Properties

Label 33.5.g.a.19.1
Level $33$
Weight $5$
Character 33.19
Analytic conductor $3.411$
Analytic rank $0$
Dimension $32$
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] = [33,5,Mod(7,33)]
 
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, 7]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("33.7");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 33.g (of order \(10\), 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: \(3.41120878177\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 19.1
Character \(\chi\) \(=\) 33.19
Dual form 33.5.g.a.7.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.37135 - 6.01665i) q^{2} +(-1.60570 - 4.94183i) q^{3} +(-12.1471 + 37.3849i) q^{4} +(-24.8968 - 18.0886i) q^{5} +(-22.7142 + 31.2634i) q^{6} +(40.6127 + 13.1959i) q^{7} +(164.863 - 53.5673i) q^{8} +(-21.8435 + 15.8702i) q^{9} +O(q^{10})\) \(q+(-4.37135 - 6.01665i) q^{2} +(-1.60570 - 4.94183i) q^{3} +(-12.1471 + 37.3849i) q^{4} +(-24.8968 - 18.0886i) q^{5} +(-22.7142 + 31.2634i) q^{6} +(40.6127 + 13.1959i) q^{7} +(164.863 - 53.5673i) q^{8} +(-21.8435 + 15.8702i) q^{9} +228.867i q^{10} +(-55.8909 + 107.318i) q^{11} +204.255 q^{12} +(-92.9028 - 127.870i) q^{13} +(-98.1376 - 302.036i) q^{14} +(-49.4140 + 152.081i) q^{15} +(-534.147 - 388.080i) q^{16} +(-52.6147 + 72.4180i) q^{17} +(190.971 + 62.0502i) q^{18} +(-624.099 + 202.782i) q^{19} +(978.664 - 711.041i) q^{20} -221.890i q^{21} +(890.015 - 132.850i) q^{22} -292.602 q^{23} +(-529.441 - 728.713i) q^{24} +(99.5185 + 306.287i) q^{25} +(-363.237 + 1117.93i) q^{26} +(113.502 + 82.4640i) q^{27} +(-986.653 + 1358.01i) q^{28} +(-646.603 - 210.094i) q^{29} +(1131.02 - 367.492i) q^{30} +(1421.82 - 1033.01i) q^{31} +2136.65i q^{32} +(620.093 + 103.883i) q^{33} +665.711 q^{34} +(-772.433 - 1063.16i) q^{35} +(-327.971 - 1009.39i) q^{36} +(56.5273 - 173.973i) q^{37} +(3948.23 + 2868.55i) q^{38} +(-482.737 + 664.431i) q^{39} +(-5073.52 - 1648.49i) q^{40} +(-553.714 + 179.912i) q^{41} +(-1335.03 + 969.960i) q^{42} +298.729i q^{43} +(-3333.17 - 3393.08i) q^{44} +830.902 q^{45} +(1279.07 + 1760.48i) q^{46} +(-662.592 - 2039.25i) q^{47} +(-1060.15 + 3262.80i) q^{48} +(-467.187 - 339.431i) q^{49} +(1407.79 - 1937.65i) q^{50} +(442.361 + 143.732i) q^{51} +(5908.90 - 1919.92i) q^{52} +(-1783.60 + 1295.86i) q^{53} -1043.38i q^{54} +(3332.74 - 1660.90i) q^{55} +7402.41 q^{56} +(2004.23 + 2758.59i) q^{57} +(1562.47 + 4808.78i) q^{58} +(1495.28 - 4602.01i) q^{59} +(-5085.29 - 3694.68i) q^{60} +(-1179.00 + 1622.76i) q^{61} +(-12430.5 - 4038.93i) q^{62} +(-1096.54 + 356.289i) q^{63} +(4309.14 - 3130.77i) q^{64} +4864.03i q^{65} +(-2085.62 - 4184.99i) q^{66} -4987.81 q^{67} +(-2068.22 - 2846.66i) q^{68} +(469.831 + 1445.99i) q^{69} +(-3020.10 + 9294.92i) q^{70} +(4378.91 + 3181.46i) q^{71} +(-2751.06 + 3786.51i) q^{72} +(1926.53 + 625.969i) q^{73} +(-1293.84 + 420.393i) q^{74} +(1353.82 - 983.608i) q^{75} -25795.1i q^{76} +(-3686.04 + 3620.96i) q^{77} +6107.86 q^{78} +(-1821.76 - 2507.43i) q^{79} +(6278.72 + 19323.9i) q^{80} +(225.273 - 693.320i) q^{81} +(3502.95 + 2545.04i) q^{82} +(-3443.51 + 4739.58i) q^{83} +(8295.34 + 2695.32i) q^{84} +(2619.88 - 851.250i) q^{85} +(1797.35 - 1305.85i) q^{86} +3532.75i q^{87} +(-3465.59 + 20686.7i) q^{88} -1483.07 q^{89} +(-3632.17 - 4999.25i) q^{90} +(-2085.68 - 6419.08i) q^{91} +(3554.26 - 10938.9i) q^{92} +(-7387.99 - 5367.69i) q^{93} +(-9373.02 + 12900.9i) q^{94} +(19206.1 + 6240.45i) q^{95} +(10559.0 - 3430.82i) q^{96} +(5297.09 - 3848.56i) q^{97} +4294.67i q^{98} +(-482.313 - 3231.20i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 76 q^{4} + 36 q^{5} + 150 q^{7} + 480 q^{8} - 216 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 76 q^{4} + 36 q^{5} + 150 q^{7} + 480 q^{8} - 216 q^{9} - 246 q^{11} + 360 q^{12} - 510 q^{13} - 1290 q^{14} - 468 q^{15} - 232 q^{16} + 2490 q^{17} + 810 q^{18} - 582 q^{20} - 510 q^{22} - 2196 q^{23} - 3510 q^{24} - 370 q^{25} - 5226 q^{26} + 4310 q^{28} + 960 q^{29} + 3780 q^{30} + 1658 q^{31} - 1008 q^{33} - 2320 q^{34} + 1920 q^{35} + 2052 q^{36} + 1374 q^{37} + 12054 q^{38} + 11070 q^{40} + 9360 q^{41} - 2844 q^{42} - 4350 q^{44} + 972 q^{45} - 12950 q^{46} - 3450 q^{47} + 4464 q^{48} - 11838 q^{49} - 11550 q^{50} + 5580 q^{51} - 19250 q^{52} - 2790 q^{53} + 12356 q^{55} - 5604 q^{56} - 6300 q^{57} + 9486 q^{58} + 2682 q^{59} - 19548 q^{60} - 17190 q^{61} - 39360 q^{62} - 4050 q^{63} + 16248 q^{64} + 2520 q^{66} + 2796 q^{67} + 68160 q^{68} + 4014 q^{69} + 18188 q^{70} + 132 q^{71} - 12150 q^{72} - 21790 q^{73} - 2130 q^{74} + 12168 q^{75} + 4542 q^{77} + 53640 q^{78} + 12270 q^{79} + 32346 q^{80} - 5832 q^{81} + 29442 q^{82} + 35430 q^{83} + 28620 q^{84} - 11990 q^{85} - 49416 q^{86} + 1176 q^{88} - 38748 q^{89} - 10260 q^{90} - 51858 q^{91} - 25590 q^{92} - 32616 q^{93} - 34510 q^{94} - 71670 q^{95} - 49950 q^{96} + 30306 q^{97} - 13932 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(13\) \(23\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.37135 6.01665i −1.09284 1.50416i −0.844550 0.535476i \(-0.820132\pi\)
−0.248288 0.968686i \(-0.579868\pi\)
\(3\) −1.60570 4.94183i −0.178411 0.549093i
\(4\) −12.1471 + 37.3849i −0.759193 + 2.33656i
\(5\) −24.8968 18.0886i −0.995873 0.723544i −0.0346733 0.999399i \(-0.511039\pi\)
−0.961199 + 0.275855i \(0.911039\pi\)
\(6\) −22.7142 + 31.2634i −0.630950 + 0.868429i
\(7\) 40.6127 + 13.1959i 0.828831 + 0.269304i 0.692553 0.721367i \(-0.256486\pi\)
0.136278 + 0.990671i \(0.456486\pi\)
\(8\) 164.863 53.5673i 2.57599 0.836989i
\(9\) −21.8435 + 15.8702i −0.269672 + 0.195928i
\(10\) 228.867i 2.28867i
\(11\) −55.8909 + 107.318i −0.461908 + 0.886928i
\(12\) 204.255 1.41843
\(13\) −92.9028 127.870i −0.549721 0.756626i 0.440253 0.897874i \(-0.354889\pi\)
−0.989974 + 0.141248i \(0.954889\pi\)
\(14\) −98.1376 302.036i −0.500702 1.54100i
\(15\) −49.4140 + 152.081i −0.219618 + 0.675915i
\(16\) −534.147 388.080i −2.08651 1.51594i
\(17\) −52.6147 + 72.4180i −0.182058 + 0.250581i −0.890285 0.455403i \(-0.849495\pi\)
0.708227 + 0.705984i \(0.249495\pi\)
\(18\) 190.971 + 62.0502i 0.589416 + 0.191513i
\(19\) −624.099 + 202.782i −1.72881 + 0.561723i −0.993276 0.115768i \(-0.963067\pi\)
−0.735531 + 0.677492i \(0.763067\pi\)
\(20\) 978.664 711.041i 2.44666 1.77760i
\(21\) 221.890i 0.503152i
\(22\) 890.015 132.850i 1.83887 0.274484i
\(23\) −292.602 −0.553123 −0.276561 0.960996i \(-0.589195\pi\)
−0.276561 + 0.960996i \(0.589195\pi\)
\(24\) −529.441 728.713i −0.919169 1.26513i
\(25\) 99.5185 + 306.287i 0.159230 + 0.490058i
\(26\) −363.237 + 1117.93i −0.537333 + 1.65374i
\(27\) 113.502 + 82.4640i 0.155695 + 0.113119i
\(28\) −986.653 + 1358.01i −1.25849 + 1.73216i
\(29\) −646.603 210.094i −0.768850 0.249815i −0.101777 0.994807i \(-0.532453\pi\)
−0.667073 + 0.744993i \(0.732453\pi\)
\(30\) 1131.02 367.492i 1.25669 0.408324i
\(31\) 1421.82 1033.01i 1.47952 1.07493i 0.501809 0.864979i \(-0.332668\pi\)
0.977711 0.209955i \(-0.0673319\pi\)
\(32\) 2136.65i 2.08657i
\(33\) 620.093 + 103.883i 0.569415 + 0.0953926i
\(34\) 665.711 0.575875
\(35\) −772.433 1063.16i −0.630557 0.867888i
\(36\) −327.971 1009.39i −0.253064 0.778852i
\(37\) 56.5273 173.973i 0.0412909 0.127080i −0.928286 0.371867i \(-0.878718\pi\)
0.969577 + 0.244786i \(0.0787178\pi\)
\(38\) 3948.23 + 2868.55i 2.73423 + 1.98653i
\(39\) −482.737 + 664.431i −0.317382 + 0.436838i
\(40\) −5073.52 1648.49i −3.17095 1.03030i
\(41\) −553.714 + 179.912i −0.329395 + 0.107027i −0.469046 0.883174i \(-0.655402\pi\)
0.139650 + 0.990201i \(0.455402\pi\)
\(42\) −1335.03 + 969.960i −0.756822 + 0.549864i
\(43\) 298.729i 0.161563i 0.996732 + 0.0807813i \(0.0257415\pi\)
−0.996732 + 0.0807813i \(0.974258\pi\)
\(44\) −3333.17 3393.08i −1.72168 1.75262i
\(45\) 830.902 0.410322
\(46\) 1279.07 + 1760.48i 0.604474 + 0.831986i
\(47\) −662.592 2039.25i −0.299951 0.923154i −0.981513 0.191394i \(-0.938699\pi\)
0.681562 0.731760i \(-0.261301\pi\)
\(48\) −1060.15 + 3262.80i −0.460134 + 1.41615i
\(49\) −467.187 339.431i −0.194580 0.141371i
\(50\) 1407.79 1937.65i 0.563115 0.775062i
\(51\) 442.361 + 143.732i 0.170073 + 0.0552602i
\(52\) 5908.90 1919.92i 2.18524 0.710029i
\(53\) −1783.60 + 1295.86i −0.634959 + 0.461325i −0.858115 0.513458i \(-0.828364\pi\)
0.223156 + 0.974783i \(0.428364\pi\)
\(54\) 1043.38i 0.357812i
\(55\) 3332.74 1660.90i 1.10173 0.549057i
\(56\) 7402.41 2.36046
\(57\) 2004.23 + 2758.59i 0.616876 + 0.849058i
\(58\) 1562.47 + 4808.78i 0.464467 + 1.42948i
\(59\) 1495.28 4602.01i 0.429556 1.32204i −0.469008 0.883194i \(-0.655389\pi\)
0.898564 0.438843i \(-0.144611\pi\)
\(60\) −5085.29 3694.68i −1.41258 1.02630i
\(61\) −1179.00 + 1622.76i −0.316851 + 0.436108i −0.937502 0.347979i \(-0.886868\pi\)
0.620652 + 0.784087i \(0.286868\pi\)
\(62\) −12430.5 4038.93i −3.23375 1.05071i
\(63\) −1096.54 + 356.289i −0.276277 + 0.0897679i
\(64\) 4309.14 3130.77i 1.05204 0.764349i
\(65\) 4864.03i 1.15125i
\(66\) −2085.62 4184.99i −0.478793 0.960742i
\(67\) −4987.81 −1.11112 −0.555559 0.831477i \(-0.687496\pi\)
−0.555559 + 0.831477i \(0.687496\pi\)
\(68\) −2068.22 2846.66i −0.447280 0.615628i
\(69\) 469.831 + 1445.99i 0.0986832 + 0.303716i
\(70\) −3020.10 + 9294.92i −0.616347 + 1.89692i
\(71\) 4378.91 + 3181.46i 0.868659 + 0.631118i 0.930227 0.366985i \(-0.119610\pi\)
−0.0615677 + 0.998103i \(0.519610\pi\)
\(72\) −2751.06 + 3786.51i −0.530682 + 0.730422i
\(73\) 1926.53 + 625.969i 0.361519 + 0.117465i 0.484144 0.874988i \(-0.339131\pi\)
−0.122625 + 0.992453i \(0.539131\pi\)
\(74\) −1293.84 + 420.393i −0.236274 + 0.0767701i
\(75\) 1353.82 983.608i 0.240679 0.174864i
\(76\) 25795.1i 4.46591i
\(77\) −3686.04 + 3620.96i −0.621697 + 0.610720i
\(78\) 6107.86 1.00392
\(79\) −1821.76 2507.43i −0.291901 0.401768i 0.637729 0.770261i \(-0.279874\pi\)
−0.929631 + 0.368493i \(0.879874\pi\)
\(80\) 6278.72 + 19323.9i 0.981051 + 3.01936i
\(81\) 225.273 693.320i 0.0343352 0.105673i
\(82\) 3502.95 + 2545.04i 0.520962 + 0.378501i
\(83\) −3443.51 + 4739.58i −0.499856 + 0.687992i −0.982168 0.188007i \(-0.939797\pi\)
0.482312 + 0.876000i \(0.339797\pi\)
\(84\) 8295.34 + 2695.32i 1.17564 + 0.381990i
\(85\) 2619.88 851.250i 0.362613 0.117820i
\(86\) 1797.35 1305.85i 0.243017 0.176562i
\(87\) 3532.75i 0.466740i
\(88\) −3465.59 + 20686.7i −0.447520 + 2.67133i
\(89\) −1483.07 −0.187233 −0.0936166 0.995608i \(-0.529843\pi\)
−0.0936166 + 0.995608i \(0.529843\pi\)
\(90\) −3632.17 4999.25i −0.448416 0.617191i
\(91\) −2085.68 6419.08i −0.251864 0.775157i
\(92\) 3554.26 10938.9i 0.419927 1.29240i
\(93\) −7387.99 5367.69i −0.854201 0.620613i
\(94\) −9373.02 + 12900.9i −1.06078 + 1.46003i
\(95\) 19206.1 + 6240.45i 2.12810 + 0.691463i
\(96\) 10559.0 3430.82i 1.14572 0.372268i
\(97\) 5297.09 3848.56i 0.562982 0.409030i −0.269567 0.962982i \(-0.586881\pi\)
0.832549 + 0.553951i \(0.186881\pi\)
\(98\) 4294.67i 0.447175i
\(99\) −482.313 3231.20i −0.0492106 0.329681i
\(100\) −12659.4 −1.26594
\(101\) −750.623 1033.14i −0.0735833 0.101279i 0.770639 0.637272i \(-0.219937\pi\)
−0.844222 + 0.535993i \(0.819937\pi\)
\(102\) −1068.93 3289.83i −0.102742 0.316209i
\(103\) 3389.37 10431.4i 0.319480 0.983260i −0.654390 0.756157i \(-0.727075\pi\)
0.973871 0.227103i \(-0.0729253\pi\)
\(104\) −22165.9 16104.5i −2.04936 1.48895i
\(105\) −4013.68 + 5524.36i −0.364053 + 0.501075i
\(106\) 15593.5 + 5066.63i 1.38781 + 0.450928i
\(107\) 12517.4 4067.16i 1.09332 0.355241i 0.293792 0.955869i \(-0.405083\pi\)
0.799529 + 0.600628i \(0.205083\pi\)
\(108\) −4461.63 + 3241.56i −0.382513 + 0.277912i
\(109\) 4675.96i 0.393566i 0.980447 + 0.196783i \(0.0630495\pi\)
−0.980447 + 0.196783i \(0.936950\pi\)
\(110\) −24561.6 12791.6i −2.02989 1.05716i
\(111\) −950.512 −0.0771457
\(112\) −16572.1 22809.5i −1.32112 1.81836i
\(113\) −1784.80 5493.06i −0.139776 0.430187i 0.856526 0.516104i \(-0.172618\pi\)
−0.996302 + 0.0859167i \(0.972618\pi\)
\(114\) 7836.26 24117.5i 0.602975 1.85577i
\(115\) 7284.85 + 5292.76i 0.550840 + 0.400208i
\(116\) 15708.7 21621.2i 1.16741 1.60680i
\(117\) 4058.64 + 1318.73i 0.296489 + 0.0963351i
\(118\) −34225.1 + 11120.4i −2.45799 + 0.798650i
\(119\) −3092.45 + 2246.79i −0.218378 + 0.158661i
\(120\) 27719.5i 1.92496i
\(121\) −8393.42 11996.2i −0.573282 0.819358i
\(122\) 14917.4 1.00224
\(123\) 1778.20 + 2447.48i 0.117536 + 0.161774i
\(124\) 21348.1 + 65702.6i 1.38840 + 4.27306i
\(125\) −2880.99 + 8866.77i −0.184383 + 0.567473i
\(126\) 6937.04 + 5040.06i 0.436952 + 0.317464i
\(127\) 7154.38 9847.15i 0.443572 0.610525i −0.527429 0.849599i \(-0.676844\pi\)
0.971001 + 0.239074i \(0.0768440\pi\)
\(128\) −5160.31 1676.69i −0.314961 0.102337i
\(129\) 1476.27 479.670i 0.0887129 0.0288246i
\(130\) 29265.2 21262.4i 1.73167 1.25813i
\(131\) 17730.8i 1.03320i −0.856226 0.516601i \(-0.827197\pi\)
0.856226 0.516601i \(-0.172803\pi\)
\(132\) −11416.0 + 21920.2i −0.655186 + 1.25805i
\(133\) −28022.3 −1.58416
\(134\) 21803.5 + 30009.9i 1.21427 + 1.67130i
\(135\) −1334.18 4106.18i −0.0732060 0.225305i
\(136\) −4795.00 + 14757.5i −0.259245 + 0.797874i
\(137\) 12286.3 + 8926.54i 0.654608 + 0.475600i 0.864838 0.502052i \(-0.167421\pi\)
−0.210230 + 0.977652i \(0.567421\pi\)
\(138\) 6646.22 9147.74i 0.348993 0.480348i
\(139\) −24706.7 8027.71i −1.27875 0.415491i −0.410611 0.911811i \(-0.634684\pi\)
−0.868140 + 0.496319i \(0.834684\pi\)
\(140\) 49129.0 15963.0i 2.50658 0.814438i
\(141\) −9013.70 + 6548.84i −0.453383 + 0.329402i
\(142\) 40253.7i 1.99631i
\(143\) 18915.2 2823.42i 0.924993 0.138071i
\(144\) 17826.5 0.859689
\(145\) 12298.0 + 16926.8i 0.584925 + 0.805080i
\(146\) −4655.32 14327.6i −0.218396 0.672153i
\(147\) −927.250 + 2853.78i −0.0429104 + 0.132065i
\(148\) 5817.32 + 4226.53i 0.265583 + 0.192957i
\(149\) −19082.2 + 26264.4i −0.859522 + 1.18303i 0.122162 + 0.992510i \(0.461017\pi\)
−0.981683 + 0.190520i \(0.938983\pi\)
\(150\) −11836.1 3845.77i −0.526047 0.170923i
\(151\) −28481.7 + 9254.25i −1.24914 + 0.405871i −0.857613 0.514296i \(-0.828053\pi\)
−0.391528 + 0.920166i \(0.628053\pi\)
\(152\) −92028.5 + 66862.6i −3.98323 + 2.89398i
\(153\) 2416.87i 0.103245i
\(154\) 37899.0 + 6349.12i 1.59804 + 0.267715i
\(155\) −54084.5 −2.25117
\(156\) −18975.8 26118.0i −0.779743 1.07322i
\(157\) 1589.28 + 4891.29i 0.0644764 + 0.198438i 0.978105 0.208112i \(-0.0667318\pi\)
−0.913629 + 0.406550i \(0.866732\pi\)
\(158\) −7122.81 + 21921.7i −0.285323 + 0.878134i
\(159\) 9267.85 + 6733.49i 0.366594 + 0.266346i
\(160\) 38649.0 53195.8i 1.50973 2.07796i
\(161\) −11883.4 3861.14i −0.458445 0.148958i
\(162\) −5156.21 + 1675.36i −0.196472 + 0.0638377i
\(163\) 22862.3 16610.5i 0.860489 0.625182i −0.0675289 0.997717i \(-0.521511\pi\)
0.928018 + 0.372535i \(0.121511\pi\)
\(164\) 22885.9i 0.850905i
\(165\) −13559.3 13803.0i −0.498044 0.506996i
\(166\) 43569.2 1.58111
\(167\) 5521.70 + 7599.96i 0.197988 + 0.272508i 0.896455 0.443135i \(-0.146134\pi\)
−0.698466 + 0.715643i \(0.746134\pi\)
\(168\) −11886.0 36581.5i −0.421133 1.29611i
\(169\) 1106.09 3404.19i 0.0387272 0.119190i
\(170\) −16574.1 12041.8i −0.573498 0.416671i
\(171\) 10414.3 14334.0i 0.356154 0.490204i
\(172\) −11168.0 3628.69i −0.377500 0.122657i
\(173\) 21544.3 7000.16i 0.719847 0.233892i 0.0738899 0.997266i \(-0.476459\pi\)
0.645957 + 0.763374i \(0.276459\pi\)
\(174\) 21255.3 15442.9i 0.702052 0.510071i
\(175\) 13752.4i 0.449057i
\(176\) 71502.0 35633.6i 2.30830 1.15036i
\(177\) −25143.3 −0.802558
\(178\) 6483.04 + 8923.14i 0.204616 + 0.281629i
\(179\) 79.4713 + 244.588i 0.00248030 + 0.00763358i 0.952289 0.305198i \(-0.0987226\pi\)
−0.949809 + 0.312831i \(0.898723\pi\)
\(180\) −10093.0 + 31063.2i −0.311514 + 0.958741i
\(181\) 41978.1 + 30498.9i 1.28134 + 0.930951i 0.999593 0.0285361i \(-0.00908454\pi\)
0.281752 + 0.959487i \(0.409085\pi\)
\(182\) −29504.1 + 40608.9i −0.890716 + 1.22597i
\(183\) 9912.52 + 3220.77i 0.295993 + 0.0961741i
\(184\) −48239.3 + 15673.9i −1.42484 + 0.462957i
\(185\) −4554.28 + 3308.88i −0.133069 + 0.0966801i
\(186\) 67915.0i 1.96309i
\(187\) −4831.09 9694.02i −0.138153 0.277218i
\(188\) 84285.6 2.38472
\(189\) 3521.44 + 4846.85i 0.0985818 + 0.135686i
\(190\) −46410.2 142836.i −1.28560 3.95667i
\(191\) 9798.08 30155.4i 0.268580 0.826605i −0.722267 0.691615i \(-0.756900\pi\)
0.990847 0.134990i \(-0.0431004\pi\)
\(192\) −22390.9 16268.0i −0.607393 0.441297i
\(193\) −27719.4 + 38152.5i −0.744166 + 1.02426i 0.254203 + 0.967151i \(0.418187\pi\)
−0.998368 + 0.0571051i \(0.981813\pi\)
\(194\) −46310.9 15047.3i −1.23050 0.399812i
\(195\) 24037.2 7810.17i 0.632143 0.205396i
\(196\) 18364.6 13342.6i 0.478044 0.347320i
\(197\) 17794.4i 0.458512i 0.973366 + 0.229256i \(0.0736293\pi\)
−0.973366 + 0.229256i \(0.926371\pi\)
\(198\) −17332.7 + 17026.6i −0.442114 + 0.434308i
\(199\) −3961.00 −0.100023 −0.0500114 0.998749i \(-0.515926\pi\)
−0.0500114 + 0.998749i \(0.515926\pi\)
\(200\) 32813.9 + 45164.4i 0.820347 + 1.12911i
\(201\) 8008.93 + 24648.9i 0.198236 + 0.610107i
\(202\) −2934.83 + 9032.47i −0.0719250 + 0.221362i
\(203\) −23487.9 17065.0i −0.569971 0.414108i
\(204\) −10746.8 + 14791.7i −0.258237 + 0.355433i
\(205\) 17040.1 + 5536.66i 0.405475 + 0.131747i
\(206\) −77578.2 + 25206.7i −1.82812 + 0.593993i
\(207\) 6391.44 4643.65i 0.149162 0.108372i
\(208\) 104355.i 2.41205i
\(209\) 13119.2 78310.9i 0.300341 1.79279i
\(210\) 50783.3 1.15155
\(211\) −985.500 1356.42i −0.0221356 0.0304671i 0.797806 0.602915i \(-0.205994\pi\)
−0.819941 + 0.572448i \(0.805994\pi\)
\(212\) −26780.1 82420.6i −0.595854 1.83385i
\(213\) 8691.06 26748.3i 0.191564 0.589573i
\(214\) −79188.8 57534.0i −1.72916 1.25631i
\(215\) 5403.60 7437.41i 0.116898 0.160896i
\(216\) 23129.7 + 7515.28i 0.495749 + 0.161079i
\(217\) 71375.4 23191.3i 1.51576 0.492499i
\(218\) 28133.6 20440.3i 0.591988 0.430104i
\(219\) 10525.7i 0.219464i
\(220\) 21609.3 + 144769.i 0.446474 + 2.99110i
\(221\) 14148.1 0.289677
\(222\) 4155.02 + 5718.90i 0.0843078 + 0.116040i
\(223\) −10870.5 33456.0i −0.218595 0.672766i −0.998879 0.0473403i \(-0.984925\pi\)
0.780284 0.625425i \(-0.215075\pi\)
\(224\) −28195.0 + 86775.3i −0.561922 + 1.72942i
\(225\) −7034.66 5110.98i −0.138956 0.100958i
\(226\) −25247.8 + 34750.6i −0.494319 + 0.680371i
\(227\) 79303.3 + 25767.2i 1.53900 + 0.500053i 0.951101 0.308879i \(-0.0999538\pi\)
0.587903 + 0.808932i \(0.299954\pi\)
\(228\) −127475. + 41419.2i −2.45220 + 0.796768i
\(229\) 17206.3 12501.1i 0.328108 0.238384i −0.411519 0.911401i \(-0.635002\pi\)
0.739627 + 0.673017i \(0.235002\pi\)
\(230\) 66966.9i 1.26592i
\(231\) 23812.9 + 12401.6i 0.446260 + 0.232410i
\(232\) −117855. −2.18964
\(233\) −41041.6 56488.9i −0.755984 1.04052i −0.997538 0.0701350i \(-0.977657\pi\)
0.241554 0.970387i \(-0.422343\pi\)
\(234\) −9807.39 30184.1i −0.179111 0.551247i
\(235\) −20390.7 + 62756.1i −0.369229 + 1.13637i
\(236\) 153882. + 111802.i 2.76290 + 2.00736i
\(237\) −9466.13 + 13029.0i −0.168529 + 0.231961i
\(238\) 27036.3 + 8784.64i 0.477303 + 0.155085i
\(239\) −96280.6 + 31283.5i −1.68556 + 0.547670i −0.985976 0.166885i \(-0.946629\pi\)
−0.699579 + 0.714555i \(0.746629\pi\)
\(240\) 85413.9 62056.8i 1.48288 1.07738i
\(241\) 73340.5i 1.26273i 0.775487 + 0.631364i \(0.217505\pi\)
−0.775487 + 0.631364i \(0.782495\pi\)
\(242\) −35486.5 + 102940.i −0.605943 + 1.75774i
\(243\) −3788.00 −0.0641500
\(244\) −46345.2 63788.7i −0.778439 1.07143i
\(245\) 5491.63 + 16901.5i 0.0914891 + 0.281574i
\(246\) 6952.49 21397.6i 0.114887 0.353585i
\(247\) 83910.3 + 60964.4i 1.37538 + 0.999269i
\(248\) 179070. 246468.i 2.91152 4.00736i
\(249\) 28951.5 + 9406.90i 0.466951 + 0.151722i
\(250\) 65942.0 21425.9i 1.05507 0.342814i
\(251\) 28293.2 20556.2i 0.449091 0.326284i −0.340146 0.940373i \(-0.610476\pi\)
0.789237 + 0.614089i \(0.210476\pi\)
\(252\) 45322.1i 0.713688i
\(253\) 16353.8 31401.5i 0.255492 0.490580i
\(254\) −90521.2 −1.40308
\(255\) −8413.47 11580.2i −0.129388 0.178088i
\(256\) −13865.6 42674.0i −0.211572 0.651153i
\(257\) 1580.93 4865.60i 0.0239357 0.0736666i −0.938375 0.345618i \(-0.887669\pi\)
0.962311 + 0.271952i \(0.0876692\pi\)
\(258\) −9339.31 6785.40i −0.140306 0.101938i
\(259\) 4591.46 6319.60i 0.0684464 0.0942084i
\(260\) −181841. 59083.8i −2.68996 0.874021i
\(261\) 17458.3 5672.54i 0.256283 0.0832715i
\(262\) −106680. + 77507.5i −1.55410 + 1.12912i
\(263\) 79876.9i 1.15481i 0.816458 + 0.577404i \(0.195934\pi\)
−0.816458 + 0.577404i \(0.804066\pi\)
\(264\) 107795. 16090.3i 1.54665 0.230864i
\(265\) 67846.2 0.966127
\(266\) 122495. + 168600.i 1.73123 + 2.38284i
\(267\) 2381.37 + 7329.11i 0.0334045 + 0.102808i
\(268\) 60587.4 186469.i 0.843554 2.59619i
\(269\) −89030.6 64684.5i −1.23037 0.893914i −0.233450 0.972369i \(-0.575002\pi\)
−0.996918 + 0.0784544i \(0.975002\pi\)
\(270\) −18873.3 + 25976.9i −0.258893 + 0.356335i
\(271\) −54208.5 17613.4i −0.738123 0.239831i −0.0842599 0.996444i \(-0.526853\pi\)
−0.653863 + 0.756613i \(0.726853\pi\)
\(272\) 56208.0 18263.1i 0.759731 0.246852i
\(273\) −28373.0 + 20614.2i −0.380698 + 0.276593i
\(274\) 112944.i 1.50439i
\(275\) −38432.3 6438.46i −0.508196 0.0851367i
\(276\) −59765.3 −0.784568
\(277\) −62705.4 86306.6i −0.817233 1.12482i −0.990167 0.139891i \(-0.955325\pi\)
0.172934 0.984933i \(-0.444675\pi\)
\(278\) 59702.0 + 183744.i 0.772501 + 2.37751i
\(279\) −14663.3 + 45129.1i −0.188375 + 0.579760i
\(280\) −184296. 133899.i −2.35072 1.70790i
\(281\) 9259.35 12744.4i 0.117265 0.161401i −0.746349 0.665554i \(-0.768195\pi\)
0.863614 + 0.504153i \(0.168195\pi\)
\(282\) 78804.1 + 25605.0i 0.990948 + 0.321978i
\(283\) −49311.7 + 16022.3i −0.615711 + 0.200057i −0.600235 0.799824i \(-0.704926\pi\)
−0.0154758 + 0.999880i \(0.504926\pi\)
\(284\) −172130. + 125060.i −2.13412 + 1.55053i
\(285\) 104934.i 1.29189i
\(286\) −99672.5 101464.i −1.21855 1.24045i
\(287\) −24861.9 −0.301836
\(288\) −33909.1 46671.9i −0.408819 0.562691i
\(289\) 23333.4 + 71812.7i 0.279371 + 0.859816i
\(290\) 48083.6 147986.i 0.571743 1.75964i
\(291\) −27524.5 19997.7i −0.325038 0.236154i
\(292\) −46803.6 + 64419.6i −0.548925 + 0.755531i
\(293\) 13682.8 + 4445.80i 0.159382 + 0.0517863i 0.387621 0.921819i \(-0.373297\pi\)
−0.228239 + 0.973605i \(0.573297\pi\)
\(294\) 21223.6 6895.95i 0.245541 0.0797810i
\(295\) −120472. + 87527.8i −1.38433 + 1.00578i
\(296\) 31709.8i 0.361917i
\(297\) −15193.6 + 7571.85i −0.172246 + 0.0858399i
\(298\) 241439. 2.71879
\(299\) 27183.5 + 37414.9i 0.304063 + 0.418507i
\(300\) 20327.1 + 62560.4i 0.225857 + 0.695116i
\(301\) −3942.00 + 12132.2i −0.0435094 + 0.133908i
\(302\) 180183. + 130911.i 1.97560 + 1.43536i
\(303\) −3900.35 + 5368.37i −0.0424833 + 0.0584733i
\(304\) 412056. + 133885.i 4.45871 + 1.44872i
\(305\) 58706.8 19075.0i 0.631086 0.205052i
\(306\) −14541.4 + 10565.0i −0.155297 + 0.112830i
\(307\) 81285.6i 0.862455i 0.902243 + 0.431228i \(0.141919\pi\)
−0.902243 + 0.431228i \(0.858081\pi\)
\(308\) −90594.6 181786.i −0.954994 1.91628i
\(309\) −56992.6 −0.596900
\(310\) 236422. + 325407.i 2.46017 + 3.38613i
\(311\) 24970.5 + 76851.3i 0.258170 + 0.794567i 0.993188 + 0.116519i \(0.0371737\pi\)
−0.735018 + 0.678048i \(0.762826\pi\)
\(312\) −43993.8 + 135399.i −0.451942 + 1.39093i
\(313\) −77100.6 56016.8i −0.786990 0.571781i 0.120079 0.992764i \(-0.461685\pi\)
−0.907069 + 0.420983i \(0.861685\pi\)
\(314\) 22481.9 30943.7i 0.228021 0.313843i
\(315\) 33745.2 + 10964.5i 0.340088 + 0.110501i
\(316\) 115869. 37648.2i 1.16036 0.377025i
\(317\) 2501.97 1817.79i 0.0248980 0.0180894i −0.575267 0.817966i \(-0.695102\pi\)
0.600165 + 0.799876i \(0.295102\pi\)
\(318\) 85195.9i 0.842489i
\(319\) 58686.1 57650.0i 0.576705 0.566523i
\(320\) −163915. −1.60073
\(321\) −40198.5 55328.4i −0.390121 0.536956i
\(322\) 28715.2 + 88376.4i 0.276950 + 0.852363i
\(323\) 18151.7 55865.3i 0.173986 0.535473i
\(324\) 23183.3 + 16843.6i 0.220844 + 0.160452i
\(325\) 29919.2 41180.3i 0.283259 0.389873i
\(326\) −199879. 64944.5i −1.88075 0.611093i
\(327\) 23107.8 7508.19i 0.216104 0.0702166i
\(328\) −81649.6 + 59321.9i −0.758938 + 0.551401i
\(329\) 91562.9i 0.845917i
\(330\) −23775.3 + 141919.i −0.218322 + 1.30320i
\(331\) −188225. −1.71799 −0.858996 0.511982i \(-0.828912\pi\)
−0.858996 + 0.511982i \(0.828912\pi\)
\(332\) −135360. 186307.i −1.22805 1.69026i
\(333\) 1526.24 + 4697.27i 0.0137636 + 0.0423601i
\(334\) 21589.0 66444.2i 0.193526 0.595613i
\(335\) 124181. + 90222.5i 1.10653 + 0.803943i
\(336\) −86111.1 + 118522.i −0.762747 + 1.04983i
\(337\) −3247.89 1055.30i −0.0285984 0.00929218i 0.294683 0.955595i \(-0.404786\pi\)
−0.323281 + 0.946303i \(0.604786\pi\)
\(338\) −25316.9 + 8225.96i −0.221604 + 0.0720034i
\(339\) −24279.9 + 17640.4i −0.211275 + 0.153500i
\(340\) 108284.i 0.936714i
\(341\) 31394.4 + 210323.i 0.269987 + 1.80875i
\(342\) −131767. −1.12656
\(343\) −74759.9 102898.i −0.635448 0.874620i
\(344\) 16002.1 + 49249.5i 0.135226 + 0.416183i
\(345\) 14458.6 44499.1i 0.121476 0.373864i
\(346\) −136295. 99024.3i −1.13849 0.827160i
\(347\) 122720. 168910.i 1.01920 1.40280i 0.106431 0.994320i \(-0.466058\pi\)
0.912766 0.408484i \(-0.133942\pi\)
\(348\) −132072. 42912.7i −1.09056 0.354346i
\(349\) 75500.1 24531.5i 0.619865 0.201406i 0.0177844 0.999842i \(-0.494339\pi\)
0.602080 + 0.798436i \(0.294339\pi\)
\(350\) 82743.2 60116.5i 0.675455 0.490747i
\(351\) 22174.6i 0.179987i
\(352\) −229302. 119419.i −1.85064 0.963805i
\(353\) −136810. −1.09792 −0.548958 0.835850i \(-0.684975\pi\)
−0.548958 + 0.835850i \(0.684975\pi\)
\(354\) 109910. + 151279.i 0.877066 + 1.20718i
\(355\) −51472.7 158417.i −0.408432 1.25703i
\(356\) 18015.0 55444.6i 0.142146 0.437481i
\(357\) 16068.8 + 11674.7i 0.126080 + 0.0916028i
\(358\) 1124.20 1547.33i 0.00877158 0.0120730i
\(359\) 150057. + 48756.5i 1.16431 + 0.378306i 0.826515 0.562914i \(-0.190320\pi\)
0.337792 + 0.941221i \(0.390320\pi\)
\(360\) 136985. 44509.2i 1.05698 0.343435i
\(361\) 242947. 176512.i 1.86422 1.35444i
\(362\) 385889.i 2.94473i
\(363\) −45806.0 + 60741.2i −0.347624 + 0.460968i
\(364\) 265312. 2.00241
\(365\) −36641.7 50432.9i −0.275036 0.378555i
\(366\) −23952.9 73719.3i −0.178811 0.550325i
\(367\) −71021.8 + 218582.i −0.527302 + 1.62287i 0.232417 + 0.972616i \(0.425337\pi\)
−0.759719 + 0.650252i \(0.774663\pi\)
\(368\) 156292. + 113553.i 1.15410 + 0.838500i
\(369\) 9239.78 12717.5i 0.0678592 0.0934002i
\(370\) 39816.7 + 12937.2i 0.290845 + 0.0945013i
\(371\) −89536.9 + 29092.3i −0.650510 + 0.211364i
\(372\) 290413. 210997.i 2.09860 1.52472i
\(373\) 72069.3i 0.518004i 0.965877 + 0.259002i \(0.0833936\pi\)
−0.965877 + 0.259002i \(0.916606\pi\)
\(374\) −37207.2 + 71443.0i −0.266001 + 0.510759i
\(375\) 48444.1 0.344491
\(376\) −218474. 300703.i −1.54534 2.12698i
\(377\) 33206.6 + 102199.i 0.233637 + 0.719060i
\(378\) 13768.3 42374.5i 0.0963602 0.296566i
\(379\) −150282. 109186.i −1.04623 0.760133i −0.0747411 0.997203i \(-0.523813\pi\)
−0.971493 + 0.237070i \(0.923813\pi\)
\(380\) −466597. + 642216.i −3.23128 + 4.44748i
\(381\) −60150.8 19544.2i −0.414373 0.134638i
\(382\) −224265. + 72868.2i −1.53686 + 0.499357i
\(383\) 58599.2 42574.8i 0.399479 0.290239i −0.369850 0.929092i \(-0.620591\pi\)
0.769329 + 0.638853i \(0.220591\pi\)
\(384\) 28193.7i 0.191201i
\(385\) 157269. 23475.1i 1.06101 0.158375i
\(386\) 350722. 2.35390
\(387\) −4740.90 6525.28i −0.0316547 0.0435690i
\(388\) 79533.9 + 244780.i 0.528310 + 1.62597i
\(389\) −53473.4 + 164574.i −0.353378 + 1.08758i 0.603567 + 0.797313i \(0.293746\pi\)
−0.956944 + 0.290272i \(0.906254\pi\)
\(390\) −152066. 110483.i −0.999779 0.726382i
\(391\) 15395.2 21189.6i 0.100700 0.138602i
\(392\) −95204.3 30933.7i −0.619561 0.201308i
\(393\) −87622.5 + 28470.3i −0.567324 + 0.184335i
\(394\) 107063. 77785.5i 0.689676 0.501079i
\(395\) 95380.1i 0.611313i
\(396\) 126657. + 21218.5i 0.807678 + 0.135308i
\(397\) 264583. 1.67873 0.839367 0.543566i \(-0.182926\pi\)
0.839367 + 0.543566i \(0.182926\pi\)
\(398\) 17314.9 + 23832.0i 0.109309 + 0.150451i
\(399\) 44995.3 + 138481.i 0.282632 + 0.869853i
\(400\) 65706.3 202223.i 0.410664 1.26389i
\(401\) −107684. 78237.2i −0.669674 0.486547i 0.200242 0.979747i \(-0.435827\pi\)
−0.869916 + 0.493200i \(0.835827\pi\)
\(402\) 113294. 155936.i 0.701061 0.964928i
\(403\) −264182. 85837.9i −1.62665 0.528529i
\(404\) 47741.9 15512.3i 0.292507 0.0950414i
\(405\) −18149.8 + 13186.6i −0.110653 + 0.0803938i
\(406\) 215916.i 1.30988i
\(407\) 15511.1 + 15789.9i 0.0936386 + 0.0953215i
\(408\) 80628.3 0.484359
\(409\) 1337.05 + 1840.29i 0.00799285 + 0.0110012i 0.812995 0.582271i \(-0.197836\pi\)
−0.805002 + 0.593272i \(0.797836\pi\)
\(410\) −41176.0 126727.i −0.244950 0.753878i
\(411\) 24385.3 75050.4i 0.144359 0.444293i
\(412\) 348806. + 253422.i 2.05489 + 1.49297i
\(413\) 121455. 167169.i 0.712058 0.980064i
\(414\) −55878.4 18156.0i −0.326020 0.105930i
\(415\) 171465. 55712.3i 0.995585 0.323485i
\(416\) 273213. 198501.i 1.57876 1.14703i
\(417\) 134987.i 0.776281i
\(418\) −528518. + 263391.i −3.02487 + 1.50747i
\(419\) −47549.2 −0.270841 −0.135421 0.990788i \(-0.543239\pi\)
−0.135421 + 0.990788i \(0.543239\pi\)
\(420\) −157773. 217156.i −0.894404 1.23104i
\(421\) −28298.3 87093.3i −0.159660 0.491383i 0.838943 0.544219i \(-0.183174\pi\)
−0.998603 + 0.0528358i \(0.983174\pi\)
\(422\) −3853.16 + 11858.8i −0.0216368 + 0.0665911i
\(423\) 46836.6 + 34028.7i 0.261761 + 0.190180i
\(424\) −224634. + 309182.i −1.24952 + 1.71982i
\(425\) −27416.8 8908.25i −0.151788 0.0493191i
\(426\) −198927. + 64635.3i −1.09616 + 0.356164i
\(427\) −69296.2 + 50346.6i −0.380061 + 0.276131i
\(428\) 517367.i 2.82430i
\(429\) −44325.0 88942.2i −0.240843 0.483274i
\(430\) −68369.3 −0.369764
\(431\) −677.399 932.359i −0.00364661 0.00501913i 0.807190 0.590292i \(-0.200987\pi\)
−0.810836 + 0.585273i \(0.800987\pi\)
\(432\) −28624.0 88095.7i −0.153378 0.472049i
\(433\) −56561.5 + 174078.i −0.301679 + 0.928473i 0.679217 + 0.733938i \(0.262320\pi\)
−0.980896 + 0.194535i \(0.937680\pi\)
\(434\) −451541. 328064.i −2.39727 1.74172i
\(435\) 63902.5 87954.3i 0.337707 0.464813i
\(436\) −174810. 56799.3i −0.919590 0.298793i
\(437\) 182613. 59334.4i 0.956242 0.310702i
\(438\) −63329.7 + 46011.7i −0.330110 + 0.239839i
\(439\) 171391.i 0.889319i 0.895700 + 0.444660i \(0.146675\pi\)
−0.895700 + 0.444660i \(0.853325\pi\)
\(440\) 460477. 452346.i 2.37849 2.33650i
\(441\) 15591.8 0.0801714
\(442\) −61846.5 85124.3i −0.316570 0.435722i
\(443\) −6465.23 19897.9i −0.0329440 0.101391i 0.933232 0.359273i \(-0.116975\pi\)
−0.966176 + 0.257882i \(0.916975\pi\)
\(444\) 11546.0 35534.8i 0.0585685 0.180255i
\(445\) 36923.8 + 26826.7i 0.186460 + 0.135471i
\(446\) −153774. + 211652.i −0.773060 + 1.06403i
\(447\) 160435. + 52128.5i 0.802941 + 0.260891i
\(448\) 216319. 70286.4i 1.07780 0.350199i
\(449\) −298589. + 216938.i −1.48109 + 1.07607i −0.503885 + 0.863771i \(0.668096\pi\)
−0.977204 + 0.212303i \(0.931904\pi\)
\(450\) 64667.0i 0.319343i
\(451\) 11639.6 69479.1i 0.0572251 0.341587i
\(452\) 227038. 1.11127
\(453\) 91466.0 + 125892.i 0.445721 + 0.613483i
\(454\) −191631. 589778.i −0.929722 2.86139i
\(455\) −64185.2 + 197542.i −0.310036 + 0.954192i
\(456\) 478194. + 347428.i 2.29972 + 1.67084i
\(457\) −18538.9 + 25516.6i −0.0887670 + 0.122177i −0.851091 0.525018i \(-0.824058\pi\)
0.762324 + 0.647196i \(0.224058\pi\)
\(458\) −150430. 48877.6i −0.717138 0.233012i
\(459\) −11943.7 + 3880.76i −0.0566911 + 0.0184201i
\(460\) −286359. + 208052.i −1.35330 + 0.983232i
\(461\) 187345.i 0.881538i −0.897621 0.440769i \(-0.854706\pi\)
0.897621 0.440769i \(-0.145294\pi\)
\(462\) −29478.1 197486.i −0.138107 0.925233i
\(463\) 406644. 1.89693 0.948466 0.316878i \(-0.102634\pi\)
0.948466 + 0.316878i \(0.102634\pi\)
\(464\) 263847. + 363155.i 1.22551 + 1.68677i
\(465\) 86843.4 + 267277.i 0.401634 + 1.23610i
\(466\) −160467. + 493866.i −0.738947 + 2.27425i
\(467\) −184337. 133929.i −0.845238 0.614102i 0.0785907 0.996907i \(-0.474958\pi\)
−0.923829 + 0.382805i \(0.874958\pi\)
\(468\) −98601.3 + 135713.i −0.450185 + 0.619626i
\(469\) −202569. 65818.6i −0.920930 0.299228i
\(470\) 466717. 151645.i 2.11280 0.686489i
\(471\) 21620.1 15707.9i 0.0974575 0.0708070i
\(472\) 838800.i 3.76508i
\(473\) −32059.1 16696.2i −0.143294 0.0746271i
\(474\) 119771. 0.533082
\(475\) −124219. 170973.i −0.550555 0.757773i
\(476\) −46431.9 142903.i −0.204929 0.630706i
\(477\) 18394.4 56612.2i 0.0808442 0.248813i
\(478\) 609098. + 442536.i 2.66582 + 1.93683i
\(479\) 113070. 155627.i 0.492806 0.678289i −0.488097 0.872790i \(-0.662309\pi\)
0.980902 + 0.194501i \(0.0623087\pi\)
\(480\) −324944. 105581.i −1.41035 0.458249i
\(481\) −27497.5 + 8934.46i −0.118851 + 0.0386170i
\(482\) 441264. 320597.i 1.89935 1.37996i
\(483\) 64925.4i 0.278305i
\(484\) 550433. 168068.i 2.34971 0.717455i
\(485\) −201496. −0.856609
\(486\) 16558.7 + 22791.0i 0.0701056 + 0.0964921i
\(487\) 69428.6 + 213679.i 0.292739 + 0.900957i 0.983972 + 0.178325i \(0.0570679\pi\)
−0.691233 + 0.722632i \(0.742932\pi\)
\(488\) −107447. + 330689.i −0.451186 + 1.38861i
\(489\) −118796. 86310.5i −0.496804 0.360949i
\(490\) 77684.6 106924.i 0.323551 0.445330i
\(491\) −28943.2 9404.21i −0.120056 0.0390085i 0.248373 0.968664i \(-0.420104\pi\)
−0.368429 + 0.929656i \(0.620104\pi\)
\(492\) −113099. + 36747.9i −0.467226 + 0.151811i
\(493\) 49235.4 35771.6i 0.202574 0.147179i
\(494\) 771356.i 3.16083i
\(495\) −46439.8 + 89171.0i −0.189531 + 0.363926i
\(496\) −1.16035e6 −4.71657
\(497\) 135857. + 186992.i 0.550010 + 0.757023i
\(498\) −69959.0 215312.i −0.282088 0.868178i
\(499\) 44849.3 138032.i 0.180117 0.554343i −0.819713 0.572774i \(-0.805867\pi\)
0.999830 + 0.0184313i \(0.00586721\pi\)
\(500\) −296488. 215411.i −1.18595 0.861643i
\(501\) 28691.6 39490.6i 0.114309 0.157332i
\(502\) −247359. 80371.8i −0.981567 0.318931i
\(503\) 30280.8 9838.83i 0.119683 0.0388873i −0.248563 0.968616i \(-0.579958\pi\)
0.368246 + 0.929728i \(0.379958\pi\)
\(504\) −161694. + 117478.i −0.636551 + 0.462482i
\(505\) 39299.7i 0.154101i
\(506\) −260420. + 38872.2i −1.01712 + 0.151823i
\(507\) −18599.0 −0.0723557
\(508\) 281230. + 387080.i 1.08977 + 1.49994i
\(509\) −47435.7 145992.i −0.183092 0.563500i 0.816818 0.576895i \(-0.195736\pi\)
−0.999910 + 0.0133953i \(0.995736\pi\)
\(510\) −32895.5 + 101242.i −0.126472 + 0.389242i
\(511\) 69981.6 + 50844.6i 0.268005 + 0.194717i
\(512\) −247171. + 340201.i −0.942882 + 1.29777i
\(513\) −87558.7 28449.5i −0.332709 0.108104i
\(514\) −36185.4 + 11757.4i −0.136964 + 0.0445024i
\(515\) −273074. + 198400.i −1.02959 + 0.748043i
\(516\) 61016.8i 0.229166i
\(517\) 255881. + 42867.1i 0.957321 + 0.160377i
\(518\) −58093.7 −0.216506
\(519\) −69187.3 95228.2i −0.256857 0.353534i
\(520\) 260553. + 801900.i 0.963584 + 2.96561i
\(521\) 67447.1 207581.i 0.248478 0.764736i −0.746567 0.665310i \(-0.768299\pi\)
0.995045 0.0994259i \(-0.0317006\pi\)
\(522\) −110446. 80243.7i −0.405330 0.294490i
\(523\) 243310. 334887.i 0.889521 1.22432i −0.0841701 0.996451i \(-0.526824\pi\)
0.973692 0.227870i \(-0.0731761\pi\)
\(524\) 662863. + 215377.i 2.41413 + 0.784400i
\(525\) 67961.9 22082.2i 0.246574 0.0801167i
\(526\) 480592. 349170.i 1.73702 1.26202i
\(527\) 157317.i 0.566440i
\(528\) −290906. 296134.i −1.04348 1.06224i
\(529\) −194225. −0.694055
\(530\) −296580. 408207.i −1.05582 1.45321i
\(531\) 40372.6 + 124254.i 0.143185 + 0.440679i
\(532\) 340389. 1.04761e6i 1.20269 3.70149i
\(533\) 74447.0 + 54088.9i 0.262055 + 0.190394i
\(534\) 33686.9 46366.0i 0.118135 0.162599i
\(535\) −385213. 125163.i −1.34584 0.437290i
\(536\) −822306. + 267184.i −2.86223 + 0.929994i
\(537\) 1081.10 785.468i 0.00374903 0.00272383i
\(538\) 818425.i 2.82758i
\(539\) 62538.6 31166.6i 0.215264 0.107278i
\(540\) 169716. 0.582015
\(541\) 235574. + 324239.i 0.804882 + 1.10783i 0.992093 + 0.125506i \(0.0400553\pi\)
−0.187211 + 0.982320i \(0.559945\pi\)
\(542\) 130991. + 403148.i 0.445904 + 1.37235i
\(543\) 83316.2 256421.i 0.282573 0.869669i
\(544\) −154732. 112419.i −0.522856 0.379877i
\(545\) 84581.6 116417.i 0.284763 0.391942i
\(546\) 248057. + 80598.6i 0.832082 + 0.270360i
\(547\) −55348.4 + 17983.8i −0.184982 + 0.0601044i −0.400043 0.916496i \(-0.631005\pi\)
0.215061 + 0.976601i \(0.431005\pi\)
\(548\) −482961. + 350892.i −1.60824 + 1.16846i
\(549\) 54157.6i 0.179686i
\(550\) 129263. + 259379.i 0.427316 + 0.857450i
\(551\) 446148. 1.46952
\(552\) 154916. + 213223.i 0.508413 + 0.699771i
\(553\) −40898.7 125873.i −0.133740 0.411608i
\(554\) −245169. + 754554.i −0.798816 + 2.45850i
\(555\) 23664.7 + 17193.4i 0.0768273 + 0.0558183i
\(556\) 600230. 826146.i 1.94164 2.67243i
\(557\) 84762.1 + 27540.9i 0.273207 + 0.0887703i 0.442416 0.896810i \(-0.354121\pi\)
−0.169209 + 0.985580i \(0.554121\pi\)
\(558\) 335625. 109051.i 1.07792 0.350236i
\(559\) 38198.5 27752.8i 0.122243 0.0888144i
\(560\) 867651.i 2.76674i
\(561\) −40149.0 + 39440.1i −0.127570 + 0.125318i
\(562\) −117155. −0.370925
\(563\) −273826. 376890.i −0.863890 1.18904i −0.980628 0.195880i \(-0.937244\pi\)
0.116737 0.993163i \(-0.462756\pi\)
\(564\) −135337. 416526.i −0.425461 1.30943i
\(565\) −54925.8 + 169044.i −0.172060 + 0.529546i
\(566\) 311959. + 226652.i 0.973790 + 0.707500i
\(567\) 18297.9 25185.0i 0.0569162 0.0783385i
\(568\) 892343. + 289940.i 2.76589 + 0.898693i
\(569\) 123667. 40181.9i 0.381970 0.124110i −0.111737 0.993738i \(-0.535641\pi\)
0.493707 + 0.869628i \(0.335641\pi\)
\(570\) −631350. + 458703.i −1.94321 + 1.41183i
\(571\) 600320.i 1.84124i −0.390457 0.920621i \(-0.627683\pi\)
0.390457 0.920621i \(-0.372317\pi\)
\(572\) −124211. + 741439.i −0.379637 + 2.26612i
\(573\) −164756. −0.501801
\(574\) 108680. + 149586.i 0.329858 + 0.454011i
\(575\) −29119.3 89620.0i −0.0880735 0.271062i
\(576\) −44440.5 + 136774.i −0.133947 + 0.412247i
\(577\) −457370. 332299.i −1.37378 0.998108i −0.997431 0.0716284i \(-0.977180\pi\)
−0.376346 0.926479i \(-0.622820\pi\)
\(578\) 330074. 454307.i 0.987996 1.35986i
\(579\) 233052. + 75723.3i 0.695179 + 0.225877i
\(580\) −782193. + 254150.i −2.32519 + 0.755499i
\(581\) −202393. + 147047.i −0.599575 + 0.435617i
\(582\) 253022.i 0.746987i
\(583\) −39382.6 263840.i −0.115869 0.776252i
\(584\) 351146. 1.02958
\(585\) −77193.2 106247.i −0.225563 0.310460i
\(586\) −33063.4 101759.i −0.0962836 0.296330i
\(587\) 122795. 377925.i 0.356374 1.09681i −0.598835 0.800873i \(-0.704369\pi\)
0.955209 0.295934i \(-0.0956307\pi\)
\(588\) −95425.0 69330.3i −0.275999 0.200525i
\(589\) −677880. + 933021.i −1.95399 + 2.68943i
\(590\) 1.05325e6 + 342221.i 3.02571 + 0.983112i
\(591\) 87936.9 28572.4i 0.251765 0.0818036i
\(592\) −97709.4 + 70990.0i −0.278800 + 0.202560i
\(593\) 351638.i 0.999970i 0.866034 + 0.499985i \(0.166661\pi\)
−0.866034 + 0.499985i \(0.833339\pi\)
\(594\) 111974. + 58315.4i 0.317354 + 0.165276i
\(595\) 117633. 0.332274
\(596\) −750100. 1.03242e6i −2.11167 2.90647i
\(597\) 6360.18 + 19574.6i 0.0178452 + 0.0549218i
\(598\) 106284. 327108.i 0.297211 0.914721i
\(599\) 17371.8 + 12621.3i 0.0484162 + 0.0351764i 0.611730 0.791067i \(-0.290474\pi\)
−0.563314 + 0.826243i \(0.690474\pi\)
\(600\) 170506. 234681.i 0.473627 0.651892i
\(601\) −13343.8 4335.67i −0.0369429 0.0120035i 0.290487 0.956879i \(-0.406183\pi\)
−0.327430 + 0.944875i \(0.606183\pi\)
\(602\) 90227.2 29316.6i 0.248968 0.0808948i
\(603\) 108951. 79157.6i 0.299638 0.217700i
\(604\) 1.17720e6i 3.22682i
\(605\) −8025.28 + 450493.i −0.0219255 + 1.23077i
\(606\) 49349.4 0.134381
\(607\) 141102. + 194211.i 0.382963 + 0.527104i 0.956367 0.292170i \(-0.0943772\pi\)
−0.573403 + 0.819273i \(0.694377\pi\)
\(608\) −433275. 1.33348e6i −1.17208 3.60728i
\(609\) −46617.8 + 143475.i −0.125695 + 0.386848i
\(610\) −371396. 269835.i −0.998107 0.725167i
\(611\) −199201. + 274177.i −0.533593 + 0.734428i
\(612\) 90354.3 + 29357.9i 0.241238 + 0.0783830i
\(613\) −242629. + 78834.9i −0.645686 + 0.209796i −0.613511 0.789686i \(-0.710243\pi\)
−0.0321752 + 0.999482i \(0.510243\pi\)
\(614\) 489067. 355328.i 1.29727 0.942524i
\(615\) 93099.4i 0.246148i
\(616\) −413727. + 794414.i −1.09032 + 2.09356i
\(617\) −715781. −1.88022 −0.940112 0.340865i \(-0.889280\pi\)
−0.940112 + 0.340865i \(0.889280\pi\)
\(618\) 249135. + 342904.i 0.652315 + 0.897834i
\(619\) 67647.5 + 208198.i 0.176551 + 0.543368i 0.999701 0.0244558i \(-0.00778531\pi\)
−0.823150 + 0.567824i \(0.807785\pi\)
\(620\) 656969. 2.02194e6i 1.70908 5.26000i
\(621\) −33210.9 24129.1i −0.0861186 0.0625689i
\(622\) 353233. 486183.i 0.913020 1.25666i
\(623\) −60231.7 19570.5i −0.155185 0.0504226i
\(624\) 515705. 167563.i 1.32444 0.430337i
\(625\) 394954. 286951.i 1.01108 0.734594i
\(626\) 708757.i 1.80862i
\(627\) −408065. + 60910.8i −1.03799 + 0.154938i
\(628\) −202166. −0.512611
\(629\) 9624.61 + 13247.1i 0.0243266 + 0.0334827i
\(630\) −81542.8 250963.i −0.205449 0.632307i
\(631\) −189769. + 584050.i −0.476614 + 1.46687i 0.367154 + 0.930160i \(0.380332\pi\)
−0.843768 + 0.536708i \(0.819668\pi\)
\(632\) −434657. 315797.i −1.08821 0.790630i
\(633\) −5120.81 + 7048.19i −0.0127800 + 0.0175902i
\(634\) −21874.0 7107.30i −0.0544189 0.0176818i
\(635\) −356242. + 115750.i −0.883483 + 0.287061i
\(636\) −364308. + 264685.i −0.900647 + 0.654359i
\(637\) 91273.2i 0.224939i
\(638\) −603397. 101086.i −1.48239 0.248341i
\(639\) −146141. −0.357907
\(640\) 98146.4 + 135087.i 0.239615 + 0.329802i
\(641\) 70528.6 + 217065.i 0.171652 + 0.528291i 0.999465 0.0327139i \(-0.0104150\pi\)
−0.827813 + 0.561005i \(0.810415\pi\)
\(642\) −157170. + 483720.i −0.381329 + 1.17361i
\(643\) 468717. + 340543.i 1.13368 + 0.823664i 0.986226 0.165405i \(-0.0528933\pi\)
0.147451 + 0.989069i \(0.452893\pi\)
\(644\) 288697. 397357.i 0.696097 0.958096i
\(645\) −45431.0 14761.4i −0.109203 0.0354821i
\(646\) −415470. + 134994.i −0.995576 + 0.323482i
\(647\) 494134. 359009.i 1.18042 0.857625i 0.188200 0.982131i \(-0.439735\pi\)
0.992219 + 0.124506i \(0.0397347\pi\)
\(648\) 126370.i 0.300950i
\(649\) 410307. + 417681.i 0.974136 + 0.991644i
\(650\) −378555. −0.895988
\(651\) −229215. 315487.i −0.540855 0.744423i
\(652\) 343269. + 1.05647e6i 0.807495 + 2.48521i
\(653\) 205996. 633991.i 0.483095 1.48681i −0.351626 0.936141i \(-0.614371\pi\)
0.834721 0.550673i \(-0.185629\pi\)
\(654\) −146187. 106211.i −0.341784 0.248321i
\(655\) −320725. + 441440.i −0.747567 + 1.02894i
\(656\) 365585. + 118786.i 0.849533 + 0.276030i
\(657\) −52016.4 + 16901.2i −0.120506 + 0.0391549i
\(658\) −550902. + 400254.i −1.27240 + 0.924450i
\(659\) 261408.i 0.601933i −0.953635 0.300967i \(-0.902691\pi\)
0.953635 0.300967i \(-0.0973093\pi\)
\(660\) 680728. 339246.i 1.56274 0.778801i
\(661\) −117901. −0.269846 −0.134923 0.990856i \(-0.543079\pi\)
−0.134923 + 0.990856i \(0.543079\pi\)
\(662\) 822798. + 1.13248e6i 1.87749 + 2.58414i
\(663\) −22717.6 69917.7i −0.0516816 0.159060i
\(664\) −313821. + 965841.i −0.711780 + 2.19063i
\(665\) 697665. + 506883.i 1.57762 + 1.14621i
\(666\) 21590.1 29716.3i 0.0486751 0.0669955i
\(667\) 189197. + 61473.9i 0.425268 + 0.138178i
\(668\) −351196. + 114111.i −0.787041 + 0.255725i
\(669\) −147879. + 107440.i −0.330411 + 0.240058i
\(670\) 1.14155e6i 2.54299i
\(671\) −108256. 217226.i −0.240440 0.482466i
\(672\) 474102. 1.04986
\(673\) −404924. 557330.i −0.894012 1.23050i −0.972339 0.233574i \(-0.924958\pi\)
0.0783272 0.996928i \(-0.475042\pi\)
\(674\) 7848.28 + 24154.5i 0.0172765 + 0.0531715i
\(675\) −13962.1 + 42970.8i −0.0306438 + 0.0943118i
\(676\) 113829. + 82701.9i 0.249093 + 0.180977i
\(677\) 363597. 500448.i 0.793310 1.09190i −0.200378 0.979719i \(-0.564217\pi\)
0.993688 0.112179i \(-0.0357830\pi\)
\(678\) 212272. + 68971.5i 0.461779 + 0.150041i
\(679\) 265915. 86400.9i 0.576770 0.187404i
\(680\) 386322. 280680.i 0.835472 0.607006i
\(681\) 433278.i 0.934271i
\(682\) 1.12820e6 1.10828e6i 2.42560 2.38277i
\(683\) 488052. 1.04622 0.523112 0.852264i \(-0.324771\pi\)
0.523112 + 0.852264i \(0.324771\pi\)
\(684\) 409373. + 563454.i 0.874999 + 1.20433i
\(685\) −144422. 444485.i −0.307788 0.947275i
\(686\) −292300. + 899608.i −0.621128 + 1.91164i
\(687\) −89406.6 64957.7i −0.189433 0.137631i
\(688\) 115931. 159565.i 0.244919 0.337102i
\(689\) 331403. + 107679.i 0.698100 + 0.226827i
\(690\) −330940. + 107529.i −0.695105 + 0.225853i
\(691\) 229190. 166516.i 0.479999 0.348739i −0.321327 0.946968i \(-0.604129\pi\)
0.801325 + 0.598229i \(0.204129\pi\)
\(692\) 890463.i 1.85953i
\(693\) 23050.5 137592.i 0.0479970 0.286502i
\(694\) −1.55273e6 −3.22386
\(695\) 469909. + 646775.i 0.972847 + 1.33901i
\(696\) 189240. + 582421.i 0.390656 + 1.20232i
\(697\) 16104.6 49564.9i 0.0331501 0.102025i
\(698\) −477635. 347022.i −0.980359 0.712273i
\(699\) −213258. + 293525.i −0.436467 + 0.600746i
\(700\) −514131. 167051.i −1.04925 0.340921i
\(701\) −723076. + 234942.i −1.47146 + 0.478106i −0.931548 0.363618i \(-0.881542\pi\)
−0.539909 + 0.841723i \(0.681542\pi\)
\(702\) −133417. + 96933.0i −0.270730 + 0.196697i
\(703\) 120039.i 0.242892i
\(704\) 95147.6 + 637431.i 0.191979 + 1.28614i
\(705\) 342872. 0.689848
\(706\) 598046. + 823139.i 1.19984 + 1.65144i
\(707\) −16851.6 51863.9i −0.0337134 0.103759i
\(708\) 305418. 939981.i 0.609297 1.87522i
\(709\) 245643. + 178470.i 0.488665 + 0.355036i 0.804671 0.593721i \(-0.202342\pi\)
−0.316006 + 0.948757i \(0.602342\pi\)
\(710\) −728133. + 1.00219e6i −1.44442 + 1.98807i
\(711\) 79586.9 + 25859.4i 0.157435 + 0.0511539i
\(712\) −244504. + 79444.3i −0.482310 + 0.156712i
\(713\) −416027. + 302261.i −0.818356 + 0.594570i
\(714\) 147715.i 0.289752i
\(715\) −522000. 271855.i −1.02108 0.531772i
\(716\) −10109.2 −0.0197193
\(717\) 309195. + 425571.i 0.601443 + 0.827816i
\(718\) −362602. 1.11597e6i −0.703365 2.16474i
\(719\) −43324.2 + 133338.i −0.0838055 + 0.257927i −0.984175 0.177199i \(-0.943296\pi\)
0.900369 + 0.435126i \(0.143296\pi\)
\(720\) −443824. 322457.i −0.856141 0.622023i
\(721\) 275303. 378922.i 0.529591 0.728919i
\(722\) −2.12402e6 690135.i −4.07459 1.32391i
\(723\) 362437. 117763.i 0.693355 0.225285i
\(724\) −1.65011e6 + 1.19888e6i −3.14801 + 2.28716i
\(725\) 218954.i 0.416559i
\(726\) 565693. + 10077.5i 1.07327 + 0.0191197i
\(727\) −69575.5 −0.131640 −0.0658199 0.997832i \(-0.520966\pi\)
−0.0658199 + 0.997832i \(0.520966\pi\)
\(728\) −687705. 946545.i −1.29760 1.78599i
\(729\) 6082.38 + 18719.6i 0.0114451 + 0.0352243i
\(730\) −143264. + 440920.i −0.268838 + 0.827398i
\(731\) −21633.4 15717.6i −0.0404846 0.0294138i
\(732\) −240817. + 331456.i −0.449432 + 0.618590i
\(733\) 8909.16 + 2894.76i 0.0165817 + 0.00538772i 0.317296 0.948327i \(-0.397225\pi\)
−0.300714 + 0.953714i \(0.597225\pi\)
\(734\) 1.62560e6 528188.i 3.01731 0.980384i
\(735\) 74706.5 54277.5i 0.138288 0.100472i
\(736\) 625188.i 1.15413i
\(737\) 278773. 535283.i 0.513235 0.985482i
\(738\) −116907. −0.214648
\(739\) 30204.8 + 41573.3i 0.0553078 + 0.0761247i 0.835775 0.549072i \(-0.185019\pi\)
−0.780467 + 0.625197i \(0.785019\pi\)
\(740\) −68380.8 210454.i −0.124874 0.384322i
\(741\) 166541. 512561.i 0.303309 0.933490i
\(742\) 566435. + 411539.i 1.02883 + 0.747487i
\(743\) 53639.0 73827.8i 0.0971635 0.133734i −0.757667 0.652641i \(-0.773661\pi\)
0.854831 + 0.518907i \(0.173661\pi\)
\(744\) −1.50554e6 489179.i −2.71986 0.883735i
\(745\) 950174. 308730.i 1.71195 0.556246i
\(746\) 433616. 315040.i 0.779162 0.566094i
\(747\) 158178.i 0.283468i
\(748\) 421094. 62855.6i 0.752620 0.112342i
\(749\) 562037. 1.00185
\(750\) −211766. 291471.i −0.376473 0.518171i
\(751\) −240883. 741361.i −0.427096 1.31447i −0.900973 0.433876i \(-0.857146\pi\)
0.473876 0.880592i \(-0.342854\pi\)
\(752\) −437470. + 1.34640e6i −0.773594 + 2.38088i
\(753\) −147016. 106813.i −0.259283 0.188380i
\(754\) 469740. 646542.i 0.826256 1.13724i
\(755\) 876499. + 284792.i 1.53765 + 0.499613i
\(756\) −223974. + 72773.6i −0.391881 + 0.127330i
\(757\) −187749. + 136407.i −0.327631 + 0.238038i −0.739425 0.673239i \(-0.764902\pi\)
0.411794 + 0.911277i \(0.364902\pi\)
\(758\) 1.38149e6i 2.40441i
\(759\) −181440. 30396.2i −0.314956 0.0527638i
\(760\) 3.50067e6 6.06071
\(761\) 483226. + 665103.i 0.834412 + 1.14847i 0.987086 + 0.160193i \(0.0512118\pi\)
−0.152673 + 0.988277i \(0.548788\pi\)
\(762\) 145350. + 447341.i 0.250325 + 0.770422i
\(763\) −61703.4 + 189904.i −0.105989 + 0.326200i
\(764\) 1.00834e6 + 732600.i 1.72751 + 1.25511i
\(765\) −43717.7 + 60172.2i −0.0747024 + 0.102819i
\(766\) −512316. 166461.i −0.873132 0.283698i
\(767\) −727374. + 236338.i −1.23642 + 0.401738i
\(768\) −188624. + 137043.i −0.319796 + 0.232346i
\(769\) 944226.i 1.59670i 0.602194 + 0.798350i \(0.294293\pi\)
−0.602194 + 0.798350i \(0.705707\pi\)
\(770\) −828718. 843613.i −1.39774 1.42286i
\(771\) −26583.5 −0.0447202
\(772\) −1.08962e6 1.49973e6i −1.82827 2.51639i
\(773\) −283782. 873390.i −0.474925 1.46167i −0.846058 0.533091i \(-0.821031\pi\)
0.371133 0.928580i \(-0.378969\pi\)
\(774\) −18536.2 + 57048.6i −0.0309414 + 0.0952277i
\(775\) 457895. + 332680.i 0.762364 + 0.553890i
\(776\) 667138. 918237.i 1.10788 1.52487i
\(777\) −38602.9 12542.8i −0.0639408 0.0207756i
\(778\) 1.22394e6 397681.i 2.02209 0.657016i
\(779\) 309089. 224567.i 0.509341 0.370058i
\(780\) 993501.i 1.63297i
\(781\) −586170. + 292122.i −0.960996 + 0.478920i
\(782\) −194788. −0.318529
\(783\) −56065.5 77167.5i −0.0914476 0.125867i
\(784\) 117820. + 362612.i 0.191684 + 0.589943i
\(785\) 48908.7 150525.i 0.0793682 0.244270i
\(786\) 554325. + 402741.i 0.897262 + 0.651899i
\(787\) −534468. + 735631.i −0.862923 + 1.18771i 0.117942 + 0.993020i \(0.462370\pi\)
−0.980865 + 0.194691i \(0.937630\pi\)
\(788\) −665241. 216150.i −1.07134 0.348099i
\(789\) 394739. 128258.i 0.634097 0.206031i
\(790\) 573869. 416940.i 0.919514 0.668066i
\(791\) 246640.i 0.394195i
\(792\) −252602. 506870.i −0.402705 0.808065i
\(793\) 317034. 0.504150
\(794\) −1.15659e6 1.59191e6i −1.83458 2.52509i
\(795\) −108941. 335285.i −0.172368 0.530493i
\(796\) 48114.7 148082.i 0.0759366 0.233709i
\(797\) −667167. 484726.i −1.05031 0.763096i −0.0780400 0.996950i \(-0.524866\pi\)
−0.972272 + 0.233854i \(0.924866\pi\)
\(798\) 636504. 876072.i 0.999529 1.37573i
\(799\) 182540. + 59310.9i 0.285933 + 0.0929054i
\(800\) −654428. + 212636.i −1.02254 + 0.332244i
\(801\) 32395.5 23536.7i 0.0504916 0.0366843i
\(802\) 989901.i 1.53902i
\(803\) −174854. + 171766.i −0.271171 + 0.266383i
\(804\) −1.01878e6 −1.57605
\(805\) 226015. + 311083.i 0.348776 + 0.480048i
\(806\) 638376. + 1.96472e6i 0.982667 + 3.02434i
\(807\) −176704. + 543839.i −0.271331 + 0.835070i
\(808\) −179093. 130119.i −0.274319 0.199304i
\(809\) −607670. + 836385.i −0.928475 + 1.27794i 0.0319759 + 0.999489i \(0.489820\pi\)
−0.960451 + 0.278448i \(0.910180\pi\)
\(810\) 158678. + 51557.7i 0.241851 + 0.0785820i
\(811\) −206959. + 67245.2i −0.314661 + 0.102240i −0.462090 0.886833i \(-0.652900\pi\)
0.147429 + 0.989073i \(0.452900\pi\)
\(812\) 923283. 670804.i 1.40031 1.01738i
\(813\) 296171.i 0.448086i
\(814\) 27197.8 162348.i 0.0410473 0.245019i
\(815\) −869659. −1.30928
\(816\) −180506. 248445.i −0.271089 0.373122i
\(817\) −60577.0 186437.i −0.0907535 0.279311i
\(818\) 5227.68 16089.1i 0.00781272 0.0240451i
\(819\) 147431. + 107115.i 0.219796 + 0.159691i
\(820\) −413975. + 569787.i −0.615667 + 0.847393i
\(821\) −299091. 97180.6i −0.443728 0.144176i 0.0786269 0.996904i \(-0.474946\pi\)
−0.522355 + 0.852728i \(0.674946\pi\)
\(822\) −558149. + 181354.i −0.826050 + 0.268400i
\(823\) 273376. 198619.i 0.403609 0.293239i −0.367400 0.930063i \(-0.619752\pi\)
0.771009 + 0.636824i \(0.219752\pi\)
\(824\) 1.90131e6i 2.80027i
\(825\) 29892.9 + 200264.i 0.0439198 + 0.294236i
\(826\) −1.53672e6 −2.25234
\(827\) −365551. 503138.i −0.534487 0.735659i 0.453319 0.891349i \(-0.350240\pi\)
−0.987806 + 0.155690i \(0.950240\pi\)
\(828\) 95965.1 + 295350.i 0.139976 + 0.430801i
\(829\) 206669. 636062.i 0.300723 0.925530i −0.680516 0.732734i \(-0.738244\pi\)
0.981239 0.192797i \(-0.0617558\pi\)
\(830\) −1.08473e6 788105.i −1.57459 1.14401i
\(831\) −325827. + 448462.i −0.471830 + 0.649418i
\(832\) −800663. 260151.i −1.15665 0.375819i
\(833\) 49161.8 15973.6i 0.0708497 0.0230205i
\(834\) 812168. 590075.i 1.16765 0.848349i
\(835\) 289095.i 0.414636i
\(836\) 2.76829e6 + 1.44171e6i 3.96094 + 2.06284i
\(837\) 246565. 0.351950
\(838\) 207854. + 286087.i 0.295986 + 0.407389i
\(839\) −106181. 326793.i −0.150843 0.464247i 0.846873 0.531795i \(-0.178482\pi\)
−0.997716 + 0.0675483i \(0.978482\pi\)
\(840\) −365783. + 1.12576e6i −0.518400 + 1.59547i
\(841\) −198247. 144035.i −0.280294 0.203645i
\(842\) −400308. + 550977.i −0.564638 + 0.777157i
\(843\) −77848.5 25294.5i −0.109546 0.0355935i
\(844\) 62680.7 20366.2i 0.0879932 0.0285907i
\(845\) −89115.0 + 64745.8i −0.124807 + 0.0906773i
\(846\) 430551.i 0.601567i
\(847\) −182579. 597958.i −0.254498 0.833497i
\(848\) 1.45560e6 2.02419
\(849\) 158359. + 217963.i 0.219699 + 0.302390i
\(850\) 66250.6 + 203898.i 0.0916963 + 0.282212i
\(851\) −16540.0 + 50904.9i −0.0228389 + 0.0702911i
\(852\) 894412. + 649829.i 1.23214 + 0.895199i
\(853\) −129864. + 178742.i −0.178480 + 0.245657i −0.888879 0.458143i \(-0.848515\pi\)
0.710398 + 0.703800i \(0.248515\pi\)
\(854\) 605836. + 196848.i 0.830691 + 0.269908i
\(855\) −518565. + 168492.i −0.709368 + 0.230488i
\(856\) 1.84580e6 1.34105e6i 2.51905 1.83019i
\(857\) 88561.8i 0.120583i −0.998181 0.0602913i \(-0.980797\pi\)
0.998181 0.0602913i \(-0.0192030\pi\)
\(858\) −341374. + 655485.i −0.463720 + 0.890407i
\(859\) 188831. 0.255909 0.127955 0.991780i \(-0.459159\pi\)
0.127955 + 0.991780i \(0.459159\pi\)
\(860\) 212409. + 292356.i 0.287194 + 0.395289i
\(861\) 39920.8 + 122864.i 0.0538509 + 0.165736i
\(862\) −2648.53 + 8151.34i −0.00356443 + 0.0109702i
\(863\) −367870. 267273.i −0.493938 0.358867i 0.312759 0.949833i \(-0.398747\pi\)
−0.806697 + 0.590966i \(0.798747\pi\)
\(864\) −176197. + 242514.i −0.236032 + 0.324870i
\(865\) −663007. 215424.i −0.886107 0.287914i
\(866\) 1.29462e6 420647.i 1.72626 0.560896i
\(867\) 317420. 230619.i 0.422276 0.306801i
\(868\) 2.95007e6i 3.91555i
\(869\) 370913. 55365.2i 0.491171 0.0733158i
\(870\) −808531. −1.06821
\(871\) 463382. + 637791.i 0.610805 + 0.840701i
\(872\) 250479. + 770894.i 0.329411 + 1.01382i
\(873\) −54629.4 + 168132.i −0.0716799 + 0.220608i
\(874\) −1.15526e6 839345.i −1.51236 1.09880i
\(875\) −234010. + 322086.i −0.305645 + 0.420684i
\(876\) 393503. + 127857.i 0.512791 + 0.166616i
\(877\) −1.42540e6 + 463140.i −1.85326 + 0.602162i −0.857050 + 0.515232i \(0.827706\pi\)
−0.996214 + 0.0869298i \(0.972294\pi\)
\(878\) 1.03120e6 749208.i 1.33768 0.971882i
\(879\) 74756.7i 0.0967547i
\(880\) −2.42473e6 406209.i −3.13111 0.524547i
\(881\) −999336. −1.28754 −0.643768 0.765220i \(-0.722630\pi\)
−0.643768 + 0.765220i \(0.722630\pi\)
\(882\) −68157.3 93810.5i −0.0876143 0.120591i
\(883\) 313137. + 963736.i 0.401618 + 1.23605i 0.923687 + 0.383149i \(0.125160\pi\)
−0.522069 + 0.852903i \(0.674840\pi\)
\(884\) −171859. + 528926.i −0.219921 + 0.676847i
\(885\) 625989. + 454808.i 0.799246 + 0.580686i
\(886\) −91457.1 + 125880.i −0.116506 + 0.160357i
\(887\) −280958. 91288.8i −0.357104 0.116030i 0.124970 0.992160i \(-0.460116\pi\)
−0.482074 + 0.876130i \(0.660116\pi\)
\(888\) −156704. + 50916.3i −0.198726 + 0.0645701i
\(889\) 420501. 305512.i 0.532063 0.386566i
\(890\) 339427.i 0.428515i
\(891\) 61815.2 + 62926.2i 0.0778646 + 0.0792640i
\(892\) 1.38279e6 1.73791
\(893\) 827046. + 1.13833e6i 1.03711 + 1.42747i
\(894\) −387679. 1.19315e6i −0.485062 1.49287i
\(895\) 2445.66 7526.98i 0.00305317 0.00939668i
\(896\) −187449. 136190.i −0.233489 0.169640i
\(897\) 141250. 194414.i 0.175551 0.241625i
\(898\) 2.61048e6 + 848195.i 3.23718 + 1.05182i
\(899\) −1.13638e6 + 369233.i −1.40606 + 0.456858i
\(900\) 276524. 200906.i 0.341388 0.248033i
\(901\) 197346.i 0.243096i
\(902\) −468912. + 233686.i −0.576340 + 0.287223i
\(903\) 66285.1 0.0812906
\(904\) −588497. 809996.i −0.720124 0.991165i
\(905\) −493440. 1.51865e6i −0.602472 1.85422i
\(906\) 357619. 1.10064e6i 0.435676 1.34087i
\(907\) 704353. + 511742.i 0.856201 + 0.622067i 0.926849 0.375435i \(-0.122507\pi\)
−0.0706476 + 0.997501i \(0.522507\pi\)
\(908\) −1.92661e6 + 2.65175e6i −2.33680 + 3.21633i
\(909\) 32792.4 + 10654.9i 0.0396868 + 0.0128950i
\(910\) 1.46912e6 477345.i 1.77408 0.576433i
\(911\) −821849. + 597108.i −0.990274 + 0.719476i −0.959981 0.280065i \(-0.909644\pi\)
−0.0302930 + 0.999541i \(0.509644\pi\)
\(912\) 2.25129e6i 2.70671i
\(913\) −316183. 634450.i −0.379312 0.761125i
\(914\) 234565. 0.280783
\(915\) −188531. 259491.i −0.225186 0.309941i
\(916\) 258346. + 795108.i 0.307901 + 0.947622i
\(917\) 233973. 720095.i 0.278245 0.856350i
\(918\) 75559.5 + 54897.2i 0.0896610 + 0.0651426i
\(919\) 233287. 321092.i 0.276223 0.380188i −0.648255 0.761423i \(-0.724501\pi\)
0.924478 + 0.381235i \(0.124501\pi\)
\(920\) 1.48452e6 + 482351.i 1.75393 + 0.569885i
\(921\) 401700. 130520.i 0.473568 0.153872i
\(922\) −1.12719e6 + 818953.i −1.32598 + 0.963378i
\(923\) 855498.i 1.00419i
\(924\) −752890. + 739598.i −0.881836 + 0.866266i
\(925\) 58911.1 0.0688516
\(926\) −1.77758e6 2.44663e6i −2.07304 2.85330i
\(927\) 91512.9 + 281648.i 0.106493 + 0.327753i
\(928\) 448898. 1.38156e6i 0.521256 1.60426i
\(929\) 583560. + 423981.i 0.676168 + 0.491264i 0.872084 0.489356i \(-0.162768\pi\)
−0.195917 + 0.980621i \(0.562768\pi\)
\(930\) 1.22849e6 1.69087e6i 1.42038 1.95499i
\(931\) 360401. + 117102.i 0.415803 + 0.135102i
\(932\) 2.61037e6 848160.i 3.00518 0.976441i
\(933\) 339691. 246800.i 0.390231 0.283519i
\(934\) 1.69454e6i 1.94249i
\(935\) −55072.6 + 328738.i −0.0629959 + 0.376034i
\(936\) 739761. 0.844383
\(937\) −503823. 693453.i −0.573850 0.789837i 0.419154 0.907915i \(-0.362327\pi\)
−0.993004 + 0.118078i \(0.962327\pi\)
\(938\) 489492. + 1.50650e6i 0.556340 + 1.71224i
\(939\) −153026. + 470965.i −0.173553 + 0.534142i
\(940\) −2.09844e6 1.52461e6i −2.37488 1.72545i
\(941\) −5816.43 + 8005.63i −0.00656867 + 0.00904099i −0.812289 0.583256i \(-0.801779\pi\)
0.805720 + 0.592297i \(0.201779\pi\)
\(942\) −189018. 61415.6i −0.213010 0.0692113i
\(943\) 162018. 52642.7i 0.182196 0.0591991i
\(944\) −2.58465e6 + 1.87786e6i −2.90040 + 2.10726i
\(945\) 184369.i 0.206454i
\(946\) 39686.3 + 265874.i 0.0443464 + 0.297093i
\(947\) 150146. 0.167423 0.0837114 0.996490i \(-0.473323\pi\)
0.0837114 + 0.996490i \(0.473323\pi\)
\(948\) −372102. 512155.i −0.414043 0.569881i
\(949\) −98938.0 304500.i −0.109858 0.338107i
\(950\) −485678. + 1.49476e6i −0.538147 + 1.65625i
\(951\) −13000.6 9445.51i −0.0143749 0.0104439i
\(952\) −389476. + 536067.i −0.429741 + 0.591487i
\(953\) 672400. + 218476.i 0.740358 + 0.240557i 0.654827 0.755779i \(-0.272741\pi\)
0.0855309 + 0.996336i \(0.472741\pi\)
\(954\) −421024. + 136799.i −0.462605 + 0.150309i
\(955\) −789409. + 573540.i −0.865557 + 0.628864i
\(956\) 3.97944e6i 4.35418i
\(957\) −379129. 197449.i −0.413964 0.215591i
\(958\) −1.43062e6 −1.55881
\(959\) 381188. + 524660.i 0.414478 + 0.570481i
\(960\) 263198. + 810041.i 0.285589 + 0.878951i
\(961\) 669071. 2.05919e6i 0.724478 2.22972i
\(962\) 173957. + 126387.i 0.187971 + 0.136569i
\(963\) −208877. + 287495.i −0.225236 + 0.310011i
\(964\) −2.74183e6 890873.i −2.95043 0.958654i
\(965\) 1.38025e6 448471.i 1.48219 0.481592i
\(966\) 390634. 283812.i 0.418616 0.304142i
\(967\) 1.59915e6i 1.71016i −0.518493 0.855082i \(-0.673507\pi\)
0.518493 0.855082i \(-0.326493\pi\)
\(968\) −2.02637e6 1.52812e6i −2.16256 1.63082i
\(969\) −305223. −0.325065
\(970\) 880810. + 1.21233e6i 0.936135 + 1.28848i
\(971\) 221471. + 681618.i 0.234898 + 0.722940i 0.997135 + 0.0756429i \(0.0241009\pi\)
−0.762237 + 0.647298i \(0.775899\pi\)
\(972\) 46013.1 141614.i 0.0487023 0.149890i
\(973\) −897476. 652054.i −0.947975 0.688744i
\(974\) 982136. 1.35179e6i 1.03527 1.42493i
\(975\) −251548. 81732.8i −0.264613 0.0859779i
\(976\) 1.25952e6 409243.i 1.32223 0.429617i
\(977\) 95869.6 69653.3i 0.100437 0.0729714i −0.536434 0.843943i \(-0.680229\pi\)
0.636870 + 0.770971i \(0.280229\pi\)
\(978\) 1.09205e6i 1.14173i
\(979\) 82890.3 159161.i 0.0864845 0.166062i
\(980\) −698568. −0.727372
\(981\) −74208.5 102139.i −0.0771108 0.106134i
\(982\) 69939.0 + 215250.i 0.0725265 + 0.223214i
\(983\) −439511. + 1.35268e6i −0.454845 + 1.39987i 0.416473 + 0.909148i \(0.363266\pi\)
−0.871317 + 0.490720i \(0.836734\pi\)
\(984\) 424264. + 308246.i 0.438173 + 0.318351i
\(985\) 321875. 443023.i 0.331753 0.456619i
\(986\) −430451. 139862.i −0.442761 0.143862i
\(987\) −452489. + 147022.i −0.464487 + 0.150921i
\(988\) −3.29841e6 + 2.39644e6i −3.37902 + 2.45500i
\(989\) 87408.8i 0.0893640i
\(990\) 739516. 110386.i 0.754531 0.112627i
\(991\) 1.18582e6 1.20746 0.603729 0.797190i \(-0.293681\pi\)
0.603729 + 0.797190i \(0.293681\pi\)
\(992\) 2.20719e6 + 3.03793e6i 2.24293 + 3.08713i
\(993\) 302233. + 930177.i 0.306509 + 0.943337i
\(994\) 531183. 1.63481e6i 0.537615 1.65461i
\(995\) 98616.4 + 71649.0i 0.0996100 + 0.0723709i
\(996\) −703352. + 968081.i −0.709013 + 0.975872i
\(997\) 219810. + 71420.5i 0.221134 + 0.0718510i 0.417489 0.908682i \(-0.362910\pi\)
−0.196354 + 0.980533i \(0.562910\pi\)
\(998\) −1.02654e6 + 333544.i −1.03066 + 0.334882i
\(999\) 20762.5 15084.8i 0.0208041 0.0151150i
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 33.5.g.a.19.1 yes 32
3.2 odd 2 99.5.k.c.19.8 32
11.2 odd 10 363.5.c.e.241.2 32
11.7 odd 10 inner 33.5.g.a.7.1 32
11.9 even 5 363.5.c.e.241.31 32
33.29 even 10 99.5.k.c.73.8 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.5.g.a.7.1 32 11.7 odd 10 inner
33.5.g.a.19.1 yes 32 1.1 even 1 trivial
99.5.k.c.19.8 32 3.2 odd 2
99.5.k.c.73.8 32 33.29 even 10
363.5.c.e.241.2 32 11.2 odd 10
363.5.c.e.241.31 32 11.9 even 5