Properties

Label 33.6.e.b.16.5
Level $33$
Weight $6$
Character 33.16
Analytic conductor $5.293$
Analytic rank $0$
Dimension $20$
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] = [33,6,Mod(4,33)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(33, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("33.4");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 33.e (of order \(5\), degree \(4\), 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: \(5.29266605383\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{19} + 78 x^{18} + 79 x^{17} + 10573 x^{16} - 33409 x^{15} + 1262953 x^{14} - 1581925 x^{13} + 89291182 x^{12} - 100741271 x^{11} + 2277268901 x^{10} + \cdots + 25599187870096 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4}\cdot 11^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 16.5
Root \(2.93057 - 9.01936i\) of defining polynomial
Character \(\chi\) \(=\) 33.16
Dual form 33.6.e.b.31.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.62155 + 8.06830i) q^{2} +(7.28115 + 5.29007i) q^{3} +(-32.3365 + 23.4938i) q^{4} +(-8.26670 + 25.4423i) q^{5} +(-23.5940 + 72.6147i) q^{6} +(-58.4588 + 42.4728i) q^{7} +(-54.7010 - 39.7426i) q^{8} +(25.0304 + 77.0356i) q^{9} +O(q^{10})\) \(q+(2.62155 + 8.06830i) q^{2} +(7.28115 + 5.29007i) q^{3} +(-32.3365 + 23.4938i) q^{4} +(-8.26670 + 25.4423i) q^{5} +(-23.5940 + 72.6147i) q^{6} +(-58.4588 + 42.4728i) q^{7} +(-54.7010 - 39.7426i) q^{8} +(25.0304 + 77.0356i) q^{9} -226.948 q^{10} +(164.972 - 365.835i) q^{11} -359.731 q^{12} +(4.13482 + 12.7257i) q^{13} +(-495.936 - 360.319i) q^{14} +(-194.782 + 141.518i) q^{15} +(-217.992 + 670.909i) q^{16} +(167.629 - 515.908i) q^{17} +(-555.928 + 403.905i) q^{18} +(1663.80 + 1208.82i) q^{19} +(-330.420 - 1016.93i) q^{20} -650.332 q^{21} +(3384.15 + 371.990i) q^{22} +2306.87 q^{23} +(-188.045 - 578.744i) q^{24} +(1949.21 + 1416.18i) q^{25} +(-91.8349 + 66.7219i) q^{26} +(-225.273 + 693.320i) q^{27} +(892.503 - 2746.84i) q^{28} +(-291.662 + 211.905i) q^{29} +(-1652.44 - 1200.57i) q^{30} +(-1796.91 - 5530.32i) q^{31} -8148.23 q^{32} +(3136.48 - 1790.99i) q^{33} +4601.95 q^{34} +(-597.344 - 1838.44i) q^{35} +(-2619.25 - 1903.00i) q^{36} +(5595.19 - 4065.14i) q^{37} +(-5391.40 + 16593.0i) q^{38} +(-37.2134 + 114.531i) q^{39} +(1463.34 - 1063.18i) q^{40} +(-2064.07 - 1499.63i) q^{41} +(-1704.88 - 5247.07i) q^{42} -7995.11 q^{43} +(3260.25 + 15705.6i) q^{44} -2166.88 q^{45} +(6047.58 + 18612.5i) q^{46} +(-10980.3 - 7977.64i) q^{47} +(-5136.39 + 3731.80i) q^{48} +(-3580.16 + 11018.6i) q^{49} +(-6316.24 + 19439.4i) q^{50} +(3949.72 - 2869.64i) q^{51} +(-432.680 - 314.360i) q^{52} +(-12058.6 - 37112.5i) q^{53} -6184.48 q^{54} +(7943.90 + 7221.51i) q^{55} +4885.74 q^{56} +(5719.63 + 17603.2i) q^{57} +(-2474.32 - 1797.70i) q^{58} +(40226.5 - 29226.3i) q^{59} +(2973.78 - 9152.36i) q^{60} +(5074.04 - 15616.3i) q^{61} +(39909.6 - 28996.0i) q^{62} +(-4735.16 - 3440.30i) q^{63} +(-14385.3 - 44273.3i) q^{64} -357.951 q^{65} +(22672.7 + 20610.9i) q^{66} -59379.1 q^{67} +(6700.13 + 20620.9i) q^{68} +(16796.7 + 12203.5i) q^{69} +(13267.1 - 9639.10i) q^{70} +(15279.1 - 47024.3i) q^{71} +(1692.41 - 5208.70i) q^{72} +(-9735.59 + 7073.32i) q^{73} +(47466.9 + 34486.7i) q^{74} +(6700.78 + 20622.9i) q^{75} -82201.2 q^{76} +(5893.97 + 28393.1i) q^{77} -1021.63 q^{78} +(31184.9 + 95977.3i) q^{79} +(-15267.4 - 11092.4i) q^{80} +(-5307.96 + 3856.46i) q^{81} +(6688.44 - 20584.9i) q^{82} +(-32932.3 + 101355. i) q^{83} +(21029.4 - 15278.8i) q^{84} +(11740.1 + 8529.71i) q^{85} +(-20959.6 - 64506.9i) q^{86} -3244.63 q^{87} +(-23563.4 + 13455.1i) q^{88} +30884.0 q^{89} +(-5680.58 - 17483.0i) q^{90} +(-782.211 - 568.310i) q^{91} +(-74596.1 + 54197.2i) q^{92} +(16172.2 - 49772.9i) q^{93} +(35580.7 - 109506. i) q^{94} +(-44509.3 + 32337.9i) q^{95} +(-59328.5 - 43104.7i) q^{96} +(3.58827 + 11.0435i) q^{97} -98286.9 q^{98} +(32311.6 + 3551.73i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9} - 424 q^{10} + 2289 q^{11} - 2682 q^{12} - 847 q^{13} + 2022 q^{14} - 396 q^{15} - 7148 q^{16} + 2482 q^{17} + 81 q^{18} + 2958 q^{19} + 8037 q^{20} - 1404 q^{21} + 7441 q^{22} + 8140 q^{23} - 4626 q^{24} - 13120 q^{25} - 13508 q^{26} + 3645 q^{27} + 27819 q^{28} - 20210 q^{29} + 11106 q^{30} + 5540 q^{31} - 4626 q^{32} + 639 q^{33} + 16540 q^{34} - 34101 q^{35} + 648 q^{36} - 25173 q^{37} - 55878 q^{38} + 7623 q^{39} + 22689 q^{40} + 54349 q^{41} + 32292 q^{42} - 21688 q^{43} + 24587 q^{44} - 5346 q^{45} + 44155 q^{46} - 48387 q^{47} - 43083 q^{48} - 78880 q^{49} + 19956 q^{50} + 7317 q^{51} + 109051 q^{52} - 74382 q^{53} + 10206 q^{54} - 47630 q^{55} + 168894 q^{56} + 52983 q^{57} + 1501 q^{58} - 108412 q^{59} - 72333 q^{60} + 16737 q^{61} + 132685 q^{62} - 11259 q^{63} - 157030 q^{64} - 134194 q^{65} - 127539 q^{66} + 20178 q^{67} + 387013 q^{68} + 19305 q^{69} - 411988 q^{70} + 143157 q^{71} + 41634 q^{72} + 164980 q^{73} + 286114 q^{74} - 96255 q^{75} + 46868 q^{76} - 367461 q^{77} - 152658 q^{78} + 369613 q^{79} - 107448 q^{80} - 32805 q^{81} - 184129 q^{82} + 267741 q^{83} + 279819 q^{84} + 379937 q^{85} - 290531 q^{86} + 214920 q^{87} - 740846 q^{88} + 205492 q^{89} + 117126 q^{90} + 394559 q^{91} - 483181 q^{92} - 49860 q^{93} + 561327 q^{94} + 267881 q^{95} + 228564 q^{96} - 300567 q^{97} - 2296174 q^{98} - 115506 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.62155 + 8.06830i 0.463429 + 1.42629i 0.860947 + 0.508694i \(0.169872\pi\)
−0.397518 + 0.917594i \(0.630128\pi\)
\(3\) 7.28115 + 5.29007i 0.467086 + 0.339358i
\(4\) −32.3365 + 23.4938i −1.01051 + 0.734182i
\(5\) −8.26670 + 25.4423i −0.147879 + 0.455125i −0.997370 0.0724781i \(-0.976909\pi\)
0.849491 + 0.527603i \(0.176909\pi\)
\(6\) −23.5940 + 72.6147i −0.267561 + 0.823468i
\(7\) −58.4588 + 42.4728i −0.450926 + 0.327617i −0.789961 0.613157i \(-0.789899\pi\)
0.339035 + 0.940774i \(0.389899\pi\)
\(8\) −54.7010 39.7426i −0.302183 0.219549i
\(9\) 25.0304 + 77.0356i 0.103006 + 0.317019i
\(10\) −226.948 −0.717671
\(11\) 164.972 365.835i 0.411082 0.911598i
\(12\) −359.731 −0.721148
\(13\) 4.13482 + 12.7257i 0.00678575 + 0.0208844i 0.954392 0.298556i \(-0.0965050\pi\)
−0.947606 + 0.319441i \(0.896505\pi\)
\(14\) −495.936 360.319i −0.676248 0.491323i
\(15\) −194.782 + 141.518i −0.223523 + 0.162399i
\(16\) −217.992 + 670.909i −0.212883 + 0.655185i
\(17\) 167.629 515.908i 0.140678 0.432962i −0.855752 0.517386i \(-0.826905\pi\)
0.996430 + 0.0844240i \(0.0269050\pi\)
\(18\) −555.928 + 403.905i −0.404424 + 0.293832i
\(19\) 1663.80 + 1208.82i 1.05735 + 0.768206i 0.973595 0.228281i \(-0.0733104\pi\)
0.0837497 + 0.996487i \(0.473310\pi\)
\(20\) −330.420 1016.93i −0.184711 0.568481i
\(21\) −650.332 −0.321800
\(22\) 3384.15 + 371.990i 1.49071 + 0.163860i
\(23\) 2306.87 0.909293 0.454647 0.890672i \(-0.349766\pi\)
0.454647 + 0.890672i \(0.349766\pi\)
\(24\) −188.045 578.744i −0.0666399 0.205097i
\(25\) 1949.21 + 1416.18i 0.623746 + 0.453178i
\(26\) −91.8349 + 66.7219i −0.0266424 + 0.0193569i
\(27\) −225.273 + 693.320i −0.0594703 + 0.183031i
\(28\) 892.503 2746.84i 0.215137 0.662123i
\(29\) −291.662 + 211.905i −0.0643998 + 0.0467892i −0.619519 0.784981i \(-0.712672\pi\)
0.555120 + 0.831771i \(0.312672\pi\)
\(30\) −1652.44 1200.57i −0.335214 0.243547i
\(31\) −1796.91 5530.32i −0.335832 1.03359i −0.966311 0.257378i \(-0.917141\pi\)
0.630478 0.776207i \(-0.282859\pi\)
\(32\) −8148.23 −1.40666
\(33\) 3136.48 1790.99i 0.501369 0.286291i
\(34\) 4601.95 0.682723
\(35\) −597.344 1838.44i −0.0824241 0.253675i
\(36\) −2619.25 1903.00i −0.336838 0.244727i
\(37\) 5595.19 4065.14i 0.671909 0.488170i −0.198755 0.980049i \(-0.563690\pi\)
0.870664 + 0.491879i \(0.163690\pi\)
\(38\) −5391.40 + 16593.0i −0.605679 + 1.86409i
\(39\) −37.2134 + 114.531i −0.00391776 + 0.0120576i
\(40\) 1463.34 1063.18i 0.144609 0.105065i
\(41\) −2064.07 1499.63i −0.191763 0.139324i 0.487761 0.872977i \(-0.337814\pi\)
−0.679524 + 0.733653i \(0.737814\pi\)
\(42\) −1704.88 5247.07i −0.149132 0.458980i
\(43\) −7995.11 −0.659406 −0.329703 0.944085i \(-0.606949\pi\)
−0.329703 + 0.944085i \(0.606949\pi\)
\(44\) 3260.25 + 15705.6i 0.253874 + 1.22299i
\(45\) −2166.88 −0.159516
\(46\) 6047.58 + 18612.5i 0.421393 + 1.29691i
\(47\) −10980.3 7977.64i −0.725052 0.526781i 0.162942 0.986636i \(-0.447902\pi\)
−0.887994 + 0.459855i \(0.847902\pi\)
\(48\) −5136.39 + 3731.80i −0.321777 + 0.233784i
\(49\) −3580.16 + 11018.6i −0.213016 + 0.655595i
\(50\) −6316.24 + 19439.4i −0.357301 + 1.09966i
\(51\) 3949.72 2869.64i 0.212638 0.154491i
\(52\) −432.680 314.360i −0.0221900 0.0161220i
\(53\) −12058.6 37112.5i −0.589667 1.81481i −0.579661 0.814858i \(-0.696815\pi\)
−0.0100060 0.999950i \(-0.503185\pi\)
\(54\) −6184.48 −0.288615
\(55\) 7943.90 + 7221.51i 0.354101 + 0.321900i
\(56\) 4885.74 0.208190
\(57\) 5719.63 + 17603.2i 0.233174 + 0.717637i
\(58\) −2474.32 1797.70i −0.0965797 0.0701692i
\(59\) 40226.5 29226.3i 1.50447 1.09306i 0.535907 0.844277i \(-0.319970\pi\)
0.968560 0.248782i \(-0.0800303\pi\)
\(60\) 2973.78 9152.36i 0.106643 0.328213i
\(61\) 5074.04 15616.3i 0.174594 0.537345i −0.825021 0.565103i \(-0.808837\pi\)
0.999615 + 0.0277574i \(0.00883658\pi\)
\(62\) 39909.6 28996.0i 1.31856 0.957987i
\(63\) −4735.16 3440.30i −0.150309 0.109206i
\(64\) −14385.3 44273.3i −0.439004 1.35111i
\(65\) −357.951 −0.0105085
\(66\) 22672.7 + 20610.9i 0.640682 + 0.582421i
\(67\) −59379.1 −1.61602 −0.808009 0.589170i \(-0.799455\pi\)
−0.808009 + 0.589170i \(0.799455\pi\)
\(68\) 6700.13 + 20620.9i 0.175716 + 0.540798i
\(69\) 16796.7 + 12203.5i 0.424718 + 0.308576i
\(70\) 13267.1 9639.10i 0.323616 0.235121i
\(71\) 15279.1 47024.3i 0.359710 1.10707i −0.593518 0.804821i \(-0.702261\pi\)
0.953228 0.302253i \(-0.0977387\pi\)
\(72\) 1692.41 5208.70i 0.0384746 0.118413i
\(73\) −9735.59 + 7073.32i −0.213823 + 0.155352i −0.689542 0.724246i \(-0.742188\pi\)
0.475718 + 0.879598i \(0.342188\pi\)
\(74\) 47466.9 + 34486.7i 1.00765 + 0.732103i
\(75\) 6700.78 + 20622.9i 0.137554 + 0.423347i
\(76\) −82201.2 −1.63247
\(77\) 5893.97 + 28393.1i 0.113287 + 0.545740i
\(78\) −1021.63 −0.0190132
\(79\) 31184.9 + 95977.3i 0.562182 + 1.73022i 0.676179 + 0.736737i \(0.263635\pi\)
−0.113997 + 0.993481i \(0.536365\pi\)
\(80\) −15267.4 11092.4i −0.266710 0.193776i
\(81\) −5307.96 + 3856.46i −0.0898908 + 0.0653095i
\(82\) 6688.44 20584.9i 0.109848 0.338076i
\(83\) −32932.3 + 101355.i −0.524719 + 1.61492i 0.240151 + 0.970735i \(0.422803\pi\)
−0.764871 + 0.644184i \(0.777197\pi\)
\(84\) 21029.4 15278.8i 0.325184 0.236260i
\(85\) 11740.1 + 8529.71i 0.176249 + 0.128052i
\(86\) −20959.6 64506.9i −0.305588 0.940503i
\(87\) −3244.63 −0.0459586
\(88\) −23563.4 + 13455.1i −0.324363 + 0.185217i
\(89\) 30884.0 0.413293 0.206647 0.978416i \(-0.433745\pi\)
0.206647 + 0.978416i \(0.433745\pi\)
\(90\) −5680.58 17483.0i −0.0739242 0.227515i
\(91\) −782.211 568.310i −0.00990194 0.00719418i
\(92\) −74596.1 + 54197.2i −0.918854 + 0.667586i
\(93\) 16172.2 49772.9i 0.193893 0.596741i
\(94\) 35580.7 109506.i 0.415331 1.27826i
\(95\) −44509.3 + 32337.9i −0.505989 + 0.367623i
\(96\) −59328.5 43104.7i −0.657030 0.477361i
\(97\) 3.58827 + 11.0435i 3.87218e−5 + 0.000119173i 0.951076 0.308957i \(-0.0999801\pi\)
−0.951037 + 0.309077i \(0.899980\pi\)
\(98\) −98286.9 −1.03379
\(99\) 32311.6 + 3551.73i 0.331338 + 0.0364210i
\(100\) −96302.0 −0.963020
\(101\) −34765.2 106996.i −0.339110 1.04367i −0.964662 0.263491i \(-0.915126\pi\)
0.625551 0.780183i \(-0.284874\pi\)
\(102\) 33507.5 + 24344.6i 0.318891 + 0.231688i
\(103\) −131066. + 95225.4i −1.21730 + 0.884422i −0.995873 0.0907544i \(-0.971072\pi\)
−0.221429 + 0.975176i \(0.571072\pi\)
\(104\) 279.572 860.435i 0.00253461 0.00780072i
\(105\) 5376.09 16545.9i 0.0475876 0.146460i
\(106\) 267823. 194585.i 2.31517 1.68207i
\(107\) 133864. + 97257.8i 1.13033 + 0.821230i 0.985742 0.168262i \(-0.0538155\pi\)
0.144584 + 0.989492i \(0.453815\pi\)
\(108\) −9004.19 27712.1i −0.0742823 0.228617i
\(109\) −34654.2 −0.279377 −0.139688 0.990196i \(-0.544610\pi\)
−0.139688 + 0.990196i \(0.544610\pi\)
\(110\) −37440.0 + 83025.4i −0.295022 + 0.654228i
\(111\) 62244.3 0.479504
\(112\) −15751.9 48479.3i −0.118655 0.365184i
\(113\) 33896.3 + 24627.1i 0.249722 + 0.181434i 0.705604 0.708607i \(-0.250676\pi\)
−0.455882 + 0.890040i \(0.650676\pi\)
\(114\) −127034. + 92295.4i −0.915497 + 0.665148i
\(115\) −19070.2 + 58692.1i −0.134465 + 0.413842i
\(116\) 4452.86 13704.5i 0.0307252 0.0945624i
\(117\) −876.832 + 637.056i −0.00592178 + 0.00430242i
\(118\) 341262. + 247942.i 2.25623 + 1.63925i
\(119\) 12112.7 + 37279.0i 0.0784104 + 0.241322i
\(120\) 16279.1 0.103199
\(121\) −106619. 120705.i −0.662023 0.749484i
\(122\) 139299. 0.847321
\(123\) −7095.64 21838.1i −0.0422891 0.130153i
\(124\) 188034. + 136615.i 1.09820 + 0.797891i
\(125\) −119777. + 87023.2i −0.685644 + 0.498150i
\(126\) 15343.9 47223.7i 0.0861012 0.264992i
\(127\) 64156.2 197453.i 0.352963 1.08631i −0.604218 0.796819i \(-0.706514\pi\)
0.957181 0.289490i \(-0.0934857\pi\)
\(128\) 108553. 78868.4i 0.585621 0.425479i
\(129\) −58213.6 42294.6i −0.308000 0.223775i
\(130\) −938.387 2888.06i −0.00486994 0.0149881i
\(131\) −41656.8 −0.212084 −0.106042 0.994362i \(-0.533818\pi\)
−0.106042 + 0.994362i \(0.533818\pi\)
\(132\) −59345.5 + 131602.i −0.296451 + 0.657397i
\(133\) −148606. −0.728461
\(134\) −155665. 479088.i −0.748910 2.30491i
\(135\) −15777.4 11462.9i −0.0745076 0.0541329i
\(136\) −29673.0 + 21558.7i −0.137567 + 0.0999483i
\(137\) 101364. 311968.i 0.461407 1.42006i −0.402039 0.915623i \(-0.631698\pi\)
0.863446 0.504442i \(-0.168302\pi\)
\(138\) −54428.2 + 167513.i −0.243291 + 0.748774i
\(139\) −95225.6 + 69185.5i −0.418039 + 0.303723i −0.776848 0.629688i \(-0.783183\pi\)
0.358809 + 0.933411i \(0.383183\pi\)
\(140\) 62507.8 + 45414.6i 0.269535 + 0.195828i
\(141\) −37746.9 116173.i −0.159894 0.492104i
\(142\) 419461. 1.74571
\(143\) 5337.62 + 586.717i 0.0218277 + 0.00239932i
\(144\) −57140.3 −0.229634
\(145\) −2980.26 9172.29i −0.0117716 0.0362291i
\(146\) −82592.1 60006.7i −0.320668 0.232979i
\(147\) −84356.7 + 61288.7i −0.321978 + 0.233931i
\(148\) −85422.9 + 262905.i −0.320568 + 0.986606i
\(149\) 30665.0 94377.2i 0.113156 0.348258i −0.878402 0.477922i \(-0.841390\pi\)
0.991558 + 0.129664i \(0.0413900\pi\)
\(150\) −148825. + 108128.i −0.540068 + 0.392382i
\(151\) 317925. + 230986.i 1.13470 + 0.824409i 0.986372 0.164529i \(-0.0526104\pi\)
0.148329 + 0.988938i \(0.452610\pi\)
\(152\) −42969.8 132247.i −0.150853 0.464278i
\(153\) 43939.1 0.151748
\(154\) −213633. + 121988.i −0.725883 + 0.414492i
\(155\) 155558. 0.520073
\(156\) −1487.42 4577.81i −0.00489353 0.0150607i
\(157\) −317651. 230787.i −1.02849 0.747244i −0.0604869 0.998169i \(-0.519265\pi\)
−0.968007 + 0.250925i \(0.919265\pi\)
\(158\) −692621. + 503219.i −2.20726 + 1.60367i
\(159\) 108527. 334013.i 0.340444 1.04778i
\(160\) 67359.0 207310.i 0.208015 0.640205i
\(161\) −134857. + 97979.4i −0.410024 + 0.297900i
\(162\) −45030.2 32716.3i −0.134808 0.0979438i
\(163\) 121580. + 374186.i 0.358422 + 1.10311i 0.953999 + 0.299811i \(0.0969236\pi\)
−0.595577 + 0.803299i \(0.703076\pi\)
\(164\) 101977. 0.296068
\(165\) 19638.5 + 94604.7i 0.0561562 + 0.270522i
\(166\) −904098. −2.54651
\(167\) 138348. + 425790.i 0.383867 + 1.18142i 0.937299 + 0.348527i \(0.113318\pi\)
−0.553432 + 0.832894i \(0.686682\pi\)
\(168\) 35573.8 + 25845.9i 0.0972427 + 0.0706510i
\(169\) 300238. 218135.i 0.808627 0.587502i
\(170\) −38042.9 + 117084.i −0.100961 + 0.310725i
\(171\) −51476.7 + 158429.i −0.134623 + 0.414328i
\(172\) 258533. 187836.i 0.666340 0.484124i
\(173\) 22830.3 + 16587.2i 0.0579957 + 0.0421364i 0.616405 0.787429i \(-0.288588\pi\)
−0.558410 + 0.829565i \(0.688588\pi\)
\(174\) −8505.95 26178.6i −0.0212985 0.0655502i
\(175\) −174098. −0.429732
\(176\) 209480. + 190430.i 0.509753 + 0.463398i
\(177\) 447505. 1.07365
\(178\) 80964.0 + 249181.i 0.191532 + 0.589475i
\(179\) 155463. + 112950.i 0.362655 + 0.263484i 0.754159 0.656692i \(-0.228045\pi\)
−0.391504 + 0.920177i \(0.628045\pi\)
\(180\) 70069.2 50908.2i 0.161193 0.117113i
\(181\) 135695. 417625.i 0.307869 0.947525i −0.670721 0.741709i \(-0.734015\pi\)
0.978591 0.205815i \(-0.0659846\pi\)
\(182\) 2534.69 7800.97i 0.00567213 0.0174570i
\(183\) 119556. 86862.6i 0.263903 0.191737i
\(184\) −126188. 91681.2i −0.274773 0.199634i
\(185\) 57172.7 + 175960.i 0.122817 + 0.377993i
\(186\) 443979. 0.940980
\(187\) −161083. 146435.i −0.336857 0.306225i
\(188\) 542489. 1.11943
\(189\) −16278.0 50098.7i −0.0331473 0.102017i
\(190\) −377595. 274339.i −0.758826 0.551319i
\(191\) 64782.9 47067.5i 0.128492 0.0933550i −0.521683 0.853140i \(-0.674696\pi\)
0.650175 + 0.759784i \(0.274696\pi\)
\(192\) 129467. 398460.i 0.253459 0.780066i
\(193\) 81668.2 251349.i 0.157819 0.485718i −0.840616 0.541631i \(-0.817807\pi\)
0.998436 + 0.0559133i \(0.0178071\pi\)
\(194\) −79.6959 + 57.9025i −0.000152031 + 0.000110457i
\(195\) −2606.30 1893.58i −0.00490837 0.00356614i
\(196\) −143099. 440414.i −0.266070 0.818880i
\(197\) −284993. −0.523201 −0.261600 0.965176i \(-0.584250\pi\)
−0.261600 + 0.965176i \(0.584250\pi\)
\(198\) 56050.1 + 270011.i 0.101605 + 0.489461i
\(199\) −597612. −1.06976 −0.534880 0.844928i \(-0.679643\pi\)
−0.534880 + 0.844928i \(0.679643\pi\)
\(200\) −50340.9 154933.i −0.0889909 0.273886i
\(201\) −432348. 314119.i −0.754820 0.548409i
\(202\) 772139. 560992.i 1.33143 0.967338i
\(203\) 8050.02 24775.4i 0.0137106 0.0421969i
\(204\) −60301.2 + 185588.i −0.101450 + 0.312230i
\(205\) 55217.1 40117.6i 0.0917676 0.0666730i
\(206\) −1.11190e6 807846.i −1.82557 1.32636i
\(207\) 57741.9 + 177711.i 0.0936624 + 0.288263i
\(208\) −9439.12 −0.0151277
\(209\) 716709. 409254.i 1.13495 0.648078i
\(210\) 147591. 0.230947
\(211\) 189339. + 582726.i 0.292775 + 0.901070i 0.983960 + 0.178391i \(0.0570893\pi\)
−0.691184 + 0.722678i \(0.742911\pi\)
\(212\) 1.26185e6 + 916785.i 1.92827 + 1.40097i
\(213\) 360011. 261564.i 0.543710 0.395028i
\(214\) −433775. + 1.33502e6i −0.647485 + 1.99275i
\(215\) 66093.1 203414.i 0.0975124 0.300112i
\(216\) 39877.1 28972.4i 0.0581552 0.0422522i
\(217\) 339934. + 246976.i 0.490055 + 0.356046i
\(218\) −90847.9 279601.i −0.129471 0.398472i
\(219\) −108305. −0.152594
\(220\) −426538. 46885.6i −0.594157 0.0653104i
\(221\) 7258.38 0.00999676
\(222\) 163177. + 502206.i 0.222216 + 0.683911i
\(223\) 43987.1 + 31958.5i 0.0592329 + 0.0430352i 0.617008 0.786957i \(-0.288345\pi\)
−0.557775 + 0.829992i \(0.688345\pi\)
\(224\) 476336. 346078.i 0.634298 0.460845i
\(225\) −60307.0 + 185606.i −0.0794166 + 0.244419i
\(226\) −109838. + 338047.i −0.143048 + 0.440257i
\(227\) −373945. + 271687.i −0.481663 + 0.349949i −0.801969 0.597365i \(-0.796214\pi\)
0.320306 + 0.947314i \(0.396214\pi\)
\(228\) −598519. 434850.i −0.762502 0.553990i
\(229\) 119754. + 368565.i 0.150904 + 0.464435i 0.997723 0.0674465i \(-0.0214852\pi\)
−0.846819 + 0.531881i \(0.821485\pi\)
\(230\) −523539. −0.652574
\(231\) −107287. + 237914.i −0.132286 + 0.293353i
\(232\) 24375.9 0.0297331
\(233\) −197781. 608709.i −0.238669 0.734547i −0.996614 0.0822284i \(-0.973796\pi\)
0.757945 0.652319i \(-0.226204\pi\)
\(234\) −7438.62 5404.48i −0.00888082 0.00645229i
\(235\) 293740. 213415.i 0.346971 0.252089i
\(236\) −614147. + 1.89015e6i −0.717781 + 2.20910i
\(237\) −280664. + 863796.i −0.324576 + 0.998942i
\(238\) −269025. + 195458.i −0.307857 + 0.223672i
\(239\) −153735. 111695.i −0.174092 0.126485i 0.497327 0.867563i \(-0.334315\pi\)
−0.671419 + 0.741078i \(0.734315\pi\)
\(240\) −52484.6 161531.i −0.0588171 0.181021i
\(241\) −1.35835e6 −1.50650 −0.753248 0.657737i \(-0.771514\pi\)
−0.753248 + 0.657737i \(0.771514\pi\)
\(242\) 694377. 1.17667e6i 0.762179 1.29157i
\(243\) −59049.0 −0.0641500
\(244\) 202810. + 624184.i 0.218079 + 0.671179i
\(245\) −250742. 182175.i −0.266877 0.193898i
\(246\) 157595. 114500.i 0.166037 0.120633i
\(247\) −8503.53 + 26171.2i −0.00886864 + 0.0272949i
\(248\) −121497. + 373928.i −0.125440 + 0.386064i
\(249\) −775961. + 563769.i −0.793125 + 0.576239i
\(250\) −1.01613e6 738263.i −1.02825 0.747069i
\(251\) −233987. 720138.i −0.234427 0.721492i −0.997197 0.0748220i \(-0.976161\pi\)
0.762770 0.646670i \(-0.223839\pi\)
\(252\) 233944. 0.232066
\(253\) 380569. 843935.i 0.373794 0.828910i
\(254\) 1.76130e6 1.71296
\(255\) 40359.0 + 124212.i 0.0388678 + 0.119623i
\(256\) −284245. 206516.i −0.271077 0.196949i
\(257\) −120563. + 87594.2i −0.113863 + 0.0827261i −0.643259 0.765648i \(-0.722418\pi\)
0.529397 + 0.848374i \(0.322418\pi\)
\(258\) 188636. 580563.i 0.176431 0.543000i
\(259\) −154430. + 475287.i −0.143048 + 0.440257i
\(260\) 11574.9 8409.63i 0.0106190 0.00771514i
\(261\) −23624.6 17164.3i −0.0214666 0.0155964i
\(262\) −109205. 336100.i −0.0982859 0.302493i
\(263\) −2.02601e6 −1.80615 −0.903074 0.429485i \(-0.858695\pi\)
−0.903074 + 0.429485i \(0.858695\pi\)
\(264\) −242747. 26683.0i −0.214360 0.0235627i
\(265\) 1.04391e6 0.913164
\(266\) −389577. 1.19900e6i −0.337590 1.03900i
\(267\) 224871. + 163378.i 0.193044 + 0.140254i
\(268\) 1.92011e6 1.39504e6i 1.63301 1.18645i
\(269\) 130374. 401250.i 0.109853 0.338091i −0.880986 0.473142i \(-0.843120\pi\)
0.990839 + 0.135051i \(0.0431197\pi\)
\(270\) 51125.2 157347.i 0.0426802 0.131356i
\(271\) −282892. + 205533.i −0.233990 + 0.170004i −0.698602 0.715511i \(-0.746194\pi\)
0.464612 + 0.885515i \(0.346194\pi\)
\(272\) 309586. + 224927.i 0.253723 + 0.184340i
\(273\) −2689.00 8275.90i −0.00218366 0.00672061i
\(274\) 2.78278e6 2.23925
\(275\) 839654. 479458.i 0.669527 0.382313i
\(276\) −829852. −0.655735
\(277\) 183353. + 564302.i 0.143578 + 0.441888i 0.996825 0.0796184i \(-0.0253702\pi\)
−0.853247 + 0.521507i \(0.825370\pi\)
\(278\) −807848. 586936.i −0.626928 0.455490i
\(279\) 381054. 276852.i 0.293073 0.212930i
\(280\) −40388.9 + 124304.i −0.0307870 + 0.0947526i
\(281\) −546959. + 1.68337e6i −0.413227 + 1.27178i 0.500600 + 0.865679i \(0.333113\pi\)
−0.913827 + 0.406104i \(0.866887\pi\)
\(282\) 838363. 609106.i 0.627783 0.456111i
\(283\) 505485. + 367256.i 0.375182 + 0.272586i 0.759357 0.650675i \(-0.225514\pi\)
−0.384174 + 0.923261i \(0.625514\pi\)
\(284\) 610708. + 1.87956e6i 0.449301 + 1.38281i
\(285\) −495148. −0.361096
\(286\) 9259.03 + 44603.7i 0.00669346 + 0.0322445i
\(287\) 184357. 0.132116
\(288\) −203953. 627704.i −0.144894 0.445937i
\(289\) 910627. + 661609.i 0.641351 + 0.465969i
\(290\) 66192.0 48091.3i 0.0462179 0.0335793i
\(291\) −32.2944 + 99.3919i −2.23560e−5 + 6.88048e-5i
\(292\) 148635. 457452.i 0.102015 0.313971i
\(293\) −902898. + 655993.i −0.614426 + 0.446406i −0.850970 0.525214i \(-0.823985\pi\)
0.236544 + 0.971621i \(0.423985\pi\)
\(294\) −715642. 519944.i −0.482867 0.350823i
\(295\) 411043. + 1.26506e6i 0.274999 + 0.846361i
\(296\) −467622. −0.310217
\(297\) 216477. + 196791.i 0.142403 + 0.129454i
\(298\) 841854. 0.549156
\(299\) 9538.49 + 29356.5i 0.00617024 + 0.0189900i
\(300\) −701189. 509444.i −0.449813 0.326808i
\(301\) 467384. 339575.i 0.297343 0.216032i
\(302\) −1.03021e6 + 3.17065e6i −0.649991 + 2.00047i
\(303\) 312887. 962966.i 0.195785 0.602566i
\(304\) −1.17370e6 + 852745.i −0.728407 + 0.529219i
\(305\) 355368. + 258190.i 0.218741 + 0.158924i
\(306\) 115189. + 354514.i 0.0703244 + 0.216436i
\(307\) 2.03999e6 1.23533 0.617663 0.786443i \(-0.288080\pi\)
0.617663 + 0.786443i \(0.288080\pi\)
\(308\) −857653. 779661.i −0.515151 0.468305i
\(309\) −1.45806e6 −0.868721
\(310\) 407805. + 1.25509e6i 0.241017 + 0.741774i
\(311\) −573467. 416648.i −0.336208 0.244269i 0.406852 0.913494i \(-0.366626\pi\)
−0.743060 + 0.669225i \(0.766626\pi\)
\(312\) 6587.37 4786.00i 0.00383112 0.00278347i
\(313\) 963156. 2.96429e6i 0.555694 1.71025i −0.138410 0.990375i \(-0.544199\pi\)
0.694104 0.719875i \(-0.255801\pi\)
\(314\) 1.02932e6 3.16793e6i 0.589152 1.81322i
\(315\) 126673. 92033.4i 0.0719297 0.0522600i
\(316\) −3.26328e6 2.37091e6i −1.83839 1.33567i
\(317\) 624464. + 1.92190e6i 0.349027 + 1.07420i 0.959392 + 0.282075i \(0.0910227\pi\)
−0.610365 + 0.792120i \(0.708977\pi\)
\(318\) 2.97942e6 1.65221
\(319\) 29406.1 + 141658.i 0.0161793 + 0.0779410i
\(320\) 1.24533e6 0.679846
\(321\) 460183. + 1.41630e6i 0.249269 + 0.767171i
\(322\) −1.14406e6 831210.i −0.614908 0.446757i
\(323\) 902541. 655734.i 0.481349 0.349721i
\(324\) 81037.7 249408.i 0.0428869 0.131992i
\(325\) −9962.23 + 30660.6i −0.00523177 + 0.0161017i
\(326\) −2.70032e6 + 1.96190e6i −1.40725 + 1.02243i
\(327\) −252323. 183323.i −0.130493 0.0948087i
\(328\) 53307.3 + 164063.i 0.0273591 + 0.0842027i
\(329\) 980728. 0.499527
\(330\) −711816. + 406460.i −0.359818 + 0.205463i
\(331\) −2.21306e6 −1.11026 −0.555129 0.831765i \(-0.687331\pi\)
−0.555129 + 0.831765i \(0.687331\pi\)
\(332\) −1.31631e6 4.05117e6i −0.655408 2.01714i
\(333\) 453210. + 329276.i 0.223970 + 0.162723i
\(334\) −3.07272e6 + 2.23246e6i −1.50715 + 1.09501i
\(335\) 490869. 1.51074e6i 0.238975 0.735491i
\(336\) 141767. 436314.i 0.0685057 0.210839i
\(337\) 556467. 404297.i 0.266910 0.193921i −0.446278 0.894894i \(-0.647251\pi\)
0.713188 + 0.700973i \(0.247251\pi\)
\(338\) 2.54707e6 + 1.85055e6i 1.21269 + 0.881070i
\(339\) 116525. + 358628.i 0.0550707 + 0.169490i
\(340\) −580030. −0.272115
\(341\) −2.31963e6 254976.i −1.08027 0.118744i
\(342\) −1.41320e6 −0.653339
\(343\) −633987. 1.95121e6i −0.290968 0.895507i
\(344\) 437341. + 317746.i 0.199262 + 0.144772i
\(345\) −449338. + 326463.i −0.203248 + 0.147668i
\(346\) −73979.6 + 227686.i −0.0332217 + 0.102246i
\(347\) −454972. + 1.40026e6i −0.202843 + 0.624288i 0.796952 + 0.604043i \(0.206444\pi\)
−0.999795 + 0.0202445i \(0.993556\pi\)
\(348\) 104920. 76228.6i 0.0464418 0.0337419i
\(349\) −2.23243e6 1.62196e6i −0.981104 0.712814i −0.0231487 0.999732i \(-0.507369\pi\)
−0.957955 + 0.286918i \(0.907369\pi\)
\(350\) −456406. 1.40467e6i −0.199150 0.612922i
\(351\) −9754.42 −0.00422604
\(352\) −1.34423e6 + 2.98091e6i −0.578252 + 1.28231i
\(353\) −334116. −0.142712 −0.0713561 0.997451i \(-0.522733\pi\)
−0.0713561 + 0.997451i \(0.522733\pi\)
\(354\) 1.17316e6 + 3.61060e6i 0.497562 + 1.53134i
\(355\) 1.07010e6 + 777471.i 0.450663 + 0.327426i
\(356\) −998679. + 725583.i −0.417639 + 0.303432i
\(357\) −109014. + 335511.i −0.0452702 + 0.139327i
\(358\) −503764. + 1.55043e6i −0.207740 + 0.639357i
\(359\) 2.97778e6 2.16348e6i 1.21943 0.885967i 0.223376 0.974732i \(-0.428292\pi\)
0.996053 + 0.0887656i \(0.0282922\pi\)
\(360\) 118530. + 86117.4i 0.0482030 + 0.0350215i
\(361\) 541822. + 1.66756e6i 0.218821 + 0.673461i
\(362\) 3.72526e6 1.49412
\(363\) −137774. 1.44290e6i −0.0548785 0.574736i
\(364\) 38645.7 0.0152879
\(365\) −99480.2 306169.i −0.0390845 0.120290i
\(366\) 1.01426e6 + 736900.i 0.395772 + 0.287545i
\(367\) −3.75578e6 + 2.72874e6i −1.45558 + 1.05754i −0.471090 + 0.882085i \(0.656139\pi\)
−0.984488 + 0.175454i \(0.943861\pi\)
\(368\) −502879. + 1.54770e6i −0.193573 + 0.595755i
\(369\) 63860.8 196543.i 0.0244156 0.0751436i
\(370\) −1.26981e6 + 922574.i −0.482210 + 0.350346i
\(371\) 2.28120e6 + 1.65739e6i 0.860457 + 0.625159i
\(372\) 646404. + 1.98943e6i 0.242185 + 0.745368i
\(373\) 3.63606e6 1.35319 0.676595 0.736355i \(-0.263455\pi\)
0.676595 + 0.736355i \(0.263455\pi\)
\(374\) 759193. 1.68355e6i 0.280655 0.622369i
\(375\) −1.33247e6 −0.489306
\(376\) 283580. + 872771.i 0.103444 + 0.318369i
\(377\) −3902.60 2835.40i −0.00141417 0.00102745i
\(378\) 361538. 262672.i 0.130144 0.0945551i
\(379\) 1.39540e6 4.29460e6i 0.499000 1.53576i −0.311628 0.950204i \(-0.600874\pi\)
0.810629 0.585561i \(-0.199126\pi\)
\(380\) 679532. 2.09138e6i 0.241408 0.742976i
\(381\) 1.51167e6 1.09829e6i 0.533512 0.387619i
\(382\) 549586. + 399298.i 0.192698 + 0.140003i
\(383\) −312297. 961152.i −0.108786 0.334807i 0.881815 0.471596i \(-0.156322\pi\)
−0.990600 + 0.136789i \(0.956322\pi\)
\(384\) 1.20761e6 0.417925
\(385\) −771109. 84761.2i −0.265133 0.0291437i
\(386\) 2.24206e6 0.765911
\(387\) −200121. 615908.i −0.0679226 0.209044i
\(388\) −375.487 272.807i −0.000126624 9.19976e-5i
\(389\) 648306. 471022.i 0.217223 0.157822i −0.473853 0.880604i \(-0.657137\pi\)
0.691076 + 0.722782i \(0.257137\pi\)
\(390\) 8445.48 25992.5i 0.00281166 0.00865340i
\(391\) 386698. 1.19013e6i 0.127918 0.393690i
\(392\) 633746. 460443.i 0.208305 0.151342i
\(393\) −303310. 220367.i −0.0990615 0.0719724i
\(394\) −747123. 2.29941e6i −0.242466 0.746235i
\(395\) −2.69968e6 −0.870601
\(396\) −1.12829e6 + 644273.i −0.361561 + 0.206458i
\(397\) 1.86106e6 0.592632 0.296316 0.955090i \(-0.404242\pi\)
0.296316 + 0.955090i \(0.404242\pi\)
\(398\) −1.56667e6 4.82171e6i −0.495758 1.52579i
\(399\) −1.08202e6 786134.i −0.340254 0.247209i
\(400\) −1.37504e6 + 999026.i −0.429700 + 0.312196i
\(401\) −1.13645e6 + 3.49762e6i −0.352929 + 1.08620i 0.604271 + 0.796779i \(0.293464\pi\)
−0.957200 + 0.289426i \(0.906536\pi\)
\(402\) 1.40099e6 4.31180e6i 0.432384 1.33074i
\(403\) 62947.1 45733.7i 0.0193069 0.0140273i
\(404\) 3.63793e6 + 2.64311e6i 1.10892 + 0.805679i
\(405\) −54237.8 166927.i −0.0164310 0.0505695i
\(406\) 220999. 0.0665389
\(407\) −564121. 2.71755e6i −0.168805 0.813189i
\(408\) −330101. −0.0981739
\(409\) −1.57052e6 4.83356e6i −0.464232 1.42876i −0.859946 0.510386i \(-0.829503\pi\)
0.395714 0.918374i \(-0.370497\pi\)
\(410\) 468436. + 340338.i 0.137623 + 0.0999888i
\(411\) 2.38838e6 1.73526e6i 0.697427 0.506710i
\(412\) 2.00102e6 6.15850e6i 0.580775 1.78744i
\(413\) −1.11027e6 + 3.41707e6i −0.320298 + 0.985777i
\(414\) −1.28246e6 + 931758.i −0.367740 + 0.267179i
\(415\) −2.30647e6 1.67575e6i −0.657395 0.477626i
\(416\) −33691.4 103692.i −0.00954523 0.0293772i
\(417\) −1.05935e6 −0.298331
\(418\) 5.18088e6 + 4.70975e6i 1.45032 + 1.31843i
\(419\) −115670. −0.0321873 −0.0160937 0.999870i \(-0.505123\pi\)
−0.0160937 + 0.999870i \(0.505123\pi\)
\(420\) 214883. + 661341.i 0.0594400 + 0.182937i
\(421\) 1.09651e6 + 796661.i 0.301514 + 0.219063i 0.728247 0.685315i \(-0.240336\pi\)
−0.426733 + 0.904378i \(0.640336\pi\)
\(422\) −4.20525e6 + 3.05529e6i −1.14950 + 0.835164i
\(423\) 339722. 1.04556e6i 0.0923150 0.284116i
\(424\) −815331. + 2.50933e6i −0.220252 + 0.677866i
\(425\) 1.05736e6 768219.i 0.283956 0.206306i
\(426\) 3.05416e6 + 2.21898e6i 0.815395 + 0.592419i
\(427\) 366646. + 1.12842e6i 0.0973143 + 0.299503i
\(428\) −6.61364e6 −1.74514
\(429\) 35760.3 + 32508.3i 0.00938118 + 0.00852809i
\(430\) 1.81447e6 0.473237
\(431\) 469344. + 1.44449e6i 0.121702 + 0.374560i 0.993286 0.115686i \(-0.0369067\pi\)
−0.871584 + 0.490247i \(0.836907\pi\)
\(432\) −416047. 302276.i −0.107259 0.0779282i
\(433\) 163420. 118732.i 0.0418877 0.0304332i −0.566644 0.823962i \(-0.691759\pi\)
0.608532 + 0.793529i \(0.291759\pi\)
\(434\) −1.10153e6 + 3.39015e6i −0.280718 + 0.863962i
\(435\) 26822.3 82550.6i 0.00679631 0.0209169i
\(436\) 1.12060e6 814160.i 0.282314 0.205113i
\(437\) 3.83817e6 + 2.78859e6i 0.961437 + 0.698525i
\(438\) −283926. 873835.i −0.0707164 0.217643i
\(439\) −5.91202e6 −1.46411 −0.732057 0.681244i \(-0.761439\pi\)
−0.732057 + 0.681244i \(0.761439\pi\)
\(440\) −147538. 710735.i −0.0363305 0.175015i
\(441\) −938436. −0.229778
\(442\) 19028.2 + 58562.9i 0.00463279 + 0.0142583i
\(443\) 2.09532e6 + 1.52234e6i 0.507272 + 0.368555i 0.811788 0.583953i \(-0.198495\pi\)
−0.304516 + 0.952507i \(0.598495\pi\)
\(444\) −2.01276e6 + 1.46236e6i −0.484545 + 0.352043i
\(445\) −255309. + 785759.i −0.0611175 + 0.188100i
\(446\) −142536. + 438682.i −0.0339304 + 0.104427i
\(447\) 722538. 524955.i 0.171038 0.124266i
\(448\) 2.72136e6 + 1.97718e6i 0.640606 + 0.465427i
\(449\) 100622. + 309683.i 0.0235547 + 0.0724939i 0.962143 0.272546i \(-0.0878655\pi\)
−0.938588 + 0.345039i \(0.887866\pi\)
\(450\) −1.65562e6 −0.385416
\(451\) −889132. + 507711.i −0.205838 + 0.117537i
\(452\) −1.67467e6 −0.385553
\(453\) 1.09293e6 + 3.36368e6i 0.250234 + 0.770140i
\(454\) −3.17237e6 2.30486e6i −0.722345 0.524814i
\(455\) 20925.4 15203.2i 0.00473855 0.00344275i
\(456\) 386728. 1.19023e6i 0.0870951 0.268051i
\(457\) −2.26999e6 + 6.98632e6i −0.508433 + 1.56480i 0.286487 + 0.958084i \(0.407512\pi\)
−0.794921 + 0.606713i \(0.792488\pi\)
\(458\) −2.65975e6 + 1.93242e6i −0.592485 + 0.430465i
\(459\) 319927. + 232441.i 0.0708793 + 0.0514968i
\(460\) −762238. 2.34593e6i −0.167956 0.516916i
\(461\) −7.99335e6 −1.75177 −0.875884 0.482521i \(-0.839721\pi\)
−0.875884 + 0.482521i \(0.839721\pi\)
\(462\) −2.20082e6 241917.i −0.479711 0.0527304i
\(463\) 2.89182e6 0.626929 0.313465 0.949600i \(-0.398510\pi\)
0.313465 + 0.949600i \(0.398510\pi\)
\(464\) −78589.1 241872.i −0.0169460 0.0521544i
\(465\) 1.13265e6 + 822915.i 0.242919 + 0.176491i
\(466\) 4.39275e6 3.19152e6i 0.937070 0.680821i
\(467\) −1.00578e6 + 3.09547e6i −0.213408 + 0.656801i 0.785855 + 0.618411i \(0.212223\pi\)
−0.999263 + 0.0383908i \(0.987777\pi\)
\(468\) 13386.8 41200.3i 0.00282528 0.00869532i
\(469\) 3.47123e6 2.52200e6i 0.728704 0.529435i
\(470\) 2.49195e6 + 1.81051e6i 0.520349 + 0.378055i
\(471\) −1.09199e6 3.36079e6i −0.226812 0.698055i
\(472\) −3.36196e6 −0.694605
\(473\) −1.31897e6 + 2.92489e6i −0.271070 + 0.601114i
\(474\) −7.70514e6 −1.57520
\(475\) 1.53118e6 + 4.71248e6i 0.311381 + 0.958332i
\(476\) −1.26751e6 920899.i −0.256409 0.186292i
\(477\) 2.55715e6 1.85788e6i 0.514589 0.373871i
\(478\) 498165. 1.53320e6i 0.0997249 0.306922i
\(479\) 2.54580e6 7.83516e6i 0.506973 1.56030i −0.290454 0.956889i \(-0.593806\pi\)
0.797427 0.603415i \(-0.206194\pi\)
\(480\) 1.58713e6 1.15312e6i 0.314420 0.228439i
\(481\) 74866.7 + 54393.8i 0.0147545 + 0.0107198i
\(482\) −3.56097e6 1.09596e7i −0.698154 2.14870i
\(483\) −1.50023e6 −0.292611
\(484\) 6.28352e6 + 1.39828e6i 1.21924 + 0.271319i
\(485\) −310.636 −5.99650e−5
\(486\) −154800. 476425.i −0.0297290 0.0914964i
\(487\) 3.47149e6 + 2.52218e6i 0.663275 + 0.481897i 0.867767 0.496971i \(-0.165554\pi\)
−0.204493 + 0.978868i \(0.565554\pi\)
\(488\) −898188. + 652572.i −0.170733 + 0.124045i
\(489\) −1.09422e6 + 3.36768e6i −0.206935 + 0.636881i
\(490\) 812507. 2.50064e6i 0.152875 0.470502i
\(491\) 6.77338e6 4.92115e6i 1.26795 0.921219i 0.268830 0.963188i \(-0.413363\pi\)
0.999119 + 0.0419692i \(0.0133631\pi\)
\(492\) 742509. + 539464.i 0.138289 + 0.100473i
\(493\) 60432.5 + 185992.i 0.0111983 + 0.0344649i
\(494\) −233450. −0.0430403
\(495\) −357474. + 792720.i −0.0655740 + 0.145414i
\(496\) 4.10206e6 0.748682
\(497\) 1.10406e6 + 3.39793e6i 0.200493 + 0.617055i
\(498\) −6.58288e6 4.78274e6i −1.18944 0.864179i
\(499\) −5.11453e6 + 3.71592e6i −0.919505 + 0.668060i −0.943401 0.331655i \(-0.892393\pi\)
0.0238957 + 0.999714i \(0.492393\pi\)
\(500\) 1.82866e6 5.62805e6i 0.327121 1.00678i
\(501\) −1.24513e6 + 3.83211e6i −0.221626 + 0.682094i
\(502\) 5.19688e6 3.77576e6i 0.920415 0.668721i
\(503\) −8.39571e6 6.09984e6i −1.47958 1.07498i −0.977693 0.210040i \(-0.932641\pi\)
−0.501883 0.864935i \(-0.667359\pi\)
\(504\) 122292. + 376376.i 0.0214448 + 0.0660002i
\(505\) 3.00962e6 0.525150
\(506\) 7.80680e6 + 858133.i 1.35549 + 0.148997i
\(507\) 3.34003e6 0.577072
\(508\) 2.56433e6 + 7.89219e6i 0.440874 + 1.35687i
\(509\) 5.91019e6 + 4.29400e6i 1.01113 + 0.734629i 0.964446 0.264281i \(-0.0851347\pi\)
0.0466838 + 0.998910i \(0.485135\pi\)
\(510\) −896379. + 651257.i −0.152604 + 0.110873i
\(511\) 268707. 826996.i 0.0455226 0.140104i
\(512\) 2.24791e6 6.91834e6i 0.378969 1.16635i
\(513\) −1.21291e6 + 881230.i −0.203486 + 0.147841i
\(514\) −1.02280e6 743107.i −0.170759 0.124063i
\(515\) −1.33926e6 4.12183e6i −0.222509 0.684813i
\(516\) 2.87608e6 0.475529
\(517\) −4.72994e6 + 2.70088e6i −0.778268 + 0.444406i
\(518\) −4.23960e6 −0.694226
\(519\) 78483.5 + 241547.i 0.0127897 + 0.0393626i
\(520\) 19580.3 + 14225.9i 0.00317549 + 0.00230713i
\(521\) 5.61791e6 4.08165e6i 0.906735 0.658782i −0.0334517 0.999440i \(-0.510650\pi\)
0.940187 + 0.340658i \(0.110650\pi\)
\(522\) 76553.6 235608.i 0.0122967 0.0378454i
\(523\) −3.40373e6 + 1.04756e7i −0.544128 + 1.67465i 0.178928 + 0.983862i \(0.442737\pi\)
−0.723055 + 0.690790i \(0.757263\pi\)
\(524\) 1.34703e6 978678.i 0.214314 0.155708i
\(525\) −1.26763e6 920988.i −0.200722 0.145833i
\(526\) −5.31130e6 1.63465e7i −0.837021 2.57609i
\(527\) −3.15435e6 −0.494748
\(528\) 517864. + 2.49471e6i 0.0808409 + 0.389436i
\(529\) −1.11468e6 −0.173186
\(530\) 2.73667e6 + 8.42259e6i 0.423187 + 1.30244i
\(531\) 3.25835e6 + 2.36733e6i 0.501489 + 0.364353i
\(532\) 4.80538e6 3.49132e6i 0.736121 0.534823i
\(533\) 10549.3 32467.4i 0.00160844 0.00495027i
\(534\) −728676. + 2.24263e6i −0.110581 + 0.340334i
\(535\) −3.58107e6 + 2.60180e6i −0.540914 + 0.392997i
\(536\) 3.24810e6 + 2.35988e6i 0.488334 + 0.354795i
\(537\) 534433. + 1.64482e6i 0.0799756 + 0.246140i
\(538\) 3.57919e6 0.533125
\(539\) 3.44036e6 + 3.12750e6i 0.510072 + 0.463688i
\(540\) 779493. 0.115034
\(541\) −1.33606e6 4.11197e6i −0.196261 0.604028i −0.999960 0.00899175i \(-0.997138\pi\)
0.803699 0.595036i \(-0.202862\pi\)
\(542\) −2.39992e6 1.74364e6i −0.350912 0.254953i
\(543\) 3.19728e6 2.32296e6i 0.465352 0.338098i
\(544\) −1.36588e6 + 4.20374e6i −0.197886 + 0.609030i
\(545\) 286476. 881683.i 0.0413140 0.127151i
\(546\) 59723.1 43391.4i 0.00857355 0.00622905i
\(547\) −539838. 392215.i −0.0771427 0.0560475i 0.548545 0.836121i \(-0.315182\pi\)
−0.625688 + 0.780073i \(0.715182\pi\)
\(548\) 4.05154e6 + 1.24694e7i 0.576327 + 1.77375i
\(549\) 1.33002e6 0.188333
\(550\) 6.06961e6 + 5.51766e6i 0.855566 + 0.777764i
\(551\) −741422. −0.104037
\(552\) −433797. 1.33509e6i −0.0605952 0.186493i
\(553\) −5.89946e6 4.28621e6i −0.820351 0.596020i
\(554\) −4.07229e6 + 2.95870e6i −0.563722 + 0.409568i
\(555\) −514554. + 1.58364e6i −0.0709086 + 0.218234i
\(556\) 1.45383e6 4.47443e6i 0.199447 0.613833i
\(557\) 2.93931e6 2.13554e6i 0.401428 0.291655i −0.368694 0.929551i \(-0.620195\pi\)
0.770123 + 0.637896i \(0.220195\pi\)
\(558\) 3.23268e6 + 2.34868e6i 0.439519 + 0.319329i
\(559\) −33058.3 101743.i −0.00447457 0.0137713i
\(560\) 1.36364e6 0.183751
\(561\) −398221. 1.91836e6i −0.0534216 0.257349i
\(562\) −1.50158e7 −2.00543
\(563\) 267094. + 822030.i 0.0355135 + 0.109299i 0.967242 0.253857i \(-0.0816992\pi\)
−0.931728 + 0.363156i \(0.881699\pi\)
\(564\) 3.94994e6 + 2.86980e6i 0.522869 + 0.379887i
\(565\) −906781. + 658815.i −0.119504 + 0.0868245i
\(566\) −1.63798e6 + 5.04119e6i −0.214916 + 0.661442i
\(567\) 146502. 450888.i 0.0191376 0.0588994i
\(568\) −2.70465e6 + 1.96505e6i −0.351755 + 0.255565i
\(569\) −8.81293e6 6.40297e6i −1.14114 0.829088i −0.153864 0.988092i \(-0.549172\pi\)
−0.987278 + 0.159004i \(0.949172\pi\)
\(570\) −1.29806e6 3.99501e6i −0.167343 0.515027i
\(571\) 2.44162e6 0.313392 0.156696 0.987647i \(-0.449916\pi\)
0.156696 + 0.987647i \(0.449916\pi\)
\(572\) −186384. + 106429.i −0.0238187 + 0.0136009i
\(573\) 720684. 0.0916977
\(574\) 483301. + 1.48745e6i 0.0612263 + 0.188435i
\(575\) 4.49657e6 + 3.26695e6i 0.567168 + 0.412072i
\(576\) 3.05055e6 2.21636e6i 0.383109 0.278345i
\(577\) 854927. 2.63119e6i 0.106903 0.329013i −0.883269 0.468866i \(-0.844663\pi\)
0.990172 + 0.139853i \(0.0446628\pi\)
\(578\) −2.95081e6 + 9.08165e6i −0.367385 + 1.13069i
\(579\) 1.92429e6 1.39808e6i 0.238547 0.173315i
\(580\) 311863. + 226582.i 0.0384941 + 0.0279676i
\(581\) −2.37966e6 7.32383e6i −0.292465 0.900115i
\(582\) −886.586 −0.000108496
\(583\) −1.55664e7 1.71107e6i −1.89678 0.208496i
\(584\) 813659. 0.0987212
\(585\) −8959.65 27575.0i −0.00108243 0.00333139i
\(586\) −7.65975e6 5.56513e6i −0.921447 0.669470i
\(587\) −4.90076e6 + 3.56061e6i −0.587041 + 0.426510i −0.841256 0.540638i \(-0.818183\pi\)
0.254215 + 0.967148i \(0.418183\pi\)
\(588\) 1.28789e6 3.96372e6i 0.153616 0.472781i
\(589\) 3.69547e6 1.13735e7i 0.438916 1.35084i
\(590\) −9.12931e6 + 6.63283e6i −1.07971 + 0.784457i
\(591\) −2.07508e6 1.50763e6i −0.244380 0.177552i
\(592\) 1.50764e6 + 4.64003e6i 0.176804 + 0.544147i
\(593\) −3.17434e6 −0.370695 −0.185348 0.982673i \(-0.559341\pi\)
−0.185348 + 0.982673i \(0.559341\pi\)
\(594\) −1.02027e6 + 2.26250e6i −0.118645 + 0.263101i
\(595\) −1.04860e6 −0.121427
\(596\) 1.22568e6 + 3.77226e6i 0.141339 + 0.434997i
\(597\) −4.35130e6 3.16141e6i −0.499670 0.363032i
\(598\) −211851. + 153919.i −0.0242258 + 0.0176011i
\(599\) 2.14578e6 6.60404e6i 0.244353 0.752042i −0.751389 0.659860i \(-0.770616\pi\)
0.995742 0.0921826i \(-0.0293844\pi\)
\(600\) 453068. 1.39440e6i 0.0513789 0.158128i
\(601\) 4.16427e6 3.02552e6i 0.470276 0.341676i −0.327273 0.944930i \(-0.606130\pi\)
0.797549 + 0.603254i \(0.206130\pi\)
\(602\) 3.96506e6 + 2.88079e6i 0.445922 + 0.323981i
\(603\) −1.48628e6 4.57430e6i −0.166459 0.512308i
\(604\) −1.57073e7 −1.75190
\(605\) 3.95240e6 1.71481e6i 0.439008 0.190470i
\(606\) 8.58975e6 0.950165
\(607\) −2.12651e6 6.54473e6i −0.234259 0.720975i −0.997219 0.0745293i \(-0.976255\pi\)
0.762960 0.646446i \(-0.223745\pi\)
\(608\) −1.35570e7 9.84975e6i −1.48732 1.08060i
\(609\) 189677. 137808.i 0.0207239 0.0150568i
\(610\) −1.15154e6 + 3.54408e6i −0.125301 + 0.385637i
\(611\) 56119.3 172717.i 0.00608148 0.0187169i
\(612\) −1.42083e6 + 1.03230e6i −0.153343 + 0.111410i
\(613\) 8.84104e6 + 6.42339e6i 0.950282 + 0.690420i 0.950873 0.309580i \(-0.100188\pi\)
−0.000591810 1.00000i \(0.500188\pi\)
\(614\) 5.34793e6 + 1.64592e7i 0.572486 + 1.76193i
\(615\) 614269. 0.0654894
\(616\) 806010. 1.78737e6i 0.0855833 0.189786i
\(617\) −2.15996e6 −0.228420 −0.114210 0.993457i \(-0.536434\pi\)
−0.114210 + 0.993457i \(0.536434\pi\)
\(618\) −3.82239e6 1.17641e7i −0.402591 1.23905i
\(619\) 1.51263e7 + 1.09899e7i 1.58674 + 1.15283i 0.908414 + 0.418071i \(0.137294\pi\)
0.678325 + 0.734762i \(0.262706\pi\)
\(620\) −5.03021e6 + 3.65466e6i −0.525542 + 0.381828i
\(621\) −519677. + 1.59940e6i −0.0540760 + 0.166429i
\(622\) 1.85827e6 5.71917e6i 0.192590 0.592731i
\(623\) −1.80544e6 + 1.31173e6i −0.186365 + 0.135402i
\(624\) −68727.7 49933.6i −0.00706594 0.00513371i
\(625\) 1.10275e6 + 3.39392e6i 0.112922 + 0.347538i
\(626\) 2.64417e7 2.69683
\(627\) 7.38345e6 + 811597.i 0.750050 + 0.0824464i
\(628\) 1.56938e7 1.58792
\(629\) −1.15933e6 3.56804e6i −0.116837 0.359586i
\(630\) 1.07463e6 + 780767.i 0.107872 + 0.0783737i
\(631\) 968726. 703821.i 0.0968562 0.0703702i −0.538303 0.842751i \(-0.680934\pi\)
0.635159 + 0.772381i \(0.280934\pi\)
\(632\) 2.10854e6 6.48943e6i 0.209986 0.646270i
\(633\) −1.70405e6 + 5.24454e6i −0.169034 + 0.520233i
\(634\) −1.38694e7 + 1.00767e7i −1.37036 + 0.995627i
\(635\) 4.49328e6 + 3.26456e6i 0.442211 + 0.321285i
\(636\) 4.33784e6 + 1.33505e7i 0.425237 + 1.30874i
\(637\) −155022. −0.0151372
\(638\) −1.06585e6 + 608623.i −0.103668 + 0.0591965i
\(639\) 4.00499e6 0.388015
\(640\) 1.10922e6 + 3.41382e6i 0.107045 + 0.329450i
\(641\) 3.56772e6 + 2.59210e6i 0.342961 + 0.249176i 0.745910 0.666046i \(-0.232015\pi\)
−0.402949 + 0.915222i \(0.632015\pi\)
\(642\) −1.02207e7 + 7.42579e6i −0.978688 + 0.711059i
\(643\) −4.08432e6 + 1.25703e7i −0.389577 + 1.19899i 0.543529 + 0.839390i \(0.317088\pi\)
−0.933105 + 0.359603i \(0.882912\pi\)
\(644\) 2.05889e6 6.33661e6i 0.195622 0.602064i
\(645\) 1.55731e6 1.13145e6i 0.147392 0.107087i
\(646\) 7.65672e6 + 5.56293e6i 0.721874 + 0.524472i
\(647\) 518851. + 1.59686e6i 0.0487284 + 0.149970i 0.972460 0.233070i \(-0.0748771\pi\)
−0.923732 + 0.383040i \(0.874877\pi\)
\(648\) 443617. 0.0415021
\(649\) −4.05574e6 1.95378e7i −0.377971 1.82081i
\(650\) −273496. −0.0253902
\(651\) 1.16859e6 + 3.59654e6i 0.108071 + 0.332608i
\(652\) −1.27225e7 9.24347e6i −1.17207 0.851561i
\(653\) 1.04355e6 758184.i 0.0957703 0.0695812i −0.538870 0.842389i \(-0.681148\pi\)
0.634640 + 0.772808i \(0.281148\pi\)
\(654\) 817631. 2.51641e6i 0.0747503 0.230058i
\(655\) 344364. 1.05984e6i 0.0313628 0.0965248i
\(656\) 1.45607e6 1.05790e6i 0.132106 0.0959806i
\(657\) −788583. 572939.i −0.0712745 0.0517839i
\(658\) 2.57103e6 + 7.91281e6i 0.231495 + 0.712469i
\(659\) 6.49514e6 0.582606 0.291303 0.956631i \(-0.405911\pi\)
0.291303 + 0.956631i \(0.405911\pi\)
\(660\) −2.85766e6 2.59780e6i −0.255359 0.232138i
\(661\) −2.12605e6 −0.189265 −0.0946325 0.995512i \(-0.530168\pi\)
−0.0946325 + 0.995512i \(0.530168\pi\)
\(662\) −5.80165e6 1.78557e7i −0.514526 1.58355i
\(663\) 52849.4 + 38397.3i 0.00466935 + 0.00339248i
\(664\) 5.82955e6 4.23542e6i 0.513115 0.372800i
\(665\) 1.22848e6 3.78087e6i 0.107724 0.331541i
\(666\) −1.46859e6 + 4.51985e6i −0.128296 + 0.394856i
\(667\) −672827. + 488837.i −0.0585583 + 0.0425451i
\(668\) −1.44771e7 1.05182e7i −1.25528 0.912015i
\(669\) 151214. + 465389.i 0.0130625 + 0.0402023i
\(670\) 1.34759e7 1.15977
\(671\) −4.87591e6 4.43251e6i −0.418070 0.380053i
\(672\) 5.29905e6 0.452663
\(673\) −5.49533e6 1.69129e7i −0.467688 1.43940i −0.855570 0.517686i \(-0.826793\pi\)
0.387883 0.921709i \(-0.373207\pi\)
\(674\) 4.72080e6 + 3.42986e6i 0.400282 + 0.290822i
\(675\) −1.42097e6 + 1.03240e6i −0.120040 + 0.0872142i
\(676\) −4.58379e6 + 1.41074e7i −0.385796 + 1.18736i
\(677\) −2.96741e6 + 9.13275e6i −0.248832 + 0.765826i 0.746151 + 0.665777i \(0.231900\pi\)
−0.994983 + 0.100049i \(0.968100\pi\)
\(678\) −2.58804e6 + 1.88032e6i −0.216221 + 0.157093i
\(679\) −678.817 493.189i −5.65038e−5 4.10524e-5i
\(680\) −303205. 933168.i −0.0251457 0.0773905i
\(681\) −4.16000e6 −0.343736
\(682\) −4.02379e6 1.93839e7i −0.331264 1.59580i
\(683\) 1.76440e7 1.44726 0.723630 0.690188i \(-0.242472\pi\)
0.723630 + 0.690188i \(0.242472\pi\)
\(684\) −2.05753e6 6.33241e6i −0.168153 0.517522i
\(685\) 7.09922e6 + 5.15788e6i 0.578075 + 0.419996i
\(686\) 1.40809e7 1.02304e7i 1.14241 0.830008i
\(687\) −1.07779e6 + 3.31708e6i −0.0871245 + 0.268142i
\(688\) 1.74287e6 5.36399e6i 0.140376 0.432033i
\(689\) 422421. 306907.i 0.0338998 0.0246297i
\(690\) −3.81197e6 2.76956e6i −0.304808 0.221456i
\(691\) 7.02007e6 + 2.16055e7i 0.559302 + 1.72135i 0.684304 + 0.729197i \(0.260106\pi\)
−0.125002 + 0.992157i \(0.539894\pi\)
\(692\) −1.12795e6 −0.0895413
\(693\) −2.03975e6 + 1.16474e6i −0.161341 + 0.0921286i
\(694\) −1.24904e7 −0.984417
\(695\) −973034. 2.99469e6i −0.0764128 0.235174i
\(696\) 177484. + 128950.i 0.0138879 + 0.0100902i
\(697\) −1.11967e6 + 813489.i −0.0872988 + 0.0634263i
\(698\) 7.23401e6 2.22640e7i 0.562006 1.72968i
\(699\) 1.78003e6 5.47838e6i 0.137796 0.424091i
\(700\) 5.62970e6 4.09022e6i 0.434250 0.315501i
\(701\) 5.69846e6 + 4.14017e6i 0.437988 + 0.318217i 0.784835 0.619705i \(-0.212748\pi\)
−0.346847 + 0.937922i \(0.612748\pi\)
\(702\) −25571.7 78701.6i −0.00195847 0.00602755i
\(703\) 1.42233e7 1.08545
\(704\) −1.85699e7 2.04122e6i −1.41214 0.155224i
\(705\) 3.26774e6 0.247614
\(706\) −875903. 2.69575e6i −0.0661369 0.203549i
\(707\) 6.57676e6 + 4.77830e6i 0.494839 + 0.359521i
\(708\) −1.44707e7 + 1.05136e7i −1.08494 + 0.788257i
\(709\) 1.83292e6 5.64115e6i 0.136939 0.421456i −0.858947 0.512064i \(-0.828881\pi\)
0.995887 + 0.0906081i \(0.0288811\pi\)
\(710\) −3.46756e6 + 1.06721e7i −0.258154 + 0.794515i
\(711\) −6.61310e6 + 4.80470e6i −0.490604 + 0.356445i
\(712\) −1.68939e6 1.22741e6i −0.124890 0.0907382i
\(713\) −4.14524e6 1.27577e7i −0.305370 0.939832i
\(714\) −2.99279e6 −0.219701
\(715\) −59051.9 + 130951.i −0.00431985 + 0.00957952i
\(716\) −7.68075e6 −0.559913
\(717\) −528494. 1.62654e6i −0.0383921 0.118159i
\(718\) 2.52620e7 + 1.83539e7i 1.82876 + 1.32867i
\(719\) −9.43232e6 + 6.85298e6i −0.680450 + 0.494376i −0.873507 0.486812i \(-0.838160\pi\)
0.193057 + 0.981188i \(0.438160\pi\)
\(720\) 472362. 1.45378e6i 0.0339581 0.104512i
\(721\) 3.61750e6 1.11335e7i 0.259162 0.797617i
\(722\) −1.20339e7 + 8.74317e6i −0.859142 + 0.624203i
\(723\) −9.89033e6 7.18574e6i −0.703663 0.511241i
\(724\) 5.42373e6 + 1.66925e7i 0.384549 + 1.18352i
\(725\) −868605. −0.0613730
\(726\) 1.12805e7 4.89423e6i 0.794307 0.344622i
\(727\) −1.37588e7 −0.965480 −0.482740 0.875764i \(-0.660358\pi\)
−0.482740 + 0.875764i \(0.660358\pi\)
\(728\) 20201.6 + 62174.2i 0.00141273 + 0.00434793i
\(729\) −429945. 312373.i −0.0299636 0.0217698i
\(730\) 2.20947e6 1.60527e6i 0.153455 0.111492i
\(731\) −1.34021e6 + 4.12474e6i −0.0927639 + 0.285498i
\(732\) −1.82529e6 + 5.61766e6i −0.125908 + 0.387505i
\(733\) 1.25336e6 910618.i 0.0861619 0.0626003i −0.543870 0.839169i \(-0.683042\pi\)
0.630032 + 0.776569i \(0.283042\pi\)
\(734\) −3.18622e7 2.31493e7i −2.18291 1.58598i
\(735\) −861974. 2.65288e6i −0.0588539 0.181134i
\(736\) −1.87969e7 −1.27906
\(737\) −9.79589e6 + 2.17229e7i −0.664317 + 1.47316i
\(738\) 1.75318e6 0.118491
\(739\) 5.26499e6 + 1.62040e7i 0.354639 + 1.09147i 0.956218 + 0.292654i \(0.0945384\pi\)
−0.601579 + 0.798813i \(0.705462\pi\)
\(740\) −5.98272e6 4.34670e6i −0.401624 0.291797i
\(741\) −200363. + 145572.i −0.0134051 + 0.00973941i
\(742\) −7.39205e6 + 2.27504e7i −0.492896 + 1.51698i
\(743\) −8.35695e6 + 2.57200e7i −0.555361 + 1.70923i 0.139626 + 0.990204i \(0.455410\pi\)
−0.694987 + 0.719022i \(0.744590\pi\)
\(744\) −2.86274e6 + 2.07990e6i −0.189605 + 0.137756i
\(745\) 2.14767e6 + 1.56037e6i 0.141768 + 0.103000i
\(746\) 9.53212e6 + 2.93368e7i 0.627108 + 1.93004i
\(747\) −8.63227e6 −0.566009
\(748\) 8.64917e6 + 950727.i 0.565224 + 0.0621301i
\(749\) −1.19563e7 −0.778742
\(750\) −3.49315e6 1.07508e7i −0.226759 0.697892i
\(751\) −1.03554e7 7.52367e6i −0.669991 0.486777i 0.200031 0.979789i \(-0.435896\pi\)
−0.870022 + 0.493013i \(0.835896\pi\)
\(752\) 7.74589e6 5.62772e6i 0.499490 0.362901i
\(753\) 2.10588e6 6.48124e6i 0.135346 0.416554i
\(754\) 12646.0 38920.5i 0.000810076 0.00249316i
\(755\) −8.50499e6 + 6.17923e6i −0.543008 + 0.394518i
\(756\) 1.70338e6 + 1.23758e6i 0.108395 + 0.0787533i
\(757\) 733288. + 2.25683e6i 0.0465088 + 0.143139i 0.971614 0.236571i \(-0.0760236\pi\)
−0.925105 + 0.379710i \(0.876024\pi\)
\(758\) 3.83083e7 2.42169
\(759\) 7.23545e6 4.13158e6i 0.455891 0.260322i
\(760\) 3.71989e6 0.233613
\(761\) 5.67225e6 + 1.74574e7i 0.355054 + 1.09274i 0.955978 + 0.293437i \(0.0947992\pi\)
−0.600925 + 0.799306i \(0.705201\pi\)
\(762\) 1.28243e7 + 9.31738e6i 0.800102 + 0.581308i
\(763\) 2.02585e6 1.47186e6i 0.125978 0.0915285i
\(764\) −989053. + 3.04399e6i −0.0613036 + 0.188673i
\(765\) −363231. + 1.11791e6i −0.0224403 + 0.0690643i
\(766\) 6.93616e6 5.03942e6i 0.427117 0.310319i
\(767\) 538253. + 391064.i 0.0330368 + 0.0240026i
\(768\) −977147. 3.00735e6i −0.0597802 0.183984i
\(769\) 2.77801e7 1.69402 0.847010 0.531577i \(-0.178400\pi\)
0.847010 + 0.531577i \(0.178400\pi\)
\(770\) −1.33762e6 6.44375e6i −0.0813030 0.391662i
\(771\) −1.34122e6 −0.0812575
\(772\) 3.26428e6 + 1.00464e7i 0.197126 + 0.606693i
\(773\) −2.46630e7 1.79187e7i −1.48456 1.07859i −0.976053 0.217534i \(-0.930199\pi\)
−0.508504 0.861060i \(-0.669801\pi\)
\(774\) 4.44470e6 3.22927e6i 0.266680 0.193754i
\(775\) 4.32939e6 1.33245e7i 0.258924 0.796887i
\(776\) 242.618 746.701i 1.44633e−5 4.45136e-5i
\(777\) −3.63873e6 + 2.64369e6i −0.216221 + 0.157093i
\(778\) 5.49992e6 + 3.99592e6i 0.325767 + 0.236684i
\(779\) −1.62141e6 4.99018e6i −0.0957301 0.294627i
\(780\) 128766. 0.00757817
\(781\) −1.46825e7 1.33473e7i −0.861336 0.783009i
\(782\) 1.06161e7 0.620796
\(783\) −81214.2 249952.i −0.00473399 0.0145697i
\(784\) −6.61203e6 4.80392e6i −0.384189 0.279129i
\(785\) 8.49768e6 6.17392e6i 0.492182 0.357591i
\(786\) 982849. 3.02490e6i 0.0567454 0.174644i
\(787\) 9.32039e6 2.86852e7i 0.536411 1.65090i −0.204171 0.978935i \(-0.565450\pi\)
0.740581 0.671967i \(-0.234550\pi\)
\(788\) 9.21566e6 6.69557e6i 0.528702 0.384124i
\(789\) −1.47517e7 1.07178e7i −0.843627 0.612931i
\(790\) −7.07734e6 2.17818e7i −0.403462 1.24173i
\(791\) −3.02752e6 −0.172047
\(792\) −1.62632e6 1.47843e6i −0.0921285 0.0837507i
\(793\) 219708. 0.0124069
\(794\) 4.87887e6 + 1.50156e7i 0.274643 + 0.845263i
\(795\) 7.60088e6 + 5.52236e6i 0.426526 + 0.309890i
\(796\) 1.93247e7 1.40402e7i 1.08101 0.785398i
\(797\) 106238. 326967.i 0.00592426 0.0182330i −0.948051 0.318119i \(-0.896949\pi\)
0.953975 + 0.299886i \(0.0969487\pi\)
\(798\) 3.50620e6 1.07910e7i 0.194908 0.599864i
\(799\) −5.95634e6 + 4.32754e6i −0.330075 + 0.239814i
\(800\) −1.58826e7 1.15394e7i −0.877398 0.637467i
\(801\) 773038. + 2.37917e6i 0.0425716 + 0.131022i
\(802\) −3.11991e7 −1.71280
\(803\) 981568. + 4.72852e6i 0.0537195 + 0.258783i
\(804\) 2.13605e7 1.16539
\(805\) −1.37800e6 4.24103e6i −0.0749477 0.230665i
\(806\) 534013. + 387983.i 0.0289544 + 0.0210366i
\(807\) 3.07191e6 2.23187e6i 0.166045 0.120638i
\(808\) −2.35062e6 + 7.23446e6i −0.126664 + 0.389832i
\(809\) 202202. 622315.i 0.0108621 0.0334302i −0.945479 0.325684i \(-0.894405\pi\)
0.956341 + 0.292254i \(0.0944053\pi\)
\(810\) 1.20463e6 875214.i 0.0645120 0.0468707i
\(811\) 3.60458e6 + 2.61888e6i 0.192443 + 0.139818i 0.679835 0.733365i \(-0.262052\pi\)
−0.487391 + 0.873184i \(0.662052\pi\)
\(812\) 321760. + 990275.i 0.0171254 + 0.0527067i
\(813\) −3.14706e6 −0.166986
\(814\) 2.04471e7 1.16757e7i 1.08161 0.617621i
\(815\) −1.05252e7 −0.555056
\(816\) 1.06426e6 + 3.27546e6i 0.0559530 + 0.172206i
\(817\) −1.33022e7 9.66465e6i −0.697220 0.506560i
\(818\) 3.48815e7 2.53429e7i 1.82268 1.32426i
\(819\) 24201.0 74483.1i 0.00126074 0.00388014i
\(820\) −843011. + 2.59452e6i −0.0437823 + 0.134748i
\(821\) 9.32589e6 6.77565e6i 0.482872 0.350827i −0.319564 0.947565i \(-0.603537\pi\)
0.802437 + 0.596737i \(0.203537\pi\)
\(822\) 2.02619e7 + 1.47211e7i 1.04592 + 0.759908i
\(823\) 805605. + 2.47940e6i 0.0414593 + 0.127599i 0.969644 0.244522i \(-0.0786309\pi\)
−0.928185 + 0.372120i \(0.878631\pi\)
\(824\) 1.09540e7 0.562023
\(825\) 8.65001e6 + 950819.i 0.442468 + 0.0486366i
\(826\) −3.04806e7 −1.55444
\(827\) 1.04299e7 + 3.20998e7i 0.530292 + 1.63207i 0.753608 + 0.657324i \(0.228312\pi\)
−0.223316 + 0.974746i \(0.571688\pi\)
\(828\) −6.04228e6 4.38998e6i −0.306285 0.222529i
\(829\) −1.09083e6 + 792534.i −0.0551278 + 0.0400527i −0.615008 0.788521i \(-0.710847\pi\)
0.559880 + 0.828574i \(0.310847\pi\)
\(830\) 7.47391e6 2.30023e7i 0.376576 1.15898i
\(831\) −1.65018e6 + 5.07872e6i −0.0828949 + 0.255124i
\(832\) 503927. 366124.i 0.0252382 0.0183367i
\(833\) 5.08444e6 + 3.69406e6i 0.253881 + 0.184456i
\(834\) −2.77714e6 8.54714e6i −0.138255 0.425506i
\(835\) −1.19768e7 −0.594460
\(836\) −1.35609e7 + 3.00721e7i −0.671077 + 1.48815i
\(837\) 4.23908e6 0.209150
\(838\) −303234. 933259.i −0.0149165 0.0459084i
\(839\) −1.68279e7 1.22262e7i −0.825324 0.599633i 0.0929087 0.995675i \(-0.470384\pi\)
−0.918232 + 0.396042i \(0.870384\pi\)
\(840\) −951656. + 691419.i −0.0465352 + 0.0338098i
\(841\) −6.29813e6 + 1.93837e7i −0.307059 + 0.945030i
\(842\) −3.55315e6 + 1.09355e7i −0.172716 + 0.531566i
\(843\) −1.28876e7 + 9.36340e6i −0.624602 + 0.453800i
\(844\) −1.98130e7 1.43950e7i −0.957403 0.695594i
\(845\) 3.06789e6 + 9.44198e6i 0.147808 + 0.454906i
\(846\) 9.32646e6 0.448013
\(847\) 1.13595e7 + 2.52785e6i 0.544066 + 0.121072i
\(848\) 2.75278e7 1.31456
\(849\) 1.73770e6 + 5.34810e6i 0.0827382 + 0.254642i
\(850\) 8.97016e6 + 6.51720e6i 0.425846 + 0.309395i
\(851\) 1.29074e7 9.37776e6i 0.610962 0.443890i
\(852\) −5.49637e6 + 1.69161e7i −0.259404 + 0.798364i
\(853\) −1.01572e7 + 3.12606e7i −0.477969 + 1.47104i 0.363941 + 0.931422i \(0.381431\pi\)
−0.841911 + 0.539617i \(0.818569\pi\)
\(854\) −8.14325e6 + 5.91642e6i −0.382079 + 0.277597i
\(855\) −3.60525e6 2.61937e6i −0.168663 0.122541i
\(856\) −3.45721e6 1.06402e7i −0.161266 0.496324i
\(857\) −1.01225e7 −0.470801 −0.235401 0.971898i \(-0.575640\pi\)
−0.235401 + 0.971898i \(0.575640\pi\)
\(858\) −168540. + 373747.i −0.00781600 + 0.0173324i
\(859\) 2.20709e7 1.02056 0.510279 0.860009i \(-0.329542\pi\)
0.510279 + 0.860009i \(0.329542\pi\)
\(860\) 2.64175e6 + 8.13046e6i 0.121799 + 0.374860i
\(861\) 1.34233e6 + 975260.i 0.0617094 + 0.0448345i
\(862\) −1.04242e7 + 7.57361e6i −0.477831 + 0.347164i
\(863\) 5.22372e6 1.60769e7i 0.238755 0.734812i −0.757846 0.652433i \(-0.773748\pi\)
0.996601 0.0823790i \(-0.0262518\pi\)
\(864\) 1.83558e6 5.64933e6i 0.0836544 0.257462i
\(865\) −610746. + 443733.i −0.0277537 + 0.0201642i
\(866\) 1.38638e6 + 1.00726e6i 0.0628184 + 0.0456403i
\(867\) 3.13046e6 + 9.63455e6i 0.141436 + 0.435295i
\(868\) −1.67947e7 −0.756610
\(869\) 4.02565e7 + 4.42504e6i 1.80837 + 0.198778i
\(870\) 736360. 0.0329831
\(871\) −245522. 755638.i −0.0109659 0.0337496i
\(872\) 1.89562e6 + 1.37725e6i 0.0844230 + 0.0613369i
\(873\) −760.931 + 552.848i −3.37917e−5 + 2.45511e-5i
\(874\) −1.24373e7 + 3.82780e7i −0.550740 + 1.69500i
\(875\) 3.30591e6 1.01745e7i 0.145972 0.449257i
\(876\) 3.50219e6 2.54449e6i 0.154198 0.112032i
\(877\) 1.04900e7 + 7.62143e6i 0.460549 + 0.334609i 0.793747 0.608248i \(-0.208128\pi\)
−0.333197 + 0.942857i \(0.608128\pi\)
\(878\) −1.54987e7 4.77000e7i −0.678513 2.08825i
\(879\) −1.00444e7 −0.438481
\(880\) −6.57668e6 + 3.75541e6i −0.286286 + 0.163475i
\(881\) −1.39444e7 −0.605285 −0.302642 0.953104i \(-0.597869\pi\)
−0.302642 + 0.953104i \(0.597869\pi\)
\(882\) −2.46016e6 7.57158e6i −0.106486 0.327729i
\(883\) −9.65393e6 7.01399e6i −0.416680 0.302736i 0.359621 0.933099i \(-0.382906\pi\)
−0.776301 + 0.630363i \(0.782906\pi\)
\(884\) −234710. + 170527.i −0.0101019 + 0.00733944i
\(885\) −3.69938e6 + 1.13855e7i −0.158771 + 0.488647i
\(886\) −6.78970e6 + 2.08966e7i −0.290580 + 0.894315i
\(887\) −3.16601e6 + 2.30024e6i −0.135115 + 0.0981666i −0.653290 0.757108i \(-0.726612\pi\)
0.518175 + 0.855275i \(0.326612\pi\)
\(888\) −3.40483e6 2.47375e6i −0.144898 0.105275i
\(889\) 4.63587e6 + 1.42677e7i 0.196733 + 0.605481i
\(890\) −7.00905e6 −0.296609
\(891\) 535162. + 2.57805e6i 0.0225835 + 0.108792i
\(892\) −2.17321e6 −0.0914514
\(893\) −8.62544e6 2.65464e7i −0.361954 1.11398i
\(894\) 6.12966e6 + 4.45346e6i 0.256503 + 0.186361i
\(895\) −4.15887e6 + 3.02160e6i −0.173547 + 0.126090i
\(896\) −2.99612e6 + 9.22110e6i −0.124678 + 0.383719i
\(897\) −85846.4 + 264208.i −0.00356239 + 0.0109639i
\(898\) −2.23483e6 + 1.62370e6i −0.0924813 + 0.0671916i
\(899\) 1.69599e6 + 1.23221e6i 0.0699882 + 0.0508494i
\(900\) −2.41047e6 7.41868e6i −0.0991965 0.305295i
\(901\) −2.11680e7 −0.868696
\(902\) −6.42727e6 5.84280e6i −0.263033 0.239114i
\(903\) 5.19947e6 0.212197
\(904\) −875418. 2.69426e6i −0.0356282 0.109652i
\(905\) 9.50359e6 + 6.90476e6i 0.385715 + 0.280238i
\(906\) −2.42741e7 + 1.76361e7i −0.982476 + 0.713811i
\(907\) 3.79702e6 1.16860e7i 0.153258 0.471681i −0.844722 0.535206i \(-0.820234\pi\)
0.997980 + 0.0635246i \(0.0202341\pi\)
\(908\) 5.70910e6 1.75708e7i 0.229802 0.707257i
\(909\) 7.37233e6 5.35631e6i 0.295934 0.215009i
\(910\) 177521. + 128976.i 0.00710634 + 0.00516306i
\(911\) −1.16375e7 3.58167e7i −0.464585 1.42985i −0.859503 0.511130i \(-0.829227\pi\)
0.394918 0.918716i \(-0.370773\pi\)
\(912\) −1.30570e7 −0.519824
\(913\) 3.16464e7 + 2.87686e7i 1.25646 + 1.14220i
\(914\) −6.23187e7 −2.46747
\(915\) 1.22165e6 + 3.75985e6i 0.0482385 + 0.148463i
\(916\) −1.25314e7 9.10460e6i −0.493470 0.358527i
\(917\) 2.43521e6 1.76928e6i 0.0956341 0.0694822i
\(918\) −1.03670e6 + 3.19063e6i −0.0406018 + 0.124959i
\(919\) 6.88121e6 2.11782e7i 0.268767 0.827180i −0.722035 0.691857i \(-0.756793\pi\)
0.990802 0.135323i \(-0.0432071\pi\)
\(920\) 3.37574e6 2.45262e6i 0.131492 0.0955345i
\(921\) 1.48534e7 + 1.07917e7i 0.577003 + 0.419217i
\(922\) −2.09550e7 6.44928e7i −0.811821 2.49853i
\(923\) 661592. 0.0255615
\(924\) −2.12024e6 1.02139e7i −0.0816969 0.393559i
\(925\) 1.66632e7 0.640329
\(926\) 7.58105e6 + 2.33321e7i 0.290537 + 0.894182i
\(927\) −1.06164e7 7.71325e6i −0.405768 0.294807i
\(928\) 2.37653e6 1.72665e6i 0.0905885 0.0658164i
\(929\) −3.80015e6 + 1.16957e7i −0.144465 + 0.444617i −0.996942 0.0781479i \(-0.975099\pi\)
0.852477 + 0.522765i \(0.175099\pi\)
\(930\) −3.67024e6 + 1.12958e7i −0.139151 + 0.428264i
\(931\) −1.92761e7 + 1.40049e7i −0.728863 + 0.529550i
\(932\) 2.06964e7 + 1.50368e7i 0.780470 + 0.567044i
\(933\) −1.97141e6 6.06736e6i −0.0741433 0.228190i
\(934\) −2.76119e7 −1.03569
\(935\) 5.05726e6 2.88779e6i 0.189185 0.108028i
\(936\) 73281.9 0.00273405
\(937\) −1.01721e7 3.13065e7i −0.378497 1.16489i −0.941089 0.338158i \(-0.890196\pi\)
0.562593 0.826734i \(-0.309804\pi\)
\(938\) 2.94482e7 + 2.13954e7i 1.09283 + 0.793987i
\(939\) 2.26942e7 1.64883e7i 0.839944 0.610255i
\(940\) −4.48459e6 + 1.38022e7i −0.165540 + 0.509480i
\(941\) 3.74402e6 1.15229e7i 0.137836 0.424217i −0.858184 0.513342i \(-0.828407\pi\)
0.996020 + 0.0891255i \(0.0284072\pi\)
\(942\) 2.42532e7 1.76210e7i 0.890516 0.646998i
\(943\) −4.76154e6 3.45946e6i −0.174369 0.126686i
\(944\) 1.08391e7 + 3.33594e7i 0.395881 + 1.21840i
\(945\) 1.40919e6 0.0513322
\(946\) −2.70566e7 2.97410e6i −0.982983 0.108051i
\(947\) 1.71819e6 0.0622582 0.0311291 0.999515i \(-0.490090\pi\)
0.0311291 + 0.999515i \(0.490090\pi\)
\(948\) −1.12182e7 3.45260e7i −0.405416 1.24774i
\(949\) −130268. 94644.9i −0.00469538 0.00341139i
\(950\) −3.40077e7 + 2.47080e7i −1.22255 + 0.888237i
\(951\) −5.62018e6 + 1.72971e7i −0.201511 + 0.620187i
\(952\) 818990. 2.52059e6i 0.0292878 0.0901385i
\(953\) 1.91302e7 1.38989e7i 0.682317 0.495733i −0.191808 0.981432i \(-0.561435\pi\)
0.874126 + 0.485700i \(0.161435\pi\)
\(954\) 2.16936e7 + 1.57614e7i 0.771723 + 0.560690i
\(955\) 661964. + 2.03732e6i 0.0234869 + 0.0722853i
\(956\) 7.59539e6 0.268785
\(957\) −535273. + 1.18700e6i −0.0188927 + 0.0418958i
\(958\) 6.98904e7 2.46039
\(959\) 7.32450e6 + 2.25425e7i 0.257177 + 0.791508i
\(960\) 9.06746e6 + 6.58789e6i 0.317547 + 0.230711i
\(961\) −4.19412e6 + 3.04720e6i −0.146498 + 0.106437i
\(962\) −242599. + 746643.i −0.00845184 + 0.0260121i
\(963\) −4.14165e6 + 1.27467e7i −0.143915 + 0.442926i
\(964\) 4.39241e7 3.19127e7i 1.52234 1.10604i
\(965\) 5.71976e6 + 4.15565e6i 0.197724 + 0.143655i
\(966\) −3.93294e6 1.21043e7i −0.135604 0.417348i
\(967\) 4.53772e7 1.56053 0.780264 0.625450i \(-0.215085\pi\)
0.780264 + 0.625450i \(0.215085\pi\)
\(968\) 1.03506e6 + 1.08400e7i 0.0355039 + 0.371828i
\(969\) 1.00404e7 0.343512
\(970\) −814.348 2506.31i −2.77895e−5 8.55273e-5i
\(971\) −2.58317e7 1.87678e7i −0.879235 0.638801i 0.0538142 0.998551i \(-0.482862\pi\)
−0.933049 + 0.359750i \(0.882862\pi\)
\(972\) 1.90944e6 1.38729e6i 0.0648245 0.0470978i
\(973\) 2.62828e6 8.08900e6i 0.0889998 0.273913i
\(974\) −1.12491e7 + 3.46211e7i −0.379944 + 1.16935i
\(975\) −234733. + 170544.i −0.00790793 + 0.00574545i
\(976\) 9.37102e6 + 6.80845e6i 0.314893 + 0.228783i
\(977\) −1.77063e6 5.44945e6i −0.0593462 0.182649i 0.916989 0.398913i \(-0.130613\pi\)
−0.976335 + 0.216265i \(0.930613\pi\)
\(978\) −3.00400e7 −1.00428
\(979\) 5.09500e6 1.12984e7i 0.169898 0.376757i
\(980\) 1.23881e7 0.412039
\(981\) −867409. 2.66961e6i −0.0287774 0.0885677i
\(982\) 5.74621e7 + 4.17486e7i 1.90153 + 1.38154i
\(983\) −3.11301e7 + 2.26174e7i −1.02754 + 0.746549i −0.967814 0.251666i \(-0.919022\pi\)
−0.0597223 + 0.998215i \(0.519022\pi\)
\(984\) −479766. + 1.47657e6i −0.0157958 + 0.0486145i
\(985\) 2.35595e6 7.25086e6i 0.0773705 0.238122i
\(986\) −1.34221e6 + 975175.i −0.0439673 + 0.0319441i
\(987\) 7.14083e6 + 5.18812e6i 0.233322 + 0.169518i
\(988\) −339887. 1.04606e6i −0.0110775 0.0340931i
\(989\) −1.84437e7 −0.599594
\(990\) −7.33304e6 806056.i −0.237791 0.0261383i
\(991\) −1.73591e7 −0.561492 −0.280746 0.959782i \(-0.590582\pi\)
−0.280746 + 0.959782i \(0.590582\pi\)
\(992\) 1.46416e7 + 4.50624e7i 0.472401 + 1.45390i
\(993\) −1.61136e7 1.17072e7i −0.518586 0.376775i
\(994\) −2.45212e7 + 1.78157e7i −0.787184 + 0.571922i
\(995\) 4.94027e6 1.52046e7i 0.158195 0.486875i
\(996\) 1.18468e7 3.64606e7i 0.378400 1.16460i
\(997\) −9.74348e6 + 7.07905e6i −0.310439 + 0.225547i −0.732085 0.681214i \(-0.761453\pi\)
0.421646 + 0.906761i \(0.361453\pi\)
\(998\) −4.33892e7 3.15241e7i −1.37897 1.00188i
\(999\) 1.55800e6 + 4.79502e6i 0.0493916 + 0.152012i
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 33.6.e.b.16.5 20
3.2 odd 2 99.6.f.b.82.1 20
11.3 even 5 363.6.a.r.1.9 10
11.8 odd 10 363.6.a.t.1.2 10
11.9 even 5 inner 33.6.e.b.31.5 yes 20
33.8 even 10 1089.6.a.bi.1.9 10
33.14 odd 10 1089.6.a.bk.1.2 10
33.20 odd 10 99.6.f.b.64.1 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.6.e.b.16.5 20 1.1 even 1 trivial
33.6.e.b.31.5 yes 20 11.9 even 5 inner
99.6.f.b.64.1 20 33.20 odd 10
99.6.f.b.82.1 20 3.2 odd 2
363.6.a.r.1.9 10 11.3 even 5
363.6.a.t.1.2 10 11.8 odd 10
1089.6.a.bi.1.9 10 33.8 even 10
1089.6.a.bk.1.2 10 33.14 odd 10