Properties

Label 74.7.d.a.31.3
Level $74$
Weight $7$
Character 74.31
Analytic conductor $17.024$
Analytic rank $0$
Dimension $18$
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: \(18\)
Relative dimension: \(9\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} + 8470 x^{16} + 28007049 x^{14} + 45282701078 x^{12} + 36580026955844 x^{10} + \cdots + 65\!\cdots\!44 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 31.3
Root \(-14.7444i\) of defining polynomial
Character \(\chi\) \(=\) 74.31
Dual form 74.7.d.a.43.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.00000 + 4.00000i) q^{2} -10.7444i q^{3} +32.0000i q^{4} +(60.1111 - 60.1111i) q^{5} +(42.9776 - 42.9776i) q^{6} -174.087 q^{7} +(-128.000 + 128.000i) q^{8} +613.558 q^{9} +O(q^{10})\) \(q+(4.00000 + 4.00000i) q^{2} -10.7444i q^{3} +32.0000i q^{4} +(60.1111 - 60.1111i) q^{5} +(42.9776 - 42.9776i) q^{6} -174.087 q^{7} +(-128.000 + 128.000i) q^{8} +613.558 q^{9} +480.889 q^{10} -1127.73i q^{11} +343.821 q^{12} +(739.616 - 739.616i) q^{13} +(-696.346 - 696.346i) q^{14} +(-645.857 - 645.857i) q^{15} -1024.00 q^{16} +(1313.72 - 1313.72i) q^{17} +(2454.23 + 2454.23i) q^{18} +(4161.36 - 4161.36i) q^{19} +(1923.55 + 1923.55i) q^{20} +1870.45i q^{21} +(4510.91 - 4510.91i) q^{22} +(14825.2 - 14825.2i) q^{23} +(1375.28 + 1375.28i) q^{24} +8398.31i q^{25} +5916.92 q^{26} -14425.0i q^{27} -5570.77i q^{28} +(-2018.87 - 2018.87i) q^{29} -5166.86i q^{30} +(10796.7 + 10796.7i) q^{31} +(-4096.00 - 4096.00i) q^{32} -12116.7 q^{33} +10509.8 q^{34} +(-10464.5 + 10464.5i) q^{35} +19633.9i q^{36} +(44063.7 + 24982.3i) q^{37} +33290.8 q^{38} +(-7946.72 - 7946.72i) q^{39} +15388.4i q^{40} +7586.85i q^{41} +(-7481.82 + 7481.82i) q^{42} +(33218.5 - 33218.5i) q^{43} +36087.3 q^{44} +(36881.6 - 36881.6i) q^{45} +118602. q^{46} -33369.3 q^{47} +11002.3i q^{48} -87342.9 q^{49} +(-33593.3 + 33593.3i) q^{50} +(-14115.2 - 14115.2i) q^{51} +(23667.7 + 23667.7i) q^{52} -248937. q^{53} +(57699.9 - 57699.9i) q^{54} +(-67788.9 - 67788.9i) q^{55} +(22283.1 - 22283.1i) q^{56} +(-44711.2 - 44711.2i) q^{57} -16150.9i q^{58} +(14581.0 - 14581.0i) q^{59} +(20667.4 - 20667.4i) q^{60} +(-55383.0 - 55383.0i) q^{61} +86373.4i q^{62} -106812. q^{63} -32768.0i q^{64} -88918.2i q^{65} +(-48467.0 - 48467.0i) q^{66} +86551.8i q^{67} +(42039.2 + 42039.2i) q^{68} +(-159288. - 159288. i) q^{69} -83716.3 q^{70} -281661. q^{71} +(-78535.4 + 78535.4i) q^{72} +645595. i q^{73} +(76325.6 + 276184. i) q^{74} +90234.8 q^{75} +(133163. + 133163. i) q^{76} +196322. i q^{77} -63573.8i q^{78} +(-194161. + 194161. i) q^{79} +(-61553.8 + 61553.8i) q^{80} +292296. q^{81} +(-30347.4 + 30347.4i) q^{82} -943610. q^{83} -59854.5 q^{84} -157939. i q^{85} +265748. q^{86} +(-21691.5 + 21691.5i) q^{87} +(144349. + 144349. i) q^{88} +(-70599.5 - 70599.5i) q^{89} +295053. q^{90} +(-128757. + 128757. i) q^{91} +(474406. + 474406. i) q^{92} +(116004. - 116004. i) q^{93} +(-133477. - 133477. i) q^{94} -500287. i q^{95} +(-44009.0 + 44009.0i) q^{96} +(-55379.7 + 55379.7i) q^{97} +(-349371. - 349371. i) q^{98} -691926. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 72 q^{2} + 294 q^{5} - 256 q^{6} - 104 q^{7} - 2304 q^{8} - 4042 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 72 q^{2} + 294 q^{5} - 256 q^{6} - 104 q^{7} - 2304 q^{8} - 4042 q^{9} + 2352 q^{10} - 2048 q^{12} - 6766 q^{13} - 416 q^{14} - 2136 q^{15} - 18432 q^{16} - 9134 q^{17} - 16168 q^{18} + 7578 q^{19} + 9408 q^{20} + 8928 q^{22} - 50578 q^{23} - 8192 q^{24} - 54128 q^{26} - 42950 q^{29} - 17358 q^{31} - 73728 q^{32} - 11056 q^{33} - 73072 q^{34} + 62152 q^{35} - 238242 q^{37} + 60624 q^{38} + 31572 q^{39} + 229024 q^{42} - 65470 q^{43} + 71424 q^{44} - 482358 q^{45} - 404624 q^{46} + 232192 q^{47} + 791686 q^{49} + 93752 q^{50} - 386848 q^{51} - 216512 q^{52} + 49972 q^{53} - 144560 q^{54} + 160168 q^{55} + 13312 q^{56} + 488476 q^{57} - 181570 q^{59} + 68352 q^{60} + 508802 q^{61} + 404788 q^{63} - 44224 q^{66} - 292288 q^{68} + 604532 q^{69} + 497216 q^{70} - 202632 q^{71} + 517376 q^{72} - 1191224 q^{74} + 2476628 q^{75} + 242496 q^{76} + 1752858 q^{79} - 301056 q^{80} + 2760658 q^{81} - 145808 q^{82} + 2371616 q^{83} + 1832192 q^{84} - 523760 q^{86} - 4188080 q^{87} + 285696 q^{88} + 1148346 q^{89} - 3858864 q^{90} + 433120 q^{91} - 1618496 q^{92} + 1589664 q^{93} + 928768 q^{94} + 262144 q^{96} - 1670270 q^{97} + 3166744 q^{98}+O(q^{100}) \) 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
\(3\) 10.7444i 0.397941i −0.980006 0.198970i \(-0.936240\pi\)
0.980006 0.198970i \(-0.0637597\pi\)
\(4\) 32.0000i 0.500000i
\(5\) 60.1111 60.1111i 0.480889 0.480889i −0.424527 0.905415i \(-0.639559\pi\)
0.905415 + 0.424527i \(0.139559\pi\)
\(6\) 42.9776 42.9776i 0.198970 0.198970i
\(7\) −174.087 −0.507541 −0.253770 0.967264i \(-0.581671\pi\)
−0.253770 + 0.967264i \(0.581671\pi\)
\(8\) −128.000 + 128.000i −0.250000 + 0.250000i
\(9\) 613.558 0.841643
\(10\) 480.889 0.480889
\(11\) 1127.73i 0.847278i −0.905831 0.423639i \(-0.860753\pi\)
0.905831 0.423639i \(-0.139247\pi\)
\(12\) 343.821 0.198970
\(13\) 739.616 739.616i 0.336648 0.336648i −0.518456 0.855104i \(-0.673493\pi\)
0.855104 + 0.518456i \(0.173493\pi\)
\(14\) −696.346 696.346i −0.253770 0.253770i
\(15\) −645.857 645.857i −0.191365 0.191365i
\(16\) −1024.00 −0.250000
\(17\) 1313.72 1313.72i 0.267397 0.267397i −0.560653 0.828051i \(-0.689450\pi\)
0.828051 + 0.560653i \(0.189450\pi\)
\(18\) 2454.23 + 2454.23i 0.420822 + 0.420822i
\(19\) 4161.36 4161.36i 0.606700 0.606700i −0.335382 0.942082i \(-0.608865\pi\)
0.942082 + 0.335382i \(0.108865\pi\)
\(20\) 1923.55 + 1923.55i 0.240444 + 0.240444i
\(21\) 1870.45i 0.201971i
\(22\) 4510.91 4510.91i 0.423639 0.423639i
\(23\) 14825.2 14825.2i 1.21848 1.21848i 0.250309 0.968166i \(-0.419468\pi\)
0.968166 0.250309i \(-0.0805324\pi\)
\(24\) 1375.28 + 1375.28i 0.0994851 + 0.0994851i
\(25\) 8398.31i 0.537492i
\(26\) 5916.92 0.336648
\(27\) 14425.0i 0.732865i
\(28\) 5570.77i 0.253770i
\(29\) −2018.87 2018.87i −0.0827777 0.0827777i 0.664506 0.747283i \(-0.268642\pi\)
−0.747283 + 0.664506i \(0.768642\pi\)
\(30\) 5166.86i 0.191365i
\(31\) 10796.7 + 10796.7i 0.362414 + 0.362414i 0.864701 0.502287i \(-0.167508\pi\)
−0.502287 + 0.864701i \(0.667508\pi\)
\(32\) −4096.00 4096.00i −0.125000 0.125000i
\(33\) −12116.7 −0.337166
\(34\) 10509.8 0.267397
\(35\) −10464.5 + 10464.5i −0.244071 + 0.244071i
\(36\) 19633.9i 0.420822i
\(37\) 44063.7 + 24982.3i 0.869913 + 0.493205i
\(38\) 33290.8 0.606700
\(39\) −7946.72 7946.72i −0.133966 0.133966i
\(40\) 15388.4i 0.240444i
\(41\) 7586.85i 0.110080i 0.998484 + 0.0550402i \(0.0175287\pi\)
−0.998484 + 0.0550402i \(0.982471\pi\)
\(42\) −7481.82 + 7481.82i −0.100986 + 0.100986i
\(43\) 33218.5 33218.5i 0.417806 0.417806i −0.466641 0.884447i \(-0.654536\pi\)
0.884447 + 0.466641i \(0.154536\pi\)
\(44\) 36087.3 0.423639
\(45\) 36881.6 36881.6i 0.404737 0.404737i
\(46\) 118602. 1.21848
\(47\) −33369.3 −0.321406 −0.160703 0.987003i \(-0.551376\pi\)
−0.160703 + 0.987003i \(0.551376\pi\)
\(48\) 11002.3i 0.0994851i
\(49\) −87342.9 −0.742402
\(50\) −33593.3 + 33593.3i −0.268746 + 0.268746i
\(51\) −14115.2 14115.2i −0.106408 0.106408i
\(52\) 23667.7 + 23667.7i 0.168324 + 0.168324i
\(53\) −248937. −1.67210 −0.836048 0.548656i \(-0.815140\pi\)
−0.836048 + 0.548656i \(0.815140\pi\)
\(54\) 57699.9 57699.9i 0.366432 0.366432i
\(55\) −67788.9 67788.9i −0.407446 0.407446i
\(56\) 22283.1 22283.1i 0.126885 0.126885i
\(57\) −44711.2 44711.2i −0.241431 0.241431i
\(58\) 16150.9i 0.0827777i
\(59\) 14581.0 14581.0i 0.0709957 0.0709957i −0.670717 0.741713i \(-0.734014\pi\)
0.741713 + 0.670717i \(0.234014\pi\)
\(60\) 20667.4 20667.4i 0.0956825 0.0956825i
\(61\) −55383.0 55383.0i −0.243998 0.243998i 0.574504 0.818502i \(-0.305195\pi\)
−0.818502 + 0.574504i \(0.805195\pi\)
\(62\) 86373.4i 0.362414i
\(63\) −106812. −0.427168
\(64\) 32768.0i 0.125000i
\(65\) 88918.2i 0.323780i
\(66\) −48467.0 48467.0i −0.168583 0.168583i
\(67\) 86551.8i 0.287774i 0.989594 + 0.143887i \(0.0459602\pi\)
−0.989594 + 0.143887i \(0.954040\pi\)
\(68\) 42039.2 + 42039.2i 0.133699 + 0.133699i
\(69\) −159288. 159288.i −0.484881 0.484881i
\(70\) −83716.3 −0.244071
\(71\) −281661. −0.786959 −0.393479 0.919333i \(-0.628729\pi\)
−0.393479 + 0.919333i \(0.628729\pi\)
\(72\) −78535.4 + 78535.4i −0.210411 + 0.210411i
\(73\) 645595.i 1.65955i 0.558095 + 0.829777i \(0.311532\pi\)
−0.558095 + 0.829777i \(0.688468\pi\)
\(74\) 76325.6 + 276184.i 0.188354 + 0.681559i
\(75\) 90234.8 0.213890
\(76\) 133163. + 133163.i 0.303350 + 0.303350i
\(77\) 196322.i 0.430028i
\(78\) 63573.8i 0.133966i
\(79\) −194161. + 194161.i −0.393804 + 0.393804i −0.876041 0.482237i \(-0.839825\pi\)
0.482237 + 0.876041i \(0.339825\pi\)
\(80\) −61553.8 + 61553.8i −0.120222 + 0.120222i
\(81\) 292296. 0.550007
\(82\) −30347.4 + 30347.4i −0.0550402 + 0.0550402i
\(83\) −943610. −1.65028 −0.825141 0.564927i \(-0.808904\pi\)
−0.825141 + 0.564927i \(0.808904\pi\)
\(84\) −59854.5 −0.100986
\(85\) 157939.i 0.257177i
\(86\) 265748. 0.417806
\(87\) −21691.5 + 21691.5i −0.0329406 + 0.0329406i
\(88\) 144349. + 144349.i 0.211819 + 0.211819i
\(89\) −70599.5 70599.5i −0.100145 0.100145i 0.655259 0.755404i \(-0.272560\pi\)
−0.755404 + 0.655259i \(0.772560\pi\)
\(90\) 295053. 0.404737
\(91\) −128757. + 128757.i −0.170863 + 0.170863i
\(92\) 474406. + 474406.i 0.609238 + 0.609238i
\(93\) 116004. 116004.i 0.144219 0.144219i
\(94\) −133477. 133477.i −0.160703 0.160703i
\(95\) 500287.i 0.583510i
\(96\) −44009.0 + 44009.0i −0.0497426 + 0.0497426i
\(97\) −55379.7 + 55379.7i −0.0606786 + 0.0606786i −0.736795 0.676116i \(-0.763662\pi\)
0.676116 + 0.736795i \(0.263662\pi\)
\(98\) −349371. 349371.i −0.371201 0.371201i
\(99\) 691926.i 0.713106i
\(100\) −268746. −0.268746
\(101\) 462045.i 0.448456i −0.974537 0.224228i \(-0.928014\pi\)
0.974537 0.224228i \(-0.0719860\pi\)
\(102\) 112921.i 0.106408i
\(103\) 410647. + 410647.i 0.375801 + 0.375801i 0.869585 0.493784i \(-0.164387\pi\)
−0.493784 + 0.869585i \(0.664387\pi\)
\(104\) 189342.i 0.168324i
\(105\) 112435. + 112435.i 0.0971256 + 0.0971256i
\(106\) −995747. 995747.i −0.836048 0.836048i
\(107\) 1.87384e6 1.52961 0.764807 0.644259i \(-0.222834\pi\)
0.764807 + 0.644259i \(0.222834\pi\)
\(108\) 461599. 0.366432
\(109\) 319902. 319902.i 0.247023 0.247023i −0.572725 0.819748i \(-0.694114\pi\)
0.819748 + 0.572725i \(0.194114\pi\)
\(110\) 542311.i 0.407446i
\(111\) 268420. 473438.i 0.196266 0.346174i
\(112\) 178265. 0.126885
\(113\) 1.63134e6 + 1.63134e6i 1.13060 + 1.13060i 0.990078 + 0.140519i \(0.0448772\pi\)
0.140519 + 0.990078i \(0.455123\pi\)
\(114\) 357690.i 0.241431i
\(115\) 1.78232e6i 1.17190i
\(116\) 64603.7 64603.7i 0.0413889 0.0413889i
\(117\) 453797. 453797.i 0.283337 0.283337i
\(118\) 116648. 0.0709957
\(119\) −228702. + 228702.i −0.135715 + 0.135715i
\(120\) 165339. 0.0956825
\(121\) 499793. 0.282120
\(122\) 443064.i 0.243998i
\(123\) 81516.1 0.0438054
\(124\) −345493. + 345493.i −0.181207 + 0.181207i
\(125\) 1.44407e6 + 1.44407e6i 0.739363 + 0.739363i
\(126\) −427249. 427249.i −0.213584 0.213584i
\(127\) 1.93108e6 0.942734 0.471367 0.881937i \(-0.343761\pi\)
0.471367 + 0.881937i \(0.343761\pi\)
\(128\) 131072. 131072.i 0.0625000 0.0625000i
\(129\) −356913. 356913.i −0.166262 0.166262i
\(130\) 355673. 355673.i 0.161890 0.161890i
\(131\) 1.94616e6 + 1.94616e6i 0.865696 + 0.865696i 0.991993 0.126296i \(-0.0403089\pi\)
−0.126296 + 0.991993i \(0.540309\pi\)
\(132\) 387736.i 0.168583i
\(133\) −724436. + 724436.i −0.307925 + 0.307925i
\(134\) −346207. + 346207.i −0.143887 + 0.143887i
\(135\) −867101. 867101.i −0.352426 0.352426i
\(136\) 336313.i 0.133699i
\(137\) −1.80552e6 −0.702167 −0.351083 0.936344i \(-0.614187\pi\)
−0.351083 + 0.936344i \(0.614187\pi\)
\(138\) 1.27430e6i 0.484881i
\(139\) 2.04030e6i 0.759713i −0.925045 0.379856i \(-0.875973\pi\)
0.925045 0.379856i \(-0.124027\pi\)
\(140\) −334865. 334865.i −0.122035 0.122035i
\(141\) 358533.i 0.127900i
\(142\) −1.12664e6 1.12664e6i −0.393479 0.393479i
\(143\) −834084. 834084.i −0.285234 0.285234i
\(144\) −628283. −0.210411
\(145\) −242712. −0.0796137
\(146\) −2.58238e6 + 2.58238e6i −0.829777 + 0.829777i
\(147\) 938446.i 0.295432i
\(148\) −799434. + 1.41004e6i −0.246602 + 0.434957i
\(149\) 1.93410e6 0.584682 0.292341 0.956314i \(-0.405566\pi\)
0.292341 + 0.956314i \(0.405566\pi\)
\(150\) 360939. + 360939.i 0.106945 + 0.106945i
\(151\) 1.33692e6i 0.388308i 0.980971 + 0.194154i \(0.0621961\pi\)
−0.980971 + 0.194154i \(0.937804\pi\)
\(152\) 1.06531e6i 0.303350i
\(153\) 806046. 806046.i 0.225053 0.225053i
\(154\) −785288. + 785288.i −0.215014 + 0.215014i
\(155\) 1.29800e6 0.348561
\(156\) 254295. 254295.i 0.0669829 0.0669829i
\(157\) −3.18578e6 −0.823222 −0.411611 0.911360i \(-0.635034\pi\)
−0.411611 + 0.911360i \(0.635034\pi\)
\(158\) −1.55329e6 −0.393804
\(159\) 2.67467e6i 0.665395i
\(160\) −492430. −0.120222
\(161\) −2.58087e6 + 2.58087e6i −0.618426 + 0.618426i
\(162\) 1.16918e6 + 1.16918e6i 0.275003 + 0.275003i
\(163\) −1.42695e6 1.42695e6i −0.329494 0.329494i 0.522900 0.852394i \(-0.324850\pi\)
−0.852394 + 0.522900i \(0.824850\pi\)
\(164\) −242779. −0.0550402
\(165\) −728350. + 728350.i −0.162139 + 0.162139i
\(166\) −3.77444e6 3.77444e6i −0.825141 0.825141i
\(167\) −493922. + 493922.i −0.106049 + 0.106049i −0.758141 0.652091i \(-0.773892\pi\)
0.652091 + 0.758141i \(0.273892\pi\)
\(168\) −239418. 239418.i −0.0504928 0.0504928i
\(169\) 3.73275e6i 0.773336i
\(170\) 631755. 631755.i 0.128588 0.128588i
\(171\) 2.55323e6 2.55323e6i 0.510625 0.510625i
\(172\) 1.06299e6 + 1.06299e6i 0.208903 + 0.208903i
\(173\) 4.16532e6i 0.804471i 0.915536 + 0.402235i \(0.131767\pi\)
−0.915536 + 0.402235i \(0.868233\pi\)
\(174\) −173532. −0.0329406
\(175\) 1.46203e6i 0.272799i
\(176\) 1.15479e6i 0.211819i
\(177\) −156664. 156664.i −0.0282521 0.0282521i
\(178\) 564796.i 0.100145i
\(179\) −2.74930e6 2.74930e6i −0.479362 0.479362i 0.425566 0.904928i \(-0.360075\pi\)
−0.904928 + 0.425566i \(0.860075\pi\)
\(180\) 1.18021e6 + 1.18021e6i 0.202368 + 0.202368i
\(181\) −8.60548e6 −1.45124 −0.725620 0.688095i \(-0.758447\pi\)
−0.725620 + 0.688095i \(0.758447\pi\)
\(182\) −1.03006e6 −0.170863
\(183\) −595056. + 595056.i −0.0970968 + 0.0970968i
\(184\) 3.79525e6i 0.609238i
\(185\) 4.15043e6 1.14700e6i 0.655508 0.181155i
\(186\) 928029. 0.144219
\(187\) −1.48152e6 1.48152e6i −0.226560 0.226560i
\(188\) 1.06782e6i 0.160703i
\(189\) 2.51119e6i 0.371959i
\(190\) 2.00115e6 2.00115e6i 0.291755 0.291755i
\(191\) 4.33614e6 4.33614e6i 0.622305 0.622305i −0.323815 0.946120i \(-0.604966\pi\)
0.946120 + 0.323815i \(0.104966\pi\)
\(192\) −352072. −0.0497426
\(193\) −3.19439e6 + 3.19439e6i −0.444341 + 0.444341i −0.893468 0.449127i \(-0.851735\pi\)
0.449127 + 0.893468i \(0.351735\pi\)
\(194\) −443037. −0.0606786
\(195\) −955372. −0.128845
\(196\) 2.79497e6i 0.371201i
\(197\) −4.04778e6 −0.529442 −0.264721 0.964325i \(-0.585280\pi\)
−0.264721 + 0.964325i \(0.585280\pi\)
\(198\) 2.76770e6 2.76770e6i 0.356553 0.356553i
\(199\) 2.50471e6 + 2.50471e6i 0.317833 + 0.317833i 0.847934 0.530101i \(-0.177846\pi\)
−0.530101 + 0.847934i \(0.677846\pi\)
\(200\) −1.07498e6 1.07498e6i −0.134373 0.134373i
\(201\) 929947. 0.114517
\(202\) 1.84818e6 1.84818e6i 0.224228 0.224228i
\(203\) 351457. + 351457.i 0.0420131 + 0.0420131i
\(204\) 451685. 451685.i 0.0532041 0.0532041i
\(205\) 456054. + 456054.i 0.0529364 + 0.0529364i
\(206\) 3.28518e6i 0.375801i
\(207\) 9.09611e6 9.09611e6i 1.02552 1.02552i
\(208\) −757366. + 757366.i −0.0841620 + 0.0841620i
\(209\) −4.69287e6 4.69287e6i −0.514043 0.514043i
\(210\) 899480.i 0.0971256i
\(211\) −8.67104e6 −0.923047 −0.461523 0.887128i \(-0.652697\pi\)
−0.461523 + 0.887128i \(0.652697\pi\)
\(212\) 7.96597e6i 0.836048i
\(213\) 3.02628e6i 0.313163i
\(214\) 7.49538e6 + 7.49538e6i 0.764807 + 0.764807i
\(215\) 3.99360e6i 0.401837i
\(216\) 1.84640e6 + 1.84640e6i 0.183216 + 0.183216i
\(217\) −1.87955e6 1.87955e6i −0.183940 0.183940i
\(218\) 2.55922e6 0.247023
\(219\) 6.93652e6 0.660404
\(220\) 2.16924e6 2.16924e6i 0.203723 0.203723i
\(221\) 1.94330e6i 0.180038i
\(222\) 2.96743e6 820073.i 0.271220 0.0749538i
\(223\) −1.41894e6 −0.127953 −0.0639764 0.997951i \(-0.520378\pi\)
−0.0639764 + 0.997951i \(0.520378\pi\)
\(224\) 713059. + 713059.i 0.0634426 + 0.0634426i
\(225\) 5.15285e6i 0.452377i
\(226\) 1.30507e7i 1.13060i
\(227\) 1.17994e7 1.17994e7i 1.00875 1.00875i 0.00878900 0.999961i \(-0.497202\pi\)
0.999961 0.00878900i \(-0.00279766\pi\)
\(228\) 1.43076e6 1.43076e6i 0.120715 0.120715i
\(229\) 1.85067e6 0.154107 0.0770536 0.997027i \(-0.475449\pi\)
0.0770536 + 0.997027i \(0.475449\pi\)
\(230\) 7.12927e6 7.12927e6i 0.585951 0.585951i
\(231\) 2.10936e6 0.171126
\(232\) 516830. 0.0413889
\(233\) 1.20765e7i 0.954710i 0.878710 + 0.477355i \(0.158404\pi\)
−0.878710 + 0.477355i \(0.841596\pi\)
\(234\) 3.63038e6 0.283337
\(235\) −2.00586e6 + 2.00586e6i −0.154560 + 0.154560i
\(236\) 466593. + 466593.i 0.0354978 + 0.0354978i
\(237\) 2.08614e6 + 2.08614e6i 0.156711 + 0.156711i
\(238\) −1.82961e6 −0.135715
\(239\) 2.81267e6 2.81267e6i 0.206027 0.206027i −0.596549 0.802577i \(-0.703462\pi\)
0.802577 + 0.596549i \(0.203462\pi\)
\(240\) 661358. + 661358.i 0.0478413 + 0.0478413i
\(241\) −7.53061e6 + 7.53061e6i −0.537996 + 0.537996i −0.922940 0.384944i \(-0.874221\pi\)
0.384944 + 0.922940i \(0.374221\pi\)
\(242\) 1.99917e6 + 1.99917e6i 0.141060 + 0.141060i
\(243\) 1.36564e7i 0.951735i
\(244\) 1.77225e6 1.77225e6i 0.121999 0.121999i
\(245\) −5.25027e6 + 5.25027e6i −0.357013 + 0.357013i
\(246\) 326064. + 326064.i 0.0219027 + 0.0219027i
\(247\) 6.15561e6i 0.408489i
\(248\) −2.76395e6 −0.181207
\(249\) 1.01385e7i 0.656714i
\(250\) 1.15525e7i 0.739363i
\(251\) −7.17086e6 7.17086e6i −0.453471 0.453471i 0.443034 0.896505i \(-0.353902\pi\)
−0.896505 + 0.443034i \(0.853902\pi\)
\(252\) 3.41799e6i 0.213584i
\(253\) −1.67188e7 1.67188e7i −1.03239 1.03239i
\(254\) 7.72432e6 + 7.72432e6i 0.471367 + 0.471367i
\(255\) −1.69696e6 −0.102341
\(256\) 1.04858e6 0.0625000
\(257\) 2.12454e7 2.12454e7i 1.25160 1.25160i 0.296599 0.955002i \(-0.404148\pi\)
0.955002 0.296599i \(-0.0958524\pi\)
\(258\) 2.85530e6i 0.166262i
\(259\) −7.67090e6 4.34908e6i −0.441517 0.250322i
\(260\) 2.84538e6 0.161890
\(261\) −1.23869e6 1.23869e6i −0.0696693 0.0696693i
\(262\) 1.55693e7i 0.865696i
\(263\) 1.66696e7i 0.916341i 0.888864 + 0.458170i \(0.151495\pi\)
−0.888864 + 0.458170i \(0.848505\pi\)
\(264\) 1.55094e6 1.55094e6i 0.0842915 0.0842915i
\(265\) −1.49639e7 + 1.49639e7i −0.804092 + 0.804092i
\(266\) −5.79549e6 −0.307925
\(267\) −758548. + 758548.i −0.0398519 + 0.0398519i
\(268\) −2.76966e6 −0.143887
\(269\) 2.99869e7 1.54055 0.770273 0.637715i \(-0.220120\pi\)
0.770273 + 0.637715i \(0.220120\pi\)
\(270\) 6.93681e6i 0.352426i
\(271\) −5.00898e6 −0.251676 −0.125838 0.992051i \(-0.540162\pi\)
−0.125838 + 0.992051i \(0.540162\pi\)
\(272\) −1.34525e6 + 1.34525e6i −0.0668494 + 0.0668494i
\(273\) 1.38342e6 + 1.38342e6i 0.0679932 + 0.0679932i
\(274\) −7.22208e6 7.22208e6i −0.351083 0.351083i
\(275\) 9.47100e6 0.455405
\(276\) 5.09721e6 5.09721e6i 0.242440 0.242440i
\(277\) 1.42910e7 + 1.42910e7i 0.672392 + 0.672392i 0.958267 0.285875i \(-0.0922842\pi\)
−0.285875 + 0.958267i \(0.592284\pi\)
\(278\) 8.16120e6 8.16120e6i 0.379856 0.379856i
\(279\) 6.62438e6 + 6.62438e6i 0.305023 + 0.305023i
\(280\) 2.67892e6i 0.122035i
\(281\) 1.57080e6 1.57080e6i 0.0707948 0.0707948i −0.670823 0.741618i \(-0.734059\pi\)
0.741618 + 0.670823i \(0.234059\pi\)
\(282\) −1.43413e6 + 1.43413e6i −0.0639502 + 0.0639502i
\(283\) −2.15634e7 2.15634e7i −0.951389 0.951389i 0.0474831 0.998872i \(-0.484880\pi\)
−0.998872 + 0.0474831i \(0.984880\pi\)
\(284\) 9.01316e6i 0.393479i
\(285\) −5.37528e6 −0.232202
\(286\) 6.67267e6i 0.285234i
\(287\) 1.32077e6i 0.0558703i
\(288\) −2.51313e6 2.51313e6i −0.105205 0.105205i
\(289\) 2.06858e7i 0.856997i
\(290\) −970850. 970850.i −0.0398069 0.0398069i
\(291\) 595021. + 595021.i 0.0241465 + 0.0241465i
\(292\) −2.06590e7 −0.829777
\(293\) 1.78427e6 0.0709343 0.0354672 0.999371i \(-0.488708\pi\)
0.0354672 + 0.999371i \(0.488708\pi\)
\(294\) −3.75378e6 + 3.75378e6i −0.147716 + 0.147716i
\(295\) 1.75296e6i 0.0682820i
\(296\) −8.83789e6 + 2.44242e6i −0.340780 + 0.0941771i
\(297\) −1.62674e7 −0.620940
\(298\) 7.73640e6 + 7.73640e6i 0.292341 + 0.292341i
\(299\) 2.19299e7i 0.820394i
\(300\) 2.88751e6i 0.106945i
\(301\) −5.78290e6 + 5.78290e6i −0.212054 + 0.212054i
\(302\) −5.34770e6 + 5.34770e6i −0.194154 + 0.194154i
\(303\) −4.96439e6 −0.178459
\(304\) −4.26123e6 + 4.26123e6i −0.151675 + 0.151675i
\(305\) −6.65826e6 −0.234672
\(306\) 6.44837e6 0.225053
\(307\) 2.20472e7i 0.761971i 0.924581 + 0.380985i \(0.124415\pi\)
−0.924581 + 0.380985i \(0.875585\pi\)
\(308\) −6.28231e6 −0.215014
\(309\) 4.41216e6 4.41216e6i 0.149546 0.149546i
\(310\) 5.19200e6 + 5.19200e6i 0.174281 + 0.174281i
\(311\) −2.22545e7 2.22545e7i −0.739838 0.739838i 0.232708 0.972547i \(-0.425241\pi\)
−0.972547 + 0.232708i \(0.925241\pi\)
\(312\) 2.03436e6 0.0669829
\(313\) −2.13882e7 + 2.13882e7i −0.697495 + 0.697495i −0.963869 0.266375i \(-0.914174\pi\)
0.266375 + 0.963869i \(0.414174\pi\)
\(314\) −1.27431e7 1.27431e7i −0.411611 0.411611i
\(315\) −6.42060e6 + 6.42060e6i −0.205420 + 0.205420i
\(316\) −6.21315e6 6.21315e6i −0.196902 0.196902i
\(317\) 2.73504e7i 0.858589i 0.903165 + 0.429294i \(0.141238\pi\)
−0.903165 + 0.429294i \(0.858762\pi\)
\(318\) −1.06987e7 + 1.06987e7i −0.332697 + 0.332697i
\(319\) −2.27673e6 + 2.27673e6i −0.0701357 + 0.0701357i
\(320\) −1.96972e6 1.96972e6i −0.0601111 0.0601111i
\(321\) 2.01333e7i 0.608696i
\(322\) −2.06469e7 −0.618426
\(323\) 1.09337e7i 0.324460i
\(324\) 9.35348e6i 0.275003i
\(325\) 6.21152e6 + 6.21152e6i 0.180946 + 0.180946i
\(326\) 1.14156e7i 0.329494i
\(327\) −3.43715e6 3.43715e6i −0.0983005 0.0983005i
\(328\) −971116. 971116.i −0.0275201 0.0275201i
\(329\) 5.80915e6 0.163127
\(330\) −5.82680e6 −0.162139
\(331\) −3.08628e6 + 3.08628e6i −0.0851043 + 0.0851043i −0.748377 0.663273i \(-0.769167\pi\)
0.663273 + 0.748377i \(0.269167\pi\)
\(332\) 3.01955e7i 0.825141i
\(333\) 2.70356e7 + 1.53281e7i 0.732157 + 0.415103i
\(334\) −3.95137e6 −0.106049
\(335\) 5.20272e6 + 5.20272e6i 0.138387 + 0.138387i
\(336\) 1.91535e6i 0.0504928i
\(337\) 2.62832e7i 0.686734i 0.939201 + 0.343367i \(0.111567\pi\)
−0.939201 + 0.343367i \(0.888433\pi\)
\(338\) −1.49310e7 + 1.49310e7i −0.386668 + 0.386668i
\(339\) 1.75277e7 1.75277e7i 0.449910 0.449910i
\(340\) 5.05404e6 0.128588
\(341\) 1.21757e7 1.21757e7i 0.307065 0.307065i
\(342\) 2.04259e7 0.510625
\(343\) 3.56863e7 0.884341
\(344\) 8.50394e6i 0.208903i
\(345\) −1.91499e7 −0.466347
\(346\) −1.66613e7 + 1.66613e7i −0.402235 + 0.402235i
\(347\) 5.19175e7 + 5.19175e7i 1.24258 + 1.24258i 0.958925 + 0.283659i \(0.0915483\pi\)
0.283659 + 0.958925i \(0.408452\pi\)
\(348\) −694128. 694128.i −0.0164703 0.0164703i
\(349\) −4.51760e7 −1.06275 −0.531376 0.847136i \(-0.678325\pi\)
−0.531376 + 0.847136i \(0.678325\pi\)
\(350\) 5.84813e6 5.84813e6i 0.136400 0.136400i
\(351\) −1.06689e7 1.06689e7i −0.246717 0.246717i
\(352\) −4.61917e6 + 4.61917e6i −0.105910 + 0.105910i
\(353\) 2.08582e6 + 2.08582e6i 0.0474191 + 0.0474191i 0.730419 0.683000i \(-0.239325\pi\)
−0.683000 + 0.730419i \(0.739325\pi\)
\(354\) 1.25331e6i 0.0282521i
\(355\) −1.69310e7 + 1.69310e7i −0.378440 + 0.378440i
\(356\) 2.25918e6 2.25918e6i 0.0500727 0.0500727i
\(357\) 2.45726e6 + 2.45726e6i 0.0540066 + 0.0540066i
\(358\) 2.19944e7i 0.479362i
\(359\) 5.88696e7 1.27235 0.636176 0.771544i \(-0.280515\pi\)
0.636176 + 0.771544i \(0.280515\pi\)
\(360\) 9.44170e6i 0.202368i
\(361\) 1.24121e7i 0.263830i
\(362\) −3.44219e7 3.44219e7i −0.725620 0.725620i
\(363\) 5.36998e6i 0.112267i
\(364\) −4.12023e6 4.12023e6i −0.0854313 0.0854313i
\(365\) 3.88074e7 + 3.88074e7i 0.798061 + 0.798061i
\(366\) −4.76045e6 −0.0970968
\(367\) −9.47358e7 −1.91653 −0.958265 0.285880i \(-0.907714\pi\)
−0.958265 + 0.285880i \(0.907714\pi\)
\(368\) −1.51810e7 + 1.51810e7i −0.304619 + 0.304619i
\(369\) 4.65497e6i 0.0926484i
\(370\) 2.11897e7 + 1.20137e7i 0.418331 + 0.237177i
\(371\) 4.33365e7 0.848657
\(372\) 3.71212e6 + 3.71212e6i 0.0721096 + 0.0721096i
\(373\) 2.54683e7i 0.490765i −0.969426 0.245382i \(-0.921086\pi\)
0.969426 0.245382i \(-0.0789135\pi\)
\(374\) 1.18522e7i 0.226560i
\(375\) 1.55156e7 1.55156e7i 0.294222 0.294222i
\(376\) 4.27127e6 4.27127e6i 0.0803514 0.0803514i
\(377\) −2.98637e6 −0.0557339
\(378\) −1.00448e7 + 1.00448e7i −0.185979 + 0.185979i
\(379\) 5.35456e7 0.983572 0.491786 0.870716i \(-0.336344\pi\)
0.491786 + 0.870716i \(0.336344\pi\)
\(380\) 1.60092e7 0.291755
\(381\) 2.07483e7i 0.375152i
\(382\) 3.46891e7 0.622305
\(383\) 3.16318e7 3.16318e7i 0.563025 0.563025i −0.367141 0.930165i \(-0.619663\pi\)
0.930165 + 0.367141i \(0.119663\pi\)
\(384\) −1.40829e6 1.40829e6i −0.0248713 0.0248713i
\(385\) 1.18011e7 + 1.18011e7i 0.206796 + 0.206796i
\(386\) −2.55551e7 −0.444341
\(387\) 2.03815e7 2.03815e7i 0.351644 0.351644i
\(388\) −1.77215e6 1.77215e6i −0.0303393 0.0303393i
\(389\) 2.53167e7 2.53167e7i 0.430089 0.430089i −0.458569 0.888659i \(-0.651638\pi\)
0.888659 + 0.458569i \(0.151638\pi\)
\(390\) −3.82149e6 3.82149e6i −0.0644227 0.0644227i
\(391\) 3.89524e7i 0.651634i
\(392\) 1.11799e7 1.11799e7i 0.185601 0.185601i
\(393\) 2.09104e7 2.09104e7i 0.344496 0.344496i
\(394\) −1.61911e7 1.61911e7i −0.264721 0.264721i
\(395\) 2.33425e7i 0.378752i
\(396\) 2.21416e7 0.356553
\(397\) 7.25089e7i 1.15883i −0.815033 0.579415i \(-0.803281\pi\)
0.815033 0.579415i \(-0.196719\pi\)
\(398\) 2.00377e7i 0.317833i
\(399\) 7.78363e6 + 7.78363e6i 0.122536 + 0.122536i
\(400\) 8.59987e6i 0.134373i
\(401\) −3.23386e7 3.23386e7i −0.501519 0.501519i 0.410390 0.911910i \(-0.365392\pi\)
−0.911910 + 0.410390i \(0.865392\pi\)
\(402\) 3.71979e6 + 3.71979e6i 0.0572585 + 0.0572585i
\(403\) 1.59708e7 0.244012
\(404\) 1.47854e7 0.224228
\(405\) 1.75702e7 1.75702e7i 0.264492 0.264492i
\(406\) 2.81166e6i 0.0420131i
\(407\) 2.81732e7 4.96918e7i 0.417882 0.737058i
\(408\) 3.61348e6 0.0532041
\(409\) 6.70387e7 + 6.70387e7i 0.979841 + 0.979841i 0.999801 0.0199599i \(-0.00635384\pi\)
−0.0199599 + 0.999801i \(0.506354\pi\)
\(410\) 3.64843e6i 0.0529364i
\(411\) 1.93992e7i 0.279421i
\(412\) −1.31407e7 + 1.31407e7i −0.187900 + 0.187900i
\(413\) −2.53836e6 + 2.53836e6i −0.0360332 + 0.0360332i
\(414\) 7.27689e7 1.02552
\(415\) −5.67214e7 + 5.67214e7i −0.793602 + 0.793602i
\(416\) −6.05893e6 −0.0841620
\(417\) −2.19218e7 −0.302321
\(418\) 3.75430e7i 0.514043i
\(419\) 1.91994e7 0.261003 0.130501 0.991448i \(-0.458341\pi\)
0.130501 + 0.991448i \(0.458341\pi\)
\(420\) −3.59792e6 + 3.59792e6i −0.0485628 + 0.0485628i
\(421\) −3.19569e7 3.19569e7i −0.428270 0.428270i 0.459768 0.888039i \(-0.347932\pi\)
−0.888039 + 0.459768i \(0.847932\pi\)
\(422\) −3.46841e7 3.46841e7i −0.461523 0.461523i
\(423\) −2.04740e7 −0.270509
\(424\) 3.18639e7 3.18639e7i 0.418024 0.418024i
\(425\) 1.10331e7 + 1.10331e7i 0.143724 + 0.143724i
\(426\) −1.21051e7 + 1.21051e7i −0.156581 + 0.156581i
\(427\) 9.64143e6 + 9.64143e6i 0.123839 + 0.123839i
\(428\) 5.99630e7i 0.764807i
\(429\) −8.96173e6 + 8.96173e6i −0.113506 + 0.113506i
\(430\) 1.59744e7 1.59744e7i 0.200918 0.200918i
\(431\) −5.49252e7 5.49252e7i −0.686025 0.686025i 0.275326 0.961351i \(-0.411214\pi\)
−0.961351 + 0.275326i \(0.911214\pi\)
\(432\) 1.47712e7i 0.183216i
\(433\) 4.30237e7 0.529962 0.264981 0.964254i \(-0.414634\pi\)
0.264981 + 0.964254i \(0.414634\pi\)
\(434\) 1.50364e7i 0.183940i
\(435\) 2.60780e6i 0.0316815i
\(436\) 1.02369e7 + 1.02369e7i 0.123512 + 0.123512i
\(437\) 1.23386e8i 1.47850i
\(438\) 2.77461e7 + 2.77461e7i 0.330202 + 0.330202i
\(439\) −9.56775e7 9.56775e7i −1.13088 1.13088i −0.990031 0.140848i \(-0.955017\pi\)
−0.140848 0.990031i \(-0.544983\pi\)
\(440\) 1.73540e7 0.203723
\(441\) −5.35899e7 −0.624838
\(442\) 7.77320e6 7.77320e6i 0.0900188 0.0900188i
\(443\) 1.32723e8i 1.52663i 0.646027 + 0.763315i \(0.276429\pi\)
−0.646027 + 0.763315i \(0.723571\pi\)
\(444\) 1.51500e7 + 8.58943e6i 0.173087 + 0.0981331i
\(445\) −8.48762e6 −0.0963177
\(446\) −5.67576e6 5.67576e6i −0.0639764 0.0639764i
\(447\) 2.07807e7i 0.232669i
\(448\) 5.70447e6i 0.0634426i
\(449\) −6.26817e7 + 6.26817e7i −0.692471 + 0.692471i −0.962775 0.270304i \(-0.912876\pi\)
0.270304 + 0.962775i \(0.412876\pi\)
\(450\) −2.06114e7 + 2.06114e7i −0.226188 + 0.226188i
\(451\) 8.55589e6 0.0932686
\(452\) −5.22027e7 + 5.22027e7i −0.565299 + 0.565299i
\(453\) 1.43644e7 0.154523
\(454\) 9.43955e7 1.00875
\(455\) 1.54795e7i 0.164332i
\(456\) 1.14461e7 0.120715
\(457\) 5.16082e7 5.16082e7i 0.540717 0.540717i −0.383022 0.923739i \(-0.625117\pi\)
0.923739 + 0.383022i \(0.125117\pi\)
\(458\) 7.40269e6 + 7.40269e6i 0.0770536 + 0.0770536i
\(459\) −1.89504e7 1.89504e7i −0.195966 0.195966i
\(460\) 5.70341e7 0.585951
\(461\) −7.61349e7 + 7.61349e7i −0.777107 + 0.777107i −0.979338 0.202231i \(-0.935181\pi\)
0.202231 + 0.979338i \(0.435181\pi\)
\(462\) 8.43745e6 + 8.43745e6i 0.0855628 + 0.0855628i
\(463\) −1.34840e8 + 1.34840e8i −1.35855 + 1.35855i −0.482852 + 0.875702i \(0.660399\pi\)
−0.875702 + 0.482852i \(0.839601\pi\)
\(464\) 2.06732e6 + 2.06732e6i 0.0206944 + 0.0206944i
\(465\) 1.39462e7i 0.138707i
\(466\) −4.83058e7 + 4.83058e7i −0.477355 + 0.477355i
\(467\) −9.32470e7 + 9.32470e7i −0.915555 + 0.915555i −0.996702 0.0811476i \(-0.974141\pi\)
0.0811476 + 0.996702i \(0.474141\pi\)
\(468\) 1.45215e7 + 1.45215e7i 0.141669 + 0.141669i
\(469\) 1.50675e7i 0.146057i
\(470\) −1.60469e7 −0.154560
\(471\) 3.42293e7i 0.327593i
\(472\) 3.73274e6i 0.0354978i
\(473\) −3.74614e7 3.74614e7i −0.353998 0.353998i
\(474\) 1.66891e7i 0.156711i
\(475\) 3.49484e7 + 3.49484e7i 0.326096 + 0.326096i
\(476\) −7.31845e6 7.31845e6i −0.0678576 0.0678576i
\(477\) −1.52737e8 −1.40731
\(478\) 2.25014e7 0.206027
\(479\) −5.94649e7 + 5.94649e7i −0.541071 + 0.541071i −0.923843 0.382772i \(-0.874969\pi\)
0.382772 + 0.923843i \(0.374969\pi\)
\(480\) 5.29086e6i 0.0478413i
\(481\) 5.10675e7 1.41129e7i 0.458891 0.126818i
\(482\) −6.02449e7 −0.537996
\(483\) 2.77298e7 + 2.77298e7i 0.246097 + 0.246097i
\(484\) 1.59934e7i 0.141060i
\(485\) 6.65787e6i 0.0583593i
\(486\) 5.46254e7 5.46254e7i 0.475867 0.475867i
\(487\) −7.43155e7 + 7.43155e7i −0.643417 + 0.643417i −0.951394 0.307977i \(-0.900348\pi\)
0.307977 + 0.951394i \(0.400348\pi\)
\(488\) 1.41780e7 0.121999
\(489\) −1.53318e7 + 1.53318e7i −0.131119 + 0.131119i
\(490\) −4.20022e7 −0.357013
\(491\) 3.06751e7 0.259144 0.129572 0.991570i \(-0.458640\pi\)
0.129572 + 0.991570i \(0.458640\pi\)
\(492\) 2.60851e6i 0.0219027i
\(493\) −5.30446e6 −0.0442691
\(494\) 2.46224e7 2.46224e7i 0.204244 0.204244i
\(495\) −4.15924e7 4.15924e7i −0.342924 0.342924i
\(496\) −1.10558e7 1.10558e7i −0.0906034 0.0906034i
\(497\) 4.90334e7 0.399414
\(498\) −4.05541e7 + 4.05541e7i −0.328357 + 0.328357i
\(499\) 2.45175e7 + 2.45175e7i 0.197322 + 0.197322i 0.798851 0.601529i \(-0.205442\pi\)
−0.601529 + 0.798851i \(0.705442\pi\)
\(500\) −4.62102e7 + 4.62102e7i −0.369681 + 0.369681i
\(501\) 5.30689e6 + 5.30689e6i 0.0422014 + 0.0422014i
\(502\) 5.73669e7i 0.453471i
\(503\) −1.85732e7 + 1.85732e7i −0.145943 + 0.145943i −0.776303 0.630360i \(-0.782907\pi\)
0.630360 + 0.776303i \(0.282907\pi\)
\(504\) 1.36720e7 1.36720e7i 0.106792 0.106792i
\(505\) −2.77740e7 2.77740e7i −0.215657 0.215657i
\(506\) 1.33750e8i 1.03239i
\(507\) 4.01061e7 0.307742
\(508\) 6.17945e7i 0.471367i
\(509\) 1.40587e8i 1.06609i 0.846087 + 0.533044i \(0.178952\pi\)
−0.846087 + 0.533044i \(0.821048\pi\)
\(510\) −6.78782e6 6.78782e6i −0.0511705 0.0511705i
\(511\) 1.12389e8i 0.842292i
\(512\) 4.19430e6 + 4.19430e6i 0.0312500 + 0.0312500i
\(513\) −6.00274e7 6.00274e7i −0.444629 0.444629i
\(514\) 1.69963e8 1.25160
\(515\) 4.93689e7 0.361436
\(516\) 1.14212e7 1.14212e7i 0.0831310 0.0831310i
\(517\) 3.76315e7i 0.272320i
\(518\) −1.32873e7 4.80799e7i −0.0955975 0.345919i
\(519\) 4.47539e7 0.320132
\(520\) 1.13815e7 + 1.13815e7i 0.0809451 + 0.0809451i
\(521\) 1.86652e8i 1.31984i −0.751338 0.659918i \(-0.770591\pi\)
0.751338 0.659918i \(-0.229409\pi\)
\(522\) 9.90953e6i 0.0696693i
\(523\) −5.86978e7 + 5.86978e7i −0.410314 + 0.410314i −0.881848 0.471534i \(-0.843701\pi\)
0.471534 + 0.881848i \(0.343701\pi\)
\(524\) −6.22773e7 + 6.22773e7i −0.432848 + 0.432848i
\(525\) −1.57087e7 −0.108558
\(526\) −6.66783e7 + 6.66783e7i −0.458170 + 0.458170i
\(527\) 2.83677e7 0.193817
\(528\) 1.24075e7 0.0842915
\(529\) 2.91537e8i 1.96936i
\(530\) −1.19711e8 −0.804092
\(531\) 8.94630e6 8.94630e6i 0.0597530 0.0597530i
\(532\) −2.31820e7 2.31820e7i −0.153963 0.153963i
\(533\) 5.61135e6 + 5.61135e6i 0.0370583 + 0.0370583i
\(534\) −6.06839e6 −0.0398519
\(535\) 1.12639e8 1.12639e8i 0.735574 0.735574i
\(536\) −1.10786e7 1.10786e7i −0.0719435 0.0719435i
\(537\) −2.95396e7 + 2.95396e7i −0.190758 + 0.190758i
\(538\) 1.19948e8 + 1.19948e8i 0.770273 + 0.770273i
\(539\) 9.84989e7i 0.629021i
\(540\) 2.77472e7 2.77472e7i 0.176213 0.176213i
\(541\) 1.26758e8 1.26758e8i 0.800541 0.800541i −0.182639 0.983180i \(-0.558464\pi\)
0.983180 + 0.182639i \(0.0584641\pi\)
\(542\) −2.00359e7 2.00359e7i −0.125838 0.125838i
\(543\) 9.24607e7i 0.577507i
\(544\) −1.07620e7 −0.0668494
\(545\) 3.84593e7i 0.237581i
\(546\) 1.10673e7i 0.0679932i
\(547\) −1.75535e8 1.75535e8i −1.07251 1.07251i −0.997157 0.0753551i \(-0.975991\pi\)
−0.0753551 0.997157i \(-0.524009\pi\)
\(548\) 5.77766e7i 0.351083i
\(549\) −3.39807e7 3.39807e7i −0.205359 0.205359i
\(550\) 3.78840e7 + 3.78840e7i 0.227703 + 0.227703i
\(551\) −1.68024e7 −0.100442
\(552\) 4.07776e7 0.242440
\(553\) 3.38008e7 3.38008e7i 0.199872 0.199872i
\(554\) 1.14328e8i 0.672392i
\(555\) −1.23239e7 4.45939e7i −0.0720888 0.260853i
\(556\) 6.52896e7 0.379856
\(557\) 2.51207e7 + 2.51207e7i 0.145367 + 0.145367i 0.776045 0.630678i \(-0.217223\pi\)
−0.630678 + 0.776045i \(0.717223\pi\)
\(558\) 5.29951e7i 0.305023i
\(559\) 4.91379e7i 0.281307i
\(560\) 1.07157e7 1.07157e7i 0.0610177 0.0610177i
\(561\) −1.59180e7 + 1.59180e7i −0.0901574 + 0.0901574i
\(562\) 1.25664e7 0.0707948
\(563\) −6.68578e6 + 6.68578e6i −0.0374651 + 0.0374651i −0.725591 0.688126i \(-0.758434\pi\)
0.688126 + 0.725591i \(0.258434\pi\)
\(564\) −1.14731e7 −0.0639502
\(565\) 1.96123e8 1.08738
\(566\) 1.72507e8i 0.951389i
\(567\) −5.08848e7 −0.279151
\(568\) 3.60526e7 3.60526e7i 0.196740 0.196740i
\(569\) 1.68698e8 + 1.68698e8i 0.915742 + 0.915742i 0.996716 0.0809745i \(-0.0258032\pi\)
−0.0809745 + 0.996716i \(0.525803\pi\)
\(570\) −2.15011e7 2.15011e7i −0.116101 0.116101i
\(571\) 5.49139e7 0.294967 0.147484 0.989064i \(-0.452883\pi\)
0.147484 + 0.989064i \(0.452883\pi\)
\(572\) 2.66907e7 2.66907e7i 0.142617 0.142617i
\(573\) −4.65892e7 4.65892e7i −0.247640 0.247640i
\(574\) 5.28307e6 5.28307e6i 0.0279351 0.0279351i
\(575\) 1.24507e8 + 1.24507e8i 0.654921 + 0.654921i
\(576\) 2.01051e7i 0.105205i
\(577\) 1.41186e8 1.41186e8i 0.734961 0.734961i −0.236637 0.971598i \(-0.576045\pi\)
0.971598 + 0.236637i \(0.0760453\pi\)
\(578\) −8.27433e7 + 8.27433e7i −0.428499 + 0.428499i
\(579\) 3.43218e7 + 3.43218e7i 0.176821 + 0.176821i
\(580\) 7.76680e6i 0.0398069i
\(581\) 1.64270e8 0.837586
\(582\) 4.76017e6i 0.0241465i
\(583\) 2.80733e8i 1.41673i
\(584\) −8.26361e7 8.26361e7i −0.414889 0.414889i
\(585\) 5.45565e7i 0.272508i
\(586\) 7.13706e6 + 7.13706e6i 0.0354672 + 0.0354672i
\(587\) 1.78196e8 + 1.78196e8i 0.881014 + 0.881014i 0.993638 0.112624i \(-0.0359255\pi\)
−0.112624 + 0.993638i \(0.535926\pi\)
\(588\) −3.00303e7 −0.147716
\(589\) 8.98575e7 0.439753
\(590\) 7.01185e6 7.01185e6i 0.0341410 0.0341410i
\(591\) 4.34910e7i 0.210686i
\(592\) −4.51212e7 2.55819e7i −0.217478 0.123301i
\(593\) 1.71632e8 0.823067 0.411533 0.911395i \(-0.364993\pi\)
0.411533 + 0.911395i \(0.364993\pi\)
\(594\) −6.50697e7 6.50697e7i −0.310470 0.310470i
\(595\) 2.74950e7i 0.130528i
\(596\) 6.18912e7i 0.292341i
\(597\) 2.69116e7 2.69116e7i 0.126479 0.126479i
\(598\) 8.77195e7 8.77195e7i 0.410197 0.410197i
\(599\) −2.12461e8 −0.988548 −0.494274 0.869306i \(-0.664566\pi\)
−0.494274 + 0.869306i \(0.664566\pi\)
\(600\) −1.15501e7 + 1.15501e7i −0.0534725 + 0.0534725i
\(601\) 2.54871e8 1.17408 0.587040 0.809558i \(-0.300293\pi\)
0.587040 + 0.809558i \(0.300293\pi\)
\(602\) −4.62632e7 −0.212054
\(603\) 5.31046e7i 0.242203i
\(604\) −4.27816e7 −0.194154
\(605\) 3.00431e7 3.00431e7i 0.135668 0.135668i
\(606\) −1.98576e7 1.98576e7i −0.0892294 0.0892294i
\(607\) 1.19721e8 + 1.19721e8i 0.535311 + 0.535311i 0.922148 0.386837i \(-0.126432\pi\)
−0.386837 + 0.922148i \(0.626432\pi\)
\(608\) −3.40898e7 −0.151675
\(609\) 3.77620e6 3.77620e6i 0.0167187 0.0167187i
\(610\) −2.66330e7 2.66330e7i −0.117336 0.117336i
\(611\) −2.46805e7 + 2.46805e7i −0.108201 + 0.108201i
\(612\) 2.57935e7 + 2.57935e7i 0.112527 + 0.112527i
\(613\) 3.86636e7i 0.167850i 0.996472 + 0.0839249i \(0.0267456\pi\)
−0.996472 + 0.0839249i \(0.973254\pi\)
\(614\) −8.81888e7 + 8.81888e7i −0.380985 + 0.380985i
\(615\) 4.90002e6 4.90002e6i 0.0210655 0.0210655i
\(616\) −2.51292e7 2.51292e7i −0.107507 0.107507i
\(617\) 8.56940e7i 0.364834i 0.983221 + 0.182417i \(0.0583921\pi\)
−0.983221 + 0.182417i \(0.941608\pi\)
\(618\) 3.52973e7 0.149546
\(619\) 1.72438e8i 0.727044i −0.931586 0.363522i \(-0.881574\pi\)
0.931586 0.363522i \(-0.118426\pi\)
\(620\) 4.15360e7i 0.174281i
\(621\) −2.13853e8 2.13853e8i −0.892977 0.892977i
\(622\) 1.78036e8i 0.739838i
\(623\) 1.22904e7 + 1.22904e7i 0.0508279 + 0.0508279i
\(624\) 8.13744e6 + 8.13744e6i 0.0334915 + 0.0334915i
\(625\) 4.23853e7 0.173610
\(626\) −1.71105e8 −0.697495
\(627\) −5.04221e7 + 5.04221e7i −0.204559 + 0.204559i
\(628\) 1.01945e8i 0.411611i
\(629\) 9.07074e7 2.50677e7i 0.364494 0.100731i
\(630\) −5.13648e7 −0.205420
\(631\) −1.06920e8 1.06920e8i −0.425570 0.425570i 0.461546 0.887116i \(-0.347295\pi\)
−0.887116 + 0.461546i \(0.847295\pi\)
\(632\) 4.97052e7i 0.196902i
\(633\) 9.31650e7i 0.367318i
\(634\) −1.09401e8 + 1.09401e8i −0.429294 + 0.429294i
\(635\) 1.16079e8 1.16079e8i 0.453350 0.453350i
\(636\) −8.55896e7 −0.332697
\(637\) −6.46001e7 + 6.46001e7i −0.249928 + 0.249928i
\(638\) −1.82138e7 −0.0701357
\(639\) −1.72815e8 −0.662339
\(640\) 1.57578e7i 0.0601111i
\(641\) −2.87915e8 −1.09318 −0.546589 0.837401i \(-0.684074\pi\)
−0.546589 + 0.837401i \(0.684074\pi\)
\(642\) 8.05333e7 8.05333e7i 0.304348 0.304348i
\(643\) 2.98112e8 + 2.98112e8i 1.12136 + 1.12136i 0.991537 + 0.129826i \(0.0414417\pi\)
0.129826 + 0.991537i \(0.458558\pi\)
\(644\) −8.25877e7 8.25877e7i −0.309213 0.309213i
\(645\) −4.29088e7 −0.159907
\(646\) 4.37350e7 4.37350e7i 0.162230 0.162230i
\(647\) −1.47868e8 1.47868e8i −0.545961 0.545961i 0.379309 0.925270i \(-0.376162\pi\)
−0.925270 + 0.379309i \(0.876162\pi\)
\(648\) −3.74139e7 + 3.74139e7i −0.137502 + 0.137502i
\(649\) −1.64434e7 1.64434e7i −0.0601531 0.0601531i
\(650\) 4.96922e7i 0.180946i
\(651\) −2.01947e7 + 2.01947e7i −0.0731971 + 0.0731971i
\(652\) 4.56625e7 4.56625e7i 0.164747 0.164747i
\(653\) 6.68189e7 + 6.68189e7i 0.239971 + 0.239971i 0.816838 0.576867i \(-0.195725\pi\)
−0.576867 + 0.816838i \(0.695725\pi\)
\(654\) 2.74972e7i 0.0983005i
\(655\) 2.33972e8 0.832607
\(656\) 7.76893e6i 0.0275201i
\(657\) 3.96110e8i 1.39675i
\(658\) 2.32366e7 + 2.32366e7i 0.0815633 + 0.0815633i
\(659\) 4.11029e7i 0.143620i −0.997418 0.0718102i \(-0.977122\pi\)
0.997418 0.0718102i \(-0.0228776\pi\)
\(660\) −2.33072e7 2.33072e7i −0.0810697 0.0810697i
\(661\) −2.13091e8 2.13091e8i −0.737839 0.737839i 0.234321 0.972159i \(-0.424713\pi\)
−0.972159 + 0.234321i \(0.924713\pi\)
\(662\) −2.46903e7 −0.0851043
\(663\) −2.08796e7 −0.0716443
\(664\) 1.20782e8 1.20782e8i 0.412570 0.412570i
\(665\) 8.70933e7i 0.296155i
\(666\) 4.68302e7 + 1.69455e8i 0.158527 + 0.573630i
\(667\) −5.98601e7 −0.201725
\(668\) −1.58055e7 1.58055e7i −0.0530247 0.0530247i
\(669\) 1.52457e7i 0.0509176i
\(670\) 4.16218e7i 0.138387i
\(671\) −6.24568e7 + 6.24568e7i −0.206734 + 0.206734i
\(672\) 7.66138e6 7.66138e6i 0.0252464 0.0252464i
\(673\) −2.78761e8 −0.914506 −0.457253 0.889337i \(-0.651167\pi\)
−0.457253 + 0.889337i \(0.651167\pi\)
\(674\) −1.05133e8 + 1.05133e8i −0.343367 + 0.343367i
\(675\) 1.21145e8 0.393909
\(676\) −1.19448e8 −0.386668
\(677\) 2.88714e8i 0.930467i −0.885188 0.465234i \(-0.845970\pi\)
0.885188 0.465234i \(-0.154030\pi\)
\(678\) 1.40222e8 0.449910
\(679\) 9.64086e6 9.64086e6i 0.0307969 0.0307969i
\(680\) 2.02162e7 + 2.02162e7i 0.0642942 + 0.0642942i
\(681\) −1.26778e8 1.26778e8i −0.401423 0.401423i
\(682\) 9.74055e7 0.307065
\(683\) 679783. 679783.i 0.00213358 0.00213358i −0.706039 0.708173i \(-0.749520\pi\)
0.708173 + 0.706039i \(0.249520\pi\)
\(684\) 8.17034e7 + 8.17034e7i 0.255312 + 0.255312i
\(685\) −1.08532e8 + 1.08532e8i −0.337664 + 0.337664i
\(686\) 1.42745e8 + 1.42745e8i 0.442170 + 0.442170i
\(687\) 1.98843e7i 0.0613255i
\(688\) −3.40158e7 + 3.40158e7i −0.104452 + 0.104452i
\(689\) −1.84117e8 + 1.84117e8i −0.562908 + 0.562908i
\(690\) −7.65996e7 7.65996e7i −0.233174 0.233174i
\(691\) 3.05221e7i 0.0925081i 0.998930 + 0.0462540i \(0.0147284\pi\)
−0.998930 + 0.0462540i \(0.985272\pi\)
\(692\) −1.33290e8 −0.402235
\(693\) 1.20455e8i 0.361930i
\(694\) 4.15340e8i 1.24258i
\(695\) −1.22645e8 1.22645e8i −0.365337 0.365337i
\(696\) 5.55302e6i 0.0164703i
\(697\) 9.96702e6 + 9.96702e6i 0.0294352 + 0.0294352i
\(698\) −1.80704e8 1.80704e8i −0.531376 0.531376i
\(699\) 1.29754e8 0.379918
\(700\) 4.67851e7 0.136400
\(701\) 1.36393e8 1.36393e8i 0.395947 0.395947i −0.480854 0.876801i \(-0.659673\pi\)
0.876801 + 0.480854i \(0.159673\pi\)
\(702\) 8.53515e7i 0.246717i
\(703\) 2.87325e8 7.94045e7i 0.827004 0.228549i
\(704\) −3.69534e7 −0.105910
\(705\) 2.15518e7 + 2.15518e7i 0.0615058 + 0.0615058i
\(706\) 1.66866e7i 0.0474191i
\(707\) 8.04357e7i 0.227610i
\(708\) 5.01326e6 5.01326e6i 0.0141260 0.0141260i
\(709\) 9.23054e7 9.23054e7i 0.258993 0.258993i −0.565651 0.824645i \(-0.691375\pi\)
0.824645 + 0.565651i \(0.191375\pi\)
\(710\) −1.35448e8 −0.378440
\(711\) −1.19129e8 + 1.19129e8i −0.331443 + 0.331443i
\(712\) 1.80735e7 0.0500727
\(713\) 3.20125e8 0.883185
\(714\) 1.96581e7i 0.0540066i
\(715\) −1.00275e8 −0.274332
\(716\) 8.79777e7 8.79777e7i 0.239681 0.239681i
\(717\) −3.02204e7 3.02204e7i −0.0819867 0.0819867i
\(718\) 2.35478e8 + 2.35478e8i 0.636176 + 0.636176i
\(719\) −5.58546e8 −1.50270 −0.751350 0.659904i \(-0.770597\pi\)
−0.751350 + 0.659904i \(0.770597\pi\)
\(720\) −3.77668e7 + 3.77668e7i −0.101184 + 0.101184i
\(721\) −7.14882e7 7.14882e7i −0.190734 0.190734i
\(722\) −4.96485e7 + 4.96485e7i −0.131915 + 0.131915i
\(723\) 8.09119e7 + 8.09119e7i 0.214090 + 0.214090i
\(724\) 2.75375e8i 0.725620i
\(725\) 1.69551e7 1.69551e7i 0.0444924 0.0444924i
\(726\) 2.14799e7 2.14799e7i 0.0561336 0.0561336i
\(727\) −3.74737e8 3.74737e8i −0.975266 0.975266i 0.0244359 0.999701i \(-0.492221\pi\)
−0.999701 + 0.0244359i \(0.992221\pi\)
\(728\) 3.29618e7i 0.0854313i
\(729\) 6.63547e7 0.171273
\(730\) 3.10459e8i 0.798061i
\(731\) 8.72799e7i 0.223441i
\(732\) −1.90418e7 1.90418e7i −0.0485484 0.0485484i
\(733\) 2.97896e8i 0.756403i 0.925723 + 0.378201i \(0.123457\pi\)
−0.925723 + 0.378201i \(0.876543\pi\)
\(734\) −3.78943e8 3.78943e8i −0.958265 0.958265i
\(735\) 5.64110e7 + 5.64110e7i 0.142070 + 0.142070i
\(736\) −1.21448e8 −0.304619
\(737\) 9.76068e7 0.243825
\(738\) −1.86199e7 + 1.86199e7i −0.0463242 + 0.0463242i
\(739\) 3.51348e8i 0.870571i −0.900293 0.435285i \(-0.856648\pi\)
0.900293 0.435285i \(-0.143352\pi\)
\(740\) 3.67041e7 + 1.32814e8i 0.0905774 + 0.327754i
\(741\) −6.61383e7 −0.162554
\(742\) 1.73346e8 + 1.73346e8i 0.424329 + 0.424329i
\(743\) 6.49894e8i 1.58444i 0.610235 + 0.792220i \(0.291075\pi\)
−0.610235 + 0.792220i \(0.708925\pi\)
\(744\) 2.96969e7i 0.0721096i
\(745\) 1.16261e8 1.16261e8i 0.281167 0.281167i
\(746\) 1.01873e8 1.01873e8i 0.245382 0.245382i
\(747\) −5.78959e8 −1.38895
\(748\) 4.74087e7 4.74087e7i 0.113280 0.113280i
\(749\) −3.26211e8 −0.776342
\(750\) 1.24125e8 0.294222
\(751\) 4.24773e8i 1.00285i −0.865200 0.501427i \(-0.832809\pi\)
0.865200 0.501427i \(-0.167191\pi\)
\(752\) 3.41702e7 0.0803514
\(753\) −7.70465e7 + 7.70465e7i −0.180455 + 0.180455i
\(754\) −1.19455e7 1.19455e7i −0.0278670 0.0278670i
\(755\) 8.03640e7 + 8.03640e7i 0.186733 + 0.186733i
\(756\) −8.03582e7 −0.185979
\(757\) −3.04769e8 + 3.04769e8i −0.702560 + 0.702560i −0.964959 0.262399i \(-0.915486\pi\)
0.262399 + 0.964959i \(0.415486\pi\)
\(758\) 2.14182e8 + 2.14182e8i 0.491786 + 0.491786i
\(759\) −1.79633e8 + 1.79633e8i −0.410829 + 0.410829i
\(760\) 6.40368e7 + 6.40368e7i 0.145878 + 0.145878i
\(761\) 6.23083e8i 1.41381i −0.707307 0.706907i \(-0.750090\pi\)
0.707307 0.706907i \(-0.249910\pi\)
\(762\) 8.29931e7 8.29931e7i 0.187576 0.187576i
\(763\) −5.56907e7 + 5.56907e7i −0.125374 + 0.125374i
\(764\) 1.38757e8 + 1.38757e8i 0.311153 + 0.311153i
\(765\) 9.69046e7i 0.216451i
\(766\) 2.53054e8 0.563025
\(767\) 2.15687e7i 0.0478011i
\(768\) 1.12663e7i 0.0248713i
\(769\) −1.62617e8 1.62617e8i −0.357592 0.357592i 0.505332 0.862925i \(-0.331370\pi\)
−0.862925 + 0.505332i \(0.831370\pi\)
\(770\) 9.44091e7i 0.206796i
\(771\) −2.28269e8 2.28269e8i −0.498063 0.498063i
\(772\) −1.02221e8 1.02221e8i −0.222170 0.222170i
\(773\) 7.37384e8 1.59645 0.798225 0.602360i \(-0.205773\pi\)
0.798225 + 0.602360i \(0.205773\pi\)
\(774\) 1.63052e8 0.351644
\(775\) −9.06738e7 + 9.06738e7i −0.194795 + 0.194795i
\(776\) 1.41772e7i 0.0303393i
\(777\) −4.67283e7 + 8.24192e7i −0.0996131 + 0.175697i
\(778\) 2.02534e8 0.430089
\(779\) 3.15716e7 + 3.15716e7i 0.0667857 + 0.0667857i
\(780\) 3.05719e7i 0.0644227i
\(781\) 3.17637e8i 0.666773i
\(782\) 1.55810e8 1.55810e8i 0.325817 0.325817i
\(783\) −2.91221e7 + 2.91221e7i −0.0606649 + 0.0606649i
\(784\) 8.94391e7 0.185601
\(785\) −1.91501e8 + 1.91501e8i −0.395878 + 0.395878i
\(786\) 1.67283e8 0.344496
\(787\) 9.66269e8 1.98232 0.991160 0.132672i \(-0.0423556\pi\)
0.991160 + 0.132672i \(0.0423556\pi\)
\(788\) 1.29529e8i 0.264721i
\(789\) 1.79104e8 0.364649
\(790\) −9.33698e7 + 9.33698e7i −0.189376 + 0.189376i
\(791\) −2.83994e8 2.83994e8i −0.573824 0.573824i
\(792\) 8.85665e7 + 8.85665e7i 0.178276 + 0.178276i
\(793\) −8.19242e7 −0.164283
\(794\) 2.90035e8 2.90035e8i 0.579415 0.579415i
\(795\) 1.60778e8 + 1.60778e8i 0.319981 + 0.319981i
\(796\) −8.01508e7 + 8.01508e7i −0.158916 + 0.158916i
\(797\) 3.97964e8 + 3.97964e8i 0.786084 + 0.786084i 0.980850 0.194766i \(-0.0623947\pi\)
−0.194766 + 0.980850i \(0.562395\pi\)
\(798\) 6.22690e7i 0.122536i
\(799\) −4.38380e7 + 4.38380e7i −0.0859431 + 0.0859431i
\(800\) 3.43995e7 3.43995e7i 0.0671865 0.0671865i
\(801\) −4.33169e7 4.33169e7i −0.0842868 0.0842868i
\(802\) 2.58709e8i 0.501519i
\(803\) 7.28055e8 1.40610
\(804\) 2.97583e7i 0.0572585i
\(805\) 3.10277e8i 0.594788i
\(806\) 6.38831e7 + 6.38831e7i 0.122006 + 0.122006i
\(807\) 3.22191e8i 0.613045i
\(808\) 5.91417e7 + 5.91417e7i 0.112114 + 0.112114i
\(809\) −2.65553e8 2.65553e8i −0.501539 0.501539i 0.410377 0.911916i \(-0.365397\pi\)
−0.911916 + 0.410377i \(0.865397\pi\)
\(810\) 1.40562e8 0.264492
\(811\) 9.25828e8 1.73567 0.867836 0.496851i \(-0.165510\pi\)
0.867836 + 0.496851i \(0.165510\pi\)
\(812\) −1.12466e7 + 1.12466e7i −0.0210065 + 0.0210065i
\(813\) 5.38185e7i 0.100152i
\(814\) 3.11460e8 8.60745e7i 0.577470 0.159588i
\(815\) −1.71552e8 −0.316900
\(816\) 1.44539e7 + 1.44539e7i 0.0266021 + 0.0266021i
\(817\) 2.76468e8i 0.506966i
\(818\) 5.36309e8i 0.979841i
\(819\) −7.90000e7 + 7.90000e7i −0.143805 + 0.143805i
\(820\) −1.45937e7 + 1.45937e7i −0.0264682 + 0.0264682i
\(821\) −7.54703e8 −1.36379 −0.681893 0.731452i \(-0.738843\pi\)
−0.681893 + 0.731452i \(0.738843\pi\)
\(822\) −7.75968e7 + 7.75968e7i −0.139710 + 0.139710i
\(823\) −8.06746e8 −1.44723 −0.723615 0.690204i \(-0.757521\pi\)
−0.723615 + 0.690204i \(0.757521\pi\)
\(824\) −1.05126e8 −0.187900
\(825\) 1.01760e8i 0.181224i
\(826\) −2.03069e7 −0.0360332
\(827\) 4.22245e7 4.22245e7i 0.0746531 0.0746531i −0.668794 0.743447i \(-0.733189\pi\)
0.743447 + 0.668794i \(0.233189\pi\)
\(828\) 2.91076e8 + 2.91076e8i 0.512761 + 0.512761i
\(829\) −2.11031e8 2.11031e8i −0.370411 0.370411i 0.497216 0.867627i \(-0.334356\pi\)
−0.867627 + 0.497216i \(0.834356\pi\)
\(830\) −4.53771e8 −0.793602
\(831\) 1.53548e8 1.53548e8i 0.267572 0.267572i
\(832\) −2.42357e7 2.42357e7i −0.0420810 0.0420810i
\(833\) −1.14744e8 + 1.14744e8i −0.198516 + 0.198516i
\(834\) −8.76871e7 8.76871e7i −0.151160 0.151160i
\(835\) 5.93803e7i 0.101996i
\(836\) 1.50172e8 1.50172e8i 0.257022 0.257022i
\(837\) 1.55742e8 1.55742e8i 0.265600 0.265600i
\(838\) 7.67976e7 + 7.67976e7i 0.130501 + 0.130501i
\(839\) 6.74327e8i 1.14179i −0.821024 0.570893i \(-0.806597\pi\)
0.821024 0.570893i \(-0.193403\pi\)
\(840\) −2.87834e7 −0.0485628
\(841\) 5.86672e8i 0.986296i
\(842\) 2.55655e8i 0.428270i
\(843\) −1.68773e7 1.68773e7i −0.0281721 0.0281721i
\(844\) 2.77473e8i 0.461523i
\(845\) 2.24379e8 + 2.24379e8i 0.371889 + 0.371889i
\(846\) −8.18960e7 8.18960e7i −0.135254 0.135254i
\(847\) −8.70073e7 −0.143188
\(848\) 2.54911e8 0.418024
\(849\) −2.31686e8 + 2.31686e8i −0.378596 + 0.378596i
\(850\) 8.82645e7i 0.143724i
\(851\) 1.02362e9 2.82886e8i 1.66093 0.459010i
\(852\) −9.68409e7 −0.156581
\(853\) 6.10544e8 + 6.10544e8i 0.983717 + 0.983717i 0.999870 0.0161525i \(-0.00514173\pi\)
−0.0161525 + 0.999870i \(0.505142\pi\)
\(854\) 7.71314e7i 0.123839i
\(855\) 3.06955e8i 0.491108i
\(856\) −2.39852e8 + 2.39852e8i −0.382404 + 0.382404i
\(857\) 7.64610e8 7.64610e8i 1.21478 1.21478i 0.245343 0.969436i \(-0.421099\pi\)
0.969436 0.245343i \(-0.0789006\pi\)
\(858\) −7.16938e7 −0.113506
\(859\) −6.32535e8 + 6.32535e8i −0.997941 + 0.997941i −0.999998 0.00205690i \(-0.999345\pi\)
0.00205690 + 0.999998i \(0.499345\pi\)
\(860\) 1.27795e8 0.200918
\(861\) −1.41909e7 −0.0222330
\(862\) 4.39402e8i 0.686025i
\(863\) 2.75363e7 0.0428424 0.0214212 0.999771i \(-0.493181\pi\)
0.0214212 + 0.999771i \(0.493181\pi\)
\(864\) −5.90847e7 + 5.90847e7i −0.0916081 + 0.0916081i
\(865\) 2.50382e8 + 2.50382e8i 0.386861 + 0.386861i
\(866\) 1.72095e8 + 1.72095e8i 0.264981 + 0.264981i
\(867\) 2.22257e8 0.341034
\(868\) 6.01458e7 6.01458e7i 0.0919699 0.0919699i
\(869\) 2.18961e8 + 2.18961e8i 0.333662 + 0.333662i
\(870\) −1.04312e7 + 1.04312e7i −0.0158408 + 0.0158408i
\(871\) 6.40151e7 + 6.40151e7i 0.0968786 + 0.0968786i
\(872\) 8.18949e7i 0.123512i
\(873\) −3.39786e7 + 3.39786e7i −0.0510697 + 0.0510697i
\(874\) 4.93543e8 4.93543e8i 0.739249 0.739249i
\(875\) −2.51393e8 2.51393e8i −0.375257 0.375257i
\(876\) 2.21969e8i 0.330202i
\(877\) −9.49722e8 −1.40798 −0.703992 0.710208i \(-0.748601\pi\)
−0.703992 + 0.710208i \(0.748601\pi\)
\(878\) 7.65420e8i 1.13088i
\(879\) 1.91709e7i 0.0282277i
\(880\) 6.94158e7 + 6.94158e7i 0.101862 + 0.101862i
\(881\) 4.13952e8i 0.605371i −0.953090 0.302686i \(-0.902117\pi\)
0.953090 0.302686i \(-0.0978832\pi\)
\(882\) −2.14360e8 2.14360e8i −0.312419 0.312419i
\(883\) 4.01091e8 + 4.01091e8i 0.582587 + 0.582587i 0.935614 0.353026i \(-0.114847\pi\)
−0.353026 + 0.935614i \(0.614847\pi\)
\(884\) 6.21856e7 0.0900188
\(885\) −1.88345e7 −0.0271722
\(886\) −5.30890e8 + 5.30890e8i −0.763315 + 0.763315i
\(887\) 6.14494e8i 0.880535i −0.897867 0.440267i \(-0.854884\pi\)
0.897867 0.440267i \(-0.145116\pi\)
\(888\) 2.62423e7 + 9.49578e7i 0.0374769 + 0.135610i
\(889\) −3.36175e8 −0.478476
\(890\) −3.39505e7 3.39505e7i −0.0481588 0.0481588i
\(891\) 3.29630e8i 0.466009i
\(892\) 4.54061e7i 0.0639764i
\(893\) −1.38862e8 + 1.38862e8i −0.194997 + 0.194997i
\(894\) 8.31229e7 8.31229e7i 0.116334 0.116334i
\(895\) −3.30527e8 −0.461040
\(896\) −2.28179e7 + 2.28179e7i −0.0317213 + 0.0317213i
\(897\) −2.35623e8 −0.326468
\(898\) −5.01454e8 −0.692471
\(899\) 4.35941e7i 0.0599996i
\(900\) −1.64891e8 −0.226188
\(901\) −3.27034e8 + 3.27034e8i −0.447114 + 0.447114i
\(902\) 3.42236e7 + 3.42236e7i 0.0466343 + 0.0466343i
\(903\) 6.21337e7 + 6.21337e7i 0.0843848 + 0.0843848i
\(904\) −4.17622e8 −0.565299
\(905\) −5.17285e8 + 5.17285e8i −0.697885 + 0.697885i
\(906\) 5.74578e7 + 5.74578e7i 0.0772617 + 0.0772617i
\(907\) 7.66542e8 7.66542e8i 1.02734 1.02734i 0.0277236 0.999616i \(-0.491174\pi\)
0.999616 0.0277236i \(-0.00882582\pi\)
\(908\) 3.77582e8 + 3.77582e8i 0.504375 + 0.504375i
\(909\) 2.83491e8i 0.377440i
\(910\) −6.19178e7 + 6.19178e7i −0.0821659 + 0.0821659i
\(911\) 1.50215e8 1.50215e8i 0.198681 0.198681i −0.600753 0.799435i \(-0.705133\pi\)
0.799435 + 0.600753i \(0.205133\pi\)
\(912\) 4.57843e7 + 4.57843e7i 0.0603576 + 0.0603576i
\(913\) 1.06413e9i 1.39825i
\(914\) 4.12866e8 0.540717
\(915\) 7.15390e7i 0.0933855i
\(916\) 5.92215e7i 0.0770536i
\(917\) −3.38801e8 3.38801e8i −0.439376 0.439376i
\(918\) 1.51603e8i 0.195966i
\(919\) −2.36187e8 2.36187e8i −0.304306 0.304306i 0.538390 0.842696i \(-0.319033\pi\)
−0.842696 + 0.538390i \(0.819033\pi\)
\(920\) 2.28137e8 + 2.28137e8i 0.292976 + 0.292976i
\(921\) 2.36884e8 0.303219
\(922\) −6.09079e8 −0.777107
\(923\) −2.08321e8 + 2.08321e8i −0.264928 + 0.264928i
\(924\) 6.74996e7i 0.0855628i
\(925\) −2.09809e8 + 3.70061e8i −0.265094 + 0.467572i
\(926\) −1.07872e9 −1.35855
\(927\) 2.51956e8 + 2.51956e8i 0.316290 + 0.316290i
\(928\) 1.65385e7i 0.0206944i
\(929\) 1.45716e9i 1.81744i 0.417408 + 0.908719i \(0.362938\pi\)
−0.417408 + 0.908719i \(0.637062\pi\)
\(930\) 5.57849e7 5.57849e7i 0.0693533 0.0693533i
\(931\) −3.63465e8 + 3.63465e8i −0.450415 + 0.450415i
\(932\) −3.86446e8 −0.477355
\(933\) −2.39111e8 + 2.39111e8i −0.294412 + 0.294412i
\(934\) −7.45976e8 −0.915555
\(935\) −1.78112e8 −0.217900
\(936\) 1.16172e8i 0.141669i
\(937\) −2.91172e7 −0.0353941 −0.0176970 0.999843i \(-0.505633\pi\)
−0.0176970 + 0.999843i \(0.505633\pi\)
\(938\) 6.02700e7 6.02700e7i 0.0730286 0.0730286i
\(939\) 2.29803e8 + 2.29803e8i 0.277561 + 0.277561i
\(940\) −6.41877e7 6.41877e7i −0.0772802 0.0772802i
\(941\) −6.56222e8 −0.787556 −0.393778 0.919205i \(-0.628832\pi\)
−0.393778 + 0.919205i \(0.628832\pi\)
\(942\) −1.36917e8 + 1.36917e8i −0.163797 + 0.163797i
\(943\) 1.12476e8 + 1.12476e8i 0.134130 + 0.134130i
\(944\) −1.49310e7 + 1.49310e7i −0.0177489 + 0.0177489i
\(945\) 1.50951e8 + 1.50951e8i 0.178871 + 0.178871i
\(946\) 2.99691e8i 0.353998i
\(947\) 6.08060e8 6.08060e8i 0.715972 0.715972i −0.251806 0.967778i \(-0.581024\pi\)
0.967778 + 0.251806i \(0.0810243\pi\)
\(948\) −6.67565e7 + 6.67565e7i −0.0783554 + 0.0783554i
\(949\) 4.77492e8 + 4.77492e8i 0.558685 + 0.558685i
\(950\) 2.79587e8i 0.326096i
\(951\) 2.93863e8 0.341667
\(952\) 5.85476e7i 0.0678576i
\(953\) 1.32808e9i 1.53443i 0.641390 + 0.767215i \(0.278358\pi\)
−0.641390 + 0.767215i \(0.721642\pi\)
\(954\) −6.10948e8 6.10948e8i −0.703654 0.703654i
\(955\) 5.21300e8i 0.598519i
\(956\) 9.00054e7 + 9.00054e7i 0.103014 + 0.103014i
\(957\) 2.44621e7 + 2.44621e7i 0.0279098 + 0.0279098i
\(958\) −4.75719e8 −0.541071
\(959\) 3.14317e8 0.356379
\(960\) −2.11634e7 + 2.11634e7i −0.0239206 + 0.0239206i
\(961\) 6.54368e8i 0.737313i
\(962\) 2.60722e8 + 1.47818e8i 0.292854 + 0.166036i
\(963\) 1.14971e9 1.28739
\(964\) −2.40980e8 2.40980e8i −0.268998 0.268998i
\(965\) 3.84037e8i 0.427357i
\(966\) 2.21839e8i 0.246097i
\(967\) −8.25481e8 + 8.25481e8i −0.912909 + 0.912909i −0.996500 0.0835907i \(-0.973361\pi\)
0.0835907 + 0.996500i \(0.473361\pi\)
\(968\) −6.39735e7 + 6.39735e7i −0.0705301 + 0.0705301i
\(969\) −1.17476e8 −0.129116
\(970\) −2.66315e7 + 2.66315e7i −0.0291796 + 0.0291796i
\(971\) −6.71474e8 −0.733452 −0.366726 0.930329i \(-0.619521\pi\)
−0.366726 + 0.930329i \(0.619521\pi\)
\(972\) 4.37003e8 0.475867
\(973\) 3.55189e8i 0.385585i
\(974\) −5.94524e8 −0.643417
\(975\) 6.67391e7 6.67391e7i 0.0720056 0.0720056i
\(976\) 5.67121e7 + 5.67121e7i 0.0609996 + 0.0609996i
\(977\) 3.73876e8 + 3.73876e8i 0.400907 + 0.400907i 0.878553 0.477646i \(-0.158510\pi\)
−0.477646 + 0.878553i \(0.658510\pi\)
\(978\) −1.22654e8 −0.131119
\(979\) −7.96169e7 + 7.96169e7i −0.0848510 + 0.0848510i
\(980\) −1.68009e8 1.68009e8i −0.178506 0.178506i
\(981\) 1.96279e8 1.96279e8i 0.207905 0.207905i
\(982\) 1.22700e8 + 1.22700e8i 0.129572 + 0.129572i
\(983\) 1.44822e9i 1.52466i −0.647187 0.762331i \(-0.724055\pi\)
0.647187 0.762331i \(-0.275945\pi\)
\(984\) −1.04341e7 + 1.04341e7i −0.0109514 + 0.0109514i
\(985\) −2.43316e8 + 2.43316e8i −0.254603 + 0.254603i
\(986\) −2.12179e7 2.12179e7i −0.0221346 0.0221346i
\(987\) 6.24158e7i 0.0649147i
\(988\) 1.96979e8 0.204244
\(989\) 9.84942e8i 1.01817i
\(990\) 3.32739e8i 0.342924i
\(991\) −1.00667e9 1.00667e9i −1.03434 1.03434i −0.999389 0.0349531i \(-0.988872\pi\)
−0.0349531 0.999389i \(-0.511128\pi\)
\(992\) 8.84463e7i 0.0906034i
\(993\) 3.31602e7 + 3.31602e7i 0.0338665 + 0.0338665i
\(994\) 1.96134e8 + 1.96134e8i 0.199707 + 0.199707i
\(995\) 3.01122e8 0.305684
\(996\) −3.24432e8 −0.328357
\(997\) −1.29813e9 + 1.29813e9i −1.30989 + 1.30989i −0.388396 + 0.921493i \(0.626971\pi\)
−0.921493 + 0.388396i \(0.873029\pi\)
\(998\) 1.96140e8i 0.197322i
\(999\) 3.60369e8 6.35618e8i 0.361452 0.637529i
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.a.31.3 18
37.6 odd 4 inner 74.7.d.a.43.7 yes 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
74.7.d.a.31.3 18 1.1 even 1 trivial
74.7.d.a.43.7 yes 18 37.6 odd 4 inner