Properties

Label 63.6.e.d.37.2
Level $63$
Weight $6$
Character 63.37
Analytic conductor $10.104$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [63,6,Mod(37,63)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(63, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([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("63.37");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 63.e (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: \(10.1041806482\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{37})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 10x^{2} + 9x + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 7)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.2
Root \(1.77069 - 3.06693i\) of defining polynomial
Character \(\chi\) \(=\) 63.37
Dual form 63.6.e.d.46.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.54138 - 6.13385i) q^{2} +(-9.08276 - 15.7318i) q^{4} +(-39.9138 + 69.1328i) q^{5} +(43.1587 + 122.247i) q^{7} +97.9863 q^{8} +O(q^{10})\) \(q+(3.54138 - 6.13385i) q^{2} +(-9.08276 - 15.7318i) q^{4} +(-39.9138 + 69.1328i) q^{5} +(43.1587 + 122.247i) q^{7} +97.9863 q^{8} +(282.700 + 489.651i) q^{10} +(175.952 + 304.757i) q^{11} -291.683 q^{13} +(902.686 + 168.194i) q^{14} +(637.655 - 1104.45i) q^{16} +(-185.038 - 320.495i) q^{17} +(-752.463 + 1303.30i) q^{19} +1450.11 q^{20} +2492.45 q^{22} +(-212.855 + 368.676i) q^{23} +(-1623.72 - 2812.37i) q^{25} +(-1032.96 + 1789.14i) q^{26} +(1531.17 - 1789.30i) q^{28} +7783.93 q^{29} +(1287.59 + 2230.17i) q^{31} +(-2948.58 - 5107.09i) q^{32} -2621.16 q^{34} +(-10173.9 - 1895.67i) q^{35} +(-369.809 + 640.528i) q^{37} +(5329.51 + 9230.99i) q^{38} +(-3911.01 + 6774.06i) q^{40} -7029.84 q^{41} +1835.23 q^{43} +(3196.26 - 5536.08i) q^{44} +(1507.60 + 2611.25i) q^{46} +(-766.342 + 1327.34i) q^{47} +(-13081.7 + 10552.0i) q^{49} -23000.9 q^{50} +(2649.28 + 4588.69i) q^{52} +(-4768.73 - 8259.68i) q^{53} -28091.6 q^{55} +(4228.96 + 11978.5i) q^{56} +(27565.9 - 47745.5i) q^{58} +(-14837.0 - 25698.5i) q^{59} +(23255.4 - 40279.5i) q^{61} +18239.4 q^{62} -958.246 q^{64} +(11642.2 - 20164.8i) q^{65} +(-13373.0 - 23162.8i) q^{67} +(-3361.31 + 5821.95i) q^{68} +(-47657.4 + 55691.9i) q^{70} +14388.8 q^{71} +(35047.6 + 60704.2i) q^{73} +(2619.27 + 4536.71i) q^{74} +27337.8 q^{76} +(-29661.8 + 34662.5i) q^{77} +(13542.9 - 23457.0i) q^{79} +(50902.5 + 88165.7i) q^{80} +(-24895.3 + 43120.0i) q^{82} +79755.4 q^{83} +29542.2 q^{85} +(6499.26 - 11257.0i) q^{86} +(17240.9 + 29862.1i) q^{88} +(21788.7 - 37739.1i) q^{89} +(-12588.6 - 35657.3i) q^{91} +7733.26 q^{92} +(5427.82 + 9401.25i) q^{94} +(-60067.3 - 104040. i) q^{95} +103374. q^{97} +(18397.5 + 117610. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 12 q^{4} - 38 q^{5} - 168 q^{7} - 192 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 12 q^{4} - 38 q^{5} - 168 q^{7} - 192 q^{8} + 778 q^{10} + 424 q^{11} - 1848 q^{13} + 2674 q^{14} + 2064 q^{16} - 2346 q^{17} + 360 q^{19} + 3416 q^{20} + 4252 q^{22} - 12 q^{23} - 1872 q^{25} + 1148 q^{26} + 2548 q^{28} + 14104 q^{29} - 3548 q^{31} - 8096 q^{32} + 14844 q^{34} - 27496 q^{35} - 11090 q^{37} + 20138 q^{38} - 15936 q^{40} - 7000 q^{41} - 25360 q^{43} + 5948 q^{44} + 5118 q^{46} - 22956 q^{47} + 4900 q^{49} - 59984 q^{50} + 1400 q^{52} + 3042 q^{53} - 50152 q^{55} + 57792 q^{56} + 58852 q^{58} - 65808 q^{59} + 42486 q^{61} + 98724 q^{62} + 70912 q^{64} - 3164 q^{65} - 42312 q^{67} + 5460 q^{68} - 113050 q^{70} + 4416 q^{71} + 50506 q^{73} - 47370 q^{74} + 77672 q^{76} - 65338 q^{77} - 9004 q^{79} + 68816 q^{80} - 67732 q^{82} + 208656 q^{83} - 106212 q^{85} + 86776 q^{86} + 20496 q^{88} - 26666 q^{89} + 135632 q^{91} + 20568 q^{92} - 98034 q^{94} - 198140 q^{95} + 418264 q^{97} - 98686 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.54138 6.13385i 0.626034 1.08432i −0.362306 0.932059i \(-0.618011\pi\)
0.988340 0.152263i \(-0.0486561\pi\)
\(3\) 0 0
\(4\) −9.08276 15.7318i −0.283836 0.491619i
\(5\) −39.9138 + 69.1328i −0.714000 + 1.23668i 0.249344 + 0.968415i \(0.419785\pi\)
−0.963344 + 0.268269i \(0.913548\pi\)
\(6\) 0 0
\(7\) 43.1587 + 122.247i 0.332907 + 0.942960i
\(8\) 97.9863 0.541303
\(9\) 0 0
\(10\) 282.700 + 489.651i 0.893976 + 1.54841i
\(11\) 175.952 + 304.757i 0.438442 + 0.759403i 0.997570 0.0696781i \(-0.0221972\pi\)
−0.559128 + 0.829082i \(0.688864\pi\)
\(12\) 0 0
\(13\) −291.683 −0.478688 −0.239344 0.970935i \(-0.576932\pi\)
−0.239344 + 0.970935i \(0.576932\pi\)
\(14\) 902.686 + 168.194i 1.23088 + 0.229346i
\(15\) 0 0
\(16\) 637.655 1104.45i 0.622710 1.07857i
\(17\) −185.038 320.495i −0.155288 0.268967i 0.777876 0.628418i \(-0.216297\pi\)
−0.933164 + 0.359451i \(0.882964\pi\)
\(18\) 0 0
\(19\) −752.463 + 1303.30i −0.478190 + 0.828250i −0.999687 0.0250030i \(-0.992040\pi\)
0.521497 + 0.853253i \(0.325374\pi\)
\(20\) 1450.11 0.810637
\(21\) 0 0
\(22\) 2492.45 1.09792
\(23\) −212.855 + 368.676i −0.0839006 + 0.145320i −0.904922 0.425577i \(-0.860071\pi\)
0.821022 + 0.570897i \(0.193404\pi\)
\(24\) 0 0
\(25\) −1623.72 2812.37i −0.519592 0.899960i
\(26\) −1032.96 + 1789.14i −0.299675 + 0.519052i
\(27\) 0 0
\(28\) 1531.17 1789.30i 0.369086 0.431310i
\(29\) 7783.93 1.71872 0.859358 0.511374i \(-0.170863\pi\)
0.859358 + 0.511374i \(0.170863\pi\)
\(30\) 0 0
\(31\) 1287.59 + 2230.17i 0.240643 + 0.416805i 0.960898 0.276904i \(-0.0893085\pi\)
−0.720255 + 0.693710i \(0.755975\pi\)
\(32\) −2948.58 5107.09i −0.509024 0.881655i
\(33\) 0 0
\(34\) −2621.16 −0.388862
\(35\) −10173.9 1895.67i −1.40384 0.261572i
\(36\) 0 0
\(37\) −369.809 + 640.528i −0.0444092 + 0.0769190i −0.887376 0.461047i \(-0.847474\pi\)
0.842966 + 0.537966i \(0.180807\pi\)
\(38\) 5329.51 + 9230.99i 0.598727 + 1.03703i
\(39\) 0 0
\(40\) −3911.01 + 6774.06i −0.386490 + 0.669421i
\(41\) −7029.84 −0.653109 −0.326554 0.945178i \(-0.605888\pi\)
−0.326554 + 0.945178i \(0.605888\pi\)
\(42\) 0 0
\(43\) 1835.23 0.151363 0.0756816 0.997132i \(-0.475887\pi\)
0.0756816 + 0.997132i \(0.475887\pi\)
\(44\) 3196.26 5536.08i 0.248891 0.431093i
\(45\) 0 0
\(46\) 1507.60 + 2611.25i 0.105049 + 0.181950i
\(47\) −766.342 + 1327.34i −0.0506032 + 0.0876473i −0.890217 0.455536i \(-0.849448\pi\)
0.839614 + 0.543183i \(0.182781\pi\)
\(48\) 0 0
\(49\) −13081.7 + 10552.0i −0.778346 + 0.627836i
\(50\) −23000.9 −1.30113
\(51\) 0 0
\(52\) 2649.28 + 4588.69i 0.135869 + 0.235332i
\(53\) −4768.73 8259.68i −0.233192 0.403900i 0.725554 0.688165i \(-0.241584\pi\)
−0.958746 + 0.284265i \(0.908250\pi\)
\(54\) 0 0
\(55\) −28091.6 −1.25219
\(56\) 4228.96 + 11978.5i 0.180204 + 0.510427i
\(57\) 0 0
\(58\) 27565.9 47745.5i 1.07597 1.86364i
\(59\) −14837.0 25698.5i −0.554903 0.961120i −0.997911 0.0646022i \(-0.979422\pi\)
0.443008 0.896517i \(-0.353911\pi\)
\(60\) 0 0
\(61\) 23255.4 40279.5i 0.800201 1.38599i −0.119282 0.992860i \(-0.538059\pi\)
0.919483 0.393129i \(-0.128607\pi\)
\(62\) 18239.4 0.602602
\(63\) 0 0
\(64\) −958.246 −0.0292434
\(65\) 11642.2 20164.8i 0.341783 0.591985i
\(66\) 0 0
\(67\) −13373.0 23162.8i −0.363951 0.630381i 0.624656 0.780900i \(-0.285239\pi\)
−0.988607 + 0.150518i \(0.951906\pi\)
\(68\) −3361.31 + 5821.95i −0.0881527 + 0.152685i
\(69\) 0 0
\(70\) −47657.4 + 55691.9i −1.16248 + 1.35846i
\(71\) 14388.8 0.338748 0.169374 0.985552i \(-0.445825\pi\)
0.169374 + 0.985552i \(0.445825\pi\)
\(72\) 0 0
\(73\) 35047.6 + 60704.2i 0.769752 + 1.33325i 0.937697 + 0.347453i \(0.112953\pi\)
−0.167946 + 0.985796i \(0.553713\pi\)
\(74\) 2619.27 + 4536.71i 0.0556033 + 0.0963078i
\(75\) 0 0
\(76\) 27337.8 0.542911
\(77\) −29661.8 + 34662.5i −0.570126 + 0.666244i
\(78\) 0 0
\(79\) 13542.9 23457.0i 0.244143 0.422868i −0.717748 0.696303i \(-0.754827\pi\)
0.961890 + 0.273436i \(0.0881601\pi\)
\(80\) 50902.5 + 88165.7i 0.889230 + 1.54019i
\(81\) 0 0
\(82\) −24895.3 + 43120.0i −0.408868 + 0.708181i
\(83\) 79755.4 1.27076 0.635382 0.772198i \(-0.280843\pi\)
0.635382 + 0.772198i \(0.280843\pi\)
\(84\) 0 0
\(85\) 29542.2 0.443502
\(86\) 6499.26 11257.0i 0.0947584 0.164126i
\(87\) 0 0
\(88\) 17240.9 + 29862.1i 0.237330 + 0.411067i
\(89\) 21788.7 37739.1i 0.291579 0.505029i −0.682605 0.730788i \(-0.739153\pi\)
0.974183 + 0.225759i \(0.0724862\pi\)
\(90\) 0 0
\(91\) −12588.6 35657.3i −0.159358 0.451383i
\(92\) 7733.26 0.0952561
\(93\) 0 0
\(94\) 5427.82 + 9401.25i 0.0633586 + 0.109740i
\(95\) −60067.3 104040.i −0.682856 1.18274i
\(96\) 0 0
\(97\) 103374. 1.11553 0.557765 0.829999i \(-0.311659\pi\)
0.557765 + 0.829999i \(0.311659\pi\)
\(98\) 18397.5 + 117610.i 0.193506 + 1.23702i
\(99\) 0 0
\(100\) −29495.8 + 51088.3i −0.294958 + 0.510883i
\(101\) 14350.1 + 24855.1i 0.139975 + 0.242444i 0.927487 0.373855i \(-0.121964\pi\)
−0.787512 + 0.616300i \(0.788631\pi\)
\(102\) 0 0
\(103\) −14614.0 + 25312.1i −0.135730 + 0.235091i −0.925876 0.377828i \(-0.876671\pi\)
0.790146 + 0.612918i \(0.210005\pi\)
\(104\) −28580.9 −0.259115
\(105\) 0 0
\(106\) −67551.6 −0.583944
\(107\) 43929.2 76087.6i 0.370932 0.642472i −0.618778 0.785566i \(-0.712372\pi\)
0.989709 + 0.143094i \(0.0457051\pi\)
\(108\) 0 0
\(109\) −110314. 191069.i −0.889333 1.54037i −0.840665 0.541555i \(-0.817836\pi\)
−0.0486678 0.998815i \(-0.515498\pi\)
\(110\) −99483.2 + 172310.i −0.783913 + 1.35778i
\(111\) 0 0
\(112\) 162536. + 30284.8i 1.22435 + 0.228128i
\(113\) −39665.6 −0.292225 −0.146113 0.989268i \(-0.546676\pi\)
−0.146113 + 0.989268i \(0.546676\pi\)
\(114\) 0 0
\(115\) −16991.7 29430.5i −0.119810 0.207517i
\(116\) −70699.6 122455.i −0.487834 0.844953i
\(117\) 0 0
\(118\) −210174. −1.38955
\(119\) 31193.5 36452.4i 0.201928 0.235971i
\(120\) 0 0
\(121\) 18607.4 32229.0i 0.115538 0.200117i
\(122\) −164712. 285290.i −1.00191 1.73535i
\(123\) 0 0
\(124\) 23389.7 40512.2i 0.136606 0.236609i
\(125\) 9774.87 0.0559546
\(126\) 0 0
\(127\) 51740.3 0.284655 0.142328 0.989820i \(-0.454541\pi\)
0.142328 + 0.989820i \(0.454541\pi\)
\(128\) 90961.0 157549.i 0.490716 0.849946i
\(129\) 0 0
\(130\) −82458.7 142823.i −0.427935 0.741206i
\(131\) −83336.9 + 144344.i −0.424286 + 0.734885i −0.996353 0.0853215i \(-0.972808\pi\)
0.572067 + 0.820207i \(0.306142\pi\)
\(132\) 0 0
\(133\) −191800. 35737.4i −0.940200 0.175184i
\(134\) −189436. −0.911382
\(135\) 0 0
\(136\) −18131.2 31404.1i −0.0840578 0.145592i
\(137\) 14129.7 + 24473.4i 0.0643178 + 0.111402i 0.896391 0.443264i \(-0.146180\pi\)
−0.832073 + 0.554666i \(0.812846\pi\)
\(138\) 0 0
\(139\) 336393. 1.47676 0.738380 0.674384i \(-0.235591\pi\)
0.738380 + 0.674384i \(0.235591\pi\)
\(140\) 62584.9 + 177272.i 0.269867 + 0.764398i
\(141\) 0 0
\(142\) 50956.1 88258.5i 0.212068 0.367312i
\(143\) −51322.1 88892.4i −0.209877 0.363517i
\(144\) 0 0
\(145\) −310686. + 538125.i −1.22716 + 2.12551i
\(146\) 496467. 1.92756
\(147\) 0 0
\(148\) 13435.5 0.0504198
\(149\) −177691. + 307769.i −0.655691 + 1.13569i 0.326030 + 0.945360i \(0.394289\pi\)
−0.981720 + 0.190330i \(0.939044\pi\)
\(150\) 0 0
\(151\) 179399. + 310727.i 0.640290 + 1.10901i 0.985368 + 0.170441i \(0.0545191\pi\)
−0.345078 + 0.938574i \(0.612148\pi\)
\(152\) −73731.0 + 127706.i −0.258846 + 0.448334i
\(153\) 0 0
\(154\) 107571. + 304694.i 0.365504 + 1.03529i
\(155\) −205570. −0.687275
\(156\) 0 0
\(157\) −229455. 397428.i −0.742932 1.28680i −0.951155 0.308714i \(-0.900101\pi\)
0.208223 0.978081i \(-0.433232\pi\)
\(158\) −95921.1 166140.i −0.305683 0.529459i
\(159\) 0 0
\(160\) 470756. 1.45377
\(161\) −54256.1 10109.3i −0.164962 0.0307368i
\(162\) 0 0
\(163\) −251220. + 435126.i −0.740603 + 1.28276i 0.211618 + 0.977353i \(0.432127\pi\)
−0.952221 + 0.305410i \(0.901206\pi\)
\(164\) 63850.3 + 110592.i 0.185376 + 0.321081i
\(165\) 0 0
\(166\) 282444. 489208.i 0.795541 1.37792i
\(167\) 676652. 1.87748 0.938738 0.344632i \(-0.111996\pi\)
0.938738 + 0.344632i \(0.111996\pi\)
\(168\) 0 0
\(169\) −286214. −0.770858
\(170\) 104620. 181208.i 0.277647 0.480900i
\(171\) 0 0
\(172\) −16669.0 28871.5i −0.0429623 0.0744130i
\(173\) −124580. + 215779.i −0.316470 + 0.548143i −0.979749 0.200230i \(-0.935831\pi\)
0.663279 + 0.748373i \(0.269164\pi\)
\(174\) 0 0
\(175\) 273726. 319874.i 0.675650 0.789557i
\(176\) 448786. 1.09209
\(177\) 0 0
\(178\) −154324. 267297.i −0.365076 0.632330i
\(179\) 69628.9 + 120601.i 0.162427 + 0.281331i 0.935738 0.352695i \(-0.114735\pi\)
−0.773312 + 0.634026i \(0.781401\pi\)
\(180\) 0 0
\(181\) 306246. 0.694823 0.347412 0.937713i \(-0.387061\pi\)
0.347412 + 0.937713i \(0.387061\pi\)
\(182\) −263298. 49059.4i −0.589209 0.109785i
\(183\) 0 0
\(184\) −20856.9 + 36125.2i −0.0454156 + 0.0786622i
\(185\) −29521.0 51131.8i −0.0634163 0.109840i
\(186\) 0 0
\(187\) 65115.4 112783.i 0.136169 0.235852i
\(188\) 27842.0 0.0574521
\(189\) 0 0
\(190\) −850885. −1.70996
\(191\) 113747. 197015.i 0.225609 0.390766i −0.730893 0.682492i \(-0.760896\pi\)
0.956502 + 0.291726i \(0.0942295\pi\)
\(192\) 0 0
\(193\) 336187. + 582293.i 0.649663 + 1.12525i 0.983203 + 0.182513i \(0.0584231\pi\)
−0.333541 + 0.942736i \(0.608244\pi\)
\(194\) 366086. 634079.i 0.698359 1.20959i
\(195\) 0 0
\(196\) 284820. + 109956.i 0.529579 + 0.204447i
\(197\) 1282.76 0.00235493 0.00117747 0.999999i \(-0.499625\pi\)
0.00117747 + 0.999999i \(0.499625\pi\)
\(198\) 0 0
\(199\) −184449. 319475.i −0.330175 0.571879i 0.652371 0.757900i \(-0.273774\pi\)
−0.982546 + 0.186020i \(0.940441\pi\)
\(200\) −159103. 275574.i −0.281257 0.487151i
\(201\) 0 0
\(202\) 203277. 0.350517
\(203\) 335944. + 951563.i 0.572173 + 1.62068i
\(204\) 0 0
\(205\) 280588. 485992.i 0.466320 0.807690i
\(206\) 103507. + 179280.i 0.169943 + 0.294349i
\(207\) 0 0
\(208\) −185993. + 322149.i −0.298084 + 0.516296i
\(209\) −529589. −0.838635
\(210\) 0 0
\(211\) 502168. 0.776503 0.388251 0.921553i \(-0.373079\pi\)
0.388251 + 0.921553i \(0.373079\pi\)
\(212\) −86626.5 + 150042.i −0.132377 + 0.229283i
\(213\) 0 0
\(214\) −311140. 538910.i −0.464431 0.804419i
\(215\) −73251.1 + 126875.i −0.108073 + 0.187188i
\(216\) 0 0
\(217\) −217061. + 253655.i −0.312919 + 0.365674i
\(218\) −1.56266e6 −2.22701
\(219\) 0 0
\(220\) 255150. + 441932.i 0.355417 + 0.615600i
\(221\) 53972.3 + 93482.7i 0.0743344 + 0.128751i
\(222\) 0 0
\(223\) −1.17328e6 −1.57993 −0.789967 0.613149i \(-0.789902\pi\)
−0.789967 + 0.613149i \(0.789902\pi\)
\(224\) 497070. 580870.i 0.661907 0.773498i
\(225\) 0 0
\(226\) −140471. + 243303.i −0.182943 + 0.316867i
\(227\) −455079. 788220.i −0.586168 1.01527i −0.994729 0.102542i \(-0.967302\pi\)
0.408560 0.912731i \(-0.366031\pi\)
\(228\) 0 0
\(229\) −260962. + 452000.i −0.328843 + 0.569573i −0.982283 0.187406i \(-0.939992\pi\)
0.653439 + 0.756979i \(0.273325\pi\)
\(230\) −240697. −0.300020
\(231\) 0 0
\(232\) 762719. 0.930346
\(233\) −521394. + 903081.i −0.629182 + 1.08977i 0.358535 + 0.933516i \(0.383277\pi\)
−0.987716 + 0.156258i \(0.950057\pi\)
\(234\) 0 0
\(235\) −61175.2 105959.i −0.0722613 0.125160i
\(236\) −269522. + 466826.i −0.315003 + 0.545601i
\(237\) 0 0
\(238\) −113126. 320428.i −0.129455 0.366681i
\(239\) 1.53447e6 1.73766 0.868830 0.495110i \(-0.164872\pi\)
0.868830 + 0.495110i \(0.164872\pi\)
\(240\) 0 0
\(241\) 503789. + 872588.i 0.558735 + 0.967758i 0.997602 + 0.0692059i \(0.0220465\pi\)
−0.438867 + 0.898552i \(0.644620\pi\)
\(242\) −131792. 228271.i −0.144661 0.250560i
\(243\) 0 0
\(244\) −844893. −0.908505
\(245\) −207353. 1.32554e6i −0.220696 1.41084i
\(246\) 0 0
\(247\) 219480. 380151.i 0.228904 0.396473i
\(248\) 126166. + 218526.i 0.130261 + 0.225618i
\(249\) 0 0
\(250\) 34616.6 59957.6i 0.0350295 0.0606729i
\(251\) −8511.89 −0.00852789 −0.00426394 0.999991i \(-0.501357\pi\)
−0.00426394 + 0.999991i \(0.501357\pi\)
\(252\) 0 0
\(253\) −149809. −0.147142
\(254\) 183232. 317367.i 0.178204 0.308658i
\(255\) 0 0
\(256\) −659587. 1.14244e6i −0.629032 1.08951i
\(257\) −263766. + 456856.i −0.249107 + 0.431466i −0.963278 0.268505i \(-0.913470\pi\)
0.714171 + 0.699971i \(0.246804\pi\)
\(258\) 0 0
\(259\) −94263.0 17563.7i −0.0873156 0.0162692i
\(260\) −422972. −0.388042
\(261\) 0 0
\(262\) 590255. + 1.02235e6i 0.531235 + 0.920126i
\(263\) −176042. 304914.i −0.156938 0.271824i 0.776825 0.629716i \(-0.216829\pi\)
−0.933763 + 0.357892i \(0.883496\pi\)
\(264\) 0 0
\(265\) 761353. 0.665996
\(266\) −898446. + 1.04991e6i −0.778552 + 0.909808i
\(267\) 0 0
\(268\) −242928. + 420764.i −0.206605 + 0.357850i
\(269\) 239770. + 415294.i 0.202029 + 0.349925i 0.949182 0.314727i \(-0.101913\pi\)
−0.747153 + 0.664652i \(0.768580\pi\)
\(270\) 0 0
\(271\) 488805. 846636.i 0.404308 0.700283i −0.589932 0.807453i \(-0.700846\pi\)
0.994241 + 0.107170i \(0.0341789\pi\)
\(272\) −471961. −0.386798
\(273\) 0 0
\(274\) 200155. 0.161061
\(275\) 571395. 989684.i 0.455622 0.789160i
\(276\) 0 0
\(277\) −484362. 838939.i −0.379289 0.656948i 0.611670 0.791113i \(-0.290498\pi\)
−0.990959 + 0.134165i \(0.957165\pi\)
\(278\) 1.19130e6 2.06339e6i 0.924502 1.60128i
\(279\) 0 0
\(280\) −996903. 185749.i −0.759902 0.141590i
\(281\) 318333. 0.240501 0.120250 0.992744i \(-0.461630\pi\)
0.120250 + 0.992744i \(0.461630\pi\)
\(282\) 0 0
\(283\) −886051. 1.53468e6i −0.657646 1.13908i −0.981223 0.192875i \(-0.938219\pi\)
0.323577 0.946202i \(-0.395115\pi\)
\(284\) −130690. 226361.i −0.0961491 0.166535i
\(285\) 0 0
\(286\) −727004. −0.525559
\(287\) −303398. 859377.i −0.217425 0.615855i
\(288\) 0 0
\(289\) 641451. 1.11103e6i 0.451771 0.782491i
\(290\) 2.20052e6 + 3.81141e6i 1.53649 + 2.66128i
\(291\) 0 0
\(292\) 636657. 1.10272e6i 0.436967 0.756849i
\(293\) −1.64148e6 −1.11703 −0.558516 0.829494i \(-0.688629\pi\)
−0.558516 + 0.829494i \(0.688629\pi\)
\(294\) 0 0
\(295\) 2.36881e6 1.58480
\(296\) −36236.2 + 62762.9i −0.0240388 + 0.0416365i
\(297\) 0 0
\(298\) 1.25854e6 + 2.17986e6i 0.820969 + 1.42196i
\(299\) 62086.2 107536.i 0.0401622 0.0695629i
\(300\) 0 0
\(301\) 79206.2 + 224352.i 0.0503898 + 0.142729i
\(302\) 2.54128e6 1.60337
\(303\) 0 0
\(304\) 959623. + 1.66212e6i 0.595548 + 1.03152i
\(305\) 1.85642e6 + 3.21542e6i 1.14269 + 1.97919i
\(306\) 0 0
\(307\) −466930. −0.282752 −0.141376 0.989956i \(-0.545153\pi\)
−0.141376 + 0.989956i \(0.545153\pi\)
\(308\) 814715. + 151803.i 0.489361 + 0.0911808i
\(309\) 0 0
\(310\) −728002. + 1.26094e6i −0.430257 + 0.745228i
\(311\) −1.21898e6 2.11134e6i −0.714654 1.23782i −0.963093 0.269169i \(-0.913251\pi\)
0.248439 0.968647i \(-0.420082\pi\)
\(312\) 0 0
\(313\) −1.21047e6 + 2.09659e6i −0.698381 + 1.20963i 0.270646 + 0.962679i \(0.412763\pi\)
−0.969028 + 0.246953i \(0.920571\pi\)
\(314\) −3.25035e6 −1.86040
\(315\) 0 0
\(316\) −492028. −0.277186
\(317\) 938057. 1.62476e6i 0.524301 0.908116i −0.475298 0.879825i \(-0.657660\pi\)
0.999600 0.0282918i \(-0.00900675\pi\)
\(318\) 0 0
\(319\) 1.36960e6 + 2.37221e6i 0.753557 + 1.30520i
\(320\) 38247.3 66246.2i 0.0208798 0.0361648i
\(321\) 0 0
\(322\) −254151. + 296998.i −0.136600 + 0.159630i
\(323\) 556936. 0.297029
\(324\) 0 0
\(325\) 473612. + 820321.i 0.248722 + 0.430800i
\(326\) 1.77933e6 + 3.08190e6i 0.927285 + 1.60611i
\(327\) 0 0
\(328\) −688828. −0.353530
\(329\) −195338. 36396.6i −0.0994940 0.0185384i
\(330\) 0 0
\(331\) 541549. 937990.i 0.271686 0.470575i −0.697607 0.716480i \(-0.745752\pi\)
0.969294 + 0.245906i \(0.0790853\pi\)
\(332\) −724399. 1.25470e6i −0.360689 0.624732i
\(333\) 0 0
\(334\) 2.39628e6 4.15048e6i 1.17536 2.03579i
\(335\) 2.13507e6 1.03944
\(336\) 0 0
\(337\) −2.59465e6 −1.24453 −0.622263 0.782809i \(-0.713786\pi\)
−0.622263 + 0.782809i \(0.713786\pi\)
\(338\) −1.01359e6 + 1.75560e6i −0.482583 + 0.835859i
\(339\) 0 0
\(340\) −268325. 464753.i −0.125882 0.218034i
\(341\) −453107. + 784804.i −0.211016 + 0.365490i
\(342\) 0 0
\(343\) −1.85454e6 1.14378e6i −0.851141 0.524938i
\(344\) 179828. 0.0819333
\(345\) 0 0
\(346\) 882371. + 1.52831e6i 0.396242 + 0.686312i
\(347\) −935255. 1.61991e6i −0.416972 0.722216i 0.578662 0.815568i \(-0.303575\pi\)
−0.995633 + 0.0933518i \(0.970242\pi\)
\(348\) 0 0
\(349\) −1.61685e6 −0.710568 −0.355284 0.934758i \(-0.615616\pi\)
−0.355284 + 0.934758i \(0.615616\pi\)
\(350\) −992689. 2.81179e6i −0.433155 1.22691i
\(351\) 0 0
\(352\) 1.03762e6 1.79720e6i 0.446354 0.773109i
\(353\) −289153. 500827.i −0.123507 0.213920i 0.797642 0.603132i \(-0.206081\pi\)
−0.921148 + 0.389212i \(0.872747\pi\)
\(354\) 0 0
\(355\) −574310. + 994734.i −0.241866 + 0.418925i
\(356\) −791605. −0.331042
\(357\) 0 0
\(358\) 986330. 0.406738
\(359\) −984090. + 1.70449e6i −0.402994 + 0.698006i −0.994086 0.108598i \(-0.965364\pi\)
0.591092 + 0.806604i \(0.298697\pi\)
\(360\) 0 0
\(361\) 105650. + 182990.i 0.0426677 + 0.0739027i
\(362\) 1.08453e6 1.87847e6i 0.434983 0.753412i
\(363\) 0 0
\(364\) −446615. + 521909.i −0.176677 + 0.206463i
\(365\) −5.59553e6 −2.19841
\(366\) 0 0
\(367\) −1.08726e6 1.88319e6i −0.421375 0.729842i 0.574700 0.818364i \(-0.305119\pi\)
−0.996074 + 0.0885223i \(0.971786\pi\)
\(368\) 271457. + 470177.i 0.104491 + 0.180985i
\(369\) 0 0
\(370\) −418180. −0.158803
\(371\) 803910. 939440.i 0.303230 0.354352i
\(372\) 0 0
\(373\) −692379. + 1.19924e6i −0.257675 + 0.446306i −0.965619 0.259963i \(-0.916290\pi\)
0.707944 + 0.706269i \(0.249623\pi\)
\(374\) −461197. 798817.i −0.170493 0.295303i
\(375\) 0 0
\(376\) −75091.0 + 130061.i −0.0273916 + 0.0474437i
\(377\) −2.27044e6 −0.822728
\(378\) 0 0
\(379\) 3.37190e6 1.20580 0.602902 0.797815i \(-0.294011\pi\)
0.602902 + 0.797815i \(0.294011\pi\)
\(380\) −1.09115e6 + 1.88993e6i −0.387639 + 0.671410i
\(381\) 0 0
\(382\) −805642. 1.39541e6i −0.282478 0.489265i
\(383\) 1.64030e6 2.84108e6i 0.571382 0.989662i −0.425043 0.905173i \(-0.639741\pi\)
0.996424 0.0844886i \(-0.0269257\pi\)
\(384\) 0 0
\(385\) −1.21240e6 3.43412e6i −0.416863 1.18076i
\(386\) 4.76227e6 1.62684
\(387\) 0 0
\(388\) −938919. 1.62626e6i −0.316628 0.548415i
\(389\) −1.47405e6 2.55313e6i −0.493899 0.855457i 0.506077 0.862488i \(-0.331095\pi\)
−0.999975 + 0.00703108i \(0.997762\pi\)
\(390\) 0 0
\(391\) 157545. 0.0521150
\(392\) −1.28182e6 + 1.03396e6i −0.421321 + 0.339849i
\(393\) 0 0
\(394\) 4542.73 7868.24i 0.00147427 0.00255351i
\(395\) 1.08110e6 + 1.87251e6i 0.348636 + 0.603855i
\(396\) 0 0
\(397\) 34635.1 59989.7i 0.0110291 0.0191030i −0.860458 0.509521i \(-0.829823\pi\)
0.871487 + 0.490418i \(0.163156\pi\)
\(398\) −2.61282e6 −0.826802
\(399\) 0 0
\(400\) −4.14151e6 −1.29422
\(401\) −1.67393e6 + 2.89933e6i −0.519848 + 0.900404i 0.479886 + 0.877331i \(0.340678\pi\)
−0.999734 + 0.0230725i \(0.992655\pi\)
\(402\) 0 0
\(403\) −375567. 650501.i −0.115193 0.199520i
\(404\) 260677. 451506.i 0.0794602 0.137629i
\(405\) 0 0
\(406\) 7.02645e6 + 1.30921e6i 2.11554 + 0.394181i
\(407\) −260274. −0.0778834
\(408\) 0 0
\(409\) −1.45608e6 2.52201e6i −0.430406 0.745485i 0.566502 0.824060i \(-0.308296\pi\)
−0.996908 + 0.0785754i \(0.974963\pi\)
\(410\) −1.98734e6 3.44217e6i −0.583864 1.01128i
\(411\) 0 0
\(412\) 530940. 0.154100
\(413\) 2.50122e6 2.92289e6i 0.721566 0.843214i
\(414\) 0 0
\(415\) −3.18334e6 + 5.51371e6i −0.907326 + 1.57153i
\(416\) 860050. + 1.48965e6i 0.243663 + 0.422037i
\(417\) 0 0
\(418\) −1.87547e6 + 3.24842e6i −0.525014 + 0.909350i
\(419\) 4.62361e6 1.28661 0.643304 0.765611i \(-0.277563\pi\)
0.643304 + 0.765611i \(0.277563\pi\)
\(420\) 0 0
\(421\) −2.63042e6 −0.723303 −0.361652 0.932313i \(-0.617787\pi\)
−0.361652 + 0.932313i \(0.617787\pi\)
\(422\) 1.77837e6 3.08023e6i 0.486117 0.841979i
\(423\) 0 0
\(424\) −467270. 809336.i −0.126227 0.218632i
\(425\) −600901. + 1.04079e6i −0.161373 + 0.279506i
\(426\) 0 0
\(427\) 5.92772e6 + 1.10449e6i 1.57332 + 0.293152i
\(428\) −1.59599e6 −0.421135
\(429\) 0 0
\(430\) 518820. + 898623.i 0.135315 + 0.234372i
\(431\) 3.77064e6 + 6.53094e6i 0.977736 + 1.69349i 0.670592 + 0.741826i \(0.266040\pi\)
0.307144 + 0.951663i \(0.400627\pi\)
\(432\) 0 0
\(433\) 5.83558e6 1.49577 0.747883 0.663830i \(-0.231070\pi\)
0.747883 + 0.663830i \(0.231070\pi\)
\(434\) 787186. + 2.22971e6i 0.200610 + 0.568229i
\(435\) 0 0
\(436\) −2.00391e6 + 3.47088e6i −0.504850 + 0.874426i
\(437\) −320331. 554830.i −0.0802409 0.138981i
\(438\) 0 0
\(439\) −84051.9 + 145582.i −0.0208155 + 0.0360535i −0.876246 0.481865i \(-0.839960\pi\)
0.855430 + 0.517918i \(0.173293\pi\)
\(440\) −2.75259e6 −0.677814
\(441\) 0 0
\(442\) 764546. 0.186143
\(443\) −1.42076e6 + 2.46082e6i −0.343962 + 0.595760i −0.985165 0.171612i \(-0.945102\pi\)
0.641203 + 0.767372i \(0.278436\pi\)
\(444\) 0 0
\(445\) 1.73934e6 + 3.01262e6i 0.416374 + 0.721181i
\(446\) −4.15503e6 + 7.19672e6i −0.989092 + 1.71316i
\(447\) 0 0
\(448\) −41356.6 117143.i −0.00973532 0.0275753i
\(449\) 1.41567e6 0.331396 0.165698 0.986177i \(-0.447012\pi\)
0.165698 + 0.986177i \(0.447012\pi\)
\(450\) 0 0
\(451\) −1.23691e6 2.14240e6i −0.286350 0.495973i
\(452\) 360273. + 624012.i 0.0829442 + 0.143664i
\(453\) 0 0
\(454\) −6.44644e6 −1.46784
\(455\) 2.96755e6 + 552933.i 0.672000 + 0.125211i
\(456\) 0 0
\(457\) −778637. + 1.34864e6i −0.174399 + 0.302068i −0.939953 0.341303i \(-0.889132\pi\)
0.765554 + 0.643372i \(0.222465\pi\)
\(458\) 1.84833e6 + 3.20141e6i 0.411734 + 0.713144i
\(459\) 0 0
\(460\) −308664. + 534621.i −0.0680129 + 0.117802i
\(461\) 4.45345e6 0.975987 0.487994 0.872847i \(-0.337729\pi\)
0.487994 + 0.872847i \(0.337729\pi\)
\(462\) 0 0
\(463\) 4.92263e6 1.06720 0.533599 0.845738i \(-0.320839\pi\)
0.533599 + 0.845738i \(0.320839\pi\)
\(464\) 4.96347e6 8.59698e6i 1.07026 1.85375i
\(465\) 0 0
\(466\) 3.69291e6 + 6.39631e6i 0.787778 + 1.36447i
\(467\) 2.54545e6 4.40885e6i 0.540098 0.935477i −0.458800 0.888540i \(-0.651720\pi\)
0.998898 0.0469376i \(-0.0149462\pi\)
\(468\) 0 0
\(469\) 2.25442e6 2.63449e6i 0.473262 0.553049i
\(470\) −866579. −0.180952
\(471\) 0 0
\(472\) −1.45383e6 2.51810e6i −0.300370 0.520257i
\(473\) 322912. + 559301.i 0.0663639 + 0.114946i
\(474\) 0 0
\(475\) 4.88717e6 0.993856
\(476\) −856786. 159642.i −0.173322 0.0322946i
\(477\) 0 0
\(478\) 5.43416e6 9.41224e6i 1.08783 1.88418i
\(479\) −4.15042e6 7.18874e6i −0.826521 1.43158i −0.900752 0.434334i \(-0.856984\pi\)
0.0742312 0.997241i \(-0.476350\pi\)
\(480\) 0 0
\(481\) 107867. 186831.i 0.0212581 0.0368202i
\(482\) 7.13644e6 1.39915
\(483\) 0 0
\(484\) −676028. −0.131175
\(485\) −4.12604e6 + 7.14651e6i −0.796488 + 1.37956i
\(486\) 0 0
\(487\) −4.31701e6 7.47727e6i −0.824822 1.42863i −0.902055 0.431621i \(-0.857942\pi\)
0.0772330 0.997013i \(-0.475391\pi\)
\(488\) 2.27871e6 3.94684e6i 0.433151 0.750240i
\(489\) 0 0
\(490\) −8.86500e6 3.42238e6i −1.66797 0.643930i
\(491\) −95039.5 −0.0177910 −0.00889550 0.999960i \(-0.502832\pi\)
−0.00889550 + 0.999960i \(0.502832\pi\)
\(492\) 0 0
\(493\) −1.44032e6 2.49471e6i −0.266896 0.462277i
\(494\) −1.55453e6 2.69252e6i −0.286603 0.496411i
\(495\) 0 0
\(496\) 3.28415e6 0.599402
\(497\) 621000. + 1.75898e6i 0.112772 + 0.319426i
\(498\) 0 0
\(499\) −1.07102e6 + 1.85506e6i −0.192551 + 0.333507i −0.946095 0.323890i \(-0.895009\pi\)
0.753544 + 0.657397i \(0.228343\pi\)
\(500\) −88782.9 153776.i −0.0158820 0.0275084i
\(501\) 0 0
\(502\) −30143.8 + 52210.7i −0.00533875 + 0.00924698i
\(503\) −5.24794e6 −0.924844 −0.462422 0.886660i \(-0.653019\pi\)
−0.462422 + 0.886660i \(0.653019\pi\)
\(504\) 0 0
\(505\) −2.29107e6 −0.399769
\(506\) −530531. + 918907.i −0.0921159 + 0.159549i
\(507\) 0 0
\(508\) −469945. 813968.i −0.0807956 0.139942i
\(509\) −5.29453e6 + 9.17040e6i −0.905802 + 1.56889i −0.0859643 + 0.996298i \(0.527397\pi\)
−0.819837 + 0.572596i \(0.805936\pi\)
\(510\) 0 0
\(511\) −5.90829e6 + 6.90437e6i −1.00094 + 1.16969i
\(512\) −3.52190e6 −0.593747
\(513\) 0 0
\(514\) 1.86819e6 + 3.23580e6i 0.311899 + 0.540225i
\(515\) −1.16660e6 2.02061e6i −0.193822 0.335709i
\(516\) 0 0
\(517\) −539357. −0.0887462
\(518\) −441554. + 515996.i −0.0723036 + 0.0844932i
\(519\) 0 0
\(520\) 1.14077e6 1.97588e6i 0.185008 0.320443i
\(521\) −2.27232e6 3.93578e6i −0.366755 0.635238i 0.622301 0.782778i \(-0.286198\pi\)
−0.989056 + 0.147540i \(0.952865\pi\)
\(522\) 0 0
\(523\) 2.63599e6 4.56566e6i 0.421394 0.729877i −0.574682 0.818377i \(-0.694874\pi\)
0.996076 + 0.0885004i \(0.0282075\pi\)
\(524\) 3.02772e6 0.481711
\(525\) 0 0
\(526\) −2.49373e6 −0.392993
\(527\) 476504. 825330.i 0.0747378 0.129450i
\(528\) 0 0
\(529\) 3.12756e6 + 5.41709e6i 0.485921 + 0.841641i
\(530\) 2.69624e6 4.67003e6i 0.416936 0.722154i
\(531\) 0 0
\(532\) 1.17986e6 + 3.34196e6i 0.180739 + 0.511943i
\(533\) 2.05048e6 0.312635
\(534\) 0 0
\(535\) 3.50676e6 + 6.07389e6i 0.529690 + 0.917451i
\(536\) −1.31037e6 2.26963e6i −0.197008 0.341227i
\(537\) 0 0
\(538\) 3.39647e6 0.505908
\(539\) −5.51755e6 2.13008e6i −0.818040 0.315809i
\(540\) 0 0
\(541\) −2.96723e6 + 5.13939e6i −0.435871 + 0.754950i −0.997366 0.0725298i \(-0.976893\pi\)
0.561496 + 0.827480i \(0.310226\pi\)
\(542\) −3.46209e6 5.99652e6i −0.506221 0.876801i
\(543\) 0 0
\(544\) −1.09120e6 + 1.89001e6i −0.158091 + 0.273821i
\(545\) 1.76122e7 2.53994
\(546\) 0 0
\(547\) −8.82017e6 −1.26040 −0.630200 0.776433i \(-0.717027\pi\)
−0.630200 + 0.776433i \(0.717027\pi\)
\(548\) 256673. 444571.i 0.0365115 0.0632397i
\(549\) 0 0
\(550\) −4.04705e6 7.00970e6i −0.570469 0.988081i
\(551\) −5.85712e6 + 1.01448e7i −0.821874 + 1.42353i
\(552\) 0 0
\(553\) 3.45204e6 + 643206.i 0.480024 + 0.0894411i
\(554\) −6.86124e6 −0.949791
\(555\) 0 0
\(556\) −3.05538e6 5.29207e6i −0.419158 0.726004i
\(557\) −591120. 1.02385e6i −0.0807304 0.139829i 0.822833 0.568283i \(-0.192392\pi\)
−0.903564 + 0.428453i \(0.859059\pi\)
\(558\) 0 0
\(559\) −535306. −0.0724556
\(560\) −8.58111e6 + 1.00278e7i −1.15631 + 1.35125i
\(561\) 0 0
\(562\) 1.12734e6 1.95261e6i 0.150561 0.260780i
\(563\) 2.03870e6 + 3.53114e6i 0.271071 + 0.469509i 0.969136 0.246525i \(-0.0792888\pi\)
−0.698065 + 0.716034i \(0.745955\pi\)
\(564\) 0 0
\(565\) 1.58321e6 2.74219e6i 0.208649 0.361391i
\(566\) −1.25514e7 −1.64684
\(567\) 0 0
\(568\) 1.40990e6 0.183366
\(569\) 4.08807e6 7.08075e6i 0.529344 0.916851i −0.470070 0.882629i \(-0.655771\pi\)
0.999414 0.0342216i \(-0.0108952\pi\)
\(570\) 0 0
\(571\) −1.65307e6 2.86321e6i −0.212179 0.367504i 0.740217 0.672368i \(-0.234723\pi\)
−0.952396 + 0.304863i \(0.901389\pi\)
\(572\) −932292. + 1.61478e6i −0.119141 + 0.206359i
\(573\) 0 0
\(574\) −6.34574e6 1.18238e6i −0.803901 0.149788i
\(575\) 1.38247e6 0.174376
\(576\) 0 0
\(577\) 3.57497e6 + 6.19203e6i 0.447026 + 0.774272i 0.998191 0.0601245i \(-0.0191498\pi\)
−0.551165 + 0.834396i \(0.685816\pi\)
\(578\) −4.54324e6 7.86913e6i −0.565648 0.979731i
\(579\) 0 0
\(580\) 1.12876e7 1.39325
\(581\) 3.44214e6 + 9.74986e6i 0.423046 + 1.19828i
\(582\) 0 0
\(583\) 1.67813e6 2.90661e6i 0.204482 0.354173i
\(584\) 3.43418e6 + 5.94818e6i 0.416669 + 0.721692i
\(585\) 0 0
\(586\) −5.81309e6 + 1.00686e7i −0.699300 + 1.21122i
\(587\) −9.69191e6 −1.16095 −0.580476 0.814277i \(-0.697133\pi\)
−0.580476 + 0.814277i \(0.697133\pi\)
\(588\) 0 0
\(589\) −3.87545e6 −0.460292
\(590\) 8.38886e6 1.45299e7i 0.992139 1.71844i
\(591\) 0 0
\(592\) 471621. + 816872.i 0.0553081 + 0.0957965i
\(593\) 3.31980e6 5.75006e6i 0.387682 0.671484i −0.604456 0.796639i \(-0.706609\pi\)
0.992137 + 0.125154i \(0.0399426\pi\)
\(594\) 0 0
\(595\) 1.27500e6 + 3.61145e6i 0.147645 + 0.418205i
\(596\) 6.45569e6 0.744435
\(597\) 0 0
\(598\) −439742. 761655.i −0.0502857 0.0870974i
\(599\) −1.62096e6 2.80758e6i −0.184588 0.319716i 0.758849 0.651266i \(-0.225762\pi\)
−0.943438 + 0.331550i \(0.892428\pi\)
\(600\) 0 0
\(601\) −5.65076e6 −0.638147 −0.319074 0.947730i \(-0.603372\pi\)
−0.319074 + 0.947730i \(0.603372\pi\)
\(602\) 1.65664e6 + 308676.i 0.186310 + 0.0347145i
\(603\) 0 0
\(604\) 3.25887e6 5.64453e6i 0.363475 0.629557i
\(605\) 1.48539e6 + 2.57277e6i 0.164988 + 0.285767i
\(606\) 0 0
\(607\) −117837. + 204100.i −0.0129811 + 0.0224839i −0.872443 0.488716i \(-0.837465\pi\)
0.859462 + 0.511200i \(0.170799\pi\)
\(608\) 8.87478e6 0.973641
\(609\) 0 0
\(610\) 2.62972e7 2.86144
\(611\) 223529. 387163.i 0.0242231 0.0419557i
\(612\) 0 0
\(613\) −394438. 683187.i −0.0423963 0.0734325i 0.844049 0.536267i \(-0.180166\pi\)
−0.886445 + 0.462834i \(0.846833\pi\)
\(614\) −1.65358e6 + 2.86408e6i −0.177012 + 0.306595i
\(615\) 0 0
\(616\) −2.90645e6 + 3.39645e6i −0.308611 + 0.360640i
\(617\) −1.67739e7 −1.77387 −0.886935 0.461894i \(-0.847170\pi\)
−0.886935 + 0.461894i \(0.847170\pi\)
\(618\) 0 0
\(619\) −4.11150e6 7.12132e6i −0.431294 0.747023i 0.565691 0.824617i \(-0.308610\pi\)
−0.996985 + 0.0775941i \(0.975276\pi\)
\(620\) 1.86714e6 + 3.23399e6i 0.195074 + 0.337878i
\(621\) 0 0
\(622\) −1.72675e7 −1.78959
\(623\) 5.55386e6 + 1.03483e6i 0.573290 + 0.106819i
\(624\) 0 0
\(625\) 4.68399e6 8.11290e6i 0.479640 0.830761i
\(626\) 8.57346e6 + 1.48497e7i 0.874420 + 1.51454i
\(627\) 0 0
\(628\) −4.16818e6 + 7.21949e6i −0.421742 + 0.730479i
\(629\) 273714. 0.0275849
\(630\) 0 0
\(631\) −5.94507e6 −0.594406 −0.297203 0.954814i \(-0.596054\pi\)
−0.297203 + 0.954814i \(0.596054\pi\)
\(632\) 1.32702e6 2.29846e6i 0.132155 0.228899i
\(633\) 0 0
\(634\) −6.64403e6 1.15078e7i −0.656460 1.13702i
\(635\) −2.06515e6 + 3.57695e6i −0.203244 + 0.352029i
\(636\) 0 0
\(637\) 3.81569e6 3.07785e6i 0.372585 0.300537i
\(638\) 1.94011e7 1.88701
\(639\) 0 0
\(640\) 7.26120e6 + 1.25768e7i 0.700743 + 1.21372i
\(641\) −5.33804e6 9.24576e6i −0.513141 0.888786i −0.999884 0.0152411i \(-0.995148\pi\)
0.486743 0.873545i \(-0.338185\pi\)
\(642\) 0 0
\(643\) −3.13159e6 −0.298701 −0.149351 0.988784i \(-0.547718\pi\)
−0.149351 + 0.988784i \(0.547718\pi\)
\(644\) 333757. + 945367.i 0.0317114 + 0.0898227i
\(645\) 0 0
\(646\) 1.97232e6 3.41616e6i 0.185950 0.322075i
\(647\) −2.46728e6 4.27346e6i −0.231717 0.401346i 0.726596 0.687065i \(-0.241101\pi\)
−0.958314 + 0.285719i \(0.907768\pi\)
\(648\) 0 0
\(649\) 5.22120e6 9.04339e6i 0.486585 0.842790i
\(650\) 6.70897e6 0.622834
\(651\) 0 0
\(652\) 9.12710e6 0.840841
\(653\) 2.86112e6 4.95561e6i 0.262575 0.454793i −0.704351 0.709852i \(-0.748762\pi\)
0.966925 + 0.255059i \(0.0820950\pi\)
\(654\) 0 0
\(655\) −6.65258e6 1.15226e7i −0.605881 1.04942i
\(656\) −4.48261e6 + 7.76411e6i −0.406698 + 0.704421i
\(657\) 0 0
\(658\) −915018. + 1.06928e6i −0.0823881 + 0.0962779i
\(659\) −362477. −0.0325137 −0.0162569 0.999868i \(-0.505175\pi\)
−0.0162569 + 0.999868i \(0.505175\pi\)
\(660\) 0 0
\(661\) 9.56053e6 + 1.65593e7i 0.851096 + 1.47414i 0.880220 + 0.474565i \(0.157395\pi\)
−0.0291249 + 0.999576i \(0.509272\pi\)
\(662\) −3.83566e6 6.64356e6i −0.340170 0.589191i
\(663\) 0 0
\(664\) 7.81494e6 0.687868
\(665\) 1.01261e7 1.18333e7i 0.887950 1.03765i
\(666\) 0 0
\(667\) −1.65685e6 + 2.86975e6i −0.144201 + 0.249764i
\(668\) −6.14587e6 1.06450e7i −0.532896 0.923003i
\(669\) 0 0
\(670\) 7.56111e6 1.30962e7i 0.650727 1.12709i
\(671\) 1.63673e7 1.40337
\(672\) 0 0
\(673\) −573374. −0.0487978 −0.0243989 0.999702i \(-0.507767\pi\)
−0.0243989 + 0.999702i \(0.507767\pi\)
\(674\) −9.18864e6 + 1.59152e7i −0.779115 + 1.34947i
\(675\) 0 0
\(676\) 2.59962e6 + 4.50267e6i 0.218798 + 0.378968i
\(677\) 5.84516e6 1.01241e7i 0.490146 0.848957i −0.509790 0.860299i \(-0.670277\pi\)
0.999936 + 0.0113419i \(0.00361030\pi\)
\(678\) 0 0
\(679\) 4.46148e6 + 1.26371e7i 0.371368 + 1.05190i
\(680\) 2.89473e6 0.240069
\(681\) 0 0
\(682\) 3.20925e6 + 5.55858e6i 0.264206 + 0.457618i
\(683\) 9.18370e6 + 1.59066e7i 0.753297 + 1.30475i 0.946217 + 0.323534i \(0.104871\pi\)
−0.192920 + 0.981214i \(0.561796\pi\)
\(684\) 0 0
\(685\) −2.25588e6 −0.183692
\(686\) −1.35834e7 + 7.32492e6i −1.10204 + 0.594282i
\(687\) 0 0
\(688\) 1.17025e6 2.02693e6i 0.0942554 0.163255i
\(689\) 1.39096e6 + 2.40921e6i 0.111626 + 0.193342i
\(690\) 0 0
\(691\) −1.17806e7 + 2.04045e7i −0.938579 + 1.62567i −0.170454 + 0.985366i \(0.554523\pi\)
−0.768125 + 0.640300i \(0.778810\pi\)
\(692\) 4.52612e6 0.359303
\(693\) 0 0
\(694\) −1.32484e7 −1.04415
\(695\) −1.34267e7 + 2.32558e7i −1.05441 + 1.82629i
\(696\) 0 0
\(697\) 1.30078e6 + 2.25303e6i 0.101420 + 0.175665i
\(698\) −5.72587e6 + 9.91750e6i −0.444839 + 0.770484i
\(699\) 0 0
\(700\) −7.51839e6 1.40087e6i −0.579935 0.108057i
\(701\) −1.32980e7 −1.02210 −0.511048 0.859552i \(-0.670743\pi\)
−0.511048 + 0.859552i \(0.670743\pi\)
\(702\) 0 0
\(703\) −556535. 963946.i −0.0424721 0.0735639i
\(704\) −168605. 292033.i −0.0128215 0.0222075i
\(705\) 0 0
\(706\) −4.09600e6 −0.309277
\(707\) −2.41913e6 + 2.82697e6i −0.182016 + 0.212703i
\(708\) 0 0
\(709\) 3.42677e6 5.93533e6i 0.256017 0.443434i −0.709154 0.705053i \(-0.750923\pi\)
0.965171 + 0.261619i \(0.0842564\pi\)
\(710\) 4.06770e6 + 7.04547e6i 0.302833 + 0.524522i
\(711\) 0 0
\(712\) 2.13499e6 3.69791e6i 0.157832 0.273374i
\(713\) −1.09628e6 −0.0807602
\(714\) 0 0
\(715\) 8.19384e6 0.599408
\(716\) 1.26485e6 2.19078e6i 0.0922051 0.159704i
\(717\) 0 0
\(718\) 6.97008e6 + 1.20725e7i 0.504576 + 0.873951i
\(719\) 1.32865e7 2.30128e7i 0.958490 1.66015i 0.232318 0.972640i \(-0.425369\pi\)
0.726172 0.687513i \(-0.241298\pi\)
\(720\) 0 0
\(721\) −3.72505e6 694075.i −0.266866 0.0497242i
\(722\) 1.49658e6 0.106846
\(723\) 0 0
\(724\) −2.78156e6 4.81781e6i −0.197216 0.341588i
\(725\) −1.26390e7 2.18913e7i −0.893031 1.54678i
\(726\) 0 0
\(727\) 2.16991e6 0.152267 0.0761335 0.997098i \(-0.475742\pi\)
0.0761335 + 0.997098i \(0.475742\pi\)
\(728\) −1.23351e6 3.49393e6i −0.0862612 0.244335i
\(729\) 0 0
\(730\) −1.98159e7 + 3.43221e7i −1.37628 + 2.38379i
\(731\) −339587. 588182.i −0.0235049 0.0407116i
\(732\) 0 0
\(733\) 8.73265e6 1.51254e7i 0.600324 1.03979i −0.392447 0.919774i \(-0.628372\pi\)
0.992772 0.120018i \(-0.0382951\pi\)
\(734\) −1.54016e7 −1.05518
\(735\) 0 0
\(736\) 2.51048e6 0.170829
\(737\) 4.70602e6 8.15106e6i 0.319143 0.552771i
\(738\) 0 0
\(739\) 6.82304e6 + 1.18178e7i 0.459586 + 0.796026i 0.998939 0.0460536i \(-0.0146645\pi\)
−0.539353 + 0.842080i \(0.681331\pi\)
\(740\) −536264. + 928836.i −0.0359997 + 0.0623533i
\(741\) 0 0
\(742\) −2.91544e6 8.25798e6i −0.194399 0.550635i
\(743\) −1.48965e7 −0.989944 −0.494972 0.868909i \(-0.664822\pi\)
−0.494972 + 0.868909i \(0.664822\pi\)
\(744\) 0 0
\(745\) −1.41846e7 2.45685e7i −0.936326 1.62176i
\(746\) 4.90396e6 + 8.49390e6i 0.322626 + 0.558805i
\(747\) 0 0
\(748\) −2.36571e6 −0.154599
\(749\) 1.11974e7 + 2.08637e6i 0.729311 + 0.135890i
\(750\) 0 0
\(751\) 1.26731e7 2.19505e7i 0.819944 1.42019i −0.0857783 0.996314i \(-0.527338\pi\)
0.905723 0.423871i \(-0.139329\pi\)
\(752\) 977324. + 1.69277e6i 0.0630222 + 0.109158i
\(753\) 0 0
\(754\) −8.04049e6 + 1.39265e7i −0.515056 + 0.892102i
\(755\) −2.86419e7 −1.82867
\(756\) 0 0
\(757\) −2.66725e7 −1.69170 −0.845852 0.533417i \(-0.820908\pi\)
−0.845852 + 0.533417i \(0.820908\pi\)
\(758\) 1.19412e7 2.06828e7i 0.754875 1.30748i
\(759\) 0 0
\(760\) −5.88577e6 1.01945e7i −0.369632 0.640221i
\(761\) 289914. 502146.i 0.0181471 0.0314318i −0.856809 0.515634i \(-0.827557\pi\)
0.874956 + 0.484202i \(0.160890\pi\)
\(762\) 0 0
\(763\) 1.85967e7 2.17319e7i 1.15644 1.35141i
\(764\) −4.13255e6 −0.256144
\(765\) 0 0
\(766\) −1.16179e7 2.01227e7i −0.715408 1.23912i
\(767\) 4.32770e6 + 7.49580e6i 0.265625 + 0.460076i
\(768\) 0 0
\(769\) 1.52438e7 0.929562 0.464781 0.885426i \(-0.346133\pi\)
0.464781 + 0.885426i \(0.346133\pi\)
\(770\) −2.53579e7 4.72485e6i −1.54130 0.287185i
\(771\) 0 0
\(772\) 6.10702e6 1.05777e7i 0.368796 0.638773i
\(773\) −9.74628e6 1.68810e7i −0.586665 1.01613i −0.994666 0.103152i \(-0.967107\pi\)
0.408001 0.912982i \(-0.366226\pi\)
\(774\) 0 0