Properties

Label 624.2.cn.f.305.7
Level $624$
Weight $2$
Character 624.305
Analytic conductor $4.983$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 624.cn (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.98266508613\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 312)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 305.7
Character \(\chi\) \(=\) 624.305
Dual form 624.2.cn.f.401.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0464265 + 1.73143i) q^{3} +(-1.33870 - 1.33870i) q^{5} +(-0.566234 + 2.11322i) q^{7} +(-2.99569 + 0.160768i) q^{9} +O(q^{10})\) \(q+(0.0464265 + 1.73143i) q^{3} +(-1.33870 - 1.33870i) q^{5} +(-0.566234 + 2.11322i) q^{7} +(-2.99569 + 0.160768i) q^{9} +(-0.256724 - 0.958107i) q^{11} +(-3.27036 + 1.51814i) q^{13} +(2.25572 - 2.38002i) q^{15} +(-2.36097 - 4.08932i) q^{17} +(-1.44252 - 0.386521i) q^{19} +(-3.68517 - 0.882285i) q^{21} +(-1.71229 + 2.96577i) q^{23} -1.41574i q^{25} +(-0.417438 - 5.17936i) q^{27} +(0.733696 + 0.423600i) q^{29} +(-3.66157 + 3.66157i) q^{31} +(1.64698 - 0.488981i) q^{33} +(3.58699 - 2.07095i) q^{35} +(-10.5491 + 2.82661i) q^{37} +(-2.78039 - 5.59191i) q^{39} +(8.93255 - 2.39347i) q^{41} +(-6.05002 + 3.49298i) q^{43} +(4.22556 + 3.79512i) q^{45} +(-0.384064 + 0.384064i) q^{47} +(1.91712 + 1.10685i) q^{49} +(6.97075 - 4.27770i) q^{51} -10.3968i q^{53} +(-0.938944 + 1.62630i) q^{55} +(0.602263 - 2.51556i) q^{57} +(-11.7285 - 3.14264i) q^{59} +(2.83411 + 4.90882i) q^{61} +(1.35652 - 6.42157i) q^{63} +(6.41038 + 2.34570i) q^{65} +(-1.52023 - 5.67359i) q^{67} +(-5.21452 - 2.82702i) q^{69} +(-2.69283 + 10.0498i) q^{71} +(-0.393272 - 0.393272i) q^{73} +(2.45126 - 0.0657280i) q^{75} +2.17005 q^{77} +10.0483 q^{79} +(8.94831 - 0.963224i) q^{81} +(-2.25706 - 2.25706i) q^{83} +(-2.31375 + 8.63503i) q^{85} +(-0.699369 + 1.29001i) q^{87} +(4.60143 + 17.1728i) q^{89} +(-1.35637 - 7.77060i) q^{91} +(-6.50974 - 6.16976i) q^{93} +(1.41367 + 2.44854i) q^{95} +(8.28096 + 2.21888i) q^{97} +(0.923099 + 2.82892i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q - 4q^{7} + O(q^{10}) \) \( 56q - 4q^{7} + 8q^{13} + 8q^{15} - 4q^{19} + 16q^{21} - 24q^{27} + 36q^{31} + 28q^{33} + 20q^{37} - 16q^{39} + 84q^{43} + 12q^{45} - 12q^{49} + 24q^{55} - 36q^{57} - 24q^{61} + 12q^{63} + 32q^{67} - 36q^{69} - 20q^{73} + 60q^{75} + 32q^{79} - 88q^{85} + 16q^{87} - 28q^{91} - 88q^{93} - 36q^{97} - 44q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(1\)

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
\(3\) 0.0464265 + 1.73143i 0.0268043 + 0.999641i
\(4\) 0 0
\(5\) −1.33870 1.33870i −0.598687 0.598687i 0.341276 0.939963i \(-0.389141\pi\)
−0.939963 + 0.341276i \(0.889141\pi\)
\(6\) 0 0
\(7\) −0.566234 + 2.11322i −0.214016 + 0.798720i 0.772494 + 0.635022i \(0.219009\pi\)
−0.986510 + 0.163698i \(0.947658\pi\)
\(8\) 0 0
\(9\) −2.99569 + 0.160768i −0.998563 + 0.0535894i
\(10\) 0 0
\(11\) −0.256724 0.958107i −0.0774052 0.288880i 0.916363 0.400349i \(-0.131111\pi\)
−0.993768 + 0.111469i \(0.964444\pi\)
\(12\) 0 0
\(13\) −3.27036 + 1.51814i −0.907034 + 0.421057i
\(14\) 0 0
\(15\) 2.25572 2.38002i 0.582424 0.614519i
\(16\) 0 0
\(17\) −2.36097 4.08932i −0.572619 0.991806i −0.996296 0.0859920i \(-0.972594\pi\)
0.423677 0.905814i \(-0.360739\pi\)
\(18\) 0 0
\(19\) −1.44252 0.386521i −0.330936 0.0886741i 0.0895251 0.995985i \(-0.471465\pi\)
−0.420461 + 0.907310i \(0.638132\pi\)
\(20\) 0 0
\(21\) −3.68517 0.882285i −0.804170 0.192530i
\(22\) 0 0
\(23\) −1.71229 + 2.96577i −0.357037 + 0.618407i −0.987464 0.157842i \(-0.949546\pi\)
0.630427 + 0.776248i \(0.282880\pi\)
\(24\) 0 0
\(25\) 1.41574i 0.283149i
\(26\) 0 0
\(27\) −0.417438 5.17936i −0.0803360 0.996768i
\(28\) 0 0
\(29\) 0.733696 + 0.423600i 0.136244 + 0.0786605i 0.566573 0.824012i \(-0.308269\pi\)
−0.430329 + 0.902672i \(0.641602\pi\)
\(30\) 0 0
\(31\) −3.66157 + 3.66157i −0.657638 + 0.657638i −0.954821 0.297183i \(-0.903953\pi\)
0.297183 + 0.954821i \(0.403953\pi\)
\(32\) 0 0
\(33\) 1.64698 0.488981i 0.286702 0.0851207i
\(34\) 0 0
\(35\) 3.58699 2.07095i 0.606312 0.350054i
\(36\) 0 0
\(37\) −10.5491 + 2.82661i −1.73425 + 0.464692i −0.981156 0.193217i \(-0.938108\pi\)
−0.753098 + 0.657909i \(0.771441\pi\)
\(38\) 0 0
\(39\) −2.78039 5.59191i −0.445218 0.895422i
\(40\) 0 0
\(41\) 8.93255 2.39347i 1.39503 0.373797i 0.518473 0.855094i \(-0.326501\pi\)
0.876558 + 0.481297i \(0.159834\pi\)
\(42\) 0 0
\(43\) −6.05002 + 3.49298i −0.922620 + 0.532675i −0.884470 0.466597i \(-0.845480\pi\)
−0.0381501 + 0.999272i \(0.512146\pi\)
\(44\) 0 0
\(45\) 4.22556 + 3.79512i 0.629910 + 0.565743i
\(46\) 0 0
\(47\) −0.384064 + 0.384064i −0.0560215 + 0.0560215i −0.734563 0.678541i \(-0.762613\pi\)
0.678541 + 0.734563i \(0.262613\pi\)
\(48\) 0 0
\(49\) 1.91712 + 1.10685i 0.273874 + 0.158121i
\(50\) 0 0
\(51\) 6.97075 4.27770i 0.976100 0.598998i
\(52\) 0 0
\(53\) 10.3968i 1.42811i −0.700090 0.714054i \(-0.746857\pi\)
0.700090 0.714054i \(-0.253143\pi\)
\(54\) 0 0
\(55\) −0.938944 + 1.62630i −0.126607 + 0.219290i
\(56\) 0 0
\(57\) 0.602263 2.51556i 0.0797717 0.333194i
\(58\) 0 0
\(59\) −11.7285 3.14264i −1.52692 0.409137i −0.604908 0.796296i \(-0.706790\pi\)
−0.922013 + 0.387159i \(0.873457\pi\)
\(60\) 0 0
\(61\) 2.83411 + 4.90882i 0.362870 + 0.628510i 0.988432 0.151665i \(-0.0484635\pi\)
−0.625562 + 0.780175i \(0.715130\pi\)
\(62\) 0 0
\(63\) 1.35652 6.42157i 0.170906 0.809042i
\(64\) 0 0
\(65\) 6.41038 + 2.34570i 0.795110 + 0.290948i
\(66\) 0 0
\(67\) −1.52023 5.67359i −0.185726 0.693139i −0.994474 0.104984i \(-0.966521\pi\)
0.808748 0.588155i \(-0.200146\pi\)
\(68\) 0 0
\(69\) −5.21452 2.82702i −0.627755 0.340333i
\(70\) 0 0
\(71\) −2.69283 + 10.0498i −0.319580 + 1.19269i 0.600069 + 0.799948i \(0.295140\pi\)
−0.919649 + 0.392741i \(0.871527\pi\)
\(72\) 0 0
\(73\) −0.393272 0.393272i −0.0460290 0.0460290i 0.683718 0.729747i \(-0.260362\pi\)
−0.729747 + 0.683718i \(0.760362\pi\)
\(74\) 0 0
\(75\) 2.45126 0.0657280i 0.283047 0.00758962i
\(76\) 0 0
\(77\) 2.17005 0.247300
\(78\) 0 0
\(79\) 10.0483 1.13052 0.565261 0.824912i \(-0.308775\pi\)
0.565261 + 0.824912i \(0.308775\pi\)
\(80\) 0 0
\(81\) 8.94831 0.963224i 0.994256 0.107025i
\(82\) 0 0
\(83\) −2.25706 2.25706i −0.247745 0.247745i 0.572300 0.820045i \(-0.306051\pi\)
−0.820045 + 0.572300i \(0.806051\pi\)
\(84\) 0 0
\(85\) −2.31375 + 8.63503i −0.250961 + 0.936600i
\(86\) 0 0
\(87\) −0.699369 + 1.29001i −0.0749803 + 0.138303i
\(88\) 0 0
\(89\) 4.60143 + 17.1728i 0.487750 + 1.82031i 0.567342 + 0.823482i \(0.307972\pi\)
−0.0795919 + 0.996828i \(0.525362\pi\)
\(90\) 0 0
\(91\) −1.35637 7.77060i −0.142186 0.814580i
\(92\) 0 0
\(93\) −6.50974 6.16976i −0.675029 0.639774i
\(94\) 0 0
\(95\) 1.41367 + 2.44854i 0.145039 + 0.251215i
\(96\) 0 0
\(97\) 8.28096 + 2.21888i 0.840804 + 0.225293i 0.653422 0.756994i \(-0.273333\pi\)
0.187383 + 0.982287i \(0.440000\pi\)
\(98\) 0 0
\(99\) 0.923099 + 2.82892i 0.0927749 + 0.284317i
\(100\) 0 0
\(101\) 1.02109 1.76859i 0.101603 0.175981i −0.810742 0.585403i \(-0.800936\pi\)
0.912345 + 0.409422i \(0.134270\pi\)
\(102\) 0 0
\(103\) 14.3415i 1.41311i 0.707656 + 0.706557i \(0.249753\pi\)
−0.707656 + 0.706557i \(0.750247\pi\)
\(104\) 0 0
\(105\) 3.75223 + 6.11447i 0.366180 + 0.596711i
\(106\) 0 0
\(107\) 0.334916 + 0.193364i 0.0323776 + 0.0186932i 0.516101 0.856527i \(-0.327383\pi\)
−0.483724 + 0.875221i \(0.660716\pi\)
\(108\) 0 0
\(109\) −8.24097 + 8.24097i −0.789342 + 0.789342i −0.981386 0.192044i \(-0.938488\pi\)
0.192044 + 0.981386i \(0.438488\pi\)
\(110\) 0 0
\(111\) −5.38383 18.1337i −0.511010 1.72117i
\(112\) 0 0
\(113\) −10.3438 + 5.97200i −0.973063 + 0.561798i −0.900169 0.435541i \(-0.856557\pi\)
−0.0728946 + 0.997340i \(0.523224\pi\)
\(114\) 0 0
\(115\) 6.26254 1.67804i 0.583985 0.156478i
\(116\) 0 0
\(117\) 9.55291 5.07365i 0.883167 0.469059i
\(118\) 0 0
\(119\) 9.97847 2.67372i 0.914725 0.245100i
\(120\) 0 0
\(121\) 8.67422 5.00806i 0.788565 0.455278i
\(122\) 0 0
\(123\) 4.55883 + 15.3550i 0.411056 + 1.38451i
\(124\) 0 0
\(125\) −8.58878 + 8.58878i −0.768204 + 0.768204i
\(126\) 0 0
\(127\) 0.109854 + 0.0634245i 0.00974800 + 0.00562801i 0.504866 0.863198i \(-0.331542\pi\)
−0.495118 + 0.868826i \(0.664875\pi\)
\(128\) 0 0
\(129\) −6.32873 10.3130i −0.557214 0.908011i
\(130\) 0 0
\(131\) 20.8758i 1.82392i 0.410274 + 0.911962i \(0.365433\pi\)
−0.410274 + 0.911962i \(0.634567\pi\)
\(132\) 0 0
\(133\) 1.63361 2.82949i 0.141652 0.245348i
\(134\) 0 0
\(135\) −6.37480 + 7.49245i −0.548655 + 0.644848i
\(136\) 0 0
\(137\) −12.2978 3.29520i −1.05068 0.281528i −0.308145 0.951340i \(-0.599708\pi\)
−0.742531 + 0.669812i \(0.766375\pi\)
\(138\) 0 0
\(139\) 9.15970 + 15.8651i 0.776915 + 1.34566i 0.933712 + 0.358026i \(0.116550\pi\)
−0.156796 + 0.987631i \(0.550117\pi\)
\(140\) 0 0
\(141\) −0.682810 0.647149i −0.0575030 0.0544998i
\(142\) 0 0
\(143\) 2.29412 + 2.74361i 0.191844 + 0.229432i
\(144\) 0 0
\(145\) −0.415127 1.54928i −0.0344744 0.128660i
\(146\) 0 0
\(147\) −1.82743 + 3.37074i −0.150724 + 0.278014i
\(148\) 0 0
\(149\) −0.550277 + 2.05366i −0.0450804 + 0.168242i −0.984796 0.173714i \(-0.944423\pi\)
0.939716 + 0.341957i \(0.111090\pi\)
\(150\) 0 0
\(151\) −2.93665 2.93665i −0.238981 0.238981i 0.577447 0.816428i \(-0.304049\pi\)
−0.816428 + 0.577447i \(0.804049\pi\)
\(152\) 0 0
\(153\) 7.73016 + 11.8708i 0.624947 + 0.959694i
\(154\) 0 0
\(155\) 9.80352 0.787438
\(156\) 0 0
\(157\) 16.1940 1.29242 0.646211 0.763159i \(-0.276353\pi\)
0.646211 + 0.763159i \(0.276353\pi\)
\(158\) 0 0
\(159\) 18.0013 0.482686i 1.42760 0.0382795i
\(160\) 0 0
\(161\) −5.29776 5.29776i −0.417522 0.417522i
\(162\) 0 0
\(163\) −0.995027 + 3.71349i −0.0779365 + 0.290863i −0.993883 0.110437i \(-0.964775\pi\)
0.915947 + 0.401300i \(0.131442\pi\)
\(164\) 0 0
\(165\) −2.85941 1.55021i −0.222605 0.120684i
\(166\) 0 0
\(167\) −6.12521 22.8596i −0.473983 1.76893i −0.625238 0.780434i \(-0.714998\pi\)
0.151255 0.988495i \(-0.451668\pi\)
\(168\) 0 0
\(169\) 8.39049 9.92974i 0.645422 0.763826i
\(170\) 0 0
\(171\) 4.38347 + 0.925987i 0.335213 + 0.0708120i
\(172\) 0 0
\(173\) −7.36150 12.7505i −0.559684 0.969401i −0.997523 0.0703477i \(-0.977589\pi\)
0.437838 0.899054i \(-0.355744\pi\)
\(174\) 0 0
\(175\) 2.99177 + 0.801643i 0.226157 + 0.0605985i
\(176\) 0 0
\(177\) 4.89675 20.4530i 0.368062 1.53734i
\(178\) 0 0
\(179\) 8.53187 14.7776i 0.637702 1.10453i −0.348234 0.937408i \(-0.613218\pi\)
0.985936 0.167125i \(-0.0534483\pi\)
\(180\) 0 0
\(181\) 3.51901i 0.261566i −0.991411 0.130783i \(-0.958251\pi\)
0.991411 0.130783i \(-0.0417491\pi\)
\(182\) 0 0
\(183\) −8.36769 + 5.13495i −0.618557 + 0.379587i
\(184\) 0 0
\(185\) 17.9061 + 10.3381i 1.31648 + 0.760070i
\(186\) 0 0
\(187\) −3.31189 + 3.31189i −0.242189 + 0.242189i
\(188\) 0 0
\(189\) 11.1815 + 2.05059i 0.813332 + 0.149159i
\(190\) 0 0
\(191\) 18.6177 10.7490i 1.34713 0.777767i 0.359290 0.933226i \(-0.383019\pi\)
0.987842 + 0.155459i \(0.0496857\pi\)
\(192\) 0 0
\(193\) −3.88032 + 1.03973i −0.279312 + 0.0748413i −0.395755 0.918356i \(-0.629517\pi\)
0.116444 + 0.993197i \(0.462851\pi\)
\(194\) 0 0
\(195\) −3.76380 + 11.2080i −0.269531 + 0.802623i
\(196\) 0 0
\(197\) −7.74656 + 2.07569i −0.551920 + 0.147886i −0.523992 0.851723i \(-0.675558\pi\)
−0.0279283 + 0.999610i \(0.508891\pi\)
\(198\) 0 0
\(199\) −9.75011 + 5.62923i −0.691167 + 0.399046i −0.804049 0.594563i \(-0.797325\pi\)
0.112882 + 0.993608i \(0.463992\pi\)
\(200\) 0 0
\(201\) 9.75283 2.89558i 0.687912 0.204238i
\(202\) 0 0
\(203\) −1.31060 + 1.31060i −0.0919862 + 0.0919862i
\(204\) 0 0
\(205\) −15.1622 8.75390i −1.05897 0.611399i
\(206\) 0 0
\(207\) 4.65269 9.15982i 0.323384 0.636651i
\(208\) 0 0
\(209\) 1.48132i 0.102465i
\(210\) 0 0
\(211\) 11.9794 20.7489i 0.824696 1.42842i −0.0774545 0.996996i \(-0.524679\pi\)
0.902151 0.431420i \(-0.141987\pi\)
\(212\) 0 0
\(213\) −17.5255 4.19587i −1.20083 0.287496i
\(214\) 0 0
\(215\) 12.7753 + 3.42312i 0.871266 + 0.233455i
\(216\) 0 0
\(217\) −5.66438 9.81100i −0.384523 0.666014i
\(218\) 0 0
\(219\) 0.662665 0.699181i 0.0447787 0.0472463i
\(220\) 0 0
\(221\) 13.9294 + 9.78925i 0.936992 + 0.658496i
\(222\) 0 0
\(223\) 0.495422 + 1.84894i 0.0331759 + 0.123814i 0.980528 0.196380i \(-0.0629185\pi\)
−0.947352 + 0.320194i \(0.896252\pi\)
\(224\) 0 0
\(225\) 0.227607 + 4.24113i 0.0151738 + 0.282742i
\(226\) 0 0
\(227\) −2.83237 + 10.5705i −0.187991 + 0.701591i 0.805980 + 0.591943i \(0.201639\pi\)
−0.993970 + 0.109648i \(0.965028\pi\)
\(228\) 0 0
\(229\) 2.18006 + 2.18006i 0.144063 + 0.144063i 0.775460 0.631397i \(-0.217518\pi\)
−0.631397 + 0.775460i \(0.717518\pi\)
\(230\) 0 0
\(231\) 0.100748 + 3.75729i 0.00662873 + 0.247212i
\(232\) 0 0
\(233\) −7.80150 −0.511093 −0.255546 0.966797i \(-0.582255\pi\)
−0.255546 + 0.966797i \(0.582255\pi\)
\(234\) 0 0
\(235\) 1.02830 0.0670787
\(236\) 0 0
\(237\) 0.466508 + 17.3979i 0.0303029 + 1.13012i
\(238\) 0 0
\(239\) −14.8365 14.8365i −0.959695 0.959695i 0.0395239 0.999219i \(-0.487416\pi\)
−0.999219 + 0.0395239i \(0.987416\pi\)
\(240\) 0 0
\(241\) −4.24837 + 15.8551i −0.273661 + 1.02132i 0.683072 + 0.730351i \(0.260644\pi\)
−0.956733 + 0.290967i \(0.906023\pi\)
\(242\) 0 0
\(243\) 2.08319 + 15.4486i 0.133637 + 0.991030i
\(244\) 0 0
\(245\) −1.08471 4.04820i −0.0692997 0.258630i
\(246\) 0 0
\(247\) 5.30434 0.925883i 0.337507 0.0589125i
\(248\) 0 0
\(249\) 3.80316 4.01273i 0.241015 0.254296i
\(250\) 0 0
\(251\) −2.11649 3.66588i −0.133592 0.231388i 0.791467 0.611212i \(-0.209318\pi\)
−0.925059 + 0.379824i \(0.875984\pi\)
\(252\) 0 0
\(253\) 3.28112 + 0.879172i 0.206282 + 0.0552731i
\(254\) 0 0
\(255\) −15.0583 3.60520i −0.942990 0.225766i
\(256\) 0 0
\(257\) 3.01424 5.22082i 0.188023 0.325666i −0.756568 0.653915i \(-0.773125\pi\)
0.944591 + 0.328249i \(0.106459\pi\)
\(258\) 0 0
\(259\) 23.8929i 1.48464i
\(260\) 0 0
\(261\) −2.26603 1.15102i −0.140264 0.0712462i
\(262\) 0 0
\(263\) −16.9076 9.76159i −1.04257 0.601925i −0.122006 0.992529i \(-0.538933\pi\)
−0.920559 + 0.390604i \(0.872266\pi\)
\(264\) 0 0
\(265\) −13.9182 + 13.9182i −0.854989 + 0.854989i
\(266\) 0 0
\(267\) −29.5198 + 8.76432i −1.80658 + 0.536367i
\(268\) 0 0
\(269\) −22.7011 + 13.1065i −1.38411 + 0.799118i −0.992644 0.121074i \(-0.961366\pi\)
−0.391469 + 0.920191i \(0.628033\pi\)
\(270\) 0 0
\(271\) −13.9542 + 3.73902i −0.847657 + 0.227129i −0.656402 0.754411i \(-0.727923\pi\)
−0.191255 + 0.981540i \(0.561256\pi\)
\(272\) 0 0
\(273\) 13.3913 2.70922i 0.810476 0.163970i
\(274\) 0 0
\(275\) −1.35643 + 0.363456i −0.0817961 + 0.0219172i
\(276\) 0 0
\(277\) −4.00445 + 2.31197i −0.240604 + 0.138913i −0.615454 0.788172i \(-0.711028\pi\)
0.374850 + 0.927085i \(0.377694\pi\)
\(278\) 0 0
\(279\) 10.3803 11.5576i 0.621450 0.691935i
\(280\) 0 0
\(281\) 2.83565 2.83565i 0.169161 0.169161i −0.617450 0.786611i \(-0.711834\pi\)
0.786611 + 0.617450i \(0.211834\pi\)
\(282\) 0 0
\(283\) −21.9372 12.6654i −1.30403 0.752883i −0.322938 0.946420i \(-0.604671\pi\)
−0.981093 + 0.193537i \(0.938004\pi\)
\(284\) 0 0
\(285\) −4.17384 + 2.56134i −0.247237 + 0.151721i
\(286\) 0 0
\(287\) 20.2317i 1.19424i
\(288\) 0 0
\(289\) −2.64835 + 4.58708i −0.155785 + 0.269828i
\(290\) 0 0
\(291\) −3.45737 + 14.4409i −0.202675 + 0.846541i
\(292\) 0 0
\(293\) 17.0816 + 4.57700i 0.997917 + 0.267391i 0.720573 0.693379i \(-0.243879\pi\)
0.277345 + 0.960770i \(0.410546\pi\)
\(294\) 0 0
\(295\) 11.4939 + 19.9081i 0.669202 + 1.15909i
\(296\) 0 0
\(297\) −4.85521 + 1.72962i −0.281728 + 0.100363i
\(298\) 0 0
\(299\) 1.09734 12.2986i 0.0634607 0.711249i
\(300\) 0 0
\(301\) −3.95569 14.7628i −0.228002 0.850917i
\(302\) 0 0
\(303\) 3.10959 + 1.68584i 0.178641 + 0.0968492i
\(304\) 0 0
\(305\) 2.77742 10.3655i 0.159035 0.593526i
\(306\) 0 0
\(307\) −16.5562 16.5562i −0.944910 0.944910i 0.0536497 0.998560i \(-0.482915\pi\)
−0.998560 + 0.0536497i \(0.982915\pi\)
\(308\) 0 0
\(309\) −24.8313 + 0.665827i −1.41261 + 0.0378776i
\(310\) 0 0
\(311\) −27.9565 −1.58527 −0.792635 0.609697i \(-0.791291\pi\)
−0.792635 + 0.609697i \(0.791291\pi\)
\(312\) 0 0
\(313\) 22.1801 1.25369 0.626846 0.779144i \(-0.284346\pi\)
0.626846 + 0.779144i \(0.284346\pi\)
\(314\) 0 0
\(315\) −10.4126 + 6.78059i −0.586681 + 0.382043i
\(316\) 0 0
\(317\) −5.44471 5.44471i −0.305805 0.305805i 0.537475 0.843280i \(-0.319378\pi\)
−0.843280 + 0.537475i \(0.819378\pi\)
\(318\) 0 0
\(319\) 0.217496 0.811708i 0.0121775 0.0454469i
\(320\) 0 0
\(321\) −0.319247 + 0.588861i −0.0178186 + 0.0328670i
\(322\) 0 0
\(323\) 1.82513 + 6.81148i 0.101553 + 0.379001i
\(324\) 0 0
\(325\) 2.14930 + 4.62999i 0.119222 + 0.256826i
\(326\) 0 0
\(327\) −14.6513 13.8861i −0.810216 0.767900i
\(328\) 0 0
\(329\) −0.594140 1.02908i −0.0327560 0.0567350i
\(330\) 0 0
\(331\) −5.61987 1.50584i −0.308896 0.0827684i 0.101041 0.994882i \(-0.467783\pi\)
−0.409937 + 0.912114i \(0.634449\pi\)
\(332\) 0 0
\(333\) 31.1473 10.1636i 1.70686 0.556962i
\(334\) 0 0
\(335\) −5.56011 + 9.63039i −0.303781 + 0.526165i
\(336\) 0 0
\(337\) 15.0629i 0.820528i −0.911967 0.410264i \(-0.865436\pi\)
0.911967 0.410264i \(-0.134564\pi\)
\(338\) 0 0
\(339\) −10.8203 17.6323i −0.587679 0.957655i
\(340\) 0 0
\(341\) 4.44819 + 2.56817i 0.240883 + 0.139074i
\(342\) 0 0
\(343\) −14.2534 + 14.2534i −0.769612 + 0.769612i
\(344\) 0 0
\(345\) 3.19616 + 10.7652i 0.172075 + 0.579581i
\(346\) 0 0
\(347\) 6.58502 3.80186i 0.353502 0.204095i −0.312724 0.949844i \(-0.601242\pi\)
0.666227 + 0.745749i \(0.267908\pi\)
\(348\) 0 0
\(349\) −13.2155 + 3.54107i −0.707407 + 0.189549i −0.594546 0.804062i \(-0.702668\pi\)
−0.112861 + 0.993611i \(0.536002\pi\)
\(350\) 0 0
\(351\) 9.22817 + 16.3046i 0.492563 + 0.870277i
\(352\) 0 0
\(353\) 6.31893 1.69315i 0.336323 0.0901174i −0.0867052 0.996234i \(-0.527634\pi\)
0.423028 + 0.906117i \(0.360967\pi\)
\(354\) 0 0
\(355\) 17.0586 9.84877i 0.905375 0.522719i
\(356\) 0 0
\(357\) 5.09263 + 17.1529i 0.269530 + 0.907827i
\(358\) 0 0
\(359\) 11.5879 11.5879i 0.611588 0.611588i −0.331772 0.943360i \(-0.607646\pi\)
0.943360 + 0.331772i \(0.107646\pi\)
\(360\) 0 0
\(361\) −14.5230 8.38487i −0.764370 0.441309i
\(362\) 0 0
\(363\) 9.07381 + 14.7863i 0.476252 + 0.776078i
\(364\) 0 0
\(365\) 1.05295i 0.0551139i
\(366\) 0 0
\(367\) 10.4529 18.1049i 0.545635 0.945068i −0.452931 0.891545i \(-0.649622\pi\)
0.998567 0.0535227i \(-0.0170449\pi\)
\(368\) 0 0
\(369\) −26.3744 + 8.60617i −1.37299 + 0.448019i
\(370\) 0 0
\(371\) 21.9707 + 5.88702i 1.14066 + 0.305639i
\(372\) 0 0
\(373\) 11.5708 + 20.0412i 0.599114 + 1.03770i 0.992952 + 0.118516i \(0.0378138\pi\)
−0.393838 + 0.919180i \(0.628853\pi\)
\(374\) 0 0
\(375\) −15.2696 14.4721i −0.788519 0.747337i
\(376\) 0 0
\(377\) −3.04253 0.271468i −0.156698 0.0139813i
\(378\) 0 0
\(379\) 3.41564 + 12.7474i 0.175450 + 0.654788i 0.996475 + 0.0838951i \(0.0267361\pi\)
−0.821025 + 0.570893i \(0.806597\pi\)
\(380\) 0 0
\(381\) −0.104715 + 0.193150i −0.00536470 + 0.00989536i
\(382\) 0 0
\(383\) −2.61140 + 9.74587i −0.133436 + 0.497991i −0.999999 0.00107658i \(-0.999657\pi\)
0.866563 + 0.499067i \(0.166324\pi\)
\(384\) 0 0
\(385\) −2.90506 2.90506i −0.148055 0.148055i
\(386\) 0 0
\(387\) 17.5624 11.4365i 0.892749 0.581352i
\(388\) 0 0
\(389\) 21.6943 1.09994 0.549971 0.835184i \(-0.314639\pi\)
0.549971 + 0.835184i \(0.314639\pi\)
\(390\) 0 0
\(391\) 16.1707 0.817786
\(392\) 0 0
\(393\) −36.1449 + 0.969189i −1.82327 + 0.0488891i
\(394\) 0 0
\(395\) −13.4517 13.4517i −0.676829 0.676829i
\(396\) 0 0
\(397\) 4.57617 17.0785i 0.229672 0.857146i −0.750807 0.660521i \(-0.770335\pi\)
0.980479 0.196625i \(-0.0629980\pi\)
\(398\) 0 0
\(399\) 4.97490 + 2.69711i 0.249056 + 0.135024i
\(400\) 0 0
\(401\) −1.42326 5.31167i −0.0710741 0.265252i 0.921240 0.388994i \(-0.127177\pi\)
−0.992314 + 0.123742i \(0.960511\pi\)
\(402\) 0 0
\(403\) 6.41587 17.5334i 0.319597 0.873403i
\(404\) 0 0
\(405\) −13.2686 10.6897i −0.659322 0.531174i
\(406\) 0 0
\(407\) 5.41639 + 9.38147i 0.268481 + 0.465022i
\(408\) 0 0
\(409\) −19.7035 5.27954i −0.974275 0.261056i −0.263643 0.964620i \(-0.584924\pi\)
−0.710632 + 0.703564i \(0.751591\pi\)
\(410\) 0 0
\(411\) 5.13445 21.4458i 0.253264 1.05784i
\(412\) 0 0
\(413\) 13.2822 23.0054i 0.653572 1.13202i
\(414\) 0 0
\(415\) 6.04308i 0.296643i
\(416\) 0 0
\(417\) −27.0440 + 16.5959i −1.32435 + 0.812706i
\(418\) 0 0
\(419\) −30.6973 17.7231i −1.49966 0.865831i −0.499663 0.866220i \(-0.666543\pi\)
−1.00000 0.000389131i \(0.999876\pi\)
\(420\) 0 0
\(421\) 26.7150 26.7150i 1.30201 1.30201i 0.374972 0.927036i \(-0.377652\pi\)
0.927036 0.374972i \(-0.122348\pi\)
\(422\) 0 0
\(423\) 1.08879 1.21228i 0.0529389 0.0589432i
\(424\) 0 0
\(425\) −5.78943 + 3.34253i −0.280829 + 0.162136i
\(426\) 0 0
\(427\) −11.9782 + 3.20954i −0.579664 + 0.155320i
\(428\) 0 0
\(429\) −4.64386 + 4.09949i −0.224208 + 0.197925i
\(430\) 0 0
\(431\) 25.5938 6.85785i 1.23281 0.330331i 0.417138 0.908843i \(-0.363033\pi\)
0.815674 + 0.578512i \(0.196366\pi\)
\(432\) 0 0
\(433\) −22.5129 + 12.9978i −1.08190 + 0.624636i −0.931409 0.363975i \(-0.881419\pi\)
−0.150493 + 0.988611i \(0.548086\pi\)
\(434\) 0 0
\(435\) 2.66319 0.790691i 0.127690 0.0379107i
\(436\) 0 0
\(437\) 3.61634 3.61634i 0.172993 0.172993i
\(438\) 0 0
\(439\) 21.2539 + 12.2710i 1.01440 + 0.585661i 0.912476 0.409131i \(-0.134168\pi\)
0.101920 + 0.994793i \(0.467501\pi\)
\(440\) 0 0
\(441\) −5.92104 3.00757i −0.281955 0.143217i
\(442\) 0 0
\(443\) 24.7493i 1.17587i 0.808907 + 0.587937i \(0.200060\pi\)
−0.808907 + 0.587937i \(0.799940\pi\)
\(444\) 0 0
\(445\) 16.8293 29.1492i 0.797785 1.38180i
\(446\) 0 0
\(447\) −3.58131 0.857420i −0.169390 0.0405546i
\(448\) 0 0
\(449\) −18.0387 4.83346i −0.851300 0.228105i −0.193316 0.981137i \(-0.561924\pi\)
−0.657985 + 0.753031i \(0.728591\pi\)
\(450\) 0 0
\(451\) −4.58640 7.94388i −0.215965 0.374063i
\(452\) 0 0
\(453\) 4.94826 5.22094i 0.232490 0.245301i
\(454\) 0 0
\(455\) −8.58675 + 12.2183i −0.402553 + 0.572803i
\(456\) 0 0
\(457\) 0.610148 + 2.27710i 0.0285415 + 0.106518i 0.978727 0.205166i \(-0.0657735\pi\)
−0.950186 + 0.311685i \(0.899107\pi\)
\(458\) 0 0
\(459\) −20.1945 + 13.9353i −0.942598 + 0.650446i
\(460\) 0 0
\(461\) −3.36375 + 12.5537i −0.156665 + 0.584683i 0.842292 + 0.539022i \(0.181206\pi\)
−0.998957 + 0.0456608i \(0.985461\pi\)
\(462\) 0 0
\(463\) −1.03011 1.03011i −0.0478733 0.0478733i 0.682765 0.730638i \(-0.260777\pi\)
−0.730638 + 0.682765i \(0.760777\pi\)
\(464\) 0 0
\(465\) 0.455143 + 16.9741i 0.0211068 + 0.787155i
\(466\) 0 0
\(467\) 36.9118 1.70808 0.854038 0.520211i \(-0.174147\pi\)
0.854038 + 0.520211i \(0.174147\pi\)
\(468\) 0 0
\(469\) 12.8503 0.593373
\(470\) 0 0
\(471\) 0.751830 + 28.0387i 0.0346425 + 1.29196i
\(472\) 0 0
\(473\) 4.89984 + 4.89984i 0.225295 + 0.225295i
\(474\) 0 0
\(475\) −0.547215 + 2.04224i −0.0251080 + 0.0937042i
\(476\) 0 0
\(477\) 1.67147 + 31.1455i 0.0765315 + 1.42606i
\(478\) 0 0
\(479\) 2.40863 + 8.98914i 0.110053 + 0.410724i 0.998869 0.0475398i \(-0.0151381\pi\)
−0.888816 + 0.458264i \(0.848471\pi\)
\(480\) 0 0
\(481\) 30.2080 25.2590i 1.37737 1.15171i
\(482\) 0 0
\(483\) 8.92674 9.41865i 0.406181 0.428563i
\(484\) 0 0
\(485\) −8.11534 14.0562i −0.368498 0.638258i
\(486\) 0 0
\(487\) −16.0328 4.29597i −0.726515 0.194669i −0.123438 0.992352i \(-0.539392\pi\)
−0.603077 + 0.797683i \(0.706059\pi\)
\(488\) 0 0
\(489\) −6.47584 1.55041i −0.292848 0.0701121i
\(490\) 0 0
\(491\) −12.3545 + 21.3987i −0.557553 + 0.965709i 0.440147 + 0.897926i \(0.354926\pi\)
−0.997700 + 0.0677839i \(0.978407\pi\)
\(492\) 0 0
\(493\) 4.00042i 0.180170i
\(494\) 0 0
\(495\) 2.55133 5.02284i 0.114674 0.225760i
\(496\) 0 0
\(497\) −19.7126 11.3811i −0.884229 0.510510i
\(498\) 0 0
\(499\) 4.69214 4.69214i 0.210049 0.210049i −0.594239 0.804288i \(-0.702547\pi\)
0.804288 + 0.594239i \(0.202547\pi\)
\(500\) 0 0
\(501\) 39.2954 11.6667i 1.75559 0.521228i
\(502\) 0 0
\(503\) −31.1321 + 17.9741i −1.38811 + 0.801427i −0.993102 0.117249i \(-0.962592\pi\)
−0.395010 + 0.918677i \(0.629259\pi\)
\(504\) 0 0
\(505\) −3.73456 + 1.00067i −0.166186 + 0.0445293i
\(506\) 0 0
\(507\) 17.5822 + 14.0665i 0.780852 + 0.624717i
\(508\) 0 0
\(509\) 17.0359 4.56477i 0.755105 0.202330i 0.139324 0.990247i \(-0.455507\pi\)
0.615781 + 0.787917i \(0.288840\pi\)
\(510\) 0 0
\(511\) 1.05375 0.608385i 0.0466153 0.0269134i
\(512\) 0 0
\(513\) −1.39977 + 7.63266i −0.0618014 + 0.336990i
\(514\) 0 0
\(515\) 19.1991 19.1991i 0.846012 0.846012i
\(516\) 0 0
\(517\) 0.466573 + 0.269376i 0.0205199 + 0.0118472i
\(518\) 0 0
\(519\) 21.7348 13.3379i 0.954051 0.585467i
\(520\) 0 0
\(521\) 22.9129i 1.00383i −0.864917 0.501915i \(-0.832629\pi\)
0.864917 0.501915i \(-0.167371\pi\)
\(522\) 0 0
\(523\) −6.11740 + 10.5957i −0.267495 + 0.463316i −0.968214 0.250122i \(-0.919529\pi\)
0.700719 + 0.713437i \(0.252863\pi\)
\(524\) 0 0
\(525\) −1.24909 + 5.21726i −0.0545147 + 0.227700i
\(526\) 0 0
\(527\) 23.6182 + 6.32848i 1.02882 + 0.275673i
\(528\) 0 0
\(529\) 5.63612 + 9.76205i 0.245049 + 0.424437i
\(530\) 0 0
\(531\) 35.6402 + 7.52881i 1.54665 + 0.326722i
\(532\) 0 0
\(533\) −25.5790 + 21.3884i −1.10795 + 0.926434i
\(534\) 0 0
\(535\) −0.189497 0.707211i −0.00819266 0.0305754i
\(536\) 0 0
\(537\) 25.9825 + 14.0863i 1.12123 + 0.607867i
\(538\) 0 0
\(539\) 0.568310 2.12096i 0.0244789 0.0913563i
\(540\) 0 0
\(541\) −17.8177 17.8177i −0.766042 0.766042i 0.211365 0.977407i \(-0.432209\pi\)
−0.977407 + 0.211365i \(0.932209\pi\)
\(542\) 0 0
\(543\) 6.09291 0.163375i 0.261472 0.00701110i
\(544\) 0 0
\(545\) 22.0644 0.945137
\(546\) 0 0
\(547\) 19.4843 0.833087 0.416543 0.909116i \(-0.363241\pi\)
0.416543 + 0.909116i \(0.363241\pi\)
\(548\) 0 0
\(549\) −9.27929 14.2497i −0.396030 0.608161i
\(550\) 0 0
\(551\) −0.894639 0.894639i −0.0381129 0.0381129i
\(552\) 0 0
\(553\) −5.68970 + 21.2342i −0.241950 + 0.902971i
\(554\) 0 0
\(555\) −17.0683 + 31.4830i −0.724509 + 1.33638i
\(556\) 0 0
\(557\) −1.33172 4.97004i −0.0564267 0.210587i 0.931956 0.362570i \(-0.118101\pi\)
−0.988383 + 0.151983i \(0.951434\pi\)
\(558\) 0 0
\(559\) 14.4829 20.6081i 0.612562 0.871630i
\(560\) 0 0
\(561\) −5.88806 5.58054i −0.248594 0.235611i
\(562\) 0 0
\(563\) −1.28809 2.23104i −0.0542866 0.0940271i 0.837605 0.546276i \(-0.183955\pi\)
−0.891892 + 0.452249i \(0.850622\pi\)
\(564\) 0 0
\(565\) 21.8420 + 5.85255i 0.918901 + 0.246219i
\(566\) 0 0
\(567\) −3.03134 + 19.4551i −0.127304 + 0.817038i
\(568\) 0 0
\(569\) −2.81100 + 4.86880i −0.117843 + 0.204111i −0.918913 0.394461i \(-0.870931\pi\)
0.801069 + 0.598572i \(0.204265\pi\)
\(570\) 0 0
\(571\) 33.8079i 1.41482i −0.706806 0.707408i \(-0.749864\pi\)
0.706806 0.707408i \(-0.250136\pi\)
\(572\) 0 0
\(573\) 19.4754 + 31.7362i 0.813597 + 1.32580i
\(574\) 0 0
\(575\) 4.19878 + 2.42417i 0.175101 + 0.101095i
\(576\) 0 0
\(577\) −5.78457 + 5.78457i −0.240815 + 0.240815i −0.817187 0.576372i \(-0.804468\pi\)
0.576372 + 0.817187i \(0.304468\pi\)
\(578\) 0 0
\(579\) −1.98037 6.67022i −0.0823012 0.277205i
\(580\) 0 0
\(581\) 6.04769 3.49163i 0.250900 0.144857i
\(582\) 0 0
\(583\) −9.96124 + 2.66911i −0.412552 + 0.110543i
\(584\) 0 0
\(585\) −19.5806 5.99640i −0.809559 0.247921i
\(586\) 0 0
\(587\) −39.0455 + 10.4622i −1.61158 + 0.431822i −0.948514 0.316737i \(-0.897413\pi\)
−0.663068 + 0.748559i \(0.730746\pi\)
\(588\) 0 0
\(589\) 6.69716 3.86661i 0.275952 0.159321i
\(590\) 0 0
\(591\) −3.95355 13.3163i −0.162627 0.547758i
\(592\) 0 0
\(593\) −8.23055 + 8.23055i −0.337988 + 0.337988i −0.855610 0.517621i \(-0.826818\pi\)
0.517621 + 0.855610i \(0.326818\pi\)
\(594\) 0 0
\(595\) −16.9375 9.77890i −0.694372 0.400896i
\(596\) 0 0
\(597\) −10.1993 16.6203i −0.417428 0.680223i
\(598\) 0 0
\(599\) 7.22852i 0.295349i −0.989036 0.147675i \(-0.952821\pi\)
0.989036 0.147675i \(-0.0471789\pi\)
\(600\) 0 0
\(601\) −1.92099 + 3.32725i −0.0783587 + 0.135721i −0.902542 0.430602i \(-0.858301\pi\)
0.824183 + 0.566323i \(0.191635\pi\)
\(602\) 0 0
\(603\) 5.46628 + 16.7519i 0.222604 + 0.682190i
\(604\) 0 0
\(605\) −18.3165 4.90790i −0.744672 0.199534i
\(606\) 0 0
\(607\) 6.01621 + 10.4204i 0.244190 + 0.422950i 0.961904 0.273389i \(-0.0881445\pi\)
−0.717713 + 0.696339i \(0.754811\pi\)
\(608\) 0 0
\(609\) −2.33006 2.20837i −0.0944187 0.0894875i
\(610\) 0 0
\(611\) 0.672964 1.83909i 0.0272252 0.0744017i
\(612\) 0 0
\(613\) 6.43463 + 24.0144i 0.259892 + 0.969931i 0.965303 + 0.261133i \(0.0840960\pi\)
−0.705411 + 0.708799i \(0.749237\pi\)
\(614\) 0 0
\(615\) 14.4528 26.6587i 0.582794 1.07498i
\(616\) 0 0
\(617\) 11.6729 43.5637i 0.469932 1.75381i −0.170066 0.985433i \(-0.554398\pi\)
0.639997 0.768377i \(-0.278935\pi\)
\(618\) 0 0
\(619\) 24.4865 + 24.4865i 0.984197 + 0.984197i 0.999877 0.0156805i \(-0.00499147\pi\)
−0.0156805 + 0.999877i \(0.504991\pi\)
\(620\) 0 0
\(621\) 16.0756 + 7.63054i 0.645091 + 0.306203i
\(622\) 0 0
\(623\) −38.8952 −1.55830
\(624\) 0 0
\(625\) 15.9169 0.636678
\(626\) 0 0
\(627\) −2.56479 + 0.0687723i −0.102428 + 0.00274650i
\(628\) 0 0
\(629\) 36.4649 + 36.4649i 1.45395 + 1.45395i
\(630\) 0 0
\(631\) −3.56833 + 13.3172i −0.142053 + 0.530149i 0.857816 + 0.513957i \(0.171821\pi\)
−0.999869 + 0.0161917i \(0.994846\pi\)
\(632\) 0 0
\(633\) 36.4815 + 19.7782i 1.45001 + 0.786112i
\(634\) 0 0
\(635\) −0.0621559 0.231969i −0.00246658 0.00920541i
\(636\) 0 0
\(637\) −7.95003 0.709336i −0.314992 0.0281049i
\(638\) 0 0
\(639\) 6.45119 30.5389i 0.255205 1.20810i
\(640\) 0 0
\(641\) 18.7773 + 32.5233i 0.741659 + 1.28459i 0.951739 + 0.306908i \(0.0992942\pi\)
−0.210080 + 0.977684i \(0.567372\pi\)
\(642\) 0 0
\(643\) 33.9096 + 9.08605i 1.33726 + 0.358319i 0.855418 0.517937i \(-0.173300\pi\)
0.481845 + 0.876256i \(0.339967\pi\)
\(644\) 0 0
\(645\) −5.33378 + 22.2784i −0.210017 + 0.877210i
\(646\) 0 0
\(647\) −4.67261 + 8.09319i −0.183699 + 0.318176i −0.943137 0.332403i \(-0.892141\pi\)
0.759438 + 0.650579i \(0.225474\pi\)
\(648\) 0 0
\(649\) 12.0440i 0.472767i
\(650\) 0 0
\(651\) 16.7241 10.2630i 0.655468 0.402237i
\(652\) 0 0
\(653\) 4.78580 + 2.76309i 0.187283 + 0.108128i 0.590710 0.806884i \(-0.298848\pi\)
−0.403427 + 0.915012i \(0.632181\pi\)
\(654\) 0 0
\(655\) 27.9465 27.9465i 1.09196 1.09196i
\(656\) 0 0
\(657\) 1.24135 + 1.11490i 0.0484296 + 0.0434962i
\(658\) 0 0
\(659\) −30.1079 + 17.3828i −1.17284 + 0.677138i −0.954347 0.298701i \(-0.903447\pi\)
−0.218491 + 0.975839i \(0.570113\pi\)
\(660\) 0 0
\(661\) −10.7464 + 2.87948i −0.417985 + 0.111999i −0.461681 0.887046i \(-0.652753\pi\)
0.0436959 + 0.999045i \(0.486087\pi\)
\(662\) 0 0
\(663\) −16.3027 + 24.5722i −0.633144 + 0.954306i
\(664\) 0 0
\(665\) −5.97476 + 1.60093i −0.231691 + 0.0620815i
\(666\) 0 0
\(667\) −2.51260 + 1.45065i −0.0972883 + 0.0561694i
\(668\) 0 0
\(669\) −3.17831 + 0.943628i −0.122881 + 0.0364828i
\(670\) 0 0
\(671\) 3.97559 3.97559i 0.153476 0.153476i
\(672\) 0 0
\(673\) 38.4396 + 22.1931i 1.48174 + 0.855482i 0.999785 0.0207144i \(-0.00659408\pi\)
0.481954 + 0.876197i \(0.339927\pi\)
\(674\) 0 0
\(675\) −7.33265 + 0.590986i −0.282234 + 0.0227470i
\(676\) 0 0
\(677\) 20.7036i 0.795704i 0.917450 + 0.397852i \(0.130244\pi\)
−0.917450 + 0.397852i \(0.869756\pi\)
\(678\) 0 0
\(679\) −9.37793 + 16.2430i −0.359892 + 0.623351i
\(680\) 0 0
\(681\) −18.4336 4.41329i −0.706378 0.169117i
\(682\) 0 0
\(683\) −3.10117 0.830957i −0.118663 0.0317957i 0.198999 0.980000i \(-0.436231\pi\)
−0.317662 + 0.948204i \(0.602898\pi\)
\(684\) 0 0
\(685\) 12.0519 + 20.8745i 0.460478 + 0.797572i
\(686\) 0 0
\(687\) −3.67341 + 3.87584i −0.140149 + 0.147872i
\(688\) 0 0
\(689\) 15.7838 + 34.0012i 0.601315 + 1.29534i
\(690\) 0 0
\(691\) 0.553429 + 2.06543i 0.0210534 + 0.0785725i 0.975653 0.219319i \(-0.0703834\pi\)
−0.954600 + 0.297891i \(0.903717\pi\)
\(692\) 0 0
\(693\) −6.50080 + 0.348876i −0.246945 + 0.0132527i
\(694\) 0 0
\(695\) 8.97649 33.5007i 0.340498 1.27076i
\(696\) 0 0
\(697\) −30.8772 30.8772i −1.16956 1.16956i
\(698\) 0 0
\(699\) −0.362196 13.5077i −0.0136995 0.510909i
\(700\) 0 0
\(701\) 21.3084 0.804808 0.402404 0.915462i \(-0.368175\pi\)
0.402404 + 0.915462i \(0.368175\pi\)
\(702\) 0 0
\(703\) 16.3097 0.615133
\(704\) 0 0
\(705\) 0.0477402 + 1.78042i 0.00179800 + 0.0670546i
\(706\) 0 0
\(707\) 3.15923 + 3.15923i 0.118815 + 0.118815i
\(708\) 0 0
\(709\) 7.30917 27.2782i 0.274502 1.02445i −0.681673 0.731657i \(-0.738747\pi\)
0.956175 0.292797i \(-0.0945859\pi\)
\(710\) 0 0
\(711\) −30.1016 + 1.61545i −1.12890 + 0.0605841i
\(712\) 0 0
\(713\) −4.58972 17.1291i −0.171886 0.641489i
\(714\) 0 0
\(715\) 0.601732 6.74403i 0.0225035 0.252213i
\(716\) 0 0
\(717\) 24.9996 26.3772i 0.933626 0.985074i
\(718\) 0 0
\(719\) 2.67277 + 4.62937i 0.0996774 + 0.172646i 0.911551 0.411187i \(-0.134886\pi\)
−0.811874 + 0.583833i \(0.801552\pi\)
\(720\) 0 0
\(721\) −30.3068 8.12067i −1.12868 0.302430i
\(722\) 0 0
\(723\) −27.6492 6.61964i −1.02829 0.246187i
\(724\) 0 0
\(725\) 0.599709 1.03873i 0.0222726 0.0385773i
\(726\) 0 0
\(727\) 3.49159i 0.129496i 0.997902 + 0.0647480i \(0.0206244\pi\)
−0.997902 + 0.0647480i \(0.979376\pi\)
\(728\) 0 0
\(729\) −26.6515 + 4.32412i −0.987092 + 0.160153i
\(730\) 0 0
\(731\) 28.5678 + 16.4937i 1.05662 + 0.610040i
\(732\) 0 0
\(733\) −1.07662 + 1.07662i −0.0397658 + 0.0397658i −0.726710 0.686944i \(-0.758952\pi\)
0.686944 + 0.726710i \(0.258952\pi\)
\(734\) 0 0
\(735\) 6.95881 2.06605i 0.256680 0.0762072i
\(736\) 0 0
\(737\) −5.04562 + 2.91309i −0.185858 + 0.107305i
\(738\) 0 0
\(739\) −32.6118 + 8.73832i −1.19965 + 0.321444i −0.802692 0.596394i \(-0.796599\pi\)
−0.396954 + 0.917838i \(0.629933\pi\)
\(740\) 0 0
\(741\) 1.84936 + 9.14111i 0.0679380 + 0.335807i
\(742\) 0 0
\(743\) −9.87756 + 2.64668i −0.362372 + 0.0970974i −0.435411 0.900232i \(-0.643397\pi\)
0.0730388 + 0.997329i \(0.476730\pi\)
\(744\) 0 0
\(745\) 3.48590 2.01259i 0.127713 0.0737354i
\(746\) 0 0
\(747\) 7.12432 + 6.39859i 0.260665 + 0.234112i
\(748\) 0 0
\(749\) −0.598261 + 0.598261i −0.0218600 + 0.0218600i
\(750\) 0 0
\(751\) −29.4768 17.0185i −1.07563 0.621012i −0.145912 0.989298i \(-0.546612\pi\)
−0.929713 + 0.368285i \(0.879945\pi\)
\(752\) 0 0
\(753\) 6.24894 3.83475i 0.227724 0.139746i
\(754\) 0 0
\(755\) 7.86261i 0.286150i
\(756\) 0 0
\(757\) 4.15573 7.19794i 0.151043 0.261614i −0.780568 0.625070i \(-0.785070\pi\)
0.931611 + 0.363457i \(0.118404\pi\)
\(758\) 0 0
\(759\) −1.36989 + 5.72183i −0.0497240 + 0.207689i
\(760\) 0 0
\(761\) −30.3530 8.13305i −1.10029 0.294823i −0.337409 0.941358i \(-0.609551\pi\)
−0.762884 + 0.646535i \(0.776217\pi\)
\(762\) 0 0
\(763\) −12.7486 22.0813i −0.461531 0.799395i
\(764\) 0 0
\(765\) 5.54303 26.2398i 0.200409 0.948703i
\(766\) 0 0
\(767\) 43.1274 7.52796i 1.55724 0.271819i
\(768\) 0 0
\(769\) 12.2950 + 45.8856i 0.443370 + 1.65468i 0.720205 + 0.693761i \(0.244048\pi\)
−0.276835 + 0.960917i \(0.589286\pi\)
\(770\) 0 0
\(771\) 9.17942 + 4.97656i 0.330589 + 0.179227i
\(772\) 0 0
\(773\) −2.09638 + 7.82380i −0.0754015 + 0.281402i −0.993324 0.115357i \(-0.963199\pi\)
0.917923 + 0.396760i \(0.129865\pi\)
\(774\) 0 0
\(775\) 5.18385 + 5.18385i 0.186209 + 0.186209i
\(776\) 0 0
\(777\) 41.3689 1.10927i 1.48410 0.0397947i
\(778\) 0 0
\(779\) −13.8105 −0.494812
\(780\) 0 0
\(781\) 10.3201 0.369281
\(782\) 0 0
\(783\) 1.88770 3.97690i 0.0674609 0.142123i
\(784\) 0 0
\(785\) −21.6790 21.6790i −0.773755 0.773755i
\(786\) 0 0
\(787\) 5.53321 20.6502i 0.197238 0.736101i −0.794439 0.607344i \(-0.792235\pi\)
0.991676 0.128756i \(-0.0410985\pi\)
\(788\) 0 0
\(789\) 16.1165 29.7274i 0.573764 1.05832i
\(790\) 0 0
\(791\) −6.76310 25.2402i −0.240468 0.897439i
\(792\) 0 0
\(793\) −16.7208 11.7510i −0.593774 0.417291i
\(794\) 0 0
\(795\) −24.7446 23.4522i −0.877600 0.831765i
\(796\) 0 0
\(797\)