Properties

Label 147.7.f.d.31.4
Level $147$
Weight $7$
Character 147.31
Analytic conductor $33.818$
Analytic rank $0$
Dimension $8$
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] = [147,7,Mod(19,147)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(147, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("147.19");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 147.f (of order \(6\), degree \(2\), not 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: \(33.8179502921\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 212x^{6} + 473x^{5} + 39800x^{4} + 36821x^{3} + 985651x^{2} - 601290x + 21068100 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3\cdot 7^{2} \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.4
Root \(-6.30797 - 10.9257i\) of defining polynomial
Character \(\chi\) \(=\) 147.31
Dual form 147.7.f.d.19.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(5.80797 + 10.0597i) q^{2} +(13.5000 + 7.79423i) q^{3} +(-35.4650 + 61.4271i) q^{4} +(165.302 - 95.4373i) q^{5} +181.074i q^{6} -80.4975 q^{8} +(121.500 + 210.444i) q^{9} +O(q^{10})\) \(q+(5.80797 + 10.0597i) q^{2} +(13.5000 + 7.79423i) q^{3} +(-35.4650 + 61.4271i) q^{4} +(165.302 - 95.4373i) q^{5} +181.074i q^{6} -80.4975 q^{8} +(121.500 + 210.444i) q^{9} +(1920.14 + 1108.59i) q^{10} +(1027.55 - 1779.77i) q^{11} +(-957.554 + 552.844i) q^{12} -3059.97i q^{13} +2975.44 q^{15} +(1802.23 + 3121.55i) q^{16} +(-2468.38 - 1425.12i) q^{17} +(-1411.34 + 2444.51i) q^{18} +(3420.04 - 1974.56i) q^{19} +13538.7i q^{20} +23872.0 q^{22} +(-330.272 - 572.047i) q^{23} +(-1086.72 - 627.416i) q^{24} +(10404.0 - 18020.3i) q^{25} +(30782.3 - 17772.2i) q^{26} +3788.00i q^{27} -9282.66 q^{29} +(17281.3 + 29932.0i) q^{30} +(-2426.36 - 1400.86i) q^{31} +(-23510.5 + 40721.4i) q^{32} +(27743.9 - 16018.0i) q^{33} -33108.2i q^{34} -17236.0 q^{36} +(18466.2 + 31984.5i) q^{37} +(39727.0 + 22936.4i) q^{38} +(23850.1 - 41309.5i) q^{39} +(-13306.4 + 7682.46i) q^{40} +67941.3i q^{41} +12336.3 q^{43} +(72884.2 + 126239. i) q^{44} +(40168.4 + 23191.3i) q^{45} +(3836.41 - 6644.86i) q^{46} +(-127836. + 73806.3i) q^{47} +56188.0i q^{48} +241705. q^{50} +(-22215.4 - 38478.3i) q^{51} +(187965. + 108522. i) q^{52} +(-109818. + 190210. i) q^{53} +(-38106.1 + 22000.6i) q^{54} -392267. i q^{55} +61560.8 q^{57} +(-53913.4 - 93380.8i) q^{58} +(-166725. - 96258.8i) q^{59} +(-105524. + 182773. i) q^{60} +(-288244. + 166418. i) q^{61} -32544.5i q^{62} -315508. q^{64} +(-292035. - 505819. i) q^{65} +(322271. + 186063. i) q^{66} +(-174592. + 302402. i) q^{67} +(175082. - 101084. i) q^{68} -10296.9i q^{69} +305650. q^{71} +(-9780.45 - 16940.2i) q^{72} +(204814. + 118249. i) q^{73} +(-214503. + 371529. i) q^{74} +(280909. - 162183. i) q^{75} +280111. i q^{76} +554082. q^{78} +(293218. + 507869. i) q^{79} +(595825. + 344000. i) q^{80} +(-29524.5 + 51137.9i) q^{81} +(-683468. + 394601. i) q^{82} -106377. i q^{83} -544039. q^{85} +(71648.8 + 124099. i) q^{86} +(-125316. - 72351.2i) q^{87} +(-82715.4 + 143267. i) q^{88} +(-11308.5 + 6528.95i) q^{89} +538776. i q^{90} +46852.3 q^{92} +(-21837.2 - 37823.2i) q^{93} +(-1.48494e6 - 857329. i) q^{94} +(376894. - 652799. i) q^{95} +(-634784. + 366493. i) q^{96} -205209. i q^{97} +499390. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 5 q^{2} + 108 q^{3} - 173 q^{4} + 294 q^{5} + 3326 q^{8} + 972 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 5 q^{2} + 108 q^{3} - 173 q^{4} + 294 q^{5} + 3326 q^{8} + 972 q^{9} + 3411 q^{10} - 314 q^{11} - 4671 q^{12} + 5292 q^{15} - 12721 q^{16} + 5532 q^{17} + 1215 q^{18} + 18234 q^{19} + 86106 q^{22} + 3928 q^{23} + 44901 q^{24} - 17038 q^{25} - 12366 q^{26} - 8300 q^{29} + 30699 q^{30} + 89508 q^{31} - 186207 q^{32} - 8478 q^{33} - 84078 q^{36} + 64706 q^{37} + 77136 q^{38} + 29106 q^{39} - 221823 q^{40} + 45740 q^{43} + 92529 q^{44} + 71442 q^{45} - 111504 q^{46} - 483276 q^{47} + 967216 q^{50} + 49788 q^{51} + 1673988 q^{52} - 540974 q^{53} + 32805 q^{54} + 328212 q^{57} + 539799 q^{58} + 181770 q^{59} - 146367 q^{60} - 418224 q^{61} + 2378626 q^{64} - 414204 q^{65} + 1162431 q^{66} - 1158902 q^{67} + 821250 q^{68} + 1442344 q^{71} + 404109 q^{72} + 378666 q^{73} - 432940 q^{74} - 460026 q^{75} - 222588 q^{78} + 611452 q^{79} + 2094945 q^{80} - 236196 q^{81} + 1561266 q^{82} - 275112 q^{85} + 816224 q^{86} - 112050 q^{87} - 366441 q^{88} + 989196 q^{89} + 678720 q^{92} + 805572 q^{93} + 716148 q^{94} - 591792 q^{95} - 5027589 q^{96} - 152604 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.80797 + 10.0597i 0.725996 + 1.25746i 0.958563 + 0.284881i \(0.0919542\pi\)
−0.232567 + 0.972580i \(0.574712\pi\)
\(3\) 13.5000 + 7.79423i 0.500000 + 0.288675i
\(4\) −35.4650 + 61.4271i −0.554140 + 0.959799i
\(5\) 165.302 95.4373i 1.32242 0.763498i 0.338304 0.941037i \(-0.390147\pi\)
0.984114 + 0.177539i \(0.0568136\pi\)
\(6\) 181.074i 0.838308i
\(7\) 0 0
\(8\) −80.4975 −0.157222
\(9\) 121.500 + 210.444i 0.166667 + 0.288675i
\(10\) 1920.14 + 1108.59i 1.92014 + 1.10859i
\(11\) 1027.55 1779.77i 0.772015 1.33717i −0.164442 0.986387i \(-0.552582\pi\)
0.936457 0.350783i \(-0.114084\pi\)
\(12\) −957.554 + 552.844i −0.554140 + 0.319933i
\(13\) 3059.97i 1.39279i −0.717657 0.696396i \(-0.754786\pi\)
0.717657 0.696396i \(-0.245214\pi\)
\(14\) 0 0
\(15\) 2975.44 0.881612
\(16\) 1802.23 + 3121.55i 0.439998 + 0.762098i
\(17\) −2468.38 1425.12i −0.502419 0.290072i 0.227293 0.973826i \(-0.427012\pi\)
−0.729712 + 0.683755i \(0.760346\pi\)
\(18\) −1411.34 + 2444.51i −0.241999 + 0.419154i
\(19\) 3420.04 1974.56i 0.498622 0.287879i −0.229523 0.973303i \(-0.573716\pi\)
0.728144 + 0.685424i \(0.240383\pi\)
\(20\) 13538.7i 1.69234i
\(21\) 0 0
\(22\) 23872.0 2.24192
\(23\) −330.272 572.047i −0.0271449 0.0470163i 0.852134 0.523324i \(-0.175308\pi\)
−0.879279 + 0.476308i \(0.841975\pi\)
\(24\) −1086.72 627.416i −0.0786109 0.0453860i
\(25\) 10404.0 18020.3i 0.665859 1.15330i
\(26\) 30782.3 17772.2i 1.75138 1.01116i
\(27\) 3788.00i 0.192450i
\(28\) 0 0
\(29\) −9282.66 −0.380609 −0.190304 0.981725i \(-0.560947\pi\)
−0.190304 + 0.981725i \(0.560947\pi\)
\(30\) 17281.3 + 29932.0i 0.640046 + 1.10859i
\(31\) −2426.36 1400.86i −0.0814460 0.0470229i 0.458724 0.888579i \(-0.348307\pi\)
−0.540170 + 0.841556i \(0.681640\pi\)
\(32\) −23510.5 + 40721.4i −0.717484 + 1.24272i
\(33\) 27743.9 16018.0i 0.772015 0.445723i
\(34\) 33108.2i 0.842363i
\(35\) 0 0
\(36\) −17236.0 −0.369427
\(37\) 18466.2 + 31984.5i 0.364563 + 0.631442i 0.988706 0.149868i \(-0.0478849\pi\)
−0.624143 + 0.781310i \(0.714552\pi\)
\(38\) 39727.0 + 22936.4i 0.723994 + 0.417998i
\(39\) 23850.1 41309.5i 0.402065 0.696396i
\(40\) −13306.4 + 7682.46i −0.207913 + 0.120039i
\(41\) 67941.3i 0.985785i 0.870090 + 0.492892i \(0.164060\pi\)
−0.870090 + 0.492892i \(0.835940\pi\)
\(42\) 0 0
\(43\) 12336.3 0.155160 0.0775799 0.996986i \(-0.475281\pi\)
0.0775799 + 0.996986i \(0.475281\pi\)
\(44\) 72884.2 + 126239.i 0.855609 + 1.48196i
\(45\) 40168.4 + 23191.3i 0.440806 + 0.254499i
\(46\) 3836.41 6644.86i 0.0394141 0.0682673i
\(47\) −127836. + 73806.3i −1.23129 + 0.710886i −0.967299 0.253639i \(-0.918372\pi\)
−0.263991 + 0.964525i \(0.585039\pi\)
\(48\) 56188.0i 0.508066i
\(49\) 0 0
\(50\) 241705. 1.93364
\(51\) −22215.4 38478.3i −0.167473 0.290072i
\(52\) 187965. + 108522.i 1.33680 + 0.771802i
\(53\) −109818. + 190210.i −0.737641 + 1.27763i 0.215914 + 0.976412i \(0.430727\pi\)
−0.953555 + 0.301219i \(0.902607\pi\)
\(54\) −38106.1 + 22000.6i −0.241999 + 0.139718i
\(55\) 392267.i 2.35773i
\(56\) 0 0
\(57\) 61560.8 0.332414
\(58\) −53913.4 93380.8i −0.276320 0.478601i
\(59\) −166725. 96258.8i −0.811792 0.468689i 0.0357855 0.999359i \(-0.488607\pi\)
−0.847578 + 0.530671i \(0.821940\pi\)
\(60\) −105524. + 182773.i −0.488536 + 0.846170i
\(61\) −288244. + 166418.i −1.26990 + 0.733180i −0.974970 0.222338i \(-0.928631\pi\)
−0.294935 + 0.955517i \(0.595298\pi\)
\(62\) 32544.5i 0.136554i
\(63\) 0 0
\(64\) −315508. −1.20357
\(65\) −292035. 505819.i −1.06339 1.84185i
\(66\) 322271. + 186063.i 1.12096 + 0.647186i
\(67\) −174592. + 302402.i −0.580496 + 1.00545i 0.414924 + 0.909856i \(0.363808\pi\)
−0.995420 + 0.0955931i \(0.969525\pi\)
\(68\) 175082. 101084.i 0.556821 0.321481i
\(69\) 10296.9i 0.0313442i
\(70\) 0 0
\(71\) 305650. 0.853984 0.426992 0.904255i \(-0.359573\pi\)
0.426992 + 0.904255i \(0.359573\pi\)
\(72\) −9780.45 16940.2i −0.0262036 0.0453860i
\(73\) 204814. + 118249.i 0.526490 + 0.303969i 0.739586 0.673062i \(-0.235021\pi\)
−0.213096 + 0.977031i \(0.568355\pi\)
\(74\) −214503. + 371529.i −0.529343 + 0.916849i
\(75\) 280909. 162183.i 0.665859 0.384434i
\(76\) 280111.i 0.638102i
\(77\) 0 0
\(78\) 554082. 1.16759
\(79\) 293218. + 507869.i 0.594716 + 1.03008i 0.993587 + 0.113072i \(0.0360690\pi\)
−0.398871 + 0.917007i \(0.630598\pi\)
\(80\) 595825. + 344000.i 1.16372 + 0.671875i
\(81\) −29524.5 + 51137.9i −0.0555556 + 0.0962250i
\(82\) −683468. + 394601.i −1.23959 + 0.715675i
\(83\) 106377.i 0.186044i −0.995664 0.0930218i \(-0.970347\pi\)
0.995664 0.0930218i \(-0.0296526\pi\)
\(84\) 0 0
\(85\) −544039. −0.885876
\(86\) 71648.8 + 124099.i 0.112645 + 0.195108i
\(87\) −125316. 72351.2i −0.190304 0.109872i
\(88\) −82715.4 + 143267.i −0.121378 + 0.210232i
\(89\) −11308.5 + 6528.95i −0.0160411 + 0.00926134i −0.507999 0.861358i \(-0.669615\pi\)
0.491958 + 0.870619i \(0.336281\pi\)
\(90\) 538776.i 0.739062i
\(91\) 0 0
\(92\) 46852.3 0.0601682
\(93\) −21837.2 37823.2i −0.0271487 0.0470229i
\(94\) −1.48494e6 857329.i −1.78782 1.03220i
\(95\) 376894. 652799.i 0.439591 0.761393i
\(96\) −634784. + 366493.i −0.717484 + 0.414240i
\(97\) 205209.i 0.224844i −0.993661 0.112422i \(-0.964139\pi\)
0.993661 0.112422i \(-0.0358609\pi\)
\(98\) 0 0
\(99\) 499390. 0.514677
\(100\) 737958. + 1.27818e6i 0.737958 + 1.27818i
\(101\) 1.21339e6 + 700549.i 1.17770 + 0.679946i 0.955482 0.295050i \(-0.0953364\pi\)
0.222220 + 0.974997i \(0.428670\pi\)
\(102\) 258053. 446961.i 0.243169 0.421182i
\(103\) −448291. + 258821.i −0.410250 + 0.236858i −0.690897 0.722953i \(-0.742784\pi\)
0.280647 + 0.959811i \(0.409451\pi\)
\(104\) 246320.i 0.218977i
\(105\) 0 0
\(106\) −2.55127e6 −2.14210
\(107\) −323372. 560097.i −0.263968 0.457206i 0.703325 0.710869i \(-0.251698\pi\)
−0.967293 + 0.253663i \(0.918365\pi\)
\(108\) −232686. 134341.i −0.184713 0.106644i
\(109\) 343631. 595186.i 0.265346 0.459593i −0.702308 0.711873i \(-0.747847\pi\)
0.967654 + 0.252280i \(0.0811805\pi\)
\(110\) 3.94609e6 2.27827e6i 2.96475 1.71170i
\(111\) 575720.i 0.420962i
\(112\) 0 0
\(113\) 2.11668e6 1.46697 0.733483 0.679708i \(-0.237893\pi\)
0.733483 + 0.679708i \(0.237893\pi\)
\(114\) 357543. + 619283.i 0.241331 + 0.417998i
\(115\) −109189. 63040.4i −0.0717937 0.0414501i
\(116\) 329209. 570207.i 0.210910 0.365308i
\(117\) 643952. 371786.i 0.402065 0.232132i
\(118\) 2.23627e6i 1.36106i
\(119\) 0 0
\(120\) −239516. −0.138609
\(121\) −1.22595e6 2.12340e6i −0.692015 1.19860i
\(122\) −3.34823e6 1.93310e6i −1.84389 1.06457i
\(123\) −529550. + 917207.i −0.284571 + 0.492892i
\(124\) 172101. 99362.7i 0.0902649 0.0521145i
\(125\) 989318.i 0.506531i
\(126\) 0 0
\(127\) 3.29012e6 1.60620 0.803102 0.595841i \(-0.203181\pi\)
0.803102 + 0.595841i \(0.203181\pi\)
\(128\) −327785. 567740.i −0.156300 0.270720i
\(129\) 166540. + 96151.9i 0.0775799 + 0.0447908i
\(130\) 3.39226e6 5.87556e6i 1.54404 2.67436i
\(131\) −193424. + 111674.i −0.0860394 + 0.0496748i −0.542402 0.840119i \(-0.682485\pi\)
0.456363 + 0.889794i \(0.349152\pi\)
\(132\) 2.27230e6i 0.987972i
\(133\) 0 0
\(134\) −4.05609e6 −1.68575
\(135\) 361516. + 626164.i 0.146935 + 0.254499i
\(136\) 198699. + 114719.i 0.0789912 + 0.0456056i
\(137\) 1.58525e6 2.74573e6i 0.616504 1.06782i −0.373615 0.927584i \(-0.621882\pi\)
0.990119 0.140232i \(-0.0447849\pi\)
\(138\) 103583. 59803.8i 0.0394141 0.0227558i
\(139\) 774740.i 0.288477i −0.989543 0.144239i \(-0.953927\pi\)
0.989543 0.144239i \(-0.0460733\pi\)
\(140\) 0 0
\(141\) −2.30105e6 −0.820860
\(142\) 1.77521e6 + 3.07475e6i 0.619989 + 1.07385i
\(143\) −5.44604e6 3.14427e6i −1.86240 1.07526i
\(144\) −437942. + 758538.i −0.146666 + 0.254033i
\(145\) −1.53444e6 + 885912.i −0.503323 + 0.290594i
\(146\) 2.74715e6i 0.882722i
\(147\) 0 0
\(148\) −2.61962e6 −0.808077
\(149\) −1.75461e6 3.03907e6i −0.530421 0.918716i −0.999370 0.0354908i \(-0.988701\pi\)
0.468949 0.883225i \(-0.344633\pi\)
\(150\) 3.26302e6 + 1.88391e6i 0.966821 + 0.558194i
\(151\) −3.22601e6 + 5.58761e6i −0.936989 + 1.62291i −0.165940 + 0.986136i \(0.553066\pi\)
−0.771049 + 0.636776i \(0.780268\pi\)
\(152\) −275305. + 158948.i −0.0783942 + 0.0452609i
\(153\) 692609.i 0.193381i
\(154\) 0 0
\(155\) −534776. −0.143607
\(156\) 1.69168e6 + 2.93008e6i 0.445600 + 0.771802i
\(157\) 4.05557e6 + 2.34148e6i 1.04798 + 0.605051i 0.922083 0.386992i \(-0.126486\pi\)
0.125896 + 0.992043i \(0.459819\pi\)
\(158\) −3.40600e6 + 5.89937e6i −0.863523 + 1.49567i
\(159\) −2.96508e6 + 1.71189e6i −0.737641 + 0.425877i
\(160\) 8.97512e6i 2.19119i
\(161\) 0 0
\(162\) −685909. −0.161332
\(163\) −2.59116e6 4.48803e6i −0.598318 1.03632i −0.993069 0.117529i \(-0.962503\pi\)
0.394752 0.918788i \(-0.370831\pi\)
\(164\) −4.17344e6 2.40953e6i −0.946155 0.546263i
\(165\) 3.05742e6 5.29560e6i 0.680617 1.17886i
\(166\) 1.07012e6 617836.i 0.233943 0.135067i
\(167\) 1.56630e6i 0.336298i −0.985762 0.168149i \(-0.946221\pi\)
0.985762 0.168149i \(-0.0537790\pi\)
\(168\) 0 0
\(169\) −4.53658e6 −0.939871
\(170\) −3.15976e6 5.47286e6i −0.643143 1.11396i
\(171\) 831071. + 479819.i 0.166207 + 0.0959598i
\(172\) −437506. + 757783.i −0.0859803 + 0.148922i
\(173\) 1.07788e6 622312.i 0.208176 0.120190i −0.392287 0.919843i \(-0.628316\pi\)
0.600463 + 0.799652i \(0.294983\pi\)
\(174\) 1.68085e6i 0.319067i
\(175\) 0 0
\(176\) 7.40754e6 1.35874
\(177\) −1.50053e6 2.59899e6i −0.270597 0.468689i
\(178\) −131359. 75839.9i −0.0232916 0.0134474i
\(179\) −1.12800e6 + 1.95375e6i −0.196675 + 0.340651i −0.947448 0.319909i \(-0.896348\pi\)
0.750773 + 0.660560i \(0.229681\pi\)
\(180\) −2.84914e6 + 1.64495e6i −0.488536 + 0.282057i
\(181\) 7.97198e6i 1.34441i −0.740367 0.672203i \(-0.765348\pi\)
0.740367 0.672203i \(-0.234652\pi\)
\(182\) 0 0
\(183\) −5.18839e6 −0.846603
\(184\) 26586.1 + 46048.4i 0.00426776 + 0.00739199i
\(185\) 6.10502e6 + 3.52473e6i 0.964210 + 0.556687i
\(186\) 253660. 439351.i 0.0394196 0.0682768i
\(187\) −5.07278e6 + 2.92877e6i −0.775750 + 0.447879i
\(188\) 1.04701e7i 1.57572i
\(189\) 0 0
\(190\) 8.75595e6 1.27656
\(191\) −2.13087e6 3.69078e6i −0.305814 0.529685i 0.671628 0.740888i \(-0.265595\pi\)
−0.977442 + 0.211203i \(0.932262\pi\)
\(192\) −4.25935e6 2.45914e6i −0.601783 0.347440i
\(193\) 72886.7 126243.i 0.0101386 0.0175605i −0.860912 0.508755i \(-0.830106\pi\)
0.871050 + 0.491194i \(0.163439\pi\)
\(194\) 2.06434e6 1.19185e6i 0.282733 0.163236i
\(195\) 9.10474e6i 1.22790i
\(196\) 0 0
\(197\) −7.21313e6 −0.943463 −0.471732 0.881742i \(-0.656371\pi\)
−0.471732 + 0.881742i \(0.656371\pi\)
\(198\) 2.90044e6 + 5.02371e6i 0.373653 + 0.647186i
\(199\) −1.52836e6 882399.i −0.193940 0.111971i 0.399886 0.916565i \(-0.369050\pi\)
−0.593826 + 0.804594i \(0.702383\pi\)
\(200\) −837500. + 1.45059e6i −0.104687 + 0.181324i
\(201\) −4.71398e6 + 2.72162e6i −0.580496 + 0.335150i
\(202\) 1.62751e7i 1.97455i
\(203\) 0 0
\(204\) 3.15148e6 0.371214
\(205\) 6.48413e6 + 1.12308e7i 0.752645 + 1.30362i
\(206\) −5.20732e6 3.00645e6i −0.595680 0.343916i
\(207\) 80256.0 139007.i 0.00904829 0.0156721i
\(208\) 9.55185e6 5.51476e6i 1.06144 0.612825i
\(209\) 8.11587e6i 0.888989i
\(210\) 0 0
\(211\) 1.37033e7 1.45874 0.729369 0.684121i \(-0.239814\pi\)
0.729369 + 0.684121i \(0.239814\pi\)
\(212\) −7.78936e6 1.34916e7i −0.817512 1.41597i
\(213\) 4.12628e6 + 2.38231e6i 0.426992 + 0.246524i
\(214\) 3.75627e6 6.50605e6i 0.383279 0.663859i
\(215\) 2.03922e6 1.17734e6i 0.205186 0.118464i
\(216\) 304924.i 0.0302573i
\(217\) 0 0
\(218\) 7.98318e6 0.770560
\(219\) 1.84332e6 + 3.19273e6i 0.175497 + 0.303969i
\(220\) 2.40958e7 + 1.39117e7i 2.26294 + 1.30651i
\(221\) −4.36082e6 + 7.55317e6i −0.404010 + 0.699765i
\(222\) −5.79157e6 + 3.34376e6i −0.529343 + 0.305616i
\(223\) 2.15029e7i 1.93902i 0.245055 + 0.969509i \(0.421194\pi\)
−0.245055 + 0.969509i \(0.578806\pi\)
\(224\) 0 0
\(225\) 5.05636e6 0.443906
\(226\) 1.22936e7 + 2.12932e7i 1.06501 + 1.84465i
\(227\) −3.40461e6 1.96565e6i −0.291065 0.168046i 0.347357 0.937733i \(-0.387079\pi\)
−0.638422 + 0.769687i \(0.720412\pi\)
\(228\) −2.18325e6 + 3.78150e6i −0.184204 + 0.319051i
\(229\) −486988. + 281163.i −0.0405520 + 0.0234127i −0.520139 0.854082i \(-0.674120\pi\)
0.479587 + 0.877494i \(0.340787\pi\)
\(230\) 1.46455e6i 0.120370i
\(231\) 0 0
\(232\) 747232. 0.0598400
\(233\) 8.16657e6 + 1.41449e7i 0.645612 + 1.11823i 0.984160 + 0.177284i \(0.0567310\pi\)
−0.338548 + 0.940949i \(0.609936\pi\)
\(234\) 7.48010e6 + 4.31864e6i 0.583794 + 0.337054i
\(235\) −1.40877e7 + 2.44007e7i −1.08552 + 1.88018i
\(236\) 1.18258e7 6.82763e6i 0.899693 0.519438i
\(237\) 9.14164e6i 0.686719i
\(238\) 0 0
\(239\) −1.96132e7 −1.43666 −0.718331 0.695702i \(-0.755094\pi\)
−0.718331 + 0.695702i \(0.755094\pi\)
\(240\) 5.36243e6 + 9.28800e6i 0.387907 + 0.671875i
\(241\) −3.11683e6 1.79950e6i −0.222670 0.128559i 0.384516 0.923118i \(-0.374368\pi\)
−0.607186 + 0.794560i \(0.707702\pi\)
\(242\) 1.42405e7 2.46653e7i 1.00480 1.74036i
\(243\) −797162. + 460241.i −0.0555556 + 0.0320750i
\(244\) 2.36080e7i 1.62514i
\(245\) 0 0
\(246\) −1.23024e7 −0.826391
\(247\) −6.04210e6 1.04652e7i −0.400956 0.694476i
\(248\) 195316. + 112766.i 0.0128051 + 0.00739302i
\(249\) 829129. 1.43609e6i 0.0537061 0.0930218i
\(250\) 9.95223e6 5.74592e6i 0.636943 0.367739i
\(251\) 6.49855e6i 0.410956i 0.978662 + 0.205478i \(0.0658749\pi\)
−0.978662 + 0.205478i \(0.934125\pi\)
\(252\) 0 0
\(253\) −1.35749e6 −0.0838250
\(254\) 1.91089e7 + 3.30976e7i 1.16610 + 2.01974i
\(255\) −7.34452e6 4.24036e6i −0.442938 0.255730i
\(256\) −6.28871e6 + 1.08924e7i −0.374837 + 0.649236i
\(257\) −2.47506e6 + 1.42897e6i −0.145810 + 0.0841832i −0.571130 0.820860i \(-0.693495\pi\)
0.425320 + 0.905043i \(0.360161\pi\)
\(258\) 2.23379e6i 0.130072i
\(259\) 0 0
\(260\) 4.14280e7 2.35708
\(261\) −1.12784e6 1.95348e6i −0.0634348 0.109872i
\(262\) −2.24680e6 1.29719e6i −0.124928 0.0721275i
\(263\) 2.49913e6 4.32862e6i 0.137380 0.237948i −0.789124 0.614233i \(-0.789465\pi\)
0.926504 + 0.376285i \(0.122799\pi\)
\(264\) −2.23332e6 + 1.28941e6i −0.121378 + 0.0700774i
\(265\) 4.19228e7i 2.25275i
\(266\) 0 0
\(267\) −203553. −0.0106941
\(268\) −1.23838e7 2.14493e7i −0.643352 1.11432i
\(269\) 1.76842e7 + 1.02100e7i 0.908507 + 0.524527i 0.879951 0.475065i \(-0.157576\pi\)
0.0285567 + 0.999592i \(0.490909\pi\)
\(270\) −4.19934e6 + 7.27348e6i −0.213349 + 0.369531i
\(271\) −1.06885e7 + 6.17102e6i −0.537044 + 0.310062i −0.743880 0.668313i \(-0.767017\pi\)
0.206836 + 0.978376i \(0.433683\pi\)
\(272\) 1.02736e7i 0.510523i
\(273\) 0 0
\(274\) 3.68283e7 1.79032
\(275\) −2.13814e7 3.70336e7i −1.02811 1.78073i
\(276\) 632506. + 365177.i 0.0300841 + 0.0173691i
\(277\) 1.04151e7 1.80395e7i 0.490031 0.848758i −0.509903 0.860232i \(-0.670319\pi\)
0.999934 + 0.0114733i \(0.00365216\pi\)
\(278\) 7.79365e6 4.49966e6i 0.362749 0.209433i
\(279\) 680817.i 0.0313486i
\(280\) 0 0
\(281\) 2.10143e7 0.947100 0.473550 0.880767i \(-0.342972\pi\)
0.473550 + 0.880767i \(0.342972\pi\)
\(282\) −1.33644e7 2.31479e7i −0.595941 1.03220i
\(283\) −9.02737e6 5.21195e6i −0.398292 0.229954i 0.287455 0.957794i \(-0.407191\pi\)
−0.685747 + 0.727840i \(0.740524\pi\)
\(284\) −1.08399e7 + 1.87752e7i −0.473227 + 0.819653i
\(285\) 1.01761e7 5.87519e6i 0.439591 0.253798i
\(286\) 7.30474e7i 3.12253i
\(287\) 0 0
\(288\) −1.14261e7 −0.478323
\(289\) −8.00684e6 1.38683e7i −0.331717 0.574551i
\(290\) −1.78240e7 1.02907e7i −0.730821 0.421940i
\(291\) 1.59945e6 2.77033e6i 0.0649070 0.112422i
\(292\) −1.45274e7 + 8.38741e6i −0.583499 + 0.336883i
\(293\) 2.85328e7i 1.13433i −0.823603 0.567167i \(-0.808039\pi\)
0.823603 0.567167i \(-0.191961\pi\)
\(294\) 0 0
\(295\) −3.67467e7 −1.43137
\(296\) −1.48649e6 2.57467e6i −0.0573173 0.0992765i
\(297\) 6.74177e6 + 3.89236e6i 0.257338 + 0.148574i
\(298\) 2.03814e7 3.53016e7i 0.770167 1.33397i
\(299\) −1.75044e6 + 1.01062e6i −0.0654839 + 0.0378072i
\(300\) 2.30072e7i 0.852120i
\(301\) 0 0
\(302\) −7.49461e7 −2.72100
\(303\) 1.09205e7 + 1.89148e7i 0.392567 + 0.679946i
\(304\) 1.23274e7 + 7.11724e6i 0.438785 + 0.253332i
\(305\) −3.17649e7 + 5.50185e7i −1.11956 + 1.93914i
\(306\) 6.96744e6 4.02265e6i 0.243169 0.140394i
\(307\) 1.02269e7i 0.353450i −0.984260 0.176725i \(-0.943450\pi\)
0.984260 0.176725i \(-0.0565503\pi\)
\(308\) 0 0
\(309\) −8.06925e6 −0.273500
\(310\) −3.10596e6 5.37968e6i −0.104258 0.180581i
\(311\) 1.36331e7 + 7.87108e6i 0.453225 + 0.261669i 0.709191 0.705016i \(-0.249060\pi\)
−0.255966 + 0.966686i \(0.582394\pi\)
\(312\) −1.91987e6 + 3.32532e6i −0.0632133 + 0.109489i
\(313\) −4.80881e7 + 2.77637e7i −1.56821 + 0.905408i −0.571834 + 0.820369i \(0.693768\pi\)
−0.996378 + 0.0850387i \(0.972899\pi\)
\(314\) 5.43970e7i 1.75706i
\(315\) 0 0
\(316\) −4.15959e7 −1.31822
\(317\) 3.01539e6 + 5.22282e6i 0.0946600 + 0.163956i 0.909467 0.415777i \(-0.136490\pi\)
−0.814807 + 0.579733i \(0.803157\pi\)
\(318\) −3.44422e7 1.98852e7i −1.07105 0.618370i
\(319\) −9.53842e6 + 1.65210e7i −0.293836 + 0.508938i
\(320\) −5.21541e7 + 3.01112e7i −1.59162 + 0.918920i
\(321\) 1.00817e7i 0.304804i
\(322\) 0 0
\(323\) −1.12560e7 −0.334022
\(324\) −2.09417e6 3.62721e6i −0.0615711 0.106644i
\(325\) −5.51416e7 3.18360e7i −1.60631 0.927403i
\(326\) 3.00988e7 5.21326e7i 0.868752 1.50472i
\(327\) 9.27803e6 5.35667e6i 0.265346 0.153198i
\(328\) 5.46910e6i 0.154987i
\(329\) 0 0
\(330\) 7.10295e7 1.97650
\(331\) −4.88277e6 8.45720e6i −0.134643 0.233208i 0.790818 0.612051i \(-0.209655\pi\)
−0.925461 + 0.378843i \(0.876322\pi\)
\(332\) 6.53445e6 + 3.77267e6i 0.178564 + 0.103094i
\(333\) −4.48729e6 + 7.77222e6i −0.121521 + 0.210481i
\(334\) 1.57564e7 9.09699e6i 0.422882 0.244151i
\(335\) 6.66502e7i 1.77283i
\(336\) 0 0
\(337\) −5.70025e7 −1.48938 −0.744688 0.667412i \(-0.767402\pi\)
−0.744688 + 0.667412i \(0.767402\pi\)
\(338\) −2.63483e7 4.56366e7i −0.682343 1.18185i
\(339\) 2.85752e7 + 1.64979e7i 0.733483 + 0.423477i
\(340\) 1.92943e7 3.34187e7i 0.490900 0.850263i
\(341\) −4.98642e6 + 2.87891e6i −0.125755 + 0.0726047i
\(342\) 1.11471e7i 0.278666i
\(343\) 0 0
\(344\) −993041. −0.0243945
\(345\) −982703. 1.70209e6i −0.0239312 0.0414501i
\(346\) 1.25205e7 + 7.22874e6i 0.302270 + 0.174516i
\(347\) 1.83677e7 3.18139e7i 0.439610 0.761426i −0.558050 0.829808i \(-0.688450\pi\)
0.997659 + 0.0683813i \(0.0217834\pi\)
\(348\) 8.88865e6 5.13187e6i 0.210910 0.121769i
\(349\) 6.58421e7i 1.54891i −0.632626 0.774457i \(-0.718023\pi\)
0.632626 0.774457i \(-0.281977\pi\)
\(350\) 0 0
\(351\) 1.15911e7 0.268043
\(352\) 4.83166e7 + 8.36867e7i 1.10782 + 1.91879i
\(353\) −2.76008e7 1.59353e7i −0.627476 0.362273i 0.152298 0.988335i \(-0.451333\pi\)
−0.779774 + 0.626061i \(0.784666\pi\)
\(354\) 1.74300e7 3.01897e7i 0.392905 0.680532i
\(355\) 5.05247e7 2.91704e7i 1.12932 0.652015i
\(356\) 926197.i 0.0205283i
\(357\) 0 0
\(358\) −2.62055e7 −0.571141
\(359\) 1.91128e7 + 3.31044e7i 0.413087 + 0.715488i 0.995226 0.0976018i \(-0.0311171\pi\)
−0.582138 + 0.813090i \(0.697784\pi\)
\(360\) −3.23346e6 1.86684e6i −0.0693043 0.0400128i
\(361\) −1.57251e7 + 2.72367e7i −0.334251 + 0.578940i
\(362\) 8.01957e7 4.63010e7i 1.69054 0.976033i
\(363\) 3.82212e7i 0.799070i
\(364\) 0 0
\(365\) 4.51415e7 0.928320
\(366\) −3.01340e7 5.21937e7i −0.614630 1.06457i
\(367\) −8.43371e7 4.86920e7i −1.70616 0.985053i −0.939206 0.343354i \(-0.888437\pi\)
−0.766956 0.641699i \(-0.778230\pi\)
\(368\) 1.19045e6 2.06192e6i 0.0238874 0.0413741i
\(369\) −1.42978e7 + 8.25486e6i −0.284571 + 0.164297i
\(370\) 8.18861e7i 1.61661i
\(371\) 0 0
\(372\) 3.09782e6 0.0601766
\(373\) −1.05213e7 1.82235e7i −0.202742 0.351160i 0.746669 0.665196i \(-0.231652\pi\)
−0.949411 + 0.314036i \(0.898319\pi\)
\(374\) −5.89251e7 3.40204e7i −1.12638 0.650317i
\(375\) 7.71097e6 1.33558e7i 0.146223 0.253265i
\(376\) 1.02905e7 5.94122e6i 0.193586 0.111767i
\(377\) 2.84046e7i 0.530109i
\(378\) 0 0
\(379\) −4.11794e7 −0.756418 −0.378209 0.925720i \(-0.623460\pi\)
−0.378209 + 0.925720i \(0.623460\pi\)
\(380\) 2.67331e7 + 4.63030e7i 0.487189 + 0.843837i
\(381\) 4.44166e7 + 2.56440e7i 0.803102 + 0.463671i
\(382\) 2.47521e7 4.28718e7i 0.444039 0.769098i
\(383\) 1.31798e7 7.60939e6i 0.234592 0.135442i −0.378096 0.925766i \(-0.623421\pi\)
0.612689 + 0.790324i \(0.290088\pi\)
\(384\) 1.02193e7i 0.180480i
\(385\) 0 0
\(386\) 1.69329e6 0.0294422
\(387\) 1.49886e6 + 2.59610e6i 0.0258600 + 0.0447908i
\(388\) 1.26054e7 + 7.27774e6i 0.215805 + 0.124595i
\(389\) 3.37497e7 5.84563e7i 0.573353 0.993076i −0.422866 0.906192i \(-0.638976\pi\)
0.996218 0.0868835i \(-0.0276908\pi\)
\(390\) 9.15909e7 5.28800e7i 1.54404 0.891452i
\(391\) 1.88271e6i 0.0314958i
\(392\) 0 0
\(393\) −3.48164e6 −0.0573596
\(394\) −4.18936e7 7.25619e7i −0.684951 1.18637i
\(395\) 9.69393e7 + 5.59679e7i 1.57293 + 0.908130i
\(396\) −1.77109e7 + 3.06761e7i −0.285203 + 0.493986i
\(397\) −8.14198e6 + 4.70078e6i −0.130124 + 0.0751273i −0.563649 0.826014i \(-0.690603\pi\)
0.433525 + 0.901142i \(0.357270\pi\)
\(398\) 2.04998e7i 0.325162i
\(399\) 0 0
\(400\) 7.50019e7 1.17190
\(401\) 2.77486e7 + 4.80620e7i 0.430336 + 0.745364i 0.996902 0.0786521i \(-0.0250616\pi\)
−0.566566 + 0.824016i \(0.691728\pi\)
\(402\) −5.47573e7 3.16141e7i −0.842876 0.486635i
\(403\) −4.28658e6 + 7.42457e6i −0.0654931 + 0.113437i
\(404\) −8.60654e7 + 4.96899e7i −1.30522 + 0.753571i
\(405\) 1.12709e7i 0.169666i
\(406\) 0 0
\(407\) 7.59001e7 1.12579
\(408\) 1.78829e6 + 3.09741e6i 0.0263304 + 0.0456056i
\(409\) −1.41570e7 8.17357e6i −0.206920 0.119465i 0.392959 0.919556i \(-0.371451\pi\)
−0.599879 + 0.800091i \(0.704785\pi\)
\(410\) −7.53192e7 + 1.30457e8i −1.09283 + 1.89284i
\(411\) 4.28017e7 2.47116e7i 0.616504 0.355939i
\(412\) 3.67163e7i 0.525010i
\(413\) 0 0
\(414\) 1.86450e6 0.0262761
\(415\) −1.01524e7 1.75844e7i −0.142044 0.246027i
\(416\) 1.24606e8 + 7.19413e7i 1.73085 + 0.999306i
\(417\) 6.03850e6 1.04590e7i 0.0832762 0.144239i
\(418\) 8.16432e7 4.71367e7i 1.11787 0.645402i
\(419\) 3.75022e7i 0.509818i −0.966965 0.254909i \(-0.917955\pi\)
0.966965 0.254909i \(-0.0820455\pi\)
\(420\) 0 0
\(421\) 9.17501e7 1.22959 0.614795 0.788687i \(-0.289239\pi\)
0.614795 + 0.788687i \(0.289239\pi\)
\(422\) 7.95882e7 + 1.37851e8i 1.05904 + 1.83431i
\(423\) −3.10642e7 1.79349e7i −0.410430 0.236962i
\(424\) 8.84006e6 1.53114e7i 0.115973 0.200871i
\(425\) −5.13623e7 + 2.96540e7i −0.669080 + 0.386293i
\(426\) 5.53455e7i 0.715902i
\(427\) 0 0
\(428\) 4.58735e7 0.585101
\(429\) −4.90144e7 8.48954e7i −0.620800 1.07526i
\(430\) 2.36874e7 + 1.36759e7i 0.297928 + 0.172009i
\(431\) 6.89035e7 1.19344e8i 0.860616 1.49063i −0.0107202 0.999943i \(-0.503412\pi\)
0.871336 0.490687i \(-0.163254\pi\)
\(432\) −1.18244e7 + 6.82684e6i −0.146666 + 0.0846776i
\(433\) 2.00324e7i 0.246757i 0.992360 + 0.123378i \(0.0393729\pi\)
−0.992360 + 0.123378i \(0.960627\pi\)
\(434\) 0 0
\(435\) −2.76200e7 −0.335549
\(436\) 2.43737e7 + 4.22165e7i 0.294078 + 0.509357i
\(437\) −2.25909e6 1.30428e6i −0.0270700 0.0156289i
\(438\) −2.14119e7 + 3.70865e7i −0.254820 + 0.441361i
\(439\) −7.45669e7 + 4.30512e7i −0.881359 + 0.508853i −0.871106 0.491095i \(-0.836597\pi\)
−0.0102525 + 0.999947i \(0.503264\pi\)
\(440\) 3.15765e7i 0.370686i
\(441\) 0 0
\(442\) −1.01310e8 −1.17324
\(443\) 4.03937e6 + 6.99640e6i 0.0464625 + 0.0804754i 0.888321 0.459222i \(-0.151872\pi\)
−0.841859 + 0.539698i \(0.818539\pi\)
\(444\) −3.53648e7 2.04179e7i −0.404038 0.233272i
\(445\) −1.24621e6 + 2.15850e6i −0.0141420 + 0.0244947i
\(446\) −2.16312e8 + 1.24888e8i −2.43824 + 1.40772i
\(447\) 5.47032e7i 0.612477i
\(448\) 0 0
\(449\) −5.16486e7 −0.570584 −0.285292 0.958441i \(-0.592091\pi\)
−0.285292 + 0.958441i \(0.592091\pi\)
\(450\) 2.93672e7 + 5.08655e7i 0.322274 + 0.558194i
\(451\) 1.20920e8 + 6.98132e7i 1.31816 + 0.761041i
\(452\) −7.50680e7 + 1.30022e8i −0.812904 + 1.40799i
\(453\) −8.71022e7 + 5.02885e7i −0.936989 + 0.540971i
\(454\) 4.56657e7i 0.488004i
\(455\) 0 0
\(456\) −4.95549e6 −0.0522628
\(457\) 1.99697e7 + 3.45885e7i 0.209229 + 0.362396i 0.951472 0.307735i \(-0.0995711\pi\)
−0.742243 + 0.670131i \(0.766238\pi\)
\(458\) −5.65682e6 3.26597e6i −0.0588811 0.0339950i
\(459\) 5.39835e6 9.35022e6i 0.0558243 0.0966905i
\(460\) 7.74478e6 4.47145e6i 0.0795675 0.0459383i
\(461\) 1.40914e7i 0.143831i −0.997411 0.0719153i \(-0.977089\pi\)
0.997411 0.0719153i \(-0.0229111\pi\)
\(462\) 0 0
\(463\) 1.25200e8 1.26142 0.630712 0.776017i \(-0.282763\pi\)
0.630712 + 0.776017i \(0.282763\pi\)
\(464\) −1.67295e7 2.89763e7i −0.167467 0.290061i
\(465\) −7.21948e6 4.16817e6i −0.0718037 0.0414559i
\(466\) −9.48623e7 + 1.64306e8i −0.937423 + 1.62367i
\(467\) 8.96567e7 5.17633e7i 0.880303 0.508243i 0.00954455 0.999954i \(-0.496962\pi\)
0.870758 + 0.491711i \(0.163628\pi\)
\(468\) 5.27415e7i 0.514535i
\(469\) 0 0
\(470\) −3.27284e8 −3.15233
\(471\) 3.65001e7 + 6.32200e7i 0.349326 + 0.605051i
\(472\) 1.34210e7 + 7.74860e6i 0.127631 + 0.0736880i
\(473\) 1.26762e7 2.19558e7i 0.119786 0.207475i
\(474\) −9.19621e7 + 5.30944e7i −0.863523 + 0.498555i
\(475\) 8.21738e7i 0.766747i
\(476\) 0 0
\(477\) −5.33714e7 −0.491760
\(478\) −1.13913e8 1.97303e8i −1.04301 1.80655i
\(479\) 6.75301e7 + 3.89885e7i 0.614456 + 0.354757i 0.774708 0.632320i \(-0.217897\pi\)
−0.160251 + 0.987076i \(0.551230\pi\)
\(480\) −6.99541e7 + 1.21164e8i −0.632542 + 1.09560i
\(481\) 9.78713e7 5.65060e7i 0.879468 0.507761i
\(482\) 4.18058e7i 0.373333i
\(483\) 0 0
\(484\) 1.73913e8 1.53389
\(485\) −1.95846e7 3.39216e7i −0.171668 0.297338i
\(486\) −9.25978e6 5.34613e6i −0.0806662 0.0465727i
\(487\) −7.13992e7 + 1.23667e8i −0.618168 + 1.07070i 0.371651 + 0.928372i \(0.378792\pi\)
−0.989820 + 0.142327i \(0.954542\pi\)
\(488\) 2.32029e7 1.33962e7i 0.199657 0.115272i
\(489\) 8.07845e7i 0.690878i
\(490\) 0 0
\(491\) 5.07818e7 0.429006 0.214503 0.976723i \(-0.431187\pi\)
0.214503 + 0.976723i \(0.431187\pi\)
\(492\) −3.75609e7 6.50574e7i −0.315385 0.546263i
\(493\) 2.29132e7 + 1.32289e7i 0.191225 + 0.110404i
\(494\) 7.01846e7 1.21563e8i 0.582185 1.00837i
\(495\) 8.25503e7 4.76604e7i 0.680617 0.392955i
\(496\) 1.00987e7i 0.0827598i
\(497\) 0 0
\(498\) 1.92622e7 0.155962
\(499\) −6.32522e7 1.09556e8i −0.509065 0.881727i −0.999945 0.0104998i \(-0.996658\pi\)
0.490879 0.871228i \(-0.336676\pi\)
\(500\) 6.07709e7 + 3.50861e7i 0.486167 + 0.280689i
\(501\) 1.22081e7 2.11450e7i 0.0970808 0.168149i
\(502\) −6.53735e7 + 3.77434e7i −0.516762 + 0.298353i
\(503\) 7.36652e6i 0.0578840i −0.999581 0.0289420i \(-0.990786\pi\)
0.999581 0.0289420i \(-0.00921381\pi\)
\(504\) 0 0
\(505\) 2.67434e8 2.07655
\(506\) −7.88423e6 1.36559e7i −0.0608566 0.105407i
\(507\) −6.12438e7 3.53591e7i −0.469936 0.271317i
\(508\) −1.16684e8 + 2.02103e8i −0.890062 + 1.54163i
\(509\) 1.98695e8 1.14716e8i 1.50672 0.869906i 0.506753 0.862092i \(-0.330846\pi\)
0.999969 0.00781491i \(-0.00248759\pi\)
\(510\) 9.85116e7i 0.742637i
\(511\) 0 0
\(512\) −1.88055e8 −1.40112
\(513\) 7.47964e6 + 1.29551e7i 0.0554024 + 0.0959598i
\(514\) −2.87501e7 1.65989e7i −0.211714 0.122233i
\(515\) −4.94024e7 + 8.55674e7i −0.361681 + 0.626450i
\(516\) −1.18127e7 + 6.82004e6i −0.0859803 + 0.0496407i
\(517\) 3.03359e8i 2.19526i
\(518\) 0 0
\(519\) 1.94018e7 0.138784
\(520\) 2.35081e7 + 4.07172e7i 0.167189 + 0.289579i
\(521\) 9.29834e7 + 5.36840e7i 0.657495 + 0.379605i 0.791322 0.611400i \(-0.209393\pi\)
−0.133827 + 0.991005i \(0.542727\pi\)
\(522\) 1.31010e7 2.26915e7i 0.0921068 0.159534i
\(523\) −1.30357e8 + 7.52614e7i −0.911230 + 0.526099i −0.880827 0.473439i \(-0.843013\pi\)
−0.0304034 + 0.999538i \(0.509679\pi\)
\(524\) 1.58420e7i 0.110107i
\(525\) 0 0
\(526\) 5.80595e7 0.398948
\(527\) 3.99279e6 + 6.91571e6i 0.0272800 + 0.0472503i
\(528\) 1.00002e8 + 5.77361e7i 0.679370 + 0.392234i
\(529\) 7.37998e7 1.27825e8i 0.498526 0.863473i
\(530\) −4.21731e8 + 2.43486e8i −2.83275 + 1.63549i
\(531\) 4.67818e7i 0.312459i
\(532\) 0 0
\(533\) 2.07898e8 1.37299
\(534\) −1.18223e6 2.04768e6i −0.00776385 0.0134474i
\(535\) −1.06908e8 6.17235e7i −0.698151 0.403078i
\(536\) 1.40542e7 2.43426e7i 0.0912666 0.158078i
\(537\) −3.04560e7 + 1.75838e7i −0.196675 + 0.113550i
\(538\) 2.37197e8i 1.52322i
\(539\) 0 0
\(540\) −5.12846e7 −0.325691
\(541\) 3.02874e7 + 5.24593e7i 0.191280 + 0.331307i 0.945675 0.325114i \(-0.105403\pi\)
−0.754395 + 0.656421i \(0.772069\pi\)
\(542\) −1.24157e8 7.16821e7i −0.779783 0.450208i
\(543\) 6.21354e7 1.07622e8i 0.388097 0.672203i
\(544\) 1.16066e8 6.70107e7i 0.720955 0.416243i
\(545\) 1.31181e8i 0.810365i
\(546\) 0 0
\(547\) −2.68955e8 −1.64330 −0.821651 0.569992i \(-0.806946\pi\)
−0.821651 + 0.569992i \(0.806946\pi\)
\(548\) 1.12442e8 + 1.94755e8i 0.683259 + 1.18344i
\(549\) −7.00433e7 4.04395e7i −0.423301 0.244393i
\(550\) 2.48365e8 4.30180e8i 1.49280 2.58561i
\(551\) −3.17471e7 + 1.83292e7i −0.189780 + 0.109569i
\(552\) 828871.i 0.00492799i
\(553\) 0 0
\(554\) 2.41962e8 1.42304
\(555\) 5.49451e7 + 9.51678e7i 0.321403 + 0.556687i
\(556\) 4.75900e7 + 2.74761e7i 0.276880 + 0.159857i
\(557\) −1.00886e8 + 1.74739e8i −0.583800 + 1.01117i 0.411223 + 0.911535i \(0.365102\pi\)
−0.995024 + 0.0996375i \(0.968232\pi\)
\(558\) 6.84881e6 3.95416e6i 0.0394196 0.0227589i
\(559\) 3.77486e7i 0.216105i
\(560\) 0 0
\(561\) −9.13101e7 −0.517166
\(562\) 1.22050e8 + 2.11397e8i 0.687591 + 1.19094i
\(563\) −1.52694e8 8.81577e7i −0.855650 0.494010i 0.00690346 0.999976i \(-0.497803\pi\)
−0.862553 + 0.505967i \(0.831136\pi\)
\(564\) 8.16067e7 1.41347e8i 0.454871 0.787860i
\(565\) 3.49892e8 2.02010e8i 1.93994 1.12003i
\(566\) 1.21083e8i 0.667783i
\(567\) 0 0
\(568\) −2.46041e7 −0.134265
\(569\) −1.00368e8 1.73843e8i −0.544828 0.943669i −0.998618 0.0525605i \(-0.983262\pi\)
0.453790 0.891109i \(-0.350072\pi\)
\(570\) 1.18205e8 + 6.82459e7i 0.638282 + 0.368512i
\(571\) 2.23204e7 3.86600e7i 0.119893 0.207660i −0.799832 0.600224i \(-0.795078\pi\)
0.919725 + 0.392563i \(0.128412\pi\)
\(572\) 3.86287e8 2.23023e8i 2.06406 1.19169i
\(573\) 6.64340e7i 0.353123i
\(574\) 0 0
\(575\) −1.37446e7 −0.0722986
\(576\) −3.83342e7 6.63967e7i −0.200594 0.347440i
\(577\) 2.24118e8 + 1.29395e8i 1.16668 + 0.673581i 0.952895 0.303301i \(-0.0980887\pi\)
0.213781 + 0.976882i \(0.431422\pi\)
\(578\) 9.30069e7 1.61093e8i 0.481650 0.834243i
\(579\) 1.96794e6 1.13619e6i 0.0101386 0.00585350i
\(580\) 1.25675e8i 0.644119i
\(581\) 0 0
\(582\) 3.71582e7 0.188489
\(583\) 2.25687e8 + 3.90901e8i 1.13894 + 1.97270i
\(584\) −1.64870e7 9.51877e6i −0.0827757 0.0477906i
\(585\) 7.09644e7 1.22914e8i 0.354465 0.613951i
\(586\) 2.87031e8 1.65717e8i 1.42638 0.823522i
\(587\) 3.41902e8i 1.69039i 0.534457 + 0.845196i \(0.320516\pi\)
−0.534457 + 0.845196i \(0.679484\pi\)
\(588\) 0 0
\(589\) −1.10643e7 −0.0541476
\(590\) −2.13424e8 3.69661e8i −1.03917 1.79989i
\(591\) −9.73773e7 5.62208e7i −0.471732 0.272354i
\(592\) −6.65608e7 + 1.15287e8i −0.320814 + 0.555666i
\(593\) −1.27791e8 + 7.37803e7i −0.612826 + 0.353815i −0.774071 0.633099i \(-0.781782\pi\)
0.161245 + 0.986914i \(0.448449\pi\)
\(594\) 9.04268e7i 0.431458i
\(595\) 0 0
\(596\) 2.48908e8 1.17571
\(597\) −1.37552e7 2.38248e7i −0.0646465 0.111971i
\(598\) −2.03331e7 1.17393e7i −0.0950822 0.0548957i
\(599\) 3.32461e7 5.75840e7i 0.154690 0.267930i −0.778256 0.627947i \(-0.783896\pi\)
0.932946 + 0.360017i \(0.117229\pi\)
\(600\) −2.26125e7 + 1.30553e7i −0.104687 + 0.0604413i
\(601\) 3.71302e7i 0.171042i 0.996336 + 0.0855212i \(0.0272555\pi\)
−0.996336 + 0.0855212i \(0.972744\pi\)
\(602\) 0 0
\(603\) −8.48516e7 −0.386998
\(604\) −2.28820e8 3.96328e8i −1.03845 1.79864i
\(605\) −4.05303e8 2.34002e8i −1.83026 1.05670i
\(606\) −1.26852e8 + 2.19713e8i −0.570004 + 0.987276i
\(607\) −1.10132e8 + 6.35850e7i −0.492436 + 0.284308i −0.725584 0.688133i \(-0.758430\pi\)
0.233149 + 0.972441i \(0.425097\pi\)
\(608\) 1.85692e8i 0.826195i
\(609\) 0 0
\(610\) −7.37959e8 −3.25119
\(611\) 2.25845e8 + 3.91174e8i 0.990116 + 1.71493i
\(612\) 4.25450e7 + 2.45634e7i 0.185607 + 0.107160i
\(613\) 7.14975e7 1.23837e8i 0.310391 0.537614i −0.668056 0.744111i \(-0.732873\pi\)
0.978447 + 0.206498i \(0.0662066\pi\)
\(614\) 1.02879e8 5.93974e7i 0.444450 0.256603i
\(615\) 2.02155e8i 0.869079i
\(616\) 0 0
\(617\) −2.96115e8 −1.26068 −0.630339 0.776320i \(-0.717084\pi\)
−0.630339 + 0.776320i \(0.717084\pi\)
\(618\) −4.68659e7 8.11742e7i −0.198560 0.343916i
\(619\) −2.81343e8 1.62433e8i −1.18622 0.684862i −0.228771 0.973480i \(-0.573471\pi\)
−0.957444 + 0.288619i \(0.906804\pi\)
\(620\) 1.89658e7 3.28498e7i 0.0795786 0.137834i
\(621\) 2.16691e6 1.25107e6i 0.00904829 0.00522403i
\(622\) 1.82860e8i 0.759884i
\(623\) 0 0
\(624\) 1.71933e8 0.707630
\(625\) 6.81453e7 + 1.18031e8i 0.279123 + 0.483456i
\(626\) −5.58588e8 3.22501e8i −2.27703 1.31464i
\(627\) 6.32569e7 1.09564e8i 0.256629 0.444494i
\(628\) −2.87661e8 + 1.66081e8i −1.16145 + 0.670566i
\(629\) 1.05267e8i 0.422998i
\(630\) 0 0
\(631\) −1.40735e8 −0.560163 −0.280082 0.959976i \(-0.590362\pi\)
−0.280082 + 0.959976i \(0.590362\pi\)
\(632\) −2.36034e7 4.08822e7i −0.0935023 0.161951i
\(633\) 1.84994e8 + 1.06806e8i 0.729369 + 0.421101i
\(634\) −3.50266e7 + 6.06679e7i −0.137446 + 0.238063i
\(635\) 5.43864e8 3.14000e8i 2.12407 1.22633i
\(636\) 2.42848e8i 0.943982i
\(637\) 0 0
\(638\) −2.21595e8 −0.853294
\(639\) 3.71365e7 + 6.43224e7i 0.142331 + 0.246524i
\(640\) −1.08367e8 6.25658e7i −0.413388 0.238670i
\(641\) 1.08339e8 1.87648e8i 0.411348 0.712476i −0.583689 0.811977i \(-0.698391\pi\)
0.995037 + 0.0995014i \(0.0317248\pi\)
\(642\) 1.01419e8 5.85544e7i 0.383279 0.221286i
\(643\) 2.61645e8i 0.984192i −0.870541 0.492096i \(-0.836231\pi\)
0.870541 0.492096i \(-0.163769\pi\)
\(644\) 0 0
\(645\) 3.67059e7 0.136791
\(646\) −6.53743e7 1.13232e8i −0.242499 0.420020i
\(647\) 9.29409e7 + 5.36595e7i 0.343158 + 0.198122i 0.661668 0.749797i \(-0.269849\pi\)
−0.318510 + 0.947920i \(0.603182\pi\)
\(648\) 2.37665e6 4.11648e6i 0.00873454 0.0151287i
\(649\) −3.42637e8 + 1.97822e8i −1.25343 + 0.723669i
\(650\) 7.39610e8i 2.69316i
\(651\) 0 0
\(652\) 3.67582e8 1.32621
\(653\) −2.21977e8 3.84475e8i −0.797200 1.38079i −0.921432 0.388539i \(-0.872980\pi\)
0.124232 0.992253i \(-0.460353\pi\)
\(654\) 1.07773e8 + 6.22228e7i 0.385280 + 0.222442i
\(655\) −2.13156e7 + 3.69198e7i −0.0758533 + 0.131382i
\(656\) −2.12082e8 + 1.22446e8i −0.751265 + 0.433743i
\(657\) 5.74691e7i 0.202646i
\(658\) 0 0
\(659\) −1.87037e7 −0.0653538 −0.0326769 0.999466i \(-0.510403\pi\)
−0.0326769 + 0.999466i \(0.510403\pi\)
\(660\) 2.16862e8 + 3.75617e8i 0.754315 + 1.30651i
\(661\) 1.85577e7 + 1.07143e7i 0.0642570 + 0.0370988i 0.531784 0.846880i \(-0.321522\pi\)
−0.467527 + 0.883979i \(0.654855\pi\)
\(662\) 5.67179e7 9.82383e7i 0.195500 0.338616i
\(663\) −1.17742e8 + 6.79785e7i −0.404010 + 0.233255i
\(664\) 8.56311e6i 0.0292501i
\(665\) 0 0
\(666\) −1.04248e8 −0.352895
\(667\) 3.06580e6 + 5.31012e6i 0.0103316 + 0.0178948i
\(668\) 9.62130e7 + 5.55486e7i 0.322778 + 0.186356i
\(669\) −1.67598e8 + 2.90289e8i −0.559746 + 0.969509i
\(670\) −6.70481e8 + 3.87102e8i −2.22927 + 1.28707i
\(671\) 6.84012e8i 2.26410i
\(672\) 0 0
\(673\) 2.29593e8 0.753205 0.376603 0.926375i \(-0.377092\pi\)
0.376603 + 0.926375i \(0.377092\pi\)
\(674\) −3.31069e8 5.73428e8i −1.08128 1.87283i
\(675\) 6.82609e7 + 3.94105e7i 0.221953 + 0.128145i
\(676\) 1.60890e8 2.78669e8i 0.520820 0.902087i
\(677\) −1.96110e7 + 1.13224e7i −0.0632024 + 0.0364899i −0.531268 0.847204i \(-0.678284\pi\)
0.468066 + 0.883694i \(0.344951\pi\)
\(678\) 3.83277e8i 1.22977i
\(679\) 0 0
\(680\) 4.37938e7 0.139279
\(681\) −3.06415e7 5.30726e7i −0.0970216 0.168046i
\(682\) −5.79219e7 3.34412e7i −0.182595 0.105421i
\(683\) −1.12310e8 + 1.94527e8i −0.352499 + 0.610546i −0.986687 0.162633i \(-0.948001\pi\)
0.634188 + 0.773179i \(0.281335\pi\)
\(684\) −5.89478e7 + 3.40335e7i −0.184204 + 0.106350i
\(685\) 6.05167e8i 1.88280i
\(686\) 0 0
\(687\) −8.76579e6 −0.0270346
\(688\) 2.22328e7 + 3.85084e7i 0.0682700 + 0.118247i
\(689\) 5.82036e8 + 3.36038e8i 1.77947 + 1.02738i
\(690\) 1.14150e7 1.97714e7i 0.0347480 0.0601852i
\(691\) −2.19279e8 + 1.26601e8i −0.664603 + 0.383709i −0.794029 0.607880i \(-0.792020\pi\)
0.129426 + 0.991589i \(0.458687\pi\)
\(692\) 8.82811e7i 0.266409i
\(693\) 0 0
\(694\) 4.26717e8 1.27662
\(695\) −7.39390e7 1.28066e8i −0.220252 0.381487i
\(696\) 1.00876e7 + 5.82409e6i 0.0299200 + 0.0172743i
\(697\) 9.68246e7 1.67705e8i 0.285948 0.495277i
\(698\) 6.62351e8 3.82409e8i 1.94770 1.12451i
\(699\) 2.54608e8i 0.745489i
\(700\) 0 0
\(701\) 3.18180e8 0.923674 0.461837 0.886965i \(-0.347191\pi\)
0.461837 + 0.886965i \(0.347191\pi\)
\(702\) 6.73209e7 + 1.16603e8i 0.194598 + 0.337054i
\(703\) 1.26311e8 + 7.29255e7i 0.363558 + 0.209900i
\(704\) −3.24201e8 + 5.61532e8i −0.929171 + 1.60937i
\(705\) −3.80369e8 + 2.19606e8i −1.08552 + 0.626725i
\(706\) 3.70207e8i 1.05204i
\(707\) 0 0
\(708\) 2.12864e8 0.599796
\(709\) −1.35142e8 2.34072e8i −0.379185 0.656767i 0.611759 0.791044i \(-0.290462\pi\)
−0.990944 + 0.134277i \(0.957129\pi\)
\(710\) 5.86891e8 + 3.38842e8i 1.63977 + 0.946721i
\(711\) −7.12521e7 + 1.23412e8i −0.198239 + 0.343360i
\(712\) 910305. 525565.i 0.00252201 0.00145608i
\(713\) 1.85065e6i 0.00510572i
\(714\) 0 0
\(715\) −1.20032e9 −3.28383
\(716\) −8.00089e7 1.38579e8i −0.217971 0.377537i
\(717\) −2.64778e8 1.52870e8i −0.718331 0.414728i
\(718\) −2.22013e8 + 3.84538e8i −0.599799 + 1.03888i
\(719\) −9.13702e7 + 5.27526e7i −0.245820 + 0.141924i −0.617849 0.786297i \(-0.711996\pi\)
0.372029 + 0.928221i \(0.378662\pi\)
\(720\) 1.67184e8i 0.447916i
\(721\) 0 0
\(722\) −3.65324e8 −0.970660
\(723\) −2.80515e7 4.85866e7i −0.0742234 0.128559i
\(724\) 4.89696e8 + 2.82726e8i 1.29036 + 0.744989i
\(725\) −9.65772e7 + 1.67277e8i −0.253431 + 0.438956i
\(726\) 3.84494e8 2.21988e8i 1.00480 0.580121i
\(727\) 3.47133e8i 0.903425i 0.892164 + 0.451713i \(0.149187\pi\)
−0.892164 + 0.451713i \(0.850813\pi\)
\(728\) 0 0
\(729\) −1.43489e7 −0.0370370
\(730\) 2.62180e8 + 4.54110e8i 0.673956 + 1.16733i
\(731\) −3.04507e7 1.75807e7i −0.0779552 0.0450074i
\(732\) 1.84006e8 3.18708e8i 0.469137 0.812568i
\(733\) 4.04599e8 2.33596e8i 1.02734 0.593134i 0.111117 0.993807i \(-0.464557\pi\)
0.916221 + 0.400673i \(0.131224\pi\)
\(734\) 1.13121e9i 2.86058i
\(735\) 0 0
\(736\) 3.10594e7 0.0779040
\(737\) 3.58804e8 + 6.21467e8i 0.896304 + 1.55244i
\(738\) −1.66083e8 9.58879e7i −0.413195 0.238558i
\(739\) −1.98814e8 + 3.44356e8i −0.492623 + 0.853247i −0.999964 0.00849788i \(-0.997295\pi\)
0.507341 + 0.861745i \(0.330628\pi\)
\(740\) −4.33028e8 + 2.50009e8i −1.06861 + 0.616965i
\(741\) 1.88374e8i 0.462984i
\(742\) 0 0
\(743\) 6.88913e8 1.67957 0.839784 0.542920i \(-0.182681\pi\)
0.839784 + 0.542920i \(0.182681\pi\)
\(744\) 1.75784e6 + 3.04467e6i 0.00426836 + 0.00739302i
\(745\) −5.80080e8 3.34909e8i −1.40288 0.809951i
\(746\) 1.22215e8 2.11683e8i 0.294380 0.509881i
\(747\) 2.23865e7 1.29248e7i 0.0537061 0.0310073i
\(748\) 4.15475e8i 0.992751i
\(749\) 0 0
\(750\) 1.79140e8 0.424629
\(751\) −1.83282e8 3.17453e8i −0.432712 0.749480i 0.564393 0.825506i \(-0.309110\pi\)
−0.997106 + 0.0760260i \(0.975777\pi\)
\(752\) −4.60781e8 2.66032e8i −1.08353 0.625576i
\(753\) −5.06512e7 + 8.77305e7i −0.118633 + 0.205478i
\(754\) −2.85742e8 + 1.64973e8i −0.666592 + 0.384857i
\(755\) 1.23152e9i 2.86156i
\(756\) 0 0
\(757\) −2.07241e8 −0.477735 −0.238868 0.971052i \(-0.576776\pi\)
−0.238868 + 0.971052i \(0.576776\pi\)
\(758\) −2.39168e8 4.14252e8i −0.549157 0.951167i
\(759\) −1.83261e7 1.05806e7i −0.0419125 0.0241982i
\(760\) −3.03390e7 + 5.25487e7i −0.0691132 + 0.119708i
\(761\) 5.86021e8 3.38339e8i 1.32972 0.767712i 0.344461 0.938801i \(-0.388062\pi\)
0.985256 + 0.171088i \(0.0547283\pi\)
\(762\) 5.95757e8i 1.34649i
\(763\) 0 0
\(764\) 3.02285e8 0.677854
\(765\) −6.61007e7 1.14490e8i −0.147646 0.255730i
\(766\) 1.53096e8 + 8.83901e7i 0.340626 + 0.196661i
\(767\) −2.94549e8 + 5.10173e8i −0.652786 + 1.13066i
\(768\) −1.69795e8 + 9.80314e7i −0.374837 + 0.216412i
\(769\) 5.58023e8i 1.22708i −0.789663 0.613540i \(-0.789745\pi\)
0.789663 0.613540i \(-0.210255\pi\)
\(770\) 0 0
\(771\) −4.45510e7 −0.0972063
\(772\) 5.16985e6 + 8.95443e6i 0.0112364 + 0.0194619i
\(773\) −7.17689e7 4.14358e7i −0.155381 0.0897093i 0.420293 0.907388i \(-0.361927\pi\)
−0.575675 + 0.817679i \(0.695260\pi\)
\(774\) −1.74107e7 + 3.01561e7i −0.0375485 + 0.0650358i
\(775\) −5.04878e7 + 2.91492e7i −0.108463 + 0.0626211i
\(776\) 1.65188e7i 0.0353504i
\(777\) 0 0
\(778\) 7.84070e8 1.66501
\(779\) 1.34154e8 + 2.32362e8i 0.283787 + 0.491533i
\(780\) 5.59278e8 + 3.22899e8i 1.17854 + 0.680430i
\(781\) 3.14072e8 5.43988e8i 0.659289 1.14192i
\(782\) −1.89395e7 + 1.09347e7i −0.0396048 + 0.0228658i
\(783\) 3.51627e7i 0.0732482i
\(784\) 0 0
\(785\) 8.93859e8 1.84782
\(786\) −2.02212e7 3.50242e7i −0.0416428 0.0721275i
\(787\) 4.59435e8 + 2.65255e8i 0.942541 + 0.544176i 0.890756 0.454482i \(-0.150176\pi\)
0.0517851 + 0.998658i \(0.483509\pi\)
\(788\) 2.55813e8 4.43082e8i 0.522811 0.905535i
\(789\) 6.74766e7 3.89576e7i 0.137380 0.0793161i
\(790\) 1.30024e9i 2.63719i
\(791\) 0 0
\(792\) −4.01997e7 −0.0809184
\(793\) 5.09233e8 + 8.82017e8i 1.02117 + 1.76871i
\(794\) −9.45767e7 5.46039e7i −0.188939 0.109084i
\(795\) −3.26756e8 + 5.65958e8i −0.650313 + 1.12637i
\(796\) 1.08406e8 6.25885e7i 0.214939 0.124095i
\(797\) 4.96880e8i 0.981469i −0.871309 0.490735i \(-0.836728\pi\)
0.871309 0.490735i \(-0.163272\pi\)
\(798\) 0 0
\(799\) 4.20732e8 0.824831
\(800\) 4.89209e8 + 8.47334e8i 0.955486 + 1.65495i
\(801\) −2.74796e6 1.58654e6i −0.00534703 0.00308711i
\(802\) −3.22326e8 + 5.58285e8i −0.624845 + 1.08226i
\(803\) 4.20913e8 2.43014e8i 0.812917 0.469338i
\(804\) 3.86088e8i 0.742879i
\(805\) 0 0
\(806\) −9.95852e7 −0.190191
\(807\) 1.59158e8 + 2.75669e8i 0.302836 + 0.524527i
\(808\) −9.76747e7 5.63925e7i −0.185160 0.106902i
\(809\) 2.10152e8 3.63994e8i 0.396906 0.687461i −0.596437 0.802660i \(-0.703417\pi\)
0.993342 + 0.115199i \(0.0367506\pi\)
\(810\) −1.13382e8 + 6.54613e7i −0.213349 + 0.123177i
\(811\) 4.27809e8i 0.802025i 0.916073 + 0.401012i \(0.131342\pi\)
−0.916073 + 0.401012i \(0.868658\pi\)
\(812\) 0 0
\(813\) −1.92393e8 −0.358029
\(814\) 4.40825e8 + 7.63531e8i 0.817322 + 1.41564i
\(815\) −8.56650e8 4.94587e8i −1.58245 0.913629i
\(816\) 8.00747e7 1.38693e8i 0.147375 0.255262i
\(817\) 4.21907e7 2.43588e7i 0.0773660 0.0446673i
\(818\) 1.89887e8i 0.346925i
\(819\) 0 0
\(820\) −9.19837e8 −1.66828
\(821\) −4.76401e8 8.25152e8i −0.860882 1.49109i −0.871079 0.491143i \(-0.836579\pi\)
0.0101968 0.999948i \(-0.496754\pi\)
\(822\) 4.97182e8 + 2.87048e8i 0.895159 + 0.516820i
\(823\) 3.70614e8 6.41923e8i 0.664848 1.15155i −0.314478 0.949265i \(-0.601829\pi\)
0.979326 0.202287i \(-0.0648372\pi\)
\(824\) 3.60864e7 2.08345e7i 0.0645003 0.0372392i
\(825\) 6.66606e8i 1.18715i
\(826\) 0 0
\(827\) −7.61072e8 −1.34558 −0.672790 0.739834i \(-0.734904\pi\)
−0.672790 + 0.739834i \(0.734904\pi\)
\(828\) 5.69255e6 + 9.85979e6i 0.0100280 + 0.0173691i
\(829\) 7.06469e8 + 4.07880e8i 1.24002 + 0.715928i 0.969099 0.246673i \(-0.0793373\pi\)
0.270924 + 0.962601i \(0.412671\pi\)
\(830\) 1.17929e8 2.04259e8i 0.206247 0.357230i
\(831\) 2.81207e8 1.62355e8i 0.490031 0.282919i
\(832\) 9.65442e8i 1.67632i
\(833\) 0 0
\(834\) 1.40286e8 0.241833
\(835\) −1.49483e8 2.58912e8i −0.256763 0.444726i
\(836\) 4.98534e8 + 2.87829e8i 0.853250 + 0.492624i
\(837\) 5.30644e6 9.19103e6i 0.00904955 0.0156743i
\(838\) 3.77261e8 2.17812e8i 0.641076 0.370126i
\(839\) 1.07654e9i 1.82283i −0.411491 0.911414i \(-0.634992\pi\)
0.411491 0.911414i \(-0.365008\pi\)
\(840\) 0 0
\(841\) −5.08655e8 −0.855137
\(842\) 5.32881e8 + 9.22978e8i 0.892677 + 1.54616i
\(843\) 2.83693e8 + 1.63790e8i 0.473550 + 0.273404i
\(844\) −4.85986e8 + 8.41753e8i −0.808345 + 1.40009i
\(845\) −7.49906e8 + 4.32959e8i −1.24290 + 0.717590i
\(846\) 4.16662e8i 0.688133i
\(847\) 0 0
\(848\) −7.91667e8 −1.29824
\(849\) −8.12463e7 1.40723e8i −0.132764 0.229954i
\(850\) −5.96621e8 3.44459e8i −0.971498 0.560895i
\(851\) 1.21977e7 2.11271e7i 0.0197921 0.0342808i
\(852\) −2.92677e8 + 1.68977e8i −0.473227 + 0.273218i
\(853\) 9.74565e8i 1.57023i −0.619349 0.785116i \(-0.712603\pi\)
0.619349 0.785116i \(-0.287397\pi\)
\(854\) 0 0
\(855\) 1.83170e8 0.293060
\(856\) 2.60307e7 + 4.50864e7i 0.0415015 + 0.0718827i
\(857\) 8.31953e8 + 4.80328e8i 1.32177 + 0.763125i 0.984011 0.178107i \(-0.0569974\pi\)
0.337760 + 0.941232i \(0.390331\pi\)
\(858\) 5.69348e8 9.86139e8i 0.901396 1.56126i
\(859\) −4.22688e8 + 2.44039e8i −0.666869 + 0.385017i −0.794889 0.606755i \(-0.792471\pi\)
0.128020 + 0.991772i \(0.459138\pi\)
\(860\) 1.67018e8i 0.262583i
\(861\) 0 0
\(862\) 1.60076e9 2.49921
\(863\) −1.61373e8 2.79507e8i −0.251073 0.434871i 0.712749 0.701420i \(-0.247450\pi\)
−0.963821 + 0.266549i \(0.914117\pi\)
\(864\) −1.54252e8 8.90577e7i −0.239161 0.138080i
\(865\) 1.18784e8 2.05739e8i 0.183530 0.317884i
\(866\) −2.01520e8 + 1.16348e8i −0.310287 + 0.179144i
\(867\) 2.49629e8i 0.383034i
\(868\) 0 0
\(869\) 1.20519e9 1.83652
\(870\) −1.60416e8 2.77849e8i −0.243607 0.421940i
\(871\) 9.25339e8 + 5.34245e8i 1.40038 + 0.808511i
\(872\) −2.76614e7 + 4.79110e7i −0.0417182 + 0.0722580i
\(873\) 4.31851e7 2.49329e7i 0.0649070 0.0374741i
\(874\) 3.03010e7i 0.0453860i
\(875\) 0 0
\(876\) −2.61494e8 −0.388999
\(877\) −4.68948e8 8.12242e8i −0.695226 1.20417i −0.970104 0.242688i \(-0.921971\pi\)
0.274878 0.961479i \(-0.411362\pi\)
\(878\) −8.66164e8 5.00080e8i −1.27973 0.738850i
\(879\) 2.22391e8 3.85192e8i 0.327454 0.567167i
\(880\) 1.22448e9 7.06956e8i 1.79682 1.03739i
\(881\) 9.47337e8i 1.38540i 0.721224 + 0.692702i \(0.243580\pi\)
−0.721224 + 0.692702i \(0.756420\pi\)
\(882\) 0 0
\(883\) 1.52054e8 0.220860 0.110430 0.993884i \(-0.464777\pi\)
0.110430 + 0.993884i \(0.464777\pi\)
\(884\) −3.09313e8 5.35746e8i −0.447756 0.775536i
\(885\) −4.96080e8 2.86412e8i −0.715686 0.413201i
\(886\) −4.69211e7 + 8.12697e7i −0.0674632 + 0.116850i
\(887\) −1.02528e9 + 5.91948e8i −1.46917 + 0.848228i −0.999403 0.0345605i \(-0.988997\pi\)
−0.469771 + 0.882788i \(0.655664\pi\)
\(888\) 4.63441e7i 0.0661843i
\(889\) 0 0
\(890\) −2.89518e7 −0.0410682
\(891\) 6.06759e7 + 1.05094e8i 0.0857795 + 0.148574i
\(892\) −1.32086e9 7.62599e8i −1.86107 1.07449i
\(893\) −2.91470e8 + 5.04842e8i −0.409298 + 0.708926i
\(894\) 5.50297e8 3.17714e8i 0.770167 0.444656i
\(895\) 4.30612e8i 0.600644i
\(896\) 0 0
\(897\) −3.15080e7 −0.0436560
\(898\) −2.99974e8 5.19569e8i −0.414242 0.717488i
\(899\) 2.25231e7 + 1.30037e7i 0.0309990 + 0.0178973i
\(900\) −1.79324e8 + 3.10598e8i −0.245986 + 0.426060i
\(901\) 5.42144e8 3.13007e8i 0.741209 0.427937i
\(902\) 1.62189e9i 2.21005i
\(903\) 0 0
\(904\) −1.70388e8 −0.230639
\(905\) −7.60824e8 1.31779e9i −1.02645 1.77787i
\(906\) −1.01177e9 5.84147e8i −1.36050 0.785485i
\(907\) −1.69886e8 + 2.94252e8i −0.227686 + 0.394364i −0.957122 0.289685i \(-0.906449\pi\)
0.729436 + 0.684049i \(0.239783\pi\)
\(908\) 2.41489e8 1.39423e8i 0.322581 0.186242i
\(909\) 3.40467e8i 0.453297i
\(910\) 0 0
\(911\) −9.44286e8 −1.24896 −0.624480 0.781041i \(-0.714689\pi\)
−0.624480 + 0.781041i \(0.714689\pi\)
\(912\) 1.10947e8 + 1.92165e8i 0.146262 + 0.253332i
\(913\) −1.89327e8 1.09308e8i −0.248772 0.143628i
\(914\) −2.31967e8 + 4.01778e8i −0.303799 + 0.526196i
\(915\) −8.57653e8 + 4.95166e8i −1.11956 + 0.646380i
\(916\) 3.98857e7i 0.0518956i
\(917\) 0 0
\(918\) 1.25414e8 0.162113
\(919\) 1.87277e8 + 3.24374e8i 0.241290 + 0.417926i 0.961082 0.276264i \(-0.0890963\pi\)
−0.719792 + 0.694189i \(0.755763\pi\)
\(920\) 8.78947e6 + 5.07460e6i 0.0112875 + 0.00651686i
\(921\) 7.97106e7 1.38063e8i 0.102032 0.176725i
\(922\) 1.41755e8 8.18424e7i 0.180862 0.104420i
\(923\) 9.35280e8i 1.18942i
\(924\) 0 0
\(925\) 7.68494e8 0.970991
\(926\) 7.27157e8 + 1.25947e9i 0.915788 + 1.58619i
\(927\) −1.08935e8 6.28936e7i −0.136750 0.0789527i
\(928\) 2.18240e8 3.78003e8i 0.273081 0.472989i
\(929\) −7.89503e8 + 4.55820e8i −0.984707 + 0.568521i −0.903688 0.428192i \(-0.859151\pi\)
−0.0810189 + 0.996713i \(0.525817\pi\)
\(930\) 9.68343e7i 0.120387i
\(931\) 0 0
\(932\) −1.15851e9 −1.43104
\(933\) 1.22698e8 + 2.12519e8i 0.151075 + 0.261669i
\(934\) 1.04145e9 + 6.01279e8i 1.27819 + 0.737965i
\(935\) −5.59028e8 + 9.68265e8i −0.683910 + 1.18457i
\(936\) −5.18365e7 + 2.99278e7i −0.0632133 + 0.0364962i
\(937\) 3.76597e8i 0.457781i −0.973452 0.228890i \(-0.926490\pi\)
0.973452 0.228890i \(-0.0735097\pi\)
\(938\) 0 0
\(939\) −8.65586e8 −1.04547
\(940\) −9.99242e8 1.73074e9i −1.20306 2.08376i
\(941\) −2.17999e8 1.25862e8i −0.261629 0.151051i 0.363449 0.931614i \(-0.381599\pi\)
−0.625077 + 0.780563i \(0.714933\pi\)
\(942\) −4.23983e8 + 7.34360e8i −0.507219 + 0.878529i
\(943\) 3.88656e7 2.24391e7i 0.0463479 0.0267590i
\(944\) 6.93922e8i 0.824888i
\(945\) 0 0
\(946\) 2.94491e8 0.347856
\(947\) 1.32933e8 + 2.30247e8i 0.156525 + 0.271109i 0.933613 0.358282i \(-0.116637\pi\)
−0.777088 + 0.629392i \(0.783304\pi\)
\(948\) −5.61545e8 3.24208e8i −0.659112 0.380539i
\(949\) 3.61838e8 6.26723e8i 0.423366 0.733292i
\(950\) 8.26643e8 4.77262e8i 0.964156 0.556655i
\(951\) 9.40107e7i 0.109304i
\(952\) 0 0
\(953\) −5.38039e8 −0.621635 −0.310817 0.950470i \(-0.600603\pi\)
−0.310817 + 0.950470i \(0.600603\pi\)
\(954\) −3.09979e8 5.36900e8i −0.357016 0.618370i
\(955\) −7.04475e8 4.06729e8i −0.808827 0.466976i
\(956\) 6.95581e8 1.20478e9i 0.796112 1.37891i
\(957\) −2.57537e8 + 1.48689e8i −0.293836 + 0.169646i
\(958\) 9.05777e8i 1.03021i
\(959\) 0 0
\(960\) −9.38774e8 −1.06108
\(961\) −4.39827e8 7.61803e8i −0.495578 0.858366i
\(962\) 1.13687e9 + 6.56370e8i 1.27698 + 0.737265i
\(963\) 7.85794e7 1.36104e8i 0.0879893 0.152402i
\(964\) 2.21077e8 1.27639e8i 0.246781 0.142479i
\(965\) 2.78244e7i 0.0309631i
\(966\) 0 0
\(967\) −1.16138e9 −1.28439 −0.642194 0.766542i \(-0.721976\pi\)
−0.642194 + 0.766542i \(0.721976\pi\)
\(968\) 9.86856e7 + 1.70929e8i 0.108800 + 0.188447i
\(969\) −1.51956e8 8.77316e7i −0.167011 0.0964240i
\(970\) 2.27494e8 3.94031e8i 0.249261 0.431732i
\(971\) −1.30640e9 + 7.54248e8i −1.42698 + 0.823866i −0.996881 0.0789166i \(-0.974854\pi\)
−0.430097 + 0.902783i \(0.641521\pi\)
\(972\) 6.52898e7i 0.0710962i
\(973\) 0 0
\(974\) −1.65874e9 −1.79515
\(975\) −4.96274e8 8.59572e8i −0.535436 0.927403i
\(976\) −1.03896e9 5.99847e8i −1.11751 0.645195i
\(977\) 6.03772e7 1.04576e8i 0.0647425 0.112137i −0.831837 0.555020i \(-0.812711\pi\)
0.896580 + 0.442882i \(0.146044\pi\)
\(978\) 8.12667e8 4.69194e8i 0.868752 0.501574i
\(979\) 2.68354e7i 0.0285996i
\(980\) 0 0
\(981\) 1.67005e8 0.176897
\(982\) 2.94939e8 + 5.10849e8i 0.311457 + 0.539459i
\(983\) 1.86333e7 + 1.07580e7i 0.0196169 + 0.0113258i 0.509776 0.860307i \(-0.329728\pi\)
−0.490159 + 0.871633i \(0.663061\pi\)
\(984\) 4.26274e7 7.38329e7i 0.0447408 0.0774934i
\(985\) −1.19235e9 + 6.88401e8i −1.24765 + 0.720333i
\(986\) 3.07333e8i 0.320611i
\(987\) 0 0
\(988\) 8.57131e8 0.888743
\(989\) −4.07433e6 7.05694e6i −0.00421179 0.00729504i
\(990\) 9.58899e8 + 5.53621e8i 0.988251 + 0.570567i
\(991\) 3.07940e7 5.33368e7i 0.0316407 0.0548033i −0.849771 0.527151i \(-0.823260\pi\)
0.881412 + 0.472348i \(0.156593\pi\)
\(992\) 1.14090e8 6.58698e7i 0.116872 0.0674763i
\(993\) 1.52230e8i 0.155472i
\(994\) 0 0
\(995\) −3.36855e8 −0.341959
\(996\) 5.88100e7 + 1.01862e8i 0.0595215 + 0.103094i
\(997\) −6.72319e8 3.88164e8i −0.678406 0.391678i 0.120848 0.992671i \(-0.461439\pi\)
−0.799254 + 0.600993i \(0.794772\pi\)
\(998\) 7.34733e8 1.27259e9i 0.739159 1.28026i
\(999\) −1.21157e8 + 6.99500e7i −0.121521 + 0.0701603i
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 147.7.f.d.31.4 8
7.2 even 3 21.7.f.a.19.4 yes 8
7.3 odd 6 147.7.d.b.97.2 8
7.4 even 3 147.7.d.b.97.1 8
7.5 odd 6 inner 147.7.f.d.19.4 8
7.6 odd 2 21.7.f.a.10.4 8
21.2 odd 6 63.7.m.d.19.1 8
21.11 odd 6 441.7.d.c.244.7 8
21.17 even 6 441.7.d.c.244.8 8
21.20 even 2 63.7.m.d.10.1 8
28.23 odd 6 336.7.bh.d.145.1 8
28.27 even 2 336.7.bh.d.241.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.7.f.a.10.4 8 7.6 odd 2
21.7.f.a.19.4 yes 8 7.2 even 3
63.7.m.d.10.1 8 21.20 even 2
63.7.m.d.19.1 8 21.2 odd 6
147.7.d.b.97.1 8 7.4 even 3
147.7.d.b.97.2 8 7.3 odd 6
147.7.f.d.19.4 8 7.5 odd 6 inner
147.7.f.d.31.4 8 1.1 even 1 trivial
336.7.bh.d.145.1 8 28.23 odd 6
336.7.bh.d.241.1 8 28.27 even 2
441.7.d.c.244.7 8 21.11 odd 6
441.7.d.c.244.8 8 21.17 even 6