Properties

Label 784.2.bb.b.111.18
Level $784$
Weight $2$
Character 784.111
Analytic conductor $6.260$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.bb (of order \(14\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.26027151847\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(20\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 111.18
Character \(\chi\) \(=\) 784.111
Dual form 784.2.bb.b.671.18

$q$-expansion

\(f(q)\) \(=\) \(q+(1.44547 + 1.81256i) q^{3} +(2.77297 - 2.21137i) q^{5} +(1.94347 + 1.79525i) q^{7} +(-0.528427 + 2.31519i) q^{9} +O(q^{10})\) \(q+(1.44547 + 1.81256i) q^{3} +(2.77297 - 2.21137i) q^{5} +(1.94347 + 1.79525i) q^{7} +(-0.528427 + 2.31519i) q^{9} +(4.57508 - 1.04423i) q^{11} +(-5.78881 + 1.32126i) q^{13} +(8.01646 + 1.82970i) q^{15} +(0.938958 - 1.94977i) q^{17} -4.08024 q^{19} +(-0.444763 + 6.11762i) q^{21} +(-1.07860 - 2.23974i) q^{23} +(1.68660 - 7.38948i) q^{25} +(1.30604 - 0.628957i) q^{27} +(3.94588 + 1.90024i) q^{29} -6.72715 q^{31} +(8.50585 + 6.78319i) q^{33} +(9.35915 + 0.680429i) q^{35} +(-8.04808 - 3.87575i) q^{37} +(-10.7624 - 8.58271i) q^{39} +(0.210900 - 0.168187i) q^{41} +(3.94188 + 3.14354i) q^{43} +(3.65443 + 7.58849i) q^{45} +(-0.0216980 - 0.0950654i) q^{47} +(0.554176 + 6.97803i) q^{49} +(4.89129 - 1.11641i) q^{51} +(-10.4093 + 5.01284i) q^{53} +(10.3774 - 13.0128i) q^{55} +(-5.89784 - 7.39566i) q^{57} +(-1.91773 + 2.40476i) q^{59} +(1.79731 - 3.73215i) q^{61} +(-5.18332 + 3.55085i) q^{63} +(-13.1304 + 16.4650i) q^{65} +4.19011i q^{67} +(2.50058 - 5.19250i) q^{69} +(3.95100 + 8.20434i) q^{71} +(-1.51164 - 0.345021i) q^{73} +(15.8318 - 7.62418i) q^{75} +(10.7662 + 6.18396i) q^{77} +14.9599i q^{79} +(9.44652 + 4.54921i) q^{81} +(0.959887 - 4.20554i) q^{83} +(-1.70795 - 7.48302i) q^{85} +(2.25935 + 9.89885i) q^{87} +(-16.4153 - 3.74669i) q^{89} +(-13.6224 - 7.82452i) q^{91} +(-9.72386 - 12.1933i) q^{93} +(-11.3144 + 9.02292i) q^{95} +15.2923i q^{97} +11.1440i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q - 24 q^{9} + O(q^{10}) \) \( 120 q - 24 q^{9} - 14 q^{17} + 16 q^{21} + 40 q^{25} + 32 q^{29} - 62 q^{37} - 28 q^{41} - 60 q^{49} + 14 q^{53} - 34 q^{57} - 112 q^{61} - 32 q^{65} + 112 q^{69} + 42 q^{73} + 66 q^{77} - 44 q^{81} - 12 q^{85} + 28 q^{89} - 58 q^{93} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(687\) \(689\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{11}{14}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.44547 + 1.81256i 0.834540 + 1.04648i 0.998201 + 0.0599630i \(0.0190983\pi\)
−0.163661 + 0.986517i \(0.552330\pi\)
\(4\) 0 0
\(5\) 2.77297 2.21137i 1.24011 0.988954i 0.240276 0.970705i \(-0.422762\pi\)
0.999833 0.0182499i \(-0.00580943\pi\)
\(6\) 0 0
\(7\) 1.94347 + 1.79525i 0.734564 + 0.678540i
\(8\) 0 0
\(9\) −0.528427 + 2.31519i −0.176142 + 0.771730i
\(10\) 0 0
\(11\) 4.57508 1.04423i 1.37944 0.314848i 0.532451 0.846461i \(-0.321271\pi\)
0.846988 + 0.531613i \(0.178414\pi\)
\(12\) 0 0
\(13\) −5.78881 + 1.32126i −1.60553 + 0.366451i −0.929033 0.369997i \(-0.879359\pi\)
−0.676494 + 0.736448i \(0.736502\pi\)
\(14\) 0 0
\(15\) 8.01646 + 1.82970i 2.06984 + 0.472428i
\(16\) 0 0
\(17\) 0.938958 1.94977i 0.227731 0.472888i −0.755525 0.655120i \(-0.772618\pi\)
0.983255 + 0.182232i \(0.0583323\pi\)
\(18\) 0 0
\(19\) −4.08024 −0.936071 −0.468036 0.883710i \(-0.655038\pi\)
−0.468036 + 0.883710i \(0.655038\pi\)
\(20\) 0 0
\(21\) −0.444763 + 6.11762i −0.0970553 + 1.33497i
\(22\) 0 0
\(23\) −1.07860 2.23974i −0.224904 0.467019i 0.757731 0.652567i \(-0.226308\pi\)
−0.982635 + 0.185548i \(0.940594\pi\)
\(24\) 0 0
\(25\) 1.68660 7.38948i 0.337320 1.47790i
\(26\) 0 0
\(27\) 1.30604 0.628957i 0.251348 0.121043i
\(28\) 0 0
\(29\) 3.94588 + 1.90024i 0.732732 + 0.352865i 0.762758 0.646684i \(-0.223845\pi\)
−0.0300263 + 0.999549i \(0.509559\pi\)
\(30\) 0 0
\(31\) −6.72715 −1.20823 −0.604116 0.796897i \(-0.706474\pi\)
−0.604116 + 0.796897i \(0.706474\pi\)
\(32\) 0 0
\(33\) 8.50585 + 6.78319i 1.48068 + 1.18080i
\(34\) 0 0
\(35\) 9.35915 + 0.680429i 1.58198 + 0.115013i
\(36\) 0 0
\(37\) −8.04808 3.87575i −1.32310 0.637169i −0.366999 0.930221i \(-0.619615\pi\)
−0.956097 + 0.293052i \(0.905329\pi\)
\(38\) 0 0
\(39\) −10.7624 8.58271i −1.72336 1.37433i
\(40\) 0 0
\(41\) 0.210900 0.168187i 0.0329371 0.0262664i −0.606883 0.794791i \(-0.707580\pi\)
0.639820 + 0.768525i \(0.279009\pi\)
\(42\) 0 0
\(43\) 3.94188 + 3.14354i 0.601130 + 0.479385i 0.876140 0.482056i \(-0.160110\pi\)
−0.275010 + 0.961441i \(0.588681\pi\)
\(44\) 0 0
\(45\) 3.65443 + 7.58849i 0.544770 + 1.13123i
\(46\) 0 0
\(47\) −0.0216980 0.0950654i −0.00316499 0.0138667i 0.973321 0.229449i \(-0.0736923\pi\)
−0.976486 + 0.215582i \(0.930835\pi\)
\(48\) 0 0
\(49\) 0.554176 + 6.97803i 0.0791679 + 0.996861i
\(50\) 0 0
\(51\) 4.89129 1.11641i 0.684918 0.156328i
\(52\) 0 0
\(53\) −10.4093 + 5.01284i −1.42982 + 0.688566i −0.978965 0.204030i \(-0.934596\pi\)
−0.450857 + 0.892596i \(0.648882\pi\)
\(54\) 0 0
\(55\) 10.3774 13.0128i 1.39929 1.75465i
\(56\) 0 0
\(57\) −5.89784 7.39566i −0.781188 0.979579i
\(58\) 0 0
\(59\) −1.91773 + 2.40476i −0.249668 + 0.313074i −0.890834 0.454328i \(-0.849879\pi\)
0.641167 + 0.767402i \(0.278451\pi\)
\(60\) 0 0
\(61\) 1.79731 3.73215i 0.230122 0.477853i −0.753650 0.657276i \(-0.771709\pi\)
0.983772 + 0.179423i \(0.0574230\pi\)
\(62\) 0 0
\(63\) −5.18332 + 3.55085i −0.653037 + 0.447365i
\(64\) 0 0
\(65\) −13.1304 + 16.4650i −1.62863 + 2.04223i
\(66\) 0 0
\(67\) 4.19011i 0.511903i 0.966690 + 0.255951i \(0.0823887\pi\)
−0.966690 + 0.255951i \(0.917611\pi\)
\(68\) 0 0
\(69\) 2.50058 5.19250i 0.301034 0.625104i
\(70\) 0 0
\(71\) 3.95100 + 8.20434i 0.468897 + 0.973676i 0.992561 + 0.121750i \(0.0388507\pi\)
−0.523663 + 0.851925i \(0.675435\pi\)
\(72\) 0 0
\(73\) −1.51164 0.345021i −0.176924 0.0403817i 0.133141 0.991097i \(-0.457494\pi\)
−0.310065 + 0.950715i \(0.600351\pi\)
\(74\) 0 0
\(75\) 15.8318 7.62418i 1.82809 0.880364i
\(76\) 0 0
\(77\) 10.7662 + 6.18396i 1.22692 + 0.704728i
\(78\) 0 0
\(79\) 14.9599i 1.68312i 0.540165 + 0.841559i \(0.318362\pi\)
−0.540165 + 0.841559i \(0.681638\pi\)
\(80\) 0 0
\(81\) 9.44652 + 4.54921i 1.04961 + 0.505467i
\(82\) 0 0
\(83\) 0.959887 4.20554i 0.105361 0.461618i −0.894532 0.447004i \(-0.852491\pi\)
0.999893 0.0146138i \(-0.00465188\pi\)
\(84\) 0 0
\(85\) −1.70795 7.48302i −0.185253 0.811648i
\(86\) 0 0
\(87\) 2.25935 + 9.89885i 0.242228 + 1.06127i
\(88\) 0 0
\(89\) −16.4153 3.74669i −1.74002 0.397148i −0.769592 0.638536i \(-0.779540\pi\)
−0.970429 + 0.241387i \(0.922398\pi\)
\(90\) 0 0
\(91\) −13.6224 7.82452i −1.42801 0.820232i
\(92\) 0 0
\(93\) −9.72386 12.1933i −1.00832 1.26439i
\(94\) 0 0
\(95\) −11.3144 + 9.02292i −1.16083 + 0.925732i
\(96\) 0 0
\(97\) 15.2923i 1.55269i 0.630306 + 0.776347i \(0.282930\pi\)
−0.630306 + 0.776347i \(0.717070\pi\)
\(98\) 0 0
\(99\) 11.1440i 1.12001i
\(100\) 0 0
\(101\) 9.05001 7.21714i 0.900510 0.718132i −0.0594617 0.998231i \(-0.518938\pi\)
0.959971 + 0.280098i \(0.0903670\pi\)
\(102\) 0 0
\(103\) −1.58264 1.98457i −0.155942 0.195545i 0.697723 0.716368i \(-0.254197\pi\)
−0.853665 + 0.520823i \(0.825625\pi\)
\(104\) 0 0
\(105\) 12.2950 + 17.9475i 1.19987 + 1.75150i
\(106\) 0 0
\(107\) −3.20491 0.731501i −0.309831 0.0707169i 0.0647784 0.997900i \(-0.479366\pi\)
−0.374609 + 0.927183i \(0.622223\pi\)
\(108\) 0 0
\(109\) −1.59774 7.00016i −0.153036 0.670494i −0.991993 0.126296i \(-0.959691\pi\)
0.838957 0.544198i \(-0.183166\pi\)
\(110\) 0 0
\(111\) −4.60820 20.1898i −0.437391 1.91634i
\(112\) 0 0
\(113\) 0.836189 3.66358i 0.0786621 0.344641i −0.920247 0.391338i \(-0.872012\pi\)
0.998909 + 0.0466969i \(0.0148695\pi\)
\(114\) 0 0
\(115\) −7.94384 3.82555i −0.740767 0.356734i
\(116\) 0 0
\(117\) 14.1004i 1.30358i
\(118\) 0 0
\(119\) 5.32515 2.10366i 0.488156 0.192842i
\(120\) 0 0
\(121\) 9.93029 4.78218i 0.902754 0.434743i
\(122\) 0 0
\(123\) 0.609698 + 0.139159i 0.0549746 + 0.0125476i
\(124\) 0 0
\(125\) −3.96957 8.24289i −0.355049 0.737267i
\(126\) 0 0
\(127\) 8.81828 18.3114i 0.782496 1.62487i 0.00176879 0.999998i \(-0.499437\pi\)
0.780727 0.624872i \(-0.214849\pi\)
\(128\) 0 0
\(129\) 11.6887i 1.02914i
\(130\) 0 0
\(131\) 4.71658 5.91440i 0.412089 0.516744i −0.531861 0.846832i \(-0.678507\pi\)
0.943950 + 0.330088i \(0.107078\pi\)
\(132\) 0 0
\(133\) −7.92984 7.32504i −0.687604 0.635161i
\(134\) 0 0
\(135\) 2.23076 4.63222i 0.191993 0.398678i
\(136\) 0 0
\(137\) 10.6554 13.3615i 0.910356 1.14155i −0.0791213 0.996865i \(-0.525211\pi\)
0.989478 0.144686i \(-0.0462171\pi\)
\(138\) 0 0
\(139\) 10.5434 + 13.2210i 0.894276 + 1.12139i 0.992008 + 0.126174i \(0.0402697\pi\)
−0.0977321 + 0.995213i \(0.531159\pi\)
\(140\) 0 0
\(141\) 0.140948 0.176743i 0.0118699 0.0148844i
\(142\) 0 0
\(143\) −25.1046 + 12.0897i −2.09935 + 1.01099i
\(144\) 0 0
\(145\) 15.1439 3.45650i 1.25763 0.287047i
\(146\) 0 0
\(147\) −11.8470 + 11.0910i −0.977126 + 0.914768i
\(148\) 0 0
\(149\) −4.16013 18.2267i −0.340811 1.49319i −0.797367 0.603495i \(-0.793774\pi\)
0.456556 0.889695i \(-0.349083\pi\)
\(150\) 0 0
\(151\) 5.47498 + 11.3689i 0.445548 + 0.925189i 0.995917 + 0.0902682i \(0.0287724\pi\)
−0.550370 + 0.834921i \(0.685513\pi\)
\(152\) 0 0
\(153\) 4.01791 + 3.20417i 0.324828 + 0.259042i
\(154\) 0 0
\(155\) −18.6542 + 14.8762i −1.49834 + 1.19489i
\(156\) 0 0
\(157\) −15.2811 12.1863i −1.21957 0.972571i −0.219570 0.975597i \(-0.570465\pi\)
−0.999995 + 0.00302581i \(0.999037\pi\)
\(158\) 0 0
\(159\) −24.1323 11.6215i −1.91381 0.921644i
\(160\) 0 0
\(161\) 1.92466 6.28924i 0.151684 0.495662i
\(162\) 0 0
\(163\) −11.3087 9.01835i −0.885762 0.706372i 0.0709277 0.997481i \(-0.477404\pi\)
−0.956690 + 0.291110i \(0.905975\pi\)
\(164\) 0 0
\(165\) 38.5866 3.00396
\(166\) 0 0
\(167\) 7.49174 + 3.60783i 0.579728 + 0.279183i 0.700680 0.713476i \(-0.252880\pi\)
−0.120951 + 0.992658i \(0.538594\pi\)
\(168\) 0 0
\(169\) 20.0520 9.65654i 1.54246 0.742811i
\(170\) 0 0
\(171\) 2.15611 9.44652i 0.164882 0.722394i
\(172\) 0 0
\(173\) −9.11432 18.9261i −0.692949 1.43892i −0.888802 0.458291i \(-0.848462\pi\)
0.195853 0.980633i \(-0.437252\pi\)
\(174\) 0 0
\(175\) 16.5438 11.3334i 1.25059 0.856724i
\(176\) 0 0
\(177\) −7.13079 −0.535983
\(178\) 0 0
\(179\) 1.33194 2.76580i 0.0995540 0.206726i −0.845243 0.534382i \(-0.820544\pi\)
0.944797 + 0.327656i \(0.106259\pi\)
\(180\) 0 0
\(181\) 12.6788 + 2.89386i 0.942410 + 0.215099i 0.666009 0.745943i \(-0.268001\pi\)
0.276401 + 0.961042i \(0.410858\pi\)
\(182\) 0 0
\(183\) 9.36268 2.13697i 0.692109 0.157969i
\(184\) 0 0
\(185\) −30.8878 + 7.04994i −2.27092 + 0.518322i
\(186\) 0 0
\(187\) 2.25980 9.90083i 0.165253 0.724020i
\(188\) 0 0
\(189\) 3.66739 + 1.12231i 0.266763 + 0.0816359i
\(190\) 0 0
\(191\) −12.0193 + 9.58505i −0.869684 + 0.693550i −0.952999 0.302973i \(-0.902021\pi\)
0.0833147 + 0.996523i \(0.473449\pi\)
\(192\) 0 0
\(193\) 4.00270 + 5.01923i 0.288121 + 0.361292i 0.904736 0.425973i \(-0.140068\pi\)
−0.616615 + 0.787265i \(0.711497\pi\)
\(194\) 0 0
\(195\) −48.8233 −3.49631
\(196\) 0 0
\(197\) −10.1071 −0.720102 −0.360051 0.932933i \(-0.617241\pi\)
−0.360051 + 0.932933i \(0.617241\pi\)
\(198\) 0 0
\(199\) −6.24464 7.83052i −0.442670 0.555091i 0.509574 0.860427i \(-0.329803\pi\)
−0.952245 + 0.305335i \(0.901231\pi\)
\(200\) 0 0
\(201\) −7.59480 + 6.05665i −0.535696 + 0.427203i
\(202\) 0 0
\(203\) 4.25732 + 10.7769i 0.298805 + 0.756389i
\(204\) 0 0
\(205\) 0.212896 0.932756i 0.0148693 0.0651465i
\(206\) 0 0
\(207\) 5.75539 1.31363i 0.400028 0.0913037i
\(208\) 0 0
\(209\) −18.6674 + 4.26072i −1.29125 + 0.294720i
\(210\) 0 0
\(211\) 8.32839 + 1.90090i 0.573350 + 0.130863i 0.499359 0.866395i \(-0.333569\pi\)
0.0739916 + 0.997259i \(0.476426\pi\)
\(212\) 0 0
\(213\) −9.15979 + 19.0205i −0.627618 + 1.30326i
\(214\) 0 0
\(215\) 17.8822 1.21956
\(216\) 0 0
\(217\) −13.0740 12.0769i −0.887523 0.819833i
\(218\) 0 0
\(219\) −1.55965 3.23864i −0.105391 0.218847i
\(220\) 0 0
\(221\) −2.85930 + 12.5274i −0.192338 + 0.842686i
\(222\) 0 0
\(223\) −22.4477 + 10.8102i −1.50321 + 0.723906i −0.990863 0.134875i \(-0.956937\pi\)
−0.512343 + 0.858781i \(0.671222\pi\)
\(224\) 0 0
\(225\) 16.2168 + 7.80960i 1.08112 + 0.520640i
\(226\) 0 0
\(227\) 6.92816 0.459838 0.229919 0.973210i \(-0.426154\pi\)
0.229919 + 0.973210i \(0.426154\pi\)
\(228\) 0 0
\(229\) −4.28471 3.41695i −0.283142 0.225798i 0.471612 0.881806i \(-0.343672\pi\)
−0.754754 + 0.656008i \(0.772244\pi\)
\(230\) 0 0
\(231\) 4.35339 + 28.4530i 0.286432 + 1.87207i
\(232\) 0 0
\(233\) −5.13534 2.47305i −0.336427 0.162015i 0.258041 0.966134i \(-0.416923\pi\)
−0.594468 + 0.804119i \(0.702637\pi\)
\(234\) 0 0
\(235\) −0.270393 0.215631i −0.0176385 0.0140662i
\(236\) 0 0
\(237\) −27.1156 + 21.6240i −1.76135 + 1.40463i
\(238\) 0 0
\(239\) 6.51054 + 5.19198i 0.421132 + 0.335841i 0.811017 0.585022i \(-0.198914\pi\)
−0.389886 + 0.920863i \(0.627486\pi\)
\(240\) 0 0
\(241\) 9.87007 + 20.4954i 0.635787 + 1.32023i 0.931079 + 0.364819i \(0.118869\pi\)
−0.295291 + 0.955407i \(0.595417\pi\)
\(242\) 0 0
\(243\) 4.44123 + 19.4583i 0.284905 + 1.24825i
\(244\) 0 0
\(245\) 16.9677 + 18.1244i 1.08403 + 1.15792i
\(246\) 0 0
\(247\) 23.6197 5.39105i 1.50289 0.343024i
\(248\) 0 0
\(249\) 9.01026 4.33911i 0.571002 0.274980i
\(250\) 0 0
\(251\) −2.20871 + 2.76963i −0.139413 + 0.174818i −0.846636 0.532172i \(-0.821376\pi\)
0.707224 + 0.706990i \(0.249947\pi\)
\(252\) 0 0
\(253\) −7.27352 9.12070i −0.457282 0.573414i
\(254\) 0 0
\(255\) 11.0946 13.9122i 0.694772 0.871216i
\(256\) 0 0
\(257\) 9.27941 19.2689i 0.578833 1.20196i −0.381827 0.924234i \(-0.624705\pi\)
0.960660 0.277726i \(-0.0895808\pi\)
\(258\) 0 0
\(259\) −8.68329 21.9807i −0.539554 1.36581i
\(260\) 0 0
\(261\) −6.48451 + 8.13132i −0.401381 + 0.503316i
\(262\) 0 0
\(263\) 15.6121i 0.962683i 0.876533 + 0.481342i \(0.159850\pi\)
−0.876533 + 0.481342i \(0.840150\pi\)
\(264\) 0 0
\(265\) −17.7793 + 36.9192i −1.09218 + 2.26793i
\(266\) 0 0
\(267\) −16.9367 35.1694i −1.03651 2.15233i
\(268\) 0 0
\(269\) 1.57546 + 0.359588i 0.0960573 + 0.0219245i 0.270279 0.962782i \(-0.412884\pi\)
−0.174222 + 0.984706i \(0.555741\pi\)
\(270\) 0 0
\(271\) −11.2359 + 5.41095i −0.682535 + 0.328692i −0.742822 0.669489i \(-0.766513\pi\)
0.0602863 + 0.998181i \(0.480799\pi\)
\(272\) 0 0
\(273\) −5.50831 36.0014i −0.333378 2.17890i
\(274\) 0 0
\(275\) 35.5687i 2.14487i
\(276\) 0 0
\(277\) 7.01008 + 3.37588i 0.421195 + 0.202837i 0.632462 0.774592i \(-0.282045\pi\)
−0.211267 + 0.977428i \(0.567759\pi\)
\(278\) 0 0
\(279\) 3.55480 15.5746i 0.212821 0.932428i
\(280\) 0 0
\(281\) 4.35932 + 19.0994i 0.260056 + 1.13938i 0.921191 + 0.389111i \(0.127218\pi\)
−0.661135 + 0.750267i \(0.729925\pi\)
\(282\) 0 0
\(283\) −4.86056 21.2955i −0.288930 1.26589i −0.885996 0.463693i \(-0.846524\pi\)
0.597066 0.802192i \(-0.296333\pi\)
\(284\) 0 0
\(285\) −32.7091 7.46563i −1.93752 0.442226i
\(286\) 0 0
\(287\) 0.711816 + 0.0517505i 0.0420172 + 0.00305473i
\(288\) 0 0
\(289\) 7.67938 + 9.62964i 0.451728 + 0.566449i
\(290\) 0 0
\(291\) −27.7181 + 22.1044i −1.62486 + 1.29579i
\(292\) 0 0
\(293\) 29.5755i 1.72782i −0.503648 0.863909i \(-0.668009\pi\)
0.503648 0.863909i \(-0.331991\pi\)
\(294\) 0 0
\(295\) 10.9092i 0.635156i
\(296\) 0 0
\(297\) 5.31847 4.24134i 0.308609 0.246107i
\(298\) 0 0
\(299\) 9.20312 + 11.5403i 0.532230 + 0.667395i
\(300\) 0 0
\(301\) 2.01750 + 13.1860i 0.116287 + 0.760030i
\(302\) 0 0
\(303\) 26.1629 + 5.97152i 1.50302 + 0.343055i
\(304\) 0 0
\(305\) −3.26928 14.3236i −0.187198 0.820170i
\(306\) 0 0
\(307\) −1.17334 5.14075i −0.0669662 0.293398i 0.930345 0.366686i \(-0.119508\pi\)
−0.997311 + 0.0732883i \(0.976651\pi\)
\(308\) 0 0
\(309\) 1.30949 5.73725i 0.0744942 0.326381i
\(310\) 0 0
\(311\) −22.3697 10.7727i −1.26847 0.610862i −0.326068 0.945346i \(-0.605724\pi\)
−0.942401 + 0.334484i \(0.891438\pi\)
\(312\) 0 0
\(313\) 3.86468i 0.218445i −0.994017 0.109222i \(-0.965164\pi\)
0.994017 0.109222i \(-0.0348361\pi\)
\(314\) 0 0
\(315\) −6.52094 + 21.3086i −0.367414 + 1.20061i
\(316\) 0 0
\(317\) 27.1510 13.0752i 1.52495 0.734379i 0.531334 0.847163i \(-0.321691\pi\)
0.993620 + 0.112784i \(0.0359767\pi\)
\(318\) 0 0
\(319\) 20.0370 + 4.57332i 1.12186 + 0.256057i
\(320\) 0 0
\(321\) −3.30671 6.86645i −0.184562 0.383248i
\(322\) 0 0
\(323\) −3.83117 + 7.95551i −0.213172 + 0.442657i
\(324\) 0 0
\(325\) 45.0047i 2.49641i
\(326\) 0 0
\(327\) 10.3787 13.0145i 0.573944 0.719703i
\(328\) 0 0
\(329\) 0.128496 0.223710i 0.00708423 0.0123335i
\(330\) 0 0
\(331\) 8.98135 18.6500i 0.493660 1.02510i −0.494142 0.869381i \(-0.664518\pi\)
0.987802 0.155714i \(-0.0497679\pi\)
\(332\) 0 0
\(333\) 13.2259 16.5848i 0.724775 0.908840i
\(334\) 0 0
\(335\) 9.26587 + 11.6190i 0.506249 + 0.634816i
\(336\) 0 0
\(337\) 9.01619 11.3059i 0.491143 0.615874i −0.473063 0.881029i \(-0.656852\pi\)
0.964206 + 0.265155i \(0.0854230\pi\)
\(338\) 0 0
\(339\) 7.84913 3.77994i 0.426306 0.205298i
\(340\) 0 0
\(341\) −30.7772 + 7.02471i −1.66668 + 0.380409i
\(342\) 0 0
\(343\) −11.4503 + 14.5565i −0.618256 + 0.785977i
\(344\) 0 0
\(345\) −4.54852 19.9284i −0.244884 1.07291i
\(346\) 0 0
\(347\) 2.59238 + 5.38314i 0.139166 + 0.288982i 0.958890 0.283777i \(-0.0915874\pi\)
−0.819724 + 0.572759i \(0.805873\pi\)
\(348\) 0 0
\(349\) 14.7441 + 11.7581i 0.789236 + 0.629395i 0.932861 0.360237i \(-0.117304\pi\)
−0.143624 + 0.989632i \(0.545876\pi\)
\(350\) 0 0
\(351\) −6.72941 + 5.36653i −0.359190 + 0.286444i
\(352\) 0 0
\(353\) 14.2625 + 11.3740i 0.759119 + 0.605377i 0.924646 0.380828i \(-0.124361\pi\)
−0.165527 + 0.986205i \(0.552932\pi\)
\(354\) 0 0
\(355\) 29.0988 + 14.0133i 1.54441 + 0.743746i
\(356\) 0 0
\(357\) 11.5103 + 6.61137i 0.609190 + 0.349911i
\(358\) 0 0
\(359\) 19.2838 + 15.3783i 1.01776 + 0.811638i 0.982221 0.187730i \(-0.0601131\pi\)
0.0355411 + 0.999368i \(0.488685\pi\)
\(360\) 0 0
\(361\) −2.35165 −0.123771
\(362\) 0 0
\(363\) 23.0219 + 11.0867i 1.20833 + 0.581903i
\(364\) 0 0
\(365\) −4.95469 + 2.38605i −0.259340 + 0.124892i
\(366\) 0 0
\(367\) 3.93605 17.2450i 0.205460 0.900179i −0.762084 0.647478i \(-0.775824\pi\)
0.967544 0.252702i \(-0.0813191\pi\)
\(368\) 0 0
\(369\) 0.277940 + 0.577148i 0.0144690 + 0.0300451i
\(370\) 0 0
\(371\) −29.2294 8.94488i −1.51751 0.464395i
\(372\) 0 0
\(373\) 0.708793 0.0366999 0.0183500 0.999832i \(-0.494159\pi\)
0.0183500 + 0.999832i \(0.494159\pi\)
\(374\) 0 0
\(375\) 9.20283 19.1099i 0.475232 0.986830i
\(376\) 0 0
\(377\) −25.3527 5.78658i −1.30573 0.298024i
\(378\) 0 0
\(379\) 15.9228 3.63427i 0.817899 0.186680i 0.206951 0.978351i \(-0.433646\pi\)
0.610948 + 0.791671i \(0.290789\pi\)
\(380\) 0 0
\(381\) 45.9369 10.4848i 2.35342 0.537152i
\(382\) 0 0
\(383\) −4.12178 + 18.0587i −0.210613 + 0.922757i 0.753538 + 0.657404i \(0.228346\pi\)
−0.964151 + 0.265353i \(0.914512\pi\)
\(384\) 0 0
\(385\) 43.5294 6.66011i 2.21846 0.339431i
\(386\) 0 0
\(387\) −9.36088 + 7.46505i −0.475840 + 0.379470i
\(388\) 0 0
\(389\) 10.4114 + 13.0555i 0.527878 + 0.661938i 0.972261 0.233899i \(-0.0751484\pi\)
−0.444383 + 0.895837i \(0.646577\pi\)
\(390\) 0 0
\(391\) −5.37974 −0.272065
\(392\) 0 0
\(393\) 17.5378 0.884667
\(394\) 0 0
\(395\) 33.0818 + 41.4833i 1.66453 + 2.08725i
\(396\) 0 0
\(397\) 17.8317 14.2203i 0.894948 0.713697i −0.0637976 0.997963i \(-0.520321\pi\)
0.958746 + 0.284266i \(0.0917498\pi\)
\(398\) 0 0
\(399\) 1.81474 24.9614i 0.0908506 1.24963i
\(400\) 0 0
\(401\) −0.942528 + 4.12948i −0.0470676 + 0.206217i −0.992994 0.118165i \(-0.962299\pi\)
0.945926 + 0.324381i \(0.105156\pi\)
\(402\) 0 0
\(403\) 38.9422 8.88830i 1.93985 0.442758i
\(404\) 0 0
\(405\) 36.2549 8.27494i 1.80152 0.411185i
\(406\) 0 0
\(407\) −40.8678 9.32781i −2.02574 0.462362i
\(408\) 0 0
\(409\) 1.40849 2.92476i 0.0696455 0.144620i −0.863240 0.504794i \(-0.831568\pi\)
0.932885 + 0.360174i \(0.117283\pi\)
\(410\) 0 0
\(411\) 39.6206 1.95434
\(412\) 0 0
\(413\) −8.04421 + 1.23079i −0.395830 + 0.0605630i
\(414\) 0 0
\(415\) −6.63826 13.7845i −0.325859 0.676654i
\(416\) 0 0
\(417\) −8.72366 + 38.2209i −0.427199 + 1.87168i
\(418\) 0 0
\(419\) −8.42438 + 4.05697i −0.411558 + 0.198196i −0.628194 0.778056i \(-0.716206\pi\)
0.216636 + 0.976252i \(0.430491\pi\)
\(420\) 0 0
\(421\) −13.2167 6.36482i −0.644142 0.310202i 0.0831435 0.996538i \(-0.473504\pi\)
−0.727285 + 0.686335i \(0.759218\pi\)
\(422\) 0 0
\(423\) 0.231560 0.0112588
\(424\) 0 0
\(425\) −12.8241 10.2269i −0.622061 0.496077i
\(426\) 0 0
\(427\) 10.1932 4.02672i 0.493281 0.194867i
\(428\) 0 0
\(429\) −58.2011 28.0282i −2.80998 1.35321i
\(430\) 0 0
\(431\) 25.2127 + 20.1065i 1.21445 + 0.968495i 0.999966 0.00823097i \(-0.00262003\pi\)
0.214489 + 0.976726i \(0.431191\pi\)
\(432\) 0 0
\(433\) −16.2970 + 12.9964i −0.783183 + 0.624567i −0.931238 0.364412i \(-0.881270\pi\)
0.148055 + 0.988979i \(0.452699\pi\)
\(434\) 0 0
\(435\) 28.1551 + 22.4530i 1.34993 + 1.07654i
\(436\) 0 0
\(437\) 4.40096 + 9.13869i 0.210527 + 0.437163i
\(438\) 0 0
\(439\) −5.34531 23.4193i −0.255118 1.11774i −0.926400 0.376541i \(-0.877113\pi\)
0.671282 0.741202i \(-0.265744\pi\)
\(440\) 0 0
\(441\) −16.4483 2.40436i −0.783252 0.114493i
\(442\) 0 0
\(443\) 5.60975 1.28039i 0.266527 0.0608331i −0.0871687 0.996194i \(-0.527782\pi\)
0.353696 + 0.935360i \(0.384925\pi\)
\(444\) 0 0
\(445\) −53.8045 + 25.9109i −2.55058 + 1.22829i
\(446\) 0 0
\(447\) 27.0236 33.8865i 1.27817 1.60278i
\(448\) 0 0
\(449\) −4.88694 6.12803i −0.230629 0.289199i 0.653029 0.757333i \(-0.273498\pi\)
−0.883658 + 0.468134i \(0.844927\pi\)
\(450\) 0 0
\(451\) 0.789259 0.989699i 0.0371647 0.0466031i
\(452\) 0 0
\(453\) −12.6929 + 26.3571i −0.596364 + 1.23836i
\(454\) 0 0
\(455\) −55.0773 + 8.42698i −2.58207 + 0.395063i
\(456\) 0 0
\(457\) −2.11019 + 2.64610i −0.0987107 + 0.123779i −0.828733 0.559644i \(-0.810938\pi\)
0.730023 + 0.683423i \(0.239509\pi\)
\(458\) 0 0
\(459\) 3.13704i 0.146424i
\(460\) 0 0
\(461\) −4.49068 + 9.32499i −0.209152 + 0.434308i −0.978984 0.203939i \(-0.934626\pi\)
0.769832 + 0.638247i \(0.220340\pi\)
\(462\) 0 0
\(463\) 0.944376 + 1.96102i 0.0438889 + 0.0911362i 0.921760 0.387760i \(-0.126751\pi\)
−0.877871 + 0.478897i \(0.841037\pi\)
\(464\) 0 0
\(465\) −53.9279 12.3087i −2.50085 0.570802i
\(466\) 0 0
\(467\) −21.2648 + 10.2406i −0.984020 + 0.473879i −0.855486 0.517826i \(-0.826741\pi\)
−0.128534 + 0.991705i \(0.541027\pi\)
\(468\) 0 0
\(469\) −7.52227 + 8.14336i −0.347346 + 0.376025i
\(470\) 0 0
\(471\) 45.3127i 2.08790i
\(472\) 0 0
\(473\) 21.3170 + 10.2657i 0.980156 + 0.472018i
\(474\) 0 0
\(475\) −6.88173 + 30.1508i −0.315756 + 1.38342i
\(476\) 0 0
\(477\) −6.10513 26.7483i −0.279535 1.22472i
\(478\) 0 0
\(479\) 5.15270 + 22.5755i 0.235433 + 1.03150i 0.945054 + 0.326915i \(0.106009\pi\)
−0.709621 + 0.704584i \(0.751134\pi\)
\(480\) 0 0
\(481\) 51.7097 + 11.8024i 2.35776 + 0.538143i
\(482\) 0 0
\(483\) 14.1816 5.60233i 0.645287 0.254915i
\(484\) 0 0
\(485\) 33.8168 + 42.4050i 1.53554 + 1.92551i
\(486\) 0 0
\(487\) −9.74360 + 7.77026i −0.441524 + 0.352104i −0.818880 0.573964i \(-0.805405\pi\)
0.377356 + 0.926068i \(0.376833\pi\)
\(488\) 0 0
\(489\) 33.5333i 1.51643i
\(490\) 0 0
\(491\) 17.7714i 0.802011i −0.916076 0.401005i \(-0.868661\pi\)
0.916076 0.401005i \(-0.131339\pi\)
\(492\) 0 0
\(493\) 7.41003 5.90930i 0.333731 0.266142i
\(494\) 0 0
\(495\) 24.6434 + 30.9019i 1.10764 + 1.38894i
\(496\) 0 0
\(497\) −7.05015 + 23.0379i −0.316242 + 1.03339i
\(498\) 0 0
\(499\) 15.2651 + 3.48416i 0.683359 + 0.155972i 0.550087 0.835107i \(-0.314595\pi\)
0.133272 + 0.991080i \(0.457452\pi\)
\(500\) 0 0
\(501\) 4.28965 + 18.7942i 0.191648 + 0.839663i
\(502\) 0 0
\(503\) 5.07467 + 22.2336i 0.226268 + 0.991346i 0.952653 + 0.304058i \(0.0983418\pi\)
−0.726385 + 0.687288i \(0.758801\pi\)
\(504\) 0 0
\(505\) 9.13563 40.0258i 0.406530 1.78113i
\(506\) 0 0
\(507\) 46.4875 + 22.3872i 2.06458 + 0.994251i
\(508\) 0 0
\(509\) 24.9810i 1.10726i 0.832762 + 0.553631i \(0.186758\pi\)
−0.832762 + 0.553631i \(0.813242\pi\)
\(510\) 0 0
\(511\) −2.31843 3.38430i −0.102561 0.149713i
\(512\) 0 0
\(513\) −5.32896 + 2.56629i −0.235279 + 0.113305i
\(514\) 0 0
\(515\) −8.77723 2.00334i −0.386771 0.0882779i
\(516\) 0 0
\(517\) −0.198541 0.412274i −0.00873181 0.0181318i
\(518\) 0 0
\(519\) 21.1302 43.8772i 0.927511 1.92600i
\(520\) 0 0
\(521\) 14.9010i 0.652823i 0.945228 + 0.326412i \(0.105840\pi\)
−0.945228 + 0.326412i \(0.894160\pi\)
\(522\) 0 0
\(523\) −7.43614 + 9.32463i −0.325160 + 0.407737i −0.917363 0.398051i \(-0.869687\pi\)
0.592204 + 0.805788i \(0.298258\pi\)
\(524\) 0 0
\(525\) 44.4559 + 13.6045i 1.94021 + 0.593751i
\(526\) 0 0
\(527\) −6.31651 + 13.1164i −0.275151 + 0.571358i
\(528\) 0 0
\(529\) 10.4872 13.1505i 0.455965 0.571762i
\(530\) 0 0
\(531\) −4.55410 5.71066i −0.197631 0.247821i
\(532\) 0 0
\(533\) −0.998642 + 1.25226i −0.0432560 + 0.0542413i
\(534\) 0 0
\(535\) −10.5047 + 5.05882i −0.454160 + 0.218712i
\(536\) 0 0
\(537\) 6.93845 1.58366i 0.299416 0.0683398i
\(538\) 0 0
\(539\) 9.82208 + 31.3464i 0.423067 + 1.35018i
\(540\) 0 0
\(541\) 7.30131 + 31.9891i 0.313908 + 1.37532i 0.848046 + 0.529923i \(0.177779\pi\)
−0.534138 + 0.845397i \(0.679364\pi\)
\(542\) 0 0
\(543\) 13.0815 + 27.1641i 0.561382 + 1.16572i
\(544\) 0 0
\(545\) −19.9104 15.8780i −0.852869 0.680141i
\(546\) 0 0
\(547\) 14.1530 11.2867i 0.605140 0.482583i −0.272337 0.962202i \(-0.587797\pi\)
0.877477 + 0.479619i \(0.159225\pi\)
\(548\) 0 0
\(549\) 7.69088 + 6.13328i 0.328239 + 0.261762i
\(550\) 0 0
\(551\) −16.1001 7.75342i −0.685889 0.330307i
\(552\) 0 0
\(553\) −26.8567 + 29.0741i −1.14206 + 1.23636i
\(554\) 0 0
\(555\) −57.4256 45.7954i −2.43758 1.94391i
\(556\) 0 0
\(557\) −2.04282 −0.0865570 −0.0432785 0.999063i \(-0.513780\pi\)
−0.0432785 + 0.999063i \(0.513780\pi\)
\(558\) 0 0
\(559\) −26.9722 12.9891i −1.14080 0.549382i
\(560\) 0 0
\(561\) 21.2123 10.2153i 0.895583 0.431290i
\(562\) 0 0
\(563\) 2.75162 12.0556i 0.115967 0.508084i −0.883264 0.468876i \(-0.844659\pi\)
0.999231 0.0392085i \(-0.0124836\pi\)
\(564\) 0 0
\(565\) −5.78281 12.0081i −0.243285 0.505186i
\(566\) 0 0
\(567\) 10.1921 + 25.8001i 0.428029 + 1.08350i
\(568\) 0 0
\(569\) −28.3263 −1.18750 −0.593750 0.804650i \(-0.702353\pi\)
−0.593750 + 0.804650i \(0.702353\pi\)
\(570\) 0 0
\(571\) 11.0645 22.9756i 0.463034 0.961500i −0.530470 0.847704i \(-0.677985\pi\)
0.993504 0.113796i \(-0.0363012\pi\)
\(572\) 0 0
\(573\) −34.7469 7.93075i −1.45157 0.331312i
\(574\) 0 0
\(575\) −18.3697 + 4.19277i −0.766070 + 0.174851i
\(576\) 0 0
\(577\) −14.3858 + 3.28347i −0.598890 + 0.136693i −0.511210 0.859456i \(-0.670802\pi\)
−0.0876801 + 0.996149i \(0.527945\pi\)
\(578\) 0 0
\(579\) −3.31187 + 14.5102i −0.137636 + 0.603025i
\(580\) 0 0
\(581\) 9.41549 6.45012i 0.390621 0.267596i
\(582\) 0 0
\(583\) −42.3887 + 33.8038i −1.75556 + 1.40001i
\(584\) 0 0
\(585\) −31.1811 39.0999i −1.28918 1.61658i
\(586\) 0 0
\(587\) −16.6979 −0.689196 −0.344598 0.938750i \(-0.611985\pi\)
−0.344598 + 0.938750i \(0.611985\pi\)
\(588\) 0 0
\(589\) 27.4484 1.13099
\(590\) 0 0
\(591\) −14.6095 18.3197i −0.600954 0.753572i
\(592\) 0 0
\(593\) −9.64991 + 7.69554i −0.396274 + 0.316018i −0.801273 0.598299i \(-0.795843\pi\)
0.404999 + 0.914317i \(0.367272\pi\)
\(594\) 0 0
\(595\) 10.1145 17.6093i 0.414655 0.721909i
\(596\) 0 0
\(597\) 5.16686 22.6375i 0.211466 0.926491i
\(598\) 0 0
\(599\) 44.6409 10.1890i 1.82398 0.416311i 0.833332 0.552773i \(-0.186430\pi\)
0.990645 + 0.136462i \(0.0435730\pi\)
\(600\) 0 0
\(601\) 17.6526 4.02910i 0.720066 0.164350i 0.153241 0.988189i \(-0.451029\pi\)
0.566825 + 0.823838i \(0.308172\pi\)
\(602\) 0 0
\(603\) −9.70088 2.21416i −0.395051 0.0901677i
\(604\) 0 0
\(605\) 16.9612 35.2204i 0.689572 1.43191i
\(606\) 0 0
\(607\) −20.6711 −0.839016 −0.419508 0.907752i \(-0.637797\pi\)
−0.419508 + 0.907752i \(0.637797\pi\)
\(608\) 0 0
\(609\) −13.3799 + 23.2942i −0.542181 + 0.943930i
\(610\) 0 0
\(611\) 0.251212 + 0.521647i 0.0101629 + 0.0211036i
\(612\) 0 0
\(613\) 1.73100 7.58402i 0.0699146 0.306316i −0.927865 0.372916i \(-0.878358\pi\)
0.997780 + 0.0666000i \(0.0212152\pi\)
\(614\) 0 0
\(615\) 1.99841 0.962381i 0.0805835 0.0388070i
\(616\) 0 0
\(617\) 1.30129 + 0.626666i 0.0523878 + 0.0252286i 0.459894 0.887974i \(-0.347887\pi\)
−0.407506 + 0.913202i \(0.633602\pi\)
\(618\) 0 0
\(619\) −46.8049 −1.88125 −0.940624 0.339449i \(-0.889759\pi\)
−0.940624 + 0.339449i \(0.889759\pi\)
\(620\) 0 0
\(621\) −2.81740 2.24680i −0.113059 0.0901612i
\(622\) 0 0
\(623\) −25.1765 36.7512i −1.00868 1.47240i
\(624\) 0 0
\(625\) 4.90897 + 2.36403i 0.196359 + 0.0945613i
\(626\) 0 0
\(627\) −34.7059 27.6770i −1.38602 1.10531i
\(628\) 0 0
\(629\) −15.1136 + 12.0527i −0.602619 + 0.480573i
\(630\) 0 0
\(631\) 1.07685 + 0.858762i 0.0428688 + 0.0341868i 0.644690 0.764444i \(-0.276987\pi\)
−0.601821 + 0.798631i \(0.705558\pi\)
\(632\) 0 0
\(633\) 8.59291 + 17.8434i 0.341538 + 0.709210i
\(634\) 0 0
\(635\) −16.0403 70.2773i −0.636541 2.78887i
\(636\) 0 0
\(637\) −12.4278 39.6623i −0.492407 1.57148i
\(638\) 0 0
\(639\) −21.0824 + 4.81192i −0.834007 + 0.190357i
\(640\) 0 0
\(641\) 23.5537 11.3429i 0.930316 0.448017i 0.0935731 0.995612i \(-0.470171\pi\)
0.836743 + 0.547596i \(0.184457\pi\)
\(642\) 0 0
\(643\) 0.582816 0.730828i 0.0229840 0.0288210i −0.770207 0.637794i \(-0.779847\pi\)
0.793191 + 0.608973i \(0.208418\pi\)
\(644\) 0 0
\(645\) 25.8481 + 32.4125i 1.01777 + 1.27624i
\(646\) 0 0
\(647\) 2.59651 3.25592i 0.102079 0.128003i −0.728168 0.685399i \(-0.759628\pi\)
0.830247 + 0.557396i \(0.188199\pi\)
\(648\) 0 0
\(649\) −6.26266 + 13.0046i −0.245831 + 0.510473i
\(650\) 0 0
\(651\) 2.99199 41.1541i 0.117265 1.61296i
\(652\) 0 0
\(653\) −22.3678 + 28.0484i −0.875321 + 1.09762i 0.119178 + 0.992873i \(0.461974\pi\)
−0.994499 + 0.104745i \(0.966597\pi\)
\(654\) 0 0
\(655\) 26.8305i 1.04836i
\(656\) 0 0
\(657\) 1.59758 3.31740i 0.0623274 0.129424i
\(658\) 0 0
\(659\) 16.7166 + 34.7125i 0.651188 + 1.35221i 0.921102 + 0.389321i \(0.127290\pi\)
−0.269914 + 0.962884i \(0.586995\pi\)
\(660\) 0 0
\(661\) −22.1532 5.05633i −0.861661 0.196668i −0.231216 0.972902i \(-0.574270\pi\)
−0.630445 + 0.776234i \(0.717128\pi\)
\(662\) 0 0
\(663\) −26.8397 + 12.9253i −1.04237 + 0.501978i
\(664\) 0 0
\(665\) −38.1876 2.77631i −1.48085 0.107661i
\(666\) 0 0
\(667\) 10.8874i 0.421561i
\(668\) 0 0
\(669\) −52.0414 25.0618i −2.01204 0.968946i
\(670\) 0 0
\(671\) 4.32560 18.9517i 0.166988 0.731622i
\(672\) 0 0
\(673\) −4.15134 18.1882i −0.160022 0.701103i −0.989735 0.142913i \(-0.954353\pi\)
0.829713 0.558190i \(-0.188504\pi\)
\(674\) 0 0
\(675\) −2.44489 10.7118i −0.0941039 0.412296i
\(676\) 0 0
\(677\) 38.4347 + 8.77246i 1.47716 + 0.337153i 0.883832 0.467804i \(-0.154955\pi\)
0.593333 + 0.804957i \(0.297812\pi\)
\(678\) 0 0
\(679\) −27.4534 + 29.7201i −1.05356 + 1.14055i
\(680\) 0 0
\(681\) 10.0144 + 12.5577i 0.383753 + 0.481211i
\(682\) 0 0
\(683\) −33.4691 + 26.6907i −1.28066 + 1.02129i −0.282584 + 0.959242i \(0.591192\pi\)
−0.998073 + 0.0620479i \(0.980237\pi\)
\(684\) 0 0
\(685\) 60.6142i 2.31595i
\(686\) 0 0
\(687\) 12.7054i 0.484740i
\(688\) 0 0
\(689\) 53.6340 42.7717i 2.04329 1.62947i
\(690\) 0 0
\(691\) 0.131609 + 0.165032i 0.00500663 + 0.00627811i 0.784328 0.620346i \(-0.213008\pi\)
−0.779322 + 0.626624i \(0.784436\pi\)
\(692\) 0 0
\(693\) −20.0062 + 21.6580i −0.759972 + 0.822720i
\(694\) 0 0
\(695\) 58.4728 + 13.3460i 2.21800 + 0.506244i
\(696\) 0 0
\(697\) −0.129899 0.569127i −0.00492029 0.0215572i
\(698\) 0 0
\(699\) −2.94041 12.8828i −0.111217 0.487272i
\(700\) 0 0
\(701\) −0.842697 + 3.69210i −0.0318282 + 0.139449i −0.988346 0.152227i \(-0.951356\pi\)
0.956517 + 0.291675i \(0.0942127\pi\)
\(702\) 0 0
\(703\) 32.8381 + 15.8140i 1.23851 + 0.596436i
\(704\) 0 0
\(705\) 0.801789i 0.0301971i
\(706\) 0 0
\(707\) 30.5450 + 2.22068i 1.14876 + 0.0835174i
\(708\) 0 0
\(709\) 29.1913 14.0578i 1.09630 0.527952i 0.203809 0.979011i \(-0.434668\pi\)
0.892494 + 0.451059i \(0.148953\pi\)
\(710\) 0 0
\(711\) −34.6350 7.90520i −1.29891 0.296468i
\(712\) 0 0
\(713\) 7.25593 + 15.0671i 0.271737 + 0.564267i
\(714\) 0 0
\(715\) −42.8794 + 89.0400i −1.60360 + 3.32991i
\(716\) 0 0
\(717\) 19.3055i 0.720978i
\(718\) 0 0
\(719\) 2.20568 2.76583i 0.0822579 0.103148i −0.739000 0.673706i \(-0.764701\pi\)
0.821258 + 0.570558i \(0.193273\pi\)
\(720\) 0 0
\(721\) 0.486971 6.69818i 0.0181358 0.249453i
\(722\) 0 0
\(723\) −22.8822 + 47.5155i −0.851000 + 1.76712i
\(724\) 0 0
\(725\) 20.6969 25.9531i 0.768663 0.963873i
\(726\) 0 0
\(727\) 6.61384 + 8.29350i 0.245294 + 0.307589i 0.889203 0.457513i \(-0.151260\pi\)
−0.643909 + 0.765102i \(0.722688\pi\)
\(728\) 0 0
\(729\) −9.23804 + 11.5841i −0.342150 + 0.429042i
\(730\) 0 0
\(731\) 9.83042 4.73408i 0.363591 0.175096i
\(732\) 0 0
\(733\) 37.0589 8.45845i 1.36880 0.312420i 0.525927 0.850530i \(-0.323719\pi\)
0.842875 + 0.538110i \(0.180861\pi\)
\(734\) 0 0
\(735\) −8.32521 + 56.9531i −0.307080 + 2.10075i
\(736\) 0 0
\(737\) 4.37544 + 19.1701i 0.161172 + 0.706139i
\(738\) 0 0
\(739\) 0.846493 + 1.75776i 0.0311387 + 0.0646602i 0.915958 0.401274i \(-0.131433\pi\)
−0.884819 + 0.465934i \(0.845718\pi\)
\(740\) 0 0
\(741\) 43.9131 + 35.0195i 1.61319 + 1.28647i
\(742\) 0 0
\(743\) 12.9913 10.3602i 0.476604 0.380079i −0.355520 0.934669i \(-0.615696\pi\)
0.832124 + 0.554590i \(0.187125\pi\)
\(744\) 0 0
\(745\) −51.8419 41.3425i −1.89934 1.51467i
\(746\) 0 0
\(747\) 9.22938 + 4.44464i 0.337685 + 0.162621i
\(748\) 0 0
\(749\) −4.91544 7.17527i −0.179606 0.262179i
\(750\) 0 0
\(751\) 12.7896 + 10.1993i 0.466697 + 0.372179i 0.828420 0.560107i \(-0.189240\pi\)
−0.361723 + 0.932286i \(0.617811\pi\)
\(752\) 0 0
\(753\) −8.21273 −0.299288
\(754\) 0 0
\(755\) 40.3228 + 19.4184i 1.46750 + 0.706710i
\(756\) 0 0
\(757\) −5.24086 + 2.52387i −0.190482 + 0.0917314i −0.526694 0.850055i \(-0.676569\pi\)
0.336212 + 0.941786i \(0.390854\pi\)
\(758\) 0 0
\(759\) 6.01817 26.3673i 0.218446 0.957073i
\(760\) 0 0
\(761\) 3.37651 + 7.01139i 0.122398 + 0.254163i 0.953161 0.302465i \(-0.0978094\pi\)
−0.830762 + 0.556627i \(0.812095\pi\)
\(762\) 0 0
\(763\) 9.46186 16.4730i 0.342542 0.596362i
\(764\) 0 0
\(765\) 18.2271 0.659004
\(766\) 0 0
\(767\) 7.92409 16.4545i 0.286122 0.594139i
\(768\) 0 0
\(769\) 5.27239 + 1.20339i 0.190127 + 0.0433953i 0.316524 0.948584i \(-0.397484\pi\)
−0.126397 + 0.991980i \(0.540341\pi\)
\(770\) 0 0
\(771\) 48.3390 11.0331i 1.74089 0.397346i
\(772\) 0 0
\(773\) 45.0160 10.2746i 1.61911 0.369552i 0.685566 0.728010i \(-0.259555\pi\)
0.933546 + 0.358459i \(0.116698\pi\)
\(774\) 0 0
\(775\) −11.3460 + 49.7101i −0.407561 + 1.78564i
\(776\) 0 0
\(777\) 27.2899 47.5113i 0.979018 1.70446i
\(778\) 0 0
\(779\) −0.860523 + 0.686244i −0.0308314 + 0.0245873i
\(780\) 0 0
\(781\) 26.6434 + 33.4097i 0.953375 + 1.19549i
\(782\) 0 0
\(783\) 6.34865 0.226882
\(784\) 0 0
\(785\) −69.3224 −2.47422
\(786\) 0 0
\(787\) −1.41984 1.78042i −0.0506118 0.0634652i 0.755881 0.654709i \(-0.227209\pi\)
−0.806493 + 0.591243i \(0.798637\pi\)
\(788\) 0 0
\(789\) −28.2978 + 22.5667i −1.00743 + 0.803398i
\(790\) 0 0
\(791\) 8.20215 5.61891i 0.291635 0.199785i
\(792\) 0 0
\(793\) −5.47315 + 23.9794i −0.194357 + 0.851534i
\(794\) 0 0
\(795\) −92.6174 + 21.1393i −3.28480 + 0.749735i
\(796\) 0 0
\(797\) −13.5857 + 3.10085i −0.4