Properties

Label 84.6.i.c.37.1
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 37.1
Root \(4.59067 + 7.95128i\) of defining polynomial
Character \(\chi\) \(=\) 84.37
Dual form 84.6.i.c.25.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.50000 + 7.79423i) q^{3} +(-39.3359 + 68.1317i) q^{5} +(-100.606 - 81.7641i) q^{7} +(-40.5000 + 70.1481i) q^{9} +(-345.759 - 598.873i) q^{11} +818.732 q^{13} -708.046 q^{15} +(-554.638 - 960.661i) q^{17} +(286.523 - 496.273i) q^{19} +(184.559 - 1152.09i) q^{21} +(-1258.80 + 2180.30i) q^{23} +(-1532.12 - 2653.71i) q^{25} -729.000 q^{27} -3258.19 q^{29} +(-5059.55 - 8763.40i) q^{31} +(3111.84 - 5389.86i) q^{33} +(9528.17 - 3638.23i) q^{35} +(-2434.81 + 4217.21i) q^{37} +(3684.30 + 6381.39i) q^{39} -13094.3 q^{41} -9303.64 q^{43} +(-3186.21 - 5518.67i) q^{45} +(-6452.90 + 11176.8i) q^{47} +(3436.28 + 16452.0i) q^{49} +(4991.74 - 8645.95i) q^{51} +(9770.12 + 16922.3i) q^{53} +54403.0 q^{55} +5157.42 q^{57} +(12560.2 + 21755.0i) q^{59} +(15681.1 - 27160.5i) q^{61} +(9810.15 - 3745.90i) q^{63} +(-32205.6 + 55781.7i) q^{65} +(-27971.9 - 48448.8i) q^{67} -22658.4 q^{69} +20501.0 q^{71} +(33825.0 + 58586.6i) q^{73} +(13789.1 - 23883.4i) q^{75} +(-14180.7 + 88521.1i) q^{77} +(-7039.95 + 12193.5i) q^{79} +(-3280.50 - 5681.99i) q^{81} -77129.1 q^{83} +87268.6 q^{85} +(-14661.9 - 25395.1i) q^{87} +(-160.396 + 277.815i) q^{89} +(-82369.7 - 66942.9i) q^{91} +(45536.0 - 78870.6i) q^{93} +(22541.3 + 39042.6i) q^{95} -112009. q^{97} +56013.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 36 q^{3} - 42 q^{7} - 324 q^{9} - 462 q^{11} - 1204 q^{13} + 228 q^{17} + 358 q^{19} + 1404 q^{21} - 2148 q^{23} - 5454 q^{25} - 5832 q^{27} - 11064 q^{29} + 830 q^{31} + 4158 q^{33} + 7692 q^{35}+ \cdots + 74844 q^{99}+O(q^{100}) \) 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
\(5\) −39.3359 + 68.1317i −0.703662 + 1.21878i 0.263511 + 0.964656i \(0.415120\pi\)
−0.967172 + 0.254121i \(0.918214\pi\)
\(6\) 0 0
\(7\) −100.606 81.7641i −0.776033 0.630692i
\(8\) 0 0
\(9\) −40.5000 + 70.1481i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −345.759 598.873i −0.861574 1.49229i −0.870410 0.492328i \(-0.836146\pi\)
0.00883597 0.999961i \(-0.497187\pi\)
\(12\) 0 0
\(13\) 818.732 1.34364 0.671821 0.740714i \(-0.265512\pi\)
0.671821 + 0.740714i \(0.265512\pi\)
\(14\) 0 0
\(15\) −708.046 −0.812518
\(16\) 0 0
\(17\) −554.638 960.661i −0.465465 0.806209i 0.533757 0.845638i \(-0.320780\pi\)
−0.999222 + 0.0394286i \(0.987446\pi\)
\(18\) 0 0
\(19\) 286.523 496.273i 0.182086 0.315382i −0.760505 0.649332i \(-0.775049\pi\)
0.942591 + 0.333951i \(0.108382\pi\)
\(20\) 0 0
\(21\) 184.559 1152.09i 0.0913245 0.570082i
\(22\) 0 0
\(23\) −1258.80 + 2180.30i −0.496177 + 0.859403i −0.999990 0.00440926i \(-0.998596\pi\)
0.503814 + 0.863812i \(0.331930\pi\)
\(24\) 0 0
\(25\) −1532.12 2653.71i −0.490279 0.849189i
\(26\) 0 0
\(27\) −729.000 −0.192450
\(28\) 0 0
\(29\) −3258.19 −0.719419 −0.359710 0.933064i \(-0.617124\pi\)
−0.359710 + 0.933064i \(0.617124\pi\)
\(30\) 0 0
\(31\) −5059.55 8763.40i −0.945601 1.63783i −0.754544 0.656249i \(-0.772142\pi\)
−0.191056 0.981579i \(-0.561191\pi\)
\(32\) 0 0
\(33\) 3111.84 5389.86i 0.497430 0.861574i
\(34\) 0 0
\(35\) 9528.17 3638.23i 1.31474 0.502018i
\(36\) 0 0
\(37\) −2434.81 + 4217.21i −0.292389 + 0.506432i −0.974374 0.224934i \(-0.927783\pi\)
0.681985 + 0.731366i \(0.261117\pi\)
\(38\) 0 0
\(39\) 3684.30 + 6381.39i 0.387876 + 0.671821i
\(40\) 0 0
\(41\) −13094.3 −1.21653 −0.608265 0.793734i \(-0.708134\pi\)
−0.608265 + 0.793734i \(0.708134\pi\)
\(42\) 0 0
\(43\) −9303.64 −0.767329 −0.383664 0.923473i \(-0.625338\pi\)
−0.383664 + 0.923473i \(0.625338\pi\)
\(44\) 0 0
\(45\) −3186.21 5518.67i −0.234554 0.406259i
\(46\) 0 0
\(47\) −6452.90 + 11176.8i −0.426099 + 0.738025i −0.996522 0.0833256i \(-0.973446\pi\)
0.570423 + 0.821351i \(0.306779\pi\)
\(48\) 0 0
\(49\) 3436.28 + 16452.0i 0.204455 + 0.978876i
\(50\) 0 0
\(51\) 4991.74 8645.95i 0.268736 0.465465i
\(52\) 0 0
\(53\) 9770.12 + 16922.3i 0.477760 + 0.827505i 0.999675 0.0254926i \(-0.00811542\pi\)
−0.521915 + 0.852998i \(0.674782\pi\)
\(54\) 0 0
\(55\) 54403.0 2.42503
\(56\) 0 0
\(57\) 5157.42 0.210254
\(58\) 0 0
\(59\) 12560.2 + 21755.0i 0.469751 + 0.813632i 0.999402 0.0345835i \(-0.0110105\pi\)
−0.529651 + 0.848216i \(0.677677\pi\)
\(60\) 0 0
\(61\) 15681.1 27160.5i 0.539575 0.934571i −0.459352 0.888254i \(-0.651918\pi\)
0.998927 0.0463168i \(-0.0147484\pi\)
\(62\) 0 0
\(63\) 9810.15 3745.90i 0.311404 0.118906i
\(64\) 0 0
\(65\) −32205.6 + 55781.7i −0.945469 + 1.63760i
\(66\) 0 0
\(67\) −27971.9 48448.8i −0.761264 1.31855i −0.942200 0.335052i \(-0.891246\pi\)
0.180936 0.983495i \(-0.442087\pi\)
\(68\) 0 0
\(69\) −22658.4 −0.572935
\(70\) 0 0
\(71\) 20501.0 0.482647 0.241323 0.970445i \(-0.422419\pi\)
0.241323 + 0.970445i \(0.422419\pi\)
\(72\) 0 0
\(73\) 33825.0 + 58586.6i 0.742900 + 1.28674i 0.951170 + 0.308669i \(0.0998835\pi\)
−0.208270 + 0.978071i \(0.566783\pi\)
\(74\) 0 0
\(75\) 13789.1 23883.4i 0.283063 0.490279i
\(76\) 0 0
\(77\) −14180.7 + 88521.1i −0.272565 + 1.70145i
\(78\) 0 0
\(79\) −7039.95 + 12193.5i −0.126912 + 0.219818i −0.922479 0.386048i \(-0.873840\pi\)
0.795567 + 0.605866i \(0.207173\pi\)
\(80\) 0 0
\(81\) −3280.50 5681.99i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −77129.1 −1.22892 −0.614459 0.788949i \(-0.710626\pi\)
−0.614459 + 0.788949i \(0.710626\pi\)
\(84\) 0 0
\(85\) 87268.6 1.31012
\(86\) 0 0
\(87\) −14661.9 25395.1i −0.207678 0.359710i
\(88\) 0 0
\(89\) −160.396 + 277.815i −0.00214644 + 0.00371775i −0.867097 0.498140i \(-0.834017\pi\)
0.864950 + 0.501858i \(0.167350\pi\)
\(90\) 0 0
\(91\) −82369.7 66942.9i −1.04271 0.847424i
\(92\) 0 0
\(93\) 45536.0 78870.6i 0.545943 0.945601i
\(94\) 0 0
\(95\) 22541.3 + 39042.6i 0.256253 + 0.443844i
\(96\) 0 0
\(97\) −112009. −1.20871 −0.604355 0.796715i \(-0.706569\pi\)
−0.604355 + 0.796715i \(0.706569\pi\)
\(98\) 0 0
\(99\) 56013.0 0.574382
\(100\) 0 0
\(101\) −33627.0 58243.7i −0.328008 0.568127i 0.654108 0.756401i \(-0.273044\pi\)
−0.982117 + 0.188274i \(0.939711\pi\)
\(102\) 0 0
\(103\) 58317.6 101009.i 0.541635 0.938140i −0.457175 0.889377i \(-0.651139\pi\)
0.998810 0.0487630i \(-0.0155279\pi\)
\(104\) 0 0
\(105\) 71233.9 + 57892.7i 0.630541 + 0.512449i
\(106\) 0 0
\(107\) 80322.6 139123.i 0.678232 1.17473i −0.297281 0.954790i \(-0.596080\pi\)
0.975513 0.219942i \(-0.0705869\pi\)
\(108\) 0 0
\(109\) −59668.3 103349.i −0.481036 0.833179i 0.518727 0.854940i \(-0.326406\pi\)
−0.999763 + 0.0217610i \(0.993073\pi\)
\(110\) 0 0
\(111\) −43826.6 −0.337622
\(112\) 0 0
\(113\) −110893. −0.816972 −0.408486 0.912765i \(-0.633943\pi\)
−0.408486 + 0.912765i \(0.633943\pi\)
\(114\) 0 0
\(115\) −99031.8 171528.i −0.698281 1.20946i
\(116\) 0 0
\(117\) −33158.7 + 57432.5i −0.223940 + 0.387876i
\(118\) 0 0
\(119\) −22747.4 + 141998.i −0.147253 + 0.919210i
\(120\) 0 0
\(121\) −158574. + 274658.i −0.984618 + 1.70541i
\(122\) 0 0
\(123\) −58924.4 102060.i −0.351182 0.608265i
\(124\) 0 0
\(125\) −4779.64 −0.0273603
\(126\) 0 0
\(127\) 315184. 1.73402 0.867012 0.498287i \(-0.166038\pi\)
0.867012 + 0.498287i \(0.166038\pi\)
\(128\) 0 0
\(129\) −41866.4 72514.7i −0.221509 0.383664i
\(130\) 0 0
\(131\) −42832.3 + 74187.6i −0.218068 + 0.377705i −0.954217 0.299114i \(-0.903309\pi\)
0.736149 + 0.676819i \(0.236642\pi\)
\(132\) 0 0
\(133\) −69403.3 + 26500.9i −0.340213 + 0.129907i
\(134\) 0 0
\(135\) 28675.9 49668.0i 0.135420 0.234554i
\(136\) 0 0
\(137\) 16316.1 + 28260.3i 0.0742703 + 0.128640i 0.900769 0.434299i \(-0.143004\pi\)
−0.826498 + 0.562939i \(0.809671\pi\)
\(138\) 0 0
\(139\) 206590. 0.906925 0.453462 0.891275i \(-0.350189\pi\)
0.453462 + 0.891275i \(0.350189\pi\)
\(140\) 0 0
\(141\) −116152. −0.492017
\(142\) 0 0
\(143\) −283084. 490317.i −1.15765 2.00510i
\(144\) 0 0
\(145\) 128164. 221986.i 0.506228 0.876812i
\(146\) 0 0
\(147\) −112767. + 100817.i −0.430417 + 0.384805i
\(148\) 0 0
\(149\) −241855. + 418906.i −0.892463 + 1.54579i −0.0555495 + 0.998456i \(0.517691\pi\)
−0.836913 + 0.547335i \(0.815642\pi\)
\(150\) 0 0
\(151\) 83610.4 + 144818.i 0.298413 + 0.516867i 0.975773 0.218785i \(-0.0702093\pi\)
−0.677360 + 0.735652i \(0.736876\pi\)
\(152\) 0 0
\(153\) 89851.3 0.310310
\(154\) 0 0
\(155\) 796087. 2.66153
\(156\) 0 0
\(157\) 7054.26 + 12218.3i 0.0228403 + 0.0395606i 0.877220 0.480089i \(-0.159396\pi\)
−0.854379 + 0.519650i \(0.826062\pi\)
\(158\) 0 0
\(159\) −87931.0 + 152301.i −0.275835 + 0.477760i
\(160\) 0 0
\(161\) 304913. 116428.i 0.927068 0.353991i
\(162\) 0 0
\(163\) −327188. + 566706.i −0.964558 + 1.67066i −0.253762 + 0.967267i \(0.581668\pi\)
−0.710797 + 0.703397i \(0.751665\pi\)
\(164\) 0 0
\(165\) 244814. + 424030.i 0.700044 + 1.21251i
\(166\) 0 0
\(167\) 182945. 0.507610 0.253805 0.967255i \(-0.418318\pi\)
0.253805 + 0.967255i \(0.418318\pi\)
\(168\) 0 0
\(169\) 299030. 0.805374
\(170\) 0 0
\(171\) 23208.4 + 40198.1i 0.0606952 + 0.105127i
\(172\) 0 0
\(173\) 146004. 252887.i 0.370894 0.642407i −0.618809 0.785541i \(-0.712385\pi\)
0.989703 + 0.143134i \(0.0457180\pi\)
\(174\) 0 0
\(175\) −62837.2 + 392253.i −0.155103 + 0.968214i
\(176\) 0 0
\(177\) −113042. + 195795.i −0.271211 + 0.469751i
\(178\) 0 0
\(179\) −97383.8 168674.i −0.227172 0.393473i 0.729797 0.683664i \(-0.239615\pi\)
−0.956969 + 0.290191i \(0.906281\pi\)
\(180\) 0 0
\(181\) −256634. −0.582261 −0.291130 0.956683i \(-0.594031\pi\)
−0.291130 + 0.956683i \(0.594031\pi\)
\(182\) 0 0
\(183\) 282260. 0.623047
\(184\) 0 0
\(185\) −191551. 331776.i −0.411486 0.712714i
\(186\) 0 0
\(187\) −383542. + 664315.i −0.802065 + 1.38922i
\(188\) 0 0
\(189\) 73342.0 + 59606.0i 0.149348 + 0.121377i
\(190\) 0 0
\(191\) 146975. 254567.i 0.291513 0.504916i −0.682654 0.730741i \(-0.739175\pi\)
0.974168 + 0.225825i \(0.0725079\pi\)
\(192\) 0 0
\(193\) 34565.0 + 59868.4i 0.0667950 + 0.115692i 0.897489 0.441037i \(-0.145389\pi\)
−0.830694 + 0.556730i \(0.812056\pi\)
\(194\) 0 0
\(195\) −579700. −1.09173
\(196\) 0 0
\(197\) 331748. 0.609037 0.304518 0.952506i \(-0.401505\pi\)
0.304518 + 0.952506i \(0.401505\pi\)
\(198\) 0 0
\(199\) −287214. 497470.i −0.514130 0.890500i −0.999866 0.0163939i \(-0.994781\pi\)
0.485735 0.874106i \(-0.338552\pi\)
\(200\) 0 0
\(201\) 251747. 436039.i 0.439516 0.761264i
\(202\) 0 0
\(203\) 327795. + 266403.i 0.558293 + 0.453732i
\(204\) 0 0
\(205\) 515076. 892138.i 0.856025 1.48268i
\(206\) 0 0
\(207\) −101963. 176604.i −0.165392 0.286468i
\(208\) 0 0
\(209\) −396272. −0.627521
\(210\) 0 0
\(211\) −383999. −0.593777 −0.296889 0.954912i \(-0.595949\pi\)
−0.296889 + 0.954912i \(0.595949\pi\)
\(212\) 0 0
\(213\) 92254.5 + 159790.i 0.139328 + 0.241323i
\(214\) 0 0
\(215\) 365967. 633873.i 0.539940 0.935203i
\(216\) 0 0
\(217\) −207508. + 1.29534e6i −0.299148 + 1.86739i
\(218\) 0 0
\(219\) −304425. + 527279.i −0.428913 + 0.742900i
\(220\) 0 0
\(221\) −454100. 786524.i −0.625418 1.08326i
\(222\) 0 0
\(223\) −347165. −0.467492 −0.233746 0.972298i \(-0.575098\pi\)
−0.233746 + 0.972298i \(0.575098\pi\)
\(224\) 0 0
\(225\) 248204. 0.326853
\(226\) 0 0
\(227\) −180641. 312879.i −0.232676 0.403006i 0.725919 0.687780i \(-0.241415\pi\)
−0.958595 + 0.284774i \(0.908081\pi\)
\(228\) 0 0
\(229\) 376492. 652102.i 0.474424 0.821726i −0.525147 0.851011i \(-0.675990\pi\)
0.999571 + 0.0292852i \(0.00932309\pi\)
\(230\) 0 0
\(231\) −753767. + 287818.i −0.929410 + 0.354885i
\(232\) 0 0
\(233\) −357199. + 618686.i −0.431042 + 0.746587i −0.996963 0.0778721i \(-0.975187\pi\)
0.565921 + 0.824460i \(0.308521\pi\)
\(234\) 0 0
\(235\) −507661. 879295.i −0.599659 1.03864i
\(236\) 0 0
\(237\) −126719. −0.146545
\(238\) 0 0
\(239\) 343587. 0.389083 0.194541 0.980894i \(-0.437678\pi\)
0.194541 + 0.980894i \(0.437678\pi\)
\(240\) 0 0
\(241\) 38152.5 + 66082.0i 0.0423136 + 0.0732893i 0.886407 0.462908i \(-0.153194\pi\)
−0.844093 + 0.536197i \(0.819860\pi\)
\(242\) 0 0
\(243\) 29524.5 51137.9i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) −1.25607e6 413033.i −1.33690 0.439612i
\(246\) 0 0
\(247\) 234586. 406314.i 0.244658 0.423760i
\(248\) 0 0
\(249\) −347081. 601162.i −0.354758 0.614459i
\(250\) 0 0
\(251\) 196249. 0.196618 0.0983090 0.995156i \(-0.468657\pi\)
0.0983090 + 0.995156i \(0.468657\pi\)
\(252\) 0 0
\(253\) 1.74096e6 1.70997
\(254\) 0 0
\(255\) 392709. + 680192.i 0.378199 + 0.655060i
\(256\) 0 0
\(257\) 854554. 1.48013e6i 0.807062 1.39787i −0.107828 0.994170i \(-0.534390\pi\)
0.914890 0.403703i \(-0.132277\pi\)
\(258\) 0 0
\(259\) 589774. 225199.i 0.546306 0.208601i
\(260\) 0 0
\(261\) 131957. 228556.i 0.119903 0.207678i
\(262\) 0 0
\(263\) 395762. + 685481.i 0.352814 + 0.611091i 0.986741 0.162301i \(-0.0518917\pi\)
−0.633928 + 0.773392i \(0.718558\pi\)
\(264\) 0 0
\(265\) −1.53726e6 −1.34473
\(266\) 0 0
\(267\) −2887.13 −0.00247850
\(268\) 0 0
\(269\) −579502. 1.00373e6i −0.488286 0.845736i 0.511623 0.859210i \(-0.329044\pi\)
−0.999909 + 0.0134740i \(0.995711\pi\)
\(270\) 0 0
\(271\) −111567. + 193240.i −0.0922811 + 0.159836i −0.908471 0.417949i \(-0.862749\pi\)
0.816190 + 0.577784i \(0.196083\pi\)
\(272\) 0 0
\(273\) 151105. 943251.i 0.122707 0.765986i
\(274\) 0 0
\(275\) −1.05949e6 + 1.83509e6i −0.844823 + 1.46328i
\(276\) 0 0
\(277\) 234523. + 406205.i 0.183648 + 0.318087i 0.943120 0.332452i \(-0.107876\pi\)
−0.759472 + 0.650540i \(0.774543\pi\)
\(278\) 0 0
\(279\) 819647. 0.630400
\(280\) 0 0
\(281\) −1.51447e6 −1.14418 −0.572090 0.820191i \(-0.693867\pi\)
−0.572090 + 0.820191i \(0.693867\pi\)
\(282\) 0 0
\(283\) 535303. + 927171.i 0.397314 + 0.688167i 0.993393 0.114758i \(-0.0366092\pi\)
−0.596080 + 0.802925i \(0.703276\pi\)
\(284\) 0 0
\(285\) −202871. + 351384.i −0.147948 + 0.256253i
\(286\) 0 0
\(287\) 1.31737e6 + 1.07064e6i 0.944068 + 0.767256i
\(288\) 0 0
\(289\) 94682.6 163995.i 0.0666846 0.115501i
\(290\) 0 0
\(291\) −504039. 873021.i −0.348925 0.604355i
\(292\) 0 0
\(293\) 1.45450e6 0.989794 0.494897 0.868952i \(-0.335206\pi\)
0.494897 + 0.868952i \(0.335206\pi\)
\(294\) 0 0
\(295\) −1.97627e6 −1.32218
\(296\) 0 0
\(297\) 252059. + 436578.i 0.165810 + 0.287191i
\(298\) 0 0
\(299\) −1.03062e6 + 1.78508e6i −0.666684 + 1.15473i
\(300\) 0 0
\(301\) 936005. + 760703.i 0.595473 + 0.483948i
\(302\) 0 0
\(303\) 302643. 524193.i 0.189376 0.328008i
\(304\) 0 0
\(305\) 1.23366e6 + 2.13676e6i 0.759356 + 1.31524i
\(306\) 0 0
\(307\) −2.23869e6 −1.35565 −0.677824 0.735224i \(-0.737077\pi\)
−0.677824 + 0.735224i \(0.737077\pi\)
\(308\) 0 0
\(309\) 1.04972e6 0.625426
\(310\) 0 0
\(311\) 750695. + 1.30024e6i 0.440111 + 0.762295i 0.997697 0.0678240i \(-0.0216056\pi\)
−0.557586 + 0.830119i \(0.688272\pi\)
\(312\) 0 0
\(313\) 890067. 1.54164e6i 0.513525 0.889452i −0.486352 0.873763i \(-0.661673\pi\)
0.999877 0.0156888i \(-0.00499410\pi\)
\(314\) 0 0
\(315\) −130676. + 815731.i −0.0742028 + 0.463202i
\(316\) 0 0
\(317\) −735500. + 1.27392e6i −0.411088 + 0.712025i −0.995009 0.0997854i \(-0.968184\pi\)
0.583921 + 0.811810i \(0.301518\pi\)
\(318\) 0 0
\(319\) 1.12655e6 + 1.95124e6i 0.619832 + 1.07358i
\(320\) 0 0
\(321\) 1.44581e6 0.783155
\(322\) 0 0
\(323\) −635666. −0.339018
\(324\) 0 0
\(325\) −1.25440e6 2.17268e6i −0.658760 1.14101i
\(326\) 0 0
\(327\) 537015. 930137.i 0.277726 0.481036i
\(328\) 0 0
\(329\) 1.56306e6 596837.i 0.796134 0.303995i
\(330\) 0 0
\(331\) 914873. 1.58461e6i 0.458977 0.794971i −0.539930 0.841710i \(-0.681549\pi\)
0.998907 + 0.0467386i \(0.0148828\pi\)
\(332\) 0 0
\(333\) −197220. 341594.i −0.0974629 0.168811i
\(334\) 0 0
\(335\) 4.40120e6 2.14269
\(336\) 0 0
\(337\) 3.18627e6 1.52830 0.764148 0.645041i \(-0.223160\pi\)
0.764148 + 0.645041i \(0.223160\pi\)
\(338\) 0 0
\(339\) −499018. 864324.i −0.235840 0.408486i
\(340\) 0 0
\(341\) −3.49878e6 + 6.06006e6i −1.62941 + 2.82222i
\(342\) 0 0
\(343\) 999468. 1.93614e6i 0.458705 0.888589i
\(344\) 0 0
\(345\) 891286. 1.54375e6i 0.403153 0.698281i
\(346\) 0 0
\(347\) −1.23895e6 2.14592e6i −0.552370 0.956732i −0.998103 0.0615664i \(-0.980390\pi\)
0.445733 0.895166i \(-0.352943\pi\)
\(348\) 0 0
\(349\) 1.81720e6 0.798618 0.399309 0.916816i \(-0.369250\pi\)
0.399309 + 0.916816i \(0.369250\pi\)
\(350\) 0 0
\(351\) −596856. −0.258584
\(352\) 0 0
\(353\) −1.57678e6 2.73106e6i −0.673493 1.16652i −0.976907 0.213666i \(-0.931460\pi\)
0.303413 0.952859i \(-0.401874\pi\)
\(354\) 0 0
\(355\) −806425. + 1.39677e6i −0.339620 + 0.588239i
\(356\) 0 0
\(357\) −1.20913e6 + 461692.i −0.502113 + 0.191726i
\(358\) 0 0
\(359\) −1.35105e6 + 2.34008e6i −0.553266 + 0.958285i 0.444770 + 0.895645i \(0.353285\pi\)
−0.998036 + 0.0626404i \(0.980048\pi\)
\(360\) 0 0
\(361\) 1.07386e6 + 1.85998e6i 0.433690 + 0.751173i
\(362\) 0 0
\(363\) −2.85433e6 −1.13694
\(364\) 0 0
\(365\) −5.32214e6 −2.09100
\(366\) 0 0
\(367\) 1.80573e6 + 3.12762e6i 0.699824 + 1.21213i 0.968527 + 0.248908i \(0.0800716\pi\)
−0.268703 + 0.963223i \(0.586595\pi\)
\(368\) 0 0
\(369\) 530319. 918540.i 0.202755 0.351182i
\(370\) 0 0
\(371\) 400703. 2.50134e6i 0.151143 0.943491i
\(372\) 0 0
\(373\) 216759. 375438.i 0.0806688 0.139722i −0.822869 0.568232i \(-0.807628\pi\)
0.903537 + 0.428509i \(0.140961\pi\)
\(374\) 0 0
\(375\) −21508.4 37253.6i −0.00789823 0.0136801i
\(376\) 0 0
\(377\) −2.66759e6 −0.966642
\(378\) 0 0
\(379\) −2.12163e6 −0.758704 −0.379352 0.925252i \(-0.623853\pi\)
−0.379352 + 0.925252i \(0.623853\pi\)
\(380\) 0 0
\(381\) 1.41833e6 + 2.45662e6i 0.500570 + 0.867012i
\(382\) 0 0
\(383\) 2.12339e6 3.67782e6i 0.739662 1.28113i −0.212985 0.977055i \(-0.568319\pi\)
0.952647 0.304077i \(-0.0983480\pi\)
\(384\) 0 0
\(385\) −5.47329e6 4.44821e6i −1.88190 1.52944i
\(386\) 0 0
\(387\) 376797. 652632.i 0.127888 0.221509i
\(388\) 0 0
\(389\) 1.76088e6 + 3.04994e6i 0.590006 + 1.02192i 0.994231 + 0.107261i \(0.0342081\pi\)
−0.404224 + 0.914660i \(0.632459\pi\)
\(390\) 0 0
\(391\) 2.79271e6 0.923811
\(392\) 0 0
\(393\) −770981. −0.251804
\(394\) 0 0
\(395\) −553845. 959288.i −0.178606 0.309354i
\(396\) 0 0
\(397\) 367025. 635706.i 0.116874 0.202432i −0.801653 0.597790i \(-0.796046\pi\)
0.918527 + 0.395357i \(0.129379\pi\)
\(398\) 0 0
\(399\) −518869. 421691.i −0.163164 0.132606i
\(400\) 0 0
\(401\) 111135. 192492.i 0.0345136 0.0597793i −0.848253 0.529592i \(-0.822345\pi\)
0.882766 + 0.469812i \(0.155678\pi\)
\(402\) 0 0
\(403\) −4.14242e6 7.17488e6i −1.27055 2.20065i
\(404\) 0 0
\(405\) 516165. 0.156369
\(406\) 0 0
\(407\) 3.36743e6 1.00766
\(408\) 0 0
\(409\) 1.75379e6 + 3.03765e6i 0.518405 + 0.897904i 0.999771 + 0.0213846i \(0.00680745\pi\)
−0.481366 + 0.876520i \(0.659859\pi\)
\(410\) 0 0
\(411\) −146845. + 254343.i −0.0428800 + 0.0742703i
\(412\) 0 0
\(413\) 515134. 3.21566e6i 0.148609 0.927674i
\(414\) 0 0
\(415\) 3.03394e6 5.25494e6i 0.864742 1.49778i
\(416\) 0 0
\(417\) 929653. + 1.61021e6i 0.261807 + 0.453462i
\(418\) 0 0
\(419\) −1.97040e6 −0.548302 −0.274151 0.961687i \(-0.588397\pi\)
−0.274151 + 0.961687i \(0.588397\pi\)
\(420\) 0 0
\(421\) −7.19318e6 −1.97795 −0.988976 0.148079i \(-0.952691\pi\)
−0.988976 + 0.148079i \(0.952691\pi\)
\(422\) 0 0
\(423\) −522685. 905317.i −0.142033 0.246008i
\(424\) 0 0
\(425\) −1.69955e6 + 2.94370e6i −0.456416 + 0.790535i
\(426\) 0 0
\(427\) −3.79837e6 + 1.45036e6i −1.00815 + 0.384953i
\(428\) 0 0
\(429\) 2.54776e6 4.41285e6i 0.668367 1.15765i
\(430\) 0 0
\(431\) −262091. 453955.i −0.0679608 0.117712i 0.830043 0.557700i \(-0.188316\pi\)
−0.898004 + 0.439988i \(0.854983\pi\)
\(432\) 0 0
\(433\) 1.49326e6 0.382750 0.191375 0.981517i \(-0.438705\pi\)
0.191375 + 0.981517i \(0.438705\pi\)
\(434\) 0 0
\(435\) 2.30695e6 0.584541
\(436\) 0 0
\(437\) 721349. + 1.24941e6i 0.180693 + 0.312970i
\(438\) 0 0
\(439\) −1.32835e6 + 2.30077e6i −0.328966 + 0.569786i −0.982307 0.187278i \(-0.940034\pi\)
0.653341 + 0.757064i \(0.273367\pi\)
\(440\) 0 0
\(441\) −1.29324e6 425256.i −0.316653 0.104125i
\(442\) 0 0
\(443\) 2.34399e6 4.05991e6i 0.567474 0.982895i −0.429340 0.903143i \(-0.641254\pi\)
0.996815 0.0797518i \(-0.0254128\pi\)
\(444\) 0 0
\(445\) −12618.7 21856.2i −0.00302074 0.00523207i
\(446\) 0 0
\(447\) −4.35340e6 −1.03053
\(448\) 0 0
\(449\) −3.45899e6 −0.809716 −0.404858 0.914379i \(-0.632679\pi\)
−0.404858 + 0.914379i \(0.632679\pi\)
\(450\) 0 0
\(451\) 4.52748e6 + 7.84182e6i 1.04813 + 1.81541i
\(452\) 0 0
\(453\) −752494. + 1.30336e6i −0.172289 + 0.298413i
\(454\) 0 0
\(455\) 7.80102e6 2.97873e6i 1.76654 0.674533i
\(456\) 0 0
\(457\) −359140. + 622048.i −0.0804401 + 0.139326i −0.903439 0.428717i \(-0.858966\pi\)
0.822999 + 0.568043i \(0.192299\pi\)
\(458\) 0 0
\(459\) 404331. + 700322.i 0.0895788 + 0.155155i
\(460\) 0 0
\(461\) 5.07998e6 1.11329 0.556647 0.830749i \(-0.312088\pi\)
0.556647 + 0.830749i \(0.312088\pi\)
\(462\) 0 0
\(463\) 3.40607e6 0.738416 0.369208 0.929347i \(-0.379629\pi\)
0.369208 + 0.929347i \(0.379629\pi\)
\(464\) 0 0
\(465\) 3.58239e6 + 6.20489e6i 0.768318 + 1.33077i
\(466\) 0 0
\(467\) −921342. + 1.59581e6i −0.195492 + 0.338602i −0.947062 0.321052i \(-0.895964\pi\)
0.751570 + 0.659654i \(0.229297\pi\)
\(468\) 0 0
\(469\) −1.14722e6 + 7.16135e6i −0.240831 + 1.50336i
\(470\) 0 0
\(471\) −63488.3 + 109965.i −0.0131869 + 0.0228403i
\(472\) 0 0
\(473\) 3.21682e6 + 5.57170e6i 0.661110 + 1.14508i
\(474\) 0 0
\(475\) −1.75595e6 −0.357091
\(476\) 0 0
\(477\) −1.58276e6 −0.318507
\(478\) 0 0
\(479\) −4.55714e6 7.89319e6i −0.907514 1.57186i −0.817507 0.575919i \(-0.804644\pi\)
−0.0900071 0.995941i \(-0.528689\pi\)
\(480\) 0 0
\(481\) −1.99346e6 + 3.45277e6i −0.392866 + 0.680464i
\(482\) 0 0
\(483\) 2.27957e6 + 1.85264e6i 0.444617 + 0.361346i
\(484\) 0 0
\(485\) 4.40596e6 7.63134e6i 0.850523 1.47315i
\(486\) 0 0
\(487\) −2.19220e6 3.79701e6i −0.418850 0.725469i 0.576974 0.816762i \(-0.304233\pi\)
−0.995824 + 0.0912933i \(0.970900\pi\)
\(488\) 0 0
\(489\) −5.88939e6 −1.11378
\(490\) 0 0
\(491\) −9.50592e6 −1.77947 −0.889735 0.456478i \(-0.849111\pi\)
−0.889735 + 0.456478i \(0.849111\pi\)
\(492\) 0 0
\(493\) 1.80712e6 + 3.13002e6i 0.334864 + 0.580002i
\(494\) 0 0
\(495\) −2.20332e6 + 3.81627e6i −0.404171 + 0.700044i
\(496\) 0 0
\(497\) −2.06253e6 1.67625e6i −0.374550 0.304401i
\(498\) 0 0
\(499\) −1.68783e6 + 2.92341e6i −0.303444 + 0.525580i −0.976914 0.213635i \(-0.931470\pi\)
0.673470 + 0.739215i \(0.264803\pi\)
\(500\) 0 0
\(501\) 823255. + 1.42592e6i 0.146535 + 0.253805i
\(502\) 0 0
\(503\) 7.82645e6 1.37926 0.689628 0.724164i \(-0.257774\pi\)
0.689628 + 0.724164i \(0.257774\pi\)
\(504\) 0 0
\(505\) 5.29099e6 0.923227
\(506\) 0 0
\(507\) 1.34563e6 + 2.33070e6i 0.232491 + 0.402687i
\(508\) 0 0
\(509\) 3.71219e6 6.42969e6i 0.635090 1.10001i −0.351406 0.936223i \(-0.614296\pi\)
0.986496 0.163785i \(-0.0523703\pi\)
\(510\) 0 0
\(511\) 1.38727e6 8.65985e6i 0.235022 1.46709i
\(512\) 0 0
\(513\) −208875. + 361783.i −0.0350424 + 0.0606952i
\(514\) 0 0
\(515\) 4.58795e6 + 7.94656e6i 0.762256 + 1.32027i
\(516\) 0 0
\(517\) 8.92461e6 1.46846
\(518\) 0 0
\(519\) 2.62807e6 0.428272
\(520\) 0 0
\(521\) 530710. + 919217.i 0.0856570 + 0.148362i 0.905671 0.423981i \(-0.139368\pi\)
−0.820014 + 0.572344i \(0.806034\pi\)
\(522\) 0 0
\(523\) 956760. 1.65716e6i 0.152950 0.264917i −0.779361 0.626575i \(-0.784456\pi\)
0.932311 + 0.361659i \(0.117789\pi\)
\(524\) 0 0
\(525\) −3.34008e6 + 1.27537e6i −0.528881 + 0.201948i
\(526\) 0 0
\(527\) −5.61243e6 + 9.72102e6i −0.880288 + 1.52470i
\(528\) 0 0
\(529\) 49029.1 + 84921.0i 0.00761755 + 0.0131940i
\(530\) 0 0
\(531\) −2.03476e6 −0.313167
\(532\) 0 0
\(533\) −1.07207e7 −1.63458
\(534\) 0 0
\(535\) 6.31912e6 + 1.09450e7i 0.954492 + 1.65323i
\(536\) 0 0
\(537\) 876454. 1.51806e6i 0.131158 0.227172i
\(538\) 0 0
\(539\) 8.66451e6 7.74632e6i 1.28461 1.14848i
\(540\) 0 0
\(541\) −5.83140e6 + 1.01003e7i −0.856603 + 1.48368i 0.0185472 + 0.999828i \(0.494096\pi\)
−0.875150 + 0.483852i \(0.839237\pi\)
\(542\) 0 0
\(543\) −1.15485e6 2.00026e6i −0.168084 0.291130i
\(544\) 0 0
\(545\) 9.38842e6 1.35395
\(546\) 0 0
\(547\) −6.36659e6 −0.909785 −0.454893 0.890546i \(-0.650322\pi\)
−0.454893 + 0.890546i \(0.650322\pi\)
\(548\) 0 0
\(549\) 1.27017e6 + 2.20000e6i 0.179858 + 0.311524i
\(550\) 0 0
\(551\) −933548. + 1.61695e6i −0.130996 + 0.226891i
\(552\) 0 0
\(553\) 1.70526e6 651134.i 0.237125 0.0905435i
\(554\) 0 0
\(555\) 1.72396e6 2.98598e6i 0.237571 0.411486i
\(556\) 0 0
\(557\) −4.86221e6 8.42159e6i −0.664042 1.15015i −0.979544 0.201230i \(-0.935506\pi\)
0.315502 0.948925i \(-0.397827\pi\)
\(558\) 0 0
\(559\) −7.61719e6 −1.03102
\(560\) 0 0
\(561\) −6.90376e6 −0.926145
\(562\) 0 0
\(563\) −3.15133e6 5.45826e6i −0.419008 0.725744i 0.576832 0.816863i \(-0.304289\pi\)
−0.995840 + 0.0911193i \(0.970956\pi\)
\(564\) 0 0
\(565\) 4.36207e6 7.55532e6i 0.574872 0.995708i
\(566\) 0 0
\(567\) −134544. + 839872.i −0.0175754 + 0.109712i
\(568\) 0 0
\(569\) −4.08244e6 + 7.07099e6i −0.528614 + 0.915586i 0.470829 + 0.882224i \(0.343955\pi\)
−0.999443 + 0.0333620i \(0.989379\pi\)
\(570\) 0 0
\(571\) 6.43857e6 + 1.11519e7i 0.826416 + 1.43139i 0.900832 + 0.434168i \(0.142957\pi\)
−0.0744158 + 0.997227i \(0.523709\pi\)
\(572\) 0 0
\(573\) 2.64554e6 0.336611
\(574\) 0 0
\(575\) 7.71453e6 0.973061
\(576\) 0 0
\(577\) −5.70887e6 9.88805e6i −0.713856 1.23643i −0.963399 0.268071i \(-0.913614\pi\)
0.249543 0.968364i \(-0.419720\pi\)
\(578\) 0 0
\(579\) −311085. + 538816.i −0.0385641 + 0.0667950i
\(580\) 0 0
\(581\) 7.75968e6 + 6.30639e6i 0.953681 + 0.775069i
\(582\) 0 0
\(583\) 6.75622e6 1.17021e7i 0.823251 1.42591i
\(584\) 0 0
\(585\) −2.60865e6 4.51831e6i −0.315156 0.545867i
\(586\) 0 0
\(587\) 2.12781e6 0.254882 0.127441 0.991846i \(-0.459324\pi\)
0.127441 + 0.991846i \(0.459324\pi\)
\(588\) 0 0
\(589\) −5.79871e6 −0.688721
\(590\) 0 0
\(591\) 1.49287e6 + 2.58572e6i 0.175814 + 0.304518i
\(592\) 0 0
\(593\) 4.28689e6 7.42511e6i 0.500617 0.867094i −0.499383 0.866382i \(-0.666440\pi\)
1.00000 0.000712836i \(-0.000226903\pi\)
\(594\) 0 0
\(595\) −8.77978e6 7.13544e6i −1.01670 0.826282i
\(596\) 0 0
\(597\) 2.58493e6 4.47723e6i 0.296833 0.514130i
\(598\) 0 0
\(599\) −5.64372e6 9.77521e6i −0.642686 1.11316i −0.984831 0.173517i \(-0.944487\pi\)
0.342145 0.939647i \(-0.388846\pi\)
\(600\) 0 0
\(601\) −1.58260e7 −1.78725 −0.893625 0.448814i \(-0.851847\pi\)
−0.893625 + 0.448814i \(0.851847\pi\)
\(602\) 0 0
\(603\) 4.53145e6 0.507509
\(604\) 0 0
\(605\) −1.24753e7 2.16078e7i −1.38568 2.40006i
\(606\) 0 0
\(607\) −4.87183e6 + 8.43826e6i −0.536686 + 0.929568i 0.462393 + 0.886675i \(0.346991\pi\)
−0.999080 + 0.0428932i \(0.986342\pi\)
\(608\) 0 0
\(609\) −601329. + 3.75372e6i −0.0657006 + 0.410128i
\(610\) 0 0
\(611\) −5.28320e6 + 9.15077e6i −0.572525 + 0.991642i
\(612\) 0 0
\(613\) −3.07524e6 5.32647e6i −0.330543 0.572517i 0.652075 0.758154i \(-0.273899\pi\)
−0.982618 + 0.185637i \(0.940565\pi\)
\(614\) 0 0
\(615\) 9.27137e6 0.988453
\(616\) 0 0
\(617\) −3.36084e6 −0.355414 −0.177707 0.984083i \(-0.556868\pi\)
−0.177707 + 0.984083i \(0.556868\pi\)
\(618\) 0 0
\(619\) −3.44329e6 5.96396e6i −0.361200 0.625616i 0.626959 0.779052i \(-0.284299\pi\)
−0.988159 + 0.153436i \(0.950966\pi\)
\(620\) 0 0
\(621\) 917663. 1.58944e6i 0.0954892 0.165392i
\(622\) 0 0
\(623\) 38852.1 14835.3i 0.00401046 0.00153135i
\(624\) 0 0
\(625\) 4.97590e6 8.61850e6i 0.509532 0.882535i
\(626\) 0 0
\(627\) −1.78323e6 3.08864e6i −0.181150 0.313760i
\(628\) 0 0
\(629\) 5.40175e6 0.544387
\(630\) 0 0
\(631\) 3.59545e6 0.359484 0.179742 0.983714i \(-0.442474\pi\)
0.179742 + 0.983714i \(0.442474\pi\)
\(632\) 0 0
\(633\) −1.72799e6 2.99297e6i −0.171409 0.296889i
\(634\) 0 0
\(635\) −1.23980e7 + 2.14740e7i −1.22017 + 2.11339i
\(636\) 0 0
\(637\) 2.81339e6 + 1.34698e7i 0.274715 + 1.31526i
\(638\) 0 0
\(639\) −830291. + 1.43811e6i −0.0804411 + 0.139328i
\(640\) 0 0
\(641\) 9.91433e6 + 1.71721e7i 0.953056 + 1.65074i 0.738756 + 0.673973i \(0.235413\pi\)
0.214299 + 0.976768i \(0.431253\pi\)
\(642\) 0 0
\(643\) −8.10851e6 −0.773417 −0.386708 0.922202i \(-0.626388\pi\)
−0.386708 + 0.922202i \(0.626388\pi\)
\(644\) 0 0
\(645\) 6.58740e6 0.623469
\(646\) 0 0
\(647\) −1.01373e6 1.75583e6i −0.0952053 0.164900i 0.814489 0.580179i \(-0.197017\pi\)
−0.909694 + 0.415279i \(0.863684\pi\)
\(648\) 0 0
\(649\) 8.68564e6 1.50440e7i 0.809450 1.40201i
\(650\) 0 0
\(651\) −1.10300e7 + 4.21168e6i −1.02005 + 0.389496i
\(652\) 0 0
\(653\) −757133. + 1.31139e6i −0.0694847 + 0.120351i −0.898675 0.438616i \(-0.855469\pi\)
0.829190 + 0.558967i \(0.188802\pi\)
\(654\) 0 0
\(655\) −3.36969e6 5.83647e6i −0.306893 0.531554i
\(656\) 0 0
\(657\) −5.47965e6 −0.495267
\(658\) 0 0
\(659\) −3.22358e6 −0.289151 −0.144576 0.989494i \(-0.546182\pi\)
−0.144576 + 0.989494i \(0.546182\pi\)
\(660\) 0 0
\(661\) 7.19538e6 + 1.24628e7i 0.640546 + 1.10946i 0.985311 + 0.170769i \(0.0546253\pi\)
−0.344765 + 0.938689i \(0.612041\pi\)
\(662\) 0 0
\(663\) 4.08690e6 7.07872e6i 0.361085 0.625418i
\(664\) 0 0
\(665\) 924488. 5.77100e6i 0.0810676 0.506054i
\(666\) 0 0
\(667\) 4.10141e6 7.10384e6i 0.356959 0.618271i
\(668\) 0 0
\(669\) −1.56224e6 2.70589e6i −0.134953 0.233746i
\(670\) 0 0
\(671\) −2.16875e7 −1.85953
\(672\) 0 0
\(673\) 7.33478e6 0.624237 0.312118 0.950043i \(-0.398961\pi\)
0.312118 + 0.950043i \(0.398961\pi\)
\(674\) 0 0
\(675\) 1.11692e6 + 1.93456e6i 0.0943543 + 0.163426i
\(676\) 0 0
\(677\) 1.52642e6 2.64384e6i 0.127998 0.221699i −0.794903 0.606737i \(-0.792478\pi\)
0.922901 + 0.385038i \(0.125812\pi\)
\(678\) 0 0
\(679\) 1.12688e7 + 9.15828e6i 0.937999 + 0.762324i
\(680\) 0 0
\(681\) 1.62577e6 2.81591e6i 0.134335 0.232676i
\(682\) 0 0
\(683\) −7.98793e6 1.38355e7i −0.655213 1.13486i −0.981840 0.189709i \(-0.939245\pi\)
0.326627 0.945153i \(-0.394088\pi\)
\(684\) 0 0
\(685\) −2.56724e6 −0.209045
\(686\) 0 0
\(687\) 6.77685e6 0.547817
\(688\) 0 0
\(689\) 7.99911e6 + 1.38549e7i 0.641939 + 1.11187i
\(690\) 0 0
\(691\) 1.23267e6 2.13504e6i 0.0982087 0.170103i −0.812735 0.582634i \(-0.802022\pi\)
0.910943 + 0.412532i \(0.135355\pi\)
\(692\) 0 0
\(693\) −5.63527e6 4.57985e6i −0.445740 0.362258i
\(694\) 0 0
\(695\) −8.12638e6 + 1.40753e7i −0.638168 + 1.10534i
\(696\) 0 0
\(697\) 7.26259e6 + 1.25792e7i 0.566252 + 0.980777i
\(698\) 0 0
\(699\) −6.42958e6 −0.497725
\(700\) 0 0
\(701\) 1.74893e7 1.34424 0.672122 0.740440i \(-0.265383\pi\)
0.672122 + 0.740440i \(0.265383\pi\)
\(702\) 0 0
\(703\) 1.39526e6 + 2.41666e6i 0.106480 + 0.184428i
\(704\) 0 0
\(705\) 4.56895e6 7.91366e6i 0.346213 0.599659i
\(706\) 0 0
\(707\) −1.37915e6 + 8.60916e6i −0.103768 + 0.647757i
\(708\) 0 0
\(709\) 1.09216e7 1.89167e7i 0.815961 1.41329i −0.0926752 0.995696i \(-0.529542\pi\)
0.908636 0.417589i \(-0.137125\pi\)
\(710\) 0 0
\(711\) −570236. 987677.i −0.0423039 0.0732725i
\(712\) 0 0
\(713\) 2.54758e7 1.87674
\(714\) 0 0
\(715\) 4.45415e7 3.25837
\(716\) 0 0
\(717\) 1.54614e6 + 2.67800e6i 0.112319 + 0.194541i
\(718\) 0 0
\(719\) −9.55868e6 + 1.65561e7i −0.689566 + 1.19436i 0.282413 + 0.959293i \(0.408865\pi\)
−0.971978 + 0.235070i \(0.924468\pi\)
\(720\) 0 0
\(721\) −1.41260e7 + 5.39387e6i −1.01200 + 0.386423i
\(722\) 0 0
\(723\) −343372. + 594738.i −0.0244298 + 0.0423136i
\(724\) 0 0
\(725\) 4.99195e6 + 8.64632e6i 0.352716 + 0.610923i
\(726\) 0 0
\(727\) −4.08900e6 −0.286933 −0.143467 0.989655i \(-0.545825\pi\)
−0.143467 + 0.989655i \(0.545825\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 0 0
\(731\) 5.16015e6 + 8.93764e6i 0.357165 + 0.618628i
\(732\) 0 0
\(733\) 1.81634e6 3.14599e6i 0.124864 0.216271i −0.796816 0.604222i \(-0.793484\pi\)
0.921680 + 0.387952i \(0.126817\pi\)
\(734\) 0 0
\(735\) −2.43304e6 1.16487e7i −0.166124 0.795355i
\(736\) 0 0
\(737\) −1.93431e7 + 3.35032e7i −1.31177 + 2.27205i
\(738\) 0 0
\(739\) −1.08978e6 1.88756e6i −0.0734056 0.127142i 0.826986 0.562222i \(-0.190053\pi\)
−0.900392 + 0.435080i \(0.856720\pi\)
\(740\) 0 0
\(741\) 4.22254e6 0.282507
\(742\) 0 0
\(743\) 1.21595e7 0.808060 0.404030 0.914746i \(-0.367609\pi\)
0.404030 + 0.914746i \(0.367609\pi\)
\(744\) 0 0
\(745\) −1.90272e7 3.29561e7i −1.25598 2.17543i
\(746\) 0 0
\(747\) 3.12373e6 5.41045e6i 0.204820 0.354758i
\(748\) 0 0
\(749\) −1.94562e7 + 7.42914e6i −1.26722 + 0.483876i
\(750\) 0 0
\(751\) −1.16248e7 + 2.01347e7i −0.752115 + 1.30270i 0.194681 + 0.980867i \(0.437633\pi\)
−0.946796 + 0.321835i \(0.895701\pi\)
\(752\) 0 0
\(753\) 883121. + 1.52961e6i 0.0567587 + 0.0983090i
\(754\) 0 0
\(755\) −1.31556e7 −0.839928
\(756\) 0 0
\(757\) −1.49939e7 −0.950985 −0.475492 0.879720i \(-0.657730\pi\)
−0.475492 + 0.879720i \(0.657730\pi\)
\(758\) 0 0
\(759\) 7.83434e6 + 1.35695e7i 0.493626 + 0.854985i
\(760\) 0 0
\(761\) 6.36596e6 1.10262e7i 0.398476 0.690181i −0.595062 0.803680i \(-0.702873\pi\)
0.993538 + 0.113499i \(0.0362058\pi\)
\(762\) 0 0
\(763\) −2.44719e6 + 1.52762e7i −0.152179 + 0.949960i
\(764\) 0 0
\(765\) −3.53438e6 + 6.12173e6i −0.218353 + 0.378199i
\(766\) 0 0
\(767\) 1.02835e7 + 1.78115e7i 0.631177 + 1.09323i
\(768\) 0 0
\(769\) 2.34653e6 0.143090 0.0715451 0.997437i \(-0.477207\pi\)
0.0715451 + 0.997437i \(0.477207\pi\)
\(770\) 0 0
\(771\) 1.53820e7 0.931915
\(772\) 0 0
\(773\) −1.35931e7 2.35440e7i −0.818222 1.41720i −0.906991 0.421150i \(-0.861627\pi\)
0.0887694 0.996052i \(-0.471707\pi\)
\(774\) 0 0
\(775\) −1.55037e7 + 2.68532e7i −0.927217 + 1.60599i
\(776\) 0 0
\(777\) 4.40923e6 + 3.58344e6i 0.262006 + 0.212935i
\(778\) 0 0
\(779\) −3.75182e6 + 6.49834e6i −0.221513 + 0.383671i
\(780\) 0 0
\(781\) −7.08842e6 1.22775e7i −0.415836 0.720249i
\(782\) 0 0
\(783\) 2.37522e6 0.138452
\(784\) 0 0