Properties

Label 49.6.c.h.18.4
Level $49$
Weight $6$
Character 49.18
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 18.4
Root \(6.52218 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 49.18
Dual form 49.6.c.h.30.4

$q$-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 \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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 0.971589 + 0.236676i \(0.0760578\pi\)
−0.280827 + 0.959758i \(0.590609\pi\)
\(3\) 11.7593 20.3677i 0.754359 1.30659i −0.191334 0.981525i \(-0.561281\pi\)
0.945692 0.325063i \(-0.105385\pi\)
\(4\) −14.5377 + 25.1800i −0.454303 + 0.786875i
\(5\) −37.1377 64.3243i −0.664339 1.15067i −0.979464 0.201618i \(-0.935380\pi\)
0.315125 0.949050i \(-0.397953\pi\)
\(6\) 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 −0.470905 0.882184i \(-0.656073\pi\)
0.999446 0.0332758i \(-0.0105940\pi\)
\(12\) 341.906 + 592.198i 0.685414 + 1.18717i
\(13\) 252.233 0.413946 0.206973 0.978347i \(-0.433639\pi\)
0.206973 + 0.978347i \(0.433639\pi\)
\(14\) 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 \(-0.986703\pi\)
0.535731 + 0.844389i \(0.320036\pi\)
\(18\) 1211.82 2098.93i 0.881569 1.52692i
\(19\) −3.23550 5.60405i −0.00205616 0.00356138i 0.864995 0.501780i \(-0.167321\pi\)
−0.867052 + 0.498218i \(0.833988\pi\)
\(20\) 2159.58 1.20724
\(21\) 0 0
\(22\) 3315.30 1.46038
\(23\) 1806.19 + 3128.42i 0.711942 + 1.23312i 0.964127 + 0.265440i \(0.0855173\pi\)
−0.252186 + 0.967679i \(0.581149\pi\)
\(24\) 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 \(-0.748397\pi\)
0.967217 + 0.253953i \(0.0817308\pi\)
\(32\) −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 0.920911 0.389774i \(-0.127447\pi\)
−0.798009 + 0.602645i \(0.794113\pi\)
\(38\) 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 \(-0.643735\pi\)
−0.436367 + 0.899769i \(0.643735\pi\)
\(42\) 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 0.997282 + 0.0736781i \(0.0234737\pi\)
−0.434834 + 0.900511i \(0.643193\pi\)
\(48\) 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 0.258877 0.965910i \(-0.416648\pi\)
0.707064 0.707149i \(-0.250019\pi\)
\(54\) −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 −0.351687 0.936118i \(-0.614392\pi\)
0.986545 0.163489i \(-0.0522750\pi\)
\(60\) 25395.1 43985.7i 0.910694 1.57737i
\(61\) 14147.6 + 24504.4i 0.486809 + 0.843178i 0.999885 0.0151652i \(-0.00482741\pi\)
−0.513076 + 0.858343i \(0.671494\pi\)
\(62\) 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 0.177686 + 0.984087i \(0.443139\pi\)
−0.941088 + 0.338163i \(0.890194\pi\)
\(68\) −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 0.0139419 + 0.999903i \(0.495562\pi\)
−0.872912 + 0.487877i \(0.837771\pi\)
\(74\) −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 0.994738 0.102456i \(-0.0326700\pi\)
−0.586098 + 0.810240i \(0.699337\pi\)
\(80\) 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 \(-0.503504\pi\)
−0.0110085 + 0.999939i \(0.503504\pi\)
\(84\) 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 \(-0.319132\pi\)
−0.999005 + 0.0446014i \(0.985798\pi\)
\(90\) −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 \(-0.699829\pi\)
−0.587351 + 0.809332i \(0.699829\pi\)
\(98\) 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 \(-0.805396\pi\)
0.906519 + 0.422165i \(0.138730\pi\)
\(102\) −101489. + 175784.i −0.965871 + 1.67294i
\(103\) 15886.8 + 27516.8i 0.147552 + 0.255567i 0.930322 0.366744i \(-0.119527\pi\)
−0.782770 + 0.622311i \(0.786194\pi\)
\(104\) 5765.11 0.0522666
\(105\) 0 0
\(106\) 308747. 2.66894
\(107\) −4114.68 7126.84i −0.0347438 0.0601780i 0.848131 0.529787i \(-0.177728\pi\)
−0.882874 + 0.469609i \(0.844395\pi\)
\(108\) 22949.9 39750.4i 0.189331 0.327931i
\(109\) 5534.34 9585.75i 0.0446169 0.0772787i −0.842855 0.538141i \(-0.819127\pi\)
0.887471 + 0.460863i \(0.152460\pi\)
\(110\) −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 −0.992511 0.122156i \(-0.961019\pi\)
0.390465 0.920618i \(-0.372314\pi\)
\(132\) 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 −0.541563 0.840660i \(-0.682167\pi\)
0.998815 + 0.0486772i \(0.0155005\pi\)
\(138\) 331977. + 575001.i 1.48392 + 2.57022i
\(139\) −52985.2 −0.232604 −0.116302 0.993214i \(-0.537104\pi\)
−0.116302 + 0.993214i \(0.537104\pi\)
\(140\) 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 0.943888 0.330266i \(-0.107139\pi\)
−0.757963 + 0.652298i \(0.773805\pi\)
\(150\) −219808. + 380718.i −0.797655 + 1.38158i
\(151\) 228952. 396556.i 0.817150 1.41535i −0.0906234 0.995885i \(-0.528886\pi\)
0.907774 0.419460i \(-0.137781\pi\)
\(152\) −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 \(-0.926937\pi\)
0.683928 + 0.729549i \(0.260270\pi\)
\(158\) −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 0.628724 0.777629i \(-0.283578\pi\)
−0.987808 + 0.155677i \(0.950244\pi\)
\(164\) 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 \(-0.551911\pi\)
−0.162362 + 0.986731i \(0.551911\pi\)
\(168\) 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 \(-0.0553586\pi\)
−0.642313 + 0.766442i \(0.722025\pi\)
\(174\) −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 −0.997626 0.0688718i \(-0.978060\pi\)
0.558457 + 0.829533i \(0.311393\pi\)
\(180\) −334869. 580009.i −0.770359 1.33430i
\(181\) 434641. 0.986131 0.493065 0.869992i \(-0.335876\pi\)
0.493065 + 0.869992i \(0.335876\pi\)
\(182\) 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 −0.997388 0.0722342i \(-0.976987\pi\)
0.436137 0.899880i \(-0.356346\pi\)
\(192\) −311970. + 540348.i −0.610744 + 1.05784i
\(193\) −257231. + 445537.i −0.497084 + 0.860974i −0.999994 0.00336433i \(-0.998929\pi\)
0.502911 + 0.864338i \(0.332262\pi\)
\(194\) −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 0.469612 + 0.882873i \(0.344394\pi\)
−0.999396 + 0.0347408i \(0.988939\pi\)
\(200\) −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 \(-0.500105\pi\)
−0.000330271 1.00000i \(0.500105\pi\)
\(224\) 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 \(-0.708401\pi\)
0.991417 + 0.130736i \(0.0417342\pi\)
\(228\) 2212.47 3832.11i 0.00281865 0.00488204i
\(229\) −17940.2 31073.3i −0.0226067 0.0391560i 0.854501 0.519450i \(-0.173863\pi\)
−0.877107 + 0.480294i \(0.840530\pi\)
\(230\) 2.09687e6 2.61368
\(231\) 0 0
\(232\) −114396. −0.139537
\(233\) −624109. 1.08099e6i −0.753131 1.30446i −0.946298 0.323295i \(-0.895209\pi\)
0.193167 0.981166i \(-0.438124\pi\)
\(234\) 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 0.172809 + 0.984955i \(0.444716\pi\)
−0.939401 + 0.342820i \(0.888618\pi\)
\(242\) 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 \(-0.551766\pi\)
−0.161912 + 0.986805i \(0.551766\pi\)
\(252\) 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 0.860226 + 0.509913i \(0.170322\pi\)
0.0114847 + 0.999934i \(0.496344\pi\)
\(258\) 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 −0.745645 0.666343i \(-0.767859\pi\)
0.949893 + 0.312576i \(0.101192\pi\)
\(264\) −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 \(-0.777126\pi\)
0.940391 + 0.340096i \(0.110460\pi\)
\(270\) −458177. + 793586.i −0.382493 + 0.662498i
\(271\) −450189. 779751.i −0.372368 0.644960i 0.617562 0.786523i \(-0.288121\pi\)
−0.989929 + 0.141563i \(0.954787\pi\)
\(272\) −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 −0.764986 0.644046i \(-0.777254\pi\)
0.940254 + 0.340475i \(0.110588\pi\)
\(278\) −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 0.133892 + 0.990996i \(0.457253\pi\)
−0.925173 + 0.379544i \(0.876081\pi\)
\(284\) 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 \(-0.190787\pi\)
0.825688 + 0.564128i \(0.190787\pi\)
\(294\) 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 \(-0.765067\pi\)
−0.739772 + 0.672857i \(0.765067\pi\)
\(308\) 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 \(-0.943242\pi\)
0.645676 + 0.763611i \(0.276576\pi\)
\(312\) 67793.5 117422.i 0.0394277 0.0682908i
\(313\) −828531. 1.43506e6i −0.478022 0.827959i 0.521660 0.853153i \(-0.325313\pi\)
−0.999683 + 0.0251945i \(0.991980\pi\)
\(314\) −1.39919e6 −0.800852
\(315\) 0 0
\(316\) −1.31815e6 −0.742584
\(317\) −410680. 711319.i −0.229539 0.397573i 0.728133 0.685436i \(-0.240388\pi\)
−0.957671 + 0.287863i \(0.907055\pi\)
\(318\) 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 0.877775 0.479073i \(-0.159027\pi\)
−0.853777 + 0.520639i \(0.825694\pi\)
\(332\) 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 −0.915510 0.402295i \(-0.868213\pi\)
0.806153 + 0.591708i \(0.201546\pi\)
\(348\) −1.71124e6 2.96396e6i −0.757467 1.31197i
\(349\) 4.21208e6 1.85111 0.925557 0.378607i \(-0.123597\pi\)
0.925557 + 0.378607i \(0.123597\pi\)
\(350\) 0 0
\(351\) −398188. −0.172512
\(352\) 1.68326e6 + 2.91549e6i 0.724092 + 1.25416i
\(353\) 1.58689e6 2.74858e6i 0.677814 1.17401i −0.297824 0.954621i \(-0.596261\pi\)
0.975638 0.219387i \(-0.0704058\pi\)
\(354\) 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 0.969718 + 0.244227i \(0.0785343\pi\)
−0.273352 + 0.961914i \(0.588132\pi\)
\(360\) −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 \(-0.708743\pi\)
0.991276 + 0.131802i \(0.0420763\pi\)
\(368\) −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 0.983754 + 0.179523i \(0.0574556\pi\)
−0.336405 + 0.941717i \(0.609211\pi\)
\(374\) −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 \(-0.0127653\pi\)
−0.534319 + 0.845283i \(0.679432\pi\)
\(384\) 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 0.480095 + 0.877217i \(0.340602\pi\)
−0.999739 + 0.0228343i \(0.992731\pi\)
\(390\) −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 \(-0.135537\pi\)
−0.813066 + 0.582171i \(0.802203\pi\)
\(398\) −4.62589e6 −1.46382
\(399\) 0 0
\(400\) −2.65262e6 −0.828942
\(401\) −1.41111e6 2.44412e6i −0.438229 0.759035i 0.559324 0.828949i \(-0.311061\pi\)
−0.997553 + 0.0699139i \(0.977728\pi\)
\(402\) −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 \(-0.723755\pi\)
0.983960 + 0.178388i \(0.0570882\pi\)
\(410\) −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 \(-0.379672\pi\)
0.369082 + 0.929397i \(0.379672\pi\)
\(420\) 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 −0.662796 0.748800i \(-0.730630\pi\)
0.979878 + 0.199598i \(0.0639636\pi\)
\(432\) −875389. 1.51622e6i −0.225679 0.390888i
\(433\) 2.11718e6 0.542673 0.271336 0.962485i \(-0.412534\pi\)
0.271336 + 0.962485i \(0.412534\pi\)
\(434\) 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 0.995988 + 0.0894902i \(0.0285238\pi\)
−0.420493 + 0.907296i \(0.638143\pi\)
\(440\) −720178. −0.177340
\(441\) 0 0
\(442\) −2.17691e6 −0.530012
\(443\) −2.21462e6 3.83584e6i −0.536155 0.928648i −0.999106 0.0422645i \(-0.986543\pi\)
0.462951 0.886384i \(-0.346791\pi\)
\(444\) −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 0.980904 + 0.194491i \(0.0623057\pi\)
−0.322018 + 0.946734i \(0.604361\pi\)
\(458\) 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 \(-0.554243\pi\)
−0.169585 + 0.985515i \(0.554243\pi\)
\(462\) 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 −0.959751 0.280852i \(-0.909383\pi\)
0.236651 0.971595i \(-0.423950\pi\)
\(468\) 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 0.481606 + 0.876388i \(0.340054\pi\)
−0.999777 + 0.0211112i \(0.993280\pi\)
\(480\) 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 −0.858527 0.512769i \(-0.828620\pi\)
0.873334 + 0.487122i \(0.161953\pi\)
\(488\) 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 0.620274 0.784385i \(-0.287022\pi\)
−0.989435 + 0.144980i \(0.953688\pi\)
\(500\) 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 \(-0.402930\pi\)
0.300250 + 0.953860i \(0.402930\pi\)
\(504\) 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 0.805332 + 0.592825i \(0.201987\pi\)
0.110735 + 0.993850i \(0.464679\pi\)
\(510\) 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 −0.346472 0.938060i \(-0.612621\pi\)
0.985620 0.168976i \(-0.0540461\pi\)
\(522\) −6.06517e6 + 1.05052e7i −0.974242 + 1.68744i
\(523\) −4.16373e6 7.21179e6i −0.665623 1.15289i −0.979116 0.203303i \(-0.934832\pi\)
0.313493 0.949591i \(-0.398501\pi\)
\(524\) 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 0.842229 0.539120i \(-0.181243\pi\)
−0.888006 + 0.459832i \(0.847910\pi\)
\(542\) 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 0.132341 0.991204i \(-0.457751\pi\)
0.792237 0.610213i \(-0.208916\pi\)
\(558\) −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 −0.144327 + 0.989530i \(0.546102\pi\)
−0.784795 + 0.619756i \(0.787232\pi\)
\(564\) −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 0.988591 0.150627i \(-0.0481293\pi\)
−0.624742 + 0.780831i \(0.714796\pi\)
\(570\) −44170.3 + 76505.1i −0.00569433 + 0.00986287i
\(571\) −4.35395e6 + 7.54126e6i −0.558847 + 0.967951i 0.438746 + 0.898611i \(0.355423\pi\)
−0.997593 + 0.0693403i \(0.977911\pi\)
\(572\) 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 \(-0.969600\pi\)
0.580304 + 0.814400i \(0.302934\pi\)
\(578\) −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 \(-0.194836\pi\)
0.818446 + 0.574583i \(0.194836\pi\)
\(588\) 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 \(-0.301221\pi\)
−0.994915 + 0.100714i \(0.967887\pi\)
\(594\) −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 −0.745667 0.666319i \(-0.767869\pi\)
0.949883 + 0.312607i \(0.101202\pi\)
\(600\) 642858. + 1.11346e6i 0.0729016 + 0.126269i
\(601\) −1.58600e7 −1.79108 −0.895542 0.444977i \(-0.853212\pi\)
−0.895542 + 0.444977i \(0.853212\pi\)
\(602\) 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 \(-0.0512114\pi\)
−0.632274 + 0.774745i \(0.717878\pi\)
\(608\) 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 −0.715976 0.698125i \(-0.754018\pi\)
0.962582 + 0.270991i \(0.0873513\pi\)
\(614\) −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 \(-0.885923\pi\)
0.772000 + 0.635623i \(0.219257\pi\)
\(620\) 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 −0.929804 0.368055i \(-0.880024\pi\)
0.783647 + 0.621206i \(0.213357\pi\)
\(642\) −756276. 1.30991e6i −0.0724174 0.125431i
\(643\) −5.25888e6 −0.501609 −0.250805 0.968038i \(-0.580695\pi\)
−0.250805 + 0.968038i \(0.580695\pi\)
\(644\) 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 0.414425 0.910083i \(-0.363983\pi\)
0.580942 0.813945i \(-0.302684\pi\)
\(648\) 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 −0.993259 0.115912i \(-0.963021\pi\)
0.396247 0.918144i \(-0.370313\pi\)
\(654\) 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 \(-0.775904\pi\)
0.941690 + 0.336483i \(0.109237\pi\)
\(662\) −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 \(-0.140654\pi\)
−0.822320 + 0.569026i \(0.807320\pi\)
\(678\) 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 −0.999957 0.00932092i \(-0.997033\pi\)
0.508050 + 0.861327i \(0.330366\pi\)
\(684\) −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 \(-0.278822\pi\)
−0.985372 + 0.170417i \(0.945488\pi\)
\(692\) −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 −0.900556 0.434739i \(-0.856841\pi\)
0.0737829 0.997274i \(-0.476493\pi\)
\(710\) −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 \(-0.250672\pi\)
−0.966470 + 0.256779i \(0.917339\pi\)
\(720\) −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 \(-0.296295\pi\)
0.597163 + 0.802120i \(0.296295\pi\)
\(728\) 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 \(-0.155722\pi\)
−0.848325 + 0.529475i \(0.822389\pi\)
\(734\) 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 −0.915684 0.401900i \(-0.868350\pi\)
0.805897 + 0.592055i \(0.201683\pi\)
\(740\) 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 0.740072 0.672528i \(-0.234791\pi\)
−0.952462 + 0.304657i \(0.901458\pi\)
\(752\) −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 \(-0.219218\pi\)
−0.936423 + 0.350874i \(0.885885\pi\)
\(762\) −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 \(-0.318195\pi\)
0.540605 + 0.841277i \(0.318195\pi\)
\(770\)