Properties

Label 26.6.b.b.25.2
Level $26$
Weight $6$
Character 26.25
Analytic conductor $4.170$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [26,6,Mod(25,26)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(26, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("26.25");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 26 = 2 \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 26.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.16997931514\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 25.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 26.25
Dual form 26.6.b.b.25.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.00000i q^{2} +4.00000 q^{3} -16.0000 q^{4} +68.0000i q^{5} +16.0000i q^{6} +82.0000i q^{7} -64.0000i q^{8} -227.000 q^{9} +O(q^{10})\) \(q+4.00000i q^{2} +4.00000 q^{3} -16.0000 q^{4} +68.0000i q^{5} +16.0000i q^{6} +82.0000i q^{7} -64.0000i q^{8} -227.000 q^{9} -272.000 q^{10} +390.000i q^{11} -64.0000 q^{12} +(507.000 - 338.000i) q^{13} -328.000 q^{14} +272.000i q^{15} +256.000 q^{16} +1738.00 q^{17} -908.000i q^{18} -1074.00i q^{19} -1088.00i q^{20} +328.000i q^{21} -1560.00 q^{22} +2104.00 q^{23} -256.000i q^{24} -1499.00 q^{25} +(1352.00 + 2028.00i) q^{26} -1880.00 q^{27} -1312.00i q^{28} -1690.00 q^{29} -1088.00 q^{30} -1430.00i q^{31} +1024.00i q^{32} +1560.00i q^{33} +6952.00i q^{34} -5576.00 q^{35} +3632.00 q^{36} +8852.00i q^{37} +4296.00 q^{38} +(2028.00 - 1352.00i) q^{39} +4352.00 q^{40} +6760.00i q^{41} -1312.00 q^{42} -16916.0 q^{43} -6240.00i q^{44} -15436.0i q^{45} +8416.00i q^{46} -25158.0i q^{47} +1024.00 q^{48} +10083.0 q^{49} -5996.00i q^{50} +6952.00 q^{51} +(-8112.00 + 5408.00i) q^{52} +38214.0 q^{53} -7520.00i q^{54} -26520.0 q^{55} +5248.00 q^{56} -4296.00i q^{57} -6760.00i q^{58} +21286.0i q^{59} -4352.00i q^{60} -5458.00 q^{61} +5720.00 q^{62} -18614.0i q^{63} -4096.00 q^{64} +(22984.0 + 34476.0i) q^{65} -6240.00 q^{66} +44542.0i q^{67} -27808.0 q^{68} +8416.00 q^{69} -22304.0i q^{70} -17790.0i q^{71} +14528.0i q^{72} +31064.0i q^{73} -35408.0 q^{74} -5996.00 q^{75} +17184.0i q^{76} -31980.0 q^{77} +(5408.00 + 8112.00i) q^{78} -45360.0 q^{79} +17408.0i q^{80} +47641.0 q^{81} -27040.0 q^{82} -124546. i q^{83} -5248.00i q^{84} +118184. i q^{85} -67664.0i q^{86} -6760.00 q^{87} +24960.0 q^{88} -18744.0i q^{89} +61744.0 q^{90} +(27716.0 + 41574.0i) q^{91} -33664.0 q^{92} -5720.00i q^{93} +100632. q^{94} +73032.0 q^{95} +4096.00i q^{96} -121488. i q^{97} +40332.0i q^{98} -88530.0i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 8 q^{3} - 32 q^{4} - 454 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 8 q^{3} - 32 q^{4} - 454 q^{9} - 544 q^{10} - 128 q^{12} + 1014 q^{13} - 656 q^{14} + 512 q^{16} + 3476 q^{17} - 3120 q^{22} + 4208 q^{23} - 2998 q^{25} + 2704 q^{26} - 3760 q^{27} - 3380 q^{29} - 2176 q^{30} - 11152 q^{35} + 7264 q^{36} + 8592 q^{38} + 4056 q^{39} + 8704 q^{40} - 2624 q^{42} - 33832 q^{43} + 2048 q^{48} + 20166 q^{49} + 13904 q^{51} - 16224 q^{52} + 76428 q^{53} - 53040 q^{55} + 10496 q^{56} - 10916 q^{61} + 11440 q^{62} - 8192 q^{64} + 45968 q^{65} - 12480 q^{66} - 55616 q^{68} + 16832 q^{69} - 70816 q^{74} - 11992 q^{75} - 63960 q^{77} + 10816 q^{78} - 90720 q^{79} + 95282 q^{81} - 54080 q^{82} - 13520 q^{87} + 49920 q^{88} + 123488 q^{90} + 55432 q^{91} - 67328 q^{92} + 201264 q^{94} + 146064 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/26\mathbb{Z}\right)^\times\).

\(n\) \(15\)
\(\chi(n)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000i 0.707107i
\(3\) 4.00000 0.256600 0.128300 0.991735i \(-0.459048\pi\)
0.128300 + 0.991735i \(0.459048\pi\)
\(4\) −16.0000 −0.500000
\(5\) 68.0000i 1.21642i 0.793776 + 0.608210i \(0.208112\pi\)
−0.793776 + 0.608210i \(0.791888\pi\)
\(6\) 16.0000i 0.181444i
\(7\) 82.0000i 0.632512i 0.948674 + 0.316256i \(0.102426\pi\)
−0.948674 + 0.316256i \(0.897574\pi\)
\(8\) 64.0000i 0.353553i
\(9\) −227.000 −0.934156
\(10\) −272.000 −0.860140
\(11\) 390.000i 0.971813i 0.874011 + 0.485907i \(0.161511\pi\)
−0.874011 + 0.485907i \(0.838489\pi\)
\(12\) −64.0000 −0.128300
\(13\) 507.000 338.000i 0.832050 0.554700i
\(14\) −328.000 −0.447254
\(15\) 272.000i 0.312134i
\(16\) 256.000 0.250000
\(17\) 1738.00 1.45857 0.729285 0.684210i \(-0.239853\pi\)
0.729285 + 0.684210i \(0.239853\pi\)
\(18\) 908.000i 0.660548i
\(19\) 1074.00i 0.682528i −0.939968 0.341264i \(-0.889145\pi\)
0.939968 0.341264i \(-0.110855\pi\)
\(20\) 1088.00i 0.608210i
\(21\) 328.000i 0.162303i
\(22\) −1560.00 −0.687176
\(23\) 2104.00 0.829328 0.414664 0.909975i \(-0.363899\pi\)
0.414664 + 0.909975i \(0.363899\pi\)
\(24\) 256.000i 0.0907218i
\(25\) −1499.00 −0.479680
\(26\) 1352.00 + 2028.00i 0.392232 + 0.588348i
\(27\) −1880.00 −0.496305
\(28\) 1312.00i 0.316256i
\(29\) −1690.00 −0.373157 −0.186579 0.982440i \(-0.559740\pi\)
−0.186579 + 0.982440i \(0.559740\pi\)
\(30\) −1088.00 −0.220712
\(31\) 1430.00i 0.267259i −0.991031 0.133629i \(-0.957337\pi\)
0.991031 0.133629i \(-0.0426632\pi\)
\(32\) 1024.00i 0.176777i
\(33\) 1560.00i 0.249367i
\(34\) 6952.00i 1.03137i
\(35\) −5576.00 −0.769401
\(36\) 3632.00 0.467078
\(37\) 8852.00i 1.06301i 0.847055 + 0.531505i \(0.178373\pi\)
−0.847055 + 0.531505i \(0.821627\pi\)
\(38\) 4296.00 0.482620
\(39\) 2028.00 1352.00i 0.213504 0.142336i
\(40\) 4352.00 0.430070
\(41\) 6760.00i 0.628040i 0.949416 + 0.314020i \(0.101676\pi\)
−0.949416 + 0.314020i \(0.898324\pi\)
\(42\) −1312.00 −0.114765
\(43\) −16916.0 −1.39517 −0.697584 0.716503i \(-0.745742\pi\)
−0.697584 + 0.716503i \(0.745742\pi\)
\(44\) 6240.00i 0.485907i
\(45\) 15436.0i 1.13633i
\(46\) 8416.00i 0.586423i
\(47\) 25158.0i 1.66124i −0.556842 0.830618i \(-0.687987\pi\)
0.556842 0.830618i \(-0.312013\pi\)
\(48\) 1024.00 0.0641500
\(49\) 10083.0 0.599929
\(50\) 5996.00i 0.339185i
\(51\) 6952.00 0.374269
\(52\) −8112.00 + 5408.00i −0.416025 + 0.277350i
\(53\) 38214.0 1.86867 0.934335 0.356395i \(-0.115994\pi\)
0.934335 + 0.356395i \(0.115994\pi\)
\(54\) 7520.00i 0.350940i
\(55\) −26520.0 −1.18213
\(56\) 5248.00 0.223627
\(57\) 4296.00i 0.175137i
\(58\) 6760.00i 0.263862i
\(59\) 21286.0i 0.796093i 0.917365 + 0.398047i \(0.130312\pi\)
−0.917365 + 0.398047i \(0.869688\pi\)
\(60\) 4352.00i 0.156067i
\(61\) −5458.00 −0.187806 −0.0939029 0.995581i \(-0.529934\pi\)
−0.0939029 + 0.995581i \(0.529934\pi\)
\(62\) 5720.00 0.188980
\(63\) 18614.0i 0.590865i
\(64\) −4096.00 −0.125000
\(65\) 22984.0 + 34476.0i 0.674749 + 1.01212i
\(66\) −6240.00 −0.176329
\(67\) 44542.0i 1.21222i 0.795379 + 0.606112i \(0.207272\pi\)
−0.795379 + 0.606112i \(0.792728\pi\)
\(68\) −27808.0 −0.729285
\(69\) 8416.00 0.212806
\(70\) 22304.0i 0.544049i
\(71\) 17790.0i 0.418823i −0.977828 0.209411i \(-0.932845\pi\)
0.977828 0.209411i \(-0.0671547\pi\)
\(72\) 14528.0i 0.330274i
\(73\) 31064.0i 0.682260i 0.940016 + 0.341130i \(0.110810\pi\)
−0.940016 + 0.341130i \(0.889190\pi\)
\(74\) −35408.0 −0.751661
\(75\) −5996.00 −0.123086
\(76\) 17184.0i 0.341264i
\(77\) −31980.0 −0.614684
\(78\) 5408.00 + 8112.00i 0.100647 + 0.150970i
\(79\) −45360.0 −0.817721 −0.408861 0.912597i \(-0.634074\pi\)
−0.408861 + 0.912597i \(0.634074\pi\)
\(80\) 17408.0i 0.304105i
\(81\) 47641.0 0.806805
\(82\) −27040.0 −0.444091
\(83\) 124546.i 1.98442i −0.124559 0.992212i \(-0.539752\pi\)
0.124559 0.992212i \(-0.460248\pi\)
\(84\) 5248.00i 0.0811513i
\(85\) 118184.i 1.77424i
\(86\) 67664.0i 0.986533i
\(87\) −6760.00 −0.0957522
\(88\) 24960.0 0.343588
\(89\) 18744.0i 0.250834i −0.992104 0.125417i \(-0.959973\pi\)
0.992104 0.125417i \(-0.0400270\pi\)
\(90\) 61744.0 0.803505
\(91\) 27716.0 + 41574.0i 0.350855 + 0.526282i
\(92\) −33664.0 −0.414664
\(93\) 5720.00i 0.0685786i
\(94\) 100632. 1.17467
\(95\) 73032.0 0.830241
\(96\) 4096.00i 0.0453609i
\(97\) 121488.i 1.31100i −0.755193 0.655502i \(-0.772457\pi\)
0.755193 0.655502i \(-0.227543\pi\)
\(98\) 40332.0i 0.424214i
\(99\) 88530.0i 0.907826i
\(100\) 23984.0 0.239840
\(101\) −14218.0 −0.138687 −0.0693434 0.997593i \(-0.522090\pi\)
−0.0693434 + 0.997593i \(0.522090\pi\)
\(102\) 27808.0i 0.264648i
\(103\) −62776.0 −0.583043 −0.291521 0.956564i \(-0.594161\pi\)
−0.291521 + 0.956564i \(0.594161\pi\)
\(104\) −21632.0 32448.0i −0.196116 0.294174i
\(105\) −22304.0 −0.197428
\(106\) 152856.i 1.32135i
\(107\) −79252.0 −0.669192 −0.334596 0.942362i \(-0.608600\pi\)
−0.334596 + 0.942362i \(0.608600\pi\)
\(108\) 30080.0 0.248152
\(109\) 218084.i 1.75816i −0.476677 0.879078i \(-0.658159\pi\)
0.476677 0.879078i \(-0.341841\pi\)
\(110\) 106080.i 0.835895i
\(111\) 35408.0i 0.272768i
\(112\) 20992.0i 0.158128i
\(113\) 44234.0 0.325882 0.162941 0.986636i \(-0.447902\pi\)
0.162941 + 0.986636i \(0.447902\pi\)
\(114\) 17184.0 0.123840
\(115\) 143072.i 1.00881i
\(116\) 27040.0 0.186579
\(117\) −115089. + 76726.0i −0.777265 + 0.518177i
\(118\) −85144.0 −0.562923
\(119\) 142516.i 0.922563i
\(120\) 17408.0 0.110356
\(121\) 8951.00 0.0555787
\(122\) 21832.0i 0.132799i
\(123\) 27040.0i 0.161155i
\(124\) 22880.0i 0.133629i
\(125\) 110568.i 0.632928i
\(126\) 74456.0 0.417805
\(127\) −310432. −1.70788 −0.853940 0.520372i \(-0.825793\pi\)
−0.853940 + 0.520372i \(0.825793\pi\)
\(128\) 16384.0i 0.0883883i
\(129\) −67664.0 −0.358000
\(130\) −137904. + 91936.0i −0.715679 + 0.477120i
\(131\) 310372. 1.58017 0.790086 0.612996i \(-0.210036\pi\)
0.790086 + 0.612996i \(0.210036\pi\)
\(132\) 24960.0i 0.124684i
\(133\) 88068.0 0.431707
\(134\) −178168. −0.857171
\(135\) 127840.i 0.603716i
\(136\) 111232.i 0.515683i
\(137\) 281032.i 1.27925i 0.768688 + 0.639623i \(0.220910\pi\)
−0.768688 + 0.639623i \(0.779090\pi\)
\(138\) 33664.0i 0.150476i
\(139\) 363820. 1.59716 0.798582 0.601886i \(-0.205584\pi\)
0.798582 + 0.601886i \(0.205584\pi\)
\(140\) 89216.0 0.384700
\(141\) 100632.i 0.426273i
\(142\) 71160.0 0.296152
\(143\) 131820. + 197730.i 0.539065 + 0.808598i
\(144\) −58112.0 −0.233539
\(145\) 114920.i 0.453916i
\(146\) −124256. −0.482431
\(147\) 40332.0 0.153942
\(148\) 141632.i 0.531505i
\(149\) 274204.i 1.01183i −0.862583 0.505916i \(-0.831155\pi\)
0.862583 0.505916i \(-0.168845\pi\)
\(150\) 23984.0i 0.0870349i
\(151\) 344030.i 1.22787i −0.789355 0.613937i \(-0.789585\pi\)
0.789355 0.613937i \(-0.210415\pi\)
\(152\) −68736.0 −0.241310
\(153\) −394526. −1.36253
\(154\) 127920.i 0.434647i
\(155\) 97240.0 0.325099
\(156\) −32448.0 + 21632.0i −0.106752 + 0.0711681i
\(157\) 20518.0 0.0664333 0.0332167 0.999448i \(-0.489425\pi\)
0.0332167 + 0.999448i \(0.489425\pi\)
\(158\) 181440.i 0.578216i
\(159\) 152856. 0.479501
\(160\) −69632.0 −0.215035
\(161\) 172528.i 0.524560i
\(162\) 190564.i 0.570497i
\(163\) 36626.0i 0.107974i −0.998542 0.0539872i \(-0.982807\pi\)
0.998542 0.0539872i \(-0.0171930\pi\)
\(164\) 108160.i 0.314020i
\(165\) −106080. −0.303336
\(166\) 498184. 1.40320
\(167\) 269442.i 0.747608i 0.927508 + 0.373804i \(0.121947\pi\)
−0.927508 + 0.373804i \(0.878053\pi\)
\(168\) 20992.0 0.0573827
\(169\) 142805. 342732.i 0.384615 0.923077i
\(170\) −472736. −1.25457
\(171\) 243798.i 0.637588i
\(172\) 270656. 0.697584
\(173\) 282654. 0.718026 0.359013 0.933333i \(-0.383113\pi\)
0.359013 + 0.933333i \(0.383113\pi\)
\(174\) 27040.0i 0.0677070i
\(175\) 122918.i 0.303403i
\(176\) 99840.0i 0.242953i
\(177\) 85144.0i 0.204278i
\(178\) 74976.0 0.177367
\(179\) 333780. 0.778624 0.389312 0.921106i \(-0.372713\pi\)
0.389312 + 0.921106i \(0.372713\pi\)
\(180\) 246976.i 0.568164i
\(181\) −459938. −1.04352 −0.521762 0.853091i \(-0.674725\pi\)
−0.521762 + 0.853091i \(0.674725\pi\)
\(182\) −166296. + 110864.i −0.372137 + 0.248092i
\(183\) −21832.0 −0.0481910
\(184\) 134656.i 0.293212i
\(185\) −601936. −1.29307
\(186\) 22880.0 0.0484924
\(187\) 677820.i 1.41746i
\(188\) 402528.i 0.830618i
\(189\) 154160.i 0.313919i
\(190\) 292128.i 0.587069i
\(191\) −917088. −1.81898 −0.909489 0.415727i \(-0.863527\pi\)
−0.909489 + 0.415727i \(0.863527\pi\)
\(192\) −16384.0 −0.0320750
\(193\) 639056.i 1.23494i −0.786595 0.617470i \(-0.788158\pi\)
0.786595 0.617470i \(-0.211842\pi\)
\(194\) 485952. 0.927020
\(195\) 91936.0 + 137904.i 0.173141 + 0.259711i
\(196\) −161328. −0.299964
\(197\) 358292.i 0.657766i 0.944371 + 0.328883i \(0.106672\pi\)
−0.944371 + 0.328883i \(0.893328\pi\)
\(198\) 354120. 0.641930
\(199\) 370440. 0.663109 0.331555 0.943436i \(-0.392427\pi\)
0.331555 + 0.943436i \(0.392427\pi\)
\(200\) 95936.0i 0.169592i
\(201\) 178168.i 0.311057i
\(202\) 56872.0i 0.0980664i
\(203\) 138580.i 0.236026i
\(204\) −111232. −0.187135
\(205\) −459680. −0.763961
\(206\) 251104.i 0.412274i
\(207\) −477608. −0.774722
\(208\) 129792. 86528.0i 0.208013 0.138675i
\(209\) 418860. 0.663290
\(210\) 89216.0i 0.139603i
\(211\) −177228. −0.274048 −0.137024 0.990568i \(-0.543754\pi\)
−0.137024 + 0.990568i \(0.543754\pi\)
\(212\) −611424. −0.934335
\(213\) 71160.0i 0.107470i
\(214\) 317008.i 0.473190i
\(215\) 1.15029e6i 1.69711i
\(216\) 120320.i 0.175470i
\(217\) 117260. 0.169044
\(218\) 872336. 1.24320
\(219\) 124256.i 0.175068i
\(220\) 424320. 0.591067
\(221\) 881166. 587444.i 1.21360 0.809069i
\(222\) −141632. −0.192876
\(223\) 1.11297e6i 1.49872i −0.662164 0.749359i \(-0.730362\pi\)
0.662164 0.749359i \(-0.269638\pi\)
\(224\) −83968.0 −0.111813
\(225\) 340273. 0.448096
\(226\) 176936.i 0.230433i
\(227\) 1.39158e6i 1.79244i 0.443612 + 0.896219i \(0.353697\pi\)
−0.443612 + 0.896219i \(0.646303\pi\)
\(228\) 68736.0i 0.0875683i
\(229\) 909796.i 1.14645i 0.819398 + 0.573225i \(0.194308\pi\)
−0.819398 + 0.573225i \(0.805692\pi\)
\(230\) −572288. −0.713337
\(231\) −127920. −0.157728
\(232\) 108160.i 0.131931i
\(233\) 266154. 0.321176 0.160588 0.987022i \(-0.448661\pi\)
0.160588 + 0.987022i \(0.448661\pi\)
\(234\) −306904. 460356.i −0.366406 0.549609i
\(235\) 1.71074e6 2.02076
\(236\) 340576.i 0.398047i
\(237\) −181440. −0.209827
\(238\) −570064. −0.652351
\(239\) 254614.i 0.288328i −0.989554 0.144164i \(-0.953951\pi\)
0.989554 0.144164i \(-0.0460494\pi\)
\(240\) 69632.0i 0.0780334i
\(241\) 313600.i 0.347803i −0.984763 0.173902i \(-0.944363\pi\)
0.984763 0.173902i \(-0.0556375\pi\)
\(242\) 35804.0i 0.0393001i
\(243\) 647404. 0.703331
\(244\) 87328.0 0.0939029
\(245\) 685644.i 0.729766i
\(246\) −108160. −0.113954
\(247\) −363012. 544518.i −0.378598 0.567897i
\(248\) −91520.0 −0.0944902
\(249\) 498184.i 0.509204i
\(250\) −442272. −0.447548
\(251\) −1.07127e6 −1.07328 −0.536641 0.843811i \(-0.680307\pi\)
−0.536641 + 0.843811i \(0.680307\pi\)
\(252\) 297824.i 0.295433i
\(253\) 820560.i 0.805952i
\(254\) 1.24173e6i 1.20765i
\(255\) 472736.i 0.455269i
\(256\) 65536.0 0.0625000
\(257\) −188382. −0.177913 −0.0889563 0.996036i \(-0.528353\pi\)
−0.0889563 + 0.996036i \(0.528353\pi\)
\(258\) 270656.i 0.253144i
\(259\) −725864. −0.672366
\(260\) −367744. 551616.i −0.337374 0.506062i
\(261\) 383630. 0.348587
\(262\) 1.24149e6i 1.11735i
\(263\) −1.48678e6 −1.32543 −0.662714 0.748873i \(-0.730596\pi\)
−0.662714 + 0.748873i \(0.730596\pi\)
\(264\) 99840.0 0.0881647
\(265\) 2.59855e6i 2.27309i
\(266\) 352272.i 0.305263i
\(267\) 74976.0i 0.0643642i
\(268\) 712672.i 0.606112i
\(269\) 743990. 0.626883 0.313441 0.949608i \(-0.398518\pi\)
0.313441 + 0.949608i \(0.398518\pi\)
\(270\) 511360. 0.426891
\(271\) 455590.i 0.376835i −0.982089 0.188417i \(-0.939664\pi\)
0.982089 0.188417i \(-0.0603358\pi\)
\(272\) 444928. 0.364643
\(273\) 110864. + 166296.i 0.0900293 + 0.135044i
\(274\) −1.12413e6 −0.904564
\(275\) 584610.i 0.466159i
\(276\) −134656. −0.106403
\(277\) 460198. 0.360367 0.180184 0.983633i \(-0.442331\pi\)
0.180184 + 0.983633i \(0.442331\pi\)
\(278\) 1.45528e6i 1.12937i
\(279\) 324610.i 0.249661i
\(280\) 356864.i 0.272024i
\(281\) 49240.0i 0.0372008i −0.999827 0.0186004i \(-0.994079\pi\)
0.999827 0.0186004i \(-0.00592103\pi\)
\(282\) 402528. 0.301421
\(283\) −544196. −0.403914 −0.201957 0.979394i \(-0.564730\pi\)
−0.201957 + 0.979394i \(0.564730\pi\)
\(284\) 284640.i 0.209411i
\(285\) 292128. 0.213040
\(286\) −790920. + 527280.i −0.571765 + 0.381177i
\(287\) −554320. −0.397243
\(288\) 232448.i 0.165137i
\(289\) 1.60079e6 1.12743
\(290\) 459680. 0.320967
\(291\) 485952.i 0.336404i
\(292\) 497024.i 0.341130i
\(293\) 1.02504e6i 0.697542i −0.937208 0.348771i \(-0.886599\pi\)
0.937208 0.348771i \(-0.113401\pi\)
\(294\) 161328.i 0.108853i
\(295\) −1.44745e6 −0.968385
\(296\) 566528. 0.375831
\(297\) 733200.i 0.482316i
\(298\) 1.09682e6 0.715473
\(299\) 1.06673e6 711152.i 0.690042 0.460028i
\(300\) 95936.0 0.0615430
\(301\) 1.38711e6i 0.882461i
\(302\) 1.37612e6 0.868238
\(303\) −56872.0 −0.0355870
\(304\) 274944.i 0.170632i
\(305\) 371144.i 0.228451i
\(306\) 1.57810e6i 0.963456i
\(307\) 1.57766e6i 0.955362i 0.878533 + 0.477681i \(0.158523\pi\)
−0.878533 + 0.477681i \(0.841477\pi\)
\(308\) 511680. 0.307342
\(309\) −251104. −0.149609
\(310\) 388960.i 0.229880i
\(311\) −330088. −0.193521 −0.0967606 0.995308i \(-0.530848\pi\)
−0.0967606 + 0.995308i \(0.530848\pi\)
\(312\) −86528.0 129792.i −0.0503234 0.0754851i
\(313\) −1.78677e6 −1.03088 −0.515438 0.856927i \(-0.672371\pi\)
−0.515438 + 0.856927i \(0.672371\pi\)
\(314\) 82072.0i 0.0469754i
\(315\) 1.26575e6 0.718741
\(316\) 725760. 0.408861
\(317\) 182148.i 0.101807i −0.998704 0.0509033i \(-0.983790\pi\)
0.998704 0.0509033i \(-0.0162100\pi\)
\(318\) 611424.i 0.339059i
\(319\) 659100.i 0.362639i
\(320\) 278528.i 0.152053i
\(321\) −317008. −0.171715
\(322\) −690112. −0.370920
\(323\) 1.86661e6i 0.995515i
\(324\) −762256. −0.403402
\(325\) −759993. + 506662.i −0.399118 + 0.266079i
\(326\) 146504. 0.0763494
\(327\) 872336.i 0.451143i
\(328\) 432640. 0.222046
\(329\) 2.06296e6 1.05075
\(330\) 424320.i 0.214491i
\(331\) 216230.i 0.108479i 0.998528 + 0.0542395i \(0.0172735\pi\)
−0.998528 + 0.0542395i \(0.982727\pi\)
\(332\) 1.99274e6i 0.992212i
\(333\) 2.00940e6i 0.993017i
\(334\) −1.07777e6 −0.528639
\(335\) −3.02886e6 −1.47457
\(336\) 83968.0i 0.0405757i
\(337\) −2.05314e6 −0.984791 −0.492396 0.870371i \(-0.663879\pi\)
−0.492396 + 0.870371i \(0.663879\pi\)
\(338\) 1.37093e6 + 571220.i 0.652714 + 0.271964i
\(339\) 176936. 0.0836213
\(340\) 1.89094e6i 0.887118i
\(341\) 557700. 0.259726
\(342\) −975192. −0.450843
\(343\) 2.20498e6i 1.01197i
\(344\) 1.08262e6i 0.493266i
\(345\) 572288.i 0.258861i
\(346\) 1.13062e6i 0.507721i
\(347\) 4.28819e6 1.91183 0.955917 0.293637i \(-0.0948658\pi\)
0.955917 + 0.293637i \(0.0948658\pi\)
\(348\) 108160. 0.0478761
\(349\) 3.55152e6i 1.56081i 0.625274 + 0.780405i \(0.284987\pi\)
−0.625274 + 0.780405i \(0.715013\pi\)
\(350\) 491672. 0.214539
\(351\) −953160. + 635440.i −0.412951 + 0.275300i
\(352\) −399360. −0.171794
\(353\) 2.08678e6i 0.891335i 0.895199 + 0.445667i \(0.147034\pi\)
−0.895199 + 0.445667i \(0.852966\pi\)
\(354\) −340576. −0.144446
\(355\) 1.20972e6 0.509465
\(356\) 299904.i 0.125417i
\(357\) 570064.i 0.236730i
\(358\) 1.33512e6i 0.550570i
\(359\) 500654.i 0.205023i −0.994732 0.102511i \(-0.967312\pi\)
0.994732 0.102511i \(-0.0326878\pi\)
\(360\) −987904. −0.401752
\(361\) 1.32262e6 0.534156
\(362\) 1.83975e6i 0.737884i
\(363\) 35804.0 0.0142615
\(364\) −443456. 665184.i −0.175427 0.263141i
\(365\) −2.11235e6 −0.829916
\(366\) 87328.0i 0.0340762i
\(367\) −1.28027e6 −0.496178 −0.248089 0.968737i \(-0.579802\pi\)
−0.248089 + 0.968737i \(0.579802\pi\)
\(368\) 538624. 0.207332
\(369\) 1.53452e6i 0.586687i
\(370\) 2.40774e6i 0.914336i
\(371\) 3.13355e6i 1.18196i
\(372\) 91520.0i 0.0342893i
\(373\) −405666. −0.150972 −0.0754860 0.997147i \(-0.524051\pi\)
−0.0754860 + 0.997147i \(0.524051\pi\)
\(374\) −2.71128e6 −1.00229
\(375\) 442272.i 0.162409i
\(376\) −1.61011e6 −0.587336
\(377\) −856830. + 571220.i −0.310485 + 0.206990i
\(378\) 616640. 0.221974
\(379\) 4.66217e6i 1.66721i 0.552363 + 0.833604i \(0.313726\pi\)
−0.552363 + 0.833604i \(0.686274\pi\)
\(380\) −1.16851e6 −0.415121
\(381\) −1.24173e6 −0.438242
\(382\) 3.66835e6i 1.28621i
\(383\) 4.35473e6i 1.51692i −0.651717 0.758462i \(-0.725951\pi\)
0.651717 0.758462i \(-0.274049\pi\)
\(384\) 65536.0i 0.0226805i
\(385\) 2.17464e6i 0.747714i
\(386\) 2.55622e6 0.873234
\(387\) 3.83993e6 1.30331
\(388\) 1.94381e6i 0.655502i
\(389\) 786990. 0.263691 0.131845 0.991270i \(-0.457910\pi\)
0.131845 + 0.991270i \(0.457910\pi\)
\(390\) −551616. + 367744.i −0.183643 + 0.122429i
\(391\) 3.65675e6 1.20963
\(392\) 645312.i 0.212107i
\(393\) 1.24149e6 0.405472
\(394\) −1.43317e6 −0.465111
\(395\) 3.08448e6i 0.994693i
\(396\) 1.41648e6i 0.453913i
\(397\) 3.97023e6i 1.26427i −0.774859 0.632134i \(-0.782179\pi\)
0.774859 0.632134i \(-0.217821\pi\)
\(398\) 1.48176e6i 0.468889i
\(399\) 352272. 0.110776
\(400\) −383744. −0.119920
\(401\) 344640.i 0.107030i −0.998567 0.0535149i \(-0.982958\pi\)
0.998567 0.0535149i \(-0.0170425\pi\)
\(402\) −712672. −0.219950
\(403\) −483340. 725010.i −0.148248 0.222373i
\(404\) 227488. 0.0693434
\(405\) 3.23959e6i 0.981414i
\(406\) 554320. 0.166896
\(407\) −3.45228e6 −1.03305
\(408\) 444928.i 0.132324i
\(409\) 2.55466e6i 0.755137i −0.925982 0.377568i \(-0.876760\pi\)
0.925982 0.377568i \(-0.123240\pi\)
\(410\) 1.83872e6i 0.540202i
\(411\) 1.12413e6i 0.328255i
\(412\) 1.00442e6 0.291521
\(413\) −1.74545e6 −0.503539
\(414\) 1.91043e6i 0.547811i
\(415\) 8.46913e6 2.41390
\(416\) 346112. + 519168.i 0.0980581 + 0.147087i
\(417\) 1.45528e6 0.409833
\(418\) 1.67544e6i 0.469017i
\(419\) −2.51894e6 −0.700943 −0.350472 0.936573i \(-0.613979\pi\)
−0.350472 + 0.936573i \(0.613979\pi\)
\(420\) 356864. 0.0987142
\(421\) 4.83670e6i 1.32998i −0.746854 0.664988i \(-0.768437\pi\)
0.746854 0.664988i \(-0.231563\pi\)
\(422\) 708912.i 0.193781i
\(423\) 5.71087e6i 1.55185i
\(424\) 2.44570e6i 0.660675i
\(425\) −2.60526e6 −0.699647
\(426\) 284640. 0.0759927
\(427\) 447556.i 0.118789i
\(428\) 1.26803e6 0.334596
\(429\) 527280. + 790920.i 0.138324 + 0.207486i
\(430\) 4.60115e6 1.20004
\(431\) 219110.i 0.0568158i −0.999596 0.0284079i \(-0.990956\pi\)
0.999596 0.0284079i \(-0.00904373\pi\)
\(432\) −481280. −0.124076
\(433\) −3.03477e6 −0.777867 −0.388934 0.921266i \(-0.627156\pi\)
−0.388934 + 0.921266i \(0.627156\pi\)
\(434\) 469040.i 0.119532i
\(435\) 459680.i 0.116475i
\(436\) 3.48934e6i 0.879078i
\(437\) 2.25970e6i 0.566039i
\(438\) −497024. −0.123792
\(439\) 4.16940e6 1.03255 0.516276 0.856422i \(-0.327318\pi\)
0.516276 + 0.856422i \(0.327318\pi\)
\(440\) 1.69728e6i 0.417948i
\(441\) −2.28884e6 −0.560427
\(442\) 2.34978e6 + 3.52466e6i 0.572098 + 0.858148i
\(443\) −6.30548e6 −1.52654 −0.763271 0.646079i \(-0.776408\pi\)
−0.763271 + 0.646079i \(0.776408\pi\)
\(444\) 566528.i 0.136384i
\(445\) 1.27459e6 0.305120
\(446\) 4.45186e6 1.05975
\(447\) 1.09682e6i 0.259636i
\(448\) 335872.i 0.0790640i
\(449\) 7.41586e6i 1.73598i 0.496579 + 0.867991i \(0.334589\pi\)
−0.496579 + 0.867991i \(0.665411\pi\)
\(450\) 1.36109e6i 0.316852i
\(451\) −2.63640e6 −0.610337
\(452\) −707744. −0.162941
\(453\) 1.37612e6i 0.315073i
\(454\) −5.56633e6 −1.26745
\(455\) −2.82703e6 + 1.88469e6i −0.640180 + 0.426787i
\(456\) −274944. −0.0619202
\(457\) 4.71529e6i 1.05613i −0.849204 0.528065i \(-0.822918\pi\)
0.849204 0.528065i \(-0.177082\pi\)
\(458\) −3.63918e6 −0.810663
\(459\) −3.26744e6 −0.723896
\(460\) 2.28915e6i 0.504406i
\(461\) 3.34566e6i 0.733212i 0.930376 + 0.366606i \(0.119480\pi\)
−0.930376 + 0.366606i \(0.880520\pi\)
\(462\) 511680.i 0.111530i
\(463\) 1.65791e6i 0.359426i 0.983719 + 0.179713i \(0.0575169\pi\)
−0.983719 + 0.179713i \(0.942483\pi\)
\(464\) −432640. −0.0932893
\(465\) 388960. 0.0834205
\(466\) 1.06462e6i 0.227106i
\(467\) 823668. 0.174767 0.0873836 0.996175i \(-0.472149\pi\)
0.0873836 + 0.996175i \(0.472149\pi\)
\(468\) 1.84142e6 1.22762e6i 0.388633 0.259088i
\(469\) −3.65244e6 −0.766746
\(470\) 6.84298e6i 1.42890i
\(471\) 82072.0 0.0170468
\(472\) 1.36230e6 0.281462
\(473\) 6.59724e6i 1.35584i
\(474\) 725760.i 0.148370i
\(475\) 1.60993e6i 0.327395i
\(476\) 2.28026e6i 0.461282i
\(477\) −8.67458e6 −1.74563
\(478\) 1.01846e6 0.203879
\(479\) 3.59011e6i 0.714938i 0.933925 + 0.357469i \(0.116360\pi\)
−0.933925 + 0.357469i \(0.883640\pi\)
\(480\) −278528. −0.0551780
\(481\) 2.99198e6 + 4.48796e6i 0.589652 + 0.884477i
\(482\) 1.25440e6 0.245934
\(483\) 690112.i 0.134602i
\(484\) −143216. −0.0277893
\(485\) 8.26118e6 1.59473
\(486\) 2.58962e6i 0.497330i
\(487\) 9.67688e6i 1.84890i −0.381306 0.924449i \(-0.624526\pi\)
0.381306 0.924449i \(-0.375474\pi\)
\(488\) 349312.i 0.0663994i
\(489\) 146504.i 0.0277062i
\(490\) −2.74258e6 −0.516022
\(491\) 3.45633e6 0.647011 0.323506 0.946226i \(-0.395139\pi\)
0.323506 + 0.946226i \(0.395139\pi\)
\(492\) 432640.i 0.0805775i
\(493\) −2.93722e6 −0.544276
\(494\) 2.17807e6 1.45205e6i 0.401564 0.267709i
\(495\) 6.02004e6 1.10430
\(496\) 366080.i 0.0668147i
\(497\) 1.45878e6 0.264910
\(498\) 1.99274e6 0.360061
\(499\) 2.09109e6i 0.375942i 0.982175 + 0.187971i \(0.0601911\pi\)
−0.982175 + 0.187971i \(0.939809\pi\)
\(500\) 1.76909e6i 0.316464i
\(501\) 1.07777e6i 0.191836i
\(502\) 4.28507e6i 0.758925i
\(503\) 5.58626e6 0.984468 0.492234 0.870463i \(-0.336180\pi\)
0.492234 + 0.870463i \(0.336180\pi\)
\(504\) −1.19130e6 −0.208902
\(505\) 966824.i 0.168702i
\(506\) −3.28224e6 −0.569894
\(507\) 571220. 1.37093e6i 0.0986924 0.236862i
\(508\) 4.96691e6 0.853940
\(509\) 4.15504e6i 0.710854i 0.934704 + 0.355427i \(0.115665\pi\)
−0.934704 + 0.355427i \(0.884335\pi\)
\(510\) −1.89094e6 −0.321924
\(511\) −2.54725e6 −0.431538
\(512\) 262144.i 0.0441942i
\(513\) 2.01912e6i 0.338742i
\(514\) 753528.i 0.125803i
\(515\) 4.26877e6i 0.709226i
\(516\) 1.08262e6 0.179000
\(517\) 9.81162e6 1.61441
\(518\) 2.90346e6i 0.475435i
\(519\) 1.13062e6 0.184245
\(520\) 2.20646e6 1.47098e6i 0.357840 0.238560i
\(521\) −9.84416e6 −1.58886 −0.794428 0.607359i \(-0.792229\pi\)
−0.794428 + 0.607359i \(0.792229\pi\)
\(522\) 1.53452e6i 0.246488i
\(523\) 481324. 0.0769455 0.0384728 0.999260i \(-0.487751\pi\)
0.0384728 + 0.999260i \(0.487751\pi\)
\(524\) −4.96595e6 −0.790086
\(525\) 491672.i 0.0778533i
\(526\) 5.94710e6i 0.937219i
\(527\) 2.48534e6i 0.389816i
\(528\) 399360.i 0.0623419i
\(529\) −2.00953e6 −0.312216
\(530\) −1.03942e7 −1.60732
\(531\) 4.83192e6i 0.743676i
\(532\) −1.40909e6 −0.215853
\(533\) 2.28488e6 + 3.42732e6i 0.348374 + 0.522561i
\(534\) 299904. 0.0455123
\(535\) 5.38914e6i 0.814019i
\(536\) 2.85069e6 0.428586
\(537\) 1.33512e6 0.199795
\(538\) 2.97596e6i 0.443273i
\(539\) 3.93237e6i 0.583019i
\(540\) 2.04544e6i 0.301858i
\(541\) 263980.i 0.0387773i 0.999812 + 0.0193887i \(0.00617199\pi\)
−0.999812 + 0.0193887i \(0.993828\pi\)
\(542\) 1.82236e6 0.266462
\(543\) −1.83975e6 −0.267769
\(544\) 1.77971e6i 0.257841i
\(545\) 1.48297e7 2.13866
\(546\) −665184. + 443456.i −0.0954905 + 0.0636603i
\(547\) 2.80023e6 0.400152 0.200076 0.979780i \(-0.435881\pi\)
0.200076 + 0.979780i \(0.435881\pi\)
\(548\) 4.49651e6i 0.639623i
\(549\) 1.23897e6 0.175440
\(550\) 2.33844e6 0.329625
\(551\) 1.81506e6i 0.254690i
\(552\) 538624.i 0.0752381i
\(553\) 3.71952e6i 0.517219i
\(554\) 1.84079e6i 0.254818i
\(555\) −2.40774e6 −0.331801
\(556\) −5.82112e6 −0.798582
\(557\) 2.70983e6i 0.370087i −0.982730 0.185043i \(-0.940757\pi\)
0.982730 0.185043i \(-0.0592426\pi\)
\(558\) −1.29844e6 −0.176537
\(559\) −8.57641e6 + 5.71761e6i −1.16085 + 0.773900i
\(560\) −1.42746e6 −0.192350
\(561\) 2.71128e6i 0.363720i
\(562\) 196960. 0.0263049
\(563\) −1.14870e7 −1.52733 −0.763667 0.645610i \(-0.776603\pi\)
−0.763667 + 0.645610i \(0.776603\pi\)
\(564\) 1.61011e6i 0.213137i
\(565\) 3.00791e6i 0.396409i
\(566\) 2.17678e6i 0.285611i
\(567\) 3.90656e6i 0.510314i
\(568\) −1.13856e6 −0.148076
\(569\) 7.85065e6 1.01654 0.508271 0.861197i \(-0.330285\pi\)
0.508271 + 0.861197i \(0.330285\pi\)
\(570\) 1.16851e6i 0.150642i
\(571\) −6.34071e6 −0.813856 −0.406928 0.913460i \(-0.633400\pi\)
−0.406928 + 0.913460i \(0.633400\pi\)
\(572\) −2.10912e6 3.16368e6i −0.269533 0.404299i
\(573\) −3.66835e6 −0.466750
\(574\) 2.21728e6i 0.280893i
\(575\) −3.15390e6 −0.397812
\(576\) 929792. 0.116770
\(577\) 7.20867e6i 0.901396i 0.892676 + 0.450698i \(0.148825\pi\)
−0.892676 + 0.450698i \(0.851175\pi\)
\(578\) 6.40315e6i 0.797212i
\(579\) 2.55622e6i 0.316886i
\(580\) 1.83872e6i 0.226958i
\(581\) 1.02128e7 1.25517
\(582\) 1.94381e6 0.237873
\(583\) 1.49035e7i 1.81600i
\(584\) 1.98810e6 0.241216
\(585\) −5.21737e6 7.82605e6i −0.630321 0.945482i
\(586\) 4.10014e6 0.493236
\(587\) 2.48138e6i 0.297234i 0.988895 + 0.148617i \(0.0474821\pi\)
−0.988895 + 0.148617i \(0.952518\pi\)
\(588\) −645312. −0.0769709
\(589\) −1.53582e6 −0.182411
\(590\) 5.78979e6i 0.684751i
\(591\) 1.43317e6i 0.168783i
\(592\) 2.26611e6i 0.265752i
\(593\) 1.38811e7i 1.62102i 0.585728 + 0.810508i \(0.300809\pi\)
−0.585728 + 0.810508i \(0.699191\pi\)
\(594\) 2.93280e6 0.341049
\(595\) −9.69109e6 −1.12223
\(596\) 4.38726e6i 0.505916i
\(597\) 1.48176e6 0.170154
\(598\) 2.84461e6 + 4.26691e6i 0.325289 + 0.487934i
\(599\) 3.85356e6 0.438829 0.219414 0.975632i \(-0.429585\pi\)
0.219414 + 0.975632i \(0.429585\pi\)
\(600\) 383744.i 0.0435175i
\(601\) 1.32728e6 0.149892 0.0749458 0.997188i \(-0.476122\pi\)
0.0749458 + 0.997188i \(0.476122\pi\)
\(602\) 5.54845e6 0.623994
\(603\) 1.01110e7i 1.13241i
\(604\) 5.50448e6i 0.613937i
\(605\) 608668.i 0.0676071i
\(606\) 227488.i 0.0251638i
\(607\) 9.73197e6 1.07208 0.536042 0.844191i \(-0.319919\pi\)
0.536042 + 0.844191i \(0.319919\pi\)
\(608\) 1.09978e6 0.120655
\(609\) 554320.i 0.0605644i
\(610\) 1.48458e6 0.161539
\(611\) −8.50340e6 1.27551e7i −0.921488 1.38223i
\(612\) 6.31242e6 0.681267
\(613\) 1.40465e7i 1.50979i −0.655846 0.754894i \(-0.727688\pi\)
0.655846 0.754894i \(-0.272312\pi\)
\(614\) −6.31065e6 −0.675543
\(615\) −1.83872e6 −0.196032
\(616\) 2.04672e6i 0.217323i
\(617\) 3.72561e6i 0.393989i −0.980405 0.196995i \(-0.936882\pi\)
0.980405 0.196995i \(-0.0631181\pi\)
\(618\) 1.00442e6i 0.105789i
\(619\) 8.96911e6i 0.940855i −0.882439 0.470428i \(-0.844100\pi\)
0.882439 0.470428i \(-0.155900\pi\)
\(620\) −1.55584e6 −0.162550
\(621\) −3.95552e6 −0.411599
\(622\) 1.32035e6i 0.136840i
\(623\) 1.53701e6 0.158656
\(624\) 519168. 346112.i 0.0533761 0.0355840i
\(625\) −1.22030e7 −1.24959
\(626\) 7.14706e6i 0.728940i
\(627\) 1.67544e6 0.170200
\(628\) −328288. −0.0332167
\(629\) 1.53848e7i 1.55047i
\(630\) 5.06301e6i 0.508226i
\(631\) 1.72189e7i 1.72160i −0.508943 0.860800i \(-0.669964\pi\)
0.508943 0.860800i \(-0.330036\pi\)
\(632\) 2.90304e6i 0.289108i
\(633\) −708912. −0.0703207
\(634\) 728592. 0.0719882
\(635\) 2.11094e7i 2.07750i
\(636\) −2.44570e6 −0.239751
\(637\) 5.11208e6 3.40805e6i 0.499171 0.332781i
\(638\) 2.63640e6 0.256425
\(639\) 4.03833e6i 0.391246i
\(640\) 1.11411e6 0.107517
\(641\) 8.51692e6 0.818724 0.409362 0.912372i \(-0.365751\pi\)
0.409362 + 0.912372i \(0.365751\pi\)
\(642\) 1.26803e6i 0.121421i
\(643\) 8.14145e6i 0.776559i 0.921542 + 0.388280i \(0.126931\pi\)
−0.921542 + 0.388280i \(0.873069\pi\)
\(644\) 2.76045e6i 0.262280i
\(645\) 4.60115e6i 0.435479i
\(646\) 7.46645e6 0.703935
\(647\) −2.39391e6 −0.224826 −0.112413 0.993662i \(-0.535858\pi\)
−0.112413 + 0.993662i \(0.535858\pi\)
\(648\) 3.04902e6i 0.285248i
\(649\) −8.30154e6 −0.773654
\(650\) −2.02665e6 3.03997e6i −0.188146 0.282219i
\(651\) 469040. 0.0433768
\(652\) 586016.i 0.0539872i
\(653\) 1.17900e7 1.08201 0.541003 0.841020i \(-0.318045\pi\)
0.541003 + 0.841020i \(0.318045\pi\)
\(654\) 3.48934e6 0.319006
\(655\) 2.11053e7i 1.92215i
\(656\) 1.73056e6i 0.157010i
\(657\) 7.05153e6i 0.637338i
\(658\) 8.25182e6i 0.742994i
\(659\) 4.84562e6 0.434646 0.217323 0.976100i \(-0.430267\pi\)
0.217323 + 0.976100i \(0.430267\pi\)
\(660\) 1.69728e6 0.151668
\(661\) 1.14461e7i 1.01895i 0.860485 + 0.509476i \(0.170161\pi\)
−0.860485 + 0.509476i \(0.829839\pi\)
\(662\) −864920. −0.0767063
\(663\) 3.52466e6 2.34978e6i 0.311411 0.207607i
\(664\) −7.97094e6 −0.701600
\(665\) 5.98862e6i 0.525137i
\(666\) 8.03762e6 0.702169
\(667\) −3.55576e6 −0.309470
\(668\) 4.31107e6i 0.373804i
\(669\) 4.45186e6i 0.384571i
\(670\) 1.21154e7i 1.04268i
\(671\) 2.12862e6i 0.182512i
\(672\) −335872. −0.0286913
\(673\) −5.34001e6 −0.454469 −0.227234 0.973840i \(-0.572968\pi\)
−0.227234 + 0.973840i \(0.572968\pi\)
\(674\) 8.21257e6i 0.696353i
\(675\) 2.81812e6 0.238067
\(676\) −2.28488e6 + 5.48371e6i −0.192308 + 0.461538i
\(677\) −7.06132e6 −0.592126 −0.296063 0.955168i \(-0.595674\pi\)
−0.296063 + 0.955168i \(0.595674\pi\)
\(678\) 707744.i 0.0591292i
\(679\) 9.96202e6 0.829226
\(680\) 7.56378e6 0.627287
\(681\) 5.56633e6i 0.459940i
\(682\) 2.23080e6i 0.183654i
\(683\) 3.50035e6i 0.287117i −0.989642 0.143559i \(-0.954145\pi\)
0.989642 0.143559i \(-0.0458546\pi\)
\(684\) 3.90077e6i 0.318794i
\(685\) −1.91102e7 −1.55610
\(686\) −8.81992e6 −0.715574
\(687\) 3.63918e6i 0.294179i
\(688\) −4.33050e6 −0.348792
\(689\) 1.93745e7 1.29163e7i 1.55483 1.03655i
\(690\) −2.28915e6 −0.183042
\(691\) 302510.i 0.0241015i 0.999927 + 0.0120508i \(0.00383597\pi\)
−0.999927 + 0.0120508i \(0.996164\pi\)
\(692\) −4.52246e6 −0.359013
\(693\) 7.25946e6 0.574211
\(694\) 1.71528e7i 1.35187i
\(695\) 2.47398e7i 1.94282i
\(696\) 432640.i 0.0338535i
\(697\) 1.17489e7i 0.916040i
\(698\) −1.42061e7 −1.10366
\(699\) 1.06462e6 0.0824138
\(700\) 1.96669e6i 0.151702i
\(701\) −1.03212e7 −0.793294 −0.396647 0.917971i \(-0.629826\pi\)
−0.396647 + 0.917971i \(0.629826\pi\)
\(702\) −2.54176e6 3.81264e6i −0.194667 0.292000i
\(703\) 9.50705e6 0.725533
\(704\) 1.59744e6i 0.121477i
\(705\) 6.84298e6 0.518528
\(706\) −8.34714e6 −0.630269
\(707\) 1.16588e6i 0.0877211i
\(708\) 1.36230e6i 0.102139i
\(709\) 5.27524e6i 0.394118i 0.980392 + 0.197059i \(0.0631391\pi\)
−0.980392 + 0.197059i \(0.936861\pi\)
\(710\) 4.83888e6i 0.360246i
\(711\) 1.02967e7 0.763880
\(712\) −1.19962e6 −0.0886834
\(713\) 3.00872e6i 0.221645i
\(714\) −2.28026e6 −0.167393
\(715\) −1.34456e7 + 8.96376e6i −0.983595 + 0.655730i
\(716\) −5.34048e6 −0.389312
\(717\) 1.01846e6i 0.0739851i
\(718\) 2.00262e6 0.144973
\(719\) −5.02216e6 −0.362300 −0.181150 0.983455i \(-0.557982\pi\)
−0.181150 + 0.983455i \(0.557982\pi\)
\(720\) 3.95162e6i 0.284082i
\(721\) 5.14763e6i 0.368782i
\(722\) 5.29049e6i 0.377705i
\(723\) 1.25440e6i 0.0892463i
\(724\) 7.35901e6 0.521762
\(725\) 2.53331e6 0.178996
\(726\) 143216.i 0.0100844i
\(727\) 8.80441e6 0.617823 0.308912 0.951091i \(-0.400035\pi\)
0.308912 + 0.951091i \(0.400035\pi\)
\(728\) 2.66074e6 1.77382e6i 0.186069 0.124046i
\(729\) −8.98715e6 −0.626330
\(730\) 8.44941e6i 0.586839i
\(731\) −2.94000e7 −2.03495
\(732\) 349312. 0.0240955
\(733\) 3.05052e6i 0.209708i 0.994488 + 0.104854i \(0.0334375\pi\)
−0.994488 + 0.104854i \(0.966563\pi\)
\(734\) 5.12109e6i 0.350850i
\(735\) 2.74258e6i 0.187258i
\(736\) 2.15450e6i 0.146606i
\(737\) −1.73714e7 −1.17806
\(738\) 6.13808e6 0.414851
\(739\) 7.62605e6i 0.513675i 0.966455 + 0.256837i \(0.0826805\pi\)
−0.966455 + 0.256837i \(0.917320\pi\)
\(740\) 9.63098e6 0.646533
\(741\) −1.45205e6 2.17807e6i −0.0971484 0.145723i
\(742\) −1.25342e7 −0.835770
\(743\) 2.18236e7i 1.45029i −0.688595 0.725146i \(-0.741772\pi\)
0.688595 0.725146i \(-0.258228\pi\)
\(744\) −366080. −0.0242462
\(745\) 1.86459e7 1.23081
\(746\) 1.62266e6i 0.106753i
\(747\) 2.82719e7i 1.85376i
\(748\) 1.08451e7i 0.708729i
\(749\) 6.49866e6i 0.423272i
\(750\) −1.76909e6 −0.114841
\(751\) 1.69030e7 1.09361 0.546807 0.837259i \(-0.315843\pi\)
0.546807 + 0.837259i \(0.315843\pi\)
\(752\) 6.44045e6i 0.415309i
\(753\) −4.28507e6 −0.275404
\(754\) −2.28488e6 3.42732e6i −0.146364 0.219546i
\(755\) 2.33940e7 1.49361
\(756\) 2.46656e6i 0.156959i
\(757\) −8.90252e6 −0.564642 −0.282321 0.959320i \(-0.591104\pi\)
−0.282321 + 0.959320i \(0.591104\pi\)
\(758\) −1.86487e7 −1.17889
\(759\) 3.28224e6i 0.206807i
\(760\) 4.67405e6i 0.293535i
\(761\) 6.98052e6i 0.436944i −0.975843 0.218472i \(-0.929893\pi\)
0.975843 0.218472i \(-0.0701073\pi\)
\(762\) 4.96691e6i 0.309884i
\(763\) 1.78829e7 1.11206
\(764\) 1.46734e7 0.909489
\(765\) 2.68278e7i 1.65741i
\(766\) 1.74189e7 1.07263
\(767\) 7.19467e6 + 1.07920e7i 0.441593 + 0.662390i
\(768\) 262144. 0.0160375
\(769\) 2.67789e7i 1.63296i −0.577372 0.816481i \(-0.695922\pi\)
0.577372 0.816481i \(-0.304078\pi\)
\(770\) 8.69856e6 0.528714
\(771\) −753528. −0.0456524
\(772\) 1.02249e7i 0.617470i
\(773\) 710244.i 0.0427522i 0.999772 + 0.0213761i \(0.00680475\pi\)
−0.999772 + 0.0213761i \(0.993195\pi\)
\(774\) 1.53597e7i 0.921576i
\(775\) 2.14357e6i 0.128199i
\(776\) −7.77523e6