Properties

Label 171.3.p.c.145.3
Level $171$
Weight $3$
Character 171.145
Analytic conductor $4.659$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 171.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.65941252056\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{6})\)
Coefficient field: 6.0.92607408.1
Defining polynomial: \( x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 94x^{2} - 77x + 43 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 57)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 145.3
Root \(0.500000 + 2.93068i\) of defining polynomial
Character \(\chi\) \(=\) 171.145
Dual form 171.3.p.c.46.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.78805 - 1.03233i) q^{2} +(0.131406 - 0.227602i) q^{4} +(3.20750 + 5.55555i) q^{5} -2.26281 q^{7} +7.71601i q^{8} +O(q^{10})\) \(q+(1.78805 - 1.03233i) q^{2} +(0.131406 - 0.227602i) q^{4} +(3.20750 + 5.55555i) q^{5} -2.26281 q^{7} +7.71601i q^{8} +(11.4703 + 6.62239i) q^{10} +20.0928 q^{11} +(-0.135471 - 0.0782143i) q^{13} +(-4.04601 + 2.33597i) q^{14} +(8.49109 + 14.7070i) q^{16} +(-12.3133 - 21.3272i) q^{17} +(-18.9317 - 1.60945i) q^{19} +1.68594 q^{20} +(35.9269 - 20.7424i) q^{22} +(2.62250 - 4.54230i) q^{23} +(-8.07609 + 13.9882i) q^{25} -0.322972 q^{26} +(-0.297347 + 0.515021i) q^{28} +(31.4573 + 18.1619i) q^{29} -17.1105i q^{31} +(3.63586 + 2.09917i) q^{32} +(-44.0334 - 25.4227i) q^{34} +(-7.25797 - 12.5712i) q^{35} -42.7124i q^{37} +(-35.5123 + 16.6660i) q^{38} +(-42.8667 + 24.7491i) q^{40} +(-30.0928 + 17.3741i) q^{41} +(12.5553 + 21.7464i) q^{43} +(2.64032 - 4.57316i) q^{44} -10.8291i q^{46} +(14.6778 - 25.4227i) q^{47} -43.8797 q^{49} +33.3487i q^{50} +(-0.0356035 + 0.0205557i) q^{52} +(-48.4176 - 27.9539i) q^{53} +(64.4476 + 111.627i) q^{55} -17.4599i q^{56} +74.9962 q^{58} +(29.9269 - 17.2783i) q^{59} +(27.3805 - 47.4244i) q^{61} +(-17.6637 - 30.5944i) q^{62} -59.2606 q^{64} -1.00349i q^{65} +(66.0698 + 38.1454i) q^{67} -6.47216 q^{68} +(-25.9552 - 14.9852i) q^{70} +(-63.6080 + 36.7241i) q^{71} +(-45.9053 - 79.5103i) q^{73} +(-44.0932 - 76.3717i) q^{74} +(-2.85406 + 4.09740i) q^{76} -45.4662 q^{77} +(-53.1300 + 30.6746i) q^{79} +(-54.4703 + 94.3453i) q^{80} +(-35.8716 + 62.1313i) q^{82} +148.793 q^{83} +(78.9897 - 136.814i) q^{85} +(44.8990 + 25.9224i) q^{86} +155.036i q^{88} +(62.7829 + 36.2477i) q^{89} +(0.306546 + 0.176984i) q^{91} +(-0.689224 - 1.19377i) q^{92} -60.6093i q^{94} +(-51.7820 - 110.338i) q^{95} +(-70.0326 + 40.4334i) q^{97} +(-78.4589 + 45.2983i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} + 5 q^{4} - 4 q^{5} - 22 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{2} + 5 q^{4} - 4 q^{5} - 22 q^{7} + 54 q^{10} + 36 q^{11} - 3 q^{13} + 57 q^{14} - 23 q^{16} - 38 q^{17} - 10 q^{19} - 32 q^{20} + 36 q^{22} - 54 q^{23} - 21 q^{25} - 118 q^{26} - 101 q^{28} + 102 q^{29} + 63 q^{32} - 150 q^{34} + 24 q^{35} - 119 q^{38} + 30 q^{40} - 96 q^{41} + 107 q^{43} + 94 q^{44} + 50 q^{47} - 48 q^{49} + 399 q^{52} + 90 q^{53} + 148 q^{55} - 116 q^{58} + 27 q^{61} + 121 q^{62} + 46 q^{64} - 39 q^{67} + 388 q^{68} - 354 q^{70} - 84 q^{71} - 77 q^{73} - 219 q^{74} + 215 q^{76} - 260 q^{77} + 9 q^{79} - 312 q^{80} - 4 q^{82} + 348 q^{83} + 68 q^{85} - 249 q^{86} + 72 q^{89} - 393 q^{91} + 118 q^{92} - 104 q^{95} - 228 q^{97} - 540 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).

\(n\) \(20\) \(154\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.78805 1.03233i 0.894023 0.516164i 0.0187668 0.999824i \(-0.494026\pi\)
0.875256 + 0.483659i \(0.160693\pi\)
\(3\) 0 0
\(4\) 0.131406 0.227602i 0.0328515 0.0569005i
\(5\) 3.20750 + 5.55555i 0.641500 + 1.11111i 0.985098 + 0.171993i \(0.0550208\pi\)
−0.343598 + 0.939117i \(0.611646\pi\)
\(6\) 0 0
\(7\) −2.26281 −0.323259 −0.161629 0.986852i \(-0.551675\pi\)
−0.161629 + 0.986852i \(0.551675\pi\)
\(8\) 7.71601i 0.964502i
\(9\) 0 0
\(10\) 11.4703 + 6.62239i 1.14703 + 0.662239i
\(11\) 20.0928 1.82662 0.913309 0.407267i \(-0.133518\pi\)
0.913309 + 0.407267i \(0.133518\pi\)
\(12\) 0 0
\(13\) −0.135471 0.0782143i −0.0104209 0.00601649i 0.494781 0.869018i \(-0.335248\pi\)
−0.505201 + 0.863001i \(0.668582\pi\)
\(14\) −4.04601 + 2.33597i −0.289001 + 0.166855i
\(15\) 0 0
\(16\) 8.49109 + 14.7070i 0.530693 + 0.919187i
\(17\) −12.3133 21.3272i −0.724311 1.25454i −0.959257 0.282534i \(-0.908825\pi\)
0.234947 0.972008i \(-0.424508\pi\)
\(18\) 0 0
\(19\) −18.9317 1.60945i −0.996406 0.0847081i
\(20\) 1.68594 0.0842970
\(21\) 0 0
\(22\) 35.9269 20.7424i 1.63304 0.942836i
\(23\) 2.62250 4.54230i 0.114022 0.197491i −0.803367 0.595485i \(-0.796960\pi\)
0.917388 + 0.397994i \(0.130293\pi\)
\(24\) 0 0
\(25\) −8.07609 + 13.9882i −0.323044 + 0.559528i
\(26\) −0.322972 −0.0124220
\(27\) 0 0
\(28\) −0.297347 + 0.515021i −0.0106195 + 0.0183936i
\(29\) 31.4573 + 18.1619i 1.08474 + 0.626272i 0.932170 0.362021i \(-0.117913\pi\)
0.152566 + 0.988293i \(0.451246\pi\)
\(30\) 0 0
\(31\) 17.1105i 0.551952i −0.961165 0.275976i \(-0.910999\pi\)
0.961165 0.275976i \(-0.0890010\pi\)
\(32\) 3.63586 + 2.09917i 0.113621 + 0.0655989i
\(33\) 0 0
\(34\) −44.0334 25.4227i −1.29510 0.747727i
\(35\) −7.25797 12.5712i −0.207370 0.359176i
\(36\) 0 0
\(37\) 42.7124i 1.15439i −0.816607 0.577194i \(-0.804148\pi\)
0.816607 0.577194i \(-0.195852\pi\)
\(38\) −35.5123 + 16.6660i −0.934533 + 0.438578i
\(39\) 0 0
\(40\) −42.8667 + 24.7491i −1.07167 + 0.618728i
\(41\) −30.0928 + 17.3741i −0.733971 + 0.423758i −0.819873 0.572545i \(-0.805956\pi\)
0.0859022 + 0.996304i \(0.472623\pi\)
\(42\) 0 0
\(43\) 12.5553 + 21.7464i 0.291984 + 0.505731i 0.974279 0.225346i \(-0.0723512\pi\)
−0.682295 + 0.731077i \(0.739018\pi\)
\(44\) 2.64032 4.57316i 0.0600072 0.103936i
\(45\) 0 0
\(46\) 10.8291i 0.235415i
\(47\) 14.6778 25.4227i 0.312294 0.540909i −0.666565 0.745447i \(-0.732236\pi\)
0.978859 + 0.204538i \(0.0655693\pi\)
\(48\) 0 0
\(49\) −43.8797 −0.895504
\(50\) 33.3487i 0.666975i
\(51\) 0 0
\(52\) −0.0356035 + 0.0205557i −0.000684682 + 0.000395301i
\(53\) −48.4176 27.9539i −0.913540 0.527433i −0.0319716 0.999489i \(-0.510179\pi\)
−0.881568 + 0.472056i \(0.843512\pi\)
\(54\) 0 0
\(55\) 64.4476 + 111.627i 1.17178 + 2.02957i
\(56\) 17.4599i 0.311784i
\(57\) 0 0
\(58\) 74.9962 1.29304
\(59\) 29.9269 17.2783i 0.507235 0.292852i −0.224461 0.974483i \(-0.572062\pi\)
0.731696 + 0.681631i \(0.238729\pi\)
\(60\) 0 0
\(61\) 27.3805 47.4244i 0.448860 0.777448i −0.549452 0.835525i \(-0.685164\pi\)
0.998312 + 0.0580769i \(0.0184968\pi\)
\(62\) −17.6637 30.5944i −0.284898 0.493457i
\(63\) 0 0
\(64\) −59.2606 −0.925947
\(65\) 1.00349i 0.0154383i
\(66\) 0 0
\(67\) 66.0698 + 38.1454i 0.986117 + 0.569335i 0.904111 0.427297i \(-0.140534\pi\)
0.0820054 + 0.996632i \(0.473868\pi\)
\(68\) −6.47216 −0.0951788
\(69\) 0 0
\(70\) −25.9552 14.9852i −0.370788 0.214075i
\(71\) −63.6080 + 36.7241i −0.895887 + 0.517240i −0.875863 0.482559i \(-0.839707\pi\)
−0.0200233 + 0.999800i \(0.506374\pi\)
\(72\) 0 0
\(73\) −45.9053 79.5103i −0.628840 1.08918i −0.987785 0.155824i \(-0.950197\pi\)
0.358945 0.933359i \(-0.383137\pi\)
\(74\) −44.0932 76.3717i −0.595854 1.03205i
\(75\) 0 0
\(76\) −2.85406 + 4.09740i −0.0375534 + 0.0539132i
\(77\) −45.4662 −0.590471
\(78\) 0 0
\(79\) −53.1300 + 30.6746i −0.672531 + 0.388286i −0.797035 0.603933i \(-0.793599\pi\)
0.124504 + 0.992219i \(0.460266\pi\)
\(80\) −54.4703 + 94.3453i −0.680879 + 1.17932i
\(81\) 0 0
\(82\) −35.8716 + 62.1313i −0.437458 + 0.757699i
\(83\) 148.793 1.79268 0.896342 0.443363i \(-0.146215\pi\)
0.896342 + 0.443363i \(0.146215\pi\)
\(84\) 0 0
\(85\) 78.9897 136.814i 0.929290 1.60958i
\(86\) 44.8990 + 25.9224i 0.522081 + 0.301424i
\(87\) 0 0
\(88\) 155.036i 1.76178i
\(89\) 62.7829 + 36.2477i 0.705426 + 0.407278i 0.809365 0.587306i \(-0.199811\pi\)
−0.103939 + 0.994584i \(0.533145\pi\)
\(90\) 0 0
\(91\) 0.306546 + 0.176984i 0.00336864 + 0.00194488i
\(92\) −0.689224 1.19377i −0.00749156 0.0129758i
\(93\) 0 0
\(94\) 60.6093i 0.644780i
\(95\) −51.7820 110.338i −0.545074 1.16146i
\(96\) 0 0
\(97\) −70.0326 + 40.4334i −0.721986 + 0.416839i −0.815483 0.578781i \(-0.803529\pi\)
0.0934972 + 0.995620i \(0.470195\pi\)
\(98\) −78.4589 + 45.2983i −0.800601 + 0.462227i
\(99\) 0 0
\(100\) 2.12250 + 3.67627i 0.0212250 + 0.0367627i
\(101\) 76.6770 132.809i 0.759178 1.31494i −0.184092 0.982909i \(-0.558934\pi\)
0.943270 0.332027i \(-0.107732\pi\)
\(102\) 0 0
\(103\) 168.948i 1.64027i −0.572169 0.820136i \(-0.693898\pi\)
0.572169 0.820136i \(-0.306102\pi\)
\(104\) 0.603503 1.04530i 0.00580291 0.0100509i
\(105\) 0 0
\(106\) −115.431 −1.08897
\(107\) 139.060i 1.29963i 0.760093 + 0.649815i \(0.225154\pi\)
−0.760093 + 0.649815i \(0.774846\pi\)
\(108\) 0 0
\(109\) −9.15888 + 5.28788i −0.0840264 + 0.0485127i −0.541424 0.840749i \(-0.682115\pi\)
0.457398 + 0.889262i \(0.348781\pi\)
\(110\) 230.471 + 133.062i 2.09519 + 1.20966i
\(111\) 0 0
\(112\) −19.2137 33.2792i −0.171551 0.297135i
\(113\) 69.1581i 0.612018i −0.952029 0.306009i \(-0.901006\pi\)
0.952029 0.306009i \(-0.0989938\pi\)
\(114\) 0 0
\(115\) 33.6466 0.292579
\(116\) 8.26737 4.77317i 0.0712704 0.0411480i
\(117\) 0 0
\(118\) 35.6737 61.7887i 0.302320 0.523633i
\(119\) 27.8626 + 48.2595i 0.234140 + 0.405542i
\(120\) 0 0
\(121\) 282.721 2.33654
\(122\) 113.063i 0.926742i
\(123\) 0 0
\(124\) −3.89438 2.24842i −0.0314063 0.0181324i
\(125\) 56.7587 0.454070
\(126\) 0 0
\(127\) −25.6547 14.8118i −0.202006 0.116628i 0.395585 0.918429i \(-0.370542\pi\)
−0.597591 + 0.801801i \(0.703875\pi\)
\(128\) −120.504 + 69.5731i −0.941438 + 0.543540i
\(129\) 0 0
\(130\) −1.03593 1.79428i −0.00796870 0.0138022i
\(131\) 28.6526 + 49.6278i 0.218722 + 0.378838i 0.954418 0.298474i \(-0.0964777\pi\)
−0.735695 + 0.677313i \(0.763144\pi\)
\(132\) 0 0
\(133\) 42.8389 + 3.64189i 0.322097 + 0.0273826i
\(134\) 157.514 1.17548
\(135\) 0 0
\(136\) 164.561 95.0094i 1.21001 0.698599i
\(137\) −47.4499 + 82.1856i −0.346349 + 0.599895i −0.985598 0.169105i \(-0.945912\pi\)
0.639249 + 0.769000i \(0.279245\pi\)
\(138\) 0 0
\(139\) −91.2747 + 158.092i −0.656652 + 1.13736i 0.324824 + 0.945774i \(0.394695\pi\)
−0.981477 + 0.191581i \(0.938639\pi\)
\(140\) −3.81496 −0.0272497
\(141\) 0 0
\(142\) −75.8226 + 131.329i −0.533962 + 0.924850i
\(143\) −2.72200 1.57155i −0.0190349 0.0109898i
\(144\) 0 0
\(145\) 233.017i 1.60701i
\(146\) −164.162 94.7788i −1.12439 0.649170i
\(147\) 0 0
\(148\) −9.72142 5.61266i −0.0656852 0.0379234i
\(149\) 5.50439 + 9.53389i 0.0369422 + 0.0639858i 0.883905 0.467666i \(-0.154905\pi\)
−0.846963 + 0.531652i \(0.821572\pi\)
\(150\) 0 0
\(151\) 238.846i 1.58176i 0.611968 + 0.790882i \(0.290378\pi\)
−0.611968 + 0.790882i \(0.709622\pi\)
\(152\) 12.4186 146.077i 0.0817011 0.961035i
\(153\) 0 0
\(154\) −81.2957 + 46.9361i −0.527894 + 0.304780i
\(155\) 95.0582 54.8819i 0.613279 0.354077i
\(156\) 0 0
\(157\) 22.8125 + 39.5124i 0.145303 + 0.251671i 0.929486 0.368858i \(-0.120251\pi\)
−0.784183 + 0.620529i \(0.786918\pi\)
\(158\) −63.3326 + 109.695i −0.400839 + 0.694273i
\(159\) 0 0
\(160\) 26.9323i 0.168327i
\(161\) −5.93421 + 10.2784i −0.0368585 + 0.0638407i
\(162\) 0 0
\(163\) 5.89159 0.0361447 0.0180724 0.999837i \(-0.494247\pi\)
0.0180724 + 0.999837i \(0.494247\pi\)
\(164\) 9.13224i 0.0556844i
\(165\) 0 0
\(166\) 266.048 153.603i 1.60270 0.925320i
\(167\) −142.140 82.0646i −0.851138 0.491405i 0.00989689 0.999951i \(-0.496850\pi\)
−0.861035 + 0.508546i \(0.830183\pi\)
\(168\) 0 0
\(169\) −84.4878 146.337i −0.499928 0.865900i
\(170\) 326.173i 1.91867i
\(171\) 0 0
\(172\) 6.59938 0.0383685
\(173\) −234.355 + 135.305i −1.35465 + 0.782109i −0.988897 0.148603i \(-0.952522\pi\)
−0.365755 + 0.930711i \(0.619189\pi\)
\(174\) 0 0
\(175\) 18.2747 31.6527i 0.104427 0.180872i
\(176\) 170.610 + 295.505i 0.969374 + 1.67900i
\(177\) 0 0
\(178\) 149.678 0.840890
\(179\) 186.439i 1.04156i 0.853691 + 0.520779i \(0.174359\pi\)
−0.853691 + 0.520779i \(0.825641\pi\)
\(180\) 0 0
\(181\) −40.1939 23.2059i −0.222066 0.128210i 0.384841 0.922983i \(-0.374256\pi\)
−0.606906 + 0.794773i \(0.707590\pi\)
\(182\) 0.730824 0.00401552
\(183\) 0 0
\(184\) 35.0484 + 20.2352i 0.190481 + 0.109974i
\(185\) 237.291 137.000i 1.28265 0.740539i
\(186\) 0 0
\(187\) −247.408 428.524i −1.32304 2.29157i
\(188\) −3.85751 6.68140i −0.0205187 0.0355393i
\(189\) 0 0
\(190\) −206.494 143.834i −1.08681 0.757021i
\(191\) 36.7222 0.192263 0.0961315 0.995369i \(-0.469353\pi\)
0.0961315 + 0.995369i \(0.469353\pi\)
\(192\) 0 0
\(193\) −173.472 + 100.154i −0.898817 + 0.518932i −0.876816 0.480826i \(-0.840337\pi\)
−0.0220009 + 0.999758i \(0.507004\pi\)
\(194\) −83.4811 + 144.593i −0.430315 + 0.745327i
\(195\) 0 0
\(196\) −5.76606 + 9.98710i −0.0294187 + 0.0509546i
\(197\) 171.512 0.870620 0.435310 0.900281i \(-0.356639\pi\)
0.435310 + 0.900281i \(0.356639\pi\)
\(198\) 0 0
\(199\) −43.7500 + 75.7772i −0.219849 + 0.380790i −0.954762 0.297372i \(-0.903890\pi\)
0.734913 + 0.678162i \(0.237223\pi\)
\(200\) −107.933 62.3152i −0.539666 0.311576i
\(201\) 0 0
\(202\) 316.624i 1.56744i
\(203\) −71.1820 41.0970i −0.350650 0.202448i
\(204\) 0 0
\(205\) −193.045 111.455i −0.941684 0.543682i
\(206\) −174.410 302.087i −0.846650 1.46644i
\(207\) 0 0
\(208\) 2.65650i 0.0127716i
\(209\) −380.391 32.3384i −1.82005 0.154729i
\(210\) 0 0
\(211\) 16.3950 9.46566i 0.0777014 0.0448609i −0.460646 0.887584i \(-0.652382\pi\)
0.538347 + 0.842723i \(0.319049\pi\)
\(212\) −12.7247 + 7.34663i −0.0600224 + 0.0346539i
\(213\) 0 0
\(214\) 143.556 + 248.646i 0.670823 + 1.16190i
\(215\) −80.5423 + 139.503i −0.374615 + 0.648853i
\(216\) 0 0
\(217\) 38.7178i 0.178423i
\(218\) −10.9177 + 18.9100i −0.0500810 + 0.0867429i
\(219\) 0 0
\(220\) 33.8752 0.153978
\(221\) 3.85230i 0.0174312i
\(222\) 0 0
\(223\) −224.162 + 129.420i −1.00521 + 0.580358i −0.909786 0.415078i \(-0.863754\pi\)
−0.0954244 + 0.995437i \(0.530421\pi\)
\(224\) −8.22727 4.75002i −0.0367289 0.0212054i
\(225\) 0 0
\(226\) −71.3939 123.658i −0.315902 0.547159i
\(227\) 129.054i 0.568522i 0.958747 + 0.284261i \(0.0917482\pi\)
−0.958747 + 0.284261i \(0.908252\pi\)
\(228\) 0 0
\(229\) −98.8946 −0.431854 −0.215927 0.976409i \(-0.569277\pi\)
−0.215927 + 0.976409i \(0.569277\pi\)
\(230\) 60.1617 34.7344i 0.261572 0.151019i
\(231\) 0 0
\(232\) −140.137 + 242.725i −0.604041 + 1.04623i
\(233\) −174.731 302.644i −0.749920 1.29890i −0.947861 0.318685i \(-0.896759\pi\)
0.197941 0.980214i \(-0.436575\pi\)
\(234\) 0 0
\(235\) 188.316 0.801346
\(236\) 9.08189i 0.0384826i
\(237\) 0 0
\(238\) 99.6394 + 57.5268i 0.418653 + 0.241709i
\(239\) −301.091 −1.25979 −0.629897 0.776679i \(-0.716903\pi\)
−0.629897 + 0.776679i \(0.716903\pi\)
\(240\) 0 0
\(241\) 110.242 + 63.6485i 0.457438 + 0.264102i 0.710966 0.703226i \(-0.248258\pi\)
−0.253529 + 0.967328i \(0.581591\pi\)
\(242\) 505.518 291.861i 2.08892 1.20604i
\(243\) 0 0
\(244\) −7.19592 12.4637i −0.0294915 0.0510807i
\(245\) −140.744 243.776i −0.574465 0.995003i
\(246\) 0 0
\(247\) 2.43882 + 1.69877i 0.00987376 + 0.00687759i
\(248\) 132.025 0.532358
\(249\) 0 0
\(250\) 101.487 58.5937i 0.405949 0.234375i
\(251\) −177.023 + 306.613i −0.705271 + 1.22157i 0.261322 + 0.965252i \(0.415841\pi\)
−0.966594 + 0.256314i \(0.917492\pi\)
\(252\) 0 0
\(253\) 52.6933 91.2675i 0.208274 0.360741i
\(254\) −61.1625 −0.240797
\(255\) 0 0
\(256\) −25.1234 + 43.5151i −0.0981384 + 0.169981i
\(257\) 236.669 + 136.641i 0.920889 + 0.531676i 0.883919 0.467641i \(-0.154896\pi\)
0.0369706 + 0.999316i \(0.488229\pi\)
\(258\) 0 0
\(259\) 96.6500i 0.373166i
\(260\) −0.228396 0.131865i −0.000878447 0.000507171i
\(261\) 0 0
\(262\) 102.464 + 59.1579i 0.391086 + 0.225793i
\(263\) 75.5642 + 130.881i 0.287316 + 0.497646i 0.973168 0.230095i \(-0.0739036\pi\)
−0.685852 + 0.727741i \(0.740570\pi\)
\(264\) 0 0
\(265\) 358.649i 1.35339i
\(266\) 80.3576 37.7120i 0.302096 0.141774i
\(267\) 0 0
\(268\) 17.3639 10.0251i 0.0647909 0.0374070i
\(269\) −58.9364 + 34.0269i −0.219094 + 0.126494i −0.605531 0.795822i \(-0.707039\pi\)
0.386437 + 0.922316i \(0.373706\pi\)
\(270\) 0 0
\(271\) 56.8991 + 98.5521i 0.209960 + 0.363661i 0.951702 0.307025i \(-0.0993334\pi\)
−0.741742 + 0.670685i \(0.766000\pi\)
\(272\) 209.106 362.183i 0.768773 1.33155i
\(273\) 0 0
\(274\) 195.935i 0.715093i
\(275\) −162.271 + 281.062i −0.590078 + 1.02204i
\(276\) 0 0
\(277\) 440.910 1.59173 0.795867 0.605472i \(-0.207016\pi\)
0.795867 + 0.605472i \(0.207016\pi\)
\(278\) 376.902i 1.35576i
\(279\) 0 0
\(280\) 96.9993 56.0026i 0.346426 0.200009i
\(281\) −78.0928 45.0869i −0.277910 0.160452i 0.354567 0.935031i \(-0.384628\pi\)
−0.632477 + 0.774579i \(0.717962\pi\)
\(282\) 0 0
\(283\) 34.5331 + 59.8131i 0.122025 + 0.211354i 0.920566 0.390587i \(-0.127728\pi\)
−0.798541 + 0.601940i \(0.794394\pi\)
\(284\) 19.3031i 0.0679685i
\(285\) 0 0
\(286\) −6.48941 −0.0226902
\(287\) 68.0944 39.3143i 0.237263 0.136984i
\(288\) 0 0
\(289\) −158.734 + 274.935i −0.549252 + 0.951332i
\(290\) 240.550 + 416.645i 0.829484 + 1.43671i
\(291\) 0 0
\(292\) −24.1289 −0.0826334
\(293\) 410.238i 1.40013i −0.714079 0.700065i \(-0.753154\pi\)
0.714079 0.700065i \(-0.246846\pi\)
\(294\) 0 0
\(295\) 191.981 + 110.840i 0.650782 + 0.375729i
\(296\) 329.569 1.11341
\(297\) 0 0
\(298\) 19.6842 + 11.3647i 0.0660544 + 0.0381365i
\(299\) −0.710545 + 0.410233i −0.00237640 + 0.00137202i
\(300\) 0 0
\(301\) −28.4103 49.2081i −0.0943864 0.163482i
\(302\) 246.568 + 427.068i 0.816451 + 1.41413i
\(303\) 0 0
\(304\) −137.081 292.095i −0.450923 0.960838i
\(305\) 351.291 1.15177
\(306\) 0 0
\(307\) −201.882 + 116.556i −0.657595 + 0.379663i −0.791360 0.611350i \(-0.790627\pi\)
0.133765 + 0.991013i \(0.457293\pi\)
\(308\) −5.97454 + 10.3482i −0.0193979 + 0.0335981i
\(309\) 0 0
\(310\) 113.312 196.263i 0.365524 0.633106i
\(311\) 441.280 1.41891 0.709454 0.704752i \(-0.248942\pi\)
0.709454 + 0.704752i \(0.248942\pi\)
\(312\) 0 0
\(313\) −60.6339 + 105.021i −0.193719 + 0.335530i −0.946480 0.322763i \(-0.895388\pi\)
0.752761 + 0.658294i \(0.228722\pi\)
\(314\) 81.5796 + 47.1000i 0.259808 + 0.150000i
\(315\) 0 0
\(316\) 16.1233i 0.0510232i
\(317\) −286.409 165.358i −0.903499 0.521635i −0.0251649 0.999683i \(-0.508011\pi\)
−0.878334 + 0.478048i \(0.841344\pi\)
\(318\) 0 0
\(319\) 632.066 + 364.924i 1.98140 + 1.14396i
\(320\) −190.078 329.225i −0.593995 1.02883i
\(321\) 0 0
\(322\) 24.5042i 0.0761001i
\(323\) 198.786 + 423.579i 0.615437 + 1.31139i
\(324\) 0 0
\(325\) 2.18816 1.26333i 0.00673279 0.00388718i
\(326\) 10.5344 6.08206i 0.0323142 0.0186566i
\(327\) 0 0
\(328\) −134.059 232.197i −0.408716 0.707916i
\(329\) −33.2131 + 57.5268i −0.100952 + 0.174854i
\(330\) 0 0
\(331\) 436.308i 1.31815i −0.752077 0.659075i \(-0.770948\pi\)
0.752077 0.659075i \(-0.229052\pi\)
\(332\) 19.5523 33.8655i 0.0588924 0.102005i
\(333\) 0 0
\(334\) −338.870 −1.01458
\(335\) 489.406i 1.46091i
\(336\) 0 0
\(337\) −217.027 + 125.301i −0.643997 + 0.371812i −0.786153 0.618033i \(-0.787930\pi\)
0.142156 + 0.989844i \(0.454597\pi\)
\(338\) −302.136 174.438i −0.893894 0.516090i
\(339\) 0 0
\(340\) −20.7594 35.9564i −0.0610572 0.105754i
\(341\) 343.798i 1.00821i
\(342\) 0 0
\(343\) 210.169 0.612738
\(344\) −167.796 + 96.8770i −0.487779 + 0.281619i
\(345\) 0 0
\(346\) −279.358 + 483.862i −0.807393 + 1.39845i
\(347\) 83.6670 + 144.915i 0.241115 + 0.417624i 0.961032 0.276436i \(-0.0891535\pi\)
−0.719917 + 0.694060i \(0.755820\pi\)
\(348\) 0 0
\(349\) −486.776 −1.39477 −0.697387 0.716695i \(-0.745654\pi\)
−0.697387 + 0.716695i \(0.745654\pi\)
\(350\) 75.4619i 0.215605i
\(351\) 0 0
\(352\) 73.0547 + 42.1781i 0.207542 + 0.119824i
\(353\) −30.1507 −0.0854128 −0.0427064 0.999088i \(-0.513598\pi\)
−0.0427064 + 0.999088i \(0.513598\pi\)
\(354\) 0 0
\(355\) −408.045 235.585i −1.14942 0.663619i
\(356\) 16.5001 9.52635i 0.0463486 0.0267594i
\(357\) 0 0
\(358\) 192.466 + 333.361i 0.537615 + 0.931177i
\(359\) 75.0088 + 129.919i 0.208938 + 0.361891i 0.951380 0.308019i \(-0.0996659\pi\)
−0.742442 + 0.669910i \(0.766333\pi\)
\(360\) 0 0
\(361\) 355.819 + 60.9394i 0.985649 + 0.168807i
\(362\) −95.8247 −0.264709
\(363\) 0 0
\(364\) 0.0805640 0.0465136i 0.000221330 0.000127785i
\(365\) 294.482 510.058i 0.806801 1.39742i
\(366\) 0 0
\(367\) 248.090 429.704i 0.675994 1.17086i −0.300183 0.953882i \(-0.597048\pi\)
0.976177 0.216975i \(-0.0696189\pi\)
\(368\) 89.0714 0.242042
\(369\) 0 0
\(370\) 282.858 489.924i 0.764480 1.32412i
\(371\) 109.560 + 63.2545i 0.295310 + 0.170497i
\(372\) 0 0
\(373\) 449.613i 1.20540i 0.797969 + 0.602698i \(0.205908\pi\)
−0.797969 + 0.602698i \(0.794092\pi\)
\(374\) −884.755 510.814i −2.36566 1.36581i
\(375\) 0 0
\(376\) 196.162 + 113.254i 0.521707 + 0.301208i
\(377\) −2.84104 4.92083i −0.00753592 0.0130526i
\(378\) 0 0
\(379\) 471.336i 1.24363i −0.783163 0.621816i \(-0.786395\pi\)
0.783163 0.621816i \(-0.213605\pi\)
\(380\) −31.9177 2.71344i −0.0839940 0.00714064i
\(381\) 0 0
\(382\) 65.6611 37.9094i 0.171888 0.0992393i
\(383\) 23.4258 13.5249i 0.0611641 0.0353131i −0.469106 0.883142i \(-0.655424\pi\)
0.530270 + 0.847829i \(0.322090\pi\)
\(384\) 0 0
\(385\) −145.833 252.590i −0.378787 0.656078i
\(386\) −206.784 + 358.160i −0.535709 + 0.927875i
\(387\) 0 0
\(388\) 21.2528i 0.0547752i
\(389\) −177.144 + 306.822i −0.455382 + 0.788745i −0.998710 0.0507758i \(-0.983831\pi\)
0.543328 + 0.839520i \(0.317164\pi\)
\(390\) 0 0
\(391\) −129.166 −0.330348
\(392\) 338.576i 0.863715i
\(393\) 0 0
\(394\) 306.672 177.057i 0.778354 0.449383i
\(395\) −340.829 196.777i −0.862857 0.498171i
\(396\) 0 0
\(397\) −79.5105 137.716i −0.200278 0.346892i 0.748340 0.663316i \(-0.230851\pi\)
−0.948618 + 0.316423i \(0.897518\pi\)
\(398\) 180.657i 0.453913i
\(399\) 0 0
\(400\) −274.299 −0.685748
\(401\) 277.534 160.234i 0.692105 0.399587i −0.112295 0.993675i \(-0.535820\pi\)
0.804400 + 0.594088i \(0.202487\pi\)
\(402\) 0 0
\(403\) −1.33829 + 2.31798i −0.00332081 + 0.00575181i
\(404\) −20.1517 34.9037i −0.0498803 0.0863953i
\(405\) 0 0
\(406\) −169.702 −0.417986
\(407\) 858.211i 2.10863i
\(408\) 0 0
\(409\) −251.776 145.363i −0.615590 0.355411i 0.159560 0.987188i \(-0.448992\pi\)
−0.775150 + 0.631777i \(0.782326\pi\)
\(410\) −460.232 −1.12252
\(411\) 0 0
\(412\) −38.4529 22.2008i −0.0933323 0.0538854i
\(413\) −67.7189 + 39.0975i −0.163968 + 0.0946671i
\(414\) 0 0
\(415\) 477.253 + 826.626i 1.15001 + 1.99187i
\(416\) −0.328370 0.568753i −0.000789350 0.00136719i
\(417\) 0 0
\(418\) −713.541 + 334.866i −1.70704 + 0.801115i
\(419\) 141.846 0.338535 0.169267 0.985570i \(-0.445860\pi\)
0.169267 + 0.985570i \(0.445860\pi\)
\(420\) 0 0
\(421\) 98.6666 56.9652i 0.234362 0.135309i −0.378220 0.925716i \(-0.623464\pi\)
0.612583 + 0.790406i \(0.290131\pi\)
\(422\) 19.5433 33.8501i 0.0463112 0.0802134i
\(423\) 0 0
\(424\) 215.693 373.591i 0.508710 0.881111i
\(425\) 397.773 0.935936
\(426\) 0 0
\(427\) −61.9568 + 107.312i −0.145098 + 0.251317i
\(428\) 31.6504 + 18.2734i 0.0739496 + 0.0426948i
\(429\) 0 0
\(430\) 332.585i 0.773453i
\(431\) −229.263 132.365i −0.531932 0.307111i 0.209871 0.977729i \(-0.432696\pi\)
−0.741803 + 0.670618i \(0.766029\pi\)
\(432\) 0 0
\(433\) −631.333 364.500i −1.45804 0.841802i −0.459129 0.888369i \(-0.651839\pi\)
−0.998915 + 0.0465669i \(0.985172\pi\)
\(434\) 39.9695 + 69.2293i 0.0920957 + 0.159514i
\(435\) 0 0
\(436\) 2.77944i 0.00637486i
\(437\) −56.9589 + 81.7726i −0.130341 + 0.187123i
\(438\) 0 0
\(439\) 319.591 184.516i 0.727998 0.420310i −0.0896911 0.995970i \(-0.528588\pi\)
0.817689 + 0.575660i \(0.195255\pi\)
\(440\) −861.312 + 497.279i −1.95753 + 1.13018i
\(441\) 0 0
\(442\) 3.97684 + 6.88809i 0.00899738 + 0.0155839i
\(443\) 291.547 504.975i 0.658120 1.13990i −0.322982 0.946405i \(-0.604685\pi\)
0.981102 0.193492i \(-0.0619815\pi\)
\(444\) 0 0
\(445\) 465.058i 1.04507i
\(446\) −267.208 + 462.818i −0.599121 + 1.03771i
\(447\) 0 0
\(448\) 134.096 0.299321
\(449\) 314.423i 0.700273i 0.936699 + 0.350137i \(0.113865\pi\)
−0.936699 + 0.350137i \(0.886135\pi\)
\(450\) 0 0
\(451\) −604.649 + 349.094i −1.34068 + 0.774045i
\(452\) −15.7405 9.08779i −0.0348242 0.0201057i
\(453\) 0 0
\(454\) 133.227 + 230.755i 0.293451 + 0.508272i
\(455\) 2.27071i 0.00499057i
\(456\) 0 0
\(457\) 505.253 1.10559 0.552793 0.833319i \(-0.313562\pi\)
0.552793 + 0.833319i \(0.313562\pi\)
\(458\) −176.828 + 102.092i −0.386088 + 0.222908i
\(459\) 0 0
\(460\) 4.42137 7.65803i 0.00961167 0.0166479i
\(461\) −136.902 237.122i −0.296968 0.514364i 0.678473 0.734626i \(-0.262642\pi\)
−0.975441 + 0.220262i \(0.929309\pi\)
\(462\) 0 0
\(463\) 319.780 0.690669 0.345334 0.938480i \(-0.387765\pi\)
0.345334 + 0.938480i \(0.387765\pi\)
\(464\) 616.857i 1.32943i
\(465\) 0 0
\(466\) −624.855 360.760i −1.34089 0.774164i
\(467\) 295.510 0.632785 0.316392 0.948628i \(-0.397528\pi\)
0.316392 + 0.948628i \(0.397528\pi\)
\(468\) 0 0
\(469\) −149.504 86.3159i −0.318771 0.184042i
\(470\) 336.718 194.404i 0.716421 0.413626i
\(471\) 0 0
\(472\) 133.319 + 230.916i 0.282457 + 0.489229i
\(473\) 252.271 + 436.947i 0.533344 + 0.923778i
\(474\) 0 0
\(475\) 175.408 251.822i 0.369279 0.530153i
\(476\) 14.6453 0.0307674
\(477\) 0 0
\(478\) −538.364 + 310.825i −1.12629 + 0.650261i
\(479\) −204.559 + 354.306i −0.427054 + 0.739679i −0.996610 0.0822735i \(-0.973782\pi\)
0.569556 + 0.821953i \(0.307115\pi\)
\(480\) 0 0
\(481\) −3.34072 + 5.78629i −0.00694536 + 0.0120297i
\(482\) 262.825 0.545280
\(483\) 0 0
\(484\) 37.1512 64.3478i 0.0767588 0.132950i
\(485\) −449.259 259.380i −0.926308 0.534804i
\(486\) 0 0
\(487\) 638.208i 1.31049i −0.755417 0.655244i \(-0.772566\pi\)
0.755417 0.655244i \(-0.227434\pi\)
\(488\) 365.927 + 211.268i 0.749850 + 0.432926i
\(489\) 0 0
\(490\) −503.314 290.588i −1.02717 0.593037i
\(491\) 173.278 + 300.126i 0.352908 + 0.611255i 0.986758 0.162202i \(-0.0518595\pi\)
−0.633850 + 0.773456i \(0.718526\pi\)
\(492\) 0 0
\(493\) 894.530i 1.81446i
\(494\) 6.11440 + 0.519808i 0.0123773 + 0.00105224i
\(495\) 0 0
\(496\) 251.644 145.287i 0.507347 0.292917i
\(497\) 143.933 83.0997i 0.289603 0.167203i
\(498\) 0 0
\(499\) −40.3510 69.8900i −0.0808638 0.140060i 0.822757 0.568393i \(-0.192435\pi\)
−0.903621 + 0.428333i \(0.859101\pi\)
\(500\) 7.45844 12.9184i 0.0149169 0.0258368i
\(501\) 0 0
\(502\) 730.984i 1.45614i
\(503\) 247.050 427.903i 0.491153 0.850701i −0.508796 0.860887i \(-0.669909\pi\)
0.999948 + 0.0101862i \(0.00324242\pi\)
\(504\) 0 0
\(505\) 983.766 1.94805
\(506\) 217.587i 0.430014i
\(507\) 0 0
\(508\) −6.74237 + 3.89271i −0.0132724 + 0.00766282i
\(509\) −63.9084 36.8975i −0.125557 0.0724902i 0.435906 0.899992i \(-0.356428\pi\)
−0.561463 + 0.827502i \(0.689761\pi\)
\(510\) 0 0
\(511\) 103.875 + 179.917i 0.203278 + 0.352088i
\(512\) 452.842i 0.884457i
\(513\) 0 0
\(514\) 564.232 1.09773
\(515\) 938.599 541.900i 1.82252 1.05223i
\(516\) 0 0
\(517\) 294.918 510.814i 0.570442 0.988034i
\(518\) 99.7746 + 172.815i 0.192615 + 0.333619i
\(519\) 0 0
\(520\) 7.74294 0.0148903
\(521\) 357.582i 0.686337i 0.939274 + 0.343169i \(0.111500\pi\)
−0.939274 + 0.343169i \(0.888500\pi\)
\(522\) 0 0
\(523\) 382.935 + 221.088i 0.732190 + 0.422730i 0.819223 0.573475i \(-0.194405\pi\)
−0.0870328 + 0.996205i \(0.527739\pi\)
\(524\) 15.0605 0.0287415
\(525\) 0 0
\(526\) 270.225 + 156.014i 0.513735 + 0.296605i
\(527\) −364.919 + 210.686i −0.692447 + 0.399784i
\(528\) 0 0
\(529\) 250.745 + 434.303i 0.473998 + 0.820989i
\(530\) −370.243 641.281i −0.698573 1.20996i
\(531\) 0 0
\(532\) 6.45819 9.27165i 0.0121395 0.0174279i
\(533\) 5.43561 0.0101981
\(534\) 0 0
\(535\) −772.557 + 446.036i −1.44403 + 0.833712i
\(536\) −294.331 + 509.796i −0.549124 + 0.951111i
\(537\) 0 0
\(538\) −70.2539 + 121.683i −0.130584 + 0.226177i
\(539\) −881.666 −1.63574
\(540\) 0 0
\(541\) −487.737 + 844.785i −0.901547 + 1.56152i −0.0760596 + 0.997103i \(0.524234\pi\)
−0.825487 + 0.564421i \(0.809099\pi\)
\(542\) 203.476 + 117.477i 0.375418 + 0.216747i
\(543\) 0 0
\(544\) 103.390i 0.190056i
\(545\) −58.7542 33.9217i −0.107806 0.0622417i
\(546\) 0 0
\(547\) 350.050 + 202.102i 0.639945 + 0.369473i 0.784594 0.620010i \(-0.212872\pi\)
−0.144648 + 0.989483i \(0.546205\pi\)
\(548\) 12.4704 + 21.5994i 0.0227562 + 0.0394149i
\(549\) 0 0
\(550\) 670.070i 1.21831i
\(551\) −566.310 394.465i −1.02779 0.715907i
\(552\) 0 0
\(553\) 120.223 69.4109i 0.217402 0.125517i
\(554\) 788.368 455.164i 1.42305 0.821596i
\(555\) 0 0
\(556\) 23.9881 + 41.5486i 0.0431441 + 0.0747277i
\(557\) 29.9352 51.8492i 0.0537435 0.0930866i −0.837902 0.545821i \(-0.816218\pi\)
0.891646 + 0.452734i \(0.149551\pi\)
\(558\) 0 0
\(559\) 3.92802i 0.00702687i
\(560\) 123.256 213.486i 0.220100 0.381225i
\(561\) 0 0
\(562\) −186.178 −0.331278
\(563\) 247.579i 0.439749i −0.975528 0.219874i \(-0.929435\pi\)
0.975528 0.219874i \(-0.0705648\pi\)
\(564\) 0 0
\(565\) 384.211 221.824i 0.680020 0.392610i
\(566\) 123.494 + 71.2990i 0.218186 + 0.125970i
\(567\) 0 0
\(568\) −283.363 490.800i −0.498879 0.864084i
\(569\) 76.4991i 0.134445i 0.997738 + 0.0672224i \(0.0214137\pi\)
−0.997738 + 0.0672224i \(0.978586\pi\)
\(570\) 0 0
\(571\) −624.523 −1.09373 −0.546867 0.837219i \(-0.684180\pi\)
−0.546867 + 0.837219i \(0.684180\pi\)
\(572\) −0.715374 + 0.413021i −0.00125065 + 0.000722065i
\(573\) 0 0
\(574\) 81.1706 140.592i 0.141412 0.244933i
\(575\) 42.3590 + 73.3680i 0.0736679 + 0.127597i
\(576\) 0 0
\(577\) 185.550 0.321577 0.160789 0.986989i \(-0.448596\pi\)
0.160789 + 0.986989i \(0.448596\pi\)
\(578\) 655.462i 1.13402i
\(579\) 0 0
\(580\) 53.0352 + 30.6199i 0.0914399 + 0.0527929i
\(581\) −336.690 −0.579501
\(582\) 0 0
\(583\) −972.846 561.673i −1.66869 0.963418i
\(584\) 613.503 354.206i 1.05052 0.606517i
\(585\) 0 0
\(586\) −423.501 733.525i −0.722698 1.25175i
\(587\) 130.891 + 226.710i 0.222983 + 0.386218i 0.955712 0.294302i \(-0.0950872\pi\)
−0.732729 + 0.680520i \(0.761754\pi\)
\(588\) 0 0
\(589\) −27.5386 + 323.931i −0.0467548 + 0.549968i
\(590\) 457.694 0.775752
\(591\) 0 0
\(592\) 628.170 362.674i 1.06110 0.612626i
\(593\) 124.254 215.215i 0.209535 0.362925i −0.742033 0.670363i \(-0.766138\pi\)
0.951568 + 0.307438i \(0.0994717\pi\)
\(594\) 0 0
\(595\) −178.739 + 309.585i −0.300401 + 0.520310i
\(596\) 2.89324 0.00485443
\(597\) 0 0
\(598\) −0.846992 + 1.46703i −0.00141637 + 0.00245323i
\(599\) 167.646 + 96.7905i 0.279877 + 0.161587i 0.633368 0.773851i \(-0.281672\pi\)
−0.353491 + 0.935438i \(0.615005\pi\)
\(600\) 0 0
\(601\) 675.975i 1.12475i −0.826882 0.562375i \(-0.809888\pi\)
0.826882 0.562375i \(-0.190112\pi\)
\(602\) −101.598 58.6576i −0.168767 0.0974378i
\(603\) 0 0
\(604\) 54.3619 + 31.3859i 0.0900032 + 0.0519634i
\(605\) 906.827 + 1570.67i 1.49889 + 2.59615i
\(606\) 0 0
\(607\) 383.052i 0.631057i 0.948916 + 0.315528i \(0.102182\pi\)
−0.948916 + 0.315528i \(0.897818\pi\)
\(608\) −65.4546 45.5925i −0.107656 0.0749877i
\(609\) 0 0
\(610\) 628.125 362.648i 1.02971 0.594505i
\(611\) −3.97684 + 2.29603i −0.00650874 + 0.00375782i
\(612\) 0 0
\(613\) −27.5410 47.7025i −0.0449283 0.0778180i 0.842687 0.538404i \(-0.180973\pi\)
−0.887615 + 0.460586i \(0.847639\pi\)
\(614\) −240.649 + 416.817i −0.391937 + 0.678854i
\(615\) 0 0
\(616\) 350.818i 0.569510i
\(617\) 51.7851 89.6944i 0.0839305 0.145372i −0.821004 0.570922i \(-0.806586\pi\)
0.904935 + 0.425550i \(0.139919\pi\)
\(618\) 0 0
\(619\) −263.102 −0.425043 −0.212521 0.977156i \(-0.568168\pi\)
−0.212521 + 0.977156i \(0.568168\pi\)
\(620\) 28.8473i 0.0465278i
\(621\) 0 0
\(622\) 789.030 455.547i 1.26854 0.732390i
\(623\) −142.066 82.0218i −0.228035 0.131656i
\(624\) 0 0
\(625\) 383.956 + 665.031i 0.614329 + 1.06405i
\(626\) 250.377i 0.399963i
\(627\) 0 0
\(628\) 11.9908 0.0190936
\(629\) −910.936 + 525.929i −1.44823 + 0.836135i
\(630\) 0 0
\(631\) 72.5474 125.656i 0.114972 0.199137i −0.802797 0.596253i \(-0.796655\pi\)
0.917769 + 0.397116i \(0.129989\pi\)
\(632\) −236.686 409.952i −0.374503 0.648658i
\(633\) 0 0
\(634\) −682.817 −1.07700
\(635\) 190.035i 0.299267i
\(636\) 0 0
\(637\) 5.94443 + 3.43202i 0.00933192 + 0.00538779i
\(638\) 1506.88 2.36189
\(639\) 0 0
\(640\) −773.034 446.311i −1.20787 0.697361i
\(641\) 583.796 337.055i 0.910758 0.525826i 0.0300832 0.999547i \(-0.490423\pi\)
0.880675 + 0.473721i \(0.157089\pi\)
\(642\) 0 0
\(643\) 0.719856 + 1.24683i 0.00111953 + 0.00193908i 0.866585 0.499030i \(-0.166310\pi\)
−0.865465 + 0.500969i \(0.832977\pi\)
\(644\) 1.55958 + 2.70128i 0.00242171 + 0.00419453i
\(645\) 0 0
\(646\) 792.711 + 552.165i 1.22711 + 0.854745i
\(647\) 614.044 0.949063 0.474532 0.880239i \(-0.342617\pi\)
0.474532 + 0.880239i \(0.342617\pi\)
\(648\) 0 0
\(649\) 601.315 347.169i 0.926525 0.534929i
\(650\) 2.60835 4.51779i 0.00401284 0.00695045i
\(651\) 0 0
\(652\) 0.774191 1.34094i 0.00118741 0.00205665i
\(653\) −822.374 −1.25938 −0.629689 0.776847i \(-0.716818\pi\)
−0.629689 + 0.776847i \(0.716818\pi\)
\(654\) 0 0
\(655\) −183.807 + 318.362i −0.280621 + 0.486049i
\(656\) −511.041 295.050i −0.779027 0.449771i
\(657\) 0 0
\(658\) 137.147i 0.208431i
\(659\) 549.386 + 317.188i 0.833666 + 0.481317i 0.855106 0.518453i \(-0.173492\pi\)
−0.0214404 + 0.999770i \(0.506825\pi\)
\(660\) 0 0
\(661\) −818.470 472.544i −1.23823 0.714893i −0.269498 0.963001i \(-0.586858\pi\)
−0.968732 + 0.248108i \(0.920191\pi\)
\(662\) −450.413 780.138i −0.680382 1.17846i
\(663\) 0 0
\(664\) 1148.09i 1.72905i
\(665\) 117.173 + 249.675i 0.176200 + 0.375451i
\(666\) 0 0
\(667\) 164.993 95.2590i 0.247366 0.142817i
\(668\) −37.3561 + 21.5676i −0.0559223 + 0.0322868i
\(669\) 0 0
\(670\) 505.228 + 875.080i 0.754071 + 1.30609i
\(671\) 550.150 952.888i 0.819896 1.42010i
\(672\) 0 0
\(673\) 570.803i 0.848147i −0.905628 0.424074i \(-0.860600\pi\)
0.905628 0.424074i \(-0.139400\pi\)
\(674\) −258.703 + 448.086i −0.383832 + 0.664817i
\(675\) 0 0
\(676\) −44.4088 −0.0656935
\(677\) 275.976i 0.407646i 0.979008 + 0.203823i \(0.0653367\pi\)
−0.979008 + 0.203823i \(0.934663\pi\)
\(678\) 0 0
\(679\) 158.471 91.4931i 0.233388 0.134747i
\(680\) 1055.66 + 609.485i 1.55244 + 0.896302i
\(681\) 0 0
\(682\) −354.913 614.727i −0.520400 0.901359i
\(683\) 106.224i 0.155525i −0.996972 0.0777627i \(-0.975222\pi\)
0.996972 0.0777627i \(-0.0247776\pi\)
\(684\) 0 0
\(685\) −608.781 −0.888732
\(686\) 375.792 216.964i 0.547802 0.316274i
\(687\) 0 0
\(688\) −213.217 + 369.302i −0.309908 + 0.536776i
\(689\) 4.37279 + 7.57390i 0.00634658 + 0.0109926i
\(690\) 0 0
\(691\) 244.177 0.353367 0.176684 0.984268i \(-0.443463\pi\)
0.176684 + 0.984268i \(0.443463\pi\)
\(692\) 71.1195i 0.102774i
\(693\) 0 0
\(694\) 299.201 + 172.744i 0.431125 + 0.248910i
\(695\) −1171.05 −1.68497
\(696\) 0 0
\(697\) 741.082 + 427.864i 1.06325 + 0.613865i
\(698\) −870.378 + 502.513i −1.24696 + 0.719932i
\(699\) 0 0
\(700\) −4.80281 8.31871i −0.00686115 0.0118839i
\(701\) −143.276 248.161i −0.204388 0.354010i 0.745550 0.666450i \(-0.232187\pi\)
−0.949938 + 0.312440i \(0.898854\pi\)
\(702\) 0 0
\(703\) −68.7436 + 808.618i −0.0977860 + 1.15024i
\(704\) −1190.71 −1.69135
\(705\) 0 0
\(706\) −53.9108 + 31.1254i −0.0763610 + 0.0440870i
\(707\) −173.506 + 300.521i −0.245411 + 0.425065i
\(708\) 0 0
\(709\) −5.70585 + 9.88282i −0.00804774 + 0.0139391i −0.870021 0.493014i \(-0.835895\pi\)
0.861973 + 0.506953i \(0.169228\pi\)
\(710\) −972.804 −1.37015
\(711\) 0 0
\(712\) −279.688 + 484.434i −0.392820 + 0.680385i
\(713\) −77.7209 44.8722i −0.109006 0.0629344i
\(714\) 0 0
\(715\) 20.1629i 0.0281999i
\(716\) 42.4339 + 24.4992i 0.0592652 + 0.0342168i
\(717\) 0 0
\(718\) 268.238 + 154.867i 0.373591 + 0.215693i
\(719\) −438.491 759.488i −0.609862 1.05631i −0.991263 0.131902i \(-0.957892\pi\)
0.381401 0.924410i \(-0.375442\pi\)
\(720\) 0 0
\(721\) 382.298i 0.530232i
\(722\) 699.131 258.360i 0.968325 0.357839i
\(723\) 0 0
\(724\) −10.5634 + 6.09880i −0.0145904 + 0.00842376i
\(725\) −508.105 + 293.354i −0.700834 + 0.404627i
\(726\) 0 0
\(727\) −360.167 623.827i −0.495415 0.858084i 0.504571 0.863370i \(-0.331651\pi\)
−0.999986 + 0.00528653i \(0.998317\pi\)
\(728\) −1.36561 + 2.36531i −0.00187584 + 0.00324905i
\(729\) 0 0
\(730\) 1216.01i 1.66577i
\(731\) 309.194 535.540i 0.422974 0.732613i
\(732\) 0 0
\(733\) −170.651 −0.232812 −0.116406 0.993202i \(-0.537137\pi\)
−0.116406 + 0.993202i \(0.537137\pi\)
\(734\) 1024.44i 1.39570i
\(735\) 0 0
\(736\) 19.0701 11.0101i 0.0259104 0.0149594i
\(737\) 1327.53 + 766.449i 1.80126 + 1.03996i
\(738\) 0 0
\(739\) 530.334 + 918.566i 0.717637 + 1.24298i 0.961933 + 0.273284i \(0.0881098\pi\)
−0.244296 + 0.969701i \(0.578557\pi\)
\(740\) 72.0104i 0.0973114i
\(741\) 0 0
\(742\) 261.198 0.352019
\(743\) −290.537 + 167.742i −0.391033 + 0.225763i −0.682607 0.730785i \(-0.739154\pi\)
0.291575 + 0.956548i \(0.405821\pi\)
\(744\) 0 0
\(745\) −35.3107 + 61.1599i −0.0473969 + 0.0820938i
\(746\) 464.148 + 803.928i 0.622182 + 1.07765i
\(747\) 0 0
\(748\) −130.044 −0.173855
\(749\) 314.668i 0.420117i
\(750\) 0 0
\(751\) −1128.41 651.490i −1.50255 0.867497i −0.999996 0.00295120i \(-0.999061\pi\)
−0.502554 0.864546i \(-0.667606\pi\)
\(752\) 498.522 0.662929
\(753\) 0 0
\(754\) −10.1598 5.86578i −0.0134746 0.00777955i
\(755\) −1326.92 + 766.100i −1.75751 + 1.01470i
\(756\) 0 0
\(757\) −60.1511 104.185i −0.0794598 0.137628i 0.823557 0.567233i \(-0.191986\pi\)
−0.903017 + 0.429605i \(0.858653\pi\)
\(758\) −486.574 842.771i −0.641919 1.11184i
\(759\) 0 0
\(760\) 851.373 399.551i 1.12023 0.525725i
\(761\) −1346.45 −1.76932 −0.884658 0.466240i \(-0.845608\pi\)
−0.884658 + 0.466240i \(0.845608\pi\)
\(762\) 0 0
\(763\) 20.7248 11.9655i 0.0271623 0.0156822i
\(764\) 4.82553 8.35805i 0.00631613 0.0109399i
\(765\) 0 0
\(766\) 27.9243 48.3663i 0.0364547 0.0631414i
\(767\) −5.40564 −0.00704777
\(768\) 0 0
\(769\) 109.016 188.821i 0.141763 0.245541i −0.786398 0.617721i \(-0.788056\pi\)
0.928161 + 0.372180i \(0.121390\pi\)
\(770\) −521.512 301.095i −0.677288 0.391033i
\(771\) 0 0
\(772\) 52.6433i 0.0681909i
\(773\) 48.6422 + 28.0836i 0.0629266 + 0.0363307i 0.531133 0.847288i \(-0.321766\pi\)
−0.468207 + 0.883619i \(0.655100\pi\)
\(774\) 0 0
\(775\) 239.345 + 138.186i 0.308832 + 0.178304i
\(776\) −311.984 540.373i −0.402042 0.696357i
\(777\) 0 0
\(778\) 731.482i 0.940208i
\(779\) 597.671 280.488i 0.767229 0.360062i
\(780\) 0 0
\(781\) −1278.06 + 737.890i −1.63644 + 0.944801i
\(782\) −230.955 + 133.342i −0.295339 + 0.170514i
\(783\) 0 0
\(784\) −372.586 645.338i −0.475238 0.823136i