Properties

Label 22.8.c.a.5.1
Level $22$
Weight $8$
Character 22.5
Analytic conductor $6.872$
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] = [22,8,Mod(3,22)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(22, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("22.3");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 22.c (of order \(5\), degree \(4\), 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: \(6.87247056065\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(3\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2 x^{11} + 718 x^{10} - 5886 x^{9} + 371698 x^{8} + 6317266 x^{7} + 171079947 x^{6} + 3212289784 x^{5} + 91377152203 x^{4} + \cdots + 475277889155161 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4}\cdot 11^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 5.1
Root \(-8.68746 + 26.7373i\) of defining polynomial
Character \(\chi\) \(=\) 22.5
Dual form 22.8.c.a.9.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.47214 + 7.60845i) q^{2} +(-26.1922 - 19.0297i) q^{3} +(-51.7771 + 37.6183i) q^{4} +(40.3475 - 124.177i) q^{5} +(80.0362 - 246.326i) q^{6} +(972.268 - 706.394i) q^{7} +(-414.217 - 300.946i) q^{8} +(-351.920 - 1083.10i) q^{9} +O(q^{10})\) \(q+(2.47214 + 7.60845i) q^{2} +(-26.1922 - 19.0297i) q^{3} +(-51.7771 + 37.6183i) q^{4} +(40.3475 - 124.177i) q^{5} +(80.0362 - 246.326i) q^{6} +(972.268 - 706.394i) q^{7} +(-414.217 - 300.946i) q^{8} +(-351.920 - 1083.10i) q^{9} +1044.54 q^{10} +(4274.89 - 1101.11i) q^{11} +2072.02 q^{12} +(-427.622 - 1316.08i) q^{13} +(7778.15 + 5651.15i) q^{14} +(-3419.84 + 2484.66i) q^{15} +(1265.73 - 3895.53i) q^{16} +(4175.04 - 12849.4i) q^{17} +(7370.71 - 5355.13i) q^{18} +(-23358.1 - 16970.6i) q^{19} +(2582.24 + 7947.31i) q^{20} -38908.4 q^{21} +(18945.9 + 29803.2i) q^{22} -73858.7 q^{23} +(5122.32 + 15764.9i) q^{24} +(49412.5 + 35900.3i) q^{25} +(8956.22 - 6507.08i) q^{26} +(-33273.4 + 102405. i) q^{27} +(-23767.9 + 73150.1i) q^{28} +(8105.27 - 5888.82i) q^{29} +(-27358.7 - 19877.3i) q^{30} +(-9452.74 - 29092.5i) q^{31} +32768.0 q^{32} +(-132923. - 52509.7i) q^{33} +108086. q^{34} +(-48489.2 - 149234. i) q^{35} +(58965.7 + 42841.1i) q^{36} +(429947. - 312375. i) q^{37} +(71375.9 - 219672. i) q^{38} +(-13844.4 + 42608.7i) q^{39} +(-54083.1 + 39293.7i) q^{40} +(201430. + 146347. i) q^{41} +(-96186.7 - 296032. i) q^{42} -118661. q^{43} +(-179920. + 217826. i) q^{44} -148695. q^{45} +(-182589. - 561950. i) q^{46} +(977962. + 710531. i) q^{47} +(-107283. + 77945.8i) q^{48} +(191824. - 590374. i) q^{49} +(-150991. + 464703. i) q^{50} +(-353875. + 257105. i) q^{51} +(71649.8 + 52056.6i) q^{52} +(240735. + 740907. i) q^{53} -861401. q^{54} +(35748.9 - 575270. i) q^{55} -615316. q^{56} +(288852. + 888996. i) q^{57} +(64842.1 + 47110.6i) q^{58} +(-1.11318e6 + 808770. i) q^{59} +(83600.8 - 257297. i) q^{60} +(-189639. + 583649. i) q^{61} +(197981. - 143841. i) q^{62} +(-1.10726e6 - 804468. i) q^{63} +(81007.0 + 249314. i) q^{64} -180680. q^{65} +(70914.1 - 1.14115e6i) q^{66} -2.89521e6 q^{67} +(267202. + 822364. i) q^{68} +(1.93452e6 + 1.40551e6i) q^{69} +(1.01557e6 - 737855. i) q^{70} +(1.13294e6 - 3.48683e6i) q^{71} +(-180183. + 554546. i) q^{72} +(576001. - 418489. i) q^{73} +(3.43957e6 + 2.49900e6i) q^{74} +(-611049. - 1.88062e6i) q^{75} +1.84782e6 q^{76} +(3.37853e6 - 4.09034e6i) q^{77} -358411. q^{78} +(-342404. - 1.05381e6i) q^{79} +(-432665. - 314349. i) q^{80} +(805281. - 585071. i) q^{81} +(-615514. + 1.89436e6i) q^{82} +(-2.47574e6 + 7.61953e6i) q^{83} +(2.01456e6 - 1.46366e6i) q^{84} +(-1.42715e6 - 1.03688e6i) q^{85} +(-293345. - 902825. i) q^{86} -324358. q^{87} +(-2.10211e6 - 830414. i) q^{88} +3.06471e6 q^{89} +(-367594. - 1.13134e6i) q^{90} +(-1.34544e6 - 977517. i) q^{91} +(3.82419e6 - 2.77844e6i) q^{92} +(-306036. + 941881. i) q^{93} +(-2.98838e6 + 9.19730e6i) q^{94} +(-3.04980e6 + 2.21581e6i) q^{95} +(-858266. - 623567. i) q^{96} +(-5.12585e6 - 1.57758e7i) q^{97} +4.96604e6 q^{98} +(-2.69703e6 - 4.24263e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 24 q^{2} + 44 q^{3} - 192 q^{4} + 220 q^{5} - 248 q^{6} + 534 q^{7} - 1536 q^{8} - 3745 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 24 q^{2} + 44 q^{3} - 192 q^{4} + 220 q^{5} - 248 q^{6} + 534 q^{7} - 1536 q^{8} - 3745 q^{9} - 6080 q^{10} - 12881 q^{11} - 1664 q^{12} - 1834 q^{13} + 4272 q^{14} - 50174 q^{15} - 12288 q^{16} + 49128 q^{17} + 28720 q^{18} - 24453 q^{19} + 14080 q^{20} + 135280 q^{21} - 10648 q^{22} + 1212 q^{23} - 15872 q^{24} + 233893 q^{25} - 2352 q^{26} + 24029 q^{27} + 25216 q^{28} + 410548 q^{29} - 401392 q^{30} - 285894 q^{31} + 393216 q^{32} - 561803 q^{33} - 416016 q^{34} + 40188 q^{35} + 229760 q^{36} - 229440 q^{37} + 559696 q^{38} + 102742 q^{39} + 81920 q^{40} - 838292 q^{41} - 547200 q^{42} - 774698 q^{43} + 30976 q^{44} - 3155228 q^{45} + 438176 q^{46} + 1107540 q^{47} + 180224 q^{48} + 4281299 q^{49} - 625416 q^{50} + 2561801 q^{51} - 18816 q^{52} - 3013626 q^{53} - 2622208 q^{54} - 4505512 q^{55} - 950272 q^{56} + 10084223 q^{57} + 3284384 q^{58} + 2583885 q^{59} + 3746304 q^{60} + 418618 q^{61} + 1193008 q^{62} + 4045264 q^{63} - 786432 q^{64} - 11397748 q^{65} + 1076416 q^{66} - 18354554 q^{67} + 3144192 q^{68} + 11135006 q^{69} + 207744 q^{70} + 22870340 q^{71} - 1917440 q^{72} - 7374584 q^{73} - 1835520 q^{74} - 19671977 q^{75} - 5825152 q^{76} - 2121482 q^{77} - 20124544 q^{78} + 4715278 q^{79} + 655360 q^{80} - 745714 q^{81} + 12958184 q^{82} - 13257515 q^{83} + 48640 q^{84} + 8622056 q^{85} - 6992984 q^{86} + 6788612 q^{87} + 613888 q^{88} - 34864794 q^{89} + 11604816 q^{90} + 31631268 q^{91} - 3544192 q^{92} + 41624776 q^{93} + 6007840 q^{94} + 2925362 q^{95} + 1441792 q^{96} - 28563397 q^{97} - 5044288 q^{98} + 28188523 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/22\mathbb{Z}\right)^\times\).

\(n\) \(13\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.47214 + 7.60845i 0.218508 + 0.672499i
\(3\) −26.1922 19.0297i −0.560077 0.406920i 0.271410 0.962464i \(-0.412510\pi\)
−0.831487 + 0.555544i \(0.812510\pi\)
\(4\) −51.7771 + 37.6183i −0.404508 + 0.293893i
\(5\) 40.3475 124.177i 0.144351 0.444268i −0.852576 0.522604i \(-0.824961\pi\)
0.996927 + 0.0783358i \(0.0249606\pi\)
\(6\) 80.0362 246.326i 0.151272 0.465566i
\(7\) 972.268 706.394i 1.07138 0.778402i 0.0952191 0.995456i \(-0.469645\pi\)
0.976160 + 0.217054i \(0.0696448\pi\)
\(8\) −414.217 300.946i −0.286031 0.207813i
\(9\) −351.920 1083.10i −0.160915 0.495244i
\(10\) 1044.54 0.330312
\(11\) 4274.89 1101.11i 0.968392 0.249435i
\(12\) 2072.02 0.346147
\(13\) −427.622 1316.08i −0.0539831 0.166143i 0.920430 0.390907i \(-0.127839\pi\)
−0.974413 + 0.224764i \(0.927839\pi\)
\(14\) 7778.15 + 5651.15i 0.757579 + 0.550413i
\(15\) −3419.84 + 2484.66i −0.261629 + 0.190085i
\(16\) 1265.73 3895.53i 0.0772542 0.237764i
\(17\) 4175.04 12849.4i 0.206105 0.634327i −0.793561 0.608491i \(-0.791775\pi\)
0.999666 0.0258359i \(-0.00822475\pi\)
\(18\) 7370.71 5355.13i 0.297890 0.216430i
\(19\) −23358.1 16970.6i −0.781267 0.567623i 0.124092 0.992271i \(-0.460398\pi\)
−0.905359 + 0.424647i \(0.860398\pi\)
\(20\) 2582.24 + 7947.31i 0.0721757 + 0.222134i
\(21\) −38908.4 −0.916802
\(22\) 18945.9 + 29803.2i 0.379346 + 0.596739i
\(23\) −73858.7 −1.26577 −0.632884 0.774246i \(-0.718129\pi\)
−0.632884 + 0.774246i \(0.718129\pi\)
\(24\) 5122.32 + 15764.9i 0.0756358 + 0.232783i
\(25\) 49412.5 + 35900.3i 0.632480 + 0.459524i
\(26\) 8956.22 6507.08i 0.0999351 0.0726071i
\(27\) −33273.4 + 102405.i −0.325330 + 1.00126i
\(28\) −23767.9 + 73150.1i −0.204615 + 0.629741i
\(29\) 8105.27 5888.82i 0.0617127 0.0448369i −0.556501 0.830847i \(-0.687857\pi\)
0.618214 + 0.786010i \(0.287857\pi\)
\(30\) −27358.7 19877.3i −0.185000 0.134410i
\(31\) −9452.74 29092.5i −0.0569891 0.175394i 0.918510 0.395398i \(-0.129393\pi\)
−0.975499 + 0.220003i \(0.929393\pi\)
\(32\) 32768.0 0.176777
\(33\) −132923. 52509.7i −0.643874 0.254355i
\(34\) 108086. 0.471619
\(35\) −48489.2 149234.i −0.191164 0.588343i
\(36\) 58965.7 + 42841.1i 0.210640 + 0.153039i
\(37\) 429947. 312375.i 1.39543 1.01384i 0.400187 0.916433i \(-0.368945\pi\)
0.995245 0.0974075i \(-0.0310550\pi\)
\(38\) 71375.9 219672.i 0.211013 0.649431i
\(39\) −13844.4 + 42608.7i −0.0373721 + 0.115020i
\(40\) −54083.1 + 39293.7i −0.133614 + 0.0970762i
\(41\) 201430. + 146347.i 0.456436 + 0.331620i 0.792132 0.610350i \(-0.208971\pi\)
−0.335695 + 0.941971i \(0.608971\pi\)
\(42\) −96186.7 296032.i −0.200328 0.616548i
\(43\) −118661. −0.227597 −0.113799 0.993504i \(-0.536302\pi\)
−0.113799 + 0.993504i \(0.536302\pi\)
\(44\) −179920. + 217826.i −0.318416 + 0.385502i
\(45\) −148695. −0.243249
\(46\) −182589. 561950.i −0.276581 0.851227i
\(47\) 977962. + 710531.i 1.37398 + 0.998252i 0.997415 + 0.0718608i \(0.0228937\pi\)
0.376562 + 0.926392i \(0.377106\pi\)
\(48\) −107283. + 77945.8i −0.140019 + 0.101730i
\(49\) 191824. 590374.i 0.232925 0.716870i
\(50\) −150991. + 464703.i −0.170827 + 0.525752i
\(51\) −353875. + 257105.i −0.373555 + 0.271403i
\(52\) 71649.8 + 52056.6i 0.0706648 + 0.0513410i
\(53\) 240735. + 740907.i 0.222113 + 0.683594i 0.998572 + 0.0534255i \(0.0170140\pi\)
−0.776459 + 0.630168i \(0.782986\pi\)
\(54\) −861401. −0.744436
\(55\) 35748.9 575270.i 0.0289730 0.466232i
\(56\) −615316. −0.468210
\(57\) 288852. + 888996.i 0.206592 + 0.635826i
\(58\) 64842.1 + 47110.6i 0.0436375 + 0.0317045i
\(59\) −1.11318e6 + 808770.i −0.705638 + 0.512676i −0.881763 0.471692i \(-0.843643\pi\)
0.176126 + 0.984368i \(0.443643\pi\)
\(60\) 83600.8 257297.i 0.0499668 0.153782i
\(61\) −189639. + 583649.i −0.106973 + 0.329229i −0.990188 0.139739i \(-0.955374\pi\)
0.883216 + 0.468967i \(0.155374\pi\)
\(62\) 197981. 143841.i 0.105500 0.0766502i
\(63\) −1.10726e6 804468.i −0.557899 0.405338i
\(64\) 81007.0 + 249314.i 0.0386271 + 0.118882i
\(65\) −180680. −0.0816046
\(66\) 70914.1 1.14115e6i 0.0303619 0.488583i
\(67\) −2.89521e6 −1.17603 −0.588015 0.808850i \(-0.700090\pi\)
−0.588015 + 0.808850i \(0.700090\pi\)
\(68\) 267202. + 822364.i 0.103053 + 0.317163i
\(69\) 1.93452e6 + 1.40551e6i 0.708928 + 0.515066i
\(70\) 1.01557e6 737855.i 0.353889 0.257115i
\(71\) 1.13294e6 3.48683e6i 0.375667 1.15618i −0.567361 0.823469i \(-0.692036\pi\)
0.943028 0.332714i \(-0.107964\pi\)
\(72\) −180183. + 554546.i −0.0568919 + 0.175095i
\(73\) 576001. 418489.i 0.173298 0.125908i −0.497755 0.867318i \(-0.665842\pi\)
0.671053 + 0.741409i \(0.265842\pi\)
\(74\) 3.43957e6 + 2.49900e6i 0.986719 + 0.716894i
\(75\) −611049. 1.88062e6i −0.167248 0.514737i
\(76\) 1.84782e6 0.482849
\(77\) 3.37853e6 4.09034e6i 0.843354 1.02104i
\(78\) −358411. −0.0855166
\(79\) −342404. 1.05381e6i −0.0781348 0.240474i 0.904358 0.426775i \(-0.140350\pi\)
−0.982493 + 0.186300i \(0.940350\pi\)
\(80\) −432665. 314349.i −0.0944793 0.0686432i
\(81\) 805281. 585071.i 0.168364 0.122324i
\(82\) −615514. + 1.89436e6i −0.123279 + 0.379414i
\(83\) −2.47574e6 + 7.61953e6i −0.475260 + 1.46270i 0.370347 + 0.928893i \(0.379239\pi\)
−0.845607 + 0.533806i \(0.820761\pi\)
\(84\) 2.01456e6 1.46366e6i 0.370854 0.269441i
\(85\) −1.42715e6 1.03688e6i −0.252060 0.183132i
\(86\) −293345. 902825.i −0.0497319 0.153059i
\(87\) −324358. −0.0528089
\(88\) −2.10211e6 830414.i −0.328826 0.129899i
\(89\) 3.06471e6 0.460813 0.230406 0.973094i \(-0.425994\pi\)
0.230406 + 0.973094i \(0.425994\pi\)
\(90\) −367594. 1.13134e6i −0.0531519 0.163585i
\(91\) −1.34544e6 977517.i −0.187162 0.135981i
\(92\) 3.82419e6 2.77844e6i 0.512014 0.372000i
\(93\) −306036. + 941881.i −0.0394532 + 0.121424i
\(94\) −2.98838e6 + 9.19730e6i −0.371098 + 1.14212i
\(95\) −3.04980e6 + 2.21581e6i −0.364954 + 0.265155i
\(96\) −858266. 623567.i −0.0990085 0.0719339i
\(97\) −5.12585e6 1.57758e7i −0.570250 1.75505i −0.651813 0.758380i \(-0.725991\pi\)
0.0815632 0.996668i \(-0.474009\pi\)
\(98\) 4.96604e6 0.532990
\(99\) −2.69703e6 4.24263e6i −0.279359 0.439453i
\(100\) −3.90894e6 −0.390894
\(101\) 3.42361e6 + 1.05368e7i 0.330643 + 1.01761i 0.968829 + 0.247731i \(0.0796850\pi\)
−0.638186 + 0.769882i \(0.720315\pi\)
\(102\) −2.83100e6 2.05684e6i −0.264143 0.191911i
\(103\) −1.62526e7 + 1.18082e7i −1.46552 + 1.06476i −0.483636 + 0.875269i \(0.660684\pi\)
−0.981882 + 0.189492i \(0.939316\pi\)
\(104\) −218942. + 673835.i −0.0190859 + 0.0587404i
\(105\) −1.56985e6 + 4.83151e6i −0.132342 + 0.407306i
\(106\) −5.04202e6 + 3.66324e6i −0.411182 + 0.298741i
\(107\) 9.70373e6 + 7.05018e6i 0.765765 + 0.556361i 0.900673 0.434497i \(-0.143074\pi\)
−0.134908 + 0.990858i \(0.543074\pi\)
\(108\) −2.12950e6 6.55393e6i −0.162665 0.500632i
\(109\) 2.11255e7 1.56248 0.781240 0.624231i \(-0.214588\pi\)
0.781240 + 0.624231i \(0.214588\pi\)
\(110\) 4.46529e6 1.15015e6i 0.319871 0.0823911i
\(111\) −1.72057e7 −1.19410
\(112\) −1.52115e6 4.68160e6i −0.102308 0.314870i
\(113\) 2.07290e7 + 1.50605e7i 1.35146 + 0.981896i 0.998937 + 0.0460940i \(0.0146774\pi\)
0.352527 + 0.935802i \(0.385323\pi\)
\(114\) −6.04980e6 + 4.39544e6i −0.382450 + 0.277866i
\(115\) −2.98001e6 + 9.17153e6i −0.182716 + 0.562341i
\(116\) −198140. + 609812.i −0.0117861 + 0.0362738i
\(117\) −1.27496e6 + 926313.i −0.0735946 + 0.0534696i
\(118\) −8.90541e6 6.47016e6i −0.498961 0.362517i
\(119\) −5.01752e6 1.54423e7i −0.272945 0.840037i
\(120\) 2.16430e6 0.114336
\(121\) 1.70623e7 9.41426e6i 0.875565 0.483101i
\(122\) −4.90948e6 −0.244780
\(123\) −2.49094e6 7.66631e6i −0.120697 0.371466i
\(124\) 1.58385e6 + 1.15073e6i 0.0745997 + 0.0541998i
\(125\) 1.47041e7 1.06831e7i 0.673368 0.489231i
\(126\) 3.38347e6 1.04133e7i 0.150683 0.463756i
\(127\) 9.62956e6 2.96367e7i 0.417151 1.28386i −0.493161 0.869938i \(-0.664159\pi\)
0.910313 0.413922i \(-0.135841\pi\)
\(128\) −1.69663e6 + 1.23268e6i −0.0715077 + 0.0519534i
\(129\) 3.10799e6 + 2.25808e6i 0.127472 + 0.0926139i
\(130\) −446667. 1.37470e6i −0.0178312 0.0548789i
\(131\) 4.26368e7 1.65705 0.828524 0.559953i \(-0.189181\pi\)
0.828524 + 0.559953i \(0.189181\pi\)
\(132\) 8.85768e6 2.28153e6i 0.335205 0.0863409i
\(133\) −3.46983e7 −1.27887
\(134\) −7.15735e6 2.20281e7i −0.256972 0.790878i
\(135\) 1.13738e7 + 8.26358e6i 0.397868 + 0.289068i
\(136\) −5.59636e6 + 4.06599e6i −0.190774 + 0.138605i
\(137\) −423305. + 1.30280e6i −0.0140647 + 0.0432868i −0.957843 0.287294i \(-0.907244\pi\)
0.943778 + 0.330580i \(0.107244\pi\)
\(138\) −5.91137e6 + 1.81933e7i −0.191475 + 0.589299i
\(139\) −4.08738e7 + 2.96965e7i −1.29090 + 0.937894i −0.999823 0.0188053i \(-0.994014\pi\)
−0.291077 + 0.956699i \(0.594014\pi\)
\(140\) 8.12456e6 + 5.90284e6i 0.250237 + 0.181808i
\(141\) −1.20937e7 3.72207e7i −0.363324 1.11820i
\(142\) 2.93302e7 0.859617
\(143\) −3.27719e6 5.15526e6i −0.0937186 0.147426i
\(144\) −4.66468e6 −0.130183
\(145\) −404228. 1.24408e6i −0.0110113 0.0338893i
\(146\) 4.60801e6 + 3.34791e6i 0.122540 + 0.0890306i
\(147\) −1.62590e7 + 1.18128e7i −0.422165 + 0.306721i
\(148\) −1.05104e7 + 3.23477e7i −0.266504 + 0.820214i
\(149\) −1.93736e7 + 5.96260e7i −0.479799 + 1.47667i 0.359575 + 0.933116i \(0.382922\pi\)
−0.839374 + 0.543554i \(0.817078\pi\)
\(150\) 1.27980e7 9.29827e6i 0.309615 0.224948i
\(151\) 3.24820e7 + 2.35996e7i 0.767757 + 0.557808i 0.901280 0.433238i \(-0.142629\pi\)
−0.133523 + 0.991046i \(0.542629\pi\)
\(152\) 4.56806e6 + 1.40590e7i 0.105506 + 0.324715i
\(153\) −1.53865e7 −0.347312
\(154\) 3.94733e7 + 1.55935e7i 0.870925 + 0.344049i
\(155\) −3.99401e6 −0.0861486
\(156\) −886041. 2.72695e6i −0.0186861 0.0575098i
\(157\) −4.20074e7 3.05201e7i −0.866317 0.629416i 0.0632794 0.997996i \(-0.479844\pi\)
−0.929596 + 0.368580i \(0.879844\pi\)
\(158\) 7.17141e6 5.21033e6i 0.144645 0.105091i
\(159\) 7.79388e6 2.39871e7i 0.153767 0.473247i
\(160\) 1.32211e6 4.06902e6i 0.0255180 0.0785363i
\(161\) −7.18105e7 + 5.21734e7i −1.35612 + 0.985277i
\(162\) 6.44225e6 + 4.68057e6i 0.119051 + 0.0864959i
\(163\) −1.78203e7 5.48452e7i −0.322298 0.991932i −0.972645 0.232295i \(-0.925377\pi\)
0.650347 0.759637i \(-0.274623\pi\)
\(164\) −1.59348e7 −0.282093
\(165\) −1.18836e7 + 1.43873e7i −0.205946 + 0.249336i
\(166\) −6.40932e7 −1.08751
\(167\) −1.27195e7 3.91467e7i −0.211331 0.650410i −0.999394 0.0348150i \(-0.988916\pi\)
0.788063 0.615595i \(-0.211084\pi\)
\(168\) 1.61165e7 + 1.17093e7i 0.262233 + 0.190524i
\(169\) 4.92154e7 3.57571e7i 0.784328 0.569847i
\(170\) 4.36098e6 1.34217e7i 0.0680790 0.209526i
\(171\) −1.01607e7 + 3.12714e7i −0.155395 + 0.478257i
\(172\) 6.14391e6 4.46381e6i 0.0920651 0.0668892i
\(173\) −1.61017e7 1.16986e7i −0.236434 0.171780i 0.463259 0.886223i \(-0.346680\pi\)
−0.699693 + 0.714443i \(0.746680\pi\)
\(174\) −801856. 2.46786e6i −0.0115392 0.0355139i
\(175\) 7.34020e7 1.03532
\(176\) 1.12147e6 1.80467e7i 0.0155058 0.249519i
\(177\) 4.45472e7 0.603829
\(178\) 7.57638e6 + 2.33177e7i 0.100691 + 0.309896i
\(179\) 5.70672e7 + 4.14617e7i 0.743705 + 0.540333i 0.893869 0.448328i \(-0.147980\pi\)
−0.150164 + 0.988661i \(0.547980\pi\)
\(180\) 7.69898e6 5.59364e6i 0.0983965 0.0714892i
\(181\) 5.84482e6 1.79885e7i 0.0732650 0.225486i −0.907718 0.419581i \(-0.862177\pi\)
0.980983 + 0.194095i \(0.0621769\pi\)
\(182\) 4.11129e6 1.26532e7i 0.0505508 0.155579i
\(183\) 1.60738e7 1.16783e7i 0.193883 0.140864i
\(184\) 3.05935e7 + 2.22275e7i 0.362049 + 0.263044i
\(185\) −2.14424e7 6.59929e7i −0.248985 0.766296i
\(186\) −7.92282e6 −0.0902785
\(187\) 3.69919e6 5.95272e7i 0.0413676 0.665686i
\(188\) −7.73649e7 −0.849164
\(189\) 3.99877e7 + 1.23069e8i 0.430834 + 1.32597i
\(190\) −2.43984e7 1.77265e7i −0.258062 0.187493i
\(191\) −2.59759e7 + 1.88726e7i −0.269745 + 0.195981i −0.714432 0.699705i \(-0.753315\pi\)
0.444687 + 0.895686i \(0.353315\pi\)
\(192\) 2.62263e6 8.07162e6i 0.0267413 0.0823012i
\(193\) 1.65659e7 5.09845e7i 0.165868 0.510490i −0.833231 0.552925i \(-0.813512\pi\)
0.999099 + 0.0424350i \(0.0135116\pi\)
\(194\) 1.07357e8 7.79996e7i 1.05566 0.766984i
\(195\) 4.73242e6 + 3.43830e6i 0.0457048 + 0.0332065i
\(196\) 1.22767e7 + 3.77839e7i 0.116463 + 0.358435i
\(197\) −1.16546e8 −1.08609 −0.543043 0.839705i \(-0.682728\pi\)
−0.543043 + 0.839705i \(0.682728\pi\)
\(198\) 2.56124e7 3.10086e7i 0.234489 0.283893i
\(199\) 1.94701e8 1.75138 0.875692 0.482870i \(-0.160406\pi\)
0.875692 + 0.482870i \(0.160406\pi\)
\(200\) −9.66344e6 2.97410e7i −0.0854135 0.262876i
\(201\) 7.58319e7 + 5.50951e7i 0.658667 + 0.478549i
\(202\) −7.17049e7 + 5.20967e7i −0.612095 + 0.444713i
\(203\) 3.72067e6 1.14510e7i 0.0312165 0.0960746i
\(204\) 8.65077e6 2.66243e7i 0.0713426 0.219570i
\(205\) 2.63001e7 1.91081e7i 0.213216 0.154910i
\(206\) −1.30020e8 9.44654e7i −1.03628 0.752900i
\(207\) 2.59924e7 + 7.99963e7i 0.203681 + 0.626864i
\(208\) −5.66810e6 −0.0436732
\(209\) −1.18540e8 4.68278e7i −0.898157 0.354807i
\(210\) −4.06412e7 −0.302830
\(211\) 2.41832e7 + 7.44281e7i 0.177225 + 0.545442i 0.999728 0.0233184i \(-0.00742317\pi\)
−0.822503 + 0.568760i \(0.807423\pi\)
\(212\) −4.03362e7 2.93060e7i −0.290750 0.211242i
\(213\) −9.60277e7 + 6.97682e7i −0.680876 + 0.494685i
\(214\) −2.96520e7 + 9.12594e7i −0.206826 + 0.636545i
\(215\) −4.78766e6 + 1.47349e7i −0.0328540 + 0.101114i
\(216\) 4.46008e7 3.24044e7i 0.301131 0.218784i
\(217\) −2.97414e7 2.16084e7i −0.197584 0.143553i
\(218\) 5.22251e7 + 1.60732e8i 0.341414 + 1.05076i
\(219\) −2.30505e7 −0.148295
\(220\) 1.97897e7 + 3.11306e7i 0.125302 + 0.197110i
\(221\) −1.86963e7 −0.116515
\(222\) −4.25347e7 1.30908e8i −0.260921 0.803031i
\(223\) −6.20838e7 4.51066e7i −0.374897 0.272378i 0.384342 0.923191i \(-0.374428\pi\)
−0.759239 + 0.650812i \(0.774428\pi\)
\(224\) 3.18593e7 2.31471e7i 0.189395 0.137603i
\(225\) 2.14943e7 6.61526e7i 0.125801 0.387176i
\(226\) −6.33423e7 + 1.94947e8i −0.365018 + 1.12341i
\(227\) −4.21645e7 + 3.06343e7i −0.239252 + 0.173827i −0.700950 0.713210i \(-0.747240\pi\)
0.461698 + 0.887037i \(0.347240\pi\)
\(228\) −4.83984e7 3.51635e7i −0.270433 0.196481i
\(229\) 2.94227e7 + 9.05539e7i 0.161904 + 0.498291i 0.998795 0.0490798i \(-0.0156289\pi\)
−0.836890 + 0.547371i \(0.815629\pi\)
\(230\) −7.71482e7 −0.418098
\(231\) −1.66329e8 + 4.28424e7i −0.887823 + 0.228682i
\(232\) −5.12956e6 −0.0269694
\(233\) 1.28111e7 + 3.94285e7i 0.0663500 + 0.204204i 0.978735 0.205129i \(-0.0657614\pi\)
−0.912385 + 0.409333i \(0.865761\pi\)
\(234\) −1.01997e7 7.41050e6i −0.0520392 0.0378087i
\(235\) 1.27690e8 9.27720e7i 0.641827 0.466315i
\(236\) 2.72125e7 8.37515e7i 0.134765 0.414763i
\(237\) −1.10855e7 + 3.41175e7i −0.0540922 + 0.166479i
\(238\) 1.05088e8 7.63511e7i 0.505283 0.367110i
\(239\) 6.98060e7 + 5.07171e7i 0.330750 + 0.240304i 0.740749 0.671782i \(-0.234471\pi\)
−0.409999 + 0.912086i \(0.634471\pi\)
\(240\) 5.35045e6 + 1.64670e7i 0.0249834 + 0.0768909i
\(241\) −1.36121e8 −0.626422 −0.313211 0.949684i \(-0.601405\pi\)
−0.313211 + 0.949684i \(0.601405\pi\)
\(242\) 1.13808e8 + 1.06544e8i 0.516202 + 0.483255i
\(243\) 2.03260e8 0.908718
\(244\) −1.21369e7 3.73536e7i −0.0534864 0.164614i
\(245\) −6.55711e7 4.76402e7i −0.284860 0.206963i
\(246\) 5.21708e7 3.79043e7i 0.223437 0.162336i
\(247\) −1.23464e7 + 3.79982e7i −0.0521314 + 0.160444i
\(248\) −4.83980e6 + 1.48954e7i −0.0201487 + 0.0620113i
\(249\) 2.09843e8 1.52460e8i 0.861383 0.625831i
\(250\) 1.17633e8 + 8.54651e7i 0.476143 + 0.345938i
\(251\) −1.47259e7 4.53216e7i −0.0587791 0.180904i 0.917356 0.398068i \(-0.130319\pi\)
−0.976135 + 0.217164i \(0.930319\pi\)
\(252\) 8.75931e7 0.344801
\(253\) −3.15738e8 + 8.13266e7i −1.22576 + 0.315726i
\(254\) 2.49295e8 0.954544
\(255\) 1.76485e7 + 5.43166e7i 0.0666527 + 0.205136i
\(256\) −1.35731e7 9.86140e6i −0.0505636 0.0367366i
\(257\) 7.81487e7 5.67784e7i 0.287181 0.208649i −0.434862 0.900497i \(-0.643203\pi\)
0.722044 + 0.691848i \(0.243203\pi\)
\(258\) −9.49716e6 + 2.92293e7i −0.0344290 + 0.105962i
\(259\) 1.97364e8 6.07424e8i 0.705860 2.17241i
\(260\) 9.35511e6 6.79688e6i 0.0330097 0.0239830i
\(261\) −9.23058e6 6.70641e6i −0.0321357 0.0233479i
\(262\) 1.05404e8 + 3.24400e8i 0.362078 + 1.11436i
\(263\) −5.39929e8 −1.83017 −0.915085 0.403261i \(-0.867877\pi\)
−0.915085 + 0.403261i \(0.867877\pi\)
\(264\) 3.92563e7 + 6.17530e7i 0.131309 + 0.206559i
\(265\) 1.01716e8 0.335761
\(266\) −8.57788e7 2.64000e8i −0.279444 0.860039i
\(267\) −8.02715e7 5.83207e7i −0.258091 0.187514i
\(268\) 1.49905e8 1.08913e8i 0.475714 0.345626i
\(269\) 9.29554e7 2.86087e8i 0.291167 0.896119i −0.693316 0.720634i \(-0.743851\pi\)
0.984482 0.175484i \(-0.0561492\pi\)
\(270\) −3.47553e7 + 1.06966e8i −0.107460 + 0.330729i
\(271\) −2.08684e8 + 1.51618e8i −0.636939 + 0.462763i −0.858797 0.512316i \(-0.828788\pi\)
0.221858 + 0.975079i \(0.428788\pi\)
\(272\) −4.47709e7 3.25279e7i −0.134898 0.0980089i
\(273\) 1.66380e7 + 5.12067e7i 0.0494918 + 0.152320i
\(274\) −1.09587e7 −0.0321836
\(275\) 2.50763e8 + 9.90613e7i 0.727110 + 0.287237i
\(276\) −1.53037e8 −0.438141
\(277\) 1.36977e8 + 4.21573e8i 0.387230 + 1.19177i 0.934850 + 0.355044i \(0.115534\pi\)
−0.547619 + 0.836728i \(0.684466\pi\)
\(278\) −3.26990e8 2.37572e8i −0.912805 0.663191i
\(279\) −2.81835e7 + 2.04765e7i −0.0776926 + 0.0564470i
\(280\) −2.48265e7 + 7.64080e7i −0.0675868 + 0.208011i
\(281\) 1.89936e8 5.84563e8i 0.510664 1.57166i −0.280372 0.959891i \(-0.590458\pi\)
0.791036 0.611770i \(-0.209542\pi\)
\(282\) 2.53295e8 1.84029e8i 0.672596 0.488670i
\(283\) −1.82383e8 1.32509e8i −0.478335 0.347530i 0.322346 0.946622i \(-0.395529\pi\)
−0.800681 + 0.599091i \(0.795529\pi\)
\(284\) 7.25081e7 + 2.23157e8i 0.187833 + 0.578091i
\(285\) 1.22047e8 0.312299
\(286\) 3.11219e7 3.76789e7i 0.0786656 0.0952394i
\(287\) 2.99223e8 0.747150
\(288\) −1.15317e7 3.54910e7i −0.0284459 0.0875476i
\(289\) 1.84294e8 + 1.33897e8i 0.449126 + 0.326309i
\(290\) 8.46625e6 6.15109e6i 0.0203844 0.0148101i
\(291\) −1.65951e8 + 5.10745e8i −0.394780 + 1.21501i
\(292\) −1.40808e7 + 4.33363e7i −0.0330970 + 0.101862i
\(293\) −6.66220e8 + 4.84037e8i −1.54732 + 1.12420i −0.601797 + 0.798649i \(0.705548\pi\)
−0.945526 + 0.325547i \(0.894452\pi\)
\(294\) −1.30072e8 9.45026e7i −0.298516 0.216884i
\(295\) 5.55166e7 + 1.70862e8i 0.125906 + 0.387498i
\(296\) −2.72099e8 −0.609826
\(297\) −2.94811e7 + 4.74409e8i −0.0652974 + 1.05076i
\(298\) −5.01556e8 −1.09790
\(299\) 3.15836e7 + 9.72042e7i 0.0683301 + 0.210298i
\(300\) 1.02384e8 + 7.43862e7i 0.218931 + 0.159063i
\(301\) −1.15370e8 + 8.38213e7i −0.243843 + 0.177162i
\(302\) −9.92562e7 + 3.05479e8i −0.207364 + 0.638201i
\(303\) 1.10840e8 3.41132e8i 0.228902 0.704487i
\(304\) −9.56746e7 + 6.95117e7i −0.195317 + 0.141906i
\(305\) 6.48242e7 + 4.70975e7i 0.130824 + 0.0950493i
\(306\) −3.80375e7 1.17067e8i −0.0758904 0.233567i
\(307\) −6.34750e8 −1.25204 −0.626020 0.779807i \(-0.715317\pi\)
−0.626020 + 0.779807i \(0.715317\pi\)
\(308\) −2.10590e7 + 3.38880e8i −0.0410685 + 0.660874i
\(309\) 6.50397e8 1.25408
\(310\) −9.87374e6 3.03882e7i −0.0188242 0.0579348i
\(311\) 2.50379e8 + 1.81911e8i 0.471994 + 0.342924i 0.798218 0.602369i \(-0.205776\pi\)
−0.326224 + 0.945293i \(0.605776\pi\)
\(312\) 1.85575e7 1.34828e7i 0.0345922 0.0251327i
\(313\) 1.75984e8 5.41624e8i 0.324391 0.998373i −0.647324 0.762215i \(-0.724112\pi\)
0.971715 0.236158i \(-0.0758882\pi\)
\(314\) 1.28363e8 3.95061e8i 0.233984 0.720129i
\(315\) −1.44571e8 + 1.05037e8i −0.260612 + 0.189346i
\(316\) 5.73713e7 + 4.16827e7i 0.102280 + 0.0743106i
\(317\) 1.35304e8 + 4.16423e8i 0.238563 + 0.734221i 0.996629 + 0.0820433i \(0.0261446\pi\)
−0.758066 + 0.652178i \(0.773855\pi\)
\(318\) 2.01772e8 0.351857
\(319\) 2.81649e7 3.40989e7i 0.0485782 0.0588129i
\(320\) 3.42274e7 0.0583914
\(321\) −1.19999e8 3.69319e8i −0.202493 0.623210i
\(322\) −5.74484e8 4.17387e8i −0.958920 0.696696i
\(323\) −3.15584e8 + 2.29285e8i −0.521082 + 0.378588i
\(324\) −1.96857e7 + 6.05865e7i −0.0321547 + 0.0989620i
\(325\) 2.61179e7 8.03827e7i 0.0422034 0.129889i
\(326\) 3.73233e8 2.71169e8i 0.596648 0.433490i
\(327\) −5.53323e8 4.02013e8i −0.875108 0.635804i
\(328\) −3.93929e7 1.21239e8i −0.0616396 0.189707i
\(329\) 1.45276e9 2.24909
\(330\) −1.38843e8 5.48483e7i −0.212679 0.0840165i
\(331\) 2.39866e8 0.363555 0.181777 0.983340i \(-0.441815\pi\)
0.181777 + 0.983340i \(0.441815\pi\)
\(332\) −1.58447e8 4.87650e8i −0.237630 0.731350i
\(333\) −4.89639e8 3.55744e8i −0.726644 0.527938i
\(334\) 2.66401e8 1.93552e8i 0.391222 0.284240i
\(335\) −1.16814e8 + 3.59518e8i −0.169762 + 0.522472i
\(336\) −4.92476e7 + 1.51569e8i −0.0708268 + 0.217983i
\(337\) 7.86441e8 5.71383e8i 1.11934 0.813247i 0.135230 0.990814i \(-0.456823\pi\)
0.984109 + 0.177567i \(0.0568226\pi\)
\(338\) 3.93723e8 + 2.86057e8i 0.554603 + 0.402943i
\(339\) −2.56341e8 7.88936e8i −0.357371 1.09987i
\(340\) 1.12899e8 0.155781
\(341\) −7.24436e7 1.13959e8i −0.0989372 0.155635i
\(342\) −2.63046e8 −0.355582
\(343\) 7.53099e7 + 2.31780e8i 0.100768 + 0.310132i
\(344\) 4.91513e7 + 3.57105e7i 0.0650999 + 0.0472978i
\(345\) 2.52585e8 1.83514e8i 0.331162 0.240603i
\(346\) 4.92025e7 1.51430e8i 0.0638588 0.196537i
\(347\) −1.68468e8 + 5.18490e8i −0.216453 + 0.666173i 0.782594 + 0.622532i \(0.213896\pi\)
−0.999047 + 0.0436414i \(0.986104\pi\)
\(348\) 1.67943e7 1.22018e7i 0.0213616 0.0155201i
\(349\) 3.14354e8 + 2.28392e8i 0.395850 + 0.287602i 0.767848 0.640632i \(-0.221327\pi\)
−0.371999 + 0.928233i \(0.621327\pi\)
\(350\) 1.81460e8 + 5.58475e8i 0.226226 + 0.696251i
\(351\) 1.49002e8 0.183915
\(352\) 1.40080e8 3.60812e7i 0.171189 0.0440942i
\(353\) 3.13795e8 0.379694 0.189847 0.981814i \(-0.439201\pi\)
0.189847 + 0.981814i \(0.439201\pi\)
\(354\) 1.10127e8 + 3.38935e8i 0.131942 + 0.406074i
\(355\) −3.87272e8 2.81369e8i −0.459427 0.333793i
\(356\) −1.58682e8 + 1.15289e8i −0.186403 + 0.135429i
\(357\) −1.62444e8 + 4.99951e8i −0.188958 + 0.581552i
\(358\) −1.74382e8 + 5.36692e8i −0.200868 + 0.618208i
\(359\) −1.35295e8 + 9.82974e7i −0.154330 + 0.112127i −0.662270 0.749265i \(-0.730407\pi\)
0.507940 + 0.861392i \(0.330407\pi\)
\(360\) 6.15918e7 + 4.47491e7i 0.0695768 + 0.0505505i
\(361\) −1.86245e7 5.73203e7i −0.0208357 0.0641258i
\(362\) 1.51314e8 0.167648
\(363\) −6.26050e8 7.81106e7i −0.686967 0.0857111i
\(364\) 1.06435e8 0.115673
\(365\) −2.87264e7 8.84109e7i −0.0309212 0.0951658i
\(366\) 1.28590e8 + 9.34262e7i 0.137096 + 0.0996059i
\(367\) −5.57645e7 + 4.05153e7i −0.0588880 + 0.0427846i −0.616840 0.787089i \(-0.711587\pi\)
0.557952 + 0.829873i \(0.311587\pi\)
\(368\) −9.34854e7 + 2.87719e8i −0.0977860 + 0.300954i
\(369\) 8.76213e7 2.69671e8i 0.0907857 0.279410i
\(370\) 4.49095e8 3.26287e8i 0.460928 0.334883i
\(371\) 7.57431e8 + 5.50306e8i 0.770078 + 0.559494i
\(372\) −1.95863e7 6.02804e7i −0.0197266 0.0607122i
\(373\) −6.05815e8 −0.604449 −0.302224 0.953237i \(-0.597729\pi\)
−0.302224 + 0.953237i \(0.597729\pi\)
\(374\) 4.62055e8 1.19014e8i 0.456712 0.117638i
\(375\) −5.88430e8 −0.576216
\(376\) −1.91257e8 5.88627e8i −0.185549 0.571062i
\(377\) −1.12162e7 8.14903e6i −0.0107808 0.00783269i
\(378\) −8.37513e8 + 6.08489e8i −0.797573 + 0.579470i
\(379\) 5.40324e7 1.66295e8i 0.0509820 0.156906i −0.922324 0.386417i \(-0.873713\pi\)
0.973306 + 0.229511i \(0.0737126\pi\)
\(380\) 7.45548e7 2.29456e8i 0.0697000 0.214515i
\(381\) −8.16199e8 + 5.93003e8i −0.756064 + 0.549313i
\(382\) −2.07807e8 1.50981e8i −0.190739 0.138580i
\(383\) −3.20870e8 9.87537e8i −0.291832 0.898168i −0.984267 0.176687i \(-0.943462\pi\)
0.692435 0.721481i \(-0.256538\pi\)
\(384\) 6.78960e7 0.0611906
\(385\) −3.71610e8 5.84569e8i −0.331875 0.522064i
\(386\) 4.28866e8 0.379547
\(387\) 4.17591e7 + 1.28521e8i 0.0366237 + 0.112716i
\(388\) 8.58858e8 + 6.23997e8i 0.746467 + 0.542340i
\(389\) −3.91828e8 + 2.84680e8i −0.337499 + 0.245207i −0.743606 0.668618i \(-0.766886\pi\)
0.406107 + 0.913826i \(0.366886\pi\)
\(390\) −1.44610e7 + 4.45063e7i −0.0123444 + 0.0379923i
\(391\) −3.08363e8 + 9.49043e8i −0.260881 + 0.802911i
\(392\) −2.57127e8 + 1.86814e8i −0.215599 + 0.156642i
\(393\) −1.11675e9 8.11368e8i −0.928074 0.674285i
\(394\) −2.88117e8 8.86733e8i −0.237319 0.730392i
\(395\) −1.44674e8 −0.118114
\(396\) 2.99245e8 + 1.18213e8i 0.242155 + 0.0956607i
\(397\) −2.46863e9 −1.98011 −0.990056 0.140674i \(-0.955073\pi\)
−0.990056 + 0.140674i \(0.955073\pi\)
\(398\) 4.81326e8 + 1.48137e9i 0.382692 + 1.17780i
\(399\) 9.08824e8 + 6.60299e8i 0.716267 + 0.520398i
\(400\) 2.02394e8 1.47048e8i 0.158120 0.114881i
\(401\) 6.45919e7 1.98793e8i 0.0500234 0.153956i −0.922924 0.384981i \(-0.874208\pi\)
0.972948 + 0.231025i \(0.0742079\pi\)
\(402\) −2.31722e8 + 7.13166e8i −0.177900 + 0.547519i
\(403\) −3.42460e7 + 2.48812e7i −0.0260641 + 0.0189367i
\(404\) −5.73639e8 4.16773e8i −0.432817 0.314460i
\(405\) −4.01611e7 1.23603e8i −0.0300409 0.0924565i
\(406\) 9.63226e7 0.0714311
\(407\) 1.49402e9 1.80879e9i 1.09844 1.32986i
\(408\) 2.23956e8 0.163249
\(409\) 5.72328e8 + 1.76144e9i 0.413631 + 1.27303i 0.913470 + 0.406907i \(0.133393\pi\)
−0.499839 + 0.866119i \(0.666607\pi\)
\(410\) 2.10401e8 + 1.52865e8i 0.150766 + 0.109538i
\(411\) 3.58792e7 2.60678e7i 0.0254916 0.0185207i
\(412\) 3.97307e8 1.22279e9i 0.279889 0.861410i
\(413\) −5.10995e8 + 1.57268e9i −0.356937 + 1.09854i
\(414\) −5.44391e8 + 3.95523e8i −0.377059 + 0.273950i
\(415\) 8.46279e8 + 6.14858e8i 0.581226 + 0.422286i
\(416\) −1.40123e7 4.31254e7i −0.00954295 0.0293702i
\(417\) 1.63569e9 1.10465
\(418\) 6.32408e7 1.01767e9i 0.0423527 0.681537i
\(419\) 5.37641e8 0.357062 0.178531 0.983934i \(-0.442866\pi\)
0.178531 + 0.983934i \(0.442866\pi\)
\(420\) −1.00471e8 3.09217e8i −0.0661708 0.203653i
\(421\) 3.08599e8 + 2.24210e8i 0.201561 + 0.146443i 0.683987 0.729494i \(-0.260244\pi\)
−0.482426 + 0.875937i \(0.660244\pi\)
\(422\) −5.06499e8 + 3.67993e8i −0.328084 + 0.238367i
\(423\) 4.25410e8 1.30928e9i 0.273286 0.841087i
\(424\) 1.23256e8 3.79344e8i 0.0785288 0.241687i
\(425\) 6.67598e8 4.85038e8i 0.421846 0.306489i
\(426\) −7.68221e8 5.58145e8i −0.481452 0.349795i
\(427\) 2.27906e8 + 7.01424e8i 0.141664 + 0.435996i
\(428\) −7.67646e8 −0.473269
\(429\) −1.22665e7 + 1.97392e8i −0.00750100 + 0.120706i
\(430\) −1.23946e8 −0.0751781
\(431\) −5.62883e8 1.73238e9i −0.338647 1.04225i −0.964897 0.262627i \(-0.915411\pi\)
0.626250 0.779622i \(-0.284589\pi\)
\(432\) 3.56807e8 + 2.59235e8i 0.212931 + 0.154704i
\(433\) 1.64159e9 1.19268e9i 0.971755 0.706021i 0.0159038 0.999874i \(-0.494937\pi\)
0.955851 + 0.293852i \(0.0949374\pi\)
\(434\) 9.08816e7 2.79705e8i 0.0533657 0.164243i
\(435\) −1.30870e7 + 4.02777e7i −0.00762304 + 0.0234613i
\(436\) −1.09382e9 + 7.94704e8i −0.632036 + 0.459201i
\(437\) 1.72520e9 + 1.25343e9i 0.988903 + 0.718480i
\(438\) −5.69839e7 1.75378e8i −0.0324036 0.0997280i
\(439\) −2.50280e8 −0.141189 −0.0705944 0.997505i \(-0.522490\pi\)
−0.0705944 + 0.997505i \(0.522490\pi\)
\(440\) −1.87933e8 + 2.27528e8i −0.105176 + 0.127336i
\(441\) −7.06940e8 −0.392507
\(442\) −4.62197e7 1.42250e8i −0.0254595 0.0783562i
\(443\) 1.35047e9 + 9.81175e8i 0.738027 + 0.536208i 0.892093 0.451853i \(-0.149237\pi\)
−0.154066 + 0.988061i \(0.549237\pi\)
\(444\) 8.90859e8 6.47247e8i 0.483024 0.350937i
\(445\) 1.23653e8 3.80566e8i 0.0665190 0.204724i
\(446\) 1.89711e8 5.83871e8i 0.101256 0.311634i
\(447\) 1.64211e9 1.19306e9i 0.869610 0.631809i
\(448\) 2.54874e8 + 1.85177e8i 0.133922 + 0.0973003i
\(449\) −1.07014e9 3.29355e9i −0.557929 1.71713i −0.688081 0.725634i \(-0.741547\pi\)
0.130152 0.991494i \(-0.458453\pi\)
\(450\) 5.56456e8 0.287864
\(451\) 1.02224e9 + 4.03823e8i 0.524726 + 0.207287i
\(452\) −1.63984e9 −0.835250
\(453\) −4.01682e8 1.23625e9i −0.203020 0.624831i
\(454\) −3.37316e8 2.45074e8i −0.169177 0.122914i
\(455\) −1.75670e8 + 1.27632e8i −0.0874294 + 0.0635212i
\(456\) 1.47892e8 4.55166e8i 0.0730414 0.224798i
\(457\) −1.18309e9 + 3.64118e9i −0.579845 + 1.78458i 0.0392085 + 0.999231i \(0.487516\pi\)
−0.619054 + 0.785349i \(0.712484\pi\)
\(458\) −6.16238e8 + 4.47723e8i −0.299722 + 0.217761i
\(459\) 1.17693e9 + 8.55090e8i 0.568076 + 0.412731i
\(460\) −1.90721e8 5.86978e8i −0.0913578 0.281170i
\(461\) −1.40758e9 −0.669143 −0.334572 0.942370i \(-0.608592\pi\)
−0.334572 + 0.942370i \(0.608592\pi\)
\(462\) −7.37153e8 1.15959e9i −0.347785 0.547091i
\(463\) −1.55804e9 −0.729532 −0.364766 0.931099i \(-0.618851\pi\)
−0.364766 + 0.931099i \(0.618851\pi\)
\(464\) −1.26810e7 3.90280e7i −0.00589304 0.0181369i
\(465\) 1.04612e8 + 7.60050e7i 0.0482498 + 0.0350556i
\(466\) −2.68319e8 + 1.94945e8i −0.122829 + 0.0892405i
\(467\) 3.20806e7 9.87339e7i 0.0145758 0.0448598i −0.943504 0.331361i \(-0.892492\pi\)
0.958080 + 0.286501i \(0.0924922\pi\)
\(468\) 3.11674e7 9.59235e7i 0.0140553 0.0432578i
\(469\) −2.81492e9 + 2.04516e9i −1.25997 + 0.915424i
\(470\) 1.02152e9 + 7.42176e8i 0.453840 + 0.329734i
\(471\) 5.19475e8 + 1.59878e9i 0.229082 + 0.705043i
\(472\) 7.04492e8 0.308375
\(473\) −5.07262e8 + 1.30659e8i −0.220404 + 0.0567707i
\(474\) −2.86986e8 −0.123776
\(475\) −5.44930e8 1.67712e9i −0.233299 0.718021i
\(476\) 8.40706e8 + 6.10808e8i 0.357289 + 0.259586i
\(477\) 7.17755e8 5.21480e8i 0.302804 0.220000i
\(478\) −2.13308e8 + 6.56495e8i −0.0893326 + 0.274938i
\(479\) −6.05751e8 + 1.86431e9i −0.251837 + 0.775076i 0.742599 + 0.669736i \(0.233593\pi\)
−0.994436 + 0.105339i \(0.966407\pi\)
\(480\) −1.12061e8 + 8.14173e7i −0.0462500 + 0.0336026i
\(481\) −5.94966e8 4.32268e8i −0.243772 0.177111i
\(482\) −3.36511e8 1.03567e9i −0.136878 0.421268i
\(483\) 2.87372e9 1.16046
\(484\) −5.29287e8 + 1.12930e9i −0.212194 + 0.452740i
\(485\) −2.16580e9 −0.862028
\(486\) 5.02486e8 + 1.54649e9i 0.198562 + 0.611112i
\(487\) 1.41052e9 + 1.02480e9i 0.553385 + 0.402058i 0.829032 0.559201i \(-0.188892\pi\)
−0.275647 + 0.961259i \(0.588892\pi\)
\(488\) 2.54199e8 1.84686e8i 0.0990157 0.0719391i
\(489\) −5.76937e8 + 1.77563e9i −0.223125 + 0.686707i
\(490\) 2.00367e8 6.16667e8i 0.0769380 0.236791i
\(491\) 6.17985e6 4.48992e6i 0.00235609 0.00171180i −0.586607 0.809872i \(-0.699536\pi\)
0.588963 + 0.808160i \(0.299536\pi\)
\(492\) 4.17367e8 + 3.03235e8i 0.157994 + 0.114789i
\(493\) −4.18283e7 1.28734e8i −0.0157219 0.0483871i
\(494\) −3.19629e8 −0.119289
\(495\) −6.35654e8 + 1.63729e8i −0.235561 + 0.0606748i
\(496\) −1.25295e8 −0.0461051
\(497\) −1.36156e9 4.19044e9i −0.497494 1.53113i
\(498\) 1.67874e9 + 1.21968e9i 0.609090 + 0.442530i
\(499\) −2.21957e9 + 1.61261e9i −0.799681 + 0.581002i −0.910821 0.412802i \(-0.864550\pi\)
0.111139 + 0.993805i \(0.464550\pi\)
\(500\) −3.59453e8 + 1.10628e9i −0.128602 + 0.395796i
\(501\) −4.11799e8 + 1.26739e9i −0.146303 + 0.450274i
\(502\) 3.08423e8 2.24082e8i 0.108814 0.0790577i
\(503\) −1.50991e9 1.09701e9i −0.529008 0.384347i 0.290978 0.956730i \(-0.406019\pi\)
−0.819987 + 0.572383i \(0.806019\pi\)
\(504\) 2.16542e8 + 6.66448e8i 0.0753417 + 0.231878i
\(505\) 1.44656e9 0.499822
\(506\) −1.39932e9 2.20123e9i −0.480164 0.755333i
\(507\) −1.96951e9 −0.671166
\(508\) 6.16292e8 + 1.89675e9i 0.208576 + 0.641930i
\(509\) −3.48384e9 2.53116e9i −1.17097 0.850760i −0.179846 0.983695i \(-0.557560\pi\)
−0.991125 + 0.132934i \(0.957560\pi\)
\(510\) −3.69636e8 + 2.68556e8i −0.123389 + 0.0896477i
\(511\) 2.64409e8 8.13768e8i 0.0876604 0.269791i
\(512\) 4.14756e7 1.27649e8i 0.0136568 0.0420312i
\(513\) 2.51508e9 1.82731e9i 0.822511 0.597589i
\(514\) 6.25190e8 + 4.54227e8i 0.203068 + 0.147537i
\(515\) 8.10551e8 + 2.49462e9i 0.261490 + 0.804783i
\(516\) −2.45868e8 −0.0787821
\(517\) 4.96306e9 + 1.96060e9i 1.57955 + 0.623982i
\(518\) 5.10947e9 1.61518
\(519\) 1.99118e8 + 6.12823e8i 0.0625209 + 0.192420i
\(520\) 7.48409e7 + 5.43751e7i 0.0233414 + 0.0169585i
\(521\) −1.34933e9 + 9.80345e8i −0.418009 + 0.303701i −0.776836 0.629703i \(-0.783177\pi\)
0.358827 + 0.933404i \(0.383177\pi\)
\(522\) 2.82061e7 8.68096e7i 0.00867955 0.0267129i
\(523\) 1.53830e9 4.73439e9i 0.470201 1.44713i −0.382120 0.924113i \(-0.624806\pi\)
0.852322 0.523018i \(-0.175194\pi\)
\(524\) −2.20761e9 + 1.60392e9i −0.670290 + 0.486994i
\(525\) −1.92256e9 1.39682e9i −0.579859 0.421292i
\(526\) −1.33478e9 4.10802e9i −0.399907 1.23079i
\(527\) −4.13288e8 −0.123003
\(528\) −3.72798e8 + 4.51341e8i −0.110218 + 0.133440i
\(529\) 2.05028e9 0.602170
\(530\) 2.51457e8 + 7.73905e8i 0.0733665 + 0.225799i
\(531\) 1.26773e9 + 9.21057e8i 0.367447 + 0.266966i
\(532\) 1.79658e9 1.30529e9i 0.517315 0.375851i
\(533\) 1.06470e8 3.27680e8i 0.0304565 0.0937355i
\(534\) 2.45288e8 7.54919e8i 0.0697079 0.214539i
\(535\) 1.26699e9 9.20521e8i 0.357713 0.259894i
\(536\) 1.19924e9 + 8.71302e8i 0.336380 + 0.244395i
\(537\) −7.05709e8 2.17195e9i −0.196660 0.605257i
\(538\) 2.40648e9 0.666261
\(539\) 1.69961e8 2.73500e9i 0.0467507 0.752311i
\(540\) −8.99765e8 −0.245896
\(541\) 1.29459e9 + 3.98433e9i 0.351513 + 1.08185i 0.958004 + 0.286755i \(0.0925766\pi\)
−0.606491 + 0.795090i \(0.707423\pi\)
\(542\) −1.66948e9 1.21295e9i −0.450384 0.327223i
\(543\) −4.95406e8 + 3.59933e8i −0.132789 + 0.0964767i
\(544\) 1.36808e8 4.21050e8i 0.0364346 0.112134i
\(545\) 8.52360e8 2.62330e9i 0.225546 0.694160i
\(546\) −3.48472e8 + 2.53180e8i −0.0916207 + 0.0665663i
\(547\) −5.30576e9 3.85486e9i −1.38609 1.00705i −0.996281 0.0861586i \(-0.972541\pi\)
−0.389810 0.920895i \(-0.627459\pi\)
\(548\) −2.70915e7 8.33791e7i −0.00703236 0.0216434i
\(549\) 6.98888e8 0.180262
\(550\) −1.33782e8 + 2.15281e9i −0.0342869 + 0.551744i
\(551\) −2.89260e8 −0.0736645
\(552\) −3.78328e8 1.16437e9i −0.0957374 0.294649i
\(553\) −1.07732e9 7.82716e8i −0.270898 0.196819i
\(554\) −2.86889e9 + 2.08437e9i −0.716852 + 0.520823i
\(555\) −6.94205e8 + 2.13654e9i −0.172370 + 0.530501i
\(556\) 9.99193e8 3.07520e9i 0.246540 0.758772i
\(557\) 1.63925e9 1.19099e9i 0.401932 0.292020i −0.368396 0.929669i \(-0.620093\pi\)
0.770327 + 0.637649i \(0.220093\pi\)
\(558\) −2.25468e8 1.63812e8i −0.0549370 0.0399141i
\(559\) 5.07419e7 + 1.56167e8i 0.0122864 + 0.0378137i
\(560\) −6.42721e8 −0.154655
\(561\) −1.22968e9 + 1.48875e9i −0.294050 + 0.356002i
\(562\) 4.91716e9 1.16852
\(563\) 2.15464e8 + 6.63129e8i 0.0508855 + 0.156610i 0.973270 0.229663i \(-0.0737624\pi\)
−0.922385 + 0.386273i \(0.873762\pi\)
\(564\) 2.02636e9 + 1.47224e9i 0.475597 + 0.345542i
\(565\) 2.70653e9 1.96641e9i 0.631311 0.458674i
\(566\) 5.57313e8 1.71523e9i 0.129194 0.397618i
\(567\) 3.69658e8 1.13769e9i 0.0851647 0.262110i
\(568\) −1.51863e9 + 1.10335e9i −0.347723 + 0.252635i
\(569\) 2.90461e9 + 2.11032e9i 0.660989 + 0.480237i 0.866997 0.498314i \(-0.166047\pi\)
−0.206008 + 0.978550i \(0.566047\pi\)
\(570\) 3.01717e8 + 9.28590e8i 0.0682398 + 0.210021i
\(571\) 2.88290e9 0.648042 0.324021 0.946050i \(-0.394965\pi\)
0.324021 + 0.946050i \(0.394965\pi\)
\(572\) 3.63615e8 + 1.43642e8i 0.0812374 + 0.0320919i
\(573\) 1.03951e9 0.230827
\(574\) 7.39719e8 + 2.27662e9i 0.163258 + 0.502457i
\(575\) −3.64954e9 2.65155e9i −0.800573 0.581651i
\(576\) 2.41523e8 1.75477e8i 0.0526600 0.0382597i
\(577\) −2.25559e9 + 6.94198e9i −0.488815 + 1.50442i 0.337565 + 0.941302i \(0.390397\pi\)
−0.826379 + 0.563114i \(0.809603\pi\)
\(578\) −5.63152e8 + 1.73320e9i −0.121305 + 0.373338i
\(579\) −1.40412e9 + 1.02015e9i −0.300627 + 0.218419i
\(580\) 6.77300e7 + 4.92088e7i 0.0144140 + 0.0104724i
\(581\) 2.97531e9 + 9.15708e9i 0.629385 + 1.93705i
\(582\) −4.29624e9 −0.903353
\(583\) 1.84494e9 + 2.90222e9i 0.385604 + 0.606584i
\(584\) −3.64532e8 −0.0757340
\(585\) 6.35851e7 + 1.95695e8i 0.0131314 + 0.0404142i
\(586\) −5.32976e9 3.87230e9i −1.09412 0.794927i
\(587\) −8.44558e8 + 6.13607e8i −0.172344 + 0.125215i −0.670613 0.741807i \(-0.733969\pi\)
0.498269 + 0.867022i \(0.333969\pi\)
\(588\) 3.97464e8 1.22327e9i 0.0806263 0.248142i
\(589\) −2.72921e8 + 8.39964e8i −0.0550343 + 0.169378i
\(590\) −1.16275e9 + 8.44790e8i −0.233080 + 0.169343i
\(591\) 3.05259e9 + 2.21784e9i 0.608292 + 0.441950i
\(592\) −6.72666e8 2.07025e9i −0.133252 0.410107i
\(593\) −6.96907e9 −1.37241 −0.686204 0.727409i \(-0.740724\pi\)
−0.686204 + 0.727409i \(0.740724\pi\)
\(594\) −3.68240e9 + 9.48498e8i −0.720905 + 0.185688i
\(595\) −2.12002e9 −0.412602
\(596\) −1.23991e9 3.81606e9i −0.239900 0.738335i
\(597\) −5.09964e9 3.70510e9i −0.980910 0.712673i
\(598\) −6.61495e8 + 4.80604e8i −0.126495 + 0.0919038i
\(599\) −1.61399e9 + 4.96735e9i −0.306837 + 0.944346i 0.672149 + 0.740416i \(0.265372\pi\)
−0.978985 + 0.203930i \(0.934628\pi\)
\(600\) −3.12857e8 + 9.62875e8i −0.0591312 + 0.181987i
\(601\) 5.50926e9 4.00271e9i 1.03522 0.752131i 0.0658730 0.997828i \(-0.479017\pi\)
0.969347 + 0.245697i \(0.0790168\pi\)
\(602\) −9.22961e8 6.70570e8i −0.172423 0.125273i
\(603\) 1.01888e9 + 3.13580e9i 0.189240 + 0.582421i
\(604\) −2.56960e9 −0.474500
\(605\) −4.80613e8 2.49858e9i −0.0882371 0.458722i
\(606\) 2.86950e9 0.523783
\(607\) 3.30794e8 + 1.01808e9i 0.0600340 + 0.184766i 0.976576 0.215173i \(-0.0690315\pi\)
−0.916542 + 0.399938i \(0.869032\pi\)
\(608\) −7.65397e8 5.56094e8i −0.138110 0.100343i
\(609\) −3.15363e8 + 2.29124e8i −0.0565783 + 0.0411065i
\(610\) −1.98085e8 + 6.09643e8i −0.0353344 + 0.108748i
\(611\) 5.16920e8 1.59092e9i 0.0916810 0.282165i
\(612\) 7.96668e8 5.78813e8i 0.140491 0.102072i
\(613\) 3.46212e9 + 2.51537e9i 0.607058 + 0.441053i 0.848377 0.529393i \(-0.177580\pi\)
−0.241319 + 0.970446i \(0.577580\pi\)
\(614\) −1.56919e9 4.82946e9i −0.273581 0.841995i
\(615\) −1.05248e9 −0.182453
\(616\) −2.63041e9 + 6.77531e8i −0.453410 + 0.116788i
\(617\) 5.99720e9 1.02790 0.513949 0.857821i \(-0.328182\pi\)
0.513949 + 0.857821i \(0.328182\pi\)
\(618\) 1.60787e9 + 4.94851e9i 0.274025 + 0.843364i
\(619\) −5.88254e9 4.27391e9i −0.996890 0.724283i −0.0354712 0.999371i \(-0.511293\pi\)
−0.961419 + 0.275087i \(0.911293\pi\)
\(620\) 2.06798e8 1.50248e8i 0.0348478 0.0253184i
\(621\) 2.45753e9 7.56351e9i 0.411793 1.26737i
\(622\) −7.65090e8 + 2.35471e9i −0.127481 + 0.392347i
\(623\) 2.97972e9 2.16489e9i 0.493705 0.358698i
\(624\) 1.48460e8 + 1.07862e8i 0.0244604 + 0.0177715i
\(625\) 7.41198e8 + 2.28117e9i 0.121438 + 0.373748i
\(626\) 4.55598e9 0.742286
\(627\) 2.21370e9 + 3.48231e9i 0.358659 + 0.564197i
\(628\) 3.32313e9 0.535413
\(629\) −2.21880e9 6.82875e9i −0.355500 1.09412i
\(630\) −1.15657e9 8.40297e8i −0.184281 0.133888i
\(631\) 6.57613e8 4.77784e8i 0.104200 0.0757058i −0.534465 0.845191i \(-0.679487\pi\)
0.638665 + 0.769485i \(0.279487\pi\)
\(632\) −1.75311e8 + 5.39552e8i −0.0276248 + 0.0850205i
\(633\) 7.82938e8 2.40964e9i 0.122692 0.377606i
\(634\) −2.83384e9 + 2.05891e9i −0.441635 + 0.320867i
\(635\) −3.29167e9 2.39154e9i −0.510162 0.370654i
\(636\) 4.98808e8 + 1.53517e9i 0.0768836 + 0.236624i
\(637\) −8.59009e8 −0.131677
\(638\) 3.29067e8 + 1.29994e8i 0.0501663 + 0.0198177i
\(639\) −4.17528e9 −0.633043
\(640\) 8.46148e7 + 2.60418e8i 0.0127590 + 0.0392681i
\(641\) 7.42710e9 + 5.39611e9i 1.11382 + 0.809240i 0.983261 0.182200i \(-0.0583219\pi\)
0.130562 + 0.991440i \(0.458322\pi\)
\(642\) 2.51329e9 1.82601e9i 0.374861 0.272353i
\(643\) 2.11543e9 6.51062e9i 0.313805 0.965793i −0.662438 0.749116i \(-0.730478\pi\)
0.976243 0.216676i \(-0.0695216\pi\)
\(644\) 1.75547e9 5.40277e9i 0.258995 0.797106i
\(645\) 4.05801e8 2.94832e8i 0.0595462 0.0432628i
\(646\) −2.52467e9 1.83428e9i −0.368461 0.267702i
\(647\) 3.62950e9 + 1.11704e10i 0.526843 + 1.62146i 0.760642 + 0.649172i \(0.224884\pi\)
−0.233799 + 0.972285i \(0.575116\pi\)
\(648\) −5.09635e8 −0.0735778
\(649\) −3.86817e9 + 4.68314e9i −0.555455 + 0.672481i
\(650\) 6.76155e8 0.0965717
\(651\) 3.67790e8 + 1.13194e9i 0.0522477 + 0.160802i
\(652\) 2.98586e9 + 2.16936e9i 0.421894 + 0.306524i
\(653\) 4.87060e9 3.53870e9i 0.684520 0.497333i −0.190334 0.981719i \(-0.560957\pi\)
0.874854 + 0.484386i \(0.160957\pi\)
\(654\) 1.69081e9 5.20377e9i 0.236359 0.727437i
\(655\) 1.72029e9 5.29450e9i 0.239197 0.736174i
\(656\) 8.25056e8 5.99438e8i 0.114109 0.0829051i
\(657\) −6.55971e8 4.76591e8i −0.0902415 0.0655643i
\(658\) 3.59141e9 + 1.10532e10i 0.491444 + 1.51251i
\(659\) −9.59456e9 −1.30595 −0.652974 0.757380i \(-0.726479\pi\)
−0.652974 + 0.757380i \(0.726479\pi\)
\(660\) 7.40724e7 1.19197e9i 0.0100289 0.161385i
\(661\) 5.99941e9 0.807985 0.403993 0.914762i \(-0.367622\pi\)
0.403993 + 0.914762i \(0.367622\pi\)
\(662\) 5.92980e8 + 1.82501e9i 0.0794396 + 0.244490i
\(663\) 4.89697e8 + 3.55785e8i 0.0652574 + 0.0474123i
\(664\) 3.31856e9 2.41107e9i 0.439907 0.319611i
\(665\) −1.39999e9 + 4.30872e9i −0.184607 + 0.568162i
\(666\) 1.49621e9 4.60485e9i 0.196260 0.604025i
\(667\) −5.98645e8 + 4.34941e8i −0.0781140 + 0.0567531i
\(668\) 2.13121e9 + 1.54841e9i 0.276636 + 0.200988i
\(669\) 7.67746e8 + 2.36288e9i 0.0991348 + 0.305106i
\(670\) −3.02415e9 −0.388456
\(671\) −1.68025e8 + 2.70385e9i −0.0214707 + 0.345505i
\(672\) −1.27495e9 −0.162069
\(673\) −2.68055e9 8.24987e9i −0.338977 1.04326i −0.964730 0.263243i \(-0.915208\pi\)
0.625752 0.780022i \(-0.284792\pi\)
\(674\) 6.29153e9 + 4.57106e9i 0.791492 + 0.575053i
\(675\) −5.32050e9 + 3.86557e9i −0.665869 + 0.483782i
\(676\) −1.20311e9 + 3.70280e9i −0.149793 + 0.461016i
\(677\) 7.64238e8 2.35208e9i 0.0946603 0.291335i −0.892505 0.451038i \(-0.851054\pi\)
0.987165 + 0.159704i \(0.0510538\pi\)
\(678\) 5.36887e9 3.90072e9i 0.661575 0.480663i
\(679\) −1.61276e10 1.17174e10i −1.97709 1.43644i
\(680\) 2.79103e8 + 8.58990e8i 0.0340395 + 0.104763i
\(681\) 1.68734e9 0.204733
\(682\) 6.87961e8 8.32906e8i 0.0830460 0.100543i
\(683\) 6.47279e9 0.777355 0.388677 0.921374i \(-0.372932\pi\)
0.388677 + 0.921374i \(0.372932\pi\)
\(684\) −6.50284e8 2.00137e9i −0.0776975 0.239128i
\(685\) 1.44698e8 + 1.05129e8i 0.0172007 + 0.0124970i
\(686\) −1.57731e9 + 1.14598e9i −0.186545 + 0.135533i
\(687\) 9.52571e8 2.93171e9i 0.112085 0.344963i
\(688\) −1.50193e8 + 4.62246e8i −0.0175829 + 0.0541145i
\(689\) 8.72152e8 6.33655e8i 0.101584 0.0738050i
\(690\) 2.02068e9 + 1.46811e9i 0.234167 + 0.170132i
\(691\) −3.62923e9 1.11696e10i −0.418448 1.28785i −0.909130 0.416512i \(-0.863252\pi\)
0.490682 0.871339i \(-0.336748\pi\)
\(692\) 1.27378e9 0.146125
\(693\) −5.61921e9 2.21981e9i −0.641370 0.253366i
\(694\) −4.36138e9 −0.495297
\(695\) 2.03847e9 + 6.27375e9i 0.230333 + 0.708893i
\(696\) 1.34354e8 + 9.76142e7i 0.0151050 + 0.0109744i
\(697\) 2.72146e9 1.97725e9i 0.304429 0.221181i
\(698\) −9.60581e8 + 2.95636e9i −0.106915 + 0.329051i
\(699\) 4.14764e8 1.27651e9i 0.0459336 0.141369i
\(700\) −3.80054e9 + 2.76125e9i −0.418796 + 0.304273i
\(701\) 5.94755e9 + 4.32115e9i 0.652116 + 0.473790i 0.863991 0.503506i \(-0.167957\pi\)
−0.211875 + 0.977297i \(0.567957\pi\)
\(702\) 3.68354e8 + 1.13368e9i 0.0401869 + 0.123683i
\(703\) −1.53439e10 −1.66568
\(704\) 6.20818e8 + 9.76593e8i 0.0670595 + 0.105489i
\(705\) −5.10990e9 −0.549225
\(706\) 7.75743e8 + 2.38749e9i 0.0829663 + 0.255344i
\(707\) 1.07718e10 + 7.82616e9i 1.14636 + 0.832876i
\(708\) −2.30652e9 + 1.67579e9i −0.244254 + 0.177461i
\(709\) 1.83597e9 5.65055e9i 0.193466 0.595427i −0.806525 0.591200i \(-0.798654\pi\)
0.999991 0.00422723i \(-0.00134557\pi\)
\(710\) 1.18340e9 3.64212e9i 0.124087 0.381901i
\(711\) −1.02088e9 + 7.41715e8i −0.106520 + 0.0773916i
\(712\) −1.26945e9 9.22313e8i −0.131807 0.0957631i
\(713\) 6.98167e8 + 2.14874e9i 0.0721350 + 0.222009i
\(714\) −4.20543e9 −0.432381
\(715\) −7.72390e8 + 1.98949e8i −0.0790252 + 0.0203550i
\(716\) −4.51449e9 −0.459635
\(717\) −8.63241e8 2.65678e9i −0.0874611 0.269178i
\(718\) −1.08236e9 7.86380e8i −0.109128 0.0792860i
\(719\) −2.89701e9 + 2.10480e9i −0.290669 + 0.211183i −0.723558 0.690264i \(-0.757494\pi\)
0.432889 + 0.901447i \(0.357494\pi\)
\(720\) −1.88208e8 + 5.79244e8i −0.0187921 + 0.0578360i
\(721\) −7.46062e9 + 2.29614e10i −0.741312 + 2.28153i
\(722\) 3.90076e8 2.83407e8i 0.0385717 0.0280240i
\(723\) 3.56532e9 + 2.59036e9i 0.350844 + 0.254903i
\(724\) 3.74069e8 + 1.15126e9i 0.0366325 + 0.112743i
\(725\) 6.11912e8 0.0596357
\(726\) −9.53379e8 4.95637e9i −0.0924672 0.480713i
\(727\) −4.43149e9 −0.427740 −0.213870 0.976862i \(-0.568607\pi\)
−0.213870 + 0.976862i \(0.568607\pi\)
\(728\) 2.63123e8 + 8.09808e8i 0.0252754 + 0.0777897i
\(729\) −7.08497e9 5.14753e9i −0.677316 0.492099i
\(730\) 6.01655e8 4.37128e8i 0.0572423 0.0415890i
\(731\) −4.95413e8 + 1.52472e9i −0.0469090 + 0.144371i
\(732\) −3.92936e8 + 1.20933e9i −0.0370283 + 0.113961i
\(733\) 3.50172e8 2.54415e8i 0.0328411 0.0238605i −0.571244 0.820781i \(-0.693539\pi\)
0.604085 + 0.796920i \(0.293539\pi\)
\(734\) −4.46116e8 3.24122e8i −0.0416401 0.0302533i
\(735\) 8.10870e8 + 2.49560e9i 0.0753261 + 0.231830i
\(736\) −2.42020e9 −0.223758
\(737\) −1.23767e10 + 3.18794e9i −1.13886 + 0.293342i
\(738\) 2.26839e9 0.207740
\(739\) 5.64555e9 + 1.73752e10i 0.514577 + 1.58371i 0.784050 + 0.620697i \(0.213150\pi\)
−0.269473 + 0.963008i \(0.586850\pi\)
\(740\) 3.59276e9 + 2.61030e9i 0.325925 + 0.236798i
\(741\) 1.04647e9 7.60308e8i 0.0944854 0.0686477i
\(742\) −2.31450e9 + 7.12331e9i −0.207991 + 0.640130i
\(743\) 2.29194e9 7.05388e9i 0.204995 0.630910i −0.794719 0.606978i \(-0.792382\pi\)
0.999714 0.0239316i \(-0.00761840\pi\)
\(744\) 4.10220e8 2.98043e8i 0.0365184 0.0265322i
\(745\) 6.62248e9 + 4.81151e9i 0.586778 + 0.426319i
\(746\) −1.49766e9 4.60932e9i −0.132077 0.406491i
\(747\) 9.12397e9 0.800869
\(748\) 2.04778e9 + 3.22130e9i 0.178907 + 0.281433i
\(749\) 1.44148e10 1.25350
\(750\) −1.45468e9 4.47704e9i −0.125908 0.387504i
\(751\) 4.51095e9 + 3.27740e9i 0.388623 + 0.282351i 0.764891 0.644160i \(-0.222793\pi\)
−0.376268 + 0.926511i \(0.622793\pi\)
\(752\) 4.00573e9 2.91033e9i 0.343494 0.249563i
\(753\) −4.76755e8 + 1.46730e9i −0.0406924 + 0.125238i
\(754\) 3.42736e7 1.05483e8i 0.00291179 0.00896156i
\(755\) 4.24108e9 3.08133e9i 0.358643 0.260570i
\(756\) −6.70010e9 4.86791e9i −0.563969 0.409747i
\(757\) −3.47079e9 1.06820e10i −0.290799 0.894988i −0.984600 0.174821i \(-0.944065\pi\)
0.693801 0.720167i \(-0.255935\pi\)
\(758\) 1.39882e9 0.116659
\(759\) 9.81750e9 + 3.87830e9i 0.814995 + 0.321955i
\(760\) 1.93011e9 0.159491
\(761\) −5.50749e9 1.69503e10i −0.453010 1.39422i −0.873456 0.486903i \(-0.838126\pi\)
0.420446 0.907317i \(-0.361874\pi\)
\(762\) −6.52959e9 4.74403e9i −0.534618 0.388423i
\(763\) 2.05397e10 1.49229e10i 1.67401 1.21624i
\(764\) 6.35002e8 1.95434e9i 0.0515168 0.158552i
\(765\) −6.20806e8 + 1.91064e9i −0.0501350 + 0.154300i
\(766\) 6.72039e9 4.88265e9i 0.540249 0.392514i
\(767\) 1.54043e9 + 1.11919e9i 0.123270 + 0.0895609i
\(768\) 1.67848e8 + 5.16584e8i 0.0133706 + 0.0411506i
\(769\) −4.95220e9 −0.392696 −0.196348 0.980534i \(-0.562908\pi\)
−0.196348 + 0.980534i \(0.562908\pi\)
\(770\) 3.52900e9 4.27251e9i 0.278570 0.337260i
\(771\) −3.12737e9 −0.245747
\(772\) 1.06021e9 + 3.26301e9i 0.0829341 + 0.255245i
\(773\) −5.95318e9 4.32524e9i −0.463576 0.336808i 0.331357 0.943506i \(-0.392494\pi\)
−0.794932 + 0.606698i \(0.792494\pi\)
\(774\) −8.74614e8 + 6.35444e8i −0.0677990 + 0.0492588i
\(775\) 5.77347e8 1.77689e9i 0.0445534 0.137121i
\(776\) −2.62444e9 + 8.07718e9i −0.201614 + 0.620503i
\(777\) −1.67285e10 + 1.21540e10i −1.27933 + 0.929491i
\(778\) −3.13463e9 2.27744e9i −0.238648 0.173388i
\(779\) −2.22140e9 6.83678e9i −0.168363 0.518168i
\(780\) −3.74374e8 −0.0282471
\(781\) 1.00381e9 1.61533e10i 0.0754005 1.21334i
\(782\) −7.98306e9 −0.596961
\(783\) 3.33355e8 + 1.02596e9i 0.0248165 + 0.0763775i
\(784\) −2.05702e9 1.49451e9i −0.152452 0.110763i
\(785\) −5.48478e9 + 3.98493e9i −0.404684 + 0.294020i
\(786\) 3.41249e9 1.05026e10i 0.250664 0.771465i
\(787\) −5.64937e8 + 1.73870e9i −0.0413132 + 0.127149i −0.969586 0.244751i \(-0.921294\pi\)
0.928273 + 0.371900i \(0.121294\pi\)
\(788\) 6.03440e9 4.38425e9i 0.439331 0.319193i
\(789\) 1.41419e10 + 1.02747e10i 1.02504 + 0.744732i
\(790\) −3.57654e8 1.10075e9i −0.0258088 0.0794314i
\(791\) 3.07928e10 2.21224
\(792\) −1.59647e8 + 2.56903e9i −0.0114188 + 0.183752i
\(793\) 8.49225e8 0.0604737
\(794\) −6.10280e9 1.87825e10i −0.432670 1.33162i
\(795\) −2.66418e9 1.93564e9i −0.188052 0.136628i
\(796\) −1.00810e10 + 7.32430e9i −0.708450 + 0.514719i
\(797\) −1.56309e7 + 4.81070e7i −0.00109365 + 0.00336592i −0.951602 0.307334i \(-0.900563\pi\)
0.950508 + 0.310699i \(0.100563\pi\)
\(798\) −2.77712e9 + 8.54709e9i −0.193457 + 0.595399i
\(799\) 1.32129e10 9.59977e9i 0.916402 0.665805i
\(800\) 1.61915e9 + 1.17638e9i 0.111808 + 0.0812331i
\(801\) −1.07853e9 3.31938e9i −0.0741515 0.228215i
\(802\) 1.67219e9 0.114466
\(803\) 2.00154e9 2.42324e9i 0.136414 0.165155i
\(804\) −5.99894e9 −0.407078
\(805\) 3.58135e9 + 1.10223e10i 0.241970 + 0.744706i
\(806\) −2.73968e8 1.99050e8i −0.0184301 0.0133902i
\(807\) −7.87887e9 + 5.72434e9i −0.527724 + 0.383414i
\(808\) 1.75289e9 5.39483e9i 0.116900 0.359781i
\(809\) −3.00115e9 + 9.23660e9i −0.199282 + 0.613327i 0.800618 + 0.599175i \(0.204505\pi\)
−0.999900 + 0.0141518i \(0.995495\pi\)
\(810\) 8.41146e8 6.11128e8i 0.0556127 0.0404050i
\(811\) −3.21882e9 2.33861e9i −0.211896 0.153952i 0.476775 0.879025i \(-0.341806\pi\)
−0.688671 + 0.725074i \(0.741806\pi\)
\(812\) 2.38123e8 + 7.32866e8i 0.0156083 + 0.0480373i
\(813\) 8.35116e9 0.545042
\(814\) 1.74555e10 + 6.89560e9i 1.13435 + 0.448112i
\(815\) −7.52950e9 −0.487208
\(816\) 5.53649e8 + 1.70396e9i 0.0356713 + 0.109785i
\(817\) 2.77169e9 + 2.01375e9i 0.177814 + 0.129190i
\(818\) −1.19870e10 + 8.70906e9i −0.765726 + 0.556333i
\(819\) −5.85261e8 + 1.80125e9i −0.0372268 + 0.114572i
\(820\) −6.42928e8 + 1.97873e9i −0.0407206 + 0.125325i
\(821\) −1.99985e10 + 1.45298e10i −1.26124 + 0.916344i −0.998818 0.0486096i \(-0.984521\pi\)
−0.262421 + 0.964953i \(0.584521\pi\)
\(822\) 2.87034e8 + 2.08542e8i 0.0180253 + 0.0130961i
\(823\) −4.35565e9 1.34053e10i −0.272366 0.838257i −0.989904 0.141738i \(-0.954731\pi\)
0.717538 0.696519i \(-0.245269\pi\)
\(824\) 1.02857e10 0.640455
\(825\) −4.68294e9 7.36660e9i −0.290355 0.456750i
\(826\) −1.32289e10 −0.816760
\(827\) 5.54827e9 + 1.70758e10i 0.341105 + 1.04981i 0.963636 + 0.267219i \(0.0861047\pi\)
−0.622530 + 0.782596i \(0.713895\pi\)
\(828\) −4.35513e9 3.16419e9i −0.266621 0.193712i
\(829\) 1.40345e9 1.01966e9i 0.0855570 0.0621608i −0.544184 0.838966i \(-0.683161\pi\)
0.629741 + 0.776805i \(0.283161\pi\)
\(830\) −2.58600e9 + 7.95888e9i −0.156984 + 0.483147i
\(831\) 4.43468e9 1.36486e10i 0.268077 0.825055i
\(832\) 2.93477e8 2.13224e8i 0.0176662 0.0128352i
\(833\) −6.78510e9 4.92966e9i −0.406723 0.295501i
\(834\) 4.04365e9 + 1.24451e10i 0.241375 + 0.742876i
\(835\) −5.37431e9 −0.319462
\(836\) 7.89923e9 2.03465e9i 0.467587 0.120439i
\(837\) 3.29375e9 0.194156
\(838\) 1.32912e9 + 4.09061e9i 0.0780208 + 0.240123i
\(839\) 3.42752e9 + 2.49024e9i 0.200361 + 0.145571i 0.683442 0.730005i \(-0.260482\pi\)
−0.483081 + 0.875576i \(0.660482\pi\)
\(840\) 2.10428e9 1.52885e9i 0.122497 0.0889996i
\(841\) −5.29949e9 + 1.63101e10i −0.307219 + 0.945523i
\(842\) −9.42994e8 + 2.90224e9i −0.0544398 + 0.167548i
\(843\) −1.60989e10 + 1.16965e10i −0.925551 + 0.672452i
\(844\) −4.05199e9 2.94394e9i −0.231990 0.168551i
\(845\) −2.45448e9 7.55412e9i −0.139946 0.430710i
\(846\) 1.10133e10 0.625345
\(847\) 9.93893e9 2.12059e10i 0.562015 1.19913i
\(848\) 3.19093e9 0.179693
\(849\) 2.25540e9 + 6.94141e9i 0.126487 + 0.389288i
\(850\) 5.34078e9 + 3.88030e9i 0.298290 + 0.216720i
\(851\) −3.17553e10 + 2.30716e10i −1.76629 + 1.28329i
\(852\) 2.34748e9 7.22479e9i 0.130036 0.400209i
\(853\) −1.27517e9 + 3.92457e9i −0.0703472 + 0.216506i −0.980049 0.198755i \(-0.936310\pi\)
0.909702 + 0.415262i \(0.136310\pi\)
\(854\) −4.77333e9 + 3.46803e9i −0.262252 + 0.190537i
\(855\) 3.47322e9 + 2.52344e9i 0.190043 + 0.138074i
\(856\) −1.89773e9 5.84060e9i −0.103413 0.318273i
\(857\) −1.30313e9 −0.0707221 −0.0353611 0.999375i \(-0.511258\pi\)
−0.0353611 + 0.999375i \(0.511258\pi\)
\(858\) −1.53217e9 + 3.94650e8i −0.0828136 + 0.0213308i
\(859\) −1.28413e10 −0.691249 −0.345624 0.938373i \(-0.612333\pi\)
−0.345624 + 0.938373i \(0.612333\pi\)
\(860\) −3.06410e8 9.43034e8i −0.0164270 0.0505572i
\(861\) −7.83730e9 5.69413e9i −0.418461 0.304030i
\(862\) 1.17892e10 8.56534e9i 0.626914 0.455480i
\(863\) 9.22065e8 2.83782e9i 0.0488342 0.150296i −0.923666 0.383199i \(-0.874822\pi\)
0.972500 + 0.232903i \(0.0748224\pi\)
\(864\) −1.09030e9 + 3.35561e9i −0.0575108 + 0.177000i
\(865\) −2.10235e9 + 1.52745e9i −0.110446 + 0.0802436i
\(866\) 1.31327e10 + 9.54147e9i 0.687134 + 0.499232i
\(867\) −2.27903e9 7.01413e9i −0.118763 0.365516i
\(868\) 2.35279e9 0.122114
\(869\) −2.62411e9 4.12791e9i −0.135648 0.213384i
\(870\) −3.38804e8 −0.0174434
\(871\) 1.23805e9 + 3.81034e9i 0.0634857 + 0.195389i
\(872\) −8.75054e9 6.35764e9i −0.446917 0.324704i
\(873\) −1.52828e10 + 1.11036e10i −0.777416 + 0.564825i
\(874\) −5.27173e9 + 1.62247e10i −0.267093 + 0.822029i
\(875\) 6.74980e9 2.07738e10i 0.340614 1.04830i
\(876\) 1.19349e9 8.67119e8i 0.0599865 0.0435827i
\(877\) 7.09951e8 + 5.15810e8i 0.0355410 + 0.0258221i 0.605414 0.795911i \(-0.293008\pi\)
−0.569873 + 0.821733i \(0.693008\pi\)
\(878\) −6.18726e8 1.90424e9i −0.0308509 0.0949492i
\(879\) 2.66609e10 1.32408
\(880\) −2.19573e9 8.67399e8i −0.108615 0.0429071i
\(881\) −2.29360e10 −1.13006 −0.565029 0.825071i \(-0.691135\pi\)
−0.565029 + 0.825071i \(0.691135\pi\)
\(882\) −1.74765e9 5.37872e9i −0.0857659 0.263960i
\(883\) 2.55508e10 + 1.85637e10i 1.24894 + 0.907407i 0.998160 0.0606368i \(-0.0193132\pi\)
0.250779 + 0.968044i \(0.419313\pi\)
\(884\) 9.68039e8 7.03321e8i 0.0471313 0.0342429i
\(885\) 1.79737e9 5.53173e9i 0.0871636 0.268262i
\(886\) −4.12667e9 + 1.27006e10i −0.199334 + 0.613488i
\(887\) −2.57080e10 + 1.86780e10i −1.23690 + 0.898663i −0.997388 0.0722295i \(-0.976989\pi\)
−0.239516 + 0.970893i \(0.576989\pi\)
\(888\) 7.12687e9 + 5.17798e9i 0.341550 + 0.248150i
\(889\) −1.15727e10 3.56171e10i −0.552432 1.70021i
\(890\) 3.20120e9 0.152212
\(891\) 2.79826e9 3.38782e9i 0.132531 0.160453i
\(892\) 4.91135e9 0.231699
\(893\) −1.07851e10 3.31932e10i −0.506811 1.55980i
\(894\) 1.31368e10 + 9.54448e9i 0.614907 + 0.446756i
\(895\) 7.45110e9 5.41354e9i 0.347408 0.252407i
\(896\) −7.78827e8 + 2.39698e9i −0.0361712 + 0.111323i
\(897\) 1.02253e9 3.14702e9i 0.0473045 0.145588i
\(898\) 2.24133e10 1.62842e10i 1.03285 0.750412i
\(899\) −2.47938e8 1.80137e8i −0.0113811 0.00826884i
\(900\) 1.37564e9 + 4.23377e9i 0.0629006 + 0.193588i
\(901\) 1.05253e10 0.479400
\(902\) −5.45361e8 + 8.77593e9i −0.0247435 + 0.398172i
\(903\) 4.61689e9 0.208662
\(904\) −4.05391e9 1.24766e10i −0.182509 0.561705i
\(905\) −1.99793e9 1.45158e9i −0.0896005 0.0650986i
\(906\) 8.41293e9 6.11235e9i 0.375836 0.273061i
\(907\) 3.73818e9 1.15049e10i 0.166355 0.511987i −0.832779 0.553605i \(-0.813252\pi\)
0.999134 + 0.0416190i \(0.0132516\pi\)
\(908\) 1.03074e9 3.17231e9i 0.0456931 0.140629i
\(909\) 1.02075e10 7.41620e9i 0.450762 0.327498i
\(910\) −1.40536e9 1.02105e9i −0.0618219 0.0449162i
\(911\) −3.68351e9 1.13367e10i −0.161416 0.496788i 0.837338 0.546685i \(-0.184111\pi\)
−0.998754 + 0.0498971i \(0.984111\pi\)
\(912\) 3.82872e9 0.167137
\(913\) −2.19356e9 + 3.52988e10i −0.0953900 + 1.53501i
\(914\) −3.06285e10 −1.32683
\(915\) −8.01634e8 2.46718e9i −0.0345941 0.106470i
\(916\) −4.92990e9 3.58178e9i −0.211936 0.153980i
\(917\) 4.14544e10 3.01184e10i 1.77533 1.28985i
\(918\) −3.59638e9 + 1.10685e10i −0.153432 + 0.472215i
\(919\) −3.32800e9 + 1.02425e10i −0.141442 + 0.435314i −0.996536 0.0831586i \(-0.973499\pi\)
0.855094 + 0.518473i \(0.173499\pi\)
\(920\) 3.99451e9 2.90218e9i 0.169124 0.122876i
\(921\) 1.66255e10 + 1.20791e10i 0.701238 + 0.509480i
\(922\) −3.47972e9 1.07095e10i −0.146213 0.449998i
\(923\) −5.07343e9 −0.212371
\(924\) 7.00038e9 8.47527e9i 0.291924 0.353428i
\(925\) 3.24591e10 1.34847
\(926\) −3.85168e9 1.18543e10i −0.159409 0.490609i
\(927\) 1.85090e10 + 1.34476e10i 0.763140 + 0.554454i
\(928\) 2.65593e8 1.92965e8i 0.0109094 0.00792612i
\(929\) 6.84976e9 2.10814e10i 0.280298 0.862669i −0.707470 0.706743i \(-0.750164\pi\)
0.987769 0.155926i \(-0.0498362\pi\)
\(930\) −3.19666e8 + 9.83830e8i −0.0130318 + 0.0401079i
\(931\) −1.44997e10 + 1.05346e10i −0.588889 + 0.427853i
\(932\) −2.14655e9 1.55956e9i −0.0868533 0.0631026i
\(933\) −3.09626e9 9.52930e9i −0.124811 0.384127i
\(934\) 8.30520e8 0.0333531
\(935\) −7.24264e9 2.86112e9i −0.289772 0.114471i
\(936\) 8.06880e8 0.0321620
\(937\) 1.35254e10 + 4.16269e10i 0.537108 + 1.65305i 0.739049 + 0.673652i \(0.235275\pi\)
−0.201941 + 0.979398i \(0.564725\pi\)
\(938\) −2.25194e10 1.63613e10i −0.890935 0.647302i
\(939\) −1.49164e10 + 1.08374e10i −0.587941 + 0.427164i
\(940\) −3.12148e9 + 9.60692e9i −0.122578 + 0.377257i
\(941\) −9.08109e9 + 2.79487e10i −0.355283 + 1.09345i 0.600562 + 0.799578i \(0.294944\pi\)
−0.955845 + 0.293871i \(0.905056\pi\)
\(942\) −1.08800e10 + 7.90480e9i −0.424084 + 0.308115i
\(943\) −1.48773e10 1.08090e10i −0.577742 0.419754i
\(944\) 1.74160e9 + 5.36009e9i 0.0673824 + 0.207382i
\(945\) 1.68958e10 0.651278
\(946\) −2.24813e9 3.53647e9i −0.0863381 0.135816i
\(947\) 1.10450e10 0.422612 0.211306 0.977420i \(-0.432228\pi\)
0.211306 + 0.977420i \(0.432228\pi\)
\(948\) −7.09469e8 2.18352e9i −0.0270461 0.0832393i
\(949\) −7.97077e8 5.79111e8i −0.0302739 0.0219953i
\(950\) 1.14132e10 8.29215e9i 0.431890 0.313787i
\(951\) 4.38051e9 1.34818e10i 0.165156 0.508296i
\(952\) −2.56897e9 + 7.90647e9i −0.0965005 + 0.296998i
\(953\) 3.02857e9 2.20039e9i 0.113348 0.0823519i −0.529667 0.848205i \(-0.677683\pi\)
0.643015 + 0.765854i \(0.277683\pi\)
\(954\) 5.74204e9 + 4.17184e9i 0.214115 + 0.155564i
\(955\) 1.29548e9 + 3.98706e9i 0.0481302 + 0.148129i
\(956\) −5.52224e9 −0.204415
\(957\) −1.38659e9 + 3.57154e8i −0.0511397 + 0.0131724i
\(958\) −1.56820e10 −0.576266
\(959\) 5.08724e8 + 1.56569e9i 0.0186259 + 0.0573245i
\(960\) −8.96491e8 6.51339e8i −0.0327037 0.0237606i
\(961\) 2.15012e10 1.56215e10i 0.781502 0.567794i
\(962\) 1.81805e9 5.59539e9i 0.0658406 0.202637i
\(963\) 4.22110e9 1.29912e10i 0.152312 0.468767i
\(964\) 7.04797e9 5.12065e9i 0.253393 0.184101i
\(965\) −5.66269e9 4.11419e9i −0.202851 0.147380i
\(966\) 7.10423e9 + 2.18646e10i 0.253569 + 0.780407i
\(967\) −3.59199e10 −1.27745 −0.638723 0.769437i \(-0.720537\pi\)
−0.638723 + 0.769437i \(0.720537\pi\)
\(968\) −9.90067e9 1.23528e9i −0.350833 0.0437726i
\(969\) 1.26291e10 0.445901
\(970\) −5.35414e9 1.64784e10i −0.188360 0.579713i
\(971\) 3.25415e10 + 2.36428e10i 1.14070 + 0.828765i 0.987216 0.159386i \(-0.0509515\pi\)
0.153481 + 0.988152i \(0.450951\pi\)
\(972\) −1.05242e10 + 7.64627e9i −0.367584 + 0.267066i
\(973\) −1.87628e10 + 5.77460e10i −0.652985 + 2.00968i
\(974\) −4.31016e9 + 1.32653e10i −0.149464 + 0.460003i
\(975\) −2.21375e9 + 1.60838e9i −0.0764913 + 0.0555742i
\(976\) 2.03359e9 + 1.47749e9i 0.0700146 + 0.0508686i
\(977\) −7.19918e9 2.21568e10i −0.246974 0.760109i −0.995305 0.0967836i \(-0.969145\pi\)
0.748331 0.663325i \(-0.230855\pi\)
\(978\) −1.49361e10 −0.510564
\(979\) 1.31013e10 3.37459e9i 0.446247 0.114943i
\(980\) 5.18722e9 0.176053
\(981\) −7.43449e9 2.28810e10i −0.251426 0.773808i
\(982\) 4.94388e7 + 3.59194e7i 0.00166601 + 0.00121043i
\(983\) −4.52018e10 + 3.28410e10i −1.51781 + 1.10276i −0.555257 + 0.831679i \(0.687380\pi\)
−0.962557 + 0.271078i \(0.912620\pi\)
\(984\) −1.27536e9 + 3.92515e9i −0.0426727 + 0.131333i
\(985\) −4.70232e9 + 1.44723e10i −0.156778 + 0.482514i
\(986\) 8.76063e8 6.36497e8i 0.0291049 0.0211459i
\(987\) −3.80509e10 2.76456e10i −1.25966 0.915199i
\(988\) −7.90167e8 2.43188e9i −0.0260657 0.0802220i
\(989\) 8.76413e9 0.288086
\(990\) −2.81715e9 4.43158e9i −0.0922756 0.145156i
\(991\) −3.98681e10 −1.30127 −0.650636 0.759390i \(-0.725498\pi\)
−0.650636 + 0.759390i \(0.725498\pi\)
\(992\) −3.09747e8 9.53304e8i −0.0100743 0.0310056i
\(993\) −6.28261e9 4.56458e9i −0.203619 0.147938i
\(994\) 2.85168e10 2.07187e10i 0.920976 0.669128i
\(995\) 7.85568e9 2.41773e10i 0.252815 0.778084i
\(996\) −5.12978e9 + 1.57878e10i −0.164509 + 0.506308i
\(997\) −1.00885e10 + 7.32971e9i −0.322398 + 0.234236i −0.737198 0.675677i \(-0.763852\pi\)
0.414800 + 0.909913i \(0.363852\pi\)
\(998\) −1.77566e10 1.29009e10i −0.565460 0.410831i
\(999\) 1.76830e10 + 5.44225e10i 0.561146 + 1.72703i
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 22.8.c.a.5.1 12
11.3 even 5 242.8.a.q.1.5 6
11.8 odd 10 242.8.a.o.1.5 6
11.9 even 5 inner 22.8.c.a.9.1 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
22.8.c.a.5.1 12 1.1 even 1 trivial
22.8.c.a.9.1 yes 12 11.9 even 5 inner
242.8.a.o.1.5 6 11.8 odd 10
242.8.a.q.1.5 6 11.3 even 5