Properties

Label 1152.2.i.i.385.4
Level $1152$
Weight $2$
Character 1152.385
Analytic conductor $9.199$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 2 x^{11} + 3 x^{10} - 8 x^{9} + 22 x^{8} - 42 x^{7} + 51 x^{6} - 126 x^{5} + 198 x^{4} - 216 x^{3} + 243 x^{2} - 486 x + 729\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 385.4
Root \(-1.28252 + 1.16410i\) of defining polynomial
Character \(\chi\) \(=\) 1152.385
Dual form 1152.2.i.i.769.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.366879 + 1.69275i) q^{3} +(-1.05471 - 1.82681i) q^{5} +(1.43914 - 2.49267i) q^{7} +(-2.73080 - 1.24207i) q^{9} +O(q^{10})\) \(q+(-0.366879 + 1.69275i) q^{3} +(-1.05471 - 1.82681i) q^{5} +(1.43914 - 2.49267i) q^{7} +(-2.73080 - 1.24207i) q^{9} +(1.21325 - 2.10141i) q^{11} +(3.30008 + 5.71590i) q^{13} +(3.47929 - 1.11514i) q^{15} -7.56848 q^{17} -6.25779 q^{19} +(3.69147 + 3.35061i) q^{21} +(-2.63611 - 4.56587i) q^{23} +(0.275172 - 0.476612i) q^{25} +(3.10438 - 4.16687i) q^{27} +(-1.57821 + 2.73353i) q^{29} +(-1.79039 - 3.10104i) q^{31} +(3.11204 + 2.82469i) q^{33} -6.07151 q^{35} -6.70957 q^{37} +(-10.8863 + 3.48916i) q^{39} +(-1.74537 - 3.02306i) q^{41} +(-3.12570 + 5.41388i) q^{43} +(0.611180 + 6.29868i) q^{45} +(1.32972 - 2.30314i) q^{47} +(-0.642255 - 1.11242i) q^{49} +(2.77671 - 12.8115i) q^{51} +0.953009 q^{53} -5.11850 q^{55} +(2.29585 - 10.5929i) q^{57} +(-4.84757 - 8.39624i) q^{59} +(2.57821 - 4.46558i) q^{61} +(-7.02607 + 5.01946i) q^{63} +(6.96125 - 12.0572i) q^{65} +(-0.949546 - 1.64466i) q^{67} +(8.69601 - 2.78715i) q^{69} +5.82491 q^{71} -5.01222 q^{73} +(0.705829 + 0.640656i) q^{75} +(-3.49207 - 6.04844i) q^{77} +(6.49996 - 11.2583i) q^{79} +(5.91454 + 6.78368i) q^{81} +(-1.54502 + 2.67606i) q^{83} +(7.98256 + 13.8262i) q^{85} +(-4.04818 - 3.67438i) q^{87} -2.95301 q^{89} +18.9971 q^{91} +(5.90614 - 1.89297i) q^{93} +(6.60015 + 11.4318i) q^{95} +(-5.51242 + 9.54779i) q^{97} +(-5.92323 + 4.23159i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 4 q^{3} - 2 q^{5} - 6 q^{7} - 2 q^{9} + O(q^{10}) \) \( 12 q - 4 q^{3} - 2 q^{5} - 6 q^{7} - 2 q^{9} - 4 q^{11} + 10 q^{13} - 4 q^{15} + 4 q^{17} - 4 q^{19} + 2 q^{21} - 8 q^{23} - 14 q^{25} + 14 q^{27} - 2 q^{29} - 8 q^{31} - 10 q^{33} - 8 q^{35} - 22 q^{39} - 2 q^{41} + 2 q^{43} + 10 q^{45} + 14 q^{47} - 18 q^{49} + 38 q^{51} + 24 q^{53} + 16 q^{55} - 38 q^{57} - 6 q^{59} + 14 q^{61} + 16 q^{63} - 8 q^{65} - 4 q^{67} - 50 q^{69} + 28 q^{71} + 60 q^{73} - 50 q^{75} + 2 q^{77} - 16 q^{79} + 22 q^{81} - 24 q^{83} + 16 q^{85} + 36 q^{87} - 48 q^{89} + 52 q^{91} + 42 q^{93} + 20 q^{95} - 14 q^{97} - 68 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) −0.366879 + 1.69275i −0.211818 + 0.977309i
\(4\) 0 0
\(5\) −1.05471 1.82681i −0.471681 0.816975i 0.527794 0.849372i \(-0.323019\pi\)
−0.999475 + 0.0323971i \(0.989686\pi\)
\(6\) 0 0
\(7\) 1.43914 2.49267i 0.543944 0.942139i −0.454728 0.890630i \(-0.650264\pi\)
0.998673 0.0515089i \(-0.0164031\pi\)
\(8\) 0 0
\(9\) −2.73080 1.24207i −0.910267 0.414022i
\(10\) 0 0
\(11\) 1.21325 2.10141i 0.365808 0.633598i −0.623097 0.782144i \(-0.714126\pi\)
0.988905 + 0.148546i \(0.0474594\pi\)
\(12\) 0 0
\(13\) 3.30008 + 5.71590i 0.915277 + 1.58531i 0.806496 + 0.591240i \(0.201361\pi\)
0.108781 + 0.994066i \(0.465305\pi\)
\(14\) 0 0
\(15\) 3.47929 1.11514i 0.898348 0.287928i
\(16\) 0 0
\(17\) −7.56848 −1.83563 −0.917813 0.397013i \(-0.870047\pi\)
−0.917813 + 0.397013i \(0.870047\pi\)
\(18\) 0 0
\(19\) −6.25779 −1.43563 −0.717817 0.696231i \(-0.754859\pi\)
−0.717817 + 0.696231i \(0.754859\pi\)
\(20\) 0 0
\(21\) 3.69147 + 3.35061i 0.805544 + 0.731163i
\(22\) 0 0
\(23\) −2.63611 4.56587i −0.549666 0.952050i −0.998297 0.0583329i \(-0.981422\pi\)
0.448631 0.893717i \(-0.351912\pi\)
\(24\) 0 0
\(25\) 0.275172 0.476612i 0.0550344 0.0953223i
\(26\) 0 0
\(27\) 3.10438 4.16687i 0.597438 0.801915i
\(28\) 0 0
\(29\) −1.57821 + 2.73353i −0.293065 + 0.507604i −0.974533 0.224244i \(-0.928009\pi\)
0.681468 + 0.731848i \(0.261342\pi\)
\(30\) 0 0
\(31\) −1.79039 3.10104i −0.321563 0.556964i 0.659248 0.751926i \(-0.270875\pi\)
−0.980811 + 0.194962i \(0.937542\pi\)
\(32\) 0 0
\(33\) 3.11204 + 2.82469i 0.541737 + 0.491715i
\(34\) 0 0
\(35\) −6.07151 −1.02627
\(36\) 0 0
\(37\) −6.70957 −1.10305 −0.551524 0.834159i \(-0.685953\pi\)
−0.551524 + 0.834159i \(0.685953\pi\)
\(38\) 0 0
\(39\) −10.8863 + 3.48916i −1.74321 + 0.558713i
\(40\) 0 0
\(41\) −1.74537 3.02306i −0.272580 0.472123i 0.696941 0.717128i \(-0.254544\pi\)
−0.969522 + 0.245005i \(0.921210\pi\)
\(42\) 0 0
\(43\) −3.12570 + 5.41388i −0.476665 + 0.825608i −0.999642 0.0267383i \(-0.991488\pi\)
0.522977 + 0.852347i \(0.324821\pi\)
\(44\) 0 0
\(45\) 0.611180 + 6.29868i 0.0911093 + 0.938952i
\(46\) 0 0
\(47\) 1.32972 2.30314i 0.193960 0.335948i −0.752599 0.658479i \(-0.771200\pi\)
0.946559 + 0.322531i \(0.104534\pi\)
\(48\) 0 0
\(49\) −0.642255 1.11242i −0.0917508 0.158917i
\(50\) 0 0
\(51\) 2.77671 12.8115i 0.388818 1.79397i
\(52\) 0 0
\(53\) 0.953009 0.130906 0.0654529 0.997856i \(-0.479151\pi\)
0.0654529 + 0.997856i \(0.479151\pi\)
\(54\) 0 0
\(55\) −5.11850 −0.690178
\(56\) 0 0
\(57\) 2.29585 10.5929i 0.304093 1.40306i
\(58\) 0 0
\(59\) −4.84757 8.39624i −0.631100 1.09310i −0.987327 0.158698i \(-0.949270\pi\)
0.356227 0.934400i \(-0.384063\pi\)
\(60\) 0 0
\(61\) 2.57821 4.46558i 0.330105 0.571759i −0.652427 0.757852i \(-0.726249\pi\)
0.982532 + 0.186092i \(0.0595824\pi\)
\(62\) 0 0
\(63\) −7.02607 + 5.01946i −0.885201 + 0.632393i
\(64\) 0 0
\(65\) 6.96125 12.0572i 0.863437 1.49552i
\(66\) 0 0
\(67\) −0.949546 1.64466i −0.116005 0.200927i 0.802176 0.597088i \(-0.203676\pi\)
−0.918181 + 0.396161i \(0.870342\pi\)
\(68\) 0 0
\(69\) 8.69601 2.78715i 1.04688 0.335533i
\(70\) 0 0
\(71\) 5.82491 0.691290 0.345645 0.938365i \(-0.387660\pi\)
0.345645 + 0.938365i \(0.387660\pi\)
\(72\) 0 0
\(73\) −5.01222 −0.586636 −0.293318 0.956015i \(-0.594760\pi\)
−0.293318 + 0.956015i \(0.594760\pi\)
\(74\) 0 0
\(75\) 0.705829 + 0.640656i 0.0815021 + 0.0739765i
\(76\) 0 0
\(77\) −3.49207 6.04844i −0.397958 0.689284i
\(78\) 0 0
\(79\) 6.49996 11.2583i 0.731303 1.26665i −0.225024 0.974353i \(-0.572246\pi\)
0.956327 0.292301i \(-0.0944207\pi\)
\(80\) 0 0
\(81\) 5.91454 + 6.78368i 0.657171 + 0.753742i
\(82\) 0 0
\(83\) −1.54502 + 2.67606i −0.169588 + 0.293735i −0.938275 0.345890i \(-0.887577\pi\)
0.768687 + 0.639625i \(0.220910\pi\)
\(84\) 0 0
\(85\) 7.98256 + 13.8262i 0.865830 + 1.49966i
\(86\) 0 0
\(87\) −4.04818 3.67438i −0.434010 0.393935i
\(88\) 0 0
\(89\) −2.95301 −0.313018 −0.156509 0.987677i \(-0.550024\pi\)
−0.156509 + 0.987677i \(0.550024\pi\)
\(90\) 0 0
\(91\) 18.9971 1.99144
\(92\) 0 0
\(93\) 5.90614 1.89297i 0.612439 0.196292i
\(94\) 0 0
\(95\) 6.60015 + 11.4318i 0.677161 + 1.17288i
\(96\) 0 0
\(97\) −5.51242 + 9.54779i −0.559702 + 0.969432i 0.437820 + 0.899063i \(0.355751\pi\)
−0.997521 + 0.0703686i \(0.977582\pi\)
\(98\) 0 0
\(99\) −5.92323 + 4.23159i −0.595307 + 0.425290i
\(100\) 0 0
\(101\) 1.82357 3.15852i 0.181452 0.314284i −0.760923 0.648842i \(-0.775254\pi\)
0.942375 + 0.334558i \(0.108587\pi\)
\(102\) 0 0
\(103\) −5.43914 9.42087i −0.535935 0.928266i −0.999117 0.0420031i \(-0.986626\pi\)
0.463183 0.886263i \(-0.346707\pi\)
\(104\) 0 0
\(105\) 2.22751 10.2775i 0.217382 1.00299i
\(106\) 0 0
\(107\) 5.94922 0.575133 0.287567 0.957761i \(-0.407154\pi\)
0.287567 + 0.957761i \(0.407154\pi\)
\(108\) 0 0
\(109\) 9.87113 0.945483 0.472741 0.881201i \(-0.343265\pi\)
0.472741 + 0.881201i \(0.343265\pi\)
\(110\) 0 0
\(111\) 2.46160 11.3576i 0.233645 1.07802i
\(112\) 0 0
\(113\) −7.51518 13.0167i −0.706969 1.22451i −0.965976 0.258630i \(-0.916729\pi\)
0.259008 0.965875i \(-0.416604\pi\)
\(114\) 0 0
\(115\) −5.56066 + 9.63134i −0.518534 + 0.898128i
\(116\) 0 0
\(117\) −1.91232 19.7079i −0.176794 1.82200i
\(118\) 0 0
\(119\) −10.8921 + 18.8657i −0.998478 + 1.72942i
\(120\) 0 0
\(121\) 2.55606 + 4.42722i 0.232369 + 0.402475i
\(122\) 0 0
\(123\) 5.75763 1.84537i 0.519148 0.166391i
\(124\) 0 0
\(125\) −11.7080 −1.04720
\(126\) 0 0
\(127\) 8.07789 0.716797 0.358398 0.933569i \(-0.383323\pi\)
0.358398 + 0.933569i \(0.383323\pi\)
\(128\) 0 0
\(129\) −8.01758 7.27727i −0.705909 0.640728i
\(130\) 0 0
\(131\) −11.1329 19.2827i −0.972684 1.68474i −0.687375 0.726303i \(-0.741237\pi\)
−0.285309 0.958435i \(-0.592096\pi\)
\(132\) 0 0
\(133\) −9.00584 + 15.5986i −0.780905 + 1.35257i
\(134\) 0 0
\(135\) −10.8863 1.27628i −0.936945 0.109844i
\(136\) 0 0
\(137\) −4.62365 + 8.00839i −0.395025 + 0.684203i −0.993104 0.117234i \(-0.962597\pi\)
0.598079 + 0.801437i \(0.295931\pi\)
\(138\) 0 0
\(139\) −4.20256 7.27905i −0.356456 0.617401i 0.630910 0.775856i \(-0.282682\pi\)
−0.987366 + 0.158456i \(0.949349\pi\)
\(140\) 0 0
\(141\) 3.41080 + 3.09586i 0.287241 + 0.260718i
\(142\) 0 0
\(143\) 16.0152 1.33926
\(144\) 0 0
\(145\) 6.65820 0.552934
\(146\) 0 0
\(147\) 2.11868 0.679055i 0.174745 0.0560075i
\(148\) 0 0
\(149\) 6.17836 + 10.7012i 0.506151 + 0.876679i 0.999975 + 0.00711709i \(0.00226546\pi\)
−0.493824 + 0.869562i \(0.664401\pi\)
\(150\) 0 0
\(151\) −4.91424 + 8.51171i −0.399915 + 0.692673i −0.993715 0.111940i \(-0.964294\pi\)
0.593800 + 0.804613i \(0.297627\pi\)
\(152\) 0 0
\(153\) 20.6680 + 9.40056i 1.67091 + 0.759990i
\(154\) 0 0
\(155\) −3.77668 + 6.54141i −0.303350 + 0.525418i
\(156\) 0 0
\(157\) −0.108083 0.187206i −0.00862598 0.0149406i 0.861680 0.507452i \(-0.169412\pi\)
−0.870306 + 0.492511i \(0.836079\pi\)
\(158\) 0 0
\(159\) −0.349639 + 1.61321i −0.0277282 + 0.127935i
\(160\) 0 0
\(161\) −15.1749 −1.19595
\(162\) 0 0
\(163\) 5.78116 0.452815 0.226408 0.974033i \(-0.427302\pi\)
0.226408 + 0.974033i \(0.427302\pi\)
\(164\) 0 0
\(165\) 1.87787 8.66434i 0.146192 0.674518i
\(166\) 0 0
\(167\) 0.818646 + 1.41794i 0.0633487 + 0.109723i 0.895960 0.444134i \(-0.146489\pi\)
−0.832612 + 0.553857i \(0.813155\pi\)
\(168\) 0 0
\(169\) −15.2810 + 26.4675i −1.17546 + 2.03596i
\(170\) 0 0
\(171\) 17.0888 + 7.77259i 1.30681 + 0.594385i
\(172\) 0 0
\(173\) −2.99228 + 5.18278i −0.227499 + 0.394040i −0.957066 0.289869i \(-0.906388\pi\)
0.729567 + 0.683909i \(0.239721\pi\)
\(174\) 0 0
\(175\) −0.792022 1.37182i −0.0598713 0.103700i
\(176\) 0 0
\(177\) 15.9912 5.12532i 1.20197 0.385243i
\(178\) 0 0
\(179\) −9.51313 −0.711045 −0.355522 0.934668i \(-0.615697\pi\)
−0.355522 + 0.934668i \(0.615697\pi\)
\(180\) 0 0
\(181\) −23.7526 −1.76551 −0.882757 0.469830i \(-0.844315\pi\)
−0.882757 + 0.469830i \(0.844315\pi\)
\(182\) 0 0
\(183\) 6.61322 + 6.00258i 0.488864 + 0.443724i
\(184\) 0 0
\(185\) 7.07666 + 12.2571i 0.520286 + 0.901162i
\(186\) 0 0
\(187\) −9.18244 + 15.9045i −0.671487 + 1.16305i
\(188\) 0 0
\(189\) −5.91898 13.7349i −0.430542 0.999067i
\(190\) 0 0
\(191\) 4.14164 7.17352i 0.299678 0.519058i −0.676384 0.736549i \(-0.736454\pi\)
0.976062 + 0.217491i \(0.0697873\pi\)
\(192\) 0 0
\(193\) 5.00315 + 8.66572i 0.360135 + 0.623772i 0.987983 0.154564i \(-0.0493973\pi\)
−0.627848 + 0.778336i \(0.716064\pi\)
\(194\) 0 0
\(195\) 17.8559 + 16.2072i 1.27869 + 1.16062i
\(196\) 0 0
\(197\) 0.556259 0.0396318 0.0198159 0.999804i \(-0.493692\pi\)
0.0198159 + 0.999804i \(0.493692\pi\)
\(198\) 0 0
\(199\) 21.5526 1.52782 0.763912 0.645320i \(-0.223276\pi\)
0.763912 + 0.645320i \(0.223276\pi\)
\(200\) 0 0
\(201\) 3.13237 1.00395i 0.220940 0.0708133i
\(202\) 0 0
\(203\) 4.54252 + 7.86788i 0.318823 + 0.552217i
\(204\) 0 0
\(205\) −3.68171 + 6.37691i −0.257142 + 0.445383i
\(206\) 0 0
\(207\) 1.52756 + 15.7427i 0.106173 + 1.09419i
\(208\) 0 0
\(209\) −7.59225 + 13.1502i −0.525167 + 0.909615i
\(210\) 0 0
\(211\) 8.32984 + 14.4277i 0.573450 + 0.993245i 0.996208 + 0.0870022i \(0.0277287\pi\)
−0.422758 + 0.906243i \(0.638938\pi\)
\(212\) 0 0
\(213\) −2.13704 + 9.86011i −0.146427 + 0.675604i
\(214\) 0 0
\(215\) 13.1868 0.899335
\(216\) 0 0
\(217\) −10.3065 −0.699650
\(218\) 0 0
\(219\) 1.83888 8.48443i 0.124260 0.573325i
\(220\) 0 0
\(221\) −24.9766 43.2607i −1.68011 2.91003i
\(222\) 0 0
\(223\) −4.49251 + 7.78126i −0.300841 + 0.521072i −0.976327 0.216301i \(-0.930601\pi\)
0.675486 + 0.737373i \(0.263934\pi\)
\(224\) 0 0
\(225\) −1.34342 + 0.959749i −0.0895615 + 0.0639833i
\(226\) 0 0
\(227\) −5.32448 + 9.22226i −0.353398 + 0.612103i −0.986842 0.161685i \(-0.948307\pi\)
0.633445 + 0.773788i \(0.281640\pi\)
\(228\) 0 0
\(229\) −5.50786 9.53988i −0.363969 0.630413i 0.624641 0.780912i \(-0.285245\pi\)
−0.988610 + 0.150499i \(0.951912\pi\)
\(230\) 0 0
\(231\) 11.5197 3.69215i 0.757938 0.242926i
\(232\) 0 0
\(233\) 27.2595 1.78583 0.892915 0.450225i \(-0.148656\pi\)
0.892915 + 0.450225i \(0.148656\pi\)
\(234\) 0 0
\(235\) −5.60988 −0.365948
\(236\) 0 0
\(237\) 16.6727 + 15.1332i 1.08301 + 0.983009i
\(238\) 0 0
\(239\) 5.82295 + 10.0856i 0.376655 + 0.652386i 0.990573 0.136984i \(-0.0437407\pi\)
−0.613918 + 0.789370i \(0.710407\pi\)
\(240\) 0 0
\(241\) 9.83554 17.0356i 0.633563 1.09736i −0.353255 0.935527i \(-0.614925\pi\)
0.986818 0.161835i \(-0.0517414\pi\)
\(242\) 0 0
\(243\) −13.6530 + 7.52304i −0.875839 + 0.482603i
\(244\) 0 0
\(245\) −1.35479 + 2.34656i −0.0865542 + 0.149916i
\(246\) 0 0
\(247\) −20.6512 35.7689i −1.31400 2.27592i
\(248\) 0 0
\(249\) −3.96306 3.59712i −0.251149 0.227958i
\(250\) 0 0
\(251\) −23.3802 −1.47575 −0.737873 0.674940i \(-0.764170\pi\)
−0.737873 + 0.674940i \(0.764170\pi\)
\(252\) 0 0
\(253\) −12.7930 −0.804289
\(254\) 0 0
\(255\) −26.3329 + 8.43993i −1.64903 + 0.528529i
\(256\) 0 0
\(257\) −1.89037 3.27421i −0.117918 0.204240i 0.801024 0.598632i \(-0.204289\pi\)
−0.918942 + 0.394392i \(0.870955\pi\)
\(258\) 0 0
\(259\) −9.65603 + 16.7247i −0.599996 + 1.03922i
\(260\) 0 0
\(261\) 7.70500 5.50449i 0.476927 0.340720i
\(262\) 0 0
\(263\) 10.3638 17.9507i 0.639060 1.10689i −0.346579 0.938021i \(-0.612657\pi\)
0.985639 0.168864i \(-0.0540100\pi\)
\(264\) 0 0
\(265\) −1.00515 1.74097i −0.0617458 0.106947i
\(266\) 0 0
\(267\) 1.08340 4.99870i 0.0663028 0.305916i
\(268\) 0 0
\(269\) 0.965772 0.0588842 0.0294421 0.999566i \(-0.490627\pi\)
0.0294421 + 0.999566i \(0.490627\pi\)
\(270\) 0 0
\(271\) 4.28219 0.260124 0.130062 0.991506i \(-0.458482\pi\)
0.130062 + 0.991506i \(0.458482\pi\)
\(272\) 0 0
\(273\) −6.96963 + 32.1573i −0.421821 + 1.94625i
\(274\) 0 0
\(275\) −0.667703 1.15650i −0.0402640 0.0697393i
\(276\) 0 0
\(277\) 4.83619 8.37653i 0.290579 0.503297i −0.683368 0.730074i \(-0.739486\pi\)
0.973947 + 0.226777i \(0.0728189\pi\)
\(278\) 0 0
\(279\) 1.03749 + 10.6921i 0.0621128 + 0.640120i
\(280\) 0 0
\(281\) 7.34848 12.7279i 0.438373 0.759285i −0.559191 0.829039i \(-0.688888\pi\)
0.997564 + 0.0697540i \(0.0222214\pi\)
\(282\) 0 0
\(283\) 7.90174 + 13.6862i 0.469710 + 0.813561i 0.999400 0.0346299i \(-0.0110252\pi\)
−0.529690 + 0.848191i \(0.677692\pi\)
\(284\) 0 0
\(285\) −21.7726 + 6.97832i −1.28970 + 0.413360i
\(286\) 0 0
\(287\) −10.0473 −0.593074
\(288\) 0 0
\(289\) 40.2819 2.36952
\(290\) 0 0
\(291\) −14.1396 12.8340i −0.828880 0.752344i
\(292\) 0 0
\(293\) −2.99866 5.19384i −0.175184 0.303427i 0.765041 0.643981i \(-0.222719\pi\)
−0.940225 + 0.340554i \(0.889385\pi\)
\(294\) 0 0
\(295\) −10.2256 + 17.7112i −0.595356 + 1.03119i
\(296\) 0 0
\(297\) −4.98991 11.5790i −0.289544 0.671883i
\(298\) 0 0
\(299\) 17.3987 30.1355i 1.00619 1.74278i
\(300\) 0 0
\(301\) 8.99666 + 15.5827i 0.518559 + 0.898170i
\(302\) 0 0
\(303\) 4.67755 + 4.24564i 0.268718 + 0.243906i
\(304\) 0 0
\(305\) −10.8770 −0.622818
\(306\) 0 0
\(307\) 11.7568 0.670994 0.335497 0.942041i \(-0.391096\pi\)
0.335497 + 0.942041i \(0.391096\pi\)
\(308\) 0 0
\(309\) 17.9427 5.75079i 1.02072 0.327151i
\(310\) 0 0
\(311\) 16.1797 + 28.0240i 0.917465 + 1.58910i 0.803252 + 0.595640i \(0.203101\pi\)
0.114213 + 0.993456i \(0.463565\pi\)
\(312\) 0 0
\(313\) −14.6062 + 25.2987i −0.825591 + 1.42997i 0.0758750 + 0.997117i \(0.475825\pi\)
−0.901466 + 0.432849i \(0.857508\pi\)
\(314\) 0 0
\(315\) 16.5801 + 7.54122i 0.934182 + 0.424900i
\(316\) 0 0
\(317\) 13.7011 23.7310i 0.769530 1.33286i −0.168288 0.985738i \(-0.553824\pi\)
0.937818 0.347127i \(-0.112843\pi\)
\(318\) 0 0
\(319\) 3.82951 + 6.63291i 0.214411 + 0.371371i
\(320\) 0 0
\(321\) −2.18264 + 10.0705i −0.121823 + 0.562083i
\(322\) 0 0
\(323\) 47.3619 2.63529
\(324\) 0 0
\(325\) 3.63235 0.201487
\(326\) 0 0
\(327\) −3.62151 + 16.7093i −0.200270 + 0.924029i
\(328\) 0 0
\(329\) −3.82731 6.62910i −0.211007 0.365474i
\(330\) 0 0
\(331\) 1.08930 1.88673i 0.0598735 0.103704i −0.834535 0.550955i \(-0.814264\pi\)
0.894408 + 0.447251i \(0.147597\pi\)
\(332\) 0 0
\(333\) 18.3225 + 8.33374i 1.00407 + 0.456686i
\(334\) 0 0
\(335\) −2.00299 + 3.46928i −0.109435 + 0.189547i
\(336\) 0 0
\(337\) −0.715700 1.23963i −0.0389866 0.0675268i 0.845874 0.533383i \(-0.179080\pi\)
−0.884860 + 0.465856i \(0.845746\pi\)
\(338\) 0 0
\(339\) 24.7911 7.94577i 1.34647 0.431555i
\(340\) 0 0
\(341\) −8.68874 −0.470522
\(342\) 0 0
\(343\) 16.4508 0.888259
\(344\) 0 0
\(345\) −14.2634 12.9463i −0.767914 0.697007i
\(346\) 0 0
\(347\) 13.1223 + 22.7285i 0.704441 + 1.22013i 0.966893 + 0.255183i \(0.0821357\pi\)
−0.262452 + 0.964945i \(0.584531\pi\)
\(348\) 0 0
\(349\) 17.1673 29.7346i 0.918944 1.59166i 0.117923 0.993023i \(-0.462377\pi\)
0.801022 0.598635i \(-0.204290\pi\)
\(350\) 0 0
\(351\) 34.0621 + 3.99334i 1.81810 + 0.213149i
\(352\) 0 0
\(353\) −2.28933 + 3.96523i −0.121849 + 0.211048i −0.920497 0.390750i \(-0.872216\pi\)
0.798648 + 0.601798i \(0.205549\pi\)
\(354\) 0 0
\(355\) −6.14359 10.6410i −0.326068 0.564766i
\(356\) 0 0
\(357\) −27.9388 25.3590i −1.47868 1.34214i
\(358\) 0 0
\(359\) −13.0591 −0.689231 −0.344616 0.938744i \(-0.611991\pi\)
−0.344616 + 0.938744i \(0.611991\pi\)
\(360\) 0 0
\(361\) 20.1599 1.06105
\(362\) 0 0
\(363\) −8.43195 + 2.70251i −0.442562 + 0.141845i
\(364\) 0 0
\(365\) 5.28644 + 9.15639i 0.276705 + 0.479267i
\(366\) 0 0
\(367\) −1.70626 + 2.95533i −0.0890660 + 0.154267i −0.907117 0.420879i \(-0.861722\pi\)
0.818051 + 0.575146i \(0.195055\pi\)
\(368\) 0 0
\(369\) 1.01140 + 10.4232i 0.0526513 + 0.542612i
\(370\) 0 0
\(371\) 1.37151 2.37553i 0.0712055 0.123332i
\(372\) 0 0
\(373\) 6.42179 + 11.1229i 0.332508 + 0.575921i 0.983003 0.183590i \(-0.0587719\pi\)
−0.650495 + 0.759511i \(0.725439\pi\)
\(374\) 0 0
\(375\) 4.29542 19.8187i 0.221815 1.02343i
\(376\) 0 0
\(377\) −20.8328 −1.07294
\(378\) 0 0
\(379\) −12.1642 −0.624833 −0.312417 0.949945i \(-0.601138\pi\)
−0.312417 + 0.949945i \(0.601138\pi\)
\(380\) 0 0
\(381\) −2.96361 + 13.6738i −0.151830 + 0.700532i
\(382\) 0 0
\(383\) −8.84072 15.3126i −0.451740 0.782436i 0.546755 0.837293i \(-0.315863\pi\)
−0.998494 + 0.0548568i \(0.982530\pi\)
\(384\) 0 0
\(385\) −7.36625 + 12.7587i −0.375419 + 0.650244i
\(386\) 0 0
\(387\) 15.2601 10.9019i 0.775713 0.554174i
\(388\) 0 0
\(389\) −3.77658 + 6.54123i −0.191480 + 0.331654i −0.945741 0.324921i \(-0.894662\pi\)
0.754261 + 0.656575i \(0.227995\pi\)
\(390\) 0 0
\(391\) 19.9513 + 34.5567i 1.00898 + 1.74761i
\(392\) 0 0
\(393\) 36.7252 11.7708i 1.85254 0.593756i
\(394\) 0 0
\(395\) −27.4223 −1.37977
\(396\) 0 0
\(397\) 7.97075 0.400040 0.200020 0.979792i \(-0.435899\pi\)
0.200020 + 0.979792i \(0.435899\pi\)
\(398\) 0 0
\(399\) −23.1004 20.9674i −1.15647 1.04968i
\(400\) 0 0
\(401\) −3.53771 6.12750i −0.176665 0.305993i 0.764071 0.645132i \(-0.223198\pi\)
−0.940736 + 0.339139i \(0.889864\pi\)
\(402\) 0 0
\(403\) 11.8168 20.4674i 0.588639 1.01955i
\(404\) 0 0
\(405\) 6.15438 17.9596i 0.305813 0.892418i
\(406\) 0 0
\(407\) −8.14038 + 14.0995i −0.403503 + 0.698889i
\(408\) 0 0
\(409\) −16.0499 27.7993i −0.793619 1.37459i −0.923713 0.383086i \(-0.874861\pi\)
0.130094 0.991502i \(-0.458472\pi\)
\(410\) 0 0
\(411\) −11.8599 10.7648i −0.585005 0.530988i
\(412\) 0 0
\(413\) −27.9054 −1.37313
\(414\) 0 0
\(415\) 6.51820 0.319966
\(416\) 0 0
\(417\) 13.8634 4.44335i 0.678895 0.217592i
\(418\) 0 0
\(419\) 5.63571 + 9.76133i 0.275322 + 0.476872i 0.970216 0.242240i \(-0.0778821\pi\)
−0.694894 + 0.719112i \(0.744549\pi\)
\(420\) 0 0
\(421\) 4.82872 8.36359i 0.235337 0.407616i −0.724033 0.689765i \(-0.757714\pi\)
0.959371 + 0.282149i \(0.0910471\pi\)
\(422\) 0 0
\(423\) −6.49186 + 4.63782i −0.315645 + 0.225499i
\(424\) 0 0
\(425\) −2.08263 + 3.60723i −0.101023 + 0.174976i
\(426\) 0 0
\(427\) −7.42081 12.8532i −0.359118 0.622011i
\(428\) 0 0
\(429\) −5.87565 + 27.1098i −0.283679 + 1.30887i
\(430\) 0 0
\(431\) −40.1842 −1.93560 −0.967802 0.251711i \(-0.919007\pi\)
−0.967802 + 0.251711i \(0.919007\pi\)
\(432\) 0 0
\(433\) 16.1510 0.776168 0.388084 0.921624i \(-0.373137\pi\)
0.388084 + 0.921624i \(0.373137\pi\)
\(434\) 0 0
\(435\) −2.44275 + 11.2707i −0.117121 + 0.540387i
\(436\) 0 0
\(437\) 16.4962 + 28.5723i 0.789120 + 1.36680i
\(438\) 0 0
\(439\) 9.25383 16.0281i 0.441661 0.764980i −0.556152 0.831081i \(-0.687723\pi\)
0.997813 + 0.0661011i \(0.0210560\pi\)
\(440\) 0 0
\(441\) 0.372172 + 3.83552i 0.0177225 + 0.182644i
\(442\) 0 0
\(443\) −1.72586 + 2.98927i −0.0819979 + 0.142025i −0.904108 0.427304i \(-0.859463\pi\)
0.822110 + 0.569329i \(0.192797\pi\)
\(444\) 0 0
\(445\) 3.11457 + 5.39459i 0.147645 + 0.255728i
\(446\) 0 0
\(447\) −20.3812 + 6.53236i −0.963998 + 0.308970i
\(448\) 0 0
\(449\) 9.83790 0.464279 0.232140 0.972682i \(-0.425427\pi\)
0.232140 + 0.972682i \(0.425427\pi\)
\(450\) 0 0
\(451\) −8.47025 −0.398848
\(452\) 0 0
\(453\) −12.6053 11.4413i −0.592247 0.537561i
\(454\) 0 0
\(455\) −20.0364 34.7041i −0.939323 1.62696i
\(456\) 0 0
\(457\) 0.0111990 0.0193973i 0.000523869 0.000907367i −0.865763 0.500454i \(-0.833167\pi\)
0.866287 + 0.499546i \(0.166500\pi\)
\(458\) 0 0
\(459\) −23.4954 + 31.5369i −1.09667 + 1.47202i
\(460\) 0 0
\(461\) −7.50986 + 13.0075i −0.349769 + 0.605818i −0.986208 0.165509i \(-0.947073\pi\)
0.636439 + 0.771327i \(0.280407\pi\)
\(462\) 0 0
\(463\) −16.2691 28.1790i −0.756091 1.30959i −0.944830 0.327561i \(-0.893773\pi\)
0.188738 0.982027i \(-0.439560\pi\)
\(464\) 0 0
\(465\) −9.68738 8.79288i −0.449241 0.407760i
\(466\) 0 0
\(467\) −10.2983 −0.476550 −0.238275 0.971198i \(-0.576582\pi\)
−0.238275 + 0.971198i \(0.576582\pi\)
\(468\) 0 0
\(469\) −5.46612 −0.252402
\(470\) 0 0
\(471\) 0.356545 0.114276i 0.0164287 0.00526556i
\(472\) 0 0
\(473\) 7.58450 + 13.1367i 0.348736 + 0.604028i
\(474\) 0 0
\(475\) −1.72197 + 2.98253i −0.0790093 + 0.136848i
\(476\) 0 0
\(477\) −2.60248 1.18370i −0.119159 0.0541980i
\(478\) 0 0
\(479\) 3.79020 6.56481i 0.173178 0.299954i −0.766351 0.642422i \(-0.777930\pi\)
0.939529 + 0.342468i \(0.111263\pi\)
\(480\) 0 0
\(481\) −22.1421 38.3513i −1.00959 1.74867i
\(482\) 0 0
\(483\) 5.56736 25.6873i 0.253323 1.16881i
\(484\) 0 0
\(485\) 23.2560 1.05600
\(486\) 0 0
\(487\) 20.6214 0.934444 0.467222 0.884140i \(-0.345255\pi\)
0.467222 + 0.884140i \(0.345255\pi\)
\(488\) 0 0
\(489\) −2.12098 + 9.78605i −0.0959142 + 0.442541i
\(490\) 0 0
\(491\) 3.98229 + 6.89752i 0.179718 + 0.311281i 0.941784 0.336219i \(-0.109148\pi\)
−0.762066 + 0.647499i \(0.775815\pi\)
\(492\) 0 0
\(493\) 11.9446 20.6887i 0.537959 0.931772i
\(494\) 0 0
\(495\) 13.9776 + 6.35752i 0.628246 + 0.285749i
\(496\) 0 0
\(497\) 8.38287 14.5196i 0.376023 0.651291i
\(498\) 0 0
\(499\) −10.5911 18.3444i −0.474125 0.821208i 0.525436 0.850833i \(-0.323902\pi\)
−0.999561 + 0.0296248i \(0.990569\pi\)
\(500\) 0 0
\(501\) −2.70055 + 0.865552i −0.120652 + 0.0386700i
\(502\) 0 0
\(503\) 19.0876 0.851073 0.425536 0.904941i \(-0.360085\pi\)
0.425536 + 0.904941i \(0.360085\pi\)
\(504\) 0 0
\(505\) −7.69336 −0.342350
\(506\) 0 0
\(507\) −39.1965 35.5773i −1.74078 1.58004i
\(508\) 0 0
\(509\) 18.3596 + 31.7998i 0.813776 + 1.40950i 0.910204 + 0.414161i \(0.135925\pi\)
−0.0964283 + 0.995340i \(0.530742\pi\)
\(510\) 0 0
\(511\) −7.21330 + 12.4938i −0.319097 + 0.552693i
\(512\) 0 0
\(513\) −19.4266 + 26.0754i −0.857703 + 1.15126i
\(514\) 0 0
\(515\) −11.4734 + 19.8726i −0.505580 + 0.875690i
\(516\) 0 0
\(517\) −3.22656 5.58857i −0.141904 0.245785i
\(518\) 0 0
\(519\) −7.67535 6.96663i −0.336910 0.305801i
\(520\) 0 0
\(521\) 20.5620 0.900839 0.450419 0.892817i \(-0.351275\pi\)
0.450419 + 0.892817i \(0.351275\pi\)
\(522\) 0 0
\(523\) 16.2754 0.711672 0.355836 0.934548i \(-0.384196\pi\)
0.355836 + 0.934548i \(0.384196\pi\)
\(524\) 0 0
\(525\) 2.61273 0.837403i 0.114029 0.0365472i
\(526\) 0 0
\(527\) 13.5505 + 23.4702i 0.590270 + 1.02238i
\(528\) 0 0
\(529\) −2.39812 + 4.15367i −0.104266 + 0.180594i
\(530\) 0 0
\(531\) 2.80905 + 28.9495i 0.121903 + 1.25630i
\(532\) 0 0
\(533\) 11.5197 19.9527i 0.498973 0.864246i
\(534\) 0 0
\(535\) −6.27471 10.8681i −0.271279 0.469870i
\(536\) 0 0
\(537\) 3.49017 16.1033i 0.150612 0.694911i
\(538\) 0 0
\(539\) −3.11686 −0.134253
\(540\) 0 0
\(541\) −3.19402 −0.137322 −0.0686609 0.997640i \(-0.521873\pi\)
−0.0686609 + 0.997640i \(0.521873\pi\)
\(542\) 0 0
\(543\) 8.71431 40.2071i 0.373967 1.72545i
\(544\) 0 0
\(545\) −10.4112 18.0327i −0.445966 0.772436i
\(546\) 0 0
\(547\) 7.43936 12.8854i 0.318084 0.550938i −0.662004 0.749500i \(-0.730294\pi\)
0.980088 + 0.198562i \(0.0636272\pi\)
\(548\) 0 0
\(549\) −12.5871 + 8.99231i −0.537205 + 0.383782i
\(550\) 0 0
\(551\) 9.87608 17.1059i 0.420735 0.728734i
\(552\) 0 0
\(553\) −18.7087 32.4045i −0.795576 1.37798i
\(554\) 0 0
\(555\) −23.3445 + 7.48213i −0.990920 + 0.317599i
\(556\) 0 0
\(557\) −5.76686 −0.244350 −0.122175 0.992509i \(-0.538987\pi\)
−0.122175 + 0.992509i \(0.538987\pi\)
\(558\) 0 0
\(559\) −41.2602 −1.74512
\(560\) 0 0
\(561\) −23.5534 21.3786i −0.994426 0.902604i
\(562\) 0 0
\(563\) −4.76738 8.25734i −0.200921 0.348005i 0.747904 0.663806i \(-0.231060\pi\)
−0.948825 + 0.315801i \(0.897727\pi\)
\(564\) 0 0
\(565\) −15.8527 + 27.4576i −0.666927 + 1.15515i
\(566\) 0 0
\(567\) 25.4213 4.98030i 1.06759 0.209153i
\(568\) 0 0
\(569\) −4.27200 + 7.39933i −0.179092 + 0.310196i −0.941570 0.336818i \(-0.890649\pi\)
0.762478 + 0.647014i \(0.223983\pi\)
\(570\) 0 0
\(571\) −18.1444 31.4270i −0.759318 1.31518i −0.943199 0.332229i \(-0.892199\pi\)
0.183881 0.982949i \(-0.441134\pi\)
\(572\) 0 0
\(573\) 10.6235 + 9.64256i 0.443803 + 0.402824i
\(574\) 0 0
\(575\) −2.90153 −0.121002
\(576\) 0 0
\(577\) −6.11652 −0.254634 −0.127317 0.991862i \(-0.540637\pi\)
−0.127317 + 0.991862i \(0.540637\pi\)
\(578\) 0 0
\(579\) −16.5044 + 5.28982i −0.685901 + 0.219837i
\(580\) 0 0
\(581\) 4.44701 + 7.70245i 0.184493 + 0.319551i
\(582\) 0 0
\(583\) 1.15624 2.00266i 0.0478864 0.0829417i
\(584\) 0 0
\(585\) −33.9857 + 24.2796i −1.40514 + 1.00384i
\(586\) 0 0
\(587\) −1.92500 + 3.33419i −0.0794532 + 0.137617i −0.903014 0.429611i \(-0.858651\pi\)
0.823561 + 0.567228i \(0.191984\pi\)
\(588\) 0 0
\(589\) 11.2039 + 19.4057i 0.461647 + 0.799597i
\(590\) 0 0
\(591\) −0.204079 + 0.941606i −0.00839471 + 0.0387325i
\(592\) 0 0
\(593\) 16.6462 0.683579 0.341789 0.939777i \(-0.388967\pi\)
0.341789 + 0.939777i \(0.388967\pi\)
\(594\) 0 0
\(595\) 45.9521 1.88385
\(596\) 0 0
\(597\) −7.90720 + 36.4832i −0.323620 + 1.49316i
\(598\) 0 0
\(599\) −17.8791 30.9675i −0.730520 1.26530i −0.956661 0.291203i \(-0.905944\pi\)
0.226141 0.974095i \(-0.427389\pi\)
\(600\) 0 0
\(601\) 6.77202 11.7295i 0.276236 0.478455i −0.694210 0.719773i \(-0.744246\pi\)
0.970446 + 0.241317i \(0.0775794\pi\)
\(602\) 0 0
\(603\) 0.550239 + 5.67064i 0.0224075 + 0.230926i
\(604\) 0 0
\(605\) 5.39181 9.33888i 0.219208 0.379679i
\(606\) 0 0
\(607\) −14.0131 24.2714i −0.568775 0.985147i −0.996688 0.0813266i \(-0.974084\pi\)
0.427913 0.903820i \(-0.359249\pi\)
\(608\) 0 0
\(609\) −14.9849 + 4.80279i −0.607219 + 0.194619i
\(610\) 0 0
\(611\) 17.5527 0.710107
\(612\) 0 0
\(613\) −37.6283 −1.51979 −0.759897 0.650043i \(-0.774751\pi\)
−0.759897 + 0.650043i \(0.774751\pi\)
\(614\) 0 0
\(615\) −9.44377 8.57177i −0.380810 0.345647i
\(616\) 0 0
\(617\) 5.57241 + 9.65169i 0.224337 + 0.388562i 0.956120 0.292975i \(-0.0946451\pi\)
−0.731784 + 0.681537i \(0.761312\pi\)
\(618\) 0 0
\(619\) −9.54119 + 16.5258i −0.383493 + 0.664229i −0.991559 0.129658i \(-0.958612\pi\)
0.608066 + 0.793886i \(0.291946\pi\)
\(620\) 0 0
\(621\) −27.2089 3.18989i −1.09185 0.128006i
\(622\) 0 0
\(623\) −4.24980 + 7.36086i −0.170265 + 0.294907i
\(624\) 0 0
\(625\) 10.9727 + 19.0053i 0.438908 + 0.760211i
\(626\) 0 0
\(627\) −19.4745 17.6763i −0.777736 0.705923i
\(628\) 0 0
\(629\) 50.7813 2.02478
\(630\) 0 0
\(631\) −29.7049 −1.18253 −0.591267 0.806476i \(-0.701372\pi\)
−0.591267 + 0.806476i \(0.701372\pi\)
\(632\) 0 0
\(633\) −27.4785 + 8.80712i −1.09217 + 0.350051i
\(634\) 0 0
\(635\) −8.51984 14.7568i −0.338099 0.585605i
\(636\) 0 0
\(637\) 4.23898 7.34214i 0.167955 0.290906i
\(638\) 0 0
\(639\) −15.9067 7.23493i −0.629258 0.286209i
\(640\) 0 0
\(641\) −9.60138 + 16.6301i −0.379232 + 0.656848i −0.990951 0.134227i \(-0.957145\pi\)
0.611719 + 0.791075i \(0.290478\pi\)
\(642\) 0 0
\(643\) −3.52181 6.09995i −0.138887 0.240559i 0.788189 0.615434i \(-0.211019\pi\)
−0.927075 + 0.374875i \(0.877686\pi\)
\(644\) 0 0
\(645\) −4.83797 + 22.3220i −0.190495 + 0.878929i
\(646\) 0 0
\(647\) 36.8474 1.44862 0.724311 0.689473i \(-0.242158\pi\)
0.724311 + 0.689473i \(0.242158\pi\)
\(648\) 0 0
\(649\) −23.5252 −0.923446
\(650\) 0 0
\(651\) 3.78123 17.4463i 0.148198 0.683774i
\(652\) 0 0
\(653\) 20.6354 + 35.7416i 0.807526 + 1.39868i 0.914572 + 0.404422i \(0.132527\pi\)
−0.107046 + 0.994254i \(0.534139\pi\)
\(654\) 0 0
\(655\) −23.4839 + 40.6754i −0.917593 + 1.58932i
\(656\) 0 0
\(657\) 13.6874 + 6.22552i 0.533995 + 0.242881i
\(658\) 0 0
\(659\) 7.79606 13.5032i 0.303691 0.526009i −0.673278 0.739390i \(-0.735114\pi\)
0.976969 + 0.213381i \(0.0684475\pi\)
\(660\) 0 0
\(661\) −0.273228 0.473246i −0.0106274 0.0184071i 0.860663 0.509175i \(-0.170050\pi\)
−0.871290 + 0.490768i \(0.836716\pi\)
\(662\) 0 0
\(663\) 82.3929 26.4076i 3.19987 1.02559i
\(664\) 0 0
\(665\) 37.9942 1.47335
\(666\) 0 0
\(667\) 16.6413 0.644353
\(668\) 0 0
\(669\) −11.5235 10.4595i −0.445525 0.404387i
\(670\) 0 0
\(671\) −6.25601 10.8357i −0.241510 0.418308i
\(672\) 0 0
\(673\) 7.71994 13.3713i 0.297582 0.515427i −0.678000 0.735061i \(-0.737153\pi\)
0.975582 + 0.219635i \(0.0704866\pi\)
\(674\) 0 0
\(675\) −1.13174 2.62619i −0.0435607 0.101082i
\(676\) 0 0
\(677\) −20.7394 + 35.9216i −0.797079 + 1.38058i 0.124432 + 0.992228i \(0.460289\pi\)
−0.921511 + 0.388353i \(0.873044\pi\)
\(678\) 0 0
\(679\) 15.8663 + 27.4812i 0.608893 + 1.05463i
\(680\) 0 0
\(681\) −13.6575 12.3965i −0.523358 0.475033i
\(682\) 0 0
\(683\) −7.83506 −0.299800 −0.149900 0.988701i \(-0.547895\pi\)
−0.149900 + 0.988701i \(0.547895\pi\)
\(684\) 0 0
\(685\) 19.5064 0.745303
\(686\) 0 0
\(687\) 18.1693 5.82344i 0.693204 0.222178i
\(688\) 0 0
\(689\) 3.14500 + 5.44730i 0.119815 + 0.207526i
\(690\) 0 0
\(691\) −11.8366 + 20.5016i −0.450286 + 0.779918i −0.998404 0.0564831i \(-0.982011\pi\)
0.548118 + 0.836401i \(0.315345\pi\)
\(692\) 0 0
\(693\) 2.02357 + 20.8545i 0.0768691 + 0.792196i
\(694\) 0 0
\(695\) −8.86497 + 15.3546i −0.336267 + 0.582432i
\(696\) 0 0
\(697\) 13.2098 + 22.8800i 0.500356 + 0.866642i
\(698\) 0 0
\(699\) −10.0009 + 46.1435i −0.378270 + 1.74531i
\(700\) 0 0
\(701\) −7.14909 −0.270017 −0.135009 0.990844i \(-0.543106\pi\)
−0.135009 + 0.990844i \(0.543106\pi\)
\(702\) 0 0
\(703\) 41.9871 1.58357
\(704\) 0 0
\(705\) 2.05815 9.49612i 0.0775143 0.357645i
\(706\) 0 0
\(707\) −5.24876 9.09111i −0.197400 0.341906i
\(708\) 0 0
\(709\) 19.3826 33.5716i 0.727928 1.26081i −0.229830 0.973231i \(-0.573817\pi\)
0.957757 0.287577i \(-0.0928498\pi\)
\(710\) 0 0
\(711\) −31.7336 + 22.6707i −1.19010 + 0.850217i
\(712\) 0 0
\(713\) −9.43931 + 16.3494i −0.353505 + 0.612289i
\(714\) 0 0
\(715\) −16.8914 29.2568i −0.631704 1.09414i
\(716\) 0 0
\(717\) −19.2088 + 6.15659i −0.717365 + 0.229922i
\(718\) 0 0
\(719\) −38.3429 −1.42995 −0.714975 0.699151i \(-0.753562\pi\)
−0.714975 + 0.699151i \(0.753562\pi\)
\(720\) 0 0
\(721\) −31.3108 −1.16607
\(722\) 0 0
\(723\) 25.2286 + 22.8991i 0.938263 + 0.851627i
\(724\) 0 0
\(725\) 0.868556 + 1.50438i 0.0322574 + 0.0558714i
\(726\) 0 0
\(727\) −21.9734 + 38.0591i −0.814950 + 1.41154i 0.0944136 + 0.995533i \(0.469902\pi\)
−0.909364 + 0.416002i \(0.863431\pi\)
\(728\) 0 0
\(729\) −7.72564 25.8711i −0.286135 0.958189i
\(730\) 0 0
\(731\) 23.6568 40.9748i 0.874979 1.51551i
\(732\) 0 0
\(733\) −24.7222 42.8202i −0.913137 1.58160i −0.809606 0.586973i \(-0.800319\pi\)
−0.103531 0.994626i \(-0.533014\pi\)
\(734\) 0 0
\(735\) −3.47510 3.15422i −0.128181 0.116345i
\(736\) 0 0
\(737\) −4.60814 −0.169743
\(738\) 0 0
\(739\) −9.25073 −0.340294 −0.170147 0.985419i \(-0.554424\pi\)
−0.170147 + 0.985419i \(0.554424\pi\)
\(740\) 0 0
\(741\) 68.1242 21.8344i 2.50261 0.802107i
\(742\) 0 0
\(743\) −20.6473 35.7621i −0.757475 1.31198i −0.944135 0.329560i \(-0.893100\pi\)
0.186660 0.982425i \(-0.440234\pi\)
\(744\) 0 0
\(745\) 13.0328 22.5734i 0.477483 0.827025i
\(746\) 0 0
\(747\) 7.54299 5.38875i 0.275984 0.197164i
\(748\) 0 0
\(749\) 8.56178 14.8294i 0.312840 0.541856i
\(750\) 0 0
\(751\) 10.2101 + 17.6845i 0.372573 + 0.645315i 0.989961 0.141344i \(-0.0451423\pi\)
−0.617388 + 0.786659i \(0.711809\pi\)
\(752\) 0 0
\(753\) 8.57770 39.5768i 0.312589 1.44226i
\(754\) 0 0
\(755\) 20.7324 0.754529
\(756\) 0 0
\(757\) 7.74944 0.281658 0.140829 0.990034i \(-0.455023\pi\)
0.140829 + 0.990034i \(0.455023\pi\)
\(758\) 0 0
\(759\) 4.69348 21.6554i 0.170363 0.786039i
\(760\) 0 0
\(761\) 13.3416 + 23.1084i 0.483634 + 0.837679i 0.999823 0.0187955i \(-0.00598315\pi\)
−0.516189 + 0.856475i \(0.672650\pi\)
\(762\) 0 0
\(763\) 14.2059 24.6054i 0.514290 0.890776i
\(764\) 0 0
\(765\) −4.62570 47.6714i −0.167243 1.72356i
\(766\) 0 0
\(767\) 31.9947 55.4165i 1.15526 2.00097i
\(768\) 0 0
\(769\) −24.5226 42.4744i −0.884307 1.53166i −0.846506 0.532379i \(-0.821298\pi\)
−0.0378010 0.999285i \(-0.512035\pi\)
\(770\) 0 0
\(771\) 6.23596 1.99868i 0.224583 0.0719807i
\(772\) 0 0
\(773\) 12.1406 0.436665 0.218333 0.975874i \(-0.429938\pi\)
0.218333 + 0.975874i \(0.429938\pi\)
\(774\) 0 0
\(775\) −1.97066 −0.0707881
\(776\) 0 0
\(777\) −24.7682 22.4812i −0.888553 0.806508i
\(778\) 0 0
\(779\) 10.9221 + 18.9177i 0.391326 + 0.677796i
\(780\) 0 0
\(781\) 7.06706 12.2405i 0.252879 0.438000i
\(782\) 0 0
\(783\) 6.49093 + 15.0621i 0.231967 + 0.538276i
\(784\) 0 0
\(785\) −0.227993 + 0.394895i −0.00813742 + 0.0140944i
\(786\) 0 0
\(787\) −24.2553 42.0114i −0.864608 1.49754i −0.867436 0.497549i \(-0.834234\pi\)
0.00282812 0.999996i \(-0.499100\pi\)
\(788\) 0 0
\(789\) 26.5837 + 24.1291i 0.946405 + 0.859017i
\(790\) 0 0
\(791\) −43.2616 −1.53821
\(792\) 0 0
\(793\) 34.0331 1.20855
\(794\) 0 0
\(795\) 3.31579 1.06274i 0.117599 0.0376915i
\(796\)