Properties

Label 13.7.d.a.5.1
Level $13$
Weight $7$
Character 13.5
Analytic conductor $2.991$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [13,7,Mod(5,13)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(13, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("13.5");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 13 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 13.d (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: \(2.99070308706\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 18 x^{10} + 488 x^{9} + 36205 x^{8} - 155430 x^{7} + 399962 x^{6} + 9502784 x^{5} + 275595012 x^{4} - 541321656 x^{3} + 523196552 x^{2} + \cdots + 56070144 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 5^{2}\cdot 13^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.1
Root \(9.50218 + 9.50218i\) of defining polynomial
Character \(\chi\) \(=\) 13.5
Dual form 13.7.d.a.8.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-8.50218 + 8.50218i) q^{2} -17.1101 q^{3} -80.5742i q^{4} +(73.6481 - 73.6481i) q^{5} +(145.473 - 145.473i) q^{6} +(-214.232 - 214.232i) q^{7} +(140.917 + 140.917i) q^{8} -436.244 q^{9} +O(q^{10})\) \(q+(-8.50218 + 8.50218i) q^{2} -17.1101 q^{3} -80.5742i q^{4} +(73.6481 - 73.6481i) q^{5} +(145.473 - 145.473i) q^{6} +(-214.232 - 214.232i) q^{7} +(140.917 + 140.917i) q^{8} -436.244 q^{9} +1252.34i q^{10} +(231.998 + 231.998i) q^{11} +1378.63i q^{12} +(-2079.64 - 708.440i) q^{13} +3642.88 q^{14} +(-1260.13 + 1260.13i) q^{15} +2760.55 q^{16} -7527.26i q^{17} +(3709.02 - 3709.02i) q^{18} +(-8308.11 + 8308.11i) q^{19} +(-5934.13 - 5934.13i) q^{20} +(3665.53 + 3665.53i) q^{21} -3944.99 q^{22} -2393.16i q^{23} +(-2411.10 - 2411.10i) q^{24} +4776.92i q^{25} +(23704.8 - 11658.2i) q^{26} +19937.5 q^{27} +(-17261.6 + 17261.6i) q^{28} -923.972 q^{29} -21427.7i q^{30} +(-16413.9 + 16413.9i) q^{31} +(-32489.4 + 32489.4i) q^{32} +(-3969.52 - 3969.52i) q^{33} +(63998.2 + 63998.2i) q^{34} -31555.5 q^{35} +35150.0i q^{36} +(-36119.9 - 36119.9i) q^{37} -141274. i q^{38} +(35583.0 + 12121.5i) q^{39} +20756.5 q^{40} +(44410.3 - 44410.3i) q^{41} -62330.1 q^{42} -97972.1i q^{43} +(18693.1 - 18693.1i) q^{44} +(-32128.5 + 32128.5i) q^{45} +(20347.1 + 20347.1i) q^{46} +(112049. + 112049. i) q^{47} -47233.3 q^{48} -25858.3i q^{49} +(-40614.2 - 40614.2i) q^{50} +128792. i q^{51} +(-57081.9 + 167566. i) q^{52} -57734.9 q^{53} +(-169512. + 169512. i) q^{54} +34172.5 q^{55} -60377.7i q^{56} +(142153. - 142153. i) q^{57} +(7855.78 - 7855.78i) q^{58} +(-57409.6 - 57409.6i) q^{59} +(101534. + 101534. i) q^{60} +413374. q^{61} -279108. i q^{62} +(93457.4 + 93457.4i) q^{63} -375786. i q^{64} +(-205337. + 100987. i) q^{65} +67499.2 q^{66} +(-265261. + 265261. i) q^{67} -606503. q^{68} +40947.3i q^{69} +(268291. - 268291. i) q^{70} +(-28896.4 + 28896.4i) q^{71} +(-61474.0 - 61474.0i) q^{72} +(-395624. - 395624. i) q^{73} +614195. q^{74} -81733.7i q^{75} +(669419. + 669419. i) q^{76} -99403.0i q^{77} +(-405592. + 199474. i) q^{78} -419351. q^{79} +(203309. - 203309. i) q^{80} -23110.5 q^{81} +755169. i q^{82} +(59175.0 - 59175.0i) q^{83} +(295347. - 295347. i) q^{84} +(-554369. - 554369. i) q^{85} +(832977. + 832977. i) q^{86} +15809.3 q^{87} +65384.9i q^{88} +(-61088.3 - 61088.3i) q^{89} -546325. i q^{90} +(293756. + 597297. i) q^{91} -192827. q^{92} +(280844. - 280844. i) q^{93} -1.90533e6 q^{94} +1.22375e6i q^{95} +(555897. - 555897. i) q^{96} +(-235474. + 235474. i) q^{97} +(219852. + 219852. i) q^{98} +(-101208. - 101208. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{2} - 4 q^{3} + 108 q^{5} - 640 q^{6} + 398 q^{7} - 912 q^{8} + 1940 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{2} - 4 q^{3} + 108 q^{5} - 640 q^{6} + 398 q^{7} - 912 q^{8} + 1940 q^{9} + 1686 q^{11} - 3926 q^{13} + 5484 q^{14} - 15268 q^{15} + 2132 q^{16} + 15254 q^{18} + 1766 q^{19} - 19044 q^{20} + 3428 q^{21} + 28832 q^{22} + 31608 q^{24} - 58266 q^{26} - 20464 q^{27} + 4092 q^{28} - 90108 q^{29} + 61014 q^{31} - 64932 q^{32} - 44452 q^{33} + 259896 q^{34} + 158772 q^{35} - 40212 q^{37} + 137852 q^{39} - 104196 q^{40} - 190416 q^{41} - 959204 q^{42} + 489372 q^{44} - 151444 q^{45} - 44412 q^{46} + 562446 q^{47} + 930308 q^{48} + 82422 q^{50} - 578500 q^{52} + 509136 q^{53} - 871432 q^{54} - 1264036 q^{55} + 939908 q^{57} - 1019980 q^{58} - 994458 q^{59} + 2407804 q^{60} + 1013696 q^{61} + 865778 q^{63} - 1130064 q^{65} - 418352 q^{66} - 1442386 q^{67} - 2313132 q^{68} + 2958968 q^{70} - 655866 q^{71} - 1706508 q^{72} + 2588228 q^{73} + 3373752 q^{74} + 246984 q^{76} + 77480 q^{78} - 75316 q^{79} - 2685408 q^{80} - 4016140 q^{81} + 894966 q^{83} - 3220504 q^{84} + 105396 q^{85} + 3704832 q^{86} + 2109064 q^{87} - 977376 q^{89} + 1088750 q^{91} + 3682872 q^{92} - 216268 q^{93} - 6238300 q^{94} + 896384 q^{96} + 983388 q^{97} + 1039302 q^{98} + 2894714 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.50218 + 8.50218i −1.06277 + 1.06277i −0.0648795 + 0.997893i \(0.520666\pi\)
−0.997893 + 0.0648795i \(0.979334\pi\)
\(3\) −17.1101 −0.633708 −0.316854 0.948474i \(-0.602627\pi\)
−0.316854 + 0.948474i \(0.602627\pi\)
\(4\) 80.5742i 1.25897i
\(5\) 73.6481 73.6481i 0.589185 0.589185i −0.348226 0.937411i \(-0.613216\pi\)
0.937411 + 0.348226i \(0.113216\pi\)
\(6\) 145.473 145.473i 0.673488 0.673488i
\(7\) −214.232 214.232i −0.624583 0.624583i 0.322117 0.946700i \(-0.395606\pi\)
−0.946700 + 0.322117i \(0.895606\pi\)
\(8\) 140.917 + 140.917i 0.275228 + 0.275228i
\(9\) −436.244 −0.598414
\(10\) 1252.34i 1.25234i
\(11\) 231.998 + 231.998i 0.174304 + 0.174304i 0.788867 0.614563i \(-0.210668\pi\)
−0.614563 + 0.788867i \(0.710668\pi\)
\(12\) 1378.63i 0.797820i
\(13\) −2079.64 708.440i −0.946584 0.322458i
\(14\) 3642.88 1.32758
\(15\) −1260.13 + 1260.13i −0.373371 + 0.373371i
\(16\) 2760.55 0.673962
\(17\) 7527.26i 1.53211i −0.642774 0.766056i \(-0.722217\pi\)
0.642774 0.766056i \(-0.277783\pi\)
\(18\) 3709.02 3709.02i 0.635978 0.635978i
\(19\) −8308.11 + 8308.11i −1.21127 + 1.21127i −0.240662 + 0.970609i \(0.577364\pi\)
−0.970609 + 0.240662i \(0.922636\pi\)
\(20\) −5934.13 5934.13i −0.741767 0.741767i
\(21\) 3665.53 + 3665.53i 0.395803 + 0.395803i
\(22\) −3944.99 −0.370491
\(23\) 2393.16i 0.196693i −0.995152 0.0983465i \(-0.968645\pi\)
0.995152 0.0983465i \(-0.0313554\pi\)
\(24\) −2411.10 2411.10i −0.174414 0.174414i
\(25\) 4776.92i 0.305723i
\(26\) 23704.8 11658.2i 1.34870 0.663304i
\(27\) 19937.5 1.01293
\(28\) −17261.6 + 17261.6i −0.786332 + 0.786332i
\(29\) −923.972 −0.0378848 −0.0189424 0.999821i \(-0.506030\pi\)
−0.0189424 + 0.999821i \(0.506030\pi\)
\(30\) 21427.7i 0.793617i
\(31\) −16413.9 + 16413.9i −0.550968 + 0.550968i −0.926720 0.375752i \(-0.877384\pi\)
0.375752 + 0.926720i \(0.377384\pi\)
\(32\) −32489.4 + 32489.4i −0.991497 + 0.991497i
\(33\) −3969.52 3969.52i −0.110458 0.110458i
\(34\) 63998.2 + 63998.2i 1.62829 + 1.62829i
\(35\) −31555.5 −0.735989
\(36\) 35150.0i 0.753386i
\(37\) −36119.9 36119.9i −0.713085 0.713085i 0.254095 0.967179i \(-0.418222\pi\)
−0.967179 + 0.254095i \(0.918222\pi\)
\(38\) 141274.i 2.57461i
\(39\) 35583.0 + 12121.5i 0.599858 + 0.204344i
\(40\) 20756.5 0.324320
\(41\) 44410.3 44410.3i 0.644366 0.644366i −0.307260 0.951626i \(-0.599412\pi\)
0.951626 + 0.307260i \(0.0994121\pi\)
\(42\) −62330.1 −0.841298
\(43\) 97972.1i 1.23225i −0.787650 0.616123i \(-0.788703\pi\)
0.787650 0.616123i \(-0.211297\pi\)
\(44\) 18693.1 18693.1i 0.219444 0.219444i
\(45\) −32128.5 + 32128.5i −0.352576 + 0.352576i
\(46\) 20347.1 + 20347.1i 0.209040 + 0.209040i
\(47\) 112049. + 112049.i 1.07923 + 1.07923i 0.996578 + 0.0826547i \(0.0263398\pi\)
0.0826547 + 0.996578i \(0.473660\pi\)
\(48\) −47233.3 −0.427095
\(49\) 25858.3i 0.219792i
\(50\) −40614.2 40614.2i −0.324914 0.324914i
\(51\) 128792.i 0.970912i
\(52\) −57081.9 + 167566.i −0.405965 + 1.19172i
\(53\) −57734.9 −0.387803 −0.193901 0.981021i \(-0.562114\pi\)
−0.193901 + 0.981021i \(0.562114\pi\)
\(54\) −169512. + 169512.i −1.07651 + 1.07651i
\(55\) 34172.5 0.205394
\(56\) 60377.7i 0.343805i
\(57\) 142153. 142153.i 0.767592 0.767592i
\(58\) 7855.78 7855.78i 0.0402629 0.0402629i
\(59\) −57409.6 57409.6i −0.279530 0.279530i 0.553391 0.832921i \(-0.313333\pi\)
−0.832921 + 0.553391i \(0.813333\pi\)
\(60\) 101534. + 101534.i 0.470064 + 0.470064i
\(61\) 413374. 1.82118 0.910591 0.413309i \(-0.135627\pi\)
0.910591 + 0.413309i \(0.135627\pi\)
\(62\) 279108.i 1.17111i
\(63\) 93457.4 + 93457.4i 0.373759 + 0.373759i
\(64\) 375786.i 1.43351i
\(65\) −205337. + 100987.i −0.747700 + 0.367725i
\(66\) 67499.2 0.234783
\(67\) −265261. + 265261.i −0.881960 + 0.881960i −0.993734 0.111774i \(-0.964347\pi\)
0.111774 + 0.993734i \(0.464347\pi\)
\(68\) −606503. −1.92888
\(69\) 40947.3i 0.124646i
\(70\) 268291. 268291.i 0.782189 0.782189i
\(71\) −28896.4 + 28896.4i −0.0807364 + 0.0807364i −0.746322 0.665585i \(-0.768182\pi\)
0.665585 + 0.746322i \(0.268182\pi\)
\(72\) −61474.0 61474.0i −0.164700 0.164700i
\(73\) −395624. 395624.i −1.01698 1.01698i −0.999853 0.0171315i \(-0.994547\pi\)
−0.0171315 0.999853i \(-0.505453\pi\)
\(74\) 614195. 1.51569
\(75\) 81733.7i 0.193739i
\(76\) 669419. + 669419.i 1.52496 + 1.52496i
\(77\) 99403.0i 0.217734i
\(78\) −405592. + 199474.i −0.854684 + 0.420341i
\(79\) −419351. −0.850543 −0.425271 0.905066i \(-0.639821\pi\)
−0.425271 + 0.905066i \(0.639821\pi\)
\(80\) 203309. 203309.i 0.397088 0.397088i
\(81\) −23110.5 −0.0434865
\(82\) 755169.i 1.36963i
\(83\) 59175.0 59175.0i 0.103491 0.103491i −0.653465 0.756957i \(-0.726685\pi\)
0.756957 + 0.653465i \(0.226685\pi\)
\(84\) 295347. 295347.i 0.498305 0.498305i
\(85\) −554369. 554369.i −0.902697 0.902697i
\(86\) 832977. + 832977.i 1.30960 + 1.30960i
\(87\) 15809.3 0.0240079
\(88\) 65384.9i 0.0959465i
\(89\) −61088.3 61088.3i −0.0866538 0.0866538i 0.662451 0.749105i \(-0.269516\pi\)
−0.749105 + 0.662451i \(0.769516\pi\)
\(90\) 546325.i 0.749417i
\(91\) 293756. + 597297.i 0.389818 + 0.792622i
\(92\) −192827. −0.247631
\(93\) 280844. 280844.i 0.349153 0.349153i
\(94\) −1.90533e6 −2.29396
\(95\) 1.22375e6i 1.42732i
\(96\) 555897. 555897.i 0.628319 0.628319i
\(97\) −235474. + 235474.i −0.258004 + 0.258004i −0.824242 0.566238i \(-0.808398\pi\)
0.566238 + 0.824242i \(0.308398\pi\)
\(98\) 219852. + 219852.i 0.233589 + 0.233589i
\(99\) −101208. 101208.i −0.104306 0.104306i
\(100\) 384896. 0.384896
\(101\) 1.08351e6i 1.05165i −0.850594 0.525823i \(-0.823757\pi\)
0.850594 0.525823i \(-0.176243\pi\)
\(102\) −1.09502e6 1.09502e6i −1.03186 1.03186i
\(103\) 228949.i 0.209521i 0.994497 + 0.104760i \(0.0334076\pi\)
−0.994497 + 0.104760i \(0.966592\pi\)
\(104\) −193226. 392887.i −0.171777 0.349275i
\(105\) 539919. 0.466402
\(106\) 490873. 490873.i 0.412146 0.412146i
\(107\) 1.77111e6 1.44575 0.722876 0.690978i \(-0.242820\pi\)
0.722876 + 0.690978i \(0.242820\pi\)
\(108\) 1.60644e6i 1.27525i
\(109\) 539118. 539118.i 0.416298 0.416298i −0.467627 0.883926i \(-0.654891\pi\)
0.883926 + 0.467627i \(0.154891\pi\)
\(110\) −290541. + 290541.i −0.218288 + 0.218288i
\(111\) 618015. + 618015.i 0.451887 + 0.451887i
\(112\) −591398. 591398.i −0.420945 0.420945i
\(113\) −1.11945e6 −0.775832 −0.387916 0.921695i \(-0.626805\pi\)
−0.387916 + 0.921695i \(0.626805\pi\)
\(114\) 2.41722e6i 1.63155i
\(115\) −176252. 176252.i −0.115889 0.115889i
\(116\) 74448.3i 0.0476959i
\(117\) 907232. + 309052.i 0.566449 + 0.192963i
\(118\) 976214. 0.594154
\(119\) −1.61258e6 + 1.61258e6i −0.956931 + 0.956931i
\(120\) −355146. −0.205524
\(121\) 1.66391e6i 0.939236i
\(122\) −3.51458e6 + 3.51458e6i −1.93550 + 1.93550i
\(123\) −759866. + 759866.i −0.408340 + 0.408340i
\(124\) 1.32254e6 + 1.32254e6i 0.693653 + 0.693653i
\(125\) 1.50256e6 + 1.50256e6i 0.769312 + 0.769312i
\(126\) −1.58918e6 −0.794442
\(127\) 2.01939e6i 0.985846i −0.870073 0.492923i \(-0.835928\pi\)
0.870073 0.492923i \(-0.164072\pi\)
\(128\) 1.11568e6 + 1.11568e6i 0.531997 + 0.531997i
\(129\) 1.67631e6i 0.780884i
\(130\) 887207. 2.60442e6i 0.403826 1.18544i
\(131\) 589259. 0.262115 0.131058 0.991375i \(-0.458163\pi\)
0.131058 + 0.991375i \(0.458163\pi\)
\(132\) −319841. + 319841.i −0.139063 + 0.139063i
\(133\) 3.55972e6 1.51308
\(134\) 4.51059e6i 1.87465i
\(135\) 1.46836e6 1.46836e6i 0.596802 0.596802i
\(136\) 1.06072e6 1.06072e6i 0.421680 0.421680i
\(137\) −2.66749e6 2.66749e6i −1.03739 1.03739i −0.999273 0.0381144i \(-0.987865\pi\)
−0.0381144 0.999273i \(-0.512135\pi\)
\(138\) −348142. 348142.i −0.132470 0.132470i
\(139\) −1.55840e6 −0.580277 −0.290139 0.956985i \(-0.593701\pi\)
−0.290139 + 0.956985i \(0.593701\pi\)
\(140\) 2.54256e6i 0.926590i
\(141\) −1.91718e6 1.91718e6i −0.683919 0.683919i
\(142\) 491366.i 0.171609i
\(143\) −318117. 646831.i −0.108788 0.221199i
\(144\) −1.20427e6 −0.403309
\(145\) −68048.8 + 68048.8i −0.0223211 + 0.0223211i
\(146\) 6.72734e6 2.16165
\(147\) 442439.i 0.139284i
\(148\) −2.91033e6 + 2.91033e6i −0.897753 + 0.897753i
\(149\) −962956. + 962956.i −0.291104 + 0.291104i −0.837516 0.546413i \(-0.815993\pi\)
0.546413 + 0.837516i \(0.315993\pi\)
\(150\) 694914. + 694914.i 0.205901 + 0.205901i
\(151\) −2.31936e6 2.31936e6i −0.673655 0.673655i 0.284902 0.958557i \(-0.408039\pi\)
−0.958557 + 0.284902i \(0.908039\pi\)
\(152\) −2.34150e6 −0.666751
\(153\) 3.28372e6i 0.916837i
\(154\) 845142. + 845142.i 0.231402 + 0.231402i
\(155\) 2.41770e6i 0.649244i
\(156\) 976679. 2.86707e6i 0.257263 0.755204i
\(157\) −3.16541e6 −0.817958 −0.408979 0.912544i \(-0.634115\pi\)
−0.408979 + 0.912544i \(0.634115\pi\)
\(158\) 3.56540e6 3.56540e6i 0.903934 0.903934i
\(159\) 987851. 0.245754
\(160\) 4.78556e6i 1.16835i
\(161\) −512692. + 512692.i −0.122851 + 0.122851i
\(162\) 196490. 196490.i 0.0462163 0.0462163i
\(163\) 3.38001e6 + 3.38001e6i 0.780467 + 0.780467i 0.979910 0.199442i \(-0.0639130\pi\)
−0.199442 + 0.979910i \(0.563913\pi\)
\(164\) −3.57833e6 3.57833e6i −0.811238 0.811238i
\(165\) −584695. −0.130160
\(166\) 1.00623e6i 0.219976i
\(167\) −3.82024e6 3.82024e6i −0.820241 0.820241i 0.165902 0.986142i \(-0.446947\pi\)
−0.986142 + 0.165902i \(0.946947\pi\)
\(168\) 1.03307e6i 0.217872i
\(169\) 3.82304e6 + 2.94661e6i 0.792042 + 0.610467i
\(170\) 9.42668e6 1.91872
\(171\) 3.62436e6 3.62436e6i 0.724842 0.724842i
\(172\) −7.89402e6 −1.55136
\(173\) 7.45195e6i 1.43923i 0.694371 + 0.719617i \(0.255683\pi\)
−0.694371 + 0.719617i \(0.744317\pi\)
\(174\) −134413. + 134413.i −0.0255149 + 0.0255149i
\(175\) 1.02337e6 1.02337e6i 0.190949 0.190949i
\(176\) 640443. + 640443.i 0.117474 + 0.117474i
\(177\) 982285. + 982285.i 0.177141 + 0.177141i
\(178\) 1.03877e6 0.184187
\(179\) 9.93321e6i 1.73193i −0.500104 0.865966i \(-0.666705\pi\)
0.500104 0.865966i \(-0.333295\pi\)
\(180\) 2.58873e6 + 2.58873e6i 0.443884 + 0.443884i
\(181\) 8.22334e6i 1.38680i 0.720555 + 0.693398i \(0.243887\pi\)
−0.720555 + 0.693398i \(0.756113\pi\)
\(182\) −7.57589e6 2.58076e6i −1.25667 0.428088i
\(183\) −7.07287e6 −1.15410
\(184\) 337237. 337237.i 0.0541354 0.0541354i
\(185\) −5.32032e6 −0.840277
\(186\) 4.77557e6i 0.742141i
\(187\) 1.74631e6 1.74631e6i 0.267053 0.267053i
\(188\) 9.02827e6 9.02827e6i 1.35872 1.35872i
\(189\) −4.27124e6 4.27124e6i −0.632657 0.632657i
\(190\) −1.04046e7 1.04046e7i −1.51692 1.51692i
\(191\) −1.03422e6 −0.148427 −0.0742136 0.997242i \(-0.523645\pi\)
−0.0742136 + 0.997242i \(0.523645\pi\)
\(192\) 6.42974e6i 0.908426i
\(193\) 5.78870e6 + 5.78870e6i 0.805210 + 0.805210i 0.983905 0.178695i \(-0.0571875\pi\)
−0.178695 + 0.983905i \(0.557187\pi\)
\(194\) 4.00408e6i 0.548400i
\(195\) 3.51334e6 1.72789e6i 0.473823 0.233031i
\(196\) −2.08351e6 −0.276712
\(197\) 3.82189e6 3.82189e6i 0.499896 0.499896i −0.411510 0.911405i \(-0.634998\pi\)
0.911405 + 0.411510i \(0.134998\pi\)
\(198\) 1.72098e6 0.221707
\(199\) 893097.i 0.113329i 0.998393 + 0.0566643i \(0.0180465\pi\)
−0.998393 + 0.0566643i \(0.981954\pi\)
\(200\) −673147. + 673147.i −0.0841434 + 0.0841434i
\(201\) 4.53865e6 4.53865e6i 0.558905 0.558905i
\(202\) 9.21222e6 + 9.21222e6i 1.11766 + 1.11766i
\(203\) 197944. + 197944.i 0.0236622 + 0.0236622i
\(204\) 1.03773e7 1.22235
\(205\) 6.54147e6i 0.759301i
\(206\) −1.94657e6 1.94657e6i −0.222673 0.222673i
\(207\) 1.04400e6i 0.117704i
\(208\) −5.74096e6 1.95568e6i −0.637962 0.217324i
\(209\) −3.85494e6 −0.422258
\(210\) −4.59049e6 + 4.59049e6i −0.495680 + 0.495680i
\(211\) −92262.9 −0.00982154 −0.00491077 0.999988i \(-0.501563\pi\)
−0.00491077 + 0.999988i \(0.501563\pi\)
\(212\) 4.65194e6i 0.488233i
\(213\) 494422. 494422.i 0.0511633 0.0511633i
\(214\) −1.50583e7 + 1.50583e7i −1.53651 + 1.53651i
\(215\) −7.21546e6 7.21546e6i −0.726020 0.726020i
\(216\) 2.80952e6 + 2.80952e6i 0.278786 + 0.278786i
\(217\) 7.03276e6 0.688251
\(218\) 9.16736e6i 0.884861i
\(219\) 6.76918e6 + 6.76918e6i 0.644471 + 0.644471i
\(220\) 2.75342e6i 0.258586i
\(221\) −5.33261e6 + 1.56540e7i −0.494041 + 1.45027i
\(222\) −1.05090e7 −0.960507
\(223\) −8.85625e6 + 8.85625e6i −0.798611 + 0.798611i −0.982876 0.184266i \(-0.941009\pi\)
0.184266 + 0.982876i \(0.441009\pi\)
\(224\) 1.39205e7 1.23854
\(225\) 2.08390e6i 0.182949i
\(226\) 9.51773e6 9.51773e6i 0.824533 0.824533i
\(227\) 7.90170e6 7.90170e6i 0.675527 0.675527i −0.283457 0.958985i \(-0.591481\pi\)
0.958985 + 0.283457i \(0.0914815\pi\)
\(228\) −1.14538e7 1.14538e7i −0.966377 0.966377i
\(229\) 2.28875e6 + 2.28875e6i 0.190587 + 0.190587i 0.795950 0.605363i \(-0.206972\pi\)
−0.605363 + 0.795950i \(0.706972\pi\)
\(230\) 2.99705e6 0.246326
\(231\) 1.70080e6i 0.137980i
\(232\) −130203. 130203.i −0.0104269 0.0104269i
\(233\) 1.13768e7i 0.899401i −0.893179 0.449701i \(-0.851531\pi\)
0.893179 0.449701i \(-0.148469\pi\)
\(234\) −1.03411e7 + 5.08583e6i −0.807083 + 0.396931i
\(235\) 1.65044e7 1.27173
\(236\) −4.62573e6 + 4.62573e6i −0.351920 + 0.351920i
\(237\) 7.17514e6 0.538996
\(238\) 2.74209e7i 2.03400i
\(239\) −7.79723e6 + 7.79723e6i −0.571145 + 0.571145i −0.932448 0.361303i \(-0.882332\pi\)
0.361303 + 0.932448i \(0.382332\pi\)
\(240\) −3.47864e6 + 3.47864e6i −0.251638 + 0.251638i
\(241\) 81950.5 + 81950.5i 0.00585464 + 0.00585464i 0.710028 0.704173i \(-0.248682\pi\)
−0.704173 + 0.710028i \(0.748682\pi\)
\(242\) 1.41469e7 + 1.41469e7i 0.998195 + 0.998195i
\(243\) −1.41390e7 −0.985370
\(244\) 3.33072e7i 2.29282i
\(245\) −1.90442e6 1.90442e6i −0.129498 0.129498i
\(246\) 1.29210e7i 0.867945i
\(247\) 2.31637e7 1.13921e7i 1.53715 0.755986i
\(248\) −4.62598e6 −0.303284
\(249\) −1.01249e6 + 1.01249e6i −0.0655833 + 0.0655833i
\(250\) −2.55501e7 −1.63521
\(251\) 9.96309e6i 0.630047i −0.949084 0.315023i \(-0.897988\pi\)
0.949084 0.315023i \(-0.102012\pi\)
\(252\) 7.53025e6 7.53025e6i 0.470552 0.470552i
\(253\) 555210. 555210.i 0.0342844 0.0342844i
\(254\) 1.71692e7 + 1.71692e7i 1.04773 + 1.04773i
\(255\) 9.48531e6 + 9.48531e6i 0.572046 + 0.572046i
\(256\) 5.07888e6 0.302725
\(257\) 1.76493e7i 1.03975i 0.854242 + 0.519875i \(0.174022\pi\)
−0.854242 + 0.519875i \(0.825978\pi\)
\(258\) −1.42523e7 1.42523e7i −0.829902 0.829902i
\(259\) 1.54761e7i 0.890761i
\(260\) 8.13691e6 + 1.65449e7i 0.462956 + 0.941333i
\(261\) 403077. 0.0226708
\(262\) −5.00999e6 + 5.00999e6i −0.278569 + 0.278569i
\(263\) −2.69228e7 −1.47997 −0.739985 0.672624i \(-0.765167\pi\)
−0.739985 + 0.672624i \(0.765167\pi\)
\(264\) 1.11874e6i 0.0608021i
\(265\) −4.25207e6 + 4.25207e6i −0.228487 + 0.228487i
\(266\) −3.02654e7 + 3.02654e7i −1.60806 + 1.60806i
\(267\) 1.04523e6 + 1.04523e6i 0.0549132 + 0.0549132i
\(268\) 2.13732e7 + 2.13732e7i 1.11036 + 1.11036i
\(269\) −2.28689e7 −1.17487 −0.587433 0.809273i \(-0.699861\pi\)
−0.587433 + 0.809273i \(0.699861\pi\)
\(270\) 2.49685e7i 1.26853i
\(271\) −1.13591e7 1.13591e7i −0.570736 0.570736i 0.361598 0.932334i \(-0.382231\pi\)
−0.932334 + 0.361598i \(0.882231\pi\)
\(272\) 2.07794e7i 1.03259i
\(273\) −5.02620e6 1.02198e7i −0.247031 0.502291i
\(274\) 4.53590e7 2.20501
\(275\) −1.10824e6 + 1.10824e6i −0.0532887 + 0.0532887i
\(276\) 3.29930e6 0.156926
\(277\) 1.30080e7i 0.612028i −0.952027 0.306014i \(-0.901005\pi\)
0.952027 0.306014i \(-0.0989955\pi\)
\(278\) 1.32498e7 1.32498e7i 0.616703 0.616703i
\(279\) 7.16046e6 7.16046e6i 0.329707 0.329707i
\(280\) −4.44670e6 4.44670e6i −0.202565 0.202565i
\(281\) 2.37985e7 + 2.37985e7i 1.07258 + 1.07258i 0.997151 + 0.0754330i \(0.0240339\pi\)
0.0754330 + 0.997151i \(0.475966\pi\)
\(282\) 3.26003e7 1.45370
\(283\) 1.24423e7i 0.548959i −0.961593 0.274480i \(-0.911494\pi\)
0.961593 0.274480i \(-0.0885056\pi\)
\(284\) 2.32831e6 + 2.32831e6i 0.101645 + 0.101645i
\(285\) 2.09385e7i 0.904507i
\(286\) 8.20417e6 + 2.79479e6i 0.350701 + 0.119468i
\(287\) −1.90282e7 −0.804920
\(288\) 1.41733e7 1.41733e7i 0.593325 0.593325i
\(289\) −3.25221e7 −1.34737
\(290\) 1.15713e6i 0.0474446i
\(291\) 4.02898e6 4.02898e6i 0.163499 0.163499i
\(292\) −3.18771e7 + 3.18771e7i −1.28035 + 1.28035i
\(293\) −9.08257e6 9.08257e6i −0.361082 0.361082i 0.503129 0.864211i \(-0.332182\pi\)
−0.864211 + 0.503129i \(0.832182\pi\)
\(294\) −3.76170e6 3.76170e6i −0.148027 0.148027i
\(295\) −8.45622e6 −0.329390
\(296\) 1.01798e7i 0.392521i
\(297\) 4.62546e6 + 4.62546e6i 0.176557 + 0.176557i
\(298\) 1.63745e7i 0.618754i
\(299\) −1.69541e6 + 4.97693e6i −0.0634252 + 0.186186i
\(300\) −6.58562e6 −0.243912
\(301\) −2.09888e7 + 2.09888e7i −0.769639 + 0.769639i
\(302\) 3.94392e7 1.43188
\(303\) 1.85390e7i 0.666437i
\(304\) −2.29349e7 + 2.29349e7i −0.816351 + 0.816351i
\(305\) 3.04442e7 3.04442e7i 1.07301 1.07301i
\(306\) −2.79188e7 2.79188e7i −0.974389 0.974389i
\(307\) −9.60324e6 9.60324e6i −0.331897 0.331897i 0.521410 0.853306i \(-0.325406\pi\)
−0.853306 + 0.521410i \(0.825406\pi\)
\(308\) −8.00931e6 −0.274121
\(309\) 3.91735e6i 0.132775i
\(310\) −2.05558e7 2.05558e7i −0.689999 0.689999i
\(311\) 3.04628e7i 1.01272i 0.862323 + 0.506359i \(0.169009\pi\)
−0.862323 + 0.506359i \(0.830991\pi\)
\(312\) 3.30611e6 + 6.72235e6i 0.108856 + 0.221339i
\(313\) 2.06729e7 0.674170 0.337085 0.941474i \(-0.390559\pi\)
0.337085 + 0.941474i \(0.390559\pi\)
\(314\) 2.69129e7 2.69129e7i 0.869303 0.869303i
\(315\) 1.37659e7 0.440426
\(316\) 3.37888e7i 1.07081i
\(317\) 3.69040e7 3.69040e7i 1.15850 1.15850i 0.173701 0.984798i \(-0.444427\pi\)
0.984798 0.173701i \(-0.0555727\pi\)
\(318\) −8.39889e6 + 8.39889e6i −0.261180 + 0.261180i
\(319\) −214360. 214360.i −0.00660347 0.00660347i
\(320\) −2.76759e7 2.76759e7i −0.844601 0.844601i
\(321\) −3.03039e7 −0.916184
\(322\) 8.71800e6i 0.261126i
\(323\) 6.25373e7 + 6.25373e7i 1.85580 + 1.85580i
\(324\) 1.86211e6i 0.0547483i
\(325\) 3.38416e6 9.93430e6i 0.0985827 0.289392i
\(326\) −5.74749e7 −1.65892
\(327\) −9.22438e6 + 9.22438e6i −0.263812 + 0.263812i
\(328\) 1.25163e7 0.354695
\(329\) 4.80090e7i 1.34814i
\(330\) 4.97119e6 4.97119e6i 0.138331 0.138331i
\(331\) 1.82030e7 1.82030e7i 0.501949 0.501949i −0.410094 0.912043i \(-0.634504\pi\)
0.912043 + 0.410094i \(0.134504\pi\)
\(332\) −4.76798e6 4.76798e6i −0.130293 0.130293i
\(333\) 1.57571e7 + 1.57571e7i 0.426720 + 0.426720i
\(334\) 6.49608e7 1.74346
\(335\) 3.90719e7i 1.03927i
\(336\) 1.01189e7 + 1.01189e7i 0.266757 + 0.266757i
\(337\) 2.14657e7i 0.560860i 0.959874 + 0.280430i \(0.0904771\pi\)
−0.959874 + 0.280430i \(0.909523\pi\)
\(338\) −5.75567e7 + 7.45156e6i −1.49055 + 0.192973i
\(339\) 1.91538e7 0.491651
\(340\) −4.46678e7 + 4.46678e7i −1.13647 + 1.13647i
\(341\) −7.61600e6 −0.192072
\(342\) 6.16299e7i 1.54068i
\(343\) −3.07439e7 + 3.07439e7i −0.761861 + 0.761861i
\(344\) 1.38059e7 1.38059e7i 0.339148 0.339148i
\(345\) 3.01569e6 + 3.01569e6i 0.0734395 + 0.0734395i
\(346\) −6.33578e7 6.33578e7i −1.52958 1.52958i
\(347\) 5.37467e7 1.28636 0.643181 0.765714i \(-0.277614\pi\)
0.643181 + 0.765714i \(0.277614\pi\)
\(348\) 1.27382e6i 0.0302253i
\(349\) 3.37710e7 + 3.37710e7i 0.794452 + 0.794452i 0.982214 0.187762i \(-0.0601235\pi\)
−0.187762 + 0.982214i \(0.560123\pi\)
\(350\) 1.74017e7i 0.405871i
\(351\) −4.14628e7 1.41245e7i −0.958821 0.326626i
\(352\) −1.50750e7 −0.345643
\(353\) 9.93725e6 9.93725e6i 0.225914 0.225914i −0.585070 0.810983i \(-0.698933\pi\)
0.810983 + 0.585070i \(0.198933\pi\)
\(354\) −1.67031e7 −0.376520
\(355\) 4.25634e6i 0.0951373i
\(356\) −4.92214e6 + 4.92214e6i −0.109095 + 0.109095i
\(357\) 2.75914e7 2.75914e7i 0.606415 0.606415i
\(358\) 8.44540e7 + 8.44540e7i 1.84065 + 1.84065i
\(359\) −3.97856e7 3.97856e7i −0.859890 0.859890i 0.131435 0.991325i \(-0.458042\pi\)
−0.991325 + 0.131435i \(0.958042\pi\)
\(360\) −9.05488e6 −0.194078
\(361\) 9.10034e7i 1.93435i
\(362\) −6.99163e7 6.99163e7i −1.47385 1.47385i
\(363\) 2.84698e7i 0.595202i
\(364\) 4.81267e7 2.36691e7i 0.997888 0.490770i
\(365\) −5.82739e7 −1.19838
\(366\) 6.01348e7 6.01348e7i 1.22654 1.22654i
\(367\) −2.88272e7 −0.583183 −0.291591 0.956543i \(-0.594185\pi\)
−0.291591 + 0.956543i \(0.594185\pi\)
\(368\) 6.60645e6i 0.132564i
\(369\) −1.93737e7 + 1.93737e7i −0.385597 + 0.385597i
\(370\) 4.52343e7 4.52343e7i 0.893023 0.893023i
\(371\) 1.23687e7 + 1.23687e7i 0.242215 + 0.242215i
\(372\) −2.26287e7 2.26287e7i −0.439574 0.439574i
\(373\) −1.80799e7 −0.348393 −0.174196 0.984711i \(-0.555733\pi\)
−0.174196 + 0.984711i \(0.555733\pi\)
\(374\) 2.96950e7i 0.567633i
\(375\) −2.57090e7 2.57090e7i −0.487519 0.487519i
\(376\) 3.15792e7i 0.594070i
\(377\) 1.92153e6 + 654579.i 0.0358611 + 0.0122162i
\(378\) 7.26297e7 1.34474
\(379\) 3.50989e7 3.50989e7i 0.644727 0.644727i −0.306987 0.951714i \(-0.599321\pi\)
0.951714 + 0.306987i \(0.0993208\pi\)
\(380\) 9.86028e7 1.79696
\(381\) 3.45520e7i 0.624738i
\(382\) 8.79314e6 8.79314e6i 0.157744 0.157744i
\(383\) 2.88898e7 2.88898e7i 0.514219 0.514219i −0.401597 0.915816i \(-0.631545\pi\)
0.915816 + 0.401597i \(0.131545\pi\)
\(384\) −1.90894e7 1.90894e7i −0.337131 0.337131i
\(385\) −7.32084e6 7.32084e6i −0.128286 0.128286i
\(386\) −9.84331e7 −1.71151
\(387\) 4.27397e7i 0.737393i
\(388\) 1.89731e7 + 1.89731e7i 0.324820 + 0.324820i
\(389\) 2.20087e7i 0.373891i −0.982370 0.186945i \(-0.940141\pi\)
0.982370 0.186945i \(-0.0598587\pi\)
\(390\) −1.51802e7 + 4.45619e7i −0.255908 + 0.751225i
\(391\) −1.80140e7 −0.301356
\(392\) 3.64387e6 3.64387e6i 0.0604929 0.0604929i
\(393\) −1.00823e7 −0.166105
\(394\) 6.49888e7i 1.06255i
\(395\) −3.08844e7 + 3.08844e7i −0.501127 + 0.501127i
\(396\) −8.15474e6 + 8.15474e6i −0.131318 + 0.131318i
\(397\) −1.81293e7 1.81293e7i −0.289740 0.289740i 0.547237 0.836977i \(-0.315679\pi\)
−0.836977 + 0.547237i \(0.815679\pi\)
\(398\) −7.59327e6 7.59327e6i −0.120442 0.120442i
\(399\) −6.09073e7 −0.958850
\(400\) 1.31869e7i 0.206046i
\(401\) 1.55442e7 + 1.55442e7i 0.241066 + 0.241066i 0.817291 0.576225i \(-0.195475\pi\)
−0.576225 + 0.817291i \(0.695475\pi\)
\(402\) 7.71768e7i 1.18798i
\(403\) 4.57633e7 2.25068e7i 0.699202 0.343874i
\(404\) −8.73032e7 −1.32399
\(405\) −1.70205e6 + 1.70205e6i −0.0256216 + 0.0256216i
\(406\) −3.36592e6 −0.0502951
\(407\) 1.67595e7i 0.248587i
\(408\) −1.81490e7 + 1.81490e7i −0.267222 + 0.267222i
\(409\) −7.10021e7 + 7.10021e7i −1.03777 + 1.03777i −0.0385117 + 0.999258i \(0.512262\pi\)
−0.999258 + 0.0385117i \(0.987738\pi\)
\(410\) 5.56168e7 + 5.56168e7i 0.806964 + 0.806964i
\(411\) 4.56411e7 + 4.56411e7i 0.657401 + 0.657401i
\(412\) 1.84474e7 0.263781
\(413\) 2.45979e7i 0.349180i
\(414\) −8.87630e6 8.87630e6i −0.125092 0.125092i
\(415\) 8.71626e6i 0.121951i
\(416\) 9.05831e7 4.45496e7i 1.25825 0.618819i
\(417\) 2.66645e7 0.367726
\(418\) 3.27754e7 3.27754e7i 0.448765 0.448765i
\(419\) 8.55705e7 1.16327 0.581637 0.813448i \(-0.302412\pi\)
0.581637 + 0.813448i \(0.302412\pi\)
\(420\) 4.35035e7i 0.587187i
\(421\) −2.05616e6 + 2.05616e6i −0.0275557 + 0.0275557i −0.720750 0.693195i \(-0.756203\pi\)
0.693195 + 0.720750i \(0.256203\pi\)
\(422\) 784436. 784436.i 0.0104381 0.0104381i
\(423\) −4.88808e7 4.88808e7i −0.645828 0.645828i
\(424\) −8.13581e6 8.13581e6i −0.106734 0.106734i
\(425\) 3.59571e7 0.468402
\(426\) 8.40732e6i 0.108750i
\(427\) −8.85578e7 8.85578e7i −1.13748 1.13748i
\(428\) 1.42706e8i 1.82016i
\(429\) 5.44303e6 + 1.10674e7i 0.0689396 + 0.140176i
\(430\) 1.22694e8 1.54319
\(431\) −1.77261e7 + 1.77261e7i −0.221402 + 0.221402i −0.809089 0.587687i \(-0.800039\pi\)
0.587687 + 0.809089i \(0.300039\pi\)
\(432\) 5.50384e7 0.682675
\(433\) 2.97891e7i 0.366939i 0.983025 + 0.183470i \(0.0587329\pi\)
−0.983025 + 0.183470i \(0.941267\pi\)
\(434\) −5.97938e7 + 5.97938e7i −0.731454 + 0.731454i
\(435\) 1.16432e6 1.16432e6i 0.0141451 0.0141451i
\(436\) −4.34390e7 4.34390e7i −0.524108 0.524108i
\(437\) 1.98827e7 + 1.98827e7i 0.238249 + 0.238249i
\(438\) −1.15106e8 −1.36985
\(439\) 3.81149e7i 0.450507i 0.974300 + 0.225254i \(0.0723210\pi\)
−0.974300 + 0.225254i \(0.927679\pi\)
\(440\) 4.81547e6 + 4.81547e6i 0.0565302 + 0.0565302i
\(441\) 1.12805e7i 0.131527i
\(442\) −8.77546e7 1.78432e8i −1.01626 2.06636i
\(443\) −3.81620e6 −0.0438955 −0.0219478 0.999759i \(-0.506987\pi\)
−0.0219478 + 0.999759i \(0.506987\pi\)
\(444\) 4.97961e7 4.97961e7i 0.568913 0.568913i
\(445\) −8.99807e6 −0.102110
\(446\) 1.50595e8i 1.69748i
\(447\) 1.64763e7 1.64763e7i 0.184475 0.184475i
\(448\) −8.05053e7 + 8.05053e7i −0.895345 + 0.895345i
\(449\) 6.41269e6 + 6.41269e6i 0.0708437 + 0.0708437i 0.741641 0.670797i \(-0.234048\pi\)
−0.670797 + 0.741641i \(0.734048\pi\)
\(450\) 1.77177e7 + 1.77177e7i 0.194433 + 0.194433i
\(451\) 2.06063e7 0.224631
\(452\) 9.01984e7i 0.976750i
\(453\) 3.96845e7 + 3.96845e7i 0.426900 + 0.426900i
\(454\) 1.34363e8i 1.43586i
\(455\) 6.56243e7 + 2.23552e7i 0.696676 + 0.237326i
\(456\) 4.00634e7 0.422525
\(457\) −9.92694e7 + 9.92694e7i −1.04008 + 1.04008i −0.0409178 + 0.999163i \(0.513028\pi\)
−0.999163 + 0.0409178i \(0.986972\pi\)
\(458\) −3.89188e7 −0.405101
\(459\) 1.50075e8i 1.55192i
\(460\) −1.42014e7 + 1.42014e7i −0.145900 + 0.145900i
\(461\) −9.89943e6 + 9.89943e6i −0.101043 + 0.101043i −0.755821 0.654778i \(-0.772762\pi\)
0.654778 + 0.755821i \(0.272762\pi\)
\(462\) −1.44605e7 1.44605e7i −0.146641 0.146641i
\(463\) −3.23972e7 3.23972e7i −0.326411 0.326411i 0.524809 0.851220i \(-0.324137\pi\)
−0.851220 + 0.524809i \(0.824137\pi\)
\(464\) −2.55067e6 −0.0255329
\(465\) 4.13672e7i 0.411431i
\(466\) 9.67279e7 + 9.67279e7i 0.955859 + 0.955859i
\(467\) 4.30021e7i 0.422220i 0.977462 + 0.211110i \(0.0677079\pi\)
−0.977462 + 0.211110i \(0.932292\pi\)
\(468\) 2.49016e7 7.30995e7i 0.242935 0.713143i
\(469\) 1.13655e8 1.10171
\(470\) −1.40324e8 + 1.40324e8i −1.35157 + 1.35157i
\(471\) 5.41605e7 0.518346
\(472\) 1.61799e7i 0.153869i
\(473\) 2.27294e7 2.27294e7i 0.214785 0.214785i
\(474\) −6.10043e7 + 6.10043e7i −0.572830 + 0.572830i
\(475\) −3.96872e7 3.96872e7i −0.370313 0.370313i
\(476\) 1.29932e8 + 1.29932e8i 1.20475 + 1.20475i
\(477\) 2.51865e7 0.232067
\(478\) 1.32587e8i 1.21400i
\(479\) −7.79320e7 7.79320e7i −0.709103 0.709103i 0.257243 0.966347i \(-0.417186\pi\)
−0.966347 + 0.257243i \(0.917186\pi\)
\(480\) 8.18815e7i 0.740392i
\(481\) 4.95277e7 + 1.00705e8i 0.445055 + 0.904934i
\(482\) −1.39352e6 −0.0124443
\(483\) 8.77222e6 8.77222e6i 0.0778517 0.0778517i
\(484\) −1.34069e8 −1.18247
\(485\) 3.46843e7i 0.304024i
\(486\) 1.20212e8 1.20212e8i 1.04722 1.04722i
\(487\) 1.40906e6 1.40906e6i 0.0121995 0.0121995i −0.700981 0.713180i \(-0.747254\pi\)
0.713180 + 0.700981i \(0.247254\pi\)
\(488\) 5.82512e7 + 5.82512e7i 0.501240 + 0.501240i
\(489\) −5.78323e7 5.78323e7i −0.494589 0.494589i
\(490\) 3.23834e7 0.275254
\(491\) 3.42671e7i 0.289490i −0.989469 0.144745i \(-0.953764\pi\)
0.989469 0.144745i \(-0.0462362\pi\)
\(492\) 6.12256e7 + 6.12256e7i 0.514088 + 0.514088i
\(493\) 6.95498e6i 0.0580437i
\(494\) −1.00084e8 + 2.93800e8i −0.830203 + 2.43709i
\(495\) −1.49075e7 −0.122911
\(496\) −4.53114e7 + 4.53114e7i −0.371332 + 0.371332i
\(497\) 1.23811e7 0.100853
\(498\) 1.72168e7i 0.139400i
\(499\) 9.89459e7 9.89459e7i 0.796336 0.796336i −0.186180 0.982516i \(-0.559611\pi\)
0.982516 + 0.186180i \(0.0596108\pi\)
\(500\) 1.21068e8 1.21068e8i 0.968542 0.968542i
\(501\) 6.53648e7 + 6.53648e7i 0.519793 + 0.519793i
\(502\) 8.47080e7 + 8.47080e7i 0.669597 + 0.669597i
\(503\) −7.51556e7 −0.590551 −0.295276 0.955412i \(-0.595411\pi\)
−0.295276 + 0.955412i \(0.595411\pi\)
\(504\) 2.63394e7i 0.205738i
\(505\) −7.97986e7 7.97986e7i −0.619614 0.619614i
\(506\) 9.44100e6i 0.0728730i
\(507\) −6.54126e7 5.04168e7i −0.501923 0.386858i
\(508\) −1.62711e8 −1.24115
\(509\) 1.63158e8 1.63158e8i 1.23724 1.23724i 0.276117 0.961124i \(-0.410952\pi\)
0.961124 0.276117i \(-0.0890477\pi\)
\(510\) −1.61292e8 −1.21591
\(511\) 1.69511e8i 1.27038i
\(512\) −1.14585e8 + 1.14585e8i −0.853725 + 0.853725i
\(513\) −1.65643e8 + 1.65643e8i −1.22693 + 1.22693i
\(514\) −1.50058e8 1.50058e8i −1.10502 1.10502i
\(515\) 1.68617e7 + 1.68617e7i 0.123447 + 0.123447i
\(516\) 1.35068e8 0.983110
\(517\) 5.19905e7i 0.376229i
\(518\) −1.31580e8 1.31580e8i −0.946676 0.946676i
\(519\) 1.27504e8i 0.912055i
\(520\) −4.31661e7 1.47047e7i −0.306996 0.104579i
\(521\) 6.71801e6 0.0475037 0.0237518 0.999718i \(-0.492439\pi\)
0.0237518 + 0.999718i \(0.492439\pi\)
\(522\) −3.42704e6 + 3.42704e6i −0.0240939 + 0.0240939i
\(523\) 1.17314e8 0.820060 0.410030 0.912072i \(-0.365518\pi\)
0.410030 + 0.912072i \(0.365518\pi\)
\(524\) 4.74791e7i 0.329996i
\(525\) −1.75100e7 + 1.75100e7i −0.121006 + 0.121006i
\(526\) 2.28902e8 2.28902e8i 1.57287 1.57287i
\(527\) 1.23552e8 + 1.23552e8i 0.844145 + 0.844145i
\(528\) −1.09581e7 1.09581e7i −0.0744444 0.0744444i
\(529\) 1.42309e8 0.961312
\(530\) 7.23037e7i 0.485660i
\(531\) 2.50446e7 + 2.50446e7i 0.167275 + 0.167275i
\(532\) 2.86822e8i 1.90492i
\(533\) −1.23820e8 + 6.08957e7i −0.817727 + 0.402165i
\(534\) −1.77734e7 −0.116721
\(535\) 1.30439e8 1.30439e8i 0.851815 0.851815i
\(536\) −7.47593e7 −0.485480
\(537\) 1.69958e8i 1.09754i
\(538\) 1.94436e8 1.94436e8i 1.24862 1.24862i
\(539\) 5.99910e6 5.99910e6i 0.0383107 0.0383107i
\(540\) −1.18312e8 1.18312e8i −0.751356 0.751356i
\(541\) −2.04171e7 2.04171e7i −0.128944 0.128944i 0.639689 0.768634i \(-0.279063\pi\)
−0.768634 + 0.639689i \(0.779063\pi\)
\(542\) 1.93154e8 1.21312
\(543\) 1.40702e8i 0.878824i
\(544\) 2.44556e8 + 2.44556e8i 1.51908 + 1.51908i
\(545\) 7.94101e7i 0.490553i
\(546\) 1.29624e8 + 4.41571e7i 0.796359 + 0.271283i
\(547\) −2.99984e8 −1.83289 −0.916444 0.400162i \(-0.868954\pi\)
−0.916444 + 0.400162i \(0.868954\pi\)
\(548\) −2.14931e8 + 2.14931e8i −1.30604 + 1.30604i
\(549\) −1.80332e8 −1.08982
\(550\) 1.88449e7i 0.113268i
\(551\) 7.67646e6 7.67646e6i 0.0458887 0.0458887i
\(552\) −5.77016e6 + 5.77016e6i −0.0343060 + 0.0343060i
\(553\) 8.98383e7 + 8.98383e7i 0.531234 + 0.531234i
\(554\) 1.10596e8 + 1.10596e8i 0.650447 + 0.650447i
\(555\) 9.10313e7 0.532490
\(556\) 1.25567e8i 0.730552i
\(557\) −4.42993e7 4.42993e7i −0.256349 0.256349i 0.567218 0.823567i \(-0.308020\pi\)
−0.823567 + 0.567218i \(0.808020\pi\)
\(558\) 1.21759e8i 0.700808i
\(559\) −6.94073e7 + 2.03747e8i −0.397347 + 1.16642i
\(560\) −8.71107e7 −0.496029
\(561\) −2.98796e7 + 2.98796e7i −0.169234 + 0.169234i
\(562\) −4.04679e8 −2.27983
\(563\) 2.83040e8i 1.58607i 0.609176 + 0.793035i \(0.291500\pi\)
−0.609176 + 0.793035i \(0.708500\pi\)
\(564\) −1.54475e8 + 1.54475e8i −0.861034 + 0.861034i
\(565\) −8.24450e7 + 8.24450e7i −0.457108 + 0.457108i
\(566\) 1.05786e8 + 1.05786e8i 0.583419 + 0.583419i
\(567\) 4.95101e6 + 4.95101e6i 0.0271609 + 0.0271609i
\(568\) −8.14398e6 −0.0444418
\(569\) 2.74227e8i 1.48858i −0.667854 0.744292i \(-0.732787\pi\)
0.667854 0.744292i \(-0.267213\pi\)
\(570\) 1.78023e8 + 1.78023e8i 0.961285 + 0.961285i
\(571\) 5.50772e7i 0.295845i −0.988999 0.147922i \(-0.952741\pi\)
0.988999 0.147922i \(-0.0472585\pi\)
\(572\) −5.21179e7 + 2.56321e7i −0.278483 + 0.136960i
\(573\) 1.76956e7 0.0940595
\(574\) 1.61781e8 1.61781e8i 0.855447 0.855447i
\(575\) 1.14320e7 0.0601336
\(576\) 1.63934e8i 0.857832i
\(577\) 8.09540e7 8.09540e7i 0.421416 0.421416i −0.464275 0.885691i \(-0.653685\pi\)
0.885691 + 0.464275i \(0.153685\pi\)
\(578\) 2.76509e8 2.76509e8i 1.43194 1.43194i
\(579\) −9.90453e7 9.90453e7i −0.510268 0.510268i
\(580\) 5.48297e6 + 5.48297e6i 0.0281017 + 0.0281017i
\(581\) −2.53544e7 −0.129278
\(582\) 6.85102e7i 0.347525i
\(583\) −1.33944e7 1.33944e7i −0.0675955 0.0675955i
\(584\) 1.11500e8i 0.559805i
\(585\) 8.95770e7 4.40548e7i 0.447434 0.220052i
\(586\) 1.54443e8 0.767497
\(587\) −2.01036e8 + 2.01036e8i −0.993938 + 0.993938i −0.999982 0.00604390i \(-0.998076\pi\)
0.00604390 + 0.999982i \(0.498076\pi\)
\(588\) 3.56492e7 0.175355
\(589\) 2.72737e8i 1.33474i
\(590\) 7.18963e7 7.18963e7i 0.350066 0.350066i
\(591\) −6.53930e7 + 6.53930e7i −0.316788 + 0.316788i
\(592\) −9.97107e7 9.97107e7i −0.480592 0.480592i
\(593\) −1.05754e8 1.05754e8i −0.507147 0.507147i 0.406503 0.913650i \(-0.366748\pi\)
−0.913650 + 0.406503i \(0.866748\pi\)
\(594\) −7.86530e7 −0.375281
\(595\) 2.37527e8i 1.12762i
\(596\) 7.75894e7 + 7.75894e7i 0.366491 + 0.366491i
\(597\) 1.52810e7i 0.0718172i
\(598\) −2.79001e7 5.67295e7i −0.130467 0.265280i
\(599\) 9.05205e7 0.421179 0.210589 0.977575i \(-0.432462\pi\)
0.210589 + 0.977575i \(0.432462\pi\)
\(600\) 1.15176e7 1.15176e7i 0.0533224 0.0533224i
\(601\) 2.05850e8 0.948262 0.474131 0.880454i \(-0.342762\pi\)
0.474131 + 0.880454i \(0.342762\pi\)
\(602\) 3.56900e8i 1.63590i
\(603\) 1.15718e8 1.15718e8i 0.527777 0.527777i
\(604\) −1.86881e8 + 1.86881e8i −0.848112 + 0.848112i
\(605\) −1.22544e8 1.22544e8i −0.553384 0.553384i
\(606\) −1.57622e8 1.57622e8i −0.708271 0.708271i
\(607\) 1.14080e8 0.510085 0.255043 0.966930i \(-0.417910\pi\)
0.255043 + 0.966930i \(0.417910\pi\)
\(608\) 5.39850e8i 2.40194i
\(609\) −3.38685e6 3.38685e6i −0.0149949 0.0149949i
\(610\) 5.17684e8i 2.28074i
\(611\) −1.53642e8 3.12403e8i −0.673577 1.36959i
\(612\) 2.64583e8 1.15427
\(613\) −1.12421e6 + 1.12421e6i −0.00488052 + 0.00488052i −0.709543 0.704662i \(-0.751099\pi\)
0.704662 + 0.709543i \(0.251099\pi\)
\(614\) 1.63297e8 0.705461
\(615\) 1.11925e8i 0.481175i
\(616\) 1.40075e7 1.40075e7i 0.0599266 0.0599266i
\(617\) −1.05308e8 + 1.05308e8i −0.448336 + 0.448336i −0.894801 0.446465i \(-0.852683\pi\)
0.446465 + 0.894801i \(0.352683\pi\)
\(618\) 3.33060e7 + 3.33060e7i 0.141110 + 0.141110i
\(619\) 3.88419e6 + 3.88419e6i 0.0163768 + 0.0163768i 0.715248 0.698871i \(-0.246314\pi\)
−0.698871 + 0.715248i \(0.746314\pi\)
\(620\) 1.94804e8 0.817380
\(621\) 4.77136e7i 0.199236i
\(622\) −2.59000e8 2.59000e8i −1.07629 1.07629i
\(623\) 2.61741e7i 0.108245i
\(624\) 9.82286e7 + 3.34620e7i 0.404282 + 0.137720i
\(625\) 1.46682e8 0.600811
\(626\) −1.75765e8 + 1.75765e8i −0.716489 + 0.716489i
\(627\) 6.59584e7 0.267589
\(628\) 2.55050e8i 1.02979i
\(629\) −2.71884e8 + 2.71884e8i −1.09253 + 1.09253i
\(630\) −1.17040e8 + 1.17040e8i −0.468073 + 0.468073i
\(631\) −2.27959e7 2.27959e7i −0.0907336 0.0907336i 0.660283 0.751017i \(-0.270436\pi\)
−0.751017 + 0.660283i \(0.770436\pi\)
\(632\) −5.90935e7 5.90935e7i −0.234093 0.234093i
\(633\) 1.57863e6 0.00622399
\(634\) 6.27529e8i 2.46244i
\(635\) −1.48724e8 1.48724e8i −0.580845 0.580845i
\(636\) 7.95953e7i 0.309397i
\(637\) −1.83191e7 + 5.37762e7i −0.0708737 + 0.208052i
\(638\) 3.64506e6 0.0140360
\(639\) 1.26059e7 1.26059e7i 0.0483138 0.0483138i
\(640\) 1.64335e8 0.626889
\(641\) 4.33034e8i 1.64417i −0.569363 0.822086i \(-0.692810\pi\)
0.569363 0.822086i \(-0.307190\pi\)
\(642\) 2.57649e8 2.57649e8i 0.973696 0.973696i
\(643\) −1.52097e8 + 1.52097e8i −0.572122 + 0.572122i −0.932721 0.360599i \(-0.882572\pi\)
0.360599 + 0.932721i \(0.382572\pi\)
\(644\) 4.13097e7 + 4.13097e7i 0.154666 + 0.154666i
\(645\) 1.23457e8 + 1.23457e8i 0.460085 + 0.460085i
\(646\) −1.06341e9 −3.94459
\(647\) 3.36634e8i 1.24293i 0.783444 + 0.621463i \(0.213461\pi\)
−0.783444 + 0.621463i \(0.786539\pi\)
\(648\) −3.25666e6 3.25666e6i −0.0119687 0.0119687i
\(649\) 2.66379e7i 0.0974464i
\(650\) 5.56904e7 + 1.13236e8i 0.202787 + 0.412329i
\(651\) −1.20331e8 −0.436150
\(652\) 2.72341e8 2.72341e8i 0.982586 0.982586i
\(653\) 2.78026e8 0.998496 0.499248 0.866459i \(-0.333610\pi\)
0.499248 + 0.866459i \(0.333610\pi\)
\(654\) 1.56855e8i 0.560744i
\(655\) 4.33978e7 4.33978e7i 0.154434 0.154434i
\(656\) 1.22597e8 1.22597e8i 0.434278 0.434278i
\(657\) 1.72589e8 + 1.72589e8i 0.608578 + 0.608578i
\(658\) 4.08182e8 + 4.08182e8i 1.43277 + 1.43277i
\(659\) 3.97164e8 1.38776 0.693878 0.720093i \(-0.255901\pi\)
0.693878 + 0.720093i \(0.255901\pi\)
\(660\) 4.71113e7i 0.163868i
\(661\) 1.57276e8 + 1.57276e8i 0.544577 + 0.544577i 0.924867 0.380290i \(-0.124176\pi\)
−0.380290 + 0.924867i \(0.624176\pi\)
\(662\) 3.09531e8i 1.06692i
\(663\) 9.12416e7 2.67842e8i 0.313078 0.919049i
\(664\) 1.66775e7 0.0569674
\(665\) 2.62167e8 2.62167e8i 0.891483 0.891483i
\(666\) −2.67939e8 −0.907012
\(667\) 2.21122e6i 0.00745167i
\(668\) −3.07813e8 + 3.07813e8i −1.03266 + 1.03266i
\(669\) 1.51531e8 1.51531e8i 0.506086 0.506086i
\(670\) −3.32196e8 3.32196e8i −1.10451 1.10451i
\(671\) 9.59021e7 + 9.59021e7i 0.317439 + 0.317439i
\(672\) −2.38182e8 −0.784875
\(673\) 1.93344e8i 0.634285i 0.948378 + 0.317143i \(0.102723\pi\)
−0.948378 + 0.317143i \(0.897277\pi\)
\(674\) −1.82505e8 1.82505e8i −0.596067 0.596067i
\(675\) 9.52396e7i 0.309675i
\(676\) 2.37420e8 3.08038e8i 0.768560 0.997158i
\(677\) −4.36390e7 −0.140640 −0.0703201 0.997524i \(-0.522402\pi\)
−0.0703201 + 0.997524i \(0.522402\pi\)
\(678\) −1.62849e8 + 1.62849e8i −0.522513 + 0.522513i
\(679\) 1.00892e8 0.322290
\(680\) 1.56239e8i 0.496894i
\(681\) −1.35199e8 + 1.35199e8i −0.428087 + 0.428087i
\(682\) 6.47526e7 6.47526e7i 0.204129 0.204129i
\(683\) 4.34212e8 + 4.34212e8i 1.36282 + 1.36282i 0.870299 + 0.492523i \(0.163925\pi\)
0.492523 + 0.870299i \(0.336075\pi\)
\(684\) −2.92030e8 2.92030e8i −0.912555 0.912555i
\(685\) −3.92911e8 −1.22243
\(686\) 5.22780e8i 1.61937i
\(687\) −3.91609e7 3.91609e7i −0.120776 0.120776i
\(688\) 2.70457e8i 0.830487i
\(689\) 1.20068e8 + 4.09017e7i 0.367088 + 0.125050i
\(690\) −5.12799e7 −0.156099
\(691\) −4.86878e7 + 4.86878e7i −0.147566 + 0.147566i −0.777030 0.629464i \(-0.783275\pi\)
0.629464 + 0.777030i \(0.283275\pi\)
\(692\) 6.00435e8 1.81196
\(693\) 4.33639e7i 0.130295i
\(694\) −4.56964e8 + 4.56964e8i −1.36711 + 1.36711i
\(695\) −1.14773e8 + 1.14773e8i −0.341890 + 0.341890i
\(696\) 2.22779e6 + 2.22779e6i 0.00660764 + 0.00660764i
\(697\) −3.34288e8 3.34288e8i −0.987240 0.987240i
\(698\) −5.74255e8 −1.68864
\(699\) 1.94659e8i 0.569958i
\(700\) −8.24571e7 8.24571e7i −0.240400 0.240400i
\(701\) 2.55548e8i 0.741853i −0.928662 0.370926i \(-0.879040\pi\)
0.928662 0.370926i \(-0.120960\pi\)
\(702\) 4.72613e8 2.32436e8i 1.36614 0.671879i
\(703\) 6.00176e8 1.72748
\(704\) 8.71817e7 8.71817e7i 0.249866 0.249866i
\(705\) −2.82393e8 −0.805909
\(706\) 1.68977e8i 0.480190i
\(707\) −2.32123e8 + 2.32123e8i −0.656841 + 0.656841i
\(708\) 7.91468e7 7.91468e7i 0.223015 0.223015i
\(709\) −2.99236e8 2.99236e8i −0.839604 0.839604i 0.149202 0.988807i \(-0.452329\pi\)
−0.988807 + 0.149202i \(0.952329\pi\)
\(710\) −3.61881e7 3.61881e7i −0.101109 0.101109i
\(711\) 1.82939e8 0.508977
\(712\) 1.72167e7i 0.0476991i
\(713\) 3.92811e7 + 3.92811e7i 0.108372 + 0.108372i
\(714\) 4.69175e8i 1.28896i
\(715\) −7.10666e7 2.42091e7i −0.194423 0.0662310i
\(716\) −8.00360e8 −2.18045
\(717\) 1.33412e8 1.33412e8i 0.361939 0.361939i
\(718\) 6.76530e8 1.82774
\(719\) 3.54786e8i 0.954508i −0.878766 0.477254i \(-0.841632\pi\)
0.878766 0.477254i \(-0.158368\pi\)
\(720\) −8.86924e7 + 8.86924e7i −0.237623 + 0.237623i
\(721\) 4.90482e7 4.90482e7i 0.130863 0.130863i
\(722\) 7.73727e8 + 7.73727e8i 2.05578 + 2.05578i
\(723\) −1.40218e6 1.40218e6i −0.00371013 0.00371013i
\(724\) 6.62589e8 1.74594
\(725\) 4.41374e6i 0.0115822i
\(726\) −2.42055e8 2.42055e8i −0.632564 0.632564i
\(727\) 6.94762e8i 1.80814i −0.427380 0.904072i \(-0.640563\pi\)
0.427380 0.904072i \(-0.359437\pi\)
\(728\) −4.27739e7 + 1.25564e8i −0.110863 + 0.325440i
\(729\) 2.58767e8 0.667924
\(730\) 4.95456e8 4.95456e8i 1.27361 1.27361i
\(731\) −7.37462e8 −1.88794
\(732\) 5.69891e8i 1.45298i
\(733\) 1.25593e8 1.25593e8i 0.318898 0.318898i −0.529446 0.848344i \(-0.677600\pi\)
0.848344 + 0.529446i \(0.177600\pi\)
\(734\) 2.45094e8 2.45094e8i 0.619791 0.619791i
\(735\) 3.25848e7 + 3.25848e7i 0.0820641 + 0.0820641i
\(736\) 7.77524e7 + 7.77524e7i 0.195020 + 0.195020i
\(737\) −1.23080e8 −0.307458
\(738\) 3.29438e8i 0.819605i
\(739\) −1.66032e8 1.66032e8i −0.411395 0.411395i 0.470829 0.882224i \(-0.343955\pi\)
−0.882224 + 0.470829i \(0.843955\pi\)
\(740\) 4.28680e8i 1.05788i
\(741\) −3.96334e8 + 1.94920e8i −0.974106 + 0.479074i
\(742\) −2.10321e8 −0.514839
\(743\) −4.33230e8 + 4.33230e8i −1.05621 + 1.05621i −0.0578917 + 0.998323i \(0.518438\pi\)
−0.998323 + 0.0578917i \(0.981562\pi\)
\(744\) 7.91511e7 0.192193
\(745\) 1.41840e8i 0.343028i
\(746\) 1.53718e8 1.53718e8i 0.370262 0.370262i
\(747\) −2.58148e7 + 2.58148e7i −0.0619307 + 0.0619307i
\(748\) −1.40708e8 1.40708e8i −0.336212 0.336212i
\(749\) −3.79428e8 3.79428e8i −0.902992 0.902992i
\(750\) 4.37165e8 1.03624
\(751\) 4.61949e8i 1.09062i 0.838234 + 0.545311i \(0.183588\pi\)
−0.838234 + 0.545311i \(0.816412\pi\)
\(752\) 3.09317e8 + 3.09317e8i 0.727362 + 0.727362i
\(753\) 1.70470e8i 0.399266i
\(754\) −2.19026e7 + 1.07719e7i −0.0510953 + 0.0251291i
\(755\) −3.41633e8 −0.793814
\(756\) −3.44152e8 + 3.44152e8i −0.796498 + 0.796498i
\(757\) 3.67377e8 0.846885 0.423443 0.905923i \(-0.360821\pi\)
0.423443 + 0.905923i \(0.360821\pi\)
\(758\) 5.96834e8i 1.37040i
\(759\) −9.49972e6 + 9.49972e6i −0.0217263 + 0.0217263i
\(760\) −1.72447e8 + 1.72447e8i −0.392839 + 0.392839i
\(761\) 2.78595e8 + 2.78595e8i 0.632150 + 0.632150i 0.948607 0.316457i \(-0.102493\pi\)
−0.316457 + 0.948607i \(0.602493\pi\)
\(762\) −2.93767e8 2.93767e8i −0.663955 0.663955i
\(763\) −2.30993e8 −0.520026
\(764\) 8.33315e7i 0.186866i
\(765\) 2.41840e8 + 2.41840e8i 0.540186 + 0.540186i
\(766\) 4.91253e8i 1.09300i
\(767\) 7.87204e7 + 1.60063e8i 0.174462 + 0.354735i
\(768\) −8.69002e7 −0.191839
\(769\) 4.33883e7 4.33883e7i 0.0954098 0.0954098i −0.657791 0.753201i \(-0.728509\pi\)
0.753201 + 0.657791i \(0.228509\pi\)
\(770\) 1.24486e8 0.272677
\(771\) 3.01982e8i 0.658899i
\(772\) 4.66420e8 4.66420e8i 1.01374 1.01374i
\(773\) 1.03754e8 1.03754e8i 0.224629 0.224629i −0.585815 0.810444i \(-0.699226\pi\)
0.810444 + 0.585815i \(0.199226\pi\)
\(774\) −3.63381e8 3.63381e8i −0.783681 0.783681i
\(775\) −7.84079e7 7.84079e7i −0.168444 0.168444i
\(776\) −6.63643e7 −0.142020
\(777\) 2.64797e8i 0.564482i
\(778\) 1.87122e8 + 1.87122e8i 0.397361 + 0.397361i
\(779\) 7.37932e8i 1.56100i
\(780\) −1.39224e8 2.83085e8i −0.293379 0.596530i
\(781\) −1.34079e7 −0.0281453
\(782\) 1.53158e8 1.53158e8i 0.320273 0.320273i
\(783\) −1.84217e7 −0.0383746
\(784\) 7.13832e7i 0.148132i
\(785\) −2.33126e8 + 2.33126e8i −0.481928 + 0.481928i
\(786\) 8.57215e7 8.57215e7i 0.176531 0.176531i
\(787\) −5.52470e8 5.52470e8i −1.13340 1.13340i −0.989608 0.143795i \(-0.954069\pi\)
−0.143795 0.989608i \(-0.545931\pi\)
\(788\) −3.07946e8 3.07946e8i −0.629355 0.629355i
\(789\) 4.60652e8 0.937868
\(790\) 5.25169e8i 1.06517i
\(791\) 2.39821e8 + 2.39821e8i 0.484571 + 0.484571i
\(792\) 2.85238e7i 0.0574158i
\(793\) −8.59670e8 2.92850e8i −1.72390 0.587254i
\(794\) 3.08277e8 0.615856
\(795\) 7.27533e7 7.27533e7i 0.144794 0.144794i
\(796\) 7.19605e7 0.142677
\(797\) 1.61019e7i 0.0318054i −0.999874 0.0159027i \(-0.994938\pi\)
0.999874 0.0159027i \(-0.00506220\pi\)
\(798\) 5.17845e8 5.17845e8i 1.01904 1.01904i
\(799\) 8.43424e8 8.43424e8i 1.65351 1.65351i
\(800\) −1.55199e8 1.55199e8i −0.303123 0.303123i
\(801\) 2.66494e7 + 2.66494e7i 0.0518549 + 0.0518549i
\(802\) −2.64320e8 −0.512397
\(803\) 1.83568e8i 0.354529i
\(804\) −3.65698e8 3.65698e8i −0.703646 0.703646i
\(805\) 7.55176e7i 0.144764i
\(806\) −1.97731e8 + 5.80445e8i −0.377633 + 1.10855i
\(807\) 3.91290e8 0.744522
\(808\) 1.52685e8 1.52685e8i 0.289442 0.289442i
\(809\) −4.23919e8 −0.800640 −0.400320 0.916375i \(-0.631101\pi\)
−0.400320 + 0.916375i \(0.631101\pi\)
\(810\) 2.89422e7i 0.0544599i
\(811\) 3.13841e8 3.13841e8i 0.588365 0.588365i −0.348823 0.937189i \(-0.613419\pi\)
0.937189 + 0.348823i \(0.113419\pi\)
\(812\) 1.59492e7 1.59492e7i 0.0297900 0.0297900i
\(813\) 1.94355e8 + 1.94355e8i 0.361680 + 0.361680i
\(814\) 1.42492e8 + 1.42492e8i 0.264191 + 0.264191i
\(815\) 4.97862e8 0.919679
\(816\) 3.55538e8i 0.654358i
\(817\) 8.13963e8 + 8.13963e8i 1.49258 + 1.49258i
\(818\) 1.20734e9i 2.20583i
\(819\) −1.28149e8 2.60567e8i −0.233273 0.474316i
\(820\) −5.27074e8 −0.955938
\(821\) 3.18406e8 3.18406e8i 0.575376 0.575376i −0.358250 0.933626i \(-0.616626\pi\)
0.933626 + 0.358250i \(0.116626\pi\)
\(822\) −7.76097e8 −1.39734
\(823\) 5.96016e8i 1.06920i 0.845106 + 0.534599i \(0.179537\pi\)
−0.845106 + 0.534599i \(0.820463\pi\)
\(824\) −3.22627e7 + 3.22627e7i −0.0576660 + 0.0576660i
\(825\) 1.89621e7 1.89621e7i 0.0337695 0.0337695i
\(826\) −2.09136e8 2.09136e8i −0.371098 0.371098i
\(827\) 3.09467e8 + 3.09467e8i 0.547140 + 0.547140i 0.925612 0.378473i \(-0.123551\pi\)
−0.378473 + 0.925612i \(0.623551\pi\)
\(828\) 8.41197e7 0.148186
\(829\) 6.94933e8i 1.21977i 0.792489 + 0.609887i \(0.208785\pi\)
−0.792489 + 0.609887i \(0.791215\pi\)
\(830\) 7.41072e7 + 7.41072e7i 0.129606 + 0.129606i
\(831\) 2.22569e8i 0.387847i
\(832\) −2.66221e8 + 7.81501e8i −0.462246 + 1.35694i
\(833\) −1.94643e8 −0.336746
\(834\) −2.26706e8 + 2.26706e8i −0.390809 + 0.390809i
\(835\) −5.62707e8 −0.966547
\(836\) 3.10608e8i 0.531611i
\(837\) −3.27251e8 + 3.27251e8i −0.558091 + 0.558091i
\(838\) −7.27536e8 + 7.27536e8i −1.23630 + 1.23630i
\(839\) 1.75155e6 + 1.75155e6i 0.00296577 + 0.00296577i 0.708588 0.705622i \(-0.249332\pi\)
−0.705622 + 0.708588i \(0.749332\pi\)
\(840\) 7.60836e7 + 7.60836e7i 0.128367 + 0.128367i
\(841\) −5.93970e8 −0.998565
\(842\) 3.49638e7i 0.0585709i
\(843\) −4.07196e8 4.07196e8i −0.679705 0.679705i
\(844\) 7.43400e6i 0.0123650i
\(845\) 4.98571e8 6.45473e7i 0.826337 0.106981i
\(846\) 8.31186e8 1.37274
\(847\) −3.56464e8 + 3.56464e8i −0.586631 + 0.586631i
\(848\) −1.59380e8 −0.261364
\(849\) 2.12889e8i 0.347880i
\(850\) −3.05714e8 + 3.05714e8i −0.497804 + 0.497804i
\(851\) −8.64408e7 + 8.64408e7i −0.140259 + 0.140259i
\(852\) −3.98376e7 3.98376e7i −0.0644131 0.0644131i
\(853\) 3.99606e8 + 3.99606e8i 0.643850 + 0.643850i 0.951500 0.307650i \(-0.0995425\pi\)
−0.307650 + 0.951500i \(0.599543\pi\)
\(854\) 1.50587e9 2.41776
\(855\) 5.33854e8i 0.854131i
\(856\) 2.49578e8 + 2.49578e8i 0.397911 + 0.397911i
\(857\) 9.84583e8i 1.56426i −0.623113 0.782132i \(-0.714132\pi\)
0.623113 0.782132i \(-0.285868\pi\)
\(858\) −1.40374e8 4.78191e7i −0.222242 0.0757076i
\(859\) −4.66714e8 −0.736328 −0.368164 0.929761i \(-0.620013\pi\)
−0.368164 + 0.929761i \(0.620013\pi\)
\(860\) −5.81380e8 + 5.81380e8i −0.914038 + 0.914038i
\(861\) 3.25575e8 0.510084
\(862\) 3.01421e8i 0.470600i
\(863\) 6.18379e8 6.18379e8i 0.962104 0.962104i −0.0372036 0.999308i \(-0.511845\pi\)
0.999308 + 0.0372036i \(0.0118450\pi\)
\(864\) −6.47755e8 + 6.47755e8i −1.00431 + 1.00431i
\(865\) 5.48822e8 + 5.48822e8i 0.847975 + 0.847975i
\(866\) −2.53273e8 2.53273e8i −0.389973 0.389973i
\(867\) 5.56458e8 0.853837
\(868\) 5.66659e8i 0.866488i
\(869\) −9.72887e7 9.72887e7i −0.148253 0.148253i
\(870\) 1.97986e7i 0.0300660i
\(871\) 7.39570e8 3.63727e8i 1.11924 0.550454i
\(872\) 1.51941e8 0.229154
\(873\) 1.02724e8 1.02724e8i 0.154393 0.154393i
\(874\) −3.38092e8 −0.506408
\(875\) 6.43794e8i 0.960998i
\(876\) 5.45421e8 5.45421e8i 0.811371 0.811371i
\(877\) −3.05312e8 + 3.05312e8i −0.452632 + 0.452632i −0.896227 0.443595i \(-0.853703\pi\)
0.443595 + 0.896227i \(0.353703\pi\)
\(878\) −3.24060e8 3.24060e8i −0.478787 0.478787i
\(879\) 1.55404e8 + 1.55404e8i 0.228821 + 0.228821i
\(880\) 9.43349e7 0.138428
\(881\) 5.29881e6i 0.00774908i −0.999992 0.00387454i \(-0.998767\pi\)
0.999992 0.00387454i \(-0.00123331\pi\)
\(882\) −9.59092e7 9.59092e7i −0.139783 0.139783i
\(883\) 7.31615e8i 1.06268i −0.847160 0.531338i \(-0.821690\pi\)
0.847160 0.531338i \(-0.178310\pi\)
\(884\) 1.26131e9 + 4.29671e8i 1.82585 + 0.621984i
\(885\) 1.44687e8 0.208737
\(886\) 3.24460e7 3.24460e7i 0.0466509 0.0466509i
\(887\) −2.32665e8 −0.333396 −0.166698 0.986008i \(-0.553311\pi\)
−0.166698 + 0.986008i \(0.553311\pi\)
\(888\) 1.74177e8i 0.248744i
\(889\) −4.32618e8 + 4.32618e8i −0.615742 + 0.615742i
\(890\) 7.65032e7 7.65032e7i 0.108520 0.108520i
\(891\) −5.36161e6 5.36161e6i −0.00757987 0.00757987i
\(892\) 7.13585e8 + 7.13585e8i 1.00543 + 1.00543i
\(893\) −1.86183e9 −2.61449
\(894\) 2.80169e8i 0.392109i
\(895\) −7.31562e8 7.31562e8i −1.02043 1.02043i
\(896\) 4.78028e8i 0.664553i
\(897\) 2.90087e7 8.51559e7i 0.0401931 0.117988i
\(898\) −1.09044e8 −0.150582
\(899\) 1.51660e7 1.51660e7i 0.0208733 0.0208733i
\(900\) −1.67909e8 −0.230327
\(901\) 4.34586e8i 0.594157i
\(902\) −1.75198e8 + 1.75198e8i −0.238732 + 0.238732i
\(903\) 3.59120e8 3.59120e8i 0.487727 0.487727i
\(904\) −1.57748e8 1.57748e8i −0.213530 0.213530i
\(905\) 6.05633e8 + 6.05633e8i 0.817079 + 0.817079i
\(906\) −6.74810e8 −0.907396
\(907\) 5.05806e8i 0.677894i −0.940805 0.338947i \(-0.889929\pi\)
0.940805 0.338947i \(-0.110071\pi\)
\(908\) −6.36673e8 6.36673e8i −0.850470 0.850470i
\(909\) 4.72676e8i 0.629320i
\(910\) −7.48018e8 + 3.67882e8i −0.992631 + 0.488185i
\(911\) −1.00881e9 −1.33431 −0.667154 0.744920i \(-0.732488\pi\)
−0.667154 + 0.744920i \(0.732488\pi\)
\(912\) 3.92420e8 3.92420e8i 0.517328 0.517328i
\(913\) 2.74570e7 0.0360779
\(914\) 1.68801e9i 2.21074i
\(915\) −5.20903e8 + 5.20903e8i −0.679977 + 0.679977i
\(916\) 1.84414e8 1.84414e8i 0.239943 0.239943i
\(917\) −1.26238e8 1.26238e8i −0.163713 0.163713i
\(918\) 1.27596e9 + 1.27596e9i 1.64934 + 1.64934i
\(919\) 1.36736e9 1.76172 0.880860 0.473378i \(-0.156965\pi\)
0.880860 + 0.473378i \(0.156965\pi\)
\(920\) 4.96737e7i 0.0637915i
\(921\) 1.64313e8 + 1.64313e8i 0.210326 + 0.210326i
\(922\) 1.68334e8i 0.214772i
\(923\) 8.05657e7 3.96229e7i 0.102458 0.0503897i
\(924\) 1.37040e8 0.173713
\(925\) 1.72542e8 1.72542e8i 0.218006 0.218006i
\(926\) 5.50894e8 0.693801
\(927\) 9.98777e7i 0.125380i
\(928\) 3.00193e7 3.00193e7i 0.0375626 0.0375626i
\(929\) −7.69217e8 + 7.69217e8i −0.959404 + 0.959404i −0.999208 0.0398032i \(-0.987327\pi\)
0.0398032 + 0.999208i \(0.487327\pi\)
\(930\) 3.51711e8 + 3.51711e8i 0.437258 + 0.437258i
\(931\) 2.14834e8 + 2.14834e8i 0.266228 + 0.266228i
\(932\) −9.16679e8 −1.13232
\(933\) 5.21222e8i 0.641768i
\(934\) −3.65612e8 3.65612e8i −0.448724 0.448724i
\(935\) 2.57225e8i 0.314687i
\(936\) 8.42935e7 + 1.71395e8i 0.102794 + 0.209011i
\(937\) 1.42415e9 1.73116 0.865581 0.500769i \(-0.166949\pi\)
0.865581 + 0.500769i \(0.166949\pi\)
\(938\) −9.66313e8 + 9.66313e8i −1.17087 + 1.17087i
\(939\) −3.53717e8 −0.427227
\(940\) 1.32983e9i 1.60108i
\(941\) 1.07583e9 1.07583e9i 1.29115 1.29115i 0.357072 0.934077i \(-0.383775\pi\)
0.934077 0.357072i \(-0.116225\pi\)
\(942\) −4.60483e8 + 4.60483e8i −0.550884 + 0.550884i
\(943\) −1.06281e8 1.06281e8i −0.126742 0.126742i
\(944\) −1.58482e8 1.58482e8i −0.188393 0.188393i
\(945\) −6.29137e8 −0.745504
\(946\) 3.86499e8i 0.456536i
\(947\) 3.72519e8 + 3.72519e8i 0.438630 + 0.438630i 0.891551 0.452921i \(-0.149618\pi\)
−0.452921 + 0.891551i \(0.649618\pi\)
\(948\) 5.78131e8i 0.678580i
\(949\) 5.42482e8 + 1.10303e9i 0.634727 + 1.29060i
\(950\) 6.74855e8 0.787118
\(951\) −6.31432e8 + 6.31432e8i −0.734151 + 0.734151i
\(952\) −4.54479e8 −0.526748
\(953\) 6.36621e8i 0.735534i −0.929918 0.367767i \(-0.880122\pi\)
0.929918 0.367767i \(-0.119878\pi\)
\(954\) −2.14140e8 + 2.14140e8i −0.246634 + 0.246634i
\(955\) −7.61684e7 + 7.61684e7i −0.0874510 + 0.0874510i
\(956\) 6.28255e8 + 6.28255e8i 0.719056 + 0.719056i
\(957\) 3.66773e6 + 3.66773e6i 0.00418467 + 0.00418467i
\(958\) 1.32518e9 1.50723
\(959\) 1.14292e9i 1.29587i
\(960\) 4.73538e8 + 4.73538e8i 0.535231 + 0.535231i
\(961\) 3.48672e8i 0.392868i
\(962\) −1.27731e9 4.35120e8i −1.43473 0.488747i
\(963\) −7.72635e8 −0.865158
\(964\) 6.60309e6 6.60309e6i 0.00737083 0.00737083i
\(965\) 8.52653e8 0.948834
\(966\) 1.49166e8i 0.165477i
\(967\) −1.65872e8 + 1.65872e8i −0.183440 + 0.183440i −0.792853 0.609413i \(-0.791405\pi\)
0.609413 + 0.792853i \(0.291405\pi\)
\(968\) 2.34473e8 2.34473e8i 0.258504 0.258504i
\(969\) −1.07002e9 1.07002e9i −1.17604 1.17604i
\(970\) −2.94893e8 2.94893e8i −0.323109 0.323109i
\(971\) −2.03038e8 −0.221779 −0.110889 0.993833i \(-0.535370\pi\)
−0.110889 + 0.993833i \(0.535370\pi\)
\(972\) 1.13924e9i 1.24055i
\(973\) 3.33860e8 + 3.33860e8i 0.362431 + 0.362431i
\(974\) 2.39602e7i 0.0259306i
\(975\) −5.79034e7 + 1.69977e8i −0.0624727 + 0.183390i
\(976\) 1.14114e9 1.22741
\(977\) 2.63431e8 2.63431e8i 0.282477 0.282477i −0.551619 0.834096i \(-0.685990\pi\)
0.834096 + 0.551619i \(0.185990\pi\)
\(978\) 9.83402e8 1.05127
\(979\) 2.83448e7i 0.0302082i
\(980\) −1.53447e8 + 1.53447e8i −0.163035 + 0.163035i
\(981\) −2.35187e8 + 2.35187e8i −0.249119 + 0.249119i
\(982\) 2.91346e8 + 2.91346e8i 0.307662 + 0.307662i
\(983\) 3.97286e8 + 3.97286e8i 0.418256 + 0.418256i 0.884602 0.466346i \(-0.154430\pi\)
−0.466346 + 0.884602i \(0.654430\pi\)
\(984\) −2.14155e8 −0.224773
\(985\) 5.62950e8i 0.589062i
\(986\) −5.91325e7 5.91325e7i −0.0616873 0.0616873i
\(987\) 8.21440e8i 0.854328i
\(988\) −9.17910e8 1.86640e9i −0.951764 1.93523i
\(989\) −2.34463e8 −0.242374
\(990\) 1.26747e8 1.26747e8i 0.130626 0.130626i
\(991\) 1.89931e8 0.195153 0.0975763 0.995228i \(-0.468891\pi\)
0.0975763 + 0.995228i \(0.468891\pi\)
\(992\) 1.06655e9i 1.09257i
\(993\) −3.11456e8 + 3.11456e8i −0.318089 + 0.318089i
\(994\) −1.05266e8 + 1.05266e8i −0.107184 + 0.107184i
\(995\) 6.57749e7 + 6.57749e7i 0.0667714 + 0.0667714i
\(996\) 8.15807e7 + 8.15807e7i 0.0825676 + 0.0825676i
\(997\) −1.93733e9 −1.95487 −0.977433 0.211244i \(-0.932249\pi\)
−0.977433 + 0.211244i \(0.932249\pi\)
\(998\) 1.68251e9i 1.69265i
\(999\) −7.20139e8 7.20139e8i −0.722303 0.722303i
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 13.7.d.a.5.1 12
3.2 odd 2 117.7.j.b.109.6 12
4.3 odd 2 208.7.t.c.161.4 12
13.8 odd 4 inner 13.7.d.a.8.1 yes 12
39.8 even 4 117.7.j.b.73.6 12
52.47 even 4 208.7.t.c.177.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
13.7.d.a.5.1 12 1.1 even 1 trivial
13.7.d.a.8.1 yes 12 13.8 odd 4 inner
117.7.j.b.73.6 12 39.8 even 4
117.7.j.b.109.6 12 3.2 odd 2
208.7.t.c.161.4 12 4.3 odd 2
208.7.t.c.177.4 12 52.47 even 4