Properties

Label 1600.2.l.f.401.1
Level $1600$
Weight $2$
Character 1600.401
Analytic conductor $12.776$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1600.l (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.7760643234\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.4767670494822400.1
Defining polynomial: \(x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + 112 x^{2} - 128 x + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: no (minimal twist has level 400)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 401.1
Root \(0.618969 - 1.27156i\) of defining polynomial
Character \(\chi\) \(=\) 1600.401
Dual form 1600.2.l.f.1201.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.16859 - 2.16859i) q^{3} -3.30519i q^{7} +6.40553i q^{9} +O(q^{10})\) \(q+(-2.16859 - 2.16859i) q^{3} -3.30519i q^{7} +6.40553i q^{9} +(-2.01163 + 2.01163i) q^{11} +(0.794042 + 0.794042i) q^{13} +4.61575 q^{17} +(3.48786 + 3.48786i) q^{19} +(-7.16759 + 7.16759i) q^{21} +7.99801i q^{23} +(7.38518 - 7.38518i) q^{27} +(-1.95065 - 1.95065i) q^{29} +5.12695 q^{31} +8.72480 q^{33} +(0.448156 - 0.448156i) q^{37} -3.44390i q^{39} +4.02230i q^{41} +(-4.97000 + 4.97000i) q^{43} +5.49112 q^{47} -3.92429 q^{49} +(-10.0096 - 10.0096i) q^{51} +(-3.35125 + 3.35125i) q^{53} -15.1274i q^{57} +(-2.07673 + 2.07673i) q^{59} +(-0.557208 - 0.557208i) q^{61} +21.1715 q^{63} +(0.636094 + 0.636094i) q^{67} +(17.3444 - 17.3444i) q^{69} +6.85258i q^{71} -10.5177i q^{73} +(6.64883 + 6.64883i) q^{77} +17.3005 q^{79} -12.8142 q^{81} +(-9.48015 - 9.48015i) q^{83} +8.46030i q^{87} +7.62073i q^{89} +(2.62446 - 2.62446i) q^{91} +(-11.1182 - 11.1182i) q^{93} +0.709082 q^{97} +(-12.8856 - 12.8856i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{3} + O(q^{10}) \) \( 12q - 2q^{3} + 2q^{11} - 4q^{13} - 8q^{17} + 14q^{19} - 20q^{21} + 10q^{27} + 4q^{31} + 28q^{33} + 8q^{37} - 8q^{47} + 4q^{49} - 10q^{51} - 16q^{53} - 20q^{59} + 4q^{61} + 8q^{63} - 50q^{67} - 8q^{77} - 12q^{79} - 8q^{81} + 2q^{83} - 44q^{93} - 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(901\) \(1151\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.16859 2.16859i −1.25203 1.25203i −0.954807 0.297227i \(-0.903938\pi\)
−0.297227 0.954807i \(-0.596062\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 3.30519i 1.24924i −0.780927 0.624622i \(-0.785253\pi\)
0.780927 0.624622i \(-0.214747\pi\)
\(8\) 0 0
\(9\) 6.40553i 2.13518i
\(10\) 0 0
\(11\) −2.01163 + 2.01163i −0.606530 + 0.606530i −0.942038 0.335507i \(-0.891092\pi\)
0.335507 + 0.942038i \(0.391092\pi\)
\(12\) 0 0
\(13\) 0.794042 + 0.794042i 0.220228 + 0.220228i 0.808594 0.588367i \(-0.200229\pi\)
−0.588367 + 0.808594i \(0.700229\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.61575 1.11948 0.559741 0.828667i \(-0.310900\pi\)
0.559741 + 0.828667i \(0.310900\pi\)
\(18\) 0 0
\(19\) 3.48786 + 3.48786i 0.800169 + 0.800169i 0.983122 0.182953i \(-0.0585655\pi\)
−0.182953 + 0.983122i \(0.558566\pi\)
\(20\) 0 0
\(21\) −7.16759 + 7.16759i −1.56410 + 1.56410i
\(22\) 0 0
\(23\) 7.99801i 1.66770i 0.551991 + 0.833850i \(0.313868\pi\)
−0.551991 + 0.833850i \(0.686132\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 7.38518 7.38518i 1.42128 1.42128i
\(28\) 0 0
\(29\) −1.95065 1.95065i −0.362227 0.362227i 0.502406 0.864632i \(-0.332448\pi\)
−0.864632 + 0.502406i \(0.832448\pi\)
\(30\) 0 0
\(31\) 5.12695 0.920828 0.460414 0.887704i \(-0.347701\pi\)
0.460414 + 0.887704i \(0.347701\pi\)
\(32\) 0 0
\(33\) 8.72480 1.51879
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0.448156 0.448156i 0.0736764 0.0736764i −0.669308 0.742985i \(-0.733409\pi\)
0.742985 + 0.669308i \(0.233409\pi\)
\(38\) 0 0
\(39\) 3.44390i 0.551465i
\(40\) 0 0
\(41\) 4.02230i 0.628177i 0.949394 + 0.314089i \(0.101699\pi\)
−0.949394 + 0.314089i \(0.898301\pi\)
\(42\) 0 0
\(43\) −4.97000 + 4.97000i −0.757918 + 0.757918i −0.975943 0.218025i \(-0.930039\pi\)
0.218025 + 0.975943i \(0.430039\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5.49112 0.800962 0.400481 0.916305i \(-0.368843\pi\)
0.400481 + 0.916305i \(0.368843\pi\)
\(48\) 0 0
\(49\) −3.92429 −0.560612
\(50\) 0 0
\(51\) −10.0096 10.0096i −1.40163 1.40163i
\(52\) 0 0
\(53\) −3.35125 + 3.35125i −0.460330 + 0.460330i −0.898763 0.438434i \(-0.855533\pi\)
0.438434 + 0.898763i \(0.355533\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 15.1274i 2.00368i
\(58\) 0 0
\(59\) −2.07673 + 2.07673i −0.270367 + 0.270367i −0.829248 0.558881i \(-0.811231\pi\)
0.558881 + 0.829248i \(0.311231\pi\)
\(60\) 0 0
\(61\) −0.557208 0.557208i −0.0713432 0.0713432i 0.670535 0.741878i \(-0.266065\pi\)
−0.741878 + 0.670535i \(0.766065\pi\)
\(62\) 0 0
\(63\) 21.1715 2.66736
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 0.636094 + 0.636094i 0.0777112 + 0.0777112i 0.744894 0.667183i \(-0.232500\pi\)
−0.667183 + 0.744894i \(0.732500\pi\)
\(68\) 0 0
\(69\) 17.3444 17.3444i 2.08802 2.08802i
\(70\) 0 0
\(71\) 6.85258i 0.813252i 0.913595 + 0.406626i \(0.133295\pi\)
−0.913595 + 0.406626i \(0.866705\pi\)
\(72\) 0 0
\(73\) 10.5177i 1.23101i −0.788134 0.615504i \(-0.788953\pi\)
0.788134 0.615504i \(-0.211047\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 6.64883 + 6.64883i 0.757705 + 0.757705i
\(78\) 0 0
\(79\) 17.3005 1.94646 0.973230 0.229833i \(-0.0738179\pi\)
0.973230 + 0.229833i \(0.0738179\pi\)
\(80\) 0 0
\(81\) −12.8142 −1.42380
\(82\) 0 0
\(83\) −9.48015 9.48015i −1.04058 1.04058i −0.999141 0.0414412i \(-0.986805\pi\)
−0.0414412 0.999141i \(-0.513195\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 8.46030i 0.907040i
\(88\) 0 0
\(89\) 7.62073i 0.807796i 0.914804 + 0.403898i \(0.132345\pi\)
−0.914804 + 0.403898i \(0.867655\pi\)
\(90\) 0 0
\(91\) 2.62446 2.62446i 0.275118 0.275118i
\(92\) 0 0
\(93\) −11.1182 11.1182i −1.15291 1.15291i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0.709082 0.0719964 0.0359982 0.999352i \(-0.488539\pi\)
0.0359982 + 0.999352i \(0.488539\pi\)
\(98\) 0 0
\(99\) −12.8856 12.8856i −1.29505 1.29505i
\(100\) 0 0
\(101\) 6.16223 6.16223i 0.613164 0.613164i −0.330605 0.943769i \(-0.607253\pi\)
0.943769 + 0.330605i \(0.107253\pi\)
\(102\) 0 0
\(103\) 15.9410i 1.57072i −0.619040 0.785359i \(-0.712478\pi\)
0.619040 0.785359i \(-0.287522\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.38717 3.38717i 0.327450 0.327450i −0.524166 0.851616i \(-0.675623\pi\)
0.851616 + 0.524166i \(0.175623\pi\)
\(108\) 0 0
\(109\) −2.43964 2.43964i −0.233675 0.233675i 0.580550 0.814225i \(-0.302838\pi\)
−0.814225 + 0.580550i \(0.802838\pi\)
\(110\) 0 0
\(111\) −1.94373 −0.184491
\(112\) 0 0
\(113\) 1.09801 0.103292 0.0516461 0.998665i \(-0.483553\pi\)
0.0516461 + 0.998665i \(0.483553\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −5.08626 + 5.08626i −0.470225 + 0.470225i
\(118\) 0 0
\(119\) 15.2559i 1.39851i
\(120\) 0 0
\(121\) 2.90666i 0.264242i
\(122\) 0 0
\(123\) 8.72270 8.72270i 0.786499 0.786499i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 1.51159 0.134131 0.0670657 0.997749i \(-0.478636\pi\)
0.0670657 + 0.997749i \(0.478636\pi\)
\(128\) 0 0
\(129\) 21.5557 1.89788
\(130\) 0 0
\(131\) 9.21660 + 9.21660i 0.805258 + 0.805258i 0.983912 0.178654i \(-0.0571743\pi\)
−0.178654 + 0.983912i \(0.557174\pi\)
\(132\) 0 0
\(133\) 11.5280 11.5280i 0.999607 0.999607i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.38639i 0.289318i 0.989482 + 0.144659i \(0.0462086\pi\)
−0.989482 + 0.144659i \(0.953791\pi\)
\(138\) 0 0
\(139\) 2.09626 2.09626i 0.177802 0.177802i −0.612595 0.790397i \(-0.709874\pi\)
0.790397 + 0.612595i \(0.209874\pi\)
\(140\) 0 0
\(141\) −11.9080 11.9080i −1.00283 1.00283i
\(142\) 0 0
\(143\) −3.19464 −0.267149
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 8.51015 + 8.51015i 0.701906 + 0.701906i
\(148\) 0 0
\(149\) −2.45247 + 2.45247i −0.200915 + 0.200915i −0.800392 0.599477i \(-0.795375\pi\)
0.599477 + 0.800392i \(0.295375\pi\)
\(150\) 0 0
\(151\) 1.11727i 0.0909222i 0.998966 + 0.0454611i \(0.0144757\pi\)
−0.998966 + 0.0454611i \(0.985524\pi\)
\(152\) 0 0
\(153\) 29.5663i 2.39029i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 15.8377 + 15.8377i 1.26398 + 1.26398i 0.949145 + 0.314839i \(0.101950\pi\)
0.314839 + 0.949145i \(0.398050\pi\)
\(158\) 0 0
\(159\) 14.5349 1.15270
\(160\) 0 0
\(161\) 26.4349 2.08337
\(162\) 0 0
\(163\) 7.22102 + 7.22102i 0.565594 + 0.565594i 0.930891 0.365297i \(-0.119033\pi\)
−0.365297 + 0.930891i \(0.619033\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 13.2304i 1.02380i −0.859044 0.511901i \(-0.828941\pi\)
0.859044 0.511901i \(-0.171059\pi\)
\(168\) 0 0
\(169\) 11.7390i 0.903000i
\(170\) 0 0
\(171\) −22.3416 + 22.3416i −1.70850 + 1.70850i
\(172\) 0 0
\(173\) 11.7503 + 11.7503i 0.893355 + 0.893355i 0.994837 0.101482i \(-0.0323585\pi\)
−0.101482 + 0.994837i \(0.532359\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 9.00712 0.677017
\(178\) 0 0
\(179\) −4.84732 4.84732i −0.362306 0.362306i 0.502355 0.864661i \(-0.332467\pi\)
−0.864661 + 0.502355i \(0.832467\pi\)
\(180\) 0 0
\(181\) 10.5742 10.5742i 0.785976 0.785976i −0.194856 0.980832i \(-0.562424\pi\)
0.980832 + 0.194856i \(0.0624240\pi\)
\(182\) 0 0
\(183\) 2.41671i 0.178648i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −9.28519 + 9.28519i −0.679000 + 0.679000i
\(188\) 0 0
\(189\) −24.4094 24.4094i −1.77553 1.77553i
\(190\) 0 0
\(191\) −7.94268 −0.574712 −0.287356 0.957824i \(-0.592776\pi\)
−0.287356 + 0.957824i \(0.592776\pi\)
\(192\) 0 0
\(193\) −20.8617 −1.50166 −0.750829 0.660496i \(-0.770346\pi\)
−0.750829 + 0.660496i \(0.770346\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2.07707 2.07707i 0.147985 0.147985i −0.629232 0.777217i \(-0.716631\pi\)
0.777217 + 0.629232i \(0.216631\pi\)
\(198\) 0 0
\(199\) 23.2807i 1.65033i 0.564893 + 0.825164i \(0.308917\pi\)
−0.564893 + 0.825164i \(0.691083\pi\)
\(200\) 0 0
\(201\) 2.75885i 0.194594i
\(202\) 0 0
\(203\) −6.44727 + 6.44727i −0.452510 + 0.452510i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −51.2315 −3.56083
\(208\) 0 0
\(209\) −14.0326 −0.970653
\(210\) 0 0
\(211\) 2.51586 + 2.51586i 0.173199 + 0.173199i 0.788383 0.615184i \(-0.210918\pi\)
−0.615184 + 0.788383i \(0.710918\pi\)
\(212\) 0 0
\(213\) 14.8604 14.8604i 1.01822 1.01822i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 16.9456i 1.15034i
\(218\) 0 0
\(219\) −22.8086 + 22.8086i −1.54126 + 1.54126i
\(220\) 0 0
\(221\) 3.66510 + 3.66510i 0.246541 + 0.246541i
\(222\) 0 0
\(223\) −10.9088 −0.730507 −0.365253 0.930908i \(-0.619018\pi\)
−0.365253 + 0.930908i \(0.619018\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 11.6347 + 11.6347i 0.772220 + 0.772220i 0.978494 0.206275i \(-0.0661340\pi\)
−0.206275 + 0.978494i \(0.566134\pi\)
\(228\) 0 0
\(229\) −1.60760 + 1.60760i −0.106233 + 0.106233i −0.758226 0.651992i \(-0.773933\pi\)
0.651992 + 0.758226i \(0.273933\pi\)
\(230\) 0 0
\(231\) 28.8371i 1.89734i
\(232\) 0 0
\(233\) 23.8100i 1.55985i 0.625875 + 0.779924i \(0.284742\pi\)
−0.625875 + 0.779924i \(0.715258\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −37.5177 37.5177i −2.43703 2.43703i
\(238\) 0 0
\(239\) 0.199630 0.0129130 0.00645649 0.999979i \(-0.497945\pi\)
0.00645649 + 0.999979i \(0.497945\pi\)
\(240\) 0 0
\(241\) −16.8755 −1.08705 −0.543525 0.839393i \(-0.682911\pi\)
−0.543525 + 0.839393i \(0.682911\pi\)
\(242\) 0 0
\(243\) 5.63317 + 5.63317i 0.361368 + 0.361368i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 5.53901i 0.352439i
\(248\) 0 0
\(249\) 41.1171i 2.60569i
\(250\) 0 0
\(251\) 6.10023 6.10023i 0.385043 0.385043i −0.487872 0.872915i \(-0.662227\pi\)
0.872915 + 0.487872i \(0.162227\pi\)
\(252\) 0 0
\(253\) −16.0891 16.0891i −1.01151 1.01151i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −19.8360 −1.23733 −0.618667 0.785653i \(-0.712327\pi\)
−0.618667 + 0.785653i \(0.712327\pi\)
\(258\) 0 0
\(259\) −1.48124 1.48124i −0.0920399 0.0920399i
\(260\) 0 0
\(261\) 12.4949 12.4949i 0.773418 0.773418i
\(262\) 0 0
\(263\) 7.14438i 0.440542i −0.975439 0.220271i \(-0.929306\pi\)
0.975439 0.220271i \(-0.0706941\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 16.5262 16.5262i 1.01139 1.01139i
\(268\) 0 0
\(269\) 21.7716 + 21.7716i 1.32744 + 1.32744i 0.907596 + 0.419844i \(0.137915\pi\)
0.419844 + 0.907596i \(0.362085\pi\)
\(270\) 0 0
\(271\) 4.71328 0.286312 0.143156 0.989700i \(-0.454275\pi\)
0.143156 + 0.989700i \(0.454275\pi\)
\(272\) 0 0
\(273\) −11.3827 −0.688915
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 20.4588 20.4588i 1.22925 1.22925i 0.265006 0.964247i \(-0.414626\pi\)
0.964247 0.265006i \(-0.0853739\pi\)
\(278\) 0 0
\(279\) 32.8409i 1.96613i
\(280\) 0 0
\(281\) 17.6481i 1.05280i 0.850239 + 0.526398i \(0.176458\pi\)
−0.850239 + 0.526398i \(0.823542\pi\)
\(282\) 0 0
\(283\) −18.1525 + 18.1525i −1.07906 + 1.07906i −0.0824607 + 0.996594i \(0.526278\pi\)
−0.996594 + 0.0824607i \(0.973722\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 13.2945 0.784747
\(288\) 0 0
\(289\) 4.30511 0.253242
\(290\) 0 0
\(291\) −1.53771 1.53771i −0.0901419 0.0901419i
\(292\) 0 0
\(293\) −0.638480 + 0.638480i −0.0373004 + 0.0373004i −0.725511 0.688211i \(-0.758397\pi\)
0.688211 + 0.725511i \(0.258397\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 29.7126i 1.72410i
\(298\) 0 0
\(299\) −6.35076 + 6.35076i −0.367274 + 0.367274i
\(300\) 0 0
\(301\) 16.4268 + 16.4268i 0.946825 + 0.946825i
\(302\) 0 0
\(303\) −26.7266 −1.53540
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −4.52224 4.52224i −0.258098 0.258098i 0.566182 0.824280i \(-0.308420\pi\)
−0.824280 + 0.566182i \(0.808420\pi\)
\(308\) 0 0
\(309\) −34.5695 + 34.5695i −1.96659 + 1.96659i
\(310\) 0 0
\(311\) 14.1014i 0.799620i 0.916598 + 0.399810i \(0.130924\pi\)
−0.916598 + 0.399810i \(0.869076\pi\)
\(312\) 0 0
\(313\) 11.9204i 0.673779i 0.941544 + 0.336889i \(0.109375\pi\)
−0.941544 + 0.336889i \(0.890625\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 17.6516 + 17.6516i 0.991410 + 0.991410i 0.999963 0.00855359i \(-0.00272272\pi\)
−0.00855359 + 0.999963i \(0.502723\pi\)
\(318\) 0 0
\(319\) 7.84798 0.439403
\(320\) 0 0
\(321\) −14.6907 −0.819958
\(322\) 0 0
\(323\) 16.0991 + 16.0991i 0.895775 + 0.895775i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 10.5811i 0.585138i
\(328\) 0 0
\(329\) 18.1492i 1.00060i
\(330\) 0 0
\(331\) 24.9785 24.9785i 1.37294 1.37294i 0.516888 0.856053i \(-0.327090\pi\)
0.856053 0.516888i \(-0.172910\pi\)
\(332\) 0 0
\(333\) 2.87068 + 2.87068i 0.157312 + 0.157312i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −24.3167 −1.32462 −0.662308 0.749231i \(-0.730423\pi\)
−0.662308 + 0.749231i \(0.730423\pi\)
\(338\) 0 0
\(339\) −2.38113 2.38113i −0.129325 0.129325i
\(340\) 0 0
\(341\) −10.3136 + 10.3136i −0.558510 + 0.558510i
\(342\) 0 0
\(343\) 10.1658i 0.548903i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −17.3818 + 17.3818i −0.933106 + 0.933106i −0.997899 0.0647931i \(-0.979361\pi\)
0.0647931 + 0.997899i \(0.479361\pi\)
\(348\) 0 0
\(349\) −0.773103 0.773103i −0.0413832 0.0413832i 0.686112 0.727496i \(-0.259316\pi\)
−0.727496 + 0.686112i \(0.759316\pi\)
\(350\) 0 0
\(351\) 11.7283 0.626010
\(352\) 0 0
\(353\) 13.3720 0.711720 0.355860 0.934539i \(-0.384188\pi\)
0.355860 + 0.934539i \(0.384188\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −33.0838 + 33.0838i −1.75098 + 1.75098i
\(358\) 0 0
\(359\) 28.5413i 1.50635i −0.657818 0.753177i \(-0.728520\pi\)
0.657818 0.753177i \(-0.271480\pi\)
\(360\) 0 0
\(361\) 5.33027i 0.280541i
\(362\) 0 0
\(363\) 6.30335 6.30335i 0.330840 0.330840i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0.909186 0.0474591 0.0237296 0.999718i \(-0.492446\pi\)
0.0237296 + 0.999718i \(0.492446\pi\)
\(368\) 0 0
\(369\) −25.7649 −1.34127
\(370\) 0 0
\(371\) 11.0765 + 11.0765i 0.575064 + 0.575064i
\(372\) 0 0
\(373\) −26.5010 + 26.5010i −1.37217 + 1.37217i −0.514946 + 0.857223i \(0.672188\pi\)
−0.857223 + 0.514946i \(0.827812\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3.09780i 0.159545i
\(378\) 0 0
\(379\) −1.23724 + 1.23724i −0.0635529 + 0.0635529i −0.738169 0.674616i \(-0.764309\pi\)
0.674616 + 0.738169i \(0.264309\pi\)
\(380\) 0 0
\(381\) −3.27800 3.27800i −0.167937 0.167937i
\(382\) 0 0
\(383\) 15.7161 0.803057 0.401529 0.915846i \(-0.368479\pi\)
0.401529 + 0.915846i \(0.368479\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −31.8355 31.8355i −1.61829 1.61829i
\(388\) 0 0
\(389\) 16.2799 16.2799i 0.825423 0.825423i −0.161457 0.986880i \(-0.551619\pi\)
0.986880 + 0.161457i \(0.0516193\pi\)
\(390\) 0 0
\(391\) 36.9168i 1.86696i
\(392\) 0 0
\(393\) 39.9740i 2.01642i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 22.8944 + 22.8944i 1.14903 + 1.14903i 0.986743 + 0.162292i \(0.0518887\pi\)
0.162292 + 0.986743i \(0.448111\pi\)
\(398\) 0 0
\(399\) −49.9990 −2.50308
\(400\) 0 0
\(401\) 15.8553 0.791778 0.395889 0.918298i \(-0.370437\pi\)
0.395889 + 0.918298i \(0.370437\pi\)
\(402\) 0 0
\(403\) 4.07102 + 4.07102i 0.202792 + 0.202792i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.80305i 0.0893740i
\(408\) 0 0
\(409\) 10.0220i 0.495557i 0.968817 + 0.247779i \(0.0797006\pi\)
−0.968817 + 0.247779i \(0.920299\pi\)
\(410\) 0 0
\(411\) 7.34367 7.34367i 0.362236 0.362236i
\(412\) 0 0
\(413\) 6.86398 + 6.86398i 0.337754 + 0.337754i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −9.09182 −0.445228
\(418\) 0 0
\(419\) −14.4998 14.4998i −0.708362 0.708362i 0.257829 0.966191i \(-0.416993\pi\)
−0.966191 + 0.257829i \(0.916993\pi\)
\(420\) 0 0
\(421\) 12.9983 12.9983i 0.633498 0.633498i −0.315446 0.948944i \(-0.602154\pi\)
0.948944 + 0.315446i \(0.102154\pi\)
\(422\) 0 0
\(423\) 35.1735i 1.71020i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −1.84168 + 1.84168i −0.0891251 + 0.0891251i
\(428\) 0 0
\(429\) 6.92786 + 6.92786i 0.334480 + 0.334480i
\(430\) 0 0
\(431\) 34.4404 1.65894 0.829469 0.558553i \(-0.188643\pi\)
0.829469 + 0.558553i \(0.188643\pi\)
\(432\) 0 0
\(433\) −14.5895 −0.701128 −0.350564 0.936539i \(-0.614010\pi\)
−0.350564 + 0.936539i \(0.614010\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −27.8959 + 27.8959i −1.33444 + 1.33444i
\(438\) 0 0
\(439\) 5.70179i 0.272131i 0.990700 + 0.136066i \(0.0434458\pi\)
−0.990700 + 0.136066i \(0.956554\pi\)
\(440\) 0 0
\(441\) 25.1371i 1.19701i
\(442\) 0 0
\(443\) −5.03375 + 5.03375i −0.239161 + 0.239161i −0.816503 0.577342i \(-0.804090\pi\)
0.577342 + 0.816503i \(0.304090\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 10.6368 0.503104
\(448\) 0 0
\(449\) 22.2502 1.05005 0.525025 0.851087i \(-0.324056\pi\)
0.525025 + 0.851087i \(0.324056\pi\)
\(450\) 0 0
\(451\) −8.09139 8.09139i −0.381009 0.381009i
\(452\) 0 0
\(453\) 2.42290 2.42290i 0.113838 0.113838i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 8.92927i 0.417694i 0.977948 + 0.208847i \(0.0669710\pi\)
−0.977948 + 0.208847i \(0.933029\pi\)
\(458\) 0 0
\(459\) 34.0881 34.0881i 1.59110 1.59110i
\(460\) 0 0
\(461\) −8.14776 8.14776i −0.379479 0.379479i 0.491435 0.870914i \(-0.336472\pi\)
−0.870914 + 0.491435i \(0.836472\pi\)
\(462\) 0 0
\(463\) 31.7058 1.47349 0.736747 0.676168i \(-0.236361\pi\)
0.736747 + 0.676168i \(0.236361\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 17.7683 + 17.7683i 0.822219 + 0.822219i 0.986426 0.164207i \(-0.0525065\pi\)
−0.164207 + 0.986426i \(0.552506\pi\)
\(468\) 0 0
\(469\) 2.10241 2.10241i 0.0970803 0.0970803i
\(470\) 0 0
\(471\) 68.6907i 3.16510i
\(472\) 0 0
\(473\) 19.9956i 0.919401i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −21.4665 21.4665i −0.982885 0.982885i
\(478\) 0 0
\(479\) 7.80806 0.356759 0.178380 0.983962i \(-0.442914\pi\)
0.178380 + 0.983962i \(0.442914\pi\)
\(480\) 0 0
\(481\) 0.711710 0.0324512
\(482\) 0 0
\(483\) −57.3264 57.3264i −2.60844 2.60844i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 27.6753i 1.25409i −0.778984 0.627044i \(-0.784265\pi\)
0.778984 0.627044i \(-0.215735\pi\)
\(488\) 0 0
\(489\) 31.3188i 1.41629i
\(490\) 0 0
\(491\) 11.7995 11.7995i 0.532505 0.532505i −0.388812 0.921317i \(-0.627114\pi\)
0.921317 + 0.388812i \(0.127114\pi\)
\(492\) 0 0
\(493\) −9.00370 9.00370i −0.405506 0.405506i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 22.6491 1.01595
\(498\) 0 0
\(499\) 25.0477 + 25.0477i 1.12129 + 1.12129i 0.991548 + 0.129743i \(0.0414153\pi\)
0.129743 + 0.991548i \(0.458585\pi\)
\(500\) 0 0
\(501\) −28.6914 + 28.6914i −1.28184 + 1.28184i
\(502\) 0 0
\(503\) 22.8644i 1.01947i 0.860331 + 0.509736i \(0.170257\pi\)
−0.860331 + 0.509736i \(0.829743\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −25.4570 + 25.4570i −1.13059 + 1.13059i
\(508\) 0 0
\(509\) −17.1633 17.1633i −0.760748 0.760748i 0.215710 0.976458i \(-0.430794\pi\)
−0.976458 + 0.215710i \(0.930794\pi\)
\(510\) 0 0
\(511\) −34.7631 −1.53783
\(512\) 0 0
\(513\) 51.5169 2.27453
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −11.0461 + 11.0461i −0.485808 + 0.485808i
\(518\) 0 0
\(519\) 50.9629i 2.23702i
\(520\) 0 0
\(521\) 11.5206i 0.504726i −0.967633 0.252363i \(-0.918792\pi\)
0.967633 0.252363i \(-0.0812077\pi\)
\(522\) 0 0
\(523\) 25.4249 25.4249i 1.11175 1.11175i 0.118841 0.992913i \(-0.462082\pi\)
0.992913 0.118841i \(-0.0379180\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 23.6647 1.03085
\(528\) 0 0
\(529\) −40.9681 −1.78122
\(530\) 0 0
\(531\) −13.3025 13.3025i −0.577281 0.577281i
\(532\) 0 0
\(533\) −3.19387 + 3.19387i −0.138342 + 0.138342i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 21.0237i 0.907239i
\(538\) 0 0
\(539\) 7.89423 7.89423i 0.340028 0.340028i
\(540\) 0 0
\(541\) −29.7997 29.7997i −1.28119 1.28119i −0.939992 0.341196i \(-0.889168\pi\)
−0.341196 0.939992i \(-0.610832\pi\)
\(542\) 0 0
\(543\) −45.8622 −1.96814
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −28.3699 28.3699i −1.21301 1.21301i −0.970032 0.242979i \(-0.921875\pi\)
−0.242979 0.970032i \(-0.578125\pi\)
\(548\) 0 0
\(549\) 3.56921 3.56921i 0.152330 0.152330i
\(550\) 0 0
\(551\) 13.6072i 0.579685i
\(552\) 0 0
\(553\) 57.1815i 2.43161i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −21.7769 21.7769i −0.922718 0.922718i 0.0745028 0.997221i \(-0.476263\pi\)
−0.997221 + 0.0745028i \(0.976263\pi\)
\(558\) 0 0
\(559\) −7.89278 −0.333829
\(560\) 0 0
\(561\) 40.2715 1.70026
\(562\) 0 0
\(563\) 10.9022 + 10.9022i 0.459473 + 0.459473i 0.898482 0.439010i \(-0.144671\pi\)
−0.439010 + 0.898482i \(0.644671\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 42.3534i 1.77868i
\(568\) 0 0
\(569\) 31.1881i 1.30747i −0.756723 0.653736i \(-0.773201\pi\)
0.756723 0.653736i \(-0.226799\pi\)
\(570\) 0 0
\(571\) 2.20354 2.20354i 0.0922153 0.0922153i −0.659494 0.751710i \(-0.729230\pi\)
0.751710 + 0.659494i \(0.229230\pi\)
\(572\) 0 0
\(573\) 17.2244 + 17.2244i 0.719559 + 0.719559i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −8.42524 −0.350747 −0.175374 0.984502i \(-0.556113\pi\)
−0.175374 + 0.984502i \(0.556113\pi\)
\(578\) 0 0
\(579\) 45.2404 + 45.2404i 1.88013 + 1.88013i
\(580\) 0 0
\(581\) −31.3337 + 31.3337i −1.29994 + 1.29994i
\(582\) 0 0
\(583\) 13.4830i 0.558408i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −19.3370 + 19.3370i −0.798125 + 0.798125i −0.982800 0.184675i \(-0.940877\pi\)
0.184675 + 0.982800i \(0.440877\pi\)
\(588\) 0 0
\(589\) 17.8821 + 17.8821i 0.736818 + 0.736818i
\(590\) 0 0
\(591\) −9.00862 −0.370565
\(592\) 0 0
\(593\) −18.1804 −0.746580 −0.373290 0.927715i \(-0.621770\pi\)
−0.373290 + 0.927715i \(0.621770\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 50.4863 50.4863i 2.06627 2.06627i
\(598\) 0 0
\(599\) 1.64695i 0.0672927i −0.999434 0.0336463i \(-0.989288\pi\)
0.999434 0.0336463i \(-0.0107120\pi\)
\(600\) 0 0
\(601\) 12.7485i 0.520021i −0.965606 0.260011i \(-0.916274\pi\)
0.965606 0.260011i \(-0.0837261\pi\)
\(602\) 0 0
\(603\) −4.07452 + 4.07452i −0.165927 + 0.165927i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 15.6773 0.636322 0.318161 0.948037i \(-0.396935\pi\)
0.318161 + 0.948037i \(0.396935\pi\)
\(608\) 0 0
\(609\) 27.9629 1.13311
\(610\) 0 0
\(611\) 4.36018 + 4.36018i 0.176394 + 0.176394i
\(612\) 0 0
\(613\) −8.29399 + 8.29399i −0.334991 + 0.334991i −0.854478 0.519487i \(-0.826123\pi\)
0.519487 + 0.854478i \(0.326123\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 20.3330i 0.818575i −0.912406 0.409287i \(-0.865777\pi\)
0.912406 0.409287i \(-0.134223\pi\)
\(618\) 0 0
\(619\) −12.5878 + 12.5878i −0.505946 + 0.505946i −0.913280 0.407333i \(-0.866459\pi\)
0.407333 + 0.913280i \(0.366459\pi\)
\(620\) 0 0
\(621\) 59.0667 + 59.0667i 2.37027 + 2.37027i
\(622\) 0 0
\(623\) 25.1880 1.00914
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 30.4308 + 30.4308i 1.21529 + 1.21529i
\(628\) 0 0
\(629\) 2.06858 2.06858i 0.0824795 0.0824795i
\(630\) 0 0
\(631\) 21.4887i 0.855453i 0.903908 + 0.427726i \(0.140685\pi\)
−0.903908 + 0.427726i \(0.859315\pi\)
\(632\) 0 0
\(633\) 10.9117i 0.433702i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −3.11605 3.11605i −0.123462 0.123462i
\(638\) 0 0
\(639\) −43.8944 −1.73644
\(640\) 0 0
\(641\) 26.1687 1.03360 0.516800 0.856106i \(-0.327123\pi\)
0.516800 + 0.856106i \(0.327123\pi\)
\(642\) 0 0
\(643\) −14.6501 14.6501i −0.577743 0.577743i 0.356538 0.934281i \(-0.383957\pi\)
−0.934281 + 0.356538i \(0.883957\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 16.2623i 0.639337i 0.947530 + 0.319668i \(0.103571\pi\)
−0.947530 + 0.319668i \(0.896429\pi\)
\(648\) 0 0
\(649\) 8.35522i 0.327971i
\(650\) 0 0
\(651\) −36.7479 + 36.7479i −1.44026 + 1.44026i
\(652\) 0 0
\(653\) 32.0639 + 32.0639i 1.25476 + 1.25476i 0.953563 + 0.301194i \(0.0973851\pi\)
0.301194 + 0.953563i \(0.402615\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 67.3717 2.62842
\(658\) 0 0
\(659\) 7.04696 + 7.04696i 0.274511 + 0.274511i 0.830913 0.556402i \(-0.187819\pi\)
−0.556402 + 0.830913i \(0.687819\pi\)
\(660\) 0 0
\(661\) 5.78655 5.78655i 0.225071 0.225071i −0.585559 0.810630i \(-0.699125\pi\)
0.810630 + 0.585559i \(0.199125\pi\)
\(662\) 0 0
\(663\) 15.8962i 0.617355i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 15.6013 15.6013i 0.604085 0.604085i
\(668\) 0 0
\(669\) 23.6567 + 23.6567i 0.914619 + 0.914619i
\(670\) 0 0
\(671\) 2.24180 0.0865436
\(672\) 0 0
\(673\) 35.3380 1.36218 0.681090 0.732200i \(-0.261506\pi\)
0.681090 + 0.732200i \(0.261506\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 7.72259 7.72259i 0.296803 0.296803i −0.542957 0.839760i \(-0.682695\pi\)
0.839760 + 0.542957i \(0.182695\pi\)
\(678\) 0 0
\(679\) 2.34365i 0.0899411i
\(680\) 0 0
\(681\) 50.4615i 1.93369i
\(682\) 0 0
\(683\) 15.6011 15.6011i 0.596958 0.596958i −0.342544 0.939502i \(-0.611289\pi\)
0.939502 + 0.342544i \(0.111289\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 6.97246 0.266016
\(688\) 0 0
\(689\) −5.32207 −0.202755
\(690\) 0 0
\(691\) −30.0975 30.0975i −1.14496 1.14496i −0.987530 0.157433i \(-0.949678\pi\)
−0.157433 0.987530i \(-0.550322\pi\)
\(692\) 0 0
\(693\) −42.5893 + 42.5893i −1.61783 + 1.61783i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 18.5659i 0.703234i
\(698\) 0 0
\(699\) 51.6341 51.6341i 1.95298 1.95298i
\(700\) 0 0
\(701\) 14.8151 + 14.8151i 0.559559 + 0.559559i 0.929182 0.369623i \(-0.120513\pi\)
−0.369623 + 0.929182i \(0.620513\pi\)
\(702\) 0 0
\(703\) 3.12621 0.117907
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −20.3673 20.3673i −0.765992 0.765992i
\(708\) 0 0
\(709\) 9.26566 9.26566i 0.347979 0.347979i −0.511377 0.859356i \(-0.670864\pi\)
0.859356 + 0.511377i \(0.170864\pi\)
\(710\) 0 0
\(711\) 110.819i 4.15604i
\(712\) 0 0
\(713\) 41.0054i 1.53567i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −0.432914 0.432914i −0.0161675 0.0161675i
\(718\) 0 0
\(719\) −40.8143 −1.52212 −0.761058 0.648684i \(-0.775320\pi\)
−0.761058 + 0.648684i \(0.775320\pi\)
\(720\) 0 0
\(721\) −52.6882 −1.96221
\(722\) 0 0
\(723\) 36.5961 + 36.5961i 1.36102 + 1.36102i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 5.20944i 0.193208i 0.995323 + 0.0966038i \(0.0307980\pi\)
−0.995323 + 0.0966038i \(0.969202\pi\)
\(728\) 0 0
\(729\) 14.0106i 0.518911i
\(730\) 0 0
\(731\) −22.9403 + 22.9403i −0.848476 + 0.848476i
\(732\) 0 0
\(733\) −14.7039 14.7039i −0.543099 0.543099i 0.381337 0.924436i \(-0.375464\pi\)
−0.924436 + 0.381337i \(0.875464\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2.55917 −0.0942684
\(738\) 0 0
\(739\) −7.68017 7.68017i −0.282520 0.282520i 0.551594 0.834113i \(-0.314020\pi\)
−0.834113 + 0.551594i \(0.814020\pi\)
\(740\) 0 0
\(741\) 12.0118 12.0118i 0.441265 0.441265i
\(742\) 0 0
\(743\) 34.9882i 1.28359i 0.766876 + 0.641796i \(0.221810\pi\)
−0.766876 + 0.641796i \(0.778190\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 60.7254 60.7254i 2.22183 2.22183i
\(748\) 0 0
\(749\) −11.1953 11.1953i −0.409066 0.409066i
\(750\) 0 0
\(751\) 33.1447 1.20947 0.604733 0.796428i \(-0.293280\pi\)
0.604733 + 0.796428i \(0.293280\pi\)
\(752\) 0 0
\(753\) −26.4577 −0.964174
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 22.1553 22.1553i 0.805248 0.805248i −0.178663 0.983910i \(-0.557177\pi\)
0.983910 + 0.178663i \(0.0571771\pi\)
\(758\) 0 0
\(759\) 69.7810i 2.53289i
\(760\) 0 0
\(761\) 48.1426i 1.74517i 0.488466 + 0.872583i \(0.337557\pi\)
−0.488466 + 0.872583i \(0.662443\pi\)
\(762\) 0 0
\(763\) −8.06347 + 8.06347i −0.291917 + 0.291917i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −3.29802 −0.119084
\(768\) 0 0
\(769\) −41.1054 −1.48230 −0.741150 0.671339i \(-0.765719\pi\)
−0.741150 + 0.671339i \(0.765719\pi\)
\(770\) 0 0
\(771\) 43.0160 + 43.0160i 1.54918 + 1.54918i
\(772\) 0 0
\(773\) 10.8044 10.8044i 0.388607 0.388607i −0.485583 0.874190i \(-0.661393\pi\)
0.874190 + 0.485583i \(0.161393\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 6.42440i 0.230474i
\(778\) 0 0
\(779\) −14.0292 + 14.0292i −0.502648 + 0.502648i
\(780\) 0 0
\(781\) −13.7849 13.7849i −0.493262 0.493262i
\(782\) 0 0
\(783\) −28.8118 −1.02965
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −11.7496 11.7496i −0.418826 0.418826i 0.465973 0.884799i \(-0.345704\pi\)
−0.884799 + 0.465973i \(0.845704\pi\)
\(788\) 0 0
\(789\) −15.4932 + 15.4932i −0.551573 + 0.551573i
\(790\) 0 0
\(791\) 3.62914i 0.129037i
\(792\) 0 0
\(793\) 0.884894i 0.0314235i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 15.9126 + 15.9126i 0.563652 + 0.563652i 0.930343 0.366691i \(-0.119509\pi\)
−0.366691 + 0.930343i \(0.619509\pi\)
\(798\) 0 0
\(799\) 25.3456 0.896663
\(800\) 0 0
\(801\) −48.8148 −1.72479
\(802\) 0 0
\(803\) 21.1578 + 21.1578i 0.746643 + 0.746643i