Properties

Label 520.2.q.d.321.1
Level $520$
Weight $2$
Character 520.321
Analytic conductor $4.152$
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] = [520,2,Mod(81,520)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(520, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("520.81");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 520.q (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.15222090511\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 321.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 520.321
Dual form 520.2.q.d.81.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} +1.00000 q^{5} +(1.50000 + 2.59808i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} +1.00000 q^{5} +(1.50000 + 2.59808i) q^{7} +(1.00000 + 1.73205i) q^{9} +(-2.50000 + 4.33013i) q^{11} +(1.00000 + 3.46410i) q^{13} +(0.500000 - 0.866025i) q^{15} +(-2.50000 - 4.33013i) q^{17} +(0.500000 + 0.866025i) q^{19} +3.00000 q^{21} +(0.500000 - 0.866025i) q^{23} +1.00000 q^{25} +5.00000 q^{27} +(4.50000 - 7.79423i) q^{29} -4.00000 q^{31} +(2.50000 + 4.33013i) q^{33} +(1.50000 + 2.59808i) q^{35} +(1.50000 - 2.59808i) q^{37} +(3.50000 + 0.866025i) q^{39} +(0.500000 - 0.866025i) q^{41} +(1.50000 + 2.59808i) q^{43} +(1.00000 + 1.73205i) q^{45} -8.00000 q^{47} +(-1.00000 + 1.73205i) q^{49} -5.00000 q^{51} +10.0000 q^{53} +(-2.50000 + 4.33013i) q^{55} +1.00000 q^{57} +(-1.50000 - 2.59808i) q^{59} +(-3.50000 - 6.06218i) q^{61} +(-3.00000 + 5.19615i) q^{63} +(1.00000 + 3.46410i) q^{65} +(4.50000 - 7.79423i) q^{67} +(-0.500000 - 0.866025i) q^{69} +(-3.50000 - 6.06218i) q^{71} +10.0000 q^{73} +(0.500000 - 0.866025i) q^{75} -15.0000 q^{77} -16.0000 q^{79} +(-0.500000 + 0.866025i) q^{81} +12.0000 q^{83} +(-2.50000 - 4.33013i) q^{85} +(-4.50000 - 7.79423i) q^{87} +(-7.50000 + 12.9904i) q^{89} +(-7.50000 + 7.79423i) q^{91} +(-2.00000 + 3.46410i) q^{93} +(0.500000 + 0.866025i) q^{95} +(3.50000 + 6.06218i) q^{97} -10.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{3} + 2 q^{5} + 3 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{3} + 2 q^{5} + 3 q^{7} + 2 q^{9} - 5 q^{11} + 2 q^{13} + q^{15} - 5 q^{17} + q^{19} + 6 q^{21} + q^{23} + 2 q^{25} + 10 q^{27} + 9 q^{29} - 8 q^{31} + 5 q^{33} + 3 q^{35} + 3 q^{37} + 7 q^{39} + q^{41} + 3 q^{43} + 2 q^{45} - 16 q^{47} - 2 q^{49} - 10 q^{51} + 20 q^{53} - 5 q^{55} + 2 q^{57} - 3 q^{59} - 7 q^{61} - 6 q^{63} + 2 q^{65} + 9 q^{67} - q^{69} - 7 q^{71} + 20 q^{73} + q^{75} - 30 q^{77} - 32 q^{79} - q^{81} + 24 q^{83} - 5 q^{85} - 9 q^{87} - 15 q^{89} - 15 q^{91} - 4 q^{93} + q^{95} + 7 q^{97} - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/520\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(261\) \(391\) \(417\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.500000 0.866025i 0.288675 0.500000i −0.684819 0.728714i \(-0.740119\pi\)
0.973494 + 0.228714i \(0.0734519\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 1.50000 + 2.59808i 0.566947 + 0.981981i 0.996866 + 0.0791130i \(0.0252088\pi\)
−0.429919 + 0.902867i \(0.641458\pi\)
\(8\) 0 0
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 0 0
\(11\) −2.50000 + 4.33013i −0.753778 + 1.30558i 0.192201 + 0.981356i \(0.438437\pi\)
−0.945979 + 0.324227i \(0.894896\pi\)
\(12\) 0 0
\(13\) 1.00000 + 3.46410i 0.277350 + 0.960769i
\(14\) 0 0
\(15\) 0.500000 0.866025i 0.129099 0.223607i
\(16\) 0 0
\(17\) −2.50000 4.33013i −0.606339 1.05021i −0.991838 0.127502i \(-0.959304\pi\)
0.385499 0.922708i \(-0.374029\pi\)
\(18\) 0 0
\(19\) 0.500000 + 0.866025i 0.114708 + 0.198680i 0.917663 0.397360i \(-0.130073\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 0 0
\(21\) 3.00000 0.654654
\(22\) 0 0
\(23\) 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
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) 4.50000 7.79423i 0.835629 1.44735i −0.0578882 0.998323i \(-0.518437\pi\)
0.893517 0.449029i \(-0.148230\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0 0
\(33\) 2.50000 + 4.33013i 0.435194 + 0.753778i
\(34\) 0 0
\(35\) 1.50000 + 2.59808i 0.253546 + 0.439155i
\(36\) 0 0
\(37\) 1.50000 2.59808i 0.246598 0.427121i −0.715981 0.698119i \(-0.754020\pi\)
0.962580 + 0.270998i \(0.0873538\pi\)
\(38\) 0 0
\(39\) 3.50000 + 0.866025i 0.560449 + 0.138675i
\(40\) 0 0
\(41\) 0.500000 0.866025i 0.0780869 0.135250i −0.824338 0.566099i \(-0.808452\pi\)
0.902424 + 0.430848i \(0.141786\pi\)
\(42\) 0 0
\(43\) 1.50000 + 2.59808i 0.228748 + 0.396203i 0.957437 0.288641i \(-0.0932035\pi\)
−0.728689 + 0.684844i \(0.759870\pi\)
\(44\) 0 0
\(45\) 1.00000 + 1.73205i 0.149071 + 0.258199i
\(46\) 0 0
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) 0 0
\(49\) −1.00000 + 1.73205i −0.142857 + 0.247436i
\(50\) 0 0
\(51\) −5.00000 −0.700140
\(52\) 0 0
\(53\) 10.0000 1.37361 0.686803 0.726844i \(-0.259014\pi\)
0.686803 + 0.726844i \(0.259014\pi\)
\(54\) 0 0
\(55\) −2.50000 + 4.33013i −0.337100 + 0.583874i
\(56\) 0 0
\(57\) 1.00000 0.132453
\(58\) 0 0
\(59\) −1.50000 2.59808i −0.195283 0.338241i 0.751710 0.659494i \(-0.229229\pi\)
−0.946993 + 0.321253i \(0.895896\pi\)
\(60\) 0 0
\(61\) −3.50000 6.06218i −0.448129 0.776182i 0.550135 0.835076i \(-0.314576\pi\)
−0.998264 + 0.0588933i \(0.981243\pi\)
\(62\) 0 0
\(63\) −3.00000 + 5.19615i −0.377964 + 0.654654i
\(64\) 0 0
\(65\) 1.00000 + 3.46410i 0.124035 + 0.429669i
\(66\) 0 0
\(67\) 4.50000 7.79423i 0.549762 0.952217i −0.448528 0.893769i \(-0.648052\pi\)
0.998290 0.0584478i \(-0.0186151\pi\)
\(68\) 0 0
\(69\) −0.500000 0.866025i −0.0601929 0.104257i
\(70\) 0 0
\(71\) −3.50000 6.06218i −0.415374 0.719448i 0.580094 0.814550i \(-0.303016\pi\)
−0.995468 + 0.0951014i \(0.969682\pi\)
\(72\) 0 0
\(73\) 10.0000 1.17041 0.585206 0.810885i \(-0.301014\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) 0 0
\(75\) 0.500000 0.866025i 0.0577350 0.100000i
\(76\) 0 0
\(77\) −15.0000 −1.70941
\(78\) 0 0
\(79\) −16.0000 −1.80014 −0.900070 0.435745i \(-0.856485\pi\)
−0.900070 + 0.435745i \(0.856485\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) −2.50000 4.33013i −0.271163 0.469668i
\(86\) 0 0
\(87\) −4.50000 7.79423i −0.482451 0.835629i
\(88\) 0 0
\(89\) −7.50000 + 12.9904i −0.794998 + 1.37698i 0.127842 + 0.991795i \(0.459195\pi\)
−0.922840 + 0.385183i \(0.874138\pi\)
\(90\) 0 0
\(91\) −7.50000 + 7.79423i −0.786214 + 0.817057i
\(92\) 0 0
\(93\) −2.00000 + 3.46410i −0.207390 + 0.359211i
\(94\) 0 0
\(95\) 0.500000 + 0.866025i 0.0512989 + 0.0888523i
\(96\) 0 0
\(97\) 3.50000 + 6.06218i 0.355371 + 0.615521i 0.987181 0.159602i \(-0.0510211\pi\)
−0.631810 + 0.775123i \(0.717688\pi\)
\(98\) 0 0
\(99\) −10.0000 −1.00504
\(100\) 0 0
\(101\) 6.50000 11.2583i 0.646774 1.12025i −0.337115 0.941464i \(-0.609451\pi\)
0.983889 0.178782i \(-0.0572157\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 0 0
\(105\) 3.00000 0.292770
\(106\) 0 0
\(107\) −3.50000 + 6.06218i −0.338358 + 0.586053i −0.984124 0.177482i \(-0.943205\pi\)
0.645766 + 0.763535i \(0.276538\pi\)
\(108\) 0 0
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) −1.50000 2.59808i −0.142374 0.246598i
\(112\) 0 0
\(113\) −8.50000 14.7224i −0.799613 1.38497i −0.919868 0.392227i \(-0.871705\pi\)
0.120256 0.992743i \(-0.461629\pi\)
\(114\) 0 0
\(115\) 0.500000 0.866025i 0.0466252 0.0807573i
\(116\) 0 0
\(117\) −5.00000 + 5.19615i −0.462250 + 0.480384i
\(118\) 0 0
\(119\) 7.50000 12.9904i 0.687524 1.19083i
\(120\) 0 0
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) 0 0
\(123\) −0.500000 0.866025i −0.0450835 0.0780869i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 0.500000 0.866025i 0.0443678 0.0768473i −0.842989 0.537931i \(-0.819206\pi\)
0.887357 + 0.461084i \(0.152539\pi\)
\(128\) 0 0
\(129\) 3.00000 0.264135
\(130\) 0 0
\(131\) −4.00000 −0.349482 −0.174741 0.984614i \(-0.555909\pi\)
−0.174741 + 0.984614i \(0.555909\pi\)
\(132\) 0 0
\(133\) −1.50000 + 2.59808i −0.130066 + 0.225282i
\(134\) 0 0
\(135\) 5.00000 0.430331
\(136\) 0 0
\(137\) −0.500000 0.866025i −0.0427179 0.0739895i 0.843876 0.536538i \(-0.180268\pi\)
−0.886594 + 0.462549i \(0.846935\pi\)
\(138\) 0 0
\(139\) 6.50000 + 11.2583i 0.551323 + 0.954919i 0.998179 + 0.0603135i \(0.0192101\pi\)
−0.446857 + 0.894606i \(0.647457\pi\)
\(140\) 0 0
\(141\) −4.00000 + 6.92820i −0.336861 + 0.583460i
\(142\) 0 0
\(143\) −17.5000 4.33013i −1.46342 0.362103i
\(144\) 0 0
\(145\) 4.50000 7.79423i 0.373705 0.647275i
\(146\) 0 0
\(147\) 1.00000 + 1.73205i 0.0824786 + 0.142857i
\(148\) 0 0
\(149\) −7.50000 12.9904i −0.614424 1.06421i −0.990485 0.137619i \(-0.956055\pi\)
0.376061 0.926595i \(-0.377278\pi\)
\(150\) 0 0
\(151\) −16.0000 −1.30206 −0.651031 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) 0 0
\(153\) 5.00000 8.66025i 0.404226 0.700140i
\(154\) 0 0
\(155\) −4.00000 −0.321288
\(156\) 0 0
\(157\) −18.0000 −1.43656 −0.718278 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) 0 0
\(159\) 5.00000 8.66025i 0.396526 0.686803i
\(160\) 0 0
\(161\) 3.00000 0.236433
\(162\) 0 0
\(163\) 11.5000 + 19.9186i 0.900750 + 1.56014i 0.826523 + 0.562902i \(0.190315\pi\)
0.0742262 + 0.997241i \(0.476351\pi\)
\(164\) 0 0
\(165\) 2.50000 + 4.33013i 0.194625 + 0.337100i
\(166\) 0 0
\(167\) 8.50000 14.7224i 0.657750 1.13926i −0.323447 0.946246i \(-0.604842\pi\)
0.981197 0.193010i \(-0.0618249\pi\)
\(168\) 0 0
\(169\) −11.0000 + 6.92820i −0.846154 + 0.532939i
\(170\) 0 0
\(171\) −1.00000 + 1.73205i −0.0764719 + 0.132453i
\(172\) 0 0
\(173\) 11.5000 + 19.9186i 0.874329 + 1.51438i 0.857476 + 0.514524i \(0.172031\pi\)
0.0168528 + 0.999858i \(0.494635\pi\)
\(174\) 0 0
\(175\) 1.50000 + 2.59808i 0.113389 + 0.196396i
\(176\) 0 0
\(177\) −3.00000 −0.225494
\(178\) 0 0
\(179\) 9.50000 16.4545i 0.710063 1.22987i −0.254770 0.967002i \(-0.582000\pi\)
0.964833 0.262864i \(-0.0846670\pi\)
\(180\) 0 0
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) 0 0
\(183\) −7.00000 −0.517455
\(184\) 0 0
\(185\) 1.50000 2.59808i 0.110282 0.191014i
\(186\) 0 0
\(187\) 25.0000 1.82818
\(188\) 0 0
\(189\) 7.50000 + 12.9904i 0.545545 + 0.944911i
\(190\) 0 0
\(191\) −7.50000 12.9904i −0.542681 0.939951i −0.998749 0.0500060i \(-0.984076\pi\)
0.456068 0.889945i \(-0.349257\pi\)
\(192\) 0 0
\(193\) −6.50000 + 11.2583i −0.467880 + 0.810392i −0.999326 0.0366998i \(-0.988315\pi\)
0.531446 + 0.847092i \(0.321649\pi\)
\(194\) 0 0
\(195\) 3.50000 + 0.866025i 0.250640 + 0.0620174i
\(196\) 0 0
\(197\) −0.500000 + 0.866025i −0.0356235 + 0.0617018i −0.883287 0.468832i \(-0.844675\pi\)
0.847664 + 0.530534i \(0.178008\pi\)
\(198\) 0 0
\(199\) 10.5000 + 18.1865i 0.744325 + 1.28921i 0.950509 + 0.310696i \(0.100562\pi\)
−0.206184 + 0.978513i \(0.566105\pi\)
\(200\) 0 0
\(201\) −4.50000 7.79423i −0.317406 0.549762i
\(202\) 0 0
\(203\) 27.0000 1.89503
\(204\) 0 0
\(205\) 0.500000 0.866025i 0.0349215 0.0604858i
\(206\) 0 0
\(207\) 2.00000 0.139010
\(208\) 0 0
\(209\) −5.00000 −0.345857
\(210\) 0 0
\(211\) 9.50000 16.4545i 0.654007 1.13277i −0.328135 0.944631i \(-0.606420\pi\)
0.982142 0.188142i \(-0.0602466\pi\)
\(212\) 0 0
\(213\) −7.00000 −0.479632
\(214\) 0 0
\(215\) 1.50000 + 2.59808i 0.102299 + 0.177187i
\(216\) 0 0
\(217\) −6.00000 10.3923i −0.407307 0.705476i
\(218\) 0 0
\(219\) 5.00000 8.66025i 0.337869 0.585206i
\(220\) 0 0
\(221\) 12.5000 12.9904i 0.840841 0.873828i
\(222\) 0 0
\(223\) 0.500000 0.866025i 0.0334825 0.0579934i −0.848799 0.528716i \(-0.822674\pi\)
0.882281 + 0.470723i \(0.156007\pi\)
\(224\) 0 0
\(225\) 1.00000 + 1.73205i 0.0666667 + 0.115470i
\(226\) 0 0
\(227\) 1.50000 + 2.59808i 0.0995585 + 0.172440i 0.911502 0.411296i \(-0.134924\pi\)
−0.811943 + 0.583736i \(0.801590\pi\)
\(228\) 0 0
\(229\) −14.0000 −0.925146 −0.462573 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) 0 0
\(231\) −7.50000 + 12.9904i −0.493464 + 0.854704i
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) −8.00000 −0.521862
\(236\) 0 0
\(237\) −8.00000 + 13.8564i −0.519656 + 0.900070i
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 12.5000 + 21.6506i 0.805196 + 1.39464i 0.916159 + 0.400815i \(0.131273\pi\)
−0.110963 + 0.993825i \(0.535394\pi\)
\(242\) 0 0
\(243\) 8.00000 + 13.8564i 0.513200 + 0.888889i
\(244\) 0 0
\(245\) −1.00000 + 1.73205i −0.0638877 + 0.110657i
\(246\) 0 0
\(247\) −2.50000 + 2.59808i −0.159071 + 0.165312i
\(248\) 0 0
\(249\) 6.00000 10.3923i 0.380235 0.658586i
\(250\) 0 0
\(251\) −1.50000 2.59808i −0.0946792 0.163989i 0.814795 0.579748i \(-0.196849\pi\)
−0.909475 + 0.415759i \(0.863516\pi\)
\(252\) 0 0
\(253\) 2.50000 + 4.33013i 0.157174 + 0.272233i
\(254\) 0 0
\(255\) −5.00000 −0.313112
\(256\) 0 0
\(257\) −4.50000 + 7.79423i −0.280702 + 0.486191i −0.971558 0.236802i \(-0.923901\pi\)
0.690856 + 0.722993i \(0.257234\pi\)
\(258\) 0 0
\(259\) 9.00000 0.559233
\(260\) 0 0
\(261\) 18.0000 1.11417
\(262\) 0 0
\(263\) 4.50000 7.79423i 0.277482 0.480613i −0.693276 0.720672i \(-0.743833\pi\)
0.970758 + 0.240059i \(0.0771668\pi\)
\(264\) 0 0
\(265\) 10.0000 0.614295
\(266\) 0 0
\(267\) 7.50000 + 12.9904i 0.458993 + 0.794998i
\(268\) 0 0
\(269\) 12.5000 + 21.6506i 0.762138 + 1.32006i 0.941746 + 0.336324i \(0.109184\pi\)
−0.179608 + 0.983738i \(0.557483\pi\)
\(270\) 0 0
\(271\) 5.50000 9.52628i 0.334101 0.578680i −0.649211 0.760609i \(-0.724901\pi\)
0.983312 + 0.181928i \(0.0582339\pi\)
\(272\) 0 0
\(273\) 3.00000 + 10.3923i 0.181568 + 0.628971i
\(274\) 0 0
\(275\) −2.50000 + 4.33013i −0.150756 + 0.261116i
\(276\) 0 0
\(277\) 3.50000 + 6.06218i 0.210295 + 0.364241i 0.951807 0.306699i \(-0.0992243\pi\)
−0.741512 + 0.670940i \(0.765891\pi\)
\(278\) 0 0
\(279\) −4.00000 6.92820i −0.239474 0.414781i
\(280\) 0 0
\(281\) 14.0000 0.835170 0.417585 0.908638i \(-0.362877\pi\)
0.417585 + 0.908638i \(0.362877\pi\)
\(282\) 0 0
\(283\) 2.50000 4.33013i 0.148610 0.257399i −0.782104 0.623148i \(-0.785854\pi\)
0.930714 + 0.365748i \(0.119187\pi\)
\(284\) 0 0
\(285\) 1.00000 0.0592349
\(286\) 0 0
\(287\) 3.00000 0.177084
\(288\) 0 0
\(289\) −4.00000 + 6.92820i −0.235294 + 0.407541i
\(290\) 0 0
\(291\) 7.00000 0.410347
\(292\) 0 0
\(293\) −4.50000 7.79423i −0.262893 0.455344i 0.704117 0.710084i \(-0.251343\pi\)
−0.967009 + 0.254741i \(0.918010\pi\)
\(294\) 0 0
\(295\) −1.50000 2.59808i −0.0873334 0.151266i
\(296\) 0 0
\(297\) −12.5000 + 21.6506i −0.725324 + 1.25630i
\(298\) 0 0
\(299\) 3.50000 + 0.866025i 0.202410 + 0.0500835i
\(300\) 0 0
\(301\) −4.50000 + 7.79423i −0.259376 + 0.449252i
\(302\) 0 0
\(303\) −6.50000 11.2583i −0.373415 0.646774i
\(304\) 0 0
\(305\) −3.50000 6.06218i −0.200409 0.347119i
\(306\) 0 0
\(307\) 4.00000 0.228292 0.114146 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 0 0
\(309\) 4.00000 6.92820i 0.227552 0.394132i
\(310\) 0 0
\(311\) −32.0000 −1.81455 −0.907277 0.420534i \(-0.861843\pi\)
−0.907277 + 0.420534i \(0.861843\pi\)
\(312\) 0 0
\(313\) −6.00000 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) 0 0
\(315\) −3.00000 + 5.19615i −0.169031 + 0.292770i
\(316\) 0 0
\(317\) 30.0000 1.68497 0.842484 0.538721i \(-0.181092\pi\)
0.842484 + 0.538721i \(0.181092\pi\)
\(318\) 0 0
\(319\) 22.5000 + 38.9711i 1.25976 + 2.18197i
\(320\) 0 0
\(321\) 3.50000 + 6.06218i 0.195351 + 0.338358i
\(322\) 0 0
\(323\) 2.50000 4.33013i 0.139104 0.240935i
\(324\) 0 0
\(325\) 1.00000 + 3.46410i 0.0554700 + 0.192154i
\(326\) 0 0
\(327\) 1.00000 1.73205i 0.0553001 0.0957826i
\(328\) 0 0
\(329\) −12.0000 20.7846i −0.661581 1.14589i
\(330\) 0 0
\(331\) 14.5000 + 25.1147i 0.796992 + 1.38043i 0.921567 + 0.388221i \(0.126910\pi\)
−0.124574 + 0.992210i \(0.539757\pi\)
\(332\) 0 0
\(333\) 6.00000 0.328798
\(334\) 0 0
\(335\) 4.50000 7.79423i 0.245861 0.425844i
\(336\) 0 0
\(337\) −18.0000 −0.980522 −0.490261 0.871576i \(-0.663099\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) 0 0
\(339\) −17.0000 −0.923313
\(340\) 0 0
\(341\) 10.0000 17.3205i 0.541530 0.937958i
\(342\) 0 0
\(343\) 15.0000 0.809924
\(344\) 0 0
\(345\) −0.500000 0.866025i −0.0269191 0.0466252i
\(346\) 0 0
\(347\) −16.5000 28.5788i −0.885766 1.53419i −0.844833 0.535031i \(-0.820300\pi\)
−0.0409337 0.999162i \(-0.513033\pi\)
\(348\) 0 0
\(349\) 2.50000 4.33013i 0.133822 0.231786i −0.791325 0.611396i \(-0.790608\pi\)
0.925147 + 0.379610i \(0.123942\pi\)
\(350\) 0 0
\(351\) 5.00000 + 17.3205i 0.266880 + 0.924500i
\(352\) 0 0
\(353\) 7.50000 12.9904i 0.399185 0.691408i −0.594441 0.804139i \(-0.702627\pi\)
0.993626 + 0.112731i \(0.0359599\pi\)
\(354\) 0 0
\(355\) −3.50000 6.06218i −0.185761 0.321747i
\(356\) 0 0
\(357\) −7.50000 12.9904i −0.396942 0.687524i
\(358\) 0 0
\(359\) −8.00000 −0.422224 −0.211112 0.977462i \(-0.567708\pi\)
−0.211112 + 0.977462i \(0.567708\pi\)
\(360\) 0 0
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) 0 0
\(363\) −14.0000 −0.734809
\(364\) 0 0
\(365\) 10.0000 0.523424
\(366\) 0 0
\(367\) 8.50000 14.7224i 0.443696 0.768505i −0.554264 0.832341i \(-0.687000\pi\)
0.997960 + 0.0638362i \(0.0203335\pi\)
\(368\) 0 0
\(369\) 2.00000 0.104116
\(370\) 0 0
\(371\) 15.0000 + 25.9808i 0.778761 + 1.34885i
\(372\) 0 0
\(373\) −10.5000 18.1865i −0.543669 0.941663i −0.998689 0.0511818i \(-0.983701\pi\)
0.455020 0.890481i \(-0.349632\pi\)
\(374\) 0 0
\(375\) 0.500000 0.866025i 0.0258199 0.0447214i
\(376\) 0 0
\(377\) 31.5000 + 7.79423i 1.62233 + 0.401423i
\(378\) 0 0
\(379\) 7.50000 12.9904i 0.385249 0.667271i −0.606555 0.795042i \(-0.707449\pi\)
0.991804 + 0.127771i \(0.0407822\pi\)
\(380\) 0 0
\(381\) −0.500000 0.866025i −0.0256158 0.0443678i
\(382\) 0 0
\(383\) −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
\(385\) −15.0000 −0.764471
\(386\) 0 0
\(387\) −3.00000 + 5.19615i −0.152499 + 0.264135i
\(388\) 0 0
\(389\) −30.0000 −1.52106 −0.760530 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) 0 0
\(391\) −5.00000 −0.252861
\(392\) 0 0
\(393\) −2.00000 + 3.46410i −0.100887 + 0.174741i
\(394\) 0 0
\(395\) −16.0000 −0.805047
\(396\) 0 0
\(397\) −4.50000 7.79423i −0.225849 0.391181i 0.730725 0.682672i \(-0.239182\pi\)
−0.956574 + 0.291491i \(0.905849\pi\)
\(398\) 0 0
\(399\) 1.50000 + 2.59808i 0.0750939 + 0.130066i
\(400\) 0 0
\(401\) −11.5000 + 19.9186i −0.574283 + 0.994687i 0.421837 + 0.906672i \(0.361386\pi\)
−0.996119 + 0.0880147i \(0.971948\pi\)
\(402\) 0 0
\(403\) −4.00000 13.8564i −0.199254 0.690237i
\(404\) 0 0
\(405\) −0.500000 + 0.866025i −0.0248452 + 0.0430331i
\(406\) 0 0
\(407\) 7.50000 + 12.9904i 0.371761 + 0.643909i
\(408\) 0 0
\(409\) −3.50000 6.06218i −0.173064 0.299755i 0.766426 0.642333i \(-0.222033\pi\)
−0.939490 + 0.342578i \(0.888700\pi\)
\(410\) 0 0
\(411\) −1.00000 −0.0493264
\(412\) 0 0
\(413\) 4.50000 7.79423i 0.221431 0.383529i
\(414\) 0 0
\(415\) 12.0000 0.589057
\(416\) 0 0
\(417\) 13.0000 0.636613
\(418\) 0 0
\(419\) −12.5000 + 21.6506i −0.610665 + 1.05770i 0.380464 + 0.924796i \(0.375764\pi\)
−0.991129 + 0.132907i \(0.957569\pi\)
\(420\) 0 0
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 0 0
\(423\) −8.00000 13.8564i −0.388973 0.673722i
\(424\) 0 0
\(425\) −2.50000 4.33013i −0.121268 0.210042i
\(426\) 0 0
\(427\) 10.5000 18.1865i 0.508131 0.880108i
\(428\) 0 0
\(429\) −12.5000 + 12.9904i −0.603506 + 0.627182i
\(430\) 0 0
\(431\) 1.50000 2.59808i 0.0722525 0.125145i −0.827636 0.561266i \(-0.810315\pi\)
0.899888 + 0.436121i \(0.143648\pi\)
\(432\) 0 0
\(433\) 5.50000 + 9.52628i 0.264313 + 0.457804i 0.967383 0.253317i \(-0.0815214\pi\)
−0.703070 + 0.711120i \(0.748188\pi\)
\(434\) 0 0
\(435\) −4.50000 7.79423i −0.215758 0.373705i
\(436\) 0 0
\(437\) 1.00000 0.0478365
\(438\) 0 0
\(439\) 7.50000 12.9904i 0.357955 0.619997i −0.629664 0.776868i \(-0.716807\pi\)
0.987619 + 0.156871i \(0.0501406\pi\)
\(440\) 0 0
\(441\) −4.00000 −0.190476
\(442\) 0 0
\(443\) −32.0000 −1.52037 −0.760183 0.649709i \(-0.774891\pi\)
−0.760183 + 0.649709i \(0.774891\pi\)
\(444\) 0 0
\(445\) −7.50000 + 12.9904i −0.355534 + 0.615803i
\(446\) 0 0
\(447\) −15.0000 −0.709476
\(448\) 0 0
\(449\) −9.50000 16.4545i −0.448333 0.776535i 0.549945 0.835201i \(-0.314649\pi\)
−0.998278 + 0.0586659i \(0.981315\pi\)
\(450\) 0 0
\(451\) 2.50000 + 4.33013i 0.117720 + 0.203898i
\(452\) 0 0
\(453\) −8.00000 + 13.8564i −0.375873 + 0.651031i
\(454\) 0 0
\(455\) −7.50000 + 7.79423i −0.351605 + 0.365399i
\(456\) 0 0
\(457\) −2.50000 + 4.33013i −0.116945 + 0.202555i −0.918556 0.395292i \(-0.870643\pi\)
0.801611 + 0.597847i \(0.203977\pi\)
\(458\) 0 0
\(459\) −12.5000 21.6506i −0.583450 1.01057i
\(460\) 0 0
\(461\) −7.50000 12.9904i −0.349310 0.605022i 0.636817 0.771015i \(-0.280251\pi\)
−0.986127 + 0.165992i \(0.946917\pi\)
\(462\) 0 0
\(463\) −4.00000 −0.185896 −0.0929479 0.995671i \(-0.529629\pi\)
−0.0929479 + 0.995671i \(0.529629\pi\)
\(464\) 0 0
\(465\) −2.00000 + 3.46410i −0.0927478 + 0.160644i
\(466\) 0 0
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 0 0
\(469\) 27.0000 1.24674
\(470\) 0 0
\(471\) −9.00000 + 15.5885i −0.414698 + 0.718278i
\(472\) 0 0
\(473\) −15.0000 −0.689701
\(474\) 0 0
\(475\) 0.500000 + 0.866025i 0.0229416 + 0.0397360i
\(476\) 0 0
\(477\) 10.0000 + 17.3205i 0.457869 + 0.793052i
\(478\) 0 0
\(479\) 5.50000 9.52628i 0.251301 0.435267i −0.712583 0.701588i \(-0.752475\pi\)
0.963884 + 0.266321i \(0.0858081\pi\)
\(480\) 0 0
\(481\) 10.5000 + 2.59808i 0.478759 + 0.118462i
\(482\) 0 0
\(483\) 1.50000 2.59808i 0.0682524 0.118217i
\(484\) 0 0
\(485\) 3.50000 + 6.06218i 0.158927 + 0.275269i
\(486\) 0 0
\(487\) −12.5000 21.6506i −0.566429 0.981084i −0.996915 0.0784867i \(-0.974991\pi\)
0.430486 0.902597i \(-0.358342\pi\)
\(488\) 0 0
\(489\) 23.0000 1.04010
\(490\) 0 0
\(491\) −4.50000 + 7.79423i −0.203082 + 0.351749i −0.949520 0.313707i \(-0.898429\pi\)
0.746438 + 0.665455i \(0.231763\pi\)
\(492\) 0 0
\(493\) −45.0000 −2.02670
\(494\) 0 0
\(495\) −10.0000 −0.449467
\(496\) 0 0
\(497\) 10.5000 18.1865i 0.470989 0.815778i
\(498\) 0 0
\(499\) −32.0000 −1.43252 −0.716258 0.697835i \(-0.754147\pi\)
−0.716258 + 0.697835i \(0.754147\pi\)
\(500\) 0 0
\(501\) −8.50000 14.7224i −0.379752 0.657750i
\(502\) 0 0
\(503\) −14.5000 25.1147i −0.646523 1.11981i −0.983948 0.178458i \(-0.942889\pi\)
0.337424 0.941353i \(-0.390444\pi\)
\(504\) 0 0
\(505\) 6.50000 11.2583i 0.289246 0.500989i
\(506\) 0 0
\(507\) 0.500000 + 12.9904i 0.0222058 + 0.576923i
\(508\) 0 0
\(509\) −13.5000 + 23.3827i −0.598377 + 1.03642i 0.394684 + 0.918817i \(0.370854\pi\)
−0.993061 + 0.117602i \(0.962479\pi\)
\(510\) 0 0
\(511\) 15.0000 + 25.9808i 0.663561 + 1.14932i
\(512\) 0 0
\(513\) 2.50000 + 4.33013i 0.110378 + 0.191180i
\(514\) 0 0
\(515\) 8.00000 0.352522
\(516\) 0 0
\(517\) 20.0000 34.6410i 0.879599 1.52351i
\(518\) 0 0
\(519\) 23.0000 1.00959
\(520\) 0 0
\(521\) −10.0000 −0.438108 −0.219054 0.975713i \(-0.570297\pi\)
−0.219054 + 0.975713i \(0.570297\pi\)
\(522\) 0 0
\(523\) −9.50000 + 16.4545i −0.415406 + 0.719504i −0.995471 0.0950659i \(-0.969694\pi\)
0.580065 + 0.814570i \(0.303027\pi\)
\(524\) 0 0
\(525\) 3.00000 0.130931
\(526\) 0 0
\(527\) 10.0000 + 17.3205i 0.435607 + 0.754493i
\(528\) 0 0
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) 0 0
\(531\) 3.00000 5.19615i 0.130189 0.225494i
\(532\) 0 0
\(533\) 3.50000 + 0.866025i 0.151602 + 0.0375117i
\(534\) 0 0
\(535\) −3.50000 + 6.06218i −0.151318 + 0.262091i
\(536\) 0 0
\(537\) −9.50000 16.4545i −0.409955 0.710063i
\(538\) 0 0
\(539\) −5.00000 8.66025i −0.215365 0.373024i
\(540\) 0 0
\(541\) 10.0000 0.429934 0.214967 0.976621i \(-0.431036\pi\)
0.214967 + 0.976621i \(0.431036\pi\)
\(542\) 0 0
\(543\) −7.00000 + 12.1244i −0.300399 + 0.520306i
\(544\) 0 0
\(545\) 2.00000 0.0856706
\(546\) 0 0
\(547\) −8.00000 −0.342055 −0.171028 0.985266i \(-0.554709\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(548\) 0 0
\(549\) 7.00000 12.1244i 0.298753 0.517455i
\(550\) 0 0
\(551\) 9.00000 0.383413
\(552\) 0 0
\(553\) −24.0000 41.5692i −1.02058 1.76770i
\(554\) 0 0
\(555\) −1.50000 2.59808i −0.0636715 0.110282i
\(556\) 0 0
\(557\) −6.50000 + 11.2583i −0.275414 + 0.477031i −0.970239 0.242147i \(-0.922148\pi\)
0.694826 + 0.719178i \(0.255482\pi\)
\(558\) 0 0
\(559\) −7.50000 + 7.79423i −0.317216 + 0.329661i
\(560\) 0 0
\(561\) 12.5000 21.6506i 0.527750 0.914091i
\(562\) 0 0
\(563\) 19.5000 + 33.7750i 0.821827 + 1.42345i 0.904320 + 0.426855i \(0.140378\pi\)
−0.0824933 + 0.996592i \(0.526288\pi\)
\(564\) 0 0
\(565\) −8.50000 14.7224i −0.357598 0.619377i
\(566\) 0 0
\(567\) −3.00000 −0.125988
\(568\) 0 0
\(569\) 18.5000 32.0429i 0.775560 1.34331i −0.158919 0.987292i \(-0.550801\pi\)
0.934479 0.356018i \(-0.115866\pi\)
\(570\) 0 0
\(571\) 8.00000 0.334790 0.167395 0.985890i \(-0.446465\pi\)
0.167395 + 0.985890i \(0.446465\pi\)
\(572\) 0 0
\(573\) −15.0000 −0.626634
\(574\) 0 0
\(575\) 0.500000 0.866025i 0.0208514 0.0361158i
\(576\) 0 0
\(577\) −38.0000 −1.58196 −0.790980 0.611842i \(-0.790429\pi\)
−0.790980 + 0.611842i \(0.790429\pi\)
\(578\) 0 0
\(579\) 6.50000 + 11.2583i 0.270131 + 0.467880i
\(580\) 0 0
\(581\) 18.0000 + 31.1769i 0.746766 + 1.29344i
\(582\) 0 0
\(583\) −25.0000 + 43.3013i −1.03539 + 1.79336i
\(584\) 0 0
\(585\) −5.00000 + 5.19615i −0.206725 + 0.214834i
\(586\) 0 0
\(587\) −11.5000 + 19.9186i −0.474656 + 0.822128i −0.999579 0.0290218i \(-0.990761\pi\)
0.524923 + 0.851150i \(0.324094\pi\)
\(588\) 0 0
\(589\) −2.00000 3.46410i −0.0824086 0.142736i
\(590\) 0 0
\(591\) 0.500000 + 0.866025i 0.0205673 + 0.0356235i
\(592\) 0 0
\(593\) 18.0000 0.739171 0.369586 0.929197i \(-0.379500\pi\)
0.369586 + 0.929197i \(0.379500\pi\)
\(594\) 0 0
\(595\) 7.50000 12.9904i 0.307470 0.532554i
\(596\) 0 0
\(597\) 21.0000 0.859473
\(598\) 0 0
\(599\) 48.0000 1.96123 0.980613 0.195952i \(-0.0627798\pi\)
0.980613 + 0.195952i \(0.0627798\pi\)
\(600\) 0 0
\(601\) 2.50000 4.33013i 0.101977 0.176630i −0.810522 0.585708i \(-0.800816\pi\)
0.912499 + 0.409079i \(0.134150\pi\)
\(602\) 0 0
\(603\) 18.0000 0.733017
\(604\) 0 0
\(605\) −7.00000 12.1244i −0.284590 0.492925i
\(606\) 0 0
\(607\) 7.50000 + 12.9904i 0.304416 + 0.527263i 0.977131 0.212638i \(-0.0682055\pi\)
−0.672715 + 0.739901i \(0.734872\pi\)
\(608\) 0 0
\(609\) 13.5000 23.3827i 0.547048 0.947514i
\(610\) 0 0
\(611\) −8.00000 27.7128i −0.323645 1.12114i
\(612\) 0 0
\(613\) 11.5000 19.9186i 0.464481 0.804504i −0.534697 0.845044i \(-0.679574\pi\)
0.999178 + 0.0405396i \(0.0129077\pi\)
\(614\) 0 0
\(615\) −0.500000 0.866025i −0.0201619 0.0349215i
\(616\) 0 0
\(617\) 7.50000 + 12.9904i 0.301939 + 0.522973i 0.976575 0.215177i \(-0.0690329\pi\)
−0.674636 + 0.738150i \(0.735700\pi\)
\(618\) 0 0
\(619\) −36.0000 −1.44696 −0.723481 0.690344i \(-0.757459\pi\)
−0.723481 + 0.690344i \(0.757459\pi\)
\(620\) 0 0
\(621\) 2.50000 4.33013i 0.100322 0.173762i
\(622\) 0 0
\(623\) −45.0000 −1.80289
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −2.50000 + 4.33013i −0.0998404 + 0.172929i
\(628\) 0 0
\(629\) −15.0000 −0.598089
\(630\) 0 0
\(631\) −5.50000 9.52628i −0.218952 0.379235i 0.735536 0.677485i \(-0.236930\pi\)
−0.954488 + 0.298250i \(0.903597\pi\)
\(632\) 0 0
\(633\) −9.50000 16.4545i −0.377591 0.654007i
\(634\) 0 0
\(635\) 0.500000 0.866025i 0.0198419 0.0343672i
\(636\) 0 0
\(637\) −7.00000 1.73205i −0.277350 0.0686264i
\(638\) 0 0
\(639\) 7.00000 12.1244i 0.276916 0.479632i
\(640\) 0 0
\(641\) 22.5000 + 38.9711i 0.888697 + 1.53927i 0.841417 + 0.540386i \(0.181722\pi\)
0.0472793 + 0.998882i \(0.484945\pi\)
\(642\) 0 0
\(643\) −18.5000 32.0429i −0.729569 1.26365i −0.957066 0.289871i \(-0.906387\pi\)
0.227497 0.973779i \(-0.426946\pi\)
\(644\) 0 0
\(645\) 3.00000 0.118125
\(646\) 0 0
\(647\) −7.50000 + 12.9904i −0.294855 + 0.510705i −0.974951 0.222419i \(-0.928605\pi\)
0.680096 + 0.733123i \(0.261938\pi\)
\(648\) 0 0
\(649\) 15.0000 0.588802
\(650\) 0 0
\(651\) −12.0000 −0.470317
\(652\) 0 0
\(653\) 1.50000 2.59808i 0.0586995 0.101671i −0.835182 0.549973i \(-0.814638\pi\)
0.893882 + 0.448303i \(0.147971\pi\)
\(654\) 0 0
\(655\) −4.00000 −0.156293
\(656\) 0 0
\(657\) 10.0000 + 17.3205i 0.390137 + 0.675737i
\(658\) 0 0
\(659\) −11.5000 19.9186i −0.447976 0.775918i 0.550278 0.834982i \(-0.314522\pi\)
−0.998254 + 0.0590638i \(0.981188\pi\)
\(660\) 0 0
\(661\) −17.5000 + 30.3109i −0.680671 + 1.17896i 0.294105 + 0.955773i \(0.404978\pi\)
−0.974776 + 0.223184i \(0.928355\pi\)
\(662\) 0 0
\(663\) −5.00000 17.3205i −0.194184 0.672673i
\(664\) 0 0
\(665\) −1.50000 + 2.59808i −0.0581675 + 0.100749i
\(666\) 0 0
\(667\) −4.50000 7.79423i −0.174241 0.301794i
\(668\) 0 0
\(669\) −0.500000 0.866025i −0.0193311 0.0334825i
\(670\) 0 0
\(671\) 35.0000 1.35116
\(672\) 0 0
\(673\) 3.50000 6.06218i 0.134915 0.233680i −0.790650 0.612268i \(-0.790257\pi\)
0.925565 + 0.378589i \(0.123591\pi\)
\(674\) 0 0
\(675\) 5.00000 0.192450
\(676\) 0 0
\(677\) −2.00000 −0.0768662 −0.0384331 0.999261i \(-0.512237\pi\)
−0.0384331 + 0.999261i \(0.512237\pi\)
\(678\) 0 0
\(679\) −10.5000 + 18.1865i −0.402953 + 0.697935i
\(680\) 0 0
\(681\) 3.00000 0.114960
\(682\) 0 0
\(683\) −10.5000 18.1865i −0.401771 0.695888i 0.592168 0.805814i \(-0.298272\pi\)
−0.993940 + 0.109926i \(0.964939\pi\)
\(684\) 0 0
\(685\) −0.500000 0.866025i −0.0191040 0.0330891i
\(686\) 0 0
\(687\) −7.00000 + 12.1244i −0.267067 + 0.462573i
\(688\) 0 0
\(689\) 10.0000 + 34.6410i 0.380970 + 1.31972i
\(690\) 0 0
\(691\) 3.50000 6.06218i 0.133146 0.230616i −0.791742 0.610856i \(-0.790825\pi\)
0.924888 + 0.380240i \(0.124159\pi\)
\(692\) 0 0
\(693\) −15.0000 25.9808i −0.569803 0.986928i
\(694\) 0 0
\(695\) 6.50000 + 11.2583i 0.246559 + 0.427053i
\(696\) 0 0
\(697\) −5.00000 −0.189389
\(698\) 0 0
\(699\) −3.00000 + 5.19615i −0.113470 + 0.196537i
\(700\) 0 0
\(701\) 10.0000 0.377695 0.188847 0.982006i \(-0.439525\pi\)
0.188847 + 0.982006i \(0.439525\pi\)
\(702\) 0 0
\(703\) 3.00000 0.113147
\(704\) 0 0
\(705\) −4.00000 + 6.92820i −0.150649 + 0.260931i
\(706\) 0 0
\(707\) 39.0000 1.46675
\(708\) 0 0
\(709\) 8.50000 + 14.7224i 0.319224 + 0.552913i 0.980326 0.197383i \(-0.0632444\pi\)
−0.661102 + 0.750296i \(0.729911\pi\)
\(710\) 0 0
\(711\) −16.0000 27.7128i −0.600047 1.03931i
\(712\) 0 0
\(713\) −2.00000 + 3.46410i −0.0749006 + 0.129732i
\(714\) 0 0
\(715\) −17.5000 4.33013i −0.654463 0.161938i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 10.5000 + 18.1865i 0.391584 + 0.678243i 0.992659 0.120950i \(-0.0385939\pi\)
−0.601075 + 0.799193i \(0.705261\pi\)
\(720\) 0 0
\(721\) 12.0000 + 20.7846i 0.446903 + 0.774059i
\(722\) 0 0
\(723\) 25.0000 0.929760
\(724\) 0 0
\(725\) 4.50000 7.79423i 0.167126 0.289470i
\(726\) 0 0
\(727\) 12.0000 0.445055 0.222528 0.974926i \(-0.428569\pi\)
0.222528 + 0.974926i \(0.428569\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 7.50000 12.9904i 0.277398 0.480467i
\(732\) 0 0
\(733\) 46.0000 1.69905 0.849524 0.527549i \(-0.176889\pi\)
0.849524 + 0.527549i \(0.176889\pi\)
\(734\) 0 0
\(735\) 1.00000 + 1.73205i 0.0368856 + 0.0638877i
\(736\) 0 0
\(737\) 22.5000 + 38.9711i 0.828798 + 1.43552i
\(738\) 0 0
\(739\) 7.50000 12.9904i 0.275892 0.477859i −0.694468 0.719524i \(-0.744360\pi\)
0.970360 + 0.241665i \(0.0776935\pi\)
\(740\) 0 0
\(741\) 1.00000 + 3.46410i 0.0367359 + 0.127257i
\(742\) 0 0
\(743\) 8.50000 14.7224i 0.311835 0.540114i −0.666925 0.745125i \(-0.732390\pi\)
0.978760 + 0.205011i \(0.0657231\pi\)
\(744\) 0 0
\(745\) −7.50000 12.9904i −0.274779 0.475931i
\(746\) 0 0
\(747\) 12.0000 + 20.7846i 0.439057 + 0.760469i
\(748\) 0 0
\(749\) −21.0000 −0.767323
\(750\) 0 0
\(751\) −16.5000 + 28.5788i −0.602094 + 1.04286i 0.390410 + 0.920641i \(0.372333\pi\)
−0.992504 + 0.122216i \(0.961000\pi\)
\(752\) 0 0
\(753\) −3.00000 −0.109326
\(754\) 0 0
\(755\) −16.0000 −0.582300
\(756\) 0 0
\(757\) 23.5000 40.7032i 0.854122 1.47938i −0.0233351 0.999728i \(-0.507428\pi\)
0.877457 0.479655i \(-0.159238\pi\)
\(758\) 0 0
\(759\) 5.00000 0.181489
\(760\) 0 0
\(761\) 18.5000 + 32.0429i 0.670624 + 1.16156i 0.977727 + 0.209879i \(0.0673071\pi\)
−0.307103 + 0.951676i \(0.599360\pi\)
\(762\) 0 0
\(763\) 3.00000 + 5.19615i 0.108607 + 0.188113i
\(764\) 0 0
\(765\) 5.00000 8.66025i 0.180775 0.313112i
\(766\) 0 0
\(767\) 7.50000 7.79423i 0.270809 0.281433i
\(768\) 0 0
\(769\) −21.5000 + 37.2391i −0.775310 + 1.34288i 0.159310 + 0.987229i \(0.449073\pi\)
−0.934620 + 0.355647i \(0.884260\pi\)
\(770\) 0 0
\(771\) 4.50000 + 7.79423i 0.162064 + 0.280702i
\(772\) 0 0
\(773\) 19.5000 + 33.7750i 0.701366 + 1.21480i 0.967987 + 0.251000i \(0.0807596\pi\)
−0.266621 + 0.963802i \(0.585907\pi\)
\(774\) 0 0
\(775\) −4.00000 −0.143684
\(776\) 0 0
\(777\) 4.50000 7.79423i 0.161437 0.279616i
\(778\) 0 0
\(779\) 1.00000 0.0358287
\(780\) 0 0
\(781\) 35.0000 1.25240
\(782\) 0 0
\(783\) 22.5000 38.9711i 0.804084 1.39272i
\(784\) 0 0
\(785\) −18.0000 −0.642448
\(786\) 0 0
\(787\) −2.50000 4.33013i −0.0891154 0.154352i 0.818022 0.575187i \(-0.195071\pi\)
−0.907137 + 0.420834i \(0.861737\pi\)
\(788\) 0 0
\(789\) −4.50000 7.79423i −0.160204 0.277482i
\(790\) 0