Properties

Label 49.6.c.h.30.3
Level $49$
Weight $6$
Character 49.30
Analytic conductor $7.859$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [49,6,Mod(18,49)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(49, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("49.18");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 49.c (of order \(3\), degree \(2\), not 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: \(7.85880717084\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.54095201243136.19
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{7} - 102x^{6} + 320x^{5} + 4283x^{4} - 9104x^{3} - 85298x^{2} + 89904x + 714364 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 30.3
Root \(5.10797 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 49.30
Dual form 49.6.c.h.18.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.90754 - 6.76805i) q^{2} +(-11.7593 - 20.3677i) q^{3} +(-14.5377 - 25.1800i) q^{4} +(37.1377 - 64.3243i) q^{5} -183.799 q^{6} +22.8562 q^{8} +(-155.062 + 268.575i) q^{9} +O(q^{10})\) \(q+(3.90754 - 6.76805i) q^{2} +(-11.7593 - 20.3677i) q^{3} +(-14.5377 - 25.1800i) q^{4} +(37.1377 - 64.3243i) q^{5} -183.799 q^{6} +22.8562 q^{8} +(-155.062 + 268.575i) q^{9} +(-290.234 - 502.699i) q^{10} +(212.110 + 367.385i) q^{11} +(-341.906 + 592.198i) q^{12} -252.233 q^{13} -1746.85 q^{15} +(554.517 - 960.452i) q^{16} +(552.173 + 956.392i) q^{17} +(1211.82 + 2098.93i) q^{18} +(3.23550 - 5.60405i) q^{19} -2159.58 q^{20} +3315.30 q^{22} +(1806.19 - 3128.42i) q^{23} +(-268.773 - 465.529i) q^{24} +(-1195.91 - 2071.38i) q^{25} +(-985.611 + 1707.13i) q^{26} +1578.65 q^{27} -5005.02 q^{29} +(-6825.88 + 11822.8i) q^{30} +(-1410.85 - 2443.66i) q^{31} +(-3967.89 - 6872.59i) q^{32} +(4988.52 - 8640.36i) q^{33} +8630.55 q^{34} +9016.95 q^{36} +(1023.44 - 1772.65i) q^{37} +(-25.2857 - 43.7961i) q^{38} +(2966.08 + 5137.41i) q^{39} +(848.827 - 1470.21i) q^{40} +9393.81 q^{41} +10320.8 q^{43} +(6167.16 - 10681.8i) q^{44} +(11517.3 + 19948.5i) q^{45} +(-14115.5 - 24448.8i) q^{46} +(-8517.79 + 14753.3i) q^{47} -26082.9 q^{48} -18692.3 q^{50} +(12986.3 - 22493.0i) q^{51} +(3666.89 + 6351.24i) q^{52} +(19753.3 + 34213.8i) q^{53} +(6168.63 - 10684.4i) q^{54} +31509.0 q^{55} -152.189 q^{57} +(-19557.3 + 33874.2i) q^{58} +(-16974.9 - 29401.4i) q^{59} +(25395.1 + 43985.7i) q^{60} +(-14147.6 + 24504.4i) q^{61} -22051.7 q^{62} -26529.7 q^{64} +(-9367.36 + 16224.7i) q^{65} +(-38985.6 - 67525.1i) q^{66} +(-28050.5 - 48584.8i) q^{67} +(16054.6 - 27807.5i) q^{68} -84958.2 q^{69} -15537.4 q^{71} +(-3544.13 + 6138.61i) q^{72} +(39109.8 + 67740.1i) q^{73} +(-7998.24 - 13853.4i) q^{74} +(-28126.1 + 48715.9i) q^{75} -188.147 q^{76} +46360.3 q^{78} +(22667.7 - 39261.7i) q^{79} +(-41187.0 - 71337.9i) q^{80} +(19116.2 + 33110.3i) q^{81} +(36706.6 - 63577.8i) q^{82} +1381.82 q^{83} +82025.7 q^{85} +(40328.8 - 69851.5i) q^{86} +(58855.4 + 101941. i) q^{87} +(4848.03 + 8397.03i) q^{88} +(34439.7 - 59651.3i) q^{89} +180016. q^{90} -105031. q^{92} +(-33181.1 + 57471.3i) q^{93} +(66567.2 + 115298. i) q^{94} +(-240.318 - 416.243i) q^{95} +(-93319.2 + 161634. i) q^{96} +108857. q^{97} -131560. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 10 q^{2} - 10 q^{4} - 540 q^{8} - 220 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 10 q^{2} - 10 q^{4} - 540 q^{8} - 220 q^{9} + 1952 q^{11} - 8192 q^{15} + 1566 q^{16} + 5974 q^{18} + 7048 q^{22} + 7136 q^{23} - 2764 q^{25} - 6704 q^{29} - 25608 q^{30} - 27810 q^{32} + 55340 q^{36} + 9208 q^{37} - 2464 q^{39} + 40896 q^{43} - 1900 q^{44} - 56712 q^{46} - 86140 q^{50} + 67408 q^{51} + 102920 q^{53} - 31152 q^{57} - 96972 q^{58} + 87080 q^{60} - 80636 q^{64} + 63168 q^{65} + 22896 q^{67} - 307648 q^{71} - 77358 q^{72} - 17596 q^{74} + 266112 q^{78} + 90688 q^{79} + 17204 q^{81} + 545312 q^{85} + 161860 q^{86} - 154812 q^{88} - 424400 q^{92} - 247760 q^{93} - 108224 q^{95} - 84544 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.90754 6.76805i 0.690761 1.19643i −0.280827 0.959758i \(-0.590609\pi\)
0.971589 0.236676i \(-0.0760578\pi\)
\(3\) −11.7593 20.3677i −0.754359 1.30659i −0.945692 0.325063i \(-0.894615\pi\)
0.191334 0.981525i \(-0.438719\pi\)
\(4\) −14.5377 25.1800i −0.454303 0.786875i
\(5\) 37.1377 64.3243i 0.664339 1.15067i −0.315125 0.949050i \(-0.602047\pi\)
0.979464 0.201618i \(-0.0646201\pi\)
\(6\) −183.799 −2.08433
\(7\) 0 0
\(8\) 22.8562 0.126264
\(9\) −155.062 + 268.575i −0.638114 + 1.10525i
\(10\) −290.234 502.699i −0.917799 1.58967i
\(11\) 212.110 + 367.385i 0.528541 + 0.915460i 0.999446 + 0.0332758i \(0.0105940\pi\)
−0.470905 + 0.882184i \(0.656073\pi\)
\(12\) −341.906 + 592.198i −0.685414 + 1.18717i
\(13\) −252.233 −0.413946 −0.206973 0.978347i \(-0.566361\pi\)
−0.206973 + 0.978347i \(0.566361\pi\)
\(14\) 0 0
\(15\) −1746.85 −2.00460
\(16\) 554.517 960.452i 0.541521 0.937942i
\(17\) 552.173 + 956.392i 0.463397 + 0.802627i 0.999128 0.0417619i \(-0.0132971\pi\)
−0.535731 + 0.844389i \(0.679964\pi\)
\(18\) 1211.82 + 2098.93i 0.881569 + 1.52692i
\(19\) 3.23550 5.60405i 0.00205616 0.00356138i −0.864995 0.501780i \(-0.832679\pi\)
0.867052 + 0.498218i \(0.166012\pi\)
\(20\) −2159.58 −1.20724
\(21\) 0 0
\(22\) 3315.30 1.46038
\(23\) 1806.19 3128.42i 0.711942 1.23312i −0.252186 0.967679i \(-0.581149\pi\)
0.964127 0.265440i \(-0.0855173\pi\)
\(24\) −268.773 465.529i −0.0952484 0.164975i
\(25\) −1195.91 2071.38i −0.382692 0.662842i
\(26\) −985.611 + 1707.13i −0.285938 + 0.495260i
\(27\) 1578.65 0.416751
\(28\) 0 0
\(29\) −5005.02 −1.10512 −0.552561 0.833472i \(-0.686350\pi\)
−0.552561 + 0.833472i \(0.686350\pi\)
\(30\) −6825.88 + 11822.8i −1.38470 + 2.39837i
\(31\) −1410.85 2443.66i −0.263679 0.456705i 0.703538 0.710658i \(-0.251603\pi\)
−0.967217 + 0.253953i \(0.918269\pi\)
\(32\) −3967.89 6872.59i −0.684991 1.18644i
\(33\) 4988.52 8640.36i 0.797419 1.38117i
\(34\) 8630.55 1.28039
\(35\) 0 0
\(36\) 9016.95 1.15959
\(37\) 1023.44 1772.65i 0.122902 0.212872i −0.798009 0.602645i \(-0.794113\pi\)
0.920911 + 0.389774i \(0.127447\pi\)
\(38\) −25.2857 43.7961i −0.00284063 0.00492012i
\(39\) 2966.08 + 5137.41i 0.312264 + 0.540857i
\(40\) 848.827 1470.21i 0.0838821 0.145288i
\(41\) 9393.81 0.872734 0.436367 0.899769i \(-0.356265\pi\)
0.436367 + 0.899769i \(0.356265\pi\)
\(42\) 0 0
\(43\) 10320.8 0.851218 0.425609 0.904907i \(-0.360060\pi\)
0.425609 + 0.904907i \(0.360060\pi\)
\(44\) 6167.16 10681.8i 0.480235 0.831791i
\(45\) 11517.3 + 19948.5i 0.847848 + 1.46852i
\(46\) −14115.5 24448.8i −0.983564 1.70358i
\(47\) −8517.79 + 14753.3i −0.562448 + 0.974189i 0.434834 + 0.900511i \(0.356807\pi\)
−0.997282 + 0.0736781i \(0.976526\pi\)
\(48\) −26082.9 −1.63400
\(49\) 0 0
\(50\) −18692.3 −1.05739
\(51\) 12986.3 22493.0i 0.699135 1.21094i
\(52\) 3666.89 + 6351.24i 0.188057 + 0.325724i
\(53\) 19753.3 + 34213.8i 0.965941 + 1.67306i 0.707064 + 0.707149i \(0.250019\pi\)
0.258877 + 0.965910i \(0.416648\pi\)
\(54\) 6168.63 10684.4i 0.287875 0.498615i
\(55\) 31509.0 1.40452
\(56\) 0 0
\(57\) −152.189 −0.00620433
\(58\) −19557.3 + 33874.2i −0.763376 + 1.32221i
\(59\) −16974.9 29401.4i −0.634859 1.09961i −0.986545 0.163489i \(-0.947725\pi\)
0.351687 0.936118i \(-0.385608\pi\)
\(60\) 25395.1 + 43985.7i 0.910694 + 1.57737i
\(61\) −14147.6 + 24504.4i −0.486809 + 0.843178i −0.999885 0.0151652i \(-0.995173\pi\)
0.513076 + 0.858343i \(0.328506\pi\)
\(62\) −22051.7 −0.728556
\(63\) 0 0
\(64\) −26529.7 −0.809621
\(65\) −9367.36 + 16224.7i −0.275001 + 0.476315i
\(66\) −38985.6 67525.1i −1.10165 1.90812i
\(67\) −28050.5 48584.8i −0.763402 1.32225i −0.941088 0.338163i \(-0.890194\pi\)
0.177686 0.984087i \(-0.443139\pi\)
\(68\) 16054.6 27807.5i 0.421045 0.729271i
\(69\) −84958.2 −2.14824
\(70\) 0 0
\(71\) −15537.4 −0.365791 −0.182895 0.983132i \(-0.558547\pi\)
−0.182895 + 0.983132i \(0.558547\pi\)
\(72\) −3544.13 + 6138.61i −0.0805709 + 0.139553i
\(73\) 39109.8 + 67740.1i 0.858970 + 1.48778i 0.872912 + 0.487877i \(0.162229\pi\)
−0.0139419 + 0.999903i \(0.504438\pi\)
\(74\) −7998.24 13853.4i −0.169791 0.294087i
\(75\) −28126.1 + 48715.9i −0.577374 + 1.00004i
\(76\) −188.147 −0.00373648
\(77\) 0 0
\(78\) 46360.3 0.862800
\(79\) 22667.7 39261.7i 0.408640 0.707784i −0.586098 0.810240i \(-0.699337\pi\)
0.994738 + 0.102456i \(0.0326700\pi\)
\(80\) −41187.0 71337.9i −0.719507 1.24622i
\(81\) 19116.2 + 33110.3i 0.323735 + 0.560725i
\(82\) 36706.6 63577.8i 0.602851 1.04417i
\(83\) 1381.82 0.0220169 0.0110085 0.999939i \(-0.496496\pi\)
0.0110085 + 0.999939i \(0.496496\pi\)
\(84\) 0 0
\(85\) 82025.7 1.23141
\(86\) 40328.8 69851.5i 0.587989 1.01843i
\(87\) 58855.4 + 101941.i 0.833659 + 1.44394i
\(88\) 4848.03 + 8397.03i 0.0667357 + 0.115590i
\(89\) 34439.7 59651.3i 0.460876 0.798261i −0.538128 0.842863i \(-0.680868\pi\)
0.999005 + 0.0446014i \(0.0142018\pi\)
\(90\) 180016. 2.34264
\(91\) 0 0
\(92\) −105031. −1.29375
\(93\) −33181.1 + 57471.3i −0.397817 + 0.689039i
\(94\) 66567.2 + 115298.i 0.777035 + 1.34586i
\(95\) −240.318 416.243i −0.00273198 0.00473192i
\(96\) −93319.2 + 161634.i −1.03346 + 1.79000i
\(97\) 108857. 1.17470 0.587351 0.809332i \(-0.300171\pi\)
0.587351 + 0.809332i \(0.300171\pi\)
\(98\) 0 0
\(99\) −131560. −1.34908
\(100\) −34771.6 + 60226.1i −0.347716 + 0.602261i
\(101\) −8986.13 15564.4i −0.0876535 0.151820i 0.818865 0.573986i \(-0.194604\pi\)
−0.906519 + 0.422165i \(0.861270\pi\)
\(102\) −101489. 175784.i −0.965871 1.67294i
\(103\) −15886.8 + 27516.8i −0.147552 + 0.255567i −0.930322 0.366744i \(-0.880473\pi\)
0.782770 + 0.622311i \(0.213806\pi\)
\(104\) −5765.11 −0.0522666
\(105\) 0 0
\(106\) 308747. 2.66894
\(107\) −4114.68 + 7126.84i −0.0347438 + 0.0601780i −0.882874 0.469609i \(-0.844395\pi\)
0.848131 + 0.529787i \(0.177728\pi\)
\(108\) −22949.9 39750.4i −0.189331 0.327931i
\(109\) 5534.34 + 9585.75i 0.0446169 + 0.0772787i 0.887471 0.460863i \(-0.152460\pi\)
−0.842855 + 0.538141i \(0.819127\pi\)
\(110\) 123123. 213255.i 0.970188 1.68042i
\(111\) −48139.6 −0.370847
\(112\) 0 0
\(113\) 65184.3 0.480228 0.240114 0.970745i \(-0.422815\pi\)
0.240114 + 0.970745i \(0.422815\pi\)
\(114\) −594.683 + 1030.02i −0.00428571 + 0.00742308i
\(115\) −134156. 232364.i −0.945941 1.63842i
\(116\) 72761.3 + 126026.i 0.502060 + 0.869594i
\(117\) 39111.7 67743.5i 0.264145 0.457513i
\(118\) −265320. −1.75414
\(119\) 0 0
\(120\) −39926.4 −0.253109
\(121\) −9455.43 + 16377.3i −0.0587108 + 0.101690i
\(122\) 110565. + 191504.i 0.672538 + 1.16487i
\(123\) −110464. 191330.i −0.658355 1.14030i
\(124\) −41020.8 + 71050.2i −0.239580 + 0.414964i
\(125\) 54456.9 0.311730
\(126\) 0 0
\(127\) −194777. −1.07159 −0.535796 0.844348i \(-0.679988\pi\)
−0.535796 + 0.844348i \(0.679988\pi\)
\(128\) 23307.0 40369.0i 0.125737 0.217782i
\(129\) −121365. 210210.i −0.642124 1.11219i
\(130\) 73206.6 + 126798.i 0.379920 + 0.658040i
\(131\) 118252. 204818.i 0.602046 1.04277i −0.390465 0.920618i \(-0.627686\pi\)
0.992511 0.122156i \(-0.0389808\pi\)
\(132\) −290086. −1.44908
\(133\) 0 0
\(134\) −438433. −2.10931
\(135\) 58627.3 101546.i 0.276864 0.479542i
\(136\) 12620.6 + 21859.5i 0.0585104 + 0.101343i
\(137\) 100452. + 173987.i 0.457252 + 0.791983i 0.998815 0.0486772i \(-0.0155005\pi\)
−0.541563 + 0.840660i \(0.682167\pi\)
\(138\) −331977. + 575001.i −1.48392 + 2.57022i
\(139\) 52985.2 0.232604 0.116302 0.993214i \(-0.462896\pi\)
0.116302 + 0.993214i \(0.462896\pi\)
\(140\) 0 0
\(141\) 400653. 1.69715
\(142\) −60713.0 + 105158.i −0.252674 + 0.437644i
\(143\) −53501.1 92666.6i −0.218788 0.378951i
\(144\) 171969. + 297859.i 0.691104 + 1.19703i
\(145\) −185875. + 321944.i −0.734176 + 1.27163i
\(146\) 611291. 2.37337
\(147\) 0 0
\(148\) −59513.7 −0.223338
\(149\) 50385.2 87269.7i 0.185925 0.322031i −0.757963 0.652298i \(-0.773805\pi\)
0.943888 + 0.330266i \(0.107139\pi\)
\(150\) 219808. + 380718.i 0.797655 + 1.38158i
\(151\) 228952. + 396556.i 0.817150 + 1.41535i 0.907774 + 0.419460i \(0.137781\pi\)
−0.0906234 + 0.995885i \(0.528886\pi\)
\(152\) 73.9513 128.087i 0.000259619 0.000449674i
\(153\) −342484. −1.18280
\(154\) 0 0
\(155\) −209582. −0.700688
\(156\) 86240.0 149372.i 0.283725 0.491426i
\(157\) 89518.6 + 155051.i 0.289844 + 0.502024i 0.973772 0.227525i \(-0.0730633\pi\)
−0.683928 + 0.729549i \(0.739730\pi\)
\(158\) −177150. 306833.i −0.564545 0.977820i
\(159\) 464570. 804659.i 1.45733 2.52417i
\(160\) −589433. −1.82027
\(161\) 0 0
\(162\) 298789. 0.894494
\(163\) −121805. + 210972.i −0.359084 + 0.621952i −0.987808 0.155677i \(-0.950244\pi\)
0.628724 + 0.777629i \(0.283578\pi\)
\(164\) −136564. 236536.i −0.396485 0.686733i
\(165\) −370524. 641766.i −1.05951 1.83513i
\(166\) 5399.52 9352.24i 0.0152085 0.0263418i
\(167\) 117033. 0.324725 0.162362 0.986731i \(-0.448089\pi\)
0.162362 + 0.986731i \(0.448089\pi\)
\(168\) 0 0
\(169\) −307671. −0.828648
\(170\) 320518. 555154.i 0.850610 1.47330i
\(171\) 1003.40 + 1737.95i 0.00262413 + 0.00454513i
\(172\) −150040. 259877.i −0.386711 0.669803i
\(173\) −134867. + 233596.i −0.342602 + 0.593403i −0.984915 0.173039i \(-0.944641\pi\)
0.642313 + 0.766442i \(0.277975\pi\)
\(174\) 919919. 2.30344
\(175\) 0 0
\(176\) 470474. 1.14486
\(177\) −399225. + 691479.i −0.957822 + 1.65900i
\(178\) −269149. 466180.i −0.636711 1.10282i
\(179\) −188262. 326080.i −0.439168 0.760661i 0.558457 0.829533i \(-0.311393\pi\)
−0.997626 + 0.0688718i \(0.978060\pi\)
\(180\) 334869. 580009.i 0.770359 1.33430i
\(181\) −434641. −0.986131 −0.493065 0.869992i \(-0.664124\pi\)
−0.493065 + 0.869992i \(0.664124\pi\)
\(182\) 0 0
\(183\) 665464. 1.46891
\(184\) 41282.8 71503.9i 0.0898927 0.155699i
\(185\) −76016.2 131664.i −0.163296 0.282838i
\(186\) 259312. + 449142.i 0.549593 + 0.951923i
\(187\) −234243. + 405720.i −0.489848 + 0.848442i
\(188\) 495316. 1.02209
\(189\) 0 0
\(190\) −3756.20 −0.00754857
\(191\) −282970. + 490118.i −0.561250 + 0.972114i 0.436137 + 0.899880i \(0.356346\pi\)
−0.997388 + 0.0722342i \(0.976987\pi\)
\(192\) 311970. + 540348.i 0.610744 + 1.05784i
\(193\) −257231. 445537.i −0.497084 0.860974i 0.502911 0.864338i \(-0.332262\pi\)
−0.999994 + 0.00336433i \(0.998929\pi\)
\(194\) 425363. 736751.i 0.811439 1.40545i
\(195\) 440614. 0.829796
\(196\) 0 0
\(197\) −298541. −0.548073 −0.274037 0.961719i \(-0.588359\pi\)
−0.274037 + 0.961719i \(0.588359\pi\)
\(198\) −514077. + 890407.i −0.931891 + 1.61408i
\(199\) 295959. + 512617.i 0.529785 + 0.917614i 0.999396 + 0.0347408i \(0.0110606\pi\)
−0.469612 + 0.882873i \(0.655606\pi\)
\(200\) −27334.0 47344.0i −0.0483202 0.0836931i
\(201\) −659707. + 1.14265e6i −1.15176 + 1.99490i
\(202\) −140455. −0.242191
\(203\) 0 0
\(204\) −755165. −1.27048
\(205\) 348864. 604250.i 0.579791 1.00423i
\(206\) 124157. + 215046.i 0.203846 + 0.353072i
\(207\) 560143. + 970196.i 0.908600 + 1.57374i
\(208\) −139868. + 242258.i −0.224161 + 0.388258i
\(209\) 2745.12 0.00434706
\(210\) 0 0
\(211\) −140535. −0.217309 −0.108655 0.994080i \(-0.534654\pi\)
−0.108655 + 0.994080i \(0.534654\pi\)
\(212\) 574335. 994778.i 0.877659 1.52015i
\(213\) 182709. + 316461.i 0.275937 + 0.477938i
\(214\) 32156.5 + 55696.8i 0.0479993 + 0.0831372i
\(215\) 383289. 663877.i 0.565497 0.979470i
\(216\) 36082.0 0.0526206
\(217\) 0 0
\(218\) 86502.5 0.123278
\(219\) 919806. 1.59315e6i 1.29594 2.24464i
\(220\) −458068. 793397.i −0.638077 1.10518i
\(221\) −139277. 241234.i −0.191822 0.332245i
\(222\) −188107. + 325811.i −0.256167 + 0.443694i
\(223\) 490.526 0.000660541 0.000330271 1.00000i \(-0.499895\pi\)
0.000330271 1.00000i \(0.499895\pi\)
\(224\) 0 0
\(225\) 741761. 0.976804
\(226\) 254710. 441171.i 0.331723 0.574561i
\(227\) −296949. 514331.i −0.382488 0.662488i 0.608930 0.793224i \(-0.291599\pi\)
−0.991417 + 0.130736i \(0.958266\pi\)
\(228\) 2212.47 + 3832.11i 0.00281865 + 0.00488204i
\(229\) 17940.2 31073.3i 0.0226067 0.0391560i −0.854501 0.519450i \(-0.826137\pi\)
0.877107 + 0.480294i \(0.159470\pi\)
\(230\) −2.09687e6 −2.61368
\(231\) 0 0
\(232\) −114396. −0.139537
\(233\) −624109. + 1.08099e6i −0.753131 + 1.30446i 0.193167 + 0.981166i \(0.438124\pi\)
−0.946298 + 0.323295i \(0.895209\pi\)
\(234\) −305661. 529421.i −0.364922 0.632064i
\(235\) 632662. + 1.09580e6i 0.747312 + 1.29438i
\(236\) −493551. + 854856.i −0.576836 + 0.999109i
\(237\) −1.06623e6 −1.23304
\(238\) 0 0
\(239\) −576943. −0.653339 −0.326669 0.945139i \(-0.605926\pi\)
−0.326669 + 0.945139i \(0.605926\pi\)
\(240\) −968659. + 1.67777e6i −1.08553 + 1.88020i
\(241\) 691205. + 1.19720e6i 0.766592 + 1.32778i 0.939401 + 0.342820i \(0.111382\pi\)
−0.172809 + 0.984955i \(0.555284\pi\)
\(242\) 73894.9 + 127990.i 0.0811103 + 0.140487i
\(243\) 641392. 1.11092e6i 0.696800 1.20689i
\(244\) 822694. 0.884634
\(245\) 0 0
\(246\) −1.72658e6 −1.81906
\(247\) −816.101 + 1413.53i −0.000851141 + 0.00147422i
\(248\) −32246.6 55852.8i −0.0332932 0.0576654i
\(249\) −16249.2 28144.5i −0.0166087 0.0287671i
\(250\) 212792. 368567.i 0.215331 0.372964i
\(251\) 323217. 0.323824 0.161912 0.986805i \(-0.448234\pi\)
0.161912 + 0.986805i \(0.448234\pi\)
\(252\) 0 0
\(253\) 1.53244e6 1.50516
\(254\) −761100. + 1.31826e6i −0.740214 + 1.28209i
\(255\) −964564. 1.67067e6i −0.928925 1.60895i
\(256\) −606621. 1.05070e6i −0.578519 1.00202i
\(257\) −923007. + 1.59870e6i −0.871711 + 1.50985i −0.0114847 + 0.999934i \(0.503656\pi\)
−0.860226 + 0.509913i \(0.829678\pi\)
\(258\) −1.89695e6 −1.77422
\(259\) 0 0
\(260\) 544719. 0.499734
\(261\) 776087. 1.34422e6i 0.705195 1.22143i
\(262\) −924146. 1.60067e6i −0.831740 1.44062i
\(263\) 229111. + 396832.i 0.204248 + 0.353767i 0.949893 0.312576i \(-0.101192\pi\)
−0.745645 + 0.666343i \(0.767859\pi\)
\(264\) 114019. 197486.i 0.100685 0.174392i
\(265\) 2.93437e6 2.56685
\(266\) 0 0
\(267\) −1.61995e6 −1.39066
\(268\) −815577. + 1.41262e6i −0.693631 + 1.20140i
\(269\) −208479. 361096.i −0.175663 0.304258i 0.764727 0.644354i \(-0.222874\pi\)
−0.940391 + 0.340096i \(0.889540\pi\)
\(270\) −458177. 793586.i −0.382493 0.662498i
\(271\) 450189. 779751.i 0.372368 0.644960i −0.617562 0.786523i \(-0.711879\pi\)
0.989929 + 0.141563i \(0.0452127\pi\)
\(272\) 1.22476e6 1.00376
\(273\) 0 0
\(274\) 1.57007e6 1.26341
\(275\) 507329. 878719.i 0.404536 0.700678i
\(276\) 1.23509e6 + 2.13925e6i 0.975950 + 1.69039i
\(277\) 223821. + 387669.i 0.175267 + 0.303572i 0.940254 0.340475i \(-0.110588\pi\)
−0.764986 + 0.644046i \(0.777254\pi\)
\(278\) 207042. 358607.i 0.160674 0.278295i
\(279\) 875072. 0.673029
\(280\) 0 0
\(281\) −768521. −0.580617 −0.290309 0.956933i \(-0.593758\pi\)
−0.290309 + 0.956933i \(0.593758\pi\)
\(282\) 1.56557e6 2.71164e6i 1.17233 2.03053i
\(283\) 1.06610e6 + 1.84654e6i 0.791282 + 1.37054i 0.925173 + 0.379544i \(0.123919\pi\)
−0.133892 + 0.990996i \(0.542747\pi\)
\(284\) 225878. + 391232.i 0.166180 + 0.287832i
\(285\) −5651.93 + 9789.43i −0.00412178 + 0.00713913i
\(286\) −836230. −0.604520
\(287\) 0 0
\(288\) 2.46107e6 1.74841
\(289\) 100138. 173443.i 0.0705266 0.122156i
\(290\) 1.45262e6 + 2.51602e6i 1.01428 + 1.75679i
\(291\) −1.28008e6 2.21717e6i −0.886147 1.53485i
\(292\) 1.13713e6 1.96957e6i 0.780465 1.35180i
\(293\) −2.42669e6 −1.65138 −0.825688 0.564128i \(-0.809213\pi\)
−0.825688 + 0.564128i \(0.809213\pi\)
\(294\) 0 0
\(295\) −2.52163e6 −1.68704
\(296\) 23391.9 40516.0i 0.0155180 0.0268781i
\(297\) 334847. + 579971.i 0.220270 + 0.381518i
\(298\) −393764. 682019.i −0.256859 0.444893i
\(299\) −455582. + 789091.i −0.294706 + 0.510445i
\(300\) 1.63556e6 1.04921
\(301\) 0 0
\(302\) 3.57855e6 2.25782
\(303\) −211341. + 366054.i −0.132244 + 0.229054i
\(304\) −3588.28 6215.09i −0.00222691 0.00385712i
\(305\) 1.05082e6 + 1.82007e6i 0.646812 + 1.12031i
\(306\) −1.33827e6 + 2.31795e6i −0.817033 + 1.41514i
\(307\) 2.44328e6 1.47954 0.739772 0.672857i \(-0.234933\pi\)
0.739772 + 0.672857i \(0.234933\pi\)
\(308\) 0 0
\(309\) 747271. 0.445228
\(310\) −818949. + 1.41846e6i −0.484008 + 0.838327i
\(311\) 577324. + 999955.i 0.338469 + 0.586245i 0.984145 0.177366i \(-0.0567577\pi\)
−0.645676 + 0.763611i \(0.723424\pi\)
\(312\) 67793.5 + 117422.i 0.0394277 + 0.0682908i
\(313\) 828531. 1.43506e6i 0.478022 0.827959i −0.521660 0.853153i \(-0.674687\pi\)
0.999683 + 0.0251945i \(0.00802050\pi\)
\(314\) 1.39919e6 0.800852
\(315\) 0 0
\(316\) −1.31815e6 −0.742584
\(317\) −410680. + 711319.i −0.229539 + 0.397573i −0.957671 0.287863i \(-0.907055\pi\)
0.728133 + 0.685436i \(0.240388\pi\)
\(318\) −3.63065e6 6.28847e6i −2.01334 3.48720i
\(319\) −1.06161e6 1.83877e6i −0.584103 1.01170i
\(320\) −985249. + 1.70650e6i −0.537862 + 0.931605i
\(321\) 193543. 0.104837
\(322\) 0 0
\(323\) 7146.23 0.00381128
\(324\) 555811. 962693.i 0.294147 0.509478i
\(325\) 301649. + 522471.i 0.158414 + 0.274381i
\(326\) 951915. + 1.64877e6i 0.496083 + 0.859241i
\(327\) 130160. 225443.i 0.0673143 0.116592i
\(328\) 214707. 0.110195
\(329\) 0 0
\(330\) −5.79134e6 −2.92748
\(331\) 47835.3 82853.2i 0.0239982 0.0415661i −0.853777 0.520639i \(-0.825694\pi\)
0.877775 + 0.479073i \(0.159027\pi\)
\(332\) −20088.5 34794.3i −0.0100024 0.0173246i
\(333\) 317392. + 549740.i 0.156850 + 0.271673i
\(334\) 457309. 792082.i 0.224307 0.388512i
\(335\) −4.16691e6 −2.02863
\(336\) 0 0
\(337\) 2.37020e6 1.13687 0.568435 0.822728i \(-0.307549\pi\)
0.568435 + 0.822728i \(0.307549\pi\)
\(338\) −1.20224e6 + 2.08234e6i −0.572398 + 0.991423i
\(339\) −766522. 1.32765e6i −0.362264 0.627460i
\(340\) −1.19246e6 2.06541e6i −0.559433 0.968966i
\(341\) 598507. 1.03665e6i 0.278730 0.482774i
\(342\) 15683.4 0.00725060
\(343\) 0 0
\(344\) 235894. 0.107478
\(345\) −3.15515e6 + 5.46488e6i −1.42716 + 2.47191i
\(346\) 1.05399e6 + 1.82557e6i 0.473312 + 0.819800i
\(347\) −245286. 424847.i −0.109358 0.189413i 0.806153 0.591708i \(-0.201546\pi\)
−0.915510 + 0.402295i \(0.868213\pi\)
\(348\) 1.71124e6 2.96396e6i 0.757467 1.31197i
\(349\) −4.21208e6 −1.85111 −0.925557 0.378607i \(-0.876403\pi\)
−0.925557 + 0.378607i \(0.876403\pi\)
\(350\) 0 0
\(351\) −398188. −0.172512
\(352\) 1.68326e6 2.91549e6i 0.724092 1.25416i
\(353\) −1.58689e6 2.74858e6i −0.677814 1.17401i −0.975638 0.219387i \(-0.929594\pi\)
0.297824 0.954621i \(-0.403739\pi\)
\(354\) 3.11997e6 + 5.40396e6i 1.32325 + 2.29194i
\(355\) −577023. + 999433.i −0.243009 + 0.420904i
\(356\) −2.00269e6 −0.837509
\(357\) 0 0
\(358\) −2.94257e6 −1.21344
\(359\) 1.70049e6 2.94533e6i 0.696366 1.20614i −0.273352 0.961914i \(-0.588132\pi\)
0.969718 0.244227i \(-0.0785343\pi\)
\(360\) 263241. + 455947.i 0.107053 + 0.185421i
\(361\) 1.23803e6 + 2.14433e6i 0.499992 + 0.866011i
\(362\) −1.69838e6 + 2.94167e6i −0.681181 + 1.17984i
\(363\) 444757. 0.177156
\(364\) 0 0
\(365\) 5.80978e6 2.28259
\(366\) 2.60032e6 4.50389e6i 1.01467 1.75746i
\(367\) −984358. 1.70496e6i −0.381494 0.660767i 0.609782 0.792569i \(-0.291257\pi\)
−0.991276 + 0.131802i \(0.957924\pi\)
\(368\) −2.00313e6 3.46952e6i −0.771063 1.33552i
\(369\) −1.45662e6 + 2.52294e6i −0.556904 + 0.964586i
\(370\) −1.18814e6 −0.451196
\(371\) 0 0
\(372\) 1.92950e6 0.722917
\(373\) 1.73944e6 3.01280e6i 0.647349 1.12124i −0.336405 0.941717i \(-0.609211\pi\)
0.983754 0.179523i \(-0.0574556\pi\)
\(374\) 1.83062e6 + 3.17073e6i 0.676737 + 1.17214i
\(375\) −640375. 1.10916e6i −0.235156 0.407302i
\(376\) −194685. + 337204.i −0.0710170 + 0.123005i
\(377\) 1.26243e6 0.457462
\(378\) 0 0
\(379\) −421294. −0.150656 −0.0753281 0.997159i \(-0.524000\pi\)
−0.0753281 + 0.997159i \(0.524000\pi\)
\(380\) −6987.33 + 12102.4i −0.00248229 + 0.00429945i
\(381\) 2.29044e6 + 3.96716e6i 0.808364 + 1.40013i
\(382\) 2.21143e6 + 3.83031e6i 0.775380 + 1.34300i
\(383\) −1.33455e6 + 2.31151e6i −0.464877 + 0.805190i −0.999196 0.0400925i \(-0.987235\pi\)
0.534319 + 0.845283i \(0.320568\pi\)
\(384\) −1.09630e6 −0.379402
\(385\) 0 0
\(386\) −4.02055e6 −1.37346
\(387\) −1.60036e6 + 2.77190e6i −0.543175 + 0.940806i
\(388\) −1.58253e6 2.74102e6i −0.533670 0.924344i
\(389\) −1.55089e6 2.68622e6i −0.519645 0.900051i −0.999739 0.0228343i \(-0.992731\pi\)
0.480095 0.877217i \(-0.340602\pi\)
\(390\) 1.72171e6 2.98210e6i 0.573191 0.992797i
\(391\) 3.98933e6 1.31965
\(392\) 0 0
\(393\) −5.56223e6 −1.81663
\(394\) −1.16656e6 + 2.02054e6i −0.378588 + 0.655733i
\(395\) −1.68365e6 2.91617e6i −0.542950 0.940417i
\(396\) 1.91258e6 + 3.31269e6i 0.612889 + 1.06156i
\(397\) −306629. + 531096.i −0.0976419 + 0.169121i −0.910708 0.413050i \(-0.864463\pi\)
0.813066 + 0.582171i \(0.197797\pi\)
\(398\) 4.62589e6 1.46382
\(399\) 0 0
\(400\) −2.65262e6 −0.828942
\(401\) −1.41111e6 + 2.44412e6i −0.438229 + 0.759035i −0.997553 0.0699139i \(-0.977728\pi\)
0.559324 + 0.828949i \(0.311061\pi\)
\(402\) 5.15566e6 + 8.92986e6i 1.59118 + 2.75600i
\(403\) 355862. + 616371.i 0.109149 + 0.189051i
\(404\) −261275. + 452542.i −0.0796425 + 0.137945i
\(405\) 2.83973e6 0.860278
\(406\) 0 0
\(407\) 868324. 0.259834
\(408\) 296819. 514105.i 0.0882756 0.152898i
\(409\) −1.14175e6 1.97757e6i −0.337492 0.584553i 0.646469 0.762941i \(-0.276245\pi\)
−0.983960 + 0.178388i \(0.942912\pi\)
\(410\) −2.72640e6 4.72226e6i −0.800994 1.38736i
\(411\) 2.36248e6 4.09193e6i 0.689864 1.19488i
\(412\) 923831. 0.268132
\(413\) 0 0
\(414\) 8.75511e6 2.51050
\(415\) 51317.6 88884.8i 0.0146267 0.0253342i
\(416\) 1.00084e6 + 1.73350e6i 0.283550 + 0.491123i
\(417\) −623068. 1.07919e6i −0.175467 0.303918i
\(418\) 10726.7 18579.1i 0.00300278 0.00520097i
\(419\) −2.65270e6 −0.738163 −0.369082 0.929397i \(-0.620328\pi\)
−0.369082 + 0.929397i \(0.620328\pi\)
\(420\) 0 0
\(421\) 2.93674e6 0.807532 0.403766 0.914862i \(-0.367701\pi\)
0.403766 + 0.914862i \(0.367701\pi\)
\(422\) −549146. + 951148.i −0.150109 + 0.259996i
\(423\) −2.64157e6 4.57533e6i −0.717812 1.24329i
\(424\) 451487. + 781998.i 0.121964 + 0.211247i
\(425\) 1.32070e6 2.28752e6i 0.354676 0.614317i
\(426\) 2.85577e6 0.762428
\(427\) 0 0
\(428\) 239272. 0.0631367
\(429\) −1.25827e6 + 2.17939e6i −0.330089 + 0.571730i
\(430\) −2.99543e6 5.18824e6i −0.781247 1.35316i
\(431\) 1.22283e6 + 2.11800e6i 0.317082 + 0.549202i 0.979878 0.199598i \(-0.0639636\pi\)
−0.662796 + 0.748800i \(0.730630\pi\)
\(432\) 875389. 1.51622e6i 0.225679 0.390888i
\(433\) −2.11718e6 −0.542673 −0.271336 0.962485i \(-0.587466\pi\)
−0.271336 + 0.962485i \(0.587466\pi\)
\(434\) 0 0
\(435\) 8.74301e6 2.21533
\(436\) 160913. 278709.i 0.0405391 0.0702158i
\(437\) −11687.9 20244.0i −0.00292773 0.00507099i
\(438\) −7.18835e6 1.24506e7i −1.79038 3.10102i
\(439\) −2.32382e6 + 4.02498e6i −0.575495 + 0.996786i 0.420493 + 0.907296i \(0.361857\pi\)
−0.995988 + 0.0894902i \(0.971476\pi\)
\(440\) 720178. 0.177340
\(441\) 0 0
\(442\) −2.17691e6 −0.530012
\(443\) −2.21462e6 + 3.83584e6i −0.536155 + 0.928648i 0.462951 + 0.886384i \(0.346791\pi\)
−0.999106 + 0.0422645i \(0.986543\pi\)
\(444\) 699839. + 1.21216e6i 0.168477 + 0.291811i
\(445\) −2.55802e6 4.43062e6i −0.612356 1.06063i
\(446\) 1916.75 3319.91i 0.000456276 0.000790294i
\(447\) −2.36998e6 −0.561016
\(448\) 0 0
\(449\) −6.70171e6 −1.56881 −0.784404 0.620250i \(-0.787031\pi\)
−0.784404 + 0.620250i \(0.787031\pi\)
\(450\) 2.89846e6 5.02027e6i 0.674739 1.16868i
\(451\) 1.99252e6 + 3.45114e6i 0.461276 + 0.798953i
\(452\) −947629. 1.64134e6i −0.218169 0.377879i
\(453\) 5.38462e6 9.32644e6i 1.23285 2.13536i
\(454\) −4.64136e6 −1.05683
\(455\) 0 0
\(456\) −3478.46 −0.000783385
\(457\) 2.94172e6 5.09521e6i 0.658887 1.14123i −0.322018 0.946734i \(-0.604361\pi\)
0.980904 0.194491i \(-0.0623057\pi\)
\(458\) −140204. 242840.i −0.0312317 0.0540949i
\(459\) 871688. + 1.50981e6i 0.193121 + 0.334495i
\(460\) −3.90062e6 + 6.75607e6i −0.859487 + 1.48867i
\(461\) 1.54764e6 0.339171 0.169585 0.985515i \(-0.445757\pi\)
0.169585 + 0.985515i \(0.445757\pi\)
\(462\) 0 0
\(463\) −3.93764e6 −0.853656 −0.426828 0.904333i \(-0.640369\pi\)
−0.426828 + 0.904333i \(0.640369\pi\)
\(464\) −2.77537e6 + 4.80708e6i −0.598447 + 1.03654i
\(465\) 2.46453e6 + 4.26870e6i 0.528570 + 0.915510i
\(466\) 4.87746e6 + 8.44800e6i 1.04047 + 1.80214i
\(467\) 3.40793e6 5.90271e6i 0.723100 1.25245i −0.236651 0.971595i \(-0.576050\pi\)
0.959751 0.280852i \(-0.0906170\pi\)
\(468\) −2.27438e6 −0.480007
\(469\) 0 0
\(470\) 9.88860e6 2.06486
\(471\) 2.10535e6 3.64657e6i 0.437293 0.757413i
\(472\) −387982. 672005.i −0.0801598 0.138841i
\(473\) 2.18913e6 + 3.79169e6i 0.449904 + 0.779256i
\(474\) −4.16632e6 + 7.21627e6i −0.851739 + 1.47525i
\(475\) −15477.5 −0.00314750
\(476\) 0 0
\(477\) −1.22519e7 −2.46552
\(478\) −2.25443e6 + 3.90478e6i −0.451301 + 0.781677i
\(479\) 2.60203e6 + 4.50685e6i 0.518171 + 0.897499i 0.999777 + 0.0211112i \(0.00672039\pi\)
−0.481606 + 0.876388i \(0.659946\pi\)
\(480\) 6.93132e6 + 1.20054e7i 1.37313 + 2.37834i
\(481\) −258145. + 447121.i −0.0508747 + 0.0881175i
\(482\) 1.08036e7 2.11813
\(483\) 0 0
\(484\) 549840. 0.106690
\(485\) 4.04270e6 7.00216e6i 0.780400 1.35169i
\(486\) −5.01253e6 8.68195e6i −0.962644 1.66735i
\(487\) 77499.2 + 134233.i 0.0148073 + 0.0256469i 0.873334 0.487122i \(-0.161953\pi\)
−0.858527 + 0.512769i \(0.828620\pi\)
\(488\) −323361. + 560078.i −0.0614665 + 0.106463i
\(489\) 5.72936e6 1.08351
\(490\) 0 0
\(491\) −1.61951e6 −0.303165 −0.151583 0.988445i \(-0.548437\pi\)
−0.151583 + 0.988445i \(0.548437\pi\)
\(492\) −3.21179e6 + 5.56299e6i −0.598184 + 1.03609i
\(493\) −2.76364e6 4.78676e6i −0.512111 0.887002i
\(494\) 6377.89 + 11046.8i 0.00117587 + 0.00203667i
\(495\) −4.88584e6 + 8.46253e6i −0.896244 + 1.55234i
\(496\) −3.12935e6 −0.571150
\(497\) 0 0
\(498\) −253978. −0.0458905
\(499\) −2.05337e6 + 3.55654e6i −0.369161 + 0.639405i −0.989435 0.144980i \(-0.953688\pi\)
0.620274 + 0.784385i \(0.287022\pi\)
\(500\) −791678. 1.37123e6i −0.141620 0.245292i
\(501\) −1.37622e6 2.38368e6i −0.244959 0.424281i
\(502\) 1.26298e6 2.18755e6i 0.223685 0.387435i
\(503\) −3.40748e6 −0.600501 −0.300250 0.953860i \(-0.597070\pi\)
−0.300250 + 0.953860i \(0.597070\pi\)
\(504\) 0 0
\(505\) −1.33490e6 −0.232927
\(506\) 5.98808e6 1.03717e7i 1.03971 1.80083i
\(507\) 3.61800e6 + 6.26655e6i 0.625098 + 1.08270i
\(508\) 2.83161e6 + 4.90450e6i 0.486827 + 0.843209i
\(509\) −5.35453e6 + 9.27432e6i −0.916067 + 1.58667i −0.110735 + 0.993850i \(0.535321\pi\)
−0.805332 + 0.592825i \(0.798013\pi\)
\(510\) −1.50763e7 −2.56666
\(511\) 0 0
\(512\) −7.98992e6 −1.34700
\(513\) 5107.72 8846.83i 0.000856907 0.00148421i
\(514\) 7.21337e6 + 1.24939e7i 1.20429 + 2.08589i
\(515\) 1.18000e6 + 2.04382e6i 0.196049 + 0.339566i
\(516\) −3.52873e6 + 6.11194e6i −0.583437 + 1.01054i
\(517\) −7.22682e6 −1.18911
\(518\) 0 0
\(519\) 6.34374e6 1.03378
\(520\) −214103. + 370836.i −0.0347227 + 0.0601415i
\(521\) −3.96000e6 6.85893e6i −0.639148 1.10704i −0.985620 0.168976i \(-0.945954\pi\)
0.346472 0.938060i \(-0.387379\pi\)
\(522\) −6.06517e6 1.05052e7i −0.974242 1.68744i
\(523\) 4.16373e6 7.21179e6i 0.665623 1.15289i −0.313493 0.949591i \(-0.601499\pi\)
0.979116 0.203303i \(-0.0651675\pi\)
\(524\) −6.87643e6 −1.09404
\(525\) 0 0
\(526\) 3.58104e6 0.564345
\(527\) 1.55806e6 2.69864e6i 0.244376 0.423271i
\(528\) −5.53244e6 9.58246e6i −0.863638 1.49586i
\(529\) −3.30649e6 5.72701e6i −0.513722 0.889793i
\(530\) 1.14662e7 1.98600e7i 1.77308 3.07106i
\(531\) 1.05286e7 1.62045
\(532\) 0 0
\(533\) −2.36943e6 −0.361265
\(534\) −6.33000e6 + 1.09639e7i −0.960618 + 1.66384i
\(535\) 305619. + 529348.i 0.0461632 + 0.0799571i
\(536\) −641128. 1.11047e6i −0.0963902 0.166953i
\(537\) −4.42766e6 + 7.66893e6i −0.662581 + 1.14762i
\(538\) −3.25856e6 −0.485366
\(539\) 0 0
\(540\) −3.40922e6 −0.503119
\(541\) −311631. + 539760.i −0.0457770 + 0.0792880i −0.888006 0.459832i \(-0.847910\pi\)
0.842229 + 0.539120i \(0.181243\pi\)
\(542\) −3.51826e6 6.09381e6i −0.514434 0.891027i
\(543\) 5.11107e6 + 8.85264e6i 0.743896 + 1.28847i
\(544\) 4.38193e6 7.58973e6i 0.634846 1.09959i
\(545\) 822129. 0.118563
\(546\) 0 0
\(547\) 1.05691e7 1.51032 0.755159 0.655541i \(-0.227559\pi\)
0.755159 + 0.655541i \(0.227559\pi\)
\(548\) 2.92067e6 5.05874e6i 0.415461 0.719600i
\(549\) −4.38751e6 7.59939e6i −0.621280 1.07609i
\(550\) −3.96481e6 6.86725e6i −0.558876 0.968002i
\(551\) −16193.7 + 28048.4i −0.00227231 + 0.00393576i
\(552\) −1.94182e6 −0.271245
\(553\) 0 0
\(554\) 3.49835e6 0.484272
\(555\) −1.78779e6 + 3.09655e6i −0.246368 + 0.426722i
\(556\) −770282. 1.33417e6i −0.105673 0.183030i
\(557\) 6.76989e6 + 1.17258e7i 0.924579 + 1.60142i 0.792237 + 0.610213i \(0.208916\pi\)
0.132341 + 0.991204i \(0.457751\pi\)
\(558\) 3.41938e6 5.92254e6i 0.464902 0.805234i
\(559\) −2.60324e6 −0.352359
\(560\) 0 0
\(561\) 1.10181e7 1.47809
\(562\) −3.00302e6 + 5.20139e6i −0.401068 + 0.694670i
\(563\) 6.98785e6 + 1.21033e7i 0.929122 + 1.60929i 0.784795 + 0.619756i \(0.212768\pi\)
0.144327 + 0.989530i \(0.453898\pi\)
\(564\) −5.82456e6 1.00884e7i −0.771020 1.33545i
\(565\) 2.42079e6 4.19294e6i 0.319034 0.552583i
\(566\) 1.66633e7 2.18635
\(567\) 0 0
\(568\) −355127. −0.0461862
\(569\) 2.80997e6 4.86701e6i 0.363848 0.630204i −0.624742 0.780831i \(-0.714796\pi\)
0.988591 + 0.150627i \(0.0481293\pi\)
\(570\) 44170.3 + 76505.1i 0.00569433 + 0.00986287i
\(571\) −4.35395e6 7.54126e6i −0.558847 0.967951i −0.997593 0.0693403i \(-0.977911\pi\)
0.438746 0.898611i \(-0.355423\pi\)
\(572\) −1.55556e6 + 2.69432e6i −0.198792 + 0.344317i
\(573\) 1.33101e7 1.69354
\(574\) 0 0
\(575\) −8.64019e6 −1.08982
\(576\) 4.11373e6 7.12520e6i 0.516630 0.894830i
\(577\) 3.31996e6 + 5.75034e6i 0.415139 + 0.719042i 0.995443 0.0953580i \(-0.0303996\pi\)
−0.580304 + 0.814400i \(0.697066\pi\)
\(578\) −782583. 1.35547e6i −0.0974340 0.168761i
\(579\) −6.04970e6 + 1.04784e7i −0.749959 + 1.29897i
\(580\) 1.08087e7 1.33415
\(581\) 0 0
\(582\) −2.00079e7 −2.44846
\(583\) −8.37974e6 + 1.45141e7i −1.02108 + 1.76856i
\(584\) 893902. + 1.54828e6i 0.108457 + 0.187853i
\(585\) −2.90504e6 5.03167e6i −0.350964 0.607887i
\(586\) −9.48239e6 + 1.64240e7i −1.14071 + 1.97576i
\(587\) −1.36652e7 −1.63689 −0.818446 0.574583i \(-0.805164\pi\)
−0.818446 + 0.574583i \(0.805164\pi\)
\(588\) 0 0
\(589\) −18259.2 −0.00216866
\(590\) −9.85337e6 + 1.70665e7i −1.16535 + 2.01844i
\(591\) 3.51063e6 + 6.08059e6i 0.413444 + 0.716106i
\(592\) −1.13503e6 1.96593e6i −0.133108 0.230549i
\(593\) 3.51295e6 6.08460e6i 0.410237 0.710551i −0.584678 0.811265i \(-0.698779\pi\)
0.994915 + 0.100714i \(0.0321126\pi\)
\(594\) 5.23370e6 0.608615
\(595\) 0 0
\(596\) −2.92994e6 −0.337864
\(597\) 6.96054e6 1.20560e7i 0.799295 1.38442i
\(598\) 3.56041e6 + 6.16681e6i 0.407143 + 0.705192i
\(599\) 1.79331e6 + 3.10611e6i 0.204216 + 0.353712i 0.949883 0.312607i \(-0.101202\pi\)
−0.745667 + 0.666319i \(0.767869\pi\)
\(600\) −642858. + 1.11346e6i −0.0729016 + 0.126269i
\(601\) 1.58600e7 1.79108 0.895542 0.444977i \(-0.146788\pi\)
0.895542 + 0.444977i \(0.146788\pi\)
\(602\) 0 0
\(603\) 1.73982e7 1.94855
\(604\) 6.65686e6 1.15300e7i 0.742467 1.28599i
\(605\) 702305. + 1.21643e6i 0.0780077 + 0.135113i
\(606\) 1.65165e6 + 2.86073e6i 0.182699 + 0.316443i
\(607\) −3.22085e6 + 5.57867e6i −0.354812 + 0.614553i −0.987086 0.160192i \(-0.948789\pi\)
0.632274 + 0.774745i \(0.282122\pi\)
\(608\) −51352.5 −0.00563381
\(609\) 0 0
\(610\) 1.64244e7 1.78717
\(611\) 2.14847e6 3.72126e6i 0.232823 0.403262i
\(612\) 4.97892e6 + 8.62375e6i 0.537349 + 0.930716i
\(613\) 2.29433e6 + 3.97389e6i 0.246606 + 0.427134i 0.962582 0.270991i \(-0.0873513\pi\)
−0.715976 + 0.698125i \(0.754018\pi\)
\(614\) 9.54722e6 1.65363e7i 1.02201 1.77018i
\(615\) −1.64096e7 −1.74948
\(616\) 0 0
\(617\) 1.47104e6 0.155565 0.0777825 0.996970i \(-0.475216\pi\)
0.0777825 + 0.996970i \(0.475216\pi\)
\(618\) 2.91999e6 5.05757e6i 0.307546 0.532685i
\(619\) 1.56784e6 + 2.71558e6i 0.164466 + 0.284863i 0.936465 0.350760i \(-0.114077\pi\)
−0.772000 + 0.635623i \(0.780743\pi\)
\(620\) 3.04684e6 + 5.27727e6i 0.318324 + 0.551354i
\(621\) 2.85134e6 4.93867e6i 0.296702 0.513903i
\(622\) 9.02366e6 0.935205
\(623\) 0 0
\(624\) 6.57898e6 0.676390
\(625\) 5.75963e6 9.97597e6i 0.589786 1.02154i
\(626\) −6.47503e6 1.12151e7i −0.660399 1.14384i
\(627\) −32280.7 55911.8i −0.00327924 0.00567982i
\(628\) 2.60279e6 4.50816e6i 0.263354 0.456142i
\(629\) 2.26046e6 0.227809
\(630\) 0 0
\(631\) 484547. 0.0484465 0.0242233 0.999707i \(-0.492289\pi\)
0.0242233 + 0.999707i \(0.492289\pi\)
\(632\) 518099. 897374.i 0.0515965 0.0893678i
\(633\) 1.65259e6 + 2.86237e6i 0.163929 + 0.283934i
\(634\) 3.20950e6 + 5.55901e6i 0.317113 + 0.549256i
\(635\) −7.23358e6 + 1.25289e7i −0.711900 + 1.23305i
\(636\) −2.70151e7 −2.64828
\(637\) 0 0
\(638\) −1.65932e7 −1.61390
\(639\) 2.40926e6 4.17296e6i 0.233416 0.404289i
\(640\) −1.73114e6 2.99842e6i −0.167064 0.289363i
\(641\) −1.52042e6 2.63345e6i −0.146157 0.253151i 0.783647 0.621206i \(-0.213357\pi\)
−0.929804 + 0.368055i \(0.880024\pi\)
\(642\) 756276. 1.30991e6i 0.0724174 0.125431i
\(643\) 5.25888e6 0.501609 0.250805 0.968038i \(-0.419305\pi\)
0.250805 + 0.968038i \(0.419305\pi\)
\(644\) 0 0
\(645\) −1.80288e7 −1.70635
\(646\) 27924.1 48366.0i 0.00263268 0.00455994i
\(647\) −1.05985e7 1.83571e7i −0.995368 1.72403i −0.580942 0.813945i \(-0.697316\pi\)
−0.414425 0.910083i \(-0.636017\pi\)
\(648\) 436925. + 756776.i 0.0408761 + 0.0707994i
\(649\) 7.20107e6 1.24726e7i 0.671097 1.16237i
\(650\) 4.71481e6 0.437705
\(651\) 0 0
\(652\) 7.08305e6 0.652531
\(653\) −6.50529e6 + 1.12675e7i −0.597013 + 1.03406i 0.396247 + 0.918144i \(0.370313\pi\)
−0.993259 + 0.115912i \(0.963021\pi\)
\(654\) −1.01721e6 1.76186e6i −0.0929962 0.161074i
\(655\) −8.78319e6 1.52129e7i −0.799924 1.38551i
\(656\) 5.20903e6 9.02230e6i 0.472604 0.818574i
\(657\) −2.42577e7 −2.19248
\(658\) 0 0
\(659\) −1.59874e7 −1.43405 −0.717024 0.697049i \(-0.754496\pi\)
−0.717024 + 0.697049i \(0.754496\pi\)
\(660\) −1.07731e7 + 1.86596e7i −0.962678 + 1.66741i
\(661\) −2.01571e6 3.49131e6i −0.179442 0.310803i 0.762248 0.647286i \(-0.224096\pi\)
−0.941690 + 0.336483i \(0.890763\pi\)
\(662\) −373837. 647504.i −0.0331541 0.0574245i
\(663\) −3.27559e6 + 5.67348e6i −0.289404 + 0.501263i
\(664\) 31583.3 0.00277995
\(665\) 0 0
\(666\) 4.96089e6 0.433385
\(667\) −9.04002e6 + 1.56578e7i −0.786783 + 1.36275i
\(668\) −1.70138e6 2.94688e6i −0.147523 0.255518i
\(669\) −5768.24 9990.88i −0.000498285 0.000863055i
\(670\) −1.62824e7 + 2.82019e7i −1.40130 + 2.42712i
\(671\) −1.20034e7 −1.02919
\(672\) 0 0
\(673\) 2.98234e6 0.253816 0.126908 0.991914i \(-0.459495\pi\)
0.126908 + 0.991914i \(0.459495\pi\)
\(674\) 9.26165e6 1.60416e7i 0.785305 1.36019i
\(675\) −1.88793e6 3.26998e6i −0.159487 0.276240i
\(676\) 4.47283e6 + 7.74717e6i 0.376457 + 0.652043i
\(677\) −973478. + 1.68611e6i −0.0816309 + 0.141389i −0.903951 0.427637i \(-0.859346\pi\)
0.822320 + 0.569026i \(0.192680\pi\)
\(678\) −1.19808e7 −1.00095
\(679\) 0 0
\(680\) 1.87480e6 0.155483
\(681\) −6.98382e6 + 1.20963e7i −0.577066 + 0.999507i
\(682\) −4.67738e6 8.10146e6i −0.385072 0.666964i
\(683\) −5.99700e6 1.03871e7i −0.491906 0.852006i 0.508050 0.861327i \(-0.330366\pi\)
−0.999957 + 0.00932092i \(0.997033\pi\)
\(684\) 29174.3 50531.4i 0.00238430 0.00412973i
\(685\) 1.49221e7 1.21508
\(686\) 0 0
\(687\) −843854. −0.0682143
\(688\) 5.72305e6 9.91261e6i 0.460953 0.798393i
\(689\) −4.98245e6 8.62986e6i −0.399848 0.692557i
\(690\) 2.46577e7 + 4.27084e7i 1.97165 + 3.41500i
\(691\) 4.33152e6 7.50242e6i 0.345100 0.597731i −0.640272 0.768149i \(-0.721178\pi\)
0.985372 + 0.170417i \(0.0545115\pi\)
\(692\) 7.84260e6 0.622579
\(693\) 0 0
\(694\) −3.83385e6 −0.302160
\(695\) 1.96775e6 3.40824e6i 0.154528 0.267650i
\(696\) 1.34521e6 + 2.32998e6i 0.105261 + 0.182318i
\(697\) 5.18701e6 + 8.98416e6i 0.404422 + 0.700480i
\(698\) −1.64589e7 + 2.85076e7i −1.27868 + 2.21474i
\(699\) 2.93563e7 2.27252
\(700\) 0 0
\(701\) −8.13382e6 −0.625172 −0.312586 0.949889i \(-0.601195\pi\)
−0.312586 + 0.949889i \(0.601195\pi\)
\(702\) −1.55593e6 + 2.69496e6i −0.119165 + 0.206400i
\(703\) −6622.67 11470.8i −0.000505411 0.000875397i
\(704\) −5.62719e6 9.74658e6i −0.427918 0.741175i
\(705\) 1.48793e7 2.57717e7i 1.12748 1.95286i
\(706\) −2.48033e7 −1.87283
\(707\) 0 0
\(708\) 2.32152e7 1.74056
\(709\) −1.10663e7 + 1.91674e7i −0.826773 + 1.43201i 0.0737829 + 0.997274i \(0.476493\pi\)
−0.900556 + 0.434739i \(0.856841\pi\)
\(710\) 4.50948e6 + 7.81064e6i 0.335722 + 0.581488i
\(711\) 7.02980e6 + 1.21760e7i 0.521517 + 0.903295i
\(712\) 787162. 1.36341e6i 0.0581921 0.100792i
\(713\) −1.01930e7 −0.750896
\(714\) 0 0
\(715\) −7.94762e6 −0.581396
\(716\) −5.47379e6 + 9.48089e6i −0.399030 + 0.691141i
\(717\) 6.78444e6 + 1.17510e7i 0.492852 + 0.853644i
\(718\) −1.32894e7 2.30180e7i −0.962046 1.66631i
\(719\) 3.61598e6 6.26306e6i 0.260858 0.451819i −0.705612 0.708598i \(-0.749328\pi\)
0.966470 + 0.256779i \(0.0826613\pi\)
\(720\) 2.55461e7 1.83651
\(721\) 0 0
\(722\) 1.93506e7 1.38150
\(723\) 1.62562e7 2.81565e7i 1.15657 2.00324i
\(724\) 6.31868e6 + 1.09443e7i 0.448002 + 0.775962i
\(725\) 5.98556e6 + 1.03673e7i 0.422921 + 0.732521i
\(726\) 1.73790e6 3.01014e6i 0.122373 0.211955i
\(727\) −1.70200e7 −1.19433 −0.597163 0.802120i \(-0.703705\pi\)
−0.597163 + 0.802120i \(0.703705\pi\)
\(728\) 0 0
\(729\) −2.08788e7 −1.45508
\(730\) 2.27019e7 3.93209e7i 1.57672 2.73097i
\(731\) 5.69886e6 + 9.87071e6i 0.394452 + 0.683211i
\(732\) −9.67430e6 1.67564e7i −0.667332 1.15585i
\(733\) −500056. + 866123.i −0.0343763 + 0.0595415i −0.882702 0.469934i \(-0.844278\pi\)
0.848325 + 0.529475i \(0.177611\pi\)
\(734\) −1.53857e7 −1.05409
\(735\) 0 0
\(736\) −2.86671e7 −1.95070
\(737\) 1.18995e7 2.06106e7i 0.806978 1.39773i
\(738\) 1.13836e7 + 1.97170e7i 0.769376 + 1.33260i
\(739\) −1.62989e6 2.82306e6i −0.109786 0.190155i 0.805897 0.592055i \(-0.201683\pi\)
−0.915684 + 0.401900i \(0.868350\pi\)
\(740\) −2.21020e6 + 3.82818e6i −0.148372 + 0.256988i
\(741\) 38387.1 0.00256826
\(742\) 0 0
\(743\) 1.36125e7 0.904617 0.452309 0.891861i \(-0.350601\pi\)
0.452309 + 0.891861i \(0.350601\pi\)
\(744\) −758394. + 1.31358e6i −0.0502300 + 0.0870008i
\(745\) −3.74238e6 6.48199e6i −0.247034 0.427875i
\(746\) −1.35939e7 2.35453e7i −0.894327 1.54902i
\(747\) −214268. + 371123.i −0.0140493 + 0.0243341i
\(748\) 1.36214e7 0.890158
\(749\) 0 0
\(750\) −1.00092e7 −0.649747
\(751\) −3.28272e6 + 5.68584e6i −0.212390 + 0.367870i −0.952462 0.304657i \(-0.901458\pi\)
0.740072 + 0.672528i \(0.234791\pi\)
\(752\) 9.44653e6 + 1.63619e7i 0.609155 + 1.05509i
\(753\) −3.80080e6 6.58318e6i −0.244280 0.423105i
\(754\) 4.93300e6 8.54421e6i 0.315997 0.547323i
\(755\) 3.40110e7 2.17146
\(756\) 0 0
\(757\) 2.62531e7 1.66510 0.832551 0.553948i \(-0.186879\pi\)
0.832551 + 0.553948i \(0.186879\pi\)
\(758\) −1.64622e6 + 2.85134e6i −0.104068 + 0.180250i
\(759\) −1.80204e7 3.12123e7i −1.13543 1.96662i
\(760\) −5492.76 9513.74i −0.000344950 0.000597472i
\(761\) 2.62555e6 4.54759e6i 0.164346 0.284656i −0.772077 0.635529i \(-0.780782\pi\)
0.936423 + 0.350874i \(0.114115\pi\)
\(762\) 3.58000e7 2.23355
\(763\) 0 0
\(764\) 1.64549e7 1.01991
\(765\) −1.27191e7 + 2.20300e7i −0.785780 + 1.36101i
\(766\) 1.04296e7 + 1.80646e7i 0.642238 + 1.11239i
\(767\) 4.28163e6 + 7.41601e6i 0.262797 + 0.455179i
\(768\) −1.42669e7 + 2.47109e7i −0.872821 + 1.51177i
\(769\) −1.77307e7 −1.08121 −0.540605 0.841277i \(-0.681805\pi\)
−0.540605 + 0.841277i \(0.681805\pi\)
\(770\)