Properties

Label 16.7.f.a.11.2
Level $16$
Weight $7$
Character 16.11
Analytic conductor $3.681$
Analytic rank $0$
Dimension $22$
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] = [16,7,Mod(3,16)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(16, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("16.3");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 16.f (of order \(4\), 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: \(3.68086533792\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 11.2
Character \(\chi\) \(=\) 16.11
Dual form 16.7.f.a.3.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-7.06494 + 3.75322i) q^{2} +(-9.43202 - 9.43202i) q^{3} +(35.8267 - 53.0325i) q^{4} +(46.6419 + 46.6419i) q^{5} +(102.037 + 31.2362i) q^{6} +647.751 q^{7} +(-54.0705 + 509.137i) q^{8} -551.074i q^{9} +O(q^{10})\) \(q+(-7.06494 + 3.75322i) q^{2} +(-9.43202 - 9.43202i) q^{3} +(35.8267 - 53.0325i) q^{4} +(46.6419 + 46.6419i) q^{5} +(102.037 + 31.2362i) q^{6} +647.751 q^{7} +(-54.0705 + 509.137i) q^{8} -551.074i q^{9} +(-504.579 - 154.465i) q^{10} +(260.052 - 260.052i) q^{11} +(-838.121 + 162.286i) q^{12} +(626.285 - 626.285i) q^{13} +(-4576.32 + 2431.15i) q^{14} -879.853i q^{15} +(-1528.90 - 3799.96i) q^{16} -1507.54 q^{17} +(2068.30 + 3893.30i) q^{18} +(5914.78 + 5914.78i) q^{19} +(4144.56 - 802.513i) q^{20} +(-6109.59 - 6109.59i) q^{21} +(-861.220 + 2813.29i) q^{22} +10951.0 q^{23} +(5312.18 - 4292.19i) q^{24} -11274.1i q^{25} +(-2074.08 + 6775.25i) q^{26} +(-12073.7 + 12073.7i) q^{27} +(23206.8 - 34351.9i) q^{28} +(-24532.3 + 24532.3i) q^{29} +(3302.28 + 6216.11i) q^{30} -1877.01i q^{31} +(25063.7 + 21108.2i) q^{32} -4905.63 q^{33} +(10650.6 - 5658.11i) q^{34} +(30212.3 + 30212.3i) q^{35} +(-29224.9 - 19743.2i) q^{36} +(-62335.0 - 62335.0i) q^{37} +(-63987.1 - 19588.1i) q^{38} -11814.3 q^{39} +(-26269.0 + 21225.1i) q^{40} +58050.6i q^{41} +(66094.6 + 20233.3i) q^{42} +(-5771.32 + 5771.32i) q^{43} +(-4474.42 - 23108.0i) q^{44} +(25703.1 - 25703.1i) q^{45} +(-77368.2 + 41101.5i) q^{46} -151739. i q^{47} +(-21420.7 + 50261.9i) q^{48} +301932. q^{49} +(42314.1 + 79650.6i) q^{50} +(14219.1 + 14219.1i) q^{51} +(-10775.8 - 55651.2i) q^{52} +(64565.8 + 64565.8i) q^{53} +(39984.6 - 130615. i) q^{54} +24258.6 q^{55} +(-35024.2 + 329794. i) q^{56} -111577. i q^{57} +(81244.2 - 265395. i) q^{58} +(-199692. + 199692. i) q^{59} +(-46660.9 - 31522.2i) q^{60} +(-226842. + 226842. i) q^{61} +(7044.84 + 13261.0i) q^{62} -356959. i q^{63} +(-256297. - 55058.6i) q^{64} +58422.2 q^{65} +(34658.0 - 18411.9i) q^{66} +(-53695.6 - 53695.6i) q^{67} +(-54010.0 + 79948.4i) q^{68} +(-103290. - 103290. i) q^{69} +(-326841. - 100055. i) q^{70} -294503. q^{71} +(280572. + 29796.9i) q^{72} +476283. i q^{73} +(674350. + 206436. i) q^{74} +(-106337. + 106337. i) q^{75} +(525583. - 101769. i) q^{76} +(168449. - 168449. i) q^{77} +(83467.0 - 44341.5i) q^{78} +291918. i q^{79} +(105926. - 248548. i) q^{80} -173975. q^{81} +(-217877. - 410124. i) q^{82} +(199292. + 199292. i) q^{83} +(-542894. + 105121. i) q^{84} +(-70314.2 - 70314.2i) q^{85} +(19113.0 - 62435.0i) q^{86} +462779. q^{87} +(118341. + 146463. i) q^{88} -713623. i q^{89} +(-85121.5 + 278060. i) q^{90} +(405677. - 405677. i) q^{91} +(392338. - 580759. i) q^{92} +(-17704.0 + 17704.0i) q^{93} +(569509. + 1.07202e6i) q^{94} +551753. i q^{95} +(-37308.1 - 435493. i) q^{96} -237368. q^{97} +(-2.13313e6 + 1.13322e6i) q^{98} +(-143308. - 143308. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8} - 1124 q^{10} + 1358 q^{11} - 2348 q^{12} - 2 q^{13} + 7564 q^{14} - 7976 q^{16} - 4 q^{17} - 1874 q^{18} + 3934 q^{19} - 16564 q^{20} - 1460 q^{21} + 25252 q^{22} - 13124 q^{23} - 32592 q^{24} + 58952 q^{26} + 35776 q^{27} + 45176 q^{28} - 33202 q^{29} + 8452 q^{30} - 39672 q^{32} - 4 q^{33} - 52588 q^{34} - 112420 q^{35} - 138484 q^{36} + 3598 q^{37} - 187280 q^{38} + 254396 q^{39} + 165160 q^{40} + 353496 q^{42} - 267986 q^{43} + 380724 q^{44} + 32706 q^{45} + 248156 q^{46} - 460824 q^{48} + 168066 q^{49} - 719674 q^{50} + 301788 q^{51} - 784892 q^{52} - 221842 q^{53} - 547552 q^{54} - 232708 q^{55} + 366424 q^{56} + 1441912 q^{58} + 39150 q^{59} + 2405600 q^{60} + 326494 q^{61} + 182832 q^{62} - 318656 q^{64} + 186412 q^{65} - 3392732 q^{66} - 122786 q^{67} - 2504400 q^{68} - 543188 q^{69} - 1186816 q^{70} - 267012 q^{71} + 1748596 q^{72} + 3610396 q^{74} - 275278 q^{75} + 4245988 q^{76} + 231180 q^{77} + 3179052 q^{78} - 2898968 q^{80} - 354298 q^{81} - 5004624 q^{82} - 288322 q^{83} - 7602776 q^{84} + 340748 q^{85} - 3240476 q^{86} + 2029884 q^{87} + 3308152 q^{88} + 10273400 q^{90} + 302396 q^{91} + 7253656 q^{92} - 1173344 q^{93} + 3859056 q^{94} - 5689424 q^{96} - 4 q^{97} - 9176950 q^{98} - 271522 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.06494 + 3.75322i −0.883117 + 0.469153i
\(3\) −9.43202 9.43202i −0.349334 0.349334i 0.510528 0.859861i \(-0.329450\pi\)
−0.859861 + 0.510528i \(0.829450\pi\)
\(4\) 35.8267 53.0325i 0.559792 0.828633i
\(5\) 46.6419 + 46.6419i 0.373135 + 0.373135i 0.868618 0.495483i \(-0.165009\pi\)
−0.495483 + 0.868618i \(0.665009\pi\)
\(6\) 102.037 + 31.2362i 0.472394 + 0.144612i
\(7\) 647.751 1.88849 0.944243 0.329249i \(-0.106796\pi\)
0.944243 + 0.329249i \(0.106796\pi\)
\(8\) −54.0705 + 509.137i −0.105606 + 0.994408i
\(9\) 551.074i 0.755932i
\(10\) −504.579 154.465i −0.504579 0.154465i
\(11\) 260.052 260.052i 0.195381 0.195381i −0.602635 0.798017i \(-0.705883\pi\)
0.798017 + 0.602635i \(0.205883\pi\)
\(12\) −838.121 + 162.286i −0.485024 + 0.0939154i
\(13\) 626.285 626.285i 0.285064 0.285064i −0.550061 0.835125i \(-0.685395\pi\)
0.835125 + 0.550061i \(0.185395\pi\)
\(14\) −4576.32 + 2431.15i −1.66775 + 0.885988i
\(15\) 879.853i 0.260697i
\(16\) −1528.90 3799.96i −0.373266 0.927724i
\(17\) −1507.54 −0.306846 −0.153423 0.988161i \(-0.549030\pi\)
−0.153423 + 0.988161i \(0.549030\pi\)
\(18\) 2068.30 + 3893.30i 0.354647 + 0.667576i
\(19\) 5914.78 + 5914.78i 0.862339 + 0.862339i 0.991609 0.129270i \(-0.0412635\pi\)
−0.129270 + 0.991609i \(0.541263\pi\)
\(20\) 4144.56 802.513i 0.518070 0.100314i
\(21\) −6109.59 6109.59i −0.659712 0.659712i
\(22\) −861.220 + 2813.29i −0.0808809 + 0.264208i
\(23\) 10951.0 0.900058 0.450029 0.893014i \(-0.351414\pi\)
0.450029 + 0.893014i \(0.351414\pi\)
\(24\) 5312.18 4292.19i 0.384272 0.310489i
\(25\) 11274.1i 0.721541i
\(26\) −2074.08 + 6775.25i −0.118006 + 0.385483i
\(27\) −12073.7 + 12073.7i −0.613406 + 0.613406i
\(28\) 23206.8 34351.9i 1.05716 1.56486i
\(29\) −24532.3 + 24532.3i −1.00588 + 1.00588i −0.00589441 + 0.999983i \(0.501876\pi\)
−0.999983 + 0.00589441i \(0.998124\pi\)
\(30\) 3302.28 + 6216.11i 0.122307 + 0.230226i
\(31\) 1877.01i 0.0630060i −0.999504 0.0315030i \(-0.989971\pi\)
0.999504 0.0315030i \(-0.0100294\pi\)
\(32\) 25063.7 + 21108.2i 0.764882 + 0.644171i
\(33\) −4905.63 −0.136507
\(34\) 10650.6 5658.11i 0.270981 0.143958i
\(35\) 30212.3 + 30212.3i 0.704660 + 0.704660i
\(36\) −29224.9 19743.2i −0.626390 0.423164i
\(37\) −62335.0 62335.0i −1.23063 1.23063i −0.963723 0.266905i \(-0.913999\pi\)
−0.266905 0.963723i \(-0.586001\pi\)
\(38\) −63987.1 19588.1i −1.16612 0.356978i
\(39\) −11814.3 −0.199165
\(40\) −26269.0 + 21225.1i −0.410454 + 0.331643i
\(41\) 58050.6i 0.842278i 0.906996 + 0.421139i \(0.138369\pi\)
−0.906996 + 0.421139i \(0.861631\pi\)
\(42\) 66094.6 + 20233.3i 0.892109 + 0.273098i
\(43\) −5771.32 + 5771.32i −0.0725888 + 0.0725888i −0.742469 0.669880i \(-0.766345\pi\)
0.669880 + 0.742469i \(0.266345\pi\)
\(44\) −4474.42 23108.0i −0.0525265 0.271272i
\(45\) 25703.1 25703.1i 0.282064 0.282064i
\(46\) −77368.2 + 41101.5i −0.794857 + 0.422264i
\(47\) 151739.i 1.46151i −0.682638 0.730757i \(-0.739167\pi\)
0.682638 0.730757i \(-0.260833\pi\)
\(48\) −21420.7 + 50261.9i −0.193691 + 0.454480i
\(49\) 301932. 2.56638
\(50\) 42314.1 + 79650.6i 0.338513 + 0.637205i
\(51\) 14219.1 + 14219.1i 0.107192 + 0.107192i
\(52\) −10775.8 55651.2i −0.0766370 0.395790i
\(53\) 64565.8 + 64565.8i 0.433685 + 0.433685i 0.889880 0.456195i \(-0.150788\pi\)
−0.456195 + 0.889880i \(0.650788\pi\)
\(54\) 39984.6 130615.i 0.253929 0.829491i
\(55\) 24258.6 0.145807
\(56\) −35024.2 + 329794.i −0.199436 + 1.87793i
\(57\) 111577.i 0.602489i
\(58\) 81244.2 265395.i 0.416398 1.36022i
\(59\) −199692. + 199692.i −0.972309 + 0.972309i −0.999627 0.0273181i \(-0.991303\pi\)
0.0273181 + 0.999627i \(0.491303\pi\)
\(60\) −46660.9 31522.2i −0.216022 0.145936i
\(61\) −226842. + 226842.i −0.999386 + 0.999386i −1.00000 0.000613806i \(-0.999805\pi\)
0.000613806 1.00000i \(0.499805\pi\)
\(62\) 7044.84 + 13261.0i 0.0295594 + 0.0556417i
\(63\) 356959.i 1.42757i
\(64\) −256297. 55058.6i −0.977695 0.210032i
\(65\) 58422.2 0.212735
\(66\) 34658.0 18411.9i 0.120551 0.0640424i
\(67\) −53695.6 53695.6i −0.178531 0.178531i 0.612184 0.790715i \(-0.290291\pi\)
−0.790715 + 0.612184i \(0.790291\pi\)
\(68\) −54010.0 + 79948.4i −0.171770 + 0.254263i
\(69\) −103290. 103290.i −0.314421 0.314421i
\(70\) −326841. 100055.i −0.952890 0.291704i
\(71\) −294503. −0.822838 −0.411419 0.911446i \(-0.634967\pi\)
−0.411419 + 0.911446i \(0.634967\pi\)
\(72\) 280572. + 29796.9i 0.751704 + 0.0798312i
\(73\) 476283.i 1.22432i 0.790732 + 0.612162i \(0.209700\pi\)
−0.790732 + 0.612162i \(0.790300\pi\)
\(74\) 674350. + 206436.i 1.66414 + 0.509436i
\(75\) −106337. + 106337.i −0.252059 + 0.252059i
\(76\) 525583. 101769.i 1.19729 0.231832i
\(77\) 168449. 168449.i 0.368975 0.368975i
\(78\) 83467.0 44341.5i 0.175886 0.0934387i
\(79\) 291918.i 0.592079i 0.955176 + 0.296039i \(0.0956660\pi\)
−0.955176 + 0.296039i \(0.904334\pi\)
\(80\) 105926. 248548.i 0.206888 0.485445i
\(81\) −173975. −0.327364
\(82\) −217877. 410124.i −0.395157 0.743830i
\(83\) 199292. + 199292.i 0.348542 + 0.348542i 0.859566 0.511024i \(-0.170734\pi\)
−0.511024 + 0.859566i \(0.670734\pi\)
\(84\) −542894. + 105121.i −0.915961 + 0.177358i
\(85\) −70314.2 70314.2i −0.114495 0.114495i
\(86\) 19113.0 62435.0i 0.0300492 0.0981596i
\(87\) 462779. 0.702774
\(88\) 118341. + 146463.i 0.173655 + 0.214922i
\(89\) 713623.i 1.01228i −0.862453 0.506138i \(-0.831073\pi\)
0.862453 0.506138i \(-0.168927\pi\)
\(90\) −85121.5 + 278060.i −0.116765 + 0.381427i
\(91\) 405677. 405677.i 0.538339 0.538339i
\(92\) 392338. 580759.i 0.503845 0.745818i
\(93\) −17704.0 + 17704.0i −0.0220101 + 0.0220101i
\(94\) 569509. + 1.07202e6i 0.685673 + 1.29069i
\(95\) 551753.i 0.643538i
\(96\) −37308.1 435493.i −0.0421686 0.492230i
\(97\) −237368. −0.260080 −0.130040 0.991509i \(-0.541511\pi\)
−0.130040 + 0.991509i \(0.541511\pi\)
\(98\) −2.13313e6 + 1.13322e6i −2.26641 + 1.20402i
\(99\) −143308. 143308.i −0.147695 0.147695i
\(100\) −597893. 403913.i −0.597893 0.403913i
\(101\) 55572.6 + 55572.6i 0.0539382 + 0.0539382i 0.733561 0.679623i \(-0.237857\pi\)
−0.679623 + 0.733561i \(0.737857\pi\)
\(102\) −153824. 47089.6i −0.144952 0.0443736i
\(103\) 682690. 0.624758 0.312379 0.949958i \(-0.398874\pi\)
0.312379 + 0.949958i \(0.398874\pi\)
\(104\) 285001. + 352728.i 0.253365 + 0.313574i
\(105\) 569926.i 0.492323i
\(106\) −698483. 213824.i −0.586460 0.179530i
\(107\) 908570. 908570.i 0.741664 0.741664i −0.231234 0.972898i \(-0.574276\pi\)
0.972898 + 0.231234i \(0.0742764\pi\)
\(108\) 207738. + 1.07286e6i 0.164909 + 0.851669i
\(109\) 413854. 413854.i 0.319571 0.319571i −0.529031 0.848602i \(-0.677445\pi\)
0.848602 + 0.529031i \(0.177445\pi\)
\(110\) −171386. + 91048.0i −0.128765 + 0.0684057i
\(111\) 1.17589e6i 0.859800i
\(112\) −990345. 2.46143e6i −0.704908 1.75199i
\(113\) −2.22714e6 −1.54352 −0.771761 0.635913i \(-0.780624\pi\)
−0.771761 + 0.635913i \(0.780624\pi\)
\(114\) 418772. + 788282.i 0.282659 + 0.532068i
\(115\) 510775. + 510775.i 0.335843 + 0.335843i
\(116\) 422100. + 2.17992e6i 0.270421 + 1.39658i
\(117\) −345130. 345130.i −0.215489 0.215489i
\(118\) 661323. 2.16030e6i 0.402501 1.31482i
\(119\) −976507. −0.579475
\(120\) 447966. + 47574.1i 0.259239 + 0.0275313i
\(121\) 1.63631e6i 0.923652i
\(122\) 751235. 2.45401e6i 0.413710 1.35144i
\(123\) 547534. 547534.i 0.294236 0.294236i
\(124\) −99542.7 67247.1i −0.0522089 0.0352703i
\(125\) 1.25462e6 1.25462e6i 0.642367 0.642367i
\(126\) 1.33974e6 + 2.52189e6i 0.669746 + 1.26071i
\(127\) 1.14502e6i 0.558988i 0.960147 + 0.279494i \(0.0901666\pi\)
−0.960147 + 0.279494i \(0.909833\pi\)
\(128\) 2.01737e6 572953.i 0.961956 0.273205i
\(129\) 108870. 0.0507154
\(130\) −412749. + 219271.i −0.187869 + 0.0998049i
\(131\) −2.23091e6 2.23091e6i −0.992357 0.992357i 0.00761414 0.999971i \(-0.497576\pi\)
−0.999971 + 0.00761414i \(0.997576\pi\)
\(132\) −175753. + 260158.i −0.0764152 + 0.113114i
\(133\) 3.83131e6 + 3.83131e6i 1.62852 + 1.62852i
\(134\) 580887. + 177825.i 0.241422 + 0.0739056i
\(135\) −1.12628e6 −0.457767
\(136\) 81513.2 767542.i 0.0324049 0.305130i
\(137\) 1.66105e6i 0.645984i −0.946402 0.322992i \(-0.895311\pi\)
0.946402 0.322992i \(-0.104689\pi\)
\(138\) 1.11741e6 + 342067.i 0.425182 + 0.130159i
\(139\) −1.78332e6 + 1.78332e6i −0.664024 + 0.664024i −0.956326 0.292302i \(-0.905579\pi\)
0.292302 + 0.956326i \(0.405579\pi\)
\(140\) 2.68464e6 519828.i 0.978368 0.189442i
\(141\) −1.43120e6 + 1.43120e6i −0.510556 + 0.510556i
\(142\) 2.08064e6 1.10533e6i 0.726662 0.386036i
\(143\) 325734.i 0.111392i
\(144\) −2.09406e6 + 842536.i −0.701296 + 0.282164i
\(145\) −2.28847e6 −0.750656
\(146\) −1.78760e6 3.36491e6i −0.574395 1.08122i
\(147\) −2.84783e6 2.84783e6i −0.896523 0.896523i
\(148\) −5.53904e6 + 1.07253e6i −1.70863 + 0.330844i
\(149\) −702022. 702022.i −0.212223 0.212223i 0.592988 0.805211i \(-0.297948\pi\)
−0.805211 + 0.592988i \(0.797948\pi\)
\(150\) 352159. 1.15037e6i 0.104343 0.340851i
\(151\) 772090. 0.224252 0.112126 0.993694i \(-0.464234\pi\)
0.112126 + 0.993694i \(0.464234\pi\)
\(152\) −3.33125e6 + 2.69162e6i −0.948586 + 0.766448i
\(153\) 830764.i 0.231955i
\(154\) −557856. + 1.82231e6i −0.152742 + 0.498953i
\(155\) 87547.4 87547.4i 0.0235097 0.0235097i
\(156\) −423266. + 626540.i −0.111491 + 0.165035i
\(157\) 809459. 809459.i 0.209168 0.209168i −0.594746 0.803914i \(-0.702747\pi\)
0.803914 + 0.594746i \(0.202747\pi\)
\(158\) −1.09563e6 2.06238e6i −0.277775 0.522875i
\(159\) 1.21797e6i 0.303002i
\(160\) 184491. + 2.15354e6i 0.0450416 + 0.525767i
\(161\) 7.09352e6 1.69975
\(162\) 1.22912e6 652966.i 0.289101 0.153584i
\(163\) 3.28693e6 + 3.28693e6i 0.758976 + 0.758976i 0.976136 0.217160i \(-0.0696794\pi\)
−0.217160 + 0.976136i \(0.569679\pi\)
\(164\) 3.07857e6 + 2.07976e6i 0.697939 + 0.471500i
\(165\) −228808. 228808.i −0.0509353 0.0509353i
\(166\) −2.15597e6 659998.i −0.471323 0.144284i
\(167\) −3.17737e6 −0.682210 −0.341105 0.940025i \(-0.610801\pi\)
−0.341105 + 0.940025i \(0.610801\pi\)
\(168\) 3.44097e6 2.78027e6i 0.725693 0.586353i
\(169\) 4.04234e6i 0.837477i
\(170\) 760671. + 232861.i 0.154828 + 0.0473969i
\(171\) 3.25949e6 3.25949e6i 0.651870 0.651870i
\(172\) 99300.4 + 512835.i 0.0195149 + 0.100784i
\(173\) 2.66328e6 2.66328e6i 0.514372 0.514372i −0.401491 0.915863i \(-0.631508\pi\)
0.915863 + 0.401491i \(0.131508\pi\)
\(174\) −3.26950e6 + 1.73691e6i −0.620632 + 0.329708i
\(175\) 7.30279e6i 1.36262i
\(176\) −1.38578e6 590595.i −0.254189 0.108331i
\(177\) 3.76699e6 0.679321
\(178\) 2.67838e6 + 5.04170e6i 0.474912 + 0.893958i
\(179\) 5.19151e6 + 5.19151e6i 0.905180 + 0.905180i 0.995878 0.0906987i \(-0.0289100\pi\)
−0.0906987 + 0.995878i \(0.528910\pi\)
\(180\) −442244. 2.28396e6i −0.0758306 0.391625i
\(181\) −4.48348e6 4.48348e6i −0.756101 0.756101i 0.219509 0.975610i \(-0.429554\pi\)
−0.975610 + 0.219509i \(0.929554\pi\)
\(182\) −1.34349e6 + 4.38867e6i −0.222853 + 0.727980i
\(183\) 4.27915e6 0.698239
\(184\) −592126. + 5.57556e6i −0.0950519 + 0.895025i
\(185\) 5.81484e6i 0.918380i
\(186\) 58630.7 191525.i 0.00911142 0.0297637i
\(187\) −392038. + 392038.i −0.0599520 + 0.0599520i
\(188\) −8.04709e6 5.43629e6i −1.21106 0.818143i
\(189\) −7.82073e6 + 7.82073e6i −1.15841 + 1.15841i
\(190\) −2.07085e6 3.89810e6i −0.301917 0.568319i
\(191\) 6.68684e6i 0.959667i 0.877360 + 0.479833i \(0.159303\pi\)
−0.877360 + 0.479833i \(0.840697\pi\)
\(192\) 1.89808e6 + 2.93671e6i 0.268171 + 0.414913i
\(193\) −4.36959e6 −0.607812 −0.303906 0.952702i \(-0.598291\pi\)
−0.303906 + 0.952702i \(0.598291\pi\)
\(194\) 1.67699e6 890893.i 0.229681 0.122017i
\(195\) −551039. 551039.i −0.0743154 0.0743154i
\(196\) 1.08172e7 1.60122e7i 1.43664 2.12659i
\(197\) −6.87265e6 6.87265e6i −0.898930 0.898930i 0.0964119 0.995342i \(-0.469263\pi\)
−0.995342 + 0.0964119i \(0.969263\pi\)
\(198\) 1.55033e6 + 474596.i 0.199723 + 0.0611404i
\(199\) 4.69869e6 0.596236 0.298118 0.954529i \(-0.403641\pi\)
0.298118 + 0.954529i \(0.403641\pi\)
\(200\) 5.74005e6 + 609595.i 0.717506 + 0.0761994i
\(201\) 1.01292e6i 0.124734i
\(202\) −601193. 184041.i −0.0729390 0.0223285i
\(203\) −1.58908e7 + 1.58908e7i −1.89958 + 1.89958i
\(204\) 1.26350e6 244652.i 0.148828 0.0288176i
\(205\) −2.70759e6 + 2.70759e6i −0.314283 + 0.314283i
\(206\) −4.82316e6 + 2.56229e6i −0.551735 + 0.293107i
\(207\) 6.03482e6i 0.680382i
\(208\) −3.33738e6 1.42233e6i −0.370865 0.158056i
\(209\) 3.07631e6 0.336970
\(210\) 2.13906e6 + 4.02649e6i 0.230975 + 0.434779i
\(211\) −650778. 650778.i −0.0692764 0.0692764i 0.671620 0.740896i \(-0.265599\pi\)
−0.740896 + 0.671620i \(0.765599\pi\)
\(212\) 5.73727e6 1.11091e6i 0.602140 0.116593i
\(213\) 2.77775e6 + 2.77775e6i 0.287445 + 0.287445i
\(214\) −3.00893e6 + 9.82906e6i −0.307023 + 1.00293i
\(215\) −538370. −0.0541708
\(216\) −5.49433e6 6.79999e6i −0.545197 0.674756i
\(217\) 1.21584e6i 0.118986i
\(218\) −1.37057e6 + 4.47713e6i −0.132291 + 0.432146i
\(219\) 4.49231e6 4.49231e6i 0.427698 0.427698i
\(220\) 869107. 1.28650e6i 0.0816216 0.120821i
\(221\) −944147. + 944147.i −0.0874707 + 0.0874707i
\(222\) −4.41337e6 8.30758e6i −0.403377 0.759304i
\(223\) 4.10370e6i 0.370050i −0.982734 0.185025i \(-0.940763\pi\)
0.982734 0.185025i \(-0.0592366\pi\)
\(224\) 1.62350e7 + 1.36728e7i 1.44447 + 1.21651i
\(225\) −6.21285e6 −0.545435
\(226\) 1.57346e7 8.35896e6i 1.36311 0.724147i
\(227\) 9.14949e6 + 9.14949e6i 0.782203 + 0.782203i 0.980202 0.197999i \(-0.0634444\pi\)
−0.197999 + 0.980202i \(0.563444\pi\)
\(228\) −5.91719e6 3.99742e6i −0.499242 0.337268i
\(229\) −1.00525e7 1.00525e7i −0.837080 0.837080i 0.151393 0.988474i \(-0.451624\pi\)
−0.988474 + 0.151393i \(0.951624\pi\)
\(230\) −5.52565e6 1.69154e6i −0.454150 0.139027i
\(231\) −3.17763e6 −0.257791
\(232\) −1.11638e7 1.38168e7i −0.894025 1.10648i
\(233\) 2.40216e6i 0.189904i 0.995482 + 0.0949519i \(0.0302697\pi\)
−0.995482 + 0.0949519i \(0.969730\pi\)
\(234\) 3.73367e6 + 1.14297e6i 0.291399 + 0.0892047i
\(235\) 7.07737e6 7.07737e6i 0.545341 0.545341i
\(236\) 3.43587e6 + 1.77445e7i 0.261397 + 1.34998i
\(237\) 2.75337e6 2.75337e6i 0.206833 0.206833i
\(238\) 6.89896e6 3.66505e6i 0.511744 0.271862i
\(239\) 4.88169e6i 0.357583i −0.983887 0.178791i \(-0.942781\pi\)
0.983887 0.178791i \(-0.0572188\pi\)
\(240\) −3.34341e6 + 1.34521e6i −0.241855 + 0.0973095i
\(241\) 1.42451e7 1.01768 0.508842 0.860860i \(-0.330074\pi\)
0.508842 + 0.860860i \(0.330074\pi\)
\(242\) −6.14142e6 1.15604e7i −0.433334 0.815693i
\(243\) 1.04426e7 + 1.04426e7i 0.727766 + 0.727766i
\(244\) 3.90300e6 + 2.01570e7i 0.268676 + 1.38757i
\(245\) 1.40827e7 + 1.40827e7i 0.957606 + 0.957606i
\(246\) −1.81328e6 + 5.92331e6i −0.121803 + 0.397887i
\(247\) 7.40869e6 0.491643
\(248\) 955657. + 101491.i 0.0626537 + 0.00665384i
\(249\) 3.75945e6i 0.243515i
\(250\) −4.15496e6 + 1.35727e7i −0.265917 + 0.868653i
\(251\) 1.32246e6 1.32246e6i 0.0836296 0.0836296i −0.664055 0.747684i \(-0.731166\pi\)
0.747684 + 0.664055i \(0.231166\pi\)
\(252\) −1.89304e7 1.27886e7i −1.18293 0.799140i
\(253\) 2.84783e6 2.84783e6i 0.175854 0.175854i
\(254\) −4.29751e6 8.08950e6i −0.262250 0.493652i
\(255\) 1.32641e6i 0.0799940i
\(256\) −1.21022e7 + 1.16195e7i −0.721345 + 0.692576i
\(257\) 4.59304e6 0.270583 0.135292 0.990806i \(-0.456803\pi\)
0.135292 + 0.990806i \(0.456803\pi\)
\(258\) −769162. + 408614.i −0.0447877 + 0.0237933i
\(259\) −4.03775e7 4.03775e7i −2.32402 2.32402i
\(260\) 2.09307e6 3.09828e6i 0.119087 0.176279i
\(261\) 1.35191e7 + 1.35191e7i 0.760374 + 0.760374i
\(262\) 2.41343e7 + 7.38814e6i 1.34193 + 0.410801i
\(263\) −1.60609e7 −0.882880 −0.441440 0.897291i \(-0.645532\pi\)
−0.441440 + 0.897291i \(0.645532\pi\)
\(264\) 265250. 2.49764e6i 0.0144160 0.135743i
\(265\) 6.02294e6i 0.323646i
\(266\) −4.14477e7 1.26882e7i −2.20219 0.674148i
\(267\) −6.73090e6 + 6.73090e6i −0.353622 + 0.353622i
\(268\) −4.77135e6 + 923878.i −0.247877 + 0.0479966i
\(269\) 1.00869e7 1.00869e7i 0.518203 0.518203i −0.398824 0.917027i \(-0.630582\pi\)
0.917027 + 0.398824i \(0.130582\pi\)
\(270\) 7.95708e6 4.22717e6i 0.404262 0.214762i
\(271\) 6.63437e6i 0.333344i 0.986012 + 0.166672i \(0.0533020\pi\)
−0.986012 + 0.166672i \(0.946698\pi\)
\(272\) 2.30487e6 + 5.72857e6i 0.114535 + 0.284669i
\(273\) −7.65270e6 −0.376120
\(274\) 6.23429e6 + 1.17352e7i 0.303065 + 0.570479i
\(275\) −2.93185e6 2.93185e6i −0.140975 0.140975i
\(276\) −9.17827e6 + 1.77719e6i −0.436550 + 0.0845293i
\(277\) −517807. 517807.i −0.0243629 0.0243629i 0.694820 0.719183i \(-0.255484\pi\)
−0.719183 + 0.694820i \(0.755484\pi\)
\(278\) 5.90584e6 1.92922e7i 0.274882 0.897940i
\(279\) −1.03437e6 −0.0476283
\(280\) −1.70158e7 + 1.37486e7i −0.775136 + 0.626303i
\(281\) 872957.i 0.0393436i 0.999806 + 0.0196718i \(0.00626213\pi\)
−0.999806 + 0.0196718i \(0.993738\pi\)
\(282\) 4.73973e6 1.54830e7i 0.211352 0.690409i
\(283\) 1.78268e7 1.78268e7i 0.786529 0.786529i −0.194395 0.980923i \(-0.562274\pi\)
0.980923 + 0.194395i \(0.0622743\pi\)
\(284\) −1.05511e7 + 1.56182e7i −0.460618 + 0.681831i
\(285\) 5.20414e6 5.20414e6i 0.224810 0.224810i
\(286\) 1.22255e6 + 2.30129e6i 0.0522599 + 0.0983724i
\(287\) 3.76023e7i 1.59063i
\(288\) 1.16322e7 1.38119e7i 0.486949 0.578198i
\(289\) −2.18649e7 −0.905845
\(290\) 1.61679e7 8.58912e6i 0.662917 0.352172i
\(291\) 2.23886e6 + 2.23886e6i 0.0908547 + 0.0908547i
\(292\) 2.52585e7 + 1.70636e7i 1.01452 + 0.685367i
\(293\) 1.17082e7 + 1.17082e7i 0.465466 + 0.465466i 0.900442 0.434976i \(-0.143243\pi\)
−0.434976 + 0.900442i \(0.643243\pi\)
\(294\) 3.08082e7 + 9.43120e6i 1.21234 + 0.371129i
\(295\) −1.86280e7 −0.725605
\(296\) 3.51075e7 2.83666e7i 1.35371 1.09378i
\(297\) 6.27958e6i 0.239696i
\(298\) 7.59459e6 + 2.32490e6i 0.286983 + 0.0878528i
\(299\) 6.85845e6 6.85845e6i 0.256574 0.256574i
\(300\) 1.82962e6 + 9.44904e6i 0.0677638 + 0.349965i
\(301\) −3.73837e6 + 3.73837e6i −0.137083 + 0.137083i
\(302\) −5.45477e6 + 2.89782e6i −0.198041 + 0.105209i
\(303\) 1.04832e6i 0.0376849i
\(304\) 1.34328e7 3.15190e7i 0.478131 1.12190i
\(305\) −2.11606e7 −0.745811
\(306\) −3.11804e6 5.86929e6i −0.108822 0.204843i
\(307\) 9.99969e6 + 9.99969e6i 0.345598 + 0.345598i 0.858467 0.512869i \(-0.171417\pi\)
−0.512869 + 0.858467i \(0.671417\pi\)
\(308\) −2.89831e6 1.49683e7i −0.0991956 0.512294i
\(309\) −6.43914e6 6.43914e6i −0.218249 0.218249i
\(310\) −289932. + 947101.i −0.00973221 + 0.0317915i
\(311\) 6.41019e6 0.213103 0.106552 0.994307i \(-0.466019\pi\)
0.106552 + 0.994307i \(0.466019\pi\)
\(312\) 638803. 6.01508e6i 0.0210331 0.198051i
\(313\) 4.05196e7i 1.32139i 0.750654 + 0.660696i \(0.229739\pi\)
−0.750654 + 0.660696i \(0.770261\pi\)
\(314\) −2.68070e6 + 8.75685e6i −0.0865883 + 0.282852i
\(315\) 1.66492e7 1.66492e7i 0.532675 0.532675i
\(316\) 1.54811e7 + 1.04585e7i 0.490616 + 0.331441i
\(317\) 1.45001e7 1.45001e7i 0.455191 0.455191i −0.441882 0.897073i \(-0.645689\pi\)
0.897073 + 0.441882i \(0.145689\pi\)
\(318\) 4.57131e6 + 8.60489e6i 0.142154 + 0.267586i
\(319\) 1.27594e7i 0.393059i
\(320\) −9.38612e6 1.45222e7i −0.286442 0.443182i
\(321\) −1.71393e7 −0.518177
\(322\) −5.01153e7 + 2.66235e7i −1.50108 + 0.797440i
\(323\) −8.91675e6 8.91675e6i −0.264605 0.264605i
\(324\) −6.23294e6 + 9.22632e6i −0.183256 + 0.271265i
\(325\) −7.06079e6 7.06079e6i −0.205685 0.205685i
\(326\) −3.55586e7 1.08854e7i −1.02634 0.314189i
\(327\) −7.80695e6 −0.223274
\(328\) −2.95557e7 3.13883e6i −0.837568 0.0889499i
\(329\) 9.82888e7i 2.76005i
\(330\) 2.47528e6 + 757747.i 0.0688783 + 0.0210854i
\(331\) −3.64653e7 + 3.64653e7i −1.00553 + 1.00553i −0.00554753 + 0.999985i \(0.501766\pi\)
−0.999985 + 0.00554753i \(0.998234\pi\)
\(332\) 1.77089e7 3.42899e6i 0.483925 0.0937025i
\(333\) −3.43512e7 + 3.43512e7i −0.930271 + 0.930271i
\(334\) 2.24479e7 1.19254e7i 0.602472 0.320061i
\(335\) 5.00892e6i 0.133232i
\(336\) −1.38753e7 + 3.25572e7i −0.365783 + 0.858279i
\(337\) −3.24205e7 −0.847091 −0.423545 0.905875i \(-0.639215\pi\)
−0.423545 + 0.905875i \(0.639215\pi\)
\(338\) −1.51718e7 2.85589e7i −0.392905 0.739590i
\(339\) 2.10065e7 + 2.10065e7i 0.539205 + 0.539205i
\(340\) −6.24807e6 + 1.20982e6i −0.158968 + 0.0307810i
\(341\) −488122. 488122.i −0.0123102 0.0123102i
\(342\) −1.07945e7 + 3.52616e7i −0.269851 + 0.881503i
\(343\) 1.19369e8 2.95809
\(344\) −2.62633e6 3.25045e6i −0.0645170 0.0798487i
\(345\) 9.63528e6i 0.234643i
\(346\) −8.82001e6 + 2.88117e7i −0.212932 + 0.695570i
\(347\) 1.34860e7 1.34860e7i 0.322772 0.322772i −0.527058 0.849829i \(-0.676705\pi\)
0.849829 + 0.527058i \(0.176705\pi\)
\(348\) 1.65798e7 2.45423e7i 0.393407 0.582342i
\(349\) 3.44786e7 3.44786e7i 0.811098 0.811098i −0.173701 0.984798i \(-0.555573\pi\)
0.984798 + 0.173701i \(0.0555726\pi\)
\(350\) 2.74090e7 + 5.15938e7i 0.639276 + 1.20335i
\(351\) 1.51231e7i 0.349720i
\(352\) 1.20071e7 1.02863e6i 0.275302 0.0235847i
\(353\) 4.98234e7 1.13268 0.566342 0.824170i \(-0.308358\pi\)
0.566342 + 0.824170i \(0.308358\pi\)
\(354\) −2.66136e7 + 1.41384e7i −0.599920 + 0.318705i
\(355\) −1.37362e7 1.37362e7i −0.307030 0.307030i
\(356\) −3.78452e7 2.55667e7i −0.838805 0.566663i
\(357\) 9.21043e6 + 9.21043e6i 0.202430 + 0.202430i
\(358\) −5.61626e7 1.71928e7i −1.22405 0.374712i
\(359\) −5.17087e7 −1.11758 −0.558792 0.829308i \(-0.688735\pi\)
−0.558792 + 0.829308i \(0.688735\pi\)
\(360\) 1.16966e7 + 1.44762e7i 0.250699 + 0.310275i
\(361\) 2.29235e7i 0.487258i
\(362\) 4.85030e7 + 1.48480e7i 1.02245 + 0.312999i
\(363\) 1.54337e7 1.54337e7i 0.322663 0.322663i
\(364\) −6.98001e6 3.60481e7i −0.144728 0.747444i
\(365\) −2.22147e7 + 2.22147e7i −0.456838 + 0.456838i
\(366\) −3.02319e7 + 1.60606e7i −0.616627 + 0.327580i
\(367\) 6.17256e7i 1.24873i −0.781135 0.624363i \(-0.785359\pi\)
0.781135 0.624363i \(-0.214641\pi\)
\(368\) −1.67430e7 4.16134e7i −0.335961 0.835006i
\(369\) 3.19902e7 0.636704
\(370\) 2.18244e7 + 4.10815e7i 0.430860 + 0.811037i
\(371\) 4.18225e7 + 4.18225e7i 0.819009 + 0.819009i
\(372\) 304613. + 1.57316e6i 0.00591724 + 0.0305594i
\(373\) −2.24042e7 2.24042e7i −0.431720 0.431720i 0.457493 0.889213i \(-0.348747\pi\)
−0.889213 + 0.457493i \(0.848747\pi\)
\(374\) 1.29832e6 4.24113e6i 0.0248180 0.0810712i
\(375\) −2.36672e7 −0.448801
\(376\) 7.72558e7 + 8.20459e6i 1.45334 + 0.154345i
\(377\) 3.07285e7i 0.573478i
\(378\) 2.59001e7 8.46059e7i 0.479541 1.56648i
\(379\) −1.89722e7 + 1.89722e7i −0.348498 + 0.348498i −0.859550 0.511052i \(-0.829256\pi\)
0.511052 + 0.859550i \(0.329256\pi\)
\(380\) 2.92609e7 + 1.97675e7i 0.533257 + 0.360247i
\(381\) 1.07999e7 1.07999e7i 0.195273 0.195273i
\(382\) −2.50972e7 4.72421e7i −0.450230 0.847498i
\(383\) 1.75005e7i 0.311498i 0.987797 + 0.155749i \(0.0497790\pi\)
−0.987797 + 0.155749i \(0.950221\pi\)
\(384\) −2.44319e7 1.36237e7i −0.431484 0.240604i
\(385\) 1.57136e7 0.275355
\(386\) 3.08709e7 1.64000e7i 0.536769 0.285156i
\(387\) 3.18042e6 + 3.18042e6i 0.0548721 + 0.0548721i
\(388\) −8.50410e6 + 1.25882e7i −0.145590 + 0.215511i
\(389\) −4.09463e7 4.09463e7i −0.695610 0.695610i 0.267850 0.963461i \(-0.413687\pi\)
−0.963461 + 0.267850i \(0.913687\pi\)
\(390\) 5.96123e6 + 1.82489e6i 0.100494 + 0.0307639i
\(391\) −1.65090e7 −0.276179
\(392\) −1.63256e7 + 1.53725e8i −0.271026 + 2.55203i
\(393\) 4.20839e7i 0.693328i
\(394\) 7.43494e7 + 2.27603e7i 1.21560 + 0.372125i
\(395\) −1.36156e7 + 1.36156e7i −0.220925 + 0.220925i
\(396\) −1.27342e7 + 2.46574e6i −0.205063 + 0.0397065i
\(397\) 1.82356e7 1.82356e7i 0.291439 0.291439i −0.546209 0.837649i \(-0.683930\pi\)
0.837649 + 0.546209i \(0.183930\pi\)
\(398\) −3.31960e7 + 1.76352e7i −0.526546 + 0.279725i
\(399\) 7.22739e7i 1.13779i
\(400\) −4.28410e7 + 1.72369e7i −0.669391 + 0.269327i
\(401\) 3.03064e7 0.470004 0.235002 0.971995i \(-0.424490\pi\)
0.235002 + 0.971995i \(0.424490\pi\)
\(402\) −3.80169e6 7.15618e6i −0.0585193 0.110155i
\(403\) −1.17555e6 1.17555e6i −0.0179607 0.0179607i
\(404\) 4.93814e6 956174.i 0.0748892 0.0145008i
\(405\) −8.11451e6 8.11451e6i −0.122151 0.122151i
\(406\) 5.26260e7 1.71910e8i 0.786361 2.56875i
\(407\) −3.24207e7 −0.480883
\(408\) −8.00830e6 + 6.47063e6i −0.117912 + 0.0952722i
\(409\) 2.93910e7i 0.429580i 0.976660 + 0.214790i \(0.0689068\pi\)
−0.976660 + 0.214790i \(0.931093\pi\)
\(410\) 8.96677e6 2.92911e7i 0.130102 0.424996i
\(411\) −1.56671e7 + 1.56671e7i −0.225664 + 0.225664i
\(412\) 2.44585e7 3.62048e7i 0.349734 0.517695i
\(413\) −1.29350e8 + 1.29350e8i −1.83619 + 1.83619i
\(414\) 2.26500e7 + 4.26356e7i 0.319203 + 0.600857i
\(415\) 1.85907e7i 0.260106i
\(416\) 2.89167e7 2.47725e6i 0.401670 0.0344105i
\(417\) 3.36405e7 0.463932
\(418\) −2.17339e7 + 1.15461e7i −0.297584 + 0.158090i
\(419\) −6.77130e7 6.77130e7i −0.920513 0.920513i 0.0765522 0.997066i \(-0.475609\pi\)
−0.997066 + 0.0765522i \(0.975609\pi\)
\(420\) −3.02246e7 2.04185e7i −0.407955 0.275599i
\(421\) 5.22594e6 + 5.22594e6i 0.0700354 + 0.0700354i 0.741257 0.671221i \(-0.234230\pi\)
−0.671221 + 0.741257i \(0.734230\pi\)
\(422\) 7.04021e6 + 2.15519e6i 0.0936804 + 0.0286780i
\(423\) −8.36193e7 −1.10480
\(424\) −3.63639e7 + 2.93817e7i −0.477060 + 0.385460i
\(425\) 1.69961e7i 0.221402i
\(426\) −3.00502e7 9.19914e6i −0.388703 0.118992i
\(427\) −1.46937e8 + 1.46937e8i −1.88733 + 1.88733i
\(428\) −1.56327e7 8.07348e7i −0.199390 1.02974i
\(429\) −3.07233e6 + 3.07233e6i −0.0389131 + 0.0389131i
\(430\) 3.80355e6 2.02062e6i 0.0478392 0.0254144i
\(431\) 1.23404e8i 1.54134i −0.637237 0.770668i \(-0.719923\pi\)
0.637237 0.770668i \(-0.280077\pi\)
\(432\) 6.43389e7 + 2.74201e7i 0.798036 + 0.340108i
\(433\) 1.19816e8 1.47587 0.737937 0.674869i \(-0.235800\pi\)
0.737937 + 0.674869i \(0.235800\pi\)
\(434\) 4.56330e6 + 8.58981e6i 0.0558226 + 0.105079i
\(435\) 2.15849e7 + 2.15849e7i 0.262229 + 0.262229i
\(436\) −7.12071e6 3.67747e7i −0.0859139 0.443700i
\(437\) 6.47728e7 + 6.47728e7i 0.776155 + 0.776155i
\(438\) −1.48773e7 + 4.85985e7i −0.177052 + 0.578363i
\(439\) 9.07146e7 1.07222 0.536109 0.844148i \(-0.319893\pi\)
0.536109 + 0.844148i \(0.319893\pi\)
\(440\) −1.31168e6 + 1.23510e7i −0.0153982 + 0.144992i
\(441\) 1.66387e8i 1.94001i
\(442\) 3.12675e6 1.02139e7i 0.0362098 0.118284i
\(443\) 1.14367e8 1.14367e8i 1.31550 1.31550i 0.398205 0.917296i \(-0.369633\pi\)
0.917296 0.398205i \(-0.130367\pi\)
\(444\) 6.23604e7 + 4.21282e7i 0.712459 + 0.481309i
\(445\) 3.32847e7 3.32847e7i 0.377715 0.377715i
\(446\) 1.54021e7 + 2.89924e7i 0.173610 + 0.326798i
\(447\) 1.32430e7i 0.148273i
\(448\) −1.66016e8 3.56642e7i −1.84636 0.396642i
\(449\) −3.25572e7 −0.359673 −0.179836 0.983697i \(-0.557557\pi\)
−0.179836 + 0.983697i \(0.557557\pi\)
\(450\) 4.38934e7 2.33182e7i 0.481683 0.255892i
\(451\) 1.50962e7 + 1.50962e7i 0.164565 + 0.164565i
\(452\) −7.97912e7 + 1.18111e8i −0.864051 + 1.27901i
\(453\) −7.28236e6 7.28236e6i −0.0783389 0.0783389i
\(454\) −9.89806e7 3.03005e7i −1.05775 0.323804i
\(455\) 3.78430e7 0.401746
\(456\) 5.68078e7 + 6.03301e6i 0.599120 + 0.0636267i
\(457\) 1.26635e8i 1.32680i 0.748267 + 0.663398i \(0.230886\pi\)
−0.748267 + 0.663398i \(0.769114\pi\)
\(458\) 1.08749e8 + 3.32910e7i 1.13196 + 0.346522i
\(459\) 1.82015e7 1.82015e7i 0.188221 0.188221i
\(460\) 4.53871e7 8.78832e6i 0.466293 0.0902885i
\(461\) 8.58153e7 8.58153e7i 0.875915 0.875915i −0.117194 0.993109i \(-0.537390\pi\)
0.993109 + 0.117194i \(0.0373899\pi\)
\(462\) 2.24497e7 1.19263e7i 0.227659 0.120943i
\(463\) 5.28474e7i 0.532452i 0.963911 + 0.266226i \(0.0857768\pi\)
−0.963911 + 0.266226i \(0.914223\pi\)
\(464\) 1.30729e8 + 5.57144e7i 1.30864 + 0.557717i
\(465\) −1.65150e6 −0.0164255
\(466\) −9.01582e6 1.69711e7i −0.0890938 0.167707i
\(467\) 1.01218e8 + 1.01218e8i 0.993821 + 0.993821i 0.999981 0.00615974i \(-0.00196072\pi\)
−0.00615974 + 0.999981i \(0.501961\pi\)
\(468\) −3.06679e7 + 5.93825e6i −0.299190 + 0.0579323i
\(469\) −3.47814e7 3.47814e7i −0.337154 0.337154i
\(470\) −2.34383e7 + 7.65641e7i −0.225752 + 0.737449i
\(471\) −1.52697e7 −0.146139
\(472\) −9.08730e7 1.12468e8i −0.864189 1.06955i
\(473\) 3.00169e6i 0.0283650i
\(474\) −9.11840e6 + 2.97864e7i −0.0856216 + 0.279694i
\(475\) 6.66837e7 6.66837e7i 0.622213 0.622213i
\(476\) −3.49850e7 + 5.17866e7i −0.324385 + 0.480172i
\(477\) 3.55805e7 3.55805e7i 0.327837 0.327837i
\(478\) 1.83221e7 + 3.44889e7i 0.167761 + 0.315788i
\(479\) 1.70178e7i 0.154845i 0.996998 + 0.0774223i \(0.0246690\pi\)
−0.996998 + 0.0774223i \(0.975331\pi\)
\(480\) 1.85721e7 2.20523e7i 0.167934 0.199403i
\(481\) −7.80790e7 −0.701615
\(482\) −1.00640e8 + 5.34648e7i −0.898734 + 0.477449i
\(483\) −6.69062e7 6.69062e7i −0.593779 0.593779i
\(484\) 8.67775e7 + 5.86234e7i 0.765369 + 0.517053i
\(485\) −1.10713e7 1.10713e7i −0.0970448 0.0970448i
\(486\) −1.12970e8 3.45831e7i −0.984136 0.301269i
\(487\) 4.54795e7 0.393758 0.196879 0.980428i \(-0.436919\pi\)
0.196879 + 0.980428i \(0.436919\pi\)
\(488\) −1.03228e8 1.27759e8i −0.888256 1.09934i
\(489\) 6.20048e7i 0.530272i
\(490\) −1.52349e8 4.66378e7i −1.29494 0.396415i
\(491\) −6.79748e7 + 6.79748e7i −0.574254 + 0.574254i −0.933314 0.359061i \(-0.883097\pi\)
0.359061 + 0.933314i \(0.383097\pi\)
\(492\) −9.42079e6 4.86535e7i −0.0791028 0.408525i
\(493\) 3.69834e7 3.69834e7i 0.308650 0.308650i
\(494\) −5.23419e7 + 2.78064e7i −0.434179 + 0.230656i
\(495\) 1.33683e7i 0.110220i
\(496\) −7.13257e6 + 2.86976e6i −0.0584522 + 0.0235180i
\(497\) −1.90764e8 −1.55392
\(498\) 1.41100e7 + 2.65603e7i 0.114246 + 0.215052i
\(499\) −7.37425e7 7.37425e7i −0.593494 0.593494i 0.345079 0.938573i \(-0.387852\pi\)
−0.938573 + 0.345079i \(0.887852\pi\)
\(500\) −2.15869e7 1.11485e8i −0.172695 0.891878i
\(501\) 2.99690e7 + 2.99690e7i 0.238319 + 0.238319i
\(502\) −4.37960e6 + 1.43065e7i −0.0346197 + 0.113090i
\(503\) 9.21484e7 0.724076 0.362038 0.932163i \(-0.382081\pi\)
0.362038 + 0.932163i \(0.382081\pi\)
\(504\) 1.81741e8 + 1.93009e7i 1.41958 + 0.150760i
\(505\) 5.18402e6i 0.0402525i
\(506\) −9.43122e6 + 3.08083e7i −0.0727975 + 0.237803i
\(507\) 3.81274e7 3.81274e7i 0.292559 0.292559i
\(508\) 6.07233e7 + 4.10223e7i 0.463196 + 0.312917i
\(509\) −1.40774e8 + 1.40774e8i −1.06750 + 1.06750i −0.0699519 + 0.997550i \(0.522285\pi\)
−0.997550 + 0.0699519i \(0.977715\pi\)
\(510\) −4.97831e6 9.37100e6i −0.0375294 0.0706440i
\(511\) 3.08513e8i 2.31212i
\(512\) 4.18904e7 1.27513e8i 0.312108 0.950047i
\(513\) −1.42826e8 −1.05793
\(514\) −3.24495e7 + 1.72387e7i −0.238957 + 0.126945i
\(515\) 3.18419e7 + 3.18419e7i 0.233119 + 0.233119i
\(516\) 3.90046e6 5.77367e6i 0.0283901 0.0420245i
\(517\) −3.94600e7 3.94600e7i −0.285552 0.285552i
\(518\) 4.36811e8 + 1.33719e8i 3.14271 + 0.962064i
\(519\) −5.02401e7 −0.359376
\(520\) −3.15892e6 + 2.97449e7i −0.0224661 + 0.211545i
\(521\) 1.20829e8i 0.854390i −0.904159 0.427195i \(-0.859502\pi\)
0.904159 0.427195i \(-0.140498\pi\)
\(522\) −1.46252e8 4.47716e7i −1.02823 0.314768i
\(523\) 5.99028e7 5.99028e7i 0.418738 0.418738i −0.466031 0.884769i \(-0.654316\pi\)
0.884769 + 0.466031i \(0.154316\pi\)
\(524\) −1.98237e8 + 3.83847e7i −1.37781 + 0.266787i
\(525\) −6.88800e7 + 6.88800e7i −0.476009 + 0.476009i
\(526\) 1.13469e8 6.02800e7i 0.779687 0.414206i
\(527\) 2.82966e6i 0.0193332i
\(528\) 7.50022e6 + 1.86412e7i 0.0509533 + 0.126640i
\(529\) −2.81114e7 −0.189896
\(530\) −2.26054e7 4.25517e7i −0.151839 0.285818i
\(531\) 1.10045e8 + 1.10045e8i 0.734999 + 0.734999i
\(532\) 3.40447e8 6.59209e7i 2.26107 0.437812i
\(533\) 3.63562e7 + 3.63562e7i 0.240103 + 0.240103i
\(534\) 2.22908e7 7.28159e7i 0.146387 0.478192i
\(535\) 8.47548e7 0.553481
\(536\) 3.02418e7 2.44351e7i 0.196387 0.158679i
\(537\) 9.79329e7i 0.632420i
\(538\) −3.34049e7 + 1.09122e8i −0.214518 + 0.700751i
\(539\) 7.85181e7 7.85181e7i 0.501422 0.501422i
\(540\) −4.03508e7 + 5.97294e7i −0.256254 + 0.379321i
\(541\) 1.29579e8 1.29579e8i 0.818354 0.818354i −0.167515 0.985870i \(-0.553574\pi\)
0.985870 + 0.167515i \(0.0535743\pi\)
\(542\) −2.49003e7 4.68714e7i −0.156389 0.294381i
\(543\) 8.45766e7i 0.528263i
\(544\) −3.77843e7 3.18213e7i −0.234701 0.197661i
\(545\) 3.86058e7 0.238486
\(546\) 5.40658e7 2.87223e7i 0.332158 0.176458i
\(547\) −1.60668e8 1.60668e8i −0.981674 0.981674i 0.0181616 0.999835i \(-0.494219\pi\)
−0.999835 + 0.0181616i \(0.994219\pi\)
\(548\) −8.80898e7 5.95100e7i −0.535284 0.361616i
\(549\) 1.25007e8 + 1.25007e8i 0.755468 + 0.755468i
\(550\) 3.17172e7 + 9.70946e6i 0.190637 + 0.0583589i
\(551\) −2.90207e8 −1.73481
\(552\) 5.81737e7 4.70038e7i 0.345867 0.279458i
\(553\) 1.89090e8i 1.11813i
\(554\) 5.60172e6 + 1.71483e6i 0.0329452 + 0.0100854i
\(555\) −5.48457e7 + 5.48457e7i −0.320821 + 0.320821i
\(556\) 3.06835e7 + 1.58464e8i 0.178517 + 0.921948i
\(557\) 1.18841e8 1.18841e8i 0.687701 0.687701i −0.274023 0.961723i \(-0.588354\pi\)
0.961723 + 0.274023i \(0.0883543\pi\)
\(558\) 7.30778e6 3.88223e6i 0.0420613 0.0223449i
\(559\) 7.22898e6i 0.0413849i
\(560\) 6.86140e7 1.60997e8i 0.390704 0.916756i
\(561\) 7.39542e6 0.0418865
\(562\) −3.27640e6 6.16739e6i −0.0184581 0.0347450i
\(563\) −6.62416e7 6.62416e7i −0.371198 0.371198i 0.496716 0.867913i \(-0.334539\pi\)
−0.867913 + 0.496716i \(0.834539\pi\)
\(564\) 2.46250e7 + 1.27175e8i 0.137259 + 0.708869i
\(565\) −1.03878e8 1.03878e8i −0.575942 0.575942i
\(566\) −5.90374e7 + 1.92853e8i −0.325595 + 1.06360i
\(567\) −1.12692e8 −0.618223
\(568\) 1.59239e7 1.49942e8i 0.0868970 0.818237i
\(569\) 2.58863e8i 1.40518i 0.711593 + 0.702592i \(0.247974\pi\)
−0.711593 + 0.702592i \(0.752026\pi\)
\(570\) −1.72347e7 + 5.62992e7i −0.0930632 + 0.304003i
\(571\) −7.06719e6 + 7.06719e6i −0.0379611 + 0.0379611i −0.725833 0.687871i \(-0.758545\pi\)
0.687871 + 0.725833i \(0.258545\pi\)
\(572\) −1.72745e7 1.16700e7i −0.0923033 0.0623564i
\(573\) 6.30703e7 6.30703e7i 0.335244 0.335244i
\(574\) −1.41130e8 2.65658e8i −0.746248 1.40471i
\(575\) 1.23462e8i 0.649428i
\(576\) −3.03414e7 + 1.41239e8i −0.158770 + 0.739070i
\(577\) 1.43515e8 0.747085 0.373542 0.927613i \(-0.378143\pi\)
0.373542 + 0.927613i \(0.378143\pi\)
\(578\) 1.54474e8 8.20638e7i 0.799968 0.424980i
\(579\) 4.12141e7 + 4.12141e7i 0.212329 + 0.212329i
\(580\) −8.19882e7 + 1.21363e8i −0.420211 + 0.622018i
\(581\) 1.29091e8 + 1.29091e8i 0.658217 + 0.658217i
\(582\) −2.42203e7 7.41446e6i −0.122860 0.0376106i
\(583\) 3.35810e7 0.169468
\(584\) −2.42493e8 2.57529e7i −1.21748 0.129297i
\(585\) 3.21950e7i 0.160813i
\(586\) −1.26661e8 3.87743e7i −0.629436 0.192687i
\(587\) 1.93835e8 1.93835e8i 0.958337 0.958337i −0.0408294 0.999166i \(-0.513000\pi\)
0.999166 + 0.0408294i \(0.0130000\pi\)
\(588\) −2.53056e8 + 4.89993e7i −1.24476 + 0.241023i
\(589\) 1.11021e7 1.11021e7i 0.0543326 0.0543326i
\(590\) 1.31606e8 6.99150e7i 0.640794 0.340419i
\(591\) 1.29646e8i 0.628053i
\(592\) −1.41567e8 + 3.32174e8i −0.682332 + 1.60104i
\(593\) −2.25213e8 −1.08002 −0.540008 0.841660i \(-0.681579\pi\)
−0.540008 + 0.841660i \(0.681579\pi\)
\(594\) −2.35686e7 4.43648e7i −0.112454 0.211680i
\(595\) −4.55461e7 4.55461e7i −0.216222 0.216222i
\(596\) −6.23812e7 + 1.20789e7i −0.294656 + 0.0570543i
\(597\) −4.43182e7 4.43182e7i −0.208285 0.208285i
\(598\) −2.27133e7 + 7.41958e7i −0.106213 + 0.346957i
\(599\) 2.40971e8 1.12120 0.560602 0.828085i \(-0.310570\pi\)
0.560602 + 0.828085i \(0.310570\pi\)
\(600\) −4.83905e7 5.98899e7i −0.224030 0.277268i
\(601\) 1.50780e8i 0.694577i −0.937758 0.347288i \(-0.887102\pi\)
0.937758 0.347288i \(-0.112898\pi\)
\(602\) 1.23804e7 4.04423e7i 0.0567475 0.185373i
\(603\) −2.95903e7 + 2.95903e7i −0.134957 + 0.134957i
\(604\) 2.76614e7 4.09459e7i 0.125535 0.185823i
\(605\) −7.63204e7 + 7.63204e7i −0.344647 + 0.344647i
\(606\) 3.93459e6 + 7.40634e6i 0.0176800 + 0.0332802i
\(607\) 1.43273e8i 0.640615i −0.947314 0.320307i \(-0.896214\pi\)
0.947314 0.320307i \(-0.103786\pi\)
\(608\) 2.33958e7 + 2.73096e8i 0.104094 + 1.21508i
\(609\) 2.99765e8 1.32718
\(610\) 1.49499e8 7.94205e7i 0.658639 0.349899i
\(611\) −9.50317e7 9.50317e7i −0.416625 0.416625i
\(612\) 4.40575e7 + 2.97635e7i 0.192205 + 0.129846i
\(613\) 1.41675e8 + 1.41675e8i 0.615052 + 0.615052i 0.944258 0.329206i \(-0.106781\pi\)
−0.329206 + 0.944258i \(0.606781\pi\)
\(614\) −1.08178e8 3.31161e7i −0.467342 0.143065i
\(615\) 5.10760e7 0.219580
\(616\) 7.66555e7 + 9.48718e7i 0.327945 + 0.405877i
\(617\) 2.02179e8i 0.860758i −0.902648 0.430379i \(-0.858380\pi\)
0.902648 0.430379i \(-0.141620\pi\)
\(618\) 6.96597e7 + 2.13246e7i 0.295132 + 0.0903474i
\(619\) −2.64754e8 + 2.64754e8i −1.11627 + 1.11627i −0.123991 + 0.992283i \(0.539569\pi\)
−0.992283 + 0.123991i \(0.960431\pi\)
\(620\) −1.50633e6 7.77939e6i −0.00632039 0.0326415i
\(621\) −1.32219e8 + 1.32219e8i −0.552101 + 0.552101i
\(622\) −4.52876e7 + 2.40589e7i −0.188195 + 0.0999779i
\(623\) 4.62250e8i 1.91167i
\(624\) 1.80628e7 + 4.48937e7i 0.0743415 + 0.184770i
\(625\) −5.91215e7 −0.242162
\(626\) −1.52079e8 2.86268e8i −0.619934 1.16694i
\(627\) −2.90158e7 2.90158e7i −0.117715 0.117715i
\(628\) −1.39274e7 7.19279e7i −0.0562331 0.290414i
\(629\) 9.39722e7 + 9.39722e7i 0.377613 + 0.377613i
\(630\) −5.51375e7 + 1.80114e8i −0.220509 + 0.720320i
\(631\) −7.09583e7 −0.282433 −0.141216 0.989979i \(-0.545101\pi\)
−0.141216 + 0.989979i \(0.545101\pi\)
\(632\) −1.48626e8 1.57841e7i −0.588768 0.0625273i
\(633\) 1.22763e7i 0.0484012i
\(634\) −4.80203e7 + 1.56865e8i −0.188433 + 0.615542i
\(635\) −5.34059e7 + 5.34059e7i −0.208578 + 0.208578i
\(636\) −6.45921e7 4.36359e7i −0.251078 0.169618i
\(637\) 1.89096e8 1.89096e8i 0.731582 0.731582i
\(638\) −4.78888e7 9.01442e7i −0.184405 0.347117i
\(639\) 1.62293e8i 0.622009i
\(640\) 1.20817e8 + 6.73702e7i 0.460882 + 0.256997i
\(641\) 4.01929e8 1.52607 0.763036 0.646355i \(-0.223708\pi\)
0.763036 + 0.646355i \(0.223708\pi\)
\(642\) 1.21088e8 6.43276e7i 0.457611 0.243104i
\(643\) 5.01109e7 + 5.01109e7i 0.188495 + 0.188495i 0.795045 0.606550i \(-0.207447\pi\)
−0.606550 + 0.795045i \(0.707447\pi\)
\(644\) 2.54137e8 3.76187e8i 0.951504 1.40847i
\(645\) 5.07791e6 + 5.07791e6i 0.0189237 + 0.0189237i
\(646\) 9.64628e7 + 2.95297e7i 0.357818 + 0.109537i
\(647\) −4.28809e7 −0.158326 −0.0791628 0.996862i \(-0.525225\pi\)
−0.0791628 + 0.996862i \(0.525225\pi\)
\(648\) 9.40690e6 8.85770e7i 0.0345718 0.325534i
\(649\) 1.03861e8i 0.379942i
\(650\) 7.63847e7 + 2.33833e7i 0.278142 + 0.0851464i
\(651\) −1.14678e7 + 1.14678e7i −0.0415659 + 0.0415659i
\(652\) 2.92074e8 5.65545e7i 1.05378 0.204044i
\(653\) −3.42700e8 + 3.42700e8i −1.23076 + 1.23076i −0.267091 + 0.963671i \(0.586062\pi\)
−0.963671 + 0.267091i \(0.913938\pi\)
\(654\) 5.51556e7 2.93012e7i 0.197177 0.104750i
\(655\) 2.08107e8i 0.740566i
\(656\) 2.20590e8 8.87535e7i 0.781401 0.314394i
\(657\) 2.62467e8 0.925506
\(658\) 3.68900e8 + 6.94404e8i 1.29488 + 2.43744i
\(659\) 2.86479e8 + 2.86479e8i 1.00101 + 1.00101i 0.999999 + 0.00100682i \(0.000320482\pi\)
0.00100682 + 0.999999i \(0.499680\pi\)
\(660\) −2.03317e7 + 3.93683e6i −0.0707199 + 0.0136935i
\(661\) −3.22988e8 3.22988e8i −1.11836 1.11836i −0.991982 0.126379i \(-0.959664\pi\)
−0.126379 0.991982i \(-0.540336\pi\)
\(662\) 1.20763e8 3.94487e8i 0.416255 1.35975i
\(663\) 1.78104e7 0.0611130
\(664\) −1.12243e8 + 9.06910e7i −0.383401 + 0.309785i
\(665\) 3.57398e8i 1.21531i
\(666\) 1.13761e8 3.71617e8i 0.385099 1.25798i
\(667\) −2.68654e8 + 2.68654e8i −0.905348 + 0.905348i
\(668\) −1.13835e8 + 1.68504e8i −0.381896 + 0.565302i
\(669\) −3.87061e7 + 3.87061e7i −0.129271 + 0.129271i
\(670\) 1.87996e7 + 3.53877e7i 0.0625064 + 0.117660i
\(671\) 1.17981e8i 0.390522i
\(672\) −2.41663e7 2.82091e8i −0.0796348 0.929569i
\(673\) −5.37871e8 −1.76455 −0.882273 0.470738i \(-0.843988\pi\)
−0.882273 + 0.470738i \(0.843988\pi\)
\(674\) 2.29049e8 1.21681e8i 0.748080 0.397415i
\(675\) 1.36120e8 + 1.36120e8i 0.442598 + 0.442598i
\(676\) 2.14376e8 + 1.44824e8i 0.693961 + 0.468813i
\(677\) −4.29706e8 4.29706e8i −1.38486 1.38486i −0.835756 0.549101i \(-0.814970\pi\)
−0.549101 0.835756i \(-0.685030\pi\)
\(678\) −2.27251e8 6.95674e7i −0.729150 0.223212i
\(679\) −1.53755e8 −0.491157
\(680\) 3.96015e7 3.19976e7i 0.125946 0.101763i
\(681\) 1.72596e8i 0.546500i
\(682\) 5.28058e6 + 1.61652e6i 0.0166467 + 0.00509598i
\(683\) 1.13185e8 1.13185e8i 0.355244 0.355244i −0.506813 0.862056i \(-0.669176\pi\)
0.862056 + 0.506813i \(0.169176\pi\)
\(684\) −5.60822e7 2.89635e8i −0.175250 0.905072i
\(685\) 7.74745e7 7.74745e7i 0.241039 0.241039i
\(686\) −8.43337e8 + 4.48020e8i −2.61234 + 1.38779i
\(687\) 1.89630e8i 0.584841i
\(688\) 3.07545e7 + 1.31070e7i 0.0944373 + 0.0402474i
\(689\) 8.08732e7 0.247256
\(690\) 3.61633e7 + 6.80726e7i 0.110083 + 0.207217i
\(691\) 1.55965e8 + 1.55965e8i 0.472707 + 0.472707i 0.902789 0.430083i \(-0.141516\pi\)
−0.430083 + 0.902789i \(0.641516\pi\)
\(692\) −4.58239e7 2.36657e8i −0.138285 0.714168i
\(693\) −9.28279e7 9.28279e7i −0.278920 0.278920i
\(694\) −4.46619e7 + 1.45894e8i −0.133616 + 0.436474i
\(695\) −1.66354e8 −0.495541
\(696\) −2.50227e7 + 2.35618e8i −0.0742175 + 0.698844i
\(697\) 8.75133e7i 0.258450i
\(698\) −1.14183e8 + 3.72995e8i −0.335766 + 1.09682i
\(699\) 2.26572e7 2.26572e7i 0.0663398 0.0663398i
\(700\) −3.87285e8 2.61635e8i −1.12911 0.762783i
\(701\) −2.01715e8 + 2.01715e8i −0.585577 + 0.585577i −0.936430 0.350853i \(-0.885892\pi\)
0.350853 + 0.936430i \(0.385892\pi\)
\(702\) −5.67605e7 1.06844e8i −0.164072 0.308844i
\(703\) 7.37396e8i 2.12244i
\(704\) −8.09687e7 + 5.23325e7i −0.232059 + 0.149987i
\(705\) −1.33508e8 −0.381013
\(706\) −3.51999e8 + 1.86998e8i −1.00029 + 0.531402i
\(707\) 3.59972e7 + 3.59972e7i 0.101862 + 0.101862i
\(708\) 1.34959e8 1.99773e8i 0.380278 0.562908i
\(709\) −1.65167e8 1.65167e8i −0.463430 0.463430i 0.436348 0.899778i \(-0.356272\pi\)
−0.899778 + 0.436348i \(0.856272\pi\)
\(710\) 1.48600e8 + 4.54903e7i 0.415187 + 0.127099i
\(711\) 1.60868e8 0.447571
\(712\) 3.63332e8 + 3.85859e7i 1.00661 + 0.106903i
\(713\) 2.05552e7i 0.0567091i
\(714\) −9.96399e7 3.05023e7i −0.273740 0.0837989i
\(715\) 1.51928e7 1.51928e7i 0.0415643 0.0415643i
\(716\) 4.61314e8 8.93244e7i 1.25677 0.243350i
\(717\) −4.60442e7 + 4.60442e7i −0.124916 + 0.124916i
\(718\) 3.65318e8 1.94074e8i 0.986957 0.524317i
\(719\) 7.08800e8i 1.90694i 0.301488 + 0.953470i \(0.402517\pi\)
−0.301488 + 0.953470i \(0.597483\pi\)
\(720\) −1.36968e8 5.83733e7i −0.366963 0.156393i
\(721\) 4.42213e8 1.17985
\(722\) −8.60368e7 1.61953e8i −0.228598 0.430306i
\(723\) −1.34360e8 1.34360e8i −0.355512 0.355512i
\(724\) −3.98399e8 + 7.71421e7i −1.04979 + 0.203271i
\(725\) 2.76579e8 + 2.76579e8i 0.725781 + 0.725781i
\(726\) −5.11119e7 + 1.66964e8i −0.133571 + 0.436328i
\(727\) 5.12736e8 1.33441 0.667207 0.744872i \(-0.267490\pi\)
0.667207 + 0.744872i \(0.267490\pi\)
\(728\) 1.84610e8 + 2.28480e8i 0.478477 + 0.592181i
\(729\) 7.01628e7i 0.181102i
\(730\) 7.35689e7 2.40322e8i 0.189115 0.617769i
\(731\) 8.70046e6 8.70046e6i 0.0222736 0.0222736i
\(732\) 1.53308e8 2.26934e8i 0.390868 0.578584i
\(733\) −1.48045e8 + 1.48045e8i −0.375909 + 0.375909i −0.869624 0.493715i \(-0.835639\pi\)
0.493715 + 0.869624i \(0.335639\pi\)
\(734\) 2.31670e8 + 4.36087e8i 0.585843 + 1.10277i
\(735\) 2.65656e8i 0.669048i
\(736\) 2.74472e8 + 2.31156e8i 0.688438 + 0.579791i
\(737\) −2.79273e7 −0.0697633
\(738\) −2.26009e8 + 1.20066e8i −0.562284 + 0.298711i
\(739\) 1.05650e8 + 1.05650e8i 0.261779 + 0.261779i 0.825776 0.563998i \(-0.190737\pi\)
−0.563998 + 0.825776i \(0.690737\pi\)
\(740\) −3.08376e8 2.08326e8i −0.761000 0.514102i
\(741\) −6.98788e7 6.98788e7i −0.171748 0.171748i
\(742\) −4.52443e8 1.38504e8i −1.10752 0.339041i
\(743\) 5.34342e8 1.30273 0.651363 0.758767i \(-0.274198\pi\)
0.651363 + 0.758767i \(0.274198\pi\)
\(744\) −8.05650e6 9.97103e6i −0.0195627 0.0242115i
\(745\) 6.54873e7i 0.158375i
\(746\) 2.42372e8 + 7.41962e7i 0.583802 + 0.178717i
\(747\) 1.09825e8 1.09825e8i 0.263474 0.263474i
\(748\) 6.74535e6 + 3.48362e7i 0.0161176 + 0.0832388i
\(749\) 5.88527e8 5.88527e8i 1.40062 1.40062i
\(750\) 1.67208e8 8.88284e7i 0.396344 0.210556i
\(751\) 1.43733e8i 0.339342i 0.985501 + 0.169671i \(0.0542705\pi\)
−0.985501 + 0.169671i \(0.945729\pi\)
\(752\) −5.76601e8 + 2.31993e8i −1.35588 + 0.545533i
\(753\) −2.49469e7 −0.0584293
\(754\) −1.15331e8 2.17095e8i −0.269049 0.506449i
\(755\) 3.60117e7 + 3.60117e7i 0.0836764 + 0.0836764i
\(756\) 1.34562e8 + 6.94944e8i 0.311428 + 1.60836i
\(757\) 2.49169e8 + 2.49169e8i 0.574390 + 0.574390i 0.933352 0.358962i \(-0.116869\pi\)
−0.358962 + 0.933352i \(0.616869\pi\)
\(758\) 6.28307e7 2.05245e8i 0.144266 0.471264i
\(759\) −5.37216e7 −0.122864
\(760\) −2.80918e8 2.98336e7i −0.639939 0.0679617i
\(761\) 6.34316e8i 1.43930i −0.694336 0.719651i \(-0.744302\pi\)
0.694336 0.719651i \(-0.255698\pi\)
\(762\) −3.57661e7 + 1.16835e8i −0.0808363 + 0.264062i
\(763\) 2.68074e8 2.68074e8i 0.603505 0.603505i
\(764\) 3.54620e8 + 2.39567e8i 0.795212 + 0.537214i
\(765\) −3.87484e7 + 3.87484e7i −0.0865504 + 0.0865504i
\(766\) −6.56833e7 1.23640e8i −0.146140 0.275089i
\(767\) 2.50128e8i 0.554340i
\(768\) 2.23743e8 + 4.55243e6i 0.493931 + 0.0100499i
\(769\) −1.21386e8 −0.266925 −0.133463 0.991054i \(-0.542610\pi\)
−0.133463 + 0.991054i \(0.542610\pi\)
\(770\) −1.11015e8 + 5.89764e7i −0.243170 + 0.129183i
\(771\) −4.33216e7 4.33216e7i −0.0945239 0.0945239i
\(772\) −1.56548e8 + 2.31731e8i −0.340248 + 0.503653i
\(773\) −4.26822e7 4.26822e7i −0.0924077 0.0924077i 0.659392 0.751799i \(-0.270814\pi\)
−0.751799 + 0.659392i \(0.770814\pi\)
\(774\) −3.44063e7 1.05327e7i −0.0742019 0.0227151i
\(775\) −2.11616e7 −0.0454614
\(776\) 1.28346e7 1.20853e8i 0.0274661 0.258625i
\(777\) 7.61683e8i 1.62372i
\(778\) 4.42964e8 + 1.35603e8i 0.940653 + 0.287958i
\(779\) −3.43357e8 + 3.43357e8i −0.726329 + 0.726329i
\(780\) −4.89649e7 + 9.48110e6i −0.103181 + 0.0199790i
\(781\) −7.65861e7 + 7.65861e7i −0.160767 + 0.160767i
\(782\) 1.16635e8 6.19620e7i 0.243899 0.129570i
\(783\) 5.92391e8i 1.23402i
\(784\) −4.61623e8 1.14733e9i −0.957943 2.38089i
\(785\) 7.55093e7 0.156096
\(786\) −1.57950e8 2.97320e8i −0.325276 0.612290i
\(787\) −5.60115e8 5.60115e8i −1.14909 1.14909i −0.986732 0.162355i \(-0.948091\pi\)
−0.162355 0.986732i \(-0.551909\pi\)
\(788\) −6.10698e8 + 1.18250e8i −1.24810 + 0.241669i
\(789\) 1.51486e8 + 1.51486e8i 0.308420 + 0.308420i
\(790\) 4.50910e7 1.47296e8i 0.0914552 0.298751i
\(791\) −1.44263e9 −2.91492
\(792\) 8.07122e7 6.52147e7i 0.162466 0.131271i
\(793\) 2.84135e8i 0.569778i
\(794\) −6.03911e7 + 1.97275e8i −0.120646 + 0.394104i
\(795\) 5.68084e7 5.68084e7i 0.113061 0.113061i
\(796\) 1.68339e8 2.49184e8i 0.333768 0.494061i
\(797\) 2.63384e8 2.63384e8i 0.520253 0.520253i −0.397395 0.917648i \(-0.630086\pi\)
0.917648 + 0.397395i \(0.130086\pi\)
\(798\) 2.71260e8 + 5.10610e8i 0.533798 + 1.00480i
\(799\) 2.28751e8i 0.448460i
\(800\) 2.37975e8 2.82569e8i 0.464795 0.551893i
\(801\) −3.93259e8 −0.765211
\(802\) −2.14113e8 + 1.13747e8i −0.415068 + 0.220503i
\(803\) 1.23859e8 + 1.23859e8i 0.239210 + 0.239210i
\(804\) 5.37175e7 + 3.62894e7i 0.103359 + 0.0698251i
\(805\) 3.30855e8 + 3.30855e8i 0.634235 + 0.634235i
\(806\) 1.27172e7 + 3.89307e6i 0.0242878 + 0.00743511i
\(807\) −1.90279e8 −0.362052
\(808\) −3.12989e7 + 2.52892e7i −0.0593328 + 0.0479404i
\(809\) 2.56780e7i 0.0484970i 0.999706 + 0.0242485i \(0.00771929\pi\)
−0.999706 + 0.0242485i \(0.992281\pi\)
\(810\) 8.77840e7 + 2.68730e7i 0.165181 + 0.0505662i
\(811\) 5.67098e8 5.67098e8i 1.06315 1.06315i 0.0652852 0.997867i \(-0.479204\pi\)
0.997867 0.0652852i \(-0.0207957\pi\)
\(812\) 2.73415e8 + 1.41205e9i 0.510687 + 2.63743i
\(813\) 6.25755e7 6.25755e7i 0.116448 0.116448i
\(814\) 2.29050e8 1.21682e8i 0.424676 0.225607i
\(815\) 3.06617e8i 0.566401i
\(816\) 3.22924e7 7.57715e7i 0.0594334 0.139455i
\(817\) −6.82722e7 −0.125192
\(818\) −1.10311e8 2.07646e8i −0.201539 0.379370i
\(819\) −2.23558e8 2.23558e8i −0.406948 0.406948i
\(820\) 4.65864e7 + 2.40594e8i 0.0844923 + 0.436359i
\(821\) 5.18326e8 + 5.18326e8i 0.936642 + 0.936642i 0.998109 0.0614672i \(-0.0195779\pi\)
−0.0614672 + 0.998109i \(0.519578\pi\)
\(822\) 5.18849e7 1.69489e8i 0.0934169 0.305159i
\(823\) −3.68387e8 −0.660852 −0.330426 0.943832i \(-0.607192\pi\)
−0.330426 + 0.943832i \(0.607192\pi\)
\(824\) −3.69134e7 + 3.47583e8i −0.0659785 + 0.621264i
\(825\) 5.53065e7i 0.0984950i
\(826\) 4.28372e8 1.39933e9i 0.760118 2.48303i
\(827\) −7.47044e8 + 7.47044e8i −1.32078 + 1.32078i −0.407632 + 0.913146i \(0.633645\pi\)
−0.913146 + 0.407632i \(0.866355\pi\)
\(828\) −3.20042e8 2.16207e8i −0.563787 0.380872i
\(829\) −2.21415e8 + 2.21415e8i −0.388636 + 0.388636i −0.874201 0.485565i \(-0.838614\pi\)
0.485565 + 0.874201i \(0.338614\pi\)
\(830\) −6.97749e7 1.31342e8i −0.122030 0.229704i
\(831\) 9.76793e6i 0.0170216i
\(832\) −1.94997e8 + 1.26033e8i −0.338578 + 0.218833i
\(833\) −4.55173e8 −0.787484
\(834\) −2.37668e8 + 1.26260e8i −0.409707 + 0.217655i
\(835\) −1.48198e8 1.48198e8i −0.254556 0.254556i
\(836\) 1.10214e8 1.63144e8i 0.188633 0.279224i
\(837\) 2.26625e7 + 2.26625e7i 0.0386483 + 0.0386483i
\(838\) 7.32530e8 + 2.24246e8i 1.24478 + 0.381060i
\(839\) 7.96655e8 1.34891 0.674457 0.738314i \(-0.264378\pi\)
0.674457 + 0.738314i \(0.264378\pi\)
\(840\) 2.90170e8 + 3.08162e7i 0.489570 + 0.0519925i
\(841\) 6.08848e8i 1.02358i
\(842\) −5.65350e7 1.73068e7i −0.0947068 0.0289922i
\(843\) 8.23375e6 8.23375e6i 0.0137441 0.0137441i
\(844\) −5.78276e7 + 1.11972e7i −0.0961851 + 0.0186244i
\(845\) −1.88542e8 + 1.88542e8i −0.312492 + 0.312492i
\(846\) 5.90765e8 3.13841e8i 0.975671 0.518322i
\(847\) 1.05992e9i 1.74430i
\(848\) 1.46633e8 3.44062e8i 0.240460 0.564221i
\(849\) −3.36286e8 −0.549522
\(850\) −6.37900e7 1.20076e8i −0.103871 0.195524i
\(851\) −6.82631e8 6.82631e8i −1.10764 1.10764i
\(852\) 2.46829e8 4.77936e7i 0.399096 0.0772772i
\(853\) 8.87177e6 + 8.87177e6i 0.0142943 + 0.0142943i 0.714218 0.699924i \(-0.246783\pi\)
−0.699924 + 0.714218i \(0.746783\pi\)
\(854\) 4.86613e8 1.58959e9i 0.781286 2.55217i
\(855\) 3.04057e8 0.486470
\(856\) 4.13460e8 + 5.11713e8i 0.659192 + 0.815841i
\(857\) 9.23287e6i 0.0146688i 0.999973 + 0.00733439i \(0.00233463\pi\)
−0.999973 + 0.00733439i \(0.997665\pi\)
\(858\) 1.01747e7 3.32369e7i 0.0161086 0.0526210i
\(859\) 2.99359e8 2.99359e8i 0.472294 0.472294i −0.430362 0.902656i \(-0.641614\pi\)
0.902656 + 0.430362i \(0.141614\pi\)
\(860\) −1.92880e7 + 2.85511e7i −0.0303244 + 0.0448877i
\(861\) 3.54666e8 3.54666e8i 0.555661 0.555661i
\(862\) 4.63162e8 + 8.71842e8i 0.723122 + 1.36118i
\(863\) 1.67298e8i 0.260290i −0.991495 0.130145i \(-0.958456\pi\)
0.991495 0.130145i \(-0.0415443\pi\)
\(864\) −5.57464e8 + 4.77571e7i −0.864322 + 0.0740452i
\(865\) 2.48440e8 0.383861
\(866\) −8.46489e8 + 4.49694e8i −1.30337 + 0.692410i
\(867\) 2.06230e8 + 2.06230e8i 0.316443 + 0.316443i
\(868\) −6.44789e7 4.35594e7i −0.0985958 0.0666074i
\(869\) 7.59139e7 + 7.59139e7i 0.115681 + 0.115681i
\(870\) −2.33508e8 7.14830e7i −0.354605 0.108554i
\(871\) −6.72575e7 −0.101786
\(872\) 1.88331e8 + 2.33085e8i 0.284035 + 0.351533i
\(873\) 1.30807e8i 0.196602i
\(874\) −7.00723e8 2.14509e8i −1.04957 0.321301i
\(875\) 8.12683e8 8.12683e8i 1.21310 1.21310i
\(876\) −7.72940e7 3.99183e8i −0.114983 0.593827i
\(877\) −8.11413e7 + 8.11413e7i −0.120294 + 0.120294i −0.764691 0.644397i \(-0.777108\pi\)
0.644397 + 0.764691i \(0.277108\pi\)
\(878\) −6.40893e8 + 3.40472e8i −0.946895 + 0.503034i
\(879\) 2.20864e8i 0.325206i
\(880\) −3.70890e7 9.21819e7i −0.0544248 0.135269i
\(881\) −4.06058e7 −0.0593827 −0.0296914 0.999559i \(-0.509452\pi\)
−0.0296914 + 0.999559i \(0.509452\pi\)
\(882\) 6.24487e8 + 1.17551e9i 0.910159 + 1.71325i
\(883\) 7.93005e7 + 7.93005e7i 0.115184 + 0.115184i 0.762350 0.647165i \(-0.224046\pi\)
−0.647165 + 0.762350i \(0.724046\pi\)
\(884\) 1.62449e7 + 8.38962e7i 0.0235158 + 0.121447i
\(885\) 1.75700e8 + 1.75700e8i 0.253478 + 0.253478i
\(886\) −3.78753e8 + 1.23725e9i −0.544571 + 1.77891i
\(887\) 4.93378e8 0.706983 0.353491 0.935438i \(-0.384994\pi\)
0.353491 + 0.935438i \(0.384994\pi\)
\(888\) −5.98689e8 6.35809e7i −0.854992 0.0908004i
\(889\) 7.41688e8i 1.05564i
\(890\) −1.10229e8 + 3.60079e8i −0.156361 + 0.510773i
\(891\) −4.52425e7 + 4.52425e7i −0.0639608 + 0.0639608i
\(892\) −2.17629e8 1.47022e8i −0.306636 0.207151i
\(893\) 8.97502e8 8.97502e8i 1.26032 1.26032i
\(894\) −4.97038e7 9.35608e7i −0.0695628 0.130943i
\(895\) 4.84284e8i 0.675508i
\(896\) 1.30675e9 3.71131e8i 1.81664 0.515944i
\(897\) −1.29378e8 −0.179260
\(898\) 2.30014e8 1.22194e8i 0.317633 0.168741i
\(899\) 4.60475e7 + 4.60475e7i 0.0633763 + 0.0633763i
\(900\) −2.22586e8 + 3.29483e8i −0.305330 + 0.451966i
\(901\) −9.73352e7 9.73352e7i −0.133075 0.133075i
\(902\) −1.63313e8 4.99943e7i −0.222536 0.0681242i
\(903\) 7.05208e7 0.0957754
\(904\) 1.20423e8 1.13392e9i 0.163006 1.53489i
\(905\) 4.18236e8i 0.564255i
\(906\) 7.87817e7 + 2.41171e7i 0.105935 + 0.0324296i
\(907\) 6.47306e7 6.47306e7i 0.0867536 0.0867536i −0.662398 0.749152i \(-0.730461\pi\)
0.749152 + 0.662398i \(0.230461\pi\)
\(908\) 8.13017e8 1.57425e8i 1.08603 0.210288i
\(909\) 3.06246e7 3.06246e7i 0.0407736 0.0407736i
\(910\) −2.67359e8 + 1.42033e8i −0.354789 + 0.188480i
\(911\) 1.45778e8i 0.192813i −0.995342 0.0964065i \(-0.969265\pi\)
0.995342 0.0964065i \(-0.0307349\pi\)
\(912\) −4.23987e8 + 1.70589e8i −0.558943 + 0.224889i
\(913\) 1.03653e8 0.136197
\(914\) −4.75288e8 8.94666e8i −0.622469 1.17172i
\(915\) 1.99587e8 + 1.99587e8i 0.260537 + 0.260537i
\(916\) −8.93256e8 + 1.72962e8i −1.16222 + 0.225042i
\(917\) −1.44507e9 1.44507e9i −1.87405 1.87405i
\(918\) −6.02782e7 + 1.96907e8i −0.0779170 + 0.254526i
\(919\) −7.81393e8 −1.00675 −0.503376 0.864067i \(-0.667909\pi\)
−0.503376 + 0.864067i \(0.667909\pi\)
\(920\) −2.87672e8 + 2.32437e8i −0.369432 + 0.298498i
\(921\) 1.88634e8i 0.241458i
\(922\) −2.84196e8 + 9.28363e8i −0.362598 + 1.18447i
\(923\) −1.84443e8 + 1.84443e8i −0.234561 + 0.234561i
\(924\) −1.13844e8 + 1.68518e8i −0.144309 + 0.213614i
\(925\) −7.02769e8 + 7.02769e8i −0.887948 + 0.887948i
\(926\) −1.98348e8 3.73364e8i −0.249801 0.470218i
\(927\) 3.76213e8i 0.472274i
\(928\) −1.13270e9 + 9.70369e7i −1.41733 + 0.121421i
\(929\) 2.80896e8 0.350347 0.175173 0.984538i \(-0.443951\pi\)
0.175173 + 0.984538i \(0.443951\pi\)
\(930\) 1.16677e7 6.19843e6i 0.0145056 0.00770607i
\(931\) 1.78586e9 + 1.78586e9i 2.21309 + 2.21309i
\(932\) 1.27392e8 + 8.60613e7i 0.157361 + 0.106307i
\(933\) −6.04610e7 6.04610e7i −0.0744442 0.0744442i
\(934\) −1.09500e9 3.35206e8i −1.34391 0.411407i
\(935\) −3.65708e7 −0.0447403
\(936\) 1.94380e8 1.57057e8i 0.237041 0.191527i
\(937\) 5.11375e8i 0.621614i −0.950473 0.310807i \(-0.899401\pi\)
0.950473 0.310807i \(-0.100599\pi\)
\(938\) 3.76270e8 + 1.15186e8i 0.455923 + 0.139570i
\(939\) 3.82181e8 3.82181e8i 0.461607 0.461607i
\(940\) −1.21772e8 6.28890e8i −0.146610 0.757166i
\(941\) −1.83103e7 + 1.83103e7i −0.0219749 + 0.0219749i −0.718009 0.696034i \(-0.754946\pi\)
0.696034 + 0.718009i \(0.254946\pi\)
\(942\) 1.07879e8 5.73104e7i 0.129058 0.0685615i
\(943\) 6.35713e8i 0.758099i
\(944\) 1.06413e9 + 4.53512e8i 1.26496 + 0.539104i
\(945\) −7.29547e8 −0.864486
\(946\) −1.12660e7 2.12067e7i −0.0133075 0.0250496i
\(947\) −3.21710e8 3.21710e8i −0.378804 0.378804i 0.491867 0.870671i \(-0.336315\pi\)
−0.870671 + 0.491867i \(0.836315\pi\)
\(948\) −4.73741e7 2.44663e8i −0.0556053 0.287172i
\(949\) 2.98289e8 + 2.98289e8i 0.349011 + 0.349011i
\(950\) −2.20838e8 + 7.21395e8i −0.257574 + 0.841400i
\(951\) −2.73531e8 −0.318028
\(952\) 5.28002e7 4.97176e8i 0.0611963 0.576234i
\(953\) 3.71293e7i 0.0428981i −0.999770 0.0214491i \(-0.993172\pi\)
0.999770 0.0214491i \(-0.00682797\pi\)
\(954\) −1.17833e8 + 3.84916e8i −0.135713 + 0.443323i
\(955\) −3.11886e8 + 3.11886e8i −0.358085 + 0.358085i
\(956\) −2.58889e8 1.74895e8i −0.296305 0.200172i
\(957\) 1.20347e8 1.20347e8i 0.137309 0.137309i
\(958\) −6.38714e7 1.20229e8i −0.0726457 0.136746i
\(959\) 1.07595e9i 1.21993i
\(960\) −4.84435e7 + 2.25504e8i −0.0547547 + 0.254882i
\(961\) 8.83981e8 0.996030
\(962\) 5.51623e8 2.93048e8i 0.619608 0.329164i
\(963\) −5.00690e8 5.00690e8i −0.560647 0.560647i
\(964\) 5.10353e8 7.55451e8i 0.569691 0.843287i
\(965\) −2.03806e8 2.03806e8i −0.226796 0.226796i
\(966\) 7.23802e8 + 2.21574e8i 0.802950 + 0.245804i
\(967\) 1.34053e9 1.48251 0.741255 0.671224i \(-0.234231\pi\)
0.741255 + 0.671224i \(0.234231\pi\)
\(968\) −8.33104e8 8.84759e7i −0.918487 0.0975436i
\(969\) 1.68206e8i 0.184871i
\(970\) 1.19771e8 + 3.66649e7i 0.131231 + 0.0401731i
\(971\) −8.32694e8 + 8.32694e8i −0.909553 + 0.909553i −0.996236 0.0866830i \(-0.972373\pi\)
0.0866830 + 0.996236i \(0.472373\pi\)
\(972\) 9.27925e8 1.79675e8i 1.01045 0.195654i
\(973\) −1.15514e9 + 1.15514e9i −1.25400 + 1.25400i
\(974\) −3.21310e8 + 1.70695e8i −0.347734 + 0.184732i
\(975\) 1.33195e8i 0.143706i
\(976\) 1.20881e9 + 5.15171e8i 1.30019 + 0.554118i
\(977\) 3.01728e8 0.323543 0.161771 0.986828i \(-0.448279\pi\)
0.161771 + 0.986828i \(0.448279\pi\)
\(978\) 2.32718e8 + 4.38060e8i 0.248778 + 0.468292i
\(979\) −1.85579e8 1.85579e8i −0.197780 0.197780i
\(980\) 1.25137e9 2.42304e8i 1.32956 0.257444i
\(981\) −2.28064e8 2.28064e8i −0.241574 0.241574i
\(982\) 2.25113e8 7.35363e8i 0.237721 0.776546i
\(983\) 5.16672e8 0.543944 0.271972 0.962305i \(-0.412324\pi\)
0.271972 + 0.962305i \(0.412324\pi\)
\(984\) 2.49164e8 + 3.08375e8i 0.261518 + 0.323664i
\(985\) 6.41106e8i 0.670844i
\(986\) −1.22478e8 + 4.00092e8i −0.127770 + 0.417377i
\(987\) −9.27062e8 + 9.27062e8i −0.964178 + 0.964178i
\(988\) 2.65429e8 3.92901e8i 0.275218 0.407392i
\(989\) −6.32017e7 + 6.32017e7i −0.0653341 + 0.0653341i
\(990\) 5.01742e7 + 9.44463e7i 0.0517101 + 0.0973373i
\(991\) 1.63508e9i 1.68003i −0.542561 0.840016i \(-0.682545\pi\)
0.542561 0.840016i \(-0.317455\pi\)
\(992\) 3.96203e7 4.70448e7i 0.0405866 0.0481922i
\(993\) 6.87883e8 0.702533
\(994\) 1.34774e9 7.15981e8i 1.37229 0.729025i
\(995\) 2.19156e8 + 2.19156e8i 0.222476 + 0.222476i
\(996\) −1.99373e8 1.34689e8i −0.201785 0.136318i
\(997\) 1.09613e9 + 1.09613e9i 1.10606 + 1.10606i 0.993664 + 0.112396i \(0.0358524\pi\)
0.112396 + 0.993664i \(0.464148\pi\)
\(998\) 7.97758e8 + 2.44214e8i 0.802564 + 0.245686i
\(999\) 1.50523e9 1.50975
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 16.7.f.a.11.2 yes 22
4.3 odd 2 64.7.f.a.15.8 22
8.3 odd 2 128.7.f.a.31.4 22
8.5 even 2 128.7.f.b.31.8 22
16.3 odd 4 inner 16.7.f.a.3.2 22
16.5 even 4 128.7.f.a.95.4 22
16.11 odd 4 128.7.f.b.95.8 22
16.13 even 4 64.7.f.a.47.8 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
16.7.f.a.3.2 22 16.3 odd 4 inner
16.7.f.a.11.2 yes 22 1.1 even 1 trivial
64.7.f.a.15.8 22 4.3 odd 2
64.7.f.a.47.8 22 16.13 even 4
128.7.f.a.31.4 22 8.3 odd 2
128.7.f.a.95.4 22 16.5 even 4
128.7.f.b.31.8 22 8.5 even 2
128.7.f.b.95.8 22 16.11 odd 4