Properties

Label 380.2.i.c.201.3
Level $380$
Weight $2$
Character 380.201
Analytic conductor $3.034$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [380,2,Mod(121,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("380.121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.i (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 9x^{6} + 2x^{5} + 65x^{4} - 20x^{3} + 25x^{2} + 6x + 4 \) Copy content Toggle raw display
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 201.3
Root \(-0.176725 + 0.306096i\) of defining polynomial
Character \(\chi\) \(=\) 380.201
Dual form 380.2.i.c.121.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.176725 - 0.306096i) q^{3} +(-0.500000 + 0.866025i) q^{5} -4.30507 q^{7} +(1.43754 + 2.48989i) q^{9} +O(q^{10})\) \(q+(0.176725 - 0.306096i) q^{3} +(-0.500000 + 0.866025i) q^{5} -4.30507 q^{7} +(1.43754 + 2.48989i) q^{9} +6.01196 q^{11} +(2.97581 + 5.15425i) q^{13} +(0.176725 + 0.306096i) q^{15} +(-1.93754 + 3.35591i) q^{17} +(4.19835 + 1.17212i) q^{19} +(-0.760812 + 1.31776i) q^{21} +(-0.391721 - 0.678480i) q^{23} +(-0.500000 - 0.866025i) q^{25} +2.07654 q^{27} +(-3.98179 - 6.89666i) q^{29} -4.49034 q^{31} +(1.06246 - 1.84024i) q^{33} +(2.15253 - 3.72830i) q^{35} -0.988035 q^{37} +2.10360 q^{39} +(-3.15253 + 5.46035i) q^{41} +(0.785004 - 1.35967i) q^{43} -2.87507 q^{45} +(0.630909 + 1.09277i) q^{47} +11.5336 q^{49} +(0.684822 + 1.18615i) q^{51} +(4.07443 + 7.05712i) q^{53} +(-3.00598 + 5.20651i) q^{55} +(1.10073 - 1.07796i) q^{57} +(-2.62834 + 4.55242i) q^{59} +(-2.80507 - 4.85852i) q^{61} +(-6.18869 - 10.7191i) q^{63} -5.95162 q^{65} +(-3.52162 - 6.09963i) q^{67} -0.276907 q^{69} +(2.90736 - 5.03570i) q^{71} +(4.62024 - 8.00250i) q^{73} -0.353450 q^{75} -25.8819 q^{77} +(6.99743 - 12.1199i) q^{79} +(-3.94563 + 6.83404i) q^{81} +6.58197 q^{83} +(-1.93754 - 3.35591i) q^{85} -2.81472 q^{87} +(1.69237 + 2.93126i) q^{89} +(-12.8110 - 22.1894i) q^{91} +(-0.793555 + 1.37448i) q^{93} +(-3.11426 + 3.04982i) q^{95} +(3.69835 - 6.40573i) q^{97} +(8.64242 + 14.9691i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - q^{3} - 4 q^{5} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - q^{3} - 4 q^{5} - 5 q^{9} + 4 q^{11} + 9 q^{13} - q^{15} + q^{17} + 3 q^{19} + 8 q^{21} - 4 q^{25} + 20 q^{27} + 5 q^{29} - 20 q^{31} + 25 q^{33} - 52 q^{37} - 54 q^{39} - 8 q^{41} + 7 q^{43} + 10 q^{45} + 16 q^{47} + 20 q^{49} + 12 q^{51} + 5 q^{53} - 2 q^{55} + 27 q^{57} + 11 q^{59} + 12 q^{61} - 3 q^{63} - 18 q^{65} + 6 q^{69} + 14 q^{71} - 4 q^{73} + 2 q^{75} - 44 q^{77} + 13 q^{79} - 24 q^{81} + 10 q^{83} + q^{85} - 4 q^{87} + 5 q^{89} - 46 q^{91} - 28 q^{93} - 6 q^{95} - q^{97} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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
\(3\) 0.176725 0.306096i 0.102032 0.176725i −0.810490 0.585753i \(-0.800799\pi\)
0.912522 + 0.409028i \(0.134132\pi\)
\(4\) 0 0
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) −4.30507 −1.62716 −0.813581 0.581452i \(-0.802485\pi\)
−0.813581 + 0.581452i \(0.802485\pi\)
\(8\) 0 0
\(9\) 1.43754 + 2.48989i 0.479179 + 0.829962i
\(10\) 0 0
\(11\) 6.01196 1.81268 0.906338 0.422554i \(-0.138866\pi\)
0.906338 + 0.422554i \(0.138866\pi\)
\(12\) 0 0
\(13\) 2.97581 + 5.15425i 0.825341 + 1.42953i 0.901659 + 0.432448i \(0.142350\pi\)
−0.0763181 + 0.997084i \(0.524316\pi\)
\(14\) 0 0
\(15\) 0.176725 + 0.306096i 0.0456301 + 0.0790337i
\(16\) 0 0
\(17\) −1.93754 + 3.35591i −0.469922 + 0.813928i −0.999408 0.0343900i \(-0.989051\pi\)
0.529487 + 0.848318i \(0.322385\pi\)
\(18\) 0 0
\(19\) 4.19835 + 1.17212i 0.963167 + 0.268903i
\(20\) 0 0
\(21\) −0.760812 + 1.31776i −0.166023 + 0.287560i
\(22\) 0 0
\(23\) −0.391721 0.678480i −0.0816794 0.141473i 0.822292 0.569066i \(-0.192695\pi\)
−0.903971 + 0.427593i \(0.859362\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 2.07654 0.399631
\(28\) 0 0
\(29\) −3.98179 6.89666i −0.739400 1.28068i −0.952766 0.303706i \(-0.901776\pi\)
0.213366 0.976972i \(-0.431557\pi\)
\(30\) 0 0
\(31\) −4.49034 −0.806489 −0.403245 0.915092i \(-0.632118\pi\)
−0.403245 + 0.915092i \(0.632118\pi\)
\(32\) 0 0
\(33\) 1.06246 1.84024i 0.184951 0.320345i
\(34\) 0 0
\(35\) 2.15253 3.72830i 0.363844 0.630197i
\(36\) 0 0
\(37\) −0.988035 −0.162432 −0.0812160 0.996697i \(-0.525880\pi\)
−0.0812160 + 0.996697i \(0.525880\pi\)
\(38\) 0 0
\(39\) 2.10360 0.336845
\(40\) 0 0
\(41\) −3.15253 + 5.46035i −0.492343 + 0.852763i −0.999961 0.00881921i \(-0.997193\pi\)
0.507618 + 0.861582i \(0.330526\pi\)
\(42\) 0 0
\(43\) 0.785004 1.35967i 0.119712 0.207347i −0.799942 0.600078i \(-0.795136\pi\)
0.919654 + 0.392731i \(0.128470\pi\)
\(44\) 0 0
\(45\) −2.87507 −0.428591
\(46\) 0 0
\(47\) 0.630909 + 1.09277i 0.0920275 + 0.159396i 0.908364 0.418180i \(-0.137332\pi\)
−0.816337 + 0.577576i \(0.803999\pi\)
\(48\) 0 0
\(49\) 11.5336 1.64766
\(50\) 0 0
\(51\) 0.684822 + 1.18615i 0.0958942 + 0.166094i
\(52\) 0 0
\(53\) 4.07443 + 7.05712i 0.559666 + 0.969369i 0.997524 + 0.0703255i \(0.0224038\pi\)
−0.437858 + 0.899044i \(0.644263\pi\)
\(54\) 0 0
\(55\) −3.00598 + 5.20651i −0.405327 + 0.702046i
\(56\) 0 0
\(57\) 1.10073 1.07796i 0.145796 0.142779i
\(58\) 0 0
\(59\) −2.62834 + 4.55242i −0.342181 + 0.592675i −0.984837 0.173480i \(-0.944499\pi\)
0.642657 + 0.766154i \(0.277832\pi\)
\(60\) 0 0
\(61\) −2.80507 4.85852i −0.359152 0.622069i 0.628668 0.777674i \(-0.283601\pi\)
−0.987819 + 0.155605i \(0.950267\pi\)
\(62\) 0 0
\(63\) −6.18869 10.7191i −0.779702 1.35048i
\(64\) 0 0
\(65\) −5.95162 −0.738207
\(66\) 0 0
\(67\) −3.52162 6.09963i −0.430235 0.745189i 0.566658 0.823953i \(-0.308236\pi\)
−0.996893 + 0.0787642i \(0.974903\pi\)
\(68\) 0 0
\(69\) −0.276907 −0.0333357
\(70\) 0 0
\(71\) 2.90736 5.03570i 0.345040 0.597628i −0.640321 0.768108i \(-0.721199\pi\)
0.985361 + 0.170480i \(0.0545319\pi\)
\(72\) 0 0
\(73\) 4.62024 8.00250i 0.540759 0.936621i −0.458102 0.888900i \(-0.651471\pi\)
0.998861 0.0477218i \(-0.0151961\pi\)
\(74\) 0 0
\(75\) −0.353450 −0.0408128
\(76\) 0 0
\(77\) −25.8819 −2.94952
\(78\) 0 0
\(79\) 6.99743 12.1199i 0.787273 1.36360i −0.140359 0.990101i \(-0.544826\pi\)
0.927632 0.373495i \(-0.121841\pi\)
\(80\) 0 0
\(81\) −3.94563 + 6.83404i −0.438404 + 0.759338i
\(82\) 0 0
\(83\) 6.58197 0.722465 0.361233 0.932476i \(-0.382356\pi\)
0.361233 + 0.932476i \(0.382356\pi\)
\(84\) 0 0
\(85\) −1.93754 3.35591i −0.210155 0.364000i
\(86\) 0 0
\(87\) −2.81472 −0.301770
\(88\) 0 0
\(89\) 1.69237 + 2.93126i 0.179390 + 0.310713i 0.941672 0.336532i \(-0.109254\pi\)
−0.762281 + 0.647246i \(0.775921\pi\)
\(90\) 0 0
\(91\) −12.8110 22.1894i −1.34296 2.32608i
\(92\) 0 0
\(93\) −0.793555 + 1.37448i −0.0822878 + 0.142527i
\(94\) 0 0
\(95\) −3.11426 + 3.04982i −0.319516 + 0.312904i
\(96\) 0 0
\(97\) 3.69835 6.40573i 0.375510 0.650403i −0.614893 0.788611i \(-0.710801\pi\)
0.990403 + 0.138208i \(0.0441341\pi\)
\(98\) 0 0
\(99\) 8.64242 + 14.9691i 0.868596 + 1.50445i
\(100\) 0 0
\(101\) 4.90369 + 8.49343i 0.487935 + 0.845128i 0.999904 0.0138759i \(-0.00441699\pi\)
−0.511969 + 0.859004i \(0.671084\pi\)
\(102\) 0 0
\(103\) 14.4368 1.42250 0.711251 0.702938i \(-0.248129\pi\)
0.711251 + 0.702938i \(0.248129\pi\)
\(104\) 0 0
\(105\) −0.760812 1.31776i −0.0742476 0.128601i
\(106\) 0 0
\(107\) −9.49034 −0.917466 −0.458733 0.888574i \(-0.651697\pi\)
−0.458733 + 0.888574i \(0.651697\pi\)
\(108\) 0 0
\(109\) 1.30920 2.26759i 0.125398 0.217196i −0.796490 0.604651i \(-0.793312\pi\)
0.921889 + 0.387455i \(0.126646\pi\)
\(110\) 0 0
\(111\) −0.174610 + 0.302434i −0.0165733 + 0.0287058i
\(112\) 0 0
\(113\) −13.6705 −1.28601 −0.643005 0.765862i \(-0.722313\pi\)
−0.643005 + 0.765862i \(0.722313\pi\)
\(114\) 0 0
\(115\) 0.783442 0.0730563
\(116\) 0 0
\(117\) −8.55567 + 14.8188i −0.790972 + 1.37000i
\(118\) 0 0
\(119\) 8.34122 14.4474i 0.764639 1.32439i
\(120\) 0 0
\(121\) 25.1437 2.28579
\(122\) 0 0
\(123\) 1.11426 + 1.92996i 0.100470 + 0.174018i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −6.53359 11.3165i −0.579762 1.00418i −0.995506 0.0946960i \(-0.969812\pi\)
0.415744 0.909482i \(-0.363521\pi\)
\(128\) 0 0
\(129\) −0.277459 0.480574i −0.0244289 0.0423122i
\(130\) 0 0
\(131\) 3.75070 6.49640i 0.327700 0.567593i −0.654355 0.756188i \(-0.727060\pi\)
0.982055 + 0.188594i \(0.0603931\pi\)
\(132\) 0 0
\(133\) −18.0742 5.04606i −1.56723 0.437549i
\(134\) 0 0
\(135\) −1.03827 + 1.79834i −0.0893602 + 0.154776i
\(136\) 0 0
\(137\) 4.21500 + 7.30059i 0.360111 + 0.623731i 0.987979 0.154589i \(-0.0494053\pi\)
−0.627867 + 0.778320i \(0.716072\pi\)
\(138\) 0 0
\(139\) −4.38961 7.60302i −0.372322 0.644880i 0.617601 0.786492i \(-0.288105\pi\)
−0.989922 + 0.141612i \(0.954771\pi\)
\(140\) 0 0
\(141\) 0.445989 0.0375591
\(142\) 0 0
\(143\) 17.8905 + 30.9872i 1.49607 + 2.59128i
\(144\) 0 0
\(145\) 7.96358 0.661339
\(146\) 0 0
\(147\) 2.03827 3.53039i 0.168114 0.291182i
\(148\) 0 0
\(149\) 0.915913 1.58641i 0.0750345 0.129964i −0.826067 0.563572i \(-0.809427\pi\)
0.901101 + 0.433609i \(0.142760\pi\)
\(150\) 0 0
\(151\) −0.389869 −0.0317271 −0.0158635 0.999874i \(-0.505050\pi\)
−0.0158635 + 0.999874i \(0.505050\pi\)
\(152\) 0 0
\(153\) −11.1411 −0.900706
\(154\) 0 0
\(155\) 2.24517 3.88875i 0.180336 0.312352i
\(156\) 0 0
\(157\) 1.37608 2.38344i 0.109823 0.190219i −0.805875 0.592085i \(-0.798305\pi\)
0.915698 + 0.401866i \(0.131638\pi\)
\(158\) 0 0
\(159\) 2.88021 0.228416
\(160\) 0 0
\(161\) 1.68638 + 2.92090i 0.132906 + 0.230199i
\(162\) 0 0
\(163\) −15.0953 −1.18236 −0.591179 0.806540i \(-0.701337\pi\)
−0.591179 + 0.806540i \(0.701337\pi\)
\(164\) 0 0
\(165\) 1.06246 + 1.84024i 0.0827127 + 0.143263i
\(166\) 0 0
\(167\) −1.49402 2.58771i −0.115611 0.200243i 0.802413 0.596769i \(-0.203549\pi\)
−0.918024 + 0.396526i \(0.870216\pi\)
\(168\) 0 0
\(169\) −11.2109 + 19.4178i −0.862374 + 1.49368i
\(170\) 0 0
\(171\) 3.11683 + 12.1384i 0.238350 + 0.928245i
\(172\) 0 0
\(173\) 11.5945 20.0822i 0.881513 1.52682i 0.0318535 0.999493i \(-0.489859\pi\)
0.849659 0.527332i \(-0.176808\pi\)
\(174\) 0 0
\(175\) 2.15253 + 3.72830i 0.162716 + 0.281833i
\(176\) 0 0
\(177\) 0.928986 + 1.60905i 0.0698269 + 0.120944i
\(178\) 0 0
\(179\) −13.5091 −1.00972 −0.504860 0.863201i \(-0.668456\pi\)
−0.504860 + 0.863201i \(0.668456\pi\)
\(180\) 0 0
\(181\) 10.1559 + 17.5906i 0.754886 + 1.30750i 0.945431 + 0.325822i \(0.105641\pi\)
−0.190546 + 0.981678i \(0.561026\pi\)
\(182\) 0 0
\(183\) −1.98290 −0.146580
\(184\) 0 0
\(185\) 0.494018 0.855664i 0.0363209 0.0629096i
\(186\) 0 0
\(187\) −11.6484 + 20.1756i −0.851816 + 1.47539i
\(188\) 0 0
\(189\) −8.93965 −0.650264
\(190\) 0 0
\(191\) −7.04838 −0.510003 −0.255002 0.966941i \(-0.582076\pi\)
−0.255002 + 0.966941i \(0.582076\pi\)
\(192\) 0 0
\(193\) 11.8892 20.5926i 0.855800 1.48229i −0.0201010 0.999798i \(-0.506399\pi\)
0.875901 0.482491i \(-0.160268\pi\)
\(194\) 0 0
\(195\) −1.05180 + 1.82177i −0.0753208 + 0.130460i
\(196\) 0 0
\(197\) 23.7428 1.69160 0.845802 0.533497i \(-0.179122\pi\)
0.845802 + 0.533497i \(0.179122\pi\)
\(198\) 0 0
\(199\) 11.4893 + 19.9001i 0.814457 + 1.41068i 0.909717 + 0.415229i \(0.136299\pi\)
−0.0952595 + 0.995452i \(0.530368\pi\)
\(200\) 0 0
\(201\) −2.48943 −0.175591
\(202\) 0 0
\(203\) 17.1419 + 29.6906i 1.20312 + 2.08387i
\(204\) 0 0
\(205\) −3.15253 5.46035i −0.220182 0.381367i
\(206\) 0 0
\(207\) 1.12623 1.95068i 0.0782781 0.135582i
\(208\) 0 0
\(209\) 25.2403 + 7.04675i 1.74591 + 0.487434i
\(210\) 0 0
\(211\) 0.692366 1.19921i 0.0476645 0.0825573i −0.841209 0.540710i \(-0.818156\pi\)
0.888873 + 0.458153i \(0.151489\pi\)
\(212\) 0 0
\(213\) −1.02761 1.77987i −0.0704104 0.121954i
\(214\) 0 0
\(215\) 0.785004 + 1.35967i 0.0535368 + 0.0927285i
\(216\) 0 0
\(217\) 19.3312 1.31229
\(218\) 0 0
\(219\) −1.63302 2.82848i −0.110349 0.191131i
\(220\) 0 0
\(221\) −23.0629 −1.55138
\(222\) 0 0
\(223\) 11.6500 20.1783i 0.780139 1.35124i −0.151721 0.988423i \(-0.548481\pi\)
0.931860 0.362818i \(-0.118185\pi\)
\(224\) 0 0
\(225\) 1.43754 2.48989i 0.0958358 0.165992i
\(226\) 0 0
\(227\) −4.48943 −0.297974 −0.148987 0.988839i \(-0.547601\pi\)
−0.148987 + 0.988839i \(0.547601\pi\)
\(228\) 0 0
\(229\) 9.20830 0.608501 0.304251 0.952592i \(-0.401594\pi\)
0.304251 + 0.952592i \(0.401594\pi\)
\(230\) 0 0
\(231\) −4.57397 + 7.92236i −0.300945 + 0.521253i
\(232\) 0 0
\(233\) 2.16265 3.74581i 0.141680 0.245396i −0.786450 0.617654i \(-0.788083\pi\)
0.928129 + 0.372258i \(0.121416\pi\)
\(234\) 0 0
\(235\) −1.26182 −0.0823119
\(236\) 0 0
\(237\) −2.47324 4.28378i −0.160654 0.278261i
\(238\) 0 0
\(239\) −14.8267 −0.959059 −0.479529 0.877526i \(-0.659193\pi\)
−0.479529 + 0.877526i \(0.659193\pi\)
\(240\) 0 0
\(241\) −1.44453 2.50199i −0.0930500 0.161167i 0.815743 0.578414i \(-0.196328\pi\)
−0.908793 + 0.417247i \(0.862995\pi\)
\(242\) 0 0
\(243\) 4.50940 + 7.81050i 0.289278 + 0.501044i
\(244\) 0 0
\(245\) −5.76679 + 9.98838i −0.368427 + 0.638134i
\(246\) 0 0
\(247\) 6.45207 + 25.1273i 0.410535 + 1.59881i
\(248\) 0 0
\(249\) 1.16320 2.01472i 0.0737147 0.127678i
\(250\) 0 0
\(251\) −7.65253 13.2546i −0.483024 0.836621i 0.516786 0.856114i \(-0.327128\pi\)
−0.999810 + 0.0194930i \(0.993795\pi\)
\(252\) 0 0
\(253\) −2.35501 4.07900i −0.148058 0.256445i
\(254\) 0 0
\(255\) −1.36964 −0.0857704
\(256\) 0 0
\(257\) −6.54214 11.3313i −0.408087 0.706828i 0.586588 0.809886i \(-0.300471\pi\)
−0.994675 + 0.103057i \(0.967137\pi\)
\(258\) 0 0
\(259\) 4.25356 0.264303
\(260\) 0 0
\(261\) 11.4479 19.8284i 0.708610 1.22735i
\(262\) 0 0
\(263\) −9.68980 + 16.7832i −0.597499 + 1.03490i 0.395691 + 0.918384i \(0.370505\pi\)
−0.993189 + 0.116514i \(0.962828\pi\)
\(264\) 0 0
\(265\) −8.14886 −0.500580
\(266\) 0 0
\(267\) 1.19633 0.0732144
\(268\) 0 0
\(269\) 0.728523 1.26184i 0.0444188 0.0769357i −0.842961 0.537974i \(-0.819190\pi\)
0.887380 + 0.461039i \(0.152523\pi\)
\(270\) 0 0
\(271\) −6.28133 + 10.8796i −0.381563 + 0.660887i −0.991286 0.131728i \(-0.957948\pi\)
0.609722 + 0.792615i \(0.291281\pi\)
\(272\) 0 0
\(273\) −9.05612 −0.548101
\(274\) 0 0
\(275\) −3.00598 5.20651i −0.181268 0.313965i
\(276\) 0 0
\(277\) −4.39448 −0.264039 −0.132019 0.991247i \(-0.542146\pi\)
−0.132019 + 0.991247i \(0.542146\pi\)
\(278\) 0 0
\(279\) −6.45503 11.1804i −0.386453 0.669355i
\(280\) 0 0
\(281\) −2.16265 3.74581i −0.129013 0.223456i 0.794282 0.607550i \(-0.207847\pi\)
−0.923294 + 0.384093i \(0.874514\pi\)
\(282\) 0 0
\(283\) −3.74885 + 6.49319i −0.222846 + 0.385980i −0.955671 0.294437i \(-0.904868\pi\)
0.732825 + 0.680417i \(0.238201\pi\)
\(284\) 0 0
\(285\) 0.383170 + 1.49224i 0.0226970 + 0.0883928i
\(286\) 0 0
\(287\) 13.5719 23.5072i 0.801122 1.38758i
\(288\) 0 0
\(289\) 0.991903 + 1.71803i 0.0583472 + 0.101060i
\(290\) 0 0
\(291\) −1.30718 2.26410i −0.0766282 0.132724i
\(292\) 0 0
\(293\) −22.2837 −1.30183 −0.650915 0.759151i \(-0.725615\pi\)
−0.650915 + 0.759151i \(0.725615\pi\)
\(294\) 0 0
\(295\) −2.62834 4.55242i −0.153028 0.265052i
\(296\) 0 0
\(297\) 12.4841 0.724401
\(298\) 0 0
\(299\) 2.33137 4.03805i 0.134827 0.233527i
\(300\) 0 0
\(301\) −3.37949 + 5.85345i −0.194791 + 0.337387i
\(302\) 0 0
\(303\) 3.46641 0.199140
\(304\) 0 0
\(305\) 5.61013 0.321235
\(306\) 0 0
\(307\) 15.1403 26.2238i 0.864103 1.49667i −0.00383236 0.999993i \(-0.501220\pi\)
0.867935 0.496677i \(-0.165447\pi\)
\(308\) 0 0
\(309\) 2.55134 4.41906i 0.145141 0.251391i
\(310\) 0 0
\(311\) −5.37224 −0.304632 −0.152316 0.988332i \(-0.548673\pi\)
−0.152316 + 0.988332i \(0.548673\pi\)
\(312\) 0 0
\(313\) 2.40369 + 4.16331i 0.135864 + 0.235324i 0.925927 0.377702i \(-0.123286\pi\)
−0.790063 + 0.613026i \(0.789952\pi\)
\(314\) 0 0
\(315\) 12.3774 0.697386
\(316\) 0 0
\(317\) 14.8855 + 25.7824i 0.836052 + 1.44808i 0.893171 + 0.449717i \(0.148475\pi\)
−0.0571197 + 0.998367i \(0.518192\pi\)
\(318\) 0 0
\(319\) −23.9384 41.4625i −1.34029 2.32145i
\(320\) 0 0
\(321\) −1.67718 + 2.90496i −0.0936110 + 0.162139i
\(322\) 0 0
\(323\) −12.0680 + 11.8183i −0.671481 + 0.657586i
\(324\) 0 0
\(325\) 2.97581 5.15425i 0.165068 0.285906i
\(326\) 0 0
\(327\) −0.462735 0.801480i −0.0255893 0.0443220i
\(328\) 0 0
\(329\) −2.71610 4.70443i −0.149744 0.259364i
\(330\) 0 0
\(331\) 30.8042 1.69315 0.846577 0.532266i \(-0.178659\pi\)
0.846577 + 0.532266i \(0.178659\pi\)
\(332\) 0 0
\(333\) −1.42034 2.46010i −0.0778340 0.134812i
\(334\) 0 0
\(335\) 7.04325 0.384814
\(336\) 0 0
\(337\) 3.32529 5.75957i 0.181140 0.313744i −0.761129 0.648601i \(-0.775355\pi\)
0.942269 + 0.334857i \(0.108688\pi\)
\(338\) 0 0
\(339\) −2.41591 + 4.18448i −0.131214 + 0.227270i
\(340\) 0 0
\(341\) −26.9958 −1.46190
\(342\) 0 0
\(343\) −19.5174 −1.05384
\(344\) 0 0
\(345\) 0.138454 0.239809i 0.00745409 0.0129109i
\(346\) 0 0
\(347\) −7.70534 + 13.3460i −0.413644 + 0.716453i −0.995285 0.0969930i \(-0.969078\pi\)
0.581641 + 0.813446i \(0.302411\pi\)
\(348\) 0 0
\(349\) −27.0157 −1.44612 −0.723058 0.690788i \(-0.757264\pi\)
−0.723058 + 0.690788i \(0.757264\pi\)
\(350\) 0 0
\(351\) 6.17939 + 10.7030i 0.329832 + 0.571285i
\(352\) 0 0
\(353\) 19.7783 1.05269 0.526346 0.850270i \(-0.323561\pi\)
0.526346 + 0.850270i \(0.323561\pi\)
\(354\) 0 0
\(355\) 2.90736 + 5.03570i 0.154307 + 0.267267i
\(356\) 0 0
\(357\) −2.94820 5.10644i −0.156035 0.270261i
\(358\) 0 0
\(359\) −17.8408 + 30.9011i −0.941600 + 1.63090i −0.179179 + 0.983816i \(0.557344\pi\)
−0.762420 + 0.647082i \(0.775989\pi\)
\(360\) 0 0
\(361\) 16.2523 + 9.84195i 0.855382 + 0.517997i
\(362\) 0 0
\(363\) 4.44352 7.69640i 0.233224 0.403956i
\(364\) 0 0
\(365\) 4.62024 + 8.00250i 0.241835 + 0.418870i
\(366\) 0 0
\(367\) 1.05235 + 1.82272i 0.0549322 + 0.0951454i 0.892184 0.451672i \(-0.149172\pi\)
−0.837252 + 0.546818i \(0.815839\pi\)
\(368\) 0 0
\(369\) −18.1275 −0.943681
\(370\) 0 0
\(371\) −17.5407 30.3813i −0.910667 1.57732i
\(372\) 0 0
\(373\) −32.0208 −1.65797 −0.828987 0.559268i \(-0.811082\pi\)
−0.828987 + 0.559268i \(0.811082\pi\)
\(374\) 0 0
\(375\) 0.176725 0.306096i 0.00912603 0.0158067i
\(376\) 0 0
\(377\) 23.6981 41.0463i 1.22051 2.11399i
\(378\) 0 0
\(379\) −2.24784 −0.115464 −0.0577319 0.998332i \(-0.518387\pi\)
−0.0577319 + 0.998332i \(0.518387\pi\)
\(380\) 0 0
\(381\) −4.61859 −0.236617
\(382\) 0 0
\(383\) −1.33479 + 2.31192i −0.0682044 + 0.118133i −0.898111 0.439769i \(-0.855060\pi\)
0.829907 + 0.557902i \(0.188394\pi\)
\(384\) 0 0
\(385\) 12.9410 22.4144i 0.659532 1.14234i
\(386\) 0 0
\(387\) 4.51389 0.229454
\(388\) 0 0
\(389\) −7.76036 13.4413i −0.393466 0.681503i 0.599438 0.800421i \(-0.295391\pi\)
−0.992904 + 0.118918i \(0.962057\pi\)
\(390\) 0 0
\(391\) 3.03589 0.153532
\(392\) 0 0
\(393\) −1.32568 2.29615i −0.0668719 0.115825i
\(394\) 0 0
\(395\) 6.99743 + 12.1199i 0.352079 + 0.609819i
\(396\) 0 0
\(397\) −1.24839 + 2.16228i −0.0626551 + 0.108522i −0.895651 0.444757i \(-0.853290\pi\)
0.832996 + 0.553278i \(0.186623\pi\)
\(398\) 0 0
\(399\) −4.73873 + 4.64067i −0.237233 + 0.232324i
\(400\) 0 0
\(401\) 10.8590 18.8083i 0.542271 0.939242i −0.456502 0.889723i \(-0.650898\pi\)
0.998773 0.0495192i \(-0.0157689\pi\)
\(402\) 0 0
\(403\) −13.3624 23.1443i −0.665628 1.15290i
\(404\) 0 0
\(405\) −3.94563 6.83404i −0.196060 0.339586i
\(406\) 0 0
\(407\) −5.94003 −0.294437
\(408\) 0 0
\(409\) −12.1200 20.9924i −0.599294 1.03801i −0.992925 0.118740i \(-0.962115\pi\)
0.393631 0.919269i \(-0.371219\pi\)
\(410\) 0 0
\(411\) 2.97958 0.146972
\(412\) 0 0
\(413\) 11.3152 19.5985i 0.556784 0.964377i
\(414\) 0 0
\(415\) −3.29099 + 5.70016i −0.161548 + 0.279810i
\(416\) 0 0
\(417\) −3.10301 −0.151955
\(418\) 0 0
\(419\) −37.6543 −1.83953 −0.919766 0.392467i \(-0.871622\pi\)
−0.919766 + 0.392467i \(0.871622\pi\)
\(420\) 0 0
\(421\) 18.6884 32.3693i 0.910818 1.57758i 0.0979071 0.995196i \(-0.468785\pi\)
0.812911 0.582388i \(-0.197881\pi\)
\(422\) 0 0
\(423\) −1.81391 + 3.14178i −0.0881953 + 0.152759i
\(424\) 0 0
\(425\) 3.87507 0.187969
\(426\) 0 0
\(427\) 12.0760 + 20.9162i 0.584398 + 1.01221i
\(428\) 0 0
\(429\) 12.6467 0.610591
\(430\) 0 0
\(431\) −5.41491 9.37889i −0.260827 0.451765i 0.705635 0.708576i \(-0.250662\pi\)
−0.966462 + 0.256810i \(0.917329\pi\)
\(432\) 0 0
\(433\) −5.71031 9.89055i −0.274420 0.475310i 0.695569 0.718460i \(-0.255153\pi\)
−0.969989 + 0.243150i \(0.921819\pi\)
\(434\) 0 0
\(435\) 1.40736 2.43762i 0.0674779 0.116875i
\(436\) 0 0
\(437\) −0.849319 3.30764i −0.0406284 0.158226i
\(438\) 0 0
\(439\) −15.0612 + 26.0868i −0.718832 + 1.24505i 0.242631 + 0.970119i \(0.421989\pi\)
−0.961463 + 0.274934i \(0.911344\pi\)
\(440\) 0 0
\(441\) 16.5800 + 28.7173i 0.789522 + 1.36749i
\(442\) 0 0
\(443\) 10.3045 + 17.8479i 0.489582 + 0.847981i 0.999928 0.0119880i \(-0.00381598\pi\)
−0.510346 + 0.859969i \(0.670483\pi\)
\(444\) 0 0
\(445\) −3.38473 −0.160452
\(446\) 0 0
\(447\) −0.323729 0.560715i −0.0153119 0.0265209i
\(448\) 0 0
\(449\) −3.61436 −0.170572 −0.0852861 0.996357i \(-0.527180\pi\)
−0.0852861 + 0.996357i \(0.527180\pi\)
\(450\) 0 0
\(451\) −18.9529 + 32.8274i −0.892458 + 1.54578i
\(452\) 0 0
\(453\) −0.0688995 + 0.119338i −0.00323718 + 0.00560697i
\(454\) 0 0
\(455\) 25.6221 1.20118
\(456\) 0 0
\(457\) 5.50452 0.257491 0.128745 0.991678i \(-0.458905\pi\)
0.128745 + 0.991678i \(0.458905\pi\)
\(458\) 0 0
\(459\) −4.02338 + 6.96869i −0.187795 + 0.325271i
\(460\) 0 0
\(461\) −9.66053 + 16.7325i −0.449936 + 0.779312i −0.998381 0.0568746i \(-0.981886\pi\)
0.548446 + 0.836186i \(0.315220\pi\)
\(462\) 0 0
\(463\) 1.05722 0.0491334 0.0245667 0.999698i \(-0.492179\pi\)
0.0245667 + 0.999698i \(0.492179\pi\)
\(464\) 0 0
\(465\) −0.793555 1.37448i −0.0368002 0.0637398i
\(466\) 0 0
\(467\) 21.9413 1.01532 0.507662 0.861556i \(-0.330510\pi\)
0.507662 + 0.861556i \(0.330510\pi\)
\(468\) 0 0
\(469\) 15.1608 + 26.2593i 0.700062 + 1.21254i
\(470\) 0 0
\(471\) −0.486375 0.842426i −0.0224110 0.0388169i
\(472\) 0 0
\(473\) 4.71942 8.17427i 0.216999 0.375853i
\(474\) 0 0
\(475\) −1.08409 4.22194i −0.0497413 0.193716i
\(476\) 0 0
\(477\) −11.7143 + 20.2897i −0.536360 + 0.929003i
\(478\) 0 0
\(479\) 6.60203 + 11.4351i 0.301655 + 0.522481i 0.976511 0.215468i \(-0.0691277\pi\)
−0.674856 + 0.737949i \(0.735794\pi\)
\(480\) 0 0
\(481\) −2.94020 5.09258i −0.134062 0.232202i
\(482\) 0 0
\(483\) 1.19210 0.0542426
\(484\) 0 0
\(485\) 3.69835 + 6.40573i 0.167933 + 0.290869i
\(486\) 0 0
\(487\) 15.5627 0.705211 0.352606 0.935772i \(-0.385296\pi\)
0.352606 + 0.935772i \(0.385296\pi\)
\(488\) 0 0
\(489\) −2.66772 + 4.62063i −0.120638 + 0.208952i
\(490\) 0 0
\(491\) 14.7978 25.6306i 0.667816 1.15669i −0.310698 0.950509i \(-0.600563\pi\)
0.978514 0.206182i \(-0.0661040\pi\)
\(492\) 0 0
\(493\) 30.8595 1.38984
\(494\) 0 0
\(495\) −17.2848 −0.776896
\(496\) 0 0
\(497\) −12.5164 + 21.6790i −0.561437 + 0.972437i
\(498\) 0 0
\(499\) 2.92190 5.06087i 0.130802 0.226556i −0.793184 0.608982i \(-0.791578\pi\)
0.923986 + 0.382426i \(0.124911\pi\)
\(500\) 0 0
\(501\) −1.05612 −0.0471840
\(502\) 0 0
\(503\) −3.14544 5.44807i −0.140248 0.242917i 0.787342 0.616517i \(-0.211457\pi\)
−0.927590 + 0.373600i \(0.878123\pi\)
\(504\) 0 0
\(505\) −9.80737 −0.436422
\(506\) 0 0
\(507\) 3.96248 + 6.86321i 0.175980 + 0.304806i
\(508\) 0 0
\(509\) 1.84591 + 3.19720i 0.0818183 + 0.141713i 0.904031 0.427467i \(-0.140594\pi\)
−0.822213 + 0.569180i \(0.807261\pi\)
\(510\) 0 0
\(511\) −19.8905 + 34.4513i −0.879902 + 1.52403i
\(512\) 0 0
\(513\) 8.71805 + 2.43396i 0.384911 + 0.107462i
\(514\) 0 0
\(515\) −7.21841 + 12.5027i −0.318081 + 0.550933i
\(516\) 0 0
\(517\) 3.79300 + 6.56967i 0.166816 + 0.288934i
\(518\) 0 0
\(519\) −4.09807 7.09806i −0.179885 0.311570i
\(520\) 0 0
\(521\) 29.0510 1.27275 0.636373 0.771381i \(-0.280434\pi\)
0.636373 + 0.771381i \(0.280434\pi\)
\(522\) 0 0
\(523\) −9.21685 15.9640i −0.403025 0.698059i 0.591065 0.806624i \(-0.298708\pi\)
−0.994089 + 0.108565i \(0.965374\pi\)
\(524\) 0 0
\(525\) 1.52162 0.0664091
\(526\) 0 0
\(527\) 8.70020 15.0692i 0.378987 0.656424i
\(528\) 0 0
\(529\) 11.1931 19.3870i 0.486657 0.842915i
\(530\) 0 0
\(531\) −15.1133 −0.655863
\(532\) 0 0
\(533\) −37.5253 −1.62540
\(534\) 0 0
\(535\) 4.74517 8.21888i 0.205152 0.355333i
\(536\) 0 0
\(537\) −2.38740 + 4.13510i −0.103024 + 0.178443i
\(538\) 0 0
\(539\) 69.3395 2.98666
\(540\) 0 0
\(541\) 21.0875 + 36.5246i 0.906622 + 1.57032i 0.818724 + 0.574187i \(0.194682\pi\)
0.0878981 + 0.996129i \(0.471985\pi\)
\(542\) 0 0
\(543\) 7.17923 0.308090
\(544\) 0 0
\(545\) 1.30920 + 2.26759i 0.0560798 + 0.0971331i
\(546\) 0 0
\(547\) −7.87719 13.6437i −0.336804 0.583362i 0.647025 0.762468i \(-0.276013\pi\)
−0.983830 + 0.179106i \(0.942679\pi\)
\(548\) 0 0
\(549\) 8.06477 13.9686i 0.344196 0.596165i
\(550\) 0 0
\(551\) −8.63321 33.6217i −0.367787 1.43233i
\(552\) 0 0
\(553\) −30.1244 + 52.1770i −1.28102 + 2.21879i
\(554\) 0 0
\(555\) −0.174610 0.302434i −0.00741180 0.0128376i
\(556\) 0 0
\(557\) −11.5924 20.0786i −0.491185 0.850757i 0.508764 0.860906i \(-0.330103\pi\)
−0.999948 + 0.0101493i \(0.996769\pi\)
\(558\) 0 0
\(559\) 9.34408 0.395213
\(560\) 0 0
\(561\) 4.11712 + 7.13107i 0.173825 + 0.301074i
\(562\) 0 0
\(563\) −0.970934 −0.0409200 −0.0204600 0.999791i \(-0.506513\pi\)
−0.0204600 + 0.999791i \(0.506513\pi\)
\(564\) 0 0
\(565\) 6.83524 11.8390i 0.287561 0.498070i
\(566\) 0 0
\(567\) 16.9862 29.4210i 0.713354 1.23556i
\(568\) 0 0
\(569\) −30.1395 −1.26351 −0.631757 0.775167i \(-0.717666\pi\)
−0.631757 + 0.775167i \(0.717666\pi\)
\(570\) 0 0
\(571\) −31.8976 −1.33487 −0.667436 0.744667i \(-0.732608\pi\)
−0.667436 + 0.744667i \(0.732608\pi\)
\(572\) 0 0
\(573\) −1.24562 + 2.15748i −0.0520367 + 0.0901302i
\(574\) 0 0
\(575\) −0.391721 + 0.678480i −0.0163359 + 0.0282946i
\(576\) 0 0
\(577\) 23.2889 0.969528 0.484764 0.874645i \(-0.338905\pi\)
0.484764 + 0.874645i \(0.338905\pi\)
\(578\) 0 0
\(579\) −4.20222 7.27845i −0.174638 0.302482i
\(580\) 0 0
\(581\) −28.3358 −1.17557
\(582\) 0 0
\(583\) 24.4953 + 42.4271i 1.01449 + 1.75715i
\(584\) 0 0
\(585\) −8.55567 14.8188i −0.353733 0.612684i
\(586\) 0 0
\(587\) −4.74059 + 8.21094i −0.195665 + 0.338902i −0.947118 0.320885i \(-0.896020\pi\)
0.751453 + 0.659786i \(0.229353\pi\)
\(588\) 0 0
\(589\) −18.8520 5.26323i −0.776784 0.216867i
\(590\) 0 0
\(591\) 4.19594 7.26758i 0.172598 0.298948i
\(592\) 0 0
\(593\) 21.2234 + 36.7600i 0.871540 + 1.50955i 0.860403 + 0.509614i \(0.170212\pi\)
0.0111366 + 0.999938i \(0.496455\pi\)
\(594\) 0 0
\(595\) 8.34122 + 14.4474i 0.341957 + 0.592287i
\(596\) 0 0
\(597\) 8.12180 0.332403
\(598\) 0 0
\(599\) 12.8961 + 22.3368i 0.526922 + 0.912656i 0.999508 + 0.0313711i \(0.00998736\pi\)
−0.472586 + 0.881285i \(0.656679\pi\)
\(600\) 0 0
\(601\) 0.206080 0.00840619 0.00420310 0.999991i \(-0.498662\pi\)
0.00420310 + 0.999991i \(0.498662\pi\)
\(602\) 0 0
\(603\) 10.1249 17.5369i 0.412319 0.714157i
\(604\) 0 0
\(605\) −12.5719 + 21.7751i −0.511119 + 0.885284i
\(606\) 0 0
\(607\) 0.100472 0.00407802 0.00203901 0.999998i \(-0.499351\pi\)
0.00203901 + 0.999998i \(0.499351\pi\)
\(608\) 0 0
\(609\) 12.1176 0.491029
\(610\) 0 0
\(611\) −3.75493 + 6.50373i −0.151908 + 0.263113i
\(612\) 0 0
\(613\) 19.7400 34.1907i 0.797292 1.38095i −0.124081 0.992272i \(-0.539598\pi\)
0.921373 0.388679i \(-0.127068\pi\)
\(614\) 0 0
\(615\) −2.22852 −0.0898627
\(616\) 0 0
\(617\) 14.1658 + 24.5359i 0.570294 + 0.987777i 0.996536 + 0.0831682i \(0.0265039\pi\)
−0.426242 + 0.904609i \(0.640163\pi\)
\(618\) 0 0
\(619\) −1.39670 −0.0561380 −0.0280690 0.999606i \(-0.508936\pi\)
−0.0280690 + 0.999606i \(0.508936\pi\)
\(620\) 0 0
\(621\) −0.813425 1.40889i −0.0326416 0.0565369i
\(622\) 0 0
\(623\) −7.28575 12.6193i −0.291897 0.505581i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 6.61758 6.48063i 0.264281 0.258812i
\(628\) 0 0
\(629\) 1.91435 3.31576i 0.0763303 0.132208i
\(630\) 0 0
\(631\) −4.07397 7.05633i −0.162182 0.280908i 0.773469 0.633834i \(-0.218520\pi\)
−0.935651 + 0.352926i \(0.885187\pi\)
\(632\) 0 0
\(633\) −0.244717 0.423862i −0.00972661 0.0168470i
\(634\) 0 0
\(635\) 13.0672 0.518555
\(636\) 0 0
\(637\) 34.3217 + 59.4470i 1.35988 + 2.35538i
\(638\) 0 0
\(639\) 16.7178 0.661344
\(640\) 0 0
\(641\) −9.76367 + 16.9112i −0.385642 + 0.667951i −0.991858 0.127349i \(-0.959353\pi\)
0.606216 + 0.795300i \(0.292687\pi\)
\(642\) 0 0
\(643\) −21.5945 + 37.4028i −0.851604 + 1.47502i 0.0281570 + 0.999604i \(0.491036\pi\)
−0.879761 + 0.475417i \(0.842297\pi\)
\(644\) 0 0
\(645\) 0.554919 0.0218499
\(646\) 0 0
\(647\) 27.4390 1.07874 0.539370 0.842069i \(-0.318662\pi\)
0.539370 + 0.842069i \(0.318662\pi\)
\(648\) 0 0
\(649\) −15.8015 + 27.3690i −0.620263 + 1.07433i
\(650\) 0 0
\(651\) 3.41630 5.91721i 0.133896 0.231914i
\(652\) 0 0
\(653\) −3.40515 −0.133254 −0.0666270 0.997778i \(-0.521224\pi\)
−0.0666270 + 0.997778i \(0.521224\pi\)
\(654\) 0 0
\(655\) 3.75070 + 6.49640i 0.146552 + 0.253835i
\(656\) 0 0
\(657\) 26.5671 1.03648
\(658\) 0 0
\(659\) −6.09862 10.5631i −0.237569 0.411481i 0.722448 0.691426i \(-0.243017\pi\)
−0.960016 + 0.279945i \(0.909684\pi\)
\(660\) 0 0
\(661\) 19.0683 + 33.0272i 0.741670 + 1.28461i 0.951734 + 0.306923i \(0.0992994\pi\)
−0.210064 + 0.977688i \(0.567367\pi\)
\(662\) 0 0
\(663\) −4.07580 + 7.05948i −0.158291 + 0.274168i
\(664\) 0 0
\(665\) 13.4071 13.1297i 0.519905 0.509146i
\(666\) 0 0
\(667\) −3.11950 + 5.40313i −0.120788 + 0.209210i
\(668\) 0 0
\(669\) −4.11768 7.13202i −0.159199 0.275740i
\(670\) 0 0
\(671\) −16.8640 29.2092i −0.651026 1.12761i
\(672\) 0 0
\(673\) −37.9505 −1.46288 −0.731442 0.681903i \(-0.761152\pi\)
−0.731442 + 0.681903i \(0.761152\pi\)
\(674\) 0 0
\(675\) −1.03827 1.79834i −0.0399631 0.0692181i
\(676\) 0 0
\(677\) −32.4499 −1.24715 −0.623575 0.781763i \(-0.714321\pi\)
−0.623575 + 0.781763i \(0.714321\pi\)
\(678\) 0 0
\(679\) −15.9216 + 27.5771i −0.611016 + 1.05831i
\(680\) 0 0
\(681\) −0.793394 + 1.37420i −0.0304029 + 0.0526594i
\(682\) 0 0
\(683\) 40.5283 1.55077 0.775385 0.631488i \(-0.217556\pi\)
0.775385 + 0.631488i \(0.217556\pi\)
\(684\) 0 0
\(685\) −8.42999 −0.322093
\(686\) 0 0
\(687\) 1.62733 2.81863i 0.0620867 0.107537i
\(688\) 0 0
\(689\) −24.2494 + 42.0012i −0.923830 + 1.60012i
\(690\) 0 0
\(691\) 1.78657 0.0679642 0.0339821 0.999422i \(-0.489181\pi\)
0.0339821 + 0.999422i \(0.489181\pi\)
\(692\) 0 0
\(693\) −37.2062 64.4430i −1.41335 2.44799i
\(694\) 0 0
\(695\) 8.77921 0.333015
\(696\) 0 0
\(697\) −12.2163 21.1592i −0.462725 0.801464i
\(698\) 0 0
\(699\) −0.764386 1.32396i −0.0289117 0.0500766i
\(700\) 0 0
\(701\) 21.8614 37.8650i 0.825693 1.43014i −0.0756952 0.997131i \(-0.524118\pi\)
0.901388 0.433011i \(-0.142549\pi\)
\(702\) 0 0
\(703\) −4.14812 1.15810i −0.156449 0.0436785i
\(704\) 0 0
\(705\) −0.222995 + 0.386238i −0.00839846 + 0.0145466i
\(706\) 0 0
\(707\) −21.1107 36.5648i −0.793949 1.37516i
\(708\) 0 0
\(709\) −7.32015 12.6789i −0.274914 0.476165i 0.695199 0.718817i \(-0.255316\pi\)
−0.970113 + 0.242652i \(0.921983\pi\)
\(710\) 0 0
\(711\) 40.2363 1.50898
\(712\) 0 0
\(713\) 1.75896 + 3.04661i 0.0658736 + 0.114096i
\(714\) 0 0
\(715\) −35.7809 −1.33813
\(716\) 0 0
\(717\) −2.62024 + 4.53840i −0.0978548 + 0.169489i
\(718\) 0 0
\(719\) 11.1778 19.3606i 0.416863 0.722028i −0.578759 0.815499i \(-0.696463\pi\)
0.995622 + 0.0934709i \(0.0297962\pi\)
\(720\) 0 0
\(721\) −62.1515 −2.31464
\(722\) 0 0
\(723\) −1.02113 −0.0379764
\(724\) 0 0
\(725\) −3.98179 + 6.89666i −0.147880 + 0.256136i
\(726\) 0 0
\(727\) −4.15042 + 7.18874i −0.153930 + 0.266615i −0.932669 0.360733i \(-0.882527\pi\)
0.778739 + 0.627349i \(0.215860\pi\)
\(728\) 0 0
\(729\) −20.4861 −0.758745
\(730\) 0 0
\(731\) 3.04195 + 5.26881i 0.112511 + 0.194874i
\(732\) 0 0
\(733\) 35.7912 1.32198 0.660989 0.750396i \(-0.270137\pi\)
0.660989 + 0.750396i \(0.270137\pi\)
\(734\) 0 0
\(735\) 2.03827 + 3.53039i 0.0751828 + 0.130220i
\(736\) 0 0
\(737\) −21.1719 36.6708i −0.779876 1.35079i
\(738\) 0 0
\(739\) 16.6216 28.7895i 0.611437 1.05904i −0.379561 0.925167i \(-0.623925\pi\)
0.990998 0.133873i \(-0.0427415\pi\)
\(740\) 0 0
\(741\) 8.83163 + 2.46567i 0.324438 + 0.0905787i
\(742\) 0 0
\(743\) 9.27444 16.0638i 0.340246 0.589324i −0.644232 0.764830i \(-0.722823\pi\)
0.984478 + 0.175506i \(0.0561563\pi\)
\(744\) 0 0
\(745\) 0.915913 + 1.58641i 0.0335565 + 0.0581215i
\(746\) 0 0
\(747\) 9.46183 + 16.3884i 0.346190 + 0.599619i
\(748\) 0 0
\(749\) 40.8565 1.49287
\(750\) 0 0
\(751\) −21.5748 37.3687i −0.787276 1.36360i −0.927630 0.373501i \(-0.878157\pi\)
0.140353 0.990101i \(-0.455176\pi\)
\(752\) 0 0
\(753\) −5.40957 −0.197136
\(754\) 0 0
\(755\) 0.194935 0.337637i 0.00709440 0.0122879i
\(756\) 0 0
\(757\) −4.77434 + 8.26940i −0.173526 + 0.300556i −0.939650 0.342136i \(-0.888849\pi\)
0.766124 + 0.642693i \(0.222183\pi\)
\(758\) 0 0
\(759\) −1.66476 −0.0604268
\(760\) 0 0
\(761\) 35.8512 1.29960 0.649802 0.760103i \(-0.274852\pi\)
0.649802 + 0.760103i \(0.274852\pi\)
\(762\) 0 0
\(763\) −5.63617 + 9.76214i −0.204043 + 0.353413i
\(764\) 0 0
\(765\) 5.57056 9.64849i 0.201404 0.348842i
\(766\) 0 0
\(767\) −31.2857 −1.12966
\(768\) 0 0
\(769\) 8.93698 + 15.4793i 0.322276 + 0.558198i 0.980957 0.194224i \(-0.0622188\pi\)
−0.658681 + 0.752422i \(0.728886\pi\)
\(770\) 0 0
\(771\) −4.62463 −0.166552
\(772\) 0 0
\(773\) −0.926769 1.60521i −0.0333336 0.0577354i 0.848877 0.528590i \(-0.177279\pi\)
−0.882211 + 0.470854i \(0.843946\pi\)
\(774\) 0 0
\(775\) 2.24517 + 3.88875i 0.0806489 + 0.139688i
\(776\) 0 0
\(777\) 0.751709 1.30200i 0.0269674 0.0467089i
\(778\) 0 0
\(779\) −19.6356 + 19.2293i −0.703519 + 0.688961i
\(780\) 0 0
\(781\) 17.4790 30.2744i 0.625446 1.08330i
\(782\) 0 0
\(783\) −8.26836 14.3212i −0.295487 0.511798i
\(784\) 0 0
\(785\) 1.37608 + 2.38344i 0.0491144 + 0.0850686i
\(786\) 0 0
\(787\) −53.8501 −1.91955 −0.959774 0.280773i \(-0.909409\pi\)
−0.959774 + 0.280773i \(0.909409\pi\)
\(788\) 0 0
\(789\) 3.42486 + 5.93202i 0.121928 + 0.211186i