Properties

Label 108.3.k.a.5.1
Level 108
Weight 3
Character 108.5
Analytic conductor 2.943
Analytic rank 0
Dimension 36
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.94278685509\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.1
Character \(\chi\) \(=\) 108.5
Dual form 108.3.k.a.65.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.92720 - 0.656882i) q^{3} +(0.740753 + 2.03520i) q^{5} +(1.08248 + 6.13906i) q^{7} +(8.13701 + 3.84565i) q^{9} +O(q^{10})\) \(q+(-2.92720 - 0.656882i) q^{3} +(0.740753 + 2.03520i) q^{5} +(1.08248 + 6.13906i) q^{7} +(8.13701 + 3.84565i) q^{9} +(-5.10694 + 14.0312i) q^{11} +(9.95988 + 8.35733i) q^{13} +(-0.831446 - 6.44403i) q^{15} +(-3.36308 - 1.94167i) q^{17} +(6.39866 + 11.0828i) q^{19} +(0.863993 - 18.6813i) q^{21} +(-35.3663 - 6.23604i) q^{23} +(15.5578 - 13.0545i) q^{25} +(-21.2925 - 16.6020i) q^{27} +(7.13197 + 8.49955i) q^{29} +(6.25720 - 35.4864i) q^{31} +(24.1659 - 37.7175i) q^{33} +(-11.6924 + 6.75059i) q^{35} +(-16.3431 + 28.3071i) q^{37} +(-23.6648 - 31.0060i) q^{39} +(-14.5164 + 17.3000i) q^{41} +(58.2594 + 21.2047i) q^{43} +(-1.79915 + 19.4091i) q^{45} +(-3.36255 + 0.592908i) q^{47} +(9.52866 - 3.46815i) q^{49} +(8.56895 + 7.89281i) q^{51} -79.3144i q^{53} -32.3393 q^{55} +(-11.4501 - 36.6448i) q^{57} +(7.36318 + 20.2302i) q^{59} +(13.7025 + 77.7109i) q^{61} +(-14.8005 + 54.1165i) q^{63} +(-9.63104 + 26.4611i) q^{65} +(-84.5379 - 70.9357i) q^{67} +(99.4280 + 41.4856i) q^{69} +(71.2183 + 41.1179i) q^{71} +(-3.09644 - 5.36320i) q^{73} +(-54.1160 + 27.9936i) q^{75} +(-91.6666 - 16.1633i) q^{77} +(49.2237 - 41.3036i) q^{79} +(51.4220 + 62.5842i) q^{81} +(97.6080 + 116.325i) q^{83} +(1.46049 - 8.28284i) q^{85} +(-15.2935 - 29.5648i) q^{87} +(97.5489 - 56.3199i) q^{89} +(-40.5248 + 70.1909i) q^{91} +(-41.6264 + 99.7655i) q^{93} +(-17.8159 + 21.2322i) q^{95} +(-52.0684 - 18.9513i) q^{97} +(-95.5143 + 94.5326i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 9q^{5} + 6q^{9} + O(q^{10}) \) \( 36q - 9q^{5} + 6q^{9} + 36q^{11} + 45q^{15} + 42q^{21} - 18q^{23} - 9q^{25} - 18q^{29} + 45q^{31} - 153q^{33} - 243q^{35} - 123q^{39} - 198q^{41} + 90q^{43} - 333q^{45} - 243q^{47} + 72q^{49} - 99q^{51} + 243q^{57} + 252q^{59} - 144q^{61} + 381q^{63} + 747q^{65} + 108q^{67} + 585q^{69} + 324q^{71} - 63q^{73} + 597q^{75} + 495q^{77} + 36q^{79} - 54q^{81} - 27q^{83} - 180q^{85} - 441q^{87} - 567q^{89} + 99q^{91} - 699q^{93} - 1044q^{95} - 216q^{97} - 945q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.92720 0.656882i −0.975734 0.218961i
\(4\) 0 0
\(5\) 0.740753 + 2.03520i 0.148151 + 0.407040i 0.991464 0.130382i \(-0.0416204\pi\)
−0.843313 + 0.537422i \(0.819398\pi\)
\(6\) 0 0
\(7\) 1.08248 + 6.13906i 0.154640 + 0.877008i 0.959114 + 0.283020i \(0.0913363\pi\)
−0.804474 + 0.593988i \(0.797553\pi\)
\(8\) 0 0
\(9\) 8.13701 + 3.84565i 0.904113 + 0.427294i
\(10\) 0 0
\(11\) −5.10694 + 14.0312i −0.464267 + 1.27556i 0.457979 + 0.888963i \(0.348573\pi\)
−0.922247 + 0.386601i \(0.873649\pi\)
\(12\) 0 0
\(13\) 9.95988 + 8.35733i 0.766144 + 0.642871i 0.939718 0.341949i \(-0.111087\pi\)
−0.173574 + 0.984821i \(0.555532\pi\)
\(14\) 0 0
\(15\) −0.831446 6.44403i −0.0554297 0.429602i
\(16\) 0 0
\(17\) −3.36308 1.94167i −0.197828 0.114216i 0.397814 0.917466i \(-0.369769\pi\)
−0.595642 + 0.803250i \(0.703102\pi\)
\(18\) 0 0
\(19\) 6.39866 + 11.0828i 0.336772 + 0.583306i 0.983824 0.179140i \(-0.0573316\pi\)
−0.647052 + 0.762446i \(0.723998\pi\)
\(20\) 0 0
\(21\) 0.863993 18.6813i 0.0411425 0.889587i
\(22\) 0 0
\(23\) −35.3663 6.23604i −1.53767 0.271132i −0.660318 0.750986i \(-0.729578\pi\)
−0.877348 + 0.479854i \(0.840690\pi\)
\(24\) 0 0
\(25\) 15.5578 13.0545i 0.622311 0.522181i
\(26\) 0 0
\(27\) −21.2925 16.6020i −0.788613 0.614890i
\(28\) 0 0
\(29\) 7.13197 + 8.49955i 0.245930 + 0.293088i 0.874862 0.484372i \(-0.160952\pi\)
−0.628932 + 0.777460i \(0.716508\pi\)
\(30\) 0 0
\(31\) 6.25720 35.4864i 0.201845 1.14472i −0.700482 0.713670i \(-0.747032\pi\)
0.902327 0.431052i \(-0.141857\pi\)
\(32\) 0 0
\(33\) 24.1659 37.7175i 0.732300 1.14295i
\(34\) 0 0
\(35\) −11.6924 + 6.75059i −0.334068 + 0.192874i
\(36\) 0 0
\(37\) −16.3431 + 28.3071i −0.441705 + 0.765056i −0.997816 0.0660523i \(-0.978960\pi\)
0.556111 + 0.831108i \(0.312293\pi\)
\(38\) 0 0
\(39\) −23.6648 31.0060i −0.606789 0.795027i
\(40\) 0 0
\(41\) −14.5164 + 17.3000i −0.354059 + 0.421951i −0.913449 0.406954i \(-0.866591\pi\)
0.559390 + 0.828905i \(0.311036\pi\)
\(42\) 0 0
\(43\) 58.2594 + 21.2047i 1.35487 + 0.493133i 0.914465 0.404666i \(-0.132612\pi\)
0.440406 + 0.897799i \(0.354834\pi\)
\(44\) 0 0
\(45\) −1.79915 + 19.4091i −0.0399812 + 0.431314i
\(46\) 0 0
\(47\) −3.36255 + 0.592908i −0.0715435 + 0.0126151i −0.209305 0.977850i \(-0.567120\pi\)
0.137762 + 0.990465i \(0.456009\pi\)
\(48\) 0 0
\(49\) 9.52866 3.46815i 0.194462 0.0707785i
\(50\) 0 0
\(51\) 8.56895 + 7.89281i 0.168019 + 0.154761i
\(52\) 0 0
\(53\) 79.3144i 1.49650i −0.663418 0.748249i \(-0.730895\pi\)
0.663418 0.748249i \(-0.269105\pi\)
\(54\) 0 0
\(55\) −32.3393 −0.587987
\(56\) 0 0
\(57\) −11.4501 36.6448i −0.200879 0.642891i
\(58\) 0 0
\(59\) 7.36318 + 20.2302i 0.124800 + 0.342884i 0.986321 0.164838i \(-0.0527100\pi\)
−0.861521 + 0.507722i \(0.830488\pi\)
\(60\) 0 0
\(61\) 13.7025 + 77.7109i 0.224632 + 1.27395i 0.863388 + 0.504540i \(0.168338\pi\)
−0.638757 + 0.769409i \(0.720551\pi\)
\(62\) 0 0
\(63\) −14.8005 + 54.1165i −0.234929 + 0.858991i
\(64\) 0 0
\(65\) −9.63104 + 26.4611i −0.148170 + 0.407093i
\(66\) 0 0
\(67\) −84.5379 70.9357i −1.26176 1.05874i −0.995492 0.0948429i \(-0.969765\pi\)
−0.266267 0.963899i \(-0.585790\pi\)
\(68\) 0 0
\(69\) 99.4280 + 41.4856i 1.44099 + 0.601241i
\(70\) 0 0
\(71\) 71.2183 + 41.1179i 1.00307 + 0.579125i 0.909157 0.416455i \(-0.136728\pi\)
0.0939180 + 0.995580i \(0.470061\pi\)
\(72\) 0 0
\(73\) −3.09644 5.36320i −0.0424170 0.0734685i 0.844037 0.536284i \(-0.180172\pi\)
−0.886454 + 0.462816i \(0.846839\pi\)
\(74\) 0 0
\(75\) −54.1160 + 27.9936i −0.721547 + 0.373248i
\(76\) 0 0
\(77\) −91.6666 16.1633i −1.19048 0.209913i
\(78\) 0 0
\(79\) 49.2237 41.3036i 0.623085 0.522830i −0.275687 0.961248i \(-0.588905\pi\)
0.898772 + 0.438417i \(0.144461\pi\)
\(80\) 0 0
\(81\) 51.4220 + 62.5842i 0.634839 + 0.772644i
\(82\) 0 0
\(83\) 97.6080 + 116.325i 1.17600 + 1.40150i 0.897470 + 0.441075i \(0.145403\pi\)
0.278530 + 0.960428i \(0.410153\pi\)
\(84\) 0 0
\(85\) 1.46049 8.28284i 0.0171822 0.0974451i
\(86\) 0 0
\(87\) −15.2935 29.5648i −0.175788 0.339825i
\(88\) 0 0
\(89\) 97.5489 56.3199i 1.09606 0.632808i 0.160873 0.986975i \(-0.448569\pi\)
0.935182 + 0.354167i \(0.115236\pi\)
\(90\) 0 0
\(91\) −40.5248 + 70.1909i −0.445327 + 0.771329i
\(92\) 0 0
\(93\) −41.6264 + 99.7655i −0.447596 + 1.07275i
\(94\) 0 0
\(95\) −17.8159 + 21.2322i −0.187536 + 0.223497i
\(96\) 0 0
\(97\) −52.0684 18.9513i −0.536787 0.195375i 0.0593790 0.998236i \(-0.481088\pi\)
−0.596166 + 0.802861i \(0.703310\pi\)
\(98\) 0 0
\(99\) −95.5143 + 94.5326i −0.964791 + 0.954875i
\(100\) 0 0
\(101\) 77.5927 13.6817i 0.768245 0.135462i 0.224228 0.974537i \(-0.428014\pi\)
0.544017 + 0.839074i \(0.316903\pi\)
\(102\) 0 0
\(103\) 49.2174 17.9137i 0.477839 0.173919i −0.0918613 0.995772i \(-0.529282\pi\)
0.569700 + 0.821853i \(0.307059\pi\)
\(104\) 0 0
\(105\) 38.6603 12.0798i 0.368193 0.115046i
\(106\) 0 0
\(107\) 189.920i 1.77495i −0.460854 0.887476i \(-0.652457\pi\)
0.460854 0.887476i \(-0.347543\pi\)
\(108\) 0 0
\(109\) −161.394 −1.48068 −0.740338 0.672234i \(-0.765335\pi\)
−0.740338 + 0.672234i \(0.765335\pi\)
\(110\) 0 0
\(111\) 66.4339 72.1250i 0.598504 0.649775i
\(112\) 0 0
\(113\) −71.3701 196.088i −0.631594 1.73529i −0.676649 0.736306i \(-0.736568\pi\)
0.0450545 0.998985i \(-0.485654\pi\)
\(114\) 0 0
\(115\) −13.5061 76.5969i −0.117444 0.666060i
\(116\) 0 0
\(117\) 48.9043 + 106.306i 0.417985 + 0.908597i
\(118\) 0 0
\(119\) 8.27958 22.7480i 0.0695763 0.191159i
\(120\) 0 0
\(121\) −78.1025 65.5358i −0.645475 0.541618i
\(122\) 0 0
\(123\) 53.8565 41.1050i 0.437858 0.334187i
\(124\) 0 0
\(125\) 84.9844 + 49.0657i 0.679875 + 0.392526i
\(126\) 0 0
\(127\) −28.4088 49.2055i −0.223691 0.387445i 0.732235 0.681052i \(-0.238477\pi\)
−0.955926 + 0.293608i \(0.905144\pi\)
\(128\) 0 0
\(129\) −156.608 100.340i −1.21402 0.777829i
\(130\) 0 0
\(131\) 136.396 + 24.0503i 1.04119 + 0.183590i 0.667998 0.744163i \(-0.267151\pi\)
0.373194 + 0.927753i \(0.378263\pi\)
\(132\) 0 0
\(133\) −61.1116 + 51.2787i −0.459486 + 0.385554i
\(134\) 0 0
\(135\) 18.0160 55.6326i 0.133452 0.412093i
\(136\) 0 0
\(137\) −34.3399 40.9247i −0.250656 0.298720i 0.626014 0.779811i \(-0.284685\pi\)
−0.876671 + 0.481091i \(0.840241\pi\)
\(138\) 0 0
\(139\) 34.7093 196.846i 0.249707 1.41616i −0.559595 0.828767i \(-0.689043\pi\)
0.809302 0.587393i \(-0.199846\pi\)
\(140\) 0 0
\(141\) 10.2323 + 0.473235i 0.0725696 + 0.00335627i
\(142\) 0 0
\(143\) −168.128 + 97.0687i −1.17572 + 0.678802i
\(144\) 0 0
\(145\) −12.0153 + 20.8111i −0.0828639 + 0.143525i
\(146\) 0 0
\(147\) −30.1705 + 3.89277i −0.205241 + 0.0264814i
\(148\) 0 0
\(149\) −43.0873 + 51.3494i −0.289176 + 0.344627i −0.891001 0.454001i \(-0.849996\pi\)
0.601825 + 0.798628i \(0.294441\pi\)
\(150\) 0 0
\(151\) 209.460 + 76.2371i 1.38715 + 0.504881i 0.924338 0.381575i \(-0.124618\pi\)
0.462812 + 0.886456i \(0.346840\pi\)
\(152\) 0 0
\(153\) −19.8984 28.7326i −0.130055 0.187795i
\(154\) 0 0
\(155\) 76.8569 13.5520i 0.495851 0.0874320i
\(156\) 0 0
\(157\) −113.832 + 41.4314i −0.725043 + 0.263894i −0.678065 0.735002i \(-0.737181\pi\)
−0.0469779 + 0.998896i \(0.514959\pi\)
\(158\) 0 0
\(159\) −52.1002 + 232.169i −0.327674 + 1.46018i
\(160\) 0 0
\(161\) 223.866i 1.39047i
\(162\) 0 0
\(163\) 70.9962 0.435560 0.217780 0.975998i \(-0.430119\pi\)
0.217780 + 0.975998i \(0.430119\pi\)
\(164\) 0 0
\(165\) 94.6637 + 21.2431i 0.573719 + 0.128746i
\(166\) 0 0
\(167\) 57.0403 + 156.717i 0.341559 + 0.938425i 0.984943 + 0.172882i \(0.0553078\pi\)
−0.643384 + 0.765544i \(0.722470\pi\)
\(168\) 0 0
\(169\) 0.00765212 + 0.0433973i 4.52788e−5 + 0.000256789i
\(170\) 0 0
\(171\) 9.44541 + 114.788i 0.0552363 + 0.671275i
\(172\) 0 0
\(173\) −78.3577 + 215.286i −0.452935 + 1.24443i 0.477714 + 0.878515i \(0.341465\pi\)
−0.930649 + 0.365913i \(0.880757\pi\)
\(174\) 0 0
\(175\) 96.9835 + 81.3789i 0.554192 + 0.465022i
\(176\) 0 0
\(177\) −8.26468 64.0545i −0.0466931 0.361890i
\(178\) 0 0
\(179\) 129.909 + 75.0033i 0.725751 + 0.419013i 0.816866 0.576828i \(-0.195710\pi\)
−0.0911147 + 0.995840i \(0.529043\pi\)
\(180\) 0 0
\(181\) 74.7777 + 129.519i 0.413137 + 0.715574i 0.995231 0.0975476i \(-0.0310998\pi\)
−0.582094 + 0.813121i \(0.697767\pi\)
\(182\) 0 0
\(183\) 10.9368 236.476i 0.0597639 1.29222i
\(184\) 0 0
\(185\) −69.7168 12.2929i −0.376847 0.0664483i
\(186\) 0 0
\(187\) 44.4191 37.2720i 0.237535 0.199316i
\(188\) 0 0
\(189\) 78.8721 148.688i 0.417313 0.786707i
\(190\) 0 0
\(191\) −48.7526 58.1011i −0.255249 0.304194i 0.623169 0.782087i \(-0.285845\pi\)
−0.878418 + 0.477893i \(0.841401\pi\)
\(192\) 0 0
\(193\) −23.6459 + 134.103i −0.122518 + 0.694833i 0.860234 + 0.509900i \(0.170318\pi\)
−0.982751 + 0.184932i \(0.940793\pi\)
\(194\) 0 0
\(195\) 45.5738 71.1304i 0.233712 0.364771i
\(196\) 0 0
\(197\) −285.910 + 165.070i −1.45132 + 0.837919i −0.998556 0.0537122i \(-0.982895\pi\)
−0.452762 + 0.891631i \(0.649561\pi\)
\(198\) 0 0
\(199\) −29.8782 + 51.7505i −0.150141 + 0.260053i −0.931279 0.364306i \(-0.881306\pi\)
0.781138 + 0.624359i \(0.214640\pi\)
\(200\) 0 0
\(201\) 200.863 + 263.175i 0.999319 + 1.30933i
\(202\) 0 0
\(203\) −44.4590 + 52.9842i −0.219010 + 0.261006i
\(204\) 0 0
\(205\) −45.9621 16.7288i −0.224205 0.0816040i
\(206\) 0 0
\(207\) −263.795 186.749i −1.27437 0.902170i
\(208\) 0 0
\(209\) −188.183 + 33.1817i −0.900396 + 0.158764i
\(210\) 0 0
\(211\) 10.6114 3.86224i 0.0502911 0.0183045i −0.316752 0.948508i \(-0.602592\pi\)
0.367043 + 0.930204i \(0.380370\pi\)
\(212\) 0 0
\(213\) −181.461 167.142i −0.851928 0.784706i
\(214\) 0 0
\(215\) 134.277i 0.624545i
\(216\) 0 0
\(217\) 224.626 1.03514
\(218\) 0 0
\(219\) 5.54093 + 17.7332i 0.0253010 + 0.0809733i
\(220\) 0 0
\(221\) −17.2686 47.4452i −0.0781386 0.214684i
\(222\) 0 0
\(223\) 19.2101 + 108.946i 0.0861441 + 0.488547i 0.997104 + 0.0760521i \(0.0242315\pi\)
−0.910960 + 0.412495i \(0.864657\pi\)
\(224\) 0 0
\(225\) 176.797 46.3951i 0.785764 0.206200i
\(226\) 0 0
\(227\) 112.933 310.280i 0.497500 1.36687i −0.396182 0.918172i \(-0.629665\pi\)
0.893683 0.448699i \(-0.148113\pi\)
\(228\) 0 0
\(229\) 346.931 + 291.110i 1.51498 + 1.27122i 0.853273 + 0.521464i \(0.174614\pi\)
0.661711 + 0.749759i \(0.269831\pi\)
\(230\) 0 0
\(231\) 257.709 + 107.527i 1.11562 + 0.465486i
\(232\) 0 0
\(233\) 312.892 + 180.648i 1.34289 + 0.775315i 0.987230 0.159302i \(-0.0509243\pi\)
0.355655 + 0.934617i \(0.384258\pi\)
\(234\) 0 0
\(235\) −3.69750 6.40426i −0.0157340 0.0272522i
\(236\) 0 0
\(237\) −171.219 + 88.5698i −0.722444 + 0.373712i
\(238\) 0 0
\(239\) −125.627 22.1514i −0.525636 0.0926838i −0.0954677 0.995433i \(-0.530435\pi\)
−0.430168 + 0.902749i \(0.641546\pi\)
\(240\) 0 0
\(241\) −100.014 + 83.9215i −0.414995 + 0.348222i −0.826255 0.563296i \(-0.809533\pi\)
0.411260 + 0.911518i \(0.365089\pi\)
\(242\) 0 0
\(243\) −109.412 216.975i −0.450255 0.892900i
\(244\) 0 0
\(245\) 14.1168 + 16.8237i 0.0576194 + 0.0686681i
\(246\) 0 0
\(247\) −28.8928 + 163.859i −0.116975 + 0.663397i
\(248\) 0 0
\(249\) −209.307 404.623i −0.840589 1.62499i
\(250\) 0 0
\(251\) −376.247 + 217.226i −1.49899 + 0.865444i −0.999999 0.00116146i \(-0.999630\pi\)
−0.498994 + 0.866606i \(0.666297\pi\)
\(252\) 0 0
\(253\) 268.113 464.385i 1.05973 1.83551i
\(254\) 0 0
\(255\) −9.71598 + 23.2862i −0.0381019 + 0.0913183i
\(256\) 0 0
\(257\) 104.428 124.452i 0.406334 0.484250i −0.523606 0.851960i \(-0.675414\pi\)
0.929941 + 0.367710i \(0.119858\pi\)
\(258\) 0 0
\(259\) −191.470 69.6893i −0.739266 0.269071i
\(260\) 0 0
\(261\) 25.3466 + 96.5880i 0.0971136 + 0.370069i
\(262\) 0 0
\(263\) −297.767 + 52.5043i −1.13219 + 0.199636i −0.708188 0.706024i \(-0.750487\pi\)
−0.424005 + 0.905660i \(0.639376\pi\)
\(264\) 0 0
\(265\) 161.421 58.7524i 0.609135 0.221707i
\(266\) 0 0
\(267\) −322.541 + 100.782i −1.20802 + 0.377459i
\(268\) 0 0
\(269\) 252.041i 0.936956i −0.883475 0.468478i \(-0.844803\pi\)
0.883475 0.468478i \(-0.155197\pi\)
\(270\) 0 0
\(271\) 107.217 0.395635 0.197818 0.980239i \(-0.436615\pi\)
0.197818 + 0.980239i \(0.436615\pi\)
\(272\) 0 0
\(273\) 164.731 178.843i 0.603411 0.655103i
\(274\) 0 0
\(275\) 103.718 + 284.963i 0.377157 + 1.03623i
\(276\) 0 0
\(277\) −46.8272 265.570i −0.169051 0.958738i −0.944788 0.327681i \(-0.893733\pi\)
0.775737 0.631056i \(-0.217378\pi\)
\(278\) 0 0
\(279\) 187.383 264.690i 0.671624 0.948710i
\(280\) 0 0
\(281\) −5.79982 + 15.9349i −0.0206399 + 0.0567077i −0.949585 0.313511i \(-0.898495\pi\)
0.928945 + 0.370218i \(0.120717\pi\)
\(282\) 0 0
\(283\) −250.525 210.215i −0.885247 0.742810i 0.0820041 0.996632i \(-0.473868\pi\)
−0.967251 + 0.253822i \(0.918312\pi\)
\(284\) 0 0
\(285\) 66.0978 50.4479i 0.231922 0.177010i
\(286\) 0 0
\(287\) −121.919 70.3903i −0.424807 0.245262i
\(288\) 0 0
\(289\) −136.960 237.221i −0.473909 0.820835i
\(290\) 0 0
\(291\) 139.966 + 89.6771i 0.480982 + 0.308169i
\(292\) 0 0
\(293\) 264.414 + 46.6234i 0.902437 + 0.159124i 0.605568 0.795794i \(-0.292946\pi\)
0.296870 + 0.954918i \(0.404057\pi\)
\(294\) 0 0
\(295\) −35.7182 + 29.9711i −0.121078 + 0.101597i
\(296\) 0 0
\(297\) 341.686 213.974i 1.15046 0.720452i
\(298\) 0 0
\(299\) −300.128 357.678i −1.00377 1.19625i
\(300\) 0 0
\(301\) −67.1121 + 380.612i −0.222964 + 1.26449i
\(302\) 0 0
\(303\) −236.117 10.9202i −0.779263 0.0360401i
\(304\) 0 0
\(305\) −148.007 + 85.4519i −0.485269 + 0.280170i
\(306\) 0 0
\(307\) −51.1411 + 88.5790i −0.166583 + 0.288531i −0.937216 0.348748i \(-0.886607\pi\)
0.770633 + 0.637279i \(0.219940\pi\)
\(308\) 0 0
\(309\) −155.836 + 20.1069i −0.504325 + 0.0650709i
\(310\) 0 0
\(311\) 300.925 358.629i 0.967605 1.15315i −0.0205661 0.999788i \(-0.506547\pi\)
0.988171 0.153358i \(-0.0490087\pi\)
\(312\) 0 0
\(313\) −173.348 63.0934i −0.553827 0.201576i 0.0499192 0.998753i \(-0.484104\pi\)
−0.603746 + 0.797177i \(0.706326\pi\)
\(314\) 0 0
\(315\) −121.101 + 9.96492i −0.384449 + 0.0316347i
\(316\) 0 0
\(317\) 96.3583 16.9906i 0.303969 0.0535980i −0.0195831 0.999808i \(-0.506234\pi\)
0.323552 + 0.946210i \(0.395123\pi\)
\(318\) 0 0
\(319\) −155.682 + 56.6634i −0.488030 + 0.177628i
\(320\) 0 0
\(321\) −124.755 + 555.933i −0.388644 + 1.73188i
\(322\) 0 0
\(323\) 49.6965i 0.153859i
\(324\) 0 0
\(325\) 264.055 0.812476
\(326\) 0 0
\(327\) 472.432 + 106.017i 1.44475 + 0.324210i
\(328\) 0 0
\(329\) −7.27979 20.0011i −0.0221270 0.0607935i
\(330\) 0 0
\(331\) −18.3892 104.290i −0.0555564 0.315076i 0.944347 0.328950i \(-0.106695\pi\)
−0.999904 + 0.0138738i \(0.995584\pi\)
\(332\) 0 0
\(333\) −241.843 + 167.485i −0.726255 + 0.502958i
\(334\) 0 0
\(335\) 81.7468 224.597i 0.244020 0.670440i
\(336\) 0 0
\(337\) −3.17508 2.66420i −0.00942159 0.00790565i 0.638065 0.769983i \(-0.279735\pi\)
−0.647486 + 0.762077i \(0.724180\pi\)
\(338\) 0 0
\(339\) 80.1083 + 620.870i 0.236308 + 1.83148i
\(340\) 0 0
\(341\) 465.961 + 269.023i 1.36646 + 0.788924i
\(342\) 0 0
\(343\) 184.333 + 319.274i 0.537414 + 0.930828i
\(344\) 0 0
\(345\) −10.7800 + 233.087i −0.0312464 + 0.675613i
\(346\) 0 0
\(347\) 387.103 + 68.2568i 1.11557 + 0.196705i 0.700896 0.713264i \(-0.252784\pi\)
0.414676 + 0.909969i \(0.363895\pi\)
\(348\) 0 0
\(349\) −246.286 + 206.658i −0.705690 + 0.592144i −0.923386 0.383872i \(-0.874590\pi\)
0.217696 + 0.976017i \(0.430146\pi\)
\(350\) 0 0
\(351\) −73.3223 343.303i −0.208896 0.978071i
\(352\) 0 0
\(353\) 112.600 + 134.192i 0.318982 + 0.380147i 0.901580 0.432613i \(-0.142408\pi\)
−0.582598 + 0.812760i \(0.697964\pi\)
\(354\) 0 0
\(355\) −30.9281 + 175.402i −0.0871213 + 0.494089i
\(356\) 0 0
\(357\) −39.1787 + 61.1491i −0.109744 + 0.171286i
\(358\) 0 0
\(359\) −455.354 + 262.899i −1.26840 + 0.732309i −0.974684 0.223586i \(-0.928224\pi\)
−0.293711 + 0.955894i \(0.594890\pi\)
\(360\) 0 0
\(361\) 98.6142 170.805i 0.273170 0.473143i
\(362\) 0 0
\(363\) 185.573 + 243.141i 0.511219 + 0.669809i
\(364\) 0 0
\(365\) 8.62149 10.2747i 0.0236205 0.0281498i
\(366\) 0 0
\(367\) −304.854 110.958i −0.830664 0.302337i −0.108533 0.994093i \(-0.534615\pi\)
−0.722131 + 0.691756i \(0.756837\pi\)
\(368\) 0 0
\(369\) −184.650 + 84.9453i −0.500407 + 0.230204i
\(370\) 0 0
\(371\) 486.916 85.8564i 1.31244 0.231419i
\(372\) 0 0
\(373\) 227.629 82.8503i 0.610267 0.222119i −0.0183533 0.999832i \(-0.505842\pi\)
0.628620 + 0.777713i \(0.283620\pi\)
\(374\) 0 0
\(375\) −216.536 199.450i −0.577429 0.531866i
\(376\) 0 0
\(377\) 144.259i 0.382649i
\(378\) 0 0
\(379\) −605.266 −1.59701 −0.798504 0.601989i \(-0.794375\pi\)
−0.798504 + 0.601989i \(0.794375\pi\)
\(380\) 0 0
\(381\) 50.8361 + 162.696i 0.133428 + 0.427023i
\(382\) 0 0
\(383\) 92.4520 + 254.010i 0.241389 + 0.663211i 0.999933 + 0.0115889i \(0.00368896\pi\)
−0.758544 + 0.651622i \(0.774089\pi\)
\(384\) 0 0
\(385\) −35.0067 198.533i −0.0909265 0.515670i
\(386\) 0 0
\(387\) 392.512 + 396.588i 1.01424 + 1.02478i
\(388\) 0 0
\(389\) 56.4976 155.226i 0.145238 0.399038i −0.845648 0.533741i \(-0.820786\pi\)
0.990886 + 0.134703i \(0.0430079\pi\)
\(390\) 0 0
\(391\) 106.831 + 89.6421i 0.273226 + 0.229264i
\(392\) 0 0
\(393\) −383.461 159.996i −0.975727 0.407115i
\(394\) 0 0
\(395\) 120.524 + 69.5844i 0.305123 + 0.176163i
\(396\) 0 0
\(397\) −192.854 334.032i −0.485778 0.841392i 0.514089 0.857737i \(-0.328130\pi\)
−0.999866 + 0.0163455i \(0.994797\pi\)
\(398\) 0 0
\(399\) 212.570 109.960i 0.532757 0.275589i
\(400\) 0 0
\(401\) 238.103 + 41.9840i 0.593773 + 0.104698i 0.462456 0.886642i \(-0.346968\pi\)
0.131317 + 0.991340i \(0.458079\pi\)
\(402\) 0 0
\(403\) 358.892 301.146i 0.890551 0.747261i
\(404\) 0 0
\(405\) −89.2805 + 151.013i −0.220446 + 0.372873i
\(406\) 0 0
\(407\) −313.719 373.876i −0.770808 0.918614i
\(408\) 0 0
\(409\) 26.9195 152.668i 0.0658180 0.373272i −0.934052 0.357137i \(-0.883753\pi\)
0.999870 0.0161348i \(-0.00513609\pi\)
\(410\) 0 0
\(411\) 73.6371 + 142.352i 0.179166 + 0.346355i
\(412\) 0 0
\(413\) −116.224 + 67.1018i −0.281413 + 0.162474i
\(414\) 0 0
\(415\) −164.441 + 284.820i −0.396243 + 0.686313i
\(416\) 0 0
\(417\) −230.906 + 553.409i −0.553731 + 1.32712i
\(418\) 0 0
\(419\) 308.155 367.245i 0.735453 0.876479i −0.260581 0.965452i \(-0.583914\pi\)
0.996034 + 0.0889728i \(0.0283584\pi\)
\(420\) 0 0
\(421\) −647.463 235.657i −1.53792 0.559756i −0.572372 0.819994i \(-0.693977\pi\)
−0.965545 + 0.260238i \(0.916199\pi\)
\(422\) 0 0
\(423\) −29.6412 8.10667i −0.0700737 0.0191647i
\(424\) 0 0
\(425\) −77.6696 + 13.6953i −0.182752 + 0.0322241i
\(426\) 0 0
\(427\) −462.239 + 168.241i −1.08253 + 0.394008i
\(428\) 0 0
\(429\) 555.907 173.699i 1.29582 0.404894i
\(430\) 0 0
\(431\) 506.298i 1.17471i −0.809331 0.587353i \(-0.800170\pi\)
0.809331 0.587353i \(-0.199830\pi\)
\(432\) 0 0
\(433\) 425.824 0.983427 0.491714 0.870757i \(-0.336371\pi\)
0.491714 + 0.870757i \(0.336371\pi\)
\(434\) 0 0
\(435\) 48.8415 53.0256i 0.112279 0.121898i
\(436\) 0 0
\(437\) −157.184 431.861i −0.359690 0.988239i
\(438\) 0 0
\(439\) 79.7889 + 452.505i 0.181751 + 1.03076i 0.930059 + 0.367411i \(0.119756\pi\)
−0.748307 + 0.663353i \(0.769133\pi\)
\(440\) 0 0
\(441\) 90.8721 + 8.42351i 0.206059 + 0.0191009i
\(442\) 0 0
\(443\) 18.6549 51.2541i 0.0421105 0.115698i −0.916855 0.399220i \(-0.869281\pi\)
0.958966 + 0.283523i \(0.0915031\pi\)
\(444\) 0 0
\(445\) 186.882 + 156.813i 0.419959 + 0.352388i
\(446\) 0 0
\(447\) 159.856 122.007i 0.357619 0.272946i
\(448\) 0 0
\(449\) 182.250 + 105.222i 0.405902 + 0.234348i 0.689027 0.724735i \(-0.258038\pi\)
−0.283125 + 0.959083i \(0.591371\pi\)
\(450\) 0 0
\(451\) −168.605 292.033i −0.373848 0.647523i
\(452\) 0 0
\(453\) −563.052 360.751i −1.24294 0.796361i
\(454\) 0 0
\(455\) −172.871 30.4819i −0.379937 0.0669932i
\(456\) 0 0
\(457\) −150.910 + 126.628i −0.330218 + 0.277086i −0.792789 0.609497i \(-0.791372\pi\)
0.462571 + 0.886582i \(0.346927\pi\)
\(458\) 0 0
\(459\) 39.3727 + 97.1771i 0.0857793 + 0.211715i
\(460\) 0 0
\(461\) 128.532 + 153.179i 0.278812 + 0.332275i 0.887218 0.461351i \(-0.152635\pi\)
−0.608406 + 0.793626i \(0.708191\pi\)
\(462\) 0 0
\(463\) 67.1681 380.929i 0.145071 0.822741i −0.822238 0.569143i \(-0.807275\pi\)
0.967310 0.253598i \(-0.0816139\pi\)
\(464\) 0 0
\(465\) −233.878 10.8166i −0.502963 0.0232615i
\(466\) 0 0
\(467\) 300.701 173.610i 0.643900 0.371756i −0.142215 0.989836i \(-0.545423\pi\)
0.786115 + 0.618080i \(0.212089\pi\)
\(468\) 0 0
\(469\) 343.968 595.770i 0.733407 1.27030i
\(470\) 0 0
\(471\) 360.424 46.5040i 0.765231 0.0987346i
\(472\) 0 0
\(473\) −595.055 + 709.159i −1.25804 + 1.49928i
\(474\) 0 0
\(475\) 244.230 + 88.8924i 0.514168 + 0.187142i
\(476\) 0 0
\(477\) 305.015 645.382i 0.639445 1.35300i
\(478\) 0 0
\(479\) −239.163 + 42.1710i −0.499297 + 0.0880396i −0.417625 0.908620i \(-0.637137\pi\)
−0.0816727 + 0.996659i \(0.526026\pi\)
\(480\) 0 0
\(481\) −399.347 + 145.350i −0.830242 + 0.302183i
\(482\) 0 0
\(483\) −147.054 + 655.302i −0.304459 + 1.35673i
\(484\) 0 0
\(485\) 120.008i 0.247439i
\(486\) 0 0
\(487\) 294.321 0.604355 0.302177 0.953252i \(-0.402287\pi\)
0.302177 + 0.953252i \(0.402287\pi\)
\(488\) 0 0
\(489\) −207.820 46.6361i −0.424990 0.0953704i
\(490\) 0 0
\(491\) −81.7251 224.538i −0.166446 0.457307i 0.828226 0.560394i \(-0.189350\pi\)
−0.994672 + 0.103087i \(0.967128\pi\)
\(492\) 0 0
\(493\) −7.48201 42.4326i −0.0151765 0.0860702i
\(494\) 0 0
\(495\) −263.145 124.366i −0.531607 0.251244i
\(496\) 0 0
\(497\) −175.333 + 481.723i −0.352782 + 0.969261i
\(498\) 0 0
\(499\) −184.698 154.980i −0.370136 0.310581i 0.438679 0.898644i \(-0.355446\pi\)
−0.808815 + 0.588063i \(0.799891\pi\)
\(500\) 0 0
\(501\) −64.0240 496.211i −0.127792 0.990441i
\(502\) 0 0
\(503\) −138.798 80.1352i −0.275941 0.159314i 0.355644 0.934622i \(-0.384262\pi\)
−0.631584 + 0.775307i \(0.717595\pi\)
\(504\) 0 0
\(505\) 85.3220 + 147.782i 0.168954 + 0.292638i
\(506\) 0 0
\(507\) 0.00610761 0.132059i 1.20466e−5 0.000260472i
\(508\) 0 0
\(509\) 78.7326 + 13.8827i 0.154681 + 0.0272744i 0.250452 0.968129i \(-0.419421\pi\)
−0.0957713 + 0.995403i \(0.530532\pi\)
\(510\) 0 0
\(511\) 29.5731 24.8148i 0.0578731 0.0485613i
\(512\) 0 0
\(513\) 47.7535 342.212i 0.0930867 0.667080i
\(514\) 0 0
\(515\) 72.9158 + 86.8977i 0.141584 + 0.168733i
\(516\) 0 0
\(517\) 8.85312 50.2085i 0.0171240 0.0971151i
\(518\) 0 0
\(519\) 370.786 578.714i 0.714424 1.11506i
\(520\) 0 0
\(521\) 599.564 346.158i 1.15079 0.664411i 0.201713 0.979445i \(-0.435349\pi\)
0.949081 + 0.315033i \(0.102016\pi\)
\(522\) 0 0
\(523\) −33.5131 + 58.0464i −0.0640786 + 0.110987i −0.896285 0.443479i \(-0.853744\pi\)
0.832206 + 0.554466i \(0.187077\pi\)
\(524\) 0 0
\(525\) −230.434 301.919i −0.438922 0.575084i
\(526\) 0 0
\(527\) −89.9464 + 107.194i −0.170676 + 0.203404i
\(528\) 0 0
\(529\) 714.791 + 260.163i 1.35121 + 0.491801i
\(530\) 0 0
\(531\) −17.8838 + 192.929i −0.0336795 + 0.363332i
\(532\) 0 0
\(533\) −289.164 + 50.9873i −0.542521 + 0.0956611i
\(534\) 0 0
\(535\) 386.525 140.684i 0.722477 0.262960i
\(536\) 0 0
\(537\) −331.003 304.885i −0.616393 0.567756i
\(538\) 0 0
\(539\) 151.410i 0.280909i
\(540\) 0 0
\(541\) −584.288 −1.08002 −0.540008 0.841660i \(-0.681579\pi\)
−0.540008 + 0.841660i \(0.681579\pi\)
\(542\) 0 0
\(543\) −133.811 428.248i −0.246429 0.788670i
\(544\) 0 0
\(545\) −119.553 328.469i −0.219363 0.602695i
\(546\) 0 0
\(547\) 13.0135 + 73.8033i 0.0237907 + 0.134924i 0.994390 0.105778i \(-0.0337334\pi\)
−0.970599 + 0.240702i \(0.922622\pi\)
\(548\) 0 0
\(549\) −187.351 + 685.030i −0.341259 + 1.24778i
\(550\) 0 0
\(551\) −48.5638 + 133.428i −0.0881377 + 0.242156i
\(552\) 0 0
\(553\) 306.849 + 257.477i 0.554881 + 0.465600i
\(554\) 0 0
\(555\) 196.000 + 81.7796i 0.353153 + 0.147351i
\(556\) 0 0
\(557\) −460.828 266.059i −0.827340 0.477665i 0.0256012 0.999672i \(-0.491850\pi\)
−0.852941 + 0.522007i \(0.825183\pi\)
\(558\) 0 0
\(559\) 403.042 + 698.090i 0.721006 + 1.24882i
\(560\) 0 0
\(561\) −154.507 + 79.9246i −0.275413 + 0.142468i
\(562\) 0 0
\(563\) −457.883 80.7371i −0.813291 0.143405i −0.248492 0.968634i \(-0.579935\pi\)
−0.564799 + 0.825229i \(0.691046\pi\)
\(564\) 0 0
\(565\) 346.211 290.505i 0.612762 0.514168i
\(566\) 0 0
\(567\) −328.545 + 383.429i −0.579444 + 0.676241i
\(568\) 0 0
\(569\) 324.973 + 387.288i 0.571130 + 0.680647i 0.971863 0.235549i \(-0.0756887\pi\)
−0.400732 + 0.916195i \(0.631244\pi\)
\(570\) 0 0
\(571\) 4.63998 26.3146i 0.00812605 0.0460851i −0.980475 0.196643i \(-0.936996\pi\)
0.988601 + 0.150558i \(0.0481070\pi\)
\(572\) 0 0
\(573\) 104.543 + 202.098i 0.182449 + 0.352702i
\(574\) 0 0
\(575\) −631.630 + 364.672i −1.09849 + 0.634212i
\(576\) 0 0
\(577\) −568.853 + 985.283i −0.985881 + 1.70760i −0.347926 + 0.937522i \(0.613114\pi\)
−0.637955 + 0.770074i \(0.720219\pi\)
\(578\) 0 0
\(579\) 157.306 377.013i 0.271686 0.651145i
\(580\) 0 0
\(581\) −608.465 + 725.141i −1.04727 + 1.24809i
\(582\) 0 0
\(583\) 1112.88 + 405.054i 1.90888 + 0.694775i
\(584\) 0 0
\(585\) −180.128 + 178.276i −0.307911 + 0.304746i
\(586\) 0 0
\(587\) 413.543 72.9187i 0.704502 0.124223i 0.190091 0.981767i \(-0.439122\pi\)
0.514411 + 0.857544i \(0.328011\pi\)
\(588\) 0 0
\(589\) 433.327 157.718i 0.735699 0.267772i
\(590\) 0 0
\(591\) 945.347 295.384i 1.59957 0.499805i
\(592\) 0 0
\(593\) 608.635i 1.02637i 0.858279 + 0.513183i \(0.171534\pi\)
−0.858279 + 0.513183i \(0.828466\pi\)
\(594\) 0 0
\(595\) 52.4298 0.0881173
\(596\) 0 0
\(597\) 121.453 131.858i 0.203439 0.220867i
\(598\) 0 0
\(599\) 222.904 + 612.422i 0.372126 + 1.02241i 0.974538 + 0.224223i \(0.0719843\pi\)
−0.602412 + 0.798185i \(0.705794\pi\)
\(600\) 0 0
\(601\) 29.5147 + 167.386i 0.0491092 + 0.278512i 0.999467 0.0326472i \(-0.0103938\pi\)
−0.950358 + 0.311160i \(0.899283\pi\)
\(602\) 0 0
\(603\) −415.092 902.308i −0.688378 1.49636i
\(604\) 0 0
\(605\) 75.5239 207.500i 0.124833 0.342976i
\(606\) 0 0
\(607\) −275.061 230.804i −0.453149 0.380237i 0.387454 0.921889i \(-0.373355\pi\)
−0.840603 + 0.541652i \(0.817799\pi\)
\(608\) 0 0
\(609\) 164.945 125.891i 0.270845 0.206718i
\(610\) 0 0
\(611\) −38.4457 22.1966i −0.0629225 0.0363283i
\(612\) 0 0
\(613\) 112.374 + 194.637i 0.183317 + 0.317515i 0.943008 0.332769i \(-0.107983\pi\)
−0.759691 + 0.650284i \(0.774650\pi\)
\(614\) 0 0
\(615\) 123.551 + 79.1603i 0.200897 + 0.128716i
\(616\) 0 0
\(617\) −369.095 65.0815i −0.598210 0.105481i −0.133660 0.991027i \(-0.542673\pi\)
−0.464550 + 0.885547i \(0.653784\pi\)
\(618\) 0 0
\(619\) −511.061 + 428.831i −0.825623 + 0.692780i −0.954282 0.298909i \(-0.903377\pi\)
0.128658 + 0.991689i \(0.458933\pi\)
\(620\) 0 0
\(621\) 649.508 + 719.934i 1.04591 + 1.15931i
\(622\) 0 0
\(623\) 451.346 + 537.893i 0.724472 + 0.863392i
\(624\) 0 0
\(625\) 51.2603 290.712i 0.0820165 0.465139i
\(626\) 0 0
\(627\) 572.645 + 26.4843i 0.913310 + 0.0422397i
\(628\) 0 0
\(629\) 109.926 63.4659i 0.174763 0.100900i
\(630\) 0 0
\(631\) −288.004 + 498.837i −0.456425 + 0.790551i −0.998769 0.0496058i \(-0.984204\pi\)
0.542344 + 0.840156i \(0.317537\pi\)
\(632\) 0 0
\(633\) −33.5988 + 4.33511i −0.0530786 + 0.00684851i
\(634\) 0 0
\(635\) 79.0992 94.2667i 0.124566 0.148452i
\(636\) 0 0
\(637\) 123.889 + 45.0918i 0.194488 + 0.0707877i
\(638\) 0 0
\(639\) 421.379 + 608.457i 0.659435 + 0.952203i
\(640\) 0 0
\(641\) −732.193 + 129.105i −1.14227 + 0.201412i −0.712597 0.701574i \(-0.752481\pi\)
−0.429670 + 0.902986i \(0.641370\pi\)
\(642\) 0 0
\(643\) 717.060 260.989i 1.11518 0.405892i 0.282289 0.959330i \(-0.408906\pi\)
0.832891 + 0.553437i \(0.186684\pi\)
\(644\) 0 0
\(645\) 88.2042 393.056i 0.136751 0.609389i
\(646\) 0 0
\(647\) 128.575i 0.198725i −0.995051 0.0993624i \(-0.968320\pi\)
0.995051 0.0993624i \(-0.0316803\pi\)
\(648\) 0 0
\(649\) −321.457 −0.495311
\(650\) 0 0
\(651\) −657.526 147.553i −1.01002 0.226656i
\(652\) 0 0
\(653\) −61.1625 168.042i −0.0936638 0.257339i 0.884010 0.467468i \(-0.154834\pi\)
−0.977674 + 0.210129i \(0.932612\pi\)
\(654\) 0 0
\(655\) 52.0886 + 295.409i 0.0795245 + 0.451006i
\(656\) 0 0
\(657\) −4.57083 55.5482i −0.00695712 0.0845483i
\(658\) 0 0
\(659\) −69.7138 + 191.537i −0.105787 + 0.290648i −0.981281 0.192581i \(-0.938314\pi\)
0.875494 + 0.483229i \(0.160536\pi\)
\(660\) 0 0
\(661\) −588.511 493.819i −0.890334 0.747079i 0.0779433 0.996958i \(-0.475165\pi\)
−0.968277 + 0.249879i \(0.919609\pi\)
\(662\) 0 0
\(663\) 19.3829 + 150.225i 0.0292351 + 0.226584i
\(664\) 0 0
\(665\) −149.631 86.3896i −0.225009 0.129909i
\(666\) 0 0
\(667\) −199.228 345.073i −0.298693 0.517351i
\(668\) 0 0
\(669\) 15.3327 331.526i 0.0229189 0.495554i
\(670\) 0 0
\(671\) −1160.36 204.602i −1.72929 0.304921i
\(672\) 0 0
\(673\) 897.798 753.342i 1.33402 1.11938i 0.350905 0.936411i \(-0.385874\pi\)
0.983119 0.182967i \(-0.0585703\pi\)
\(674\) 0 0
\(675\) −547.997 + 19.6731i −0.811847 + 0.0291454i
\(676\) 0 0
\(677\) 192.459 + 229.364i 0.284283 + 0.338795i 0.889221 0.457477i \(-0.151247\pi\)
−0.604939 + 0.796272i \(0.706802\pi\)
\(678\) 0 0
\(679\) 59.9803 340.165i 0.0883363 0.500980i
\(680\) 0 0
\(681\) −534.393 + 834.068i −0.784719 + 1.22477i
\(682\) 0 0
\(683\) 812.585 469.146i 1.18973 0.686890i 0.231484 0.972839i \(-0.425642\pi\)
0.958245 + 0.285949i \(0.0923087\pi\)
\(684\) 0 0
\(685\) 57.8526 100.204i 0.0844564 0.146283i
\(686\) 0 0
\(687\) −824.313 1080.03i −1.19987 1.57210i
\(688\) 0 0
\(689\) 662.856 789.962i 0.962056 1.14653i
\(690\) 0 0
\(691\) −31.6500 11.5197i −0.0458032 0.0166710i 0.319017 0.947749i \(-0.396647\pi\)
−0.364820 + 0.931078i \(0.618870\pi\)
\(692\) 0 0
\(693\) −683.734 484.038i −0.986629 0.698468i
\(694\) 0 0
\(695\) 426.333 75.1739i 0.613428 0.108164i
\(696\) 0 0
\(697\) 82.4108 29.9951i 0.118236 0.0430345i
\(698\) 0 0
\(699\) −797.234 734.328i −1.14054 1.05054i
\(700\) 0 0
\(701\) 1259.81i 1.79716i −0.438814 0.898578i \(-0.644601\pi\)
0.438814 0.898578i \(-0.355399\pi\)
\(702\) 0 0
\(703\) −418.296 −0.595015
\(704\) 0 0
\(705\) 6.61649 + 21.1754i 0.00938509 + 0.0300360i
\(706\) 0 0
\(707\) 167.985 + 461.536i 0.237603 + 0.652809i
\(708\) 0 0
\(709\) 51.2300 + 290.540i 0.0722567 + 0.409788i 0.999386 + 0.0350457i \(0.0111577\pi\)
−0.927129 + 0.374742i \(0.877731\pi\)
\(710\) 0 0
\(711\) 559.373 146.791i 0.786742 0.206457i
\(712\) 0 0
\(713\) −442.589 + 1216.00i −0.620741 + 1.70547i
\(714\) 0 0
\(715\) −322.096 270.270i −0.450483 0.378000i
\(716\) 0 0
\(717\) 353.185 + 147.364i 0.492587 + 0.205528i
\(718\) 0 0
\(719\) −719.610 415.467i −1.00085 0.577840i −0.0923493 0.995727i \(-0.529438\pi\)
−0.908499 + 0.417886i \(0.862771\pi\)
\(720\) 0 0
\(721\) 163.250 + 282.757i 0.226422 + 0.392174i
\(722\) 0 0
\(723\) 347.887 179.958i 0.481172 0.248905i
\(724\) 0 0
\(725\) 221.915 + 39.1297i 0.306090 + 0.0539719i
\(726\) 0 0
\(727\) 171.551 143.949i 0.235972 0.198004i −0.517132 0.855906i \(-0.673000\pi\)
0.753104 + 0.657902i \(0.228556\pi\)
\(728\) 0 0
\(729\) 177.744 + 706.999i 0.243820 + 0.969821i
\(730\) 0 0
\(731\) −154.758 184.434i −0.211708 0.252303i
\(732\) 0 0
\(733\) −47.7555 + 270.835i −0.0651508 + 0.369488i 0.934749 + 0.355309i \(0.115625\pi\)
−0.999899 + 0.0141788i \(0.995487\pi\)
\(734\) 0 0
\(735\) −30.2714 58.5194i −0.0411856 0.0796182i
\(736\) 0 0
\(737\) 1427.04 823.904i 1.93629 1.11792i
\(738\) 0 0
\(739\) 235.936 408.653i 0.319264 0.552981i −0.661071 0.750323i \(-0.729898\pi\)
0.980335 + 0.197343i \(0.0632311\pi\)
\(740\) 0 0
\(741\) 192.211 460.670i 0.259394 0.621686i
\(742\) 0 0
\(743\) −245.380 + 292.432i −0.330255 + 0.393583i −0.905464 0.424424i \(-0.860477\pi\)
0.575208 + 0.818007i \(0.304921\pi\)
\(744\) 0 0
\(745\) −136.423 49.6541i −0.183119 0.0666497i
\(746\) 0 0
\(747\) 346.894 + 1321.90i 0.464383 + 1.76961i
\(748\) 0 0
\(749\) 1165.93 205.585i 1.55665 0.274479i
\(750\) 0 0
\(751\) −1053.31 + 383.374i −1.40255 + 0.510485i −0.928933 0.370248i \(-0.879273\pi\)
−0.473613 + 0.880733i \(0.657051\pi\)
\(752\) 0 0
\(753\) 1244.04 388.716i 1.65212 0.516223i
\(754\) 0 0
\(755\) 482.765i 0.639424i
\(756\) 0 0
\(757\) 157.155 0.207602 0.103801 0.994598i \(-0.466899\pi\)
0.103801 + 0.994598i \(0.466899\pi\)
\(758\) 0 0
\(759\) −1089.87 + 1183.23i −1.43592 + 1.55893i
\(760\) 0 0
\(761\) −440.078 1209.11i −0.578290 1.58884i −0.791062 0.611736i \(-0.790472\pi\)
0.212773 0.977102i \(-0.431751\pi\)
\(762\) 0 0
\(763\) −174.706 990.806i −0.228972 1.29857i
\(764\) 0 0
\(765\) 43.7369 61.7810i 0.0571724 0.0807595i
\(766\) 0 0
\(767\) −95.7338 + 263.026i −0.124816 + 0.342929i
\(768\) 0 0
\(769\) −687.236 576.660i −0.893675 0.749882i 0.0752688 0.997163i \(-0.476019\pi\)
−0.968944 + 0.247281i \(0.920463\pi\)
\(770\) 0 0
\(771\) −387.432 + 295.700i −0.502506 + 0.383528i
\(772\) 0 0
\(773\) −211.789 122.276i −0.273983 0.158184i 0.356713 0.934214i \(-0.383897\pi\)
−0.630696 + 0.776030i \(0.717231\pi\)
\(774\) 0 0
\(775\) −365.910 633.774i −0.472141 0.817773i
\(776\) 0 0
\(777\) 514.693 + 329.768i 0.662411 + 0.424411i
\(778\) 0 0
\(779\) −284.618 50.1859i −0.365364 0.0644235i
\(780\) 0 0
\(781\) −940.641 + 789.292i −1.20441 + 1.01062i
\(782\) 0 0
\(783\) −10.7479 299.382i −0.0137265 0.382353i
\(784\)