Properties

Label 60.7.f.a.19.1
Level $60$
Weight $7$
Character 60.19
Analytic conductor $13.803$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

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

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(13.8032450172\)
Analytic rank: \(0\)
Dimension: \(36\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 19.1
Character \(\chi\) \(=\) 60.19
Dual form 60.7.f.a.19.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-7.93273 - 1.03526i) q^{2} +15.5885 q^{3} +(61.8565 + 16.4248i) q^{4} +(-80.2400 + 95.8465i) q^{5} +(-123.659 - 16.1381i) q^{6} -143.606 q^{7} +(-473.687 - 194.331i) q^{8} +243.000 q^{9} +O(q^{10})\) \(q+(-7.93273 - 1.03526i) q^{2} +15.5885 q^{3} +(61.8565 + 16.4248i) q^{4} +(-80.2400 + 95.8465i) q^{5} +(-123.659 - 16.1381i) q^{6} -143.606 q^{7} +(-473.687 - 194.331i) q^{8} +243.000 q^{9} +(735.748 - 677.255i) q^{10} -1568.78i q^{11} +(964.247 + 256.038i) q^{12} +3878.76i q^{13} +(1139.19 + 148.669i) q^{14} +(-1250.82 + 1494.10i) q^{15} +(3556.45 + 2031.96i) q^{16} -5035.60i q^{17} +(-1927.65 - 251.567i) q^{18} -11740.4i q^{19} +(-6537.63 + 4610.80i) q^{20} -2238.59 q^{21} +(-1624.09 + 12444.7i) q^{22} -21747.5 q^{23} +(-7384.05 - 3029.32i) q^{24} +(-2748.09 - 15381.4i) q^{25} +(4015.52 - 30769.2i) q^{26} +3788.00 q^{27} +(-8882.95 - 2358.70i) q^{28} -40105.7 q^{29} +(11469.2 - 10557.4i) q^{30} +223.114i q^{31} +(-26108.8 - 19800.9i) q^{32} -24454.9i q^{33} +(-5213.14 + 39946.1i) q^{34} +(11522.9 - 13764.1i) q^{35} +(15031.1 + 3991.23i) q^{36} -17396.7i q^{37} +(-12154.3 + 93133.1i) q^{38} +60464.0i q^{39} +(56634.6 - 29808.1i) q^{40} +2197.54 q^{41} +(17758.2 + 2317.52i) q^{42} -3196.47 q^{43} +(25766.9 - 97039.2i) q^{44} +(-19498.3 + 23290.7i) q^{45} +(172517. + 22514.2i) q^{46} +10495.8 q^{47} +(55439.6 + 31675.2i) q^{48} -97026.4 q^{49} +(5876.12 + 124862. i) q^{50} -78497.3i q^{51} +(-63708.0 + 239927. i) q^{52} -199848. i q^{53} +(-30049.2 - 3921.55i) q^{54} +(150362. + 125879. i) q^{55} +(68024.2 + 27907.1i) q^{56} -183014. i q^{57} +(318148. + 41519.7i) q^{58} +149784. i q^{59} +(-101911. + 71875.2i) q^{60} +226558. q^{61} +(230.980 - 1769.90i) q^{62} -34896.2 q^{63} +(186615. + 184104. i) q^{64} +(-371766. - 311232. i) q^{65} +(-25317.0 + 193994. i) q^{66} -235597. q^{67} +(82708.9 - 311485. i) q^{68} -339009. q^{69} +(-105658. + 97257.8i) q^{70} +170700. i q^{71} +(-115106. - 47222.5i) q^{72} +245829. i q^{73} +(-18010.0 + 138003. i) q^{74} +(-42838.5 - 239773. i) q^{75} +(192833. - 726217. i) q^{76} +225286. i q^{77} +(62595.7 - 479644. i) q^{78} -373075. i q^{79} +(-480126. + 177828. i) q^{80} +59049.0 q^{81} +(-17432.5 - 2275.02i) q^{82} +380458. q^{83} +(-138471. - 36768.5i) q^{84} +(482645. + 404057. i) q^{85} +(25356.8 + 3309.17i) q^{86} -625186. q^{87} +(-304863. + 743111. i) q^{88} +421299. q^{89} +(178787. - 164573. i) q^{90} -557013. i q^{91} +(-1.34522e6 - 357198. i) q^{92} +3478.00i q^{93} +(-83260.6 - 10865.9i) q^{94} +(1.12527e6 + 942046. i) q^{95} +(-406995. - 308665. i) q^{96} +855309. i q^{97} +(769684. + 100447. i) q^{98} -381213. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9} - 1422 q^{10} + 15484 q^{14} + 1266 q^{16} - 2188 q^{20} - 9234 q^{24} + 13812 q^{25} - 32052 q^{26} - 36920 q^{29} - 24300 q^{30} - 156204 q^{34} - 16038 q^{36} + 7674 q^{40} + 341848 q^{41} + 74892 q^{44} + 10692 q^{45} + 478080 q^{46} + 482556 q^{49} - 191448 q^{50} - 39366 q^{54} - 926132 q^{56} + 126846 q^{60} - 455976 q^{61} - 618 q^{64} - 624192 q^{65} - 127332 q^{66} - 541728 q^{69} - 1871304 q^{70} - 612324 q^{74} - 1566456 q^{76} + 2360972 q^{80} + 2125764 q^{81} + 858276 q^{84} + 2280864 q^{85} + 5157592 q^{86} - 1806104 q^{89} - 345546 q^{90} - 3121992 q^{94} - 4040118 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.93273 1.03526i −0.991592 0.129407i
\(3\) 15.5885 0.577350
\(4\) 61.8565 + 16.4248i 0.966508 + 0.256638i
\(5\) −80.2400 + 95.8465i −0.641920 + 0.766772i
\(6\) −123.659 16.1381i −0.572496 0.0747132i
\(7\) −143.606 −0.418676 −0.209338 0.977843i \(-0.567131\pi\)
−0.209338 + 0.977843i \(0.567131\pi\)
\(8\) −473.687 194.331i −0.925170 0.379553i
\(9\) 243.000 0.333333
\(10\) 735.748 677.255i 0.735748 0.677255i
\(11\) 1568.78i 1.17865i −0.807897 0.589324i \(-0.799394\pi\)
0.807897 0.589324i \(-0.200606\pi\)
\(12\) 964.247 + 256.038i 0.558013 + 0.148170i
\(13\) 3878.76i 1.76548i 0.469860 + 0.882741i \(0.344305\pi\)
−0.469860 + 0.882741i \(0.655695\pi\)
\(14\) 1139.19 + 148.669i 0.415155 + 0.0541796i
\(15\) −1250.82 + 1494.10i −0.370613 + 0.442696i
\(16\) 3556.45 + 2031.96i 0.868274 + 0.496085i
\(17\) 5035.60i 1.02495i −0.858701 0.512477i \(-0.828728\pi\)
0.858701 0.512477i \(-0.171272\pi\)
\(18\) −1927.65 251.567i −0.330531 0.0431357i
\(19\) 11740.4i 1.71167i −0.517247 0.855836i \(-0.673043\pi\)
0.517247 0.855836i \(-0.326957\pi\)
\(20\) −6537.63 + 4610.80i −0.817203 + 0.576350i
\(21\) −2238.59 −0.241723
\(22\) −1624.09 + 12444.7i −0.152525 + 1.16874i
\(23\) −21747.5 −1.78741 −0.893706 0.448652i \(-0.851904\pi\)
−0.893706 + 0.448652i \(0.851904\pi\)
\(24\) −7384.05 3029.32i −0.534147 0.219135i
\(25\) −2748.09 15381.4i −0.175878 0.984412i
\(26\) 4015.52 30769.2i 0.228466 1.75064i
\(27\) 3788.00 0.192450
\(28\) −8882.95 2358.70i −0.404653 0.107448i
\(29\) −40105.7 −1.64442 −0.822208 0.569187i \(-0.807258\pi\)
−0.822208 + 0.569187i \(0.807258\pi\)
\(30\) 11469.2 10557.4i 0.424784 0.391014i
\(31\) 223.114i 0.00748930i 0.999993 + 0.00374465i \(0.00119196\pi\)
−0.999993 + 0.00374465i \(0.998808\pi\)
\(32\) −26108.8 19800.9i −0.796776 0.604275i
\(33\) 24454.9i 0.680492i
\(34\) −5213.14 + 39946.1i −0.132636 + 1.01634i
\(35\) 11522.9 13764.1i 0.268756 0.321029i
\(36\) 15031.1 + 3991.23i 0.322169 + 0.0855460i
\(37\) 17396.7i 0.343448i −0.985145 0.171724i \(-0.945066\pi\)
0.985145 0.171724i \(-0.0549337\pi\)
\(38\) −12154.3 + 93133.1i −0.221503 + 1.69728i
\(39\) 60464.0i 1.01930i
\(40\) 56634.6 29808.1i 0.884915 0.465752i
\(41\) 2197.54 0.0318849 0.0159425 0.999873i \(-0.494925\pi\)
0.0159425 + 0.999873i \(0.494925\pi\)
\(42\) 17758.2 + 2317.52i 0.239690 + 0.0312806i
\(43\) −3196.47 −0.0402036 −0.0201018 0.999798i \(-0.506399\pi\)
−0.0201018 + 0.999798i \(0.506399\pi\)
\(44\) 25766.9 97039.2i 0.302486 1.13917i
\(45\) −19498.3 + 23290.7i −0.213973 + 0.255591i
\(46\) 172517. + 22514.2i 1.77238 + 0.231304i
\(47\) 10495.8 0.101093 0.0505467 0.998722i \(-0.483904\pi\)
0.0505467 + 0.998722i \(0.483904\pi\)
\(48\) 55439.6 + 31675.2i 0.501298 + 0.286415i
\(49\) −97026.4 −0.824711
\(50\) 5876.12 + 124862.i 0.0470090 + 0.998894i
\(51\) 78497.3i 0.591758i
\(52\) −63708.0 + 239927.i −0.453090 + 1.70635i
\(53\) 199848.i 1.34237i −0.741289 0.671186i \(-0.765785\pi\)
0.741289 0.671186i \(-0.234215\pi\)
\(54\) −30049.2 3921.55i −0.190832 0.0249044i
\(55\) 150362. + 125879.i 0.903753 + 0.756597i
\(56\) 68024.2 + 27907.1i 0.387346 + 0.158910i
\(57\) 183014.i 0.988235i
\(58\) 318148. + 41519.7i 1.63059 + 0.212799i
\(59\) 149784.i 0.729304i 0.931144 + 0.364652i \(0.118812\pi\)
−0.931144 + 0.364652i \(0.881188\pi\)
\(60\) −101911. + 71875.2i −0.471812 + 0.332756i
\(61\) 226558. 0.998137 0.499068 0.866563i \(-0.333676\pi\)
0.499068 + 0.866563i \(0.333676\pi\)
\(62\) 230.980 1769.90i 0.000969168 0.00742632i
\(63\) −34896.2 −0.139559
\(64\) 186615. + 184104.i 0.711879 + 0.702302i
\(65\) −371766. 311232.i −1.35372 1.13330i
\(66\) −25317.0 + 193994.i −0.0880605 + 0.674770i
\(67\) −235597. −0.783330 −0.391665 0.920108i \(-0.628101\pi\)
−0.391665 + 0.920108i \(0.628101\pi\)
\(68\) 82708.9 311485.i 0.263042 0.990626i
\(69\) −339009. −1.03196
\(70\) −105658. + 97257.8i −0.308040 + 0.283550i
\(71\) 170700.i 0.476934i 0.971151 + 0.238467i \(0.0766448\pi\)
−0.971151 + 0.238467i \(0.923355\pi\)
\(72\) −115106. 47222.5i −0.308390 0.126518i
\(73\) 245829.i 0.631923i 0.948772 + 0.315962i \(0.102327\pi\)
−0.948772 + 0.315962i \(0.897673\pi\)
\(74\) −18010.0 + 138003.i −0.0444446 + 0.340560i
\(75\) −42838.5 239773.i −0.101543 0.568351i
\(76\) 192833. 726217.i 0.439280 1.65434i
\(77\) 225286.i 0.493471i
\(78\) 62595.7 479644.i 0.131905 1.01073i
\(79\) 373075.i 0.756684i −0.925666 0.378342i \(-0.876494\pi\)
0.925666 0.378342i \(-0.123506\pi\)
\(80\) −480126. + 177828.i −0.937746 + 0.347321i
\(81\) 59049.0 0.111111
\(82\) −17432.5 2275.02i −0.0316168 0.00412614i
\(83\) 380458. 0.665384 0.332692 0.943036i \(-0.392043\pi\)
0.332692 + 0.943036i \(0.392043\pi\)
\(84\) −138471. 36768.5i −0.233627 0.0620352i
\(85\) 482645. + 404057.i 0.785906 + 0.657939i
\(86\) 25356.8 + 3309.17i 0.0398656 + 0.00520264i
\(87\) −625186. −0.949404
\(88\) −304863. + 743111.i −0.447359 + 1.09045i
\(89\) 421299. 0.597614 0.298807 0.954314i \(-0.403411\pi\)
0.298807 + 0.954314i \(0.403411\pi\)
\(90\) 178787. 164573.i 0.245249 0.225752i
\(91\) 557013.i 0.739165i
\(92\) −1.34522e6 357198.i −1.72755 0.458718i
\(93\) 3478.00i 0.00432395i
\(94\) −83260.6 10865.9i −0.100243 0.0130822i
\(95\) 1.12527e6 + 942046.i 1.31246 + 1.09876i
\(96\) −406995. 308665.i −0.460019 0.348878i
\(97\) 855309.i 0.937147i 0.883425 + 0.468573i \(0.155232\pi\)
−0.883425 + 0.468573i \(0.844768\pi\)
\(98\) 769684. + 100447.i 0.817776 + 0.106723i
\(99\) 381213.i 0.392882i
\(100\) 82650.3 996579.i 0.0826503 0.996579i
\(101\) 514825. 0.499684 0.249842 0.968287i \(-0.419621\pi\)
0.249842 + 0.968287i \(0.419621\pi\)
\(102\) −81264.8 + 622698.i −0.0765776 + 0.586782i
\(103\) −1.35064e6 −1.23603 −0.618015 0.786166i \(-0.712063\pi\)
−0.618015 + 0.786166i \(0.712063\pi\)
\(104\) 753765. 1.83732e6i 0.670094 1.63337i
\(105\) 179625. 214561.i 0.155166 0.185346i
\(106\) −206894. + 1.58534e6i −0.173712 + 1.33108i
\(107\) −717435. −0.585641 −0.292820 0.956167i \(-0.594594\pi\)
−0.292820 + 0.956167i \(0.594594\pi\)
\(108\) 234312. + 62217.2i 0.186004 + 0.0493900i
\(109\) 339995. 0.262538 0.131269 0.991347i \(-0.458095\pi\)
0.131269 + 0.991347i \(0.458095\pi\)
\(110\) −1.06246e6 1.15423e6i −0.798245 0.867187i
\(111\) 271187.i 0.198290i
\(112\) −510727. 291802.i −0.363525 0.207699i
\(113\) 465203.i 0.322409i 0.986921 + 0.161205i \(0.0515379\pi\)
−0.986921 + 0.161205i \(0.948462\pi\)
\(114\) −189467. + 1.45180e6i −0.127885 + 0.979925i
\(115\) 1.74502e6 2.08442e6i 1.14738 1.37054i
\(116\) −2.48080e6 658729.i −1.58934 0.422020i
\(117\) 942540.i 0.588494i
\(118\) 155065. 1.18819e6i 0.0943771 0.723171i
\(119\) 723141.i 0.429124i
\(120\) 882846. 464662.i 0.510906 0.268902i
\(121\) −689508. −0.389209
\(122\) −1.79722e6 234546.i −0.989744 0.129166i
\(123\) 34256.3 0.0184088
\(124\) −3664.60 + 13801.0i −0.00192204 + 0.00723846i
\(125\) 1.69476e6 + 970812.i 0.867719 + 0.497056i
\(126\) 276822. + 36126.5i 0.138385 + 0.0180599i
\(127\) −1.03009e6 −0.502878 −0.251439 0.967873i \(-0.580904\pi\)
−0.251439 + 0.967873i \(0.580904\pi\)
\(128\) −1.28977e6 1.65364e6i −0.615010 0.788519i
\(129\) −49828.1 −0.0232116
\(130\) 2.62691e6 + 2.85379e6i 1.19568 + 1.29895i
\(131\) 2.41236e6i 1.07307i 0.843878 + 0.536536i \(0.180267\pi\)
−0.843878 + 0.536536i \(0.819733\pi\)
\(132\) 401667. 1.51269e6i 0.174640 0.657701i
\(133\) 1.68598e6i 0.716636i
\(134\) 1.86892e6 + 243903.i 0.776743 + 0.101368i
\(135\) −303949. + 363066.i −0.123538 + 0.147565i
\(136\) −978574. + 2.38530e6i −0.389024 + 0.948257i
\(137\) 527604.i 0.205185i 0.994723 + 0.102593i \(0.0327138\pi\)
−0.994723 + 0.102593i \(0.967286\pi\)
\(138\) 2.68927e6 + 350962.i 1.02329 + 0.133543i
\(139\) 2.19739e6i 0.818204i 0.912489 + 0.409102i \(0.134158\pi\)
−0.912489 + 0.409102i \(0.865842\pi\)
\(140\) 938841. 662137.i 0.342143 0.241304i
\(141\) 163614. 0.0583663
\(142\) 176718. 1.35412e6i 0.0617186 0.472924i
\(143\) 6.08493e6 2.08088
\(144\) 864217. + 493767.i 0.289425 + 0.165362i
\(145\) 3.21808e6 3.84399e6i 1.05558 1.26089i
\(146\) 254496. 1.95009e6i 0.0817753 0.626610i
\(147\) −1.51249e6 −0.476147
\(148\) 285737. 1.07610e6i 0.0881417 0.331945i
\(149\) −3.55467e6 −1.07458 −0.537292 0.843396i \(-0.680553\pi\)
−0.537292 + 0.843396i \(0.680553\pi\)
\(150\) 91599.7 + 1.94640e6i 0.0271406 + 0.576712i
\(151\) 28179.2i 0.00818459i 0.999992 + 0.00409230i \(0.00130262\pi\)
−0.999992 + 0.00409230i \(0.998697\pi\)
\(152\) −2.28152e6 + 5.56126e6i −0.649670 + 1.58359i
\(153\) 1.22365e6i 0.341652i
\(154\) 233229. 1.78713e6i 0.0638586 0.489322i
\(155\) −21384.7 17902.6i −0.00574258 0.00480753i
\(156\) −993110. + 3.74009e6i −0.261591 + 0.985163i
\(157\) 2.51703e6i 0.650413i −0.945643 0.325207i \(-0.894566\pi\)
0.945643 0.325207i \(-0.105434\pi\)
\(158\) −386228. + 2.95950e6i −0.0979203 + 0.750322i
\(159\) 3.11533e6i 0.775019i
\(160\) 3.99281e6 913611.i 0.974807 0.223050i
\(161\) 3.12306e6 0.748346
\(162\) −468420. 61130.9i −0.110177 0.0143786i
\(163\) −2.44319e6 −0.564150 −0.282075 0.959392i \(-0.591023\pi\)
−0.282075 + 0.959392i \(0.591023\pi\)
\(164\) 135932. + 36094.2i 0.0308170 + 0.00818288i
\(165\) 2.34391e6 + 1.96226e6i 0.521782 + 0.436822i
\(166\) −3.01807e6 393871.i −0.659789 0.0861054i
\(167\) −595753. −0.127914 −0.0639569 0.997953i \(-0.520372\pi\)
−0.0639569 + 0.997953i \(0.520372\pi\)
\(168\) 1.06039e6 + 435028.i 0.223634 + 0.0917465i
\(169\) −1.02180e7 −2.11693
\(170\) −3.41039e6 3.70493e6i −0.694156 0.754108i
\(171\) 2.85291e6i 0.570557i
\(172\) −197722. 52501.5i −0.0388571 0.0103178i
\(173\) 3.88556e6i 0.750440i −0.926936 0.375220i \(-0.877567\pi\)
0.926936 0.375220i \(-0.122433\pi\)
\(174\) 4.95943e6 + 647228.i 0.941421 + 0.122860i
\(175\) 394641. + 2.20886e6i 0.0736357 + 0.412149i
\(176\) 3.18770e6 5.57929e6i 0.584709 1.02339i
\(177\) 2.33490e6i 0.421064i
\(178\) −3.34205e6 436153.i −0.592589 0.0773354i
\(179\) 4.77301e6i 0.832211i 0.909316 + 0.416106i \(0.136605\pi\)
−0.909316 + 0.416106i \(0.863395\pi\)
\(180\) −1.58864e6 + 1.12042e6i −0.272401 + 0.192117i
\(181\) −5.55733e6 −0.937196 −0.468598 0.883412i \(-0.655241\pi\)
−0.468598 + 0.883412i \(0.655241\pi\)
\(182\) −576651. + 4.41863e6i −0.0956531 + 0.732949i
\(183\) 3.53169e6 0.576275
\(184\) 1.03015e7 + 4.22621e6i 1.65366 + 0.678418i
\(185\) 1.66741e6 + 1.39591e6i 0.263346 + 0.220466i
\(186\) 3600.62 27590.0i 0.000559549 0.00428759i
\(187\) −7.89975e6 −1.20806
\(188\) 649235. + 172392.i 0.0977076 + 0.0259444i
\(189\) −543978. −0.0805742
\(190\) −7.95122e6 8.63795e6i −1.15924 1.25936i
\(191\) 2.75996e6i 0.396098i 0.980192 + 0.198049i \(0.0634605\pi\)
−0.980192 + 0.198049i \(0.936540\pi\)
\(192\) 2.90904e6 + 2.86990e6i 0.411004 + 0.405474i
\(193\) 1.01132e7i 1.40675i −0.710820 0.703374i \(-0.751676\pi\)
0.710820 0.703374i \(-0.248324\pi\)
\(194\) 885464. 6.78493e6i 0.121273 0.929267i
\(195\) −5.79526e6 4.85163e6i −0.781572 0.654310i
\(196\) −6.00171e6 1.59364e6i −0.797089 0.211652i
\(197\) 5.31570e6i 0.695284i −0.937627 0.347642i \(-0.886983\pi\)
0.937627 0.347642i \(-0.113017\pi\)
\(198\) −394654. + 3.02406e6i −0.0508418 + 0.389579i
\(199\) 1.03986e7i 1.31952i −0.751477 0.659759i \(-0.770658\pi\)
0.751477 0.659759i \(-0.229342\pi\)
\(200\) −1.68736e6 + 7.82003e6i −0.210920 + 0.977503i
\(201\) −3.67259e6 −0.452256
\(202\) −4.08397e6 532976.i −0.495483 0.0646627i
\(203\) 5.75941e6 0.688477
\(204\) 1.28930e6 4.85556e6i 0.151867 0.571938i
\(205\) −176331. + 210627.i −0.0204676 + 0.0244485i
\(206\) 1.07143e7 + 1.39826e6i 1.22564 + 0.159951i
\(207\) −5.28463e6 −0.595804
\(208\) −7.88151e6 + 1.37946e7i −0.875829 + 1.53292i
\(209\) −1.84180e7 −2.01746
\(210\) −1.64704e6 + 1.51610e6i −0.177847 + 0.163708i
\(211\) 5.65069e6i 0.601525i −0.953699 0.300763i \(-0.902759\pi\)
0.953699 0.300763i \(-0.0972412\pi\)
\(212\) 3.28247e6 1.23619e7i 0.344504 1.29741i
\(213\) 2.66095e6i 0.275358i
\(214\) 5.69122e6 + 742729.i 0.580716 + 0.0757860i
\(215\) 256485. 306370.i 0.0258075 0.0308270i
\(216\) −1.79432e6 736125.i −0.178049 0.0730450i
\(217\) 32040.4i 0.00313559i
\(218\) −2.69709e6 351982.i −0.260331 0.0339743i
\(219\) 3.83209e6i 0.364841i
\(220\) 7.23332e6 + 1.02561e7i 0.679313 + 0.963194i
\(221\) 1.95319e7 1.80954
\(222\) −280748. + 2.15125e6i −0.0256601 + 0.196622i
\(223\) −1.20891e7 −1.09013 −0.545065 0.838394i \(-0.683495\pi\)
−0.545065 + 0.838394i \(0.683495\pi\)
\(224\) 3.74937e6 + 2.84352e6i 0.333591 + 0.252995i
\(225\) −667786. 3.73769e6i −0.0586259 0.328137i
\(226\) 481604. 3.69033e6i 0.0417220 0.319698i
\(227\) 5.54653e6 0.474181 0.237090 0.971488i \(-0.423806\pi\)
0.237090 + 0.971488i \(0.423806\pi\)
\(228\) 3.00598e6 1.13206e7i 0.253618 0.955136i
\(229\) −5.82739e6 −0.485252 −0.242626 0.970120i \(-0.578009\pi\)
−0.242626 + 0.970120i \(0.578009\pi\)
\(230\) −1.60006e7 + 1.47286e7i −1.31509 + 1.21053i
\(231\) 3.51186e6i 0.284906i
\(232\) 1.89975e7 + 7.79378e6i 1.52136 + 0.624143i
\(233\) 6.44278e6i 0.509338i 0.967028 + 0.254669i \(0.0819664\pi\)
−0.967028 + 0.254669i \(0.918034\pi\)
\(234\) 975771. 7.47692e6i 0.0761553 0.583546i
\(235\) −842185. + 1.00599e6i −0.0648939 + 0.0775156i
\(236\) −2.46017e6 + 9.26509e6i −0.187167 + 0.704878i
\(237\) 5.81566e6i 0.436872i
\(238\) 748637. 5.73649e6i 0.0555316 0.425515i
\(239\) 2.58807e7i 1.89576i 0.318632 + 0.947878i \(0.396777\pi\)
−0.318632 + 0.947878i \(0.603223\pi\)
\(240\) −7.48443e6 + 2.77207e6i −0.541408 + 0.200526i
\(241\) 2.39919e7 1.71401 0.857005 0.515308i \(-0.172323\pi\)
0.857005 + 0.515308i \(0.172323\pi\)
\(242\) 5.46968e6 + 713818.i 0.385937 + 0.0503664i
\(243\) 920483. 0.0641500
\(244\) 1.40141e7 + 3.72118e6i 0.964707 + 0.256160i
\(245\) 7.78540e6 9.29964e6i 0.529398 0.632365i
\(246\) −271746. 35464.0i −0.0182540 0.00238223i
\(247\) 4.55381e7 3.02193
\(248\) 43357.9 105686.i 0.00284258 0.00692887i
\(249\) 5.93075e6 0.384159
\(250\) −1.24391e7 9.45570e6i −0.796100 0.605165i
\(251\) 2.34272e7i 1.48149i −0.671787 0.740744i \(-0.734473\pi\)
0.671787 0.740744i \(-0.265527\pi\)
\(252\) −2.15856e6 573164.i −0.134884 0.0358160i
\(253\) 3.41170e7i 2.10673i
\(254\) 8.17141e6 + 1.06640e6i 0.498650 + 0.0650760i
\(255\) 7.52368e6 + 6.29862e6i 0.453743 + 0.379861i
\(256\) 8.51946e6 + 1.44532e7i 0.507799 + 0.861475i
\(257\) 1.57956e7i 0.930544i 0.885168 + 0.465272i \(0.154043\pi\)
−0.885168 + 0.465272i \(0.845957\pi\)
\(258\) 395273. + 51584.8i 0.0230164 + 0.00300374i
\(259\) 2.49826e6i 0.143793i
\(260\) −1.78842e7 2.53579e7i −1.01754 1.44276i
\(261\) −9.74568e6 −0.548139
\(262\) 2.49741e6 1.91366e7i 0.138863 1.06405i
\(263\) −8.68016e6 −0.477156 −0.238578 0.971123i \(-0.576681\pi\)
−0.238578 + 0.971123i \(0.576681\pi\)
\(264\) −4.75234e6 + 1.15839e7i −0.258283 + 0.629571i
\(265\) 1.91548e7 + 1.60358e7i 1.02929 + 0.861695i
\(266\) 1.74543e6 1.33745e7i 0.0927377 0.710610i
\(267\) 6.56740e6 0.345032
\(268\) −1.45732e7 3.86963e6i −0.757094 0.201032i
\(269\) −3.33952e7 −1.71564 −0.857822 0.513946i \(-0.828183\pi\)
−0.857822 + 0.513946i \(0.828183\pi\)
\(270\) 2.78701e6 2.56544e6i 0.141595 0.130338i
\(271\) 2.69520e7i 1.35420i 0.735889 + 0.677102i \(0.236764\pi\)
−0.735889 + 0.677102i \(0.763236\pi\)
\(272\) 1.02322e7 1.79089e7i 0.508465 0.889941i
\(273\) 8.68297e6i 0.426757i
\(274\) 546205. 4.18534e6i 0.0265524 0.203460i
\(275\) −2.41301e7 + 4.31115e6i −1.16027 + 0.207298i
\(276\) −2.09699e7 5.56817e6i −0.997400 0.264841i
\(277\) 9.32384e6i 0.438688i −0.975648 0.219344i \(-0.929608\pi\)
0.975648 0.219344i \(-0.0703917\pi\)
\(278\) 2.27486e6 1.74313e7i 0.105881 0.811324i
\(279\) 54216.6i 0.00249643i
\(280\) −8.13305e6 + 4.28062e6i −0.370493 + 0.194999i
\(281\) 2.95827e7 1.33327 0.666636 0.745384i \(-0.267734\pi\)
0.666636 + 0.745384i \(0.267734\pi\)
\(282\) −1.29790e6 169382.i −0.0578756 0.00755302i
\(283\) −8.93801e6 −0.394350 −0.197175 0.980368i \(-0.563177\pi\)
−0.197175 + 0.980368i \(0.563177\pi\)
\(284\) −2.80372e6 + 1.05589e7i −0.122399 + 0.460960i
\(285\) 1.75413e7 + 1.46851e7i 0.757750 + 0.634367i
\(286\) −4.82701e7 6.29946e6i −2.06338 0.269281i
\(287\) −315580. −0.0133494
\(288\) −6.34443e6 4.81161e6i −0.265592 0.201425i
\(289\) −1.21971e6 −0.0505318
\(290\) −2.95077e7 + 2.71618e7i −1.20988 + 1.11369i
\(291\) 1.33329e7i 0.541062i
\(292\) −4.03770e6 + 1.52061e7i −0.162175 + 0.610759i
\(293\) 2.26330e7i 0.899787i −0.893082 0.449894i \(-0.851462\pi\)
0.893082 0.449894i \(-0.148538\pi\)
\(294\) 1.19982e7 + 1.56582e6i 0.472143 + 0.0616168i
\(295\) −1.43562e7 1.20186e7i −0.559209 0.468155i
\(296\) −3.38071e6 + 8.24057e6i −0.130357 + 0.317748i
\(297\) 5.94253e6i 0.226831i
\(298\) 2.81982e7 + 3.68000e6i 1.06555 + 0.139059i
\(299\) 8.43532e7i 3.15565i
\(300\) 1.28839e6 1.55351e7i 0.0477182 0.575375i
\(301\) 459032. 0.0168323
\(302\) 29172.7 223538.i 0.00105914 0.00811577i
\(303\) 8.02533e6 0.288493
\(304\) 2.38560e7 4.17540e7i 0.849135 1.48620i
\(305\) −1.81790e7 + 2.17148e7i −0.640724 + 0.765343i
\(306\) −1.26679e6 + 9.70690e6i −0.0442121 + 0.338779i
\(307\) 9.53548e6 0.329555 0.164777 0.986331i \(-0.447309\pi\)
0.164777 + 0.986331i \(0.447309\pi\)
\(308\) −3.70028e6 + 1.39354e7i −0.126643 + 0.476943i
\(309\) −2.10544e7 −0.713622
\(310\) 151105. + 164155.i 0.00507217 + 0.00551024i
\(311\) 1.49513e7i 0.497047i −0.968626 0.248523i \(-0.920055\pi\)
0.968626 0.248523i \(-0.0799453\pi\)
\(312\) 1.17500e7 2.86410e7i 0.386879 0.943027i
\(313\) 5.65882e6i 0.184541i 0.995734 + 0.0922706i \(0.0294125\pi\)
−0.995734 + 0.0922706i \(0.970588\pi\)
\(314\) −2.60577e6 + 1.99669e7i −0.0841681 + 0.644944i
\(315\) 2.80007e6 3.34468e6i 0.0895854 0.107010i
\(316\) 6.12769e6 2.30771e7i 0.194194 0.731341i
\(317\) 1.34418e7i 0.421969i 0.977489 + 0.210984i \(0.0676669\pi\)
−0.977489 + 0.210984i \(0.932333\pi\)
\(318\) −3.22516e6 + 2.47131e7i −0.100293 + 0.768502i
\(319\) 6.29170e7i 1.93819i
\(320\) −3.26197e7 + 3.11385e6i −0.995475 + 0.0950272i
\(321\) −1.11837e7 −0.338120
\(322\) −2.47744e7 3.23317e6i −0.742054 0.0968413i
\(323\) −5.91198e7 −1.75439
\(324\) 3.65256e6 + 969870.i 0.107390 + 0.0285153i
\(325\) 5.96610e7 1.06592e7i 1.73796 0.310509i
\(326\) 1.93812e7 + 2.52933e6i 0.559407 + 0.0730050i
\(327\) 5.29999e6 0.151577
\(328\) −1.04095e6 427051.i −0.0294990 0.0121020i
\(329\) −1.50726e6 −0.0423254
\(330\) −1.65622e7 1.79926e7i −0.460867 0.500671i
\(331\) 4.96648e7i 1.36951i −0.728774 0.684755i \(-0.759909\pi\)
0.728774 0.684755i \(-0.240091\pi\)
\(332\) 2.35338e7 + 6.24895e6i 0.643098 + 0.170763i
\(333\) 4.22739e6i 0.114483i
\(334\) 4.72595e6 + 616758.i 0.126838 + 0.0165529i
\(335\) 1.89043e7 2.25811e7i 0.502835 0.600635i
\(336\) −7.96144e6 4.54874e6i −0.209881 0.119915i
\(337\) 2.90061e7i 0.757878i 0.925422 + 0.378939i \(0.123711\pi\)
−0.925422 + 0.378939i \(0.876289\pi\)
\(338\) 8.10567e7 + 1.05783e7i 2.09913 + 0.273945i
\(339\) 7.25180e6i 0.186143i
\(340\) 2.32181e7 + 3.29209e7i 0.590732 + 0.837596i
\(341\) 350016. 0.00882724
\(342\) −2.95349e6 + 2.26314e7i −0.0738342 + 0.565760i
\(343\) 3.08286e7 0.763962
\(344\) 1.51413e6 + 621174.i 0.0371952 + 0.0152594i
\(345\) 2.72021e7 3.24928e7i 0.662438 0.791280i
\(346\) −4.02256e6 + 3.08231e7i −0.0971122 + 0.744130i
\(347\) −2.93928e7 −0.703481 −0.351740 0.936098i \(-0.614410\pi\)
−0.351740 + 0.936098i \(0.614410\pi\)
\(348\) −3.86718e7 1.02686e7i −0.917607 0.243653i
\(349\) −4.15224e7 −0.976801 −0.488401 0.872620i \(-0.662419\pi\)
−0.488401 + 0.872620i \(0.662419\pi\)
\(350\) −843845. 1.79309e7i −0.0196815 0.418213i
\(351\) 1.46927e7i 0.339767i
\(352\) −3.10632e7 + 4.09589e7i −0.712226 + 0.939118i
\(353\) 5.41710e7i 1.23152i 0.787933 + 0.615761i \(0.211152\pi\)
−0.787933 + 0.615761i \(0.788848\pi\)
\(354\) 2.41722e6 1.85221e7i 0.0544886 0.417523i
\(355\) −1.63610e7 1.36970e7i −0.365699 0.306153i
\(356\) 2.60601e7 + 6.91976e6i 0.577598 + 0.153370i
\(357\) 1.12727e7i 0.247755i
\(358\) 4.94130e6 3.78630e7i 0.107694 0.825214i
\(359\) 5.22320e7i 1.12890i 0.825469 + 0.564448i \(0.190911\pi\)
−0.825469 + 0.564448i \(0.809089\pi\)
\(360\) 1.37622e7 7.24337e6i 0.294972 0.155251i
\(361\) −9.07902e7 −1.92982
\(362\) 4.40848e7 + 5.75326e6i 0.929315 + 0.121280i
\(363\) −1.07484e7 −0.224710
\(364\) 9.14884e6 3.44549e7i 0.189698 0.714408i
\(365\) −2.35618e7 1.97253e7i −0.484541 0.405644i
\(366\) −2.80160e7 3.65621e6i −0.571429 0.0745740i
\(367\) 3.08439e7 0.623980 0.311990 0.950085i \(-0.399004\pi\)
0.311990 + 0.950085i \(0.399004\pi\)
\(368\) −7.73437e7 4.41900e7i −1.55196 0.886709i
\(369\) 534003. 0.0106283
\(370\) −1.17820e7 1.27996e7i −0.232602 0.252691i
\(371\) 2.86994e7i 0.562019i
\(372\) −57125.5 + 215137.i −0.00110969 + 0.00417913i
\(373\) 9.32456e7i 1.79681i −0.439170 0.898404i \(-0.644727\pi\)
0.439170 0.898404i \(-0.355273\pi\)
\(374\) 6.26666e7 + 8.17827e6i 1.19790 + 0.156331i
\(375\) 2.64187e7 + 1.51335e7i 0.500978 + 0.286975i
\(376\) −4.97174e6 2.03967e6i −0.0935287 0.0383703i
\(377\) 1.55560e8i 2.90319i
\(378\) 4.31523e6 + 563157.i 0.0798967 + 0.0104269i
\(379\) 3.66043e7i 0.672379i −0.941794 0.336189i \(-0.890862\pi\)
0.941794 0.336189i \(-0.109138\pi\)
\(380\) 5.41324e7 + 7.67541e7i 0.986522 + 1.39878i
\(381\) −1.60575e7 −0.290337
\(382\) 2.85726e6 2.18940e7i 0.0512578 0.392767i
\(383\) 3.75898e7 0.669073 0.334537 0.942383i \(-0.391420\pi\)
0.334537 + 0.942383i \(0.391420\pi\)
\(384\) −2.01055e7 2.57778e7i −0.355076 0.455252i
\(385\) −2.15928e7 1.80769e7i −0.378380 0.316769i
\(386\) −1.04698e7 + 8.02253e7i −0.182043 + 1.39492i
\(387\) −776743. −0.0134012
\(388\) −1.40483e7 + 5.29064e7i −0.240507 + 0.905760i
\(389\) −1.40687e7 −0.239005 −0.119502 0.992834i \(-0.538130\pi\)
−0.119502 + 0.992834i \(0.538130\pi\)
\(390\) 4.09495e7 + 4.44862e7i 0.690328 + 0.749949i
\(391\) 1.09511e8i 1.83202i
\(392\) 4.59601e7 + 1.88552e7i 0.762998 + 0.313021i
\(393\) 3.76050e7i 0.619538i
\(394\) −5.50312e6 + 4.21680e7i −0.0899746 + 0.689437i
\(395\) 3.57579e7 + 2.99355e7i 0.580204 + 0.485731i
\(396\) 6.26136e6 2.35805e7i 0.100829 0.379724i
\(397\) 5.35899e7i 0.856469i −0.903668 0.428234i \(-0.859136\pi\)
0.903668 0.428234i \(-0.140864\pi\)
\(398\) −1.07652e7 + 8.24893e7i −0.170755 + 1.30842i
\(399\) 2.62819e7i 0.413750i
\(400\) 2.14811e7 6.02873e7i 0.335642 0.941990i
\(401\) 6.63361e7 1.02877 0.514384 0.857560i \(-0.328021\pi\)
0.514384 + 0.857560i \(0.328021\pi\)
\(402\) 2.91337e7 + 3.80207e6i 0.448453 + 0.0585251i
\(403\) −865405. −0.0132222
\(404\) 3.18453e7 + 8.45591e6i 0.482949 + 0.128238i
\(405\) −4.73809e6 + 5.65964e6i −0.0713244 + 0.0851969i
\(406\) −4.56878e7 5.96246e6i −0.682688 0.0890938i
\(407\) −2.72915e7 −0.404804
\(408\) −1.52545e7 + 3.71831e7i −0.224603 + 0.547477i
\(409\) 4.77129e7 0.697374 0.348687 0.937239i \(-0.386628\pi\)
0.348687 + 0.937239i \(0.386628\pi\)
\(410\) 1.61684e6 1.48830e6i 0.0234593 0.0215942i
\(411\) 8.22453e6i 0.118464i
\(412\) −8.35460e7 2.21841e7i −1.19463 0.317212i
\(413\) 2.15098e7i 0.305342i
\(414\) 4.19216e7 + 5.47095e6i 0.590794 + 0.0771013i
\(415\) −3.05279e7 + 3.64655e7i −0.427123 + 0.510197i
\(416\) 7.68029e7 1.01270e8i 1.06684 1.40669i
\(417\) 3.42538e7i 0.472390i
\(418\) 1.46105e8 + 1.90674e7i 2.00049 + 0.261073i
\(419\) 4.33308e7i 0.589053i −0.955643 0.294526i \(-0.904838\pi\)
0.955643 0.294526i \(-0.0951619\pi\)
\(420\) 1.46351e7 1.03217e7i 0.197536 0.139317i
\(421\) −5.83065e7 −0.781395 −0.390697 0.920519i \(-0.627766\pi\)
−0.390697 + 0.920519i \(0.627766\pi\)
\(422\) −5.84991e6 + 4.48254e7i −0.0778416 + 0.596467i
\(423\) 2.55049e6 0.0336978
\(424\) −3.88367e7 + 9.46656e7i −0.509501 + 1.24192i
\(425\) −7.74548e7 + 1.38383e7i −1.00898 + 0.180267i
\(426\) 2.75476e6 2.11086e7i 0.0356333 0.273043i
\(427\) −3.25350e7 −0.417896
\(428\) −4.43780e7 1.17837e7i −0.566026 0.150298i
\(429\) 9.48546e7 1.20140
\(430\) −2.35180e6 + 2.16483e6i −0.0295798 + 0.0272281i
\(431\) 1.41316e8i 1.76506i −0.470255 0.882531i \(-0.655838\pi\)
0.470255 0.882531i \(-0.344162\pi\)
\(432\) 1.34718e7 + 7.69707e6i 0.167099 + 0.0954716i
\(433\) 6.37747e7i 0.785569i −0.919631 0.392785i \(-0.871512\pi\)
0.919631 0.392785i \(-0.128488\pi\)
\(434\) −33170.0 + 254168.i −0.000405767 + 0.00310922i
\(435\) 5.01649e7 5.99218e7i 0.609442 0.727976i
\(436\) 2.10309e7 + 5.58435e6i 0.253745 + 0.0673773i
\(437\) 2.55323e8i 3.05947i
\(438\) 3.96720e6 3.03990e7i 0.0472130 0.361773i
\(439\) 8.13434e7i 0.961455i −0.876870 0.480728i \(-0.840373\pi\)
0.876870 0.480728i \(-0.159627\pi\)
\(440\) −4.67623e7 8.88472e7i −0.548957 1.04300i
\(441\) −2.35774e7 −0.274904
\(442\) −1.54941e8 2.02205e7i −1.79432 0.234167i
\(443\) −2.93915e7 −0.338073 −0.169036 0.985610i \(-0.554066\pi\)
−0.169036 + 0.985610i \(0.554066\pi\)
\(444\) 4.45420e6 1.67747e7i 0.0508887 0.191648i
\(445\) −3.38050e7 + 4.03800e7i −0.383620 + 0.458233i
\(446\) 9.58993e7 + 1.25153e7i 1.08096 + 0.141070i
\(447\) −5.54118e7 −0.620412
\(448\) −2.67990e7 2.64384e7i −0.298046 0.294037i
\(449\) −6.13990e6 −0.0678300 −0.0339150 0.999425i \(-0.510798\pi\)
−0.0339150 + 0.999425i \(0.510798\pi\)
\(450\) 1.42790e6 + 3.03414e7i 0.0156697 + 0.332965i
\(451\) 3.44746e6i 0.0375811i
\(452\) −7.64088e6 + 2.87758e7i −0.0827424 + 0.311611i
\(453\) 439270.i 0.00472538i
\(454\) −4.39991e7 5.74208e6i −0.470193 0.0613623i
\(455\) 5.33877e7 + 4.46947e7i 0.566770 + 0.474484i
\(456\) −3.55653e7 + 8.66914e7i −0.375087 + 0.914285i
\(457\) 1.81452e7i 0.190113i 0.995472 + 0.0950567i \(0.0303032\pi\)
−0.995472 + 0.0950567i \(0.969697\pi\)
\(458\) 4.62271e7 + 6.03284e6i 0.481172 + 0.0627951i
\(459\) 1.90748e7i 0.197253i
\(460\) 1.42177e8 1.00273e8i 1.46068 1.03017i
\(461\) 1.58024e8 1.61294 0.806472 0.591272i \(-0.201374\pi\)
0.806472 + 0.591272i \(0.201374\pi\)
\(462\) 3.63567e6 2.78586e7i 0.0368688 0.282510i
\(463\) 1.30644e8 1.31627 0.658137 0.752898i \(-0.271345\pi\)
0.658137 + 0.752898i \(0.271345\pi\)
\(464\) −1.42634e8 8.14933e7i −1.42780 0.815770i
\(465\) −333354. 279074.i −0.00331548 0.00277563i
\(466\) 6.66993e6 5.11089e7i 0.0659119 0.505055i
\(467\) −1.60687e8 −1.57772 −0.788859 0.614574i \(-0.789328\pi\)
−0.788859 + 0.614574i \(0.789328\pi\)
\(468\) −1.54811e7 + 5.83022e7i −0.151030 + 0.568784i
\(469\) 3.38330e7 0.327961
\(470\) 7.72229e6 7.10836e6i 0.0743793 0.0684661i
\(471\) 3.92366e7i 0.375516i
\(472\) 2.91076e7 7.09506e7i 0.276809 0.674730i
\(473\) 5.01456e6i 0.0473859i
\(474\) −6.02070e6 + 4.61341e7i −0.0565343 + 0.433199i
\(475\) −1.80584e8 + 3.22636e7i −1.68499 + 0.301045i
\(476\) −1.18775e7 + 4.47310e7i −0.110129 + 0.414751i
\(477\) 4.85631e7i 0.447457i
\(478\) 2.67932e7 2.05305e8i 0.245324 1.87982i
\(479\) 8.69380e7i 0.791048i 0.918456 + 0.395524i \(0.129437\pi\)
−0.918456 + 0.395524i \(0.870563\pi\)
\(480\) 6.22417e7 1.42418e7i 0.562805 0.128778i
\(481\) 6.74776e7 0.606351
\(482\) −1.90321e8 2.48378e7i −1.69960 0.221805i
\(483\) 4.86837e7 0.432058
\(484\) −4.26505e7 1.13250e7i −0.376174 0.0998859i
\(485\) −8.19783e7 6.86300e7i −0.718578 0.601573i
\(486\) −7.30194e6 952936.i −0.0636106 0.00830147i
\(487\) 9.33645e6 0.0808342 0.0404171 0.999183i \(-0.487131\pi\)
0.0404171 + 0.999183i \(0.487131\pi\)
\(488\) −1.07318e8 4.40273e7i −0.923446 0.378846i
\(489\) −3.80856e7 −0.325712
\(490\) −7.13870e7 + 6.57116e7i −0.606779 + 0.558540i
\(491\) 4.23949e7i 0.358154i −0.983835 0.179077i \(-0.942689\pi\)
0.983835 0.179077i \(-0.0573111\pi\)
\(492\) 2.11897e6 + 562653.i 0.0177922 + 0.00472439i
\(493\) 2.01956e8i 1.68545i
\(494\) −3.61242e8 4.71436e7i −2.99652 0.391059i
\(495\) 3.65380e7 + 3.05886e7i 0.301251 + 0.252199i
\(496\) −453359. + 793493.i −0.00371533 + 0.00650276i
\(497\) 2.45135e7i 0.199681i
\(498\) −4.70470e7 6.13985e6i −0.380929 0.0497130i
\(499\) 2.31844e7i 0.186592i 0.995638 + 0.0932962i \(0.0297404\pi\)
−0.995638 + 0.0932962i \(0.970260\pi\)
\(500\) 8.88867e7 + 8.78872e7i 0.711093 + 0.703098i
\(501\) −9.28688e6 −0.0738510
\(502\) −2.42531e7 + 1.85841e8i −0.191715 + 1.46903i
\(503\) 1.79093e8 1.40726 0.703632 0.710565i \(-0.251561\pi\)
0.703632 + 0.710565i \(0.251561\pi\)
\(504\) 1.65299e7 + 6.78142e6i 0.129115 + 0.0529699i
\(505\) −4.13096e7 + 4.93442e7i −0.320757 + 0.383144i
\(506\) 3.53198e7 2.70641e8i 0.272626 2.08901i
\(507\) −1.59283e8 −1.22221
\(508\) −6.37176e7 1.69190e7i −0.486036 0.129058i
\(509\) 1.21665e8 0.922595 0.461298 0.887245i \(-0.347384\pi\)
0.461298 + 0.887245i \(0.347384\pi\)
\(510\) −5.31627e7 5.77542e7i −0.400771 0.435385i
\(511\) 3.53024e7i 0.264571i
\(512\) −5.26199e7 1.23473e8i −0.392048 0.919945i
\(513\) 4.44724e7i 0.329412i
\(514\) 1.63525e7 1.25302e8i 0.120419 0.922719i
\(515\) 1.08376e8 1.29454e8i 0.793432 0.947753i
\(516\) −3.08219e6 818417.i −0.0224342 0.00595697i
\(517\) 1.64656e7i 0.119154i
\(518\) 2.58634e6 1.98180e7i 0.0186079 0.142584i
\(519\) 6.05700e7i 0.433267i
\(520\) 1.15619e8 + 2.19672e8i 0.822276 + 1.56230i
\(521\) −6.60811e7 −0.467266 −0.233633 0.972325i \(-0.575061\pi\)
−0.233633 + 0.972325i \(0.575061\pi\)
\(522\) 7.73099e7 + 1.00893e7i 0.543530 + 0.0709330i
\(523\) −7.09676e7 −0.496083 −0.248042 0.968749i \(-0.579787\pi\)
−0.248042 + 0.968749i \(0.579787\pi\)
\(524\) −3.96226e7 + 1.49220e8i −0.275391 + 1.03713i
\(525\) 6.15185e6 + 3.44328e7i 0.0425136 + 0.237955i
\(526\) 6.88574e7 + 8.98619e6i 0.473144 + 0.0617474i
\(527\) 1.12351e6 0.00767619
\(528\) 4.96914e7 8.69725e7i 0.337582 0.590854i
\(529\) 3.24916e8 2.19484
\(530\) −1.35348e8 1.47038e8i −0.909129 0.987648i
\(531\) 3.63974e7i 0.243101i
\(532\) −2.76920e7 + 1.04289e8i −0.183916 + 0.692634i
\(533\) 8.52375e6i 0.0562923i
\(534\) −5.20974e7 6.79895e6i −0.342131 0.0446496i
\(535\) 5.75670e7 6.87636e7i 0.375934 0.449053i
\(536\) 1.11599e8 + 4.57837e7i 0.724713 + 0.297315i
\(537\) 7.44039e7i 0.480478i
\(538\) 2.64915e8 + 3.45726e7i 1.70122 + 0.222017i
\(539\) 1.52213e8i 0.972043i
\(540\) −2.47645e7 + 1.74657e7i −0.157271 + 0.110919i
\(541\) −1.30210e7 −0.0822345 −0.0411172 0.999154i \(-0.513092\pi\)
−0.0411172 + 0.999154i \(0.513092\pi\)
\(542\) 2.79023e7 2.13803e8i 0.175243 1.34282i
\(543\) −8.66302e7 −0.541090
\(544\) −9.97093e7 + 1.31473e8i −0.619354 + 0.816659i
\(545\) −2.72812e7 + 3.25873e7i −0.168529 + 0.201307i
\(546\) −8.98910e6 + 6.88797e7i −0.0552254 + 0.423168i
\(547\) 2.06228e8 1.26004 0.630021 0.776578i \(-0.283046\pi\)
0.630021 + 0.776578i \(0.283046\pi\)
\(548\) −8.66580e6 + 3.26357e7i −0.0526583 + 0.198313i
\(549\) 5.50536e7 0.332712
\(550\) 1.95881e8 9.21834e6i 1.17734 0.0554070i
\(551\) 4.70855e8i 2.81470i
\(552\) 1.60584e8 + 6.58800e7i 0.954741 + 0.391685i
\(553\) 5.35757e7i 0.316805i
\(554\) −9.65257e6 + 7.39635e7i −0.0567693 + 0.434999i
\(555\) 2.59923e7 + 2.17601e7i 0.152043 + 0.127286i
\(556\) −3.60917e7 + 1.35923e8i −0.209982 + 0.790801i
\(557\) 2.48107e6i 0.0143573i 0.999974 + 0.00717865i \(0.00228505\pi\)
−0.999974 + 0.00717865i \(0.997715\pi\)
\(558\) 56128.1 430086.i 0.000323056 0.00247544i
\(559\) 1.23984e7i 0.0709788i
\(560\) 6.89489e7 2.55372e7i 0.392612 0.145415i
\(561\) −1.23145e8 −0.697474
\(562\) −2.34671e8 3.06257e7i −1.32206 0.172535i
\(563\) 1.47289e8 0.825361 0.412680 0.910876i \(-0.364593\pi\)
0.412680 + 0.910876i \(0.364593\pi\)
\(564\) 1.01206e7 + 2.68733e6i 0.0564115 + 0.0149790i
\(565\) −4.45881e7 3.73279e7i −0.247214 0.206961i
\(566\) 7.09028e7 + 9.25313e6i 0.391034 + 0.0510316i
\(567\) −8.47978e6 −0.0465195
\(568\) 3.31723e7 8.08583e7i 0.181022 0.441245i
\(569\) 9.59654e7 0.520928 0.260464 0.965484i \(-0.416124\pi\)
0.260464 + 0.965484i \(0.416124\pi\)
\(570\) −1.23947e8 1.34652e8i −0.669287 0.727092i
\(571\) 3.67358e8i 1.97325i −0.163011 0.986624i \(-0.552121\pi\)
0.163011 0.986624i \(-0.447879\pi\)
\(572\) 3.76392e8 + 9.99439e7i 2.01119 + 0.534033i
\(573\) 4.30235e7i 0.228687i
\(574\) 2.50341e6 + 326706.i 0.0132372 + 0.00172751i
\(575\) 5.97639e7 + 3.34507e8i 0.314366 + 1.75955i
\(576\) 4.53474e7 + 4.47373e7i 0.237293 + 0.234101i
\(577\) 2.14798e8i 1.11816i 0.829115 + 0.559078i \(0.188845\pi\)
−0.829115 + 0.559078i \(0.811155\pi\)
\(578\) 9.67567e6 + 1.26272e6i 0.0501069 + 0.00653917i
\(579\) 1.57649e8i 0.812187i
\(580\) 2.62196e8 1.84919e8i 1.34382 0.947759i
\(581\) −5.46359e7 −0.278580
\(582\) 1.38030e7 1.05767e8i 0.0700173 0.536513i
\(583\) −3.13518e8 −1.58218
\(584\) 4.77722e7 1.16446e8i 0.239848 0.584636i
\(585\) −9.03391e7 7.56294e7i −0.451241 0.377766i
\(586\) −2.34310e7 + 1.79542e8i −0.116439 + 0.892222i
\(587\) 1.34919e8 0.667050 0.333525 0.942741i \(-0.391762\pi\)
0.333525 + 0.942741i \(0.391762\pi\)
\(588\) −9.35574e7 2.48424e7i −0.460200 0.122197i
\(589\) 2.61943e6 0.0128192
\(590\) 1.01442e8 + 1.10203e8i 0.493925 + 0.536584i
\(591\) 8.28636e7i 0.401422i
\(592\) 3.53494e7 6.18704e7i 0.170379 0.298207i
\(593\) 2.80226e8i 1.34383i −0.740628 0.671915i \(-0.765472\pi\)
0.740628 0.671915i \(-0.234528\pi\)
\(594\) −6.15204e6 + 4.71405e7i −0.0293535 + 0.224923i
\(595\) −6.93105e7 5.80249e7i −0.329040 0.275463i
\(596\) −2.19879e8 5.83848e7i −1.03859 0.275779i
\(597\) 1.62098e8i 0.761824i
\(598\) −8.73273e7 + 6.69152e8i −0.408363 + 3.12911i
\(599\) 1.49142e8i 0.693937i −0.937877 0.346969i \(-0.887211\pi\)
0.937877 0.346969i \(-0.112789\pi\)
\(600\) −2.63033e7 + 1.21902e8i −0.121775 + 0.564362i
\(601\) −2.09302e8 −0.964161 −0.482080 0.876127i \(-0.660119\pi\)
−0.482080 + 0.876127i \(0.660119\pi\)
\(602\) −3.64138e6 475216.i −0.0166908 0.00217822i
\(603\) −5.72500e7 −0.261110
\(604\) −462838. + 1.74306e6i −0.00210048 + 0.00791047i
\(605\) 5.53261e7 6.60869e7i 0.249841 0.298435i
\(606\) −6.36628e7 8.30828e6i −0.286067 0.0373330i
\(607\) 1.45876e8 0.652258 0.326129 0.945325i \(-0.394256\pi\)
0.326129 + 0.945325i \(0.394256\pi\)
\(608\) −2.32469e8 + 3.06526e8i −1.03432 + 1.36382i
\(609\) 8.97803e7 0.397493
\(610\) 1.66690e8 1.53438e8i 0.734377 0.675993i
\(611\) 4.07108e7i 0.178479i
\(612\) 2.00983e7 7.56908e7i 0.0876807 0.330209i
\(613\) 2.18756e8i 0.949684i −0.880071 0.474842i \(-0.842505\pi\)
0.880071 0.474842i \(-0.157495\pi\)
\(614\) −7.56424e7 9.87167e6i −0.326784 0.0426467i
\(615\) −2.74872e6 + 3.28334e6i −0.0118170 + 0.0141153i
\(616\) 4.37800e7 1.06715e8i 0.187298 0.456545i
\(617\) 2.56428e8i 1.09172i −0.837877 0.545859i \(-0.816203\pi\)
0.837877 0.545859i \(-0.183797\pi\)
\(618\) 1.67019e8 + 2.17968e7i 0.707622 + 0.0923478i
\(619\) 5.25164e7i 0.221423i −0.993853 0.110712i \(-0.964687\pi\)
0.993853 0.110712i \(-0.0353130\pi\)
\(620\) −1.02873e6 1.45863e6i −0.00431645 0.00612028i
\(621\) −8.23792e7 −0.343988
\(622\) −1.54784e7 + 1.18605e8i −0.0643214 + 0.492867i
\(623\) −6.05010e7 −0.250206
\(624\) −1.22861e8 + 2.15037e8i −0.505660 + 0.885033i
\(625\) −2.29037e8 + 8.45391e7i −0.938134 + 0.346272i
\(626\) 5.85834e6 4.48899e7i 0.0238809 0.182989i
\(627\) −2.87109e8 −1.16478
\(628\) 4.13418e7 1.55695e8i 0.166921 0.628629i
\(629\) −8.76027e7 −0.352018
\(630\) −2.56748e7 + 2.36336e7i −0.102680 + 0.0945168i
\(631\) 3.92931e8i 1.56397i 0.623297 + 0.781985i \(0.285793\pi\)
−0.623297 + 0.781985i \(0.714207\pi\)
\(632\) −7.25001e7 + 1.76721e8i −0.287202 + 0.700062i
\(633\) 8.80855e7i 0.347291i
\(634\) 1.39157e7 1.06630e8i 0.0546058 0.418421i
\(635\) 8.26542e7 9.87302e7i 0.322807 0.385593i
\(636\) 5.11687e7 1.92703e8i 0.198899 0.749062i
\(637\) 3.76343e8i 1.45601i
\(638\) 6.51352e7 4.99103e8i 0.250815 1.92189i
\(639\) 4.14801e7i 0.158978i
\(640\) 2.61987e8 + 9.06843e6i 0.999401 + 0.0345933i
\(641\) −4.43610e8 −1.68433 −0.842165 0.539219i \(-0.818719\pi\)
−0.842165 + 0.539219i \(0.818719\pi\)
\(642\) 8.87173e7 + 1.15780e7i 0.335277 + 0.0437551i
\(643\) −4.69895e8 −1.76753 −0.883767 0.467927i \(-0.845001\pi\)
−0.883767 + 0.467927i \(0.845001\pi\)
\(644\) 1.93181e8 + 5.12957e7i 0.723282 + 0.192054i
\(645\) 3.99820e6 4.77584e6i 0.0149000 0.0177980i
\(646\) 4.68981e8 + 6.12041e7i 1.73963 + 0.227030i
\(647\) −7.12899e7 −0.263218 −0.131609 0.991302i \(-0.542014\pi\)
−0.131609 + 0.991302i \(0.542014\pi\)
\(648\) −2.79707e7 1.14751e7i −0.102797 0.0421725i
\(649\) 2.34978e8 0.859592
\(650\) −4.84310e8 + 2.27921e7i −1.76353 + 0.0829935i
\(651\) 499460.i 0.00181033i
\(652\) −1.51127e8 4.01290e7i −0.545255 0.144782i
\(653\) 3.07313e8i 1.10367i 0.833952 + 0.551837i \(0.186073\pi\)
−0.833952 + 0.551837i \(0.813927\pi\)
\(654\) −4.20434e7 5.48685e6i −0.150302 0.0196151i
\(655\) −2.31216e8 1.93568e8i −0.822801 0.688826i
\(656\) 7.81545e6 + 4.46533e6i 0.0276849 + 0.0158176i
\(657\) 5.97364e7i 0.210641i
\(658\) 1.19567e7 + 1.56040e6i 0.0419695 + 0.00547720i
\(659\) 1.56295e8i 0.546122i 0.961997 + 0.273061i \(0.0880360\pi\)
−0.961997 + 0.273061i \(0.911964\pi\)
\(660\) 1.12756e8 + 1.59877e8i 0.392202 + 0.556100i
\(661\) 2.76572e7 0.0957644 0.0478822 0.998853i \(-0.484753\pi\)
0.0478822 + 0.998853i \(0.484753\pi\)
\(662\) −5.14158e7 + 3.93978e8i −0.177224 + 1.35799i
\(663\) 3.04472e8 1.04474
\(664\) −1.80218e8 7.39348e7i −0.615593 0.252548i
\(665\) −1.61596e8 1.35283e8i −0.549496 0.460023i
\(666\) −4.37643e6 + 3.35347e7i −0.0148149 + 0.113520i
\(667\) 8.72196e8 2.93925
\(668\) −3.68512e7 9.78515e6i −0.123630 0.0328275i
\(669\) −1.88450e8 −0.629386
\(670\) −1.73340e8 + 1.59559e8i −0.576333 + 0.530514i
\(671\) 3.55420e8i 1.17645i
\(672\) 5.84469e7 + 4.43261e7i 0.192599 + 0.146067i
\(673\) 2.88925e8i 0.947851i 0.880565 + 0.473926i \(0.157163\pi\)
−0.880565 + 0.473926i \(0.842837\pi\)
\(674\) 3.00288e7 2.30098e8i 0.0980748 0.751506i
\(675\) −1.04097e7 5.82648e7i −0.0338477 0.189450i
\(676\) −6.32050e8 1.67829e8i −2.04603 0.543284i
\(677\) 1.02252e8i 0.329540i −0.986332 0.164770i \(-0.947312\pi\)
0.986332 0.164770i \(-0.0526881\pi\)
\(678\) 7.50747e6 5.75266e7i 0.0240882 0.184578i
\(679\) 1.22827e8i 0.392361i
\(680\) −1.50102e8 2.85189e8i −0.477374 0.906998i
\(681\) 8.64618e7 0.273768
\(682\) −2.77658e6 362356.i −0.00875302 0.00114231i
\(683\) −1.71355e8 −0.537818 −0.268909 0.963166i \(-0.586663\pi\)
−0.268909 + 0.963166i \(0.586663\pi\)
\(684\) 4.68585e7 1.76471e8i 0.146427 0.551448i
\(685\) −5.05690e7 4.23349e7i −0.157330 0.131712i
\(686\) −2.44555e8 3.19155e7i −0.757538 0.0988621i
\(687\) −9.08400e7 −0.280161
\(688\) −1.13681e7 6.49512e6i −0.0349078 0.0199444i
\(689\) 7.75165e8 2.36993
\(690\) −2.49425e8 + 2.29596e8i −0.759265 + 0.698903i
\(691\) 1.78401e8i 0.540708i 0.962761 + 0.270354i \(0.0871408\pi\)
−0.962761 + 0.270354i \(0.912859\pi\)
\(692\) 6.38197e7 2.40347e8i 0.192591 0.725306i
\(693\) 5.47444e7i 0.164490i
\(694\) 2.33165e8 + 3.04291e7i 0.697566 + 0.0910354i
\(695\) −2.10612e8 1.76318e8i −0.627376 0.525222i
\(696\) 2.96142e8 + 1.21493e8i 0.878360 + 0.360349i
\(697\) 1.10659e7i 0.0326806i
\(698\) 3.29386e8 + 4.29863e7i 0.968588 + 0.126405i
\(699\) 1.00433e8i 0.294066i
\(700\) −1.18691e7 + 1.43114e8i −0.0346037 + 0.417243i
\(701\) −3.64044e8 −1.05682 −0.528408 0.848991i \(-0.677211\pi\)
−0.528408 + 0.848991i \(0.677211\pi\)
\(702\) 1.52108e7 1.16554e8i 0.0439683 0.336910i
\(703\) −2.04243e8 −0.587870
\(704\) 2.88819e8 2.92758e8i 0.827766 0.839054i
\(705\) −1.31284e7 + 1.56818e7i −0.0374665 + 0.0447537i
\(706\) 5.60809e7 4.29724e8i 0.159368 1.22117i
\(707\) −7.39319e7 −0.209206
\(708\) −3.83503e7 + 1.44428e8i −0.108061 + 0.406961i
\(709\) −4.12018e8 −1.15605 −0.578026 0.816018i \(-0.696177\pi\)
−0.578026 + 0.816018i \(0.696177\pi\)
\(710\) 1.15607e8 + 1.25592e8i 0.323006 + 0.350903i
\(711\) 9.06572e7i 0.252228i
\(712\) −1.99564e8 8.18715e7i −0.552894 0.226826i
\(713\) 4.85215e6i 0.0133865i
\(714\) 1.16701e7 8.94230e7i 0.0320612 0.245671i
\(715\) −4.88254e8 + 5.83219e8i −1.33576 + 1.59556i
\(716\) −7.83959e7 + 2.95242e8i −0.213577 + 0.804339i
\(717\) 4.03440e8i 1.09452i
\(718\) 5.40736e7 4.14343e8i 0.146087 1.11940i
\(719\) 3.87039e8i 1.04128i −0.853776 0.520641i \(-0.825693\pi\)
0.853776 0.520641i \(-0.174307\pi\)
\(720\) −1.16671e8 + 4.32123e7i −0.312582 + 0.115774i
\(721\) 1.93960e8 0.517496
\(722\) 7.20214e8 + 9.39912e7i 1.91360 + 0.249733i
\(723\) 3.73997e8 0.989584
\(724\) −3.43757e8 9.12781e7i −0.905807 0.240520i
\(725\) 1.10214e8 + 6.16883e8i 0.289216 + 1.61878i
\(726\) 8.52639e7 + 1.11273e7i 0.222821 + 0.0290791i
\(727\) 4.91602e8 1.27941 0.639706 0.768619i \(-0.279056\pi\)
0.639706 + 0.768619i \(0.279056\pi\)
\(728\) −1.08245e8 + 2.63850e8i −0.280552 + 0.683853i
\(729\) 1.43489e7 0.0370370
\(730\) 1.66489e8 + 1.80868e8i 0.427973 + 0.464936i
\(731\) 1.60962e7i 0.0412069i
\(732\) 2.18458e8 + 5.80074e7i 0.556974 + 0.147894i
\(733\) 2.92669e8i 0.743130i −0.928407 0.371565i \(-0.878821\pi\)
0.928407 0.371565i \(-0.121179\pi\)
\(734\) −2.44676e8 3.19313e7i −0.618733 0.0807474i
\(735\) 1.21362e8 1.44967e8i 0.305648 0.365096i
\(736\) 5.67799e8 + 4.30618e8i 1.42417 + 1.08009i
\(737\) 3.69599e8i 0.923269i
\(738\) −4.23610e6 552830.i −0.0105389 0.00137538i
\(739\) 2.64415e8i 0.655167i 0.944822 + 0.327583i \(0.106234\pi\)
−0.944822 + 0.327583i \(0.893766\pi\)
\(740\) 8.02125e7 + 1.13733e8i 0.197946 + 0.280667i
\(741\) 7.09869e8 1.74471
\(742\) 2.97112e7 2.27664e8i 0.0727292 0.557293i
\(743\) 2.47114e8 0.602464 0.301232 0.953551i \(-0.402602\pi\)
0.301232 + 0.953551i \(0.402602\pi\)
\(744\) 675883. 1.64748e6i 0.00164117 0.00400039i
\(745\) 2.85227e8 3.40703e8i 0.689797 0.823961i
\(746\) −9.65331e7 + 7.39692e8i −0.232520 + 1.78170i
\(747\) 9.24512e7 0.221795
\(748\) −4.88651e8 1.29752e8i −1.16760 0.310034i
\(749\) 1.03028e8 0.245193
\(750\) −1.93906e8 1.47400e8i −0.459629 0.349392i
\(751\) 3.88949e8i 0.918276i −0.888365 0.459138i \(-0.848158\pi\)
0.888365 0.459138i \(-0.151842\pi\)
\(752\) 3.73279e7 + 2.13271e7i 0.0877768 + 0.0501510i
\(753\) 3.65193e8i 0.855338i
\(754\) −1.61045e8 + 1.23402e9i −0.375693 + 2.87878i
\(755\) −2.70087e6 2.26110e6i −0.00627572 0.00525385i
\(756\) −3.36486e7 8.93474e6i −0.0778756 0.0206784i
\(757\) 3.98638e8i 0.918948i −0.888191 0.459474i \(-0.848038\pi\)
0.888191 0.459474i \(-0.151962\pi\)
\(758\) −3.78948e7 + 2.90372e8i −0.0870106 + 0.666725i
\(759\) 5.31831e8i 1.21632i
\(760\) −3.49958e8 6.64911e8i −0.797214 1.51469i
\(761\) 2.05271e8 0.465773 0.232887 0.972504i \(-0.425183\pi\)
0.232887 + 0.972504i \(0.425183\pi\)
\(762\) 1.27380e8 + 1.66236e7i 0.287896 + 0.0375716i
\(763\) −4.88252e7 −0.109918
\(764\) −4.53318e7 + 1.70721e8i −0.101654 + 0.382831i
\(765\) 1.17283e8 + 9.81858e7i 0.261969 + 0.219313i
\(766\) −2.98190e8 3.89151e7i −0.663447 0.0865828i
\(767\) −5.80976e8 −1.28757
\(768\) 1.32805e8 + 2.25302e8i 0.293178 + 0.497373i
\(769\) −5.15212e8 −1.13294 −0.566470 0.824082i \(-0.691691\pi\)
−0.566470 + 0.824082i \(0.691691\pi\)
\(770\) 1.52576e8 + 1.65754e8i 0.334206 + 0.363070i
\(771\) 2.46229e8i 0.537250i
\(772\) 1.66107e8 6.25567e8i 0.361025 1.35963i
\(773\) 2.25469e8i 0.488145i −0.969757 0.244072i \(-0.921517\pi\)
0.969757 0.244072i \(-0.0784834\pi\)
\(774\) 6.16169e6 + 804128.i 0.0132885 + 0.00173421i
\(775\) 3.43181e6 613136.i 0.00737255 0.00131720i
\(776\) 1.66213e8 4.05149e8i 0.355697 0.867020i
\(777\) 3.89440e7i 0.0830191i
\(778\) 1.11603e8 + 1.45647e7i 0.236995 + 0.0309289i
\(779\) 2.57999e7i 0.0545766i
\(780\) −2.78787e8 3.95291e8i −0.587474 0.832977i
\(781\) 2.67790e8 0.562137
\(782\) 1.13373e8 8.68725e8i 0.237076 1.81661i
\(783\) −1.51920e8 −0.316468
\(784\) −3.45069e8 1.97154e8i −0.716075 0.409127i
\(785\) 2.41248e8 + 2.01966e8i 0.498718 + 0.417513i
\(786\) 3.89308e7 2.98310e8i 0.0801726 0.614329i
\(787\) 8.23340e8 1.68910 0.844549 0.535478i \(-0.179869\pi\)
0.844549 + 0.535478i \(0.179869\pi\)
\(788\) 8.73095e7 3.28811e8i 0.178436 0.671997i
\(789\) −1.35310e8 −0.275486
\(790\) −2.52667e8 2.74489e8i −0.512469 0.556729i
\(791\) 6.68058e7i 0.134985i
\(792\) −7.40816e7 + 1.80576e8i −0.149120 + 0.363483i
\(793\) 8.78765e8i 1.76219i
\(794\) −5.54793e7 + 4.25114e8i −0.110833 + 0.849267i
\(795\) 2.98593e8 + 2.49974e8i 0.594262 + 0.497500i
\(796\) 1.70795e8 6.43221e8i 0.338638 1.27532i
\(797\) 1.31438e8i 0.259624i 0.991539 + 0.129812i \(0.0414374\pi\)
−0.991539 + 0.129812i \(0.958563\pi\)
\(798\) 2.72085e7 2.08487e8i 0.0535421 0.410271i
\(799\) 5.28528e7i 0.103616i
\(800\) −2.32817e8 + 4.56005e8i −0.454720 + 0.890634i
\(801\) 1.02376e8 0.199205
\(802\) −5.26227e8 6.86749e7i −1.02012 0.133130i
\(803\) 3.85651e8 0.744814
\(804\) −2.27173e8 6.03216e7i −0.437108 0.116066i
\(805\) −2.50594e8 + 2.99334e8i −0.480378 + 0.573811i
\(806\) 6.86503e6 + 895917.i 0.0131110 + 0.00171105i
\(807\) −5.20580e8 −0.990528
\(808\) −2.43866e8 1.00047e8i −0.462293 0.189657i
\(809\) −6.41573e8 −1.21172 −0.605858 0.795573i \(-0.707170\pi\)
−0.605858 + 0.795573i \(0.707170\pi\)
\(810\) 4.34452e7 3.99913e7i 0.0817498 0.0752506i
\(811\) 3.32626e8i 0.623582i 0.950151 + 0.311791i \(0.100929\pi\)
−0.950151 + 0.311791i \(0.899071\pi\)
\(812\) 3.56257e8 + 9.45973e7i 0.665418 + 0.176689i
\(813\) 4.20141e8i 0.781850i
\(814\) 2.16496e8 + 2.82537e7i 0.401400 + 0.0523845i
\(815\) 1.96042e8 2.34171e8i 0.362139 0.432574i
\(816\) 1.59504e8 2.79172e8i 0.293562 0.513808i
\(817\) 3.75277e7i 0.0688155i
\(818\) −3.78494e8 4.93951e7i −0.691511 0.0902452i
\(819\) 1.35354e8i 0.246388i
\(820\) −1.43667e7 + 1.01324e7i −0.0260565 + 0.0183769i
\(821\) 6.97205e8 1.25988 0.629942 0.776642i \(-0.283078\pi\)
0.629942 + 0.776642i \(0.283078\pi\)
\(822\) 8.51450e6 6.52430e7i 0.0153300 0.117468i
\(823\) −5.53566e8 −0.993047 −0.496523 0.868023i \(-0.665390\pi\)
−0.496523 + 0.868023i \(0.665390\pi\)
\(824\) 6.39782e8 + 2.62472e8i 1.14354 + 0.469139i
\(825\) −3.76151e8 + 6.72041e7i −0.669885 + 0.119683i
\(826\) −2.22682e7 + 1.70631e8i −0.0395134 + 0.302774i
\(827\) −4.25348e8 −0.752018 −0.376009 0.926616i \(-0.622704\pi\)
−0.376009 + 0.926616i \(0.622704\pi\)
\(828\) −3.26889e8 8.67991e7i −0.575849 0.152906i
\(829\) −1.52812e8 −0.268222 −0.134111 0.990966i \(-0.542818\pi\)
−0.134111 + 0.990966i \(0.542818\pi\)
\(830\) 2.79921e8 2.57667e8i 0.489555 0.450635i
\(831\) 1.45344e8i 0.253277i
\(832\) −7.14097e8 + 7.23835e8i −1.23990 + 1.25681i
\(833\) 4.88586e8i 0.845291i
\(834\) 3.54615e7 2.71727e8i 0.0611307 0.468418i
\(835\) 4.78032e7 5.71009e7i 0.0821104 0.0980806i
\(836\) −1.13928e9 3.02513e8i −1.94989 0.517756i
\(837\) 845153.i 0.00144132i
\(838\) −4.48585e7 + 3.43731e8i −0.0762276 + 0.584100i
\(839\) 3.56914e8i 0.604334i −0.953255 0.302167i \(-0.902290\pi\)
0.953255 0.302167i \(-0.0977101\pi\)
\(840\) −1.26782e8 + 6.67282e7i −0.213904 + 0.112583i
\(841\) 1.01364e9 1.70411
\(842\) 4.62530e8 + 6.03622e7i 0.774824 + 0.101118i
\(843\) 4.61148e8 0.769765
\(844\) 9.28116e7 3.49532e8i 0.154374 0.581379i
\(845\) 8.19893e8 9.79360e8i 1.35890 1.62320i
\(846\) −2.02323e7 2.64041e6i −0.0334145 0.00436074i
\(847\) 9.90173e7 0.162952
\(848\) 4.06085e8 7.10751e8i 0.665931 1.16555i
\(849\) −1.39330e8 −0.227678
\(850\) 6.28754e8 2.95898e7i 1.02382 0.0481821i
\(851\) 3.78333e8i 0.613883i
\(852\) −4.37056e7 + 1.64597e8i −0.0706673 + 0.266135i
\(853\) 5.26433e8i 0.848195i −0.905617 0.424098i \(-0.860591\pi\)
0.905617 0.424098i \(-0.139409\pi\)
\(854\) 2.58092e8 + 3.36821e7i 0.414382 + 0.0540786i
\(855\) 2.73441e8 + 2.28917e8i 0.437487 + 0.366252i
\(856\) 3.39840e8 + 1.39420e8i 0.541817 + 0.222282i
\(857\) 6.08907e8i 0.967405i 0.875233 + 0.483702i \(0.160708\pi\)
−0.875233 + 0.483702i \(0.839292\pi\)
\(858\) −7.52456e8 9.81989e7i −1.19130 0.155469i
\(859\) 1.36881e8i 0.215956i 0.994153 + 0.107978i \(0.0344376\pi\)
−0.994153 + 0.107978i \(0.965562\pi\)
\(860\) 2.08973e7 1.47383e7i 0.0328545 0.0231714i
\(861\) −4.91940e6 −0.00770731
\(862\) −1.46298e8 + 1.12102e9i −0.228411 + 1.75022i
\(863\) −1.14016e8 −0.177391 −0.0886956 0.996059i \(-0.528270\pi\)
−0.0886956 + 0.996059i \(0.528270\pi\)
\(864\) −9.88999e7 7.50056e7i −0.153340 0.116293i
\(865\) 3.72418e8 + 3.11778e8i 0.575416 + 0.481722i
\(866\) −6.60231e7 + 5.05907e8i −0.101658 + 0.778964i
\(867\) −1.90135e7 −0.0291745
\(868\) 526258. 1.98191e6i 0.000804710 0.00303057i
\(869\) −5.85272e8 −0.891864
\(870\) −4.59979e8 + 4.23410e8i −0.698522 + 0.642989i
\(871\) 9.13824e8i 1.38295i
\(872\) −1.61051e8 6.60715e7i −0.242893 0.0996472i
\(873\) 2.07840e8i 0.312382i
\(874\) 2.64325e8 2.02541e9i 0.395916 3.03374i
\(875\) −2.43378e8 1.39414e8i −0.363293 0.208105i
\(876\) −6.29415e7 + 2.37040e8i −0.0936320 + 0.352622i
\(877\) 4.75175e8i 0.704457i 0.935914 + 0.352229i \(0.114576\pi\)
−0.935914 + 0.352229i \(0.885424\pi\)
\(878\) −8.42113e7 + 6.45276e8i −0.124419 + 0.953371i
\(879\) 3.52814e8i 0.519493i
\(880\) 2.78974e8 + 7.53212e8i 0.409369 + 1.10527i
\(881\) −1.06776e9 −1.56151 −0.780755 0.624837i \(-0.785165\pi\)
−0.780755 + 0.624837i \(0.785165\pi\)
\(882\) 1.87033e8 + 2.44087e7i 0.272592 + 0.0355745i
\(883\) 1.10522e9 1.60534 0.802671 0.596422i \(-0.203411\pi\)
0.802671 + 0.596422i \(0.203411\pi\)
\(884\) 1.20818e9 + 3.20808e8i 1.74893 + 0.464396i
\(885\) −2.23792e8 1.87352e8i −0.322860 0.270289i
\(886\) 2.33155e8 + 3.04277e7i 0.335230 + 0.0437490i
\(887\) −1.10318e9 −1.58079 −0.790395 0.612598i \(-0.790124\pi\)
−0.790395 + 0.612598i \(0.790124\pi\)
\(888\) −5.27001e7 + 1.28458e8i −0.0752614 + 0.183452i
\(889\) 1.47926e8 0.210543
\(890\) 3.09970e8 2.85327e8i 0.439693 0.404737i
\(891\) 9.26349e7i 0.130961i
\(892\) −7.47787e8 1.98561e8i −1.05362 0.279768i
\(893\) 1.23225e8i 0.173039i
\(894\) 4.39567e8 + 5.73655e7i 0.615195 + 0.0802856i
\(895\) −4.57477e8 3.82987e8i −0.638116 0.534213i
\(896\) 1.85218e8 + 2.37473e8i 0.257490 + 0.330134i
\(897\) 1.31494e9i 1.82191i
\(898\) 4.87062e7 + 6.35637e6i 0.0672597 + 0.00877769i
\(899\) 8.94812e6i 0.0123155i
\(900\) 2.00840e7 2.42169e8i 0.0275501 0.332193i
\(901\) −1.00636e9 −1.37587
\(902\) −3.56900e6 + 2.73478e7i −0.00486326 + 0.0372651i
\(903\) 7.15560e6 0.00971813
\(904\) 9.04034e7 2.20361e8i 0.122371 0.298283i
\(905\) 4.45920e8 5.32650e8i 0.601605 0.718615i
\(906\) 454757. 3.48461e6i 0.000611497 0.00468564i
\(907\) −9.34213e8 −1.25206 −0.626028 0.779800i \(-0.715321\pi\)
−0.626028 + 0.779800i \(0.715321\pi\)
\(908\) 3.43089e8 + 9.11008e7i 0.458299 + 0.121693i
\(909\) 1.25103e8 0.166561
\(910\) −3.77240e8 4.09821e8i −0.500603 0.543839i
\(911\) 1.26470e9i 1.67275i −0.548155 0.836377i \(-0.684669\pi\)
0.548155 0.836377i \(-0.315331\pi\)
\(912\) 3.71878e8 6.50881e8i 0.490248 0.858058i
\(913\) 5.96854e8i 0.784253i
\(914\) 1.87849e7 1.43941e8i 0.0246020 0.188515i
\(915\) −2.83383e8 + 3.38500e8i −0.369922 + 0.441871i
\(916\) −3.60462e8 9.57139e7i −0.469000 0.124534i
\(917\) 3.46429e8i 0.449269i
\(918\) −1.97473e7 + 1.51316e8i −0.0255259 + 0.195594i
\(919\) 1.39700e9i 1.79990i 0.435993 + 0.899950i \(0.356397\pi\)
−0.435993 + 0.899950i \(0.643603\pi\)
\(920\) −1.23166e9 + 6.48250e8i −1.58171 + 0.832490i
\(921\) 1.48643e8 0.190269
\(922\) −1.25356e9 1.63595e8i −1.59938 0.208726i
\(923\) −6.62105e8 −0.842018
\(924\) −5.76817e7 + 2.17231e8i −0.0731176 + 0.275363i
\(925\) −2.67586e8 + 4.78076e7i −0.338094 + 0.0604048i
\(926\) −1.03636e9 1.35250e8i −1.30521 0.170335i
\(927\) −3.28206e8 −0.412010
\(928\) 1.04711e9 + 7.94127e8i 1.31023 + 0.993679i
\(929\) −1.13181e9 −1.41165 −0.705825 0.708386i \(-0.749423\pi\)
−0.705825 + 0.708386i \(0.749423\pi\)
\(930\) 2.35549e6 + 2.55893e6i 0.00292842 + 0.00318134i
\(931\) 1.13912e9i 1.41163i
\(932\) −1.05822e8 + 3.98528e8i −0.130715 + 0.492279i
\(933\) 2.33067e8i 0.286970i
\(934\) 1.27468e9 + 1.66352e8i 1.56445 + 0.204168i
\(935\) 6.33876e8 7.57163e8i 0.775478 0.926306i
\(936\) 1.83165e8 4.46469e8i 0.223365 0.544457i
\(937\) 4.15887e8i 0.505541i −0.967526 0.252770i \(-0.918658\pi\)
0.967526 0.252770i \(-0.0813417\pi\)
\(938\) −2.68388e8 3.50259e7i −0.325203 0.0424405i
\(939\) 8.82123e7i 0.106545i
\(940\) −6.86178e7 + 4.83941e7i −0.0826139 + 0.0582652i
\(941\) −9.66470e8 −1.15990 −0.579949 0.814653i \(-0.696927\pi\)
−0.579949 + 0.814653i \(0.696927\pi\)
\(942\) −4.06199e7 + 3.11253e8i −0.0485944 + 0.372359i
\(943\) −4.77909e7 −0.0569915
\(944\) −3.04355e8 + 5.32698e8i −0.361797 + 0.633235i
\(945\) 4.36488e7 5.21384e7i 0.0517222 0.0617820i
\(946\) 5.19136e6 3.97792e7i 0.00613207 0.0469875i
\(947\) 7.38750e8 0.869857 0.434928 0.900465i \(-0.356774\pi\)
0.434928 + 0.900465i \(0.356774\pi\)
\(948\) 9.55213e7 3.59736e8i 0.112118 0.422240i
\(949\) −9.53512e8 −1.11565
\(950\) 1.46592e9 6.89878e7i 1.70978 0.0804640i
\(951\) 2.09537e8i 0.243624i
\(952\) 1.40529e8 3.42543e8i 0.162875 0.397012i
\(953\) 1.55167e9i 1.79275i −0.443293 0.896377i \(-0.646190\pi\)
0.443293 0.896377i \(-0.353810\pi\)
\(954\) −5.02753e7 + 3.85238e8i −0.0579041 + 0.443695i
\(955\) −2.64532e8 2.21459e8i −0.303716 0.254263i
\(956\) −4.25086e8 + 1.60089e9i −0.486523 + 1.83226i
\(957\) 9.80778e8i 1.11901i
\(958\) 9.00031e7 6.89656e8i 0.102367 0.784397i
\(959\) 7.57669e7i 0.0859061i
\(960\) −5.08491e8 + 4.85401e7i −0.574738 + 0.0548640i
\(961\) 8.87454e8 0.999944
\(962\) −5.35281e8 6.98566e7i −0.601253 0.0784661i
\(963\) −1.74337e8 −0.195214
\(964\) 1.48405e9 + 3.94063e8i 1.65660 + 0.439880i
\(965\) 9.69314e8 + 8.11483e8i 1.07865 + 0.903020i
\(966\) −3.86195e8 5.04001e7i −0.428425 0.0559114i
\(967\) 7.67779e8 0.849096 0.424548 0.905405i \(-0.360433\pi\)
0.424548 + 0.905405i \(0.360433\pi\)
\(968\) 3.26611e8 + 1.33993e8i 0.360085 + 0.147726i
\(969\) −9.21586e8 −1.01290
\(970\) 5.79262e8 + 6.29292e8i 0.634688 + 0.689504i
\(971\) 8.79174e8i 0.960323i 0.877180 + 0.480161i \(0.159422\pi\)
−0.877180 + 0.480161i \(0.840578\pi\)
\(972\) 5.69378e7 + 1.51188e7i 0.0620015 + 0.0164633i
\(973\) 3.15557e8i 0.342562i
\(974\) −7.40636e7 9.66562e6i −0.0801545 0.0104605i
\(975\) 9.30023e8 1.66160e8i 1.00341 0.179272i
\(976\) 8.05742e8 + 4.60358e8i 0.866656 + 0.495161i
\(977\) 4.02377e8i 0.431469i −0.976452 0.215734i \(-0.930785\pi\)
0.976452 0.215734i \(-0.0692146\pi\)
\(978\) 3.02123e8 + 3.94284e7i 0.322974 + 0.0421495i
\(979\) 6.60925e8i 0.704376i
\(980\) 6.34322e8 4.47369e8i 0.673956 0.475322i
\(981\) 8.26187e7 0.0875127
\(982\) −4.38896e7 + 3.36308e8i −0.0463476 + 0.355142i
\(983\) 2.86965e8 0.302112 0.151056 0.988525i \(-0.451733\pi\)
0.151056 + 0.988525i \(0.451733\pi\)
\(984\) −1.62268e7 6.65706e6i −0.0170312 0.00698710i
\(985\) 5.09491e8 + 4.26532e8i 0.533124 + 0.446316i
\(986\) 2.09076e8 1.60206e9i 0.218109 1.67128i
\(987\) −2.34959e7 −0.0244366
\(988\) 2.81683e9 + 7.47955e8i 2.92072 + 0.775541i
\(989\) 6.95151e7 0.0718605
\(990\) −2.58179e8 2.80477e8i −0.266082 0.289062i
\(991\) 5.51206e8i 0.566360i 0.959067 + 0.283180i \(0.0913894\pi\)
−0.959067 + 0.283180i \(0.908611\pi\)
\(992\) 4.41784e6 5.82522e6i 0.00452559 0.00596729i
\(993\) 7.74198e8i 0.790686i
\(994\) −2.53777e7 + 1.94459e8i −0.0258401 + 0.198002i
\(995\) 9.96669e8 + 8.34383e8i 1.01177 + 0.847025i
\(996\) 3.66855e8 + 9.74115e7i 0.371293 + 0.0985899i
\(997\) 7.29498e8i 0.736103i 0.929805 + 0.368052i \(0.119975\pi\)
−0.929805 + 0.368052i \(0.880025\pi\)
\(998\) 2.40018e7 1.83916e8i 0.0241464 0.185023i
\(999\) 6.58985e7i 0.0660966i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 60.7.f.a.19.1 36
3.2 odd 2 180.7.f.g.19.36 36
4.3 odd 2 inner 60.7.f.a.19.35 yes 36
5.4 even 2 inner 60.7.f.a.19.36 yes 36
12.11 even 2 180.7.f.g.19.2 36
15.14 odd 2 180.7.f.g.19.1 36
20.19 odd 2 inner 60.7.f.a.19.2 yes 36
60.59 even 2 180.7.f.g.19.35 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.7.f.a.19.1 36 1.1 even 1 trivial
60.7.f.a.19.2 yes 36 20.19 odd 2 inner
60.7.f.a.19.35 yes 36 4.3 odd 2 inner
60.7.f.a.19.36 yes 36 5.4 even 2 inner
180.7.f.g.19.1 36 15.14 odd 2
180.7.f.g.19.2 36 12.11 even 2
180.7.f.g.19.35 36 60.59 even 2
180.7.f.g.19.36 36 3.2 odd 2