Properties

Label 22.8.c.a.3.1
Level $22$
Weight $8$
Character 22.3
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 3.1
Root \(-7.43190 - 5.39959i\) of defining polynomial
Character \(\chi\) \(=\) 22.3
Dual form 22.8.c.a.15.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-6.47214 + 4.70228i) q^{2} +(-19.8857 - 61.2018i) q^{3} +(19.7771 - 60.8676i) q^{4} +(-37.7557 - 27.4311i) q^{5} +(416.491 + 302.598i) q^{6} +(-204.857 + 630.484i) q^{7} +(158.217 + 486.941i) q^{8} +(-1580.90 + 1148.59i) q^{9} +O(q^{10})\) \(q+(-6.47214 + 4.70228i) q^{2} +(-19.8857 - 61.2018i) q^{3} +(19.7771 - 60.8676i) q^{4} +(-37.7557 - 27.4311i) q^{5} +(416.491 + 302.598i) q^{6} +(-204.857 + 630.484i) q^{7} +(158.217 + 486.941i) q^{8} +(-1580.90 + 1148.59i) q^{9} +373.349 q^{10} +(-3878.93 + 2107.38i) q^{11} -4118.49 q^{12} +(-6223.82 + 4521.87i) q^{13} +(-1638.85 - 5043.87i) q^{14} +(-928.036 + 2856.20i) q^{15} +(-3313.73 - 2407.57i) q^{16} +(12653.3 + 9193.17i) q^{17} +(4830.80 - 14867.7i) q^{18} +(8445.74 + 25993.3i) q^{19} +(-2416.36 + 1755.59i) q^{20} +42660.4 q^{21} +(15195.5 - 31879.1i) q^{22} -15120.2 q^{23} +(26655.4 - 19366.3i) q^{24} +(-23468.9 - 72229.9i) q^{25} +(19018.3 - 58532.3i) q^{26} +(-12125.1 - 8809.39i) q^{27} +(34324.6 + 24938.3i) q^{28} +(28560.9 - 87901.5i) q^{29} +(-7424.29 - 22849.6i) q^{30} +(-263357. + 191340. i) q^{31} +32768.0 q^{32} +(206110. + 195491. i) q^{33} -125123. q^{34} +(25029.4 - 18184.9i) q^{35} +(38646.4 + 118941. i) q^{36} +(21604.8 - 66492.6i) q^{37} +(-176890. - 128518. i) q^{38} +(400511. + 290988. i) q^{39} +(7383.75 - 22724.9i) q^{40} +(-86391.8 - 265887. i) q^{41} +(-276104. + 200601. i) q^{42} -861451. q^{43} +(51556.9 + 277779. i) q^{44} +91195.1 q^{45} +(97859.8 - 71099.3i) q^{46} +(-199698. - 614607. i) q^{47} +(-81451.7 + 250683. i) q^{48} +(310717. + 225749. i) q^{49} +(491540. + 357124. i) q^{50} +(311019. - 957218. i) q^{51} +(152146. + 468258. i) q^{52} +(-849513. + 617208. i) q^{53} +119899. q^{54} +(204260. + 26838.1i) q^{55} -339420. q^{56} +(1.42289e6 - 1.03379e6i) q^{57} +(228487. + 703212. i) q^{58} +(571152. - 1.75783e6i) q^{59} +(155496. + 112975. i) q^{60} +(777106. + 564601. i) q^{61} +(804746. - 2.47675e6i) q^{62} +(-400310. - 1.23203e6i) q^{63} +(-212079. + 154084. i) q^{64} +359024. q^{65} +(-2.25323e6 - 296056. i) q^{66} -1.19782e6 q^{67} +(809812. - 588363. i) q^{68} +(300675. + 925382. i) q^{69} +(-76482.9 + 235390. i) q^{70} +(4.05030e6 + 2.94272e6i) q^{71} +(-809421. - 588079. i) q^{72} +(-1.85870e6 + 5.72050e6i) q^{73} +(172838. + 531941. i) q^{74} +(-3.95391e6 + 2.87268e6i) q^{75} +1.74918e6 q^{76} +(-534041. - 2.87731e6i) q^{77} -3.96047e6 q^{78} +(-410136. + 297981. i) q^{79} +(59070.0 + 181799. i) q^{80} +(-1.61866e6 + 4.98171e6i) q^{81} +(1.80941e6 + 1.31462e6i) q^{82} +(-6.60960e6 - 4.80216e6i) q^{83} +(843699. - 2.59664e6i) q^{84} +(-225556. - 694189. i) q^{85} +(5.57543e6 - 4.05079e6i) q^{86} -5.94768e6 q^{87} +(-1.63988e6 - 1.55539e6i) q^{88} +608839. q^{89} +(-590227. + 428825. i) q^{90} +(-1.57597e6 - 4.85035e6i) q^{91} +(-299033. + 920329. i) q^{92} +(1.69474e7 + 1.23130e7i) q^{93} +(4.18252e6 + 3.03878e6i) q^{94} +(394151. - 1.21307e6i) q^{95} +(-651614. - 2.00546e6i) q^{96} +(8.55176e6 - 6.21322e6i) q^{97} -3.07254e6 q^{98} +(3.71169e6 - 7.78686e6i) 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 \(\left(\mathbb{Z}/22\mathbb{Z}\right)^\times\).

\(n\) \(13\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.47214 + 4.70228i −0.572061 + 0.415627i
\(3\) −19.8857 61.2018i −0.425222 1.30870i −0.902781 0.430100i \(-0.858478\pi\)
0.477559 0.878599i \(-0.341522\pi\)
\(4\) 19.7771 60.8676i 0.154508 0.475528i
\(5\) −37.7557 27.4311i −0.135079 0.0981405i 0.518194 0.855263i \(-0.326605\pi\)
−0.653273 + 0.757123i \(0.726605\pi\)
\(6\) 416.491 + 302.598i 0.787184 + 0.571922i
\(7\) −204.857 + 630.484i −0.225739 + 0.694753i 0.772477 + 0.635043i \(0.219018\pi\)
−0.998216 + 0.0597102i \(0.980982\pi\)
\(8\) 158.217 + 486.941i 0.109254 + 0.336249i
\(9\) −1580.90 + 1148.59i −0.722862 + 0.525190i
\(10\) 373.349 0.118063
\(11\) −3878.93 + 2107.38i −0.878695 + 0.477384i
\(12\) −4118.49 −0.688024
\(13\) −6223.82 + 4521.87i −0.785697 + 0.570842i −0.906683 0.421812i \(-0.861394\pi\)
0.120986 + 0.992654i \(0.461394\pi\)
\(14\) −1638.85 5043.87i −0.159622 0.491265i
\(15\) −928.036 + 2856.20i −0.0709979 + 0.218509i
\(16\) −3313.73 2407.57i −0.202254 0.146946i
\(17\) 12653.3 + 9193.17i 0.624645 + 0.453831i 0.854541 0.519384i \(-0.173839\pi\)
−0.229896 + 0.973215i \(0.573839\pi\)
\(18\) 4830.80 14867.7i 0.195238 0.600882i
\(19\) 8445.74 + 25993.3i 0.282488 + 0.869409i 0.987140 + 0.159856i \(0.0511030\pi\)
−0.704652 + 0.709553i \(0.748897\pi\)
\(20\) −2416.36 + 1755.59i −0.0675394 + 0.0490703i
\(21\) 42660.4 1.00521
\(22\) 15195.5 31879.1i 0.304254 0.638302i
\(23\) −15120.2 −0.259125 −0.129563 0.991571i \(-0.541357\pi\)
−0.129563 + 0.991571i \(0.541357\pi\)
\(24\) 26655.4 19366.3i 0.393592 0.285961i
\(25\) −23468.9 72229.9i −0.300402 0.924543i
\(26\) 19018.3 58532.3i 0.212210 0.653114i
\(27\) −12125.1 8809.39i −0.118553 0.0861336i
\(28\) 34324.6 + 24938.3i 0.295496 + 0.214691i
\(29\) 28560.9 87901.5i 0.217460 0.669273i −0.781510 0.623893i \(-0.785550\pi\)
0.998970 0.0453799i \(-0.0144498\pi\)
\(30\) −7424.29 22849.6i −0.0502031 0.154509i
\(31\) −263357. + 191340.i −1.58774 + 1.15356i −0.680653 + 0.732606i \(0.738304\pi\)
−0.907083 + 0.420952i \(0.861696\pi\)
\(32\) 32768.0 0.176777
\(33\) 206110. + 195491.i 0.998392 + 0.946953i
\(34\) −125123. −0.545960
\(35\) 25029.4 18184.9i 0.0986760 0.0716923i
\(36\) 38646.4 + 118941.i 0.138054 + 0.424888i
\(37\) 21604.8 66492.6i 0.0701203 0.215808i −0.909855 0.414926i \(-0.863808\pi\)
0.979976 + 0.199118i \(0.0638076\pi\)
\(38\) −176890. 128518.i −0.522950 0.379946i
\(39\) 400511. + 290988.i 1.08116 + 0.785506i
\(40\) 7383.75 22724.9i 0.0182418 0.0561424i
\(41\) −86391.8 265887.i −0.195762 0.602494i −0.999967 0.00814181i \(-0.997408\pi\)
0.804205 0.594353i \(-0.202592\pi\)
\(42\) −276104. + 200601.i −0.575043 + 0.417793i
\(43\) −861451. −1.65231 −0.826154 0.563444i \(-0.809476\pi\)
−0.826154 + 0.563444i \(0.809476\pi\)
\(44\) 51556.9 + 277779.i 0.0912437 + 0.491604i
\(45\) 91195.1 0.149186
\(46\) 97859.8 71099.3i 0.148235 0.107699i
\(47\) −199698. 614607.i −0.280563 0.863485i −0.987694 0.156402i \(-0.950011\pi\)
0.707130 0.707083i \(-0.249989\pi\)
\(48\) −81451.7 + 250683.i −0.106306 + 0.327175i
\(49\) 310717. + 225749.i 0.377293 + 0.274119i
\(50\) 491540. + 357124.i 0.556114 + 0.404040i
\(51\) 311019. 957218.i 0.328315 1.01045i
\(52\) 152146. + 468258.i 0.150055 + 0.461821i
\(53\) −849513. + 617208.i −0.783799 + 0.569463i −0.906117 0.423028i \(-0.860967\pi\)
0.122318 + 0.992491i \(0.460967\pi\)
\(54\) 119899. 0.103619
\(55\) 204260. + 26838.1i 0.165544 + 0.0217511i
\(56\) −339420. −0.258273
\(57\) 1.42289e6 1.03379e6i 1.01767 0.739384i
\(58\) 228487. + 703212.i 0.153767 + 0.473247i
\(59\) 571152. 1.75783e6i 0.362051 1.11428i −0.589756 0.807581i \(-0.700776\pi\)
0.951807 0.306697i \(-0.0992239\pi\)
\(60\) 155496. + 112975.i 0.0929375 + 0.0675230i
\(61\) 777106. + 564601.i 0.438355 + 0.318484i 0.784981 0.619520i \(-0.212673\pi\)
−0.346626 + 0.938003i \(0.612673\pi\)
\(62\) 804746. 2.47675e6i 0.428833 1.31981i
\(63\) −400310. 1.23203e6i −0.201699 0.620767i
\(64\) −212079. + 154084.i −0.101127 + 0.0734732i
\(65\) 359024. 0.162154
\(66\) −2.25323e6 296056.i −0.964721 0.126757i
\(67\) −1.19782e6 −0.486553 −0.243276 0.969957i \(-0.578222\pi\)
−0.243276 + 0.969957i \(0.578222\pi\)
\(68\) 809812. 588363.i 0.312322 0.226915i
\(69\) 300675. + 925382.i 0.110186 + 0.339117i
\(70\) −76482.9 + 235390.i −0.0266515 + 0.0820248i
\(71\) 4.05030e6 + 2.94272e6i 1.34302 + 0.975762i 0.999327 + 0.0366810i \(0.0116785\pi\)
0.343695 + 0.939081i \(0.388321\pi\)
\(72\) −809421. 588079.i −0.255570 0.185683i
\(73\) −1.85870e6 + 5.72050e6i −0.559217 + 1.72109i 0.125322 + 0.992116i \(0.460004\pi\)
−0.684539 + 0.728977i \(0.739996\pi\)
\(74\) 172838. + 531941.i 0.0495825 + 0.152599i
\(75\) −3.95391e6 + 2.87268e6i −1.08221 + 0.786272i
\(76\) 1.74918e6 0.457075
\(77\) −534041. 2.87731e6i −0.133308 0.718240i
\(78\) −3.96047e6 −0.944966
\(79\) −410136. + 297981.i −0.0935907 + 0.0679976i −0.633596 0.773664i \(-0.718422\pi\)
0.540006 + 0.841661i \(0.318422\pi\)
\(80\) 59070.0 + 181799.i 0.0128989 + 0.0396987i
\(81\) −1.61866e6 + 4.98171e6i −0.338421 + 1.04155i
\(82\) 1.80941e6 + 1.31462e6i 0.362401 + 0.263300i
\(83\) −6.60960e6 4.80216e6i −1.26883 0.921856i −0.269671 0.962953i \(-0.586915\pi\)
−0.999155 + 0.0410968i \(0.986915\pi\)
\(84\) 843699. 2.59664e6i 0.155314 0.478007i
\(85\) −225556. 694189.i −0.0398371 0.122606i
\(86\) 5.57543e6 4.05079e6i 0.945222 0.686744i
\(87\) −5.94768e6 −0.968345
\(88\) −1.63988e6 1.55539e6i −0.256521 0.243304i
\(89\) 608839. 0.0915456 0.0457728 0.998952i \(-0.485425\pi\)
0.0457728 + 0.998952i \(0.485425\pi\)
\(90\) −590227. + 428825.i −0.0853435 + 0.0620057i
\(91\) −1.57597e6 4.85035e6i −0.219232 0.674727i
\(92\) −299033. + 920329.i −0.0400370 + 0.123221i
\(93\) 1.69474e7 + 1.23130e7i 2.18480 + 1.58735i
\(94\) 4.18252e6 + 3.03878e6i 0.519387 + 0.377357i
\(95\) 394151. 1.21307e6i 0.0471661 0.145162i
\(96\) −651614. 2.00546e6i −0.0751694 0.231347i
\(97\) 8.55176e6 6.21322e6i 0.951381 0.691218i 0.000247580 1.00000i \(-0.499921\pi\)
0.951133 + 0.308782i \(0.0999212\pi\)
\(98\) −3.07254e6 −0.329766
\(99\) 3.71169e6 7.78686e6i 0.384458 0.806565i
\(100\) −4.86061e6 −0.486061
\(101\) 1.33572e7 9.70455e6i 1.29000 0.937240i 0.290195 0.956968i \(-0.406280\pi\)
0.999805 + 0.0197276i \(0.00627991\pi\)
\(102\) 2.48815e6 + 7.65774e6i 0.232154 + 0.714497i
\(103\) −5.14609e6 + 1.58380e7i −0.464031 + 1.42814i 0.396167 + 0.918179i \(0.370340\pi\)
−0.860198 + 0.509961i \(0.829660\pi\)
\(104\) −3.18660e6 2.31520e6i −0.277786 0.201823i
\(105\) −1.61067e6 1.17022e6i −0.135783 0.0986521i
\(106\) 2.59588e6 7.98930e6i 0.211697 0.651536i
\(107\) −3.01459e6 9.27795e6i −0.237895 0.732164i −0.996724 0.0808752i \(-0.974228\pi\)
0.758830 0.651289i \(-0.225772\pi\)
\(108\) −776005. + 563801.i −0.0592764 + 0.0430668i
\(109\) −9.09015e6 −0.672323 −0.336162 0.941804i \(-0.609129\pi\)
−0.336162 + 0.941804i \(0.609129\pi\)
\(110\) −1.44820e6 + 786786.i −0.103742 + 0.0563615i
\(111\) −4.49909e6 −0.312244
\(112\) 2.19677e6 1.59605e6i 0.147748 0.107345i
\(113\) −4.00988e6 1.23412e7i −0.261431 0.804602i −0.992494 0.122292i \(-0.960975\pi\)
0.731063 0.682310i \(-0.239025\pi\)
\(114\) −4.34796e6 + 1.33816e7i −0.274864 + 0.845946i
\(115\) 570873. + 414763.i 0.0350023 + 0.0254307i
\(116\) −4.78550e6 3.47687e6i −0.284659 0.206817i
\(117\) 4.64546e6 1.42972e7i 0.268150 0.825281i
\(118\) 4.56922e6 + 1.40626e7i 0.256009 + 0.787914i
\(119\) −8.38826e6 + 6.09443e6i −0.456307 + 0.331527i
\(120\) −1.53763e6 −0.0812303
\(121\) 1.06051e7 1.63488e7i 0.544209 0.838949i
\(122\) −7.68445e6 −0.383136
\(123\) −1.45548e7 + 1.05747e7i −0.705241 + 0.512388i
\(124\) 6.43797e6 + 1.98140e7i 0.303231 + 0.933248i
\(125\) −2.22193e6 + 6.83841e6i −0.101753 + 0.313163i
\(126\) 8.38421e6 + 6.09148e6i 0.373392 + 0.271285i
\(127\) −1.02339e6 743536.i −0.0443331 0.0322099i 0.565398 0.824818i \(-0.308723\pi\)
−0.609731 + 0.792608i \(0.708723\pi\)
\(128\) 648056. 1.99451e6i 0.0273135 0.0840623i
\(129\) 1.71305e7 + 5.27224e7i 0.702598 + 2.16237i
\(130\) −2.32366e6 + 1.68823e6i −0.0927620 + 0.0673955i
\(131\) −1.37648e7 −0.534958 −0.267479 0.963564i \(-0.586191\pi\)
−0.267479 + 0.963564i \(0.586191\pi\)
\(132\) 1.59753e7 8.67921e6i 0.604563 0.328451i
\(133\) −1.81185e7 −0.667793
\(134\) 7.75245e6 5.63249e6i 0.278338 0.202224i
\(135\) 216140. + 665209.i 0.00756077 + 0.0232697i
\(136\) −2.47457e6 + 7.61593e6i −0.0843554 + 0.259619i
\(137\) 3.27915e6 + 2.38244e6i 0.108953 + 0.0791590i 0.640928 0.767601i \(-0.278550\pi\)
−0.531975 + 0.846760i \(0.678550\pi\)
\(138\) −6.29741e6 4.57534e6i −0.203979 0.148199i
\(139\) 1.64965e7 5.07711e7i 0.521004 1.60349i −0.251081 0.967966i \(-0.580786\pi\)
0.772085 0.635519i \(-0.219214\pi\)
\(140\) −611864. 1.88312e6i −0.0188454 0.0580003i
\(141\) −3.36439e7 + 2.44437e7i −1.01074 + 0.734346i
\(142\) −4.00516e7 −1.17384
\(143\) 1.46125e7 3.06560e7i 0.417877 0.876675i
\(144\) 8.00399e6 0.223377
\(145\) −3.48957e6 + 2.53532e6i −0.0950570 + 0.0690630i
\(146\) −1.48696e7 4.57640e7i −0.395426 1.21700i
\(147\) 7.63743e6 2.35056e7i 0.198306 0.610324i
\(148\) −3.61997e6 2.63006e6i −0.0917886 0.0666883i
\(149\) 3.54889e7 + 2.57842e7i 0.878902 + 0.638560i 0.932961 0.359978i \(-0.117216\pi\)
−0.0540588 + 0.998538i \(0.517216\pi\)
\(150\) 1.20821e7 3.71848e7i 0.292295 0.899592i
\(151\) 2.35137e7 + 7.23679e7i 0.555779 + 1.71051i 0.693876 + 0.720094i \(0.255902\pi\)
−0.138097 + 0.990419i \(0.544098\pi\)
\(152\) −1.13209e7 + 8.22515e6i −0.261475 + 0.189973i
\(153\) −3.05628e7 −0.689880
\(154\) 1.69863e7 + 1.61112e7i 0.374781 + 0.355471i
\(155\) 1.51919e7 0.327680
\(156\) 2.56327e7 1.86233e7i 0.540578 0.392753i
\(157\) −1.45880e7 4.48974e7i −0.300849 0.925917i −0.981194 0.193025i \(-0.938170\pi\)
0.680345 0.732892i \(-0.261830\pi\)
\(158\) 1.25326e6 3.85715e6i 0.0252780 0.0777976i
\(159\) 5.46674e7 + 3.97182e7i 1.07854 + 0.783609i
\(160\) −1.23718e6 898863.i −0.0238788 0.0173490i
\(161\) 3.09747e6 9.53302e6i 0.0584946 0.180028i
\(162\) −1.29492e7 3.98537e7i −0.239300 0.736488i
\(163\) −1.56352e7 + 1.13596e7i −0.282779 + 0.205451i −0.720128 0.693841i \(-0.755917\pi\)
0.437350 + 0.899291i \(0.355917\pi\)
\(164\) −1.78925e7 −0.316750
\(165\) −2.41930e6 1.30347e7i −0.0419272 0.225896i
\(166\) 6.53593e7 1.10899
\(167\) 1.98729e7 1.44385e7i 0.330182 0.239891i −0.410326 0.911939i \(-0.634585\pi\)
0.740508 + 0.672048i \(0.234585\pi\)
\(168\) 6.74959e6 + 2.07731e7i 0.109823 + 0.338002i
\(169\) −1.10174e6 + 3.39080e6i −0.0175580 + 0.0540380i
\(170\) 4.72410e6 + 3.43226e6i 0.0737476 + 0.0535808i
\(171\) −4.32076e7 3.13921e7i −0.660805 0.480103i
\(172\) −1.70370e7 + 5.24345e7i −0.255296 + 0.785720i
\(173\) 4.96854e6 + 1.52916e7i 0.0729571 + 0.224539i 0.980885 0.194587i \(-0.0623366\pi\)
−0.907928 + 0.419126i \(0.862337\pi\)
\(174\) 3.84942e7 2.79677e7i 0.553953 0.402470i
\(175\) 5.03475e7 0.710142
\(176\) 1.79274e7 + 2.35552e6i 0.247870 + 0.0325681i
\(177\) −1.18940e8 −1.61221
\(178\) −3.94049e6 + 2.86293e6i −0.0523697 + 0.0380488i
\(179\) 2.49535e7 + 7.67991e7i 0.325197 + 1.00085i 0.971352 + 0.237647i \(0.0763761\pi\)
−0.646155 + 0.763207i \(0.723624\pi\)
\(180\) 1.80357e6 5.55083e6i 0.0230505 0.0709421i
\(181\) −4.97413e7 3.61392e7i −0.623508 0.453005i 0.230637 0.973040i \(-0.425919\pi\)
−0.854145 + 0.520035i \(0.825919\pi\)
\(182\) 3.30076e7 + 2.39814e7i 0.405849 + 0.294867i
\(183\) 1.91013e7 5.87878e7i 0.230401 0.709101i
\(184\) −2.39226e6 7.36263e6i −0.0283104 0.0871306i
\(185\) −2.63967e6 + 1.91783e6i −0.0306513 + 0.0222695i
\(186\) −1.67585e8 −1.90959
\(187\) −6.84549e7 8.99441e6i −0.765524 0.100584i
\(188\) −4.13591e7 −0.453961
\(189\) 8.03808e6 5.84001e6i 0.0866036 0.0629212i
\(190\) 3.15321e6 + 9.70457e6i 0.0333515 + 0.102645i
\(191\) −4.40152e7 + 1.35465e8i −0.457074 + 1.40673i 0.411610 + 0.911360i \(0.364967\pi\)
−0.868683 + 0.495368i \(0.835033\pi\)
\(192\) 1.36476e7 + 9.91554e6i 0.139156 + 0.101103i
\(193\) −3.30071e7 2.39811e7i −0.330489 0.240114i 0.410149 0.912019i \(-0.365477\pi\)
−0.740638 + 0.671904i \(0.765477\pi\)
\(194\) −2.61318e7 + 8.04255e7i −0.256959 + 0.790839i
\(195\) −7.13944e6 2.19729e7i −0.0689514 0.212211i
\(196\) 1.98859e7 1.44479e7i 0.188646 0.137060i
\(197\) 1.24454e8 1.15978 0.579892 0.814694i \(-0.303095\pi\)
0.579892 + 0.814694i \(0.303095\pi\)
\(198\) 1.25934e7 + 6.78511e7i 0.115296 + 0.621196i
\(199\) 2.16245e7 0.194518 0.0972592 0.995259i \(-0.468992\pi\)
0.0972592 + 0.995259i \(0.468992\pi\)
\(200\) 3.14585e7 2.28560e7i 0.278057 0.202020i
\(201\) 2.38195e7 + 7.33087e7i 0.206893 + 0.636751i
\(202\) −4.08159e7 + 1.25618e8i −0.348417 + 1.07232i
\(203\) 4.95695e7 + 3.60144e7i 0.415890 + 0.302162i
\(204\) −5.21125e7 3.78620e7i −0.429770 0.312247i
\(205\) −4.03178e6 + 1.24086e7i −0.0326858 + 0.100596i
\(206\) −4.11687e7 1.26704e8i −0.328119 1.00985i
\(207\) 2.39035e7 1.73669e7i 0.187312 0.136090i
\(208\) 3.15108e7 0.242794
\(209\) −8.75382e7 8.30280e7i −0.663262 0.629090i
\(210\) 1.59272e7 0.118679
\(211\) −1.69714e7 + 1.23304e7i −0.124374 + 0.0903628i −0.648233 0.761442i \(-0.724492\pi\)
0.523859 + 0.851805i \(0.324492\pi\)
\(212\) 2.07671e7 + 6.39144e7i 0.149692 + 0.460706i
\(213\) 9.95566e7 3.06404e8i 0.705897 2.17253i
\(214\) 6.31383e7 + 4.58727e7i 0.440398 + 0.319968i
\(215\) 3.25247e7 + 2.36306e7i 0.223192 + 0.162158i
\(216\) 2.37126e6 7.29799e6i 0.0160100 0.0492737i
\(217\) −6.66863e7 2.05239e8i −0.443024 1.36349i
\(218\) 5.88327e7 4.27444e7i 0.384610 0.279436i
\(219\) 3.87067e8 2.49018
\(220\) 5.67323e6 1.19020e7i 0.0359212 0.0753600i
\(221\) −1.20322e8 −0.749848
\(222\) 2.91188e7 2.11560e7i 0.178623 0.129777i
\(223\) −1.01635e8 3.12800e8i −0.613727 1.88886i −0.418949 0.908010i \(-0.637601\pi\)
−0.194778 0.980847i \(-0.562399\pi\)
\(224\) −6.71274e6 + 2.06597e7i −0.0399054 + 0.122816i
\(225\) 1.20065e8 + 8.72321e7i 0.702711 + 0.510549i
\(226\) 8.39841e7 + 6.10180e7i 0.483969 + 0.351624i
\(227\) −6.76118e7 + 2.08088e8i −0.383647 + 1.18074i 0.553810 + 0.832643i \(0.313173\pi\)
−0.937457 + 0.348101i \(0.886827\pi\)
\(228\) −3.47837e7 1.07053e8i −0.194358 0.598174i
\(229\) 8.58949e7 6.24063e7i 0.472654 0.343403i −0.325821 0.945431i \(-0.605641\pi\)
0.798475 + 0.602029i \(0.205641\pi\)
\(230\) −5.64510e6 −0.0305931
\(231\) −1.65477e8 + 8.99016e7i −0.883275 + 0.479872i
\(232\) 4.73216e7 0.248801
\(233\) −2.42929e8 + 1.76498e8i −1.25815 + 0.914102i −0.998666 0.0516439i \(-0.983554\pi\)
−0.259488 + 0.965746i \(0.583554\pi\)
\(234\) 3.71637e7 + 1.14378e8i 0.189611 + 0.583562i
\(235\) −9.31962e6 + 2.86828e7i −0.0468447 + 0.144173i
\(236\) −9.56989e7 6.95294e7i −0.473931 0.344331i
\(237\) 2.63928e7 + 1.91755e7i 0.128785 + 0.0935680i
\(238\) 2.56322e7 7.88879e7i 0.123244 0.379307i
\(239\) 2.35874e7 + 7.25947e7i 0.111760 + 0.343963i 0.991258 0.131941i \(-0.0421209\pi\)
−0.879497 + 0.475904i \(0.842121\pi\)
\(240\) 9.95177e6 7.23038e6i 0.0464687 0.0337615i
\(241\) 5.09450e7 0.234445 0.117223 0.993106i \(-0.462601\pi\)
0.117223 + 0.993106i \(0.462601\pi\)
\(242\) 8.23879e6 + 1.55680e8i 0.0373689 + 0.706119i
\(243\) 3.04300e8 1.36044
\(244\) 4.97348e7 3.61344e7i 0.219177 0.159242i
\(245\) −5.53878e6 1.70466e7i −0.0240621 0.0740555i
\(246\) 4.44755e7 1.36881e8i 0.190479 0.586235i
\(247\) −1.70103e8 1.23587e8i −0.718245 0.521836i
\(248\) −1.34839e8 9.79660e7i −0.561349 0.407844i
\(249\) −1.62464e8 + 5.00014e8i −0.666899 + 2.05250i
\(250\) −1.77755e7 5.47073e7i −0.0719500 0.221439i
\(251\) −2.92702e8 + 2.12661e8i −1.16834 + 0.848846i −0.990809 0.135270i \(-0.956810\pi\)
−0.177528 + 0.984116i \(0.556810\pi\)
\(252\) −8.29076e7 −0.326357
\(253\) 5.86502e7 3.18639e7i 0.227692 0.123702i
\(254\) 1.01198e7 0.0387485
\(255\) −3.80003e7 + 2.76088e7i −0.143515 + 0.104270i
\(256\) 5.18444e6 + 1.59561e7i 0.0193136 + 0.0594410i
\(257\) 3.46749e7 1.06718e8i 0.127423 0.392169i −0.866912 0.498462i \(-0.833898\pi\)
0.994335 + 0.106294i \(0.0338983\pi\)
\(258\) −3.58787e8 2.60674e8i −1.30067 0.944993i
\(259\) 3.74966e7 + 2.72429e7i 0.134104 + 0.0974326i
\(260\) 7.10046e6 2.18530e7i 0.0250541 0.0771087i
\(261\) 5.58109e7 + 1.71768e8i 0.194302 + 0.598000i
\(262\) 8.90874e7 6.47258e7i 0.306029 0.222343i
\(263\) 4.50529e7 0.152713 0.0763567 0.997081i \(-0.475671\pi\)
0.0763567 + 0.997081i \(0.475671\pi\)
\(264\) −6.25826e7 + 1.31294e8i −0.209334 + 0.439167i
\(265\) 4.90047e7 0.161762
\(266\) 1.17266e8 8.51984e7i 0.382019 0.277553i
\(267\) −1.21072e7 3.72620e7i −0.0389272 0.119806i
\(268\) −2.36894e7 + 7.29084e7i −0.0751765 + 0.231369i
\(269\) −1.10615e8 8.03668e7i −0.346484 0.251735i 0.400909 0.916118i \(-0.368694\pi\)
−0.747392 + 0.664383i \(0.768694\pi\)
\(270\) −4.52689e6 3.28898e6i −0.0139967 0.0101692i
\(271\) 2.13371e7 6.56688e7i 0.0651243 0.200432i −0.913200 0.407513i \(-0.866396\pi\)
0.978324 + 0.207081i \(0.0663963\pi\)
\(272\) −1.97965e7 6.09274e7i −0.0596483 0.183578i
\(273\) −2.65511e8 + 1.92905e8i −0.789792 + 0.573818i
\(274\) −3.24260e7 −0.0952284
\(275\) 2.43250e8 + 2.30717e8i 0.705324 + 0.668984i
\(276\) 6.22723e7 0.178284
\(277\) −1.36711e8 + 9.93265e7i −0.386478 + 0.280793i −0.764011 0.645203i \(-0.776773\pi\)
0.377533 + 0.925996i \(0.376773\pi\)
\(278\) 1.31972e8 + 4.06169e8i 0.368405 + 1.13384i
\(279\) 1.96569e8 6.04978e8i 0.541877 1.66773i
\(280\) 1.28150e7 + 9.31067e6i 0.0348872 + 0.0253471i
\(281\) 3.99435e8 + 2.90207e8i 1.07393 + 0.780253i 0.976614 0.215001i \(-0.0689756\pi\)
0.0973118 + 0.995254i \(0.468976\pi\)
\(282\) 1.02807e8 3.16406e8i 0.272992 0.840182i
\(283\) 2.85481e7 + 8.78619e7i 0.0748728 + 0.230435i 0.981488 0.191523i \(-0.0613428\pi\)
−0.906615 + 0.421958i \(0.861343\pi\)
\(284\) 2.59219e8 1.88334e8i 0.671511 0.487881i
\(285\) −8.20801e7 −0.210030
\(286\) 4.95789e7 + 2.67122e8i 0.125319 + 0.675193i
\(287\) 1.85335e8 0.462776
\(288\) −5.18029e7 + 3.76370e7i −0.127785 + 0.0928414i
\(289\) −5.12096e7 1.57607e8i −0.124798 0.384090i
\(290\) 1.06632e7 3.28179e7i 0.0256740 0.0790165i
\(291\) −5.50317e8 3.99829e8i −1.30915 0.951150i
\(292\) 3.11434e8 + 2.26270e8i 0.732024 + 0.531847i
\(293\) −4.95767e6 + 1.52581e7i −0.0115144 + 0.0354377i −0.956649 0.291245i \(-0.905931\pi\)
0.945134 + 0.326682i \(0.105931\pi\)
\(294\) 6.10995e7 + 1.88045e8i 0.140224 + 0.431565i
\(295\) −6.97834e7 + 5.07006e7i −0.158261 + 0.114984i
\(296\) 3.57962e7 0.0802262
\(297\) 6.55971e7 + 8.61893e6i 0.145290 + 0.0190900i
\(298\) −3.50933e8 −0.768188
\(299\) 9.41052e7 6.83714e7i 0.203594 0.147920i
\(300\) 9.66565e7 + 2.97478e8i 0.206684 + 0.636108i
\(301\) 1.76474e8 5.43131e8i 0.372991 1.14795i
\(302\) −4.92478e8 3.57806e8i −1.02888 0.747522i
\(303\) −8.59553e8 6.24501e8i −1.77510 1.28969i
\(304\) 3.45937e7 1.06469e8i 0.0706220 0.217352i
\(305\) −1.38526e7 4.26338e7i −0.0279563 0.0860408i
\(306\) 1.97807e8 1.43715e8i 0.394654 0.286733i
\(307\) 4.87741e8 0.962066 0.481033 0.876703i \(-0.340262\pi\)
0.481033 + 0.876703i \(0.340262\pi\)
\(308\) −1.85697e8 2.43991e7i −0.362141 0.0475824i
\(309\) 1.07165e9 2.06632
\(310\) −9.83239e7 + 7.14365e7i −0.187453 + 0.136193i
\(311\) −2.22745e8 6.85539e8i −0.419901 1.29232i −0.907793 0.419418i \(-0.862234\pi\)
0.487892 0.872904i \(-0.337766\pi\)
\(312\) −7.83266e7 + 2.41065e8i −0.146005 + 0.449358i
\(313\) −1.89881e8 1.37956e8i −0.350006 0.254295i 0.398865 0.917010i \(-0.369404\pi\)
−0.748872 + 0.662715i \(0.769404\pi\)
\(314\) 3.05536e8 + 2.21985e8i 0.556940 + 0.404641i
\(315\) −1.86819e7 + 5.74970e7i −0.0336771 + 0.103647i
\(316\) 1.00261e7 + 3.08572e7i 0.0178742 + 0.0550112i
\(317\) 5.35521e8 3.89079e8i 0.944212 0.686010i −0.00521915 0.999986i \(-0.501661\pi\)
0.949431 + 0.313976i \(0.101661\pi\)
\(318\) −5.40581e8 −0.942683
\(319\) 7.44555e7 + 4.01153e8i 0.128419 + 0.691898i
\(320\) 1.22339e7 0.0208708
\(321\) −5.07880e8 + 3.68996e8i −0.857025 + 0.622665i
\(322\) 2.47797e7 + 7.62642e7i 0.0413620 + 0.127299i
\(323\) −1.32094e8 + 4.06545e8i −0.218110 + 0.671273i
\(324\) 2.71212e8 + 1.97047e8i 0.442998 + 0.321857i
\(325\) 4.72681e8 + 3.43423e8i 0.763794 + 0.554929i
\(326\) 4.77769e7 1.47042e8i 0.0763759 0.235061i
\(327\) 1.80764e8 + 5.56333e8i 0.285887 + 0.879869i
\(328\) 1.15802e8 8.41354e7i 0.181200 0.131650i
\(329\) 4.28409e8 0.663243
\(330\) 7.69511e7 + 7.29864e7i 0.117873 + 0.111800i
\(331\) −1.40023e8 −0.212227 −0.106113 0.994354i \(-0.533841\pi\)
−0.106113 + 0.994354i \(0.533841\pi\)
\(332\) −4.23015e8 + 3.07338e8i −0.634413 + 0.460928i
\(333\) 4.22179e7 + 1.29933e8i 0.0626530 + 0.192826i
\(334\) −6.07261e7 + 1.86896e8i −0.0891790 + 0.274465i
\(335\) 4.52245e7 + 3.28575e7i 0.0657230 + 0.0477505i
\(336\) −1.41365e8 1.02708e8i −0.203308 0.147712i
\(337\) −3.45614e8 + 1.06369e9i −0.491911 + 1.51395i 0.329806 + 0.944049i \(0.393017\pi\)
−0.821716 + 0.569897i \(0.806983\pi\)
\(338\) −8.81391e6 2.71264e7i −0.0124154 0.0382106i
\(339\) −6.75562e8 + 4.90824e8i −0.941816 + 0.684269i
\(340\) −4.67145e7 −0.0644578
\(341\) 6.18318e8 1.29719e9i 0.844446 1.77158i
\(342\) 4.27260e8 0.577565
\(343\) −6.47667e8 + 4.70558e8i −0.866608 + 0.629627i
\(344\) −1.36296e8 4.19476e8i −0.180521 0.555588i
\(345\) 1.40321e7 4.31863e7i 0.0183973 0.0566212i
\(346\) −1.04062e8 7.56058e7i −0.135060 0.0981271i
\(347\) −8.82931e8 6.41487e8i −1.13442 0.824204i −0.148087 0.988974i \(-0.547312\pi\)
−0.986332 + 0.164771i \(0.947312\pi\)
\(348\) −1.17628e8 + 3.62021e8i −0.149618 + 0.460476i
\(349\) −8.93081e7 2.74862e8i −0.112461 0.346119i 0.878948 0.476918i \(-0.158246\pi\)
−0.991409 + 0.130798i \(0.958246\pi\)
\(350\) −3.25856e8 + 2.36748e8i −0.406245 + 0.295154i
\(351\) 1.15299e8 0.142315
\(352\) −1.27105e8 + 6.90545e7i −0.155333 + 0.0843903i
\(353\) −1.22512e9 −1.48241 −0.741204 0.671279i \(-0.765745\pi\)
−0.741204 + 0.671279i \(0.765745\pi\)
\(354\) 7.69795e8 5.59289e8i 0.922282 0.670077i
\(355\) −7.21999e7 2.22209e8i −0.0856520 0.263610i
\(356\) 1.20411e7 3.70586e7i 0.0141446 0.0435325i
\(357\) 5.39796e8 + 3.92185e8i 0.627901 + 0.456196i
\(358\) −5.22634e8 3.79716e8i −0.602014 0.437389i
\(359\) 5.74309e7 1.76754e8i 0.0655112 0.201623i −0.912943 0.408087i \(-0.866196\pi\)
0.978454 + 0.206465i \(0.0661959\pi\)
\(360\) 1.44286e7 + 4.44066e7i 0.0162992 + 0.0501636i
\(361\) 1.18836e8 8.63393e7i 0.132945 0.0965902i
\(362\) 4.91869e8 0.544966
\(363\) −1.21146e9 3.23945e8i −1.32934 0.355466i
\(364\) −3.26397e8 −0.354725
\(365\) 2.27096e8 1.64995e8i 0.244447 0.177601i
\(366\) 1.52810e8 + 4.70302e8i 0.162918 + 0.501410i
\(367\) −5.49861e8 + 1.69230e9i −0.580659 + 1.78709i 0.0353842 + 0.999374i \(0.488735\pi\)
−0.616044 + 0.787712i \(0.711265\pi\)
\(368\) 5.01042e7 + 3.64029e7i 0.0524091 + 0.0380775i
\(369\) 4.41972e8 + 3.21111e8i 0.457933 + 0.332708i
\(370\) 8.06611e6 2.48249e7i 0.00827863 0.0254790i
\(371\) −2.15111e8 6.62043e8i −0.218703 0.673097i
\(372\) 1.08463e9 7.88031e8i 1.09240 0.793675i
\(373\) 1.37112e8 0.136802 0.0684011 0.997658i \(-0.478210\pi\)
0.0684011 + 0.997658i \(0.478210\pi\)
\(374\) 4.85343e8 2.63681e8i 0.479732 0.260632i
\(375\) 4.62707e8 0.453103
\(376\) 2.67682e8 1.94482e8i 0.259693 0.188678i
\(377\) 2.19721e8 + 6.76232e8i 0.211192 + 0.649981i
\(378\) −2.45622e7 + 7.55946e7i −0.0233908 + 0.0719896i
\(379\) 1.57355e9 + 1.14325e9i 1.48472 + 1.07871i 0.975999 + 0.217777i \(0.0698804\pi\)
0.508718 + 0.860933i \(0.330120\pi\)
\(380\) −6.60416e7 4.79820e7i −0.0617412 0.0448576i
\(381\) −2.51550e7 + 7.74190e7i −0.0233016 + 0.0717150i
\(382\) −3.52122e8 1.08372e9i −0.323200 0.994707i
\(383\) 1.33359e9 9.68910e8i 1.21290 0.881227i 0.217413 0.976080i \(-0.430238\pi\)
0.995491 + 0.0948527i \(0.0302380\pi\)
\(384\) −1.34955e8 −0.121627
\(385\) −5.87649e7 + 1.23284e8i −0.0524814 + 0.110102i
\(386\) 3.26393e8 0.288858
\(387\) 1.36187e9 9.89456e8i 1.19439 0.867777i
\(388\) −2.09055e8 6.43404e8i −0.181698 0.559207i
\(389\) 1.82011e8 5.60171e8i 0.156774 0.482500i −0.841563 0.540160i \(-0.818364\pi\)
0.998336 + 0.0576599i \(0.0183639\pi\)
\(390\) 1.49530e8 + 1.08640e8i 0.127645 + 0.0927394i
\(391\) −1.91320e8 1.39002e8i −0.161861 0.117599i
\(392\) −6.07659e7 + 1.87018e8i −0.0509517 + 0.156813i
\(393\) 2.73722e8 + 8.42429e8i 0.227476 + 0.700099i
\(394\) −8.05483e8 + 5.85217e8i −0.663467 + 0.482037i
\(395\) 2.36589e7 0.0193154
\(396\) −4.00561e8 3.79923e8i −0.324142 0.307442i
\(397\) −1.18729e9 −0.952340 −0.476170 0.879353i \(-0.657975\pi\)
−0.476170 + 0.879353i \(0.657975\pi\)
\(398\) −1.39957e8 + 1.01685e8i −0.111277 + 0.0808471i
\(399\) 3.60299e8 + 1.10889e9i 0.283960 + 0.873940i
\(400\) −9.61287e7 + 2.95854e8i −0.0751006 + 0.231136i
\(401\) −3.57933e8 2.60054e8i −0.277202 0.201399i 0.440494 0.897756i \(-0.354803\pi\)
−0.717696 + 0.696356i \(0.754803\pi\)
\(402\) −4.98881e8 3.62458e8i −0.383006 0.278270i
\(403\) 7.73870e8 2.38173e9i 0.588980 1.81269i
\(404\) −3.26527e8 1.00495e9i −0.246368 0.758243i
\(405\) 1.97767e8 1.43686e8i 0.147932 0.107479i
\(406\) −4.90171e8 −0.363501
\(407\) 5.63215e7 + 3.03450e8i 0.0414089 + 0.223104i
\(408\) 5.15317e8 0.375633
\(409\) −1.69436e7 + 1.23103e7i −0.0122454 + 0.00889684i −0.593891 0.804545i \(-0.702409\pi\)
0.581646 + 0.813442i \(0.302409\pi\)
\(410\) −3.22543e7 9.92685e7i −0.0231123 0.0711325i
\(411\) 8.06016e7 2.48066e8i 0.0572661 0.176247i
\(412\) 8.62248e8 + 6.26460e8i 0.607424 + 0.441319i
\(413\) 9.91276e8 + 7.20204e8i 0.692420 + 0.503072i
\(414\) −7.30426e7 + 2.24802e8i −0.0505912 + 0.155704i
\(415\) 1.17822e8 + 3.62617e8i 0.0809201 + 0.249046i
\(416\) −2.03942e8 + 1.48173e8i −0.138893 + 0.100912i
\(417\) −3.43533e9 −2.32002
\(418\) 9.56980e8 + 1.25739e8i 0.640893 + 0.0842082i
\(419\) −2.00155e9 −1.32928 −0.664642 0.747162i \(-0.731416\pi\)
−0.664642 + 0.747162i \(0.731416\pi\)
\(420\) −1.03083e8 + 7.48943e7i −0.0678915 + 0.0493260i
\(421\) −7.98203e7 2.45662e8i −0.0521346 0.160454i 0.921599 0.388142i \(-0.126883\pi\)
−0.973734 + 0.227689i \(0.926883\pi\)
\(422\) 5.18599e7 1.59608e8i 0.0335922 0.103386i
\(423\) 1.02163e9 + 7.42261e8i 0.656303 + 0.476832i
\(424\) −4.34951e8 3.16010e8i −0.277115 0.201336i
\(425\) 3.67062e8 1.12970e9i 0.231942 0.713843i
\(426\) 7.96452e8 + 2.45123e9i 0.499144 + 1.53621i
\(427\) −5.15167e8 + 3.74291e8i −0.320221 + 0.232654i
\(428\) −6.24346e8 −0.384922
\(429\) −2.16678e9 2.84697e8i −1.32499 0.174094i
\(430\) −3.21622e8 −0.195077
\(431\) −6.87037e8 + 4.99162e8i −0.413342 + 0.300311i −0.774954 0.632018i \(-0.782227\pi\)
0.361611 + 0.932329i \(0.382227\pi\)
\(432\) 1.89701e7 + 5.83839e7i 0.0113208 + 0.0348418i
\(433\) −5.06723e8 + 1.55953e9i −0.299960 + 0.923181i 0.681551 + 0.731771i \(0.261306\pi\)
−0.981510 + 0.191410i \(0.938694\pi\)
\(434\) 1.39670e9 + 1.01476e9i 0.820139 + 0.595866i
\(435\) 2.24559e8 + 1.63152e8i 0.130803 + 0.0950339i
\(436\) −1.79777e8 + 5.53295e8i −0.103880 + 0.319709i
\(437\) −1.27701e8 3.93023e8i −0.0731997 0.225286i
\(438\) −2.50515e9 + 1.82010e9i −1.42454 + 1.03499i
\(439\) 1.73535e9 0.978954 0.489477 0.872016i \(-0.337188\pi\)
0.489477 + 0.872016i \(0.337188\pi\)
\(440\) 1.92487e7 + 1.03709e8i 0.0107725 + 0.0580404i
\(441\) −7.50506e8 −0.416696
\(442\) 7.78742e8 5.65789e8i 0.428959 0.311657i
\(443\) 1.05749e8 + 3.25463e8i 0.0577916 + 0.177864i 0.975785 0.218731i \(-0.0701917\pi\)
−0.917994 + 0.396595i \(0.870192\pi\)
\(444\) −8.89790e7 + 2.73849e8i −0.0482444 + 0.148481i
\(445\) −2.29871e7 1.67011e7i −0.0123659 0.00898433i
\(446\) 2.12867e9 + 1.54657e9i 1.13615 + 0.825461i
\(447\) 8.72318e8 2.68472e9i 0.461954 1.42175i
\(448\) −5.37019e7 1.65277e8i −0.0282174 0.0868442i
\(449\) −2.05961e9 + 1.49640e9i −1.07380 + 0.780161i −0.976591 0.215103i \(-0.930991\pi\)
−0.0972080 + 0.995264i \(0.530991\pi\)
\(450\) −1.18726e9 −0.614192
\(451\) 8.95431e8 + 8.49297e8i 0.459636 + 0.435955i
\(452\) −8.30480e8 −0.423004
\(453\) 3.96146e9 2.87817e9i 2.00222 1.45470i
\(454\) −5.40894e8 1.66470e9i −0.271279 0.834912i
\(455\) −7.35485e7 + 2.26359e8i −0.0366045 + 0.112657i
\(456\) 7.28519e8 + 5.29300e8i 0.359802 + 0.261412i
\(457\) −6.12009e8 4.44651e8i −0.299952 0.217928i 0.427621 0.903958i \(-0.359352\pi\)
−0.727573 + 0.686030i \(0.759352\pi\)
\(458\) −2.62471e8 + 8.07804e8i −0.127659 + 0.392895i
\(459\) −7.24363e7 2.22936e8i −0.0349632 0.107606i
\(460\) 3.65358e7 2.65448e7i 0.0175012 0.0127153i
\(461\) −1.99223e9 −0.947079 −0.473539 0.880773i \(-0.657024\pi\)
−0.473539 + 0.880773i \(0.657024\pi\)
\(462\) 6.48247e8 1.35998e9i 0.305840 0.641629i
\(463\) 1.44558e9 0.676876 0.338438 0.940989i \(-0.390101\pi\)
0.338438 + 0.940989i \(0.390101\pi\)
\(464\) −3.06272e8 + 2.22520e8i −0.142329 + 0.103408i
\(465\) −3.02101e8 9.29770e8i −0.139337 0.428835i
\(466\) 7.42325e8 2.28464e9i 0.339816 1.04585i
\(467\) 8.65301e7 + 6.28678e7i 0.0393150 + 0.0285640i 0.607269 0.794496i \(-0.292265\pi\)
−0.567954 + 0.823060i \(0.692265\pi\)
\(468\) −7.78366e8 5.65516e8i −0.351013 0.255026i
\(469\) 2.45381e8 7.55206e8i 0.109834 0.338034i
\(470\) −7.45569e7 2.29463e8i −0.0331242 0.101946i
\(471\) −2.45771e9 + 1.78563e9i −1.08382 + 0.787441i
\(472\) 9.46323e8 0.414231
\(473\) 3.34151e9 1.81540e9i 1.45188 0.788786i
\(474\) −2.60986e8 −0.112562
\(475\) 1.67928e9 1.22007e9i 0.718946 0.522345i
\(476\) 2.05058e8 + 6.31103e8i 0.0871469 + 0.268211i
\(477\) 6.34077e8 1.95149e9i 0.267502 0.823287i
\(478\) −4.94022e8 3.58928e8i −0.206894 0.150317i
\(479\) 2.36540e9 + 1.71856e9i 0.983400 + 0.714482i 0.958466 0.285208i \(-0.0920625\pi\)
0.0249338 + 0.999689i \(0.492063\pi\)
\(480\) −3.04099e7 + 9.35920e7i −0.0125508 + 0.0386273i
\(481\) 1.66207e8 + 5.11532e8i 0.0680991 + 0.209587i
\(482\) −3.29723e8 + 2.39558e8i −0.134117 + 0.0974418i
\(483\) −6.45033e8 −0.260476
\(484\) −7.85372e8 9.68838e8i −0.314859 0.388412i
\(485\) −4.93313e8 −0.196348
\(486\) −1.96947e9 + 1.43090e9i −0.778257 + 0.565436i
\(487\) 3.72249e8 + 1.14567e9i 0.146044 + 0.449476i 0.997144 0.0755274i \(-0.0240640\pi\)
−0.851100 + 0.525003i \(0.824064\pi\)
\(488\) −1.51976e8 + 4.67734e8i −0.0591978 + 0.182192i
\(489\) 1.00615e9 + 7.31008e8i 0.389117 + 0.282710i
\(490\) 1.16006e8 + 8.42831e7i 0.0445444 + 0.0323634i
\(491\) 1.22772e8 3.77854e8i 0.0468075 0.144059i −0.924921 0.380159i \(-0.875869\pi\)
0.971729 + 0.236100i \(0.0758693\pi\)
\(492\) 3.55804e8 + 1.09505e9i 0.134689 + 0.414531i
\(493\) 1.16948e9 8.49680e8i 0.439572 0.319368i
\(494\) 1.68207e9 0.627769
\(495\) −3.53740e8 + 1.92182e8i −0.131089 + 0.0712189i
\(496\) 1.33336e9 0.490637
\(497\) −2.68506e9 + 1.95081e9i −0.981087 + 0.712801i
\(498\) −1.29971e9 4.00011e9i −0.471569 1.45134i
\(499\) −6.44844e8 + 1.98463e9i −0.232329 + 0.715034i 0.765136 + 0.643869i \(0.222672\pi\)
−0.997465 + 0.0711652i \(0.977328\pi\)
\(500\) 3.72294e8 + 2.70488e8i 0.133196 + 0.0967726i
\(501\) −1.27885e9 9.29136e8i −0.454346 0.330101i
\(502\) 8.94418e8 2.75274e9i 0.315557 0.971184i
\(503\) 7.35759e8 + 2.26443e9i 0.257779 + 0.793363i 0.993269 + 0.115827i \(0.0369519\pi\)
−0.735490 + 0.677535i \(0.763048\pi\)
\(504\) 5.36589e8 3.89855e8i 0.186696 0.135643i
\(505\) −7.70516e8 −0.266233
\(506\) −2.29759e8 + 4.82017e8i −0.0788398 + 0.165400i
\(507\) 2.29432e8 0.0781855
\(508\) −6.54969e7 + 4.75863e7i −0.0221665 + 0.0161049i
\(509\) 3.53191e7 + 1.08701e8i 0.0118713 + 0.0365361i 0.956817 0.290692i \(-0.0938855\pi\)
−0.944945 + 0.327228i \(0.893885\pi\)
\(510\) 1.16119e8 3.57376e8i 0.0387620 0.119297i
\(511\) −3.22592e9 2.34377e9i −1.06950 0.777036i
\(512\) −1.08584e8 7.88912e7i −0.0357538 0.0259767i
\(513\) 1.26580e8 3.89573e8i 0.0413956 0.127402i
\(514\) 2.77399e8 + 8.53746e8i 0.0901019 + 0.277305i
\(515\) 6.28749e8 4.56813e8i 0.202839 0.147371i
\(516\) 3.54788e9 1.13683
\(517\) 2.06982e9 + 1.96318e9i 0.658743 + 0.624803i
\(518\) −3.70787e8 −0.117212
\(519\) 8.37071e8 6.08167e8i 0.262831 0.190958i
\(520\) 5.68037e7 + 1.74824e8i 0.0177160 + 0.0545241i
\(521\) −1.01255e9 + 3.11630e9i −0.313677 + 0.965399i 0.662618 + 0.748957i \(0.269445\pi\)
−0.976295 + 0.216442i \(0.930555\pi\)
\(522\) −1.16892e9 8.49269e8i −0.359698 0.261336i
\(523\) −6.78224e7 4.92759e7i −0.0207309 0.0150618i 0.577372 0.816482i \(-0.304078\pi\)
−0.598102 + 0.801420i \(0.704078\pi\)
\(524\) −2.72227e8 + 8.37829e8i −0.0826555 + 0.254387i
\(525\) −1.00119e9 3.08136e9i −0.301968 0.929362i
\(526\) −2.91588e8 + 2.11851e8i −0.0873615 + 0.0634718i
\(527\) −5.09135e9 −1.51529
\(528\) −2.12337e8 1.14403e9i −0.0627778 0.338235i
\(529\) −3.17621e9 −0.932854
\(530\) −3.17165e8 + 2.30434e8i −0.0925379 + 0.0672327i
\(531\) 1.11609e9 + 3.43497e9i 0.323495 + 0.995616i
\(532\) −3.58332e8 + 1.10283e9i −0.103180 + 0.317555i
\(533\) 1.73999e9 + 1.26418e9i 0.497739 + 0.361629i
\(534\) 2.53576e8 + 1.84234e8i 0.0720632 + 0.0523570i
\(535\) −1.40687e8 + 4.32989e8i −0.0397205 + 0.122247i
\(536\) −1.89515e8 5.83268e8i −0.0531578 0.163603i
\(537\) 4.20402e9 3.05440e9i 1.17153 0.851170i
\(538\) 1.09383e9 0.302838
\(539\) −1.68099e9 2.20868e8i −0.462385 0.0607537i
\(540\) 4.47643e7 0.0122336
\(541\) −1.59805e9 + 1.16105e9i −0.433910 + 0.315254i −0.783211 0.621756i \(-0.786419\pi\)
0.349300 + 0.937011i \(0.386419\pi\)
\(542\) 1.70697e8 + 5.25351e8i 0.0460498 + 0.141727i
\(543\) −1.22264e9 + 3.76291e9i −0.327718 + 1.00861i
\(544\) 4.14624e8 + 3.01242e8i 0.110423 + 0.0802267i
\(545\) 3.43205e8 + 2.49353e8i 0.0908167 + 0.0659822i
\(546\) 8.11329e8 2.49701e9i 0.213316 0.656518i
\(547\) −3.34030e6 1.02804e7i −0.000872628 0.00268567i 0.950619 0.310360i \(-0.100449\pi\)
−0.951492 + 0.307674i \(0.900449\pi\)
\(548\) 2.09866e8 1.52476e8i 0.0544765 0.0395795i
\(549\) −1.87702e9 −0.484135
\(550\) −2.65925e9 3.49403e8i −0.681536 0.0895484i
\(551\) 2.52607e9 0.643301
\(552\) −4.03035e8 + 2.92822e8i −0.101990 + 0.0740997i
\(553\) −1.03853e8 3.19627e8i −0.0261145 0.0803722i
\(554\) 4.17752e8 1.28571e9i 0.104384 0.321261i
\(555\) 1.69866e8 + 1.23415e8i 0.0421776 + 0.0306438i
\(556\) −2.76406e9 2.00821e9i −0.682003 0.495504i
\(557\) −2.42689e9 + 7.46921e9i −0.595056 + 1.83139i −0.0406062 + 0.999175i \(0.512929\pi\)
−0.554449 + 0.832217i \(0.687071\pi\)
\(558\) 1.57255e9 + 4.83983e9i 0.383165 + 1.17926i
\(559\) 5.36152e9 3.89537e9i 1.29821 0.943208i
\(560\) −1.26722e8 −0.0304926
\(561\) 8.10796e8 + 4.36842e9i 0.193884 + 1.04461i
\(562\) −3.94983e9 −0.938645
\(563\) −1.19590e9 + 8.68870e8i −0.282432 + 0.205199i −0.719978 0.693997i \(-0.755848\pi\)
0.437545 + 0.899196i \(0.355848\pi\)
\(564\) 8.22453e8 + 2.53125e9i 0.193034 + 0.594098i
\(565\) −1.87136e8 + 5.75944e8i −0.0436503 + 0.134342i
\(566\) −5.97919e8 4.34413e8i −0.138607 0.100704i
\(567\) −2.80929e9 2.04107e9i −0.647227 0.470238i
\(568\) −7.92104e8 + 2.43784e9i −0.181369 + 0.558196i
\(569\) −1.89632e9 5.83627e9i −0.431537 1.32814i −0.896594 0.442854i \(-0.853966\pi\)
0.465056 0.885281i \(-0.346034\pi\)
\(570\) 5.31234e8 3.85964e8i 0.120150 0.0872940i
\(571\) 9.86349e8 0.221720 0.110860 0.993836i \(-0.464640\pi\)
0.110860 + 0.993836i \(0.464640\pi\)
\(572\) −1.57696e9 1.49571e9i −0.352318 0.334166i
\(573\) 9.16597e9 2.03534
\(574\) −1.19951e9 + 8.71498e8i −0.264736 + 0.192342i
\(575\) 3.54854e8 + 1.09213e9i 0.0778417 + 0.239572i
\(576\) 1.58296e8 4.87184e8i 0.0345136 0.106222i
\(577\) −1.43110e9 1.03976e9i −0.310139 0.225329i 0.421817 0.906681i \(-0.361392\pi\)
−0.731956 + 0.681352i \(0.761392\pi\)
\(578\) 1.07255e9 + 7.79252e8i 0.231031 + 0.167854i
\(579\) −8.11317e8 + 2.49698e9i −0.173706 + 0.534613i
\(580\) 8.53055e7 + 2.62543e8i 0.0181543 + 0.0558731i
\(581\) 4.38170e9 3.18349e9i 0.926886 0.673422i
\(582\) 5.44184e9 1.14423
\(583\) 1.99452e9 4.18435e9i 0.416868 0.874558i
\(584\) −3.07963e9 −0.639813
\(585\) −5.67582e8 + 4.12372e8i −0.117215 + 0.0851616i
\(586\) −3.96614e7 1.22065e8i −0.00814191 0.0250582i
\(587\) 2.11267e9 6.50214e9i 0.431121 1.32685i −0.465889 0.884843i \(-0.654265\pi\)
0.897010 0.442010i \(-0.145735\pi\)
\(588\) −1.27968e9 9.29745e8i −0.259587 0.188601i
\(589\) −7.19780e9 5.22950e9i −1.45143 1.05453i
\(590\) 2.13239e8 6.56282e8i 0.0427449 0.131555i
\(591\) −2.47485e9 7.61680e9i −0.493165 1.51781i
\(592\) −2.31678e8 + 1.68324e8i −0.0458943 + 0.0333442i
\(593\) 3.33993e9 0.657727 0.328863 0.944378i \(-0.393334\pi\)
0.328863 + 0.944378i \(0.393334\pi\)
\(594\) −4.65082e8 + 2.52673e8i −0.0910494 + 0.0494660i
\(595\) 4.83881e8 0.0941737
\(596\) 2.27129e9 1.65019e9i 0.439451 0.319280i
\(597\) −4.30018e8 1.32346e9i −0.0827136 0.254566i
\(598\) −2.87560e8 + 8.85019e8i −0.0549888 + 0.169238i
\(599\) −6.75239e9 4.90590e9i −1.28370 0.932663i −0.284042 0.958812i \(-0.591676\pi\)
−0.999658 + 0.0261487i \(0.991676\pi\)
\(600\) −2.02440e9 1.47081e9i −0.382619 0.277989i
\(601\) −1.81539e9 + 5.58718e9i −0.341121 + 1.04986i 0.622507 + 0.782614i \(0.286114\pi\)
−0.963628 + 0.267248i \(0.913886\pi\)
\(602\) 1.41179e9 + 4.34505e9i 0.263744 + 0.811721i
\(603\) 1.89363e9 1.37581e9i 0.351711 0.255533i
\(604\) 4.86989e9 0.899270
\(605\) −8.48867e8 + 3.26349e8i −0.155846 + 0.0599153i
\(606\) 8.49972e9 1.55150
\(607\) 2.78491e9 2.02336e9i 0.505419 0.367208i −0.305664 0.952139i \(-0.598878\pi\)
0.811083 + 0.584931i \(0.198878\pi\)
\(608\) 2.76750e8 + 8.51749e8i 0.0499373 + 0.153691i
\(609\) 1.21842e9 3.74992e9i 0.218593 0.672761i
\(610\) 2.90132e8 + 2.10793e8i 0.0517536 + 0.0376012i
\(611\) 4.02205e9 + 2.92219e9i 0.713352 + 0.518280i
\(612\) −6.04444e8 + 1.86029e9i −0.106592 + 0.328057i
\(613\) 3.00142e9 + 9.23742e9i 0.526278 + 1.61972i 0.761775 + 0.647842i \(0.224328\pi\)
−0.235497 + 0.971875i \(0.575672\pi\)
\(614\) −3.15672e9 + 2.29349e9i −0.550361 + 0.399860i
\(615\) 8.39601e8 0.145549
\(616\) 1.31659e9 7.15286e8i 0.226943 0.123295i
\(617\) 1.03976e10 1.78212 0.891058 0.453890i \(-0.149964\pi\)
0.891058 + 0.453890i \(0.149964\pi\)
\(618\) −6.93586e9 + 5.03919e9i −1.18206 + 0.858819i
\(619\) −1.78748e9 5.50128e9i −0.302916 0.932281i −0.980447 0.196786i \(-0.936950\pi\)
0.677530 0.735495i \(-0.263050\pi\)
\(620\) 3.00451e8 9.24693e8i 0.0506294 0.155821i
\(621\) 1.83333e8 + 1.33200e8i 0.0307200 + 0.0223194i
\(622\) 4.66523e9 + 3.38949e9i 0.777333 + 0.564765i
\(623\) −1.24725e8 + 3.83863e8i −0.0206654 + 0.0636016i
\(624\) −6.26613e8 1.92852e9i −0.103241 0.317744i
\(625\) −4.52872e9 + 3.29030e9i −0.741985 + 0.539083i
\(626\) 1.87764e9 0.305917
\(627\) −3.34071e9 + 7.00856e9i −0.541255 + 1.13551i
\(628\) −3.02131e9 −0.486783
\(629\) 8.84650e8 6.42736e8i 0.141741 0.102981i
\(630\) −1.49455e8 4.59976e8i −0.0238133 0.0732898i
\(631\) 9.52598e8 2.93179e9i 0.150941 0.464548i −0.846786 0.531933i \(-0.821466\pi\)
0.997727 + 0.0673853i \(0.0214657\pi\)
\(632\) −2.09989e8 1.52566e8i −0.0330893 0.0240408i
\(633\) 1.09213e9 + 7.93480e8i 0.171144 + 0.124343i
\(634\) −1.63641e9 + 5.03634e9i −0.255023 + 0.784880i
\(635\) 1.82428e7 + 5.61454e7i 0.00282737 + 0.00870175i
\(636\) 3.49871e9 2.54196e9i 0.539272 0.391804i
\(637\) −2.95465e9 −0.452917
\(638\) −2.36822e9 2.24620e9i −0.361035 0.342434i
\(639\) −9.78310e9 −1.48328
\(640\) −7.91794e7 + 5.75272e7i −0.0119394 + 0.00867448i
\(641\) 5.22764e8 + 1.60890e9i 0.0783976 + 0.241283i 0.982573 0.185879i \(-0.0595133\pi\)
−0.904175 + 0.427162i \(0.859513\pi\)
\(642\) 1.55194e9 4.77639e9i 0.231475 0.712405i
\(643\) −1.30195e9 9.45925e8i −0.193133 0.140320i 0.487016 0.873393i \(-0.338085\pi\)
−0.680150 + 0.733073i \(0.738085\pi\)
\(644\) −5.18993e8 3.77071e8i −0.0765705 0.0556317i
\(645\) 7.99458e8 2.46048e9i 0.117310 0.361045i
\(646\) −1.05675e9 3.25236e9i −0.154227 0.474662i
\(647\) 8.21735e8 5.97025e8i 0.119280 0.0866618i −0.526546 0.850147i \(-0.676513\pi\)
0.645826 + 0.763485i \(0.276513\pi\)
\(648\) −2.68190e9 −0.387195
\(649\) 1.48894e9 + 8.02212e9i 0.213806 + 1.15195i
\(650\) −4.67412e9 −0.667580
\(651\) −1.12349e10 + 8.16264e9i −1.59601 + 1.15957i
\(652\) 3.82215e8 + 1.17634e9i 0.0540059 + 0.166213i
\(653\) −8.61861e8 + 2.65253e9i −0.121127 + 0.372791i −0.993176 0.116629i \(-0.962791\pi\)
0.872049 + 0.489419i \(0.162791\pi\)
\(654\) −3.78596e9 2.75066e9i −0.529242 0.384517i
\(655\) 5.19698e8 + 3.77583e8i 0.0722615 + 0.0525010i
\(656\) −3.53861e8 + 1.08907e9i −0.0489406 + 0.150624i
\(657\) −3.63209e9 1.11784e10i −0.499664 1.53781i
\(658\) −2.77272e9 + 2.01450e9i −0.379416 + 0.275662i
\(659\) −1.67394e9 −0.227846 −0.113923 0.993490i \(-0.536342\pi\)
−0.113923 + 0.993490i \(0.536342\pi\)
\(660\) −8.41241e8 1.10532e8i −0.113898 0.0149653i
\(661\) 7.26540e9 0.978485 0.489243 0.872148i \(-0.337273\pi\)
0.489243 + 0.872148i \(0.337273\pi\)
\(662\) 9.06245e8 6.58426e8i 0.121407 0.0882072i
\(663\) 2.39269e9 + 7.36394e9i 0.318852 + 0.981325i
\(664\) 1.29262e9 3.97827e9i 0.171349 0.527358i
\(665\) 6.84077e8 + 4.97011e8i 0.0902047 + 0.0655376i
\(666\) −8.84223e8 6.42425e8i −0.115985 0.0842681i
\(667\) −4.31846e8 + 1.32909e9i −0.0563493 + 0.173425i
\(668\) −4.85809e8 1.49517e9i −0.0630591 0.194076i
\(669\) −1.71228e10 + 1.24405e10i −2.21098 + 1.60637i
\(670\) −4.47205e8 −0.0574440
\(671\) −4.20417e9 5.52394e8i −0.537219 0.0705862i
\(672\) 1.39790e9 0.177698
\(673\) 7.61378e9 5.53174e9i 0.962826 0.699534i 0.00902030 0.999959i \(-0.497129\pi\)
0.953805 + 0.300426i \(0.0971287\pi\)
\(674\) −2.76491e9 8.50952e9i −0.347833 1.07052i
\(675\) −3.51739e8 + 1.08254e9i −0.0440207 + 0.135482i
\(676\) 1.84601e8 + 1.34120e8i 0.0229837 + 0.0166987i
\(677\) 6.45850e9 + 4.69237e9i 0.799965 + 0.581209i 0.910904 0.412619i \(-0.135386\pi\)
−0.110939 + 0.993827i \(0.535386\pi\)
\(678\) 2.06433e9 6.35336e9i 0.254376 0.782888i
\(679\) 2.16545e9 + 6.66456e9i 0.265463 + 0.817010i
\(680\) 3.02342e8 2.19665e8i 0.0368738 0.0267904i
\(681\) 1.40798e10 1.70837
\(682\) 2.09790e9 + 1.13031e10i 0.253244 + 1.36443i
\(683\) −9.00646e9 −1.08164 −0.540819 0.841139i \(-0.681886\pi\)
−0.540819 + 0.841139i \(0.681886\pi\)
\(684\) −2.76528e9 + 2.00910e9i −0.330402 + 0.240051i
\(685\) −5.84535e7 1.79901e8i −0.00694854 0.0213854i
\(686\) 1.97909e9 6.09103e9i 0.234063 0.720371i
\(687\) −5.52745e9 4.01593e9i −0.650394 0.472539i
\(688\) 2.85462e9 + 2.07400e9i 0.334186 + 0.242801i
\(689\) 2.49629e9 7.68278e9i 0.290755 0.894851i
\(690\) 1.12257e8 + 3.45490e8i 0.0130089 + 0.0400372i
\(691\) 6.84117e9 4.97040e9i 0.788783 0.573084i −0.118819 0.992916i \(-0.537911\pi\)
0.907602 + 0.419832i \(0.137911\pi\)
\(692\) 1.02903e9 0.118047
\(693\) 4.14912e9 + 3.93535e9i 0.473576 + 0.449177i
\(694\) 8.73090e9 0.991519
\(695\) −2.01555e9 + 1.46438e9i −0.227744 + 0.165465i
\(696\) −9.41022e8 2.89617e9i −0.105796 0.325605i
\(697\) 1.35120e9 4.15856e9i 0.151149 0.465188i
\(698\) 1.87049e9 + 1.35899e9i 0.208191 + 0.151260i
\(699\) 1.56328e10 + 1.13579e10i 1.73128 + 1.25785i
\(700\) 9.95728e8 3.06454e9i 0.109723 0.337693i
\(701\) −8.70304e8 2.67852e9i −0.0954241 0.293685i 0.891940 0.452154i \(-0.149344\pi\)
−0.987364 + 0.158469i \(0.949344\pi\)
\(702\) −7.46232e8 + 5.42170e8i −0.0814131 + 0.0591501i
\(703\) 1.91083e9 0.207433
\(704\) 4.97927e8 1.04461e9i 0.0537850 0.112837i
\(705\) 1.94077e9 0.208599
\(706\) 7.92916e9 5.76087e9i 0.848029 0.616129i
\(707\) 3.38226e9 + 1.04095e10i 0.359947 + 1.10780i
\(708\) −2.35228e9 + 7.23959e9i −0.249100 + 0.766650i
\(709\) −1.26588e10 9.19717e9i −1.33393 0.969154i −0.999644 0.0266803i \(-0.991506\pi\)
−0.334282 0.942473i \(-0.608494\pi\)
\(710\) 1.51217e9 + 1.09866e9i 0.158562 + 0.115202i
\(711\) 3.06125e8 9.42156e8i 0.0319415 0.0983058i
\(712\) 9.63285e7 + 2.96469e8i 0.0100017 + 0.0307821i
\(713\) 3.98200e9 2.89309e9i 0.411422 0.298916i
\(714\) −5.33780e9 −0.548805
\(715\) −1.39263e9 + 7.56600e8i −0.142484 + 0.0774096i
\(716\) 5.16809e9 0.526180
\(717\) 3.97387e9 2.88719e9i 0.402621 0.292522i
\(718\) 4.59448e8 + 1.41403e9i 0.0463234 + 0.142569i
\(719\) 4.58017e9 1.40963e10i 0.459548 1.41434i −0.406164 0.913800i \(-0.633134\pi\)
0.865712 0.500542i \(-0.166866\pi\)
\(720\) −3.02196e8 2.19558e8i −0.0301735 0.0219223i
\(721\) −8.93140e9 6.48904e9i −0.887455 0.644774i
\(722\) −3.63130e8 + 1.11760e9i −0.0359072 + 0.110511i
\(723\) −1.01307e9 3.11792e9i −0.0996914 0.306818i
\(724\) −3.18344e9 + 2.31291e9i −0.311754 + 0.226503i
\(725\) −7.01941e9 −0.684097
\(726\) 9.36403e9 3.60002e9i 0.908207 0.349162i
\(727\) −1.44416e10 −1.39394 −0.696972 0.717099i \(-0.745470\pi\)
−0.696972 + 0.717099i \(0.745470\pi\)
\(728\) 2.11249e9 1.53481e9i 0.202925 0.147433i
\(729\) −2.51121e9 7.72872e9i −0.240070 0.738858i
\(730\) −6.93945e8 + 2.13574e9i −0.0660230 + 0.203198i
\(731\) −1.09002e10 7.91947e9i −1.03211 0.749869i
\(732\) −3.20050e9 2.32530e9i −0.301599 0.219124i
\(733\) −9.27457e8 + 2.85442e9i −0.0869821 + 0.267703i −0.985081 0.172090i \(-0.944948\pi\)
0.898099 + 0.439793i \(0.144948\pi\)
\(734\) −4.39889e9 1.35384e10i −0.410588 1.26366i
\(735\) −9.33142e8 + 6.77967e8i −0.0866846 + 0.0629800i
\(736\) −4.95458e8 −0.0458073
\(737\) 4.64627e9 2.52426e9i 0.427531 0.232272i
\(738\) −4.37046e9 −0.400249
\(739\) 9.86637e9 7.16833e9i 0.899294 0.653375i −0.0389906 0.999240i \(-0.512414\pi\)
0.938285 + 0.345864i \(0.112414\pi\)
\(740\) 6.45289e7 + 1.98600e8i 0.00585387 + 0.0180164i
\(741\) −4.18114e9 + 1.28682e10i −0.377512 + 1.16186i
\(742\) 4.50534e9 + 3.27332e9i 0.404869 + 0.294154i
\(743\) 1.62916e9 + 1.18365e9i 0.145714 + 0.105868i 0.658254 0.752796i \(-0.271295\pi\)
−0.512540 + 0.858664i \(0.671295\pi\)
\(744\) −3.31434e9 + 1.02005e10i −0.295047 + 0.908062i
\(745\) −6.32618e8 1.94700e9i −0.0560525 0.172512i
\(746\) −8.87405e8 + 6.44737e8i −0.0782593 + 0.0568587i
\(747\) 1.59648e10 1.40134
\(748\) −1.90131e9 + 3.98880e9i −0.166110 + 0.348487i
\(749\) 6.46715e9 0.562376
\(750\) −2.99471e9 + 2.17578e9i −0.259203 + 0.188322i
\(751\) 1.31591e9 + 4.04996e9i 0.113367 + 0.348908i 0.991603 0.129320i \(-0.0412794\pi\)
−0.878236 + 0.478228i \(0.841279\pi\)
\(752\) −8.17962e8 + 2.51743e9i −0.0701408 + 0.215871i
\(753\) 1.88358e10 + 1.36850e10i 1.60769 + 1.16805i
\(754\) −4.60190e9 3.34347e9i −0.390964 0.284052i
\(755\) 1.09735e9 3.37731e9i 0.0927966 0.285599i
\(756\) −1.96497e8 6.04757e8i −0.0165398 0.0509043i
\(757\) −8.84068e9 + 6.42313e9i −0.740713 + 0.538160i −0.892934 0.450187i \(-0.851357\pi\)
0.152221 + 0.988346i \(0.451357\pi\)
\(758\) −1.55601e10 −1.29769
\(759\) −3.11643e9 2.95586e9i −0.258708 0.245379i
\(760\) 6.53055e8 0.0539638
\(761\) −1.09107e10 + 7.92710e9i −0.897443 + 0.652030i −0.937808 0.347155i \(-0.887148\pi\)
0.0403650 + 0.999185i \(0.487148\pi\)
\(762\) −2.01240e8 6.19352e8i −0.0164767 0.0507102i
\(763\) 1.86218e9 5.73119e9i 0.151770 0.467099i
\(764\) 7.37494e9 + 5.35821e9i 0.598317 + 0.434703i
\(765\) 1.15392e9 + 8.38372e8i 0.0931882 + 0.0677052i
\(766\) −4.07509e9 + 1.25418e10i −0.327594 + 1.00823i
\(767\) 4.39391e9 + 1.35231e10i 0.351615 + 1.08216i
\(768\) 8.73445e8 6.34595e8i 0.0695779 0.0505513i
\(769\) −6.51045e9 −0.516261 −0.258130 0.966110i \(-0.583106\pi\)
−0.258130 + 0.966110i \(0.583106\pi\)
\(770\) −1.99384e8 1.07424e9i −0.0157388 0.0847978i
\(771\) −7.22088e9 −0.567414
\(772\) −2.11246e9 + 1.53479e9i −0.165245 + 0.120057i
\(773\) −3.23352e9 9.95177e9i −0.251796 0.774947i −0.994444 0.105266i \(-0.966431\pi\)
0.742649 0.669681i \(-0.233569\pi\)
\(774\) −4.16150e9 + 1.28078e10i −0.322594 + 0.992843i
\(775\) 2.00012e10 + 1.45317e10i 1.54347 + 1.12140i
\(776\) 4.37850e9 + 3.18117e9i 0.336364 + 0.244383i
\(777\) 9.21669e8 2.83661e9i 0.0704858 0.216933i
\(778\) 1.45608e9 + 4.48137e9i 0.110856 + 0.341179i
\(779\) 6.18163e9 4.49122e9i 0.468513 0.340395i
\(780\) −1.47864e9 −0.111566
\(781\) −2.19123e10 2.87909e9i −1.64592 0.216261i
\(782\) 1.89188e9 0.141472
\(783\) −1.12066e9 + 8.14209e8i −0.0834273 + 0.0606135i
\(784\) −4.86127e8 1.49614e9i −0.0360283 0.110884i
\(785\) −6.80803e8 + 2.09530e9i −0.0502317 + 0.154597i
\(786\) −5.73290e9 4.16520e9i −0.421110 0.305954i
\(787\) −8.23701e9 5.98454e9i −0.602362 0.437642i 0.244354 0.969686i \(-0.421424\pi\)
−0.846717 + 0.532044i \(0.821424\pi\)
\(788\) 2.46134e9 7.57521e9i 0.179196 0.551510i
\(789\) −8.95906e8 2.75732e9i −0.0649371 0.199856i
\(790\) −1.53124e8 + 1.11251e8i −0.0110496 + 0.00802802i
\(791\) 8.60235e9 0.618015
\(792\) 4.37899e9 + 5.75364e8i 0.313210 + 0.0411533i
\(793\) −7.38962e9 −0.526218
\(794\) 7.68433e9 5.58300e9i 0.544797 0.395818i
\(795\) −9.74491e8 2.99917e9i −0.0687848 0.211698i
\(796\) 4.27670e8 1.31623e9i 0.0300548 0.0924990i
\(797\) 5.32005e9 + 3.86525e9i 0.372230 + 0.270441i 0.758135 0.652097i \(-0.226111\pi\)
−0.385905 + 0.922539i \(0.626111\pi\)
\(798\) −7.54620e9 5.48263e9i −0.525676 0.381926i
\(799\) 3.12334e9 9.61267e9i 0.216624 0.666700i
\(800\) −7.69030e8 2.36683e9i −0.0531041 0.163438i
\(801\) −9.62513e8 + 6.99307e8i −0.0661748 + 0.0480788i
\(802\) 3.53944e9 0.242284
\(803\) −4.84546e9 2.61065e10i −0.330241 1.77928i
\(804\) 4.93321e9 0.334760
\(805\) −3.78448e8 + 2.74959e8i −0.0255694 + 0.0185773i
\(806\) 6.19096e9 + 1.90538e10i 0.416472 + 1.28177i
\(807\) −2.71893e9 + 8.36801e9i −0.182113 + 0.560486i
\(808\) 6.83887e9 + 4.96873e9i 0.456084 + 0.331364i
\(809\) −1.94536e10 1.41339e10i −1.29176 0.938515i −0.291916 0.956444i \(-0.594293\pi\)
−0.999839 + 0.0179287i \(0.994293\pi\)
\(810\) −6.04323e8 + 1.85992e9i −0.0399550 + 0.122969i
\(811\) 6.43379e9 + 1.98012e10i 0.423539 + 1.30352i 0.904386 + 0.426716i \(0.140329\pi\)
−0.480846 + 0.876805i \(0.659671\pi\)
\(812\) 3.17245e9 2.30492e9i 0.207945 0.151081i
\(813\) −4.44335e9 −0.289997
\(814\) −1.79143e9 1.69913e9i −0.116416 0.110418i
\(815\) 9.01925e8 0.0583605
\(816\) −3.33520e9 + 2.42317e9i −0.214885 + 0.156123i
\(817\) −7.27559e9 2.23920e10i −0.466757 1.43653i
\(818\) 5.17751e7 1.59347e8i 0.00330738 0.0101791i
\(819\) 8.06253e9 + 5.85777e9i 0.512835 + 0.372596i
\(820\) 6.75542e8 + 4.90810e8i 0.0427862 + 0.0310860i
\(821\) −5.74381e9 + 1.76776e10i −0.362242 + 1.11487i 0.589448 + 0.807806i \(0.299345\pi\)
−0.951690 + 0.307060i \(0.900655\pi\)
\(822\) 6.44813e8 + 1.98453e9i 0.0404932 + 0.124625i
\(823\) 1.49261e10 1.08444e10i 0.933354 0.678121i −0.0134580 0.999909i \(-0.504284\pi\)
0.946812 + 0.321788i \(0.104284\pi\)
\(824\) −8.52638e9 −0.530908
\(825\) 9.28312e9 1.94753e10i 0.575580 1.20752i
\(826\) −9.80228e9 −0.605197
\(827\) −1.64272e10 + 1.19351e10i −1.00994 + 0.733764i −0.964196 0.265189i \(-0.914566\pi\)
−0.0457433 + 0.998953i \(0.514566\pi\)
\(828\) −5.84340e8 1.79841e9i −0.0357734 0.110099i
\(829\) −4.00110e9 + 1.23141e10i −0.243915 + 0.750692i 0.751898 + 0.659279i \(0.229138\pi\)
−0.995813 + 0.0914133i \(0.970862\pi\)
\(830\) −2.46769e9 1.79288e9i −0.149802 0.108837i
\(831\) 8.79755e9 + 6.39180e9i 0.531812 + 0.386384i
\(832\) 6.23192e8 1.91799e9i 0.0375137 0.115455i
\(833\) 1.85625e9 + 5.71295e9i 0.111270 + 0.342454i
\(834\) 2.22339e10 1.61539e10i 1.32720 0.964264i
\(835\) −1.14638e9 −0.0681436
\(836\) −6.78497e9 + 3.68619e9i −0.401630 + 0.218200i
\(837\) 4.87881e9 0.287591
\(838\) 1.29543e10 9.41186e9i 0.760432 0.552486i
\(839\) 8.96664e9 + 2.75965e10i 0.524159 + 1.61319i 0.765974 + 0.642872i \(0.222257\pi\)
−0.241815 + 0.970322i \(0.577743\pi\)
\(840\) 3.14994e8 9.69452e8i 0.0183369 0.0564350i
\(841\) 7.04450e9 + 5.11813e9i 0.408380 + 0.296705i
\(842\) 1.67178e9 + 1.21462e9i 0.0965131 + 0.0701209i
\(843\) 9.81813e9 3.02171e10i 0.564459 1.73723i
\(844\) 4.14879e8 + 1.27687e9i 0.0237533 + 0.0731050i
\(845\) 1.34610e8 9.78002e7i 0.00767504 0.00557624i
\(846\) −1.01025e10 −0.573629
\(847\) 8.13510e9 + 1.00355e10i 0.460014 + 0.567475i
\(848\) 4.30103e9 0.242207
\(849\) 4.80961e9 3.49439e9i 0.269732 0.195972i
\(850\) 2.93650e9 + 9.03762e9i 0.164007 + 0.504763i
\(851\) −3.26668e8 + 1.00538e9i −0.0181699 + 0.0559213i
\(852\) −1.66811e10 1.21195e10i −0.924031 0.671348i
\(853\) −1.47323e10 1.07036e10i −0.812732 0.590485i 0.101889 0.994796i \(-0.467511\pi\)
−0.914621 + 0.404311i \(0.867511\pi\)
\(854\) 1.57421e9 4.84492e9i 0.0864888 0.266185i
\(855\) 7.70210e8 + 2.37046e9i 0.0421432 + 0.129704i
\(856\) 4.04085e9 2.93585e9i 0.220199 0.159984i
\(857\) 6.60403e8 0.0358407 0.0179203 0.999839i \(-0.494295\pi\)
0.0179203 + 0.999839i \(0.494295\pi\)
\(858\) 1.53624e10 8.34621e9i 0.830336 0.451111i
\(859\) −7.93116e9 −0.426934 −0.213467 0.976950i \(-0.568476\pi\)
−0.213467 + 0.976950i \(0.568476\pi\)
\(860\) 2.08158e9 1.51236e9i 0.111596 0.0810792i
\(861\) −3.68551e9 1.13428e10i −0.196783 0.605635i
\(862\) 2.09940e9 6.46129e9i 0.111640 0.343592i
\(863\) 1.28258e10 + 9.31847e9i 0.679275 + 0.493522i 0.873117 0.487510i \(-0.162095\pi\)
−0.193842 + 0.981033i \(0.562095\pi\)
\(864\) −3.97315e8 2.88666e8i −0.0209574 0.0152264i
\(865\) 2.31875e8 7.13638e8i 0.0121814 0.0374905i
\(866\) −4.05378e9 1.24763e10i −0.212104 0.652787i
\(867\) −8.62750e9 + 6.26825e9i −0.449592 + 0.326647i
\(868\) −1.38113e10 −0.716828
\(869\) 9.62931e8 2.02016e9i 0.0497767 0.104428i
\(870\) −2.22056e9 −0.114326
\(871\) 7.45501e9 5.41638e9i 0.382283 0.277745i
\(872\) −1.43821e9 4.42636e9i −0.0734540 0.226068i
\(873\) −6.38303e9 + 1.96449e10i −0.324696 + 0.999312i
\(874\) 2.67461e9 + 1.94321e9i 0.135509 + 0.0984534i
\(875\) −3.85633e9 2.80178e9i −0.194601 0.141386i
\(876\) 7.65505e9 2.35598e10i 0.384755 1.18415i
\(877\) 5.00630e9 + 1.54078e10i 0.250622 + 0.771334i 0.994661 + 0.103198i \(0.0329076\pi\)
−0.744039 + 0.668136i \(0.767092\pi\)
\(878\) −1.12315e10 + 8.16013e9i −0.560022 + 0.406880i
\(879\) 1.03241e9 0.0512734
\(880\) −6.12247e8 5.80703e8i −0.0302857 0.0287253i
\(881\) 3.01828e10 1.48711 0.743555 0.668675i \(-0.233138\pi\)
0.743555 + 0.668675i \(0.233138\pi\)
\(882\) 4.85738e9 3.52909e9i 0.238376 0.173190i
\(883\) −9.24712e7 2.84597e8i −0.00452006 0.0139113i 0.948771 0.315964i \(-0.102328\pi\)
−0.953291 + 0.302053i \(0.902328\pi\)
\(884\) −2.37962e9 + 7.32373e9i −0.115858 + 0.356574i
\(885\) 4.49066e9 + 3.26265e9i 0.217775 + 0.158223i
\(886\) −2.21484e9 1.60918e9i −0.106986 0.0777295i
\(887\) −4.53943e8 + 1.39709e9i −0.0218408 + 0.0672191i −0.961383 0.275214i \(-0.911251\pi\)
0.939542 + 0.342434i \(0.111251\pi\)
\(888\) −7.11832e8 2.19079e9i −0.0341140 0.104992i
\(889\) 6.78435e8 4.92912e8i 0.0323856 0.0235295i
\(890\) 2.27309e8 0.0108082
\(891\) −4.21968e9 2.27348e10i −0.199851 1.07676i
\(892\) −2.10494e10 −0.993031
\(893\) 1.42891e10 1.03816e10i 0.671465 0.487848i
\(894\) 6.97855e9 + 2.14778e10i 0.326651 + 1.00533i
\(895\) 1.16455e9 3.58411e9i 0.0542971 0.167109i
\(896\) 1.12475e9 + 8.17177e8i 0.0522369 + 0.0379523i
\(897\) −6.05580e9 4.39980e9i −0.280155 0.203544i
\(898\) 6.29361e9 1.93697e10i 0.290023 0.892600i
\(899\) 9.29734e9 + 2.86143e10i 0.426776 + 1.31348i
\(900\) 7.68414e9 5.58285e9i 0.351355 0.255275i
\(901\) −1.64233e10 −0.748036
\(902\) −9.78899e9 1.28619e9i −0.444135 0.0583557i
\(903\) −3.67499e10 −1.66092
\(904\) 5.37498e9 3.90515e9i 0.241984 0.175812i
\(905\) 8.86680e8 + 2.72892e9i 0.0397646 + 0.122383i
\(906\) −1.21051e10 + 3.72558e10i −0.540780 + 1.66435i
\(907\) −9.25427e9 6.72362e9i −0.411829 0.299211i 0.362513 0.931979i \(-0.381919\pi\)
−0.774342 + 0.632768i \(0.781919\pi\)
\(908\) 1.13286e10 + 8.23074e9i 0.502201 + 0.364870i
\(909\) −9.96979e9 + 3.06839e10i −0.440263 + 1.35499i
\(910\) −5.88388e8 1.81087e9i −0.0258833 0.0796605i
\(911\) −3.11857e10 + 2.26578e10i −1.36660 + 0.992893i −0.368607 + 0.929586i \(0.620165\pi\)
−0.997994 + 0.0633079i \(0.979835\pi\)
\(912\) −7.20399e9 −0.314479
\(913\) 3.57582e10 + 4.69833e9i 1.55499 + 0.204313i
\(914\) 6.05188e9 0.262167
\(915\) −2.33380e9 + 1.69560e9i −0.100714 + 0.0731729i
\(916\) −2.09977e9 6.46243e9i −0.0902688 0.277819i
\(917\) 2.81980e9 8.67846e9i 0.120761 0.371664i
\(918\) 1.51713e9 + 1.10226e9i 0.0647250 + 0.0470255i
\(919\) 2.83975e10 + 2.06320e10i 1.20691 + 0.876873i 0.994947 0.100404i \(-0.0320136\pi\)
0.211965 + 0.977277i \(0.432014\pi\)
\(920\) −1.11644e8 + 3.43604e8i −0.00472690 + 0.0145479i
\(921\) −9.69905e9 2.98506e10i −0.409092 1.25905i
\(922\) 1.28940e10 9.36803e9i 0.541787 0.393631i
\(923\) −3.85149e10 −1.61221
\(924\) 2.19944e9 + 1.18502e10i 0.0917193 + 0.494166i
\(925\) −5.30980e9 −0.220588
\(926\) −9.35600e9 + 6.79754e9i −0.387215 + 0.281328i
\(927\) −1.00560e10 3.09491e10i −0.414615 1.27605i
\(928\) 9.35884e8 2.88036e9i 0.0384418 0.118312i
\(929\) 1.59975e10 + 1.16229e10i 0.654631 + 0.475617i 0.864846 0.502038i \(-0.167416\pi\)
−0.210214 + 0.977655i \(0.567416\pi\)
\(930\) 6.32728e9 + 4.59704e9i 0.257945 + 0.187408i
\(931\) −3.24373e9 + 9.98318e9i −0.131741 + 0.405457i
\(932\) 5.93860e9 + 1.82771e10i 0.240286 + 0.739524i
\(933\) −3.75268e10 + 2.72648e10i −1.51271 + 1.09905i
\(934\) −8.55657e8 −0.0343626
\(935\) 2.33783e9 + 2.21738e9i 0.0935347 + 0.0887156i
\(936\) 7.69690e9 0.306797
\(937\) −2.11428e10 + 1.53612e10i −0.839604 + 0.610008i −0.922260 0.386570i \(-0.873660\pi\)
0.0826562 + 0.996578i \(0.473660\pi\)
\(938\) 1.96305e9 + 6.04165e9i 0.0776643 + 0.239026i
\(939\) −4.66728e9 + 1.43644e10i −0.183965 + 0.566185i
\(940\) 1.56154e9 + 1.13453e9i 0.0613205 + 0.0445520i
\(941\) 3.58041e9 + 2.60132e9i 0.140078 + 0.101772i 0.655617 0.755093i \(-0.272409\pi\)
−0.515540 + 0.856866i \(0.672409\pi\)
\(942\) 7.51008e9 2.31137e10i 0.292730 0.900929i
\(943\) 1.30626e9 + 4.02025e9i 0.0507269 + 0.156121i
\(944\) −6.12473e9 + 4.44988e9i −0.236966 + 0.172166i
\(945\) −4.63681e8 −0.0178734
\(946\) −1.30902e10 + 2.74623e10i −0.502721 + 1.05467i
\(947\) 1.37318e10 0.525413 0.262707 0.964876i \(-0.415385\pi\)
0.262707 + 0.964876i \(0.415385\pi\)
\(948\) 1.68914e9 1.22723e9i 0.0643926 0.0467840i
\(949\) −1.42991e10 4.40082e10i −0.543098 1.67148i
\(950\) −5.13143e9 + 1.57929e10i −0.194181 + 0.597626i
\(951\) −3.44615e10 2.50378e10i −1.29928 0.943982i
\(952\) −4.29479e9 3.12035e9i −0.161329 0.117212i
\(953\) 7.51281e9 2.31221e10i 0.281176 0.865369i −0.706343 0.707869i \(-0.749657\pi\)
0.987519 0.157500i \(-0.0503434\pi\)
\(954\) 5.07261e9 + 1.56119e10i 0.189153 + 0.582152i
\(955\) 5.37778e9 3.90719e9i 0.199798 0.145162i
\(956\) 4.88515e9 0.180832
\(957\) 2.30707e10 1.25340e10i 0.850880 0.462272i
\(958\) −2.33903e10 −0.859523
\(959\) −2.17385e9 + 1.57939e9i −0.0795909 + 0.0578262i
\(960\) −2.43279e8 7.48736e8i −0.00887474 0.0273136i
\(961\) 2.42439e10 7.46152e10i 0.881193 2.71203i
\(962\) −3.48108e9 2.52915e9i −0.126067 0.0915930i
\(963\) 1.54223e10 + 1.12050e10i 0.556491 + 0.404314i
\(964\) 1.00754e9 3.10090e9i 0.0362238 0.111485i
\(965\) 5.88379e8 + 1.81085e9i 0.0210771 + 0.0648688i
\(966\) 4.17474e9 3.03313e9i 0.149008 0.108261i
\(967\) 3.87137e10 1.37680 0.688402 0.725329i \(-0.258312\pi\)
0.688402 + 0.725329i \(0.258312\pi\)
\(968\) 9.63878e9 + 2.57741e9i 0.341553 + 0.0913314i
\(969\) 2.75080e10 0.971240
\(970\) 3.19279e9 2.31970e9i 0.112323 0.0816075i
\(971\) −2.63837e9 8.12007e9i −0.0924844 0.284638i 0.894106 0.447856i \(-0.147812\pi\)
−0.986590 + 0.163219i \(0.947812\pi\)
\(972\) 6.01817e9 1.85220e10i 0.210200 0.646929i
\(973\) 2.86309e10 + 2.08016e10i 0.996416 + 0.723938i
\(974\) −7.79649e9 5.66448e9i −0.270360 0.196428i
\(975\) 1.16185e10 3.57581e10i 0.401453 1.23554i
\(976\) −1.21581e9 3.74187e9i −0.0418592 0.128829i
\(977\) −7.59772e9 + 5.52007e9i −0.260647 + 0.189371i −0.710432 0.703766i \(-0.751500\pi\)
0.449785 + 0.893137i \(0.351500\pi\)
\(978\) −9.94932e9 −0.340101
\(979\) −2.36165e9 + 1.28305e9i −0.0804406 + 0.0437024i
\(980\) −1.14713e9 −0.0389333
\(981\) 1.43706e10 1.04409e10i 0.485997 0.353098i
\(982\) 9.82179e8 + 3.02284e9i 0.0330979 + 0.101865i
\(983\) −4.22154e9 + 1.29926e10i −0.141753 + 0.436272i −0.996579 0.0826430i \(-0.973664\pi\)
0.854826 + 0.518915i \(0.173664\pi\)
\(984\) −7.45205e9 5.41423e9i −0.249341 0.181156i
\(985\) −4.69884e9 3.41391e9i −0.156662 0.113822i
\(986\) −3.57362e9 + 1.09985e10i −0.118724 + 0.365396i
\(987\) −8.51920e9 2.62194e10i −0.282026 0.867986i
\(988\) −1.08866e10 + 7.90958e9i −0.359123 + 0.260918i
\(989\) 1.30253e10 0.428155
\(990\) 1.38576e9 2.90722e9i 0.0453904 0.0952257i
\(991\) −5.18430e8 −0.0169213 −0.00846063 0.999964i \(-0.502693\pi\)
−0.00846063 + 0.999964i \(0.502693\pi\)
\(992\) −8.62967e9 + 6.26982e9i −0.280675 + 0.203922i
\(993\) 2.78444e9 + 8.56964e9i 0.0902435 + 0.277741i
\(994\) 8.20483e9 2.52519e10i 0.264982 0.815532i
\(995\) −8.16449e8 5.93185e8i −0.0262753 0.0190901i
\(996\) 2.72216e10 + 1.97776e10i 0.872982 + 0.634259i
\(997\) −1.52878e10 + 4.70511e10i −0.488555 + 1.50362i 0.338211 + 0.941070i \(0.390178\pi\)
−0.826766 + 0.562546i \(0.809822\pi\)
\(998\) −5.15875e9 1.58770e10i −0.164281 0.505605i
\(999\) −8.47719e8 + 6.15904e8i −0.0269013 + 0.0195449i
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.3.1 12
11.2 odd 10 242.8.a.o.1.1 6
11.4 even 5 inner 22.8.c.a.15.1 yes 12
11.9 even 5 242.8.a.q.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
22.8.c.a.3.1 12 1.1 even 1 trivial
22.8.c.a.15.1 yes 12 11.4 even 5 inner
242.8.a.o.1.1 6 11.2 odd 10
242.8.a.q.1.1 6 11.9 even 5