Properties

Label 74.7.d.b.31.7
Level $74$
Weight $7$
Character 74.31
Analytic conductor $17.024$
Analytic rank $0$
Dimension $20$
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] = [74,7,Mod(31,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.31");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 74.d (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(17.0240021879\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 10424 x^{18} + 44844916 x^{16} + 103219343022 x^{14} + 138101513095620 x^{12} + \cdots + 73\!\cdots\!36 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{9}\cdot 3^{2}\cdot 11^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 31.7
Root \(-17.1892i\) of defining polynomial
Character \(\chi\) \(=\) 74.31
Dual form 74.7.d.b.43.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.00000 - 4.00000i) q^{2} +20.1892i q^{3} +32.0000i q^{4} +(9.27541 - 9.27541i) q^{5} +(80.7569 - 80.7569i) q^{6} +8.30790 q^{7} +(128.000 - 128.000i) q^{8} +321.395 q^{9} +O(q^{10})\) \(q+(-4.00000 - 4.00000i) q^{2} +20.1892i q^{3} +32.0000i q^{4} +(9.27541 - 9.27541i) q^{5} +(80.7569 - 80.7569i) q^{6} +8.30790 q^{7} +(128.000 - 128.000i) q^{8} +321.395 q^{9} -74.2032 q^{10} +243.820i q^{11} -646.055 q^{12} +(1658.09 - 1658.09i) q^{13} +(-33.2316 - 33.2316i) q^{14} +(187.263 + 187.263i) q^{15} -1024.00 q^{16} +(-6733.96 + 6733.96i) q^{17} +(-1285.58 - 1285.58i) q^{18} +(-2804.19 + 2804.19i) q^{19} +(296.813 + 296.813i) q^{20} +167.730i q^{21} +(975.281 - 975.281i) q^{22} +(4070.88 - 4070.88i) q^{23} +(2584.22 + 2584.22i) q^{24} +15452.9i q^{25} -13264.7 q^{26} +21206.7i q^{27} +265.853i q^{28} +(29954.3 + 29954.3i) q^{29} -1498.11i q^{30} +(-4347.19 - 4347.19i) q^{31} +(4096.00 + 4096.00i) q^{32} -4922.54 q^{33} +53871.7 q^{34} +(77.0591 - 77.0591i) q^{35} +10284.6i q^{36} +(-10586.5 + 49534.4i) q^{37} +22433.5 q^{38} +(33475.5 + 33475.5i) q^{39} -2374.50i q^{40} -10298.7i q^{41} +(670.920 - 670.920i) q^{42} +(-76826.5 + 76826.5i) q^{43} -7802.25 q^{44} +(2981.07 - 2981.07i) q^{45} -32567.0 q^{46} +124505. q^{47} -20673.8i q^{48} -117580. q^{49} +(61811.7 - 61811.7i) q^{50} +(-135953. - 135953. i) q^{51} +(53058.7 + 53058.7i) q^{52} -82881.1 q^{53} +(84826.7 - 84826.7i) q^{54} +(2261.53 + 2261.53i) q^{55} +(1063.41 - 1063.41i) q^{56} +(-56614.4 - 56614.4i) q^{57} -239635. i q^{58} +(-144216. + 144216. i) q^{59} +(-5992.43 + 5992.43i) q^{60} +(-70415.2 - 70415.2i) q^{61} +34777.6i q^{62} +2670.12 q^{63} -32768.0i q^{64} -30758.8i q^{65} +(19690.2 + 19690.2i) q^{66} -483835. i q^{67} +(-215487. - 215487. i) q^{68} +(82187.9 + 82187.9i) q^{69} -616.473 q^{70} +172911. q^{71} +(41138.6 - 41138.6i) q^{72} +526876. i q^{73} +(240483. - 155791. i) q^{74} -311983. q^{75} +(-89734.1 - 89734.1i) q^{76} +2025.63i q^{77} -267804. i q^{78} +(616752. - 616752. i) q^{79} +(-9498.02 + 9498.02i) q^{80} -193849. q^{81} +(-41194.9 + 41194.9i) q^{82} +359323. q^{83} -5367.36 q^{84} +124920. i q^{85} +614612. q^{86} +(-604755. + 604755. i) q^{87} +(31209.0 + 31209.0i) q^{88} +(312844. + 312844. i) q^{89} -23848.6 q^{90} +(13775.2 - 13775.2i) q^{91} +(130268. + 130268. i) q^{92} +(87766.5 - 87766.5i) q^{93} +(-498020. - 498020. i) q^{94} +52020.0i q^{95} +(-82695.1 + 82695.1i) q^{96} +(34447.0 - 34447.0i) q^{97} +(470320. + 470320. i) q^{98} +78362.6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 80 q^{2} + 60 q^{5} + 256 q^{6} + 104 q^{7} + 2560 q^{8} - 6472 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 80 q^{2} + 60 q^{5} + 256 q^{6} + 104 q^{7} + 2560 q^{8} - 6472 q^{9} - 480 q^{10} - 2048 q^{12} + 1560 q^{13} - 416 q^{14} - 2136 q^{15} - 20480 q^{16} + 16000 q^{17} + 25888 q^{18} + 3838 q^{19} + 1920 q^{20} + 8928 q^{22} - 6478 q^{23} + 8192 q^{24} - 12480 q^{26} - 1964 q^{29} + 117662 q^{31} + 81920 q^{32} - 92624 q^{33} - 128000 q^{34} - 104456 q^{35} - 17618 q^{37} - 30704 q^{38} + 121012 q^{39} + 213472 q^{42} + 65582 q^{43} - 71424 q^{44} - 466848 q^{45} + 51824 q^{46} - 168176 q^{47} + 563124 q^{49} - 379904 q^{50} + 560888 q^{51} + 49920 q^{52} + 561604 q^{53} - 139120 q^{54} - 1395304 q^{55} + 13312 q^{56} + 631036 q^{57} - 376510 q^{59} + 68352 q^{60} + 836700 q^{61} - 275908 q^{63} + 370496 q^{66} + 512000 q^{68} - 1616748 q^{69} + 835648 q^{70} - 94584 q^{71} - 828416 q^{72} + 133200 q^{74} + 20340 q^{75} + 122816 q^{76} - 2525594 q^{79} - 61440 q^{80} + 2933572 q^{81} - 1816480 q^{82} + 715304 q^{83} - 1707776 q^{84} - 524656 q^{86} + 900256 q^{87} + 285696 q^{88} - 952068 q^{89} + 3734784 q^{90} - 1351840 q^{91} - 207296 q^{92} + 580320 q^{93} + 672704 q^{94} - 262144 q^{96} + 178132 q^{97} - 2252496 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.00000 4.00000i −0.500000 0.500000i
\(3\) 20.1892i 0.747749i 0.927479 + 0.373875i \(0.121971\pi\)
−0.927479 + 0.373875i \(0.878029\pi\)
\(4\) 32.0000i 0.500000i
\(5\) 9.27541 9.27541i 0.0742032 0.0742032i −0.669031 0.743234i \(-0.733291\pi\)
0.743234 + 0.669031i \(0.233291\pi\)
\(6\) 80.7569 80.7569i 0.373875 0.373875i
\(7\) 8.30790 0.0242213 0.0121106 0.999927i \(-0.496145\pi\)
0.0121106 + 0.999927i \(0.496145\pi\)
\(8\) 128.000 128.000i 0.250000 0.250000i
\(9\) 321.395 0.440871
\(10\) −74.2032 −0.0742032
\(11\) 243.820i 0.183186i 0.995797 + 0.0915929i \(0.0291958\pi\)
−0.995797 + 0.0915929i \(0.970804\pi\)
\(12\) −646.055 −0.373875
\(13\) 1658.09 1658.09i 0.754704 0.754704i −0.220649 0.975353i \(-0.570817\pi\)
0.975353 + 0.220649i \(0.0708175\pi\)
\(14\) −33.2316 33.2316i −0.0121106 0.0121106i
\(15\) 187.263 + 187.263i 0.0554854 + 0.0554854i
\(16\) −1024.00 −0.250000
\(17\) −6733.96 + 6733.96i −1.37064 + 1.37064i −0.511150 + 0.859492i \(0.670780\pi\)
−0.859492 + 0.511150i \(0.829220\pi\)
\(18\) −1285.58 1285.58i −0.220436 0.220436i
\(19\) −2804.19 + 2804.19i −0.408834 + 0.408834i −0.881332 0.472498i \(-0.843352\pi\)
0.472498 + 0.881332i \(0.343352\pi\)
\(20\) 296.813 + 296.813i 0.0371016 + 0.0371016i
\(21\) 167.730i 0.0181114i
\(22\) 975.281 975.281i 0.0915929 0.0915929i
\(23\) 4070.88 4070.88i 0.334584 0.334584i −0.519740 0.854324i \(-0.673971\pi\)
0.854324 + 0.519740i \(0.173971\pi\)
\(24\) 2584.22 + 2584.22i 0.186937 + 0.186937i
\(25\) 15452.9i 0.988988i
\(26\) −13264.7 −0.754704
\(27\) 21206.7i 1.07741i
\(28\) 265.853i 0.0121106i
\(29\) 29954.3 + 29954.3i 1.22819 + 1.22819i 0.964648 + 0.263542i \(0.0848908\pi\)
0.263542 + 0.964648i \(0.415109\pi\)
\(30\) 1498.11i 0.0554854i
\(31\) −4347.19 4347.19i −0.145923 0.145923i 0.630371 0.776294i \(-0.282903\pi\)
−0.776294 + 0.630371i \(0.782903\pi\)
\(32\) 4096.00 + 4096.00i 0.125000 + 0.125000i
\(33\) −4922.54 −0.136977
\(34\) 53871.7 1.37064
\(35\) 77.0591 77.0591i 0.00179730 0.00179730i
\(36\) 10284.6i 0.220436i
\(37\) −10586.5 + 49534.4i −0.209001 + 0.977915i
\(38\) 22433.5 0.408834
\(39\) 33475.5 + 33475.5i 0.564330 + 0.564330i
\(40\) 2374.50i 0.0371016i
\(41\) 10298.7i 0.149428i −0.997205 0.0747139i \(-0.976196\pi\)
0.997205 0.0747139i \(-0.0238044\pi\)
\(42\) 670.920 670.920i 0.00905572 0.00905572i
\(43\) −76826.5 + 76826.5i −0.966286 + 0.966286i −0.999450 0.0331642i \(-0.989442\pi\)
0.0331642 + 0.999450i \(0.489442\pi\)
\(44\) −7802.25 −0.0915929
\(45\) 2981.07 2981.07i 0.0327141 0.0327141i
\(46\) −32567.0 −0.334584
\(47\) 124505. 1.19920 0.599602 0.800299i \(-0.295326\pi\)
0.599602 + 0.800299i \(0.295326\pi\)
\(48\) 20673.8i 0.186937i
\(49\) −117580. −0.999413
\(50\) 61811.7 61811.7i 0.494494 0.494494i
\(51\) −135953. 135953.i −1.02490 1.02490i
\(52\) 53058.7 + 53058.7i 0.377352 + 0.377352i
\(53\) −82881.1 −0.556708 −0.278354 0.960478i \(-0.589789\pi\)
−0.278354 + 0.960478i \(0.589789\pi\)
\(54\) 84826.7 84826.7i 0.538705 0.538705i
\(55\) 2261.53 + 2261.53i 0.0135930 + 0.0135930i
\(56\) 1063.41 1063.41i 0.00605532 0.00605532i
\(57\) −56614.4 56614.4i −0.305705 0.305705i
\(58\) 239635.i 1.22819i
\(59\) −144216. + 144216.i −0.702192 + 0.702192i −0.964881 0.262688i \(-0.915391\pi\)
0.262688 + 0.964881i \(0.415391\pi\)
\(60\) −5992.43 + 5992.43i −0.0277427 + 0.0277427i
\(61\) −70415.2 70415.2i −0.310225 0.310225i 0.534772 0.844997i \(-0.320398\pi\)
−0.844997 + 0.534772i \(0.820398\pi\)
\(62\) 34777.6i 0.145923i
\(63\) 2670.12 0.0106785
\(64\) 32768.0i 0.125000i
\(65\) 30758.8i 0.112003i
\(66\) 19690.2 + 19690.2i 0.0684885 + 0.0684885i
\(67\) 483835.i 1.60869i −0.594161 0.804346i \(-0.702516\pi\)
0.594161 0.804346i \(-0.297484\pi\)
\(68\) −215487. 215487.i −0.685321 0.685321i
\(69\) 82187.9 + 82187.9i 0.250185 + 0.250185i
\(70\) −616.473 −0.00179730
\(71\) 172911. 0.483112 0.241556 0.970387i \(-0.422342\pi\)
0.241556 + 0.970387i \(0.422342\pi\)
\(72\) 41138.6 41138.6i 0.110218 0.110218i
\(73\) 526876.i 1.35438i 0.735810 + 0.677189i \(0.236802\pi\)
−0.735810 + 0.677189i \(0.763198\pi\)
\(74\) 240483. 155791.i 0.593458 0.384457i
\(75\) −311983. −0.739515
\(76\) −89734.1 89734.1i −0.204417 0.204417i
\(77\) 2025.63i 0.00443699i
\(78\) 267804.i 0.564330i
\(79\) 616752. 616752.i 1.25092 1.25092i 0.295612 0.955308i \(-0.404477\pi\)
0.955308 0.295612i \(-0.0955234\pi\)
\(80\) −9498.02 + 9498.02i −0.0185508 + 0.0185508i
\(81\) −193849. −0.364762
\(82\) −41194.9 + 41194.9i −0.0747139 + 0.0747139i
\(83\) 359323. 0.628422 0.314211 0.949353i \(-0.398260\pi\)
0.314211 + 0.949353i \(0.398260\pi\)
\(84\) −5367.36 −0.00905572
\(85\) 124920.i 0.203412i
\(86\) 614612. 0.966286
\(87\) −604755. + 604755.i −0.918378 + 0.918378i
\(88\) 31209.0 + 31209.0i 0.0457964 + 0.0457964i
\(89\) 312844. + 312844.i 0.443770 + 0.443770i 0.893277 0.449507i \(-0.148400\pi\)
−0.449507 + 0.893277i \(0.648400\pi\)
\(90\) −23848.6 −0.0327141
\(91\) 13775.2 13775.2i 0.0182799 0.0182799i
\(92\) 130268. + 130268.i 0.167292 + 0.167292i
\(93\) 87766.5 87766.5i 0.109114 0.109114i
\(94\) −498020. 498020.i −0.599602 0.599602i
\(95\) 52020.0i 0.0606736i
\(96\) −82695.1 + 82695.1i −0.0934687 + 0.0934687i
\(97\) 34447.0 34447.0i 0.0377430 0.0377430i −0.687983 0.725726i \(-0.741504\pi\)
0.725726 + 0.687983i \(0.241504\pi\)
\(98\) 470320. + 470320.i 0.499707 + 0.499707i
\(99\) 78362.6i 0.0807613i
\(100\) −494494. −0.494494
\(101\) 434158.i 0.421389i 0.977552 + 0.210695i \(0.0675726\pi\)
−0.977552 + 0.210695i \(0.932427\pi\)
\(102\) 1.08763e6i 1.02490i
\(103\) −111529. 111529.i −0.102065 0.102065i 0.654230 0.756295i \(-0.272993\pi\)
−0.756295 + 0.654230i \(0.772993\pi\)
\(104\) 424470.i 0.377352i
\(105\) 1555.76 + 1555.76i 0.00134393 + 0.00134393i
\(106\) 331524. + 331524.i 0.278354 + 0.278354i
\(107\) 219793. 0.179416 0.0897081 0.995968i \(-0.471407\pi\)
0.0897081 + 0.995968i \(0.471407\pi\)
\(108\) −678613. −0.538705
\(109\) −806861. + 806861.i −0.623044 + 0.623044i −0.946309 0.323264i \(-0.895220\pi\)
0.323264 + 0.946309i \(0.395220\pi\)
\(110\) 18092.3i 0.0135930i
\(111\) −1.00006e6 213734.i −0.731236 0.156280i
\(112\) −8507.29 −0.00605532
\(113\) −298812. 298812.i −0.207092 0.207092i 0.595938 0.803030i \(-0.296780\pi\)
−0.803030 + 0.595938i \(0.796780\pi\)
\(114\) 452916.i 0.305705i
\(115\) 75518.1i 0.0496544i
\(116\) −958538. + 958538.i −0.614095 + 0.614095i
\(117\) 532901. 532901.i 0.332727 0.332727i
\(118\) 1.15372e6 0.702192
\(119\) −55945.1 + 55945.1i −0.0331987 + 0.0331987i
\(120\) 47939.4 0.0277427
\(121\) 1.71211e6 0.966443
\(122\) 563321.i 0.310225i
\(123\) 207923. 0.111735
\(124\) 139110. 139110.i 0.0729615 0.0729615i
\(125\) 288260. + 288260.i 0.147589 + 0.147589i
\(126\) −10680.5 10680.5i −0.00533923 0.00533923i
\(127\) −1.72567e6 −0.842456 −0.421228 0.906955i \(-0.638401\pi\)
−0.421228 + 0.906955i \(0.638401\pi\)
\(128\) −131072. + 131072.i −0.0625000 + 0.0625000i
\(129\) −1.55107e6 1.55107e6i −0.722539 0.722539i
\(130\) −123035. + 123035.i −0.0560015 + 0.0560015i
\(131\) 2.54435e6 + 2.54435e6i 1.13178 + 1.13178i 0.989881 + 0.141900i \(0.0453211\pi\)
0.141900 + 0.989881i \(0.454679\pi\)
\(132\) 157521.i 0.0684885i
\(133\) −23296.9 + 23296.9i −0.00990247 + 0.00990247i
\(134\) −1.93534e6 + 1.93534e6i −0.804346 + 0.804346i
\(135\) 196700. + 196700.i 0.0799473 + 0.0799473i
\(136\) 1.72389e6i 0.685321i
\(137\) 2.65306e6 1.03178 0.515889 0.856656i \(-0.327462\pi\)
0.515889 + 0.856656i \(0.327462\pi\)
\(138\) 657503.i 0.250185i
\(139\) 3.85559e6i 1.43564i −0.696227 0.717822i \(-0.745139\pi\)
0.696227 0.717822i \(-0.254861\pi\)
\(140\) 2465.89 + 2465.89i 0.000898649 + 0.000898649i
\(141\) 2.51366e6i 0.896703i
\(142\) −691644. 691644.i −0.241556 0.241556i
\(143\) 404275. + 404275.i 0.138251 + 0.138251i
\(144\) −329109. −0.110218
\(145\) 555677. 0.182271
\(146\) 2.10750e6 2.10750e6i 0.677189 0.677189i
\(147\) 2.37385e6i 0.747311i
\(148\) −1.58510e6 338768.i −0.488958 0.104500i
\(149\) 3.78950e6 1.14557 0.572787 0.819704i \(-0.305862\pi\)
0.572787 + 0.819704i \(0.305862\pi\)
\(150\) 1.24793e6 + 1.24793e6i 0.369757 + 0.369757i
\(151\) 3.87072e6i 1.12425i −0.827054 0.562123i \(-0.809985\pi\)
0.827054 0.562123i \(-0.190015\pi\)
\(152\) 717873.i 0.204417i
\(153\) −2.16426e6 + 2.16426e6i −0.604276 + 0.604276i
\(154\) 8102.53 8102.53i 0.00221850 0.00221850i
\(155\) −80644.0 −0.0216559
\(156\) −1.07122e6 + 1.07122e6i −0.282165 + 0.282165i
\(157\) 5.05290e6 1.30570 0.652848 0.757489i \(-0.273574\pi\)
0.652848 + 0.757489i \(0.273574\pi\)
\(158\) −4.93402e6 −1.25092
\(159\) 1.67331e6i 0.416278i
\(160\) 75984.1 0.0185508
\(161\) 33820.5 33820.5i 0.00810405 0.00810405i
\(162\) 775397. + 775397.i 0.182381 + 0.182381i
\(163\) −3.01651e6 3.01651e6i −0.696535 0.696535i 0.267127 0.963661i \(-0.413926\pi\)
−0.963661 + 0.267127i \(0.913926\pi\)
\(164\) 329559. 0.0747139
\(165\) −45658.6 + 45658.6i −0.0101641 + 0.0101641i
\(166\) −1.43729e6 1.43729e6i −0.314211 0.314211i
\(167\) −3.98933e6 + 3.98933e6i −0.856545 + 0.856545i −0.990929 0.134384i \(-0.957094\pi\)
0.134384 + 0.990929i \(0.457094\pi\)
\(168\) 21469.4 + 21469.4i 0.00452786 + 0.00452786i
\(169\) 671687.i 0.139158i
\(170\) 499682. 499682.i 0.101706 0.101706i
\(171\) −901253. + 901253.i −0.180243 + 0.180243i
\(172\) −2.45845e6 2.45845e6i −0.483143 0.483143i
\(173\) 8.15262e6i 1.57456i −0.616597 0.787279i \(-0.711489\pi\)
0.616597 0.787279i \(-0.288511\pi\)
\(174\) 4.83804e6 0.918378
\(175\) 128381.i 0.0239545i
\(176\) 249672.i 0.0457964i
\(177\) −2.91160e6 2.91160e6i −0.525064 0.525064i
\(178\) 2.50275e6i 0.443770i
\(179\) −254389. 254389.i −0.0443546 0.0443546i 0.684582 0.728936i \(-0.259985\pi\)
−0.728936 + 0.684582i \(0.759985\pi\)
\(180\) 95394.2 + 95394.2i 0.0163570 + 0.0163570i
\(181\) 827492. 0.139549 0.0697747 0.997563i \(-0.477772\pi\)
0.0697747 + 0.997563i \(0.477772\pi\)
\(182\) −110202. −0.0182799
\(183\) 1.42163e6 1.42163e6i 0.231971 0.231971i
\(184\) 1.04215e6i 0.167292i
\(185\) 361257. + 557645.i 0.0570560 + 0.0880730i
\(186\) −702132. −0.109114
\(187\) −1.64188e6 1.64188e6i −0.251082 0.251082i
\(188\) 3.98416e6i 0.599602i
\(189\) 176183.i 0.0260963i
\(190\) 208080. 208080.i 0.0303368 0.0303368i
\(191\) −5.09562e6 + 5.09562e6i −0.731302 + 0.731302i −0.970878 0.239576i \(-0.922992\pi\)
0.239576 + 0.970878i \(0.422992\pi\)
\(192\) 661561. 0.0934687
\(193\) 1.99638e6 1.99638e6i 0.277696 0.277696i −0.554492 0.832189i \(-0.687088\pi\)
0.832189 + 0.554492i \(0.187088\pi\)
\(194\) −275576. −0.0377430
\(195\) 620997. 0.0837502
\(196\) 3.76256e6i 0.499707i
\(197\) 1.62058e6 0.211969 0.105984 0.994368i \(-0.466201\pi\)
0.105984 + 0.994368i \(0.466201\pi\)
\(198\) 313450. 313450.i 0.0403806 0.0403806i
\(199\) −3.85892e6 3.85892e6i −0.489673 0.489673i 0.418530 0.908203i \(-0.362546\pi\)
−0.908203 + 0.418530i \(0.862546\pi\)
\(200\) 1.97798e6 + 1.97798e6i 0.247247 + 0.247247i
\(201\) 9.76825e6 1.20290
\(202\) 1.73663e6 1.73663e6i 0.210695 0.210695i
\(203\) 248857. + 248857.i 0.0297483 + 0.0297483i
\(204\) 4.35051e6 4.35051e6i 0.512448 0.512448i
\(205\) −95524.8 95524.8i −0.0110880 0.0110880i
\(206\) 892232.i 0.102065i
\(207\) 1.30836e6 1.30836e6i 0.147508 0.147508i
\(208\) −1.69788e6 + 1.69788e6i −0.188676 + 0.188676i
\(209\) −683718. 683718.i −0.0748925 0.0748925i
\(210\) 12446.1i 0.00134393i
\(211\) −5.98273e6 −0.636872 −0.318436 0.947944i \(-0.603158\pi\)
−0.318436 + 0.947944i \(0.603158\pi\)
\(212\) 2.65219e6i 0.278354i
\(213\) 3.49094e6i 0.361247i
\(214\) −879170. 879170.i −0.0897081 0.0897081i
\(215\) 1.42519e6i 0.143403i
\(216\) 2.71445e6 + 2.71445e6i 0.269353 + 0.269353i
\(217\) −36116.0 36116.0i −0.00353444 0.00353444i
\(218\) 6.45488e6 0.623044
\(219\) −1.06372e7 −1.01273
\(220\) −72369.0 + 72369.0i −0.00679649 + 0.00679649i
\(221\) 2.23310e7i 2.06886i
\(222\) 3.14531e6 + 4.85518e6i 0.287478 + 0.443758i
\(223\) −1.19672e7 −1.07914 −0.539570 0.841941i \(-0.681413\pi\)
−0.539570 + 0.841941i \(0.681413\pi\)
\(224\) 34029.1 + 34029.1i 0.00302766 + 0.00302766i
\(225\) 4.96650e6i 0.436016i
\(226\) 2.39050e6i 0.207092i
\(227\) −9.17918e6 + 9.17918e6i −0.784741 + 0.784741i −0.980627 0.195886i \(-0.937242\pi\)
0.195886 + 0.980627i \(0.437242\pi\)
\(228\) 1.81166e6 1.81166e6i 0.152853 0.152853i
\(229\) 430968. 0.0358871 0.0179436 0.999839i \(-0.494288\pi\)
0.0179436 + 0.999839i \(0.494288\pi\)
\(230\) −302073. + 302073.i −0.0248272 + 0.0248272i
\(231\) −40896.0 −0.00331776
\(232\) 7.66831e6 0.614095
\(233\) 1.94580e7i 1.53826i 0.639093 + 0.769130i \(0.279310\pi\)
−0.639093 + 0.769130i \(0.720690\pi\)
\(234\) −4.26320e6 −0.332727
\(235\) 1.15483e6 1.15483e6i 0.0889848 0.0889848i
\(236\) −4.61490e6 4.61490e6i −0.351096 0.351096i
\(237\) 1.24518e7 + 1.24518e7i 0.935374 + 0.935374i
\(238\) 447560. 0.0331987
\(239\) 1.68305e7 1.68305e7i 1.23283 1.23283i 0.269957 0.962872i \(-0.412990\pi\)
0.962872 0.269957i \(-0.0870095\pi\)
\(240\) −191758. 191758.i −0.0138714 0.0138714i
\(241\) −4.80533e6 + 4.80533e6i −0.343299 + 0.343299i −0.857606 0.514307i \(-0.828049\pi\)
0.514307 + 0.857606i \(0.328049\pi\)
\(242\) −6.84845e6 6.84845e6i −0.483221 0.483221i
\(243\) 1.15460e7i 0.804660i
\(244\) 2.25329e6 2.25329e6i 0.155113 0.155113i
\(245\) −1.09060e6 + 1.09060e6i −0.0741597 + 0.0741597i
\(246\) −831692. 831692.i −0.0558673 0.0558673i
\(247\) 9.29918e6i 0.617097i
\(248\) −1.11288e6 −0.0729615
\(249\) 7.25446e6i 0.469902i
\(250\) 2.30608e6i 0.147589i
\(251\) −6.57840e6 6.57840e6i −0.416005 0.416005i 0.467819 0.883824i \(-0.345040\pi\)
−0.883824 + 0.467819i \(0.845040\pi\)
\(252\) 85443.7i 0.00533923i
\(253\) 992563. + 992563.i 0.0612910 + 0.0612910i
\(254\) 6.90269e6 + 6.90269e6i 0.421228 + 0.421228i
\(255\) −2.52205e6 −0.152101
\(256\) 1.04858e6 0.0625000
\(257\) 8.58905e6 8.58905e6i 0.505994 0.505994i −0.407300 0.913294i \(-0.633530\pi\)
0.913294 + 0.407300i \(0.133530\pi\)
\(258\) 1.24085e7i 0.722539i
\(259\) −87951.7 + 411526.i −0.00506226 + 0.0236864i
\(260\) 984283. 0.0560015
\(261\) 9.62717e6 + 9.62717e6i 0.541474 + 0.541474i
\(262\) 2.03548e7i 1.13178i
\(263\) 7.85817e6i 0.431970i −0.976397 0.215985i \(-0.930704\pi\)
0.976397 0.215985i \(-0.0692963\pi\)
\(264\) −630085. + 630085.i −0.0342442 + 0.0342442i
\(265\) −768756. + 768756.i −0.0413096 + 0.0413096i
\(266\) 186375. 0.00990247
\(267\) −6.31608e6 + 6.31608e6i −0.331829 + 0.331829i
\(268\) 1.54827e7 0.804346
\(269\) 1.61362e7 0.828983 0.414491 0.910053i \(-0.363960\pi\)
0.414491 + 0.910053i \(0.363960\pi\)
\(270\) 1.57360e6i 0.0799473i
\(271\) 1.77920e7 0.893955 0.446978 0.894545i \(-0.352500\pi\)
0.446978 + 0.894545i \(0.352500\pi\)
\(272\) 6.89558e6 6.89558e6i 0.342660 0.342660i
\(273\) 278111. + 278111.i 0.0136688 + 0.0136688i
\(274\) −1.06123e7 1.06123e7i −0.515889 0.515889i
\(275\) −3.76774e6 −0.181168
\(276\) −2.63001e6 + 2.63001e6i −0.125092 + 0.125092i
\(277\) −1.30922e7 1.30922e7i −0.615990 0.615990i 0.328511 0.944500i \(-0.393453\pi\)
−0.944500 + 0.328511i \(0.893453\pi\)
\(278\) −1.54224e7 + 1.54224e7i −0.717822 + 0.717822i
\(279\) −1.39717e6 1.39717e6i −0.0643333 0.0643333i
\(280\) 19727.1i 0.000898649i
\(281\) −1.08811e7 + 1.08811e7i −0.490404 + 0.490404i −0.908434 0.418029i \(-0.862721\pi\)
0.418029 + 0.908434i \(0.362721\pi\)
\(282\) 1.00546e7 1.00546e7i 0.448352 0.448352i
\(283\) −6.68314e6 6.68314e6i −0.294864 0.294864i 0.544134 0.838998i \(-0.316858\pi\)
−0.838998 + 0.544134i \(0.816858\pi\)
\(284\) 5.53315e6i 0.241556i
\(285\) −1.05024e6 −0.0453686
\(286\) 3.23420e6i 0.138251i
\(287\) 85560.7i 0.00361933i
\(288\) 1.31643e6 + 1.31643e6i 0.0551089 + 0.0551089i
\(289\) 6.65549e7i 2.75732i
\(290\) −2.22271e6 2.22271e6i −0.0911357 0.0911357i
\(291\) 695458. + 695458.i 0.0282223 + 0.0282223i
\(292\) −1.68600e7 −0.677189
\(293\) 9.50505e6 0.377878 0.188939 0.981989i \(-0.439495\pi\)
0.188939 + 0.981989i \(0.439495\pi\)
\(294\) −9.49540e6 + 9.49540e6i −0.373655 + 0.373655i
\(295\) 2.67532e6i 0.104210i
\(296\) 4.98532e6 + 7.69547e6i 0.192229 + 0.296729i
\(297\) −5.17061e6 −0.197366
\(298\) −1.51580e7 1.51580e7i −0.572787 0.572787i
\(299\) 1.34997e7i 0.505024i
\(300\) 9.98345e6i 0.369757i
\(301\) −638267. + 638267.i −0.0234047 + 0.0234047i
\(302\) −1.54829e7 + 1.54829e7i −0.562123 + 0.562123i
\(303\) −8.76531e6 −0.315093
\(304\) 2.87149e6 2.87149e6i 0.102208 0.102208i
\(305\) −1.30626e6 −0.0460394
\(306\) 1.73141e7 0.604276
\(307\) 3.80384e7i 1.31464i −0.753611 0.657321i \(-0.771690\pi\)
0.753611 0.657321i \(-0.228310\pi\)
\(308\) −64820.3 −0.00221850
\(309\) 2.25168e6 2.25168e6i 0.0763189 0.0763189i
\(310\) 322576. + 322576.i 0.0108280 + 0.0108280i
\(311\) −3.91219e7 3.91219e7i −1.30058 1.30058i −0.927997 0.372588i \(-0.878470\pi\)
−0.372588 0.927997i \(-0.621530\pi\)
\(312\) 8.56972e6 0.282165
\(313\) −2.13307e7 + 2.13307e7i −0.695619 + 0.695619i −0.963462 0.267844i \(-0.913689\pi\)
0.267844 + 0.963462i \(0.413689\pi\)
\(314\) −2.02116e7 2.02116e7i −0.652848 0.652848i
\(315\) 24766.4 24766.4i 0.000792376 0.000792376i
\(316\) 1.97361e7 + 1.97361e7i 0.625460 + 0.625460i
\(317\) 1.11986e7i 0.351548i 0.984431 + 0.175774i \(0.0562427\pi\)
−0.984431 + 0.175774i \(0.943757\pi\)
\(318\) −6.69322e6 + 6.69322e6i −0.208139 + 0.208139i
\(319\) −7.30347e6 + 7.30347e6i −0.224987 + 0.224987i
\(320\) −303937. 303937.i −0.00927541 0.00927541i
\(321\) 4.43744e6i 0.134158i
\(322\) −270564. −0.00810405
\(323\) 3.77666e7i 1.12073i
\(324\) 6.20318e6i 0.182381i
\(325\) 2.56223e7 + 2.56223e7i 0.746393 + 0.746393i
\(326\) 2.41321e7i 0.696535i
\(327\) −1.62899e7 1.62899e7i −0.465881 0.465881i
\(328\) −1.31824e6 1.31824e6i −0.0373570 0.0373570i
\(329\) 1.03437e6 0.0290462
\(330\) 365269. 0.0101641
\(331\) 4.88035e7 4.88035e7i 1.34576 1.34576i 0.455545 0.890213i \(-0.349444\pi\)
0.890213 0.455545i \(-0.150556\pi\)
\(332\) 1.14983e7i 0.314211i
\(333\) −3.40245e6 + 1.59201e7i −0.0921424 + 0.431135i
\(334\) 3.19146e7 0.856545
\(335\) −4.48777e6 4.48777e6i −0.119370 0.119370i
\(336\) 171756.i 0.00452786i
\(337\) 1.93250e7i 0.504928i −0.967606 0.252464i \(-0.918759\pi\)
0.967606 0.252464i \(-0.0812409\pi\)
\(338\) −2.68675e6 + 2.68675e6i −0.0695788 + 0.0695788i
\(339\) 6.03279e6 6.03279e6i 0.154853 0.154853i
\(340\) −3.99745e6 −0.101706
\(341\) 1.05993e6 1.05993e6i 0.0267310 0.0267310i
\(342\) 7.21002e6 0.180243
\(343\) −1.95426e6 −0.0484283
\(344\) 1.96676e7i 0.483143i
\(345\) 1.52465e6 0.0371290
\(346\) −3.26105e7 + 3.26105e7i −0.787279 + 0.787279i
\(347\) 1.17866e7 + 1.17866e7i 0.282099 + 0.282099i 0.833946 0.551847i \(-0.186077\pi\)
−0.551847 + 0.833946i \(0.686077\pi\)
\(348\) −1.93522e7 1.93522e7i −0.459189 0.459189i
\(349\) 6.10844e7 1.43699 0.718496 0.695531i \(-0.244831\pi\)
0.718496 + 0.695531i \(0.244831\pi\)
\(350\) 513526. 513526.i 0.0119773 0.0119773i
\(351\) 3.51625e7 + 3.51625e7i 0.813126 + 0.813126i
\(352\) −998688. + 998688.i −0.0228982 + 0.0228982i
\(353\) 7.87288e6 + 7.87288e6i 0.178982 + 0.178982i 0.790912 0.611930i \(-0.209607\pi\)
−0.611930 + 0.790912i \(0.709607\pi\)
\(354\) 2.32928e7i 0.525064i
\(355\) 1.60382e6 1.60382e6i 0.0358485 0.0358485i
\(356\) −1.00110e7 + 1.00110e7i −0.221885 + 0.221885i
\(357\) −1.12949e6 1.12949e6i −0.0248243 0.0248243i
\(358\) 2.03511e6i 0.0443546i
\(359\) 6.52112e7 1.40942 0.704708 0.709498i \(-0.251078\pi\)
0.704708 + 0.709498i \(0.251078\pi\)
\(360\) 763154.i 0.0163570i
\(361\) 3.13189e7i 0.665710i
\(362\) −3.30997e6 3.30997e6i −0.0697747 0.0697747i
\(363\) 3.45662e7i 0.722657i
\(364\) 440807. + 440807.i 0.00913995 + 0.00913995i
\(365\) 4.88699e6 + 4.88699e6i 0.100499 + 0.100499i
\(366\) −1.13730e7 −0.231971
\(367\) −9.42630e7 −1.90697 −0.953483 0.301447i \(-0.902530\pi\)
−0.953483 + 0.301447i \(0.902530\pi\)
\(368\) −4.16858e6 + 4.16858e6i −0.0836459 + 0.0836459i
\(369\) 3.30996e6i 0.0658784i
\(370\) 785554. 3.67561e6i 0.0155085 0.0725645i
\(371\) −688568. −0.0134842
\(372\) 2.80853e6 + 2.80853e6i 0.0545569 + 0.0545569i
\(373\) 3.92074e7i 0.755512i −0.925905 0.377756i \(-0.876696\pi\)
0.925905 0.377756i \(-0.123304\pi\)
\(374\) 1.31350e7i 0.251082i
\(375\) −5.81976e6 + 5.81976e6i −0.110360 + 0.110360i
\(376\) 1.59366e7 1.59366e7i 0.299801 0.299801i
\(377\) 9.93337e7 1.85384
\(378\) 704731. 704731.i 0.0130481 0.0130481i
\(379\) 3.68081e7 0.676122 0.338061 0.941124i \(-0.390229\pi\)
0.338061 + 0.941124i \(0.390229\pi\)
\(380\) −1.66464e6 −0.0303368
\(381\) 3.48400e7i 0.629946i
\(382\) 4.07649e7 0.731302
\(383\) −2.45374e7 + 2.45374e7i −0.436749 + 0.436749i −0.890916 0.454168i \(-0.849937\pi\)
0.454168 + 0.890916i \(0.349937\pi\)
\(384\) −2.64624e6 2.64624e6i −0.0467343 0.0467343i
\(385\) 18788.6 + 18788.6i 0.000329239 + 0.000329239i
\(386\) −1.59710e7 −0.277696
\(387\) −2.46917e7 + 2.46917e7i −0.426007 + 0.426007i
\(388\) 1.10230e6 + 1.10230e6i 0.0188715 + 0.0188715i
\(389\) −6.32206e7 + 6.32206e7i −1.07401 + 1.07401i −0.0769809 + 0.997033i \(0.524528\pi\)
−0.997033 + 0.0769809i \(0.975472\pi\)
\(390\) −2.48399e6 2.48399e6i −0.0418751 0.0418751i
\(391\) 5.48263e7i 0.917189i
\(392\) −1.50502e7 + 1.50502e7i −0.249853 + 0.249853i
\(393\) −5.13684e7 + 5.13684e7i −0.846288 + 0.846288i
\(394\) −6.48232e6 6.48232e6i −0.105984 0.105984i
\(395\) 1.14413e7i 0.185645i
\(396\) −2.50760e6 −0.0403806
\(397\) 1.08622e7i 0.173599i 0.996226 + 0.0867994i \(0.0276639\pi\)
−0.996226 + 0.0867994i \(0.972336\pi\)
\(398\) 3.08714e7i 0.489673i
\(399\) −470347. 470347.i −0.00740457 0.00740457i
\(400\) 1.58238e7i 0.247247i
\(401\) −4.52618e7 4.52618e7i −0.701937 0.701937i 0.262889 0.964826i \(-0.415325\pi\)
−0.964826 + 0.262889i \(0.915325\pi\)
\(402\) −3.90730e7 3.90730e7i −0.601449 0.601449i
\(403\) −1.44160e7 −0.220258
\(404\) −1.38930e7 −0.210695
\(405\) −1.79803e6 + 1.79803e6i −0.0270665 + 0.0270665i
\(406\) 1.99086e6i 0.0297483i
\(407\) −1.20775e7 2.58121e6i −0.179140 0.0382859i
\(408\) −3.48041e7 −0.512448
\(409\) −1.64004e7 1.64004e7i −0.239709 0.239709i 0.577020 0.816730i \(-0.304215\pi\)
−0.816730 + 0.577020i \(0.804215\pi\)
\(410\) 764198.i 0.0110880i
\(411\) 5.35633e7i 0.771511i
\(412\) 3.56893e6 3.56893e6i 0.0510324 0.0510324i
\(413\) −1.19813e6 + 1.19813e6i −0.0170080 + 0.0170080i
\(414\) −1.04669e7 −0.147508
\(415\) 3.33287e6 3.33287e6i 0.0466309 0.0466309i
\(416\) 1.35830e7 0.188676
\(417\) 7.78415e7 1.07350
\(418\) 5.46975e6i 0.0748925i
\(419\) 8.17876e7 1.11185 0.555924 0.831233i \(-0.312365\pi\)
0.555924 + 0.831233i \(0.312365\pi\)
\(420\) −49784.5 + 49784.5i −0.000671964 + 0.000671964i
\(421\) 4.36761e7 + 4.36761e7i 0.585326 + 0.585326i 0.936362 0.351036i \(-0.114171\pi\)
−0.351036 + 0.936362i \(0.614171\pi\)
\(422\) 2.39309e7 + 2.39309e7i 0.318436 + 0.318436i
\(423\) 4.00153e7 0.528694
\(424\) −1.06088e7 + 1.06088e7i −0.139177 + 0.139177i
\(425\) −1.04059e8 1.04059e8i −1.35555 1.35555i
\(426\) 1.39638e7 1.39638e7i 0.180623 0.180623i
\(427\) −585002. 585002.i −0.00751405 0.00751405i
\(428\) 7.03336e6i 0.0897081i
\(429\) −8.16200e6 + 8.16200e6i −0.103377 + 0.103377i
\(430\) 5.70077e6 5.70077e6i 0.0717015 0.0717015i
\(431\) −4.06283e7 4.06283e7i −0.507454 0.507454i 0.406290 0.913744i \(-0.366822\pi\)
−0.913744 + 0.406290i \(0.866822\pi\)
\(432\) 2.17156e7i 0.269353i
\(433\) −1.37685e8 −1.69599 −0.847995 0.530004i \(-0.822191\pi\)
−0.847995 + 0.530004i \(0.822191\pi\)
\(434\) 288928.i 0.00353444i
\(435\) 1.12187e7i 0.136293i
\(436\) −2.58195e7 2.58195e7i −0.311522 0.311522i
\(437\) 2.28310e7i 0.273578i
\(438\) 4.25489e7 + 4.25489e7i 0.506367 + 0.506367i
\(439\) 8.19502e6 + 8.19502e6i 0.0968626 + 0.0968626i 0.753878 0.657015i \(-0.228181\pi\)
−0.657015 + 0.753878i \(0.728181\pi\)
\(440\) 578952. 0.00679649
\(441\) −3.77896e7 −0.440612
\(442\) 8.93239e7 8.93239e7i 1.03443 1.03443i
\(443\) 1.24481e8i 1.43183i 0.698187 + 0.715915i \(0.253990\pi\)
−0.698187 + 0.715915i \(0.746010\pi\)
\(444\) 6.83947e6 3.20019e7i 0.0781401 0.365618i
\(445\) 5.80351e6 0.0658583
\(446\) 4.78688e7 + 4.78688e7i 0.539570 + 0.539570i
\(447\) 7.65071e7i 0.856602i
\(448\) 272233.i 0.00302766i
\(449\) −1.48915e7 + 1.48915e7i −0.164513 + 0.164513i −0.784563 0.620050i \(-0.787112\pi\)
0.620050 + 0.784563i \(0.287112\pi\)
\(450\) 1.98660e7 1.98660e7i 0.218008 0.218008i
\(451\) 2.51103e6 0.0273730
\(452\) 9.56199e6 9.56199e6i 0.103546 0.103546i
\(453\) 7.81469e7 0.840653
\(454\) 7.34334e7 0.784741
\(455\) 255541.i 0.00271286i
\(456\) −1.44933e7 −0.152853
\(457\) 6.38802e7 6.38802e7i 0.669295 0.669295i −0.288258 0.957553i \(-0.593076\pi\)
0.957553 + 0.288258i \(0.0930760\pi\)
\(458\) −1.72387e6 1.72387e6i −0.0179436 0.0179436i
\(459\) −1.42805e8 1.42805e8i −1.47674 1.47674i
\(460\) 2.41658e6 0.0248272
\(461\) 1.26741e8 1.26741e8i 1.29365 1.29365i 0.361131 0.932515i \(-0.382391\pi\)
0.932515 0.361131i \(-0.117609\pi\)
\(462\) 163584. + 163584.i 0.00165888 + 0.00165888i
\(463\) 1.91810e7 1.91810e7i 0.193254 0.193254i −0.603847 0.797100i \(-0.706366\pi\)
0.797100 + 0.603847i \(0.206366\pi\)
\(464\) −3.06732e7 3.06732e7i −0.307048 0.307048i
\(465\) 1.62814e6i 0.0161932i
\(466\) 7.78319e7 7.78319e7i 0.769130 0.769130i
\(467\) 5.31830e7 5.31830e7i 0.522182 0.522182i −0.396048 0.918230i \(-0.629618\pi\)
0.918230 + 0.396048i \(0.129618\pi\)
\(468\) 1.70528e7 + 1.70528e7i 0.166364 + 0.166364i
\(469\) 4.01965e6i 0.0389646i
\(470\) −9.23867e6 −0.0889848
\(471\) 1.02014e8i 0.976333i
\(472\) 3.69192e7i 0.351096i
\(473\) −1.87318e7 1.87318e7i −0.177010 0.177010i
\(474\) 9.96140e7i 0.935374i
\(475\) −4.33330e7 4.33330e7i −0.404332 0.404332i
\(476\) −1.79024e6 1.79024e6i −0.0165993 0.0165993i
\(477\) −2.66376e7 −0.245437
\(478\) −1.34644e8 −1.23283
\(479\) 3.57644e7 3.57644e7i 0.325420 0.325420i −0.525422 0.850842i \(-0.676092\pi\)
0.850842 + 0.525422i \(0.176092\pi\)
\(480\) 1.53406e6i 0.0138714i
\(481\) 6.45789e7 + 9.96855e7i 0.580303 + 0.895771i
\(482\) 3.84426e7 0.343299
\(483\) 682809. + 682809.i 0.00605979 + 0.00605979i
\(484\) 5.47876e7i 0.483221i
\(485\) 639020.i 0.00560130i
\(486\) 4.61840e7 4.61840e7i 0.402330 0.402330i
\(487\) −1.06035e8 + 1.06035e8i −0.918044 + 0.918044i −0.996887 0.0788427i \(-0.974878\pi\)
0.0788427 + 0.996887i \(0.474878\pi\)
\(488\) −1.80263e7 −0.155113
\(489\) 6.09011e7 6.09011e7i 0.520833 0.520833i
\(490\) 8.72482e6 0.0741597
\(491\) 1.16072e8 0.980579 0.490290 0.871560i \(-0.336891\pi\)
0.490290 + 0.871560i \(0.336891\pi\)
\(492\) 6.65354e6i 0.0558673i
\(493\) −4.03423e8 −3.36682
\(494\) 3.71967e7 3.71967e7i 0.308549 0.308549i
\(495\) 726845. + 726845.i 0.00599275 + 0.00599275i
\(496\) 4.45153e6 + 4.45153e6i 0.0364808 + 0.0364808i
\(497\) 1.43653e6 0.0117016
\(498\) 2.90178e7 2.90178e7i 0.234951 0.234951i
\(499\) 5.94999e7 + 5.94999e7i 0.478867 + 0.478867i 0.904769 0.425902i \(-0.140043\pi\)
−0.425902 + 0.904769i \(0.640043\pi\)
\(500\) −9.22433e6 + 9.22433e6i −0.0737947 + 0.0737947i
\(501\) −8.05414e7 8.05414e7i −0.640481 0.640481i
\(502\) 5.26272e7i 0.416005i
\(503\) −6.36091e7 + 6.36091e7i −0.499822 + 0.499822i −0.911382 0.411561i \(-0.864984\pi\)
0.411561 + 0.911382i \(0.364984\pi\)
\(504\) 341775. 341775.i 0.00266962 0.00266962i
\(505\) 4.02699e6 + 4.02699e6i 0.0312684 + 0.0312684i
\(506\) 7.94050e6i 0.0612910i
\(507\) 1.35609e7 0.104055
\(508\) 5.52215e7i 0.421228i
\(509\) 8.59204e7i 0.651543i −0.945449 0.325771i \(-0.894376\pi\)
0.945449 0.325771i \(-0.105624\pi\)
\(510\) 1.00882e7 + 1.00882e7i 0.0760506 + 0.0760506i
\(511\) 4.37723e6i 0.0328047i
\(512\) −4.19430e6 4.19430e6i −0.0312500 0.0312500i
\(513\) −5.94675e7 5.94675e7i −0.440482 0.440482i
\(514\) −6.87124e7 −0.505994
\(515\) −2.06895e6 −0.0151471
\(516\) 4.96342e7 4.96342e7i 0.361270 0.361270i
\(517\) 3.03568e7i 0.219677i
\(518\) 1.99791e6 1.29430e6i 0.0143743 0.00931205i
\(519\) 1.64595e8 1.17737
\(520\) −3.93713e6 3.93713e6i −0.0280008 0.0280008i
\(521\) 1.09155e8i 0.771845i −0.922531 0.385922i \(-0.873883\pi\)
0.922531 0.385922i \(-0.126117\pi\)
\(522\) 7.70174e7i 0.541474i
\(523\) 4.80117e7 4.80117e7i 0.335616 0.335616i −0.519099 0.854714i \(-0.673732\pi\)
0.854714 + 0.519099i \(0.173732\pi\)
\(524\) −8.14191e7 + 8.14191e7i −0.565890 + 0.565890i
\(525\) −2.59192e6 −0.0179120
\(526\) −3.14327e7 + 3.14327e7i −0.215985 + 0.215985i
\(527\) 5.85477e7 0.400016
\(528\) 5.04068e6 0.0342442
\(529\) 1.14892e8i 0.776107i
\(530\) 6.15005e6 0.0413096
\(531\) −4.63502e7 + 4.63502e7i −0.309576 + 0.309576i
\(532\) −745502. 745502.i −0.00495124 0.00495124i
\(533\) −1.70762e7 1.70762e7i −0.112774 0.112774i
\(534\) 5.05286e7 0.331829
\(535\) 2.03866e6 2.03866e6i 0.0133133 0.0133133i
\(536\) −6.19309e7 6.19309e7i −0.402173 0.402173i
\(537\) 5.13591e6 5.13591e6i 0.0331661 0.0331661i
\(538\) −6.45449e7 6.45449e7i −0.414491 0.414491i
\(539\) 2.86684e7i 0.183078i
\(540\) −6.29441e6 + 6.29441e6i −0.0399737 + 0.0399737i
\(541\) 4.71584e7 4.71584e7i 0.297829 0.297829i −0.542334 0.840163i \(-0.682459\pi\)
0.840163 + 0.542334i \(0.182459\pi\)
\(542\) −7.11678e7 7.11678e7i −0.446978 0.446978i
\(543\) 1.67064e7i 0.104348i
\(544\) −5.51646e7 −0.342660
\(545\) 1.49679e7i 0.0924638i
\(546\) 2.22489e6i 0.0136688i
\(547\) −2.83095e7 2.83095e7i −0.172970 0.172970i 0.615313 0.788283i \(-0.289030\pi\)
−0.788283 + 0.615313i \(0.789030\pi\)
\(548\) 8.48980e7i 0.515889i
\(549\) −2.26311e7 2.26311e7i −0.136769 0.136769i
\(550\) 1.50709e7 + 1.50709e7i 0.0905842 + 0.0905842i
\(551\) −1.67995e8 −1.00425
\(552\) 2.10401e7 0.125092
\(553\) 5.12391e6 5.12391e6i 0.0302989 0.0302989i
\(554\) 1.04738e8i 0.615990i
\(555\) −1.12584e7 + 7.29350e6i −0.0658565 + 0.0426636i
\(556\) 1.23379e8 0.717822
\(557\) 1.45283e8 + 1.45283e8i 0.840716 + 0.840716i 0.988952 0.148236i \(-0.0473595\pi\)
−0.148236 + 0.988952i \(0.547359\pi\)
\(558\) 1.11773e7i 0.0643333i
\(559\) 2.54770e8i 1.45852i
\(560\) −78908.5 + 78908.5i −0.000449324 + 0.000449324i
\(561\) 3.31482e7 3.31482e7i 0.187746 0.187746i
\(562\) 8.70489e7 0.490404
\(563\) 5.63680e7 5.63680e7i 0.315869 0.315869i −0.531309 0.847178i \(-0.678300\pi\)
0.847178 + 0.531309i \(0.178300\pi\)
\(564\) −8.04371e7 −0.448352
\(565\) −5.54321e6 −0.0307338
\(566\) 5.34651e7i 0.294864i
\(567\) −1.61048e6 −0.00883499
\(568\) 2.21326e7 2.21326e7i 0.120778 0.120778i
\(569\) 3.84710e7 + 3.84710e7i 0.208832 + 0.208832i 0.803771 0.594939i \(-0.202824\pi\)
−0.594939 + 0.803771i \(0.702824\pi\)
\(570\) 4.20098e6 + 4.20098e6i 0.0226843 + 0.0226843i
\(571\) 2.43126e8 1.30594 0.652970 0.757384i \(-0.273523\pi\)
0.652970 + 0.757384i \(0.273523\pi\)
\(572\) −1.29368e7 + 1.29368e7i −0.0691255 + 0.0691255i
\(573\) −1.02877e8 1.02877e8i −0.546830 0.546830i
\(574\) −342243. + 342243.i −0.00180967 + 0.00180967i
\(575\) 6.29070e7 + 6.29070e7i 0.330899 + 0.330899i
\(576\) 1.05315e7i 0.0551089i
\(577\) −2.09577e8 + 2.09577e8i −1.09098 + 1.09098i −0.0955517 + 0.995424i \(0.530462\pi\)
−0.995424 + 0.0955517i \(0.969538\pi\)
\(578\) −2.66220e8 + 2.66220e8i −1.37866 + 1.37866i
\(579\) 4.03053e7 + 4.03053e7i 0.207647 + 0.207647i
\(580\) 1.77817e7i 0.0911357i
\(581\) 2.98522e6 0.0152212
\(582\) 5.56367e6i 0.0282223i
\(583\) 2.02081e7i 0.101981i
\(584\) 6.74401e7 + 6.74401e7i 0.338594 + 0.338594i
\(585\) 9.88574e6i 0.0493789i
\(586\) −3.80202e7 3.80202e7i −0.188939 0.188939i
\(587\) 1.24110e8 + 1.24110e8i 0.613610 + 0.613610i 0.943885 0.330275i \(-0.107142\pi\)
−0.330275 + 0.943885i \(0.607142\pi\)
\(588\) 7.59632e7 0.373655
\(589\) 2.43807e7 0.119317
\(590\) 1.07013e7 1.07013e7i 0.0521050 0.0521050i
\(591\) 3.27182e7i 0.158499i
\(592\) 1.08406e7 5.07232e7i 0.0522502 0.244479i
\(593\) −2.45373e8 −1.17669 −0.588345 0.808610i \(-0.700220\pi\)
−0.588345 + 0.808610i \(0.700220\pi\)
\(594\) 2.06825e7 + 2.06825e7i 0.0986831 + 0.0986831i
\(595\) 1.03783e6i 0.00492690i
\(596\) 1.21264e8i 0.572787i
\(597\) 7.79086e7 7.79086e7i 0.366153 0.366153i
\(598\) −5.39989e7 + 5.39989e7i −0.252512 + 0.252512i
\(599\) 3.44657e8 1.60364 0.801819 0.597567i \(-0.203866\pi\)
0.801819 + 0.597567i \(0.203866\pi\)
\(600\) −3.99338e7 + 3.99338e7i −0.184879 + 0.184879i
\(601\) 1.91557e8 0.882421 0.441210 0.897404i \(-0.354549\pi\)
0.441210 + 0.897404i \(0.354549\pi\)
\(602\) 5.10613e6 0.0234047
\(603\) 1.55502e8i 0.709226i
\(604\) 1.23863e8 0.562123
\(605\) 1.58805e7 1.58805e7i 0.0717132 0.0717132i
\(606\) 3.50612e7 + 3.50612e7i 0.157547 + 0.157547i
\(607\) −3.62425e7 3.62425e7i −0.162051 0.162051i 0.621424 0.783475i \(-0.286555\pi\)
−0.783475 + 0.621424i \(0.786555\pi\)
\(608\) −2.29719e7 −0.102208
\(609\) −5.02424e6 + 5.02424e6i −0.0222443 + 0.0222443i
\(610\) 5.22504e6 + 5.22504e6i 0.0230197 + 0.0230197i
\(611\) 2.06440e8 2.06440e8i 0.905044 0.905044i
\(612\) −6.92564e7 6.92564e7i −0.302138 0.302138i
\(613\) 4.08087e8i 1.77162i 0.464047 + 0.885811i \(0.346397\pi\)
−0.464047 + 0.885811i \(0.653603\pi\)
\(614\) −1.52154e8 + 1.52154e8i −0.657321 + 0.657321i
\(615\) 1.92857e6 1.92857e6i 0.00829107 0.00829107i
\(616\) 259281. + 259281.i 0.00110925 + 0.00110925i
\(617\) 2.02329e8i 0.861396i −0.902496 0.430698i \(-0.858267\pi\)
0.902496 0.430698i \(-0.141733\pi\)
\(618\) −1.80135e7 −0.0763189
\(619\) 1.53352e8i 0.646574i 0.946301 + 0.323287i \(0.104788\pi\)
−0.946301 + 0.323287i \(0.895212\pi\)
\(620\) 2.58061e6i 0.0108280i
\(621\) 8.63298e7 + 8.63298e7i 0.360484 + 0.360484i
\(622\) 3.12975e8i 1.30058i
\(623\) 2.59908e6 + 2.59908e6i 0.0107487 + 0.0107487i
\(624\) −3.42789e7 3.42789e7i −0.141082 0.141082i
\(625\) −2.36105e8 −0.967085
\(626\) 1.70645e8 0.695619
\(627\) 1.38037e7 1.38037e7i 0.0560008 0.0560008i
\(628\) 1.61693e8i 0.652848i
\(629\) −2.62273e8 4.04852e8i −1.05391 1.62684i
\(630\) −198131. −0.000792376
\(631\) −1.36434e8 1.36434e8i −0.543042 0.543042i 0.381378 0.924419i \(-0.375450\pi\)
−0.924419 + 0.381378i \(0.875450\pi\)
\(632\) 1.57889e8i 0.625460i
\(633\) 1.20787e8i 0.476221i
\(634\) 4.47942e7 4.47942e7i 0.175774 0.175774i
\(635\) −1.60063e7 + 1.60063e7i −0.0625130 + 0.0625130i
\(636\) 5.35458e7 0.208139
\(637\) −1.94958e8 + 1.94958e8i −0.754262 + 0.754262i
\(638\) 5.84278e7 0.224987
\(639\) 5.55728e7 0.212990
\(640\) 2.43149e6i 0.00927541i
\(641\) 3.98764e8 1.51406 0.757028 0.653382i \(-0.226650\pi\)
0.757028 + 0.653382i \(0.226650\pi\)
\(642\) 1.77498e7 1.77498e7i 0.0670791 0.0670791i
\(643\) 2.88666e8 + 2.88666e8i 1.08583 + 1.08583i 0.995953 + 0.0898795i \(0.0286482\pi\)
0.0898795 + 0.995953i \(0.471352\pi\)
\(644\) 1.08225e6 + 1.08225e6i 0.00405202 + 0.00405202i
\(645\) −2.87736e7 −0.107230
\(646\) −1.51066e8 + 1.51066e8i −0.560364 + 0.560364i
\(647\) 8.75493e6 + 8.75493e6i 0.0323251 + 0.0323251i 0.723085 0.690759i \(-0.242724\pi\)
−0.690759 + 0.723085i \(0.742724\pi\)
\(648\) −2.48127e7 + 2.48127e7i −0.0911904 + 0.0911904i
\(649\) −3.51627e7 3.51627e7i −0.128632 0.128632i
\(650\) 2.04978e8i 0.746393i
\(651\) 729155. 729155.i 0.00264288 0.00264288i
\(652\) 9.65285e7 9.65285e7i 0.348267 0.348267i
\(653\) −1.85611e8 1.85611e8i −0.666599 0.666599i 0.290328 0.956927i \(-0.406236\pi\)
−0.956927 + 0.290328i \(0.906236\pi\)
\(654\) 1.30319e8i 0.465881i
\(655\) 4.71997e7 0.167964
\(656\) 1.05459e7i 0.0373570i
\(657\) 1.69335e8i 0.597106i
\(658\) −4.13750e6 4.13750e6i −0.0145231 0.0145231i
\(659\) 3.74110e8i 1.30720i −0.756839 0.653601i \(-0.773257\pi\)
0.756839 0.653601i \(-0.226743\pi\)
\(660\) −1.46107e6 1.46107e6i −0.00508207 0.00508207i
\(661\) −2.47910e8 2.47910e8i −0.858400 0.858400i 0.132749 0.991150i \(-0.457619\pi\)
−0.991150 + 0.132749i \(0.957619\pi\)
\(662\) −3.90428e8 −1.34576
\(663\) −4.50845e8 −1.54699
\(664\) 4.59934e7 4.59934e7i 0.157105 0.157105i
\(665\) 432177.i 0.00146959i
\(666\) 7.72902e7 5.00706e7i 0.261639 0.169496i
\(667\) 2.43881e8 0.821865
\(668\) −1.27658e8 1.27658e8i −0.428272 0.428272i
\(669\) 2.41608e8i 0.806926i
\(670\) 3.59021e7i 0.119370i
\(671\) 1.71686e7 1.71686e7i 0.0568288 0.0568288i
\(672\) −687022. + 687022.i −0.00226393 + 0.00226393i
\(673\) 3.46494e8 1.13671 0.568356 0.822782i \(-0.307579\pi\)
0.568356 + 0.822782i \(0.307579\pi\)
\(674\) −7.72999e7 + 7.72999e7i −0.252464 + 0.252464i
\(675\) −3.27705e8 −1.06555
\(676\) 2.14940e7 0.0695788
\(677\) 3.89453e7i 0.125513i −0.998029 0.0627565i \(-0.980011\pi\)
0.998029 0.0627565i \(-0.0199892\pi\)
\(678\) −4.82623e7 −0.154853
\(679\) 286182. 286182.i 0.000914183 0.000914183i
\(680\) 1.59898e7 + 1.59898e7i 0.0508530 + 0.0508530i
\(681\) −1.85320e8 1.85320e8i −0.586789 0.586789i
\(682\) −8.47947e6 −0.0267310
\(683\) 2.57774e8 2.57774e8i 0.809054 0.809054i −0.175437 0.984491i \(-0.556134\pi\)
0.984491 + 0.175437i \(0.0561338\pi\)
\(684\) −2.88401e7 2.88401e7i −0.0901215 0.0901215i
\(685\) 2.46082e7 2.46082e7i 0.0765612 0.0765612i
\(686\) 7.81703e6 + 7.81703e6i 0.0242142 + 0.0242142i
\(687\) 8.70091e6i 0.0268346i
\(688\) 7.86703e7 7.86703e7i 0.241571 0.241571i
\(689\) −1.37424e8 + 1.37424e8i −0.420150 + 0.420150i
\(690\) −6.09861e6 6.09861e6i −0.0185645 0.0185645i
\(691\) 3.05557e7i 0.0926100i 0.998927 + 0.0463050i \(0.0147446\pi\)
−0.998927 + 0.0463050i \(0.985255\pi\)
\(692\) 2.60884e8 0.787279
\(693\) 651029.i 0.00195614i
\(694\) 9.42932e7i 0.282099i
\(695\) −3.57622e7 3.57622e7i −0.106529 0.106529i
\(696\) 1.54817e8i 0.459189i
\(697\) 6.93512e7 + 6.93512e7i 0.204812 + 0.204812i
\(698\) −2.44338e8 2.44338e8i −0.718496 0.718496i
\(699\) −3.92841e8 −1.15023
\(700\) −4.10820e6 −0.0119773
\(701\) 1.93439e8 1.93439e8i 0.561551 0.561551i −0.368197 0.929748i \(-0.620025\pi\)
0.929748 + 0.368197i \(0.120025\pi\)
\(702\) 2.81300e8i 0.813126i
\(703\) −1.09217e8 1.68590e8i −0.314358 0.485251i
\(704\) 7.98950e6 0.0228982
\(705\) 2.33152e7 + 2.33152e7i 0.0665383 + 0.0665383i
\(706\) 6.29830e7i 0.178982i
\(707\) 3.60694e6i 0.0102066i
\(708\) 9.31712e7 9.31712e7i 0.262532 0.262532i
\(709\) 3.90628e8 3.90628e8i 1.09604 1.09604i 0.101166 0.994870i \(-0.467743\pi\)
0.994870 0.101166i \(-0.0322573\pi\)
\(710\) −1.28306e7 −0.0358485
\(711\) 1.98221e8 1.98221e8i 0.551494 0.551494i
\(712\) 8.00881e7 0.221885
\(713\) −3.53938e7 −0.0976470
\(714\) 9.03590e6i 0.0248243i
\(715\) 7.49963e6 0.0205174
\(716\) 8.14043e6 8.14043e6i 0.0221773 0.0221773i
\(717\) 3.39795e8 + 3.39795e8i 0.921847 + 0.921847i
\(718\) −2.60845e8 2.60845e8i −0.704708 0.704708i
\(719\) −2.40488e8 −0.647003 −0.323501 0.946228i \(-0.604860\pi\)
−0.323501 + 0.946228i \(0.604860\pi\)
\(720\) −3.05262e6 + 3.05262e6i −0.00817852 + 0.00817852i
\(721\) −926571. 926571.i −0.00247214 0.00247214i
\(722\) 1.25276e8 1.25276e8i 0.332855 0.332855i
\(723\) −9.70159e7 9.70159e7i −0.256701 0.256701i
\(724\) 2.64797e7i 0.0697747i
\(725\) −4.62882e8 + 4.62882e8i −1.21466 + 1.21466i
\(726\) 1.38265e8 1.38265e8i 0.361328 0.361328i
\(727\) 4.28916e8 + 4.28916e8i 1.11627 + 1.11627i 0.992284 + 0.123986i \(0.0395677\pi\)
0.123986 + 0.992284i \(0.460432\pi\)
\(728\) 3.52645e6i 0.00913995i
\(729\) −3.74421e8 −0.966445
\(730\) 3.90959e7i 0.100499i
\(731\) 1.03469e9i 2.64886i
\(732\) 4.54921e7 + 4.54921e7i 0.115985 + 0.115985i
\(733\) 3.86581e8i 0.981586i 0.871276 + 0.490793i \(0.163293\pi\)
−0.871276 + 0.490793i \(0.836707\pi\)
\(734\) 3.77052e8 + 3.77052e8i 0.953483 + 0.953483i
\(735\) −2.20184e7 2.20184e7i −0.0554529 0.0554529i
\(736\) 3.33487e7 0.0836459
\(737\) 1.17969e8 0.294689
\(738\) −1.32398e7 + 1.32398e7i −0.0329392 + 0.0329392i
\(739\) 2.15335e8i 0.533556i 0.963758 + 0.266778i \(0.0859591\pi\)
−0.963758 + 0.266778i \(0.914041\pi\)
\(740\) −1.78447e7 + 1.15602e7i −0.0440365 + 0.0285280i
\(741\) −1.87743e8 −0.461434
\(742\) 2.75427e6 + 2.75427e6i 0.00674209 + 0.00674209i
\(743\) 5.62436e8i 1.37122i 0.727970 + 0.685609i \(0.240464\pi\)
−0.727970 + 0.685609i \(0.759536\pi\)
\(744\) 2.24682e7i 0.0545569i
\(745\) 3.51492e7 3.51492e7i 0.0850053 0.0850053i
\(746\) −1.56830e8 + 1.56830e8i −0.377756 + 0.377756i
\(747\) 1.15485e8 0.277053
\(748\) 5.25400e7 5.25400e7i 0.125541 0.125541i
\(749\) 1.82601e6 0.00434569
\(750\) 4.65580e7 0.110360
\(751\) 1.10982e8i 0.262020i 0.991381 + 0.131010i \(0.0418219\pi\)
−0.991381 + 0.131010i \(0.958178\pi\)
\(752\) −1.27493e8 −0.299801
\(753\) 1.32813e8 1.32813e8i 0.311068 0.311068i
\(754\) −3.97335e8 3.97335e8i −0.926921 0.926921i
\(755\) −3.59025e7 3.59025e7i −0.0834226 0.0834226i
\(756\) −5.63785e6 −0.0130481
\(757\) 2.08014e8 2.08014e8i 0.479518 0.479518i −0.425459 0.904978i \(-0.639887\pi\)
0.904978 + 0.425459i \(0.139887\pi\)
\(758\) −1.47232e8 1.47232e8i −0.338061 0.338061i
\(759\) −2.00391e7 + 2.00391e7i −0.0458303 + 0.0458303i
\(760\) 6.65856e6 + 6.65856e6i 0.0151684 + 0.0151684i
\(761\) 2.96475e8i 0.672719i 0.941734 + 0.336359i \(0.109196\pi\)
−0.941734 + 0.336359i \(0.890804\pi\)
\(762\) −1.39360e8 + 1.39360e8i −0.314973 + 0.314973i
\(763\) −6.70331e6 + 6.70331e6i −0.0150909 + 0.0150909i
\(764\) −1.63060e8 1.63060e8i −0.365651 0.365651i
\(765\) 4.01488e7i 0.0896785i
\(766\) 1.96299e8 0.436749
\(767\) 4.78244e8i 1.05990i
\(768\) 2.11699e7i 0.0467343i
\(769\) 4.29336e8 + 4.29336e8i 0.944101 + 0.944101i 0.998518 0.0544175i \(-0.0173302\pi\)
−0.0544175 + 0.998518i \(0.517330\pi\)
\(770\) 150309.i 0.000329239i
\(771\) 1.73406e8 + 1.73406e8i 0.378357 + 0.378357i
\(772\) 6.38840e7 + 6.38840e7i 0.138848 + 0.138848i
\(773\) −3.70319e8 −0.801746 −0.400873 0.916134i \(-0.631293\pi\)
−0.400873 + 0.916134i \(0.631293\pi\)
\(774\) 1.97533e8 0.426007
\(775\) 6.71769e7 6.71769e7i 0.144316 0.144316i
\(776\) 8.81843e6i 0.0188715i
\(777\) −8.30840e6 1.77568e6i −0.0177115 0.00378530i
\(778\) 5.05765e8 1.07401
\(779\) 2.88796e7 + 2.88796e7i 0.0610911 + 0.0610911i
\(780\) 1.98719e7i 0.0418751i
\(781\) 4.21592e7i 0.0884992i
\(782\) 2.19305e8 2.19305e8i 0.458594 0.458594i
\(783\) −6.35231e8 + 6.35231e8i −1.32326 + 1.32326i
\(784\) 1.20402e8 0.249853
\(785\) 4.68677e7 4.68677e7i 0.0968869 0.0968869i
\(786\) 4.10947e8 0.846288
\(787\) −3.63995e8 −0.746744 −0.373372 0.927682i \(-0.621798\pi\)
−0.373372 + 0.927682i \(0.621798\pi\)
\(788\) 5.18585e7i 0.105984i
\(789\) 1.58650e8 0.323006
\(790\) −4.57650e7 + 4.57650e7i −0.0928223 + 0.0928223i
\(791\) −2.48250e6 2.48250e6i −0.00501603 0.00501603i
\(792\) 1.00304e7 + 1.00304e7i 0.0201903 + 0.0201903i
\(793\) −2.33509e8 −0.468256
\(794\) 4.34488e7 4.34488e7i 0.0867994 0.0867994i
\(795\) −1.55206e7 1.55206e7i −0.0308892 0.0308892i
\(796\) 1.23485e8 1.23485e8i 0.244837 0.244837i
\(797\) −4.55860e8 4.55860e8i −0.900444 0.900444i 0.0950306 0.995474i \(-0.469705\pi\)
−0.995474 + 0.0950306i \(0.969705\pi\)
\(798\) 3.76278e6i 0.00740457i
\(799\) −8.38411e8 + 8.38411e8i −1.64368 + 1.64368i
\(800\) −6.32952e7 + 6.32952e7i −0.123623 + 0.123623i
\(801\) 1.00547e8 + 1.00547e8i 0.195645 + 0.195645i
\(802\) 3.62094e8i 0.701937i
\(803\) −1.28463e8 −0.248103
\(804\) 3.12584e8i 0.601449i
\(805\) 627397.i 0.00120269i
\(806\) 5.76642e7 + 5.76642e7i 0.110129 + 0.110129i
\(807\) 3.25778e8i 0.619871i
\(808\) 5.55722e7 + 5.55722e7i 0.105347 + 0.105347i
\(809\) 4.76133e8 + 4.76133e8i 0.899255 + 0.899255i 0.995370 0.0961157i \(-0.0306419\pi\)
−0.0961157 + 0.995370i \(0.530642\pi\)
\(810\) 1.43842e7 0.0270665
\(811\) 2.09397e8 0.392561 0.196281 0.980548i \(-0.437114\pi\)
0.196281 + 0.980548i \(0.437114\pi\)
\(812\) −7.96344e6 + 7.96344e6i −0.0148742 + 0.0148742i
\(813\) 3.59206e8i 0.668454i
\(814\) 3.79851e7 + 5.86347e7i 0.0704271 + 0.108713i
\(815\) −5.59588e7 −0.103370
\(816\) 1.39216e8 + 1.39216e8i 0.256224 + 0.256224i
\(817\) 4.30872e8i 0.790100i
\(818\) 1.31203e8i 0.239709i
\(819\) 4.42728e6 4.42728e6i 0.00805908 0.00805908i
\(820\) 3.05679e6 3.05679e6i 0.00554402 0.00554402i
\(821\) 1.68790e8 0.305013 0.152506 0.988302i \(-0.451266\pi\)
0.152506 + 0.988302i \(0.451266\pi\)
\(822\) 2.14253e8 2.14253e8i 0.385755 0.385755i
\(823\) −4.01876e8 −0.720928 −0.360464 0.932773i \(-0.617382\pi\)
−0.360464 + 0.932773i \(0.617382\pi\)
\(824\) −2.85514e7 −0.0510324
\(825\) 7.60677e7i 0.135469i
\(826\) 9.58503e6 0.0170080
\(827\) 2.23264e8 2.23264e8i 0.394731 0.394731i −0.481639 0.876370i \(-0.659958\pi\)
0.876370 + 0.481639i \(0.159958\pi\)
\(828\) 4.18675e7 + 4.18675e7i 0.0737542 + 0.0737542i
\(829\) 4.07300e8 + 4.07300e8i 0.714909 + 0.714909i 0.967558 0.252649i \(-0.0813018\pi\)
−0.252649 + 0.967558i \(0.581302\pi\)
\(830\) −2.66630e7 −0.0466309
\(831\) 2.64322e8 2.64322e8i 0.460606 0.460606i
\(832\) −5.43322e7 5.43322e7i −0.0943381 0.0943381i
\(833\) 7.91779e8 7.91779e8i 1.36984 1.36984i
\(834\) −3.11366e8 3.11366e8i −0.536751 0.536751i
\(835\) 7.40052e7i 0.127117i
\(836\) 2.18790e7 2.18790e7i 0.0374463 0.0374463i
\(837\) 9.21895e7 9.21895e7i 0.157219 0.157219i
\(838\) −3.27150e8 3.27150e8i −0.555924 0.555924i
\(839\) 2.92272e7i 0.0494881i −0.999694 0.0247441i \(-0.992123\pi\)
0.999694 0.0247441i \(-0.00787708\pi\)
\(840\) 398276. 0.000671964
\(841\) 1.19970e9i 2.01690i
\(842\) 3.49409e8i 0.585326i
\(843\) −2.19681e8 2.19681e8i −0.366699 0.366699i
\(844\) 1.91447e8i 0.318436i
\(845\) −6.23017e6 6.23017e6i −0.0103260 0.0103260i
\(846\) −1.60061e8 1.60061e8i −0.264347 0.264347i
\(847\) 1.42241e7 0.0234085
\(848\) 8.48702e7 0.139177
\(849\) 1.34927e8 1.34927e8i 0.220484 0.220484i
\(850\) 8.32476e8i 1.35555i
\(851\) 1.58552e8 + 2.44745e8i 0.257266 + 0.397123i
\(852\) −1.11710e8 −0.180623
\(853\) −4.61668e8 4.61668e8i −0.743845 0.743845i 0.229471 0.973316i \(-0.426300\pi\)
−0.973316 + 0.229471i \(0.926300\pi\)
\(854\) 4.68002e6i 0.00751405i
\(855\) 1.67190e7i 0.0267492i
\(856\) 2.81334e7 2.81334e7i 0.0448540 0.0448540i
\(857\) −2.21175e8 + 2.21175e8i −0.351393 + 0.351393i −0.860628 0.509235i \(-0.829929\pi\)
0.509235 + 0.860628i \(0.329929\pi\)
\(858\) 6.52960e7 0.103377
\(859\) 1.54957e8 1.54957e8i 0.244474 0.244474i −0.574224 0.818698i \(-0.694696\pi\)
0.818698 + 0.574224i \(0.194696\pi\)
\(860\) −4.56062e7 −0.0717015
\(861\) 1.72740e6 0.00270635
\(862\) 3.25027e8i 0.507454i
\(863\) −1.02709e9 −1.59800 −0.798999 0.601332i \(-0.794637\pi\)
−0.798999 + 0.601332i \(0.794637\pi\)
\(864\) −8.68625e7 + 8.68625e7i −0.134676 + 0.134676i
\(865\) −7.56188e7 7.56188e7i −0.116837 0.116837i
\(866\) 5.50741e8 + 5.50741e8i 0.847995 + 0.847995i
\(867\) 1.34369e9 2.06178
\(868\) 1.15571e6 1.15571e6i 0.00176722 0.00176722i
\(869\) 1.50377e8 + 1.50377e8i 0.229151 + 0.229151i
\(870\) 4.48748e7 4.48748e7i 0.0681466 0.0681466i
\(871\) −8.02240e8 8.02240e8i −1.21409 1.21409i
\(872\) 2.06556e8i 0.311522i
\(873\) 1.10711e7 1.10711e7i 0.0166398 0.0166398i
\(874\) 9.13242e7 9.13242e7i 0.136789 0.136789i
\(875\) 2.39484e6 + 2.39484e6i 0.00357480 + 0.00357480i
\(876\) 3.40391e8i 0.506367i
\(877\) −1.81172e8 −0.268591 −0.134296 0.990941i \(-0.542877\pi\)
−0.134296 + 0.990941i \(0.542877\pi\)
\(878\) 6.55601e7i 0.0968626i
\(879\) 1.91900e8i 0.282558i
\(880\) −2.31581e6 2.31581e6i −0.00339824 0.00339824i
\(881\) 8.94016e8i 1.30743i 0.756742 + 0.653714i \(0.226790\pi\)
−0.756742 + 0.653714i \(0.773210\pi\)
\(882\) 1.51158e8 + 1.51158e8i 0.220306 + 0.220306i
\(883\) −9.00390e8 9.00390e8i −1.30782 1.30782i −0.922984 0.384838i \(-0.874257\pi\)
−0.384838 0.922984i \(-0.625743\pi\)
\(884\) −7.14591e8 −1.03443
\(885\) −5.40126e7 −0.0779229
\(886\) 4.97924e8 4.97924e8i 0.715915 0.715915i
\(887\) 2.33052e8i 0.333950i −0.985961 0.166975i \(-0.946600\pi\)
0.985961 0.166975i \(-0.0534000\pi\)
\(888\) −1.55366e8 + 1.00650e8i −0.221879 + 0.143739i
\(889\) −1.43367e7 −0.0204054
\(890\) −2.32140e7 2.32140e7i −0.0329292 0.0329292i
\(891\) 4.72644e7i 0.0668191i
\(892\) 3.82950e8i 0.539570i
\(893\) −3.49135e8 + 3.49135e8i −0.490275 + 0.490275i
\(894\) 3.06028e8 3.06028e8i 0.428301 0.428301i
\(895\) −4.71911e6 −0.00658251
\(896\) −1.08893e6 + 1.08893e6i −0.00151383 + 0.00151383i
\(897\) 2.72549e8 0.377631
\(898\) 1.19132e8 0.164513
\(899\) 2.60435e8i 0.358442i
\(900\) −1.58928e8 −0.218008
\(901\) 5.58118e8 5.58118e8i 0.763048 0.763048i
\(902\) −1.00441e7 1.00441e7i −0.0136865 0.0136865i
\(903\) −1.28861e7 1.28861e7i −0.0175008 0.0175008i
\(904\) −7.64959e7 −0.103546
\(905\) 7.67532e6 7.67532e6i 0.0103550 0.0103550i
\(906\) −3.12587e8 3.12587e8i −0.420327 0.420327i
\(907\) 8.26420e8 8.26420e8i 1.10759 1.10759i 0.114124 0.993467i \(-0.463594\pi\)
0.993467 0.114124i \(-0.0364061\pi\)
\(908\) −2.93734e8 2.93734e8i −0.392370 0.392370i
\(909\) 1.39536e8i 0.185778i
\(910\) −1.02217e6 + 1.02217e6i −0.00135643 + 0.00135643i
\(911\) −4.57595e8 + 4.57595e8i −0.605237 + 0.605237i −0.941698 0.336460i \(-0.890770\pi\)
0.336460 + 0.941698i \(0.390770\pi\)
\(912\) 5.79732e7 + 5.79732e7i 0.0764263 + 0.0764263i
\(913\) 8.76103e7i 0.115118i
\(914\) −5.11042e8 −0.669295
\(915\) 2.63724e7i 0.0344259i
\(916\) 1.37910e7i 0.0179436i
\(917\) 2.11382e7 + 2.11382e7i 0.0274132 + 0.0274132i
\(918\) 1.14244e9i 1.47674i
\(919\) −5.96266e8 5.96266e8i −0.768233 0.768233i 0.209562 0.977795i \(-0.432796\pi\)
−0.977795 + 0.209562i \(0.932796\pi\)
\(920\) −9.66632e6 9.66632e6i −0.0124136 0.0124136i
\(921\) 7.67967e8 0.983022
\(922\) −1.01393e9 −1.29365
\(923\) 2.86701e8 2.86701e8i 0.364607 0.364607i
\(924\) 1.30867e6i 0.00165888i
\(925\) −7.65451e8 1.63593e8i −0.967146 0.206699i
\(926\) −1.53448e8 −0.193254
\(927\) −3.58449e7 3.58449e7i −0.0449974 0.0449974i
\(928\) 2.45386e8i 0.307048i
\(929\) 1.45466e7i 0.0181432i 0.999959 + 0.00907159i \(0.00288762\pi\)
−0.999959 + 0.00907159i \(0.997112\pi\)
\(930\) −6.51256e6 + 6.51256e6i −0.00809660 + 0.00809660i
\(931\) 3.29717e8 3.29717e8i 0.408594 0.408594i
\(932\) −6.22655e8 −0.769130
\(933\) 7.89841e8 7.89841e8i 0.972511 0.972511i
\(934\) −4.25464e8 −0.522182
\(935\) −3.04581e7 −0.0372622
\(936\) 1.36423e8i 0.166364i
\(937\) −3.48928e7 −0.0424147 −0.0212074 0.999775i \(-0.506751\pi\)
−0.0212074 + 0.999775i \(0.506751\pi\)
\(938\) −1.60786e7 + 1.60786e7i −0.0194823 + 0.0194823i
\(939\) −4.30650e8 4.30650e8i −0.520148 0.520148i
\(940\) 3.69547e7 + 3.69547e7i 0.0444924 + 0.0444924i
\(941\) 1.25247e9 1.50313 0.751567 0.659657i \(-0.229298\pi\)
0.751567 + 0.659657i \(0.229298\pi\)
\(942\) 4.08057e8 4.08057e8i 0.488167 0.488167i
\(943\) −4.19248e7 4.19248e7i −0.0499961 0.0499961i
\(944\) 1.47677e8 1.47677e8i 0.175548 0.175548i
\(945\) 1.63417e6 + 1.63417e6i 0.00193643 + 0.00193643i
\(946\) 1.49855e8i 0.177010i
\(947\) −5.62450e8 + 5.62450e8i −0.662269 + 0.662269i −0.955914 0.293646i \(-0.905131\pi\)
0.293646 + 0.955914i \(0.405131\pi\)
\(948\) −3.98456e8 + 3.98456e8i −0.467687 + 0.467687i
\(949\) 8.73605e8 + 8.73605e8i 1.02215 + 1.02215i
\(950\) 3.46664e8i 0.404332i
\(951\) −2.26090e8 −0.262870
\(952\) 1.43219e7i 0.0165993i
\(953\) 8.73569e8i 1.00930i −0.863325 0.504648i \(-0.831622\pi\)
0.863325 0.504648i \(-0.168378\pi\)
\(954\) 1.06550e8 + 1.06550e8i 0.122718 + 0.122718i
\(955\) 9.45278e7i 0.108530i
\(956\) 5.38576e8 + 5.38576e8i 0.616415 + 0.616415i
\(957\) −1.47451e8 1.47451e8i −0.168234 0.168234i
\(958\) −2.86115e8 −0.325420
\(959\) 2.20414e7 0.0249910
\(960\) 6.13624e6 6.13624e6i 0.00693568 0.00693568i
\(961\) 8.49707e8i 0.957413i
\(962\) 1.40427e8 6.57058e8i 0.157734 0.738037i
\(963\) 7.06402e7 0.0790994
\(964\) −1.53771e8 1.53771e8i −0.171649 0.171649i
\(965\) 3.70344e7i 0.0412119i
\(966\) 5.46247e6i 0.00605979i
\(967\) 9.51226e8 9.51226e8i 1.05197 1.05197i 0.0533996 0.998573i \(-0.482994\pi\)
0.998573 0.0533996i \(-0.0170057\pi\)
\(968\) 2.19150e8 2.19150e8i 0.241611 0.241611i
\(969\) 7.62479e8 0.838024
\(970\) −2.55608e6 + 2.55608e6i −0.00280065 + 0.00280065i
\(971\) 7.81268e8 0.853380 0.426690 0.904398i \(-0.359680\pi\)
0.426690 + 0.904398i \(0.359680\pi\)
\(972\) −3.69472e8 −0.402330
\(973\) 3.20319e7i 0.0347731i
\(974\) 8.48283e8 0.918044
\(975\) −5.17294e8 + 5.17294e8i −0.558115 + 0.558115i
\(976\) 7.21051e7 + 7.21051e7i 0.0775563 + 0.0775563i
\(977\) −1.11773e9 1.11773e9i −1.19854 1.19854i −0.974603 0.223939i \(-0.928109\pi\)
−0.223939 0.974603i \(-0.571891\pi\)
\(978\) −4.87209e8 −0.520833
\(979\) −7.62777e7 + 7.62777e7i −0.0812923 + 0.0812923i
\(980\) −3.48993e7 3.48993e7i −0.0370799 0.0370799i
\(981\) −2.59321e8 + 2.59321e8i −0.274682 + 0.274682i
\(982\) −4.64288e8 4.64288e8i −0.490290 0.490290i
\(983\) 5.46258e8i 0.575091i 0.957767 + 0.287546i \(0.0928393\pi\)
−0.957767 + 0.287546i \(0.907161\pi\)
\(984\) 2.66142e7 2.66142e7i 0.0279336 0.0279336i
\(985\) 1.50315e7 1.50315e7i 0.0157288 0.0157288i
\(986\) 1.61369e9 + 1.61369e9i 1.68341 + 1.68341i
\(987\) 2.08832e7i 0.0217193i
\(988\) −2.97574e8 −0.308549
\(989\) 6.25503e8i 0.646607i
\(990\) 5.81476e6i 0.00599275i
\(991\) 7.28375e8 + 7.28375e8i 0.748400 + 0.748400i 0.974179 0.225778i \(-0.0724925\pi\)
−0.225778 + 0.974179i \(0.572492\pi\)
\(992\) 3.56122e7i 0.0364808i
\(993\) 9.85305e8 + 9.85305e8i 1.00629 + 1.00629i
\(994\) −5.74611e6 5.74611e6i −0.00585079 0.00585079i
\(995\) −7.15861e7 −0.0726707
\(996\) −2.32143e8 −0.234951
\(997\) 4.98472e8 4.98472e8i 0.502985 0.502985i −0.409379 0.912364i \(-0.634255\pi\)
0.912364 + 0.409379i \(0.134255\pi\)
\(998\) 4.75999e8i 0.478867i
\(999\) −1.05046e9 2.24505e8i −1.05362 0.225179i
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 74.7.d.b.31.7 20
37.6 odd 4 inner 74.7.d.b.43.4 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
74.7.d.b.31.7 20 1.1 even 1 trivial
74.7.d.b.43.4 yes 20 37.6 odd 4 inner