Properties

Label 350.2.e.j.51.1
Level $350$
Weight $2$
Character 350.51
Analytic conductor $2.795$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 350.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.79476407074\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 51.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 350.51
Dual form 350.2.e.j.151.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.50000 - 2.59808i) q^{11} +5.00000 q^{13} +(2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +(-1.50000 - 2.59808i) q^{18} +(2.50000 - 4.33013i) q^{19} -3.00000 q^{22} +(-3.50000 + 6.06218i) q^{23} +(2.50000 - 4.33013i) q^{26} +(0.500000 - 2.59808i) q^{28} -4.00000 q^{29} +(1.00000 + 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} -2.00000 q^{34} -3.00000 q^{36} +(0.500000 - 0.866025i) q^{37} +(-2.50000 - 4.33013i) q^{38} +3.00000 q^{41} -2.00000 q^{43} +(-1.50000 + 2.59808i) q^{44} +(3.50000 + 6.06218i) q^{46} +(-3.50000 + 6.06218i) q^{47} +(1.00000 + 6.92820i) q^{49} +(-2.50000 - 4.33013i) q^{52} +(4.50000 + 7.79423i) q^{53} +(-2.00000 - 1.73205i) q^{56} +(-2.00000 + 3.46410i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-3.00000 + 5.19615i) q^{61} +2.00000 q^{62} +(7.50000 - 2.59808i) q^{63} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{67} +(-1.00000 + 1.73205i) q^{68} -6.00000 q^{71} +(-1.50000 + 2.59808i) q^{72} +(-8.00000 - 13.8564i) q^{73} +(-0.500000 - 0.866025i) q^{74} -5.00000 q^{76} +(1.50000 - 7.79423i) q^{77} +(-7.00000 + 12.1244i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(1.50000 - 2.59808i) q^{82} +6.00000 q^{83} +(-1.00000 + 1.73205i) q^{86} +(1.50000 + 2.59808i) q^{88} +(-1.00000 + 1.73205i) q^{89} +(10.0000 + 8.66025i) q^{91} +7.00000 q^{92} +(3.50000 + 6.06218i) q^{94} +12.0000 q^{97} +(6.50000 + 2.59808i) q^{98} -9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{4} + 4 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - q^{4} + 4 q^{7} - 2 q^{8} + 3 q^{9} - 3 q^{11} + 10 q^{13} + 5 q^{14} - q^{16} - 2 q^{17} - 3 q^{18} + 5 q^{19} - 6 q^{22} - 7 q^{23} + 5 q^{26} + q^{28} - 8 q^{29} + 2 q^{31} + q^{32} - 4 q^{34} - 6 q^{36} + q^{37} - 5 q^{38} + 6 q^{41} - 4 q^{43} - 3 q^{44} + 7 q^{46} - 7 q^{47} + 2 q^{49} - 5 q^{52} + 9 q^{53} - 4 q^{56} - 4 q^{58} + 4 q^{59} - 6 q^{61} + 4 q^{62} + 15 q^{63} + 2 q^{64} + 2 q^{67} - 2 q^{68} - 12 q^{71} - 3 q^{72} - 16 q^{73} - q^{74} - 10 q^{76} + 3 q^{77} - 14 q^{79} - 9 q^{81} + 3 q^{82} + 12 q^{83} - 2 q^{86} + 3 q^{88} - 2 q^{89} + 20 q^{91} + 14 q^{92} + 7 q^{94} + 24 q^{97} + 13 q^{98} - 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) 2.00000 + 1.73205i 0.755929 + 0.654654i
\(8\) −1.00000 −0.353553
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) 0 0
\(11\) −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) 0 0
\(13\) 5.00000 1.38675 0.693375 0.720577i \(-0.256123\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 2.50000 0.866025i 0.668153 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.00000 1.73205i −0.242536 0.420084i 0.718900 0.695113i \(-0.244646\pi\)
−0.961436 + 0.275029i \(0.911312\pi\)
\(18\) −1.50000 2.59808i −0.353553 0.612372i
\(19\) 2.50000 4.33013i 0.573539 0.993399i −0.422659 0.906289i \(-0.638903\pi\)
0.996199 0.0871106i \(-0.0277634\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −3.00000 −0.639602
\(23\) −3.50000 + 6.06218i −0.729800 + 1.26405i 0.227167 + 0.973856i \(0.427054\pi\)
−0.956967 + 0.290196i \(0.906280\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 2.50000 4.33013i 0.490290 0.849208i
\(27\) 0 0
\(28\) 0.500000 2.59808i 0.0944911 0.490990i
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) 1.00000 + 1.73205i 0.179605 + 0.311086i 0.941745 0.336327i \(-0.109185\pi\)
−0.762140 + 0.647412i \(0.775851\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −2.00000 −0.342997
\(35\) 0 0
\(36\) −3.00000 −0.500000
\(37\) 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) −2.50000 4.33013i −0.405554 0.702439i
\(39\) 0 0
\(40\) 0 0
\(41\) 3.00000 0.468521 0.234261 0.972174i \(-0.424733\pi\)
0.234261 + 0.972174i \(0.424733\pi\)
\(42\) 0 0
\(43\) −2.00000 −0.304997 −0.152499 0.988304i \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) −1.50000 + 2.59808i −0.226134 + 0.391675i
\(45\) 0 0
\(46\) 3.50000 + 6.06218i 0.516047 + 0.893819i
\(47\) −3.50000 + 6.06218i −0.510527 + 0.884260i 0.489398 + 0.872060i \(0.337217\pi\)
−0.999926 + 0.0121990i \(0.996117\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 0 0
\(51\) 0 0
\(52\) −2.50000 4.33013i −0.346688 0.600481i
\(53\) 4.50000 + 7.79423i 0.618123 + 1.07062i 0.989828 + 0.142269i \(0.0454398\pi\)
−0.371706 + 0.928351i \(0.621227\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −2.00000 1.73205i −0.267261 0.231455i
\(57\) 0 0
\(58\) −2.00000 + 3.46410i −0.262613 + 0.454859i
\(59\) 2.00000 + 3.46410i 0.260378 + 0.450988i 0.966342 0.257260i \(-0.0828195\pi\)
−0.705965 + 0.708247i \(0.749486\pi\)
\(60\) 0 0
\(61\) −3.00000 + 5.19615i −0.384111 + 0.665299i −0.991645 0.128994i \(-0.958825\pi\)
0.607535 + 0.794293i \(0.292159\pi\)
\(62\) 2.00000 0.254000
\(63\) 7.50000 2.59808i 0.944911 0.327327i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 1.00000 + 1.73205i 0.122169 + 0.211604i 0.920623 0.390453i \(-0.127682\pi\)
−0.798454 + 0.602056i \(0.794348\pi\)
\(68\) −1.00000 + 1.73205i −0.121268 + 0.210042i
\(69\) 0 0
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) −1.50000 + 2.59808i −0.176777 + 0.306186i
\(73\) −8.00000 13.8564i −0.936329 1.62177i −0.772246 0.635323i \(-0.780867\pi\)
−0.164083 0.986447i \(-0.552466\pi\)
\(74\) −0.500000 0.866025i −0.0581238 0.100673i
\(75\) 0 0
\(76\) −5.00000 −0.573539
\(77\) 1.50000 7.79423i 0.170941 0.888235i
\(78\) 0 0
\(79\) −7.00000 + 12.1244i −0.787562 + 1.36410i 0.139895 + 0.990166i \(0.455323\pi\)
−0.927457 + 0.373930i \(0.878010\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 1.50000 2.59808i 0.165647 0.286910i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −1.00000 + 1.73205i −0.107833 + 0.186772i
\(87\) 0 0
\(88\) 1.50000 + 2.59808i 0.159901 + 0.276956i
\(89\) −1.00000 + 1.73205i −0.106000 + 0.183597i −0.914146 0.405385i \(-0.867138\pi\)
0.808146 + 0.588982i \(0.200471\pi\)
\(90\) 0 0
\(91\) 10.0000 + 8.66025i 1.04828 + 0.907841i
\(92\) 7.00000 0.729800
\(93\) 0 0
\(94\) 3.50000 + 6.06218i 0.360997 + 0.625266i
\(95\) 0 0
\(96\) 0 0
\(97\) 12.0000 1.21842 0.609208 0.793011i \(-0.291488\pi\)
0.609208 + 0.793011i \(0.291488\pi\)
\(98\) 6.50000 + 2.59808i 0.656599 + 0.262445i
\(99\) −9.00000 −0.904534
\(100\) 0 0
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) 0 0
\(103\) −4.00000 + 6.92820i −0.394132 + 0.682656i −0.992990 0.118199i \(-0.962288\pi\)
0.598858 + 0.800855i \(0.295621\pi\)
\(104\) −5.00000 −0.490290
\(105\) 0 0
\(106\) 9.00000 0.874157
\(107\) −8.00000 + 13.8564i −0.773389 + 1.33955i 0.162306 + 0.986740i \(0.448107\pi\)
−0.935695 + 0.352809i \(0.885227\pi\)
\(108\) 0 0
\(109\) −1.00000 1.73205i −0.0957826 0.165900i 0.814152 0.580651i \(-0.197202\pi\)
−0.909935 + 0.414751i \(0.863869\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −2.50000 + 0.866025i −0.236228 + 0.0818317i
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 2.00000 + 3.46410i 0.185695 + 0.321634i
\(117\) 7.50000 12.9904i 0.693375 1.20096i
\(118\) 4.00000 0.368230
\(119\) 1.00000 5.19615i 0.0916698 0.476331i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 3.00000 + 5.19615i 0.271607 + 0.470438i
\(123\) 0 0
\(124\) 1.00000 1.73205i 0.0898027 0.155543i
\(125\) 0 0
\(126\) 1.50000 7.79423i 0.133631 0.694365i
\(127\) −7.00000 −0.621150 −0.310575 0.950549i \(-0.600522\pi\)
−0.310575 + 0.950549i \(0.600522\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) 0.500000 0.866025i 0.0436852 0.0756650i −0.843356 0.537355i \(-0.819423\pi\)
0.887041 + 0.461690i \(0.152757\pi\)
\(132\) 0 0
\(133\) 12.5000 4.33013i 1.08389 0.375470i
\(134\) 2.00000 0.172774
\(135\) 0 0
\(136\) 1.00000 + 1.73205i 0.0857493 + 0.148522i
\(137\) −4.00000 6.92820i −0.341743 0.591916i 0.643013 0.765855i \(-0.277684\pi\)
−0.984757 + 0.173939i \(0.944351\pi\)
\(138\) 0 0
\(139\) 16.0000 1.35710 0.678551 0.734553i \(-0.262608\pi\)
0.678551 + 0.734553i \(0.262608\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −3.00000 + 5.19615i −0.251754 + 0.436051i
\(143\) −7.50000 12.9904i −0.627182 1.08631i
\(144\) 1.50000 + 2.59808i 0.125000 + 0.216506i
\(145\) 0 0
\(146\) −16.0000 −1.32417
\(147\) 0 0
\(148\) −1.00000 −0.0821995
\(149\) 9.00000 15.5885i 0.737309 1.27706i −0.216394 0.976306i \(-0.569430\pi\)
0.953703 0.300750i \(-0.0972370\pi\)
\(150\) 0 0
\(151\) 3.00000 + 5.19615i 0.244137 + 0.422857i 0.961888 0.273442i \(-0.0881622\pi\)
−0.717752 + 0.696299i \(0.754829\pi\)
\(152\) −2.50000 + 4.33013i −0.202777 + 0.351220i
\(153\) −6.00000 −0.485071
\(154\) −6.00000 5.19615i −0.483494 0.418718i
\(155\) 0 0
\(156\) 0 0
\(157\) −4.50000 7.79423i −0.359139 0.622047i 0.628678 0.777666i \(-0.283596\pi\)
−0.987817 + 0.155618i \(0.950263\pi\)
\(158\) 7.00000 + 12.1244i 0.556890 + 0.964562i
\(159\) 0 0
\(160\) 0 0
\(161\) −17.5000 + 6.06218i −1.37919 + 0.477767i
\(162\) −9.00000 −0.707107
\(163\) −6.00000 + 10.3923i −0.469956 + 0.813988i −0.999410 0.0343508i \(-0.989064\pi\)
0.529454 + 0.848339i \(0.322397\pi\)
\(164\) −1.50000 2.59808i −0.117130 0.202876i
\(165\) 0 0
\(166\) 3.00000 5.19615i 0.232845 0.403300i
\(167\) −15.0000 −1.16073 −0.580367 0.814355i \(-0.697091\pi\)
−0.580367 + 0.814355i \(0.697091\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) −7.50000 12.9904i −0.573539 0.993399i
\(172\) 1.00000 + 1.73205i 0.0762493 + 0.132068i
\(173\) 4.50000 7.79423i 0.342129 0.592584i −0.642699 0.766119i \(-0.722185\pi\)
0.984828 + 0.173534i \(0.0555188\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 3.00000 0.226134
\(177\) 0 0
\(178\) 1.00000 + 1.73205i 0.0749532 + 0.129823i
\(179\) −6.50000 11.2583i −0.485833 0.841487i 0.514035 0.857769i \(-0.328150\pi\)
−0.999867 + 0.0162823i \(0.994817\pi\)
\(180\) 0 0
\(181\) 26.0000 1.93256 0.966282 0.257485i \(-0.0828937\pi\)
0.966282 + 0.257485i \(0.0828937\pi\)
\(182\) 12.5000 4.33013i 0.926562 0.320970i
\(183\) 0 0
\(184\) 3.50000 6.06218i 0.258023 0.446910i
\(185\) 0 0
\(186\) 0 0
\(187\) −3.00000 + 5.19615i −0.219382 + 0.379980i
\(188\) 7.00000 0.510527
\(189\) 0 0
\(190\) 0 0
\(191\) 10.0000 17.3205i 0.723575 1.25327i −0.235983 0.971757i \(-0.575831\pi\)
0.959558 0.281511i \(-0.0908356\pi\)
\(192\) 0 0
\(193\) −5.00000 8.66025i −0.359908 0.623379i 0.628037 0.778183i \(-0.283859\pi\)
−0.987945 + 0.154805i \(0.950525\pi\)
\(194\) 6.00000 10.3923i 0.430775 0.746124i
\(195\) 0 0
\(196\) 5.50000 4.33013i 0.392857 0.309295i
\(197\) 5.00000 0.356235 0.178118 0.984009i \(-0.442999\pi\)
0.178118 + 0.984009i \(0.442999\pi\)
\(198\) −4.50000 + 7.79423i −0.319801 + 0.553912i
\(199\) −9.00000 15.5885i −0.637993 1.10504i −0.985873 0.167497i \(-0.946431\pi\)
0.347879 0.937539i \(-0.386902\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −8.00000 6.92820i −0.561490 0.486265i
\(204\) 0 0
\(205\) 0 0
\(206\) 4.00000 + 6.92820i 0.278693 + 0.482711i
\(207\) 10.5000 + 18.1865i 0.729800 + 1.26405i
\(208\) −2.50000 + 4.33013i −0.173344 + 0.300240i
\(209\) −15.0000 −1.03757
\(210\) 0 0
\(211\) −9.00000 −0.619586 −0.309793 0.950804i \(-0.600260\pi\)
−0.309793 + 0.950804i \(0.600260\pi\)
\(212\) 4.50000 7.79423i 0.309061 0.535310i
\(213\) 0 0
\(214\) 8.00000 + 13.8564i 0.546869 + 0.947204i
\(215\) 0 0
\(216\) 0 0
\(217\) −1.00000 + 5.19615i −0.0678844 + 0.352738i
\(218\) −2.00000 −0.135457
\(219\) 0 0
\(220\) 0 0
\(221\) −5.00000 8.66025i −0.336336 0.582552i
\(222\) 0 0
\(223\) 8.00000 0.535720 0.267860 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) −0.500000 + 2.59808i −0.0334077 + 0.173591i
\(225\) 0 0
\(226\) −7.00000 + 12.1244i −0.465633 + 0.806500i
\(227\) −3.00000 5.19615i −0.199117 0.344881i 0.749125 0.662428i \(-0.230474\pi\)
−0.948242 + 0.317547i \(0.897141\pi\)
\(228\) 0 0
\(229\) −8.00000 + 13.8564i −0.528655 + 0.915657i 0.470787 + 0.882247i \(0.343970\pi\)
−0.999442 + 0.0334101i \(0.989363\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 4.00000 0.262613
\(233\) −4.00000 + 6.92820i −0.262049 + 0.453882i −0.966786 0.255586i \(-0.917731\pi\)
0.704737 + 0.709468i \(0.251065\pi\)
\(234\) −7.50000 12.9904i −0.490290 0.849208i
\(235\) 0 0
\(236\) 2.00000 3.46410i 0.130189 0.225494i
\(237\) 0 0
\(238\) −4.00000 3.46410i −0.259281 0.224544i
\(239\) 20.0000 1.29369 0.646846 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) 0 0
\(241\) 4.50000 + 7.79423i 0.289870 + 0.502070i 0.973779 0.227498i \(-0.0730544\pi\)
−0.683908 + 0.729568i \(0.739721\pi\)
\(242\) −1.00000 1.73205i −0.0642824 0.111340i
\(243\) 0 0
\(244\) 6.00000 0.384111
\(245\) 0 0
\(246\) 0 0
\(247\) 12.5000 21.6506i 0.795356 1.37760i
\(248\) −1.00000 1.73205i −0.0635001 0.109985i
\(249\) 0 0
\(250\) 0 0
\(251\) 5.00000 0.315597 0.157799 0.987471i \(-0.449560\pi\)
0.157799 + 0.987471i \(0.449560\pi\)
\(252\) −6.00000 5.19615i −0.377964 0.327327i
\(253\) 21.0000 1.32026
\(254\) −3.50000 + 6.06218i −0.219610 + 0.380375i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −3.00000 + 5.19615i −0.187135 + 0.324127i −0.944294 0.329104i \(-0.893253\pi\)
0.757159 + 0.653231i \(0.226587\pi\)
\(258\) 0 0
\(259\) 2.50000 0.866025i 0.155342 0.0538122i
\(260\) 0 0
\(261\) −6.00000 + 10.3923i −0.371391 + 0.643268i
\(262\) −0.500000 0.866025i −0.0308901 0.0535032i
\(263\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 2.50000 12.9904i 0.153285 0.796491i
\(267\) 0 0
\(268\) 1.00000 1.73205i 0.0610847 0.105802i
\(269\) 5.00000 + 8.66025i 0.304855 + 0.528025i 0.977229 0.212187i \(-0.0680585\pi\)
−0.672374 + 0.740212i \(0.734725\pi\)
\(270\) 0 0
\(271\) −12.0000 + 20.7846i −0.728948 + 1.26258i 0.228380 + 0.973572i \(0.426657\pi\)
−0.957328 + 0.289003i \(0.906676\pi\)
\(272\) 2.00000 0.121268
\(273\) 0 0
\(274\) −8.00000 −0.483298
\(275\) 0 0
\(276\) 0 0
\(277\) −1.00000 1.73205i −0.0600842 0.104069i 0.834419 0.551131i \(-0.185804\pi\)
−0.894503 + 0.447062i \(0.852470\pi\)
\(278\) 8.00000 13.8564i 0.479808 0.831052i
\(279\) 6.00000 0.359211
\(280\) 0 0
\(281\) 9.00000 0.536895 0.268447 0.963294i \(-0.413489\pi\)
0.268447 + 0.963294i \(0.413489\pi\)
\(282\) 0 0
\(283\) 7.00000 + 12.1244i 0.416107 + 0.720718i 0.995544 0.0942988i \(-0.0300609\pi\)
−0.579437 + 0.815017i \(0.696728\pi\)
\(284\) 3.00000 + 5.19615i 0.178017 + 0.308335i
\(285\) 0 0
\(286\) −15.0000 −0.886969
\(287\) 6.00000 + 5.19615i 0.354169 + 0.306719i
\(288\) 3.00000 0.176777
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) 0 0
\(291\) 0 0
\(292\) −8.00000 + 13.8564i −0.468165 + 0.810885i
\(293\) 9.00000 0.525786 0.262893 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −0.500000 + 0.866025i −0.0290619 + 0.0503367i
\(297\) 0 0
\(298\) −9.00000 15.5885i −0.521356 0.903015i
\(299\) −17.5000 + 30.3109i −1.01205 + 1.75292i
\(300\) 0 0
\(301\) −4.00000 3.46410i −0.230556 0.199667i
\(302\) 6.00000 0.345261
\(303\) 0 0
\(304\) 2.50000 + 4.33013i 0.143385 + 0.248350i
\(305\) 0 0
\(306\) −3.00000 + 5.19615i −0.171499 + 0.297044i
\(307\) 22.0000 1.25561 0.627803 0.778372i \(-0.283954\pi\)
0.627803 + 0.778372i \(0.283954\pi\)
\(308\) −7.50000 + 2.59808i −0.427352 + 0.148039i
\(309\) 0 0
\(310\) 0 0
\(311\) −3.00000 5.19615i −0.170114 0.294647i 0.768345 0.640036i \(-0.221080\pi\)
−0.938460 + 0.345389i \(0.887747\pi\)
\(312\) 0 0
\(313\) −11.0000 + 19.0526i −0.621757 + 1.07691i 0.367402 + 0.930062i \(0.380247\pi\)
−0.989158 + 0.146852i \(0.953086\pi\)
\(314\) −9.00000 −0.507899
\(315\) 0 0
\(316\) 14.0000 0.787562
\(317\) −1.00000 + 1.73205i −0.0561656 + 0.0972817i −0.892741 0.450570i \(-0.851221\pi\)
0.836576 + 0.547852i \(0.184554\pi\)
\(318\) 0 0
\(319\) 6.00000 + 10.3923i 0.335936 + 0.581857i
\(320\) 0 0
\(321\) 0 0
\(322\) −3.50000 + 18.1865i −0.195047 + 1.01350i
\(323\) −10.0000 −0.556415
\(324\) −4.50000 + 7.79423i −0.250000 + 0.433013i
\(325\) 0 0
\(326\) 6.00000 + 10.3923i 0.332309 + 0.575577i
\(327\) 0 0
\(328\) −3.00000 −0.165647
\(329\) −17.5000 + 6.06218i −0.964806 + 0.334219i
\(330\) 0 0
\(331\) −2.50000 + 4.33013i −0.137412 + 0.238005i −0.926516 0.376254i \(-0.877212\pi\)
0.789104 + 0.614260i \(0.210545\pi\)
\(332\) −3.00000 5.19615i −0.164646 0.285176i
\(333\) −1.50000 2.59808i −0.0821995 0.142374i
\(334\) −7.50000 + 12.9904i −0.410382 + 0.710802i
\(335\) 0 0
\(336\) 0 0
\(337\) −10.0000 −0.544735 −0.272367 0.962193i \(-0.587807\pi\)
−0.272367 + 0.962193i \(0.587807\pi\)
\(338\) 6.00000 10.3923i 0.326357 0.565267i
\(339\) 0 0
\(340\) 0 0
\(341\) 3.00000 5.19615i 0.162459 0.281387i
\(342\) −15.0000 −0.811107
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 2.00000 0.107833
\(345\) 0 0
\(346\) −4.50000 7.79423i −0.241921 0.419020i
\(347\) −6.00000 10.3923i −0.322097 0.557888i 0.658824 0.752297i \(-0.271054\pi\)
−0.980921 + 0.194409i \(0.937721\pi\)
\(348\) 0 0
\(349\) −12.0000 −0.642345 −0.321173 0.947021i \(-0.604077\pi\)
−0.321173 + 0.947021i \(0.604077\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.50000 2.59808i 0.0799503 0.138478i
\(353\) 12.0000 + 20.7846i 0.638696 + 1.10625i 0.985719 + 0.168397i \(0.0538590\pi\)
−0.347024 + 0.937856i \(0.612808\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 2.00000 0.106000
\(357\) 0 0
\(358\) −13.0000 −0.687071
\(359\) −8.00000 + 13.8564i −0.422224 + 0.731313i −0.996157 0.0875892i \(-0.972084\pi\)
0.573933 + 0.818902i \(0.305417\pi\)
\(360\) 0 0
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) 13.0000 22.5167i 0.683265 1.18345i
\(363\) 0 0
\(364\) 2.50000 12.9904i 0.131036 0.680881i
\(365\) 0 0
\(366\) 0 0
\(367\) 6.50000 + 11.2583i 0.339297 + 0.587680i 0.984301 0.176500i \(-0.0564774\pi\)
−0.645003 + 0.764180i \(0.723144\pi\)
\(368\) −3.50000 6.06218i −0.182450 0.316013i
\(369\) 4.50000 7.79423i 0.234261 0.405751i
\(370\) 0 0
\(371\) −4.50000 + 23.3827i −0.233628 + 1.21397i
\(372\) 0 0
\(373\) 13.0000 22.5167i 0.673114 1.16587i −0.303902 0.952703i \(-0.598289\pi\)
0.977016 0.213165i \(-0.0683772\pi\)
\(374\) 3.00000 + 5.19615i 0.155126 + 0.268687i
\(375\) 0 0
\(376\) 3.50000 6.06218i 0.180499 0.312633i
\(377\) −20.0000 −1.03005
\(378\) 0 0
\(379\) −29.0000 −1.48963 −0.744815 0.667271i \(-0.767462\pi\)
−0.744815 + 0.667271i \(0.767462\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −10.0000 17.3205i −0.511645 0.886194i
\(383\) 10.5000 18.1865i 0.536525 0.929288i −0.462563 0.886586i \(-0.653070\pi\)
0.999088 0.0427020i \(-0.0135966\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −10.0000 −0.508987
\(387\) −3.00000 + 5.19615i −0.152499 + 0.264135i
\(388\) −6.00000 10.3923i −0.304604 0.527589i
\(389\) 3.00000 + 5.19615i 0.152106 + 0.263455i 0.932002 0.362454i \(-0.118061\pi\)
−0.779895 + 0.625910i \(0.784728\pi\)
\(390\) 0 0
\(391\) 14.0000 0.708010
\(392\) −1.00000 6.92820i −0.0505076 0.349927i
\(393\) 0 0
\(394\) 2.50000 4.33013i 0.125948 0.218149i
\(395\) 0 0
\(396\) 4.50000 + 7.79423i 0.226134 + 0.391675i
\(397\) −7.00000 + 12.1244i −0.351320 + 0.608504i −0.986481 0.163876i \(-0.947600\pi\)
0.635161 + 0.772380i \(0.280934\pi\)
\(398\) −18.0000 −0.902258
\(399\) 0 0
\(400\) 0 0
\(401\) 7.50000 12.9904i 0.374532 0.648709i −0.615725 0.787961i \(-0.711137\pi\)
0.990257 + 0.139253i \(0.0444700\pi\)
\(402\) 0 0
\(403\) 5.00000 + 8.66025i 0.249068 + 0.431398i
\(404\) 0 0
\(405\) 0 0
\(406\) −10.0000 + 3.46410i −0.496292 + 0.171920i
\(407\) −3.00000 −0.148704
\(408\) 0 0
\(409\) 7.00000 + 12.1244i 0.346128 + 0.599511i 0.985558 0.169338i \(-0.0541630\pi\)
−0.639430 + 0.768849i \(0.720830\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 8.00000 0.394132
\(413\) −2.00000 + 10.3923i −0.0984136 + 0.511372i
\(414\) 21.0000 1.03209
\(415\) 0 0
\(416\) 2.50000 + 4.33013i 0.122573 + 0.212302i
\(417\) 0 0
\(418\) −7.50000 + 12.9904i −0.366837 + 0.635380i
\(419\) 35.0000 1.70986 0.854931 0.518742i \(-0.173599\pi\)
0.854931 + 0.518742i \(0.173599\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) −4.50000 + 7.79423i −0.219057 + 0.379417i
\(423\) 10.5000 + 18.1865i 0.510527 + 0.884260i
\(424\) −4.50000 7.79423i −0.218539 0.378521i
\(425\) 0 0
\(426\) 0 0
\(427\) −15.0000 + 5.19615i −0.725901 + 0.251459i
\(428\) 16.0000 0.773389
\(429\) 0 0
\(430\) 0 0
\(431\) −1.00000 1.73205i −0.0481683 0.0834300i 0.840936 0.541135i \(-0.182005\pi\)
−0.889104 + 0.457705i \(0.848672\pi\)
\(432\) 0 0
\(433\) −28.0000 −1.34559 −0.672797 0.739827i \(-0.734907\pi\)
−0.672797 + 0.739827i \(0.734907\pi\)
\(434\) 4.00000 + 3.46410i 0.192006 + 0.166282i
\(435\) 0 0
\(436\) −1.00000 + 1.73205i −0.0478913 + 0.0829502i
\(437\) 17.5000 + 30.3109i 0.837139 + 1.44997i
\(438\) 0 0
\(439\) 14.0000 24.2487i 0.668184 1.15733i −0.310228 0.950662i \(-0.600405\pi\)
0.978412 0.206666i \(-0.0662612\pi\)
\(440\) 0 0
\(441\) 19.5000 + 7.79423i 0.928571 + 0.371154i
\(442\) −10.0000 −0.475651
\(443\) 15.0000 25.9808i 0.712672 1.23438i −0.251179 0.967941i \(-0.580818\pi\)
0.963851 0.266443i \(-0.0858483\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 4.00000 6.92820i 0.189405 0.328060i
\(447\) 0 0
\(448\) 2.00000 + 1.73205i 0.0944911 + 0.0818317i
\(449\) 5.00000 0.235965 0.117982 0.993016i \(-0.462357\pi\)
0.117982 + 0.993016i \(0.462357\pi\)
\(450\) 0 0
\(451\) −4.50000 7.79423i −0.211897 0.367016i
\(452\) 7.00000 + 12.1244i 0.329252 + 0.570282i
\(453\) 0 0
\(454\) −6.00000 −0.281594
\(455\) 0 0
\(456\) 0 0
\(457\) −5.00000 + 8.66025i −0.233890 + 0.405110i −0.958950 0.283577i \(-0.908479\pi\)
0.725059 + 0.688686i \(0.241812\pi\)
\(458\) 8.00000 + 13.8564i 0.373815 + 0.647467i
\(459\) 0 0
\(460\) 0 0
\(461\) −32.0000 −1.49039 −0.745194 0.666847i \(-0.767643\pi\)
−0.745194 + 0.666847i \(0.767643\pi\)
\(462\) 0 0
\(463\) 17.0000 0.790057 0.395029 0.918669i \(-0.370735\pi\)
0.395029 + 0.918669i \(0.370735\pi\)
\(464\) 2.00000 3.46410i 0.0928477 0.160817i
\(465\) 0 0
\(466\) 4.00000 + 6.92820i 0.185296 + 0.320943i
\(467\) 17.0000 29.4449i 0.786666 1.36255i −0.141332 0.989962i \(-0.545139\pi\)
0.927999 0.372584i \(-0.121528\pi\)
\(468\) −15.0000 −0.693375
\(469\) −1.00000 + 5.19615i −0.0461757 + 0.239936i
\(470\) 0 0
\(471\) 0 0
\(472\) −2.00000 3.46410i −0.0920575 0.159448i
\(473\) 3.00000 + 5.19615i 0.137940 + 0.238919i
\(474\) 0 0
\(475\) 0 0
\(476\) −5.00000 + 1.73205i −0.229175 + 0.0793884i
\(477\) 27.0000 1.23625
\(478\) 10.0000 17.3205i 0.457389 0.792222i
\(479\) −18.0000 31.1769i −0.822441 1.42451i −0.903859 0.427830i \(-0.859278\pi\)
0.0814184 0.996680i \(-0.474055\pi\)
\(480\) 0 0
\(481\) 2.50000 4.33013i 0.113990 0.197437i
\(482\) 9.00000 0.409939
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) 0 0
\(486\) 0 0
\(487\) −16.0000 27.7128i −0.725029 1.25579i −0.958962 0.283535i \(-0.908493\pi\)
0.233933 0.972253i \(-0.424840\pi\)
\(488\) 3.00000 5.19615i 0.135804 0.235219i
\(489\) 0 0
\(490\) 0 0
\(491\) 24.0000 1.08310 0.541552 0.840667i \(-0.317837\pi\)
0.541552 + 0.840667i \(0.317837\pi\)
\(492\) 0 0
\(493\) 4.00000 + 6.92820i 0.180151 + 0.312031i
\(494\) −12.5000 21.6506i −0.562402 0.974108i
\(495\) 0 0
\(496\) −2.00000 −0.0898027
\(497\) −12.0000 10.3923i −0.538274 0.466159i
\(498\) 0 0
\(499\) −2.00000 + 3.46410i −0.0895323 + 0.155074i −0.907314 0.420455i \(-0.861871\pi\)
0.817781 + 0.575529i \(0.195204\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 2.50000 4.33013i 0.111580 0.193263i
\(503\) −40.0000 −1.78351 −0.891756 0.452517i \(-0.850526\pi\)
−0.891756 + 0.452517i \(0.850526\pi\)
\(504\) −7.50000 + 2.59808i −0.334077 + 0.115728i
\(505\) 0 0
\(506\) 10.5000 18.1865i 0.466782 0.808490i
\(507\) 0 0
\(508\) 3.50000 + 6.06218i 0.155287 + 0.268966i
\(509\) 17.0000 29.4449i 0.753512 1.30512i −0.192599 0.981278i \(-0.561692\pi\)
0.946111 0.323843i \(-0.104975\pi\)
\(510\) 0 0
\(511\) 8.00000 41.5692i 0.353899 1.83891i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 3.00000 + 5.19615i 0.132324 + 0.229192i
\(515\) 0 0
\(516\) 0 0
\(517\) 21.0000 0.923579
\(518\) 0.500000 2.59808i 0.0219687 0.114153i
\(519\) 0 0
\(520\) 0 0
\(521\) 13.5000 + 23.3827i 0.591446 + 1.02441i 0.994038 + 0.109035i \(0.0347759\pi\)
−0.402592 + 0.915379i \(0.631891\pi\)
\(522\) 6.00000 + 10.3923i 0.262613 + 0.454859i
\(523\) 8.00000 13.8564i 0.349816 0.605898i −0.636401 0.771358i \(-0.719578\pi\)
0.986216 + 0.165460i \(0.0529109\pi\)
\(524\) −1.00000 −0.0436852
\(525\) 0 0
\(526\) 0 0
\(527\) 2.00000 3.46410i 0.0871214 0.150899i
\(528\) 0 0
\(529\) −13.0000 22.5167i −0.565217 0.978985i
\(530\) 0 0
\(531\) 12.0000 0.520756
\(532\) −10.0000 8.66025i −0.433555 0.375470i
\(533\) 15.0000 0.649722
\(534\) 0 0
\(535\) 0 0
\(536\) −1.00000 1.73205i −0.0431934 0.0748132i
\(537\) 0 0
\(538\) 10.0000 0.431131
\(539\) 16.5000 12.9904i 0.710705 0.559535i
\(540\) 0 0
\(541\) 8.00000 13.8564i 0.343947 0.595733i −0.641215 0.767361i \(-0.721569\pi\)
0.985162 + 0.171628i \(0.0549027\pi\)
\(542\) 12.0000 + 20.7846i 0.515444 + 0.892775i
\(543\) 0 0
\(544\) 1.00000 1.73205i 0.0428746 0.0742611i
\(545\) 0 0
\(546\) 0 0
\(547\) 26.0000 1.11168 0.555840 0.831289i \(-0.312397\pi\)
0.555840 + 0.831289i \(0.312397\pi\)
\(548\) −4.00000 + 6.92820i −0.170872 + 0.295958i
\(549\) 9.00000 + 15.5885i 0.384111 + 0.665299i
\(550\) 0 0
\(551\) −10.0000 + 17.3205i −0.426014 + 0.737878i
\(552\) 0 0
\(553\) −35.0000 + 12.1244i −1.48835 + 0.515580i
\(554\) −2.00000 −0.0849719
\(555\) 0 0
\(556\) −8.00000 13.8564i −0.339276 0.587643i
\(557\) 11.5000 + 19.9186i 0.487271 + 0.843978i 0.999893 0.0146368i \(-0.00465919\pi\)
−0.512622 + 0.858614i \(0.671326\pi\)
\(558\) 3.00000 5.19615i 0.127000 0.219971i
\(559\) −10.0000 −0.422955
\(560\) 0 0
\(561\) 0 0
\(562\) 4.50000 7.79423i 0.189821 0.328780i
\(563\) 1.00000 + 1.73205i 0.0421450 + 0.0729972i 0.886328 0.463057i \(-0.153248\pi\)
−0.844183 + 0.536054i \(0.819914\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 14.0000 0.588464
\(567\) 4.50000 23.3827i 0.188982 0.981981i
\(568\) 6.00000 0.251754
\(569\) 7.50000 12.9904i 0.314416 0.544585i −0.664897 0.746935i \(-0.731525\pi\)
0.979313 + 0.202350i \(0.0648579\pi\)
\(570\) 0 0
\(571\) −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i \(-0.933141\pi\)
0.308443 0.951243i \(-0.400192\pi\)
\(572\) −7.50000 + 12.9904i −0.313591 + 0.543155i
\(573\) 0 0
\(574\) 7.50000 2.59808i 0.313044 0.108442i
\(575\) 0 0
\(576\) 1.50000 2.59808i 0.0625000 0.108253i
\(577\) −2.00000 3.46410i −0.0832611 0.144212i 0.821388 0.570370i \(-0.193200\pi\)
−0.904649 + 0.426158i \(0.859867\pi\)
\(578\) −6.50000 11.2583i −0.270364 0.468285i
\(579\) 0 0
\(580\) 0 0
\(581\) 12.0000 + 10.3923i 0.497844 + 0.431145i
\(582\) 0 0
\(583\) 13.5000 23.3827i 0.559113 0.968412i
\(584\) 8.00000 + 13.8564i 0.331042 + 0.573382i
\(585\) 0 0
\(586\) 4.50000 7.79423i 0.185893 0.321977i
\(587\) −34.0000 −1.40333 −0.701665 0.712507i \(-0.747560\pi\)
−0.701665 + 0.712507i \(0.747560\pi\)
\(588\) 0 0
\(589\) 10.0000 0.412043
\(590\) 0 0
\(591\) 0 0
\(592\) 0.500000 + 0.866025i 0.0205499 + 0.0355934i
\(593\) −3.00000 + 5.19615i −0.123195 + 0.213380i −0.921026 0.389501i \(-0.872647\pi\)
0.797831 + 0.602881i \(0.205981\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −18.0000 −0.737309
\(597\) 0 0
\(598\) 17.5000 + 30.3109i 0.715628 + 1.23950i
\(599\) 6.00000 + 10.3923i 0.245153 + 0.424618i 0.962175 0.272433i \(-0.0878284\pi\)
−0.717021 + 0.697051i \(0.754495\pi\)
\(600\) 0 0
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) −5.00000 + 1.73205i −0.203785 + 0.0705931i
\(603\) 6.00000 0.244339
\(604\) 3.00000 5.19615i 0.122068 0.211428i
\(605\) 0 0
\(606\) 0 0
\(607\) −6.50000 + 11.2583i −0.263827 + 0.456962i −0.967256 0.253804i \(-0.918318\pi\)
0.703429 + 0.710766i \(0.251651\pi\)
\(608\) 5.00000 0.202777
\(609\) 0 0
\(610\) 0 0
\(611\) −17.5000 + 30.3109i −0.707974 + 1.22625i
\(612\) 3.00000 + 5.19615i 0.121268 + 0.210042i
\(613\) −7.50000 12.9904i −0.302922 0.524677i 0.673874 0.738846i \(-0.264629\pi\)
−0.976797 + 0.214169i \(0.931296\pi\)
\(614\) 11.0000 19.0526i 0.443924 0.768899i
\(615\) 0 0
\(616\) −1.50000 + 7.79423i −0.0604367 + 0.314038i
\(617\) −14.0000 −0.563619 −0.281809 0.959470i \(-0.590935\pi\)
−0.281809 + 0.959470i \(0.590935\pi\)
\(618\) 0 0
\(619\) −9.50000 16.4545i −0.381837 0.661361i 0.609488 0.792796i \(-0.291375\pi\)
−0.991325 + 0.131434i \(0.958042\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −6.00000 −0.240578
\(623\) −5.00000 + 1.73205i −0.200321 + 0.0693932i
\(624\) 0 0
\(625\) 0 0
\(626\) 11.0000 + 19.0526i 0.439648 + 0.761493i
\(627\) 0 0
\(628\) −4.50000 + 7.79423i −0.179570 + 0.311024i
\(629\) −2.00000 −0.0797452
\(630\) 0 0
\(631\) −18.0000 −0.716569 −0.358284 0.933613i \(-0.616638\pi\)
−0.358284 + 0.933613i \(0.616638\pi\)
\(632\) 7.00000 12.1244i 0.278445 0.482281i
\(633\) 0 0
\(634\) 1.00000 + 1.73205i 0.0397151 + 0.0687885i
\(635\) 0 0
\(636\) 0 0
\(637\) 5.00000 + 34.6410i 0.198107 + 1.37253i
\(638\) 12.0000 0.475085
\(639\) −9.00000 + 15.5885i −0.356034 + 0.616670i
\(640\) 0 0
\(641\) 2.50000 + 4.33013i 0.0987441 + 0.171030i 0.911165 0.412042i \(-0.135184\pi\)
−0.812421 + 0.583071i \(0.801851\pi\)
\(642\) 0 0
\(643\) 14.0000 0.552106 0.276053 0.961142i \(-0.410973\pi\)
0.276053 + 0.961142i \(0.410973\pi\)
\(644\) 14.0000 + 12.1244i 0.551677 + 0.477767i
\(645\) 0 0
\(646\) −5.00000 + 8.66025i −0.196722 + 0.340733i
\(647\) −13.5000 23.3827i −0.530740 0.919268i −0.999357 0.0358667i \(-0.988581\pi\)
0.468617 0.883402i \(-0.344753\pi\)
\(648\) 4.50000 + 7.79423i 0.176777 + 0.306186i
\(649\) 6.00000 10.3923i 0.235521 0.407934i
\(650\) 0 0
\(651\) 0 0
\(652\) 12.0000 0.469956
\(653\) 1.50000 2.59808i 0.0586995 0.101671i −0.835182 0.549973i \(-0.814638\pi\)
0.893882 + 0.448303i \(0.147971\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.50000 + 2.59808i −0.0585652 + 0.101438i
\(657\) −48.0000 −1.87266
\(658\) −3.50000 + 18.1865i −0.136444 + 0.708985i
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) −8.00000 13.8564i −0.311164 0.538952i 0.667451 0.744654i \(-0.267385\pi\)
−0.978615 + 0.205702i \(0.934052\pi\)
\(662\) 2.50000 + 4.33013i 0.0971653 + 0.168295i
\(663\) 0 0
\(664\) −6.00000 −0.232845
\(665\) 0 0
\(666\) −3.00000 −0.116248
\(667\) 14.0000 24.2487i 0.542082 0.938914i
\(668\) 7.50000 + 12.9904i 0.290184 + 0.502613i
\(669\) 0 0
\(670\) 0 0
\(671\) 18.0000 0.694882
\(672\) 0 0
\(673\) −32.0000 −1.23351 −0.616755 0.787155i \(-0.711553\pi\)
−0.616755 + 0.787155i \(0.711553\pi\)
\(674\) −5.00000 + 8.66025i −0.192593 + 0.333581i
\(675\) 0 0
\(676\) −6.00000 10.3923i −0.230769 0.399704i
\(677\) −8.50000 + 14.7224i −0.326682 + 0.565829i −0.981851 0.189653i \(-0.939264\pi\)
0.655170 + 0.755482i \(0.272597\pi\)
\(678\) 0 0
\(679\) 24.0000 + 20.7846i 0.921035 + 0.797640i
\(680\) 0 0
\(681\) 0 0
\(682\) −3.00000 5.19615i −0.114876 0.198971i
\(683\) −22.0000 38.1051i −0.841807 1.45805i −0.888366 0.459136i \(-0.848159\pi\)
0.0465592 0.998916i \(-0.485174\pi\)
\(684\) −7.50000 + 12.9904i −0.286770 + 0.496700i
\(685\) 0 0
\(686\) 8.50000 + 16.4545i 0.324532 + 0.628235i
\(687\) 0 0
\(688\) 1.00000 1.73205i 0.0381246 0.0660338i
\(689\) 22.5000 + 38.9711i 0.857182 + 1.48468i
\(690\) 0 0
\(691\) 22.0000 38.1051i 0.836919 1.44959i −0.0555386 0.998457i \(-0.517688\pi\)
0.892458 0.451130i \(-0.148979\pi\)
\(692\) −9.00000 −0.342129
\(693\) −18.0000 15.5885i −0.683763 0.592157i
\(694\) −12.0000 −0.455514
\(695\) 0 0
\(696\) 0 0
\(697\) −3.00000 5.19615i −0.113633 0.196818i
\(698\) −6.00000 + 10.3923i −0.227103 + 0.393355i
\(699\) 0 0
\(700\) 0 0
\(701\) 26.0000 0.982006 0.491003 0.871158i \(-0.336630\pi\)
0.491003 + 0.871158i \(0.336630\pi\)
\(702\) 0 0
\(703\) −2.50000 4.33013i −0.0942893 0.163314i
\(704\) −1.50000 2.59808i −0.0565334 0.0979187i
\(705\) 0 0
\(706\) 24.0000 0.903252
\(707\) 0 0
\(708\) 0 0
\(709\) −6.00000 + 10.3923i −0.225335 + 0.390291i −0.956420 0.291995i \(-0.905681\pi\)
0.731085 + 0.682286i \(0.239014\pi\)
\(710\) 0 0
\(711\) 21.0000 + 36.3731i 0.787562 + 1.36410i
\(712\) 1.00000 1.73205i 0.0374766 0.0649113i
\(713\) −14.0000 −0.524304
\(714\) 0 0
\(715\) 0 0
\(716\) −6.50000 + 11.2583i −0.242916 + 0.420744i
\(717\) 0 0
\(718\) 8.00000 + 13.8564i 0.298557 + 0.517116i
\(719\) −13.0000 + 22.5167i −0.484818 + 0.839730i −0.999848 0.0174426i \(-0.994448\pi\)
0.515030 + 0.857172i \(0.327781\pi\)
\(720\) 0 0
\(721\) −20.0000 + 6.92820i −0.744839 + 0.258020i
\(722\) −6.00000 −0.223297
\(723\) 0 0
\(724\) −13.0000 22.5167i −0.483141 0.836825i
\(725\) 0 0
\(726\) 0 0
\(727\) 29.0000 1.07555 0.537775 0.843088i \(-0.319265\pi\)
0.537775 + 0.843088i \(0.319265\pi\)
\(728\) −10.0000 8.66025i −0.370625 0.320970i
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 2.00000 + 3.46410i 0.0739727 + 0.128124i
\(732\) 0 0
\(733\) 20.5000 35.5070i 0.757185 1.31148i −0.187096 0.982342i \(-0.559908\pi\)
0.944281 0.329141i \(-0.106759\pi\)
\(734\) 13.0000 0.479839
\(735\) 0 0
\(736\) −7.00000 −0.258023
\(737\) 3.00000 5.19615i 0.110506 0.191403i
\(738\) −4.50000 7.79423i −0.165647 0.286910i
\(739\) 14.5000 + 25.1147i 0.533391 + 0.923861i 0.999239 + 0.0389959i \(0.0124159\pi\)
−0.465848 + 0.884865i \(0.654251\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 18.0000 + 15.5885i 0.660801 + 0.572270i
\(743\) 21.0000 0.770415 0.385208 0.922830i \(-0.374130\pi\)
0.385208 + 0.922830i \(0.374130\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −13.0000 22.5167i −0.475964 0.824394i
\(747\) 9.00000 15.5885i 0.329293 0.570352i
\(748\) 6.00000 0.219382
\(749\) −40.0000 + 13.8564i −1.46157 + 0.506302i
\(750\) 0 0
\(751\) −14.0000 + 24.2487i −0.510867 + 0.884848i 0.489053 + 0.872254i \(0.337342\pi\)
−0.999921 + 0.0125942i \(0.995991\pi\)
\(752\) −3.50000 6.06218i −0.127632 0.221065i
\(753\) 0 0
\(754\) −10.0000 + 17.3205i −0.364179 + 0.630776i
\(755\) 0 0
\(756\) 0 0
\(757\) −42.0000 −1.52652 −0.763258 0.646094i \(-0.776401\pi\)
−0.763258 + 0.646094i \(0.776401\pi\)
\(758\) −14.5000 + 25.1147i −0.526664 + 0.912208i
\(759\) 0 0
\(760\) 0 0
\(761\) −0.500000 + 0.866025i −0.0181250 + 0.0313934i −0.874946 0.484221i \(-0.839103\pi\)
0.856821 + 0.515615i \(0.172436\pi\)
\(762\) 0 0
\(763\) 1.00000 5.19615i 0.0362024 0.188113i
\(764\) −20.0000 −0.723575
\(765\) 0 0
\(766\) −10.5000 18.1865i −0.379380 0.657106i
\(767\) 10.0000 + 17.3205i 0.361079 + 0.625407i
\(768\) 0 0
\(769\) −29.0000 −1.04577 −0.522883 0.852404i \(-0.675144\pi\)
−0.522883 + 0.852404i \(0.675144\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −5.00000 + 8.66025i −0.179954 + 0.311689i
\(773\) 22.5000 + 38.9711i 0.809269 + 1.40169i 0.913371 + 0.407128i \(0.133470\pi\)
−0.104102 + 0.994567i \(0.533197\pi\)
\(774\) 3.00000 + 5.19615i 0.107833 + 0.186772i
\(775\) 0 0
\(776\) −12.0000 −0.430775
\(777\) 0 0
\(778\) 6.00000 0.215110
\(779\) 7.50000 12.9904i 0.268715 0.465429i
\(780\) 0 0
\(781\) 9.00000 + 15.5885i 0.322045 + 0.557799i
\(782\) 7.00000 12.1244i 0.250319 0.433566i
\(783\) 0 0
\(784\) −6.50000 2.59808i −0.232143 0.0927884i
\(785\) 0 0
\(786\) 0 0
\(787\) 9.00000 + 15.5885i 0.320815 + 0.555668i 0.980656 0.195737i \(-0.0627098\pi\)
−0.659841 + 0.751405i \(0.729376\pi\)
\(788\) −2.50000 4.33013i −0.0890588 0.154254i
\(789\) 0 0
\(790\) 0