Properties

Label 6.7.b.a.5.2
Level $6$
Weight $7$
Character 6.5
Analytic conductor $1.380$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6,7,Mod(5,6)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6.5");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 6.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: \(1.38032450172\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-2}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.2
Root \(1.41421i\) of defining polynomial
Character \(\chi\) \(=\) 6.5
Dual form 6.7.b.a.5.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+5.65685i q^{2} +(21.0000 + 16.9706i) q^{3} -32.0000 q^{4} -169.706i q^{5} +(-96.0000 + 118.794i) q^{6} +2.00000 q^{7} -181.019i q^{8} +(153.000 + 712.764i) q^{9} +O(q^{10})\) \(q+5.65685i q^{2} +(21.0000 + 16.9706i) q^{3} -32.0000 q^{4} -169.706i q^{5} +(-96.0000 + 118.794i) q^{6} +2.00000 q^{7} -181.019i q^{8} +(153.000 + 712.764i) q^{9} +960.000 q^{10} -33.9411i q^{11} +(-672.000 - 543.058i) q^{12} -2950.00 q^{13} +11.3137i q^{14} +(2880.00 - 3563.82i) q^{15} +1024.00 q^{16} +4480.23i q^{17} +(-4032.00 + 865.499i) q^{18} +5258.00 q^{19} +5430.58i q^{20} +(42.0000 + 33.9411i) q^{21} +192.000 q^{22} -10250.2i q^{23} +(3072.00 - 3801.41i) q^{24} -13175.0 q^{25} -16687.7i q^{26} +(-8883.00 + 17564.5i) q^{27} -64.0000 q^{28} +2206.17i q^{29} +(20160.0 + 16291.7i) q^{30} +22898.0 q^{31} +5792.62i q^{32} +(576.000 - 712.764i) q^{33} -25344.0 q^{34} -339.411i q^{35} +(-4896.00 - 22808.4i) q^{36} +34058.0 q^{37} +29743.7i q^{38} +(-61950.0 - 50063.2i) q^{39} -30720.0 q^{40} -16766.9i q^{41} +(-192.000 + 237.588i) q^{42} -6406.00 q^{43} +1086.12i q^{44} +(120960. - 25965.0i) q^{45} +57984.0 q^{46} +179888. i q^{47} +(21504.0 + 17377.9i) q^{48} -117645. q^{49} -74529.1i q^{50} +(-76032.0 + 94084.8i) q^{51} +94400.0 q^{52} -192548. i q^{53} +(-99360.0 - 50249.8i) q^{54} -5760.00 q^{55} -362.039i q^{56} +(110418. + 89231.2i) q^{57} -12480.0 q^{58} -326819. i q^{59} +(-92160.0 + 114042. i) q^{60} -62566.0 q^{61} +129531. i q^{62} +(306.000 + 1425.53i) q^{63} -32768.0 q^{64} +500632. i q^{65} +(4032.00 + 3258.35i) q^{66} +438698. q^{67} -143367. i q^{68} +(173952. - 215255. i) q^{69} +1920.00 q^{70} -68221.7i q^{71} +(129024. - 27696.0i) q^{72} -730510. q^{73} +192661. i q^{74} +(-276675. - 223587. i) q^{75} -168256. q^{76} -67.8823i q^{77} +(283200. - 350442. i) q^{78} +340562. q^{79} -173779. i q^{80} +(-484623. + 218106. i) q^{81} +94848.0 q^{82} +496253. i q^{83} +(-1344.00 - 1086.12i) q^{84} +760320. q^{85} -36237.8i q^{86} +(-37440.0 + 46329.6i) q^{87} -6144.00 q^{88} -386725. i q^{89} +(146880. + 684253. i) q^{90} -5900.00 q^{91} +328007. i q^{92} +(480858. + 388592. i) q^{93} -1.01760e6 q^{94} -892312. i q^{95} +(-98304.0 + 121645. i) q^{96} -281086. q^{97} -665501. i q^{98} +(24192.0 - 5192.99i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 42 q^{3} - 64 q^{4} - 192 q^{6} + 4 q^{7} + 306 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 42 q^{3} - 64 q^{4} - 192 q^{6} + 4 q^{7} + 306 q^{9} + 1920 q^{10} - 1344 q^{12} - 5900 q^{13} + 5760 q^{15} + 2048 q^{16} - 8064 q^{18} + 10516 q^{19} + 84 q^{21} + 384 q^{22} + 6144 q^{24} - 26350 q^{25} - 17766 q^{27} - 128 q^{28} + 40320 q^{30} + 45796 q^{31} + 1152 q^{33} - 50688 q^{34} - 9792 q^{36} + 68116 q^{37} - 123900 q^{39} - 61440 q^{40} - 384 q^{42} - 12812 q^{43} + 241920 q^{45} + 115968 q^{46} + 43008 q^{48} - 235290 q^{49} - 152064 q^{51} + 188800 q^{52} - 198720 q^{54} - 11520 q^{55} + 220836 q^{57} - 24960 q^{58} - 184320 q^{60} - 125132 q^{61} + 612 q^{63} - 65536 q^{64} + 8064 q^{66} + 877396 q^{67} + 347904 q^{69} + 3840 q^{70} + 258048 q^{72} - 1461020 q^{73} - 553350 q^{75} - 336512 q^{76} + 566400 q^{78} + 681124 q^{79} - 969246 q^{81} + 189696 q^{82} - 2688 q^{84} + 1520640 q^{85} - 74880 q^{87} - 12288 q^{88} + 293760 q^{90} - 11800 q^{91} + 961716 q^{93} - 2035200 q^{94} - 196608 q^{96} - 562172 q^{97} + 48384 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.65685i 0.707107i
\(3\) 21.0000 + 16.9706i 0.777778 + 0.628539i
\(4\) −32.0000 −0.500000
\(5\) 169.706i 1.35765i −0.734302 0.678823i \(-0.762491\pi\)
0.734302 0.678823i \(-0.237509\pi\)
\(6\) −96.0000 + 118.794i −0.444444 + 0.549972i
\(7\) 2.00000 0.00583090 0.00291545 0.999996i \(-0.499072\pi\)
0.00291545 + 0.999996i \(0.499072\pi\)
\(8\) 181.019i 0.353553i
\(9\) 153.000 + 712.764i 0.209877 + 0.977728i
\(10\) 960.000 0.960000
\(11\) 33.9411i 0.0255005i −0.999919 0.0127502i \(-0.995941\pi\)
0.999919 0.0127502i \(-0.00405864\pi\)
\(12\) −672.000 543.058i −0.388889 0.314270i
\(13\) −2950.00 −1.34274 −0.671370 0.741122i \(-0.734294\pi\)
−0.671370 + 0.741122i \(0.734294\pi\)
\(14\) 11.3137i 0.00412307i
\(15\) 2880.00 3563.82i 0.853333 1.05595i
\(16\) 1024.00 0.250000
\(17\) 4480.23i 0.911913i 0.890002 + 0.455956i \(0.150703\pi\)
−0.890002 + 0.455956i \(0.849297\pi\)
\(18\) −4032.00 + 865.499i −0.691358 + 0.148405i
\(19\) 5258.00 0.766584 0.383292 0.923627i \(-0.374790\pi\)
0.383292 + 0.923627i \(0.374790\pi\)
\(20\) 5430.58i 0.678823i
\(21\) 42.0000 + 33.9411i 0.00453515 + 0.00366495i
\(22\) 192.000 0.0180316
\(23\) 10250.2i 0.842461i −0.906954 0.421230i \(-0.861598\pi\)
0.906954 0.421230i \(-0.138402\pi\)
\(24\) 3072.00 3801.41i 0.222222 0.274986i
\(25\) −13175.0 −0.843200
\(26\) 16687.7i 0.949461i
\(27\) −8883.00 + 17564.5i −0.451303 + 0.892371i
\(28\) −64.0000 −0.00291545
\(29\) 2206.17i 0.0904577i 0.998977 + 0.0452289i \(0.0144017\pi\)
−0.998977 + 0.0452289i \(0.985598\pi\)
\(30\) 20160.0 + 16291.7i 0.746667 + 0.603398i
\(31\) 22898.0 0.768621 0.384311 0.923204i \(-0.374439\pi\)
0.384311 + 0.923204i \(0.374439\pi\)
\(32\) 5792.62i 0.176777i
\(33\) 576.000 712.764i 0.0160280 0.0198337i
\(34\) −25344.0 −0.644820
\(35\) 339.411i 0.00791630i
\(36\) −4896.00 22808.4i −0.104938 0.488864i
\(37\) 34058.0 0.672379 0.336189 0.941794i \(-0.390862\pi\)
0.336189 + 0.941794i \(0.390862\pi\)
\(38\) 29743.7i 0.542057i
\(39\) −61950.0 50063.2i −1.04435 0.843965i
\(40\) −30720.0 −0.480000
\(41\) 16766.9i 0.243277i −0.992574 0.121639i \(-0.961185\pi\)
0.992574 0.121639i \(-0.0388149\pi\)
\(42\) −192.000 + 237.588i −0.00259151 + 0.00320683i
\(43\) −6406.00 −0.0805715 −0.0402858 0.999188i \(-0.512827\pi\)
−0.0402858 + 0.999188i \(0.512827\pi\)
\(44\) 1086.12i 0.0127502i
\(45\) 120960. 25965.0i 1.32741 0.284938i
\(46\) 57984.0 0.595710
\(47\) 179888.i 1.73264i 0.499489 + 0.866320i \(0.333521\pi\)
−0.499489 + 0.866320i \(0.666479\pi\)
\(48\) 21504.0 + 17377.9i 0.194444 + 0.157135i
\(49\) −117645. −0.999966
\(50\) 74529.1i 0.596232i
\(51\) −76032.0 + 94084.8i −0.573173 + 0.709266i
\(52\) 94400.0 0.671370
\(53\) 192548.i 1.29334i −0.762772 0.646668i \(-0.776162\pi\)
0.762772 0.646668i \(-0.223838\pi\)
\(54\) −99360.0 50249.8i −0.631001 0.319120i
\(55\) −5760.00 −0.0346206
\(56\) 362.039i 0.00206154i
\(57\) 110418. + 89231.2i 0.596232 + 0.481828i
\(58\) −12480.0 −0.0639633
\(59\) 326819.i 1.59130i −0.605758 0.795649i \(-0.707130\pi\)
0.605758 0.795649i \(-0.292870\pi\)
\(60\) −92160.0 + 114042.i −0.426667 + 0.527973i
\(61\) −62566.0 −0.275644 −0.137822 0.990457i \(-0.544010\pi\)
−0.137822 + 0.990457i \(0.544010\pi\)
\(62\) 129531.i 0.543497i
\(63\) 306.000 + 1425.53i 0.00122377 + 0.00570104i
\(64\) −32768.0 −0.125000
\(65\) 500632.i 1.82296i
\(66\) 4032.00 + 3258.35i 0.0140245 + 0.0113335i
\(67\) 438698. 1.45862 0.729308 0.684185i \(-0.239842\pi\)
0.729308 + 0.684185i \(0.239842\pi\)
\(68\) 143367.i 0.455956i
\(69\) 173952. 215255.i 0.529520 0.655247i
\(70\) 1920.00 0.00559767
\(71\) 68221.7i 0.190611i −0.995448 0.0953053i \(-0.969617\pi\)
0.995448 0.0953053i \(-0.0303827\pi\)
\(72\) 129024. 27696.0i 0.345679 0.0742026i
\(73\) −730510. −1.87784 −0.938918 0.344141i \(-0.888170\pi\)
−0.938918 + 0.344141i \(0.888170\pi\)
\(74\) 192661.i 0.475444i
\(75\) −276675. 223587.i −0.655822 0.529984i
\(76\) −168256. −0.383292
\(77\) 67.8823i 0.000148691i
\(78\) 283200. 350442.i 0.596773 0.738469i
\(79\) 340562. 0.690740 0.345370 0.938467i \(-0.387753\pi\)
0.345370 + 0.938467i \(0.387753\pi\)
\(80\) 173779.i 0.339411i
\(81\) −484623. + 218106.i −0.911904 + 0.410404i
\(82\) 94848.0 0.172023
\(83\) 496253.i 0.867899i 0.900937 + 0.433949i \(0.142880\pi\)
−0.900937 + 0.433949i \(0.857120\pi\)
\(84\) −1344.00 1086.12i −0.00226757 0.00183248i
\(85\) 760320. 1.23805
\(86\) 36237.8i 0.0569727i
\(87\) −37440.0 + 46329.6i −0.0568562 + 0.0703560i
\(88\) −6144.00 −0.00901578
\(89\) 386725.i 0.548570i −0.961648 0.274285i \(-0.911559\pi\)
0.961648 0.274285i \(-0.0884412\pi\)
\(90\) 146880. + 684253.i 0.201481 + 0.938619i
\(91\) −5900.00 −0.00782939
\(92\) 328007.i 0.421230i
\(93\) 480858. + 388592.i 0.597817 + 0.483109i
\(94\) −1.01760e6 −1.22516
\(95\) 892312.i 1.04075i
\(96\) −98304.0 + 121645.i −0.111111 + 0.137493i
\(97\) −281086. −0.307981 −0.153991 0.988072i \(-0.549213\pi\)
−0.153991 + 0.988072i \(0.549213\pi\)
\(98\) 665501.i 0.707083i
\(99\) 24192.0 5192.99i 0.0249325 0.00535195i
\(100\) 421600. 0.421600
\(101\) 945362.i 0.917559i −0.888550 0.458780i \(-0.848287\pi\)
0.888550 0.458780i \(-0.151713\pi\)
\(102\) −532224. 430102.i −0.501527 0.405295i
\(103\) −865726. −0.792262 −0.396131 0.918194i \(-0.629647\pi\)
−0.396131 + 0.918194i \(0.629647\pi\)
\(104\) 534007.i 0.474730i
\(105\) 5760.00 7127.64i 0.00497570 0.00615712i
\(106\) 1.08922e6 0.914527
\(107\) 1.47410e6i 1.20330i 0.798759 + 0.601651i \(0.205490\pi\)
−0.798759 + 0.601651i \(0.794510\pi\)
\(108\) 284256. 562065.i 0.225652 0.446185i
\(109\) 650810. 0.502545 0.251272 0.967916i \(-0.419151\pi\)
0.251272 + 0.967916i \(0.419151\pi\)
\(110\) 32583.5i 0.0244805i
\(111\) 715218. + 577983.i 0.522961 + 0.422616i
\(112\) 2048.00 0.00145773
\(113\) 1.74417e6i 1.20879i 0.796683 + 0.604397i \(0.206586\pi\)
−0.796683 + 0.604397i \(0.793414\pi\)
\(114\) −504768. + 624619.i −0.340704 + 0.421600i
\(115\) −1.73952e6 −1.14376
\(116\) 70597.5i 0.0452289i
\(117\) −451350. 2.10265e6i −0.281810 1.31283i
\(118\) 1.84877e6 1.12522
\(119\) 8960.46i 0.00531728i
\(120\) −645120. 521336.i −0.373333 0.301699i
\(121\) 1.77041e6 0.999350
\(122\) 353927.i 0.194910i
\(123\) 284544. 352105.i 0.152909 0.189216i
\(124\) −732736. −0.384311
\(125\) 415779.i 0.212879i
\(126\) −8064.00 + 1731.00i −0.00403124 + 0.000865336i
\(127\) −2.28053e6 −1.11333 −0.556665 0.830737i \(-0.687919\pi\)
−0.556665 + 0.830737i \(0.687919\pi\)
\(128\) 185364.i 0.0883883i
\(129\) −134526. 108713.i −0.0626667 0.0506424i
\(130\) −2.83200e6 −1.28903
\(131\) 1.07196e6i 0.476832i −0.971163 0.238416i \(-0.923372\pi\)
0.971163 0.238416i \(-0.0766282\pi\)
\(132\) −18432.0 + 22808.4i −0.00801402 + 0.00991685i
\(133\) 10516.0 0.00446988
\(134\) 2.48165e6i 1.03140i
\(135\) 2.98080e6 + 1.50750e6i 1.21152 + 0.612709i
\(136\) 811008. 0.322410
\(137\) 2.78338e6i 1.08246i −0.840876 0.541228i \(-0.817960\pi\)
0.840876 0.541228i \(-0.182040\pi\)
\(138\) 1.21766e6 + 984021.i 0.463330 + 0.374427i
\(139\) 4.57395e6 1.70313 0.851563 0.524253i \(-0.175655\pi\)
0.851563 + 0.524253i \(0.175655\pi\)
\(140\) 10861.2i 0.00395815i
\(141\) −3.05280e6 + 3.77765e6i −1.08903 + 1.34761i
\(142\) 385920. 0.134782
\(143\) 100126.i 0.0342405i
\(144\) 156672. + 729870.i 0.0524691 + 0.244432i
\(145\) 374400. 0.122809
\(146\) 4.13239e6i 1.32783i
\(147\) −2.47054e6 1.99650e6i −0.777751 0.628518i
\(148\) −1.08986e6 −0.336189
\(149\) 4.46010e6i 1.34830i 0.738595 + 0.674149i \(0.235489\pi\)
−0.738595 + 0.674149i \(0.764511\pi\)
\(150\) 1.26480e6 1.56511e6i 0.374756 0.463736i
\(151\) −2.20809e6 −0.641338 −0.320669 0.947191i \(-0.603908\pi\)
−0.320669 + 0.947191i \(0.603908\pi\)
\(152\) 951800.i 0.271028i
\(153\) −3.19334e6 + 685475.i −0.891603 + 0.191389i
\(154\) 384.000 0.000105140
\(155\) 3.88592e6i 1.04352i
\(156\) 1.98240e6 + 1.60202e6i 0.522177 + 0.421983i
\(157\) −1.28887e6 −0.333051 −0.166525 0.986037i \(-0.553255\pi\)
−0.166525 + 0.986037i \(0.553255\pi\)
\(158\) 1.92651e6i 0.488427i
\(159\) 3.26765e6 4.04351e6i 0.812913 1.00593i
\(160\) 983040. 0.240000
\(161\) 20500.4i 0.00491231i
\(162\) −1.23379e6 2.74144e6i −0.290200 0.644813i
\(163\) 879914. 0.203178 0.101589 0.994826i \(-0.467607\pi\)
0.101589 + 0.994826i \(0.467607\pi\)
\(164\) 536541.i 0.121639i
\(165\) −120960. 97750.4i −0.0269271 0.0217604i
\(166\) −2.80723e6 −0.613697
\(167\) 5.96760e6i 1.28130i 0.767834 + 0.640649i \(0.221335\pi\)
−0.767834 + 0.640649i \(0.778665\pi\)
\(168\) 6144.00 7602.81i 0.00129576 0.00160342i
\(169\) 3.87569e6 0.802951
\(170\) 4.30102e6i 0.875436i
\(171\) 804474. + 3.74771e6i 0.160888 + 0.749511i
\(172\) 204992. 0.0402858
\(173\) 418867.i 0.0808981i 0.999182 + 0.0404490i \(0.0128788\pi\)
−0.999182 + 0.0404490i \(0.987121\pi\)
\(174\) −262080. 211793.i −0.0497492 0.0402034i
\(175\) −26350.0 −0.00491662
\(176\) 34755.7i 0.00637512i
\(177\) 5.54630e6 6.86320e6i 1.00019 1.23768i
\(178\) 2.18765e6 0.387898
\(179\) 302110.i 0.0526752i 0.999653 + 0.0263376i \(0.00838448\pi\)
−0.999653 + 0.0263376i \(0.991616\pi\)
\(180\) −3.87072e6 + 830879.i −0.663704 + 0.142469i
\(181\) −6.47618e6 −1.09215 −0.546076 0.837735i \(-0.683879\pi\)
−0.546076 + 0.837735i \(0.683879\pi\)
\(182\) 33375.4i 0.00553621i
\(183\) −1.31389e6 1.06178e6i −0.214390 0.173253i
\(184\) −1.85549e6 −0.297855
\(185\) 5.77983e6i 0.912852i
\(186\) −2.19821e6 + 2.72014e6i −0.341610 + 0.422720i
\(187\) 152064. 0.0232542
\(188\) 5.75641e6i 0.866320i
\(189\) −17766.0 + 35129.1i −0.00263151 + 0.00520333i
\(190\) 5.04768e6 0.735921
\(191\) 5.02166e6i 0.720687i −0.932820 0.360344i \(-0.882659\pi\)
0.932820 0.360344i \(-0.117341\pi\)
\(192\) −688128. 556091.i −0.0972222 0.0785674i
\(193\) 3.50093e6 0.486980 0.243490 0.969903i \(-0.421708\pi\)
0.243490 + 0.969903i \(0.421708\pi\)
\(194\) 1.59006e6i 0.217775i
\(195\) −8.49600e6 + 1.05133e7i −1.14580 + 1.41786i
\(196\) 3.76464e6 0.499983
\(197\) 4.85423e6i 0.634923i 0.948271 + 0.317462i \(0.102830\pi\)
−0.948271 + 0.317462i \(0.897170\pi\)
\(198\) 29376.0 + 136851.i 0.00378440 + 0.0176300i
\(199\) −9.50976e6 −1.20673 −0.603365 0.797465i \(-0.706174\pi\)
−0.603365 + 0.797465i \(0.706174\pi\)
\(200\) 2.38493e6i 0.298116i
\(201\) 9.21266e6 + 7.44495e6i 1.13448 + 0.916798i
\(202\) 5.34778e6 0.648812
\(203\) 4412.35i 0.000527450i
\(204\) 2.43302e6 3.01071e6i 0.286587 0.354633i
\(205\) −2.84544e6 −0.330284
\(206\) 4.89729e6i 0.560214i
\(207\) 7.30598e6 1.56828e6i 0.823697 0.176813i
\(208\) −3.02080e6 −0.335685
\(209\) 178462.i 0.0195483i
\(210\) 40320.0 + 32583.5i 0.00435374 + 0.00351835i
\(211\) 7.06414e6 0.751990 0.375995 0.926622i \(-0.377301\pi\)
0.375995 + 0.926622i \(0.377301\pi\)
\(212\) 6.16154e6i 0.646668i
\(213\) 1.15776e6 1.43265e6i 0.119806 0.148253i
\(214\) −8.33875e6 −0.850863
\(215\) 1.08713e6i 0.109388i
\(216\) 3.17952e6 + 1.60799e6i 0.315501 + 0.159560i
\(217\) 45796.0 0.00448176
\(218\) 3.68154e6i 0.355353i
\(219\) −1.53407e7 1.23972e7i −1.46054 1.18029i
\(220\) 184320. 0.0173103
\(221\) 1.32167e7i 1.22446i
\(222\) −3.26957e6 + 4.04588e6i −0.298835 + 0.369789i
\(223\) 4.66891e6 0.421019 0.210509 0.977592i \(-0.432488\pi\)
0.210509 + 0.977592i \(0.432488\pi\)
\(224\) 11585.2i 0.00103077i
\(225\) −2.01578e6 9.39066e6i −0.176968 0.824420i
\(226\) −9.86650e6 −0.854747
\(227\) 1.96525e7i 1.68012i 0.542494 + 0.840059i \(0.317480\pi\)
−0.542494 + 0.840059i \(0.682520\pi\)
\(228\) −3.53338e6 2.85540e6i −0.298116 0.240914i
\(229\) −4.48178e6 −0.373202 −0.186601 0.982436i \(-0.559747\pi\)
−0.186601 + 0.982436i \(0.559747\pi\)
\(230\) 9.84021e6i 0.808762i
\(231\) 1152.00 1425.53i 9.34580e−5 0.000115648i
\(232\) 399360. 0.0319816
\(233\) 2.29286e6i 0.181263i 0.995884 + 0.0906316i \(0.0288886\pi\)
−0.995884 + 0.0906316i \(0.971111\pi\)
\(234\) 1.18944e7 2.55322e6i 0.928314 0.199270i
\(235\) 3.05280e7 2.35231
\(236\) 1.04582e7i 0.795649i
\(237\) 7.15180e6 + 5.77953e6i 0.537243 + 0.434158i
\(238\) −50688.0 −0.00375988
\(239\) 2.64564e6i 0.193793i −0.995294 0.0968964i \(-0.969108\pi\)
0.995294 0.0968964i \(-0.0308915\pi\)
\(240\) 2.94912e6 3.64935e6i 0.213333 0.263987i
\(241\) −6.99581e6 −0.499789 −0.249894 0.968273i \(-0.580396\pi\)
−0.249894 + 0.968273i \(0.580396\pi\)
\(242\) 1.00149e7i 0.706647i
\(243\) −1.38785e7 3.64411e6i −0.967214 0.253964i
\(244\) 2.00211e6 0.137822
\(245\) 1.99650e7i 1.35760i
\(246\) 1.99181e6 + 1.60962e6i 0.133796 + 0.108123i
\(247\) −1.55111e7 −1.02932
\(248\) 4.14498e6i 0.271749i
\(249\) −8.42170e6 + 1.04213e7i −0.545508 + 0.675032i
\(250\) 2.35200e6 0.150528
\(251\) 2.84990e7i 1.80223i −0.433585 0.901113i \(-0.642752\pi\)
0.433585 0.901113i \(-0.357248\pi\)
\(252\) −9792.00 45616.9i −0.000611885 0.00285052i
\(253\) −347904. −0.0214831
\(254\) 1.29006e7i 0.787243i
\(255\) 1.59667e7 + 1.29031e7i 0.962931 + 0.778166i
\(256\) 1.04858e6 0.0625000
\(257\) 186812.i 0.0110054i −0.999985 0.00550269i \(-0.998248\pi\)
0.999985 0.00550269i \(-0.00175157\pi\)
\(258\) 614976. 760994.i 0.0358096 0.0443121i
\(259\) 68116.0 0.00392058
\(260\) 1.60202e7i 0.911482i
\(261\) −1.57248e6 + 337544.i −0.0884430 + 0.0189850i
\(262\) 6.06394e6 0.337171
\(263\) 8.61541e6i 0.473597i −0.971559 0.236798i \(-0.923902\pi\)
0.971559 0.236798i \(-0.0760981\pi\)
\(264\) −129024. 104267.i −0.00701227 0.00566677i
\(265\) −3.26765e7 −1.75589
\(266\) 59487.5i 0.00316068i
\(267\) 6.56294e6 8.12123e6i 0.344798 0.426666i
\(268\) −1.40383e7 −0.729308
\(269\) 7.55132e6i 0.387941i −0.981007 0.193971i \(-0.937863\pi\)
0.981007 0.193971i \(-0.0621367\pi\)
\(270\) −8.52768e6 + 1.68620e7i −0.433251 + 0.856676i
\(271\) 1.39445e7 0.700642 0.350321 0.936630i \(-0.386073\pi\)
0.350321 + 0.936630i \(0.386073\pi\)
\(272\) 4.58775e6i 0.227978i
\(273\) −123900. 100126.i −0.00608952 0.00492108i
\(274\) 1.57452e7 0.765412
\(275\) 447174.i 0.0215020i
\(276\) −5.56646e6 + 6.88815e6i −0.264760 + 0.327624i
\(277\) 2.81293e7 1.32349 0.661744 0.749730i \(-0.269817\pi\)
0.661744 + 0.749730i \(0.269817\pi\)
\(278\) 2.58741e7i 1.20429i
\(279\) 3.50339e6 + 1.63209e7i 0.161316 + 0.751503i
\(280\) −61440.0 −0.00279883
\(281\) 2.23430e7i 1.00698i 0.864000 + 0.503491i \(0.167951\pi\)
−0.864000 + 0.503491i \(0.832049\pi\)
\(282\) −2.13696e7 1.72692e7i −0.952904 0.770063i
\(283\) 1.01418e7 0.447464 0.223732 0.974651i \(-0.428176\pi\)
0.223732 + 0.974651i \(0.428176\pi\)
\(284\) 2.18309e6i 0.0953053i
\(285\) 1.51430e7 1.87386e7i 0.654152 0.809471i
\(286\) −566400. −0.0242117
\(287\) 33533.8i 0.00141853i
\(288\) −4.12877e6 + 886271.i −0.172840 + 0.0371013i
\(289\) 4.06512e6 0.168415
\(290\) 2.11793e6i 0.0868394i
\(291\) −5.90281e6 4.77019e6i −0.239541 0.193578i
\(292\) 2.33763e7 0.938918
\(293\) 2.78468e7i 1.10706i −0.832828 0.553532i \(-0.813280\pi\)
0.832828 0.553532i \(-0.186720\pi\)
\(294\) 1.12939e7 1.39755e7i 0.444429 0.549953i
\(295\) −5.54630e7 −2.16042
\(296\) 6.16516e6i 0.237722i
\(297\) 596160. + 301499.i 0.0227559 + 0.0115084i
\(298\) −2.52301e7 −0.953391
\(299\) 3.02381e7i 1.13121i
\(300\) 8.85360e6 + 7.15479e6i 0.327911 + 0.264992i
\(301\) −12812.0 −0.000469805
\(302\) 1.24909e7i 0.453494i
\(303\) 1.60433e7 1.98526e7i 0.576722 0.713657i
\(304\) 5.38419e6 0.191646
\(305\) 1.06178e7i 0.374227i
\(306\) −3.87763e6 1.80643e7i −0.135333 0.630458i
\(307\) −3.63254e7 −1.25544 −0.627718 0.778440i \(-0.716011\pi\)
−0.627718 + 0.778440i \(0.716011\pi\)
\(308\) 2172.23i 7.43454e-5i
\(309\) −1.81802e7 1.46919e7i −0.616204 0.497968i
\(310\) 2.19821e7 0.737877
\(311\) 3.59921e7i 1.19654i 0.801296 + 0.598268i \(0.204144\pi\)
−0.801296 + 0.598268i \(0.795856\pi\)
\(312\) −9.06240e6 + 1.12141e7i −0.298387 + 0.369235i
\(313\) 4.01099e7 1.30803 0.654016 0.756480i \(-0.273083\pi\)
0.654016 + 0.756480i \(0.273083\pi\)
\(314\) 7.29095e6i 0.235502i
\(315\) 241920. 51929.9i 0.00773998 0.00166145i
\(316\) −1.08980e7 −0.345370
\(317\) 3.94377e7i 1.23804i −0.785377 0.619018i \(-0.787531\pi\)
0.785377 0.619018i \(-0.212469\pi\)
\(318\) 2.28735e7 + 1.84846e7i 0.711299 + 0.574816i
\(319\) 74880.0 0.00230671
\(320\) 5.56091e6i 0.169706i
\(321\) −2.50163e7 + 3.09560e7i −0.756323 + 0.935902i
\(322\) 115968. 0.00347353
\(323\) 2.35570e7i 0.699058i
\(324\) 1.55079e7 6.97938e6i 0.455952 0.205202i
\(325\) 3.88662e7 1.13220
\(326\) 4.97755e6i 0.143669i
\(327\) 1.36670e7 + 1.10446e7i 0.390868 + 0.315869i
\(328\) −3.03514e6 −0.0860115
\(329\) 359776.i 0.0101029i
\(330\) 552960. 684253.i 0.0153869 0.0190404i
\(331\) 2.78363e7 0.767586 0.383793 0.923419i \(-0.374618\pi\)
0.383793 + 0.923419i \(0.374618\pi\)
\(332\) 1.58801e7i 0.433949i
\(333\) 5.21087e6 + 2.42753e7i 0.141117 + 0.657403i
\(334\) −3.37578e7 −0.906014
\(335\) 7.44495e7i 1.98028i
\(336\) 43008.0 + 34755.7i 0.00113379 + 0.000916238i
\(337\) −2.37897e7 −0.621582 −0.310791 0.950478i \(-0.600594\pi\)
−0.310791 + 0.950478i \(0.600594\pi\)
\(338\) 2.19242e7i 0.567772i
\(339\) −2.95995e7 + 3.66275e7i −0.759775 + 0.940174i
\(340\) −2.43302e7 −0.619027
\(341\) 777184.i 0.0196002i
\(342\) −2.12003e7 + 4.55079e6i −0.529984 + 0.113765i
\(343\) −470588. −0.0116616
\(344\) 1.15961e6i 0.0284863i
\(345\) −3.65299e7 2.95206e7i −0.889593 0.718900i
\(346\) −2.36947e6 −0.0572036
\(347\) 5.34078e7i 1.27825i −0.769103 0.639125i \(-0.779297\pi\)
0.769103 0.639125i \(-0.220703\pi\)
\(348\) 1.19808e6 1.48255e6i 0.0284281 0.0351780i
\(349\) 4.71677e7 1.10961 0.554803 0.831982i \(-0.312794\pi\)
0.554803 + 0.831982i \(0.312794\pi\)
\(350\) 149058.i 0.00347657i
\(351\) 2.62048e7 5.18154e7i 0.605983 1.19822i
\(352\) 196608. 0.00450789
\(353\) 1.75443e7i 0.398852i −0.979913 0.199426i \(-0.936092\pi\)
0.979913 0.199426i \(-0.0639078\pi\)
\(354\) 3.88241e7 + 3.13746e7i 0.875169 + 0.707243i
\(355\) −1.15776e7 −0.258782
\(356\) 1.23752e7i 0.274285i
\(357\) −152064. + 188170.i −0.00334212 + 0.00413566i
\(358\) −1.70899e6 −0.0372470
\(359\) 6.18249e7i 1.33623i 0.744059 + 0.668113i \(0.232898\pi\)
−0.744059 + 0.668113i \(0.767102\pi\)
\(360\) −4.70016e6 2.18961e7i −0.100741 0.469309i
\(361\) −1.93993e7 −0.412349
\(362\) 3.66348e7i 0.772269i
\(363\) 3.71786e7 + 3.00448e7i 0.777272 + 0.628131i
\(364\) 188800. 0.00391469
\(365\) 1.23972e8i 2.54943i
\(366\) 6.00634e6 7.43246e6i 0.122509 0.151597i
\(367\) −3.40461e7 −0.688761 −0.344381 0.938830i \(-0.611911\pi\)
−0.344381 + 0.938830i \(0.611911\pi\)
\(368\) 1.04962e7i 0.210615i
\(369\) 1.19508e7 2.56534e6i 0.237859 0.0510582i
\(370\) 3.26957e7 0.645484
\(371\) 385096.i 0.00754132i
\(372\) −1.53875e7 1.24349e7i −0.298908 0.241554i
\(373\) −5.15781e7 −0.993892 −0.496946 0.867782i \(-0.665545\pi\)
−0.496946 + 0.867782i \(0.665545\pi\)
\(374\) 860204.i 0.0164432i
\(375\) 7.05600e6 8.73135e6i 0.133803 0.165572i
\(376\) 3.25632e7 0.612581
\(377\) 6.50821e6i 0.121461i
\(378\) −198720. 100500.i −0.00367931 0.00186076i
\(379\) 4.28828e7 0.787709 0.393855 0.919173i \(-0.371141\pi\)
0.393855 + 0.919173i \(0.371141\pi\)
\(380\) 2.85540e7i 0.520375i
\(381\) −4.78910e7 3.87018e7i −0.865923 0.699772i
\(382\) 2.84068e7 0.509603
\(383\) 1.51307e7i 0.269316i 0.990892 + 0.134658i \(0.0429936\pi\)
−0.990892 + 0.134658i \(0.957006\pi\)
\(384\) 3.14573e6 3.89264e6i 0.0555556 0.0687465i
\(385\) −11520.0 −0.000201869
\(386\) 1.98043e7i 0.344347i
\(387\) −980118. 4.56596e6i −0.0169101 0.0787770i
\(388\) 8.99475e6 0.153991
\(389\) 6.15319e7i 1.04533i −0.852540 0.522663i \(-0.824939\pi\)
0.852540 0.522663i \(-0.175061\pi\)
\(390\) −5.94720e7 4.80606e7i −1.00258 0.810206i
\(391\) 4.59233e7 0.768251
\(392\) 2.12960e7i 0.353541i
\(393\) 1.81918e7 2.25112e7i 0.299708 0.370870i
\(394\) −2.74596e7 −0.448959
\(395\) 5.77953e7i 0.937780i
\(396\) −774144. + 166176.i −0.0124663 + 0.00267598i
\(397\) −8.55816e7 −1.36776 −0.683878 0.729596i \(-0.739708\pi\)
−0.683878 + 0.729596i \(0.739708\pi\)
\(398\) 5.37953e7i 0.853287i
\(399\) 220836. + 178462.i 0.00347657 + 0.00280949i
\(400\) −1.34912e7 −0.210800
\(401\) 4.09739e7i 0.635439i 0.948185 + 0.317719i \(0.102917\pi\)
−0.948185 + 0.317719i \(0.897083\pi\)
\(402\) −4.21150e7 + 5.21147e7i −0.648274 + 0.802198i
\(403\) −6.75491e7 −1.03206
\(404\) 3.02516e7i 0.458780i
\(405\) 3.70138e7 + 8.22433e7i 0.557183 + 1.23804i
\(406\) −24960.0 −0.000372964
\(407\) 1.15597e6i 0.0171460i
\(408\) 1.70312e7 + 1.37633e7i 0.250763 + 0.202647i
\(409\) 6.10556e7 0.892391 0.446196 0.894935i \(-0.352779\pi\)
0.446196 + 0.894935i \(0.352779\pi\)
\(410\) 1.60962e7i 0.233546i
\(411\) 4.72355e7 5.84509e7i 0.680366 0.841910i
\(412\) 2.77032e7 0.396131
\(413\) 653638.i 0.00927870i
\(414\) 8.87155e6 + 4.13289e7i 0.125025 + 0.582442i
\(415\) 8.42170e7 1.17830
\(416\) 1.70882e7i 0.237365i
\(417\) 9.60529e7 + 7.76224e7i 1.32465 + 1.07048i
\(418\) 1.00954e6 0.0138227
\(419\) 3.38860e7i 0.460657i −0.973113 0.230329i \(-0.926020\pi\)
0.973113 0.230329i \(-0.0739801\pi\)
\(420\) −184320. + 228084.i −0.00248785 + 0.00307856i
\(421\) −1.96156e7 −0.262879 −0.131439 0.991324i \(-0.541960\pi\)
−0.131439 + 0.991324i \(0.541960\pi\)
\(422\) 3.99608e7i 0.531737i
\(423\) −1.28218e8 + 2.75229e7i −1.69405 + 0.363641i
\(424\) −3.48549e7 −0.457263
\(425\) 5.90270e7i 0.768925i
\(426\) 8.10432e6 + 6.54928e6i 0.104831 + 0.0847159i
\(427\) −125132. −0.00160725
\(428\) 4.71711e7i 0.601651i
\(429\) −1.69920e6 + 2.10265e6i −0.0215215 + 0.0266315i
\(430\) −6.14976e6 −0.0773487
\(431\) 4.01587e7i 0.501589i 0.968040 + 0.250795i \(0.0806919\pi\)
−0.968040 + 0.250795i \(0.919308\pi\)
\(432\) −9.09619e6 + 1.79861e7i −0.112826 + 0.223093i
\(433\) −845854. −0.0104191 −0.00520957 0.999986i \(-0.501658\pi\)
−0.00520957 + 0.999986i \(0.501658\pi\)
\(434\) 259061.i 0.00316908i
\(435\) 7.86240e6 + 6.35378e6i 0.0955185 + 0.0771906i
\(436\) −2.08259e7 −0.251272
\(437\) 5.38957e7i 0.645817i
\(438\) 7.01290e7 8.67802e7i 0.834594 1.03276i
\(439\) −7.48204e7 −0.884354 −0.442177 0.896928i \(-0.645794\pi\)
−0.442177 + 0.896928i \(0.645794\pi\)
\(440\) 1.04267e6i 0.0122402i
\(441\) −1.79997e7 8.38531e7i −0.209869 0.977695i
\(442\) 7.47648e7 0.865825
\(443\) 1.25246e8i 1.44063i 0.693649 + 0.720313i \(0.256002\pi\)
−0.693649 + 0.720313i \(0.743998\pi\)
\(444\) −2.28870e7 1.84955e7i −0.261481 0.211308i
\(445\) −6.56294e7 −0.744764
\(446\) 2.64114e7i 0.297705i
\(447\) −7.56904e7 + 9.36621e7i −0.847458 + 1.04868i
\(448\) −65536.0 −0.000728863
\(449\) 1.12812e8i 1.24628i −0.782109 0.623142i \(-0.785856\pi\)
0.782109 0.623142i \(-0.214144\pi\)
\(450\) 5.31216e7 1.14029e7i 0.582953 0.125135i
\(451\) −569088. −0.00620369
\(452\) 5.58133e7i 0.604397i
\(453\) −4.63700e7 3.74726e7i −0.498818 0.403106i
\(454\) −1.11171e8 −1.18802
\(455\) 1.00126e6i 0.0106295i
\(456\) 1.61526e7 1.99878e7i 0.170352 0.210800i
\(457\) 1.57358e8 1.64870 0.824350 0.566081i \(-0.191541\pi\)
0.824350 + 0.566081i \(0.191541\pi\)
\(458\) 2.53528e7i 0.263894i
\(459\) −7.86931e7 3.97979e7i −0.813764 0.411549i
\(460\) 5.56646e7 0.571881
\(461\) 1.83107e8i 1.86897i 0.356002 + 0.934485i \(0.384140\pi\)
−0.356002 + 0.934485i \(0.615860\pi\)
\(462\) 8064.00 + 6516.70i 8.17758e−5 + 6.60848e-5i
\(463\) 1.77978e8 1.79318 0.896588 0.442866i \(-0.146038\pi\)
0.896588 + 0.442866i \(0.146038\pi\)
\(464\) 2.25912e6i 0.0226144i
\(465\) 6.59462e7 8.16043e7i 0.655890 0.811623i
\(466\) −1.29704e7 −0.128172
\(467\) 9.35797e7i 0.918821i 0.888224 + 0.459410i \(0.151939\pi\)
−0.888224 + 0.459410i \(0.848061\pi\)
\(468\) 1.44432e7 + 6.72849e7i 0.140905 + 0.656417i
\(469\) 877396. 0.00850505
\(470\) 1.72692e8i 1.66334i
\(471\) −2.70663e7 2.18728e7i −0.259039 0.209335i
\(472\) −5.91606e7 −0.562609
\(473\) 217427.i 0.00205461i
\(474\) −3.26940e7 + 4.04567e7i −0.306996 + 0.379888i
\(475\) −6.92742e7 −0.646384
\(476\) 286735.i 0.00265864i
\(477\) 1.37241e8 2.94598e7i 1.26453 0.271441i
\(478\) 1.49660e7 0.137032
\(479\) 1.07662e8i 0.979617i −0.871830 0.489808i \(-0.837067\pi\)
0.871830 0.489808i \(-0.162933\pi\)
\(480\) 2.06438e7 + 1.66827e7i 0.186667 + 0.150849i
\(481\) −1.00471e8 −0.902830
\(482\) 3.95743e7i 0.353404i
\(483\) 347904. 430509.i 0.00308758 0.00382068i
\(484\) −5.66531e7 −0.499675
\(485\) 4.77019e7i 0.418129i
\(486\) 2.06142e7 7.85084e7i 0.179580 0.683923i
\(487\) −4.14432e6 −0.0358811 −0.0179406 0.999839i \(-0.505711\pi\)
−0.0179406 + 0.999839i \(0.505711\pi\)
\(488\) 1.13257e7i 0.0974549i
\(489\) 1.84782e7 + 1.49326e7i 0.158028 + 0.127706i
\(490\) −1.12939e8 −0.959967
\(491\) 1.19347e8i 1.00824i −0.863633 0.504122i \(-0.831816\pi\)
0.863633 0.504122i \(-0.168184\pi\)
\(492\) −9.10541e6 + 1.12674e7i −0.0764547 + 0.0946078i
\(493\) −9.88416e6 −0.0824896
\(494\) 8.77440e7i 0.727841i
\(495\) −881280. 4.10552e6i −0.00726605 0.0338495i
\(496\) 2.34476e7 0.192155
\(497\) 136443.i 0.00111143i
\(498\) −5.89519e7 4.76403e7i −0.477320 0.385733i
\(499\) 1.17436e8 0.945144 0.472572 0.881292i \(-0.343326\pi\)
0.472572 + 0.881292i \(0.343326\pi\)
\(500\) 1.33049e7i 0.106439i
\(501\) −1.01273e8 + 1.25320e8i −0.805346 + 0.996565i
\(502\) 1.61215e8 1.27437
\(503\) 1.99753e8i 1.56960i −0.619747 0.784802i \(-0.712765\pi\)
0.619747 0.784802i \(-0.287235\pi\)
\(504\) 258048. 55391.9i 0.00201562 0.000432668i
\(505\) −1.60433e8 −1.24572
\(506\) 1.96804e6i 0.0151909i
\(507\) 8.13895e7 + 6.57727e7i 0.624517 + 0.504686i
\(508\) 7.29768e7 0.556665
\(509\) 1.12725e8i 0.854804i −0.904062 0.427402i \(-0.859429\pi\)
0.904062 0.427402i \(-0.140571\pi\)
\(510\) −7.29907e7 + 9.03214e7i −0.550246 + 0.680895i
\(511\) −1.46102e6 −0.0109495
\(512\) 5.93164e6i 0.0441942i
\(513\) −4.67068e7 + 9.23543e7i −0.345962 + 0.684077i
\(514\) 1.05677e6 0.00778198
\(515\) 1.46919e8i 1.07561i
\(516\) 4.30483e6 + 3.47883e6i 0.0313334 + 0.0253212i
\(517\) 6.10560e6 0.0441832
\(518\) 385322.i 0.00277227i
\(519\) −7.10842e6 + 8.79622e6i −0.0508476 + 0.0629207i
\(520\) 9.06240e7 0.644515
\(521\) 1.14581e8i 0.810215i 0.914269 + 0.405108i \(0.132766\pi\)
−0.914269 + 0.405108i \(0.867234\pi\)
\(522\) −1.90944e6 8.89529e6i −0.0134244 0.0625387i
\(523\) −1.49806e8 −1.04719 −0.523594 0.851968i \(-0.675409\pi\)
−0.523594 + 0.851968i \(0.675409\pi\)
\(524\) 3.43028e7i 0.238416i
\(525\) −553350. 447174.i −0.00382404 0.00309029i
\(526\) 4.87361e7 0.334884
\(527\) 1.02588e8i 0.700916i
\(528\) 589824. 729870.i 0.00400701 0.00495842i
\(529\) 4.29689e7 0.290260
\(530\) 1.84846e8i 1.24160i
\(531\) 2.32945e8 5.00033e7i 1.55586 0.333976i
\(532\) −336512. −0.00223494
\(533\) 4.94624e7i 0.326658i
\(534\) 4.59406e7 + 3.71256e7i 0.301698 + 0.243809i
\(535\) 2.50163e8 1.63366
\(536\) 7.94128e7i 0.515699i
\(537\) −5.12698e6 + 6.34431e6i −0.0331084 + 0.0409696i
\(538\) 4.27167e7 0.274316
\(539\) 3.99300e6i 0.0254996i
\(540\) −9.53856e7 4.82398e7i −0.605761 0.306355i
\(541\) −1.57017e8 −0.991644 −0.495822 0.868424i \(-0.665133\pi\)
−0.495822 + 0.868424i \(0.665133\pi\)
\(542\) 7.88822e7i 0.495429i
\(543\) −1.36000e8 1.09904e8i −0.849452 0.686461i
\(544\) −2.59523e7 −0.161205
\(545\) 1.10446e8i 0.682277i
\(546\) 566400. 700884.i 0.00347973 0.00430594i
\(547\) −2.79469e8 −1.70754 −0.853770 0.520650i \(-0.825690\pi\)
−0.853770 + 0.520650i \(0.825690\pi\)
\(548\) 8.90680e7i 0.541228i
\(549\) −9.57260e6 4.45948e7i −0.0578513 0.269505i
\(550\) −2.52960e6 −0.0152042
\(551\) 1.16001e7i 0.0693434i
\(552\) −3.89652e7 3.14887e7i −0.231665 0.187213i
\(553\) 681124. 0.00402764
\(554\) 1.59123e8i 0.935847i
\(555\) 9.80870e7 1.21377e8i 0.573763 0.709996i
\(556\) −1.46366e8 −0.851563
\(557\) 1.50294e8i 0.869712i −0.900500 0.434856i \(-0.856799\pi\)
0.900500 0.434856i \(-0.143201\pi\)
\(558\) −9.23247e7 + 1.98182e7i −0.531393 + 0.114067i
\(559\) 1.88977e7 0.108187
\(560\) 347557.i 0.00197907i
\(561\) 3.19334e6 + 2.58061e6i 0.0180866 + 0.0146162i
\(562\) −1.26391e8 −0.712044
\(563\) 8.27836e7i 0.463894i −0.972728 0.231947i \(-0.925490\pi\)
0.972728 0.231947i \(-0.0745097\pi\)
\(564\) 9.76896e7 1.20885e8i 0.544516 0.673805i
\(565\) 2.95995e8 1.64111
\(566\) 5.73710e7i 0.316405i
\(567\) −969246. + 436211.i −0.00531722 + 0.00239303i
\(568\) −1.23494e7 −0.0673911
\(569\) 2.57230e8i 1.39632i 0.715942 + 0.698160i \(0.245997\pi\)
−0.715942 + 0.698160i \(0.754003\pi\)
\(570\) 1.06001e8 + 8.56620e7i 0.572383 + 0.462555i
\(571\) 2.84039e7 0.152570 0.0762852 0.997086i \(-0.475694\pi\)
0.0762852 + 0.997086i \(0.475694\pi\)
\(572\) 3.20404e6i 0.0171203i
\(573\) 8.52204e7 1.05455e8i 0.452980 0.560535i
\(574\) 189696. 0.00100305
\(575\) 1.35047e8i 0.710363i
\(576\) −5.01350e6 2.33558e7i −0.0262346 0.122216i
\(577\) 6.52476e7 0.339654 0.169827 0.985474i \(-0.445679\pi\)
0.169827 + 0.985474i \(0.445679\pi\)
\(578\) 2.29958e7i 0.119087i
\(579\) 7.35195e7 + 5.94128e7i 0.378763 + 0.306086i
\(580\) −1.19808e7 −0.0614047
\(581\) 992506.i 0.00506063i
\(582\) 2.69843e7 3.33913e7i 0.136880 0.169381i
\(583\) −6.53530e6 −0.0329807
\(584\) 1.32236e8i 0.663915i
\(585\) −3.56832e8 + 7.65966e7i −1.78236 + 0.382597i
\(586\) 1.57525e8 0.782813
\(587\) 6.66740e7i 0.329642i −0.986324 0.164821i \(-0.947295\pi\)
0.986324 0.164821i \(-0.0527046\pi\)
\(588\) 7.90574e7 + 6.38881e7i 0.388876 + 0.314259i
\(589\) 1.20398e8 0.589213
\(590\) 3.13746e8i 1.52765i
\(591\) −8.23789e7 + 1.01939e8i −0.399074 + 0.493829i
\(592\) 3.48754e7 0.168095
\(593\) 1.53324e8i 0.735271i 0.929970 + 0.367635i \(0.119833\pi\)
−0.929970 + 0.367635i \(0.880167\pi\)
\(594\) −1.70554e6 + 3.37239e6i −0.00813770 + 0.0160908i
\(595\) 1.52064e6 0.00721897
\(596\) 1.42723e8i 0.674149i
\(597\) −1.99705e8 1.61386e8i −0.938568 0.758478i
\(598\) −1.71053e8 −0.799883
\(599\) 2.18294e8i 1.01569i 0.861448 + 0.507846i \(0.169558\pi\)
−0.861448 + 0.507846i \(0.830442\pi\)
\(600\) −4.04736e7 + 5.00835e7i −0.187378 + 0.231868i
\(601\) 1.08478e8 0.499709 0.249854 0.968283i \(-0.419617\pi\)
0.249854 + 0.968283i \(0.419617\pi\)
\(602\) 72475.6i 0.000332202i
\(603\) 6.71208e7 + 3.12688e8i 0.306129 + 1.42613i
\(604\) 7.06590e7 0.320669
\(605\) 3.00448e8i 1.35676i
\(606\) 1.12303e8 + 9.07548e7i 0.504632 + 0.407804i
\(607\) −3.43321e8 −1.53509 −0.767547 0.640993i \(-0.778523\pi\)
−0.767547 + 0.640993i \(0.778523\pi\)
\(608\) 3.04576e7i 0.135514i
\(609\) −74880.0 + 92659.3i −0.000331523 + 0.000410239i
\(610\) −6.00634e7 −0.264618
\(611\) 5.30669e8i 2.32649i
\(612\) 1.02187e8 2.19352e7i 0.445801 0.0956946i
\(613\) 2.96325e8 1.28643 0.643216 0.765685i \(-0.277600\pi\)
0.643216 + 0.765685i \(0.277600\pi\)
\(614\) 2.05487e8i 0.887728i
\(615\) −5.97542e7 4.82887e7i −0.256888 0.207597i
\(616\) −12288.0 −5.25701e−5
\(617\) 1.32676e8i 0.564853i −0.959289 0.282426i \(-0.908861\pi\)
0.959289 0.282426i \(-0.0911393\pi\)
\(618\) 8.31097e7 1.02843e8i 0.352116 0.435722i
\(619\) −4.14773e8 −1.74879 −0.874397 0.485211i \(-0.838743\pi\)
−0.874397 + 0.485211i \(0.838743\pi\)
\(620\) 1.24349e8i 0.521758i
\(621\) 1.80040e8 + 9.10527e7i 0.751787 + 0.380205i
\(622\) −2.03602e8 −0.846078
\(623\) 773450.i 0.00319866i
\(624\) −6.34368e7 5.12647e7i −0.261088 0.210991i
\(625\) −2.76419e8 −1.13221
\(626\) 2.26896e8i 0.924919i
\(627\) 3.02861e6 3.74771e6i 0.0122868 0.0152042i
\(628\) 4.12438e7 0.166525
\(629\) 1.52588e8i 0.613151i
\(630\) 293760. + 1.36851e6i 0.00117482 + 0.00547300i
\(631\) 3.03858e8 1.20944 0.604718 0.796440i \(-0.293286\pi\)
0.604718 + 0.796440i \(0.293286\pi\)
\(632\) 6.16483e7i 0.244214i
\(633\) 1.48347e8 + 1.19882e8i 0.584881 + 0.472655i
\(634\) 2.23093e8 0.875424
\(635\) 3.87018e8i 1.51151i
\(636\) −1.04565e8 + 1.29392e8i −0.406456 + 0.502964i
\(637\) 3.47053e8 1.34269
\(638\) 423585.i 0.00163109i
\(639\) 4.86259e7 1.04379e7i 0.186365 0.0400047i
\(640\) −3.14573e7 −0.120000
\(641\) 1.81629e8i 0.689622i −0.938672 0.344811i \(-0.887943\pi\)
0.938672 0.344811i \(-0.112057\pi\)
\(642\) −1.75114e8 1.41513e8i −0.661782 0.534801i
\(643\) 1.73811e8 0.653798 0.326899 0.945059i \(-0.393996\pi\)
0.326899 + 0.945059i \(0.393996\pi\)
\(644\) 656014.i 0.00245615i
\(645\) −1.84493e7 + 2.28298e7i −0.0687544 + 0.0850792i
\(646\) −1.33259e8 −0.494309
\(647\) 2.43137e8i 0.897713i 0.893604 + 0.448856i \(0.148168\pi\)
−0.893604 + 0.448856i \(0.851832\pi\)
\(648\) 3.94813e7 + 8.77261e7i 0.145100 + 0.322407i
\(649\) −1.10926e7 −0.0405788
\(650\) 2.19861e8i 0.800585i
\(651\) 961716. + 777184.i 0.00348581 + 0.00281696i
\(652\) −2.81572e7 −0.101589
\(653\) 4.47562e7i 0.160736i −0.996765 0.0803681i \(-0.974390\pi\)
0.996765 0.0803681i \(-0.0256096\pi\)
\(654\) −6.24778e7 + 7.73123e7i −0.223353 + 0.276386i
\(655\) −1.81918e8 −0.647369
\(656\) 1.71693e7i 0.0608193i
\(657\) −1.11768e8 5.20681e8i −0.394114 1.83601i
\(658\) −2.03520e6 −0.00714380
\(659\) 1.13574e8i 0.396845i −0.980117 0.198423i \(-0.936418\pi\)
0.980117 0.198423i \(-0.0635819\pi\)
\(660\) 3.87072e6 + 3.12801e6i 0.0134636 + 0.0108802i
\(661\) −9.93464e7 −0.343992 −0.171996 0.985098i \(-0.555022\pi\)
−0.171996 + 0.985098i \(0.555022\pi\)
\(662\) 1.57466e8i 0.542766i
\(663\) 2.24294e8 2.77550e8i 0.769623 0.952359i
\(664\) 8.98314e7 0.306849
\(665\) 1.78462e6i 0.00606851i
\(666\) −1.37322e8 + 2.94772e7i −0.464854 + 0.0997845i
\(667\) 2.26138e7 0.0762071
\(668\) 1.90963e8i 0.640649i
\(669\) 9.80472e7 + 7.92341e7i 0.327459 + 0.264627i
\(670\) 4.21150e8 1.40027
\(671\) 2.12356e6i 0.00702906i
\(672\) −196608. + 243290.i −0.000647878 + 0.000801708i
\(673\) −2.79412e8 −0.916642 −0.458321 0.888787i \(-0.651549\pi\)
−0.458321 + 0.888787i \(0.651549\pi\)
\(674\) 1.34575e8i 0.439525i
\(675\) 1.17034e8 2.31413e8i 0.380539 0.752447i
\(676\) −1.24022e8 −0.401475
\(677\) 4.09293e7i 0.131907i 0.997823 + 0.0659536i \(0.0210089\pi\)
−0.997823 + 0.0659536i \(0.978991\pi\)
\(678\) −2.07196e8 1.67440e8i −0.664803 0.537242i
\(679\) −562172. −0.00179581
\(680\) 1.37633e8i 0.437718i
\(681\) −3.33514e8 + 4.12702e8i −1.05602 + 1.30676i
\(682\) 4.39642e6 0.0138594
\(683\) 3.74260e8i 1.17466i 0.809348 + 0.587329i \(0.199820\pi\)
−0.809348 + 0.587329i \(0.800180\pi\)
\(684\) −2.57432e7 1.19927e8i −0.0804440 0.374755i
\(685\) −4.72355e8 −1.46959
\(686\) 2.66205e6i 0.00824600i
\(687\) −9.41174e7 7.60584e7i −0.290268 0.234572i
\(688\) −6.55974e6 −0.0201429
\(689\) 5.68017e8i 1.73661i
\(690\) 1.66994e8 2.06644e8i 0.508339 0.629037i
\(691\) 1.15164e8 0.349047 0.174524 0.984653i \(-0.444161\pi\)
0.174524 + 0.984653i \(0.444161\pi\)
\(692\) 1.34038e7i 0.0404490i
\(693\) 48384.0 10386.0i 0.000145379 3.12067e-5i
\(694\) 3.02120e8 0.903859
\(695\) 7.76224e8i 2.31224i
\(696\) 8.38656e6 + 6.77736e6i 0.0248746 + 0.0201017i
\(697\) 7.51196e7 0.221848
\(698\) 2.66821e8i 0.784609i
\(699\) −3.89111e7 + 4.81500e7i −0.113931 + 0.140982i
\(700\) 843200. 0.00245831
\(701\) 5.65717e7i 0.164227i 0.996623 + 0.0821137i \(0.0261671\pi\)
−0.996623 + 0.0821137i \(0.973833\pi\)
\(702\) 2.93112e8 + 1.48237e8i 0.847271 + 0.428495i
\(703\) 1.79077e8 0.515435
\(704\) 1.11218e6i 0.00318756i
\(705\) 6.41088e8 + 5.18077e8i 1.82958 + 1.47852i
\(706\) 9.92456e7 0.282031
\(707\) 1.89072e6i 0.00535020i
\(708\) −1.77482e8 + 2.19622e8i −0.500097 + 0.618838i
\(709\) −1.28652e8 −0.360975 −0.180488 0.983577i \(-0.557768\pi\)
−0.180488 + 0.983577i \(0.557768\pi\)
\(710\) 6.54928e7i 0.182986i
\(711\) 5.21060e7 + 2.42740e8i 0.144970 + 0.675356i
\(712\) −7.00047e7 −0.193949
\(713\) 2.34710e8i 0.647533i
\(714\) −1.06445e6 860204.i −0.00292435 0.00236323i
\(715\) 1.69920e7 0.0464864
\(716\) 9.66752e6i 0.0263376i
\(717\) 4.48980e7 5.55585e7i 0.121806 0.150728i
\(718\) −3.49735e8 −0.944855
\(719\) 2.01053e8i 0.540908i −0.962733 0.270454i \(-0.912826\pi\)
0.962733 0.270454i \(-0.0871738\pi\)
\(720\) 1.23863e8 2.65881e7i 0.331852 0.0712345i
\(721\) −1.73145e6 −0.00461960
\(722\) 1.09739e8i 0.291575i
\(723\) −1.46912e8 1.18723e8i −0.388725 0.314137i
\(724\) 2.07238e8 0.546076
\(725\) 2.90663e7i 0.0762739i
\(726\) −1.69959e8 + 2.10314e8i −0.444155 + 0.549614i
\(727\) 5.23208e8 1.36167 0.680833 0.732438i \(-0.261618\pi\)
0.680833 + 0.732438i \(0.261618\pi\)
\(728\) 1.06801e6i 0.00276811i
\(729\) −2.29605e8 3.12051e8i −0.592651 0.805459i
\(730\) −7.01290e8 −1.80272
\(731\) 2.87003e7i 0.0734742i
\(732\) 4.20444e7 + 3.39770e7i 0.107195 + 0.0866266i
\(733\) −6.57372e8 −1.66917 −0.834583 0.550882i \(-0.814291\pi\)
−0.834583 + 0.550882i \(0.814291\pi\)
\(734\) 1.92594e8i 0.487028i
\(735\) −3.38818e8 + 4.19265e8i −0.853304 + 1.05591i
\(736\) 5.93756e7 0.148927
\(737\) 1.48899e7i 0.0371954i
\(738\) 1.45117e7 + 6.76042e7i 0.0361036 + 0.168192i
\(739\) 3.50495e8 0.868458 0.434229 0.900803i \(-0.357021\pi\)
0.434229 + 0.900803i \(0.357021\pi\)
\(740\) 1.84955e8i 0.456426i
\(741\) −3.25733e8 2.63232e8i −0.800585 0.646970i
\(742\) 2.17843e6 0.00533252
\(743\) 4.66667e8i 1.13773i −0.822429 0.568867i \(-0.807382\pi\)
0.822429 0.568867i \(-0.192618\pi\)
\(744\) 7.03427e7 8.70446e7i 0.170805 0.211360i
\(745\) 7.56904e8 1.83051
\(746\) 2.91770e8i 0.702788i
\(747\) −3.53711e8 + 7.59267e7i −0.848569 + 0.182152i
\(748\) −4.86605e6 −0.0116271
\(749\) 2.94819e6i 0.00701634i
\(750\) 4.93920e7 + 3.99148e7i 0.117077 + 0.0946128i
\(751\) −3.36993e7 −0.0795612 −0.0397806 0.999208i \(-0.512666\pi\)
−0.0397806 + 0.999208i \(0.512666\pi\)
\(752\) 1.84205e8i 0.433160i
\(753\) 4.83645e8 5.98480e8i 1.13277 1.40173i
\(754\) 3.68160e7 0.0858860
\(755\) 3.74726e8i 0.870709i
\(756\) 568512. 1.12413e6i 0.00131575 0.00260166i
\(757\) 2.98552e8 0.688227 0.344113 0.938928i \(-0.388180\pi\)
0.344113 + 0.938928i \(0.388180\pi\)
\(758\) 2.42582e8i 0.556995i
\(759\) −7.30598e6 5.90413e6i −0.0167091 0.0135030i
\(760\) −1.61526e8 −0.367960
\(761\) 3.98702e8i 0.904679i −0.891846 0.452340i \(-0.850590\pi\)
0.891846 0.452340i \(-0.149410\pi\)
\(762\) 2.18930e8 2.70913e8i 0.494813 0.612300i
\(763\) 1.30162e6 0.00293029
\(764\) 1.60693e8i 0.360344i
\(765\) 1.16329e8 + 5.41928e8i 0.259839 + 1.21048i
\(766\) −8.55921e7 −0.190435
\(767\) 9.64116e8i 2.13670i
\(768\) 2.20201e7 + 1.77949e7i 0.0486111 + 0.0392837i
\(769\) −5.17372e8 −1.13769 −0.568845 0.822444i \(-0.692610\pi\)
−0.568845 + 0.822444i \(0.692610\pi\)
\(770\) 65167.0i 0.000142743i
\(771\) 3.17030e6 3.92305e6i 0.00691732 0.00855974i
\(772\) −1.12030e8 −0.243490
\(773\) 1.83241e8i 0.396719i 0.980129 + 0.198360i \(0.0635614\pi\)
−0.980129 + 0.198360i \(0.936439\pi\)
\(774\) 2.58290e7 5.54438e6i 0.0557038 0.0119572i
\(775\) −3.01681e8 −0.648102
\(776\) 5.08820e7i 0.108888i
\(777\) 1.43044e6 + 1.15597e6i 0.00304934 + 0.00246424i
\(778\) 3.48077e8 0.739157
\(779\) 8.81604e7i 0.186493i
\(780\) 2.71872e8 3.36424e8i 0.572902 0.708931i
\(781\) −2.31552e6 −0.00486066
\(782\) 2.59782e8i 0.543235i
\(783\) −3.87504e7 1.95974e7i −0.0807218 0.0408239i
\(784\) −1.20468e8 −0.249992
\(785\) 2.18728e8i 0.452164i
\(786\) 1.27343e8 + 1.02908e8i 0.262244 + 0.211925i
\(787\) 3.14718e8 0.645650 0.322825 0.946459i \(-0.395367\pi\)
0.322825 + 0.946459i \(0.395367\pi\)
\(788\) 1.55335e8i 0.317462i
\(789\) 1.46208e8 1.80924e8i 0.297674 0.368353i
\(790\) 3.26940e8 0.663111
\(791\) 3.48833e6i 0.00704837i
\(792\) −940032. 4.37922e6i −0.00189220 0.00881498i
\(793\) 1.84570e8 0.370119
\(794\) 4.84122e8i 0.967150i
\(795\) −6.86206e8 5.54538e8i −1.36569 1.10365i
\(796\) 3.04312e8 0.603365
\(797\) 7.88168e8i 1.55684i 0.627744 + 0.778420i \(0.283979\pi\)
−0.627744 + 0.778420i \(0.716021\pi\)
\(798\) −1.00954e6 + 1.24924e6i −0.00198661 + 0.00245831i
\(799\) −8.05939e8 −1.58002
\(800\) 7.63178e7i 0.149058i
\(801\) 2.75644e8 5.91690e7i 0.536353 0.115132i
\(802\) −2.31783e8 −0.449323
\(803\) 2.47943e7i 0.0478857i
\(804\) −2.94805e8 2.38238e8i −0.567240 0.458399i
\(805\) −3.47904e6 −0.00666917
\(806\) 3.82115e8i 0.729776i
\(807\) 1.28150e8 1.58578e8i 0.243836 0.301732i
\(808\) −1.71129e8 −0.324406
\(809\) 1.04745e9i 1.97828i −0.146993 0.989138i \(-0.546959\pi\)
0.146993 0.989138i \(-0.453041\pi\)
\(810\) −4.65238e8 + 2.09381e8i −0.875428 + 0.393988i
\(811\) −1.17930e8 −0.221086 −0.110543 0.993871i \(-0.535259\pi\)
−0.110543 + 0.993871i \(0.535259\pi\)
\(812\) 141195.i 0.000263725i
\(813\) 2.92835e8 + 2.36647e8i 0.544944 + 0.440381i
\(814\) 6.53914e6 0.0121240
\(815\) 1.49326e8i 0.275844i
\(816\) −7.78568e7 + 9.63428e7i −0.143293 + 0.177316i
\(817\) −3.36827e7 −0.0617648
\(818\) 3.45382e8i 0.631016i
\(819\) −902700. 4.20531e6i −0.00164320 0.00765501i
\(820\) 9.10541e7 0.165142
\(821\) 6.01939e7i 0.108774i −0.998520 0.0543868i \(-0.982680\pi\)
0.998520 0.0543868i \(-0.0173204\pi\)
\(822\) 3.30648e8 + 2.67204e8i 0.595320 + 0.481091i
\(823\) 1.60620e7 0.0288139 0.0144069 0.999896i \(-0.495414\pi\)
0.0144069 + 0.999896i \(0.495414\pi\)
\(824\) 1.56713e8i 0.280107i
\(825\) −7.58880e6 + 9.39066e6i −0.0135149 + 0.0167238i
\(826\) 3.69754e6 0.00656103
\(827\) 3.66665e8i 0.648266i −0.946012 0.324133i \(-0.894928\pi\)
0.946012 0.324133i \(-0.105072\pi\)
\(828\) −2.33791e8 + 5.01851e7i −0.411849 + 0.0884064i
\(829\) −3.63153e8 −0.637421 −0.318711 0.947852i \(-0.603250\pi\)
−0.318711 + 0.947852i \(0.603250\pi\)
\(830\) 4.76403e8i 0.833183i
\(831\) 5.90716e8 + 4.77370e8i 1.02938 + 0.831864i
\(832\) 9.66656e7 0.167843
\(833\) 5.27076e8i 0.911882i
\(834\) −4.39099e8 + 5.43357e8i −0.756945 + 0.936671i
\(835\) 1.01273e9 1.73955
\(836\) 5.71080e6i 0.00977413i
\(837\) −2.03403e8 + 4.02193e8i −0.346881 + 0.685895i
\(838\) 1.91688e8 0.325734
\(839\) 8.80700e8i 1.49122i 0.666382 + 0.745611i \(0.267842\pi\)
−0.666382 + 0.745611i \(0.732158\pi\)
\(840\) −1.29024e6 1.04267e6i −0.00217687 0.00175918i
\(841\) 5.89956e8 0.991817
\(842\) 1.10963e8i 0.185883i
\(843\) −3.79173e8 + 4.69202e8i −0.632928 + 0.783209i
\(844\) −2.26052e8 −0.375995
\(845\) 6.57727e8i 1.09012i
\(846\) −1.55693e8 7.25308e8i −0.257133 1.19788i
\(847\) 3.54082e6 0.00582711
\(848\) 1.97169e8i 0.323334i
\(849\) 2.12979e8 + 1.72113e8i 0.348027 + 0.281249i
\(850\) 3.33907e8 0.543712
\(851\) 3.49102e8i 0.566453i
\(852\) −3.70483e7 + 4.58450e7i −0.0599032 + 0.0741264i
\(853\) −3.84724e8 −0.619873 −0.309936 0.950757i \(-0.600308\pi\)
−0.309936 + 0.950757i \(0.600308\pi\)
\(854\) 707853.i 0.00113650i
\(855\) 6.36008e8 1.36524e8i 1.01757 0.218429i
\(856\) 2.66840e8 0.425432
\(857\) 3.42647e8i 0.544382i 0.962243 + 0.272191i \(0.0877483\pi\)
−0.962243 + 0.272191i \(0.912252\pi\)
\(858\) −1.18944e7 9.61213e6i −0.0188313 0.0152180i
\(859\) −3.87443e8 −0.611263 −0.305631 0.952150i \(-0.598868\pi\)
−0.305631 + 0.952150i \(0.598868\pi\)
\(860\) 3.47883e7i 0.0546938i
\(861\) 569088. 704210.i 0.000891600 0.00110330i
\(862\) −2.27172e8 −0.354677
\(863\) 6.46530e7i 0.100590i −0.998734 0.0502951i \(-0.983984\pi\)
0.998734 0.0502951i \(-0.0160162\pi\)
\(864\) −1.01745e8 5.14558e7i −0.157750 0.0797799i
\(865\) 7.10842e7 0.109831
\(866\) 4.78487e6i 0.00736744i
\(867\) 8.53675e7 + 6.89874e7i 0.130989 + 0.105855i
\(868\) −1.46547e6 −0.00224088
\(869\) 1.15591e7i 0.0176142i
\(870\) −3.59424e7 + 4.44765e7i −0.0545820 + 0.0675418i
\(871\) −1.29416e9 −1.95854
\(872\) 1.17809e8i 0.177676i
\(873\) −4.30062e7 2.00348e8i −0.0646380 0.301122i
\(874\) 3.04880e8 0.456662
\(875\) 831558.i 0.00124128i
\(876\) 4.90903e8 + 3.96709e8i 0.730269 + 0.590147i
\(877\) −4.99281e8 −0.740196 −0.370098 0.928993i \(-0.620676\pi\)
−0.370098 + 0.928993i \(0.620676\pi\)
\(878\) 4.23248e8i 0.625333i
\(879\) 4.72576e8 5.84783e8i 0.695833 0.861050i
\(880\) −5.89824e6 −0.00865515
\(881\) 9.14796e8i 1.33782i 0.743345 + 0.668908i \(0.233238\pi\)
−0.743345 + 0.668908i \(0.766762\pi\)
\(882\) 4.74345e8 1.01822e8i 0.691335 0.148400i
\(883\) 7.85211e6 0.0114052 0.00570261 0.999984i \(-0.498185\pi\)
0.00570261 + 0.999984i \(0.498185\pi\)
\(884\) 4.22934e8i 0.612231i
\(885\) −1.16472e9 9.41239e8i −1.68032 1.35791i
\(886\) −7.08496e8 −1.01868
\(887\) 1.10737e9i 1.58679i −0.608704 0.793397i \(-0.708310\pi\)
0.608704 0.793397i \(-0.291690\pi\)
\(888\) 1.04626e8 1.29468e8i 0.149417 0.184895i
\(889\) −4.56105e6 −0.00649172
\(890\) 3.71256e8i 0.526628i
\(891\) 7.40275e6 + 1.64487e7i 0.0104655 + 0.0232540i
\(892\) −1.49405e8 −0.210509
\(893\) 9.45851e8i 1.32821i
\(894\) −5.29833e8 4.28170e8i −0.741526 0.599244i
\(895\) 5.12698e7 0.0715142
\(896\) 370728.i 0.000515384i
\(897\) −5.13158e8 + 6.35001e8i −0.711007 + 0.879827i
\(898\) 6.38162e8 0.881256
\(899\) 5.05170e7i 0.0695277i
\(900\) 6.45048e7 + 3.00501e8i 0.0884840 + 0.412210i
\(901\) 8.62659e8 1.17941
\(902\) 3.21925e6i 0.00438667i
\(903\) −269052. 217427.i −0.000365404 0.000295291i
\(904\) 3.15728e8 0.427374
\(905\) 1.09904e9i 1.48276i
\(906\) 2.11977e8 2.62308e8i 0.285039 0.352718i
\(907\) 1.16193e9 1.55725 0.778623 0.627492i \(-0.215918\pi\)
0.778623 + 0.627492i \(0.215918\pi\)
\(908\) 6.28880e8i 0.840059i
\(909\) 6.73820e8 1.44640e8i 0.897123 0.192574i
\(910\) −5.66400e6 −0.00751621
\(911\) 3.61439e8i 0.478057i 0.971013 + 0.239028i \(0.0768289\pi\)
−0.971013 + 0.239028i \(0.923171\pi\)
\(912\) 1.13068e8 + 9.13728e7i 0.149058 + 0.120457i
\(913\) 1.68434e7 0.0221318
\(914\) 8.90154e8i 1.16581i
\(915\) −1.80190e8 + 2.22974e8i −0.235216 + 0.291065i
\(916\) 1.43417e8 0.186601
\(917\) 2.14393e6i 0.00278036i
\(918\) 2.25131e8 4.45156e8i 0.291009 0.575418i
\(919\) 1.20431e9 1.55164 0.775820 0.630954i \(-0.217336\pi\)
0.775820 + 0.630954i \(0.217336\pi\)
\(920\) 3.14887e8i 0.404381i
\(921\) −7.62833e8 6.16462e8i −0.976451 0.789091i
\(922\) −1.03581e9 −1.32156
\(923\) 2.01254e8i 0.255941i
\(924\) −36864.0 + 45616.9i −4.67290e−5 + 5.78242e-5i
\(925\) −4.48714e8 −0.566950
\(926\) 1.00679e9i 1.26797i
\(927\) −1.32456e8 6.17058e8i −0.166277 0.774617i
\(928\) −1.27795e7 −0.0159908
\(929\) 6.33924e8i 0.790661i −0.918539 0.395330i \(-0.870630\pi\)
0.918539 0.395330i \(-0.129370\pi\)
\(930\) 4.61624e8 + 3.73048e8i 0.573904 + 0.463784i
\(931\) −6.18577e8 −0.766558
\(932\) 7.33715e7i 0.0906316i
\(933\) −6.10805e8 + 7.55833e8i −0.752069 + 0.930638i
\(934\) −5.29366e8 −0.649704
\(935\) 2.58061e7i 0.0315710i
\(936\) −3.80621e8 + 8.17031e7i −0.464157 + 0.0996348i
\(937\) −2.47138e8 −0.300414 −0.150207 0.988655i \(-0.547994\pi\)
−0.150207 + 0.988655i \(0.547994\pi\)
\(938\) 4.96330e6i 0.00601398i
\(939\) 8.42308e8 + 6.80688e8i 1.01736 + 0.822150i
\(940\) −9.76896e8 −1.17616
\(941\) 9.37355e8i 1.12496i −0.826812 0.562478i \(-0.809848\pi\)
0.826812 0.562478i \(-0.190152\pi\)
\(942\) 1.23732e8 1.53110e8i 0.148022 0.183168i
\(943\) −1.71865e8 −0.204952
\(944\) 3.34663e8i 0.397824i
\(945\) 5.96160e6 + 3.01499e6i 0.00706427 + 0.00357265i
\(946\) −1.22995e6 −0.00145283
\(947\) 1.49756e9i 1.76333i −0.471877 0.881664i \(-0.656424\pi\)
0.471877 0.881664i \(-0.343576\pi\)
\(948\) −2.28858e8 1.84945e8i −0.268621 0.217079i
\(949\) 2.15500e9 2.52145
\(950\) 3.91874e8i 0.457062i
\(951\) 6.69279e8 8.28191e8i 0.778154 0.962917i
\(952\) 1.62202e6 0.00187994
\(953\) 4.28296e7i 0.0494840i 0.999694 + 0.0247420i \(0.00787643\pi\)
−0.999694 + 0.0247420i \(0.992124\pi\)
\(954\) 1.66650e8 + 7.76354e8i 0.191938 + 0.894158i
\(955\) −8.52204e8 −0.978438
\(956\) 8.46606e7i 0.0968964i
\(957\) 1.57248e6 + 1.27076e6i 0.00179411 + 0.00144986i
\(958\) 6.09029e8 0.692694
\(959\) 5.56675e6i 0.00631170i
\(960\) −9.43718e7 + 1.16779e8i −0.106667 + 0.131993i
\(961\) −3.63185e8 −0.409221
\(962\) 5.68350e8i 0.638397i
\(963\) −1.05068e9 + 2.25537e8i −1.17650 + 0.252545i
\(964\) 2.23866e8 0.249894
\(965\) 5.94128e8i 0.661147i
\(966\) 2.43533e6 + 1.96804e6i 0.00270163 + 0.00218325i
\(967\) −1.16322e9 −1.28642 −0.643210 0.765690i \(-0.722398\pi\)
−0.643210 + 0.765690i \(0.722398\pi\)
\(968\) 3.20478e8i 0.353323i
\(969\) −3.99776e8 + 4.94698e8i −0.439385 + 0.543712i
\(970\) −2.69843e8 −0.295662
\(971\) 1.39293e9i 1.52150i 0.649045 + 0.760750i \(0.275169\pi\)
−0.649045 + 0.760750i \(0.724831\pi\)
\(972\) 4.44111e8 + 1.16611e8i 0.483607 + 0.126982i
\(973\) 9.14789e6 0.00993076
\(974\) 2.34438e7i 0.0253718i
\(975\) 8.16191e8 + 6.59582e8i 0.880599 + 0.711631i
\(976\) −6.40676e7 −0.0689111
\(977\) 7.81956e8i 0.838492i −0.907873 0.419246i \(-0.862295\pi\)
0.907873 0.419246i \(-0.137705\pi\)
\(978\) −8.44717e7 + 1.04528e8i −0.0903015 + 0.111742i
\(979\) −1.31259e7 −0.0139888
\(980\) 6.38881e8i 0.678799i
\(981\) 9.95739e7 + 4.63874e8i 0.105472 + 0.491352i
\(982\) 6.75126e8 0.712936
\(983\) 8.80220e8i 0.926682i 0.886180 + 0.463341i \(0.153349\pi\)
−0.886180 + 0.463341i \(0.846651\pi\)
\(984\) −6.37379e7 5.15080e7i −0.0668978 0.0540616i
\(985\) 8.23789e8 0.862001
\(986\) 5.59133e7i 0.0583289i
\(987\) −6.10560e6 + 7.55529e6i −0.00635005 + 0.00785778i
\(988\) 4.96355e8 0.514662
\(989\) 6.56629e7i 0.0678783i
\(990\) 2.32243e7 4.98527e6i 0.0239352 0.00513787i
\(991\) −1.83915e9 −1.88971 −0.944857 0.327483i \(-0.893800\pi\)
−0.944857 + 0.327483i \(0.893800\pi\)
\(992\) 1.32639e8i 0.135874i
\(993\) 5.84562e8 + 4.72397e8i 0.597012 + 0.482458i
\(994\) 771840. 0.000785902
\(995\) 1.61386e9i 1.63831i
\(996\) 2.69494e8 3.33482e8i 0.272754 0.337516i
\(997\) 5.69927e8 0.575088 0.287544 0.957767i \(-0.407161\pi\)
0.287544 + 0.957767i \(0.407161\pi\)
\(998\) 6.64316e8i 0.668318i
\(999\) −3.02537e8 + 5.98213e8i −0.303447 + 0.600011i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 6.7.b.a.5.2 yes 2
3.2 odd 2 inner 6.7.b.a.5.1 2
4.3 odd 2 48.7.e.b.17.1 2
5.2 odd 4 150.7.b.a.149.1 4
5.3 odd 4 150.7.b.a.149.4 4
5.4 even 2 150.7.d.a.101.1 2
7.6 odd 2 294.7.b.a.197.2 2
8.3 odd 2 192.7.e.f.65.2 2
8.5 even 2 192.7.e.c.65.1 2
9.2 odd 6 162.7.d.b.53.1 4
9.4 even 3 162.7.d.b.107.1 4
9.5 odd 6 162.7.d.b.107.2 4
9.7 even 3 162.7.d.b.53.2 4
12.11 even 2 48.7.e.b.17.2 2
15.2 even 4 150.7.b.a.149.3 4
15.8 even 4 150.7.b.a.149.2 4
15.14 odd 2 150.7.d.a.101.2 2
21.20 even 2 294.7.b.a.197.1 2
24.5 odd 2 192.7.e.c.65.2 2
24.11 even 2 192.7.e.f.65.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6.7.b.a.5.1 2 3.2 odd 2 inner
6.7.b.a.5.2 yes 2 1.1 even 1 trivial
48.7.e.b.17.1 2 4.3 odd 2
48.7.e.b.17.2 2 12.11 even 2
150.7.b.a.149.1 4 5.2 odd 4
150.7.b.a.149.2 4 15.8 even 4
150.7.b.a.149.3 4 15.2 even 4
150.7.b.a.149.4 4 5.3 odd 4
150.7.d.a.101.1 2 5.4 even 2
150.7.d.a.101.2 2 15.14 odd 2
162.7.d.b.53.1 4 9.2 odd 6
162.7.d.b.53.2 4 9.7 even 3
162.7.d.b.107.1 4 9.4 even 3
162.7.d.b.107.2 4 9.5 odd 6
192.7.e.c.65.1 2 8.5 even 2
192.7.e.c.65.2 2 24.5 odd 2
192.7.e.f.65.1 2 24.11 even 2
192.7.e.f.65.2 2 8.3 odd 2
294.7.b.a.197.1 2 21.20 even 2
294.7.b.a.197.2 2 7.6 odd 2