Properties

Label 37.7.i.a.2.4
Level $37$
Weight $7$
Character 37.2
Analytic conductor $8.512$
Analytic rank $0$
Dimension $216$
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] = [37,7,Mod(2,37)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(37, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("37.2");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 37 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 37.i (of order \(36\), degree \(12\), 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: \(8.51200109393\)
Analytic rank: \(0\)
Dimension: \(216\)
Relative dimension: \(18\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 2.4
Character \(\chi\) \(=\) 37.2
Dual form 37.7.i.a.19.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-8.95954 - 0.783858i) q^{2} +(21.0804 - 25.1226i) q^{3} +(16.6313 + 2.93254i) q^{4} +(74.3976 - 159.546i) q^{5} +(-208.563 + 208.563i) q^{6} +(147.602 - 53.7227i) q^{7} +(409.278 + 109.666i) q^{8} +(-60.1738 - 341.262i) q^{9} +O(q^{10})\) \(q+(-8.95954 - 0.783858i) q^{2} +(21.0804 - 25.1226i) q^{3} +(16.6313 + 2.93254i) q^{4} +(74.3976 - 159.546i) q^{5} +(-208.563 + 208.563i) q^{6} +(147.602 - 53.7227i) q^{7} +(409.278 + 109.666i) q^{8} +(-60.1738 - 341.262i) q^{9} +(-791.630 + 1371.14i) q^{10} +(348.212 - 201.040i) q^{11} +(424.266 - 356.002i) q^{12} +(-1232.83 - 1760.66i) q^{13} +(-1364.56 + 365.632i) q^{14} +(-2439.89 - 5232.35i) q^{15} +(-4596.62 - 1673.03i) q^{16} +(-2665.20 - 1866.19i) q^{17} +(271.628 + 3104.72i) q^{18} +(-2573.12 + 225.119i) q^{19} +(1705.20 - 2435.28i) q^{20} +(1761.85 - 4840.64i) q^{21} +(-3277.41 + 1528.28i) q^{22} +(-1216.04 - 4538.32i) q^{23} +(11382.8 - 7970.34i) q^{24} +(-9876.43 - 11770.3i) q^{25} +(9665.49 + 16741.1i) q^{26} +(10862.8 + 6271.64i) q^{27} +(2612.35 - 460.628i) q^{28} +(-10334.6 + 38569.2i) q^{29} +(17758.8 + 48792.0i) q^{30} +(16557.7 + 16557.7i) q^{31} +(15295.1 + 7132.23i) q^{32} +(2289.78 - 12986.0i) q^{33} +(22416.1 + 18809.4i) q^{34} +(2409.98 - 27546.2i) q^{35} -5852.09i q^{36} +(-8724.70 - 49896.0i) q^{37} +23230.5 q^{38} +(-70221.0 - 6143.54i) q^{39} +(47946.1 - 57139.9i) q^{40} +(-36903.0 - 6507.00i) q^{41} +(-19579.7 + 41988.9i) q^{42} +(76062.3 - 76062.3i) q^{43} +(6380.77 - 2322.41i) q^{44} +(-58923.9 - 15788.6i) q^{45} +(7337.75 + 41614.5i) q^{46} +(11539.3 - 19986.6i) q^{47} +(-138929. + 80210.9i) q^{48} +(-71224.2 + 59764.2i) q^{49} +(79262.0 + 113198. i) q^{50} +(-103067. + 27616.7i) q^{51} +(-15340.3 - 32897.4i) q^{52} +(162869. + 59279.6i) q^{53} +(-92409.7 - 64706.0i) q^{54} +(-6169.07 - 70512.8i) q^{55} +(66301.8 - 5800.65i) q^{56} +(-48586.8 + 69389.1i) q^{57} +(122826. - 337461. i) q^{58} +(-140692. + 65605.8i) q^{59} +(-25234.3 - 94175.8i) q^{60} +(336449. - 235584. i) q^{61} +(-135370. - 161328. i) q^{62} +(-27215.3 - 47138.3i) q^{63} +(139675. + 80641.2i) q^{64} +(-372627. + 65704.2i) q^{65} +(-30694.6 + 114554. i) q^{66} +(161937. + 444919. i) q^{67} +(-38852.9 - 38852.9i) q^{68} +(-139649. - 65119.4i) q^{69} +(-43184.6 + 244912. i) q^{70} +(-37425.7 - 31403.9i) q^{71} +(12797.0 - 146270. i) q^{72} -602585. i q^{73} +(39058.0 + 453884. i) q^{74} -503898. q^{75} +(-43454.5 - 3801.77i) q^{76} +(40596.3 - 48380.8i) q^{77} +(624332. + 110087. i) q^{78} +(321121. - 688646. i) q^{79} +(-608904. + 608904. i) q^{80} +(623935. - 227094. i) q^{81} +(325534. + 87226.5i) q^{82} +(-83012.3 - 470786. i) q^{83} +(43497.2 - 75339.3i) q^{84} +(-496028. + 286382. i) q^{85} +(-741106. + 621862. i) q^{86} +(751102. + 1.07268e6i) q^{87} +(164563. - 44094.4i) q^{88} +(388275. + 832657. i) q^{89} +(515555. + 187647. i) q^{90} +(-276556. - 193646. i) q^{91} +(-6915.46 - 79044.1i) q^{92} +(765015. - 66930.1i) q^{93} +(-119053. + 170025. i) q^{94} +(-155517. + 427280. i) q^{95} +(501607. - 233903. i) q^{96} +(-312431. - 1.16601e6i) q^{97} +(684983. - 479630. i) q^{98} +(-89560.7 - 106734. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216 q - 12 q^{2} - 12 q^{3} - 282 q^{4} + 186 q^{5} - 12 q^{6} - 12 q^{7} + 1782 q^{8} - 972 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 216 q - 12 q^{2} - 12 q^{3} - 282 q^{4} + 186 q^{5} - 12 q^{6} - 12 q^{7} + 1782 q^{8} - 972 q^{9} - 6 q^{10} - 18 q^{11} - 12300 q^{12} - 12 q^{13} - 2508 q^{14} - 5724 q^{15} + 21138 q^{16} + 14652 q^{17} - 36462 q^{18} + 25692 q^{19} + 15156 q^{20} + 22308 q^{21} - 396 q^{22} - 45372 q^{23} - 130632 q^{24} + 54042 q^{25} + 48834 q^{26} - 18 q^{27} - 261132 q^{28} - 63852 q^{29} + 140076 q^{30} + 255300 q^{31} + 444198 q^{32} + 151134 q^{33} + 121740 q^{34} + 64380 q^{35} - 323412 q^{37} - 530748 q^{38} - 734844 q^{39} - 873996 q^{40} + 143244 q^{41} + 682356 q^{42} + 298788 q^{43} + 410502 q^{44} - 296748 q^{45} + 1696848 q^{46} + 97674 q^{47} - 18 q^{48} - 827124 q^{49} - 701574 q^{50} + 1150788 q^{51} + 452802 q^{52} + 147876 q^{53} - 1733052 q^{54} - 481266 q^{55} - 1608972 q^{56} + 238596 q^{57} + 2880600 q^{58} + 1700916 q^{59} - 2913120 q^{60} - 212628 q^{61} - 3373512 q^{62} - 1185486 q^{63} - 2139876 q^{64} - 2189010 q^{65} + 4562748 q^{66} - 486876 q^{67} + 6077478 q^{68} + 3324612 q^{69} + 6153942 q^{70} + 2088276 q^{71} + 1397046 q^{72} - 212106 q^{74} - 5357160 q^{75} - 2036850 q^{76} - 4623426 q^{77} - 7419738 q^{78} - 2895996 q^{79} - 8321832 q^{80} - 337890 q^{81} - 5343312 q^{82} + 2697348 q^{83} + 1737582 q^{84} + 6365610 q^{85} + 9282138 q^{86} + 9292260 q^{87} + 11436912 q^{88} - 618732 q^{89} - 2893080 q^{90} - 2103804 q^{91} - 1911270 q^{92} + 2397036 q^{93} + 751476 q^{94} - 8155788 q^{95} - 5338512 q^{96} - 8958252 q^{97} + 1386858 q^{98} - 12128778 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{36}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.95954 0.783858i −1.11994 0.0979823i −0.487888 0.872906i \(-0.662233\pi\)
−0.632055 + 0.774924i \(0.717788\pi\)
\(3\) 21.0804 25.1226i 0.780754 0.930467i −0.218213 0.975901i \(-0.570023\pi\)
0.998967 + 0.0454344i \(0.0144672\pi\)
\(4\) 16.6313 + 2.93254i 0.259864 + 0.0458210i
\(5\) 74.3976 159.546i 0.595181 1.27637i −0.345926 0.938262i \(-0.612435\pi\)
0.941107 0.338108i \(-0.109787\pi\)
\(6\) −208.563 + 208.563i −0.965569 + 0.965569i
\(7\) 147.602 53.7227i 0.430326 0.156626i −0.117771 0.993041i \(-0.537575\pi\)
0.548097 + 0.836415i \(0.315353\pi\)
\(8\) 409.278 + 109.666i 0.799371 + 0.214191i
\(9\) −60.1738 341.262i −0.0825429 0.468124i
\(10\) −791.630 + 1371.14i −0.791630 + 1.37114i
\(11\) 348.212 201.040i 0.261617 0.151044i −0.363455 0.931612i \(-0.618403\pi\)
0.625072 + 0.780567i \(0.285070\pi\)
\(12\) 424.266 356.002i 0.245525 0.206020i
\(13\) −1232.83 1760.66i −0.561143 0.801395i 0.433888 0.900967i \(-0.357142\pi\)
−0.995030 + 0.0995721i \(0.968253\pi\)
\(14\) −1364.56 + 365.632i −0.497287 + 0.133248i
\(15\) −2439.89 5232.35i −0.722929 1.55033i
\(16\) −4596.62 1673.03i −1.12222 0.408455i
\(17\) −2665.20 1866.19i −0.542479 0.379848i 0.269981 0.962866i \(-0.412983\pi\)
−0.812459 + 0.583018i \(0.801872\pi\)
\(18\) 271.628 + 3104.72i 0.0465755 + 0.532360i
\(19\) −2573.12 + 225.119i −0.375145 + 0.0328210i −0.273170 0.961966i \(-0.588072\pi\)
−0.101976 + 0.994787i \(0.532516\pi\)
\(20\) 1705.20 2435.28i 0.213150 0.304410i
\(21\) 1761.85 4840.64i 0.190244 0.522691i
\(22\) −3277.41 + 1528.28i −0.307795 + 0.143527i
\(23\) −1216.04 4538.32i −0.0999457 0.373002i 0.897777 0.440450i \(-0.145181\pi\)
−0.997723 + 0.0674477i \(0.978514\pi\)
\(24\) 11382.8 7970.34i 0.823410 0.576558i
\(25\) −9876.43 11770.3i −0.632091 0.753297i
\(26\) 9665.49 + 16741.1i 0.549925 + 0.952499i
\(27\) 10862.8 + 6271.64i 0.551888 + 0.318633i
\(28\) 2612.35 460.628i 0.119003 0.0209834i
\(29\) −10334.6 + 38569.2i −0.423739 + 1.58142i 0.342921 + 0.939364i \(0.388584\pi\)
−0.766660 + 0.642053i \(0.778083\pi\)
\(30\) 17758.8 + 48792.0i 0.657735 + 1.80711i
\(31\) 16557.7 + 16557.7i 0.555795 + 0.555795i 0.928107 0.372312i \(-0.121435\pi\)
−0.372312 + 0.928107i \(0.621435\pi\)
\(32\) 15295.1 + 7132.23i 0.466770 + 0.217658i
\(33\) 2289.78 12986.0i 0.0637165 0.361354i
\(34\) 22416.1 + 18809.4i 0.570327 + 0.478561i
\(35\) 2409.98 27546.2i 0.0562094 0.642476i
\(36\) 5852.09i 0.125431i
\(37\) −8724.70 49896.0i −0.172245 0.985054i
\(38\) 23230.5 0.423357
\(39\) −70221.0 6143.54i −1.18379 0.103568i
\(40\) 47946.1 57139.9i 0.749157 0.892811i
\(41\) −36903.0 6507.00i −0.535440 0.0944125i −0.100611 0.994926i \(-0.532080\pi\)
−0.434828 + 0.900513i \(0.643191\pi\)
\(42\) −19579.7 + 41988.9i −0.264277 + 0.566743i
\(43\) 76062.3 76062.3i 0.956675 0.956675i −0.0424250 0.999100i \(-0.513508\pi\)
0.999100 + 0.0424250i \(0.0135083\pi\)
\(44\) 6380.77 2322.41i 0.0749057 0.0272634i
\(45\) −58923.9 15788.6i −0.646627 0.173263i
\(46\) 7337.75 + 41614.5i 0.0753858 + 0.427534i
\(47\) 11539.3 19986.6i 0.111144 0.192506i −0.805088 0.593155i \(-0.797882\pi\)
0.916232 + 0.400649i \(0.131215\pi\)
\(48\) −138929. + 80210.9i −1.25623 + 0.725287i
\(49\) −71224.2 + 59764.2i −0.605395 + 0.507987i
\(50\) 79262.0 + 113198.i 0.634096 + 0.905583i
\(51\) −103067. + 27616.7i −0.776978 + 0.208191i
\(52\) −15340.3 32897.4i −0.109100 0.233966i
\(53\) 162869. + 59279.6i 1.09399 + 0.398179i 0.825096 0.564992i \(-0.191121\pi\)
0.268890 + 0.963171i \(0.413343\pi\)
\(54\) −92409.7 64706.0i −0.586862 0.410925i
\(55\) −6169.07 70512.8i −0.0370793 0.423818i
\(56\) 66301.8 5800.65i 0.377538 0.0330303i
\(57\) −48586.8 + 69389.1i −0.262358 + 0.374685i
\(58\) 122826. 337461.i 0.629515 1.72958i
\(59\) −140692. + 65605.8i −0.685037 + 0.319438i −0.733793 0.679373i \(-0.762252\pi\)
0.0487566 + 0.998811i \(0.484474\pi\)
\(60\) −25234.3 94175.8i −0.116826 0.435999i
\(61\) 336449. 235584.i 1.48228 1.03790i 0.496847 0.867838i \(-0.334491\pi\)
0.985433 0.170065i \(-0.0543979\pi\)
\(62\) −135370. 161328.i −0.568001 0.676917i
\(63\) −27215.3 47138.3i −0.108841 0.188518i
\(64\) 139675. + 80641.2i 0.532816 + 0.307622i
\(65\) −372627. + 65704.2i −1.35686 + 0.239251i
\(66\) −30694.6 + 114554.i −0.106765 + 0.398453i
\(67\) 161937. + 444919.i 0.538421 + 1.47930i 0.848814 + 0.528692i \(0.177317\pi\)
−0.310393 + 0.950608i \(0.600461\pi\)
\(68\) −38852.9 38852.9i −0.123565 0.123565i
\(69\) −139649. 65119.4i −0.425099 0.198227i
\(70\) −43184.6 + 244912.i −0.125903 + 0.714029i
\(71\) −37425.7 31403.9i −0.104567 0.0877422i 0.589005 0.808129i \(-0.299520\pi\)
−0.693572 + 0.720387i \(0.743964\pi\)
\(72\) 12797.0 146270.i 0.0342855 0.391885i
\(73\) 602585.i 1.54899i −0.632578 0.774496i \(-0.718003\pi\)
0.632578 0.774496i \(-0.281997\pi\)
\(74\) 39058.0 + 453884.i 0.0963862 + 1.12008i
\(75\) −503898. −1.19443
\(76\) −43454.5 3801.77i −0.0989905 0.00866055i
\(77\) 40596.3 48380.8i 0.0889231 0.105974i
\(78\) 624332. + 110087.i 1.31562 + 0.231980i
\(79\) 321121. 688646.i 0.651310 1.39674i −0.251991 0.967730i \(-0.581085\pi\)
0.903300 0.429009i \(-0.141137\pi\)
\(80\) −608904. + 608904.i −1.18927 + 1.18927i
\(81\) 623935. 227094.i 1.17404 0.427317i
\(82\) 325534. + 87226.5i 0.590411 + 0.158200i
\(83\) −83012.3 470786.i −0.145180 0.823359i −0.967222 0.253932i \(-0.918276\pi\)
0.822042 0.569427i \(-0.192835\pi\)
\(84\) 43497.2 75339.3i 0.0733876 0.127111i
\(85\) −496028. + 286382.i −0.807699 + 0.466325i
\(86\) −741106. + 621862.i −1.16516 + 0.977684i
\(87\) 751102. + 1.07268e6i 1.14062 + 1.62897i
\(88\) 164563. 44094.4i 0.241481 0.0647047i
\(89\) 388275. + 832657.i 0.550768 + 1.18113i 0.962864 + 0.269986i \(0.0870190\pi\)
−0.412096 + 0.911140i \(0.635203\pi\)
\(90\) 515555. + 187647.i 0.707209 + 0.257403i
\(91\) −276556. 193646.i −0.366994 0.256972i
\(92\) −6915.46 79044.1i −0.00888092 0.101509i
\(93\) 765015. 66930.1i 0.951088 0.0832094i
\(94\) −119053. + 170025.i −0.143337 + 0.204706i
\(95\) −155517. + 427280.i −0.181388 + 0.498358i
\(96\) 501607. 233903.i 0.566957 0.264376i
\(97\) −312431. 1.16601e6i −0.342326 1.27758i −0.895706 0.444648i \(-0.853329\pi\)
0.553380 0.832929i \(-0.313338\pi\)
\(98\) 684983. 479630.i 0.727782 0.509598i
\(99\) −89560.7 106734.i −0.0923022 0.110001i
\(100\) −129741. 224718.i −0.129741 0.224718i
\(101\) 82793.4 + 47800.8i 0.0803584 + 0.0463950i 0.539641 0.841895i \(-0.318560\pi\)
−0.459282 + 0.888290i \(0.651893\pi\)
\(102\) 945080. 166643.i 0.890570 0.157032i
\(103\) −241124. + 899886.i −0.220662 + 0.823523i 0.763434 + 0.645886i \(0.223512\pi\)
−0.984096 + 0.177637i \(0.943155\pi\)
\(104\) −311486. 855801.i −0.276910 0.760804i
\(105\) −641228. 641228.i −0.553917 0.553917i
\(106\) −1.41277e6 658785.i −1.18619 0.553129i
\(107\) −245377. + 1.39160e6i −0.200301 + 1.13596i 0.704363 + 0.709840i \(0.251233\pi\)
−0.904665 + 0.426124i \(0.859879\pi\)
\(108\) 162270. + 136161.i 0.128816 + 0.108089i
\(109\) 66748.8 762942.i 0.0515423 0.589131i −0.925877 0.377824i \(-0.876672\pi\)
0.977420 0.211307i \(-0.0677720\pi\)
\(110\) 636598.i 0.478286i
\(111\) −1.43744e6 832638.i −1.05104 0.608817i
\(112\) −768350. −0.546896
\(113\) 1.99514e6 + 174552.i 1.38273 + 0.120973i 0.754115 0.656742i \(-0.228066\pi\)
0.628617 + 0.777715i \(0.283621\pi\)
\(114\) 489707. 583610.i 0.330538 0.393920i
\(115\) −814542. 143626.i −0.535575 0.0944362i
\(116\) −284983. + 611148.i −0.182577 + 0.391537i
\(117\) −526665. + 526665.i −0.328834 + 0.328834i
\(118\) 1.31196e6 477515.i 0.798501 0.290631i
\(119\) −493645. 132272.i −0.292937 0.0784922i
\(120\) −424782. 2.40906e6i −0.245823 1.39413i
\(121\) −804946. + 1.39421e6i −0.454371 + 0.786994i
\(122\) −3.19910e6 + 1.84700e6i −1.76176 + 1.01716i
\(123\) −941402. + 789930.i −0.505895 + 0.424496i
\(124\) 226819. + 323932.i 0.118964 + 0.169898i
\(125\) 44212.2 11846.6i 0.0226366 0.00606547i
\(126\) 206887. + 443671.i 0.103424 + 0.221794i
\(127\) −899140. 327260.i −0.438951 0.159765i 0.113085 0.993585i \(-0.463927\pi\)
−0.552036 + 0.833820i \(0.686149\pi\)
\(128\) −2.07296e6 1.45150e6i −0.988465 0.692131i
\(129\) −307462. 3.51431e6i −0.143226 1.63708i
\(130\) 3.39007e6 296593.i 1.54305 0.134999i
\(131\) 62192.0 88819.4i 0.0276644 0.0395088i −0.805082 0.593164i \(-0.797879\pi\)
0.832746 + 0.553655i \(0.186767\pi\)
\(132\) 76163.9 209259.i 0.0331152 0.0909833i
\(133\) −367704. + 171463.i −0.156294 + 0.0728812i
\(134\) −1.10213e6 4.11320e6i −0.458056 1.70949i
\(135\) 1.80878e6 1.26652e6i 0.735166 0.514769i
\(136\) −886150. 1.05607e6i −0.352282 0.419833i
\(137\) 2.01201e6 + 3.48490e6i 0.782470 + 1.35528i 0.930499 + 0.366294i \(0.119374\pi\)
−0.148029 + 0.988983i \(0.547293\pi\)
\(138\) 1.20015e6 + 692905.i 0.456664 + 0.263655i
\(139\) 2.25773e6 398098.i 0.840672 0.148233i 0.263300 0.964714i \(-0.415189\pi\)
0.577372 + 0.816481i \(0.304078\pi\)
\(140\) 120861. 451060.i 0.0440456 0.164381i
\(141\) −258863. 711221.i −0.0923449 0.253715i
\(142\) 310701. + 310701.i 0.108512 + 0.108512i
\(143\) −783251. 365236.i −0.267851 0.124901i
\(144\) −294347. + 1.66933e6i −0.0985764 + 0.559054i
\(145\) 5.38470e6 + 4.51830e6i 1.76627 + 1.48208i
\(146\) −472341. + 5.39888e6i −0.151774 + 1.73478i
\(147\) 3.04919e6i 0.959913i
\(148\) 1219.05 855419.i 0.000376041 0.263872i
\(149\) −582711. −0.176155 −0.0880773 0.996114i \(-0.528072\pi\)
−0.0880773 + 0.996114i \(0.528072\pi\)
\(150\) 4.51470e6 + 394985.i 1.33769 + 0.117033i
\(151\) −553030. + 659076.i −0.160627 + 0.191428i −0.840355 0.542037i \(-0.817653\pi\)
0.679728 + 0.733464i \(0.262098\pi\)
\(152\) −1.07781e6 190047.i −0.306910 0.0541166i
\(153\) −476486. + 1.02183e6i −0.133038 + 0.285301i
\(154\) −401648. + 401648.i −0.109972 + 0.109972i
\(155\) 3.87357e6 1.40986e6i 1.04020 0.378601i
\(156\) −1.14985e6 308101.i −0.302877 0.0811557i
\(157\) 794132. + 4.50374e6i 0.205208 + 1.16379i 0.897113 + 0.441802i \(0.145661\pi\)
−0.691905 + 0.721988i \(0.743228\pi\)
\(158\) −3.41690e6 + 5.91824e6i −0.866285 + 1.50045i
\(159\) 4.92261e6 2.84207e6i 1.22463 0.707039i
\(160\) 2.27584e6 1.90966e6i 0.555625 0.466225i
\(161\) −423300. 604536.i −0.101431 0.144859i
\(162\) −5.76819e6 + 1.54558e6i −1.35673 + 0.363535i
\(163\) −2.51835e6 5.40062e6i −0.581505 1.24704i −0.948488 0.316814i \(-0.897387\pi\)
0.366982 0.930228i \(-0.380391\pi\)
\(164\) −594662. 216439.i −0.134815 0.0490687i
\(165\) −1.90151e6 1.33145e6i −0.423299 0.296397i
\(166\) 374722. + 4.28310e6i 0.0819191 + 0.936340i
\(167\) 1.38773e6 121411.i 0.297959 0.0260680i 0.0628038 0.998026i \(-0.479996\pi\)
0.235155 + 0.971958i \(0.424440\pi\)
\(168\) 1.25194e6 1.78795e6i 0.264031 0.377075i
\(169\) 70797.2 194514.i 0.0146675 0.0402986i
\(170\) 4.66867e6 2.17704e6i 0.950268 0.443117i
\(171\) 231659. + 864564.i 0.0463299 + 0.172905i
\(172\) 1.48807e6 1.04196e6i 0.292441 0.204769i
\(173\) 2.72930e6 + 3.25265e6i 0.527124 + 0.628202i 0.962250 0.272168i \(-0.0877405\pi\)
−0.435126 + 0.900370i \(0.643296\pi\)
\(174\) −5.88869e6 1.01995e7i −1.11782 1.93612i
\(175\) −2.09011e6 1.20673e6i −0.389991 0.225162i
\(176\) −1.93695e6 + 341536.i −0.355287 + 0.0626467i
\(177\) −1.31765e6 + 4.91755e6i −0.237619 + 0.886806i
\(178\) −2.82608e6 7.76458e6i −0.501099 1.37676i
\(179\) −2.77840e6 2.77840e6i −0.484435 0.484435i 0.422110 0.906545i \(-0.361290\pi\)
−0.906545 + 0.422110i \(0.861290\pi\)
\(180\) −933679. 435382.i −0.160096 0.0746539i
\(181\) −1.88517e6 + 1.06913e7i −0.317918 + 1.80300i 0.237451 + 0.971400i \(0.423688\pi\)
−0.555369 + 0.831604i \(0.687423\pi\)
\(182\) 2.32602e6 + 1.95176e6i 0.385833 + 0.323753i
\(183\) 1.17398e6 1.34187e7i 0.191562 2.18956i
\(184\) 1.99079e6i 0.319575i
\(185\) −8.60981e6 2.32015e6i −1.35981 0.366438i
\(186\) −6.90664e6 −1.07332
\(187\) −1.30323e6 114018.i −0.199295 0.0174361i
\(188\) 250524. 298563.i 0.0377030 0.0449327i
\(189\) 1.94030e6 + 342127.i 0.287398 + 0.0506760i
\(190\) 1.72829e6 3.70633e6i 0.251974 0.540360i
\(191\) 9.21660e6 9.21660e6i 1.32273 1.32273i 0.411169 0.911559i \(-0.365121\pi\)
0.911559 0.411169i \(-0.134879\pi\)
\(192\) 4.97031e6 1.80904e6i 0.702230 0.255591i
\(193\) 431736. + 115683.i 0.0600546 + 0.0160916i 0.288721 0.957413i \(-0.406770\pi\)
−0.228667 + 0.973505i \(0.573437\pi\)
\(194\) 1.88526e6 + 1.06918e7i 0.258205 + 1.46435i
\(195\) −6.20445e6 + 1.07464e7i −0.836758 + 1.44931i
\(196\) −1.35981e6 + 785086.i −0.180597 + 0.104268i
\(197\) −5.01394e6 + 4.20719e6i −0.655813 + 0.550292i −0.908829 0.417170i \(-0.863022\pi\)
0.253016 + 0.967462i \(0.418578\pi\)
\(198\) 718758. + 1.02649e6i 0.0925950 + 0.132239i
\(199\) −2.33335e6 + 625219.i −0.296088 + 0.0793365i −0.403805 0.914845i \(-0.632313\pi\)
0.107717 + 0.994182i \(0.465646\pi\)
\(200\) −2.75141e6 5.90042e6i −0.343926 0.737552i
\(201\) 1.45912e7 + 5.31077e6i 1.79681 + 0.653987i
\(202\) −704322. 493171.i −0.0854510 0.0598334i
\(203\) 546637. + 6.24809e6i 0.0653448 + 0.746894i
\(204\) −1.79512e6 + 157053.i −0.211448 + 0.0184993i
\(205\) −3.78367e6 + 5.40363e6i −0.439189 + 0.627226i
\(206\) 2.86574e6 7.87356e6i 0.327820 0.900678i
\(207\) −1.47558e6 + 688076.i −0.166362 + 0.0775757i
\(208\) 2.72121e6 + 1.01557e7i 0.302393 + 1.12854i
\(209\) −850734. + 595690.i −0.0931869 + 0.0652502i
\(210\) 5.24248e6 + 6.24774e6i 0.566081 + 0.674629i
\(211\) −6.71518e6 1.16310e7i −0.714843 1.23814i −0.963020 0.269429i \(-0.913165\pi\)
0.248177 0.968715i \(-0.420168\pi\)
\(212\) 2.53489e6 + 1.46352e6i 0.266042 + 0.153600i
\(213\) −1.57789e6 + 278225.i −0.163282 + 0.0287911i
\(214\) 3.28929e6 1.22758e7i 0.335630 1.25259i
\(215\) −6.47660e6 1.77943e7i −0.651676 1.79046i
\(216\) 3.75812e6 + 3.75812e6i 0.372915 + 0.372915i
\(217\) 3.33347e6 + 1.55442e6i 0.326225 + 0.152121i
\(218\) −1.19608e6 + 6.78329e6i −0.115449 + 0.654743i
\(219\) −1.51385e7 1.27027e7i −1.44129 1.20938i
\(220\) 104182. 1.19081e6i 0.00978421 0.111834i
\(221\) 6.99322e6i 0.647888i
\(222\) 1.22261e7 + 8.58680e6i 1.11745 + 0.784824i
\(223\) 1.22292e7 1.10277 0.551383 0.834252i \(-0.314100\pi\)
0.551383 + 0.834252i \(0.314100\pi\)
\(224\) 2.64075e6 + 231036.i 0.234954 + 0.0205558i
\(225\) −3.42245e6 + 4.07872e6i −0.300462 + 0.358077i
\(226\) −1.77387e7 3.12781e6i −1.53673 0.270967i
\(227\) −313196. + 671652.i −0.0267756 + 0.0574204i −0.919241 0.393696i \(-0.871196\pi\)
0.892465 + 0.451116i \(0.148974\pi\)
\(228\) −1.01155e6 + 1.01155e6i −0.0853456 + 0.0853456i
\(229\) 1.01980e7 3.71178e6i 0.849200 0.309083i 0.119486 0.992836i \(-0.461875\pi\)
0.729714 + 0.683753i \(0.239653\pi\)
\(230\) 7.18534e6 + 1.92531e6i 0.590560 + 0.158240i
\(231\) −359667. 2.03977e6i −0.0291786 0.165480i
\(232\) −8.45943e6 + 1.46522e7i −0.677450 + 1.17338i
\(233\) 169550. 97890.0i 0.0134039 0.00773875i −0.493283 0.869869i \(-0.664203\pi\)
0.506687 + 0.862130i \(0.330870\pi\)
\(234\) 5.13151e6 4.30584e6i 0.400495 0.336055i
\(235\) −2.33029e6 3.32800e6i −0.179559 0.256436i
\(236\) −2.53228e6 + 678523.i −0.192653 + 0.0516212i
\(237\) −1.05312e7 2.25843e7i −0.791106 1.69653i
\(238\) 4.31915e6 + 1.57204e6i 0.320382 + 0.116609i
\(239\) −4.38364e6 3.06946e6i −0.321101 0.224837i 0.401902 0.915683i \(-0.368349\pi\)
−0.723002 + 0.690846i \(0.757238\pi\)
\(240\) 2.46133e6 + 2.81332e7i 0.178048 + 2.03510i
\(241\) −3.17302e6 + 277603.i −0.226684 + 0.0198323i −0.199932 0.979810i \(-0.564072\pi\)
−0.0267524 + 0.999642i \(0.508517\pi\)
\(242\) 8.30481e6 1.18605e7i 0.585981 0.836868i
\(243\) 4.32015e6 1.18695e7i 0.301078 0.827206i
\(244\) 6.28644e6 2.93142e6i 0.432748 0.201794i
\(245\) 4.23624e6 + 1.58099e7i 0.288059 + 1.07505i
\(246\) 9.05373e6 6.33949e6i 0.608166 0.425842i
\(247\) 3.56858e6 + 4.25287e6i 0.236813 + 0.282222i
\(248\) 4.96089e6 + 8.59251e6i 0.325240 + 0.563333i
\(249\) −1.35773e7 7.83886e6i −0.879458 0.507756i
\(250\) −405407. + 71484.2i −0.0259460 + 0.00457499i
\(251\) −2.54440e6 + 9.49582e6i −0.160903 + 0.600498i 0.837624 + 0.546247i \(0.183944\pi\)
−0.998527 + 0.0542511i \(0.982723\pi\)
\(252\) −314390. 863780.i −0.0196457 0.0539761i
\(253\) −1.33582e6 1.33582e6i −0.0824874 0.0824874i
\(254\) 7.79936e6 + 3.63690e6i 0.475946 + 0.221937i
\(255\) −3.26179e6 + 1.84986e7i −0.196714 + 1.11562i
\(256\) 9.52785e6 + 7.99482e6i 0.567904 + 0.476528i
\(257\) 860040. 9.83030e6i 0.0506663 0.579119i −0.927851 0.372952i \(-0.878346\pi\)
0.978517 0.206166i \(-0.0660988\pi\)
\(258\) 3.17276e7i 1.84747i
\(259\) −3.96833e6 6.89602e6i −0.228406 0.396917i
\(260\) −6.38994e6 −0.363561
\(261\) 1.37841e7 + 1.20595e6i 0.775276 + 0.0678279i
\(262\) −626834. + 747031.i −0.0348537 + 0.0415370i
\(263\) −2.39943e7 4.23085e6i −1.31899 0.232574i −0.530534 0.847664i \(-0.678008\pi\)
−0.788457 + 0.615090i \(0.789120\pi\)
\(264\) 2.36127e6 5.06377e6i 0.128332 0.275209i
\(265\) 2.15749e7 2.15749e7i 1.15934 1.15934i
\(266\) 3.42886e6 1.24800e6i 0.182182 0.0663087i
\(267\) 2.91035e7 + 7.79826e6i 1.52901 + 0.409698i
\(268\) 1.38848e6 + 7.87445e6i 0.0721331 + 0.409087i
\(269\) −6.65457e6 + 1.15261e7i −0.341872 + 0.592139i −0.984780 0.173804i \(-0.944394\pi\)
0.642909 + 0.765943i \(0.277728\pi\)
\(270\) −1.71987e7 + 9.92965e6i −0.873782 + 0.504478i
\(271\) 7.93837e6 6.66108e6i 0.398863 0.334686i −0.421191 0.906972i \(-0.638388\pi\)
0.820054 + 0.572286i \(0.193943\pi\)
\(272\) 9.12870e6 + 1.30371e7i 0.453631 + 0.647852i
\(273\) −1.06948e7 + 2.86566e6i −0.525636 + 0.140844i
\(274\) −1.52950e7 3.28002e7i −0.743528 1.59450i
\(275\) −5.80539e6 2.11299e6i −0.279147 0.101601i
\(276\) −2.13157e6 1.49254e6i −0.101385 0.0709905i
\(277\) 480906. + 5.49678e6i 0.0226267 + 0.258624i 0.999080 + 0.0428937i \(0.0136577\pi\)
−0.976453 + 0.215730i \(0.930787\pi\)
\(278\) −2.05402e7 + 1.79704e6i −0.956029 + 0.0836417i
\(279\) 4.65418e6 6.64686e6i 0.214304 0.306058i
\(280\) 4.00722e6 1.10097e7i 0.182545 0.501537i
\(281\) 3.16462e7 1.47569e7i 1.42627 0.665082i 0.452324 0.891854i \(-0.350595\pi\)
0.973948 + 0.226772i \(0.0728172\pi\)
\(282\) 1.76180e6 + 6.57512e6i 0.0785614 + 0.293195i
\(283\) −2.39444e7 + 1.67660e7i −1.05644 + 0.739726i −0.966615 0.256232i \(-0.917519\pi\)
−0.0898225 + 0.995958i \(0.528630\pi\)
\(284\) −530344. 632039.i −0.0231527 0.0275924i
\(285\) 7.45603e6 + 1.29142e7i 0.322087 + 0.557871i
\(286\) 6.73128e6 + 3.88630e6i 0.287739 + 0.166126i
\(287\) −5.79653e6 + 1.02209e6i −0.245201 + 0.0432356i
\(288\) 1.51360e6 5.64882e6i 0.0633626 0.236472i
\(289\) −4.63493e6 1.27344e7i −0.192021 0.527574i
\(290\) −4.47027e7 4.47027e7i −1.83291 1.83291i
\(291\) −3.58794e7 1.67308e7i −1.45601 0.678951i
\(292\) 1.76710e6 1.00217e7i 0.0709764 0.402527i
\(293\) 1.70754e7 + 1.43280e7i 0.678842 + 0.569616i 0.915668 0.401936i \(-0.131662\pi\)
−0.236825 + 0.971552i \(0.576107\pi\)
\(294\) 2.39013e6 2.73193e7i 0.0940545 1.07505i
\(295\) 2.73278e7i 1.06448i
\(296\) 1.90105e6 2.13781e7i 0.0733023 0.824317i
\(297\) 5.04341e6 0.192511
\(298\) 5.22082e6 + 456763.i 0.197283 + 0.0172600i
\(299\) −6.49129e6 + 7.73602e6i −0.242838 + 0.289404i
\(300\) −8.38047e6 1.47770e6i −0.310388 0.0547297i
\(301\) 7.14067e6 1.53132e7i 0.261842 0.561522i
\(302\) 5.47152e6 5.47152e6i 0.198649 0.198649i
\(303\) 2.94619e6 1.07233e6i 0.105909 0.0385478i
\(304\) 1.22043e7 + 3.27013e6i 0.434402 + 0.116398i
\(305\) −1.25556e7 7.12061e7i −0.442524 2.50968i
\(306\) 5.07007e6 8.78161e6i 0.176949 0.306485i
\(307\) −4.16564e7 + 2.40504e7i −1.43968 + 0.831202i −0.997827 0.0658843i \(-0.979013\pi\)
−0.441856 + 0.897086i \(0.645680\pi\)
\(308\) 817047. 685584.i 0.0279637 0.0234643i
\(309\) 1.75245e7 + 2.50276e7i 0.593978 + 0.848289i
\(310\) −3.58105e7 + 9.59541e6i −1.20206 + 0.322091i
\(311\) 4.09726e6 + 8.78661e6i 0.136211 + 0.292106i 0.962568 0.271042i \(-0.0873681\pi\)
−0.826356 + 0.563147i \(0.809590\pi\)
\(312\) −2.80662e7 1.02153e7i −0.924101 0.336345i
\(313\) 2.43688e7 + 1.70632e7i 0.794696 + 0.556452i 0.898926 0.438101i \(-0.144349\pi\)
−0.104229 + 0.994553i \(0.533238\pi\)
\(314\) −3.58476e6 4.09740e7i −0.115790 1.32349i
\(315\) −9.54549e6 + 835122.i −0.305398 + 0.0267189i
\(316\) 7.36014e6 1.05114e7i 0.233252 0.333118i
\(317\) −1.50488e7 + 4.13463e7i −0.472416 + 1.29795i 0.443390 + 0.896329i \(0.353776\pi\)
−0.915805 + 0.401622i \(0.868446\pi\)
\(318\) −4.63321e7 + 2.16050e7i −1.44079 + 0.671851i
\(319\) 4.15533e6 + 1.55079e7i 0.128007 + 0.477729i
\(320\) 2.32574e7 1.62850e7i 0.709761 0.496980i
\(321\) 2.97881e7 + 3.55001e7i 0.900591 + 1.07328i
\(322\) 3.31871e6 + 5.74817e6i 0.0994034 + 0.172172i
\(323\) 7.27799e6 + 4.20195e6i 0.215975 + 0.124693i
\(324\) 1.10428e7 1.94714e6i 0.324672 0.0572484i
\(325\) −8.54753e6 + 3.18998e7i −0.248995 + 0.929262i
\(326\) 1.83300e7 + 5.03612e7i 0.529065 + 1.45359i
\(327\) −1.77600e7 1.77600e7i −0.507925 0.507925i
\(328\) −1.43900e7 6.71017e6i −0.407793 0.190157i
\(329\) 629483. 3.56998e6i 0.0176765 0.100248i
\(330\) 1.59930e7 + 1.34197e7i 0.445029 + 0.373423i
\(331\) −717045. + 8.19586e6i −0.0197725 + 0.226001i 0.979879 + 0.199594i \(0.0639623\pi\)
−0.999651 + 0.0264073i \(0.991593\pi\)
\(332\) 8.07321e6i 0.220613i
\(333\) −1.65026e7 + 5.97984e6i −0.446910 + 0.161941i
\(334\) −1.25286e7 −0.336251
\(335\) 8.30328e7 + 7.26443e6i 2.20859 + 0.193227i
\(336\) −1.61971e7 + 1.93030e7i −0.426992 + 0.508869i
\(337\) 5.59951e7 + 9.87344e6i 1.46305 + 0.257976i 0.847784 0.530342i \(-0.177936\pi\)
0.615269 + 0.788317i \(0.289047\pi\)
\(338\) −786781. + 1.68726e6i −0.0203753 + 0.0436950i
\(339\) 4.64435e7 4.64435e7i 1.19214 1.19214i
\(340\) −9.08940e6 + 3.30827e6i −0.231259 + 0.0841714i
\(341\) 9.09435e6 + 2.43682e6i 0.229355 + 0.0614555i
\(342\) −1.39786e6 7.92768e6i −0.0349451 0.198184i
\(343\) −1.65420e7 + 2.86515e7i −0.409925 + 0.710012i
\(344\) 3.94721e7 2.27892e7i 0.969649 0.559827i
\(345\) −2.07791e7 + 1.74357e7i −0.506022 + 0.424603i
\(346\) −2.19037e7 3.12817e7i −0.528796 0.755199i
\(347\) 6.72303e7 1.80143e7i 1.60908 0.431151i 0.661309 0.750114i \(-0.270001\pi\)
0.947767 + 0.318963i \(0.103335\pi\)
\(348\) 9.34608e6 + 2.00427e7i 0.221764 + 0.475575i
\(349\) 2.62547e7 + 9.55594e6i 0.617634 + 0.224800i 0.631840 0.775099i \(-0.282300\pi\)
−0.0142062 + 0.999899i \(0.504522\pi\)
\(350\) 1.77805e7 + 1.24501e7i 0.414706 + 0.290380i
\(351\) −2.34974e6 2.68576e7i −0.0543373 0.621078i
\(352\) 6.75981e6 591407.i 0.154991 0.0135600i
\(353\) 2.15110e6 3.07209e6i 0.0489031 0.0698409i −0.793956 0.607975i \(-0.791982\pi\)
0.842859 + 0.538135i \(0.180871\pi\)
\(354\) 1.56602e7 4.30261e7i 0.353011 0.969890i
\(355\) −7.79475e6 + 3.63475e6i −0.174228 + 0.0812437i
\(356\) 4.01570e6 + 1.49868e7i 0.0890043 + 0.332168i
\(357\) −1.37292e7 + 9.61331e6i −0.301746 + 0.211285i
\(358\) 2.27153e7 + 2.70711e7i 0.495074 + 0.590006i
\(359\) −4.82379e6 8.35505e6i −0.104257 0.180578i 0.809177 0.587564i \(-0.199913\pi\)
−0.913434 + 0.406986i \(0.866580\pi\)
\(360\) −2.23848e7 1.29239e7i −0.479784 0.277003i
\(361\) −3.97609e7 + 7.01091e6i −0.845151 + 0.149023i
\(362\) 2.52708e7 9.43119e7i 0.532713 1.98811i
\(363\) 1.80576e7 + 4.96128e7i 0.377519 + 1.03723i
\(364\) −4.03160e6 4.03160e6i −0.0835936 0.0835936i
\(365\) −9.61401e7 4.48309e7i −1.97709 0.921931i
\(366\) −2.10367e7 + 1.19305e8i −0.429076 + 2.43341i
\(367\) −4.66117e7 3.91118e7i −0.942967 0.791243i 0.0351322 0.999383i \(-0.488815\pi\)
−0.978099 + 0.208139i \(0.933259\pi\)
\(368\) −2.00309e6 + 2.28954e7i −0.0401936 + 0.459415i
\(369\) 1.29852e7i 0.258445i
\(370\) 7.53213e7 + 2.75363e7i 1.48700 + 0.543627i
\(371\) 2.72245e7 0.533136
\(372\) 1.29194e7 + 1.13030e6i 0.250966 + 0.0219567i
\(373\) −4.50389e7 + 5.36753e7i −0.867883 + 1.03430i 0.131194 + 0.991357i \(0.458119\pi\)
−0.999077 + 0.0429460i \(0.986326\pi\)
\(374\) 1.15870e7 + 2.04310e6i 0.221491 + 0.0390548i
\(375\) 634391. 1.36046e6i 0.0120299 0.0257983i
\(376\) 6.91461e6 6.91461e6i 0.130078 0.130078i
\(377\) 8.06482e7 2.93535e7i 1.50512 0.547818i
\(378\) −1.71160e7 4.58623e6i −0.316904 0.0849141i
\(379\) −1.19498e7 6.77705e7i −0.219504 1.24487i −0.872918 0.487867i \(-0.837775\pi\)
0.653415 0.757000i \(-0.273336\pi\)
\(380\) −3.83947e6 + 6.65015e6i −0.0699713 + 0.121194i
\(381\) −2.71758e7 + 1.56900e7i −0.491369 + 0.283692i
\(382\) −8.98010e7 + 7.53520e7i −1.61098 + 1.35178i
\(383\) 4.74683e7 + 6.77917e7i 0.844903 + 1.20665i 0.976537 + 0.215349i \(0.0690888\pi\)
−0.131634 + 0.991298i \(0.542022\pi\)
\(384\) −8.01643e7 + 2.14800e7i −1.41575 + 0.379350i
\(385\) −4.69870e6 1.00764e7i −0.0823372 0.176573i
\(386\) −3.77748e6 1.37489e6i −0.0656811 0.0239060i
\(387\) −3.05342e7 2.13803e7i −0.526809 0.368876i
\(388\) −1.77676e6 2.03084e7i −0.0304182 0.347681i
\(389\) −5.39506e7 + 4.72006e6i −0.916531 + 0.0801861i −0.535652 0.844439i \(-0.679934\pi\)
−0.380879 + 0.924625i \(0.624379\pi\)
\(390\) 6.40127e7 9.14197e7i 1.07913 1.54115i
\(391\) −5.22839e6 + 1.43649e7i −0.0874657 + 0.240310i
\(392\) −3.57046e7 + 1.66493e7i −0.592742 + 0.276400i
\(393\) −920344. 3.43477e6i −0.0151626 0.0565874i
\(394\) 4.82204e7 3.37643e7i 0.788392 0.552038i
\(395\) −8.59803e7 1.02467e8i −1.39511 1.66262i
\(396\) −1.17651e6 2.03777e6i −0.0189456 0.0328148i
\(397\) 5.74663e7 + 3.31782e7i 0.918420 + 0.530250i 0.883131 0.469127i \(-0.155431\pi\)
0.0352893 + 0.999377i \(0.488765\pi\)
\(398\) 2.13958e7 3.77266e6i 0.339375 0.0598410i
\(399\) −3.44373e6 + 1.28522e7i −0.0542139 + 0.202329i
\(400\) 2.57061e7 + 7.06271e7i 0.401659 + 1.10355i
\(401\) −2.81102e7 2.81102e7i −0.435944 0.435944i 0.454701 0.890644i \(-0.349746\pi\)
−0.890644 + 0.454701i \(0.849746\pi\)
\(402\) −1.26568e8 5.90195e7i −1.94825 0.908484i
\(403\) 8.73971e6 4.95654e7i 0.133531 0.757292i
\(404\) 1.23678e6 + 1.03778e6i 0.0187564 + 0.0157385i
\(405\) 1.01873e7 1.16442e8i 0.153354 1.75285i
\(406\) 5.64085e7i 0.842881i
\(407\) −1.30691e7 1.56203e7i −0.193849 0.231690i
\(408\) −4.52116e7 −0.665686
\(409\) 3.50679e6 + 306804.i 0.0512554 + 0.00448426i 0.112755 0.993623i \(-0.464033\pi\)
−0.0614992 + 0.998107i \(0.519588\pi\)
\(410\) 3.81356e7 4.54482e7i 0.553323 0.659425i
\(411\) 1.29964e8 + 2.29161e7i 1.87196 + 0.330077i
\(412\) −6.64915e6 + 1.42591e7i −0.0950768 + 0.203893i
\(413\) −1.72419e7 + 1.72419e7i −0.244757 + 0.244757i
\(414\) 1.37599e7 5.00820e6i 0.193917 0.0705798i
\(415\) −8.12880e7 2.17811e7i −1.13732 0.304744i
\(416\) −6.29883e6 3.57224e7i −0.0874943 0.496205i
\(417\) 3.75924e7 6.51120e7i 0.518432 0.897951i
\(418\) 8.08912e6 4.67026e6i 0.110757 0.0639458i
\(419\) −6.05332e7 + 5.07934e7i −0.822908 + 0.690502i −0.953651 0.300914i \(-0.902708\pi\)
0.130743 + 0.991416i \(0.458264\pi\)
\(420\) −8.78401e6 1.25449e7i −0.118562 0.169324i
\(421\) −9.48289e7 + 2.54093e7i −1.27085 + 0.340523i −0.830356 0.557233i \(-0.811863\pi\)
−0.440493 + 0.897756i \(0.645197\pi\)
\(422\) 5.10479e7 + 1.09473e8i 0.679267 + 1.45669i
\(423\) −7.51503e6 2.73525e6i −0.0992909 0.0361389i
\(424\) 6.01579e7 + 4.21230e7i 0.789215 + 0.552614i
\(425\) 4.35706e6 + 4.98014e7i 0.0567579 + 0.648746i
\(426\) 1.43553e7 1.25593e6i 0.185688 0.0162456i
\(427\) 3.70043e7 5.28477e7i 0.475301 0.678801i
\(428\) −8.16188e6 + 2.24246e7i −0.104102 + 0.286018i
\(429\) −2.56869e7 + 1.19780e7i −0.325342 + 0.151709i
\(430\) 4.40791e7 + 1.64506e8i 0.554406 + 2.06907i
\(431\) −1.10022e8 + 7.70384e7i −1.37420 + 0.962222i −0.374812 + 0.927101i \(0.622293\pi\)
−0.999383 + 0.0351210i \(0.988818\pi\)
\(432\) −3.94395e7 4.70022e7i −0.489193 0.582998i
\(433\) −5.15051e6 8.92095e6i −0.0634434 0.109887i 0.832559 0.553936i \(-0.186875\pi\)
−0.896002 + 0.444049i \(0.853542\pi\)
\(434\) −2.86479e7 1.65399e7i −0.350448 0.202331i
\(435\) 2.27023e8 4.00302e7i 2.75805 0.486318i
\(436\) 3.34748e6 1.24929e7i 0.0403885 0.150732i
\(437\) 4.15068e6 + 1.14039e7i 0.0497365 + 0.136650i
\(438\) 1.25677e8 + 1.25677e8i 1.49566 + 1.49566i
\(439\) −5.79962e7 2.70441e7i −0.685497 0.319653i 0.0484823 0.998824i \(-0.484562\pi\)
−0.733980 + 0.679171i \(0.762339\pi\)
\(440\) 5.20797e6 2.95359e7i 0.0611379 0.346730i
\(441\) 2.46811e7 + 2.07099e7i 0.287772 + 0.241469i
\(442\) 5.48169e6 6.26560e7i 0.0634816 0.725598i
\(443\) 3.53897e7i 0.407067i −0.979068 0.203533i \(-0.934757\pi\)
0.979068 0.203533i \(-0.0652426\pi\)
\(444\) −2.14646e7 1.80632e7i −0.245231 0.206369i
\(445\) 1.61734e8 1.83536
\(446\) −1.09568e8 9.58596e6i −1.23503 0.108052i
\(447\) −1.22838e7 + 1.46392e7i −0.137533 + 0.163906i
\(448\) 2.49485e7 + 4.39909e6i 0.277466 + 0.0489248i
\(449\) −3.31007e7 + 7.09846e7i −0.365677 + 0.784197i 0.634262 + 0.773119i \(0.281304\pi\)
−0.999939 + 0.0110785i \(0.996474\pi\)
\(450\) 3.38607e7 3.38607e7i 0.371585 0.371585i
\(451\) −1.41582e7 + 5.15318e6i −0.154340 + 0.0561753i
\(452\) 3.26698e7 + 8.75386e6i 0.353779 + 0.0947947i
\(453\) 4.89962e6 + 2.77871e7i 0.0527069 + 0.298916i
\(454\) 3.33258e6 5.77219e6i 0.0356133 0.0616841i
\(455\) −5.14707e7 + 2.97166e7i −0.546419 + 0.315475i
\(456\) −2.74951e7 + 2.30711e7i −0.289975 + 0.243318i
\(457\) −5.31832e7 7.59535e7i −0.557219 0.795792i 0.437413 0.899261i \(-0.355895\pi\)
−0.994633 + 0.103469i \(0.967006\pi\)
\(458\) −9.42792e7 + 2.52620e7i −0.981340 + 0.262949i
\(459\) −1.72474e7 3.69872e7i −0.178355 0.382485i
\(460\) −1.31257e7 4.77736e6i −0.134849 0.0490811i
\(461\) 3.56906e7 + 2.49908e7i 0.364294 + 0.255081i 0.741363 0.671104i \(-0.234179\pi\)
−0.377070 + 0.926185i \(0.623068\pi\)
\(462\) 1.62356e6 + 1.85573e7i 0.0164642 + 0.188187i
\(463\) −3.64226e7 + 3.18657e6i −0.366968 + 0.0321056i −0.269149 0.963099i \(-0.586742\pi\)
−0.0978194 + 0.995204i \(0.531187\pi\)
\(464\) 1.12032e8 1.59998e8i 1.12147 1.60162i
\(465\) 4.62368e7 1.27035e8i 0.459864 1.26346i
\(466\) −1.59583e6 + 744146.i −0.0157699 + 0.00735361i
\(467\) 2.42830e7 + 9.06254e7i 0.238425 + 0.889814i 0.976575 + 0.215177i \(0.0690330\pi\)
−0.738150 + 0.674637i \(0.764300\pi\)
\(468\) −1.03036e7 + 7.21464e6i −0.100519 + 0.0703845i
\(469\) 4.78045e7 + 5.69711e7i 0.463394 + 0.552251i
\(470\) 1.82696e7 + 3.16440e7i 0.175969 + 0.304788i
\(471\) 1.29886e8 + 7.49899e7i 1.24308 + 0.717695i
\(472\) −6.47769e7 + 1.14219e7i −0.616019 + 0.108621i
\(473\) 1.11942e7 4.17774e7i 0.105782 0.394783i
\(474\) 7.66522e7 + 2.10600e8i 0.719763 + 1.97753i
\(475\) 2.80630e7 + 2.80630e7i 0.261850 + 0.261850i
\(476\) −7.82205e6 3.64748e6i −0.0725270 0.0338199i
\(477\) 1.04294e7 5.91483e7i 0.0960962 0.544988i
\(478\) 3.68694e7 + 3.09371e7i 0.337584 + 0.283267i
\(479\) −1.82252e7 + 2.08315e8i −0.165831 + 1.89546i 0.224031 + 0.974582i \(0.428078\pi\)
−0.389862 + 0.920873i \(0.627477\pi\)
\(480\) 9.74313e7i 0.880998i
\(481\) −7.70940e7 + 7.68745e7i −0.692764 + 0.690792i
\(482\) 2.86464e7 0.255817
\(483\) −2.41108e7 2.10943e6i −0.213979 0.0187207i
\(484\) −1.74759e7 + 2.08269e7i −0.154135 + 0.183691i
\(485\) −2.09277e8 3.69011e7i −1.83441 0.323455i
\(486\) −4.80105e7 + 1.02959e8i −0.418242 + 0.896923i
\(487\) −1.37633e7 + 1.37633e7i −0.119161 + 0.119161i −0.764173 0.645012i \(-0.776853\pi\)
0.645012 + 0.764173i \(0.276853\pi\)
\(488\) 1.63537e8 5.95226e7i 1.40720 0.512179i
\(489\) −1.88766e8 5.05796e7i −1.61434 0.432562i
\(490\) −2.55621e7 1.44970e8i −0.217274 1.23222i
\(491\) −2.19023e7 + 3.79359e7i −0.185031 + 0.320483i −0.943587 0.331125i \(-0.892572\pi\)
0.758556 + 0.651608i \(0.225905\pi\)
\(492\) −1.79732e7 + 1.03768e7i −0.150914 + 0.0871305i
\(493\) 9.95212e7 8.35082e7i 0.830567 0.696929i
\(494\) −2.86392e7 4.09010e7i −0.237564 0.339276i
\(495\) −2.36922e7 + 6.34829e6i −0.195339 + 0.0523409i
\(496\) −4.84079e7 1.03811e8i −0.396708 0.850743i
\(497\) −7.21120e6 2.62466e6i −0.0587406 0.0213798i
\(498\) 1.15502e8 + 8.08752e7i 0.935192 + 0.654829i
\(499\) −1.19193e7 1.36238e8i −0.0959288 1.09647i −0.879734 0.475465i \(-0.842280\pi\)
0.783806 0.621006i \(-0.213276\pi\)
\(500\) 770045. 67370.2i 0.00616036 0.000538962i
\(501\) 2.62037e7 3.74228e7i 0.208377 0.297593i
\(502\) 3.02400e7 8.30838e7i 0.239040 0.656757i
\(503\) 2.59059e7 1.20801e7i 0.203561 0.0949220i −0.318164 0.948036i \(-0.603066\pi\)
0.521725 + 0.853114i \(0.325289\pi\)
\(504\) −5.96917e6 2.22773e7i −0.0466254 0.174008i
\(505\) 1.37861e7 9.65310e6i 0.107045 0.0749537i
\(506\) 1.09213e7 + 1.30155e7i 0.0842989 + 0.100463i
\(507\) −3.39426e6 5.87903e6i −0.0260448 0.0451109i
\(508\) −1.39941e7 8.07952e6i −0.106747 0.0616303i
\(509\) 8.26478e7 1.45730e7i 0.626726 0.110509i 0.148741 0.988876i \(-0.452478\pi\)
0.477986 + 0.878367i \(0.341367\pi\)
\(510\) 4.37244e7 1.63182e8i 0.329620 1.23016i
\(511\) −3.23725e7 8.89426e7i −0.242612 0.666572i
\(512\) 3.54244e7 + 3.54244e7i 0.263932 + 0.263932i
\(513\) −2.93632e7 1.36923e7i −0.217496 0.101420i
\(514\) −1.54111e7 + 8.74009e7i −0.113487 + 0.643615i
\(515\) 1.25634e8 + 1.05420e8i 0.919786 + 0.771792i
\(516\) 5.19237e6 5.93490e7i 0.0377934 0.431981i
\(517\) 9.27942e6i 0.0671505i
\(518\) 3.01489e7 + 6.48958e7i 0.216911 + 0.466904i
\(519\) 1.39250e8 0.996075
\(520\) −1.59714e8 1.39731e7i −1.13588 0.0993765i
\(521\) −1.36264e8 + 1.62393e8i −0.963533 + 1.14829i 0.0253620 + 0.999678i \(0.491926\pi\)
−0.988895 + 0.148616i \(0.952518\pi\)
\(522\) −1.22554e8 2.16095e7i −0.861619 0.151927i
\(523\) 3.41264e7 7.31843e7i 0.238553 0.511579i −0.750186 0.661227i \(-0.770036\pi\)
0.988739 + 0.149648i \(0.0478140\pi\)
\(524\) 1.29480e6 1.29480e6i 0.00899929 0.00899929i
\(525\) −7.43764e7 + 2.70708e7i −0.513993 + 0.187078i
\(526\) 2.11662e8 + 5.67147e7i 1.45441 + 0.389707i
\(527\) −1.32297e7 7.50293e7i −0.0903895 0.512624i
\(528\) −3.22512e7 + 5.58608e7i −0.219101 + 0.379494i
\(529\) 1.09085e8 6.29804e7i 0.736884 0.425440i
\(530\) −2.10213e8 + 1.76390e8i −1.41199 + 1.18480i
\(531\) 3.08548e7 + 4.40652e7i 0.206081 + 0.294315i
\(532\) −6.61820e6 + 1.77334e6i −0.0439547 + 0.0117776i
\(533\) 3.40386e7 + 7.29959e7i 0.224796 + 0.482078i
\(534\) −2.54641e8 9.26818e7i −1.67226 0.608654i
\(535\) 2.03770e8 + 1.42681e8i 1.33069 + 0.931762i
\(536\) 1.74850e7 + 1.99854e8i 0.113546 + 1.29783i
\(537\) −1.28370e8 + 1.12310e7i −0.828976 + 0.0725260i
\(538\) 6.86567e7 9.80519e7i 0.440896 0.629665i
\(539\) −1.27861e7 + 3.51295e7i −0.0816529 + 0.224340i
\(540\) 3.37965e7 1.57596e7i 0.214630 0.100084i
\(541\) −8.43228e6 3.14697e7i −0.0532541 0.198747i 0.934173 0.356819i \(-0.116139\pi\)
−0.987428 + 0.158072i \(0.949472\pi\)
\(542\) −7.63455e7 + 5.34577e7i −0.479497 + 0.335747i
\(543\) 2.28854e8 + 2.72738e8i 1.42942 + 1.70352i
\(544\) −2.74544e7 4.75524e7i −0.170536 0.295377i
\(545\) −1.16759e8 6.74106e7i −0.721272 0.416427i
\(546\) 9.80668e7 1.72918e7i 0.602482 0.106234i
\(547\) 5.82083e7 2.17236e8i 0.355650 1.32731i −0.524014 0.851710i \(-0.675566\pi\)
0.879664 0.475595i \(-0.157767\pi\)
\(548\) 2.32426e7 + 6.38586e7i 0.141235 + 0.388041i
\(549\) −1.00642e8 1.00642e8i −0.608219 0.608219i
\(550\) 5.03573e7 + 2.34820e7i 0.302674 + 0.141139i
\(551\) 1.79095e7 1.01570e8i 0.107060 0.607169i
\(552\) −5.00139e7 4.19666e7i −0.297354 0.249509i
\(553\) 1.04021e7 1.18897e8i 0.0615102 0.703065i
\(554\) 4.96256e7i 0.291861i
\(555\) −2.39786e8 + 1.67391e8i −1.40264 + 0.979160i
\(556\) 3.87163e7 0.225252
\(557\) 7.10204e6 + 621348.i 0.0410977 + 0.00359558i 0.107686 0.994185i \(-0.465656\pi\)
−0.0665884 + 0.997781i \(0.521211\pi\)
\(558\) −4.69095e7 + 5.59046e7i −0.269997 + 0.321769i
\(559\) −2.27692e8 4.01483e7i −1.30351 0.229843i
\(560\) −5.71634e7 + 1.22587e8i −0.325502 + 0.698042i
\(561\) −3.03371e7 + 3.03371e7i −0.171824 + 0.171824i
\(562\) −2.95103e8 + 1.07409e8i −1.66251 + 0.605104i
\(563\) −3.31025e8 8.86979e7i −1.85496 0.497036i −0.855190 0.518314i \(-0.826560\pi\)
−0.999774 + 0.0212778i \(0.993227\pi\)
\(564\) −2.21954e6 1.25876e7i −0.0123716 0.0701628i
\(565\) 1.76283e8 3.05331e8i 0.977382 1.69288i
\(566\) 2.27673e8 1.31447e8i 1.25563 0.724938i
\(567\) 7.98940e7 6.70390e7i 0.438293 0.367772i
\(568\) −1.18736e7 1.69572e7i −0.0647943 0.0925358i
\(569\) 1.29582e8 3.47214e7i 0.703410 0.188478i 0.110652 0.993859i \(-0.464706\pi\)
0.592757 + 0.805381i \(0.298039\pi\)
\(570\) −5.66797e7 1.21550e8i −0.306057 0.656342i
\(571\) −2.54440e8 9.26086e7i −1.36671 0.497442i −0.448589 0.893738i \(-0.648073\pi\)
−0.918123 + 0.396296i \(0.870295\pi\)
\(572\) −1.19554e7 8.37125e6i −0.0638816 0.0447304i
\(573\) −3.72557e7 4.25834e8i −0.198029 2.26348i
\(574\) 5.27355e7 4.61375e6i 0.278848 0.0243960i
\(575\) −4.14071e7 + 5.91355e7i −0.217807 + 0.311060i
\(576\) 1.91151e7 5.25182e7i 0.100025 0.274816i
\(577\) 3.13922e8 1.46384e8i 1.63416 0.762020i 0.634219 0.773153i \(-0.281322\pi\)
0.999938 + 0.0111335i \(0.00354398\pi\)
\(578\) 3.15449e7 + 1.17727e8i 0.163360 + 0.609668i
\(579\) 1.20074e7 8.40769e6i 0.0618606 0.0433153i
\(580\) 7.63043e7 + 9.09359e7i 0.391079 + 0.466070i
\(581\) −3.75447e7 6.50293e7i −0.191434 0.331574i
\(582\) 3.08348e8 + 1.78025e8i 1.56413 + 0.903050i
\(583\) 6.86307e7 1.21014e7i 0.346348 0.0610705i
\(584\) 6.60829e7 2.46625e8i 0.331780 1.23822i
\(585\) 4.48448e7 + 1.23210e8i 0.223998 + 0.615429i
\(586\) −1.41757e8 1.41757e8i −0.704452 0.704452i
\(587\) 1.86381e7 + 8.69107e6i 0.0921481 + 0.0429694i 0.468146 0.883651i \(-0.344922\pi\)
−0.375998 + 0.926621i \(0.622700\pi\)
\(588\) −8.94187e6 + 5.07119e7i −0.0439842 + 0.249447i
\(589\) −4.63324e7 3.88775e7i −0.226746 0.190262i
\(590\) 2.14211e7 2.44845e8i 0.104301 1.19216i
\(591\) 2.14652e8i 1.03986i
\(592\) −4.33734e7 + 2.43950e8i −0.209054 + 1.17580i
\(593\) −1.37369e8 −0.658756 −0.329378 0.944198i \(-0.606839\pi\)
−0.329378 + 0.944198i \(0.606839\pi\)
\(594\) −4.51867e7 3.95332e6i −0.215601 0.0188626i
\(595\) −5.78295e7 + 6.89185e7i −0.274535 + 0.327179i
\(596\) −9.69122e6 1.70882e6i −0.0457762 0.00807158i
\(597\) −3.34807e7 + 7.17996e7i −0.157352 + 0.337442i
\(598\) 6.42229e7 6.42229e7i 0.300322 0.300322i
\(599\) −1.02003e8 + 3.71259e7i −0.474604 + 0.172742i −0.568237 0.822865i \(-0.692374\pi\)
0.0936331 + 0.995607i \(0.470152\pi\)
\(600\) −2.06235e8 5.52604e7i −0.954790 0.255835i
\(601\) 5.09194e7 + 2.88778e8i 0.234563 + 1.33027i 0.843532 + 0.537079i \(0.180472\pi\)
−0.608969 + 0.793194i \(0.708416\pi\)
\(602\) −7.59805e7 + 1.31602e8i −0.348267 + 0.603217i
\(603\) 1.42090e8 8.20355e7i 0.648053 0.374154i
\(604\) −1.11304e7 + 9.33948e6i −0.0505125 + 0.0423850i
\(605\) 1.62554e8 + 2.32152e8i 0.734062 + 1.04835i
\(606\) −2.72371e7 + 7.29816e6i −0.122389 + 0.0327941i
\(607\) 1.02642e8 + 2.20117e8i 0.458944 + 0.984208i 0.990542 + 0.137211i \(0.0438138\pi\)
−0.531598 + 0.846997i \(0.678408\pi\)
\(608\) −4.09618e7 1.49089e7i −0.182250 0.0663337i
\(609\) 1.68492e8 + 1.17979e8i 0.745978 + 0.522340i
\(610\) 5.66766e7 + 6.47816e8i 0.249697 + 2.85405i
\(611\) −4.94156e7 + 4.32331e6i −0.216641 + 0.0189536i
\(612\) −1.09211e7 + 1.55970e7i −0.0476445 + 0.0680434i
\(613\) −9.56992e7 + 2.62932e8i −0.415458 + 1.14146i 0.538789 + 0.842441i \(0.318882\pi\)
−0.954247 + 0.299020i \(0.903340\pi\)
\(614\) 3.92075e8 1.82827e8i 1.69381 0.789835i
\(615\) 5.59923e7 + 2.08966e8i 0.240715 + 0.898360i
\(616\) 2.19209e7 1.53492e7i 0.0937813 0.0656664i
\(617\) 1.62711e8 + 1.93912e8i 0.692727 + 0.825560i 0.991683 0.128707i \(-0.0410826\pi\)
−0.298955 + 0.954267i \(0.596638\pi\)
\(618\) −1.37393e8 2.37972e8i −0.582104 1.00823i
\(619\) 2.15079e8 + 1.24176e8i 0.906832 + 0.523560i 0.879411 0.476064i \(-0.157937\pi\)
0.0274215 + 0.999624i \(0.491270\pi\)
\(620\) 6.85569e7 1.20884e7i 0.287658 0.0507218i
\(621\) 1.52531e7 5.69255e7i 0.0636919 0.237701i
\(622\) −2.98221e7 8.19357e7i −0.123927 0.340488i
\(623\) 1.02043e8 + 1.02043e8i 0.422005 + 0.422005i
\(624\) 3.12501e8 + 1.45722e8i 1.28617 + 0.599750i
\(625\) 4.30883e7 2.44366e8i 0.176490 1.00092i
\(626\) −2.04958e8 1.71980e8i −0.835492 0.701061i
\(627\) −2.96849e6 + 3.39300e7i −0.0120430 + 0.137652i
\(628\) 7.72318e7i 0.311830i
\(629\) −6.98623e7 + 1.49265e8i −0.280731 + 0.599798i
\(630\) 8.61778e7 0.344647
\(631\) 4.91238e8 + 4.29778e7i 1.95526 + 0.171063i 0.994377 0.105900i \(-0.0337725\pi\)
0.960881 + 0.276963i \(0.0893280\pi\)
\(632\) 2.06949e8 2.46632e8i 0.819807 0.977008i
\(633\) −4.33761e8 7.64837e7i −1.71017 0.301549i
\(634\) 1.67240e8 3.58647e8i 0.656255 1.40734i
\(635\) −1.19107e8 + 1.19107e8i −0.465175 + 0.465175i
\(636\) 9.02037e7 3.28315e7i 0.350633 0.127620i
\(637\) 1.93032e8 + 5.17228e7i 0.746812 + 0.200108i
\(638\) −2.50739e7 1.42201e8i −0.0965516 0.547571i
\(639\) −8.46492e6 + 1.46617e7i −0.0324430 + 0.0561928i
\(640\) −3.85805e8 + 2.22745e8i −1.47173 + 0.849704i
\(641\) −3.35499e6 + 2.81517e6i −0.0127385 + 0.0106888i −0.649135 0.760674i \(-0.724869\pi\)
0.636396 + 0.771362i \(0.280424\pi\)
\(642\) −2.39061e8 3.41414e8i −0.903447 1.29026i
\(643\) 3.90204e7 1.04555e7i 0.146777 0.0393289i −0.184682 0.982798i \(-0.559126\pi\)
0.331460 + 0.943469i \(0.392459\pi\)
\(644\) −5.26720e6 1.12955e7i −0.0197207 0.0422912i
\(645\) −5.83569e8 2.12402e8i −2.17477 0.791550i
\(646\) −6.19137e7 4.33525e7i −0.229662 0.160811i
\(647\) 3.99647e7 + 4.56798e8i 0.147558 + 1.68660i 0.604110 + 0.796901i \(0.293529\pi\)
−0.456551 + 0.889697i \(0.650916\pi\)
\(648\) 2.80267e8 2.45202e7i 1.03002 0.0901155i
\(649\) −3.58013e7 + 5.11295e7i −0.130968 + 0.187041i
\(650\) 1.01587e8 2.79108e8i 0.369911 1.01632i
\(651\) 1.09322e8 5.09777e7i 0.396246 0.184772i
\(652\) −2.60458e7 9.72044e7i −0.0939714 0.350706i
\(653\) 2.98009e7 2.08668e7i 0.107026 0.0749405i −0.518838 0.854872i \(-0.673635\pi\)
0.625864 + 0.779932i \(0.284746\pi\)
\(654\) 1.45200e8 + 1.73043e8i 0.519079 + 0.618615i
\(655\) −9.54386e6 1.65304e7i −0.0339625 0.0588248i
\(656\) 1.58743e8 + 9.16502e7i 0.562319 + 0.324655i
\(657\) −2.05640e8 + 3.62598e7i −0.725121 + 0.127858i
\(658\) −8.43824e6 + 3.14919e7i −0.0296193 + 0.110541i
\(659\) 1.34498e8 + 3.69531e8i 0.469960 + 1.29120i 0.917783 + 0.397082i \(0.129977\pi\)
−0.447823 + 0.894122i \(0.647800\pi\)
\(660\) −2.77200e7 2.77200e7i −0.0964188 0.0964188i
\(661\) −3.76747e8 1.75680e8i −1.30450 0.608300i −0.358825 0.933405i \(-0.616823\pi\)
−0.945678 + 0.325105i \(0.894600\pi\)
\(662\) 1.28488e7 7.28691e7i 0.0442882 0.251171i
\(663\) 1.75688e8 + 1.47420e8i 0.602839 + 0.505842i
\(664\) 1.76540e7 2.01786e8i 0.0603029 0.689266i
\(665\) 7.14222e7i 0.242867i
\(666\) 1.52543e8 4.06409e7i 0.516381 0.137575i
\(667\) 1.87607e8 0.632223
\(668\) 2.34358e7 + 2.05037e6i 0.0786231 + 0.00687863i
\(669\) 2.57796e8 3.07229e8i 0.860989 1.02609i
\(670\) −7.38242e8 1.30172e8i −2.45456 0.432806i
\(671\) 6.97937e7 1.49673e8i 0.231020 0.495423i
\(672\) 6.14722e7 6.14722e7i 0.202568 0.202568i
\(673\) 6.94528e7 2.52788e7i 0.227848 0.0829298i −0.225573 0.974226i \(-0.572426\pi\)
0.453421 + 0.891296i \(0.350203\pi\)
\(674\) −4.93951e8 1.32354e8i −1.61326 0.432271i
\(675\) −3.34668e7 1.89800e8i −0.108818 0.617140i
\(676\) 1.74787e6 3.02739e6i 0.00565807 0.00980006i
\(677\) −1.25083e8 + 7.22165e7i −0.403117 + 0.232740i −0.687828 0.725874i \(-0.741436\pi\)
0.284711 + 0.958613i \(0.408102\pi\)
\(678\) −4.52517e8 + 3.79707e8i −1.45193 + 1.21832i
\(679\) −1.08757e8 1.55321e8i −0.347413 0.496158i
\(680\) −2.34420e8 + 6.28126e7i −0.745534 + 0.199765i
\(681\) 1.02713e7 + 2.20270e7i 0.0325227 + 0.0697451i
\(682\) −7.95711e7 2.89615e7i −0.250843 0.0912994i
\(683\) −4.57914e8 3.20635e8i −1.43721 1.00635i −0.993936 0.109965i \(-0.964926\pi\)
−0.443279 0.896384i \(-0.646185\pi\)
\(684\) 1.31742e6 + 1.50581e7i 0.00411675 + 0.0470547i
\(685\) 7.05690e8 6.17399e7i 2.19555 0.192085i
\(686\) 1.70667e8 2.43738e8i 0.528662 0.755007i
\(687\) 1.21729e8 3.34447e8i 0.375424 1.03147i
\(688\) −4.76885e8 + 2.22375e8i −1.46436 + 0.682842i
\(689\) −9.64189e7 3.59840e8i −0.294784 1.10015i
\(690\) 1.99838e8 1.39928e8i 0.608319 0.425950i
\(691\) 1.43250e7 + 1.70719e7i 0.0434170 + 0.0517424i 0.787316 0.616550i \(-0.211470\pi\)
−0.743899 + 0.668292i \(0.767026\pi\)
\(692\) 3.58532e7 + 6.20995e7i 0.108196 + 0.187400i
\(693\) −1.89534e7 1.09427e7i −0.0569491 0.0328796i
\(694\) −6.16473e8 + 1.08701e8i −1.84432 + 0.325203i
\(695\) 1.04454e8 3.89829e8i 0.311152 1.16123i
\(696\) 1.89773e8 + 5.21396e8i 0.562867 + 1.54646i
\(697\) 8.62106e7 + 8.62106e7i 0.254602 + 0.254602i
\(698\) −2.27740e8 1.06197e8i −0.669688 0.312281i
\(699\) 1.11493e6 6.32311e6i 0.00326451 0.0185139i
\(700\) −3.12224e7 2.61987e7i −0.0910274 0.0763811i
\(701\) 1.50271e7 1.71760e8i 0.0436235 0.498619i −0.942682 0.333692i \(-0.891706\pi\)
0.986306 0.164927i \(-0.0527389\pi\)
\(702\) 2.42474e8i 0.700896i
\(703\) 3.36823e7 + 1.26424e8i 0.0969472 + 0.363885i
\(704\) 6.48485e7 0.185858
\(705\) −1.32731e8 1.16125e7i −0.378797 0.0331404i
\(706\) −2.16809e7 + 2.58383e7i −0.0616118 + 0.0734261i
\(707\) 1.47884e7 + 2.60760e6i 0.0418470 + 0.00737875i
\(708\) −3.63352e7 + 7.79210e7i −0.102383 + 0.219561i
\(709\) −6.06419e7 + 6.06419e7i −0.170151 + 0.170151i −0.787046 0.616895i \(-0.788390\pi\)
0.616895 + 0.787046i \(0.288390\pi\)
\(710\) 7.26865e7 2.64557e7i 0.203086 0.0739171i
\(711\) −2.54332e8 6.81481e7i −0.707608 0.189603i
\(712\) 6.75983e7 + 3.83369e8i 0.187282 + 1.06213i
\(713\) 5.50093e7 9.52789e7i 0.151764 0.262862i
\(714\) 1.30543e8 7.53691e7i 0.358640 0.207061i
\(715\) −1.16544e8 + 9.77920e7i −0.318839 + 0.267538i
\(716\) −3.80606e7 5.43561e7i −0.103690 0.148084i
\(717\) −1.69521e8 + 4.54231e7i −0.459904 + 0.123231i
\(718\) 3.66698e7 + 7.86386e7i 0.0990683 + 0.212453i
\(719\) −2.75165e8 1.00152e8i −0.740298 0.269446i −0.0557807 0.998443i \(-0.517765\pi\)
−0.684517 + 0.728997i \(0.739987\pi\)
\(720\) 2.44436e8 + 1.71156e8i 0.654889 + 0.458558i
\(721\) 1.27540e7 + 1.45779e8i 0.0340283 + 0.388945i
\(722\) 3.61735e8 3.16477e7i 0.961122 0.0840873i
\(723\) −5.99143e7 + 8.55665e7i −0.158532 + 0.226406i
\(724\) −6.27056e7 + 1.72282e8i −0.165231 + 0.453968i
\(725\) 5.56038e8 2.59285e8i 1.45912 0.680398i
\(726\) −1.22898e8 4.58662e8i −0.321170 1.19862i
\(727\) −5.27275e8 + 3.69202e8i −1.37225 + 0.960862i −0.372796 + 0.927913i \(0.621601\pi\)
−0.999457 + 0.0329488i \(0.989510\pi\)
\(728\) −9.19518e7 1.09584e8i −0.238323 0.284023i
\(729\) 3.48975e7 + 6.04443e7i 0.0900766 + 0.156017i
\(730\) 8.26230e8 + 4.77024e8i 2.12389 + 1.22623i
\(731\) −3.44668e8 + 6.07743e7i −0.882366 + 0.155585i
\(732\) 5.88757e7 2.19727e8i 0.150108 0.560209i
\(733\) −1.08518e8 2.98149e8i −0.275542 0.757046i −0.997854 0.0654782i \(-0.979143\pi\)
0.722312 0.691567i \(-0.243079\pi\)
\(734\) 3.86961e8 + 3.86961e8i 0.978541 + 0.978541i
\(735\) 4.86486e8 + 2.26852e8i 1.22520 + 0.571322i
\(736\) 1.37689e7 7.80872e7i 0.0345355 0.195860i
\(737\) 1.45835e8 + 1.22370e8i 0.364300 + 0.305684i
\(738\) 1.01785e7 1.16341e8i 0.0253231 0.289444i
\(739\) 1.43211e8i 0.354850i −0.984134 0.177425i \(-0.943223\pi\)
0.984134 0.177425i \(-0.0567766\pi\)
\(740\) −1.36388e8 6.38356e7i −0.336575 0.157532i
\(741\) 1.82070e8 0.447491
\(742\) −2.43919e8 2.13402e7i −0.597082 0.0522379i
\(743\) 4.01199e8 4.78130e8i 0.978122 1.16568i −0.00805147 0.999968i \(-0.502563\pi\)
0.986174 0.165713i \(-0.0529927\pi\)
\(744\) 3.20444e8 + 5.65029e7i 0.778095 + 0.137199i
\(745\) −4.33523e7 + 9.29693e7i −0.104844 + 0.224838i
\(746\) 4.45602e8 4.45602e8i 1.07332 1.07332i
\(747\) −1.55666e8 + 5.66579e7i −0.373451 + 0.135925i
\(748\) −2.13401e7 5.71805e6i −0.0509907 0.0136629i
\(749\) 3.85426e7 + 2.18586e8i 0.0917266 + 0.520207i
\(750\) −6.75026e6 + 1.16918e7i −0.0160006 + 0.0277139i
\(751\) −2.82840e8 + 1.63298e8i −0.667760 + 0.385532i −0.795227 0.606311i \(-0.792649\pi\)
0.127467 + 0.991843i \(0.459315\pi\)
\(752\) −8.64798e7 + 7.25652e7i −0.203358 + 0.170638i
\(753\) 1.84923e8 + 2.64097e8i 0.433117 + 0.618556i
\(754\) −7.45580e8 + 1.99778e8i −1.73932 + 0.466050i
\(755\) 6.40089e7 + 1.37268e8i 0.148730 + 0.318953i
\(756\) 3.12664e7 + 1.13800e7i 0.0723622 + 0.0263377i
\(757\) 1.09640e8 + 7.67709e7i 0.252745 + 0.176974i 0.693082 0.720859i \(-0.256252\pi\)
−0.440337 + 0.897832i \(0.645141\pi\)
\(758\) 5.39420e7 + 6.16559e8i 0.123857 + 1.41569i
\(759\) −6.17190e7 + 5.39972e6i −0.141154 + 0.0123494i
\(760\) −1.10508e8 + 1.57821e8i −0.251740 + 0.359522i
\(761\) −9.69082e6 + 2.66253e7i −0.0219891 + 0.0604144i −0.950202 0.311636i \(-0.899123\pi\)
0.928212 + 0.372051i \(0.121345\pi\)
\(762\) 2.55782e8 1.19273e8i 0.578102 0.269574i
\(763\) −3.11351e7 1.16198e8i −0.0700932 0.261591i
\(764\) 1.80312e8 1.26256e8i 0.404338 0.283120i
\(765\) 1.27579e8 + 1.52043e8i 0.284968 + 0.339611i
\(766\) −3.72155e8 6.44591e8i −0.828013 1.43416i
\(767\) 2.88959e8 + 1.66831e8i 0.640399 + 0.369735i
\(768\) 4.01701e8 7.08308e7i 0.886787 0.156365i
\(769\) −9.03860e7 + 3.37325e8i −0.198757 + 0.741771i 0.792505 + 0.609865i \(0.208776\pi\)
−0.991262 + 0.131906i \(0.957890\pi\)
\(770\) 3.41998e7 + 9.39631e7i 0.0749119 + 0.205819i
\(771\) −2.28833e8 2.28833e8i −0.499293 0.499293i
\(772\) 6.84108e6 + 3.19005e6i 0.0148687 + 0.00693338i
\(773\) 2.42157e7 1.37334e8i 0.0524273 0.297330i −0.947308 0.320323i \(-0.896208\pi\)
0.999736 + 0.0229931i \(0.00731956\pi\)
\(774\) 2.56813e8 + 2.15492e8i 0.553853 + 0.464738i
\(775\) 3.13576e7 3.58419e8i 0.0673656 0.769992i
\(776\) 5.11485e8i 1.09458i
\(777\) −2.56900e8 4.56760e7i −0.547647 0.0973699i
\(778\) 4.87072e8 1.03432
\(779\) 9.64209e7 + 8.43573e6i 0.203966 + 0.0178447i
\(780\) −1.34702e8 + 1.60532e8i −0.283852 + 0.338281i
\(781\) −1.93455e7 3.41114e6i −0.0406095 0.00716054i
\(782\) 5.81040e7 1.24604e8i 0.121503 0.260563i
\(783\) −3.54155e8 + 3.54155e8i −0.737748 + 0.737748i
\(784\) 4.27378e8 1.55553e8i 0.886878 0.322797i
\(785\) 7.77637e8 + 2.08367e8i 1.60756 + 0.430745i
\(786\) 5.55349e6 + 3.14954e7i 0.0114366 + 0.0648603i
\(787\) −1.69453e7 + 2.93500e7i −0.0347635 + 0.0602122i −0.882884 0.469592i \(-0.844401\pi\)
0.848120 + 0.529804i \(0.177734\pi\)
\(788\) −9.57259e7 + 5.52674e7i −0.195637 + 0.112951i
\(789\) −6.12100e8 + 5.13613e8i −1.24621 + 1.04569i
\(790\) 6.90024e8 + 9.85456e8i 1.39953 + 1.99874i
\(791\) 3.03864e8 8.14201e7i 0.613973 0.164514i
\(792\) −2.49501e7 5.35057e7i −0.0502224 0.107702i
\(793\) −8.29570e8 3.01939e8i −1.66354 0.605480i
\(794\) −4.88864e8 3.42306e8i −0.976623 0.683839i
\(795\) −8.72110e7 9.96826e8i −0.173568 1.98389i
\(796\) −4.06400e7 + 3.55554e6i −0.0805777 + 0.00704964i
\(797\) 3.68708e7 5.26570e7i 0.0728296 0.104011i −0.781085 0.624425i \(-0.785333\pi\)
0.853914 + 0.520414i \(0.174222\pi\)
\(798\) 4.09285e7 1.12450e8i 0.0805411 0.221285i
\(799\) −6.80532e7 + 3.17337e7i −0.133416 + 0.0622129i
\(800\) −6.71129e7 2.50469e8i −0.131080 0.489197i
\(801\) 2.60791e8 1.82608e8i 0.507452 0.355321i
\(802\) 2.29820e8 + 2.73889e8i 0.445517 + 0.530947i
\(803\) −1.21144e8 2.09827e8i −0.233967 0.405242i
\(804\) 2.27096e8 + 1.31114e8i 0.436960 + 0.252279i
\(805\) −1.27944e8 + 2.25600e7i −0.245263 + 0.0432465i
\(806\) −1.17156e8 + 4.37232e8i −0.223748 + 0.835040i
\(807\) 1.49284e8 + 4.10154e8i 0.284048 + 0.780416i
\(808\) 2.86434e7 + 2.86434e7i 0.0542988 + 0.0542988i
\(809\) −6.76404e8 3.15412e8i −1.27750 0.595707i −0.338934 0.940810i \(-0.610066\pi\)
−0.938565 + 0.345103i \(0.887844\pi\)
\(810\) −1.82548e8 + 1.03528e9i −0.343496 + 1.94806i
\(811\) 2.05475e8 + 1.72414e8i 0.385209 + 0.323228i 0.814743 0.579822i \(-0.196878\pi\)
−0.429535 + 0.903050i \(0.641322\pi\)
\(812\) −9.23151e6 + 1.05517e8i −0.0172427 + 0.197085i
\(813\) 3.39851e8i 0.632436i
\(814\) 1.04849e8 + 1.50196e8i 0.194398 + 0.278473i
\(815\) −1.04901e9 −1.93779
\(816\) 5.19963e8 + 4.54909e7i 0.956979 + 0.0837248i
\(817\) −1.78595e8 + 2.12841e8i −0.327493 + 0.390291i
\(818\) −3.11787e7 5.49765e6i −0.0569637 0.0100442i
\(819\) −4.94429e7 + 1.06031e8i −0.0900020 + 0.193010i
\(820\) −7.87735e7 + 7.87735e7i −0.142869 + 0.142869i
\(821\) 5.19163e8 1.88960e8i 0.938154 0.341460i 0.172718 0.984971i \(-0.444745\pi\)
0.765437 + 0.643511i \(0.222523\pi\)
\(822\) −1.14645e9 3.07191e8i −2.06414 0.553086i
\(823\) −9.59506e7 5.44163e8i −0.172127 0.976179i −0.941408 0.337269i \(-0.890497\pi\)
0.769281 0.638910i \(-0.220614\pi\)
\(824\) −1.97373e8 + 3.41861e8i −0.352782 + 0.611037i
\(825\) −1.75463e8 + 1.01304e8i −0.312482 + 0.180411i
\(826\) 1.67995e8 1.40964e8i 0.298096 0.250132i
\(827\) −3.21751e8 4.59509e8i −0.568858 0.812414i 0.426912 0.904293i \(-0.359601\pi\)
−0.995770 + 0.0918796i \(0.970712\pi\)
\(828\) −2.65587e7 + 7.11637e6i −0.0467859 + 0.0125362i
\(829\) 5.61088e7 + 1.20326e8i 0.0984845 + 0.211201i 0.949377 0.314139i \(-0.101716\pi\)
−0.850892 + 0.525340i \(0.823938\pi\)
\(830\) 7.11230e8 + 2.58867e8i 1.24387 + 0.452733i
\(831\) 1.48231e8 + 1.03793e8i 0.258307 + 0.180869i
\(832\) −3.02131e7 3.45337e8i −0.0524596 0.599616i
\(833\) 3.01358e8 2.63654e7i 0.521372 0.0456141i
\(834\) −3.87849e8 + 5.53906e8i −0.668598 + 0.954857i
\(835\) 8.38733e7 2.30440e8i 0.144067 0.395821i
\(836\) −1.58957e7 + 7.41227e6i −0.0272057 + 0.0126862i
\(837\) 7.60191e7 + 2.83707e8i 0.129642 + 0.483831i
\(838\) 5.82165e8 4.07636e8i 0.989267 0.692692i
\(839\) −1.81412e8 2.16199e8i −0.307172 0.366073i 0.590270 0.807206i \(-0.299021\pi\)
−0.897442 + 0.441133i \(0.854577\pi\)
\(840\) −1.92120e8 3.32761e8i −0.324141 0.561429i
\(841\) −8.65646e8 4.99781e8i −1.45530 0.840218i
\(842\) 8.69541e8 1.53323e8i 1.45664 0.256846i
\(843\) 2.96382e8 1.10611e9i 0.494732 1.84636i
\(844\) −7.75735e7 2.13132e8i −0.129029 0.354503i
\(845\) −2.57668e7 2.57668e7i −0.0427061 0.0427061i
\(846\) 6.51872e7 + 3.03973e7i 0.107659 + 0.0502023i
\(847\) −4.39110e7 + 2.49032e8i −0.0722642 + 0.409830i
\(848\) −6.49472e8 5.44972e8i −1.06506 0.893690i
\(849\) −8.35498e7 + 9.54979e8i −0.136528 + 1.56052i
\(850\) 4.49613e8i 0.732120i
\(851\) −2.15834e8 + 1.00271e8i −0.350212 + 0.162700i
\(852\) −2.70583e7 −0.0437504
\(853\) 8.80803e8 + 7.70603e7i 1.41916 + 0.124161i 0.770754 0.637133i \(-0.219880\pi\)
0.648407 + 0.761294i \(0.275435\pi\)
\(854\) −3.72967e8 + 4.44485e8i −0.598821 + 0.713647i
\(855\) 1.55173e8 + 2.73611e7i 0.248266 + 0.0437760i
\(856\) −2.53039e8 + 5.42644e8i −0.403428 + 0.865154i
\(857\) −8.15181e8 + 8.15181e8i −1.29513 + 1.29513i −0.363551 + 0.931574i \(0.618436\pi\)
−0.931574 + 0.363551i \(0.881564\pi\)
\(858\) 2.39532e8 8.71824e7i 0.379229 0.138028i
\(859\) 7.20082e8 + 1.92945e8i 1.13606 + 0.304407i 0.777367 0.629048i \(-0.216555\pi\)
0.358696 + 0.933455i \(0.383222\pi\)
\(860\) −5.55315e7 3.14935e8i −0.0873060 0.495137i
\(861\) −9.65156e7 + 1.67170e8i −0.151213 + 0.261908i
\(862\) 1.04614e9 6.03987e8i 1.63330 0.942987i
\(863\) 5.74030e8 4.81668e8i 0.893104 0.749403i −0.0757262 0.997129i \(-0.524127\pi\)
0.968830 + 0.247725i \(0.0796830\pi\)
\(864\) 1.21417e8 + 1.73402e8i 0.188252 + 0.268851i
\(865\) 7.22002e8 1.93460e8i 1.11555 0.298911i
\(866\) 3.91535e7 + 8.39649e7i 0.0602860 + 0.129284i
\(867\) −4.17626e8 1.52004e8i −0.640812 0.233236i
\(868\) 5.08814e7 + 3.56276e7i 0.0778037 + 0.0544787i
\(869\) −2.66274e7 3.04353e8i −0.0405761 0.463787i
\(870\) −2.06540e9 + 1.80699e8i −3.13651 + 0.274409i
\(871\) 5.83712e8 8.33627e8i 0.883372 1.26159i
\(872\) 1.10987e8 3.04935e8i 0.167388 0.459894i
\(873\) −3.79115e8 + 1.76784e8i −0.569808 + 0.265706i
\(874\) −2.82491e7 1.05427e8i −0.0423127 0.157913i
\(875\) 5.88937e6 4.12378e6i 0.00879113 0.00615562i
\(876\) −2.14521e8 2.55656e8i −0.319123 0.380316i
\(877\) 2.18253e7 + 3.78025e7i 0.0323565 + 0.0560431i 0.881750 0.471717i \(-0.156365\pi\)
−0.849394 + 0.527760i \(0.823032\pi\)
\(878\) 4.98421e8 + 2.87763e8i 0.736398 + 0.425159i
\(879\) 7.19913e8 1.26940e8i 1.06002 0.186910i
\(880\) −8.96134e7 + 3.34442e8i −0.131500 + 0.490764i
\(881\) −1.37948e8 3.79008e8i −0.201737 0.554269i 0.797028 0.603942i \(-0.206404\pi\)
−0.998766 + 0.0496733i \(0.984182\pi\)
\(882\) −2.04898e8 2.04898e8i −0.298629 0.298629i
\(883\) −5.92832e8 2.76442e8i −0.861092 0.401534i −0.0586607 0.998278i \(-0.518683\pi\)
−0.802432 + 0.596744i \(0.796461\pi\)
\(884\) −2.05079e7 + 1.16306e8i −0.0296869 + 0.168363i
\(885\) 6.86546e8 + 5.76080e8i 0.990466 + 0.831100i
\(886\) −2.77405e7 + 3.17076e8i −0.0398854 + 0.455892i
\(887\) 5.96329e8i 0.854506i 0.904132 + 0.427253i \(0.140519\pi\)
−0.904132 + 0.427253i \(0.859481\pi\)
\(888\) −4.96999e8 4.98418e8i −0.709769 0.711795i
\(889\) −1.50296e8 −0.213916
\(890\) −1.44906e9 1.26777e8i −2.05550 0.179833i
\(891\) 1.71607e8 2.04513e8i 0.242606 0.289126i
\(892\) 2.03387e8 + 3.58626e7i 0.286569 + 0.0505298i
\(893\) −2.51926e7 + 5.40256e7i −0.0353767 + 0.0758657i
\(894\) 1.21532e8 1.21532e8i 0.170090 0.170090i
\(895\) −6.49990e8 + 2.36577e8i −0.906645 + 0.329992i
\(896\) −3.83952e8 1.02880e8i −0.533768 0.143023i
\(897\) 5.75101e7 + 3.26156e8i 0.0796832 + 0.451906i
\(898\) 3.52209e8 6.10043e8i 0.486375 0.842426i
\(899\) −8.09733e8 + 4.67500e8i −1.11446 + 0.643432i
\(900\) −6.88807e7 + 5.77977e7i −0.0944865 + 0.0792836i
\(901\) −3.23452e8 4.61937e8i −0.442217 0.631552i
\(902\) 1.30891e8 3.50721e7i 0.178357 0.0477905i
\(903\) −2.34180e8 5.02201e8i −0.318043 0.682046i
\(904\) 7.97425e8 + 2.90239e8i 1.07940 + 0.392871i
\(905\) 1.56551e9 + 1.09618e9i 2.11208 + 1.47889i
\(906\) −2.21172e7 2.52800e8i −0.0297403 0.339933i
\(907\) 6.74253e8 5.89895e7i 0.903651 0.0790592i 0.374150 0.927368i \(-0.377935\pi\)
0.529501 + 0.848309i \(0.322379\pi\)
\(908\) −7.17850e6 + 1.02520e7i −0.00958906 + 0.0136946i
\(909\) 1.13306e7 3.11306e7i 0.0150856 0.0414473i
\(910\) 4.84447e8 2.25901e8i 0.642869 0.299775i
\(911\) 2.41266e8 + 9.00416e8i 0.319110 + 1.19093i 0.920102 + 0.391679i \(0.128106\pi\)
−0.600992 + 0.799255i \(0.705228\pi\)
\(912\) 3.39425e8 2.37668e8i 0.447466 0.313319i
\(913\) −1.23553e8 1.47244e8i −0.162345 0.193476i
\(914\) 4.16961e8 + 7.22197e8i 0.546080 + 0.945839i
\(915\) −2.05356e9 1.18562e9i −2.68067 1.54769i
\(916\) 1.80491e8 3.18255e7i 0.234839 0.0414084i
\(917\) 4.40804e6 1.64510e7i 0.00571660 0.0213346i
\(918\) 1.25536e8 + 3.44908e8i 0.162271 + 0.445837i
\(919\) 2.01780e8 + 2.01780e8i 0.259975 + 0.259975i 0.825044 0.565069i \(-0.191150\pi\)
−0.565069 + 0.825044i \(0.691150\pi\)
\(920\) −3.17623e8 1.48110e8i −0.407895 0.190205i
\(921\) −2.73925e8 + 1.55351e9i −0.350634 + 1.98854i
\(922\) −3.00182e8 2.51883e8i −0.382994 0.321371i
\(923\) −9.15217e6 + 1.04610e8i −0.0116391 + 0.133035i
\(924\) 3.49787e7i 0.0443392i
\(925\) −5.01120e8 + 5.95486e8i −0.633164 + 0.752395i
\(926\) 3.28828e8 0.414129
\(927\) 3.21607e8 + 2.81369e7i 0.403725 + 0.0353214i
\(928\) −4.33153e8 + 5.16212e8i −0.541998 + 0.645928i
\(929\) 5.63437e8 + 9.93491e7i 0.702746 + 0.123913i 0.513592 0.858034i \(-0.328314\pi\)
0.189154 + 0.981948i \(0.439426\pi\)
\(930\) −5.13838e8 + 1.10193e9i −0.638818 + 1.36995i
\(931\) 1.69814e8 1.69814e8i 0.210439 0.210439i
\(932\) 3.10691e6 1.13082e6i 0.00383778 0.00139684i
\(933\) 3.07114e8 + 8.22910e7i 0.378142 + 0.101323i
\(934\) −1.46527e8 8.30996e8i −0.179836 1.01990i
\(935\) −1.15149e8 + 1.99443e8i −0.140872 + 0.243997i
\(936\) −2.73309e8 + 1.57795e8i −0.333294 + 0.192427i
\(937\) 7.68877e6 6.45165e6i 0.00934627 0.00784245i −0.638103 0.769951i \(-0.720280\pi\)
0.647449 + 0.762109i \(0.275836\pi\)
\(938\) −3.83649e8 5.47907e8i −0.464863 0.663894i
\(939\) 9.42376e8 2.52509e8i 1.13822 0.304986i
\(940\) −2.89962e7 6.21825e7i −0.0349106 0.0748660i
\(941\) 7.48659e8 + 2.72489e8i 0.898494 + 0.327025i 0.749649 0.661836i \(-0.230222\pi\)
0.148845 + 0.988861i \(0.452445\pi\)
\(942\) −1.10494e9 7.73688e8i −1.32186 0.925578i
\(943\) 1.53447e7 + 1.75391e8i 0.0182988 + 0.209156i
\(944\) 7.56469e8 6.61825e7i 0.899239 0.0786733i
\(945\) 1.98939e8 2.84114e8i 0.235735 0.336665i
\(946\) −1.33043e8 + 3.65532e8i −0.157151 + 0.431769i
\(947\) −5.88891e7 + 2.74605e7i −0.0693402 + 0.0323339i −0.456979 0.889477i \(-0.651069\pi\)
0.387639 + 0.921811i \(0.373291\pi\)
\(948\) −1.08918e8 4.06489e8i −0.127843 0.477116i
\(949\) −1.06095e9 + 7.42885e8i −1.24136 + 0.869206i
\(950\) −2.29434e8 2.73429e8i −0.267600 0.318914i
\(951\) 7.21491e8 + 1.24966e9i 0.838860 + 1.45295i
\(952\) −1.87532e8 1.08272e8i −0.217353 0.125489i
\(953\) 1.10783e9 1.95341e8i 1.27996 0.225691i 0.507997 0.861359i \(-0.330386\pi\)
0.771963 + 0.635667i \(0.219275\pi\)
\(954\) −1.39807e8 + 5.21767e8i −0.161021 + 0.600940i
\(955\) −7.84780e8 2.15617e9i −0.901027 2.47555i
\(956\) −6.39042e7 6.39042e7i −0.0731401 0.0731401i
\(957\) 4.77195e8 + 2.22520e8i 0.544453 + 0.253882i
\(958\) 3.26579e8 1.85212e9i 0.371442 2.10655i
\(959\) 4.84194e8 + 4.06287e8i 0.548989 + 0.460656i
\(960\) 8.11529e7 9.27582e8i 0.0917256 1.04843i
\(961\) 3.39189e8i 0.382184i
\(962\) 7.50985e8 6.28330e8i 0.843541 0.705769i
\(963\) 4.89668e8 0.548306
\(964\) −5.35854e7 4.68812e6i −0.0598158 0.00523320i
\(965\) 5.05770e7 6.02753e7i 0.0562822 0.0670745i
\(966\) 2.14369e8 + 3.77990e7i 0.237810 + 0.0419323i
\(967\) −7.14850e7 + 1.53300e8i −0.0790562 + 0.169537i −0.941863 0.335997i \(-0.890927\pi\)
0.862807 + 0.505534i \(0.168704\pi\)
\(968\) −4.82344e8 + 4.82344e8i −0.531778 + 0.531778i
\(969\) 2.58987e8 9.42634e7i 0.284647 0.103603i
\(970\) 1.84610e9 + 4.94660e8i 2.02274 + 0.541991i
\(971\) −9.03616e7 5.12466e8i −0.0987021 0.559767i −0.993550 0.113396i \(-0.963827\pi\)
0.894848 0.446371i \(-0.147284\pi\)
\(972\) 1.06657e8 1.84736e8i 0.116143 0.201165i
\(973\) 3.11858e8 1.80051e8i 0.338546 0.195460i
\(974\) 1.34101e8 1.12524e8i 0.145130 0.121778i
\(975\) 6.21221e8 + 8.87196e8i 0.670243 + 0.957207i
\(976\) −1.94067e9 + 5.20001e8i −2.08738 + 0.559313i
\(977\) −5.97731e8 1.28184e9i −0.640947 1.37452i −0.911296 0.411753i \(-0.864917\pi\)
0.270348 0.962763i \(-0.412861\pi\)
\(978\) 1.65161e9 + 6.01135e8i 1.76559 + 0.642622i
\(979\) 3.02599e8 + 2.11882e8i 0.322493 + 0.225812i
\(980\) 2.40910e7 + 2.75361e8i 0.0255962 + 0.292566i
\(981\) −2.64380e8 + 2.31302e7i −0.280041 + 0.0245004i
\(982\) 2.25971e8 3.22720e8i 0.238626 0.340793i
\(983\) −1.18766e8 + 3.26308e8i −0.125035 + 0.343532i −0.986378 0.164492i \(-0.947402\pi\)
0.861343 + 0.508024i \(0.169624\pi\)
\(984\) −4.71924e8 + 2.20062e8i −0.495321 + 0.230972i
\(985\) 2.98217e8 + 1.11296e9i 0.312049 + 1.16458i
\(986\) −9.57123e8 + 6.70185e8i −0.998474 + 0.699139i
\(987\) −7.64174e7 9.10707e7i −0.0794769 0.0947168i
\(988\) 4.68783e7 + 8.11957e7i 0.0486073 + 0.0841903i
\(989\) −4.37690e8 2.52700e8i −0.452457 0.261226i
\(990\) 2.17247e8 3.83065e7i 0.223897 0.0394791i
\(991\) −4.12678e8 + 1.54013e9i −0.424023 + 1.58248i 0.342023 + 0.939692i \(0.388888\pi\)
−0.766046 + 0.642785i \(0.777779\pi\)
\(992\) 1.35159e8 + 3.71345e8i 0.138455 + 0.380402i
\(993\) 1.90786e8 + 1.90786e8i 0.194849 + 0.194849i
\(994\) 6.25517e7 + 2.91683e7i 0.0636913 + 0.0296997i
\(995\) −7.38443e7 + 4.18792e8i −0.0749631 + 0.425137i
\(996\) −2.02820e8 1.70186e8i −0.205273 0.172245i
\(997\) −1.24018e8 + 1.41754e9i −0.125141 + 1.43037i 0.630909 + 0.775857i \(0.282682\pi\)
−0.756050 + 0.654513i \(0.772874\pi\)
\(998\) 1.22998e9i 1.23738i
\(999\) 2.18155e8 5.96728e8i 0.218811 0.598522i
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 37.7.i.a.2.4 216
37.19 odd 36 inner 37.7.i.a.19.4 yes 216
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
37.7.i.a.2.4 216 1.1 even 1 trivial
37.7.i.a.19.4 yes 216 37.19 odd 36 inner