Properties

Label 1078.2.i.d.901.4
Level $1078$
Weight $2$
Character 1078.901
Analytic conductor $8.608$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.i (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 901.4
Character \(\chi\) \(=\) 1078.901
Dual form 1078.2.i.d.1011.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(1.60021 - 0.923880i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.80322 - 1.61844i) q^{5} -1.84776 q^{6} -1.00000i q^{8} +(0.207107 - 0.358719i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(1.60021 - 0.923880i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.80322 - 1.61844i) q^{5} -1.84776 q^{6} -1.00000i q^{8} +(0.207107 - 0.358719i) q^{9} +(1.61844 + 2.80322i) q^{10} +(-1.23604 - 3.07769i) q^{11} +(1.60021 + 0.923880i) q^{12} -6.10838 q^{13} -5.98098 q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.06577 + 7.04213i) q^{17} +(-0.358719 + 0.207107i) q^{18} +(-3.30769 + 5.72908i) q^{19} -3.23688i q^{20} +(-0.468406 + 3.28338i) q^{22} +(2.65291 - 4.59498i) q^{23} +(-0.923880 - 1.60021i) q^{24} +(2.73870 + 4.74357i) q^{25} +(5.29001 + 3.05419i) q^{26} +4.77791i q^{27} +1.32485i q^{29} +(5.17968 + 2.99049i) q^{30} +(2.03928 - 1.17738i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-4.82134 - 3.78300i) q^{33} -8.13155i q^{34} +0.414214 q^{36} +(-2.64340 + 4.57851i) q^{37} +(5.72908 - 3.30769i) q^{38} +(-9.77466 + 5.64340i) q^{39} +(-1.61844 + 2.80322i) q^{40} +1.22400 q^{41} -3.73834i q^{43} +(2.04734 - 2.60929i) q^{44} +(-1.16113 + 0.670380i) q^{45} +(-4.59498 + 2.65291i) q^{46} +(-1.47757 - 0.853074i) q^{47} +1.84776i q^{48} -5.47740i q^{50} +(13.0122 + 7.51257i) q^{51} +(-3.05419 - 5.29001i) q^{52} +(1.99049 + 3.44763i) q^{53} +(2.38896 - 4.13779i) q^{54} +(-1.51617 + 10.6279i) q^{55} +12.2236i q^{57} +(0.662426 - 1.14736i) q^{58} +(-7.82759 + 4.51926i) q^{59} +(-2.99049 - 5.17968i) q^{60} +(-4.27819 + 7.41004i) q^{61} -2.35476 q^{62} -1.00000 q^{64} +(17.1231 + 9.88604i) q^{65} +(2.28390 + 5.68684i) q^{66} +(-1.17551 - 2.03605i) q^{67} +(-4.06577 + 7.04213i) q^{68} -9.80389i q^{69} -7.17945 q^{71} +(-0.358719 - 0.207107i) q^{72} +(-5.49637 - 9.52000i) q^{73} +(4.57851 - 2.64340i) q^{74} +(8.76497 + 5.06046i) q^{75} -6.61537 q^{76} +11.2868 q^{78} +(-7.34847 - 4.24264i) q^{79} +(2.80322 - 1.61844i) q^{80} +(5.03553 + 8.72180i) q^{81} +(-1.06002 - 0.612002i) q^{82} -5.60138 q^{83} -26.3209i q^{85} +(-1.86917 + 3.23749i) q^{86} +(1.22400 + 2.12004i) q^{87} +(-3.07769 + 1.23604i) q^{88} +(4.03668 + 2.33058i) q^{89} +1.34076 q^{90} +5.30583 q^{92} +(2.17551 - 3.76810i) q^{93} +(0.853074 + 1.47757i) q^{94} +(18.5444 - 10.7066i) q^{95} +(0.923880 - 1.60021i) q^{96} +3.82683i q^{97} +(-1.36002 - 0.194020i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{4} - 16 q^{9} + O(q^{10}) \) \( 32 q + 16 q^{4} - 16 q^{9} - 16 q^{11} - 16 q^{16} - 16 q^{22} + 16 q^{23} + 64 q^{25} - 32 q^{36} + 80 q^{37} + 16 q^{44} - 32 q^{53} + 48 q^{58} - 32 q^{64} - 16 q^{67} - 96 q^{71} + 32 q^{78} + 48 q^{81} - 32 q^{86} - 8 q^{88} + 32 q^{92} + 48 q^{93} + 48 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 1.60021 0.923880i 0.923880 0.533402i 0.0390089 0.999239i \(-0.487580\pi\)
0.884871 + 0.465837i \(0.154247\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −2.80322 1.61844i −1.25364 0.723789i −0.281809 0.959471i \(-0.590934\pi\)
−0.971830 + 0.235682i \(0.924268\pi\)
\(6\) −1.84776 −0.754344
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0.207107 0.358719i 0.0690356 0.119573i
\(10\) 1.61844 + 2.80322i 0.511796 + 0.886457i
\(11\) −1.23604 3.07769i −0.372680 0.927960i
\(12\) 1.60021 + 0.923880i 0.461940 + 0.266701i
\(13\) −6.10838 −1.69416 −0.847079 0.531467i \(-0.821641\pi\)
−0.847079 + 0.531467i \(0.821641\pi\)
\(14\) 0 0
\(15\) −5.98098 −1.54428
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 4.06577 + 7.04213i 0.986095 + 1.70797i 0.636965 + 0.770892i \(0.280189\pi\)
0.349130 + 0.937074i \(0.386477\pi\)
\(18\) −0.358719 + 0.207107i −0.0845510 + 0.0488155i
\(19\) −3.30769 + 5.72908i −0.758835 + 1.31434i 0.184609 + 0.982812i \(0.440898\pi\)
−0.943445 + 0.331530i \(0.892435\pi\)
\(20\) 3.23688i 0.723789i
\(21\) 0 0
\(22\) −0.468406 + 3.28338i −0.0998645 + 0.700019i
\(23\) 2.65291 4.59498i 0.553171 0.958120i −0.444872 0.895594i \(-0.646751\pi\)
0.998043 0.0625262i \(-0.0199157\pi\)
\(24\) −0.923880 1.60021i −0.188586 0.326641i
\(25\) 2.73870 + 4.74357i 0.547740 + 0.948714i
\(26\) 5.29001 + 3.05419i 1.03746 + 0.598975i
\(27\) 4.77791i 0.919509i
\(28\) 0 0
\(29\) 1.32485i 0.246019i 0.992406 + 0.123009i \(0.0392545\pi\)
−0.992406 + 0.123009i \(0.960745\pi\)
\(30\) 5.17968 + 2.99049i 0.945676 + 0.545986i
\(31\) 2.03928 1.17738i 0.366266 0.211464i −0.305560 0.952173i \(-0.598844\pi\)
0.671826 + 0.740709i \(0.265510\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) −4.82134 3.78300i −0.839287 0.658535i
\(34\) 8.13155i 1.39455i
\(35\) 0 0
\(36\) 0.414214 0.0690356
\(37\) −2.64340 + 4.57851i −0.434573 + 0.752702i −0.997261 0.0739673i \(-0.976434\pi\)
0.562688 + 0.826669i \(0.309767\pi\)
\(38\) 5.72908 3.30769i 0.929380 0.536578i
\(39\) −9.77466 + 5.64340i −1.56520 + 0.903668i
\(40\) −1.61844 + 2.80322i −0.255898 + 0.443228i
\(41\) 1.22400 0.191157 0.0955786 0.995422i \(-0.469530\pi\)
0.0955786 + 0.995422i \(0.469530\pi\)
\(42\) 0 0
\(43\) 3.73834i 0.570091i −0.958514 0.285045i \(-0.907991\pi\)
0.958514 0.285045i \(-0.0920087\pi\)
\(44\) 2.04734 2.60929i 0.308648 0.393365i
\(45\) −1.16113 + 0.670380i −0.173091 + 0.0999344i
\(46\) −4.59498 + 2.65291i −0.677493 + 0.391151i
\(47\) −1.47757 0.853074i −0.215525 0.124434i 0.388351 0.921511i \(-0.373045\pi\)
−0.603877 + 0.797078i \(0.706378\pi\)
\(48\) 1.84776i 0.266701i
\(49\) 0 0
\(50\) 5.47740i 0.774622i
\(51\) 13.0122 + 7.51257i 1.82207 + 1.05197i
\(52\) −3.05419 5.29001i −0.423540 0.733592i
\(53\) 1.99049 + 3.44763i 0.273415 + 0.473568i 0.969734 0.244164i \(-0.0785136\pi\)
−0.696319 + 0.717732i \(0.745180\pi\)
\(54\) 2.38896 4.13779i 0.325096 0.563082i
\(55\) −1.51617 + 10.6279i −0.204441 + 1.43307i
\(56\) 0 0
\(57\) 12.2236i 1.61906i
\(58\) 0.662426 1.14736i 0.0869808 0.150655i
\(59\) −7.82759 + 4.51926i −1.01907 + 0.588358i −0.913833 0.406090i \(-0.866892\pi\)
−0.105233 + 0.994448i \(0.533559\pi\)
\(60\) −2.99049 5.17968i −0.386070 0.668694i
\(61\) −4.27819 + 7.41004i −0.547766 + 0.948759i 0.450661 + 0.892695i \(0.351188\pi\)
−0.998427 + 0.0560638i \(0.982145\pi\)
\(62\) −2.35476 −0.299055
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 17.1231 + 9.88604i 2.12386 + 1.22621i
\(66\) 2.28390 + 5.68684i 0.281129 + 0.700001i
\(67\) −1.17551 2.03605i −0.143612 0.248743i 0.785242 0.619188i \(-0.212538\pi\)
−0.928854 + 0.370446i \(0.879205\pi\)
\(68\) −4.06577 + 7.04213i −0.493048 + 0.853983i
\(69\) 9.80389i 1.18025i
\(70\) 0 0
\(71\) −7.17945 −0.852044 −0.426022 0.904713i \(-0.640085\pi\)
−0.426022 + 0.904713i \(0.640085\pi\)
\(72\) −0.358719 0.207107i −0.0422755 0.0244078i
\(73\) −5.49637 9.52000i −0.643302 1.11423i −0.984691 0.174309i \(-0.944231\pi\)
0.341389 0.939922i \(-0.389103\pi\)
\(74\) 4.57851 2.64340i 0.532241 0.307289i
\(75\) 8.76497 + 5.06046i 1.01209 + 0.584332i
\(76\) −6.61537 −0.758835
\(77\) 0 0
\(78\) 11.2868 1.27798
\(79\) −7.34847 4.24264i −0.826767 0.477334i 0.0259772 0.999663i \(-0.491730\pi\)
−0.852745 + 0.522328i \(0.825064\pi\)
\(80\) 2.80322 1.61844i 0.313410 0.180947i
\(81\) 5.03553 + 8.72180i 0.559504 + 0.969089i
\(82\) −1.06002 0.612002i −0.117059 0.0675843i
\(83\) −5.60138 −0.614831 −0.307415 0.951575i \(-0.599464\pi\)
−0.307415 + 0.951575i \(0.599464\pi\)
\(84\) 0 0
\(85\) 26.3209i 2.85490i
\(86\) −1.86917 + 3.23749i −0.201558 + 0.349108i
\(87\) 1.22400 + 2.12004i 0.131227 + 0.227292i
\(88\) −3.07769 + 1.23604i −0.328083 + 0.131762i
\(89\) 4.03668 + 2.33058i 0.427887 + 0.247041i 0.698446 0.715663i \(-0.253875\pi\)
−0.270559 + 0.962703i \(0.587209\pi\)
\(90\) 1.34076 0.141329
\(91\) 0 0
\(92\) 5.30583 0.553171
\(93\) 2.17551 3.76810i 0.225590 0.390734i
\(94\) 0.853074 + 1.47757i 0.0879879 + 0.152399i
\(95\) 18.5444 10.7066i 1.90261 1.09847i
\(96\) 0.923880 1.60021i 0.0942931 0.163320i
\(97\) 3.82683i 0.388556i 0.980946 + 0.194278i \(0.0622364\pi\)
−0.980946 + 0.194278i \(0.937764\pi\)
\(98\) 0 0
\(99\) −1.36002 0.194020i −0.136687 0.0194997i
\(100\) −2.73870 + 4.74357i −0.273870 + 0.474357i
\(101\) 1.83018 + 3.16997i 0.182110 + 0.315424i 0.942599 0.333927i \(-0.108374\pi\)
−0.760489 + 0.649351i \(0.775041\pi\)
\(102\) −7.51257 13.0122i −0.743855 1.28840i
\(103\) −12.6193 7.28575i −1.24342 0.717887i −0.273628 0.961836i \(-0.588224\pi\)
−0.969788 + 0.243949i \(0.921557\pi\)
\(104\) 6.10838i 0.598975i
\(105\) 0 0
\(106\) 3.98098i 0.386667i
\(107\) −6.81876 3.93681i −0.659194 0.380586i 0.132776 0.991146i \(-0.457611\pi\)
−0.791970 + 0.610560i \(0.790944\pi\)
\(108\) −4.13779 + 2.38896i −0.398159 + 0.229877i
\(109\) 5.19615 3.00000i 0.497701 0.287348i −0.230063 0.973176i \(-0.573893\pi\)
0.727764 + 0.685828i \(0.240560\pi\)
\(110\) 6.62700 8.44596i 0.631860 0.805291i
\(111\) 9.76874i 0.927208i
\(112\) 0 0
\(113\) 13.5216 1.27200 0.636001 0.771688i \(-0.280587\pi\)
0.636001 + 0.771688i \(0.280587\pi\)
\(114\) 6.11181 10.5860i 0.572423 0.991466i
\(115\) −14.8734 + 8.58717i −1.38695 + 0.800758i
\(116\) −1.14736 + 0.662426i −0.106529 + 0.0615047i
\(117\) −1.26509 + 2.19119i −0.116957 + 0.202576i
\(118\) 9.03853 0.832064
\(119\) 0 0
\(120\) 5.98098i 0.545986i
\(121\) −7.94441 + 7.60831i −0.722219 + 0.691664i
\(122\) 7.41004 4.27819i 0.670874 0.387329i
\(123\) 1.95866 1.13083i 0.176606 0.101964i
\(124\) 2.03928 + 1.17738i 0.183133 + 0.105732i
\(125\) 1.54529i 0.138215i
\(126\) 0 0
\(127\) 8.63710i 0.766419i 0.923661 + 0.383209i \(0.125181\pi\)
−0.923661 + 0.383209i \(0.874819\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) −3.45377 5.98211i −0.304088 0.526695i
\(130\) −9.88604 17.1231i −0.867063 1.50180i
\(131\) 3.10109 5.37125i 0.270944 0.469288i −0.698160 0.715942i \(-0.745998\pi\)
0.969104 + 0.246654i \(0.0793310\pi\)
\(132\) 0.865501 6.06690i 0.0753322 0.528056i
\(133\) 0 0
\(134\) 2.35103i 0.203098i
\(135\) 7.73276 13.3935i 0.665530 1.15273i
\(136\) 7.04213 4.06577i 0.603857 0.348637i
\(137\) 4.51257 + 7.81600i 0.385535 + 0.667766i 0.991843 0.127464i \(-0.0406836\pi\)
−0.606308 + 0.795230i \(0.707350\pi\)
\(138\) −4.90195 + 8.49042i −0.417281 + 0.722753i
\(139\) −8.34638 −0.707930 −0.353965 0.935259i \(-0.615167\pi\)
−0.353965 + 0.935259i \(0.615167\pi\)
\(140\) 0 0
\(141\) −3.15255 −0.265493
\(142\) 6.21759 + 3.58973i 0.521768 + 0.301243i
\(143\) 7.55019 + 18.7997i 0.631379 + 1.57211i
\(144\) 0.207107 + 0.358719i 0.0172589 + 0.0298933i
\(145\) 2.14419 3.71385i 0.178066 0.308419i
\(146\) 10.9927i 0.909766i
\(147\) 0 0
\(148\) −5.28681 −0.434573
\(149\) −18.4020 10.6244i −1.50755 0.870383i −0.999961 0.00878227i \(-0.997204\pi\)
−0.507586 0.861601i \(-0.669462\pi\)
\(150\) −5.06046 8.76497i −0.413185 0.715657i
\(151\) −14.4411 + 8.33757i −1.17520 + 0.678502i −0.954899 0.296930i \(-0.904037\pi\)
−0.220301 + 0.975432i \(0.570704\pi\)
\(152\) 5.72908 + 3.30769i 0.464690 + 0.268289i
\(153\) 3.36820 0.272303
\(154\) 0 0
\(155\) −7.62207 −0.612220
\(156\) −9.77466 5.64340i −0.782599 0.451834i
\(157\) −10.8335 + 6.25474i −0.864610 + 0.499183i −0.865553 0.500817i \(-0.833033\pi\)
0.000943620 1.00000i \(0.499700\pi\)
\(158\) 4.24264 + 7.34847i 0.337526 + 0.584613i
\(159\) 6.37038 + 3.67794i 0.505204 + 0.291680i
\(160\) −3.23688 −0.255898
\(161\) 0 0
\(162\) 10.0711i 0.791258i
\(163\) −4.19796 + 7.27108i −0.328810 + 0.569515i −0.982276 0.187441i \(-0.939981\pi\)
0.653466 + 0.756956i \(0.273314\pi\)
\(164\) 0.612002 + 1.06002i 0.0477893 + 0.0827735i
\(165\) 7.39272 + 18.4076i 0.575523 + 1.43303i
\(166\) 4.85093 + 2.80069i 0.376506 + 0.217376i
\(167\) 4.04635 0.313116 0.156558 0.987669i \(-0.449960\pi\)
0.156558 + 0.987669i \(0.449960\pi\)
\(168\) 0 0
\(169\) 24.3123 1.87017
\(170\) −13.1604 + 22.7945i −1.00936 + 1.74826i
\(171\) 1.37009 + 2.37306i 0.104773 + 0.181473i
\(172\) 3.23749 1.86917i 0.246857 0.142523i
\(173\) −1.53801 + 2.66392i −0.116933 + 0.202534i −0.918551 0.395303i \(-0.870640\pi\)
0.801618 + 0.597837i \(0.203973\pi\)
\(174\) 2.44801i 0.185583i
\(175\) 0 0
\(176\) 3.28338 + 0.468406i 0.247494 + 0.0353074i
\(177\) −8.35051 + 14.4635i −0.627663 + 1.08714i
\(178\) −2.33058 4.03668i −0.174684 0.302562i
\(179\) 5.73276 + 9.92944i 0.428487 + 0.742161i 0.996739 0.0806934i \(-0.0257135\pi\)
−0.568252 + 0.822855i \(0.692380\pi\)
\(180\) −1.16113 0.670380i −0.0865457 0.0499672i
\(181\) 13.2743i 0.986670i −0.869839 0.493335i \(-0.835778\pi\)
0.869839 0.493335i \(-0.164222\pi\)
\(182\) 0 0
\(183\) 15.8101i 1.16872i
\(184\) −4.59498 2.65291i −0.338747 0.195575i
\(185\) 14.8201 8.55638i 1.08959 0.629078i
\(186\) −3.76810 + 2.17551i −0.276290 + 0.159516i
\(187\) 16.6481 21.2176i 1.21743 1.55158i
\(188\) 1.70615i 0.124434i
\(189\) 0 0
\(190\) −21.4132 −1.55348
\(191\) 6.10735 10.5782i 0.441913 0.765415i −0.555919 0.831237i \(-0.687633\pi\)
0.997831 + 0.0658215i \(0.0209668\pi\)
\(192\) −1.60021 + 0.923880i −0.115485 + 0.0666753i
\(193\) −4.38485 + 2.53159i −0.315628 + 0.182228i −0.649442 0.760411i \(-0.724998\pi\)
0.333814 + 0.942639i \(0.391664\pi\)
\(194\) 1.91342 3.31414i 0.137375 0.237941i
\(195\) 36.5341 2.61626
\(196\) 0 0
\(197\) 20.0883i 1.43123i 0.698493 + 0.715617i \(0.253854\pi\)
−0.698493 + 0.715617i \(0.746146\pi\)
\(198\) 1.08080 + 0.848037i 0.0768093 + 0.0602674i
\(199\) 12.8341 7.40979i 0.909788 0.525266i 0.0294248 0.999567i \(-0.490632\pi\)
0.880363 + 0.474301i \(0.157299\pi\)
\(200\) 4.74357 2.73870i 0.335421 0.193655i
\(201\) −3.76213 2.17206i −0.265360 0.153206i
\(202\) 3.66037i 0.257543i
\(203\) 0 0
\(204\) 15.0251i 1.05197i
\(205\) −3.43115 1.98098i −0.239642 0.138357i
\(206\) 7.28575 + 12.6193i 0.507623 + 0.879228i
\(207\) −1.09887 1.90330i −0.0763770 0.132289i
\(208\) 3.05419 5.29001i 0.211770 0.366796i
\(209\) 21.7208 + 3.09868i 1.50246 + 0.214340i
\(210\) 0 0
\(211\) 9.19848i 0.633249i 0.948551 + 0.316625i \(0.102550\pi\)
−0.948551 + 0.316625i \(0.897450\pi\)
\(212\) −1.99049 + 3.44763i −0.136707 + 0.236784i
\(213\) −11.4886 + 6.63295i −0.787186 + 0.454482i
\(214\) 3.93681 + 6.81876i 0.269115 + 0.466121i
\(215\) −6.05028 + 10.4794i −0.412625 + 0.714688i
\(216\) 4.77791 0.325096
\(217\) 0 0
\(218\) −6.00000 −0.406371
\(219\) −17.5907 10.1560i −1.18867 0.686277i
\(220\) −9.96213 + 4.00091i −0.671647 + 0.269742i
\(221\) −24.8353 43.0160i −1.67060 2.89357i
\(222\) 4.88437 8.45998i 0.327818 0.567797i
\(223\) 10.8760i 0.728310i −0.931338 0.364155i \(-0.881358\pi\)
0.931338 0.364155i \(-0.118642\pi\)
\(224\) 0 0
\(225\) 2.26881 0.151254
\(226\) −11.7100 6.76078i −0.778939 0.449721i
\(227\) −11.7396 20.3337i −0.779187 1.34959i −0.932411 0.361400i \(-0.882299\pi\)
0.153224 0.988192i \(-0.451035\pi\)
\(228\) −10.5860 + 6.11181i −0.701073 + 0.404764i
\(229\) −19.7715 11.4151i −1.30653 0.754328i −0.325018 0.945708i \(-0.605370\pi\)
−0.981516 + 0.191380i \(0.938704\pi\)
\(230\) 17.1743 1.13244
\(231\) 0 0
\(232\) 1.32485 0.0869808
\(233\) −12.7383 7.35445i −0.834512 0.481806i 0.0208827 0.999782i \(-0.493352\pi\)
−0.855395 + 0.517976i \(0.826686\pi\)
\(234\) 2.19119 1.26509i 0.143243 0.0827013i
\(235\) 2.76130 + 4.78271i 0.180127 + 0.311990i
\(236\) −7.82759 4.51926i −0.509533 0.294179i
\(237\) −15.6788 −1.01844
\(238\) 0 0
\(239\) 22.4218i 1.45035i −0.688567 0.725173i \(-0.741760\pi\)
0.688567 0.725173i \(-0.258240\pi\)
\(240\) 2.99049 5.17968i 0.193035 0.334347i
\(241\) 7.73437 + 13.3963i 0.498215 + 0.862933i 0.999998 0.00206005i \(-0.000655735\pi\)
−0.501783 + 0.864994i \(0.667322\pi\)
\(242\) 10.6842 2.61678i 0.686807 0.168213i
\(243\) 3.70241 + 2.13759i 0.237510 + 0.137126i
\(244\) −8.55638 −0.547766
\(245\) 0 0
\(246\) −2.26166 −0.144198
\(247\) 20.2046 34.9954i 1.28559 2.22670i
\(248\) −1.17738 2.03928i −0.0747636 0.129494i
\(249\) −8.96336 + 5.17500i −0.568030 + 0.327952i
\(250\) −0.772647 + 1.33826i −0.0488665 + 0.0846392i
\(251\) 4.87408i 0.307649i 0.988098 + 0.153825i \(0.0491590\pi\)
−0.988098 + 0.153825i \(0.950841\pi\)
\(252\) 0 0
\(253\) −17.4211 2.48528i −1.09525 0.156248i
\(254\) 4.31855 7.47995i 0.270970 0.469334i
\(255\) −24.3173 42.1188i −1.52281 2.63758i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −17.1250 9.88713i −1.06823 0.616742i −0.140532 0.990076i \(-0.544881\pi\)
−0.927697 + 0.373334i \(0.878214\pi\)
\(258\) 6.90755i 0.430045i
\(259\) 0 0
\(260\) 19.7721i 1.22621i
\(261\) 0.475250 + 0.274386i 0.0294172 + 0.0169841i
\(262\) −5.37125 + 3.10109i −0.331837 + 0.191586i
\(263\) 7.34847 4.24264i 0.453126 0.261612i −0.256023 0.966671i \(-0.582412\pi\)
0.709150 + 0.705058i \(0.249079\pi\)
\(264\) −3.78300 + 4.82134i −0.232827 + 0.296733i
\(265\) 12.8860i 0.791578i
\(266\) 0 0
\(267\) 8.61269 0.527088
\(268\) 1.17551 2.03605i 0.0718059 0.124371i
\(269\) 6.40809 3.69971i 0.390708 0.225575i −0.291759 0.956492i \(-0.594240\pi\)
0.682467 + 0.730916i \(0.260907\pi\)
\(270\) −13.3935 + 7.73276i −0.815105 + 0.470601i
\(271\) 7.18047 12.4369i 0.436183 0.755491i −0.561209 0.827674i \(-0.689663\pi\)
0.997391 + 0.0721838i \(0.0229968\pi\)
\(272\) −8.13155 −0.493048
\(273\) 0 0
\(274\) 9.02514i 0.545229i
\(275\) 11.2141 14.2921i 0.676237 0.861848i
\(276\) 8.49042 4.90195i 0.511063 0.295063i
\(277\) 1.89648 1.09493i 0.113948 0.0657882i −0.441943 0.897043i \(-0.645711\pi\)
0.555891 + 0.831255i \(0.312377\pi\)
\(278\) 7.22817 + 4.17319i 0.433517 + 0.250291i
\(279\) 0.975373i 0.0583940i
\(280\) 0 0
\(281\) 25.7003i 1.53315i −0.642154 0.766575i \(-0.721959\pi\)
0.642154 0.766575i \(-0.278041\pi\)
\(282\) 2.73019 + 1.57628i 0.162580 + 0.0938658i
\(283\) 7.77887 + 13.4734i 0.462406 + 0.800910i 0.999080 0.0428792i \(-0.0136531\pi\)
−0.536675 + 0.843789i \(0.680320\pi\)
\(284\) −3.58973 6.21759i −0.213011 0.368946i
\(285\) 19.7832 34.2655i 1.17186 2.02971i
\(286\) 2.86120 20.0561i 0.169186 1.18594i
\(287\) 0 0
\(288\) 0.414214i 0.0244078i
\(289\) −24.5610 + 42.5410i −1.44477 + 2.50241i
\(290\) −3.71385 + 2.14419i −0.218085 + 0.125911i
\(291\) 3.53553 + 6.12372i 0.207257 + 0.358979i
\(292\) 5.49637 9.52000i 0.321651 0.557116i
\(293\) 3.11451 0.181952 0.0909759 0.995853i \(-0.471001\pi\)
0.0909759 + 0.995853i \(0.471001\pi\)
\(294\) 0 0
\(295\) 29.2566 1.70339
\(296\) 4.57851 + 2.64340i 0.266120 + 0.153645i
\(297\) 14.7050 5.90569i 0.853268 0.342683i
\(298\) 10.6244 + 18.4020i 0.615454 + 1.06600i
\(299\) −16.2050 + 28.0679i −0.937159 + 1.62321i
\(300\) 10.1209i 0.584332i
\(301\) 0 0
\(302\) 16.6751 0.959547
\(303\) 5.85734 + 3.38174i 0.336496 + 0.194276i
\(304\) −3.30769 5.72908i −0.189709 0.328585i
\(305\) 23.9854 13.8480i 1.37340 0.792934i
\(306\) −2.91694 1.68410i −0.166751 0.0962735i
\(307\) −8.93072 −0.509703 −0.254852 0.966980i \(-0.582027\pi\)
−0.254852 + 0.966980i \(0.582027\pi\)
\(308\) 0 0
\(309\) −26.9246 −1.53169
\(310\) 6.60091 + 3.81104i 0.374906 + 0.216452i
\(311\) 16.5710 9.56730i 0.939658 0.542512i 0.0498046 0.998759i \(-0.484140\pi\)
0.889853 + 0.456247i \(0.150807\pi\)
\(312\) 5.64340 + 9.77466i 0.319495 + 0.553381i
\(313\) −1.02066 0.589279i −0.0576912 0.0333080i 0.470877 0.882199i \(-0.343938\pi\)
−0.528568 + 0.848891i \(0.677271\pi\)
\(314\) 12.5095 0.705951
\(315\) 0 0
\(316\) 8.48528i 0.477334i
\(317\) 4.54847 7.87818i 0.255468 0.442483i −0.709555 0.704650i \(-0.751104\pi\)
0.965022 + 0.262167i \(0.0844373\pi\)
\(318\) −3.67794 6.37038i −0.206249 0.357233i
\(319\) 4.07749 1.63757i 0.228296 0.0916863i
\(320\) 2.80322 + 1.61844i 0.156705 + 0.0904736i
\(321\) −14.5486 −0.812021
\(322\) 0 0
\(323\) −53.7932 −2.99314
\(324\) −5.03553 + 8.72180i −0.279752 + 0.484544i
\(325\) −16.7290 28.9755i −0.927959 1.60727i
\(326\) 7.27108 4.19796i 0.402708 0.232503i
\(327\) 5.54328 9.60124i 0.306544 0.530950i
\(328\) 1.22400i 0.0675843i
\(329\) 0 0
\(330\) 2.80152 19.6378i 0.154219 1.08103i
\(331\) −1.36486 + 2.36401i −0.0750197 + 0.129938i −0.901095 0.433622i \(-0.857235\pi\)
0.826075 + 0.563560i \(0.190569\pi\)
\(332\) −2.80069 4.85093i −0.153708 0.266230i
\(333\) 1.09493 + 1.89648i 0.0600020 + 0.103926i
\(334\) −3.50424 2.02317i −0.191743 0.110703i
\(335\) 7.60999i 0.415778i
\(336\) 0 0
\(337\) 20.3209i 1.10695i 0.832867 + 0.553474i \(0.186698\pi\)
−0.832867 + 0.553474i \(0.813302\pi\)
\(338\) −21.0550 12.1561i −1.14524 0.661206i
\(339\) 21.6373 12.4923i 1.17518 0.678489i
\(340\) 22.7945 13.1604i 1.23621 0.713725i
\(341\) −6.14424 4.82100i −0.332729 0.261072i
\(342\) 2.74018i 0.148172i
\(343\) 0 0
\(344\) −3.73834 −0.201558
\(345\) −15.8670 + 27.4825i −0.854252 + 1.47961i
\(346\) 2.66392 1.53801i 0.143213 0.0826841i
\(347\) 21.1642 12.2192i 1.13615 0.655959i 0.190679 0.981652i \(-0.438931\pi\)
0.945475 + 0.325693i \(0.105598\pi\)
\(348\) −1.22400 + 2.12004i −0.0656135 + 0.113646i
\(349\) 3.07603 0.164656 0.0823280 0.996605i \(-0.473764\pi\)
0.0823280 + 0.996605i \(0.473764\pi\)
\(350\) 0 0
\(351\) 29.1853i 1.55779i
\(352\) −2.60929 2.04734i −0.139076 0.109124i
\(353\) −29.2196 + 16.8700i −1.55520 + 0.897897i −0.557499 + 0.830178i \(0.688239\pi\)
−0.997704 + 0.0677191i \(0.978428\pi\)
\(354\) 14.4635 8.35051i 0.768727 0.443825i
\(355\) 20.1256 + 11.6195i 1.06816 + 0.616700i
\(356\) 4.66115i 0.247041i
\(357\) 0 0
\(358\) 11.4655i 0.605972i
\(359\) −25.8928 14.9492i −1.36657 0.788990i −0.376083 0.926586i \(-0.622729\pi\)
−0.990488 + 0.137596i \(0.956063\pi\)
\(360\) 0.670380 + 1.16113i 0.0353321 + 0.0611971i
\(361\) −12.3816 21.4455i −0.651663 1.12871i
\(362\) −6.63714 + 11.4959i −0.348841 + 0.604210i
\(363\) −5.68354 + 19.5145i −0.298309 + 1.02425i
\(364\) 0 0
\(365\) 35.5822i 1.86246i
\(366\) 7.90507 13.6920i 0.413204 0.715691i
\(367\) −3.07894 + 1.77763i −0.160719 + 0.0927914i −0.578202 0.815893i \(-0.696246\pi\)
0.417483 + 0.908685i \(0.362912\pi\)
\(368\) 2.65291 + 4.59498i 0.138293 + 0.239530i
\(369\) 0.253499 0.439074i 0.0131967 0.0228573i
\(370\) −17.1128 −0.889650
\(371\) 0 0
\(372\) 4.35103 0.225590
\(373\) 18.2705 + 10.5485i 0.946010 + 0.546179i 0.891839 0.452353i \(-0.149415\pi\)
0.0541707 + 0.998532i \(0.482748\pi\)
\(374\) −25.0264 + 10.0509i −1.29409 + 0.519720i
\(375\) −1.42766 2.47279i −0.0737243 0.127694i
\(376\) −0.853074 + 1.47757i −0.0439939 + 0.0761997i
\(377\) 8.09269i 0.416795i
\(378\) 0 0
\(379\) 8.61063 0.442298 0.221149 0.975240i \(-0.429019\pi\)
0.221149 + 0.975240i \(0.429019\pi\)
\(380\) 18.5444 + 10.7066i 0.951306 + 0.549237i
\(381\) 7.97964 + 13.8211i 0.408809 + 0.708079i
\(382\) −10.5782 + 6.10735i −0.541230 + 0.312479i
\(383\) 29.6432 + 17.1145i 1.51470 + 0.874510i 0.999852 + 0.0172267i \(0.00548369\pi\)
0.514845 + 0.857284i \(0.327850\pi\)
\(384\) 1.84776 0.0942931
\(385\) 0 0
\(386\) 5.06319 0.257709
\(387\) −1.34101 0.774235i −0.0681676 0.0393566i
\(388\) −3.31414 + 1.91342i −0.168250 + 0.0971390i
\(389\) −11.4126 19.7672i −0.578641 1.00224i −0.995636 0.0933265i \(-0.970250\pi\)
0.416995 0.908909i \(-0.363083\pi\)
\(390\) −31.6394 18.2670i −1.60212 0.924987i
\(391\) 43.1446 2.18192
\(392\) 0 0
\(393\) 11.4601i 0.578088i
\(394\) 10.0442 17.3970i 0.506018 0.876448i
\(395\) 13.7329 + 23.7861i 0.690978 + 1.19681i
\(396\) −0.511984 1.27482i −0.0257282 0.0640623i
\(397\) 10.9477 + 6.32068i 0.549451 + 0.317226i 0.748901 0.662682i \(-0.230582\pi\)
−0.199450 + 0.979908i \(0.563915\pi\)
\(398\) −14.8196 −0.742839
\(399\) 0 0
\(400\) −5.47740 −0.273870
\(401\) 2.60875 4.51849i 0.130275 0.225642i −0.793508 0.608560i \(-0.791747\pi\)
0.923782 + 0.382918i \(0.125081\pi\)
\(402\) 2.17206 + 3.76213i 0.108333 + 0.187638i
\(403\) −12.4567 + 7.19187i −0.620512 + 0.358253i
\(404\) −1.83018 + 3.16997i −0.0910551 + 0.157712i
\(405\) 32.5989i 1.61985i
\(406\) 0 0
\(407\) 17.3586 + 2.47637i 0.860434 + 0.122749i
\(408\) 7.51257 13.0122i 0.371928 0.644198i
\(409\) −10.1741 17.6221i −0.503079 0.871359i −0.999994 0.00355936i \(-0.998867\pi\)
0.496914 0.867800i \(-0.334466\pi\)
\(410\) 1.98098 + 3.43115i 0.0978335 + 0.169453i
\(411\) 14.4421 + 8.33814i 0.712376 + 0.411290i
\(412\) 14.5715i 0.717887i
\(413\) 0 0
\(414\) 2.19775i 0.108013i
\(415\) 15.7019 + 9.06550i 0.770776 + 0.445008i
\(416\) −5.29001 + 3.05419i −0.259364 + 0.149744i
\(417\) −13.3559 + 7.71105i −0.654042 + 0.377612i
\(418\) −17.2614 13.5439i −0.844284 0.662456i
\(419\) 20.3391i 0.993631i −0.867856 0.496816i \(-0.834503\pi\)
0.867856 0.496816i \(-0.165497\pi\)
\(420\) 0 0
\(421\) −15.3327 −0.747272 −0.373636 0.927575i \(-0.621889\pi\)
−0.373636 + 0.927575i \(0.621889\pi\)
\(422\) 4.59924 7.96611i 0.223887 0.387784i
\(423\) −0.612028 + 0.353355i −0.0297578 + 0.0171807i
\(424\) 3.44763 1.99049i 0.167432 0.0966667i
\(425\) −22.2699 + 38.5726i −1.08025 + 1.87104i
\(426\) 13.2659 0.642735
\(427\) 0 0
\(428\) 7.87362i 0.380586i
\(429\) 29.4505 + 23.1080i 1.42189 + 1.11566i
\(430\) 10.4794 6.05028i 0.505361 0.291770i
\(431\) −1.87844 + 1.08452i −0.0904814 + 0.0522394i −0.544558 0.838723i \(-0.683303\pi\)
0.454077 + 0.890963i \(0.349969\pi\)
\(432\) −4.13779 2.38896i −0.199080 0.114939i
\(433\) 38.4356i 1.84710i 0.383479 + 0.923550i \(0.374726\pi\)
−0.383479 + 0.923550i \(0.625274\pi\)
\(434\) 0 0
\(435\) 7.92391i 0.379922i
\(436\) 5.19615 + 3.00000i 0.248851 + 0.143674i
\(437\) 17.5500 + 30.3975i 0.839531 + 1.45411i
\(438\) 10.1560 + 17.5907i 0.485271 + 0.840514i
\(439\) −2.86120 + 4.95574i −0.136558 + 0.236525i −0.926191 0.377054i \(-0.876937\pi\)
0.789634 + 0.613578i \(0.210271\pi\)
\(440\) 10.6279 + 1.51617i 0.506666 + 0.0722808i
\(441\) 0 0
\(442\) 49.6706i 2.36259i
\(443\) −3.59367 + 6.22441i −0.170740 + 0.295731i −0.938679 0.344793i \(-0.887949\pi\)
0.767939 + 0.640523i \(0.221283\pi\)
\(444\) −8.45998 + 4.88437i −0.401493 + 0.231802i
\(445\) −7.54380 13.0662i −0.357610 0.619399i
\(446\) −5.43800 + 9.41888i −0.257497 + 0.445997i
\(447\) −39.2626 −1.85706
\(448\) 0 0
\(449\) 8.63068 0.407307 0.203654 0.979043i \(-0.434718\pi\)
0.203654 + 0.979043i \(0.434718\pi\)
\(450\) −1.96485 1.13441i −0.0926239 0.0534765i
\(451\) −1.51292 3.76711i −0.0712405 0.177386i
\(452\) 6.76078 + 11.7100i 0.318001 + 0.550793i
\(453\) −15.4058 + 26.6837i −0.723829 + 1.25371i
\(454\) 23.4793i 1.10194i
\(455\) 0 0
\(456\) 12.2236 0.572423
\(457\) 24.6833 + 14.2509i 1.15464 + 0.666629i 0.950013 0.312211i \(-0.101070\pi\)
0.204623 + 0.978841i \(0.434403\pi\)
\(458\) 11.4151 + 19.7715i 0.533390 + 0.923859i
\(459\) −33.6467 + 19.4259i −1.57049 + 0.906724i
\(460\) −14.8734 8.58717i −0.693477 0.400379i
\(461\) 35.6022 1.65816 0.829080 0.559129i \(-0.188865\pi\)
0.829080 + 0.559129i \(0.188865\pi\)
\(462\) 0 0
\(463\) 32.2369 1.49818 0.749088 0.662471i \(-0.230492\pi\)
0.749088 + 0.662471i \(0.230492\pi\)
\(464\) −1.14736 0.662426i −0.0532646 0.0307524i
\(465\) −12.1969 + 7.04188i −0.565617 + 0.326559i
\(466\) 7.35445 + 12.7383i 0.340688 + 0.590089i
\(467\) 22.3972 + 12.9310i 1.03642 + 0.598376i 0.918817 0.394685i \(-0.129146\pi\)
0.117601 + 0.993061i \(0.462479\pi\)
\(468\) −2.53017 −0.116957
\(469\) 0 0
\(470\) 5.52260i 0.254738i
\(471\) −11.5573 + 20.0177i −0.532530 + 0.922369i
\(472\) 4.51926 + 7.82759i 0.208016 + 0.360294i
\(473\) −11.5055 + 4.62073i −0.529022 + 0.212461i
\(474\) 13.5782 + 7.83938i 0.623667 + 0.360075i
\(475\) −36.2351 −1.66258
\(476\) 0 0
\(477\) 1.64897 0.0755014
\(478\) −11.2109 + 19.4178i −0.512774 + 0.888151i
\(479\) −6.26028 10.8431i −0.286040 0.495435i 0.686821 0.726826i \(-0.259006\pi\)
−0.972861 + 0.231391i \(0.925672\pi\)
\(480\) −5.17968 + 2.99049i −0.236419 + 0.136497i
\(481\) 16.1469 27.9672i 0.736235 1.27520i
\(482\) 15.4687i 0.704582i
\(483\) 0 0
\(484\) −10.5612 3.07591i −0.480054 0.139814i
\(485\) 6.19350 10.7275i 0.281233 0.487109i
\(486\) −2.13759 3.70241i −0.0969630 0.167945i
\(487\) −10.3542 17.9341i −0.469195 0.812670i 0.530185 0.847882i \(-0.322123\pi\)
−0.999380 + 0.0352123i \(0.988789\pi\)
\(488\) 7.41004 + 4.27819i 0.335437 + 0.193665i
\(489\) 15.5136i 0.701551i
\(490\) 0 0
\(491\) 23.6712i 1.06826i 0.845401 + 0.534132i \(0.179362\pi\)
−0.845401 + 0.534132i \(0.820638\pi\)
\(492\) 1.95866 + 1.13083i 0.0883031 + 0.0509818i
\(493\) −9.32978 + 5.38655i −0.420192 + 0.242598i
\(494\) −34.9954 + 20.2046i −1.57452 + 0.909048i
\(495\) 3.49843 + 2.74500i 0.157243 + 0.123378i
\(496\) 2.35476i 0.105732i
\(497\) 0 0
\(498\) 10.3500 0.463794
\(499\) −5.80619 + 10.0566i −0.259921 + 0.450196i −0.966220 0.257717i \(-0.917030\pi\)
0.706300 + 0.707913i \(0.250363\pi\)
\(500\) 1.33826 0.772647i 0.0598489 0.0345538i
\(501\) 6.47499 3.73834i 0.289281 0.167017i
\(502\) 2.43704 4.22107i 0.108770 0.188396i
\(503\) −11.7871 −0.525561 −0.262780 0.964856i \(-0.584639\pi\)
−0.262780 + 0.964856i \(0.584639\pi\)
\(504\) 0 0
\(505\) 11.8482i 0.527237i
\(506\) 13.8444 + 10.8628i 0.615461 + 0.482912i
\(507\) 38.9046 22.4616i 1.72781 0.997554i
\(508\) −7.47995 + 4.31855i −0.331869 + 0.191605i
\(509\) −0.783816 0.452537i −0.0347421 0.0200583i 0.482528 0.875880i \(-0.339719\pi\)
−0.517270 + 0.855822i \(0.673052\pi\)
\(510\) 48.6346i 2.15358i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) −27.3730 15.8038i −1.20855 0.697756i
\(514\) 9.88713 + 17.1250i 0.436102 + 0.755352i
\(515\) 23.5831 + 40.8472i 1.03920 + 1.79994i
\(516\) 3.45377 5.98211i 0.152044 0.263348i
\(517\) −0.799170 + 5.60193i −0.0351474 + 0.246373i
\(518\) 0 0
\(519\) 5.68376i 0.249489i
\(520\) 9.88604 17.1231i 0.433532 0.750899i
\(521\) 6.98727 4.03410i 0.306118 0.176737i −0.339070 0.940761i \(-0.610112\pi\)
0.645188 + 0.764024i \(0.276779\pi\)
\(522\) −0.274386 0.475250i −0.0120095 0.0208011i
\(523\) 8.91730 15.4452i 0.389926 0.675372i −0.602513 0.798109i \(-0.705834\pi\)
0.992439 + 0.122737i \(0.0391672\pi\)
\(524\) 6.20218 0.270944
\(525\) 0 0
\(526\) −8.48528 −0.369976
\(527\) 16.5825 + 9.57391i 0.722345 + 0.417046i
\(528\) 5.68684 2.28390i 0.247488 0.0993941i
\(529\) −2.57591 4.46161i −0.111996 0.193983i
\(530\) −6.44298 + 11.1596i −0.279865 + 0.484740i
\(531\) 3.74388i 0.162471i
\(532\) 0 0
\(533\) −7.47667 −0.323851
\(534\) −7.45881 4.30634i −0.322774 0.186354i
\(535\) 12.7430 + 22.0715i 0.550928 + 0.954235i
\(536\) −2.03605 + 1.17551i −0.0879439 + 0.0507744i
\(537\) 18.3472 + 10.5928i 0.791741 + 0.457112i
\(538\) −7.39943 −0.319012
\(539\) 0 0
\(540\) 15.4655 0.665530
\(541\) 1.27884 + 0.738336i 0.0549815 + 0.0317436i 0.527239 0.849717i \(-0.323227\pi\)
−0.472257 + 0.881461i \(0.656561\pi\)
\(542\) −12.4369 + 7.18047i −0.534212 + 0.308428i
\(543\) −12.2638 21.2416i −0.526292 0.911564i
\(544\) 7.04213 + 4.06577i 0.301929 + 0.174319i
\(545\) −19.4213 −0.831917
\(546\) 0 0
\(547\) 16.3374i 0.698536i 0.937023 + 0.349268i \(0.113570\pi\)
−0.937023 + 0.349268i \(0.886430\pi\)
\(548\) −4.51257 + 7.81600i −0.192767 + 0.333883i
\(549\) 1.77208 + 3.06934i 0.0756307 + 0.130996i
\(550\) −16.8578 + 6.77029i −0.718818 + 0.288686i
\(551\) −7.59019 4.38220i −0.323353 0.186688i
\(552\) −9.80389 −0.417281
\(553\) 0 0
\(554\) −2.18987 −0.0930385
\(555\) 15.8101 27.3840i 0.671103 1.16238i
\(556\) −4.17319 7.22817i −0.176983 0.306543i
\(557\) −15.0253 + 8.67485i −0.636641 + 0.367565i −0.783320 0.621619i \(-0.786475\pi\)
0.146678 + 0.989184i \(0.453142\pi\)
\(558\) −0.487686 + 0.844698i −0.0206454 + 0.0357589i
\(559\) 22.8352i 0.965824i
\(560\) 0 0
\(561\) 7.03786 49.3333i 0.297139 2.08285i
\(562\) −12.8501 + 22.2571i −0.542051 + 0.938859i
\(563\) 4.46536 + 7.73423i 0.188192 + 0.325959i 0.944648 0.328087i \(-0.106404\pi\)
−0.756455 + 0.654046i \(0.773070\pi\)
\(564\) −1.57628 2.73019i −0.0663732 0.114962i
\(565\) −37.9039 21.8839i −1.59463 0.920661i
\(566\) 15.5577i 0.653940i
\(567\) 0 0
\(568\) 7.17945i 0.301243i
\(569\) 8.36434 + 4.82916i 0.350652 + 0.202449i 0.664972 0.746868i \(-0.268443\pi\)
−0.314321 + 0.949317i \(0.601777\pi\)
\(570\) −34.2655 + 19.7832i −1.43522 + 0.828627i
\(571\) −10.3301 + 5.96410i −0.432302 + 0.249590i −0.700327 0.713822i \(-0.746962\pi\)
0.268025 + 0.963412i \(0.413629\pi\)
\(572\) −12.5059 + 15.9385i −0.522899 + 0.666423i
\(573\) 22.5698i 0.942868i
\(574\) 0 0
\(575\) 29.0622 1.21198
\(576\) −0.207107 + 0.358719i −0.00862945 + 0.0149466i
\(577\) −32.5171 + 18.7737i −1.35370 + 0.781561i −0.988766 0.149471i \(-0.952243\pi\)
−0.364938 + 0.931032i \(0.618910\pi\)
\(578\) 42.5410 24.5610i 1.76947 1.02160i
\(579\) −4.67778 + 8.10215i −0.194402 + 0.336714i
\(580\) 4.28839 0.178066
\(581\) 0 0
\(582\) 7.07107i 0.293105i
\(583\) 8.15042 10.3875i 0.337556 0.430207i
\(584\) −9.52000 + 5.49637i −0.393940 + 0.227442i
\(585\) 7.09263 4.09493i 0.293244 0.169305i
\(586\) −2.69725 1.55726i −0.111422 0.0643297i
\(587\) 29.1914i 1.20486i −0.798173 0.602429i \(-0.794200\pi\)
0.798173 0.602429i \(-0.205800\pi\)
\(588\) 0 0
\(589\) 15.5776i 0.641864i
\(590\) −25.3370 14.6283i −1.04311 0.602238i
\(591\) 18.5592 + 32.1455i 0.763423 + 1.32229i
\(592\) −2.64340 4.57851i −0.108643 0.188176i
\(593\) −14.3449 + 24.8461i −0.589076 + 1.02031i 0.405278 + 0.914193i \(0.367175\pi\)
−0.994354 + 0.106115i \(0.966159\pi\)
\(594\) −15.6877 2.23800i −0.643674 0.0918263i
\(595\) 0 0
\(596\) 21.2488i 0.870383i
\(597\) 13.6915 23.7144i 0.560356 0.970565i
\(598\) 28.0679 16.2050i 1.14778 0.662672i
\(599\) 5.32806 + 9.22848i 0.217699 + 0.377065i 0.954104 0.299475i \(-0.0968116\pi\)
−0.736405 + 0.676541i \(0.763478\pi\)
\(600\) 5.06046 8.76497i 0.206592 0.357829i
\(601\) −43.5354 −1.77585 −0.887923 0.459992i \(-0.847852\pi\)
−0.887923 + 0.459992i \(0.847852\pi\)
\(602\) 0 0
\(603\) −0.973827 −0.0396573
\(604\) −14.4411 8.33757i −0.587600 0.339251i
\(605\) 34.5835 8.47020i 1.40602 0.344363i
\(606\) −3.38174 5.85734i −0.137374 0.237938i
\(607\) −13.6748 + 23.6855i −0.555044 + 0.961365i 0.442856 + 0.896593i \(0.353965\pi\)
−0.997900 + 0.0647718i \(0.979368\pi\)
\(608\) 6.61537i 0.268289i
\(609\) 0 0
\(610\) −27.6960 −1.12138
\(611\) 9.02554 + 5.21090i 0.365134 + 0.210810i
\(612\) 1.68410 + 2.91694i 0.0680757 + 0.117911i
\(613\) −24.1278 + 13.9302i −0.974514 + 0.562636i −0.900609 0.434629i \(-0.856879\pi\)
−0.0739045 + 0.997265i \(0.523546\pi\)
\(614\) 7.73423 + 4.46536i 0.312128 + 0.180207i
\(615\) −7.32074 −0.295201
\(616\) 0 0
\(617\) 32.0263 1.28933 0.644665 0.764465i \(-0.276997\pi\)
0.644665 + 0.764465i \(0.276997\pi\)
\(618\) 23.3174 + 13.4623i 0.937964 + 0.541534i
\(619\) 17.3213 10.0005i 0.696203 0.401953i −0.109729 0.993962i \(-0.534998\pi\)
0.805932 + 0.592009i \(0.201665\pi\)
\(620\) −3.81104 6.60091i −0.153055 0.265099i
\(621\) 21.9544 + 12.6754i 0.881000 + 0.508646i
\(622\) −19.1346 −0.767227
\(623\) 0 0
\(624\) 11.2868i 0.451834i
\(625\) 11.1925 19.3860i 0.447702 0.775442i
\(626\) 0.589279 + 1.02066i 0.0235523 + 0.0407938i
\(627\) 37.6206 15.1089i 1.50242 0.603390i
\(628\) −10.8335 6.25474i −0.432305 0.249591i
\(629\) −42.9899 −1.71412
\(630\) 0 0
\(631\) 25.3751 1.01017 0.505084 0.863070i \(-0.331461\pi\)
0.505084 + 0.863070i \(0.331461\pi\)
\(632\) −4.24264 + 7.34847i −0.168763 + 0.292306i
\(633\) 8.49828 + 14.7195i 0.337776 + 0.585046i
\(634\) −7.87818 + 4.54847i −0.312883 + 0.180643i
\(635\) 13.9786 24.2117i 0.554725 0.960812i
\(636\) 7.35589i 0.291680i
\(637\) 0 0
\(638\) −4.34999 0.620568i −0.172218 0.0245685i
\(639\) −1.48691 + 2.57541i −0.0588214 + 0.101882i
\(640\) −1.61844 2.80322i −0.0639745 0.110807i
\(641\) −14.6685 25.4067i −0.579373 1.00350i −0.995551 0.0942201i \(-0.969964\pi\)
0.416179 0.909283i \(-0.363369\pi\)
\(642\) 12.5994 + 7.27428i 0.497260 + 0.287093i
\(643\) 7.53612i 0.297196i 0.988898 + 0.148598i \(0.0474760\pi\)
−0.988898 + 0.148598i \(0.952524\pi\)
\(644\) 0 0
\(645\) 22.3589i 0.880381i
\(646\) 46.5863 + 26.8966i 1.83291 + 1.05823i
\(647\) 25.1631 14.5279i 0.989262 0.571151i 0.0842084 0.996448i \(-0.473164\pi\)
0.905054 + 0.425297i \(0.139831\pi\)
\(648\) 8.72180 5.03553i 0.342625 0.197814i
\(649\) 23.5841 + 18.5050i 0.925758 + 0.726383i
\(650\) 33.4580i 1.31233i
\(651\) 0 0
\(652\) −8.39592 −0.328810
\(653\) −14.7920 + 25.6205i −0.578856 + 1.00261i 0.416755 + 0.909019i \(0.363167\pi\)
−0.995611 + 0.0935894i \(0.970166\pi\)
\(654\) −9.60124 + 5.54328i −0.375438 + 0.216759i
\(655\) −17.3861 + 10.0379i −0.679331 + 0.392212i
\(656\) −0.612002 + 1.06002i −0.0238947 + 0.0413868i
\(657\) −4.55335 −0.177643
\(658\) 0 0
\(659\) 5.39725i 0.210247i −0.994459 0.105124i \(-0.966476\pi\)
0.994459 0.105124i \(-0.0335238\pi\)
\(660\) −12.2451 + 15.6061i −0.476640 + 0.607467i
\(661\) −25.5047 + 14.7252i −0.992018 + 0.572742i −0.905877 0.423541i \(-0.860787\pi\)
−0.0861414 + 0.996283i \(0.527454\pi\)
\(662\) 2.36401 1.36486i 0.0918800 0.0530469i
\(663\) −79.4831 45.8896i −3.08687 1.78220i
\(664\) 5.60138i 0.217376i
\(665\) 0 0
\(666\) 2.18987i 0.0848556i
\(667\) 6.08767 + 3.51472i 0.235716 + 0.136090i
\(668\) 2.02317 + 3.50424i 0.0782789 + 0.135583i
\(669\) −10.0481 17.4038i −0.388482 0.672871i
\(670\) 3.80500 6.59044i 0.147000 0.254611i
\(671\) 28.0939 + 4.00786i 1.08455 + 0.154722i
\(672\) 0 0
\(673\) 5.21501i 0.201024i −0.994936 0.100512i \(-0.967952\pi\)
0.994936 0.100512i \(-0.0320481\pi\)
\(674\) 10.1604 17.5984i 0.391365 0.677864i
\(675\) −22.6643 + 13.0853i −0.872351 + 0.503652i
\(676\) 12.1561 + 21.0550i 0.467543 + 0.809809i
\(677\) −4.86736 + 8.43051i −0.187068 + 0.324011i −0.944271 0.329168i \(-0.893232\pi\)
0.757204 + 0.653179i \(0.226565\pi\)
\(678\) −24.9846 −0.959528
\(679\) 0 0
\(680\) −26.3209 −1.00936
\(681\) −37.5717 21.6920i −1.43975 0.831240i
\(682\) 2.91057 + 7.24723i 0.111452 + 0.277511i
\(683\) 8.75076 + 15.1568i 0.334838 + 0.579957i 0.983454 0.181159i \(-0.0579849\pi\)
−0.648615 + 0.761116i \(0.724652\pi\)
\(684\) −1.37009 + 2.37306i −0.0523867 + 0.0907364i
\(685\) 29.2133i 1.11618i
\(686\) 0 0
\(687\) −42.1845 −1.60944
\(688\) 3.23749 + 1.86917i 0.123428 + 0.0712614i
\(689\) −12.1587 21.0594i −0.463208 0.802299i
\(690\) 27.4825 15.8670i 1.04624 0.604047i
\(691\) 40.0753 + 23.1375i 1.52454 + 0.880192i 0.999577 + 0.0290659i \(0.00925328\pi\)
0.524961 + 0.851127i \(0.324080\pi\)
\(692\) −3.07603 −0.116933
\(693\) 0 0
\(694\) −24.4383 −0.927666
\(695\) 23.3967 + 13.5081i 0.887489 + 0.512392i
\(696\) 2.12004 1.22400i 0.0803598 0.0463957i
\(697\) 4.97652 + 8.61959i 0.188499 + 0.326490i
\(698\) −2.66392 1.53801i −0.100831 0.0582147i
\(699\) −27.1785 −1.02799
\(700\) 0 0
\(701\) 28.7883i 1.08732i −0.839306 0.543660i \(-0.817038\pi\)
0.839306 0.543660i \(-0.182962\pi\)
\(702\) −14.5926 + 25.2752i −0.550764 + 0.953950i
\(703\) −17.4871 30.2885i −0.659538 1.14235i
\(704\) 1.23604 + 3.07769i 0.0465850 + 0.115995i
\(705\) 8.83730 + 5.10222i 0.332832 + 0.192161i
\(706\) 33.7399 1.26982
\(707\) 0 0
\(708\) −16.7010 −0.627663
\(709\) −1.25142 + 2.16753i −0.0469982 + 0.0814032i −0.888568 0.458746i \(-0.848299\pi\)
0.841569 + 0.540149i \(0.181632\pi\)
\(710\) −11.6195 20.1256i −0.436073 0.755300i
\(711\) −3.04384 + 1.75736i −0.114153 + 0.0659061i
\(712\) 2.33058 4.03668i 0.0873421 0.151281i
\(713\) 12.4939i 0.467902i
\(714\) 0 0
\(715\) 9.26136 64.9193i 0.346355 2.42784i
\(716\) −5.73276 + 9.92944i −0.214243 + 0.371081i
\(717\) −20.7150 35.8795i −0.773617 1.33994i
\(718\) 14.9492 + 25.8928i 0.557900 + 0.966312i
\(719\) 1.84966 + 1.06790i 0.0689807 + 0.0398260i 0.534094 0.845425i \(-0.320653\pi\)
−0.465113 + 0.885251i \(0.653986\pi\)
\(720\) 1.34076i 0.0499672i
\(721\) 0 0
\(722\) 24.7632i 0.921590i
\(723\) 24.7532 + 14.2913i 0.920581 + 0.531498i
\(724\) 11.4959 6.63714i 0.427241 0.246668i
\(725\) −6.28453 + 3.62837i −0.233401 + 0.134754i
\(726\) 14.6794 14.0583i 0.544802 0.521753i
\(727\) 35.5296i 1.31772i 0.752266 + 0.658859i \(0.228961\pi\)
−0.752266 + 0.658859i \(0.771039\pi\)
\(728\) 0 0
\(729\) −22.3137 −0.826434
\(730\) 17.7911 30.8151i 0.658479 1.14052i
\(731\) 26.3258 15.1992i 0.973696 0.562164i
\(732\) −13.6920 + 7.90507i −0.506070 + 0.292180i
\(733\) 1.17128 2.02871i 0.0432622 0.0749323i −0.843584 0.536998i \(-0.819558\pi\)
0.886846 + 0.462066i \(0.152892\pi\)
\(734\) 3.55525 0.131227
\(735\) 0 0
\(736\) 5.30583i 0.195575i
\(737\) −4.81335 + 6.13450i −0.177302 + 0.225967i
\(738\) −0.439074 + 0.253499i −0.0161625 + 0.00933144i
\(739\) 11.8757 6.85645i 0.436855 0.252218i −0.265408 0.964136i \(-0.585507\pi\)
0.702263 + 0.711918i \(0.252173\pi\)
\(740\) 14.8201 + 8.55638i 0.544797 + 0.314539i
\(741\) 74.6664i 2.74294i
\(742\) 0 0
\(743\) 44.2193i 1.62225i 0.584873 + 0.811125i \(0.301144\pi\)
−0.584873 + 0.811125i \(0.698856\pi\)
\(744\) −3.76810 2.17551i −0.138145 0.0797582i
\(745\) 34.3899 + 59.5650i 1.25995 + 2.18229i
\(746\) −10.5485 18.2705i −0.386207 0.668930i
\(747\) −1.16008 + 2.00932i −0.0424452 + 0.0735173i
\(748\) 26.6990 + 3.80886i 0.976211 + 0.139266i
\(749\) 0 0
\(750\) 2.85533i 0.104262i
\(751\) −4.83164 + 8.36864i −0.176309 + 0.305376i −0.940613 0.339479i \(-0.889749\pi\)
0.764305 + 0.644855i \(0.223082\pi\)
\(752\) 1.47757 0.853074i 0.0538813 0.0311084i
\(753\) 4.50306 + 7.79953i 0.164101 + 0.284231i
\(754\) −4.04635 + 7.00848i −0.147359 + 0.255234i
\(755\) 53.9755 1.96437
\(756\) 0 0
\(757\) −29.0384 −1.05542 −0.527710 0.849425i \(-0.676949\pi\)
−0.527710 + 0.849425i \(0.676949\pi\)
\(758\) −7.45702 4.30531i −0.270851 0.156376i
\(759\) −30.1734 + 12.1180i −1.09522 + 0.439856i
\(760\) −10.7066 18.5444i −0.388369 0.672675i
\(761\) 10.6811 18.5003i 0.387191 0.670635i −0.604879 0.796317i \(-0.706779\pi\)
0.992071 + 0.125682i \(0.0401120\pi\)
\(762\) 15.9593i 0.578144i
\(763\) 0 0
\(764\) 12.2147 0.441913
\(765\) −9.44180 5.45123i −0.341369 0.197090i
\(766\) −17.1145 29.6432i −0.618372 1.07105i
\(767\) 47.8139 27.6054i 1.72646 0.996772i
\(768\) −1.60021 0.923880i −0.0577425 0.0333376i
\(769\) 15.7726 0.568773 0.284387 0.958710i \(-0.408210\pi\)
0.284387 + 0.958710i \(0.408210\pi\)
\(770\) 0 0
\(771\) −36.5381 −1.31589
\(772\) −4.38485 2.53159i −0.157814 0.0911141i
\(773\) −5.81924 + 3.35974i −0.209303 + 0.120841i −0.600988 0.799258i \(-0.705226\pi\)
0.391684 + 0.920100i \(0.371893\pi\)
\(774\) 0.774235 + 1.34101i 0.0278293 + 0.0482018i
\(775\) 11.1700 + 6.44898i 0.401237 + 0.231654i
\(776\) 3.82683 0.137375
\(777\) 0 0
\(778\) 22.8252i 0.818322i
\(779\) −4.04862 + 7.01242i −0.145057 + 0.251246i
\(780\) 18.2670 + 31.6394i 0.654064 + 1.13287i
\(781\) 8.87409 + 22.0962i 0.317540 + 0.790663i
\(782\) −37.3643 21.5723i −1.33615 0.771424i
\(783\) −6.33002 −0.226217
\(784\) 0