Properties

Label 76.7.b.a.39.8
Level $76$
Weight $7$
Character 76.39
Analytic conductor $17.484$
Analytic rank $0$
Dimension $54$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [76,7,Mod(39,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.39");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 76.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(17.4841103551\)
Analytic rank: \(0\)
Dimension: \(54\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 39.8
Character \(\chi\) \(=\) 76.39
Dual form 76.7.b.a.39.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-7.53857 + 2.67768i) q^{2} -14.2612i q^{3} +(49.6600 - 40.3718i) q^{4} -201.264 q^{5} +(38.1869 + 107.509i) q^{6} +304.241i q^{7} +(-266.263 + 437.319i) q^{8} +525.619 q^{9} +O(q^{10})\) \(q+(-7.53857 + 2.67768i) q^{2} -14.2612i q^{3} +(49.6600 - 40.3718i) q^{4} -201.264 q^{5} +(38.1869 + 107.509i) q^{6} +304.241i q^{7} +(-266.263 + 437.319i) q^{8} +525.619 q^{9} +(1517.25 - 538.922i) q^{10} +933.491i q^{11} +(-575.749 - 708.210i) q^{12} -219.305 q^{13} +(-814.660 - 2293.54i) q^{14} +2870.26i q^{15} +(836.237 - 4009.73i) q^{16} -4130.81 q^{17} +(-3962.42 + 1407.44i) q^{18} -1573.56i q^{19} +(-9994.79 + 8125.40i) q^{20} +4338.82 q^{21} +(-2499.59 - 7037.19i) q^{22} -11056.4i q^{23} +(6236.68 + 3797.21i) q^{24} +24882.3 q^{25} +(1653.24 - 587.229i) q^{26} -17892.3i q^{27} +(12282.7 + 15108.6i) q^{28} +13109.4 q^{29} +(-7685.66 - 21637.7i) q^{30} -47617.4i q^{31} +(4432.76 + 32466.8i) q^{32} +13312.7 q^{33} +(31140.4 - 11061.0i) q^{34} -61232.8i q^{35} +(26102.3 - 21220.2i) q^{36} +48926.0 q^{37} +(4213.50 + 11862.4i) q^{38} +3127.54i q^{39} +(53589.2 - 88016.8i) q^{40} +30436.0 q^{41} +(-32708.5 + 11618.0i) q^{42} -50390.6i q^{43} +(37686.7 + 46357.2i) q^{44} -105788. q^{45} +(29605.5 + 83349.3i) q^{46} +117012. i q^{47} +(-57183.4 - 11925.7i) q^{48} +25086.7 q^{49} +(-187577. + 66627.0i) q^{50} +58910.1i q^{51} +(-10890.7 + 8853.73i) q^{52} -135594. q^{53} +(47910.0 + 134883. i) q^{54} -187879. i q^{55} +(-133050. - 81007.9i) q^{56} -22440.8 q^{57} +(-98826.0 + 35102.8i) q^{58} -326096. i q^{59} +(115878. + 142537. i) q^{60} +282709. q^{61} +(127504. + 358967. i) q^{62} +159915. i q^{63} +(-120352. - 232884. i) q^{64} +44138.2 q^{65} +(-100358. + 35647.1i) q^{66} -359557. i q^{67} +(-205136. + 166768. i) q^{68} -157677. q^{69} +(163962. + 461607. i) q^{70} +133998. i q^{71} +(-139953. + 229863. i) q^{72} -227670. q^{73} +(-368832. + 131008. i) q^{74} -354851. i q^{75} +(-63527.5 - 78143.2i) q^{76} -284006. q^{77} +(-8374.56 - 23577.2i) q^{78} +746350. i q^{79} +(-168305. + 807016. i) q^{80} +128011. q^{81} +(-229444. + 81497.9i) q^{82} -459386. i q^{83} +(215466. - 175166. i) q^{84} +831384. q^{85} +(134930. + 379873. i) q^{86} -186955. i q^{87} +(-408234. - 248554. i) q^{88} +905466. q^{89} +(797493. - 283268. i) q^{90} -66721.4i q^{91} +(-446366. - 549060. i) q^{92} -679079. q^{93} +(-313321. - 882103. i) q^{94} +316702. i q^{95} +(463014. - 63216.2i) q^{96} +1.58577e6 q^{97} +(-189118. + 67174.3i) q^{98} +490661. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9} - 2088 q^{10} - 2384 q^{12} - 828 q^{13} + 4116 q^{14} - 7782 q^{16} + 12220 q^{17} + 15790 q^{18} - 7000 q^{20} - 16048 q^{21} - 51864 q^{22} + 19294 q^{24} + 218346 q^{25} - 18110 q^{26} + 97926 q^{28} - 101996 q^{29} + 50076 q^{30} - 235160 q^{32} + 9072 q^{33} - 51156 q^{34} - 48028 q^{36} - 63420 q^{37} + 157260 q^{40} - 135700 q^{41} + 302290 q^{42} + 137784 q^{44} - 50348 q^{45} - 177084 q^{46} + 111320 q^{48} - 1099338 q^{49} + 485770 q^{50} + 232980 q^{52} + 892932 q^{53} - 730010 q^{54} - 298644 q^{56} - 702534 q^{58} + 1231628 q^{60} + 323700 q^{61} + 1573116 q^{62} - 1065942 q^{64} + 587512 q^{65} - 74604 q^{66} - 1235974 q^{68} + 217376 q^{69} + 1163796 q^{70} - 1228320 q^{72} - 739428 q^{73} - 1852264 q^{74} - 563144 q^{77} - 2516852 q^{78} - 1597436 q^{80} + 4660886 q^{81} - 919236 q^{82} + 4928476 q^{84} - 737904 q^{85} - 1444124 q^{86} + 2679960 q^{88} - 3415940 q^{89} + 4702636 q^{90} - 3230670 q^{92} - 5021584 q^{93} + 1881960 q^{94} + 1838870 q^{96} + 3483660 q^{97} - 3419858 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.53857 + 2.67768i −0.942321 + 0.334710i
\(3\) 14.2612i 0.528191i −0.964497 0.264096i \(-0.914927\pi\)
0.964497 0.264096i \(-0.0850734\pi\)
\(4\) 49.6600 40.3718i 0.775938 0.630809i
\(5\) −201.264 −1.61011 −0.805057 0.593197i \(-0.797866\pi\)
−0.805057 + 0.593197i \(0.797866\pi\)
\(6\) 38.1869 + 107.509i 0.176791 + 0.497726i
\(7\) 304.241i 0.886999i 0.896275 + 0.443499i \(0.146263\pi\)
−0.896275 + 0.443499i \(0.853737\pi\)
\(8\) −266.263 + 437.319i −0.520044 + 0.854139i
\(9\) 525.619 0.721014
\(10\) 1517.25 538.922i 1.51725 0.538922i
\(11\) 933.491i 0.701346i 0.936498 + 0.350673i \(0.114047\pi\)
−0.936498 + 0.350673i \(0.885953\pi\)
\(12\) −575.749 708.210i −0.333188 0.409843i
\(13\) −219.305 −0.0998201 −0.0499100 0.998754i \(-0.515893\pi\)
−0.0499100 + 0.998754i \(0.515893\pi\)
\(14\) −814.660 2293.54i −0.296888 0.835837i
\(15\) 2870.26i 0.850448i
\(16\) 836.237 4009.73i 0.204159 0.978938i
\(17\) −4130.81 −0.840791 −0.420396 0.907341i \(-0.638109\pi\)
−0.420396 + 0.907341i \(0.638109\pi\)
\(18\) −3962.42 + 1407.44i −0.679427 + 0.241331i
\(19\) 1573.56i 0.229416i
\(20\) −9994.79 + 8125.40i −1.24935 + 1.01568i
\(21\) 4338.82 0.468505
\(22\) −2499.59 7037.19i −0.234748 0.660893i
\(23\) 11056.4i 0.908719i −0.890818 0.454359i \(-0.849868\pi\)
0.890818 0.454359i \(-0.150132\pi\)
\(24\) 6236.68 + 3797.21i 0.451149 + 0.274683i
\(25\) 24882.3 1.59247
\(26\) 1653.24 587.229i 0.0940626 0.0334108i
\(27\) 17892.3i 0.909024i
\(28\) 12282.7 + 15108.6i 0.559527 + 0.688256i
\(29\) 13109.4 0.537512 0.268756 0.963208i \(-0.413387\pi\)
0.268756 + 0.963208i \(0.413387\pi\)
\(30\) −7685.66 21637.7i −0.284654 0.801395i
\(31\) 47617.4i 1.59838i −0.601078 0.799191i \(-0.705262\pi\)
0.601078 0.799191i \(-0.294738\pi\)
\(32\) 4432.76 + 32466.8i 0.135277 + 0.990808i
\(33\) 13312.7 0.370445
\(34\) 31140.4 11061.0i 0.792295 0.281422i
\(35\) 61232.8i 1.42817i
\(36\) 26102.3 21220.2i 0.559462 0.454822i
\(37\) 48926.0 0.965906 0.482953 0.875646i \(-0.339564\pi\)
0.482953 + 0.875646i \(0.339564\pi\)
\(38\) 4213.50 + 11862.4i 0.0767878 + 0.216183i
\(39\) 3127.54i 0.0527241i
\(40\) 53589.2 88016.8i 0.837331 1.37526i
\(41\) 30436.0 0.441607 0.220803 0.975318i \(-0.429132\pi\)
0.220803 + 0.975318i \(0.429132\pi\)
\(42\) −32708.5 + 11618.0i −0.441482 + 0.156813i
\(43\) 50390.6i 0.633789i −0.948461 0.316894i \(-0.897360\pi\)
0.948461 0.316894i \(-0.102640\pi\)
\(44\) 37686.7 + 46357.2i 0.442416 + 0.544201i
\(45\) −105788. −1.16092
\(46\) 29605.5 + 83349.3i 0.304158 + 0.856305i
\(47\) 117012.i 1.12703i 0.826105 + 0.563517i \(0.190552\pi\)
−0.826105 + 0.563517i \(0.809448\pi\)
\(48\) −57183.4 11925.7i −0.517066 0.107835i
\(49\) 25086.7 0.213234
\(50\) −187577. + 66627.0i −1.50062 + 0.533016i
\(51\) 58910.1i 0.444098i
\(52\) −10890.7 + 8853.73i −0.0774542 + 0.0629674i
\(53\) −135594. −0.910778 −0.455389 0.890293i \(-0.650500\pi\)
−0.455389 + 0.890293i \(0.650500\pi\)
\(54\) 47910.0 + 134883.i 0.304260 + 0.856593i
\(55\) 187879.i 1.12925i
\(56\) −133050. 81007.9i −0.757620 0.461278i
\(57\) −22440.8 −0.121175
\(58\) −98826.0 + 35102.8i −0.506509 + 0.179911i
\(59\) 326096.i 1.58778i −0.608065 0.793888i \(-0.708054\pi\)
0.608065 0.793888i \(-0.291946\pi\)
\(60\) 115878. + 142537.i 0.536471 + 0.659895i
\(61\) 282709. 1.24552 0.622758 0.782414i \(-0.286012\pi\)
0.622758 + 0.782414i \(0.286012\pi\)
\(62\) 127504. + 358967.i 0.534995 + 1.50619i
\(63\) 159915.i 0.639539i
\(64\) −120352. 232884.i −0.459108 0.888380i
\(65\) 44138.2 0.160722
\(66\) −100358. + 35647.1i −0.349078 + 0.123992i
\(67\) 359557.i 1.19548i −0.801689 0.597742i \(-0.796065\pi\)
0.801689 0.597742i \(-0.203935\pi\)
\(68\) −205136. + 166768.i −0.652402 + 0.530379i
\(69\) −157677. −0.479977
\(70\) 163962. + 461607.i 0.478023 + 1.34579i
\(71\) 133998.i 0.374390i 0.982323 + 0.187195i \(0.0599396\pi\)
−0.982323 + 0.187195i \(0.940060\pi\)
\(72\) −139953. + 229863.i −0.374959 + 0.615847i
\(73\) −227670. −0.585244 −0.292622 0.956228i \(-0.594528\pi\)
−0.292622 + 0.956228i \(0.594528\pi\)
\(74\) −368832. + 131008.i −0.910194 + 0.323299i
\(75\) 354851.i 0.841129i
\(76\) −63527.5 78143.2i −0.144718 0.178012i
\(77\) −284006. −0.622093
\(78\) −8374.56 23577.2i −0.0176473 0.0496830i
\(79\) 746350.i 1.51377i 0.653545 + 0.756887i \(0.273281\pi\)
−0.653545 + 0.756887i \(0.726719\pi\)
\(80\) −168305. + 807016.i −0.328720 + 1.57620i
\(81\) 128011. 0.240876
\(82\) −229444. + 81497.9i −0.416135 + 0.147810i
\(83\) 459386.i 0.803421i −0.915767 0.401710i \(-0.868416\pi\)
0.915767 0.401710i \(-0.131584\pi\)
\(84\) 215466. 175166.i 0.363531 0.295537i
\(85\) 831384. 1.35377
\(86\) 134930. + 379873.i 0.212136 + 0.597232i
\(87\) 186955.i 0.283909i
\(88\) −408234. 248554.i −0.599047 0.364731i
\(89\) 905466. 1.28440 0.642202 0.766535i \(-0.278021\pi\)
0.642202 + 0.766535i \(0.278021\pi\)
\(90\) 797493. 283268.i 1.09396 0.388571i
\(91\) 66721.4i 0.0885403i
\(92\) −446366. 549060.i −0.573228 0.705109i
\(93\) −679079. −0.844251
\(94\) −313321. 882103.i −0.377230 1.06203i
\(95\) 316702.i 0.369386i
\(96\) 463014. 63216.2i 0.523336 0.0714521i
\(97\) 1.58577e6 1.73750 0.868752 0.495247i \(-0.164922\pi\)
0.868752 + 0.495247i \(0.164922\pi\)
\(98\) −189118. + 67174.3i −0.200934 + 0.0713715i
\(99\) 490661.i 0.505680i
\(100\) 1.23566e6 1.00454e6i 1.23566 1.00454i
\(101\) −924935. −0.897732 −0.448866 0.893599i \(-0.648172\pi\)
−0.448866 + 0.893599i \(0.648172\pi\)
\(102\) −157743. 444098.i −0.148644 0.418483i
\(103\) 72807.1i 0.0666288i 0.999445 + 0.0333144i \(0.0106063\pi\)
−0.999445 + 0.0333144i \(0.989394\pi\)
\(104\) 58392.7 95906.2i 0.0519109 0.0852603i
\(105\) −873250. −0.754346
\(106\) 1.02218e6 363077.i 0.858245 0.304847i
\(107\) 1.36704e6i 1.11591i −0.829871 0.557955i \(-0.811586\pi\)
0.829871 0.557955i \(-0.188414\pi\)
\(108\) −722345. 888533.i −0.573421 0.705346i
\(109\) −382830. −0.295615 −0.147808 0.989016i \(-0.547222\pi\)
−0.147808 + 0.989016i \(0.547222\pi\)
\(110\) 503079. + 1.41634e6i 0.377971 + 1.06411i
\(111\) 697742.i 0.510183i
\(112\) 1.21992e6 + 254417.i 0.868316 + 0.181089i
\(113\) −1.55925e6 −1.08064 −0.540318 0.841461i \(-0.681696\pi\)
−0.540318 + 0.841461i \(0.681696\pi\)
\(114\) 169172. 60089.4i 0.114186 0.0405586i
\(115\) 2.22526e6i 1.46314i
\(116\) 651012. 529249.i 0.417076 0.339068i
\(117\) −115271. −0.0719717
\(118\) 873181. + 2.45829e6i 0.531445 + 1.49619i
\(119\) 1.25676e6i 0.745780i
\(120\) −1.25522e6 764244.i −0.726401 0.442271i
\(121\) 900155. 0.508114
\(122\) −2.13122e6 + 757004.i −1.17368 + 0.416887i
\(123\) 434052.i 0.233253i
\(124\) −1.92240e6 2.36468e6i −1.00827 1.24024i
\(125\) −1.86317e6 −0.953945
\(126\) −428201. 1.20553e6i −0.214060 0.602651i
\(127\) 1.85216e6i 0.904208i 0.891965 + 0.452104i \(0.149326\pi\)
−0.891965 + 0.452104i \(0.850674\pi\)
\(128\) 1.53087e6 + 1.43334e6i 0.729977 + 0.683471i
\(129\) −718629. −0.334762
\(130\) −332739. + 118188.i −0.151452 + 0.0537953i
\(131\) 226361.i 0.100690i −0.998732 0.0503451i \(-0.983968\pi\)
0.998732 0.0503451i \(-0.0160321\pi\)
\(132\) 661108. 537456.i 0.287442 0.233680i
\(133\) 478741. 0.203491
\(134\) 962781. + 2.71055e6i 0.400141 + 1.12653i
\(135\) 3.60109e6i 1.46363i
\(136\) 1.09988e6 1.80648e6i 0.437249 0.718153i
\(137\) 4.89900e6 1.90522 0.952611 0.304192i \(-0.0983863\pi\)
0.952611 + 0.304192i \(0.0983863\pi\)
\(138\) 1.18866e6 422209.i 0.452293 0.160653i
\(139\) 5.05499e6i 1.88224i −0.338066 0.941122i \(-0.609773\pi\)
0.338066 0.941122i \(-0.390227\pi\)
\(140\) −2.47208e6 3.04082e6i −0.900903 1.10817i
\(141\) 1.66873e6 0.595289
\(142\) −358805. 1.01016e6i −0.125312 0.352796i
\(143\) 204719.i 0.0700084i
\(144\) 439542. 2.10759e6i 0.147202 0.705828i
\(145\) −2.63845e6 −0.865456
\(146\) 1.71630e6 609627.i 0.551487 0.195887i
\(147\) 357766.i 0.112628i
\(148\) 2.42967e6 1.97523e6i 0.749483 0.609302i
\(149\) 2.74913e6 0.831066 0.415533 0.909578i \(-0.363595\pi\)
0.415533 + 0.909578i \(0.363595\pi\)
\(150\) 950179. + 2.67507e6i 0.281534 + 0.792613i
\(151\) 3.60493e6i 1.04705i 0.852011 + 0.523523i \(0.175383\pi\)
−0.852011 + 0.523523i \(0.824617\pi\)
\(152\) 688149. + 418981.i 0.195953 + 0.119306i
\(153\) −2.17123e6 −0.606222
\(154\) 2.14100e6 760478.i 0.586211 0.208221i
\(155\) 9.58368e6i 2.57358i
\(156\) 126264. + 155314.i 0.0332588 + 0.0409106i
\(157\) −3.36977e6 −0.870766 −0.435383 0.900245i \(-0.643387\pi\)
−0.435383 + 0.900245i \(0.643387\pi\)
\(158\) −1.99849e6 5.62641e6i −0.506676 1.42646i
\(159\) 1.93373e6i 0.481065i
\(160\) −892156. 6.53441e6i −0.217811 1.59531i
\(161\) 3.36380e6 0.806032
\(162\) −965021. + 342773.i −0.226982 + 0.0806236i
\(163\) 1.68728e6i 0.389606i 0.980842 + 0.194803i \(0.0624067\pi\)
−0.980842 + 0.194803i \(0.937593\pi\)
\(164\) 1.51145e6 1.22876e6i 0.342659 0.278570i
\(165\) −2.67937e6 −0.596458
\(166\) 1.23009e6 + 3.46311e6i 0.268913 + 0.757080i
\(167\) 12054.9i 0.00258830i 0.999999 + 0.00129415i \(0.000411941\pi\)
−0.999999 + 0.00129415i \(0.999588\pi\)
\(168\) −1.15527e6 + 1.89745e6i −0.243643 + 0.400168i
\(169\) −4.77871e6 −0.990036
\(170\) −6.26745e6 + 2.22618e6i −1.27569 + 0.453121i
\(171\) 827095.i 0.165412i
\(172\) −2.03436e6 2.50240e6i −0.399800 0.491781i
\(173\) −2.14415e6 −0.414110 −0.207055 0.978329i \(-0.566388\pi\)
−0.207055 + 0.978329i \(0.566388\pi\)
\(174\) 500606. + 1.40937e6i 0.0950273 + 0.267533i
\(175\) 7.57022e6i 1.41252i
\(176\) 3.74305e6 + 780620.i 0.686574 + 0.143186i
\(177\) −4.65050e6 −0.838649
\(178\) −6.82592e6 + 2.42455e6i −1.21032 + 0.429904i
\(179\) 351257.i 0.0612443i 0.999531 + 0.0306221i \(0.00974885\pi\)
−0.999531 + 0.0306221i \(0.990251\pi\)
\(180\) −5.25346e6 + 4.27087e6i −0.900799 + 0.732316i
\(181\) 6.47595e6 1.09211 0.546057 0.837748i \(-0.316128\pi\)
0.546057 + 0.837748i \(0.316128\pi\)
\(182\) 178659. + 502984.i 0.0296353 + 0.0834334i
\(183\) 4.03175e6i 0.657871i
\(184\) 4.83517e6 + 2.94390e6i 0.776173 + 0.472574i
\(185\) −9.84707e6 −1.55522
\(186\) 5.11928e6 1.81836e6i 0.795555 0.282579i
\(187\) 3.85607e6i 0.589685i
\(188\) 4.72399e6 + 5.81082e6i 0.710943 + 0.874508i
\(189\) 5.44357e6 0.806303
\(190\) −848028. 2.38748e6i −0.123637 0.348080i
\(191\) 2.10096e6i 0.301521i −0.988570 0.150761i \(-0.951828\pi\)
0.988570 0.150761i \(-0.0481722\pi\)
\(192\) −3.32119e6 + 1.71636e6i −0.469235 + 0.242497i
\(193\) 1.09660e7 1.52538 0.762689 0.646765i \(-0.223879\pi\)
0.762689 + 0.646765i \(0.223879\pi\)
\(194\) −1.19545e7 + 4.24620e6i −1.63729 + 0.581561i
\(195\) 629462.i 0.0848918i
\(196\) 1.24581e6 1.01280e6i 0.165456 0.134510i
\(197\) −963490. −0.126023 −0.0630113 0.998013i \(-0.520070\pi\)
−0.0630113 + 0.998013i \(0.520070\pi\)
\(198\) −1.31383e6 3.69888e6i −0.169256 0.476513i
\(199\) 1.30813e7i 1.65994i −0.557807 0.829971i \(-0.688357\pi\)
0.557807 0.829971i \(-0.311643\pi\)
\(200\) −6.62524e6 + 1.08815e7i −0.828155 + 1.36019i
\(201\) −5.12770e6 −0.631444
\(202\) 6.97268e6 2.47668e6i 0.845952 0.300480i
\(203\) 3.98840e6i 0.476772i
\(204\) 2.37831e6 + 2.92548e6i 0.280141 + 0.344593i
\(205\) −6.12568e6 −0.711038
\(206\) −194954. 548861.i −0.0223013 0.0627857i
\(207\) 5.81145e6i 0.655199i
\(208\) −183391. + 879352.i −0.0203792 + 0.0977176i
\(209\) 1.46891e6 0.160900
\(210\) 6.58306e6 2.33829e6i 0.710837 0.252488i
\(211\) 4.72673e6i 0.503168i −0.967835 0.251584i \(-0.919049\pi\)
0.967835 0.251584i \(-0.0809515\pi\)
\(212\) −6.73359e6 + 5.47417e6i −0.706707 + 0.574527i
\(213\) 1.91097e6 0.197749
\(214\) 3.66049e6 + 1.03055e7i 0.373507 + 1.05155i
\(215\) 1.01418e7i 1.02047i
\(216\) 7.82466e6 + 4.76406e6i 0.776433 + 0.472733i
\(217\) 1.44871e7 1.41776
\(218\) 2.88599e6 1.02510e6i 0.278565 0.0989455i
\(219\) 3.24683e6i 0.309121i
\(220\) −7.58499e6 9.33005e6i −0.712340 0.876226i
\(221\) 905905. 0.0839278
\(222\) 1.86833e6 + 5.25998e6i 0.170764 + 0.480756i
\(223\) 1.60135e7i 1.44401i −0.691886 0.722007i \(-0.743220\pi\)
0.691886 0.722007i \(-0.256780\pi\)
\(224\) −9.87771e6 + 1.34862e6i −0.878845 + 0.119990i
\(225\) 1.30786e7 1.14819
\(226\) 1.17545e7 4.17517e6i 1.01831 0.361700i
\(227\) 1.44440e7i 1.23484i 0.786635 + 0.617419i \(0.211822\pi\)
−0.786635 + 0.617419i \(0.788178\pi\)
\(228\) −1.11441e6 + 905976.i −0.0940245 + 0.0764385i
\(229\) −2.13524e7 −1.77804 −0.889018 0.457873i \(-0.848611\pi\)
−0.889018 + 0.457873i \(0.848611\pi\)
\(230\) −5.95853e6 1.67752e7i −0.489729 1.37875i
\(231\) 4.05025e6i 0.328584i
\(232\) −3.49054e6 + 5.73299e6i −0.279530 + 0.459110i
\(233\) −2.21591e7 −1.75180 −0.875901 0.482491i \(-0.839732\pi\)
−0.875901 + 0.482491i \(0.839732\pi\)
\(234\) 868977. 308659.i 0.0678204 0.0240897i
\(235\) 2.35504e7i 1.81465i
\(236\) −1.31651e7 1.61939e7i −1.00158 1.23201i
\(237\) 1.06438e7 0.799562
\(238\) 3.36520e6 + 9.47416e6i 0.249620 + 0.702765i
\(239\) 1.95371e7i 1.43109i −0.698567 0.715544i \(-0.746179\pi\)
0.698567 0.715544i \(-0.253821\pi\)
\(240\) 1.15090e7 + 2.40022e6i 0.832536 + 0.173627i
\(241\) 2.28838e7 1.63485 0.817424 0.576036i \(-0.195401\pi\)
0.817424 + 0.576036i \(0.195401\pi\)
\(242\) −6.78588e6 + 2.41033e6i −0.478806 + 0.170071i
\(243\) 1.48691e7i 1.03625i
\(244\) 1.40393e7 1.14135e7i 0.966444 0.785683i
\(245\) −5.04906e6 −0.343331
\(246\) 1.16225e6 + 3.27213e6i 0.0780721 + 0.219799i
\(247\) 345090.i 0.0229003i
\(248\) 2.08240e7 + 1.26787e7i 1.36524 + 0.831229i
\(249\) −6.55137e6 −0.424360
\(250\) 1.40457e7 4.98899e6i 0.898923 0.319295i
\(251\) 1.64716e7i 1.04163i −0.853670 0.520815i \(-0.825628\pi\)
0.853670 0.520815i \(-0.174372\pi\)
\(252\) 6.45604e6 + 7.94137e6i 0.403427 + 0.496242i
\(253\) 1.03210e7 0.637326
\(254\) −4.95951e6 1.39627e7i −0.302648 0.852054i
\(255\) 1.18565e7i 0.715049i
\(256\) −1.53786e7 6.70616e6i −0.916638 0.399719i
\(257\) 2.44386e7 1.43972 0.719859 0.694120i \(-0.244206\pi\)
0.719859 + 0.694120i \(0.244206\pi\)
\(258\) 5.41743e6 1.92426e6i 0.315453 0.112048i
\(259\) 1.48853e7i 0.856757i
\(260\) 2.19191e6 1.78194e6i 0.124710 0.101385i
\(261\) 6.89054e6 0.387554
\(262\) 606123. + 1.70644e6i 0.0337021 + 0.0948825i
\(263\) 2.00725e7i 1.10340i 0.834041 + 0.551702i \(0.186021\pi\)
−0.834041 + 0.551702i \(0.813979\pi\)
\(264\) −3.54467e6 + 5.82189e6i −0.192648 + 0.316411i
\(265\) 2.72902e7 1.46646
\(266\) −3.60903e6 + 1.28192e6i −0.191754 + 0.0681107i
\(267\) 1.29130e7i 0.678411i
\(268\) −1.45160e7 1.78556e7i −0.754122 0.927621i
\(269\) 796563. 0.0409226 0.0204613 0.999791i \(-0.493487\pi\)
0.0204613 + 0.999791i \(0.493487\pi\)
\(270\) −9.64257e6 2.71470e7i −0.489893 1.37921i
\(271\) 1.04185e6i 0.0523474i −0.999657 0.0261737i \(-0.991668\pi\)
0.999657 0.0261737i \(-0.00833230\pi\)
\(272\) −3.45433e6 + 1.65634e7i −0.171655 + 0.823082i
\(273\) −951524. −0.0467662
\(274\) −3.69314e7 + 1.31180e7i −1.79533 + 0.637698i
\(275\) 2.32275e7i 1.11687i
\(276\) −7.83024e6 + 6.36570e6i −0.372433 + 0.302774i
\(277\) −2.26267e7 −1.06459 −0.532293 0.846560i \(-0.678670\pi\)
−0.532293 + 0.846560i \(0.678670\pi\)
\(278\) 1.35357e7 + 3.81074e7i 0.630007 + 1.77368i
\(279\) 2.50286e7i 1.15246i
\(280\) 2.67783e7 + 1.63040e7i 1.21986 + 0.742711i
\(281\) 2.62054e6 0.118106 0.0590531 0.998255i \(-0.481192\pi\)
0.0590531 + 0.998255i \(0.481192\pi\)
\(282\) −1.25798e7 + 4.46832e6i −0.560954 + 0.199249i
\(283\) 1.42323e7i 0.627935i −0.949434 0.313967i \(-0.898342\pi\)
0.949434 0.313967i \(-0.101658\pi\)
\(284\) 5.40975e6 + 6.65436e6i 0.236169 + 0.290503i
\(285\) 4.51654e6 0.195106
\(286\) 548173. + 1.54329e6i 0.0234325 + 0.0659704i
\(287\) 9.25986e6i 0.391705i
\(288\) 2.32994e6 + 1.70652e7i 0.0975366 + 0.714386i
\(289\) −7.07401e6 −0.293070
\(290\) 1.98901e7 7.06494e6i 0.815538 0.289677i
\(291\) 2.26150e7i 0.917734i
\(292\) −1.13061e7 + 9.19144e6i −0.454113 + 0.369177i
\(293\) −9.23155e6 −0.367005 −0.183502 0.983019i \(-0.558743\pi\)
−0.183502 + 0.983019i \(0.558743\pi\)
\(294\) 957983. + 2.69704e6i 0.0376978 + 0.106132i
\(295\) 6.56314e7i 2.55650i
\(296\) −1.30272e7 + 2.13963e7i −0.502314 + 0.825018i
\(297\) 1.67023e7 0.637541
\(298\) −2.07245e7 + 7.36129e6i −0.783131 + 0.278167i
\(299\) 2.42472e6i 0.0907084i
\(300\) −1.43260e7 1.76219e7i −0.530592 0.652664i
\(301\) 1.53309e7 0.562170
\(302\) −9.65286e6 2.71760e7i −0.350457 0.986654i
\(303\) 1.31906e7i 0.474174i
\(304\) −6.30956e6 1.31587e6i −0.224584 0.0468374i
\(305\) −5.68992e7 −2.00543
\(306\) 1.63680e7 5.81387e6i 0.571256 0.202909i
\(307\) 4.33908e7i 1.49962i 0.661651 + 0.749812i \(0.269856\pi\)
−0.661651 + 0.749812i \(0.730144\pi\)
\(308\) −1.41037e7 + 1.14658e7i −0.482705 + 0.392422i
\(309\) 1.03831e6 0.0351927
\(310\) −2.56621e7 7.22472e7i −0.861403 2.42514i
\(311\) 3.03615e7i 1.00935i −0.863309 0.504676i \(-0.831612\pi\)
0.863309 0.504676i \(-0.168388\pi\)
\(312\) −1.36773e6 832747.i −0.0450337 0.0274189i
\(313\) −4.96666e7 −1.61969 −0.809844 0.586645i \(-0.800448\pi\)
−0.809844 + 0.586645i \(0.800448\pi\)
\(314\) 2.54032e7 9.02318e6i 0.820541 0.291454i
\(315\) 3.21851e7i 1.02973i
\(316\) 3.01315e7 + 3.70638e7i 0.954903 + 1.17460i
\(317\) −3.88885e7 −1.22080 −0.610398 0.792095i \(-0.708991\pi\)
−0.610398 + 0.792095i \(0.708991\pi\)
\(318\) −5.17790e6 1.45775e7i −0.161017 0.453317i
\(319\) 1.22375e7i 0.376982i
\(320\) 2.42227e7 + 4.68712e7i 0.739217 + 1.43039i
\(321\) −1.94955e7 −0.589414
\(322\) −2.53582e7 + 9.00719e6i −0.759541 + 0.269787i
\(323\) 6.50008e6i 0.192891i
\(324\) 6.35704e6 5.16804e6i 0.186905 0.151947i
\(325\) −5.45682e6 −0.158961
\(326\) −4.51801e6 1.27197e7i −0.130405 0.367134i
\(327\) 5.45961e6i 0.156141i
\(328\) −8.10397e6 + 1.33102e7i −0.229655 + 0.377194i
\(329\) −3.55998e7 −0.999677
\(330\) 2.01986e7 7.17449e6i 0.562055 0.199641i
\(331\) 2.42937e7i 0.669900i 0.942236 + 0.334950i \(0.108719\pi\)
−0.942236 + 0.334950i \(0.891281\pi\)
\(332\) −1.85462e7 2.28131e7i −0.506805 0.623405i
\(333\) 2.57165e7 0.696432
\(334\) −32279.2 90876.7i −0.000866330 0.00243901i
\(335\) 7.23661e7i 1.92487i
\(336\) 3.62828e6 1.73975e7i 0.0956496 0.458637i
\(337\) −3.56079e7 −0.930373 −0.465186 0.885213i \(-0.654013\pi\)
−0.465186 + 0.885213i \(0.654013\pi\)
\(338\) 3.60247e7 1.27959e7i 0.932932 0.331375i
\(339\) 2.22367e7i 0.570783i
\(340\) 4.12866e7 3.35645e7i 1.05044 0.853971i
\(341\) 4.44504e7 1.12102
\(342\) 2.21470e6 + 6.23511e6i 0.0553651 + 0.155871i
\(343\) 4.34260e7i 1.07614i
\(344\) 2.20368e7 + 1.34171e7i 0.541344 + 0.329598i
\(345\) 3.17347e7 0.772818
\(346\) 1.61638e7 5.74134e6i 0.390225 0.138607i
\(347\) 1.40341e6i 0.0335890i −0.999859 0.0167945i \(-0.994654\pi\)
0.999859 0.0167945i \(-0.00534610\pi\)
\(348\) −7.54771e6 9.28419e6i −0.179092 0.220296i
\(349\) −1.27027e7 −0.298827 −0.149413 0.988775i \(-0.547739\pi\)
−0.149413 + 0.988775i \(0.547739\pi\)
\(350\) −2.02706e7 5.70686e7i −0.472785 1.33105i
\(351\) 3.92387e6i 0.0907389i
\(352\) −3.03075e7 + 4.13794e6i −0.694899 + 0.0948760i
\(353\) 4.78227e7 1.08720 0.543601 0.839344i \(-0.317061\pi\)
0.543601 + 0.839344i \(0.317061\pi\)
\(354\) 3.50581e7 1.24526e7i 0.790276 0.280704i
\(355\) 2.69691e7i 0.602811i
\(356\) 4.49655e7 3.65553e7i 0.996619 0.810215i
\(357\) −1.79228e7 −0.393915
\(358\) −940554. 2.64797e6i −0.0204991 0.0577118i
\(359\) 7.00860e7i 1.51477i 0.652966 + 0.757387i \(0.273525\pi\)
−0.652966 + 0.757387i \(0.726475\pi\)
\(360\) 2.81675e7 4.62633e7i 0.603728 0.991584i
\(361\) −2.47610e6 −0.0526316
\(362\) −4.88194e7 + 1.73406e7i −1.02912 + 0.365542i
\(363\) 1.28373e7i 0.268381i
\(364\) −2.69366e6 3.31339e6i −0.0558520 0.0687018i
\(365\) 4.58218e7 0.942310
\(366\) 1.07958e7 + 3.03936e7i 0.220196 + 0.619926i
\(367\) 1.78296e7i 0.360699i −0.983603 0.180349i \(-0.942277\pi\)
0.983603 0.180349i \(-0.0577228\pi\)
\(368\) −4.43331e7 9.24575e6i −0.889579 0.185523i
\(369\) 1.59977e7 0.318405
\(370\) 7.42328e7 2.63673e7i 1.46552 0.520548i
\(371\) 4.12531e7i 0.807858i
\(372\) −3.37231e7 + 2.74156e7i −0.655086 + 0.532561i
\(373\) −3.47591e7 −0.669795 −0.334898 0.942254i \(-0.608702\pi\)
−0.334898 + 0.942254i \(0.608702\pi\)
\(374\) 1.03253e7 + 2.90693e7i 0.197374 + 0.555673i
\(375\) 2.65710e7i 0.503865i
\(376\) −5.11716e7 3.11559e7i −0.962644 0.586107i
\(377\) −2.87495e6 −0.0536545
\(378\) −4.10367e7 + 1.45762e7i −0.759797 + 0.269878i
\(379\) 4.69020e7i 0.861536i −0.902463 0.430768i \(-0.858243\pi\)
0.902463 0.430768i \(-0.141757\pi\)
\(380\) 1.27858e7 + 1.57274e7i 0.233012 + 0.286620i
\(381\) 2.64140e7 0.477595
\(382\) 5.62570e6 + 1.58382e7i 0.100922 + 0.284130i
\(383\) 2.59506e7i 0.461903i −0.972965 0.230952i \(-0.925816\pi\)
0.972965 0.230952i \(-0.0741839\pi\)
\(384\) 2.04411e7 2.18320e7i 0.361003 0.385568i
\(385\) 5.71603e7 1.00164
\(386\) −8.26682e7 + 2.93636e7i −1.43740 + 0.510560i
\(387\) 2.64863e7i 0.456971i
\(388\) 7.87496e7 6.40205e7i 1.34820 1.09603i
\(389\) 5.98509e7 1.01677 0.508384 0.861130i \(-0.330243\pi\)
0.508384 + 0.861130i \(0.330243\pi\)
\(390\) 1.68550e6 + 4.74524e6i 0.0284142 + 0.0799954i
\(391\) 4.56718e7i 0.764043i
\(392\) −6.67966e6 + 1.09709e7i −0.110891 + 0.182131i
\(393\) −3.22817e6 −0.0531837
\(394\) 7.26333e6 2.57992e6i 0.118754 0.0421811i
\(395\) 1.50214e8i 2.43735i
\(396\) 1.98089e7 + 2.43662e7i 0.318988 + 0.392377i
\(397\) −5.66329e7 −0.905101 −0.452551 0.891739i \(-0.649486\pi\)
−0.452551 + 0.891739i \(0.649486\pi\)
\(398\) 3.50277e7 + 9.86145e7i 0.555600 + 1.56420i
\(399\) 6.82741e6i 0.107482i
\(400\) 2.08075e7 9.97715e7i 0.325118 1.55893i
\(401\) −2.81556e7 −0.436649 −0.218324 0.975876i \(-0.570059\pi\)
−0.218324 + 0.975876i \(0.570059\pi\)
\(402\) 3.86556e7 1.37304e7i 0.595023 0.211351i
\(403\) 1.04427e7i 0.159551i
\(404\) −4.59323e7 + 3.73413e7i −0.696585 + 0.566298i
\(405\) −2.57641e7 −0.387837
\(406\) −1.06797e7 3.00669e7i −0.159581 0.449273i
\(407\) 4.56720e7i 0.677434i
\(408\) −2.57625e7 1.56856e7i −0.379322 0.230951i
\(409\) −5.69492e7 −0.832373 −0.416187 0.909279i \(-0.636634\pi\)
−0.416187 + 0.909279i \(0.636634\pi\)
\(410\) 4.61788e7 1.64026e7i 0.670026 0.237992i
\(411\) 6.98654e7i 1.00632i
\(412\) 2.93935e6 + 3.61560e6i 0.0420301 + 0.0516998i
\(413\) 9.92115e7 1.40835
\(414\) 1.55612e7 + 4.38100e7i 0.219302 + 0.617408i
\(415\) 9.24580e7i 1.29360i
\(416\) −972124. 7.12012e6i −0.0135034 0.0989025i
\(417\) −7.20901e7 −0.994185
\(418\) −1.10735e7 + 3.93327e6i −0.151619 + 0.0538548i
\(419\) 1.28188e8i 1.74263i −0.490724 0.871315i \(-0.663268\pi\)
0.490724 0.871315i \(-0.336732\pi\)
\(420\) −4.33656e7 + 3.52547e7i −0.585326 + 0.475849i
\(421\) 1.38826e8 1.86048 0.930238 0.366957i \(-0.119600\pi\)
0.930238 + 0.366957i \(0.119600\pi\)
\(422\) 1.26567e7 + 3.56327e7i 0.168416 + 0.474146i
\(423\) 6.15038e7i 0.812607i
\(424\) 3.61036e7 5.92978e7i 0.473645 0.777931i
\(425\) −1.02784e8 −1.33893
\(426\) −1.44060e7 + 5.11698e6i −0.186344 + 0.0661888i
\(427\) 8.60114e7i 1.10477i
\(428\) −5.51897e7 6.78871e7i −0.703926 0.865877i
\(429\) −2.91953e6 −0.0369778
\(430\) −2.71566e7 7.64550e7i −0.341563 0.961613i
\(431\) 5.38586e7i 0.672703i 0.941737 + 0.336351i \(0.109193\pi\)
−0.941737 + 0.336351i \(0.890807\pi\)
\(432\) −7.17434e7 1.49622e7i −0.889878 0.185586i
\(433\) −2.00516e7 −0.246994 −0.123497 0.992345i \(-0.539411\pi\)
−0.123497 + 0.992345i \(0.539411\pi\)
\(434\) −1.09212e8 + 3.87920e7i −1.33599 + 0.474540i
\(435\) 3.76274e7i 0.457126i
\(436\) −1.90114e7 + 1.54556e7i −0.229379 + 0.186477i
\(437\) −1.73979e7 −0.208474
\(438\) −8.69399e6 2.44765e7i −0.103466 0.291291i
\(439\) 4.22684e7i 0.499600i 0.968297 + 0.249800i \(0.0803649\pi\)
−0.968297 + 0.249800i \(0.919635\pi\)
\(440\) 8.21629e7 + 5.00250e7i 0.964535 + 0.587259i
\(441\) 1.31861e7 0.153744
\(442\) −6.82923e6 + 2.42573e6i −0.0790870 + 0.0280915i
\(443\) 1.28540e8i 1.47852i −0.673418 0.739262i \(-0.735174\pi\)
0.673418 0.739262i \(-0.264826\pi\)
\(444\) −2.81691e7 3.46499e7i −0.321828 0.395870i
\(445\) −1.82238e8 −2.06804
\(446\) 4.28790e7 + 1.20719e8i 0.483326 + 1.36072i
\(447\) 3.92057e7i 0.438962i
\(448\) 7.08526e7 3.66161e7i 0.787992 0.407228i
\(449\) 7.85801e7 0.868108 0.434054 0.900887i \(-0.357083\pi\)
0.434054 + 0.900887i \(0.357083\pi\)
\(450\) −9.85942e7 + 3.50205e7i −1.08197 + 0.384312i
\(451\) 2.84117e7i 0.309719i
\(452\) −7.74323e7 + 6.29496e7i −0.838507 + 0.681675i
\(453\) 5.14105e7 0.553041
\(454\) −3.86764e7 1.08887e8i −0.413313 1.16361i
\(455\) 1.34286e7i 0.142560i
\(456\) 5.97515e6 9.81381e6i 0.0630165 0.103501i
\(457\) −3.52825e6 −0.0369667 −0.0184833 0.999829i \(-0.505884\pi\)
−0.0184833 + 0.999829i \(0.505884\pi\)
\(458\) 1.60967e8 5.71750e7i 1.67548 0.595127i
\(459\) 7.39097e7i 0.764300i
\(460\) 8.98376e7 + 1.10506e8i 0.922963 + 1.13531i
\(461\) 1.35044e8 1.37839 0.689194 0.724577i \(-0.257965\pi\)
0.689194 + 0.724577i \(0.257965\pi\)
\(462\) −1.08453e7 3.05331e7i −0.109980 0.309632i
\(463\) 1.53732e8i 1.54890i −0.632637 0.774448i \(-0.718027\pi\)
0.632637 0.774448i \(-0.281973\pi\)
\(464\) 1.09625e7 5.25651e7i 0.109738 0.526191i
\(465\) 1.36674e8 1.35934
\(466\) 1.67048e8 5.93351e7i 1.65076 0.586346i
\(467\) 4.70204e7i 0.461675i −0.972992 0.230837i \(-0.925854\pi\)
0.972992 0.230837i \(-0.0741465\pi\)
\(468\) −5.72435e6 + 4.65369e6i −0.0558456 + 0.0454004i
\(469\) 1.09392e8 1.06039
\(470\) 6.30604e7 + 1.77536e8i 0.607383 + 1.70999i
\(471\) 4.80568e7i 0.459931i
\(472\) 1.42608e8 + 8.68271e7i 1.35618 + 0.825713i
\(473\) 4.70392e7 0.444505
\(474\) −8.02391e7 + 2.85008e7i −0.753444 + 0.267622i
\(475\) 3.91539e7i 0.365338i
\(476\) −5.07376e7 6.24107e7i −0.470445 0.578679i
\(477\) −7.12707e7 −0.656683
\(478\) 5.23142e7 + 1.47282e8i 0.479000 + 1.34854i
\(479\) 1.05499e8i 0.959938i −0.877285 0.479969i \(-0.840648\pi\)
0.877285 0.479969i \(-0.159352\pi\)
\(480\) −9.31882e7 + 1.27232e7i −0.842631 + 0.115046i
\(481\) −1.07297e7 −0.0964168
\(482\) −1.72511e8 + 6.12756e7i −1.54055 + 0.547201i
\(483\) 4.79717e7i 0.425739i
\(484\) 4.47017e7 3.63409e7i 0.394265 0.320523i
\(485\) −3.19160e8 −2.79758
\(486\) 3.98147e7 + 1.12092e8i 0.346845 + 0.976483i
\(487\) 7.29337e7i 0.631454i 0.948850 + 0.315727i \(0.102248\pi\)
−0.948850 + 0.315727i \(0.897752\pi\)
\(488\) −7.52747e7 + 1.23634e8i −0.647724 + 1.06384i
\(489\) 2.40626e7 0.205786
\(490\) 3.80627e7 1.35198e7i 0.323528 0.114916i
\(491\) 1.76733e8i 1.49305i −0.665359 0.746524i \(-0.731722\pi\)
0.665359 0.746524i \(-0.268278\pi\)
\(492\) −1.75235e7 2.15551e7i −0.147138 0.180990i
\(493\) −5.41523e7 −0.451935
\(494\) −924041. 2.60148e6i −0.00766497 0.0215794i
\(495\) 9.87526e7i 0.814203i
\(496\) −1.90933e8 3.98194e7i −1.56472 0.326324i
\(497\) −4.07677e7 −0.332083
\(498\) 4.93880e7 1.75425e7i 0.399883 0.142038i
\(499\) 4.09661e7i 0.329703i 0.986318 + 0.164852i \(0.0527145\pi\)
−0.986318 + 0.164852i \(0.947285\pi\)
\(500\) −9.25253e7 + 7.52197e7i −0.740202 + 0.601757i
\(501\) 171917. 0.00136712
\(502\) 4.41056e7 + 1.24172e8i 0.348644 + 0.981550i
\(503\) 2.79451e7i 0.219584i 0.993955 + 0.109792i \(0.0350185\pi\)
−0.993955 + 0.109792i \(0.964981\pi\)
\(504\) −6.99338e7 4.25793e7i −0.546255 0.332588i
\(505\) 1.86156e8 1.44545
\(506\) −7.78058e7 + 2.76365e7i −0.600566 + 0.213320i
\(507\) 6.81500e7i 0.522928i
\(508\) 7.47752e7 + 9.19785e7i 0.570383 + 0.701609i
\(509\) −1.06277e7 −0.0805911 −0.0402956 0.999188i \(-0.512830\pi\)
−0.0402956 + 0.999188i \(0.512830\pi\)
\(510\) 3.17480e7 + 8.93811e7i 0.239334 + 0.673806i
\(511\) 6.92664e7i 0.519110i
\(512\) 1.33890e8 + 9.37577e6i 0.997557 + 0.0698549i
\(513\) −2.81547e7 −0.208544
\(514\) −1.84232e8 + 6.54389e7i −1.35668 + 0.481889i
\(515\) 1.46535e7i 0.107280i
\(516\) −3.56871e7 + 2.90123e7i −0.259754 + 0.211171i
\(517\) −1.09230e8 −0.790441
\(518\) −3.98581e7 1.12214e8i −0.286766 0.807340i
\(519\) 3.05780e7i 0.218729i
\(520\) −1.17524e7 + 1.93025e7i −0.0835825 + 0.137279i
\(521\) −3.34642e7 −0.236629 −0.118314 0.992976i \(-0.537749\pi\)
−0.118314 + 0.992976i \(0.537749\pi\)
\(522\) −5.19448e7 + 1.84507e7i −0.365200 + 0.129718i
\(523\) 2.51990e8i 1.76148i −0.473601 0.880740i \(-0.657046\pi\)
0.473601 0.880740i \(-0.342954\pi\)
\(524\) −9.13859e6 1.12411e7i −0.0635163 0.0781294i
\(525\) 1.07960e8 0.746080
\(526\) −5.37478e7 1.51318e8i −0.369321 1.03976i
\(527\) 1.96698e8i 1.34390i
\(528\) 1.11325e7 5.33802e7i 0.0756297 0.362642i
\(529\) 2.57923e7 0.174230
\(530\) −2.05729e8 + 7.30745e7i −1.38187 + 0.490838i
\(531\) 1.71402e8i 1.14481i
\(532\) 2.37743e7 1.93277e7i 0.157897 0.128364i
\(533\) −6.67476e6 −0.0440812
\(534\) 3.45769e7 + 9.73455e7i 0.227071 + 0.639281i
\(535\) 2.75136e8i 1.79674i
\(536\) 1.57241e8 + 9.57367e7i 1.02111 + 0.621705i
\(537\) 5.00933e6 0.0323487
\(538\) −6.00494e6 + 2.13294e6i −0.0385622 + 0.0136972i
\(539\) 2.34182e7i 0.149550i
\(540\) 1.45382e8 + 1.78830e8i 0.923274 + 1.13569i
\(541\) −1.23124e8 −0.777593 −0.388796 0.921324i \(-0.627109\pi\)
−0.388796 + 0.921324i \(0.627109\pi\)
\(542\) 2.78973e6 + 7.85402e6i 0.0175212 + 0.0493281i
\(543\) 9.23546e7i 0.576845i
\(544\) −1.83109e7 1.34114e8i −0.113740 0.833062i
\(545\) 7.70501e7 0.475975
\(546\) 7.17313e6 2.54788e6i 0.0440688 0.0156531i
\(547\) 1.61396e8i 0.986120i 0.869995 + 0.493060i \(0.164122\pi\)
−0.869995 + 0.493060i \(0.835878\pi\)
\(548\) 2.43284e8 1.97781e8i 1.47833 1.20183i
\(549\) 1.48597e8 0.898035
\(550\) −6.21958e7 1.75102e8i −0.373829 1.05245i
\(551\) 2.06284e7i 0.123314i
\(552\) 4.19834e7 6.89551e7i 0.249609 0.409967i
\(553\) −2.27070e8 −1.34272
\(554\) 1.70573e8 6.05870e7i 1.00318 0.356328i
\(555\) 1.40431e8i 0.821453i
\(556\) −2.04079e8 2.51031e8i −1.18734 1.46051i
\(557\) 6.79124e7 0.392992 0.196496 0.980505i \(-0.437044\pi\)
0.196496 + 0.980505i \(0.437044\pi\)
\(558\) 6.70187e7 + 1.88680e8i 0.385739 + 1.08598i
\(559\) 1.10509e7i 0.0632648i
\(560\) −2.45527e8 5.12051e7i −1.39809 0.291574i
\(561\) −5.49921e7 −0.311467
\(562\) −1.97552e7 + 7.01699e6i −0.111294 + 0.0395314i
\(563\) 1.63874e8i 0.918300i 0.888359 + 0.459150i \(0.151846\pi\)
−0.888359 + 0.459150i \(0.848154\pi\)
\(564\) 8.28690e7 6.73695e7i 0.461907 0.375514i
\(565\) 3.13821e8 1.73995
\(566\) 3.81095e7 + 1.07291e8i 0.210176 + 0.591716i
\(567\) 3.89462e7i 0.213656i
\(568\) −5.86001e7 3.56787e7i −0.319781 0.194699i
\(569\) 4.76512e7 0.258664 0.129332 0.991601i \(-0.458717\pi\)
0.129332 + 0.991601i \(0.458717\pi\)
\(570\) −3.40482e7 + 1.20939e7i −0.183853 + 0.0653041i
\(571\) 2.89473e8i 1.55489i 0.628950 + 0.777446i \(0.283485\pi\)
−0.628950 + 0.777446i \(0.716515\pi\)
\(572\) −8.26488e6 1.01664e7i −0.0441620 0.0543222i
\(573\) −2.99621e7 −0.159261
\(574\) −2.47950e7 6.98061e7i −0.131108 0.369111i
\(575\) 2.75109e8i 1.44711i
\(576\) −6.32596e7 1.22408e8i −0.331023 0.640535i
\(577\) −1.68949e8 −0.879487 −0.439744 0.898123i \(-0.644931\pi\)
−0.439744 + 0.898123i \(0.644931\pi\)
\(578\) 5.33279e7 1.89419e7i 0.276166 0.0980937i
\(579\) 1.56388e8i 0.805691i
\(580\) −1.31026e8 + 1.06519e8i −0.671540 + 0.545938i
\(581\) 1.39764e8 0.712633
\(582\) 6.05557e7 + 1.70484e8i 0.307175 + 0.864801i
\(583\) 1.26576e8i 0.638770i
\(584\) 6.06199e7 9.95644e7i 0.304353 0.499880i
\(585\) 2.31999e7 0.115883
\(586\) 6.95926e7 2.47192e7i 0.345836 0.122840i
\(587\) 887448.i 0.00438762i −0.999998 0.00219381i \(-0.999302\pi\)
0.999998 0.00219381i \(-0.000698311\pi\)
\(588\) −1.44436e7 1.77667e7i −0.0710468 0.0873924i
\(589\) −7.49289e7 −0.366694
\(590\) −1.75740e8 4.94767e8i −0.855687 2.40904i
\(591\) 1.37405e7i 0.0665640i
\(592\) 4.09137e7 1.96180e8i 0.197199 0.945562i
\(593\) −2.75935e7 −0.132325 −0.0661627 0.997809i \(-0.521076\pi\)
−0.0661627 + 0.997809i \(0.521076\pi\)
\(594\) −1.25912e8 + 4.47236e7i −0.600768 + 0.213391i
\(595\) 2.52941e8i 1.20079i
\(596\) 1.36522e8 1.10987e8i 0.644856 0.524244i
\(597\) −1.86555e8 −0.876766
\(598\) −6.49262e6 1.82789e7i −0.0303610 0.0854764i
\(599\) 1.16393e8i 0.541562i −0.962641 0.270781i \(-0.912718\pi\)
0.962641 0.270781i \(-0.0872819\pi\)
\(600\) 1.55183e8 + 9.44836e7i 0.718441 + 0.437424i
\(601\) 1.62465e8 0.748402 0.374201 0.927348i \(-0.377917\pi\)
0.374201 + 0.927348i \(0.377917\pi\)
\(602\) −1.15573e8 + 4.10512e7i −0.529744 + 0.188164i
\(603\) 1.88990e8i 0.861961i
\(604\) 1.45538e8 + 1.79021e8i 0.660487 + 0.812443i
\(605\) −1.81169e8 −0.818122
\(606\) −3.53204e7 9.94385e7i −0.158711 0.446824i
\(607\) 1.74742e8i 0.781324i 0.920534 + 0.390662i \(0.127754\pi\)
−0.920534 + 0.390662i \(0.872246\pi\)
\(608\) 5.10885e7 6.97522e6i 0.227307 0.0310347i
\(609\) 5.68793e7 0.251827
\(610\) 4.28938e8 1.52358e8i 1.88975 0.671237i
\(611\) 2.56613e7i 0.112501i
\(612\) −1.07823e8 + 8.76565e7i −0.470391 + 0.382411i
\(613\) 7.67842e7 0.333342 0.166671 0.986013i \(-0.446698\pi\)
0.166671 + 0.986013i \(0.446698\pi\)
\(614\) −1.16187e8 3.27105e8i −0.501940 1.41313i
\(615\) 8.73593e7i 0.375564i
\(616\) 7.56202e7 1.24201e8i 0.323516 0.531354i
\(617\) 2.39522e8 1.01974 0.509872 0.860251i \(-0.329693\pi\)
0.509872 + 0.860251i \(0.329693\pi\)
\(618\) −7.82740e6 + 2.78027e6i −0.0331629 + 0.0117794i
\(619\) 2.49504e8i 1.05198i 0.850492 + 0.525988i \(0.176304\pi\)
−0.850492 + 0.525988i \(0.823696\pi\)
\(620\) 3.86910e8 + 4.75926e8i 1.62344 + 1.99694i
\(621\) −1.97824e8 −0.826048
\(622\) 8.12985e7 + 2.28882e8i 0.337840 + 0.951133i
\(623\) 2.75479e8i 1.13927i
\(624\) 1.25406e7 + 2.61536e6i 0.0516136 + 0.0107641i
\(625\) −1.37961e7 −0.0565089
\(626\) 3.74415e8 1.32991e8i 1.52627 0.542126i
\(627\) 2.09483e7i 0.0849858i
\(628\) −1.67343e8 + 1.36044e8i −0.675660 + 0.549287i
\(629\) −2.02104e8 −0.812125
\(630\) 8.61816e7 + 2.42630e8i 0.344662 + 0.970337i
\(631\) 1.47158e8i 0.585727i −0.956154 0.292863i \(-0.905392\pi\)
0.956154 0.292863i \(-0.0946081\pi\)
\(632\) −3.26393e8 1.98725e8i −1.29297 0.787230i
\(633\) −6.74086e7 −0.265769
\(634\) 2.93163e8 1.04131e8i 1.15038 0.408613i
\(635\) 3.72775e8i 1.45588i
\(636\) 7.80680e7 + 9.60288e7i 0.303460 + 0.373276i
\(637\) −5.50164e6 −0.0212850
\(638\) −3.27681e7 9.22532e7i −0.126180 0.355238i
\(639\) 7.04321e7i 0.269941i
\(640\) −3.08110e8 2.88481e8i −1.17535 1.10047i
\(641\) 1.03678e8 0.393653 0.196826 0.980438i \(-0.436936\pi\)
0.196826 + 0.980438i \(0.436936\pi\)
\(642\) 1.46968e8 5.22029e7i 0.555417 0.197283i
\(643\) 2.23604e8i 0.841098i 0.907270 + 0.420549i \(0.138163\pi\)
−0.907270 + 0.420549i \(0.861837\pi\)
\(644\) 1.67046e8 1.35803e8i 0.625431 0.508453i
\(645\) 1.44634e8 0.539005
\(646\) −1.74052e7 4.90013e7i −0.0645625 0.181765i
\(647\) 4.10400e8i 1.51529i −0.652670 0.757643i \(-0.726351\pi\)
0.652670 0.757643i \(-0.273649\pi\)
\(648\) −3.40846e7 + 5.59818e7i −0.125266 + 0.205741i
\(649\) 3.04407e8 1.11358
\(650\) 4.11366e7 1.46116e7i 0.149792 0.0532057i
\(651\) 2.06603e8i 0.748849i
\(652\) 6.81187e7 + 8.37905e7i 0.245767 + 0.302310i
\(653\) 2.37002e8 0.851164 0.425582 0.904920i \(-0.360069\pi\)
0.425582 + 0.904920i \(0.360069\pi\)
\(654\) −1.46191e7 4.11576e7i −0.0522621 0.147135i
\(655\) 4.55584e7i 0.162123i
\(656\) 2.54517e7 1.22040e8i 0.0901581 0.432306i
\(657\) −1.19668e8 −0.421969
\(658\) 2.68372e8 9.53250e7i 0.942017 0.334602i
\(659\) 2.57956e8i 0.901342i −0.892690 0.450671i \(-0.851185\pi\)
0.892690 0.450671i \(-0.148815\pi\)
\(660\) −1.33057e8 + 1.08171e8i −0.462815 + 0.376252i
\(661\) −1.44446e8 −0.500152 −0.250076 0.968226i \(-0.580456\pi\)
−0.250076 + 0.968226i \(0.580456\pi\)
\(662\) −6.50509e7 1.83140e8i −0.224222 0.631261i
\(663\) 1.29193e7i 0.0443299i
\(664\) 2.00898e8 + 1.22317e8i 0.686233 + 0.417814i
\(665\) −9.63536e7 −0.327645
\(666\) −1.93865e8 + 6.88606e7i −0.656262 + 0.233103i
\(667\) 1.44942e8i 0.488447i
\(668\) 486678. + 598647.i 0.00163272 + 0.00200836i
\(669\) −2.28371e8 −0.762715
\(670\) −1.93773e8 5.45537e8i −0.644273 1.81384i
\(671\) 2.63906e8i 0.873538i
\(672\) 1.92329e7 + 1.40868e8i 0.0633779 + 0.464198i
\(673\) 1.41439e8 0.464006 0.232003 0.972715i \(-0.425472\pi\)
0.232003 + 0.972715i \(0.425472\pi\)
\(674\) 2.68433e8 9.53467e7i 0.876710 0.311405i
\(675\) 4.45203e8i 1.44759i
\(676\) −2.37311e8 + 1.92925e8i −0.768206 + 0.624524i
\(677\) 1.65808e8 0.534368 0.267184 0.963645i \(-0.413907\pi\)
0.267184 + 0.963645i \(0.413907\pi\)
\(678\) −5.95428e7 1.67633e8i −0.191047 0.537860i
\(679\) 4.82457e8i 1.54116i
\(680\) −2.21367e8 + 3.63580e8i −0.704020 + 1.15631i
\(681\) 2.05988e8 0.652230
\(682\) −3.35092e8 + 1.19024e8i −1.05636 + 0.375216i
\(683\) 4.13870e8i 1.29898i 0.760371 + 0.649490i \(0.225017\pi\)
−0.760371 + 0.649490i \(0.774983\pi\)
\(684\) −3.33913e7 4.10736e7i −0.104343 0.128349i
\(685\) −9.85994e8 −3.06763
\(686\) −1.16281e8 3.27370e8i −0.360194 1.01407i
\(687\) 3.04510e8i 0.939142i
\(688\) −2.02053e8 4.21385e7i −0.620440 0.129394i
\(689\) 2.97364e7 0.0909139
\(690\) −2.39234e8 + 8.49755e7i −0.728243 + 0.258670i
\(691\) 1.36723e8i 0.414388i 0.978300 + 0.207194i \(0.0664331\pi\)
−0.978300 + 0.207194i \(0.933567\pi\)
\(692\) −1.06478e8 + 8.65630e7i −0.321324 + 0.261225i
\(693\) −1.49279e8 −0.448538
\(694\) 3.75789e6 + 1.05797e7i 0.0112426 + 0.0316516i
\(695\) 1.01739e9i 3.03063i
\(696\) 8.17590e7 + 4.97791e7i 0.242498 + 0.147645i
\(697\) −1.25725e8 −0.371299
\(698\) 9.57602e7 3.40138e7i 0.281591 0.100020i
\(699\) 3.16015e8i 0.925286i
\(700\) 3.05623e8 + 3.75937e8i 0.891030 + 1.09603i
\(701\) 1.37569e8 0.399361 0.199680 0.979861i \(-0.436010\pi\)
0.199680 + 0.979861i \(0.436010\pi\)
\(702\) −1.05069e7 2.95804e7i −0.0303712 0.0855052i
\(703\) 7.69882e7i 0.221594i
\(704\) 2.17395e8 1.12348e8i 0.623062 0.321994i
\(705\) −3.35855e8 −0.958484
\(706\) −3.60515e8 + 1.28054e8i −1.02449 + 0.363898i
\(707\) 2.81403e8i 0.796287i
\(708\) −2.30944e8 + 1.87749e8i −0.650739 + 0.529027i
\(709\) 3.87826e8 1.08817 0.544087 0.839029i \(-0.316876\pi\)
0.544087 + 0.839029i \(0.316876\pi\)
\(710\) 7.22147e7 + 2.03308e8i 0.201767 + 0.568042i
\(711\) 3.92296e8i 1.09145i
\(712\) −2.41092e8 + 3.95978e8i −0.667947 + 1.09706i
\(713\) −5.26476e8 −1.45248
\(714\) 1.35113e8 4.79917e7i 0.371194 0.131847i
\(715\) 4.12027e7i 0.112722i
\(716\) 1.41809e7 + 1.74434e7i 0.0386334 + 0.0475217i
\(717\) −2.78622e8 −0.755888
\(718\) −1.87668e8 5.28348e8i −0.507011 1.42740i
\(719\) 1.23338e8i 0.331826i 0.986140 + 0.165913i \(0.0530571\pi\)
−0.986140 + 0.165913i \(0.946943\pi\)
\(720\) −8.84642e7 + 4.24183e8i −0.237012 + 1.13646i
\(721\) −2.21509e7 −0.0590996
\(722\) 1.86662e7 6.63021e6i 0.0495958 0.0176163i
\(723\) 3.26350e8i 0.863512i
\(724\) 3.21596e8 2.61446e8i 0.847413 0.688916i
\(725\) 3.26192e8 0.855972
\(726\) 3.43741e7 + 9.67745e7i 0.0898300 + 0.252901i
\(727\) 6.02562e8i 1.56819i 0.620641 + 0.784095i \(0.286873\pi\)
−0.620641 + 0.784095i \(0.713127\pi\)
\(728\) 2.91786e7 + 1.77654e7i 0.0756257 + 0.0460449i
\(729\) −1.18730e8 −0.306464
\(730\) −3.45431e8 + 1.22696e8i −0.887958 + 0.315401i
\(731\) 2.08154e8i 0.532884i
\(732\) −1.62769e8 2.00217e8i −0.414991 0.510467i
\(733\) −3.48940e7 −0.0886010 −0.0443005 0.999018i \(-0.514106\pi\)
−0.0443005 + 0.999018i \(0.514106\pi\)
\(734\) 4.77421e7 + 1.34410e8i 0.120730 + 0.339894i
\(735\) 7.20055e7i 0.181344i
\(736\) 3.58965e8 4.90102e7i 0.900366 0.122929i
\(737\) 3.35644e8 0.838448
\(738\) −1.20600e8 + 4.28369e7i −0.300040 + 0.106573i
\(739\) 2.60560e8i 0.645616i −0.946464 0.322808i \(-0.895373\pi\)
0.946464 0.322808i \(-0.104627\pi\)
\(740\) −4.89006e8 + 3.97544e8i −1.20675 + 0.981047i
\(741\) 4.92138e6 0.0120957
\(742\) 1.10463e8 + 3.10990e8i 0.270399 + 0.761262i
\(743\) 6.93870e8i 1.69166i −0.533456 0.845828i \(-0.679107\pi\)
0.533456 0.845828i \(-0.320893\pi\)
\(744\) 1.80813e8 2.96974e8i 0.439048 0.721108i
\(745\) −5.53301e8 −1.33811
\(746\) 2.62034e8 9.30739e7i 0.631162 0.224187i
\(747\) 2.41462e8i 0.579278i
\(748\) −1.55677e8 1.91493e8i −0.371979 0.457559i
\(749\) 4.15908e8 0.989810
\(750\) −7.11488e7 2.00307e8i −0.168649 0.474803i
\(751\) 3.01857e8i 0.712658i 0.934361 + 0.356329i \(0.115972\pi\)
−0.934361 + 0.356329i \(0.884028\pi\)
\(752\) 4.69186e8 + 9.78497e7i 1.10330 + 0.230094i
\(753\) −2.34903e8 −0.550180
\(754\) 2.16730e7 7.69820e6i 0.0505598 0.0179587i
\(755\) 7.25544e8i 1.68587i
\(756\) 2.70328e8 2.19767e8i 0.625641 0.508624i
\(757\) 4.78490e8 1.10302 0.551512 0.834167i \(-0.314051\pi\)
0.551512 + 0.834167i \(0.314051\pi\)
\(758\) 1.25589e8 + 3.53574e8i 0.288365 + 0.811844i
\(759\) 1.47190e8i 0.336630i
\(760\) −1.38500e8 8.43259e7i −0.315507 0.192097i
\(761\) −5.95860e8 −1.35204 −0.676021 0.736882i \(-0.736297\pi\)
−0.676021 + 0.736882i \(0.736297\pi\)
\(762\) −1.99124e8 + 7.07283e7i −0.450047 + 0.159856i
\(763\) 1.16473e8i 0.262210i
\(764\) −8.48195e7 1.04334e8i −0.190202 0.233962i
\(765\) 4.36992e8 0.976088
\(766\) 6.94875e7 + 1.95630e8i 0.154604 + 0.435261i
\(767\) 7.15143e7i 0.158492i
\(768\) −9.56377e7 + 2.19317e8i −0.211128 + 0.484160i
\(769\) 6.50131e8 1.42962 0.714812 0.699317i \(-0.246512\pi\)
0.714812 + 0.699317i \(0.246512\pi\)
\(770\) −4.30907e8 + 1.53057e8i −0.943867 + 0.335260i
\(771\) 3.48523e8i 0.760446i
\(772\) 5.44574e8 4.42718e8i 1.18360 0.962223i
\(773\) 5.61377e8 1.21539 0.607696 0.794170i \(-0.292094\pi\)
0.607696 + 0.794170i \(0.292094\pi\)
\(774\) 7.09219e7 + 1.99669e8i 0.152953 + 0.430613i
\(775\) 1.18483e9i 2.54537i
\(776\) −4.22232e8 + 6.93489e8i −0.903579 + 1.48407i
\(777\) 2.12281e8 0.452532
\(778\) −4.51190e8 + 1.60262e8i −0.958122 + 0.340323i
\(779\) 4.78929e7i 0.101312i
\(780\) −2.54125e7 3.12591e7i −0.0535506 0.0658708i
\(781\) −1.25086e8 −0.262577
\(782\) −1.22295e8 3.44300e8i −0.255733 0.719974i
\(783\) 2.34557e8i 0.488612i
\(784\) 2.09784e7 1.00591e8i 0.0435336 0.208742i
\(785\) 6.78215e8 1.40203
\(786\) 2.43358e7 8.64401e6i 0.0501161 0.0178011i
\(787\) 2.56259e8i 0.525721i 0.964834 + 0.262860i \(0.0846658\pi\)
−0.964834 + 0.262860i \(0.915334\pi\)
\(788\) −4.78469e7 + 3.88978e7i −0.0977857 + 0.0794962i
\(789\) 2.86257e8 0.582808
\(790\) 4.02225e8 + 1.13240e9i 0.815807 + 2.29677i
\(791\) 4.74386e8i 0.958523i
\(792\) −2.14576e8 1.30645e8i −0.431921 0.262976i
\(793\) −6.19993e7 −0.124328
\(794\) 4.26931e8 1.51645e8i 0.852896 0.302947i
\(795\) 3.89190e8i 0.774569i
\(796\) −5.28117e8 6.49619e8i −1.04711 1.28801i
\(797\) −3.41309e7 −0.0674176 −0.0337088 0.999432i \(-0.510732\pi\)
−0.0337088 + 0.999432i \(0.510732\pi\)
\(798\) 1.82816e7 + 5.14689e7i 0.0359755 + 0.101283i
\(799\) 4.83354e8i 0.947600i
\(800\) 1.10297e8 + 8.07850e8i 0.215425 + 1.57783i
\(801\) 4.75930e8 0.926074
\(802\) 2.12253e8 7.53918e7i 0.411463 0.146151i
\(803\) 2.12528e8i 0.410458i
\(804\) −2.54642e8 + 2.07015e8i −0.489961 + 0.398321i
\(805\) −6.77013e8 −1.29780
\(806\) −2.79623e7 7.87231e7i −0.0534032 0.150348i
\(807\) 1.13599e7i 0.0216149i
\(808\) 2.46276e8 4.04492e8i 0.466861 0.766789i
\(809\) 1.12820e8 0.213078 0.106539 0.994308i \(-0.466023\pi\)
0.106539 + 0.994308i \(0.466023\pi\)
\(810\) 1.94224e8 6.89881e7i 0.365467 0.129813i
\(811\) 1.85497e8i 0.347756i 0.984767 + 0.173878i \(0.0556299\pi\)
−0.984767 + 0.173878i \(0.944370\pi\)
\(812\) 1.61019e8 + 1.98064e8i 0.300752 + 0.369946i
\(813\) −1.48579e7 −0.0276494
\(814\) −1.22295e8 3.44302e8i −0.226744 0.638361i
\(815\) 3.39590e8i 0.627310i
\(816\) 2.36213e8 + 4.92628e7i 0.434745 + 0.0906668i
\(817\) −7.92928e7 −0.145401
\(818\) 4.29316e8 1.52492e8i 0.784363 0.278604i
\(819\) 3.50700e7i 0.0638388i
\(820\) −3.04201e8 + 2.47305e8i −0.551721 + 0.448529i
\(821\) 6.47897e8 1.17078 0.585391 0.810751i \(-0.300941\pi\)
0.585391 + 0.810751i \(0.300941\pi\)
\(822\) 1.87077e8 + 5.26685e8i 0.336826 + 0.948278i
\(823\) 4.02842e8i 0.722661i 0.932438 + 0.361331i \(0.117677\pi\)
−0.932438 + 0.361331i \(0.882323\pi\)
\(824\) −3.18399e7 1.93858e7i −0.0569103 0.0346499i
\(825\) 3.31250e8 0.589922
\(826\) −7.47913e8 + 2.65657e8i −1.32712 + 0.471391i
\(827\) 2.64980e7i 0.0468486i −0.999726 0.0234243i \(-0.992543\pi\)
0.999726 0.0234243i \(-0.00745687\pi\)
\(828\) −2.34619e8 2.88597e8i −0.413306 0.508394i
\(829\) −5.15025e8 −0.903992 −0.451996 0.892020i \(-0.649288\pi\)
−0.451996 + 0.892020i \(0.649288\pi\)
\(830\) −2.47573e8 6.97001e8i −0.432981 1.21899i
\(831\) 3.22682e8i 0.562305i
\(832\) 2.63939e7 + 5.10725e7i 0.0458282 + 0.0886782i
\(833\) −1.03628e8 −0.179285
\(834\) 5.43456e8 1.93034e8i 0.936841 0.332764i
\(835\) 2.42622e6i 0.00416746i
\(836\) 7.29460e7 5.93024e7i 0.124848 0.101497i
\(837\) −8.51986e8 −1.45297
\(838\) 3.43247e8 + 9.66354e8i 0.583277 + 1.64212i
\(839\) 6.99663e8i 1.18468i −0.805686 0.592342i \(-0.798203\pi\)
0.805686 0.592342i \(-0.201797\pi\)
\(840\) 2.32514e8 3.81889e8i 0.392294 0.644317i
\(841\) −4.22967e8 −0.711081
\(842\) −1.04655e9 + 3.71732e8i −1.75317 + 0.622721i
\(843\) 3.73720e7i 0.0623826i
\(844\) −1.90826e8 2.34729e8i −0.317403 0.390427i
\(845\) 9.61785e8 1.59407
\(846\) −1.64688e8 4.63650e8i −0.271988 0.765737i
\(847\) 2.73864e8i 0.450696i
\(848\) −1.13389e8 + 5.43694e8i −0.185944 + 0.891594i
\(849\) −2.02969e8 −0.331670
\(850\) 7.74845e8 2.75223e8i 1.26171 0.448155i
\(851\) 5.40945e8i 0.877737i
\(852\) 9.48989e7 7.71493e7i 0.153441 0.124742i
\(853\) −9.64213e8 −1.55355 −0.776776 0.629777i \(-0.783146\pi\)
−0.776776 + 0.629777i \(0.783146\pi\)
\(854\) −2.30311e8 6.48403e8i −0.369778 1.04105i
\(855\) 1.66465e8i 0.266332i
\(856\) 5.97832e8 + 3.63991e8i 0.953142 + 0.580322i
\(857\) −2.61569e7 −0.0415570 −0.0207785 0.999784i \(-0.506614\pi\)
−0.0207785 + 0.999784i \(0.506614\pi\)
\(858\) 2.20091e7 7.81758e6i 0.0348450 0.0123769i
\(859\) 9.37229e8i 1.47865i 0.673347 + 0.739326i \(0.264856\pi\)
−0.673347 + 0.739326i \(0.735144\pi\)
\(860\) 4.09444e8 + 5.03644e8i 0.643724 + 0.791823i
\(861\) 1.32056e8 0.206895
\(862\) −1.44216e8 4.06017e8i −0.225161 0.633902i
\(863\) 1.49852e8i 0.233147i −0.993182 0.116574i \(-0.962809\pi\)
0.993182 0.116574i \(-0.0371911\pi\)
\(864\) 5.80906e8 7.93123e7i 0.900668 0.122970i
\(865\) 4.31540e8 0.666765
\(866\) 1.51161e8 5.36920e7i 0.232748 0.0826714i
\(867\) 1.00884e8i 0.154797i
\(868\) 7.19431e8 5.84872e8i 1.10010 0.894337i
\(869\) −6.96711e8 −1.06168
\(870\) −1.00754e8 2.83657e8i −0.153005 0.430760i
\(871\) 7.88526e7i 0.119333i
\(872\) 1.01933e8 1.67419e8i 0.153733 0.252497i
\(873\) 8.33513e8 1.25277
\(874\) 1.31155e8 4.65861e7i 0.196450 0.0697785i
\(875\) 5.66853e8i 0.846148i
\(876\) 1.31081e8 + 1.61238e8i 0.194996 + 0.239858i
\(877\) −3.76755e7 −0.0558547 −0.0279274 0.999610i \(-0.508891\pi\)
−0.0279274 + 0.999610i \(0.508891\pi\)
\(878\) −1.13182e8 3.18644e8i −0.167221 0.470784i
\(879\) 1.31653e8i 0.193849i
\(880\) −7.53342e8 1.57111e8i −1.10546 0.230546i
\(881\) −4.58408e8 −0.670386 −0.335193 0.942150i \(-0.608801\pi\)
−0.335193 + 0.942150i \(0.608801\pi\)
\(882\) −9.94040e7 + 3.53081e7i −0.144877 + 0.0514599i
\(883\) 2.11933e8i 0.307834i 0.988084 + 0.153917i \(0.0491889\pi\)
−0.988084 + 0.153917i \(0.950811\pi\)
\(884\) 4.49873e7 3.65730e7i 0.0651228 0.0529425i
\(885\) 9.35980e8 1.35032
\(886\) 3.44190e8 + 9.69011e8i 0.494877 + 1.39324i
\(887\) 2.52427e8i 0.361713i 0.983509 + 0.180857i \(0.0578870\pi\)
−0.983509 + 0.180857i \(0.942113\pi\)
\(888\) 3.05136e8 + 1.85783e8i 0.435767 + 0.265318i
\(889\) −5.63503e8 −0.802031
\(890\) 1.37381e9 4.87976e8i 1.94876 0.692194i
\(891\) 1.19497e8i 0.168937i
\(892\) −6.46493e8 7.95230e8i −0.910897 1.12046i
\(893\) 1.84126e8 0.258559
\(894\) 1.04980e8 + 2.95555e8i 0.146925 + 0.413643i
\(895\) 7.06954e7i 0.0986103i
\(896\) −4.36081e8 + 4.65754e8i −0.606238 + 0.647489i
\(897\) 3.45793e7 0.0479114
\(898\) −5.92382e8 + 2.10413e8i −0.818036 + 0.290565i
\(899\) 6.24234e8i 0.859149i
\(900\) 6.49486e8 5.28008e8i 0.890927 0.724291i
\(901\) 5.60112e8 0.765774
\(902\) −7.60776e7 2.14184e8i −0.103666 0.291855i
\(903\) 2.18636e8i 0.296933i
\(904\) 4.15169e8 6.81889e8i 0.561979 0.923014i
\(905\) −1.30338e9 −1.75843
\(906\) −3.87561e8 + 1.37661e8i −0.521142 + 0.185108i
\(907\) 1.27485e9i 1.70859i 0.519789 + 0.854294i \(0.326010\pi\)
−0.519789 + 0.854294i \(0.673990\pi\)
\(908\) 5.83130e8 + 7.17289e8i 0.778947 + 0.958157i
\(909\) −4.86164e8 −0.647278
\(910\) −3.59576e7 1.01233e8i −0.0477163 0.134337i
\(911\) 9.61222e7i 0.127136i 0.997978 + 0.0635680i \(0.0202480\pi\)
−0.997978 + 0.0635680i \(0.979752\pi\)
\(912\) −1.87658e7 + 8.99816e7i −0.0247391 + 0.118623i
\(913\) 4.28833e8 0.563476
\(914\) 2.65979e7 9.44753e6i 0.0348345 0.0123731i
\(915\) 8.11448e8i 1.05925i
\(916\) −1.06036e9 + 8.62035e8i −1.37964 + 1.12160i
\(917\) 6.88681e7 0.0893121
\(918\) −1.97907e8 5.57174e8i −0.255819 0.720216i
\(919\) 1.40009e9i 1.80389i −0.431849 0.901946i \(-0.642139\pi\)
0.431849 0.901946i \(-0.357861\pi\)
\(920\) −9.73147e8 5.92502e8i −1.24973 0.760898i
\(921\) 6.18803e8 0.792088
\(922\) −1.01804e9 + 3.61604e8i −1.29888 + 0.461361i
\(923\) 2.93865e7i 0.0373716i
\(924\) 1.63516e8 + 2.01136e8i 0.207274 + 0.254961i
\(925\) 1.21739e9 1.53818
\(926\) 4.11647e8 + 1.15892e9i 0.518432 + 1.45956i
\(927\) 3.82688e7i 0.0480403i
\(928\) 5.81107e7 + 4.25620e8i 0.0727130 + 0.532571i
\(929\) −9.90092e8 −1.23489 −0.617445 0.786614i \(-0.711832\pi\)
−0.617445 + 0.786614i \(0.711832\pi\)
\(930\) −1.03033e9 + 3.65971e8i −1.28094 + 0.454985i
\(931\) 3.94755e7i 0.0489191i
\(932\) −1.10042e9 + 8.94604e8i −1.35929 + 1.10505i
\(933\) −4.32990e8 −0.533130
\(934\) 1.25906e8 + 3.54467e8i 0.154527 + 0.435046i
\(935\) 7.76090e8i 0.949461i
\(936\) 3.06923e7 5.04102e7i 0.0374285 0.0614739i
\(937\) 6.25355e8 0.760165 0.380082 0.924953i \(-0.375896\pi\)
0.380082 + 0.924953i \(0.375896\pi\)
\(938\) −8.24658e8 + 2.92917e8i −0.999230 + 0.354924i
\(939\) 7.08303e8i 0.855505i
\(940\) −9.50770e8 1.16951e9i −1.14470 1.40806i
\(941\) −8.66106e8 −1.03945 −0.519724 0.854335i \(-0.673965\pi\)
−0.519724 + 0.854335i \(0.673965\pi\)
\(942\) −1.28681e8 3.62280e8i −0.153944 0.433402i
\(943\) 3.36512e8i 0.401296i
\(944\) −1.30756e9 2.72693e8i −1.55433 0.324159i
\(945\) −1.09560e9 −1.29824
\(946\) −3.54608e8 + 1.25956e8i −0.418867 + 0.148780i
\(947\) 1.05653e9i 1.24403i 0.783006 + 0.622014i \(0.213685\pi\)
−0.783006 + 0.622014i \(0.786315\pi\)
\(948\) 5.28572e8 4.29710e8i 0.620411 0.504371i
\(949\) 4.99291e7 0.0584191
\(950\) 1.04842e8 + 2.95165e8i 0.122282 + 0.344265i
\(951\) 5.54595e8i 0.644814i
\(952\) 5.49605e8 + 3.34628e8i 0.637000 + 0.387839i
\(953\) 1.53579e9 1.77441 0.887205 0.461376i \(-0.152644\pi\)
0.887205 + 0.461376i \(0.152644\pi\)
\(954\) 5.37279e8 1.90840e8i 0.618807 0.219799i
\(955\) 4.22848e8i 0.485483i
\(956\) −7.88748e8 9.70213e8i −0.902744 1.11044i
\(957\) 1.74521e8 0.199118
\(958\) 2.82494e8 + 7.95314e8i 0.321301 + 0.904570i
\(959\) 1.49047e9i 1.68993i
\(960\) 6.68437e8 3.45443e8i 0.755522 0.390448i
\(961\) −1.37991e9 −1.55482
\(962\) 8.08867e7 2.87308e7i 0.0908556 0.0322717i
\(963\) 7.18541e8i 0.804587i
\(964\) 1.13641e9 9.23861e8i 1.26854 1.03128i
\(965\) −2.20707e9 −2.45604
\(966\) 1.28453e8 + 3.61638e8i 0.142499 + 0.401183i
\(967\) 9.05532e8i 1.00144i −0.865610 0.500719i \(-0.833069\pi\)
0.865610 0.500719i \(-0.166931\pi\)
\(968\) −2.39678e8 + 3.93655e8i −0.264242 + 0.434000i
\(969\) 9.26987e7 0.101883
\(970\) 2.40601e9 8.54609e8i 2.63622 0.936380i
\(971\) 4.03780e8i 0.441049i −0.975381 0.220524i \(-0.929223\pi\)
0.975381 0.220524i \(-0.0707769\pi\)
\(972\) −6.00292e8 7.38400e8i −0.653678 0.804068i
\(973\) 1.53793e9 1.66955
\(974\) −1.95293e8 5.49816e8i −0.211354 0.595032i
\(975\) 7.78205e7i 0.0839615i
\(976\) 2.36411e8 1.13358e9i 0.254284 1.21928i
\(977\) 6.46229e8 0.692951 0.346475 0.938059i \(-0.387378\pi\)
0.346475 + 0.938059i \(0.387378\pi\)
\(978\) −1.81398e8 + 6.44321e7i −0.193917 + 0.0688788i
\(979\) 8.45244e8i 0.900812i
\(980\) −2.50737e8 + 2.03840e8i −0.266403 + 0.216576i
\(981\) −2.01223e8 −0.213143
\(982\) 4.73235e8 + 1.33231e9i 0.499738 + 1.40693i
\(983\) 1.04005e9i 1.09495i −0.836822 0.547475i \(-0.815589\pi\)
0.836822 0.547475i \(-0.184411\pi\)
\(984\) 1.89820e8 + 1.15572e8i 0.199230 + 0.121302i
\(985\) 1.93916e8 0.202911
\(986\) 4.08231e8 1.45003e8i 0.425868 0.151267i
\(987\) 5.07694e8i 0.528021i
\(988\) 1.39319e7 + 1.71372e7i 0.0144457 + 0.0177692i
\(989\) −5.57138e8 −0.575936
\(990\) 2.64428e8 + 7.44453e8i 0.272522 + 0.767241i
\(991\) 1.59559e9i 1.63946i −0.572750 0.819730i \(-0.694123\pi\)
0.572750 0.819730i \(-0.305877\pi\)
\(992\) 1.54598e9 2.11076e8i 1.58369 0.216224i
\(993\) 3.46456e8 0.353835
\(994\) 3.07330e8 1.09163e8i 0.312929 0.111152i
\(995\) 2.63281e9i 2.67270i
\(996\) −3.25341e8 + 2.64491e8i −0.329277 + 0.267690i
\(997\) 3.15622e8 0.318480 0.159240 0.987240i \(-0.449096\pi\)
0.159240 + 0.987240i \(0.449096\pi\)
\(998\) −1.09694e8 3.08826e8i −0.110355 0.310686i
\(999\) 8.75401e8i 0.878032i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 76.7.b.a.39.8 yes 54
4.3 odd 2 inner 76.7.b.a.39.7 54
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.7.b.a.39.7 54 4.3 odd 2 inner
76.7.b.a.39.8 yes 54 1.1 even 1 trivial