Properties

Label 804.2.ba.b.41.5
Level 804
Weight 2
Character 804.41
Analytic conductor 6.420
Analytic rank 0
Dimension 440
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.ba (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(440\)
Relative dimension: \(22\) over \(\Q(\zeta_{66})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label 41.5
Character \(\chi\) = 804.41
Dual form 804.2.ba.b.353.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.32247 - 1.11851i) q^{3} +(0.102406 - 0.712247i) q^{5} +(0.0729329 + 0.763788i) q^{7} +(0.497878 + 2.95840i) q^{9} +O(q^{10})\) \(q+(-1.32247 - 1.11851i) q^{3} +(0.102406 - 0.712247i) q^{5} +(0.0729329 + 0.763788i) q^{7} +(0.497878 + 2.95840i) q^{9} +(-0.457848 + 0.183294i) q^{11} +(3.42746 + 3.59462i) q^{13} +(-0.932083 + 0.827387i) q^{15} +(-6.00843 + 2.07954i) q^{17} +(1.10984 + 0.105977i) q^{19} +(0.757851 - 1.09167i) q^{21} +(7.01892 - 0.334352i) q^{23} +(4.30066 + 1.26279i) q^{25} +(2.65056 - 4.46929i) q^{27} +(-7.80897 + 4.50851i) q^{29} +(2.71627 - 2.84874i) q^{31} +(0.810508 + 0.269704i) q^{33} +(0.551474 + 0.0262700i) q^{35} +(0.597753 - 1.03534i) q^{37} +(-0.512121 - 8.58744i) q^{39} +(8.84237 + 1.70423i) q^{41} +(3.66095 + 3.17223i) q^{43} +(2.15810 - 0.0516556i) q^{45} +(2.65699 - 5.15385i) q^{47} +(6.29545 - 1.21335i) q^{49} +(10.2720 + 3.97034i) q^{51} +(1.01898 + 1.17596i) q^{53} +(0.0836648 + 0.344871i) q^{55} +(-1.34920 - 1.38152i) q^{57} +(1.87800 + 6.39587i) q^{59} +(-2.71070 + 6.77100i) q^{61} +(-2.22328 + 0.596038i) q^{63} +(2.91125 - 2.07309i) q^{65} +(-0.562265 - 8.16602i) q^{67} +(-9.65632 - 7.40855i) q^{69} +(-8.12417 - 2.81180i) q^{71} +(10.8460 + 4.34209i) q^{73} +(-4.27507 - 6.48032i) q^{75} +(-0.173390 - 0.336330i) q^{77} +(7.69406 - 1.86656i) q^{79} +(-8.50423 + 2.94584i) q^{81} +(-9.04632 + 11.5033i) q^{83} +(0.865847 + 4.49244i) q^{85} +(15.3700 + 2.77201i) q^{87} +(2.00976 - 3.12725i) q^{89} +(-2.49555 + 2.88002i) q^{91} +(-6.77854 + 0.729218i) q^{93} +(0.189136 - 0.779630i) q^{95} +(1.81643 + 1.04871i) q^{97} +(-0.770210 - 1.26324i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440q - 12q^{7} + 4q^{9} + O(q^{10}) \) \( 440q - 12q^{7} + 4q^{9} - 2q^{15} - 10q^{19} + 22q^{21} - 68q^{25} + 50q^{31} + 11q^{33} - 22q^{37} - 45q^{39} + 22q^{43} + 22q^{45} - 18q^{49} - 6q^{51} + 126q^{55} - 183q^{57} - 56q^{61} - 141q^{63} - 12q^{67} + 33q^{69} + 356q^{73} + 165q^{75} + 228q^{79} + 24q^{81} - 6q^{85} + 75q^{87} - 4q^{91} - 75q^{93} + 12q^{97} + 88q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{53}{66}\right)\) \(1\)

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
\(3\) −1.32247 1.11851i −0.763531 0.645771i
\(4\) 0 0
\(5\) 0.102406 0.712247i 0.0457972 0.318527i −0.954026 0.299724i \(-0.903105\pi\)
0.999823 0.0188027i \(-0.00598544\pi\)
\(6\) 0 0
\(7\) 0.0729329 + 0.763788i 0.0275660 + 0.288685i 0.998735 + 0.0502909i \(0.0160148\pi\)
−0.971169 + 0.238394i \(0.923379\pi\)
\(8\) 0 0
\(9\) 0.497878 + 2.95840i 0.165959 + 0.986133i
\(10\) 0 0
\(11\) −0.457848 + 0.183294i −0.138046 + 0.0552654i −0.439657 0.898166i \(-0.644900\pi\)
0.301611 + 0.953431i \(0.402476\pi\)
\(12\) 0 0
\(13\) 3.42746 + 3.59462i 0.950607 + 0.996968i 0.999998 0.00181138i \(-0.000576581\pi\)
−0.0493912 + 0.998780i \(0.515728\pi\)
\(14\) 0 0
\(15\) −0.932083 + 0.827387i −0.240663 + 0.213630i
\(16\) 0 0
\(17\) −6.00843 + 2.07954i −1.45726 + 0.504362i −0.936903 0.349589i \(-0.886321\pi\)
−0.520354 + 0.853951i \(0.674200\pi\)
\(18\) 0 0
\(19\) 1.10984 + 0.105977i 0.254616 + 0.0243128i 0.221583 0.975141i \(-0.428878\pi\)
0.0330323 + 0.999454i \(0.489484\pi\)
\(20\) 0 0
\(21\) 0.757851 1.09167i 0.165377 0.238221i
\(22\) 0 0
\(23\) 7.01892 0.334352i 1.46355 0.0697173i 0.699386 0.714744i \(-0.253457\pi\)
0.764160 + 0.645027i \(0.223154\pi\)
\(24\) 0 0
\(25\) 4.30066 + 1.26279i 0.860131 + 0.252557i
\(26\) 0 0
\(27\) 2.65056 4.46929i 0.510101 0.860115i
\(28\) 0 0
\(29\) −7.80897 + 4.50851i −1.45009 + 0.837210i −0.998486 0.0550091i \(-0.982481\pi\)
−0.451604 + 0.892219i \(0.649148\pi\)
\(30\) 0 0
\(31\) 2.71627 2.84874i 0.487857 0.511649i −0.433083 0.901354i \(-0.642574\pi\)
0.920940 + 0.389705i \(0.127423\pi\)
\(32\) 0 0
\(33\) 0.810508 + 0.269704i 0.141091 + 0.0469494i
\(34\) 0 0
\(35\) 0.551474 + 0.0262700i 0.0932162 + 0.00444043i
\(36\) 0 0
\(37\) 0.597753 1.03534i 0.0982700 0.170209i −0.812699 0.582684i \(-0.802002\pi\)
0.910969 + 0.412476i \(0.135336\pi\)
\(38\) 0 0
\(39\) −0.512121 8.58744i −0.0820049 1.37509i
\(40\) 0 0
\(41\) 8.84237 + 1.70423i 1.38095 + 0.266156i 0.825033 0.565085i \(-0.191157\pi\)
0.555913 + 0.831240i \(0.312369\pi\)
\(42\) 0 0
\(43\) 3.66095 + 3.17223i 0.558289 + 0.483761i 0.887698 0.460427i \(-0.152304\pi\)
−0.329408 + 0.944188i \(0.606849\pi\)
\(44\) 0 0
\(45\) 2.15810 0.0516556i 0.321710 0.00770036i
\(46\) 0 0
\(47\) 2.65699 5.15385i 0.387562 0.751766i −0.611663 0.791118i \(-0.709499\pi\)
0.999225 + 0.0393523i \(0.0125295\pi\)
\(48\) 0 0
\(49\) 6.29545 1.21335i 0.899350 0.173335i
\(50\) 0 0
\(51\) 10.2720 + 3.97034i 1.43836 + 0.555959i
\(52\) 0 0
\(53\) 1.01898 + 1.17596i 0.139967 + 0.161531i 0.821405 0.570345i \(-0.193191\pi\)
−0.681438 + 0.731876i \(0.738645\pi\)
\(54\) 0 0
\(55\) 0.0836648 + 0.344871i 0.0112814 + 0.0465024i
\(56\) 0 0
\(57\) −1.34920 1.38152i −0.178706 0.182987i
\(58\) 0 0
\(59\) 1.87800 + 6.39587i 0.244495 + 0.832672i 0.986707 + 0.162508i \(0.0519582\pi\)
−0.742213 + 0.670164i \(0.766224\pi\)
\(60\) 0 0
\(61\) −2.71070 + 6.77100i −0.347070 + 0.866938i 0.647423 + 0.762131i \(0.275847\pi\)
−0.994493 + 0.104807i \(0.966578\pi\)
\(62\) 0 0
\(63\) −2.22328 + 0.596038i −0.280107 + 0.0750937i
\(64\) 0 0
\(65\) 2.91125 2.07309i 0.361096 0.257135i
\(66\) 0 0
\(67\) −0.562265 8.16602i −0.0686916 0.997638i
\(68\) 0 0
\(69\) −9.65632 7.40855i −1.16248 0.891884i
\(70\) 0 0
\(71\) −8.12417 2.81180i −0.964162 0.333700i −0.200772 0.979638i \(-0.564345\pi\)
−0.763390 + 0.645938i \(0.776466\pi\)
\(72\) 0 0
\(73\) 10.8460 + 4.34209i 1.26943 + 0.508203i 0.905945 0.423396i \(-0.139162\pi\)
0.363486 + 0.931600i \(0.381586\pi\)
\(74\) 0 0
\(75\) −4.27507 6.48032i −0.493643 0.748283i
\(76\) 0 0
\(77\) −0.173390 0.336330i −0.0197597 0.0383284i
\(78\) 0 0
\(79\) 7.69406 1.86656i 0.865649 0.210004i 0.221740 0.975106i \(-0.428826\pi\)
0.643909 + 0.765102i \(0.277311\pi\)
\(80\) 0 0
\(81\) −8.50423 + 2.94584i −0.944915 + 0.327316i
\(82\) 0 0
\(83\) −9.04632 + 11.5033i −0.992963 + 1.26265i −0.0281811 + 0.999603i \(0.508972\pi\)
−0.964782 + 0.263052i \(0.915271\pi\)
\(84\) 0 0
\(85\) 0.865847 + 4.49244i 0.0939143 + 0.487273i
\(86\) 0 0
\(87\) 15.3700 + 2.77201i 1.64783 + 0.297190i
\(88\) 0 0
\(89\) 2.00976 3.12725i 0.213034 0.331487i −0.718248 0.695788i \(-0.755055\pi\)
0.931282 + 0.364300i \(0.118692\pi\)
\(90\) 0 0
\(91\) −2.49555 + 2.88002i −0.261605 + 0.301908i
\(92\) 0 0
\(93\) −6.77854 + 0.729218i −0.702902 + 0.0756164i
\(94\) 0 0
\(95\) 0.189136 0.779630i 0.0194050 0.0799884i
\(96\) 0 0
\(97\) 1.81643 + 1.04871i 0.184430 + 0.106481i 0.589372 0.807861i \(-0.299375\pi\)
−0.404942 + 0.914342i \(0.632708\pi\)
\(98\) 0 0
\(99\) −0.770210 1.26324i −0.0774090 0.126960i
\(100\) 0 0
\(101\) 9.01742 12.6632i 0.897267 1.26004i −0.0677112 0.997705i \(-0.521570\pi\)
0.964978 0.262330i \(-0.0844909\pi\)
\(102\) 0 0
\(103\) 0.855334 + 0.815559i 0.0842786 + 0.0803594i 0.731048 0.682326i \(-0.239032\pi\)
−0.646769 + 0.762686i \(0.723880\pi\)
\(104\) 0 0
\(105\) −0.699928 0.651570i −0.0683059 0.0635867i
\(106\) 0 0
\(107\) 14.7662 2.12306i 1.42750 0.205244i 0.615149 0.788411i \(-0.289096\pi\)
0.812352 + 0.583168i \(0.198187\pi\)
\(108\) 0 0
\(109\) −5.42033 + 18.4599i −0.519173 + 1.76814i 0.113302 + 0.993561i \(0.463857\pi\)
−0.632475 + 0.774581i \(0.717961\pi\)
\(110\) 0 0
\(111\) −1.94855 + 0.700617i −0.184948 + 0.0664997i
\(112\) 0 0
\(113\) −13.0375 + 10.2528i −1.22646 + 0.964499i −0.999955 0.00951088i \(-0.996973\pi\)
−0.226505 + 0.974010i \(0.572730\pi\)
\(114\) 0 0
\(115\) 0.480636 5.03344i 0.0448195 0.469371i
\(116\) 0 0
\(117\) −8.92786 + 11.9295i −0.825381 + 1.10288i
\(118\) 0 0
\(119\) −2.02654 4.43750i −0.185772 0.406785i
\(120\) 0 0
\(121\) −7.78505 + 7.42303i −0.707732 + 0.674821i
\(122\) 0 0
\(123\) −9.78762 12.1441i −0.882520 1.09499i
\(124\) 0 0
\(125\) 2.83443 6.20654i 0.253519 0.555130i
\(126\) 0 0
\(127\) −8.51309 + 0.812901i −0.755414 + 0.0721333i −0.465655 0.884966i \(-0.654181\pi\)
−0.289759 + 0.957100i \(0.593575\pi\)
\(128\) 0 0
\(129\) −1.29335 8.29000i −0.113873 0.729893i
\(130\) 0 0
\(131\) −10.2167 15.8976i −0.892640 1.38898i −0.921077 0.389380i \(-0.872689\pi\)
0.0284368 0.999596i \(-0.490947\pi\)
\(132\) 0 0
\(133\) 0.855415i 0.0741739i
\(134\) 0 0
\(135\) −2.91180 2.34553i −0.250608 0.201871i
\(136\) 0 0
\(137\) −5.35826 + 3.44355i −0.457787 + 0.294202i −0.749138 0.662414i \(-0.769532\pi\)
0.291350 + 0.956616i \(0.405895\pi\)
\(138\) 0 0
\(139\) −13.1584 1.89189i −1.11608 0.160468i −0.440498 0.897754i \(-0.645198\pi\)
−0.675581 + 0.737286i \(0.736107\pi\)
\(140\) 0 0
\(141\) −9.27843 + 3.84396i −0.781385 + 0.323720i
\(142\) 0 0
\(143\) −2.22813 1.01755i −0.186326 0.0850920i
\(144\) 0 0
\(145\) 2.41149 + 6.02361i 0.200263 + 0.500234i
\(146\) 0 0
\(147\) −9.68271 5.43689i −0.798616 0.448427i
\(148\) 0 0
\(149\) −0.935127 + 0.427058i −0.0766086 + 0.0349860i −0.453351 0.891332i \(-0.649772\pi\)
0.376742 + 0.926318i \(0.377044\pi\)
\(150\) 0 0
\(151\) 2.20202 + 6.36232i 0.179198 + 0.517758i 0.998449 0.0556768i \(-0.0177316\pi\)
−0.819251 + 0.573435i \(0.805610\pi\)
\(152\) 0 0
\(153\) −9.14356 16.7400i −0.739213 1.35335i
\(154\) 0 0
\(155\) −1.75085 2.22638i −0.140631 0.178827i
\(156\) 0 0
\(157\) 0.123241 + 2.58715i 0.00983570 + 0.206477i 0.998436 + 0.0559113i \(0.0178064\pi\)
−0.988600 + 0.150565i \(0.951891\pi\)
\(158\) 0 0
\(159\) −0.0322477 2.69491i −0.00255741 0.213720i
\(160\) 0 0
\(161\) 0.767285 + 5.33658i 0.0604705 + 0.420582i
\(162\) 0 0
\(163\) −2.86411 4.96079i −0.224335 0.388559i 0.731785 0.681536i \(-0.238688\pi\)
−0.956120 + 0.292977i \(0.905354\pi\)
\(164\) 0 0
\(165\) 0.275096 0.549663i 0.0214162 0.0427912i
\(166\) 0 0
\(167\) 13.2822 + 9.45824i 1.02781 + 0.731901i 0.963957 0.266058i \(-0.0857214\pi\)
0.0638540 + 0.997959i \(0.479661\pi\)
\(168\) 0 0
\(169\) −0.555224 + 11.6556i −0.0427095 + 0.896583i
\(170\) 0 0
\(171\) 0.239044 + 3.33612i 0.0182802 + 0.255120i
\(172\) 0 0
\(173\) 9.36076 + 2.27090i 0.711685 + 0.172653i 0.575228 0.817993i \(-0.304913\pi\)
0.136457 + 0.990646i \(0.456428\pi\)
\(174\) 0 0
\(175\) −0.650842 + 3.37689i −0.0491990 + 0.255269i
\(176\) 0 0
\(177\) 4.67023 10.5589i 0.351036 0.793658i
\(178\) 0 0
\(179\) 4.29867 + 2.76259i 0.321298 + 0.206486i 0.691340 0.722529i \(-0.257021\pi\)
−0.370043 + 0.929015i \(0.620657\pi\)
\(180\) 0 0
\(181\) −22.5091 11.6043i −1.67309 0.862537i −0.991396 0.130899i \(-0.958214\pi\)
−0.681693 0.731638i \(-0.738756\pi\)
\(182\) 0 0
\(183\) 11.1583 5.92254i 0.824842 0.437806i
\(184\) 0 0
\(185\) −0.676204 0.531772i −0.0497155 0.0390967i
\(186\) 0 0
\(187\) 2.36978 2.05342i 0.173295 0.150161i
\(188\) 0 0
\(189\) 3.60690 + 1.69851i 0.262363 + 0.123548i
\(190\) 0 0
\(191\) −12.7980 + 6.59782i −0.926030 + 0.477402i −0.854159 0.520012i \(-0.825927\pi\)
−0.0718711 + 0.997414i \(0.522897\pi\)
\(192\) 0 0
\(193\) 6.27247 1.84176i 0.451502 0.132573i −0.0480724 0.998844i \(-0.515308\pi\)
0.499575 + 0.866271i \(0.333490\pi\)
\(194\) 0 0
\(195\) −6.16882 0.514646i −0.441758 0.0368546i
\(196\) 0 0
\(197\) 3.40216 9.82990i 0.242394 0.700351i −0.756529 0.653960i \(-0.773107\pi\)
0.998923 0.0463916i \(-0.0147722\pi\)
\(198\) 0 0
\(199\) −5.47924 7.69451i −0.388413 0.545449i 0.573358 0.819305i \(-0.305640\pi\)
−0.961771 + 0.273856i \(0.911701\pi\)
\(200\) 0 0
\(201\) −8.39018 + 11.4282i −0.591798 + 0.806087i
\(202\) 0 0
\(203\) −4.01308 5.63558i −0.281663 0.395540i
\(204\) 0 0
\(205\) 2.11934 6.12343i 0.148021 0.427679i
\(206\) 0 0
\(207\) 4.48371 + 20.5983i 0.311640 + 1.43168i
\(208\) 0 0
\(209\) −0.527564 + 0.154907i −0.0364924 + 0.0107151i
\(210\) 0 0
\(211\) −16.6300 + 8.57337i −1.14486 + 0.590215i −0.922975 0.384859i \(-0.874250\pi\)
−0.221882 + 0.975074i \(0.571220\pi\)
\(212\) 0 0
\(213\) 7.59899 + 12.8055i 0.520674 + 0.877418i
\(214\) 0 0
\(215\) 2.63431 2.28265i 0.179659 0.155675i
\(216\) 0 0
\(217\) 2.37394 + 1.86689i 0.161154 + 0.126733i
\(218\) 0 0
\(219\) −9.48692 17.8737i −0.641067 1.20779i
\(220\) 0 0
\(221\) −28.0688 14.4705i −1.88811 0.973389i
\(222\) 0 0
\(223\) 17.2618 + 11.0935i 1.15593 + 0.742873i 0.970812 0.239843i \(-0.0770960\pi\)
0.185121 + 0.982716i \(0.440732\pi\)
\(224\) 0 0
\(225\) −1.59462 + 13.3518i −0.106308 + 0.890118i
\(226\) 0 0
\(227\) 3.55785 18.4599i 0.236143 1.22522i −0.649321 0.760515i \(-0.724947\pi\)
0.885463 0.464709i \(-0.153841\pi\)
\(228\) 0 0
\(229\) −6.29360 1.52681i −0.415892 0.100894i 0.0223522 0.999750i \(-0.492884\pi\)
−0.438245 + 0.898856i \(0.644400\pi\)
\(230\) 0 0
\(231\) −0.146884 + 0.638727i −0.00966425 + 0.0420251i
\(232\) 0 0
\(233\) −0.455903 + 9.57058i −0.0298672 + 0.626990i 0.933463 + 0.358673i \(0.116771\pi\)
−0.963331 + 0.268317i \(0.913532\pi\)
\(234\) 0 0
\(235\) −3.39872 2.42022i −0.221708 0.157878i
\(236\) 0 0
\(237\) −12.2630 6.13739i −0.796565 0.398666i
\(238\) 0 0
\(239\) 6.97831 + 12.0868i 0.451389 + 0.781829i 0.998473 0.0552490i \(-0.0175953\pi\)
−0.547083 + 0.837078i \(0.684262\pi\)
\(240\) 0 0
\(241\) −2.34857 16.3347i −0.151285 1.05221i −0.914070 0.405557i \(-0.867078\pi\)
0.762785 0.646652i \(-0.223831\pi\)
\(242\) 0 0
\(243\) 14.5416 + 5.61625i 0.932843 + 0.360283i
\(244\) 0 0
\(245\) −0.219514 4.60817i −0.0140242 0.294405i
\(246\) 0 0
\(247\) 3.42300 + 4.35270i 0.217800 + 0.276956i
\(248\) 0 0
\(249\) 24.8301 5.09448i 1.57354 0.322850i
\(250\) 0 0
\(251\) −0.505431 1.46035i −0.0319025 0.0921763i 0.927925 0.372767i \(-0.121591\pi\)
−0.959828 + 0.280591i \(0.909470\pi\)
\(252\) 0 0
\(253\) −3.15231 + 1.43961i −0.198184 + 0.0905076i
\(254\) 0 0
\(255\) 3.87977 6.90959i 0.242961 0.432696i
\(256\) 0 0
\(257\) 1.80024 + 4.49679i 0.112296 + 0.280502i 0.973861 0.227146i \(-0.0729393\pi\)
−0.861565 + 0.507648i \(0.830515\pi\)
\(258\) 0 0
\(259\) 0.834375 + 0.381046i 0.0518455 + 0.0236771i
\(260\) 0 0
\(261\) −17.2259 20.8574i −1.06626 1.29104i
\(262\) 0 0
\(263\) 15.9211 + 2.28910i 0.981735 + 0.141152i 0.614450 0.788956i \(-0.289378\pi\)
0.367286 + 0.930108i \(0.380287\pi\)
\(264\) 0 0
\(265\) 0.941924 0.605338i 0.0578619 0.0371856i
\(266\) 0 0
\(267\) −6.15570 + 1.88777i −0.376723 + 0.115530i
\(268\) 0 0
\(269\) 9.53004i 0.581057i 0.956866 + 0.290528i \(0.0938311\pi\)
−0.956866 + 0.290528i \(0.906169\pi\)
\(270\) 0 0
\(271\) 4.36800 + 6.79675i 0.265337 + 0.412873i 0.948200 0.317674i \(-0.102902\pi\)
−0.682863 + 0.730547i \(0.739265\pi\)
\(272\) 0 0
\(273\) 6.52163 1.01746i 0.394707 0.0615794i
\(274\) 0 0
\(275\) −2.20051 + 0.210123i −0.132696 + 0.0126709i
\(276\) 0 0
\(277\) 3.07594 6.73536i 0.184815 0.404689i −0.794434 0.607351i \(-0.792232\pi\)
0.979249 + 0.202662i \(0.0649594\pi\)
\(278\) 0 0
\(279\) 9.78009 + 6.61748i 0.585518 + 0.396178i
\(280\) 0 0
\(281\) 11.3790 10.8499i 0.678817 0.647251i −0.270080 0.962838i \(-0.587050\pi\)
0.948897 + 0.315587i \(0.102202\pi\)
\(282\) 0 0
\(283\) −0.121689 0.266462i −0.00723367 0.0158395i 0.905981 0.423319i \(-0.139135\pi\)
−0.913214 + 0.407480i \(0.866408\pi\)
\(284\) 0 0
\(285\) −1.12215 + 0.819491i −0.0664705 + 0.0485424i
\(286\) 0 0
\(287\) −0.656768 + 6.87799i −0.0387678 + 0.405995i
\(288\) 0 0
\(289\) 18.4138 14.4808i 1.08317 0.851810i
\(290\) 0 0
\(291\) −1.22918 3.41858i −0.0720559 0.200401i
\(292\) 0 0
\(293\) 1.94667 6.62975i 0.113726 0.387314i −0.882884 0.469591i \(-0.844401\pi\)
0.996609 + 0.0822776i \(0.0262194\pi\)
\(294\) 0 0
\(295\) 4.74776 0.682625i 0.276425 0.0397439i
\(296\) 0 0
\(297\) −0.394357 + 2.53209i −0.0228829 + 0.146926i
\(298\) 0 0
\(299\) 25.2590 + 24.0844i 1.46076 + 1.39284i
\(300\) 0 0
\(301\) −2.15591 + 3.02755i −0.124264 + 0.174505i
\(302\) 0 0
\(303\) −26.0892 + 6.66069i −1.49879 + 0.382647i
\(304\) 0 0
\(305\) 4.54503 + 2.62408i 0.260248 + 0.150254i
\(306\) 0 0
\(307\) 5.52792 22.7864i 0.315495 1.30049i −0.564472 0.825452i \(-0.690920\pi\)
0.879967 0.475035i \(-0.157565\pi\)
\(308\) 0 0
\(309\) −0.218948 2.03525i −0.0124555 0.115782i
\(310\) 0 0
\(311\) −17.5008 + 20.1970i −0.992382 + 1.14527i −0.00299002 + 0.999996i \(0.500952\pi\)
−0.989391 + 0.145274i \(0.953594\pi\)
\(312\) 0 0
\(313\) 11.9394 18.5781i 0.674857 1.05010i −0.319862 0.947464i \(-0.603637\pi\)
0.994719 0.102634i \(-0.0327269\pi\)
\(314\) 0 0
\(315\) 0.196850 + 1.64456i 0.0110912 + 0.0926604i
\(316\) 0 0
\(317\) 2.09975 + 10.8945i 0.117934 + 0.611897i 0.992015 + 0.126118i \(0.0402519\pi\)
−0.874082 + 0.485779i \(0.838536\pi\)
\(318\) 0 0
\(319\) 2.74893 3.49555i 0.153911 0.195713i
\(320\) 0 0
\(321\) −21.9026 13.7084i −1.22248 0.765129i
\(322\) 0 0
\(323\) −6.88880 + 1.67120i −0.383303 + 0.0929883i
\(324\) 0 0
\(325\) 10.2011 + 19.7874i 0.565855 + 1.09761i
\(326\) 0 0
\(327\) 27.8158 18.3501i 1.53822 1.01476i
\(328\) 0 0
\(329\) 4.13023 + 1.65349i 0.227707 + 0.0911601i
\(330\) 0 0
\(331\) −21.2921 7.36927i −1.17032 0.405052i −0.328340 0.944560i \(-0.606489\pi\)
−0.841980 + 0.539508i \(0.818610\pi\)
\(332\) 0 0
\(333\) 3.36055 + 1.25292i 0.184157 + 0.0686595i
\(334\) 0 0
\(335\) −5.87380 0.435775i −0.320920 0.0238089i
\(336\) 0 0
\(337\) −1.41006 + 1.00410i −0.0768111 + 0.0546969i −0.617817 0.786322i \(-0.711983\pi\)
0.541006 + 0.841019i \(0.318044\pi\)
\(338\) 0 0
\(339\) 28.7095 + 1.02348i 1.55929 + 0.0555876i
\(340\) 0 0
\(341\) −0.721479 + 1.80217i −0.0390703 + 0.0975928i
\(342\) 0 0
\(343\) 2.89903 + 9.87317i 0.156533 + 0.533101i
\(344\) 0 0
\(345\) −6.26558 + 6.11901i −0.337327 + 0.329436i
\(346\) 0 0
\(347\) 0.318692 + 1.31367i 0.0171083 + 0.0705213i 0.979726 0.200343i \(-0.0642057\pi\)
−0.962618 + 0.270864i \(0.912691\pi\)
\(348\) 0 0
\(349\) 16.6287 + 19.1905i 0.890112 + 1.02724i 0.999447 + 0.0332396i \(0.0105824\pi\)
−0.109335 + 0.994005i \(0.534872\pi\)
\(350\) 0 0
\(351\) 25.1501 5.79055i 1.34241 0.309077i
\(352\) 0 0
\(353\) 6.98868 1.34696i 0.371970 0.0716913i 0.000159442 1.00000i \(-0.499949\pi\)
0.371810 + 0.928309i \(0.378737\pi\)
\(354\) 0 0
\(355\) −2.83466 + 5.49847i −0.150448 + 0.291829i
\(356\) 0 0
\(357\) −2.28333 + 8.13517i −0.120847 + 0.430559i
\(358\) 0 0
\(359\) −25.8420 22.3923i −1.36389 1.18182i −0.964202 0.265167i \(-0.914573\pi\)
−0.399689 0.916651i \(-0.630882\pi\)
\(360\) 0 0
\(361\) −17.4361 3.36054i −0.917691 0.176870i
\(362\) 0 0
\(363\) 18.5982 1.10913i 0.976155 0.0582140i
\(364\) 0 0
\(365\) 4.20333 7.28039i 0.220013 0.381073i
\(366\) 0 0
\(367\) 10.0097 + 0.476822i 0.522504 + 0.0248899i 0.307178 0.951652i \(-0.400615\pi\)
0.215326 + 0.976542i \(0.430918\pi\)
\(368\) 0 0
\(369\) −0.639359 + 27.0077i −0.0332837 + 1.40597i
\(370\) 0 0
\(371\) −0.823868 + 0.864048i −0.0427731 + 0.0448591i
\(372\) 0 0
\(373\) 0.674775 0.389582i 0.0349385 0.0201718i −0.482429 0.875935i \(-0.660245\pi\)
0.517368 + 0.855763i \(0.326912\pi\)
\(374\) 0 0
\(375\) −10.6905 + 5.03765i −0.552056 + 0.260143i
\(376\) 0 0
\(377\) −42.9713 12.6175i −2.21314 0.649836i
\(378\) 0 0
\(379\) −14.7383 + 0.702071i −0.757055 + 0.0360630i −0.422561 0.906335i \(-0.638869\pi\)
−0.334495 + 0.942398i \(0.608566\pi\)
\(380\) 0 0
\(381\) 12.1676 + 8.44692i 0.623364 + 0.432749i
\(382\) 0 0
\(383\) −12.4215 1.18611i −0.634710 0.0606075i −0.227259 0.973834i \(-0.572976\pi\)
−0.407451 + 0.913227i \(0.633582\pi\)
\(384\) 0 0
\(385\) −0.257306 + 0.0890546i −0.0131135 + 0.00453864i
\(386\) 0 0
\(387\) −7.56201 + 12.4099i −0.384399 + 0.630832i
\(388\) 0 0
\(389\) −6.30391 6.61135i −0.319621 0.335209i 0.544249 0.838924i \(-0.316815\pi\)
−0.863870 + 0.503715i \(0.831966\pi\)
\(390\) 0 0
\(391\) −41.4774 + 16.6050i −2.09760 + 0.839753i
\(392\) 0 0
\(393\) −4.27017 + 32.4516i −0.215402 + 1.63697i
\(394\) 0 0
\(395\) −0.541535 5.67122i −0.0272476 0.285350i
\(396\) 0 0
\(397\) 3.68724 25.6453i 0.185057 1.28710i −0.659527 0.751681i \(-0.729243\pi\)
0.844585 0.535422i \(-0.179848\pi\)
\(398\) 0 0
\(399\) 0.956788 1.13126i 0.0478993 0.0566340i
\(400\) 0 0
\(401\) 37.9003 1.89265 0.946325 0.323218i \(-0.104765\pi\)
0.946325 + 0.323218i \(0.104765\pi\)
\(402\) 0 0
\(403\) 19.5501 0.973858
\(404\) 0 0
\(405\) 1.22729 + 6.35879i 0.0609843 + 0.315971i
\(406\) 0 0
\(407\) −0.0839079 + 0.583592i −0.00415916 + 0.0289276i
\(408\) 0 0
\(409\) −0.00694953 0.0727787i −0.000343632 0.00359868i 0.995298 0.0968552i \(-0.0308784\pi\)
−0.995642 + 0.0932565i \(0.970272\pi\)
\(410\) 0 0
\(411\) 10.9378 + 1.43926i 0.539522 + 0.0709934i
\(412\) 0 0
\(413\) −4.74812 + 1.90086i −0.233640 + 0.0935353i
\(414\) 0 0
\(415\) 7.26682 + 7.62122i 0.356714 + 0.374111i
\(416\) 0 0
\(417\) 15.2855 + 17.2197i 0.748536 + 0.843254i
\(418\) 0 0
\(419\) 22.3142 7.72303i 1.09012 0.377295i 0.277880 0.960616i \(-0.410368\pi\)
0.812242 + 0.583321i \(0.198247\pi\)
\(420\) 0 0
\(421\) 1.13680 + 0.108551i 0.0554044 + 0.00529048i 0.122721 0.992441i \(-0.460838\pi\)
−0.0673170 + 0.997732i \(0.521444\pi\)
\(422\) 0 0
\(423\) 16.5700 + 5.29445i 0.805661 + 0.257425i
\(424\) 0 0
\(425\) −28.4662 + 1.35601i −1.38081 + 0.0657762i
\(426\) 0 0
\(427\) −5.36931 1.57657i −0.259839 0.0762956i
\(428\) 0 0
\(429\) 1.80850 + 3.83787i 0.0873154 + 0.185294i
\(430\) 0 0
\(431\) 21.1776 12.2269i 1.02009 0.588949i 0.105959 0.994370i \(-0.466209\pi\)
0.914130 + 0.405422i \(0.132875\pi\)
\(432\) 0 0
\(433\) 18.9387 19.8624i 0.910137 0.954525i −0.0890008 0.996032i \(-0.528367\pi\)
0.999138 + 0.0415069i \(0.0132159\pi\)
\(434\) 0 0
\(435\) 3.54833 10.6633i 0.170129 0.511268i
\(436\) 0 0
\(437\) 7.82534 + 0.372767i 0.374337 + 0.0178319i
\(438\) 0 0
\(439\) 18.3953 31.8617i 0.877962 1.52067i 0.0243886 0.999703i \(-0.492236\pi\)
0.853574 0.520972i \(-0.174431\pi\)
\(440\) 0 0
\(441\) 6.72393 + 18.0203i 0.320187 + 0.858111i
\(442\) 0 0
\(443\) 7.27332 + 1.40182i 0.345566 + 0.0666024i 0.359081 0.933306i \(-0.383090\pi\)
−0.0135154 + 0.999909i \(0.504302\pi\)
\(444\) 0 0
\(445\) −2.02156 1.75169i −0.0958312 0.0830382i
\(446\) 0 0
\(447\) 1.71435 + 0.481174i 0.0810860 + 0.0227587i
\(448\) 0 0
\(449\) −1.84954 + 3.58761i −0.0872852 + 0.169310i −0.928438 0.371489i \(-0.878847\pi\)
0.841152 + 0.540798i \(0.181878\pi\)
\(450\) 0 0
\(451\) −4.36083 + 0.840482i −0.205344 + 0.0395767i
\(452\) 0 0
\(453\) 4.20419 10.8770i 0.197530 0.511046i
\(454\) 0 0
\(455\) 1.79573 + 2.07238i 0.0841850 + 0.0971547i
\(456\) 0 0
\(457\) 0.138080 + 0.569175i 0.00645913 + 0.0266249i 0.974950 0.222424i \(-0.0713970\pi\)
−0.968491 + 0.249049i \(0.919882\pi\)
\(458\) 0 0
\(459\) −6.63166 + 32.3653i −0.309539 + 1.51068i
\(460\) 0 0
\(461\) 6.48390 + 22.0821i 0.301985 + 1.02847i 0.961049 + 0.276380i \(0.0891347\pi\)
−0.659063 + 0.752087i \(0.729047\pi\)
\(462\) 0 0
\(463\) −12.1602 + 30.3748i −0.565135 + 1.41164i 0.320497 + 0.947250i \(0.396150\pi\)
−0.885632 + 0.464389i \(0.846274\pi\)
\(464\) 0 0
\(465\) −0.174777 + 4.90267i −0.00810510 + 0.227356i
\(466\) 0 0
\(467\) 6.68274 4.75876i 0.309240 0.220209i −0.414891 0.909871i \(-0.636180\pi\)
0.724131 + 0.689662i \(0.242241\pi\)
\(468\) 0 0
\(469\) 6.19610 1.02502i 0.286109 0.0473311i
\(470\) 0 0
\(471\) 2.73076 3.55928i 0.125827 0.164003i
\(472\) 0 0
\(473\) −2.25761 0.781366i −0.103805 0.0359272i
\(474\) 0 0
\(475\) 4.63923 + 1.85727i 0.212862 + 0.0852173i
\(476\) 0 0
\(477\) −2.97163 + 3.60002i −0.136062 + 0.164834i
\(478\) 0 0
\(479\) −6.19309 12.0129i −0.282970 0.548885i 0.703920 0.710279i \(-0.251431\pi\)
−0.986890 + 0.161394i \(0.948401\pi\)
\(480\) 0 0
\(481\) 5.77043 1.39989i 0.263109 0.0638295i
\(482\) 0 0
\(483\) 4.95430 7.91571i 0.225428 0.360177i
\(484\) 0 0
\(485\) 0.932955 1.18635i 0.0423633 0.0538693i
\(486\) 0 0
\(487\) −0.665348 3.45215i −0.0301498 0.156432i 0.963734 0.266866i \(-0.0859881\pi\)
−0.993883 + 0.110434i \(0.964776\pi\)
\(488\) 0 0
\(489\) −1.76097 + 9.76405i −0.0796337 + 0.441546i
\(490\) 0 0
\(491\) −12.7512 + 19.8412i −0.575453 + 0.895422i −0.999950 0.0100070i \(-0.996815\pi\)
0.424497 + 0.905429i \(0.360451\pi\)
\(492\) 0 0
\(493\) 37.5440 43.3281i 1.69090 1.95140i
\(494\) 0 0
\(495\) −0.978610 + 0.419217i −0.0439853 + 0.0188424i
\(496\) 0 0
\(497\) 1.55510 6.41022i 0.0697559 0.287538i
\(498\) 0 0
\(499\) −33.2615 19.2035i −1.48899 0.859668i −0.489068 0.872246i \(-0.662663\pi\)
−0.999921 + 0.0125777i \(0.995996\pi\)
\(500\) 0 0
\(501\) −6.98631 27.3646i −0.312125 1.22256i
\(502\) 0 0
\(503\) −8.66130 + 12.1631i −0.386188 + 0.542325i −0.961212 0.275811i \(-0.911053\pi\)
0.575024 + 0.818137i \(0.304993\pi\)
\(504\) 0 0
\(505\) −8.09589 7.71941i −0.360262 0.343509i
\(506\) 0 0
\(507\) 13.7711 14.7932i 0.611597 0.656988i
\(508\) 0 0
\(509\) 0.747224 0.107435i 0.0331201 0.00476196i −0.125735 0.992064i \(-0.540129\pi\)
0.158855 + 0.987302i \(0.449220\pi\)
\(510\) 0 0
\(511\) −2.52541 + 8.60074i −0.111717 + 0.380474i
\(512\) 0 0
\(513\) 3.41535 4.67931i 0.150791 0.206597i
\(514\) 0 0
\(515\) 0.668471 0.525691i 0.0294563 0.0231647i
\(516\) 0 0
\(517\) −0.271826 + 2.84669i −0.0119549 + 0.125197i
\(518\) 0 0
\(519\) −9.83935 13.4733i −0.431899 0.591412i
\(520\) 0 0
\(521\) −0.681593 1.49248i −0.0298611 0.0653867i 0.894114 0.447840i \(-0.147807\pi\)
−0.923975 + 0.382453i \(0.875079\pi\)
\(522\) 0 0
\(523\) −8.39247 + 8.00221i −0.366977 + 0.349912i −0.851021 0.525132i \(-0.824016\pi\)
0.484044 + 0.875044i \(0.339168\pi\)
\(524\) 0 0
\(525\) 4.63780 3.73788i 0.202410 0.163134i
\(526\) 0 0
\(527\) −10.3964 + 22.7650i −0.452876 + 0.991661i
\(528\) 0 0
\(529\) 26.2576 2.50730i 1.14163 0.109013i
\(530\) 0 0
\(531\) −17.9865 + 8.74023i −0.780549 + 0.379294i
\(532\) 0 0
\(533\) 24.1808 + 37.6261i 1.04739 + 1.62977i
\(534\) 0 0
\(535\) 10.7346i 0.464096i
\(536\) 0 0
\(537\) −2.59491 8.46155i −0.111978 0.365143i
\(538\) 0 0
\(539\) −2.65996 + 1.70945i −0.114572 + 0.0736312i
\(540\) 0 0
\(541\) −0.802131 0.115329i −0.0344863 0.00495839i 0.125050 0.992150i \(-0.460091\pi\)
−0.159536 + 0.987192i \(0.551000\pi\)
\(542\) 0 0
\(543\) 16.7883 + 40.5230i 0.720454 + 1.73901i
\(544\) 0 0
\(545\) 12.5930 + 5.75101i 0.539423 + 0.246346i
\(546\) 0 0
\(547\) −0.289443 0.722993i −0.0123757 0.0309129i 0.922051 0.387067i \(-0.126512\pi\)
−0.934427 + 0.356154i \(0.884088\pi\)
\(548\) 0 0
\(549\) −21.3809 4.64819i −0.912515 0.198380i
\(550\) 0 0
\(551\) −9.14454 + 4.17617i −0.389570 + 0.177911i
\(552\) 0 0
\(553\) 1.98680 + 5.74050i 0.0844875 + 0.244111i
\(554\) 0 0
\(555\) 0.299470 + 1.45959i 0.0127118 + 0.0619563i
\(556\) 0 0
\(557\) 25.5617 + 32.5044i 1.08309 + 1.37726i 0.920583 + 0.390547i \(0.127714\pi\)
0.162503 + 0.986708i \(0.448043\pi\)
\(558\) 0 0
\(559\) 1.14481 + 24.0324i 0.0484201 + 1.01646i
\(560\) 0 0
\(561\) −5.43074 + 0.0649850i −0.229286 + 0.00274367i
\(562\) 0 0
\(563\) −2.56815 17.8618i −0.108234 0.752787i −0.969581 0.244770i \(-0.921288\pi\)
0.861347 0.508017i \(-0.169621\pi\)
\(564\) 0 0
\(565\) 5.96739 + 10.3358i 0.251050 + 0.434831i
\(566\) 0 0
\(567\) −2.87024 6.28058i −0.120539 0.263760i
\(568\) 0 0
\(569\) −20.0817 14.3001i −0.841868 0.599491i 0.0756733 0.997133i \(-0.475889\pi\)
−0.917541 + 0.397641i \(0.869829\pi\)
\(570\) 0 0
\(571\) 0.459882 9.65412i 0.0192455 0.404012i −0.968605 0.248605i \(-0.920028\pi\)
0.987850 0.155407i \(-0.0496690\pi\)
\(572\) 0 0
\(573\) 24.3047 + 5.58921i 1.01534 + 0.233492i
\(574\) 0 0
\(575\) 30.6082 + 7.42546i 1.27645 + 0.309663i
\(576\) 0 0
\(577\) 7.93038 41.1467i 0.330146 1.71296i −0.315162 0.949038i \(-0.602059\pi\)
0.645308 0.763922i \(-0.276729\pi\)
\(578\) 0 0
\(579\) −10.3552 4.58012i −0.430348 0.190343i
\(580\) 0 0
\(581\) −9.44588 6.07050i −0.391881 0.251847i
\(582\) 0 0
\(583\) −0.682083 0.351638i −0.0282490 0.0145634i
\(584\) 0 0
\(585\) 7.58247 + 7.58048i 0.313497 + 0.313414i
\(586\) 0 0
\(587\) −34.6085 27.2165i −1.42845 1.12334i −0.972382 0.233397i \(-0.925016\pi\)
−0.456066 0.889946i \(-0.650742\pi\)
\(588\) 0 0
\(589\) 3.31654 2.87380i 0.136656 0.118413i
\(590\) 0 0
\(591\) −15.4941 + 9.19445i −0.637342 + 0.378209i
\(592\) 0 0
\(593\) −1.02148 + 0.526611i −0.0419473 + 0.0216253i −0.479073 0.877775i \(-0.659027\pi\)
0.437125 + 0.899401i \(0.355997\pi\)
\(594\) 0 0
\(595\) −3.36812 + 0.988970i −0.138080 + 0.0405438i
\(596\) 0 0
\(597\) −1.36022 + 16.3044i −0.0556702 + 0.667293i
\(598\) 0 0
\(599\) 7.05909 20.3959i 0.288427 0.833354i −0.703965 0.710235i \(-0.748589\pi\)
0.992392 0.123120i \(-0.0392899\pi\)
\(600\) 0 0
\(601\) −22.9755 32.2645i −0.937189 1.31610i −0.948705 0.316164i \(-0.897605\pi\)
0.0115161 0.999934i \(-0.496334\pi\)
\(602\) 0 0
\(603\) 23.8784 5.72909i 0.972403 0.233306i
\(604\) 0 0
\(605\) 4.48980 + 6.30504i 0.182536 + 0.256336i
\(606\) 0 0
\(607\) 7.86388 22.7212i 0.319185 0.922225i −0.665272 0.746601i \(-0.731684\pi\)
0.984457 0.175624i \(-0.0561943\pi\)
\(608\) 0 0
\(609\) −0.996249 + 11.9416i −0.0403700 + 0.483897i
\(610\) 0 0
\(611\) 27.6329 8.11374i 1.11791 0.328247i
\(612\) 0 0
\(613\) −11.3349 + 5.84355i −0.457812 + 0.236019i −0.671676 0.740845i \(-0.734425\pi\)
0.213864 + 0.976863i \(0.431395\pi\)
\(614\) 0 0
\(615\) −9.65188 + 5.72758i −0.389201 + 0.230958i
\(616\) 0 0
\(617\) 25.5107 22.1051i 1.02702 0.889919i 0.0330383 0.999454i \(-0.489482\pi\)
0.993983 + 0.109535i \(0.0349362\pi\)
\(618\) 0 0
\(619\) −15.0547 11.8391i −0.605099 0.475855i 0.267986 0.963423i \(-0.413642\pi\)
−0.873085 + 0.487568i \(0.837884\pi\)
\(620\) 0 0
\(621\) 17.1098 32.2558i 0.686591 1.29438i
\(622\) 0 0
\(623\) 2.53513 + 1.30695i 0.101568 + 0.0523619i
\(624\) 0 0
\(625\) 14.7231 + 9.46195i 0.588923 + 0.378478i
\(626\) 0 0
\(627\) 0.870955 + 0.385225i 0.0347826 + 0.0153844i
\(628\) 0 0
\(629\) −1.43853 + 7.46380i −0.0573580 + 0.297601i
\(630\) 0 0
\(631\) −29.6306 7.18830i −1.17958 0.286162i −0.402411 0.915459i \(-0.631828\pi\)
−0.777165 + 0.629297i \(0.783343\pi\)
\(632\) 0 0
\(633\) 31.5821 + 7.26275i 1.25528 + 0.288668i
\(634\) 0 0
\(635\) −0.292802 + 6.14667i −0.0116195 + 0.243923i
\(636\) 0 0
\(637\) 25.9389 + 18.4710i 1.02774 + 0.731849i
\(638\) 0 0
\(639\) 4.27359 25.4345i 0.169060 1.00617i
\(640\) 0 0
\(641\) −12.4842 21.6233i −0.493098 0.854070i 0.506871 0.862022i \(-0.330802\pi\)
−0.999968 + 0.00795173i \(0.997469\pi\)
\(642\) 0 0
\(643\) −4.85325 33.7551i −0.191394 1.33117i −0.828323 0.560250i \(-0.810705\pi\)
0.636930 0.770922i \(-0.280204\pi\)
\(644\) 0 0
\(645\) −6.03697 + 0.0722392i −0.237705 + 0.00284442i
\(646\) 0 0
\(647\) 1.46370 + 30.7268i 0.0575439 + 1.20800i 0.824336 + 0.566101i \(0.191549\pi\)
−0.766792 + 0.641895i \(0.778148\pi\)
\(648\) 0 0
\(649\) −2.03217 2.58411i −0.0797695 0.101435i
\(650\) 0 0
\(651\) −1.05135 5.12418i −0.0412055 0.200833i
\(652\) 0 0
\(653\) −11.9399 34.4979i −0.467243 1.35001i −0.894980 0.446106i \(-0.852811\pi\)
0.427738 0.903903i \(-0.359311\pi\)
\(654\) 0 0
\(655\) −12.3692 + 5.64884i −0.483306 + 0.220718i
\(656\) 0 0
\(657\) −7.44564 + 34.2487i −0.290482 + 1.33617i
\(658\) 0 0
\(659\) −11.1980 27.9712i −0.436211 1.08960i −0.969809 0.243865i \(-0.921585\pi\)
0.533598 0.845738i \(-0.320840\pi\)
\(660\) 0 0
\(661\) −14.5054 6.62441i −0.564196 0.257660i 0.112836 0.993614i \(-0.464007\pi\)
−0.677032 + 0.735954i \(0.736734\pi\)
\(662\) 0 0
\(663\) 20.9349 + 50.5320i 0.813045 + 1.96250i
\(664\) 0 0
\(665\) 0.609266 + 0.0875993i 0.0236263 + 0.00339695i
\(666\) 0 0
\(667\) −53.3031 + 34.2558i −2.06390 + 1.32639i
\(668\) 0 0
\(669\) −10.4201 33.9782i −0.402865 1.31367i
\(670\) 0 0
\(671\) 3.59694i 0.138858i
\(672\) 0 0
\(673\) −11.7725 18.3184i −0.453797 0.706122i 0.536682 0.843785i \(-0.319677\pi\)
−0.990479 + 0.137662i \(0.956041\pi\)
\(674\) 0 0
\(675\) 17.0429 15.8738i 0.655982 0.610982i
\(676\) 0 0
\(677\) −18.8041 + 1.79557i −0.722701 + 0.0690095i −0.449923 0.893068i \(-0.648548\pi\)
−0.272778 + 0.962077i \(0.587942\pi\)
\(678\) 0 0
\(679\) −0.668518 + 1.46385i −0.0256554 + 0.0561774i
\(680\) 0 0
\(681\) −25.3527 + 20.4332i −0.971516 + 0.783002i
\(682\) 0 0
\(683\) −3.78334 + 3.60741i −0.144765 + 0.138034i −0.759002 0.651089i \(-0.774313\pi\)
0.614236 + 0.789122i \(0.289464\pi\)
\(684\) 0 0
\(685\) 1.90394 + 4.16904i 0.0727457 + 0.159291i
\(686\) 0 0
\(687\) 6.61537 + 9.05861i 0.252392 + 0.345607i
\(688\) 0 0
\(689\) −0.734630 + 7.69339i −0.0279872 + 0.293095i
\(690\) 0 0
\(691\) 18.4389 14.5005i 0.701449 0.551625i −0.202492 0.979284i \(-0.564904\pi\)
0.903940 + 0.427659i \(0.140661\pi\)
\(692\) 0 0
\(693\) 0.908671 0.680409i 0.0345176 0.0258466i
\(694\) 0 0
\(695\) −2.69499 + 9.17828i −0.102227 + 0.348152i
\(696\) 0 0
\(697\) −56.6727 + 8.14831i −2.14663 + 0.308639i
\(698\) 0 0
\(699\) 11.3077 12.1469i 0.427696 0.459439i
\(700\) 0 0
\(701\) −3.03624 2.89505i −0.114677 0.109345i 0.630571 0.776131i \(-0.282821\pi\)
−0.745249 + 0.666787i \(0.767669\pi\)
\(702\) 0 0
\(703\) 0.773135 1.08572i 0.0291593 0.0409486i
\(704\) 0 0
\(705\) 1.78769 + 7.00218i 0.0673282 + 0.263717i
\(706\) 0 0
\(707\) 10.3297 + 5.96383i 0.388487 + 0.224293i
\(708\) 0 0
\(709\) −2.63551 + 10.8637i −0.0989785 + 0.407995i −0.999649 0.0265087i \(-0.991561\pi\)
0.900670 + 0.434504i \(0.143076\pi\)
\(710\) 0 0
\(711\) 9.35273 + 21.8328i 0.350755 + 0.818793i
\(712\) 0 0
\(713\) 18.1128 20.9033i 0.678330 0.782834i
\(714\) 0 0
\(715\) −0.952922 + 1.48278i −0.0356373 + 0.0554526i
\(716\) 0 0
\(717\) 4.29053 23.7898i 0.160233 0.888445i
\(718\) 0 0
\(719\) −4.48842 23.2881i −0.167390 0.868501i −0.964382 0.264512i \(-0.914789\pi\)
0.796993 0.603989i \(-0.206423\pi\)
\(720\) 0 0
\(721\) −0.560532 + 0.712775i −0.0208753 + 0.0265451i
\(722\) 0 0
\(723\) −15.1645 + 24.2291i −0.563975 + 0.901090i
\(724\) 0 0
\(725\) −39.2770 + 9.52849i −1.45871 + 0.353879i
\(726\) 0 0
\(727\) 14.2934 + 27.7254i 0.530113 + 1.02828i 0.990102 + 0.140352i \(0.0448233\pi\)
−0.459988 + 0.887925i \(0.652146\pi\)
\(728\) 0 0
\(729\) −12.9490 23.6922i −0.479594 0.877490i
\(730\) 0 0
\(731\) −28.5933 11.4470i −1.05756 0.423384i
\(732\) 0 0
\(733\) 12.0707 + 4.17770i 0.445841 + 0.154307i 0.540758 0.841178i \(-0.318137\pi\)
−0.0949174 + 0.995485i \(0.530259\pi\)
\(734\) 0 0
\(735\) −4.86397 + 6.33971i −0.179410 + 0.233844i
\(736\) 0 0
\(737\) 1.75422 + 3.63573i 0.0646174 + 0.133924i
\(738\) 0 0
\(739\) −13.9275 + 9.91775i −0.512332 + 0.364830i −0.806794 0.590833i \(-0.798799\pi\)
0.294461 + 0.955663i \(0.404860\pi\)
\(740\) 0 0
\(741\) 0.341699 9.58499i 0.0125526 0.352113i
\(742\) 0 0
\(743\) 2.89884 7.24096i 0.106348 0.265645i −0.865643 0.500661i \(-0.833090\pi\)
0.971991 + 0.235016i \(0.0755144\pi\)
\(744\) 0 0
\(745\) 0.208409 + 0.709775i 0.00763550 + 0.0260041i
\(746\) 0 0
\(747\) −38.5354 21.0354i −1.40994 0.769643i
\(748\) 0 0
\(749\) 2.69850 + 11.1234i 0.0986012 + 0.406440i
\(750\) 0 0
\(751\) −21.2733 24.5507i −0.776275 0.895869i 0.220560 0.975373i \(-0.429212\pi\)
−0.996834 + 0.0795047i \(0.974666\pi\)
\(752\) 0 0
\(753\) −0.964991 + 2.49660i −0.0351662 + 0.0909812i
\(754\) 0 0
\(755\) 4.75704 0.916845i 0.173127 0.0333674i
\(756\) 0 0
\(757\) −12.8973 + 25.0173i −0.468762 + 0.909271i 0.529383 + 0.848383i \(0.322423\pi\)
−0.998145 + 0.0608878i \(0.980607\pi\)
\(758\) 0 0
\(759\) 5.77907 + 1.62204i 0.209767 + 0.0588761i
\(760\) 0 0
\(761\) 35.4724 + 30.7370i 1.28587 + 1.11422i 0.987137 + 0.159879i \(0.0511105\pi\)
0.298736 + 0.954336i \(0.403435\pi\)
\(762\) 0 0
\(763\) −14.4948 2.79364i −0.524747 0.101137i
\(764\) 0 0
\(765\) −12.8593 + 4.79821i −0.464930 + 0.173480i
\(766\) 0 0
\(767\) −16.5540 + 28.6723i −0.597729 + 1.03530i
\(768\) 0 0
\(769\) −53.7049 2.55828i −1.93665 0.0922539i −0.956647 0.291251i \(-0.905929\pi\)
−0.980000 + 0.198997i \(0.936232\pi\)
\(770\) 0 0
\(771\) 2.64892 7.96048i 0.0953986 0.286690i
\(772\) 0 0
\(773\) 10.5107 11.0233i 0.378042 0.396479i −0.507034 0.861926i \(-0.669258\pi\)
0.885076 + 0.465447i \(0.154107\pi\)