Properties

Label 27.7.f.a.2.5
Level $27$
Weight $7$
Character 27.2
Analytic conductor $6.211$
Analytic rank $0$
Dimension $102$
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] = [27,7,Mod(2,27)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(27, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("27.2");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 27.f (of order \(18\), degree \(6\), 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: \(6.21146025774\)
Analytic rank: \(0\)
Dimension: \(102\)
Relative dimension: \(17\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 2.5
Character \(\chi\) \(=\) 27.2
Dual form 27.7.f.a.14.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-9.42516 - 1.66191i) q^{2} +(-26.9402 - 1.79573i) q^{3} +(25.9314 + 9.43824i) q^{4} +(-132.788 - 158.250i) q^{5} +(250.932 + 61.6973i) q^{6} +(-462.855 + 168.465i) q^{7} +(301.732 + 174.205i) q^{8} +(722.551 + 96.7550i) q^{9} +O(q^{10})\) \(q+(-9.42516 - 1.66191i) q^{2} +(-26.9402 - 1.79573i) q^{3} +(25.9314 + 9.43824i) q^{4} +(-132.788 - 158.250i) q^{5} +(250.932 + 61.6973i) q^{6} +(-462.855 + 168.465i) q^{7} +(301.732 + 174.205i) q^{8} +(722.551 + 96.7550i) q^{9} +(988.548 + 1712.22i) q^{10} +(867.186 - 1033.47i) q^{11} +(-681.648 - 300.834i) q^{12} +(162.872 + 923.694i) q^{13} +(4642.46 - 818.590i) q^{14} +(3293.16 + 4501.75i) q^{15} +(-3907.29 - 3278.60i) q^{16} +(-5293.41 + 3056.15i) q^{17} +(-6649.36 - 2112.75i) q^{18} +(59.2073 - 102.550i) q^{19} +(-1949.76 - 5356.93i) q^{20} +(12771.9 - 3707.33i) q^{21} +(-9890.91 + 8299.46i) q^{22} +(7053.70 - 19379.9i) q^{23} +(-7815.91 - 5234.96i) q^{24} +(-4697.32 + 26639.8i) q^{25} -8976.64i q^{26} +(-19291.9 - 3904.11i) q^{27} -13592.5 q^{28} +(1904.97 + 335.898i) q^{29} +(-23557.0 - 47902.6i) q^{30} +(9740.86 + 3545.38i) q^{31} +(17045.0 + 20313.4i) q^{32} +(-25218.0 + 26284.7i) q^{33} +(54970.3 - 20007.5i) q^{34} +(88121.2 + 50876.8i) q^{35} +(17823.5 + 9328.60i) q^{36} +(25963.3 + 44969.7i) q^{37} +(-728.467 + 868.153i) q^{38} +(-2729.10 - 25177.0i) q^{39} +(-12498.3 - 70881.6i) q^{40} +(-56718.7 + 10001.0i) q^{41} +(-126539. + 13716.4i) q^{42} +(40875.2 + 34298.4i) q^{43} +(32241.5 - 18614.6i) q^{44} +(-80634.4 - 127192. i) q^{45} +(-98689.9 + 170936. i) q^{46} +(24295.3 + 66750.9i) q^{47} +(99375.7 + 95342.7i) q^{48} +(95729.8 - 80326.8i) q^{49} +(88545.9 - 243278. i) q^{50} +(148094. - 72827.8i) q^{51} +(-4494.55 + 25489.9i) q^{52} +210667. i q^{53} +(175341. + 68858.3i) q^{54} -278699. q^{55} +(-169006. - 29800.3i) q^{56} +(-1779.21 + 2656.40i) q^{57} +(-17396.4 - 6331.78i) q^{58} +(-132806. - 158271. i) q^{59} +(42907.4 + 147818. i) q^{60} +(279772. - 101829. i) q^{61} +(-85917.0 - 49604.2i) q^{62} +(-350736. + 76941.3i) q^{63} +(36326.5 + 62919.3i) q^{64} +(124547. - 148430. i) q^{65} +(281367. - 205828. i) q^{66} +(-11379.9 - 64538.6i) q^{67} +(-166110. + 29289.7i) q^{68} +(-224829. + 509432. i) q^{69} +(-746004. - 625971. i) q^{70} +(19112.3 - 11034.5i) q^{71} +(201162. + 155066. i) q^{72} +(2485.07 - 4304.27i) q^{73} +(-169972. - 466995. i) q^{74} +(174385. - 709247. i) q^{75} +(2503.22 - 2100.45i) q^{76} +(-227277. + 624439. i) q^{77} +(-16119.7 + 241833. i) q^{78} +(-14021.5 + 79519.8i) q^{79} +1.05369e6i q^{80} +(512718. + 139821. i) q^{81} +551204. q^{82} +(72010.5 + 12697.4i) q^{83} +(366184. + 24408.5i) q^{84} +(1.18654e6 + 431864. i) q^{85} +(-328254. - 391198. i) q^{86} +(-50717.2 - 12470.0i) q^{87} +(441695. - 160764. i) q^{88} +(118458. + 68392.0i) q^{89} +(548611. + 1.33281e6i) q^{90} +(-230997. - 400098. i) q^{91} +(365824. - 435972. i) q^{92} +(-256054. - 113005. i) q^{93} +(-118053. - 669514. i) q^{94} +(-24090.6 + 4247.82i) q^{95} +(-422719. - 577857. i) q^{96} +(-148727. - 124797. i) q^{97} +(-1.03576e6 + 597999. i) q^{98} +(726580. - 662832. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −9.42516 1.66191i −1.17814 0.207739i −0.449915 0.893071i \(-0.648546\pi\)
−0.728230 + 0.685333i \(0.759657\pi\)
\(3\) −26.9402 1.79573i −0.997786 0.0665087i
\(4\) 25.9314 + 9.43824i 0.405178 + 0.147473i
\(5\) −132.788 158.250i −1.06230 1.26600i −0.962583 0.270987i \(-0.912650\pi\)
−0.0997193 0.995016i \(-0.531794\pi\)
\(6\) 250.932 + 61.6973i 1.16172 + 0.285636i
\(7\) −462.855 + 168.465i −1.34943 + 0.491153i −0.912770 0.408473i \(-0.866061\pi\)
−0.436661 + 0.899626i \(0.643839\pi\)
\(8\) 301.732 + 174.205i 0.589321 + 0.340245i
\(9\) 722.551 + 96.7550i 0.991153 + 0.132723i
\(10\) 988.548 + 1712.22i 0.988548 + 1.71222i
\(11\) 867.186 1033.47i 0.651530 0.776463i −0.334614 0.942355i \(-0.608606\pi\)
0.986144 + 0.165892i \(0.0530503\pi\)
\(12\) −681.648 300.834i −0.394472 0.174094i
\(13\) 162.872 + 923.694i 0.0741339 + 0.420434i 0.999177 + 0.0405711i \(0.0129177\pi\)
−0.925043 + 0.379863i \(0.875971\pi\)
\(14\) 4642.46 818.590i 1.69186 0.298320i
\(15\) 3293.16 + 4501.75i 0.975750 + 1.33385i
\(16\) −3907.29 3278.60i −0.953928 0.800440i
\(17\) −5293.41 + 3056.15i −1.07743 + 0.622054i −0.930202 0.367049i \(-0.880368\pi\)
−0.147227 + 0.989103i \(0.547035\pi\)
\(18\) −6649.36 2112.75i −1.14015 0.362268i
\(19\) 59.2073 102.550i 0.00863206 0.0149512i −0.861677 0.507457i \(-0.830586\pi\)
0.870309 + 0.492506i \(0.163919\pi\)
\(20\) −1949.76 5356.93i −0.243720 0.669616i
\(21\) 12771.9 3707.33i 1.37911 0.400316i
\(22\) −9890.91 + 8299.46i −0.928898 + 0.779438i
\(23\) 7053.70 19379.9i 0.579741 1.59282i −0.208878 0.977942i \(-0.566981\pi\)
0.788619 0.614883i \(-0.210797\pi\)
\(24\) −7815.91 5234.96i −0.565387 0.378686i
\(25\) −4697.32 + 26639.8i −0.300628 + 1.70495i
\(26\) 8976.64i 0.510733i
\(27\) −19291.9 3904.11i −0.980131 0.198349i
\(28\) −13592.5 −0.619191
\(29\) 1904.97 + 335.898i 0.0781078 + 0.0137725i 0.212566 0.977147i \(-0.431818\pi\)
−0.134458 + 0.990919i \(0.542929\pi\)
\(30\) −23557.0 47902.6i −0.872482 1.77417i
\(31\) 9740.86 + 3545.38i 0.326973 + 0.119008i 0.500291 0.865858i \(-0.333226\pi\)
−0.173318 + 0.984866i \(0.555449\pi\)
\(32\) 17045.0 + 20313.4i 0.520172 + 0.619917i
\(33\) −25218.0 + 26284.7i −0.701729 + 0.731412i
\(34\) 54970.3 20007.5i 1.39859 0.509046i
\(35\) 88121.2 + 50876.8i 2.05531 + 1.18663i
\(36\) 17823.5 + 9328.60i 0.382020 + 0.199944i
\(37\) 25963.3 + 44969.7i 0.512571 + 0.887799i 0.999894 + 0.0145772i \(0.00464023\pi\)
−0.487323 + 0.873222i \(0.662026\pi\)
\(38\) −728.467 + 868.153i −0.0132758 + 0.0158214i
\(39\) −2729.10 25177.0i −0.0460072 0.424434i
\(40\) −12498.3 70881.6i −0.195287 1.10752i
\(41\) −56718.7 + 10001.0i −0.822952 + 0.145109i −0.569240 0.822171i \(-0.692763\pi\)
−0.253712 + 0.967280i \(0.581651\pi\)
\(42\) −126539. + 13716.4i −1.70795 + 0.185136i
\(43\) 40875.2 + 34298.4i 0.514108 + 0.431388i 0.862572 0.505934i \(-0.168852\pi\)
−0.348464 + 0.937322i \(0.613297\pi\)
\(44\) 32241.5 18614.6i 0.378492 0.218523i
\(45\) −80634.4 127192.i −0.884877 1.39579i
\(46\) −98689.9 + 170936.i −1.01391 + 1.75614i
\(47\) 24295.3 + 66750.9i 0.234007 + 0.642929i 1.00000 8.02683e-5i \(2.55502e-5\pi\)
−0.765993 + 0.642849i \(0.777752\pi\)
\(48\) 99375.7 + 95342.7i 0.898579 + 0.862112i
\(49\) 95729.8 80326.8i 0.813690 0.682767i
\(50\) 88545.9 243278.i 0.708367 1.94622i
\(51\) 148094. 72827.8i 1.11642 0.549018i
\(52\) −4494.55 + 25489.9i −0.0319651 + 0.181283i
\(53\) 210667.i 1.41504i 0.706692 + 0.707521i \(0.250187\pi\)
−0.706692 + 0.707521i \(0.749813\pi\)
\(54\) 175341. + 68858.3i 1.11353 + 0.437295i
\(55\) −278699. −1.67513
\(56\) −169006. 29800.3i −0.962361 0.169690i
\(57\) −1779.21 + 2656.40i −0.00960733 + 0.0143440i
\(58\) −17396.4 6331.78i −0.0891613 0.0324520i
\(59\) −132806. 158271.i −0.646636 0.770631i 0.338766 0.940870i \(-0.389990\pi\)
−0.985403 + 0.170239i \(0.945546\pi\)
\(60\) 42907.4 + 147818.i 0.198645 + 0.684343i
\(61\) 279772. 101829.i 1.23258 0.448622i 0.358100 0.933683i \(-0.383425\pi\)
0.874480 + 0.485061i \(0.161203\pi\)
\(62\) −85917.0 49604.2i −0.360499 0.208134i
\(63\) −350736. + 76941.3i −1.40268 + 0.307707i
\(64\) 36326.5 + 62919.3i 0.138574 + 0.240018i
\(65\) 124547. 148430.i 0.453518 0.540482i
\(66\) 281367. 205828.i 0.978681 0.715933i
\(67\) −11379.9 64538.6i −0.0378368 0.214583i 0.960027 0.279906i \(-0.0903033\pi\)
−0.997864 + 0.0653230i \(0.979192\pi\)
\(68\) −166110. + 29289.7i −0.528286 + 0.0931511i
\(69\) −224829. + 509432.i −0.684394 + 1.55074i
\(70\) −746004. 625971.i −2.17494 1.82499i
\(71\) 19112.3 11034.5i 0.0533995 0.0308302i −0.473063 0.881029i \(-0.656852\pi\)
0.526462 + 0.850199i \(0.323518\pi\)
\(72\) 201162. + 155066.i 0.538949 + 0.415451i
\(73\) 2485.07 4304.27i 0.00638807 0.0110645i −0.862814 0.505522i \(-0.831300\pi\)
0.869202 + 0.494458i \(0.164633\pi\)
\(74\) −169972. 466995.i −0.419453 1.15244i
\(75\) 174385. 709247.i 0.413356 1.68118i
\(76\) 2503.22 2100.45i 0.00570240 0.00478488i
\(77\) −227277. + 624439.i −0.497833 + 1.36778i
\(78\) −16119.7 + 241833.i −0.0339682 + 0.509602i
\(79\) −14021.5 + 79519.8i −0.0284389 + 0.161285i −0.995720 0.0924225i \(-0.970539\pi\)
0.967281 + 0.253708i \(0.0816501\pi\)
\(80\) 1.05369e6i 2.05798i
\(81\) 512718. + 139821.i 0.964769 + 0.263097i
\(82\) 551204. 0.999702
\(83\) 72010.5 + 12697.4i 0.125939 + 0.0222065i 0.236263 0.971689i \(-0.424077\pi\)
−0.110323 + 0.993896i \(0.535189\pi\)
\(84\) 366184. + 24408.5i 0.617820 + 0.0411816i
\(85\) 1.18654e6 + 431864.i 1.93208 + 0.703219i
\(86\) −328254. 391198.i −0.516078 0.615038i
\(87\) −50717.2 12470.0i −0.0770189 0.0189369i
\(88\) 441695. 160764.i 0.648148 0.235907i
\(89\) 118458. + 68392.0i 0.168034 + 0.0970142i 0.581658 0.813433i \(-0.302404\pi\)
−0.413625 + 0.910447i \(0.635737\pi\)
\(90\) 548611. + 1.33281e6i 0.752553 + 1.82827i
\(91\) −230997. 400098.i −0.306536 0.530936i
\(92\) 365824. 435972.i 0.469796 0.559881i
\(93\) −256054. 113005.i −0.318334 0.140492i
\(94\) −118053. 669514.i −0.142133 0.806076i
\(95\) −24090.6 + 4247.82i −0.0280981 + 0.00495445i
\(96\) −422719. 577857.i −0.477791 0.653141i
\(97\) −148727. 124797.i −0.162958 0.136738i 0.557663 0.830068i \(-0.311698\pi\)
−0.720620 + 0.693330i \(0.756143\pi\)
\(98\) −1.03576e6 + 597999.i −1.10048 + 0.635363i
\(99\) 726580. 662832.i 0.748821 0.683121i
\(100\) −373241. + 646472.i −0.373241 + 0.646472i
\(101\) 562443. + 1.54530e6i 0.545901 + 1.49985i 0.839196 + 0.543829i \(0.183026\pi\)
−0.293295 + 0.956022i \(0.594752\pi\)
\(102\) −1.51684e6 + 440296.i −1.42935 + 0.414900i
\(103\) −433960. + 364136.i −0.397135 + 0.333236i −0.819385 0.573244i \(-0.805685\pi\)
0.422250 + 0.906479i \(0.361240\pi\)
\(104\) −111769. + 307082.i −0.0993618 + 0.272994i
\(105\) −2.28264e6 1.52887e6i −1.97183 1.32070i
\(106\) 350110. 1.98557e6i 0.293959 1.66713i
\(107\) 1.40996e6i 1.15095i −0.817819 0.575475i \(-0.804817\pi\)
0.817819 0.575475i \(-0.195183\pi\)
\(108\) −463418. 283321.i −0.367876 0.224909i
\(109\) −635387. −0.490635 −0.245318 0.969443i \(-0.578892\pi\)
−0.245318 + 0.969443i \(0.578892\pi\)
\(110\) 2.62678e6 + 463173.i 1.97354 + 0.347989i
\(111\) −618702. 1.25812e6i −0.452390 0.919924i
\(112\) 2.36084e6 + 859275.i 1.68040 + 0.611615i
\(113\) −1.15293e6 1.37401e6i −0.799037 0.952255i 0.200587 0.979676i \(-0.435715\pi\)
−0.999624 + 0.0274205i \(0.991271\pi\)
\(114\) 21184.0 22080.1i 0.0142986 0.0149034i
\(115\) −4.00352e6 + 1.45716e6i −2.63238 + 0.958108i
\(116\) 46228.2 + 26689.9i 0.0296165 + 0.0170991i
\(117\) 28311.4 + 683174.i 0.0176768 + 0.426554i
\(118\) 988680. + 1.71244e6i 0.601741 + 1.04225i
\(119\) 1.93523e6 2.30631e6i 1.14839 1.36860i
\(120\) 209423. + 1.93201e6i 0.121194 + 1.11806i
\(121\) −8424.90 47780.0i −0.00475564 0.0269706i
\(122\) −2.80613e6 + 494796.i −1.54535 + 0.272488i
\(123\) 1.54597e6 167578.i 0.830781 0.0900539i
\(124\) 219132. + 183873.i 0.114932 + 0.0964391i
\(125\) 2.04412e6 1.18017e6i 1.04659 0.604249i
\(126\) 3.43361e6 142292.i 1.71648 0.0711328i
\(127\) −886641. + 1.53571e6i −0.432849 + 0.749717i −0.997117 0.0758748i \(-0.975825\pi\)
0.564268 + 0.825592i \(0.309158\pi\)
\(128\) −818262. 2.24816e6i −0.390178 1.07200i
\(129\) −1.03960e6 997406.i −0.484279 0.464625i
\(130\) −1.42056e6 + 1.19199e6i −0.646589 + 0.542553i
\(131\) −87440.9 + 240242.i −0.0388956 + 0.106865i −0.957620 0.288034i \(-0.906998\pi\)
0.918724 + 0.394899i \(0.129220\pi\)
\(132\) −902020. + 443585.i −0.392188 + 0.192866i
\(133\) −10128.3 + 57440.2i −0.00430506 + 0.0244152i
\(134\) 627199.i 0.260670i
\(135\) 1.94391e6 + 3.57137e6i 0.790085 + 1.45156i
\(136\) −2.12959e6 −0.846602
\(137\) 95387.6 + 16819.4i 0.0370963 + 0.00654108i 0.192166 0.981363i \(-0.438449\pi\)
−0.155069 + 0.987904i \(0.549560\pi\)
\(138\) 2.96568e6 4.42783e6i 1.12846 1.68482i
\(139\) 3.32992e6 + 1.21199e6i 1.23991 + 0.451289i 0.876980 0.480528i \(-0.159555\pi\)
0.362928 + 0.931817i \(0.381777\pi\)
\(140\) 1.80492e6 + 2.15101e6i 0.657768 + 0.783897i
\(141\) −534655. 1.84191e6i −0.190729 0.657069i
\(142\) −198474. + 72238.8i −0.0693169 + 0.0252293i
\(143\) 1.09585e6 + 632691.i 0.374752 + 0.216363i
\(144\) −2.50599e6 2.74701e6i −0.839252 0.919967i
\(145\) −199801. 346066.i −0.0655381 0.113515i
\(146\) −30575.5 + 36438.4i −0.00982460 + 0.0117085i
\(147\) −2.72323e6 + 1.99212e6i −0.857298 + 0.627138i
\(148\) 248828. + 1.41117e6i 0.0767563 + 0.435306i
\(149\) 4.50565e6 794468.i 1.36207 0.240169i 0.555601 0.831449i \(-0.312488\pi\)
0.806467 + 0.591280i \(0.201377\pi\)
\(150\) −2.82231e6 + 6.39495e6i −0.836240 + 1.89480i
\(151\) 1.24649e6 + 1.04593e6i 0.362041 + 0.303789i 0.805604 0.592455i \(-0.201841\pi\)
−0.443562 + 0.896244i \(0.646286\pi\)
\(152\) 35729.5 20628.4i 0.0101741 0.00587403i
\(153\) −4.12045e6 + 1.69606e6i −1.15046 + 0.473551i
\(154\) 3.17988e6 5.50772e6i 0.870661 1.50803i
\(155\) −732409. 2.01228e6i −0.196679 0.540372i
\(156\) 166857. 678631.i 0.0439512 0.178756i
\(157\) −4.02841e6 + 3.38024e6i −1.04096 + 0.873470i −0.992114 0.125336i \(-0.959999\pi\)
−0.0488467 + 0.998806i \(0.515555\pi\)
\(158\) 264309. 726184.i 0.0670103 0.184109i
\(159\) 378303. 5.67542e6i 0.0941126 1.41191i
\(160\) 951241. 5.39475e6i 0.232237 1.31708i
\(161\) 1.01584e7i 2.43415i
\(162\) −4.60008e6 2.16992e6i −1.08198 0.510387i
\(163\) 3.25383e6 0.751333 0.375666 0.926755i \(-0.377414\pi\)
0.375666 + 0.926755i \(0.377414\pi\)
\(164\) −1.56519e6 275984.i −0.354841 0.0625681i
\(165\) 7.50822e6 + 500470.i 1.67142 + 0.111410i
\(166\) −657609. 239350.i −0.143762 0.0523250i
\(167\) 622389. + 741735.i 0.133633 + 0.159257i 0.828711 0.559677i \(-0.189075\pi\)
−0.695078 + 0.718934i \(0.744630\pi\)
\(168\) 4.49954e6 + 1.10632e6i 0.948944 + 0.233320i
\(169\) 3.70903e6 1.34998e6i 0.768424 0.279683i
\(170\) −1.04656e7 6.04231e6i −2.13018 1.22986i
\(171\) 52702.5 68369.0i 0.0105401 0.0136732i
\(172\) 736233. + 1.27519e6i 0.144687 + 0.250606i
\(173\) −5.39396e6 + 6.42827e6i −1.04176 + 1.24153i −0.0720193 + 0.997403i \(0.522944\pi\)
−0.969744 + 0.244122i \(0.921500\pi\)
\(174\) 457294. + 201819.i 0.0868055 + 0.0383102i
\(175\) −2.31371e6 1.31217e7i −0.431713 2.44836i
\(176\) −6.77669e6 + 1.19491e6i −1.24302 + 0.219179i
\(177\) 3.29360e6 + 4.50235e6i 0.593951 + 0.811932i
\(178\) −1.00283e6 841473.i −0.177814 0.149204i
\(179\) 5.25825e6 3.03585e6i 0.916815 0.529324i 0.0341976 0.999415i \(-0.489112\pi\)
0.882618 + 0.470092i \(0.155779\pi\)
\(180\) −890493. 4.05930e6i −0.152691 0.696040i
\(181\) −4.75293e6 + 8.23232e6i −0.801541 + 1.38831i 0.117061 + 0.993125i \(0.462653\pi\)
−0.918602 + 0.395185i \(0.870680\pi\)
\(182\) 1.51225e6 + 4.15488e6i 0.250848 + 0.689199i
\(183\) −7.71998e6 + 2.24089e6i −1.25969 + 0.365652i
\(184\) 5.50441e6 4.61875e6i 0.883604 0.741431i
\(185\) 3.66886e6 1.00801e7i 0.579451 1.59203i
\(186\) 2.22555e6 + 1.49063e6i 0.345858 + 0.231650i
\(187\) −1.43192e6 + 8.12085e6i −0.218975 + 1.24187i
\(188\) 1.96025e6i 0.295010i
\(189\) 9.58707e6 1.44299e6i 1.42004 0.213736i
\(190\) 234117. 0.0341328
\(191\) −8.02752e6 1.41547e6i −1.15208 0.203142i −0.435194 0.900337i \(-0.643320\pi\)
−0.716882 + 0.697195i \(0.754431\pi\)
\(192\) −865657. 1.76029e6i −0.122304 0.248703i
\(193\) −1.14809e6 417869.i −0.159699 0.0581257i 0.260934 0.965357i \(-0.415970\pi\)
−0.420633 + 0.907231i \(0.638192\pi\)
\(194\) 1.19437e6 + 1.42340e6i 0.163582 + 0.194949i
\(195\) −3.62187e6 + 3.77508e6i −0.488461 + 0.509122i
\(196\) 3.24055e6 1.17946e6i 0.430378 0.156645i
\(197\) 4.78394e6 + 2.76201e6i 0.625730 + 0.361265i 0.779096 0.626904i \(-0.215678\pi\)
−0.153367 + 0.988169i \(0.549012\pi\)
\(198\) −7.94970e6 + 5.03978e6i −1.02413 + 0.649257i
\(199\) −6.74102e6 1.16758e7i −0.855394 1.48159i −0.876279 0.481804i \(-0.839982\pi\)
0.0208852 0.999782i \(-0.493352\pi\)
\(200\) −6.05813e6 + 7.21980e6i −0.757266 + 0.902474i
\(201\) 190683. + 1.75912e6i 0.0234814 + 0.216624i
\(202\) −2.73296e6 1.54994e7i −0.331574 1.88045i
\(203\) −938313. + 165450.i −0.112166 + 0.0197778i
\(204\) 4.52764e6 490781.i 0.533312 0.0578092i
\(205\) 9.11422e6 + 7.64774e6i 1.05793 + 0.887710i
\(206\) 4.69530e6 2.71083e6i 0.537108 0.310100i
\(207\) 6.97176e6 1.33205e7i 0.786016 1.50179i
\(208\) 2.39204e6 4.14313e6i 0.265814 0.460403i
\(209\) −54638.9 150119.i −0.00598498 0.0164436i
\(210\) 1.89734e7 + 1.82034e7i 2.04874 + 1.96560i
\(211\) −1.01063e7 + 8.48019e6i −1.07583 + 0.902731i −0.995568 0.0940424i \(-0.970021\pi\)
−0.0802649 + 0.996774i \(0.525577\pi\)
\(212\) −1.98833e6 + 5.46289e6i −0.208680 + 0.573343i
\(213\) −534703. + 262950.i −0.0553317 + 0.0272104i
\(214\) −2.34323e6 + 1.32891e7i −0.239097 + 1.35599i
\(215\) 1.10229e7i 1.10913i
\(216\) −5.14088e6 4.53875e6i −0.510125 0.450376i
\(217\) −5.10588e6 −0.499679
\(218\) 5.98863e6 + 1.05596e6i 0.578040 + 0.101924i
\(219\) −74677.6 + 111495.i −0.00710981 + 0.0106151i
\(220\) −7.22705e6 2.63043e6i −0.678724 0.247035i
\(221\) −3.68510e6 4.39173e6i −0.341407 0.406873i
\(222\) 3.74049e6 + 1.28862e7i 0.341877 + 1.17778i
\(223\) 1.68061e7 6.11692e6i 1.51549 0.551592i 0.555471 0.831536i \(-0.312538\pi\)
0.960016 + 0.279944i \(0.0903158\pi\)
\(224\) −1.13115e7 6.53069e6i −1.00641 0.581052i
\(225\) −5.97158e6 + 1.87941e7i −0.524254 + 1.64996i
\(226\) 8.58306e6 + 1.48663e7i 0.743561 + 1.28789i
\(227\) −1.98248e6 + 2.36263e6i −0.169485 + 0.201985i −0.844101 0.536185i \(-0.819865\pi\)
0.674615 + 0.738169i \(0.264309\pi\)
\(228\) −71209.1 + 52091.4i −0.00600801 + 0.00439503i
\(229\) 2.42442e6 + 1.37496e7i 0.201884 + 1.14494i 0.902268 + 0.431175i \(0.141901\pi\)
−0.700385 + 0.713766i \(0.746988\pi\)
\(230\) 4.01555e7 7.08050e6i 3.30036 0.581943i
\(231\) 7.24422e6 1.64144e7i 0.587700 1.33165i
\(232\) 516277. + 433208.i 0.0413446 + 0.0346922i
\(233\) 1.01782e7 5.87637e6i 0.804641 0.464560i −0.0404506 0.999182i \(-0.512879\pi\)
0.845091 + 0.534622i \(0.179546\pi\)
\(234\) 868534. 6.48608e6i 0.0677859 0.506214i
\(235\) 7.33722e6 1.27084e7i 0.565364 0.979239i
\(236\) −1.95002e6 5.35765e6i −0.148356 0.407604i
\(237\) 520538. 2.11710e6i 0.0391028 0.159036i
\(238\) −2.20727e7 + 1.85212e7i −1.63729 + 1.37385i
\(239\) −6.77238e6 + 1.86070e7i −0.496075 + 1.36296i 0.398963 + 0.916967i \(0.369370\pi\)
−0.895038 + 0.445989i \(0.852852\pi\)
\(240\) 1.89214e6 2.83866e7i 0.136874 2.05343i
\(241\) −954656. + 5.41412e6i −0.0682018 + 0.386791i 0.931531 + 0.363663i \(0.118474\pi\)
−0.999732 + 0.0231288i \(0.992637\pi\)
\(242\) 464335.i 0.0327632i
\(243\) −1.35617e7 4.68751e6i −0.945135 0.326680i
\(244\) 8.21596e6 0.565573
\(245\) −2.54235e7 4.48285e6i −1.72877 0.304829i
\(246\) −1.48495e7 989815.i −0.997488 0.0664888i
\(247\) 104368. + 37986.9i 0.00692591 + 0.00252082i
\(248\) 2.32151e6 + 2.76667e6i 0.152200 + 0.181385i
\(249\) −1.91718e6 471382.i −0.124184 0.0305334i
\(250\) −2.12275e7 + 7.72618e6i −1.35856 + 0.494476i
\(251\) −5.54881e6 3.20361e6i −0.350896 0.202590i 0.314184 0.949362i \(-0.398269\pi\)
−0.665080 + 0.746772i \(0.731603\pi\)
\(252\) −9.82125e6 1.31514e6i −0.613713 0.0821808i
\(253\) −1.39117e7 2.40958e7i −0.859051 1.48792i
\(254\) 1.09089e7 1.30008e7i 0.665704 0.793355i
\(255\) −3.11901e7 1.37652e7i −1.88103 0.830162i
\(256\) 3.16859e6 + 1.79700e7i 0.188863 + 1.07109i
\(257\) −1.25273e7 + 2.20890e6i −0.738004 + 0.130130i −0.530000 0.847998i \(-0.677808\pi\)
−0.208004 + 0.978128i \(0.566697\pi\)
\(258\) 8.14076e6 + 1.11284e7i 0.474030 + 0.648000i
\(259\) −1.95931e7 1.64405e7i −1.12772 0.946273i
\(260\) 4.63060e6 2.67348e6i 0.263462 0.152110i
\(261\) 1.34394e6 + 427019.i 0.0755889 + 0.0240174i
\(262\) 1.22341e6 2.11900e6i 0.0680247 0.117822i
\(263\) 5.73899e6 + 1.57677e7i 0.315477 + 0.866767i 0.991526 + 0.129910i \(0.0414687\pi\)
−0.676049 + 0.736857i \(0.736309\pi\)
\(264\) −1.21880e7 + 3.53784e6i −0.662403 + 0.192277i
\(265\) 3.33382e7 2.79740e7i 1.79145 1.50320i
\(266\) 190921. 524551.i 0.0101440 0.0278704i
\(267\) −3.06848e6 2.05522e6i −0.161209 0.107975i
\(268\) 314035. 1.78098e6i 0.0163145 0.0925241i
\(269\) 2.12720e7i 1.09283i 0.837515 + 0.546414i \(0.184007\pi\)
−0.837515 + 0.546414i \(0.815993\pi\)
\(270\) −1.23863e7 3.68913e7i −0.629290 1.87427i
\(271\) 3.86080e7 1.93986 0.969928 0.243390i \(-0.0782595\pi\)
0.969928 + 0.243390i \(0.0782595\pi\)
\(272\) 3.07028e7 + 5.41373e6i 1.52571 + 0.269023i
\(273\) 5.50463e6 + 1.11935e7i 0.270545 + 0.550148i
\(274\) −871091. 317051.i −0.0423460 0.0154127i
\(275\) 2.34581e7 + 2.79562e7i 1.12796 + 1.34425i
\(276\) −1.06383e7 + 1.10883e7i −0.505993 + 0.527396i
\(277\) 5.10597e6 1.85842e6i 0.240237 0.0874390i −0.219096 0.975703i \(-0.570311\pi\)
0.459333 + 0.888264i \(0.348089\pi\)
\(278\) −2.93708e7 1.69572e7i −1.36704 0.789261i
\(279\) 6.69523e6 + 3.50419e6i 0.308285 + 0.161352i
\(280\) 1.77260e7 + 3.07024e7i 0.807490 + 1.39861i
\(281\) 9.09776e6 1.08423e7i 0.410030 0.488655i −0.521021 0.853544i \(-0.674449\pi\)
0.931051 + 0.364889i \(0.118893\pi\)
\(282\) 1.97811e6 + 1.82488e7i 0.0882072 + 0.813745i
\(283\) 5.04812e6 + 2.86293e7i 0.222726 + 1.26314i 0.866986 + 0.498333i \(0.166054\pi\)
−0.644260 + 0.764807i \(0.722834\pi\)
\(284\) 599753. 105753.i 0.0261829 0.00461675i
\(285\) 656633. 71176.9i 0.0283654 0.00307471i
\(286\) −9.27711e6 7.78442e6i −0.396565 0.332758i
\(287\) 2.45677e7 1.41842e7i 1.03925 0.600010i
\(288\) 1.03505e7 + 1.63267e7i 0.433293 + 0.683472i
\(289\) 6.61134e6 1.14512e7i 0.273902 0.474413i
\(290\) 1.30803e6 + 3.59377e6i 0.0536318 + 0.147352i
\(291\) 3.78264e6 + 3.62913e6i 0.153503 + 0.147273i
\(292\) 105066. 88160.8i 0.00422001 0.00354101i
\(293\) 2.00959e6 5.52130e6i 0.0798922 0.219502i −0.893315 0.449430i \(-0.851627\pi\)
0.973208 + 0.229928i \(0.0738492\pi\)
\(294\) 2.89776e7 1.42503e7i 1.14030 0.560765i
\(295\) −7.41156e6 + 4.20330e7i −0.288698 + 1.63729i
\(296\) 1.80918e7i 0.697598i
\(297\) −2.07645e7 + 1.65521e7i −0.792596 + 0.631806i
\(298\) −4.37868e7 −1.65461
\(299\) 1.90499e7 + 3.35902e6i 0.712656 + 0.125660i
\(300\) 1.12161e7 1.67459e7i 0.415410 0.620217i
\(301\) −2.46974e7 8.98911e6i −0.905631 0.329623i
\(302\) −1.00101e7 1.19296e7i −0.363429 0.433117i
\(303\) −1.23774e7 4.26407e7i −0.444939 1.53284i
\(304\) −567561. + 206575.i −0.0202019 + 0.00735288i
\(305\) −5.32648e7 3.07524e7i −1.87733 1.08388i
\(306\) 4.16546e7 9.13782e6i 1.45378 0.318917i
\(307\) −1.24038e7 2.14841e7i −0.428687 0.742508i 0.568070 0.822980i \(-0.307690\pi\)
−0.996757 + 0.0804725i \(0.974357\pi\)
\(308\) −1.17872e7 + 1.40475e7i −0.403421 + 0.480779i
\(309\) 1.23449e7 9.03062e6i 0.418419 0.306085i
\(310\) 3.55885e6 + 2.01832e7i 0.119461 + 0.677494i
\(311\) −4.37561e7 + 7.71538e6i −1.45465 + 0.256493i −0.844397 0.535717i \(-0.820041\pi\)
−0.610248 + 0.792210i \(0.708930\pi\)
\(312\) 3.56251e6 8.07214e6i 0.117298 0.265782i
\(313\) 3.75231e7 + 3.14856e7i 1.22367 + 1.02678i 0.998624 + 0.0524373i \(0.0166990\pi\)
0.225050 + 0.974347i \(0.427745\pi\)
\(314\) 4.35860e7 2.51644e7i 1.40786 0.812826i
\(315\) 5.87495e7 + 4.52872e7i 1.87963 + 1.44892i
\(316\) −1.11412e6 + 1.92972e6i −0.0353079 + 0.0611551i
\(317\) −1.53658e6 4.22173e6i −0.0482368 0.132530i 0.913235 0.407433i \(-0.133576\pi\)
−0.961472 + 0.274904i \(0.911354\pi\)
\(318\) −1.29976e7 + 5.28631e7i −0.404187 + 1.64388i
\(319\) 1.99911e6 1.67745e6i 0.0615835 0.0516747i
\(320\) 5.13329e6 1.41036e7i 0.156655 0.430407i
\(321\) −2.53192e6 + 3.79847e7i −0.0765482 + 1.14840i
\(322\) 1.68823e7 9.57444e7i 0.505667 2.86778i
\(323\) 723786.i 0.0214784i
\(324\) 1.19758e7 + 8.46490e6i 0.352103 + 0.248878i
\(325\) −2.53721e7 −0.739105
\(326\) −3.06679e7 5.40758e6i −0.885179 0.156081i
\(327\) 1.71175e7 + 1.14099e6i 0.489549 + 0.0326315i
\(328\) −1.88561e7 6.86306e6i −0.534356 0.194490i
\(329\) −2.24904e7 2.68030e7i −0.631553 0.752656i
\(330\) −6.99344e7 1.71950e7i −1.94603 0.478476i
\(331\) −4.32899e7 + 1.57562e7i −1.19372 + 0.434479i −0.861028 0.508557i \(-0.830179\pi\)
−0.332692 + 0.943036i \(0.607957\pi\)
\(332\) 1.74749e6 + 1.00891e6i 0.0477530 + 0.0275702i
\(333\) 1.44087e7 + 3.50050e7i 0.390205 + 0.947975i
\(334\) −4.63342e6 8.02532e6i −0.124355 0.215389i
\(335\) −8.70215e6 + 1.03708e7i −0.231469 + 0.275854i
\(336\) −6.20585e7 2.73885e7i −1.63600 0.722022i
\(337\) −7.46362e6 4.23283e7i −0.195011 1.10596i −0.912402 0.409294i \(-0.865775\pi\)
0.717391 0.696671i \(-0.245336\pi\)
\(338\) −3.72018e7 + 6.55968e6i −0.963415 + 0.169876i
\(339\) 2.85928e7 + 3.90864e7i 0.733935 + 1.00329i
\(340\) 2.66925e7 + 2.23977e7i 0.679129 + 0.569857i
\(341\) 1.21112e7 6.99240e6i 0.305439 0.176345i
\(342\) −610353. + 556802.i −0.0152582 + 0.0139195i
\(343\) −1.80212e6 + 3.12136e6i −0.0446581 + 0.0773502i
\(344\) 6.35842e6 + 1.74696e7i 0.156197 + 0.429149i
\(345\) 1.10472e8 3.20670e7i 2.69027 0.780910i
\(346\) 6.15221e7 5.16232e7i 1.48526 1.24628i
\(347\) −6.38668e6 + 1.75473e7i −0.152857 + 0.419972i −0.992359 0.123385i \(-0.960625\pi\)
0.839501 + 0.543357i \(0.182847\pi\)
\(348\) −1.19747e6 802045.i −0.0284137 0.0190310i
\(349\) 1.31282e7 7.44540e7i 0.308838 1.75151i −0.296028 0.955179i \(-0.595662\pi\)
0.604866 0.796327i \(-0.293227\pi\)
\(350\) 1.27519e8i 2.97421i
\(351\) 464084. 1.84557e7i 0.0107319 0.426785i
\(352\) 3.57746e7 0.820251
\(353\) −1.45221e7 2.56063e6i −0.330145 0.0582135i 0.00611887 0.999981i \(-0.498052\pi\)
−0.336264 + 0.941768i \(0.609163\pi\)
\(354\) −2.35602e7 4.79090e7i −0.531091 1.07996i
\(355\) −4.28408e6 1.55928e6i −0.0957575 0.0348529i
\(356\) 2.42629e6 + 2.89154e6i 0.0537765 + 0.0640883i
\(357\) −5.62769e7 + 5.86574e7i −1.23687 + 1.28919i
\(358\) −5.46051e7 + 1.98746e7i −1.19010 + 0.433162i
\(359\) 3.78992e7 + 2.18811e7i 0.819119 + 0.472919i 0.850113 0.526601i \(-0.176534\pi\)
−0.0309935 + 0.999520i \(0.509867\pi\)
\(360\) −2.17254e6 5.24248e7i −0.0465650 1.12365i
\(361\) 2.35159e7 + 4.07308e7i 0.499851 + 0.865767i
\(362\) 5.84785e7 6.96920e7i 1.23274 1.46912i
\(363\) 141168. + 1.30233e6i 0.00295133 + 0.0272271i
\(364\) −2.21384e6 1.25553e7i −0.0459030 0.260329i
\(365\) −1.01114e6 + 178291.i −0.0207937 + 0.00366649i
\(366\) 7.64862e7 8.29085e6i 1.56006 0.169105i
\(367\) −3.60397e7 3.02409e7i −0.729093 0.611782i 0.200791 0.979634i \(-0.435649\pi\)
−0.929884 + 0.367852i \(0.880093\pi\)
\(368\) −9.10998e7 + 5.25965e7i −1.82799 + 1.05539i
\(369\) −4.19498e7 + 1.73844e6i −0.834931 + 0.0346004i
\(370\) −5.13319e7 + 8.89094e7i −1.01340 + 1.75526i
\(371\) −3.54902e7 9.75084e7i −0.695002 1.90950i
\(372\) −5.57326e6 5.34709e6i −0.108263 0.103870i
\(373\) 6.04115e6 5.06913e6i 0.116411 0.0976803i −0.582724 0.812670i \(-0.698013\pi\)
0.699135 + 0.714990i \(0.253569\pi\)
\(374\) 2.69922e7 7.41605e7i 0.515969 1.41761i
\(375\) −5.71883e7 + 2.81234e7i −1.08446 + 0.533304i
\(376\) −4.29767e6 + 2.43733e7i −0.0808480 + 0.458512i
\(377\) 1.81432e6i 0.0338602i
\(378\) −9.27578e7 2.33247e6i −1.71741 0.0431858i
\(379\) −3.61708e7 −0.664417 −0.332208 0.943206i \(-0.607794\pi\)
−0.332208 + 0.943206i \(0.607794\pi\)
\(380\) −664794. 117221.i −0.0121154 0.00213626i
\(381\) 2.66440e7 3.97801e7i 0.481753 0.719269i
\(382\) 7.33082e7 + 2.66820e7i 1.31511 + 0.478662i
\(383\) 6.88915e6 + 8.21017e6i 0.122622 + 0.146135i 0.823863 0.566789i \(-0.191815\pi\)
−0.701241 + 0.712925i \(0.747370\pi\)
\(384\) 1.80071e7 + 6.20352e7i 0.318016 + 1.09558i
\(385\) 1.28997e8 4.69512e7i 2.26047 0.822743i
\(386\) 1.01264e7 + 5.84650e6i 0.176074 + 0.101656i
\(387\) 2.62159e7 + 2.87372e7i 0.452305 + 0.495805i
\(388\) −2.67883e6 4.63987e6i −0.0458617 0.0794348i
\(389\) −4.48292e7 + 5.34253e7i −0.761574 + 0.907608i −0.997946 0.0640544i \(-0.979597\pi\)
0.236373 + 0.971662i \(0.424041\pi\)
\(390\) 4.04106e7 2.95615e7i 0.681242 0.498348i
\(391\) 2.18897e7 + 1.24143e8i 0.366193 + 2.07679i
\(392\) 4.28781e7 7.56057e6i 0.711832 0.125515i
\(393\) 2.78709e6 6.31515e6i 0.0459170 0.104041i
\(394\) −4.04992e7 3.39828e7i −0.662152 0.555611i
\(395\) 1.44459e7 8.34035e6i 0.234398 0.135330i
\(396\) 2.50972e7 1.03305e7i 0.404147 0.166355i
\(397\) −574096. + 994363.i −0.00917514 + 0.0158918i −0.870577 0.492033i \(-0.836254\pi\)
0.861401 + 0.507925i \(0.169587\pi\)
\(398\) 4.41311e7 + 1.21249e8i 0.699995 + 1.92322i
\(399\) 376005. 1.52926e6i 0.00591936 0.0240748i
\(400\) 1.05695e8 8.86887e7i 1.65149 1.38576i
\(401\) −1.79655e7 + 4.93597e7i −0.278615 + 0.765489i 0.718905 + 0.695108i \(0.244644\pi\)
−0.997520 + 0.0703808i \(0.977579\pi\)
\(402\) 1.12628e6 1.68969e7i 0.0173368 0.260093i
\(403\) −1.68833e6 + 9.57501e6i −0.0257954 + 0.146293i
\(404\) 4.53802e7i 0.688211i
\(405\) −4.59560e7 9.97043e7i −0.691795 1.50089i
\(406\) 9.11871e6 0.136256
\(407\) 6.89899e7 + 1.21648e7i 1.02330 + 0.180435i
\(408\) 5.73716e7 + 3.82418e6i 0.844728 + 0.0563064i
\(409\) −7.36691e7 2.68134e7i −1.07675 0.391906i −0.258054 0.966130i \(-0.583081\pi\)
−0.818698 + 0.574225i \(0.805304\pi\)
\(410\) −7.31931e7 8.72281e7i −1.06199 1.26562i
\(411\) −2.53956e6 624410.i −0.0365791 0.00899382i
\(412\) −1.46900e7 + 5.34671e6i −0.210053 + 0.0764531i
\(413\) 8.81330e7 + 5.08836e7i 1.25109 + 0.722317i
\(414\) −8.78474e7 + 1.13961e8i −1.23802 + 1.60604i
\(415\) −7.55275e6 1.30817e7i −0.105672 0.183030i
\(416\) −1.59872e7 + 1.90529e7i −0.222072 + 0.264655i
\(417\) −8.75323e7 3.86310e7i −1.20715 0.532755i
\(418\) 265496. + 1.50570e6i 0.00363520 + 0.0206163i
\(419\) 1.03973e8 1.83332e7i 1.41344 0.249228i 0.585786 0.810466i \(-0.300786\pi\)
0.827654 + 0.561238i \(0.189675\pi\)
\(420\) −4.47622e7 6.11899e7i −0.604176 0.825909i
\(421\) −3.14656e6 2.64028e6i −0.0421687 0.0353837i 0.621460 0.783446i \(-0.286540\pi\)
−0.663628 + 0.748062i \(0.730984\pi\)
\(422\) 1.09347e8 6.31314e7i 1.45502 0.840056i
\(423\) 1.10961e7 + 5.05816e7i 0.146606 + 0.668300i
\(424\) −3.66994e7 + 6.35652e7i −0.481461 + 0.833915i
\(425\) −5.65504e7 1.55371e8i −0.736664 2.02397i
\(426\) 5.47666e6 1.58972e6i 0.0708414 0.0205633i
\(427\) −1.12339e8 + 9.42639e7i −1.44294 + 1.21077i
\(428\) 1.33076e7 3.65623e7i 0.169734 0.466339i
\(429\) −2.83864e7 1.90127e7i −0.359532 0.240808i
\(430\) −1.83191e7 + 1.03893e8i −0.230409 + 1.30671i
\(431\) 5.35958e7i 0.669420i 0.942321 + 0.334710i \(0.108638\pi\)
−0.942321 + 0.334710i \(0.891362\pi\)
\(432\) 6.25791e7 + 7.85050e7i 0.776208 + 0.973747i
\(433\) −3.01190e7 −0.371003 −0.185501 0.982644i \(-0.559391\pi\)
−0.185501 + 0.982644i \(0.559391\pi\)
\(434\) 4.81237e7 + 8.48551e6i 0.588695 + 0.103803i
\(435\) 4.76124e6 + 9.68187e6i 0.0578432 + 0.117623i
\(436\) −1.64765e7 5.99694e6i −0.198794 0.0723553i
\(437\) −1.56978e6 1.87079e6i −0.0188102 0.0224171i
\(438\) 889144. 926754.i 0.0105816 0.0110292i
\(439\) 8.84886e7 3.22072e7i 1.04591 0.380680i 0.238792 0.971071i \(-0.423249\pi\)
0.807117 + 0.590391i \(0.201026\pi\)
\(440\) −8.40926e7 4.85509e7i −0.987187 0.569953i
\(441\) 7.69416e7 4.87779e7i 0.897110 0.568731i
\(442\) 2.74340e7 + 4.75170e7i 0.317703 + 0.550278i
\(443\) 1.05943e8 1.26258e8i 1.21860 1.45227i 0.365266 0.930903i \(-0.380978\pi\)
0.853333 0.521367i \(-0.174578\pi\)
\(444\) −4.16939e6 3.84641e7i −0.0476347 0.439448i
\(445\) −4.90678e6 2.78277e7i −0.0556822 0.315789i
\(446\) −1.68566e8 + 2.97227e7i −1.90005 + 0.335030i
\(447\) −1.22810e8 + 1.33122e7i −1.37503 + 0.149048i
\(448\) −2.74136e7 2.30028e7i −0.304882 0.255827i
\(449\) 3.52133e7 2.03304e7i 0.389016 0.224598i −0.292718 0.956199i \(-0.594560\pi\)
0.681734 + 0.731600i \(0.261226\pi\)
\(450\) 8.75172e7 1.67213e8i 0.960409 1.83499i
\(451\) −3.88499e7 + 6.72900e7i −0.423507 + 0.733535i
\(452\) −1.69288e7 4.65115e7i −0.183320 0.503669i
\(453\) −3.17025e7 3.04159e7i −0.341035 0.327195i
\(454\) 2.26117e7 1.89735e7i 0.241638 0.202758i
\(455\) −3.26421e7 + 8.96834e7i −0.346532 + 0.952090i
\(456\) −999604. + 491574.i −0.0105423 + 0.00518435i
\(457\) −1.04389e7 + 5.92022e7i −0.109372 + 0.620282i 0.880011 + 0.474953i \(0.157535\pi\)
−0.989383 + 0.145329i \(0.953576\pi\)
\(458\) 1.33621e8i 1.39084i
\(459\) 1.14052e8 3.82930e7i 1.17941 0.395987i
\(460\) −1.17570e8 −1.20788
\(461\) −8.15152e7 1.43733e7i −0.832024 0.146708i −0.258618 0.965980i \(-0.583267\pi\)
−0.573406 + 0.819271i \(0.694378\pi\)
\(462\) −9.55572e7 + 1.42669e8i −0.969031 + 1.44678i
\(463\) −5.78267e7 2.10472e7i −0.582620 0.212056i 0.0338605 0.999427i \(-0.489220\pi\)
−0.616480 + 0.787370i \(0.711442\pi\)
\(464\) −6.34200e6 7.55810e6i −0.0634851 0.0756586i
\(465\) 1.61177e7 + 5.55264e7i 0.160304 + 0.552256i
\(466\) −1.05697e8 + 3.84705e7i −1.04449 + 0.380163i
\(467\) −9.75841e7 5.63402e7i −0.958139 0.553182i −0.0625394 0.998042i \(-0.519920\pi\)
−0.895600 + 0.444861i \(0.853253\pi\)
\(468\) −5.71381e6 + 1.79828e7i −0.0557427 + 0.175437i
\(469\) 1.61398e7 + 2.79549e7i 0.156451 + 0.270981i
\(470\) −9.02748e7 + 1.07585e8i −0.869507 + 1.03624i
\(471\) 1.14596e8 8.38303e7i 1.09675 0.802303i
\(472\) −1.25000e7 7.08911e7i −0.118873 0.674164i
\(473\) 7.08928e7 1.25003e7i 0.669914 0.118124i
\(474\) −8.42459e6 + 1.90889e7i −0.0791068 + 0.179245i
\(475\) 2.45380e6 + 2.05898e6i 0.0228959 + 0.0192119i
\(476\) 7.19506e7 4.15407e7i 0.667134 0.385170i
\(477\) −2.03831e7 + 1.52218e8i −0.187808 + 1.40252i
\(478\) 9.47539e7 1.64119e8i 0.867588 1.50271i
\(479\) 4.68718e7 + 1.28779e8i 0.426487 + 1.17176i 0.947931 + 0.318477i \(0.103171\pi\)
−0.521444 + 0.853285i \(0.674607\pi\)
\(480\) −3.53142e7 + 1.43628e8i −0.319320 + 1.29872i
\(481\) −3.73095e7 + 3.13064e7i −0.335262 + 0.281318i
\(482\) 1.79956e7 4.94424e7i 0.160703 0.441528i
\(483\) 1.82418e7 2.73669e8i 0.161892 2.42876i
\(484\) 232490. 1.31852e6i 0.00205054 0.0116292i
\(485\) 4.01076e7i 0.351561i
\(486\) 1.20031e8 + 6.67187e7i 1.04564 + 0.581218i
\(487\) 9.83197e7 0.851243 0.425622 0.904901i \(-0.360055\pi\)
0.425622 + 0.904901i \(0.360055\pi\)
\(488\) 1.02155e8 + 1.80128e7i 0.879027 + 0.154996i
\(489\) −8.76590e7 5.84302e6i −0.749669 0.0499702i
\(490\) 2.32170e8 + 8.45031e7i 1.97342 + 0.718265i
\(491\) 4.01777e6 + 4.78819e6i 0.0339422 + 0.0404508i 0.782749 0.622338i \(-0.213817\pi\)
−0.748806 + 0.662789i \(0.769373\pi\)
\(492\) 4.16708e7 + 1.02457e7i 0.349894 + 0.0860296i
\(493\) −1.11104e7 + 4.04384e6i −0.0927229 + 0.0337484i
\(494\) −920555. 531482.i −0.00763605 0.00440868i
\(495\) −2.01374e8 2.69655e7i −1.66031 0.222328i
\(496\) −2.64364e7 4.57892e7i −0.216649 0.375248i
\(497\) −6.98728e6 + 8.32711e6i −0.0569166 + 0.0678305i
\(498\) 1.72863e7 + 7.62903e6i 0.139963 + 0.0617705i
\(499\) 6.39969e6 + 3.62944e7i 0.0515059 + 0.292105i 0.999670 0.0256756i \(-0.00817369\pi\)
−0.948164 + 0.317780i \(0.897063\pi\)
\(500\) 6.41456e7 1.13106e7i 0.513165 0.0904848i
\(501\) −1.54353e7 2.11001e7i −0.122745 0.167792i
\(502\) 4.69743e7 + 3.94161e7i 0.371321 + 0.311575i
\(503\) −7.30091e7 + 4.21518e7i −0.573684 + 0.331217i −0.758620 0.651534i \(-0.774126\pi\)
0.184935 + 0.982751i \(0.440793\pi\)
\(504\) −1.19232e8 3.78844e7i −0.931325 0.295916i
\(505\) 1.69858e8 2.94203e8i 1.31890 2.28441i
\(506\) 9.10751e7 + 2.50227e8i 0.702988 + 1.93144i
\(507\) −1.02346e8 + 2.97083e7i −0.785324 + 0.227957i
\(508\) −3.74862e7 + 3.14546e7i −0.285943 + 0.239935i
\(509\) −5.39214e7 + 1.48148e8i −0.408891 + 1.12342i 0.548884 + 0.835899i \(0.315053\pi\)
−0.957775 + 0.287520i \(0.907169\pi\)
\(510\) 2.71095e8 + 1.81574e8i 2.04367 + 1.36881i
\(511\) −425107. + 2.41090e6i −0.00318592 + 0.0180683i
\(512\) 2.15196e7i 0.160334i
\(513\) −1.54259e6 + 1.74724e6i −0.0114261 + 0.0129419i
\(514\) 1.21743e8 0.896509
\(515\) 1.15249e8 + 2.03215e7i 0.843755 + 0.148777i
\(516\) −1.75444e7 3.56761e7i −0.127699 0.259674i
\(517\) 9.00538e7 + 3.27769e7i 0.651674 + 0.237190i
\(518\) 1.57345e8 + 1.87517e8i 1.13205 + 1.34912i
\(519\) 1.56858e8 1.63493e8i 1.12203 1.16949i
\(520\) 6.34373e7 2.30893e7i 0.451164 0.164210i
\(521\) −1.80546e8 1.04238e8i −1.27666 0.737079i −0.300426 0.953805i \(-0.597129\pi\)
−0.976233 + 0.216726i \(0.930462\pi\)
\(522\) −1.19572e7 6.25823e6i −0.0840653 0.0439987i
\(523\) −2.89704e6 5.01782e6i −0.0202511 0.0350760i 0.855722 0.517435i \(-0.173113\pi\)
−0.875973 + 0.482359i \(0.839780\pi\)
\(524\) −4.53492e6 + 5.40451e6i −0.0315193 + 0.0375632i
\(525\) 3.87688e7 + 3.57656e8i 0.267919 + 2.47166i
\(526\) −2.78863e7 1.58151e8i −0.191617 1.08671i
\(527\) −6.23976e7 + 1.10024e7i −0.426320 + 0.0751717i
\(528\) 1.84711e8 2.00221e7i 1.25485 0.136022i
\(529\) −2.12423e8 1.78244e8i −1.43495 1.20406i
\(530\) −3.60708e8 + 2.08255e8i −2.42286 + 1.39884i
\(531\) −8.06452e7 1.27209e8i −0.538635 0.849637i
\(532\) −804774. + 1.39391e6i −0.00534489 + 0.00925762i
\(533\) −1.84758e7 5.07618e7i −0.122017 0.335240i
\(534\) 2.55053e7 + 2.44703e7i 0.167497 + 0.160700i
\(535\) −2.23127e8 + 1.87226e8i −1.45711 + 1.22266i
\(536\) 7.80929e6 2.14558e7i 0.0507127 0.139332i
\(537\) −1.47110e8 + 7.23440e7i −0.949990 + 0.467175i
\(538\) 3.53522e7 2.00492e8i 0.227023 1.28751i
\(539\) 1.68592e8i 1.07664i
\(540\) 1.67006e7 + 1.10958e8i 0.106060 + 0.704654i
\(541\) 2.99767e8 1.89318 0.946589 0.322443i \(-0.104504\pi\)
0.946589 + 0.322443i \(0.104504\pi\)
\(542\) −3.63887e8 6.41631e7i −2.28543 0.402983i
\(543\) 1.42828e8 2.13245e8i 0.892101 1.33193i
\(544\) −1.52307e8 5.54353e7i −0.946071 0.344342i
\(545\) 8.43717e7 + 1.00550e8i 0.521203 + 0.621146i
\(546\) −3.32794e7 1.14649e8i −0.204455 0.704356i
\(547\) 3.66493e7 1.33392e7i 0.223925 0.0815021i −0.227621 0.973750i \(-0.573095\pi\)
0.451546 + 0.892248i \(0.350873\pi\)
\(548\) 2.31479e6 + 1.33644e6i 0.0140660 + 0.00812098i
\(549\) 2.12002e8 4.65071e7i 1.28122 0.281062i
\(550\) −1.74635e8 3.02477e8i −1.04965 1.81804i
\(551\) 147235. 175467.i 0.000880147 0.00104892i
\(552\) −1.56584e8 + 1.14546e8i −0.930959 + 0.681022i
\(553\) −6.90642e6 3.91683e7i −0.0408393 0.231611i
\(554\) −5.12131e7 + 9.03026e6i −0.301198 + 0.0531093i
\(555\) −1.16941e8 + 2.64972e8i −0.684051 + 1.54996i
\(556\) 7.49103e7 + 6.28572e7i 0.435830 + 0.365705i
\(557\) 1.22491e8 7.07204e7i 0.708826 0.409241i −0.101800 0.994805i \(-0.532460\pi\)
0.810626 + 0.585564i \(0.199127\pi\)
\(558\) −5.72799e7 4.41545e7i −0.329686 0.254139i
\(559\) −2.50237e7 + 4.33424e7i −0.143257 + 0.248129i
\(560\) −1.77510e8 4.87705e8i −1.01078 2.77711i
\(561\) 5.31592e7 2.16206e8i 0.301086 1.22456i
\(562\) −1.03767e8 + 8.70707e7i −0.584587 + 0.490527i
\(563\) −1.78446e7 + 4.90275e7i −0.0999955 + 0.274735i −0.979596 0.200978i \(-0.935588\pi\)
0.879600 + 0.475714i \(0.157810\pi\)
\(564\) 3.52008e6 5.28095e7i 0.0196207 0.294357i
\(565\) −6.43422e7 + 3.64903e8i −0.356739 + 2.02317i
\(566\) 2.78225e8i 1.53443i
\(567\) −2.60869e8 + 2.16585e7i −1.43111 + 0.118817i
\(568\) 7.68905e6 0.0419593
\(569\) −1.96431e8 3.46362e7i −1.06629 0.188015i −0.387143 0.922020i \(-0.626538\pi\)
−0.679145 + 0.734004i \(0.737649\pi\)
\(570\) −6.30716e6 420412.i −0.0340573 0.00227013i
\(571\) 1.54906e8 + 5.63813e7i 0.832071 + 0.302849i 0.722709 0.691153i \(-0.242897\pi\)
0.109363 + 0.994002i \(0.465119\pi\)
\(572\) 2.24455e7 + 2.67495e7i 0.119933 + 0.142931i
\(573\) 2.13721e8 + 5.25483e7i 1.13601 + 0.279315i
\(574\) −2.55127e8 + 9.28587e7i −1.34903 + 0.491006i
\(575\) 4.83143e8 + 2.78943e8i 2.54140 + 1.46728i
\(576\) 2.01600e7 + 4.89771e7i 0.105493 + 0.256287i
\(577\) 6.71573e7 + 1.16320e8i 0.349596 + 0.605517i 0.986178 0.165692i \(-0.0529857\pi\)
−0.636582 + 0.771209i \(0.719652\pi\)
\(578\) −8.13437e7 + 9.69417e7i −0.421251 + 0.502027i
\(579\) 3.01793e7 + 1.33191e7i 0.155480 + 0.0686184i
\(580\) −1.91486e6 1.08597e7i −0.00981417 0.0556589i
\(581\) −3.54695e7 + 6.25423e6i −0.180853 + 0.0318893i
\(582\) −2.96207e7 4.04915e7i −0.150254 0.205397i
\(583\) 2.17719e8 + 1.82688e8i 1.09873 + 0.921943i
\(584\) 1.49965e6 865824.i 0.00752925 0.00434702i
\(585\) 1.04353e8 9.51975e7i 0.521240 0.475508i
\(586\) −2.81166e7 + 4.86994e7i −0.139724 + 0.242008i
\(587\) 1.07746e8 + 2.96031e8i 0.532707 + 1.46360i 0.855837 + 0.517246i \(0.173043\pi\)
−0.323130 + 0.946355i \(0.604735\pi\)
\(588\) −8.94191e7 + 2.59558e7i −0.439843 + 0.127674i
\(589\) 940309. 789013.i 0.00460177 0.00386134i
\(590\) 1.39710e8 3.83851e8i 0.680256 1.86899i
\(591\) −1.23920e8 8.29998e7i −0.600317 0.402082i
\(592\) 4.59918e7 2.60833e8i 0.221675 1.25718i
\(593\) 3.36778e8i 1.61503i −0.589850 0.807513i \(-0.700813\pi\)
0.589850 0.807513i \(-0.299187\pi\)
\(594\) 2.23217e8 1.21497e8i 1.06504 0.579706i
\(595\) −6.21949e8 −2.95259
\(596\) 1.24336e8 + 2.19238e7i 0.587298 + 0.103556i
\(597\) 1.60638e8 + 3.26653e8i 0.754962 + 1.53520i
\(598\) −1.73966e8 6.33186e7i −0.813508 0.296093i
\(599\) 1.70304e8 + 2.02961e8i 0.792401 + 0.944347i 0.999422 0.0339894i \(-0.0108213\pi\)
−0.207021 + 0.978337i \(0.566377\pi\)
\(600\) 1.76172e8 1.83624e8i 0.815612 0.850111i
\(601\) 1.75894e8 6.40201e7i 0.810265 0.294912i 0.0965319 0.995330i \(-0.469225\pi\)
0.713733 + 0.700417i \(0.247003\pi\)
\(602\) 2.17838e8 + 1.25769e8i 0.998489 + 0.576478i
\(603\) −1.97812e6 4.77335e7i −0.00902197 0.217706i
\(604\) 2.24515e7 + 3.88871e7i 0.101891 + 0.176480i
\(605\) −6.44247e6 + 7.67784e6i −0.0290929 + 0.0346715i
\(606\) 4.57938e7 + 4.22465e8i 0.205773 + 1.89834i
\(607\) −7.37813e7 4.18434e8i −0.329898 1.87095i −0.472742 0.881201i \(-0.656736\pi\)
0.142844 0.989745i \(-0.454375\pi\)
\(608\) 3.09233e6 545262.i 0.0137586 0.00242602i
\(609\) 2.55755e7 2.77230e6i 0.113233 0.0122740i
\(610\) 4.50921e8 + 3.78368e8i 1.98660 + 1.66696i
\(611\) −5.77003e7 + 3.33133e7i −0.252962 + 0.146047i
\(612\) −1.22857e8 + 5.09131e6i −0.535976 + 0.0222114i
\(613\) 9.21125e6 1.59544e7i 0.0399887 0.0692625i −0.845338 0.534231i \(-0.820601\pi\)
0.885327 + 0.464969i \(0.153934\pi\)
\(614\) 8.12035e7 + 2.23105e8i 0.350808 + 0.963837i
\(615\) −2.31806e8 2.22398e8i −0.996549 0.956106i
\(616\) −1.77357e8 + 1.48821e8i −0.758765 + 0.636680i
\(617\) 2.29579e7 6.30763e7i 0.0977410 0.268541i −0.881180 0.472781i \(-0.843250\pi\)
0.978921 + 0.204240i \(0.0654723\pi\)
\(618\) −1.31360e8 + 6.45990e7i −0.556544 + 0.273691i
\(619\) −1.26311e7 + 7.16343e7i −0.0532559 + 0.302029i −0.999788 0.0205797i \(-0.993449\pi\)
0.946532 + 0.322609i \(0.104560\pi\)
\(620\) 5.90937e7i 0.247951i
\(621\) −2.11741e8 + 3.46337e8i −0.884158 + 1.44619i
\(622\) 4.25230e8 1.76707
\(623\) −6.63508e7 1.16994e7i −0.274399 0.0483839i
\(624\) −7.18820e7 + 1.07321e8i −0.295846 + 0.441705i
\(625\) −6.10189e7 2.22091e7i −0.249934 0.0909684i
\(626\) −3.01335e8 3.59117e8i −1.22836 1.46391i
\(627\) 1.20241e6 + 4.14236e6i 0.00487809 + 0.0168053i
\(628\) −1.36366e8 + 4.96330e7i −0.550587 + 0.200397i
\(629\) −2.74868e8 1.58695e8i −1.10452 0.637694i
\(630\) −4.78460e8 5.24476e8i −1.91348 2.09751i
\(631\) −476315. 825002.i −0.00189586 0.00328373i 0.865076 0.501641i \(-0.167270\pi\)
−0.866972 + 0.498357i \(0.833937\pi\)
\(632\) −1.80835e7 + 2.15511e7i −0.0716360 + 0.0853725i
\(633\) 2.87494e8 2.10310e8i 1.13349 0.829180i
\(634\) 7.46642e6 + 4.23441e7i 0.0292984 + 0.166160i
\(635\) 3.60761e8 6.36119e7i 1.40896 0.248438i
\(636\) 6.33759e7 1.43601e8i 0.246350 0.558195i
\(637\) 8.97891e7 + 7.53420e7i 0.347380 + 0.291487i
\(638\) −2.16297e7 + 1.24879e7i −0.0832891 + 0.0480870i
\(639\) 1.48772e7 6.12376e6i 0.0570189 0.0234701i
\(640\) −2.47116e8 + 4.28018e8i −0.942674 + 1.63276i
\(641\) 6.85669e7 + 1.88386e8i 0.260340 + 0.715278i 0.999144 + 0.0413579i \(0.0131684\pi\)
−0.738805 + 0.673920i \(0.764609\pi\)
\(642\) 8.69909e7 3.53804e8i 0.328752 1.33708i
\(643\) 1.49120e8 1.25126e8i 0.560921 0.470669i −0.317698 0.948192i \(-0.602910\pi\)
0.878619 + 0.477523i \(0.158465\pi\)
\(644\) −9.58773e7 + 2.63421e8i −0.358970 + 0.986262i
\(645\) −1.97942e7 + 2.96960e8i −0.0737666 + 1.10667i
\(646\) 1.20287e6 6.82180e6i 0.00446190 0.0253047i
\(647\) 3.61439e7i 0.133451i −0.997771 0.0667255i \(-0.978745\pi\)
0.997771 0.0667255i \(-0.0212552\pi\)
\(648\) 1.30346e8 + 1.31507e8i 0.479041 + 0.483307i
\(649\) −2.78736e8 −1.01967
\(650\) 2.39136e8 + 4.21661e7i 0.870772 + 0.153541i
\(651\) 1.37553e8 + 9.16880e6i 0.498573 + 0.0332330i
\(652\) 8.43763e7 + 3.07105e7i 0.304423 + 0.110801i
\(653\) −2.30639e8 2.74865e8i −0.828311 0.987142i −0.999998 0.00199079i \(-0.999366\pi\)
0.171687 0.985151i \(-0.445078\pi\)
\(654\) −1.59439e8 3.92017e7i −0.569981 0.140143i
\(655\) 4.96295e7 1.80636e7i 0.176610 0.0642808i
\(656\) 2.54406e8 + 1.46881e8i 0.901188 + 0.520301i
\(657\) 2.21205e6 2.86961e6i 0.00780007 0.0101187i
\(658\) 1.67432e8 + 2.90000e8i 0.587705 + 1.01794i
\(659\) −8.27062e7 + 9.85655e7i −0.288989 + 0.344404i −0.890933 0.454134i \(-0.849949\pi\)
0.601944 + 0.798538i \(0.294393\pi\)
\(660\) 1.89975e8 + 8.38422e7i 0.660791 + 0.291629i
\(661\) 3.71995e7 + 2.10969e8i 0.128805 + 0.730490i 0.978975 + 0.203981i \(0.0653881\pi\)
−0.850170 + 0.526509i \(0.823501\pi\)
\(662\) 4.34200e8 7.65611e7i 1.49663 0.263897i
\(663\) 9.13909e7 + 1.24932e8i 0.313590 + 0.428678i
\(664\) 1.95160e7 + 1.63758e7i 0.0666631 + 0.0559370i
\(665\) 1.04348e7 6.02455e6i 0.0354830 0.0204861i
\(666\) −7.76295e7 3.53873e8i −0.262787 1.19791i
\(667\) 1.99468e7 3.45488e7i 0.0672195 0.116428i
\(668\) 9.13873e6 + 2.51085e7i 0.0306589 + 0.0842346i
\(669\) −4.63744e8 + 1.34612e8i −1.54882 + 0.449578i
\(670\) 9.92545e7 8.32844e7i 0.330009 0.276910i
\(671\) 1.37377e8 3.77441e8i 0.454724 1.24934i
\(672\) 2.93006e8 + 1.96250e8i 0.965538 + 0.646700i
\(673\) −391195. + 2.21858e6i −0.00128336 + 0.00727828i −0.985443 0.170008i \(-0.945621\pi\)
0.984159 + 0.177286i \(0.0567318\pi\)
\(674\) 4.11355e8i 1.34350i
\(675\) 1.94625e8 4.95594e8i 0.632830 1.61144i
\(676\) 1.08922e8 0.352594
\(677\) −1.63935e8 2.89061e7i −0.528330 0.0931588i −0.0968807 0.995296i \(-0.530887\pi\)
−0.431449 + 0.902137i \(0.641998\pi\)
\(678\) −2.04534e8 4.15914e8i −0.656259 1.33449i
\(679\) 8.98630e7 + 3.27074e7i 0.287059 + 0.104481i
\(680\) 2.82784e8 + 3.37008e8i 0.899348 + 1.07180i
\(681\) 5.76511e7 6.00898e7i 0.182544 0.190265i
\(682\) −1.25771e8 + 4.57768e7i −0.396485 + 0.144309i
\(683\) 3.63059e8 + 2.09612e8i 1.13950 + 0.657892i 0.946307 0.323269i \(-0.104782\pi\)
0.193195 + 0.981160i \(0.438115\pi\)
\(684\) 2.01193e6 1.27548e6i 0.00628702 0.00398571i
\(685\) −1.00046e7 1.73285e7i −0.0311264 0.0539126i
\(686\) 2.21727e7 2.64243e7i 0.0686824 0.0818525i
\(687\) −4.06238e7 3.74770e8i −0.125288 1.15583i
\(688\) −4.72604e7 2.68027e8i −0.145122 0.823026i
\(689\) −1.94592e8 + 3.43118e7i −0.594932 + 0.104903i
\(690\) −1.09451e9 + 1.18642e8i −3.33176 + 0.361151i
\(691\) −2.27571e8 1.90955e8i −0.689736 0.578757i 0.229097 0.973404i \(-0.426423\pi\)
−0.918833 + 0.394646i \(0.870867\pi\)
\(692\) −2.00544e8 + 1.15784e8i −0.605190 + 0.349407i
\(693\) −2.24637e8 + 4.29199e8i −0.674965 + 1.28961i
\(694\) 8.93574e7 1.54772e8i 0.267333 0.463034i
\(695\) −2.50375e8 6.87899e8i −0.745823 2.04913i
\(696\) −1.31307e7 1.25978e7i −0.0389457 0.0373652i
\(697\) 2.69671e8 2.26280e8i 0.796407 0.668265i
\(698\) −2.47472e8 + 6.79923e8i −0.727712 + 1.99937i
\(699\) −2.84755e8 + 1.40033e8i −0.833756 + 0.410015i
\(700\) 6.38482e7 3.62101e8i 0.186146 1.05569i
\(701\) 2.55553e8i 0.741868i 0.928659 + 0.370934i \(0.120962\pi\)
−0.928659 + 0.370934i \(0.879038\pi\)
\(702\) −3.50458e7 + 1.73177e8i −0.101303 + 0.500585i
\(703\) 6.14886e6 0.0176982
\(704\) 9.65272e7 + 1.70203e7i 0.276651 + 0.0487810i
\(705\) −2.20487e8 + 3.29192e8i −0.629240 + 0.939469i
\(706\) 1.32617e8 + 4.82688e7i 0.376865 + 0.137168i
\(707\) −5.20659e8 6.20497e8i −1.47331 1.75583i
\(708\) 4.29131e7 + 1.47838e8i 0.120918 + 0.416568i
\(709\) −7.92755e7 + 2.88539e7i −0.222433 + 0.0809592i −0.450833 0.892608i \(-0.648873\pi\)
0.228400 + 0.973567i \(0.426651\pi\)
\(710\) 3.77868e7 + 2.18162e7i 0.105576 + 0.0609543i
\(711\) −1.78252e7 + 5.61004e7i −0.0495935 + 0.156084i
\(712\) 2.38285e7 + 4.12722e7i 0.0660171 + 0.114345i
\(713\) 1.37418e8 1.63769e8i 0.379119 0.451817i
\(714\) 6.27902e8 4.59328e8i 1.72503 1.26191i
\(715\) −4.53923e7 2.57433e8i −0.124184 0.704280i
\(716\) 1.65007e8 2.90951e7i 0.449534 0.0792649i
\(717\) 2.15863e8 4.89114e8i 0.585626 1.32695i
\(718\) −3.20842e8 2.69218e8i −0.866798 0.727330i
\(719\) −4.61555e8 + 2.66479e8i −1.24176 + 0.716928i −0.969452 0.245283i \(-0.921119\pi\)
−0.272305 + 0.962211i \(0.587786\pi\)
\(720\) −1.01950e8 + 7.61343e8i −0.273142 + 2.03978i
\(721\) 1.39516e8 2.41649e8i 0.372237 0.644733i
\(722\) −1.53950e8 4.22976e8i −0.409043 1.12384i
\(723\) 3.54410e7 1.44143e8i 0.0937758 0.381399i
\(724\) −2.00949e8 + 1.68616e8i −0.529504 + 0.444307i
\(725\) −1.78965e7 + 4.91703e7i −0.0469628 + 0.129029i
\(726\) 833823. 1.25093e7i 0.00217903 0.0326906i
\(727\) −3.87788e7 + 2.19925e8i −0.100923 + 0.572364i 0.891847 + 0.452336i \(0.149409\pi\)
−0.992771 + 0.120027i \(0.961702\pi\)
\(728\) 1.60963e8i 0.417189i
\(729\) 3.56936e8 + 1.50636e8i 0.921315 + 0.388817i
\(730\) 9.82644e6 0.0252597
\(731\) −3.21190e8 5.66345e7i −0.822262 0.144987i
\(732\) −2.21340e8 1.47537e7i −0.564321 0.0376155i
\(733\) −9.66757e7 3.51871e7i −0.245474 0.0893452i 0.216353 0.976315i \(-0.430584\pi\)
−0.461827 + 0.886970i \(0.652806\pi\)
\(734\) 2.89422e8 + 3.44920e8i 0.731886 + 0.872228i
\(735\) 6.76864e8 + 1.66423e8i 1.70467 + 0.419132i
\(736\) 5.13903e8 1.87045e8i 1.28898 0.469152i
\(737\) −7.65674e7 4.42062e7i −0.191268 0.110428i
\(738\) 3.98272e8 + 5.33317e7i 0.990858 + 0.132683i
\(739\) −1.61111e8 2.79053e8i −0.399201 0.691437i 0.594426 0.804150i \(-0.297379\pi\)
−0.993628 + 0.112713i \(0.964046\pi\)
\(740\) 1.90277e8 2.26764e8i 0.469561 0.559601i
\(741\) −2.74348e6 1.21079e6i −0.00674292 0.00297588i
\(742\) 1.72450e8 + 9.78014e8i 0.422136 + 2.39405i
\(743\) −4.50982e8 + 7.95203e7i −1.09949 + 0.193870i −0.693821 0.720148i \(-0.744074\pi\)
−0.405673 + 0.914018i \(0.632963\pi\)
\(744\) −5.75737e7 7.87034e7i −0.139799 0.191106i
\(745\) −7.24020e8 6.07525e8i −1.75098 1.46925i
\(746\) −6.53633e7 + 3.77375e7i −0.157441 + 0.0908985i
\(747\) 5.08027e7 + 1.61419e7i 0.121878 + 0.0387251i
\(748\) −1.13778e8 + 1.97070e8i −0.271866 + 0.470885i
\(749\) 2.37530e8 + 6.52609e8i 0.565293 + 1.55313i
\(750\) 5.85748e8 1.70026e8i 1.38844 0.403025i
\(751\) −4.81122e8 + 4.03709e8i −1.13589 + 0.953123i −0.999296 0.0375046i \(-0.988059\pi\)
−0.136591 + 0.990628i \(0.543615\pi\)
\(752\) 1.23921e8 3.40469e8i 0.291401 0.800617i
\(753\) 1.43733e8 + 9.62700e7i 0.336645 + 0.225479i
\(754\) 3.01524e6 1.71002e7i 0.00703408 0.0398922i
\(755\) 3.36144e8i 0.781061i
\(756\) 2.62225e8 + 5.30665e7i 0.606888 + 0.122816i
\(757\) 3.68074e7 0.0848493 0.0424246 0.999100i \(-0.486492\pi\)
0.0424246 + 0.999100i \(0.486492\pi\)
\(758\) 3.40916e8 + 6.01126e7i 0.782779 + 0.138025i
\(759\) 3.31515e8 + 6.74128e8i 0.758189 + 1.54176i
\(760\) −8.00890e6 2.91500e6i −0.0182445 0.00664046i
\(761\) 5.73398e7 + 6.83349e7i 0.130107 + 0.155056i 0.827165 0.561959i \(-0.189952\pi\)
−0.697057 + 0.717015i \(0.745508\pi\)
\(762\) −3.17235e8 + 3.30654e8i −0.716995 + 0.747324i
\(763\) 2.94092e8 1.07041e8i 0.662079 0.240977i
\(764\) −1.94805e8 1.12471e8i −0.436837 0.252208i
\(765\) 8.15548e8 + 4.26847e8i 1.82165 + 0.953428i
\(766\) −5.12868e7 8.88313e7i −0.114109 0.197642i
\(767\) 1.24564e8 1.48450e8i 0.276062 0.328998i
\(768\) −5.30932e7 4.89805e8i −0.117207 1.08128i
\(769\) 1.01552e8 + 5.75932e8i 0.223312 + 1.26646i 0.865887 + 0.500240i \(0.166755\pi\)
−0.642575 + 0.766223i \(0.722134\pi\)
\(770\) −1.29385e9 + 2.28140e8i −2.83407 + 0.499724i
\(771\) 3.41455e8 3.70126e7i 0.745025 0.0807582i
\(772\) −2.58275e7 2.16718e7i −0.0561345 0.0471025i
\(773\) −1.70479e8 + 9.84259e7i −0.369089 + 0.213094i −0.673060 0.739587i \(-0.735021\pi\)
0.303971 + 0.952681i \(0.401687\pi\)
\(774\) −1.99330e8 3.14421e8i −0.429883 0.678092i
\(775\) −1.40204e8 + 2.42841e8i −0.301201 + 0.521695i
\(776\) −2.31355e7 6.35643e7i −0.0495101 0.136028i
\(777\) 4.98319e8 + 4.78096e8i 1.06229 + 1.01918i
\(778\) 5.11310e8 4.29040e8i 1.08579 0.911086i
\(779\) −2.33255e6 + 6.40864e6i −0.00493423 + 0.0135567i
\(780\) −1.29550e8 + 6.37088e7i −0.272995 + 0.134250i
\(781\) 5.17007e6 2.93209e7i 0.0108528 0.0615495i
\(782\) 1.20645e9i 2.52283i
\(783\) −3.54392e7 1.39173e7i −0.0738242 0.0289915i
\(784\) −6.37404e8 −1.32271
\(785\) 1.06985e9 + 1.88643e8i 2.21163 + 0.389970i
\(786\) −3.67640e7 + 5.48894e7i −0.0757102 + 0.113037i
\(787\) 8.34997e8 + 3.03914e8i 1.71301 + 0.623486i 0.997198 0.0748033i \(-0.0238329\pi\)
0.715816 + 0.698289i \(0.246055\pi\)
\(788\) 9.79855e7 + 1.16775e8i 0.200255 + 0.238655i
\(789\) −1.26295e8 4.35092e8i −0.257131 0.885829i
\(790\) −1.50016e8 + 5.46014e7i −0.304268 + 0.110744i
\(791\) 7.65111e8 + 4.41737e8i 1.54595 + 0.892554i
\(792\) 3.34702e8 7.34238e7i 0.673724 0.147796i
\(793\) 1.39626e8 + 2.41839e8i 0.279992 + 0.484961i
\(794\) 7.06348e6 8.41793e6i 0.0141110 0.0168168i
\(795\) −9.48371e8 + 6.93760e8i −1.88746 + 1.38073i
\(796\) −6.46049e7 3.66392e8i −0.128093 0.726452i
\(797\) −3.14104e8 + 5.53851e7i −0.620439 + 0.109400i −0.475027 0.879971i \(-0.657562\pi\)
−0.145412 + 0.989371i \(0.546451\pi\)
\(798\) −6.08540e6 + 1.37887e7i −0.0119751 + 0.0271340i
\(799\) −3.32606e8 2.79089e8i −0.652063 0.547146i
\(800\) −6.21212e8 + 3.58657e8i −1.21330 + 0.700502i
\(801\) 7.89749e7 + 6.08781e7i 0.153671 + 0.118458i
\(802\) 2.51359e8 4.35366e8i 0.487271 0.843978i
\(803\) −2.29332e6 6.30085e6i −0.00442913 0.0121689i
\(804\) −1.16583e7 + 4.74161e7i −0.0224320 + 0.0912342i
\(805\) 1.60757e9 1.34891e9i 3.08164 2.58580i
\(806\) 3.18256e7 8.74402e7i 0.0607815 0.166996i
\(807\) 3.81989e7 5.73073e8i 0.0726825 1.09041i
\(808\) −9.94920e7 + 5.64247e8i −0.188605 + 1.06963i
\(809\) 5.93505e8i 1.12093i 0.828178 + 0.560465i \(0.189378\pi\)
−0.828178 + 0.560465i \(0.810622\pi\)
\(810\) 2.67443e8 + 1.01610e9i 0.503242 + 1.91198i
\(811\) 4.10582e8 0.769728 0.384864 0.922973i \(-0.374248\pi\)
0.384864 + 0.922973i \(0.374248\pi\)
\(812\) −2.58933e7 4.56569e6i −0.0483637 0.00852782i
\(813\) −1.04011e9 6.93298e7i −1.93556 0.129017i
\(814\) −6.30024e8 2.29310e8i −1.16811 0.425158i
\(815\) −4.32069e8 5.14920e8i −0.798143 0.951189i
\(816\) −8.17418e8 2.00981e8i −1.50444 0.369900i
\(817\) 5.93741e6 2.16104e6i 0.0108876 0.00396275i
\(818\) 6.49782e8 + 3.75152e8i 1.18716 + 0.685405i
\(819\) −1.28195e8 3.11441e8i −0.233357 0.566923i
\(820\) 1.64163e8 + 2.84338e8i 0.297737 + 0.515696i
\(821\) −2.17404e8 + 2.59092e8i −0.392860 + 0.468192i −0.925829 0.377942i \(-0.876632\pi\)
0.532969 + 0.846135i \(0.321076\pi\)
\(822\) 2.28981e7 + 1.01057e7i 0.0412271 + 0.0181949i
\(823\) −9.58192e7 5.43418e8i −0.171891 0.974842i −0.941672 0.336533i \(-0.890746\pi\)
0.769781 0.638309i \(-0.220366\pi\)
\(824\) −1.94374e8 + 3.42734e7i −0.347422 + 0.0612598i
\(825\) −5.81763e8 7.95271e8i −1.03606 1.41629i
\(826\) −7.46103e8 6.26055e8i −1.32391 1.11089i
\(827\) −4.57220e8 + 2.63976e8i −0.808367 + 0.466711i −0.846389 0.532566i \(-0.821228\pi\)
0.0380214 + 0.999277i \(0.487894\pi\)
\(828\) 3.06509e8 2.79617e8i 0.539949 0.492575i
\(829\) −4.33550e8 + 7.50931e8i −0.760984 + 1.31806i 0.181359 + 0.983417i \(0.441950\pi\)
−0.942344 + 0.334647i \(0.891383\pi\)
\(830\) 4.94452e7 + 1.35850e8i 0.0864748 + 0.237588i
\(831\) −1.40893e8 + 4.08973e7i −0.245520 + 0.0712675i
\(832\) −5.22016e7 + 4.38023e7i −0.0906387 + 0.0760549i
\(833\) −2.61246e8 + 7.17767e8i −0.451975 + 1.24179i
\(834\) 7.60805e8 + 5.09574e8i 1.31152 + 0.878434i
\(835\) 3.47341e7 1.96987e8i 0.0596618 0.338359i
\(836\) 4.40849e6i 0.00754520i
\(837\) −1.74078e8 1.06427e8i −0.296871 0.181499i
\(838\) −1.01043e9 −1.71701
\(839\) −6.23986e7 1.10026e7i −0.105655 0.0186298i 0.120571 0.992705i \(-0.461528\pi\)
−0.226226 + 0.974075i \(0.572639\pi\)
\(840\) −4.22409e8 8.58960e8i −0.712682 1.44922i
\(841\) −5.55435e8 2.02162e8i −0.933781 0.339869i
\(842\) 2.52689e7 + 3.01143e7i 0.0423302 + 0.0504472i
\(843\) −2.64566e8 + 2.75757e8i −0.441622 + 0.460302i
\(844\) −3.42108e8 + 1.24517e8i −0.569031 + 0.207111i
\(845\) −7.06149e8 4.07695e8i −1.17038 0.675718i
\(846\) −2.05208e7 4.95180e8i −0.0338908 0.817809i
\(847\) 1.19488e7 + 2.06959e7i 0.0196641 + 0.0340592i
\(848\) 6.90694e8 8.23138e8i 1.13266 1.34985i
\(849\) −8.45868e7 7.80345e8i −0.138223 1.27516i
\(850\) 2.74784e8 + 1.55838e9i 0.447440 + 2.53756i
\(851\) 1.05465e9 1.85962e8i 1.71127 0.301742i
\(852\) −1.63474e7 + 1.77200e6i −0.0264320 + 0.00286514i
\(853\) 5.24127e8 + 4.39795e8i 0.844480 + 0.708603i 0.958567 0.284868i \(-0.0919498\pi\)
−0.114087 + 0.993471i \(0.536394\pi\)
\(854\) 1.21547e9 7.01754e8i 1.95152 1.12671i
\(855\) −1.78177e7 + 738382.i −0.0285071 + 0.00118136i
\(856\) 2.45623e8 4.25432e8i 0.391605 0.678279i
\(857\) −1.10120e8 3.02552e8i −0.174954 0.480681i 0.820961 0.570985i \(-0.193438\pi\)
−0.995914 + 0.0903037i \(0.971216\pi\)
\(858\) 2.35949e8 + 2.26373e8i 0.373556 + 0.358396i
\(859\) 1.71618e8 1.44005e8i 0.270760 0.227195i −0.497290 0.867584i \(-0.665672\pi\)
0.768050 + 0.640390i \(0.221227\pi\)
\(860\) 1.04037e8 2.85839e8i 0.163566 0.449393i
\(861\) −6.87330e8 + 3.38008e8i −1.07685 + 0.529562i
\(862\) 8.90714e7 5.05149e8i 0.139064 0.788674i
\(863\) 1.89355e8i 0.294608i 0.989091 + 0.147304i \(0.0470596\pi\)
−0.989091 + 0.147304i \(0.952940\pi\)
\(864\) −2.49525e8 4.58431e8i −0.386877 0.710776i
\(865\) 1.73353e9 2.67844
\(866\) 2.83877e8 + 5.00551e7i 0.437095 + 0.0770717i
\(867\) −1.98674e8 + 2.96625e8i −0.304848 + 0.455145i
\(868\) −1.32402e8 4.81905e7i −0.202459 0.0736890i
\(869\) 7.00223e7 + 8.34493e7i 0.106703 + 0.127164i
\(870\) −2.87851e7 9.91659e7i −0.0437129 0.150593i
\(871\) 5.77605e7 2.10231e7i 0.0874130 0.0318157i
\(872\) −1.91717e8 1.10688e8i −0.289142 0.166936i
\(873\) −9.53881e7 1.04562e8i −0.143368 0.157156i
\(874\) 1.16863e7 + 2.02413e7i 0.0175043 + 0.0303183i
\(875\) −7.47313e8 + 8.90613e8i −1.11552 + 1.32943i
\(876\) −2.98881e6 + 2.18640e6i −0.00444617 + 0.00325250i
\(877\) 2.24289e8 + 1.27201e9i 0.332514 + 1.88578i 0.450518 + 0.892767i \(0.351239\pi\)
−0.118004 + 0.993013i \(0.537650\pi\)
\(878\) −8.87545e8 + 1.56498e8i −1.31131 + 0.231220i
\(879\) −6.40535e7 + 1.45136e8i −0.0943141 + 0.213702i
\(880\) 1.08896e9 + 9.13744e8i 1.59795 + 1.34084i
\(881\) −4.35981e8 + 2.51714e8i −0.637587 + 0.368111i −0.783684 0.621159i \(-0.786662\pi\)
0.146097 + 0.989270i \(0.453329\pi\)
\(882\) −8.06252e8 + 3.31869e8i −1.17507 + 0.483683i
\(883\) −3.76563e8 + 6.52227e8i −0.546961 + 0.947363i 0.451520 + 0.892261i \(0.350882\pi\)
−0.998481 + 0.0551025i \(0.982451\pi\)
\(884\) −5.41094e7 1.48664e8i −0.0783278 0.215204i
\(885\) 2.75149e8 1.11907e9i 0.396952 1.61446i
\(886\) −1.20836e9 + 1.01393e9i −1.73738 + 1.45783i
\(887\) 1.11979e8 3.07661e8i 0.160460 0.440860i −0.833243 0.552907i \(-0.813518\pi\)
0.993703 + 0.112047i \(0.0357406\pi\)
\(888\) 3.24880e7 4.87396e8i 0.0463964 0.696054i
\(889\) 1.51673e8 8.60178e8i 0.215875 1.22429i
\(890\) 2.70435e8i 0.383613i
\(891\) 5.89123e8 4.08629e8i 0.832862 0.577692i
\(892\) 4.93538e8 0.695386
\(893\) 8.28376e6 + 1.46065e6i 0.0116325 + 0.00205112i
\(894\) 1.17963e9 + 7.86295e7i 1.65094 + 0.110046i
\(895\) −1.17866e9 4.28995e8i −1.64406 0.598389i
\(896\) 7.57473e8 + 9.02721e8i 1.05304 + 1.25496i
\(897\) −5.07178e8 1.24701e8i −0.702721 0.172780i
\(898\) −3.65678e8 + 1.33096e8i −0.504975 + 0.183796i
\(899\) 1.73652e7 + 1.00258e7i 0.0239001 + 0.0137987i
\(900\) −3.32235e8 + 4.30996e8i −0.455740 + 0.591215i
\(901\) −6.43831e8 1.11515e9i −0.880233 1.52461i
\(902\) 4.77996e8 5.69654e8i 0.651336 0.776232i
\(903\) 6.49211e8 + 2.86518e8i 0.881703 + 0.389125i
\(904\) −1.08517e8 6.15429e8i −0.146890 0.833053i
\(905\) 1.93390e9 3.40998e8i 2.60908 0.460052i
\(906\) 2.48253e8 + 3.39362e8i 0.333818 + 0.456329i
\(907\) 5.63036e8 + 4.72443e8i 0.754595 + 0.633181i 0.936714 0.350096i \(-0.113851\pi\)
−0.182118 + 0.983277i \(0.558295\pi\)
\(908\) −7.37075e7 + 4.25551e7i −0.0984588 + 0.0568452i
\(909\) 2.56878e8 + 1.17098e9i 0.342007 + 1.55904i
\(910\) 4.56703e8 7.91032e8i 0.606051 1.04971i
\(911\) 1.76524e8 + 4.84995e8i 0.233479 + 0.641479i 1.00000 0.000741119i \(-0.000235906\pi\)
−0.766521 + 0.642220i \(0.778014\pi\)
\(912\) 1.56612e7 4.54599e6i 0.0206462 0.00599300i
\(913\) 7.55690e7 6.34099e7i 0.0992959 0.0833191i
\(914\) 1.96777e8 5.40642e8i 0.257713 0.708061i
\(915\) 1.37974e9 + 9.24127e8i 1.80109 + 1.20634i
\(916\) −6.69033e7 + 3.79428e8i −0.0870485 + 0.493676i
\(917\) 1.25928e8i 0.163311i
\(918\) −1.13859e9 + 1.71374e8i −1.47177 + 0.221522i
\(919\) −2.27188e8 −0.292711 −0.146355 0.989232i \(-0.546754\pi\)
−0.146355 + 0.989232i \(0.546754\pi\)
\(920\) −1.46184e9 2.57761e8i −1.87731 0.331020i
\(921\) 2.95582e8 + 6.01059e8i 0.378355 + 0.769375i
\(922\) 7.44406e8 + 2.70942e8i 0.949768 + 0.345687i
\(923\) 1.33053e7 + 1.58567e7i 0.0169208 + 0.0201654i
\(924\) 3.42776e8 3.57275e8i 0.434504 0.452883i
\(925\) −1.31994e9 + 4.80419e8i −1.66774 + 0.607009i
\(926\) 5.10047e8 + 2.94476e8i 0.642358 + 0.370866i
\(927\) −3.48790e8 + 2.21119e8i −0.437850 + 0.277579i
\(928\) 2.56470e7 + 4.44219e7i 0.0320917 + 0.0555845i
\(929\) −4.55586e7 + 5.42946e7i −0.0568229 + 0.0677189i −0.793707 0.608300i \(-0.791852\pi\)
0.736884 + 0.676019i \(0.236296\pi\)
\(930\) −5.96324e7 5.50131e8i −0.0741368 0.683939i
\(931\) −2.56962e6 1.45730e7i −0.00318434 0.0180593i
\(932\) 3.19396e8 5.63182e7i 0.394532 0.0695667i
\(933\) 1.19265e9 1.29280e8i 1.46848 0.159179i
\(934\) 8.26114e8 + 6.93192e8i 1.01391 + 0.850771i
\(935\) 1.47527e9 8.51747e8i 1.80483 1.04202i
\(936\) −1.10470e8 + 2.11068e8i −0.134715 + 0.257392i
\(937\) −3.78328e8 + 6.55284e8i −0.459886 + 0.796545i −0.998954 0.0457164i \(-0.985443\pi\)
0.539069 + 0.842262i \(0.318776\pi\)
\(938\) −1.05661e8 2.90302e8i −0.128029 0.351756i
\(939\) −9.54341e8 9.15611e8i −1.15267 1.10590i
\(940\) 3.10210e8 2.60297e8i 0.373484 0.313390i
\(941\) 3.68526e8 1.01252e9i 0.442282 1.21516i −0.495706 0.868490i \(-0.665091\pi\)
0.937988 0.346668i \(-0.112687\pi\)
\(942\) −1.21941e9 + 5.99666e8i −1.45880 + 0.717392i
\(943\) −2.06258e8 + 1.16975e9i −0.245966 + 1.39494i
\(944\) 1.05383e9i 1.25272i
\(945\) −1.50140e9 1.32555e9i −1.77910 1.57072i
\(946\) −6.88951e8 −0.813794
\(947\) −2.23337e8 3.93803e7i −0.262973 0.0463692i 0.0406071 0.999175i \(-0.487071\pi\)
−0.303580 + 0.952806i \(0.598182\pi\)
\(948\) 3.34800e7 4.99864e7i 0.0392971 0.0586714i
\(949\) 4.38057e6 + 1.59440e6i 0.00512545 + 0.00186551i
\(950\) −1.97056e7 2.34842e7i −0.0229836 0.0273908i
\(951\) 3.38148e7 + 1.16494e8i 0.0393156 + 0.135444i
\(952\) 9.85692e8 3.58762e8i 1.14243 0.415811i
\(953\) −1.31937e9 7.61739e8i −1.52436 0.880091i −0.999584 0.0288519i \(-0.990815\pi\)
−0.524778 0.851239i \(-0.675852\pi\)
\(954\) 4.45086e8 1.40080e9i 0.512624 1.61336i
\(955\) 8.41958e8 + 1.45831e9i 0.966674 + 1.67433i
\(956\) −3.51234e8 + 4.18585e8i −0.401997 + 0.479082i
\(957\) −5.68686e7 + 4.16010e7i −0.0648839 + 0.0474644i
\(958\) −2.27755e8 1.29166e9i −0.259043 1.46910i
\(959\) −4.69841e7 + 8.28457e6i −0.0532716 + 0.00939321i
\(960\) −1.63618e8 + 3.70736e8i −0.184934 + 0.419035i
\(961\) −5.97553e8 5.01406e8i −0.673296 0.564962i
\(962\) 4.03677e8 2.33063e8i 0.453428 0.261787i
\(963\) 1.36421e8 1.01877e9i 0.152757 1.14077i
\(964\) −7.58553e7 + 1.31385e8i −0.0846750 + 0.146661i
\(965\) 8.63239e7 + 2.37173e8i 0.0960614 + 0.263927i
\(966\) −6.26745e8 + 2.54906e9i −0.695280 + 2.82780i
\(967\) −2.53850e8 + 2.13005e8i −0.280735 + 0.235565i −0.772272 0.635292i \(-0.780880\pi\)
0.491537 + 0.870857i \(0.336435\pi\)
\(968\) 5.78146e6 1.58844e7i 0.00637399 0.0175124i
\(969\) 1.29973e6 1.94989e7i 0.00142850 0.0214309i
\(970\) 6.66552e7 3.78020e8i 0.0730329 0.414190i
\(971\) 6.86482e8i 0.749845i 0.927056 + 0.374922i \(0.122331\pi\)
−0.927056 + 0.374922i \(0.877669\pi\)
\(972\) −3.07430e8 2.49552e8i −0.334771 0.271745i
\(973\) −1.74545e9 −1.89482
\(974\) −9.26679e8 1.63399e8i −1.00289 0.176836i
\(975\) 6.83529e8 + 4.55615e7i 0.737468 + 0.0491569i
\(976\) −1.42701e9 5.19388e8i −1.53489 0.558653i
\(977\) −1.02868e9 1.22593e9i −1.10305 1.31456i −0.944978 0.327135i \(-0.893917\pi\)
−0.158071 0.987428i \(-0.550528\pi\)
\(978\) 8.16489e8 + 2.00753e8i 0.872838 + 0.214607i
\(979\) 1.73407e8 6.31149e7i 0.184807 0.0672642i
\(980\) −6.16956e8 3.56199e8i −0.655504 0.378456i
\(981\) −4.59099e8 6.14769e7i −0.486295 0.0651185i
\(982\) −2.99106e7 5.18066e7i −0.0315857 0.0547080i
\(983\) 8.76617e8 1.04471e9i 0.922889 1.09986i −0.0718506 0.997415i \(-0.522890\pi\)
0.994739 0.102440i \(-0.0326651\pi\)
\(984\) 4.95663e8 + 2.18753e8i 0.520237 + 0.229598i
\(985\) −1.98160e8 1.12382e9i −0.207351 1.17595i
\(986\) 1.11437e8 1.96494e7i 0.116252 0.0204983i
\(987\) 5.57766e8 + 7.62467e8i 0.580097 + 0.792993i
\(988\) 2.34788e6 + 1.97010e6i 0.00243447 + 0.00204276i
\(989\) 9.53020e8 5.50226e8i 0.985175 0.568791i
\(990\) 1.85317e9 + 5.88820e8i 1.90990 + 0.606844i
\(991\) 2.88959e8 5.00491e8i 0.296903 0.514252i −0.678523 0.734580i \(-0.737379\pi\)
0.975426 + 0.220328i \(0.0707128\pi\)
\(992\) 9.40140e7 + 2.58301e8i 0.0963069 + 0.264601i
\(993\) 1.19453e9 3.46739e8i 1.21997 0.354124i
\(994\) 7.96951e7 6.68721e7i 0.0811470 0.0680904i
\(995\) −9.52572e8 + 2.61717e9i −0.967004 + 2.65682i
\(996\) −4.52660e7 3.03184e7i −0.0458136 0.0306851i
\(997\) −1.37662e8 + 7.80719e8i −0.138908 + 0.787788i 0.833150 + 0.553047i \(0.186535\pi\)
−0.972058 + 0.234741i \(0.924576\pi\)
\(998\) 3.52717e8i 0.354841i
\(999\) −3.25315e8 9.68915e8i −0.326293 0.971828i
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 27.7.f.a.2.5 102
3.2 odd 2 81.7.f.a.8.13 102
27.13 even 9 81.7.f.a.71.13 102
27.14 odd 18 inner 27.7.f.a.14.5 yes 102
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.7.f.a.2.5 102 1.1 even 1 trivial
27.7.f.a.14.5 yes 102 27.14 odd 18 inner
81.7.f.a.8.13 102 3.2 odd 2
81.7.f.a.71.13 102 27.13 even 9