\(368\) −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 0.459883 0.887980i \(-0.347891\pi\)
−0.384625 + 0.923073i \(0.625669\pi\)
\(374\) 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 \(-0.862924\pi\)
0.908700 0.417451i \(-0.137076\pi\)
\(380\) −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 −0.118066 0.993006i \(-0.537669\pi\)
0.836578 0.547848i \(-0.184553\pi\)
\(384\) 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 0.0446865 0.999001i \(-0.485771\pi\)
−0.607914 + 0.794003i \(0.707993\pi\)
\(390\) 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 0.557998 0.829842i \(-0.311570\pi\)
0.0683192 + 0.997664i \(0.478236\pi\)
\(398\) 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 0.369758 0.929128i \(-0.379440\pi\)
0.0296788 + 0.999559i \(0.490552\pi\)
\(402\) 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 0.667793 0.744347i \(-0.267239\pi\)
0.372938 + 0.927856i \(0.378350\pi\)
\(410\) −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 0.693842 0.720127i \(-0.255917\pi\)
−0.588703 + 0.808350i \(0.700361\pi\)
\(420\) 0 0
\(421\) −4.87917 1.77587i −0.237796 0.0865507i 0.220373 0.975416i \(-0.429272\pi\)
−0.458169 + 0.888865i \(0.651495\pi\)
\(422\) −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 \(0.0955783\pi\)
−0.955257 + 0.295776i \(0.904422\pi\)
\(432\) 0 0
\(433\) 10.5318 + 10.5318i 0.506127 + 0.506127i 0.913335 0.407209i \(-0.133498\pi\)
−0.407209 + 0.913335i \(0.633498\pi\)
\(434\) 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 −0.187660 0.982234i \(-0.560090\pi\)
0.159601 + 0.987182i \(0.448979\pi\)
\(440\) −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 −0.837068 0.547098i \(-0.815732\pi\)
−0.118956 + 0.992900i \(0.537955\pi\)
\(444\) 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 −0.790137 0.612930i \(-0.789991\pi\)
0.925881 + 0.377814i \(0.123324\pi\)
\(450\) 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 −0.730440 0.682977i \(-0.760685\pi\)
0.837941 0.545761i \(-0.183759\pi\)
\(458\) 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 0.977518 + 0.210853i \(0.0676242\pi\)
0.0379057 + 0.999281i \(0.487931\pi\)
\(462\) 0 0
\(463\) −14.3797 + 10.0688i −0.668283 + 0.467937i −0.857829 0.513935i \(-0.828187\pi\)
0.189546 + 0.981872i \(0.439298\pi\)
\(464\) −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 −0.996264 0.0863616i \(-0.972476\pi\)
0.905971 + 0.423341i \(0.139143\pi\)
\(468\) 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 −0.989887 0.141858i \(-0.954692\pi\)
0.881671 0.471864i \(-0.156419\pi\)
\(480\) 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 −0.201743 0.979439i \(-0.564661\pi\)
0.979439 + 0.201743i \(0.0646605\pi\)
\(488\) −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 −0.837282 0.546771i \(-0.815857\pi\)
0.289938 0.957046i \(-0.406365\pi\)
\(492\) 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 −0.242815 + 0.970073i \(0.578071\pi\)
−0.913171 + 0.407578i \(0.866374\pi\)
\(500\) 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 0.984808 0.173648i \(-0.0555555\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(504\) 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 −0.661190 0.750219i \(-0.729948\pi\)
0.877905 0.478835i \(-0.158941\pi\)
\(510\) 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 −0.880390 0.474251i \(-0.842719\pi\)
−0.0294818 + 0.999565i \(0.509386\pi\)
\(522\) 0 0
\(523\) −8.27760 + 2.21798i −0.361954 + 0.0969853i −0.435213 0.900328i \(-0.643327\pi\)
0.0732586 + 0.997313i \(0.476660\pi\)
\(524\) −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 0.379190 0.925319i \(-0.376203\pi\)
−0.739825 + 0.672800i \(0.765092\pi\)
\(548\) −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 −0.259108 0.965848i \(-0.583428\pi\)
0.258530 + 0.966003i \(0.416762\pi\)
\(558\) 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 0.957783 0.287490i \(-0.0928210\pi\)
−0.597734 + 0.801695i \(0.703932\pi\)
\(564\) 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 −0.967117 0.254331i \(-0.918145\pi\)
0.0825286 + 0.996589i \(0.473700\pi\)
\(570\) 0 0
\(571\) −3.36410 + 19.0788i −0.140783 + 0.798421i 0.829873 + 0.557952i \(0.188413\pi\)
−0.970657 + 0.240470i \(0.922699\pi\)
\(572\) 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 −0.949785 0.312904i \(-0.898698\pi\)
0.666086 0.745875i \(-0.267968\pi\)
\(578\) −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 −0.985621 0.168969i \(-0.945956\pi\)
0.495882 + 0.868390i \(0.334845\pi\)
\(588\) 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 −0.0335886 + 0.999436i \(0.510694\pi\)
−0.999436 + 0.0335886i \(0.989306\pi\)
\(594\) 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 0.150723 0.988576i \(-0.451840\pi\)
0.750905 + 0.660410i \(0.229617\pi\)
\(600\) 0 0
\(601\) −0.359287 2.03762i −0.0146556 0.0831161i 0.976603 0.215052i \(-0.0689920\pi\)
−0.991258 + 0.131935i \(0.957881\pi\)
\(602\) 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 0.480651 0.876912i \(-0.340401\pi\)
0.625623 + 0.780126i \(0.284845\pi\)
\(608\) −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 −0.997562 0.0697805i \(-0.977770\pi\)
0.898805 + 0.438350i \(0.144437\pi\)
\(614\) 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 −0.967516 0.252808i \(-0.918646\pi\)
−0.0933483 + 0.995634i \(0.529757\pi\)
\(618\) 0 0
\(619\) 19.6122 + 23.3729i 0.788279 + 0.939435i 0.999276 0.0380520i \(-0.0121153\pi\)
−0.210996 + 0.977487i \(0.567671\pi\)
\(620\) 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 0.457490 + 0.889215i \(0.348749\pi\)
−0.998828 + 0.0484094i \(0.984585\pi\)
\(632\) −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 −0.989823 0.142304i \(-0.954549\pi\)
−0.881459 + 0.472261i \(0.843438\pi\)
\(642\) 0 0
\(643\) 1.29754 + 0.605053i 0.0511700 + 0.0238610i 0.448035 0.894016i \(-0.352124\pi\)
−0.396865 + 0.917877i \(0.629902\pi\)
\(644\) −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 0.777158 0.629305i \(-0.216660\pi\)
−0.629305 + 0.777158i \(0.716660\pi\)
\(648\) 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 −0.377997 0.925807i \(-0.623387\pi\)
0.952181 0.305535i \(-0.0988353\pi\)
\(654\) 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 −0.305254 0.952271i \(-0.598742\pi\)
−0.845946 + 0.533268i \(0.820964\pi\)
\(660\) 0 0
\(661\) 18.2275 + 15.2947i 0.708967 + 0.594894i 0.924309 0.381645i \(-0.124642\pi\)
−0.215342 + 0.976539i \(0.569087\pi\)
\(662\) 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 0.0517472 0.998660i \(-0.483521\pi\)
−0.122454 + 0.992474i \(0.539077\pi\)
\(674\) −2.80899 −0.108198
\(675\) 0 0
\(676\) 6.31265 0.242794
\(677\) −11.1662 0.976915i −0.429151 0.0375459i −0.129466 0.991584i \(-0.541326\pi\)
−0.299686 + 0.954038i \(0.596882\pi\)
\(678\) 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 −0.406216 0.913777i \(-0.633152\pi\)
−0.808682 + 0.588246i \(0.799819\pi\)
\(684\) 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 0.909742 0.415175i \(-0.136280\pi\)
0.430033 + 0.902813i \(0.358502\pi\)
\(692\) −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 \(-0.947128\pi\)
0.986237 0.165341i \(-0.0528724\pi\)
\(702\) 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 −0.0244124 0.999702i \(-0.507771\pi\)
0.318978 + 0.947762i \(0.396660\pi\)
\(710\) 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 −0.773338 0.633994i \(-0.781414\pi\)
0.935724 + 0.352733i \(0.114748\pi\)
\(720\) 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 0.700774 + 0.713383i \(0.252838\pi\)
−0.814005 + 0.580857i \(0.802717\pi\)
\(728\) 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 −0.253090 0.967443i \(-0.581447\pi\)
0.822537 + 0.568711i \(0.192558\pi\)
\(734\) 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 0.657281 0.753645i \(-0.271706\pi\)
−0.324035 + 0.946045i \(0.605040\pi\)
\(740\) −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 −0.563048 0.826424i \(-0.690371\pi\)
−0.410987 + 0.911641i \(0.634816\pi\)
\(744\) 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 −0.870621 0.491954i \(-0.836283\pi\)
−0.350712 + 0.936483i \(0.614061\pi\)
\(752\) −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 −0.989400 0.145215i \(-0.953613\pi\)
0.145215 + 0.989400i \(0.453613\pi\)
\(758\) 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 0.962041 + 0.272904i \(0.0879842\pi\)
−0.561547 + 0.827445i \(0.689794\pi\)
\(762\) 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 0.125492 + 0.992095i \(0.459949\pi\)
−0.998814 + 0.0486900i \(0.984495\pi\)
\(770\) 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 0.925759 0.378113i \(-0.123427\pi\)
−0.990788 + 0.135424i \(0.956760\pi\)
\(774\) 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
\(787\) −8.41019