Properties

Label 804.2.ba.b.41.15
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 41.15
Character \(\chi\) = 804.41
Dual form 804.2.ba.b.353.15

$q$-expansion

\(f(q)\) \(=\) \(q+(0.774432 + 1.54928i) q^{3} +(-0.177548 + 1.23488i) q^{5} +(0.271050 + 2.83857i) q^{7} +(-1.80051 + 2.39962i) q^{9} +O(q^{10})\) \(q+(0.774432 + 1.54928i) q^{3} +(-0.177548 + 1.23488i) q^{5} +(0.271050 + 2.83857i) q^{7} +(-1.80051 + 2.39962i) q^{9} +(5.62239 - 2.25086i) q^{11} +(0.830910 + 0.871434i) q^{13} +(-2.05066 + 0.681255i) q^{15} +(4.76535 - 1.64930i) q^{17} +(-3.22750 - 0.308189i) q^{19} +(-4.18781 + 2.61821i) q^{21} +(-4.74225 + 0.225901i) q^{23} +(3.30407 + 0.970163i) q^{25} +(-5.11204 - 0.931149i) q^{27} +(-7.03437 + 4.06129i) q^{29} +(-6.90458 + 7.24131i) q^{31} +(7.84136 + 6.96749i) q^{33} +(-3.55340 - 0.169269i) q^{35} +(3.38398 - 5.86123i) q^{37} +(-0.706608 + 1.96218i) q^{39} +(-4.19811 - 0.809119i) q^{41} +(4.51548 + 3.91269i) q^{43} +(-2.64355 - 2.64945i) q^{45} +(2.74131 - 5.31740i) q^{47} +(-1.11049 + 0.214029i) q^{49} +(6.24567 + 6.10557i) q^{51} +(-6.19918 - 7.15424i) q^{53} +(1.78129 + 7.34258i) q^{55} +(-2.02201 - 5.23896i) q^{57} +(1.03031 + 3.50891i) q^{59} +(0.285957 - 0.714285i) q^{61} +(-7.29950 - 4.46045i) q^{63} +(-1.22364 + 0.871349i) q^{65} +(6.77031 - 4.60032i) q^{67} +(-4.02253 - 7.17211i) q^{69} +(13.6640 + 4.72917i) q^{71} +(-7.42126 - 2.97103i) q^{73} +(1.05573 + 5.87024i) q^{75} +(7.91317 + 15.3494i) q^{77} +(5.89134 - 1.42922i) q^{79} +(-2.51632 - 8.64107i) q^{81} +(-4.48418 + 5.70210i) q^{83} +(1.19061 + 6.17745i) q^{85} +(-11.7397 - 7.75298i) q^{87} +(8.56425 - 13.3262i) q^{89} +(-2.24840 + 2.59480i) q^{91} +(-16.5659 - 5.08919i) q^{93} +(0.953612 - 3.93084i) q^{95} +(4.86960 + 2.81147i) q^{97} +(-4.72196 + 17.5443i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440q - 12q^{7} + 4q^{9} + O(q^{10}) \) \( 440q - 12q^{7} + 4q^{9} - 2q^{15} - 10q^{19} + 22q^{21} - 68q^{25} + 50q^{31} + 11q^{33} - 22q^{37} - 45q^{39} + 22q^{43} + 22q^{45} - 18q^{49} - 6q^{51} + 126q^{55} - 183q^{57} - 56q^{61} - 141q^{63} - 12q^{67} + 33q^{69} + 356q^{73} + 165q^{75} + 228q^{79} + 24q^{81} - 6q^{85} + 75q^{87} - 4q^{91} - 75q^{93} + 12q^{97} + 88q^{99} + O(q^{100}) \)

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
\(3\) 0.774432 + 1.54928i 0.447118 + 0.894475i
\(4\) 0 0
\(5\) −0.177548 + 1.23488i −0.0794020 + 0.552253i 0.910826 + 0.412792i \(0.135446\pi\)
−0.990228 + 0.139461i \(0.955463\pi\)
\(6\) 0 0
\(7\) 0.271050 + 2.83857i 0.102447 + 1.07288i 0.889793 + 0.456365i \(0.150849\pi\)
−0.787345 + 0.616512i \(0.788545\pi\)
\(8\) 0 0
\(9\) −1.80051 + 2.39962i −0.600170 + 0.799872i
\(10\) 0 0
\(11\) 5.62239 2.25086i 1.69521 0.678661i 0.695989 0.718052i \(-0.254966\pi\)
0.999224 + 0.0393914i \(0.0125419\pi\)
\(12\) 0 0
\(13\) 0.830910 + 0.871434i 0.230453 + 0.241692i 0.828800 0.559545i \(-0.189024\pi\)
−0.598347 + 0.801237i \(0.704176\pi\)
\(14\) 0 0
\(15\) −2.05066 + 0.681255i −0.529478 + 0.175899i
\(16\) 0 0
\(17\) 4.76535 1.64930i 1.15577 0.400015i 0.319098 0.947722i \(-0.396620\pi\)
0.836670 + 0.547707i \(0.184499\pi\)
\(18\) 0 0
\(19\) −3.22750 0.308189i −0.740439 0.0707034i −0.281982 0.959420i \(-0.590992\pi\)
−0.458457 + 0.888716i \(0.651598\pi\)
\(20\) 0 0
\(21\) −4.18781 + 2.61821i −0.913855 + 0.571340i
\(22\) 0 0
\(23\) −4.74225 + 0.225901i −0.988828 + 0.0471037i −0.535758 0.844371i \(-0.679974\pi\)
−0.453070 + 0.891475i \(0.649671\pi\)
\(24\) 0 0
\(25\) 3.30407 + 0.970163i 0.660814 + 0.194033i
\(26\) 0 0
\(27\) −5.11204 0.931149i −0.983813 0.179200i
\(28\) 0 0
\(29\) −7.03437 + 4.06129i −1.30625 + 0.754163i −0.981468 0.191626i \(-0.938624\pi\)
−0.324781 + 0.945789i \(0.605291\pi\)
\(30\) 0 0
\(31\) −6.90458 + 7.24131i −1.24010 + 1.30058i −0.302378 + 0.953188i \(0.597780\pi\)
−0.937721 + 0.347390i \(0.887068\pi\)
\(32\) 0 0
\(33\) 7.84136 + 6.96749i 1.36501 + 1.21288i
\(34\) 0 0
\(35\) −3.55340 0.169269i −0.600634 0.0286117i
\(36\) 0 0
\(37\) 3.38398 5.86123i 0.556323 0.963580i −0.441476 0.897273i \(-0.645545\pi\)
0.997799 0.0663071i \(-0.0211217\pi\)
\(38\) 0 0
\(39\) −0.706608 + 1.96218i −0.113148 + 0.314200i
\(40\) 0 0
\(41\) −4.19811 0.809119i −0.655634 0.126363i −0.149424 0.988773i \(-0.547742\pi\)
−0.506210 + 0.862410i \(0.668954\pi\)
\(42\) 0 0
\(43\) 4.51548 + 3.91269i 0.688604 + 0.596679i 0.927257 0.374426i \(-0.122160\pi\)
−0.238652 + 0.971105i \(0.576706\pi\)
\(44\) 0 0
\(45\) −2.64355 2.64945i −0.394077 0.394957i
\(46\) 0 0
\(47\) 2.74131 5.31740i 0.399861 0.775623i −0.599838 0.800121i \(-0.704768\pi\)
0.999700 + 0.0244981i \(0.00779878\pi\)
\(48\) 0 0
\(49\) −1.11049 + 0.214029i −0.158641 + 0.0305755i
\(50\) 0 0
\(51\) 6.24567 + 6.10557i 0.874569 + 0.854951i
\(52\) 0 0
\(53\) −6.19918 7.15424i −0.851523 0.982710i 0.148458 0.988919i \(-0.452569\pi\)
−0.999981 + 0.00620868i \(0.998024\pi\)
\(54\) 0 0
\(55\) 1.78129 + 7.34258i 0.240189 + 0.990073i
\(56\) 0 0
\(57\) −2.02201 5.23896i −0.267822 0.693917i
\(58\) 0 0
\(59\) 1.03031 + 3.50891i 0.134135 + 0.456821i 0.998977 0.0452228i \(-0.0143998\pi\)
−0.864842 + 0.502044i \(0.832582\pi\)
\(60\) 0 0
\(61\) 0.285957 0.714285i 0.0366130 0.0914548i −0.908935 0.416939i \(-0.863103\pi\)
0.945548 + 0.325484i \(0.105527\pi\)
\(62\) 0 0
\(63\) −7.29950 4.46045i −0.919650 0.561964i
\(64\) 0 0
\(65\) −1.22364 + 0.871349i −0.151774 + 0.108078i
\(66\) 0 0
\(67\) 6.77031 4.60032i 0.827125 0.562018i
\(68\) 0 0
\(69\) −4.02253 7.17211i −0.484256 0.863421i
\(70\) 0 0
\(71\) 13.6640 + 4.72917i 1.62162 + 0.561250i 0.978810 0.204772i \(-0.0656454\pi\)
0.642814 + 0.766022i \(0.277767\pi\)
\(72\) 0 0
\(73\) −7.42126 2.97103i −0.868593 0.347732i −0.105810 0.994386i \(-0.533743\pi\)
−0.762783 + 0.646654i \(0.776168\pi\)
\(74\) 0 0
\(75\) 1.05573 + 5.87024i 0.121905 + 0.677837i
\(76\) 0 0
\(77\) 7.91317 + 15.3494i 0.901790 + 1.74923i
\(78\) 0 0
\(79\) 5.89134 1.42922i 0.662827 0.160800i 0.109788 0.993955i \(-0.464983\pi\)
0.553040 + 0.833155i \(0.313468\pi\)
\(80\) 0 0
\(81\) −2.51632 8.64107i −0.279591 0.960119i
\(82\) 0 0
\(83\) −4.48418 + 5.70210i −0.492203 + 0.625887i −0.967174 0.254114i \(-0.918216\pi\)
0.474971 + 0.880001i \(0.342458\pi\)
\(84\) 0 0
\(85\) 1.19061 + 6.17745i 0.129139 + 0.670038i
\(86\) 0 0
\(87\) −11.7397 7.75298i −1.25863 0.831207i
\(88\) 0 0
\(89\) 8.56425 13.3262i 0.907809 1.41258i −0.00311057 0.999995i \(-0.500990\pi\)
0.910920 0.412584i \(-0.135374\pi\)
\(90\) 0 0
\(91\) −2.24840 + 2.59480i −0.235697 + 0.272009i
\(92\) 0 0
\(93\) −16.5659 5.08919i −1.71781 0.527725i
\(94\) 0 0
\(95\) 0.953612 3.93084i 0.0978385 0.403296i
\(96\) 0 0
\(97\) 4.86960 + 2.81147i 0.494433 + 0.285461i 0.726412 0.687260i \(-0.241187\pi\)
−0.231979 + 0.972721i \(0.574520\pi\)
\(98\) 0 0
\(99\) −4.72196 + 17.5443i −0.474575 + 1.76327i
\(100\) 0 0
\(101\) 4.60755 6.47040i 0.458468 0.643829i −0.519034 0.854754i \(-0.673708\pi\)
0.977502 + 0.210925i \(0.0676476\pi\)
\(102\) 0 0
\(103\) −0.947981 0.903898i −0.0934073 0.0890637i 0.641937 0.766757i \(-0.278131\pi\)
−0.735344 + 0.677694i \(0.762980\pi\)
\(104\) 0 0
\(105\) −2.48962 5.63628i −0.242962 0.550045i
\(106\) 0 0
\(107\) 1.97204 0.283536i 0.190644 0.0274105i −0.0463313 0.998926i \(-0.514753\pi\)
0.236975 + 0.971516i \(0.423844\pi\)
\(108\) 0 0
\(109\) −0.666913 + 2.27130i −0.0638787 + 0.217551i −0.985247 0.171141i \(-0.945255\pi\)
0.921368 + 0.388692i \(0.127073\pi\)
\(110\) 0 0
\(111\) 11.7013 + 0.703600i 1.11064 + 0.0667828i
\(112\) 0 0
\(113\) −16.4421 + 12.9302i −1.54674 + 1.21637i −0.662779 + 0.748815i \(0.730623\pi\)
−0.883963 + 0.467557i \(0.845134\pi\)
\(114\) 0 0
\(115\) 0.563019 5.89620i 0.0525017 0.549823i
\(116\) 0 0
\(117\) −3.58717 + 0.424840i −0.331634 + 0.0392765i
\(118\) 0 0
\(119\) 5.97331 + 13.0797i 0.547572 + 1.19902i
\(120\) 0 0
\(121\) 18.5838 17.7196i 1.68943 1.61087i
\(122\) 0 0
\(123\) −1.99760 7.13063i −0.180117 0.642947i
\(124\) 0 0
\(125\) −4.37597 + 9.58203i −0.391398 + 0.857043i
\(126\) 0 0
\(127\) 9.97022 0.952041i 0.884714 0.0844800i 0.357202 0.934027i \(-0.383731\pi\)
0.527513 + 0.849547i \(0.323125\pi\)
\(128\) 0 0
\(129\) −2.56490 + 10.0258i −0.225827 + 0.882725i
\(130\) 0 0
\(131\) −12.1678 18.9335i −1.06311 1.65423i −0.685138 0.728414i \(-0.740258\pi\)
−0.377972 0.925817i \(-0.623378\pi\)
\(132\) 0 0
\(133\) 9.24501i 0.801644i
\(134\) 0 0
\(135\) 2.05749 6.14741i 0.177080 0.529085i
\(136\) 0 0
\(137\) 1.42346 0.914800i 0.121614 0.0781566i −0.478420 0.878131i \(-0.658790\pi\)
0.600034 + 0.799975i \(0.295154\pi\)
\(138\) 0 0
\(139\) 19.3972 + 2.78890i 1.64525 + 0.236551i 0.901772 0.432211i \(-0.142267\pi\)
0.743476 + 0.668762i \(0.233176\pi\)
\(140\) 0 0
\(141\) 10.3611 + 0.129082i 0.872561 + 0.0108707i
\(142\) 0 0
\(143\) 6.63318 + 3.02927i 0.554694 + 0.253320i
\(144\) 0 0
\(145\) −3.76625 9.40764i −0.312770 0.781262i
\(146\) 0 0
\(147\) −1.19158 1.55470i −0.0982803 0.128229i
\(148\) 0 0
\(149\) 7.36263 3.36240i 0.603170 0.275459i −0.0903335 0.995912i \(-0.528793\pi\)
0.693504 + 0.720453i \(0.256066\pi\)
\(150\) 0 0
\(151\) 4.84507 + 13.9989i 0.394286 + 1.13922i 0.951181 + 0.308633i \(0.0998714\pi\)
−0.556895 + 0.830583i \(0.688007\pi\)
\(152\) 0 0
\(153\) −4.62237 + 14.4046i −0.373697 + 1.16454i
\(154\) 0 0
\(155\) −7.71622 9.81197i −0.619782 0.788117i
\(156\) 0 0
\(157\) −0.180626 3.79180i −0.0144155 0.302619i −0.994548 0.104277i \(-0.966747\pi\)
0.980133 0.198342i \(-0.0635557\pi\)
\(158\) 0 0
\(159\) 6.28304 15.1447i 0.498278 1.20105i
\(160\) 0 0
\(161\) −1.92662 13.4000i −0.151839 1.05606i
\(162\) 0 0
\(163\) 3.69900 + 6.40685i 0.289728 + 0.501823i 0.973745 0.227643i \(-0.0731019\pi\)
−0.684017 + 0.729466i \(0.739769\pi\)
\(164\) 0 0
\(165\) −9.99620 + 8.44604i −0.778203 + 0.657523i
\(166\) 0 0
\(167\) −7.94281 5.65605i −0.614633 0.437678i 0.229876 0.973220i \(-0.426168\pi\)
−0.844509 + 0.535542i \(0.820107\pi\)
\(168\) 0 0
\(169\) 0.549580 11.5371i 0.0422754 0.887470i
\(170\) 0 0
\(171\) 6.55069 7.18987i 0.500943 0.549823i
\(172\) 0 0
\(173\) 8.60933 + 2.08860i 0.654555 + 0.158793i 0.549265 0.835648i \(-0.314908\pi\)
0.105290 + 0.994442i \(0.466423\pi\)
\(174\) 0 0
\(175\) −1.85830 + 9.64179i −0.140474 + 0.728851i
\(176\) 0 0
\(177\) −4.63836 + 4.31364i −0.348641 + 0.324233i
\(178\) 0 0
\(179\) 15.4083 + 9.90233i 1.15167 + 0.740135i 0.969971 0.243219i \(-0.0782035\pi\)
0.181700 + 0.983354i \(0.441840\pi\)
\(180\) 0 0
\(181\) 4.72348 + 2.43512i 0.351094 + 0.181001i 0.624747 0.780827i \(-0.285202\pi\)
−0.273654 + 0.961828i \(0.588232\pi\)
\(182\) 0 0
\(183\) 1.32808 0.110139i 0.0981744 0.00814174i
\(184\) 0 0
\(185\) 6.63707 + 5.21945i 0.487967 + 0.383741i
\(186\) 0 0
\(187\) 23.0803 19.9992i 1.68780 1.46249i
\(188\) 0 0
\(189\) 1.25751 14.7633i 0.0914702 1.07387i
\(190\) 0 0
\(191\) −11.9859 + 6.17917i −0.867271 + 0.447109i −0.833629 0.552325i \(-0.813741\pi\)
−0.0336417 + 0.999434i \(0.510710\pi\)
\(192\) 0 0
\(193\) 1.59036 0.466972i 0.114477 0.0336134i −0.223992 0.974591i \(-0.571909\pi\)
0.338469 + 0.940977i \(0.390091\pi\)
\(194\) 0 0
\(195\) −2.29758 1.22095i −0.164533 0.0874343i
\(196\) 0 0
\(197\) −0.0834813 + 0.241203i −0.00594779 + 0.0171850i −0.947936 0.318462i \(-0.896834\pi\)
0.941988 + 0.335647i \(0.108955\pi\)
\(198\) 0 0
\(199\) −3.88124 5.45044i −0.275134 0.386371i 0.653770 0.756694i \(-0.273187\pi\)
−0.928903 + 0.370322i \(0.879247\pi\)
\(200\) 0 0
\(201\) 12.3703 + 6.92645i 0.872534 + 0.488554i
\(202\) 0 0
\(203\) −13.4349 18.8667i −0.942946 1.32418i
\(204\) 0 0
\(205\) 1.74453 5.04048i 0.121843 0.352042i
\(206\) 0 0
\(207\) 7.99640 11.7863i 0.555788 0.819206i
\(208\) 0 0
\(209\) −18.8399 + 5.53191i −1.30319 + 0.382650i
\(210\) 0 0
\(211\) 1.54063 0.794251i 0.106061 0.0546785i −0.404380 0.914591i \(-0.632512\pi\)
0.510441 + 0.859913i \(0.329482\pi\)
\(212\) 0 0
\(213\) 3.25508 + 24.8318i 0.223034 + 1.70145i
\(214\) 0 0
\(215\) −5.63340 + 4.88136i −0.384194 + 0.332906i
\(216\) 0 0
\(217\) −22.4264 17.6363i −1.52240 1.19723i
\(218\) 0 0
\(219\) −1.14432 13.7984i −0.0773262 0.932412i
\(220\) 0 0
\(221\) 5.39684 + 2.78227i 0.363031 + 0.187155i
\(222\) 0 0
\(223\) −20.0793 12.9042i −1.34461 0.864130i −0.347326 0.937745i \(-0.612910\pi\)
−0.997287 + 0.0736148i \(0.976546\pi\)
\(224\) 0 0
\(225\) −8.27704 + 6.18172i −0.551802 + 0.412114i
\(226\) 0 0
\(227\) −3.87856 + 20.1239i −0.257429 + 1.33567i 0.591134 + 0.806574i \(0.298681\pi\)
−0.848563 + 0.529095i \(0.822532\pi\)
\(228\) 0 0
\(229\) −5.04776 1.22457i −0.333565 0.0809220i 0.0654785 0.997854i \(-0.479143\pi\)
−0.399044 + 0.916932i \(0.630658\pi\)
\(230\) 0 0
\(231\) −17.6523 + 24.1468i −1.16143 + 1.58874i
\(232\) 0 0
\(233\) 0.778718 16.3473i 0.0510155 1.07095i −0.817703 0.575641i \(-0.804753\pi\)
0.868718 0.495307i \(-0.164944\pi\)
\(234\) 0 0
\(235\) 6.07961 + 4.32927i 0.396590 + 0.282411i
\(236\) 0 0
\(237\) 6.77670 + 8.02047i 0.440194 + 0.520986i
\(238\) 0 0
\(239\) −1.49234 2.58480i −0.0965313 0.167197i 0.813715 0.581264i \(-0.197441\pi\)
−0.910247 + 0.414066i \(0.864108\pi\)
\(240\) 0 0
\(241\) −3.09140 21.5012i −0.199135 1.38501i −0.806802 0.590821i \(-0.798804\pi\)
0.607668 0.794191i \(-0.292105\pi\)
\(242\) 0 0
\(243\) 11.4387 10.5904i 0.733792 0.679374i
\(244\) 0 0
\(245\) −0.0671338 1.40931i −0.00428902 0.0900376i
\(246\) 0 0
\(247\) −2.41320 3.06863i −0.153548 0.195252i
\(248\) 0 0
\(249\) −12.3068 2.53135i −0.779913 0.160418i
\(250\) 0 0
\(251\) 4.13319 + 11.9421i 0.260885 + 0.753776i 0.997034 + 0.0769577i \(0.0245207\pi\)
−0.736150 + 0.676819i \(0.763358\pi\)
\(252\) 0 0
\(253\) −26.1543 + 11.9443i −1.64431 + 0.750930i
\(254\) 0 0
\(255\) −8.64853 + 6.62859i −0.541592 + 0.415098i
\(256\) 0 0
\(257\) 0.837662 + 2.09238i 0.0522519 + 0.130519i 0.952197 0.305484i \(-0.0988181\pi\)
−0.899945 + 0.436003i \(0.856394\pi\)
\(258\) 0 0
\(259\) 17.5547 + 8.01697i 1.09080 + 0.498150i
\(260\) 0 0
\(261\) 2.91991 24.1922i 0.180738 1.49746i
\(262\) 0 0
\(263\) 12.2448 + 1.76054i 0.755047 + 0.108559i 0.509081 0.860719i \(-0.329985\pi\)
0.245967 + 0.969278i \(0.420895\pi\)
\(264\) 0 0
\(265\) 9.93524 6.38499i 0.610317 0.392227i
\(266\) 0 0
\(267\) 27.2785 + 2.94813i 1.66941 + 0.180423i
\(268\) 0 0
\(269\) 26.0117i 1.58596i −0.609246 0.792981i \(-0.708528\pi\)
0.609246 0.792981i \(-0.291472\pi\)
\(270\) 0 0
\(271\) 5.96421 + 9.28049i 0.362300 + 0.563749i 0.973775 0.227514i \(-0.0730599\pi\)
−0.611475 + 0.791264i \(0.709423\pi\)
\(272\) 0 0
\(273\) −5.76129 1.47390i −0.348689 0.0892048i
\(274\) 0 0
\(275\) 20.7605 1.98238i 1.25190 0.119542i
\(276\) 0 0
\(277\) 12.6487 27.6969i 0.759990 1.66414i 0.0124546 0.999922i \(-0.496035\pi\)
0.747535 0.664223i \(-0.231237\pi\)
\(278\) 0 0
\(279\) −4.94461 29.6064i −0.296026 1.77249i
\(280\) 0 0
\(281\) −1.23763 + 1.18007i −0.0738306 + 0.0703973i −0.726096 0.687593i \(-0.758667\pi\)
0.652265 + 0.757991i \(0.273819\pi\)
\(282\) 0 0
\(283\) 6.29421 + 13.7824i 0.374152 + 0.819278i 0.999250 + 0.0387317i \(0.0123318\pi\)
−0.625098 + 0.780546i \(0.714941\pi\)
\(284\) 0 0
\(285\) 6.82847 1.56676i 0.404483 0.0928069i
\(286\) 0 0
\(287\) 1.15884 12.1359i 0.0684041 0.716360i
\(288\) 0 0
\(289\) 6.62548 5.21034i 0.389734 0.306490i
\(290\) 0 0
\(291\) −0.584562 + 9.72164i −0.0342676 + 0.569893i
\(292\) 0 0
\(293\) 4.96968 16.9252i 0.290332 0.988779i −0.677152 0.735844i \(-0.736786\pi\)
0.967483 0.252935i \(-0.0813960\pi\)
\(294\) 0 0
\(295\) −4.51599 + 0.649302i −0.262931 + 0.0378038i
\(296\) 0 0
\(297\) −30.8378 + 6.27123i −1.78939 + 0.363894i
\(298\) 0 0
\(299\) −4.13724 3.94485i −0.239263 0.228137i
\(300\) 0 0
\(301\) −9.88250 + 13.8780i −0.569618 + 0.799916i
\(302\) 0 0
\(303\) 13.5927 + 2.12748i 0.780878 + 0.122221i
\(304\) 0 0
\(305\) 0.831282 + 0.479941i 0.0475991 + 0.0274813i
\(306\) 0 0
\(307\) 2.13694 8.80857i 0.121961 0.502732i −0.877759 0.479102i \(-0.840963\pi\)
0.999721 0.0236299i \(-0.00752233\pi\)
\(308\) 0 0
\(309\) 0.666241 2.16869i 0.0379011 0.123372i
\(310\) 0 0
\(311\) −15.3682 + 17.7358i −0.871450 + 1.00571i 0.128452 + 0.991716i \(0.458999\pi\)
−0.999902 + 0.0139911i \(0.995546\pi\)
\(312\) 0 0
\(313\) −1.83055 + 2.84839i −0.103469 + 0.161000i −0.889127 0.457660i \(-0.848688\pi\)
0.785659 + 0.618660i \(0.212324\pi\)
\(314\) 0 0
\(315\) 6.80411 8.22202i 0.383368 0.463259i
\(316\) 0 0
\(317\) −1.89899 9.85288i −0.106658 0.553393i −0.995466 0.0951144i \(-0.969678\pi\)
0.888809 0.458279i \(-0.151534\pi\)
\(318\) 0 0
\(319\) −30.4085 + 38.6676i −1.70255 + 2.16497i
\(320\) 0 0
\(321\) 1.96648 + 2.83565i 0.109758 + 0.158271i
\(322\) 0 0
\(323\) −15.8885 + 3.85450i −0.884058 + 0.214470i
\(324\) 0 0
\(325\) 1.89995 + 3.68540i 0.105391 + 0.204429i
\(326\) 0 0
\(327\) −4.03535 + 0.725733i −0.223155 + 0.0401331i
\(328\) 0 0
\(329\) 15.8368 + 6.34011i 0.873113 + 0.349542i
\(330\) 0 0
\(331\) 23.5013 + 8.13388i 1.29175 + 0.447079i 0.884629 0.466296i \(-0.154412\pi\)
0.407120 + 0.913375i \(0.366533\pi\)
\(332\) 0 0
\(333\) 7.97181 + 18.6735i 0.436852 + 1.02330i
\(334\) 0 0
\(335\) 4.47876 + 9.17727i 0.244701 + 0.501408i
\(336\) 0 0
\(337\) −27.8821 + 19.8548i −1.51884 + 1.08156i −0.549598 + 0.835429i \(0.685219\pi\)
−0.969237 + 0.246129i \(0.920841\pi\)
\(338\) 0 0
\(339\) −32.7657 15.4598i −1.77959 0.839660i
\(340\) 0 0
\(341\) −22.5210 + 56.2547i −1.21958 + 3.04636i
\(342\) 0 0
\(343\) 4.71495 + 16.0576i 0.254583 + 0.867031i
\(344\) 0 0
\(345\) 9.57085 3.69393i 0.515277 0.198875i
\(346\) 0 0
\(347\) −3.60288 14.8513i −0.193413 0.797258i −0.982998 0.183617i \(-0.941219\pi\)
0.789585 0.613641i \(-0.210296\pi\)
\(348\) 0 0
\(349\) 12.8926 + 14.8788i 0.690123 + 0.796445i 0.987383 0.158352i \(-0.0506181\pi\)
−0.297259 + 0.954797i \(0.596073\pi\)
\(350\) 0 0
\(351\) −3.43621 5.22851i −0.183412 0.279077i
\(352\) 0 0
\(353\) 5.06534 0.976265i 0.269601 0.0519613i −0.0526590 0.998613i \(-0.516770\pi\)
0.322260 + 0.946651i \(0.395558\pi\)
\(354\) 0 0
\(355\) −8.26597 + 16.0337i −0.438712 + 0.850982i
\(356\) 0 0
\(357\) −15.6382 + 19.3837i −0.827660 + 1.02589i
\(358\) 0 0
\(359\) 14.2243 + 12.3254i 0.750730 + 0.650511i 0.943741 0.330685i \(-0.107280\pi\)
−0.193011 + 0.981197i \(0.561825\pi\)
\(360\) 0 0
\(361\) −8.33487 1.60641i −0.438677 0.0845481i
\(362\) 0 0
\(363\) 41.8444 + 15.0688i 2.19626 + 0.790905i
\(364\) 0 0
\(365\) 4.98648 8.63683i 0.261004 0.452073i
\(366\) 0 0
\(367\) −24.4248 1.16350i −1.27497 0.0607341i −0.600851 0.799361i \(-0.705172\pi\)
−0.674115 + 0.738627i \(0.735475\pi\)
\(368\) 0 0
\(369\) 9.50031 8.61702i 0.494566 0.448584i
\(370\) 0 0
\(371\) 18.6275 19.5359i 0.967091 1.01426i
\(372\) 0 0
\(373\) −12.1758 + 7.02967i −0.630437 + 0.363983i −0.780921 0.624630i \(-0.785250\pi\)
0.150485 + 0.988612i \(0.451917\pi\)
\(374\) 0 0
\(375\) −18.2341 + 0.641049i −0.941605 + 0.0331036i
\(376\) 0 0
\(377\) −9.38408 2.75541i −0.483305 0.141911i
\(378\) 0 0
\(379\) 15.7523 0.750375i 0.809142 0.0385442i 0.361067 0.932540i \(-0.382413\pi\)
0.448075 + 0.893996i \(0.352110\pi\)
\(380\) 0 0
\(381\) 9.19623 + 14.7093i 0.471137 + 0.753582i
\(382\) 0 0
\(383\) −12.6317 1.20618i −0.645447 0.0616327i −0.232801 0.972524i \(-0.574789\pi\)
−0.412646 + 0.910892i \(0.635395\pi\)
\(384\) 0 0
\(385\) −20.3596 + 7.04652i −1.03762 + 0.359124i
\(386\) 0 0
\(387\) −17.5191 + 3.79059i −0.890547 + 0.192686i
\(388\) 0 0
\(389\) 16.4064 + 17.2065i 0.831837 + 0.872406i 0.993429 0.114452i \(-0.0365112\pi\)
−0.161591 + 0.986858i \(0.551663\pi\)
\(390\) 0 0
\(391\) −22.2259 + 8.89792i −1.12401 + 0.449987i
\(392\) 0 0
\(393\) 19.9101 33.5141i 1.00433 1.69056i
\(394\) 0 0
\(395\) 0.718915 + 7.52882i 0.0361726 + 0.378816i
\(396\) 0 0
\(397\) −2.30702 + 16.0457i −0.115786 + 0.805311i 0.846328 + 0.532663i \(0.178809\pi\)
−0.962114 + 0.272648i \(0.912101\pi\)
\(398\) 0 0
\(399\) 14.3231 7.15963i 0.717050 0.358430i
\(400\) 0 0
\(401\) −9.84306 −0.491539 −0.245770 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(402\) 0 0
\(403\) −12.0474 −0.600124
\(404\) 0 0
\(405\) 11.1174 1.57313i 0.552429 0.0781697i
\(406\) 0 0
\(407\) 5.83323 40.5710i 0.289142 2.01103i
\(408\) 0 0
\(409\) −0.952292 9.97285i −0.0470878 0.493126i −0.987998 0.154469i \(-0.950633\pi\)
0.940910 0.338657i \(-0.109973\pi\)
\(410\) 0 0
\(411\) 2.51965 + 1.49688i 0.124285 + 0.0738355i
\(412\) 0 0
\(413\) −9.68100 + 3.87569i −0.476371 + 0.190710i
\(414\) 0 0
\(415\) −6.24522 6.54980i −0.306566 0.321517i
\(416\) 0 0
\(417\) 10.7010 + 32.2114i 0.524032 + 1.57740i
\(418\) 0 0
\(419\) 9.38589 3.24849i 0.458531 0.158699i −0.0880313 0.996118i \(-0.528058\pi\)
0.546562 + 0.837419i \(0.315936\pi\)
\(420\) 0 0
\(421\) 26.5655 + 2.53670i 1.29472 + 0.123631i 0.719573 0.694417i \(-0.244338\pi\)
0.575150 + 0.818048i \(0.304944\pi\)
\(422\) 0 0
\(423\) 7.82397 + 16.1521i 0.380414 + 0.785344i
\(424\) 0 0
\(425\) 17.3452 0.826252i 0.841364 0.0400791i
\(426\) 0 0
\(427\) 2.10505 + 0.618100i 0.101871 + 0.0299119i
\(428\) 0 0
\(429\) 0.443767 + 12.6226i 0.0214253 + 0.609424i
\(430\) 0 0
\(431\) 6.87919 3.97170i 0.331359 0.191310i −0.325085 0.945685i \(-0.605393\pi\)
0.656444 + 0.754375i \(0.272060\pi\)
\(432\) 0 0
\(433\) −8.68654 + 9.11018i −0.417448 + 0.437807i −0.898559 0.438853i \(-0.855385\pi\)
0.481111 + 0.876660i \(0.340234\pi\)
\(434\) 0 0
\(435\) 11.6583 13.1205i 0.558974 0.629082i
\(436\) 0 0
\(437\) 15.3752 + 0.732413i 0.735497 + 0.0350361i
\(438\) 0 0
\(439\) −2.96472 + 5.13504i −0.141498 + 0.245082i −0.928061 0.372428i \(-0.878525\pi\)
0.786563 + 0.617510i \(0.211859\pi\)
\(440\) 0 0
\(441\) 1.48586 3.05010i 0.0707550 0.145243i
\(442\) 0 0
\(443\) 9.59946 + 1.85014i 0.456084 + 0.0879030i 0.412119 0.911130i \(-0.364789\pi\)
0.0439651 + 0.999033i \(0.486001\pi\)
\(444\) 0 0
\(445\) 14.9357 + 12.9418i 0.708019 + 0.613502i
\(446\) 0 0
\(447\) 10.9111 + 8.80280i 0.516079 + 0.416358i
\(448\) 0 0
\(449\) −12.6532 + 24.5438i −0.597141 + 1.15829i 0.375683 + 0.926748i \(0.377408\pi\)
−0.972824 + 0.231544i \(0.925622\pi\)
\(450\) 0 0
\(451\) −25.4246 + 4.90019i −1.19720 + 0.230741i
\(452\) 0 0
\(453\) −17.9360 + 18.3476i −0.842707 + 0.862043i
\(454\) 0 0
\(455\) −2.80505 3.23720i −0.131503 0.151762i
\(456\) 0 0
\(457\) −6.78293 27.9596i −0.317292 1.30790i −0.877513 0.479552i \(-0.840799\pi\)
0.560221 0.828343i \(-0.310716\pi\)
\(458\) 0 0
\(459\) −25.8964 + 3.99406i −1.20874 + 0.186427i
\(460\) 0 0
\(461\) −7.46037 25.4077i −0.347464 1.18335i −0.929077 0.369888i \(-0.879396\pi\)
0.581613 0.813466i \(-0.302422\pi\)
\(462\) 0 0
\(463\) −5.24553 + 13.1027i −0.243781 + 0.608935i −0.998912 0.0466391i \(-0.985149\pi\)
0.755131 + 0.655574i \(0.227573\pi\)
\(464\) 0 0
\(465\) 9.22577 19.5533i 0.427835 0.906761i
\(466\) 0 0
\(467\) −21.5349 + 15.3349i −0.996516 + 0.709616i −0.957145 0.289609i \(-0.906475\pi\)
−0.0393712 + 0.999225i \(0.512535\pi\)
\(468\) 0 0
\(469\) 14.8934 + 17.9711i 0.687713 + 0.829826i
\(470\) 0 0
\(471\) 5.73466 3.21633i 0.264239 0.148201i
\(472\) 0 0
\(473\) 34.1947 + 11.8349i 1.57227 + 0.544169i
\(474\) 0 0
\(475\) −10.3649 4.14948i −0.475574 0.190391i
\(476\) 0 0
\(477\) 28.3291 1.99438i 1.29710 0.0913163i
\(478\) 0 0
\(479\) −14.2559 27.6526i −0.651368 1.26348i −0.950932 0.309401i \(-0.899871\pi\)
0.299563 0.954076i \(-0.403159\pi\)
\(480\) 0 0
\(481\) 7.91946 1.92124i 0.361096 0.0876010i
\(482\) 0 0
\(483\) 19.2682 13.3622i 0.876733 0.608002i
\(484\) 0 0
\(485\) −4.33640 + 5.51418i −0.196906 + 0.250386i
\(486\) 0 0
\(487\) 1.33028 + 6.90213i 0.0602806 + 0.312765i 0.999536 0.0304531i \(-0.00969504\pi\)
−0.939256 + 0.343218i \(0.888483\pi\)
\(488\) 0 0
\(489\) −7.06136 + 10.6924i −0.319326 + 0.483529i
\(490\) 0 0
\(491\) 9.07689 14.1239i 0.409634 0.637403i −0.573731 0.819044i \(-0.694504\pi\)
0.983365 + 0.181641i \(0.0581408\pi\)
\(492\) 0 0
\(493\) −26.8229 + 30.9553i −1.20804 + 1.39416i
\(494\) 0 0
\(495\) −20.8266 8.94598i −0.936087 0.402092i
\(496\) 0 0
\(497\) −9.72043 + 40.0681i −0.436021 + 1.79730i
\(498\) 0 0
\(499\) −28.5971 16.5105i −1.28018 0.739113i −0.303300 0.952895i \(-0.598089\pi\)
−0.976881 + 0.213782i \(0.931422\pi\)
\(500\) 0 0
\(501\) 2.61162 16.6858i 0.116678 0.745468i
\(502\) 0 0
\(503\) −2.49099 + 3.49810i −0.111068 + 0.155973i −0.866368 0.499406i \(-0.833552\pi\)
0.755300 + 0.655379i \(0.227491\pi\)
\(504\) 0 0
\(505\) 7.17207 + 6.83856i 0.319153 + 0.304312i
\(506\) 0 0
\(507\) 18.2998 8.08325i 0.812722 0.358990i
\(508\) 0 0
\(509\) −21.5661 + 3.10074i −0.955903 + 0.137438i −0.602576 0.798062i \(-0.705859\pi\)
−0.353327 + 0.935500i \(0.614950\pi\)
\(510\) 0 0
\(511\) 6.42192 21.8710i 0.284089 0.967518i
\(512\) 0 0
\(513\) 16.2121 + 4.58076i 0.715784 + 0.202245i
\(514\) 0 0
\(515\) 1.28451 1.01015i 0.0566024 0.0445126i
\(516\) 0 0
\(517\) 3.44396 36.0668i 0.151465 1.58622i
\(518\) 0 0
\(519\) 3.43152 + 14.9557i 0.150627 + 0.656482i
\(520\) 0 0
\(521\) −4.00476 8.76920i −0.175452 0.384186i 0.801392 0.598139i \(-0.204093\pi\)
−0.976844 + 0.213954i \(0.931366\pi\)
\(522\) 0 0
\(523\) −6.02032 + 5.74036i −0.263250 + 0.251009i −0.810195 0.586160i \(-0.800639\pi\)
0.546945 + 0.837168i \(0.315791\pi\)
\(524\) 0 0
\(525\) −16.3769 + 4.58788i −0.714747 + 0.200232i
\(526\) 0 0
\(527\) −20.9596 + 45.8952i −0.913015 + 1.99922i
\(528\) 0 0
\(529\) −0.457938 + 0.0437278i −0.0199104 + 0.00190121i
\(530\) 0 0
\(531\) −10.2751 3.84548i −0.445902 0.166880i
\(532\) 0 0
\(533\) −2.78316 4.33068i −0.120552 0.187582i
\(534\) 0 0
\(535\) 2.48556i 0.107460i
\(536\) 0 0
\(537\) −3.40874 + 31.5404i −0.147098 + 1.36107i
\(538\) 0 0
\(539\) −5.76183 + 3.70290i −0.248180 + 0.159495i
\(540\) 0 0
\(541\) −2.16925 0.311891i −0.0932634 0.0134092i 0.0955251 0.995427i \(-0.469547\pi\)
−0.188788 + 0.982018i \(0.560456\pi\)
\(542\) 0 0
\(543\) −0.114665 + 9.20382i −0.00492073 + 0.394974i
\(544\) 0 0
\(545\) −2.68636 1.22682i −0.115071 0.0525512i
\(546\) 0 0
\(547\) −9.88563 24.6931i −0.422679 1.05580i −0.975007 0.222174i \(-0.928685\pi\)
0.552328 0.833627i \(-0.313740\pi\)
\(548\) 0 0
\(549\) 1.19914 + 1.97226i 0.0511781 + 0.0841742i
\(550\) 0 0
\(551\) 23.9551 10.9399i 1.02052 0.466056i
\(552\) 0 0
\(553\) 5.65379 + 16.3356i 0.240424 + 0.694659i
\(554\) 0 0
\(555\) −2.94641 + 14.3248i −0.125068 + 0.608052i
\(556\) 0 0
\(557\) −5.97109 7.59286i −0.253003 0.321720i 0.642916 0.765937i \(-0.277724\pi\)
−0.895919 + 0.444217i \(0.853482\pi\)
\(558\) 0 0
\(559\) 0.342313 + 7.18603i 0.0144783 + 0.303937i
\(560\) 0 0
\(561\) 48.8584 + 20.2697i 2.06280 + 0.855789i
\(562\) 0 0
\(563\) 1.64096 + 11.4132i 0.0691584 + 0.481007i 0.994738 + 0.102454i \(0.0326693\pi\)
−0.925579 + 0.378553i \(0.876422\pi\)
\(564\) 0 0
\(565\) −13.0479 22.5997i −0.548930 0.950775i
\(566\) 0 0
\(567\) 23.8462 9.48490i 1.00145 0.398329i
\(568\) 0 0
\(569\) −11.1066 7.90898i −0.465613 0.331562i 0.323056 0.946380i \(-0.395290\pi\)
−0.788669 + 0.614818i \(0.789229\pi\)
\(570\) 0 0
\(571\) −0.284062 + 5.96320i −0.0118876 + 0.249552i 0.985100 + 0.171985i \(0.0550182\pi\)
−0.996987 + 0.0775669i \(0.975285\pi\)
\(572\) 0 0
\(573\) −18.8555 13.7841i −0.787700 0.575841i
\(574\) 0 0
\(575\) −15.8879 3.85436i −0.662571 0.160738i
\(576\) 0 0
\(577\) 4.96863 25.7797i 0.206847 1.07322i −0.718910 0.695103i \(-0.755359\pi\)
0.925757 0.378119i \(-0.123429\pi\)
\(578\) 0 0
\(579\) 1.95510 + 2.10227i 0.0812510 + 0.0873674i
\(580\) 0 0
\(581\) −17.4012 11.1831i −0.721924 0.463953i
\(582\) 0 0
\(583\) −50.9574 26.2704i −2.11044 1.08801i
\(584\) 0 0
\(585\) 0.112271 4.50514i 0.00464183 0.186265i
\(586\) 0 0
\(587\) −23.1431 18.1999i −0.955217 0.751191i 0.0133582 0.999911i \(-0.495748\pi\)
−0.968576 + 0.248720i \(0.919990\pi\)
\(588\) 0 0
\(589\) 24.5162 21.2434i 1.01017 0.875320i
\(590\) 0 0
\(591\) −0.438341 + 0.0574600i −0.0180309 + 0.00236359i
\(592\) 0 0
\(593\) 33.4171 17.2277i 1.37227 0.707457i 0.394851 0.918745i \(-0.370796\pi\)
0.977424 + 0.211288i \(0.0677659\pi\)
\(594\) 0 0
\(595\) −17.2124 + 5.05401i −0.705639 + 0.207194i
\(596\) 0 0
\(597\) 5.43848 10.2341i 0.222582 0.418854i
\(598\) 0 0
\(599\) −1.91514 + 5.53343i −0.0782505 + 0.226090i −0.977340 0.211674i \(-0.932108\pi\)
0.899090 + 0.437764i \(0.144230\pi\)
\(600\) 0 0
\(601\) −6.08524 8.54552i −0.248222 0.348579i 0.671601 0.740913i \(-0.265607\pi\)
−0.919823 + 0.392334i \(0.871668\pi\)
\(602\) 0 0
\(603\) −1.15102 + 24.5291i −0.0468733 + 0.998901i
\(604\) 0 0
\(605\) 18.5820 + 26.0947i 0.755464 + 1.06090i
\(606\) 0 0
\(607\) −13.1542 + 38.0064i −0.533911 + 1.54263i 0.279027 + 0.960283i \(0.409988\pi\)
−0.812938 + 0.582350i \(0.802133\pi\)
\(608\) 0 0
\(609\) 18.8253 35.4254i 0.762840 1.43551i
\(610\) 0 0
\(611\) 6.91155 2.02941i 0.279611 0.0821013i
\(612\) 0 0
\(613\) 1.05817 0.545524i 0.0427390 0.0220335i −0.436725 0.899595i \(-0.643862\pi\)
0.479464 + 0.877562i \(0.340831\pi\)
\(614\) 0 0
\(615\) 9.16011 1.20075i 0.369371 0.0484191i
\(616\) 0 0
\(617\) 6.20162 5.37373i 0.249668 0.216338i −0.521031 0.853537i \(-0.674453\pi\)
0.770699 + 0.637199i \(0.219907\pi\)
\(618\) 0 0
\(619\) −30.7540 24.1852i −1.23611 0.972086i −1.00000 0.000359445i \(-0.999886\pi\)
−0.236108 0.971727i \(-0.575872\pi\)
\(620\) 0 0
\(621\) 24.4529 + 3.26093i 0.981262 + 0.130856i
\(622\) 0 0
\(623\) 40.1488 + 20.6981i 1.60853 + 0.829253i
\(624\) 0 0
\(625\) 3.42887 + 2.20360i 0.137155 + 0.0881440i
\(626\) 0 0
\(627\) −23.1607 24.9042i −0.924949 0.994577i
\(628\) 0 0
\(629\) 6.45892 33.5120i 0.257534 1.33621i
\(630\) 0 0
\(631\) −2.77883 0.674138i −0.110624 0.0268370i 0.180065 0.983655i \(-0.442369\pi\)
−0.290689 + 0.956818i \(0.593884\pi\)
\(632\) 0 0
\(633\) 2.42363 + 1.77177i 0.0963305 + 0.0704215i
\(634\) 0 0
\(635\) −0.594544 + 12.4810i −0.0235938 + 0.495294i
\(636\) 0 0
\(637\) −1.10923 0.789876i −0.0439491 0.0312960i
\(638\) 0 0
\(639\) −35.9505 + 24.2735i −1.42218 + 0.960247i
\(640\) 0 0
\(641\) −17.5025 30.3151i −0.691305 1.19738i −0.971410 0.237407i \(-0.923703\pi\)
0.280105 0.959969i \(-0.409631\pi\)
\(642\) 0 0
\(643\) −3.61977 25.1761i −0.142750 0.992848i −0.927710 0.373301i \(-0.878226\pi\)
0.784960 0.619546i \(-0.212683\pi\)
\(644\) 0 0
\(645\) −11.9253 4.94740i −0.469557 0.194804i
\(646\) 0 0
\(647\) −0.0372958 0.782935i −0.00146625 0.0307804i 0.998016 0.0629665i \(-0.0200561\pi\)
−0.999482 + 0.0321861i \(0.989753\pi\)
\(648\) 0 0
\(649\) 13.6909 + 17.4094i 0.537414 + 0.683377i
\(650\) 0 0
\(651\) 9.95581 48.4029i 0.390199 1.89706i
\(652\) 0 0
\(653\) −4.66960 13.4919i −0.182735 0.527979i 0.816011 0.578036i \(-0.196181\pi\)
−0.998746 + 0.0500571i \(0.984060\pi\)
\(654\) 0 0
\(655\) 25.5409 11.6642i 0.997967 0.455756i
\(656\) 0 0
\(657\) 20.4914 12.4588i 0.799445 0.486065i
\(658\) 0 0
\(659\) 6.02945 + 15.0608i 0.234874 + 0.586687i 0.998242 0.0592776i \(-0.0188797\pi\)
−0.763368 + 0.645964i \(0.776455\pi\)
\(660\) 0 0
\(661\) 19.7598 + 9.02398i 0.768566 + 0.350992i 0.760807 0.648978i \(-0.224803\pi\)
0.00775838 + 0.999970i \(0.497530\pi\)
\(662\) 0 0
\(663\) −0.131011 + 10.5159i −0.00508804 + 0.408403i
\(664\) 0 0
\(665\) 11.4164 + 1.64143i 0.442710 + 0.0636521i
\(666\) 0 0
\(667\) 32.4413 20.8488i 1.25613 0.807267i
\(668\) 0 0
\(669\) 4.44210 41.1019i 0.171742 1.58909i
\(670\) 0 0
\(671\) 4.65964i 0.179883i
\(672\) 0 0
\(673\) 18.9480 + 29.4836i 0.730391 + 1.13651i 0.985513 + 0.169602i \(0.0542482\pi\)
−0.255121 + 0.966909i \(0.582115\pi\)
\(674\) 0 0
\(675\) −15.9872 8.03609i −0.615347 0.309309i
\(676\) 0 0
\(677\) −44.6510 + 4.26366i −1.71608 + 0.163866i −0.906233 0.422778i \(-0.861055\pi\)
−0.809845 + 0.586644i \(0.800449\pi\)
\(678\) 0 0
\(679\) −6.66062 + 14.5847i −0.255611 + 0.559710i
\(680\) 0 0
\(681\) −34.1811 + 9.57561i −1.30982 + 0.366938i
\(682\) 0 0
\(683\) −4.89897 + 4.67116i −0.187454 + 0.178737i −0.777995 0.628271i \(-0.783763\pi\)
0.590541 + 0.807008i \(0.298915\pi\)
\(684\) 0 0
\(685\) 0.876931 + 1.92021i 0.0335058 + 0.0733675i
\(686\) 0 0
\(687\) −2.01194 8.76871i −0.0767604 0.334547i
\(688\) 0 0
\(689\) 1.08348 11.3467i 0.0412773 0.432275i
\(690\) 0 0
\(691\) 16.3921 12.8909i 0.623583 0.490391i −0.255658 0.966767i \(-0.582292\pi\)
0.879242 + 0.476376i \(0.158050\pi\)
\(692\) 0 0
\(693\) −51.0805 8.64821i −1.94039 0.328518i
\(694\) 0 0
\(695\) −6.88788 + 23.4580i −0.261272 + 0.889811i
\(696\) 0 0
\(697\) −21.3399 + 3.06822i −0.808308 + 0.116217i
\(698\) 0 0
\(699\) 25.9295 11.4534i 0.980745 0.433208i
\(700\) 0 0
\(701\) 25.8412 + 24.6396i 0.976009 + 0.930623i 0.997607 0.0691436i \(-0.0220267\pi\)
−0.0215972 + 0.999767i \(0.506875\pi\)
\(702\) 0 0
\(703\) −12.7282 + 17.8742i −0.480052 + 0.674139i
\(704\) 0 0
\(705\) −1.99899 + 12.7717i −0.0752864 + 0.481011i
\(706\) 0 0
\(707\) 19.6155 + 11.3250i 0.737718 + 0.425922i
\(708\) 0 0
\(709\) 5.74258 23.6712i 0.215667 0.888992i −0.756366 0.654148i \(-0.773027\pi\)
0.972033 0.234843i \(-0.0754577\pi\)
\(710\) 0 0
\(711\) −7.17783 + 16.7103i −0.269190 + 0.626685i
\(712\) 0 0
\(713\) 31.1074 35.8999i 1.16498 1.34446i
\(714\) 0 0
\(715\) −4.91848 + 7.65330i −0.183941 + 0.286217i
\(716\) 0 0
\(717\) 2.84886 4.31380i 0.106393 0.161102i
\(718\) 0 0
\(719\) 0.787928 + 4.08816i 0.0293847 + 0.152463i 0.993658 0.112449i \(-0.0358694\pi\)
−0.964273 + 0.264911i \(0.914657\pi\)
\(720\) 0 0
\(721\) 2.30882 2.93591i 0.0859850 0.109339i
\(722\) 0 0
\(723\) 30.9172 21.4406i 1.14982 0.797386i
\(724\) 0 0
\(725\) −27.1822 + 6.59432i −1.00952 + 0.244907i
\(726\) 0 0
\(727\) −5.16258 10.0140i −0.191470 0.371399i 0.773486 0.633814i \(-0.218511\pi\)
−0.964955 + 0.262415i \(0.915481\pi\)
\(728\) 0 0
\(729\) 25.2659 + 9.52014i 0.935775 + 0.352598i
\(730\) 0 0
\(731\) 27.9711 + 11.1979i 1.03455 + 0.414170i
\(732\) 0 0
\(733\) 5.54878 + 1.92045i 0.204949 + 0.0709336i 0.427614 0.903962i \(-0.359354\pi\)
−0.222665 + 0.974895i \(0.571476\pi\)
\(734\) 0 0
\(735\) 2.13142 1.19542i 0.0786187 0.0440939i
\(736\) 0 0
\(737\) 27.7106 41.1038i 1.02073 1.51408i
\(738\) 0 0
\(739\) −11.0929 + 7.89920i −0.408058 + 0.290577i −0.765596 0.643322i \(-0.777556\pi\)
0.357538 + 0.933899i \(0.383616\pi\)
\(740\) 0 0
\(741\) 2.88530 6.11515i 0.105994 0.224646i
\(742\) 0 0
\(743\) 7.33380 18.3190i 0.269051 0.672057i −0.730894 0.682490i \(-0.760897\pi\)
0.999946 + 0.0104334i \(0.00332110\pi\)
\(744\) 0 0
\(745\) 2.84492 + 9.68892i 0.104230 + 0.354975i
\(746\) 0 0
\(747\) −5.60904 21.0270i −0.205224 0.769338i
\(748\) 0 0
\(749\) 1.33936 + 5.52091i 0.0489391 + 0.201730i
\(750\) 0 0
\(751\) −24.5196 28.2972i −0.894734 1.03258i −0.999276 0.0380577i \(-0.987883\pi\)
0.104541 0.994521i \(-0.466663\pi\)
\(752\) 0 0
\(753\) −15.3007 + 15.6518i −0.557588 + 0.570382i
\(754\) 0 0
\(755\) −18.1471 + 3.49758i −0.660442 + 0.127290i
\(756\) 0 0
\(757\) 9.05969 17.5733i 0.329280 0.638714i −0.664842 0.746984i \(-0.731501\pi\)
0.994121 + 0.108270i \(0.0345313\pi\)
\(758\) 0 0
\(759\) −38.7597 31.2702i −1.40689 1.13504i
\(760\) 0 0
\(761\) 10.5028 + 9.10074i 0.380727 + 0.329902i 0.824109 0.566431i \(-0.191676\pi\)
−0.443382 + 0.896333i \(0.646222\pi\)
\(762\) 0 0
\(763\) −6.62800 1.27744i −0.239950 0.0462465i
\(764\) 0 0
\(765\) −16.9672 8.26557i −0.613451 0.298842i
\(766\) 0 0
\(767\) −2.20169 + 3.81344i −0.0794983 + 0.137695i
\(768\) 0 0
\(769\) −0.686755 0.0327142i −0.0247650 0.00117970i 0.0351958 0.999380i \(-0.488795\pi\)
−0.0599608 + 0.998201i \(0.519098\pi\)
\(770\) 0 0
\(771\) −2.59296 + 2.91817i −0.0933831 + 0.105095i
\(772\) 0 0
\(773\) −15.8781 + 16.6525i −0.571095 + 0.598947i −0.944415 0.328755i \(-0.893371\pi\)
0.373320 + 0.927703i \(0.378219\pi\)