Properties

Label 33.6.e.b.4.2
Level $33$
Weight $6$
Character 33.4
Analytic conductor $5.293$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [33,6,Mod(4,33)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(33, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("33.4");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 33.e (of order \(5\), degree \(4\), 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: \(5.29266605383\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{19} + 78 x^{18} + 79 x^{17} + 10573 x^{16} - 33409 x^{15} + 1262953 x^{14} - 1581925 x^{13} + 89291182 x^{12} - 100741271 x^{11} + 2277268901 x^{10} + \cdots + 25599187870096 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4}\cdot 11^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 4.2
Root \(-3.89647 + 2.83095i\) of defining polynomial
Character \(\chi\) \(=\) 33.4
Dual form 33.6.e.b.25.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.08746 - 2.24317i) q^{2} +(-2.78115 + 8.55951i) q^{3} +(-5.38796 - 16.5824i) q^{4} +(3.77724 - 2.74432i) q^{5} +(27.7871 - 20.1885i) q^{6} +(49.4196 + 152.098i) q^{7} +(-58.2998 + 179.428i) q^{8} +(-65.5304 - 47.6106i) q^{9} +O(q^{10})\) \(q+(-3.08746 - 2.24317i) q^{2} +(-2.78115 + 8.55951i) q^{3} +(-5.38796 - 16.5824i) q^{4} +(3.77724 - 2.74432i) q^{5} +(27.7871 - 20.1885i) q^{6} +(49.4196 + 152.098i) q^{7} +(-58.2998 + 179.428i) q^{8} +(-65.5304 - 47.6106i) q^{9} -17.8180 q^{10} +(85.6495 + 392.065i) q^{11} +156.922 q^{12} +(821.799 + 597.072i) q^{13} +(188.600 - 580.452i) q^{14} +(12.9850 + 39.9637i) q^{15} +(131.099 - 95.2491i) q^{16} +(-1647.76 + 1197.17i) q^{17} +(95.5236 + 293.991i) q^{18} +(919.594 - 2830.22i) q^{19} +(-65.8591 - 47.8494i) q^{20} -1439.33 q^{21} +(615.029 - 1402.61i) q^{22} -1906.44 q^{23} +(-1373.68 - 998.036i) q^{24} +(-958.942 + 2951.32i) q^{25} +(-1197.94 - 3686.87i) q^{26} +(589.773 - 428.495i) q^{27} +(2255.88 - 1638.99i) q^{28} +(-487.060 - 1499.02i) q^{29} +(49.5547 - 152.514i) q^{30} +(1910.76 + 1388.25i) q^{31} +5418.77 q^{32} +(-3594.09 - 357.275i) q^{33} +7772.83 q^{34} +(604.075 + 438.886i) q^{35} +(-436.425 + 1343.18i) q^{36} +(1230.94 + 3788.44i) q^{37} +(-9187.87 + 6675.37i) q^{38} +(-7396.19 + 5373.65i) q^{39} +(272.197 + 837.737i) q^{40} +(1063.73 - 3273.84i) q^{41} +(4443.86 + 3228.65i) q^{42} -2635.68 q^{43} +(6039.92 - 3532.71i) q^{44} -378.182 q^{45} +(5886.06 + 4276.47i) q^{46} +(-5004.26 + 15401.5i) q^{47} +(450.679 + 1387.05i) q^{48} +(-7094.31 + 5154.32i) q^{49} +(9581.00 - 6961.01i) q^{50} +(-5664.49 - 17433.5i) q^{51} +(5473.08 - 16844.4i) q^{52} +(17823.6 + 12949.6i) q^{53} -2782.09 q^{54} +(1399.47 + 1245.87i) q^{55} -30171.8 q^{56} +(21667.7 + 15742.5i) q^{57} +(-1858.77 + 5720.71i) q^{58} +(-9001.20 - 27702.8i) q^{59} +(592.732 - 430.645i) q^{60} +(-3584.49 + 2604.29i) q^{61} +(-2785.31 - 8572.30i) q^{62} +(4002.99 - 12319.9i) q^{63} +(-20925.4 - 15203.2i) q^{64} +4742.69 q^{65} +(10295.2 + 9165.23i) q^{66} -28092.8 q^{67} +(28730.0 + 20873.5i) q^{68} +(5302.10 - 16318.2i) q^{69} +(-880.560 - 2710.08i) q^{70} +(4871.81 - 3539.58i) q^{71} +(12363.1 - 8982.32i) q^{72} +(-14764.6 - 45440.8i) q^{73} +(4697.64 - 14457.8i) q^{74} +(-22594.9 - 16416.1i) q^{75} -51886.6 q^{76} +(-55399.5 + 32402.8i) q^{77} +34889.4 q^{78} +(43127.4 + 31333.9i) q^{79} +(233.798 - 719.557i) q^{80} +(2027.46 + 6239.88i) q^{81} +(-10628.0 + 7721.70i) q^{82} +(65158.7 - 47340.6i) q^{83} +(7755.03 + 23867.5i) q^{84} +(-2938.56 + 9043.95i) q^{85} +(8137.56 + 5912.29i) q^{86} +14185.4 q^{87} +(-75341.0 - 7489.37i) q^{88} +37942.9 q^{89} +(1167.62 + 848.327i) q^{90} +(-50200.4 + 154501. i) q^{91} +(10271.8 + 31613.4i) q^{92} +(-17196.8 + 12494.2i) q^{93} +(49998.6 - 36326.1i) q^{94} +(-4293.51 - 13214.1i) q^{95} +(-15070.4 + 46382.0i) q^{96} +(78089.3 + 56735.2i) q^{97} +33465.4 q^{98} +(13053.8 - 29770.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9} - 424 q^{10} + 2289 q^{11} - 2682 q^{12} - 847 q^{13} + 2022 q^{14} - 396 q^{15} - 7148 q^{16} + 2482 q^{17} + 81 q^{18} + 2958 q^{19} + 8037 q^{20} - 1404 q^{21} + 7441 q^{22} + 8140 q^{23} - 4626 q^{24} - 13120 q^{25} - 13508 q^{26} + 3645 q^{27} + 27819 q^{28} - 20210 q^{29} + 11106 q^{30} + 5540 q^{31} - 4626 q^{32} + 639 q^{33} + 16540 q^{34} - 34101 q^{35} + 648 q^{36} - 25173 q^{37} - 55878 q^{38} + 7623 q^{39} + 22689 q^{40} + 54349 q^{41} + 32292 q^{42} - 21688 q^{43} + 24587 q^{44} - 5346 q^{45} + 44155 q^{46} - 48387 q^{47} - 43083 q^{48} - 78880 q^{49} + 19956 q^{50} + 7317 q^{51} + 109051 q^{52} - 74382 q^{53} + 10206 q^{54} - 47630 q^{55} + 168894 q^{56} + 52983 q^{57} + 1501 q^{58} - 108412 q^{59} - 72333 q^{60} + 16737 q^{61} + 132685 q^{62} - 11259 q^{63} - 157030 q^{64} - 134194 q^{65} - 127539 q^{66} + 20178 q^{67} + 387013 q^{68} + 19305 q^{69} - 411988 q^{70} + 143157 q^{71} + 41634 q^{72} + 164980 q^{73} + 286114 q^{74} - 96255 q^{75} + 46868 q^{76} - 367461 q^{77} - 152658 q^{78} + 369613 q^{79} - 107448 q^{80} - 32805 q^{81} - 184129 q^{82} + 267741 q^{83} + 279819 q^{84} + 379937 q^{85} - 290531 q^{86} + 214920 q^{87} - 740846 q^{88} + 205492 q^{89} + 117126 q^{90} + 394559 q^{91} - 483181 q^{92} - 49860 q^{93} + 561327 q^{94} + 267881 q^{95} + 228564 q^{96} - 300567 q^{97} - 2296174 q^{98} - 115506 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.08746 2.24317i −0.545791 0.396540i 0.280441 0.959871i \(-0.409519\pi\)
−0.826231 + 0.563331i \(0.809519\pi\)
\(3\) −2.78115 + 8.55951i −0.178411 + 0.549093i
\(4\) −5.38796 16.5824i −0.168374 0.518201i
\(5\) 3.77724 2.74432i 0.0675692 0.0490919i −0.553488 0.832857i \(-0.686703\pi\)
0.621057 + 0.783765i \(0.286703\pi\)
\(6\) 27.7871 20.1885i 0.315112 0.228943i
\(7\) 49.4196 + 152.098i 0.381201 + 1.17322i 0.939199 + 0.343374i \(0.111570\pi\)
−0.557998 + 0.829842i \(0.688430\pi\)
\(8\) −58.2998 + 179.428i −0.322064 + 0.991211i
\(9\) −65.5304 47.6106i −0.269672 0.195928i
\(10\) −17.8180 −0.0563456
\(11\) 85.6495 + 392.065i 0.213424 + 0.976960i
\(12\) 156.922 0.314580
\(13\) 821.799 + 597.072i 1.34867 + 0.979869i 0.999076 + 0.0429698i \(0.0136819\pi\)
0.349598 + 0.936900i \(0.386318\pi\)
\(14\) 188.600 580.452i 0.257171 0.791492i
\(15\) 12.9850 + 39.9637i 0.0149009 + 0.0458603i
\(16\) 131.099 95.2491i 0.128027 0.0930167i
\(17\) −1647.76 + 1197.17i −1.38284 + 1.00469i −0.386228 + 0.922403i \(0.626222\pi\)
−0.996609 + 0.0822865i \(0.973778\pi\)
\(18\) 95.5236 + 293.991i 0.0694911 + 0.213872i
\(19\) 919.594 2830.22i 0.584402 1.79861i −0.0172548 0.999851i \(-0.505493\pi\)
0.601657 0.798754i \(-0.294507\pi\)
\(20\) −65.8591 47.8494i −0.0368164 0.0267487i
\(21\) −1439.33 −0.712215
\(22\) 615.029 1402.61i 0.270919 0.617847i
\(23\) −1906.44 −0.751456 −0.375728 0.926730i \(-0.622607\pi\)
−0.375728 + 0.926730i \(0.622607\pi\)
\(24\) −1373.68 998.036i −0.486807 0.353686i
\(25\) −958.942 + 2951.32i −0.306861 + 0.944422i
\(26\) −1197.94 3686.87i −0.347536 1.06961i
\(27\) 589.773 428.495i 0.155695 0.113119i
\(28\) 2255.88 1638.99i 0.543777 0.395077i
\(29\) −487.060 1499.02i −0.107544 0.330988i 0.882775 0.469796i \(-0.155673\pi\)
−0.990319 + 0.138809i \(0.955673\pi\)
\(30\) 49.5547 152.514i 0.0100527 0.0309389i
\(31\) 1910.76 + 1388.25i 0.357109 + 0.259455i 0.751845 0.659340i \(-0.229164\pi\)
−0.394736 + 0.918794i \(0.629164\pi\)
\(32\) 5418.77 0.935461
\(33\) −3594.09 357.275i −0.574519 0.0571108i
\(34\) 7772.83 1.15314
\(35\) 604.075 + 438.886i 0.0833529 + 0.0605594i
\(36\) −436.425 + 1343.18i −0.0561246 + 0.172734i
\(37\) 1230.94 + 3788.44i 0.147819 + 0.454942i 0.997363 0.0725773i \(-0.0231224\pi\)
−0.849543 + 0.527519i \(0.823122\pi\)
\(38\) −9187.87 + 6675.37i −1.03218 + 0.749923i
\(39\) −7396.19 + 5373.65i −0.778658 + 0.565728i
\(40\) 272.197 + 837.737i 0.0268988 + 0.0827861i
\(41\) 1063.73 3273.84i 0.0988265 0.304157i −0.889406 0.457119i \(-0.848881\pi\)
0.988232 + 0.152962i \(0.0488813\pi\)
\(42\) 4443.86 + 3228.65i 0.388720 + 0.282422i
\(43\) −2635.68 −0.217381 −0.108691 0.994076i \(-0.534666\pi\)
−0.108691 + 0.994076i \(0.534666\pi\)
\(44\) 6039.92 3532.71i 0.470326 0.275091i
\(45\) −378.182 −0.0278401
\(46\) 5886.06 + 4276.47i 0.410138 + 0.297983i
\(47\) −5004.26 + 15401.5i −0.330442 + 1.01700i 0.638482 + 0.769637i \(0.279563\pi\)
−0.968924 + 0.247359i \(0.920437\pi\)
\(48\) 450.679 + 1387.05i 0.0282335 + 0.0868937i
\(49\) −7094.31 + 5154.32i −0.422104 + 0.306677i
\(50\) 9581.00 6961.01i 0.541983 0.393774i
\(51\) −5664.49 17433.5i −0.304954 0.938553i
\(52\) 5473.08 16844.4i 0.280688 0.863869i
\(53\) 17823.6 + 12949.6i 0.871576 + 0.633237i 0.931009 0.364995i \(-0.118929\pi\)
−0.0594334 + 0.998232i \(0.518929\pi\)
\(54\) −2782.09 −0.129833
\(55\) 1399.47 + 1245.87i 0.0623817 + 0.0555350i
\(56\) −30171.8 −1.28568
\(57\) 21667.7 + 15742.5i 0.883337 + 0.641782i
\(58\) −1858.77 + 5720.71i −0.0725531 + 0.223296i
\(59\) −9001.20 27702.8i −0.336644 1.03608i −0.965907 0.258890i \(-0.916643\pi\)
0.629263 0.777192i \(-0.283357\pi\)
\(60\) 592.732 430.645i 0.0212559 0.0154433i
\(61\) −3584.49 + 2604.29i −0.123340 + 0.0896116i −0.647745 0.761857i \(-0.724288\pi\)
0.524405 + 0.851469i \(0.324288\pi\)
\(62\) −2785.31 8572.30i −0.0920225 0.283216i
\(63\) 4002.99 12319.9i 0.127067 0.391072i
\(64\) −20925.4 15203.2i −0.638592 0.463964i
\(65\) 4742.69 0.139233
\(66\) 10295.2 + 9165.23i 0.290920 + 0.258990i
\(67\) −28092.8 −0.764555 −0.382278 0.924048i \(-0.624860\pi\)
−0.382278 + 0.924048i \(0.624860\pi\)
\(68\) 28730.0 + 20873.5i 0.753464 + 0.547424i
\(69\) 5302.10 16318.2i 0.134068 0.412619i
\(70\) −880.560 2710.08i −0.0214790 0.0661055i
\(71\) 4871.81 3539.58i 0.114695 0.0833308i −0.528959 0.848647i \(-0.677418\pi\)
0.643654 + 0.765316i \(0.277418\pi\)
\(72\) 12363.1 8982.32i 0.281058 0.204201i
\(73\) −14764.6 45440.8i −0.324276 0.998020i −0.971766 0.235946i \(-0.924181\pi\)
0.647490 0.762074i \(-0.275819\pi\)
\(74\) 4697.64 14457.8i 0.0997241 0.306919i
\(75\) −22594.9 16416.1i −0.463828 0.336991i
\(76\) −51886.6 −1.03044
\(77\) −55399.5 + 32402.8i −1.06483 + 0.622810i
\(78\) 34889.4 0.649318
\(79\) 43127.4 + 31333.9i 0.777473 + 0.564867i 0.904220 0.427068i \(-0.140453\pi\)
−0.126746 + 0.991935i \(0.540453\pi\)
\(80\) 233.798 719.557i 0.00408429 0.0125701i
\(81\) 2027.46 + 6239.88i 0.0343352 + 0.105673i
\(82\) −10628.0 + 7721.70i −0.174549 + 0.126817i
\(83\) 65158.7 47340.6i 1.03819 0.754290i 0.0682592 0.997668i \(-0.478256\pi\)
0.969932 + 0.243378i \(0.0782555\pi\)
\(84\) 7755.03 + 23867.5i 0.119918 + 0.369070i
\(85\) −2938.56 + 9043.95i −0.0441151 + 0.135772i
\(86\) 8137.56 + 5912.29i 0.118645 + 0.0862004i
\(87\) 14185.4 0.200930
\(88\) −75341.0 7489.37i −1.03711 0.103095i
\(89\) 37942.9 0.507756 0.253878 0.967236i \(-0.418294\pi\)
0.253878 + 0.967236i \(0.418294\pi\)
\(90\) 1167.62 + 848.327i 0.0151948 + 0.0110397i
\(91\) −50200.4 + 154501.i −0.635482 + 1.95581i
\(92\) 10271.8 + 31613.4i 0.126525 + 0.389405i
\(93\) −17196.8 + 12494.2i −0.206177 + 0.149796i
\(94\) 49998.6 36326.1i 0.583631 0.424033i
\(95\) −4293.51 13214.1i −0.0488094 0.150220i
\(96\) −15070.4 + 46382.0i −0.166897 + 0.513655i
\(97\) 78089.3 + 56735.2i 0.842679 + 0.612242i 0.923118 0.384518i \(-0.125632\pi\)
−0.0804389 + 0.996760i \(0.525632\pi\)
\(98\) 33465.4 0.351990
\(99\) 13053.8 29770.0i 0.133860 0.305275i
\(100\) 54106.8 0.541068
\(101\) 120205. + 87334.4i 1.17252 + 0.851886i 0.991309 0.131557i \(-0.0419978\pi\)
0.181213 + 0.983444i \(0.441998\pi\)
\(102\) −21617.4 + 66531.6i −0.205733 + 0.633180i
\(103\) −46107.0 141903.i −0.428227 1.31795i −0.899870 0.436158i \(-0.856339\pi\)
0.471643 0.881790i \(-0.343661\pi\)
\(104\) −155042. + 112645.i −1.40562 + 1.02124i
\(105\) −5436.67 + 3949.97i −0.0481238 + 0.0349640i
\(106\) −25981.4 79962.6i −0.224594 0.691230i
\(107\) 21316.2 65604.4i 0.179990 0.553954i −0.819836 0.572599i \(-0.805935\pi\)
0.999826 + 0.0186451i \(0.00593526\pi\)
\(108\) −10283.2 7471.16i −0.0848335 0.0616352i
\(109\) 107017. 0.862752 0.431376 0.902172i \(-0.358028\pi\)
0.431376 + 0.902172i \(0.358028\pi\)
\(110\) −1526.11 6985.83i −0.0120255 0.0550473i
\(111\) −35850.6 −0.276178
\(112\) 20966.1 + 15232.7i 0.157933 + 0.114745i
\(113\) 56341.2 173400.i 0.415078 1.27748i −0.497103 0.867692i \(-0.665603\pi\)
0.912181 0.409788i \(-0.134397\pi\)
\(114\) −31585.1 97208.8i −0.227625 0.700557i
\(115\) −7201.08 + 5231.89i −0.0507753 + 0.0368904i
\(116\) −22233.1 + 16153.3i −0.153410 + 0.111459i
\(117\) −25425.8 78252.7i −0.171716 0.528487i
\(118\) −34351.3 + 105723.i −0.227111 + 0.698977i
\(119\) −263518. 191457.i −1.70586 1.23938i
\(120\) −7927.64 −0.0502563
\(121\) −146379. + 67160.4i −0.908900 + 0.417013i
\(122\) 16908.8 0.102852
\(123\) 25064.0 + 18210.1i 0.149378 + 0.108530i
\(124\) 12725.4 39164.8i 0.0743220 0.228740i
\(125\) 8985.90 + 27655.7i 0.0514383 + 0.158311i
\(126\) −39994.7 + 29057.9i −0.224428 + 0.163056i
\(127\) 174180. 126549.i 0.958272 0.696226i 0.00552360 0.999985i \(-0.498242\pi\)
0.952749 + 0.303759i \(0.0982418\pi\)
\(128\) −23080.8 71035.4i −0.124516 0.383221i
\(129\) 7330.24 22560.2i 0.0387832 0.119363i
\(130\) −14642.8 10638.6i −0.0759918 0.0552113i
\(131\) −211266. −1.07560 −0.537800 0.843072i \(-0.680744\pi\)
−0.537800 + 0.843072i \(0.680744\pi\)
\(132\) 13440.3 + 61523.7i 0.0671389 + 0.307332i
\(133\) 475916. 2.33293
\(134\) 86735.5 + 63017.0i 0.417287 + 0.303177i
\(135\) 1051.78 3237.06i 0.00496697 0.0152868i
\(136\) −118742. 365449.i −0.550498 1.69426i
\(137\) −75687.9 + 54990.5i −0.344528 + 0.250315i −0.746570 0.665307i \(-0.768301\pi\)
0.402042 + 0.915621i \(0.368301\pi\)
\(138\) −52974.5 + 38488.2i −0.236793 + 0.172040i
\(139\) 88715.3 + 273038.i 0.389459 + 1.19863i 0.933194 + 0.359374i \(0.117010\pi\)
−0.543735 + 0.839257i \(0.682990\pi\)
\(140\) 4023.07 12381.7i 0.0173475 0.0533901i
\(141\) −117912. 85668.0i −0.499470 0.362886i
\(142\) −22981.4 −0.0956434
\(143\) −163704. + 373338.i −0.669453 + 1.52673i
\(144\) −13125.8 −0.0527498
\(145\) −5953.53 4325.49i −0.0235155 0.0170850i
\(146\) −56346.3 + 173416.i −0.218768 + 0.673298i
\(147\) −24388.1 75058.7i −0.0930859 0.286489i
\(148\) 56189.2 40823.9i 0.210862 0.153200i
\(149\) 93015.5 67579.7i 0.343233 0.249374i −0.402791 0.915292i \(-0.631960\pi\)
0.746025 + 0.665918i \(0.231960\pi\)
\(150\) 32936.6 + 101368.i 0.119523 + 0.367853i
\(151\) 62414.5 192092.i 0.222763 0.685594i −0.775748 0.631043i \(-0.782627\pi\)
0.998511 0.0545514i \(-0.0173729\pi\)
\(152\) 454209. + 330002.i 1.59458 + 1.15853i
\(153\) 164976. 0.569760
\(154\) 243729. + 24228.2i 0.828142 + 0.0823226i
\(155\) 11027.2 0.0368667
\(156\) 128958. + 93693.8i 0.424266 + 0.308247i
\(157\) −115078. + 354173.i −0.372600 + 1.14674i 0.572484 + 0.819916i \(0.305980\pi\)
−0.945084 + 0.326829i \(0.894020\pi\)
\(158\) −62866.8 193484.i −0.200345 0.616599i
\(159\) −160412. + 116546.i −0.503205 + 0.365600i
\(160\) 20468.0 14870.8i 0.0632084 0.0459236i
\(161\) −94215.5 289966.i −0.286456 0.881620i
\(162\) 7737.41 23813.3i 0.0231637 0.0712906i
\(163\) −59669.4 43352.4i −0.175907 0.127804i 0.496348 0.868124i \(-0.334674\pi\)
−0.672255 + 0.740320i \(0.734674\pi\)
\(164\) −60019.5 −0.174254
\(165\) −14556.2 + 8513.83i −0.0416235 + 0.0243453i
\(166\) −307368. −0.865741
\(167\) −110445. 80243.1i −0.306447 0.222647i 0.423923 0.905698i \(-0.360653\pi\)
−0.730370 + 0.683051i \(0.760653\pi\)
\(168\) 83912.5 258256.i 0.229379 0.705955i
\(169\) 204123. + 628225.i 0.549762 + 1.69199i
\(170\) 29359.8 21331.1i 0.0779167 0.0566098i
\(171\) −195010. + 141683.i −0.509995 + 0.370533i
\(172\) 14201.0 + 43706.0i 0.0366013 + 0.112647i
\(173\) −33254.0 + 102345.i −0.0844750 + 0.259987i −0.984368 0.176123i \(-0.943644\pi\)
0.899893 + 0.436110i \(0.143644\pi\)
\(174\) −43797.0 31820.4i −0.109666 0.0796768i
\(175\) −496280. −1.22499
\(176\) 48572.5 + 43241.4i 0.118198 + 0.105225i
\(177\) 262156. 0.628966
\(178\) −117147. 85112.2i −0.277128 0.201346i
\(179\) 45261.2 139300.i 0.105583 0.324951i −0.884284 0.466950i \(-0.845353\pi\)
0.989867 + 0.141999i \(0.0453530\pi\)
\(180\) 2037.63 + 6271.18i 0.00468753 + 0.0144267i
\(181\) −274921. + 199742.i −0.623752 + 0.453182i −0.854230 0.519895i \(-0.825971\pi\)
0.230478 + 0.973078i \(0.425971\pi\)
\(182\) 501563. 364407.i 1.12240 0.815470i
\(183\) −12322.4 37924.4i −0.0271999 0.0837127i
\(184\) 111145. 342070.i 0.242017 0.744852i
\(185\) 15046.2 + 10931.7i 0.0323220 + 0.0234833i
\(186\) 81121.0 0.171930
\(187\) −610497. 543492.i −1.27667 1.13655i
\(188\) 282357. 0.582645
\(189\) 94319.6 + 68527.2i 0.192065 + 0.139543i
\(190\) −16385.4 + 50428.9i −0.0329285 + 0.101343i
\(191\) 76981.1 + 236924.i 0.152687 + 0.469921i 0.997919 0.0644776i \(-0.0205381\pi\)
−0.845233 + 0.534399i \(0.820538\pi\)
\(192\) 188328. 136829.i 0.368691 0.267870i
\(193\) −26781.4 + 19457.8i −0.0517535 + 0.0376012i −0.613361 0.789802i \(-0.710183\pi\)
0.561608 + 0.827404i \(0.310183\pi\)
\(194\) −113831. 350335.i −0.217148 0.668312i
\(195\) −13190.1 + 40595.1i −0.0248406 + 0.0764516i
\(196\) 123695. + 89869.6i 0.229991 + 0.167099i
\(197\) 245814. 0.451274 0.225637 0.974211i \(-0.427554\pi\)
0.225637 + 0.974211i \(0.427554\pi\)
\(198\) −107082. + 62631.7i −0.194113 + 0.113535i
\(199\) −72399.8 −0.129600 −0.0648000 0.997898i \(-0.520641\pi\)
−0.0648000 + 0.997898i \(0.520641\pi\)
\(200\) −473644. 344123.i −0.837293 0.608329i
\(201\) 78130.5 240461.i 0.136405 0.419812i
\(202\) −175223. 539282.i −0.302144 0.929903i
\(203\) 203927. 148162.i 0.347324 0.252346i
\(204\) −258570. + 187862.i −0.435013 + 0.316055i
\(205\) −4966.49 15285.3i −0.00825401 0.0254032i
\(206\) −175959. + 541545.i −0.288897 + 0.889133i
\(207\) 124930. + 90766.8i 0.202647 + 0.147232i
\(208\) 164608. 0.263810
\(209\) 1.18839e6 + 118134.i 1.88189 + 0.187072i
\(210\) 25646.0 0.0401301
\(211\) −241483. 175448.i −0.373406 0.271295i 0.385216 0.922826i \(-0.374127\pi\)
−0.758622 + 0.651531i \(0.774127\pi\)
\(212\) 118703. 365330.i 0.181394 0.558272i
\(213\) 16747.8 + 51544.4i 0.0252935 + 0.0778453i
\(214\) −212975. + 154735.i −0.317902 + 0.230969i
\(215\) −9955.60 + 7233.17i −0.0146883 + 0.0106717i
\(216\) 42500.6 + 130803.i 0.0619813 + 0.190759i
\(217\) −116720. + 359228.i −0.168266 + 0.517871i
\(218\) −330410. 240057.i −0.470882 0.342116i
\(219\) 430014. 0.605860
\(220\) 13119.3 29919.3i 0.0182749 0.0416769i
\(221\) −2.06892e6 −2.84946
\(222\) 110687. + 80418.9i 0.150735 + 0.109516i
\(223\) −21477.6 + 66101.3i −0.0289217 + 0.0890118i −0.964475 0.264173i \(-0.914901\pi\)
0.935554 + 0.353184i \(0.114901\pi\)
\(224\) 267793. + 824183.i 0.356599 + 1.09750i
\(225\) 203354. 147745.i 0.267791 0.194562i
\(226\) −562917. + 408983.i −0.733118 + 0.532641i
\(227\) −115985. 356966.i −0.149396 0.459793i 0.848154 0.529749i \(-0.177714\pi\)
−0.997550 + 0.0699563i \(0.977714\pi\)
\(228\) 144305. 444124.i 0.183841 0.565805i
\(229\) −242301. 176042.i −0.305328 0.221834i 0.424561 0.905399i \(-0.360428\pi\)
−0.729889 + 0.683565i \(0.760428\pi\)
\(230\) 33969.0 0.0423412
\(231\) −123278. 564310.i −0.152004 0.695805i
\(232\) 297362. 0.362715
\(233\) 1.02768e6 + 746656.i 1.24014 + 0.901012i 0.997608 0.0691322i \(-0.0220230\pi\)
0.242529 + 0.970144i \(0.422023\pi\)
\(234\) −97032.8 + 298636.i −0.115845 + 0.356536i
\(235\) 23364.5 + 71908.4i 0.0275986 + 0.0849396i
\(236\) −410882. + 298523.i −0.480217 + 0.348898i
\(237\) −388147. + 282005.i −0.448874 + 0.326126i
\(238\) 384130. + 1.18223e6i 0.439578 + 1.35288i
\(239\) 68696.4 211426.i 0.0777927 0.239421i −0.904596 0.426270i \(-0.859827\pi\)
0.982389 + 0.186849i \(0.0598274\pi\)
\(240\) 5508.82 + 4002.39i 0.00617349 + 0.00448530i
\(241\) 527531. 0.585067 0.292533 0.956255i \(-0.405502\pi\)
0.292533 + 0.956255i \(0.405502\pi\)
\(242\) 602592. + 120999.i 0.661432 + 0.132813i
\(243\) −59049.0 −0.0641500
\(244\) 62498.5 + 45407.8i 0.0672040 + 0.0488265i
\(245\) −12651.8 + 38938.1i −0.0134659 + 0.0414438i
\(246\) −36535.8 112446.i −0.0384929 0.118469i
\(247\) 2.44556e6 1.77681e6i 2.55057 1.85310i
\(248\) −360487. + 261909.i −0.372187 + 0.270409i
\(249\) 223996. + 689388.i 0.228950 + 0.704637i
\(250\) 34292.9 105543.i 0.0347020 0.106802i
\(251\) 689843. + 501201.i 0.691140 + 0.502143i 0.877035 0.480427i \(-0.159518\pi\)
−0.185895 + 0.982570i \(0.559518\pi\)
\(252\) −225862. −0.224049
\(253\) −163286. 747449.i −0.160379 0.734143i
\(254\) −821645. −0.799097
\(255\) −69239.2 50305.2i −0.0666809 0.0484465i
\(256\) −343853. + 1.05827e6i −0.327923 + 1.00924i
\(257\) 375280. + 1.15499e6i 0.354424 + 1.09080i 0.956343 + 0.292247i \(0.0944030\pi\)
−0.601919 + 0.798557i \(0.705597\pi\)
\(258\) −73238.1 + 53210.6i −0.0684995 + 0.0497678i
\(259\) −515380. + 374446.i −0.477396 + 0.346848i
\(260\) −25553.4 78645.2i −0.0234431 0.0721505i
\(261\) −39451.9 + 121420.i −0.0358481 + 0.110329i
\(262\) 652274. + 473905.i 0.587052 + 0.426518i
\(263\) −1.21904e6 −1.08675 −0.543374 0.839491i \(-0.682853\pi\)
−0.543374 + 0.839491i \(0.682853\pi\)
\(264\) 273640. 624053.i 0.241641 0.551076i
\(265\) 102862. 0.0899786
\(266\) −1.46937e6 1.06756e6i −1.27329 0.925099i
\(267\) −105525. + 324772.i −0.0905893 + 0.278805i
\(268\) 151363. + 465848.i 0.128731 + 0.396193i
\(269\) 1.59215e6 1.15676e6i 1.34154 0.974683i 0.342150 0.939645i \(-0.388845\pi\)
0.999386 0.0350377i \(-0.0111551\pi\)
\(270\) −10508.6 + 7634.95i −0.00877275 + 0.00637377i
\(271\) 63636.5 + 195853.i 0.0526360 + 0.161997i 0.973919 0.226896i \(-0.0728577\pi\)
−0.921283 + 0.388893i \(0.872858\pi\)
\(272\) −101991. + 313895.i −0.0835869 + 0.257254i
\(273\) −1.18284e6 859381.i −0.960546 0.697878i
\(274\) 357036. 0.287300
\(275\) −1.23924e6 123189.i −0.988154 0.0982288i
\(276\) −299163. −0.236393
\(277\) −905248. 657701.i −0.708873 0.515026i 0.173937 0.984757i \(-0.444351\pi\)
−0.882810 + 0.469731i \(0.844351\pi\)
\(278\) 338565. 1.04200e6i 0.262742 0.808637i
\(279\) −59117.3 181944.i −0.0454678 0.139936i
\(280\) −113966. + 82801.2i −0.0868721 + 0.0631163i
\(281\) 765645. 556273.i 0.578444 0.420264i −0.259719 0.965684i \(-0.583630\pi\)
0.838163 + 0.545420i \(0.183630\pi\)
\(282\) 171880. + 528992.i 0.128707 + 0.396120i
\(283\) −194822. + 599602.i −0.144602 + 0.445038i −0.996960 0.0779210i \(-0.975172\pi\)
0.852358 + 0.522959i \(0.175172\pi\)
\(284\) −84943.9 61715.3i −0.0624937 0.0454043i
\(285\) 125047. 0.0911928
\(286\) 1.34289e6 785448.i 0.970790 0.567809i
\(287\) 550513. 0.394514
\(288\) −355094. 257991.i −0.252268 0.183283i
\(289\) 843138. 2.59491e6i 0.593819 1.82759i
\(290\) 8678.46 + 26709.5i 0.00605965 + 0.0186497i
\(291\) −702803. + 510617.i −0.486521 + 0.353478i
\(292\) −673968. + 489667.i −0.462575 + 0.336081i
\(293\) −177501. 546290.i −0.120790 0.371753i 0.872321 0.488934i \(-0.162614\pi\)
−0.993111 + 0.117181i \(0.962614\pi\)
\(294\) −93072.3 + 286447.i −0.0627989 + 0.193275i
\(295\) −110025. 79938.0i −0.0736100 0.0534808i
\(296\) −751516. −0.498551
\(297\) 218512. + 194529.i 0.143742 + 0.127966i
\(298\) −438774. −0.286220
\(299\) −1.56671e6 1.13828e6i −1.01347 0.736329i
\(300\) −150479. + 463127.i −0.0965325 + 0.297096i
\(301\) −130254. 400882.i −0.0828660 0.255035i
\(302\) −623597. + 453070.i −0.393448 + 0.285856i
\(303\) −1.08185e6 + 786009.i −0.676955 + 0.491837i
\(304\) −149018. 458630.i −0.0924814 0.284628i
\(305\) −6392.47 + 19674.0i −0.00393477 + 0.0121100i
\(306\) −509356. 370069.i −0.310970 0.225933i
\(307\) 2.24566e6 1.35987 0.679935 0.733272i \(-0.262008\pi\)
0.679935 + 0.733272i \(0.262008\pi\)
\(308\) 835807. + 744073.i 0.502030 + 0.446929i
\(309\) 1.34285e6 0.800076
\(310\) −34045.9 24735.8i −0.0201215 0.0146191i
\(311\) 385338. 1.18595e6i 0.225913 0.695288i −0.772285 0.635277i \(-0.780886\pi\)
0.998198 0.0600119i \(-0.0191139\pi\)
\(312\) −532988. 1.64037e6i −0.309978 0.954015i
\(313\) −1.07441e6 + 780607.i −0.619884 + 0.450372i −0.852881 0.522105i \(-0.825147\pi\)
0.232997 + 0.972477i \(0.425147\pi\)
\(314\) 1.14977e6 835356.i 0.658092 0.478132i
\(315\) −18689.6 57520.7i −0.0106127 0.0326624i
\(316\) 287223. 883982.i 0.161809 0.497996i
\(317\) 1.60262e6 + 1.16437e6i 0.895740 + 0.650793i 0.937368 0.348340i \(-0.113255\pi\)
−0.0416285 + 0.999133i \(0.513255\pi\)
\(318\) 756699. 0.419619
\(319\) 545996. 319350.i 0.300409 0.175707i
\(320\) −120763. −0.0659261
\(321\) 502258. + 364912.i 0.272060 + 0.197663i
\(322\) −359555. + 1.10660e6i −0.193253 + 0.594771i
\(323\) 1.87297e6 + 5.76442e6i 0.998907 + 3.07432i
\(324\) 92548.5 67240.4i 0.0489787 0.0355851i
\(325\) −2.55021e6 + 1.85283e6i −1.33927 + 0.973034i
\(326\) 86980.1 + 267697.i 0.0453290 + 0.139508i
\(327\) −297630. + 916012.i −0.153925 + 0.473731i
\(328\) 525404. + 381728.i 0.269655 + 0.195916i
\(329\) −2.58985e6 −1.31912
\(330\) 64039.6 + 6365.95i 0.0323716 + 0.00321794i
\(331\) −232513. −0.116648 −0.0583240 0.998298i \(-0.518576\pi\)
−0.0583240 + 0.998298i \(0.518576\pi\)
\(332\) −1.13609e6 825420.i −0.565678 0.410989i
\(333\) 99705.9 306863.i 0.0492732 0.151647i
\(334\) 160996. + 495494.i 0.0789675 + 0.243037i
\(335\) −106113. + 77095.8i −0.0516604 + 0.0375335i
\(336\) −188694. + 137095.i −0.0911824 + 0.0662479i
\(337\) 348433. + 1.07237e6i 0.167126 + 0.514362i 0.999187 0.0403232i \(-0.0128388\pi\)
−0.832060 + 0.554685i \(0.812839\pi\)
\(338\) 778995. 2.39750e6i 0.370888 1.14148i
\(339\) 1.32753e6 + 964506.i 0.627400 + 0.455833i
\(340\) 165804. 0.0777851
\(341\) −380627. + 868043.i −0.177261 + 0.404255i
\(342\) 919903. 0.425282
\(343\) 1.03997e6 + 755581.i 0.477293 + 0.346773i
\(344\) 153660. 472917.i 0.0700107 0.215471i
\(345\) −24755.1 76188.3i −0.0111974 0.0344620i
\(346\) 332248. 241392.i 0.149201 0.108401i
\(347\) 2.99900e6 2.17890e6i 1.33707 0.971436i 0.337521 0.941318i \(-0.390412\pi\)
0.999546 0.0301180i \(-0.00958829\pi\)
\(348\) −76430.6 235229.i −0.0338313 0.104122i
\(349\) −777364. + 2.39248e6i −0.341634 + 1.05144i 0.621728 + 0.783233i \(0.286431\pi\)
−0.963361 + 0.268207i \(0.913569\pi\)
\(350\) 1.53224e6 + 1.11324e6i 0.668586 + 0.485756i
\(351\) 740518. 0.320825
\(352\) 464115. + 2.12451e6i 0.199650 + 0.913907i
\(353\) −3.02523e6 −1.29218 −0.646088 0.763263i \(-0.723596\pi\)
−0.646088 + 0.763263i \(0.723596\pi\)
\(354\) −809397. 588061.i −0.343284 0.249410i
\(355\) 8688.23 26739.6i 0.00365898 0.0112612i
\(356\) −204434. 629185.i −0.0854927 0.263120i
\(357\) 2.37166e6 1.72311e6i 0.984877 0.715555i
\(358\) −452215. + 328553.i −0.186482 + 0.135487i
\(359\) 398330. + 1.22593e6i 0.163120 + 0.502031i 0.998893 0.0470441i \(-0.0149801\pi\)
−0.835773 + 0.549075i \(0.814980\pi\)
\(360\) 22048.0 67856.7i 0.00896628 0.0275954i
\(361\) −5.16128e6 3.74989e6i −2.08444 1.51443i
\(362\) 1.29686e6 0.520143
\(363\) −167757. 1.43972e6i −0.0668211 0.573470i
\(364\) 2.83248e6 1.12050
\(365\) −180474. 131122.i −0.0709058 0.0515161i
\(366\) −47026.0 + 144731.i −0.0183500 + 0.0564754i
\(367\) −1.37513e6 4.23221e6i −0.532940 1.64022i −0.748059 0.663633i \(-0.769014\pi\)
0.215119 0.976588i \(-0.430986\pi\)
\(368\) −249933. + 181587.i −0.0962064 + 0.0698980i
\(369\) −225576. + 163891.i −0.0862437 + 0.0626597i
\(370\) −21932.9 67502.5i −0.00832897 0.0256339i
\(371\) −1.08877e6 + 3.35089e6i −0.410678 + 1.26394i
\(372\) 299840. + 217846.i 0.112339 + 0.0816194i
\(373\) −3.32452e6 −1.23725 −0.618625 0.785687i \(-0.712310\pi\)
−0.618625 + 0.785687i \(0.712310\pi\)
\(374\) 665739. + 3.04746e6i 0.246108 + 1.12657i
\(375\) −261711. −0.0961044
\(376\) −2.47172e6 1.79581e6i −0.901634 0.655075i
\(377\) 494756. 1.52270e6i 0.179282 0.551774i
\(378\) −137490. 423150.i −0.0494926 0.152323i
\(379\) −1.70859e6 + 1.24136e6i −0.610998 + 0.443916i −0.849766 0.527161i \(-0.823257\pi\)
0.238768 + 0.971077i \(0.423257\pi\)
\(380\) −195988. + 142394.i −0.0696258 + 0.0505861i
\(381\) 598778. + 1.84285e6i 0.211326 + 0.650395i
\(382\) 293784. 904173.i 0.103008 0.317025i
\(383\) −1.05344e6 765370.i −0.366955 0.266609i 0.388992 0.921241i \(-0.372823\pi\)
−0.755947 + 0.654632i \(0.772823\pi\)
\(384\) 672219. 0.232639
\(385\) −120333. + 274427.i −0.0413746 + 0.0943572i
\(386\) 126334. 0.0431570
\(387\) 172717. + 125487.i 0.0586217 + 0.0425912i
\(388\) 520065. 1.60060e6i 0.175379 0.539762i
\(389\) −1.46703e6 4.51504e6i −0.491546 1.51282i −0.822272 0.569095i \(-0.807294\pi\)
0.330726 0.943727i \(-0.392706\pi\)
\(390\) 131786. 95747.8i 0.0438739 0.0318763i
\(391\) 3.14135e6 2.28233e6i 1.03914 0.754980i
\(392\) −511234. 1.57342e6i −0.168037 0.517164i
\(393\) 587562. 1.80833e6i 0.191899 0.590604i
\(394\) −758939. 551401.i −0.246301 0.178948i
\(395\) 248893. 0.0802637
\(396\) −563992. 56064.4i −0.180732 0.0179659i
\(397\) 2.09629e6 0.667536 0.333768 0.942655i \(-0.391680\pi\)
0.333768 + 0.942655i \(0.391680\pi\)
\(398\) 223531. + 162405.i 0.0707344 + 0.0513916i
\(399\) −1.32360e6 + 4.07361e6i −0.416220 + 1.28099i
\(400\) 155394. + 478254.i 0.0485607 + 0.149454i
\(401\) −7494.54 + 5445.10i −0.00232747 + 0.00169100i −0.588948 0.808171i \(-0.700458\pi\)
0.586621 + 0.809862i \(0.300458\pi\)
\(402\) −780619. + 567153.i −0.240921 + 0.175039i
\(403\) 741375. + 2.28172e6i 0.227392 + 0.699841i
\(404\) 800554. 2.46385e6i 0.244027 0.751037i
\(405\) 24782.4 + 18005.5i 0.00750769 + 0.00545466i
\(406\) −961968. −0.289631
\(407\) −1.37988e6 + 807085.i −0.412911 + 0.241509i
\(408\) 3.45830e6 1.02852
\(409\) 2.75737e6 + 2.00335e6i 0.815055 + 0.592172i 0.915292 0.402791i \(-0.131960\pi\)
−0.100237 + 0.994964i \(0.531960\pi\)
\(410\) −18953.6 + 58333.3i −0.00556844 + 0.0171379i
\(411\) −260192. 800788.i −0.0759782 0.233837i
\(412\) −2.10467e6 + 1.52913e6i −0.610860 + 0.443815i
\(413\) 3.76871e6 2.73813e6i 1.08722 0.789911i
\(414\) −182110. 560477.i −0.0522196 0.160715i
\(415\) 116202. 357633.i 0.0331202 0.101934i
\(416\) 4.45314e6 + 3.23539e6i 1.26163 + 0.916629i
\(417\) −2.58380e6 −0.727643
\(418\) −3.40412e6 3.03050e6i −0.952937 0.848347i
\(419\) −630609. −0.175479 −0.0877395 0.996143i \(-0.527964\pi\)
−0.0877395 + 0.996143i \(0.527964\pi\)
\(420\) 94792.7 + 68871.0i 0.0262212 + 0.0190508i
\(421\) −537621. + 1.65463e6i −0.147833 + 0.454983i −0.997364 0.0725550i \(-0.976885\pi\)
0.849531 + 0.527538i \(0.176885\pi\)
\(422\) 352010. + 1.08338e6i 0.0962220 + 0.296141i
\(423\) 1.06121e6 771012.i 0.288369 0.209513i
\(424\) −3.36264e6 + 2.44310e6i −0.908375 + 0.659973i
\(425\) −1.95312e6 6.01107e6i −0.524512 1.61428i
\(426\) 63914.7 196709.i 0.0170638 0.0525171i
\(427\) −573250. 416491.i −0.152151 0.110544i
\(428\) −1.20273e6 −0.317365
\(429\) −2.74030e6 2.43954e6i −0.718878 0.639977i
\(430\) 46962.7 0.0122485
\(431\) 2.33920e6 + 1.69953e6i 0.606561 + 0.440693i 0.848202 0.529673i \(-0.177685\pi\)
−0.241640 + 0.970366i \(0.577685\pi\)
\(432\) 36505.0 112351.i 0.00941115 0.0289646i
\(433\) 1.17677e6 + 3.62174e6i 0.301629 + 0.928320i 0.980914 + 0.194444i \(0.0622904\pi\)
−0.679284 + 0.733875i \(0.737710\pi\)
\(434\) 1.16618e6 847279.i 0.297195 0.215924i
\(435\) 53581.8 38929.4i 0.0135767 0.00986404i
\(436\) −576603. 1.77460e6i −0.145265 0.447079i
\(437\) −1.75315e6 + 5.39564e6i −0.439153 + 1.35157i
\(438\) −1.32765e6 964594.i −0.330673 0.240248i
\(439\) 5.05208e6 1.25115 0.625575 0.780164i \(-0.284865\pi\)
0.625575 + 0.780164i \(0.284865\pi\)
\(440\) −305134. + 178471.i −0.0751379 + 0.0439476i
\(441\) 710293. 0.173917
\(442\) 6.38770e6 + 4.64094e6i 1.55521 + 1.12993i
\(443\) −468192. + 1.44095e6i −0.113348 + 0.348850i −0.991599 0.129351i \(-0.958711\pi\)
0.878251 + 0.478200i \(0.158711\pi\)
\(444\) 193161. + 594490.i 0.0465011 + 0.143116i
\(445\) 143319. 104127.i 0.0343087 0.0249267i
\(446\) 214588. 155907.i 0.0510819 0.0371132i
\(447\) 319759. + 984116.i 0.0756926 + 0.232958i
\(448\) 1.27825e6 3.93404e6i 0.300898 0.926070i
\(449\) −2.16345e6 1.57184e6i −0.506444 0.367953i 0.305029 0.952343i \(-0.401334\pi\)
−0.811473 + 0.584390i \(0.801334\pi\)
\(450\) −959264. −0.223309
\(451\) 1.37467e6 + 136651.i 0.318241 + 0.0316352i
\(452\) −3.17896e6 −0.731879
\(453\) 1.47063e6 + 1.06848e6i 0.336712 + 0.244635i
\(454\) −442636. + 1.36229e6i −0.100788 + 0.310192i
\(455\) 234382. + 721352.i 0.0530756 + 0.163350i
\(456\) −4.08788e6 + 2.97002e6i −0.920633 + 0.668879i
\(457\) −2.09292e6 + 1.52059e6i −0.468772 + 0.340582i −0.796962 0.604029i \(-0.793561\pi\)
0.328191 + 0.944611i \(0.393561\pi\)
\(458\) 353203. + 1.08705e6i 0.0786792 + 0.242150i
\(459\) −458823. + 1.41211e6i −0.101651 + 0.312851i
\(460\) 125556. + 91222.1i 0.0276659 + 0.0201004i
\(461\) 5.12106e6 1.12230 0.561148 0.827715i \(-0.310360\pi\)
0.561148 + 0.827715i \(0.310360\pi\)
\(462\) −885228. + 2.01881e6i −0.192952 + 0.440039i
\(463\) −50847.5 −0.0110234 −0.00551172 0.999985i \(-0.501754\pi\)
−0.00551172 + 0.999985i \(0.501754\pi\)
\(464\) −206633. 150128.i −0.0445559 0.0323718i
\(465\) −30668.2 + 94387.1i −0.00657743 + 0.0202433i
\(466\) −1.49805e6 4.61054e6i −0.319567 0.983528i
\(467\) −7.50041e6 + 5.44937e6i −1.59145 + 1.15626i −0.689612 + 0.724179i \(0.742219\pi\)
−0.901837 + 0.432076i \(0.857781\pi\)
\(468\) −1.16063e6 + 843244.i −0.244950 + 0.177967i
\(469\) −1.38834e6 4.27286e6i −0.291449 0.896988i
\(470\) 89166.0 274425.i 0.0186189 0.0573032i
\(471\) −2.71150e6 1.97002e6i −0.563193 0.409184i
\(472\) 5.49545e6 1.13540
\(473\) −225745. 1.03336e6i −0.0463944 0.212373i
\(474\) 1.83097e6 0.374314
\(475\) 7.47104e6 + 5.42803e6i 1.51931 + 1.10385i
\(476\) −1.75500e6 + 5.40133e6i −0.355025 + 1.09265i
\(477\) −551448. 1.69718e6i −0.110971 0.341533i
\(478\) −686361. + 498670.i −0.137399 + 0.0998260i
\(479\) 7.70294e6 5.59652e6i 1.53397 1.11450i 0.579997 0.814619i \(-0.303054\pi\)
0.953977 0.299878i \(-0.0969461\pi\)
\(480\) 70362.6 + 216554.i 0.0139392 + 0.0429005i
\(481\) −1.25039e6 + 3.84829e6i −0.246423 + 0.758412i
\(482\) −1.62873e6 1.18334e6i −0.319324 0.232002i
\(483\) 2.74399e6 0.535198
\(484\) 1.90237e6 + 2.06547e6i 0.369132 + 0.400779i
\(485\) 450661. 0.0869953
\(486\) 182311. + 132457.i 0.0350125 + 0.0254381i
\(487\) 1.99874e6 6.15148e6i 0.381885 1.17532i −0.556829 0.830627i \(-0.687982\pi\)
0.938715 0.344695i \(-0.112018\pi\)
\(488\) −258308. 794989.i −0.0491007 0.151116i
\(489\) 537025. 390171.i 0.101560 0.0737876i
\(490\) 126407. 91839.8i 0.0237837 0.0172799i
\(491\) −853226. 2.62596e6i −0.159720 0.491569i 0.838888 0.544304i \(-0.183206\pi\)
−0.998609 + 0.0527350i \(0.983206\pi\)
\(492\) 166923. 513738.i 0.0310888 0.0956816i
\(493\) 2.59713e6 + 1.88693e6i 0.481256 + 0.349653i
\(494\) −1.15363e7 −2.12690
\(495\) −32391.2 148272.i −0.00594174 0.0271986i
\(496\) 382728. 0.0698531
\(497\) 779125. + 566067.i 0.141487 + 0.102796i
\(498\) 854836. 2.63092e6i 0.154458 0.475372i
\(499\) −168800. 519514.i −0.0303474 0.0933998i 0.934736 0.355344i \(-0.115636\pi\)
−0.965083 + 0.261944i \(0.915636\pi\)
\(500\) 410184. 298016.i 0.0733759 0.0533107i
\(501\) 994006. 722188.i 0.176927 0.128545i
\(502\) −1.00558e6 3.09487e6i −0.178098 0.548130i
\(503\) 1.93426e6 5.95305e6i 0.340875 1.04911i −0.622880 0.782317i \(-0.714038\pi\)
0.963755 0.266788i \(-0.0859625\pi\)
\(504\) 1.97717e6 + 1.43650e6i 0.346711 + 0.251900i
\(505\) 693718. 0.121047
\(506\) −1.17252e6 + 2.67400e6i −0.203584 + 0.464285i
\(507\) −5.94500e6 −1.02715
\(508\) −3.03697e6 2.20649e6i −0.522133 0.379352i
\(509\) −2.77372e6 + 8.53662e6i −0.474534 + 1.46047i 0.372050 + 0.928213i \(0.378655\pi\)
−0.846585 + 0.532254i \(0.821345\pi\)
\(510\) 100930. + 310631.i 0.0171828 + 0.0528833i
\(511\) 6.18179e6 4.49133e6i 1.04728 0.760892i
\(512\) 1.50187e6 1.09117e6i 0.253196 0.183958i
\(513\) −670384. 2.06323e6i −0.112468 0.346142i
\(514\) 1.43218e6 4.40781e6i 0.239106 0.735894i
\(515\) −563584. 409468.i −0.0936356 0.0680302i
\(516\) −413597. −0.0683838
\(517\) −6.46701e6 642862.i −1.06409 0.105777i
\(518\) 2.43116e6 0.398097
\(519\) −783540. 569275.i −0.127686 0.0927692i
\(520\) −276498. + 850973.i −0.0448418 + 0.138009i
\(521\) −664892. 2.04633e6i −0.107314 0.330279i 0.882953 0.469462i \(-0.155552\pi\)
−0.990267 + 0.139184i \(0.955552\pi\)
\(522\) 394173. 286383.i 0.0633155 0.0460014i
\(523\) −191274. + 138968.i −0.0305774 + 0.0222158i −0.602969 0.797765i \(-0.706016\pi\)
0.572392 + 0.819980i \(0.306016\pi\)
\(524\) 1.13829e6 + 3.50330e6i 0.181103 + 0.557377i
\(525\) 1.38023e6 4.24791e6i 0.218551 0.672631i
\(526\) 3.76373e6 + 2.73451e6i 0.593136 + 0.430939i
\(527\) −4.81042e6 −0.754495
\(528\) −505212. + 295495.i −0.0788659 + 0.0461281i
\(529\) −2.80183e6 −0.435313
\(530\) −317581. 230736.i −0.0491094 0.0356801i
\(531\) −729097. + 2.24393e6i −0.112215 + 0.345361i
\(532\) −2.56422e6 7.89184e6i −0.392804 1.20892i
\(533\) 2.82889e6 2.05531e6i 0.431319 0.313371i
\(534\) 1.05432e6 766010.i 0.160000 0.116247i
\(535\) −99523.4 306302.i −0.0150328 0.0462663i
\(536\) 1.63781e6 5.04066e6i 0.246236 0.757836i
\(537\) 1.06646e6 + 774827.i 0.159591 + 0.115950i
\(538\) −7.51050e6 −1.11870
\(539\) −2.62845e6 2.33997e6i −0.389698 0.346927i
\(540\) −59345.2 −0.00875793
\(541\) 1.46666e6 + 1.06559e6i 0.215445 + 0.156530i 0.690274 0.723548i \(-0.257490\pi\)
−0.474829 + 0.880078i \(0.657490\pi\)
\(542\) 242856. 747435.i 0.0355101 0.109289i
\(543\) −945095. 2.90870e6i −0.137555 0.423350i
\(544\) −8.92881e6 + 6.48716e6i −1.29359 + 0.939848i
\(545\) 404228. 293689.i 0.0582955 0.0423542i
\(546\) 1.72422e6 + 5.30661e6i 0.247521 + 0.761790i
\(547\) 202383. 622870.i 0.0289204 0.0890079i −0.935554 0.353182i \(-0.885099\pi\)
0.964475 + 0.264175i \(0.0850995\pi\)
\(548\) 1.31968e6 + 958803.i 0.187723 + 0.136389i
\(549\) 358885. 0.0508188
\(550\) 3.54978e6 + 3.16017e6i 0.500374 + 0.445455i
\(551\) −4.69045e6 −0.658165
\(552\) 2.61884e6 + 1.90270e6i 0.365814 + 0.265780i
\(553\) −2.63448e6 + 8.10809e6i −0.366338 + 1.12747i
\(554\) 1.31958e6 + 4.06125e6i 0.182668 + 0.562193i
\(555\) −135416. + 98385.5i −0.0186611 + 0.0135581i
\(556\) 4.04963e6 2.94223e6i 0.555557 0.403636i
\(557\) −3.67152e6 1.12998e7i −0.501427 1.54323i −0.806695 0.590968i \(-0.798746\pi\)
0.305268 0.952267i \(-0.401254\pi\)
\(558\) −225610. + 694356.i −0.0306742 + 0.0944054i
\(559\) −2.16600e6 1.57369e6i −0.293177 0.213005i
\(560\) 120997. 0.0163044
\(561\) 6.34991e6 3.71402e6i 0.851844 0.498238i
\(562\) −3.61171e6 −0.482361
\(563\) 9.87469e6 + 7.17438e6i 1.31296 + 0.953923i 0.999991 + 0.00416105i \(0.00132451\pi\)
0.312972 + 0.949762i \(0.398675\pi\)
\(564\) −785279. + 2.41684e6i −0.103950 + 0.319926i
\(565\) −263053. 809592.i −0.0346674 0.106695i
\(566\) 1.94651e6 1.41423e6i 0.255397 0.185557i
\(567\) −848876. + 616745.i −0.110889 + 0.0805653i
\(568\) 351075. + 1.08050e6i 0.0456593 + 0.140525i
\(569\) −698849. + 2.15084e6i −0.0904904 + 0.278501i −0.986052 0.166436i \(-0.946774\pi\)
0.895562 + 0.444937i \(0.146774\pi\)
\(570\) −386077. 280501.i −0.0497721 0.0361616i
\(571\) 4.20948e6 0.540304 0.270152 0.962818i \(-0.412926\pi\)
0.270152 + 0.962818i \(0.412926\pi\)
\(572\) 7.07288e6 + 703089.i 0.903870 + 0.0898505i
\(573\) −2.24205e6 −0.285271
\(574\) −1.69968e6 1.23489e6i −0.215322 0.156441i
\(575\) 1.82817e6 5.62652e6i 0.230593 0.709692i
\(576\) 647416. + 1.99254e6i 0.0813068 + 0.250237i
\(577\) −5.61704e6 + 4.08101e6i −0.702373 + 0.510304i −0.880704 0.473667i \(-0.842930\pi\)
0.178331 + 0.983970i \(0.442930\pi\)
\(578\) −8.42398e6 + 6.12038e6i −1.04881 + 0.762007i
\(579\) −92066.3 283351.i −0.0114131 0.0351260i
\(580\) −39649.8 + 122030.i −0.00489408 + 0.0150624i
\(581\) 1.04205e7 + 7.57095e6i 1.28070 + 0.930486i
\(582\) 3.31528e6 0.405707
\(583\) −3.55050e6 + 8.09713e6i −0.432632 + 0.986643i
\(584\) 9.01415e6 1.09369
\(585\) −310790. 225802.i −0.0375472 0.0272796i
\(586\) −677397. + 2.08481e6i −0.0814890 + 0.250797i
\(587\) 1.80686e6 + 5.56095e6i 0.216436 + 0.666122i 0.999049 + 0.0436127i \(0.0138868\pi\)
−0.782612 + 0.622509i \(0.786113\pi\)
\(588\) −1.11325e6 + 808826.i −0.132786 + 0.0964744i
\(589\) 5.68616e6 4.13123e6i 0.675352 0.490672i
\(590\) 160384. + 493610.i 0.0189684 + 0.0583787i
\(591\) −683645. + 2.10404e6i −0.0805122 + 0.247791i
\(592\) 522220. + 379415.i 0.0612420 + 0.0444949i
\(593\) 8.85114e6 1.03362 0.516812 0.856099i \(-0.327119\pi\)
0.516812 + 0.856099i \(0.327119\pi\)
\(594\) −238285. 1.09076e6i −0.0277096 0.126842i
\(595\) −1.52079e6 −0.176107
\(596\) −1.62180e6 1.17831e6i −0.187017 0.135876i
\(597\) 201355. 619707.i 0.0231221 0.0711624i
\(598\) 2.28379e6 + 7.02880e6i 0.261158 + 0.803763i
\(599\) 4.21259e6 3.06063e6i 0.479714 0.348532i −0.321501 0.946909i \(-0.604187\pi\)
0.801215 + 0.598377i \(0.204187\pi\)
\(600\) 4.26280e6 3.09711e6i 0.483411 0.351219i
\(601\) 3.65187e6 + 1.12393e7i 0.412410 + 1.26927i 0.914547 + 0.404480i \(0.132548\pi\)
−0.502136 + 0.864789i \(0.667452\pi\)
\(602\) −497091. + 1.52989e6i −0.0559042 + 0.172055i
\(603\) 1.84093e6 + 1.33752e6i 0.206179 + 0.149798i
\(604\) −3.52164e6 −0.392783
\(605\) −368599. + 655393.i −0.0409417 + 0.0727969i
\(606\) 5.10331e6 0.564509
\(607\) −1.36089e7 9.88746e6i −1.49917 1.08921i −0.970709 0.240259i \(-0.922768\pi\)
−0.528466 0.848955i \(-0.677232\pi\)
\(608\) 4.98306e6 1.53363e7i 0.546685 1.68252i
\(609\) 701039. + 2.15758e6i 0.0765947 + 0.235734i
\(610\) 63868.6 46403.3i 0.00694965 0.00504922i
\(611\) −1.33083e7 + 9.66905e6i −1.44218 + 1.04781i
\(612\) −888883. 2.73570e6i −0.0959326 0.295250i
\(613\) −3.93335e6 + 1.21056e7i −0.422777 + 1.30118i 0.482329 + 0.875990i \(0.339791\pi\)
−0.905106 + 0.425185i \(0.860209\pi\)
\(614\) −6.93337e6 5.03739e6i −0.742205 0.539243i
\(615\) 144647. 0.0154213
\(616\) −2.58420e6 1.18293e7i −0.274394 1.25605i
\(617\) 9.06047e6 0.958160 0.479080 0.877771i \(-0.340970\pi\)
0.479080 + 0.877771i \(0.340970\pi\)
\(618\) −4.14599e6 3.01224e6i −0.436674 0.317262i
\(619\) 400128. 1.23147e6i 0.0419733 0.129180i −0.927874 0.372894i \(-0.878366\pi\)
0.969847 + 0.243713i \(0.0783656\pi\)
\(620\) −59413.9 182857.i −0.00620739 0.0191044i
\(621\) −1.12437e6 + 816901.i −0.116998 + 0.0850042i
\(622\) −3.85000e6 + 2.79719e6i −0.399011 + 0.289898i
\(623\) 1.87512e6 + 5.77103e6i 0.193557 + 0.595707i
\(624\) −457799. + 1.40896e6i −0.0470667 + 0.144856i
\(625\) −7.73561e6 5.62025e6i −0.792126 0.575513i
\(626\) 5.06824e6 0.516917
\(627\) −4.31627e6 + 9.84351e6i −0.438470 + 0.999957i
\(628\) 6.49309e6 0.656980
\(629\) −6.56367e6 4.76879e6i −0.661485 0.480597i
\(630\) −71325.3 + 219517.i −0.00715966 + 0.0220352i
\(631\) −1.00779e6 3.10167e6i −0.100762 0.310114i 0.887950 0.459940i \(-0.152129\pi\)
−0.988713 + 0.149825i \(0.952129\pi\)
\(632\) −8.13651e6 + 5.91152e6i −0.810299 + 0.588717i
\(633\) 2.17335e6 1.57903e6i 0.215586 0.156632i
\(634\) −2.33614e6 7.18989e6i −0.230821 0.710393i
\(635\) 310627. 956012.i 0.0305707 0.0940869i
\(636\) 2.79691e6 + 2.03208e6i 0.274180 + 0.199204i
\(637\) −8.90759e6 −0.869784
\(638\) −2.40210e6 238784.i −0.233635 0.0232248i
\(639\) −487773. −0.0472569
\(640\) −282125. 204976.i −0.0272265 0.0197812i
\(641\) 174692. 537647.i 0.0167930 0.0516836i −0.942309 0.334745i \(-0.891350\pi\)
0.959102 + 0.283061i \(0.0913499\pi\)
\(642\) −732141. 2.25330e6i −0.0701063 0.215765i
\(643\) 5.00366e6 3.63537e6i 0.477266 0.346754i −0.323000 0.946399i \(-0.604692\pi\)
0.800266 + 0.599645i \(0.204692\pi\)
\(644\) −4.30070e6 + 3.12464e6i −0.408625 + 0.296883i
\(645\) −34224.3 105332.i −0.00323918 0.00996918i
\(646\) 7.14784e6 2.19988e7i 0.673897 2.07404i
\(647\) −1.54995e7 1.12610e7i −1.45565 1.05759i −0.984470 0.175556i \(-0.943828\pi\)
−0.471181 0.882037i \(-0.656172\pi\)
\(648\) −1.23781e6 −0.115802
\(649\) 1.00904e7 5.90179e6i 0.940363 0.550012i
\(650\) 1.20299e7 1.11681
\(651\) −2.75020e6 1.99814e6i −0.254338 0.184788i
\(652\) −397391. + 1.22304e6i −0.0366100 + 0.112674i
\(653\) −2.79448e6 8.60052e6i −0.256459 0.789299i −0.993539 0.113494i \(-0.963796\pi\)
0.737080 0.675806i \(-0.236204\pi\)
\(654\) 2.97369e6 2.16051e6i 0.271864 0.197521i
\(655\) −798000. + 579781.i −0.0726775 + 0.0528033i
\(656\) −172375. 530517.i −0.0156392 0.0481326i
\(657\) −1.19593e6 + 3.68071e6i −0.108092 + 0.332673i
\(658\) 7.99604e6 + 5.80946e6i 0.719963 + 0.523084i
\(659\) 486261. 0.0436170 0.0218085 0.999762i \(-0.493058\pi\)
0.0218085 + 0.999762i \(0.493058\pi\)
\(660\) 219608. + 195505.i 0.0196240 + 0.0174702i
\(661\) 1.75953e6 0.156637 0.0783184 0.996928i \(-0.475045\pi\)
0.0783184 + 0.996928i \(0.475045\pi\)
\(662\) 717874. + 521566.i 0.0636654 + 0.0462556i
\(663\) 5.75398e6 1.77089e7i 0.508375 1.56462i
\(664\) 4.69550e6 + 1.44513e7i 0.413297 + 1.27200i
\(665\) 1.79765e6 1.30607e6i 0.157634 0.114528i
\(666\) −996184. + 723770.i −0.0870270 + 0.0632288i
\(667\) 928552. + 2.85779e6i 0.0808149 + 0.248723i
\(668\) −735552. + 2.26380e6i −0.0637782 + 0.196289i
\(669\) −506062. 367676.i −0.0437158 0.0317614i
\(670\) 500559. 0.0430793
\(671\) −1.32806e6 1.18230e6i −0.113871 0.101373i
\(672\) −7.79937e6 −0.666249
\(673\) −1.07451e7 7.80674e6i −0.914474 0.664404i 0.0276687 0.999617i \(-0.491192\pi\)
−0.942142 + 0.335213i \(0.891192\pi\)
\(674\) 1.32973e6 4.09248e6i 0.112749 0.347006i
\(675\) 699069. + 2.15151e6i 0.0590555 + 0.181754i
\(676\) 9.31770e6 6.76970e6i 0.784227 0.569774i
\(677\) 1.51718e6 1.10230e6i 0.127223 0.0924329i −0.522354 0.852729i \(-0.674946\pi\)
0.649577 + 0.760296i \(0.274946\pi\)
\(678\) −1.93514e6 5.95574e6i −0.161673 0.497579i
\(679\) −4.77016e6 + 1.46810e7i −0.397062 + 1.22203i
\(680\) −1.45142e6 1.05452e6i −0.120371 0.0874547i
\(681\) 3.37803e6 0.279123
\(682\) 3.12234e6 1.82624e6i 0.257051 0.150347i
\(683\) −2.03885e7 −1.67237 −0.836185 0.548447i \(-0.815219\pi\)
−0.836185 + 0.548447i \(0.815219\pi\)
\(684\) 3.40015e6 + 2.47035e6i 0.277880 + 0.201892i
\(685\) −134979. + 415424.i −0.0109911 + 0.0338271i
\(686\) −1.51596e6 4.66565e6i −0.122992 0.378531i
\(687\) 2.18071e6 1.58438e6i 0.176281 0.128076i
\(688\) −345536. + 251047.i −0.0278306 + 0.0202201i
\(689\) 6.91556e6 + 2.12839e7i 0.554983 + 1.70806i
\(690\) −94473.1 + 290758.i −0.00755414 + 0.0232493i
\(691\) 888566. + 645581.i 0.0707937 + 0.0514346i 0.622619 0.782525i \(-0.286069\pi\)
−0.551826 + 0.833960i \(0.686069\pi\)
\(692\) 1.87630e6 0.148949
\(693\) 5.17307e6 + 514236.i 0.409181 + 0.0406752i
\(694\) −1.41469e7 −1.11497
\(695\) 1.08440e6 + 787864.i 0.0851585 + 0.0618713i
\(696\) −827009. + 2.54527e6i −0.0647123 + 0.199164i
\(697\) 2.16655e6 + 6.66795e6i 0.168922 + 0.519889i
\(698\) 7.76681e6 5.64292e6i 0.603399 0.438395i
\(699\) −9.24915e6 + 6.71990e6i −0.715993 + 0.520199i
\(700\) 2.67393e6 + 8.22952e6i 0.206256 + 0.634789i
\(701\) −4.49292e6 + 1.38278e7i −0.345330 + 1.06282i 0.616077 + 0.787686i \(0.288721\pi\)
−0.961407 + 0.275130i \(0.911279\pi\)
\(702\) −2.28632e6 1.66111e6i −0.175103 0.127220i
\(703\) 1.18541e7 0.904646
\(704\) 4.16839e6 9.50626e6i 0.316984 0.722900i
\(705\) −680481. −0.0515636
\(706\) 9.34027e6 + 6.78610e6i 0.705258 + 0.512400i
\(707\) −7.34286e6 + 2.25990e7i −0.552481 + 1.70036i
\(708\) −1.41249e6 4.34719e6i −0.105901 0.325931i
\(709\) 1.73149e7 1.25800e7i 1.29361 0.939862i 0.293738 0.955886i \(-0.405101\pi\)
0.999872 + 0.0160234i \(0.00510064\pi\)
\(710\) −86806.1 + 63068.3i −0.00646255 + 0.00469532i
\(711\) −1.33433e6 4.10664e6i −0.0989894 0.304658i
\(712\) −2.21206e6 + 6.80803e6i −0.163530 + 0.503293i
\(713\) −3.64274e6 2.64661e6i −0.268352 0.194969i
\(714\) −1.11876e7 −0.821283
\(715\) 406209. + 1.85944e6i 0.0297156 + 0.136025i
\(716\) −2.55379e6 −0.186167
\(717\) 1.61864e6 + 1.17601e6i 0.117585 + 0.0854308i
\(718\) 1.52015e6 4.67854e6i 0.110046 0.338687i
\(719\) −3.72195e6 1.14550e7i −0.268503 0.826367i −0.990866 0.134852i \(-0.956944\pi\)
0.722363 0.691514i \(-0.243056\pi\)
\(720\) −49579.4 + 36021.6i −0.00356427 + 0.00258959i
\(721\) 1.93045e7 1.40256e7i 1.38300 1.00481i
\(722\) 7.52359e6 + 2.31552e7i 0.537133 + 1.65313i
\(723\) −1.46714e6 + 4.51541e6i −0.104382 + 0.321256i
\(724\) 4.79347e6 + 3.48266e6i 0.339863 + 0.246925i
\(725\) 4.89114e6 0.345593
\(726\) −2.71159e6 + 4.82138e6i −0.190934 + 0.339492i
\(727\) 1.47037e7 1.03179 0.515896 0.856651i \(-0.327459\pi\)
0.515896 + 0.856651i \(0.327459\pi\)
\(728\) −2.47952e7 1.80147e7i −1.73396 1.25979i
\(729\) 164224. 505430.i 0.0114451 0.0352243i
\(730\) 263077. + 809666.i 0.0182715 + 0.0562340i
\(731\) 4.34297e6 3.15535e6i 0.300603 0.218401i
\(732\) −562486. + 408670.i −0.0388002 + 0.0281900i
\(733\) 3.11861e6 + 9.59809e6i 0.214388 + 0.659819i 0.999196 + 0.0400806i \(0.0127615\pi\)
−0.784808 + 0.619739i \(0.787239\pi\)
\(734\) −5.24791e6 + 1.61514e7i −0.359540 + 1.10655i
\(735\) −298105. 216586.i −0.0203540 0.0147881i
\(736\) −1.03306e7 −0.702958
\(737\) −2.40614e6 1.10142e7i −0.163174 0.746939i
\(738\) 1.06409e6 0.0719181
\(739\) −2.19803e7 1.59696e7i −1.48055 1.07568i −0.977380 0.211489i \(-0.932169\pi\)
−0.503165 0.864190i \(-0.667831\pi\)
\(740\) 100206. 308403.i 0.00672690 0.0207033i
\(741\) 8.40710e6 + 2.58744e7i 0.562472 + 1.73111i
\(742\) 1.08781e7 7.90344e6i 0.725346 0.526995i
\(743\) −7.48446e6 + 5.43778e6i −0.497380 + 0.361368i −0.808015 0.589161i \(-0.799458\pi\)
0.310635 + 0.950529i \(0.399458\pi\)
\(744\) −1.23925e6 3.81400e6i −0.0820777 0.252609i
\(745\) 165881. 510529.i 0.0109498 0.0337000i
\(746\) 1.02643e7 + 7.45747e6i 0.675279 + 0.490619i
\(747\) −6.52379e6 −0.427758
\(748\) −5.72308e6 + 1.30518e7i −0.374004 + 0.852938i
\(749\) 1.10317e7 0.718520
\(750\) 808021. + 587061.i 0.0524529 + 0.0381093i
\(751\) 6.24335e6 1.92151e7i 0.403941 1.24320i −0.517835 0.855480i \(-0.673262\pi\)
0.921776 0.387722i \(-0.126738\pi\)
\(752\) 810927. + 2.49578e6i 0.0522922 + 0.160939i
\(753\) −6.20859e6 + 4.51080e6i −0.399030 + 0.289912i
\(754\) −4.94321e6 + 3.59146e6i −0.316651 + 0.230061i
\(755\) −291408. 896863.i −0.0186052 0.0572610i
\(756\) 628157. 1.93327e6i 0.0399727 0.123023i
\(757\) 5.67188e6 + 4.12086e6i 0.359739 + 0.261365i 0.752943 0.658086i \(-0.228634\pi\)
−0.393204 + 0.919451i \(0.628634\pi\)
\(758\) 8.05979e6 0.509507
\(759\) 6.85192e6 + 681124.i 0.431726 + 0.0429163i
\(760\) 2.62129e6 0.164619
\(761\) 9.16713e6 + 6.66031e6i 0.573815 + 0.416901i 0.836489 0.547984i \(-0.184604\pi\)
−0.262674 + 0.964885i \(0.584604\pi\)
\(762\) 2.28512e6 7.03287e6i 0.142568 0.438779i
\(763\) 5.28873e6 + 1.62770e7i 0.328882 + 1.01219i
\(764\) 3.51400e6 2.55307e6i 0.217805 0.158245i
\(765\) 623153. 452747.i 0.0384983 0.0279706i
\(766\) 1.53560e6 + 4.72609e6i 0.0945598 + 0.291025i
\(767\) 9.14341e6 2.81405e7i 0.561203 1.72720i
\(768\) −8.10196e6 5.88642e6i −0.495664 0.360121i
\(769\) −1.87008e7 −1.14036 −0.570182 0.821519i \(-0.693127\pi\)
−0.570182 + 0.821519i \(0.693127\pi\)
\(770\) 987110. 577354.i 0.0599983 0.0350926i
\(771\) −1.09299e7 −0.662186
\(772\) 466955. + 339263.i 0.0281989 + 0.0204877i
\(773\) 4.58096e6 1.40987e7i 0.275745 0.848656i −0.713276 0.700883i \(-0.752789\pi\)
0.989021 0.147773i \(-0.0472105\pi\)
\(774\) −251770. 774869.i −0.0151061 0.0464917i
\(775\) −5.92946e6 + 4.30800e6i −0.354618 + 0.257645i
\(776\) −1.47325e7 + 1.07038e7i −0.878258 + 0.638092i
\(777\) −1.77172e6 5.45279e6i −0.105279 0.324016i
\(778\) −5.59862e6 + 1.72308e7i −0.331614 + 1.02060i
\(779\) −8.28747e6 6.02120e6i −0.489303 0.355500i
\(780\) 744233. 0.0437998
\(781\) 1.80501e6 + 1.60690e6i 0.105889 + 0.0942676i
\(782\) −1.48184e7 −0.866534
\(783\) −929578. 675378.i −0.0541853 0.0393679i
\(784\) −439114. + 1.35145e6i −0.0255145 + 0.0785255i
\(785\) 537290. + 1.65361e6i 0.0311196 + 0.0957763i
\(786\) −5.87047e6 + 4.26514e6i −0.338935 + 0.246251i
\(787\) 7.97608e6 5.79496e6i 0.459042 0.333514i −0.334113 0.942533i \(-0.608437\pi\)
0.793155 + 0.609019i \(0.208437\pi\)
\(788\) −1.32443e6 4.07619e6i −0.0759826 0.233851i
\(789\) 3.39034e6 1.04344e7i 0.193888 0.596725i
\(790\) −768445. 558308.i −0.0438072 0.0318278i
\(791\) 2.91582e7 1.65699
\(792\) 4.58055e6 + 4.07781e6i 0.259480 + 0.231001i
\(793\) −4.50068e6 −0.254153
\(794\) −6.47220e6 4.70233e6i −0.364335 0.264705i
\(795\) −286074. + 880446.i −0.0160532 + 0.0494066i
\(796\) 390087. + 1.20057e6i 0.0218212 + 0.0671588i
\(797\) −75476.8 + 54837.1i −0.00420889 + 0.00305794i −0.589888 0.807485i \(-0.700828\pi\)
0.585679 + 0.810543i \(0.300828\pi\)
\(798\) 1.32243e7 9.60804e6i 0.735134 0.534106i
\(799\) −1.01924e7 3.13689e7i −0.564818 1.73833i
\(800\) −5.19628e6 + 1.59925e7i −0.287057 + 0.883470i
\(801\) −2.48641e6 1.80648e6i −0.136928 0.0994838i
\(802\) 35353.3 0.00194086
\(803\) 1.65512e7 9.68068e6i 0.905817 0.529806i
\(804\) −4.40839e6 −0.240514
\(805\) −1.15163e6 836710.i −0.0626360 0.0455078i
\(806\) 2.82931e6 8.70773e6i 0.153406 0.472136i
\(807\) 5.47331e6 + 1.68451e7i 0.295847 + 0.910522i
\(808\) −2.26782e7 + 1.64767e7i −1.22203 + 0.887854i
\(809\) −2.46700e7 + 1.79238e7i −1.32525 + 0.962849i −0.325397 + 0.945578i \(0.605498\pi\)
−0.999851 + 0.0172710i \(0.994502\pi\)
\(810\) −36125.4 111182.i −0.00193464 0.00595420i
\(811\) 6.03765e6 1.85820e7i 0.322341 0.992064i −0.650286 0.759690i \(-0.725351\pi\)
0.972627 0.232374i \(-0.0746492\pi\)
\(812\) −3.55563e6 2.58332e6i −0.189246 0.137495i
\(813\) −1.85339e6 −0.0983422
\(814\) 6.07076e6 + 603473.i 0.321131 + 0.0319225i
\(815\) −344358. −0.0181600
\(816\) −2.40313e6 1.74598e6i −0.126343 0.0917939i
\(817\) −2.42376e6 + 7.45956e6i −0.127038 + 0.390983i
\(818\) −4.01942e6 1.23705e7i −0.210029 0.646404i
\(819\) 1.06455e7 7.73443e6i 0.554571 0.402920i
\(820\) −226708. + 164713.i −0.0117742 + 0.00855447i
\(821\) −1.32430e6 4.07577e6i −0.0685691 0.211034i 0.910900 0.412626i \(-0.135388\pi\)
−0.979470 + 0.201592i \(0.935388\pi\)
\(822\) −992972. + 3.05605e6i −0.0512575 + 0.157754i
\(823\) 6.17852e6 + 4.48896e6i 0.317969 + 0.231018i 0.735308 0.677733i \(-0.237037\pi\)
−0.417339 + 0.908751i \(0.637037\pi\)
\(824\) 2.81494e7 1.44428
\(825\) 4.50096e6 1.02647e7i 0.230234 0.525063i
\(826\) −1.77778e7 −0.906626
\(827\) 1.82364e7 + 1.32495e7i 0.927202 + 0.673652i 0.945306 0.326184i \(-0.105763\pi\)
−0.0181038 + 0.999836i \(0.505763\pi\)
\(828\) 832018. 2.56069e6i 0.0421752 0.129802i
\(829\) 1.74640e6 + 5.37488e6i 0.0882588 + 0.271633i 0.985438 0.170033i \(-0.0543876\pi\)
−0.897179 + 0.441666i \(0.854388\pi\)
\(830\) −1.16100e6 + 843516.i −0.0584974 + 0.0425009i
\(831\) 8.14724e6 5.91931e6i 0.409268 0.297351i
\(832\) −8.11907e6 2.49879e7i −0.406629 1.25147i
\(833\) 5.51913e6 1.69861e7i 0.275586 0.848168i
\(834\) 7.97737e6 + 5.79590e6i 0.397141 + 0.288540i
\(835\) −637390. −0.0316366
\(836\) −4.44407e6 2.03429e7i −0.219920 1.00670i
\(837\) 1.72177e6 0.0849496
\(838\) 1.94698e6 + 1.41456e6i 0.0957748 + 0.0695844i
\(839\) 1.40846e6 4.33479e6i 0.0690780 0.212600i −0.910558 0.413381i \(-0.864348\pi\)
0.979636 + 0.200781i \(0.0643479\pi\)
\(840\) −391781. 1.20578e6i −0.0191578 0.0589615i
\(841\) 1.45840e7 1.05959e7i 0.711030 0.516594i
\(842\) 5.37149e6 3.90262e6i 0.261105 0.189704i
\(843\) 2.63205e6 + 8.10062e6i 0.127563 + 0.392599i
\(844\) −1.60825e6 + 4.94969e6i −0.0777137 + 0.239178i
\(845\) 2.49507e6 + 1.81278e6i 0.120210 + 0.0873379i
\(846\) −5.00594e6 −0.240469
\(847\) −1.74490e7 1.89449e7i −0.835720 0.907370i
\(848\) 3.57009e6 0.170486
\(849\) −4.59047e6 3.33517e6i −0.218568 0.158799i
\(850\) −7.45369e6 + 2.29401e7i −0.353854 + 1.08905i
\(851\) −2.34671e6 7.22243e6i −0.111080 0.341869i
\(852\) 764495. 555438.i 0.0360808 0.0262142i
\(853\) −2.08517e7 + 1.51497e7i −0.981228 + 0.712904i −0.957983 0.286826i \(-0.907400\pi\)
−0.0232450 + 0.999730i \(0.507400\pi\)
\(854\) 835627. + 2.57180e6i 0.0392074 + 0.120668i
\(855\) −347774. + 1.07034e6i −0.0162698 + 0.0500733i
\(856\) 1.05286e7 + 7.64945e6i 0.491117 + 0.356817i
\(857\) −4.17864e7 −1.94349 −0.971746 0.236028i \(-0.924154\pi\)
−0.971746 + 0.236028i \(0.924154\pi\)
\(858\) 2.98826e6 + 1.36789e7i 0.138580 + 0.634357i
\(859\) −2.10963e7 −0.975491 −0.487745 0.872986i \(-0.662181\pi\)
−0.487745 + 0.872986i \(0.662181\pi\)
\(860\) 173584. + 126116.i 0.00800319 + 0.00581466i
\(861\) −1.53106e6 + 4.71212e6i −0.0703857 + 0.216625i
\(862\) −3.40986e6 1.04945e7i −0.156303 0.481052i
\(863\) −2.79883e7 + 2.03347e7i −1.27923 + 0.929416i −0.999530 0.0306713i \(-0.990235\pi\)
−0.279701 + 0.960087i \(0.590235\pi\)
\(864\) 3.19584e6 2.32192e6i 0.145647 0.105819i
\(865\) 155260. + 477842.i 0.00705537 + 0.0217142i
\(866\) 4.49093e6 1.38217e7i 0.203489 0.626276i
\(867\) 1.98663e7 + 1.44337e7i 0.897571 + 0.652124i
\(868\) 6.58576e6 0.296693
\(869\) −8.59109e6 + 1.95925e7i −0.385921 + 0.880116i
\(870\) −252757. −0.0113215
\(871\) −2.30867e7 1.67734e7i −1.03114 0.749164i
\(872\) −6.23907e6 + 1.92019e7i −0.277862 + 0.855170i
\(873\) −2.41602e6 7.43576e6i −0.107292 0.330209i
\(874\) 1.75161e7 1.27262e7i 0.775638 0.563534i
\(875\) −3.76230e6 + 2.73347e6i −0.166124 + 0.120696i
\(876\) −2.31690e6 7.13067e6i −0.102011 0.313957i
\(877\) 5.55530e6 1.70975e7i 0.243898 0.750641i −0.751918 0.659257i \(-0.770871\pi\)
0.995816 0.0913843i \(-0.0291292\pi\)
\(878\) −1.55981e7 1.13327e7i −0.682866 0.496131i
\(879\) 5.16963e6 0.225677
\(880\) 302138. + 30034.4i 0.0131522 + 0.00130741i
\(881\) 4.11396e7 1.78575 0.892875 0.450305i \(-0.148685\pi\)
0.892875 + 0.450305i \(0.148685\pi\)
\(882\) −2.19300e6 1.59331e6i −0.0949220 0.0689649i
\(883\) −4.67324e6 + 1.43827e7i −0.201705 + 0.620783i 0.798128 + 0.602488i \(0.205824\pi\)
−0.999833 + 0.0182953i \(0.994176\pi\)
\(884\) 1.11472e7 + 3.43077e7i 0.479774 + 1.47659i
\(885\) 990226. 719442.i 0.0424988 0.0308772i
\(886\) 4.67781e6 3.39863e6i 0.200197 0.145452i
\(887\) 1.35128e7 + 4.15881e7i 0.576682 + 1.77484i 0.630380 + 0.776287i \(0.282899\pi\)
−0.0536981 + 0.998557i \(0.517101\pi\)
\(888\) 2.09008e6 6.43261e6i 0.0889469 0.273750i
\(889\) 2.78558e7 + 2.02384e7i 1.18212 + 0.858859i
\(890\) −676067. −0.0286098
\(891\) −2.27279e6 + 1.32934e6i −0.0959102 + 0.0560973i
\(892\) 1.21184e6 0.0509957
\(893\) 3.89878e7 + 2.83263e7i 1.63606 + 1.18867i
\(894\) 1.22030e6 3.75569e6i 0.0510648 0.157161i
\(895\) −211321. 650379.i −0.00881830 0.0271399i
\(896\) 9.66368e6 7.02107e6i 0.402136 0.292169i
\(897\) 1.41004e7 1.02445e7i 0.585127 0.425120i
\(898\) 3.15366e6 + 9.70598e6i 0.130504 + 0.401651i
\(899\) 1.15035e6 3.54042e6i 0.0474713 0.146102i
\(900\) −3.54564e6 2.57606e6i −0.145911 0.106011i
\(901\) −4.48717e7 −1.84145
\(902\) −3.93769e6 3.50551e6i −0.161148 0.143461i
\(903\) 3.79361e6 0.154822
\(904\) 2.78283e7 + 2.02184e7i 1.13257 + 0.822860i
\(905\) −490286. + 1.50895e6i −0.0198989 + 0.0612424i
\(906\) −2.14374e6 6.59774e6i −0.0867663 0.267039i
\(907\) −2.47567e7 + 1.79868e7i −0.999252 + 0.725999i −0.961928 0.273304i \(-0.911883\pi\)
−0.0373243 + 0.999303i \(0.511883\pi\)
\(908\) −5.29444e6 + 3.84664e6i −0.213111 + 0.154834i
\(909\) −3.71907e6 1.14461e7i −0.149288 0.459460i
\(910\) 894472. 2.75290e6i 0.0358066 0.110201i
\(911\) −1.22385e7 8.89178e6i −0.488575 0.354971i 0.316061 0.948739i \(-0.397640\pi\)
−0.804636 + 0.593768i \(0.797640\pi\)
\(912\) 4.34009e6 0.172787
\(913\) 2.41414e7 + 2.14918e7i 0.958485 + 0.853287i
\(914\) 9.87273e6 0.390906
\(915\) −150621. 109433.i −0.00594749 0.00432111i
\(916\) −1.61370e6 + 4.96645e6i −0.0635453 + 0.195572i
\(917\) −1.04407e7 3.21331e7i −0.410020 1.26191i
\(918\) 4.58421e6 3.33062e6i 0.179538 0.130442i
\(919\) −3.87760e6 + 2.81724e6i −0.151452 + 0.110036i −0.660931 0.750447i \(-0.729838\pi\)
0.509479 + 0.860483i \(0.329838\pi\)
\(920\) −518928. 1.59710e6i −0.0202133 0.0622102i
\(921\) −6.24552e6 + 1.92217e7i −0.242616 + 0.746695i
\(922\) −1.58111e7 1.14874e7i −0.612539 0.445036i
\(923\) 6.11703e6 0.236340
\(924\) −8.69341e6 + 5.08472e6i −0.334973 + 0.195924i
\(925\) −1.23613e7 −0.475017
\(926\) 156989. + 114060.i 0.00601649 + 0.00437123i
\(927\) −3.73467e6 + 1.14941e7i −0.142742 + 0.439316i
\(928\) −2.63927e6 8.12283e6i −0.100604 0.309626i
\(929\) 8.08331e6 5.87287e6i 0.307291 0.223260i −0.423442 0.905923i \(-0.639178\pi\)
0.730733 + 0.682663i \(0.239178\pi\)
\(930\) 306413. 222622.i 0.0116172 0.00844036i
\(931\) 8.06396e6 + 2.48183e7i 0.304912 + 0.938422i
\(932\) 6.84425e6 2.10644e7i 0.258099 0.794347i
\(933\) 9.07946e6 + 6.59661e6i 0.341472 + 0.248094i
\(934\) 3.53810e7 1.32710
\(935\) −3.79751e6 377496.i −0.142059 0.0141216i
\(936\) 1.55231e7 0.579146
\(937\) 6.26693e6 + 4.55319e6i 0.233188 + 0.169421i 0.698243 0.715861i \(-0.253966\pi\)
−0.465055 + 0.885282i \(0.653966\pi\)
\(938\) −5.29832e6 + 1.63066e7i −0.196622 + 0.605139i
\(939\) −3.69350e6 1.13674e7i −0.136702 0.420725i
\(940\) 1.06653e6 774879.i 0.0393689 0.0286032i
\(941\) −2.63129e7 + 1.91174e7i −0.968712 + 0.703810i −0.955158 0.296098i \(-0.904315\pi\)
−0.0135542 + 0.999908i \(0.504315\pi\)
\(942\) 3.95255e6 + 1.21647e7i 0.145128 + 0.446657i
\(943\) −2.02795e6 + 6.24138e6i −0.0742638 + 0.228560i
\(944\) −3.81872e6 2.77446e6i −0.139472 0.101333i
\(945\) 544328. 0.0198281
\(946\) −1.62102e6 + 3.69684e6i −0.0588927 + 0.134308i
\(947\) 3.09940e7 1.12306 0.561530 0.827456i \(-0.310213\pi\)
0.561530 + 0.827456i \(0.310213\pi\)
\(948\) 6.76764e6 + 4.91698e6i 0.244578 + 0.177696i
\(949\) 1.49979e7 4.61588e7i 0.540586 1.66375i
\(950\) −1.08905e7 3.35176e7i −0.391508 1.20494i
\(951\) −1.44236e7 + 1.04793e7i −0.517156 + 0.375736i
\(952\) 4.97158e7 3.61207e7i 1.77788 1.29171i
\(953\) −1.04509e7 3.21646e7i −0.372754 1.14722i −0.944981 0.327124i \(-0.893921\pi\)
0.572227 0.820095i \(-0.306079\pi\)
\(954\) −2.10450e6 + 6.47697e6i −0.0748647 + 0.230410i
\(955\) 940970. + 683655.i 0.0333862 + 0.0242565i
\(956\) −3.87608e6 −0.137167
\(957\) 1.21498e6 + 5.56162e6i 0.0428833 + 0.196301i
\(958\) −3.63364e7 −1.27917
\(959\) −1.21044e7 8.79436e6i −0.425008 0.308786i
\(960\) 335859. 1.03367e6i 0.0117619 0.0361995i
\(961\) −7.12313e6 2.19227e7i −0.248807 0.765749i
\(962\) 1.24929e7 9.07661e6i 0.435236 0.316217i
\(963\) −4.52032e6 + 3.28421e6i −0.157074 + 0.114121i
\(964\) −2.84231e6 8.74775e6i −0.0985098 0.303182i
\(965\) −47761.1 + 146994.i −0.00165103 + 0.00508136i
\(966\) −8.47195e6 6.15523e6i −0.292106 0.212228i
\(967\) 1.45003e7 0.498668 0.249334 0.968418i \(-0.419788\pi\)
0.249334 + 0.968418i \(0.419788\pi\)
\(968\) −3.51660e6 3.01800e7i −0.120624 1.03522i
\(969\) −5.45496e7 −1.86630
\(970\) −1.39140e6 1.01091e6i −0.0474812 0.0344971i
\(971\) −1.75820e7 + 5.41117e7i −0.598438 + 1.84180i −0.0616293 + 0.998099i \(0.519630\pi\)
−0.536809 + 0.843704i \(0.680370\pi\)
\(972\) 318154. + 979176.i 0.0108012 + 0.0332426i
\(973\) −3.71441e7 + 2.69868e7i −1.25779 + 0.913838i
\(974\) −1.99698e7 + 1.45089e7i −0.674492 + 0.490047i
\(975\) −8.76683e6 2.69815e7i −0.295346 0.908982i
\(976\) −221868. + 682840.i −0.00745539 + 0.0229453i
\(977\) 2.51461e7 + 1.82697e7i 0.842817 + 0.612343i 0.923156 0.384425i \(-0.125600\pi\)
−0.0803390 + 0.996768i \(0.525600\pi\)
\(978\) −2.53326e6 −0.0846901
\(979\) 3.24979e6 + 1.48761e7i 0.108367 + 0.496057i
\(980\) 713856. 0.0237435
\(981\) −7.01286e6 5.09514e6i −0.232660 0.169038i
\(982\) −3.25617e6 + 1.00215e7i −0.107753 + 0.331629i
\(983\) −9.08813e6 2.79704e7i −0.299979 0.923240i −0.981503 0.191445i \(-0.938683\pi\)
0.681525 0.731795i \(-0.261317\pi\)
\(984\) −4.72863e6 + 3.43555e6i −0.155685 + 0.113112i
\(985\) 928496. 674591.i 0.0304922 0.0221539i
\(986\) −3.78584e6 1.16516e7i −0.124014 0.381675i
\(987\) 7.20276e6 2.21678e7i 0.235345 0.724319i
\(988\) −4.26404e7 3.09800e7i −1.38972 1.00969i
\(989\) 5.02478e6 0.163353
\(990\) −232593. + 530443.i −0.00754240 + 0.0172009i
\(991\) 5.86096e7 1.89576 0.947882 0.318620i \(-0.103219\pi\)
0.947882 + 0.318620i \(0.103219\pi\)
\(992\) 1.03539e7 + 7.52258e6i 0.334062 + 0.242710i
\(993\) 646655. 1.99020e6i 0.0208113 0.0640506i
\(994\) −1.13573e6 3.49542e6i −0.0364594 0.112210i
\(995\) −273471. + 198688.i −0.00875697 + 0.00636231i
\(996\) 1.02248e7 7.42878e6i 0.326594 0.237285i
\(997\) −1.22917e7 3.78301e7i −0.391630 1.20531i −0.931555 0.363599i \(-0.881548\pi\)
0.539926 0.841713i \(-0.318452\pi\)
\(998\) −644194. + 1.98263e6i −0.0204734 + 0.0630107i
\(999\) 2.34930e6 + 1.70687e6i 0.0744775 + 0.0541111i
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 33.6.e.b.4.2 20
3.2 odd 2 99.6.f.b.37.4 20
11.3 even 5 inner 33.6.e.b.25.2 yes 20
11.5 even 5 363.6.a.r.1.8 10
11.6 odd 10 363.6.a.t.1.3 10
33.5 odd 10 1089.6.a.bk.1.3 10
33.14 odd 10 99.6.f.b.91.4 20
33.17 even 10 1089.6.a.bi.1.8 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.6.e.b.4.2 20 1.1 even 1 trivial
33.6.e.b.25.2 yes 20 11.3 even 5 inner
99.6.f.b.37.4 20 3.2 odd 2
99.6.f.b.91.4 20 33.14 odd 10
363.6.a.r.1.8 10 11.5 even 5
363.6.a.t.1.3 10 11.6 odd 10
1089.6.a.bi.1.8 10 33.17 even 10
1089.6.a.bk.1.3 10 33.5 odd 10