Properties

Label 225.3.g.e.82.2
Level $225$
Weight $3$
Character 225.82
Analytic conductor $6.131$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,3,Mod(82,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.82");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 225.g (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.13080594811\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 25)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 82.2
Root \(1.22474 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 225.82
Dual form 225.3.g.e.118.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.22474 + 1.22474i) q^{2} -1.00000i q^{4} +(4.89898 + 4.89898i) q^{7} +(6.12372 - 6.12372i) q^{8} +O(q^{10})\) \(q+(1.22474 + 1.22474i) q^{2} -1.00000i q^{4} +(4.89898 + 4.89898i) q^{7} +(6.12372 - 6.12372i) q^{8} +3.00000 q^{11} +(7.34847 - 7.34847i) q^{13} +12.0000i q^{14} +11.0000 q^{16} +(13.4722 + 13.4722i) q^{17} +5.00000i q^{19} +(3.67423 + 3.67423i) q^{22} +(17.1464 - 17.1464i) q^{23} +18.0000 q^{26} +(4.89898 - 4.89898i) q^{28} +30.0000i q^{29} -38.0000 q^{31} +(-11.0227 - 11.0227i) q^{32} +33.0000i q^{34} +(-19.5959 - 19.5959i) q^{37} +(-6.12372 + 6.12372i) q^{38} -57.0000 q^{41} +(-4.89898 + 4.89898i) q^{43} -3.00000i q^{44} +42.0000 q^{46} +(7.34847 + 7.34847i) q^{47} -1.00000i q^{49} +(-7.34847 - 7.34847i) q^{52} +(-31.8434 + 31.8434i) q^{53} +60.0000 q^{56} +(-36.7423 + 36.7423i) q^{58} -90.0000i q^{59} -28.0000 q^{61} +(-46.5403 - 46.5403i) q^{62} -71.0000i q^{64} +(47.7650 + 47.7650i) q^{67} +(13.4722 - 13.4722i) q^{68} -42.0000 q^{71} +(13.4722 - 13.4722i) q^{73} -48.0000i q^{74} +5.00000 q^{76} +(14.6969 + 14.6969i) q^{77} -80.0000i q^{79} +(-69.8105 - 69.8105i) q^{82} +(-111.452 + 111.452i) q^{83} -12.0000 q^{86} +(18.3712 - 18.3712i) q^{88} +15.0000i q^{89} +72.0000 q^{91} +(-17.1464 - 17.1464i) q^{92} +18.0000i q^{94} +(53.8888 + 53.8888i) q^{97} +(1.22474 - 1.22474i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 12 q^{11} + 44 q^{16} + 72 q^{26} - 152 q^{31} - 228 q^{41} + 168 q^{46} + 240 q^{56} - 112 q^{61} - 168 q^{71} + 20 q^{76} - 48 q^{86} + 288 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 + 1.22474i 0.612372 + 0.612372i 0.943564 0.331191i \(-0.107451\pi\)
−0.331191 + 0.943564i \(0.607451\pi\)
\(3\) 0 0
\(4\) 1.00000i 0.250000i
\(5\) 0 0
\(6\) 0 0
\(7\) 4.89898 + 4.89898i 0.699854 + 0.699854i 0.964379 0.264525i \(-0.0852151\pi\)
−0.264525 + 0.964379i \(0.585215\pi\)
\(8\) 6.12372 6.12372i 0.765466 0.765466i
\(9\) 0 0
\(10\) 0 0
\(11\) 3.00000 0.272727 0.136364 0.990659i \(-0.456458\pi\)
0.136364 + 0.990659i \(0.456458\pi\)
\(12\) 0 0
\(13\) 7.34847 7.34847i 0.565267 0.565267i −0.365532 0.930799i \(-0.619113\pi\)
0.930799 + 0.365532i \(0.119113\pi\)
\(14\) 12.0000i 0.857143i
\(15\) 0 0
\(16\) 11.0000 0.687500
\(17\) 13.4722 + 13.4722i 0.792482 + 0.792482i 0.981897 0.189415i \(-0.0606592\pi\)
−0.189415 + 0.981897i \(0.560659\pi\)
\(18\) 0 0
\(19\) 5.00000i 0.263158i 0.991306 + 0.131579i \(0.0420047\pi\)
−0.991306 + 0.131579i \(0.957995\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 3.67423 + 3.67423i 0.167011 + 0.167011i
\(23\) 17.1464 17.1464i 0.745497 0.745497i −0.228133 0.973630i \(-0.573262\pi\)
0.973630 + 0.228133i \(0.0732621\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 18.0000 0.692308
\(27\) 0 0
\(28\) 4.89898 4.89898i 0.174964 0.174964i
\(29\) 30.0000i 1.03448i 0.855840 + 0.517241i \(0.173041\pi\)
−0.855840 + 0.517241i \(0.826959\pi\)
\(30\) 0 0
\(31\) −38.0000 −1.22581 −0.612903 0.790158i \(-0.709998\pi\)
−0.612903 + 0.790158i \(0.709998\pi\)
\(32\) −11.0227 11.0227i −0.344459 0.344459i
\(33\) 0 0
\(34\) 33.0000i 0.970588i
\(35\) 0 0
\(36\) 0 0
\(37\) −19.5959 19.5959i −0.529619 0.529619i 0.390839 0.920459i \(-0.372185\pi\)
−0.920459 + 0.390839i \(0.872185\pi\)
\(38\) −6.12372 + 6.12372i −0.161151 + 0.161151i
\(39\) 0 0
\(40\) 0 0
\(41\) −57.0000 −1.39024 −0.695122 0.718892i \(-0.744650\pi\)
−0.695122 + 0.718892i \(0.744650\pi\)
\(42\) 0 0
\(43\) −4.89898 + 4.89898i −0.113930 + 0.113930i −0.761773 0.647844i \(-0.775671\pi\)
0.647844 + 0.761773i \(0.275671\pi\)
\(44\) 3.00000i 0.0681818i
\(45\) 0 0
\(46\) 42.0000 0.913043
\(47\) 7.34847 + 7.34847i 0.156350 + 0.156350i 0.780947 0.624597i \(-0.214737\pi\)
−0.624597 + 0.780947i \(0.714737\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.0204082i
\(50\) 0 0
\(51\) 0 0
\(52\) −7.34847 7.34847i −0.141317 0.141317i
\(53\) −31.8434 + 31.8434i −0.600818 + 0.600818i −0.940530 0.339711i \(-0.889671\pi\)
0.339711 + 0.940530i \(0.389671\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 60.0000 1.07143
\(57\) 0 0
\(58\) −36.7423 + 36.7423i −0.633489 + 0.633489i
\(59\) 90.0000i 1.52542i −0.646738 0.762712i \(-0.723867\pi\)
0.646738 0.762712i \(-0.276133\pi\)
\(60\) 0 0
\(61\) −28.0000 −0.459016 −0.229508 0.973307i \(-0.573712\pi\)
−0.229508 + 0.973307i \(0.573712\pi\)
\(62\) −46.5403 46.5403i −0.750650 0.750650i
\(63\) 0 0
\(64\) 71.0000i 1.10938i
\(65\) 0 0
\(66\) 0 0
\(67\) 47.7650 + 47.7650i 0.712911 + 0.712911i 0.967143 0.254232i \(-0.0818227\pi\)
−0.254232 + 0.967143i \(0.581823\pi\)
\(68\) 13.4722 13.4722i 0.198120 0.198120i
\(69\) 0 0
\(70\) 0 0
\(71\) −42.0000 −0.591549 −0.295775 0.955258i \(-0.595578\pi\)
−0.295775 + 0.955258i \(0.595578\pi\)
\(72\) 0 0
\(73\) 13.4722 13.4722i 0.184551 0.184551i −0.608785 0.793335i \(-0.708343\pi\)
0.793335 + 0.608785i \(0.208343\pi\)
\(74\) 48.0000i 0.648649i
\(75\) 0 0
\(76\) 5.00000 0.0657895
\(77\) 14.6969 + 14.6969i 0.190869 + 0.190869i
\(78\) 0 0
\(79\) 80.0000i 1.01266i −0.862340 0.506329i \(-0.831002\pi\)
0.862340 0.506329i \(-0.168998\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −69.8105 69.8105i −0.851347 0.851347i
\(83\) −111.452 + 111.452i −1.34279 + 1.34279i −0.449525 + 0.893268i \(0.648407\pi\)
−0.893268 + 0.449525i \(0.851593\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −12.0000 −0.139535
\(87\) 0 0
\(88\) 18.3712 18.3712i 0.208763 0.208763i
\(89\) 15.0000i 0.168539i 0.996443 + 0.0842697i \(0.0268557\pi\)
−0.996443 + 0.0842697i \(0.973144\pi\)
\(90\) 0 0
\(91\) 72.0000 0.791209
\(92\) −17.1464 17.1464i −0.186374 0.186374i
\(93\) 0 0
\(94\) 18.0000i 0.191489i
\(95\) 0 0
\(96\) 0 0
\(97\) 53.8888 + 53.8888i 0.555554 + 0.555554i 0.928039 0.372484i \(-0.121494\pi\)
−0.372484 + 0.928039i \(0.621494\pi\)
\(98\) 1.22474 1.22474i 0.0124974 0.0124974i
\(99\) 0 0
\(100\) 0 0
\(101\) 48.0000 0.475248 0.237624 0.971357i \(-0.423631\pi\)
0.237624 + 0.971357i \(0.423631\pi\)
\(102\) 0 0
\(103\) −90.6311 + 90.6311i −0.879914 + 0.879914i −0.993525 0.113611i \(-0.963758\pi\)
0.113611 + 0.993525i \(0.463758\pi\)
\(104\) 90.0000i 0.865385i
\(105\) 0 0
\(106\) −78.0000 −0.735849
\(107\) 25.7196 + 25.7196i 0.240370 + 0.240370i 0.817003 0.576633i \(-0.195634\pi\)
−0.576633 + 0.817003i \(0.695634\pi\)
\(108\) 0 0
\(109\) 40.0000i 0.366972i 0.983022 + 0.183486i \(0.0587383\pi\)
−0.983022 + 0.183486i \(0.941262\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 53.8888 + 53.8888i 0.481150 + 0.481150i
\(113\) 84.5074 84.5074i 0.747853 0.747853i −0.226223 0.974076i \(-0.572638\pi\)
0.974076 + 0.226223i \(0.0726377\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 30.0000 0.258621
\(117\) 0 0
\(118\) 110.227 110.227i 0.934127 0.934127i
\(119\) 132.000i 1.10924i
\(120\) 0 0
\(121\) −112.000 −0.925620
\(122\) −34.2929 34.2929i −0.281089 0.281089i
\(123\) 0 0
\(124\) 38.0000i 0.306452i
\(125\) 0 0
\(126\) 0 0
\(127\) −154.318 154.318i −1.21510 1.21510i −0.969327 0.245774i \(-0.920958\pi\)
−0.245774 0.969327i \(-0.579042\pi\)
\(128\) 42.8661 42.8661i 0.334891 0.334891i
\(129\) 0 0
\(130\) 0 0
\(131\) −162.000 −1.23664 −0.618321 0.785926i \(-0.712187\pi\)
−0.618321 + 0.785926i \(0.712187\pi\)
\(132\) 0 0
\(133\) −24.4949 + 24.4949i −0.184172 + 0.184172i
\(134\) 117.000i 0.873134i
\(135\) 0 0
\(136\) 165.000 1.21324
\(137\) 50.2145 + 50.2145i 0.366529 + 0.366529i 0.866210 0.499680i \(-0.166549\pi\)
−0.499680 + 0.866210i \(0.666549\pi\)
\(138\) 0 0
\(139\) 185.000i 1.33094i 0.746427 + 0.665468i \(0.231768\pi\)
−0.746427 + 0.665468i \(0.768232\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −51.4393 51.4393i −0.362248 0.362248i
\(143\) 22.0454 22.0454i 0.154164 0.154164i
\(144\) 0 0
\(145\) 0 0
\(146\) 33.0000 0.226027
\(147\) 0 0
\(148\) −19.5959 + 19.5959i −0.132405 + 0.132405i
\(149\) 150.000i 1.00671i 0.864079 + 0.503356i \(0.167901\pi\)
−0.864079 + 0.503356i \(0.832099\pi\)
\(150\) 0 0
\(151\) 52.0000 0.344371 0.172185 0.985065i \(-0.444917\pi\)
0.172185 + 0.985065i \(0.444917\pi\)
\(152\) 30.6186 + 30.6186i 0.201438 + 0.201438i
\(153\) 0 0
\(154\) 36.0000i 0.233766i
\(155\) 0 0
\(156\) 0 0
\(157\) 188.611 + 188.611i 1.20134 + 1.20134i 0.973759 + 0.227584i \(0.0730825\pi\)
0.227584 + 0.973759i \(0.426918\pi\)
\(158\) 97.9796 97.9796i 0.620124 0.620124i
\(159\) 0 0
\(160\) 0 0
\(161\) 168.000 1.04348
\(162\) 0 0
\(163\) 99.2043 99.2043i 0.608616 0.608616i −0.333969 0.942584i \(-0.608388\pi\)
0.942584 + 0.333969i \(0.108388\pi\)
\(164\) 57.0000i 0.347561i
\(165\) 0 0
\(166\) −273.000 −1.64458
\(167\) −17.1464 17.1464i −0.102673 0.102673i 0.653904 0.756577i \(-0.273130\pi\)
−0.756577 + 0.653904i \(0.773130\pi\)
\(168\) 0 0
\(169\) 61.0000i 0.360947i
\(170\) 0 0
\(171\) 0 0
\(172\) 4.89898 + 4.89898i 0.0284824 + 0.0284824i
\(173\) 78.3837 78.3837i 0.453085 0.453085i −0.443292 0.896377i \(-0.646190\pi\)
0.896377 + 0.443292i \(0.146190\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 33.0000 0.187500
\(177\) 0 0
\(178\) −18.3712 + 18.3712i −0.103209 + 0.103209i
\(179\) 195.000i 1.08939i −0.838636 0.544693i \(-0.816646\pi\)
0.838636 0.544693i \(-0.183354\pi\)
\(180\) 0 0
\(181\) 262.000 1.44751 0.723757 0.690055i \(-0.242414\pi\)
0.723757 + 0.690055i \(0.242414\pi\)
\(182\) 88.1816 + 88.1816i 0.484514 + 0.484514i
\(183\) 0 0
\(184\) 210.000i 1.14130i
\(185\) 0 0
\(186\) 0 0
\(187\) 40.4166 + 40.4166i 0.216131 + 0.216131i
\(188\) 7.34847 7.34847i 0.0390876 0.0390876i
\(189\) 0 0
\(190\) 0 0
\(191\) 18.0000 0.0942408 0.0471204 0.998889i \(-0.484996\pi\)
0.0471204 + 0.998889i \(0.484996\pi\)
\(192\) 0 0
\(193\) 86.9569 86.9569i 0.450554 0.450554i −0.444984 0.895538i \(-0.646791\pi\)
0.895538 + 0.444984i \(0.146791\pi\)
\(194\) 132.000i 0.680412i
\(195\) 0 0
\(196\) −1.00000 −0.00510204
\(197\) 129.823 + 129.823i 0.659000 + 0.659000i 0.955143 0.296144i \(-0.0957007\pi\)
−0.296144 + 0.955143i \(0.595701\pi\)
\(198\) 0 0
\(199\) 200.000i 1.00503i −0.864570 0.502513i \(-0.832409\pi\)
0.864570 0.502513i \(-0.167591\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 58.7878 + 58.7878i 0.291028 + 0.291028i
\(203\) −146.969 + 146.969i −0.723987 + 0.723987i
\(204\) 0 0
\(205\) 0 0
\(206\) −222.000 −1.07767
\(207\) 0 0
\(208\) 80.8332 80.8332i 0.388621 0.388621i
\(209\) 15.0000i 0.0717703i
\(210\) 0 0
\(211\) −103.000 −0.488152 −0.244076 0.969756i \(-0.578485\pi\)
−0.244076 + 0.969756i \(0.578485\pi\)
\(212\) 31.8434 + 31.8434i 0.150205 + 0.150205i
\(213\) 0 0
\(214\) 63.0000i 0.294393i
\(215\) 0 0
\(216\) 0 0
\(217\) −186.161 186.161i −0.857886 0.857886i
\(218\) −48.9898 + 48.9898i −0.224724 + 0.224724i
\(219\) 0 0
\(220\) 0 0
\(221\) 198.000 0.895928
\(222\) 0 0
\(223\) −200.858 + 200.858i −0.900709 + 0.900709i −0.995497 0.0947882i \(-0.969783\pi\)
0.0947882 + 0.995497i \(0.469783\pi\)
\(224\) 108.000i 0.482143i
\(225\) 0 0
\(226\) 207.000 0.915929
\(227\) −274.343 274.343i −1.20856 1.20856i −0.971494 0.237065i \(-0.923815\pi\)
−0.237065 0.971494i \(-0.576185\pi\)
\(228\) 0 0
\(229\) 20.0000i 0.0873362i 0.999046 + 0.0436681i \(0.0139044\pi\)
−0.999046 + 0.0436681i \(0.986096\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 183.712 + 183.712i 0.791861 + 0.791861i
\(233\) 102.879 102.879i 0.441539 0.441539i −0.450990 0.892529i \(-0.648929\pi\)
0.892529 + 0.450990i \(0.148929\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −90.0000 −0.381356
\(237\) 0 0
\(238\) −161.666 + 161.666i −0.679270 + 0.679270i
\(239\) 210.000i 0.878661i −0.898325 0.439331i \(-0.855216\pi\)
0.898325 0.439331i \(-0.144784\pi\)
\(240\) 0 0
\(241\) −43.0000 −0.178423 −0.0892116 0.996013i \(-0.528435\pi\)
−0.0892116 + 0.996013i \(0.528435\pi\)
\(242\) −137.171 137.171i −0.566824 0.566824i
\(243\) 0 0
\(244\) 28.0000i 0.114754i
\(245\) 0 0
\(246\) 0 0
\(247\) 36.7423 + 36.7423i 0.148754 + 0.148754i
\(248\) −232.702 + 232.702i −0.938313 + 0.938313i
\(249\) 0 0
\(250\) 0 0
\(251\) 123.000 0.490040 0.245020 0.969518i \(-0.421205\pi\)
0.245020 + 0.969518i \(0.421205\pi\)
\(252\) 0 0
\(253\) 51.4393 51.4393i 0.203317 0.203317i
\(254\) 378.000i 1.48819i
\(255\) 0 0
\(256\) −179.000 −0.699219
\(257\) −4.89898 4.89898i −0.0190622 0.0190622i 0.697511 0.716574i \(-0.254291\pi\)
−0.716574 + 0.697511i \(0.754291\pi\)
\(258\) 0 0
\(259\) 192.000i 0.741313i
\(260\) 0 0
\(261\) 0 0
\(262\) −198.409 198.409i −0.757285 0.757285i
\(263\) −7.34847 + 7.34847i −0.0279409 + 0.0279409i −0.720939 0.692998i \(-0.756289\pi\)
0.692998 + 0.720939i \(0.256289\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −60.0000 −0.225564
\(267\) 0 0
\(268\) 47.7650 47.7650i 0.178228 0.178228i
\(269\) 120.000i 0.446097i 0.974807 + 0.223048i \(0.0716008\pi\)
−0.974807 + 0.223048i \(0.928399\pi\)
\(270\) 0 0
\(271\) −58.0000 −0.214022 −0.107011 0.994258i \(-0.534128\pi\)
−0.107011 + 0.994258i \(0.534128\pi\)
\(272\) 148.194 + 148.194i 0.544831 + 0.544831i
\(273\) 0 0
\(274\) 123.000i 0.448905i
\(275\) 0 0
\(276\) 0 0
\(277\) −276.792 276.792i −0.999250 0.999250i 0.000749391 1.00000i \(-0.499761\pi\)
−1.00000 0.000749391i \(0.999761\pi\)
\(278\) −226.578 + 226.578i −0.815028 + 0.815028i
\(279\) 0 0
\(280\) 0 0
\(281\) −462.000 −1.64413 −0.822064 0.569395i \(-0.807178\pi\)
−0.822064 + 0.569395i \(0.807178\pi\)
\(282\) 0 0
\(283\) −72.2599 + 72.2599i −0.255336 + 0.255336i −0.823154 0.567818i \(-0.807788\pi\)
0.567818 + 0.823154i \(0.307788\pi\)
\(284\) 42.0000i 0.147887i
\(285\) 0 0
\(286\) 54.0000 0.188811
\(287\) −279.242 279.242i −0.972968 0.972968i
\(288\) 0 0
\(289\) 74.0000i 0.256055i
\(290\) 0 0
\(291\) 0 0
\(292\) −13.4722 13.4722i −0.0461376 0.0461376i
\(293\) 4.89898 4.89898i 0.0167201 0.0167201i −0.698697 0.715417i \(-0.746237\pi\)
0.715417 + 0.698697i \(0.246237\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −240.000 −0.810811
\(297\) 0 0
\(298\) −183.712 + 183.712i −0.616482 + 0.616482i
\(299\) 252.000i 0.842809i
\(300\) 0 0
\(301\) −48.0000 −0.159468
\(302\) 63.6867 + 63.6867i 0.210883 + 0.210883i
\(303\) 0 0
\(304\) 55.0000i 0.180921i
\(305\) 0 0
\(306\) 0 0
\(307\) −86.9569 86.9569i −0.283247 0.283247i 0.551155 0.834403i \(-0.314187\pi\)
−0.834403 + 0.551155i \(0.814187\pi\)
\(308\) 14.6969 14.6969i 0.0477173 0.0477173i
\(309\) 0 0
\(310\) 0 0
\(311\) 528.000 1.69775 0.848875 0.528594i \(-0.177281\pi\)
0.848875 + 0.528594i \(0.177281\pi\)
\(312\) 0 0
\(313\) 191.060 191.060i 0.610416 0.610416i −0.332638 0.943054i \(-0.607939\pi\)
0.943054 + 0.332638i \(0.107939\pi\)
\(314\) 462.000i 1.47134i
\(315\) 0 0
\(316\) −80.0000 −0.253165
\(317\) −200.858 200.858i −0.633622 0.633622i 0.315353 0.948975i \(-0.397877\pi\)
−0.948975 + 0.315353i \(0.897877\pi\)
\(318\) 0 0
\(319\) 90.0000i 0.282132i
\(320\) 0 0
\(321\) 0 0
\(322\) 205.757 + 205.757i 0.638997 + 0.638997i
\(323\) −67.3610 + 67.3610i −0.208548 + 0.208548i
\(324\) 0 0
\(325\) 0 0
\(326\) 243.000 0.745399
\(327\) 0 0
\(328\) −349.052 + 349.052i −1.06418 + 1.06418i
\(329\) 72.0000i 0.218845i
\(330\) 0 0
\(331\) −313.000 −0.945619 −0.472810 0.881165i \(-0.656760\pi\)
−0.472810 + 0.881165i \(0.656760\pi\)
\(332\) 111.452 + 111.452i 0.335698 + 0.335698i
\(333\) 0 0
\(334\) 42.0000i 0.125749i
\(335\) 0 0
\(336\) 0 0
\(337\) 194.734 + 194.734i 0.577847 + 0.577847i 0.934310 0.356463i \(-0.116017\pi\)
−0.356463 + 0.934310i \(0.616017\pi\)
\(338\) −74.7094 + 74.7094i −0.221034 + 0.221034i
\(339\) 0 0
\(340\) 0 0
\(341\) −114.000 −0.334311
\(342\) 0 0
\(343\) 244.949 244.949i 0.714137 0.714137i
\(344\) 60.0000i 0.174419i
\(345\) 0 0
\(346\) 192.000 0.554913
\(347\) 99.2043 + 99.2043i 0.285891 + 0.285891i 0.835453 0.549562i \(-0.185205\pi\)
−0.549562 + 0.835453i \(0.685205\pi\)
\(348\) 0 0
\(349\) 100.000i 0.286533i −0.989684 0.143266i \(-0.954239\pi\)
0.989684 0.143266i \(-0.0457606\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −33.0681 33.0681i −0.0939435 0.0939435i
\(353\) 396.817 396.817i 1.12413 1.12413i 0.133014 0.991114i \(-0.457534\pi\)
0.991114 0.133014i \(-0.0424656\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 15.0000 0.0421348
\(357\) 0 0
\(358\) 238.825 238.825i 0.667110 0.667110i
\(359\) 540.000i 1.50418i −0.659061 0.752089i \(-0.729046\pi\)
0.659061 0.752089i \(-0.270954\pi\)
\(360\) 0 0
\(361\) 336.000 0.930748
\(362\) 320.883 + 320.883i 0.886418 + 0.886418i
\(363\) 0 0
\(364\) 72.0000i 0.197802i
\(365\) 0 0
\(366\) 0 0
\(367\) −44.0908 44.0908i −0.120138 0.120138i 0.644481 0.764620i \(-0.277073\pi\)
−0.764620 + 0.644481i \(0.777073\pi\)
\(368\) 188.611 188.611i 0.512529 0.512529i
\(369\) 0 0
\(370\) 0 0
\(371\) −312.000 −0.840970
\(372\) 0 0
\(373\) 350.277 350.277i 0.939081 0.939081i −0.0591675 0.998248i \(-0.518845\pi\)
0.998248 + 0.0591675i \(0.0188446\pi\)
\(374\) 99.0000i 0.264706i
\(375\) 0 0
\(376\) 90.0000 0.239362
\(377\) 220.454 + 220.454i 0.584759 + 0.584759i
\(378\) 0 0
\(379\) 505.000i 1.33245i −0.745749 0.666227i \(-0.767908\pi\)
0.745749 0.666227i \(-0.232092\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 22.0454 + 22.0454i 0.0577105 + 0.0577105i
\(383\) −142.070 + 142.070i −0.370941 + 0.370941i −0.867820 0.496879i \(-0.834479\pi\)
0.496879 + 0.867820i \(0.334479\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 213.000 0.551813
\(387\) 0 0
\(388\) 53.8888 53.8888i 0.138889 0.138889i
\(389\) 690.000i 1.77378i 0.461982 + 0.886889i \(0.347139\pi\)
−0.461982 + 0.886889i \(0.652861\pi\)
\(390\) 0 0
\(391\) 462.000 1.18159
\(392\) −6.12372 6.12372i −0.0156217 0.0156217i
\(393\) 0 0
\(394\) 318.000i 0.807107i
\(395\) 0 0
\(396\) 0 0
\(397\) 421.312 + 421.312i 1.06124 + 1.06124i 0.997998 + 0.0632416i \(0.0201439\pi\)
0.0632416 + 0.997998i \(0.479856\pi\)
\(398\) 244.949 244.949i 0.615450 0.615450i
\(399\) 0 0
\(400\) 0 0
\(401\) 573.000 1.42893 0.714464 0.699672i \(-0.246671\pi\)
0.714464 + 0.699672i \(0.246671\pi\)
\(402\) 0 0
\(403\) −279.242 + 279.242i −0.692908 + 0.692908i
\(404\) 48.0000i 0.118812i
\(405\) 0 0
\(406\) −360.000 −0.886700
\(407\) −58.7878 58.7878i −0.144442 0.144442i
\(408\) 0 0
\(409\) 365.000i 0.892421i 0.894928 + 0.446210i \(0.147227\pi\)
−0.894928 + 0.446210i \(0.852773\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 90.6311 + 90.6311i 0.219978 + 0.219978i
\(413\) 440.908 440.908i 1.06757 1.06757i
\(414\) 0 0
\(415\) 0 0
\(416\) −162.000 −0.389423
\(417\) 0 0
\(418\) −18.3712 + 18.3712i −0.0439502 + 0.0439502i
\(419\) 645.000i 1.53938i 0.638418 + 0.769690i \(0.279589\pi\)
−0.638418 + 0.769690i \(0.720411\pi\)
\(420\) 0 0
\(421\) −8.00000 −0.0190024 −0.00950119 0.999955i \(-0.503024\pi\)
−0.00950119 + 0.999955i \(0.503024\pi\)
\(422\) −126.149 126.149i −0.298931 0.298931i
\(423\) 0 0
\(424\) 390.000i 0.919811i
\(425\) 0 0
\(426\) 0 0
\(427\) −137.171 137.171i −0.321245 0.321245i
\(428\) 25.7196 25.7196i 0.0600926 0.0600926i
\(429\) 0 0
\(430\) 0 0
\(431\) −12.0000 −0.0278422 −0.0139211 0.999903i \(-0.504431\pi\)
−0.0139211 + 0.999903i \(0.504431\pi\)
\(432\) 0 0
\(433\) −439.683 + 439.683i −1.01544 + 1.01544i −0.0155561 + 0.999879i \(0.504952\pi\)
−0.999879 + 0.0155561i \(0.995048\pi\)
\(434\) 456.000i 1.05069i
\(435\) 0 0
\(436\) 40.0000 0.0917431
\(437\) 85.7321 + 85.7321i 0.196183 + 0.196183i
\(438\) 0 0
\(439\) 10.0000i 0.0227790i 0.999935 + 0.0113895i \(0.00362548\pi\)
−0.999935 + 0.0113895i \(0.996375\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 242.499 + 242.499i 0.548641 + 0.548641i
\(443\) −86.9569 + 86.9569i −0.196291 + 0.196291i −0.798408 0.602117i \(-0.794324\pi\)
0.602117 + 0.798408i \(0.294324\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −492.000 −1.10314
\(447\) 0 0
\(448\) 347.828 347.828i 0.776401 0.776401i
\(449\) 75.0000i 0.167038i 0.996506 + 0.0835189i \(0.0266159\pi\)
−0.996506 + 0.0835189i \(0.973384\pi\)
\(450\) 0 0
\(451\) −171.000 −0.379157
\(452\) −84.5074 84.5074i −0.186963 0.186963i
\(453\) 0 0
\(454\) 672.000i 1.48018i
\(455\) 0 0
\(456\) 0 0
\(457\) −209.431 209.431i −0.458274 0.458274i 0.439814 0.898089i \(-0.355044\pi\)
−0.898089 + 0.439814i \(0.855044\pi\)
\(458\) −24.4949 + 24.4949i −0.0534823 + 0.0534823i
\(459\) 0 0
\(460\) 0 0
\(461\) 228.000 0.494577 0.247289 0.968942i \(-0.420460\pi\)
0.247289 + 0.968942i \(0.420460\pi\)
\(462\) 0 0
\(463\) 436.009 436.009i 0.941704 0.941704i −0.0566875 0.998392i \(-0.518054\pi\)
0.998392 + 0.0566875i \(0.0180539\pi\)
\(464\) 330.000i 0.711207i
\(465\) 0 0
\(466\) 252.000 0.540773
\(467\) 533.989 + 533.989i 1.14344 + 1.14344i 0.987816 + 0.155629i \(0.0497406\pi\)
0.155629 + 0.987816i \(0.450259\pi\)
\(468\) 0 0
\(469\) 468.000i 0.997868i
\(470\) 0 0
\(471\) 0 0
\(472\) −551.135 551.135i −1.16766 1.16766i
\(473\) −14.6969 + 14.6969i −0.0310718 + 0.0310718i
\(474\) 0 0
\(475\) 0 0
\(476\) 132.000 0.277311
\(477\) 0 0
\(478\) 257.196 257.196i 0.538068 0.538068i
\(479\) 270.000i 0.563674i −0.959462 0.281837i \(-0.909056\pi\)
0.959462 0.281837i \(-0.0909438\pi\)
\(480\) 0 0
\(481\) −288.000 −0.598753
\(482\) −52.6640 52.6640i −0.109261 0.109261i
\(483\) 0 0
\(484\) 112.000i 0.231405i
\(485\) 0 0
\(486\) 0 0
\(487\) −80.8332 80.8332i −0.165982 0.165982i 0.619229 0.785211i \(-0.287445\pi\)
−0.785211 + 0.619229i \(0.787445\pi\)
\(488\) −171.464 + 171.464i −0.351361 + 0.351361i
\(489\) 0 0
\(490\) 0 0
\(491\) −582.000 −1.18534 −0.592668 0.805447i \(-0.701925\pi\)
−0.592668 + 0.805447i \(0.701925\pi\)
\(492\) 0 0
\(493\) −404.166 + 404.166i −0.819809 + 0.819809i
\(494\) 90.0000i 0.182186i
\(495\) 0 0
\(496\) −418.000 −0.842742
\(497\) −205.757 205.757i −0.413998 0.413998i
\(498\) 0 0
\(499\) 250.000i 0.501002i 0.968116 + 0.250501i \(0.0805953\pi\)
−0.968116 + 0.250501i \(0.919405\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 150.644 + 150.644i 0.300087 + 0.300087i
\(503\) −460.504 + 460.504i −0.915515 + 0.915515i −0.996699 0.0811841i \(-0.974130\pi\)
0.0811841 + 0.996699i \(0.474130\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 126.000 0.249012
\(507\) 0 0
\(508\) −154.318 + 154.318i −0.303775 + 0.303775i
\(509\) 390.000i 0.766208i −0.923705 0.383104i \(-0.874855\pi\)
0.923705 0.383104i \(-0.125145\pi\)
\(510\) 0 0
\(511\) 132.000 0.258317
\(512\) −390.694 390.694i −0.763073 0.763073i
\(513\) 0 0
\(514\) 12.0000i 0.0233463i
\(515\) 0 0
\(516\) 0 0
\(517\) 22.0454 + 22.0454i 0.0426410 + 0.0426410i
\(518\) 235.151 235.151i 0.453959 0.453959i
\(519\) 0 0
\(520\) 0 0
\(521\) 183.000 0.351248 0.175624 0.984457i \(-0.443806\pi\)
0.175624 + 0.984457i \(0.443806\pi\)
\(522\) 0 0
\(523\) −476.426 + 476.426i −0.910948 + 0.910948i −0.996347 0.0853989i \(-0.972784\pi\)
0.0853989 + 0.996347i \(0.472784\pi\)
\(524\) 162.000i 0.309160i
\(525\) 0 0
\(526\) −18.0000 −0.0342205
\(527\) −511.943 511.943i −0.971430 0.971430i
\(528\) 0 0
\(529\) 59.0000i 0.111531i
\(530\) 0 0
\(531\) 0 0
\(532\) 24.4949 + 24.4949i 0.0460430 + 0.0460430i
\(533\) −418.863 + 418.863i −0.785859 + 0.785859i
\(534\) 0 0
\(535\) 0 0
\(536\) 585.000 1.09142
\(537\) 0 0
\(538\) −146.969 + 146.969i −0.273177 + 0.273177i
\(539\) 3.00000i 0.00556586i
\(540\) 0 0
\(541\) −568.000 −1.04991 −0.524954 0.851131i \(-0.675917\pi\)
−0.524954 + 0.851131i \(0.675917\pi\)
\(542\) −71.0352 71.0352i −0.131061 0.131061i
\(543\) 0 0
\(544\) 297.000i 0.545956i
\(545\) 0 0
\(546\) 0 0
\(547\) −160.442 160.442i −0.293312 0.293312i 0.545075 0.838387i \(-0.316501\pi\)
−0.838387 + 0.545075i \(0.816501\pi\)
\(548\) 50.2145 50.2145i 0.0916324 0.0916324i
\(549\) 0 0
\(550\) 0 0
\(551\) −150.000 −0.272232
\(552\) 0 0
\(553\) 391.918 391.918i 0.708713 0.708713i
\(554\) 678.000i 1.22383i
\(555\) 0 0
\(556\) 185.000 0.332734
\(557\) −66.1362 66.1362i −0.118736 0.118736i 0.645242 0.763978i \(-0.276757\pi\)
−0.763978 + 0.645242i \(0.776757\pi\)
\(558\) 0 0
\(559\) 72.0000i 0.128801i
\(560\) 0 0
\(561\) 0 0
\(562\) −565.832 565.832i −1.00682 1.00682i
\(563\) −191.060 + 191.060i −0.339361 + 0.339361i −0.856127 0.516766i \(-0.827136\pi\)
0.516766 + 0.856127i \(0.327136\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −177.000 −0.312721
\(567\) 0 0
\(568\) −257.196 + 257.196i −0.452811 + 0.452811i
\(569\) 45.0000i 0.0790861i 0.999218 + 0.0395431i \(0.0125902\pi\)
−0.999218 + 0.0395431i \(0.987410\pi\)
\(570\) 0 0
\(571\) 542.000 0.949212 0.474606 0.880198i \(-0.342591\pi\)
0.474606 + 0.880198i \(0.342591\pi\)
\(572\) −22.0454 22.0454i −0.0385409 0.0385409i
\(573\) 0 0
\(574\) 684.000i 1.19164i
\(575\) 0 0
\(576\) 0 0
\(577\) 549.910 + 549.910i 0.953051 + 0.953051i 0.998946 0.0458952i \(-0.0146140\pi\)
−0.0458952 + 0.998946i \(0.514614\pi\)
\(578\) −90.6311 + 90.6311i −0.156801 + 0.156801i
\(579\) 0 0
\(580\) 0 0
\(581\) −1092.00 −1.87952
\(582\) 0 0
\(583\) −95.5301 + 95.5301i −0.163860 + 0.163860i
\(584\) 165.000i 0.282534i
\(585\) 0 0
\(586\) 12.0000 0.0204778
\(587\) 417.638 + 417.638i 0.711479 + 0.711479i 0.966845 0.255366i \(-0.0821959\pi\)
−0.255366 + 0.966845i \(0.582196\pi\)
\(588\) 0 0
\(589\) 190.000i 0.322581i
\(590\) 0 0
\(591\) 0 0
\(592\) −215.555 215.555i −0.364113 0.364113i
\(593\) −331.906 + 331.906i −0.559706 + 0.559706i −0.929224 0.369517i \(-0.879523\pi\)
0.369517 + 0.929224i \(0.379523\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 150.000 0.251678
\(597\) 0 0
\(598\) 308.636 308.636i 0.516113 0.516113i
\(599\) 900.000i 1.50250i −0.660015 0.751252i \(-0.729450\pi\)
0.660015 0.751252i \(-0.270550\pi\)
\(600\) 0 0
\(601\) 577.000 0.960067 0.480033 0.877250i \(-0.340625\pi\)
0.480033 + 0.877250i \(0.340625\pi\)
\(602\) −58.7878 58.7878i −0.0976541 0.0976541i
\(603\) 0 0
\(604\) 52.0000i 0.0860927i
\(605\) 0 0
\(606\) 0 0
\(607\) 127.373 + 127.373i 0.209841 + 0.209841i 0.804200 0.594359i \(-0.202594\pi\)
−0.594359 + 0.804200i \(0.702594\pi\)
\(608\) 55.1135 55.1135i 0.0906472 0.0906472i
\(609\) 0 0
\(610\) 0 0
\(611\) 108.000 0.176759
\(612\) 0 0
\(613\) −237.601 + 237.601i −0.387603 + 0.387603i −0.873832 0.486229i \(-0.838372\pi\)
0.486229 + 0.873832i \(0.338372\pi\)
\(614\) 213.000i 0.346906i
\(615\) 0 0
\(616\) 180.000 0.292208
\(617\) 656.463 + 656.463i 1.06396 + 1.06396i 0.997810 + 0.0661502i \(0.0210717\pi\)
0.0661502 + 0.997810i \(0.478928\pi\)
\(618\) 0 0
\(619\) 470.000i 0.759289i −0.925132 0.379645i \(-0.876046\pi\)
0.925132 0.379645i \(-0.123954\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 646.665 + 646.665i 1.03965 + 1.03965i
\(623\) −73.4847 + 73.4847i −0.117953 + 0.117953i
\(624\) 0 0
\(625\) 0 0
\(626\) 468.000 0.747604
\(627\) 0 0
\(628\) 188.611 188.611i 0.300336 0.300336i
\(629\) 528.000i 0.839428i
\(630\) 0 0
\(631\) −838.000 −1.32805 −0.664025 0.747710i \(-0.731153\pi\)
−0.664025 + 0.747710i \(0.731153\pi\)
\(632\) −489.898 489.898i −0.775155 0.775155i
\(633\) 0 0
\(634\) 492.000i 0.776025i
\(635\) 0 0
\(636\) 0 0
\(637\) −7.34847 7.34847i −0.0115361 0.0115361i
\(638\) −110.227 + 110.227i −0.172770 + 0.172770i
\(639\) 0 0
\(640\) 0 0
\(641\) 618.000 0.964119 0.482059 0.876139i \(-0.339889\pi\)
0.482059 + 0.876139i \(0.339889\pi\)
\(642\) 0 0
\(643\) −249.848 + 249.848i −0.388566 + 0.388566i −0.874176 0.485610i \(-0.838598\pi\)
0.485610 + 0.874176i \(0.338598\pi\)
\(644\) 168.000i 0.260870i
\(645\) 0 0
\(646\) −165.000 −0.255418
\(647\) −421.312 421.312i −0.651178 0.651178i 0.302099 0.953277i \(-0.402313\pi\)
−0.953277 + 0.302099i \(0.902313\pi\)
\(648\) 0 0
\(649\) 270.000i 0.416025i
\(650\) 0 0
\(651\) 0 0
\(652\) −99.2043 99.2043i −0.152154 0.152154i
\(653\) 519.292 519.292i 0.795240 0.795240i −0.187101 0.982341i \(-0.559909\pi\)
0.982341 + 0.187101i \(0.0599090\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −627.000 −0.955793
\(657\) 0 0
\(658\) −88.1816 + 88.1816i −0.134015 + 0.134015i
\(659\) 885.000i 1.34294i 0.741030 + 0.671472i \(0.234338\pi\)
−0.741030 + 0.671472i \(0.765662\pi\)
\(660\) 0 0
\(661\) 922.000 1.39486 0.697428 0.716655i \(-0.254328\pi\)
0.697428 + 0.716655i \(0.254328\pi\)
\(662\) −383.345 383.345i −0.579071 0.579071i
\(663\) 0 0
\(664\) 1365.00i 2.05572i
\(665\) 0 0
\(666\) 0 0
\(667\) 514.393 + 514.393i 0.771204 + 0.771204i
\(668\) −17.1464 + 17.1464i −0.0256683 + 0.0256683i
\(669\) 0 0
\(670\) 0 0
\(671\) −84.0000 −0.125186
\(672\) 0 0
\(673\) −78.3837 + 78.3837i −0.116469 + 0.116469i −0.762939 0.646470i \(-0.776244\pi\)
0.646470 + 0.762939i \(0.276244\pi\)
\(674\) 477.000i 0.707715i
\(675\) 0 0
\(676\) 61.0000 0.0902367
\(677\) 705.453 + 705.453i 1.04203 + 1.04203i 0.999077 + 0.0429510i \(0.0136759\pi\)
0.0429510 + 0.999077i \(0.486324\pi\)
\(678\) 0 0
\(679\) 528.000i 0.777614i
\(680\) 0 0
\(681\) 0 0
\(682\) −139.621 139.621i −0.204723 0.204723i
\(683\) 133.497 133.497i 0.195457 0.195457i −0.602592 0.798049i \(-0.705865\pi\)
0.798049 + 0.602592i \(0.205865\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 600.000 0.874636
\(687\) 0 0
\(688\) −53.8888 + 53.8888i −0.0783267 + 0.0783267i
\(689\) 468.000i 0.679245i
\(690\) 0 0
\(691\) −893.000 −1.29233 −0.646165 0.763198i \(-0.723628\pi\)
−0.646165 + 0.763198i \(0.723628\pi\)
\(692\) −78.3837 78.3837i −0.113271 0.113271i
\(693\) 0 0
\(694\) 243.000i 0.350144i
\(695\) 0 0
\(696\) 0 0
\(697\) −767.915 767.915i −1.10174 1.10174i
\(698\) 122.474 122.474i 0.175465 0.175465i
\(699\) 0 0
\(700\) 0 0
\(701\) −402.000 −0.573466 −0.286733 0.958010i \(-0.592569\pi\)
−0.286733 + 0.958010i \(0.592569\pi\)
\(702\) 0 0
\(703\) 97.9796 97.9796i 0.139374 0.139374i
\(704\) 213.000i 0.302557i
\(705\) 0 0
\(706\) 972.000 1.37677
\(707\) 235.151 + 235.151i 0.332604 + 0.332604i
\(708\) 0 0
\(709\) 1060.00i 1.49506i −0.664226 0.747532i \(-0.731239\pi\)
0.664226 0.747532i \(-0.268761\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 91.8559 + 91.8559i 0.129011 + 0.129011i
\(713\) −651.564 + 651.564i −0.913835 + 0.913835i
\(714\) 0 0
\(715\) 0 0
\(716\) −195.000 −0.272346
\(717\) 0 0
\(718\) 661.362 661.362i 0.921117 0.921117i
\(719\) 1320.00i 1.83588i 0.396716 + 0.917942i \(0.370150\pi\)
−0.396716 + 0.917942i \(0.629850\pi\)
\(720\) 0 0
\(721\) −888.000 −1.23162
\(722\) 411.514 + 411.514i 0.569964 + 0.569964i
\(723\) 0 0
\(724\) 262.000i 0.361878i
\(725\) 0 0
\(726\) 0 0
\(727\) −31.8434 31.8434i −0.0438011 0.0438011i 0.684867 0.728668i \(-0.259860\pi\)
−0.728668 + 0.684867i \(0.759860\pi\)
\(728\) 440.908 440.908i 0.605643 0.605643i
\(729\) 0 0
\(730\) 0 0
\(731\) −132.000 −0.180575
\(732\) 0 0
\(733\) 815.680 815.680i 1.11280 1.11280i 0.120026 0.992771i \(-0.461702\pi\)
0.992771 0.120026i \(-0.0382978\pi\)
\(734\) 108.000i 0.147139i
\(735\) 0 0
\(736\) −378.000 −0.513587
\(737\) 143.295 + 143.295i 0.194430 + 0.194430i
\(738\) 0 0
\(739\) 710.000i 0.960758i 0.877061 + 0.480379i \(0.159501\pi\)
−0.877061 + 0.480379i \(0.840499\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −382.120 382.120i −0.514987 0.514987i
\(743\) 800.983 800.983i 1.07804 1.07804i 0.0813540 0.996685i \(-0.474076\pi\)
0.996685 0.0813540i \(-0.0259244\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 858.000 1.15013
\(747\) 0 0
\(748\) 40.4166 40.4166i 0.0540329 0.0540329i
\(749\) 252.000i 0.336449i
\(750\) 0 0
\(751\) 502.000 0.668442 0.334221 0.942495i \(-0.391527\pi\)
0.334221 + 0.942495i \(0.391527\pi\)
\(752\) 80.8332 + 80.8332i 0.107491 + 0.107491i
\(753\) 0 0
\(754\) 540.000i 0.716180i
\(755\) 0 0
\(756\) 0 0
\(757\) 4.89898 + 4.89898i 0.00647157 + 0.00647157i 0.710335 0.703864i \(-0.248543\pi\)
−0.703864 + 0.710335i \(0.748543\pi\)
\(758\) 618.496 618.496i 0.815958 0.815958i
\(759\) 0 0
\(760\) 0 0
\(761\) −747.000 −0.981603 −0.490802 0.871271i \(-0.663296\pi\)
−0.490802 + 0.871271i \(0.663296\pi\)
\(762\) 0 0
\(763\) −195.959 + 195.959i −0.256827 + 0.256827i
\(764\) 18.0000i 0.0235602i
\(765\) 0 0
\(766\) −348.000 −0.454308
\(767\) −661.362 661.362i −0.862271 0.862271i
\(768\) 0 0
\(769\) 1255.00i 1.63199i 0.578059 + 0.815995i \(0.303810\pi\)
−0.578059 + 0.815995i \(0.696190\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −86.9569 86.9569i −0.112638 0.112638i
\(773\) 17.1464 17.1464i 0.0221817 0.0221817i −0.695929 0.718111i \(-0.745007\pi\)
0.718111 + 0.695929i \(0.245007\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 660.000 0.850515
\(777\) 0 0
\(778\) −845.074 + 845.074i −1.08621 + 1.08621i
\(779\) 285.000i 0.365854i
\(780\) 0 0
\(781\) −126.000 −0.161332
\(782\) 565.832 + 565.832i 0.723570 + 0.723570i
\(783\) 0 0
\(784\) 11.0000i 0.0140306i
\(785\) 0 0
\(786\) 0 0
\(787\) 592.777 + 592.777i 0.753210 + 0.753210i 0.975077 0.221867i \(-0.0712150\pi\)
−0.221867 + 0.975077i \(0.571215\pi\)
\(788\) 129.823 129.823i 0.164750 0.164750i
\(789\) 0 0
\(790\)