Properties

Label 75.9.f.b.43.1
Level $75$
Weight $9$
Character 75.43
Analytic conductor $30.553$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [75,9,Mod(7,75)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(75, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.7");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 75.f (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(30.5533957546\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.1485512441856.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 119x^{4} + 625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.1
Root \(-2.30795 + 2.30795i\) of defining polynomial
Character \(\chi\) \(=\) 75.43
Dual form 75.9.f.b.7.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-10.7561 + 10.7561i) q^{2} +(-33.0681 - 33.0681i) q^{3} +24.6120i q^{4} +711.369 q^{6} +(986.622 - 986.622i) q^{7} +(-3018.29 - 3018.29i) q^{8} +2187.00i q^{9} +O(q^{10})\) \(q+(-10.7561 + 10.7561i) q^{2} +(-33.0681 - 33.0681i) q^{3} +24.6120i q^{4} +711.369 q^{6} +(986.622 - 986.622i) q^{7} +(-3018.29 - 3018.29i) q^{8} +2187.00i q^{9} -7119.87 q^{11} +(813.874 - 813.874i) q^{12} +(21548.2 + 21548.2i) q^{13} +21224.4i q^{14} +58629.6 q^{16} +(73737.3 - 73737.3i) q^{17} +(-23523.6 - 23523.6i) q^{18} +118517. i q^{19} -65251.5 q^{21} +(76582.1 - 76582.1i) q^{22} +(115753. + 115753. i) q^{23} +199619. i q^{24} -463549. q^{26} +(72320.0 - 72320.0i) q^{27} +(24282.8 + 24282.8i) q^{28} +471964. i q^{29} -1.10387e6 q^{31} +(142057. - 142057. i) q^{32} +(235441. + 235441. i) q^{33} +1.58625e6i q^{34} -53826.5 q^{36} +(-437375. + 437375. i) q^{37} +(-1.27479e6 - 1.27479e6i) q^{38} -1.42511e6i q^{39} -2.59091e6 q^{41} +(701852. - 701852. i) q^{42} +(-4.52928e6 - 4.52928e6i) q^{43} -175235. i q^{44} -2.49011e6 q^{46} +(-1.05817e6 + 1.05817e6i) q^{47} +(-1.93877e6 - 1.93877e6i) q^{48} +3.81795e6i q^{49} -4.87671e6 q^{51} +(-530344. + 530344. i) q^{52} +(-1.00150e7 - 1.00150e7i) q^{53} +1.55576e6i q^{54} -5.95583e6 q^{56} +(3.91915e6 - 3.91915e6i) q^{57} +(-5.07649e6 - 5.07649e6i) q^{58} -6.33938e6i q^{59} +8.28532e6 q^{61} +(1.18733e7 - 1.18733e7i) q^{62} +(2.15774e6 + 2.15774e6i) q^{63} +1.80651e7i q^{64} -5.06485e6 q^{66} +(-2.32318e7 + 2.32318e7i) q^{67} +(1.81483e6 + 1.81483e6i) q^{68} -7.65549e6i q^{69} -3.22536e7 q^{71} +(6.60101e6 - 6.60101e6i) q^{72} +(1.49231e7 + 1.49231e7i) q^{73} -9.40892e6i q^{74} -2.91696e6 q^{76} +(-7.02462e6 + 7.02462e6i) q^{77} +(1.53287e7 + 1.53287e7i) q^{78} +7.17598e7i q^{79} -4.78297e6 q^{81} +(2.78681e7 - 2.78681e7i) q^{82} +(2.46934e7 + 2.46934e7i) q^{83} -1.60597e6i q^{84} +9.74350e7 q^{86} +(1.56069e7 - 1.56069e7i) q^{87} +(2.14899e7 + 2.14899e7i) q^{88} -8.60547e7i q^{89} +4.25198e7 q^{91} +(-2.84892e6 + 2.84892e6i) q^{92} +(3.65028e7 + 3.65028e7i) q^{93} -2.27636e7i q^{94} -9.39513e6 q^{96} +(-7.27492e7 + 7.27492e7i) q^{97} +(-4.10664e7 - 4.10664e7i) q^{98} -1.55712e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 1296 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 1296 q^{6} + 52752 q^{11} + 164320 q^{16} + 31752 q^{21} - 3637584 q^{26} - 6842152 q^{31} - 1854576 q^{36} - 29029152 q^{41} - 18397632 q^{46} - 10226736 q^{51} - 46814880 q^{56} - 73982120 q^{61} - 51725952 q^{66} + 33100896 q^{71} + 13636624 q^{76} - 38263752 q^{81} + 271592592 q^{86} + 507032568 q^{91} + 165488832 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

\(n\) \(26\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.7561 + 10.7561i −0.672257 + 0.672257i −0.958236 0.285979i \(-0.907681\pi\)
0.285979 + 0.958236i \(0.407681\pi\)
\(3\) −33.0681 33.0681i −0.408248 0.408248i
\(4\) 24.6120i 0.0961408i
\(5\) 0 0
\(6\) 711.369 0.548896
\(7\) 986.622 986.622i 0.410921 0.410921i −0.471138 0.882059i \(-0.656157\pi\)
0.882059 + 0.471138i \(0.156157\pi\)
\(8\) −3018.29 3018.29i −0.736888 0.736888i
\(9\) 2187.00i 0.333333i
\(10\) 0 0
\(11\) −7119.87 −0.486297 −0.243148 0.969989i \(-0.578180\pi\)
−0.243148 + 0.969989i \(0.578180\pi\)
\(12\) 813.874 813.874i 0.0392493 0.0392493i
\(13\) 21548.2 + 21548.2i 0.754461 + 0.754461i 0.975308 0.220847i \(-0.0708823\pi\)
−0.220847 + 0.975308i \(0.570882\pi\)
\(14\) 21224.4i 0.552490i
\(15\) 0 0
\(16\) 58629.6 0.894616
\(17\) 73737.3 73737.3i 0.882860 0.882860i −0.110965 0.993824i \(-0.535394\pi\)
0.993824 + 0.110965i \(0.0353941\pi\)
\(18\) −23523.6 23523.6i −0.224086 0.224086i
\(19\) 118517.i 0.909427i 0.890638 + 0.454714i \(0.150258\pi\)
−0.890638 + 0.454714i \(0.849742\pi\)
\(20\) 0 0
\(21\) −65251.5 −0.335516
\(22\) 76582.1 76582.1i 0.326916 0.326916i
\(23\) 115753. + 115753.i 0.413640 + 0.413640i 0.883004 0.469365i \(-0.155517\pi\)
−0.469365 + 0.883004i \(0.655517\pi\)
\(24\) 199619.i 0.601667i
\(25\) 0 0
\(26\) −463549. −1.01438
\(27\) 72320.0 72320.0i 0.136083 0.136083i
\(28\) 24282.8 + 24282.8i 0.0395063 + 0.0395063i
\(29\) 471964.i 0.667293i 0.942698 + 0.333646i \(0.108279\pi\)
−0.942698 + 0.333646i \(0.891721\pi\)
\(30\) 0 0
\(31\) −1.10387e6 −1.19528 −0.597641 0.801764i \(-0.703895\pi\)
−0.597641 + 0.801764i \(0.703895\pi\)
\(32\) 142057. 142057.i 0.135476 0.135476i
\(33\) 235441. + 235441.i 0.198530 + 0.198530i
\(34\) 1.58625e6i 1.18702i
\(35\) 0 0
\(36\) −53826.5 −0.0320469
\(37\) −437375. + 437375.i −0.233371 + 0.233371i −0.814098 0.580727i \(-0.802768\pi\)
0.580727 + 0.814098i \(0.302768\pi\)
\(38\) −1.27479e6 1.27479e6i −0.611369 0.611369i
\(39\) 1.42511e6i 0.616015i
\(40\) 0 0
\(41\) −2.59091e6 −0.916888 −0.458444 0.888723i \(-0.651593\pi\)
−0.458444 + 0.888723i \(0.651593\pi\)
\(42\) 701852. 701852.i 0.225553 0.225553i
\(43\) −4.52928e6 4.52928e6i −1.32482 1.32482i −0.909826 0.414990i \(-0.863785\pi\)
−0.414990 0.909826i \(-0.636215\pi\)
\(44\) 175235.i 0.0467530i
\(45\) 0 0
\(46\) −2.49011e6 −0.556144
\(47\) −1.05817e6 + 1.05817e6i −0.216852 + 0.216852i −0.807170 0.590318i \(-0.799002\pi\)
0.590318 + 0.807170i \(0.299002\pi\)
\(48\) −1.93877e6 1.93877e6i −0.365226 0.365226i
\(49\) 3.81795e6i 0.662287i
\(50\) 0 0
\(51\) −4.87671e6 −0.720852
\(52\) −530344. + 530344.i −0.0725345 + 0.0725345i
\(53\) −1.00150e7 1.00150e7i −1.26925 1.26925i −0.946478 0.322767i \(-0.895387\pi\)
−0.322767 0.946478i \(-0.604613\pi\)
\(54\) 1.55576e6i 0.182965i
\(55\) 0 0
\(56\) −5.95583e6 −0.605606
\(57\) 3.91915e6 3.91915e6i 0.371272 0.371272i
\(58\) −5.07649e6 5.07649e6i −0.448592 0.448592i
\(59\) 6.33938e6i 0.523165i −0.965181 0.261583i \(-0.915756\pi\)
0.965181 0.261583i \(-0.0842444\pi\)
\(60\) 0 0
\(61\) 8.28532e6 0.598398 0.299199 0.954191i \(-0.403281\pi\)
0.299199 + 0.954191i \(0.403281\pi\)
\(62\) 1.18733e7 1.18733e7i 0.803537 0.803537i
\(63\) 2.15774e6 + 2.15774e6i 0.136974 + 0.136974i
\(64\) 1.80651e7i 1.07677i
\(65\) 0 0
\(66\) −5.06485e6 −0.266926
\(67\) −2.32318e7 + 2.32318e7i −1.15288 + 1.15288i −0.166904 + 0.985973i \(0.553377\pi\)
−0.985973 + 0.166904i \(0.946623\pi\)
\(68\) 1.81483e6 + 1.81483e6i 0.0848788 + 0.0848788i
\(69\) 7.65549e6i 0.337735i
\(70\) 0 0
\(71\) −3.22536e7 −1.26924 −0.634621 0.772823i \(-0.718844\pi\)
−0.634621 + 0.772823i \(0.718844\pi\)
\(72\) 6.60101e6 6.60101e6i 0.245629 0.245629i
\(73\) 1.49231e7 + 1.49231e7i 0.525493 + 0.525493i 0.919225 0.393732i \(-0.128816\pi\)
−0.393732 + 0.919225i \(0.628816\pi\)
\(74\) 9.40892e6i 0.313771i
\(75\) 0 0
\(76\) −2.91696e6 −0.0874330
\(77\) −7.02462e6 + 7.02462e6i −0.199830 + 0.199830i
\(78\) 1.53287e7 + 1.53287e7i 0.414120 + 0.414120i
\(79\) 7.17598e7i 1.84235i 0.389146 + 0.921176i \(0.372770\pi\)
−0.389146 + 0.921176i \(0.627230\pi\)
\(80\) 0 0
\(81\) −4.78297e6 −0.111111
\(82\) 2.78681e7 2.78681e7i 0.616385 0.616385i
\(83\) 2.46934e7 + 2.46934e7i 0.520318 + 0.520318i 0.917667 0.397349i \(-0.130070\pi\)
−0.397349 + 0.917667i \(0.630070\pi\)
\(84\) 1.60597e6i 0.0322568i
\(85\) 0 0
\(86\) 9.74350e7 1.78123
\(87\) 1.56069e7 1.56069e7i 0.272421 0.272421i
\(88\) 2.14899e7 + 2.14899e7i 0.358346 + 0.358346i
\(89\) 8.60547e7i 1.37156i −0.727810 0.685779i \(-0.759462\pi\)
0.727810 0.685779i \(-0.240538\pi\)
\(90\) 0 0
\(91\) 4.25198e7 0.620048
\(92\) −2.84892e6 + 2.84892e6i −0.0397676 + 0.0397676i
\(93\) 3.65028e7 + 3.65028e7i 0.487972 + 0.487972i
\(94\) 2.27636e7i 0.291561i
\(95\) 0 0
\(96\) −9.39513e6 −0.110616
\(97\) −7.27492e7 + 7.27492e7i −0.821753 + 0.821753i −0.986359 0.164607i \(-0.947364\pi\)
0.164607 + 0.986359i \(0.447364\pi\)
\(98\) −4.10664e7 4.10664e7i −0.445227 0.445227i
\(99\) 1.55712e7i 0.162099i
\(100\) 0 0
\(101\) 4.96287e7 0.476922 0.238461 0.971152i \(-0.423357\pi\)
0.238461 + 0.971152i \(0.423357\pi\)
\(102\) 5.24544e7 5.24544e7i 0.484598 0.484598i
\(103\) 6.23246e7 + 6.23246e7i 0.553746 + 0.553746i 0.927520 0.373774i \(-0.121936\pi\)
−0.373774 + 0.927520i \(0.621936\pi\)
\(104\) 1.30077e8i 1.11191i
\(105\) 0 0
\(106\) 2.15444e8 1.70652
\(107\) −9.91772e7 + 9.91772e7i −0.756618 + 0.756618i −0.975705 0.219087i \(-0.929692\pi\)
0.219087 + 0.975705i \(0.429692\pi\)
\(108\) 1.77994e6 + 1.77994e6i 0.0130831 + 0.0130831i
\(109\) 9.28159e7i 0.657531i −0.944412 0.328766i \(-0.893367\pi\)
0.944412 0.328766i \(-0.106633\pi\)
\(110\) 0 0
\(111\) 2.89263e7 0.190547
\(112\) 5.78452e7 5.78452e7i 0.367617 0.367617i
\(113\) −1.25548e8 1.25548e8i −0.770009 0.770009i 0.208099 0.978108i \(-0.433272\pi\)
−0.978108 + 0.208099i \(0.933272\pi\)
\(114\) 8.43096e7i 0.499181i
\(115\) 0 0
\(116\) −1.16160e7 −0.0641541
\(117\) −4.71258e7 + 4.71258e7i −0.251487 + 0.251487i
\(118\) 6.81871e7 + 6.81871e7i 0.351702 + 0.351702i
\(119\) 1.45502e8i 0.725572i
\(120\) 0 0
\(121\) −1.63666e8 −0.763515
\(122\) −8.91178e7 + 8.91178e7i −0.402277 + 0.402277i
\(123\) 8.56764e7 + 8.56764e7i 0.374318 + 0.374318i
\(124\) 2.71685e7i 0.114915i
\(125\) 0 0
\(126\) −4.64178e7 −0.184163
\(127\) 7.80666e7 7.80666e7i 0.300089 0.300089i −0.540959 0.841049i \(-0.681939\pi\)
0.841049 + 0.540959i \(0.181939\pi\)
\(128\) −1.57944e8 1.57944e8i −0.588387 0.588387i
\(129\) 2.99550e8i 1.08171i
\(130\) 0 0
\(131\) 1.86914e8 0.634682 0.317341 0.948311i \(-0.397210\pi\)
0.317341 + 0.948311i \(0.397210\pi\)
\(132\) −5.79468e6 + 5.79468e6i −0.0190868 + 0.0190868i
\(133\) 1.16932e8 + 1.16932e8i 0.373703 + 0.373703i
\(134\) 4.99767e8i 1.55006i
\(135\) 0 0
\(136\) −4.45122e8 −1.30114
\(137\) −3.19732e8 + 3.19732e8i −0.907619 + 0.907619i −0.996080 0.0884605i \(-0.971805\pi\)
0.0884605 + 0.996080i \(0.471805\pi\)
\(138\) 8.23433e7 + 8.23433e7i 0.227045 + 0.227045i
\(139\) 5.44849e8i 1.45954i 0.683691 + 0.729772i \(0.260374\pi\)
−0.683691 + 0.729772i \(0.739626\pi\)
\(140\) 0 0
\(141\) 6.99833e7 0.177059
\(142\) 3.46923e8 3.46923e8i 0.853257 0.853257i
\(143\) −1.53420e8 1.53420e8i −0.366892 0.366892i
\(144\) 1.28223e8i 0.298205i
\(145\) 0 0
\(146\) −3.21028e8 −0.706532
\(147\) 1.26253e8 1.26253e8i 0.270378 0.270378i
\(148\) −1.07647e7 1.07647e7i −0.0224365 0.0224365i
\(149\) 8.49730e8i 1.72400i 0.506912 + 0.861998i \(0.330787\pi\)
−0.506912 + 0.861998i \(0.669213\pi\)
\(150\) 0 0
\(151\) −5.53942e8 −1.06551 −0.532754 0.846270i \(-0.678843\pi\)
−0.532754 + 0.846270i \(0.678843\pi\)
\(152\) 3.57721e8 3.57721e8i 0.670146 0.670146i
\(153\) 1.61263e8 + 1.61263e8i 0.294287 + 0.294287i
\(154\) 1.51115e8i 0.268674i
\(155\) 0 0
\(156\) 3.50750e7 0.0592241
\(157\) 6.53141e8 6.53141e8i 1.07500 1.07500i 0.0780506 0.996949i \(-0.475130\pi\)
0.996949 0.0780506i \(-0.0248696\pi\)
\(158\) −7.71856e8 7.71856e8i −1.23853 1.23853i
\(159\) 6.62352e8i 1.03633i
\(160\) 0 0
\(161\) 2.28410e8 0.339947
\(162\) 5.14462e7 5.14462e7i 0.0746952 0.0746952i
\(163\) −1.36520e8 1.36520e8i −0.193395 0.193395i 0.603766 0.797161i \(-0.293666\pi\)
−0.797161 + 0.603766i \(0.793666\pi\)
\(164\) 6.37675e7i 0.0881503i
\(165\) 0 0
\(166\) −5.31211e8 −0.699575
\(167\) −8.46479e8 + 8.46479e8i −1.08830 + 1.08830i −0.0926003 + 0.995703i \(0.529518\pi\)
−0.995703 + 0.0926003i \(0.970482\pi\)
\(168\) 1.96948e8 + 1.96948e8i 0.247238 + 0.247238i
\(169\) 1.12916e8i 0.138423i
\(170\) 0 0
\(171\) −2.59198e8 −0.303142
\(172\) 1.11475e8 1.11475e8i 0.127369 0.127369i
\(173\) −9.98204e8 9.98204e8i −1.11438 1.11438i −0.992551 0.121833i \(-0.961123\pi\)
−0.121833 0.992551i \(-0.538877\pi\)
\(174\) 3.35740e8i 0.366274i
\(175\) 0 0
\(176\) −4.17435e8 −0.435049
\(177\) −2.09631e8 + 2.09631e8i −0.213581 + 0.213581i
\(178\) 9.25614e8 + 9.25614e8i 0.922040 + 0.922040i
\(179\) 1.26965e9i 1.23672i −0.785896 0.618359i \(-0.787798\pi\)
0.785896 0.618359i \(-0.212202\pi\)
\(180\) 0 0
\(181\) 6.81618e8 0.635077 0.317539 0.948245i \(-0.397144\pi\)
0.317539 + 0.948245i \(0.397144\pi\)
\(182\) −4.57348e8 + 4.57348e8i −0.416832 + 0.416832i
\(183\) −2.73980e8 2.73980e8i −0.244295 0.244295i
\(184\) 6.98755e8i 0.609612i
\(185\) 0 0
\(186\) −7.85258e8 −0.656085
\(187\) −5.25000e8 + 5.25000e8i −0.429332 + 0.429332i
\(188\) −2.60437e7 2.60437e7i −0.0208483 0.0208483i
\(189\) 1.42705e8i 0.111839i
\(190\) 0 0
\(191\) 1.18866e9 0.893150 0.446575 0.894746i \(-0.352644\pi\)
0.446575 + 0.894746i \(0.352644\pi\)
\(192\) 5.97380e8 5.97380e8i 0.439588 0.439588i
\(193\) −1.09555e9 1.09555e9i −0.789594 0.789594i 0.191833 0.981428i \(-0.438557\pi\)
−0.981428 + 0.191833i \(0.938557\pi\)
\(194\) 1.56500e9i 1.10486i
\(195\) 0 0
\(196\) −9.39677e7 −0.0636728
\(197\) 9.26327e7 9.26327e7i 0.0615034 0.0615034i −0.675686 0.737189i \(-0.736152\pi\)
0.737189 + 0.675686i \(0.236152\pi\)
\(198\) 1.67485e8 + 1.67485e8i 0.108972 + 0.108972i
\(199\) 1.76224e9i 1.12371i 0.827237 + 0.561854i \(0.189912\pi\)
−0.827237 + 0.561854i \(0.810088\pi\)
\(200\) 0 0
\(201\) 1.53646e9 0.941320
\(202\) −5.33812e8 + 5.33812e8i −0.320614 + 0.320614i
\(203\) 4.65650e8 + 4.65650e8i 0.274205 + 0.274205i
\(204\) 1.20026e8i 0.0693033i
\(205\) 0 0
\(206\) −1.34074e9 −0.744520
\(207\) −2.53152e8 + 2.53152e8i −0.137880 + 0.137880i
\(208\) 1.26336e9 + 1.26336e9i 0.674953 + 0.674953i
\(209\) 8.43829e8i 0.442251i
\(210\) 0 0
\(211\) 1.02674e9 0.518001 0.259000 0.965877i \(-0.416607\pi\)
0.259000 + 0.965877i \(0.416607\pi\)
\(212\) 2.46489e8 2.46489e8i 0.122026 0.122026i
\(213\) 1.06657e9 + 1.06657e9i 0.518166 + 0.518166i
\(214\) 2.13352e9i 1.01728i
\(215\) 0 0
\(216\) −4.36566e8 −0.200556
\(217\) −1.08910e9 + 1.08910e9i −0.491167 + 0.491167i
\(218\) 9.98338e8 + 9.98338e8i 0.442030 + 0.442030i
\(219\) 9.86955e8i 0.429063i
\(220\) 0 0
\(221\) 3.17781e9 1.33217
\(222\) −3.11135e8 + 3.11135e8i −0.128096 + 0.128096i
\(223\) −1.83455e8 1.83455e8i −0.0741841 0.0741841i 0.669041 0.743225i \(-0.266705\pi\)
−0.743225 + 0.669041i \(0.766705\pi\)
\(224\) 2.80314e8i 0.111340i
\(225\) 0 0
\(226\) 2.70082e9 1.03529
\(227\) 7.64853e8 7.64853e8i 0.288055 0.288055i −0.548256 0.836311i \(-0.684708\pi\)
0.836311 + 0.548256i \(0.184708\pi\)
\(228\) 9.64582e7 + 9.64582e7i 0.0356944 + 0.0356944i
\(229\) 4.06794e9i 1.47922i 0.673037 + 0.739609i \(0.264989\pi\)
−0.673037 + 0.739609i \(0.735011\pi\)
\(230\) 0 0
\(231\) 4.64582e8 0.163160
\(232\) 1.42453e9 1.42453e9i 0.491720 0.491720i
\(233\) 1.88027e9 + 1.88027e9i 0.637964 + 0.637964i 0.950053 0.312089i \(-0.101029\pi\)
−0.312089 + 0.950053i \(0.601029\pi\)
\(234\) 1.01378e9i 0.338128i
\(235\) 0 0
\(236\) 1.56025e8 0.0502975
\(237\) 2.37296e9 2.37296e9i 0.752137 0.752137i
\(238\) 1.56503e9 + 1.56503e9i 0.487771 + 0.487771i
\(239\) 1.27628e9i 0.391160i 0.980688 + 0.195580i \(0.0626589\pi\)
−0.980688 + 0.195580i \(0.937341\pi\)
\(240\) 0 0
\(241\) 3.56750e9 1.05754 0.528768 0.848766i \(-0.322654\pi\)
0.528768 + 0.848766i \(0.322654\pi\)
\(242\) 1.76041e9 1.76041e9i 0.513279 0.513279i
\(243\) 1.58164e8 + 1.58164e8i 0.0453609 + 0.0453609i
\(244\) 2.03919e8i 0.0575304i
\(245\) 0 0
\(246\) −1.84309e9 −0.503276
\(247\) −2.55383e9 + 2.55383e9i −0.686127 + 0.686127i
\(248\) 3.33180e9 + 3.33180e9i 0.880790 + 0.880790i
\(249\) 1.63313e9i 0.424838i
\(250\) 0 0
\(251\) −1.90299e9 −0.479447 −0.239724 0.970841i \(-0.577057\pi\)
−0.239724 + 0.970841i \(0.577057\pi\)
\(252\) −5.31064e7 + 5.31064e7i −0.0131688 + 0.0131688i
\(253\) −8.24149e8 8.24149e8i −0.201152 0.201152i
\(254\) 1.67939e9i 0.403474i
\(255\) 0 0
\(256\) −1.22695e9 −0.285671
\(257\) −7.71199e8 + 7.71199e8i −0.176780 + 0.176780i −0.789951 0.613170i \(-0.789894\pi\)
0.613170 + 0.789951i \(0.289894\pi\)
\(258\) −3.22199e9 3.22199e9i −0.727186 0.727186i
\(259\) 8.63048e8i 0.191794i
\(260\) 0 0
\(261\) −1.03218e9 −0.222431
\(262\) −2.01047e9 + 2.01047e9i −0.426669 + 0.426669i
\(263\) 7.60308e8 + 7.60308e8i 0.158916 + 0.158916i 0.782086 0.623170i \(-0.214156\pi\)
−0.623170 + 0.782086i \(0.714156\pi\)
\(264\) 1.42126e9i 0.292589i
\(265\) 0 0
\(266\) −2.51547e9 −0.502449
\(267\) −2.84566e9 + 2.84566e9i −0.559936 + 0.559936i
\(268\) −5.71781e8 5.71781e8i −0.110839 0.110839i
\(269\) 6.05851e9i 1.15706i 0.815660 + 0.578531i \(0.196374\pi\)
−0.815660 + 0.578531i \(0.803626\pi\)
\(270\) 0 0
\(271\) −4.99620e9 −0.926324 −0.463162 0.886274i \(-0.653285\pi\)
−0.463162 + 0.886274i \(0.653285\pi\)
\(272\) 4.32319e9 4.32319e9i 0.789820 0.789820i
\(273\) −1.40605e9 1.40605e9i −0.253134 0.253134i
\(274\) 6.87814e9i 1.22031i
\(275\) 0 0
\(276\) 1.88417e8 0.0324701
\(277\) −1.30830e9 + 1.30830e9i −0.222222 + 0.222222i −0.809434 0.587211i \(-0.800226\pi\)
0.587211 + 0.809434i \(0.300226\pi\)
\(278\) −5.86046e9 5.86046e9i −0.981189 0.981189i
\(279\) 2.41416e9i 0.398428i
\(280\) 0 0
\(281\) −6.91480e9 −1.10906 −0.554529 0.832164i \(-0.687102\pi\)
−0.554529 + 0.832164i \(0.687102\pi\)
\(282\) −7.52748e8 + 7.52748e8i −0.119029 + 0.119029i
\(283\) −5.90916e9 5.90916e9i −0.921255 0.921255i 0.0758636 0.997118i \(-0.475829\pi\)
−0.997118 + 0.0758636i \(0.975829\pi\)
\(284\) 7.93827e8i 0.122026i
\(285\) 0 0
\(286\) 3.30041e9 0.493291
\(287\) −2.55625e9 + 2.55625e9i −0.376769 + 0.376769i
\(288\) 3.10679e8 + 3.10679e8i 0.0451588 + 0.0451588i
\(289\) 3.89862e9i 0.558882i
\(290\) 0 0
\(291\) 4.81135e9 0.670958
\(292\) −3.67287e8 + 3.67287e8i −0.0505213 + 0.0505213i
\(293\) 4.72997e9 + 4.72997e9i 0.641783 + 0.641783i 0.950994 0.309211i \(-0.100065\pi\)
−0.309211 + 0.950994i \(0.600065\pi\)
\(294\) 2.71597e9i 0.363527i
\(295\) 0 0
\(296\) 2.64026e9 0.343937
\(297\) −5.14909e8 + 5.14909e8i −0.0661766 + 0.0661766i
\(298\) −9.13980e9 9.13980e9i −1.15897 1.15897i
\(299\) 4.98854e9i 0.624150i
\(300\) 0 0
\(301\) −8.93738e9 −1.08879
\(302\) 5.95826e9 5.95826e9i 0.716295 0.716295i
\(303\) −1.64113e9 1.64113e9i −0.194703 0.194703i
\(304\) 6.94863e9i 0.813588i
\(305\) 0 0
\(306\) −3.46914e9 −0.395672
\(307\) 5.52832e9 5.52832e9i 0.622357 0.622357i −0.323777 0.946133i \(-0.604953\pi\)
0.946133 + 0.323777i \(0.104953\pi\)
\(308\) −1.72890e8 1.72890e8i −0.0192118 0.0192118i
\(309\) 4.12192e9i 0.452132i
\(310\) 0 0
\(311\) −5.99042e9 −0.640347 −0.320174 0.947359i \(-0.603741\pi\)
−0.320174 + 0.947359i \(0.603741\pi\)
\(312\) −4.30141e9 + 4.30141e9i −0.453934 + 0.453934i
\(313\) −6.95852e9 6.95852e9i −0.725003 0.725003i 0.244617 0.969620i \(-0.421338\pi\)
−0.969620 + 0.244617i \(0.921338\pi\)
\(314\) 1.40505e10i 1.44535i
\(315\) 0 0
\(316\) −1.76615e9 −0.177125
\(317\) 1.67452e9 1.67452e9i 0.165826 0.165826i −0.619316 0.785142i \(-0.712590\pi\)
0.785142 + 0.619316i \(0.212590\pi\)
\(318\) −7.12433e9 7.12433e9i −0.696683 0.696683i
\(319\) 3.36032e9i 0.324502i
\(320\) 0 0
\(321\) 6.55921e9 0.617776
\(322\) −2.45680e9 + 2.45680e9i −0.228532 + 0.228532i
\(323\) 8.73916e9 + 8.73916e9i 0.802896 + 0.802896i
\(324\) 1.17719e8i 0.0106823i
\(325\) 0 0
\(326\) 2.93685e9 0.260023
\(327\) −3.06925e9 + 3.06925e9i −0.268436 + 0.268436i
\(328\) 7.82012e9 + 7.82012e9i 0.675644 + 0.675644i
\(329\) 2.08802e9i 0.178218i
\(330\) 0 0
\(331\) −1.77038e10 −1.47487 −0.737436 0.675417i \(-0.763964\pi\)
−0.737436 + 0.675417i \(0.763964\pi\)
\(332\) −6.07756e8 + 6.07756e8i −0.0500238 + 0.0500238i
\(333\) −9.56540e8 9.56540e8i −0.0777904 0.0777904i
\(334\) 1.82096e10i 1.46324i
\(335\) 0 0
\(336\) −3.82566e9 −0.300158
\(337\) 1.30214e10 1.30214e10i 1.00957 1.00957i 0.00961969 0.999954i \(-0.496938\pi\)
0.999954 0.00961969i \(-0.00306209\pi\)
\(338\) −1.21454e9 1.21454e9i −0.0930558 0.0930558i
\(339\) 8.30327e9i 0.628710i
\(340\) 0 0
\(341\) 7.85940e9 0.581262
\(342\) 2.78796e9 2.78796e9i 0.203790 0.203790i
\(343\) 9.45456e9 + 9.45456e9i 0.683069 + 0.683069i
\(344\) 2.73414e10i 1.95248i
\(345\) 0 0
\(346\) 2.14736e10 1.49830
\(347\) 1.29834e9 1.29834e9i 0.0895509 0.0895509i −0.660912 0.750463i \(-0.729830\pi\)
0.750463 + 0.660912i \(0.229830\pi\)
\(348\) 3.84119e8 + 3.84119e8i 0.0261908 + 0.0261908i
\(349\) 8.25437e9i 0.556394i −0.960524 0.278197i \(-0.910263\pi\)
0.960524 0.278197i \(-0.0897368\pi\)
\(350\) 0 0
\(351\) 3.11672e9 0.205338
\(352\) −1.01143e9 + 1.01143e9i −0.0658817 + 0.0658817i
\(353\) 9.06303e9 + 9.06303e9i 0.583679 + 0.583679i 0.935912 0.352233i \(-0.114578\pi\)
−0.352233 + 0.935912i \(0.614578\pi\)
\(354\) 4.50964e9i 0.287163i
\(355\) 0 0
\(356\) 2.11798e9 0.131863
\(357\) −4.81147e9 + 4.81147e9i −0.296213 + 0.296213i
\(358\) 1.36565e10 + 1.36565e10i 0.831393 + 0.831393i
\(359\) 7.06291e9i 0.425212i −0.977138 0.212606i \(-0.931805\pi\)
0.977138 0.212606i \(-0.0681951\pi\)
\(360\) 0 0
\(361\) 2.93718e9 0.172943
\(362\) −7.33156e9 + 7.33156e9i −0.426935 + 0.426935i
\(363\) 5.41214e9 + 5.41214e9i 0.311704 + 0.311704i
\(364\) 1.04650e9i 0.0596119i
\(365\) 0 0
\(366\) 5.89392e9 0.328458
\(367\) −1.17036e9 + 1.17036e9i −0.0645144 + 0.0645144i −0.738628 0.674113i \(-0.764526\pi\)
0.674113 + 0.738628i \(0.264526\pi\)
\(368\) 6.78657e9 + 6.78657e9i 0.370049 + 0.370049i
\(369\) 5.66631e9i 0.305629i
\(370\) 0 0
\(371\) −1.97620e10 −1.04312
\(372\) −8.98410e8 + 8.98410e8i −0.0469140 + 0.0469140i
\(373\) −8.36934e8 8.36934e8i −0.0432370 0.0432370i 0.685158 0.728395i \(-0.259733\pi\)
−0.728395 + 0.685158i \(0.759733\pi\)
\(374\) 1.12939e10i 0.577243i
\(375\) 0 0
\(376\) 6.38773e9 0.319591
\(377\) −1.01699e10 + 1.01699e10i −0.503447 + 0.503447i
\(378\) 1.53495e9 + 1.53495e9i 0.0751843 + 0.0751843i
\(379\) 7.43822e9i 0.360506i −0.983620 0.180253i \(-0.942308\pi\)
0.983620 0.180253i \(-0.0576916\pi\)
\(380\) 0 0
\(381\) −5.16303e9 −0.245022
\(382\) −1.27854e10 + 1.27854e10i −0.600426 + 0.600426i
\(383\) 8.80678e9 + 8.80678e9i 0.409281 + 0.409281i 0.881488 0.472207i \(-0.156542\pi\)
−0.472207 + 0.881488i \(0.656542\pi\)
\(384\) 1.04458e10i 0.480416i
\(385\) 0 0
\(386\) 2.35678e10 1.06162
\(387\) 9.90554e9 9.90554e9i 0.441605 0.441605i
\(388\) −1.79051e9 1.79051e9i −0.0790039 0.0790039i
\(389\) 3.67525e10i 1.60505i −0.596620 0.802524i \(-0.703490\pi\)
0.596620 0.802524i \(-0.296510\pi\)
\(390\) 0 0
\(391\) 1.70707e10 0.730371
\(392\) 1.15237e10 1.15237e10i 0.488032 0.488032i
\(393\) −6.18089e9 6.18089e9i −0.259108 0.259108i
\(394\) 1.99274e9i 0.0826922i
\(395\) 0 0
\(396\) 3.83238e8 0.0155843
\(397\) −8.61053e8 + 8.61053e8i −0.0346631 + 0.0346631i −0.724226 0.689563i \(-0.757803\pi\)
0.689563 + 0.724226i \(0.257803\pi\)
\(398\) −1.89549e10 1.89549e10i −0.755420 0.755420i
\(399\) 7.73344e9i 0.305127i
\(400\) 0 0
\(401\) 4.86650e10 1.88208 0.941042 0.338290i \(-0.109849\pi\)
0.941042 + 0.338290i \(0.109849\pi\)
\(402\) −1.65264e10 + 1.65264e10i −0.632809 + 0.632809i
\(403\) −2.37863e10 2.37863e10i −0.901794 0.901794i
\(404\) 1.22146e9i 0.0458517i
\(405\) 0 0
\(406\) −1.00172e10 −0.368672
\(407\) 3.11406e9 3.11406e9i 0.113488 0.113488i
\(408\) 1.47193e10 + 1.47193e10i 0.531187 + 0.531187i
\(409\) 1.40974e10i 0.503785i −0.967755 0.251892i \(-0.918947\pi\)
0.967755 0.251892i \(-0.0810529\pi\)
\(410\) 0 0
\(411\) 2.11459e10 0.741068
\(412\) −1.53394e9 + 1.53394e9i −0.0532376 + 0.0532376i
\(413\) −6.25458e9 6.25458e9i −0.214980 0.214980i
\(414\) 5.44587e9i 0.185381i
\(415\) 0 0
\(416\) 6.12215e9 0.204423
\(417\) 1.80171e10 1.80171e10i 0.595856 0.595856i
\(418\) 9.07632e9 + 9.07632e9i 0.297307 + 0.297307i
\(419\) 4.51696e10i 1.46551i −0.680491 0.732757i \(-0.738233\pi\)
0.680491 0.732757i \(-0.261767\pi\)
\(420\) 0 0
\(421\) 5.87369e9 0.186975 0.0934873 0.995620i \(-0.470199\pi\)
0.0934873 + 0.995620i \(0.470199\pi\)
\(422\) −1.10437e10 + 1.10437e10i −0.348230 + 0.348230i
\(423\) −2.31421e9 2.31421e9i −0.0722840 0.0722840i
\(424\) 6.04562e10i 1.87058i
\(425\) 0 0
\(426\) −2.29442e10 −0.696682
\(427\) 8.17448e9 8.17448e9i 0.245894 0.245894i
\(428\) −2.44095e9 2.44095e9i −0.0727419 0.0727419i
\(429\) 1.01466e10i 0.299566i
\(430\) 0 0
\(431\) −6.34592e10 −1.83902 −0.919508 0.393072i \(-0.871412\pi\)
−0.919508 + 0.393072i \(0.871412\pi\)
\(432\) 4.24009e9 4.24009e9i 0.121742 0.121742i
\(433\) 1.88003e10 + 1.88003e10i 0.534828 + 0.534828i 0.922005 0.387177i \(-0.126550\pi\)
−0.387177 + 0.922005i \(0.626550\pi\)
\(434\) 2.34290e10i 0.660381i
\(435\) 0 0
\(436\) 2.28439e9 0.0632156
\(437\) −1.37188e10 + 1.37188e10i −0.376175 + 0.376175i
\(438\) 1.06158e10 + 1.06158e10i 0.288441 + 0.288441i
\(439\) 3.57969e10i 0.963800i 0.876226 + 0.481900i \(0.160053\pi\)
−0.876226 + 0.481900i \(0.839947\pi\)
\(440\) 0 0
\(441\) −8.34987e9 −0.220762
\(442\) −3.41809e10 + 3.41809e10i −0.895558 + 0.895558i
\(443\) −4.37162e10 4.37162e10i −1.13508 1.13508i −0.989319 0.145764i \(-0.953436\pi\)
−0.145764 0.989319i \(-0.546564\pi\)
\(444\) 7.11936e8i 0.0183193i
\(445\) 0 0
\(446\) 3.94653e9 0.0997416
\(447\) 2.80990e10 2.80990e10i 0.703818 0.703818i
\(448\) 1.78235e10 + 1.78235e10i 0.442466 + 0.442466i
\(449\) 1.65888e9i 0.0408159i 0.999792 + 0.0204079i \(0.00649650\pi\)
−0.999792 + 0.0204079i \(0.993504\pi\)
\(450\) 0 0
\(451\) 1.84469e10 0.445880
\(452\) 3.08999e9 3.08999e9i 0.0740293 0.0740293i
\(453\) 1.83178e10 + 1.83178e10i 0.434992 + 0.434992i
\(454\) 1.64537e10i 0.387293i
\(455\) 0 0
\(456\) −2.36583e10 −0.547172
\(457\) 2.84520e10 2.84520e10i 0.652302 0.652302i −0.301245 0.953547i \(-0.597402\pi\)
0.953547 + 0.301245i \(0.0974021\pi\)
\(458\) −4.37552e10 4.37552e10i −0.994415 0.994415i
\(459\) 1.06654e10i 0.240284i
\(460\) 0 0
\(461\) −6.07445e10 −1.34494 −0.672471 0.740124i \(-0.734767\pi\)
−0.672471 + 0.740124i \(0.734767\pi\)
\(462\) −4.99710e9 + 4.99710e9i −0.109686 + 0.109686i
\(463\) −1.71916e10 1.71916e10i −0.374104 0.374104i 0.494865 0.868970i \(-0.335217\pi\)
−0.868970 + 0.494865i \(0.835217\pi\)
\(464\) 2.76710e10i 0.596971i
\(465\) 0 0
\(466\) −4.04488e10 −0.857752
\(467\) 3.12336e10 3.12336e10i 0.656680 0.656680i −0.297913 0.954593i \(-0.596290\pi\)
0.954593 + 0.297913i \(0.0962905\pi\)
\(468\) −1.15986e9 1.15986e9i −0.0241782 0.0241782i
\(469\) 4.58420e10i 0.947484i
\(470\) 0 0
\(471\) −4.31963e10 −0.877734
\(472\) −1.91341e10 + 1.91341e10i −0.385514 + 0.385514i
\(473\) 3.22479e10 + 3.22479e10i 0.644254 + 0.644254i
\(474\) 5.10477e10i 1.01126i
\(475\) 0 0
\(476\) 3.58109e9 0.0697570
\(477\) 2.19027e10 2.19027e10i 0.423082 0.423082i
\(478\) −1.37278e10 1.37278e10i −0.262960 0.262960i
\(479\) 4.02757e10i 0.765069i 0.923941 + 0.382535i \(0.124949\pi\)
−0.923941 + 0.382535i \(0.875051\pi\)
\(480\) 0 0
\(481\) −1.88493e10 −0.352139
\(482\) −3.83724e10 + 3.83724e10i −0.710937 + 0.710937i
\(483\) −7.55307e9 7.55307e9i −0.138783 0.138783i
\(484\) 4.02816e9i 0.0734050i
\(485\) 0 0
\(486\) −3.40245e9 −0.0609884
\(487\) 2.78327e10 2.78327e10i 0.494811 0.494811i −0.415007 0.909818i \(-0.636221\pi\)
0.909818 + 0.415007i \(0.136221\pi\)
\(488\) −2.50075e10 2.50075e10i −0.440952 0.440952i
\(489\) 9.02891e9i 0.157907i
\(490\) 0 0
\(491\) 3.48952e10 0.600399 0.300199 0.953876i \(-0.402947\pi\)
0.300199 + 0.953876i \(0.402947\pi\)
\(492\) −2.10867e9 + 2.10867e9i −0.0359872 + 0.0359872i
\(493\) 3.48013e10 + 3.48013e10i 0.589126 + 0.589126i
\(494\) 5.49386e10i 0.922508i
\(495\) 0 0
\(496\) −6.47193e10 −1.06932
\(497\) −3.18221e10 + 3.18221e10i −0.521559 + 0.521559i
\(498\) 1.75661e10 + 1.75661e10i 0.285600 + 0.285600i
\(499\) 8.29525e10i 1.33791i 0.743302 + 0.668956i \(0.233258\pi\)
−0.743302 + 0.668956i \(0.766742\pi\)
\(500\) 0 0
\(501\) 5.59829e10 0.888596
\(502\) 2.04687e10 2.04687e10i 0.322312 0.322312i
\(503\) −3.75026e10 3.75026e10i −0.585855 0.585855i 0.350651 0.936506i \(-0.385960\pi\)
−0.936506 + 0.350651i \(0.885960\pi\)
\(504\) 1.30254e10i 0.201869i
\(505\) 0 0
\(506\) 1.77293e10 0.270451
\(507\) 3.73391e9 3.73391e9i 0.0565109 0.0565109i
\(508\) 1.92138e9 + 1.92138e9i 0.0288508 + 0.0288508i
\(509\) 1.07216e11i 1.59730i −0.601795 0.798651i \(-0.705548\pi\)
0.601795 0.798651i \(-0.294452\pi\)
\(510\) 0 0
\(511\) 2.94469e10 0.431872
\(512\) 5.36309e10 5.36309e10i 0.780432 0.780432i
\(513\) 8.57118e9 + 8.57118e9i 0.123757 + 0.123757i
\(514\) 1.65902e10i 0.237684i
\(515\) 0 0
\(516\) −7.37253e9 −0.103996
\(517\) 7.53402e9 7.53402e9i 0.105454 0.105454i
\(518\) −9.28304e9 9.28304e9i −0.128935 0.128935i
\(519\) 6.60174e10i 0.909890i
\(520\) 0 0
\(521\) −7.65990e10 −1.03961 −0.519807 0.854284i \(-0.673996\pi\)
−0.519807 + 0.854284i \(0.673996\pi\)
\(522\) 1.11023e10 1.11023e10i 0.149531 0.149531i
\(523\) −3.31472e10 3.31472e10i −0.443038 0.443038i 0.449994 0.893032i \(-0.351426\pi\)
−0.893032 + 0.449994i \(0.851426\pi\)
\(524\) 4.60033e9i 0.0610188i
\(525\) 0 0
\(526\) −1.63559e10 −0.213664
\(527\) −8.13963e10 + 8.13963e10i −1.05527 + 1.05527i
\(528\) 1.38038e10 + 1.38038e10i 0.177608 + 0.177608i
\(529\) 5.15133e10i 0.657805i
\(530\) 0 0
\(531\) 1.38642e10 0.174388
\(532\) −2.87793e9 + 2.87793e9i −0.0359281 + 0.0359281i
\(533\) −5.58293e10 5.58293e10i −0.691756 0.691756i
\(534\) 6.12166e10i 0.752842i
\(535\) 0 0
\(536\) 1.40241e11 1.69908
\(537\) −4.19848e10 + 4.19848e10i −0.504888 + 0.504888i
\(538\) −6.51660e10 6.51660e10i −0.777843 0.777843i
\(539\) 2.71833e10i 0.322068i
\(540\) 0 0
\(541\) 1.00235e11 1.17012 0.585061 0.810989i \(-0.301071\pi\)
0.585061 + 0.810989i \(0.301071\pi\)
\(542\) 5.37397e10 5.37397e10i 0.622728 0.622728i
\(543\) −2.25398e10 2.25398e10i −0.259269 0.259269i
\(544\) 2.09498e10i 0.239213i
\(545\) 0 0
\(546\) 3.02472e10 0.340342
\(547\) −5.03272e9 + 5.03272e9i −0.0562151 + 0.0562151i −0.734655 0.678440i \(-0.762656\pi\)
0.678440 + 0.734655i \(0.262656\pi\)
\(548\) −7.86925e9 7.86925e9i −0.0872592 0.0872592i
\(549\) 1.81200e10i 0.199466i
\(550\) 0 0
\(551\) −5.59359e10 −0.606854
\(552\) −2.31065e10 + 2.31065e10i −0.248873 + 0.248873i
\(553\) 7.07998e10 + 7.07998e10i 0.757062 + 0.757062i
\(554\) 2.81444e10i 0.298781i
\(555\) 0 0
\(556\) −1.34099e10 −0.140322
\(557\) −8.75954e10 + 8.75954e10i −0.910040 + 0.910040i −0.996275 0.0862350i \(-0.972516\pi\)
0.0862350 + 0.996275i \(0.472516\pi\)
\(558\) 2.59670e10 + 2.59670e10i 0.267846 + 0.267846i
\(559\) 1.95195e11i 1.99904i
\(560\) 0 0
\(561\) 3.47215e10 0.350548
\(562\) 7.43764e10 7.43764e10i 0.745572 0.745572i
\(563\) 9.70300e10 + 9.70300e10i 0.965767 + 0.965767i 0.999433 0.0336664i \(-0.0107184\pi\)
−0.0336664 + 0.999433i \(0.510718\pi\)
\(564\) 1.72243e9i 0.0170226i
\(565\) 0 0
\(566\) 1.27119e11 1.23864
\(567\) −4.71898e9 + 4.71898e9i −0.0456579 + 0.0456579i
\(568\) 9.73508e10 + 9.73508e10i 0.935290 + 0.935290i
\(569\) 1.41438e11i 1.34932i 0.738127 + 0.674662i \(0.235711\pi\)
−0.738127 + 0.674662i \(0.764289\pi\)
\(570\) 0 0
\(571\) −3.01297e10 −0.283433 −0.141716 0.989907i \(-0.545262\pi\)
−0.141716 + 0.989907i \(0.545262\pi\)
\(572\) 3.77598e9 3.77598e9i 0.0352733 0.0352733i
\(573\) −3.93068e10 3.93068e10i −0.364627 0.364627i
\(574\) 5.49905e10i 0.506571i
\(575\) 0 0
\(576\) −3.95085e10 −0.358922
\(577\) −6.35231e10 + 6.35231e10i −0.573097 + 0.573097i −0.932993 0.359896i \(-0.882812\pi\)
0.359896 + 0.932993i \(0.382812\pi\)
\(578\) 4.19340e10 + 4.19340e10i 0.375712 + 0.375712i
\(579\) 7.24557e10i 0.644701i
\(580\) 0 0
\(581\) 4.87262e10 0.427620
\(582\) −5.17515e10 + 5.17515e10i −0.451056 + 0.451056i
\(583\) 7.13052e10 + 7.13052e10i 0.617230 + 0.617230i
\(584\) 9.00844e10i 0.774459i
\(585\) 0 0
\(586\) −1.01752e11 −0.862886
\(587\) −6.15149e10 + 6.15149e10i −0.518117 + 0.518117i −0.917001 0.398884i \(-0.869398\pi\)
0.398884 + 0.917001i \(0.369398\pi\)
\(588\) 3.10733e9 + 3.10733e9i 0.0259943 + 0.0259943i
\(589\) 1.30828e11i 1.08702i
\(590\) 0 0
\(591\) −6.12638e9 −0.0502173
\(592\) −2.56431e10 + 2.56431e10i −0.208778 + 0.208778i
\(593\) 1.54470e11 + 1.54470e11i 1.24918 + 1.24918i 0.956082 + 0.293098i \(0.0946863\pi\)
0.293098 + 0.956082i \(0.405314\pi\)
\(594\) 1.10768e10i 0.0889754i
\(595\) 0 0
\(596\) −2.09136e10 −0.165746
\(597\) 5.82740e10 5.82740e10i 0.458752 0.458752i
\(598\) −5.36573e10 5.36573e10i −0.419589 0.419589i
\(599\) 1.71649e11i 1.33332i 0.745363 + 0.666658i \(0.232276\pi\)
−0.745363 + 0.666658i \(0.767724\pi\)
\(600\) 0 0
\(601\) 2.52528e11 1.93558 0.967790 0.251759i \(-0.0810090\pi\)
0.967790 + 0.251759i \(0.0810090\pi\)
\(602\) 9.61315e10 9.61315e10i 0.731947 0.731947i
\(603\) −5.08079e10 5.08079e10i −0.384292 0.384292i
\(604\) 1.36336e10i 0.102439i
\(605\) 0 0
\(606\) 3.53043e10 0.261780
\(607\) 8.26378e10 8.26378e10i 0.608729 0.608729i −0.333885 0.942614i \(-0.608360\pi\)
0.942614 + 0.333885i \(0.108360\pi\)
\(608\) 1.68363e10 + 1.68363e10i 0.123206 + 0.123206i
\(609\) 3.07963e10i 0.223887i
\(610\) 0 0
\(611\) −4.56032e10 −0.327213
\(612\) −3.96902e9 + 3.96902e9i −0.0282929 + 0.0282929i
\(613\) 5.27356e10 + 5.27356e10i 0.373476 + 0.373476i 0.868741 0.495266i \(-0.164929\pi\)
−0.495266 + 0.868741i \(0.664929\pi\)
\(614\) 1.18926e11i 0.836767i
\(615\) 0 0
\(616\) 4.24048e10 0.294504
\(617\) −2.53400e10 + 2.53400e10i −0.174850 + 0.174850i −0.789107 0.614256i \(-0.789456\pi\)
0.614256 + 0.789107i \(0.289456\pi\)
\(618\) 4.43358e10 + 4.43358e10i 0.303949 + 0.303949i
\(619\) 1.55331e11i 1.05802i 0.848614 + 0.529012i \(0.177437\pi\)
−0.848614 + 0.529012i \(0.822563\pi\)
\(620\) 0 0
\(621\) 1.67425e10 0.112578
\(622\) 6.44336e10 6.44336e10i 0.430478 0.430478i
\(623\) −8.49034e10 8.49034e10i −0.563603 0.563603i
\(624\) 8.35538e10i 0.551097i
\(625\) 0 0
\(626\) 1.49693e11 0.974777
\(627\) −2.79038e10 + 2.79038e10i −0.180548 + 0.180548i
\(628\) 1.60751e10 + 1.60751e10i 0.103351 + 0.103351i
\(629\) 6.45018e10i 0.412068i
\(630\) 0 0
\(631\) −2.06463e11 −1.30234 −0.651171 0.758931i \(-0.725722\pi\)
−0.651171 + 0.758931i \(0.725722\pi\)
\(632\) 2.16592e11 2.16592e11i 1.35761 1.35761i
\(633\) −3.39523e10 3.39523e10i −0.211473 0.211473i
\(634\) 3.60227e10i 0.222956i
\(635\) 0 0
\(636\) −1.63018e10 −0.0996340
\(637\) −8.22699e10 + 8.22699e10i −0.499670 + 0.499670i
\(638\) 3.61440e10 + 3.61440e10i 0.218149 + 0.218149i
\(639\) 7.05386e10i 0.423081i
\(640\) 0 0
\(641\) −1.81421e11 −1.07462 −0.537311 0.843384i \(-0.680560\pi\)
−0.537311 + 0.843384i \(0.680560\pi\)
\(642\) −7.05516e10 + 7.05516e10i −0.415304 + 0.415304i
\(643\) −2.13170e11 2.13170e11i −1.24704 1.24704i −0.957019 0.290025i \(-0.906337\pi\)
−0.290025 0.957019i \(-0.593663\pi\)
\(644\) 5.62162e9i 0.0326827i
\(645\) 0 0
\(646\) −1.87999e11 −1.07951
\(647\) −5.73225e10 + 5.73225e10i −0.327120 + 0.327120i −0.851491 0.524370i \(-0.824301\pi\)
0.524370 + 0.851491i \(0.324301\pi\)
\(648\) 1.44364e10 + 1.44364e10i 0.0818765 + 0.0818765i
\(649\) 4.51356e10i 0.254414i
\(650\) 0 0
\(651\) 7.20290e10 0.401036
\(652\) 3.36003e9 3.36003e9i 0.0185932 0.0185932i
\(653\) 2.36175e11 + 2.36175e11i 1.29892 + 1.29892i 0.929109 + 0.369807i \(0.120576\pi\)
0.369807 + 0.929109i \(0.379424\pi\)
\(654\) 6.60263e10i 0.360916i
\(655\) 0 0
\(656\) −1.51904e11 −0.820263
\(657\) −3.26367e10 + 3.26367e10i −0.175164 + 0.175164i
\(658\) −2.24590e10 2.24590e10i −0.119808 0.119808i
\(659\) 1.35776e11i 0.719918i 0.932968 + 0.359959i \(0.117209\pi\)
−0.932968 + 0.359959i \(0.882791\pi\)
\(660\) 0 0
\(661\) 2.20549e11 1.15531 0.577655 0.816281i \(-0.303968\pi\)
0.577655 + 0.816281i \(0.303968\pi\)
\(662\) 1.90424e11 1.90424e11i 0.991494 0.991494i
\(663\) −1.05084e11 1.05084e11i −0.543855 0.543855i
\(664\) 1.49064e11i 0.766833i
\(665\) 0 0
\(666\) 2.05773e10 0.104590
\(667\) −5.46313e10 + 5.46313e10i −0.276019 + 0.276019i
\(668\) −2.08336e10 2.08336e10i −0.104630 0.104630i
\(669\) 1.21330e10i 0.0605711i
\(670\) 0 0
\(671\) −5.89904e10 −0.290999
\(672\) −9.26944e9 + 9.26944e9i −0.0454545 + 0.0454545i
\(673\) −1.71937e11 1.71937e11i −0.838124 0.838124i 0.150488 0.988612i \(-0.451916\pi\)
−0.988612 + 0.150488i \(0.951916\pi\)
\(674\) 2.80119e11i 1.35739i
\(675\) 0 0
\(676\) −2.77909e9 −0.0133081
\(677\) −5.77761e10 + 5.77761e10i −0.275038 + 0.275038i −0.831125 0.556086i \(-0.812302\pi\)
0.556086 + 0.831125i \(0.312302\pi\)
\(678\) −8.93109e10 8.93109e10i −0.422655 0.422655i
\(679\) 1.43552e11i 0.675351i
\(680\) 0 0
\(681\) −5.05845e10 −0.235196
\(682\) −8.45366e10 + 8.45366e10i −0.390758 + 0.390758i
\(683\) −1.41107e11 1.41107e11i −0.648432 0.648432i 0.304182 0.952614i \(-0.401617\pi\)
−0.952614 + 0.304182i \(0.901617\pi\)
\(684\) 6.37938e9i 0.0291443i
\(685\) 0 0
\(686\) −2.03389e11 −0.918396
\(687\) 1.34519e11 1.34519e11i 0.603888 0.603888i
\(688\) −2.65550e11 2.65550e11i −1.18520 1.18520i
\(689\) 4.31608e11i 1.91519i
\(690\) 0 0
\(691\) 1.42595e10 0.0625450 0.0312725 0.999511i \(-0.490044\pi\)
0.0312725 + 0.999511i \(0.490044\pi\)
\(692\) 2.45678e10 2.45678e10i 0.107138 0.107138i
\(693\) −1.53628e10 1.53628e10i −0.0666099 0.0666099i
\(694\) 2.79302e10i 0.120402i
\(695\) 0 0
\(696\) −9.42127e10 −0.401488
\(697\) −1.91046e11 + 1.91046e11i −0.809483 + 0.809483i
\(698\) 8.87850e10 + 8.87850e10i 0.374040 + 0.374040i
\(699\) 1.24354e11i 0.520896i
\(700\) 0 0
\(701\) 6.57751e10 0.272389 0.136195 0.990682i \(-0.456513\pi\)
0.136195 + 0.990682i \(0.456513\pi\)
\(702\) −3.35238e10 + 3.35238e10i −0.138040 + 0.138040i
\(703\) −5.18366e10 5.18366e10i −0.212234 0.212234i
\(704\) 1.28621e11i 0.523628i
\(705\) 0 0
\(706\) −1.94966e11 −0.784765
\(707\) 4.89648e10 4.89648e10i 0.195977 0.195977i
\(708\) −5.15946e9 5.15946e9i −0.0205339 0.0205339i
\(709\) 5.22271e10i 0.206686i 0.994646 + 0.103343i \(0.0329539\pi\)
−0.994646 + 0.103343i \(0.967046\pi\)
\(710\) 0 0
\(711\) −1.56939e11 −0.614118
\(712\) −2.59738e11 + 2.59738e11i −1.01069 + 1.01069i
\(713\) −1.27776e11 1.27776e11i −0.494416 0.494416i
\(714\) 1.03505e11i 0.398263i
\(715\) 0 0
\(716\) 3.12486e10 0.118899
\(717\) 4.22042e10 4.22042e10i 0.159690 0.159690i
\(718\) 7.59694e10 + 7.59694e10i 0.285852 + 0.285852i
\(719\) 4.96442e11i 1.85760i 0.370579 + 0.928801i \(0.379159\pi\)
−0.370579 + 0.928801i \(0.620841\pi\)
\(720\) 0 0
\(721\) 1.22982e11 0.455092
\(722\) −3.15926e10 + 3.15926e10i −0.116262 + 0.116262i
\(723\) −1.17970e11 1.17970e11i −0.431738 0.431738i
\(724\) 1.67760e10i 0.0610568i
\(725\) 0 0
\(726\) −1.16427e11 −0.419090
\(727\) 1.06405e10 1.06405e10i 0.0380911 0.0380911i −0.687805 0.725896i \(-0.741425\pi\)
0.725896 + 0.687805i \(0.241425\pi\)
\(728\) −1.28337e11 1.28337e11i −0.456906 0.456906i
\(729\) 1.04604e10i 0.0370370i
\(730\) 0 0
\(731\) −6.67954e11 −2.33925
\(732\) 6.74320e9 6.74320e9i 0.0234867 0.0234867i
\(733\) 1.39079e11 + 1.39079e11i 0.481778 + 0.481778i 0.905699 0.423921i \(-0.139347\pi\)
−0.423921 + 0.905699i \(0.639347\pi\)
\(734\) 2.51771e10i 0.0867405i
\(735\) 0 0
\(736\) 3.28872e10 0.112077
\(737\) 1.65407e11 1.65407e11i 0.560641 0.560641i
\(738\) 6.09475e10 + 6.09475e10i 0.205462 + 0.205462i
\(739\) 1.49124e11i 0.500001i 0.968246 + 0.250000i \(0.0804308\pi\)
−0.968246 + 0.250000i \(0.919569\pi\)
\(740\) 0 0
\(741\) 1.68901e11 0.560221
\(742\) 2.12562e11 2.12562e11i 0.701245 0.701245i
\(743\) 3.03305e11 + 3.03305e11i 0.995231 + 0.995231i 0.999989 0.00475782i \(-0.00151447\pi\)
−0.00475782 + 0.999989i \(0.501514\pi\)
\(744\) 2.20353e11i 0.719162i
\(745\) 0 0
\(746\) 1.80043e10 0.0581328
\(747\) −5.40045e10 + 5.40045e10i −0.173439 + 0.173439i
\(748\) −1.29213e10 1.29213e10i −0.0412763 0.0412763i
\(749\) 1.95701e11i 0.621821i
\(750\) 0 0
\(751\) 4.43851e11 1.39533 0.697666 0.716424i \(-0.254222\pi\)
0.697666 + 0.716424i \(0.254222\pi\)
\(752\) −6.20400e10 + 6.20400e10i −0.193999 + 0.193999i
\(753\) 6.29282e10 + 6.29282e10i 0.195733 + 0.195733i
\(754\) 2.18778e11i 0.676891i
\(755\) 0 0
\(756\) 3.51226e9 0.0107523
\(757\) 5.37427e10 5.37427e10i 0.163658 0.163658i −0.620527 0.784185i \(-0.713081\pi\)
0.784185 + 0.620527i \(0.213081\pi\)
\(758\) 8.00063e10 + 8.00063e10i 0.242353 + 0.242353i
\(759\) 5.45061e10i 0.164240i
\(760\) 0 0
\(761\) 5.87151e11 1.75070 0.875349 0.483492i \(-0.160632\pi\)
0.875349 + 0.483492i \(0.160632\pi\)
\(762\) 5.55341e10 5.55341e10i 0.164718 0.164718i
\(763\) −9.15742e10 9.15742e10i −0.270194 0.270194i
\(764\) 2.92554e10i 0.0858681i
\(765\) 0 0
\(766\) −1.89453e11 −0.550285
\(767\) 1.36602e11 1.36602e11i 0.394708 0.394708i
\(768\) 4.05728e10 + 4.05728e10i 0.116625 + 0.116625i
\(769\) 4.98735e10i 0.142615i 0.997454 + 0.0713074i \(0.0227171\pi\)
−0.997454 + 0.0713074i \(0.977283\pi\)
\(770\) 0 0
\(771\) 5.10042e10 0.144341
\(772\) 2.69638e10 2.69638e10i 0.0759122 0.0759122i
\(773\) 1.45752e11 + 1.45752e11i 0.408223 + 0.408223i 0.881119 0.472895i \(-0.156791\pi\)
−0.472895 + 0.881119i \(0.656791\pi\)
\(774\) 2.13090e11i 0.593745i
\(775\) 0 0
\(776\) 4.39157e11 1.21108
\(777\) 2.85394e10 2.85394e10i 0.0782998 0.0782998i
\(778\) 3.95314e11 + 3.95314e11i 1.07900 + 1.07900i
\(779\) 3.07068e11i 0.833843i
\(780\) 0 0
\(781\) 2.29641e11 0.617229
\(782\) −1.83614e11 + 1.83614e11i −0.490997 + 0.490997i
\(783\) 3.41324e10 + 3.41324e10i 0.0908071 + 0.0908071i
\(784\) 2.23845e11i 0.592493i
\(785\) 0 0
\(786\) 1.32965e11 0.348374
\(787\) 3.40029e11 3.40029e11i 0.886374 0.886374i −0.107798 0.994173i \(-0.534380\pi\)
0.994173 + 0.107798i \(0.0343801\pi\)
\(788\) 2.27988e9 + 2.27988e9i 0.00591299 + 0.00591299i
\(789\) 5.02839e10i 0.129754i
\(790\) 0 0
\(791\) −2.47737e11 −0.632826
\(792\) −4.69983e10 + 4.69983e10i −0.119449 + 0.119449i
\(793\) 1.78533e11 + 1.78533e11i 0.451468 + 0.451468i
\(794\) 1.85232e10i 0.0466051i
\(795\) 0 0
\(796\) −4.33724e10 −0.108034
\(797\) 5.24767e10 5.24767e10i 0.130057 0.130057i −0.639082 0.769139i \(-0.720685\pi\)
0.769139 + 0.639082i \(0.220685\pi\)
\(798\) 8.31817e10 + 8.31817e10i 0.205124 + 0.205124i
\(799\) 1.56053e11i 0.382900i
\(800\) 0 0
\(801\) 1.88202e11 0.457186
\(802\) −5.23446e11 + 5.23446e11i −1.26524 + 1.26524i
\(803\) −1.06250e11 1.06250e11i −0.255545 0.255545i
\(804\) 3.78155e10i 0.0904993i
\(805\) 0 0
\(806\) 5.11697e11 1.21247
\(807\) 2.00343e11 2.00343e11i 0.472369 0.472369i
\(808\) −1.49794e11 1.49794e11i −0.351438 0.351438i
\(809\) 5.20379e11i 1.21486i −0.794374 0.607429i \(-0.792201\pi\)
0.794374 0.607429i \(-0.207799\pi\)
\(810\) 0 0
\(811\) −5.64818e11 −1.30565 −0.652823 0.757511i \(-0.726415\pi\)
−0.652823 + 0.757511i \(0.726415\pi\)
\(812\) −1.14606e10 + 1.14606e10i −0.0263623 + 0.0263623i
\(813\) 1.65215e11 + 1.65215e11i 0.378170 + 0.378170i
\(814\) 6.69903e10i 0.152586i
\(815\) 0 0
\(816\) −2.85919e11 −0.644886
\(817\) 5.36799e11 5.36799e11i 1.20482 1.20482i
\(818\) 1.51633e11 + 1.51633e11i 0.338673 + 0.338673i
\(819\) 9.29908e10i 0.206683i
\(820\) 0 0
\(821\) 2.29433e11 0.504990 0.252495 0.967598i \(-0.418749\pi\)
0.252495 + 0.967598i \(0.418749\pi\)
\(822\) −2.27447e11 + 2.27447e11i −0.498188 + 0.498188i
\(823\) −6.02259e10 6.02259e10i −0.131276 0.131276i 0.638416 0.769692i \(-0.279590\pi\)
−0.769692 + 0.638416i \(0.779590\pi\)
\(824\) 3.76228e11i 0.816099i
\(825\) 0 0
\(826\) 1.34550e11 0.289043
\(827\) −3.29701e11 + 3.29701e11i −0.704853 + 0.704853i −0.965448 0.260595i \(-0.916081\pi\)
0.260595 + 0.965448i \(0.416081\pi\)
\(828\) −6.23060e9 6.23060e9i −0.0132559 0.0132559i
\(829\) 7.15909e11i 1.51579i −0.652375 0.757897i \(-0.726227\pi\)
0.652375 0.757897i \(-0.273773\pi\)
\(830\) 0 0
\(831\) 8.65260e10 0.181444
\(832\) −3.89270e11 + 3.89270e11i −0.812378 + 0.812378i
\(833\) 2.81526e11 + 2.81526e11i 0.584707 + 0.584707i
\(834\) 3.87589e11i 0.801137i
\(835\) 0 0
\(836\) 2.07684e10 0.0425184
\(837\) −7.98317e10 + 7.98317e10i −0.162657 + 0.162657i
\(838\) 4.85849e11 + 4.85849e11i 0.985202 + 0.985202i
\(839\) 6.38354e10i 0.128829i −0.997923 0.0644145i \(-0.979482\pi\)
0.997923 0.0644145i \(-0.0205180\pi\)
\(840\) 0 0
\(841\) 2.77497e11 0.554720
\(842\) −6.31781e10 + 6.31781e10i −0.125695 + 0.125695i
\(843\) 2.28659e11 + 2.28659e11i 0.452771 + 0.452771i
\(844\) 2.52701e10i 0.0498010i
\(845\) 0 0
\(846\) 4.97839e10 0.0971869
\(847\) −1.61477e11 + 1.61477e11i −0.313745 + 0.313745i
\(848\) −5.87173e11 5.87173e11i −1.13549 1.13549i
\(849\) 3.90809e11i 0.752201i
\(850\) 0 0
\(851\) −1.01255e11 −0.193063
\(852\) −2.62503e10 + 2.62503e10i −0.0498169 + 0.0498169i
\(853\) 2.89736e11 + 2.89736e11i 0.547276 + 0.547276i 0.925652 0.378376i \(-0.123517\pi\)
−0.378376 + 0.925652i \(0.623517\pi\)
\(854\) 1.75851e11i 0.330608i
\(855\) 0 0
\(856\) 5.98692e11 1.11509
\(857\) −3.42707e11 + 3.42707e11i −0.635330 + 0.635330i −0.949400 0.314070i \(-0.898307\pi\)
0.314070 + 0.949400i \(0.398307\pi\)
\(858\) −1.09138e11 1.09138e11i −0.201385 0.201385i
\(859\) 7.22659e11i 1.32727i −0.748054 0.663637i \(-0.769012\pi\)
0.748054 0.663637i \(-0.230988\pi\)
\(860\) 0 0
\(861\) 1.69060e11 0.307631
\(862\) 6.82574e11 6.82574e11i 1.23629 1.23629i
\(863\) −7.53219e11 7.53219e11i −1.35793 1.35793i −0.876463 0.481469i \(-0.840103\pi\)
−0.481469 0.876463i \(-0.659897\pi\)
\(864\) 2.05471e10i 0.0368720i
\(865\) 0 0
\(866\) −4.04437e11 −0.719084
\(867\) −1.28920e11 + 1.28920e11i −0.228163 + 0.228163i
\(868\) −2.68050e10 2.68050e10i −0.0472212 0.0472212i
\(869\) 5.10920e11i 0.895930i
\(870\) 0 0
\(871\) −1.00120e12 −1.73960
\(872\) −2.80146e11 + 2.80146e11i −0.484527 + 0.484527i
\(873\) −1.59102e11 1.59102e11i −0.273918 0.273918i
\(874\) 2.95122e11i 0.505773i
\(875\) 0 0
\(876\) 2.42910e10 0.0412505
\(877\) 4.95750e11 4.95750e11i 0.838039 0.838039i −0.150562 0.988601i \(-0.548108\pi\)
0.988601 + 0.150562i \(0.0481082\pi\)
\(878\) −3.85035e11 3.85035e11i −0.647921 0.647921i
\(879\) 3.12823e11i 0.524014i
\(880\) 0 0
\(881\) 6.59305e11 1.09442 0.547208 0.836997i \(-0.315691\pi\)
0.547208 + 0.836997i \(0.315691\pi\)
\(882\) 8.98121e10 8.98121e10i 0.148409 0.148409i
\(883\) −9.31998e10 9.31998e10i −0.153311 0.153311i 0.626284 0.779595i \(-0.284575\pi\)
−0.779595 + 0.626284i \(0.784575\pi\)
\(884\) 7.82123e10i 0.128075i
\(885\) 0 0
\(886\) 9.40433e11 1.52614
\(887\) −3.56333e11 + 3.56333e11i −0.575654 + 0.575654i −0.933703 0.358049i \(-0.883442\pi\)
0.358049 + 0.933703i \(0.383442\pi\)
\(888\) −8.73083e10 8.73083e10i −0.140412 0.140412i
\(889\) 1.54044e11i 0.246626i
\(890\) 0 0
\(891\) 3.40541e10 0.0540330
\(892\) 4.51521e9 4.51521e9i 0.00713212 0.00713212i
\(893\) −1.25411e11 1.25411e11i −0.197211 0.197211i
\(894\) 6.04472e11i 0.946294i
\(895\) 0 0
\(896\) −3.11662e11 −0.483562
\(897\) 1.64962e11 1.64962e11i 0.254808 0.254808i
\(898\) −1.78431e10 1.78431e10i −0.0274388 0.0274388i
\(899\) 5.20986e11i 0.797604i
\(900\) 0 0
\(901\) −1.47695e12 −2.24113
\(902\) −1.98417e11 + 1.98417e11i −0.299746 + 0.299746i
\(903\) 2.95542e11 + 2.95542e11i 0.444497 + 0.444497i
\(904\) 7.57881e11i 1.13482i
\(905\) 0 0
\(906\) −3.94057e11 −0.584852
\(907\) −4.99028e11 + 4.99028e11i −0.737388 + 0.737388i −0.972072 0.234684i \(-0.924595\pi\)
0.234684 + 0.972072i \(0.424595\pi\)
\(908\) 1.88246e10 + 1.88246e10i 0.0276938 + 0.0276938i
\(909\) 1.08538e11i 0.158974i
\(910\) 0 0
\(911\) −2.35231e11 −0.341523 −0.170762 0.985312i \(-0.554623\pi\)
−0.170762 + 0.985312i \(0.554623\pi\)
\(912\) 2.29778e11 2.29778e11i 0.332146 0.332146i
\(913\) −1.75814e11 1.75814e11i −0.253029 0.253029i
\(914\) 6.12067e11i 0.877029i
\(915\) 0 0
\(916\) −1.00120e11 −0.142213
\(917\) 1.84413e11 1.84413e11i 0.260804 0.260804i
\(918\) 1.14718e11 + 1.14718e11i 0.161533 + 0.161533i
\(919\) 6.55314e11i 0.918729i 0.888248 + 0.459364i \(0.151923\pi\)
−0.888248 + 0.459364i \(0.848077\pi\)
\(920\) 0 0
\(921\) −3.65622e11 −0.508152
\(922\) 6.53375e11 6.53375e11i 0.904147 0.904147i
\(923\) −6.95006e11 6.95006e11i −0.957594 0.957594i
\(924\) 1.14343e10i 0.0156864i
\(925\) 0 0
\(926\) 3.69830e11 0.502988
\(927\) −1.36304e11 + 1.36304e11i −0.184582 + 0.184582i
\(928\) 6.70459e10 + 6.70459e10i 0.0904024 + 0.0904024i
\(929\) 6.37954e10i 0.0856498i −0.999083 0.0428249i \(-0.986364\pi\)
0.999083 0.0428249i \(-0.0136358\pi\)
\(930\) 0 0
\(931\) −4.52494e11 −0.602302
\(932\) −4.62773e10 + 4.62773e10i −0.0613344 + 0.0613344i
\(933\) 1.98092e11 + 1.98092e11i 0.261421 + 0.261421i
\(934\) 6.71903e11i 0.882916i
\(935\) 0 0
\(936\) 2.84479e11 0.370636
\(937\) 2.92340e11 2.92340e11i 0.379253 0.379253i −0.491580 0.870833i \(-0.663580\pi\)
0.870833 + 0.491580i \(0.163580\pi\)
\(938\) −4.93081e11 4.93081e11i −0.636953 0.636953i
\(939\) 4.60210e11i 0.591962i
\(940\) 0 0
\(941\) 8.59770e10 0.109654 0.0548269 0.998496i \(-0.482539\pi\)
0.0548269 + 0.998496i \(0.482539\pi\)
\(942\) 4.64624e11 4.64624e11i 0.590063 0.590063i
\(943\) −2.99906e11 2.99906e11i −0.379261 0.379261i
\(944\) 3.71675e11i 0.468032i
\(945\) 0 0
\(946\) −6.93724e11 −0.866208
\(947\) 7.18344e11 7.18344e11i 0.893167 0.893167i −0.101653 0.994820i \(-0.532413\pi\)
0.994820 + 0.101653i \(0.0324131\pi\)
\(948\) 5.84034e10 + 5.84034e10i 0.0723111 + 0.0723111i
\(949\) 6.43129e11i 0.792927i
\(950\) 0 0
\(951\) −1.10747e11 −0.135397
\(952\) −4.39167e11 + 4.39167e11i −0.534665 + 0.534665i
\(953\) 3.85444e11 + 3.85444e11i 0.467294 + 0.467294i 0.901037 0.433743i \(-0.142807\pi\)
−0.433743 + 0.901037i \(0.642807\pi\)
\(954\) 4.71176e11i 0.568840i
\(955\) 0 0
\(956\) −3.14118e10 −0.0376064
\(957\) −1.11119e11 + 1.11119e11i −0.132478 + 0.132478i
\(958\) −4.33210e11 4.33210e11i −0.514323 0.514323i
\(959\) 6.30909e11i 0.745920i
\(960\) 0 0
\(961\) 3.65635e11 0.428700
\(962\) 2.02745e11 2.02745e11i 0.236728 0.236728i
\(963\) −2.16901e11 2.16901e11i −0.252206 0.252206i
\(964\) 8.78034e10i 0.101672i
\(965\) 0 0
\(966\) 1.62483e11 0.186595
\(967\) 1.01381e12 1.01381e12i 1.15944 1.15944i 0.174849 0.984595i \(-0.444056\pi\)
0.984595 0.174849i \(-0.0559439\pi\)
\(968\) 4.93993e11 + 4.93993e11i 0.562626 + 0.562626i
\(969\) 5.77975e11i 0.655562i
\(970\) 0 0
\(971\) −1.08935e12 −1.22543 −0.612716 0.790303i \(-0.709923\pi\)
−0.612716 + 0.790303i \(0.709923\pi\)
\(972\) −3.89273e9 + 3.89273e9i −0.00436103 + 0.00436103i
\(973\) 5.37560e11 + 5.37560e11i 0.599758 + 0.599758i
\(974\) 5.98744e11i 0.665281i
\(975\) 0 0
\(976\) 4.85765e11 0.535336
\(977\) −8.57679e11 + 8.57679e11i −0.941340 + 0.941340i −0.998372 0.0570321i \(-0.981836\pi\)
0.0570321 + 0.998372i \(0.481836\pi\)
\(978\) −9.71160e10 9.71160e10i −0.106154 0.106154i
\(979\) 6.12698e11i 0.666984i
\(980\) 0 0
\(981\) 2.02988e11 0.219177
\(982\) −3.75337e11 + 3.75337e11i −0.403622 + 0.403622i
\(983\) 7.84557e11 + 7.84557e11i 0.840253 + 0.840253i 0.988892 0.148638i \(-0.0474890\pi\)
−0.148638 + 0.988892i \(0.547489\pi\)
\(984\) 5.17193e11i 0.551661i
\(985\) 0 0
\(986\) −7.48654e11 −0.792088
\(987\) 6.90470e10 6.90470e10i 0.0727573 0.0727573i
\(988\) −6.28550e10 6.28550e10i −0.0659648 0.0659648i
\(989\) 1.04856e12i 1.09599i
\(990\) 0 0
\(991\) −1.18172e12 −1.22523 −0.612617 0.790380i \(-0.709883\pi\)
−0.612617 + 0.790380i \(0.709883\pi\)
\(992\) −1.56813e11 + 1.56813e11i −0.161933 + 0.161933i
\(993\) 5.85431e11 + 5.85431e11i 0.602114 + 0.602114i
\(994\) 6.84564e11i 0.701243i
\(995\) 0 0
\(996\) 4.01947e10 0.0408443
\(997\) −1.19697e12 + 1.19697e12i −1.21145 + 1.21145i −0.240894 + 0.970552i \(0.577440\pi\)
−0.970552 + 0.240894i \(0.922560\pi\)
\(998\) −8.92246e11 8.92246e11i −0.899420 0.899420i
\(999\) 6.32619e10i 0.0635156i
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 75.9.f.b.43.1 yes 8
5.2 odd 4 inner 75.9.f.b.7.1 8
5.3 odd 4 inner 75.9.f.b.7.4 yes 8
5.4 even 2 inner 75.9.f.b.43.4 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.9.f.b.7.1 8 5.2 odd 4 inner
75.9.f.b.7.4 yes 8 5.3 odd 4 inner
75.9.f.b.43.1 yes 8 1.1 even 1 trivial
75.9.f.b.43.4 yes 8 5.4 even 2 inner