Properties

Label 520.2.d.c.209.7
Level $520$
Weight $2$
Character 520.209
Analytic conductor $4.152$
Analytic rank $0$
Dimension $10$
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(209,520)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(520, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("520.209");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 520.d (of order \(2\), degree \(1\), 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: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 4x^{9} + 2x^{8} + 16x^{7} - 15x^{6} - 40x^{5} - 75x^{4} + 400x^{3} + 250x^{2} - 2500x + 3125 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 209.7
Root \(-2.16128 + 0.573465i\) of defining polynomial
Character \(\chi\) \(=\) 520.209
Dual form 520.2.d.c.209.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.76881i q^{3} +(2.16128 - 0.573465i) q^{5} -2.87131i q^{7} -0.128689 q^{9} +O(q^{10})\) \(q+1.76881i q^{3} +(2.16128 - 0.573465i) q^{5} -2.87131i q^{7} -0.128689 q^{9} +4.07313 q^{11} -1.00000i q^{13} +(1.01435 + 3.82290i) q^{15} -6.32256i q^{17} -5.46449 q^{19} +5.07880 q^{21} +4.09137i q^{23} +(4.34228 - 2.47884i) q^{25} +5.07880i q^{27} +8.31210 q^{29} -2.82937 q^{31} +7.20460i q^{33} +(-1.64660 - 6.20571i) q^{35} +7.77382i q^{37} +1.76881 q^{39} -12.0365 q^{41} +6.06267i q^{43} +(-0.278133 + 0.0737987i) q^{45} +6.87131i q^{47} -1.24443 q^{49} +11.1834 q^{51} +1.24376i q^{53} +(8.80318 - 2.33580i) q^{55} -9.66564i q^{57} -10.5720 q^{59} +8.22324 q^{61} +0.369506i q^{63} +(-0.573465 - 2.16128i) q^{65} -5.38313i q^{67} -7.23686 q^{69} +11.0308 q^{71} -2.77448i q^{73} +(4.38460 + 7.68066i) q^{75} -11.6952i q^{77} -9.83148 q^{79} -9.36951 q^{81} -10.0547i q^{83} +(-3.62577 - 13.6648i) q^{85} +14.7025i q^{87} -12.9390 q^{89} -2.87131 q^{91} -5.00462i q^{93} +(-11.8103 + 3.13369i) q^{95} -0.205002i q^{97} -0.524168 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 4 q^{5} - 30 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 4 q^{5} - 30 q^{9} + 16 q^{11} + 4 q^{15} - 36 q^{19} + 4 q^{21} + 12 q^{25} - 4 q^{29} - 8 q^{31} + 18 q^{35} - 4 q^{39} - 24 q^{41} + 36 q^{45} - 38 q^{49} - 4 q^{51} + 32 q^{55} - 28 q^{59} + 20 q^{61} + 4 q^{65} - 72 q^{69} + 36 q^{71} + 62 q^{75} - 16 q^{79} + 18 q^{81} + 8 q^{85} + 12 q^{89} + 52 q^{95} - 68 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(41\) \(261\) \(391\) \(417\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

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
\(3\) 1.76881i 1.02122i 0.859812 + 0.510611i \(0.170581\pi\)
−0.859812 + 0.510611i \(0.829419\pi\)
\(4\) 0 0
\(5\) 2.16128 0.573465i 0.966554 0.256461i
\(6\) 0 0
\(7\) 2.87131i 1.08525i −0.839974 0.542627i \(-0.817430\pi\)
0.839974 0.542627i \(-0.182570\pi\)
\(8\) 0 0
\(9\) −0.128689 −0.0428964
\(10\) 0 0
\(11\) 4.07313 1.22810 0.614048 0.789269i \(-0.289540\pi\)
0.614048 + 0.789269i \(0.289540\pi\)
\(12\) 0 0
\(13\) 1.00000i 0.277350i
\(14\) 0 0
\(15\) 1.01435 + 3.82290i 0.261904 + 0.987068i
\(16\) 0 0
\(17\) 6.32256i 1.53345i −0.641978 0.766723i \(-0.721886\pi\)
0.641978 0.766723i \(-0.278114\pi\)
\(18\) 0 0
\(19\) −5.46449 −1.25364 −0.626820 0.779164i \(-0.715644\pi\)
−0.626820 + 0.779164i \(0.715644\pi\)
\(20\) 0 0
\(21\) 5.07880 1.10829
\(22\) 0 0
\(23\) 4.09137i 0.853110i 0.904462 + 0.426555i \(0.140273\pi\)
−0.904462 + 0.426555i \(0.859727\pi\)
\(24\) 0 0
\(25\) 4.34228 2.47884i 0.868455 0.495768i
\(26\) 0 0
\(27\) 5.07880i 0.977416i
\(28\) 0 0
\(29\) 8.31210 1.54352 0.771759 0.635915i \(-0.219377\pi\)
0.771759 + 0.635915i \(0.219377\pi\)
\(30\) 0 0
\(31\) −2.82937 −0.508170 −0.254085 0.967182i \(-0.581774\pi\)
−0.254085 + 0.967182i \(0.581774\pi\)
\(32\) 0 0
\(33\) 7.20460i 1.25416i
\(34\) 0 0
\(35\) −1.64660 6.20571i −0.278326 1.04896i
\(36\) 0 0
\(37\) 7.77382i 1.27801i 0.769204 + 0.639004i \(0.220653\pi\)
−0.769204 + 0.639004i \(0.779347\pi\)
\(38\) 0 0
\(39\) 1.76881 0.283236
\(40\) 0 0
\(41\) −12.0365 −1.87978 −0.939891 0.341474i \(-0.889074\pi\)
−0.939891 + 0.341474i \(0.889074\pi\)
\(42\) 0 0
\(43\) 6.06267i 0.924549i 0.886737 + 0.462274i \(0.152966\pi\)
−0.886737 + 0.462274i \(0.847034\pi\)
\(44\) 0 0
\(45\) −0.278133 + 0.0737987i −0.0414617 + 0.0110013i
\(46\) 0 0
\(47\) 6.87131i 1.00228i 0.865365 + 0.501142i \(0.167087\pi\)
−0.865365 + 0.501142i \(0.832913\pi\)
\(48\) 0 0
\(49\) −1.24443 −0.177775
\(50\) 0 0
\(51\) 11.1834 1.56599
\(52\) 0 0
\(53\) 1.24376i 0.170843i 0.996345 + 0.0854217i \(0.0272238\pi\)
−0.996345 + 0.0854217i \(0.972776\pi\)
\(54\) 0 0
\(55\) 8.80318 2.33580i 1.18702 0.314959i
\(56\) 0 0
\(57\) 9.66564i 1.28025i
\(58\) 0 0
\(59\) −10.5720 −1.37636 −0.688178 0.725542i \(-0.741589\pi\)
−0.688178 + 0.725542i \(0.741589\pi\)
\(60\) 0 0
\(61\) 8.22324 1.05288 0.526439 0.850213i \(-0.323527\pi\)
0.526439 + 0.850213i \(0.323527\pi\)
\(62\) 0 0
\(63\) 0.369506i 0.0465534i
\(64\) 0 0
\(65\) −0.573465 2.16128i −0.0711296 0.268074i
\(66\) 0 0
\(67\) 5.38313i 0.657653i −0.944390 0.328827i \(-0.893347\pi\)
0.944390 0.328827i \(-0.106653\pi\)
\(68\) 0 0
\(69\) −7.23686 −0.871216
\(70\) 0 0
\(71\) 11.0308 1.30912 0.654558 0.756012i \(-0.272855\pi\)
0.654558 + 0.756012i \(0.272855\pi\)
\(72\) 0 0
\(73\) 2.77448i 0.324729i −0.986731 0.162364i \(-0.948088\pi\)
0.986731 0.162364i \(-0.0519120\pi\)
\(74\) 0 0
\(75\) 4.38460 + 7.68066i 0.506290 + 0.886886i
\(76\) 0 0
\(77\) 11.6952i 1.33279i
\(78\) 0 0
\(79\) −9.83148 −1.10613 −0.553064 0.833139i \(-0.686542\pi\)
−0.553064 + 0.833139i \(0.686542\pi\)
\(80\) 0 0
\(81\) −9.36951 −1.04106
\(82\) 0 0
\(83\) 10.0547i 1.10365i −0.833960 0.551825i \(-0.813932\pi\)
0.833960 0.551825i \(-0.186068\pi\)
\(84\) 0 0
\(85\) −3.62577 13.6648i −0.393270 1.48216i
\(86\) 0 0
\(87\) 14.7025i 1.57628i
\(88\) 0 0
\(89\) −12.9390 −1.37153 −0.685765 0.727823i \(-0.740532\pi\)
−0.685765 + 0.727823i \(0.740532\pi\)
\(90\) 0 0
\(91\) −2.87131 −0.300995
\(92\) 0 0
\(93\) 5.00462i 0.518955i
\(94\) 0 0
\(95\) −11.8103 + 3.13369i −1.21171 + 0.321510i
\(96\) 0 0
\(97\) 0.205002i 0.0208148i −0.999946 0.0104074i \(-0.996687\pi\)
0.999946 0.0104074i \(-0.00331283\pi\)
\(98\) 0 0
\(99\) −0.524168 −0.0526808
\(100\) 0 0
\(101\) −4.44012 −0.441809 −0.220904 0.975295i \(-0.570901\pi\)
−0.220904 + 0.975295i \(0.570901\pi\)
\(102\) 0 0
\(103\) 8.34875i 0.822627i −0.911494 0.411313i \(-0.865070\pi\)
0.911494 0.411313i \(-0.134930\pi\)
\(104\) 0 0
\(105\) 10.9767 2.91252i 1.07122 0.284233i
\(106\) 0 0
\(107\) 10.2390i 0.989839i −0.868939 0.494919i \(-0.835198\pi\)
0.868939 0.494919i \(-0.164802\pi\)
\(108\) 0 0
\(109\) −4.28608 −0.410532 −0.205266 0.978706i \(-0.565806\pi\)
−0.205266 + 0.978706i \(0.565806\pi\)
\(110\) 0 0
\(111\) −13.7504 −1.30513
\(112\) 0 0
\(113\) 9.36488i 0.880974i 0.897759 + 0.440487i \(0.145194\pi\)
−0.897759 + 0.440487i \(0.854806\pi\)
\(114\) 0 0
\(115\) 2.34626 + 8.84261i 0.218790 + 0.824578i
\(116\) 0 0
\(117\) 0.128689i 0.0118973i
\(118\) 0 0
\(119\) −18.1540 −1.66418
\(120\) 0 0
\(121\) 5.59040 0.508218
\(122\) 0 0
\(123\) 21.2903i 1.91968i
\(124\) 0 0
\(125\) 7.96335 7.84761i 0.712264 0.701912i
\(126\) 0 0
\(127\) 8.23897i 0.731090i 0.930794 + 0.365545i \(0.119117\pi\)
−0.930794 + 0.365545i \(0.880883\pi\)
\(128\) 0 0
\(129\) −10.7237 −0.944170
\(130\) 0 0
\(131\) −2.51181 −0.219458 −0.109729 0.993962i \(-0.534998\pi\)
−0.109729 + 0.993962i \(0.534998\pi\)
\(132\) 0 0
\(133\) 15.6902i 1.36052i
\(134\) 0 0
\(135\) 2.91252 + 10.9767i 0.250670 + 0.944726i
\(136\) 0 0
\(137\) 18.6816i 1.59608i 0.602606 + 0.798039i \(0.294129\pi\)
−0.602606 + 0.798039i \(0.705871\pi\)
\(138\) 0 0
\(139\) 10.2222 0.867033 0.433517 0.901146i \(-0.357273\pi\)
0.433517 + 0.901146i \(0.357273\pi\)
\(140\) 0 0
\(141\) −12.1540 −1.02356
\(142\) 0 0
\(143\) 4.07313i 0.340612i
\(144\) 0 0
\(145\) 17.9648 4.76670i 1.49189 0.395853i
\(146\) 0 0
\(147\) 2.20115i 0.181548i
\(148\) 0 0
\(149\) −19.6315 −1.60828 −0.804138 0.594443i \(-0.797373\pi\)
−0.804138 + 0.594443i \(0.797373\pi\)
\(150\) 0 0
\(151\) 12.6322 1.02799 0.513995 0.857793i \(-0.328165\pi\)
0.513995 + 0.857793i \(0.328165\pi\)
\(152\) 0 0
\(153\) 0.813645i 0.0657793i
\(154\) 0 0
\(155\) −6.11507 + 1.62255i −0.491174 + 0.130326i
\(156\) 0 0
\(157\) 4.35127i 0.347269i 0.984810 + 0.173634i \(0.0555511\pi\)
−0.984810 + 0.173634i \(0.944449\pi\)
\(158\) 0 0
\(159\) −2.19997 −0.174469
\(160\) 0 0
\(161\) 11.7476 0.925841
\(162\) 0 0
\(163\) 13.0935i 1.02556i −0.858520 0.512780i \(-0.828616\pi\)
0.858520 0.512780i \(-0.171384\pi\)
\(164\) 0 0
\(165\) 4.13159 + 15.5712i 0.321643 + 1.21221i
\(166\) 0 0
\(167\) 11.9595i 0.925454i 0.886501 + 0.462727i \(0.153129\pi\)
−0.886501 + 0.462727i \(0.846871\pi\)
\(168\) 0 0
\(169\) −1.00000 −0.0769231
\(170\) 0 0
\(171\) 0.703220 0.0537766
\(172\) 0 0
\(173\) 5.83148i 0.443359i −0.975120 0.221680i \(-0.928846\pi\)
0.975120 0.221680i \(-0.0711539\pi\)
\(174\) 0 0
\(175\) −7.11752 12.4680i −0.538034 0.942494i
\(176\) 0 0
\(177\) 18.6998i 1.40557i
\(178\) 0 0
\(179\) −5.32546 −0.398044 −0.199022 0.979995i \(-0.563776\pi\)
−0.199022 + 0.979995i \(0.563776\pi\)
\(180\) 0 0
\(181\) 9.46700 0.703677 0.351838 0.936061i \(-0.385557\pi\)
0.351838 + 0.936061i \(0.385557\pi\)
\(182\) 0 0
\(183\) 14.5454i 1.07522i
\(184\) 0 0
\(185\) 4.45801 + 16.8014i 0.327760 + 1.23526i
\(186\) 0 0
\(187\) 25.7526i 1.88322i
\(188\) 0 0
\(189\) 14.5828 1.06074
\(190\) 0 0
\(191\) −11.7204 −0.848056 −0.424028 0.905649i \(-0.639384\pi\)
−0.424028 + 0.905649i \(0.639384\pi\)
\(192\) 0 0
\(193\) 11.6064i 0.835445i 0.908575 + 0.417722i \(0.137172\pi\)
−0.908575 + 0.417722i \(0.862828\pi\)
\(194\) 0 0
\(195\) 3.82290 1.01435i 0.273763 0.0726392i
\(196\) 0 0
\(197\) 15.6235i 1.11313i 0.830804 + 0.556565i \(0.187881\pi\)
−0.830804 + 0.556565i \(0.812119\pi\)
\(198\) 0 0
\(199\) 0.0888592 0.00629906 0.00314953 0.999995i \(-0.498997\pi\)
0.00314953 + 0.999995i \(0.498997\pi\)
\(200\) 0 0
\(201\) 9.52173 0.671611
\(202\) 0 0
\(203\) 23.8666i 1.67511i
\(204\) 0 0
\(205\) −26.0142 + 6.90250i −1.81691 + 0.482092i
\(206\) 0 0
\(207\) 0.526515i 0.0365953i
\(208\) 0 0
\(209\) −22.2576 −1.53959
\(210\) 0 0
\(211\) 7.61932 0.524536 0.262268 0.964995i \(-0.415530\pi\)
0.262268 + 0.964995i \(0.415530\pi\)
\(212\) 0 0
\(213\) 19.5114i 1.33690i
\(214\) 0 0
\(215\) 3.47673 + 13.1031i 0.237111 + 0.893627i
\(216\) 0 0
\(217\) 8.12401i 0.551494i
\(218\) 0 0
\(219\) 4.90753 0.331620
\(220\) 0 0
\(221\) −6.32256 −0.425302
\(222\) 0 0
\(223\) 2.46131i 0.164821i 0.996598 + 0.0824107i \(0.0262619\pi\)
−0.996598 + 0.0824107i \(0.973738\pi\)
\(224\) 0 0
\(225\) −0.558803 + 0.319000i −0.0372536 + 0.0212666i
\(226\) 0 0
\(227\) 8.77448i 0.582383i −0.956665 0.291191i \(-0.905948\pi\)
0.956665 0.291191i \(-0.0940517\pi\)
\(228\) 0 0
\(229\) 12.6738 0.837510 0.418755 0.908099i \(-0.362467\pi\)
0.418755 + 0.908099i \(0.362467\pi\)
\(230\) 0 0
\(231\) 20.6866 1.36108
\(232\) 0 0
\(233\) 18.7992i 1.23157i −0.787912 0.615787i \(-0.788838\pi\)
0.787912 0.615787i \(-0.211162\pi\)
\(234\) 0 0
\(235\) 3.94046 + 14.8508i 0.257047 + 0.968762i
\(236\) 0 0
\(237\) 17.3900i 1.12960i
\(238\) 0 0
\(239\) 8.44807 0.546460 0.273230 0.961949i \(-0.411908\pi\)
0.273230 + 0.961949i \(0.411908\pi\)
\(240\) 0 0
\(241\) 11.4278 0.736132 0.368066 0.929800i \(-0.380020\pi\)
0.368066 + 0.929800i \(0.380020\pi\)
\(242\) 0 0
\(243\) 1.33647i 0.0857344i
\(244\) 0 0
\(245\) −2.68956 + 0.713635i −0.171829 + 0.0455925i
\(246\) 0 0
\(247\) 5.46449i 0.347697i
\(248\) 0 0
\(249\) 17.7849 1.12707
\(250\) 0 0
\(251\) −12.5512 −0.792227 −0.396114 0.918202i \(-0.629641\pi\)
−0.396114 + 0.918202i \(0.629641\pi\)
\(252\) 0 0
\(253\) 16.6647i 1.04770i
\(254\) 0 0
\(255\) 24.1705 6.41330i 1.51362 0.401616i
\(256\) 0 0
\(257\) 18.1540i 1.13242i −0.824262 0.566209i \(-0.808409\pi\)
0.824262 0.566209i \(-0.191591\pi\)
\(258\) 0 0
\(259\) 22.3210 1.38696
\(260\) 0 0
\(261\) −1.06968 −0.0662113
\(262\) 0 0
\(263\) 26.5902i 1.63962i −0.572633 0.819812i \(-0.694078\pi\)
0.572633 0.819812i \(-0.305922\pi\)
\(264\) 0 0
\(265\) 0.713253 + 2.68811i 0.0438148 + 0.165130i
\(266\) 0 0
\(267\) 22.8866i 1.40064i
\(268\) 0 0
\(269\) 15.5154 0.945988 0.472994 0.881066i \(-0.343173\pi\)
0.472994 + 0.881066i \(0.343173\pi\)
\(270\) 0 0
\(271\) −4.57977 −0.278202 −0.139101 0.990278i \(-0.544421\pi\)
−0.139101 + 0.990278i \(0.544421\pi\)
\(272\) 0 0
\(273\) 5.07880i 0.307383i
\(274\) 0 0
\(275\) 17.6867 10.0966i 1.06655 0.608850i
\(276\) 0 0
\(277\) 16.7340i 1.00545i 0.864447 + 0.502724i \(0.167669\pi\)
−0.864447 + 0.502724i \(0.832331\pi\)
\(278\) 0 0
\(279\) 0.364109 0.0217987
\(280\) 0 0
\(281\) −13.5699 −0.809512 −0.404756 0.914425i \(-0.632643\pi\)
−0.404756 + 0.914425i \(0.632643\pi\)
\(282\) 0 0
\(283\) 10.3488i 0.615169i −0.951521 0.307585i \(-0.900479\pi\)
0.951521 0.307585i \(-0.0995207\pi\)
\(284\) 0 0
\(285\) −5.54291 20.8902i −0.328334 1.23743i
\(286\) 0 0
\(287\) 34.5605i 2.04004i
\(288\) 0 0
\(289\) −22.9748 −1.35146
\(290\) 0 0
\(291\) 0.362609 0.0212565
\(292\) 0 0
\(293\) 18.5930i 1.08622i −0.839663 0.543108i \(-0.817248\pi\)
0.839663 0.543108i \(-0.182752\pi\)
\(294\) 0 0
\(295\) −22.8491 + 6.06267i −1.33032 + 0.352982i
\(296\) 0 0
\(297\) 20.6866i 1.20036i
\(298\) 0 0
\(299\) 4.09137 0.236610
\(300\) 0 0
\(301\) 17.4078 1.00337
\(302\) 0 0
\(303\) 7.85374i 0.451185i
\(304\) 0 0
\(305\) 17.7727 4.71574i 1.01766 0.270023i
\(306\) 0 0
\(307\) 5.37312i 0.306660i 0.988175 + 0.153330i \(0.0489997\pi\)
−0.988175 + 0.153330i \(0.951000\pi\)
\(308\) 0 0
\(309\) 14.7674 0.840085
\(310\) 0 0
\(311\) −16.7814 −0.951585 −0.475792 0.879558i \(-0.657839\pi\)
−0.475792 + 0.879558i \(0.657839\pi\)
\(312\) 0 0
\(313\) 31.2393i 1.76575i 0.469609 + 0.882875i \(0.344395\pi\)
−0.469609 + 0.882875i \(0.655605\pi\)
\(314\) 0 0
\(315\) 0.211899 + 0.798607i 0.0119392 + 0.0449964i
\(316\) 0 0
\(317\) 2.15028i 0.120772i −0.998175 0.0603858i \(-0.980767\pi\)
0.998175 0.0603858i \(-0.0192331\pi\)
\(318\) 0 0
\(319\) 33.8563 1.89559
\(320\) 0 0
\(321\) 18.1108 1.01085
\(322\) 0 0
\(323\) 34.5496i 1.92239i
\(324\) 0 0
\(325\) −2.47884 4.34228i −0.137501 0.240866i
\(326\) 0 0
\(327\) 7.58126i 0.419245i
\(328\) 0 0
\(329\) 19.7297 1.08773
\(330\) 0 0
\(331\) 21.1597 1.16304 0.581522 0.813531i \(-0.302458\pi\)
0.581522 + 0.813531i \(0.302458\pi\)
\(332\) 0 0
\(333\) 1.00041i 0.0548219i
\(334\) 0 0
\(335\) −3.08704 11.6344i −0.168663 0.635658i
\(336\) 0 0
\(337\) 33.7869i 1.84049i 0.391344 + 0.920244i \(0.372010\pi\)
−0.391344 + 0.920244i \(0.627990\pi\)
\(338\) 0 0
\(339\) −16.5647 −0.899671
\(340\) 0 0
\(341\) −11.5244 −0.624082
\(342\) 0 0
\(343\) 16.5260i 0.892322i
\(344\) 0 0
\(345\) −15.6409 + 4.15009i −0.842078 + 0.223433i
\(346\) 0 0
\(347\) 25.2331i 1.35459i 0.735714 + 0.677293i \(0.236847\pi\)
−0.735714 + 0.677293i \(0.763153\pi\)
\(348\) 0 0
\(349\) −9.20415 −0.492687 −0.246343 0.969183i \(-0.579229\pi\)
−0.246343 + 0.969183i \(0.579229\pi\)
\(350\) 0 0
\(351\) 5.07880 0.271086
\(352\) 0 0
\(353\) 2.53936i 0.135156i 0.997714 + 0.0675782i \(0.0215272\pi\)
−0.997714 + 0.0675782i \(0.978473\pi\)
\(354\) 0 0
\(355\) 23.8407 6.32579i 1.26533 0.335738i
\(356\) 0 0
\(357\) 32.1111i 1.69950i
\(358\) 0 0
\(359\) −26.7547 −1.41206 −0.706031 0.708181i \(-0.749516\pi\)
−0.706031 + 0.708181i \(0.749516\pi\)
\(360\) 0 0
\(361\) 10.8606 0.571612
\(362\) 0 0
\(363\) 9.88836i 0.519004i
\(364\) 0 0
\(365\) −1.59107 5.99644i −0.0832804 0.313868i
\(366\) 0 0
\(367\) 16.3643i 0.854210i 0.904202 + 0.427105i \(0.140467\pi\)
−0.904202 + 0.427105i \(0.859533\pi\)
\(368\) 0 0
\(369\) 1.54896 0.0806358
\(370\) 0 0
\(371\) 3.57122 0.185408
\(372\) 0 0
\(373\) 15.9568i 0.826213i 0.910683 + 0.413106i \(0.135556\pi\)
−0.910683 + 0.413106i \(0.864444\pi\)
\(374\) 0 0
\(375\) 13.8809 + 14.0857i 0.716809 + 0.727380i
\(376\) 0 0
\(377\) 8.31210i 0.428095i
\(378\) 0 0
\(379\) −33.0473 −1.69752 −0.848762 0.528775i \(-0.822652\pi\)
−0.848762 + 0.528775i \(0.822652\pi\)
\(380\) 0 0
\(381\) −14.5732 −0.746606
\(382\) 0 0
\(383\) 14.5287i 0.742383i 0.928556 + 0.371191i \(0.121051\pi\)
−0.928556 + 0.371191i \(0.878949\pi\)
\(384\) 0 0
\(385\) −6.70681 25.2767i −0.341810 1.28822i
\(386\) 0 0
\(387\) 0.780200i 0.0396598i
\(388\) 0 0
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) 25.8680 1.30820
\(392\) 0 0
\(393\) 4.44292i 0.224116i
\(394\) 0 0
\(395\) −21.2486 + 5.63801i −1.06913 + 0.283679i
\(396\) 0 0
\(397\) 21.1672i 1.06235i −0.847262 0.531176i \(-0.821750\pi\)
0.847262 0.531176i \(-0.178250\pi\)
\(398\) 0 0
\(399\) −27.7531 −1.38939
\(400\) 0 0
\(401\) −23.6064 −1.17885 −0.589423 0.807825i \(-0.700645\pi\)
−0.589423 + 0.807825i \(0.700645\pi\)
\(402\) 0 0
\(403\) 2.82937i 0.140941i
\(404\) 0 0
\(405\) −20.2501 + 5.37309i −1.00624 + 0.266991i
\(406\) 0 0
\(407\) 31.6638i 1.56951i
\(408\) 0 0
\(409\) −18.3232 −0.906025 −0.453012 0.891504i \(-0.649651\pi\)
−0.453012 + 0.891504i \(0.649651\pi\)
\(410\) 0 0
\(411\) −33.0442 −1.62995
\(412\) 0 0
\(413\) 30.3555i 1.49370i
\(414\) 0 0
\(415\) −5.76603 21.7311i −0.283043 1.06674i
\(416\) 0 0
\(417\) 18.0811i 0.885434i
\(418\) 0 0
\(419\) 37.2500 1.81978 0.909891 0.414847i \(-0.136165\pi\)
0.909891 + 0.414847i \(0.136165\pi\)
\(420\) 0 0
\(421\) −4.35905 −0.212447 −0.106223 0.994342i \(-0.533876\pi\)
−0.106223 + 0.994342i \(0.533876\pi\)
\(422\) 0 0
\(423\) 0.884263i 0.0429943i
\(424\) 0 0
\(425\) −15.6726 27.4543i −0.760234 1.33173i
\(426\) 0 0
\(427\) 23.6115i 1.14264i
\(428\) 0 0
\(429\) 7.20460 0.347841
\(430\) 0 0
\(431\) −23.4500 −1.12955 −0.564774 0.825246i \(-0.691037\pi\)
−0.564774 + 0.825246i \(0.691037\pi\)
\(432\) 0 0
\(433\) 2.47016i 0.118708i −0.998237 0.0593542i \(-0.981096\pi\)
0.998237 0.0593542i \(-0.0189041\pi\)
\(434\) 0 0
\(435\) 8.43139 + 31.7763i 0.404254 + 1.52356i
\(436\) 0 0
\(437\) 22.3573i 1.06949i
\(438\) 0 0
\(439\) 27.6939 1.32176 0.660879 0.750493i \(-0.270184\pi\)
0.660879 + 0.750493i \(0.270184\pi\)
\(440\) 0 0
\(441\) 0.160144 0.00762591
\(442\) 0 0
\(443\) 23.7730i 1.12949i −0.825265 0.564745i \(-0.808974\pi\)
0.825265 0.564745i \(-0.191026\pi\)
\(444\) 0 0
\(445\) −27.9648 + 7.42006i −1.32566 + 0.351745i
\(446\) 0 0
\(447\) 34.7244i 1.64241i
\(448\) 0 0
\(449\) 26.9181 1.27034 0.635171 0.772372i \(-0.280930\pi\)
0.635171 + 0.772372i \(0.280930\pi\)
\(450\) 0 0
\(451\) −49.0262 −2.30855
\(452\) 0 0
\(453\) 22.3439i 1.04981i
\(454\) 0 0
\(455\) −6.20571 + 1.64660i −0.290928 + 0.0771937i
\(456\) 0 0
\(457\) 10.1463i 0.474622i −0.971434 0.237311i \(-0.923734\pi\)
0.971434 0.237311i \(-0.0762661\pi\)
\(458\) 0 0
\(459\) 32.1111 1.49882
\(460\) 0 0
\(461\) 30.8034 1.43466 0.717328 0.696735i \(-0.245365\pi\)
0.717328 + 0.696735i \(0.245365\pi\)
\(462\) 0 0
\(463\) 24.3695i 1.13255i −0.824217 0.566274i \(-0.808385\pi\)
0.824217 0.566274i \(-0.191615\pi\)
\(464\) 0 0
\(465\) −2.86998 10.8164i −0.133092 0.501598i
\(466\) 0 0
\(467\) 25.7229i 1.19031i −0.803610 0.595156i \(-0.797090\pi\)
0.803610 0.595156i \(-0.202910\pi\)
\(468\) 0 0
\(469\) −15.4566 −0.713721
\(470\) 0 0
\(471\) −7.69656 −0.354639
\(472\) 0 0
\(473\) 24.6941i 1.13543i
\(474\) 0 0
\(475\) −23.7283 + 13.5456i −1.08873 + 0.621514i
\(476\) 0 0
\(477\) 0.160058i 0.00732856i
\(478\) 0 0
\(479\) 16.6531 0.760898 0.380449 0.924802i \(-0.375769\pi\)
0.380449 + 0.924802i \(0.375769\pi\)
\(480\) 0 0
\(481\) 7.77382 0.354455
\(482\) 0 0
\(483\) 20.7793i 0.945490i
\(484\) 0 0
\(485\) −0.117561 0.443066i −0.00533818 0.0201186i
\(486\) 0 0
\(487\) 15.6505i 0.709192i −0.935020 0.354596i \(-0.884618\pi\)
0.935020 0.354596i \(-0.115382\pi\)
\(488\) 0 0
\(489\) 23.1599 1.04733
\(490\) 0 0
\(491\) −15.1834 −0.685218 −0.342609 0.939478i \(-0.611311\pi\)
−0.342609 + 0.939478i \(0.611311\pi\)
\(492\) 0 0
\(493\) 52.5538i 2.36690i
\(494\) 0 0
\(495\) −1.13287 + 0.300592i −0.0509189 + 0.0135106i
\(496\) 0 0
\(497\) 31.6729i 1.42072i
\(498\) 0 0
\(499\) −4.13685 −0.185191 −0.0925955 0.995704i \(-0.529516\pi\)
−0.0925955 + 0.995704i \(0.529516\pi\)
\(500\) 0 0
\(501\) −21.1541 −0.945095
\(502\) 0 0
\(503\) 2.34875i 0.104726i −0.998628 0.0523628i \(-0.983325\pi\)
0.998628 0.0523628i \(-0.0166752\pi\)
\(504\) 0 0
\(505\) −9.59636 + 2.54626i −0.427032 + 0.113307i
\(506\) 0 0
\(507\) 1.76881i 0.0785556i
\(508\) 0 0
\(509\) 23.5964 1.04589 0.522945 0.852366i \(-0.324833\pi\)
0.522945 + 0.852366i \(0.324833\pi\)
\(510\) 0 0
\(511\) −7.96640 −0.352413
\(512\) 0 0
\(513\) 27.7531i 1.22533i
\(514\) 0 0
\(515\) −4.78772 18.0440i −0.210972 0.795114i
\(516\) 0 0
\(517\) 27.9878i 1.23090i
\(518\) 0 0
\(519\) 10.3148 0.452769
\(520\) 0 0
\(521\) −2.49224 −0.109187 −0.0545935 0.998509i \(-0.517386\pi\)
−0.0545935 + 0.998509i \(0.517386\pi\)
\(522\) 0 0
\(523\) 37.9006i 1.65728i 0.559784 + 0.828639i \(0.310884\pi\)
−0.559784 + 0.828639i \(0.689116\pi\)
\(524\) 0 0
\(525\) 22.0536 12.5895i 0.962496 0.549453i
\(526\) 0 0
\(527\) 17.8889i 0.779252i
\(528\) 0 0
\(529\) 6.26067 0.272203
\(530\) 0 0
\(531\) 1.36050 0.0590407
\(532\) 0 0
\(533\) 12.0365i 0.521358i
\(534\) 0 0
\(535\) −5.87169 22.1293i −0.253855 0.956733i
\(536\) 0 0
\(537\) 9.41973i 0.406491i
\(538\) 0 0
\(539\) −5.06871 −0.218325
\(540\) 0 0
\(541\) −8.41778 −0.361909 −0.180954 0.983491i \(-0.557919\pi\)
−0.180954 + 0.983491i \(0.557919\pi\)
\(542\) 0 0
\(543\) 16.7453i 0.718611i
\(544\) 0 0
\(545\) −9.26343 + 2.45792i −0.396802 + 0.105286i
\(546\) 0 0
\(547\) 19.4627i 0.832165i 0.909327 + 0.416083i \(0.136597\pi\)
−0.909327 + 0.416083i \(0.863403\pi\)
\(548\) 0 0
\(549\) −1.05824 −0.0451647
\(550\) 0 0
\(551\) −45.4214 −1.93502
\(552\) 0 0
\(553\) 28.2292i 1.20043i
\(554\) 0 0
\(555\) −29.7185 + 7.88538i −1.26148 + 0.334716i
\(556\) 0 0
\(557\) 15.0289i 0.636796i −0.947957 0.318398i \(-0.896855\pi\)
0.947957 0.318398i \(-0.103145\pi\)
\(558\) 0 0
\(559\) 6.06267 0.256424
\(560\) 0 0
\(561\) 45.5515 1.92319
\(562\) 0 0
\(563\) 8.03543i 0.338653i 0.985560 + 0.169327i \(0.0541593\pi\)
−0.985560 + 0.169327i \(0.945841\pi\)
\(564\) 0 0
\(565\) 5.37044 + 20.2402i 0.225936 + 0.851510i
\(566\) 0 0
\(567\) 26.9028i 1.12981i
\(568\) 0 0
\(569\) −36.4568 −1.52835 −0.764173 0.645011i \(-0.776853\pi\)
−0.764173 + 0.645011i \(0.776853\pi\)
\(570\) 0 0
\(571\) 35.7061 1.49425 0.747126 0.664682i \(-0.231433\pi\)
0.747126 + 0.664682i \(0.231433\pi\)
\(572\) 0 0
\(573\) 20.7311i 0.866054i
\(574\) 0 0
\(575\) 10.1419 + 17.7659i 0.422945 + 0.740888i
\(576\) 0 0
\(577\) 13.2985i 0.553623i −0.960924 0.276812i \(-0.910722\pi\)
0.960924 0.276812i \(-0.0892778\pi\)
\(578\) 0 0
\(579\) −20.5295 −0.853175
\(580\) 0 0
\(581\) −28.8702 −1.19774
\(582\) 0 0
\(583\) 5.06600i 0.209812i
\(584\) 0 0
\(585\) 0.0737987 + 0.278133i 0.00305120 + 0.0114994i
\(586\) 0 0
\(587\) 14.0182i 0.578595i 0.957239 + 0.289297i \(0.0934216\pi\)
−0.957239 + 0.289297i \(0.906578\pi\)
\(588\) 0 0
\(589\) 15.4611 0.637062
\(590\) 0 0
\(591\) −27.6351 −1.13675
\(592\) 0 0
\(593\) 22.7125i 0.932692i −0.884602 0.466346i \(-0.845570\pi\)
0.884602 0.466346i \(-0.154430\pi\)
\(594\) 0 0
\(595\) −39.2360 + 10.4107i −1.60852 + 0.426798i
\(596\) 0 0
\(597\) 0.157175i 0.00643275i
\(598\) 0 0
\(599\) 6.11614 0.249899 0.124949 0.992163i \(-0.460123\pi\)
0.124949 + 0.992163i \(0.460123\pi\)
\(600\) 0 0
\(601\) −10.7848 −0.439919 −0.219960 0.975509i \(-0.570593\pi\)
−0.219960 + 0.975509i \(0.570593\pi\)
\(602\) 0 0
\(603\) 0.692750i 0.0282109i
\(604\) 0 0
\(605\) 12.0824 3.20590i 0.491221 0.130338i
\(606\) 0 0
\(607\) 30.0847i 1.22110i −0.791978 0.610550i \(-0.790949\pi\)
0.791978 0.610550i \(-0.209051\pi\)
\(608\) 0 0
\(609\) 42.2155 1.71066
\(610\) 0 0
\(611\) 6.87131 0.277983
\(612\) 0 0
\(613\) 26.5282i 1.07146i −0.844388 0.535732i \(-0.820036\pi\)
0.844388 0.535732i \(-0.179964\pi\)
\(614\) 0 0
\(615\) −12.2092 46.0142i −0.492323 1.85547i
\(616\) 0 0
\(617\) 46.8179i 1.88482i −0.334465 0.942408i \(-0.608556\pi\)
0.334465 0.942408i \(-0.391444\pi\)
\(618\) 0 0
\(619\) −27.8048 −1.11757 −0.558785 0.829312i \(-0.688732\pi\)
−0.558785 + 0.829312i \(0.688732\pi\)
\(620\) 0 0
\(621\) −20.7793 −0.833844
\(622\) 0 0
\(623\) 37.1519i 1.48846i
\(624\) 0 0
\(625\) 12.7107 21.5276i 0.508428 0.861104i
\(626\) 0 0
\(627\) 39.3694i 1.57226i
\(628\) 0 0
\(629\) 49.1504 1.95976
\(630\) 0 0
\(631\) 28.9260 1.15153 0.575763 0.817617i \(-0.304705\pi\)
0.575763 + 0.817617i \(0.304705\pi\)
\(632\) 0 0
\(633\) 13.4771i 0.535668i
\(634\) 0 0
\(635\) 4.72476 + 17.8067i 0.187496 + 0.706639i
\(636\) 0 0
\(637\) 1.24443i 0.0493060i
\(638\) 0 0
\(639\) −1.41955 −0.0561563
\(640\) 0 0
\(641\) −4.37271 −0.172712 −0.0863558 0.996264i \(-0.527522\pi\)
−0.0863558 + 0.996264i \(0.527522\pi\)
\(642\) 0 0
\(643\) 14.9824i 0.590847i −0.955366 0.295423i \(-0.904539\pi\)
0.955366 0.295423i \(-0.0954607\pi\)
\(644\) 0 0
\(645\) −23.1770 + 6.14968i −0.912592 + 0.242143i
\(646\) 0 0
\(647\) 25.1981i 0.990638i 0.868711 + 0.495319i \(0.164949\pi\)
−0.868711 + 0.495319i \(0.835051\pi\)
\(648\) 0 0
\(649\) −43.0611 −1.69030
\(650\) 0 0
\(651\) −14.3698 −0.563198
\(652\) 0 0
\(653\) 7.66163i 0.299823i −0.988699 0.149911i \(-0.952101\pi\)
0.988699 0.149911i \(-0.0478988\pi\)
\(654\) 0 0
\(655\) −5.42874 + 1.44044i −0.212118 + 0.0562826i
\(656\) 0 0
\(657\) 0.357046i 0.0139297i
\(658\) 0 0
\(659\) 30.1870 1.17592 0.587959 0.808891i \(-0.299932\pi\)
0.587959 + 0.808891i \(0.299932\pi\)
\(660\) 0 0
\(661\) 3.61149 0.140471 0.0702353 0.997530i \(-0.477625\pi\)
0.0702353 + 0.997530i \(0.477625\pi\)
\(662\) 0 0
\(663\) 11.1834i 0.434328i
\(664\) 0 0
\(665\) 8.99781 + 33.9110i 0.348920 + 1.31501i
\(666\) 0 0
\(667\) 34.0079i 1.31679i
\(668\) 0 0
\(669\) −4.35359 −0.168319
\(670\) 0 0
\(671\) 33.4944 1.29304
\(672\) 0 0
\(673\) 19.9863i 0.770417i −0.922830 0.385208i \(-0.874130\pi\)
0.922830 0.385208i \(-0.125870\pi\)
\(674\) 0 0
\(675\) 12.5895 + 22.0536i 0.484572 + 0.848842i
\(676\) 0 0
\(677\) 29.9325i 1.15040i 0.818013 + 0.575200i \(0.195076\pi\)
−0.818013 + 0.575200i \(0.804924\pi\)
\(678\) 0 0
\(679\) −0.588623 −0.0225893
\(680\) 0 0
\(681\) 15.5204 0.594743
\(682\) 0 0
\(683\) 35.2770i 1.34984i 0.737892 + 0.674919i \(0.235822\pi\)
−0.737892 + 0.674919i \(0.764178\pi\)
\(684\) 0 0
\(685\) 10.7133 + 40.3762i 0.409332 + 1.54270i
\(686\) 0 0
\(687\) 22.4176i 0.855285i
\(688\) 0 0
\(689\) 1.24376 0.0473835
\(690\) 0 0
\(691\) 5.08177 0.193320 0.0966598 0.995317i \(-0.469184\pi\)
0.0966598 + 0.995317i \(0.469184\pi\)
\(692\) 0 0
\(693\) 1.50505i 0.0571721i
\(694\) 0 0
\(695\) 22.0930 5.86206i 0.838035 0.222361i
\(696\) 0 0
\(697\) 76.1014i 2.88255i
\(698\) 0 0
\(699\) 33.2522 1.25771
\(700\) 0 0
\(701\) −10.4989 −0.396537 −0.198268 0.980148i \(-0.563532\pi\)
−0.198268 + 0.980148i \(0.563532\pi\)
\(702\) 0 0
\(703\) 42.4799i 1.60216i
\(704\) 0 0
\(705\) −26.2683 + 6.96992i −0.989322 + 0.262502i
\(706\) 0 0
\(707\) 12.7490i 0.479475i
\(708\) 0 0
\(709\) 48.6644 1.82763 0.913815 0.406132i \(-0.133123\pi\)
0.913815 + 0.406132i \(0.133123\pi\)
\(710\) 0 0
\(711\) 1.26520 0.0474489
\(712\) 0 0
\(713\) 11.5760i 0.433525i
\(714\) 0 0
\(715\) −2.33580 8.80318i −0.0873539 0.329220i
\(716\) 0 0
\(717\) 14.9430i 0.558058i
\(718\) 0 0
\(719\) 16.4394 0.613085 0.306542 0.951857i \(-0.400828\pi\)
0.306542 + 0.951857i \(0.400828\pi\)
\(720\) 0 0
\(721\) −23.9719 −0.892759
\(722\) 0 0
\(723\) 20.2137i 0.751755i
\(724\) 0 0
\(725\) 36.0934 20.6044i 1.34048 0.765227i
\(726\) 0 0
\(727\) 27.0194i 1.00210i −0.865420 0.501048i \(-0.832948\pi\)
0.865420 0.501048i \(-0.167052\pi\)
\(728\) 0 0
\(729\) −25.7446 −0.953502
\(730\) 0 0
\(731\) 38.3316 1.41775
\(732\) 0 0
\(733\) 39.2522i 1.44981i −0.688848 0.724906i \(-0.741883\pi\)
0.688848 0.724906i \(-0.258117\pi\)
\(734\) 0 0
\(735\) −1.26229 4.75731i −0.0465601 0.175476i
\(736\) 0 0
\(737\) 21.9262i 0.807661i
\(738\) 0 0
\(739\) −23.9893 −0.882459 −0.441230 0.897394i \(-0.645458\pi\)
−0.441230 + 0.897394i \(0.645458\pi\)
\(740\) 0 0
\(741\) −9.66564 −0.355076
\(742\) 0 0
\(743\) 22.1997i 0.814428i −0.913333 0.407214i \(-0.866500\pi\)
0.913333 0.407214i \(-0.133500\pi\)
\(744\) 0 0
\(745\) −42.4292 + 11.2580i −1.55449 + 0.412461i
\(746\) 0 0
\(747\) 1.29393i 0.0473425i
\(748\) 0 0
\(749\) −29.3993 −1.07423
\(750\) 0 0
\(751\) −1.64375 −0.0599814 −0.0299907 0.999550i \(-0.509548\pi\)
−0.0299907 + 0.999550i \(0.509548\pi\)
\(752\) 0 0
\(753\) 22.2008i 0.809041i
\(754\) 0 0
\(755\) 27.3016 7.24410i 0.993608 0.263640i
\(756\) 0 0
\(757\) 37.2019i 1.35213i −0.736844 0.676063i \(-0.763685\pi\)
0.736844 0.676063i \(-0.236315\pi\)
\(758\) 0 0
\(759\) −29.4767 −1.06994
\(760\) 0 0
\(761\) −17.5432 −0.635939 −0.317970 0.948101i \(-0.603001\pi\)
−0.317970 + 0.948101i \(0.603001\pi\)
\(762\) 0 0
\(763\) 12.3067i 0.445531i
\(764\) 0 0
\(765\) 0.466597 + 1.75852i 0.0168699 + 0.0635793i
\(766\) 0 0
\(767\) 10.5720i 0.381733i
\(768\) 0 0
\(769\) −34.0835 −1.22908 −0.614542 0.788884i \(-0.710659\pi\)
−0.614542 + 0.788884i \(0.710659\pi\)
\(770\) 0 0
\(771\) 32.1111 1.15645
\(772\) 0 0
\(773\) 46.3178i 1.66594i 0.553321 + 0.832968i \(0.313360\pi\)
−0.553321 + 0.832968i \(0.686640\pi\)
\(774\) 0 0
\(775\) −12.2859 + 7.01356i −0.441323 + 0.251935i
\(776\) 0 0
\(777\) 39.4817i 1.41640i
\(778\) 0 0
\(779\) 65.7732 2.35657
\(780\) 0 0
\(781\) 44.9299 1.60772
\(782\) 0 0
\(783\) 42.2155i 1.50866i
\(784\) 0 0
\(785\) 2.49530 + 9.40431i 0.0890610 + 0.335654i
\(786\) 0 0
\(787\) 0.369506i 0.0131715i 0.999978 + 0.00658574i \(0.00209632\pi\)
−0.999978 + 0.00658574i \(0.997904\pi\)
\(788\) 0 0
\(789\) 47.0331 1.67442
\(790\) 0 0
\(791\) 26.8895 0.956080
\(792\) 0 0
\(793\) 8.22324i 0.292016i
\(794\) 0 0