Properties

Label 1050.2.bc.h.493.2
Level $1050$
Weight $2$
Character 1050.493
Analytic conductor $8.384$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.bc (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 493.2
Root \(-0.709944 + 0.925217i\) of defining polynomial
Character \(\chi\) \(=\) 1050.493
Dual form 1050.2.bc.h.607.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.965926 - 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(1.38658 + 2.25331i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.965926 - 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(1.38658 + 2.25331i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(0.582897 - 1.00961i) q^{11} +(0.258819 - 0.965926i) q^{12} +(1.92501 - 1.92501i) q^{13} +(-0.756134 - 2.53540i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.0209315 - 0.00560858i) q^{17} +(0.965926 - 0.258819i) q^{18} +(-0.989363 - 1.71363i) q^{19} +(1.81766 - 1.92253i) q^{21} +(-0.824341 + 0.824341i) q^{22} +(-1.85829 + 6.93525i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.35765 + 1.36119i) q^{26} +(0.707107 + 0.707107i) q^{27} +(0.0741591 + 2.64471i) q^{28} -5.60604i q^{29} +(6.86850 + 3.96553i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-1.12607 - 0.301730i) q^{33} -0.0216699 q^{34} -1.00000 q^{36} +(10.2592 + 2.74894i) q^{37} +(0.512132 + 1.91130i) q^{38} +(-2.35765 - 1.36119i) q^{39} +2.48977i q^{41} +(-2.25331 + 1.38658i) q^{42} +(7.87756 + 7.87756i) q^{43} +(1.00961 - 0.582897i) q^{44} +(3.58995 - 6.21797i) q^{46} +(1.05773 - 3.94750i) q^{47} +(0.707107 - 0.707107i) q^{48} +(-3.15479 + 6.24878i) q^{49} +(-0.0108349 - 0.0187667i) q^{51} +(2.62962 - 0.704604i) q^{52} +(-2.82745 + 0.757613i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(0.612870 - 2.57379i) q^{56} +(-1.39917 + 1.39917i) q^{57} +(-1.45095 + 5.41502i) q^{58} +(5.34623 - 9.25995i) q^{59} +(-3.15795 + 1.82324i) q^{61} +(-5.60811 - 5.60811i) q^{62} +(-2.32747 - 1.25813i) q^{63} +1.00000i q^{64} +(1.00961 + 0.582897i) q^{66} +(-3.76794 - 14.0621i) q^{67} +(0.0209315 + 0.00560858i) q^{68} +7.17989 q^{69} +7.51848 q^{71} +(0.965926 + 0.258819i) q^{72} +(-0.969376 - 3.61776i) q^{73} +(-9.19815 - 5.31055i) q^{74} -1.97873i q^{76} +(3.08319 - 0.0864543i) q^{77} +(1.92501 + 1.92501i) q^{78} +(-1.39464 + 0.805197i) q^{79} +(0.500000 - 0.866025i) q^{81} +(0.644400 - 2.40493i) q^{82} +(9.74815 - 9.74815i) q^{83} +(2.53540 - 0.756134i) q^{84} +(-5.57028 - 9.64800i) q^{86} +(-5.41502 + 1.45095i) q^{87} +(-1.12607 + 0.301730i) q^{88} +(1.80255 + 3.12211i) q^{89} +(7.00683 + 1.66846i) q^{91} +(-5.07695 + 5.07695i) q^{92} +(2.05271 - 7.66082i) q^{93} +(-2.04338 + 3.53923i) q^{94} +(-0.866025 + 0.500000i) q^{96} +(0.265501 + 0.265501i) q^{97} +(4.66460 - 5.21934i) q^{98} +1.16579i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 8q^{7} + O(q^{10}) \) \( 16q + 8q^{7} + 4q^{11} + 16q^{13} + 16q^{14} + 8q^{16} + 12q^{17} - 8q^{19} + 8q^{21} - 4q^{22} - 32q^{23} - 8q^{24} - 12q^{26} + 8q^{28} - 24q^{31} - 8q^{33} + 16q^{34} - 16q^{36} + 8q^{37} + 28q^{38} - 12q^{39} + 4q^{42} + 24q^{43} - 4q^{46} + 24q^{47} + 52q^{49} + 8q^{51} + 8q^{52} - 44q^{53} - 8q^{54} + 8q^{56} + 8q^{57} - 48q^{58} + 8q^{59} + 24q^{61} - 8q^{62} - 4q^{63} - 36q^{67} + 12q^{68} - 8q^{69} - 32q^{71} + 40q^{73} - 24q^{74} + 44q^{77} + 16q^{78} + 12q^{79} + 8q^{81} - 12q^{82} + 16q^{83} + 4q^{84} - 8q^{86} - 12q^{87} - 8q^{88} - 16q^{89} + 8q^{91} - 8q^{92} - 40q^{93} + 8q^{94} - 44q^{97} + 8q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.965926 0.258819i −0.683013 0.183013i
\(3\) −0.258819 0.965926i −0.149429 0.557678i
\(4\) 0.866025 + 0.500000i 0.433013 + 0.250000i
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) 1.38658 + 2.25331i 0.524078 + 0.851670i
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) −0.866025 + 0.500000i −0.288675 + 0.166667i
\(10\) 0 0
\(11\) 0.582897 1.00961i 0.175750 0.304408i −0.764670 0.644422i \(-0.777098\pi\)
0.940421 + 0.340013i \(0.110432\pi\)
\(12\) 0.258819 0.965926i 0.0747146 0.278839i
\(13\) 1.92501 1.92501i 0.533903 0.533903i −0.387829 0.921731i \(-0.626775\pi\)
0.921731 + 0.387829i \(0.126775\pi\)
\(14\) −0.756134 2.53540i −0.202085 0.677615i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) 0.0209315 0.00560858i 0.00507664 0.00136028i −0.256280 0.966603i \(-0.582497\pi\)
0.261356 + 0.965242i \(0.415830\pi\)
\(18\) 0.965926 0.258819i 0.227671 0.0610042i
\(19\) −0.989363 1.71363i −0.226976 0.393133i 0.729935 0.683517i \(-0.239550\pi\)
−0.956910 + 0.290384i \(0.906217\pi\)
\(20\) 0 0
\(21\) 1.81766 1.92253i 0.396645 0.419531i
\(22\) −0.824341 + 0.824341i −0.175750 + 0.175750i
\(23\) −1.85829 + 6.93525i −0.387481 + 1.44610i 0.446738 + 0.894665i \(0.352586\pi\)
−0.834219 + 0.551434i \(0.814081\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 0 0
\(26\) −2.35765 + 1.36119i −0.462373 + 0.266951i
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) 0.0741591 + 2.64471i 0.0140148 + 0.499804i
\(29\) 5.60604i 1.04102i −0.853857 0.520508i \(-0.825743\pi\)
0.853857 0.520508i \(-0.174257\pi\)
\(30\) 0 0
\(31\) 6.86850 + 3.96553i 1.23362 + 0.712231i 0.967783 0.251787i \(-0.0810183\pi\)
0.265837 + 0.964018i \(0.414352\pi\)
\(32\) −0.258819 0.965926i −0.0457532 0.170753i
\(33\) −1.12607 0.301730i −0.196024 0.0525244i
\(34\) −0.0216699 −0.00371636
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 10.2592 + 2.74894i 1.68660 + 0.451924i 0.969509 0.245054i \(-0.0788057\pi\)
0.717093 + 0.696978i \(0.245472\pi\)
\(38\) 0.512132 + 1.91130i 0.0830788 + 0.310054i
\(39\) −2.35765 1.36119i −0.377526 0.217965i
\(40\) 0 0
\(41\) 2.48977i 0.388837i 0.980919 + 0.194418i \(0.0622819\pi\)
−0.980919 + 0.194418i \(0.937718\pi\)
\(42\) −2.25331 + 1.38658i −0.347693 + 0.213954i
\(43\) 7.87756 + 7.87756i 1.20132 + 1.20132i 0.973766 + 0.227550i \(0.0730716\pi\)
0.227550 + 0.973766i \(0.426928\pi\)
\(44\) 1.00961 0.582897i 0.152204 0.0878751i
\(45\) 0 0
\(46\) 3.58995 6.21797i 0.529309 0.916790i
\(47\) 1.05773 3.94750i 0.154286 0.575802i −0.844880 0.534956i \(-0.820328\pi\)
0.999165 0.0408457i \(-0.0130052\pi\)
\(48\) 0.707107 0.707107i 0.102062 0.102062i
\(49\) −3.15479 + 6.24878i −0.450685 + 0.892683i
\(50\) 0 0
\(51\) −0.0108349 0.0187667i −0.00151720 0.00262786i
\(52\) 2.62962 0.704604i 0.364662 0.0977110i
\(53\) −2.82745 + 0.757613i −0.388380 + 0.104066i −0.447725 0.894171i \(-0.647766\pi\)
0.0593446 + 0.998238i \(0.481099\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 0 0
\(56\) 0.612870 2.57379i 0.0818981 0.343937i
\(57\) −1.39917 + 1.39917i −0.185325 + 0.185325i
\(58\) −1.45095 + 5.41502i −0.190519 + 0.711027i
\(59\) 5.34623 9.25995i 0.696020 1.20554i −0.273815 0.961782i \(-0.588286\pi\)
0.969835 0.243760i \(-0.0783810\pi\)
\(60\) 0 0
\(61\) −3.15795 + 1.82324i −0.404334 + 0.233442i −0.688352 0.725376i \(-0.741666\pi\)
0.284018 + 0.958819i \(0.408332\pi\)
\(62\) −5.60811 5.60811i −0.712231 0.712231i
\(63\) −2.32747 1.25813i −0.293233 0.158510i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 1.00961 + 0.582897i 0.124274 + 0.0717497i
\(67\) −3.76794 14.0621i −0.460327 1.71796i −0.671935 0.740610i \(-0.734537\pi\)
0.211608 0.977355i \(-0.432130\pi\)
\(68\) 0.0209315 + 0.00560858i 0.00253832 + 0.000680140i
\(69\) 7.17989 0.864358
\(70\) 0 0
\(71\) 7.51848 0.892280 0.446140 0.894963i \(-0.352798\pi\)
0.446140 + 0.894963i \(0.352798\pi\)
\(72\) 0.965926 + 0.258819i 0.113835 + 0.0305021i
\(73\) −0.969376 3.61776i −0.113457 0.423427i 0.885710 0.464239i \(-0.153672\pi\)
−0.999167 + 0.0408122i \(0.987005\pi\)
\(74\) −9.19815 5.31055i −1.06926 0.617339i
\(75\) 0 0
\(76\) 1.97873i 0.226976i
\(77\) 3.08319 0.0864543i 0.351362 0.00985238i
\(78\) 1.92501 + 1.92501i 0.217965 + 0.217965i
\(79\) −1.39464 + 0.805197i −0.156910 + 0.0905918i −0.576399 0.817169i \(-0.695543\pi\)
0.419489 + 0.907760i \(0.362209\pi\)
\(80\) 0 0
\(81\) 0.500000 0.866025i 0.0555556 0.0962250i
\(82\) 0.644400 2.40493i 0.0711620 0.265580i
\(83\) 9.74815 9.74815i 1.07000 1.07000i 0.0726405 0.997358i \(-0.476857\pi\)
0.997358 0.0726405i \(-0.0231426\pi\)
\(84\) 2.53540 0.756134i 0.276635 0.0825010i
\(85\) 0 0
\(86\) −5.57028 9.64800i −0.600658 1.04037i
\(87\) −5.41502 + 1.45095i −0.580551 + 0.155558i
\(88\) −1.12607 + 0.301730i −0.120040 + 0.0321645i
\(89\) 1.80255 + 3.12211i 0.191070 + 0.330943i 0.945605 0.325317i \(-0.105471\pi\)
−0.754535 + 0.656260i \(0.772138\pi\)
\(90\) 0 0
\(91\) 7.00683 + 1.66846i 0.734516 + 0.174903i
\(92\) −5.07695 + 5.07695i −0.529309 + 0.529309i
\(93\) 2.05271 7.66082i 0.212856 0.794390i
\(94\) −2.04338 + 3.53923i −0.210758 + 0.365044i
\(95\) 0 0
\(96\) −0.866025 + 0.500000i −0.0883883 + 0.0510310i
\(97\) 0.265501 + 0.265501i 0.0269575 + 0.0269575i 0.720457 0.693500i \(-0.243932\pi\)
−0.693500 + 0.720457i \(0.743932\pi\)
\(98\) 4.66460 5.21934i 0.471196 0.527233i
\(99\) 1.16579i 0.117167i
\(100\) 0 0
\(101\) 12.0515 + 6.95796i 1.19917 + 0.692343i 0.960371 0.278725i \(-0.0899119\pi\)
0.238802 + 0.971068i \(0.423245\pi\)
\(102\) 0.00560858 + 0.0209315i 0.000555332 + 0.00207253i
\(103\) 11.5757 + 3.10171i 1.14059 + 0.305621i 0.779189 0.626789i \(-0.215631\pi\)
0.361403 + 0.932410i \(0.382298\pi\)
\(104\) −2.72238 −0.266951
\(105\) 0 0
\(106\) 2.92719 0.284314
\(107\) 6.67031 + 1.78730i 0.644843 + 0.172785i 0.566396 0.824133i \(-0.308337\pi\)
0.0784469 + 0.996918i \(0.475004\pi\)
\(108\) 0.258819 + 0.965926i 0.0249049 + 0.0929463i
\(109\) −0.499969 0.288657i −0.0478883 0.0276483i 0.475865 0.879519i \(-0.342135\pi\)
−0.523753 + 0.851870i \(0.675469\pi\)
\(110\) 0 0
\(111\) 10.6211i 1.00811i
\(112\) −1.25813 + 2.32747i −0.118882 + 0.219925i
\(113\) −13.2689 13.2689i −1.24823 1.24823i −0.956501 0.291728i \(-0.905770\pi\)
−0.291728 0.956501i \(-0.594230\pi\)
\(114\) 1.71363 0.989363i 0.160496 0.0926624i
\(115\) 0 0
\(116\) 2.80302 4.85498i 0.260254 0.450773i
\(117\) −0.704604 + 2.62962i −0.0651406 + 0.243108i
\(118\) −7.56072 + 7.56072i −0.696020 + 0.696020i
\(119\) 0.0416611 + 0.0393884i 0.00381906 + 0.00361073i
\(120\) 0 0
\(121\) 4.82046 + 8.34928i 0.438224 + 0.759026i
\(122\) 3.52224 0.943781i 0.318888 0.0854459i
\(123\) 2.40493 0.644400i 0.216845 0.0581036i
\(124\) 3.96553 + 6.86850i 0.356115 + 0.616810i
\(125\) 0 0
\(126\) 1.92253 + 1.81766i 0.171273 + 0.161930i
\(127\) −1.36110 + 1.36110i −0.120778 + 0.120778i −0.764912 0.644134i \(-0.777218\pi\)
0.644134 + 0.764912i \(0.277218\pi\)
\(128\) 0.258819 0.965926i 0.0228766 0.0853766i
\(129\) 5.57028 9.64800i 0.490435 0.849459i
\(130\) 0 0
\(131\) −14.8522 + 8.57489i −1.29764 + 0.749192i −0.979996 0.199019i \(-0.936225\pi\)
−0.317643 + 0.948210i \(0.602891\pi\)
\(132\) −0.824341 0.824341i −0.0717497 0.0717497i
\(133\) 2.48950 4.60542i 0.215867 0.399341i
\(134\) 14.5582i 1.25764i
\(135\) 0 0
\(136\) −0.0187667 0.0108349i −0.00160923 0.000929089i
\(137\) −2.64921 9.88699i −0.226337 0.844702i −0.981864 0.189585i \(-0.939286\pi\)
0.755527 0.655117i \(-0.227381\pi\)
\(138\) −6.93525 1.85829i −0.590367 0.158188i
\(139\) 5.65119 0.479327 0.239664 0.970856i \(-0.422963\pi\)
0.239664 + 0.970856i \(0.422963\pi\)
\(140\) 0 0
\(141\) −4.08675 −0.344166
\(142\) −7.26230 1.94593i −0.609439 0.163299i
\(143\) −0.821423 3.06559i −0.0686909 0.256358i
\(144\) −0.866025 0.500000i −0.0721688 0.0416667i
\(145\) 0 0
\(146\) 3.74538i 0.309970i
\(147\) 6.85238 + 1.42999i 0.565175 + 0.117944i
\(148\) 7.51026 + 7.51026i 0.617339 + 0.617339i
\(149\) 0.191221 0.110402i 0.0156655 0.00904446i −0.492147 0.870512i \(-0.663788\pi\)
0.507812 + 0.861468i \(0.330454\pi\)
\(150\) 0 0
\(151\) 3.18442 5.51559i 0.259145 0.448852i −0.706868 0.707345i \(-0.749893\pi\)
0.966013 + 0.258493i \(0.0832260\pi\)
\(152\) −0.512132 + 1.91130i −0.0415394 + 0.155027i
\(153\) −0.0153229 + 0.0153229i −0.00123879 + 0.00123879i
\(154\) −3.00051 0.714480i −0.241788 0.0575745i
\(155\) 0 0
\(156\) −1.36119 2.35765i −0.108982 0.188763i
\(157\) 13.9830 3.74673i 1.11596 0.299022i 0.346715 0.937970i \(-0.387297\pi\)
0.769249 + 0.638949i \(0.220630\pi\)
\(158\) 1.55552 0.416801i 0.123751 0.0331589i
\(159\) 1.46360 + 2.53502i 0.116071 + 0.201040i
\(160\) 0 0
\(161\) −18.2039 + 5.42896i −1.43467 + 0.427862i
\(162\) −0.707107 + 0.707107i −0.0555556 + 0.0555556i
\(163\) −5.66960 + 21.1592i −0.444078 + 1.65732i 0.274283 + 0.961649i \(0.411560\pi\)
−0.718360 + 0.695671i \(0.755107\pi\)
\(164\) −1.24488 + 2.15620i −0.0972091 + 0.168371i
\(165\) 0 0
\(166\) −11.9390 + 6.89298i −0.926646 + 0.534999i
\(167\) 11.3917 + 11.3917i 0.881515 + 0.881515i 0.993689 0.112174i \(-0.0357814\pi\)
−0.112174 + 0.993689i \(0.535781\pi\)
\(168\) −2.64471 + 0.0741591i −0.204044 + 0.00572150i
\(169\) 5.58865i 0.429896i
\(170\) 0 0
\(171\) 1.71363 + 0.989363i 0.131044 + 0.0756585i
\(172\) 2.88339 + 10.7609i 0.219856 + 0.820515i
\(173\) −10.0874 2.70291i −0.766932 0.205499i −0.145916 0.989297i \(-0.546613\pi\)
−0.621016 + 0.783798i \(0.713280\pi\)
\(174\) 5.60604 0.424993
\(175\) 0 0
\(176\) 1.16579 0.0878751
\(177\) −10.3281 2.76741i −0.776310 0.208012i
\(178\) −0.933068 3.48226i −0.0699364 0.261006i
\(179\) 1.30513 + 0.753516i 0.0975498 + 0.0563204i 0.547981 0.836491i \(-0.315397\pi\)
−0.450431 + 0.892811i \(0.648730\pi\)
\(180\) 0 0
\(181\) 21.3457i 1.58662i −0.608821 0.793308i \(-0.708357\pi\)
0.608821 0.793308i \(-0.291643\pi\)
\(182\) −6.33625 3.42511i −0.469674 0.253886i
\(183\) 2.57846 + 2.57846i 0.190605 + 0.190605i
\(184\) 6.21797 3.58995i 0.458395 0.264654i
\(185\) 0 0
\(186\) −3.96553 + 6.86850i −0.290767 + 0.503623i
\(187\) 0.00653845 0.0244018i 0.000478139 0.00178444i
\(188\) 2.88977 2.88977i 0.210758 0.210758i
\(189\) −0.612870 + 2.57379i −0.0445797 + 0.187216i
\(190\) 0 0
\(191\) −3.22543 5.58661i −0.233384 0.404233i 0.725418 0.688309i \(-0.241647\pi\)
−0.958802 + 0.284076i \(0.908313\pi\)
\(192\) 0.965926 0.258819i 0.0697097 0.0186787i
\(193\) −4.96349 + 1.32996i −0.357280 + 0.0957328i −0.432994 0.901397i \(-0.642543\pi\)
0.0757145 + 0.997130i \(0.475876\pi\)
\(194\) −0.187737 0.325171i −0.0134788 0.0233459i
\(195\) 0 0
\(196\) −5.85652 + 3.83421i −0.418323 + 0.273872i
\(197\) −17.8347 + 17.8347i −1.27067 + 1.27067i −0.324931 + 0.945738i \(0.605341\pi\)
−0.945738 + 0.324931i \(0.894659\pi\)
\(198\) 0.301730 1.12607i 0.0214430 0.0800264i
\(199\) −2.47098 + 4.27987i −0.175163 + 0.303392i −0.940218 0.340574i \(-0.889379\pi\)
0.765054 + 0.643966i \(0.222712\pi\)
\(200\) 0 0
\(201\) −12.6078 + 7.27910i −0.889284 + 0.513428i
\(202\) −9.84004 9.84004i −0.692343 0.692343i
\(203\) 12.6321 7.77323i 0.886603 0.545574i
\(204\) 0.0216699i 0.00151720i
\(205\) 0 0
\(206\) −10.3785 5.99204i −0.723106 0.417485i
\(207\) −1.85829 6.93525i −0.129160 0.482033i
\(208\) 2.62962 + 0.704604i 0.182331 + 0.0488555i
\(209\) −2.30679 −0.159564
\(210\) 0 0
\(211\) −19.0455 −1.31115 −0.655574 0.755131i \(-0.727573\pi\)
−0.655574 + 0.755131i \(0.727573\pi\)
\(212\) −2.82745 0.757613i −0.194190 0.0520331i
\(213\) −1.94593 7.26230i −0.133333 0.497604i
\(214\) −5.98043 3.45281i −0.408814 0.236029i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 0.588161 + 20.9754i 0.0399270 + 1.42390i
\(218\) 0.408223 + 0.408223i 0.0276483 + 0.0276483i
\(219\) −3.24360 + 1.87269i −0.219182 + 0.126545i
\(220\) 0 0
\(221\) 0.0294968 0.0510900i 0.00198417 0.00343669i
\(222\) −2.74894 + 10.2592i −0.184497 + 0.688553i
\(223\) −2.94490 + 2.94490i −0.197205 + 0.197205i −0.798801 0.601596i \(-0.794532\pi\)
0.601596 + 0.798801i \(0.294532\pi\)
\(224\) 1.81766 1.92253i 0.121447 0.128455i
\(225\) 0 0
\(226\) 9.38250 + 16.2510i 0.624115 + 1.08100i
\(227\) 17.8106 4.77234i 1.18213 0.316751i 0.386360 0.922348i \(-0.373732\pi\)
0.795772 + 0.605597i \(0.207065\pi\)
\(228\) −1.91130 + 0.512132i −0.126579 + 0.0339168i
\(229\) −2.95505 5.11830i −0.195276 0.338227i 0.751715 0.659488i \(-0.229227\pi\)
−0.946991 + 0.321261i \(0.895893\pi\)
\(230\) 0 0
\(231\) −0.881497 2.95576i −0.0579983 0.194475i
\(232\) −3.96407 + 3.96407i −0.260254 + 0.260254i
\(233\) −1.87264 + 6.98879i −0.122681 + 0.457851i −0.999746 0.0225196i \(-0.992831\pi\)
0.877066 + 0.480371i \(0.159498\pi\)
\(234\) 1.36119 2.35765i 0.0889838 0.154124i
\(235\) 0 0
\(236\) 9.25995 5.34623i 0.602771 0.348010i
\(237\) 1.13872 + 1.13872i 0.0739679 + 0.0739679i
\(238\) −0.0300470 0.0488289i −0.00194766 0.00316511i
\(239\) 4.20172i 0.271787i 0.990723 + 0.135893i \(0.0433904\pi\)
−0.990723 + 0.135893i \(0.956610\pi\)
\(240\) 0 0
\(241\) −18.9970 10.9679i −1.22371 0.706507i −0.258000 0.966145i \(-0.583064\pi\)
−0.965706 + 0.259638i \(0.916397\pi\)
\(242\) −2.49525 9.31242i −0.160401 0.598625i
\(243\) −0.965926 0.258819i −0.0619642 0.0166032i
\(244\) −3.64649 −0.233442
\(245\) 0 0
\(246\) −2.48977 −0.158742
\(247\) −5.20329 1.39422i −0.331078 0.0887120i
\(248\) −2.05271 7.66082i −0.130347 0.486463i
\(249\) −11.9390 6.89298i −0.756603 0.436825i
\(250\) 0 0
\(251\) 15.1293i 0.954952i 0.878645 + 0.477476i \(0.158448\pi\)
−0.878645 + 0.477476i \(0.841552\pi\)
\(252\) −1.38658 2.25331i −0.0873463 0.141945i
\(253\) 5.91868 + 5.91868i 0.372105 + 0.372105i
\(254\) 1.66700 0.962442i 0.104597 0.0603890i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −5.95653 + 22.2301i −0.371558 + 1.38667i 0.486751 + 0.873541i \(0.338182\pi\)
−0.858309 + 0.513133i \(0.828485\pi\)
\(258\) −7.87756 + 7.87756i −0.490435 + 0.490435i
\(259\) 8.03098 + 26.9288i 0.499021 + 1.67327i
\(260\) 0 0
\(261\) 2.80302 + 4.85498i 0.173503 + 0.300516i
\(262\) 16.5654 4.43869i 1.02342 0.274223i
\(263\) −19.4349 + 5.20756i −1.19841 + 0.321112i −0.802203 0.597051i \(-0.796339\pi\)
−0.396203 + 0.918163i \(0.629672\pi\)
\(264\) 0.582897 + 1.00961i 0.0358749 + 0.0621371i
\(265\) 0 0
\(266\) −3.59664 + 3.80417i −0.220524 + 0.233248i
\(267\) 2.54919 2.54919i 0.156008 0.156008i
\(268\) 3.76794 14.0621i 0.230164 0.858982i
\(269\) 4.63479 8.02770i 0.282588 0.489457i −0.689433 0.724349i \(-0.742140\pi\)
0.972021 + 0.234892i \(0.0754736\pi\)
\(270\) 0 0
\(271\) 22.7157 13.1149i 1.37988 0.796673i 0.387734 0.921771i \(-0.373258\pi\)
0.992144 + 0.125098i \(0.0399244\pi\)
\(272\) 0.0153229 + 0.0153229i 0.000929089 + 0.000929089i
\(273\) −0.201889 7.19991i −0.0122189 0.435758i
\(274\) 10.2358i 0.618365i
\(275\) 0 0
\(276\) 6.21797 + 3.58995i 0.374278 + 0.216089i
\(277\) −3.44216 12.8463i −0.206819 0.771860i −0.988887 0.148667i \(-0.952502\pi\)
0.782068 0.623193i \(-0.214165\pi\)
\(278\) −5.45863 1.46263i −0.327387 0.0877230i
\(279\) −7.93107 −0.474821
\(280\) 0 0
\(281\) −13.5101 −0.805944 −0.402972 0.915212i \(-0.632023\pi\)
−0.402972 + 0.915212i \(0.632023\pi\)
\(282\) 3.94750 + 1.05773i 0.235070 + 0.0629868i
\(283\) −5.14819 19.2133i −0.306028 1.14211i −0.932057 0.362313i \(-0.881987\pi\)
0.626028 0.779800i \(-0.284679\pi\)
\(284\) 6.51120 + 3.75924i 0.386369 + 0.223070i
\(285\) 0 0
\(286\) 3.17374i 0.187667i
\(287\) −5.61022 + 3.45226i −0.331161 + 0.203781i
\(288\) 0.707107 + 0.707107i 0.0416667 + 0.0416667i
\(289\) −14.7220 + 8.49977i −0.866001 + 0.499986i
\(290\) 0 0
\(291\) 0.187737 0.325171i 0.0110054 0.0190618i
\(292\) 0.969376 3.61776i 0.0567284 0.211713i
\(293\) −17.4044 + 17.4044i −1.01677 + 1.01677i −0.0169176 + 0.999857i \(0.505385\pi\)
−0.999857 + 0.0169176i \(0.994615\pi\)
\(294\) −6.24878 3.15479i −0.364436 0.183991i
\(295\) 0 0
\(296\) −5.31055 9.19815i −0.308670 0.534632i
\(297\) 1.12607 0.301730i 0.0653413 0.0175081i
\(298\) −0.213280 + 0.0571481i −0.0123550 + 0.00331050i
\(299\) 9.77320 + 16.9277i 0.565199 + 0.978953i
\(300\) 0 0
\(301\) −6.82771 + 28.6734i −0.393542 + 1.65271i
\(302\) −4.50346 + 4.50346i −0.259145 + 0.259145i
\(303\) 3.60170 13.4417i 0.206913 0.772208i
\(304\) 0.989363 1.71363i 0.0567439 0.0982833i
\(305\) 0 0
\(306\) 0.0187667 0.0108349i 0.00107282 0.000619393i
\(307\) 0.566349 + 0.566349i 0.0323232 + 0.0323232i 0.723084 0.690760i \(-0.242724\pi\)
−0.690760 + 0.723084i \(0.742724\pi\)
\(308\) 2.71335 + 1.46672i 0.154607 + 0.0835744i
\(309\) 11.9841i 0.681751i
\(310\) 0 0
\(311\) 11.6023 + 6.69862i 0.657909 + 0.379844i 0.791480 0.611196i \(-0.209311\pi\)
−0.133571 + 0.991039i \(0.542644\pi\)
\(312\) 0.704604 + 2.62962i 0.0398903 + 0.148873i
\(313\) −27.7781 7.44312i −1.57011 0.420710i −0.634263 0.773117i \(-0.718697\pi\)
−0.935847 + 0.352407i \(0.885363\pi\)
\(314\) −14.4763 −0.816943
\(315\) 0 0
\(316\) −1.61039 −0.0905918
\(317\) −32.5854 8.73124i −1.83018 0.490395i −0.832232 0.554427i \(-0.812938\pi\)
−0.997948 + 0.0640314i \(0.979604\pi\)
\(318\) −0.757613 2.82745i −0.0424848 0.158556i
\(319\) −5.65991 3.26775i −0.316894 0.182959i
\(320\) 0 0
\(321\) 6.90561i 0.385434i
\(322\) 18.9888 0.532455i 1.05820 0.0296725i
\(323\) −0.0303199 0.0303199i −0.00168704 0.00168704i
\(324\) 0.866025 0.500000i 0.0481125 0.0277778i
\(325\) 0 0
\(326\) 10.9528 18.9709i 0.606621 1.05070i
\(327\) −0.149420 + 0.557643i −0.00826294 + 0.0308377i
\(328\) 1.76053 1.76053i 0.0972091 0.0972091i
\(329\) 10.3616 3.09013i 0.571251 0.170364i
\(330\) 0 0
\(331\) 5.46781 + 9.47053i 0.300538 + 0.520547i 0.976258 0.216611i \(-0.0695004\pi\)
−0.675720 + 0.737159i \(0.736167\pi\)
\(332\) 13.3162 3.56807i 0.730823 0.195823i
\(333\) −10.2592 + 2.74894i −0.562201 + 0.150641i
\(334\) −8.05513 13.9519i −0.440757 0.763414i
\(335\) 0 0
\(336\) 2.57379 + 0.612870i 0.140412 + 0.0334348i
\(337\) 10.2916 10.2916i 0.560617 0.560617i −0.368866 0.929483i \(-0.620254\pi\)
0.929483 + 0.368866i \(0.120254\pi\)
\(338\) 1.44645 5.39822i 0.0786764 0.293624i
\(339\) −9.38250 + 16.2510i −0.509587 + 0.882631i
\(340\) 0 0
\(341\) 8.00727 4.62300i 0.433618 0.250349i
\(342\) −1.39917 1.39917i −0.0756585 0.0756585i
\(343\) −18.4548 + 1.55571i −0.996466 + 0.0840004i
\(344\) 11.1406i 0.600658i
\(345\) 0 0
\(346\) 9.04413 + 5.22163i 0.486215 + 0.280717i
\(347\) 0.661173 + 2.46753i 0.0354936 + 0.132464i 0.981399 0.191978i \(-0.0614902\pi\)
−0.945906 + 0.324442i \(0.894824\pi\)
\(348\) −5.41502 1.45095i −0.290276 0.0777791i
\(349\) −18.6079 −0.996058 −0.498029 0.867160i \(-0.665943\pi\)
−0.498029 + 0.867160i \(0.665943\pi\)
\(350\) 0 0
\(351\) 2.72238 0.145310
\(352\) −1.12607 0.301730i −0.0600198 0.0160823i
\(353\) 4.09742 + 15.2918i 0.218084 + 0.813900i 0.985058 + 0.172222i \(0.0550946\pi\)
−0.766974 + 0.641678i \(0.778239\pi\)
\(354\) 9.25995 + 5.34623i 0.492161 + 0.284149i
\(355\) 0 0
\(356\) 3.60510i 0.191070i
\(357\) 0.0272636 0.0504360i 0.00144294 0.00266935i
\(358\) −1.06563 1.06563i −0.0563204 0.0563204i
\(359\) 6.50055 3.75309i 0.343086 0.198081i −0.318550 0.947906i \(-0.603196\pi\)
0.661636 + 0.749825i \(0.269863\pi\)
\(360\) 0 0
\(361\) 7.54232 13.0637i 0.396964 0.687562i
\(362\) −5.52468 + 20.6184i −0.290371 + 1.08368i
\(363\) 6.81716 6.81716i 0.357808 0.357808i
\(364\) 5.23386 + 4.94835i 0.274329 + 0.259364i
\(365\) 0 0
\(366\) −1.82324 3.15795i −0.0953025 0.165069i
\(367\) −3.81343 + 1.02181i −0.199060 + 0.0533379i −0.356971 0.934115i \(-0.616191\pi\)
0.157912 + 0.987453i \(0.449524\pi\)
\(368\) −6.93525 + 1.85829i −0.361525 + 0.0968702i
\(369\) −1.24488 2.15620i −0.0648061 0.112247i
\(370\) 0 0
\(371\) −5.62762 5.32063i −0.292172 0.276233i
\(372\) 5.60811 5.60811i 0.290767 0.290767i
\(373\) −1.39610 + 5.21031i −0.0722872 + 0.269780i −0.992605 0.121393i \(-0.961264\pi\)
0.920317 + 0.391173i \(0.127931\pi\)
\(374\) −0.0126313 + 0.0218781i −0.000653150 + 0.00113129i
\(375\) 0 0
\(376\) −3.53923 + 2.04338i −0.182522 + 0.105379i
\(377\) −10.7917 10.7917i −0.555801 0.555801i
\(378\) 1.25813 2.32747i 0.0647113 0.119712i
\(379\) 2.47403i 0.127082i 0.997979 + 0.0635411i \(0.0202394\pi\)
−0.997979 + 0.0635411i \(0.979761\pi\)
\(380\) 0 0
\(381\) 1.66700 + 0.962442i 0.0854029 + 0.0493074i
\(382\) 1.66960 + 6.23105i 0.0854244 + 0.318808i
\(383\) 23.2872 + 6.23980i 1.18992 + 0.318839i 0.798855 0.601524i \(-0.205439\pi\)
0.391067 + 0.920362i \(0.372106\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 5.13858 0.261547
\(387\) −10.7609 2.88339i −0.547010 0.146571i
\(388\) 0.0971800 + 0.362681i 0.00493357 + 0.0184123i
\(389\) 5.58638 + 3.22530i 0.283241 + 0.163529i 0.634890 0.772603i \(-0.281046\pi\)
−0.351649 + 0.936132i \(0.614379\pi\)
\(390\) 0 0
\(391\) 0.155588i 0.00786840i
\(392\) 6.64933 2.18778i 0.335842 0.110500i
\(393\) 12.1267 + 12.1267i 0.611713 + 0.611713i
\(394\) 21.8429 12.6110i 1.10043 0.635334i
\(395\) 0 0
\(396\) −0.582897 + 1.00961i −0.0292917 + 0.0507347i
\(397\) −4.84423 + 18.0789i −0.243125 + 0.907354i 0.731192 + 0.682172i \(0.238964\pi\)
−0.974317 + 0.225182i \(0.927702\pi\)
\(398\) 3.49450 3.49450i 0.175163 0.175163i
\(399\) −5.09283 1.21270i −0.254960 0.0607110i
\(400\) 0 0
\(401\) 9.36968 + 16.2288i 0.467900 + 0.810426i 0.999327 0.0366779i \(-0.0116776\pi\)
−0.531428 + 0.847104i \(0.678344\pi\)
\(402\) 14.0621 3.76794i 0.701356 0.187928i
\(403\) 20.8557 5.58826i 1.03889 0.278371i
\(404\) 6.95796 + 12.0515i 0.346171 + 0.599587i
\(405\) 0 0
\(406\) −14.2136 + 4.23892i −0.705408 + 0.210374i
\(407\) 8.75542 8.75542i 0.433990 0.433990i
\(408\) −0.00560858 + 0.0209315i −0.000277666 + 0.00103626i
\(409\) 11.6768 20.2248i 0.577381 1.00005i −0.418398 0.908264i \(-0.637408\pi\)
0.995778 0.0917890i \(-0.0292585\pi\)
\(410\) 0 0
\(411\) −8.86443 + 5.11788i −0.437250 + 0.252446i
\(412\) 8.47403 + 8.47403i 0.417485 + 0.417485i
\(413\) 28.2785 0.792944i 1.39149 0.0390182i
\(414\) 7.17989i 0.352873i
\(415\) 0 0
\(416\) −2.35765 1.36119i −0.115593 0.0667378i
\(417\) −1.46263 5.45863i −0.0716255 0.267310i
\(418\) 2.22819 + 0.597041i 0.108984 + 0.0292022i
\(419\) 8.27092 0.404061 0.202030 0.979379i \(-0.435246\pi\)
0.202030 + 0.979379i \(0.435246\pi\)
\(420\) 0 0
\(421\) −33.3728 −1.62649 −0.813246 0.581920i \(-0.802302\pi\)
−0.813246 + 0.581920i \(0.802302\pi\)
\(422\) 18.3966 + 4.92934i 0.895530 + 0.239957i
\(423\) 1.05773 + 3.94750i 0.0514285 + 0.191934i
\(424\) 2.53502 + 1.46360i 0.123112 + 0.0710785i
\(425\) 0 0
\(426\) 7.51848i 0.364272i
\(427\) −8.48708 4.58776i −0.410719 0.222017i
\(428\) 4.88300 + 4.88300i 0.236029 + 0.236029i
\(429\) −2.74854 + 1.58687i −0.132701 + 0.0766147i
\(430\) 0 0
\(431\) 12.1733 21.0848i 0.586369 1.01562i −0.408334 0.912832i \(-0.633890\pi\)
0.994703 0.102788i \(-0.0327764\pi\)
\(432\) −0.258819 + 0.965926i −0.0124524 + 0.0464731i
\(433\) 18.0803 18.0803i 0.868885 0.868885i −0.123464 0.992349i \(-0.539400\pi\)
0.992349 + 0.123464i \(0.0394002\pi\)
\(434\) 4.86071 20.4129i 0.233322 0.979850i
\(435\) 0 0
\(436\) −0.288657 0.499969i −0.0138242 0.0239442i
\(437\) 13.7230 3.67705i 0.656458 0.175897i
\(438\) 3.61776 0.969376i 0.172863 0.0463186i
\(439\) −8.11012 14.0471i −0.387075 0.670433i 0.604980 0.796241i \(-0.293181\pi\)
−0.992055 + 0.125808i \(0.959848\pi\)
\(440\) 0 0
\(441\) −0.392259 6.98900i −0.0186790 0.332810i
\(442\) −0.0417148 + 0.0417148i −0.00198417 + 0.00198417i
\(443\) −5.63860 + 21.0436i −0.267898 + 0.999810i 0.692554 + 0.721366i \(0.256485\pi\)
−0.960452 + 0.278444i \(0.910181\pi\)
\(444\) 5.31055 9.19815i 0.252028 0.436525i
\(445\) 0 0
\(446\) 3.60676 2.08236i 0.170785 0.0986027i
\(447\) −0.156132 0.156132i −0.00738477 0.00738477i
\(448\) −2.25331 + 1.38658i −0.106459 + 0.0655097i
\(449\) 10.1648i 0.479708i −0.970809 0.239854i \(-0.922900\pi\)
0.970809 0.239854i \(-0.0770996\pi\)
\(450\) 0 0
\(451\) 2.51369 + 1.45128i 0.118365 + 0.0683381i
\(452\) −4.85674 18.1256i −0.228442 0.852556i
\(453\) −6.15184 1.64838i −0.289038 0.0774476i
\(454\) −18.4389 −0.865381
\(455\) 0 0
\(456\) 1.97873 0.0926624
\(457\) −27.5526 7.38270i −1.28886 0.345348i −0.451631 0.892205i \(-0.649158\pi\)
−0.837226 + 0.546856i \(0.815824\pi\)
\(458\) 1.52965 + 5.70873i 0.0714758 + 0.266751i
\(459\) 0.0187667 + 0.0108349i 0.000875953 + 0.000505732i
\(460\) 0 0
\(461\) 20.0972i 0.936022i −0.883723 0.468011i \(-0.844971\pi\)
0.883723 0.468011i \(-0.155029\pi\)
\(462\) 0.0864543 + 3.08319i 0.00402222 + 0.143443i
\(463\) 7.34462 + 7.34462i 0.341334 + 0.341334i 0.856869 0.515535i \(-0.172407\pi\)
−0.515535 + 0.856869i \(0.672407\pi\)
\(464\) 4.85498 2.80302i 0.225387 0.130127i
\(465\) 0 0
\(466\) 3.61767 6.26598i 0.167585 0.290266i
\(467\) 6.10926 22.8001i 0.282703 1.05506i −0.667799 0.744342i \(-0.732763\pi\)
0.950502 0.310720i \(-0.100570\pi\)
\(468\) −1.92501 + 1.92501i −0.0889838 + 0.0889838i
\(469\) 26.4618 27.9886i 1.22189 1.29239i
\(470\) 0 0
\(471\) −7.23813 12.5368i −0.333515 0.577666i
\(472\) −10.3281 + 2.76741i −0.475391 + 0.127381i
\(473\) 12.5451 3.36144i 0.576822 0.154559i
\(474\) −0.805197 1.39464i −0.0369839 0.0640581i
\(475\) 0 0
\(476\) 0.0163853 + 0.0549419i 0.000751021 + 0.00251826i
\(477\) 2.06984 2.06984i 0.0947714 0.0947714i
\(478\) 1.08748 4.05855i 0.0497404 0.185634i
\(479\) −12.3892 + 21.4588i −0.566079 + 0.980478i 0.430869 + 0.902414i \(0.358207\pi\)
−0.996948 + 0.0780633i \(0.975126\pi\)
\(480\) 0 0
\(481\) 25.0409 14.4573i 1.14176 0.659198i
\(482\) 15.5110 + 15.5110i 0.706507 + 0.706507i
\(483\) 9.95550 + 16.1785i 0.452991 + 0.736148i
\(484\) 9.64092i 0.438224i
\(485\) 0 0
\(486\) 0.866025 + 0.500000i 0.0392837 + 0.0226805i
\(487\) −6.15129 22.9569i −0.278741 1.04028i −0.953292 0.302049i \(-0.902329\pi\)
0.674551 0.738228i \(-0.264337\pi\)
\(488\) 3.52224 + 0.943781i 0.159444 + 0.0427229i
\(489\) 21.9057 0.990608
\(490\) 0 0
\(491\) −0.386093 −0.0174242 −0.00871208 0.999962i \(-0.502773\pi\)
−0.00871208 + 0.999962i \(0.502773\pi\)
\(492\) 2.40493 + 0.644400i 0.108423 + 0.0290518i
\(493\) −0.0314419 0.117343i −0.00141607 0.00528486i
\(494\) 4.66514 + 2.69342i 0.209895 + 0.121183i
\(495\) 0 0
\(496\) 7.93107i 0.356115i
\(497\) 10.4250 + 16.9415i 0.467624 + 0.759928i
\(498\) 9.74815 + 9.74815i 0.436825 + 0.436825i
\(499\) −6.94992 + 4.01254i −0.311121 + 0.179626i −0.647428 0.762127i \(-0.724155\pi\)
0.336307 + 0.941752i \(0.390822\pi\)
\(500\) 0 0
\(501\) 8.05513 13.9519i 0.359877 0.623325i
\(502\) 3.91575 14.6138i 0.174768 0.652244i
\(503\) −11.5901 + 11.5901i −0.516775 + 0.516775i −0.916594 0.399819i \(-0.869073\pi\)
0.399819 + 0.916594i \(0.369073\pi\)
\(504\) 0.756134 + 2.53540i 0.0336809 + 0.112936i
\(505\) 0 0
\(506\) −4.18514 7.24888i −0.186052 0.322252i
\(507\) 5.39822 1.44645i 0.239743 0.0642390i
\(508\) −1.85929 + 0.498197i −0.0824929 + 0.0221039i
\(509\) 7.77422 + 13.4654i 0.344586 + 0.596841i 0.985279 0.170957i \(-0.0546858\pi\)
−0.640692 + 0.767798i \(0.721352\pi\)
\(510\) 0 0
\(511\) 6.80781 7.20062i 0.301160 0.318536i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 0.512132 1.91130i 0.0226112 0.0843861i
\(514\) 11.5071 19.9309i 0.507558 0.879116i
\(515\) 0 0
\(516\) 9.64800 5.57028i 0.424730 0.245218i
\(517\) −3.36888 3.36888i −0.148163 0.148163i
\(518\) −0.787652 28.0898i −0.0346074 1.23419i
\(519\) 10.4433i 0.458408i
\(520\) 0 0
\(521\) 22.8573 + 13.1967i 1.00140 + 0.578156i 0.908661 0.417535i \(-0.137106\pi\)
0.0927347 + 0.995691i \(0.470439\pi\)
\(522\) −1.45095 5.41502i −0.0635064 0.237009i
\(523\) 38.1134 + 10.2125i 1.66658 + 0.446559i 0.964186 0.265227i \(-0.0854469\pi\)
0.702396 + 0.711786i \(0.252114\pi\)
\(524\) −17.1498 −0.749192
\(525\) 0 0
\(526\) 20.1205 0.877294
\(527\) 0.166009 + 0.0444820i 0.00723147 + 0.00193767i
\(528\) −0.301730 1.12607i −0.0131311 0.0490060i
\(529\) −24.7258 14.2754i −1.07503 0.620671i
\(530\) 0 0
\(531\) 10.6925i 0.464014i
\(532\) 4.45868 2.74366i 0.193308 0.118953i
\(533\) 4.79284 + 4.79284i 0.207601 + 0.207601i
\(534\) −3.12211 + 1.80255i −0.135107 + 0.0780040i
\(535\) 0 0
\(536\) −7.27910 + 12.6078i −0.314409 + 0.544573i
\(537\) 0.390048 1.45568i 0.0168318 0.0628172i
\(538\) −6.55459 + 6.55459i −0.282588 + 0.282588i
\(539\) 4.46990 + 6.82750i 0.192532 + 0.294081i
\(540\) 0 0
\(541\) −4.06849 7.04683i −0.174918 0.302967i 0.765215 0.643775i \(-0.222633\pi\)
−0.940133 + 0.340808i \(0.889299\pi\)
\(542\) −25.3360 + 6.78877i −1.08828 + 0.291603i
\(543\) −20.6184 + 5.52468i −0.884820 + 0.237087i
\(544\) −0.0108349 0.0187667i −0.000464544 0.000804615i
\(545\) 0 0
\(546\) −1.66846 + 7.00683i −0.0714037 + 0.299865i
\(547\) −12.5204 + 12.5204i −0.535335 + 0.535335i −0.922155 0.386820i \(-0.873573\pi\)
0.386820 + 0.922155i \(0.373573\pi\)
\(548\) 2.64921 9.88699i 0.113169 0.422351i
\(549\) 1.82324 3.15795i 0.0778142 0.134778i
\(550\) 0 0
\(551\) −9.60667 + 5.54641i −0.409258 + 0.236285i
\(552\) −5.07695 5.07695i −0.216089 0.216089i
\(553\) −3.74814 2.02609i −0.159387 0.0861581i
\(554\) 13.2995i 0.565040i
\(555\) 0 0
\(556\) 4.89407 + 2.82559i 0.207555 + 0.119832i
\(557\) 4.19123 + 15.6419i 0.177588 + 0.662768i 0.996096 + 0.0882732i \(0.0281348\pi\)
−0.818508 + 0.574495i \(0.805198\pi\)
\(558\) 7.66082 + 2.05271i 0.324308 + 0.0868982i
\(559\) 30.3288 1.28277
\(560\) 0 0
\(561\) −0.0252626 −0.00106659
\(562\) 13.0497 + 3.49667i 0.550470 + 0.147498i
\(563\) −2.26573 8.45582i −0.0954892 0.356370i 0.901604 0.432562i \(-0.142390\pi\)
−0.997093 + 0.0761920i \(0.975724\pi\)
\(564\) −3.53923 2.04338i −0.149028 0.0860416i
\(565\) 0 0
\(566\) 19.8911i 0.836085i
\(567\) 2.64471 0.0741591i 0.111067 0.00311439i
\(568\) −5.31637 5.31637i −0.223070 0.223070i
\(569\) −35.9794 + 20.7727i −1.50833 + 0.870838i −0.508382 + 0.861132i \(0.669756\pi\)
−0.999953 + 0.00970591i \(0.996910\pi\)
\(570\) 0 0
\(571\) −6.59259 + 11.4187i −0.275891 + 0.477858i −0.970360 0.241666i \(-0.922306\pi\)
0.694468 + 0.719523i \(0.255640\pi\)
\(572\) 0.821423 3.06559i 0.0343454 0.128179i
\(573\) −4.56144 + 4.56144i −0.190557 + 0.190557i
\(574\) 6.31256 1.88260i 0.263481 0.0785782i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −17.3319 + 4.64406i −0.721535 + 0.193335i −0.600857 0.799357i \(-0.705174\pi\)
−0.120679 + 0.992692i \(0.538507\pi\)
\(578\) 16.4203 4.39980i 0.682994 0.183008i
\(579\) 2.56929 + 4.45014i 0.106776 + 0.184942i
\(580\) 0 0
\(581\) 35.4822 + 8.44900i 1.47205 + 0.350524i
\(582\) −0.265501 + 0.265501i −0.0110054 + 0.0110054i
\(583\) −0.883222 + 3.29623i −0.0365793 + 0.136516i
\(584\) −1.87269 + 3.24360i −0.0774925 + 0.134221i
\(585\) 0 0
\(586\) 21.3159 12.3068i 0.880553 0.508387i
\(587\) −7.68342 7.68342i −0.317129 0.317129i 0.530535 0.847663i \(-0.321991\pi\)
−0.847663 + 0.530535i \(0.821991\pi\)
\(588\) 5.21934 + 4.66460i 0.215242 + 0.192365i
\(589\) 15.6934i 0.646636i
\(590\) 0 0
\(591\) 21.8429 + 12.6110i 0.898499 + 0.518748i
\(592\) 2.74894 + 10.2592i 0.112981 + 0.421651i
\(593\) 7.58832 + 2.03328i 0.311615 + 0.0834970i 0.411237 0.911528i \(-0.365097\pi\)
−0.0996223 + 0.995025i \(0.531763\pi\)
\(594\) −1.16579 −0.0478331
\(595\) 0 0
\(596\) 0.220803 0.00904446
\(597\) 4.77357 + 1.27908i 0.195369 + 0.0523491i
\(598\) −5.05898 18.8804i −0.206877 0.772076i
\(599\) −20.5520 11.8657i −0.839731 0.484819i 0.0174418 0.999848i \(-0.494448\pi\)
−0.857173 + 0.515029i \(0.827781\pi\)
\(600\) 0 0
\(601\) 14.4348i 0.588806i −0.955681 0.294403i \(-0.904879\pi\)
0.955681 0.294403i \(-0.0951208\pi\)
\(602\) 14.0163 25.9293i 0.571261 1.05680i
\(603\) 10.2942 + 10.2942i 0.419213 + 0.419213i
\(604\) 5.51559 3.18442i 0.224426 0.129572i
\(605\) 0 0
\(606\) −6.95796 + 12.0515i −0.282648 + 0.489560i
\(607\) −0.172772 + 0.644795i −0.00701261 + 0.0261714i −0.969343 0.245710i \(-0.920979\pi\)
0.962331 + 0.271881i \(0.0876457\pi\)
\(608\) −1.39917 + 1.39917i −0.0567439 + 0.0567439i
\(609\) −10.7778 10.1899i −0.436738 0.412914i
\(610\) 0 0
\(611\) −5.56284 9.63513i −0.225049 0.389796i
\(612\) −0.0209315 + 0.00560858i −0.000846106 + 0.000226713i
\(613\) −14.2571 + 3.82018i −0.575839 + 0.154296i −0.534973 0.844869i \(-0.679678\pi\)
−0.0408659 + 0.999165i \(0.513012\pi\)
\(614\) −0.400469 0.693633i −0.0161616 0.0279927i
\(615\) 0 0
\(616\) −2.24128 2.11901i −0.0903037 0.0853775i
\(617\) 4.88322 4.88322i 0.196591 0.196591i −0.601946 0.798537i \(-0.705608\pi\)
0.798537 + 0.601946i \(0.205608\pi\)
\(618\) −3.10171 + 11.5757i −0.124769 + 0.465644i
\(619\) −13.8975 + 24.0712i −0.558589 + 0.967504i 0.439026 + 0.898474i \(0.355324\pi\)
−0.997615 + 0.0690295i \(0.978010\pi\)
\(620\) 0 0
\(621\) −6.21797 + 3.58995i −0.249519 + 0.144060i
\(622\) −9.47327 9.47327i −0.379844 0.379844i
\(623\) −4.53569 + 8.39075i −0.181719 + 0.336168i
\(624\) 2.72238i 0.108982i
\(625\) 0 0
\(626\) 24.9051 + 14.3790i 0.995410 + 0.574700i
\(627\) 0.597041 + 2.22819i 0.0238435 + 0.0889852i
\(628\) 13.9830 + 3.74673i 0.557982 + 0.149511i
\(629\) 0.230158 0.00917701
\(630\) 0 0
\(631\) 6.30112 0.250844 0.125422 0.992104i \(-0.459972\pi\)
0.125422 + 0.992104i \(0.459972\pi\)
\(632\) 1.55552 + 0.416801i 0.0618753 + 0.0165794i
\(633\) 4.92934 + 18.3966i 0.195924 + 0.731197i
\(634\) 29.2153 + 16.8675i 1.16029 + 0.669893i
\(635\) 0 0
\(636\) 2.92719i 0.116071i
\(637\) 5.95597 + 18.1020i 0.235984 + 0.717228i
\(638\) 4.62129 + 4.62129i 0.182959 + 0.182959i
\(639\) −6.51120 + 3.75924i −0.257579 + 0.148713i
\(640\) 0 0
\(641\) −2.63684 + 4.56715i −0.104149 + 0.180391i −0.913390 0.407085i \(-0.866545\pi\)
0.809241 + 0.587477i \(0.199879\pi\)
\(642\) −1.78730 + 6.67031i −0.0705393 + 0.263256i
\(643\) 5.34948 5.34948i 0.210963 0.210963i −0.593714 0.804677i \(-0.702339\pi\)
0.804677 + 0.593714i \(0.202339\pi\)
\(644\) −18.4795 4.40034i −0.728196 0.173398i
\(645\) 0 0
\(646\) 0.0214394 + 0.0371341i 0.000843522 + 0.00146102i
\(647\) 21.4035 5.73506i 0.841460 0.225469i 0.187753 0.982216i \(-0.439880\pi\)
0.653707 + 0.756748i \(0.273213\pi\)
\(648\) −0.965926 + 0.258819i −0.0379452 + 0.0101674i
\(649\) −6.23261 10.7952i −0.244651 0.423749i
\(650\) 0 0
\(651\) 20.1084 5.99695i 0.788112 0.235039i
\(652\) −15.4896 + 15.4896i −0.606621 + 0.606621i
\(653\) 11.4754 42.8267i 0.449066 1.67594i −0.255907 0.966702i \(-0.582374\pi\)
0.704972 0.709235i \(-0.250959\pi\)
\(654\) 0.288657 0.499969i 0.0112874 0.0195503i
\(655\) 0 0
\(656\) −2.15620 + 1.24488i −0.0841856 + 0.0486046i
\(657\) 2.64838 + 2.64838i 0.103323 + 0.103323i
\(658\) −10.8083 + 0.303070i −0.421351 + 0.0118149i
\(659\) 38.6387i 1.50515i −0.658507 0.752575i \(-0.728812\pi\)
0.658507 0.752575i \(-0.271188\pi\)
\(660\) 0 0
\(661\) −24.7737 14.3031i −0.963587 0.556327i −0.0663118 0.997799i \(-0.521123\pi\)
−0.897275 + 0.441472i \(0.854457\pi\)
\(662\) −2.83035 10.5630i −0.110005 0.410543i
\(663\) −0.0569835 0.0152687i −0.00221306 0.000592987i
\(664\) −13.7860 −0.534999
\(665\) 0 0
\(666\) 10.6211 0.411560
\(667\) 38.8793 + 10.4177i 1.50541 + 0.403374i
\(668\) 4.16964 + 15.5613i 0.161328 + 0.602086i
\(669\) 3.60676 + 2.08236i 0.139445 + 0.0805088i
\(670\) 0 0
\(671\) 4.25106i 0.164110i
\(672\) −2.32747 1.25813i −0.0897840 0.0485335i
\(673\) −36.6126 36.6126i −1.41131 1.41131i −0.750932 0.660379i \(-0.770396\pi\)
−0.660379 0.750932i \(-0.729604\pi\)
\(674\) −12.6045 + 7.27723i −0.485509 + 0.280309i
\(675\) 0 0
\(676\) −2.79432 + 4.83991i −0.107474 + 0.186150i
\(677\) 6.94951 25.9359i 0.267091 0.996798i −0.693867 0.720104i \(-0.744094\pi\)
0.960958 0.276695i \(-0.0892390\pi\)
\(678\) 13.2689 13.2689i 0.509587 0.509587i
\(679\) −0.230117 + 0.966393i −0.00883108 + 0.0370868i
\(680\) 0 0
\(681\) −9.21945 15.9686i −0.353290 0.611917i
\(682\) −8.93095 + 2.39304i −0.341984 + 0.0916342i
\(683\) −1.91999 + 0.514460i −0.0734664 + 0.0196853i −0.295365 0.955384i \(-0.595441\pi\)
0.221899 + 0.975070i \(0.428775\pi\)
\(684\) 0.989363 + 1.71363i 0.0378293 + 0.0655222i
\(685\) 0 0
\(686\) 18.2286 + 3.27375i 0.695972 + 0.124993i
\(687\) −4.17908 + 4.17908i −0.159442 + 0.159442i
\(688\) −2.88339 + 10.7609i −0.109928 + 0.410257i
\(689\) −3.98446 + 6.90130i −0.151796 + 0.262918i
\(690\) 0 0
\(691\) −8.33571 + 4.81262i −0.317105 + 0.183081i −0.650102 0.759847i \(-0.725274\pi\)
0.332996 + 0.942928i \(0.391940\pi\)
\(692\) −7.38450 7.38450i −0.280717 0.280717i
\(693\) −2.62690 + 1.61647i −0.0997875 + 0.0614045i
\(694\) 2.55458i 0.0969703i
\(695\) 0 0
\(696\) 4.85498 + 2.80302i 0.184027 + 0.106248i
\(697\) 0.0139641 + 0.0521146i 0.000528927 + 0.00197398i
\(698\) 17.9739 + 4.81608i 0.680320 + 0.182291i
\(699\) 7.23533 0.273665
\(700\) 0 0
\(701\) −12.4958 −0.471959 −0.235980 0.971758i \(-0.575830\pi\)
−0.235980 + 0.971758i \(0.575830\pi\)
\(702\) −2.62962 0.704604i −0.0992485 0.0265936i
\(703\) −5.43941 20.3002i −0.205151 0.765635i
\(704\) 1.00961 + 0.582897i 0.0380510 + 0.0219688i
\(705\) 0 0
\(706\) 15.8312i 0.595816i
\(707\) 1.03199 + 36.8036i 0.0388121 + 1.38414i
\(708\) −7.56072 7.56072i −0.284149 0.284149i
\(709\) 39.6174 22.8731i 1.48786 0.859018i 0.487958 0.872867i \(-0.337742\pi\)
0.999904 + 0.0138494i \(0.00440856\pi\)
\(710\) 0 0
\(711\) 0.805197 1.39464i 0.0301973 0.0523032i
\(712\) 0.933068 3.48226i 0.0349682 0.130503i
\(713\) −40.2656 + 40.2656i −1.50796 + 1.50796i
\(714\) −0.0393884 + 0.0416611i −0.00147407 + 0.00155913i
\(715\) 0 0
\(716\) 0.753516 + 1.30513i 0.0281602 + 0.0487749i
\(717\) 4.05855 1.08748i 0.151569 0.0406129i
\(718\) −7.25042 + 1.94274i −0.270583 + 0.0725025i
\(719\) −8.05439 13.9506i −0.300378 0.520270i 0.675844 0.737045i \(-0.263779\pi\)
−0.976222 + 0.216775i \(0.930446\pi\)
\(720\) 0 0
\(721\) 9.06157 + 30.3845i 0.337471 + 1.13158i
\(722\) −10.6665 + 10.6665i −0.396964 + 0.396964i
\(723\) −5.67742 + 21.1884i −0.211146 + 0.788006i
\(724\) 10.6729 18.4859i 0.396654 0.687025i
\(725\) 0 0
\(726\) −8.34928 + 4.82046i −0.309871 + 0.178904i
\(727\) −26.7345 26.7345i −0.991528 0.991528i 0.00843633 0.999964i \(-0.497315\pi\)
−0.999964 + 0.00843633i \(0.997315\pi\)
\(728\) −3.77480 6.13436i −0.139903 0.227355i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 0.209071 + 0.120707i 0.00773278 + 0.00446452i
\(732\) 0.943781 + 3.52224i 0.0348831 + 0.130186i
\(733\) 9.81640 + 2.63030i 0.362577 + 0.0971523i 0.435508 0.900185i \(-0.356569\pi\)
−0.0729311 + 0.997337i \(0.523235\pi\)
\(734\) 3.94796 0.145722
\(735\) 0 0
\(736\) 7.17989 0.264654
\(737\) −16.3936 4.39265i −0.603865 0.161805i
\(738\) 0.644400 + 2.40493i 0.0237207 + 0.0885268i
\(739\) 1.51357 + 0.873858i 0.0556775 + 0.0321454i 0.527580 0.849505i \(-0.323099\pi\)
−0.471903 + 0.881651i \(0.656433\pi\)
\(740\) 0 0
\(741\) 5.38685i 0.197891i
\(742\) 4.05879 + 6.59587i 0.149003 + 0.242142i
\(743\) −4.26452 4.26452i −0.156450 0.156450i 0.624542 0.780992i \(-0.285286\pi\)
−0.780992 + 0.624542i \(0.785286\pi\)
\(744\) −6.86850 + 3.96553i −0.251812 + 0.145383i
\(745\) 0 0
\(746\) 2.69706 4.67144i 0.0987462 0.171033i
\(747\) −3.56807 + 13.3162i −0.130549 + 0.487215i
\(748\) 0.0178634 0.0178634i 0.000653150 0.000653150i
\(749\) 5.22157 + 17.5085i 0.190792 + 0.639747i
\(750\) 0 0
\(751\) −7.54354 13.0658i −0.275268 0.476778i 0.694935 0.719073i \(-0.255433\pi\)
−0.970203 + 0.242295i \(0.922100\pi\)
\(752\) 3.94750 1.05773i 0.143950 0.0385714i
\(753\) 14.6138 3.91575i 0.532555 0.142698i
\(754\) 7.63089 + 13.2171i 0.277901 + 0.481338i
\(755\) 0 0
\(756\) −1.81766 + 1.92253i −0.0661075 + 0.0699218i
\(757\) 7.26095 7.26095i 0.263904 0.263904i −0.562734 0.826638i \(-0.690251\pi\)
0.826638 + 0.562734i \(0.190251\pi\)
\(758\) 0.640325 2.38973i 0.0232576 0.0867987i
\(759\) 4.18514 7.24888i 0.151911 0.263118i
\(760\) 0 0
\(761\) −10.7048 + 6.18041i −0.388048 + 0.224040i −0.681314 0.731991i \(-0.738591\pi\)
0.293266 + 0.956031i \(0.405258\pi\)
\(762\) −1.36110 1.36110i −0.0493074 0.0493074i
\(763\) −0.0428131 1.52683i −0.00154994 0.0552750i
\(764\) 6.45086i 0.233384i
\(765\) 0 0
\(766\) −20.8788 12.0544i −0.754380 0.435542i
\(767\) −7.53395 28.1171i −0.272035 1.01525i
\(768\) 0.965926 + 0.258819i 0.0348548 + 0.00933933i
\(769\) 17.1708 0.619196 0.309598 0.950867i \(-0.399805\pi\)
0.309598 + 0.950867i \(0.399805\pi\)
\(770\) 0 0
\(771\) 23.0143 0.828839
\(772\) −4.96349 1.32996i −0.178640 0.0478664i
\(773\) 0.327680 + 1.22292i 0.0117858 + 0.0439853i 0.971568 0.236759i \(-0.0760853\pi\)
−0.959783 + 0.280745i \(0.909419\pi\)
\(774\) 9.64800 + 5.57028i 0.346790 + 0.200219i
\(775\) 0 0
\(776\) 0.375475i 0.0134788i
\(777\) 23.9326 14.7270i 0.858578 0.528329i
\(778\) −4.56126 4.56126i −0.163529 0.163529i
\(779\) 4.26654 2.46329i 0.152865 0.0882564i
\(780\) 0 0
\(781\) 4.38251 7.59072i 0.156818