Properties

Label 252.6.k.f.109.1
Level $252$
Weight $6$
Character 252.109
Analytic conductor $40.417$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [252,6,Mod(37,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.37");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 252.k (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: \(40.4167225929\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} + 703x^{6} + 2770x^{5} + 427565x^{4} + 718170x^{3} + 42175732x^{2} - 40929504x + 3559792896 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{3}\cdot 7 \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.1
Root \(-11.2416 + 19.4709i\) of defining polynomial
Character \(\chi\) \(=\) 252.109
Dual form 252.6.k.f.37.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-46.4128 - 80.3893i) q^{5} +(-118.369 + 52.8745i) q^{7} +O(q^{10})\) \(q+(-46.4128 - 80.3893i) q^{5} +(-118.369 + 52.8745i) q^{7} +(70.3812 - 121.904i) q^{11} -1111.24 q^{13} +(27.4435 - 47.5335i) q^{17} +(855.929 + 1482.51i) q^{19} +(-1643.95 - 2847.41i) q^{23} +(-2745.79 + 4755.85i) q^{25} +3790.72 q^{29} +(2423.66 - 4197.90i) q^{31} +(9744.39 + 7061.57i) q^{35} +(5683.35 + 9843.86i) q^{37} +10385.6 q^{41} +7137.16 q^{43} +(-8207.53 - 14215.9i) q^{47} +(11215.6 - 12517.4i) q^{49} +(-10487.2 + 18164.3i) q^{53} -13066.3 q^{55} +(-18106.0 + 31360.5i) q^{59} +(-2474.35 - 4285.70i) q^{61} +(51575.9 + 89332.0i) q^{65} +(11482.8 - 19888.8i) q^{67} +26341.8 q^{71} +(-27693.7 + 47966.9i) q^{73} +(-1885.36 + 18151.0i) q^{77} +(24978.3 + 43263.7i) q^{79} -44858.9 q^{83} -5094.91 q^{85} +(63972.5 + 110804. i) q^{89} +(131537. - 58756.4i) q^{91} +(79452.1 - 137615. i) q^{95} -65685.9 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 42 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 42 q^{7} + 462 q^{11} - 1204 q^{13} - 228 q^{17} + 358 q^{19} + 2148 q^{23} - 5454 q^{25} + 11064 q^{29} + 830 q^{31} - 7692 q^{35} - 3914 q^{37} + 16632 q^{41} - 29036 q^{43} - 41700 q^{47} + 41876 q^{49} - 22164 q^{53} + 7784 q^{55} - 32886 q^{59} + 83732 q^{61} + 93192 q^{65} - 80034 q^{67} - 89544 q^{71} - 22470 q^{73} - 138732 q^{77} - 75286 q^{79} + 34836 q^{83} + 278504 q^{85} - 28944 q^{89} - 12058 q^{91} + 144120 q^{95} - 433356 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −46.4128 80.3893i −0.830257 1.43805i −0.897834 0.440333i \(-0.854860\pi\)
0.0675775 0.997714i \(-0.478473\pi\)
\(6\) 0 0
\(7\) −118.369 + 52.8745i −0.913049 + 0.407851i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 70.3812 121.904i 0.175378 0.303763i −0.764914 0.644132i \(-0.777219\pi\)
0.940292 + 0.340369i \(0.110552\pi\)
\(12\) 0 0
\(13\) −1111.24 −1.82369 −0.911844 0.410537i \(-0.865341\pi\)
−0.911844 + 0.410537i \(0.865341\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 27.4435 47.5335i 0.0230312 0.0398912i −0.854280 0.519813i \(-0.826002\pi\)
0.877311 + 0.479922i \(0.159335\pi\)
\(18\) 0 0
\(19\) 855.929 + 1482.51i 0.543943 + 0.942138i 0.998673 + 0.0515079i \(0.0164027\pi\)
−0.454729 + 0.890630i \(0.650264\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1643.95 2847.41i −0.647993 1.12236i −0.983602 0.180355i \(-0.942275\pi\)
0.335609 0.942001i \(-0.391058\pi\)
\(24\) 0 0
\(25\) −2745.79 + 4755.85i −0.878653 + 1.52187i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3790.72 0.837003 0.418501 0.908216i \(-0.362555\pi\)
0.418501 + 0.908216i \(0.362555\pi\)
\(30\) 0 0
\(31\) 2423.66 4197.90i 0.452968 0.784563i −0.545601 0.838045i \(-0.683699\pi\)
0.998569 + 0.0534817i \(0.0170319\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 9744.39 + 7061.57i 1.34457 + 0.974386i
\(36\) 0 0
\(37\) 5683.35 + 9843.86i 0.682496 + 1.18212i 0.974217 + 0.225615i \(0.0724391\pi\)
−0.291720 + 0.956504i \(0.594228\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 10385.6 0.964881 0.482440 0.875929i \(-0.339751\pi\)
0.482440 + 0.875929i \(0.339751\pi\)
\(42\) 0 0
\(43\) 7137.16 0.588646 0.294323 0.955706i \(-0.404906\pi\)
0.294323 + 0.955706i \(0.404906\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −8207.53 14215.9i −0.541961 0.938704i −0.998791 0.0491499i \(-0.984349\pi\)
0.456831 0.889554i \(-0.348985\pi\)
\(48\) 0 0
\(49\) 11215.6 12517.4i 0.667315 0.744775i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −10487.2 + 18164.3i −0.512824 + 0.888238i 0.487065 + 0.873366i \(0.338067\pi\)
−0.999889 + 0.0148720i \(0.995266\pi\)
\(54\) 0 0
\(55\) −13066.3 −0.582435
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −18106.0 + 31360.5i −0.677161 + 1.17288i 0.298672 + 0.954356i \(0.403456\pi\)
−0.975832 + 0.218521i \(0.929877\pi\)
\(60\) 0 0
\(61\) −2474.35 4285.70i −0.0851405 0.147468i 0.820311 0.571918i \(-0.193801\pi\)
−0.905451 + 0.424451i \(0.860467\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 51575.9 + 89332.0i 1.51413 + 2.62255i
\(66\) 0 0
\(67\) 11482.8 19888.8i 0.312507 0.541279i −0.666397 0.745597i \(-0.732164\pi\)
0.978905 + 0.204318i \(0.0654978\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 26341.8 0.620154 0.310077 0.950711i \(-0.399645\pi\)
0.310077 + 0.950711i \(0.399645\pi\)
\(72\) 0 0
\(73\) −27693.7 + 47966.9i −0.608238 + 1.05350i 0.383293 + 0.923627i \(0.374790\pi\)
−0.991531 + 0.129872i \(0.958543\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1885.36 + 18151.0i −0.0362383 + 0.348879i
\(78\) 0 0
\(79\) 24978.3 + 43263.7i 0.450293 + 0.779930i 0.998404 0.0564752i \(-0.0179862\pi\)
−0.548111 + 0.836406i \(0.684653\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −44858.9 −0.714749 −0.357374 0.933961i \(-0.616328\pi\)
−0.357374 + 0.933961i \(0.616328\pi\)
\(84\) 0 0
\(85\) −5094.91 −0.0764873
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 63972.5 + 110804.i 0.856087 + 1.48279i 0.875633 + 0.482978i \(0.160445\pi\)
−0.0195454 + 0.999809i \(0.506222\pi\)
\(90\) 0 0
\(91\) 131537. 58756.4i 1.66512 0.743793i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 79452.1 137615.i 0.903226 1.56443i
\(96\) 0 0
\(97\) −65685.9 −0.708831 −0.354415 0.935088i \(-0.615320\pi\)
−0.354415 + 0.935088i \(0.615320\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 87891.4 152232.i 0.857320 1.48492i −0.0171565 0.999853i \(-0.505461\pi\)
0.874476 0.485068i \(-0.161205\pi\)
\(102\) 0 0
\(103\) 77054.7 + 133463.i 0.715659 + 1.23956i 0.962705 + 0.270554i \(0.0872068\pi\)
−0.247046 + 0.969004i \(0.579460\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 91681.0 + 158796.i 0.774141 + 1.34085i 0.935276 + 0.353919i \(0.115151\pi\)
−0.161135 + 0.986932i \(0.551515\pi\)
\(108\) 0 0
\(109\) 67322.3 116606.i 0.542741 0.940055i −0.456004 0.889978i \(-0.650720\pi\)
0.998745 0.0500775i \(-0.0159468\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −176955. −1.30367 −0.651833 0.758362i \(-0.726000\pi\)
−0.651833 + 0.758362i \(0.726000\pi\)
\(114\) 0 0
\(115\) −152601. + 264313.i −1.07600 + 1.86369i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −735.153 + 7077.57i −0.00475894 + 0.0458159i
\(120\) 0 0
\(121\) 70618.5 + 122315.i 0.438485 + 0.759479i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 219679. 1.25752
\(126\) 0 0
\(127\) 144432. 0.794608 0.397304 0.917687i \(-0.369946\pi\)
0.397304 + 0.917687i \(0.369946\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −118754. 205688.i −0.604602 1.04720i −0.992114 0.125337i \(-0.959999\pi\)
0.387512 0.921865i \(-0.373335\pi\)
\(132\) 0 0
\(133\) −179703. 130227.i −0.880899 0.638370i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −48101.6 + 83314.5i −0.218957 + 0.379244i −0.954489 0.298245i \(-0.903599\pi\)
0.735533 + 0.677489i \(0.236932\pi\)
\(138\) 0 0
\(139\) −391373. −1.71812 −0.859060 0.511874i \(-0.828951\pi\)
−0.859060 + 0.511874i \(0.828951\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −78210.6 + 135465.i −0.319835 + 0.553970i
\(144\) 0 0
\(145\) −175938. 304733.i −0.694927 1.20365i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −40339.4 69869.9i −0.148855 0.257825i 0.781949 0.623342i \(-0.214225\pi\)
−0.930805 + 0.365517i \(0.880892\pi\)
\(150\) 0 0
\(151\) −47841.3 + 82863.6i −0.170750 + 0.295748i −0.938682 0.344783i \(-0.887952\pi\)
0.767932 + 0.640531i \(0.221286\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −449955. −1.50432
\(156\) 0 0
\(157\) 97812.7 169417.i 0.316699 0.548538i −0.663098 0.748532i \(-0.730759\pi\)
0.979797 + 0.199994i \(0.0640923\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 345149. + 250123.i 1.04940 + 0.760481i
\(162\) 0 0
\(163\) −18822.8 32602.1i −0.0554902 0.0961118i 0.836946 0.547286i \(-0.184339\pi\)
−0.892436 + 0.451174i \(0.851005\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −646778. −1.79458 −0.897292 0.441437i \(-0.854469\pi\)
−0.897292 + 0.441437i \(0.854469\pi\)
\(168\) 0 0
\(169\) 863568. 2.32584
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −193454. 335072.i −0.491431 0.851184i 0.508520 0.861050i \(-0.330193\pi\)
−0.999951 + 0.00986616i \(0.996859\pi\)
\(174\) 0 0
\(175\) 73554.0 708129.i 0.181556 1.74790i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 13705.3 23738.2i 0.0319709 0.0553752i −0.849597 0.527432i \(-0.823155\pi\)
0.881568 + 0.472057i \(0.156488\pi\)
\(180\) 0 0
\(181\) −196155. −0.445044 −0.222522 0.974928i \(-0.571429\pi\)
−0.222522 + 0.974928i \(0.571429\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 527560. 913761.i 1.13329 1.96292i
\(186\) 0 0
\(187\) −3863.01 6690.93i −0.00807833 0.0139921i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 133491. + 231213.i 0.264770 + 0.458595i 0.967503 0.252858i \(-0.0813706\pi\)
−0.702733 + 0.711453i \(0.748037\pi\)
\(192\) 0 0
\(193\) 50681.9 87783.6i 0.0979398 0.169637i −0.812892 0.582415i \(-0.802108\pi\)
0.910832 + 0.412778i \(0.135441\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −362366. −0.665245 −0.332623 0.943060i \(-0.607934\pi\)
−0.332623 + 0.943060i \(0.607934\pi\)
\(198\) 0 0
\(199\) −112706. + 195213.i −0.201751 + 0.349443i −0.949093 0.314997i \(-0.897997\pi\)
0.747342 + 0.664440i \(0.231330\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −448705. + 200433.i −0.764224 + 0.341372i
\(204\) 0 0
\(205\) −482026. 834894.i −0.801099 1.38754i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 240965. 0.381583
\(210\) 0 0
\(211\) −327801. −0.506878 −0.253439 0.967351i \(-0.581562\pi\)
−0.253439 + 0.967351i \(0.581562\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −331255. 573751.i −0.488727 0.846501i
\(216\) 0 0
\(217\) −64924.7 + 625053.i −0.0935968 + 0.901088i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −30496.4 + 52821.2i −0.0420017 + 0.0727492i
\(222\) 0 0
\(223\) 109690. 0.147708 0.0738538 0.997269i \(-0.476470\pi\)
0.0738538 + 0.997269i \(0.476470\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 608733. 1.05436e6i 0.784083 1.35807i −0.145463 0.989364i \(-0.546467\pi\)
0.929545 0.368708i \(-0.120200\pi\)
\(228\) 0 0
\(229\) 668013. + 1.15703e6i 0.841776 + 1.45800i 0.888392 + 0.459086i \(0.151823\pi\)
−0.0466161 + 0.998913i \(0.514844\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 23394.2 + 40520.0i 0.0282305 + 0.0488967i 0.879795 0.475352i \(-0.157679\pi\)
−0.851565 + 0.524249i \(0.824346\pi\)
\(234\) 0 0
\(235\) −761868. + 1.31959e6i −0.899933 + 1.55873i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −86350.2 −0.0977841 −0.0488921 0.998804i \(-0.515569\pi\)
−0.0488921 + 0.998804i \(0.515569\pi\)
\(240\) 0 0
\(241\) −412649. + 714730.i −0.457655 + 0.792682i −0.998837 0.0482236i \(-0.984644\pi\)
0.541181 + 0.840906i \(0.317977\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.52681e6 320642.i −1.62507 0.341276i
\(246\) 0 0
\(247\) −951145. 1.64743e6i −0.991983 1.71817i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 130188. 0.130432 0.0652162 0.997871i \(-0.479226\pi\)
0.0652162 + 0.997871i \(0.479226\pi\)
\(252\) 0 0
\(253\) −462814. −0.454574
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 51395.1 + 89018.9i 0.0485388 + 0.0840716i 0.889274 0.457375i \(-0.151210\pi\)
−0.840735 + 0.541446i \(0.817877\pi\)
\(258\) 0 0
\(259\) −1.19322e6 864706.i −1.10528 0.800975i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −17750.4 + 30744.5i −0.0158241 + 0.0274081i −0.873829 0.486233i \(-0.838370\pi\)
0.858005 + 0.513641i \(0.171704\pi\)
\(264\) 0 0
\(265\) 1.94695e6 1.70310
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 523171. 906158.i 0.440821 0.763525i −0.556929 0.830560i \(-0.688021\pi\)
0.997751 + 0.0670350i \(0.0213539\pi\)
\(270\) 0 0
\(271\) −88639.2 153528.i −0.0733167 0.126988i 0.827036 0.562148i \(-0.190025\pi\)
−0.900353 + 0.435160i \(0.856692\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 386504. + 669445.i 0.308193 + 0.533805i
\(276\) 0 0
\(277\) −72793.0 + 126081.i −0.0570020 + 0.0987304i −0.893118 0.449822i \(-0.851487\pi\)
0.836116 + 0.548552i \(0.184821\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.03073e6 0.778714 0.389357 0.921087i \(-0.372697\pi\)
0.389357 + 0.921087i \(0.372697\pi\)
\(282\) 0 0
\(283\) 558631. 967577.i 0.414628 0.718157i −0.580761 0.814074i \(-0.697245\pi\)
0.995389 + 0.0959167i \(0.0305783\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.22934e6 + 549136.i −0.880983 + 0.393527i
\(288\) 0 0
\(289\) 708422. + 1.22702e6i 0.498939 + 0.864188i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2.02032e6 1.37484 0.687418 0.726262i \(-0.258744\pi\)
0.687418 + 0.726262i \(0.258744\pi\)
\(294\) 0 0
\(295\) 3.36139e6 2.24887
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.82683e6 + 3.16417e6i 1.18174 + 2.04683i
\(300\) 0 0
\(301\) −844820. + 377374.i −0.537462 + 0.240080i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −229683. + 397822.i −0.141377 + 0.244872i
\(306\) 0 0
\(307\) −535150. −0.324063 −0.162031 0.986786i \(-0.551805\pi\)
−0.162031 + 0.986786i \(0.551805\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.15009e6 + 1.99202e6i −0.674268 + 1.16787i 0.302415 + 0.953176i \(0.402207\pi\)
−0.976682 + 0.214689i \(0.931126\pi\)
\(312\) 0 0
\(313\) 1.37863e6 + 2.38786e6i 0.795404 + 1.37768i 0.922582 + 0.385801i \(0.126075\pi\)
−0.127178 + 0.991880i \(0.540592\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.27404e6 + 2.20671e6i 0.712092 + 1.23338i 0.964070 + 0.265647i \(0.0855856\pi\)
−0.251978 + 0.967733i \(0.581081\pi\)
\(318\) 0 0
\(319\) 266795. 462103.i 0.146792 0.254251i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 93958.7 0.0501107
\(324\) 0 0
\(325\) 3.05124e6 5.28490e6i 1.60239 2.77542i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.72318e6 + 1.24875e6i 0.877688 + 0.636043i
\(330\) 0 0
\(331\) 244667. + 423776.i 0.122746 + 0.212602i 0.920849 0.389918i \(-0.127497\pi\)
−0.798104 + 0.602520i \(0.794163\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −2.13179e6 −1.03785
\(336\) 0 0
\(337\) −1.47140e6 −0.705757 −0.352878 0.935669i \(-0.614797\pi\)
−0.352878 + 0.935669i \(0.614797\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −341160. 590907.i −0.158881 0.275190i
\(342\) 0 0
\(343\) −665725. + 2.07470e6i −0.305534 + 0.952181i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.20963e6 + 2.09513e6i −0.539296 + 0.934088i 0.459646 + 0.888102i \(0.347976\pi\)
−0.998942 + 0.0459859i \(0.985357\pi\)
\(348\) 0 0
\(349\) −2.58571e6 −1.13636 −0.568180 0.822905i \(-0.692352\pi\)
−0.568180 + 0.822905i \(0.692352\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 502198. 869832.i 0.214505 0.371534i −0.738614 0.674128i \(-0.764519\pi\)
0.953119 + 0.302594i \(0.0978528\pi\)
\(354\) 0 0
\(355\) −1.22260e6 2.11760e6i −0.514887 0.891811i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.13383e6 1.96384e6i −0.464313 0.804213i 0.534858 0.844942i \(-0.320365\pi\)
−0.999170 + 0.0407292i \(0.987032\pi\)
\(360\) 0 0
\(361\) −227180. + 393487.i −0.0917490 + 0.158914i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 5.14136e6 2.01998
\(366\) 0 0
\(367\) −2.39312e6 + 4.14500e6i −0.927467 + 1.60642i −0.139923 + 0.990162i \(0.544685\pi\)
−0.787545 + 0.616258i \(0.788648\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 280929. 2.70460e6i 0.105965 1.02016i
\(372\) 0 0
\(373\) 2.31351e6 + 4.00711e6i 0.860991 + 1.49128i 0.870973 + 0.491331i \(0.163489\pi\)
−0.00998166 + 0.999950i \(0.503177\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4.21241e6 −1.52643
\(378\) 0 0
\(379\) −497760. −0.178001 −0.0890004 0.996032i \(-0.528367\pi\)
−0.0890004 + 0.996032i \(0.528367\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 693745. + 1.20160e6i 0.241659 + 0.418566i 0.961187 0.275898i \(-0.0889751\pi\)
−0.719528 + 0.694463i \(0.755642\pi\)
\(384\) 0 0
\(385\) 1.54665e6 690877.i 0.531791 0.237547i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −293028. + 507539.i −0.0981826 + 0.170057i −0.910932 0.412556i \(-0.864636\pi\)
0.812750 + 0.582613i \(0.197970\pi\)
\(390\) 0 0
\(391\) −180463. −0.0596962
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.31862e6 4.01598e6i 0.747718 1.29509i
\(396\) 0 0
\(397\) −1.52668e6 2.64429e6i −0.486151 0.842039i 0.513722 0.857957i \(-0.328266\pi\)
−0.999873 + 0.0159181i \(0.994933\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2.76158e6 + 4.78320e6i 0.857624 + 1.48545i 0.874189 + 0.485585i \(0.161393\pi\)
−0.0165657 + 0.999863i \(0.505273\pi\)
\(402\) 0 0
\(403\) −2.69327e6 + 4.66489e6i −0.826072 + 1.43080i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.60000e6 0.478779
\(408\) 0 0
\(409\) 1.67464e6 2.90055e6i 0.495008 0.857379i −0.504975 0.863134i \(-0.668498\pi\)
0.999983 + 0.00575475i \(0.00183180\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 485021. 4.66946e6i 0.139922 1.34707i
\(414\) 0 0
\(415\) 2.08203e6 + 3.60618e6i 0.593425 + 1.02784i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −2.97012e6 −0.826493 −0.413247 0.910619i \(-0.635605\pi\)
−0.413247 + 0.910619i \(0.635605\pi\)
\(420\) 0 0
\(421\) −5.41478e6 −1.48894 −0.744468 0.667658i \(-0.767297\pi\)
−0.744468 + 0.667658i \(0.767297\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 150708. + 261034.i 0.0404729 + 0.0701011i
\(426\) 0 0
\(427\) 519491. + 376465.i 0.137882 + 0.0999205i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2.52975e6 + 4.38165e6i −0.655970 + 1.13617i 0.325679 + 0.945480i \(0.394407\pi\)
−0.981650 + 0.190694i \(0.938926\pi\)
\(432\) 0 0
\(433\) 3.84174e6 0.984711 0.492355 0.870394i \(-0.336136\pi\)
0.492355 + 0.870394i \(0.336136\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.81422e6 4.87437e6i 0.704943 1.22100i
\(438\) 0 0
\(439\) 762859. + 1.32131e6i 0.188922 + 0.327223i 0.944891 0.327385i \(-0.106167\pi\)
−0.755969 + 0.654607i \(0.772834\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −735068. 1.27317e6i −0.177958 0.308233i 0.763223 0.646135i \(-0.223616\pi\)
−0.941181 + 0.337903i \(0.890283\pi\)
\(444\) 0 0
\(445\) 5.93828e6 1.02854e7i 1.42154 2.46219i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 6.05071e6 1.41641 0.708207 0.706004i \(-0.249504\pi\)
0.708207 + 0.706004i \(0.249504\pi\)
\(450\) 0 0
\(451\) 730954. 1.26605e6i 0.169219 0.293095i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.08284e7 7.84712e6i −2.45208 1.77698i
\(456\) 0 0
\(457\) 2.87710e6 + 4.98328e6i 0.644413 + 1.11616i 0.984437 + 0.175739i \(0.0562315\pi\)
−0.340024 + 0.940417i \(0.610435\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −2.83684e6 −0.621703 −0.310851 0.950458i \(-0.600614\pi\)
−0.310851 + 0.950458i \(0.600614\pi\)
\(462\) 0 0
\(463\) 5.19089e6 1.12535 0.562677 0.826677i \(-0.309771\pi\)
0.562677 + 0.826677i \(0.309771\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 544520. + 943136.i 0.115537 + 0.200116i 0.917994 0.396594i \(-0.129808\pi\)
−0.802457 + 0.596710i \(0.796474\pi\)
\(468\) 0 0
\(469\) −307600. + 2.96137e6i −0.0645734 + 0.621670i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 502322. 870047.i 0.103235 0.178809i
\(474\) 0 0
\(475\) −9.40081e6 −1.91175
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −2.84705e6 + 4.93124e6i −0.566966 + 0.982013i 0.429898 + 0.902877i \(0.358549\pi\)
−0.996864 + 0.0791359i \(0.974784\pi\)
\(480\) 0 0
\(481\) −6.31559e6 1.09389e7i −1.24466 2.15582i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 3.04866e6 + 5.28044e6i 0.588512 + 1.01933i
\(486\) 0 0
\(487\) 2.05713e6 3.56305e6i 0.393042 0.680768i −0.599807 0.800144i \(-0.704756\pi\)
0.992849 + 0.119376i \(0.0380895\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 609530. 0.114101 0.0570507 0.998371i \(-0.481830\pi\)
0.0570507 + 0.998371i \(0.481830\pi\)
\(492\) 0 0
\(493\) 104031. 180186.i 0.0192772 0.0333891i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −3.11806e6 + 1.39281e6i −0.566231 + 0.252930i
\(498\) 0 0
\(499\) −497896. 862382.i −0.0895133 0.155042i 0.817792 0.575514i \(-0.195198\pi\)
−0.907306 + 0.420472i \(0.861864\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −1.02730e7 −1.81042 −0.905209 0.424966i \(-0.860286\pi\)
−0.905209 + 0.424966i \(0.860286\pi\)
\(504\) 0 0
\(505\) −1.63171e7 −2.84718
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1.39213e6 2.41125e6i −0.238170 0.412522i 0.722020 0.691873i \(-0.243214\pi\)
−0.960189 + 0.279351i \(0.909881\pi\)
\(510\) 0 0
\(511\) 741856. 7.14210e6i 0.125680 1.20997i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 7.15264e6 1.23887e7i 1.18836 2.05830i
\(516\) 0 0
\(517\) −2.31062e6 −0.380192
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 522678. 905306.i 0.0843607 0.146117i −0.820758 0.571276i \(-0.806449\pi\)
0.905119 + 0.425159i \(0.139782\pi\)
\(522\) 0 0
\(523\) 1.81578e6 + 3.14503e6i 0.290275 + 0.502771i 0.973875 0.227086i \(-0.0729199\pi\)
−0.683600 + 0.729857i \(0.739587\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −133027. 230410.i −0.0208648 0.0361389i
\(528\) 0 0
\(529\) −2.18700e6 + 3.78800e6i −0.339789 + 0.588532i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.15410e7 −1.75964
\(534\) 0 0
\(535\) 8.51034e6 1.47403e7i 1.28547 2.22650i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −736558. 2.24821e6i −0.109203 0.333323i
\(540\) 0 0
\(541\) 4.72442e6 + 8.18294e6i 0.693994 + 1.20203i 0.970519 + 0.241025i \(0.0774837\pi\)
−0.276525 + 0.961007i \(0.589183\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.24985e7 −1.80246
\(546\) 0 0
\(547\) 2.69014e6 0.384421 0.192210 0.981354i \(-0.438434\pi\)
0.192210 + 0.981354i \(0.438434\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 3.24459e6 + 5.61979e6i 0.455282 + 0.788572i
\(552\) 0 0
\(553\) −5.24421e6 3.80038e6i −0.729235 0.528462i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −4.44490e6 + 7.69880e6i −0.607050 + 1.05144i 0.384674 + 0.923052i \(0.374314\pi\)
−0.991724 + 0.128389i \(0.959020\pi\)
\(558\) 0 0
\(559\) −7.93112e6 −1.07351
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 629963. 1.09113e6i 0.0837615 0.145079i −0.821101 0.570782i \(-0.806640\pi\)
0.904863 + 0.425703i \(0.139973\pi\)
\(564\) 0 0
\(565\) 8.21297e6 + 1.42253e7i 1.08238 + 1.87473i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −2.91019e6 5.04059e6i −0.376826 0.652681i 0.613773 0.789483i \(-0.289651\pi\)
−0.990598 + 0.136801i \(0.956318\pi\)
\(570\) 0 0
\(571\) −2.32980e6 + 4.03534e6i −0.299040 + 0.517952i −0.975917 0.218144i \(-0.930000\pi\)
0.676877 + 0.736096i \(0.263333\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.80558e7 2.27744
\(576\) 0 0
\(577\) 762391. 1.32050e6i 0.0953319 0.165120i −0.814415 0.580283i \(-0.802942\pi\)
0.909747 + 0.415163i \(0.136275\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 5.30992e6 2.37189e6i 0.652600 0.291511i
\(582\) 0 0
\(583\) 1.47620e6 + 2.55685e6i 0.179876 + 0.311554i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.50087e7 1.79783 0.898914 0.438124i \(-0.144357\pi\)
0.898914 + 0.438124i \(0.144357\pi\)
\(588\) 0 0
\(589\) 8.29792e6 0.985556
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −3.53973e6 6.13099e6i −0.413364 0.715968i 0.581891 0.813267i \(-0.302313\pi\)
−0.995255 + 0.0972987i \(0.968980\pi\)
\(594\) 0 0
\(595\) 603081. 269391.i 0.0698366 0.0311954i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1.08761e6 + 1.88379e6i −0.123853 + 0.214519i −0.921284 0.388891i \(-0.872858\pi\)
0.797431 + 0.603410i \(0.206192\pi\)
\(600\) 0 0
\(601\) 2.69785e6 0.304671 0.152336 0.988329i \(-0.451321\pi\)
0.152336 + 0.988329i \(0.451321\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 6.55520e6 1.13539e7i 0.728111 1.26112i
\(606\) 0 0
\(607\) −2.49417e6 4.32003e6i −0.274760 0.475899i 0.695314 0.718706i \(-0.255265\pi\)
−0.970075 + 0.242807i \(0.921932\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 9.12056e6 + 1.57973e7i 0.988367 + 1.71190i
\(612\) 0 0
\(613\) −556820. + 964441.i −0.0598500 + 0.103663i −0.894398 0.447272i \(-0.852396\pi\)
0.834548 + 0.550935i \(0.185729\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5.14757e6 0.544364 0.272182 0.962246i \(-0.412255\pi\)
0.272182 + 0.962246i \(0.412255\pi\)
\(618\) 0 0
\(619\) −121588. + 210597.i −0.0127545 + 0.0220915i −0.872332 0.488914i \(-0.837393\pi\)
0.859578 + 0.511005i \(0.170727\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1.34311e7 9.73322e6i −1.38641 1.00470i
\(624\) 0 0
\(625\) −1.61533e6 2.79783e6i −0.165410 0.286498i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 623884. 0.0628749
\(630\) 0 0
\(631\) 9.94255e6 0.994087 0.497044 0.867726i \(-0.334419\pi\)
0.497044 + 0.867726i \(0.334419\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −6.70347e6 1.16108e7i −0.659729 1.14268i
\(636\) 0 0
\(637\) −1.24632e7 + 1.39099e7i −1.21697 + 1.35824i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −5.77767e6 + 1.00072e7i −0.555402 + 0.961985i 0.442470 + 0.896783i \(0.354102\pi\)
−0.997872 + 0.0652017i \(0.979231\pi\)
\(642\) 0 0
\(643\) 1.35139e6 0.128900 0.0644500 0.997921i \(-0.479471\pi\)
0.0644500 + 0.997921i \(0.479471\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 8.77678e6 1.52018e7i 0.824279 1.42769i −0.0781895 0.996939i \(-0.524914\pi\)
0.902469 0.430755i \(-0.141753\pi\)
\(648\) 0 0
\(649\) 2.54864e6 + 4.41437e6i 0.237518 + 0.411393i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3.99936e6 6.92710e6i −0.367035 0.635724i 0.622065 0.782965i \(-0.286294\pi\)
−0.989101 + 0.147242i \(0.952961\pi\)
\(654\) 0 0
\(655\) −1.10234e7 + 1.90931e7i −1.00395 + 1.73889i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −229419. −0.0205786 −0.0102893 0.999947i \(-0.503275\pi\)
−0.0102893 + 0.999947i \(0.503275\pi\)
\(660\) 0 0
\(661\) 1.64279e6 2.84539e6i 0.146244 0.253302i −0.783593 0.621275i \(-0.786615\pi\)
0.929836 + 0.367973i \(0.119948\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2.12835e6 + 2.04904e7i −0.186634 + 1.79678i
\(666\) 0 0
\(667\) −6.23177e6 1.07937e7i −0.542372 0.939416i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −696590. −0.0597271
\(672\) 0 0
\(673\) 8.22188e6 0.699734 0.349867 0.936799i \(-0.386227\pi\)
0.349867 + 0.936799i \(0.386227\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.07702e7 + 1.86546e7i 0.903138 + 1.56428i 0.823397 + 0.567465i \(0.192076\pi\)
0.0797405 + 0.996816i \(0.474591\pi\)
\(678\) 0 0
\(679\) 7.77519e6 3.47311e6i 0.647197 0.289097i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −8.08706e6 + 1.40072e7i −0.663344 + 1.14895i 0.316387 + 0.948630i \(0.397530\pi\)
−0.979731 + 0.200316i \(0.935803\pi\)
\(684\) 0 0
\(685\) 8.93012e6 0.727162
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.16538e7 2.01850e7i 0.935231 1.61987i
\(690\) 0 0
\(691\) −5.32318e6 9.22002e6i −0.424108 0.734576i 0.572229 0.820094i \(-0.306079\pi\)
−0.996337 + 0.0855179i \(0.972746\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.81647e7 + 3.14622e7i 1.42648 + 2.47074i
\(696\) 0 0
\(697\) 285018. 493666.i 0.0222224 0.0384903i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 4.55461e6 0.350071 0.175035 0.984562i \(-0.443996\pi\)
0.175035 + 0.984562i \(0.443996\pi\)
\(702\) 0 0
\(703\) −9.72909e6 + 1.68513e7i −0.742479 + 1.28601i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2.35442e6 + 2.26668e7i −0.177148 + 1.70546i
\(708\) 0 0
\(709\) −6.55174e6 1.13479e7i −0.489487 0.847816i 0.510440 0.859913i \(-0.329483\pi\)
−0.999927 + 0.0120971i \(0.996149\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.59375e7 −1.17408
\(714\) 0 0
\(715\) 1.45199e7 1.06218
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 8.95942e6 + 1.55182e7i 0.646335 + 1.11949i 0.983991 + 0.178216i \(0.0570325\pi\)
−0.337656 + 0.941269i \(0.609634\pi\)
\(720\) 0 0
\(721\) −1.61777e7 1.17236e7i −1.15899 0.839894i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.04085e7 + 1.80281e7i −0.735435 + 1.27381i
\(726\) 0 0
\(727\) 1.41466e7 0.992693 0.496347 0.868125i \(-0.334675\pi\)
0.496347 + 0.868125i \(0.334675\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 195868. 339254.i 0.0135572 0.0234818i
\(732\) 0 0
\(733\) 6.22241e6 + 1.07775e7i 0.427758 + 0.740899i 0.996674 0.0814969i \(-0.0259701\pi\)
−0.568915 + 0.822396i \(0.692637\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.61634e6 2.79959e6i −0.109614 0.189857i
\(738\) 0 0
\(739\) 883322. 1.52996e6i 0.0594988 0.103055i −0.834742 0.550642i \(-0.814383\pi\)
0.894241 + 0.447587i \(0.147716\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −5.73250e6 −0.380953 −0.190477 0.981692i \(-0.561003\pi\)
−0.190477 + 0.981692i \(0.561003\pi\)
\(744\) 0 0
\(745\) −3.74453e6 + 6.48571e6i −0.247176 + 0.428122i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1.92485e7 1.39490e7i −1.25370 0.908528i
\(750\) 0 0
\(751\) −1.31566e7 2.27879e7i −0.851224 1.47436i −0.880104 0.474780i \(-0.842528\pi\)
0.0288804 0.999583i \(-0.490806\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 8.88179e6 0.567066
\(756\) 0 0
\(757\) 1.63104e7 1.03449 0.517245 0.855838i \(-0.326958\pi\)
0.517245 + 0.855838i \(0.326958\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 8.42080e6 + 1.45853e7i 0.527098 + 0.912961i 0.999501 + 0.0315785i \(0.0100534\pi\)
−0.472403 + 0.881383i \(0.656613\pi\)
\(762\) 0 0
\(763\) −1.80342e6 + 1.73622e7i −0.112147 + 1.07967i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.01201e7 3.48491e7i 1.23493 2.13896i
\(768\) 0 0
\(769\) 1.19890e7 0.731084 0.365542 0.930795i \(-0.380884\pi\)
0.365542 + 0.930795i \(0.380884\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 8.48868e6 1.47028e7i 0.510965 0.885018i −0.488954 0.872310i \(-0.662621\pi\)
0.999919 0.0127081i \(-0.00404522\pi\)
\(774\) 0 0
\(775\) 1.33097e7 + 2.30531e7i 0.796003 + 1.37872i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 8.88937e6 + 1.53968e7i 0.524841 + 0.909050i
\(780\) 0 0
\(781\) 1.85397e6 3.21117e6i 0.108761 0.188380i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1.81590e7 −1.05177
\(786\) 0 0
\(787\) 1.59750e7 2.76696e7i 0.919400 1.59245i 0.119072 0.992886i \(-0.462008\pi\)
0.800328 0.599563i \(-0.204659\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0