Properties

Label 1110.2.o.a.253.4
Level $1110$
Weight $2$
Character 1110.253
Analytic conductor $8.863$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.o (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 253.4
Character \(\chi\) \(=\) 1110.253
Dual form 1110.2.o.a.487.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-0.530977 + 2.17211i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.93388 + 1.93388i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-0.530977 + 2.17211i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.93388 + 1.93388i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(0.530977 - 2.17211i) q^{10} -2.54109i q^{11} +(-0.707107 + 0.707107i) q^{12} -2.64021 q^{13} +(1.93388 - 1.93388i) q^{14} +(-1.16046 - 1.91137i) q^{15} +1.00000 q^{16} -3.60448i q^{17} +1.00000i q^{18} +(-2.47157 - 2.47157i) q^{19} +(-0.530977 + 2.17211i) q^{20} -2.73491i q^{21} +2.54109i q^{22} -4.49206 q^{23} +(0.707107 - 0.707107i) q^{24} +(-4.43613 - 2.30668i) q^{25} +2.64021 q^{26} +(0.707107 + 0.707107i) q^{27} +(-1.93388 + 1.93388i) q^{28} +(4.58885 - 4.58885i) q^{29} +(1.16046 + 1.91137i) q^{30} +(7.33111 + 7.33111i) q^{31} -1.00000 q^{32} +(1.79682 + 1.79682i) q^{33} +3.60448i q^{34} +(-3.17375 - 5.22744i) q^{35} -1.00000i q^{36} +(5.87071 + 1.59211i) q^{37} +(2.47157 + 2.47157i) q^{38} +(1.86691 - 1.86691i) q^{39} +(0.530977 - 2.17211i) q^{40} -4.31993i q^{41} +2.73491i q^{42} -3.12360 q^{43} -2.54109i q^{44} +(2.17211 + 0.530977i) q^{45} +4.49206 q^{46} +(4.51187 - 4.51187i) q^{47} +(-0.707107 + 0.707107i) q^{48} -0.479758i q^{49} +(4.43613 + 2.30668i) q^{50} +(2.54875 + 2.54875i) q^{51} -2.64021 q^{52} +(-0.301411 - 0.301411i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(5.51953 + 1.34926i) q^{55} +(1.93388 - 1.93388i) q^{56} +3.49532 q^{57} +(-4.58885 + 4.58885i) q^{58} +(-0.813625 - 0.813625i) q^{59} +(-1.16046 - 1.91137i) q^{60} +(-0.867564 - 0.867564i) q^{61} +(-7.33111 - 7.33111i) q^{62} +(1.93388 + 1.93388i) q^{63} +1.00000 q^{64} +(1.40189 - 5.73482i) q^{65} +(-1.79682 - 1.79682i) q^{66} +(5.77261 + 5.77261i) q^{67} -3.60448i q^{68} +(3.17637 - 3.17637i) q^{69} +(3.17375 + 5.22744i) q^{70} -2.30317 q^{71} +1.00000i q^{72} +(-3.70992 + 3.70992i) q^{73} +(-5.87071 - 1.59211i) q^{74} +(4.76789 - 1.50574i) q^{75} +(-2.47157 - 2.47157i) q^{76} +(4.91416 + 4.91416i) q^{77} +(-1.86691 + 1.86691i) q^{78} +(-4.70094 - 4.70094i) q^{79} +(-0.530977 + 2.17211i) q^{80} -1.00000 q^{81} +4.31993i q^{82} +(-0.524568 - 0.524568i) q^{83} -2.73491i q^{84} +(7.82932 + 1.91389i) q^{85} +3.12360 q^{86} +6.48962i q^{87} +2.54109i q^{88} +(6.69075 - 6.69075i) q^{89} +(-2.17211 - 0.530977i) q^{90} +(5.10583 - 5.10583i) q^{91} -4.49206 q^{92} -10.3677 q^{93} +(-4.51187 + 4.51187i) q^{94} +(6.68086 - 4.05617i) q^{95} +(0.707107 - 0.707107i) q^{96} -17.0294i q^{97} +0.479758i q^{98} -2.54109 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 36q^{2} + 36q^{4} + 4q^{5} + 4q^{7} - 36q^{8} + O(q^{10}) \) \( 36q - 36q^{2} + 36q^{4} + 4q^{5} + 4q^{7} - 36q^{8} - 4q^{10} - 8q^{13} - 4q^{14} + 36q^{16} - 4q^{19} + 4q^{20} + 4q^{25} + 8q^{26} + 4q^{28} - 36q^{29} - 4q^{31} - 36q^{32} + 4q^{33} + 28q^{35} + 28q^{37} + 4q^{38} - 4q^{39} - 4q^{40} - 32q^{43} + 16q^{47} - 4q^{50} - 8q^{52} - 8q^{53} - 8q^{55} - 4q^{56} - 8q^{57} + 36q^{58} + 4q^{59} - 4q^{61} + 4q^{62} - 4q^{63} + 36q^{64} - 52q^{65} - 4q^{66} - 16q^{67} + 8q^{69} - 28q^{70} - 8q^{71} + 4q^{73} - 28q^{74} + 16q^{75} - 4q^{76} - 8q^{77} + 4q^{78} + 12q^{79} + 4q^{80} - 36q^{81} + 8q^{83} - 8q^{85} + 32q^{86} + 24q^{89} + 56q^{91} - 8q^{93} - 16q^{94} + 20q^{95} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −0.707107 + 0.707107i −0.408248 + 0.408248i
\(4\) 1.00000 0.500000
\(5\) −0.530977 + 2.17211i −0.237460 + 0.971397i
\(6\) 0.707107 0.707107i 0.288675 0.288675i
\(7\) −1.93388 + 1.93388i −0.730937 + 0.730937i −0.970805 0.239869i \(-0.922896\pi\)
0.239869 + 0.970805i \(0.422896\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000i 0.333333i
\(10\) 0.530977 2.17211i 0.167910 0.686882i
\(11\) 2.54109i 0.766168i −0.923714 0.383084i \(-0.874862\pi\)
0.923714 0.383084i \(-0.125138\pi\)
\(12\) −0.707107 + 0.707107i −0.204124 + 0.204124i
\(13\) −2.64021 −0.732261 −0.366131 0.930563i \(-0.619318\pi\)
−0.366131 + 0.930563i \(0.619318\pi\)
\(14\) 1.93388 1.93388i 0.516850 0.516850i
\(15\) −1.16046 1.91137i −0.299629 0.493514i
\(16\) 1.00000 0.250000
\(17\) 3.60448i 0.874214i −0.899410 0.437107i \(-0.856003\pi\)
0.899410 0.437107i \(-0.143997\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −2.47157 2.47157i −0.567017 0.567017i 0.364275 0.931291i \(-0.381317\pi\)
−0.931291 + 0.364275i \(0.881317\pi\)
\(20\) −0.530977 + 2.17211i −0.118730 + 0.485699i
\(21\) 2.73491i 0.596807i
\(22\) 2.54109i 0.541763i
\(23\) −4.49206 −0.936659 −0.468329 0.883554i \(-0.655144\pi\)
−0.468329 + 0.883554i \(0.655144\pi\)
\(24\) 0.707107 0.707107i 0.144338 0.144338i
\(25\) −4.43613 2.30668i −0.887225 0.461336i
\(26\) 2.64021 0.517787
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) −1.93388 + 1.93388i −0.365468 + 0.365468i
\(29\) 4.58885 4.58885i 0.852129 0.852129i −0.138266 0.990395i \(-0.544153\pi\)
0.990395 + 0.138266i \(0.0441530\pi\)
\(30\) 1.16046 + 1.91137i 0.211869 + 0.348967i
\(31\) 7.33111 + 7.33111i 1.31671 + 1.31671i 0.916368 + 0.400338i \(0.131107\pi\)
0.400338 + 0.916368i \(0.368893\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.79682 + 1.79682i 0.312787 + 0.312787i
\(34\) 3.60448i 0.618163i
\(35\) −3.17375 5.22744i −0.536461 0.883598i
\(36\) 1.00000i 0.166667i
\(37\) 5.87071 + 1.59211i 0.965138 + 0.261741i
\(38\) 2.47157 + 2.47157i 0.400941 + 0.400941i
\(39\) 1.86691 1.86691i 0.298944 0.298944i
\(40\) 0.530977 2.17211i 0.0839549 0.343441i
\(41\) 4.31993i 0.674660i −0.941387 0.337330i \(-0.890476\pi\)
0.941387 0.337330i \(-0.109524\pi\)
\(42\) 2.73491i 0.422006i
\(43\) −3.12360 −0.476344 −0.238172 0.971223i \(-0.576548\pi\)
−0.238172 + 0.971223i \(0.576548\pi\)
\(44\) 2.54109i 0.383084i
\(45\) 2.17211 + 0.530977i 0.323799 + 0.0791534i
\(46\) 4.49206 0.662318
\(47\) 4.51187 4.51187i 0.658123 0.658123i −0.296812 0.954936i \(-0.595924\pi\)
0.954936 + 0.296812i \(0.0959236\pi\)
\(48\) −0.707107 + 0.707107i −0.102062 + 0.102062i
\(49\) 0.479758i 0.0685368i
\(50\) 4.43613 + 2.30668i 0.627363 + 0.326214i
\(51\) 2.54875 + 2.54875i 0.356896 + 0.356896i
\(52\) −2.64021 −0.366131
\(53\) −0.301411 0.301411i −0.0414020 0.0414020i 0.686103 0.727505i \(-0.259320\pi\)
−0.727505 + 0.686103i \(0.759320\pi\)
\(54\) −0.707107 0.707107i −0.0962250 0.0962250i
\(55\) 5.51953 + 1.34926i 0.744253 + 0.181934i
\(56\) 1.93388 1.93388i 0.258425 0.258425i
\(57\) 3.49532 0.462967
\(58\) −4.58885 + 4.58885i −0.602546 + 0.602546i
\(59\) −0.813625 0.813625i −0.105925 0.105925i 0.652158 0.758083i \(-0.273864\pi\)
−0.758083 + 0.652158i \(0.773864\pi\)
\(60\) −1.16046 1.91137i −0.149814 0.246757i
\(61\) −0.867564 0.867564i −0.111080 0.111080i 0.649382 0.760462i \(-0.275028\pi\)
−0.760462 + 0.649382i \(0.775028\pi\)
\(62\) −7.33111 7.33111i −0.931051 0.931051i
\(63\) 1.93388 + 1.93388i 0.243646 + 0.243646i
\(64\) 1.00000 0.125000
\(65\) 1.40189 5.73482i 0.173883 0.711317i
\(66\) −1.79682 1.79682i −0.221174 0.221174i
\(67\) 5.77261 + 5.77261i 0.705237 + 0.705237i 0.965530 0.260293i \(-0.0838191\pi\)
−0.260293 + 0.965530i \(0.583819\pi\)
\(68\) 3.60448i 0.437107i
\(69\) 3.17637 3.17637i 0.382389 0.382389i
\(70\) 3.17375 + 5.22744i 0.379336 + 0.624798i
\(71\) −2.30317 −0.273336 −0.136668 0.990617i \(-0.543639\pi\)
−0.136668 + 0.990617i \(0.543639\pi\)
\(72\) 1.00000i 0.117851i
\(73\) −3.70992 + 3.70992i −0.434213 + 0.434213i −0.890059 0.455846i \(-0.849337\pi\)
0.455846 + 0.890059i \(0.349337\pi\)
\(74\) −5.87071 1.59211i −0.682456 0.185079i
\(75\) 4.76789 1.50574i 0.550548 0.173868i
\(76\) −2.47157 2.47157i −0.283508 0.283508i
\(77\) 4.91416 + 4.91416i 0.560020 + 0.560020i
\(78\) −1.86691 + 1.86691i −0.211386 + 0.211386i
\(79\) −4.70094 4.70094i −0.528897 0.528897i 0.391347 0.920243i \(-0.372009\pi\)
−0.920243 + 0.391347i \(0.872009\pi\)
\(80\) −0.530977 + 2.17211i −0.0593651 + 0.242849i
\(81\) −1.00000 −0.111111
\(82\) 4.31993i 0.477056i
\(83\) −0.524568 0.524568i −0.0575788 0.0575788i 0.677731 0.735310i \(-0.262963\pi\)
−0.735310 + 0.677731i \(0.762963\pi\)
\(84\) 2.73491i 0.298404i
\(85\) 7.82932 + 1.91389i 0.849209 + 0.207591i
\(86\) 3.12360 0.336826
\(87\) 6.48962i 0.695760i
\(88\) 2.54109i 0.270881i
\(89\) 6.69075 6.69075i 0.709218 0.709218i −0.257153 0.966371i \(-0.582784\pi\)
0.966371 + 0.257153i \(0.0827844\pi\)
\(90\) −2.17211 0.530977i −0.228961 0.0559699i
\(91\) 5.10583 5.10583i 0.535237 0.535237i
\(92\) −4.49206 −0.468329
\(93\) −10.3677 −1.07509
\(94\) −4.51187 + 4.51187i −0.465363 + 0.465363i
\(95\) 6.68086 4.05617i 0.685442 0.416154i
\(96\) 0.707107 0.707107i 0.0721688 0.0721688i
\(97\) 17.0294i 1.72908i −0.502565 0.864539i \(-0.667610\pi\)
0.502565 0.864539i \(-0.332390\pi\)
\(98\) 0.479758i 0.0484628i
\(99\) −2.54109 −0.255389
\(100\) −4.43613 2.30668i −0.443613 0.230668i
\(101\) 18.0572i 1.79675i −0.439225 0.898377i \(-0.644747\pi\)
0.439225 0.898377i \(-0.355253\pi\)
\(102\) −2.54875 2.54875i −0.252364 0.252364i
\(103\) 2.66961i 0.263044i −0.991313 0.131522i \(-0.958014\pi\)
0.991313 0.131522i \(-0.0419864\pi\)
\(104\) 2.64021 0.258894
\(105\) 5.94054 + 1.45218i 0.579737 + 0.141718i
\(106\) 0.301411 + 0.301411i 0.0292757 + 0.0292757i
\(107\) −0.404456 + 0.404456i −0.0391002 + 0.0391002i −0.726387 0.687286i \(-0.758802\pi\)
0.687286 + 0.726387i \(0.258802\pi\)
\(108\) 0.707107 + 0.707107i 0.0680414 + 0.0680414i
\(109\) −1.04982 1.04982i −0.100554 0.100554i 0.655040 0.755594i \(-0.272652\pi\)
−0.755594 + 0.655040i \(0.772652\pi\)
\(110\) −5.51953 1.34926i −0.526267 0.128647i
\(111\) −5.27701 + 3.02543i −0.500871 + 0.287161i
\(112\) −1.93388 + 1.93388i −0.182734 + 0.182734i
\(113\) 5.71763i 0.537869i −0.963158 0.268935i \(-0.913328\pi\)
0.963158 0.268935i \(-0.0866715\pi\)
\(114\) −3.49532 −0.327367
\(115\) 2.38518 9.75725i 0.222419 0.909868i
\(116\) 4.58885 4.58885i 0.426064 0.426064i
\(117\) 2.64021i 0.244087i
\(118\) 0.813625 + 0.813625i 0.0749002 + 0.0749002i
\(119\) 6.97061 + 6.97061i 0.638995 + 0.638995i
\(120\) 1.16046 + 1.91137i 0.105935 + 0.174484i
\(121\) 4.54285 0.412987
\(122\) 0.867564 + 0.867564i 0.0785456 + 0.0785456i
\(123\) 3.05465 + 3.05465i 0.275429 + 0.275429i
\(124\) 7.33111 + 7.33111i 0.658353 + 0.658353i
\(125\) 7.36585 8.41096i 0.658822 0.752299i
\(126\) −1.93388 1.93388i −0.172283 0.172283i
\(127\) 3.15767 3.15767i 0.280198 0.280198i −0.552990 0.833188i \(-0.686513\pi\)
0.833188 + 0.552990i \(0.186513\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 2.20872 2.20872i 0.194467 0.194467i
\(130\) −1.40189 + 5.73482i −0.122954 + 0.502977i
\(131\) −12.5592 12.5592i −1.09730 1.09730i −0.994725 0.102577i \(-0.967291\pi\)
−0.102577 0.994725i \(-0.532709\pi\)
\(132\) 1.79682 + 1.79682i 0.156393 + 0.156393i
\(133\) 9.55941 0.828906
\(134\) −5.77261 5.77261i −0.498678 0.498678i
\(135\) −1.91137 + 1.16046i −0.164505 + 0.0998762i
\(136\) 3.60448i 0.309081i
\(137\) −12.7858 + 12.7858i −1.09236 + 1.09236i −0.0970857 + 0.995276i \(0.530952\pi\)
−0.995276 + 0.0970857i \(0.969048\pi\)
\(138\) −3.17637 + 3.17637i −0.270390 + 0.270390i
\(139\) −3.82368 −0.324321 −0.162160 0.986764i \(-0.551846\pi\)
−0.162160 + 0.986764i \(0.551846\pi\)
\(140\) −3.17375 5.22744i −0.268231 0.441799i
\(141\) 6.38074i 0.537355i
\(142\) 2.30317 0.193278
\(143\) 6.70901i 0.561035i
\(144\) 1.00000i 0.0833333i
\(145\) 7.53092 + 12.4041i 0.625409 + 1.03010i
\(146\) 3.70992 3.70992i 0.307035 0.307035i
\(147\) 0.339240 + 0.339240i 0.0279800 + 0.0279800i
\(148\) 5.87071 + 1.59211i 0.482569 + 0.130870i
\(149\) 4.92924i 0.403819i −0.979404 0.201909i \(-0.935285\pi\)
0.979404 0.201909i \(-0.0647147\pi\)
\(150\) −4.76789 + 1.50574i −0.389296 + 0.122943i
\(151\) 2.56917i 0.209076i 0.994521 + 0.104538i \(0.0333363\pi\)
−0.994521 + 0.104538i \(0.966664\pi\)
\(152\) 2.47157 + 2.47157i 0.200471 + 0.200471i
\(153\) −3.60448 −0.291405
\(154\) −4.91416 4.91416i −0.395994 0.395994i
\(155\) −19.8166 + 12.0313i −1.59171 + 0.966379i
\(156\) 1.86691 1.86691i 0.149472 0.149472i
\(157\) 10.7956 10.7956i 0.861586 0.861586i −0.129937 0.991522i \(-0.541477\pi\)
0.991522 + 0.129937i \(0.0414774\pi\)
\(158\) 4.70094 + 4.70094i 0.373986 + 0.373986i
\(159\) 0.426260 0.0338046
\(160\) 0.530977 2.17211i 0.0419774 0.171720i
\(161\) 8.68709 8.68709i 0.684638 0.684638i
\(162\) 1.00000 0.0785674
\(163\) 2.00094i 0.156726i 0.996925 + 0.0783628i \(0.0249693\pi\)
−0.996925 + 0.0783628i \(0.975031\pi\)
\(164\) 4.31993i 0.337330i
\(165\) −4.85697 + 2.94883i −0.378115 + 0.229566i
\(166\) 0.524568 + 0.524568i 0.0407144 + 0.0407144i
\(167\) 3.34903i 0.259156i −0.991569 0.129578i \(-0.958638\pi\)
0.991569 0.129578i \(-0.0413622\pi\)
\(168\) 2.73491i 0.211003i
\(169\) −6.02931 −0.463793
\(170\) −7.82932 1.91389i −0.600481 0.146789i
\(171\) −2.47157 + 2.47157i −0.189006 + 0.189006i
\(172\) −3.12360 −0.238172
\(173\) 7.11846 7.11846i 0.541206 0.541206i −0.382676 0.923882i \(-0.624998\pi\)
0.923882 + 0.382676i \(0.124998\pi\)
\(174\) 6.48962i 0.491977i
\(175\) 13.0398 4.11808i 0.985713 0.311298i
\(176\) 2.54109i 0.191542i
\(177\) 1.15064 0.0864873
\(178\) −6.69075 + 6.69075i −0.501493 + 0.501493i
\(179\) −8.68094 + 8.68094i −0.648844 + 0.648844i −0.952714 0.303869i \(-0.901721\pi\)
0.303869 + 0.952714i \(0.401721\pi\)
\(180\) 2.17211 + 0.530977i 0.161900 + 0.0395767i
\(181\) 14.0432 1.04382 0.521912 0.852999i \(-0.325219\pi\)
0.521912 + 0.852999i \(0.325219\pi\)
\(182\) −5.10583 + 5.10583i −0.378470 + 0.378470i
\(183\) 1.22692 0.0906966
\(184\) 4.49206 0.331159
\(185\) −6.57544 + 11.9064i −0.483436 + 0.875380i
\(186\) 10.3677 0.760200
\(187\) −9.15930 −0.669795
\(188\) 4.51187 4.51187i 0.329062 0.329062i
\(189\) −2.73491 −0.198936
\(190\) −6.68086 + 4.05617i −0.484681 + 0.294266i
\(191\) −1.64289 + 1.64289i −0.118876 + 0.118876i −0.764042 0.645166i \(-0.776788\pi\)
0.645166 + 0.764042i \(0.276788\pi\)
\(192\) −0.707107 + 0.707107i −0.0510310 + 0.0510310i
\(193\) −13.9313 −1.00280 −0.501398 0.865217i \(-0.667181\pi\)
−0.501398 + 0.865217i \(0.667181\pi\)
\(194\) 17.0294i 1.22264i
\(195\) 3.06384 + 5.04642i 0.219406 + 0.361381i
\(196\) 0.479758i 0.0342684i
\(197\) 18.7947 18.7947i 1.33907 1.33907i 0.442107 0.896962i \(-0.354231\pi\)
0.896962 0.442107i \(-0.145769\pi\)
\(198\) 2.54109 0.180588
\(199\) 3.23872 3.23872i 0.229587 0.229587i −0.582933 0.812520i \(-0.698095\pi\)
0.812520 + 0.582933i \(0.198095\pi\)
\(200\) 4.43613 + 2.30668i 0.313681 + 0.163107i
\(201\) −8.16371 −0.575824
\(202\) 18.0572i 1.27050i
\(203\) 17.7486i 1.24570i
\(204\) 2.54875 + 2.54875i 0.178448 + 0.178448i
\(205\) 9.38336 + 2.29378i 0.655362 + 0.160205i
\(206\) 2.66961i 0.186000i
\(207\) 4.49206i 0.312220i
\(208\) −2.64021 −0.183065
\(209\) −6.28048 + 6.28048i −0.434430 + 0.434430i
\(210\) −5.94054 1.45218i −0.409936 0.100210i
\(211\) −13.4040 −0.922767 −0.461384 0.887201i \(-0.652647\pi\)
−0.461384 + 0.887201i \(0.652647\pi\)
\(212\) −0.301411 0.301411i −0.0207010 0.0207010i
\(213\) 1.62859 1.62859i 0.111589 0.111589i
\(214\) 0.404456 0.404456i 0.0276480 0.0276480i
\(215\) 1.65856 6.78480i 0.113113 0.462720i
\(216\) −0.707107 0.707107i −0.0481125 0.0481125i
\(217\) −28.3549 −1.92486
\(218\) 1.04982 + 1.04982i 0.0711026 + 0.0711026i
\(219\) 5.24662i 0.354534i
\(220\) 5.51953 + 1.34926i 0.372127 + 0.0909672i
\(221\) 9.51656i 0.640153i
\(222\) 5.27701 3.02543i 0.354169 0.203053i
\(223\) −18.2552 18.2552i −1.22246 1.22246i −0.966754 0.255707i \(-0.917692\pi\)
−0.255707 0.966754i \(-0.582308\pi\)
\(224\) 1.93388 1.93388i 0.129213 0.129213i
\(225\) −2.30668 + 4.43613i −0.153779 + 0.295742i
\(226\) 5.71763i 0.380331i
\(227\) 20.3161i 1.34843i 0.738535 + 0.674215i \(0.235518\pi\)
−0.738535 + 0.674215i \(0.764482\pi\)
\(228\) 3.49532 0.231484
\(229\) 23.8741i 1.57764i 0.614623 + 0.788821i \(0.289308\pi\)
−0.614623 + 0.788821i \(0.710692\pi\)
\(230\) −2.38518 + 9.75725i −0.157274 + 0.643374i
\(231\) −6.94967 −0.457255
\(232\) −4.58885 + 4.58885i −0.301273 + 0.301273i
\(233\) −0.0502450 + 0.0502450i −0.00329166 + 0.00329166i −0.708751 0.705459i \(-0.750741\pi\)
0.705459 + 0.708751i \(0.250741\pi\)
\(234\) 2.64021i 0.172596i
\(235\) 7.40457 + 12.1960i 0.483021 + 0.795577i
\(236\) −0.813625 0.813625i −0.0529625 0.0529625i
\(237\) 6.64813 0.431842
\(238\) −6.97061 6.97061i −0.451838 0.451838i
\(239\) −11.3273 11.3273i −0.732705 0.732705i 0.238450 0.971155i \(-0.423361\pi\)
−0.971155 + 0.238450i \(0.923361\pi\)
\(240\) −1.16046 1.91137i −0.0749071 0.123379i
\(241\) −3.69272 + 3.69272i −0.237869 + 0.237869i −0.815967 0.578098i \(-0.803795\pi\)
0.578098 + 0.815967i \(0.303795\pi\)
\(242\) −4.54285 −0.292026
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) −0.867564 0.867564i −0.0555401 0.0555401i
\(245\) 1.04209 + 0.254740i 0.0665765 + 0.0162748i
\(246\) −3.05465 3.05465i −0.194757 0.194757i
\(247\) 6.52545 + 6.52545i 0.415204 + 0.415204i
\(248\) −7.33111 7.33111i −0.465526 0.465526i
\(249\) 0.741852 0.0470129
\(250\) −7.36585 + 8.41096i −0.465857 + 0.531956i
\(251\) −8.29215 8.29215i −0.523396 0.523396i 0.395199 0.918595i \(-0.370675\pi\)
−0.918595 + 0.395199i \(0.870675\pi\)
\(252\) 1.93388 + 1.93388i 0.121823 + 0.121823i
\(253\) 11.4147i 0.717638i
\(254\) −3.15767 + 3.15767i −0.198130 + 0.198130i
\(255\) −6.88949 + 4.18284i −0.431437 + 0.261939i
\(256\) 1.00000 0.0625000
\(257\) 1.06813i 0.0666279i −0.999445 0.0333140i \(-0.989394\pi\)
0.999445 0.0333140i \(-0.0106061\pi\)
\(258\) −2.20872 + 2.20872i −0.137509 + 0.137509i
\(259\) −14.4322 + 8.27428i −0.896771 + 0.514139i
\(260\) 1.40189 5.73482i 0.0869415 0.355658i
\(261\) −4.58885 4.58885i −0.284043 0.284043i
\(262\) 12.5592 + 12.5592i 0.775909 + 0.775909i
\(263\) −22.2567 + 22.2567i −1.37240 + 1.37240i −0.515538 + 0.856867i \(0.672408\pi\)
−0.856867 + 0.515538i \(0.827592\pi\)
\(264\) −1.79682 1.79682i −0.110587 0.110587i
\(265\) 0.814742 0.494656i 0.0500492 0.0303865i
\(266\) −9.55941 −0.586125
\(267\) 9.46214i 0.579074i
\(268\) 5.77261 + 5.77261i 0.352618 + 0.352618i
\(269\) 1.98048i 0.120752i 0.998176 + 0.0603760i \(0.0192300\pi\)
−0.998176 + 0.0603760i \(0.980770\pi\)
\(270\) 1.91137 1.16046i 0.116322 0.0706231i
\(271\) −20.2119 −1.22779 −0.613894 0.789389i \(-0.710398\pi\)
−0.613894 + 0.789389i \(0.710398\pi\)
\(272\) 3.60448i 0.218553i
\(273\) 7.22074i 0.437019i
\(274\) 12.7858 12.7858i 0.772416 0.772416i
\(275\) −5.86149 + 11.2726i −0.353461 + 0.679763i
\(276\) 3.17637 3.17637i 0.191195 0.191195i
\(277\) −26.8225 −1.61161 −0.805805 0.592181i \(-0.798267\pi\)
−0.805805 + 0.592181i \(0.798267\pi\)
\(278\) 3.82368 0.229329
\(279\) 7.33111 7.33111i 0.438902 0.438902i
\(280\) 3.17375 + 5.22744i 0.189668 + 0.312399i
\(281\) 11.8287 11.8287i 0.705642 0.705642i −0.259974 0.965616i \(-0.583714\pi\)
0.965616 + 0.259974i \(0.0837140\pi\)
\(282\) 6.38074i 0.379968i
\(283\) 20.4845i 1.21768i −0.793293 0.608840i \(-0.791635\pi\)
0.793293 0.608840i \(-0.208365\pi\)
\(284\) −2.30317 −0.136668
\(285\) −1.85594 + 7.59223i −0.109936 + 0.449725i
\(286\) 6.70901i 0.396712i
\(287\) 8.35421 + 8.35421i 0.493133 + 0.493133i
\(288\) 1.00000i 0.0589256i
\(289\) 4.00775 0.235750
\(290\) −7.53092 12.4041i −0.442231 0.728392i
\(291\) 12.0416 + 12.0416i 0.705893 + 0.705893i
\(292\) −3.70992 + 3.70992i −0.217107 + 0.217107i
\(293\) −18.0953 18.0953i −1.05714 1.05714i −0.998266 0.0588702i \(-0.981250\pi\)
−0.0588702 0.998266i \(-0.518750\pi\)
\(294\) −0.339240 0.339240i −0.0197849 0.0197849i
\(295\) 2.19930 1.33527i 0.128048 0.0777422i
\(296\) −5.87071 1.59211i −0.341228 0.0925393i
\(297\) 1.79682 1.79682i 0.104262 0.104262i
\(298\) 4.92924i 0.285543i
\(299\) 11.8600 0.685879
\(300\) 4.76789 1.50574i 0.275274 0.0869342i
\(301\) 6.04066 6.04066i 0.348178 0.348178i
\(302\) 2.56917i 0.147839i
\(303\) 12.7683 + 12.7683i 0.733522 + 0.733522i
\(304\) −2.47157 2.47157i −0.141754 0.141754i
\(305\) 2.34510 1.42379i 0.134280 0.0815259i
\(306\) 3.60448 0.206054
\(307\) 22.5634 + 22.5634i 1.28776 + 1.28776i 0.936144 + 0.351616i \(0.114368\pi\)
0.351616 + 0.936144i \(0.385632\pi\)
\(308\) 4.91416 + 4.91416i 0.280010 + 0.280010i
\(309\) 1.88770 + 1.88770i 0.107387 + 0.107387i
\(310\) 19.8166 12.0313i 1.12551 0.683333i
\(311\) 17.2148 + 17.2148i 0.976159 + 0.976159i 0.999722 0.0235634i \(-0.00750115\pi\)
−0.0235634 + 0.999722i \(0.507501\pi\)
\(312\) −1.86691 + 1.86691i −0.105693 + 0.105693i
\(313\) −30.7702 −1.73923 −0.869616 0.493729i \(-0.835634\pi\)
−0.869616 + 0.493729i \(0.835634\pi\)
\(314\) −10.7956 + 10.7956i −0.609233 + 0.609233i
\(315\) −5.22744 + 3.17375i −0.294533 + 0.178820i
\(316\) −4.70094 4.70094i −0.264448 0.264448i
\(317\) 12.5932 + 12.5932i 0.707307 + 0.707307i 0.965968 0.258661i \(-0.0832813\pi\)
−0.258661 + 0.965968i \(0.583281\pi\)
\(318\) −0.426260 −0.0239035
\(319\) −11.6607 11.6607i −0.652874 0.652874i
\(320\) −0.530977 + 2.17211i −0.0296825 + 0.121425i
\(321\) 0.571987i 0.0319252i
\(322\) −8.68709 + 8.68709i −0.484112 + 0.484112i
\(323\) −8.90871 + 8.90871i −0.495694 + 0.495694i
\(324\) −1.00000 −0.0555556
\(325\) 11.7123 + 6.09012i 0.649681 + 0.337819i
\(326\) 2.00094i 0.110822i
\(327\) 1.48467 0.0821022
\(328\) 4.31993i 0.238528i
\(329\) 17.4508i 0.962093i
\(330\) 4.85697 2.94883i 0.267367 0.162327i
\(331\) 12.4856 12.4856i 0.686272 0.686272i −0.275134 0.961406i \(-0.588722\pi\)
0.961406 + 0.275134i \(0.0887222\pi\)
\(332\) −0.524568 0.524568i −0.0287894 0.0287894i
\(333\) 1.59211 5.87071i 0.0872469 0.321713i
\(334\) 3.34903i 0.183251i
\(335\) −15.6039 + 9.47363i −0.852531 + 0.517599i
\(336\) 2.73491i 0.149202i
\(337\) 2.01004 + 2.01004i 0.109494 + 0.109494i 0.759731 0.650237i \(-0.225331\pi\)
−0.650237 + 0.759731i \(0.725331\pi\)
\(338\) 6.02931 0.327951
\(339\) 4.04297 + 4.04297i 0.219584 + 0.219584i
\(340\) 7.82932 + 1.91389i 0.424604 + 0.103796i
\(341\) 18.6290 18.6290i 1.00882 1.00882i
\(342\) 2.47157 2.47157i 0.133647 0.133647i
\(343\) −12.6093 12.6093i −0.680841 0.680841i
\(344\) 3.12360 0.168413
\(345\) 5.21284 + 8.58599i 0.280650 + 0.462254i
\(346\) −7.11846 + 7.11846i −0.382691 + 0.382691i
\(347\) 15.1173 0.811539 0.405770 0.913975i \(-0.367004\pi\)
0.405770 + 0.913975i \(0.367004\pi\)
\(348\) 6.48962i 0.347880i
\(349\) 13.6893i 0.732771i −0.930463 0.366386i \(-0.880595\pi\)
0.930463 0.366386i \(-0.119405\pi\)
\(350\) −13.0398 + 4.11808i −0.697005 + 0.220121i
\(351\) −1.86691 1.86691i −0.0996482 0.0996482i
\(352\) 2.54109i 0.135441i
\(353\) 31.3775i 1.67006i −0.550206 0.835029i \(-0.685451\pi\)
0.550206 0.835029i \(-0.314549\pi\)
\(354\) −1.15064 −0.0611558
\(355\) 1.22293 5.00274i 0.0649065 0.265518i
\(356\) 6.69075 6.69075i 0.354609 0.354609i
\(357\) −9.85793 −0.521737
\(358\) 8.68094 8.68094i 0.458802 0.458802i
\(359\) 32.4157i 1.71083i 0.517941 + 0.855416i \(0.326699\pi\)
−0.517941 + 0.855416i \(0.673301\pi\)
\(360\) −2.17211 0.530977i −0.114480 0.0279850i
\(361\) 6.78271i 0.356985i
\(362\) −14.0432 −0.738096
\(363\) −3.21228 + 3.21228i −0.168601 + 0.168601i
\(364\) 5.10583 5.10583i 0.267618 0.267618i
\(365\) −6.08847 10.0282i −0.318685 0.524902i
\(366\) −1.22692 −0.0641322
\(367\) 9.63234 9.63234i 0.502804 0.502804i −0.409504 0.912308i \(-0.634298\pi\)
0.912308 + 0.409504i \(0.134298\pi\)
\(368\) −4.49206 −0.234165
\(369\) −4.31993 −0.224887
\(370\) 6.57544 11.9064i 0.341841 0.618987i
\(371\) 1.16579 0.0605245
\(372\) −10.3677 −0.537543
\(373\) 21.6306 21.6306i 1.11999 1.11999i 0.128250 0.991742i \(-0.459064\pi\)
0.991742 0.128250i \(-0.0409359\pi\)
\(374\) 9.15930 0.473616
\(375\) 0.739003 + 11.1559i 0.0381620 + 0.576088i
\(376\) −4.51187 + 4.51187i −0.232682 + 0.232682i
\(377\) −12.1155 + 12.1155i −0.623981 + 0.623981i
\(378\) 2.73491 0.140669
\(379\) 0.115662i 0.00594116i −0.999996 0.00297058i \(-0.999054\pi\)
0.999996 0.00297058i \(-0.000945566\pi\)
\(380\) 6.68086 4.05617i 0.342721 0.208077i
\(381\) 4.46562i 0.228781i
\(382\) 1.64289 1.64289i 0.0840578 0.0840578i
\(383\) 1.75588 0.0897211 0.0448606 0.998993i \(-0.485716\pi\)
0.0448606 + 0.998993i \(0.485716\pi\)
\(384\) 0.707107 0.707107i 0.0360844 0.0360844i
\(385\) −13.2834 + 8.06479i −0.676985 + 0.411020i
\(386\) 13.9313 0.709084
\(387\) 3.12360i 0.158781i
\(388\) 17.0294i 0.864539i
\(389\) 11.3156 + 11.3156i 0.573722 + 0.573722i 0.933166 0.359445i \(-0.117034\pi\)
−0.359445 + 0.933166i \(0.617034\pi\)
\(390\) −3.06384 5.04642i −0.155144 0.255535i
\(391\) 16.1915i 0.818840i
\(392\) 0.479758i 0.0242314i
\(393\) 17.7614 0.895943
\(394\) −18.7947 + 18.7947i −0.946865 + 0.946865i
\(395\) 12.7070 7.71486i 0.639361 0.388177i
\(396\) −2.54109 −0.127695
\(397\) −10.5898 10.5898i −0.531488 0.531488i 0.389527 0.921015i \(-0.372639\pi\)
−0.921015 + 0.389527i \(0.872639\pi\)
\(398\) −3.23872 + 3.23872i −0.162342 + 0.162342i
\(399\) −6.75953 + 6.75953i −0.338400 + 0.338400i
\(400\) −4.43613 2.30668i −0.221806 0.115334i
\(401\) 6.78291 + 6.78291i 0.338722 + 0.338722i 0.855886 0.517164i \(-0.173012\pi\)
−0.517164 + 0.855886i \(0.673012\pi\)
\(402\) 8.16371 0.407169
\(403\) −19.3556 19.3556i −0.964173 0.964173i
\(404\) 18.0572i 0.898377i
\(405\) 0.530977 2.17211i 0.0263845 0.107933i
\(406\) 17.7486i 0.880846i
\(407\) 4.04569 14.9180i 0.200537 0.739458i
\(408\) −2.54875 2.54875i −0.126182 0.126182i
\(409\) −12.5316 + 12.5316i −0.619650 + 0.619650i −0.945442 0.325792i \(-0.894369\pi\)
0.325792 + 0.945442i \(0.394369\pi\)
\(410\) −9.38336 2.29378i −0.463411 0.113282i
\(411\) 18.0818i 0.891910i
\(412\) 2.66961i 0.131522i
\(413\) 3.14690 0.154849
\(414\) 4.49206i 0.220773i
\(415\) 1.41795 0.860886i 0.0696046 0.0422592i
\(416\) 2.64021 0.129447
\(417\) 2.70375 2.70375i 0.132403 0.132403i
\(418\) 6.28048 6.28048i 0.307188 0.307188i
\(419\) 21.4066i 1.04578i −0.852400 0.522891i \(-0.824854\pi\)
0.852400 0.522891i \(-0.175146\pi\)
\(420\) 5.94054 + 1.45218i 0.289868 + 0.0708590i
\(421\) 10.7024 + 10.7024i 0.521601 + 0.521601i 0.918055 0.396454i \(-0.129759\pi\)
−0.396454 + 0.918055i \(0.629759\pi\)
\(422\) 13.4040 0.652495
\(423\) −4.51187 4.51187i −0.219374 0.219374i
\(424\) 0.301411 + 0.301411i 0.0146378 + 0.0146378i
\(425\) −8.31438 + 15.9899i −0.403307 + 0.775625i
\(426\) −1.62859 + 1.62859i −0.0789053 + 0.0789053i
\(427\) 3.35552 0.162385
\(428\) −0.404456 + 0.404456i −0.0195501 + 0.0195501i
\(429\) −4.74398 4.74398i −0.229042 0.229042i
\(430\) −1.65856 + 6.78480i −0.0799829 + 0.327192i
\(431\) −11.7768 11.7768i −0.567266 0.567266i 0.364095 0.931362i \(-0.381378\pi\)
−0.931362 + 0.364095i \(0.881378\pi\)
\(432\) 0.707107 + 0.707107i 0.0340207 + 0.0340207i
\(433\) 12.9115 + 12.9115i 0.620487 + 0.620487i 0.945656 0.325169i \(-0.105421\pi\)
−0.325169 + 0.945656i \(0.605421\pi\)
\(434\) 28.3549 1.36108
\(435\) −14.0962 3.44584i −0.675860 0.165215i
\(436\) −1.04982 1.04982i −0.0502771 0.0502771i
\(437\) 11.1024 + 11.1024i 0.531101 + 0.531101i
\(438\) 5.24662i 0.250693i
\(439\) −12.6631 + 12.6631i −0.604375 + 0.604375i −0.941471 0.337095i \(-0.890556\pi\)
0.337095 + 0.941471i \(0.390556\pi\)
\(440\) −5.51953 1.34926i −0.263133 0.0643235i
\(441\) −0.479758 −0.0228456
\(442\) 9.51656i 0.452657i
\(443\) −19.8789 + 19.8789i −0.944476 + 0.944476i −0.998538 0.0540616i \(-0.982783\pi\)
0.0540616 + 0.998538i \(0.482783\pi\)
\(444\) −5.27701 + 3.02543i −0.250436 + 0.143580i
\(445\) 10.9804 + 18.0857i 0.520521 + 0.857343i
\(446\) 18.2552 + 18.2552i 0.864411 + 0.864411i
\(447\) 3.48550 + 3.48550i 0.164858 + 0.164858i
\(448\) −1.93388 + 1.93388i −0.0913671 + 0.0913671i
\(449\) −10.2591 10.2591i −0.484159 0.484159i 0.422298 0.906457i \(-0.361224\pi\)
−0.906457 + 0.422298i \(0.861224\pi\)
\(450\) 2.30668 4.43613i 0.108738 0.209121i
\(451\) −10.9773 −0.516902
\(452\) 5.71763i 0.268935i
\(453\) −1.81667 1.81667i −0.0853548 0.0853548i
\(454\) 20.3161i 0.953483i
\(455\) 8.37935 + 13.8015i 0.392830 + 0.647025i
\(456\) −3.49532 −0.163684
\(457\) 3.03992i 0.142202i 0.997469 + 0.0711008i \(0.0226512\pi\)
−0.997469 + 0.0711008i \(0.977349\pi\)
\(458\) 23.8741i 1.11556i
\(459\) 2.54875 2.54875i 0.118965 0.118965i
\(460\) 2.38518 9.75725i 0.111210 0.454934i
\(461\) −2.13391 + 2.13391i −0.0993859 + 0.0993859i −0.755051 0.655666i \(-0.772388\pi\)
0.655666 + 0.755051i \(0.272388\pi\)
\(462\) 6.94967 0.323328
\(463\) −20.8314 −0.968118 −0.484059 0.875035i \(-0.660838\pi\)
−0.484059 + 0.875035i \(0.660838\pi\)
\(464\) 4.58885 4.58885i 0.213032 0.213032i
\(465\) 5.50504 22.5199i 0.255290 1.04434i
\(466\) 0.0502450 0.0502450i 0.00232756 0.00232756i
\(467\) 30.6842i 1.41990i −0.704253 0.709949i \(-0.748718\pi\)
0.704253 0.709949i \(-0.251282\pi\)
\(468\) 2.64021i 0.122044i
\(469\) −22.3270 −1.03097
\(470\) −7.40457 12.1960i −0.341547 0.562558i
\(471\) 15.2673i 0.703482i
\(472\) 0.813625 + 0.813625i 0.0374501 + 0.0374501i
\(473\) 7.93735i 0.364960i
\(474\) −6.64813 −0.305359
\(475\) 5.26306 + 16.6653i 0.241486 + 0.764657i
\(476\) 6.97061 + 6.97061i 0.319497 + 0.319497i
\(477\) −0.301411 + 0.301411i −0.0138007 + 0.0138007i
\(478\) 11.3273 + 11.3273i 0.518100 + 0.518100i
\(479\) 3.72623 + 3.72623i 0.170256 + 0.170256i 0.787092 0.616836i \(-0.211586\pi\)
−0.616836 + 0.787092i \(0.711586\pi\)
\(480\) 1.16046 + 1.91137i 0.0529673 + 0.0872418i
\(481\) −15.4999 4.20349i −0.706734 0.191663i
\(482\) 3.69272 3.69272i 0.168199 0.168199i
\(483\) 12.2854i 0.559005i
\(484\) 4.54285 0.206493
\(485\) 36.9898 + 9.04225i 1.67962 + 0.410587i
\(486\) −0.707107 + 0.707107i −0.0320750 + 0.0320750i
\(487\) 19.2486i 0.872239i −0.899889 0.436120i \(-0.856352\pi\)
0.899889 0.436120i \(-0.143648\pi\)
\(488\) 0.867564 + 0.867564i 0.0392728 + 0.0392728i
\(489\) −1.41488 1.41488i −0.0639830 0.0639830i
\(490\) −1.04209 0.254740i −0.0470767 0.0115080i
\(491\) −7.57274 −0.341753 −0.170877 0.985292i \(-0.554660\pi\)
−0.170877 + 0.985292i \(0.554660\pi\)
\(492\) 3.05465 + 3.05465i 0.137714 + 0.137714i
\(493\) −16.5404 16.5404i −0.744943 0.744943i
\(494\) −6.52545 6.52545i −0.293594 0.293594i
\(495\) 1.34926 5.51953i 0.0606448 0.248084i
\(496\) 7.33111 + 7.33111i 0.329176 + 0.329176i
\(497\) 4.45405 4.45405i 0.199791 0.199791i
\(498\) −0.741852 −0.0332432
\(499\) 8.46141 8.46141i 0.378785 0.378785i −0.491879 0.870664i \(-0.663690\pi\)
0.870664 + 0.491879i \(0.163690\pi\)
\(500\) 7.36585 8.41096i 0.329411 0.376150i
\(501\) 2.36812 + 2.36812i 0.105800 + 0.105800i
\(502\) 8.29215 + 8.29215i 0.370097 + 0.370097i
\(503\) −16.8793 −0.752612 −0.376306 0.926495i \(-0.622806\pi\)
−0.376306 + 0.926495i \(0.622806\pi\)
\(504\) −1.93388 1.93388i −0.0861417 0.0861417i
\(505\) 39.2221 + 9.58794i 1.74536 + 0.426658i
\(506\) 11.4147i 0.507447i
\(507\) 4.26337 4.26337i 0.189343 0.189343i
\(508\) 3.15767 3.15767i 0.140099 0.140099i
\(509\) −24.8021 −1.09933 −0.549667 0.835384i \(-0.685245\pi\)
−0.549667 + 0.835384i \(0.685245\pi\)
\(510\) 6.88949 4.18284i 0.305072 0.185219i
\(511\) 14.3491i 0.634765i
\(512\) −1.00000 −0.0441942
\(513\) 3.49532i 0.154322i
\(514\) 1.06813i 0.0471131i
\(515\) 5.79868 + 1.41750i 0.255520 + 0.0624625i
\(516\) 2.20872 2.20872i 0.0972334 0.0972334i
\(517\) −11.4651 11.4651i −0.504233 0.504233i
\(518\) 14.4322 8.27428i 0.634113 0.363551i
\(519\) 10.0670i 0.441893i
\(520\) −1.40189 + 5.73482i −0.0614769 + 0.251488i
\(521\) 25.4431i 1.11468i −0.830283 0.557342i \(-0.811821\pi\)
0.830283 0.557342i \(-0.188179\pi\)
\(522\) 4.58885 + 4.58885i 0.200849 + 0.200849i
\(523\) 43.8527 1.91755 0.958773 0.284174i \(-0.0917195\pi\)
0.958773 + 0.284174i \(0.0917195\pi\)
\(524\) −12.5592 12.5592i −0.548651 0.548651i
\(525\) −6.30858 + 12.1324i −0.275329 + 0.529502i
\(526\) 22.2567 22.2567i 0.970437 0.970437i
\(527\) 26.4248 26.4248i 1.15108 1.15108i
\(528\) 1.79682 + 1.79682i 0.0781967 + 0.0781967i
\(529\) −2.82141 −0.122670
\(530\) −0.814742 + 0.494656i −0.0353901 + 0.0214865i
\(531\) −0.813625 + 0.813625i −0.0353083 + 0.0353083i
\(532\) 9.55941 0.414453
\(533\) 11.4055i 0.494027i
\(534\) 9.46214i 0.409467i
\(535\) −0.663765 1.09328i −0.0286971 0.0472666i
\(536\) −5.77261 5.77261i −0.249339 0.249339i
\(537\) 12.2767i 0.529779i
\(538\) 1.98048i 0.0853845i
\(539\) −1.21911 −0.0525107
\(540\) −1.91137 + 1.16046i −0.0822523 + 0.0499381i
\(541\) 25.4345 25.4345i 1.09351 1.09351i 0.0983645 0.995150i \(-0.468639\pi\)
0.995150 0.0983645i \(-0.0313611\pi\)
\(542\) 20.2119 0.868177
\(543\) −9.93006 + 9.93006i −0.426140 + 0.426140i
\(544\) 3.60448i 0.154541i
\(545\) 2.83775 1.72289i 0.121556 0.0738005i
\(546\) 7.22074i 0.309019i
\(547\) −13.3671 −0.571538 −0.285769 0.958299i \(-0.592249\pi\)
−0.285769 + 0.958299i \(0.592249\pi\)
\(548\) −12.7858 + 12.7858i −0.546181 + 0.546181i
\(549\) −0.867564 + 0.867564i −0.0370267 + 0.0370267i
\(550\) 5.86149 11.2726i 0.249935 0.480665i
\(551\) −22.6833 −0.966342
\(552\) −3.17637 + 3.17637i −0.135195 + 0.135195i
\(553\) 18.1821 0.773180
\(554\) 26.8225 1.13958
\(555\) −3.76959 13.0687i −0.160010 0.554734i
\(556\) −3.82368 −0.162160
\(557\) 17.4429 0.739080 0.369540 0.929215i \(-0.379515\pi\)
0.369540 + 0.929215i \(0.379515\pi\)
\(558\) −7.33111 + 7.33111i −0.310350 + 0.310350i
\(559\) 8.24695 0.348809
\(560\) −3.17375 5.22744i −0.134115 0.220900i
\(561\) 6.47661 6.47661i 0.273442 0.273442i
\(562\) −11.8287 + 11.8287i −0.498964 + 0.498964i
\(563\) 2.58551 0.108966 0.0544831 0.998515i \(-0.482649\pi\)
0.0544831 + 0.998515i \(0.482649\pi\)
\(564\) 6.38074i 0.268678i
\(565\) 12.4193 + 3.03593i 0.522485 + 0.127723i
\(566\) 20.4845i 0.861029i
\(567\) 1.93388 1.93388i 0.0812152 0.0812152i
\(568\) 2.30317 0.0966389
\(569\) −19.1350 + 19.1350i −0.802180 + 0.802180i −0.983436 0.181256i \(-0.941984\pi\)
0.181256 + 0.983436i \(0.441984\pi\)
\(570\) 1.85594 7.59223i 0.0777367 0.318004i
\(571\) 6.72822 0.281567 0.140784 0.990040i \(-0.455038\pi\)
0.140784 + 0.990040i \(0.455038\pi\)
\(572\) 6.70901i 0.280518i
\(573\) 2.32340i 0.0970616i
\(574\) −8.35421 8.35421i −0.348698 0.348698i
\(575\) 19.9273 + 10.3618i 0.831027 + 0.432115i
\(576\) 1.00000i 0.0416667i
\(577\) 32.3098i 1.34507i −0.740063 0.672537i \(-0.765204\pi\)
0.740063 0.672537i \(-0.234796\pi\)
\(578\) −4.00775 −0.166701
\(579\) 9.85090 9.85090i 0.409390 0.409390i
\(580\) 7.53092 + 12.4041i 0.312704 + 0.515051i
\(581\) 2.02890 0.0841730
\(582\) −12.0416 12.0416i −0.499142 0.499142i
\(583\) −0.765914 + 0.765914i −0.0317209 + 0.0317209i
\(584\) 3.70992 3.70992i 0.153518 0.153518i
\(585\) −5.73482 1.40189i −0.237106 0.0579610i
\(586\) 18.0953 + 18.0953i 0.747508 + 0.747508i
\(587\) 13.1138 0.541266 0.270633 0.962683i \(-0.412767\pi\)
0.270633 + 0.962683i \(0.412767\pi\)
\(588\) 0.339240 + 0.339240i 0.0139900 + 0.0139900i
\(589\) 36.2386i 1.49319i
\(590\) −2.19930 + 1.33527i −0.0905437 + 0.0549721i
\(591\) 26.5798i 1.09335i
\(592\) 5.87071 + 1.59211i 0.241285 + 0.0654352i
\(593\) 28.5182 + 28.5182i 1.17110 + 1.17110i 0.981947 + 0.189155i \(0.0605749\pi\)
0.189155 + 0.981947i \(0.439425\pi\)
\(594\) −1.79682 + 1.79682i −0.0737245 + 0.0737245i
\(595\) −18.8422 + 11.4397i −0.772454 + 0.468982i
\(596\) 4.92924i 0.201909i
\(597\) 4.58024i 0.187457i
\(598\) −11.8600 −0.484990
\(599\) 13.3830i 0.546815i 0.961898 + 0.273407i \(0.0881507\pi\)
−0.961898 + 0.273407i \(0.911849\pi\)
\(600\) −4.76789 + 1.50574i −0.194648 + 0.0614717i
\(601\) 11.5916 0.472833 0.236417 0.971652i \(-0.424027\pi\)
0.236417 + 0.971652i \(0.424027\pi\)
\(602\) −6.04066 + 6.04066i −0.246199 + 0.246199i
\(603\) 5.77261 5.77261i 0.235079 0.235079i
\(604\) 2.56917i 0.104538i
\(605\) −2.41215 + 9.86758i −0.0980679 + 0.401174i
\(606\) −12.7683 12.7683i −0.518678 0.518678i
\(607\) −34.6374 −1.40589 −0.702944 0.711246i \(-0.748131\pi\)
−0.702944 + 0.711246i \(0.748131\pi\)
\(608\) 2.47157 + 2.47157i 0.100235 + 0.100235i
\(609\) −12.5501 12.5501i −0.508557 0.508557i
\(610\) −2.34510 + 1.42379i −0.0949504 + 0.0576475i
\(611\) −11.9123 + 11.9123i −0.481918 + 0.481918i
\(612\) −3.60448 −0.145702
\(613\) 13.5656 13.5656i 0.547908 0.547908i −0.377928 0.925835i \(-0.623363\pi\)
0.925835 + 0.377928i \(0.123363\pi\)
\(614\) −22.5634 22.5634i −0.910584 0.910584i
\(615\) −8.25699 + 5.01309i −0.332954 + 0.202147i
\(616\) −4.91416 4.91416i −0.197997 0.197997i
\(617\) −29.4000 29.4000i −1.18360 1.18360i −0.978805 0.204793i \(-0.934348\pi\)
−0.204793 0.978805i \(-0.565652\pi\)
\(618\) −1.88770 1.88770i −0.0759343 0.0759343i
\(619\) −8.71796 −0.350404 −0.175202 0.984532i \(-0.556058\pi\)
−0.175202 + 0.984532i \(0.556058\pi\)
\(620\) −19.8166 + 12.0313i −0.795855 + 0.483189i
\(621\) −3.17637 3.17637i −0.127463 0.127463i
\(622\) −17.2148 17.2148i −0.690249 0.690249i
\(623\) 25.8782i 1.03679i
\(624\) 1.86691 1.86691i 0.0747361 0.0747361i
\(625\) 14.3584 + 20.4655i 0.574337 + 0.818619i
\(626\) 30.7702 1.22982
\(627\) 8.88194i 0.354710i
\(628\) 10.7956 10.7956i 0.430793 0.430793i
\(629\) 5.73871 21.1608i 0.228817 0.843737i
\(630\) 5.22744 3.17375i 0.208266 0.126445i
\(631\) −20.3687 20.3687i −0.810867 0.810867i 0.173897 0.984764i \(-0.444364\pi\)
−0.984764 + 0.173897i \(0.944364\pi\)
\(632\) 4.70094 + 4.70094i 0.186993 + 0.186993i
\(633\) 9.47804 9.47804i 0.376718 0.376718i
\(634\) −12.5932 12.5932i −0.500141 0.500141i
\(635\) 5.18216 + 8.53546i 0.205648 + 0.338719i
\(636\) 0.426260 0.0169023
\(637\) 1.26666i 0.0501869i
\(638\) 11.6607 + 11.6607i 0.461651 + 0.461651i
\(639\) 2.30317i 0.0911120i
\(640\) 0.530977 2.17211i 0.0209887 0.0858602i
\(641\) 19.7213 0.778944 0.389472 0.921038i \(-0.372658\pi\)
0.389472 + 0.921038i \(0.372658\pi\)
\(642\) 0.571987i 0.0225745i
\(643\) 30.0934i 1.18677i −0.804919 0.593384i \(-0.797791\pi\)
0.804919 0.593384i \(-0.202209\pi\)
\(644\) 8.68709 8.68709i 0.342319 0.342319i
\(645\) 3.62480 + 5.97036i 0.142726 + 0.235083i
\(646\) 8.90871 8.90871i 0.350508 0.350508i
\(647\) 3.58012 0.140749 0.0703746 0.997521i \(-0.477581\pi\)
0.0703746 + 0.997521i \(0.477581\pi\)
\(648\) 1.00000 0.0392837
\(649\) −2.06750 + 2.06750i −0.0811563 + 0.0811563i
\(650\) −11.7123 6.09012i −0.459394 0.238874i
\(651\) 20.0499 20.0499i 0.785819 0.785819i
\(652\) 2.00094i 0.0783628i
\(653\) 21.6461i 0.847079i 0.905878 + 0.423540i \(0.139213\pi\)
−0.905878 + 0.423540i \(0.860787\pi\)
\(654\) −1.48467 −0.0580550
\(655\) 33.9486 20.6113i 1.32648 0.805350i
\(656\) 4.31993i 0.168665i
\(657\) 3.70992 + 3.70992i 0.144738 + 0.144738i
\(658\) 17.4508i 0.680302i
\(659\) −24.8071 −0.966346 −0.483173 0.875525i \(-0.660516\pi\)
−0.483173 + 0.875525i \(0.660516\pi\)
\(660\) −4.85697 + 2.94883i −0.189057 + 0.114783i
\(661\) −7.55751 7.55751i −0.293953 0.293953i 0.544687 0.838640i \(-0.316649\pi\)
−0.838640 + 0.544687i \(0.816649\pi\)
\(662\) −12.4856 + 12.4856i −0.485267 + 0.485267i
\(663\) −6.72922 6.72922i −0.261341 0.261341i
\(664\) 0.524568 + 0.524568i 0.0203572 + 0.0203572i
\(665\) −5.07583 + 20.7641i −0.196832 + 0.805197i
\(666\) −1.59211 + 5.87071i −0.0616929 + 0.227485i
\(667\) −20.6134 + 20.6134i −0.798154 + 0.798154i
\(668\) 3.34903i 0.129578i
\(669\) 25.8168 0.998135
\(670\) 15.6039 9.47363i 0.602830 0.365998i
\(671\) −2.20456 + 2.20456i −0.0851061 + 0.0851061i
\(672\) 2.73491i 0.105502i
\(673\) 23.8195 + 23.8195i 0.918173 + 0.918173i 0.996896 0.0787239i \(-0.0250846\pi\)
−0.0787239 + 0.996896i \(0.525085\pi\)
\(674\) −2.01004 2.01004i −0.0774237 0.0774237i
\(675\) −1.50574 4.76789i −0.0579561 0.183516i
\(676\) −6.02931 −0.231897
\(677\) −26.5470 26.5470i −1.02028 1.02028i −0.999790 0.0204933i \(-0.993476\pi\)
−0.0204933 0.999790i \(-0.506524\pi\)
\(678\) −4.04297 4.04297i −0.155269 0.155269i
\(679\) 32.9329 + 32.9329i 1.26385 + 1.26385i
\(680\) −7.82932 1.91389i −0.300241 0.0733945i
\(681\) −14.3657 14.3657i −0.550494 0.550494i
\(682\) −18.6290 + 18.6290i −0.713342 + 0.713342i
\(683\) −26.8136 −1.02599 −0.512997 0.858390i \(-0.671465\pi\)
−0.512997 + 0.858390i \(0.671465\pi\)
\(684\) −2.47157 + 2.47157i −0.0945028 + 0.0945028i
\(685\) −20.9831 34.5610i −0.801725 1.32051i
\(686\) 12.6093 + 12.6093i 0.481427 + 0.481427i
\(687\) −16.8815 16.8815i −0.644070 0.644070i
\(688\) −3.12360 −0.119086
\(689\) 0.795788 + 0.795788i 0.0303171 + 0.0303171i
\(690\) −5.21284 8.58599i −0.198449 0.326863i
\(691\) 39.2996i 1.49503i 0.664246 + 0.747514i \(0.268753\pi\)
−0.664246 + 0.747514i \(0.731247\pi\)
\(692\) 7.11846 7.11846i 0.270603 0.270603i
\(693\) 4.91416 4.91416i 0.186673 0.186673i
\(694\) −15.1173 −0.573845
\(695\) 2.03029 8.30546i 0.0770133 0.315044i
\(696\) 6.48962i 0.245988i
\(697\) −15.5711 −0.589797
\(698\) 13.6893i 0.518148i
\(699\) 0.0710572i 0.00268763i
\(700\) 13.0398 4.11808i 0.492857 0.155649i
\(701\) −19.5030 + 19.5030i −0.736617 + 0.736617i −0.971922 0.235305i \(-0.924391\pi\)
0.235305 + 0.971922i \(0.424391\pi\)
\(702\) 1.86691 + 1.86691i 0.0704619 + 0.0704619i
\(703\) −10.5748 18.4448i −0.398838 0.695661i
\(704\) 2.54109i 0.0957710i
\(705\) −13.8597 3.38803i −0.521986 0.127601i
\(706\) 31.3775i 1.18091i
\(707\) 34.9203 + 34.9203i 1.31331 + 1.31331i
\(708\) 1.15064 0.0432437
\(709\) 8.21814 + 8.21814i 0.308639 + 0.308639i 0.844381 0.535743i \(-0.179968\pi\)
−0.535743 + 0.844381i \(0.679968\pi\)
\(710\) −1.22293 + 5.00274i −0.0458958 + 0.187750i
\(711\) −4.70094 + 4.70094i −0.176299 + 0.176299i
\(712\) −6.69075 + 6.69075i −0.250746 + 0.250746i
\(713\) −32.9318 32.9318i −1.23330 1.23330i
\(714\) 9.85793 0.368924
\(715\) −14.5727 3.56233i −0.544988 0.133224i
\(716\) −8.68094 + 8.68094i −0.324422 + 0.324422i
\(717\) 16.0193 0.598251
\(718\) 32.4157i 1.20974i
\(719\) 9.15541i 0.341439i 0.985320 + 0.170720i \(0.0546092\pi\)
−0.985320 + 0.170720i \(0.945391\pi\)
\(720\) 2.17211 + 0.530977i 0.0809498 + 0.0197884i
\(721\) 5.16269 + 5.16269i 0.192269 + 0.192269i
\(722\) 6.78271i 0.252426i
\(723\) 5.22229i 0.194219i
\(724\) 14.0432 0.521912
\(725\) −30.9418 + 9.77171i −1.14915 + 0.362912i
\(726\) 3.21228 3.21228i 0.119219 0.119219i
\(727\) −32.4114 −1.20207 −0.601036 0.799222i \(-0.705245\pi\)
−0.601036 + 0.799222i \(0.705245\pi\)
\(728\) −5.10583 + 5.10583i −0.189235 + 0.189235i
\(729\) 1.00000i 0.0370370i
\(730\) 6.08847 + 10.0282i 0.225344 + 0.371162i
\(731\) 11.2589i 0.416427i
\(732\) 1.22692 0.0453483
\(733\) 35.1555 35.1555i 1.29850 1.29850i 0.369115 0.929384i \(-0.379661\pi\)
0.929384 0.369115i \(-0.120339\pi\)
\(734\) −9.63234 + 9.63234i −0.355536 + 0.355536i
\(735\) −0.916995 + 0.556738i −0.0338239 + 0.0205356i
\(736\) 4.49206 0.165579
\(737\) 14.6687 14.6687i 0.540330 0.540330i
\(738\) 4.31993 0.159019
\(739\) 11.5902 0.426351 0.213176 0.977014i \(-0.431619\pi\)
0.213176 + 0.977014i \(0.431619\pi\)
\(740\) −6.57544 + 11.9064i −0.241718 + 0.437690i
\(741\) −9.22838 −0.339013
\(742\) −1.16579 −0.0427973
\(743\) 21.4779 21.4779i 0.787949 0.787949i −0.193209 0.981158i \(-0.561890\pi\)
0.981158 + 0.193209i \(0.0618895\pi\)
\(744\) 10.3677 0.380100
\(745\) 10.7068 + 2.61731i 0.392269 + 0.0958909i
\(746\) −21.6306 + 21.6306i −0.791954 + 0.791954i
\(747\) −0.524568 + 0.524568i −0.0191929 + 0.0191929i
\(748\) −9.15930 −0.334897
\(749\) 1.56433i 0.0571595i
\(750\) −0.739003 11.1559i −0.0269846 0.407355i
\(751\) 46.7182i 1.70477i 0.522914 + 0.852385i \(0.324845\pi\)
−0.522914 + 0.852385i \(0.675155\pi\)
\(752\) 4.51187 4.51187i 0.164531 0.164531i
\(753\) 11.7269 0.427351
\(754\) 12.1155 12.1155i 0.441221 0.441221i
\(755\) −5.58051 1.36417i −0.203096 0.0496472i
\(756\) −2.73491 −0.0994679
\(757\) 28.5100i 1.03622i 0.855315 + 0.518108i \(0.173363\pi\)
−0.855315 + 0.518108i \(0.826637\pi\)
\(758\) 0.115662i 0.00420103i
\(759\) −8.07143 8.07143i −0.292974 0.292974i
\(760\) −6.68086 + 4.05617i −0.242340 + 0.147133i
\(761\) 19.7514i 0.715988i 0.933724 + 0.357994i \(0.116539\pi\)
−0.933724 + 0.357994i \(0.883461\pi\)
\(762\) 4.46562i 0.161772i
\(763\) 4.06043 0.146998
\(764\) −1.64289 + 1.64289i −0.0594378 + 0.0594378i
\(765\) 1.91389 7.82932i 0.0691970 0.283070i
\(766\) −1.75588 −0.0634424
\(767\) 2.14814 + 2.14814i 0.0775647 + 0.0775647i
\(768\) −0.707107 + 0.707107i −0.0255155 + 0.0255155i
\(769\) 26.6238 26.6238i 0.960078 0.960078i −0.0391547 0.999233i \(-0.512467\pi\)
0.999233 + 0.0391547i \(0.0124665\pi\)
\(770\) 13.2834 8.06479i 0.478700 0.290635i
\(771\) 0.755280 + 0.755280i 0.0272007 + 0.0272007i
\(772\) −13.9313 −0.501398
\(773\) −1.41448 1.41448i −0.0508753 0.0508753i 0.681211 0.732087i \(-0.261453\pi\)
−0.732087 + 0.681211i \(0.761453\pi\)
\(774\) 3.12360i 0.112275i
\(775\) −15.6112 49.4322i −0.560770 1.77566i
\(776\) 17.0294i 0.611322i
\(777\) 4.35428 16.0559i 0.156209 0.576002i
\(778\) −11.3156 11.3156i −0.405683 0.405683i
\(779\) −10.6770 + 10.6770i −0.382543 + 0.382543i
\(780\)