Properties

Label 150.6.g.b.31.2
Level $150$
Weight $6$
Character 150.31
Analytic conductor $24.058$
Analytic rank $0$
Dimension $24$
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] = [150,6,Mod(31,150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(150, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("150.31");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 150.g (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: \(24.0575729719\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 31.2
Character \(\chi\) \(=\) 150.31
Dual form 150.6.g.b.121.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.23607 + 3.80423i) q^{2} +(-7.28115 + 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(-55.5791 + 5.99730i) q^{5} +(-29.1246 - 21.1603i) q^{6} +161.028 q^{7} +(-51.7771 - 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +O(q^{10})\) \(q+(1.23607 + 3.80423i) q^{2} +(-7.28115 + 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(-55.5791 + 5.99730i) q^{5} +(-29.1246 - 21.1603i) q^{6} +161.028 q^{7} +(-51.7771 - 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +(-91.5146 - 204.022i) q^{10} +(-141.396 - 435.171i) q^{11} +(44.4984 - 136.952i) q^{12} +(78.8398 - 242.644i) q^{13} +(199.042 + 612.588i) q^{14} +(372.954 - 337.684i) q^{15} +(79.1084 - 243.470i) q^{16} +(-1333.75 - 969.024i) q^{17} +324.000 q^{18} +(1281.16 + 930.818i) q^{19} +(663.029 - 600.328i) q^{20} +(-1172.47 + 851.850i) q^{21} +(1480.71 - 1075.80i) q^{22} +(1033.60 + 3181.10i) q^{23} +576.000 q^{24} +(3053.06 - 666.648i) q^{25} +1020.52 q^{26} +(225.273 + 693.320i) q^{27} +(-2084.39 + 1514.40i) q^{28} +(4154.82 - 3018.65i) q^{29} +(1745.62 + 1001.40i) q^{30} +(8154.81 + 5924.81i) q^{31} +1024.00 q^{32} +(3331.61 + 2420.55i) q^{33} +(2037.78 - 6271.65i) q^{34} +(-8949.80 + 965.734i) q^{35} +(400.486 + 1232.57i) q^{36} +(-562.665 + 1731.70i) q^{37} +(-1957.44 + 6024.38i) q^{38} +(709.558 + 2183.80i) q^{39} +(3103.33 + 1780.26i) q^{40} +(577.538 - 1777.48i) q^{41} +(-4689.88 - 3407.40i) q^{42} -18541.1 q^{43} +(5922.86 + 4303.21i) q^{44} +(-929.160 + 4431.68i) q^{45} +(-10824.0 + 7864.12i) q^{46} +(21041.9 - 15287.8i) q^{47} +(711.975 + 2191.23i) q^{48} +9123.09 q^{49} +(6309.88 + 10790.5i) q^{50} +14837.4 q^{51} +(1261.44 + 3882.30i) q^{52} +(19127.7 - 13897.1i) q^{53} +(-2359.09 + 1713.98i) q^{54} +(10468.5 + 23338.4i) q^{55} +(-8337.57 - 6057.60i) q^{56} -14252.4 q^{57} +(16619.3 + 12074.6i) q^{58} +(1899.08 - 5844.78i) q^{59} +(-1651.84 + 7878.54i) q^{60} +(-1667.89 - 5133.24i) q^{61} +(-12459.4 + 38346.2i) q^{62} +(4030.60 - 12404.9i) q^{63} +(1265.73 + 3895.53i) q^{64} +(-2926.64 + 13958.8i) q^{65} +(-5090.24 + 15666.2i) q^{66} +(24919.2 + 18104.9i) q^{67} +26377.6 q^{68} +(-24354.1 - 17694.3i) q^{69} +(-14736.4 - 32853.3i) q^{70} +(-13309.9 + 9670.24i) q^{71} +(-4193.94 + 3047.08i) q^{72} +(-970.460 - 2986.77i) q^{73} -7283.29 q^{74} +(-18703.2 + 21004.9i) q^{75} -25337.6 q^{76} +(-22768.7 - 70074.8i) q^{77} +(-7430.59 + 5398.64i) q^{78} +(48397.1 - 35162.5i) q^{79} +(-2936.60 + 14006.3i) q^{80} +(-5307.96 - 3856.46i) q^{81} +7475.81 q^{82} +(27239.7 + 19790.8i) q^{83} +(7165.51 - 22053.2i) q^{84} +(79939.9 + 45858.6i) q^{85} +(-22918.1 - 70534.6i) q^{86} +(-14283.0 + 43958.6i) q^{87} +(-9049.32 + 27850.9i) q^{88} +(-40288.4 - 123995. i) q^{89} +(-18007.6 + 1943.12i) q^{90} +(12695.4 - 39072.5i) q^{91} +(-43296.1 - 31456.5i) q^{92} -90719.1 q^{93} +(84167.5 + 61151.3i) q^{94} +(-76788.1 - 44050.5i) q^{95} +(-7455.90 + 5417.03i) q^{96} +(-45908.6 + 33354.6i) q^{97} +(11276.8 + 34706.3i) q^{98} -37062.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 24 q^{2} - 54 q^{3} - 96 q^{4} + 30 q^{5} - 216 q^{6} - 212 q^{7} - 384 q^{8} - 486 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 24 q^{2} - 54 q^{3} - 96 q^{4} + 30 q^{5} - 216 q^{6} - 212 q^{7} - 384 q^{8} - 486 q^{9} - 320 q^{10} + 578 q^{11} - 864 q^{12} + 964 q^{13} + 1312 q^{14} - 1350 q^{15} - 1536 q^{16} + 3318 q^{17} + 7776 q^{18} + 3240 q^{19} - 2400 q^{20} - 1998 q^{21} - 48 q^{22} - 2566 q^{23} + 13824 q^{24} + 16120 q^{25} - 2544 q^{26} - 4374 q^{27} - 3552 q^{28} + 2220 q^{29} + 4320 q^{30} + 12918 q^{31} + 24576 q^{32} - 108 q^{33} - 5968 q^{34} - 17190 q^{35} - 7776 q^{36} + 5738 q^{37} - 3600 q^{38} + 8676 q^{39} + 7680 q^{40} - 18732 q^{41} - 7992 q^{42} - 21176 q^{43} - 192 q^{44} + 6480 q^{45} + 20736 q^{46} + 37488 q^{47} - 13824 q^{48} + 62048 q^{49} + 7880 q^{50} - 32868 q^{51} + 15424 q^{52} + 49414 q^{53} - 17496 q^{54} - 83140 q^{55} - 14208 q^{56} - 42120 q^{57} + 8880 q^{58} - 37280 q^{59} + 11520 q^{60} + 65988 q^{61} - 20008 q^{62} + 26568 q^{63} - 24576 q^{64} - 62940 q^{65} + 20808 q^{66} + 38328 q^{67} - 58432 q^{68} + 46656 q^{69} + 33360 q^{70} + 199868 q^{71} - 31104 q^{72} - 50656 q^{73} + 2912 q^{74} - 82620 q^{75} - 74880 q^{76} - 83224 q^{77} - 23256 q^{78} + 132930 q^{79} + 20480 q^{80} - 39366 q^{81} + 15712 q^{82} - 304696 q^{83} + 47232 q^{84} + 12360 q^{85} + 9256 q^{86} + 93600 q^{87} + 36992 q^{88} - 343880 q^{89} + 9720 q^{90} + 453528 q^{91} + 82944 q^{92} - 142488 q^{93} + 149952 q^{94} + 321730 q^{95} - 55296 q^{96} + 153648 q^{97} + 125152 q^{98} - 91692 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.23607 + 3.80423i 0.218508 + 0.672499i
\(3\) −7.28115 + 5.29007i −0.467086 + 0.339358i
\(4\) −12.9443 + 9.40456i −0.404508 + 0.293893i
\(5\) −55.5791 + 5.99730i −0.994229 + 0.107283i
\(6\) −29.1246 21.1603i −0.330280 0.239962i
\(7\) 161.028 1.24210 0.621051 0.783771i \(-0.286706\pi\)
0.621051 + 0.783771i \(0.286706\pi\)
\(8\) −51.7771 37.6183i −0.286031 0.207813i
\(9\) 25.0304 77.0356i 0.103006 0.317019i
\(10\) −91.5146 204.022i −0.289394 0.645175i
\(11\) −141.396 435.171i −0.352334 1.08437i −0.957539 0.288303i \(-0.906909\pi\)
0.605206 0.796069i \(-0.293091\pi\)
\(12\) 44.4984 136.952i 0.0892055 0.274546i
\(13\) 78.8398 242.644i 0.129386 0.398209i −0.865289 0.501274i \(-0.832865\pi\)
0.994675 + 0.103065i \(0.0328649\pi\)
\(14\) 199.042 + 612.588i 0.271409 + 0.835311i
\(15\) 372.954 337.684i 0.427983 0.387510i
\(16\) 79.1084 243.470i 0.0772542 0.237764i
\(17\) −1333.75 969.024i −1.11931 0.813228i −0.135207 0.990817i \(-0.543170\pi\)
−0.984105 + 0.177590i \(0.943170\pi\)
\(18\) 324.000 0.235702
\(19\) 1281.16 + 930.818i 0.814179 + 0.591535i 0.915039 0.403365i \(-0.132160\pi\)
−0.100861 + 0.994901i \(0.532160\pi\)
\(20\) 663.029 600.328i 0.370644 0.335593i
\(21\) −1172.47 + 851.850i −0.580168 + 0.421517i
\(22\) 1480.71 1075.80i 0.652251 0.473888i
\(23\) 1033.60 + 3181.10i 0.407412 + 1.25389i 0.918864 + 0.394574i \(0.129108\pi\)
−0.511452 + 0.859312i \(0.670892\pi\)
\(24\) 576.000 0.204124
\(25\) 3053.06 666.648i 0.976981 0.213327i
\(26\) 1020.52 0.296067
\(27\) 225.273 + 693.320i 0.0594703 + 0.183031i
\(28\) −2084.39 + 1514.40i −0.502440 + 0.365044i
\(29\) 4154.82 3018.65i 0.917397 0.666528i −0.0254779 0.999675i \(-0.508111\pi\)
0.942875 + 0.333148i \(0.108111\pi\)
\(30\) 1745.62 + 1001.40i 0.354117 + 0.203144i
\(31\) 8154.81 + 5924.81i 1.52409 + 1.10731i 0.959415 + 0.281997i \(0.0909968\pi\)
0.564671 + 0.825316i \(0.309003\pi\)
\(32\) 1024.00 0.176777
\(33\) 3331.61 + 2420.55i 0.532560 + 0.386928i
\(34\) 2037.78 6271.65i 0.302316 0.930432i
\(35\) −8949.80 + 965.734i −1.23493 + 0.133256i
\(36\) 400.486 + 1232.57i 0.0515028 + 0.158509i
\(37\) −562.665 + 1731.70i −0.0675687 + 0.207955i −0.979140 0.203187i \(-0.934870\pi\)
0.911571 + 0.411142i \(0.134870\pi\)
\(38\) −1957.44 + 6024.38i −0.219902 + 0.676789i
\(39\) 709.558 + 2183.80i 0.0747010 + 0.229906i
\(40\) 3103.33 + 1780.26i 0.306675 + 0.175928i
\(41\) 577.538 1777.48i 0.0536563 0.165137i −0.920637 0.390419i \(-0.872330\pi\)
0.974294 + 0.225282i \(0.0723302\pi\)
\(42\) −4689.88 3407.40i −0.410241 0.298057i
\(43\) −18541.1 −1.52920 −0.764601 0.644504i \(-0.777064\pi\)
−0.764601 + 0.644504i \(0.777064\pi\)
\(44\) 5922.86 + 4303.21i 0.461211 + 0.335089i
\(45\) −929.160 + 4431.68i −0.0684005 + 0.326240i
\(46\) −10824.0 + 7864.12i −0.754214 + 0.547968i
\(47\) 21041.9 15287.8i 1.38944 1.00949i 0.393514 0.919319i \(-0.371259\pi\)
0.995926 0.0901692i \(-0.0287408\pi\)
\(48\) 711.975 + 2191.23i 0.0446028 + 0.137273i
\(49\) 9123.09 0.542815
\(50\) 6309.88 + 10790.5i 0.356941 + 0.610404i
\(51\) 14837.4 0.798790
\(52\) 1261.44 + 3882.30i 0.0646930 + 0.199105i
\(53\) 19127.7 13897.1i 0.935350 0.679572i −0.0119468 0.999929i \(-0.503803\pi\)
0.947297 + 0.320357i \(0.103803\pi\)
\(54\) −2359.09 + 1713.98i −0.110093 + 0.0799874i
\(55\) 10468.5 + 23338.4i 0.466635 + 1.04031i
\(56\) −8337.57 6057.60i −0.355279 0.258125i
\(57\) −14252.4 −0.581034
\(58\) 16619.3 + 12074.6i 0.648697 + 0.471306i
\(59\) 1899.08 5844.78i 0.0710254 0.218594i −0.909243 0.416267i \(-0.863338\pi\)
0.980268 + 0.197673i \(0.0633383\pi\)
\(60\) −1651.84 + 7878.54i −0.0592365 + 0.282532i
\(61\) −1667.89 5133.24i −0.0573909 0.176631i 0.918252 0.395997i \(-0.129601\pi\)
−0.975643 + 0.219366i \(0.929601\pi\)
\(62\) −12459.4 + 38346.2i −0.411642 + 1.26690i
\(63\) 4030.60 12404.9i 0.127943 0.393769i
\(64\) 1265.73 + 3895.53i 0.0386271 + 0.118882i
\(65\) −2926.64 + 13958.8i −0.0859182 + 0.409792i
\(66\) −5090.24 + 15666.2i −0.143840 + 0.442693i
\(67\) 24919.2 + 18104.9i 0.678185 + 0.492730i 0.872755 0.488159i \(-0.162331\pi\)
−0.194570 + 0.980889i \(0.562331\pi\)
\(68\) 26377.6 0.691773
\(69\) −24354.1 17694.3i −0.615813 0.447414i
\(70\) −14736.4 32853.3i −0.359457 0.801373i
\(71\) −13309.9 + 9670.24i −0.313350 + 0.227662i −0.733333 0.679870i \(-0.762036\pi\)
0.419982 + 0.907532i \(0.362036\pi\)
\(72\) −4193.94 + 3047.08i −0.0953436 + 0.0692712i
\(73\) −970.460 2986.77i −0.0213143 0.0655986i 0.939834 0.341632i \(-0.110980\pi\)
−0.961148 + 0.276034i \(0.910980\pi\)
\(74\) −7283.29 −0.154614
\(75\) −18703.2 + 21004.9i −0.383940 + 0.431189i
\(76\) −25337.6 −0.503190
\(77\) −22768.7 70074.8i −0.437634 1.34690i
\(78\) −7430.59 + 5398.64i −0.138289 + 0.100473i
\(79\) 48397.1 35162.5i 0.872471 0.633888i −0.0587775 0.998271i \(-0.518720\pi\)
0.931249 + 0.364383i \(0.118720\pi\)
\(80\) −2936.60 + 14006.3i −0.0513004 + 0.244680i
\(81\) −5307.96 3856.46i −0.0898908 0.0653095i
\(82\) 7475.81 0.122779
\(83\) 27239.7 + 19790.8i 0.434018 + 0.315333i 0.783254 0.621702i \(-0.213559\pi\)
−0.349236 + 0.937035i \(0.613559\pi\)
\(84\) 7165.51 22053.2i 0.110802 0.341014i
\(85\) 79939.9 + 45858.6i 1.20010 + 0.688451i
\(86\) −22918.1 70534.6i −0.334143 1.02839i
\(87\) −14283.0 + 43958.6i −0.202312 + 0.622652i
\(88\) −9049.32 + 27850.9i −0.124569 + 0.383383i
\(89\) −40288.4 123995.i −0.539145 1.65932i −0.734519 0.678588i \(-0.762592\pi\)
0.195374 0.980729i \(-0.437408\pi\)
\(90\) −18007.6 + 1943.12i −0.234342 + 0.0252868i
\(91\) 12695.4 39072.5i 0.160710 0.494616i
\(92\) −43296.1 31456.5i −0.533310 0.387472i
\(93\) −90719.1 −1.08766
\(94\) 84167.5 + 61151.3i 0.982483 + 0.713816i
\(95\) −76788.1 44050.5i −0.872941 0.500774i
\(96\) −7455.90 + 5417.03i −0.0825700 + 0.0599906i
\(97\) −45908.6 + 33354.6i −0.495410 + 0.359937i −0.807261 0.590194i \(-0.799051\pi\)
0.311851 + 0.950131i \(0.399051\pi\)
\(98\) 11276.8 + 34706.3i 0.118609 + 0.365042i
\(99\) −37062.8 −0.380059
\(100\) −33250.2 + 37342.0i −0.332502 + 0.373420i
\(101\) 52318.0 0.510326 0.255163 0.966898i \(-0.417871\pi\)
0.255163 + 0.966898i \(0.417871\pi\)
\(102\) 18340.1 + 56444.9i 0.174542 + 0.537185i
\(103\) 131773. 95738.7i 1.22386 0.889190i 0.227450 0.973790i \(-0.426961\pi\)
0.996415 + 0.0845998i \(0.0269612\pi\)
\(104\) −13209.9 + 9597.58i −0.119762 + 0.0870119i
\(105\) 60056.1 54376.7i 0.531598 0.481326i
\(106\) 76511.0 + 55588.5i 0.661392 + 0.480530i
\(107\) 131556. 1.11084 0.555419 0.831571i \(-0.312558\pi\)
0.555419 + 0.831571i \(0.312558\pi\)
\(108\) −9436.37 6855.93i −0.0778477 0.0565597i
\(109\) 45110.4 138836.i 0.363672 1.11927i −0.587136 0.809489i \(-0.699745\pi\)
0.950808 0.309780i \(-0.100255\pi\)
\(110\) −75844.8 + 68672.3i −0.597646 + 0.541128i
\(111\) −5063.98 15585.3i −0.0390108 0.120063i
\(112\) 12738.7 39205.6i 0.0959576 0.295327i
\(113\) −45155.4 + 138974.i −0.332670 + 1.02385i 0.635188 + 0.772358i \(0.280923\pi\)
−0.967858 + 0.251496i \(0.919077\pi\)
\(114\) −17617.0 54219.4i −0.126961 0.390744i
\(115\) −76524.7 170604.i −0.539581 1.20294i
\(116\) −25392.0 + 78148.5i −0.175207 + 0.539232i
\(117\) −16718.8 12146.9i −0.112912 0.0820356i
\(118\) 24582.2 0.162524
\(119\) −214771. 156040.i −1.39030 1.01011i
\(120\) −32013.5 + 3454.44i −0.202946 + 0.0218990i
\(121\) −39088.1 + 28399.2i −0.242706 + 0.176336i
\(122\) 17466.4 12690.1i 0.106244 0.0771906i
\(123\) 5197.84 + 15997.3i 0.0309785 + 0.0953420i
\(124\) −161278. −0.941937
\(125\) −165688. + 55361.8i −0.948456 + 0.316910i
\(126\) 52173.1 0.292766
\(127\) −5067.14 15595.1i −0.0278775 0.0857981i 0.936150 0.351602i \(-0.114363\pi\)
−0.964027 + 0.265803i \(0.914363\pi\)
\(128\) −13254.9 + 9630.27i −0.0715077 + 0.0519534i
\(129\) 135001. 98083.8i 0.714269 0.518947i
\(130\) −56719.8 + 6120.38i −0.294358 + 0.0317629i
\(131\) −308400. 224065.i −1.57013 1.14077i −0.927033 0.374981i \(-0.877649\pi\)
−0.643097 0.765785i \(-0.722351\pi\)
\(132\) −65889.5 −0.329140
\(133\) 206303. + 149888.i 1.01129 + 0.734747i
\(134\) −38073.2 + 117177.i −0.183171 + 0.563744i
\(135\) −16678.5 37183.1i −0.0787632 0.175594i
\(136\) 32604.5 + 100346.i 0.151158 + 0.465216i
\(137\) −18265.0 + 56213.9i −0.0831416 + 0.255884i −0.983982 0.178266i \(-0.942951\pi\)
0.900841 + 0.434150i \(0.142951\pi\)
\(138\) 37209.7 114520.i 0.166325 0.511897i
\(139\) −88151.8 271303.i −0.386985 1.19102i −0.935030 0.354569i \(-0.884628\pi\)
0.548045 0.836449i \(-0.315372\pi\)
\(140\) 106766. 96669.7i 0.460378 0.416841i
\(141\) −72335.6 + 222626.i −0.306411 + 0.943036i
\(142\) −53239.8 38681.0i −0.221572 0.160982i
\(143\) −116739. −0.477394
\(144\) −16775.8 12188.3i −0.0674181 0.0489821i
\(145\) −212817. + 192692.i −0.840595 + 0.761102i
\(146\) 10162.8 7383.70i 0.0394576 0.0286676i
\(147\) −66426.6 + 48261.8i −0.253541 + 0.184209i
\(148\) −9002.64 27707.3i −0.0337843 0.103978i
\(149\) 359461. 1.32643 0.663217 0.748427i \(-0.269191\pi\)
0.663217 + 0.748427i \(0.269191\pi\)
\(150\) −103026. 45187.8i −0.373868 0.163981i
\(151\) 444588. 1.58678 0.793388 0.608717i \(-0.208315\pi\)
0.793388 + 0.608717i \(0.208315\pi\)
\(152\) −31319.0 96390.1i −0.109951 0.338395i
\(153\) −108033. + 78490.9i −0.373104 + 0.271076i
\(154\) 238437. 173234.i 0.810161 0.588617i
\(155\) −488769. 280389.i −1.63409 0.937414i
\(156\) −29722.4 21594.6i −0.0977849 0.0710449i
\(157\) −153037. −0.495506 −0.247753 0.968823i \(-0.579692\pi\)
−0.247753 + 0.968823i \(0.579692\pi\)
\(158\) 193588. + 140650.i 0.616931 + 0.448226i
\(159\) −65755.3 + 202374.i −0.206271 + 0.634837i
\(160\) −56913.0 + 6141.23i −0.175756 + 0.0189651i
\(161\) 166439. + 512247.i 0.506047 + 1.55745i
\(162\) 8109.84 24959.5i 0.0242787 0.0747221i
\(163\) −15985.1 + 49197.0i −0.0471244 + 0.145034i −0.971850 0.235600i \(-0.924294\pi\)
0.924726 + 0.380634i \(0.124294\pi\)
\(164\) 9240.61 + 28439.7i 0.0268282 + 0.0825686i
\(165\) −199684. 114552.i −0.570998 0.327560i
\(166\) −41618.6 + 128089.i −0.117224 + 0.360779i
\(167\) 281147. + 204265.i 0.780085 + 0.566765i 0.905005 0.425402i \(-0.139867\pi\)
−0.124919 + 0.992167i \(0.539867\pi\)
\(168\) 92752.3 0.253543
\(169\) 247722. + 179981.i 0.667187 + 0.484740i
\(170\) −75645.2 + 360794.i −0.200752 + 0.957496i
\(171\) 103774. 75396.2i 0.271393 0.197178i
\(172\) 240001. 174371.i 0.618575 0.449421i
\(173\) 44656.9 + 137440.i 0.113442 + 0.349138i 0.991619 0.129198i \(-0.0412402\pi\)
−0.878177 + 0.478336i \(0.841240\pi\)
\(174\) −184883. −0.462939
\(175\) 491630. 107349.i 1.21351 0.264974i
\(176\) −117137. −0.285044
\(177\) 17091.7 + 52603.0i 0.0410066 + 0.126205i
\(178\) 421906. 306533.i 0.998081 0.725148i
\(179\) −35475.2 + 25774.2i −0.0827546 + 0.0601247i −0.628393 0.777896i \(-0.716287\pi\)
0.545639 + 0.838021i \(0.316287\pi\)
\(180\) −29650.7 66103.2i −0.0682109 0.152069i
\(181\) −49195.6 35742.7i −0.111617 0.0810945i 0.530577 0.847637i \(-0.321975\pi\)
−0.642194 + 0.766543i \(0.721975\pi\)
\(182\) 164333. 0.367745
\(183\) 39299.4 + 28552.7i 0.0867477 + 0.0630259i
\(184\) 66150.6 203591.i 0.144042 0.443316i
\(185\) 20886.8 99621.0i 0.0448687 0.214004i
\(186\) −112135. 345116.i −0.237661 0.731446i
\(187\) −233105. + 717424.i −0.487470 + 1.50028i
\(188\) −128597. + 395780.i −0.265360 + 0.816693i
\(189\) 36275.4 + 111644.i 0.0738682 + 0.227343i
\(190\) 72662.7 346569.i 0.146025 0.696475i
\(191\) −93581.9 + 288016.i −0.185613 + 0.571258i −0.999958 0.00912237i \(-0.997096\pi\)
0.814345 + 0.580381i \(0.197096\pi\)
\(192\) −29823.6 21668.1i −0.0583858 0.0424197i
\(193\) 945331. 1.82680 0.913400 0.407064i \(-0.133447\pi\)
0.913400 + 0.407064i \(0.133447\pi\)
\(194\) −183635. 133418.i −0.350308 0.254514i
\(195\) −52533.5 117118.i −0.0989349 0.220565i
\(196\) −118092. + 85798.7i −0.219573 + 0.159529i
\(197\) −669650. + 486530.i −1.22937 + 0.893190i −0.996843 0.0794003i \(-0.974699\pi\)
−0.232527 + 0.972590i \(0.574699\pi\)
\(198\) −45812.2 140995.i −0.0830459 0.255589i
\(199\) 202054. 0.361688 0.180844 0.983512i \(-0.442117\pi\)
0.180844 + 0.983512i \(0.442117\pi\)
\(200\) −183157. 80333.9i −0.323779 0.142012i
\(201\) −277217. −0.483982
\(202\) 64668.6 + 199029.i 0.111510 + 0.343193i
\(203\) 669043. 486088.i 1.13950 0.827895i
\(204\) −192060. + 139539.i −0.323118 + 0.234759i
\(205\) −21439.0 + 102254.i −0.0356302 + 0.169940i
\(206\) 527092. + 382955.i 0.865403 + 0.628752i
\(207\) 270930. 0.439471
\(208\) −52839.8 38390.3i −0.0846842 0.0615267i
\(209\) 223914. 689138.i 0.354582 1.09129i
\(210\) 281095. + 161254.i 0.439850 + 0.252325i
\(211\) −261145. 803722.i −0.403809 1.24280i −0.921886 0.387462i \(-0.873352\pi\)
0.518077 0.855334i \(-0.326648\pi\)
\(212\) −116898. + 359776.i −0.178636 + 0.549785i
\(213\) 45755.5 140821.i 0.0691026 0.212676i
\(214\) 162612. + 500468.i 0.242727 + 0.747037i
\(215\) 1.03050e6 111197.i 1.52038 0.164057i
\(216\) 14417.5 44372.5i 0.0210259 0.0647112i
\(217\) 1.31315e6 + 954062.i 1.89307 + 1.37540i
\(218\) 583921. 0.832172
\(219\) 22866.3 + 16613.3i 0.0322170 + 0.0234070i
\(220\) −354994. 203647.i −0.494498 0.283675i
\(221\) −340280. + 247228.i −0.468658 + 0.340500i
\(222\) 53030.7 38529.1i 0.0722179 0.0524694i
\(223\) −45559.6 140218.i −0.0613505 0.188817i 0.915684 0.401899i \(-0.131650\pi\)
−0.977034 + 0.213082i \(0.931650\pi\)
\(224\) 164893. 0.219575
\(225\) 25063.7 251881.i 0.0330057 0.331695i
\(226\) −584504. −0.761231
\(227\) 119781. + 368649.i 0.154285 + 0.474842i 0.998088 0.0618124i \(-0.0196880\pi\)
−0.843802 + 0.536654i \(0.819688\pi\)
\(228\) 184487. 134038.i 0.235033 0.170762i
\(229\) 172217. 125123.i 0.217014 0.157670i −0.473968 0.880542i \(-0.657179\pi\)
0.690981 + 0.722873i \(0.257179\pi\)
\(230\) 554426. 501995.i 0.691073 0.625720i
\(231\) 536483. + 389778.i 0.661494 + 0.480603i
\(232\) −328681. −0.400917
\(233\) −555435. 403547.i −0.670260 0.486972i 0.199852 0.979826i \(-0.435954\pi\)
−0.870112 + 0.492854i \(0.835954\pi\)
\(234\) 25544.1 78616.6i 0.0304966 0.0938588i
\(235\) −1.07780e6 + 975877.i −1.27312 + 1.15272i
\(236\) 30385.3 + 93516.4i 0.0355127 + 0.109297i
\(237\) −166374. + 512047.i −0.192405 + 0.592160i
\(238\) 328141. 1.00991e6i 0.375507 1.15569i
\(239\) −518378. 1.59540e6i −0.587018 1.80666i −0.591009 0.806665i \(-0.701270\pi\)
0.00399048 0.999992i \(-0.498730\pi\)
\(240\) −52712.4 117517.i −0.0590724 0.131696i
\(241\) −484779. + 1.49200e6i −0.537652 + 1.65472i 0.200196 + 0.979756i \(0.435842\pi\)
−0.737848 + 0.674967i \(0.764158\pi\)
\(242\) −156352. 113597.i −0.171619 0.124689i
\(243\) 59049.0 0.0641500
\(244\) 69865.5 + 50760.3i 0.0751257 + 0.0545820i
\(245\) −507053. + 54713.9i −0.539682 + 0.0582348i
\(246\) −54432.5 + 39547.5i −0.0573483 + 0.0416660i
\(247\) 326864. 237480.i 0.340898 0.247677i
\(248\) −199351. 613539.i −0.205821 0.633451i
\(249\) −303032. −0.309734
\(250\) −415411. 561885.i −0.420366 0.568588i
\(251\) −1.08251e6 −1.08455 −0.542274 0.840202i \(-0.682436\pi\)
−0.542274 + 0.840202i \(0.682436\pi\)
\(252\) 64489.6 + 198478.i 0.0639717 + 0.196885i
\(253\) 1.23818e6 899588.i 1.21613 0.883573i
\(254\) 53063.8 38553.1i 0.0516076 0.0374951i
\(255\) −824650. + 88984.4i −0.794180 + 0.0856965i
\(256\) −53019.7 38521.1i −0.0505636 0.0367366i
\(257\) 854843. 0.807335 0.403667 0.914906i \(-0.367735\pi\)
0.403667 + 0.914906i \(0.367735\pi\)
\(258\) 540003. + 392335.i 0.505064 + 0.366951i
\(259\) −90604.9 + 278853.i −0.0839271 + 0.258301i
\(260\) −93392.8 208210.i −0.0856801 0.191015i
\(261\) −128547. 395627.i −0.116805 0.359488i
\(262\) 471193. 1.45018e6i 0.424077 1.30518i
\(263\) −562906. + 1.73245e6i −0.501818 + 1.54444i 0.304237 + 0.952596i \(0.401598\pi\)
−0.806055 + 0.591840i \(0.798402\pi\)
\(264\) −81443.9 250658.i −0.0719198 0.221346i
\(265\) −979757. + 887104.i −0.857045 + 0.775997i
\(266\) −315203. + 970095.i −0.273141 + 0.840640i
\(267\) 949288. + 689698.i 0.814929 + 0.592081i
\(268\) −492830. −0.419141
\(269\) −686682. 498904.i −0.578595 0.420374i 0.259622 0.965710i \(-0.416402\pi\)
−0.838217 + 0.545336i \(0.816402\pi\)
\(270\) 120837. 109410.i 0.100877 0.0913369i
\(271\) −1.94684e6 + 1.41446e6i −1.61030 + 1.16995i −0.747753 + 0.663977i \(0.768867\pi\)
−0.862548 + 0.505975i \(0.831133\pi\)
\(272\) −341439. + 248070.i −0.279828 + 0.203307i
\(273\) 114259. + 351653.i 0.0927862 + 0.285567i
\(274\) −236427. −0.190248
\(275\) −721796. 1.23434e6i −0.575550 0.984248i
\(276\) 481653. 0.380593
\(277\) −360576. 1.10974e6i −0.282357 0.869004i −0.987179 0.159620i \(-0.948973\pi\)
0.704822 0.709384i \(-0.251027\pi\)
\(278\) 923138. 670699.i 0.716398 0.520494i
\(279\) 660539. 479910.i 0.508029 0.369104i
\(280\) 499724. + 286673.i 0.380921 + 0.218520i
\(281\) 624545. + 453758.i 0.471843 + 0.342814i 0.798159 0.602447i \(-0.205807\pi\)
−0.326316 + 0.945261i \(0.605807\pi\)
\(282\) −936331. −0.701143
\(283\) −1.37183e6 996692.i −1.01820 0.739767i −0.0522884 0.998632i \(-0.516651\pi\)
−0.965913 + 0.258865i \(0.916651\pi\)
\(284\) 81343.1 250348.i 0.0598446 0.184183i
\(285\) 792136. 85476.0i 0.577680 0.0623350i
\(286\) −144298. 444102.i −0.104314 0.321047i
\(287\) 92999.9 286224.i 0.0666466 0.205117i
\(288\) 25631.1 78884.4i 0.0182090 0.0560415i
\(289\) 401114. + 1.23450e6i 0.282503 + 0.869454i
\(290\) −996099. 571425.i −0.695517 0.398992i
\(291\) 157820. 485720.i 0.109252 0.336243i
\(292\) 40651.2 + 29534.8i 0.0279007 + 0.0202711i
\(293\) −835980. −0.568888 −0.284444 0.958693i \(-0.591809\pi\)
−0.284444 + 0.958693i \(0.591809\pi\)
\(294\) −265707. 193047.i −0.179281 0.130255i
\(295\) −70496.4 + 336237.i −0.0471641 + 0.224952i
\(296\) 94276.8 68496.1i 0.0625426 0.0454398i
\(297\) 269860. 196065.i 0.177520 0.128976i
\(298\) 444318. + 1.36747e6i 0.289836 + 0.892025i
\(299\) 853365. 0.552022
\(300\) 44557.7 447789.i 0.0285838 0.287257i
\(301\) −2.98564e6 −1.89942
\(302\) 549541. + 1.69131e6i 0.346723 + 1.06710i
\(303\) −380935. + 276766.i −0.238366 + 0.173183i
\(304\) 327977. 238289.i 0.203545 0.147884i
\(305\) 123485. + 275298.i 0.0760092 + 0.169455i
\(306\) −432134. 313964.i −0.263824 0.191680i
\(307\) 774991. 0.469300 0.234650 0.972080i \(-0.424606\pi\)
0.234650 + 0.972080i \(0.424606\pi\)
\(308\) 953747. + 692938.i 0.572871 + 0.416215i
\(309\) −452995. + 1.39418e6i −0.269897 + 0.830657i
\(310\) 462510. 2.20597e6i 0.273349 1.30375i
\(311\) 139649. + 429794.i 0.0818721 + 0.251976i 0.983611 0.180305i \(-0.0577086\pi\)
−0.901739 + 0.432282i \(0.857709\pi\)
\(312\) 45411.7 139763.i 0.0264108 0.0812841i
\(313\) 256707. 790063.i 0.148107 0.455828i −0.849290 0.527927i \(-0.822970\pi\)
0.997398 + 0.0720986i \(0.0229696\pi\)
\(314\) −189165. 582189.i −0.108272 0.333227i
\(315\) −149621. + 713626.i −0.0849603 + 0.405223i
\(316\) −295777. + 910306.i −0.166627 + 0.512826i
\(317\) 319485. + 232119.i 0.178567 + 0.129737i 0.673479 0.739207i \(-0.264799\pi\)
−0.494911 + 0.868944i \(0.664799\pi\)
\(318\) −851155. −0.471999
\(319\) −1.90110e6 1.38123e6i −1.04599 0.759959i
\(320\) −93710.9 208919.i −0.0511582 0.114052i
\(321\) −957878. + 695939.i −0.518857 + 0.376972i
\(322\) −1.74297e6 + 1.26635e6i −0.936810 + 0.680632i
\(323\) −806760. 2.48295e6i −0.430267 1.32422i
\(324\) 104976. 0.0555556
\(325\) 78944.9 793366.i 0.0414587 0.416644i
\(326\) −206915. −0.107832
\(327\) 405994. + 1.24952e6i 0.209966 + 0.646210i
\(328\) −96768.9 + 70306.7i −0.0496651 + 0.0360838i
\(329\) 3.38834e6 2.46177e6i 1.72583 1.25389i
\(330\) 188956. 901238.i 0.0955161 0.455570i
\(331\) −1.96888e6 1.43048e6i −0.987757 0.717647i −0.0283279 0.999599i \(-0.509018\pi\)
−0.959429 + 0.281952i \(0.909018\pi\)
\(332\) −538723. −0.268238
\(333\) 119319. + 86690.4i 0.0589657 + 0.0428411i
\(334\) −429554. + 1.32203e6i −0.210694 + 0.648449i
\(335\) −1.49357e6 856805.i −0.727132 0.417129i
\(336\) 114648. + 352851.i 0.0554011 + 0.170507i
\(337\) −655978. + 2.01889e6i −0.314640 + 0.968363i 0.661262 + 0.750155i \(0.270021\pi\)
−0.975902 + 0.218208i \(0.929979\pi\)
\(338\) −378485. + 1.16486e6i −0.180201 + 0.554602i
\(339\) −406399. 1.25077e6i −0.192067 0.591122i
\(340\) −1.46604e6 + 158194.i −0.687780 + 0.0742154i
\(341\) 1.42525e6 4.38648e6i 0.663752 2.04282i
\(342\) 415096. + 301585.i 0.191904 + 0.139426i
\(343\) −1.23733e6 −0.567870
\(344\) 960005. + 697485.i 0.437399 + 0.317789i
\(345\) 1.45969e6 + 837372.i 0.660259 + 0.378766i
\(346\) −467653. + 339770.i −0.210007 + 0.152579i
\(347\) 3.15492e6 2.29218e6i 1.40658 1.02194i 0.412771 0.910835i \(-0.364561\pi\)
0.993809 0.111105i \(-0.0354391\pi\)
\(348\) −228528. 703337.i −0.101156 0.311326i
\(349\) 1.32819e6 0.583709 0.291854 0.956463i \(-0.405728\pi\)
0.291854 + 0.956463i \(0.405728\pi\)
\(350\) 1.01607e6 + 1.73758e6i 0.443356 + 0.758184i
\(351\) 185990. 0.0805792
\(352\) −144789. 445615.i −0.0622844 0.191692i
\(353\) −2.02432e6 + 1.47075e6i −0.864653 + 0.628207i −0.929147 0.369711i \(-0.879457\pi\)
0.0644937 + 0.997918i \(0.479457\pi\)
\(354\) −178987. + 130042.i −0.0759126 + 0.0551537i
\(355\) 681759. 617287.i 0.287118 0.259966i
\(356\) 1.68762e6 + 1.22613e6i 0.705750 + 0.512757i
\(357\) 2.38924e6 0.992178
\(358\) −141901. 103097.i −0.0585163 0.0425146i
\(359\) −58590.2 + 180322.i −0.0239932 + 0.0738436i −0.962336 0.271862i \(-0.912360\pi\)
0.938343 + 0.345706i \(0.112360\pi\)
\(360\) 214821. 194506.i 0.0873617 0.0791001i
\(361\) 9794.51 + 30144.4i 0.00395562 + 0.0121741i
\(362\) 75164.3 231332.i 0.0301467 0.0927820i
\(363\) 134373. 413557.i 0.0535236 0.164729i
\(364\) 203127. + 625161.i 0.0803552 + 0.247308i
\(365\) 71849.8 + 160182.i 0.0282289 + 0.0629333i
\(366\) −60044.1 + 184797.i −0.0234297 + 0.0721093i
\(367\) −485608. 352815.i −0.188201 0.136736i 0.489695 0.871894i \(-0.337108\pi\)
−0.677896 + 0.735158i \(0.737108\pi\)
\(368\) 856271. 0.329603
\(369\) −122473. 88981.9i −0.0468247 0.0340201i
\(370\) 404798. 43680.0i 0.153721 0.0165874i
\(371\) 3.08011e6 2.23783e6i 1.16180 0.844097i
\(372\) 1.17429e6 853173.i 0.439966 0.319654i
\(373\) 479229. + 1.47492e6i 0.178349 + 0.548903i 0.999771 0.0214192i \(-0.00681847\pi\)
−0.821421 + 0.570322i \(0.806818\pi\)
\(374\) −3.01738e6 −1.11545
\(375\) 913535. 1.27960e6i 0.335465 0.469890i
\(376\) −1.66459e6 −0.607208
\(377\) −404893. 1.24613e6i −0.146719 0.451555i
\(378\) −379881. + 275999.i −0.136747 + 0.0993525i
\(379\) 571102. 414930.i 0.204228 0.148380i −0.480970 0.876737i \(-0.659716\pi\)
0.685198 + 0.728357i \(0.259716\pi\)
\(380\) 1.40824e6 151957.i 0.500286 0.0539837i
\(381\) 119394. + 86744.5i 0.0421375 + 0.0306147i
\(382\) −1.21135e6 −0.424728
\(383\) 3.69147e6 + 2.68201e6i 1.28589 + 0.934251i 0.999714 0.0239271i \(-0.00761695\pi\)
0.286173 + 0.958178i \(0.407617\pi\)
\(384\) 45566.4 140239.i 0.0157695 0.0485334i
\(385\) 1.68572e6 + 3.75814e6i 0.579608 + 1.29218i
\(386\) 1.16849e6 + 3.59625e6i 0.399170 + 1.22852i
\(387\) −464091. + 1.42833e6i −0.157516 + 0.484786i
\(388\) 280569. 863502.i 0.0946150 0.291195i
\(389\) 683516. + 2.10364e6i 0.229021 + 0.704853i 0.997859 + 0.0654091i \(0.0208352\pi\)
−0.768838 + 0.639444i \(0.779165\pi\)
\(390\) 380608. 344615.i 0.126712 0.114729i
\(391\) 1.70400e6 5.24437e6i 0.563674 1.73481i
\(392\) −472367. 343195.i −0.155262 0.112804i
\(393\) 3.43082e6 1.12051
\(394\) −2.67860e6 1.94612e6i −0.869296 0.631580i
\(395\) −2.47898e6 + 2.24455e6i −0.799431 + 0.723830i
\(396\) 479751. 348560.i 0.153737 0.111696i
\(397\) −901076. + 654670.i −0.286936 + 0.208471i −0.721937 0.691959i \(-0.756748\pi\)
0.435001 + 0.900430i \(0.356748\pi\)
\(398\) 249752. + 768658.i 0.0790317 + 0.243235i
\(399\) −2.29504e6 −0.721703
\(400\) 79213.8 796069.i 0.0247543 0.248771i
\(401\) −3.47897e6 −1.08041 −0.540206 0.841533i \(-0.681654\pi\)
−0.540206 + 0.841533i \(0.681654\pi\)
\(402\) −342659. 1.05460e6i −0.105754 0.325477i
\(403\) 2.08054e6 1.51160e6i 0.638138 0.463634i
\(404\) −677218. + 492028.i −0.206431 + 0.149981i
\(405\) 318140. + 182505.i 0.0963786 + 0.0552888i
\(406\) 2.67617e6 + 1.94435e6i 0.805748 + 0.585410i
\(407\) 833146. 0.249307
\(408\) −768238. 558158.i −0.228479 0.165999i
\(409\) 735672. 2.26417e6i 0.217458 0.669268i −0.781511 0.623891i \(-0.785551\pi\)
0.998970 0.0453774i \(-0.0144490\pi\)
\(410\) −415498. + 44834.6i −0.122070 + 0.0131721i
\(411\) −164385. 505925.i −0.0480018 0.147734i
\(412\) −805325. + 2.47854e6i −0.233737 + 0.719370i
\(413\) 305806. 941174.i 0.0882208 0.271516i
\(414\) 334887. + 1.03068e6i 0.0960280 + 0.295544i
\(415\) −1.63265e6 936591.i −0.465343 0.266950i
\(416\) 80732.0 248467.i 0.0228724 0.0703941i
\(417\) 2.07706e6 + 1.50907e6i 0.584937 + 0.424981i
\(418\) 2.89841e6 0.811370
\(419\) 620891. + 451104.i 0.172775 + 0.125528i 0.670812 0.741627i \(-0.265946\pi\)
−0.498037 + 0.867156i \(0.665946\pi\)
\(420\) −265993. + 1.26867e6i −0.0735778 + 0.350933i
\(421\) −574949. + 417725.i −0.158097 + 0.114864i −0.664021 0.747714i \(-0.731152\pi\)
0.505924 + 0.862578i \(0.331152\pi\)
\(422\) 2.73475e6 1.98691e6i 0.747543 0.543122i
\(423\) −651020. 2.00363e6i −0.176906 0.544462i
\(424\) −1.51316e6 −0.408763
\(425\) −4.71801e6 2.06935e6i −1.26703 0.555728i
\(426\) 592272. 0.158124
\(427\) −268578. 826597.i −0.0712853 0.219394i
\(428\) −1.70289e6 + 1.23722e6i −0.449343 + 0.326467i
\(429\) 849996. 617558.i 0.222984 0.162007i
\(430\) 1.69678e6 + 3.78280e6i 0.442543 + 0.986603i
\(431\) 2.27241e6 + 1.65100e6i 0.589240 + 0.428108i 0.842044 0.539409i \(-0.181352\pi\)
−0.252803 + 0.967518i \(0.581352\pi\)
\(432\) 186624. 0.0481125
\(433\) −2.79236e6 2.02877e6i −0.715733 0.520011i 0.169285 0.985567i \(-0.445854\pi\)
−0.885018 + 0.465557i \(0.845854\pi\)
\(434\) −2.00632e6 + 6.17482e6i −0.511300 + 1.57362i
\(435\) 530203. 2.52883e6i 0.134344 0.640763i
\(436\) 721766. + 2.22137e6i 0.181836 + 0.559634i
\(437\) −1.63682e6 + 5.03760e6i −0.410012 + 1.26189i
\(438\) −34936.6 + 107524.i −0.00870152 + 0.0267805i
\(439\) 548616. + 1.68847e6i 0.135865 + 0.418149i 0.995724 0.0923832i \(-0.0294485\pi\)
−0.859859 + 0.510532i \(0.829448\pi\)
\(440\) 335922. 1.60220e6i 0.0827194 0.394535i
\(441\) 228354. 702803.i 0.0559130 0.172083i
\(442\) −1.36112e6 988912.i −0.331391 0.240770i
\(443\) −737408. −0.178525 −0.0892624 0.996008i \(-0.528451\pi\)
−0.0892624 + 0.996008i \(0.528451\pi\)
\(444\) 212123. + 154116.i 0.0510658 + 0.0371015i
\(445\) 2.98283e6 + 6.64991e6i 0.714049 + 1.59190i
\(446\) 477107. 346638.i 0.113574 0.0825162i
\(447\) −2.61729e6 + 1.90157e6i −0.619559 + 0.450136i
\(448\) 203819. + 627290.i 0.0479788 + 0.147664i
\(449\) 934181. 0.218683 0.109341 0.994004i \(-0.465126\pi\)
0.109341 + 0.994004i \(0.465126\pi\)
\(450\) 989193. 215994.i 0.230277 0.0502818i
\(451\) −855169. −0.197975
\(452\) −722487. 2.22359e6i −0.166335 0.511927i
\(453\) −3.23711e6 + 2.35190e6i −0.741161 + 0.538485i
\(454\) −1.25437e6 + 911351.i −0.285618 + 0.207513i
\(455\) −471271. + 2.24775e6i −0.106719 + 0.509003i
\(456\) 737949. + 536151.i 0.166193 + 0.120747i
\(457\) 5.75606e6 1.28924 0.644622 0.764502i \(-0.277015\pi\)
0.644622 + 0.764502i \(0.277015\pi\)
\(458\) 688868. + 500492.i 0.153452 + 0.111489i
\(459\) 371386. 1.14301e6i 0.0822799 0.253232i
\(460\) 2.59501e6 + 1.48866e6i 0.571801 + 0.328021i
\(461\) 1.53253e6 + 4.71663e6i 0.335858 + 1.03366i 0.966298 + 0.257426i \(0.0828744\pi\)
−0.630440 + 0.776238i \(0.717126\pi\)
\(462\) −819673. + 2.52269e6i −0.178663 + 0.549869i
\(463\) −1.55564e6 + 4.78777e6i −0.337254 + 1.03796i 0.628348 + 0.777933i \(0.283732\pi\)
−0.965601 + 0.260027i \(0.916268\pi\)
\(464\) −406272. 1.25038e6i −0.0876036 0.269616i
\(465\) 5.04208e6 544069.i 1.08138 0.116687i
\(466\) 848629. 2.61181e6i 0.181031 0.557156i
\(467\) −4.44494e6 3.22944e6i −0.943135 0.685228i 0.00603816 0.999982i \(-0.498078\pi\)
−0.949173 + 0.314754i \(0.898078\pi\)
\(468\) 330650. 0.0697836
\(469\) 4.01270e6 + 2.91540e6i 0.842374 + 0.612020i
\(470\) −5.04470e6 2.89395e6i −1.05339 0.604292i
\(471\) 1.11429e6 809579.i 0.231444 0.168154i
\(472\) −318199. + 231185.i −0.0657422 + 0.0477645i
\(473\) 2.62163e6 + 8.06856e6i 0.538789 + 1.65822i
\(474\) −2.15359e6 −0.440269
\(475\) 4.53199e6 + 1.98776e6i 0.921627 + 0.404232i
\(476\) 4.24754e6 0.859252
\(477\) −591798. 1.82137e6i −0.119091 0.366523i
\(478\) 5.42852e6 3.94405e6i 1.08671 0.789538i
\(479\) 2.70137e6 1.96266e6i 0.537953 0.390846i −0.285371 0.958417i \(-0.592117\pi\)
0.823324 + 0.567571i \(0.192117\pi\)
\(480\) 381904. 345789.i 0.0756574 0.0685027i
\(481\) 375827. + 273054.i 0.0740671 + 0.0538129i
\(482\) −6.27511e6 −1.23028
\(483\) −3.92169e6 2.84928e6i −0.764902 0.555734i
\(484\) 238885. 735213.i 0.0463528 0.142659i
\(485\) 2.35152e6 2.12914e6i 0.453936 0.411008i
\(486\) 72988.6 + 224636.i 0.0140173 + 0.0431408i
\(487\) 2.13892e6 6.58292e6i 0.408669 1.25775i −0.509123 0.860694i \(-0.670030\pi\)
0.917792 0.397061i \(-0.129970\pi\)
\(488\) −106745. + 328527.i −0.0202908 + 0.0624485i
\(489\) −143866. 442773.i −0.0272073 0.0837354i
\(490\) −834896. 1.86131e6i −0.157088 0.350211i
\(491\) 1.37179e6 4.22192e6i 0.256793 0.790326i −0.736679 0.676243i \(-0.763607\pi\)
0.993471 0.114083i \(-0.0363931\pi\)
\(492\) −217730. 158190.i −0.0405514 0.0294623i
\(493\) −8.46663e6 −1.56889
\(494\) 1.30746e6 + 949922.i 0.241051 + 0.175134i
\(495\) 2.05992e6 222277.i 0.377865 0.0407738i
\(496\) 2.08763e6 1.51675e6i 0.381021 0.276828i
\(497\) −2.14328e6 + 1.55718e6i −0.389213 + 0.282780i
\(498\) −374568. 1.15280e6i −0.0676795 0.208296i
\(499\) 5.19536e6 0.934037 0.467019 0.884247i \(-0.345328\pi\)
0.467019 + 0.884247i \(0.345328\pi\)
\(500\) 1.62406e6 2.27485e6i 0.290521 0.406937i
\(501\) −3.12765e6 −0.556703
\(502\) −1.33806e6 4.11812e6i −0.236982 0.729356i
\(503\) −3.70637e6 + 2.69283e6i −0.653173 + 0.474558i −0.864351 0.502889i \(-0.832270\pi\)
0.211177 + 0.977448i \(0.432270\pi\)
\(504\) −675343. + 490666.i −0.118426 + 0.0860418i
\(505\) −2.90778e6 + 313766.i −0.507380 + 0.0547492i
\(506\) 4.95271e6 + 3.59835e6i 0.859936 + 0.624780i
\(507\) −2.75581e6 −0.476134
\(508\) 212255. + 154212.i 0.0364921 + 0.0265131i
\(509\) 1.07525e6 3.30928e6i 0.183956 0.566160i −0.815972 0.578091i \(-0.803798\pi\)
0.999929 + 0.0119312i \(0.00379790\pi\)
\(510\) −1.35784e6 3.02716e6i −0.231166 0.515360i
\(511\) −156271. 480954.i −0.0264745 0.0814801i
\(512\) 81007.0 249314.i 0.0136568 0.0420312i
\(513\) −356743. + 1.09794e6i −0.0598498 + 0.184199i
\(514\) 1.05664e6 + 3.25202e6i 0.176409 + 0.542932i
\(515\) −6.74965e6 + 6.11135e6i −1.12141 + 1.01536i
\(516\) −825051. + 2.53925e6i −0.136413 + 0.419837i
\(517\) −9.62805e6 6.99519e6i −1.58421 1.15099i
\(518\) −1.17281e6 −0.192046
\(519\) −1.05222e6 764482.i −0.171470 0.124580i
\(520\) 676637. 612649.i 0.109735 0.0993581i
\(521\) 5.82323e6 4.23082e6i 0.939874 0.682858i −0.00851643 0.999964i \(-0.502711\pi\)
0.948390 + 0.317105i \(0.102711\pi\)
\(522\) 1.34616e6 978044.i 0.216232 0.157102i
\(523\) −1.33204e6 4.09960e6i −0.212943 0.655371i −0.999293 0.0375902i \(-0.988032\pi\)
0.786350 0.617781i \(-0.211968\pi\)
\(524\) 6.09924e6 0.970393
\(525\) −3.01175e6 + 3.38238e6i −0.476892 + 0.535580i
\(526\) −7.28640e6 −1.14828
\(527\) −5.13516e6 1.58044e7i −0.805430 2.47886i
\(528\) 852891. 619662.i 0.133140 0.0967320i
\(529\) −3.84397e6 + 2.79281e6i −0.597229 + 0.433912i
\(530\) −4.58579e6 2.63070e6i −0.709128 0.406800i
\(531\) −402721. 292594.i −0.0619823 0.0450328i
\(532\) −4.08007e6 −0.625013
\(533\) −385762. 280272.i −0.0588167 0.0427329i
\(534\) −1.45038e6 + 4.46382e6i −0.220105 + 0.677413i
\(535\) −7.31175e6 + 788979.i −1.10443 + 0.119174i
\(536\) −609172. 1.87484e6i −0.0915857 0.281872i
\(537\) 121953. 375332.i 0.0182497 0.0561669i
\(538\) 1.04916e6 3.22897e6i 0.156273 0.480960i
\(539\) −1.28997e6 3.97011e6i −0.191252 0.588613i
\(540\) 565582. + 324453.i 0.0834663 + 0.0478815i
\(541\) 1.87349e6 5.76600e6i 0.275206 0.846996i −0.713959 0.700187i \(-0.753100\pi\)
0.989165 0.146809i \(-0.0469002\pi\)
\(542\) −7.78736e6 5.65785e6i −1.13865 0.827281i
\(543\) 547282. 0.0796548
\(544\) −1.36576e6 992280.i −0.197868 0.143760i
\(545\) −1.67456e6 + 7.98689e6i −0.241495 + 1.15182i
\(546\) −1.19653e6 + 869334.i −0.171769 + 0.124797i
\(547\) 7.33505e6 5.32923e6i 1.04818 0.761546i 0.0763124 0.997084i \(-0.475685\pi\)
0.971865 + 0.235538i \(0.0756854\pi\)
\(548\) −292240. 899422.i −0.0415708 0.127942i
\(549\) −437190. −0.0619070
\(550\) 3.80354e6 4.27161e6i 0.536143 0.602122i
\(551\) 8.13281e6 1.14120
\(552\) 595355. + 1.83232e6i 0.0831627 + 0.255948i
\(553\) 7.79329e6 5.66216e6i 1.08370 0.787353i
\(554\) 3.77601e6 2.74343e6i 0.522707 0.379769i
\(555\) 374921. + 835848.i 0.0516663 + 0.115185i
\(556\) 3.69255e6 + 2.68279e6i 0.506570 + 0.368045i
\(557\) 2.19310e6 0.299517 0.149758 0.988723i \(-0.452150\pi\)
0.149758 + 0.988723i \(0.452150\pi\)
\(558\) 2.64216e6 + 1.91964e6i 0.359231 + 0.260996i
\(559\) −1.46178e6 + 4.49889e6i −0.197857 + 0.608942i
\(560\) −472876. + 2.25541e6i −0.0637202 + 0.303917i
\(561\) −2.09795e6 6.45681e6i −0.281441 0.866186i
\(562\) −954219. + 2.93678e6i −0.127440 + 0.392221i
\(563\) −3.42989e6 + 1.05561e7i −0.456047 + 1.40357i 0.413854 + 0.910343i \(0.364182\pi\)
−0.869902 + 0.493225i \(0.835818\pi\)
\(564\) −1.15737e6 3.56202e6i −0.153205 0.471518i
\(565\) 1.67623e6 7.99487e6i 0.220908 1.05363i
\(566\) 2.09597e6 6.45073e6i 0.275007 0.846384i
\(567\) −854732. 620999.i −0.111653 0.0811210i
\(568\) 1.05293e6 0.136939
\(569\) −2.73524e6 1.98727e6i −0.354172 0.257321i 0.396445 0.918058i \(-0.370244\pi\)
−0.750617 + 0.660737i \(0.770244\pi\)
\(570\) 1.30430e6 + 2.90781e6i 0.168148 + 0.374868i
\(571\) −2.94320e6 + 2.13836e6i −0.377772 + 0.274468i −0.760427 0.649424i \(-0.775010\pi\)
0.382654 + 0.923892i \(0.375010\pi\)
\(572\) 1.51110e6 1.09788e6i 0.193110 0.140303i
\(573\) −842237. 2.59214e6i −0.107164 0.329816i
\(574\) 1.20382e6 0.152504
\(575\) 5.27633e6 + 9.02306e6i 0.665522 + 1.13811i
\(576\) 331776. 0.0416667
\(577\) 4.01338e6 + 1.23519e7i 0.501847 + 1.54453i 0.806008 + 0.591905i \(0.201624\pi\)
−0.304161 + 0.952621i \(0.598376\pi\)
\(578\) −4.20052e6 + 3.05185e6i −0.522978 + 0.379965i
\(579\) −6.88310e6 + 5.00087e6i −0.853273 + 0.619939i
\(580\) 942584. 4.49571e6i 0.116346 0.554917i
\(581\) 4.38637e6 + 3.18688e6i 0.539094 + 0.391675i
\(582\) 2.04286e6 0.249995
\(583\) −8.75220e6 6.35885e6i −1.06646 0.774831i
\(584\) −62109.5 + 191153.i −0.00753573 + 0.0231926i
\(585\) 1.00207e6 + 574848.i 0.121062 + 0.0694486i
\(586\) −1.03333e6 3.18026e6i −0.124307 0.382576i
\(587\) −2.02396e6 + 6.22912e6i −0.242442 + 0.746160i 0.753605 + 0.657328i \(0.228313\pi\)
−0.996047 + 0.0888317i \(0.971687\pi\)
\(588\) 405963. 1.24943e6i 0.0484221 0.149028i
\(589\) 4.93270e6 + 1.51813e7i 0.585863 + 1.80310i
\(590\) −1.36626e6 + 147427.i −0.161586 + 0.0174360i
\(591\) 2.30205e6 7.08499e6i 0.271111 0.834393i
\(592\) 377107. + 273985.i 0.0442243 + 0.0321308i
\(593\) −1.48651e7 −1.73593 −0.867963 0.496629i \(-0.834571\pi\)
−0.867963 + 0.496629i \(0.834571\pi\)
\(594\) 1.07944e6 + 784260.i 0.125526 + 0.0911998i
\(595\) 1.28726e7 + 7.38452e6i 1.49064 + 0.855126i
\(596\) −4.65296e6 + 3.38057e6i −0.536554 + 0.389829i
\(597\) −1.47118e6 + 1.06888e6i −0.168939 + 0.122742i
\(598\) 1.05482e6 + 3.24639e6i 0.120621 + 0.371234i
\(599\) 965073. 0.109899 0.0549494 0.998489i \(-0.482500\pi\)
0.0549494 + 0.998489i \(0.482500\pi\)
\(600\) 1.75857e6 383989.i 0.199425 0.0435453i
\(601\) 9.02699e6 1.01943 0.509715 0.860344i \(-0.329751\pi\)
0.509715 + 0.860344i \(0.329751\pi\)
\(602\) −3.69046e6 1.13581e7i −0.415039 1.27736i
\(603\) 2.01846e6 1.46650e6i 0.226062 0.164243i
\(604\) −5.75487e6 + 4.18116e6i −0.641864 + 0.466342i
\(605\) 2.00216e6 1.81282e6i 0.222388 0.201357i
\(606\) −1.52374e6 1.10706e6i −0.168550 0.122459i
\(607\) −29976.0 −0.00330219 −0.00165110 0.999999i \(-0.500526\pi\)
−0.00165110 + 0.999999i \(0.500526\pi\)
\(608\) 1.31191e6 + 953157.i 0.143928 + 0.104570i
\(609\) −2.29997e6 + 7.07857e6i −0.251292 + 0.773397i
\(610\) −894659. + 810053.i −0.0973494 + 0.0881433i
\(611\) −2.05056e6 6.31098e6i −0.222213 0.683901i
\(612\) 660242. 2.03202e6i 0.0712565 0.219305i
\(613\) −2.76667e6 + 8.51494e6i −0.297376 + 0.915230i 0.685037 + 0.728509i \(0.259786\pi\)
−0.982413 + 0.186722i \(0.940214\pi\)
\(614\) 957941. + 2.94824e6i 0.102546 + 0.315604i
\(615\) −384832. 857943.i −0.0410283 0.0914683i
\(616\) −1.45720e6 + 4.48479e6i −0.154727 + 0.476201i
\(617\) 2.31469e6 + 1.68172e6i 0.244782 + 0.177845i 0.703411 0.710783i \(-0.251659\pi\)
−0.458629 + 0.888628i \(0.651659\pi\)
\(618\) −5.86370e6 −0.617590
\(619\) −1.06634e7 7.74738e6i −1.11858 0.812697i −0.134588 0.990902i \(-0.542971\pi\)
−0.983993 + 0.178205i \(0.942971\pi\)
\(620\) 8.96370e6 967234.i 0.936501 0.101054i
\(621\) −1.97268e6 + 1.43324e6i −0.205271 + 0.149138i
\(622\) −1.46242e6 + 1.06251e6i −0.151564 + 0.110118i
\(623\) −6.48758e6 1.99667e7i −0.669672 2.06104i
\(624\) 587822. 0.0604344
\(625\) 8.87679e6 4.07064e6i 0.908983 0.416834i
\(626\) 3.32289e6 0.338906
\(627\) 2.01523e6 + 6.20224e6i 0.204718 + 0.630057i
\(628\) 1.98096e6 1.43925e6i 0.200436 0.145625i
\(629\) 2.42851e6 1.76442e6i 0.244745 0.177818i
\(630\) −2.89973e6 + 312898.i −0.291076 + 0.0314088i
\(631\) 7.40268e6 + 5.37836e6i 0.740143 + 0.537746i 0.892756 0.450541i \(-0.148769\pi\)
−0.152613 + 0.988286i \(0.548769\pi\)
\(632\) −3.82861e6 −0.381284
\(633\) 6.15318e6 + 4.47055e6i 0.610366 + 0.443457i
\(634\) −488130. + 1.50231e6i −0.0482294 + 0.148435i
\(635\) 375155. + 836370.i 0.0369213 + 0.0823121i
\(636\) −1.05209e6 3.23799e6i −0.103136 0.317418i
\(637\) 719263. 2.21366e6i 0.0702327 0.216154i
\(638\) 2.90463e6 8.93953e6i 0.282513 0.869486i
\(639\) 411800. + 1.26739e6i 0.0398964 + 0.122789i
\(640\) 678941. 614735.i 0.0655213 0.0593251i
\(641\) −3.60931e6 + 1.11083e7i −0.346960 + 1.06783i 0.613566 + 0.789643i \(0.289734\pi\)
−0.960526 + 0.278190i \(0.910266\pi\)
\(642\) −3.83151e6 2.78376e6i −0.366887 0.266559i
\(643\) −9.13585e6 −0.871408 −0.435704 0.900090i \(-0.643501\pi\)
−0.435704 + 0.900090i \(0.643501\pi\)
\(644\) −6.97190e6 5.06538e6i −0.662424 0.481280i
\(645\) −6.91498e6 + 6.26104e6i −0.654473 + 0.592581i
\(646\) 8.44850e6 6.13819e6i 0.796523 0.578708i
\(647\) −8.61705e6 + 6.26066e6i −0.809279 + 0.587975i −0.913621 0.406566i \(-0.866726\pi\)
0.104343 + 0.994541i \(0.466726\pi\)
\(648\) 129757. + 399352.i 0.0121393 + 0.0373610i
\(649\) −2.81200e6 −0.262062
\(650\) 3.11573e6 680330.i 0.289252 0.0631592i
\(651\) −1.46083e7 −1.35098
\(652\) −255761. 787153.i −0.0235622 0.0725170i
\(653\) −1.29776e7 + 9.42875e6i −1.19100 + 0.865309i −0.993369 0.114968i \(-0.963323\pi\)
−0.197627 + 0.980277i \(0.563323\pi\)
\(654\) −4.25162e6 + 3.08898e6i −0.388696 + 0.282404i
\(655\) 1.84843e7 + 1.06038e7i 1.68345 + 0.965734i
\(656\) −387076. 281227.i −0.0351185 0.0255151i
\(657\) −254378. −0.0229915
\(658\) 1.35534e7 + 9.84709e6i 1.22034 + 0.886631i
\(659\) 2.33327e6 7.18108e6i 0.209292 0.644134i −0.790218 0.612826i \(-0.790033\pi\)
0.999510 0.0313082i \(-0.00996734\pi\)
\(660\) 3.66208e6 395159.i 0.327241 0.0353111i
\(661\) −6.41313e6 1.97376e7i −0.570908 1.75707i −0.649707 0.760184i \(-0.725109\pi\)
0.0787990 0.996891i \(-0.474891\pi\)
\(662\) 3.00819e6 9.25824e6i 0.266784 0.821076i
\(663\) 1.16978e6 3.60021e6i 0.103352 0.318086i
\(664\) −665898. 2.04942e6i −0.0586121 0.180390i
\(665\) −1.23651e7 7.09337e6i −1.08428 0.622012i
\(666\) −182303. + 561072.i −0.0159261 + 0.0490155i
\(667\) 1.38971e7 + 1.00968e7i 1.20951 + 0.878760i
\(668\) −5.56027e6 −0.482119
\(669\) 1.07349e6 + 779936.i 0.0927327 + 0.0673742i
\(670\) 1.41333e6 6.74094e6i 0.121634 0.580141i
\(671\) −1.99801e6 + 1.45164e6i −0.171313 + 0.124466i
\(672\) −1.20061e6 + 872295.i −0.102560 + 0.0745144i
\(673\) −994347. 3.06028e6i −0.0846253 0.260450i 0.899786 0.436331i \(-0.143722\pi\)
−0.984411 + 0.175881i \(0.943722\pi\)
\(674\) −8.49115e6 −0.719974
\(675\) 1.14997e6 + 1.96657e6i 0.0971469 + 0.166131i
\(676\) −4.89922e6 −0.412344
\(677\) −4.00827e6 1.23362e7i −0.336113 1.03445i −0.966171 0.257901i \(-0.916969\pi\)
0.630059 0.776548i \(-0.283031\pi\)
\(678\) 4.25587e6 3.09207e6i 0.355561 0.258330i
\(679\) −7.39259e6 + 5.37103e6i −0.615350 + 0.447078i
\(680\) −2.41394e6 5.38162e6i −0.200195 0.446315i
\(681\) −2.82233e6 2.05054e6i −0.233206 0.169434i
\(682\) 1.84489e7 1.51883
\(683\) 1.69241e7 + 1.22960e7i 1.38820 + 1.00859i 0.996060 + 0.0886837i \(0.0282660\pi\)
0.392143 + 0.919904i \(0.371734\pi\)
\(684\) −634210. + 1.95190e6i −0.0518314 + 0.159521i
\(685\) 678020. 3.23386e6i 0.0552098 0.263326i
\(686\) −1.52942e6 4.70707e6i −0.124084 0.381892i
\(687\) −592029. + 1.82208e6i −0.0478576 + 0.147291i
\(688\) −1.46676e6 + 4.51421e6i −0.118137 + 0.363589i
\(689\) −1.86403e6 5.73688e6i −0.149590 0.460392i
\(690\) −1.38127e6 + 6.58806e6i −0.110448 + 0.526786i
\(691\) −920841. + 2.83406e6i −0.0733651 + 0.225795i −0.981014 0.193935i \(-0.937875\pi\)
0.907649 + 0.419729i \(0.137875\pi\)
\(692\) −1.87061e6 1.35908e6i −0.148497 0.107890i
\(693\) −5.96816e6 −0.472071
\(694\) 1.26197e7 + 9.16873e6i 0.994602 + 0.722621i
\(695\) 6.52648e6 + 1.45501e7i 0.512527 + 1.14263i
\(696\) 2.39318e6 1.73874e6i 0.187263 0.136054i
\(697\) −2.49271e6 + 1.81106e6i −0.194352 + 0.141205i
\(698\) 1.64173e6 + 5.05273e6i 0.127545 + 0.392543i
\(699\) 6.17900e6 0.478327
\(700\) −5.35422e6 + 6.01312e6i −0.413001 + 0.463826i
\(701\) −644574. −0.0495425 −0.0247713 0.999693i \(-0.507886\pi\)
−0.0247713 + 0.999693i \(0.507886\pi\)
\(702\) 229897. + 707550.i 0.0176072 + 0.0541894i
\(703\) −2.33277e6 + 1.69485e6i −0.178026 + 0.129343i
\(704\) 1.51625e6 1.10162e6i 0.115303 0.0837723i
\(705\) 2.68519e6 1.28072e7i 0.203471 0.970466i
\(706\) −8.09727e6 5.88301e6i −0.611402 0.444210i
\(707\) 8.42467e6 0.633876
\(708\) −715948. 520167.i −0.0536783 0.0389996i
\(709\) −891372. + 2.74336e6i −0.0665953 + 0.204959i −0.978817 0.204738i \(-0.934366\pi\)
0.912221 + 0.409697i \(0.134366\pi\)
\(710\) 3.19100e6 + 1.83056e6i 0.237564 + 0.136282i
\(711\) −1.49737e6 4.60843e6i −0.111085 0.341884i
\(712\) −2.57846e6 + 7.93568e6i −0.190616 + 0.586657i
\(713\) −1.04186e7 + 3.20652e7i −0.767513 + 2.36216i
\(714\) 2.95327e6 + 9.08922e6i 0.216799 + 0.667239i
\(715\) 6.48826e6 700120.i 0.474638 0.0512162i
\(716\) 216805. 667257.i 0.0158047 0.0486419i
\(717\) 1.22142e7 + 8.87412e6i 0.887292 + 0.644655i
\(718\) −758408. −0.0549024
\(719\) 2.11167e7 + 1.53422e7i 1.52337 + 1.10679i 0.959786 + 0.280731i \(0.0905769\pi\)
0.563581 + 0.826060i \(0.309423\pi\)
\(720\) 1.00548e6 + 576806.i 0.0722839 + 0.0414666i
\(721\) 2.12192e7 1.54166e7i 1.52016 1.10446i
\(722\) −102569. + 74521.0i −0.00732276 + 0.00532030i
\(723\) −4.36301e6 1.34280e7i −0.310414 0.955355i
\(724\) 972947. 0.0689831
\(725\) 1.06726e7 1.19859e7i 0.754090 0.846891i
\(726\) 1.73936e6 0.122475
\(727\) −2.24692e6 6.91532e6i −0.157671 0.485262i 0.840751 0.541423i \(-0.182114\pi\)
−0.998422 + 0.0561608i \(0.982114\pi\)
\(728\) −2.12717e6 + 1.54548e6i −0.148756 + 0.108078i
\(729\) −429945. + 312373.i −0.0299636 + 0.0217698i
\(730\) −520556. + 471328.i −0.0361543 + 0.0327353i
\(731\) 2.47292e7 + 1.79668e7i 1.71165 + 1.24359i
\(732\) −777227. −0.0536130
\(733\) −4.54838e6 3.30459e6i −0.312678 0.227174i 0.420367 0.907354i \(-0.361901\pi\)
−0.733045 + 0.680181i \(0.761901\pi\)
\(734\) 741944. 2.28347e6i 0.0508312 0.156442i
\(735\) 3.40249e6 3.08072e6i 0.232316 0.210346i
\(736\) 1.05841e6 + 3.25745e6i 0.0720210 + 0.221658i
\(737\) 4.35525e6 1.34041e7i 0.295355 0.909010i
\(738\) 187122. 575903.i 0.0126469 0.0389232i
\(739\) −2.44824e6 7.53490e6i −0.164908 0.507535i 0.834121 0.551581i \(-0.185975\pi\)
−0.999030 + 0.0440457i \(0.985975\pi\)
\(740\) 666527. + 1.48595e6i 0.0447444 + 0.0997529i
\(741\) −1.12366e6 + 3.45826e6i −0.0751776 + 0.231373i
\(742\) 1.23204e7 + 8.95132e6i 0.821516 + 0.596866i
\(743\) 1.02748e7 0.682811 0.341406 0.939916i \(-0.389097\pi\)
0.341406 + 0.939916i \(0.389097\pi\)
\(744\) 4.69717e6 + 3.41269e6i 0.311103 + 0.226029i
\(745\) −1.99785e7 + 2.15579e6i −1.31878 + 0.142304i
\(746\) −5.01856e6 + 3.64619e6i −0.330166 + 0.239879i
\(747\) 2.20642e6 1.60306e6i 0.144673 0.105111i
\(748\) −3.72968e6 1.14788e7i −0.243735 0.750139i
\(749\) 2.11842e7 1.37977
\(750\) 5.99708e6 + 1.89362e6i 0.389302 + 0.122925i
\(751\) −2.45834e7 −1.59053 −0.795266 0.606261i \(-0.792669\pi\)
−0.795266 + 0.606261i \(0.792669\pi\)
\(752\) −2.05755e6 6.33247e6i −0.132680 0.408346i
\(753\) 7.88194e6 5.72656e6i 0.506577 0.368050i
\(754\) 4.24009e6 3.08061e6i 0.271611 0.197337i
\(755\) −2.47098e7 + 2.66633e6i −1.57762 + 0.170234i
\(756\) −1.51952e6 1.10400e6i −0.0966947 0.0702528i
\(757\) 1.99942e7 1.26813 0.634065 0.773280i \(-0.281385\pi\)
0.634065 + 0.773280i \(0.281385\pi\)
\(758\) 2.28441e6 + 1.65972e6i 0.144411 + 0.104921i
\(759\) −4.25647e6 + 1.31001e7i −0.268192 + 0.825409i
\(760\) 2.31876e6 + 5.16944e6i 0.145620 + 0.324646i
\(761\) −1.71836e6 5.28856e6i −0.107560 0.331036i 0.882763 0.469819i \(-0.155681\pi\)
−0.990323 + 0.138783i \(0.955681\pi\)
\(762\) −182417. + 561422.i −0.0113809 + 0.0350269i
\(763\) 7.26405e6 2.23564e7i 0.451718 1.39025i
\(764\) −1.49731e6 4.60825e6i −0.0928065 0.285629i
\(765\) 5.53367e6 5.01036e6i 0.341869 0.309539i
\(766\) −5.64007e6 + 1.73583e7i −0.347306 + 1.06890i
\(767\) −1.26848e6 921602.i −0.0778564 0.0565660i
\(768\) 589824. 0.0360844
\(769\) 5.85945e6 + 4.25714e6i 0.357306 + 0.259598i 0.751928 0.659246i \(-0.229124\pi\)
−0.394621 + 0.918844i \(0.629124\pi\)
\(770\) −1.22132e7 + 1.10582e7i −0.742337 + 0.672136i
\(771\) −6.22425e6 + 4.52218e6i −0.377095 + 0.273976i
\(772\) −1.22366e7 + 8.89043e6i −0.738956 + 0.536883i
\(773\) 3.32689e6 + 1.02391e7i 0.200258 + 0.616330i 0.999875 + 0.0158201i \(0.00503590\pi\)
−0.799617 + 0.600510i \(0.794964\pi\)
\(774\) −6.00732e6 −0.360436
\(775\) 2.88469e7 + 1.26525e7i 1.72522 + 0.756694i
\(776\) 3.63176e6 0.216502
\(777\) −815444. 2.50968e6i −0.0484554 0.149130i
\(778\) −7.15787e6 + 5.20050e6i −0.423970 + 0.308032i
\(779\) 2.39443e6 1.73965e6i 0.141370 0.102712i
\(780\) 1.78145e6 + 1.02195e6i 0.104842 + 0.0601442i
\(781\) 6.09018e6 + 4.42477e6i 0.357275 + 0.259575i
\(782\) 2.20570e7 1.28982
\(783\) 3.02886e6 + 2.20060e6i 0.176553 + 0.128273i
\(784\) 721713. 2.22120e6i 0.0419348 0.129062i
\(785\) 8.50568e6 917811.i 0.492646 0.0531593i
\(786\) 4.24073e6 + 1.30516e7i 0.244841 + 0.753544i
\(787\) −9.45883e6 + 2.91113e7i −0.544378 + 1.67542i 0.178085 + 0.984015i \(0.443010\pi\)
−0.722464 + 0.691409i \(0.756990\pi\)
\(788\) 4.09254e6 1.25955e7i 0.234789 0.722606i
\(789\) −5.06615e6 1.55920e7i −0.289725 0.891681i
\(790\) −1.16030e7 6.65619e6i −0.661457 0.379453i
\(791\) −7.27130e6 + 2.23788e7i −0.413210 + 1.27173i
\(792\) 1.91901e6 + 1.39424e6i 0.108708 + 0.0789813i
\(793\) −1.37705e6 −0.0777617
\(794\) −3.60430e6 2.61868e6i −0.202894 0.147411i
\(795\) 2.44092e6 1.16421e7i 0.136973 0.653302i
\(796\) −2.61544e6 + 1.90023e6i −0.146306 + 0.106297i
\(797\) 2.08713e7 1.51639e7i 1.16387 0.845601i 0.173608 0.984815i \(-0.444458\pi\)
0.990262 + 0.139214i \(0.0444575\pi\)
\(798\) −2.83683e6 8.73086e6i −0.157698 0.485344i
\(799\) −4.28788e7 −2.37616
\(800\) 3.12634e6 682648.i 0.172707 0.0377113i
\(801\) −1.05605e7 −0.581570
\(802\) −4.30024e6 1.32348e7i −0.236079 0.726576i
\(803\) −1.16254e6 + 844632.i −0.0636235 + 0.0462252i
\(804\) 3.58837e6 2.60710e6i 0.195775 0.142239i
\(805\) −1.23226e7 2.74720e7i −0.670215 1.49417i
\(806\) 8.32218e6 + 6.04641e6i 0.451231 + 0.327839i
\(807\) 7.63907e6 0.412911
\(808\) −2.70887e6 1.96811e6i −0.145969 0.106053i
\(809\) 9.65001e6 2.96997e7i 0.518390 1.59544i −0.258639 0.965974i \(-0.583274\pi\)
0.777028 0.629466i \(-0.216726\pi\)
\(810\) −301048. + 1.43586e6i −0.0161221 + 0.0768955i
\(811\) −4.18392e6 1.28768e7i −0.223373 0.687472i −0.998453 0.0556084i \(-0.982290\pi\)
0.775079 0.631864i \(-0.217710\pi\)
\(812\) −4.08883e6 + 1.25841e7i −0.217625 + 0.669781i
\(813\) 6.69264e6 2.05978e7i 0.355117 1.09294i
\(814\) 1.02982e6 + 3.16947e6i 0.0544756 + 0.167659i
\(815\) 593387. 2.83019e6i 0.0312928 0.149253i
\(816\) 1.17376e6 3.61247e6i 0.0617100 0.189924i
\(817\) −2.37542e7 1.72584e7i −1.24504 0.904577i
\(818\) 9.52274e6 0.497598
\(819\) −2.69220e6 1.95600e6i −0.140248 0.101896i
\(820\) −684145. 1.52523e6i −0.0355315 0.0792138i
\(821\) −7.39681e6 + 5.37410e6i −0.382989 + 0.278258i −0.762577 0.646898i \(-0.776066\pi\)
0.379587 + 0.925156i \(0.376066\pi\)
\(822\) 1.72146e6 1.25072e6i 0.0888624 0.0645623i
\(823\) 2.95400e6 + 9.09147e6i 0.152023 + 0.467880i 0.997847 0.0655825i \(-0.0208905\pi\)
−0.845824 + 0.533463i \(0.820891\pi\)
\(824\) −1.04243e7 −0.534849
\(825\) 1.17853e7 + 5.16910e6i 0.602844 + 0.264411i
\(826\) 3.95844e6 0.201871
\(827\) 2.74124e6 + 8.43666e6i 0.139374 + 0.428950i 0.996245 0.0865818i \(-0.0275944\pi\)
−0.856870 + 0.515532i \(0.827594\pi\)
\(828\) −3.50699e6 + 2.54797e6i −0.177770 + 0.129157i
\(829\) −8.51484e6 + 6.18639e6i −0.430319 + 0.312645i −0.781776 0.623559i \(-0.785686\pi\)
0.351458 + 0.936204i \(0.385686\pi\)
\(830\) 1.54494e6 7.36866e6i 0.0778423 0.371273i
\(831\) 8.49601e6 + 6.17271e6i 0.426788 + 0.310080i
\(832\) 1.04502e6 0.0523377
\(833\) −1.21679e7 8.84049e6i −0.607579 0.441432i
\(834\) −3.17346e6 + 9.76692e6i −0.157986 + 0.486231i
\(835\) −1.68509e7 9.66675e6i −0.836387 0.479804i
\(836\) 3.58263e6 + 1.10262e7i 0.177291 + 0.545645i
\(837\) −2.27073e6 + 6.98860e6i −0.112035 + 0.344807i
\(838\) −948637. + 2.91961e6i −0.0466649 + 0.143620i
\(839\) 8.93343e6 + 2.74943e7i 0.438141 + 1.34846i 0.889834 + 0.456285i \(0.150820\pi\)
−0.451693 + 0.892173i \(0.649180\pi\)
\(840\) −5.15508e6 + 556263.i −0.252080 + 0.0272008i
\(841\) 1.81197e6 5.57666e6i 0.0883406 0.271884i
\(842\) −2.29979e6 1.67090e6i −0.111792 0.0812213i
\(843\) −6.94782e6 −0.336728
\(844\) 1.09390e7 + 7.94764e6i 0.528593 + 0.384045i
\(845\) −1.48476e7 8.51749e6i −0.715341 0.410364i
\(846\) 6.81757e6 4.95326e6i 0.327494 0.237939i
\(847\) −6.29429e6 + 4.57307e6i −0.301466 + 0.219028i
\(848\) −1.87037e6 5.75642e6i −0.0893180 0.274892i
\(849\) 1.52611e7 0.726634
\(850\) 2.04050e6 2.05063e7i 0.0968700 0.973507i
\(851\) −6.09030e6 −0.288280
\(852\) 732088. + 2.25314e6i 0.0345513 + 0.106338i
\(853\) 1.26505e6 919116.i 0.0595301 0.0432512i −0.557622 0.830095i \(-0.688286\pi\)
0.617152 + 0.786844i \(0.288286\pi\)
\(854\) 2.81258e6 2.04346e6i 0.131966 0.0958786i
\(855\) −5.31549e6 + 4.81282e6i −0.248673 + 0.225156i
\(856\) −6.81158e6 4.94890e6i −0.317734 0.230847i
\(857\) −3.94817e6 −0.183630 −0.0918151 0.995776i \(-0.529267\pi\)
−0.0918151 + 0.995776i \(0.529267\pi\)
\(858\) 3.39998e6 + 2.47023e6i 0.157674 + 0.114557i
\(859\) 9.95622e6 3.06421e7i 0.460375 1.41689i −0.404333 0.914612i \(-0.632496\pi\)
0.864708 0.502276i \(-0.167504\pi\)
\(860\) −1.22933e7 + 1.11307e7i −0.566790 + 0.513190i
\(861\) 836999. + 2.57602e6i 0.0384784 + 0.118424i
\(862\) −3.47193e6 + 1.06855e7i −0.159148 + 0.489808i
\(863\) −1.95777e6 + 6.02539e6i −0.0894817 + 0.275396i −0.985776 0.168063i \(-0.946249\pi\)
0.896295 + 0.443459i \(0.146249\pi\)
\(864\) 230680. + 709960.i 0.0105130 + 0.0323556i
\(865\) −3.30626e6 7.37096e6i −0.150244 0.334953i
\(866\) 4.26634e6 1.31304e7i 0.193313 0.594956i
\(867\) −9.45116e6 6.86667e6i −0.427009 0.310240i
\(868\) −2.59704e7 −1.16998
\(869\) −2.21448e7 1.60892e7i −0.994771 0.722744i
\(870\) 1.02756e7 1.10880e6i 0.460267 0.0496655i
\(871\) 6.35767e6 4.61912e6i 0.283957 0.206307i
\(872\) −7.55844e6 + 5.49153e6i −0.336621 + 0.244569i
\(873\) 1.42038e6 + 4.37148e6i 0.0630766 + 0.194130i
\(874\) −2.11874e7 −0.938207
\(875\) −2.66805e7 + 8.91482e6i −1.17808 + 0.393634i
\(876\) −452228. −0.0199112
\(877\) 6.78195e6 + 2.08727e7i 0.297753 + 0.916389i 0.982283 + 0.187404i \(0.0600075\pi\)
−0.684530 + 0.728985i \(0.739993\pi\)
\(878\) −5.74518e6 + 4.17412e6i −0.251517 + 0.182738i
\(879\) 6.08690e6 4.42239e6i 0.265720 0.193057i
\(880\) 6.51036e6 702504.i 0.283399 0.0305803i
\(881\) −1.92473e7 1.39840e7i −0.835468 0.607003i 0.0856331 0.996327i \(-0.472709\pi\)
−0.921101 + 0.389324i \(0.872709\pi\)
\(882\) 2.95588e6 0.127943
\(883\) 3.77542e6 + 2.74300e6i 0.162953 + 0.118392i 0.666273 0.745708i \(-0.267888\pi\)
−0.503320 + 0.864100i \(0.667888\pi\)
\(884\) 2.07961e6 6.40037e6i 0.0895057 0.275470i
\(885\) −1.26542e6 2.82112e6i −0.0543096 0.121078i
\(886\) −911486. 2.80527e6i −0.0390091 0.120058i
\(887\) −1.82448e6 + 5.61518e6i −0.0778629 + 0.239637i −0.982410 0.186736i \(-0.940209\pi\)
0.904547 + 0.426373i \(0.140209\pi\)
\(888\) −324095. + 997462.i −0.0137924 + 0.0424486i
\(889\) −815953. 2.51124e6i −0.0346267 0.106570i
\(890\) −2.16108e7 + 1.95671e7i −0.914524 + 0.828040i
\(891\) −927697. + 2.85516e6i −0.0391482 + 0.120486i
\(892\) 1.90843e6 + 1.38655e6i 0.0803088 + 0.0583478i
\(893\) 4.11882e7 1.72840
\(894\) −1.04692e7 7.60628e6i −0.438094 0.318294i
\(895\) 1.81710e6 1.64526e6i 0.0758266 0.0686559i
\(896\) −2.13442e6 + 1.55075e6i −0.0888198 + 0.0645313i
\(897\) −6.21348e6 + 4.51436e6i −0.257842 + 0.187333i
\(898\) 1.15471e6 + 3.55383e6i 0.0477840 + 0.147064i
\(899\) 5.17667e7 2.13625
\(900\) 2.04440e6 + 3.49613e6i 0.0841317 + 0.143874i
\(901\) −3.89782e7 −1.59959
\(902\) −1.05705e6 3.25325e6i −0.0432591 0.133138i
\(903\) 2.17389e7 1.57943e7i 0.887194 0.644584i
\(904\) 7.56598e6 5.49701e6i 0.307925 0.223720i
\(905\) 2.94861e6 + 1.69151e6i 0.119673 + 0.0686518i
\(906\) −1.29485e7 9.40760e6i −0.524080 0.380766i
\(907\) 1.99300e7 0.804433 0.402216 0.915545i \(-0.368240\pi\)
0.402216 + 0.915545i \(0.368240\pi\)
\(908\) −5.01747e6 3.64541e6i −0.201962 0.146734i
\(909\) 1.30954e6 4.03035e6i 0.0525664 0.161783i
\(910\) −9.13348e6 + 985555.i −0.365623 + 0.0394527i
\(911\) −6.95947e6 2.14190e7i −0.277831 0.855075i −0.988457 0.151505i \(-0.951588\pi\)
0.710626 0.703570i \(-0.248412\pi\)
\(912\) −1.12749e6 + 3.47004e6i −0.0448873 + 0.138149i
\(913\) 4.76082e6 1.46523e7i 0.189019 0.581739i
\(914\) 7.11488e6 + 2.18974e7i 0.281710 + 0.867014i
\(915\) −2.35546e6 1.35124e6i −0.0930086 0.0533556i
\(916\) −1.05250e6 + 3.23925e6i −0.0414459 + 0.127557i
\(917\) −4.96610e7 3.60809e7i −1.95026 1.41695i
\(918\) 4.80732e6 0.188277
\(919\) −1.81507e7 1.31873e7i −0.708932 0.515070i 0.173897 0.984764i \(-0.444364\pi\)
−0.882829 + 0.469694i \(0.844364\pi\)
\(920\) −2.45559e6 + 1.17121e7i −0.0956505 + 0.456210i
\(921\) −5.64283e6 + 4.09975e6i −0.219204 + 0.159261i
\(922\) −1.60488e7 + 1.16601e7i −0.621750 + 0.451728i
\(923\) 1.29707e6 + 3.99198e6i 0.0501141 + 0.154235i
\(924\) −1.06101e7 −0.408826
\(925\) −563415. + 5.66210e6i −0.0216508 + 0.217582i
\(926\) −2.01366e7 −0.771719
\(927\) −4.07696e6 1.25476e7i −0.155825 0.479580i
\(928\) 4.25454e6 3.09110e6i 0.162174 0.117827i
\(929\) −2.21371e7 + 1.60835e7i −0.841552 + 0.611423i −0.922804 0.385270i \(-0.874108\pi\)
0.0812516 + 0.996694i \(0.474108\pi\)
\(930\) 8.30212e6 + 1.85087e7i 0.314761 + 0.701728i
\(931\) 1.16881e7 + 8.49194e6i 0.441948 + 0.321094i
\(932\) 1.09849e7 0.414243
\(933\) −3.29044e6 2.39065e6i −0.123751 0.0899107i
\(934\) 6.79127e6 2.09014e7i 0.254732 0.783985i
\(935\) 8.65316e6 4.12717e7i 0.323702 1.54392i
\(936\) 408706. + 1.25787e6i 0.0152483 + 0.0469294i
\(937\) −9.50294e6 + 2.92470e7i −0.353597 + 1.08826i 0.603221 + 0.797574i \(0.293884\pi\)
−0.956818 + 0.290686i \(0.906116\pi\)
\(938\) −6.13086e6 + 1.88689e7i −0.227517 + 0.700226i
\(939\) 2.31036e6 + 7.11057e6i 0.0855099 + 0.263172i
\(940\) 4.77367e6 2.27683e7i 0.176211 0.840448i
\(941\) −1.20548e7 + 3.71008e7i −0.443798 + 1.36587i 0.439998 + 0.897999i \(0.354979\pi\)
−0.883796 + 0.467872i \(0.845021\pi\)
\(942\) 4.45716e6 + 3.23831e6i 0.163656 + 0.118903i
\(943\) 6.25129e6 0.228923
\(944\) −1.27280e6 924741.i −0.0464868 0.0337746i
\(945\) −2.68571e6 5.98752e6i −0.0978319 0.218106i
\(946\) −2.74541e7 + 1.99466e7i −0.997423 + 0.724670i
\(947\) −2.36132e7 + 1.71560e7i −0.855619 + 0.621643i −0.926689 0.375828i \(-0.877358\pi\)
0.0710708 + 0.997471i \(0.477358\pi\)
\(948\) −2.66199e6 8.19276e6i −0.0962023 0.296080i
\(949\) −801233. −0.0288797
\(950\) −1.96005e6 + 1.96977e7i −0.0704624 + 0.708121i
\(951\) −3.55415e6 −0.127434
\(952\) 5.25025e6 + 1.61586e7i 0.187753 + 0.577845i
\(953\) 4.23458e7 3.07660e7i 1.51035 1.09734i 0.544332 0.838870i \(-0.316783\pi\)
0.966021 0.258465i \(-0.0832168\pi\)
\(954\) 6.19739e6 4.50267e6i 0.220464 0.160177i
\(955\) 3.47388e6 1.65689e7i 0.123256 0.587874i
\(956\) 2.17141e7 + 1.57762e7i 0.768417 + 0.558288i
\(957\) 2.11490e7 0.746467
\(958\) 1.08055e7 + 7.85063e6i 0.380391 + 0.276370i
\(959\) −2.94118e6 + 9.05202e6i −0.103270 + 0.317833i
\(960\) 1.78752e6 + 1.02543e6i 0.0625997 + 0.0359111i
\(961\) 2.25506e7 + 6.94035e7i 0.787678 + 2.42422i
\(962\) −574213. + 1.76725e6i −0.0200048 + 0.0615686i
\(963\) 3.29289e6 1.01345e7i 0.114423 0.352156i
\(964\) −7.75647e6 2.38719e7i −0.268826 0.827361i
\(965\) −5.25406e7 + 5.66943e6i −1.81626 + 0.195984i
\(966\) 5.99181e6 1.84409e7i 0.206593 0.635828i
\(967\) −2.68069e7 1.94764e7i −0.921894 0.669795i 0.0221007 0.999756i \(-0.492965\pi\)
−0.943995 + 0.329961i \(0.892965\pi\)
\(968\) 3.09219e6 0.106067
\(969\) 1.90091e7 + 1.38109e7i 0.650358 + 0.472513i
\(970\) 1.10064e7 + 6.31396e6i 0.375591 + 0.215463i
\(971\) 4.04998e7 2.94248e7i 1.37849 1.00153i 0.381475 0.924379i \(-0.375416\pi\)
0.997019 0.0771557i \(-0.0245838\pi\)
\(972\) −764346. + 555330.i −0.0259492 + 0.0188532i
\(973\) −1.41949e7 4.36875e7i −0.480675 1.47936i
\(974\) 2.76868e7 0.935136
\(975\) 3.62215e6 + 6.19424e6i 0.122027 + 0.208678i
\(976\) −1.38174e6 −0.0464302
\(977\) −9.46664e6 2.91353e7i −0.317292 0.976525i −0.974801 0.223078i \(-0.928390\pi\)
0.657508 0.753447i \(-0.271610\pi\)
\(978\) 1.50658e6 1.09460e6i 0.0503669 0.0365937i
\(979\) −4.82624e7 + 3.50647e7i −1.60936 + 1.16927i
\(980\) 6.04887e6 5.47684e6i 0.201191 0.182165i
\(981\) −9.56615e6 6.95021e6i −0.317369 0.230582i
\(982\) 1.77568e7 0.587605
\(983\) 4.39991e7 + 3.19672e7i 1.45231 + 1.05517i 0.985284 + 0.170925i \(0.0546755\pi\)
0.467029 + 0.884242i \(0.345325\pi\)
\(984\) 332662. 1.02383e6i 0.0109525 0.0337085i
\(985\) 3.43007e7 3.10569e7i 1.12645 1.01992i
\(986\) −1.04653e7 3.22090e7i −0.342815 1.05508i
\(987\) −1.16481e7 + 3.58491e7i −0.380593 + 1.17135i
\(988\) −1.99761e6 + 6.14802e6i −0.0651057 + 0.200375i
\(989\) −1.91642e7 5.89812e7i −0.623016 1.91745i
\(990\) 3.39179e6 + 7.56164e6i 0.109987 + 0.245204i
\(991\) 4.46307e6 1.37359e7i 0.144361 0.444297i −0.852567 0.522617i \(-0.824956\pi\)
0.996928 + 0.0783200i \(0.0249556\pi\)
\(992\) 8.35052e6 + 6.06701e6i 0.269423 + 0.195747i
\(993\) 2.19031e7 0.704907
\(994\) −8.57311e6 6.22873e6i −0.275215 0.199955i
\(995\) −1.12300e7 + 1.21178e6i −0.359601 + 0.0388029i
\(996\) 3.92252e6 2.84988e6i 0.125290 0.0910287i
\(997\) −1.57358e7 + 1.14328e7i −0.501363 + 0.364261i −0.809537 0.587068i \(-0.800282\pi\)
0.308174 + 0.951330i \(0.400282\pi\)
\(998\) 6.42182e6 + 1.97643e7i 0.204095 + 0.628139i
\(999\) −1.32738e6 −0.0420805
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 150.6.g.b.31.2 24
25.21 even 5 inner 150.6.g.b.121.2 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.6.g.b.31.2 24 1.1 even 1 trivial
150.6.g.b.121.2 yes 24 25.21 even 5 inner