Properties

Label 804.2.ba.b.41.10
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 41.10
Character \(\chi\) = 804.41
Dual form 804.2.ba.b.353.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.468055 - 1.66761i) q^{3} +(-0.102406 + 0.712247i) q^{5} +(0.0729329 + 0.763788i) q^{7} +(-2.56185 + 1.56107i) q^{9} +O(q^{10})\) \(q+(-0.468055 - 1.66761i) q^{3} +(-0.102406 + 0.712247i) q^{5} +(0.0729329 + 0.763788i) q^{7} +(-2.56185 + 1.56107i) q^{9} +(0.457848 - 0.183294i) q^{11} +(3.42746 + 3.59462i) q^{13} +(1.23568 - 0.162598i) q^{15} +(6.00843 - 2.07954i) q^{17} +(1.10984 + 0.105977i) q^{19} +(1.23956 - 0.479119i) q^{21} +(-7.01892 + 0.334352i) q^{23} +(4.30066 + 1.26279i) q^{25} +(3.80234 + 3.54150i) q^{27} +(7.80897 - 4.50851i) q^{29} +(2.71627 - 2.84874i) q^{31} +(-0.519962 - 0.677719i) q^{33} +(-0.551474 - 0.0262700i) q^{35} +(0.597753 - 1.03534i) q^{37} +(4.39018 - 7.39815i) q^{39} +(-8.84237 - 1.70423i) q^{41} +(3.66095 + 3.17223i) q^{43} +(-0.849518 - 1.98453i) q^{45} +(-2.65699 + 5.15385i) q^{47} +(6.29545 - 1.21335i) q^{49} +(-6.28013 - 9.04638i) q^{51} +(-1.01898 - 1.17596i) q^{53} +(0.0836648 + 0.344871i) q^{55} +(-0.342739 - 1.90039i) q^{57} +(-1.87800 - 6.39587i) q^{59} +(-2.71070 + 6.77100i) q^{61} +(-1.37917 - 1.84286i) q^{63} +(-2.91125 + 2.07309i) q^{65} +(-0.562265 - 8.16602i) q^{67} +(3.84281 + 11.5483i) q^{69} +(8.12417 + 2.81180i) q^{71} +(10.8460 + 4.34209i) q^{73} +(0.0928916 - 7.76287i) q^{75} +(0.173390 + 0.336330i) q^{77} +(7.69406 - 1.86656i) q^{79} +(4.12614 - 7.99844i) q^{81} +(9.04632 - 11.5033i) q^{83} +(0.865847 + 4.49244i) q^{85} +(-11.1735 - 10.9121i) q^{87} +(-2.00976 + 3.12725i) q^{89} +(-2.49555 + 2.88002i) q^{91} +(-6.02196 - 3.19631i) q^{93} +(-0.189136 + 0.779630i) q^{95} +(1.81643 + 1.04871i) q^{97} +(-0.886801 + 1.18430i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440q - 12q^{7} + 4q^{9} + O(q^{10}) \) \( 440q - 12q^{7} + 4q^{9} - 2q^{15} - 10q^{19} + 22q^{21} - 68q^{25} + 50q^{31} + 11q^{33} - 22q^{37} - 45q^{39} + 22q^{43} + 22q^{45} - 18q^{49} - 6q^{51} + 126q^{55} - 183q^{57} - 56q^{61} - 141q^{63} - 12q^{67} + 33q^{69} + 356q^{73} + 165q^{75} + 228q^{79} + 24q^{81} - 6q^{85} + 75q^{87} - 4q^{91} - 75q^{93} + 12q^{97} + 88q^{99} + O(q^{100}) \)

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
\(3\) −0.468055 1.66761i −0.270232 0.962795i
\(4\) 0 0
\(5\) −0.102406 + 0.712247i −0.0457972 + 0.318527i 0.954026 + 0.299724i \(0.0968945\pi\)
−0.999823 + 0.0188027i \(0.994015\pi\)
\(6\) 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
\(9\) −2.56185 + 1.56107i −0.853950 + 0.520356i
\(10\) 0 0
\(11\) 0.457848 0.183294i 0.138046 0.0552654i −0.301611 0.953431i \(-0.597524\pi\)
0.439657 + 0.898166i \(0.355100\pi\)
\(12\) 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
\(15\) 1.23568 0.162598i 0.319052 0.0419827i
\(16\) 0 0
\(17\) 6.00843 2.07954i 1.45726 0.504362i 0.520354 0.853951i \(-0.325800\pi\)
0.936903 + 0.349589i \(0.113679\pi\)
\(18\) 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
\(21\) 1.23956 0.479119i 0.270495 0.104552i
\(22\) 0 0
\(23\) −7.01892 + 0.334352i −1.46355 + 0.0697173i −0.764160 0.645027i \(-0.776846\pi\)
−0.699386 + 0.714744i \(0.746543\pi\)
\(24\) 0 0
\(25\) 4.30066 + 1.26279i 0.860131 + 0.252557i
\(26\) 0 0
\(27\) 3.80234 + 3.54150i 0.731760 + 0.681562i
\(28\) 0 0
\(29\) 7.80897 4.50851i 1.45009 0.837210i 0.451604 0.892219i \(-0.350852\pi\)
0.998486 + 0.0550091i \(0.0175188\pi\)
\(30\) 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
\(33\) −0.519962 0.677719i −0.0905137 0.117976i
\(34\) 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
\(39\) 4.39018 7.39815i 0.702992 1.18465i
\(40\) 0 0
\(41\) −8.84237 1.70423i −1.38095 0.266156i −0.555913 0.831240i \(-0.687631\pi\)
−0.825033 + 0.565085i \(0.808843\pi\)
\(42\) 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
\(45\) −0.849518 1.98453i −0.126639 0.295836i
\(46\) 0 0
\(47\) −2.65699 + 5.15385i −0.387562 + 0.751766i −0.999225 0.0393523i \(-0.987471\pi\)
0.611663 + 0.791118i \(0.290501\pi\)
\(48\) 0 0
\(49\) 6.29545 1.21335i 0.899350 0.173335i
\(50\) 0 0
\(51\) −6.28013 9.04638i −0.879394 1.26675i
\(52\) 0 0
\(53\) −1.01898 1.17596i −0.139967 0.161531i 0.681438 0.731876i \(-0.261355\pi\)
−0.821405 + 0.570345i \(0.806809\pi\)
\(54\) 0 0
\(55\) 0.0836648 + 0.344871i 0.0112814 + 0.0465024i
\(56\) 0 0
\(57\) −0.342739 1.90039i −0.0453969 0.251713i
\(58\) 0 0
\(59\) −1.87800 6.39587i −0.244495 0.832672i −0.986707 0.162508i \(-0.948042\pi\)
0.742213 0.670164i \(-0.233776\pi\)
\(60\) 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
\(63\) −1.37917 1.84286i −0.173759 0.232178i
\(64\) 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
\(69\) 3.84281 + 11.5483i 0.462620 + 1.39026i
\(70\) 0 0
\(71\) 8.12417 + 2.81180i 0.964162 + 0.333700i 0.763390 0.645938i \(-0.223534\pi\)
0.200772 + 0.979638i \(0.435655\pi\)
\(72\) 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
\(75\) 0.0928916 7.76287i 0.0107262 0.896379i
\(76\) 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
\(81\) 4.12614 7.99844i 0.458460 0.888715i
\(82\) 0 0
\(83\) 9.04632 11.5033i 0.992963 1.26265i 0.0281811 0.999603i \(-0.491028\pi\)
0.964782 0.263052i \(-0.0847291\pi\)
\(84\) 0 0
\(85\) 0.865847 + 4.49244i 0.0939143 + 0.487273i
\(86\) 0 0
\(87\) −11.1735 10.9121i −1.19792 1.16990i
\(88\) 0 0
\(89\) −2.00976 + 3.12725i −0.213034 + 0.331487i −0.931282 0.364300i \(-0.881308\pi\)
0.718248 + 0.695788i \(0.244945\pi\)
\(90\) 0 0
\(91\) −2.49555 + 2.88002i −0.261605 + 0.301908i
\(92\) 0 0
\(93\) −6.02196 3.19631i −0.624448 0.331442i
\(94\) 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
\(99\) −0.886801 + 1.18430i −0.0891269 + 0.119027i
\(100\) 0 0
\(101\) −9.01742 + 12.6632i −0.897267 + 1.26004i 0.0677112 + 0.997705i \(0.478430\pi\)
−0.964978 + 0.262330i \(0.915509\pi\)
\(102\) 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
\(105\) 0.214312 + 0.931940i 0.0209147 + 0.0909480i
\(106\) 0 0
\(107\) −14.7662 + 2.12306i −1.42750 + 0.205244i −0.812352 0.583168i \(-0.801813\pi\)
−0.615149 + 0.788411i \(0.710904\pi\)
\(108\) 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
\(111\) −2.00632 0.512224i −0.190432 0.0486181i
\(112\) 0 0
\(113\) 13.0375 10.2528i 1.22646 0.964499i 0.226505 0.974010i \(-0.427270\pi\)
0.999955 + 0.00951088i \(0.00302745\pi\)
\(114\) 0 0
\(115\) 0.480636 5.03344i 0.0448195 0.469371i
\(116\) 0 0
\(117\) −14.3921 3.85837i −1.33055 0.356707i
\(118\) 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
\(123\) 1.29673 + 15.5433i 0.116922 + 1.40149i
\(124\) 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
\(129\) 3.57652 7.58981i 0.314895 0.668246i
\(130\) 0 0
\(131\) 10.2167 + 15.8976i 0.892640 + 1.38898i 0.921077 + 0.389380i \(0.127311\pi\)
−0.0284368 + 0.999596i \(0.509053\pi\)
\(132\) 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 −0.291350 0.956616i \(-0.594105\pi\)
0.749138 + 0.662414i \(0.230468\pi\)
\(138\) 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
\(141\) 9.83823 + 2.01854i 0.828528 + 0.169992i
\(142\) 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
\(147\) −4.97001 9.93044i −0.409919 0.819049i
\(148\) 0 0
\(149\) 0.935127 0.427058i 0.0766086 0.0349860i −0.376742 0.926318i \(-0.622956\pi\)
0.453351 + 0.891332i \(0.350228\pi\)
\(150\) 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
\(153\) −12.1464 + 14.7070i −0.981977 + 1.18899i
\(154\) 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
\(159\) −1.48411 + 2.24967i −0.117697 + 0.178410i
\(160\) 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
\(165\) 0.535951 0.300939i 0.0417237 0.0234281i
\(166\) 0 0
\(167\) −13.2822 9.45824i −1.02781 0.731901i −0.0638540 0.997959i \(-0.520339\pi\)
−0.963957 + 0.266058i \(0.914279\pi\)
\(168\) 0 0
\(169\) −0.555224 + 11.6556i −0.0427095 + 0.896583i
\(170\) 0 0
\(171\) −3.00869 + 1.46104i −0.230080 + 0.111729i
\(172\) 0 0
\(173\) −9.36076 2.27090i −0.711685 0.172653i −0.136457 0.990646i \(-0.543572\pi\)
−0.575228 + 0.817993i \(0.695087\pi\)
\(174\) 0 0
\(175\) −0.650842 + 3.37689i −0.0491990 + 0.255269i
\(176\) 0 0
\(177\) −9.78682 + 6.12539i −0.735622 + 0.460413i
\(178\) 0 0
\(179\) −4.29867 2.76259i −0.321298 0.206486i 0.370043 0.929015i \(-0.379343\pi\)
−0.691340 + 0.722529i \(0.742979\pi\)
\(180\) 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
\(183\) 12.5601 + 1.35119i 0.928473 + 0.0998828i
\(184\) 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
\(189\) −2.42764 + 3.16247i −0.176585 + 0.230036i
\(190\) 0 0
\(191\) 12.7980 6.59782i 0.926030 0.477402i 0.0718711 0.997414i \(-0.477103\pi\)
0.854159 + 0.520012i \(0.174073\pi\)
\(192\) 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
\(195\) 4.81973 + 3.88451i 0.345148 + 0.278175i
\(196\) 0 0
\(197\) −3.40216 + 9.82990i −0.242394 + 0.700351i 0.756529 + 0.653960i \(0.226893\pi\)
−0.998923 + 0.0463916i \(0.985228\pi\)
\(198\) 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
\(201\) −13.3546 + 4.75979i −0.941958 + 0.335729i
\(202\) 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
\(207\) 17.4595 11.8136i 1.21352 0.821100i
\(208\) 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
\(213\) 0.886432 14.8640i 0.0607373 1.01847i
\(214\) 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
\(219\) 2.16438 20.1193i 0.146255 1.35953i
\(220\) 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
\(225\) −12.9889 + 3.47855i −0.865928 + 0.231903i
\(226\) 0 0
\(227\) −3.55785 + 18.4599i −0.236143 + 1.22522i 0.649321 + 0.760515i \(0.275053\pi\)
−0.885463 + 0.464709i \(0.846159\pi\)
\(228\) 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
\(231\) 0.479712 0.446569i 0.0315627 0.0293821i
\(232\) 0 0
\(233\) 0.455903 9.57058i 0.0298672 0.626990i −0.933463 0.358673i \(-0.883229\pi\)
0.963331 0.268317i \(-0.0864675\pi\)
\(234\) 0 0
\(235\) −3.39872 2.42022i −0.221708 0.157878i
\(236\) 0 0
\(237\) −6.71394 11.9570i −0.436117 0.776693i
\(238\) 0 0
\(239\) −6.97831 12.0868i −0.451389 0.781829i 0.547083 0.837078i \(-0.315738\pi\)
−0.998473 + 0.0552490i \(0.982405\pi\)
\(240\) 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
\(243\) −15.2695 3.13708i −0.979541 0.201244i
\(244\) 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
\(249\) −23.4173 9.70154i −1.48401 0.614810i
\(250\) 0 0
\(251\) 0.505431 + 1.46035i 0.0319025 + 0.0921763i 0.959828 0.280591i \(-0.0905303\pi\)
−0.927925 + 0.372767i \(0.878409\pi\)
\(252\) 0 0
\(253\) −3.15231 + 1.43961i −0.198184 + 0.0905076i
\(254\) 0 0
\(255\) 7.08637 3.54660i 0.443766 0.222097i
\(256\) 0 0
\(257\) −1.80024 4.49679i −0.112296 0.280502i 0.861565 0.507648i \(-0.169485\pi\)
−0.973861 + 0.227146i \(0.927061\pi\)
\(258\) 0 0
\(259\) 0.834375 + 0.381046i 0.0518455 + 0.0236771i
\(260\) 0 0
\(261\) −12.9673 + 23.7405i −0.802656 + 1.46950i
\(262\) 0 0
\(263\) −15.9211 2.28910i −0.981735 0.141152i −0.367286 0.930108i \(-0.619713\pi\)
−0.614450 + 0.788956i \(0.710622\pi\)
\(264\) 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 \(-0.906169\pi\)
0.956866 0.290528i \(-0.0938311\pi\)
\(270\) 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
\(273\) 5.97081 + 2.81360i 0.361370 + 0.170287i
\(274\) 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
\(279\) −2.51160 + 11.5383i −0.150365 + 0.690782i
\(280\) 0 0
\(281\) −11.3790 + 10.8499i −0.678817 + 0.647251i −0.948897 0.315587i \(-0.897798\pi\)
0.270080 + 0.962838i \(0.412950\pi\)
\(282\) 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
\(285\) 1.38865 0.0495044i 0.0822563 0.00293239i
\(286\) 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
\(291\) 0.898659 3.51995i 0.0526803 0.206343i
\(292\) 0 0
\(293\) −1.94667 + 6.62975i −0.113726 + 0.387314i −0.996609 0.0822776i \(-0.973781\pi\)
0.882884 + 0.469591i \(0.155599\pi\)
\(294\) 0 0
\(295\) 4.74776 0.682625i 0.276425 0.0397439i
\(296\) 0 0
\(297\) 2.39003 + 0.924519i 0.138684 + 0.0536460i
\(298\) 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
\(303\) 25.3379 + 9.11047i 1.45563 + 0.523383i
\(304\) 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
\(309\) 0.959692 1.80809i 0.0545950 0.102859i
\(310\) 0 0
\(311\) 17.5008 20.1970i 0.992382 1.14527i 0.00299002 0.999996i \(-0.499048\pi\)
0.989391 0.145274i \(-0.0464063\pi\)
\(312\) 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
\(315\) 1.45380 0.793589i 0.0819125 0.0447137i
\(316\) 0 0
\(317\) −2.09975 10.8945i −0.117934 0.611897i −0.992015 0.126118i \(-0.959748\pi\)
0.874082 0.485779i \(-0.161464\pi\)
\(318\) 0 0
\(319\) 2.74893 3.49555i 0.153911 0.195713i
\(320\) 0 0
\(321\) 10.4518 + 23.6305i 0.583364 + 1.31893i
\(322\) 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
\(327\) 33.3210 + 0.398724i 1.84266 + 0.0220495i
\(328\) 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
\(333\) 0.0848805 + 3.58551i 0.00465142 + 0.196485i
\(334\) 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
\(339\) −23.1999 16.9425i −1.26004 0.920192i
\(340\) 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
\(345\) −8.61879 + 1.55442i −0.464020 + 0.0836870i
\(346\) 0 0
\(347\) −0.318692 1.31367i −0.0171083 0.0705213i 0.962618 0.270864i \(-0.0873095\pi\)
−0.979726 + 0.200343i \(0.935794\pi\)
\(348\) 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
\(351\) 0.302030 + 25.8063i 0.0161211 + 1.37744i
\(352\) 0 0
\(353\) −6.98868 + 1.34696i −0.371970 + 0.0716913i −0.371810 0.928309i \(-0.621263\pi\)
−0.000159442 1.00000i \(0.500051\pi\)
\(354\) 0 0
\(355\) −2.83466 + 5.49847i −0.150448 + 0.291829i
\(356\) 0 0
\(357\) 6.45148 5.45647i 0.341449 0.288787i
\(358\) 0 0
\(359\) 25.8420 + 22.3923i 1.36389 + 1.18182i 0.964202 + 0.265167i \(0.0854272\pi\)
0.399689 + 0.916651i \(0.369118\pi\)
\(360\) 0 0
\(361\) −17.4361 3.36054i −0.917691 0.176870i
\(362\) 0 0
\(363\) 16.0225 + 9.50804i 0.840966 + 0.499043i
\(364\) 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
\(369\) 25.3132 9.43756i 1.31775 0.491300i
\(370\) 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
\(375\) 11.6768 + 1.82172i 0.602985 + 0.0940734i
\(376\) 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
\(381\) 5.34020 + 13.8160i 0.273587 + 0.707817i
\(382\) 0 0
\(383\) 12.4215 + 1.18611i 0.634710 + 0.0606075i 0.407451 0.913227i \(-0.366418\pi\)
0.227259 + 0.973834i \(0.427024\pi\)
\(384\) 0 0
\(385\) −0.257306 + 0.0890546i −0.0131135 + 0.00453864i
\(386\) 0 0
\(387\) −14.3309 2.41179i −0.728479 0.122598i
\(388\) 0 0
\(389\) 6.30391 + 6.61135i 0.319621 + 0.335209i 0.863870 0.503715i \(-0.168034\pi\)
−0.544249 + 0.838924i \(0.683185\pi\)
\(390\) 0 0
\(391\) −41.4774 + 16.6050i −2.09760 + 0.839753i
\(392\) 0 0
\(393\) 21.7289 24.4785i 1.09608 1.23478i
\(394\) 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
\(399\) 1.42650 0.400381i 0.0714142 0.0200441i
\(400\) 0 0
\(401\) −37.9003 −1.89265 −0.946325 0.323218i \(-0.895235\pi\)
−0.946325 + 0.323218i \(0.895235\pi\)
\(402\) 0 0
\(403\) 19.5501 0.973858
\(404\) 0 0
\(405\) 5.27432 + 3.75791i 0.262083 + 0.186732i
\(406\) 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
\(411\) −8.25045 7.32372i −0.406965 0.361253i
\(412\) 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
\(417\) 3.00391 + 22.8286i 0.147102 + 1.11792i
\(418\) 0 0
\(419\) −22.3142 + 7.72303i −1.09012 + 0.377295i −0.812242 0.583321i \(-0.801753\pi\)
−0.277880 + 0.960616i \(0.589632\pi\)
\(420\) 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
\(423\) −1.23869 17.3511i −0.0602271 0.843641i
\(424\) 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
\(429\) 0.653994 4.19192i 0.0315751 0.202388i
\(430\) 0 0
\(431\) −21.1776 + 12.2269i −1.02009 + 0.588949i −0.914130 0.405422i \(-0.867125\pi\)
−0.105959 + 0.994370i \(0.533791\pi\)
\(432\) 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
\(435\) 8.91633 6.84081i 0.427505 0.327992i
\(436\) 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
\(441\) −14.2339 + 12.9360i −0.677803 + 0.616002i
\(442\) 0 0
\(443\) −7.27332 1.40182i −0.345566 0.0666024i 0.0135154 0.999909i \(-0.495698\pi\)
−0.359081 + 0.933306i \(0.616910\pi\)
\(444\) 0 0
\(445\) −2.02156 1.75169i −0.0958312 0.0830382i
\(446\) 0 0
\(447\) −1.14986 1.35954i −0.0543864 0.0643041i
\(448\) 0 0
\(449\) 1.84954 3.58761i 0.0872852 0.169310i −0.841152 0.540798i \(-0.818122\pi\)
0.928438 + 0.371489i \(0.121153\pi\)
\(450\) 0 0
\(451\) −4.36083 + 0.840482i −0.205344 + 0.0395767i
\(452\) 0 0
\(453\) 9.57921 6.65003i 0.450070 0.312446i
\(454\) 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
\(459\) 30.2107 + 13.3717i 1.41012 + 0.624139i
\(460\) 0 0
\(461\) −6.48390 22.0821i −0.301985 1.02847i −0.961049 0.276380i \(-0.910865\pi\)
0.659063 0.752087i \(-0.270953\pi\)
\(462\) 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
\(465\) 2.89325 3.96180i 0.134171 0.183724i
\(466\) 0 0
\(467\) −6.68274 + 4.75876i −0.309240 + 0.220209i −0.724131 0.689662i \(-0.757759\pi\)
0.414891 + 0.909871i \(0.363820\pi\)
\(468\) 0 0
\(469\) 6.19610 1.02502i 0.286109 0.0473311i
\(470\) 0 0
\(471\) 4.25667 1.41644i 0.196137 0.0652663i
\(472\) 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
\(477\) 4.44622 + 1.42194i 0.203578 + 0.0651064i
\(478\) 0 0
\(479\) 6.19309 + 12.0129i 0.282970 + 0.548885i 0.986890 0.161394i \(-0.0515991\pi\)
−0.703920 + 0.710279i \(0.748569\pi\)
\(480\) 0 0
\(481\) 5.77043 1.39989i 0.263109 0.0638295i
\(482\) 0 0
\(483\) −8.54021 + 3.77735i −0.388593 + 0.171875i
\(484\) 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
\(489\) −6.93210 + 7.09815i −0.313480 + 0.320989i
\(490\) 0 0
\(491\) 12.7512 19.8412i 0.575453 0.895422i −0.424497 0.905429i \(-0.639549\pi\)
0.999950 + 0.0100070i \(0.00318537\pi\)
\(492\) 0 0
\(493\) 37.5440 43.3281i 1.69090 1.95140i
\(494\) 0 0
\(495\) −0.752703 0.752901i −0.0338315 0.0338404i
\(496\) 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
\(501\) −9.55584 + 26.5766i −0.426924 + 1.18735i
\(502\) 0 0
\(503\) 8.66130 12.1631i 0.386188 0.542325i −0.575024 0.818137i \(-0.695007\pi\)
0.961212 + 0.275811i \(0.0889465\pi\)
\(504\) 0 0
\(505\) −8.09589 7.71941i −0.360262 0.343509i
\(506\) 0 0
\(507\) 19.6968 4.52956i 0.874767 0.201165i
\(508\) 0 0
\(509\) −0.747224 + 0.107435i −0.0331201 + 0.00476196i −0.158855 0.987302i \(-0.550780\pi\)
0.125735 + 0.992064i \(0.459871\pi\)
\(510\) 0 0
\(511\) −2.52541 + 8.60074i −0.111717 + 0.380474i
\(512\) 0 0
\(513\) 3.84468 + 4.33347i 0.169747 + 0.191328i
\(514\) 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
\(519\) 0.594383 + 16.6730i 0.0260905 + 0.731863i
\(520\) 0 0
\(521\) 0.681593 + 1.49248i 0.0298611 + 0.0653867i 0.923975 0.382453i \(-0.124921\pi\)
−0.894114 + 0.447840i \(0.852193\pi\)
\(522\) 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
\(525\) 5.93596 0.495219i 0.259067 0.0216131i
\(526\) 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
\(531\) 14.7955 + 13.4536i 0.642072 + 0.583836i
\(532\) 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
\(543\) −8.81587 + 42.9679i −0.378325 + 1.84393i
\(544\) 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
\(549\) −3.62558 21.5779i −0.154736 0.920921i
\(550\) 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
\(555\) 0.570288 1.37654i 0.0242074 0.0584310i
\(556\) 0 0
\(557\) −25.5617 32.5044i −1.08309 1.37726i −0.920583 0.390547i \(-0.872286\pi\)
−0.162503 0.986708i \(-0.551957\pi\)
\(558\) 0 0
\(559\) 1.14481 + 24.0324i 0.0484201 + 1.01646i
\(560\) 0 0
\(561\) −4.53349 2.99075i −0.191404 0.126269i
\(562\) 0 0
\(563\) 2.56815 + 17.8618i 0.108234 + 0.752787i 0.969581 + 0.244770i \(0.0787123\pi\)
−0.861347 + 0.508017i \(0.830379\pi\)
\(564\) 0 0
\(565\) 5.96739 + 10.3358i 0.251050 + 0.434831i
\(566\) 0 0
\(567\) 6.41004 + 2.56814i 0.269196 + 0.107852i
\(568\) 0 0
\(569\) 20.0817 + 14.3001i 0.841868 + 0.599491i 0.917541 0.397641i \(-0.130171\pi\)
−0.0756733 + 0.997133i \(0.524111\pi\)
\(570\) 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
\(573\) −16.9928 18.2539i −0.709883 0.762568i
\(574\) 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
\(579\) −6.00721 9.59799i −0.249651 0.398879i
\(580\) 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
\(585\) 4.22194 9.85560i 0.174556 0.407479i
\(586\) 0 0
\(587\) 34.6085 + 27.2165i 1.42845 + 1.12334i 0.972382 + 0.233397i \(0.0749842\pi\)
0.456066 + 0.889946i \(0.349258\pi\)
\(588\) 0 0
\(589\) 3.31654 2.87380i 0.136656 0.118413i
\(590\) 0 0
\(591\) 17.9848 + 1.07254i 0.739797 + 0.0441186i
\(592\) 0 0
\(593\) 1.02148 0.526611i 0.0419473 0.0216253i −0.437125 0.899401i \(-0.644003\pi\)
0.479073 + 0.877775i \(0.340973\pi\)
\(594\) 0 0
\(595\) −3.36812 + 0.988970i −0.138080 + 0.0405438i
\(596\) 0 0
\(597\) −10.2669 + 12.7387i −0.420195 + 0.521360i
\(598\) 0 0
\(599\) −7.05909 + 20.3959i −0.288427 + 0.833354i 0.703965 + 0.710235i \(0.251411\pi\)
−0.992392 + 0.123120i \(0.960710\pi\)
\(600\) 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
\(603\) 14.1881 + 20.0424i 0.577786 + 0.816188i
\(604\) 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
\(609\) 7.51961 9.33001i 0.304710 0.378071i
\(610\) 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
\(615\) −11.2035 0.668130i −0.451767 0.0269416i
\(616\) 0 0
\(617\) −25.5107 + 22.1051i −1.02702 + 0.889919i −0.993983 0.109535i \(-0.965064\pi\)
−0.0330383 + 0.999454i \(0.510518\pi\)
\(618\) 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
\(621\) −27.8724 23.5862i −1.11848 0.946481i
\(622\) 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
\(627\) −0.505253 0.807267i −0.0201779 0.0322391i
\(628\) 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
\(633\) 22.0808 + 23.7196i 0.877633 + 0.942768i
\(634\) 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
\(639\) −25.2023 + 5.47897i −0.996988 + 0.216745i
\(640\) 0 0
\(641\) 12.4842 + 21.6233i 0.493098 + 0.854070i 0.999968 0.00795173i \(-0.00253114\pi\)
−0.506871 + 0.862022i \(0.669198\pi\)
\(642\) 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
\(645\) 5.03957 + 3.32460i 0.198433 + 0.130906i
\(646\) 0 0
\(647\) −1.46370 30.7268i −0.0575439 1.20800i −0.824336 0.566101i \(-0.808451\pi\)
0.766792 0.641895i \(-0.221852\pi\)
\(648\) 0 0
\(649\) −2.03217 2.58411i −0.0797695 0.101435i
\(650\) 0 0
\(651\) 2.00211 4.83261i 0.0784687 0.189405i
\(652\) 0 0
\(653\) 11.9399 + 34.4979i 0.467243 + 1.35001i 0.894980 + 0.446106i \(0.147189\pi\)
−0.427738 + 0.903903i \(0.640689\pi\)
\(654\) 0 0
\(655\) −12.3692 + 5.64884i −0.483306 + 0.220718i
\(656\) 0 0
\(657\) −34.5642 + 5.80759i −1.34848 + 0.226575i
\(658\) 0 0
\(659\) 11.1980 + 27.9712i 0.436211 + 1.08960i 0.969809 + 0.243865i \(0.0784154\pi\)
−0.533598 + 0.845738i \(0.679160\pi\)
\(660\) 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
\(663\) 10.9934 53.5808i 0.426947 2.08091i
\(664\) 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
\(675\) 11.8804 + 20.0323i 0.457277 + 0.771044i
\(676\) 0 0
\(677\) 18.8041 1.79557i 0.722701 0.0690095i 0.272778 0.962077i \(-0.412058\pi\)
0.449923 + 0.893068i \(0.351452\pi\)
\(678\) 0 0
\(679\) −0.668518 + 1.46385i −0.0256554 + 0.0561774i
\(680\) 0 0
\(681\) 32.4491 2.70713i 1.24345 0.103737i
\(682\) 0 0
\(683\) 3.78334 3.60741i 0.144765 0.138034i −0.614236 0.789122i \(-0.710536\pi\)
0.759002 + 0.651089i \(0.225687\pi\)
\(684\) 0 0
\(685\) 1.90394 + 4.16904i 0.0727457 + 0.159291i
\(686\) 0 0
\(687\) 0.399626 + 11.2099i 0.0152467 + 0.427684i
\(688\) 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
\(693\) −0.969234 0.590953i −0.0368181 0.0224485i
\(694\) 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
\(699\) −16.1734 + 3.71929i −0.611734 + 0.140677i
\(700\) 0 0
\(701\) 3.03624 + 2.89505i 0.114677 + 0.109345i 0.745249 0.666787i \(-0.232331\pi\)
−0.630571 + 0.776131i \(0.717179\pi\)
\(702\) 0 0
\(703\) 0.773135 1.08572i 0.0291593 0.0409486i
\(704\) 0 0
\(705\) −2.44519 + 6.80054i −0.0920913 + 0.256123i
\(706\) 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
\(711\) −16.7972 + 16.7928i −0.629944 + 0.629779i
\(712\) 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
\(717\) −16.8898 + 17.2944i −0.630762 + 0.645871i
\(718\) 0 0
\(719\) 4.48842 + 23.2881i 0.167390 + 0.868501i 0.964382 + 0.264512i \(0.0852108\pi\)
−0.796993 + 0.603989i \(0.793577\pi\)
\(720\) 0 0
\(721\) −0.560532 + 0.712775i −0.0208753 + 0.0265451i
\(722\) 0 0
\(723\) −26.1406 + 11.5620i −0.972180 + 0.429997i
\(724\) 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
\(729\) 1.91556 + 26.9320i 0.0709466 + 0.997480i
\(730\) 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
\(735\) 7.58188 2.52294i 0.279662 0.0930601i
\(736\) 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
\(741\) 5.65645 7.74554i 0.207795 0.284539i
\(742\) 0 0
\(743\) −2.89884 + 7.24096i −0.106348 + 0.265645i −0.971991 0.235016i \(-0.924486\pi\)
0.865643 + 0.500661i \(0.166910\pi\)
\(744\) 0 0
\(745\) 0.208409 + 0.709775i 0.00763550 + 0.0260041i
\(746\) 0 0
\(747\) −5.21783 + 43.5917i −0.190910 + 1.59494i
\(748\) 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
\(753\) 2.19872 1.52639i 0.0801259 0.0556246i
\(754\) 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
\(759\) 3.87617 + 4.58301i 0.140696 + 0.166353i
\(760\) 0 0
\(761\) −35.4724 30.7370i −1.28587 1.11422i −0.987137 0.159879i \(-0.948889\pi\)
−0.298736 0.954336i \(-0.596565\pi\)
\(762\) 0 0
\(763\) −14.4948 2.79364i −0.524747 0.101137i
\(764\) 0 0
\(765\) −9.23117 10.1573i −0.333754 0.367238i
\(766\) 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
\(771\) −6.65629 + 5.10685i −0.239720 + 0.183919i
\(772\) 0 0
\(773\) −10.5107 + 11.0233i −0.378042 + 0.396479i −0.885076 0.465447i \(-0.845893\pi\)
0.507034 + 0.861926i \(0.330742\pi\)