Properties

Label 32.8.g.a.13.18
Level $32$
Weight $8$
Character 32.13
Analytic conductor $9.996$
Analytic rank $0$
Dimension $108$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [32,8,Mod(5,32)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(32, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("32.5");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 32.g (of order \(8\), 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: \(9.99632081549\)
Analytic rank: \(0\)
Dimension: \(108\)
Relative dimension: \(27\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 13.18
Character \(\chi\) \(=\) 32.13
Dual form 32.8.g.a.5.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(5.84536 - 9.68668i) q^{2} +(3.37541 - 8.14896i) q^{3} +(-59.6635 - 113.244i) q^{4} +(482.880 - 200.015i) q^{5} +(-59.2059 - 80.3301i) q^{6} +(-141.209 + 141.209i) q^{7} +(-1445.72 - 84.0120i) q^{8} +(1491.43 + 1491.43i) q^{9} +O(q^{10})\) \(q+(5.84536 - 9.68668i) q^{2} +(3.37541 - 8.14896i) q^{3} +(-59.6635 - 113.244i) q^{4} +(482.880 - 200.015i) q^{5} +(-59.2059 - 80.3301i) q^{6} +(-141.209 + 141.209i) q^{7} +(-1445.72 - 84.0120i) q^{8} +(1491.43 + 1491.43i) q^{9} +(885.122 - 5846.66i) q^{10} +(-2979.30 - 7192.67i) q^{11} +(-1124.21 + 103.950i) q^{12} +(-2566.69 - 1063.16i) q^{13} +(542.427 + 2193.26i) q^{14} -4610.10i q^{15} +(-9264.53 + 13513.1i) q^{16} +6727.00i q^{17} +(23165.0 - 5729.06i) q^{18} +(-19530.1 - 8089.62i) q^{19} +(-51460.9 - 42749.7i) q^{20} +(674.066 + 1627.34i) q^{21} +(-87088.2 - 13184.2i) q^{22} +(46492.7 + 46492.7i) q^{23} +(-5564.49 + 11497.5i) q^{24} +(137924. - 137924. i) q^{25} +(-25301.7 + 18648.1i) q^{26} +(35009.6 - 14501.4i) q^{27} +(24416.1 + 7566.06i) q^{28} +(-55819.4 + 134760. i) q^{29} +(-44656.6 - 26947.7i) q^{30} +184799. q^{31} +(76742.6 + 168731. i) q^{32} -68669.1 q^{33} +(65162.3 + 39321.8i) q^{34} +(-39942.9 + 96430.6i) q^{35} +(79911.9 - 257880. i) q^{36} +(203734. - 84389.5i) q^{37} +(-192522. + 141895. i) q^{38} +(-17327.2 + 17327.2i) q^{39} +(-714911. + 248598. i) q^{40} +(491764. + 491764. i) q^{41} +(19703.7 + 2982.92i) q^{42} +(-189516. - 457531. i) q^{43} +(-636773. + 766529. i) q^{44} +(1.01849e6 + 421873. i) q^{45} +(722126. - 178593. i) q^{46} +309952. i q^{47} +(78846.1 + 121108. i) q^{48} +783663. i q^{49} +(-529810. - 2.14224e6i) q^{50} +(54818.1 + 22706.4i) q^{51} +(32741.2 + 354094. i) q^{52} +(-525171. - 1.26787e6i) q^{53} +(64172.7 - 423892. i) q^{54} +(-2.87729e6 - 2.87729e6i) q^{55} +(216011. - 192284. i) q^{56} +(-131844. + 131844. i) q^{57} +(979092. + 1.32842e6i) q^{58} +(797543. - 330353. i) q^{59} +(-522067. + 275055. i) q^{60} +(204787. - 494400. i) q^{61} +(1.08022e6 - 1.79009e6i) q^{62} -421205. q^{63} +(2.08304e6 + 242915. i) q^{64} -1.45205e6 q^{65} +(-401396. + 665176. i) q^{66} +(-1.18118e6 + 2.85162e6i) q^{67} +(761795. - 401357. i) q^{68} +(535799. - 221935. i) q^{69} +(700612. + 950586. i) q^{70} +(-2.14178e6 + 2.14178e6i) q^{71} +(-2.03089e6 - 2.28148e6i) q^{72} +(1.27197e6 + 1.27197e6i) q^{73} +(373446. - 2.46680e6i) q^{74} +(-658387. - 1.58949e6i) q^{75} +(249130. + 2.69432e6i) q^{76} +(1.43637e6 + 594964. i) q^{77} +(66559.4 + 269127. i) q^{78} -1.67355e6i q^{79} +(-1.77082e6 + 8.37825e6i) q^{80} +4.27858e6i q^{81} +(7.63809e6 - 1.88902e6i) q^{82} +(-5.03997e6 - 2.08762e6i) q^{83} +(144070. - 173427. i) q^{84} +(1.34550e6 + 3.24833e6i) q^{85} +(-5.53974e6 - 838657. i) q^{86} +(909740. + 909740. i) q^{87} +(3.70295e6 + 1.06489e7i) q^{88} +(221712. - 221712. i) q^{89} +(1.00400e7 - 7.39979e6i) q^{90} +(512565. - 212311. i) q^{91} +(2.49111e6 - 8.03895e6i) q^{92} +(623772. - 1.50592e6i) q^{93} +(3.00241e6 + 1.81178e6i) q^{94} -1.10487e7 q^{95} +(1.63402e6 - 55834.7i) q^{96} +9.62678e6 q^{97} +(7.59110e6 + 4.58079e6i) q^{98} +(6.28395e6 - 1.51708e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 13004 q^{10} - 4 q^{11} + 30668 q^{12} - 4 q^{13} - 26196 q^{14} - 52784 q^{16} + 102056 q^{18} - 4 q^{19} + 81996 q^{20} - 4 q^{21} - 374240 q^{22} - 143420 q^{23} + 380880 q^{24} - 4 q^{25} - 363984 q^{26} + 476084 q^{27} - 195464 q^{28} - 4 q^{29} + 870468 q^{30} - 714992 q^{31} + 535656 q^{32} - 8 q^{33} - 201072 q^{34} + 816500 q^{35} - 1669712 q^{36} - 4 q^{37} - 2533100 q^{38} - 283948 q^{39} + 2746344 q^{40} - 4 q^{41} + 4924936 q^{42} + 366180 q^{43} - 1585404 q^{44} + 8744 q^{45} - 2715812 q^{46} - 5044368 q^{48} - 1653804 q^{50} + 3002072 q^{51} + 8882212 q^{52} - 1815636 q^{53} + 6815776 q^{54} - 4191012 q^{55} - 3655000 q^{56} - 4 q^{57} - 12448736 q^{58} - 1835940 q^{59} - 6364808 q^{60} - 4559780 q^{61} + 12948600 q^{62} + 10001872 q^{63} + 16915544 q^{64} - 8 q^{65} - 11246068 q^{66} - 1940684 q^{67} - 8895536 q^{68} + 9580892 q^{69} - 8149480 q^{70} - 12348708 q^{71} + 12884564 q^{72} - 4 q^{73} + 10931436 q^{74} + 11573008 q^{75} + 14443516 q^{76} - 11914452 q^{77} - 38252364 q^{78} - 11333192 q^{80} + 15827196 q^{82} - 9565884 q^{83} + 8101984 q^{84} + 312496 q^{85} - 14812992 q^{86} + 40789108 q^{87} + 5716448 q^{88} - 4 q^{89} + 5335400 q^{90} - 3406996 q^{91} + 27562664 q^{92} - 8752 q^{93} - 14227032 q^{94} - 54872008 q^{95} - 25080448 q^{96} - 8 q^{97} + 57598104 q^{98} - 9738480 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(31\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.84536 9.68668i 0.516662 0.856190i
\(3\) 3.37541 8.14896i 0.0721775 0.174252i −0.883673 0.468104i \(-0.844937\pi\)
0.955851 + 0.293852i \(0.0949373\pi\)
\(4\) −59.6635 113.244i −0.466121 0.884721i
\(5\) 482.880 200.015i 1.72760 0.715597i 0.728056 0.685518i \(-0.240424\pi\)
0.999548 0.0300787i \(-0.00957578\pi\)
\(6\) −59.2059 80.3301i −0.111901 0.151827i
\(7\) −141.209 + 141.209i −0.155603 + 0.155603i −0.780615 0.625012i \(-0.785094\pi\)
0.625012 + 0.780615i \(0.285094\pi\)
\(8\) −1445.72 84.0120i −0.998316 0.0580132i
\(9\) 1491.43 + 1491.43i 0.681953 + 0.681953i
\(10\) 885.122 5846.66i 0.279900 1.84888i
\(11\) −2979.30 7192.67i −0.674901 1.62936i −0.773172 0.634196i \(-0.781331\pi\)
0.0982709 0.995160i \(-0.468669\pi\)
\(12\) −1124.21 + 103.950i −0.187808 + 0.0173656i
\(13\) −2566.69 1063.16i −0.324019 0.134213i 0.214744 0.976670i \(-0.431108\pi\)
−0.538763 + 0.842457i \(0.681108\pi\)
\(14\) 542.427 + 2193.26i 0.0528315 + 0.213620i
\(15\) 4610.10i 0.352688i
\(16\) −9264.53 + 13513.1i −0.565462 + 0.824774i
\(17\) 6727.00i 0.332086i 0.986119 + 0.166043i \(0.0530990\pi\)
−0.986119 + 0.166043i \(0.946901\pi\)
\(18\) 23165.0 5729.06i 0.936220 0.231542i
\(19\) −19530.1 8089.62i −0.653230 0.270577i 0.0313567 0.999508i \(-0.490017\pi\)
−0.684587 + 0.728932i \(0.740017\pi\)
\(20\) −51460.9 42749.7i −1.43838 1.19489i
\(21\) 674.066 + 1627.34i 0.0158831 + 0.0383452i
\(22\) −87088.2 13184.2i −1.74373 0.263982i
\(23\) 46492.7 + 46492.7i 0.796778 + 0.796778i 0.982586 0.185808i \(-0.0594903\pi\)
−0.185808 + 0.982586i \(0.559490\pi\)
\(24\) −5564.49 + 11497.5i −0.0821649 + 0.169771i
\(25\) 137924. 137924.i 1.76543 1.76543i
\(26\) −25301.7 + 18648.1i −0.282320 + 0.208079i
\(27\) 35009.6 14501.4i 0.342305 0.141787i
\(28\) 24416.1 + 7566.06i 0.210195 + 0.0651353i
\(29\) −55819.4 + 134760.i −0.425003 + 1.02605i 0.555847 + 0.831285i \(0.312394\pi\)
−0.980850 + 0.194764i \(0.937606\pi\)
\(30\) −44656.6 26947.7i −0.301968 0.182220i
\(31\) 184799. 1.11412 0.557062 0.830471i \(-0.311928\pi\)
0.557062 + 0.830471i \(0.311928\pi\)
\(32\) 76742.6 + 168731.i 0.414011 + 0.910272i
\(33\) −68669.1 −0.332631
\(34\) 65162.3 + 39321.8i 0.284328 + 0.171576i
\(35\) −39942.9 + 96430.6i −0.157471 + 0.380169i
\(36\) 79911.9 257880.i 0.285465 0.921210i
\(37\) 203734. 84389.5i 0.661239 0.273894i −0.0267210 0.999643i \(-0.508507\pi\)
0.687960 + 0.725749i \(0.258507\pi\)
\(38\) −192522. + 141895.i −0.569164 + 0.419492i
\(39\) −17327.2 + 17327.2i −0.0467738 + 0.0467738i
\(40\) −714911. + 248598.i −1.76621 + 0.614168i
\(41\) 491764. + 491764.i 1.11433 + 1.11433i 0.992558 + 0.121770i \(0.0388569\pi\)
0.121770 + 0.992558i \(0.461143\pi\)
\(42\) 19703.7 + 2982.92i 0.0410369 + 0.00621254i
\(43\) −189516. 457531.i −0.363501 0.877568i −0.994783 0.102015i \(-0.967471\pi\)
0.631282 0.775553i \(-0.282529\pi\)
\(44\) −636773. + 766529.i −1.12694 + 1.35658i
\(45\) 1.01849e6 + 421873.i 1.66615 + 0.690141i
\(46\) 722126. 178593.i 1.09386 0.270528i
\(47\) 309952.i 0.435464i 0.976009 + 0.217732i \(0.0698659\pi\)
−0.976009 + 0.217732i \(0.930134\pi\)
\(48\) 78846.1 + 121108.i 0.102905 + 0.158063i
\(49\) 783663.i 0.951575i
\(50\) −529810. 2.14224e6i −0.599412 2.42367i
\(51\) 54818.1 + 22706.4i 0.0578666 + 0.0239691i
\(52\) 32741.2 + 354094.i 0.0322911 + 0.349226i
\(53\) −525171. 1.26787e6i −0.484546 1.16980i −0.957428 0.288672i \(-0.906786\pi\)
0.472882 0.881126i \(-0.343214\pi\)
\(54\) 64172.7 423892.i 0.0554590 0.366334i
\(55\) −2.87729e6 2.87729e6i −2.33192 2.33192i
\(56\) 216011. 192284.i 0.164368 0.146314i
\(57\) −131844. + 131844.i −0.0942970 + 0.0942970i
\(58\) 979092. + 1.32842e6i 0.658909 + 0.894003i
\(59\) 797543. 330353.i 0.505559 0.209410i −0.115301 0.993331i \(-0.536783\pi\)
0.620861 + 0.783921i \(0.286783\pi\)
\(60\) −522067. + 275055.i −0.312031 + 0.164395i
\(61\) 204787. 494400.i 0.115518 0.278884i −0.855537 0.517742i \(-0.826773\pi\)
0.971055 + 0.238857i \(0.0767728\pi\)
\(62\) 1.08022e6 1.79009e6i 0.575626 0.953902i
\(63\) −421205. −0.212228
\(64\) 2.08304e6 + 242915.i 0.993269 + 0.115831i
\(65\) −1.45205e6 −0.655820
\(66\) −401396. + 665176.i −0.171858 + 0.284795i
\(67\) −1.18118e6 + 2.85162e6i −0.479793 + 1.15832i 0.479913 + 0.877316i \(0.340668\pi\)
−0.959706 + 0.281007i \(0.909332\pi\)
\(68\) 761795. 401357.i 0.293803 0.154792i
\(69\) 535799. 221935.i 0.196350 0.0813306i
\(70\) 700612. + 950586.i 0.244138 + 0.331244i
\(71\) −2.14178e6 + 2.14178e6i −0.710184 + 0.710184i −0.966574 0.256389i \(-0.917467\pi\)
0.256389 + 0.966574i \(0.417467\pi\)
\(72\) −2.03089e6 2.28148e6i −0.641242 0.720366i
\(73\) 1.27197e6 + 1.27197e6i 0.382691 + 0.382691i 0.872071 0.489380i \(-0.162777\pi\)
−0.489380 + 0.872071i \(0.662777\pi\)
\(74\) 373446. 2.46680e6i 0.107132 0.707656i
\(75\) −658387. 1.58949e6i −0.180205 0.435053i
\(76\) 249130. + 2.69432e6i 0.0650995 + 0.704048i
\(77\) 1.43637e6 + 594964.i 0.358549 + 0.148516i
\(78\) 66559.4 + 269127.i 0.0158810 + 0.0642135i
\(79\) 1.67355e6i 0.381895i −0.981600 0.190948i \(-0.938844\pi\)
0.981600 0.190948i \(-0.0611561\pi\)
\(80\) −1.77082e6 + 8.37825e6i −0.386688 + 1.82953i
\(81\) 4.27858e6i 0.894545i
\(82\) 7.63809e6 1.88902e6i 1.52981 0.378345i
\(83\) −5.03997e6 2.08762e6i −0.967508 0.400755i −0.157724 0.987483i \(-0.550416\pi\)
−0.809784 + 0.586728i \(0.800416\pi\)
\(84\) 144070. 173427.i 0.0265213 0.0319256i
\(85\) 1.34550e6 + 3.24833e6i 0.237640 + 0.573713i
\(86\) −5.53974e6 838657.i −0.939172 0.142180i
\(87\) 909740. + 909740.i 0.148115 + 0.148115i
\(88\) 3.70295e6 + 1.06489e7i 0.579241 + 1.66576i
\(89\) 221712. 221712.i 0.0333368 0.0333368i −0.690242 0.723579i \(-0.742496\pi\)
0.723579 + 0.690242i \(0.242496\pi\)
\(90\) 1.00400e7 7.39979e6i 1.45173 1.06997i
\(91\) 512565. 212311.i 0.0713024 0.0295344i
\(92\) 2.49111e6 8.03895e6i 0.333531 1.07632i
\(93\) 623772. 1.50592e6i 0.0804148 0.194138i
\(94\) 3.00241e6 + 1.81178e6i 0.372840 + 0.224988i
\(95\) −1.10487e7 −1.32215
\(96\) 1.63402e6 55834.7i 0.188499 0.00644102i
\(97\) 9.62678e6 1.07098 0.535488 0.844543i \(-0.320128\pi\)
0.535488 + 0.844543i \(0.320128\pi\)
\(98\) 7.59110e6 + 4.58079e6i 0.814729 + 0.491643i
\(99\) 6.28395e6 1.51708e7i 0.650893 1.57139i
\(100\) −2.38481e7 7.39007e6i −2.38481 0.739007i
\(101\) 728195. 301628.i 0.0703272 0.0291305i −0.347243 0.937775i \(-0.612882\pi\)
0.417570 + 0.908645i \(0.362882\pi\)
\(102\) 540381. 398278.i 0.0504196 0.0371609i
\(103\) 2.11052e6 2.11052e6i 0.190309 0.190309i −0.605521 0.795830i \(-0.707035\pi\)
0.795830 + 0.605521i \(0.207035\pi\)
\(104\) 3.62138e6 + 1.75265e6i 0.315688 + 0.152785i
\(105\) 650986. + 650986.i 0.0548793 + 0.0548793i
\(106\) −1.53513e7 2.32402e6i −1.25191 0.189526i
\(107\) 7.11467e6 + 1.71763e7i 0.561450 + 1.35546i 0.908606 + 0.417653i \(0.137147\pi\)
−0.347156 + 0.937807i \(0.612853\pi\)
\(108\) −3.73100e6 3.09942e6i −0.284998 0.236754i
\(109\) −6.39882e6 2.65048e6i −0.473268 0.196034i 0.133284 0.991078i \(-0.457448\pi\)
−0.606552 + 0.795044i \(0.707448\pi\)
\(110\) −4.46902e7 + 1.10526e7i −3.20138 + 0.791753i
\(111\) 1.94507e6i 0.134991i
\(112\) −599936. 3.21640e6i −0.0403498 0.216325i
\(113\) 6.22894e6i 0.406106i −0.979168 0.203053i \(-0.934914\pi\)
0.979168 0.203053i \(-0.0650864\pi\)
\(114\) 506454. + 2.04780e6i 0.0320165 + 0.129456i
\(115\) 3.17496e7 + 1.31511e7i 1.94669 + 0.806345i
\(116\) 1.85912e7 1.71903e6i 1.10587 0.102254i
\(117\) −2.24241e6 5.41366e6i −0.129439 0.312493i
\(118\) 1.46190e6 9.65658e6i 0.0819089 0.541049i
\(119\) −949910. 949910.i −0.0516736 0.0516736i
\(120\) −387304. + 6.66489e6i −0.0204606 + 0.352094i
\(121\) −2.90788e7 + 2.90788e7i −1.49220 + 1.49220i
\(122\) −3.59204e6 4.87366e6i −0.179094 0.242994i
\(123\) 5.66726e6 2.34746e6i 0.274603 0.113744i
\(124\) −1.10258e7 2.09274e7i −0.519317 0.985690i
\(125\) 2.33876e7 5.64627e7i 1.07103 2.58569i
\(126\) −2.46210e6 + 4.08008e6i −0.109650 + 0.181707i
\(127\) −1.27770e7 −0.553499 −0.276749 0.960942i \(-0.589257\pi\)
−0.276749 + 0.960942i \(0.589257\pi\)
\(128\) 1.45291e7 1.87578e7i 0.612357 0.790581i
\(129\) −4.36809e6 −0.179155
\(130\) −8.48775e6 + 1.40655e7i −0.338837 + 0.561506i
\(131\) 1.82759e6 4.41219e6i 0.0710279 0.171477i −0.884379 0.466770i \(-0.845418\pi\)
0.955407 + 0.295294i \(0.0954175\pi\)
\(132\) 4.09704e6 + 7.77639e6i 0.155046 + 0.294286i
\(133\) 3.90013e6 1.61549e6i 0.143747 0.0595420i
\(134\) 2.07183e7 + 2.81105e7i 0.743854 + 1.00926i
\(135\) 1.40049e7 1.40049e7i 0.489905 0.489905i
\(136\) 565149. 9.72533e6i 0.0192654 0.331527i
\(137\) −1.38701e7 1.38701e7i −0.460847 0.460847i 0.438086 0.898933i \(-0.355657\pi\)
−0.898933 + 0.438086i \(0.855657\pi\)
\(138\) 982122. 6.48740e6i 0.0318118 0.210133i
\(139\) 1.82575e7 + 4.40776e7i 0.576620 + 1.39208i 0.895828 + 0.444400i \(0.146583\pi\)
−0.319208 + 0.947685i \(0.603417\pi\)
\(140\) 1.33033e7 1.23009e6i 0.409744 0.0378869i
\(141\) 2.52579e6 + 1.04622e6i 0.0758805 + 0.0314307i
\(142\) 8.22727e6 + 3.32662e7i 0.241127 + 0.974977i
\(143\) 2.16288e7i 0.618524i
\(144\) −3.39713e7 + 6.33646e6i −0.948075 + 0.176839i
\(145\) 7.62376e7i 2.07674i
\(146\) 1.97564e7 4.88606e6i 0.525378 0.129934i
\(147\) 6.38604e6 + 2.64518e6i 0.165814 + 0.0686823i
\(148\) −2.17121e7 1.80368e7i −0.550537 0.457344i
\(149\) −8.81187e6 2.12737e7i −0.218231 0.526856i 0.776412 0.630225i \(-0.217038\pi\)
−0.994643 + 0.103370i \(0.967038\pi\)
\(150\) −1.92454e7 2.91354e6i −0.465593 0.0704858i
\(151\) −3.79656e7 3.79656e7i −0.897370 0.897370i 0.0978329 0.995203i \(-0.468809\pi\)
−0.995203 + 0.0978329i \(0.968809\pi\)
\(152\) 2.75553e7 + 1.33360e7i 0.636433 + 0.308017i
\(153\) −1.00329e7 + 1.00329e7i −0.226467 + 0.226467i
\(154\) 1.41593e7 1.04359e7i 0.312406 0.230254i
\(155\) 8.92357e7 3.69627e7i 1.92477 0.797264i
\(156\) 2.99601e6 + 928406.i 0.0631841 + 0.0195795i
\(157\) 2.19236e6 5.29283e6i 0.0452130 0.109154i −0.899660 0.436592i \(-0.856185\pi\)
0.944873 + 0.327438i \(0.106185\pi\)
\(158\) −1.62112e7 9.78251e6i −0.326975 0.197311i
\(159\) −1.21045e7 −0.238813
\(160\) 7.08063e7 + 6.61273e7i 1.36663 + 1.27632i
\(161\) −1.31303e7 −0.247962
\(162\) 4.14453e7 + 2.50099e7i 0.765901 + 0.462177i
\(163\) −3.32672e7 + 8.03142e7i −0.601673 + 1.45257i 0.270186 + 0.962808i \(0.412915\pi\)
−0.871859 + 0.489758i \(0.837085\pi\)
\(164\) 2.63491e7 8.50298e7i 0.466457 1.50528i
\(165\) −3.31589e7 + 1.37349e7i −0.574655 + 0.238030i
\(166\) −4.96826e7 + 3.66177e7i −0.842997 + 0.621316i
\(167\) −4.46578e7 + 4.46578e7i −0.741976 + 0.741976i −0.972958 0.230982i \(-0.925806\pi\)
0.230982 + 0.972958i \(0.425806\pi\)
\(168\) −837792. 2.40930e6i −0.0136318 0.0392020i
\(169\) −3.89123e7 3.89123e7i −0.620131 0.620131i
\(170\) 3.93305e7 + 5.95422e6i 0.613986 + 0.0929508i
\(171\) −1.70626e7 4.11928e7i −0.260951 0.629992i
\(172\) −4.05056e7 + 4.87595e7i −0.606967 + 0.730650i
\(173\) −7.80431e7 3.23265e7i −1.14597 0.474676i −0.272790 0.962074i \(-0.587946\pi\)
−0.873180 + 0.487397i \(0.837946\pi\)
\(174\) 1.41301e7 3.49460e6i 0.203340 0.0502892i
\(175\) 3.89521e7i 0.549412i
\(176\) 1.24797e8 + 2.63771e7i 1.72548 + 0.364697i
\(177\) 7.61422e6i 0.103209i
\(178\) −851665. 3.44363e6i −0.0113188 0.0457664i
\(179\) −7.54027e7 3.12328e7i −0.982656 0.407029i −0.167247 0.985915i \(-0.553488\pi\)
−0.815409 + 0.578886i \(0.803488\pi\)
\(180\) −1.29921e7 1.40509e8i −0.166045 1.79576i
\(181\) −2.45629e7 5.93001e7i −0.307897 0.743328i −0.999773 0.0213120i \(-0.993216\pi\)
0.691876 0.722016i \(-0.256784\pi\)
\(182\) 939535. 6.20609e6i 0.0115522 0.0763076i
\(183\) −3.33760e6 3.33760e6i −0.0402584 0.0402584i
\(184\) −6.33093e7 7.11212e7i −0.749212 0.841660i
\(185\) 8.15000e7 8.15000e7i 0.946360 0.946360i
\(186\) −1.09412e7 1.48449e7i −0.124672 0.169154i
\(187\) 4.83851e7 2.00418e7i 0.541086 0.224125i
\(188\) 3.51003e7 1.84929e7i 0.385264 0.202979i
\(189\) −2.89592e6 + 6.99138e6i −0.0312012 + 0.0753262i
\(190\) −6.45837e7 + 1.07025e8i −0.683102 + 1.13201i
\(191\) 7.10470e7 0.737783 0.368892 0.929472i \(-0.379737\pi\)
0.368892 + 0.929472i \(0.379737\pi\)
\(192\) 9.01060e6 1.61546e7i 0.0918754 0.164719i
\(193\) −7.65287e7 −0.766256 −0.383128 0.923695i \(-0.625153\pi\)
−0.383128 + 0.923695i \(0.625153\pi\)
\(194\) 5.62720e7 9.32516e7i 0.553333 0.916959i
\(195\) −4.90126e6 + 1.18327e7i −0.0473354 + 0.114278i
\(196\) 8.87454e7 4.67561e7i 0.841879 0.443550i
\(197\) −6.92775e7 + 2.86957e7i −0.645595 + 0.267414i −0.681363 0.731946i \(-0.738612\pi\)
0.0357677 + 0.999360i \(0.488612\pi\)
\(198\) −1.10223e8 1.49549e8i −1.00912 1.36917i
\(199\) 1.11038e8 1.11038e8i 0.998821 0.998821i −0.00117819 0.999999i \(-0.500375\pi\)
0.999999 + 0.00117819i \(0.000375031\pi\)
\(200\) −2.10986e8 + 1.87812e8i −1.86487 + 1.66004i
\(201\) 1.92508e7 + 1.92508e7i 0.167210 + 0.167210i
\(202\) 1.33479e6 8.81692e6i 0.0113942 0.0752640i
\(203\) −1.11471e7 2.69114e7i −0.0935244 0.225788i
\(204\) −699271. 7.56257e6i −0.00576687 0.0623683i
\(205\) 3.35823e8 + 1.39102e8i 2.72253 + 1.12771i
\(206\) −8.10719e6 3.27807e7i −0.0646152 0.261266i
\(207\) 1.38681e8i 1.08673i
\(208\) 3.81457e7 2.48343e7i 0.293916 0.191350i
\(209\) 1.64575e8i 1.24696i
\(210\) 1.01111e7 2.50064e6i 0.0753412 0.0186331i
\(211\) −1.15722e8 4.79335e7i −0.848059 0.351277i −0.0840327 0.996463i \(-0.526780\pi\)
−0.764026 + 0.645186i \(0.776780\pi\)
\(212\) −1.12246e8 + 1.35118e8i −0.809087 + 0.973955i
\(213\) 1.02239e7 + 2.46827e7i 0.0724916 + 0.175010i
\(214\) 2.07969e8 + 3.14843e7i 1.45061 + 0.219607i
\(215\) −1.83026e8 1.83026e8i −1.25597 1.25597i
\(216\) −5.18322e7 + 1.80237e7i −0.349954 + 0.121690i
\(217\) −2.60952e7 + 2.60952e7i −0.173361 + 0.173361i
\(218\) −6.30777e7 + 4.64903e7i −0.412361 + 0.303924i
\(219\) 1.46587e7 6.07183e6i 0.0943064 0.0390630i
\(220\) −1.54167e8 + 4.97506e8i −0.976142 + 3.15006i
\(221\) 7.15186e6 1.72661e7i 0.0445703 0.107602i
\(222\) −1.88413e7 1.13696e7i −0.115578 0.0697447i
\(223\) −1.35075e8 −0.815656 −0.407828 0.913059i \(-0.633714\pi\)
−0.407828 + 0.913059i \(0.633714\pi\)
\(224\) −3.46630e7 1.29896e7i −0.206062 0.0772197i
\(225\) 4.11408e8 2.40788
\(226\) −6.03378e7 3.64104e7i −0.347704 0.209820i
\(227\) 5.51550e6 1.33156e7i 0.0312964 0.0755561i −0.907459 0.420141i \(-0.861980\pi\)
0.938755 + 0.344585i \(0.111980\pi\)
\(228\) 2.27968e7 + 7.06429e6i 0.127380 + 0.0394727i
\(229\) 3.43654e7 1.42346e7i 0.189102 0.0783287i −0.286123 0.958193i \(-0.592367\pi\)
0.475225 + 0.879864i \(0.342367\pi\)
\(230\) 3.12979e8 2.30675e8i 1.69616 1.25013i
\(231\) 9.69667e6 9.69667e6i 0.0517584 0.0517584i
\(232\) 9.20204e7 1.90135e8i 0.483812 0.999664i
\(233\) −2.67221e7 2.67221e7i −0.138397 0.138397i 0.634514 0.772911i \(-0.281200\pi\)
−0.772911 + 0.634514i \(0.781200\pi\)
\(234\) −6.55481e7 9.92327e6i −0.334429 0.0506290i
\(235\) 6.19952e7 + 1.49670e8i 0.311617 + 0.752309i
\(236\) −8.49949e7 7.06072e7i −0.420921 0.349669i
\(237\) −1.36377e7 5.64892e6i −0.0665460 0.0275642i
\(238\) −1.47540e7 + 3.64891e6i −0.0709401 + 0.0175446i
\(239\) 4.44632e7i 0.210673i −0.994437 0.105336i \(-0.966408\pi\)
0.994437 0.105336i \(-0.0335919\pi\)
\(240\) 6.22968e7 + 4.27104e7i 0.290888 + 0.199432i
\(241\) 1.75636e7i 0.0808266i 0.999183 + 0.0404133i \(0.0128674\pi\)
−0.999183 + 0.0404133i \(0.987133\pi\)
\(242\) 1.11701e8 + 4.51653e8i 0.506644 + 2.04857i
\(243\) 1.11432e8 + 4.61566e7i 0.498181 + 0.206353i
\(244\) −6.82063e7 + 6.30668e6i −0.300580 + 0.0277930i
\(245\) 1.56745e8 + 3.78415e8i 0.680944 + 1.64394i
\(246\) 1.03881e7 6.86187e7i 0.0444902 0.293880i
\(247\) 4.15270e7 + 4.15270e7i 0.175344 + 0.175344i
\(248\) −2.67167e8 1.55253e7i −1.11225 0.0646339i
\(249\) −3.40239e7 + 3.40239e7i −0.139665 + 0.139665i
\(250\) −4.10227e8 5.56593e8i −1.66048 2.25293i
\(251\) 1.89285e8 7.84042e7i 0.755539 0.312955i 0.0285400 0.999593i \(-0.490914\pi\)
0.727000 + 0.686638i \(0.240914\pi\)
\(252\) 2.51306e7 + 4.76991e7i 0.0989239 + 0.187762i
\(253\) 1.95891e8 4.72923e8i 0.760488 1.83598i
\(254\) −7.46863e7 + 1.23767e8i −0.285972 + 0.473900i
\(255\) 3.10122e7 0.117123
\(256\) −9.67725e7 2.50385e8i −0.360506 0.932757i
\(257\) 1.49895e8 0.550834 0.275417 0.961325i \(-0.411184\pi\)
0.275417 + 0.961325i \(0.411184\pi\)
\(258\) −2.55331e7 + 4.23123e7i −0.0925623 + 0.153390i
\(259\) −1.68525e7 + 4.06856e7i −0.0602720 + 0.145509i
\(260\) 8.66343e7 + 1.64436e8i 0.305691 + 0.580217i
\(261\) −2.84236e8 + 1.17734e8i −0.989548 + 0.409884i
\(262\) −3.20566e7 4.34941e7i −0.110119 0.149409i
\(263\) 2.39703e8 2.39703e8i 0.812508 0.812508i −0.172501 0.985009i \(-0.555185\pi\)
0.985009 + 0.172501i \(0.0551848\pi\)
\(264\) 9.92761e7 + 5.76903e6i 0.332071 + 0.0192970i
\(265\) −5.07189e8 5.07189e8i −1.67421 1.67421i
\(266\) 7.14897e6 4.72225e7i 0.0232894 0.153838i
\(267\) −1.05835e6 2.55509e6i −0.00340283 0.00821516i
\(268\) 3.93403e8 3.63759e7i 1.24843 0.115436i
\(269\) −2.73966e8 1.13480e8i −0.858151 0.355458i −0.0901668 0.995927i \(-0.528740\pi\)
−0.767984 + 0.640469i \(0.778740\pi\)
\(270\) −5.37973e7 2.17525e8i −0.166336 0.672567i
\(271\) 4.53786e8i 1.38503i 0.721405 + 0.692513i \(0.243497\pi\)
−0.721405 + 0.692513i \(0.756503\pi\)
\(272\) −9.09027e7 6.23225e7i −0.273896 0.187782i
\(273\) 4.89351e6i 0.0145563i
\(274\) −2.15431e8 + 5.32794e7i −0.632675 + 0.156470i
\(275\) −1.40296e9 5.81125e8i −4.06800 1.68502i
\(276\) −5.71005e7 4.74347e7i −0.163478 0.135805i
\(277\) 2.29919e8 + 5.55073e8i 0.649973 + 1.56917i 0.812815 + 0.582522i \(0.197934\pi\)
−0.162842 + 0.986652i \(0.552066\pi\)
\(278\) 5.33687e8 + 8.07944e7i 1.48981 + 0.225541i
\(279\) 2.75615e8 + 2.75615e8i 0.759780 + 0.759780i
\(280\) 6.58474e7 1.36056e8i 0.179261 0.370393i
\(281\) 1.77116e8 1.77116e8i 0.476196 0.476196i −0.427717 0.903913i \(-0.640682\pi\)
0.903913 + 0.427717i \(0.140682\pi\)
\(282\) 2.48985e7 1.83510e7i 0.0661152 0.0487290i
\(283\) −3.14752e8 + 1.30374e8i −0.825498 + 0.341932i −0.755119 0.655588i \(-0.772421\pi\)
−0.0703788 + 0.997520i \(0.522421\pi\)
\(284\) 3.70331e8 + 1.14758e8i 0.959347 + 0.297283i
\(285\) −3.72939e7 + 9.00355e7i −0.0954292 + 0.230386i
\(286\) 2.09511e8 + 1.26428e8i 0.529574 + 0.319568i
\(287\) −1.38883e8 −0.346785
\(288\) −1.37195e8 + 3.66108e8i −0.338427 + 0.903098i
\(289\) 3.65086e8 0.889719
\(290\) 7.38489e8 + 4.45636e8i 1.77808 + 1.07297i
\(291\) 3.24943e7 7.84482e7i 0.0773004 0.186620i
\(292\) 6.81533e7 2.19934e8i 0.160194 0.516955i
\(293\) −7.66018e8 + 3.17295e8i −1.77911 + 0.736930i −0.786209 + 0.617961i \(0.787959\pi\)
−0.992898 + 0.118970i \(0.962041\pi\)
\(294\) 6.29517e7 4.63975e7i 0.144475 0.106483i
\(295\) 3.19042e8 3.19042e8i 0.723553 0.723553i
\(296\) −3.01632e8 + 1.04887e8i −0.676015 + 0.235072i
\(297\) −2.08608e8 2.08608e8i −0.462044 0.462044i
\(298\) −2.57580e8 3.89949e7i −0.563840 0.0853593i
\(299\) −6.99032e7 1.68761e8i −0.151233 0.365110i
\(300\) −1.40719e8 + 1.69393e8i −0.300903 + 0.362219i
\(301\) 9.13685e7 + 3.78461e7i 0.193114 + 0.0799904i
\(302\) −5.89684e8 + 1.45838e8i −1.23196 + 0.304682i
\(303\) 6.95215e6i 0.0143572i
\(304\) 2.90253e8 1.88965e8i 0.592541 0.385766i
\(305\) 2.79696e8i 0.564466i
\(306\) 3.85394e7 + 1.55831e8i 0.0768918 + 0.310905i
\(307\) 4.86790e8 + 2.01635e8i 0.960190 + 0.397724i 0.807051 0.590481i \(-0.201062\pi\)
0.153138 + 0.988205i \(0.451062\pi\)
\(308\) −1.83227e7 1.98158e8i −0.0357323 0.386442i
\(309\) −1.00747e7 2.43224e7i −0.0194257 0.0468978i
\(310\) 1.63570e8 1.08046e9i 0.311844 2.05988i
\(311\) −6.27067e7 6.27067e7i −0.118210 0.118210i 0.645528 0.763737i \(-0.276638\pi\)
−0.763737 + 0.645528i \(0.776638\pi\)
\(312\) 2.65059e7 2.35946e7i 0.0494086 0.0439816i
\(313\) −4.49748e7 + 4.49748e7i −0.0829018 + 0.0829018i −0.747342 0.664440i \(-0.768670\pi\)
0.664440 + 0.747342i \(0.268670\pi\)
\(314\) −3.84548e7 5.21752e7i −0.0700966 0.0951066i
\(315\) −2.03392e8 + 8.42476e7i −0.366645 + 0.151869i
\(316\) −1.89520e8 + 9.98500e7i −0.337871 + 0.178009i
\(317\) −2.45055e8 + 5.91615e8i −0.432072 + 1.04311i 0.546547 + 0.837429i \(0.315942\pi\)
−0.978618 + 0.205685i \(0.934058\pi\)
\(318\) −7.07553e7 + 1.17253e8i −0.123385 + 0.204469i
\(319\) 1.13559e9 1.95863
\(320\) 1.05444e9 2.99340e8i 1.79886 0.510670i
\(321\) 1.63984e8 0.276716
\(322\) −7.67515e7 + 1.27189e8i −0.128112 + 0.212303i
\(323\) 5.44189e7 1.31379e8i 0.0898547 0.216928i
\(324\) 4.84525e8 2.55275e8i 0.791423 0.416967i
\(325\) −5.00643e8 + 2.07373e8i −0.808977 + 0.335089i
\(326\) 5.83519e8 + 7.91715e8i 0.932811 + 1.26563i
\(327\) −4.31972e7 + 4.31972e7i −0.0683186 + 0.0683186i
\(328\) −6.69637e8 7.52265e8i −1.04781 1.17710i
\(329\) −4.37679e7 4.37679e7i −0.0677595 0.0677595i
\(330\) −6.07805e7 + 4.01485e8i −0.0931034 + 0.614994i
\(331\) 1.86901e8 + 4.51220e8i 0.283279 + 0.683896i 0.999908 0.0135583i \(-0.00431588\pi\)
−0.716629 + 0.697455i \(0.754316\pi\)
\(332\) 6.42910e7 + 6.95303e8i 0.0964199 + 1.04278i
\(333\) 4.29717e8 + 1.77995e8i 0.637716 + 0.264151i
\(334\) 1.71545e8 + 6.93627e8i 0.251922 + 1.01862i
\(335\) 1.61324e9i 2.34446i
\(336\) −2.82353e7 5.96780e6i −0.0406074 0.00858276i
\(337\) 2.39548e8i 0.340948i −0.985362 0.170474i \(-0.945470\pi\)
0.985362 0.170474i \(-0.0545299\pi\)
\(338\) −6.04388e8 + 1.49475e8i −0.851348 + 0.210552i
\(339\) −5.07594e7 2.10252e7i −0.0707648 0.0293118i
\(340\) 2.87578e8 3.46178e8i 0.396807 0.477664i
\(341\) −5.50572e8 1.32920e9i −0.751924 1.81531i
\(342\) −4.98759e8 7.55067e7i −0.674216 0.102069i
\(343\) −2.26951e8 2.26951e8i −0.303671 0.303671i
\(344\) 2.35547e8 + 6.77381e8i 0.311978 + 0.897178i
\(345\) 2.14336e8 2.14336e8i 0.281014 0.281014i
\(346\) −7.69327e8 + 5.67018e8i −0.998492 + 0.735920i
\(347\) 1.25659e9 5.20496e8i 1.61451 0.668751i 0.621136 0.783703i \(-0.286671\pi\)
0.993371 + 0.114952i \(0.0366715\pi\)
\(348\) 4.87445e7 1.57301e8i 0.0620010 0.200080i
\(349\) 4.16411e8 1.00530e9i 0.524364 1.26593i −0.410804 0.911724i \(-0.634752\pi\)
0.935168 0.354203i \(-0.115248\pi\)
\(350\) 3.77317e8 + 2.27689e8i 0.470400 + 0.283860i
\(351\) −1.05276e8 −0.129943
\(352\) 9.84991e8 1.05469e9i 1.20374 1.28891i
\(353\) −1.52792e9 −1.84879 −0.924397 0.381431i \(-0.875431\pi\)
−0.924397 + 0.381431i \(0.875431\pi\)
\(354\) −7.37565e7 4.45079e7i −0.0883668 0.0533243i
\(355\) −6.05834e8 + 1.46261e9i −0.718711 + 1.73512i
\(356\) −3.83357e7 1.18795e7i −0.0450327 0.0139548i
\(357\) −1.09471e7 + 4.53444e6i −0.0127339 + 0.00527455i
\(358\) −7.43298e8 + 5.47835e8i −0.856195 + 0.631043i
\(359\) 3.13976e8 3.13976e8i 0.358150 0.358150i −0.504980 0.863131i \(-0.668500\pi\)
0.863131 + 0.504980i \(0.168500\pi\)
\(360\) −1.43701e9 6.95473e8i −1.62330 0.785637i
\(361\) −3.16081e8 3.16081e8i −0.353609 0.353609i
\(362\) −7.18000e8 1.08697e8i −0.795508 0.120431i
\(363\) 1.38809e8 + 3.35115e8i 0.152316 + 0.367722i
\(364\) −5.46245e7 4.53778e7i −0.0593653 0.0493161i
\(365\) 8.68625e8 + 3.59796e8i 0.934991 + 0.387286i
\(366\) −5.18398e7 + 1.28208e7i −0.0552687 + 0.0136688i
\(367\) 9.29519e8i 0.981583i −0.871277 0.490792i \(-0.836708\pi\)
0.871277 0.490792i \(-0.163292\pi\)
\(368\) −1.05899e9 + 1.97528e8i −1.10771 + 0.206615i
\(369\) 1.46686e9i 1.51984i
\(370\) −3.13068e8 1.26586e9i −0.321316 1.29921i
\(371\) 2.53193e8 + 1.04876e8i 0.257421 + 0.106627i
\(372\) −2.07753e8 + 1.92098e7i −0.209241 + 0.0193474i
\(373\) −6.21107e7 1.49949e8i −0.0619706 0.149610i 0.889861 0.456232i \(-0.150801\pi\)
−0.951831 + 0.306622i \(0.900801\pi\)
\(374\) 8.86903e7 5.85843e8i 0.0876648 0.579069i
\(375\) −3.81169e8 3.81169e8i −0.373257 0.373257i
\(376\) 2.60397e7 4.48103e8i 0.0252627 0.434731i
\(377\) 2.86542e8 2.86542e8i 0.275419 0.275419i
\(378\) 5.07955e7 + 6.89190e7i 0.0483731 + 0.0656323i
\(379\) 1.24582e9 5.16034e8i 1.17549 0.486902i 0.292483 0.956271i \(-0.405519\pi\)
0.883002 + 0.469369i \(0.155519\pi\)
\(380\) 6.59206e8 + 1.25120e9i 0.616280 + 1.16973i
\(381\) −4.31277e7 + 1.04119e8i −0.0399502 + 0.0964482i
\(382\) 4.15295e8 6.88209e8i 0.381184 0.631682i
\(383\) 1.16962e9 1.06377 0.531887 0.846815i \(-0.321483\pi\)
0.531887 + 0.846815i \(0.321483\pi\)
\(384\) −1.03815e8 1.81712e8i −0.0935619 0.163767i
\(385\) 8.12596e8 0.725708
\(386\) −4.47338e8 + 7.41309e8i −0.395895 + 0.656060i
\(387\) 3.99726e8 9.65025e8i 0.350570 0.846350i
\(388\) −5.74368e8 1.09018e9i −0.499205 0.947515i
\(389\) 1.41462e9 5.85956e8i 1.21848 0.504709i 0.321551 0.946892i \(-0.395796\pi\)
0.896925 + 0.442183i \(0.145796\pi\)
\(390\) 8.59698e7 + 1.16643e8i 0.0733871 + 0.0995711i
\(391\) −3.12757e8 + 3.12757e8i −0.264599 + 0.264599i
\(392\) 6.58371e7 1.13295e9i 0.0552039 0.949973i
\(393\) −2.97859e7 2.97859e7i −0.0247535 0.0247535i
\(394\) −1.26986e8 + 8.38805e8i −0.104597 + 0.690914i
\(395\) −3.34736e8 8.08124e8i −0.273283 0.659763i
\(396\) −2.09293e9 + 1.93522e8i −1.69364 + 0.156602i
\(397\) −1.21161e9 5.01866e8i −0.971844 0.402551i −0.160446 0.987045i \(-0.551293\pi\)
−0.811398 + 0.584494i \(0.801293\pi\)
\(398\) −4.26534e8 1.72465e9i −0.339128 1.37123i
\(399\) 3.72350e7i 0.0293458i
\(400\) 5.85981e8 + 3.14158e9i 0.457798 + 2.45436i
\(401\) 3.11173e8i 0.240989i −0.992714 0.120495i \(-0.961552\pi\)
0.992714 0.120495i \(-0.0384480\pi\)
\(402\) 2.99004e8 7.39483e7i 0.229554 0.0567724i
\(403\) −4.74321e8 1.96470e8i −0.360998 0.149530i
\(404\) −7.76044e7 6.44677e7i −0.0585533 0.0486416i
\(405\) 8.55782e8 + 2.06604e9i 0.640134 + 1.54542i
\(406\) −3.25841e8 4.93288e7i −0.241638 0.0365813i
\(407\) −1.21397e9 1.21397e9i −0.892542 0.892542i
\(408\) −7.73437e7 3.74324e7i −0.0563786 0.0272858i
\(409\) 3.01713e8 3.01713e8i 0.218053 0.218053i −0.589624 0.807678i \(-0.700724\pi\)
0.807678 + 0.589624i \(0.200724\pi\)
\(410\) 3.31045e9 2.43991e9i 2.37216 1.74836i
\(411\) −1.59844e8 + 6.62095e7i −0.113566 + 0.0470407i
\(412\) −3.64926e8 1.13083e8i −0.257078 0.0796633i
\(413\) −6.59712e7 + 1.59269e8i −0.0460818 + 0.111251i
\(414\) 1.34336e9 + 8.10642e8i 0.930447 + 0.561472i
\(415\) −2.85126e9 −1.95825
\(416\) −1.75863e7 5.14670e8i −0.0119770 0.350512i
\(417\) 4.20813e8 0.284193
\(418\) 1.59418e9 + 9.61999e8i 1.06763 + 0.644255i
\(419\) −9.84343e8 + 2.37642e9i −0.653729 + 1.57824i 0.153596 + 0.988134i \(0.450914\pi\)
−0.807325 + 0.590107i \(0.799086\pi\)
\(420\) 3.48803e7 1.12560e8i 0.0229725 0.0741333i
\(421\) −7.05921e8 + 2.92402e8i −0.461072 + 0.190982i −0.601114 0.799163i \(-0.705276\pi\)
0.140042 + 0.990146i \(0.455276\pi\)
\(422\) −1.14075e9 + 8.40770e8i −0.738919 + 0.544607i
\(423\) −4.62272e8 + 4.62272e8i −0.296966 + 0.296966i
\(424\) 6.52731e8 + 1.87711e9i 0.415866 + 1.19594i
\(425\) 9.27815e8 + 9.27815e8i 0.586274 + 0.586274i
\(426\) 2.98856e8 + 4.52435e7i 0.187296 + 0.0283545i
\(427\) 4.08958e7 + 9.87312e7i 0.0254203 + 0.0613701i
\(428\) 1.52063e9 1.83049e9i 0.937500 1.12854i
\(429\) 1.76252e8 + 7.30060e7i 0.107779 + 0.0446435i
\(430\) −2.84277e9 + 7.03063e8i −1.72426 + 0.426437i
\(431\) 1.20805e8i 0.0726799i −0.999339 0.0363399i \(-0.988430\pi\)
0.999339 0.0363399i \(-0.0115699\pi\)
\(432\) −1.28388e8 + 6.07437e8i −0.0766178 + 0.362500i
\(433\) 1.22289e9i 0.723901i 0.932197 + 0.361950i \(0.117889\pi\)
−0.932197 + 0.361950i \(0.882111\pi\)
\(434\) 1.00240e8 + 4.05312e8i 0.0588609 + 0.237999i
\(435\) 6.21257e8 + 2.57333e8i 0.361875 + 0.149894i
\(436\) 8.16247e7 + 8.82766e8i 0.0471649 + 0.510085i
\(437\) −5.31897e8 1.28411e9i −0.304890 0.736069i
\(438\) 2.68695e7 1.77486e8i 0.0152792 0.100926i
\(439\) 1.78280e9 + 1.78280e9i 1.00572 + 1.00572i 0.999984 + 0.00573775i \(0.00182639\pi\)
0.00573775 + 0.999984i \(0.498174\pi\)
\(440\) 3.91802e9 + 4.40147e9i 2.19271 + 2.46328i
\(441\) −1.16878e9 + 1.16878e9i −0.648929 + 0.648929i
\(442\) −1.25446e8 1.70204e8i −0.0691002 0.0937546i
\(443\) −1.28845e9 + 5.33695e8i −0.704135 + 0.291662i −0.705875 0.708336i \(-0.749446\pi\)
0.00174038 + 0.999998i \(0.499446\pi\)
\(444\) −2.20268e8 + 1.16050e8i −0.119429 + 0.0629222i
\(445\) 6.27143e7 1.51406e8i 0.0337370 0.0814484i
\(446\) −7.89560e8 + 1.30842e9i −0.421418 + 0.698356i
\(447\) −2.03102e8 −0.107557
\(448\) −3.28444e8 + 2.59841e8i −0.172579 + 0.136532i
\(449\) 9.61826e8 0.501458 0.250729 0.968057i \(-0.419330\pi\)
0.250729 + 0.968057i \(0.419330\pi\)
\(450\) 2.40483e9 3.98518e9i 1.24406 2.06160i
\(451\) 2.07198e9 5.00221e9i 1.06358 2.56770i
\(452\) −7.05392e8 + 3.71641e8i −0.359291 + 0.189295i
\(453\) −4.37530e8 + 1.81231e8i −0.221138 + 0.0915985i
\(454\) −9.67437e7 1.31261e8i −0.0485207 0.0658326i
\(455\) 2.05042e8 2.05042e8i 0.102047 0.102047i
\(456\) 2.01685e8 1.79532e8i 0.0996087 0.0886677i
\(457\) 4.19740e8 + 4.19740e8i 0.205719 + 0.205719i 0.802445 0.596726i \(-0.203532\pi\)
−0.596726 + 0.802445i \(0.703532\pi\)
\(458\) 6.29919e7 4.16093e8i 0.0306377 0.202377i
\(459\) 9.75512e7 + 2.35509e8i 0.0470856 + 0.113675i
\(460\) −4.05005e8 4.38011e9i −0.194003 2.09813i
\(461\) −3.85794e8 1.59801e8i −0.183401 0.0759673i 0.289093 0.957301i \(-0.406646\pi\)
−0.472494 + 0.881334i \(0.656646\pi\)
\(462\) −3.72480e7 1.50609e8i −0.0175734 0.0710566i
\(463\) 4.27790e8i 0.200308i 0.994972 + 0.100154i \(0.0319335\pi\)
−0.994972 + 0.100154i \(0.968067\pi\)
\(464\) −1.30388e9 2.00278e9i −0.605935 0.930723i
\(465\) 8.51942e8i 0.392939i
\(466\) −4.15049e8 + 1.02648e8i −0.189998 + 0.0469895i
\(467\) −3.39235e8 1.40516e8i −0.154132 0.0638435i 0.304284 0.952581i \(-0.401583\pi\)
−0.458416 + 0.888738i \(0.651583\pi\)
\(468\) −4.79276e8 + 5.76938e8i −0.216135 + 0.260177i
\(469\) −2.35880e8 5.69466e8i −0.105581 0.254896i
\(470\) 1.81219e9 + 2.74346e8i 0.805120 + 0.121886i
\(471\) −3.57309e7 3.57309e7i −0.0157569 0.0157569i
\(472\) −1.18077e9 + 4.10594e8i −0.516857 + 0.179728i
\(473\) −2.72625e9 + 2.72625e9i −1.18454 + 1.18454i
\(474\) −1.34437e8 + 9.90840e7i −0.0579820 + 0.0427346i
\(475\) −3.80942e9 + 1.57791e9i −1.63091 + 0.675546i
\(476\) −5.08969e7 + 1.64247e8i −0.0216305 + 0.0698028i
\(477\) 1.10769e9 2.67420e9i 0.467309 1.12818i
\(478\) −4.30701e8 2.59904e8i −0.180376 0.108847i
\(479\) −4.59226e9 −1.90920 −0.954602 0.297883i \(-0.903719\pi\)
−0.954602 + 0.297883i \(0.903719\pi\)
\(480\) 7.77869e8 3.53791e8i 0.321042 0.146017i
\(481\) −6.12642e8 −0.251014
\(482\) 1.70133e8 + 1.02666e8i 0.0692029 + 0.0417600i
\(483\) −4.43202e7 + 1.06999e8i −0.0178973 + 0.0432079i
\(484\) 5.02795e9 + 1.55806e9i 2.01573 + 0.624635i
\(485\) 4.64858e9 1.92550e9i 1.85022 0.766387i
\(486\) 1.09846e9 8.09603e8i 0.434069 0.319923i
\(487\) −1.99768e9 + 1.99768e9i −0.783743 + 0.783743i −0.980460 0.196717i \(-0.936972\pi\)
0.196717 + 0.980460i \(0.436972\pi\)
\(488\) −3.37600e8 + 6.97558e8i −0.131502 + 0.271713i
\(489\) 5.42187e8 + 5.42187e8i 0.209685 + 0.209685i
\(490\) 4.58182e9 + 6.93637e8i 1.75935 + 0.266346i
\(491\) 1.00452e8 + 2.42512e8i 0.0382977 + 0.0924587i 0.941871 0.335975i \(-0.109066\pi\)
−0.903573 + 0.428433i \(0.859066\pi\)
\(492\) −6.03965e8 5.01728e8i −0.228630 0.189929i
\(493\) −9.06531e8 3.75497e8i −0.340736 0.141138i
\(494\) 6.44999e8 1.59519e8i 0.240722 0.0595342i
\(495\) 8.58256e9i 3.18052i
\(496\) −1.71208e9 + 2.49721e9i −0.629995 + 0.918902i
\(497\) 6.04876e8i 0.221014i
\(498\) 1.30697e8 + 5.28461e8i 0.0474201 + 0.191739i
\(499\) 4.82771e9 + 1.99970e9i 1.73936 + 0.720466i 0.998826 + 0.0484478i \(0.0154274\pi\)
0.740534 + 0.672019i \(0.234573\pi\)
\(500\) −7.78946e9 + 7.20250e8i −2.78684 + 0.257684i
\(501\) 2.13176e8 + 5.14653e8i 0.0757368 + 0.182845i
\(502\) 3.46960e8 2.29184e9i 0.122410 0.808577i
\(503\) −3.60445e9 3.60445e9i −1.26285 1.26285i −0.949706 0.313143i \(-0.898618\pi\)
−0.313143 0.949706i \(-0.601382\pi\)
\(504\) 6.08943e8 + 3.53863e7i 0.211870 + 0.0123120i
\(505\) 2.91301e8 2.91301e8i 0.100652 0.100652i
\(506\) −3.43600e9 4.66194e9i −1.17903 1.59970i
\(507\) −4.48440e8 + 1.85750e8i −0.152819 + 0.0632995i
\(508\) 7.62322e8 + 1.44692e9i 0.257998 + 0.489692i
\(509\) −1.47847e9 + 3.56933e9i −0.496935 + 1.19971i 0.454191 + 0.890904i \(0.349928\pi\)
−0.951126 + 0.308803i \(0.900072\pi\)
\(510\) 1.81277e8 3.00405e8i 0.0605129 0.100279i
\(511\) −3.59227e8 −0.119096
\(512\) −2.99107e9 5.26186e8i −0.984876 0.173258i
\(513\) −8.01050e8 −0.261968
\(514\) 8.76190e8 1.45198e9i 0.284595 0.471619i
\(515\) 5.96991e8 1.44126e9i 0.192594 0.464963i
\(516\) 2.60616e8 + 4.94661e8i 0.0835077 + 0.158502i
\(517\) 2.22939e9 9.23442e8i 0.709526 0.293895i
\(518\) 2.95599e8 + 4.01067e8i 0.0934434 + 0.126783i
\(519\) −5.26855e8 + 5.26855e8i −0.165427 + 0.165427i
\(520\) 2.09925e9 + 1.21990e8i 0.654715 + 0.0380462i
\(521\) 3.47362e9 + 3.47362e9i 1.07610 + 1.07610i 0.996856 + 0.0792399i \(0.0252493\pi\)
0.0792399 + 0.996856i \(0.474751\pi\)
\(522\) −5.21006e8 + 3.44150e9i −0.160323 + 1.05901i
\(523\) 9.15878e8 + 2.21113e9i 0.279951 + 0.675861i 0.999834 0.0182345i \(-0.00580453\pi\)
−0.719883 + 0.694096i \(0.755805\pi\)
\(524\) −6.08696e8 + 5.62829e7i −0.184816 + 0.0170890i
\(525\) 3.17419e8 + 1.31479e8i 0.0957360 + 0.0396552i
\(526\) −9.20775e8 3.72307e9i −0.275869 1.11545i
\(527\) 1.24314e9i 0.369985i
\(528\) 6.36187e8 9.27933e8i 0.188090 0.274346i
\(529\) 9.18317e8i 0.269710i
\(530\) −7.87767e9 + 1.94827e9i −2.29844 + 0.568440i
\(531\) 1.68218e9 + 6.96781e8i 0.487575 + 0.201960i
\(532\) −4.15641e8 3.45282e8i −0.119682 0.0994222i
\(533\) −7.39382e8 1.78503e9i −0.211506 0.510622i
\(534\) −3.09367e7 4.68349e6i −0.00879185 0.00133099i
\(535\) 6.87106e9 + 6.87106e9i 1.93993 + 1.93993i
\(536\) 1.94722e9 4.02340e9i 0.546183 1.12854i
\(537\) −5.09030e8 + 5.09030e8i −0.141851 + 0.141851i
\(538\) −2.70068e9 + 1.99049e9i −0.747713 + 0.551088i
\(539\) 5.63663e9 2.33477e9i 1.55045 0.642219i
\(540\) −2.42156e9 7.50393e8i −0.661784 0.205074i
\(541\) 7.28921e8 1.75977e9i 0.197920 0.477821i −0.793494 0.608577i \(-0.791740\pi\)
0.991415 + 0.130756i \(0.0417405\pi\)
\(542\) 4.39568e9 + 2.65254e9i 1.18585 + 0.715590i
\(543\) −5.66144e8 −0.151750
\(544\) −1.13506e9 + 5.16248e8i −0.302288 + 0.137487i
\(545\) −3.61999e9 −0.957900
\(546\) −4.74018e7 2.86043e7i −0.0124629 0.00752068i
\(547\) −1.61743e9 + 3.90483e9i −0.422543 + 1.02011i 0.559051 + 0.829133i \(0.311165\pi\)
−0.981595 + 0.190977i \(0.938835\pi\)
\(548\) −7.43169e8 + 2.39824e9i −0.192910 + 0.622532i
\(549\) 1.04279e9 4.31938e8i 0.268964 0.111408i
\(550\) −1.38300e10 + 1.01931e10i −3.54448 + 2.61239i
\(551\) 2.18031e9 2.18031e9i 0.555249 0.555249i
\(552\) −7.93258e8 + 2.75842e8i −0.200737 + 0.0698028i
\(553\) 2.36320e8 + 2.36320e8i 0.0594240 + 0.0594240i
\(554\) 6.72078e9 + 1.01745e9i 1.67933 + 0.254232i
\(555\) −3.89044e8 9.39236e8i −0.0965992 0.233211i
\(556\) 3.90222e9 4.69738e9i 0.962831 1.15903i
\(557\) −1.22526e9 5.07520e8i −0.300425 0.124440i 0.227379 0.973806i \(-0.426984\pi\)
−0.527804 + 0.849366i \(0.676984\pi\)
\(558\) 4.28086e9 1.05873e9i 1.04307 0.257967i
\(559\) 1.37582e9i 0.333136i
\(560\) −9.33025e8 1.43314e9i −0.224510 0.344849i
\(561\) 4.61938e8i 0.110462i
\(562\) −6.80359e8 2.75097e9i −0.161682 0.653746i
\(563\) 2.48705e9 + 1.03017e9i 0.587360 + 0.243293i 0.656515 0.754313i \(-0.272030\pi\)
−0.0691543 + 0.997606i \(0.522030\pi\)
\(564\) −3.22195e7 3.48452e8i −0.00756209 0.0817836i
\(565\) −1.24588e9 3.00783e9i −0.290608 0.701591i
\(566\) −5.76942e8 + 3.81099e9i −0.133744 + 0.883446i
\(567\) −6.04173e8 6.04173e8i −0.139194 0.139194i
\(568\) 3.27634e9 2.91647e9i 0.750188 0.667788i
\(569\) 3.42275e9 3.42275e9i 0.778901 0.778901i −0.200743 0.979644i \(-0.564336\pi\)
0.979644 + 0.200743i \(0.0643356\pi\)
\(570\) 6.54149e8 + 8.87544e8i 0.147950 + 0.200737i
\(571\) −2.05853e6 + 852671.i −0.000462733 + 0.000191670i −0.382915 0.923784i \(-0.625080\pi\)
0.382452 + 0.923975i \(0.375080\pi\)
\(572\) 2.44934e9 1.29045e9i 0.547221 0.288307i
\(573\) 2.39813e8 5.78959e8i 0.0532514 0.128560i
\(574\) −8.11818e8 + 1.34531e9i −0.179171 + 0.296914i
\(575\) 1.28249e10 2.81331
\(576\) 2.74441e9 + 3.46899e9i 0.598371 + 0.756354i
\(577\) −3.84842e9 −0.834002 −0.417001 0.908906i \(-0.636919\pi\)
−0.417001 + 0.908906i \(0.636919\pi\)
\(578\) 2.13406e9 3.53647e9i 0.459684 0.761768i
\(579\) −2.58316e8 + 6.23629e8i −0.0553064 + 0.133522i
\(580\) 8.63347e9 4.54860e9i 1.83733 0.968010i
\(581\) 1.00648e9 4.16897e8i 0.212906 0.0881885i
\(582\) −5.69962e8 7.73320e8i −0.119844 0.162603i
\(583\) −7.55476e9 + 7.55476e9i −1.57900 + 1.57900i
\(584\) −1.73205e9 1.94577e9i −0.359845 0.404248i
\(585\) −2.16563e9 2.16563e9i −0.447238 0.447238i
\(586\) −1.40411e9 + 9.27487e9i −0.288244 + 1.90400i
\(587\) −1.99675e9 4.82059e9i −0.407465 0.983709i −0.985802 0.167911i \(-0.946298\pi\)
0.578337 0.815798i \(-0.303702\pi\)
\(588\) −8.14617e7 8.81003e8i −0.0165247 0.178713i
\(589\) −3.60914e9 1.49495e9i −0.727780 0.301456i
\(590\) −1.22554e9 4.95537e9i −0.245667 0.993331i
\(591\) 6.61399e8i 0.131797i
\(592\) −7.47138e8 + 3.53491e9i −0.148004 + 0.700249i
\(593\) 4.01770e9i 0.791199i −0.918423 0.395599i \(-0.870537\pi\)
0.918423 0.395599i \(-0.129463\pi\)
\(594\) −3.24011e9 + 8.01331e8i −0.634318 + 0.156877i
\(595\) −6.48689e8 2.68696e8i −0.126249 0.0522940i
\(596\) −1.88338e9 + 2.26716e9i −0.364398 + 0.438652i
\(597\) −5.30047e8 1.27965e9i −0.101954 0.246139i
\(598\) −2.04334e9 3.09340e8i −0.390740 0.0591538i
\(599\) 1.85612e8 + 1.85612e8i 0.0352868 + 0.0352868i 0.724530 0.689243i \(-0.242057\pi\)
−0.689243 + 0.724530i \(0.742057\pi\)
\(600\) 8.18304e8 + 2.35326e9i 0.154663 + 0.444775i
\(601\) 3.22719e9 3.22719e9i 0.606406 0.606406i −0.335599 0.942005i \(-0.608939\pi\)
0.942005 + 0.335599i \(0.108939\pi\)
\(602\) 9.00685e8 6.63833e8i 0.168262 0.124014i
\(603\) −6.01464e9 + 2.49135e9i −1.11712 + 0.462725i
\(604\) −2.03423e9 + 6.56456e9i −0.375639 + 1.21221i
\(605\) −8.22536e9 + 1.98578e10i −1.51012 + 3.64575i
\(606\) −6.73433e7 4.06378e7i −0.0122925 0.00741782i
\(607\) 7.74615e9 1.40581 0.702903 0.711285i \(-0.251887\pi\)
0.702903 + 0.711285i \(0.251887\pi\)
\(608\) −1.33815e8 3.91615e9i −0.0241459 0.706638i
\(609\) −2.56926e8 −0.0460943
\(610\) −2.70933e9 1.63493e9i −0.483290 0.291638i
\(611\) 3.29528e8 7.95551e8i 0.0584451 0.141099i
\(612\) 1.73476e9 + 5.37568e8i 0.305921 + 0.0947989i
\(613\) −5.67809e9 + 2.35194e9i −0.995613 + 0.412396i −0.820186 0.572096i \(-0.806130\pi\)
−0.175426 + 0.984493i \(0.556130\pi\)
\(614\) 4.79863e9 3.53675e9i 0.836620 0.616616i
\(615\) 2.26708e9 2.26708e9i 0.393010 0.393010i
\(616\) −2.02660e9 9.80821e8i −0.349330 0.169066i
\(617\) 6.41988e9 + 6.41988e9i 1.10035 + 1.10035i 0.994369 + 0.105976i \(0.0337968\pi\)
0.105976 + 0.994369i \(0.466203\pi\)
\(618\) −2.94494e8 4.45831e7i −0.0501899 0.00759821i
\(619\) −2.53808e9 6.12746e9i −0.430118 1.03840i −0.979249 0.202660i \(-0.935041\pi\)
0.549131 0.835736i \(-0.314959\pi\)
\(620\) −9.50993e9 7.90011e9i −1.60253 1.33126i
\(621\) 2.30190e9 + 9.53478e8i 0.385714 + 0.159768i
\(622\) −9.73963e8 + 2.40876e8i −0.162284 + 0.0401354i
\(623\) 6.26152e7i 0.0103746i
\(624\) −7.36161e7 3.94673e8i −0.0121290 0.0650267i
\(625\) 1.67040e10i 2.73678i
\(626\) 1.72763e8 + 6.98550e8i 0.0281475 + 0.113812i
\(627\) 1.34111e9 + 5.55507e8i 0.217285 + 0.0900022i
\(628\) −7.30187e8 + 6.75165e7i −0.117645 + 0.0108781i
\(629\) 5.67689e8 + 1.37052e9i 0.0909563 + 0.219588i
\(630\) −3.72818e8 + 2.46265e9i −0.0594025 + 0.392383i
\(631\) −6.12180e8 6.12180e8i −0.0970011 0.0970011i 0.656941 0.753942i \(-0.271850\pi\)
−0.753942 + 0.656941i \(0.771850\pi\)
\(632\) −1.40598e8 + 2.41948e9i −0.0221549 + 0.381252i
\(633\) −7.81215e8 + 7.81215e8i −0.122422 + 0.122422i
\(634\) 4.29835e9 + 5.83197e9i 0.669868 + 0.908872i
\(635\) −6.16977e9 + 2.55560e9i −0.956226 + 0.396082i
\(636\) 7.22198e8 + 1.37077e9i 0.111316 + 0.211283i
\(637\) 8.33157e8 2.01142e9i 0.127714 0.308329i
\(638\) 6.63792e9 1.10001e10i 1.01195 1.67696i
\(639\) −6.38864e9 −0.968624
\(640\) 3.26398e9 1.19638e10i 0.492173 1.80401i
\(641\) −8.61409e9 −1.29183 −0.645916 0.763408i \(-0.723524\pi\)
−0.645916 + 0.763408i \(0.723524\pi\)
\(642\) 9.58546e8 1.58846e9i 0.142968 0.236921i
\(643\) 2.67840e6 6.46624e6i 0.000397317 0.000959209i −0.923681 0.383163i \(-0.874835\pi\)
0.924078 + 0.382204i \(0.124835\pi\)
\(644\) 7.83402e8 + 1.48693e9i 0.115580 + 0.219377i
\(645\) −2.10926e9 + 8.73685e8i −0.309508 + 0.128202i
\(646\) −9.54526e8 1.29509e9i −0.139307 0.189011i
\(647\) 1.93862e9 1.93862e9i 0.281402 0.281402i −0.552266 0.833668i \(-0.686237\pi\)
0.833668 + 0.552266i \(0.186237\pi\)
\(648\) 3.59452e8 6.18562e9i 0.0518954 0.893039i
\(649\) −4.75225e9 4.75225e9i −0.682405 0.682405i
\(650\) −9.17681e8 + 6.06173e9i −0.131067 + 0.865765i
\(651\) 1.24567e8 + 3.00731e8i 0.0176957 + 0.0427213i
\(652\) 1.10800e10 1.02451e9i 1.56557 0.144760i
\(653\) 5.01222e9 + 2.07613e9i 0.704424 + 0.291782i 0.705995 0.708217i \(-0.250500\pi\)
−0.00157082 + 0.999999i \(0.500500\pi\)
\(654\) 1.65934e8 + 6.70941e8i 0.0231961 + 0.0937912i
\(655\) 2.49610e9i 0.347071i
\(656\) −1.12012e10 + 2.08930e9i −1.54918 + 0.288959i
\(657\) 3.79412e9i 0.521954i
\(658\) −6.79805e8 + 1.68127e8i −0.0930238 + 0.0230063i
\(659\) −2.01567e9 8.34919e8i −0.274360 0.113644i 0.241261 0.970460i \(-0.422439\pi\)
−0.515622 + 0.856816i \(0.672439\pi\)
\(660\) 3.53378e9 + 2.93559e9i 0.478449 + 0.397458i
\(661\) −2.23091e9 5.38589e9i −0.300453 0.725358i −0.999943 0.0107150i \(-0.996589\pi\)
0.699490 0.714643i \(-0.253411\pi\)
\(662\) 5.46333e9 + 8.27089e8i 0.731904 + 0.110802i
\(663\) −1.16560e8 1.16560e8i −0.0155329 0.0155329i
\(664\) 7.11098e9 + 3.44153e9i 0.942630 + 0.456208i
\(665\) 1.56017e9 1.56017e9i 0.205730 0.205730i
\(666\) 4.23603e9 3.12209e9i 0.555647 0.409529i
\(667\) −8.86055e9 + 3.67016e9i −1.15617 + 0.478900i
\(668\) 7.72168e9 + 2.39280e9i 1.00229 + 0.310591i
\(669\) −4.55932e8 + 1.10072e9i −0.0588720 + 0.142130i
\(670\) 1.56270e10 + 9.42999e9i 2.00730 + 1.21129i
\(671\) −4.16618e9 −0.532365
\(672\) −2.22854e8 + 2.38622e8i −0.0283287 + 0.0303332i
\(673\) 2.65376e9 0.335590 0.167795 0.985822i \(-0.446335\pi\)
0.167795 + 0.985822i \(0.446335\pi\)
\(674\) −2.32043e9 1.40025e9i −0.291916 0.176155i
\(675\) 2.82856e9 6.82875e9i 0.353999 0.854630i
\(676\) −2.08495e9 + 6.72824e9i −0.259587 + 0.837700i
\(677\) 2.35923e9 9.77224e8i 0.292220 0.121041i −0.231758 0.972774i \(-0.574448\pi\)
0.523977 + 0.851732i \(0.324448\pi\)
\(678\) −5.00372e8 + 3.68790e8i −0.0616579 + 0.0454439i
\(679\) −1.35938e9 + 1.35938e9i −0.166647 + 0.166647i
\(680\) −1.67232e9 4.80921e9i −0.203956 0.586533i
\(681\) −8.98911e7 8.98911e7i −0.0109069 0.0109069i
\(682\) −1.60938e10 2.43643e9i −1.94274 0.294109i
\(683\) 8.73998e8 + 2.11002e9i 0.104963 + 0.253404i 0.967632 0.252366i \(-0.0812085\pi\)
−0.862669 + 0.505770i \(0.831209\pi\)
\(684\) −3.64683e9 + 4.38995e9i −0.435732 + 0.524522i
\(685\) −9.47181e9 3.92335e9i −1.12594 0.466380i
\(686\) −3.52502e9 + 8.71792e8i −0.416895 + 0.103105i
\(687\) 3.28089e8i 0.0386050i
\(688\) 7.93844e9 + 1.67786e9i 0.929342 + 0.196425i
\(689\) 3.81257e9i 0.444070i
\(690\) −8.23333e8 3.32907e9i −0.0954121 0.385791i
\(691\) 1.20795e9 + 5.00348e8i 0.139276 + 0.0576898i 0.451233 0.892406i \(-0.350984\pi\)
−0.311957 + 0.950096i \(0.600984\pi\)
\(692\) 9.95535e8 + 1.07666e10i 0.114205 + 1.23512i
\(693\) 1.25490e9 + 3.02959e9i 0.143233 + 0.345794i
\(694\) 2.30333e9 1.52147e10i 0.261577 1.72784i
\(695\) 1.76324e10 + 1.76324e10i 1.99234 + 1.99234i
\(696\) −1.23880e9 1.39165e9i −0.139273 0.156458i
\(697\) −3.30810e9 + 3.30810e9i −0.370053 + 0.370053i
\(698\) −7.30399e9 9.91000e9i −0.812955 1.10301i
\(699\) −3.07956e8 + 1.27559e8i −0.0341050 + 0.0141268i
\(700\) 4.41110e9 2.32402e9i 0.486076 0.256092i
\(701\) 2.97482e9 7.18185e9i 0.326172 0.787450i −0.672697 0.739918i \(-0.734864\pi\)
0.998870 0.0475322i \(-0.0151357\pi\)
\(702\) −6.15375e8 + 1.01977e9i −0.0671367 + 0.111256i
\(703\) −4.66162e9 −0.506050
\(704\) −4.45879e9 1.57063e10i −0.481629 1.69656i
\(705\) 1.42891e9 0.153583
\(706\) −8.93123e9 + 1.48005e10i −0.955202 + 1.58292i
\(707\) −6.02349e7 + 1.45420e8i −0.00641033 + 0.0154759i
\(708\) −8.62267e8 + 4.54291e8i −0.0913115 + 0.0481081i
\(709\) 1.49755e10 6.20304e9i 1.57804 0.653646i 0.589940 0.807447i \(-0.299152\pi\)
0.988102 + 0.153801i \(0.0491515\pi\)
\(710\) 1.06265e10 + 1.44180e10i 1.11426 + 1.51182i
\(711\) 2.49599e9 2.49599e9i 0.260434 0.260434i
\(712\) −3.39158e8 + 3.01906e8i −0.0352146 + 0.0313466i
\(713\) 8.59181e9 + 8.59181e9i 0.887710 + 0.887710i
\(714\) −2.00661e7 + 1.32547e8i −0.00206310 + 0.0136278i
\(715\) 4.32609e9 + 1.04441e10i 0.442613 + 1.06856i
\(716\) 9.61854e8 + 1.04024e10i 0.0979295 + 1.05910i
\(717\) −3.62329e8 1.50082e8i −0.0367101 0.0152058i
\(718\) −1.20608e9 4.87668e9i −0.121602 0.491687i
\(719\) 1.36604e10i 1.37061i −0.728258 0.685303i \(-0.759670\pi\)
0.728258 0.685303i \(-0.240330\pi\)
\(720\) −1.51366e10 + 9.85452e9i −1.51135 + 0.983947i
\(721\) 5.96047e8i 0.0592253i
\(722\) −4.90939e9 + 1.21417e9i −0.485453 + 0.120060i
\(723\) 1.43125e8 + 5.92843e7i 0.0140842 + 0.00583386i
\(724\) −5.24989e9 + 6.31966e9i −0.514121 + 0.618884i
\(725\) 1.08878e10 + 2.62855e10i 1.06110 + 2.56173i
\(726\) 4.05754e9 + 6.14267e8i 0.393536 + 0.0595771i
\(727\) −5.78643e9 5.78643e9i −0.558522 0.558522i 0.370364 0.928887i \(-0.379233\pi\)
−0.928887 + 0.370364i \(0.879233\pi\)
\(728\) −7.58860e8 + 2.63880e8i −0.0728957 + 0.0253482i
\(729\) −5.86433e9 + 5.86433e9i −0.560624 + 0.560624i
\(730\) 8.56266e9 6.31095e9i 0.814664 0.600434i
\(731\) 3.07781e9 1.27487e9i 0.291428 0.120713i
\(732\) −1.78831e8 + 5.77098e8i −0.0168521 + 0.0543827i
\(733\) −2.20425e8 + 5.32152e8i −0.0206727 + 0.0499082i −0.933879 0.357590i \(-0.883599\pi\)
0.913206 + 0.407498i \(0.133599\pi\)
\(734\) −9.00396e9 5.43338e9i −0.840421 0.507147i
\(735\) 3.61277e9 0.335609
\(736\) −4.27681e9 + 1.14128e10i −0.395410 + 1.05516i
\(737\) 2.40299e10 2.21113
\(738\) 1.42090e10 + 8.57434e9i 1.30127 + 0.785242i
\(739\) −6.89179e8 + 1.66383e9i −0.0628169 + 0.151653i −0.952171 0.305566i \(-0.901154\pi\)
0.889354 + 0.457219i \(0.151154\pi\)
\(740\) −1.40920e10 4.36683e9i −1.27838 0.396146i
\(741\) 4.78572e8 1.98231e8i 0.0432100 0.0178982i
\(742\) 2.49591e9 1.83956e9i 0.224293 0.165311i
\(743\) −1.04141e10 + 1.04141e10i −0.931454 + 0.931454i −0.997797 0.0663433i \(-0.978867\pi\)
0.0663433 + 0.997797i \(0.478867\pi\)
\(744\) −1.02831e9 + 2.12473e9i −0.0915419 + 0.189146i
\(745\) −8.51015e9 8.51015e9i −0.754033 0.754033i
\(746\) −1.81556e9 2.74857e8i −0.160113 0.0242393i
\(747\) −4.40322e9 1.06303e10i −0.386499 0.933091i
\(748\) −5.15644e9 4.28358e9i −0.450500 0.374241i
\(749\) −3.43010e9 1.42079e9i −0.298277 0.123550i
\(750\) −5.92033e9 + 1.46419e9i −0.512427 + 0.126731i
\(751\) 5.21564e9i 0.449332i −0.974436 0.224666i \(-0.927871\pi\)
0.974436 0.224666i \(-0.0721291\pi\)
\(752\) −4.18842e9 2.87156e9i −0.359160 0.246238i
\(753\) 1.80712e9i 0.154243i
\(754\) −1.10070e9 4.45058e9i −0.0935123 0.378109i
\(755\) −2.59266e10 1.07391e10i −2.19245 0.908144i
\(756\) 9.64514e8 8.91835e7i 0.0811862 0.00750686i
\(757\) 1.94976e9 + 4.70713e9i 0.163360 + 0.394385i 0.984270 0.176672i \(-0.0565333\pi\)
−0.820910 + 0.571058i \(0.806533\pi\)
\(758\) 2.28359e9 1.50842e10i 0.190448 1.25800i
\(759\) −3.19261e9 3.19261e9i −0.265033 0.265033i
\(760\) 1.59733e10 + 9.28225e8i 1.31992 + 0.0767018i
\(761\) 1.31795e10 1.31795e10i 1.08406 1.08406i 0.0879329 0.996126i \(-0.471974\pi\)
0.996126 0.0879329i \(-0.0280261\pi\)
\(762\) 7.56475e8 + 1.02638e9i 0.0619373 + 0.0840360i
\(763\) 1.27784e9 5.29298e8i 0.104145 0.0431384i
\(764\) −4.23891e9 8.04566e9i −0.343897 0.652732i
\(765\) −2.83794e9 + 6.85139e9i −0.229186 + 0.553304i
\(766\) 6.83685e9 1.13297e10i 0.549611 0.910792i
\(767\) −2.39826e9 −0.191917
\(768\) −2.36702e9 5.65565e7i −0.188555 0.00450524i
\(769\) 9.47745e9 0.751535 0.375768 0.926714i \(-0.377379\pi\)
0.375768 + 0.926714i \(0.377379\pi\)
\(770\) 4.74992e9 7.87136e9i 0.374946 0.621344i
\(771\) 5.05957e8 1.22149e9i 0.0397579 0.0959840i
\(772\) 4.56597e9 + 8.66644e9i 0.357168 + 0.677922i
\(773\) −1.86730e10 + 7.73462e9i −1.45407 + 0.602297i −0.963164 0.268914i \(-0.913335\pi\)
−0.490909 + 0.871211i \(0.663335\pi\)
\(774\) −7.01134e9 9.51294e9i −0.543510 0.737431i
\(775\) 2.54882e10 2.54882e10i 1.96691 1.96691i
\(776\) −1.39176e10 8.08765e8i −1.06917 0.0621307i
\(777\) 2.74661e8 + 2.74661e8i 0.0210050 + 0.0210050i
\(778\) 2.59301e9 1.71281e10i 0.197413 1.30401i
\(779\) −5.62600e9 1.35824e10i −0.426401 1.02942i
\(780\) 1.63241e9 1.50940e8i 0.123168 0.0113887i
\(781\) 2.17862e10 + 9.02412e9i 1.63645 + 0.677839i
\(782\) 1.20140e9 + 4.85775e9i 0.0898386 + 0.363255i
\(783\) 5.52735e9i 0.411482i
\(784\) −1.05897e10 7.26027e9i −0.784835 0.538080i
\(785\) 2.99431e9i 0.220929i
\(786\) −4.62636e8 + 1.14417e8i −0.0339829 + 0.00840450i
\(787\) 6.39792e9 + 2.65010e9i 0.467872 + 0.193799i 0.604148 0.796872i \(-0.293513\pi\)
−0.136276 + 0.990671i \(0.543513\pi\)
\(788\) 7.38296e9 + 6.13319e9i 0.537513 + 0.446524i
\(789\) −1.14423e9 2.76242e9i −0.0829363 0.200226i
\(790\) −9.78469e9 1.48130e9i −0.706077 0.106892i
\(791\) 8.79580e8 + 8.79580e8i 0.0631914 + 0.0631914i
\(792\) −1.03593e10 + 2.14047e10i −0.740958 + 1.53099i
\(793\) −1.05125e9 + 1.05125e9i −0.0748600 + 0.0748600i
\(794\) −1.19437e10 + 8.80290e9i −0.846774 + 0.624100i
\(795\) −5.84503e9 + 2.42109e9i −0.412574 + 0.170894i
\(796\) −1.91994e10 5.94952e9i −1.34925 0.418106i
\(797\) 5.86600e9 1.41618e10i 0.410429 0.990863i −0.574594 0.818439i \(-0.694840\pi\)
0.985023 0.172425i \(-0.0551601\pi\)
\(798\) −3.60683e8 2.17652e8i −0.0251256 0.0151618i
\(799\) −2.08505e9 −0.144612
\(800\) 3.38568e10 + 1.26875e10i 2.33793 + 0.876113i
\(801\) 6.61335e8 0.0454682
\(802\) −3.01424e9 1.81892e9i −0.206332 0.124510i
\(803\) 5.35930e9 1.29385e10i 0.365261 0.881819i
\(804\) 1.03147e9 3.32861e9i 0.0699939 0.225874i
\(805\) −6.34037e9 + 2.62627e9i −0.428380 + 0.177441i
\(806\) −4.67572e9 + 3.44616e9i −0.314540 + 0.231826i
\(807\) −1.84949e9 + 1.84949e9i −0.123878 + 0.123878i
\(808\) −1.07810e9 + 3.74892e8i −0.0718987 + 0.0250015i
\(809\) −7.75368e9 7.75368e9i −0.514859 0.514859i 0.401152 0.916011i \(-0.368610\pi\)
−0.916011 + 0.401152i \(0.868610\pi\)
\(810\) 2.50154e10 + 3.78707e9i 1.65390 + 0.250383i
\(811\) 5.52554e9 + 1.33398e10i 0.363749 + 0.878167i 0.994745 + 0.102381i \(0.0326462\pi\)
−0.630997 + 0.775786i \(0.717354\pi\)
\(812\) −2.38249e9 + 2.86797e9i −0.156166 + 0.187988i
\(813\) 3.69788e9 + 1.53171e9i 0.241344 + 0.0999678i
\(814\) −1.88555e10 + 4.66326e9i −1.22533 + 0.303043i
\(815\) 4.54361e10i 2.94001i
\(816\) −8.14697e8 + 5.30398e8i −0.0524905 + 0.0341733i
\(817\) 1.04687e10i 0.671608i
\(818\) −1.15898e9 4.68622e9i −0.0740352 0.299355i
\(819\) 1.08110e9 + 4.47807e8i 0.0687659 + 0.0284838i
\(820\) −4.28383e9 4.63294e10i −0.271321 2.93432i
\(821\) −6.71068e9 1.62010e10i −0.423219 1.02174i −0.981392 0.192016i \(-0.938497\pi\)
0.558173 0.829725i \(-0.311503\pi\)
\(822\) −2.92995e8 + 1.93537e9i −0.0183996 + 0.121538i
\(823\) −8.66533e9 8.66533e9i −0.541858 0.541858i 0.382215 0.924073i \(-0.375161\pi\)
−0.924073 + 0.382215i \(0.875161\pi\)
\(824\) −3.22852e9 + 2.87391e9i −0.201029 + 0.178948i
\(825\) −9.47112e9 + 9.47112e9i −0.587236 + 0.587236i
\(826\) 1.15716e9 + 1.57002e9i 0.0714435 + 0.0969341i
\(827\) 1.15482e10 4.78341e9i 0.709977 0.294082i 0.00168195 0.999999i \(-0.499465\pi\)
0.708295 + 0.705916i \(0.249465\pi\)
\(828\) 1.57049e10 8.27421e9i 0.961452 0.506548i
\(829\) 1.18942e9 2.87150e9i 0.0725092 0.175053i −0.883470 0.468489i \(-0.844799\pi\)
0.955979 + 0.293436i \(0.0947987\pi\)
\(830\) −1.66666e10 + 2.76192e10i −1.01175 + 1.67663i
\(831\) 5.29934e9 0.320345
\(832\) −5.08824e9 2.83808e9i −0.306292 0.170841i
\(833\) −5.27171e9 −0.316005
\(834\) 2.45980e9 4.07628e9i 0.146831 0.243323i
\(835\) −1.26321e10 + 3.04966e10i −0.750885 + 1.81280i
\(836\) 1.86371e10 9.81911e9i 1.10321 0.581233i
\(837\) 6.46973e9 2.67985e9i 0.381371 0.157969i
\(838\) 1.72657e10 + 2.34260e10i 1.01352 + 1.37513i
\(839\) −1.93616e10 + 1.93616e10i −1.13181 + 1.13181i −0.141934 + 0.989876i \(0.545332\pi\)
−0.989876 + 0.141934i \(0.954668\pi\)
\(840\) −8.86449e8 9.95831e8i −0.0516032 0.0579706i
\(841\) −2.84693e9 2.84693e9i −0.165041 0.165041i
\(842\) −1.29396e9 + 8.54722e9i −0.0747012 + 0.493438i
\(843\) −8.45472e8 2.04115e9i −0.0486074 0.117349i
\(844\) 1.47617e9 + 1.59647e10i 0.0845158 + 0.914033i
\(845\) −2.65730e10 1.10069e10i −1.51510 0.627577i
\(846\) 1.77574e9 + 7.18003e9i 0.100828 + 0.407690i
\(847\) 8.21235e9i 0.464382i
\(848\) 2.19984e10 + 4.64957e9i 1.23881 + 0.261835i
\(849\) 3.00497e9i 0.168524i
\(850\) 1.44109e10 3.56404e9i 0.804866 0.199056i
\(851\) 1.33957e10 + 5.54866e9i 0.745093 + 0.308628i
\(852\) 2.18518e9 2.63045e9i 0.121045 0.145711i
\(853\) −9.64007e9 2.32732e10i −0.531812 1.28391i −0.930322 0.366744i \(-0.880472\pi\)
0.398509 0.917164i \(-0.369528\pi\)
\(854\) 1.19543e9 + 1.80975e8i 0.0656782 + 0.00994297i
\(855\) −1.64784e10 1.64784e10i −0.901641 0.901641i
\(856\) −8.84277e9 2.54298e10i −0.481870 1.38575i
\(857\) 2.09744e9 2.09744e9i 0.113830 0.113830i −0.647897 0.761728i \(-0.724351\pi\)
0.761728 + 0.647897i \(0.224351\pi\)
\(858\) 1.73744e9 1.28055e9i 0.0939086 0.0692136i
\(859\) 2.24034e10 9.27979e9i 1.20597 0.499531i 0.313049 0.949737i \(-0.398650\pi\)
0.892925 + 0.450206i \(0.148650\pi\)
\(860\) −9.80669e9 + 3.16467e10i −0.525748 + 1.69662i
\(861\) −4.68785e8 + 1.13175e9i −0.0250301 + 0.0604280i
\(862\) −1.17020e9 7.06148e8i −0.0622277 0.0375509i
\(863\) 1.32809e10 0.703381 0.351691 0.936116i \(-0.385607\pi\)
0.351691 + 0.936116i \(0.385607\pi\)
\(864\) 5.13357e9 + 4.79434e9i 0.270783 + 0.252889i
\(865\) −4.41512e10 −2.31946
\(866\) 1.18457e10 + 7.14822e9i 0.619796 + 0.374012i
\(867\) 1.23231e9 2.97507e9i 0.0642177 0.155035i
\(868\) 4.51207e9 + 1.39820e9i 0.234184 + 0.0725689i
\(869\) −1.20373e10 + 4.98602e9i −0.622243 + 0.257742i
\(870\) 6.12417e9 4.51371e9i 0.315304 0.232389i
\(871\) 6.06343e9 6.06343e9i 0.310925 0.310925i
\(872\) 9.02820e9 + 4.36941e9i 0.461098 + 0.223159i
\(873\) 1.43577e10 + 1.43577e10i 0.730355 + 0.730355i
\(874\) −1.55479e10 2.35379e9i −0.787739 0.119255i
\(875\) 4.67048e9 + 1.12755e10i 0.235686 + 0.568996i
\(876\) −1.56219e9 1.29775e9i −0.0785180 0.0652267i
\(877\) 2.34530e10 + 9.71455e9i 1.17409 + 0.486322i 0.882541 0.470235i \(-0.155831\pi\)
0.291544 + 0.956557i \(0.405831\pi\)
\(878\) 2.76906e10 6.84832e9i 1.38071 0.341470i
\(879\) 7.31324e9i 0.363203i
\(880\) 6.55379e10 1.22244e10i 3.24192 0.604697i
\(881\) 2.78778e10i 1.37354i 0.726874 + 0.686771i \(0.240973\pi\)
−0.726874 + 0.686771i \(0.759027\pi\)
\(882\) 4.48965e9 + 1.81535e10i 0.220330 + 0.890884i
\(883\) 1.24844e9 + 5.17119e8i 0.0610245 + 0.0252772i 0.412987 0.910737i \(-0.364486\pi\)
−0.351962 + 0.936014i \(0.614486\pi\)
\(884\) −2.38199e9 + 2.20250e8i −0.115973 + 0.0107234i
\(885\) −1.52296e9 3.67675e9i −0.0738563 0.178305i
\(886\) −2.36174e9 + 1.56005e10i −0.114081 + 0.753563i
\(887\) −1.26393e10 1.26393e10i −0.608121 0.608121i 0.334334 0.942455i \(-0.391489\pi\)
−0.942455 + 0.334334i \(0.891489\pi\)
\(888\) −1.63409e8 + 2.81202e9i −0.00783126 + 0.134764i
\(889\) 1.80423e9 1.80423e9i 0.0861261 0.0861261i
\(890\) −1.10003e9 1.49251e9i −0.0523046 0.0709665i
\(891\) 3.07745e10 1.27472e10i 1.45753 0.603730i
\(892\) 8.05903e9 + 1.52964e10i 0.380194 + 0.721627i
\(893\) 2.50740e9 6.05339e9i 0.117826 0.284458i
\(894\) −1.18721e9 + 1.96739e9i −0.0555706 + 0.0920892i
\(895\) −4.26575e10 −1.98891
\(896\) 5.97120e8 + 4.70040e9i 0.0277322 + 0.218301i
\(897\) −1.61118e9 −0.0745367
\(898\) 5.62222e9 9.31690e9i 0.259084 0.429343i
\(899\) −1.03154e10 + 2.49035e10i −0.473507 + 1.14315i
\(900\) −2.45461e10 4.65896e10i −1.12236 2.13030i
\(901\) 8.52899e9 3.53283e9i 0.388473 0.160911i
\(902\) −3.63433e10 4.93104e10i −1.64893 2.23725i
\(903\) 6.16812e8 6.16812e8i 0.0278770 0.0278770i
\(904\) −5.23306e8 + 9.00528e9i −0.0235595 + 0.405423i
\(905\) −2.37219e10 2.37219e10i −1.06385 1.06385i
\(906\) −8.01995e8 + 5.29757e9i −0.0358280 + 0.236662i
\(907\) 1.43966e10 + 3.47564e10i 0.640668 + 1.54671i 0.825780 + 0.563993i \(0.190735\pi\)
−0.185111 + 0.982718i \(0.559265\pi\)
\(908\) −1.83699e9 + 1.69856e8i −0.0814340 + 0.00752977i
\(909\) 1.53591e9 + 6.36195e8i 0.0678254 + 0.0280942i
\(910\) −7.87631e8 3.18472e9i −0.0346480 0.140096i
\(911\) 3.22959e10i 1.41525i −0.706588 0.707625i \(-0.749767\pi\)
0.706588 0.707625i \(-0.250233\pi\)
\(912\) −5.60149e8 3.00309e9i −0.0244524 0.131095i
\(913\) 4.24705e10i 1.84689i
\(914\) 6.51943e9 1.61236e9i 0.282421 0.0698473i
\(915\) −2.27923e9 9.44090e8i −0.0983592 0.0407417i
\(916\) −3.66235e9 3.04239e9i −0.157444 0.130792i
\(917\) 3.64968e8 + 8.81110e8i 0.0156301 + 0.0377344i
\(918\) 2.85153e9 + 4.31690e8i 0.121654 + 0.0184172i
\(919\) −1.41211e10 1.41211e10i −0.600156 0.600156i 0.340198 0.940354i \(-0.389506\pi\)
−0.940354 + 0.340198i \(0.889506\pi\)
\(920\) −4.47961e10 2.16801e10i −1.89663 0.917920i
\(921\) 3.28623e9 3.28623e9i 0.138608 0.138608i
\(922\) −3.80305e9 + 2.80297e9i −0.159799 + 0.117777i
\(923\) 7.77433e9 3.22023e9i 0.325430 0.134797i
\(924\) −1.67663e9 5.19555e8i −0.0699174 0.0216660i
\(925\) 1.64605e10 3.97392e10i 0.683829 1.65091i
\(926\) 4.14387e9 + 2.50059e9i 0.171501 + 0.103491i
\(927\) 6.29539e9 0.259564
\(928\) −2.70220e10 + 9.23343e8i −1.10994 + 0.0379267i
\(929\) 1.11443e10 0.456036 0.228018 0.973657i \(-0.426776\pi\)
0.228018 + 0.973657i \(0.426776\pi\)
\(930\) −8.25249e9 4.97991e9i −0.336430 0.203016i
\(931\) 6.33953e9 1.53050e10i 0.257474 0.621597i
\(932\) −1.43179e9 + 4.62047e9i −0.0579327 + 0.186952i
\(933\) −7.22655e8 + 2.99333e8i −0.0291303 + 0.0120662i
\(934\) −3.34409e9 + 2.46470e9i −0.134296 + 0.0989805i
\(935\) 1.93555e10 1.93555e10i 0.774399 0.774399i
\(936\) 2.78708e9 + 8.01500e9i 0.111092 + 0.319476i
\(937\) −1.54037e10 1.54037e10i −0.611699 0.611699i 0.331689 0.943389i \(-0.392381\pi\)
−0.943389 + 0.331689i \(0.892381\pi\)
\(938\) −6.89504e9 1.04383e9i −0.272789 0.0412973i
\(939\) 2.14689e8 + 5.18306e8i 0.00846215 + 0.0204294i
\(940\) 1.32504e10 1.59504e10i 0.520333 0.626361i
\(941\) −5.70259e9 2.36209e9i −0.223104 0.0924129i 0.268331 0.963327i \(-0.413528\pi\)
−0.491436 + 0.870914i \(0.663528\pi\)
\(942\) −5.54974e8 + 1.37254e8i −0.0216319 + 0.00534991i
\(943\) 4.57268e10i 1.77574i
\(944\) −2.92476e9 + 1.38379e10i −0.113159 + 0.535386i
\(945\) 3.95522e9i 0.152461i
\(946\) 1.04724e10 + 4.23442e10i 0.402186 + 1.62620i
\(947\) −7.70336e9 3.19083e9i −0.294751 0.122090i 0.230408 0.973094i \(-0.425994\pi\)
−0.525159 + 0.851004i \(0.675994\pi\)
\(948\) 1.73965e8 + 1.88143e9i 0.00663184 + 0.0717229i
\(949\) −1.91245e9 4.61707e9i −0.0726371 0.175362i
\(950\) −6.98268e9 + 4.61241e10i −0.264235 + 1.74540i
\(951\) 3.99388e9 + 3.99388e9i 0.150579 + 0.150579i
\(952\) 1.29350e9 + 1.45310e9i 0.0485888 + 0.0545843i
\(953\) −9.56220e9 + 9.56220e9i −0.357876 + 0.357876i −0.863029 0.505154i \(-0.831436\pi\)
0.505154 + 0.863029i \(0.331436\pi\)
\(954\) −1.94293e10 2.63615e10i −0.724499 0.982995i
\(955\) 3.43071e10 1.42105e10i 1.27460 0.527955i
\(956\) −5.03520e9 + 2.65283e9i −0.186387 + 0.0981990i
\(957\) 3.83307e9 9.25385e9i 0.141369 0.341296i
\(958\) −2.68434e10 + 4.44838e10i −0.986413 + 1.63464i
\(959\) 3.91715e9 0.143418
\(960\) 1.11986e9 9.60300e9i 0.0408522 0.350314i
\(961\) 6.63809e9 0.241274
\(962\) −3.58111e9 + 5.93446e9i −0.129690 + 0.214916i
\(963\) −1.50063e10 + 3.62283e10i −0.541478 + 1.30724i
\(964\) 1.98898e9 1.04791e9i 0.0715089 0.0376750i
\(965\) −3.69542e10 + 1.53069e10i −1.32379 + 0.548330i
\(966\) 7.77393e8 + 1.05476e9i 0.0277473 + 0.0376473i
\(967\) −8.35425e9 + 8.35425e9i −0.297108 + 0.297108i −0.839880 0.542772i \(-0.817375\pi\)
0.542772 + 0.839880i \(0.317375\pi\)
\(968\) 4.44826e10 3.95967e10i 1.57626 1.40312i
\(969\) −8.86914e8 8.86914e8i −0.0313147 0.0313147i
\(970\) 8.52087e9 5.62846e10i 0.299766 1.98010i
\(971\) −6.03056e9 1.45591e10i −0.211393 0.510348i 0.782245 0.622971i \(-0.214075\pi\)
−0.993638 + 0.112623i \(0.964075\pi\)
\(972\) −1.42145e9 1.53729e10i −0.0496477 0.536937i
\(973\) −8.80225e9 3.64601e9i −0.306336 0.126889i
\(974\) 7.67371e9 + 3.10280e10i 0.266103 + 1.07596i
\(975\) 4.77968e9i 0.165152i
\(976\) 4.78362e9 + 7.34770e9i 0.164696 + 0.252975i
\(977\) 3.52736e10i 1.21009i −0.796190 0.605047i \(-0.793154\pi\)
0.796190 0.605047i \(-0.206846\pi\)
\(978\) 8.42126e9 2.08271e9i 0.287867 0.0711940i
\(979\) −2.25525e9 9.34153e8i −0.0768165 0.0318184i
\(980\) 3.35014e10 4.03280e10i 1.13703 1.36872i
\(981\) −5.59039e9 1.34964e10i −0.189060 0.456432i
\(982\) 2.93631e9 + 4.44526e8i 0.0989491 + 0.0149798i
\(983\) 2.10863e10 + 2.10863e10i 0.708050 + 0.708050i 0.966125 0.258075i \(-0.0830881\pi\)
−0.258075 + 0.966125i \(0.583088\pi\)
\(984\) −8.39047e9 + 2.91764e9i −0.280739 + 0.0976222i
\(985\) −2.77131e10 + 2.77131e10i −0.923971 + 0.923971i
\(986\) −8.93632e9 + 6.58635e9i −0.296886 + 0.218814i
\(987\) −5.04398e8 + 2.08928e8i −0.0166979 + 0.00691651i
\(988\) 2.22505e9 7.18034e9i 0.0733990 0.236862i
\(989\) 1.24608e10 3.00829e10i 0.409598 0.988856i
\(990\) −8.31365e10 5.01681e10i −2.72313 1.64325i
\(991\) 4.10809e10 1.34085 0.670427 0.741975i \(-0.266111\pi\)
0.670427 + 0.741975i \(0.266111\pi\)
\(992\) 1.41820e10 + 3.11814e10i 0.461260 + 1.01416i
\(993\) 4.30784e9 0.139617
\(994\) −5.85924e9 3.53572e9i −0.189229 0.114189i
\(995\) 3.14088e10 7.58276e10i 1.01081 2.44032i
\(996\) 5.88300e9 + 1.82303e9i 0.188665 + 0.0584636i
\(997\) 1.05169e10 4.35626e9i 0.336090 0.139213i −0.208255 0.978075i \(-0.566778\pi\)
0.544345 + 0.838861i \(0.316778\pi\)
\(998\) 4.75902e10 3.50755e10i 1.51552 1.11698i
\(999\) 5.90888e9 5.90888e9i 0.187511 0.187511i
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 32.8.g.a.13.18 yes 108
32.5 even 8 inner 32.8.g.a.5.18 108
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.8.g.a.5.18 108 32.5 even 8 inner
32.8.g.a.13.18 yes 108 1.1 even 1 trivial