Properties

Label 637.2.k.h.459.2
Level $637$
Weight $2$
Character 637.459
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.58891012706304.1
Defining polynomial: \( x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 459.2
Root \(1.40744 - 0.138282i\) of defining polynomial
Character \(\chi\) \(=\) 637.459
Dual form 637.2.k.h.569.5

$q$-expansion

\(f(q)\) \(=\) \(q-1.27656i q^{2} +(0.583963 + 1.01145i) q^{3} +0.370384 q^{4} +(1.57173 - 0.907437i) q^{5} +(1.29118 - 0.745466i) q^{6} -3.02595i q^{8} +(0.817975 - 1.41677i) q^{9} +O(q^{10})\) \(q-1.27656i q^{2} +(0.583963 + 1.01145i) q^{3} +0.370384 q^{4} +(1.57173 - 0.907437i) q^{5} +(1.29118 - 0.745466i) q^{6} -3.02595i q^{8} +(0.817975 - 1.41677i) q^{9} +(-1.15840 - 2.00641i) q^{10} +(2.40625 - 1.38925i) q^{11} +(0.216290 + 0.374626i) q^{12} +(-3.58305 + 0.402155i) q^{13} +(1.83566 + 1.05982i) q^{15} -3.12205 q^{16} -2.74396 q^{17} +(-1.80860 - 1.04420i) q^{18} +(5.08351 + 2.93497i) q^{19} +(0.582143 - 0.336100i) q^{20} +(-1.77346 - 3.07173i) q^{22} -6.99909 q^{23} +(3.06060 - 1.76704i) q^{24} +(-0.853117 + 1.47764i) q^{25} +(0.513376 + 4.57400i) q^{26} +5.41444 q^{27} +(1.75806 - 3.04505i) q^{29} +(1.35293 - 2.34334i) q^{30} +(1.79004 + 1.03348i) q^{31} -2.06640i q^{32} +(2.81031 + 1.62254i) q^{33} +3.50284i q^{34} +(0.302965 - 0.524751i) q^{36} -1.74302i q^{37} +(3.74667 - 6.48942i) q^{38} +(-2.49913 - 3.38925i) q^{39} +(-2.74586 - 4.75596i) q^{40} +(5.51406 + 3.18355i) q^{41} +(4.55195 + 7.88422i) q^{43} +(0.891235 - 0.514555i) q^{44} -2.96904i q^{45} +8.93479i q^{46} +(-5.76714 + 3.32966i) q^{47} +(-1.82316 - 3.15780i) q^{48} +(1.88631 + 1.08906i) q^{50} +(-1.60237 - 2.77539i) q^{51} +(-1.32711 + 0.148952i) q^{52} +(5.24396 - 9.08280i) q^{53} -6.91188i q^{54} +(2.52131 - 4.36703i) q^{55} +6.85564i q^{57} +(-3.88720 - 2.24427i) q^{58} +3.07396i q^{59} +(0.679899 + 0.392540i) q^{60} +(-0.540892 + 0.936853i) q^{61} +(1.31931 - 2.28511i) q^{62} -8.88199 q^{64} +(-5.26665 + 3.88347i) q^{65} +(2.07127 - 3.58755i) q^{66} +(-4.34568 + 2.50898i) q^{67} -1.01632 q^{68} +(-4.08721 - 7.07925i) q^{69} +(2.35453 - 1.35939i) q^{71} +(-4.28709 - 2.47515i) q^{72} +(-6.64426 - 3.83607i) q^{73} -2.22508 q^{74} -1.99275 q^{75} +(1.88285 + 1.08706i) q^{76} +(-4.32659 + 3.19030i) q^{78} +(7.86993 + 13.6311i) q^{79} +(-4.90700 + 2.83306i) q^{80} +(0.707906 + 1.22613i) q^{81} +(4.06400 - 7.03905i) q^{82} -7.97408i q^{83} +(-4.31275 + 2.48997i) q^{85} +(10.0647 - 5.81086i) q^{86} +4.10656 q^{87} +(-4.20379 - 7.28117i) q^{88} +16.0640i q^{89} -3.79017 q^{90} -2.59235 q^{92} +2.41406i q^{93} +(4.25052 + 7.36212i) q^{94} +10.6532 q^{95} +(2.09007 - 1.20670i) q^{96} +(-12.3209 + 7.11347i) q^{97} -4.54548i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 8 q^{4} + 6 q^{5} - 18 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 8 q^{4} + 6 q^{5} - 18 q^{6} - 4 q^{9} + 12 q^{10} - 6 q^{11} + 2 q^{12} + 4 q^{13} + 6 q^{15} + 16 q^{16} + 8 q^{17} + 12 q^{18} - 12 q^{20} + 6 q^{22} + 24 q^{23} - 12 q^{24} + 10 q^{25} + 18 q^{26} + 12 q^{27} + 8 q^{29} + 8 q^{30} - 18 q^{31} + 30 q^{33} - 10 q^{36} - 2 q^{38} + 14 q^{39} - 46 q^{40} + 30 q^{41} + 2 q^{43} - 24 q^{44} - 42 q^{47} - 2 q^{48} - 18 q^{50} - 26 q^{51} - 28 q^{52} + 22 q^{53} - 6 q^{55} + 12 q^{58} - 66 q^{60} + 14 q^{61} - 4 q^{62} - 52 q^{64} - 18 q^{65} + 26 q^{66} + 24 q^{67} + 16 q^{68} + 4 q^{69} - 24 q^{71} - 60 q^{72} - 30 q^{73} - 12 q^{74} - 92 q^{75} - 18 q^{76} - 10 q^{78} + 28 q^{79} + 72 q^{80} + 2 q^{81} + 14 q^{82} - 48 q^{85} + 60 q^{86} + 4 q^{87} - 14 q^{88} + 24 q^{90} + 24 q^{92} + 4 q^{94} + 44 q^{95} - 6 q^{96} + 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.27656i 0.902667i −0.892355 0.451334i \(-0.850948\pi\)
0.892355 0.451334i \(-0.149052\pi\)
\(3\) 0.583963 + 1.01145i 0.337151 + 0.583963i 0.983896 0.178744i \(-0.0572034\pi\)
−0.646745 + 0.762707i \(0.723870\pi\)
\(4\) 0.370384 0.185192
\(5\) 1.57173 0.907437i 0.702897 0.405818i −0.105528 0.994416i \(-0.533653\pi\)
0.808426 + 0.588598i \(0.200320\pi\)
\(6\) 1.29118 0.745466i 0.527124 0.304335i
\(7\) 0 0
\(8\) 3.02595i 1.06983i
\(9\) 0.817975 1.41677i 0.272658 0.472258i
\(10\) −1.15840 2.00641i −0.366319 0.634482i
\(11\) 2.40625 1.38925i 0.725510 0.418874i −0.0912671 0.995826i \(-0.529092\pi\)
0.816777 + 0.576953i \(0.195758\pi\)
\(12\) 0.216290 + 0.374626i 0.0624377 + 0.108145i
\(13\) −3.58305 + 0.402155i −0.993760 + 0.111538i
\(14\) 0 0
\(15\) 1.83566 + 1.05982i 0.473965 + 0.273644i
\(16\) −3.12205 −0.780512
\(17\) −2.74396 −0.665508 −0.332754 0.943014i \(-0.607978\pi\)
−0.332754 + 0.943014i \(0.607978\pi\)
\(18\) −1.80860 1.04420i −0.426292 0.246120i
\(19\) 5.08351 + 2.93497i 1.16624 + 0.673327i 0.952791 0.303628i \(-0.0981979\pi\)
0.213446 + 0.976955i \(0.431531\pi\)
\(20\) 0.582143 0.336100i 0.130171 0.0751543i
\(21\) 0 0
\(22\) −1.77346 3.07173i −0.378103 0.654894i
\(23\) −6.99909 −1.45941 −0.729706 0.683761i \(-0.760343\pi\)
−0.729706 + 0.683761i \(0.760343\pi\)
\(24\) 3.06060 1.76704i 0.624743 0.360696i
\(25\) −0.853117 + 1.47764i −0.170623 + 0.295528i
\(26\) 0.513376 + 4.57400i 0.100681 + 0.897035i
\(27\) 5.41444 1.04201
\(28\) 0 0
\(29\) 1.75806 3.04505i 0.326463 0.565451i −0.655344 0.755330i \(-0.727476\pi\)
0.981807 + 0.189879i \(0.0608097\pi\)
\(30\) 1.35293 2.34334i 0.247009 0.427833i
\(31\) 1.79004 + 1.03348i 0.321501 + 0.185619i 0.652062 0.758166i \(-0.273904\pi\)
−0.330560 + 0.943785i \(0.607238\pi\)
\(32\) 2.06640i 0.365292i
\(33\) 2.81031 + 1.62254i 0.489213 + 0.282447i
\(34\) 3.50284i 0.600732i
\(35\) 0 0
\(36\) 0.302965 0.524751i 0.0504942 0.0874585i
\(37\) 1.74302i 0.286551i −0.989683 0.143276i \(-0.954236\pi\)
0.989683 0.143276i \(-0.0457635\pi\)
\(38\) 3.74667 6.48942i 0.607790 1.05272i
\(39\) −2.49913 3.38925i −0.400181 0.542714i
\(40\) −2.74586 4.75596i −0.434158 0.751984i
\(41\) 5.51406 + 3.18355i 0.861152 + 0.497186i 0.864398 0.502808i \(-0.167700\pi\)
−0.00324599 + 0.999995i \(0.501033\pi\)
\(42\) 0 0
\(43\) 4.55195 + 7.88422i 0.694167 + 1.20233i 0.970461 + 0.241259i \(0.0775603\pi\)
−0.276294 + 0.961073i \(0.589106\pi\)
\(44\) 0.891235 0.514555i 0.134359 0.0775721i
\(45\) 2.96904i 0.442599i
\(46\) 8.93479i 1.31736i
\(47\) −5.76714 + 3.32966i −0.841224 + 0.485681i −0.857680 0.514184i \(-0.828095\pi\)
0.0164563 + 0.999865i \(0.494762\pi\)
\(48\) −1.82316 3.15780i −0.263150 0.455790i
\(49\) 0 0
\(50\) 1.88631 + 1.08906i 0.266764 + 0.154016i
\(51\) −1.60237 2.77539i −0.224377 0.388632i
\(52\) −1.32711 + 0.148952i −0.184037 + 0.0206559i
\(53\) 5.24396 9.08280i 0.720313 1.24762i −0.240561 0.970634i \(-0.577331\pi\)
0.960874 0.276985i \(-0.0893352\pi\)
\(54\) 6.91188i 0.940588i
\(55\) 2.52131 4.36703i 0.339973 0.588850i
\(56\) 0 0
\(57\) 6.85564i 0.908052i
\(58\) −3.88720 2.24427i −0.510414 0.294688i
\(59\) 3.07396i 0.400195i 0.979776 + 0.200097i \(0.0641259\pi\)
−0.979776 + 0.200097i \(0.935874\pi\)
\(60\) 0.679899 + 0.392540i 0.0877746 + 0.0506767i
\(61\) −0.540892 + 0.936853i −0.0692541 + 0.119952i −0.898573 0.438824i \(-0.855395\pi\)
0.829319 + 0.558775i \(0.188729\pi\)
\(62\) 1.31931 2.28511i 0.167552 0.290209i
\(63\) 0 0
\(64\) −8.88199 −1.11025
\(65\) −5.26665 + 3.88347i −0.653248 + 0.481685i
\(66\) 2.07127 3.58755i 0.254956 0.441596i
\(67\) −4.34568 + 2.50898i −0.530910 + 0.306521i −0.741387 0.671078i \(-0.765832\pi\)
0.210477 + 0.977599i \(0.432498\pi\)
\(68\) −1.01632 −0.123247
\(69\) −4.08721 7.07925i −0.492042 0.852242i
\(70\) 0 0
\(71\) 2.35453 1.35939i 0.279431 0.161330i −0.353735 0.935346i \(-0.615088\pi\)
0.633166 + 0.774016i \(0.281755\pi\)
\(72\) −4.28709 2.47515i −0.505238 0.291699i
\(73\) −6.64426 3.83607i −0.777652 0.448978i 0.0579454 0.998320i \(-0.481545\pi\)
−0.835598 + 0.549342i \(0.814878\pi\)
\(74\) −2.22508 −0.258660
\(75\) −1.99275 −0.230103
\(76\) 1.88285 + 1.08706i 0.215978 + 0.124695i
\(77\) 0 0
\(78\) −4.32659 + 3.19030i −0.489890 + 0.361230i
\(79\) 7.86993 + 13.6311i 0.885436 + 1.53362i 0.845213 + 0.534430i \(0.179474\pi\)
0.0402236 + 0.999191i \(0.487193\pi\)
\(80\) −4.90700 + 2.83306i −0.548620 + 0.316746i
\(81\) 0.707906 + 1.22613i 0.0786563 + 0.136237i
\(82\) 4.06400 7.03905i 0.448794 0.777333i
\(83\) 7.97408i 0.875269i −0.899153 0.437635i \(-0.855816\pi\)
0.899153 0.437635i \(-0.144184\pi\)
\(84\) 0 0
\(85\) −4.31275 + 2.48997i −0.467784 + 0.270075i
\(86\) 10.0647 5.81086i 1.08531 0.626601i
\(87\) 4.10656 0.440270
\(88\) −4.20379 7.28117i −0.448125 0.776176i
\(89\) 16.0640i 1.70278i 0.524537 + 0.851388i \(0.324239\pi\)
−0.524537 + 0.851388i \(0.675761\pi\)
\(90\) −3.79017 −0.399519
\(91\) 0 0
\(92\) −2.59235 −0.270271
\(93\) 2.41406i 0.250326i
\(94\) 4.25052 + 7.36212i 0.438408 + 0.759345i
\(95\) 10.6532 1.09299
\(96\) 2.09007 1.20670i 0.213317 0.123158i
\(97\) −12.3209 + 7.11347i −1.25100 + 0.722263i −0.971307 0.237827i \(-0.923565\pi\)
−0.279689 + 0.960091i \(0.590231\pi\)
\(98\) 0 0
\(99\) 4.54548i 0.456838i
\(100\) −0.315981 + 0.547295i −0.0315981 + 0.0547295i
\(101\) −0.0365612 0.0633259i −0.00363798 0.00630117i 0.864201 0.503147i \(-0.167825\pi\)
−0.867839 + 0.496846i \(0.834491\pi\)
\(102\) −3.54296 + 2.04553i −0.350805 + 0.202537i
\(103\) −6.45980 11.1887i −0.636503 1.10245i −0.986195 0.165590i \(-0.947047\pi\)
0.349692 0.936865i \(-0.386286\pi\)
\(104\) 1.21690 + 10.8421i 0.119327 + 1.06316i
\(105\) 0 0
\(106\) −11.5948 6.69425i −1.12618 0.650203i
\(107\) 4.00855 0.387521 0.193761 0.981049i \(-0.437932\pi\)
0.193761 + 0.981049i \(0.437932\pi\)
\(108\) 2.00542 0.192972
\(109\) −1.71984 0.992947i −0.164730 0.0951071i 0.415368 0.909653i \(-0.363653\pi\)
−0.580099 + 0.814546i \(0.696986\pi\)
\(110\) −5.57479 3.21861i −0.531536 0.306882i
\(111\) 1.76299 1.01786i 0.167335 0.0966110i
\(112\) 0 0
\(113\) 5.28711 + 9.15754i 0.497369 + 0.861469i 0.999995 0.00303506i \(-0.000966090\pi\)
−0.502626 + 0.864504i \(0.667633\pi\)
\(114\) 8.75166 0.819668
\(115\) −11.0007 + 6.35123i −1.02582 + 0.592256i
\(116\) 0.651157 1.12784i 0.0604584 0.104717i
\(117\) −2.36109 + 5.40533i −0.218283 + 0.499723i
\(118\) 3.92410 0.361243
\(119\) 0 0
\(120\) 3.20695 5.55461i 0.292753 0.507064i
\(121\) −1.63999 + 2.84054i −0.149090 + 0.258231i
\(122\) 1.19595 + 0.690483i 0.108276 + 0.0625134i
\(123\) 7.43629i 0.670507i
\(124\) 0.663004 + 0.382786i 0.0595395 + 0.0343752i
\(125\) 12.1710i 1.08860i
\(126\) 0 0
\(127\) 5.63478 9.75972i 0.500006 0.866035i −0.499994 0.866029i \(-0.666665\pi\)
1.00000 6.53271e-6i \(-2.07943e-6\pi\)
\(128\) 7.20562i 0.636893i
\(129\) −5.31634 + 9.20818i −0.468078 + 0.810735i
\(130\) 4.95750 + 6.72322i 0.434801 + 0.589665i
\(131\) −1.53241 2.65421i −0.133887 0.231899i 0.791285 0.611448i \(-0.209413\pi\)
−0.925172 + 0.379549i \(0.876079\pi\)
\(132\) 1.04090 + 0.600962i 0.0905984 + 0.0523070i
\(133\) 0 0
\(134\) 3.20288 + 5.54754i 0.276686 + 0.479235i
\(135\) 8.51002 4.91326i 0.732426 0.422867i
\(136\) 8.30308i 0.711983i
\(137\) 21.8830i 1.86959i 0.355185 + 0.934796i \(0.384418\pi\)
−0.355185 + 0.934796i \(0.615582\pi\)
\(138\) −9.03712 + 5.21758i −0.769291 + 0.444150i
\(139\) −5.53535 9.58750i −0.469502 0.813201i 0.529890 0.848066i \(-0.322233\pi\)
−0.999392 + 0.0348652i \(0.988900\pi\)
\(140\) 0 0
\(141\) −6.73559 3.88879i −0.567239 0.327495i
\(142\) −1.73534 3.00570i −0.145627 0.252233i
\(143\) −8.06301 + 5.94543i −0.674263 + 0.497182i
\(144\) −2.55376 + 4.42324i −0.212813 + 0.368603i
\(145\) 6.38131i 0.529939i
\(146\) −4.89699 + 8.48183i −0.405277 + 0.701961i
\(147\) 0 0
\(148\) 0.645588i 0.0530670i
\(149\) 1.99824 + 1.15369i 0.163702 + 0.0945136i 0.579613 0.814892i \(-0.303204\pi\)
−0.415911 + 0.909406i \(0.636537\pi\)
\(150\) 2.54388i 0.207707i
\(151\) −17.8538 10.3079i −1.45292 0.838845i −0.454275 0.890861i \(-0.650102\pi\)
−0.998646 + 0.0520168i \(0.983435\pi\)
\(152\) 8.88105 15.3824i 0.720348 1.24768i
\(153\) −2.24449 + 3.88757i −0.181456 + 0.314292i
\(154\) 0 0
\(155\) 3.75128 0.301310
\(156\) −0.925638 1.25532i −0.0741103 0.100506i
\(157\) −1.44824 + 2.50843i −0.115582 + 0.200194i −0.918012 0.396552i \(-0.870207\pi\)
0.802430 + 0.596746i \(0.203540\pi\)
\(158\) 17.4010 10.0465i 1.38435 0.799254i
\(159\) 12.2491 0.971417
\(160\) −1.87513 3.24782i −0.148242 0.256763i
\(161\) 0 0
\(162\) 1.56523 0.903688i 0.122976 0.0710004i
\(163\) 20.2944 + 11.7170i 1.58958 + 0.917743i 0.993376 + 0.114907i \(0.0366571\pi\)
0.596201 + 0.802835i \(0.296676\pi\)
\(164\) 2.04232 + 1.17913i 0.159478 + 0.0920750i
\(165\) 5.88939 0.458489
\(166\) −10.1794 −0.790077
\(167\) 6.58349 + 3.80098i 0.509446 + 0.294129i 0.732606 0.680653i \(-0.238304\pi\)
−0.223160 + 0.974782i \(0.571637\pi\)
\(168\) 0 0
\(169\) 12.6765 2.88188i 0.975119 0.221683i
\(170\) 3.17861 + 5.50551i 0.243788 + 0.422253i
\(171\) 8.31637 4.80146i 0.635969 0.367177i
\(172\) 1.68597 + 2.92019i 0.128554 + 0.222662i
\(173\) 2.69861 4.67412i 0.205171 0.355367i −0.745016 0.667047i \(-0.767558\pi\)
0.950187 + 0.311679i \(0.100892\pi\)
\(174\) 5.24229i 0.397417i
\(175\) 0 0
\(176\) −7.51241 + 4.33729i −0.566269 + 0.326936i
\(177\) −3.10916 + 1.79508i −0.233699 + 0.134926i
\(178\) 20.5067 1.53704
\(179\) −6.14571 10.6447i −0.459352 0.795621i 0.539575 0.841938i \(-0.318585\pi\)
−0.998927 + 0.0463168i \(0.985252\pi\)
\(180\) 1.09969i 0.0819658i
\(181\) −21.8525 −1.62428 −0.812140 0.583463i \(-0.801697\pi\)
−0.812140 + 0.583463i \(0.801697\pi\)
\(182\) 0 0
\(183\) −1.26344 −0.0933964
\(184\) 21.1789i 1.56133i
\(185\) −1.58168 2.73956i −0.116288 0.201416i
\(186\) 3.08170 0.225961
\(187\) −6.60264 + 3.81204i −0.482833 + 0.278764i
\(188\) −2.13606 + 1.23325i −0.155788 + 0.0899442i
\(189\) 0 0
\(190\) 13.5995i 0.986609i
\(191\) −1.37858 + 2.38777i −0.0997507 + 0.172773i −0.911581 0.411120i \(-0.865138\pi\)
0.811831 + 0.583893i \(0.198471\pi\)
\(192\) −5.18675 8.98371i −0.374321 0.648344i
\(193\) −11.2491 + 6.49467i −0.809728 + 0.467497i −0.846861 0.531814i \(-0.821511\pi\)
0.0371334 + 0.999310i \(0.488177\pi\)
\(194\) 9.08080 + 15.7284i 0.651963 + 1.12923i
\(195\) −7.00347 3.05917i −0.501529 0.219071i
\(196\) 0 0
\(197\) 16.4772 + 9.51312i 1.17395 + 0.677781i 0.954608 0.297866i \(-0.0962749\pi\)
0.219344 + 0.975648i \(0.429608\pi\)
\(198\) −5.80259 −0.412372
\(199\) 20.0317 1.42001 0.710006 0.704195i \(-0.248692\pi\)
0.710006 + 0.704195i \(0.248692\pi\)
\(200\) 4.47127 + 2.58149i 0.316166 + 0.182539i
\(201\) −5.07543 2.93030i −0.357993 0.206688i
\(202\) −0.0808396 + 0.0466728i −0.00568785 + 0.00328388i
\(203\) 0 0
\(204\) −0.593492 1.02796i −0.0415528 0.0719715i
\(205\) 11.5555 0.807069
\(206\) −14.2831 + 8.24634i −0.995150 + 0.574550i
\(207\) −5.72509 + 9.91614i −0.397921 + 0.689219i
\(208\) 11.1865 1.25555i 0.775642 0.0870564i
\(209\) 16.3096 1.12816
\(210\) 0 0
\(211\) −5.00015 + 8.66052i −0.344225 + 0.596215i −0.985213 0.171336i \(-0.945192\pi\)
0.640988 + 0.767551i \(0.278525\pi\)
\(212\) 1.94228 3.36413i 0.133396 0.231049i
\(213\) 2.74991 + 1.58766i 0.188421 + 0.108785i
\(214\) 5.11717i 0.349802i
\(215\) 14.3089 + 8.26122i 0.975856 + 0.563411i
\(216\) 16.3838i 1.11478i
\(217\) 0 0
\(218\) −1.26756 + 2.19548i −0.0858501 + 0.148697i
\(219\) 8.96048i 0.605493i
\(220\) 0.933852 1.61748i 0.0629603 0.109050i
\(221\) 9.83175 1.10350i 0.661355 0.0742292i
\(222\) −1.29936 2.25056i −0.0872076 0.151048i
\(223\) 7.25954 + 4.19130i 0.486135 + 0.280670i 0.722970 0.690880i \(-0.242777\pi\)
−0.236835 + 0.971550i \(0.576110\pi\)
\(224\) 0 0
\(225\) 1.39566 + 2.41735i 0.0930439 + 0.161157i
\(226\) 11.6902 6.74933i 0.777620 0.448959i
\(227\) 0.919719i 0.0610439i −0.999534 0.0305220i \(-0.990283\pi\)
0.999534 0.0305220i \(-0.00971695\pi\)
\(228\) 2.53922i 0.168164i
\(229\) −21.3222 + 12.3104i −1.40901 + 0.813494i −0.995293 0.0969108i \(-0.969104\pi\)
−0.413719 + 0.910404i \(0.635771\pi\)
\(230\) 8.10776 + 14.0430i 0.534610 + 0.925971i
\(231\) 0 0
\(232\) −9.21415 5.31979i −0.604939 0.349261i
\(233\) −8.63847 14.9623i −0.565925 0.980211i −0.996963 0.0778773i \(-0.975186\pi\)
0.431038 0.902334i \(-0.358148\pi\)
\(234\) 6.90025 + 3.01408i 0.451084 + 0.197036i
\(235\) −6.04291 + 10.4666i −0.394196 + 0.682767i
\(236\) 1.13854i 0.0741129i
\(237\) −9.19149 + 15.9201i −0.597051 + 1.03412i
\(238\) 0 0
\(239\) 14.4828i 0.936816i −0.883512 0.468408i \(-0.844828\pi\)
0.883512 0.468408i \(-0.155172\pi\)
\(240\) −5.73101 3.30880i −0.369935 0.213582i
\(241\) 8.43441i 0.543308i −0.962395 0.271654i \(-0.912429\pi\)
0.962395 0.271654i \(-0.0875706\pi\)
\(242\) 3.62614 + 2.09355i 0.233097 + 0.134579i
\(243\) 7.29488 12.6351i 0.467967 0.810543i
\(244\) −0.200338 + 0.346995i −0.0128253 + 0.0222141i
\(245\) 0 0
\(246\) 9.49290 0.605245
\(247\) −19.3948 8.47178i −1.23406 0.539046i
\(248\) 3.12726 5.41658i 0.198581 0.343953i
\(249\) 8.06541 4.65657i 0.511124 0.295098i
\(250\) 15.5370 0.982647
\(251\) −7.33631 12.7069i −0.463064 0.802050i 0.536048 0.844188i \(-0.319917\pi\)
−0.999112 + 0.0421373i \(0.986583\pi\)
\(252\) 0 0
\(253\) −16.8415 + 9.72346i −1.05882 + 0.611309i
\(254\) −12.4589 7.19315i −0.781742 0.451339i
\(255\) −5.03697 2.90810i −0.315427 0.182112i
\(256\) −8.56553 −0.535346
\(257\) −29.3286 −1.82947 −0.914733 0.404059i \(-0.867599\pi\)
−0.914733 + 0.404059i \(0.867599\pi\)
\(258\) 11.7548 + 6.78665i 0.731824 + 0.422519i
\(259\) 0 0
\(260\) −1.95068 + 1.43838i −0.120976 + 0.0892043i
\(261\) −2.87610 4.98155i −0.178026 0.308350i
\(262\) −3.38826 + 1.95622i −0.209328 + 0.120855i
\(263\) −9.95747 17.2468i −0.614004 1.06349i −0.990558 0.137091i \(-0.956225\pi\)
0.376555 0.926394i \(-0.377109\pi\)
\(264\) 4.90971 8.50386i 0.302172 0.523377i
\(265\) 19.0342i 1.16926i
\(266\) 0 0
\(267\) −16.2479 + 9.38075i −0.994357 + 0.574092i
\(268\) −1.60957 + 0.929287i −0.0983203 + 0.0567652i
\(269\) −22.3250 −1.36118 −0.680589 0.732666i \(-0.738276\pi\)
−0.680589 + 0.732666i \(0.738276\pi\)
\(270\) −6.27210 10.8636i −0.381708 0.661137i
\(271\) 9.39988i 0.571002i 0.958378 + 0.285501i \(0.0921600\pi\)
−0.958378 + 0.285501i \(0.907840\pi\)
\(272\) 8.56677 0.519437
\(273\) 0 0
\(274\) 27.9351 1.68762
\(275\) 4.74076i 0.285879i
\(276\) −1.51384 2.62204i −0.0911223 0.157828i
\(277\) 14.3427 0.861767 0.430883 0.902408i \(-0.358202\pi\)
0.430883 + 0.902408i \(0.358202\pi\)
\(278\) −12.2391 + 7.06622i −0.734050 + 0.423804i
\(279\) 2.92842 1.69073i 0.175320 0.101221i
\(280\) 0 0
\(281\) 0.0988416i 0.00589640i −0.999996 0.00294820i \(-0.999062\pi\)
0.999996 0.00294820i \(-0.000938442\pi\)
\(282\) −4.96429 + 8.59841i −0.295619 + 0.512028i
\(283\) −0.310336 0.537518i −0.0184476 0.0319521i 0.856654 0.515891i \(-0.172539\pi\)
−0.875102 + 0.483939i \(0.839206\pi\)
\(284\) 0.872079 0.503495i 0.0517484 0.0298769i
\(285\) 6.22106 + 10.7752i 0.368504 + 0.638267i
\(286\) 7.58972 + 10.2930i 0.448789 + 0.608635i
\(287\) 0 0
\(288\) −2.92763 1.69027i −0.172512 0.0995998i
\(289\) −9.47069 −0.557099
\(290\) −8.14615 −0.478358
\(291\) −14.3899 8.30800i −0.843549 0.487023i
\(292\) −2.46093 1.42082i −0.144015 0.0831471i
\(293\) 21.5586 12.4469i 1.25947 0.727153i 0.286496 0.958082i \(-0.407510\pi\)
0.972971 + 0.230928i \(0.0741762\pi\)
\(294\) 0 0
\(295\) 2.78942 + 4.83142i 0.162406 + 0.281296i
\(296\) −5.27430 −0.306562
\(297\) 13.0285 7.52200i 0.755989 0.436471i
\(298\) 1.47275 2.55088i 0.0853143 0.147769i
\(299\) 25.0781 2.81472i 1.45031 0.162779i
\(300\) −0.738085 −0.0426133
\(301\) 0 0
\(302\) −13.1587 + 22.7915i −0.757197 + 1.31150i
\(303\) 0.0427008 0.0739599i 0.00245310 0.00424889i
\(304\) −15.8710 9.16310i −0.910262 0.525540i
\(305\) 1.96330i 0.112418i
\(306\) 4.96274 + 2.86524i 0.283701 + 0.163795i
\(307\) 9.89767i 0.564890i −0.959284 0.282445i \(-0.908855\pi\)
0.959284 0.282445i \(-0.0911455\pi\)
\(308\) 0 0
\(309\) 7.54456 13.0676i 0.429195 0.743387i
\(310\) 4.78875i 0.271983i
\(311\) 3.61895 6.26820i 0.205212 0.355437i −0.744988 0.667077i \(-0.767545\pi\)
0.950200 + 0.311640i \(0.100878\pi\)
\(312\) −10.2557 + 7.56223i −0.580614 + 0.428127i
\(313\) −16.3303 28.2849i −0.923043 1.59876i −0.794678 0.607031i \(-0.792360\pi\)
−0.128365 0.991727i \(-0.540973\pi\)
\(314\) 3.20217 + 1.84877i 0.180709 + 0.104332i
\(315\) 0 0
\(316\) 2.91490 + 5.04875i 0.163976 + 0.284014i
\(317\) −14.8734 + 8.58718i −0.835375 + 0.482304i −0.855690 0.517489i \(-0.826867\pi\)
0.0203143 + 0.999794i \(0.493533\pi\)
\(318\) 15.6368i 0.876866i
\(319\) 9.76951i 0.546987i
\(320\) −13.9601 + 8.05984i −0.780391 + 0.450559i
\(321\) 2.34084 + 4.05446i 0.130653 + 0.226298i
\(322\) 0 0
\(323\) −13.9489 8.05342i −0.776140 0.448105i
\(324\) 0.262197 + 0.454139i 0.0145665 + 0.0252299i
\(325\) 2.46252 5.63756i 0.136596 0.312715i
\(326\) 14.9574 25.9071i 0.828416 1.43486i
\(327\) 2.31938i 0.128262i
\(328\) 9.63324 16.6853i 0.531907 0.921289i
\(329\) 0 0
\(330\) 7.51819i 0.413863i
\(331\) −17.2633 9.96698i −0.948877 0.547835i −0.0561454 0.998423i \(-0.517881\pi\)
−0.892732 + 0.450588i \(0.851214\pi\)
\(332\) 2.95347i 0.162093i
\(333\) −2.46947 1.42575i −0.135326 0.0781306i
\(334\) 4.85219 8.40424i 0.265500 0.459860i
\(335\) −4.55348 + 7.88687i −0.248783 + 0.430905i
\(336\) 0 0
\(337\) 1.27189 0.0692842 0.0346421 0.999400i \(-0.488971\pi\)
0.0346421 + 0.999400i \(0.488971\pi\)
\(338\) −3.67891 16.1824i −0.200106 0.880208i
\(339\) −6.17495 + 10.6953i −0.335377 + 0.580890i
\(340\) −1.59738 + 0.922245i −0.0866298 + 0.0500158i
\(341\) 5.74305 0.311004
\(342\) −6.12937 10.6164i −0.331438 0.574068i
\(343\) 0 0
\(344\) 23.8572 13.7740i 1.28630 0.742643i
\(345\) −12.8479 7.41777i −0.691710 0.399359i
\(346\) −5.96682 3.44494i −0.320778 0.185201i
\(347\) 25.8833 1.38949 0.694744 0.719257i \(-0.255518\pi\)
0.694744 + 0.719257i \(0.255518\pi\)
\(348\) 1.52101 0.0815344
\(349\) −14.9967 8.65837i −0.802757 0.463472i 0.0416774 0.999131i \(-0.486730\pi\)
−0.844434 + 0.535659i \(0.820063\pi\)
\(350\) 0 0
\(351\) −19.4002 + 2.17744i −1.03551 + 0.116223i
\(352\) −2.87074 4.97227i −0.153011 0.265023i
\(353\) 21.9533 12.6747i 1.16846 0.674608i 0.215140 0.976583i \(-0.430979\pi\)
0.953316 + 0.301975i \(0.0976459\pi\)
\(354\) 2.29153 + 3.96904i 0.121793 + 0.210952i
\(355\) 2.46711 4.27317i 0.130941 0.226796i
\(356\) 5.94983i 0.315341i
\(357\) 0 0
\(358\) −13.5886 + 7.84539i −0.718181 + 0.414642i
\(359\) 4.56434 2.63522i 0.240897 0.139082i −0.374692 0.927149i \(-0.622252\pi\)
0.615589 + 0.788068i \(0.288918\pi\)
\(360\) −8.98417 −0.473507
\(361\) 7.72804 + 13.3854i 0.406739 + 0.704493i
\(362\) 27.8961i 1.46618i
\(363\) −3.83077 −0.201063
\(364\) 0 0
\(365\) −13.9240 −0.728813
\(366\) 1.61287i 0.0843058i
\(367\) −12.6588 21.9257i −0.660783 1.14451i −0.980410 0.196967i \(-0.936891\pi\)
0.319627 0.947544i \(-0.396443\pi\)
\(368\) 21.8515 1.13909
\(369\) 9.02073 5.20812i 0.469601 0.271124i
\(370\) −3.49722 + 2.01912i −0.181812 + 0.104969i
\(371\) 0 0
\(372\) 0.894130i 0.0463585i
\(373\) 3.39391 5.87842i 0.175730 0.304373i −0.764684 0.644406i \(-0.777105\pi\)
0.940414 + 0.340033i \(0.110438\pi\)
\(374\) 4.86631 + 8.42869i 0.251631 + 0.435837i
\(375\) −12.3104 + 7.10739i −0.635704 + 0.367024i
\(376\) 10.0754 + 17.4511i 0.519598 + 0.899970i
\(377\) −5.07464 + 11.6176i −0.261357 + 0.598336i
\(378\) 0 0
\(379\) 10.6717 + 6.16130i 0.548168 + 0.316485i 0.748383 0.663267i \(-0.230831\pi\)
−0.200215 + 0.979752i \(0.564164\pi\)
\(380\) 3.94577 0.202414
\(381\) 13.1620 0.674310
\(382\) 3.04815 + 1.75985i 0.155957 + 0.0900417i
\(383\) 6.28662 + 3.62958i 0.321232 + 0.185463i 0.651941 0.758269i \(-0.273955\pi\)
−0.330710 + 0.943732i \(0.607288\pi\)
\(384\) −7.28815 + 4.20782i −0.371922 + 0.214729i
\(385\) 0 0
\(386\) 8.29086 + 14.3602i 0.421994 + 0.730915i
\(387\) 14.8935 0.757082
\(388\) −4.56346 + 2.63472i −0.231675 + 0.133757i
\(389\) −3.57406 + 6.19045i −0.181212 + 0.313868i −0.942293 0.334788i \(-0.891335\pi\)
0.761082 + 0.648656i \(0.224669\pi\)
\(390\) −3.90522 + 8.94038i −0.197749 + 0.452714i
\(391\) 19.2052 0.971250
\(392\) 0 0
\(393\) 1.78974 3.09991i 0.0902802 0.156370i
\(394\) 12.1441 21.0342i 0.611811 1.05969i
\(395\) 24.7388 + 14.2829i 1.24474 + 0.718652i
\(396\) 1.68357i 0.0846027i
\(397\) 19.4520 + 11.2306i 0.976266 + 0.563647i 0.901141 0.433527i \(-0.142731\pi\)
0.0751252 + 0.997174i \(0.476064\pi\)
\(398\) 25.5718i 1.28180i
\(399\) 0 0
\(400\) 2.66347 4.61327i 0.133174 0.230663i
\(401\) 3.05473i 0.152546i 0.997087 + 0.0762729i \(0.0243020\pi\)
−0.997087 + 0.0762729i \(0.975698\pi\)
\(402\) −3.74072 + 6.47912i −0.186570 + 0.323149i
\(403\) −6.82944 2.98315i −0.340199 0.148601i
\(404\) −0.0135417 0.0234549i −0.000673725 0.00116693i
\(405\) 2.22527 + 1.28476i 0.110575 + 0.0638403i
\(406\) 0 0
\(407\) −2.42149 4.19414i −0.120029 0.207896i
\(408\) −8.39817 + 4.84869i −0.415771 + 0.240046i
\(409\) 5.60586i 0.277192i 0.990349 + 0.138596i \(0.0442590\pi\)
−0.990349 + 0.138596i \(0.955741\pi\)
\(410\) 14.7513i 0.728514i
\(411\) −22.1336 + 12.7789i −1.09177 + 0.630335i
\(412\) −2.39261 4.14412i −0.117875 0.204166i
\(413\) 0 0
\(414\) 12.6586 + 7.30844i 0.622136 + 0.359190i
\(415\) −7.23597 12.5331i −0.355200 0.615224i
\(416\) 0.831013 + 7.40403i 0.0407437 + 0.363012i
\(417\) 6.46487 11.1975i 0.316586 0.548343i
\(418\) 20.8202i 1.01835i
\(419\) −3.06969 + 5.31687i −0.149964 + 0.259746i −0.931214 0.364473i \(-0.881249\pi\)
0.781250 + 0.624219i \(0.214583\pi\)
\(420\) 0 0
\(421\) 1.92589i 0.0938622i 0.998898 + 0.0469311i \(0.0149441\pi\)
−0.998898 + 0.0469311i \(0.985056\pi\)
\(422\) 11.0557 + 6.38302i 0.538184 + 0.310720i
\(423\) 10.8943i 0.529700i
\(424\) −27.4841 15.8679i −1.33475 0.770615i
\(425\) 2.34092 4.05459i 0.113551 0.196677i
\(426\) 2.02675 3.51044i 0.0981965 0.170081i
\(427\) 0 0
\(428\) 1.48470 0.0717658
\(429\) −10.7220 4.68345i −0.517664 0.226119i
\(430\) 10.5460 18.2662i 0.508572 0.880873i
\(431\) −9.30923 + 5.37469i −0.448410 + 0.258890i −0.707158 0.707055i \(-0.750023\pi\)
0.258749 + 0.965945i \(0.416690\pi\)
\(432\) −16.9041 −0.813301
\(433\) 20.1328 + 34.8710i 0.967520 + 1.67579i 0.702685 + 0.711501i \(0.251984\pi\)
0.264835 + 0.964294i \(0.414682\pi\)
\(434\) 0 0
\(435\) 6.45439 3.72644i 0.309464 0.178669i
\(436\) −0.637000 0.367772i −0.0305068 0.0176131i
\(437\) −35.5799 20.5421i −1.70202 0.982662i
\(438\) −11.4386 −0.546559
\(439\) 21.9508 1.04765 0.523826 0.851825i \(-0.324504\pi\)
0.523826 + 0.851825i \(0.324504\pi\)
\(440\) −13.2144 7.62934i −0.629972 0.363715i
\(441\) 0 0
\(442\) −1.40868 12.5509i −0.0670042 0.596984i
\(443\) 13.9482 + 24.1589i 0.662697 + 1.14783i 0.979904 + 0.199469i \(0.0639217\pi\)
−0.317207 + 0.948356i \(0.602745\pi\)
\(444\) 0.652982 0.376999i 0.0309892 0.0178916i
\(445\) 14.5770 + 25.2481i 0.691017 + 1.19688i
\(446\) 5.35046 9.26727i 0.253352 0.438818i
\(447\) 2.69484i 0.127461i
\(448\) 0 0
\(449\) 19.1056 11.0306i 0.901648 0.520567i 0.0239134 0.999714i \(-0.492387\pi\)
0.877734 + 0.479147i \(0.159054\pi\)
\(450\) 3.08590 1.78165i 0.145471 0.0839876i
\(451\) 17.6909 0.833033
\(452\) 1.95826 + 3.39181i 0.0921088 + 0.159537i
\(453\) 24.0777i 1.13127i
\(454\) −1.17408 −0.0551023
\(455\) 0 0
\(456\) 20.7448 0.971464
\(457\) 5.51628i 0.258041i −0.991642 0.129020i \(-0.958817\pi\)
0.991642 0.129020i \(-0.0411833\pi\)
\(458\) 15.7150 + 27.2192i 0.734314 + 1.27187i
\(459\) −14.8570 −0.693466
\(460\) −4.07447 + 2.35240i −0.189973 + 0.109681i
\(461\) 25.0092 14.4391i 1.16479 0.672494i 0.212346 0.977195i \(-0.431890\pi\)
0.952448 + 0.304700i \(0.0985562\pi\)
\(462\) 0 0
\(463\) 14.2284i 0.661251i −0.943762 0.330625i \(-0.892740\pi\)
0.943762 0.330625i \(-0.107260\pi\)
\(464\) −5.48874 + 9.50678i −0.254808 + 0.441341i
\(465\) 2.19061 + 3.79424i 0.101587 + 0.175954i
\(466\) −19.1003 + 11.0276i −0.884804 + 0.510842i
\(467\) −2.27163 3.93457i −0.105118 0.182070i 0.808668 0.588265i \(-0.200189\pi\)
−0.913787 + 0.406195i \(0.866855\pi\)
\(468\) −0.874509 + 2.00205i −0.0404242 + 0.0925448i
\(469\) 0 0
\(470\) 13.3613 + 7.71416i 0.616312 + 0.355828i
\(471\) −3.38288 −0.155875
\(472\) 9.30163 0.428142
\(473\) 21.9062 + 12.6476i 1.00725 + 0.581536i
\(474\) 20.3231 + 11.7335i 0.933469 + 0.538939i
\(475\) −8.67366 + 5.00774i −0.397975 + 0.229771i
\(476\) 0 0
\(477\) −8.57886 14.8590i −0.392799 0.680348i
\(478\) −18.4883 −0.845633
\(479\) 1.44239 0.832764i 0.0659044 0.0380499i −0.466686 0.884423i \(-0.654552\pi\)
0.532590 + 0.846373i \(0.321219\pi\)
\(480\) 2.19001 3.79321i 0.0999598 0.173135i
\(481\) 0.700965 + 6.24535i 0.0319612 + 0.284763i
\(482\) −10.7671 −0.490426
\(483\) 0 0
\(484\) −0.607426 + 1.05209i −0.0276103 + 0.0478224i
\(485\) −12.9100 + 22.3608i −0.586215 + 1.01535i
\(486\) −16.1295 9.31239i −0.731650 0.422418i
\(487\) 1.48493i 0.0672884i −0.999434 0.0336442i \(-0.989289\pi\)
0.999434 0.0336442i \(-0.0107113\pi\)
\(488\) 2.83487 + 1.63671i 0.128328 + 0.0740904i
\(489\) 27.3691i 1.23767i
\(490\) 0 0
\(491\) 7.99791 13.8528i 0.360941 0.625167i −0.627175 0.778878i \(-0.715789\pi\)
0.988116 + 0.153711i \(0.0491224\pi\)
\(492\) 2.75428i 0.124173i
\(493\) −4.82404 + 8.35548i −0.217264 + 0.376312i
\(494\) −10.8148 + 24.7587i −0.486580 + 1.11395i
\(495\) −4.12473 7.14425i −0.185393 0.321110i
\(496\) −5.58860 3.22658i −0.250936 0.144878i
\(497\) 0 0
\(498\) −5.94440 10.2960i −0.266375 0.461375i
\(499\) 15.3459 8.85997i 0.686977 0.396627i −0.115501 0.993307i \(-0.536847\pi\)
0.802479 + 0.596681i \(0.203514\pi\)
\(500\) 4.50793i 0.201601i
\(501\) 8.87852i 0.396663i
\(502\) −16.2211 + 9.36527i −0.723984 + 0.417993i
\(503\) 0.598451 + 1.03655i 0.0266836 + 0.0462174i 0.879059 0.476713i \(-0.158172\pi\)
−0.852375 + 0.522931i \(0.824839\pi\)
\(504\) 0 0
\(505\) −0.114929 0.0663540i −0.00511425 0.00295272i
\(506\) 12.4126 + 21.4993i 0.551809 + 0.955760i
\(507\) 10.3175 + 11.1388i 0.458217 + 0.494692i
\(508\) 2.08703 3.61485i 0.0925971 0.160383i
\(509\) 6.28614i 0.278628i −0.990248 0.139314i \(-0.955510\pi\)
0.990248 0.139314i \(-0.0444898\pi\)
\(510\) −3.71237 + 6.43002i −0.164387 + 0.284726i
\(511\) 0 0
\(512\) 25.3457i 1.12013i
\(513\) 27.5244 + 15.8912i 1.21523 + 0.701614i
\(514\) 37.4398i 1.65140i
\(515\) −20.3061 11.7237i −0.894792 0.516608i
\(516\) −1.96909 + 3.41056i −0.0866843 + 0.150142i
\(517\) −9.25143 + 16.0240i −0.406878 + 0.704733i
\(518\) 0 0
\(519\) 6.30354 0.276695
\(520\) 11.7512 + 15.9366i 0.515323 + 0.698866i
\(521\) 5.42367 9.39407i 0.237615 0.411562i −0.722414 0.691460i \(-0.756968\pi\)
0.960029 + 0.279899i \(0.0903010\pi\)
\(522\) −6.35926 + 3.67152i −0.278337 + 0.160698i
\(523\) 1.34726 0.0589114 0.0294557 0.999566i \(-0.490623\pi\)
0.0294557 + 0.999566i \(0.490623\pi\)
\(524\) −0.567579 0.983076i −0.0247948 0.0429459i
\(525\) 0 0
\(526\) −22.0167 + 12.7113i −0.959974 + 0.554241i
\(527\) −4.91181 2.83583i −0.213962 0.123531i
\(528\) −8.77394 5.06563i −0.381837 0.220453i
\(529\) 25.9873 1.12988
\(530\) −24.2984 −1.05546
\(531\) 4.35510 + 2.51442i 0.188995 + 0.109117i
\(532\) 0 0
\(533\) −21.0375 9.18931i −0.911233 0.398033i
\(534\) 11.9751 + 20.7415i 0.518214 + 0.897574i
\(535\) 6.30034 3.63750i 0.272388 0.157263i
\(536\) 7.59205 + 13.1498i 0.327926 + 0.567985i
\(537\) 7.17773 12.4322i 0.309742 0.536489i
\(538\) 28.4993i 1.22869i
\(539\) 0 0
\(540\) 3.15198 1.81980i 0.135640 0.0783115i
\(541\) 17.4565 10.0785i 0.750516 0.433310i −0.0753646 0.997156i \(-0.524012\pi\)
0.825880 + 0.563846i \(0.190679\pi\)
\(542\) 11.9996 0.515425
\(543\) −12.7610 22.1027i −0.547628 0.948519i
\(544\) 5.67012i 0.243104i
\(545\) −3.60415 −0.154385
\(546\) 0 0
\(547\) −3.42286 −0.146351 −0.0731755 0.997319i \(-0.523313\pi\)
−0.0731755 + 0.997319i \(0.523313\pi\)
\(548\) 8.10512i 0.346234i
\(549\) 0.884873 + 1.53264i 0.0377654 + 0.0654117i
\(550\) 6.05188 0.258053
\(551\) 17.8742 10.3197i 0.761467 0.439633i
\(552\) −21.4214 + 12.3677i −0.911757 + 0.526403i
\(553\) 0 0
\(554\) 18.3093i 0.777889i
\(555\) 1.84729 3.19960i 0.0784130 0.135815i
\(556\) −2.05020 3.55106i −0.0869480 0.150598i
\(557\) 20.4948 11.8327i 0.868394 0.501367i 0.00157977 0.999999i \(-0.499497\pi\)
0.866814 + 0.498631i \(0.166164\pi\)
\(558\) −2.15832 3.73832i −0.0913690 0.158256i
\(559\) −19.4806 26.4190i −0.823940 1.11740i
\(560\) 0 0
\(561\) −7.71139 4.45217i −0.325575 0.187971i
\(562\) −0.126178 −0.00532248
\(563\) −28.8075 −1.21409 −0.607045 0.794668i \(-0.707645\pi\)
−0.607045 + 0.794668i \(0.707645\pi\)
\(564\) −2.49475 1.44035i −0.105048 0.0606496i
\(565\) 16.6198 + 9.59543i 0.699199 + 0.403683i
\(566\) −0.686177 + 0.396164i −0.0288422 + 0.0166520i
\(567\) 0 0
\(568\) −4.11343 7.12467i −0.172596 0.298945i
\(569\) 27.6722 1.16008 0.580040 0.814588i \(-0.303037\pi\)
0.580040 + 0.814588i \(0.303037\pi\)
\(570\) 13.7552 7.94158i 0.576143 0.332636i
\(571\) 6.48273 11.2284i 0.271294 0.469895i −0.697899 0.716196i \(-0.745882\pi\)
0.969193 + 0.246301i \(0.0792151\pi\)
\(572\) −2.98641 + 2.20209i −0.124868 + 0.0920741i
\(573\) −3.22016 −0.134524
\(574\) 0 0
\(575\) 5.97105 10.3422i 0.249010 0.431298i
\(576\) −7.26525 + 12.5838i −0.302719 + 0.524324i
\(577\) −8.19301 4.73023i −0.341079 0.196922i 0.319670 0.947529i \(-0.396428\pi\)
−0.660749 + 0.750607i \(0.729761\pi\)
\(578\) 12.0899i 0.502875i
\(579\) −13.1381 7.58529i −0.546001 0.315234i
\(580\) 2.36354i 0.0981405i
\(581\) 0 0
\(582\) −10.6057 + 18.3696i −0.439620 + 0.761444i
\(583\) 29.1406i 1.20688i
\(584\) −11.6077 + 20.1052i −0.480332 + 0.831959i
\(585\) 1.19401 + 10.6382i 0.0493664 + 0.439837i
\(586\) −15.8892 27.5209i −0.656377 1.13688i
\(587\) −18.6673 10.7776i −0.770481 0.444837i 0.0625654 0.998041i \(-0.480072\pi\)
−0.833046 + 0.553204i \(0.813405\pi\)
\(588\) 0 0
\(589\) 6.06647 + 10.5074i 0.249965 + 0.432951i
\(590\) 6.16761 3.56087i 0.253917 0.146599i
\(591\) 22.2212i 0.914059i
\(592\) 5.44180i 0.223657i
\(593\) 3.44015 1.98617i 0.141270 0.0815622i −0.427699 0.903921i \(-0.640676\pi\)
0.568969 + 0.822359i \(0.307342\pi\)
\(594\) −9.60231 16.6317i −0.393988 0.682407i
\(595\) 0 0
\(596\) 0.740117 + 0.427307i 0.0303164 + 0.0175032i
\(597\) 11.6978 + 20.2612i 0.478759 + 0.829234i
\(598\) −3.59317 32.0138i −0.146936 1.30914i
\(599\) 9.75246 16.8918i 0.398475 0.690179i −0.595063 0.803679i \(-0.702873\pi\)
0.993538 + 0.113500i \(0.0362063\pi\)
\(600\) 6.02997i 0.246172i
\(601\) 13.4368 23.2733i 0.548100 0.949336i −0.450305 0.892875i \(-0.648685\pi\)
0.998405 0.0564616i \(-0.0179818\pi\)
\(602\) 0 0
\(603\) 8.20914i 0.334302i
\(604\) −6.61276 3.81788i −0.269070 0.155347i
\(605\) 5.95274i 0.242013i
\(606\) −0.0944146 0.0545103i −0.00383533 0.00221433i
\(607\) −12.5102 + 21.6682i −0.507772 + 0.879487i 0.492187 + 0.870489i \(0.336197\pi\)
−0.999960 + 0.00899773i \(0.997136\pi\)
\(608\) 6.06482 10.5046i 0.245961 0.426016i
\(609\) 0 0
\(610\) 2.50628 0.101476
\(611\) 19.3249 14.2496i 0.781803 0.576478i
\(612\) −0.831324 + 1.43990i −0.0336043 + 0.0582043i
\(613\) 18.4970 10.6793i 0.747088 0.431332i −0.0775527 0.996988i \(-0.524711\pi\)
0.824641 + 0.565657i \(0.191377\pi\)
\(614\) −12.6350 −0.509908
\(615\) 6.74796 + 11.6878i 0.272104 + 0.471298i
\(616\) 0 0
\(617\) −28.5425 + 16.4790i −1.14908 + 0.663420i −0.948662 0.316291i \(-0.897562\pi\)
−0.200415 + 0.979711i \(0.564229\pi\)
\(618\) −16.6816 9.63111i −0.671031 0.387420i
\(619\) 42.3588 + 24.4559i 1.70254 + 0.982965i 0.943170 + 0.332311i \(0.107828\pi\)
0.759375 + 0.650654i \(0.225505\pi\)
\(620\) 1.38941 0.0558002
\(621\) −37.8962 −1.52072
\(622\) −8.00176 4.61982i −0.320841 0.185238i
\(623\) 0 0
\(624\) 7.80240 + 10.5814i 0.312346 + 0.423595i
\(625\) 6.77880 + 11.7412i 0.271152 + 0.469649i
\(626\) −36.1075 + 20.8467i −1.44315 + 0.833201i
\(627\) 9.52417 + 16.4964i 0.380359 + 0.658801i
\(628\) −0.536406 + 0.929083i −0.0214049 + 0.0370744i
\(629\) 4.78278i 0.190702i
\(630\) 0 0
\(631\) 4.65076 2.68512i 0.185144 0.106893i −0.404563 0.914510i \(-0.632576\pi\)
0.589707 + 0.807617i \(0.299243\pi\)
\(632\) 41.2470 23.8140i 1.64072 0.947270i
\(633\) −11.6796 −0.464223
\(634\) 10.9621 + 18.9869i 0.435360 + 0.754066i
\(635\) 20.4528i 0.811645i
\(636\) 4.53687 0.179899
\(637\) 0 0
\(638\) −12.4714 −0.493747
\(639\) 4.44778i 0.175951i
\(640\) 6.53865 + 11.3253i 0.258463 + 0.447671i
\(641\) −39.7020 −1.56813 −0.784066 0.620677i \(-0.786858\pi\)
−0.784066 + 0.620677i \(0.786858\pi\)
\(642\) 5.17578 2.98824i 0.204272 0.117936i
\(643\) 27.8388 16.0727i 1.09785 0.633847i 0.162198 0.986758i \(-0.448142\pi\)
0.935657 + 0.352911i \(0.114808\pi\)
\(644\) 0 0
\(645\) 19.2970i 0.759818i
\(646\) −10.2807 + 17.8067i −0.404489 + 0.700596i
\(647\) −9.92502 17.1906i −0.390193 0.675833i 0.602282 0.798283i \(-0.294258\pi\)
−0.992475 + 0.122450i \(0.960925\pi\)
\(648\) 3.71020 2.14209i 0.145751 0.0841491i
\(649\) 4.27048 + 7.39669i 0.167631 + 0.290346i
\(650\) −7.19670 3.14357i −0.282278 0.123301i
\(651\) 0 0
\(652\) 7.51671 + 4.33977i 0.294377 + 0.169959i
\(653\) −19.0005 −0.743547 −0.371773 0.928324i \(-0.621250\pi\)
−0.371773 + 0.928324i \(0.621250\pi\)
\(654\) −2.96083 −0.115778
\(655\) −4.81705 2.78112i −0.188218 0.108667i
\(656\) −17.2152 9.93918i −0.672139 0.388060i
\(657\) −10.8697 + 6.27562i −0.424067 + 0.244835i
\(658\) 0 0
\(659\) 3.60729 + 6.24801i 0.140520 + 0.243388i 0.927693 0.373345i \(-0.121789\pi\)
−0.787173 + 0.616733i \(0.788456\pi\)
\(660\) 2.18134 0.0849085
\(661\) −14.5068 + 8.37548i −0.564248 + 0.325769i −0.754849 0.655899i \(-0.772290\pi\)
0.190601 + 0.981668i \(0.438956\pi\)
\(662\) −12.7235 + 22.0377i −0.494512 + 0.856520i
\(663\) 6.85751 + 9.29995i 0.266324 + 0.361180i
\(664\) −24.1291 −0.936393
\(665\) 0 0
\(666\) −1.82006 + 3.15244i −0.0705259 + 0.122155i
\(667\) −12.3048 + 21.3126i −0.476444 + 0.825226i
\(668\) 2.43842 + 1.40782i 0.0943453 + 0.0544703i
\(669\) 9.79025i 0.378513i
\(670\) 10.0681 + 5.81281i 0.388964 + 0.224569i
\(671\) 3.00573i 0.116035i
\(672\) 0 0
\(673\) −18.6684 + 32.3346i −0.719614 + 1.24641i 0.241539 + 0.970391i \(0.422348\pi\)
−0.961153 + 0.276016i \(0.910986\pi\)
\(674\) 1.62365i 0.0625406i
\(675\) −4.61916 + 8.00061i −0.177791 + 0.307944i
\(676\) 4.69519 1.06740i 0.180584 0.0410540i
\(677\) −14.0671 24.3649i −0.540641 0.936418i −0.998867 0.0475826i \(-0.984848\pi\)
0.458226 0.888836i \(-0.348485\pi\)
\(678\) 13.6533 + 7.88271i 0.524350 + 0.302734i
\(679\) 0 0
\(680\) 7.53452 + 13.0502i 0.288935 + 0.500451i
\(681\) 0.930253 0.537082i 0.0356474 0.0205810i
\(682\) 7.33137i 0.280733i
\(683\) 2.07032i 0.0792186i −0.999215 0.0396093i \(-0.987389\pi\)
0.999215 0.0396093i \(-0.0126113\pi\)
\(684\) 3.08025 1.77838i 0.117776 0.0679982i
\(685\) 19.8574 + 34.3941i 0.758714 + 1.31413i
\(686\) 0 0
\(687\) −24.9028 14.3776i −0.950100 0.548540i
\(688\) −14.2114 24.6149i −0.541805 0.938434i
\(689\) −15.1367 + 34.6531i −0.576662 + 1.32018i
\(690\) −9.46925 + 16.4012i −0.360488 + 0.624384i
\(691\) 35.8583i 1.36411i −0.731299 0.682057i \(-0.761086\pi\)
0.731299 0.682057i \(-0.238914\pi\)
\(692\) 0.999521 1.73122i 0.0379961 0.0658112i
\(693\) 0 0
\(694\) 33.0417i 1.25425i
\(695\) −17.4001 10.0460i −0.660023 0.381065i
\(696\) 12.4262i 0.471015i
\(697\) −15.1304 8.73552i −0.573103 0.330881i
\(698\) −11.0530 + 19.1443i −0.418361 + 0.724622i
\(699\) 10.0891 17.4748i 0.381604 0.660958i
\(700\) 0 0
\(701\) −44.8940 −1.69562 −0.847812 0.530297i \(-0.822081\pi\)
−0.847812 + 0.530297i \(0.822081\pi\)
\(702\) 2.77965 + 24.7657i 0.104911 + 0.934719i
\(703\) 5.11571 8.86067i 0.192943 0.334187i
\(704\) −21.3722 + 12.3393i −0.805497 + 0.465054i
\(705\) −14.1153 −0.531614
\(706\) −16.1801 28.0248i −0.608947 1.05473i
\(707\) 0 0
\(708\) −1.15158 + 0.664867i −0.0432792 + 0.0249872i
\(709\) 14.0864 + 8.13279i 0.529026 + 0.305433i 0.740620 0.671924i \(-0.234532\pi\)
−0.211594 + 0.977358i \(0.567865\pi\)
\(710\) −5.45497 3.14943i −0.204721 0.118196i
\(711\) 25.7496 0.965687
\(712\) 48.6087 1.82169
\(713\) −12.5287 7.23344i −0.469203 0.270894i
\(714\) 0 0
\(715\) −7.27775 + 16.6613i −0.272173 + 0.623096i
\(716\) −2.27627 3.94262i −0.0850683 0.147343i
\(717\) 14.6487 8.45743i 0.547066 0.315849i
\(718\) −3.36403 5.82667i −0.125544 0.217449i
\(719\) −5.00744 + 8.67314i −0.186746 + 0.323454i −0.944164 0.329477i \(-0.893127\pi\)
0.757417 + 0.652931i \(0.226461\pi\)
\(720\) 9.26949i 0.345454i
\(721\) 0 0
\(722\) 17.0873 9.86534i 0.635922 0.367150i
\(723\) 8.53100 4.92538i 0.317271 0.183177i
\(724\) −8.09380 −0.300804
\(725\) 2.99966 + 5.19556i 0.111405 + 0.192958i
\(726\) 4.89022i 0.181493i
\(727\) 34.5299 1.28064 0.640322 0.768106i \(-0.278801\pi\)
0.640322 + 0.768106i \(0.278801\pi\)
\(728\) 0 0
\(729\) 21.2872 0.788415
\(730\) 17.7748i 0.657875i
\(731\) −12.4904 21.6340i −0.461973 0.800161i
\(732\) −0.467959 −0.0172963
\(733\) −28.6966 + 16.5680i −1.05993 + 0.611953i −0.925414 0.378958i \(-0.876283\pi\)
−0.134520 + 0.990911i \(0.542949\pi\)
\(734\) −27.9895 + 16.1598i −1.03311 + 0.596468i
\(735\) 0 0
\(736\) 14.4629i 0.533111i
\(737\) −6.97119 + 12.0745i −0.256787 + 0.444768i
\(738\) −6.64850 11.5155i −0.244735 0.423893i
\(739\) 3.47767 2.00784i 0.127928 0.0738594i −0.434670 0.900590i \(-0.643135\pi\)
0.562598 + 0.826730i \(0.309802\pi\)
\(740\) −0.585830 1.01469i −0.0215356 0.0373007i
\(741\) −2.75703 24.5641i −0.101282 0.902386i
\(742\) 0 0
\(743\) 10.8361 + 6.25622i 0.397538 + 0.229519i 0.685421 0.728147i \(-0.259618\pi\)
−0.287883 + 0.957666i \(0.592952\pi\)
\(744\) 7.30482 0.267808
\(745\) 4.18759 0.153421
\(746\) −7.50418 4.33254i −0.274748 0.158626i
\(747\) −11.2975 6.52260i −0.413353 0.238650i
\(748\) −2.44551 + 1.41192i −0.0894168 + 0.0516248i
\(749\) 0 0
\(750\) 9.07304 + 15.7150i 0.331300 + 0.573829i
\(751\) −37.5158 −1.36897 −0.684486 0.729026i \(-0.739973\pi\)
−0.684486 + 0.729026i \(0.739973\pi\)
\(752\) 18.0053 10.3954i 0.656585 0.379080i
\(753\) 8.56826 14.8407i 0.312245 0.540824i
\(754\) 14.8306 + 6.47810i 0.540098 + 0.235919i
\(755\) −37.4150 −1.36167
\(756\) 0 0
\(757\) 17.5223 30.3496i 0.636860 1.10307i −0.349258 0.937027i \(-0.613566\pi\)
0.986118 0.166047i \(-0.0531004\pi\)
\(758\) 7.86530 13.6231i 0.285680 0.494813i
\(759\) −19.6697 11.3563i −0.713963 0.412207i
\(760\) 32.2360i 1.16932i
\(761\) 3.72586 + 2.15113i 0.135062 + 0.0779782i 0.566009 0.824399i \(-0.308487\pi\)
−0.430946 + 0.902378i \(0.641820\pi\)
\(762\) 16.8021i 0.608677i
\(763\) 0 0
\(764\) −0.510605 + 0.884394i −0.0184730 + 0.0319962i
\(765\) 8.14693i 0.294553i
\(766\) 4.63340 8.02528i 0.167411 0.289965i
\(767\) −1.23621 11.0141i −0.0446368 0.397698i
\(768\) −5.00195 8.66363i −0.180492 0.312622i
\(769\) 10.6146 + 6.12834i 0.382772 + 0.220994i 0.679024 0.734116i \(-0.262403\pi\)
−0.296251 + 0.955110i \(0.595737\pi\)
\(770\) 0 0
\(771\) −17.1268 29.6645i −0.616806 1.06834i
\(772\) −4.16649 + 2.40552i −0.149955 + 0.0865767i
\(773\) 3.80327i 0.136794i −0.997658 0.0683970i \(-0.978212\pi\)
0.997658 0.0683970i \(-0.0217884\pi\)
\(774\) 19.0126i 0.683393i
\(775\) −3.05424 + 1.76336i −0.109711 + 0.0633419i
\(776\) 21.5250 + 37.2824i 0.772702 + 1.33836i
\(777\) 0 0
\(778\) 7.90250 + 4.56251i 0.283318 + 0.163574i
\(779\) 18.6872