Properties

Label 1350.2.e.i.901.1
Level $1350$
Weight $2$
Character 1350.901
Analytic conductor $10.780$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1350,2,Mod(451,1350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1350, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1350.451");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1350.e (of order \(3\), degree \(2\), not 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: \(10.7798042729\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
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 90)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 901.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1350.901
Dual form 1350.2.e.i.451.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-1.00000 - 1.73205i) q^{11} +(3.00000 - 5.19615i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +2.00000 q^{17} +6.00000 q^{19} +(1.00000 - 1.73205i) q^{22} +(0.500000 - 0.866025i) q^{23} +6.00000 q^{26} -1.00000 q^{28} +(4.50000 + 7.79423i) q^{29} +(1.00000 - 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.00000 + 1.73205i) q^{34} +2.00000 q^{37} +(3.00000 + 5.19615i) q^{38} +(-5.50000 + 9.52628i) q^{41} +(2.00000 + 3.46410i) q^{43} +2.00000 q^{44} +1.00000 q^{46} +(-3.50000 - 6.06218i) q^{47} +(3.00000 - 5.19615i) q^{49} +(3.00000 + 5.19615i) q^{52} +(-0.500000 - 0.866025i) q^{56} +(-4.50000 + 7.79423i) q^{58} +(-2.00000 + 3.46410i) q^{59} +(3.50000 + 6.06218i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(5.50000 - 9.52628i) q^{67} +(-1.00000 + 1.73205i) q^{68} +6.00000 q^{71} -4.00000 q^{73} +(1.00000 + 1.73205i) q^{74} +(-3.00000 + 5.19615i) q^{76} +(1.00000 - 1.73205i) q^{77} +(6.00000 + 10.3923i) q^{79} -11.0000 q^{82} +(-5.50000 - 9.52628i) q^{83} +(-2.00000 + 3.46410i) q^{86} +(1.00000 + 1.73205i) q^{88} -1.00000 q^{89} +6.00000 q^{91} +(0.500000 + 0.866025i) q^{92} +(3.50000 - 6.06218i) q^{94} +(4.00000 + 6.92820i) q^{97} +6.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{4} + q^{7} - 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - q^{4} + q^{7} - 2 q^{8} - 2 q^{11} + 6 q^{13} - q^{14} - q^{16} + 4 q^{17} + 12 q^{19} + 2 q^{22} + q^{23} + 12 q^{26} - 2 q^{28} + 9 q^{29} + 2 q^{31} + q^{32} + 2 q^{34} + 4 q^{37} + 6 q^{38} - 11 q^{41} + 4 q^{43} + 4 q^{44} + 2 q^{46} - 7 q^{47} + 6 q^{49} + 6 q^{52} - q^{56} - 9 q^{58} - 4 q^{59} + 7 q^{61} + 4 q^{62} + 2 q^{64} + 11 q^{67} - 2 q^{68} + 12 q^{71} - 8 q^{73} + 2 q^{74} - 6 q^{76} + 2 q^{77} + 12 q^{79} - 22 q^{82} - 11 q^{83} - 4 q^{86} + 2 q^{88} - 2 q^{89} + 12 q^{91} + q^{92} + 7 q^{94} + 8 q^{97} + 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).

\(n\) \(1001\) \(1027\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i 0.944911 0.327327i \(-0.106148\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) 0 0
\(13\) 3.00000 5.19615i 0.832050 1.44115i −0.0643593 0.997927i \(-0.520500\pi\)
0.896410 0.443227i \(-0.146166\pi\)
\(14\) −0.500000 + 0.866025i −0.133631 + 0.231455i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 0 0
\(19\) 6.00000 1.37649 0.688247 0.725476i \(-0.258380\pi\)
0.688247 + 0.725476i \(0.258380\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.00000 1.73205i 0.213201 0.369274i
\(23\) 0.500000 0.866025i 0.104257 0.180579i −0.809177 0.587565i \(-0.800087\pi\)
0.913434 + 0.406986i \(0.133420\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 6.00000 1.17670
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) 4.50000 + 7.79423i 0.835629 + 1.44735i 0.893517 + 0.449029i \(0.148230\pi\)
−0.0578882 + 0.998323i \(0.518437\pi\)
\(30\) 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
\(34\) 1.00000 + 1.73205i 0.171499 + 0.297044i
\(35\) 0 0
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 3.00000 + 5.19615i 0.486664 + 0.842927i
\(39\) 0 0
\(40\) 0 0
\(41\) −5.50000 + 9.52628i −0.858956 + 1.48775i 0.0139704 + 0.999902i \(0.495553\pi\)
−0.872926 + 0.487852i \(0.837780\pi\)
\(42\) 0 0
\(43\) 2.00000 + 3.46410i 0.304997 + 0.528271i 0.977261 0.212041i \(-0.0680112\pi\)
−0.672264 + 0.740312i \(0.734678\pi\)
\(44\) 2.00000 0.301511
\(45\) 0 0
\(46\) 1.00000 0.147442
\(47\) −3.50000 6.06218i −0.510527 0.884260i −0.999926 0.0121990i \(-0.996117\pi\)
0.489398 0.872060i \(-0.337217\pi\)
\(48\) 0 0
\(49\) 3.00000 5.19615i 0.428571 0.742307i
\(50\) 0 0
\(51\) 0 0
\(52\) 3.00000 + 5.19615i 0.416025 + 0.720577i
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −0.500000 0.866025i −0.0668153 0.115728i
\(57\) 0 0
\(58\) −4.50000 + 7.79423i −0.590879 + 1.02343i
\(59\) −2.00000 + 3.46410i −0.260378 + 0.450988i −0.966342 0.257260i \(-0.917180\pi\)
0.705965 + 0.708247i \(0.250514\pi\)
\(60\) 0 0
\(61\) 3.50000 + 6.06218i 0.448129 + 0.776182i 0.998264 0.0588933i \(-0.0187572\pi\)
−0.550135 + 0.835076i \(0.685424\pi\)
\(62\) 2.00000 0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 5.50000 9.52628i 0.671932 1.16382i −0.305424 0.952217i \(-0.598798\pi\)
0.977356 0.211604i \(-0.0678686\pi\)
\(68\) −1.00000 + 1.73205i −0.121268 + 0.210042i
\(69\) 0 0
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) −4.00000 −0.468165 −0.234082 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) 1.00000 + 1.73205i 0.116248 + 0.201347i
\(75\) 0 0
\(76\) −3.00000 + 5.19615i −0.344124 + 0.596040i
\(77\) 1.00000 1.73205i 0.113961 0.197386i
\(78\) 0 0
\(79\) 6.00000 + 10.3923i 0.675053 + 1.16923i 0.976453 + 0.215728i \(0.0692125\pi\)
−0.301401 + 0.953498i \(0.597454\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −11.0000 −1.21475
\(83\) −5.50000 9.52628i −0.603703 1.04565i −0.992255 0.124218i \(-0.960358\pi\)
0.388552 0.921427i \(-0.372976\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −2.00000 + 3.46410i −0.215666 + 0.373544i
\(87\) 0 0
\(88\) 1.00000 + 1.73205i 0.106600 + 0.184637i
\(89\) −1.00000 −0.106000 −0.0529999 0.998595i \(-0.516878\pi\)
−0.0529999 + 0.998595i \(0.516878\pi\)
\(90\) 0 0
\(91\) 6.00000 0.628971
\(92\) 0.500000 + 0.866025i 0.0521286 + 0.0902894i
\(93\) 0 0
\(94\) 3.50000 6.06218i 0.360997 0.625266i
\(95\) 0 0
\(96\) 0 0
\(97\) 4.00000 + 6.92820i 0.406138 + 0.703452i 0.994453 0.105180i \(-0.0335417\pi\)
−0.588315 + 0.808632i \(0.700208\pi\)
\(98\) 6.00000 0.606092
\(99\) 0 0
\(100\) 0 0
\(101\) 1.00000 + 1.73205i 0.0995037 + 0.172345i 0.911479 0.411346i \(-0.134941\pi\)
−0.811976 + 0.583691i \(0.801608\pi\)
\(102\) 0 0
\(103\) 4.00000 6.92820i 0.394132 0.682656i −0.598858 0.800855i \(-0.704379\pi\)
0.992990 + 0.118199i \(0.0377120\pi\)
\(104\) −3.00000 + 5.19615i −0.294174 + 0.509525i
\(105\) 0 0
\(106\) 0 0
\(107\) −3.00000 −0.290021 −0.145010 0.989430i \(-0.546322\pi\)
−0.145010 + 0.989430i \(0.546322\pi\)
\(108\) 0 0
\(109\) 7.00000 0.670478 0.335239 0.942133i \(-0.391183\pi\)
0.335239 + 0.942133i \(0.391183\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.500000 0.866025i 0.0472456 0.0818317i
\(113\) 6.00000 10.3923i 0.564433 0.977626i −0.432670 0.901553i \(-0.642428\pi\)
0.997102 0.0760733i \(-0.0242383\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −9.00000 −0.835629
\(117\) 0 0
\(118\) −4.00000 −0.368230
\(119\) 1.00000 + 1.73205i 0.0916698 + 0.158777i
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) −3.50000 + 6.06218i −0.316875 + 0.548844i
\(123\) 0 0
\(124\) 1.00000 + 1.73205i 0.0898027 + 0.155543i
\(125\) 0 0
\(126\) 0 0
\(127\) −19.0000 −1.68598 −0.842989 0.537931i \(-0.819206\pi\)
−0.842989 + 0.537931i \(0.819206\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) 6.00000 10.3923i 0.524222 0.907980i −0.475380 0.879781i \(-0.657689\pi\)
0.999602 0.0281993i \(-0.00897729\pi\)
\(132\) 0 0
\(133\) 3.00000 + 5.19615i 0.260133 + 0.450564i
\(134\) 11.0000 0.950255
\(135\) 0 0
\(136\) −2.00000 −0.171499
\(137\) 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i \(0.00465636\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(138\) 0 0
\(139\) −8.00000 + 13.8564i −0.678551 + 1.17529i 0.296866 + 0.954919i \(0.404058\pi\)
−0.975417 + 0.220366i \(0.929275\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 3.00000 + 5.19615i 0.251754 + 0.436051i
\(143\) −12.0000 −1.00349
\(144\) 0 0
\(145\) 0 0
\(146\) −2.00000 3.46410i −0.165521 0.286691i
\(147\) 0 0
\(148\) −1.00000 + 1.73205i −0.0821995 + 0.142374i
\(149\) −0.500000 + 0.866025i −0.0409616 + 0.0709476i −0.885779 0.464107i \(-0.846375\pi\)
0.844818 + 0.535054i \(0.179709\pi\)
\(150\) 0 0
\(151\) −5.00000 8.66025i −0.406894 0.704761i 0.587646 0.809118i \(-0.300055\pi\)
−0.994540 + 0.104357i \(0.966722\pi\)
\(152\) −6.00000 −0.486664
\(153\) 0 0
\(154\) 2.00000 0.161165
\(155\) 0 0
\(156\) 0 0
\(157\) −2.00000 + 3.46410i −0.159617 + 0.276465i −0.934731 0.355357i \(-0.884359\pi\)
0.775113 + 0.631822i \(0.217693\pi\)
\(158\) −6.00000 + 10.3923i −0.477334 + 0.826767i
\(159\) 0 0
\(160\) 0 0
\(161\) 1.00000 0.0788110
\(162\) 0 0
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) −5.50000 9.52628i −0.429478 0.743877i
\(165\) 0 0
\(166\) 5.50000 9.52628i 0.426883 0.739383i
\(167\) −1.50000 + 2.59808i −0.116073 + 0.201045i −0.918208 0.396098i \(-0.870364\pi\)
0.802135 + 0.597143i \(0.203697\pi\)
\(168\) 0 0
\(169\) −11.5000 19.9186i −0.884615 1.53220i
\(170\) 0 0
\(171\) 0 0
\(172\) −4.00000 −0.304997
\(173\) −2.00000 3.46410i −0.152057 0.263371i 0.779926 0.625871i \(-0.215256\pi\)
−0.931984 + 0.362500i \(0.881923\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.00000 + 1.73205i −0.0753778 + 0.130558i
\(177\) 0 0
\(178\) −0.500000 0.866025i −0.0374766 0.0649113i
\(179\) −2.00000 −0.149487 −0.0747435 0.997203i \(-0.523814\pi\)
−0.0747435 + 0.997203i \(0.523814\pi\)
\(180\) 0 0
\(181\) −13.0000 −0.966282 −0.483141 0.875542i \(-0.660504\pi\)
−0.483141 + 0.875542i \(0.660504\pi\)
\(182\) 3.00000 + 5.19615i 0.222375 + 0.385164i
\(183\) 0 0
\(184\) −0.500000 + 0.866025i −0.0368605 + 0.0638442i
\(185\) 0 0
\(186\) 0 0
\(187\) −2.00000 3.46410i −0.146254 0.253320i
\(188\) 7.00000 0.510527
\(189\) 0 0
\(190\) 0 0
\(191\) 3.00000 + 5.19615i 0.217072 + 0.375980i 0.953912 0.300088i \(-0.0970159\pi\)
−0.736839 + 0.676068i \(0.763683\pi\)
\(192\) 0 0
\(193\) 5.00000 8.66025i 0.359908 0.623379i −0.628037 0.778183i \(-0.716141\pi\)
0.987945 + 0.154805i \(0.0494748\pi\)
\(194\) −4.00000 + 6.92820i −0.287183 + 0.497416i
\(195\) 0 0
\(196\) 3.00000 + 5.19615i 0.214286 + 0.371154i
\(197\) −8.00000 −0.569976 −0.284988 0.958531i \(-0.591990\pi\)
−0.284988 + 0.958531i \(0.591990\pi\)
\(198\) 0 0
\(199\) −18.0000 −1.27599 −0.637993 0.770042i \(-0.720235\pi\)
−0.637993 + 0.770042i \(0.720235\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −1.00000 + 1.73205i −0.0703598 + 0.121867i
\(203\) −4.50000 + 7.79423i −0.315838 + 0.547048i
\(204\) 0 0
\(205\) 0 0
\(206\) 8.00000 0.557386
\(207\) 0 0
\(208\) −6.00000 −0.416025
\(209\) −6.00000 10.3923i −0.415029 0.718851i
\(210\) 0 0
\(211\) −9.00000 + 15.5885i −0.619586 + 1.07315i 0.369976 + 0.929041i \(0.379366\pi\)
−0.989561 + 0.144112i \(0.953967\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −1.50000 2.59808i −0.102538 0.177601i
\(215\) 0 0
\(216\) 0 0
\(217\) 2.00000 0.135769
\(218\) 3.50000 + 6.06218i 0.237050 + 0.410582i
\(219\) 0 0
\(220\) 0 0
\(221\) 6.00000 10.3923i 0.403604 0.699062i
\(222\) 0 0
\(223\) −11.5000 19.9186i −0.770097 1.33385i −0.937509 0.347960i \(-0.886874\pi\)
0.167412 0.985887i \(-0.446459\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) 12.0000 0.798228
\(227\) −4.00000 6.92820i −0.265489 0.459841i 0.702202 0.711977i \(-0.252200\pi\)
−0.967692 + 0.252136i \(0.918867\pi\)
\(228\) 0 0
\(229\) 3.50000 6.06218i 0.231287 0.400600i −0.726900 0.686743i \(-0.759040\pi\)
0.958187 + 0.286143i \(0.0923732\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −4.50000 7.79423i −0.295439 0.511716i
\(233\) 10.0000 0.655122 0.327561 0.944830i \(-0.393773\pi\)
0.327561 + 0.944830i \(0.393773\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −2.00000 3.46410i −0.130189 0.225494i
\(237\) 0 0
\(238\) −1.00000 + 1.73205i −0.0648204 + 0.112272i
\(239\) 14.0000 24.2487i 0.905585 1.56852i 0.0854543 0.996342i \(-0.472766\pi\)
0.820130 0.572177i \(-0.193901\pi\)
\(240\) 0 0
\(241\) −0.500000 0.866025i −0.0322078 0.0557856i 0.849472 0.527633i \(-0.176921\pi\)
−0.881680 + 0.471848i \(0.843587\pi\)
\(242\) 7.00000 0.449977
\(243\) 0 0
\(244\) −7.00000 −0.448129
\(245\) 0 0
\(246\) 0 0
\(247\) 18.0000 31.1769i 1.14531 1.98374i
\(248\) −1.00000 + 1.73205i −0.0635001 + 0.109985i
\(249\) 0 0
\(250\) 0 0
\(251\) −18.0000 −1.13615 −0.568075 0.822977i \(-0.692312\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(252\) 0 0
\(253\) −2.00000 −0.125739
\(254\) −9.50000 16.4545i −0.596083 1.03245i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 6.00000 10.3923i 0.374270 0.648254i −0.615948 0.787787i \(-0.711227\pi\)
0.990217 + 0.139533i \(0.0445601\pi\)
\(258\) 0 0
\(259\) 1.00000 + 1.73205i 0.0621370 + 0.107624i
\(260\) 0 0
\(261\) 0 0
\(262\) 12.0000 0.741362
\(263\) 8.00000 + 13.8564i 0.493301 + 0.854423i 0.999970 0.00771799i \(-0.00245674\pi\)
−0.506669 + 0.862141i \(0.669123\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −3.00000 + 5.19615i −0.183942 + 0.318597i
\(267\) 0 0
\(268\) 5.50000 + 9.52628i 0.335966 + 0.581910i
\(269\) −3.00000 −0.182913 −0.0914566 0.995809i \(-0.529152\pi\)
−0.0914566 + 0.995809i \(0.529152\pi\)
\(270\) 0 0
\(271\) −14.0000 −0.850439 −0.425220 0.905090i \(-0.639803\pi\)
−0.425220 + 0.905090i \(0.639803\pi\)
\(272\) −1.00000 1.73205i −0.0606339 0.105021i
\(273\) 0 0
\(274\) −6.00000 + 10.3923i −0.362473 + 0.627822i
\(275\) 0 0
\(276\) 0 0
\(277\) 11.0000 + 19.0526i 0.660926 + 1.14476i 0.980373 + 0.197153i \(0.0631696\pi\)
−0.319447 + 0.947604i \(0.603497\pi\)
\(278\) −16.0000 −0.959616
\(279\) 0 0
\(280\) 0 0
\(281\) −1.50000 2.59808i −0.0894825 0.154988i 0.817810 0.575488i \(-0.195188\pi\)
−0.907293 + 0.420500i \(0.861855\pi\)
\(282\) 0 0
\(283\) −0.500000 + 0.866025i −0.0297219 + 0.0514799i −0.880504 0.474039i \(-0.842796\pi\)
0.850782 + 0.525519i \(0.176129\pi\)
\(284\) −3.00000 + 5.19615i −0.178017 + 0.308335i
\(285\) 0 0
\(286\) −6.00000 10.3923i −0.354787 0.614510i
\(287\) −11.0000 −0.649309
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 0 0
\(292\) 2.00000 3.46410i 0.117041 0.202721i
\(293\) −9.00000 + 15.5885i −0.525786 + 0.910687i 0.473763 + 0.880652i \(0.342895\pi\)
−0.999549 + 0.0300351i \(0.990438\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −2.00000 −0.116248
\(297\) 0 0
\(298\) −1.00000 −0.0579284
\(299\) −3.00000 5.19615i −0.173494 0.300501i
\(300\) 0 0
\(301\) −2.00000 + 3.46410i −0.115278 + 0.199667i
\(302\) 5.00000 8.66025i 0.287718 0.498342i
\(303\) 0 0
\(304\) −3.00000 5.19615i −0.172062 0.298020i
\(305\) 0 0
\(306\) 0 0
\(307\) −9.00000 −0.513657 −0.256829 0.966457i \(-0.582678\pi\)
−0.256829 + 0.966457i \(0.582678\pi\)
\(308\) 1.00000 + 1.73205i 0.0569803 + 0.0986928i
\(309\) 0 0
\(310\) 0 0
\(311\) 3.00000 5.19615i 0.170114 0.294647i −0.768345 0.640036i \(-0.778920\pi\)
0.938460 + 0.345389i \(0.112253\pi\)
\(312\) 0 0
\(313\) 11.0000 + 19.0526i 0.621757 + 1.07691i 0.989158 + 0.146852i \(0.0469141\pi\)
−0.367402 + 0.930062i \(0.619753\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) −12.0000 −0.675053
\(317\) −1.00000 1.73205i −0.0561656 0.0972817i 0.836576 0.547852i \(-0.184554\pi\)
−0.892741 + 0.450570i \(0.851221\pi\)
\(318\) 0 0
\(319\) 9.00000 15.5885i 0.503903 0.872786i
\(320\) 0 0
\(321\) 0 0
\(322\) 0.500000 + 0.866025i 0.0278639 + 0.0482617i
\(323\) 12.0000 0.667698
\(324\) 0 0
\(325\) 0 0
\(326\) 2.00000 + 3.46410i 0.110770 + 0.191859i
\(327\) 0 0
\(328\) 5.50000 9.52628i 0.303687 0.526001i
\(329\) 3.50000 6.06218i 0.192961 0.334219i
\(330\) 0 0
\(331\) 4.00000 + 6.92820i 0.219860 + 0.380808i 0.954765 0.297361i \(-0.0961066\pi\)
−0.734905 + 0.678170i \(0.762773\pi\)
\(332\) 11.0000 0.603703
\(333\) 0 0
\(334\) −3.00000 −0.164153
\(335\) 0 0
\(336\) 0 0
\(337\) −4.00000 + 6.92820i −0.217894 + 0.377403i −0.954164 0.299285i \(-0.903252\pi\)
0.736270 + 0.676688i \(0.236585\pi\)
\(338\) 11.5000 19.9186i 0.625518 1.08343i
\(339\) 0 0
\(340\) 0 0
\(341\) −4.00000 −0.216612
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) −2.00000 3.46410i −0.107833 0.186772i
\(345\) 0 0
\(346\) 2.00000 3.46410i 0.107521 0.186231i
\(347\) −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i \(-0.937721\pi\)
0.658824 + 0.752297i \(0.271054\pi\)
\(348\) 0 0
\(349\) 5.50000 + 9.52628i 0.294408 + 0.509930i 0.974847 0.222875i \(-0.0715441\pi\)
−0.680439 + 0.732805i \(0.738211\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −2.00000 −0.106600
\(353\) −8.00000 13.8564i −0.425797 0.737502i 0.570697 0.821160i \(-0.306673\pi\)
−0.996495 + 0.0836583i \(0.973340\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0.500000 0.866025i 0.0264999 0.0458993i
\(357\) 0 0
\(358\) −1.00000 1.73205i −0.0528516 0.0915417i
\(359\) −30.0000 −1.58334 −0.791670 0.610949i \(-0.790788\pi\)
−0.791670 + 0.610949i \(0.790788\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) −6.50000 11.2583i −0.341632 0.591725i
\(363\) 0 0
\(364\) −3.00000 + 5.19615i −0.157243 + 0.272352i
\(365\) 0 0
\(366\) 0 0
\(367\) 8.00000 + 13.8564i 0.417597 + 0.723299i 0.995697 0.0926670i \(-0.0295392\pi\)
−0.578101 + 0.815966i \(0.696206\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −6.00000 + 10.3923i −0.310668 + 0.538093i −0.978507 0.206213i \(-0.933886\pi\)
0.667839 + 0.744306i \(0.267219\pi\)
\(374\) 2.00000 3.46410i 0.103418 0.179124i
\(375\) 0 0
\(376\) 3.50000 + 6.06218i 0.180499 + 0.312633i
\(377\) 54.0000 2.78114
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −3.00000 + 5.19615i −0.153493 + 0.265858i
\(383\) 16.0000 27.7128i 0.817562 1.41606i −0.0899119 0.995950i \(-0.528659\pi\)
0.907474 0.420109i \(-0.138008\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 10.0000 0.508987
\(387\) 0 0
\(388\) −8.00000 −0.406138
\(389\) 9.50000 + 16.4545i 0.481669 + 0.834275i 0.999779 0.0210389i \(-0.00669738\pi\)
−0.518110 + 0.855314i \(0.673364\pi\)
\(390\) 0 0
\(391\) 1.00000 1.73205i 0.0505722 0.0875936i
\(392\) −3.00000 + 5.19615i −0.151523 + 0.262445i
\(393\) 0 0
\(394\) −4.00000 6.92820i −0.201517 0.349038i
\(395\) 0 0
\(396\) 0 0
\(397\) −4.00000 −0.200754 −0.100377 0.994949i \(-0.532005\pi\)
−0.100377 + 0.994949i \(0.532005\pi\)
\(398\) −9.00000 15.5885i −0.451129 0.781379i
\(399\) 0 0
\(400\) 0 0
\(401\) −5.00000 + 8.66025i −0.249688 + 0.432472i −0.963439 0.267927i \(-0.913661\pi\)
0.713751 + 0.700399i \(0.246995\pi\)
\(402\) 0 0
\(403\) −6.00000 10.3923i −0.298881 0.517678i
\(404\) −2.00000 −0.0995037
\(405\) 0 0
\(406\) −9.00000 −0.446663
\(407\) −2.00000 3.46410i −0.0991363 0.171709i
\(408\) 0 0
\(409\) −19.0000 + 32.9090i −0.939490 + 1.62724i −0.173064 + 0.984911i \(0.555367\pi\)
−0.766426 + 0.642333i \(0.777967\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 4.00000 + 6.92820i 0.197066 + 0.341328i
\(413\) −4.00000 −0.196827
\(414\) 0 0
\(415\) 0 0
\(416\) −3.00000 5.19615i −0.147087 0.254762i
\(417\) 0 0
\(418\) 6.00000 10.3923i 0.293470 0.508304i
\(419\) 17.0000 29.4449i 0.830504 1.43848i −0.0671345 0.997744i \(-0.521386\pi\)
0.897639 0.440732i \(-0.145281\pi\)
\(420\) 0 0
\(421\) −11.0000 19.0526i −0.536107 0.928565i −0.999109 0.0422075i \(-0.986561\pi\)
0.463002 0.886357i \(-0.346772\pi\)
\(422\) −18.0000 −0.876226
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −3.50000 + 6.06218i −0.169377 + 0.293369i
\(428\) 1.50000 2.59808i 0.0725052 0.125583i
\(429\) 0 0
\(430\) 0 0
\(431\) −16.0000 −0.770693 −0.385346 0.922772i \(-0.625918\pi\)
−0.385346 + 0.922772i \(0.625918\pi\)
\(432\) 0 0
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 1.00000 + 1.73205i 0.0480015 + 0.0831411i
\(435\) 0 0
\(436\) −3.50000 + 6.06218i −0.167620 + 0.290326i
\(437\) 3.00000 5.19615i 0.143509 0.248566i
\(438\) 0 0
\(439\) −12.0000 20.7846i −0.572729 0.991995i −0.996284 0.0861252i \(-0.972552\pi\)
0.423556 0.905870i \(-0.360782\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 12.0000 0.570782
\(443\) −4.50000 7.79423i −0.213801 0.370315i 0.739100 0.673596i \(-0.235251\pi\)
−0.952901 + 0.303281i \(0.901918\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 11.5000 19.9186i 0.544541 0.943172i
\(447\) 0 0
\(448\) 0.500000 + 0.866025i 0.0236228 + 0.0409159i
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 0 0
\(451\) 22.0000 1.03594
\(452\) 6.00000 + 10.3923i 0.282216 + 0.488813i
\(453\) 0 0
\(454\) 4.00000 6.92820i 0.187729 0.325157i
\(455\) 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 \(0.758188\pi\)
\(458\) 7.00000 0.327089
\(459\) 0 0
\(460\) 0 0
\(461\) −10.5000 18.1865i −0.489034 0.847031i 0.510887 0.859648i \(-0.329317\pi\)
−0.999920 + 0.0126168i \(0.995984\pi\)
\(462\) 0 0
\(463\) −18.0000 + 31.1769i −0.836531 + 1.44891i 0.0562469 + 0.998417i \(0.482087\pi\)
−0.892778 + 0.450497i \(0.851247\pi\)
\(464\) 4.50000 7.79423i 0.208907 0.361838i
\(465\) 0 0
\(466\) 5.00000 + 8.66025i 0.231621 + 0.401179i
\(467\) −36.0000 −1.66588 −0.832941 0.553362i \(-0.813345\pi\)
−0.832941 + 0.553362i \(0.813345\pi\)
\(468\) 0 0
\(469\) 11.0000 0.507933
\(470\) 0 0
\(471\) 0 0
\(472\) 2.00000 3.46410i 0.0920575 0.159448i
\(473\) 4.00000 6.92820i 0.183920 0.318559i
\(474\) 0 0
\(475\) 0 0
\(476\) −2.00000 −0.0916698
\(477\) 0 0
\(478\) 28.0000 1.28069
\(479\) 14.0000 + 24.2487i 0.639676 + 1.10795i 0.985504 + 0.169654i \(0.0542649\pi\)
−0.345827 + 0.938298i \(0.612402\pi\)
\(480\) 0 0
\(481\) 6.00000 10.3923i 0.273576 0.473848i
\(482\) 0.500000 0.866025i 0.0227744 0.0394464i
\(483\) 0 0
\(484\) 3.50000 + 6.06218i 0.159091 + 0.275554i
\(485\) 0 0
\(486\) 0 0
\(487\) −12.0000 −0.543772 −0.271886 0.962329i \(-0.587647\pi\)
−0.271886 + 0.962329i \(0.587647\pi\)
\(488\) −3.50000 6.06218i −0.158438 0.274422i
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(492\) 0 0
\(493\) 9.00000 + 15.5885i 0.405340 + 0.702069i
\(494\) 36.0000 1.61972
\(495\) 0 0
\(496\) −2.00000 −0.0898027
\(497\) 3.00000 + 5.19615i 0.134568 + 0.233079i
\(498\) 0 0
\(499\) 12.0000 20.7846i 0.537194 0.930447i −0.461860 0.886953i \(-0.652818\pi\)
0.999054 0.0434940i \(-0.0138489\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −9.00000 15.5885i −0.401690 0.695747i
\(503\) −27.0000 −1.20387 −0.601935 0.798545i \(-0.705603\pi\)
−0.601935 + 0.798545i \(0.705603\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −1.00000 1.73205i −0.0444554 0.0769991i
\(507\) 0 0
\(508\) 9.50000 16.4545i 0.421494 0.730050i
\(509\) −7.50000 + 12.9904i −0.332432 + 0.575789i −0.982988 0.183669i \(-0.941202\pi\)
0.650556 + 0.759458i \(0.274536\pi\)
\(510\) 0 0
\(511\) −2.00000 3.46410i −0.0884748 0.153243i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 12.0000 0.529297
\(515\) 0 0
\(516\) 0 0
\(517\) −7.00000 + 12.1244i −0.307860 + 0.533229i
\(518\) −1.00000 + 1.73205i −0.0439375 + 0.0761019i
\(519\) 0 0
\(520\) 0 0
\(521\) 37.0000 1.62100 0.810500 0.585739i \(-0.199196\pi\)
0.810500 + 0.585739i \(0.199196\pi\)
\(522\) 0 0
\(523\) −29.0000 −1.26808 −0.634041 0.773300i \(-0.718605\pi\)
−0.634041 + 0.773300i \(0.718605\pi\)
\(524\) 6.00000 + 10.3923i 0.262111 + 0.453990i
\(525\) 0 0
\(526\) −8.00000 + 13.8564i −0.348817 + 0.604168i
\(527\) 2.00000 3.46410i 0.0871214 0.150899i
\(528\) 0 0
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) 0 0
\(531\) 0 0
\(532\) −6.00000 −0.260133
\(533\) 33.0000 + 57.1577i 1.42939 + 2.47577i
\(534\) 0 0
\(535\) 0 0
\(536\) −5.50000 + 9.52628i −0.237564 + 0.411473i
\(537\) 0 0
\(538\) −1.50000 2.59808i −0.0646696 0.112011i
\(539\) −12.0000 −0.516877
\(540\) 0 0
\(541\) −17.0000 −0.730887 −0.365444 0.930834i \(-0.619083\pi\)
−0.365444 + 0.930834i \(0.619083\pi\)
\(542\) −7.00000 12.1244i −0.300676 0.520786i
\(543\) 0 0
\(544\) 1.00000 1.73205i 0.0428746 0.0742611i
\(545\) 0 0
\(546\) 0 0
\(547\) −17.5000 30.3109i −0.748246 1.29600i −0.948663 0.316289i \(-0.897563\pi\)
0.200417 0.979711i \(-0.435770\pi\)
\(548\) −12.0000 −0.512615
\(549\) 0 0
\(550\) 0 0
\(551\) 27.0000 + 46.7654i 1.15024 + 1.99227i
\(552\) 0 0
\(553\) −6.00000 + 10.3923i −0.255146 + 0.441926i
\(554\) −11.0000 + 19.0526i −0.467345 + 0.809466i
\(555\) 0 0
\(556\) −8.00000 13.8564i −0.339276 0.587643i
\(557\) 24.0000 1.01691 0.508456 0.861088i \(-0.330216\pi\)
0.508456 + 0.861088i \(0.330216\pi\)
\(558\) 0 0
\(559\) 24.0000 1.01509
\(560\) 0 0
\(561\) 0 0
\(562\) 1.50000 2.59808i 0.0632737 0.109593i
\(563\) −18.5000 + 32.0429i −0.779682 + 1.35045i 0.152443 + 0.988312i \(0.451286\pi\)
−0.932125 + 0.362137i \(0.882047\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −1.00000 −0.0420331
\(567\) 0 0
\(568\) −6.00000 −0.251754
\(569\) −1.00000 1.73205i −0.0419222 0.0726113i 0.844303 0.535866i \(-0.180015\pi\)
−0.886225 + 0.463255i \(0.846681\pi\)
\(570\) 0 0
\(571\) 10.0000 17.3205i 0.418487 0.724841i −0.577301 0.816532i \(-0.695894\pi\)
0.995788 + 0.0916910i \(0.0292272\pi\)
\(572\) 6.00000 10.3923i 0.250873 0.434524i
\(573\) 0 0
\(574\) −5.50000 9.52628i −0.229566 0.397619i
\(575\) 0 0
\(576\) 0 0
\(577\) 32.0000 1.33218 0.666089 0.745873i \(-0.267967\pi\)
0.666089 + 0.745873i \(0.267967\pi\)
\(578\) −6.50000 11.2583i −0.270364 0.468285i
\(579\) 0 0
\(580\) 0 0
\(581\) 5.50000 9.52628i 0.228178 0.395217i
\(582\) 0 0
\(583\) 0 0
\(584\) 4.00000 0.165521
\(585\) 0 0
\(586\) −18.0000 −0.743573
\(587\) 1.50000 + 2.59808i 0.0619116 + 0.107234i 0.895320 0.445424i \(-0.146947\pi\)
−0.833408 + 0.552658i \(0.813614\pi\)
\(588\) 0 0
\(589\) 6.00000 10.3923i 0.247226 0.428207i
\(590\) 0 0
\(591\) 0 0
\(592\) −1.00000 1.73205i −0.0410997 0.0711868i
\(593\) 30.0000 1.23195 0.615976 0.787765i \(-0.288762\pi\)
0.615976 + 0.787765i \(0.288762\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.500000 0.866025i −0.0204808 0.0354738i
\(597\) 0 0
\(598\) 3.00000 5.19615i 0.122679 0.212486i
\(599\) −6.00000 + 10.3923i −0.245153 + 0.424618i −0.962175 0.272433i \(-0.912172\pi\)
0.717021 + 0.697051i \(0.245505\pi\)
\(600\) 0 0
\(601\) 11.0000 + 19.0526i 0.448699 + 0.777170i 0.998302 0.0582563i \(-0.0185541\pi\)
−0.549602 + 0.835426i \(0.685221\pi\)
\(602\) −4.00000 −0.163028
\(603\) 0 0
\(604\) 10.0000 0.406894
\(605\) 0 0
\(606\) 0 0
\(607\) −0.500000 + 0.866025i −0.0202944 + 0.0351509i −0.875994 0.482322i \(-0.839794\pi\)
0.855700 + 0.517472i \(0.173127\pi\)
\(608\) 3.00000 5.19615i 0.121666 0.210732i
\(609\) 0 0
\(610\) 0 0
\(611\) −42.0000 −1.69914
\(612\) 0 0
\(613\) −34.0000 −1.37325 −0.686624 0.727013i \(-0.740908\pi\)
−0.686624 + 0.727013i \(0.740908\pi\)
\(614\) −4.50000 7.79423i −0.181605 0.314549i
\(615\) 0 0
\(616\) −1.00000 + 1.73205i −0.0402911 + 0.0697863i
\(617\) −16.0000 + 27.7128i −0.644136 + 1.11568i 0.340365 + 0.940294i \(0.389449\pi\)
−0.984500 + 0.175382i \(0.943884\pi\)
\(618\) 0 0
\(619\) 5.00000 + 8.66025i 0.200967 + 0.348085i 0.948840 0.315757i \(-0.102258\pi\)
−0.747873 + 0.663842i \(0.768925\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 6.00000 0.240578
\(623\) −0.500000 0.866025i −0.0200321 0.0346966i
\(624\) 0 0
\(625\) 0 0
\(626\) −11.0000 + 19.0526i −0.439648 + 0.761493i
\(627\) 0 0
\(628\) −2.00000 3.46410i −0.0798087 0.138233i
\(629\) 4.00000 0.159490
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) −6.00000 10.3923i −0.238667 0.413384i
\(633\) 0 0
\(634\) 1.00000 1.73205i 0.0397151 0.0687885i
\(635\) 0 0
\(636\) 0 0
\(637\) −18.0000 31.1769i −0.713186 1.23527i
\(638\) 18.0000 0.712627
\(639\) 0 0
\(640\) 0 0
\(641\) 6.50000 + 11.2583i 0.256735 + 0.444677i 0.965365 0.260902i \(-0.0840201\pi\)
−0.708631 + 0.705580i \(0.750687\pi\)
\(642\) 0 0
\(643\) 16.5000 28.5788i 0.650696 1.12704i −0.332258 0.943189i \(-0.607810\pi\)
0.982954 0.183851i \(-0.0588563\pi\)
\(644\) −0.500000 + 0.866025i −0.0197028 + 0.0341262i
\(645\) 0 0
\(646\) 6.00000 + 10.3923i 0.236067 + 0.408880i
\(647\) −33.0000 −1.29736 −0.648682 0.761060i \(-0.724679\pi\)
−0.648682 + 0.761060i \(0.724679\pi\)
\(648\) 0 0
\(649\) 8.00000 0.314027
\(650\) 0 0
\(651\) 0 0
\(652\) −2.00000 + 3.46410i −0.0783260 + 0.135665i
\(653\) −13.0000 + 22.5167i −0.508729 + 0.881145i 0.491220 + 0.871036i \(0.336551\pi\)
−0.999949 + 0.0101092i \(0.996782\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 11.0000 0.429478
\(657\) 0 0
\(658\) 7.00000 0.272888
\(659\) 10.0000 + 17.3205i 0.389545 + 0.674711i 0.992388 0.123148i \(-0.0392990\pi\)
−0.602844 + 0.797859i \(0.705966\pi\)
\(660\) 0 0
\(661\) 5.00000 8.66025i 0.194477 0.336845i −0.752252 0.658876i \(-0.771032\pi\)
0.946729 + 0.322031i \(0.104366\pi\)
\(662\) −4.00000 + 6.92820i −0.155464 + 0.269272i
\(663\) 0 0
\(664\) 5.50000 + 9.52628i 0.213441 + 0.369691i
\(665\) 0 0
\(666\) 0 0
\(667\) 9.00000 0.348481
\(668\) −1.50000 2.59808i −0.0580367 0.100523i
\(669\) 0 0
\(670\) 0 0
\(671\) 7.00000 12.1244i 0.270232 0.468056i
\(672\) 0 0
\(673\) −3.00000 5.19615i −0.115642 0.200297i 0.802395 0.596794i \(-0.203559\pi\)
−0.918036 + 0.396497i \(0.870226\pi\)
\(674\) −8.00000 −0.308148
\(675\) 0 0
\(676\) 23.0000 0.884615
\(677\) 11.0000 + 19.0526i 0.422764 + 0.732249i 0.996209 0.0869952i \(-0.0277265\pi\)
−0.573444 + 0.819244i \(0.694393\pi\)
\(678\) 0 0
\(679\) −4.00000 + 6.92820i −0.153506 + 0.265880i
\(680\) 0 0
\(681\) 0 0
\(682\) −2.00000 3.46410i −0.0765840 0.132647i
\(683\) −4.00000 −0.153056 −0.0765279 0.997067i \(-0.524383\pi\)
−0.0765279 + 0.997067i \(0.524383\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 6.50000 + 11.2583i 0.248171 + 0.429845i
\(687\) 0 0
\(688\) 2.00000 3.46410i 0.0762493 0.132068i
\(689\) 0 0
\(690\) 0 0
\(691\) 22.0000 + 38.1051i 0.836919 + 1.44959i 0.892458 + 0.451130i \(0.148979\pi\)
−0.0555386 + 0.998457i \(0.517688\pi\)
\(692\) 4.00000 0.152057
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) 0 0
\(696\) 0 0
\(697\) −11.0000 + 19.0526i −0.416655 + 0.721667i
\(698\) −5.50000 + 9.52628i −0.208178 + 0.360575i
\(699\) 0 0
\(700\) 0 0
\(701\) −13.0000 −0.491003 −0.245502 0.969396i \(-0.578953\pi\)
−0.245502 + 0.969396i \(0.578953\pi\)
\(702\) 0 0
\(703\) 12.0000 0.452589
\(704\) −1.00000 1.73205i −0.0376889 0.0652791i
\(705\) 0 0
\(706\) 8.00000 13.8564i 0.301084 0.521493i
\(707\) −1.00000 + 1.73205i −0.0376089 + 0.0651405i
\(708\) 0 0
\(709\) 13.5000 + 23.3827i 0.507003 + 0.878155i 0.999967 + 0.00810550i \(0.00258009\pi\)
−0.492964 + 0.870050i \(0.664087\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 1.00000 0.0374766
\(713\) −1.00000 1.73205i −0.0374503 0.0648658i
\(714\) 0 0
\(715\) 0 0
\(716\) 1.00000 1.73205i 0.0373718 0.0647298i
\(717\) 0 0
\(718\) −15.0000 25.9808i −0.559795 0.969593i
\(719\) 44.0000 1.64092 0.820462 0.571702i \(-0.193717\pi\)
0.820462 + 0.571702i \(0.193717\pi\)
\(720\) 0 0
\(721\) 8.00000 0.297936
\(722\) 8.50000 + 14.7224i 0.316337 + 0.547912i
\(723\) 0 0
\(724\) 6.50000 11.2583i 0.241571 0.418413i
\(725\) 0 0
\(726\) 0 0
\(727\) −10.5000 18.1865i −0.389423 0.674501i 0.602949 0.797780i \(-0.293992\pi\)
−0.992372 + 0.123279i \(0.960659\pi\)
\(728\) −6.00000 −0.222375
\(729\) 0 0
\(730\) 0 0
\(731\) 4.00000 + 6.92820i 0.147945 + 0.256249i
\(732\) 0 0
\(733\) −2.00000 + 3.46410i −0.0738717 + 0.127950i −0.900595 0.434659i \(-0.856869\pi\)
0.826723 + 0.562609i \(0.190202\pi\)
\(734\) −8.00000 + 13.8564i −0.295285 + 0.511449i
\(735\) 0 0
\(736\) −0.500000 0.866025i −0.0184302 0.0319221i
\(737\) −22.0000 −0.810380
\(738\) 0 0
\(739\) 40.0000 1.47142 0.735712 0.677295i \(-0.236848\pi\)
0.735712 + 0.677295i \(0.236848\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −7.50000 + 12.9904i −0.275148 + 0.476571i −0.970173 0.242415i \(-0.922060\pi\)
0.695024 + 0.718986i \(0.255394\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −12.0000 −0.439351
\(747\) 0 0
\(748\) 4.00000 0.146254
\(749\) −1.50000 2.59808i −0.0548088 0.0949316i
\(750\) 0 0
\(751\) −13.0000 + 22.5167i −0.474377 + 0.821645i −0.999570 0.0293387i \(-0.990660\pi\)
0.525193 + 0.850983i \(0.323993\pi\)
\(752\) −3.50000 + 6.06218i −0.127632 + 0.221065i
\(753\) 0 0
\(754\) 27.0000 + 46.7654i 0.983282 + 1.70309i
\(755\) 0 0
\(756\) 0 0
\(757\) −10.0000 −0.363456 −0.181728 0.983349i \(-0.558169\pi\)
−0.181728 + 0.983349i \(0.558169\pi\)
\(758\) −8.00000 13.8564i −0.290573 0.503287i
\(759\) 0 0
\(760\) 0 0
\(761\) −4.50000 + 7.79423i −0.163125 + 0.282541i −0.935988 0.352032i \(-0.885491\pi\)
0.772863 + 0.634573i \(0.218824\pi\)
\(762\) 0 0
\(763\) 3.50000 + 6.06218i 0.126709 + 0.219466i
\(764\) −6.00000 −0.217072
\(765\) 0 0
\(766\) 32.0000 1.15621
\(767\) 12.0000 + 20.7846i 0.433295 + 0.750489i
\(768\) 0 0
\(769\) 7.50000 12.9904i 0.270457 0.468445i −0.698522 0.715589i \(-0.746159\pi\)
0.968979 + 0.247143i \(0.0794919\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 5.00000 + 8.66025i 0.179954 + 0.311689i
\(773\) −12.0000 −0.431610 −0.215805 0.976436i \(-0.569238\pi\)
−0.215805 + 0.976436i \(0.569238\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −4.00000 6.92820i −0.143592 0.248708i
\(777\) 0 0
\(778\) −9.50000 + 16.4545i −0.340592 + 0.589922i
\(779\) −33.0000 + 57.1577i −1.18235 + 2.04789i
\(780\) 0 0
\(781\) −6.00000 10.3923i −0.214697 0.371866i
\(782\) 2.00000 0.0715199
\(783\) 0 0
\(784\) −6.00000 −0.214286
\(785\) 0 0
\(786\) 0 0
\(787\) −22.0000 + 38.1051i −0.784215 + 1.35830i 0.145251 + 0.989395i \(0.453601\pi\)
−0.929467 + 0.368906i \(0.879732\pi\)
\(788\) 4.00000 6.92820i 0.142494 0.246807i
\(789\) 0 0