Properties

Label 84.6.i.c.37.4
Level $84$
Weight $6$
Character 84.37
Analytic conductor $13.472$
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] = [84,6,Mod(25,84)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(84, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("84.25");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 84.i (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: \(13.4722408643\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.4
Root \(-11.2416 - 19.4709i\) of defining polynomial
Character \(\chi\) \(=\) 84.37
Dual form 84.6.i.c.25.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.50000 + 7.79423i) q^{3} +(46.4128 - 80.3893i) q^{5} +(-118.369 - 52.8745i) q^{7} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\) \(q+(4.50000 + 7.79423i) q^{3} +(46.4128 - 80.3893i) q^{5} +(-118.369 - 52.8745i) q^{7} +(-40.5000 + 70.1481i) q^{9} +(-70.3812 - 121.904i) q^{11} -1111.24 q^{13} +835.430 q^{15} +(-27.4435 - 47.5335i) q^{17} +(855.929 - 1482.51i) q^{19} +(-120.546 - 1160.53i) q^{21} +(1643.95 - 2847.41i) q^{23} +(-2745.79 - 4755.85i) q^{25} -729.000 q^{27} -3790.72 q^{29} +(2423.66 + 4197.90i) q^{31} +(633.431 - 1097.13i) q^{33} +(-9744.39 + 7061.57i) q^{35} +(5683.35 - 9843.86i) q^{37} +(-5000.59 - 8661.28i) q^{39} -10385.6 q^{41} +7137.16 q^{43} +(3759.43 + 6511.53i) q^{45} +(8207.53 - 14215.9i) q^{47} +(11215.6 + 12517.4i) q^{49} +(246.991 - 427.801i) q^{51} +(10487.2 + 18164.3i) q^{53} -13066.3 q^{55} +15406.7 q^{57} +(18106.0 + 31360.5i) q^{59} +(-2474.35 + 4285.70i) q^{61} +(8503.00 - 6161.96i) q^{63} +(-51575.9 + 89332.0i) q^{65} +(11482.8 + 19888.8i) q^{67} +29591.2 q^{69} -26341.8 q^{71} +(-27693.7 - 47966.9i) q^{73} +(24712.1 - 42802.6i) q^{75} +(1885.36 + 18151.0i) q^{77} +(24978.3 - 43263.7i) q^{79} +(-3280.50 - 5681.99i) q^{81} +44858.9 q^{83} -5094.91 q^{85} +(-17058.2 - 29545.8i) q^{87} +(-63972.5 + 110804. i) q^{89} +(131537. + 58756.4i) q^{91} +(-21812.9 + 37781.1i) q^{93} +(-79452.1 - 137615. i) q^{95} -65685.9 q^{97} +11401.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 36 q^{3} - 42 q^{7} - 324 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 36 q^{3} - 42 q^{7} - 324 q^{9} - 462 q^{11} - 1204 q^{13} + 228 q^{17} + 358 q^{19} + 1404 q^{21} - 2148 q^{23} - 5454 q^{25} - 5832 q^{27} - 11064 q^{29} + 830 q^{31} + 4158 q^{33} + 7692 q^{35} - 3914 q^{37} - 5418 q^{39} - 16632 q^{41} - 29036 q^{43} + 41700 q^{47} + 41876 q^{49} - 2052 q^{51} + 22164 q^{53} + 7784 q^{55} + 6444 q^{57} + 32886 q^{59} + 83732 q^{61} + 16038 q^{63} - 93192 q^{65} - 80034 q^{67} - 38664 q^{69} + 89544 q^{71} - 22470 q^{73} + 49086 q^{75} + 138732 q^{77} - 75286 q^{79} - 26244 q^{81} - 34836 q^{83} + 278504 q^{85} - 49788 q^{87} + 28944 q^{89} - 12058 q^{91} - 7470 q^{93} - 144120 q^{95} - 433356 q^{97} + 74844 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(43\) \(73\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 4.50000 + 7.79423i 0.288675 + 0.500000i
\(4\) 0 0
\(5\) 46.4128 80.3893i 0.830257 1.43805i −0.0675775 0.997714i \(-0.521527\pi\)
0.897834 0.440333i \(-0.145140\pi\)
\(6\) 0 0
\(7\) −118.369 52.8745i −0.913049 0.407851i
\(8\) 0 0
\(9\) −40.5000 + 70.1481i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −70.3812 121.904i −0.175378 0.303763i 0.764914 0.644132i \(-0.222781\pi\)
−0.940292 + 0.340369i \(0.889448\pi\)
\(12\) 0 0
\(13\) −1111.24 −1.82369 −0.911844 0.410537i \(-0.865341\pi\)
−0.911844 + 0.410537i \(0.865341\pi\)
\(14\) 0 0
\(15\) 835.430 0.958698
\(16\) 0 0
\(17\) −27.4435 47.5335i −0.0230312 0.0398912i 0.854280 0.519813i \(-0.173998\pi\)
−0.877311 + 0.479922i \(0.840665\pi\)
\(18\) 0 0
\(19\) 855.929 1482.51i 0.543943 0.942138i −0.454729 0.890630i \(-0.650264\pi\)
0.998673 0.0515079i \(-0.0164027\pi\)
\(20\) 0 0
\(21\) −120.546 1160.53i −0.0596490 0.574261i
\(22\) 0 0
\(23\) 1643.95 2847.41i 0.647993 1.12236i −0.335609 0.942001i \(-0.608942\pi\)
0.983602 0.180355i \(-0.0577247\pi\)
\(24\) 0 0
\(25\) −2745.79 4755.85i −0.878653 1.52187i
\(26\) 0 0
\(27\) −729.000 −0.192450
\(28\) 0 0
\(29\) −3790.72 −0.837003 −0.418501 0.908216i \(-0.637445\pi\)
−0.418501 + 0.908216i \(0.637445\pi\)
\(30\) 0 0
\(31\) 2423.66 + 4197.90i 0.452968 + 0.784563i 0.998569 0.0534817i \(-0.0170319\pi\)
−0.545601 + 0.838045i \(0.683699\pi\)
\(32\) 0 0
\(33\) 633.431 1097.13i 0.101254 0.175378i
\(34\) 0 0
\(35\) −9744.39 + 7061.57i −1.34457 + 0.974386i
\(36\) 0 0
\(37\) 5683.35 9843.86i 0.682496 1.18212i −0.291720 0.956504i \(-0.594228\pi\)
0.974217 0.225615i \(-0.0724391\pi\)
\(38\) 0 0
\(39\) −5000.59 8661.28i −0.526453 0.911844i
\(40\) 0 0
\(41\) −10385.6 −0.964881 −0.482440 0.875929i \(-0.660249\pi\)
−0.482440 + 0.875929i \(0.660249\pi\)
\(42\) 0 0
\(43\) 7137.16 0.588646 0.294323 0.955706i \(-0.404906\pi\)
0.294323 + 0.955706i \(0.404906\pi\)
\(44\) 0 0
\(45\) 3759.43 + 6511.53i 0.276752 + 0.479349i
\(46\) 0 0
\(47\) 8207.53 14215.9i 0.541961 0.938704i −0.456831 0.889554i \(-0.651015\pi\)
0.998791 0.0491499i \(-0.0156512\pi\)
\(48\) 0 0
\(49\) 11215.6 + 12517.4i 0.667315 + 0.744775i
\(50\) 0 0
\(51\) 246.991 427.801i 0.0132971 0.0230312i
\(52\) 0 0
\(53\) 10487.2 + 18164.3i 0.512824 + 0.888238i 0.999889 + 0.0148720i \(0.00473407\pi\)
−0.487065 + 0.873366i \(0.661933\pi\)
\(54\) 0 0
\(55\) −13066.3 −0.582435
\(56\) 0 0
\(57\) 15406.7 0.628092
\(58\) 0 0
\(59\) 18106.0 + 31360.5i 0.677161 + 1.17288i 0.975832 + 0.218521i \(0.0701231\pi\)
−0.298672 + 0.954356i \(0.596544\pi\)
\(60\) 0 0
\(61\) −2474.35 + 4285.70i −0.0851405 + 0.147468i −0.905451 0.424451i \(-0.860467\pi\)
0.820311 + 0.571918i \(0.193801\pi\)
\(62\) 0 0
\(63\) 8503.00 6161.96i 0.269911 0.195599i
\(64\) 0 0
\(65\) −51575.9 + 89332.0i −1.51413 + 2.62255i
\(66\) 0 0
\(67\) 11482.8 + 19888.8i 0.312507 + 0.541279i 0.978905 0.204318i \(-0.0654978\pi\)
−0.666397 + 0.745597i \(0.732164\pi\)
\(68\) 0 0
\(69\) 29591.2 0.748238
\(70\) 0 0
\(71\) −26341.8 −0.620154 −0.310077 0.950711i \(-0.600355\pi\)
−0.310077 + 0.950711i \(0.600355\pi\)
\(72\) 0 0
\(73\) −27693.7 47966.9i −0.608238 1.05350i −0.991531 0.129872i \(-0.958543\pi\)
0.383293 0.923627i \(-0.374790\pi\)
\(74\) 0 0
\(75\) 24712.1 42802.6i 0.507291 0.878653i
\(76\) 0 0
\(77\) 1885.36 + 18151.0i 0.0362383 + 0.348879i
\(78\) 0 0
\(79\) 24978.3 43263.7i 0.450293 0.779930i −0.548111 0.836406i \(-0.684653\pi\)
0.998404 + 0.0564752i \(0.0179862\pi\)
\(80\) 0 0
\(81\) −3280.50 5681.99i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 44858.9 0.714749 0.357374 0.933961i \(-0.383672\pi\)
0.357374 + 0.933961i \(0.383672\pi\)
\(84\) 0 0
\(85\) −5094.91 −0.0764873
\(86\) 0 0
\(87\) −17058.2 29545.8i −0.241622 0.418501i
\(88\) 0 0
\(89\) −63972.5 + 110804.i −0.856087 + 1.48279i 0.0195454 + 0.999809i \(0.493778\pi\)
−0.875633 + 0.482978i \(0.839555\pi\)
\(90\) 0 0
\(91\) 131537. + 58756.4i 1.66512 + 0.743793i
\(92\) 0 0
\(93\) −21812.9 + 37781.1i −0.261521 + 0.452968i
\(94\) 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
\(99\) 11401.8 0.116919
\(100\) 0 0
\(101\) −87891.4 152232.i −0.857320 1.48492i −0.874476 0.485068i \(-0.838795\pi\)
0.0171565 0.999853i \(-0.494539\pi\)
\(102\) 0 0
\(103\) 77054.7 133463.i 0.715659 1.23956i −0.247046 0.969004i \(-0.579460\pi\)
0.962705 0.270554i \(-0.0872068\pi\)
\(104\) 0 0
\(105\) −98889.2 44173.0i −0.875338 0.391006i
\(106\) 0 0
\(107\) −91681.0 + 158796.i −0.774141 + 1.34085i 0.161135 + 0.986932i \(0.448485\pi\)
−0.935276 + 0.353919i \(0.884849\pi\)
\(108\) 0 0
\(109\) 67322.3 + 116606.i 0.542741 + 0.940055i 0.998745 + 0.0500775i \(0.0159468\pi\)
−0.456004 + 0.889978i \(0.650720\pi\)
\(110\) 0 0
\(111\) 102300. 0.788079
\(112\) 0 0
\(113\) 176955. 1.30367 0.651833 0.758362i \(-0.274000\pi\)
0.651833 + 0.758362i \(0.274000\pi\)
\(114\) 0 0
\(115\) −152601. 264313.i −1.07600 1.86369i
\(116\) 0 0
\(117\) 45005.3 77951.5i 0.303948 0.526453i
\(118\) 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
\(123\) −46735.4 80948.0i −0.278537 0.482440i
\(124\) 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
\(129\) 32117.2 + 55628.6i 0.169927 + 0.294323i
\(130\) 0 0
\(131\) 118754. 205688.i 0.604602 1.04720i −0.387512 0.921865i \(-0.626665\pi\)
0.992114 0.125337i \(-0.0400013\pi\)
\(132\) 0 0
\(133\) −179703. + 130227.i −0.880899 + 0.638370i
\(134\) 0 0
\(135\) −33834.9 + 58603.8i −0.159783 + 0.276752i
\(136\) 0 0
\(137\) 48101.6 + 83314.5i 0.218957 + 0.379244i 0.954489 0.298245i \(-0.0964013\pi\)
−0.735533 + 0.677489i \(0.763068\pi\)
\(138\) 0 0
\(139\) −391373. −1.71812 −0.859060 0.511874i \(-0.828951\pi\)
−0.859060 + 0.511874i \(0.828951\pi\)
\(140\) 0 0
\(141\) 147736. 0.625802
\(142\) 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
\(147\) −47093.7 + 143745.i −0.179750 + 0.548656i
\(148\) 0 0
\(149\) 40339.4 69869.9i 0.148855 0.257825i −0.781949 0.623342i \(-0.785775\pi\)
0.930805 + 0.365517i \(0.119108\pi\)
\(150\) 0 0
\(151\) −47841.3 82863.6i −0.170750 0.295748i 0.767932 0.640531i \(-0.221286\pi\)
−0.938682 + 0.344783i \(0.887952\pi\)
\(152\) 0 0
\(153\) 4445.84 0.0153541
\(154\) 0 0
\(155\) 449955. 1.50432
\(156\) 0 0
\(157\) 97812.7 + 169417.i 0.316699 + 0.548538i 0.979797 0.199994i \(-0.0640923\pi\)
−0.663098 + 0.748532i \(0.730759\pi\)
\(158\) 0 0
\(159\) −94384.5 + 163479.i −0.296079 + 0.512824i
\(160\) 0 0
\(161\) −345149. + 250123.i −1.04940 + 0.760481i
\(162\) 0 0
\(163\) −18822.8 + 32602.1i −0.0554902 + 0.0961118i −0.892436 0.451174i \(-0.851005\pi\)
0.836946 + 0.547286i \(0.184339\pi\)
\(164\) 0 0
\(165\) −58798.5 101842.i −0.168134 0.291217i
\(166\) 0 0
\(167\) 646778. 1.79458 0.897292 0.441437i \(-0.145531\pi\)
0.897292 + 0.441437i \(0.145531\pi\)
\(168\) 0 0
\(169\) 863568. 2.32584
\(170\) 0 0
\(171\) 69330.3 + 120084.i 0.181314 + 0.314046i
\(172\) 0 0
\(173\) 193454. 335072.i 0.491431 0.851184i −0.508520 0.861050i \(-0.669807\pi\)
0.999951 + 0.00986616i \(0.00314055\pi\)
\(174\) 0 0
\(175\) 73554.0 + 708129.i 0.181556 + 1.74790i
\(176\) 0 0
\(177\) −162954. + 282244.i −0.390959 + 0.677161i
\(178\) 0 0
\(179\) −13705.3 23738.2i −0.0319709 0.0553752i 0.849597 0.527432i \(-0.176845\pi\)
−0.881568 + 0.472057i \(0.843512\pi\)
\(180\) 0 0
\(181\) −196155. −0.445044 −0.222522 0.974928i \(-0.571429\pi\)
−0.222522 + 0.974928i \(0.571429\pi\)
\(182\) 0 0
\(183\) −44538.3 −0.0983118
\(184\) 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
\(189\) 86291.2 + 38545.5i 0.175716 + 0.0784909i
\(190\) 0 0
\(191\) −133491. + 231213.i −0.264770 + 0.458595i −0.967503 0.252858i \(-0.918629\pi\)
0.702733 + 0.711453i \(0.251963\pi\)
\(192\) 0 0
\(193\) 50681.9 + 87783.6i 0.0979398 + 0.169637i 0.910832 0.412778i \(-0.135441\pi\)
−0.812892 + 0.582415i \(0.802108\pi\)
\(194\) 0 0
\(195\) −928366. −1.74837
\(196\) 0 0
\(197\) 362366. 0.665245 0.332623 0.943060i \(-0.392066\pi\)
0.332623 + 0.943060i \(0.392066\pi\)
\(198\) 0 0
\(199\) −112706. 195213.i −0.201751 0.349443i 0.747342 0.664440i \(-0.231330\pi\)
−0.949093 + 0.314997i \(0.897997\pi\)
\(200\) 0 0
\(201\) −103345. + 178999.i −0.180426 + 0.312507i
\(202\) 0 0
\(203\) 448705. + 200433.i 0.764224 + 0.341372i
\(204\) 0 0
\(205\) −482026. + 834894.i −0.801099 + 1.38754i
\(206\) 0 0
\(207\) 133160. + 230640.i 0.215998 + 0.374119i
\(208\) 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
\(213\) −118538. 205314.i −0.179023 0.310077i
\(214\) 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
\(219\) 249243. 431702.i 0.351166 0.608238i
\(220\) 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
\(225\) 444818. 0.585769
\(226\) 0 0
\(227\) −608733. 1.05436e6i −0.784083 1.35807i −0.929545 0.368708i \(-0.879800\pi\)
0.145463 0.989364i \(-0.453533\pi\)
\(228\) 0 0
\(229\) 668013. 1.15703e6i 0.841776 1.45800i −0.0466161 0.998913i \(-0.514844\pi\)
0.888392 0.459086i \(-0.151823\pi\)
\(230\) 0 0
\(231\) −132989. + 96374.6i −0.163978 + 0.118832i
\(232\) 0 0
\(233\) −23394.2 + 40520.0i −0.0282305 + 0.0488967i −0.879795 0.475352i \(-0.842321\pi\)
0.851565 + 0.524249i \(0.175654\pi\)
\(234\) 0 0
\(235\) −761868. 1.31959e6i −0.899933 1.55873i
\(236\) 0 0
\(237\) 449609. 0.519954
\(238\) 0 0
\(239\) 86350.2 0.0977841 0.0488921 0.998804i \(-0.484431\pi\)
0.0488921 + 0.998804i \(0.484431\pi\)
\(240\) 0 0
\(241\) −412649. 714730.i −0.457655 0.792682i 0.541181 0.840906i \(-0.317977\pi\)
−0.998837 + 0.0482236i \(0.984644\pi\)
\(242\) 0 0
\(243\) 29524.5 51137.9i 0.0320750 0.0555556i
\(244\) 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
\(249\) 201865. + 349641.i 0.206330 + 0.357374i
\(250\) 0 0
\(251\) −130188. −0.130432 −0.0652162 0.997871i \(-0.520774\pi\)
−0.0652162 + 0.997871i \(0.520774\pi\)
\(252\) 0 0
\(253\) −462814. −0.454574
\(254\) 0 0
\(255\) −22927.1 39710.9i −0.0220800 0.0382436i
\(256\) 0 0
\(257\) −51395.1 + 89018.9i −0.0485388 + 0.0840716i −0.889274 0.457375i \(-0.848790\pi\)
0.840735 + 0.541446i \(0.182123\pi\)
\(258\) 0 0
\(259\) −1.19322e6 + 864706.i −1.10528 + 0.800975i
\(260\) 0 0
\(261\) 153524. 265912.i 0.139500 0.241622i
\(262\) 0 0
\(263\) 17750.4 + 30744.5i 0.0158241 + 0.0274081i 0.873829 0.486233i \(-0.161630\pi\)
−0.858005 + 0.513641i \(0.828296\pi\)
\(264\) 0 0
\(265\) 1.94695e6 1.70310
\(266\) 0 0
\(267\) −1.15150e6 −0.988524
\(268\) 0 0
\(269\) −523171. 906158.i −0.440821 0.763525i 0.556929 0.830560i \(-0.311979\pi\)
−0.997751 + 0.0670350i \(0.978646\pi\)
\(270\) 0 0
\(271\) −88639.2 + 153528.i −0.0733167 + 0.126988i −0.900353 0.435160i \(-0.856692\pi\)
0.827036 + 0.562148i \(0.190025\pi\)
\(272\) 0 0
\(273\) 133955. + 1.28963e6i 0.108781 + 1.04727i
\(274\) 0 0
\(275\) −386504. + 669445.i −0.308193 + 0.533805i
\(276\) 0 0
\(277\) −72793.0 126081.i −0.0570020 0.0987304i 0.836116 0.548552i \(-0.184821\pi\)
−0.893118 + 0.449822i \(0.851487\pi\)
\(278\) 0 0
\(279\) −392633. −0.301979
\(280\) 0 0
\(281\) −1.03073e6 −0.778714 −0.389357 0.921087i \(-0.627303\pi\)
−0.389357 + 0.921087i \(0.627303\pi\)
\(282\) 0 0
\(283\) 558631. + 967577.i 0.414628 + 0.718157i 0.995389 0.0959167i \(-0.0305783\pi\)
−0.580761 + 0.814074i \(0.697245\pi\)
\(284\) 0 0
\(285\) 715069. 1.23854e6i 0.521478 0.903226i
\(286\) 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
\(291\) −295586. 511971.i −0.204622 0.354415i
\(292\) 0 0
\(293\) −2.02032e6 −1.37484 −0.687418 0.726262i \(-0.741256\pi\)
−0.687418 + 0.726262i \(0.741256\pi\)
\(294\) 0 0
\(295\) 3.36139e6 2.24887
\(296\) 0 0
\(297\) 51307.9 + 88867.9i 0.0337515 + 0.0584593i
\(298\) 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
\(303\) 791022. 1.37009e6i 0.494974 0.857320i
\(304\) 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
\(309\) 1.38698e6 0.826372
\(310\) 0 0
\(311\) 1.15009e6 + 1.99202e6i 0.674268 + 1.16787i 0.976682 + 0.214689i \(0.0688739\pi\)
−0.302415 + 0.953176i \(0.597793\pi\)
\(312\) 0 0
\(313\) 1.37863e6 2.38786e6i 0.795404 1.37768i −0.127178 0.991880i \(-0.540592\pi\)
0.922582 0.385801i \(-0.126075\pi\)
\(314\) 0 0
\(315\) −100707. 969544.i −0.0571853 0.550543i
\(316\) 0 0
\(317\) −1.27404e6 + 2.20671e6i −0.712092 + 1.23338i 0.251978 + 0.967733i \(0.418919\pi\)
−0.964070 + 0.265647i \(0.914414\pi\)
\(318\) 0 0
\(319\) 266795. + 462103.i 0.146792 + 0.254251i
\(320\) 0 0
\(321\) −1.65026e6 −0.893901
\(322\) 0 0
\(323\) −93958.7 −0.0501107
\(324\) 0 0
\(325\) 3.05124e6 + 5.28490e6i 1.60239 + 2.77542i
\(326\) 0 0
\(327\) −605901. + 1.04945e6i −0.313352 + 0.542741i
\(328\) 0 0
\(329\) −1.72318e6 + 1.24875e6i −0.877688 + 0.636043i
\(330\) 0 0
\(331\) 244667. 423776.i 0.122746 0.212602i −0.798104 0.602520i \(-0.794163\pi\)
0.920849 + 0.389918i \(0.127497\pi\)
\(332\) 0 0
\(333\) 460352. + 797352.i 0.227499 + 0.394039i
\(334\) 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
\(339\) 796297. + 1.37923e6i 0.376336 + 0.651833i
\(340\) 0 0
\(341\) 341160. 590907.i 0.158881 0.275190i
\(342\) 0 0
\(343\) −665725. 2.07470e6i −0.305534 0.952181i
\(344\) 0 0
\(345\) 1.37341e6 2.37881e6i 0.621229 1.07600i
\(346\) 0 0
\(347\) 1.20963e6 + 2.09513e6i 0.539296 + 0.934088i 0.998942 + 0.0459859i \(0.0146429\pi\)
−0.459646 + 0.888102i \(0.652024\pi\)
\(348\) 0 0
\(349\) −2.58571e6 −1.13636 −0.568180 0.822905i \(-0.692352\pi\)
−0.568180 + 0.822905i \(0.692352\pi\)
\(350\) 0 0
\(351\) 810096. 0.350969
\(352\) 0 0
\(353\) −502198. 869832.i −0.214505 0.371534i 0.738614 0.674128i \(-0.235481\pi\)
−0.953119 + 0.302594i \(0.902147\pi\)
\(354\) 0 0
\(355\) −1.22260e6 + 2.11760e6i −0.514887 + 0.891811i
\(356\) 0 0
\(357\) −51856.0 + 37579.0i −0.0215342 + 0.0156054i
\(358\) 0 0
\(359\) 1.13383e6 1.96384e6i 0.464313 0.804213i −0.534858 0.844942i \(-0.679635\pi\)
0.999170 + 0.0407292i \(0.0129681\pi\)
\(360\) 0 0
\(361\) −227180. 393487.i −0.0917490 0.158914i
\(362\) 0 0
\(363\) 1.27113e6 0.506319
\(364\) 0 0
\(365\) −5.14136e6 −2.01998
\(366\) 0 0
\(367\) −2.39312e6 4.14500e6i −0.927467 1.60642i −0.787545 0.616258i \(-0.788648\pi\)
−0.139923 0.990162i \(-0.544685\pi\)
\(368\) 0 0
\(369\) 420618. 728532.i 0.160813 0.278537i
\(370\) 0 0
\(371\) −280929. 2.70460e6i −0.105965 1.02016i
\(372\) 0 0
\(373\) 2.31351e6 4.00711e6i 0.860991 1.49128i −0.00998166 0.999950i \(-0.503177\pi\)
0.870973 0.491331i \(-0.163489\pi\)
\(374\) 0 0
\(375\) −988557. 1.71223e6i −0.363014 0.628759i
\(376\) 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
\(381\) 649942. + 1.12573e6i 0.229384 + 0.397304i
\(382\) 0 0
\(383\) −693745. + 1.20160e6i −0.241659 + 0.418566i −0.961187 0.275898i \(-0.911025\pi\)
0.719528 + 0.694463i \(0.244358\pi\)
\(384\) 0 0
\(385\) 1.54665e6 + 690877.i 0.531791 + 0.237547i
\(386\) 0 0
\(387\) −289055. + 500658.i −0.0981077 + 0.169927i
\(388\) 0 0
\(389\) 293028. + 507539.i 0.0981826 + 0.170057i 0.910932 0.412556i \(-0.135364\pi\)
−0.812750 + 0.582613i \(0.802030\pi\)
\(390\) 0 0
\(391\) −180463. −0.0596962
\(392\) 0 0
\(393\) 2.13757e6 0.698135
\(394\) 0 0
\(395\) −2.31862e6 4.01598e6i −0.747718 1.29509i
\(396\) 0 0
\(397\) −1.52668e6 + 2.64429e6i −0.486151 + 0.842039i −0.999873 0.0159181i \(-0.994933\pi\)
0.513722 + 0.857957i \(0.328266\pi\)
\(398\) 0 0
\(399\) −1.82368e6 814623.i −0.573478 0.256168i
\(400\) 0 0
\(401\) −2.76158e6 + 4.78320e6i −0.857624 + 1.48545i 0.0165657 + 0.999863i \(0.494727\pi\)
−0.874189 + 0.485585i \(0.838607\pi\)
\(402\) 0 0
\(403\) −2.69327e6 4.66489e6i −0.826072 1.43080i
\(404\) 0 0
\(405\) −609028. −0.184502
\(406\) 0 0
\(407\) −1.60000e6 −0.478779
\(408\) 0 0
\(409\) 1.67464e6 + 2.90055e6i 0.495008 + 0.857379i 0.999983 0.00575475i \(-0.00183180\pi\)
−0.504975 + 0.863134i \(0.668498\pi\)
\(410\) 0 0
\(411\) −432915. + 749830.i −0.126415 + 0.218957i
\(412\) 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
\(417\) −1.76118e6 3.05045e6i −0.495979 0.859060i
\(418\) 0 0
\(419\) 2.97012e6 0.826493 0.413247 0.910619i \(-0.364395\pi\)
0.413247 + 0.910619i \(0.364395\pi\)
\(420\) 0 0
\(421\) −5.41478e6 −1.48894 −0.744468 0.667658i \(-0.767297\pi\)
−0.744468 + 0.667658i \(0.767297\pi\)
\(422\) 0 0
\(423\) 664810. + 1.15148e6i 0.180654 + 0.312901i
\(424\) 0 0
\(425\) −150708. + 261034.i −0.0404729 + 0.0701011i
\(426\) 0 0
\(427\) 519491. 376465.i 0.137882 0.0999205i
\(428\) 0 0
\(429\) −703895. + 1.21918e6i −0.184657 + 0.319835i
\(430\) 0 0
\(431\) 2.52975e6 + 4.38165e6i 0.655970 + 1.13617i 0.981650 + 0.190694i \(0.0610737\pi\)
−0.325679 + 0.945480i \(0.605593\pi\)
\(432\) 0 0
\(433\) 3.84174e6 0.984711 0.492355 0.870394i \(-0.336136\pi\)
0.492355 + 0.870394i \(0.336136\pi\)
\(434\) 0 0
\(435\) −3.16688e6 −0.802433
\(436\) 0 0
\(437\) −2.81422e6 4.87437e6i −0.704943 1.22100i
\(438\) 0 0
\(439\) 762859. 1.32131e6i 0.188922 0.327223i −0.755969 0.654607i \(-0.772834\pi\)
0.944891 + 0.327385i \(0.106167\pi\)
\(440\) 0 0
\(441\) −1.33230e6 + 279794.i −0.326217 + 0.0685081i
\(442\) 0 0
\(443\) 735068. 1.27317e6i 0.177958 0.308233i −0.763223 0.646135i \(-0.776384\pi\)
0.941181 + 0.337903i \(0.109717\pi\)
\(444\) 0 0
\(445\) 5.93828e6 + 1.02854e7i 1.42154 + 2.46219i
\(446\) 0 0
\(447\) 726110. 0.171883
\(448\) 0 0
\(449\) −6.05071e6 −1.41641 −0.708207 0.706004i \(-0.750496\pi\)
−0.708207 + 0.706004i \(0.750496\pi\)
\(450\) 0 0
\(451\) 730954. + 1.26605e6i 0.169219 + 0.293095i
\(452\) 0 0
\(453\) 430572. 745772.i 0.0985826 0.170750i
\(454\) 0 0
\(455\) 1.08284e7 7.84712e6i 2.45208 1.77698i
\(456\) 0 0
\(457\) 2.87710e6 4.98328e6i 0.644413 1.11616i −0.340024 0.940417i \(-0.610435\pi\)
0.984437 0.175739i \(-0.0562315\pi\)
\(458\) 0 0
\(459\) 20006.3 + 34651.9i 0.00443236 + 0.00767707i
\(460\) 0 0
\(461\) 2.83684e6 0.621703 0.310851 0.950458i \(-0.399386\pi\)
0.310851 + 0.950458i \(0.399386\pi\)
\(462\) 0 0
\(463\) 5.19089e6 1.12535 0.562677 0.826677i \(-0.309771\pi\)
0.562677 + 0.826677i \(0.309771\pi\)
\(464\) 0 0
\(465\) 2.02480e6 + 3.50705e6i 0.434260 + 0.752160i
\(466\) 0 0
\(467\) −544520. + 943136.i −0.115537 + 0.200116i −0.917994 0.396594i \(-0.870192\pi\)
0.802457 + 0.596710i \(0.203526\pi\)
\(468\) 0 0
\(469\) −307600. 2.96137e6i −0.0645734 0.621670i
\(470\) 0 0
\(471\) −880315. + 1.52475e6i −0.182846 + 0.316699i
\(472\) 0 0
\(473\) −502322. 870047.i −0.103235 0.178809i
\(474\) 0 0
\(475\) −9.40081e6 −1.91175
\(476\) 0 0
\(477\) −1.69892e6 −0.341883
\(478\) 0 0
\(479\) 2.84705e6 + 4.93124e6i 0.566966 + 0.982013i 0.996864 + 0.0791359i \(0.0252161\pi\)
−0.429898 + 0.902877i \(0.641451\pi\)
\(480\) 0 0
\(481\) −6.31559e6 + 1.09389e7i −1.24466 + 2.15582i
\(482\) 0 0
\(483\) −3.50269e6 1.56462e6i −0.683177 0.305169i
\(484\) 0 0
\(485\) −3.04866e6 + 5.28044e6i −0.588512 + 1.01933i
\(486\) 0 0
\(487\) 2.05713e6 + 3.56305e6i 0.393042 + 0.680768i 0.992849 0.119376i \(-0.0380895\pi\)
−0.599807 + 0.800144i \(0.704756\pi\)
\(488\) 0 0
\(489\) −338811. −0.0640745
\(490\) 0 0
\(491\) −609530. −0.114101 −0.0570507 0.998371i \(-0.518170\pi\)
−0.0570507 + 0.998371i \(0.518170\pi\)
\(492\) 0 0
\(493\) 104031. + 180186.i 0.0192772 + 0.0333891i
\(494\) 0 0
\(495\) 529187. 916579.i 0.0970725 0.168134i
\(496\) 0 0
\(497\) 3.11806e6 + 1.39281e6i 0.566231 + 0.252930i
\(498\) 0 0
\(499\) −497896. + 862382.i −0.0895133 + 0.155042i −0.907306 0.420472i \(-0.861864\pi\)
0.817792 + 0.575514i \(0.195198\pi\)
\(500\) 0 0
\(501\) 2.91050e6 + 5.04113e6i 0.518052 + 0.897292i
\(502\) 0 0
\(503\) 1.02730e7 1.81042 0.905209 0.424966i \(-0.139714\pi\)
0.905209 + 0.424966i \(0.139714\pi\)
\(504\) 0 0
\(505\) −1.63171e7 −2.84718
\(506\) 0 0
\(507\) 3.88605e6 + 6.73084e6i 0.671412 + 1.16292i
\(508\) 0 0
\(509\) 1.39213e6 2.41125e6i 0.238170 0.412522i −0.722020 0.691873i \(-0.756786\pi\)
0.960189 + 0.279351i \(0.0901193\pi\)
\(510\) 0 0
\(511\) 741856. + 7.14210e6i 0.125680 + 1.20997i
\(512\) 0 0
\(513\) −623972. + 1.08075e6i −0.104682 + 0.181314i
\(514\) 0 0
\(515\) −7.15264e6 1.23887e7i −1.18836 2.05830i
\(516\) 0 0
\(517\) −2.31062e6 −0.380192
\(518\) 0 0
\(519\) 3.48218e6 0.567456
\(520\) 0 0
\(521\) −522678. 905306.i −0.0843607 0.146117i 0.820758 0.571276i \(-0.193551\pi\)
−0.905119 + 0.425159i \(0.860218\pi\)
\(522\) 0 0
\(523\) 1.81578e6 3.14503e6i 0.290275 0.502771i −0.683600 0.729857i \(-0.739587\pi\)
0.973875 + 0.227086i \(0.0729199\pi\)
\(524\) 0 0
\(525\) −5.18833e6 + 3.75988e6i −0.821540 + 0.595354i
\(526\) 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
\(531\) −2.93317e6 −0.451440
\(532\) 0 0
\(533\) 1.15410e7 1.75964
\(534\) 0 0
\(535\) 8.51034e6 + 1.47403e7i 1.28547 + 2.22650i
\(536\) 0 0
\(537\) 123347. 213644.i 0.0184584 0.0319709i
\(538\) 0 0
\(539\) 736558. 2.24821e6i 0.109203 0.333323i
\(540\) 0 0
\(541\) 4.72442e6 8.18294e6i 0.693994 1.20203i −0.276525 0.961007i \(-0.589183\pi\)
0.970519 0.241025i \(-0.0774837\pi\)
\(542\) 0 0
\(543\) −882698. 1.52888e6i −0.128473 0.222522i
\(544\) 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
\(549\) −200422. 347142.i −0.0283802 0.0491559i
\(550\) 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
\(555\) 4.74804e6 8.22385e6i 0.654308 1.13329i
\(556\) 0 0
\(557\) 4.44490e6 + 7.69880e6i 0.607050 + 1.05144i 0.991724 + 0.128389i \(0.0409805\pi\)
−0.384674 + 0.923052i \(0.625686\pi\)
\(558\) 0 0
\(559\) −7.93112e6 −1.07351
\(560\) 0 0
\(561\) −69534.1 −0.00932805
\(562\) 0 0
\(563\) −629963. 1.09113e6i −0.0837615 0.145079i 0.821101 0.570782i \(-0.193360\pi\)
−0.904863 + 0.425703i \(0.860027\pi\)
\(564\) 0 0
\(565\) 8.21297e6 1.42253e7i 1.08238 1.87473i
\(566\) 0 0
\(567\) 87877.7 + 846028.i 0.0114794 + 0.110517i
\(568\) 0 0
\(569\) 2.91019e6 5.04059e6i 0.376826 0.652681i −0.613773 0.789483i \(-0.710349\pi\)
0.990598 + 0.136801i \(0.0436822\pi\)
\(570\) 0 0
\(571\) −2.32980e6 4.03534e6i −0.299040 0.517952i 0.676877 0.736096i \(-0.263333\pi\)
−0.975917 + 0.218144i \(0.930000\pi\)
\(572\) 0 0
\(573\) −2.40284e6 −0.305730
\(574\) 0 0
\(575\) −1.80558e7 −2.27744
\(576\) 0 0
\(577\) 762391. + 1.32050e6i 0.0953319 + 0.165120i 0.909747 0.415163i \(-0.136275\pi\)
−0.814415 + 0.580283i \(0.802942\pi\)
\(578\) 0 0
\(579\) −456137. + 790052.i −0.0565456 + 0.0979398i
\(580\) 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
\(585\) −4.17764e6 7.23589e6i −0.504710 0.874183i
\(586\) 0 0
\(587\) −1.50087e7 −1.79783 −0.898914 0.438124i \(-0.855643\pi\)
−0.898914 + 0.438124i \(0.855643\pi\)
\(588\) 0 0
\(589\) 8.29792e6 0.985556
\(590\) 0 0
\(591\) 1.63065e6 + 2.82436e6i 0.192040 + 0.332623i
\(592\) 0 0
\(593\) 3.53973e6 6.13099e6i 0.413364 0.715968i −0.581891 0.813267i \(-0.697687\pi\)
0.995255 + 0.0972987i \(0.0310202\pi\)
\(594\) 0 0
\(595\) 603081. + 269391.i 0.0698366 + 0.0311954i
\(596\) 0 0
\(597\) 1.01436e6 1.75692e6i 0.116481 0.201751i
\(598\) 0 0
\(599\) 1.08761e6 + 1.88379e6i 0.123853 + 0.214519i 0.921284 0.388891i \(-0.127142\pi\)
−0.797431 + 0.603410i \(0.793808\pi\)
\(600\) 0 0
\(601\) 2.69785e6 0.304671 0.152336 0.988329i \(-0.451321\pi\)
0.152336 + 0.988329i \(0.451321\pi\)
\(602\) 0 0
\(603\) −1.86021e6 −0.208338
\(604\) 0 0
\(605\) −6.55520e6 1.13539e7i −0.728111 1.26112i
\(606\) 0 0
\(607\) −2.49417e6 + 4.32003e6i −0.274760 + 0.475899i −0.970075 0.242807i \(-0.921932\pi\)
0.695314 + 0.718706i \(0.255265\pi\)
\(608\) 0 0
\(609\) 456955. + 4.39926e6i 0.0499263 + 0.480658i
\(610\) 0 0
\(611\) −9.12056e6 + 1.57973e7i −0.988367 + 1.71190i
\(612\) 0 0
\(613\) −556820. 964441.i −0.0598500 0.103663i 0.834548 0.550935i \(-0.185729\pi\)
−0.894398 + 0.447272i \(0.852396\pi\)
\(614\) 0 0
\(615\) −8.67647e6 −0.925029
\(616\) 0 0
\(617\) −5.14757e6 −0.544364 −0.272182 0.962246i \(-0.587745\pi\)
−0.272182 + 0.962246i \(0.587745\pi\)
\(618\) 0 0
\(619\) −121588. 210597.i −0.0127545 0.0220915i 0.859578 0.511005i \(-0.170727\pi\)
−0.872332 + 0.488914i \(0.837393\pi\)
\(620\) 0 0
\(621\) −1.19844e6 + 2.07576e6i −0.124706 + 0.215998i
\(622\) 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
\(627\) −1.08434e6 1.87814e6i −0.110153 0.190791i
\(628\) 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
\(633\) −1.47510e6 2.55495e6i −0.146323 0.253439i
\(634\) 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
\(639\) 1.06684e6 1.84783e6i 0.103359 0.179023i
\(640\) 0 0
\(641\) 5.77767e6 + 1.00072e7i 0.555402 + 0.961985i 0.997872 + 0.0652017i \(0.0207691\pi\)
−0.442470 + 0.896783i \(0.645898\pi\)
\(642\) 0 0
\(643\) 1.35139e6 0.128900 0.0644500 0.997921i \(-0.479471\pi\)
0.0644500 + 0.997921i \(0.479471\pi\)
\(644\) 0 0
\(645\) 5.96260e6 0.564334
\(646\) 0 0
\(647\) −8.77678e6 1.52018e7i −0.824279 1.42769i −0.902469 0.430755i \(-0.858247\pi\)
0.0781895 0.996939i \(-0.475086\pi\)
\(648\) 0 0
\(649\) 2.54864e6 4.41437e6i 0.237518 0.411393i
\(650\) 0 0
\(651\) 4.57964e6 3.31877e6i 0.423525 0.306920i
\(652\) 0 0
\(653\) 3.99936e6 6.92710e6i 0.367035 0.635724i −0.622065 0.782965i \(-0.713706\pi\)
0.989101 + 0.147242i \(0.0470395\pi\)
\(654\) 0 0
\(655\) −1.10234e7 1.90931e7i −1.00395 1.73889i
\(656\) 0 0
\(657\) 4.48638e6 0.405492
\(658\) 0 0
\(659\) 229419. 0.0205786 0.0102893 0.999947i \(-0.496725\pi\)
0.0102893 + 0.999947i \(0.496725\pi\)
\(660\) 0 0
\(661\) 1.64279e6 + 2.84539e6i 0.146244 + 0.253302i 0.929836 0.367973i \(-0.119948\pi\)
−0.783593 + 0.621275i \(0.786615\pi\)
\(662\) 0 0
\(663\) −274467. + 475391.i −0.0242497 + 0.0420017i
\(664\) 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
\(669\) 493603. + 854945.i 0.0426395 + 0.0738538i
\(670\) 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
\(675\) 2.00168e6 + 3.46701e6i 0.169097 + 0.292884i
\(676\) 0 0
\(677\) −1.07702e7 + 1.86546e7i −0.903138 + 1.56428i −0.0797405 + 0.996816i \(0.525409\pi\)
−0.823397 + 0.567465i \(0.807924\pi\)
\(678\) 0 0
\(679\) 7.77519e6 + 3.47311e6i 0.647197 + 0.289097i
\(680\) 0 0
\(681\) 5.47859e6 9.48920e6i 0.452690 0.784083i
\(682\) 0 0
\(683\) 8.08706e6 + 1.40072e7i 0.663344 + 1.14895i 0.979731 + 0.200316i \(0.0641968\pi\)
−0.316387 + 0.948630i \(0.602470\pi\)
\(684\) 0 0
\(685\) 8.93012e6 0.727162
\(686\) 0 0
\(687\) 1.20242e7 0.971999
\(688\) 0 0
\(689\) −1.16538e7 2.01850e7i −0.935231 1.61987i
\(690\) 0 0
\(691\) −5.32318e6 + 9.22002e6i −0.424108 + 0.734576i −0.996337 0.0855179i \(-0.972746\pi\)
0.572229 + 0.820094i \(0.306079\pi\)
\(692\) 0 0
\(693\) −1.34962e6 602862.i −0.106752 0.0476854i
\(694\) 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
\(699\) −421096. −0.0325978
\(700\) 0 0
\(701\) −4.55461e6 −0.350071 −0.175035 0.984562i \(-0.556004\pi\)
−0.175035 + 0.984562i \(0.556004\pi\)
\(702\) 0 0
\(703\) −9.72909e6 1.68513e7i −0.742479 1.28601i
\(704\) 0 0
\(705\) 6.85682e6 1.18764e7i 0.519577 0.899933i
\(706\) 0 0
\(707\) 2.35442e6 + 2.26668e7i 0.177148 + 1.70546i
\(708\) 0 0
\(709\) −6.55174e6 + 1.13479e7i −0.489487 + 0.847816i −0.999927 0.0120971i \(-0.996149\pi\)
0.510440 + 0.859913i \(0.329483\pi\)
\(710\) 0 0
\(711\) 2.02324e6 + 3.50436e6i 0.150098 + 0.259977i
\(712\) 0 0
\(713\) 1.59375e7 1.17408
\(714\) 0 0
\(715\) 1.45199e7 1.06218
\(716\) 0 0
\(717\) 388576. + 673033.i 0.0282278 + 0.0488921i
\(718\) 0 0
\(719\) −8.95942e6 + 1.55182e7i −0.646335 + 1.11949i 0.337656 + 0.941269i \(0.390366\pi\)
−0.983991 + 0.178216i \(0.942968\pi\)
\(720\) 0 0
\(721\) −1.61777e7 + 1.17236e7i −1.15899 + 0.839894i
\(722\) 0 0
\(723\) 3.71384e6 6.43257e6i 0.264227 0.457655i
\(724\) 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
\(729\) 531441. 0.0370370
\(730\) 0 0
\(731\) −195868. 339254.i −0.0135572 0.0234818i
\(732\) 0 0
\(733\) 6.22241e6 1.07775e7i 0.427758 0.740899i −0.568915 0.822396i \(-0.692637\pi\)
0.996674 + 0.0814969i \(0.0259701\pi\)
\(734\) 0 0
\(735\) 9.36982e6 + 1.04574e7i 0.639754 + 0.714015i
\(736\) 0 0
\(737\) 1.61634e6 2.79959e6i 0.109614 0.189857i
\(738\) 0 0
\(739\) 883322. + 1.52996e6i 0.0594988 + 0.103055i 0.894241 0.447587i \(-0.147716\pi\)
−0.834742 + 0.550642i \(0.814383\pi\)
\(740\) 0 0
\(741\) −1.71206e7 −1.14544
\(742\) 0 0
\(743\) 5.73250e6 0.380953 0.190477 0.981692i \(-0.438997\pi\)
0.190477 + 0.981692i \(0.438997\pi\)
\(744\) 0 0
\(745\) −3.74453e6 6.48571e6i −0.247176 0.428122i
\(746\) 0 0
\(747\) −1.81679e6 + 3.14677e6i −0.119125 + 0.206330i
\(748\) 0 0
\(749\) 1.92485e7 1.39490e7i 1.25370 0.908528i
\(750\) 0 0
\(751\) −1.31566e7 + 2.27879e7i −0.851224 + 1.47436i 0.0288804 + 0.999583i \(0.490806\pi\)
−0.880104 + 0.474780i \(0.842528\pi\)
\(752\) 0 0
\(753\) −585844. 1.01471e6i −0.0376526 0.0652162i
\(754\) 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
\(759\) −2.08266e6 3.60728e6i −0.131224 0.227287i
\(760\) 0 0
\(761\) −8.42080e6 + 1.45853e7i −0.527098 + 0.912961i 0.472403 + 0.881383i \(0.343387\pi\)
−0.999501 + 0.0315785i \(0.989947\pi\)
\(762\) 0 0
\(763\) −1.80342e6 1.73622e7i −0.112147 1.07967i
\(764\) 0 0
\(765\) 206344. 357398.i 0.0127479 0.0220800i
\(766\) 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
\(771\) −925112. −0.0560477
\(772\) 0 0
\(773\) −8.48868e6 1.47028e7i −0.510965 0.885018i −0.999919 0.0127081i \(-0.995955\pi\)
0.488954 0.872310i \(-0.337379\pi\)
\(774\) 0 0
\(775\) 1.33097e7 2.30531e7i 0.796003 1.37872i
\(776\) 0 0
\(777\) −1.21092e7 5.40908e6i −0.719554 0.321419i
\(778\) 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