Properties

Label 18.7.d.a.11.6
Level $18$
Weight $7$
Character 18.11
Analytic conductor $4.141$
Analytic rank $0$
Dimension $12$
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] = [18,7,Mod(5,18)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(18, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("18.5");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 18.d (of order \(6\), degree \(2\), 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: \(4.14097350516\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 370x^{10} + 51793x^{8} + 3491832x^{6} + 117603792x^{4} + 1832032512x^{2} + 10453017600 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{10}\cdot 3^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.6
Root \(3.87527i\) of defining polynomial
Character \(\chi\) \(=\) 18.11
Dual form 18.7.d.a.5.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.89898 + 2.82843i) q^{2} +(25.6485 + 8.43532i) q^{3} +(16.0000 + 27.7128i) q^{4} +(1.59771 - 0.922438i) q^{5} +(101.793 + 113.869i) q^{6} +(6.34411 - 10.9883i) q^{7} +181.019i q^{8} +(586.691 + 432.707i) q^{9} +O(q^{10})\) \(q+(4.89898 + 2.82843i) q^{2} +(25.6485 + 8.43532i) q^{3} +(16.0000 + 27.7128i) q^{4} +(1.59771 - 0.922438i) q^{5} +(101.793 + 113.869i) q^{6} +(6.34411 - 10.9883i) q^{7} +181.019i q^{8} +(586.691 + 432.707i) q^{9} +10.4362 q^{10} +(-49.8080 - 28.7567i) q^{11} +(176.609 + 845.757i) q^{12} +(-1411.17 - 2444.23i) q^{13} +(62.1593 - 35.8877i) q^{14} +(48.7599 - 10.1820i) q^{15} +(-512.000 + 886.810i) q^{16} -7221.17i q^{17} +(1650.31 + 3779.23i) q^{18} -10648.3 q^{19} +(51.1267 + 29.5180i) q^{20} +(255.407 - 228.319i) q^{21} +(-162.672 - 281.757i) q^{22} +(11573.9 - 6682.21i) q^{23} +(-1526.96 + 4642.87i) q^{24} +(-7810.80 + 13528.7i) q^{25} -15965.6i q^{26} +(11397.7 + 16047.2i) q^{27} +406.023 q^{28} +(30795.1 + 17779.6i) q^{29} +(267.673 + 88.0326i) q^{30} +(8657.84 + 14995.8i) q^{31} +(-5016.55 + 2896.31i) q^{32} +(-1034.93 - 1157.71i) q^{33} +(20424.5 - 35376.3i) q^{34} -23.4082i q^{35} +(-2604.46 + 23182.2i) q^{36} -60441.2 q^{37} +(-52166.0 - 30118.0i) q^{38} +(-15576.7 - 74594.4i) q^{39} +(166.979 + 289.216i) q^{40} +(-75436.3 + 43553.2i) q^{41} +(1897.02 - 396.132i) q^{42} +(37932.2 - 65700.4i) q^{43} -1840.43i q^{44} +(1336.51 + 150.153i) q^{45} +75600.6 q^{46} +(61896.5 + 35736.0i) q^{47} +(-20612.6 + 18426.5i) q^{48} +(58744.0 + 101748. i) q^{49} +(-76529.9 + 44184.5i) q^{50} +(60912.8 - 185212. i) q^{51} +(45157.6 - 78215.2i) q^{52} +147761. i q^{53} +(10448.9 + 110853. i) q^{54} -106.105 q^{55} +(1989.10 + 1148.41i) q^{56} +(-273114. - 89822.1i) q^{57} +(100576. + 174203. i) q^{58} +(100224. - 57864.1i) q^{59} +(1062.33 + 1188.36i) q^{60} +(20138.6 - 34881.1i) q^{61} +97952.2i q^{62} +(8476.74 - 3701.61i) q^{63} -32768.0 q^{64} +(-4509.29 - 2603.44i) q^{65} +(-1795.59 - 8598.83i) q^{66} +(90883.7 + 157415. i) q^{67} +(200119. - 115539. i) q^{68} +(353221. - 73758.9i) q^{69} +(66.2083 - 114.676i) q^{70} -301066. i q^{71} +(-78328.3 + 106202. i) q^{72} -612635. q^{73} +(-296100. - 170954. i) q^{74} +(-314454. + 281104. i) q^{75} +(-170373. - 295095. i) q^{76} +(-631.975 + 364.871i) q^{77} +(134675. - 409494. i) q^{78} +(171651. - 297308. i) q^{79} +1889.15i q^{80} +(156971. + 507730. i) q^{81} -492748. q^{82} +(-131581. - 75968.6i) q^{83} +(10413.9 + 3424.93i) q^{84} +(-6661.07 - 11537.3i) q^{85} +(371658. - 214577. i) q^{86} +(639872. + 715786. i) q^{87} +(5205.52 - 9016.22i) q^{88} -102435. i q^{89} +(6122.82 + 4515.81i) q^{90} -35810.6 q^{91} +(370366. + 213831. i) q^{92} +(95566.0 + 457652. i) q^{93} +(202153. + 350140. i) q^{94} +(-17012.9 + 9822.43i) q^{95} +(-153098. + 31969.7i) q^{96} +(247882. - 429345. i) q^{97} +664613. i q^{98} +(-16778.7 - 38423.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 42 q^{3} + 192 q^{4} + 432 q^{5} - 144 q^{6} + 240 q^{7} + 2190 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 42 q^{3} + 192 q^{4} + 432 q^{5} - 144 q^{6} + 240 q^{7} + 2190 q^{9} + 378 q^{11} + 384 q^{12} + 1680 q^{13} - 4752 q^{14} - 10872 q^{15} - 6144 q^{16} - 2976 q^{18} - 2820 q^{19} + 13824 q^{20} + 24876 q^{21} - 3600 q^{22} - 76248 q^{23} - 6144 q^{24} + 8094 q^{25} + 127008 q^{27} + 15360 q^{28} + 97092 q^{29} + 34272 q^{30} + 21480 q^{31} - 246258 q^{33} - 27360 q^{34} + 38208 q^{36} - 25536 q^{37} + 97632 q^{38} + 42204 q^{39} - 410562 q^{41} - 222144 q^{42} + 71430 q^{43} + 13716 q^{45} - 135072 q^{46} + 347652 q^{47} + 55296 q^{48} - 135954 q^{49} + 311040 q^{50} + 336402 q^{51} - 53760 q^{52} - 173520 q^{54} + 580392 q^{55} - 152064 q^{56} - 522282 q^{57} + 159264 q^{58} + 369738 q^{59} - 170496 q^{60} + 135744 q^{61} - 103800 q^{63} - 393216 q^{64} - 753840 q^{65} + 909216 q^{66} - 289938 q^{67} + 744768 q^{68} + 2059272 q^{69} + 155952 q^{70} - 374784 q^{72} - 977700 q^{73} - 2197152 q^{74} - 2115342 q^{75} - 45120 q^{76} - 159192 q^{77} - 631488 q^{78} - 764796 q^{79} - 1428282 q^{81} + 1073088 q^{82} + 396900 q^{83} + 1441536 q^{84} + 1619568 q^{85} + 3264624 q^{86} + 3072636 q^{87} + 115200 q^{88} - 1987200 q^{90} + 355584 q^{91} - 2439936 q^{92} - 2526576 q^{93} - 736848 q^{94} - 2089260 q^{95} - 49152 q^{96} - 38874 q^{97} + 4398804 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/18\mathbb{Z}\right)^\times\).

\(n\) \(11\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.89898 + 2.82843i 0.612372 + 0.353553i
\(3\) 25.6485 + 8.43532i 0.949944 + 0.312419i
\(4\) 16.0000 + 27.7128i 0.250000 + 0.433013i
\(5\) 1.59771 0.922438i 0.0127817 0.00737950i −0.493596 0.869692i \(-0.664318\pi\)
0.506377 + 0.862312i \(0.330984\pi\)
\(6\) 101.793 + 113.869i 0.471263 + 0.527173i
\(7\) 6.34411 10.9883i 0.0184959 0.0320359i −0.856629 0.515932i \(-0.827446\pi\)
0.875125 + 0.483897i \(0.160779\pi\)
\(8\) 181.019i 0.353553i
\(9\) 586.691 + 432.707i 0.804788 + 0.593562i
\(10\) 10.4362 0.0104362
\(11\) −49.8080 28.7567i −0.0374215 0.0216053i 0.481173 0.876626i \(-0.340211\pi\)
−0.518594 + 0.855021i \(0.673544\pi\)
\(12\) 176.609 + 845.757i 0.102205 + 0.489443i
\(13\) −1411.17 2444.23i −0.642319 1.11253i −0.984914 0.173046i \(-0.944639\pi\)
0.342595 0.939483i \(-0.388694\pi\)
\(14\) 62.1593 35.8877i 0.0226528 0.0130786i
\(15\) 48.7599 10.1820i 0.0144474 0.00301687i
\(16\) −512.000 + 886.810i −0.125000 + 0.216506i
\(17\) 7221.17i 1.46981i −0.678171 0.734904i \(-0.737227\pi\)
0.678171 0.734904i \(-0.262773\pi\)
\(18\) 1650.31 + 3779.23i 0.282974 + 0.648017i
\(19\) −10648.3 −1.55246 −0.776231 0.630449i \(-0.782871\pi\)
−0.776231 + 0.630449i \(0.782871\pi\)
\(20\) 51.1267 + 29.5180i 0.00639084 + 0.00368975i
\(21\) 255.407 228.319i 0.0275787 0.0246538i
\(22\) −162.672 281.757i −0.0152773 0.0264610i
\(23\) 11573.9 6682.21i 0.951256 0.549208i 0.0577851 0.998329i \(-0.481596\pi\)
0.893471 + 0.449121i \(0.148263\pi\)
\(24\) −1526.96 + 4642.87i −0.110457 + 0.335856i
\(25\) −7810.80 + 13528.7i −0.499891 + 0.865837i
\(26\) 15965.6i 0.908376i
\(27\) 11397.7 + 16047.2i 0.579064 + 0.815282i
\(28\) 406.023 0.0184959
\(29\) 30795.1 + 17779.6i 1.26266 + 0.729000i 0.973589 0.228307i \(-0.0733190\pi\)
0.289075 + 0.957306i \(0.406652\pi\)
\(30\) 267.673 + 88.0326i 0.00991380 + 0.00326047i
\(31\) 8657.84 + 14995.8i 0.290619 + 0.503367i 0.973956 0.226736i \(-0.0728054\pi\)
−0.683337 + 0.730103i \(0.739472\pi\)
\(32\) −5016.55 + 2896.31i −0.153093 + 0.0883883i
\(33\) −1034.93 1157.71i −0.0287984 0.0322151i
\(34\) 20424.5 35376.3i 0.519656 0.900070i
\(35\) 23.4082i 0.000545963i
\(36\) −2604.46 + 23182.2i −0.0558227 + 0.496874i
\(37\) −60441.2 −1.19324 −0.596620 0.802524i \(-0.703490\pi\)
−0.596620 + 0.802524i \(0.703490\pi\)
\(38\) −52166.0 30118.0i −0.950685 0.548878i
\(39\) −15576.7 74594.4i −0.262592 1.25751i
\(40\) 166.979 + 289.216i 0.00260905 + 0.00451900i
\(41\) −75436.3 + 43553.2i −1.09453 + 0.631929i −0.934780 0.355228i \(-0.884403\pi\)
−0.159754 + 0.987157i \(0.551070\pi\)
\(42\) 1897.02 396.132i 0.0256049 0.00534677i
\(43\) 37932.2 65700.4i 0.477092 0.826348i −0.522563 0.852601i \(-0.675024\pi\)
0.999655 + 0.0262527i \(0.00835745\pi\)
\(44\) 1840.43i 0.0216053i
\(45\) 1336.51 + 150.153i 0.0146667 + 0.00164777i
\(46\) 75600.6 0.776697
\(47\) 61896.5 + 35736.0i 0.596174 + 0.344201i 0.767535 0.641007i \(-0.221483\pi\)
−0.171361 + 0.985208i \(0.554817\pi\)
\(48\) −20612.6 + 18426.5i −0.186384 + 0.166617i
\(49\) 58744.0 + 101748.i 0.499316 + 0.864840i
\(50\) −76529.9 + 44184.5i −0.612239 + 0.353476i
\(51\) 60912.8 185212.i 0.459196 1.39624i
\(52\) 45157.6 78215.2i 0.321159 0.556265i
\(53\) 147761.i 0.992505i 0.868178 + 0.496252i \(0.165291\pi\)
−0.868178 + 0.496252i \(0.834709\pi\)
\(54\) 10448.9 + 110853.i 0.0663571 + 0.703986i
\(55\) −106.105 −0.000637746
\(56\) 1989.10 + 1148.41i 0.0113264 + 0.00653930i
\(57\) −273114. 89822.1i −1.47475 0.485019i
\(58\) 100576. + 174203.i 0.515481 + 0.892838i
\(59\) 100224. 57864.1i 0.487993 0.281743i −0.235748 0.971814i \(-0.575754\pi\)
0.723742 + 0.690071i \(0.242421\pi\)
\(60\) 1062.33 + 1188.36i 0.00491819 + 0.00550168i
\(61\) 20138.6 34881.1i 0.0887239 0.153674i −0.818248 0.574865i \(-0.805054\pi\)
0.906972 + 0.421191i \(0.138388\pi\)
\(62\) 97952.2i 0.410998i
\(63\) 8476.74 3701.61i 0.0339006 0.0148036i
\(64\) −32768.0 −0.125000
\(65\) −4509.29 2603.44i −0.0164198 0.00947999i
\(66\) −1795.59 8598.83i −0.00624563 0.0299094i
\(67\) 90883.7 + 157415.i 0.302177 + 0.523386i 0.976629 0.214933i \(-0.0689533\pi\)
−0.674452 + 0.738319i \(0.735620\pi\)
\(68\) 200119. 115539.i 0.636445 0.367452i
\(69\) 353221. 73758.9i 1.07522 0.224526i
\(70\) 66.2083 114.676i 0.000193027 0.000334333i
\(71\) 301066.i 0.841175i −0.907252 0.420588i \(-0.861824\pi\)
0.907252 0.420588i \(-0.138176\pi\)
\(72\) −78328.3 + 106202.i −0.209856 + 0.284536i
\(73\) −612635. −1.57483 −0.787415 0.616424i \(-0.788581\pi\)
−0.787415 + 0.616424i \(0.788581\pi\)
\(74\) −296100. 170954.i −0.730707 0.421874i
\(75\) −314454. + 281104.i −0.745373 + 0.666321i
\(76\) −170373. 295095.i −0.388116 0.672236i
\(77\) −631.975 + 364.871i −0.00138429 + 0.000799221i
\(78\) 134675. 409494.i 0.283794 0.862907i
\(79\) 171651. 297308.i 0.348149 0.603012i −0.637772 0.770225i \(-0.720144\pi\)
0.985921 + 0.167214i \(0.0534770\pi\)
\(80\) 1889.15i 0.00368975i
\(81\) 156971. + 507730.i 0.295369 + 0.955383i
\(82\) −492748. −0.893683
\(83\) −131581. 75968.6i −0.230123 0.132862i 0.380506 0.924779i \(-0.375750\pi\)
−0.610629 + 0.791917i \(0.709083\pi\)
\(84\) 10413.9 + 3424.93i 0.0175701 + 0.00577849i
\(85\) −6661.07 11537.3i −0.0108464 0.0187866i
\(86\) 371658. 214577.i 0.584316 0.337355i
\(87\) 639872. + 715786.i 0.971707 + 1.08699i
\(88\) 5205.52 9016.22i 0.00763864 0.0132305i
\(89\) 102435.i 0.145304i −0.997357 0.0726520i \(-0.976854\pi\)
0.997357 0.0726520i \(-0.0231462\pi\)
\(90\) 6122.82 + 4515.81i 0.00839893 + 0.00619452i
\(91\) −35810.6 −0.0475212
\(92\) 370366. + 213831.i 0.475628 + 0.274604i
\(93\) 95566.0 + 457652.i 0.118810 + 0.568966i
\(94\) 202153. + 350140.i 0.243387 + 0.421558i
\(95\) −17012.9 + 9822.43i −0.0198431 + 0.0114564i
\(96\) −153098. + 31969.7i −0.173044 + 0.0361348i
\(97\) 247882. 429345.i 0.271600 0.470425i −0.697672 0.716418i \(-0.745780\pi\)
0.969272 + 0.245992i \(0.0791138\pi\)
\(98\) 664613.i 0.706139i
\(99\) −16778.7 38423.5i −0.0172923 0.0395997i
\(100\) −499891. −0.499891
\(101\) 68156.2 + 39350.0i 0.0661517 + 0.0381927i 0.532711 0.846297i \(-0.321173\pi\)
−0.466559 + 0.884490i \(0.654507\pi\)
\(102\) 822270. 735062.i 0.774843 0.692666i
\(103\) 326814. + 566059.i 0.299081 + 0.518024i 0.975926 0.218102i \(-0.0699865\pi\)
−0.676845 + 0.736126i \(0.736653\pi\)
\(104\) 442452. 255450.i 0.393338 0.227094i
\(105\) 197.455 600.384i 0.000170569 0.000518634i
\(106\) −417932. + 723879.i −0.350903 + 0.607783i
\(107\) 1.53176e6i 1.25037i −0.780476 0.625186i \(-0.785023\pi\)
0.780476 0.625186i \(-0.214977\pi\)
\(108\) −262349. + 572618.i −0.208261 + 0.454563i
\(109\) 863246. 0.666584 0.333292 0.942824i \(-0.391840\pi\)
0.333292 + 0.942824i \(0.391840\pi\)
\(110\) −519.806 300.110i −0.000390538 0.000225477i
\(111\) −1.55023e6 509841.i −1.13351 0.372791i
\(112\) 6496.36 + 11252.0i 0.00462398 + 0.00800897i
\(113\) −1.51141e6 + 872613.i −1.04748 + 0.604765i −0.921944 0.387324i \(-0.873400\pi\)
−0.125540 + 0.992089i \(0.540066\pi\)
\(114\) −1.08392e6 1.21252e6i −0.731618 0.818416i
\(115\) 12327.8 21352.5i 0.00810576 0.0140396i
\(116\) 1.13789e6i 0.729000i
\(117\) 229710. 2.04463e6i 0.143424 1.27661i
\(118\) 654658. 0.398445
\(119\) −79348.4 45811.8i −0.0470866 0.0271855i
\(120\) 1843.13 + 8826.48i 0.00106663 + 0.00510792i
\(121\) −884127. 1.53135e6i −0.499066 0.864408i
\(122\) 197318. 113921.i 0.108664 0.0627373i
\(123\) −2.30221e6 + 480744.i −1.23717 + 0.258344i
\(124\) −277051. + 479866.i −0.145310 + 0.251684i
\(125\) 57646.1i 0.0295148i
\(126\) 51997.1 + 5841.76i 0.0259937 + 0.00292033i
\(127\) 3.20463e6 1.56447 0.782234 0.622985i \(-0.214080\pi\)
0.782234 + 0.622985i \(0.214080\pi\)
\(128\) −160530. 92681.9i −0.0765466 0.0441942i
\(129\) 1.52711e6 1.36515e6i 0.711378 0.635932i
\(130\) −14727.3 25508.4i −0.00670336 0.0116106i
\(131\) −2.63987e6 + 1.52413e6i −1.17427 + 0.677967i −0.954683 0.297625i \(-0.903805\pi\)
−0.219590 + 0.975592i \(0.570472\pi\)
\(132\) 15524.6 47204.2i 0.00674992 0.0205239i
\(133\) −67554.2 + 117007.i −0.0287142 + 0.0497345i
\(134\) 1.02823e6i 0.427343i
\(135\) 33012.8 + 15125.1i 0.0134178 + 0.00614746i
\(136\) 1.30717e6 0.519656
\(137\) 3.54873e6 + 2.04886e6i 1.38010 + 0.796802i 0.992171 0.124887i \(-0.0398567\pi\)
0.387931 + 0.921689i \(0.373190\pi\)
\(138\) 1.93904e6 + 637715.i 0.737819 + 0.242655i
\(139\) 556460. + 963816.i 0.207200 + 0.358881i 0.950831 0.309709i \(-0.100232\pi\)
−0.743632 + 0.668590i \(0.766898\pi\)
\(140\) 648.706 374.531i 0.000236409 0.000136491i
\(141\) 1.28611e6 + 1.43869e6i 0.458797 + 0.513228i
\(142\) 851543. 1.47492e6i 0.297400 0.515112i
\(143\) 162323.i 0.0555100i
\(144\) −684114. + 298737.i −0.229108 + 0.100047i
\(145\) 65602.2 0.0215186
\(146\) −3.00129e6 1.73279e6i −0.964382 0.556786i
\(147\) 648422. + 3.10520e6i 0.204129 + 0.977546i
\(148\) −967059. 1.67500e6i −0.298310 0.516688i
\(149\) −440188. + 254142.i −0.133070 + 0.0768278i −0.565057 0.825052i \(-0.691146\pi\)
0.431987 + 0.901880i \(0.357812\pi\)
\(150\) −2.33559e6 + 487713.i −0.692026 + 0.144508i
\(151\) −2.81751e6 + 4.88007e6i −0.818341 + 1.41741i 0.0885624 + 0.996071i \(0.471773\pi\)
−0.906904 + 0.421338i \(0.861561\pi\)
\(152\) 1.92756e6i 0.548878i
\(153\) 3.12465e6 4.23659e6i 0.872422 1.18288i
\(154\) −4128.04 −0.00113027
\(155\) 27665.4 + 15972.6i 0.00742920 + 0.00428925i
\(156\) 1.81799e6 1.62518e6i 0.478871 0.428084i
\(157\) −2.68126e6 4.64408e6i −0.692852 1.20005i −0.970900 0.239487i \(-0.923021\pi\)
0.278048 0.960567i \(-0.410313\pi\)
\(158\) 1.68183e6 971005.i 0.426394 0.246179i
\(159\) −1.24641e6 + 3.78985e6i −0.310078 + 0.942824i
\(160\) −5343.33 + 9254.92i −0.00130452 + 0.00225950i
\(161\) 169571.i 0.0406324i
\(162\) −667079. + 2.93134e6i −0.156903 + 0.689479i
\(163\) −2.42021e6 −0.558844 −0.279422 0.960168i \(-0.590143\pi\)
−0.279422 + 0.960168i \(0.590143\pi\)
\(164\) −2.41396e6 1.39370e6i −0.547267 0.315965i
\(165\) −2721.43 895.030i −0.000605823 0.000199244i
\(166\) −429743. 744337.i −0.0939474 0.162722i
\(167\) 7.16092e6 4.13436e6i 1.53751 0.887685i 0.538532 0.842605i \(-0.318979\pi\)
0.998983 0.0450793i \(-0.0143541\pi\)
\(168\) 41330.2 + 46233.5i 0.00871645 + 0.00975056i
\(169\) −1.56942e6 + 2.71832e6i −0.325147 + 0.563171i
\(170\) 75361.5i 0.0153392i
\(171\) −6.24728e6 4.60761e6i −1.24940 0.921482i
\(172\) 2.42766e6 0.477092
\(173\) 2.27322e6 + 1.31244e6i 0.439039 + 0.253479i 0.703190 0.711002i \(-0.251758\pi\)
−0.264151 + 0.964481i \(0.585092\pi\)
\(174\) 1.11017e6 + 5.31645e6i 0.210738 + 1.00919i
\(175\) 99105.0 + 171655.i 0.0184919 + 0.0320289i
\(176\) 51003.4 29446.8i 0.00935538 0.00540133i
\(177\) 3.05869e6 638709.i 0.551588 0.115182i
\(178\) 289729. 501826.i 0.0513727 0.0889802i
\(179\) 7.60442e6i 1.32589i −0.748669 0.662944i \(-0.769307\pi\)
0.748669 0.662944i \(-0.230693\pi\)
\(180\) 17222.9 + 39440.8i 0.00295318 + 0.00676282i
\(181\) −9.89440e6 −1.66861 −0.834303 0.551306i \(-0.814130\pi\)
−0.834303 + 0.551306i \(0.814130\pi\)
\(182\) −175435. 101288.i −0.0291006 0.0168013i
\(183\) 810759. 724773.i 0.132294 0.118263i
\(184\) 1.20961e6 + 2.09511e6i 0.194174 + 0.336320i
\(185\) −96567.4 + 55753.2i −0.0152516 + 0.00880552i
\(186\) −826258. + 2.51233e6i −0.128404 + 0.390425i
\(187\) −207657. + 359672.i −0.0317557 + 0.0550024i
\(188\) 2.28710e6i 0.344201i
\(189\) 248640. 23436.6i 0.0368286 0.00347143i
\(190\) −111128. −0.0162018
\(191\) −1.09559e6 632537.i −0.157234 0.0907791i 0.419319 0.907839i \(-0.362269\pi\)
−0.576553 + 0.817060i \(0.695602\pi\)
\(192\) −840450. 276409.i −0.118743 0.0390524i
\(193\) −654987. 1.13447e6i −0.0911089 0.157805i 0.816869 0.576823i \(-0.195708\pi\)
−0.907978 + 0.419018i \(0.862374\pi\)
\(194\) 2.42874e6 1.40223e6i 0.332641 0.192050i
\(195\) −93695.7 104812.i −0.0126362 0.0141353i
\(196\) −1.87981e6 + 3.25592e6i −0.249658 + 0.432420i
\(197\) 9.83234e6i 1.28605i 0.765845 + 0.643025i \(0.222321\pi\)
−0.765845 + 0.643025i \(0.777679\pi\)
\(198\) 26479.6 235694.i 0.00341127 0.0303635i
\(199\) 1.36283e7 1.72934 0.864672 0.502336i \(-0.167526\pi\)
0.864672 + 0.502336i \(0.167526\pi\)
\(200\) −2.44896e6 1.41391e6i −0.306120 0.176738i
\(201\) 1.00318e6 + 4.80410e6i 0.123536 + 0.591594i
\(202\) 222597. + 385549.i 0.0270063 + 0.0467763i
\(203\) 390735. 225591.i 0.0467083 0.0269671i
\(204\) 6.10735e6 1.27533e6i 0.719387 0.150221i
\(205\) −80350.2 + 139171.i −0.00932664 + 0.0161542i
\(206\) 3.69748e6i 0.422965i
\(207\) 9.68176e6 + 1.08772e6i 1.09155 + 0.122633i
\(208\) 2.89009e6 0.321159
\(209\) 530373. + 306211.i 0.0580955 + 0.0335414i
\(210\) 2665.47 2382.78i 0.000287817 0.000257292i
\(211\) 1.55640e6 + 2.69577e6i 0.165682 + 0.286969i 0.936897 0.349605i \(-0.113684\pi\)
−0.771216 + 0.636574i \(0.780351\pi\)
\(212\) −4.09488e6 + 2.36418e6i −0.429767 + 0.248126i
\(213\) 2.53959e6 7.72189e6i 0.262799 0.799070i
\(214\) 4.33247e6 7.50405e6i 0.442073 0.765693i
\(215\) 139960.i 0.0140828i
\(216\) −2.90485e6 + 2.06321e6i −0.288246 + 0.204730i
\(217\) 219705. 0.0215011
\(218\) 4.22902e6 + 2.44163e6i 0.408198 + 0.235673i
\(219\) −1.57132e7 5.16778e6i −1.49600 0.492007i
\(220\) −1697.68 2940.47i −0.000159437 0.000276152i
\(221\) −1.76502e7 + 1.01903e7i −1.63520 + 0.944085i
\(222\) −6.15248e6 6.88240e6i −0.562330 0.629044i
\(223\) 1.00499e7 1.74069e7i 0.906248 1.56967i 0.0870139 0.996207i \(-0.472268\pi\)
0.819234 0.573460i \(-0.194399\pi\)
\(224\) 73498.0i 0.00653930i
\(225\) −1.04365e7 + 4.55738e6i −0.916234 + 0.400099i
\(226\) −9.87249e6 −0.855267
\(227\) −1.03090e7 5.95188e6i −0.881328 0.508835i −0.0102317 0.999948i \(-0.503257\pi\)
−0.871096 + 0.491113i \(0.836590\pi\)
\(228\) −1.88060e6 9.00591e6i −0.158669 0.759841i
\(229\) 1.55174e6 + 2.68769e6i 0.129215 + 0.223807i 0.923373 0.383905i \(-0.125421\pi\)
−0.794158 + 0.607712i \(0.792088\pi\)
\(230\) 120788. 69736.8i 0.00992749 0.00573164i
\(231\) −19287.0 + 4027.48i −0.00156469 + 0.000326736i
\(232\) −3.21845e6 + 5.57451e6i −0.257740 + 0.446419i
\(233\) 9.36024e6i 0.739979i 0.929036 + 0.369989i \(0.120639\pi\)
−0.929036 + 0.369989i \(0.879361\pi\)
\(234\) 6.90843e6 9.36688e6i 0.539177 0.731051i
\(235\) 131857. 0.0101601
\(236\) 3.20715e6 + 1.85165e6i 0.243997 + 0.140872i
\(237\) 6.91048e6 6.17758e6i 0.519115 0.464059i
\(238\) −259151. 448862.i −0.0192230 0.0332953i
\(239\) 6.05702e6 3.49702e6i 0.443676 0.256156i −0.261480 0.965209i \(-0.584211\pi\)
0.705156 + 0.709053i \(0.250877\pi\)
\(240\) −15935.6 + 48453.9i −0.00115275 + 0.00350506i
\(241\) 2.06773e6 3.58141e6i 0.147721 0.255860i −0.782664 0.622445i \(-0.786140\pi\)
0.930385 + 0.366585i \(0.119473\pi\)
\(242\) 1.00028e7i 0.705786i
\(243\) −256792. + 1.43466e7i −0.0178963 + 0.999840i
\(244\) 1.28887e6 0.0887239
\(245\) 187712. + 108375.i 0.0127642 + 0.00736940i
\(246\) −1.26382e7 4.15649e6i −0.848949 0.279204i
\(247\) 1.50267e7 + 2.60269e7i 0.997176 + 1.72716i
\(248\) −2.71453e6 + 1.56724e6i −0.177967 + 0.102749i
\(249\) −2.73405e6 3.05841e6i −0.177096 0.198106i
\(250\) −163048. + 282407.i −0.0104351 + 0.0180740i
\(251\) 6.15130e6i 0.388997i −0.980903 0.194498i \(-0.937692\pi\)
0.980903 0.194498i \(-0.0623079\pi\)
\(252\) 238210. + 175689.i 0.0148853 + 0.0109785i
\(253\) −768633. −0.0474633
\(254\) 1.56994e7 + 9.06406e6i 0.958037 + 0.553123i
\(255\) −73525.6 352103.i −0.00443423 0.0212349i
\(256\) −524288. 908093.i −0.0312500 0.0541266i
\(257\) 6.62383e6 3.82427e6i 0.390220 0.225294i −0.292035 0.956408i \(-0.594332\pi\)
0.682256 + 0.731114i \(0.260999\pi\)
\(258\) 1.13425e7 2.36852e6i 0.660464 0.137917i
\(259\) −383445. + 664147.i −0.0220701 + 0.0382265i
\(260\) 166620.i 0.00947999i
\(261\) 1.03739e7 + 2.37564e7i 0.583471 + 1.33616i
\(262\) −1.72436e7 −0.958790
\(263\) 7.24714e6 + 4.18414e6i 0.398382 + 0.230006i 0.685786 0.727804i \(-0.259459\pi\)
−0.287404 + 0.957810i \(0.592792\pi\)
\(264\) 209568. 187342.i 0.0113897 0.0101818i
\(265\) 136300. + 236079.i 0.00732419 + 0.0126859i
\(266\) −661893. + 382144.i −0.0351676 + 0.0203040i
\(267\) 864071. 2.62730e6i 0.0453958 0.138031i
\(268\) −2.90828e6 + 5.03729e6i −0.151089 + 0.261693i
\(269\) 2.26505e7i 1.16364i −0.813316 0.581822i \(-0.802340\pi\)
0.813316 0.581822i \(-0.197660\pi\)
\(270\) 118949. + 167472.i 0.00604322 + 0.00850844i
\(271\) −1.56983e7 −0.788758 −0.394379 0.918948i \(-0.629040\pi\)
−0.394379 + 0.918948i \(0.629040\pi\)
\(272\) 6.40380e6 + 3.69724e6i 0.318223 + 0.183726i
\(273\) −918487. 302074.i −0.0451424 0.0148465i
\(274\) 1.15901e7 + 2.00746e7i 0.563424 + 0.975879i
\(275\) 778081. 449225.i 0.0374134 0.0216006i
\(276\) 7.69559e6 + 8.60859e6i 0.366029 + 0.409454i
\(277\) 9.51658e6 1.64832e7i 0.447756 0.775537i −0.550483 0.834846i \(-0.685557\pi\)
0.998240 + 0.0593095i \(0.0188899\pi\)
\(278\) 6.29562e6i 0.293025i
\(279\) −1.40931e6 + 1.25442e7i −0.0648926 + 0.577605i
\(280\) 4237.33 0.000193027
\(281\) −1.12171e7 6.47622e6i −0.505549 0.291879i 0.225453 0.974254i \(-0.427614\pi\)
−0.731002 + 0.682375i \(0.760947\pi\)
\(282\) 2.23139e6 + 1.06858e7i 0.0995010 + 0.476496i
\(283\) −1.67469e7 2.90065e7i −0.738883 1.27978i −0.952999 0.302974i \(-0.902020\pi\)
0.214116 0.976808i \(-0.431313\pi\)
\(284\) 8.34338e6 4.81705e6i 0.364240 0.210294i
\(285\) −519212. + 108421.i −0.0224290 + 0.00468358i
\(286\) −459118. + 795216.i −0.0196258 + 0.0339928i
\(287\) 1.10522e6i 0.0467525i
\(288\) −4.19642e6 471458.i −0.175672 0.0197363i
\(289\) −2.80077e7 −1.16033
\(290\) 321384. + 185551.i 0.0131774 + 0.00760798i
\(291\) 9.97946e6 8.92108e6i 0.404975 0.362025i
\(292\) −9.80217e6 1.69779e7i −0.393707 0.681921i
\(293\) 1.31069e7 7.56728e6i 0.521072 0.300841i −0.216301 0.976327i \(-0.569399\pi\)
0.737373 + 0.675486i \(0.236066\pi\)
\(294\) −5.60622e6 + 1.70463e7i −0.220611 + 0.670793i
\(295\) 106752. 184900.i 0.00415825 0.00720229i
\(296\) 1.09410e7i 0.421874i
\(297\) −106234. 1.12704e6i −0.00405502 0.0430200i
\(298\) −2.87529e6 −0.108651
\(299\) −3.26657e7 1.88595e7i −1.22202 0.705533i
\(300\) −1.28215e7 4.21674e6i −0.474869 0.156176i
\(301\) −481291. 833621.i −0.0176485 0.0305682i
\(302\) −2.76058e7 + 1.59382e7i −1.00226 + 0.578655i
\(303\) 1.41617e6 + 1.58419e6i 0.0509083 + 0.0569480i
\(304\) 5.45195e6 9.44305e6i 0.194058 0.336118i
\(305\) 74306.5i 0.00261895i
\(306\) 2.72905e7 1.19171e7i 0.952460 0.415918i
\(307\) −5.41823e6 −0.187259 −0.0936294 0.995607i \(-0.529847\pi\)
−0.0936294 + 0.995607i \(0.529847\pi\)
\(308\) −20223.2 11675.9i −0.000692146 0.000399611i
\(309\) 3.60741e6 + 1.72753e7i 0.122270 + 0.585533i
\(310\) 90354.8 + 156499.i 0.00303296 + 0.00525324i
\(311\) 2.36986e7 1.36824e7i 0.787848 0.454864i −0.0513567 0.998680i \(-0.516355\pi\)
0.839204 + 0.543816i \(0.183021\pi\)
\(312\) 1.35030e7 2.81968e6i 0.444598 0.0928402i
\(313\) −1.13895e7 + 1.97272e7i −0.371426 + 0.643328i −0.989785 0.142567i \(-0.954464\pi\)
0.618360 + 0.785895i \(0.287798\pi\)
\(314\) 3.03350e7i 0.979840i
\(315\) 10128.9 13733.4i 0.000324063 0.000439385i
\(316\) 1.09857e7 0.348149
\(317\) 2.29031e7 + 1.32231e7i 0.718979 + 0.415103i 0.814377 0.580337i \(-0.197079\pi\)
−0.0953979 + 0.995439i \(0.530412\pi\)
\(318\) −1.68255e7 + 1.50410e7i −0.523222 + 0.467731i
\(319\) −1.02256e6 1.77113e6i −0.0315005 0.0545605i
\(320\) −52353.7 + 30226.4i −0.00159771 + 0.000922438i
\(321\) 1.29209e7 3.92873e7i 0.390640 1.18778i
\(322\) 479618. 830723.i 0.0143657 0.0248822i
\(323\) 7.68934e7i 2.28182i
\(324\) −1.15591e7 + 1.24738e7i −0.339851 + 0.366744i
\(325\) 4.40896e7 1.28436
\(326\) −1.18566e7 6.84539e6i −0.342221 0.197581i
\(327\) 2.21410e7 + 7.28176e6i 0.633218 + 0.208254i
\(328\) −7.88397e6 1.36554e7i −0.223421 0.386976i
\(329\) 785356. 453426.i 0.0220536 0.0127326i
\(330\) −10800.7 12082.1i −0.000300546 0.000336203i
\(331\) −2.25635e7 + 3.90812e7i −0.622190 + 1.07766i 0.366887 + 0.930265i \(0.380424\pi\)
−0.989077 + 0.147399i \(0.952910\pi\)
\(332\) 4.86199e6i 0.132862i
\(333\) −3.54603e7 2.61533e7i −0.960306 0.708262i
\(334\) 4.67749e7 1.25538
\(335\) 290411. + 167669.i 0.00772466 + 0.00445983i
\(336\) 71707.5 + 343397.i 0.00189037 + 0.00905270i
\(337\) 1.56916e7 + 2.71787e7i 0.409994 + 0.710131i 0.994889 0.100978i \(-0.0321973\pi\)
−0.584894 + 0.811110i \(0.698864\pi\)
\(338\) −1.53771e7 + 8.87800e6i −0.398222 + 0.229914i
\(339\) −4.61262e7 + 9.63199e6i −1.18399 + 0.247239i
\(340\) 213154. 369194.i 0.00542322 0.00939330i
\(341\) 995883.i 0.0251157i
\(342\) −1.75730e7 4.02425e7i −0.439307 1.00602i
\(343\) 2.98347e6 0.0739331
\(344\) 1.18931e7 + 6.86646e6i 0.292158 + 0.168678i
\(345\) 496306. 443669.i 0.0120863 0.0108044i
\(346\) 7.42430e6 + 1.28593e7i 0.179237 + 0.310447i
\(347\) 9.52685e6 5.50033e6i 0.228014 0.131644i −0.381642 0.924310i \(-0.624641\pi\)
0.609655 + 0.792667i \(0.291308\pi\)
\(348\) −9.59849e6 + 2.91852e7i −0.227753 + 0.692509i
\(349\) 1.73905e6 3.01213e6i 0.0409107 0.0708594i −0.844845 0.535011i \(-0.820307\pi\)
0.885756 + 0.464152i \(0.153641\pi\)
\(350\) 1.12125e6i 0.0261515i
\(351\) 2.31388e7 5.05040e7i 0.535081 1.16790i
\(352\) 333153. 0.00763864
\(353\) 2.33541e7 + 1.34835e7i 0.530932 + 0.306534i 0.741396 0.671068i \(-0.234164\pi\)
−0.210464 + 0.977602i \(0.567497\pi\)
\(354\) 1.67910e7 + 5.52225e6i 0.378500 + 0.124482i
\(355\) −277714. 481016.i −0.00620745 0.0107516i
\(356\) 2.83876e6 1.63896e6i 0.0629185 0.0363260i
\(357\) −1.64873e6 1.84433e6i −0.0362364 0.0405354i
\(358\) 2.15086e7 3.72539e7i 0.468773 0.811938i
\(359\) 8.82517e7i 1.90739i 0.300775 + 0.953695i \(0.402755\pi\)
−0.300775 + 0.953695i \(0.597245\pi\)
\(360\) −27180.7 + 241933.i −0.000582576 + 0.00518547i
\(361\) 6.63412e7 1.41014
\(362\) −4.84725e7 2.79856e7i −1.02181 0.589941i
\(363\) −9.75907e6 4.67348e7i −0.204027 0.977058i
\(364\) −572969. 992411.i −0.0118803 0.0205773i
\(365\) −978813. + 565118.i −0.0201290 + 0.0116215i
\(366\) 6.02186e6 1.25747e6i 0.122825 0.0256481i
\(367\) −1.50282e7 + 2.60296e7i −0.304024 + 0.526585i −0.977044 0.213040i \(-0.931664\pi\)
0.673019 + 0.739625i \(0.264997\pi\)
\(368\) 1.36852e7i 0.274604i
\(369\) −6.31036e7 7.08954e6i −1.25596 0.141104i
\(370\) −630776. −0.0124529
\(371\) 1.62365e6 + 937412.i 0.0317958 + 0.0183573i
\(372\) −1.11538e7 + 9.97083e6i −0.216667 + 0.193688i
\(373\) −1.95923e7 3.39349e7i −0.377537 0.653913i 0.613166 0.789954i \(-0.289896\pi\)
−0.990703 + 0.136041i \(0.956562\pi\)
\(374\) −2.03461e6 + 1.17468e6i −0.0388926 + 0.0224547i
\(375\) −486263. + 1.47854e6i −0.00922099 + 0.0280374i
\(376\) −6.46890e6 + 1.12045e7i −0.121693 + 0.210779i
\(377\) 1.00360e8i 1.87300i
\(378\) 1.28437e6 + 588445.i 0.0237802 + 0.0108951i
\(379\) −3.94927e7 −0.725436 −0.362718 0.931899i \(-0.618151\pi\)
−0.362718 + 0.931899i \(0.618151\pi\)
\(380\) −544414. 314318.i −0.00992153 0.00572820i
\(381\) 8.21939e7 + 2.70321e7i 1.48616 + 0.488770i
\(382\) −3.57817e6 6.19757e6i −0.0641905 0.111181i
\(383\) −5.89496e7 + 3.40346e7i −1.04926 + 0.605793i −0.922443 0.386133i \(-0.873811\pi\)
−0.126821 + 0.991926i \(0.540477\pi\)
\(384\) −3.33555e6 3.73127e6i −0.0589079 0.0658966i
\(385\) −673.141 + 1165.91i −1.17957e−5 + 2.04308e-5i
\(386\) 7.41034e6i 0.128847i
\(387\) 5.06835e7 2.21323e7i 0.874447 0.381852i
\(388\) 1.58645e7 0.271600
\(389\) −6.88443e7 3.97473e7i −1.16955 0.675241i −0.215977 0.976398i \(-0.569294\pi\)
−0.953574 + 0.301157i \(0.902627\pi\)
\(390\) −162561. 778482.i −0.00274046 0.0131236i
\(391\) −4.82534e7 8.35773e7i −0.807230 1.39816i
\(392\) −1.84183e7 + 1.06338e7i −0.305767 + 0.176535i
\(393\) −8.05653e7 + 1.68235e7i −1.32730 + 0.277165i
\(394\) −2.78101e7 + 4.81684e7i −0.454688 + 0.787542i
\(395\) 633349.i 0.0102767i
\(396\) 796365. 1.07976e6i 0.0128241 0.0173877i
\(397\) −4.50639e6 −0.0720206 −0.0360103 0.999351i \(-0.511465\pi\)
−0.0360103 + 0.999351i \(0.511465\pi\)
\(398\) 6.67646e7 + 3.85466e7i 1.05900 + 0.611416i
\(399\) −2.71966e6 + 2.43122e6i −0.0428149 + 0.0382741i
\(400\) −7.99826e6 1.38534e7i −0.124973 0.216459i
\(401\) 3.46331e7 1.99954e7i 0.537104 0.310097i −0.206801 0.978383i \(-0.566305\pi\)
0.743904 + 0.668286i \(0.232972\pi\)
\(402\) −8.67346e6 + 2.63726e7i −0.133510 + 0.405952i
\(403\) 2.44354e7 4.23234e7i 0.373340 0.646645i
\(404\) 2.51840e6i 0.0381927i
\(405\) 719143. + 666409.i 0.0108256 + 0.0100317i
\(406\) 2.55227e6 0.0381372
\(407\) 3.01046e6 + 1.73809e6i 0.0446529 + 0.0257803i
\(408\) 3.35270e7 + 1.10264e7i 0.493644 + 0.162350i
\(409\) 2.00563e7 + 3.47385e7i 0.293144 + 0.507740i 0.974551 0.224164i \(-0.0719653\pi\)
−0.681408 + 0.731904i \(0.738632\pi\)
\(410\) −787268. + 454529.i −0.0114228 + 0.00659493i
\(411\) 7.37368e7 + 8.24848e7i 1.06208 + 1.18809i
\(412\) −1.04581e7 + 1.81139e7i −0.149541 + 0.259012i
\(413\) 1.46838e6i 0.0208444i
\(414\) 4.43542e7 + 3.27129e7i 0.625077 + 0.461018i
\(415\) −280305. −0.00392181
\(416\) 1.41585e7 + 8.17440e6i 0.196669 + 0.113547i
\(417\) 6.14225e6 + 2.94144e7i 0.0847071 + 0.405650i
\(418\) 1.73219e6 + 3.00024e6i 0.0237174 + 0.0410797i
\(419\) 7.70293e7 4.44729e7i 1.04716 0.604579i 0.125309 0.992118i \(-0.460008\pi\)
0.921854 + 0.387538i \(0.126675\pi\)
\(420\) 19797.6 4134.10i 0.000267218 5.57999e-5i
\(421\) −2.31687e7 + 4.01293e7i −0.310495 + 0.537793i −0.978470 0.206391i \(-0.933828\pi\)
0.667975 + 0.744184i \(0.267161\pi\)
\(422\) 1.76087e7i 0.234309i
\(423\) 2.08509e7 + 4.77490e7i 0.275489 + 0.630875i
\(424\) −2.67476e7 −0.350903
\(425\) 9.76930e7 + 5.64031e7i 1.27261 + 0.734744i
\(426\) 3.42822e7 3.06463e7i 0.443445 0.396415i
\(427\) −255523. 442579.i −0.00328206 0.00568470i
\(428\) 4.24493e7 2.45081e7i 0.541427 0.312593i
\(429\) −1.36925e6 + 4.16334e6i −0.0173424 + 0.0527314i
\(430\) 395867. 685662.i 0.00497902 0.00862392i
\(431\) 1.17075e8i 1.46228i −0.682227 0.731140i \(-0.738988\pi\)
0.682227 0.731140i \(-0.261012\pi\)
\(432\) −2.00664e7 + 1.89144e6i −0.248897 + 0.0234608i
\(433\) 1.81236e7 0.223244 0.111622 0.993751i \(-0.464395\pi\)
0.111622 + 0.993751i \(0.464395\pi\)
\(434\) 1.07633e6 + 621419.i 0.0131667 + 0.00760178i
\(435\) 1.68260e6 + 553375.i 0.0204415 + 0.00672283i
\(436\) 1.38119e7 + 2.39230e7i 0.166646 + 0.288639i
\(437\) −1.23243e8 + 7.11545e7i −1.47679 + 0.852624i
\(438\) −6.23619e7 6.97604e7i −0.742159 0.830208i
\(439\) −3.02641e6 + 5.24189e6i −0.0357712 + 0.0619576i −0.883357 0.468701i \(-0.844722\pi\)
0.847586 + 0.530659i \(0.178055\pi\)
\(440\) 19207.1i 0.000225477i
\(441\) −9.56229e6 + 8.51133e7i −0.111493 + 0.992388i
\(442\) −1.15290e8 −1.33514
\(443\) 4.21347e6 + 2.43265e6i 0.0484651 + 0.0279813i 0.524037 0.851696i \(-0.324425\pi\)
−0.475572 + 0.879677i \(0.657759\pi\)
\(444\) −1.06745e7 5.11186e7i −0.121955 0.584023i
\(445\) −94489.7 163661.i −0.00107227 0.00185723i
\(446\) 9.84684e7 5.68508e7i 1.10992 0.640814i
\(447\) −1.34339e7 + 2.80525e6i −0.150411 + 0.0314086i
\(448\) −207884. + 360065.i −0.00231199 + 0.00400449i
\(449\) 1.43332e8i 1.58345i −0.610877 0.791725i \(-0.709183\pi\)
0.610877 0.791725i \(-0.290817\pi\)
\(450\) −6.40183e7 7.19232e6i −0.702533 0.0789280i
\(451\) 5.00978e6 0.0546121
\(452\) −4.83651e7 2.79236e7i −0.523742 0.302382i
\(453\) −1.13430e8 + 1.01400e8i −1.22020 + 1.09079i
\(454\) −3.36689e7 5.83163e7i −0.359800 0.623193i
\(455\) −57214.9 + 33033.0i −0.000607400 + 0.000350682i
\(456\) 1.62595e7 4.94389e7i 0.171480 0.521404i
\(457\) −4.87353e7 + 8.44121e7i −0.510617 + 0.884415i 0.489307 + 0.872111i \(0.337250\pi\)
−0.999924 + 0.0123031i \(0.996084\pi\)
\(458\) 1.75559e7i 0.182738i
\(459\) 1.15879e8 8.23048e7i 1.19831 0.851113i
\(460\) 788982. 0.00810576
\(461\) −4.63065e7 2.67351e7i −0.472650 0.272884i 0.244699 0.969599i \(-0.421311\pi\)
−0.717348 + 0.696715i \(0.754644\pi\)
\(462\) −105878. 34821.4i −0.00107369 0.000353118i
\(463\) −1.53890e7 2.66545e7i −0.155048 0.268552i 0.778028 0.628229i \(-0.216220\pi\)
−0.933077 + 0.359678i \(0.882887\pi\)
\(464\) −3.15342e7 + 1.82063e7i −0.315666 + 0.182250i
\(465\) 574842. + 643040.i 0.00571728 + 0.00639557i
\(466\) −2.64748e7 + 4.58556e7i −0.261622 + 0.453142i
\(467\) 1.10305e8i 1.08304i 0.840688 + 0.541519i \(0.182151\pi\)
−0.840688 + 0.541519i \(0.817849\pi\)
\(468\) 6.03378e7 2.63482e7i 0.588643 0.257047i
\(469\) 2.30630e6 0.0223562
\(470\) 645964. + 372947.i 0.00622178 + 0.00359215i
\(471\) −2.95960e7 1.41731e8i −0.283250 1.35644i
\(472\) 1.04745e7 + 1.81424e7i 0.0996112 + 0.172532i
\(473\) −3.77865e6 + 2.18161e6i −0.0357070 + 0.0206155i
\(474\) 5.13271e7 1.07180e7i 0.481961 0.100642i
\(475\) 8.31720e7 1.44058e8i 0.776062 1.34418i
\(476\) 2.93196e6i 0.0271855i
\(477\) −6.39372e7 + 8.66901e7i −0.589113 + 0.798756i
\(478\) 3.95643e7 0.362260
\(479\) −7.31282e6 4.22206e6i −0.0665393 0.0384165i 0.466361 0.884594i \(-0.345565\pi\)
−0.532901 + 0.846178i \(0.678898\pi\)
\(480\) −215117. + 192302.i −0.00194514 + 0.00173884i
\(481\) 8.52931e7 + 1.47732e8i 0.766441 + 1.32751i
\(482\) 2.02595e7 1.16968e7i 0.180920 0.104454i
\(483\) 1.43038e6 4.34923e6i 0.0126944 0.0385986i
\(484\) 2.82921e7 4.90033e7i 0.249533 0.432204i
\(485\) 914623.i 0.00801710i
\(486\) −4.18364e7 + 6.95574e7i −0.364456 + 0.605947i
\(487\) −3.58999e7 −0.310818 −0.155409 0.987850i \(-0.549669\pi\)
−0.155409 + 0.987850i \(0.549669\pi\)
\(488\) 6.31416e6 + 3.64548e6i 0.0543321 + 0.0313686i
\(489\) −6.20748e7 2.04153e7i −0.530871 0.174594i
\(490\) 613064. + 1.06186e6i 0.00521095 + 0.00902564i
\(491\) −6.98926e7 + 4.03525e7i −0.590455 + 0.340899i −0.765277 0.643701i \(-0.777398\pi\)
0.174823 + 0.984600i \(0.444065\pi\)
\(492\) −5.01582e7 5.61089e7i −0.421159 0.471125i
\(493\) 1.28389e8 2.22377e8i 1.07149 1.85587i
\(494\) 1.70007e8i 1.41022i
\(495\) −62250.8 45912.3i −0.000513251 0.000378542i
\(496\) −1.77312e7 −0.145310
\(497\) −3.30821e6 1.90999e6i −0.0269478 0.0155583i
\(498\) −4.74355e6 2.27162e7i −0.0384074 0.183928i
\(499\) 4.86033e7 + 8.41833e7i 0.391169 + 0.677524i 0.992604 0.121398i \(-0.0387376\pi\)
−0.601435 + 0.798921i \(0.705404\pi\)
\(500\) −1.59753e6 + 922337.i −0.0127803 + 0.00737870i
\(501\) 2.18541e8 4.56354e7i 1.73788 0.362902i
\(502\) 1.73985e7 3.01351e7i 0.137531 0.238211i
\(503\) 1.31021e8i 1.02952i 0.857333 + 0.514762i \(0.172120\pi\)
−0.857333 + 0.514762i \(0.827880\pi\)
\(504\) 670062. + 1.53445e6i 0.00523388 + 0.0119857i
\(505\) 145192. 0.00112737
\(506\) −3.76552e6 2.17402e6i −0.0290652 0.0167808i
\(507\) −6.31833e7 + 5.64823e7i −0.484817 + 0.433399i
\(508\) 5.12741e7 + 8.88093e7i 0.391117 + 0.677435i
\(509\) −1.64280e8 + 9.48472e7i −1.24575 + 0.719236i −0.970260 0.242067i \(-0.922175\pi\)
−0.275493 + 0.961303i \(0.588841\pi\)
\(510\) 635698. 1.93291e6i 0.00479226 0.0145714i
\(511\) −3.88662e6 + 6.73183e6i −0.0291279 + 0.0504511i
\(512\) 5.93164e6i 0.0441942i
\(513\) −1.21367e8 1.70876e8i −0.898975 1.26569i
\(514\) 4.32667e7 0.318614
\(515\) 1.04431e6 + 602931.i 0.00764552 + 0.00441414i
\(516\) 6.22658e7 + 2.04781e7i 0.453211 + 0.149053i
\(517\) −2.05530e6 3.55988e6i −0.0148731 0.0257610i
\(518\) −3.75698e6 + 2.16909e6i −0.0270302 + 0.0156059i
\(519\) 4.72337e7 + 5.28375e7i 0.337871 + 0.377955i
\(520\) 471273. 816269.i 0.00335168 0.00580528i
\(521\) 3.24426e7i 0.229405i 0.993400 + 0.114702i \(0.0365914\pi\)
−0.993400 + 0.114702i \(0.963409\pi\)
\(522\) −1.63717e7 + 1.45724e8i −0.115102 + 1.02452i
\(523\) 8.16094e7 0.570473 0.285237 0.958457i \(-0.407928\pi\)
0.285237 + 0.958457i \(0.407928\pi\)
\(524\) −8.44759e7 4.87722e7i −0.587137 0.338983i
\(525\) 1.09393e6 + 5.23868e6i 0.00755983 + 0.0362029i
\(526\) 2.36691e7 + 4.09960e7i 0.162639 + 0.281699i
\(527\) 1.08287e8 6.25197e7i 0.739853 0.427154i
\(528\) 1.55656e6 325037.i 0.0105746 0.00220816i
\(529\) 1.52860e7 2.64761e7i 0.103259 0.178849i
\(530\) 1.54206e6i 0.0103580i
\(531\) 8.38384e7 + 9.41906e6i 0.559963 + 0.0629106i
\(532\) −4.32347e6 −0.0287142
\(533\) 2.12908e8 + 1.22922e8i 1.40608 + 0.811800i
\(534\) 1.16642e7 1.04271e7i 0.0766004 0.0684764i
\(535\) −1.41295e6 2.44730e6i −0.00922712 0.0159818i
\(536\) −2.84952e7 + 1.64517e7i −0.185045 + 0.106836i
\(537\) 6.41457e7 1.95042e8i 0.414233 1.25952i
\(538\) 6.40652e7 1.10964e8i 0.411410 0.712584i
\(539\) 6.75713e6i 0.0431515i
\(540\) 109046. + 1.15688e6i 0.000692515 + 0.00734694i
\(541\) −1.52147e8 −0.960884 −0.480442 0.877027i \(-0.659524\pi\)
−0.480442 + 0.877027i \(0.659524\pi\)
\(542\) −7.69055e7 4.44014e7i −0.483014 0.278868i
\(543\) −2.53777e8 8.34625e7i −1.58508 0.521305i
\(544\) 2.09147e7 + 3.62254e7i 0.129914 + 0.225017i
\(545\) 1.37922e6 796291.i 0.00852006 0.00491906i
\(546\) −3.64526e6 4.07773e6i −0.0223950 0.0250519i
\(547\) −8.56437e7 + 1.48339e8i −0.523279 + 0.906346i 0.476354 + 0.879254i \(0.341958\pi\)
−0.999633 + 0.0270921i \(0.991375\pi\)
\(548\) 1.31127e8i 0.796802i
\(549\) 2.69084e7 1.17503e7i 0.162619 0.0710122i
\(550\) 5.08240e6 0.0305479
\(551\) −3.27917e8 1.89323e8i −1.96024 1.13174i
\(552\) 1.33518e7 + 6.39397e7i 0.0793820 + 0.380149i
\(553\) −2.17794e6 3.77231e6i −0.0128787 0.0223065i
\(554\) 9.32431e7 5.38339e7i 0.548387 0.316612i
\(555\) −2.94711e6 + 615409.i −0.0172392 + 0.00359986i
\(556\) −1.78067e7 + 3.08421e7i −0.103600 + 0.179440i
\(557\) 2.71640e8i 1.57191i −0.618283 0.785956i \(-0.712171\pi\)
0.618283 0.785956i \(-0.287829\pi\)
\(558\) −4.23846e7 + 5.74677e7i −0.243952 + 0.330766i
\(559\) −2.14116e8 −1.22578
\(560\) 20758.6 + 11985.0i 0.000118204 + 6.82454e-5i
\(561\) −8.36003e6 + 7.47340e6i −0.0473499 + 0.0423282i
\(562\) −3.66351e7 6.34538e7i −0.206390 0.357477i
\(563\) 2.27013e8 1.31066e8i 1.27211 0.734454i 0.296727 0.954962i \(-0.404105\pi\)
0.975385 + 0.220508i \(0.0707715\pi\)
\(564\) −1.92924e7 + 5.86607e7i −0.107535 + 0.326972i
\(565\) −1.60986e6 + 2.78836e6i −0.00892573 + 0.0154598i
\(566\) 1.89470e8i 1.04494i
\(567\) 6.57494e6 + 1.49624e6i 0.0360697 + 0.00820830i
\(568\) 5.44987e7 0.297400
\(569\) 2.40050e8 + 1.38593e8i 1.30306 + 0.752324i 0.980928 0.194370i \(-0.0622662\pi\)
0.322135 + 0.946694i \(0.395600\pi\)
\(570\) −2.85027e6 937401.i −0.0153908 0.00506175i
\(571\) 3.53749e7 + 6.12712e7i 0.190015 + 0.329115i 0.945255 0.326333i \(-0.105813\pi\)
−0.755240 + 0.655448i \(0.772480\pi\)
\(572\) −4.49842e6 + 2.59717e6i −0.0240366 + 0.0138775i
\(573\) −2.27645e7 2.54652e7i −0.121002 0.135358i
\(574\) −3.12605e6 + 5.41447e6i −0.0165295 + 0.0286299i
\(575\) 2.08774e8i 1.09818i
\(576\) −1.92247e7 1.41789e7i −0.100599 0.0741952i
\(577\) −1.69497e8 −0.882336 −0.441168 0.897425i \(-0.645436\pi\)
−0.441168 + 0.897425i \(0.645436\pi\)
\(578\) −1.37209e8 7.92176e7i −0.710557 0.410240i
\(579\) −7.22981e6 3.46225e7i −0.0372470 0.178370i
\(580\) 1.04963e6 + 1.81802e6i 0.00537965 + 0.00931783i
\(581\) −1.66953e6 + 963906.i −0.00851269 + 0.00491480i
\(582\) 7.41218e7 1.54780e7i 0.375991 0.0785137i
\(583\) 4.24912e6 7.35969e6i 0.0214434 0.0371410i
\(584\) 1.10899e8i 0.556786i
\(585\) −1.51903e6 3.47862e6i −0.00758752 0.0173756i
\(586\) 8.56140e7 0.425453
\(587\) 2.49955e8 + 1.44312e8i 1.23580 + 0.713489i 0.968233 0.250051i \(-0.0804474\pi\)
0.267566 + 0.963540i \(0.413781\pi\)
\(588\) −7.56790e7 + 6.76528e7i −0.372257 + 0.332777i
\(589\) −9.21916e7 1.59680e8i −0.451175 0.781458i
\(590\) 1.04595e6 603881.i 0.00509279 0.00294032i
\(591\) −8.29389e7 + 2.52185e8i −0.401787 + 1.22168i
\(592\) 3.09459e7 5.35999e7i 0.149155 0.258344i
\(593\) 1.14093e8i 0.547135i −0.961853 0.273567i \(-0.911796\pi\)
0.961853 0.273567i \(-0.0882037\pi\)
\(594\) 2.66731e6 5.82182e6i 0.0127267 0.0277779i
\(595\) −169034. −0.000802461
\(596\) −1.40860e7 8.13256e6i −0.0665348 0.0384139i
\(597\) 3.49545e8 + 1.14959e8i 1.64278 + 0.540281i
\(598\) −1.06686e8 1.84785e8i −0.498887 0.864098i
\(599\) −8.39663e7 + 4.84780e7i −0.390683 + 0.225561i −0.682456 0.730927i \(-0.739088\pi\)
0.291773 + 0.956488i \(0.405755\pi\)
\(600\) −5.08853e7 5.69223e7i −0.235580 0.263529i
\(601\) −2.05589e8 + 3.56090e8i −0.947056 + 1.64035i −0.195475 + 0.980709i \(0.562625\pi\)
−0.751581 + 0.659640i \(0.770709\pi\)
\(602\) 5.44519e6i 0.0249588i
\(603\) −1.47940e7 + 1.31680e8i −0.0674734 + 0.600576i
\(604\) −1.80321e8 −0.818341
\(605\) −2.82515e6 1.63110e6i −0.0127578 0.00736572i
\(606\) 2.45705e6 + 1.17664e7i 0.0110407 + 0.0528722i
\(607\) 5.43359e7 + 9.41126e7i 0.242952 + 0.420806i 0.961554 0.274616i \(-0.0885508\pi\)
−0.718602 + 0.695422i \(0.755217\pi\)
\(608\) 5.34180e7 3.08409e7i 0.237671 0.137220i
\(609\) 1.19247e7 2.49009e6i 0.0527953 0.0110246i
\(610\) 210171. 364026.i 0.000925939 0.00160377i
\(611\) 2.01719e8i 0.884347i
\(612\) 1.67402e8 + 1.88073e7i 0.730309 + 0.0820486i
\(613\) 2.58460e8 1.12205 0.561025 0.827799i \(-0.310407\pi\)
0.561025 + 0.827799i \(0.310407\pi\)
\(614\) −2.65438e7 1.53251e7i −0.114672 0.0662060i
\(615\) −3.23481e6 + 2.89174e6i −0.0139067 + 0.0124318i
\(616\) −66048.7 114400.i −0.000282567 0.000489421i
\(617\) 1.05483e8 6.09007e7i 0.449084 0.259278i −0.258360 0.966049i \(-0.583182\pi\)
0.707443 + 0.706770i \(0.249849\pi\)
\(618\) −3.11894e7 + 9.48348e7i −0.132142 + 0.401793i
\(619\) −6.31246e7 + 1.09335e8i −0.266150 + 0.460985i −0.967864 0.251473i \(-0.919085\pi\)
0.701714 + 0.712459i \(0.252418\pi\)
\(620\) 1.02225e6i 0.00428925i
\(621\) 2.39147e8 + 1.09567e8i 0.998597 + 0.457515i
\(622\) 1.54799e8 0.643275
\(623\) −1.12559e6 649857.i −0.00465494 0.00268753i
\(624\) 7.41264e7 + 2.43788e7i 0.305084 + 0.100336i
\(625\) −1.21991e8 2.11294e8i −0.499673 0.865460i
\(626\) −1.11594e8 + 6.44288e7i −0.454902 + 0.262638i
\(627\) 1.10203e7 + 1.23277e7i 0.0447085 + 0.0500127i
\(628\) 8.58004e7 1.48611e8i 0.346426 0.600027i
\(629\) 4.36456e8i 1.75383i
\(630\) 88464.9 38630.7i 0.000353793 0.000154494i
\(631\) 1.13561e6 0.00452003 0.00226002 0.999997i \(-0.499281\pi\)
0.00226002 + 0.999997i \(0.499281\pi\)
\(632\) 5.38186e7 + 3.10722e7i 0.213197 + 0.123089i
\(633\) 1.71797e7 + 8.22711e7i 0.0677337 + 0.324367i
\(634\) 7.48011e7 + 1.29559e8i 0.293522 + 0.508395i
\(635\) 5.12007e6 2.95607e6i 0.0199965 0.0115450i
\(636\) −1.24970e8 + 2.60960e7i −0.485774 + 0.101439i
\(637\) 1.65796e8 2.87167e8i 0.641440 1.11101i
\(638\) 1.15690e7i 0.0445485i
\(639\) 1.30273e8 1.76633e8i 0.499289 0.676968i
\(640\) −341973. −0.00130452
\(641\) −9.76272e6 5.63651e6i −0.0370678 0.0214011i 0.481352 0.876528i \(-0.340146\pi\)
−0.518419 + 0.855127i \(0.673479\pi\)
\(642\) 1.74420e8 1.55922e8i 0.659162 0.589253i
\(643\) 1.61344e7 + 2.79457e7i 0.0606905 + 0.105119i 0.894774 0.446519i \(-0.147336\pi\)
−0.834084 + 0.551638i \(0.814003\pi\)
\(644\) 4.69928e6 2.71313e6i 0.0175944 0.0101581i
\(645\) 1.18061e6 3.58977e6i 0.00439974 0.0133779i
\(646\) −2.17487e8 + 3.76699e8i −0.806745 + 1.39732i
\(647\) 4.30138e8i 1.58816i −0.607812 0.794081i \(-0.707952\pi\)
0.607812 0.794081i \(-0.292048\pi\)
\(648\) −9.19089e7 + 2.84148e7i −0.337779 + 0.104429i
\(649\) −6.65592e6 −0.0243486
\(650\) 2.15994e8 + 1.24704e8i 0.786505 + 0.454089i
\(651\) 5.63510e6 + 1.85328e6i 0.0204248 + 0.00671736i
\(652\) −3.87234e7 6.70709e7i −0.139711 0.241986i
\(653\) −4.50239e8 + 2.59945e8i −1.61697 + 0.933561i −0.629277 + 0.777181i \(0.716649\pi\)
−0.987697 + 0.156380i \(0.950018\pi\)
\(654\) 8.78722e7 + 9.82973e7i 0.314136 + 0.351405i
\(655\) −2.81183e6 + 4.87024e6i −0.0100061 + 0.0173311i
\(656\) 8.91969e7i 0.315965i
\(657\) −3.59428e8 2.65091e8i −1.26740 0.934759i
\(658\) 5.12993e6 0.0180067
\(659\) −3.59541e8 2.07581e8i −1.25630 0.725322i −0.283943 0.958841i \(-0.591643\pi\)
−0.972352 + 0.233519i \(0.924976\pi\)
\(660\) −18739.2 89739.1i −6.51806e−5 0.000312140i
\(661\) −2.11607e8 3.66515e8i −0.732700 1.26907i −0.955725 0.294261i \(-0.904926\pi\)
0.223025 0.974813i \(-0.428407\pi\)
\(662\) −2.21077e8 + 1.27639e8i −0.762024 + 0.439955i
\(663\) −5.38659e8 + 1.12482e8i −1.84830 + 0.385959i
\(664\) 1.37518e7 2.38188e7i 0.0469737 0.0813609i
\(665\) 249258.i 0.000847587i
\(666\) −9.97465e7 2.28421e8i −0.337657 0.773239i
\(667\) 4.75227e8 1.60149
\(668\) 2.29149e8 + 1.32299e8i 0.768757 + 0.443842i
\(669\) 4.04598e8 3.61687e8i 1.35128 1.20797i
\(670\) 948480. + 1.64281e6i 0.00315358 + 0.00546216i
\(671\) −2.00613e6 + 1.15824e6i −0.00664036 + 0.00383382i
\(672\) −619979. + 1.88511e6i −0.00204300 + 0.00621197i
\(673\) 862893. 1.49457e6i 0.00283082 0.00490312i −0.864607 0.502450i \(-0.832432\pi\)
0.867437 + 0.497546i \(0.165766\pi\)
\(674\) 1.77530e8i 0.579820i
\(675\) −3.06123e8 + 2.88549e7i −0.995370 + 0.0938227i
\(676\) −1.00443e8 −0.325147
\(677\) −1.62390e8 9.37561e7i −0.523352 0.302158i 0.214953 0.976624i \(-0.431040\pi\)
−0.738305 + 0.674467i \(0.764374\pi\)
\(678\) −2.53215e8 8.32776e7i −0.812456 0.267202i
\(679\) −3.14518e6 5.44761e6i −0.0100470 0.0174019i
\(680\) 2.08848e6 1.20578e6i 0.00664207 0.00383480i
\(681\) −2.14203e8 2.39616e8i −0.678242 0.758708i
\(682\) 2.81678e6 4.87881e6i 0.00887974 0.0153802i
\(683\) 3.29781e8i 1.03506i 0.855666 + 0.517528i \(0.173148\pi\)
−0.855666 + 0.517528i \(0.826852\pi\)
\(684\) 2.77332e7 2.46851e8i 0.0866626 0.771378i
\(685\) 7.55978e6 0.0235200
\(686\) 1.46159e7 + 8.43852e6i 0.0452746 + 0.0261393i
\(687\) 1.71283e7 + 8.20248e7i 0.0528254 + 0.252973i
\(688\) 3.88425e7 + 6.72773e7i 0.119273 + 0.206587i
\(689\) 3.61162e8 2.08517e8i 1.10419 0.637505i
\(690\) 3.68628e6 769762.i 0.0112212 0.00234320i
\(691\) 7.94682e7 1.37643e8i 0.240857 0.417177i −0.720102 0.693869i \(-0.755905\pi\)
0.960959 + 0.276692i \(0.0892381\pi\)
\(692\) 8.39964e7i 0.253479i
\(693\) −528656. 59393.3i −0.00158845 0.000178459i
\(694\) 6.22291e7 0.186172
\(695\) 1.77812e6 + 1.02660e6i 0.00529672 + 0.00305806i
\(696\) −1.29571e8 + 1.15829e8i −0.384309 + 0.343550i
\(697\) 3.14505e8 + 5.44738e8i 0.928814 + 1.60875i
\(698\) 1.70392e7 9.83758e6i 0.0501052 0.0289282i
\(699\) −7.89566e7 + 2.40076e8i −0.231184 + 0.702938i
\(700\) −3.17136e6 + 5.49296e6i −0.00924595 + 0.0160145i
\(701\) 1.13256e8i 0.328780i 0.986395 + 0.164390i \(0.0525656\pi\)
−0.986395 + 0.164390i \(0.947434\pi\)
\(702\) 2.56203e8 1.81972e8i 0.740583 0.526008i
\(703\) 6.43598e8 1.85246
\(704\) 1.63211e6 + 942299.i 0.00467769 + 0.00270067i
\(705\) 3.38193e6 + 1.11225e6i 0.00965155 + 0.00317422i
\(706\) 7.62742e7 + 1.32111e8i 0.216752 + 0.375426i
\(707\) 864780. 499281.i 0.00244707 0.00141282i
\(708\) 6.66394e7 + 7.45455e7i 0.187772 + 0.210049i
\(709\) −2.95239e7 + 5.11369e7i −0.0828390 + 0.143481i −0.904468 0.426541i \(-0.859732\pi\)
0.821629 + 0.570022i \(0.193065\pi\)
\(710\) 3.14198e6i 0.00877866i
\(711\) 2.29353e8 1.00154e8i 0.638111 0.278649i
\(712\) 1.85427e7 0.0513727
\(713\) 2.00410e8 + 1.15707e8i 0.552906 + 0.319221i
\(714\) −2.86053e6 1.36987e7i −0.00785872 0.0376343i
\(715\) 149733. + 259345.i 0.000409636 + 0.000709511i
\(716\) 2.10740e8 1.21671e8i 0.574127 0.331472i
\(717\) 1.84852e8 3.86005e7i 0.501495 0.104721i
\(718\) −2.49613e8 + 4.32343e8i −0.674364 + 1.16803i
\(719\) 1.17775e8i 0.316860i 0.987370 + 0.158430i \(0.0506433\pi\)
−0.987370 + 0.158430i \(0.949357\pi\)
\(720\) −817449. + 1.10835e6i −0.00219010 + 0.00296947i
\(721\) 8.29337e6 0.0221272
\(722\) 3.25004e8 + 1.87641e8i 0.863530 + 0.498559i
\(723\) 8.32444e7 7.44157e7i 0.220262 0.196902i
\(724\) −1.58310e8 2.74202e8i −0.417152 0.722528i
\(725\) −4.81069e8 + 2.77745e8i −1.26239 + 0.728841i
\(726\) 8.43764e7 2.56556e8i 0.220501 0.670458i
\(727\) −1.08321e8 + 1.87617e8i −0.281909 + 0.488281i −0.971855 0.235580i \(-0.924301\pi\)
0.689946 + 0.723861i \(0.257634\pi\)
\(728\) 6.48240e6i 0.0168013i
\(729\) −1.27605e8 + 3.65803e8i −0.329370 + 0.944201i
\(730\) −6.39358e6 −0.0164352
\(731\) −4.74434e8 2.73914e8i −1.21457 0.701234i
\(732\) 3.30576e7 + 1.08721e7i 0.0842827 + 0.0277190i
\(733\) −2.54830e8 4.41379e8i −0.647052 1.12073i −0.983824 0.179140i \(-0.942668\pi\)
0.336772 0.941586i \(-0.390665\pi\)
\(734\) −1.47245e8 + 8.50122e7i −0.372352 + 0.214978i
\(735\) 3.90034e6 + 4.36307e6i 0.00982292 + 0.0109883i
\(736\) −3.87075e7 + 6.70434e7i −0.0970872 + 0.168160i
\(737\) 1.04541e7i 0.0261145i
\(738\) −2.89091e8 2.13215e8i −0.719226 0.530456i
\(739\) 1.66066e8 0.411479 0.205740 0.978607i \(-0.434040\pi\)
0.205740 + 0.978607i \(0.434040\pi\)
\(740\) −3.09016e6 1.78410e6i −0.00762580 0.00440276i
\(741\) 1.65866e8 + 7.94307e8i 0.407664 + 1.95224i
\(742\) 5.30280e6 + 9.18473e6i 0.0129806 + 0.0224830i
\(743\) 6.45800e8 3.72853e8i 1.57446 0.909016i 0.578849 0.815434i \(-0.303502\pi\)
0.995612 0.0935810i \(-0.0298314\pi\)
\(744\) −8.28438e7 + 1.72993e7i −0.201160 + 0.0420058i
\(745\) −468861. + 812091.i −0.00113390 + 0.00196397i
\(746\) 2.21662e8i 0.533918i
\(747\) −4.43255e7 1.01506e8i −0.106339 0.243518i
\(748\) −1.32900e7 −0.0317557
\(749\) −1.68314e7 9.71764e6i −0.0400568 0.0231268i
\(750\) −6.56412e6 + 5.86795e6i −0.0155594 + 0.0139092i
\(751\) 5.23107e7 + 9.06048e7i 0.123501 + 0.213910i 0.921146 0.389217i \(-0.127254\pi\)
−0.797645 + 0.603127i \(0.793921\pi\)
\(752\) −6.33820e7 + 3.65936e7i −0.149043 + 0.0860502i
\(753\) 5.18882e7 1.57772e8i 0.121530 0.369525i
\(754\) 2.83862e8 4.91663e8i 0.662206 1.14697i
\(755\) 1.03959e7i 0.0241558i
\(756\) 4.62773e6 + 6.51553e6i 0.0107103 + 0.0150794i
\(757\) −5.24396e8 −1.20885 −0.604424 0.796663i \(-0.706597\pi\)
−0.604424 + 0.796663i \(0.706597\pi\)
\(758\) −1.93474e8 1.11702e8i −0.444237 0.256481i
\(759\) −1.97143e7 6.48367e6i −0.0450875 0.0148284i
\(760\) −1.77805e6 3.07967e6i −0.00405045 0.00701558i
\(761\) −2.36160e8 + 1.36347e8i −0.535861 + 0.309380i −0.743400 0.668847i \(-0.766788\pi\)
0.207539 + 0.978227i \(0.433455\pi\)
\(762\) 3.26208e8 + 3.64909e8i 0.737276 + 0.824745i
\(763\) 5.47652e6 9.48562e6i 0.0123291 0.0213546i
\(764\) 4.04824e7i 0.0907791i
\(765\) 1.08428e6 9.65113e6i 0.00242191 0.0215573i
\(766\) −3.85057e8 −0.856720
\(767\) −2.82866e8 1.63313e8i −0.626895 0.361938i
\(768\) −5.78714e6 2.77138e7i −0.0127756 0.0611803i
\(769\) 7.15604e6 + 1.23946e7i 0.0157360 + 0.0272555i 0.873786 0.486310i \(-0.161658\pi\)
−0.858050 + 0.513566i \(0.828324\pi\)
\(770\) −6595.41 + 3807.86i −1.44467e−5 + 8.34083e-6i
\(771\) 2.02150e8 4.22127e7i 0.441074 0.0921042i
\(772\) 2.09596e7 3.63031e7i 0.0455545 0.0789027i
\(773\) 3.91457e8i 0.847512i 0.905776 + 0.423756i \(0.139289\pi\)
−0.905776 + 0.423756i \(0.860711\pi\)
\(774\) 3.10897e8 + 3.49286e7i 0.670492 + 0.0753283i
\(775\) −2.70498e8 −0.581112
\(776\) 7.77197e7 + 4.48715e7i 0.166320 + 0.0960252i
\(777\) −1.54371e7 + 1.37999e7i −0.0329081 + 0.0294179i
\(778\) −2.24845e8 3.89442e8i −0.477468 0.826998i
\(779\) 8.03272e8 4.63769e8i 1.69922 0.981046i
\(780\) 1.40550e6 4.27356e6i 0.00296173 0.00900546i
\(781\) −8.65766e6 + 1.49955e7i −0.0181739 + 0.0314781i
\(782\) 5.45924e8i 1.14160i
\(783\) 6.56818e7 + 6.96822e8i 0.136823 + 1.45156i
\(784\) −1.20308e8 −0.249658
\(785\) −8.56775e6 4.94659e6i −0.0177116 0.0102258i
\(786\) −4.42272e8 1.45455e8i −0.910797 0.299545i
\(787\) −2.06845e8 3.58267e8i −0.424348 0.734992i 0.572012 0.820246i \(-0.306163\pi\)
−0.996359 + 0.0852538i \(0.972830\pi\)
\(788\) −2.72482e8 + 1.57317e8i −0.556876 + 0.321513i
\(789\) 1.50584e8 + 1.68449e8i 0.306582 + 0.342955i
\(790\) 1.79138e6 3.10277e6i 0.00363335 0.00629315i
\(791\) 2.21438e7i 0.0447428i
\(792\) 6.95541e6 3.03727e6i 0.0140006 0.00611375i
\(793\) −1.13677e8 −0.227956
\(794\) −2.20767e7 1.27460e7i −0.0441034 0.0254631i
\(795\) 1.50450e6 + 7.20482e6i 0.00299426 + 0.0143391i
\(796\) 2.18052e8 + 3.77678e8i 0.432336 + 0.748828i
\(797\) 4.24006e7 2.44800e7i 0.0837523 0.0483544i −0.457539 0.889190i \(-0.651269\pi\)
0.541291 + 0.840835i \(0.317936\pi\)
\(798\) −2.02001e7 + 4.21814e6i −0.0397506 + 0.00830066i
\(799\) 2.58055e8 4.46965e8i 0.505909 0.876261i
\(800\) 9.04900e7i 0.176738i
\(801\) 4.43242e7 6.00976e7i 0.0862469 0.116939i
\(802\) 2.26222e8 0.438543
\(803\) 3.05142e7 + 1.76174e7i 0.0589325 + 0.0340247i
\(804\) −1.17084e8 + 1.04667e8i −0.225284 + 0.201391i
\(805\) −156418. 270925.i −0.000299847 0.000519351i
\(806\) 2.39417e8 1.38228e8i 0.457247 0.263992i
\(807\) 1.91064e8 5.80950e8i 0.363545 1.10540i
\(808\) −7.12311e6 + 1.23376e7i −0.0135032 + 0.0233882i
\(809\) 2.59106e8i 0.489364i −0.969603 0.244682i \(-0.921316\pi\)
0.969603 0.244682i \(-0.0786836\pi\)
\(810\) 1.63818e6 + 5.29877e6i 0.00308252 + 0.00997056i
\(811\) −9.21052e8 −1.72672 −0.863359 0.504590i \(-0.831644\pi\)
−0.863359 + 0.504590i \(0.831644\pi\)
\(812\) 1.25035e7 + 7.21891e6i 0.0233542 + 0.0134835i
\(813\) −4.02637e8 1.32420e8i −0.749276 0.246423i
\(814\) 9.83211e6 + 1.70297e7i 0.0182295 + 0.0315743i
\(815\) −3.86679e6 + 2.23249e6i −0.00714296 + 0.00412399i
\(816\) 1.33061e8 + 1.48847e8i 0.244894 + 0.273948i
\(817\) −4.03915e8 + 6.99600e8i −0.740668 + 1.28287i
\(818\) 2.26911e8i 0.414568i
\(819\) −2.10097e7 1.54955e7i −0.0382445 0.0282067i
\(820\) −5.14241e6 −0.00932664
\(821\) −3.01878e8 1.74289e8i −0.545509 0.314950i 0.201800 0.979427i \(-0.435321\pi\)
−0.747309 + 0.664477i \(0.768654\pi\)
\(822\) 1.27933e8 + 6.12650e8i 0.230338 + 1.10306i
\(823\) 2.06887e8 + 3.58338e8i 0.371136 + 0.642827i 0.989741 0.142876i \(-0.0456350\pi\)
−0.618604 + 0.785703i \(0.712302\pi\)
\(824\) −1.02468e8 + 5.91597e7i −0.183149 + 0.105741i
\(825\) 2.37460e7 4.95859e6i 0.0422891 0.00883073i
\(826\) 4.15322e6 7.19358e6i 0.00736961 0.0127645i
\(827\) 3.10912e8i 0.549693i −0.961488 0.274847i \(-0.911373\pi\)
0.961488 0.274847i \(-0.0886271\pi\)
\(828\) 1.24764e8 + 2.85712e8i 0.219785 + 0.503313i
\(829\) −2.87241e8 −0.504177 −0.252089 0.967704i \(-0.581117\pi\)
−0.252089 + 0.967704i \(0.581117\pi\)
\(830\) −1.37321e6 792823.i −0.00240161 0.00138657i
\(831\) 3.83127e8 3.42494e8i 0.667636 0.596829i
\(832\) 4.62414e7 + 8.00924e7i 0.0802899 + 0.139066i
\(833\) 7.34736e8 4.24200e8i 1.27115 0.733898i
\(834\) −5.31056e7 + 1.61473e8i −0.0915466 + 0.278357i
\(835\) 7.62738e6 1.32110e7i 0.0131013 0.0226922i
\(836\) 1.95975e7i 0.0335414i
\(837\) −1.41961e8 + 3.09852e8i −0.242099 + 0.528418i
\(838\) 5.03153e8 0.855004
\(839\) 7.38621e8 + 4.26443e8i 1.25065 + 0.722064i 0.971239 0.238108i \(-0.0765271\pi\)
0.279412 + 0.960171i \(0.409860\pi\)
\(840\) 108681. + 35743.2i 0.000183365 + 6.03054e-5i
\(841\) 3.34815e8 + 5.79916e8i 0.562881 + 0.974938i
\(842\) −2.27006e8 + 1.31062e8i −0.380277 + 0.219553i
\(843\) −2.33074e8 2.60726e8i −0.389055 0.435212i
\(844\) −4.98048e7 + 8.62645e7i −0.0828408 + 0.143484i
\(845\) 5.79078e6i 0.00959770i
\(846\) −3.29063e7 + 2.92897e8i −0.0543460 + 0.483730i
\(847\) −2.24360e7 −0.0369228
\(848\) −1.31036e8 7.56537e7i −0.214884 0.124063i
\(849\) −1.84854e8 8.85239e8i −0.302069 1.44656i
\(850\) 3.19064e8 + 5.52635e8i 0.519542 + 0.899874i
\(851\) −6.99542e8 + 4.03881e8i −1.13508 + 0.655337i
\(852\) 2.54629e8 5.31711e7i 0.411707 0.0859719i
\(853\) 3.75152e8 6.49782e8i 0.604449 1.04694i −0.387689 0.921790i \(-0.626727\pi\)
0.992138 0.125146i \(-0.0399401\pi\)
\(854\) 2.89092e6i 0.00464154i
\(855\) −1.42316e7 1.59888e6i −0.0227695 0.00255811i
\(856\) 2.77278e8 0.442073
\(857\) 8.56478e8 + 4.94488e8i 1.36074 + 0.785621i 0.989722 0.143006i \(-0.0456770\pi\)
0.371014 + 0.928627i \(0.379010\pi\)
\(858\) −1.84836e7 + 1.65233e7i −0.0292634 + 0.0261598i
\(859\) 4.07993e8 + 7.06665e8i 0.643685 + 1.11490i 0.984603 + 0.174803i \(0.0559288\pi\)
−0.340918 + 0.940093i \(0.610738\pi\)
\(860\) 3.87869e6 2.23936e6i 0.00609804 0.00352070i
\(861\) −9.32292e6 + 2.83473e7i −0.0146064 + 0.0444123i
\(862\) 3.31137e8 5.73546e8i 0.516994 0.895461i
\(863\) 2.87047e8i 0.446603i 0.974749 + 0.223301i \(0.0716834\pi\)
−0.974749 + 0.223301i \(0.928317\pi\)
\(864\) −1.03655e8 4.74903e7i −0.160712 0.0736316i
\(865\) 4.84259e6 0.00748220
\(866\) 8.87870e7 + 5.12612e7i 0.136708 + 0.0789287i
\(867\) −7.18354e8 2.36254e8i −1.10225 0.362511i
\(868\) 3.51528e6 + 6.08864e6i 0.00537527 + 0.00931025i
\(869\) −1.70992e7 + 9.87223e6i −0.0260565 + 0.0150437i
\(870\) 6.67783e6 + 7.47008e6i 0.0101409 + 0.0113440i
\(871\) 2.56506e8 4.44281e8i 0.388188 0.672362i
\(872\) 1.56264e8i 0.235673i
\(873\) 3.31210e8 1.44632e8i 0.497807 0.217381i
\(874\) −8.05021e8 −1.20579
\(875\) 633433. + 365713.i 0.000945533 + 0.000545904i
\(876\) −1.08197e8 5.18141e8i −0.160955 0.770789i
\(877\) −1.17214e8 2.03021e8i −0.173772 0.300983i 0.765963 0.642884i \(-0.222262\pi\)
−0.939736 + 0.341902i \(0.888929\pi\)
\(878\) −2.96526e7 + 1.71199e7i −0.0438106 + 0.0252941i
\(879\) 4.00005e8 8.35283e7i 0.588978 0.122989i
\(880\) 54325.8 94095.0i 7.97183e−5 0.000138076i
\(881\) 6.01503e6i 0.00879651i −0.999990 0.00439825i \(-0.998600\pi\)
0.999990 0.00439825i \(-0.00140001\pi\)
\(882\) −2.87582e8 + 3.89922e8i −0.419137 + 0.568293i
\(883\) −5.07079e8 −0.736535 −0.368267 0.929720i \(-0.620049\pi\)
−0.368267 + 0.929720i \(0.620049\pi\)
\(884\) −5.64805e8 3.26090e8i −0.817602 0.472043i
\(885\) 4.29772e6 3.84192e6i 0.00620024 0.00554266i
\(886\) 1.37611e7 + 2.38350e7i 0.0197858 + 0.0342700i
\(887\) −9.89927e8 + 5.71535e8i −1.41851 + 0.818977i −0.996168 0.0874597i \(-0.972125\pi\)
−0.422342 + 0.906437i \(0.638792\pi\)
\(888\) 9.22911e7 2.80621e8i 0.131802 0.400757i
\(889\) 2.03305e7 3.52135e7i 0.0289363 0.0501191i
\(890\) 1.06903e6i 0.00151642i
\(891\) 6.78221e6 2.98030e7i 0.00958822 0.0421334i
\(892\) 6.43193e8 0.906248
\(893\) −6.59095e8 3.80529e8i −0.925537 0.534359i
\(894\) −7.37469e7 2.42540e7i −0.103212 0.0339446i
\(895\) −7.01461e6 1.21497e7i −0.00978440 0.0169471i
\(896\) −2.03684e6 + 1.17597e6i −0.00283160 + 0.00163482i
\(897\) −6.78739e8 7.59264e8i −0.940428 1.05200i
\(898\) 4.05404e8 7.02181e8i 0.559834 0.969662i
\(899\) 6.15730e8i 0.847445i
\(900\) −2.93281e8 2.16306e8i −0.402307 0.296716i
\(901\) 1.06701e9 1.45879
\(902\) 2.45428e7 + 1.41698e7i 0.0334430 + 0.0193083i
\(903\) −5.31254e6 2.54410e7i −0.00721504 0.0345518i
\(904\) −1.57960e8 2.73595e8i −0.213817 0.370341i
\(905\) −1.58084e7 + 9.12697e6i −0.0213276 + 0.0123135i
\(906\) −8.42492e8 + 1.75928e8i −1.13287 + 0.236565i
\(907\) −2.40785e8 + 4.17052e8i −0.322707 + 0.558944i −0.981046 0.193777i \(-0.937926\pi\)
0.658339 + 0.752722i \(0.271259\pi\)
\(908\) 3.80920e8i 0.508835i
\(909\) 2.29596e7 + 5.25779e7i 0.0305684 + 0.0700022i
\(910\) −373726. −0.000495940
\(911\) 6.27463e8 + 3.62266e8i 0.829914 + 0.479151i 0.853823 0.520563i \(-0.174278\pi\)
−0.0239090 + 0.999714i \(0.507611\pi\)
\(912\) 2.19489e8 1.96211e8i 0.289354 0.258666i
\(913\) 4.36921e6 + 7.56770e6i 0.00574104 + 0.00994378i
\(914\) −4.77507e8 + 2.75689e8i −0.625375 + 0.361061i
\(915\) 626799. 1.90585e6i 0.000818211 0.00248786i
\(916\) −4.96557e7 + 8.60062e7i −0.0646075 + 0.111903i
\(917\) 3.86770e7i 0.0501585i
\(918\) 8.00484e8 7.54529e7i 1.03472 0.0975322i
\(919\) 1.45033e7 0.0186862 0.00934311 0.999956i \(-0.497026\pi\)
0.00934311 + 0.999956i \(0.497026\pi\)
\(920\) 3.86521e6 + 2.23158e6i 0.00496374 + 0.00286582i
\(921\) −1.38969e8 4.57045e7i −0.177885 0.0585033i
\(922\) −1.51236e8 2.61949e8i −0.192958 0.334214i
\(923\) −7.35873e8 + 4.24856e8i −0.935832 + 0.540303i
\(924\) −420205. 470058.i −0.000532654 0.000595848i
\(925\) 4.72094e8 8.17691e8i 0.596490 1.03315i
\(926\) 1.74107e8i 0.219272i
\(927\) −5.31985e7 + 4.73516e8i −0.0667821 + 0.594423i
\(928\) −2.05981e8 −0.257740
\(929\) −4.07462e8 2.35248e8i −0.508206 0.293413i 0.223890 0.974614i \(-0.428124\pi\)
−0.732096 + 0.681201i \(0.761458\pi\)
\(930\) 997345. + 4.77614e6i 0.00123993 + 0.00593784i
\(931\) −6.25526e8 1.08344e9i −0.775169 1.34263i
\(932\) −2.59399e8 + 1.49764e8i −0.320420 + 0.184995i
\(933\) 7.23250e8 1.51028e8i 0.890520 0.185957i
\(934\) −3.11989e8 + 5.40381e8i −0.382912 + 0.663223i
\(935\) 766202.i 0.000937364i
\(936\) 3.70117e8 + 4.15819e7i 0.451349 + 0.0507080i
\(937\) 1.72677e8 0.209902 0.104951 0.994477i \(-0.466531\pi\)
0.104951 + 0.994477i \(0.466531\pi\)
\(938\) 1.12985e7 + 6.52321e6i 0.0136903 + 0.00790411i
\(939\) −4.58529e8 + 4.09899e8i −0.553822 + 0.495085i
\(940\) 2.10971e6 + 3.65412e6i 0.00254003 + 0.00439946i
\(941\) 1.62668e8 9.39166e7i 0.195224 0.112713i −0.399202 0.916863i \(-0.630713\pi\)
0.594426 + 0.804150i \(0.297379\pi\)
\(942\) 2.55886e8 7.78047e8i 0.306121 0.930794i
\(943\) −5.82063e8 + 1.00816e9i −0.694121 + 1.20225i
\(944\) 1.18506e8i 0.140872i
\(945\) 375635. 266800.i 0.000445114 0.000316148i
\(946\) −2.46821e7 −0.0291547
\(947\) −5.56583e7 3.21344e7i −0.0655361 0.0378373i 0.466874 0.884324i \(-0.345380\pi\)
−0.532410 + 0.846487i \(0.678714\pi\)
\(948\) 2.81766e8 + 9.26676e7i 0.330722 + 0.108768i
\(949\) 8.64536e8 + 1.49742e9i 1.01154 + 1.75204i
\(950\) 8.14916e8 4.70492e8i 0.950478 0.548759i
\(951\) 4.75888e8 + 5.32347e8i 0.553304 + 0.618947i
\(952\) 8.29283e6 1.43636e7i 0.00961151 0.0166476i
\(953\) 8.06493e8i 0.931798i −0.884838 0.465899i \(-0.845731\pi\)
0.884838 0.465899i \(-0.154269\pi\)
\(954\) −5.58424e8 + 2.43851e8i −0.643160 + 0.280854i
\(955\) −2.33390e6 −0.00267962
\(956\) 1.93825e8 + 1.11905e8i 0.221838 + 0.128078i
\(957\) −1.12871e7 5.40525e7i −0.0128780 0.0616709i
\(958\) −2.38836e7 4.13676e7i −0.0271646 0.0470504i
\(959\) 4.50270e7 2.59964e7i 0.0510525 0.0294752i
\(960\) −1.59776e6 + 333642.i −0.00180592 + 0.000377109i
\(961\) 2.93836e8 5.08938e8i 0.331081 0.573449i
\(962\) 9.64981e8i 1.08391i
\(963\) 6.62802e8 8.98669e8i 0.742173 1.00628i
\(964\) 1.32334e8 0.147721
\(965\) −2.09296e6 1.20837e6i −0.00232905 0.00134468i
\(966\) 1.93089e7 1.72611e7i 0.0214203 0.0191486i
\(967\) −1.31014e8 2.26923e8i −0.144890 0.250957i 0.784442 0.620203i \(-0.212950\pi\)
−0.929332 + 0.369245i \(0.879616\pi\)
\(968\) 2.77204e8 1.60044e8i 0.305615 0.176447i
\(969\) −6.48621e8 + 1.97220e9i −0.712885 + 2.16760i
\(970\) 2.58695e6 4.48072e6i 0.00283447 0.00490945i
\(971\) 6.14354e8i 0.671060i 0.942030 + 0.335530i \(0.108915\pi\)
−0.942030 + 0.335530i \(0.891085\pi\)
\(972\) −4.01694e8 + 2.22429e8i −0.437417 + 0.242211i
\(973\) 1.41210e7 0.0153294
\(974\) −1.75873e8 1.01540e8i −0.190336 0.109891i
\(975\) 1.13083e9 + 3.71910e8i 1.22007 + 0.401258i
\(976\) 2.06220e7 + 3.57183e7i 0.0221810 + 0.0384186i
\(977\) 7.27332e8 4.19925e8i 0.779918 0.450286i −0.0564832 0.998404i \(-0.517989\pi\)
0.836401 + 0.548118i \(0.184655\pi\)
\(978\) −2.46360e8 2.75588e8i −0.263362 0.294607i
\(979\) −2.94569e6 + 5.10208e6i −0.00313934 + 0.00543750i
\(980\) 6.93602e6i 0.00736940i
\(981\) 5.06458e8 + 3.73532e8i 0.536459 + 0.395659i
\(982\) −4.56536e8 −0.482104
\(983\) 1.08109e9 + 6.24168e8i 1.13816 + 0.657114i 0.945973 0.324245i \(-0.105110\pi\)
0.192182 + 0.981359i \(0.438444\pi\)
\(984\) −8.70240e7 4.16745e8i −0.0913385 0.437407i
\(985\) 9.06972e6 + 1.57092e7i 0.00949041 + 0.0164379i
\(986\) 1.25795e9 7.26279e8i 1.31230 0.757657i
\(987\) 2.39680e7 5.00495e6i 0.0249276 0.00520533i
\(988\) −4.80853e8 + 8.32862e8i −0.498588 + 0.863580i
\(989\) 1.01388e9i 1.04809i
\(990\) −175106. 400995.i −0.000180466 0.000413270i
\(991\) 1.60725e8 0.165144 0.0825719 0.996585i \(-0.473687\pi\)
0.0825719 + 0.996585i \(0.473687\pi\)
\(992\) −8.68650e7 5.01515e7i −0.0889836 0.0513747i
\(993\) −9.08383e8 + 8.12043e8i −0.927729 + 0.829337i
\(994\) −1.08046e7 1.87140e7i −0.0110014 0.0190550i
\(995\) 2.17740e7 1.25712e7i 0.0221039 0.0127617i
\(996\) 4.10124e7 1.24703e8i 0.0415086 0.126211i
\(997\) −3.43673e8 + 5.95259e8i −0.346785 + 0.600649i −0.985676 0.168648i \(-0.946060\pi\)
0.638892 + 0.769297i \(0.279393\pi\)
\(998\) 5.49883e8i 0.553196i
\(999\) −6.88892e8 9.69912e8i −0.690963 0.972827i
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 18.7.d.a.11.6 yes 12
3.2 odd 2 54.7.d.a.35.2 12
4.3 odd 2 144.7.q.c.65.2 12
9.2 odd 6 162.7.b.c.161.10 12
9.4 even 3 54.7.d.a.17.2 12
9.5 odd 6 inner 18.7.d.a.5.6 12
9.7 even 3 162.7.b.c.161.3 12
12.11 even 2 432.7.q.b.305.3 12
36.23 even 6 144.7.q.c.113.2 12
36.31 odd 6 432.7.q.b.17.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
18.7.d.a.5.6 12 9.5 odd 6 inner
18.7.d.a.11.6 yes 12 1.1 even 1 trivial
54.7.d.a.17.2 12 9.4 even 3
54.7.d.a.35.2 12 3.2 odd 2
144.7.q.c.65.2 12 4.3 odd 2
144.7.q.c.113.2 12 36.23 even 6
162.7.b.c.161.3 12 9.7 even 3
162.7.b.c.161.10 12 9.2 odd 6
432.7.q.b.17.3 12 36.31 odd 6
432.7.q.b.305.3 12 12.11 even 2