Properties

Label 76.6.k.a.3.1
Level $76$
Weight $6$
Character 76.3
Analytic conductor $12.189$
Analytic rank $0$
Dimension $288$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [76,6,Mod(3,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 13]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.3");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 76.k (of order \(18\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(12.1891703058\)
Analytic rank: \(0\)
Dimension: \(288\)
Relative dimension: \(48\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 3.1
Character \(\chi\) \(=\) 76.3
Dual form 76.6.k.a.51.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.65633 - 0.0770723i) q^{2} +(-6.62020 + 2.40955i) q^{3} +(31.9881 + 0.871892i) q^{4} +(8.57723 - 48.6439i) q^{5} +(37.6317 - 13.1190i) q^{6} +(27.9453 - 16.1342i) q^{7} +(-180.868 - 7.39710i) q^{8} +(-148.128 + 124.294i) q^{9} +O(q^{10})\) \(q+(-5.65633 - 0.0770723i) q^{2} +(-6.62020 + 2.40955i) q^{3} +(31.9881 + 0.871892i) q^{4} +(8.57723 - 48.6439i) q^{5} +(37.6317 - 13.1190i) q^{6} +(27.9453 - 16.1342i) q^{7} +(-180.868 - 7.39710i) q^{8} +(-148.128 + 124.294i) q^{9} +(-52.2648 + 274.485i) q^{10} +(638.582 + 368.686i) q^{11} +(-213.869 + 71.3050i) q^{12} +(88.0086 - 241.802i) q^{13} +(-159.311 + 89.1067i) q^{14} +(60.4272 + 342.700i) q^{15} +(1022.48 + 55.7804i) q^{16} +(-1495.60 - 1254.96i) q^{17} +(847.439 - 691.631i) q^{18} +(-809.616 - 1349.30i) q^{19} +(316.782 - 1548.55i) q^{20} +(-146.127 + 174.148i) q^{21} +(-3583.62 - 2134.62i) q^{22} +(-1705.75 + 300.770i) q^{23} +(1215.21 - 386.841i) q^{24} +(643.879 + 234.353i) q^{25} +(-516.442 + 1360.93i) q^{26} +(1537.12 - 2662.37i) q^{27} +(907.985 - 491.738i) q^{28} +(-3897.01 - 4644.27i) q^{29} +(-315.383 - 1943.08i) q^{30} +(-1934.61 - 3350.84i) q^{31} +(-5779.18 - 394.317i) q^{32} +(-5115.91 - 902.072i) q^{33} +(8362.90 + 7213.74i) q^{34} +(-545.139 - 1497.76i) q^{35} +(-4846.70 + 3846.78i) q^{36} -14166.8i q^{37} +(4475.46 + 7694.50i) q^{38} +1812.84i q^{39} +(-1911.17 + 8734.69i) q^{40} +(590.364 + 1622.01i) q^{41} +(839.965 - 973.774i) q^{42} +(17143.4 + 3022.85i) q^{43} +(20105.6 + 12350.3i) q^{44} +(4775.62 + 8271.61i) q^{45} +(9671.48 - 1569.79i) q^{46} +(-15203.7 - 18119.1i) q^{47} +(-6903.42 + 2094.44i) q^{48} +(-7882.87 + 13653.5i) q^{49} +(-3623.93 - 1375.20i) q^{50} +(12925.1 + 4704.35i) q^{51} +(3026.05 - 7658.04i) q^{52} +(-37495.2 + 6611.41i) q^{53} +(-8899.64 + 14940.7i) q^{54} +(23411.6 - 27900.8i) q^{55} +(-5173.76 + 2711.45i) q^{56} +(8611.04 + 6981.84i) q^{57} +(21684.8 + 26569.9i) q^{58} +(-2080.00 - 1745.33i) q^{59} +(1634.15 + 11015.0i) q^{60} +(2402.17 + 13623.4i) q^{61} +(10684.5 + 19102.6i) q^{62} +(-2134.09 + 5863.36i) q^{63} +(32658.6 + 2675.80i) q^{64} +(-11007.3 - 6355.07i) q^{65} +(28867.7 + 5496.71i) q^{66} +(-27194.7 + 22819.1i) q^{67} +(-46747.3 - 41447.8i) q^{68} +(10567.7 - 6101.27i) q^{69} +(2968.05 + 8513.82i) q^{70} +(1389.38 - 7879.55i) q^{71} +(27711.0 - 21385.1i) q^{72} +(13035.2 - 4744.42i) q^{73} +(-1091.87 + 80132.1i) q^{74} -4827.29 q^{75} +(-24721.7 - 43867.6i) q^{76} +23793.8 q^{77} +(139.719 - 10254.0i) q^{78} +(-37883.5 + 13788.5i) q^{79} +(11483.4 - 49259.0i) q^{80} +(4398.51 - 24945.2i) q^{81} +(-3214.28 - 9220.14i) q^{82} +(72432.4 - 41818.9i) q^{83} +(-4826.17 + 5443.25i) q^{84} +(-73874.3 + 61987.9i) q^{85} +(-96735.9 - 18419.5i) q^{86} +(36989.6 + 21355.9i) q^{87} +(-112772. - 71407.1i) q^{88} +(37782.8 - 103808. i) q^{89} +(-26374.9 - 47155.0i) q^{90} +(-1441.86 - 8177.17i) q^{91} +(-54826.1 + 8133.85i) q^{92} +(20881.5 + 17521.7i) q^{93} +(84600.9 + 103659. i) q^{94} +(-72579.7 + 27809.6i) q^{95} +(39209.5 - 11314.8i) q^{96} +(65639.4 - 78226.0i) q^{97} +(45640.4 - 76621.3i) q^{98} +(-140417. + 24759.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9} - 657 q^{10} - 9 q^{12} + 336 q^{13} - 2163 q^{14} + 1824 q^{16} - 12 q^{17} - 10242 q^{20} - 7842 q^{21} - 102 q^{22} - 11856 q^{24} - 12 q^{25} + 1317 q^{26} + 6660 q^{28} - 12 q^{29} - 40692 q^{30} - 3351 q^{32} - 8604 q^{33} - 15756 q^{34} + 81783 q^{36} + 50400 q^{38} + 39246 q^{40} - 29082 q^{41} - 123081 q^{42} - 39651 q^{44} - 6 q^{45} - 112554 q^{46} - 68403 q^{48} + 259302 q^{49} + 154188 q^{50} - 36867 q^{52} - 26280 q^{53} + 172605 q^{54} - 12 q^{57} + 229740 q^{58} - 136062 q^{60} + 169296 q^{61} + 35076 q^{62} + 63795 q^{64} - 189918 q^{65} + 73644 q^{66} + 59706 q^{68} - 200898 q^{69} - 177831 q^{70} - 188502 q^{72} + 397428 q^{73} - 530703 q^{74} - 53022 q^{76} + 159804 q^{77} - 618237 q^{78} + 18045 q^{80} - 110160 q^{81} + 155859 q^{82} + 733851 q^{84} - 645108 q^{85} + 616836 q^{86} + 598383 q^{88} - 226320 q^{89} + 546366 q^{90} - 754308 q^{92} + 558942 q^{93} - 454530 q^{96} - 177198 q^{97} - 76791 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.65633 0.0770723i −0.999907 0.0136246i
\(3\) −6.62020 + 2.40955i −0.424686 + 0.154573i −0.545516 0.838100i \(-0.683666\pi\)
0.120831 + 0.992673i \(0.461444\pi\)
\(4\) 31.9881 + 0.871892i 0.999629 + 0.0272466i
\(5\) 8.57723 48.6439i 0.153434 0.870169i −0.806769 0.590867i \(-0.798786\pi\)
0.960203 0.279302i \(-0.0901030\pi\)
\(6\) 37.6317 13.1190i 0.426752 0.148772i
\(7\) 27.9453 16.1342i 0.215558 0.124452i −0.388334 0.921519i \(-0.626949\pi\)
0.603892 + 0.797066i \(0.293616\pi\)
\(8\) −180.868 7.39710i −0.999165 0.0408636i
\(9\) −148.128 + 124.294i −0.609579 + 0.511498i
\(10\) −52.2648 + 274.485i −0.165276 + 0.867997i
\(11\) 638.582 + 368.686i 1.59124 + 0.918701i 0.993095 + 0.117312i \(0.0374276\pi\)
0.598142 + 0.801390i \(0.295906\pi\)
\(12\) −213.869 + 71.3050i −0.428740 + 0.142944i
\(13\) 88.0086 241.802i 0.144433 0.396827i −0.846290 0.532722i \(-0.821169\pi\)
0.990723 + 0.135896i \(0.0433912\pi\)
\(14\) −159.311 + 89.1067i −0.217233 + 0.121504i
\(15\) 60.4272 + 342.700i 0.0693433 + 0.393265i
\(16\) 1022.48 + 55.7804i 0.998515 + 0.0544730i
\(17\) −1495.60 1254.96i −1.25515 1.05319i −0.996182 0.0873052i \(-0.972174\pi\)
−0.258964 0.965887i \(-0.583381\pi\)
\(18\) 847.439 691.631i 0.616492 0.503145i
\(19\) −809.616 1349.30i −0.514512 0.857483i
\(20\) 316.782 1548.55i 0.177086 0.865665i
\(21\) −146.127 + 174.148i −0.0723074 + 0.0861726i
\(22\) −3583.62 2134.62i −1.57857 0.940296i
\(23\) −1705.75 + 300.770i −0.672352 + 0.118554i −0.499393 0.866375i \(-0.666444\pi\)
−0.172959 + 0.984929i \(0.555333\pi\)
\(24\) 1215.21 386.841i 0.430648 0.137090i
\(25\) 643.879 + 234.353i 0.206041 + 0.0749928i
\(26\) −516.442 + 1360.93i −0.149826 + 0.394822i
\(27\) 1537.12 2662.37i 0.405787 0.702843i
\(28\) 907.985 491.738i 0.218869 0.118533i
\(29\) −3897.01 4644.27i −0.860471 1.02547i −0.999382 0.0351641i \(-0.988805\pi\)
0.138911 0.990305i \(-0.455640\pi\)
\(30\) −315.383 1943.08i −0.0639787 0.394173i
\(31\) −1934.61 3350.84i −0.361567 0.626253i 0.626652 0.779299i \(-0.284425\pi\)
−0.988219 + 0.153047i \(0.951091\pi\)
\(32\) −5779.18 394.317i −0.997680 0.0680723i
\(33\) −5115.91 902.072i −0.817782 0.144197i
\(34\) 8362.90 + 7213.74i 1.24068 + 1.07020i
\(35\) −545.139 1497.76i −0.0752206 0.206667i
\(36\) −4846.70 + 3846.78i −0.623289 + 0.494699i
\(37\) 14166.8i 1.70125i −0.525775 0.850624i \(-0.676224\pi\)
0.525775 0.850624i \(-0.323776\pi\)
\(38\) 4475.46 + 7694.50i 0.502781 + 0.864414i
\(39\) 1812.84i 0.190852i
\(40\) −1911.17 + 8734.69i −0.188864 + 0.863172i
\(41\) 590.364 + 1622.01i 0.0548480 + 0.150694i 0.964091 0.265572i \(-0.0855608\pi\)
−0.909243 + 0.416266i \(0.863339\pi\)
\(42\) 839.965 973.774i 0.0734747 0.0851794i
\(43\) 17143.4 + 3022.85i 1.41392 + 0.249313i 0.827853 0.560946i \(-0.189562\pi\)
0.586072 + 0.810259i \(0.300673\pi\)
\(44\) 20105.6 + 12350.3i 1.56562 + 0.961716i
\(45\) 4775.62 + 8271.61i 0.351559 + 0.608918i
\(46\) 9671.48 1569.79i 0.673905 0.109382i
\(47\) −15203.7 18119.1i −1.00394 1.19644i −0.980460 0.196720i \(-0.936971\pi\)
−0.0234758 0.999724i \(-0.507473\pi\)
\(48\) −6903.42 + 2094.44i −0.432475 + 0.131210i
\(49\) −7882.87 + 13653.5i −0.469023 + 0.812372i
\(50\) −3623.93 1375.20i −0.205000 0.0777931i
\(51\) 12925.1 + 4704.35i 0.695838 + 0.253264i
\(52\) 3026.05 7658.04i 0.155192 0.392744i
\(53\) −37495.2 + 6611.41i −1.83352 + 0.323299i −0.980188 0.198069i \(-0.936533\pi\)
−0.853332 + 0.521368i \(0.825422\pi\)
\(54\) −8899.64 + 14940.7i −0.415325 + 0.697249i
\(55\) 23411.6 27900.8i 1.04358 1.24368i
\(56\) −5173.76 + 2711.45i −0.220463 + 0.115540i
\(57\) 8611.04 + 6981.84i 0.351050 + 0.284631i
\(58\) 21684.8 + 26569.9i 0.846419 + 1.03710i
\(59\) −2080.00 1745.33i −0.0777917 0.0652750i 0.603063 0.797694i \(-0.293947\pi\)
−0.680854 + 0.732419i \(0.738391\pi\)
\(60\) 1634.15 + 11015.0i 0.0586024 + 0.395008i
\(61\) 2402.17 + 13623.4i 0.0826570 + 0.468771i 0.997838 + 0.0657273i \(0.0209367\pi\)
−0.915181 + 0.403044i \(0.867952\pi\)
\(62\) 10684.5 + 19102.6i 0.353001 + 0.631121i
\(63\) −2134.09 + 5863.36i −0.0677425 + 0.186121i
\(64\) 32658.6 + 2675.80i 0.996660 + 0.0816590i
\(65\) −11007.3 6355.07i −0.323145 0.186568i
\(66\) 28867.7 + 5496.71i 0.815742 + 0.155326i
\(67\) −27194.7 + 22819.1i −0.740113 + 0.621028i −0.932868 0.360219i \(-0.882702\pi\)
0.192755 + 0.981247i \(0.438258\pi\)
\(68\) −46747.3 41447.8i −1.22598 1.08700i
\(69\) 10567.7 6101.27i 0.267213 0.154276i
\(70\) 2968.05 + 8513.82i 0.0723979 + 0.207673i
\(71\) 1389.38 7879.55i 0.0327095 0.185505i −0.964075 0.265629i \(-0.914420\pi\)
0.996785 + 0.0801238i \(0.0255316\pi\)
\(72\) 27711.0 21385.1i 0.629972 0.486161i
\(73\) 13035.2 4744.42i 0.286293 0.104202i −0.194882 0.980827i \(-0.562432\pi\)
0.481175 + 0.876625i \(0.340210\pi\)
\(74\) −1091.87 + 80132.1i −0.0231788 + 1.70109i
\(75\) −4827.29 −0.0990946
\(76\) −24721.7 43867.6i −0.490957 0.871184i
\(77\) 23793.8 0.457338
\(78\) 139.719 10254.0i 0.00260028 0.190834i
\(79\) −37883.5 + 13788.5i −0.682940 + 0.248570i −0.660109 0.751169i \(-0.729490\pi\)
−0.0228307 + 0.999739i \(0.507268\pi\)
\(80\) 11483.4 49259.0i 0.200607 0.860519i
\(81\) 4398.51 24945.2i 0.0744891 0.422449i
\(82\) −3214.28 9220.14i −0.0527897 0.151427i
\(83\) 72432.4 41818.9i 1.15408 0.666311i 0.204205 0.978928i \(-0.434539\pi\)
0.949879 + 0.312617i \(0.101206\pi\)
\(84\) −4826.17 + 5443.25i −0.0746285 + 0.0841705i
\(85\) −73874.3 + 61987.9i −1.10904 + 0.930593i
\(86\) −96735.9 18419.5i −1.41040 0.268554i
\(87\) 36989.6 + 21355.9i 0.523940 + 0.302497i
\(88\) −112772. 71407.1i −1.55237 0.982958i
\(89\) 37782.8 103808.i 0.505615 1.38916i −0.380105 0.924943i \(-0.624112\pi\)
0.885719 0.464221i \(-0.153666\pi\)
\(90\) −26374.9 47155.0i −0.343230 0.613651i
\(91\) −1441.86 8177.17i −0.0182523 0.103514i
\(92\) −54826.1 + 8133.85i −0.675333 + 0.100190i
\(93\) 20881.5 + 17521.7i 0.250354 + 0.210072i
\(94\) 84600.9 + 103659.i 0.987541 + 1.21001i
\(95\) −72579.7 + 27809.6i −0.825099 + 0.316145i
\(96\) 39209.5 11314.8i 0.434223 0.125305i
\(97\) 65639.4 78226.0i 0.708330 0.844155i −0.285112 0.958494i \(-0.592031\pi\)
0.993442 + 0.114340i \(0.0364752\pi\)
\(98\) 45640.4 76621.3i 0.480048 0.805906i
\(99\) −140417. + 24759.3i −1.43990 + 0.253893i
\(100\) 20392.1 + 8057.89i 0.203921 + 0.0805789i
\(101\) −73189.5 26638.8i −0.713913 0.259843i −0.0405734 0.999177i \(-0.512918\pi\)
−0.673339 + 0.739334i \(0.735141\pi\)
\(102\) −72746.0 27605.5i −0.692322 0.262721i
\(103\) 30650.5 53088.2i 0.284672 0.493066i −0.687858 0.725846i \(-0.741449\pi\)
0.972530 + 0.232779i \(0.0747820\pi\)
\(104\) −17706.6 + 43083.2i −0.160528 + 0.390593i
\(105\) 7217.85 + 8601.90i 0.0638903 + 0.0761414i
\(106\) 212595. 34506.5i 1.83775 0.298288i
\(107\) 56877.5 + 98514.8i 0.480265 + 0.831844i 0.999744 0.0226395i \(-0.00720700\pi\)
−0.519478 + 0.854484i \(0.673874\pi\)
\(108\) 51490.8 83823.9i 0.424786 0.691526i
\(109\) 101259. + 17854.7i 0.816335 + 0.143942i 0.566199 0.824269i \(-0.308413\pi\)
0.250136 + 0.968211i \(0.419525\pi\)
\(110\) −134574. + 156012.i −1.06042 + 1.22935i
\(111\) 34135.7 + 93787.0i 0.262967 + 0.722496i
\(112\) 29473.5 14938.1i 0.222017 0.112526i
\(113\) 1930.74i 0.0142242i 0.999975 + 0.00711211i \(0.00226388\pi\)
−0.999975 + 0.00711211i \(0.997736\pi\)
\(114\) −48168.8 40155.3i −0.347139 0.289388i
\(115\) 85554.3i 0.603250i
\(116\) −120609. 151959.i −0.832211 1.04853i
\(117\) 17018.0 + 46756.4i 0.114932 + 0.315774i
\(118\) 11630.6 + 10032.5i 0.0768951 + 0.0663288i
\(119\) −62042.9 10939.8i −0.401629 0.0708180i
\(120\) −8394.37 62430.4i −0.0532151 0.395770i
\(121\) 191333. + 331398.i 1.18802 + 2.05772i
\(122\) −12537.5 77243.6i −0.0762626 0.469854i
\(123\) −7816.66 9315.53i −0.0465863 0.0555194i
\(124\) −58962.9 108874.i −0.344370 0.635872i
\(125\) 94101.1 162988.i 0.538666 0.932998i
\(126\) 12523.0 33000.6i 0.0702720 0.185181i
\(127\) 117989. + 42944.5i 0.649131 + 0.236264i 0.645537 0.763729i \(-0.276634\pi\)
0.00359415 + 0.999994i \(0.498856\pi\)
\(128\) −184521. 17652.3i −0.995455 0.0952305i
\(129\) −120777. + 21296.2i −0.639011 + 0.112675i
\(130\) 61771.1 + 36794.7i 0.320573 + 0.190953i
\(131\) −166306. + 198195.i −0.846699 + 1.00906i 0.153084 + 0.988213i \(0.451080\pi\)
−0.999783 + 0.0208433i \(0.993365\pi\)
\(132\) −162862. 33316.1i −0.813550 0.166425i
\(133\) −44395.0 24644.2i −0.217623 0.120805i
\(134\) 155581. 126976.i 0.748505 0.610887i
\(135\) −116324. 97607.1i −0.549330 0.460943i
\(136\) 261224. + 238045.i 1.21106 + 1.10360i
\(137\) −12924.2 73296.8i −0.0588304 0.333644i 0.941160 0.337961i \(-0.109737\pi\)
−0.999991 + 0.00431665i \(0.998626\pi\)
\(138\) −60244.6 + 33696.3i −0.269290 + 0.150621i
\(139\) 27883.2 76608.4i 0.122407 0.336310i −0.863321 0.504654i \(-0.831620\pi\)
0.985728 + 0.168345i \(0.0538421\pi\)
\(140\) −16132.1 48385.7i −0.0695617 0.208640i
\(141\) 144311. + 83317.9i 0.611295 + 0.352931i
\(142\) −8466.07 + 44462.2i −0.0352339 + 0.185042i
\(143\) 145349. 121963.i 0.594392 0.498754i
\(144\) −158391. + 118825.i −0.636537 + 0.477533i
\(145\) −259341. + 149731.i −1.02436 + 0.591413i
\(146\) −74097.0 + 25831.4i −0.287686 + 0.100292i
\(147\) 19287.2 109383.i 0.0736167 0.417501i
\(148\) 12351.9 453169.i 0.0463533 1.70062i
\(149\) 58921.8 21445.8i 0.217425 0.0791363i −0.231011 0.972951i \(-0.574203\pi\)
0.448436 + 0.893815i \(0.351981\pi\)
\(150\) 27304.7 + 372.050i 0.0990854 + 0.00135012i
\(151\) 3926.98 0.0140158 0.00700788 0.999975i \(-0.497769\pi\)
0.00700788 + 0.999975i \(0.497769\pi\)
\(152\) 136453. + 250035.i 0.479042 + 0.877792i
\(153\) 377524. 1.30382
\(154\) −134586. 1833.84i −0.457296 0.00623104i
\(155\) −179592. + 65366.0i −0.600422 + 0.218536i
\(156\) −1580.60 + 57989.2i −0.00520007 + 0.190781i
\(157\) 40708.8 230871.i 0.131807 0.747516i −0.845223 0.534414i \(-0.820532\pi\)
0.977030 0.213102i \(-0.0683567\pi\)
\(158\) 215344. 75072.4i 0.686263 0.239242i
\(159\) 232295. 134115.i 0.728697 0.420713i
\(160\) −68750.5 + 277740.i −0.212313 + 0.857706i
\(161\) −42815.1 + 35926.1i −0.130176 + 0.109231i
\(162\) −26802.0 + 140759.i −0.0802379 + 0.421395i
\(163\) 95033.1 + 54867.4i 0.280160 + 0.161750i 0.633496 0.773746i \(-0.281619\pi\)
−0.353336 + 0.935497i \(0.614953\pi\)
\(164\) 17470.4 + 52399.9i 0.0507217 + 0.152132i
\(165\) −87760.7 + 241120.i −0.250952 + 0.689484i
\(166\) −412925. + 230959.i −1.16306 + 0.650525i
\(167\) 25371.2 + 143887.i 0.0703962 + 0.399237i 0.999563 + 0.0295748i \(0.00941533\pi\)
−0.929166 + 0.369662i \(0.879474\pi\)
\(168\) 27717.9 30416.8i 0.0757683 0.0831459i
\(169\) 233704. + 196101.i 0.629434 + 0.528158i
\(170\) 422635. 344930.i 1.12161 0.915396i
\(171\) 287637. + 99238.9i 0.752236 + 0.259532i
\(172\) 545750. + 111642.i 1.40661 + 0.287745i
\(173\) −398173. + 474524.i −1.01148 + 1.20543i −0.0329197 + 0.999458i \(0.510481\pi\)
−0.978558 + 0.205974i \(0.933964\pi\)
\(174\) −207579. 123647.i −0.519770 0.309607i
\(175\) 21774.5 3839.43i 0.0537468 0.00947701i
\(176\) 632372. + 412594.i 1.53883 + 1.00402i
\(177\) 17975.5 + 6542.53i 0.0431268 + 0.0156969i
\(178\) −221713. + 584257.i −0.524494 + 1.38215i
\(179\) −155123. + 268681.i −0.361863 + 0.626764i −0.988267 0.152734i \(-0.951192\pi\)
0.626405 + 0.779498i \(0.284526\pi\)
\(180\) 145551. + 268757.i 0.334837 + 0.618271i
\(181\) −290580. 346300.i −0.659280 0.785699i 0.328002 0.944677i \(-0.393625\pi\)
−0.987282 + 0.158978i \(0.949180\pi\)
\(182\) 7525.38 + 46363.9i 0.0168403 + 0.103753i
\(183\) −48729.2 84401.5i −0.107563 0.186304i
\(184\) 310741. 41782.1i 0.676635 0.0909800i
\(185\) −689129. 121512.i −1.48037 0.261030i
\(186\) −116762. 100718.i −0.247469 0.213464i
\(187\) −492380. 1.35280e6i −1.02967 2.82898i
\(188\) −470541. 592852.i −0.970964 1.22335i
\(189\) 99200.8i 0.202004i
\(190\) 412678. 151706.i 0.829330 0.304874i
\(191\) 198944.i 0.394592i 0.980344 + 0.197296i \(0.0632160\pi\)
−0.980344 + 0.197296i \(0.936784\pi\)
\(192\) −222654. + 60978.3i −0.435890 + 0.119377i
\(193\) −88275.6 242535.i −0.170587 0.468685i 0.824709 0.565557i \(-0.191339\pi\)
−0.995297 + 0.0968714i \(0.969116\pi\)
\(194\) −377307. + 437413.i −0.719765 + 0.834426i
\(195\) 88183.4 + 15549.1i 0.166073 + 0.0292832i
\(196\) −264063. + 429878.i −0.490983 + 0.799291i
\(197\) −175940. 304738.i −0.322998 0.559449i 0.658107 0.752924i \(-0.271357\pi\)
−0.981105 + 0.193475i \(0.938024\pi\)
\(198\) 796154. 129225.i 1.44322 0.234251i
\(199\) 369939. + 440876.i 0.662213 + 0.789194i 0.987701 0.156352i \(-0.0499733\pi\)
−0.325489 + 0.945546i \(0.605529\pi\)
\(200\) −114724. 47149.8i −0.202805 0.0833498i
\(201\) 125051. 216594.i 0.218321 0.378143i
\(202\) 411931. + 156319.i 0.710306 + 0.269546i
\(203\) −183835. 66910.4i −0.313103 0.113960i
\(204\) 409347. + 161752.i 0.688679 + 0.272129i
\(205\) 83964.7 14805.2i 0.139544 0.0246054i
\(206\) −177461. + 297922.i −0.291363 + 0.489142i
\(207\) 215285. 256567.i 0.349212 0.416174i
\(208\) 103475. 242328.i 0.165835 0.388370i
\(209\) −19537.8 1.16013e6i −0.0309393 1.83714i
\(210\) −40163.6 49211.5i −0.0628469 0.0770049i
\(211\) 164983. + 138437.i 0.255113 + 0.214066i 0.761371 0.648317i \(-0.224527\pi\)
−0.506257 + 0.862383i \(0.668971\pi\)
\(212\) −1.20516e6 + 178795.i −1.84165 + 0.273222i
\(213\) 9788.25 + 55511.9i 0.0147828 + 0.0838373i
\(214\) −314125. 561616.i −0.468887 0.838310i
\(215\) 294086. 807995.i 0.433889 1.19210i
\(216\) −297709. + 470167.i −0.434168 + 0.685674i
\(217\) −108126. 62426.9i −0.155877 0.0899958i
\(218\) −571380. 108797.i −0.814298 0.155051i
\(219\) −74863.6 + 62818.0i −0.105478 + 0.0885062i
\(220\) 773219. 872083.i 1.07707 1.21479i
\(221\) −435077. + 251192.i −0.599219 + 0.345959i
\(222\) −185854. 533121.i −0.253099 0.726012i
\(223\) 125502. 711760.i 0.169001 0.958454i −0.775841 0.630928i \(-0.782674\pi\)
0.944842 0.327526i \(-0.106215\pi\)
\(224\) −167863. + 82223.4i −0.223530 + 0.109490i
\(225\) −124505. + 45316.1i −0.163957 + 0.0596755i
\(226\) 148.807 10920.9i 0.000193799 0.0142229i
\(227\) −403979. −0.520348 −0.260174 0.965562i \(-0.583780\pi\)
−0.260174 + 0.965562i \(0.583780\pi\)
\(228\) 269364. + 230844.i 0.343164 + 0.294091i
\(229\) −455588. −0.574095 −0.287047 0.957916i \(-0.592674\pi\)
−0.287047 + 0.957916i \(0.592674\pi\)
\(230\) 6593.86 483923.i 0.00821902 0.603194i
\(231\) −157520. + 57332.5i −0.194225 + 0.0706922i
\(232\) 670490. + 868827.i 0.817848 + 1.05977i
\(233\) 117120. 664218.i 0.141332 0.801532i −0.828908 0.559385i \(-0.811037\pi\)
0.970240 0.242147i \(-0.0778517\pi\)
\(234\) −92655.5 265781.i −0.110620 0.317311i
\(235\) −1.01179e6 + 584158.i −1.19515 + 0.690018i
\(236\) −65013.5 57643.2i −0.0759843 0.0673703i
\(237\) 217572. 182565.i 0.251613 0.211128i
\(238\) 350092. + 66661.1i 0.400627 + 0.0762834i
\(239\) 681481. + 393453.i 0.771718 + 0.445552i 0.833487 0.552539i \(-0.186341\pi\)
−0.0617689 + 0.998090i \(0.519674\pi\)
\(240\) 42669.7 + 353774.i 0.0478180 + 0.396459i
\(241\) 91520.8 251451.i 0.101503 0.278876i −0.878538 0.477672i \(-0.841481\pi\)
0.980041 + 0.198796i \(0.0637030\pi\)
\(242\) −1.05670e6 1.88924e6i −1.15988 2.07371i
\(243\) 160710. + 911430.i 0.174593 + 0.990166i
\(244\) 64962.9 + 437882.i 0.0698539 + 0.470849i
\(245\) 596548. + 500563.i 0.634936 + 0.532775i
\(246\) 43495.6 + 53294.1i 0.0458256 + 0.0561490i
\(247\) −397517. + 77016.2i −0.414585 + 0.0803230i
\(248\) 325123. + 620371.i 0.335674 + 0.640504i
\(249\) −378752. + 451379.i −0.387130 + 0.461363i
\(250\) −544829. + 914661.i −0.551328 + 0.925572i
\(251\) 233173. 41114.6i 0.233611 0.0411919i −0.0556170 0.998452i \(-0.517713\pi\)
0.289228 + 0.957260i \(0.406601\pi\)
\(252\) −73377.7 + 185697.i −0.0727885 + 0.184206i
\(253\) −1.20015e6 436820.i −1.17879 0.429043i
\(254\) −664075. 252002.i −0.645852 0.245087i
\(255\) 339699. 588376.i 0.327148 0.566637i
\(256\) 1.04235e6 + 114069.i 0.994065 + 0.108784i
\(257\) 551966. + 657808.i 0.521291 + 0.621250i 0.960885 0.276946i \(-0.0893224\pi\)
−0.439595 + 0.898196i \(0.644878\pi\)
\(258\) 684793. 111150.i 0.640487 0.103958i
\(259\) −228571. 395896.i −0.211724 0.366717i
\(260\) −346562. 212884.i −0.317942 0.195303i
\(261\) 1.15451e6 + 203571.i 1.04905 + 0.184976i
\(262\) 955955. 1.10824e6i 0.860368 0.997427i
\(263\) −259069. 711786.i −0.230954 0.634541i 0.769035 0.639207i \(-0.220737\pi\)
−0.999989 + 0.00466531i \(0.998515\pi\)
\(264\) 918632. + 200999.i 0.811207 + 0.177494i
\(265\) 1.88062e6i 1.64508i
\(266\) 249213. + 142817.i 0.215957 + 0.123759i
\(267\) 778266.i 0.668113i
\(268\) −889804. + 706229.i −0.756759 + 0.600632i
\(269\) 488760. + 1.34286e6i 0.411827 + 1.13148i 0.956218 + 0.292654i \(0.0945383\pi\)
−0.544392 + 0.838831i \(0.683239\pi\)
\(270\) 650442. + 561063.i 0.542999 + 0.468385i
\(271\) 1.06178e6 + 187221.i 0.878239 + 0.154857i 0.594550 0.804059i \(-0.297330\pi\)
0.283690 + 0.958916i \(0.408441\pi\)
\(272\) −1.45922e6 1.36660e6i −1.19591 1.12000i
\(273\) 29248.7 + 50660.2i 0.0237520 + 0.0411397i
\(274\) 67454.4 + 415587.i 0.0542792 + 0.334415i
\(275\) 324767. + 387042.i 0.258964 + 0.308622i
\(276\) 343361. 185954.i 0.271317 0.146938i
\(277\) 590237. 1.02232e6i 0.462197 0.800549i −0.536873 0.843663i \(-0.680395\pi\)
0.999070 + 0.0431143i \(0.0137280\pi\)
\(278\) −163621. + 431173.i −0.126977 + 0.334611i
\(279\) 703058. + 255892.i 0.540731 + 0.196810i
\(280\) 87519.2 + 274929.i 0.0667126 + 0.209568i
\(281\) −1.10539e6 + 194910.i −0.835122 + 0.147254i −0.574827 0.818275i \(-0.694931\pi\)
−0.260294 + 0.965529i \(0.583820\pi\)
\(282\) −809848. 482396.i −0.606430 0.361227i
\(283\) −731696. + 872002.i −0.543081 + 0.647219i −0.965876 0.259007i \(-0.916605\pi\)
0.422794 + 0.906226i \(0.361049\pi\)
\(284\) 51313.7 250841.i 0.0377518 0.184545i
\(285\) 413483. 358990.i 0.301540 0.261800i
\(286\) −831544. + 678659.i −0.601133 + 0.490610i
\(287\) 42667.8 + 35802.6i 0.0305771 + 0.0256572i
\(288\) 905068. 659908.i 0.642984 0.468816i
\(289\) 415349. + 2.35556e6i 0.292528 + 1.65901i
\(290\) 1.47846e6 826938.i 1.03232 0.577401i
\(291\) −246056. + 676034.i −0.170334 + 0.467989i
\(292\) 421108. 140400.i 0.289026 0.0963628i
\(293\) 867329. + 500753.i 0.590221 + 0.340764i 0.765185 0.643810i \(-0.222647\pi\)
−0.174964 + 0.984575i \(0.555981\pi\)
\(294\) −117525. + 617222.i −0.0792982 + 0.416459i
\(295\) −102740. + 86209.2i −0.0687361 + 0.0576765i
\(296\) −104793. + 2.56232e6i −0.0695191 + 1.69983i
\(297\) 1.96315e6 1.13343e6i 1.29141 0.745593i
\(298\) −334934. + 116763.i −0.218483 + 0.0761667i
\(299\) −77394.2 + 438924.i −0.0500646 + 0.283930i
\(300\) −154416. 4208.87i −0.0990578 0.00269999i
\(301\) 527850. 192122.i 0.335810 0.122225i
\(302\) −22212.3 302.661i −0.0140145 0.000190959i
\(303\) 548716. 0.343353
\(304\) −752552. 1.42480e6i −0.467038 0.884237i
\(305\) 683300. 0.420593
\(306\) −2.13540e6 29096.6i −1.30369 0.0177639i
\(307\) −2.86695e6 + 1.04348e6i −1.73610 + 0.631888i −0.999034 0.0439369i \(-0.986010\pi\)
−0.737063 + 0.675825i \(0.763788\pi\)
\(308\) 761120. + 20745.7i 0.457169 + 0.0124609i
\(309\) −74993.4 + 425309.i −0.0446814 + 0.253401i
\(310\) 1.02087e6 355890.i 0.603344 0.210335i
\(311\) 462453. 266998.i 0.271123 0.156533i −0.358275 0.933616i \(-0.616635\pi\)
0.629398 + 0.777083i \(0.283302\pi\)
\(312\) 13409.7 327884.i 0.00779891 0.190693i
\(313\) −132663. + 111318.i −0.0765402 + 0.0642249i −0.680255 0.732975i \(-0.738131\pi\)
0.603715 + 0.797200i \(0.293687\pi\)
\(314\) −248056. + 1.30275e6i −0.141980 + 0.745651i
\(315\) 266912. + 154102.i 0.151563 + 0.0875047i
\(316\) −1.22384e6 + 408037.i −0.689459 + 0.229870i
\(317\) 632935. 1.73897e6i 0.353762 0.971952i −0.627389 0.778706i \(-0.715876\pi\)
0.981150 0.193246i \(-0.0619015\pi\)
\(318\) −1.32427e6 + 740698.i −0.734361 + 0.410746i
\(319\) −776283. 4.40252e6i −0.427113 2.42228i
\(320\) 410282. 1.56569e6i 0.223979 0.854733i
\(321\) −613917. 515138.i −0.332543 0.279036i
\(322\) 244945. 199910.i 0.131653 0.107447i
\(323\) −482457. + 3.03406e6i −0.257308 + 1.61815i
\(324\) 162450. 794114.i 0.0859718 0.420262i
\(325\) 113334. 135066.i 0.0595183 0.0709311i
\(326\) −533310. 317672.i −0.277930 0.165552i
\(327\) −713378. + 125788.i −0.368935 + 0.0650533i
\(328\) −94779.9 297737.i −0.0486443 0.152809i
\(329\) −717211. 261044.i −0.365306 0.132961i
\(330\) 514987. 1.35709e6i 0.260322 0.686001i
\(331\) 1.04000e6 1.80133e6i 0.521752 0.903700i −0.477928 0.878399i \(-0.658612\pi\)
0.999680 0.0253013i \(-0.00805453\pi\)
\(332\) 2.35344e6 1.27455e6i 1.17181 0.634619i
\(333\) 1.76085e6 + 2.09850e6i 0.870184 + 1.03705i
\(334\) −132418. 815828.i −0.0649502 0.400159i
\(335\) 876754. + 1.51858e6i 0.426841 + 0.739310i
\(336\) −159126. + 169911.i −0.0768941 + 0.0821058i
\(337\) −1.19154e6 210100.i −0.571521 0.100775i −0.119583 0.992824i \(-0.538156\pi\)
−0.451937 + 0.892050i \(0.649267\pi\)
\(338\) −1.30680e6 1.12723e6i −0.622180 0.536685i
\(339\) −4652.23 12781.9i −0.00219868 0.00604083i
\(340\) −2.41715e6 + 1.91847e6i −1.13398 + 0.900030i
\(341\) 2.85305e6i 1.32869i
\(342\) −1.61932e6 583497.i −0.748631 0.269757i
\(343\) 1.05107e6i 0.482389i
\(344\) −3.07834e6 673549.i −1.40256 0.306883i
\(345\) −206148. 566386.i −0.0932461 0.256192i
\(346\) 2.28877e6 2.65337e6i 1.02781 1.19154i
\(347\) 1.40427e6 + 247610.i 0.626075 + 0.110394i 0.477680 0.878534i \(-0.341478\pi\)
0.148396 + 0.988928i \(0.452589\pi\)
\(348\) 1.16461e6 + 715387.i 0.515503 + 0.316660i
\(349\) 16965.3 + 29384.7i 0.00745584 + 0.0129139i 0.869729 0.493529i \(-0.164293\pi\)
−0.862273 + 0.506443i \(0.830960\pi\)
\(350\) −123460. + 20038.9i −0.0538710 + 0.00874386i
\(351\) −508485. 605988.i −0.220298 0.262541i
\(352\) −3.54510e6 2.38250e6i −1.52501 1.02489i
\(353\) 469391. 813008.i 0.200492 0.347263i −0.748195 0.663479i \(-0.769079\pi\)
0.948687 + 0.316216i \(0.102413\pi\)
\(354\) −101171. 38392.1i −0.0429089 0.0162830i
\(355\) −371375. 135169.i −0.156402 0.0569256i
\(356\) 1.29911e6 3.28766e6i 0.543277 1.37487i
\(357\) 437096. 77071.9i 0.181513 0.0320056i
\(358\) 898135. 1.50779e6i 0.370368 0.621776i
\(359\) −1.75590e6 + 2.09259e6i −0.719056 + 0.856937i −0.994539 0.104369i \(-0.966718\pi\)
0.275483 + 0.961306i \(0.411162\pi\)
\(360\) −802571. 1.53140e6i −0.326383 0.622775i
\(361\) −1.16514e6 + 2.18484e6i −0.470555 + 0.882371i
\(362\) 1.61693e6 + 1.98118e6i 0.648514 + 0.794609i
\(363\) −2.06518e6 1.73289e6i −0.822605 0.690248i
\(364\) −38992.6 262829.i −0.0154251 0.103973i
\(365\) −118981. 674777.i −0.0467462 0.265111i
\(366\) 269123. + 481158.i 0.105014 + 0.187752i
\(367\) 688208. 1.89084e6i 0.266719 0.732805i −0.731956 0.681352i \(-0.761392\pi\)
0.998675 0.0514535i \(-0.0163854\pi\)
\(368\) −1.76088e6 + 212384.i −0.677812 + 0.0817527i
\(369\) −289056. 166886.i −0.110514 0.0638050i
\(370\) 3.88857e6 + 740425.i 1.47668 + 0.281175i
\(371\) −941144. + 789714.i −0.354994 + 0.297876i
\(372\) 652684. + 578692.i 0.244537 + 0.216815i
\(373\) −2.78370e6 + 1.60717e6i −1.03598 + 0.598122i −0.918691 0.394976i \(-0.870753\pi\)
−0.117286 + 0.993098i \(0.537420\pi\)
\(374\) 2.68080e6 + 7.68984e6i 0.991026 + 2.84275i
\(375\) −230240. + 1.30575e6i −0.0845478 + 0.479494i
\(376\) 2.61584e6 + 3.38963e6i 0.954206 + 1.23647i
\(377\) −1.46596e6 + 533566.i −0.531214 + 0.193346i
\(378\) −7645.63 + 561113.i −0.00275222 + 0.201986i
\(379\) 2.66126e6 0.951675 0.475837 0.879533i \(-0.342145\pi\)
0.475837 + 0.879533i \(0.342145\pi\)
\(380\) −2.34593e6 + 826296.i −0.833406 + 0.293546i
\(381\) −884588. −0.312197
\(382\) 15333.1 1.12530e6i 0.00537615 0.394555i
\(383\) 1.99399e6 725754.i 0.694587 0.252809i 0.0294891 0.999565i \(-0.490612\pi\)
0.665098 + 0.746756i \(0.268390\pi\)
\(384\) 1.26410e6 327753.i 0.437476 0.113427i
\(385\) 204085. 1.15742e6i 0.0701713 0.397961i
\(386\) 480623. + 1.37866e6i 0.164186 + 0.470966i
\(387\) −2.91514e6 + 1.68306e6i −0.989422 + 0.571243i
\(388\) 2.16789e6 2.44507e6i 0.731067 0.824542i
\(389\) 492803. 413511.i 0.165120 0.138552i −0.556484 0.830859i \(-0.687850\pi\)
0.721604 + 0.692306i \(0.243405\pi\)
\(390\) −497596. 94747.4i −0.165659 0.0315432i
\(391\) 2.92859e6 + 1.69082e6i 0.968760 + 0.559314i
\(392\) 1.52676e6 2.41118e6i 0.501828 0.792528i
\(393\) 623414. 1.71282e6i 0.203608 0.559409i
\(394\) 971690. + 1.73726e6i 0.315346 + 0.563798i
\(395\) 345790. + 1.96107e6i 0.111511 + 0.632412i
\(396\) −4.51327e6 + 669576.i −1.44628 + 0.214566i
\(397\) −2.78968e6 2.34082e6i −0.888337 0.745403i 0.0795388 0.996832i \(-0.474655\pi\)
−0.967876 + 0.251428i \(0.919100\pi\)
\(398\) −2.05852e6 2.52225e6i −0.651399 0.798144i
\(399\) 353285. + 56177.2i 0.111095 + 0.0176656i
\(400\) 645280. + 275537.i 0.201650 + 0.0861052i
\(401\) 673551. 802707.i 0.209175 0.249285i −0.651249 0.758864i \(-0.725755\pi\)
0.860424 + 0.509579i \(0.170199\pi\)
\(402\) −724021. + 1.21549e6i −0.223453 + 0.375134i
\(403\) −980501. + 172889.i −0.300736 + 0.0530279i
\(404\) −2.31797e6 915938.i −0.706568 0.279198i
\(405\) −1.17570e6 427921.i −0.356173 0.129636i
\(406\) 1.03467e6 + 392636.i 0.311522 + 0.118216i
\(407\) 5.22310e6 9.04667e6i 1.56294 2.70709i
\(408\) −2.30294e6 946474.i −0.684907 0.281487i
\(409\) −772035. 920076.i −0.228207 0.271966i 0.639775 0.768562i \(-0.279028\pi\)
−0.867982 + 0.496596i \(0.834583\pi\)
\(410\) −476073. + 77272.0i −0.139867 + 0.0227019i
\(411\) 262173. + 454097.i 0.0765568 + 0.132600i
\(412\) 1.02674e6 1.67147e6i 0.298001 0.485127i
\(413\) −86285.7 15214.5i −0.0248922 0.00438917i
\(414\) −1.23750e6 + 1.43464e6i −0.354850 + 0.411378i
\(415\) −1.41296e6 3.88209e6i −0.402727 1.10648i
\(416\) −603964. + 1.36271e6i −0.171111 + 0.386074i
\(417\) 574349.i 0.161747i
\(418\) 21098.2 + 6.56361e6i 0.00590617 + 1.83739i
\(419\) 3.24349e6i 0.902562i −0.892382 0.451281i \(-0.850967\pi\)
0.892382 0.451281i \(-0.149033\pi\)
\(420\) 223386. + 281452.i 0.0617919 + 0.0778540i
\(421\) 1.66367e6 + 4.57090e6i 0.457469 + 1.25689i 0.927363 + 0.374163i \(0.122070\pi\)
−0.469894 + 0.882723i \(0.655708\pi\)
\(422\) −922529. 795763.i −0.252173 0.217522i
\(423\) 4.50419e6 + 794211.i 1.22396 + 0.215817i
\(424\) 6.83059e6 918438.i 1.84520 0.248105i
\(425\) −668884. 1.15854e6i −0.179630 0.311128i
\(426\) −51087.2 314748.i −0.0136392 0.0840310i
\(427\) 286933. + 341953.i 0.0761571 + 0.0907605i
\(428\) 1.73351e6 + 3.20089e6i 0.457422 + 0.844621i
\(429\) −668366. + 1.15764e6i −0.175336 + 0.303691i
\(430\) −1.72572e6 + 4.54762e6i −0.450091 + 1.18608i
\(431\) −1.76725e6 643225.i −0.458251 0.166790i 0.102572 0.994726i \(-0.467293\pi\)
−0.560823 + 0.827936i \(0.689515\pi\)
\(432\) 1.72018e6 2.63647e6i 0.443470 0.679695i
\(433\) −1.09281e6 + 192692.i −0.280107 + 0.0493905i −0.311937 0.950103i \(-0.600978\pi\)
0.0318295 + 0.999493i \(0.489867\pi\)
\(434\) 606788. + 361440.i 0.154637 + 0.0921112i
\(435\) 1.35610e6 1.61614e6i 0.343613 0.409502i
\(436\) 3.22353e6 + 659427.i 0.812110 + 0.166131i
\(437\) 1.78684e6 + 2.05807e6i 0.447591 + 0.515533i
\(438\) 428295. 349549.i 0.106674 0.0870609i
\(439\) −4.51773e6 3.79082e6i −1.11882 0.938798i −0.120272 0.992741i \(-0.538377\pi\)
−0.998544 + 0.0539429i \(0.982821\pi\)
\(440\) −4.44079e6 + 4.87319e6i −1.09353 + 1.20000i
\(441\) −529380. 3.00226e6i −0.129620 0.735109i
\(442\) 2.48030e6 1.38729e6i 0.603877 0.337763i
\(443\) −2.54769e6 + 6.99973e6i −0.616791 + 1.69462i 0.0979152 + 0.995195i \(0.468783\pi\)
−0.714706 + 0.699425i \(0.753440\pi\)
\(444\) 1.01016e6 + 3.02983e6i 0.243184 + 0.729393i
\(445\) −4.72553e6 2.72829e6i −1.13123 0.653115i
\(446\) −764740. + 4.01628e6i −0.182044 + 0.956063i
\(447\) −338399. + 283950.i −0.0801051 + 0.0672162i
\(448\) 955826. 452145.i 0.225001 0.106435i
\(449\) 3.64541e6 2.10468e6i 0.853356 0.492685i −0.00842610 0.999964i \(-0.502682\pi\)
0.861782 + 0.507279i \(0.169349\pi\)
\(450\) 707733. 246727.i 0.164755 0.0574361i
\(451\) −221017. + 1.25345e6i −0.0511662 + 0.290178i
\(452\) −1683.40 + 61760.9i −0.000387562 + 0.0142189i
\(453\) −25997.4 + 9462.28i −0.00595229 + 0.00216646i
\(454\) 2.28504e6 + 31135.5i 0.520300 + 0.00708952i
\(455\) −410137. −0.0928753
\(456\) −1.50582e6 1.32649e6i −0.339125 0.298739i
\(457\) −3.87130e6 −0.867094 −0.433547 0.901131i \(-0.642738\pi\)
−0.433547 + 0.901131i \(0.642738\pi\)
\(458\) 2.57696e6 + 35113.2i 0.574042 + 0.00782180i
\(459\) −5.64008e6 + 2.05282e6i −1.24955 + 0.454799i
\(460\) −74594.1 + 2.73672e6i −0.0164365 + 0.603026i
\(461\) −1.28063e6 + 7.26280e6i −0.280653 + 1.59166i 0.439757 + 0.898117i \(0.355064\pi\)
−0.720411 + 0.693548i \(0.756047\pi\)
\(462\) 895403. 312151.i 0.195170 0.0680394i
\(463\) 4.03232e6 2.32806e6i 0.874184 0.504711i 0.00544788 0.999985i \(-0.498266\pi\)
0.868736 + 0.495275i \(0.164933\pi\)
\(464\) −3.72555e6 4.96605e6i −0.803333 1.07082i
\(465\) 1.03143e6 865471.i 0.221211 0.185618i
\(466\) −713660. + 3.74801e6i −0.152239 + 0.799532i
\(467\) −4.69132e6 2.70854e6i −0.995412 0.574702i −0.0885247 0.996074i \(-0.528215\pi\)
−0.906888 + 0.421372i \(0.861549\pi\)
\(468\) 503606. + 1.51049e6i 0.106286 + 0.318789i
\(469\) −391797. + 1.07645e6i −0.0822486 + 0.225976i
\(470\) 5.76804e6 3.22621e6i 1.20444 0.673671i
\(471\) 286796. + 1.62650e6i 0.0595692 + 0.337833i
\(472\) 363295. + 331060.i 0.0750593 + 0.0683993i
\(473\) 9.83300e6 + 8.25087e6i 2.02085 + 1.69569i
\(474\) −1.24473e6 + 1.01588e6i −0.254466 + 0.207681i
\(475\) −205082. 1.05852e6i −0.0417055 0.215262i
\(476\) −1.97510e6 404040.i −0.399550 0.0817347i
\(477\) 4.73232e6 5.63975e6i 0.952309 1.13492i
\(478\) −3.82435e6 2.27802e6i −0.765576 0.456025i
\(479\) 6.58921e6 1.16186e6i 1.31218 0.231373i 0.526592 0.850118i \(-0.323470\pi\)
0.785592 + 0.618745i \(0.212359\pi\)
\(480\) −214087. 2.00435e6i −0.0424119 0.397073i
\(481\) −3.42556e6 1.24680e6i −0.675100 0.245716i
\(482\) −537052. + 1.41524e6i −0.105293 + 0.277467i
\(483\) 196878. 341004.i 0.0383999 0.0665106i
\(484\) 5.83143e6 + 1.07676e7i 1.13152 + 2.08932i
\(485\) −3.24222e6 3.86392e6i −0.625875 0.745889i
\(486\) −838781. 5.16774e6i −0.161086 0.992452i
\(487\) −303627. 525897.i −0.0580120 0.100480i 0.835561 0.549398i \(-0.185143\pi\)
−0.893573 + 0.448918i \(0.851809\pi\)
\(488\) −333703. 2.48181e6i −0.0634323 0.471757i
\(489\) −761344. 134245.i −0.143982 0.0253879i
\(490\) −3.33569e6 2.87733e6i −0.627619 0.541376i
\(491\) −3.54682e6 9.74481e6i −0.663951 1.82419i −0.558041 0.829813i \(-0.688447\pi\)
−0.105909 0.994376i \(-0.533775\pi\)
\(492\) −241918. 304802.i −0.0450563 0.0567681i
\(493\) 1.18366e7i 2.19335i
\(494\) 2.25442e6 404992.i 0.415641 0.0746670i
\(495\) 7.04280e6i 1.29191i
\(496\) −1.79119e6 3.53408e6i −0.326916 0.645018i
\(497\) −88303.9 242613.i −0.0160357 0.0440578i
\(498\) 2.17713e6 2.52396e6i 0.393380 0.456046i
\(499\) 7.74879e6 + 1.36632e6i 1.39310 + 0.245641i 0.819305 0.573358i \(-0.194359\pi\)
0.573795 + 0.818999i \(0.305471\pi\)
\(500\) 3.15223e6 5.13163e6i 0.563887 0.917974i
\(501\) −514666. 891427.i −0.0916075 0.158669i
\(502\) −1.32207e6 + 214587.i −0.234150 + 0.0380052i
\(503\) 5.67144e6 + 6.75896e6i 0.999478 + 1.19113i 0.981533 + 0.191293i \(0.0612680\pi\)
0.0179451 + 0.999839i \(0.494288\pi\)
\(504\) 429360. 1.04471e6i 0.0752915 0.183197i
\(505\) −1.92358e6 + 3.33173e6i −0.335646 + 0.581356i
\(506\) 6.75480e6 + 2.56330e6i 1.17283 + 0.445064i
\(507\) −2.01969e6 735106.i −0.348951 0.127008i
\(508\) 3.73680e6 + 1.47659e6i 0.642452 + 0.253863i
\(509\) 1.66831e6 294168.i 0.285419 0.0503270i −0.0291059 0.999576i \(-0.509266\pi\)
0.314525 + 0.949249i \(0.398155\pi\)
\(510\) −1.96680e6 + 3.30187e6i −0.334838 + 0.562127i
\(511\) 287725. 342897.i 0.0487444 0.0580914i
\(512\) −5.88710e6 725546.i −0.992491 0.122318i
\(513\) −4.83681e6 + 81456.8i −0.811458 + 0.0136658i
\(514\) −3.07140e6 3.76332e6i −0.512778 0.628295i
\(515\) −2.31952e6 1.94631e6i −0.385372 0.323366i
\(516\) −3.88198e6 + 575920.i −0.641844 + 0.0952222i
\(517\) −3.02858e6 1.71759e7i −0.498325 2.82614i
\(518\) 1.26236e6 + 2.25693e6i 0.206708 + 0.369568i
\(519\) 1.49259e6 4.10086e6i 0.243233 0.668277i
\(520\) 1.94386e6 + 1.23085e6i 0.315251 + 0.199617i
\(521\) 8.02796e6 + 4.63494e6i 1.29572 + 0.748083i 0.979662 0.200657i \(-0.0643076\pi\)
0.316057 + 0.948740i \(0.397641\pi\)
\(522\) −6.51460e6 1.24045e6i −1.04643 0.199252i
\(523\) −3.50146e6 + 2.93808e6i −0.559751 + 0.469687i −0.878227 0.478244i \(-0.841274\pi\)
0.318476 + 0.947931i \(0.396829\pi\)
\(524\) −5.49261e6 + 6.19490e6i −0.873878 + 0.985612i
\(525\) −134900. + 77884.6i −0.0213606 + 0.0123326i
\(526\) 1.41052e6 + 4.04606e6i 0.222287 + 0.637629i
\(527\) −1.31176e6 + 7.43939e6i −0.205745 + 1.16684i
\(528\) −5.18059e6 1.20772e6i −0.808713 0.188530i
\(529\) −3.22905e6 + 1.17528e6i −0.501690 + 0.182600i
\(530\) 144944. 1.06374e7i 0.0224135 1.64492i
\(531\) 525039. 0.0808082
\(532\) −1.39862e6 827028.i −0.214251 0.126690i
\(533\) 444162. 0.0677211
\(534\) 59982.7 4.40213e6i 0.00910276 0.668051i
\(535\) 5.28000e6 1.92176e6i 0.797534 0.290279i
\(536\) 5.08746e6 3.92608e6i 0.764872 0.590266i
\(537\) 379543. 2.15250e6i 0.0567971 0.322112i
\(538\) −2.66109e6 7.63331e6i −0.396373 1.13699i
\(539\) −1.00677e7 + 5.81260e6i −1.49265 + 0.861785i
\(540\) −3.63587e6 3.22369e6i −0.536567 0.475739i
\(541\) 3.28472e6 2.75620e6i 0.482508 0.404873i −0.368824 0.929499i \(-0.620240\pi\)
0.851332 + 0.524627i \(0.175795\pi\)
\(542\) −5.99137e6 1.14082e6i −0.876048 0.166809i
\(543\) 2.75813e6 + 1.59241e6i 0.401435 + 0.231769i
\(544\) 8.14851e6 + 7.84238e6i 1.18054 + 1.13619i
\(545\) 1.73705e6 4.77250e6i 0.250507 0.688264i
\(546\) −161536. 288805.i −0.0231893 0.0414595i
\(547\) 882962. + 5.00753e6i 0.126175 + 0.715575i 0.980603 + 0.196005i \(0.0627968\pi\)
−0.854428 + 0.519570i \(0.826092\pi\)
\(548\) −349514. 2.35589e6i −0.0497179 0.335123i
\(549\) −2.04914e6 1.71943e6i −0.290161 0.243474i
\(550\) −1.80716e6 2.21427e6i −0.254735 0.312121i
\(551\) −3.11145e6 + 9.01832e6i −0.436600 + 1.26546i
\(552\) −1.95649e6 + 1.02535e6i −0.273294 + 0.143227i
\(553\) −836200. + 996545.i −0.116278 + 0.138575i
\(554\) −3.41737e6 + 5.73709e6i −0.473061 + 0.794177i
\(555\) 4.85496e6 856060.i 0.669041 0.117970i
\(556\) 958725. 2.42625e6i 0.131525 0.332850i
\(557\) 6.49411e6 + 2.36366e6i 0.886915 + 0.322811i 0.744997 0.667068i \(-0.232451\pi\)
0.141918 + 0.989878i \(0.454673\pi\)
\(558\) −3.95701e6 1.50160e6i −0.537999 0.204159i
\(559\) 2.23970e6 3.87927e6i 0.303152 0.525074i
\(560\) −473848. 1.56183e6i −0.0638512 0.210458i
\(561\) 6.51930e6 + 7.76940e6i 0.874569 + 1.04227i
\(562\) 6.26747e6 1.01728e6i 0.837050 0.135863i
\(563\) 2.44094e6 + 4.22783e6i 0.324553 + 0.562143i 0.981422 0.191862i \(-0.0614527\pi\)
−0.656868 + 0.754005i \(0.728119\pi\)
\(564\) 4.54359e6 + 2.79101e6i 0.601452 + 0.369456i
\(565\) 93919.0 + 16560.4i 0.0123775 + 0.00218248i
\(566\) 4.20592e6 4.87594e6i 0.551849 0.639760i
\(567\) −279554. 768067.i −0.0365180 0.100333i
\(568\) −309580. + 1.41488e6i −0.0402626 + 0.184013i
\(569\) 1.44474e6i 0.187072i −0.995616 0.0935358i \(-0.970183\pi\)
0.995616 0.0935358i \(-0.0298169\pi\)
\(570\) −2.36646e6 + 1.99870e6i −0.305079 + 0.257668i
\(571\) 171117.i 0.0219636i −0.999940 0.0109818i \(-0.996504\pi\)
0.999940 0.0109818i \(-0.00349569\pi\)
\(572\) 4.75579e6 3.77463e6i 0.607761 0.482374i
\(573\) −479368. 1.31705e6i −0.0609933 0.167578i
\(574\) −238584. 205800.i −0.0302247 0.0260714i
\(575\) −1.16878e6 206088.i −0.147423 0.0259946i
\(576\) −5.17023e6 + 3.66290e6i −0.649312 + 0.460012i
\(577\) 783652. + 1.35732e6i 0.0979904 + 0.169724i 0.910853 0.412732i \(-0.135425\pi\)
−0.812862 + 0.582456i \(0.802092\pi\)
\(578\) −2.16780e6 1.33558e7i −0.269898 1.66284i
\(579\) 1.16880e6 + 1.39293e6i 0.144892 + 0.172676i
\(580\) −8.42638e6 + 4.56348e6i −1.04009 + 0.563283i
\(581\) 1.34943e6 2.33728e6i 0.165848 0.287257i
\(582\) 1.44388e6 3.80491e6i 0.176695 0.465625i
\(583\) −2.63813e7 9.60200e6i −3.21458 1.17001i
\(584\) −2.39275e6 + 761692.i −0.290312 + 0.0924160i
\(585\) 2.42038e6 426779.i 0.292412 0.0515600i
\(586\) −4.86730e6 2.89927e6i −0.585524 0.348774i
\(587\) −5.32526e6 + 6.34639e6i −0.637889 + 0.760207i −0.984035 0.177974i \(-0.943046\pi\)
0.346146 + 0.938181i \(0.387490\pi\)
\(588\) 712333. 3.48215e6i 0.0849649 0.415340i
\(589\) −2.95501e6 + 5.32327e6i −0.350971 + 0.632252i
\(590\) 587776. 479709.i 0.0695156 0.0567346i
\(591\) 1.89904e6 + 1.59349e6i 0.223649 + 0.187663i
\(592\) 790230. 1.44853e7i 0.0926721 1.69872i
\(593\) −1.00233e6 5.68452e6i −0.117051 0.663831i −0.985714 0.168427i \(-0.946131\pi\)
0.868663 0.495404i \(-0.164980\pi\)
\(594\) −1.11916e7 + 6.25973e6i −1.30144 + 0.727929i
\(595\) −1.06431e6 + 2.92418e6i −0.123247 + 0.338619i
\(596\) 1.90349e6 634636.i 0.219501 0.0731829i
\(597\) −3.51139e6 2.02730e6i −0.403221 0.232799i
\(598\) 471596. 2.47674e6i 0.0539283 0.283222i
\(599\) 1.09878e7 9.21984e6i 1.25125 1.04992i 0.254688 0.967023i \(-0.418027\pi\)
0.996558 0.0828966i \(-0.0264171\pi\)
\(600\) 873103. + 35708.0i 0.0990119 + 0.00404936i
\(601\) 7.54051e6 4.35352e6i 0.851559 0.491648i −0.00961762 0.999954i \(-0.503061\pi\)
0.861177 + 0.508306i \(0.169728\pi\)
\(602\) −3.00050e6 + 1.04602e6i −0.337444 + 0.117638i
\(603\) 1.19202e6 6.76028e6i 0.133503 0.757132i
\(604\) 125617. + 3423.90i 0.0140106 + 0.000381882i
\(605\) 1.77616e7 6.46469e6i 1.97285 0.718057i
\(606\) −3.10372e6 42290.8i −0.343321 0.00467804i
\(607\) 3.66108e6 0.403309 0.201654 0.979457i \(-0.435368\pi\)
0.201654 + 0.979457i \(0.435368\pi\)
\(608\) 4.14687e6 + 8.11712e6i 0.454947 + 0.890518i
\(609\) 1.37825e6 0.150586
\(610\) −3.86497e6 52663.4i −0.420554 0.00573040i
\(611\) −5.71929e6 + 2.08165e6i −0.619782 + 0.225582i
\(612\) 1.20763e7 + 329160.i 1.30333 + 0.0355246i
\(613\) −625432. + 3.54700e6i −0.0672247 + 0.381250i 0.932570 + 0.360989i \(0.117561\pi\)
−0.999795 + 0.0202611i \(0.993550\pi\)
\(614\) 1.62968e7 5.68133e6i 1.74454 0.608175i
\(615\) −520189. + 300331.i −0.0554592 + 0.0320194i
\(616\) −4.30355e6 176005.i −0.456956 0.0186885i
\(617\) 1.08443e6 909946.i 0.114680 0.0962283i −0.583644 0.812010i \(-0.698374\pi\)
0.698325 + 0.715781i \(0.253929\pi\)
\(618\) 456967. 2.39991e6i 0.0481297 0.252769i
\(619\) −2.53916e6 1.46598e6i −0.266356 0.153781i 0.360874 0.932614i \(-0.382478\pi\)
−0.627231 + 0.778834i \(0.715812\pi\)
\(620\) −5.80179e6 + 1.93435e6i −0.606154 + 0.202095i
\(621\) −1.82118e6 + 5.00366e6i −0.189507 + 0.520665i
\(622\) −2.63637e6 + 1.47458e6i −0.273231 + 0.152825i
\(623\) −619001. 3.51053e6i −0.0638957 0.362370i
\(624\) −101121. + 1.85359e6i −0.0103963 + 0.190569i
\(625\) −5.48095e6 4.59906e6i −0.561249 0.470944i
\(626\) 758966. 619425.i 0.0774081 0.0631761i
\(627\) 2.92475e6 + 7.63324e6i 0.297112 + 0.775426i
\(628\) 1.50349e6 7.34964e6i 0.152126 0.743648i
\(629\) −1.77788e7 + 2.11879e7i −1.79174 + 2.13531i
\(630\) −1.49787e6 892222.i −0.150356 0.0895615i
\(631\) −1.56111e7 + 2.75266e6i −1.56085 + 0.275219i −0.886335 0.463045i \(-0.846757\pi\)
−0.674512 + 0.738264i \(0.735646\pi\)
\(632\) 6.95392e6 2.21367e6i 0.692527 0.220455i
\(633\) −1.42579e6 518946.i −0.141432 0.0514770i
\(634\) −3.71411e6 + 9.78743e6i −0.366971 + 0.967042i
\(635\) 3.10101e6 5.37110e6i 0.305189 0.528602i
\(636\) 7.54761e6 4.08757e6i 0.739889 0.400702i
\(637\) 2.60769e6 + 3.10772e6i 0.254628 + 0.303454i
\(638\) 4.05160e6 + 2.49619e7i 0.394071 + 2.42787i
\(639\) 773575. + 1.33987e6i 0.0749463 + 0.129811i
\(640\) −2.44136e6 + 8.82443e6i −0.235603 + 0.851602i
\(641\) −656667. 115788.i −0.0631248 0.0111306i 0.141997 0.989867i \(-0.454648\pi\)
−0.205121 + 0.978737i \(0.565759\pi\)
\(642\) 3.43282e6 + 2.96110e6i 0.328710 + 0.283541i
\(643\) −4.05729e6 1.11473e7i −0.386998 1.06327i −0.968346 0.249612i \(-0.919697\pi\)
0.581348 0.813655i \(-0.302525\pi\)
\(644\) −1.40090e6 + 1.11188e6i −0.133104 + 0.105644i
\(645\) 6.05771e6i 0.573336i
\(646\) 2.96278e6 1.71245e7i 0.279330 1.61449i
\(647\) 6.71786e6i 0.630914i −0.948940 0.315457i \(-0.897842\pi\)
0.948940 0.315457i \(-0.102158\pi\)
\(648\) −980072. + 4.47925e6i −0.0916897 + 0.419052i
\(649\) −684773. 1.88140e6i −0.0638168 0.175335i
\(650\) −651462. + 755242.i −0.0604792 + 0.0701137i
\(651\) 866240. + 152741.i 0.0801098 + 0.0141255i
\(652\) 2.99209e6 + 1.83796e6i 0.275649 + 0.169324i
\(653\) 3.08893e6 + 5.35018e6i 0.283482 + 0.491005i 0.972240 0.233987i \(-0.0751772\pi\)
−0.688758 + 0.724991i \(0.741844\pi\)
\(654\) 4.04480e6 656516.i 0.369788 0.0600206i
\(655\) 8.21456e6 + 9.78973e6i 0.748137 + 0.891595i
\(656\) 513159. + 1.69141e6i 0.0465578 + 0.153458i
\(657\) −1.34117e6 + 2.32298e6i −0.121219 + 0.209957i
\(658\) 4.03666e6 + 1.53183e6i 0.363461 + 0.137925i
\(659\) 2.04543e7 + 7.44474e6i 1.83472 + 0.667784i 0.991482 + 0.130247i \(0.0415769\pi\)
0.843240 + 0.537537i \(0.180645\pi\)
\(660\) −3.01753e6 + 7.63647e6i −0.269645 + 0.682390i
\(661\) 6.29417e6 1.10983e6i 0.560318 0.0987993i 0.113686 0.993517i \(-0.463734\pi\)
0.446633 + 0.894717i \(0.352623\pi\)
\(662\) −6.02142e6 + 1.01088e7i −0.534016 + 0.896508i
\(663\) 2.27504e6 2.71128e6i 0.201004 0.239547i
\(664\) −1.34101e7 + 7.02791e6i −1.18035 + 0.618595i
\(665\) −1.57957e6 + 1.94817e6i −0.138512 + 0.170833i
\(666\) −9.79820e6 1.20055e7i −0.855974 1.04880i
\(667\) 8.04419e6 + 6.74988e6i 0.700112 + 0.587464i
\(668\) 686122. + 4.62479e6i 0.0594922 + 0.401006i
\(669\) 884173. + 5.01440e6i 0.0763787 + 0.433165i
\(670\) −4.84217e6 8.65718e6i −0.416728 0.745057i
\(671\) −3.48877e6 + 9.58531e6i −0.299134 + 0.821864i
\(672\) 913165. 948810.i 0.0780056 0.0810506i
\(673\) −4.68733e6 2.70623e6i −0.398922 0.230317i 0.287097 0.957902i \(-0.407310\pi\)
−0.686019 + 0.727584i \(0.740643\pi\)
\(674\) 6.72352e6 + 1.28023e6i 0.570095 + 0.108552i
\(675\) 1.61365e6 1.35401e6i 0.136317 0.114383i
\(676\) 7.30479e6 + 6.47668e6i 0.614810 + 0.545112i
\(677\) 1.05748e7 6.10534e6i 0.886746 0.511963i 0.0138690 0.999904i \(-0.495585\pi\)
0.872877 + 0.487941i \(0.162252\pi\)
\(678\) 25329.4 + 72657.2i 0.00211617 + 0.00607022i
\(679\) 572197. 3.24509e6i 0.0476290 0.270118i
\(680\) 1.38200e7 1.06652e7i 1.14614 0.884496i
\(681\) 2.67442e6 973409.i 0.220984 0.0804317i
\(682\) −219891. + 1.61378e7i −0.0181028 + 1.32857i
\(683\) 2.36077e7 1.93643 0.968214 0.250121i \(-0.0804705\pi\)
0.968214 + 0.250121i \(0.0804705\pi\)
\(684\) 9.11444e6 + 3.42525e6i 0.744886 + 0.279932i
\(685\) −3.67629e6 −0.299353
\(686\) 81008.5 5.94521e6i 0.00657235 0.482344i
\(687\) 3.01608e6 1.09776e6i 0.243810 0.0887396i
\(688\) 1.73602e7 + 4.04707e6i 1.39824 + 0.325964i
\(689\) −1.70125e6 + 9.64825e6i −0.136527 + 0.774284i
\(690\) 1.12239e6 + 3.21956e6i 0.0897470 + 0.257438i
\(691\) 1.08708e7 6.27624e6i 0.866094 0.500039i 4.54474e−5 1.00000i \(-0.499986\pi\)
0.866048 + 0.499961i \(0.166652\pi\)
\(692\) −1.31505e7 + 1.48320e7i −1.04395 + 1.17742i
\(693\) −3.52453e6 + 2.95743e6i −0.278784 + 0.233927i
\(694\) −7.92392e6 1.50880e6i −0.624513 0.118914i
\(695\) −3.48737e6 2.01344e6i −0.273865 0.158116i
\(696\) −6.53226e6 4.13622e6i −0.511141 0.323654i
\(697\) 1.15261e6 3.16677e6i 0.0898671 0.246908i
\(698\) −93696.3 167517.i −0.00727921 0.0130143i
\(699\) 825116. + 4.67946e6i 0.0638737 + 0.362246i
\(700\) 699872. 103831.i 0.0539851 0.00800908i
\(701\) −1.71653e7 1.44034e7i −1.31934 1.10706i −0.986445 0.164092i \(-0.947531\pi\)
−0.332894 0.942964i \(-0.608025\pi\)
\(702\) 2.82945e6 + 3.46686e6i 0.216700 + 0.265518i
\(703\) −1.91153e7 + 1.14697e7i −1.45879 + 0.875312i
\(704\) 1.98686e7 + 1.37495e7i 1.51090 + 1.04557i
\(705\) 5.29069e6 6.30520e6i 0.400903 0.477778i
\(706\) −2.71769e6 + 4.56247e6i −0.205205 + 0.344499i
\(707\) −2.47510e6 + 436427.i −0.186228 + 0.0328369i
\(708\) 569297. + 224956.i 0.0426831 + 0.0168661i
\(709\) −1.71558e7 6.24421e6i −1.28173 0.466511i −0.390725 0.920507i \(-0.627776\pi\)
−0.891004 + 0.453996i \(0.849998\pi\)
\(710\) 2.09020e6 + 793186.i 0.155612 + 0.0590512i
\(711\) 3.89778e6 6.75115e6i 0.289163 0.500845i
\(712\) −7.60159e6 + 1.84960e7i −0.561959 + 1.36734i
\(713\) 4.30780e6 + 5.13384e6i 0.317345 + 0.378197i
\(714\) −2.47830e6 + 402256.i −0.181932 + 0.0295296i
\(715\) −4.68604e6 8.11647e6i −0.342800 0.593748i
\(716\) −5.19635e6 + 8.45935e6i −0.378805 + 0.616672i
\(717\) −5.45958e6 962672.i −0.396608 0.0699327i
\(718\) 1.00932e7 1.17011e7i 0.730664 0.847061i
\(719\) −5.52536e6 1.51808e7i −0.398601 1.09515i −0.962966 0.269622i \(-0.913101\pi\)
0.564366 0.825525i \(-0.309121\pi\)
\(720\) 4.42158e6 + 8.72394e6i 0.317867 + 0.627164i
\(721\) 1.97809e6i 0.141712i
\(722\) 6.75881e6 1.22684e7i 0.482534 0.875878i
\(723\) 1.88518e6i 0.134124i
\(724\) −8.99319e6 1.13308e7i −0.637628 0.803371i
\(725\) −1.42080e6 3.90362e6i −0.100390 0.275818i
\(726\) 1.15478e7 + 9.96097e6i 0.813124 + 0.701391i
\(727\) −3.84799e6 678504.i −0.270021 0.0476120i 0.0369982 0.999315i \(-0.488220\pi\)
−0.307019 + 0.951703i \(0.599332\pi\)
\(728\) 200298. + 1.48966e6i 0.0140071 + 0.104174i
\(729\) −182477. 316059.i −0.0127171 0.0220267i
\(730\) 620991. + 3.82593e6i 0.0431299 + 0.265723i
\(731\) −2.18462e7 2.60353e7i −1.51211 1.80206i
\(732\) −1.48517e6 2.74233e6i −0.102447 0.189166i
\(733\) −3.86180e6 + 6.68883e6i −0.265479 + 0.459823i −0.967689 0.252147i \(-0.918863\pi\)
0.702210 + 0.711970i \(0.252197\pi\)
\(734\) −4.03846e6 + 1.06421e7i −0.276679 + 0.729103i
\(735\) −5.15540e6 1.87641e6i −0.352001 0.128118i
\(736\) 9.97646e6 1.06560e6i 0.678863 0.0725102i
\(737\) −2.57791e7 + 4.54556e6i −1.74823 + 0.308261i
\(738\) 1.62213e6 + 966243.i 0.109634 + 0.0653048i
\(739\) 9.97978e6 1.18934e7i 0.672217 0.801117i −0.316867 0.948470i \(-0.602631\pi\)
0.989084 + 0.147353i \(0.0470752\pi\)
\(740\) −2.19380e7 4.48779e6i −1.47271 0.301268i
\(741\) 2.44607e6 1.46770e6i 0.163652 0.0981956i
\(742\) 5.38428e6 4.39434e6i 0.359020 0.293011i
\(743\) 695068. + 583231.i 0.0461908 + 0.0387586i 0.665591 0.746317i \(-0.268180\pi\)
−0.619400 + 0.785076i \(0.712624\pi\)
\(744\) −3.64719e6 3.32358e6i −0.241561 0.220127i
\(745\) −537820. 3.05013e6i −0.0355015 0.201339i
\(746\) 1.58694e7 8.87614e6i 1.04403 0.583952i
\(747\) −5.53142e6 + 1.51974e7i −0.362689 + 0.996481i
\(748\) −1.45708e7 4.37029e7i −0.952203 2.85599i
\(749\) 3.17892e6 + 1.83535e6i 0.207050 + 0.119540i
\(750\) 1.40295e6 7.36803e6i 0.0910728 0.478298i
\(751\) 5.35179e6 4.49069e6i 0.346258 0.290545i −0.453028 0.891497i \(-0.649656\pi\)
0.799285 + 0.600952i \(0.205212\pi\)
\(752\) −1.45348e7 1.93745e7i −0.937271 1.24935i
\(753\) −1.44458e6 + 834029.i −0.0928441 + 0.0536036i
\(754\) 8.33309e6 2.90504e6i 0.533799 0.186090i
\(755\) 33682.6 191024.i 0.00215050 0.0121961i
\(756\) 86492.4 3.17325e6i 0.00550394 0.201929i
\(757\) 1.89585e7 6.90032e6i 1.20244 0.437653i 0.338365 0.941015i \(-0.390126\pi\)
0.864076 + 0.503362i \(0.167904\pi\)
\(758\) −1.50529e7 205109.i −0.951587 0.0129662i
\(759\) 8.99779e6 0.566933
\(760\) 1.33331e7 4.49299e6i 0.837328 0.282164i
\(761\) −2.09585e7 −1.31189 −0.655947 0.754807i \(-0.727731\pi\)
−0.655947 + 0.754807i \(0.727731\pi\)
\(762\) 5.00352e6 + 68177.2i 0.312168 + 0.00425355i
\(763\) 3.11779e6 1.13478e6i 0.193881 0.0705670i
\(764\) −173458. + 6.36386e6i −0.0107513 + 0.394446i
\(765\) 3.23811e6 1.83643e7i 0.200050 1.13454i
\(766\) −1.13346e7 + 3.95142e6i −0.697967 + 0.243322i
\(767\) −605080. + 349343.i −0.0371385 + 0.0214419i
\(768\) −7.17544e6 + 1.75645e6i −0.438981 + 0.107457i
\(769\) −5.15701e6 + 4.32725e6i −0.314472 + 0.263874i −0.786338 0.617797i \(-0.788025\pi\)
0.471865 + 0.881671i \(0.343581\pi\)
\(770\) −1.24358e6 + 6.53105e6i −0.0755869 + 0.396968i
\(771\) −5.23915e6 3.02482e6i −0.317413 0.183259i
\(772\) −2.61230e6 7.83521e6i −0.157754 0.473159i
\(773\) 7.94483e6 2.18283e7i 0.478229 1.31392i −0.432766 0.901506i \(-0.642462\pi\)
0.910995 0.412417i \(-0.135315\pi\)
\(774\) 1.66187e7 9.29524e6i 0.997113 0.557710i
\(775\) −460375. 2.61092e6i −0.0275332 0.156149i
\(776\) −1.24507e7 + 1.36631e7i −0.742233 + 0.814505i
\(777\) 2.46711e6 + 2.07015e6i 0.146601 + 0.123013i
\(778\) −2.81933e6 + 2.30097e6i −0.166992 + 0.136290i
\(779\) 1.71062e6 2.10979e6i 0.100997 0.124565i
\(780\) 2.80726e6 + 574273.i 0.165214 + 0.0337973i
\(781\) 3.79231e6 4.51950e6i 0.222472 0.265132i
\(782\) −1.64347e7 9.78954e6i −0.961049 0.572461i
\(783\) −1.83549e7 + 3.23646e6i −1.06991 + 0.188654i
\(784\) −8.82168e6 + 1.35208e7i −0.512579 + 0.785617i
\(785\) −1.08813e7 3.96047e6i −0.630242 0.229389i
\(786\) −3.65825e6 + 9.64020e6i −0.211211 + 0.556583i
\(787\) 6.03222e6 1.04481e7i 0.347169 0.601314i −0.638577 0.769558i \(-0.720476\pi\)
0.985745 + 0.168244i \(0.0538098\pi\)
\(788\) −5.36231e6 9.90139e6i −0.307635 0.568042i
\(789\) 3.43017e6 + 4.08792e6i 0.196166 + 0.233781i
\(790\) −1.80476e6 1.11191e7i −0.102885 0.633873i
\(791\) 31151.1 + 53955.2i 0.00177024 + 0.00306614i
\(792\) 2.55801e7 3.43949e6i 1.44907 0.194841i
\(793\) 3.50557e6 + 618127.i 0.197959 + 0.0349056i
\(794\) 1.55989e7 + 1.34554e7i 0.878099 + 0.757437i
\(795\) −4.53145e6 1.24501e7i −0.254284 0.698641i
\(796\) 1.14493e7 + 1.44253e7i 0.640464 + 0.806944i
\(797\) 6.72965e6i 0.375272i −0.982239 0.187636i \(-0.939917\pi\)
0.982239 0.187636i \(-0.0600826\pi\)
\(798\) −1.99397e6 344985.i −0.110844 0.0191775i
\(799\) 4.61791e7i 2.55905i
\(800\) −3.62868e6 1.60826e6i −0.200458 0.0888446i
\(801\) 7.30596e6 + 2.00729e7i 0.402342 + 1.10543i
\(802\) −3.87169e6 + 4.48846e6i −0.212552 + 0.246412i
\(803\) 1.00732e7 + 1.77618e6i 0.551290 + 0.0972073i
\(804\) 4.18898e6 6.81941e6i 0.228543 0.372054i
\(805\) 1.38035e6 + 2.39084e6i 0.0750759 + 0.130035i
\(806\) 5.55936e6 902346.i 0.301430 0.0489255i
\(807\) −6.47137e6 7.71228e6i −0.349794 0.416868i
\(808\) 1.30406e7 + 5.35950e6i 0.702698 + 0.288799i
\(809\) 8.85660e6 1.53401e7i 0.475768 0.824055i −0.523846 0.851813i \(-0.675503\pi\)
0.999615 + 0.0277577i \(0.00883669\pi\)
\(810\) 6.61719e6 + 2.51108e6i 0.354373 + 0.134477i
\(811\) −6.06198e6 2.20638e6i −0.323640 0.117795i 0.175091 0.984552i \(-0.443978\pi\)
−0.498731 + 0.866757i \(0.666200\pi\)
\(812\) −5.82219e6 2.30062e6i −0.309882 0.122449i
\(813\) −7.48034e6 + 1.31899e6i −0.396913 + 0.0699864i
\(814\) −3.02408e7 + 5.07684e7i −1.59968 + 2.68554i
\(815\) 3.48409e6 4.15217e6i 0.183736 0.218968i
\(816\) 1.29532e7 + 5.53106e6i 0.681008 + 0.290793i
\(817\) −9.80086e6 2.55790e7i −0.513699 1.34069i
\(818\) 4.29597e6 + 5.26375e6i 0.224480 + 0.275050i
\(819\) 1.22995e6 + 1.03205e6i 0.0640735 + 0.0537640i
\(820\) 2.69878e6 400384.i 0.140163 0.0207942i
\(821\) −1.02354e6 5.80480e6i −0.0529966 0.300559i 0.946776 0.321894i \(-0.104319\pi\)
−0.999772 + 0.0213351i \(0.993208\pi\)
\(822\) −1.44794e6 2.58873e6i −0.0747431 0.133631i
\(823\) −5.25726e6 + 1.44442e7i −0.270558 + 0.743351i 0.727785 + 0.685805i \(0.240550\pi\)
−0.998343 + 0.0575459i \(0.981672\pi\)
\(824\) −5.93640e6 + 9.37525e6i −0.304583 + 0.481022i
\(825\) −3.08262e6 1.77975e6i −0.157683 0.0910384i
\(826\) 486888. + 92708.5i 0.0248301 + 0.00472791i
\(827\) 3.25626e6 2.73233e6i 0.165560 0.138921i −0.556244 0.831019i \(-0.687758\pi\)
0.721804 + 0.692098i \(0.243313\pi\)
\(828\) 7.11028e6 8.01940e6i 0.360421 0.406505i
\(829\) −6.81754e6 + 3.93611e6i −0.344541 + 0.198921i −0.662278 0.749258i \(-0.730410\pi\)
0.317737 + 0.948179i \(0.397077\pi\)
\(830\) 7.69299e6 + 2.20673e7i 0.387614 + 1.11187i
\(831\) −1.44415e6 + 8.19017e6i −0.0725453 + 0.411425i
\(832\) 3.52125e6 7.66140e6i 0.176355 0.383707i
\(833\) 2.89243e7 1.05276e7i 1.44428 0.525674i
\(834\) 44266.4 3.24871e6i 0.00220373 0.161732i
\(835\) 7.21684e6 0.358204
\(836\) 386534. 3.71276e7i 0.0191281 1.83730i
\(837\) −1.18949e7 −0.586876
\(838\) −249983. + 1.83462e7i −0.0122970 + 0.902478i
\(839\) 2.23235e7 8.12509e6i 1.09486 0.398496i 0.269439 0.963017i \(-0.413162\pi\)
0.825418 + 0.564522i \(0.190939\pi\)
\(840\) −1.24185e6 1.60920e6i −0.0607255 0.0786886i
\(841\) −2.82087e6 + 1.59980e7i −0.137529 + 0.779964i
\(842\) −9.05797e6 2.59827e7i −0.440302 1.26300i
\(843\) 6.84825e6 3.95384e6i 0.331903 0.191624i
\(844\) 5.15680e6 + 4.57220e6i 0.249186 + 0.220937i
\(845\) 1.15437e7 9.68629e6i 0.556163 0.466676i
\(846\) −2.54160e7 4.83946e6i −1.22090 0.232472i
\(847\) 1.06937e7 + 6.17401e6i 0.512176 + 0.295705i
\(848\) −3.87068e7 + 4.66854e6i −1.84841 + 0.222942i
\(849\) 2.74284e6 7.53589e6i 0.130596 0.358810i
\(850\) 3.69413e6 + 6.60464e6i 0.175374 + 0.313546i
\(851\) 4.26096e6 + 2.41651e7i 0.201689 + 1.14384i
\(852\) 264707. + 1.78426e6i 0.0124930 + 0.0842090i
\(853\) 3.10928e7 + 2.60899e7i 1.46314 + 1.22772i 0.922229 + 0.386645i \(0.126366\pi\)
0.540914 + 0.841078i \(0.318078\pi\)
\(854\) −1.59663e6 1.95631e6i −0.0749134 0.0917897i
\(855\) 7.29450e6 1.31406e7i 0.341256 0.614751i
\(856\) −9.55861e6 1.82389e7i −0.445872 0.850775i
\(857\) −2.14112e7 + 2.55169e7i −0.995840 + 1.18680i −0.0134589 + 0.999909i \(0.504284\pi\)
−0.982381 + 0.186887i \(0.940160\pi\)
\(858\) 3.86972e6 6.49650e6i 0.179457 0.301274i
\(859\) −1.39366e7 + 2.45740e6i −0.644427 + 0.113630i −0.486304 0.873790i \(-0.661655\pi\)
−0.158123 + 0.987419i \(0.550544\pi\)
\(860\) 1.01118e7 2.55898e7i 0.466209 1.17984i
\(861\) −368738. 134210.i −0.0169516 0.00616987i
\(862\) 9.94655e6 + 3.77450e6i 0.455936 + 0.173018i
\(863\) −1.33232e7 + 2.30765e7i −0.608951 + 1.05473i 0.382463 + 0.923971i \(0.375076\pi\)
−0.991414 + 0.130763i \(0.958257\pi\)
\(864\) −9.93310e6 + 1.47802e7i −0.452689 + 0.673590i
\(865\) 1.96675e7 + 2.34388e7i 0.893734 + 1.06511i
\(866\) 6.19614e6 1.00570e6i 0.280754 0.0455696i
\(867\) −8.42554e6 1.45935e7i −0.380671 0.659342i
\(868\) −3.40433e6 2.09119e6i −0.153367 0.0942095i
\(869\) −2.92754e7 5.16203e6i −1.31508 0.231884i
\(870\) −7.79513e6 + 9.03692e6i −0.349161 + 0.404783i
\(871\) 3.12432e6 + 8.58401e6i 0.139544 + 0.383393i
\(872\) −1.81825e7 3.97838e6i −0.809771 0.177180i
\(873\) 1.97460e7i 0.876888i
\(874\) −9.94832e6 1.17788e7i −0.440525 0.521584i
\(875\) 6.07300e6i 0.268153i
\(876\) −2.44952e6 + 1.94416e6i −0.107850 + 0.0855995i
\(877\) 2.28195e6 + 6.26961e6i 0.100186 + 0.275259i 0.979652 0.200702i \(-0.0643224\pi\)
−0.879466 + 0.475961i \(0.842100\pi\)
\(878\) 2.52616e7 + 2.17903e7i 1.10592 + 0.953954i
\(879\) −6.94848e6 1.22520e6i −0.303332 0.0534855i
\(880\) 2.54942e7 2.72221e7i 1.10977 1.18499i
\(881\) −521029. 902449.i −0.0226163 0.0391726i 0.854496 0.519458i \(-0.173866\pi\)
−0.877112 + 0.480286i \(0.840533\pi\)
\(882\) 2.76295e6 + 1.70226e7i 0.119592 + 0.736807i
\(883\) 8.23079e6 + 9.80907e6i 0.355254 + 0.423376i 0.913842 0.406070i \(-0.133101\pi\)
−0.558588 + 0.829446i \(0.688657\pi\)
\(884\) −1.41363e7 + 7.65582e6i −0.608423 + 0.329504i
\(885\) 472434. 818280.i 0.0202760 0.0351191i
\(886\) 1.49501e7 3.93964e7i 0.639822 1.68606i
\(887\) −1.67438e7 6.09424e6i −0.714570 0.260082i −0.0409509 0.999161i \(-0.513039\pi\)
−0.673619 + 0.739079i \(0.735261\pi\)
\(888\) −5.48031e6 1.72156e7i −0.233224 0.732638i
\(889\) 3.99012e6 703565.i 0.169329 0.0298573i
\(890\) 2.65189e7 + 1.57963e7i 1.12223 + 0.668467i
\(891\) 1.20057e7 1.43079e7i 0.506634 0.603783i
\(892\) 4.63517e6 2.26584e7i 0.195053 0.953494i
\(893\) −1.21390e7 + 3.51840e7i −0.509394 + 1.47644i
\(894\) 1.93598e6 1.58004e6i 0.0810135 0.0661185i
\(895\) 1.17392e7 + 9.85033e6i 0.489869 + 0.411049i
\(896\) −5.44131e6 + 2.48381e6i −0.226430 + 0.103359i
\(897\) −545247. 3.09225e6i −0.0226262 0.128320i
\(898\) −2.07818e7 + 1.16238e7i −0.859989 + 0.481013i
\(899\) −8.02303e6 + 2.20431e7i −0.331085 + 0.909648i
\(900\) −4.02219e6 + 1.34102e6i −0.165522 + 0.0551861i
\(901\) 6.43749e7 + 3.71669e7i 2.64183 + 1.52526i
\(902\) 1.34675e6 7.07288e6i 0.0551150 0.289454i
\(903\) −3.03154e6 + 2.54376e6i −0.123721 + 0.103814i
\(904\) 14281.9 349210.i 0.000581253 0.0142123i
\(905\) −1.93378e7 + 1.11647e7i −0.784847 + 0.453132i
\(906\) 147779. 51518.1i 0.00598126 0.00208516i
\(907\) 339174. 1.92355e6i 0.0136900 0.0776400i −0.977197 0.212333i \(-0.931894\pi\)
0.990887 + 0.134693i \(0.0430049\pi\)
\(908\) −1.29225e7 352226.i −0.520155 0.0141777i
\(909\) 1.41524e7 5.15106e6i 0.568095 0.206770i
\(910\) 2.31987e6 + 31610.2i 0.0928666 + 0.00126539i
\(911\) −5.51423e6 −0.220135 −0.110068 0.993924i \(-0.535107\pi\)
−0.110068 + 0.993924i \(0.535107\pi\)
\(912\) 8.41516e6 + 7.61912e6i 0.335024 + 0.303332i
\(913\) 6.16721e7 2.44856
\(914\) 2.18973e7 + 298370.i 0.867014 + 0.0118138i
\(915\) −4.52358e6 + 1.64645e6i −0.178620 + 0.0650123i
\(916\) −1.45734e7 397224.i −0.573882 0.0156421i
\(917\) −1.44973e6 + 8.22185e6i −0.0569331 + 0.322884i
\(918\) 3.20604e7 1.11767e7i 1.25563 0.437732i
\(919\) 4.38695e6 2.53281e6i 0.171346 0.0989266i −0.411874 0.911241i \(-0.635126\pi\)
0.583220 + 0.812314i \(0.301792\pi\)
\(920\) 632854. 1.54740e7i 0.0246510 0.602746i
\(921\) 1.64654e7 1.38161e7i 0.639623 0.536707i
\(922\) 7.80341e6 4.09821e7i 0.302313 1.58769i
\(923\) −1.78301e6 1.02942e6i −0.0688889 0.0397731i
\(924\) −5.08875e6 + 1.69662e6i −0.196079 + 0.0653739i
\(925\) 3.32003e6 9.12170e6i 0.127581 0.350527i
\(926\) −2.29876e7 + 1.28575e7i −0.880980 + 0.492753i
\(927\) 2.05836e6 + 1.16735e7i 0.0786722 + 0.446172i
\(928\) 2.06902e7 + 2.83767e7i 0.788669 + 1.08166i
\(929\) −6.80504e6 5.71010e6i −0.258697 0.217072i 0.504210 0.863581i \(-0.331784\pi\)
−0.762906 + 0.646509i \(0.776228\pi\)
\(930\) −5.90080e6 + 4.81590e6i −0.223720 + 0.182587i
\(931\) 2.48049e7 417739.i 0.937913 0.0157954i
\(932\) 4.32556e6 2.11450e7i 0.163118 0.797384i
\(933\) −2.41819e6 + 2.88188e6i −0.0909465 + 0.108386i
\(934\) 2.63269e7 + 1.56819e7i 0.987490 + 0.588210i
\(935\) −7.00288e7 + 1.23480e7i −2.61968 + 0.461920i
\(936\) −2.73214e6 8.58264e6i −0.101933 0.320207i
\(937\) −2.67899e7 9.75071e6i −0.996831 0.362817i −0.208469 0.978029i \(-0.566848\pi\)
−0.788362 + 0.615212i \(0.789070\pi\)
\(938\) 2.29910e6 6.05857e6i 0.0853198 0.224835i
\(939\) 610031. 1.05660e6i 0.0225781 0.0391064i
\(940\) −3.28746e7 + 1.78039e7i −1.21350 + 0.657198i
\(941\) −1.92888e7 2.29874e7i −0.710117 0.846285i 0.283514 0.958968i \(-0.408500\pi\)
−0.993631 + 0.112683i \(0.964055\pi\)
\(942\) −1.49686e6 9.22214e6i −0.0549608 0.338614i
\(943\) −1.49487e6 2.58919e6i −0.0547424 0.0948167i
\(944\) −2.02940e6 1.90058e6i −0.0741204 0.0694156i
\(945\) −4.82552e6 850869.i −0.175778 0.0309944i
\(946\) −5.49828e7 4.74275e7i −1.99756 1.72307i
\(947\) −4.80961e6 1.32143e7i −0.174275 0.478817i 0.821546 0.570142i \(-0.193112\pi\)
−0.995821 + 0.0913255i \(0.970890\pi\)
\(948\) 7.11891e6 5.65021e6i 0.257272 0.204194i
\(949\) 3.56948e6i 0.128659i
\(950\) 1.07843e6 + 6.00316e6i 0.0387688 + 0.215810i
\(951\) 1.30374e7i 0.467456i
\(952\) 1.11407e7 + 2.43761e6i 0.398399 + 0.0871708i
\(953\) −1.55598e6 4.27501e6i −0.0554971 0.152477i 0.908846 0.417131i \(-0.136964\pi\)
−0.964343 + 0.264654i \(0.914742\pi\)
\(954\) −2.72022e7 + 3.15356e7i −0.967683 + 1.12184i
\(955\) 9.67744e6 + 1.70639e6i 0.343362 + 0.0605439i
\(956\) 2.14562e7 + 1.31800e7i 0.759292 + 0.466413i
\(957\) 1.57473e7 + 2.72750e7i 0.555808 + 0.962688i
\(958\) −3.73603e7 + 6.06399e6i −1.31521 + 0.213474i
\(959\) −1.54376e6 1.83978e6i −0.0542041 0.0645980i
\(960\) 1.05647e6 + 1.13538e7i 0.0369980 + 0.397614i
\(961\) 6.82915e6 1.18284e7i 0.238538 0.413161i
\(962\) 1.92800e7 + 7.31633e6i 0.671690 + 0.254892i
\(963\) −2.06699e7 7.52324e6i −0.718246 0.261420i
\(964\) 3.14682e6 7.96366e6i 0.109063 0.276007i
\(965\) −1.25550e7 + 2.21379e6i −0.434009 + 0.0765275i
\(966\) −1.13989e6 + 1.91365e6i −0.0393025 + 0.0659813i
\(967\) −2.41545e7 + 2.87862e7i −0.830675 + 0.989960i 0.169315 + 0.985562i \(0.445844\pi\)
−0.999990 + 0.00439823i \(0.998600\pi\)
\(968\) −3.21546e7 6.13546e7i −1.10295 2.10455i
\(969\) −4.11677e6 2.12486e7i −0.140847 0.726977i
\(970\) 1.80412e7 + 2.21055e7i 0.615654 + 0.754347i
\(971\) 85044.9 + 71361.2i 0.00289468 + 0.00242892i 0.644234 0.764829i \(-0.277176\pi\)
−0.641339 + 0.767258i \(0.721621\pi\)
\(972\) 4.34613e6 + 2.92951e7i 0.147549 + 0.994555i
\(973\) −456814. 2.59072e6i −0.0154688 0.0877280i
\(974\) 1.67688e6 + 2.99805e6i 0.0566376 + 0.101261i
\(975\) −424843. + 1.16725e6i −0.0143125 + 0.0393234i
\(976\) 1.69626e6 + 1.40636e7i 0.0569989 + 0.472578i
\(977\) 3.21349e7 + 1.85531e7i 1.07706 + 0.621842i 0.930102 0.367301i \(-0.119718\pi\)
0.146959 + 0.989143i \(0.453051\pi\)
\(978\) 4.29607e6 + 818015.i 0.143623 + 0.0273473i
\(979\) 6.23998e7 5.23596e7i 2.08078 1.74598i
\(980\) 1.86460e7 + 1.65322e7i 0.620184 + 0.549877i
\(981\) −1.72185e7 + 9.94113e6i −0.571247 + 0.329809i
\(982\) 1.93109e7 + 5.53932e7i 0.639035 + 1.83307i
\(983\) −4.06649e6 + 2.30622e7i −0.134226 + 0.761232i 0.841170 + 0.540771i \(0.181867\pi\)
−0.975396 + 0.220461i \(0.929244\pi\)
\(984\) 1.34488e6 + 1.74270e6i 0.0442787 + 0.0573767i
\(985\) −1.63327e7 + 5.94462e6i −0.536374 + 0.195224i
\(986\) 912271. 6.69516e7i 0.0298835 2.19315i
\(987\) 5.37708e6 0.175693
\(988\) −1.27830e7 + 2.11701e6i −0.416619 + 0.0689971i
\(989\) −3.01516e7 −0.980212
\(990\) 542805. 3.98364e7i 0.0176017 1.29179i
\(991\) 3.00718e7 1.09452e7i 0.972691 0.354030i 0.193696 0.981062i \(-0.437952\pi\)
0.778994 + 0.627031i \(0.215730\pi\)
\(992\) 9.85916e6 + 2.01280e7i 0.318098 + 0.649413i
\(993\) −2.54460e6 + 1.44311e7i −0.0818928 + 0.464437i
\(994\) 480777. + 1.37910e6i 0.0154340 + 0.0442722i
\(995\) 2.46190e7 1.42138e7i 0.788338 0.455147i
\(996\) −1.25091e7 + 1.41085e7i −0.399557 + 0.450644i
\(997\) 3.68859e7 3.09509e7i 1.17523 0.986134i 0.175230 0.984528i \(-0.443933\pi\)
0.999999 0.00160638i \(-0.000511325\pi\)
\(998\) −4.37244e7 8.32557e6i −1.38962 0.264599i
\(999\) −3.77172e7 2.17760e7i −1.19571 0.690343i
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 76.6.k.a.3.1 288
4.3 odd 2 inner 76.6.k.a.3.26 yes 288
19.13 odd 18 inner 76.6.k.a.51.26 yes 288
76.51 even 18 inner 76.6.k.a.51.1 yes 288
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.6.k.a.3.1 288 1.1 even 1 trivial
76.6.k.a.3.26 yes 288 4.3 odd 2 inner
76.6.k.a.51.1 yes 288 76.51 even 18 inner
76.6.k.a.51.26 yes 288 19.13 odd 18 inner