Properties

Label 312.2.bp.a.89.2
Level $312$
Weight $2$
Character 312.89
Analytic conductor $2.491$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 312.bp (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.49133254306\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 89.2
Character \(\chi\) \(=\) 312.89
Dual form 312.2.bp.a.305.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.43902 + 0.963958i) q^{3} +(0.504580 - 0.504580i) q^{5} +(-0.836809 - 3.12301i) q^{7} +(1.14157 - 2.77431i) q^{9} +O(q^{10})\) \(q+(-1.43902 + 0.963958i) q^{3} +(0.504580 - 0.504580i) q^{5} +(-0.836809 - 3.12301i) q^{7} +(1.14157 - 2.77431i) q^{9} +(-0.296516 + 1.10661i) q^{11} +(3.23695 - 1.58812i) q^{13} +(-0.239708 + 1.21249i) q^{15} +(1.51919 - 2.63131i) q^{17} +(4.59867 - 1.23221i) q^{19} +(4.21464 + 3.68744i) q^{21} +(-2.43079 - 4.21025i) q^{23} +4.49080i q^{25} +(1.03158 + 5.09273i) q^{27} +(8.98018 - 5.18471i) q^{29} +(-1.93142 - 1.93142i) q^{31} +(-0.640035 - 1.87827i) q^{33} +(-1.99805 - 1.15357i) q^{35} +(-7.49362 - 2.00791i) q^{37} +(-3.12717 + 5.40563i) q^{39} +(-6.55081 - 1.75528i) q^{41} +(1.98070 + 1.14356i) q^{43} +(-0.823849 - 1.97588i) q^{45} +(1.27830 + 1.27830i) q^{47} +(-2.99079 + 1.72673i) q^{49} +(0.350327 + 5.25094i) q^{51} -2.42966i q^{53} +(0.408758 + 0.707990i) q^{55} +(-5.42979 + 6.20611i) q^{57} +(-5.61424 + 1.50433i) q^{59} +(-5.23702 + 9.07078i) q^{61} +(-9.61950 - 1.24357i) q^{63} +(0.831967 - 2.43463i) q^{65} +(-1.57758 + 5.88762i) q^{67} +(7.55646 + 3.71546i) q^{69} +(1.02693 + 3.83254i) q^{71} +(-4.06395 + 4.06395i) q^{73} +(-4.32894 - 6.46236i) q^{75} +3.70409 q^{77} +6.77768 q^{79} +(-6.39363 - 6.33415i) q^{81} +(11.9425 - 11.9425i) q^{83} +(-0.561154 - 2.09426i) q^{85} +(-7.92484 + 16.1174i) q^{87} +(-2.07215 + 7.73338i) q^{89} +(-7.66844 - 8.78010i) q^{91} +(4.64117 + 0.917551i) q^{93} +(1.69865 - 2.94215i) q^{95} +(-0.989115 + 0.265032i) q^{97} +(2.73160 + 2.08590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q + 4 q^{7} + O(q^{10}) \) \( 56 q + 4 q^{7} + 8 q^{13} - 8 q^{15} + 4 q^{19} + 16 q^{21} + 24 q^{27} - 36 q^{31} + 28 q^{33} + 20 q^{37} + 16 q^{39} - 84 q^{43} + 12 q^{45} - 12 q^{49} - 24 q^{55} - 36 q^{57} - 24 q^{61} - 12 q^{63} - 32 q^{67} - 36 q^{69} - 20 q^{73} - 60 q^{75} - 32 q^{79} - 88 q^{85} - 16 q^{87} + 28 q^{91} - 88 q^{93} - 36 q^{97} + 44 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/312\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(157\) \(209\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{12}\right)\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.43902 + 0.963958i −0.830820 + 0.556541i
\(4\) 0 0
\(5\) 0.504580 0.504580i 0.225655 0.225655i −0.585220 0.810875i \(-0.698992\pi\)
0.810875 + 0.585220i \(0.198992\pi\)
\(6\) 0 0
\(7\) −0.836809 3.12301i −0.316284 1.18039i −0.922788 0.385308i \(-0.874095\pi\)
0.606504 0.795080i \(-0.292571\pi\)
\(8\) 0 0
\(9\) 1.14157 2.77431i 0.380523 0.924771i
\(10\) 0 0
\(11\) −0.296516 + 1.10661i −0.0894029 + 0.333656i −0.996112 0.0881015i \(-0.971920\pi\)
0.906709 + 0.421758i \(0.138587\pi\)
\(12\) 0 0
\(13\) 3.23695 1.58812i 0.897769 0.440466i
\(14\) 0 0
\(15\) −0.239708 + 1.21249i −0.0618923 + 0.313065i
\(16\) 0 0
\(17\) 1.51919 2.63131i 0.368457 0.638186i −0.620868 0.783916i \(-0.713220\pi\)
0.989325 + 0.145729i \(0.0465529\pi\)
\(18\) 0 0
\(19\) 4.59867 1.23221i 1.05501 0.282689i 0.310688 0.950512i \(-0.399440\pi\)
0.744320 + 0.667823i \(0.232774\pi\)
\(20\) 0 0
\(21\) 4.21464 + 3.68744i 0.919710 + 0.804665i
\(22\) 0 0
\(23\) −2.43079 4.21025i −0.506854 0.877897i −0.999969 0.00793257i \(-0.997475\pi\)
0.493114 0.869964i \(-0.335858\pi\)
\(24\) 0 0
\(25\) 4.49080i 0.898160i
\(26\) 0 0
\(27\) 1.03158 + 5.09273i 0.198527 + 0.980095i
\(28\) 0 0
\(29\) 8.98018 5.18471i 1.66758 0.962776i 0.698638 0.715475i \(-0.253790\pi\)
0.968939 0.247301i \(-0.0795437\pi\)
\(30\) 0 0
\(31\) −1.93142 1.93142i −0.346894 0.346894i 0.512057 0.858951i \(-0.328884\pi\)
−0.858951 + 0.512057i \(0.828884\pi\)
\(32\) 0 0
\(33\) −0.640035 1.87827i −0.111416 0.326965i
\(34\) 0 0
\(35\) −1.99805 1.15357i −0.337731 0.194989i
\(36\) 0 0
\(37\) −7.49362 2.00791i −1.23194 0.330098i −0.416608 0.909086i \(-0.636781\pi\)
−0.815336 + 0.578988i \(0.803448\pi\)
\(38\) 0 0
\(39\) −3.12717 + 5.40563i −0.500747 + 0.865593i
\(40\) 0 0
\(41\) −6.55081 1.75528i −1.02306 0.274129i −0.291986 0.956423i \(-0.594316\pi\)
−0.731079 + 0.682293i \(0.760983\pi\)
\(42\) 0 0
\(43\) 1.98070 + 1.14356i 0.302054 + 0.174391i 0.643365 0.765559i \(-0.277538\pi\)
−0.341311 + 0.939950i \(0.610871\pi\)
\(44\) 0 0
\(45\) −0.823849 1.97588i −0.122812 0.294546i
\(46\) 0 0
\(47\) 1.27830 + 1.27830i 0.186459 + 0.186459i 0.794163 0.607704i \(-0.207909\pi\)
−0.607704 + 0.794163i \(0.707909\pi\)
\(48\) 0 0
\(49\) −2.99079 + 1.72673i −0.427256 + 0.246676i
\(50\) 0 0
\(51\) 0.350327 + 5.25094i 0.0490556 + 0.735279i
\(52\) 0 0
\(53\) 2.42966i 0.333740i −0.985979 0.166870i \(-0.946634\pi\)
0.985979 0.166870i \(-0.0533660\pi\)
\(54\) 0 0
\(55\) 0.408758 + 0.707990i 0.0551169 + 0.0954653i
\(56\) 0 0
\(57\) −5.42979 + 6.20611i −0.719194 + 0.822019i
\(58\) 0 0
\(59\) −5.61424 + 1.50433i −0.730911 + 0.195847i −0.605035 0.796199i \(-0.706841\pi\)
−0.125876 + 0.992046i \(0.540174\pi\)
\(60\) 0 0
\(61\) −5.23702 + 9.07078i −0.670531 + 1.16139i 0.307223 + 0.951638i \(0.400600\pi\)
−0.977754 + 0.209756i \(0.932733\pi\)
\(62\) 0 0
\(63\) −9.61950 1.24357i −1.21194 0.156675i
\(64\) 0 0
\(65\) 0.831967 2.43463i 0.103193 0.301979i
\(66\) 0 0
\(67\) −1.57758 + 5.88762i −0.192732 + 0.719287i 0.800110 + 0.599853i \(0.204774\pi\)
−0.992842 + 0.119433i \(0.961892\pi\)
\(68\) 0 0
\(69\) 7.55646 + 3.71546i 0.909690 + 0.447289i
\(70\) 0 0
\(71\) 1.02693 + 3.83254i 0.121874 + 0.454839i 0.999709 0.0241235i \(-0.00767950\pi\)
−0.877835 + 0.478963i \(0.841013\pi\)
\(72\) 0 0
\(73\) −4.06395 + 4.06395i −0.475650 + 0.475650i −0.903737 0.428088i \(-0.859187\pi\)
0.428088 + 0.903737i \(0.359187\pi\)
\(74\) 0 0
\(75\) −4.32894 6.46236i −0.499863 0.746209i
\(76\) 0 0
\(77\) 3.70409 0.422121
\(78\) 0 0
\(79\) 6.77768 0.762549 0.381274 0.924462i \(-0.375485\pi\)
0.381274 + 0.924462i \(0.375485\pi\)
\(80\) 0 0
\(81\) −6.39363 6.33415i −0.710404 0.703794i
\(82\) 0 0
\(83\) 11.9425 11.9425i 1.31086 1.31086i 0.390075 0.920783i \(-0.372449\pi\)
0.920783 0.390075i \(-0.127551\pi\)
\(84\) 0 0
\(85\) −0.561154 2.09426i −0.0608657 0.227154i
\(86\) 0 0
\(87\) −7.92484 + 16.1174i −0.849632 + 1.72797i
\(88\) 0 0
\(89\) −2.07215 + 7.73338i −0.219648 + 0.819737i 0.764831 + 0.644231i \(0.222823\pi\)
−0.984478 + 0.175505i \(0.943844\pi\)
\(90\) 0 0
\(91\) −7.66844 8.78010i −0.803871 0.920404i
\(92\) 0 0
\(93\) 4.64117 + 0.917551i 0.481267 + 0.0951456i
\(94\) 0 0
\(95\) 1.69865 2.94215i 0.174278 0.301858i
\(96\) 0 0
\(97\) −0.989115 + 0.265032i −0.100429 + 0.0269100i −0.308684 0.951165i \(-0.599888\pi\)
0.208254 + 0.978075i \(0.433222\pi\)
\(98\) 0 0
\(99\) 2.73160 + 2.08590i 0.274536 + 0.209641i
\(100\) 0 0
\(101\) 3.77328 + 6.53550i 0.375455 + 0.650307i 0.990395 0.138267i \(-0.0441532\pi\)
−0.614940 + 0.788574i \(0.710820\pi\)
\(102\) 0 0
\(103\) 6.31264i 0.622003i −0.950409 0.311001i \(-0.899336\pi\)
0.950409 0.311001i \(-0.100664\pi\)
\(104\) 0 0
\(105\) 3.98723 0.266016i 0.389114 0.0259605i
\(106\) 0 0
\(107\) 7.26480 4.19434i 0.702315 0.405482i −0.105894 0.994377i \(-0.533770\pi\)
0.808209 + 0.588896i \(0.200437\pi\)
\(108\) 0 0
\(109\) 10.3472 + 10.3472i 0.991084 + 0.991084i 0.999961 0.00887687i \(-0.00282563\pi\)
−0.00887687 + 0.999961i \(0.502826\pi\)
\(110\) 0 0
\(111\) 12.7190 4.33411i 1.20724 0.411375i
\(112\) 0 0
\(113\) −13.0474 7.53294i −1.22740 0.708639i −0.260914 0.965362i \(-0.584024\pi\)
−0.966485 + 0.256723i \(0.917357\pi\)
\(114\) 0 0
\(115\) −3.35093 0.897879i −0.312476 0.0837277i
\(116\) 0 0
\(117\) −0.710737 10.7933i −0.0657077 0.997839i
\(118\) 0 0
\(119\) −9.48889 2.54254i −0.869845 0.233074i
\(120\) 0 0
\(121\) 8.38961 + 4.84374i 0.762692 + 0.440340i
\(122\) 0 0
\(123\) 11.1188 3.78881i 1.00255 0.341626i
\(124\) 0 0
\(125\) 4.78886 + 4.78886i 0.428329 + 0.428329i
\(126\) 0 0
\(127\) 7.12606 4.11423i 0.632336 0.365079i −0.149320 0.988789i \(-0.547709\pi\)
0.781656 + 0.623710i \(0.214375\pi\)
\(128\) 0 0
\(129\) −3.95261 + 0.263706i −0.348008 + 0.0232181i
\(130\) 0 0
\(131\) 13.4099i 1.17163i 0.810446 + 0.585814i \(0.199225\pi\)
−0.810446 + 0.585814i \(0.800775\pi\)
\(132\) 0 0
\(133\) −7.69642 13.3306i −0.667365 1.15591i
\(134\) 0 0
\(135\) 3.09020 + 2.04917i 0.265962 + 0.176365i
\(136\) 0 0
\(137\) −13.2257 + 3.54382i −1.12995 + 0.302769i −0.774904 0.632079i \(-0.782202\pi\)
−0.355047 + 0.934849i \(0.615535\pi\)
\(138\) 0 0
\(139\) −9.49420 + 16.4444i −0.805288 + 1.39480i 0.110809 + 0.993842i \(0.464656\pi\)
−0.916097 + 0.400957i \(0.868678\pi\)
\(140\) 0 0
\(141\) −3.07172 0.607274i −0.258686 0.0511417i
\(142\) 0 0
\(143\) 0.797626 + 4.05296i 0.0667009 + 0.338925i
\(144\) 0 0
\(145\) 1.91512 7.14731i 0.159042 0.593552i
\(146\) 0 0
\(147\) 2.63932 5.36780i 0.217687 0.442729i
\(148\) 0 0
\(149\) −1.55037 5.78607i −0.127012 0.474014i 0.872892 0.487914i \(-0.162242\pi\)
−0.999903 + 0.0139002i \(0.995575\pi\)
\(150\) 0 0
\(151\) 10.9825 10.9825i 0.893741 0.893741i −0.101132 0.994873i \(-0.532247\pi\)
0.994873 + 0.101132i \(0.0322466\pi\)
\(152\) 0 0
\(153\) −5.56582 7.21853i −0.449970 0.583583i
\(154\) 0 0
\(155\) −1.94912 −0.156557
\(156\) 0 0
\(157\) 10.2214 0.815760 0.407880 0.913036i \(-0.366268\pi\)
0.407880 + 0.913036i \(0.366268\pi\)
\(158\) 0 0
\(159\) 2.34209 + 3.49634i 0.185740 + 0.277278i
\(160\) 0 0
\(161\) −11.1146 + 11.1146i −0.875950 + 0.875950i
\(162\) 0 0
\(163\) −5.56650 20.7745i −0.436002 1.62718i −0.738657 0.674082i \(-0.764540\pi\)
0.302655 0.953100i \(-0.402127\pi\)
\(164\) 0 0
\(165\) −1.27068 0.624788i −0.0989227 0.0486396i
\(166\) 0 0
\(167\) 2.83710 10.5882i 0.219542 0.819341i −0.764976 0.644058i \(-0.777249\pi\)
0.984518 0.175283i \(-0.0560839\pi\)
\(168\) 0 0
\(169\) 7.95574 10.2814i 0.611980 0.790873i
\(170\) 0 0
\(171\) 1.83117 14.1648i 0.140033 1.08321i
\(172\) 0 0
\(173\) −10.1274 + 17.5412i −0.769975 + 1.33364i 0.167601 + 0.985855i \(0.446398\pi\)
−0.937576 + 0.347781i \(0.886935\pi\)
\(174\) 0 0
\(175\) 14.0248 3.75794i 1.06018 0.284074i
\(176\) 0 0
\(177\) 6.62890 7.57665i 0.498259 0.569496i
\(178\) 0 0
\(179\) 10.5903 + 18.3430i 0.791557 + 1.37102i 0.925003 + 0.379961i \(0.124063\pi\)
−0.133445 + 0.991056i \(0.542604\pi\)
\(180\) 0 0
\(181\) 14.0377i 1.04342i 0.853124 + 0.521709i \(0.174705\pi\)
−0.853124 + 0.521709i \(0.825295\pi\)
\(182\) 0 0
\(183\) −1.20767 18.1013i −0.0892732 1.33809i
\(184\) 0 0
\(185\) −4.79428 + 2.76798i −0.352483 + 0.203506i
\(186\) 0 0
\(187\) 2.46138 + 2.46138i 0.179994 + 0.179994i
\(188\) 0 0
\(189\) 15.0414 7.48327i 1.09410 0.544328i
\(190\) 0 0
\(191\) 18.7332 + 10.8156i 1.35549 + 0.782592i 0.989012 0.147835i \(-0.0472305\pi\)
0.366477 + 0.930427i \(0.380564\pi\)
\(192\) 0 0
\(193\) −20.6023 5.52036i −1.48298 0.397364i −0.575622 0.817716i \(-0.695240\pi\)
−0.907361 + 0.420352i \(0.861907\pi\)
\(194\) 0 0
\(195\) 1.14967 + 4.30548i 0.0823293 + 0.308321i
\(196\) 0 0
\(197\) 24.7548 + 6.63302i 1.76371 + 0.472583i 0.987463 0.157851i \(-0.0504567\pi\)
0.776242 + 0.630435i \(0.217123\pi\)
\(198\) 0 0
\(199\) 13.6540 + 7.88312i 0.967904 + 0.558820i 0.898597 0.438776i \(-0.144588\pi\)
0.0693073 + 0.997595i \(0.477921\pi\)
\(200\) 0 0
\(201\) −3.40524 9.99313i −0.240187 0.704861i
\(202\) 0 0
\(203\) −23.7066 23.7066i −1.66388 1.66388i
\(204\) 0 0
\(205\) −4.19109 + 2.41973i −0.292718 + 0.169001i
\(206\) 0 0
\(207\) −14.4555 + 1.93747i −1.00472 + 0.134664i
\(208\) 0 0
\(209\) 5.45432i 0.377283i
\(210\) 0 0
\(211\) −5.20303 9.01192i −0.358192 0.620406i 0.629467 0.777027i \(-0.283273\pi\)
−0.987659 + 0.156621i \(0.949940\pi\)
\(212\) 0 0
\(213\) −5.17218 4.52520i −0.354392 0.310062i
\(214\) 0 0
\(215\) 1.57644 0.422405i 0.107512 0.0288078i
\(216\) 0 0
\(217\) −4.41563 + 7.64810i −0.299753 + 0.519187i
\(218\) 0 0
\(219\) 1.93064 9.76560i 0.130461 0.659898i
\(220\) 0 0
\(221\) 0.738700 10.9301i 0.0496903 0.735237i
\(222\) 0 0
\(223\) −5.88651 + 21.9688i −0.394190 + 1.47114i 0.428966 + 0.903321i \(0.358878\pi\)
−0.823156 + 0.567816i \(0.807789\pi\)
\(224\) 0 0
\(225\) 12.4589 + 5.12656i 0.830592 + 0.341771i
\(226\) 0 0
\(227\) 5.14469 + 19.2003i 0.341465 + 1.27437i 0.896688 + 0.442664i \(0.145967\pi\)
−0.555222 + 0.831702i \(0.687367\pi\)
\(228\) 0 0
\(229\) 1.16288 1.16288i 0.0768456 0.0768456i −0.667639 0.744485i \(-0.732695\pi\)
0.744485 + 0.667639i \(0.232695\pi\)
\(230\) 0 0
\(231\) −5.33027 + 3.57059i −0.350706 + 0.234928i
\(232\) 0 0
\(233\) 23.8148 1.56016 0.780080 0.625680i \(-0.215178\pi\)
0.780080 + 0.625680i \(0.215178\pi\)
\(234\) 0 0
\(235\) 1.29001 0.0841507
\(236\) 0 0
\(237\) −9.75323 + 6.53340i −0.633541 + 0.424390i
\(238\) 0 0
\(239\) 3.10170 3.10170i 0.200632 0.200632i −0.599639 0.800271i \(-0.704689\pi\)
0.800271 + 0.599639i \(0.204689\pi\)
\(240\) 0 0
\(241\) −2.25233 8.40583i −0.145086 0.541467i −0.999752 0.0222886i \(-0.992905\pi\)
0.854666 0.519178i \(-0.173762\pi\)
\(242\) 0 0
\(243\) 15.3064 + 2.95179i 0.981908 + 0.189357i
\(244\) 0 0
\(245\) −0.637817 + 2.38037i −0.0407487 + 0.152076i
\(246\) 0 0
\(247\) 12.9288 11.2919i 0.822640 0.718484i
\(248\) 0 0
\(249\) −5.67345 + 28.6976i −0.359540 + 1.81863i
\(250\) 0 0
\(251\) −4.34184 + 7.52029i −0.274055 + 0.474677i −0.969896 0.243519i \(-0.921698\pi\)
0.695842 + 0.718195i \(0.255032\pi\)
\(252\) 0 0
\(253\) 5.37988 1.44153i 0.338230 0.0906284i
\(254\) 0 0
\(255\) 2.82629 + 2.47275i 0.176989 + 0.154850i
\(256\) 0 0
\(257\) −2.99467 5.18692i −0.186802 0.323551i 0.757380 0.652974i \(-0.226479\pi\)
−0.944182 + 0.329423i \(0.893146\pi\)
\(258\) 0 0
\(259\) 25.0829i 1.55858i
\(260\) 0 0
\(261\) −4.13250 30.8325i −0.255796 1.90849i
\(262\) 0 0
\(263\) −16.5914 + 9.57907i −1.02307 + 0.590670i −0.914992 0.403472i \(-0.867803\pi\)
−0.108079 + 0.994142i \(0.534470\pi\)
\(264\) 0 0
\(265\) −1.22596 1.22596i −0.0753101 0.0753101i
\(266\) 0 0
\(267\) −4.47278 13.1260i −0.273730 0.803297i
\(268\) 0 0
\(269\) −22.0370 12.7231i −1.34362 0.775741i −0.356285 0.934377i \(-0.615957\pi\)
−0.987337 + 0.158637i \(0.949290\pi\)
\(270\) 0 0
\(271\) −22.0299 5.90289i −1.33822 0.358575i −0.482447 0.875925i \(-0.660252\pi\)
−0.855774 + 0.517350i \(0.826919\pi\)
\(272\) 0 0
\(273\) 19.4987 + 5.24271i 1.18011 + 0.317303i
\(274\) 0 0
\(275\) −4.96957 1.33159i −0.299677 0.0802981i
\(276\) 0 0
\(277\) −11.4444 6.60744i −0.687628 0.397002i 0.115095 0.993355i \(-0.463283\pi\)
−0.802723 + 0.596352i \(0.796616\pi\)
\(278\) 0 0
\(279\) −7.56323 + 3.15352i −0.452799 + 0.188796i
\(280\) 0 0
\(281\) −1.24623 1.24623i −0.0743436 0.0743436i 0.668957 0.743301i \(-0.266741\pi\)
−0.743301 + 0.668957i \(0.766741\pi\)
\(282\) 0 0
\(283\) −20.1262 + 11.6199i −1.19638 + 0.690728i −0.959745 0.280871i \(-0.909377\pi\)
−0.236631 + 0.971600i \(0.576043\pi\)
\(284\) 0 0
\(285\) 0.391711 + 5.87124i 0.0232030 + 0.347782i
\(286\) 0 0
\(287\) 21.9271i 1.29432i
\(288\) 0 0
\(289\) 3.88414 + 6.72753i 0.228479 + 0.395737i
\(290\) 0 0
\(291\) 1.16788 1.33485i 0.0684622 0.0782504i
\(292\) 0 0
\(293\) −2.69061 + 0.720947i −0.157187 + 0.0421182i −0.336555 0.941664i \(-0.609262\pi\)
0.179367 + 0.983782i \(0.442595\pi\)
\(294\) 0 0
\(295\) −2.07378 + 3.59188i −0.120740 + 0.209128i
\(296\) 0 0
\(297\) −5.94155 0.368518i −0.344764 0.0213836i
\(298\) 0 0
\(299\) −14.5547 9.76799i −0.841722 0.564897i
\(300\) 0 0
\(301\) 1.91388 7.14269i 0.110314 0.411698i
\(302\) 0 0
\(303\) −11.7298 5.76746i −0.673858 0.331332i
\(304\) 0 0
\(305\) 1.93444 + 7.21942i 0.110766 + 0.413383i
\(306\) 0 0
\(307\) −15.5744 + 15.5744i −0.888881 + 0.888881i −0.994416 0.105535i \(-0.966344\pi\)
0.105535 + 0.994416i \(0.466344\pi\)
\(308\) 0 0
\(309\) 6.08512 + 9.08403i 0.346170 + 0.516772i
\(310\) 0 0
\(311\) −16.8640 −0.956272 −0.478136 0.878286i \(-0.658687\pi\)
−0.478136 + 0.878286i \(0.658687\pi\)
\(312\) 0 0
\(313\) 14.7731 0.835026 0.417513 0.908671i \(-0.362902\pi\)
0.417513 + 0.908671i \(0.362902\pi\)
\(314\) 0 0
\(315\) −5.48128 + 4.22632i −0.308835 + 0.238126i
\(316\) 0 0
\(317\) 3.02944 3.02944i 0.170150 0.170150i −0.616895 0.787045i \(-0.711610\pi\)
0.787045 + 0.616895i \(0.211610\pi\)
\(318\) 0 0
\(319\) 3.07470 + 11.4749i 0.172150 + 0.642472i
\(320\) 0 0
\(321\) −6.41105 + 13.0387i −0.357830 + 0.727750i
\(322\) 0 0
\(323\) 3.74392 13.9725i 0.208317 0.777450i
\(324\) 0 0
\(325\) 7.13193 + 14.5365i 0.395609 + 0.806340i
\(326\) 0 0
\(327\) −24.8642 4.91559i −1.37499 0.271833i
\(328\) 0 0
\(329\) 2.92245 5.06183i 0.161120 0.279068i
\(330\) 0 0
\(331\) −0.735585 + 0.197099i −0.0404314 + 0.0108336i −0.278978 0.960297i \(-0.589996\pi\)
0.238547 + 0.971131i \(0.423329\pi\)
\(332\) 0 0
\(333\) −14.1251 + 18.4975i −0.774049 + 1.01366i
\(334\) 0 0
\(335\) 2.17476 + 3.76679i 0.118820 + 0.205802i
\(336\) 0 0
\(337\) 6.15955i 0.335532i −0.985827 0.167766i \(-0.946345\pi\)
0.985827 0.167766i \(-0.0536554\pi\)
\(338\) 0 0
\(339\) 26.0370 1.73711i 1.41413 0.0943468i
\(340\) 0 0
\(341\) 2.71004 1.56464i 0.146757 0.0847300i
\(342\) 0 0
\(343\) −8.10810 8.10810i −0.437796 0.437796i
\(344\) 0 0
\(345\) 5.68758 1.93809i 0.306209 0.104343i
\(346\) 0 0
\(347\) 5.68995 + 3.28509i 0.305452 + 0.176353i 0.644890 0.764276i \(-0.276903\pi\)
−0.339437 + 0.940629i \(0.610237\pi\)
\(348\) 0 0
\(349\) 1.81261 + 0.485688i 0.0970270 + 0.0259983i 0.307006 0.951708i \(-0.400673\pi\)
−0.209979 + 0.977706i \(0.567340\pi\)
\(350\) 0 0
\(351\) 11.4270 + 14.8466i 0.609930 + 0.792455i
\(352\) 0 0
\(353\) 26.6737 + 7.14721i 1.41970 + 0.380407i 0.885377 0.464873i \(-0.153900\pi\)
0.534323 + 0.845281i \(0.320567\pi\)
\(354\) 0 0
\(355\) 2.45199 + 1.41566i 0.130138 + 0.0751353i
\(356\) 0 0
\(357\) 16.1056 5.48812i 0.852400 0.290462i
\(358\) 0 0
\(359\) −10.1971 10.1971i −0.538182 0.538182i 0.384813 0.922995i \(-0.374266\pi\)
−0.922995 + 0.384813i \(0.874266\pi\)
\(360\) 0 0
\(361\) 3.17498 1.83307i 0.167104 0.0964775i
\(362\) 0 0
\(363\) −16.7420 + 1.11698i −0.878727 + 0.0586260i
\(364\) 0 0
\(365\) 4.10118i 0.214665i
\(366\) 0 0
\(367\) −2.25960 3.91375i −0.117950 0.204296i 0.801005 0.598658i \(-0.204299\pi\)
−0.918955 + 0.394362i \(0.870966\pi\)
\(368\) 0 0
\(369\) −12.3479 + 16.1702i −0.642807 + 0.841788i
\(370\) 0 0
\(371\) −7.58788 + 2.03316i −0.393943 + 0.105557i
\(372\) 0 0
\(373\) 2.40745 4.16983i 0.124653 0.215905i −0.796944 0.604053i \(-0.793552\pi\)
0.921597 + 0.388147i \(0.126885\pi\)
\(374\) 0 0
\(375\) −11.5075 2.27502i −0.594247 0.117481i
\(376\) 0 0
\(377\) 20.8345 31.0443i 1.07303 1.59886i
\(378\) 0 0
\(379\) −0.736874 + 2.75005i −0.0378507 + 0.141261i −0.982265 0.187496i \(-0.939963\pi\)
0.944415 + 0.328757i \(0.106630\pi\)
\(380\) 0 0
\(381\) −6.28861 + 12.7897i −0.322175 + 0.655236i
\(382\) 0 0
\(383\) −1.67036 6.23387i −0.0853514 0.318536i 0.910029 0.414544i \(-0.136059\pi\)
−0.995381 + 0.0960085i \(0.969392\pi\)
\(384\) 0 0
\(385\) 1.86901 1.86901i 0.0952536 0.0952536i
\(386\) 0 0
\(387\) 5.43370 4.18963i 0.276210 0.212971i
\(388\) 0 0
\(389\) 5.45516 0.276588 0.138294 0.990391i \(-0.455838\pi\)
0.138294 + 0.990391i \(0.455838\pi\)
\(390\) 0 0
\(391\) −14.7713 −0.747016
\(392\) 0 0
\(393\) −12.9266 19.2971i −0.652059 0.973412i
\(394\) 0 0
\(395\) 3.41988 3.41988i 0.172073 0.172073i
\(396\) 0 0
\(397\) −0.437429 1.63251i −0.0219539 0.0819331i 0.954080 0.299553i \(-0.0968374\pi\)
−0.976034 + 0.217620i \(0.930171\pi\)
\(398\) 0 0
\(399\) 23.9255 + 11.7640i 1.19777 + 0.588937i
\(400\) 0 0
\(401\) 5.16790 19.2869i 0.258073 0.963141i −0.708282 0.705929i \(-0.750530\pi\)
0.966355 0.257212i \(-0.0828037\pi\)
\(402\) 0 0
\(403\) −9.31927 3.18460i −0.464226 0.158636i
\(404\) 0 0
\(405\) −6.42218 + 0.0300156i −0.319121 + 0.00149149i
\(406\) 0 0
\(407\) 4.44396 7.69716i 0.220279 0.381534i
\(408\) 0 0
\(409\) 8.48733 2.27417i 0.419671 0.112451i −0.0428024 0.999084i \(-0.513629\pi\)
0.462474 + 0.886633i \(0.346962\pi\)
\(410\) 0 0
\(411\) 15.6160 17.8487i 0.770281 0.880411i
\(412\) 0 0
\(413\) 9.39609 + 16.2745i 0.462351 + 0.800816i
\(414\) 0 0
\(415\) 12.0519i 0.591603i
\(416\) 0 0
\(417\) −2.18938 32.8159i −0.107214 1.60700i
\(418\) 0 0
\(419\) 7.34045 4.23801i 0.358604 0.207040i −0.309864 0.950781i \(-0.600284\pi\)
0.668468 + 0.743741i \(0.266950\pi\)
\(420\) 0 0
\(421\) −15.5203 15.5203i −0.756412 0.756412i 0.219255 0.975667i \(-0.429637\pi\)
−0.975667 + 0.219255i \(0.929637\pi\)
\(422\) 0 0
\(423\) 5.00567 2.08713i 0.243384 0.101480i
\(424\) 0 0
\(425\) 11.8167 + 6.82236i 0.573193 + 0.330933i
\(426\) 0 0
\(427\) 32.7105 + 8.76477i 1.58297 + 0.424157i
\(428\) 0 0
\(429\) −5.05468 5.06342i −0.244042 0.244464i
\(430\) 0 0
\(431\) 26.3726 + 7.06652i 1.27032 + 0.340382i 0.830155 0.557533i \(-0.188252\pi\)
0.440169 + 0.897915i \(0.354919\pi\)
\(432\) 0 0
\(433\) 9.03766 + 5.21790i 0.434322 + 0.250756i 0.701186 0.712978i \(-0.252654\pi\)
−0.266864 + 0.963734i \(0.585987\pi\)
\(434\) 0 0
\(435\) 4.13381 + 12.1312i 0.198201 + 0.581648i
\(436\) 0 0
\(437\) −16.3663 16.3663i −0.782907 0.782907i
\(438\) 0 0
\(439\) 22.1085 12.7643i 1.05518 0.609208i 0.131084 0.991371i \(-0.458154\pi\)
0.924095 + 0.382163i \(0.124821\pi\)
\(440\) 0 0
\(441\) 1.37630 + 10.2686i 0.0655383 + 0.488980i
\(442\) 0 0
\(443\) 27.6082i 1.31170i 0.754889 + 0.655852i \(0.227691\pi\)
−0.754889 + 0.655852i \(0.772309\pi\)
\(444\) 0 0
\(445\) 2.85654 + 4.94767i 0.135413 + 0.234542i
\(446\) 0 0
\(447\) 7.80855 + 6.83179i 0.369332 + 0.323133i
\(448\) 0 0
\(449\) −26.6058 + 7.12899i −1.25560 + 0.336438i −0.824499 0.565864i \(-0.808543\pi\)
−0.431105 + 0.902302i \(0.641876\pi\)
\(450\) 0 0
\(451\) 3.88484 6.72874i 0.182930 0.316844i
\(452\) 0 0
\(453\) −5.21738 + 26.3907i −0.245134 + 1.23994i
\(454\) 0 0
\(455\) −8.29960 0.560921i −0.389091 0.0262964i
\(456\) 0 0
\(457\) 5.68707 21.2244i 0.266030 0.992838i −0.695587 0.718442i \(-0.744856\pi\)
0.961617 0.274396i \(-0.0884778\pi\)
\(458\) 0 0
\(459\) 14.9677 + 5.02240i 0.698632 + 0.234426i
\(460\) 0 0
\(461\) −5.98430 22.3337i −0.278717 1.04019i −0.953310 0.301995i \(-0.902347\pi\)
0.674593 0.738190i \(-0.264319\pi\)
\(462\) 0 0
\(463\) 8.48586 8.48586i 0.394371 0.394371i −0.481871 0.876242i \(-0.660043\pi\)
0.876242 + 0.481871i \(0.160043\pi\)
\(464\) 0 0
\(465\) 2.80482 1.87886i 0.130070 0.0871303i
\(466\) 0 0
\(467\) 26.9837 1.24866 0.624329 0.781162i \(-0.285373\pi\)
0.624329 + 0.781162i \(0.285373\pi\)
\(468\) 0 0
\(469\) 19.7072 0.909996
\(470\) 0 0
\(471\) −14.7089 + 9.85304i −0.677750 + 0.454004i
\(472\) 0 0
\(473\) −1.85278 + 1.85278i −0.0851911 + 0.0851911i
\(474\) 0 0
\(475\) 5.53361 + 20.6517i 0.253900 + 0.947566i
\(476\) 0 0
\(477\) −6.74065 2.77363i −0.308633 0.126996i
\(478\) 0 0
\(479\) 5.46091 20.3804i 0.249515 0.931203i −0.721545 0.692368i \(-0.756568\pi\)
0.971060 0.238836i \(-0.0767657\pi\)
\(480\) 0 0
\(481\) −27.4453 + 5.40127i −1.25140 + 0.246277i
\(482\) 0 0
\(483\) 5.28013 26.7081i 0.240254 1.21526i
\(484\) 0 0
\(485\) −0.365357 + 0.632817i −0.0165900 + 0.0287347i
\(486\) 0 0
\(487\) −15.7355 + 4.21633i −0.713046 + 0.191060i −0.597067 0.802192i \(-0.703667\pi\)
−0.115979 + 0.993252i \(0.537001\pi\)
\(488\) 0 0
\(489\) 28.0360 + 24.5290i 1.26783 + 1.10924i
\(490\) 0 0
\(491\) −16.2519 28.1492i −0.733440 1.27036i −0.955404 0.295300i \(-0.904580\pi\)
0.221965 0.975055i \(-0.428753\pi\)
\(492\) 0 0
\(493\) 31.5062i 1.41897i
\(494\) 0 0
\(495\) 2.43081 0.325803i 0.109257 0.0146438i
\(496\) 0 0
\(497\) 11.1097 6.41422i 0.498340 0.287717i
\(498\) 0 0
\(499\) 10.3481 + 10.3481i 0.463245 + 0.463245i 0.899718 0.436472i \(-0.143772\pi\)
−0.436472 + 0.899718i \(0.643772\pi\)
\(500\) 0 0
\(501\) 6.12394 + 17.9715i 0.273597 + 0.802909i
\(502\) 0 0
\(503\) −19.4725 11.2424i −0.868235 0.501276i −0.00147394 0.999999i \(-0.500469\pi\)
−0.866761 + 0.498723i \(0.833803\pi\)
\(504\) 0 0
\(505\) 5.20160 + 1.39376i 0.231468 + 0.0620217i
\(506\) 0 0
\(507\) −1.53770 + 22.4641i −0.0682915 + 0.997665i
\(508\) 0 0
\(509\) −27.6271 7.40267i −1.22455 0.328117i −0.412095 0.911141i \(-0.635203\pi\)
−0.812455 + 0.583023i \(0.801870\pi\)
\(510\) 0 0
\(511\) 16.0925 + 9.29103i 0.711892 + 0.411011i
\(512\) 0 0
\(513\) 11.0192 + 22.1487i 0.486509 + 0.977887i
\(514\) 0 0
\(515\) −3.18523 3.18523i −0.140358 0.140358i
\(516\) 0 0
\(517\) −1.79362 + 1.03554i −0.0788831 + 0.0455432i
\(518\) 0 0
\(519\) −2.33541 35.0047i −0.102513 1.53653i
\(520\) 0 0
\(521\) 7.17424i 0.314309i 0.987574 + 0.157155i \(0.0502321\pi\)
−0.987574 + 0.157155i \(0.949768\pi\)
\(522\) 0 0
\(523\) −11.5992 20.0904i −0.507199 0.878494i −0.999965 0.00833218i \(-0.997348\pi\)
0.492767 0.870161i \(-0.335986\pi\)
\(524\) 0 0
\(525\) −16.5595 + 18.9271i −0.722718 + 0.826047i
\(526\) 0 0
\(527\) −8.01637 + 2.14798i −0.349199 + 0.0935675i
\(528\) 0 0
\(529\) −0.317449 + 0.549837i −0.0138021 + 0.0239060i
\(530\) 0 0
\(531\) −2.23556 + 17.2930i −0.0970151 + 0.750450i
\(532\) 0 0
\(533\) −23.9923 + 4.72171i −1.03922 + 0.204520i
\(534\) 0 0
\(535\) 1.54930 5.78205i 0.0669819 0.249980i
\(536\) 0 0
\(537\) −32.9215 16.1873i −1.42067 0.698534i
\(538\) 0 0
\(539\) −1.02401 3.82165i −0.0441071 0.164610i
\(540\) 0 0
\(541\) 30.2641 30.2641i 1.30115 1.30115i 0.373539 0.927615i \(-0.378144\pi\)
0.927615 0.373539i \(-0.121856\pi\)
\(542\) 0 0
\(543\) −13.5318 20.2006i −0.580705 0.866892i
\(544\) 0 0
\(545\) 10.4420 0.447286
\(546\) 0 0
\(547\) −29.5412 −1.26309 −0.631545 0.775339i \(-0.717579\pi\)
−0.631545 + 0.775339i \(0.717579\pi\)
\(548\) 0 0
\(549\) 19.1868 + 24.8841i 0.818871 + 1.06203i
\(550\) 0 0
\(551\) 34.9083 34.9083i 1.48714 1.48714i
\(552\) 0 0
\(553\) −5.67163 21.1668i −0.241182 0.900104i
\(554\) 0 0
\(555\) 4.23086 8.60467i 0.179590 0.365248i
\(556\) 0 0
\(557\) −6.70422 + 25.0205i −0.284067 + 1.06015i 0.665451 + 0.746441i \(0.268239\pi\)
−0.949518 + 0.313712i \(0.898428\pi\)
\(558\) 0 0
\(559\) 8.22754 + 0.556051i 0.347988 + 0.0235185i
\(560\) 0 0
\(561\) −5.91464 1.16931i −0.249716 0.0493684i
\(562\) 0 0
\(563\) 2.40232 4.16095i 0.101246 0.175363i −0.810952 0.585112i \(-0.801050\pi\)
0.912198 + 0.409749i \(0.134384\pi\)
\(564\) 0 0
\(565\) −10.3844 + 2.78250i −0.436876 + 0.117061i
\(566\) 0 0
\(567\) −14.4314 + 25.2679i −0.606061 + 1.06115i
\(568\) 0 0
\(569\) −1.00204 1.73559i −0.0420078 0.0727597i 0.844257 0.535938i \(-0.180042\pi\)
−0.886265 + 0.463179i \(0.846709\pi\)
\(570\) 0 0
\(571\) 16.7105i 0.699311i 0.936878 + 0.349656i \(0.113701\pi\)
−0.936878 + 0.349656i \(0.886299\pi\)
\(572\) 0 0
\(573\) −37.3834 + 2.49411i −1.56171 + 0.104193i
\(574\) 0 0
\(575\) 18.9074 10.9162i 0.788492 0.455236i
\(576\) 0 0
\(577\) 14.2655 + 14.2655i 0.593883 + 0.593883i 0.938678 0.344795i \(-0.112052\pi\)
−0.344795 + 0.938678i \(0.612052\pi\)
\(578\) 0 0
\(579\) 34.9685 11.9158i 1.45324 0.495203i
\(580\) 0 0
\(581\) −47.2901 27.3030i −1.96193 1.13272i
\(582\) 0 0
\(583\) 2.68870 + 0.720434i 0.111354 + 0.0298373i
\(584\) 0 0
\(585\) −5.80469 5.08745i −0.239994 0.210340i
\(586\) 0 0
\(587\) −1.79654 0.481380i −0.0741509 0.0198687i 0.221553 0.975148i \(-0.428887\pi\)
−0.295704 + 0.955280i \(0.595554\pi\)
\(588\) 0 0
\(589\) −11.2619 6.50207i −0.464039 0.267913i
\(590\) 0 0
\(591\) −42.0166 + 14.3175i −1.72833 + 0.588943i
\(592\) 0 0
\(593\) 32.1956 + 32.1956i 1.32212 + 1.32212i 0.912060 + 0.410057i \(0.134491\pi\)
0.410057 + 0.912060i \(0.365509\pi\)
\(594\) 0 0
\(595\) −6.07081 + 3.50499i −0.248879 + 0.143690i
\(596\) 0 0
\(597\) −27.2474 + 1.81786i −1.11516 + 0.0744001i
\(598\) 0 0
\(599\) 14.7278i 0.601762i 0.953662 + 0.300881i \(0.0972807\pi\)
−0.953662 + 0.300881i \(0.902719\pi\)
\(600\) 0 0
\(601\) 23.2965 + 40.3507i 0.950282 + 1.64594i 0.744812 + 0.667274i \(0.232539\pi\)
0.205470 + 0.978663i \(0.434128\pi\)
\(602\) 0 0
\(603\) 14.5332 + 11.0978i 0.591837 + 0.451939i
\(604\) 0 0
\(605\) 6.67728 1.78917i 0.271470 0.0727402i
\(606\) 0 0
\(607\) 5.31772 9.21056i 0.215840 0.373845i −0.737692 0.675137i \(-0.764085\pi\)
0.953532 + 0.301292i \(0.0974178\pi\)
\(608\) 0 0
\(609\) 56.9665 + 11.2622i 2.30840 + 0.456366i
\(610\) 0 0
\(611\) 6.16788 + 2.10770i 0.249526 + 0.0852684i
\(612\) 0 0
\(613\) −4.55636 + 17.0046i −0.184030 + 0.686808i 0.810806 + 0.585314i \(0.199029\pi\)
−0.994836 + 0.101494i \(0.967638\pi\)
\(614\) 0 0
\(615\) 3.69855 7.52207i 0.149140 0.303319i
\(616\) 0 0
\(617\) 1.61026 + 6.00956i 0.0648265 + 0.241936i 0.990734 0.135813i \(-0.0433648\pi\)
−0.925908 + 0.377749i \(0.876698\pi\)
\(618\) 0 0
\(619\) −20.3122 + 20.3122i −0.816415 + 0.816415i −0.985587 0.169172i \(-0.945891\pi\)
0.169172 + 0.985587i \(0.445891\pi\)
\(620\) 0 0
\(621\) 18.9341 16.7225i 0.759799 0.671052i
\(622\) 0 0
\(623\) 25.8854 1.03708
\(624\) 0 0
\(625\) −17.6213 −0.704851
\(626\) 0 0
\(627\) −5.25773 7.84889i −0.209974 0.313454i
\(628\) 0 0
\(629\) −16.6676 + 16.6676i −0.664583 + 0.664583i
\(630\) 0 0
\(631\) 7.88943 + 29.4438i 0.314073 + 1.17214i 0.924849 + 0.380334i \(0.124191\pi\)
−0.610776 + 0.791804i \(0.709142\pi\)
\(632\) 0 0
\(633\) 16.1744 + 7.95285i 0.642875 + 0.316097i
\(634\) 0 0
\(635\) 1.51971 5.67162i 0.0603077 0.225072i
\(636\) 0 0
\(637\) −6.93879 + 10.3391i −0.274925 + 0.409650i
\(638\) 0 0
\(639\) 11.8050 + 1.52610i 0.466998 + 0.0603716i
\(640\) 0 0
\(641\) 15.6856 27.1682i 0.619543 1.07308i −0.370026 0.929021i \(-0.620651\pi\)
0.989569 0.144058i \(-0.0460153\pi\)
\(642\) 0 0
\(643\) −4.97838 + 1.33395i −0.196328 + 0.0526060i −0.355643 0.934622i \(-0.615738\pi\)
0.159315 + 0.987228i \(0.449071\pi\)
\(644\) 0 0
\(645\) −1.86135 + 2.12747i −0.0732905 + 0.0837690i
\(646\) 0 0
\(647\) 4.80729 + 8.32648i 0.188994 + 0.327348i 0.944915 0.327315i \(-0.106144\pi\)
−0.755921 + 0.654663i \(0.772811\pi\)
\(648\) 0 0
\(649\) 6.65884i 0.261382i
\(650\) 0 0
\(651\) −1.01825 15.2623i −0.0399085 0.598176i
\(652\) 0 0
\(653\) 16.4158 9.47768i 0.642401 0.370890i −0.143138 0.989703i \(-0.545719\pi\)
0.785539 + 0.618813i \(0.212386\pi\)
\(654\) 0 0
\(655\) 6.76636 + 6.76636i 0.264384 + 0.264384i
\(656\) 0 0
\(657\) 6.63539 + 15.9140i 0.258871 + 0.620863i
\(658\) 0 0
\(659\) 23.6778 + 13.6704i 0.922357 + 0.532523i 0.884386 0.466756i \(-0.154577\pi\)
0.0379709 + 0.999279i \(0.487911\pi\)
\(660\) 0 0
\(661\) −9.46548 2.53627i −0.368165 0.0986494i 0.0699932 0.997547i \(-0.477702\pi\)
−0.438158 + 0.898898i \(0.644369\pi\)
\(662\) 0 0
\(663\) 9.47313 + 16.4407i 0.367906 + 0.638504i
\(664\) 0 0
\(665\) −10.6098 2.84289i −0.411431 0.110243i
\(666\) 0 0
\(667\) −43.6578 25.2058i −1.69044 0.975974i
\(668\) 0 0
\(669\) −12.7061 37.2879i −0.491248 1.44163i
\(670\) 0 0
\(671\) −8.48497 8.48497i −0.327559 0.327559i
\(672\) 0 0
\(673\) −6.65548 + 3.84254i −0.256550 + 0.148119i −0.622760 0.782413i \(-0.713989\pi\)
0.366210 + 0.930532i \(0.380655\pi\)
\(674\) 0 0
\(675\) −22.8704 + 4.63260i −0.880282 + 0.178309i
\(676\) 0 0
\(677\) 11.5419i 0.443593i 0.975093 + 0.221797i \(0.0711921\pi\)
−0.975093 + 0.221797i \(0.928808\pi\)
\(678\) 0 0
\(679\) 1.65540 + 2.86724i 0.0635284 + 0.110034i
\(680\) 0 0
\(681\) −25.9116 22.6703i −0.992933 0.868729i
\(682\) 0 0
\(683\) −19.8376 + 5.31546i −0.759063 + 0.203390i −0.617535 0.786544i \(-0.711868\pi\)
−0.141529 + 0.989934i \(0.545202\pi\)
\(684\) 0 0
\(685\) −4.88529 + 8.46157i −0.186657 + 0.323300i
\(686\) 0 0
\(687\) −0.552445 + 2.79439i −0.0210771 + 0.106613i
\(688\) 0 0
\(689\) −3.85860 7.86471i −0.147001 0.299622i
\(690\) 0 0
\(691\) 0.529217 1.97507i 0.0201324 0.0751350i −0.955129 0.296191i \(-0.904284\pi\)
0.975261 + 0.221056i \(0.0709503\pi\)
\(692\) 0 0
\(693\) 4.22848 10.2763i 0.160627 0.390365i
\(694\) 0 0
\(695\) 3.50695 + 13.0881i 0.133026 + 0.496460i
\(696\) 0 0
\(697\) −14.5706 + 14.5706i −0.551901 + 0.551901i
\(698\) 0 0
\(699\) −34.2700 + 22.9565i −1.29621 + 0.868294i
\(700\) 0 0
\(701\) 13.4888 0.509464 0.254732 0.967012i \(-0.418013\pi\)
0.254732 + 0.967012i \(0.418013\pi\)
\(702\) 0 0
\(703\) −36.9349 −1.39303
\(704\) 0 0
\(705\) −1.85635 + 1.24351i −0.0699141 + 0.0468334i
\(706\) 0 0
\(707\) 17.2530 17.2530i 0.648864 0.648864i
\(708\) 0 0
\(709\) −3.48407 13.0027i −0.130847 0.488328i 0.869133 0.494578i \(-0.164677\pi\)
−0.999980 + 0.00624974i \(0.998011\pi\)
\(710\) 0 0
\(711\) 7.73720 18.8034i 0.290168 0.705183i
\(712\) 0 0
\(713\) −3.43689 + 12.8267i −0.128713 + 0.480362i
\(714\) 0 0
\(715\) 2.44751 + 1.64257i 0.0915315 + 0.0614287i
\(716\) 0 0
\(717\) −1.47351 + 7.45333i −0.0550291 + 0.278350i
\(718\) 0 0
\(719\) −9.18916 + 15.9161i −0.342698 + 0.593570i −0.984933 0.172938i \(-0.944674\pi\)
0.642235 + 0.766508i \(0.278007\pi\)
\(720\) 0 0
\(721\) −19.7145 + 5.28248i −0.734205 + 0.196730i
\(722\) 0 0
\(723\) 11.3440 + 9.92502i 0.421889 + 0.369115i
\(724\) 0 0
\(725\) 23.2835 + 40.3282i 0.864727 + 1.49775i
\(726\) 0 0
\(727\) 14.3838i 0.533466i 0.963770 + 0.266733i \(0.0859442\pi\)
−0.963770 + 0.266733i \(0.914056\pi\)
\(728\) 0 0
\(729\) −24.8717 + 10.5071i −0.921174 + 0.389151i
\(730\) 0 0
\(731\) 6.01811 3.47456i 0.222588 0.128511i
\(732\) 0 0
\(733\) 3.75917 + 3.75917i 0.138848 + 0.138848i 0.773114 0.634266i \(-0.218698\pi\)
−0.634266 + 0.773114i \(0.718698\pi\)
\(734\) 0 0
\(735\) −1.37674 4.04023i −0.0507818 0.149026i
\(736\) 0 0
\(737\) −6.04753 3.49154i −0.222764 0.128613i
\(738\) 0 0
\(739\) 37.0517 + 9.92797i 1.36297 + 0.365206i 0.864905 0.501935i \(-0.167378\pi\)
0.498063 + 0.867141i \(0.334045\pi\)
\(740\) 0 0
\(741\) −7.71994 + 28.7121i −0.283599 + 1.05476i
\(742\) 0 0
\(743\) −32.0441 8.58618i −1.17558 0.314996i −0.382410 0.923993i \(-0.624906\pi\)
−0.793173 + 0.608996i \(0.791572\pi\)
\(744\) 0 0
\(745\) −3.70182 2.13725i −0.135624 0.0783027i
\(746\) 0 0
\(747\) −19.4990 46.7654i −0.713432 1.71106i
\(748\) 0 0
\(749\) −19.1782 19.1782i −0.700757 0.700757i
\(750\) 0 0
\(751\) 19.2045 11.0877i 0.700782 0.404597i −0.106857 0.994274i \(-0.534079\pi\)
0.807639 + 0.589678i \(0.200745\pi\)
\(752\) 0 0
\(753\) −1.00124 15.0072i −0.0364871 0.546893i
\(754\) 0 0
\(755\) 11.0831i 0.403354i
\(756\) 0 0
\(757\) 10.5455 + 18.2654i 0.383284 + 0.663868i 0.991530 0.129881i \(-0.0414597\pi\)
−0.608245 + 0.793749i \(0.708126\pi\)
\(758\) 0 0
\(759\) −6.35218 + 7.26037i −0.230570 + 0.263535i
\(760\) 0 0
\(761\) −31.8738 + 8.54057i −1.15543 + 0.309595i −0.785137 0.619322i \(-0.787408\pi\)
−0.370288 + 0.928917i \(0.620741\pi\)
\(762\) 0 0
\(763\) 23.6559 40.9732i 0.856400 1.48333i
\(764\) 0 0
\(765\) −6.45072 0.833922i −0.233226 0.0301505i
\(766\) 0 0
\(767\) −15.7840 + 13.7855i −0.569926 + 0.497767i
\(768\) 0 0
\(769\) −1.87152 + 6.98462i −0.0674889 + 0.251872i −0.991425 0.130674i \(-0.958286\pi\)
0.923937 + 0.382546i \(0.124953\pi\)
\(770\) 0 0
\(771\) 9.30937 + 4.57736i 0.335269 + 0.164850i
\(772\) 0 0
\(773\) −2.16927 8.09584i −0.0780234 0.291187i 0.915878 0.401456i \(-0.131496\pi\)
−0.993902 + 0.110268i \(0.964829\pi\)
\(774\) 0 0
\(775\) 8.67364 8.67364i 0.311566 0.311566i
\(776\) 0 0
\(777\) −24.1789 36.0949i −0.867413 1.29490i
\(778\) 0 0
\(779\) −32.2879 −1.15684
\(780\) 0 0
\(781\) −4.54564 −0.162656
\(782\) 0 0
\(783\) 35.6680 + 40.3852i 1.27467 + 1.44325i
\(784\) 0 0
\(785\) 5.15753 5.15753i 0.184080 0.184080i
\(786\) 0 0
\(787\) 8.20017 + 30.6035i 0.292305 + 1.09090i 0.943335 + 0.331843i \(0.107671\pi\)
−0.651030 + 0.759052i \(0.725663\pi\)
\(788\) 0 0
\(789\) 14.6416 29.7779i 0.521255 1.06012i
\(790\) 0 0
\(791\) −12.6073 + 47.0509i −0.448263 + 1.67294i
\(792\) 0 0
\(793\) −2.54648 + 37.6787i −0.0904282 + 1.33801i
\(794\) 0 0
\(795\) 2.94596 + 0.582409i 0.104482 + 0.0206559i
\(796\) 0 0
\(797\)