Properties

Label 76.2.i.a.17.2
Level $76$
Weight $2$
Character 76.17
Analytic conductor $0.607$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 76.i (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.606863055362\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 6 x^{11} - 3 x^{10} + 70 x^{9} - 15 x^{8} - 426 x^{7} + 64 x^{6} + 1659 x^{5} + 267 x^{4} - 3969 x^{3} - 2088 x^{2} + 4446 x + 4161\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 17.2
Root \(-1.26253 + 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 76.17
Dual form 76.2.i.a.9.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.86622 + 1.56594i) q^{3} +(-2.06765 + 0.752564i) q^{5} +(-1.48413 - 2.57059i) q^{7} +(0.509650 + 2.89037i) q^{9} +O(q^{10})\) \(q+(1.86622 + 1.56594i) q^{3} +(-2.06765 + 0.752564i) q^{5} +(-1.48413 - 2.57059i) q^{7} +(0.509650 + 2.89037i) q^{9} +(1.34956 - 2.33751i) q^{11} +(3.64418 - 3.05783i) q^{13} +(-5.03717 - 1.83338i) q^{15} +(-1.19836 + 6.79626i) q^{17} +(-4.33264 - 0.477728i) q^{19} +(1.25569 - 7.12136i) q^{21} +(-4.86497 - 1.77070i) q^{23} +(-0.121388 + 0.101857i) q^{25} +(0.0792304 - 0.137231i) q^{27} +(1.17057 + 6.63861i) q^{29} +(2.14339 + 3.71247i) q^{31} +(6.17900 - 2.24897i) q^{33} +(5.00321 + 4.19819i) q^{35} -5.02546 q^{37} +11.5892 q^{39} +(1.42844 + 1.19860i) q^{41} +(8.50895 - 3.09700i) q^{43} +(-3.22896 - 5.59273i) q^{45} +(0.108919 + 0.617710i) q^{47} +(-0.905299 + 1.56802i) q^{49} +(-12.8790 + 10.8067i) q^{51} +(-6.42007 - 2.33671i) q^{53} +(-1.03130 + 5.84880i) q^{55} +(-7.33756 - 7.67622i) q^{57} +(0.623372 - 3.53532i) q^{59} +(9.43969 + 3.43576i) q^{61} +(6.67357 - 5.59979i) q^{63} +(-5.23369 + 9.06501i) q^{65} +(-1.58002 - 8.96073i) q^{67} +(-6.30628 - 10.9228i) q^{69} +(-0.533286 + 0.194100i) q^{71} +(-0.598968 - 0.502594i) q^{73} -0.386038 q^{75} -8.01173 q^{77} +(2.42448 + 2.03438i) q^{79} +(8.63662 - 3.14347i) q^{81} +(3.64810 + 6.31870i) q^{83} +(-2.63682 - 14.9542i) q^{85} +(-8.21115 + 14.2221i) q^{87} +(7.84414 - 6.58201i) q^{89} +(-13.2689 - 4.82948i) q^{91} +(-1.81347 + 10.2847i) q^{93} +(9.31792 - 2.27281i) q^{95} +(-1.47083 + 8.34147i) q^{97} +(7.44408 + 2.70942i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 3q^{3} + 3q^{7} - 3q^{9} + O(q^{10}) \) \( 12q - 3q^{3} + 3q^{7} - 3q^{9} + 3q^{11} - 9q^{13} - 15q^{15} - 3q^{17} - 12q^{19} - 15q^{21} - 12q^{23} - 18q^{25} - 9q^{27} + 27q^{29} + 6q^{31} + 48q^{33} + 33q^{35} - 12q^{37} + 60q^{39} + 3q^{41} + 27q^{43} + 24q^{45} - 15q^{47} + 9q^{49} - 33q^{51} - 21q^{53} - 27q^{55} - 42q^{57} - 48q^{59} - 6q^{61} - 9q^{63} - 33q^{65} + 24q^{67} - 33q^{69} + 30q^{73} + 42q^{75} + 24q^{77} + 3q^{79} + 3q^{81} + 3q^{83} - 42q^{85} - 18q^{87} - 18q^{89} - 24q^{91} - 78q^{93} + 9q^{95} + 12q^{97} - 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.86622 + 1.56594i 1.07746 + 0.904098i 0.995708 0.0925543i \(-0.0295032\pi\)
0.0817546 + 0.996652i \(0.473948\pi\)
\(4\) 0 0
\(5\) −2.06765 + 0.752564i −0.924682 + 0.336557i −0.760100 0.649806i \(-0.774850\pi\)
−0.164583 + 0.986363i \(0.552628\pi\)
\(6\) 0 0
\(7\) −1.48413 2.57059i −0.560949 0.971593i −0.997414 0.0718714i \(-0.977103\pi\)
0.436465 0.899721i \(-0.356230\pi\)
\(8\) 0 0
\(9\) 0.509650 + 2.89037i 0.169883 + 0.963456i
\(10\) 0 0
\(11\) 1.34956 2.33751i 0.406909 0.704787i −0.587633 0.809128i \(-0.699940\pi\)
0.994542 + 0.104341i \(0.0332733\pi\)
\(12\) 0 0
\(13\) 3.64418 3.05783i 1.01071 0.848090i 0.0222816 0.999752i \(-0.492907\pi\)
0.988432 + 0.151662i \(0.0484625\pi\)
\(14\) 0 0
\(15\) −5.03717 1.83338i −1.30059 0.473376i
\(16\) 0 0
\(17\) −1.19836 + 6.79626i −0.290646 + 1.64834i 0.393744 + 0.919220i \(0.371180\pi\)
−0.684390 + 0.729116i \(0.739931\pi\)
\(18\) 0 0
\(19\) −4.33264 0.477728i −0.993976 0.109598i
\(20\) 0 0
\(21\) 1.25569 7.12136i 0.274014 1.55401i
\(22\) 0 0
\(23\) −4.86497 1.77070i −1.01442 0.369217i −0.219289 0.975660i \(-0.570374\pi\)
−0.795127 + 0.606442i \(0.792596\pi\)
\(24\) 0 0
\(25\) −0.121388 + 0.101857i −0.0242776 + 0.0203713i
\(26\) 0 0
\(27\) 0.0792304 0.137231i 0.0152479 0.0264101i
\(28\) 0 0
\(29\) 1.17057 + 6.63861i 0.217369 + 1.23276i 0.876749 + 0.480949i \(0.159708\pi\)
−0.659380 + 0.751810i \(0.729181\pi\)
\(30\) 0 0
\(31\) 2.14339 + 3.71247i 0.384965 + 0.666779i 0.991764 0.128076i \(-0.0408802\pi\)
−0.606799 + 0.794855i \(0.707547\pi\)
\(32\) 0 0
\(33\) 6.17900 2.24897i 1.07563 0.391496i
\(34\) 0 0
\(35\) 5.00321 + 4.19819i 0.845696 + 0.709623i
\(36\) 0 0
\(37\) −5.02546 −0.826181 −0.413091 0.910690i \(-0.635551\pi\)
−0.413091 + 0.910690i \(0.635551\pi\)
\(38\) 0 0
\(39\) 11.5892 1.85576
\(40\) 0 0
\(41\) 1.42844 + 1.19860i 0.223085 + 0.187190i 0.747479 0.664285i \(-0.231264\pi\)
−0.524395 + 0.851475i \(0.675708\pi\)
\(42\) 0 0
\(43\) 8.50895 3.09700i 1.29760 0.472289i 0.401387 0.915908i \(-0.368528\pi\)
0.896215 + 0.443620i \(0.146306\pi\)
\(44\) 0 0
\(45\) −3.22896 5.59273i −0.481346 0.833715i
\(46\) 0 0
\(47\) 0.108919 + 0.617710i 0.0158875 + 0.0901022i 0.991720 0.128415i \(-0.0409890\pi\)
−0.975833 + 0.218518i \(0.929878\pi\)
\(48\) 0 0
\(49\) −0.905299 + 1.56802i −0.129328 + 0.224003i
\(50\) 0 0
\(51\) −12.8790 + 10.8067i −1.80342 + 1.51325i
\(52\) 0 0
\(53\) −6.42007 2.33671i −0.881864 0.320972i −0.138902 0.990306i \(-0.544357\pi\)
−0.742962 + 0.669334i \(0.766580\pi\)
\(54\) 0 0
\(55\) −1.03130 + 5.84880i −0.139061 + 0.788652i
\(56\) 0 0
\(57\) −7.33756 7.67622i −0.971884 1.01674i
\(58\) 0 0
\(59\) 0.623372 3.53532i 0.0811561 0.460259i −0.916964 0.398970i \(-0.869368\pi\)
0.998120 0.0612890i \(-0.0195211\pi\)
\(60\) 0 0
\(61\) 9.43969 + 3.43576i 1.20863 + 0.439905i 0.866228 0.499650i \(-0.166538\pi\)
0.342400 + 0.939554i \(0.388760\pi\)
\(62\) 0 0
\(63\) 6.67357 5.59979i 0.840791 0.705507i
\(64\) 0 0
\(65\) −5.23369 + 9.06501i −0.649159 + 1.12438i
\(66\) 0 0
\(67\) −1.58002 8.96073i −0.193030 1.09473i −0.915196 0.403008i \(-0.867965\pi\)
0.722167 0.691719i \(-0.243146\pi\)
\(68\) 0 0
\(69\) −6.30628 10.9228i −0.759187 1.31495i
\(70\) 0 0
\(71\) −0.533286 + 0.194100i −0.0632894 + 0.0230355i −0.373471 0.927642i \(-0.621832\pi\)
0.310181 + 0.950677i \(0.399610\pi\)
\(72\) 0 0
\(73\) −0.598968 0.502594i −0.0701039 0.0588242i 0.607062 0.794654i \(-0.292348\pi\)
−0.677166 + 0.735830i \(0.736792\pi\)
\(74\) 0 0
\(75\) −0.386038 −0.0445759
\(76\) 0 0
\(77\) −8.01173 −0.913021
\(78\) 0 0
\(79\) 2.42448 + 2.03438i 0.272775 + 0.228885i 0.768905 0.639363i \(-0.220802\pi\)
−0.496130 + 0.868248i \(0.665246\pi\)
\(80\) 0 0
\(81\) 8.63662 3.14347i 0.959625 0.349275i
\(82\) 0 0
\(83\) 3.64810 + 6.31870i 0.400431 + 0.693568i 0.993778 0.111380i \(-0.0355269\pi\)
−0.593346 + 0.804947i \(0.702194\pi\)
\(84\) 0 0
\(85\) −2.63682 14.9542i −0.286003 1.62201i
\(86\) 0 0
\(87\) −8.21115 + 14.2221i −0.880328 + 1.52477i
\(88\) 0 0
\(89\) 7.84414 6.58201i 0.831477 0.697692i −0.124152 0.992263i \(-0.539621\pi\)
0.955630 + 0.294571i \(0.0951768\pi\)
\(90\) 0 0
\(91\) −13.2689 4.82948i −1.39096 0.506267i
\(92\) 0 0
\(93\) −1.81347 + 10.2847i −0.188048 + 1.06647i
\(94\) 0 0
\(95\) 9.31792 2.27281i 0.955998 0.233186i
\(96\) 0 0
\(97\) −1.47083 + 8.34147i −0.149340 + 0.846948i 0.814440 + 0.580248i \(0.197044\pi\)
−0.963780 + 0.266700i \(0.914067\pi\)
\(98\) 0 0
\(99\) 7.44408 + 2.70942i 0.748158 + 0.272307i
\(100\) 0 0
\(101\) 7.17480 6.02037i 0.713920 0.599050i −0.211776 0.977318i \(-0.567925\pi\)
0.925696 + 0.378269i \(0.123480\pi\)
\(102\) 0 0
\(103\) −6.00311 + 10.3977i −0.591504 + 1.02452i 0.402526 + 0.915409i \(0.368132\pi\)
−0.994030 + 0.109107i \(0.965201\pi\)
\(104\) 0 0
\(105\) 2.76295 + 15.6695i 0.269637 + 1.52918i
\(106\) 0 0
\(107\) −7.15153 12.3868i −0.691364 1.19748i −0.971391 0.237486i \(-0.923677\pi\)
0.280027 0.959992i \(-0.409657\pi\)
\(108\) 0 0
\(109\) 2.08076 0.757335i 0.199301 0.0725396i −0.240441 0.970664i \(-0.577292\pi\)
0.439742 + 0.898124i \(0.355070\pi\)
\(110\) 0 0
\(111\) −9.37862 7.86960i −0.890179 0.746949i
\(112\) 0 0
\(113\) −7.64213 −0.718911 −0.359455 0.933162i \(-0.617038\pi\)
−0.359455 + 0.933162i \(0.617038\pi\)
\(114\) 0 0
\(115\) 11.3916 1.06228
\(116\) 0 0
\(117\) 10.6955 + 8.97460i 0.988800 + 0.829702i
\(118\) 0 0
\(119\) 19.2490 7.00605i 1.76455 0.642244i
\(120\) 0 0
\(121\) 1.85735 + 3.21703i 0.168850 + 0.292457i
\(122\) 0 0
\(123\) 0.788836 + 4.47371i 0.0711270 + 0.403381i
\(124\) 0 0
\(125\) 5.67521 9.82975i 0.507606 0.879200i
\(126\) 0 0
\(127\) −3.55943 + 2.98672i −0.315848 + 0.265028i −0.786904 0.617075i \(-0.788317\pi\)
0.471056 + 0.882103i \(0.343873\pi\)
\(128\) 0 0
\(129\) 20.7293 + 7.54485i 1.82511 + 0.664287i
\(130\) 0 0
\(131\) 0.00139646 0.00791975i 0.000122010 0.000691951i −0.984747 0.173994i \(-0.944333\pi\)
0.984869 + 0.173302i \(0.0554437\pi\)
\(132\) 0 0
\(133\) 5.20217 + 11.8465i 0.451085 + 1.02722i
\(134\) 0 0
\(135\) −0.0605457 + 0.343372i −0.00521095 + 0.0295528i
\(136\) 0 0
\(137\) −14.6907 5.34697i −1.25511 0.456822i −0.372984 0.927838i \(-0.621665\pi\)
−0.882125 + 0.471015i \(0.843888\pi\)
\(138\) 0 0
\(139\) −5.96207 + 5.00277i −0.505697 + 0.424330i −0.859612 0.510948i \(-0.829295\pi\)
0.353915 + 0.935278i \(0.384850\pi\)
\(140\) 0 0
\(141\) −0.764032 + 1.32334i −0.0643431 + 0.111446i
\(142\) 0 0
\(143\) −2.22967 12.6451i −0.186454 1.05743i
\(144\) 0 0
\(145\) −7.41630 12.8454i −0.615890 1.06675i
\(146\) 0 0
\(147\) −4.14493 + 1.50863i −0.341868 + 0.124430i
\(148\) 0 0
\(149\) −0.400779 0.336294i −0.0328331 0.0275502i 0.626223 0.779644i \(-0.284600\pi\)
−0.659057 + 0.752093i \(0.729044\pi\)
\(150\) 0 0
\(151\) 0.0730868 0.00594772 0.00297386 0.999996i \(-0.499053\pi\)
0.00297386 + 0.999996i \(0.499053\pi\)
\(152\) 0 0
\(153\) −20.2544 −1.63747
\(154\) 0 0
\(155\) −7.22566 6.06305i −0.580379 0.486996i
\(156\) 0 0
\(157\) −13.4211 + 4.88487i −1.07112 + 0.389855i −0.816594 0.577212i \(-0.804141\pi\)
−0.254523 + 0.967067i \(0.581918\pi\)
\(158\) 0 0
\(159\) −8.32209 14.4143i −0.659985 1.14313i
\(160\) 0 0
\(161\) 2.66850 + 15.1338i 0.210307 + 1.19271i
\(162\) 0 0
\(163\) −0.158689 + 0.274858i −0.0124295 + 0.0215286i −0.872173 0.489197i \(-0.837290\pi\)
0.859744 + 0.510726i \(0.170623\pi\)
\(164\) 0 0
\(165\) −11.0835 + 9.30018i −0.862851 + 0.724018i
\(166\) 0 0
\(167\) −0.822400 0.299329i −0.0636392 0.0231628i 0.310004 0.950735i \(-0.399669\pi\)
−0.373644 + 0.927572i \(0.621892\pi\)
\(168\) 0 0
\(169\) 1.67230 9.48408i 0.128638 0.729545i
\(170\) 0 0
\(171\) −0.827319 12.7664i −0.0632667 0.976271i
\(172\) 0 0
\(173\) 3.78253 21.4518i 0.287581 1.63095i −0.408338 0.912831i \(-0.633891\pi\)
0.695919 0.718121i \(-0.254997\pi\)
\(174\) 0 0
\(175\) 0.441988 + 0.160870i 0.0334111 + 0.0121607i
\(176\) 0 0
\(177\) 6.69946 5.62151i 0.503562 0.422539i
\(178\) 0 0
\(179\) 2.96398 5.13376i 0.221538 0.383715i −0.733737 0.679433i \(-0.762226\pi\)
0.955275 + 0.295718i \(0.0955590\pi\)
\(180\) 0 0
\(181\) 2.09038 + 11.8552i 0.155377 + 0.881187i 0.958440 + 0.285293i \(0.0920910\pi\)
−0.803063 + 0.595894i \(0.796798\pi\)
\(182\) 0 0
\(183\) 12.2363 + 21.1939i 0.904534 + 1.56670i
\(184\) 0 0
\(185\) 10.3909 3.78198i 0.763955 0.278057i
\(186\) 0 0
\(187\) 14.2691 + 11.9732i 1.04346 + 0.875566i
\(188\) 0 0
\(189\) −0.470353 −0.0342132
\(190\) 0 0
\(191\) −8.38465 −0.606692 −0.303346 0.952880i \(-0.598104\pi\)
−0.303346 + 0.952880i \(0.598104\pi\)
\(192\) 0 0
\(193\) 0.715575 + 0.600439i 0.0515082 + 0.0432205i 0.668178 0.744001i \(-0.267074\pi\)
−0.616670 + 0.787222i \(0.711519\pi\)
\(194\) 0 0
\(195\) −23.9625 + 8.72164i −1.71599 + 0.624570i
\(196\) 0 0
\(197\) 11.1803 + 19.3648i 0.796562 + 1.37969i 0.921843 + 0.387565i \(0.126684\pi\)
−0.125280 + 0.992121i \(0.539983\pi\)
\(198\) 0 0
\(199\) −2.50746 14.2205i −0.177749 1.00806i −0.934923 0.354851i \(-0.884532\pi\)
0.757174 0.653213i \(-0.226580\pi\)
\(200\) 0 0
\(201\) 11.0833 19.1969i 0.781758 1.35405i
\(202\) 0 0
\(203\) 15.3279 12.8616i 1.07581 0.902709i
\(204\) 0 0
\(205\) −3.85554 1.40330i −0.269283 0.0980109i
\(206\) 0 0
\(207\) 2.63855 14.9640i 0.183392 1.04007i
\(208\) 0 0
\(209\) −6.96387 + 9.48288i −0.481701 + 0.655945i
\(210\) 0 0
\(211\) −3.15065 + 17.8682i −0.216900 + 1.23010i 0.660679 + 0.750668i \(0.270268\pi\)
−0.877579 + 0.479432i \(0.840843\pi\)
\(212\) 0 0
\(213\) −1.29918 0.472863i −0.0890183 0.0324000i
\(214\) 0 0
\(215\) −15.2629 + 12.8071i −1.04092 + 0.873434i
\(216\) 0 0
\(217\) 6.36216 11.0196i 0.431892 0.748058i
\(218\) 0 0
\(219\) −0.330772 1.87590i −0.0223515 0.126762i
\(220\) 0 0
\(221\) 16.4148 + 28.4312i 1.10418 + 1.91249i
\(222\) 0 0
\(223\) −3.08215 + 1.12181i −0.206396 + 0.0751219i −0.443149 0.896448i \(-0.646139\pi\)
0.236754 + 0.971570i \(0.423917\pi\)
\(224\) 0 0
\(225\) −0.356268 0.298945i −0.0237512 0.0199296i
\(226\) 0 0
\(227\) 11.5190 0.764543 0.382272 0.924050i \(-0.375142\pi\)
0.382272 + 0.924050i \(0.375142\pi\)
\(228\) 0 0
\(229\) 15.3682 1.01556 0.507780 0.861487i \(-0.330466\pi\)
0.507780 + 0.861487i \(0.330466\pi\)
\(230\) 0 0
\(231\) −14.9516 12.5459i −0.983746 0.825461i
\(232\) 0 0
\(233\) −12.8920 + 4.69229i −0.844581 + 0.307402i −0.727829 0.685759i \(-0.759471\pi\)
−0.116752 + 0.993161i \(0.537248\pi\)
\(234\) 0 0
\(235\) −0.690073 1.19524i −0.0450154 0.0779689i
\(236\) 0 0
\(237\) 1.33888 + 7.59318i 0.0869698 + 0.493230i
\(238\) 0 0
\(239\) −8.39945 + 14.5483i −0.543315 + 0.941050i 0.455396 + 0.890289i \(0.349498\pi\)
−0.998711 + 0.0507604i \(0.983836\pi\)
\(240\) 0 0
\(241\) 17.2571 14.4804i 1.11163 0.932765i 0.113474 0.993541i \(-0.463802\pi\)
0.998151 + 0.0607762i \(0.0193576\pi\)
\(242\) 0 0
\(243\) 20.5936 + 7.49547i 1.32108 + 0.480834i
\(244\) 0 0
\(245\) 0.691806 3.92342i 0.0441978 0.250658i
\(246\) 0 0
\(247\) −17.2497 + 11.5076i −1.09757 + 0.732208i
\(248\) 0 0
\(249\) −3.08657 + 17.5048i −0.195603 + 1.10932i
\(250\) 0 0
\(251\) 14.5743 + 5.30463i 0.919924 + 0.334825i 0.758208 0.652012i \(-0.226075\pi\)
0.161716 + 0.986837i \(0.448297\pi\)
\(252\) 0 0
\(253\) −10.7046 + 8.98226i −0.672995 + 0.564710i
\(254\) 0 0
\(255\) 18.4965 32.0369i 1.15830 2.00623i
\(256\) 0 0
\(257\) −5.05935 28.6930i −0.315594 1.78982i −0.568870 0.822427i \(-0.692619\pi\)
0.253277 0.967394i \(-0.418492\pi\)
\(258\) 0 0
\(259\) 7.45846 + 12.9184i 0.463446 + 0.802712i
\(260\) 0 0
\(261\) −18.5914 + 6.76673i −1.15078 + 0.418850i
\(262\) 0 0
\(263\) 2.90918 + 2.44110i 0.179388 + 0.150524i 0.728060 0.685513i \(-0.240422\pi\)
−0.548672 + 0.836038i \(0.684867\pi\)
\(264\) 0 0
\(265\) 15.0330 0.923470
\(266\) 0 0
\(267\) 24.9459 1.52667
\(268\) 0 0
\(269\) −6.09243 5.11215i −0.371462 0.311693i 0.437878 0.899035i \(-0.355730\pi\)
−0.809340 + 0.587341i \(0.800175\pi\)
\(270\) 0 0
\(271\) 0.640257 0.233034i 0.0388928 0.0141558i −0.322500 0.946569i \(-0.604523\pi\)
0.361393 + 0.932413i \(0.382301\pi\)
\(272\) 0 0
\(273\) −17.2000 29.7912i −1.04099 1.80305i
\(274\) 0 0
\(275\) 0.0742704 + 0.421208i 0.00447867 + 0.0253998i
\(276\) 0 0
\(277\) 6.97191 12.0757i 0.418901 0.725558i −0.576928 0.816795i \(-0.695749\pi\)
0.995829 + 0.0912367i \(0.0290820\pi\)
\(278\) 0 0
\(279\) −9.63801 + 8.08725i −0.577013 + 0.484171i
\(280\) 0 0
\(281\) −25.1212 9.14338i −1.49861 0.545448i −0.542908 0.839792i \(-0.682677\pi\)
−0.955700 + 0.294344i \(0.904899\pi\)
\(282\) 0 0
\(283\) 0.879102 4.98563i 0.0522572 0.296365i −0.947467 0.319854i \(-0.896366\pi\)
0.999724 + 0.0234886i \(0.00747733\pi\)
\(284\) 0 0
\(285\) 20.9484 + 10.3498i 1.24087 + 0.613067i
\(286\) 0 0
\(287\) 0.961127 5.45082i 0.0567335 0.321752i
\(288\) 0 0
\(289\) −28.7784 10.4745i −1.69284 0.616145i
\(290\) 0 0
\(291\) −15.8072 + 13.2638i −0.926632 + 0.777536i
\(292\) 0 0
\(293\) −0.625879 + 1.08405i −0.0365642 + 0.0633311i −0.883728 0.468000i \(-0.844975\pi\)
0.847164 + 0.531331i \(0.178308\pi\)
\(294\) 0 0
\(295\) 1.37164 + 7.77893i 0.0798597 + 0.452907i
\(296\) 0 0
\(297\) −0.213853 0.370404i −0.0124090 0.0214930i
\(298\) 0 0
\(299\) −23.1434 + 8.42349i −1.33841 + 0.487143i
\(300\) 0 0
\(301\) −20.5895 17.2767i −1.18676 0.995811i
\(302\) 0 0
\(303\) 22.8173 1.31082
\(304\) 0 0
\(305\) −22.1036 −1.26565
\(306\) 0 0
\(307\) −18.5543 15.5689i −1.05895 0.888564i −0.0649432 0.997889i \(-0.520687\pi\)
−0.994006 + 0.109325i \(0.965131\pi\)
\(308\) 0 0
\(309\) −27.4853 + 10.0038i −1.56359 + 0.569099i
\(310\) 0 0
\(311\) 15.7119 + 27.2139i 0.890942 + 1.54316i 0.838747 + 0.544521i \(0.183288\pi\)
0.0521949 + 0.998637i \(0.483378\pi\)
\(312\) 0 0
\(313\) 3.65444 + 20.7254i 0.206561 + 1.17147i 0.894964 + 0.446139i \(0.147201\pi\)
−0.688402 + 0.725329i \(0.741688\pi\)
\(314\) 0 0
\(315\) −9.58442 + 16.6007i −0.540021 + 0.935344i
\(316\) 0 0
\(317\) 7.82632 6.56706i 0.439570 0.368843i −0.395978 0.918260i \(-0.629595\pi\)
0.835548 + 0.549417i \(0.185150\pi\)
\(318\) 0 0
\(319\) 17.0976 + 6.22301i 0.957281 + 0.348422i
\(320\) 0 0
\(321\) 6.05073 34.3154i 0.337719 1.91530i
\(322\) 0 0
\(323\) 8.43885 28.8733i 0.469550 1.60655i
\(324\) 0 0
\(325\) −0.130899 + 0.742368i −0.00726100 + 0.0411792i
\(326\) 0 0
\(327\) 5.06910 + 1.84500i 0.280322 + 0.102029i
\(328\) 0 0
\(329\) 1.42623 1.19675i 0.0786306 0.0659789i
\(330\) 0 0
\(331\) 13.6834 23.7003i 0.752105 1.30268i −0.194695 0.980864i \(-0.562372\pi\)
0.946801 0.321821i \(-0.104295\pi\)
\(332\) 0 0
\(333\) −2.56123 14.5254i −0.140354 0.795989i
\(334\) 0 0
\(335\) 10.0104 + 17.3386i 0.546929 + 0.947309i
\(336\) 0 0
\(337\) −1.26806 + 0.461535i −0.0690754 + 0.0251414i −0.376327 0.926487i \(-0.622813\pi\)
0.307251 + 0.951628i \(0.400591\pi\)
\(338\) 0 0
\(339\) −14.2619 11.9671i −0.774599 0.649966i
\(340\) 0 0
\(341\) 11.5706 0.626583
\(342\) 0 0
\(343\) −15.4035 −0.831712
\(344\) 0 0
\(345\) 21.2593 + 17.8387i 1.14456 + 0.960402i
\(346\) 0 0
\(347\) −9.33198 + 3.39656i −0.500967 + 0.182337i −0.580129 0.814525i \(-0.696998\pi\)
0.0791620 + 0.996862i \(0.474776\pi\)
\(348\) 0 0
\(349\) 3.32804 + 5.76434i 0.178146 + 0.308558i 0.941246 0.337723i \(-0.109657\pi\)
−0.763100 + 0.646281i \(0.776323\pi\)
\(350\) 0 0
\(351\) −0.130899 0.742368i −0.00698690 0.0396247i
\(352\) 0 0
\(353\) −10.8285 + 18.7556i −0.576345 + 0.998259i 0.419549 + 0.907733i \(0.362188\pi\)
−0.995894 + 0.0905262i \(0.971145\pi\)
\(354\) 0 0
\(355\) 0.956578 0.802664i 0.0507699 0.0426010i
\(356\) 0 0
\(357\) 46.8939 + 17.0680i 2.48189 + 0.903333i
\(358\) 0 0
\(359\) −1.67956 + 9.52525i −0.0886437 + 0.502724i 0.907867 + 0.419258i \(0.137710\pi\)
−0.996511 + 0.0834652i \(0.973401\pi\)
\(360\) 0 0
\(361\) 18.5436 + 4.13965i 0.975976 + 0.217876i
\(362\) 0 0
\(363\) −1.57146 + 8.91219i −0.0824802 + 0.467769i
\(364\) 0 0
\(365\) 1.61669 + 0.588428i 0.0846215 + 0.0307997i
\(366\) 0 0
\(367\) 19.8828 16.6837i 1.03788 0.870881i 0.0461083 0.998936i \(-0.485318\pi\)
0.991767 + 0.128056i \(0.0408736\pi\)
\(368\) 0 0
\(369\) −2.73640 + 4.73958i −0.142451 + 0.246733i
\(370\) 0 0
\(371\) 3.52149 + 19.9714i 0.182827 + 1.03686i
\(372\) 0 0
\(373\) −9.13616 15.8243i −0.473052 0.819351i 0.526472 0.850193i \(-0.323515\pi\)
−0.999524 + 0.0308418i \(0.990181\pi\)
\(374\) 0 0
\(375\) 25.9840 9.45741i 1.34181 0.488379i
\(376\) 0 0
\(377\) 24.5655 + 20.6129i 1.26519 + 1.06162i
\(378\) 0 0
\(379\) −31.1455 −1.59983 −0.799917 0.600110i \(-0.795123\pi\)
−0.799917 + 0.600110i \(0.795123\pi\)
\(380\) 0 0
\(381\) −11.3197 −0.579926
\(382\) 0 0
\(383\) −22.1294 18.5687i −1.13076 0.948819i −0.131661 0.991295i \(-0.542031\pi\)
−0.999097 + 0.0424761i \(0.986475\pi\)
\(384\) 0 0
\(385\) 16.5655 6.02934i 0.844255 0.307284i
\(386\) 0 0
\(387\) 13.2881 + 23.0156i 0.675470 + 1.16995i
\(388\) 0 0
\(389\) −1.07456 6.09416i −0.0544826 0.308986i 0.945373 0.325991i \(-0.105698\pi\)
−0.999855 + 0.0170051i \(0.994587\pi\)
\(390\) 0 0
\(391\) 17.8642 30.9417i 0.903431 1.56479i
\(392\) 0 0
\(393\) 0.0150080 0.0125932i 0.000757053 0.000635243i
\(394\) 0 0
\(395\) −6.54397 2.38181i −0.329263 0.119842i
\(396\) 0 0
\(397\) −1.25366 + 7.10986i −0.0629194 + 0.356834i 0.937051 + 0.349191i \(0.113544\pi\)
−0.999971 + 0.00764217i \(0.997567\pi\)
\(398\) 0 0
\(399\) −8.84252 + 30.2544i −0.442680 + 1.51462i
\(400\) 0 0
\(401\) −4.01252 + 22.7561i −0.200376 + 1.13639i 0.704177 + 0.710025i \(0.251316\pi\)
−0.904552 + 0.426362i \(0.859795\pi\)
\(402\) 0 0
\(403\) 19.1630 + 6.97477i 0.954578 + 0.347438i
\(404\) 0 0
\(405\) −15.4919 + 12.9992i −0.769797 + 0.645937i
\(406\) 0 0
\(407\) −6.78219 + 11.7471i −0.336181 + 0.582282i
\(408\) 0 0
\(409\) −1.47083 8.34147i −0.0727276 0.412459i −0.999336 0.0364315i \(-0.988401\pi\)
0.926609 0.376027i \(-0.122710\pi\)
\(410\) 0 0
\(411\) −19.0430 32.9834i −0.939321 1.62695i
\(412\) 0 0
\(413\) −10.0130 + 3.64444i −0.492709 + 0.179331i
\(414\) 0 0
\(415\) −12.2982 10.3194i −0.603697 0.506562i
\(416\) 0 0
\(417\) −18.9606 −0.928505
\(418\) 0 0
\(419\) −34.4402 −1.68251 −0.841257 0.540635i \(-0.818184\pi\)
−0.841257 + 0.540635i \(0.818184\pi\)
\(420\) 0 0
\(421\) 8.18476 + 6.86783i 0.398901 + 0.334718i 0.820069 0.572265i \(-0.193935\pi\)
−0.421168 + 0.906983i \(0.638380\pi\)
\(422\) 0 0
\(423\) −1.72990 + 0.629631i −0.0841105 + 0.0306137i
\(424\) 0 0
\(425\) −0.546777 0.947046i −0.0265226 0.0459385i
\(426\) 0 0
\(427\) −5.17779 29.3647i −0.250571 1.42106i
\(428\) 0 0
\(429\) 15.6404 27.0900i 0.755126 1.30792i
\(430\) 0 0
\(431\) −9.45533 + 7.93396i −0.455447 + 0.382166i −0.841453 0.540331i \(-0.818299\pi\)
0.386005 + 0.922497i \(0.373855\pi\)
\(432\) 0 0
\(433\) 33.6628 + 12.2522i 1.61773 + 0.588805i 0.982948 0.183886i \(-0.0588676\pi\)
0.634782 + 0.772691i \(0.281090\pi\)
\(434\) 0 0
\(435\) 6.27475 35.5859i 0.300851 1.70621i
\(436\) 0 0
\(437\) 20.2323 + 9.99596i 0.967840 + 0.478172i
\(438\) 0 0
\(439\) −3.66200 + 20.7682i −0.174778 + 0.991213i 0.763623 + 0.645663i \(0.223419\pi\)
−0.938400 + 0.345550i \(0.887692\pi\)
\(440\) 0 0
\(441\) −4.99355 1.81750i −0.237788 0.0865478i
\(442\) 0 0
\(443\) 7.17585 6.02125i 0.340935 0.286078i −0.456203 0.889876i \(-0.650791\pi\)
0.797138 + 0.603797i \(0.206346\pi\)
\(444\) 0 0
\(445\) −11.2656 + 19.5125i −0.534039 + 0.924983i
\(446\) 0 0
\(447\) −0.221325 1.25520i −0.0104683 0.0593687i
\(448\) 0 0
\(449\) −4.05742 7.02766i −0.191481 0.331656i 0.754260 0.656576i \(-0.227996\pi\)
−0.945741 + 0.324920i \(0.894663\pi\)
\(450\) 0 0
\(451\) 4.72952 1.72141i 0.222704 0.0810578i
\(452\) 0 0
\(453\) 0.136396 + 0.114450i 0.00640844 + 0.00537732i
\(454\) 0 0
\(455\) 31.0699 1.45658
\(456\) 0 0
\(457\) 4.33380 0.202727 0.101363 0.994849i \(-0.467680\pi\)
0.101363 + 0.994849i \(0.467680\pi\)
\(458\) 0 0
\(459\) 0.837711 + 0.702923i 0.0391010 + 0.0328097i
\(460\) 0 0
\(461\) 24.1245 8.78061i 1.12359 0.408954i 0.287629 0.957742i \(-0.407133\pi\)
0.835962 + 0.548788i \(0.184911\pi\)
\(462\) 0 0
\(463\) −0.875824 1.51697i −0.0407030 0.0704996i 0.844956 0.534835i \(-0.179626\pi\)
−0.885659 + 0.464336i \(0.846293\pi\)
\(464\) 0 0
\(465\) −3.99027 22.6300i −0.185044 1.04944i
\(466\) 0 0
\(467\) −8.64997 + 14.9822i −0.400273 + 0.693293i −0.993759 0.111551i \(-0.964418\pi\)
0.593486 + 0.804844i \(0.297751\pi\)
\(468\) 0 0
\(469\) −20.6894 + 17.3605i −0.955349 + 0.801633i
\(470\) 0 0
\(471\) −32.6961 11.9004i −1.50656 0.548341i
\(472\) 0 0
\(473\) 4.24408 24.0694i 0.195143 1.10671i
\(474\) 0 0
\(475\) 0.574590 0.383318i 0.0263640 0.0175878i
\(476\) 0 0
\(477\) 3.48197 19.7473i 0.159429 0.904165i
\(478\) 0 0
\(479\) −8.04717 2.92893i −0.367684 0.133826i 0.151569 0.988447i \(-0.451568\pi\)
−0.519253 + 0.854621i \(0.673790\pi\)
\(480\) 0 0
\(481\) −18.3137 + 15.3670i −0.835033 + 0.700676i
\(482\) 0 0
\(483\) −18.7187 + 32.4218i −0.851731 + 1.47524i
\(484\) 0 0
\(485\) −3.23633 18.3541i −0.146954 0.833419i
\(486\) 0 0
\(487\) −2.01043 3.48216i −0.0911011 0.157792i 0.816874 0.576817i \(-0.195705\pi\)
−0.907975 + 0.419025i \(0.862372\pi\)
\(488\) 0 0
\(489\) −0.726562 + 0.264447i −0.0328563 + 0.0119587i
\(490\) 0 0
\(491\) 6.40117 + 5.37122i 0.288881 + 0.242400i 0.775698 0.631104i \(-0.217398\pi\)
−0.486817 + 0.873504i \(0.661842\pi\)
\(492\) 0 0
\(493\) −46.5205 −2.09518
\(494\) 0 0
\(495\) −17.4308 −0.783455
\(496\) 0 0
\(497\) 1.29042 + 1.08279i 0.0578833 + 0.0485698i
\(498\) 0 0
\(499\) 7.57293 2.75632i 0.339011 0.123390i −0.166904 0.985973i \(-0.553377\pi\)
0.505915 + 0.862583i \(0.331155\pi\)
\(500\) 0 0
\(501\) −1.06605 1.84645i −0.0476274 0.0824931i
\(502\) 0 0
\(503\) −1.17379 6.65690i −0.0523367 0.296816i 0.947393 0.320073i \(-0.103708\pi\)
−0.999730 + 0.0232569i \(0.992596\pi\)
\(504\) 0 0
\(505\) −10.3043 + 17.8475i −0.458535 + 0.794205i
\(506\) 0 0
\(507\) 17.9724 15.0807i 0.798183 0.669755i
\(508\) 0 0
\(509\) −8.14794 2.96561i −0.361151 0.131448i 0.155070 0.987903i \(-0.450440\pi\)
−0.516221 + 0.856455i \(0.672662\pi\)
\(510\) 0 0
\(511\) −0.403016 + 2.28562i −0.0178284 + 0.101110i
\(512\) 0 0
\(513\) −0.408836 + 0.556722i −0.0180505 + 0.0245799i
\(514\) 0 0
\(515\) 4.58742 26.0165i 0.202146 1.14643i
\(516\) 0 0
\(517\) 1.59090 + 0.579040i 0.0699676 + 0.0254661i
\(518\) 0 0
\(519\) 40.6514 34.1106i 1.78440 1.49729i
\(520\) 0 0
\(521\) −18.9134 + 32.7589i −0.828610 + 1.43519i 0.0705193 + 0.997510i \(0.477534\pi\)
−0.899129 + 0.437684i \(0.855799\pi\)
\(522\) 0 0
\(523\) 1.16685 + 6.61751i 0.0510226 + 0.289363i 0.999633 0.0270822i \(-0.00862160\pi\)
−0.948611 + 0.316446i \(0.897510\pi\)
\(524\) 0 0
\(525\) 0.572932 + 0.992347i 0.0250048 + 0.0433096i
\(526\) 0 0
\(527\) −27.7995 + 10.1182i −1.21096 + 0.440755i
\(528\) 0 0
\(529\) 2.91353 + 2.44474i 0.126675 + 0.106293i
\(530\) 0 0
\(531\) 10.5361 0.457226
\(532\) 0 0
\(533\) 8.87062 0.384229
\(534\) 0 0
\(535\) 24.1087 + 20.2296i 1.04231 + 0.874603i
\(536\) 0 0
\(537\) 13.5706 4.93930i 0.585615 0.213146i
\(538\) 0 0
\(539\) 2.44352 + 4.23230i 0.105250 + 0.182298i
\(540\) 0 0
\(541\) 6.42812 + 36.4557i 0.276366 + 1.56735i 0.734588 + 0.678514i \(0.237376\pi\)
−0.458222 + 0.888838i \(0.651513\pi\)
\(542\) 0 0
\(543\) −14.6634 + 25.3977i −0.629267 + 1.08992i
\(544\) 0 0
\(545\) −3.73235 + 3.13181i −0.159876 + 0.134152i
\(546\) 0 0
\(547\) 32.4038 + 11.7940i 1.38549 + 0.504275i 0.923837 0.382787i \(-0.125036\pi\)
0.461649 + 0.887063i \(0.347258\pi\)
\(548\) 0 0
\(549\) −5.11969 + 29.0352i −0.218503 + 1.23919i
\(550\) 0 0
\(551\) −1.90019 29.3219i −0.0809508 1.24916i
\(552\) 0 0
\(553\) 1.63131 9.25162i 0.0693704 0.393419i
\(554\) 0 0
\(555\) 25.3141 + 9.21358i 1.07452 + 0.391095i
\(556\) 0 0
\(557\) 32.0493 26.8925i 1.35797 1.13947i 0.381369 0.924423i \(-0.375453\pi\)
0.976603 0.215051i \(-0.0689917\pi\)
\(558\) 0 0
\(559\) 21.5380 37.3050i 0.910962 1.57783i
\(560\) 0 0
\(561\) 7.87991 + 44.6892i 0.332690 + 1.88678i
\(562\) 0 0
\(563\) 7.86717 + 13.6263i 0.331562 + 0.574282i 0.982818 0.184576i \(-0.0590912\pi\)
−0.651257 + 0.758858i \(0.725758\pi\)
\(564\) 0 0
\(565\) 15.8013 5.75119i 0.664764 0.241954i
\(566\) 0 0
\(567\) −20.8985 17.5359i −0.877654 0.736439i
\(568\) 0 0
\(569\) 41.4620 1.73818 0.869089 0.494656i \(-0.164706\pi\)
0.869089 + 0.494656i \(0.164706\pi\)
\(570\) 0 0
\(571\) 12.3160 0.515408 0.257704 0.966224i \(-0.417034\pi\)
0.257704 + 0.966224i \(0.417034\pi\)
\(572\) 0 0
\(573\) −15.6476 13.1299i −0.653688 0.548509i
\(574\) 0 0
\(575\) 0.770907 0.280587i 0.0321490 0.0117013i
\(576\) 0 0
\(577\) −5.49834 9.52341i −0.228899 0.396465i 0.728583 0.684957i \(-0.240179\pi\)
−0.957482 + 0.288493i \(0.906846\pi\)
\(578\) 0 0
\(579\) 0.395167 + 2.24110i 0.0164226 + 0.0931370i
\(580\) 0 0
\(581\) 10.8285 18.7556i 0.449244 0.778113i
\(582\) 0 0
\(583\) −14.1264 + 11.8535i −0.585055 + 0.490920i
\(584\) 0 0
\(585\) −28.8686 10.5073i −1.19357 0.434423i
\(586\) 0 0
\(587\) −7.13565 + 40.4683i −0.294520 + 1.67030i 0.374628 + 0.927175i \(0.377770\pi\)
−0.669148 + 0.743129i \(0.733341\pi\)
\(588\) 0 0
\(589\) −7.51300 17.1087i −0.309568 0.704954i
\(590\) 0 0
\(591\) −9.45936 + 53.6467i −0.389106 + 2.20673i
\(592\) 0 0
\(593\) 24.1916 + 8.80504i 0.993432 + 0.361580i 0.787048 0.616892i \(-0.211608\pi\)
0.206384 + 0.978471i \(0.433831\pi\)
\(594\) 0 0
\(595\) −34.5277 + 28.9722i −1.41550 + 1.18774i
\(596\) 0 0
\(597\) 17.5890 30.4651i 0.719871 1.24685i
\(598\) 0 0
\(599\) −4.76463 27.0215i −0.194677 1.10407i −0.912877 0.408234i \(-0.866145\pi\)
0.718200 0.695837i \(-0.244966\pi\)
\(600\) 0 0
\(601\) −12.5425 21.7242i −0.511618 0.886148i −0.999909 0.0134673i \(-0.995713\pi\)
0.488292 0.872681i \(-0.337620\pi\)
\(602\) 0 0
\(603\) 25.0945 9.13366i 1.02193 0.371951i
\(604\) 0 0
\(605\) −6.26138 5.25392i −0.254561 0.213602i
\(606\) 0 0
\(607\) 7.83141 0.317867 0.158934 0.987289i \(-0.449194\pi\)
0.158934 + 0.987289i \(0.449194\pi\)
\(608\) 0 0
\(609\) 48.7458 1.97528
\(610\) 0 0
\(611\) 2.28577 + 1.91799i 0.0924725 + 0.0775936i
\(612\) 0 0
\(613\) −8.42277 + 3.06564i −0.340193 + 0.123820i −0.506466 0.862260i \(-0.669049\pi\)
0.166274 + 0.986080i \(0.446826\pi\)
\(614\) 0 0
\(615\) −4.99779 8.65643i −0.201530 0.349061i
\(616\) 0 0
\(617\) 0.703095 + 3.98745i 0.0283055 + 0.160529i 0.995684 0.0928062i \(-0.0295837\pi\)
−0.967379 + 0.253335i \(0.918473\pi\)
\(618\) 0 0
\(619\) −13.0871 + 22.6676i −0.526016 + 0.911087i 0.473525 + 0.880781i \(0.342982\pi\)
−0.999541 + 0.0303060i \(0.990352\pi\)
\(620\) 0 0
\(621\) −0.628449 + 0.527331i −0.0252188 + 0.0211611i
\(622\) 0 0
\(623\) −28.5614 10.3955i −1.14429 0.416487i
\(624\) 0 0
\(625\) −4.19926 + 23.8152i −0.167970 + 0.952608i
\(626\) 0 0
\(627\) −27.8458 + 6.79210i −1.11205 + 0.271251i
\(628\) 0 0
\(629\) 6.02234 34.1544i 0.240126 1.36182i
\(630\) 0 0
\(631\) −41.3624 15.0547i −1.64661 0.599317i −0.658435 0.752638i \(-0.728781\pi\)
−0.988177 + 0.153321i \(0.951003\pi\)
\(632\) 0 0
\(633\) −33.8605 + 28.4123i −1.34583 + 1.12929i
\(634\) 0 0
\(635\) 5.11197 8.85419i 0.202862 0.351368i
\(636\) 0 0
\(637\) 1.49568 + 8.48242i 0.0592610 + 0.336086i
\(638\) 0 0
\(639\) −0.832810 1.44247i −0.0329455 0.0570632i
\(640\) 0 0
\(641\) 4.91616 1.78934i 0.194177 0.0706745i −0.243101 0.970001i \(-0.578165\pi\)
0.437278 + 0.899326i \(0.355943\pi\)
\(642\) 0 0
\(643\) 10.2920 + 8.63602i 0.405877 + 0.340571i 0.822760 0.568389i \(-0.192433\pi\)
−0.416883 + 0.908960i \(0.636878\pi\)
\(644\) 0 0
\(645\) −48.5390 −1.91122
\(646\) 0 0
\(647\) 15.4880 0.608895 0.304448 0.952529i \(-0.401528\pi\)
0.304448 + 0.952529i \(0.401528\pi\)
\(648\) 0 0
\(649\) −7.42257 6.22828i −0.291361 0.244481i
\(650\) 0 0
\(651\) 29.1292 10.6022i 1.14167 0.415532i
\(652\) 0 0
\(653\) −5.03649 8.72346i −0.197093 0.341375i 0.750492 0.660880i \(-0.229817\pi\)
−0.947585 + 0.319505i \(0.896483\pi\)
\(654\) 0 0
\(655\) 0.00307271 + 0.0174262i 0.000120061 + 0.000680898i
\(656\) 0 0
\(657\) 1.14742 1.98738i 0.0447650 0.0775352i
\(658\) 0 0
\(659\) 18.8606 15.8259i 0.734704 0.616490i −0.196706 0.980463i \(-0.563024\pi\)
0.931410 + 0.363973i \(0.118580\pi\)
\(660\) 0 0
\(661\) −44.4545 16.1801i −1.72908 0.629333i −0.730515 0.682897i \(-0.760720\pi\)
−0.998564 + 0.0535638i \(0.982942\pi\)
\(662\) 0 0
\(663\) −13.8881 + 78.7635i −0.539370 + 3.05892i
\(664\) 0 0
\(665\) −19.6715 20.5794i −0.762828 0.798035i
\(666\) 0 0
\(667\) 6.06024 34.3694i 0.234654 1.33079i
\(668\) 0 0
\(669\) −7.50865 2.73293i −0.290301 0.105661i
\(670\) 0 0
\(671\) 20.7706 17.4286i 0.801841 0.672824i
\(672\) 0 0
\(673\) 7.44102 12.8882i 0.286830 0.496805i −0.686221 0.727393i \(-0.740732\pi\)
0.973051 + 0.230588i \(0.0740651\pi\)
\(674\) 0 0
\(675\) 0.00436027 + 0.0247283i 0.000167827 + 0.000951794i
\(676\) 0 0
\(677\) 1.25311 + 2.17046i 0.0481611 + 0.0834175i 0.889101 0.457711i \(-0.151331\pi\)
−0.840940 + 0.541129i \(0.817997\pi\)
\(678\) 0 0
\(679\) 23.6254 8.59895i 0.906660 0.329997i
\(680\) 0 0
\(681\) 21.4970 + 18.0381i 0.823766 + 0.691222i
\(682\) 0 0
\(683\) −29.5227 −1.12965 −0.564827 0.825209i \(-0.691057\pi\)
−0.564827 + 0.825209i \(0.691057\pi\)
\(684\) 0 0
\(685\) 34.3992 1.31432
\(686\) 0 0
\(687\) 28.6805 + 24.0658i 1.09423 + 0.918166i
\(688\) 0 0
\(689\) −30.5412 + 11.1161i −1.16353 + 0.423489i
\(690\) 0 0
\(691\) −20.8238 36.0678i −0.792173 1.37208i −0.924619 0.380894i \(-0.875616\pi\)
0.132445 0.991190i \(-0.457717\pi\)
\(692\) 0 0
\(693\) −4.08317 23.1568i −0.155107 0.879655i
\(694\) 0 0
\(695\) 8.56259 14.8308i 0.324798 0.562566i
\(696\) 0 0
\(697\) −9.85781 + 8.27169i −0.373391 + 0.313313i
\(698\) 0 0
\(699\) −31.4071 11.4313i −1.18793 0.432370i
\(700\) 0 0
\(701\) 7.62364 43.2358i 0.287941 1.63299i −0.406647 0.913585i \(-0.633302\pi\)
0.694588 0.719408i \(-0.255587\pi\)
\(702\) 0 0
\(703\) 21.7735 + 2.40081i 0.821204 + 0.0905481i
\(704\) 0 0
\(705\) 0.583853 3.31120i 0.0219892 0.124707i
\(706\) 0 0
\(707\) −26.1243 9.50846i −0.982505 0.357603i
\(708\) 0 0
\(709\) 15.4412 12.9567i 0.579907 0.486599i −0.305010 0.952349i \(-0.598660\pi\)
0.884916 + 0.465750i \(0.154215\pi\)
\(710\) 0 0
\(711\) −4.64446 + 8.04444i −0.174181 + 0.301690i
\(712\) 0 0
\(713\) −3.85387 21.8564i −0.144328 0.818527i
\(714\) 0 0
\(715\) 14.1264 + 24.4676i 0.528297 + 0.915038i
\(716\) 0 0
\(717\) −38.4570 + 13.9972i −1.43620 + 0.522735i
\(718\) 0 0
\(719\) 17.5142 + 14.6962i 0.653170 + 0.548074i 0.908031 0.418903i \(-0.137585\pi\)
−0.254861 + 0.966978i \(0.582030\pi\)
\(720\) 0 0
\(721\) 35.6377 1.32722
\(722\) 0 0
\(723\) 54.8810 2.04105
\(724\) 0 0
\(725\) −0.818278 0.686617i −0.0303901 0.0255003i
\(726\) 0 0
\(727\) −10.1790 + 3.70485i −0.377518 + 0.137405i −0.523808 0.851836i \(-0.675489\pi\)
0.146290 + 0.989242i \(0.453267\pi\)
\(728\) 0 0
\(729\) 12.9084 + 22.3580i 0.478088 + 0.828073i
\(730\) 0 0
\(731\) 10.8512 + 61.5404i 0.401347 + 2.27615i
\(732\) 0 0
\(733\) −11.9702 + 20.7331i −0.442131 + 0.765794i −0.997847 0.0655783i \(-0.979111\pi\)
0.555716 + 0.831372i \(0.312444\pi\)
\(734\) 0 0
\(735\) 7.43492 6.23864i 0.274241 0.230116i
\(736\) 0 0
\(737\) −23.0782 8.39976i −0.850095 0.309409i
\(738\) 0 0
\(739\) 0.980265 5.55936i 0.0360596 0.204504i −0.961455 0.274962i \(-0.911335\pi\)
0.997515 + 0.0704574i \(0.0224459\pi\)
\(740\) 0 0
\(741\) −50.2120 5.53650i −1.84458 0.203389i
\(742\) 0 0
\(743\) 7.01282 39.7717i 0.257275 1.45908i −0.532889 0.846185i \(-0.678894\pi\)
0.790164 0.612895i \(-0.209995\pi\)
\(744\) 0 0
\(745\) 1.08175 + 0.393726i 0.0396324 + 0.0144250i
\(746\) 0 0
\(747\) −16.4041 + 13.7647i −0.600195 + 0.503623i
\(748\) 0 0
\(749\) −21.2276 + 36.7673i −0.775641 + 1.34345i
\(750\) 0 0
\(751\) 4.21819 + 23.9225i 0.153924 + 0.872946i 0.959763 + 0.280811i \(0.0906036\pi\)
−0.805839 + 0.592135i \(0.798285\pi\)
\(752\) 0 0
\(753\) 18.8922 + 32.7222i 0.688469 + 1.19246i
\(754\) 0 0
\(755\) −0.151118 + 0.0550025i −0.00549975 + 0.00200174i
\(756\) 0 0
\(757\) 6.92712 + 5.81254i 0.251770 + 0.211260i 0.759934 0.650000i \(-0.225231\pi\)
−0.508164 + 0.861260i \(0.669676\pi\)
\(758\) 0 0
\(759\) −34.0429 −1.23568
\(760\) 0 0
\(761\) −42.8970 −1.55502 −0.777508 0.628874i \(-0.783516\pi\)
−0.777508 + 0.628874i \(0.783516\pi\)
\(762\) 0 0
\(763\) −5.03493 4.22481i −0.182277 0.152948i
\(764\) 0 0
\(765\) 41.8791 15.2428i 1.51414 0.551103i
\(766\) 0 0
\(767\) −8.53872 14.7895i −0.308315 0.534018i
\(768\) 0 0
\(769\) 0.909951 + 5.16059i 0.0328137 + 0.186095i 0.996809 0.0798236i \(-0.0254357\pi\)
−0.963995 + 0.265919i \(0.914325\pi\)
\(770\) 0 0
\(771\) 35.4898 61.4701i 1.27813 2.21379i
\(772\) 0 0
\(773\) 27.4974 23.0731i 0.989014 0.829881i 0.00358889 0.999994i \(-0.498858\pi\)
0.985425 + 0.170113i \(0.0544132\pi\)
\(774\) 0 0
\(775\) −0.638321 0.232330i −0.0229292 0.00834554i
\(776\) 0 0
\(777\) −6.31041 + 35.7881i −0.226385 + 1.28389i
\(778\) 0 0
\(779\) −5.61631 5.87552i −0.201225 0.210512i
\(780\) 0 0
\(781\) −0.265992 + 1.50851i −0.00951794 + 0.0539789i
\(782\) 0 0
\(783\) 1.00377 + 0.365341i 0.0358717 + 0.0130562i
\(784\) 0 0
\(785\) 24.0739 20.2004i 0.859235 0.720984i
\(786\) 0 0
\(787\) −22.6443 + 39.2211i −0.807182 + 1.39808i 0.107625 + 0.994192i \(0.465675\pi\)
−0.914808 + 0.403890i \(0.867658\pi\)
\(788\) 0 0
\(789\) 1.60656 + 9.11124i 0.0571949 + 0.324369i
\(790\) 0 0
\(791\) 11.3419 + 19.6448i 0.403273 + 0.698489i
\(792\) 0 0
\(793\) 44.9059 16.3444i 1.59466 0.580407i
\(794\) 0 0