Properties

Label 60.7.f.a.19.8
Level $60$
Weight $7$
Character 60.19
Analytic conductor $13.803$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [60,7,Mod(19,60)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(60, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("60.19");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 60.f (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: \(13.8032450172\)
Analytic rank: \(0\)
Dimension: \(36\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 19.8
Character \(\chi\) \(=\) 60.19
Dual form 60.7.f.a.19.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-6.43144 + 4.75779i) q^{2} -15.5885 q^{3} +(18.7270 - 61.1989i) q^{4} +(-121.123 - 30.8887i) q^{5} +(100.256 - 74.1665i) q^{6} -549.446 q^{7} +(170.730 + 482.696i) q^{8} +243.000 q^{9} +O(q^{10})\) \(q+(-6.43144 + 4.75779i) q^{2} -15.5885 q^{3} +(18.7270 - 61.1989i) q^{4} +(-121.123 - 30.8887i) q^{5} +(100.256 - 74.1665i) q^{6} -549.446 q^{7} +(170.730 + 482.696i) q^{8} +243.000 q^{9} +(925.960 - 377.621i) q^{10} -2553.45i q^{11} +(-291.924 + 953.996i) q^{12} +1094.42i q^{13} +(3533.73 - 2614.14i) q^{14} +(1888.13 + 481.507i) q^{15} +(-3394.60 - 2292.14i) q^{16} +1497.06i q^{17} +(-1562.84 + 1156.14i) q^{18} +9519.26i q^{19} +(-4158.63 + 6834.17i) q^{20} +8565.01 q^{21} +(12148.8 + 16422.4i) q^{22} +67.4831 q^{23} +(-2661.41 - 7524.49i) q^{24} +(13716.8 + 7482.69i) q^{25} +(-5207.00 - 7038.68i) q^{26} -3788.00 q^{27} +(-10289.4 + 33625.4i) q^{28} -6173.49 q^{29} +(-14434.3 + 5886.52i) q^{30} +20870.0i q^{31} +(32737.7 - 1409.04i) q^{32} +39804.3i q^{33} +(-7122.70 - 9628.28i) q^{34} +(66550.7 + 16971.6i) q^{35} +(4550.65 - 14871.3i) q^{36} -26680.6i q^{37} +(-45290.6 - 61222.6i) q^{38} -17060.3i q^{39} +(-5769.53 - 63739.4i) q^{40} +102914. q^{41} +(-55085.4 + 40750.5i) q^{42} -8841.12 q^{43} +(-156268. - 47818.3i) q^{44} +(-29433.0 - 7505.95i) q^{45} +(-434.014 + 321.070i) q^{46} -49099.5 q^{47} +(52916.6 + 35730.9i) q^{48} +184241. q^{49} +(-123820. + 17137.0i) q^{50} -23336.9i q^{51} +(66977.1 + 20495.1i) q^{52} -246920. i q^{53} +(24362.3 - 18022.5i) q^{54} +(-78872.7 + 309283. i) q^{55} +(-93806.7 - 265215. i) q^{56} -148391. i q^{57} +(39704.4 - 29372.1i) q^{58} +114674. i q^{59} +(64826.6 - 106534. i) q^{60} -15188.1 q^{61} +(-99295.0 - 134224. i) q^{62} -133515. q^{63} +(-203847. + 164821. i) q^{64} +(33805.1 - 132560. i) q^{65} +(-189381. - 255999. i) q^{66} +380903. q^{67} +(91618.5 + 28035.4i) q^{68} -1051.96 q^{69} +(-508765. + 207482. i) q^{70} -323615. i q^{71} +(41487.3 + 117295. i) q^{72} -361842. i q^{73} +(126940. + 171595. i) q^{74} +(-213823. - 116644. i) q^{75} +(582568. + 178267. i) q^{76} +1.40298e6i q^{77} +(81169.1 + 109722. i) q^{78} +753970. i q^{79} +(340365. + 382486. i) q^{80} +59049.0 q^{81} +(-661887. + 489644. i) q^{82} +23678.7 q^{83} +(160397. - 524169. i) q^{84} +(46242.3 - 181329. i) q^{85} +(56861.2 - 42064.1i) q^{86} +96235.2 q^{87} +(1.23254e6 - 435950. i) q^{88} -559777. q^{89} +(225008. - 91761.8i) q^{90} -601322. i q^{91} +(1263.75 - 4129.89i) q^{92} -325331. i q^{93} +(315781. - 233605. i) q^{94} +(294037. - 1.15301e6i) q^{95} +(-510330. + 21964.7i) q^{96} +843786. i q^{97} +(-1.18494e6 + 876581. i) q^{98} -620488. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9} - 1422 q^{10} + 15484 q^{14} + 1266 q^{16} - 2188 q^{20} - 9234 q^{24} + 13812 q^{25} - 32052 q^{26} - 36920 q^{29} - 24300 q^{30} - 156204 q^{34} - 16038 q^{36} + 7674 q^{40} + 341848 q^{41} + 74892 q^{44} + 10692 q^{45} + 478080 q^{46} + 482556 q^{49} - 191448 q^{50} - 39366 q^{54} - 926132 q^{56} + 126846 q^{60} - 455976 q^{61} - 618 q^{64} - 624192 q^{65} - 127332 q^{66} - 541728 q^{69} - 1871304 q^{70} - 612324 q^{74} - 1566456 q^{76} + 2360972 q^{80} + 2125764 q^{81} + 858276 q^{84} + 2280864 q^{85} + 5157592 q^{86} - 1806104 q^{89} - 345546 q^{90} - 3121992 q^{94} - 4040118 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.43144 + 4.75779i −0.803931 + 0.594723i
\(3\) −15.5885 −0.577350
\(4\) 18.7270 61.1989i 0.292609 0.956232i
\(5\) −121.123 30.8887i −0.968988 0.247109i
\(6\) 100.256 74.1665i 0.464150 0.343364i
\(7\) −549.446 −1.60188 −0.800941 0.598743i \(-0.795667\pi\)
−0.800941 + 0.598743i \(0.795667\pi\)
\(8\) 170.730 + 482.696i 0.333456 + 0.942766i
\(9\) 243.000 0.333333
\(10\) 925.960 377.621i 0.925960 0.377621i
\(11\) 2553.45i 1.91844i −0.282653 0.959222i \(-0.591214\pi\)
0.282653 0.959222i \(-0.408786\pi\)
\(12\) −291.924 + 953.996i −0.168938 + 0.552081i
\(13\) 1094.42i 0.498142i 0.968485 + 0.249071i \(0.0801252\pi\)
−0.968485 + 0.249071i \(0.919875\pi\)
\(14\) 3533.73 2614.14i 1.28780 0.952676i
\(15\) 1888.13 + 481.507i 0.559445 + 0.142669i
\(16\) −3394.60 2292.14i −0.828760 0.559604i
\(17\) 1497.06i 0.304715i 0.988325 + 0.152357i \(0.0486864\pi\)
−0.988325 + 0.152357i \(0.951314\pi\)
\(18\) −1562.84 + 1156.14i −0.267977 + 0.198241i
\(19\) 9519.26i 1.38785i 0.720048 + 0.693925i \(0.244120\pi\)
−0.720048 + 0.693925i \(0.755880\pi\)
\(20\) −4158.63 + 6834.17i −0.519828 + 0.854271i
\(21\) 8565.01 0.924847
\(22\) 12148.8 + 16422.4i 1.14094 + 1.54230i
\(23\) 67.4831 0.00554640 0.00277320 0.999996i \(-0.499117\pi\)
0.00277320 + 0.999996i \(0.499117\pi\)
\(24\) −2661.41 7524.49i −0.192521 0.544306i
\(25\) 13716.8 + 7482.69i 0.877874 + 0.478892i
\(26\) −5207.00 7038.68i −0.296256 0.400471i
\(27\) −3788.00 −0.192450
\(28\) −10289.4 + 33625.4i −0.468725 + 1.53177i
\(29\) −6173.49 −0.253126 −0.126563 0.991959i \(-0.540395\pi\)
−0.126563 + 0.991959i \(0.540395\pi\)
\(30\) −14434.3 + 5886.52i −0.534604 + 0.218019i
\(31\) 20870.0i 0.700547i 0.936647 + 0.350273i \(0.113911\pi\)
−0.936647 + 0.350273i \(0.886089\pi\)
\(32\) 32737.7 1409.04i 0.999075 0.0430004i
\(33\) 39804.3i 1.10761i
\(34\) −7122.70 9628.28i −0.181221 0.244969i
\(35\) 66550.7 + 16971.6i 1.55220 + 0.395840i
\(36\) 4550.65 14871.3i 0.0975362 0.318744i
\(37\) 26680.6i 0.526732i −0.964696 0.263366i \(-0.915167\pi\)
0.964696 0.263366i \(-0.0848327\pi\)
\(38\) −45290.6 61222.6i −0.825386 1.11573i
\(39\) 17060.3i 0.287602i
\(40\) −5769.53 63739.4i −0.0901489 0.995928i
\(41\) 102914. 1.49322 0.746610 0.665262i \(-0.231680\pi\)
0.746610 + 0.665262i \(0.231680\pi\)
\(42\) −55085.4 + 40750.5i −0.743513 + 0.550028i
\(43\) −8841.12 −0.111199 −0.0555996 0.998453i \(-0.517707\pi\)
−0.0555996 + 0.998453i \(0.517707\pi\)
\(44\) −156268. 47818.3i −1.83448 0.561354i
\(45\) −29433.0 7505.95i −0.322996 0.0823698i
\(46\) −434.014 + 321.070i −0.00445892 + 0.00329857i
\(47\) −49099.5 −0.472916 −0.236458 0.971642i \(-0.575987\pi\)
−0.236458 + 0.971642i \(0.575987\pi\)
\(48\) 52916.6 + 35730.9i 0.478485 + 0.323087i
\(49\) 184241. 1.56603
\(50\) −123820. + 17137.0i −0.990558 + 0.137096i
\(51\) 23336.9i 0.175927i
\(52\) 66977.1 + 20495.1i 0.476339 + 0.145761i
\(53\) 246920.i 1.65855i −0.558842 0.829274i \(-0.688754\pi\)
0.558842 0.829274i \(-0.311246\pi\)
\(54\) 24362.3 18022.5i 0.154717 0.114455i
\(55\) −78872.7 + 309283.i −0.474066 + 1.85895i
\(56\) −93806.7 265215.i −0.534158 1.51020i
\(57\) 148391.i 0.801275i
\(58\) 39704.4 29372.1i 0.203496 0.150540i
\(59\) 114674.i 0.558351i 0.960240 + 0.279175i \(0.0900611\pi\)
−0.960240 + 0.279175i \(0.909939\pi\)
\(60\) 64826.6 106534.i 0.300123 0.493213i
\(61\) −15188.1 −0.0669136 −0.0334568 0.999440i \(-0.510652\pi\)
−0.0334568 + 0.999440i \(0.510652\pi\)
\(62\) −99295.0 134224.i −0.416631 0.563191i
\(63\) −133515. −0.533961
\(64\) −203847. + 164821.i −0.777614 + 0.628742i
\(65\) 33805.1 132560.i 0.123095 0.482693i
\(66\) −189381. 255999.i −0.658724 0.890445i
\(67\) 380903. 1.26646 0.633228 0.773965i \(-0.281729\pi\)
0.633228 + 0.773965i \(0.281729\pi\)
\(68\) 91618.5 + 28035.4i 0.291378 + 0.0891621i
\(69\) −1051.96 −0.00320222
\(70\) −508765. + 207482.i −1.48328 + 0.604904i
\(71\) 323615.i 0.904177i −0.891973 0.452088i \(-0.850679\pi\)
0.891973 0.452088i \(-0.149321\pi\)
\(72\) 41487.3 + 117295.i 0.111152 + 0.314255i
\(73\) 361842.i 0.930145i −0.885273 0.465072i \(-0.846028\pi\)
0.885273 0.465072i \(-0.153972\pi\)
\(74\) 126940. + 171595.i 0.313260 + 0.423456i
\(75\) −213823. 116644.i −0.506841 0.276488i
\(76\) 582568. + 178267.i 1.32711 + 0.406097i
\(77\) 1.40298e6i 3.07312i
\(78\) 81169.1 + 109722.i 0.171044 + 0.231212i
\(79\) 753970.i 1.52923i 0.644488 + 0.764615i \(0.277071\pi\)
−0.644488 + 0.764615i \(0.722929\pi\)
\(80\) 340365. + 382486.i 0.664775 + 0.747044i
\(81\) 59049.0 0.111111
\(82\) −661887. + 489644.i −1.20045 + 0.888053i
\(83\) 23678.7 0.0414117 0.0207059 0.999786i \(-0.493409\pi\)
0.0207059 + 0.999786i \(0.493409\pi\)
\(84\) 160397. 524169.i 0.270618 0.884369i
\(85\) 46242.3 181329.i 0.0752979 0.295265i
\(86\) 56861.2 42064.1i 0.0893965 0.0661328i
\(87\) 96235.2 0.146142
\(88\) 1.23254e6 435950.i 1.80864 0.639718i
\(89\) −559777. −0.794045 −0.397023 0.917809i \(-0.629957\pi\)
−0.397023 + 0.917809i \(0.629957\pi\)
\(90\) 225008. 91761.8i 0.308653 0.125874i
\(91\) 601322.i 0.797964i
\(92\) 1263.75 4129.89i 0.00162293 0.00530365i
\(93\) 325331.i 0.404461i
\(94\) 315781. 233605.i 0.380191 0.281254i
\(95\) 294037. 1.15301e6i 0.342951 1.34481i
\(96\) −510330. + 21964.7i −0.576816 + 0.0248263i
\(97\) 843786.i 0.924522i 0.886744 + 0.462261i \(0.152962\pi\)
−0.886744 + 0.462261i \(0.847038\pi\)
\(98\) −1.18494e6 + 876581.i −1.25898 + 0.931352i
\(99\) 620488.i 0.639481i
\(100\) 714805. 699323.i 0.714805 0.699323i
\(101\) 490739. 0.476307 0.238153 0.971228i \(-0.423458\pi\)
0.238153 + 0.971228i \(0.423458\pi\)
\(102\) 111032. + 150090.i 0.104628 + 0.141433i
\(103\) −1.06879e6 −0.978095 −0.489047 0.872257i \(-0.662656\pi\)
−0.489047 + 0.872257i \(0.662656\pi\)
\(104\) −528271. + 186849.i −0.469631 + 0.166108i
\(105\) −1.03742e6 264562.i −0.896165 0.228538i
\(106\) 1.17479e6 + 1.58805e6i 0.986377 + 1.33336i
\(107\) 1.83486e6 1.49779 0.748896 0.662688i \(-0.230584\pi\)
0.748896 + 0.662688i \(0.230584\pi\)
\(108\) −70937.6 + 231821.i −0.0563126 + 0.184027i
\(109\) 930756. 0.718714 0.359357 0.933200i \(-0.382996\pi\)
0.359357 + 0.933200i \(0.382996\pi\)
\(110\) −964235. 2.36439e6i −0.724444 1.77640i
\(111\) 415909.i 0.304109i
\(112\) 1.86515e6 + 1.25940e6i 1.32758 + 0.896419i
\(113\) 2.29606e6i 1.59128i 0.605767 + 0.795642i \(0.292866\pi\)
−0.605767 + 0.795642i \(0.707134\pi\)
\(114\) 706010. + 954366.i 0.476537 + 0.644170i
\(115\) −8173.78 2084.46i −0.00537439 0.00137057i
\(116\) −115611. + 377811.i −0.0740669 + 0.242047i
\(117\) 265943.i 0.166047i
\(118\) −545592. 737517.i −0.332064 0.448875i
\(119\) 822554.i 0.488117i
\(120\) 89938.0 + 993599.i 0.0520475 + 0.574999i
\(121\) −4.74854e6 −2.68043
\(122\) 97681.6 72261.8i 0.0537939 0.0397951i
\(123\) −1.60427e6 −0.862111
\(124\) 1.27722e6 + 390831.i 0.669886 + 0.204986i
\(125\) −1.43029e6 1.33002e6i −0.732310 0.680971i
\(126\) 858696. 635237.i 0.429267 0.317559i
\(127\) −2.86745e6 −1.39986 −0.699931 0.714210i \(-0.746786\pi\)
−0.699931 + 0.714210i \(0.746786\pi\)
\(128\) 526846. 2.02990e6i 0.251220 0.967930i
\(129\) 137819. 0.0642009
\(130\) 413274. + 1.01339e6i 0.188108 + 0.461259i
\(131\) 1.61676e6i 0.719170i 0.933112 + 0.359585i \(0.117082\pi\)
−0.933112 + 0.359585i \(0.882918\pi\)
\(132\) 2.43598e6 + 745414.i 1.05914 + 0.324098i
\(133\) 5.23031e6i 2.22317i
\(134\) −2.44976e6 + 1.81226e6i −1.01814 + 0.753191i
\(135\) 458815. + 117006.i 0.186482 + 0.0475562i
\(136\) −722626. + 255593.i −0.287274 + 0.101609i
\(137\) 1.21351e6i 0.471934i −0.971761 0.235967i \(-0.924174\pi\)
0.971761 0.235967i \(-0.0758258\pi\)
\(138\) 6765.60 5004.99i 0.00257436 0.00190443i
\(139\) 745684.i 0.277658i −0.990316 0.138829i \(-0.955666\pi\)
0.990316 0.138829i \(-0.0443339\pi\)
\(140\) 2.28494e6 3.75500e6i 0.832703 1.36844i
\(141\) 765386. 0.273038
\(142\) 1.53969e6 + 2.08131e6i 0.537735 + 0.726895i
\(143\) 2.79454e6 0.955657
\(144\) −824888. 556989.i −0.276253 0.186535i
\(145\) 747754. + 190691.i 0.245276 + 0.0625498i
\(146\) 1.72157e6 + 2.32717e6i 0.553179 + 0.747772i
\(147\) −2.87204e6 −0.904145
\(148\) −1.63282e6 499646.i −0.503678 0.154126i
\(149\) 2.87355e6 0.868679 0.434340 0.900749i \(-0.356982\pi\)
0.434340 + 0.900749i \(0.356982\pi\)
\(150\) 1.93016e6 267139.i 0.571899 0.0791524i
\(151\) 1.70934e6i 0.496476i −0.968699 0.248238i \(-0.920149\pi\)
0.968699 0.248238i \(-0.0798515\pi\)
\(152\) −4.59491e6 + 1.62522e6i −1.30842 + 0.462787i
\(153\) 363786.i 0.101572i
\(154\) −6.67508e6 9.02320e6i −1.82766 2.47058i
\(155\) 644647. 2.52785e6i 0.173112 0.678821i
\(156\) −1.04407e6 319487.i −0.275014 0.0841549i
\(157\) 5.99085e6i 1.54807i 0.633145 + 0.774033i \(0.281764\pi\)
−0.633145 + 0.774033i \(0.718236\pi\)
\(158\) −3.58723e6 4.84911e6i −0.909468 1.22939i
\(159\) 3.84910e6i 0.957563i
\(160\) −4.00883e6 840557.i −0.978717 0.205214i
\(161\) −37078.3 −0.00888468
\(162\) −379770. + 280942.i −0.0893256 + 0.0660804i
\(163\) 3.10350e6 0.716619 0.358310 0.933603i \(-0.383353\pi\)
0.358310 + 0.933603i \(0.383353\pi\)
\(164\) 1.92727e6 6.29823e6i 0.436929 1.42787i
\(165\) 1.22950e6 4.82124e6i 0.273702 1.07326i
\(166\) −152288. + 112658.i −0.0332921 + 0.0246285i
\(167\) 6.24357e6 1.34055 0.670276 0.742112i \(-0.266176\pi\)
0.670276 + 0.742112i \(0.266176\pi\)
\(168\) 1.46230e6 + 4.13429e6i 0.308396 + 0.871914i
\(169\) 3.62906e6 0.751855
\(170\) 565322. + 1.38622e6i 0.115066 + 0.282154i
\(171\) 2.31318e6i 0.462616i
\(172\) −165567. + 541066.i −0.0325379 + 0.106332i
\(173\) 4.02510e6i 0.777389i 0.921367 + 0.388695i \(0.127074\pi\)
−0.921367 + 0.388695i \(0.872926\pi\)
\(174\) −618931. + 457866.i −0.117488 + 0.0869142i
\(175\) −7.53662e6 4.11133e6i −1.40625 0.767128i
\(176\) −5.85286e6 + 8.66795e6i −1.07357 + 1.58993i
\(177\) 1.78758e6i 0.322364i
\(178\) 3.60018e6 2.66330e6i 0.638357 0.472237i
\(179\) 5.02425e6i 0.876015i 0.898971 + 0.438008i \(0.144316\pi\)
−0.898971 + 0.438008i \(0.855684\pi\)
\(180\) −1.01055e6 + 1.66070e6i −0.173276 + 0.284757i
\(181\) 7.58820e6 1.27969 0.639843 0.768506i \(-0.279000\pi\)
0.639843 + 0.768506i \(0.279000\pi\)
\(182\) 2.86096e6 + 3.86737e6i 0.474568 + 0.641508i
\(183\) 236759. 0.0386326
\(184\) 11521.4 + 32573.8i 0.00184948 + 0.00522896i
\(185\) −824127. + 3.23164e6i −0.130160 + 0.510397i
\(186\) 1.54786e6 + 2.09235e6i 0.240542 + 0.325159i
\(187\) 3.82267e6 0.584578
\(188\) −919485. + 3.00483e6i −0.138379 + 0.452217i
\(189\) 2.08130e6 0.308282
\(190\) 3.59467e6 + 8.81446e6i 0.524080 + 1.28509i
\(191\) 5.02660e6i 0.721397i 0.932682 + 0.360699i \(0.117462\pi\)
−0.932682 + 0.360699i \(0.882538\pi\)
\(192\) 3.17766e6 2.56931e6i 0.448955 0.363005i
\(193\) 2.70300e6i 0.375988i −0.982170 0.187994i \(-0.939801\pi\)
0.982170 0.187994i \(-0.0601986\pi\)
\(194\) −4.01455e6 5.42676e6i −0.549834 0.743251i
\(195\) −526969. + 2.06640e6i −0.0710692 + 0.278683i
\(196\) 3.45028e6 1.12754e7i 0.458233 1.49748i
\(197\) 8.87040e6i 1.16023i 0.814534 + 0.580115i \(0.196993\pi\)
−0.814534 + 0.580115i \(0.803007\pi\)
\(198\) 2.95215e6 + 3.99064e6i 0.380314 + 0.514099i
\(199\) 1.00354e7i 1.27343i 0.771101 + 0.636713i \(0.219706\pi\)
−0.771101 + 0.636713i \(0.780294\pi\)
\(200\) −1.27000e6 + 7.89855e6i −0.158750 + 0.987319i
\(201\) −5.93769e6 −0.731189
\(202\) −3.15616e6 + 2.33483e6i −0.382918 + 0.283271i
\(203\) 3.39200e6 0.405478
\(204\) −1.42819e6 437029.i −0.168227 0.0514778i
\(205\) −1.24653e7 3.17888e6i −1.44691 0.368989i
\(206\) 6.87387e6 5.08508e6i 0.786320 0.581696i
\(207\) 16398.4 0.00184880
\(208\) 2.50855e6 3.71511e6i 0.278762 0.412840i
\(209\) 2.43069e7 2.66251
\(210\) 7.93086e6 3.23432e6i 0.856372 0.349241i
\(211\) 6.66623e6i 0.709631i −0.934936 0.354816i \(-0.884544\pi\)
0.934936 0.354816i \(-0.115456\pi\)
\(212\) −1.51112e7 4.62406e6i −1.58596 0.485306i
\(213\) 5.04466e6i 0.522027i
\(214\) −1.18008e7 + 8.72987e6i −1.20412 + 0.890771i
\(215\) 1.07087e6 + 273090.i 0.107751 + 0.0274784i
\(216\) −646723. 1.82845e6i −0.0641737 0.181435i
\(217\) 1.14669e7i 1.12219i
\(218\) −5.98610e6 + 4.42834e6i −0.577796 + 0.427436i
\(219\) 5.64056e6i 0.537019i
\(220\) 1.74507e7 + 1.06188e7i 1.63887 + 0.997262i
\(221\) −1.63841e6 −0.151791
\(222\) −1.97880e6 2.67489e6i −0.180861 0.244482i
\(223\) −6.53736e6 −0.589506 −0.294753 0.955574i \(-0.595237\pi\)
−0.294753 + 0.955574i \(0.595237\pi\)
\(224\) −1.79876e7 + 774189.i −1.60040 + 0.0688816i
\(225\) 3.33318e6 + 1.81829e6i 0.292625 + 0.159631i
\(226\) −1.09242e7 1.47670e7i −0.946373 1.27928i
\(227\) −4.37830e6 −0.374307 −0.187154 0.982331i \(-0.559926\pi\)
−0.187154 + 0.982331i \(0.559926\pi\)
\(228\) −9.08133e6 2.77890e6i −0.766205 0.234460i
\(229\) 5.31579e6 0.442651 0.221325 0.975200i \(-0.428962\pi\)
0.221325 + 0.975200i \(0.428962\pi\)
\(230\) 62486.7 25483.0i 0.00513575 0.00209444i
\(231\) 2.18703e7i 1.77427i
\(232\) −1.05400e6 2.97992e6i −0.0844065 0.238638i
\(233\) 604948.i 0.0478245i 0.999714 + 0.0239122i \(0.00761223\pi\)
−0.999714 + 0.0239122i \(0.992388\pi\)
\(234\) −1.26530e6 1.71040e6i −0.0987521 0.133490i
\(235\) 5.94710e6 + 1.51662e6i 0.458249 + 0.116862i
\(236\) 7.01789e6 + 2.14749e6i 0.533913 + 0.163378i
\(237\) 1.17532e7i 0.882901i
\(238\) 3.91354e6 + 5.29021e6i 0.290294 + 0.392412i
\(239\) 1.45792e6i 0.106792i 0.998573 + 0.0533962i \(0.0170046\pi\)
−0.998573 + 0.0533962i \(0.982995\pi\)
\(240\) −5.30576e6 5.96237e6i −0.383808 0.431306i
\(241\) −7.04006e6 −0.502951 −0.251475 0.967864i \(-0.580916\pi\)
−0.251475 + 0.967864i \(0.580916\pi\)
\(242\) 3.05400e7 2.25926e7i 2.15488 1.59411i
\(243\) −920483. −0.0641500
\(244\) −284427. + 929496.i −0.0195795 + 0.0639850i
\(245\) −2.23160e7 5.69097e6i −1.51746 0.386980i
\(246\) 1.03178e7 7.63279e6i 0.693077 0.512717i
\(247\) −1.04180e7 −0.691345
\(248\) −1.00739e7 + 3.56313e6i −0.660451 + 0.233602i
\(249\) −369114. −0.0239091
\(250\) 1.55268e7 + 1.74893e6i 0.993716 + 0.111932i
\(251\) 1.58945e7i 1.00514i −0.864537 0.502569i \(-0.832388\pi\)
0.864537 0.502569i \(-0.167612\pi\)
\(252\) −2.50033e6 + 8.17098e6i −0.156242 + 0.510590i
\(253\) 172315.i 0.0106405i
\(254\) 1.84419e7 1.36427e7i 1.12539 0.832531i
\(255\) −720846. + 2.82665e6i −0.0434732 + 0.170471i
\(256\) 6.26943e6 + 1.55618e7i 0.373687 + 0.927555i
\(257\) 2.27306e7i 1.33910i −0.742768 0.669549i \(-0.766487\pi\)
0.742768 0.669549i \(-0.233513\pi\)
\(258\) −886378. + 655715.i −0.0516131 + 0.0381818i
\(259\) 1.46595e7i 0.843762i
\(260\) −7.47943e6 4.55127e6i −0.425548 0.258948i
\(261\) −1.50016e6 −0.0843753
\(262\) −7.69220e6 1.03981e7i −0.427707 0.578163i
\(263\) −8.61581e6 −0.473619 −0.236809 0.971556i \(-0.576102\pi\)
−0.236809 + 0.971556i \(0.576102\pi\)
\(264\) −1.92134e7 + 6.79578e6i −1.04422 + 0.369341i
\(265\) −7.62702e6 + 2.99078e7i −0.409843 + 1.60711i
\(266\) 2.48847e7 + 3.36385e7i 1.32217 + 1.78727i
\(267\) 8.72607e6 0.458442
\(268\) 7.13316e6 2.33108e7i 0.370576 1.21103i
\(269\) −2.00001e7 −1.02748 −0.513742 0.857944i \(-0.671741\pi\)
−0.513742 + 0.857944i \(0.671741\pi\)
\(270\) −3.50753e6 + 1.43042e6i −0.178201 + 0.0726731i
\(271\) 7.07623e6i 0.355545i 0.984072 + 0.177772i \(0.0568891\pi\)
−0.984072 + 0.177772i \(0.943111\pi\)
\(272\) 3.43147e6 5.08193e6i 0.170519 0.252535i
\(273\) 9.37369e6i 0.460705i
\(274\) 5.77362e6 + 7.80462e6i 0.280670 + 0.379402i
\(275\) 1.91067e7 3.50251e7i 0.918728 1.68415i
\(276\) −19700.0 + 64378.6i −0.000936996 + 0.00306206i
\(277\) 5.31398e6i 0.250023i −0.992155 0.125012i \(-0.960103\pi\)
0.992155 0.125012i \(-0.0398968\pi\)
\(278\) 3.54781e6 + 4.79583e6i 0.165130 + 0.223218i
\(279\) 5.07141e6i 0.233516i
\(280\) 3.17004e6 + 3.50213e7i 0.144408 + 1.59536i
\(281\) −3.15126e7 −1.42025 −0.710126 0.704075i \(-0.751362\pi\)
−0.710126 + 0.704075i \(0.751362\pi\)
\(282\) −4.92254e6 + 3.64154e6i −0.219504 + 0.162382i
\(283\) 2.50051e7 1.10324 0.551620 0.834096i \(-0.314010\pi\)
0.551620 + 0.834096i \(0.314010\pi\)
\(284\) −1.98049e7 6.06032e6i −0.864603 0.264570i
\(285\) −4.58359e6 + 1.79736e7i −0.198003 + 0.776426i
\(286\) −1.79729e7 + 1.32958e7i −0.768282 + 0.568351i
\(287\) −5.65458e7 −2.39196
\(288\) 7.95526e6 342396.i 0.333025 0.0143335i
\(289\) 2.18964e7 0.907149
\(290\) −5.71641e6 + 2.33124e6i −0.234385 + 0.0955856i
\(291\) 1.31533e7i 0.533773i
\(292\) −2.21443e7 6.77620e6i −0.889434 0.272168i
\(293\) 7.88892e6i 0.313628i 0.987628 + 0.156814i \(0.0501223\pi\)
−0.987628 + 0.156814i \(0.949878\pi\)
\(294\) 1.84714e7 1.36645e7i 0.726870 0.537716i
\(295\) 3.54211e6 1.38897e7i 0.137974 0.541035i
\(296\) 1.28786e7 4.55516e6i 0.496585 0.175642i
\(297\) 9.67245e6i 0.369205i
\(298\) −1.84811e7 + 1.36717e7i −0.698358 + 0.516624i
\(299\) 73854.6i 0.00276289i
\(300\) −1.11427e7 + 1.09014e7i −0.412693 + 0.403755i
\(301\) 4.85771e6 0.178128
\(302\) 8.13268e6 + 1.09935e7i 0.295266 + 0.399132i
\(303\) −7.64987e6 −0.274996
\(304\) 2.18194e7 3.23141e7i 0.776646 1.15019i
\(305\) 1.83964e6 + 469141.i 0.0648385 + 0.0165350i
\(306\) −1.73082e6 2.33967e6i −0.0604069 0.0816565i
\(307\) 3.83562e7 1.32562 0.662812 0.748786i \(-0.269363\pi\)
0.662812 + 0.748786i \(0.269363\pi\)
\(308\) 8.58609e7 + 2.62736e7i 2.93862 + 0.899222i
\(309\) 1.66608e7 0.564703
\(310\) 7.88094e6 + 1.93248e7i 0.264541 + 0.648679i
\(311\) 4.40873e7i 1.46566i 0.680413 + 0.732829i \(0.261800\pi\)
−0.680413 + 0.732829i \(0.738200\pi\)
\(312\) 8.23492e6 2.91269e6i 0.271141 0.0959028i
\(313\) 2.98649e6i 0.0973931i 0.998814 + 0.0486965i \(0.0155067\pi\)
−0.998814 + 0.0486965i \(0.984493\pi\)
\(314\) −2.85032e7 3.85298e7i −0.920671 1.24454i
\(315\) 1.61718e7 + 4.12411e6i 0.517401 + 0.131947i
\(316\) 4.61421e7 + 1.41196e7i 1.46230 + 0.447466i
\(317\) 3.90061e7i 1.22449i −0.790668 0.612245i \(-0.790267\pi\)
0.790668 0.612245i \(-0.209733\pi\)
\(318\) −1.83132e7 2.47553e7i −0.569485 0.769815i
\(319\) 1.57637e7i 0.485608i
\(320\) 2.97817e7 1.36671e7i 0.908866 0.417088i
\(321\) −2.86026e7 −0.864750
\(322\) 238467. 176410.i 0.00714267 0.00528393i
\(323\) −1.42509e7 −0.422898
\(324\) 1.10581e6 3.61373e6i 0.0325121 0.106248i
\(325\) −8.18918e6 + 1.50119e7i −0.238556 + 0.437305i
\(326\) −1.99600e7 + 1.47658e7i −0.576112 + 0.426190i
\(327\) −1.45090e7 −0.414950
\(328\) 1.75705e7 + 4.96763e7i 0.497924 + 1.40776i
\(329\) 2.69775e7 0.757555
\(330\) 1.50309e7 + 3.68572e7i 0.418258 + 1.02561i
\(331\) 4.24129e7i 1.16954i −0.811200 0.584768i \(-0.801185\pi\)
0.811200 0.584768i \(-0.198815\pi\)
\(332\) 443430. 1.44911e6i 0.0121174 0.0395992i
\(333\) 6.48337e6i 0.175577i
\(334\) −4.01552e7 + 2.97056e7i −1.07771 + 0.797257i
\(335\) −4.61363e7 1.17656e7i −1.22718 0.312953i
\(336\) −2.90748e7 1.96322e7i −0.766476 0.517548i
\(337\) 4.59359e7i 1.20022i 0.799916 + 0.600112i \(0.204877\pi\)
−0.799916 + 0.600112i \(0.795123\pi\)
\(338\) −2.33401e7 + 1.72663e7i −0.604439 + 0.447146i
\(339\) 3.57920e7i 0.918728i
\(340\) −1.02312e7 6.22572e6i −0.260309 0.158399i
\(341\) 5.32905e7 1.34396
\(342\) −1.10056e7 1.48771e7i −0.275129 0.371911i
\(343\) −3.65889e7 −0.906707
\(344\) −1.50944e6 4.26757e6i −0.0370801 0.104835i
\(345\) 127417. + 32493.6i 0.00310291 + 0.000791298i
\(346\) −1.91506e7 2.58872e7i −0.462331 0.624967i
\(347\) 4.68864e7 1.12217 0.561085 0.827758i \(-0.310384\pi\)
0.561085 + 0.827758i \(0.310384\pi\)
\(348\) 1.80219e6 5.88948e6i 0.0427625 0.139746i
\(349\) 1.85236e7 0.435762 0.217881 0.975975i \(-0.430086\pi\)
0.217881 + 0.975975i \(0.430086\pi\)
\(350\) 6.80322e7 9.41585e6i 1.58676 0.219612i
\(351\) 4.14565e6i 0.0958674i
\(352\) −3.59790e6 8.35940e7i −0.0824939 1.91667i
\(353\) 3.87474e7i 0.880884i −0.897781 0.440442i \(-0.854822\pi\)
0.897781 0.440442i \(-0.145178\pi\)
\(354\) 8.50494e6 + 1.14967e7i 0.191717 + 0.259158i
\(355\) −9.99603e6 + 3.91973e7i −0.223431 + 0.876136i
\(356\) −1.04829e7 + 3.42577e7i −0.232345 + 0.759292i
\(357\) 1.28224e7i 0.281814i
\(358\) −2.39043e7 3.23132e7i −0.520987 0.704256i
\(359\) 7.81969e6i 0.169008i −0.996423 0.0845038i \(-0.973069\pi\)
0.996423 0.0845038i \(-0.0269305\pi\)
\(360\) −1.40200e6 1.54887e7i −0.0300496 0.331976i
\(361\) −4.35704e7 −0.926126
\(362\) −4.88031e7 + 3.61030e7i −1.02878 + 0.761058i
\(363\) 7.40225e7 1.54755
\(364\) −3.68003e7 1.12609e7i −0.763039 0.233491i
\(365\) −1.11768e7 + 4.38276e7i −0.229848 + 0.901299i
\(366\) −1.52270e6 + 1.12645e6i −0.0310579 + 0.0229757i
\(367\) 5.10078e7 1.03190 0.515951 0.856618i \(-0.327439\pi\)
0.515951 + 0.856618i \(0.327439\pi\)
\(368\) −229078. 154680.i −0.00459664 0.00310379i
\(369\) 2.50082e7 0.497740
\(370\) −1.00751e7 2.47051e7i −0.198905 0.487733i
\(371\) 1.35669e8i 2.65680i
\(372\) −1.99099e7 6.09246e6i −0.386759 0.118349i
\(373\) 2.10254e7i 0.405152i 0.979267 + 0.202576i \(0.0649313\pi\)
−0.979267 + 0.202576i \(0.935069\pi\)
\(374\) −2.45853e7 + 1.81875e7i −0.469960 + 0.347662i
\(375\) 2.22961e7 + 2.07330e7i 0.422799 + 0.393159i
\(376\) −8.38274e6 2.37001e7i −0.157697 0.445849i
\(377\) 6.75637e6i 0.126093i
\(378\) −1.33857e7 + 9.90236e6i −0.247838 + 0.183343i
\(379\) 5.39833e6i 0.0991613i 0.998770 + 0.0495806i \(0.0157885\pi\)
−0.998770 + 0.0495806i \(0.984212\pi\)
\(380\) −6.50562e7 3.95870e7i −1.18560 0.721443i
\(381\) 4.46992e7 0.808211
\(382\) −2.39155e7 3.23283e7i −0.429032 0.579953i
\(383\) −6.21222e7 −1.10573 −0.552867 0.833270i \(-0.686466\pi\)
−0.552867 + 0.833270i \(0.686466\pi\)
\(384\) −8.21271e6 + 3.16430e7i −0.145042 + 0.558835i
\(385\) 4.33362e7 1.69934e8i 0.759397 2.97782i
\(386\) 1.28603e7 + 1.73842e7i 0.223609 + 0.302269i
\(387\) −2.14839e6 −0.0370664
\(388\) 5.16387e7 + 1.58015e7i 0.884057 + 0.270523i
\(389\) −2.55535e7 −0.434113 −0.217056 0.976159i \(-0.569646\pi\)
−0.217056 + 0.976159i \(0.569646\pi\)
\(390\) −6.44231e6 1.57971e7i −0.108604 0.266308i
\(391\) 101026.i 0.00169007i
\(392\) 3.14555e7 + 8.89326e7i 0.522201 + 1.47640i
\(393\) 2.52028e7i 0.415213i
\(394\) −4.22034e7 5.70495e7i −0.690016 0.932745i
\(395\) 2.32891e7 9.13234e7i 0.377887 1.48180i
\(396\) −3.79732e7 1.16199e7i −0.611493 0.187118i
\(397\) 1.95610e7i 0.312622i −0.987708 0.156311i \(-0.950040\pi\)
0.987708 0.156311i \(-0.0499602\pi\)
\(398\) −4.77461e7 6.45419e7i −0.757336 1.02375i
\(399\) 8.15325e7i 1.28355i
\(400\) −2.94117e7 5.68415e7i −0.459557 0.888148i
\(401\) 4.67869e7 0.725589 0.362795 0.931869i \(-0.381823\pi\)
0.362795 + 0.931869i \(0.381823\pi\)
\(402\) 3.81880e7 2.82503e7i 0.587825 0.434855i
\(403\) −2.28405e7 −0.348972
\(404\) 9.19006e6 3.00327e7i 0.139372 0.455460i
\(405\) −7.15222e6 1.82395e6i −0.107665 0.0274566i
\(406\) −2.18154e7 + 1.61384e7i −0.325976 + 0.241147i
\(407\) −6.81275e7 −1.01051
\(408\) 1.12646e7 3.98430e6i 0.165858 0.0586640i
\(409\) 8.50968e7 1.24378 0.621889 0.783105i \(-0.286365\pi\)
0.621889 + 0.783105i \(0.286365\pi\)
\(410\) 9.52945e7 3.88625e7i 1.38266 0.563871i
\(411\) 1.89167e7i 0.272471i
\(412\) −2.00152e7 + 6.54088e7i −0.286199 + 0.935286i
\(413\) 6.30069e7i 0.894412i
\(414\) −105465. + 78020.0i −0.00148631 + 0.00109952i
\(415\) −2.86804e6 731403.i −0.0401274 0.0102332i
\(416\) 1.54207e6 + 3.58287e7i 0.0214203 + 0.497681i
\(417\) 1.16241e7i 0.160306i
\(418\) −1.56329e8 + 1.15647e8i −2.14047 + 1.58346i
\(419\) 6.10478e7i 0.829904i 0.909843 + 0.414952i \(0.136202\pi\)
−0.909843 + 0.414952i \(0.863798\pi\)
\(420\) −3.56187e7 + 5.85347e7i −0.480762 + 0.790070i
\(421\) −7.67905e7 −1.02911 −0.514555 0.857458i \(-0.672043\pi\)
−0.514555 + 0.857458i \(0.672043\pi\)
\(422\) 3.17165e7 + 4.28735e7i 0.422034 + 0.570494i
\(423\) −1.19312e7 −0.157639
\(424\) 1.19187e8 4.21565e7i 1.56362 0.553054i
\(425\) −1.12021e7 + 2.05349e7i −0.145925 + 0.267501i
\(426\) −2.40014e7 3.24444e7i −0.310461 0.419673i
\(427\) 8.34504e6 0.107188
\(428\) 3.43613e7 1.12291e8i 0.438267 1.43224i
\(429\) −4.35625e7 −0.551749
\(430\) −8.18652e6 + 3.33859e6i −0.102966 + 0.0419911i
\(431\) 1.61877e7i 0.202188i −0.994877 0.101094i \(-0.967766\pi\)
0.994877 0.101094i \(-0.0322342\pi\)
\(432\) 1.28587e7 + 8.68260e6i 0.159495 + 0.107696i
\(433\) 9.44401e7i 1.16330i 0.813438 + 0.581651i \(0.197593\pi\)
−0.813438 + 0.581651i \(0.802407\pi\)
\(434\) 5.45572e7 + 7.37489e7i 0.667394 + 0.902166i
\(435\) −1.16563e7 2.97258e6i −0.141610 0.0361131i
\(436\) 1.74302e7 5.69612e7i 0.210302 0.687258i
\(437\) 642389.i 0.00769757i
\(438\) −2.68366e7 3.62769e7i −0.319378 0.431726i
\(439\) 5.43621e7i 0.642543i −0.946987 0.321272i \(-0.895890\pi\)
0.946987 0.321272i \(-0.104110\pi\)
\(440\) −1.62755e8 + 1.47322e7i −1.91063 + 0.172946i
\(441\) 4.47707e7 0.522009
\(442\) 1.05373e7 7.79521e6i 0.122029 0.0902736i
\(443\) 1.25008e8 1.43789 0.718945 0.695067i \(-0.244625\pi\)
0.718945 + 0.695067i \(0.244625\pi\)
\(444\) 2.54531e7 + 7.78870e6i 0.290799 + 0.0889849i
\(445\) 6.78022e7 + 1.72908e7i 0.769420 + 0.196216i
\(446\) 4.20447e7 3.11034e7i 0.473922 0.350593i
\(447\) −4.47942e7 −0.501532
\(448\) 1.12003e8 9.05602e7i 1.24565 1.00717i
\(449\) −1.08925e8 −1.20334 −0.601672 0.798743i \(-0.705499\pi\)
−0.601672 + 0.798743i \(0.705499\pi\)
\(450\) −3.00882e7 + 4.16429e6i −0.330186 + 0.0456987i
\(451\) 2.62786e8i 2.86466i
\(452\) 1.40516e8 + 4.29982e7i 1.52164 + 0.465623i
\(453\) 2.66460e7i 0.286640i
\(454\) 2.81588e7 2.08310e7i 0.300917 0.222609i
\(455\) −1.85741e7 + 7.28343e7i −0.197184 + 0.773217i
\(456\) 7.16275e7 2.53347e7i 0.755415 0.267190i
\(457\) 1.25491e8i 1.31482i 0.753534 + 0.657408i \(0.228347\pi\)
−0.753534 + 0.657408i \(0.771653\pi\)
\(458\) −3.41882e7 + 2.52914e7i −0.355860 + 0.263255i
\(459\) 5.67087e6i 0.0586424i
\(460\) −280637. + 461191.i −0.00288318 + 0.00473813i
\(461\) 6.26253e7 0.639215 0.319608 0.947550i \(-0.396449\pi\)
0.319608 + 0.947550i \(0.396449\pi\)
\(462\) 1.04054e8 + 1.40658e8i 1.05520 + 1.42639i
\(463\) −1.61927e7 −0.163146 −0.0815731 0.996667i \(-0.525994\pi\)
−0.0815731 + 0.996667i \(0.525994\pi\)
\(464\) 2.09565e7 + 1.41505e7i 0.209781 + 0.141650i
\(465\) −1.00490e7 + 3.94052e7i −0.0999461 + 0.391918i
\(466\) −2.87821e6 3.89069e6i −0.0284423 0.0384475i
\(467\) 2.19434e6 0.0215453 0.0107727 0.999942i \(-0.496571\pi\)
0.0107727 + 0.999942i \(0.496571\pi\)
\(468\) 1.62754e7 + 4.98031e6i 0.158780 + 0.0485868i
\(469\) −2.09286e8 −2.02871
\(470\) −4.54642e7 + 1.85410e7i −0.437901 + 0.178583i
\(471\) 9.33881e7i 0.893777i
\(472\) −5.53525e7 + 1.95782e7i −0.526394 + 0.186186i
\(473\) 2.25753e7i 0.213330i
\(474\) 5.59193e7 + 7.55902e7i 0.525082 + 0.709791i
\(475\) −7.12296e7 + 1.30574e8i −0.664630 + 1.21836i
\(476\) −5.03394e7 1.54039e7i −0.466753 0.142827i
\(477\) 6.00015e7i 0.552850i
\(478\) −6.93647e6 9.37653e6i −0.0635119 0.0858536i
\(479\) 1.52962e8i 1.39180i −0.718140 0.695899i \(-0.755006\pi\)
0.718140 0.695899i \(-0.244994\pi\)
\(480\) 6.24914e7 + 1.31030e7i 0.565063 + 0.118480i
\(481\) 2.91997e7 0.262387
\(482\) 4.52778e7 3.34951e7i 0.404337 0.299116i
\(483\) 577993. 0.00512957
\(484\) −8.89258e7 + 2.90606e8i −0.784317 + 2.56311i
\(485\) 2.60634e7 1.02202e8i 0.228458 0.895850i
\(486\) 5.92003e6 4.37946e6i 0.0515722 0.0381515i
\(487\) 3.34301e7 0.289435 0.144717 0.989473i \(-0.453773\pi\)
0.144717 + 0.989473i \(0.453773\pi\)
\(488\) −2.59306e6 7.33124e6i −0.0223128 0.0630839i
\(489\) −4.83787e7 −0.413740
\(490\) 1.70600e8 6.95733e7i 1.45008 0.591364i
\(491\) 7.03915e7i 0.594670i 0.954773 + 0.297335i \(0.0960978\pi\)
−0.954773 + 0.297335i \(0.903902\pi\)
\(492\) −3.00432e7 + 9.81797e7i −0.252261 + 0.824378i
\(493\) 9.24210e6i 0.0771312i
\(494\) 6.70030e7 4.95668e7i 0.555794 0.411159i
\(495\) −1.91661e7 + 7.51557e7i −0.158022 + 0.619650i
\(496\) 4.78369e7 7.08453e7i 0.392029 0.580585i
\(497\) 1.77809e8i 1.44838i
\(498\) 2.37394e6 1.75617e6i 0.0192212 0.0142193i
\(499\) 1.54457e7i 0.124310i −0.998067 0.0621548i \(-0.980203\pi\)
0.998067 0.0621548i \(-0.0197972\pi\)
\(500\) −1.08181e8 + 6.26251e7i −0.865447 + 0.501000i
\(501\) −9.73276e7 −0.773968
\(502\) 7.56226e7 + 1.02225e8i 0.597779 + 0.808061i
\(503\) 1.32839e8 1.04381 0.521905 0.853004i \(-0.325222\pi\)
0.521905 + 0.853004i \(0.325222\pi\)
\(504\) −2.27950e7 6.44473e7i −0.178053 0.503400i
\(505\) −5.94400e7 1.51583e7i −0.461535 0.117700i
\(506\) 819836. + 1.10823e6i 0.00632813 + 0.00855419i
\(507\) −5.65715e7 −0.434084
\(508\) −5.36987e7 + 1.75485e8i −0.409612 + 1.33859i
\(509\) 7.26222e7 0.550701 0.275351 0.961344i \(-0.411206\pi\)
0.275351 + 0.961344i \(0.411206\pi\)
\(510\) −8.81249e6 2.16090e7i −0.0664337 0.162901i
\(511\) 1.98813e8i 1.48998i
\(512\) −1.14361e8 7.02562e7i −0.852057 0.523449i
\(513\) 3.60589e7i 0.267092i
\(514\) 1.08148e8 + 1.46191e8i 0.796393 + 1.07654i
\(515\) 1.29456e8 + 3.30135e7i 0.947762 + 0.241696i
\(516\) 2.58094e6 8.43439e6i 0.0187857 0.0613910i
\(517\) 1.25373e8i 0.907262i
\(518\) −6.97468e7 9.42818e7i −0.501805 0.678326i
\(519\) 6.27451e7i 0.448826i
\(520\) 6.97575e7 6.31427e6i 0.496113 0.0449069i
\(521\) −1.05596e8 −0.746682 −0.373341 0.927694i \(-0.621788\pi\)
−0.373341 + 0.927694i \(0.621788\pi\)
\(522\) 9.64818e6 7.13743e6i 0.0678319 0.0501800i
\(523\) 4.78413e7 0.334425 0.167212 0.985921i \(-0.446523\pi\)
0.167212 + 0.985921i \(0.446523\pi\)
\(524\) 9.89439e7 + 3.02770e7i 0.687694 + 0.210435i
\(525\) 1.17484e8 + 6.40893e7i 0.811899 + 0.442902i
\(526\) 5.54121e7 4.09922e7i 0.380756 0.281672i
\(527\) −3.12437e7 −0.213467
\(528\) 9.12370e7 1.35120e8i 0.619825 0.917947i
\(529\) −1.48031e8 −0.999969
\(530\) −9.32420e7 2.28638e8i −0.626302 1.53575i
\(531\) 2.78657e7i 0.186117i
\(532\) −3.20089e8 9.79479e7i −2.12587 0.650519i
\(533\) 1.12631e8i 0.743835i
\(534\) −5.61212e7 + 4.15167e7i −0.368556 + 0.272646i
\(535\) −2.22244e8 5.66764e7i −1.45134 0.370118i
\(536\) 6.50315e7 + 1.83860e8i 0.422308 + 1.19397i
\(537\) 7.83202e7i 0.505768i
\(538\) 1.28630e8 9.51562e7i 0.826027 0.611069i
\(539\) 4.70451e8i 3.00433i
\(540\) 1.57529e7 2.58878e7i 0.100041 0.164404i
\(541\) 2.07113e8 1.30802 0.654012 0.756484i \(-0.273085\pi\)
0.654012 + 0.756484i \(0.273085\pi\)
\(542\) −3.36672e7 4.55104e7i −0.211451 0.285833i
\(543\) −1.18288e8 −0.738827
\(544\) 2.10942e6 + 4.90104e7i 0.0131028 + 0.304433i
\(545\) −1.12736e8 2.87498e7i −0.696425 0.177601i
\(546\) −4.45980e7 6.02864e7i −0.273992 0.370375i
\(547\) 2.69963e8 1.64946 0.824731 0.565525i \(-0.191326\pi\)
0.824731 + 0.565525i \(0.191326\pi\)
\(548\) −7.42654e7 2.27253e7i −0.451279 0.138092i
\(549\) −3.69071e6 −0.0223045
\(550\) 4.37585e7 + 3.16167e8i 0.263011 + 1.90033i
\(551\) 5.87670e7i 0.351301i
\(552\) −179600. 507775.i −0.00106780 0.00301894i
\(553\) 4.14265e8i 2.44964i
\(554\) 2.52828e7 + 3.41766e7i 0.148695 + 0.201001i
\(555\) 1.28469e7 5.03763e7i 0.0751482 0.294678i
\(556\) −4.56350e7 1.39644e7i −0.265506 0.0812452i
\(557\) 1.22257e8i 0.707468i 0.935346 + 0.353734i \(0.115088\pi\)
−0.935346 + 0.353734i \(0.884912\pi\)
\(558\) −2.41287e7 3.26165e7i −0.138877 0.187730i
\(559\) 9.67587e6i 0.0553930i
\(560\) −1.87012e8 2.10155e8i −1.06489 1.19668i
\(561\) −5.95896e7 −0.337506
\(562\) 2.02672e8 1.49930e8i 1.14178 0.844656i
\(563\) −6.05594e7 −0.339357 −0.169678 0.985500i \(-0.554273\pi\)
−0.169678 + 0.985500i \(0.554273\pi\)
\(564\) 1.43333e7 4.68407e7i 0.0798933 0.261088i
\(565\) 7.09222e7 2.78107e8i 0.393221 1.54193i
\(566\) −1.60819e8 + 1.18969e8i −0.886928 + 0.656122i
\(567\) −3.24442e7 −0.177987
\(568\) 1.56208e8 5.52507e7i 0.852427 0.301504i
\(569\) −1.97749e8 −1.07344 −0.536719 0.843761i \(-0.680336\pi\)
−0.536719 + 0.843761i \(0.680336\pi\)
\(570\) −5.60353e7 1.37404e8i −0.302578 0.741949i
\(571\) 2.35693e8i 1.26601i 0.774146 + 0.633007i \(0.218179\pi\)
−0.774146 + 0.633007i \(0.781821\pi\)
\(572\) 5.23332e7 1.71023e8i 0.279634 0.913830i
\(573\) 7.83570e7i 0.416499i
\(574\) 3.63671e8 2.69033e8i 1.92297 1.42256i
\(575\) 925650. + 504955.i 0.00486904 + 0.00265613i
\(576\) −4.95348e7 + 4.00515e7i −0.259205 + 0.209581i
\(577\) 1.18751e8i 0.618171i −0.951034 0.309085i \(-0.899977\pi\)
0.951034 0.309085i \(-0.100023\pi\)
\(578\) −1.40825e8 + 1.04178e8i −0.729285 + 0.539503i
\(579\) 4.21356e7i 0.217077i
\(580\) 2.56732e7 4.21907e7i 0.131582 0.216238i
\(581\) −1.30101e7 −0.0663367
\(582\) 6.25807e7 + 8.45948e7i 0.317447 + 0.429116i
\(583\) −6.30497e8 −3.18183
\(584\) 1.74660e8 6.17772e7i 0.876908 0.310163i
\(585\) 8.21464e6 3.22120e7i 0.0410318 0.160898i
\(586\) −3.75338e7 5.07372e7i −0.186522 0.252135i
\(587\) 3.48828e7 0.172464 0.0862318 0.996275i \(-0.472517\pi\)
0.0862318 + 0.996275i \(0.472517\pi\)
\(588\) −5.37845e7 + 1.75766e8i −0.264561 + 0.864573i
\(589\) −1.98667e8 −0.972254
\(590\) 4.33031e7 + 1.06183e8i 0.210845 + 0.517011i
\(591\) 1.38276e8i 0.669859i
\(592\) −6.11555e7 + 9.05699e7i −0.294761 + 0.436535i
\(593\) 2.91576e8i 1.39826i 0.714994 + 0.699130i \(0.246429\pi\)
−0.714994 + 0.699130i \(0.753571\pi\)
\(594\) −4.60195e7 6.22079e7i −0.219575 0.296815i
\(595\) −2.54076e7 + 9.96306e7i −0.120618 + 0.472979i
\(596\) 5.38128e7 1.75858e8i 0.254183 0.830659i
\(597\) 1.56436e8i 0.735213i
\(598\) −351384. 474992.i −0.00164316 0.00222117i
\(599\) 4.20347e8i 1.95582i 0.209036 + 0.977908i \(0.432967\pi\)
−0.209036 + 0.977908i \(0.567033\pi\)
\(600\) 1.97974e7 1.23126e8i 0.0916544 0.570029i
\(601\) 3.31489e8 1.52702 0.763511 0.645794i \(-0.223474\pi\)
0.763511 + 0.645794i \(0.223474\pi\)
\(602\) −3.12421e7 + 2.31120e7i −0.143203 + 0.105937i
\(603\) 9.25595e7 0.422152
\(604\) −1.04610e8 3.20108e7i −0.474746 0.145273i
\(605\) 5.75160e8 + 1.46676e8i 2.59730 + 0.662359i
\(606\) 4.91997e7 3.63964e7i 0.221078 0.163546i
\(607\) 2.17689e8 0.973355 0.486677 0.873582i \(-0.338209\pi\)
0.486677 + 0.873582i \(0.338209\pi\)
\(608\) 1.34130e7 + 3.11639e8i 0.0596781 + 1.38657i
\(609\) −5.28760e7 −0.234103
\(610\) −1.40636e7 + 5.73535e6i −0.0619594 + 0.0252680i
\(611\) 5.37353e7i 0.235579i
\(612\) 2.22633e7 + 6.81261e6i 0.0971260 + 0.0297207i
\(613\) 7.52134e7i 0.326523i 0.986583 + 0.163261i \(0.0522014\pi\)
−0.986583 + 0.163261i \(0.947799\pi\)
\(614\) −2.46686e8 + 1.82490e8i −1.06571 + 0.788379i
\(615\) 1.94315e8 + 4.95539e7i 0.835375 + 0.213036i
\(616\) −6.77213e8 + 2.39531e8i −2.89723 + 1.02475i
\(617\) 3.12798e8i 1.33171i −0.746083 0.665853i \(-0.768068\pi\)
0.746083 0.665853i \(-0.231932\pi\)
\(618\) −1.07153e8 + 7.92685e7i −0.453982 + 0.335842i
\(619\) 8.50021e7i 0.358392i 0.983813 + 0.179196i \(0.0573495\pi\)
−0.983813 + 0.179196i \(0.942650\pi\)
\(620\) −1.42629e8 8.67905e7i −0.598457 0.364164i
\(621\) −255626. −0.00106741
\(622\) −2.09758e8 2.83545e8i −0.871660 1.17829i
\(623\) 3.07567e8 1.27197
\(624\) −3.91045e7 + 5.79128e7i −0.160943 + 0.238353i
\(625\) 1.32159e8 + 2.05277e8i 0.541325 + 0.840813i
\(626\) −1.42091e7 1.92074e7i −0.0579219 0.0782973i
\(627\) −3.78908e8 −1.53720
\(628\) 3.66633e8 + 1.12190e8i 1.48031 + 0.452978i
\(629\) 3.99425e7 0.160503
\(630\) −1.23630e8 + 5.04181e7i −0.494426 + 0.201635i
\(631\) 4.70789e8i 1.87386i 0.349513 + 0.936932i \(0.386347\pi\)
−0.349513 + 0.936932i \(0.613653\pi\)
\(632\) −3.63938e8 + 1.28725e8i −1.44170 + 0.509931i
\(633\) 1.03916e8i 0.409706i
\(634\) 1.85583e8 + 2.50866e8i 0.728232 + 0.984404i
\(635\) 3.47316e8 + 8.85719e7i 1.35645 + 0.345919i
\(636\) 2.35560e8 + 7.20819e7i 0.915653 + 0.280191i
\(637\) 2.01637e8i 0.780103i
\(638\) −7.50003e7 1.01383e8i −0.288802 0.390395i
\(639\) 7.86384e7i 0.301392i
\(640\) −1.26514e8 + 2.29594e8i −0.482613 + 0.875833i
\(641\) 2.62768e8 0.997698 0.498849 0.866689i \(-0.333756\pi\)
0.498849 + 0.866689i \(0.333756\pi\)
\(642\) 1.83956e8 1.36085e8i 0.695199 0.514287i
\(643\) 4.31165e8 1.62185 0.810926 0.585149i \(-0.198964\pi\)
0.810926 + 0.585149i \(0.198964\pi\)
\(644\) −694363. + 2.26915e6i −0.00259974 + 0.00849582i
\(645\) −1.66932e7 4.25706e6i −0.0622099 0.0158646i
\(646\) 9.16541e7 6.78029e7i 0.339981 0.251507i
\(647\) −2.35225e7 −0.0868501 −0.0434250 0.999057i \(-0.513827\pi\)
−0.0434250 + 0.999057i \(0.513827\pi\)
\(648\) 1.00814e7 + 2.85027e7i 0.0370507 + 0.104752i
\(649\) 2.92813e8 1.07117
\(650\) −1.87550e7 1.35510e8i −0.0682932 0.493438i
\(651\) 1.78752e8i 0.647899i
\(652\) 5.81190e7 1.89930e8i 0.209689 0.685254i
\(653\) 1.76583e8i 0.634174i −0.948396 0.317087i \(-0.897295\pi\)
0.948396 0.317087i \(-0.102705\pi\)
\(654\) 9.33141e7 6.90309e7i 0.333591 0.246780i
\(655\) 4.99396e7 1.95828e8i 0.177714 0.696867i
\(656\) −3.49353e8 2.35894e8i −1.23752 0.835612i
\(657\) 8.79276e7i 0.310048i
\(658\) −1.73504e8 + 1.28353e8i −0.609022 + 0.450536i
\(659\) 8.34343e7i 0.291533i −0.989319 0.145767i \(-0.953435\pi\)
0.989319 0.145767i \(-0.0465649\pi\)
\(660\) −2.72029e8 1.65531e8i −0.946203 0.575769i
\(661\) −4.88849e8 −1.69266 −0.846332 0.532656i \(-0.821194\pi\)
−0.846332 + 0.532656i \(0.821194\pi\)
\(662\) 2.01791e8 + 2.72776e8i 0.695550 + 0.940226i
\(663\) 2.55403e7 0.0876366
\(664\) 4.04265e6 + 1.14296e7i 0.0138090 + 0.0390415i
\(665\) −1.61557e8 + 6.33514e8i −0.549366 + 2.15422i
\(666\) 3.08465e7 + 4.16975e7i 0.104420 + 0.141152i
\(667\) −416606. −0.00140394
\(668\) 1.16923e8 3.82099e8i 0.392257 1.28188i
\(669\) 1.01907e8 0.340351
\(670\) 3.52701e8 1.43837e8i 1.17269 0.478240i
\(671\) 3.87821e7i 0.128370i
\(672\) 2.80399e8 1.20684e7i 0.923992 0.0397688i
\(673\) 8.80898e7i 0.288988i 0.989506 + 0.144494i \(0.0461555\pi\)
−0.989506 + 0.144494i \(0.953844\pi\)
\(674\) −2.18553e8 2.95434e8i −0.713801 0.964896i
\(675\) −5.19591e7 2.83444e7i −0.168947 0.0921628i
\(676\) 6.79613e7 2.22094e8i 0.219999 0.718948i
\(677\) 4.30417e8i 1.38715i −0.720384 0.693575i \(-0.756035\pi\)
0.720384 0.693575i \(-0.243965\pi\)
\(678\) 1.70291e8 + 2.30194e8i 0.546389 + 0.738594i
\(679\) 4.63614e8i 1.48097i
\(680\) 9.54219e7 8.63734e6i 0.303474 0.0274697i
\(681\) 6.82510e7 0.216106
\(682\) −3.42735e8 + 2.53545e8i −1.08045 + 0.799284i
\(683\) −5.22431e8 −1.63971 −0.819854 0.572572i \(-0.805946\pi\)
−0.819854 + 0.572572i \(0.805946\pi\)
\(684\) 1.41564e8 + 4.33188e7i 0.442369 + 0.135366i
\(685\) −3.74837e7 + 1.46984e8i −0.116619 + 0.457298i
\(686\) 2.35319e8 1.74082e8i 0.728929 0.539239i
\(687\) −8.28649e7 −0.255564
\(688\) 3.00121e7 + 2.02651e7i 0.0921575 + 0.0622275i
\(689\) 2.70233e8 0.826192
\(690\) −974071. + 397241.i −0.00296513 + 0.00120922i
\(691\) 2.74162e8i 0.830947i −0.909605 0.415473i \(-0.863616\pi\)
0.909605 0.415473i \(-0.136384\pi\)
\(692\) 2.46332e8 + 7.53779e7i 0.743365 + 0.227471i
\(693\) 3.40924e8i 1.02437i
\(694\) −3.01547e8 + 2.23076e8i −0.902147 + 0.667380i
\(695\) −2.30332e7 + 9.03198e7i −0.0686120 + 0.269047i
\(696\) 1.64302e7 + 4.64523e7i 0.0487321 + 0.137778i
\(697\) 1.54069e8i 0.455006i
\(698\) −1.19134e8 + 8.81314e7i −0.350322 + 0.259158i
\(699\) 9.43020e6i 0.0276115i
\(700\) −3.92747e8 + 3.84240e8i −1.14503 + 1.12023i
\(701\) −1.41906e8 −0.411952 −0.205976 0.978557i \(-0.566037\pi\)
−0.205976 + 0.978557i \(0.566037\pi\)
\(702\) 1.97241e7 + 2.66625e7i 0.0570146 + 0.0770707i
\(703\) 2.53979e8 0.731025
\(704\) 4.20862e8 + 5.20512e8i 1.20621 + 1.49181i
\(705\) −9.27062e7 2.36418e7i −0.264570 0.0674703i
\(706\) 1.84352e8 + 2.49202e8i 0.523882 + 0.708169i
\(707\) −2.69635e8 −0.762987
\(708\) −1.09398e8 3.34760e7i −0.308255 0.0943265i
\(709\) −1.21569e8 −0.341102 −0.170551 0.985349i \(-0.554555\pi\)
−0.170551 + 0.985349i \(0.554555\pi\)
\(710\) −1.22204e8 2.99655e8i −0.341436 0.837232i
\(711\) 1.83215e8i 0.509743i
\(712\) −9.55706e7 2.70202e8i −0.264780 0.748599i
\(713\) 1.40837e6i 0.00388551i
\(714\) −6.10060e7 8.24663e7i −0.167602 0.226559i
\(715\) −3.38484e8 8.63196e7i −0.926020 0.236152i
\(716\) 3.07478e8 + 9.40888e7i 0.837674 + 0.256330i
\(717\) 2.27267e7i 0.0616566i
\(718\) 3.72044e7 + 5.02919e7i 0.100513 + 0.135870i
\(719\) 6.64252e7i 0.178709i −0.996000 0.0893545i \(-0.971520\pi\)
0.996000 0.0893545i \(-0.0284804\pi\)
\(720\) 8.27087e7 + 9.29442e7i 0.221592 + 0.249015i
\(721\) 5.87242e8 1.56679
\(722\) 2.80221e8 2.07299e8i 0.744541 0.550788i
\(723\) 1.09744e8 0.290379
\(724\) 1.42104e8 4.64389e8i 0.374447 1.22368i
\(725\) −8.46804e7 4.61943e7i −0.222213 0.121220i
\(726\) −4.76071e8 + 3.52183e8i −1.24412 + 0.920362i
\(727\) −9.71701e7 −0.252889 −0.126444 0.991974i \(-0.540357\pi\)
−0.126444 + 0.991974i \(0.540357\pi\)
\(728\) 2.90256e8 1.02664e8i 0.752293 0.266086i
\(729\) 1.43489e7 0.0370370
\(730\) −1.36639e8 3.35051e8i −0.351242 0.861277i
\(731\) 1.32357e7i 0.0338840i
\(732\) 4.43378e6 1.44894e7i 0.0113042 0.0369417i
\(733\) 7.38776e8i 1.87586i −0.346821 0.937931i \(-0.612739\pi\)
0.346821 0.937931i \(-0.387261\pi\)
\(734\) −3.28054e8 + 2.42684e8i −0.829577 + 0.613696i
\(735\) 3.47871e8 + 8.87135e7i 0.876106 + 0.223423i
\(736\) 2.20924e6 95086.1i 0.00554127 0.000238497i
\(737\) 9.72617e8i 2.42963i
\(738\) −1.60839e8 + 1.18983e8i −0.400148 + 0.296018i
\(739\) 9.03695e7i 0.223918i −0.993713 0.111959i \(-0.964288\pi\)
0.993713 0.111959i \(-0.0357125\pi\)
\(740\) 1.82339e8 + 1.10954e8i 0.449972 + 0.273810i
\(741\) 1.62401e8 0.399148
\(742\) −6.45484e8 8.72547e8i −1.58006 2.13588i
\(743\) 5.29875e8 1.29183 0.645917 0.763408i \(-0.276475\pi\)
0.645917 + 0.763408i \(0.276475\pi\)
\(744\) 1.57036e8 5.55437e7i 0.381312 0.134870i
\(745\) −3.48054e8 8.87600e7i −0.841739 0.214659i
\(746\) −1.00034e8 1.35224e8i −0.240953 0.325714i
\(747\) 5.75392e6 0.0138039
\(748\) 7.15871e7 2.33943e8i 0.171053 0.558992i
\(749\) −1.00816e9 −2.39929
\(750\) −2.42039e8 2.72632e7i −0.573722 0.0646239i
\(751\) 4.01846e8i 0.948723i −0.880330 0.474362i \(-0.842679\pi\)
0.880330 0.474362i \(-0.157321\pi\)
\(752\) 1.66673e8 + 1.12543e8i 0.391934 + 0.264645i
\(753\) 2.47771e8i 0.580317i
\(754\) 3.21454e7 + 4.34532e7i 0.0749902 + 0.101370i
\(755\) −5.27993e7 + 2.07041e8i −0.122684 + 0.481079i
\(756\) 3.89764e7 1.27373e8i 0.0902061 0.294790i
\(757\) 6.84418e8i 1.57773i 0.614564 + 0.788867i \(0.289332\pi\)
−0.614564 + 0.788867i \(0.710668\pi\)
\(758\) −2.56841e7 3.47191e7i −0.0589735 0.0797188i
\(759\) 2.68612e6i 0.00614327i
\(760\) 6.06752e8 5.49216e7i 1.38220 0.125113i
\(761\) −3.75375e8 −0.851748 −0.425874 0.904782i \(-0.640033\pi\)
−0.425874 + 0.904782i \(0.640033\pi\)
\(762\) −2.87480e8 + 2.12669e8i −0.649746 + 0.480662i
\(763\) −5.11400e8 −1.15130
\(764\) 3.07622e8 + 9.41330e7i 0.689823 + 0.211087i
\(765\) 1.12369e7 4.40630e7i 0.0250993 0.0984216i
\(766\) 3.99536e8 2.95564e8i 0.888933 0.657606i
\(767\) −1.25501e8 −0.278138
\(768\) −9.77308e7 2.42584e8i −0.215748 0.535524i
\(769\) 4.59463e7 0.101035 0.0505175 0.998723i \(-0.483913\pi\)
0.0505175 + 0.998723i \(0.483913\pi\)
\(770\) 5.29795e8 + 1.29911e9i 1.16047 + 2.84559i
\(771\) 3.54336e8i 0.773129i
\(772\) −1.65421e8 5.06190e7i −0.359532 0.110017i
\(773\) 3.78255e8i 0.818930i 0.912326 + 0.409465i \(0.134285\pi\)
−0.912326 + 0.409465i \(0.865715\pi\)
\(774\) 1.38173e7 1.02216e7i 0.0297988 0.0220443i
\(775\) −1.56164e8 + 2.86269e8i −0.335486 + 0.614992i
\(776\) −4.07292e8 + 1.44059e8i −0.871607 + 0.308288i
\(777\) 2.28519e8i 0.487146i
\(778\) 1.64346e8 1.21578e8i 0.348996 0.258177i
\(779\) 9.79667e8i 2.07236i
\(780\) 1.16593e8 + 7.09473e7i 0.245690 + 0.149504i
\(781\) −8.26334e8 −1.73461
\(782\) −480662. 649746.i −0.00100512 0.00135870i
\(783\) 2.33851e7 0.0487141
\(784\) −6.25426e8 4.22306e8i −1.29786 0.876354i
\(785\) 1.85050e8 7.25633e8i 0.382542 1.50006i
\(786\) 1.19909e8 + 1.62090e8i 0.246937 + 0.333802i
\(787\) 1.56045e8 0.320129 0.160065 0.987107i \(-0.448830\pi\)
0.160065 + 0.987107i \(0.448830\pi\)
\(788\) 5.42858e8 + 1.66116e8i 1.10945 + 0.339494i
\(789\) 1.34307e8 0.273444
\(790\) 2.84714e8 + 6.98146e8i 0.577468 + 1.41601i
\(791\) 1.26156e9i 2.54905i
\(792\) 2.99507e8 1.05936e8i 0.602881 0.213239i
\(793\) 1.66221e7i 0.0333325i
\(794\) 9.30670e7 + 1.25805e8i 0.185923 + 0.251326i
\(795\) 1.18894e8 4.66216e8i 0.236623 0.927867i
\(796\) 6.14153e8 + 1.87932e8i 1.21769 + 0.372616i
\(797\) 3.23272e8i 0.638548i 0.947662 + 0.319274i \(0.103439\pi\)
−0.947662 + 0.319274i \(0.896561\pi\)
\(798\) −3.87914e8 5.24372e8i −0.763356 1.03188i
\(799\) 7.35051e7i 0.144104i
\(800\) 4.59599e8 + 2.25638e8i 0.897654 + 0.440700i
\(801\) −1.36026e8 −0.264682
\(802\) −3.00907e8 + 2.22602e8i −0.583323 + 0.431525i
\(803\) −9.23946e8 −1.78443
\(804\) −1.11195e8 + 3.63380e8i −0.213952 + 0.699187i
\(805\) 4.49105e6 + 1.14530e6i 0.00860915 + 0.00219549i
\(806\) 1.46897e8 1.08670e8i 0.280549 0.207541i
\(807\) 3.11771e8 0.593219
\(808\) 8.37838e7 + 2.36878e8i 0.158828 + 0.449046i
\(809\) 1.51271e8 0.285700 0.142850 0.989744i \(-0.454373\pi\)
0.142850 + 0.989744i \(0.454373\pi\)
\(810\) 5.46770e7 2.22981e7i 0.102884 0.0419578i
\(811\) 7.39372e8i 1.38612i −0.720880 0.693060i \(-0.756262\pi\)
0.720880 0.693060i \(-0.243738\pi\)
\(812\) 6.35218e7 2.07586e8i 0.118646 0.387731i
\(813\) 1.10308e8i 0.205274i
\(814\) 4.38158e8 3.24136e8i 0.812377 0.600971i
\(815\) −3.75906e8 9.58629e7i −0.694395 0.177083i
\(816\) −5.34914e7 + 7.92195e7i −0.0984494 + 0.145801i
\(817\) 8.41609e7i 0.154328i
\(818\) −5.47295e8 + 4.04872e8i −0.999912 + 0.739704i
\(819\) 1.46121e8i 0.265988i
\(820\) −4.27982e8 + 7.03333e8i −0.776218 + 1.27561i
\(821\) 2.62161e8 0.473739 0.236870 0.971541i \(-0.423879\pi\)
0.236870 + 0.971541i \(0.423879\pi\)
\(822\) −9.00018e7 1.21662e8i −0.162045 0.219048i
\(823\) 1.57030e8 0.281698 0.140849 0.990031i \(-0.455017\pi\)
0.140849 + 0.990031i \(0.455017\pi\)
\(824\) −1.82474e8 5.15901e8i −0.326152 0.922114i
\(825\) −2.97843e8 + 5.45987e8i −0.530428 + 0.972346i
\(826\) 2.99773e8 + 4.05225e8i 0.531928 + 0.719045i
\(827\) −7.49865e8 −1.32576 −0.662882 0.748724i \(-0.730667\pi\)
−0.662882 + 0.748724i \(0.730667\pi\)
\(828\) 307092. 1.00356e6i 0.000540975 0.00176788i
\(829\) −2.21793e8 −0.389299 −0.194650 0.980873i \(-0.562357\pi\)
−0.194650 + 0.980873i \(0.562357\pi\)
\(830\) 2.19255e7 8.94155e6i 0.0383456 0.0156379i
\(831\) 8.28367e7i 0.144351i
\(832\) −1.80383e8 2.23093e8i −0.313203 0.387362i
\(833\) 2.75821e8i 0.477191i
\(834\) −5.53048e7 7.47595e7i −0.0953377 0.128875i
\(835\) −7.56243e8 1.92856e8i −1.29898 0.331263i
\(836\) 4.55195e8 1.48756e9i 0.779074 2.54598i
\(837\) 7.90554e7i 0.134820i
\(838\) −2.90452e8 3.92625e8i −0.493563 0.667185i
\(839\) 3.85183e7i 0.0652201i 0.999468 + 0.0326101i \(0.0103819\pi\)
−0.999468 + 0.0326101i \(0.989618\pi\)
\(840\) −4.94160e7 5.45929e8i −0.0833739 0.921081i
\(841\) −5.56711e8 −0.935927
\(842\) 4.93874e8 3.65353e8i 0.827332 0.612035i
\(843\) 4.91233e8 0.819983
\(844\) −4.07965e8 1.24838e8i −0.678572 0.207644i
\(845\) −4.39564e8 1.12097e8i −0.728538 0.185790i
\(846\) 7.67347e7 5.67660e7i 0.126730 0.0937513i
\(847\) 2.60907e9 4.29373
\(848\) −5.65974e8 + 8.38194e8i −0.928130 + 1.37454i
\(849\) −3.89791e8 −0.636956
\(850\) −2.56552e7 1.85366e8i −0.0417752 0.301837i
\(851\) 1.80049e6i 0.00292147i
\(852\) 3.08727e8 + 9.44711e7i 0.499179 + 0.152750i
\(853\) 6.04161e8i 0.973433i 0.873560 + 0.486716i \(0.161805\pi\)
−0.873560 + 0.486716i \(0.838195\pi\)
\(854\) −5.36707e7 + 3.97039e7i −0.0861715 + 0.0637470i
\(855\) 7.14511e7 2.80180e8i 0.114317 0.448270i
\(856\) 3.13265e8 + 8.85679e8i 0.499448 + 1.41207i
\(857\) 1.07405e9i 1.70641i 0.521576 + 0.853205i \(0.325344\pi\)
−0.521576 + 0.853205i \(0.674656\pi\)
\(858\) 2.80170e8 2.07261e8i 0.443568 0.328138i
\(859\) 4.18661e8i 0.660516i 0.943891 + 0.330258i \(0.107136\pi\)
−0.943891 + 0.330258i \(0.892864\pi\)
\(860\) 3.67669e7 6.04217e7i 0.0578045 0.0949943i
\(861\) 8.81461e8 1.38100
\(862\) 7.70178e7 + 1.04111e8i 0.120246 + 0.162545i
\(863\) 6.54898e8 1.01892 0.509461 0.860493i \(-0.329845\pi\)
0.509461 + 0.860493i \(0.329845\pi\)
\(864\) −1.24010e8 + 5.33742e6i −0.192272 + 0.00827543i
\(865\) 1.24330e8 4.87534e8i 0.192100 0.753281i
\(866\) −4.49326e8 6.07386e8i −0.691843 0.935214i
\(867\) −3.41331e8 −0.523743
\(868\) −7.01763e8 2.14741e8i −1.07308 0.328364i
\(869\) 1.92522e9 2.93374
\(870\) 8.91100e7 3.63404e7i 0.135322 0.0551863i
\(871\) 4.16867e8i 0.630875i
\(872\) 1.58908e8 + 4.49272e8i 0.239660 + 0.677579i
\(873\) 2.05040e8i 0.308174i
\(874\) −3.05635e6 4.13149e6i −0.00457792 0.00618831i
\(875\) 7.85868e8 + 7.30775e8i 1.17307 + 1.09084i
\(876\) 3.45196e8 + 1.05631e8i 0.513515 + 0.157137i
\(877\) 3.34585e8i 0.496030i 0.968756 + 0.248015i \(0.0797783\pi\)
−0.968756 + 0.248015i \(0.920222\pi\)
\(878\) 2.58643e8 + 3.49627e8i 0.382135 + 0.516560i
\(879\) 1.22976e8i 0.181073i
\(880\) 9.76660e8 8.69104e8i 1.43316 1.27533i
\(881\) −2.23304e8 −0.326564 −0.163282 0.986579i \(-0.552208\pi\)
−0.163282 + 0.986579i \(0.552208\pi\)
\(882\) −2.87940e8 + 2.13009e8i −0.419659 + 0.310451i
\(883\) −2.19587e8 −0.318952 −0.159476 0.987202i \(-0.550980\pi\)
−0.159476 + 0.987202i \(0.550980\pi\)
\(884\) −3.06824e7 + 1.00269e8i −0.0444154 + 0.145147i
\(885\) −5.52161e7 + 2.16518e8i −0.0796592 + 0.312367i
\(886\) −8.03981e8 + 5.94760e8i −1.15596 + 0.855147i
\(887\) −1.05645e9 −1.51383 −0.756915 0.653514i \(-0.773294\pi\)
−0.756915 + 0.653514i \(0.773294\pi\)
\(888\) −2.00757e8 + 7.10080e7i −0.286703 + 0.101407i
\(889\) 1.57551e9 2.24241
\(890\) −5.18332e8 + 2.11383e8i −0.735255 + 0.299848i
\(891\) 1.50779e8i 0.213160i
\(892\) −1.22425e8 + 4.00079e8i −0.172495 + 0.563705i
\(893\) 4.67391e8i 0.656336i
\(894\) 2.88091e8 2.13121e8i 0.403197 0.298273i
\(895\) 1.55192e8 6.08554e8i 0.216472 0.848848i
\(896\) −2.89473e8 + 1.11532e9i −0.402424 + 1.55051i
\(897\) 1.15128e6i 0.00159516i
\(898\) 7.00548e8 5.18244e8i 0.967406 0.715657i
\(899\) 1.28841e8i 0.177327i
\(900\) 1.73698e8 1.69936e8i 0.238268 0.233108i
\(901\) 3.69654e8 0.505384
\(902\) 1.25028e9 + 1.69010e9i 1.70368 + 2.30299i
\(903\) −7.57242e7 −0.102842
\(904\) −1.10830e9 + 3.92005e8i −1.50021 + 0.530624i
\(905\) −9.19109e8 2.34390e8i −1.24000 0.316222i
\(906\) −1.26776e8 1.71372e8i −0.170472 0.230439i
\(907\) −7.33082e8 −0.982495 −0.491248 0.871020i \(-0.663459\pi\)
−0.491248 + 0.871020i \(0.663459\pi\)
\(908\) −8.19923e7 + 2.67947e8i −0.109526 + 0.357925i
\(909\) 1.19250e8 0.158769
\(910\) −2.27072e8 5.56801e8i −0.301328 0.738883i
\(911\) 4.35193e8i 0.575608i 0.957689 + 0.287804i \(0.0929252\pi\)
−0.957689 + 0.287804i \(0.907075\pi\)
\(912\) −3.40131e8 + 5.03727e8i −0.448397 + 0.664065i
\(913\) 6.04623e7i 0.0794461i
\(914\) −5.97061e8 8.07091e8i −0.781952 1.05702i
\(915\) −2.86771e7 7.31318e6i −0.0374345 0.00954648i
\(916\) 9.95485e7 3.25320e8i 0.129523 0.423277i
\(917\) 8.88321e8i 1.15203i
\(918\) 2.69808e7 + 3.64719e7i 0.0348760 + 0.0471444i
\(919\) 9.37380e8i 1.20773i 0.797087 + 0.603864i \(0.206373\pi\)
−0.797087 + 0.603864i \(0.793627\pi\)
\(920\) −389345. 4.30133e6i −0.000500002 0.00552382i
\(921\) −5.97913e8 −0.765349
\(922\) −4.02771e8 + 2.97958e8i −0.513885 + 0.380156i
\(923\) 3.54170e8 0.450408
\(924\) −1.33844e9 4.09564e8i −1.69661 0.519166i
\(925\) 1.99642e8 3.65971e8i 0.252248 0.462404i
\(926\) 1.04143e8 7.70415e7i 0.131158 0.0970268i
\(927\) −2.59716e8 −0.326032
\(928\) −2.02106e8 + 8.69867e6i −0.252892 + 0.0108845i
\(929\) 1.90323e8 0.237380 0.118690 0.992931i \(-0.462131\pi\)
0.118690 + 0.992931i \(0.462131\pi\)
\(930\) −1.22852e8 3.01244e8i −0.152733 0.374515i
\(931\) 1.75384e9i 2.17341i
\(932\) 3.70221e7 + 1.13288e7i 0.0457313 + 0.0139939i
\(933\) 6.87253e8i 0.846198i
\(934\) −1.41128e7 + 1.04402e7i −0.0173209 + 0.0128135i
\(935\) −4.63016e8 1.18077e8i −0.566449 0.144455i
\(936\) −1.28370e8 + 4.54044e7i −0.156544 + 0.0553695i
\(937\) 1.56976e9i 1.90816i 0.299558 + 0.954078i \(0.403161\pi\)
−0.299558 + 0.954078i \(0.596839\pi\)
\(938\) 1.34601e9 9.95736e8i 1.63095 1.20652i
\(939\) 4.65548e7i 0.0562299i
\(940\) 2.04187e8 3.35554e8i 0.245835 0.403998i
\(941\) −3.37518e8 −0.405069 −0.202534 0.979275i \(-0.564918\pi\)
−0.202534 + 0.979275i \(0.564918\pi\)
\(942\) 4.44321e8 + 6.00621e8i 0.531550 + 0.718534i
\(943\) 6.94497e6 0.00828200
\(944\) 2.62848e8 3.89271e8i 0.312455 0.462739i
\(945\) −2.52094e8 6.42885e7i −0.298722 0.0761795i
\(946\) −1.07409e8 1.45192e8i −0.126872 0.171502i
\(947\) −9.84991e8 −1.15980 −0.579899 0.814689i \(-0.696908\pi\)
−0.579899 + 0.814689i \(0.696908\pi\)
\(948\) −7.19284e8 2.20102e8i −0.844258 0.258344i
\(949\) 3.96006e8 0.463344
\(950\) −1.63132e8 1.17867e9i −0.190269 1.37474i
\(951\) 6.08045e8i 0.706959i
\(952\) 3.97044e8 1.40434e8i 0.460180 0.162766i
\(953\) 1.46230e9i 1.68950i −0.535165 0.844748i \(-0.679751\pi\)
0.535165 0.844748i \(-0.320249\pi\)
\(954\) 2.85474e8 + 3.85896e8i 0.328792 + 0.444453i
\(955\) 1.55265e8 6.08840e8i 0.178264 0.699025i
\(956\) 8.92231e7 + 2.73024e7i 0.102118 + 0.0312484i
\(957\) 2.45732e8i 0.280366i
\(958\) 7.27759e8 + 9.83764e8i 0.827734 + 1.11891i
\(959\) 6.66757e8i 0.755983i
\(960\) −4.64251e8 + 2.13050e8i −0.524734 + 0.240806i
\(961\) 4.51947e8 0.509234
\(962\) −1.87796e8 + 1.38926e8i −0.210941 + 0.156048i
\(963\) 4.45871e8 0.499264
\(964\) −1.31839e8 + 4.30844e8i −0.147168 + 0.480938i
\(965\) −8.34922e7 + 3.27397e8i −0.0929103 + 0.364328i
\(966\) −3.71733e6 + 2.74997e6i −0.00412382 + 0.00305068i
\(967\) 1.00253e9 1.10871 0.554355 0.832280i \(-0.312965\pi\)
0.554355 + 0.832280i \(0.312965\pi\)
\(968\) −8.10717e8 2.29210e9i −0.893806 2.52702i
\(969\) 2.22150e8 0.244160
\(970\) 3.18631e8 + 7.81312e8i 0.349118 + 0.856070i
\(971\) 8.17160e8i 0.892585i −0.894887 0.446293i \(-0.852744\pi\)
0.894887 0.446293i \(-0.147256\pi\)
\(972\) −1.72378e7 + 5.63325e7i −0.0187709 + 0.0613423i
\(973\) 4.09713e8i 0.444776i
\(974\) −2.15004e8 + 1.59053e8i −0.232685 + 0.172134i
\(975\) 1.27657e8 2.34012e8i 0.137730 0.252478i
\(976\) 5.15576e7 + 3.48133e7i 0.0554554 + 0.0374451i
\(977\) 2.61374e8i 0.280272i 0.990132 + 0.140136i \(0.0447539\pi\)
−0.990132 + 0.140136i \(0.955246\pi\)
\(978\) 3.11145e8 2.30176e8i 0.332618 0.246061i
\(979\) 1.42936e9i 1.52333i
\(980\) −7.66191e8 + 1.25914e9i −0.814064 + 1.33781i
\(981\) 2.26174e8 0.239571
\(982\) −3.34908e8 4.52719e8i −0.353664 0.478073i
\(983\) 8.00824e7 0.0843095 0.0421548 0.999111i \(-0.486578\pi\)
0.0421548 + 0.999111i \(0.486578\pi\)
\(984\) −2.73897e8 7.74377e8i −0.287476 0.812769i
\(985\) 2.73995e8 1.07441e9i 0.286704 1.12425i
\(986\) 4.39719e7 + 5.94401e7i 0.0458717 + 0.0620081i
\(987\) −4.20538e8 −0.437375
\(988\) −1.95098e8 + 6.37572e8i −0.202294 + 0.661087i
\(989\) −596626. −0.000616756
\(990\) −2.34309e8 5.74548e8i −0.241481 0.592135i
\(991\) 6.18860e8i 0.635874i −0.948112 0.317937i \(-0.897010\pi\)
0.948112 0.317937i \(-0.102990\pi\)
\(992\) 2.94066e7 + 6.83235e8i 0.0301238 + 0.699899i
\(993\) 6.61151e8i 0.675232i
\(994\) −8.45976e8 1.14357e9i −0.861388 1.16440i
\(995\) 3.09979e8 1.21552e9i 0.314676 1.23393i
\(996\) −6.91238e6 + 2.25894e7i −0.00699600 + 0.0228626i
\(997\) 1.35069e9i 1.36292i −0.731854 0.681461i \(-0.761345\pi\)
0.731854 0.681461i \(-0.238655\pi\)
\(998\) 7.34871e7 + 9.93378e7i 0.0739298 + 0.0999363i
\(999\) 1.01066e8i 0.101370i
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 60.7.f.a.19.8 yes 36
3.2 odd 2 180.7.f.g.19.29 36
4.3 odd 2 inner 60.7.f.a.19.30 yes 36
5.4 even 2 inner 60.7.f.a.19.29 yes 36
12.11 even 2 180.7.f.g.19.7 36
15.14 odd 2 180.7.f.g.19.8 36
20.19 odd 2 inner 60.7.f.a.19.7 36
60.59 even 2 180.7.f.g.19.30 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.7.f.a.19.7 36 20.19 odd 2 inner
60.7.f.a.19.8 yes 36 1.1 even 1 trivial
60.7.f.a.19.29 yes 36 5.4 even 2 inner
60.7.f.a.19.30 yes 36 4.3 odd 2 inner
180.7.f.g.19.7 36 12.11 even 2
180.7.f.g.19.8 36 15.14 odd 2
180.7.f.g.19.29 36 3.2 odd 2
180.7.f.g.19.30 36 60.59 even 2