Properties

Label 350.2.e.c.151.1
Level $350$
Weight $2$
Character 350.151
Analytic conductor $2.795$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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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 151.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 350.151
Dual form 350.2.e.c.51.1

$q$-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 \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(4\) −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 −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) 0 0
\(13\) −5.00000 −1.38675 −0.693375 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 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 \(-0.755354\pi\)
0.961436 + 0.275029i \(0.0886875\pi\)
\(18\) 1.50000 2.59808i 0.353553 0.612372i
\(19\) 2.50000 + 4.33013i 0.573539 + 0.993399i 0.996199 + 0.0871106i \(0.0277634\pi\)
−0.422659 + 0.906289i \(0.638903\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 3.00000 0.639602
\(23\) 3.50000 + 6.06218i 0.729800 + 1.26405i 0.956967 + 0.290196i \(0.0937204\pi\)
−0.227167 + 0.973856i \(0.572946\pi\)
\(24\) 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 −0.762140 0.647412i \(-0.775851\pi\)
0.941745 + 0.336327i \(0.109185\pi\)
\(32\) −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 \(-0.192861\pi\)
−0.904194 + 0.427121i \(0.859528\pi\)
\(38\) 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 \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) −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 0.999926 + 0.0121990i \(0.00388317\pi\)
−0.489398 + 0.872060i \(0.662783\pi\)
\(48\) 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 0.371706 + 0.928351i \(0.378773\pi\)
−0.989828 + 0.142269i \(0.954560\pi\)
\(54\) 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 −0.705965 0.708247i \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) 0 0
\(61\) −3.00000 5.19615i −0.384111 0.665299i 0.607535 0.794293i \(-0.292159\pi\)
−0.991645 + 0.128994i \(0.958825\pi\)
\(62\) −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 \(-0.872318\pi\)
0.798454 + 0.602056i \(0.205652\pi\)
\(68\) 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 0.164083 0.986447i \(-0.447534\pi\)
0.772246 0.635323i \(-0.219133\pi\)
\(74\) −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 −0.927457 0.373930i \(-0.878010\pi\)
0.139895 0.990166i \(-0.455323\pi\)
\(80\) 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 \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 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 0.808146 0.588982i \(-0.200471\pi\)
−0.914146 + 0.405385i \(0.867138\pi\)
\(90\) 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 \(-0.708512\pi\)
−0.609208 + 0.793011i \(0.708512\pi\)
\(98\) −6.50000 + 2.59808i −0.656599 + 0.262445i
\(99\) −9.00000 −0.904534
\(100\) 0 0
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 0 0
\(103\) 4.00000 + 6.92820i 0.394132 + 0.682656i 0.992990 0.118199i \(-0.0377120\pi\)
−0.598858 + 0.800855i \(0.704379\pi\)
\(104\) −5.00000 −0.490290
\(105\) 0 0
\(106\) 9.00000 0.874157
\(107\) 8.00000 + 13.8564i 0.773389 + 1.33955i 0.935695 + 0.352809i \(0.114773\pi\)
−0.162306 + 0.986740i \(0.551893\pi\)
\(108\) 0 0
\(109\) −1.00000 + 1.73205i −0.0957826 + 0.165900i −0.909935 0.414751i \(-0.863869\pi\)
0.814152 + 0.580651i \(0.197202\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.50000 + 0.866025i 0.236228 + 0.0818317i
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 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 \(-0.399478\pi\)
0.310575 + 0.950549i \(0.399478\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) 0.500000 + 0.866025i 0.0436852 + 0.0756650i 0.887041 0.461690i \(-0.152757\pi\)
−0.843356 + 0.537355i \(0.819423\pi\)
\(132\) 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 \(-0.722316\pi\)
0.984757 + 0.173939i \(0.0556494\pi\)
\(138\) 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 0.953703 + 0.300750i \(0.0972370\pi\)
−0.216394 + 0.976306i \(0.569430\pi\)
\(150\) 0 0
\(151\) 3.00000 5.19615i 0.244137 0.422857i −0.717752 0.696299i \(-0.754829\pi\)
0.961888 + 0.273442i \(0.0881622\pi\)
\(152\) 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 \(-0.716404\pi\)
0.987817 + 0.155618i \(0.0497370\pi\)
\(158\) −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 \(-0.0109363\pi\)
−0.529454 + 0.848339i \(0.677603\pi\)
\(164\) −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 \(-0.302909\pi\)
0.580367 + 0.814355i \(0.302909\pi\)
\(168\) 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 \(-0.277815\pi\)
−0.984828 + 0.173534i \(0.944481\pi\)
\(174\) 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 −0.999867 0.0162823i \(-0.994817\pi\)
0.514035 + 0.857769i \(0.328150\pi\)
\(180\) 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 0.959558 + 0.281511i \(0.0908356\pi\)
−0.235983 + 0.971757i \(0.575831\pi\)
\(192\) 0 0
\(193\) 5.00000 8.66025i 0.359908 0.623379i −0.628037 0.778183i \(-0.716141\pi\)
0.987945 + 0.154805i \(0.0494748\pi\)
\(194\) 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 \(-0.557001\pi\)
−0.178118 + 0.984009i \(0.557001\pi\)
\(198\) 4.50000 + 7.79423i 0.319801 + 0.553912i
\(199\) −9.00000 + 15.5885i −0.637993 + 1.10504i 0.347879 + 0.937539i \(0.386902\pi\)
−0.985873 + 0.167497i \(0.946431\pi\)
\(200\) 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 \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) −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 \(-0.769526\pi\)
0.948242 + 0.317547i \(0.102859\pi\)
\(228\) 0 0
\(229\) −8.00000 13.8564i −0.528655 0.915657i −0.999442 0.0334101i \(-0.989363\pi\)
0.470787 0.882247i \(-0.343970\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −4.00000 −0.262613
\(233\) 4.00000 + 6.92820i 0.262049 + 0.453882i 0.966786 0.255586i \(-0.0822686\pi\)
−0.704737 + 0.709468i \(0.748935\pi\)
\(234\) −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 −0.683908 0.729568i \(-0.739721\pi\)
0.973779 + 0.227498i \(0.0730544\pi\)
\(242\) 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 \(-0.106747\pi\)
−0.757159 + 0.653231i \(0.773413\pi\)
\(258\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(264\) 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 −0.672374 0.740212i \(-0.734725\pi\)
0.977229 + 0.212187i \(0.0680585\pi\)
\(270\) 0 0
\(271\) −12.0000 20.7846i −0.728948 1.26258i −0.957328 0.289003i \(-0.906676\pi\)
0.228380 0.973572i \(-0.426657\pi\)
\(272\) −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 \(-0.814196\pi\)
0.894503 + 0.447062i \(0.147530\pi\)
\(278\) −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 \(-0.969939\pi\)
0.579437 + 0.815017i \(0.303272\pi\)
\(284\) 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 \(-0.584677\pi\)
−0.262893 + 0.964825i \(0.584677\pi\)
\(294\) 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 \(-0.716046\pi\)
−0.627803 + 0.778372i \(0.716046\pi\)
\(308\) 7.50000 + 2.59808i 0.427352 + 0.148039i
\(309\) 0 0
\(310\) 0 0
\(311\) −3.00000 + 5.19615i −0.170114 + 0.294647i −0.938460 0.345389i \(-0.887747\pi\)
0.768345 + 0.640036i \(0.221080\pi\)
\(312\) 0 0
\(313\) 11.0000 + 19.0526i 0.621757 + 1.07691i 0.989158 + 0.146852i \(0.0469141\pi\)
−0.367402 + 0.930062i \(0.619753\pi\)
\(314\) −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 \(-0.148779\pi\)
−0.836576 + 0.547852i \(0.815446\pi\)
\(318\) 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 0.789104 0.614260i \(-0.210545\pi\)
−0.926516 + 0.376254i \(0.877212\pi\)
\(332\) 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 \(-0.412193\pi\)
0.272367 + 0.962193i \(0.412193\pi\)
\(338\) −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 \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) 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 0.347024 + 0.937856i \(0.387192\pi\)
−0.985719 + 0.168397i \(0.946141\pi\)
\(354\) 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 0.573933 0.818902i \(-0.305417\pi\)
−0.996157 + 0.0875892i \(0.972084\pi\)
\(360\) 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 \(-0.943523\pi\)
0.645003 + 0.764180i \(0.276856\pi\)
\(368\) 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 −0.977016 0.213165i \(-0.931623\pi\)
0.303902 0.952703i \(-0.401711\pi\)
\(374\) 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 −0.999088 0.0427020i \(-0.986403\pi\)
0.462563 0.886586i \(-0.346930\pi\)
\(384\) 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 −0.779895 0.625910i \(-0.784728\pi\)
0.932002 + 0.362454i \(0.118061\pi\)
\(390\) 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 \(-0.0523996\pi\)
−0.635161 + 0.772380i \(0.719066\pi\)
\(398\) 18.0000 0.902258
\(399\) 0 0
\(400\) 0 0
\(401\) 7.50000 + 12.9904i 0.374532 + 0.648709i 0.990257 0.139253i \(-0.0444700\pi\)
−0.615725 + 0.787961i \(0.711137\pi\)
\(402\) 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 −0.639430 0.768849i \(-0.720830\pi\)
0.985558 + 0.169338i \(0.0541630\pi\)
\(410\) 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 −0.889104 0.457705i \(-0.848672\pi\)
0.840936 + 0.541135i \(0.182005\pi\)
\(432\) 0 0
\(433\) 28.0000 1.34559 0.672797 0.739827i \(-0.265093\pi\)
0.672797 + 0.739827i \(0.265093\pi\)
\(434\) 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 0.978412 + 0.206666i \(0.0662612\pi\)
−0.310228 + 0.950662i \(0.600405\pi\)
\(440\) 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 −0.963851 0.266443i \(-0.914152\pi\)
0.251179 0.967941i \(-0.419182\pi\)
\(444\) 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 \(-0.0915211\pi\)
−0.725059 + 0.688686i \(0.758188\pi\)
\(458\) −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 \(-0.629265\pi\)
−0.395029 + 0.918669i \(0.629265\pi\)
\(464\) 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 −0.927999 0.372584i \(-0.878472\pi\)
0.141332 0.989962i \(-0.454861\pi\)
\(468\) 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 0.0814184 + 0.996680i \(0.474055\pi\)
−0.903859 + 0.427830i \(0.859278\pi\)
\(480\) 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 −0.233933 0.972253i \(-0.575160\pi\)
0.958962 0.283535i \(-0.0915071\pi\)
\(488\) −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 0.817781 0.575529i \(-0.195204\pi\)
−0.907314 + 0.420455i \(0.861871\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −2.50000 4.33013i −0.111580 0.193263i
\(503\) 40.0000 1.78351 0.891756 0.452517i \(-0.149474\pi\)
0.891756 + 0.452517i \(0.149474\pi\)
\(504\) −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 0.946111 + 0.323843i \(0.104975\pi\)
−0.192599 + 0.981278i \(0.561692\pi\)
\(510\) 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 −0.402592 0.915379i \(-0.631891\pi\)
0.994038 0.109035i \(-0.0347759\pi\)
\(522\) −6.00000 + 10.3923i −0.262613 + 0.454859i
\(523\) −8.00000 13.8564i −0.349816 0.605898i 0.636401 0.771358i \(-0.280422\pi\)
−0.986216 + 0.165460i \(0.947089\pi\)
\(524\) −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 0.985162 0.171628i \(-0.0549027\pi\)
−0.641215 + 0.767361i \(0.721569\pi\)
\(542\) −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 \(-0.687603\pi\)
−0.555840 + 0.831289i \(0.687603\pi\)
\(548\) 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 \(-0.995341\pi\)
0.512622 + 0.858614i \(0.328674\pi\)
\(558\) −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 \(-0.846752\pi\)
0.844183 + 0.536054i \(0.180086\pi\)
\(564\) 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 0.979313 0.202350i \(-0.0648579\pi\)
−0.664897 + 0.746935i \(0.731525\pi\)
\(570\) 0 0
\(571\) −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i \(0.400192\pi\)
−0.978022 + 0.208502i \(0.933141\pi\)
\(572\) 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 \(-0.806800\pi\)
0.904649 + 0.426158i \(0.140133\pi\)
\(578\) 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 \(-0.252440\pi\)
0.701665 + 0.712507i \(0.252440\pi\)
\(588\) 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 \(-0.127353\pi\)
−0.797831 + 0.602881i \(0.794019\pi\)
\(594\) 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 −0.717021 0.697051i \(-0.754495\pi\)
0.962175 + 0.272433i \(0.0878284\pi\)
\(600\) 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 \(-0.0816819\pi\)
−0.703429 + 0.710766i \(0.748349\pi\)
\(608\) −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 \(-0.735371\pi\)
0.976797 + 0.214169i \(0.0687045\pi\)
\(614\) 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 \(-0.409065\pi\)
0.281809 + 0.959470i \(0.409065\pi\)
\(618\) 0 0
\(619\) −9.50000 + 16.4545i −0.381837 + 0.661361i −0.991325 0.131434i \(-0.958042\pi\)
0.609488 + 0.792796i \(0.291375\pi\)
\(620\) 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 −0.812421 0.583071i \(-0.801851\pi\)
0.911165 + 0.412042i \(0.135184\pi\)
\(642\) 0 0
\(643\) −14.0000 −0.552106 −0.276053 0.961142i \(-0.589027\pi\)
−0.276053 + 0.961142i \(0.589027\pi\)
\(644\) 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 −0.468617 0.883402i \(-0.655247\pi\)
0.999357 0.0358667i \(-0.0114192\pi\)
\(648\) −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 \(-0.185362\pi\)
−0.893882 + 0.448303i \(0.852029\pi\)
\(654\) 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 −0.978615 0.205702i \(-0.934052\pi\)
0.667451 + 0.744654i \(0.267385\pi\)
\(662\) −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 \(-0.288447\pi\)
0.616755 + 0.787155i \(0.288447\pi\)
\(674\) −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 \(-0.0607362\pi\)
−0.655170 + 0.755482i \(0.727403\pi\)
\(678\) 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 −0.0465592 0.998916i \(-0.514826\pi\)
0.888366 0.459136i \(-0.151841\pi\)
\(684\) −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 0.892458 + 0.451130i \(0.148979\pi\)
−0.0555386 + 0.998457i \(0.517688\pi\)
\(692\) 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 0.731085 0.682286i \(-0.239014\pi\)
−0.956420 + 0.291995i \(0.905681\pi\)
\(710\) 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 0.515030 0.857172i \(-0.327781\pi\)
−0.999848 + 0.0174426i \(0.994448\pi\)
\(720\) 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 \(-0.680735\pi\)
−0.537775 + 0.843088i \(0.680735\pi\)
\(728\) 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 −0.944281 0.329141i \(-0.893241\pi\)
0.187096 0.982342i \(-0.440092\pi\)
\(734\) 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 −0.465848 0.884865i \(-0.654251\pi\)
0.999239 0.0389959i \(-0.0124159\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −18.0000 + 15.5885i −0.660801 + 0.572270i
\(743\) −21.0000 −0.770415 −0.385208 0.922830i \(-0.625870\pi\)
−0.385208 + 0.922830i \(0.625870\pi\)
\(744\) 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 −0.999921 0.0125942i \(-0.995991\pi\)
0.489053 0.872254i \(-0.337342\pi\)
\(752\) 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 \(-0.223599\pi\)
0.763258 + 0.646094i \(0.223599\pi\)
\(758\) 14.5000 + 25.1147i 0.526664 + 0.912208i
\(759\) 0 0
\(760\) 0 0
\(761\) −0.500000 0.866025i −0.0181250 0.0313934i 0.856821 0.515615i \(-0.172436\pi\)
−0.874946 + 0.484221i \(0.839103\pi\)
\(762\) 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 0.104102 + 0.994567i \(0.466803\pi\)
−0.913371 + 0.407128i \(0.866530\pi\)
\(774\) 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 \(-0.937290\pi\)
0.659841 + 0.751405i \(0.270624\pi\)
\(788\) 2.50000 4.33013i 0.0890588 0.154254i
\(789\) 0 0
\(790\)