Properties

Label 9.5.d.a.2.1
Level $9$
Weight $5$
Character 9.2
Analytic conductor $0.930$
Analytic rank $0$
Dimension $6$
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] = [9,5,Mod(2,9)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("9.2");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9 = 3^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 9.d (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.930329667755\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{6})\)
Coefficient field: 6.0.39400128.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 11x^{4} + 14x^{3} + 98x^{2} + 20x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 2.1
Root \(1.89154 - 3.27625i\) of defining polynomial
Character \(\chi\) \(=\) 9.2
Dual form 9.5.d.a.5.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.67463 - 3.27625i) q^{2} +(-1.11837 - 8.93024i) q^{3} +(13.4676 + 23.3266i) q^{4} +(10.2044 - 5.89150i) q^{5} +(-22.9114 + 54.3399i) q^{6} +(26.6364 - 46.1356i) q^{7} -71.6534i q^{8} +(-78.4985 + 19.9746i) q^{9} +O(q^{10})\) \(q+(-5.67463 - 3.27625i) q^{2} +(-1.11837 - 8.93024i) q^{3} +(13.4676 + 23.3266i) q^{4} +(10.2044 - 5.89150i) q^{5} +(-22.9114 + 54.3399i) q^{6} +(26.6364 - 46.1356i) q^{7} -71.6534i q^{8} +(-78.4985 + 19.9746i) q^{9} -77.2081 q^{10} +(108.228 + 62.4856i) q^{11} +(193.251 - 146.357i) q^{12} +(37.3052 + 64.6145i) q^{13} +(-302.304 + 174.535i) q^{14} +(-64.0248 - 84.5387i) q^{15} +(-19.2722 + 33.3805i) q^{16} +7.70989i q^{17} +(510.892 + 143.832i) q^{18} -54.1307 q^{19} +(274.858 + 158.689i) q^{20} +(-441.792 - 186.273i) q^{21} +(-409.437 - 709.166i) q^{22} +(346.370 - 199.977i) q^{23} +(-639.882 + 80.1350i) q^{24} +(-243.080 + 421.028i) q^{25} -488.885i q^{26} +(266.169 + 678.672i) q^{27} +1434.92 q^{28} +(-468.219 - 270.326i) q^{29} +(86.3473 + 689.487i) q^{30} +(766.083 + 1326.89i) q^{31} +(-774.133 + 446.946i) q^{32} +(436.973 - 1036.39i) q^{33} +(25.2595 - 43.7508i) q^{34} -627.714i q^{35} +(-1523.13 - 1562.09i) q^{36} -1719.10 q^{37} +(307.172 + 177.346i) q^{38} +(535.302 - 405.408i) q^{39} +(-422.146 - 731.178i) q^{40} +(1090.87 - 629.816i) q^{41} +(1896.73 + 2504.45i) q^{42} +(1303.89 - 2258.41i) q^{43} +3366.13i q^{44} +(-683.348 + 666.303i) q^{45} -2620.70 q^{46} +(-692.850 - 400.017i) q^{47} +(319.649 + 134.774i) q^{48} +(-218.498 - 378.449i) q^{49} +(2758.78 - 1592.79i) q^{50} +(68.8512 - 8.62251i) q^{51} +(-1004.83 + 1740.41i) q^{52} +4229.81i q^{53} +(713.088 - 4723.25i) q^{54} +1472.54 q^{55} +(-3305.77 - 1908.59i) q^{56} +(60.5381 + 483.400i) q^{57} +(1771.31 + 3068.01i) q^{58} +(-2886.63 + 1666.60i) q^{59} +(1109.74 - 2632.02i) q^{60} +(7.50843 - 13.0050i) q^{61} -10039.5i q^{62} +(-1169.38 + 4153.63i) q^{63} +6473.94 q^{64} +(761.353 + 439.567i) q^{65} +(-5875.12 + 4449.48i) q^{66} +(-2591.20 - 4488.08i) q^{67} +(-179.846 + 103.834i) q^{68} +(-2173.21 - 2869.52i) q^{69} +(-2056.55 + 3562.05i) q^{70} +1924.16i q^{71} +(1431.25 + 5624.68i) q^{72} +949.554 q^{73} +(9755.28 + 5632.21i) q^{74} +(4031.73 + 1699.90i) q^{75} +(-729.012 - 1262.69i) q^{76} +(5765.63 - 3328.79i) q^{77} +(-4365.86 + 546.754i) q^{78} +(118.990 - 206.097i) q^{79} +454.169i q^{80} +(5763.03 - 3135.96i) q^{81} -8253.75 q^{82} +(-11402.0 - 6582.95i) q^{83} +(-1604.77 - 12814.2i) q^{84} +(45.4228 + 78.6746i) q^{85} +(-14798.2 + 8543.77i) q^{86} +(-1890.44 + 4483.64i) q^{87} +(4477.31 - 7754.92i) q^{88} +575.925i q^{89} +(6060.72 - 1542.20i) q^{90} +3974.71 q^{91} +(9329.58 + 5386.44i) q^{92} +(10992.7 - 8325.27i) q^{93} +(2621.11 + 4539.90i) q^{94} +(-552.370 + 318.911i) q^{95} +(4857.10 + 6413.34i) q^{96} +(-7561.70 + 13097.3i) q^{97} +2863.41i q^{98} +(-9743.88 - 2743.21i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} - 3 q^{3} + 15 q^{4} - 12 q^{5} - 99 q^{6} + 12 q^{7} + 99 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{2} - 3 q^{3} + 15 q^{4} - 12 q^{5} - 99 q^{6} + 12 q^{7} + 99 q^{9} - 36 q^{10} + 483 q^{11} + 330 q^{12} - 6 q^{13} - 1146 q^{14} - 1026 q^{15} + 15 q^{16} + 1404 q^{18} - 258 q^{19} + 1614 q^{20} + 480 q^{21} - 369 q^{22} - 282 q^{23} - 1449 q^{24} - 273 q^{25} + 54 q^{27} + 1308 q^{28} - 1056 q^{29} - 1278 q^{30} + 1290 q^{31} - 1161 q^{32} + 279 q^{33} + 513 q^{34} - 2385 q^{36} + 12 q^{37} - 789 q^{38} + 1974 q^{39} - 1314 q^{40} + 7629 q^{41} + 9612 q^{42} - 285 q^{43} - 4212 q^{45} - 5760 q^{46} - 9642 q^{47} - 6771 q^{48} - 1863 q^{49} + 3027 q^{50} + 2457 q^{51} - 240 q^{52} - 405 q^{54} + 2016 q^{55} - 462 q^{56} + 5367 q^{57} + 6462 q^{58} + 6225 q^{59} + 7470 q^{60} + 3630 q^{61} - 7578 q^{63} + 15450 q^{64} - 7158 q^{65} - 13734 q^{66} - 5055 q^{67} - 10503 q^{68} - 13878 q^{69} - 9684 q^{70} + 8451 q^{72} - 14622 q^{73} + 26454 q^{74} + 21021 q^{75} - 4047 q^{76} + 2580 q^{77} - 12060 q^{78} + 4764 q^{79} + 18387 q^{81} - 9702 q^{82} - 1866 q^{83} - 6486 q^{84} + 12366 q^{85} - 37731 q^{86} - 21564 q^{87} + 14787 q^{88} + 20790 q^{90} + 34836 q^{91} + 33636 q^{92} + 19254 q^{93} - 12708 q^{94} - 13362 q^{95} - 3672 q^{96} - 28959 q^{97} - 9126 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/9\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.67463 3.27625i −1.41866 0.819063i −0.422477 0.906374i \(-0.638839\pi\)
−0.996181 + 0.0873110i \(0.972173\pi\)
\(3\) −1.11837 8.93024i −0.124263 0.992249i
\(4\) 13.4676 + 23.3266i 0.841727 + 1.45791i
\(5\) 10.2044 5.89150i 0.408175 0.235660i −0.281830 0.959464i \(-0.590942\pi\)
0.690005 + 0.723804i \(0.257608\pi\)
\(6\) −22.9114 + 54.3399i −0.636427 + 1.50944i
\(7\) 26.6364 46.1356i 0.543600 0.941544i −0.455093 0.890444i \(-0.650394\pi\)
0.998694 0.0510997i \(-0.0162726\pi\)
\(8\) 71.6534i 1.11958i
\(9\) −78.4985 + 19.9746i −0.969117 + 0.246601i
\(10\) −77.2081 −0.772081
\(11\) 108.228 + 62.4856i 0.894449 + 0.516410i 0.875395 0.483408i \(-0.160601\pi\)
0.0190536 + 0.999818i \(0.493935\pi\)
\(12\) 193.251 146.357i 1.34202 1.01637i
\(13\) 37.3052 + 64.6145i 0.220741 + 0.382334i 0.955033 0.296499i \(-0.0958192\pi\)
−0.734292 + 0.678833i \(0.762486\pi\)
\(14\) −302.304 + 174.535i −1.54237 + 0.890486i
\(15\) −64.0248 84.5387i −0.284555 0.375727i
\(16\) −19.2722 + 33.3805i −0.0752822 + 0.130393i
\(17\) 7.70989i 0.0266778i 0.999911 + 0.0133389i \(0.00424603\pi\)
−0.999911 + 0.0133389i \(0.995754\pi\)
\(18\) 510.892 + 143.832i 1.57683 + 0.443926i
\(19\) −54.1307 −0.149946 −0.0749732 0.997186i \(-0.523887\pi\)
−0.0749732 + 0.997186i \(0.523887\pi\)
\(20\) 274.858 + 158.689i 0.687144 + 0.396723i
\(21\) −441.792 186.273i −1.00180 0.422388i
\(22\) −409.437 709.166i −0.845944 1.46522i
\(23\) 346.370 199.977i 0.654765 0.378029i −0.135515 0.990775i \(-0.543269\pi\)
0.790279 + 0.612747i \(0.209935\pi\)
\(24\) −639.882 + 80.1350i −1.11091 + 0.139123i
\(25\) −243.080 + 421.028i −0.388929 + 0.673644i
\(26\) 488.885i 0.723202i
\(27\) 266.169 + 678.672i 0.365115 + 0.930962i
\(28\) 1434.92 1.83025
\(29\) −468.219 270.326i −0.556741 0.321435i 0.195095 0.980784i \(-0.437498\pi\)
−0.751836 + 0.659350i \(0.770832\pi\)
\(30\) 86.3473 + 689.487i 0.0959414 + 0.766097i
\(31\) 766.083 + 1326.89i 0.797173 + 1.38074i 0.921450 + 0.388496i \(0.127005\pi\)
−0.124278 + 0.992247i \(0.539661\pi\)
\(32\) −774.133 + 446.946i −0.755989 + 0.436470i
\(33\) 436.973 1036.39i 0.401260 0.951687i
\(34\) 25.2595 43.7508i 0.0218508 0.0378467i
\(35\) 627.714i 0.512419i
\(36\) −1523.13 1562.09i −1.17525 1.20532i
\(37\) −1719.10 −1.25574 −0.627868 0.778320i \(-0.716072\pi\)
−0.627868 + 0.778320i \(0.716072\pi\)
\(38\) 307.172 + 177.346i 0.212723 + 0.122816i
\(39\) 535.302 405.408i 0.351941 0.266540i
\(40\) −422.146 731.178i −0.263841 0.456986i
\(41\) 1090.87 629.816i 0.648944 0.374668i −0.139108 0.990277i \(-0.544423\pi\)
0.788051 + 0.615610i \(0.211090\pi\)
\(42\) 1896.73 + 2504.45i 1.07524 + 1.41976i
\(43\) 1303.89 2258.41i 0.705189 1.22142i −0.261434 0.965221i \(-0.584196\pi\)
0.966623 0.256202i \(-0.0824711\pi\)
\(44\) 3366.13i 1.73871i
\(45\) −683.348 + 666.303i −0.337456 + 0.329038i
\(46\) −2620.70 −1.23852
\(47\) −692.850 400.017i −0.313649 0.181085i 0.334909 0.942250i \(-0.391294\pi\)
−0.648558 + 0.761165i \(0.724628\pi\)
\(48\) 319.649 + 134.774i 0.138737 + 0.0584957i
\(49\) −218.498 378.449i −0.0910029 0.157622i
\(50\) 2758.78 1592.79i 1.10351 0.637114i
\(51\) 68.8512 8.62251i 0.0264710 0.00331508i
\(52\) −1004.83 + 1740.41i −0.371607 + 0.643643i
\(53\) 4229.81i 1.50581i 0.658131 + 0.752904i \(0.271347\pi\)
−0.658131 + 0.752904i \(0.728653\pi\)
\(54\) 713.088 4723.25i 0.244543 1.61977i
\(55\) 1472.54 0.486789
\(56\) −3305.77 1908.59i −1.05414 0.608606i
\(57\) 60.5381 + 483.400i 0.0186329 + 0.148784i
\(58\) 1771.31 + 3068.01i 0.526550 + 0.912011i
\(59\) −2886.63 + 1666.60i −0.829253 + 0.478769i −0.853597 0.520934i \(-0.825584\pi\)
0.0243441 + 0.999704i \(0.492250\pi\)
\(60\) 1109.74 2632.02i 0.308261 0.731116i
\(61\) 7.50843 13.0050i 0.00201785 0.00349502i −0.865015 0.501746i \(-0.832691\pi\)
0.867033 + 0.498251i \(0.166024\pi\)
\(62\) 10039.5i 2.61174i
\(63\) −1169.38 + 4153.63i −0.294627 + 1.04652i
\(64\) 6473.94 1.58055
\(65\) 761.353 + 439.567i 0.180202 + 0.104040i
\(66\) −5875.12 + 4449.48i −1.34874 + 1.02146i
\(67\) −2591.20 4488.08i −0.577233 0.999796i −0.995795 0.0916081i \(-0.970799\pi\)
0.418563 0.908188i \(-0.362534\pi\)
\(68\) −179.846 + 103.834i −0.0388940 + 0.0224554i
\(69\) −2173.21 2869.52i −0.456462 0.602715i
\(70\) −2056.55 + 3562.05i −0.419704 + 0.726948i
\(71\) 1924.16i 0.381701i 0.981619 + 0.190851i \(0.0611246\pi\)
−0.981619 + 0.190851i \(0.938875\pi\)
\(72\) 1431.25 + 5624.68i 0.276090 + 1.08501i
\(73\) 949.554 0.178186 0.0890931 0.996023i \(-0.471603\pi\)
0.0890931 + 0.996023i \(0.471603\pi\)
\(74\) 9755.28 + 5632.21i 1.78146 + 1.02853i
\(75\) 4031.73 + 1699.90i 0.716753 + 0.302205i
\(76\) −729.012 1262.69i −0.126214 0.218609i
\(77\) 5765.63 3328.79i 0.972445 0.561442i
\(78\) −4365.86 + 546.754i −0.717597 + 0.0898676i
\(79\) 118.990 206.097i 0.0190659 0.0330231i −0.856335 0.516421i \(-0.827264\pi\)
0.875401 + 0.483398i \(0.160597\pi\)
\(80\) 454.169i 0.0709640i
\(81\) 5763.03 3135.96i 0.878376 0.477970i
\(82\) −8253.75 −1.22751
\(83\) −11402.0 6582.95i −1.65510 0.955574i −0.974927 0.222526i \(-0.928570\pi\)
−0.680177 0.733048i \(-0.738097\pi\)
\(84\) −1604.77 12814.2i −0.227433 1.81607i
\(85\) 45.4228 + 78.6746i 0.00628689 + 0.0108892i
\(86\) −14798.2 + 8543.77i −2.00084 + 1.15519i
\(87\) −1890.44 + 4483.64i −0.249761 + 0.592368i
\(88\) 4477.31 7754.92i 0.578164 1.00141i
\(89\) 575.925i 0.0727086i 0.999339 + 0.0363543i \(0.0115745\pi\)
−0.999339 + 0.0363543i \(0.988426\pi\)
\(90\) 6060.72 1542.20i 0.748237 0.190396i
\(91\) 3974.71 0.479979
\(92\) 9329.58 + 5386.44i 1.10227 + 0.636394i
\(93\) 10992.7 8325.27i 1.27098 0.962570i
\(94\) 2621.11 + 4539.90i 0.296640 + 0.513796i
\(95\) −552.370 + 318.911i −0.0612044 + 0.0353364i
\(96\) 4857.10 + 6413.34i 0.527029 + 0.695892i
\(97\) −7561.70 + 13097.3i −0.803667 + 1.39199i 0.113520 + 0.993536i \(0.463787\pi\)
−0.917187 + 0.398456i \(0.869546\pi\)
\(98\) 2863.41i 0.298148i
\(99\) −9743.88 2743.21i −0.994172 0.279890i
\(100\) −13094.9 −1.30949
\(101\) 9578.90 + 5530.38i 0.939016 + 0.542141i 0.889652 0.456640i \(-0.150947\pi\)
0.0493643 + 0.998781i \(0.484280\pi\)
\(102\) −418.955 176.644i −0.0402686 0.0169785i
\(103\) 1781.46 + 3085.58i 0.167920 + 0.290846i 0.937688 0.347478i \(-0.112962\pi\)
−0.769769 + 0.638323i \(0.779628\pi\)
\(104\) 4629.85 2673.04i 0.428055 0.247138i
\(105\) −5605.64 + 702.017i −0.508448 + 0.0636750i
\(106\) 13857.9 24002.6i 1.23335 2.13623i
\(107\) 11432.7i 0.998576i −0.866436 0.499288i \(-0.833595\pi\)
0.866436 0.499288i \(-0.166405\pi\)
\(108\) −12246.5 + 15348.9i −1.04994 + 1.31592i
\(109\) −4780.43 −0.402359 −0.201180 0.979554i \(-0.564478\pi\)
−0.201180 + 0.979554i \(0.564478\pi\)
\(110\) −8356.10 4824.40i −0.690587 0.398710i
\(111\) 1922.59 + 15352.0i 0.156042 + 1.24600i
\(112\) 1026.69 + 1778.27i 0.0818468 + 0.141763i
\(113\) 3889.66 2245.69i 0.304617 0.175871i −0.339898 0.940462i \(-0.610393\pi\)
0.644515 + 0.764592i \(0.277059\pi\)
\(114\) 1240.21 2941.46i 0.0954300 0.226335i
\(115\) 2356.33 4081.28i 0.178172 0.308604i
\(116\) 14562.6i 1.08224i
\(117\) −4219.05 4326.98i −0.308208 0.316092i
\(118\) 21840.7 1.56857
\(119\) 355.701 + 205.364i 0.0251183 + 0.0145021i
\(120\) −6057.48 + 4587.59i −0.420658 + 0.318583i
\(121\) 488.406 + 845.944i 0.0333588 + 0.0577791i
\(122\) −85.2151 + 49.1990i −0.00572528 + 0.00330549i
\(123\) −6844.42 9037.40i −0.452404 0.597356i
\(124\) −20634.7 + 35740.3i −1.34200 + 2.32442i
\(125\) 13092.8i 0.837940i
\(126\) 20244.1 19739.2i 1.27514 1.24333i
\(127\) 13521.3 0.838322 0.419161 0.907912i \(-0.362324\pi\)
0.419161 + 0.907912i \(0.362324\pi\)
\(128\) −24351.1 14059.1i −1.48627 0.858100i
\(129\) −21626.4 9118.35i −1.29959 0.547945i
\(130\) −2880.26 4988.76i −0.170430 0.295193i
\(131\) 2941.86 1698.48i 0.171427 0.0989735i −0.411831 0.911260i \(-0.635111\pi\)
0.583259 + 0.812287i \(0.301777\pi\)
\(132\) 30060.4 3764.59i 1.72523 0.216057i
\(133\) −1441.85 + 2497.35i −0.0815110 + 0.141181i
\(134\) 33957.6i 1.89116i
\(135\) 6714.48 + 5357.29i 0.368421 + 0.293953i
\(136\) 552.439 0.0298680
\(137\) 3310.98 + 1911.60i 0.176407 + 0.101849i 0.585603 0.810598i \(-0.300858\pi\)
−0.409197 + 0.912446i \(0.634191\pi\)
\(138\) 2930.91 + 23403.5i 0.153902 + 1.22892i
\(139\) −1738.31 3010.85i −0.0899702 0.155833i 0.817528 0.575889i \(-0.195344\pi\)
−0.907498 + 0.420056i \(0.862010\pi\)
\(140\) 14642.4 8453.82i 0.747064 0.431317i
\(141\) −2797.39 + 6634.68i −0.140707 + 0.333720i
\(142\) 6304.02 10918.9i 0.312637 0.541504i
\(143\) 9324.16i 0.455971i
\(144\) 846.078 3005.27i 0.0408024 0.144930i
\(145\) −6370.51 −0.302997
\(146\) −5388.37 3110.98i −0.252785 0.145946i
\(147\) −3135.28 + 2374.49i −0.145092 + 0.109884i
\(148\) −23152.3 40100.9i −1.05699 1.83076i
\(149\) 7717.10 4455.47i 0.347602 0.200688i −0.316027 0.948750i \(-0.602349\pi\)
0.663628 + 0.748062i \(0.269016\pi\)
\(150\) −17309.3 22855.3i −0.769302 1.01579i
\(151\) 4957.66 8586.92i 0.217432 0.376603i −0.736590 0.676339i \(-0.763565\pi\)
0.954022 + 0.299736i \(0.0968987\pi\)
\(152\) 3878.65i 0.167878i
\(153\) −154.002 605.215i −0.00657876 0.0258539i
\(154\) −43623.8 −1.83942
\(155\) 15634.8 + 9026.75i 0.650772 + 0.375723i
\(156\) 16666.0 + 7026.92i 0.684831 + 0.288746i
\(157\) −2823.47 4890.39i −0.114547 0.198401i 0.803052 0.595909i \(-0.203208\pi\)
−0.917599 + 0.397508i \(0.869875\pi\)
\(158\) −1350.45 + 779.684i −0.0540960 + 0.0312323i
\(159\) 37773.3 4730.50i 1.49414 0.187117i
\(160\) −5266.36 + 9121.60i −0.205717 + 0.356313i
\(161\) 21306.7i 0.821986i
\(162\) −42977.2 1085.71i −1.63760 0.0413698i
\(163\) −2153.55 −0.0810552 −0.0405276 0.999178i \(-0.512904\pi\)
−0.0405276 + 0.999178i \(0.512904\pi\)
\(164\) 29383.0 + 16964.3i 1.09247 + 0.630736i
\(165\) −1646.84 13150.1i −0.0604900 0.483016i
\(166\) 43134.8 + 74711.7i 1.56535 + 2.71127i
\(167\) −32060.4 + 18510.1i −1.14957 + 0.663706i −0.948783 0.315929i \(-0.897684\pi\)
−0.200789 + 0.979635i \(0.564351\pi\)
\(168\) −13347.1 + 31655.9i −0.472899 + 1.12159i
\(169\) 11497.1 19913.6i 0.402547 0.697232i
\(170\) 595.266i 0.0205974i
\(171\) 4249.18 1081.24i 0.145316 0.0369769i
\(172\) 70241.5 2.37431
\(173\) −42076.2 24292.7i −1.40587 0.811678i −0.410882 0.911689i \(-0.634779\pi\)
−0.994986 + 0.100010i \(0.968112\pi\)
\(174\) 25417.1 19249.4i 0.839512 0.635799i
\(175\) 12949.6 + 22429.3i 0.422844 + 0.732387i
\(176\) −4171.60 + 2408.48i −0.134672 + 0.0777530i
\(177\) 18111.4 + 23914.4i 0.578104 + 0.763332i
\(178\) 1886.87 3268.16i 0.0595529 0.103149i
\(179\) 47717.9i 1.48928i −0.667468 0.744639i \(-0.732622\pi\)
0.667468 0.744639i \(-0.267378\pi\)
\(180\) −24745.7 6966.68i −0.763755 0.215021i
\(181\) −45767.2 −1.39700 −0.698502 0.715608i \(-0.746150\pi\)
−0.698502 + 0.715608i \(0.746150\pi\)
\(182\) −22555.0 13022.1i −0.680927 0.393133i
\(183\) −124.535 52.5077i −0.00371868 0.00156791i
\(184\) −14329.0 24818.6i −0.423235 0.733064i
\(185\) −17542.4 + 10128.1i −0.512560 + 0.295927i
\(186\) −89655.3 + 11227.9i −2.59149 + 0.324543i
\(187\) −481.757 + 834.428i −0.0137767 + 0.0238619i
\(188\) 21549.1i 0.609697i
\(189\) 38400.7 + 5797.52i 1.07502 + 0.162300i
\(190\) 4179.33 0.115771
\(191\) 40460.3 + 23359.7i 1.10908 + 0.640326i 0.938590 0.345034i \(-0.112133\pi\)
0.170487 + 0.985360i \(0.445466\pi\)
\(192\) −7240.26 57813.8i −0.196405 1.56830i
\(193\) 13603.9 + 23562.6i 0.365215 + 0.632571i 0.988811 0.149176i \(-0.0476621\pi\)
−0.623596 + 0.781747i \(0.714329\pi\)
\(194\) 85819.8 49548.1i 2.28026 1.31651i
\(195\) 3073.97 7290.66i 0.0808407 0.191733i
\(196\) 5885.30 10193.6i 0.153199 0.265349i
\(197\) 64665.2i 1.66624i 0.553090 + 0.833122i \(0.313449\pi\)
−0.553090 + 0.833122i \(0.686551\pi\)
\(198\) 46305.5 + 47490.1i 1.18114 + 1.21136i
\(199\) −25841.3 −0.652542 −0.326271 0.945276i \(-0.605792\pi\)
−0.326271 + 0.945276i \(0.605792\pi\)
\(200\) 30168.1 + 17417.5i 0.754201 + 0.435438i
\(201\) −37181.8 + 28159.4i −0.920318 + 0.696997i
\(202\) −36237.8 62765.8i −0.888095 1.53823i
\(203\) −24943.4 + 14401.1i −0.605289 + 0.349464i
\(204\) 1128.40 + 1489.94i 0.0271145 + 0.0358021i
\(205\) 7421.13 12853.8i 0.176588 0.305860i
\(206\) 23346.0i 0.550147i
\(207\) −23195.1 + 22616.5i −0.541322 + 0.527819i
\(208\) −2875.82 −0.0664714
\(209\) −5858.47 3382.39i −0.134119 0.0774339i
\(210\) 34109.9 + 14381.8i 0.773467 + 0.326118i
\(211\) −23029.3 39888.0i −0.517269 0.895936i −0.999799 0.0200565i \(-0.993615\pi\)
0.482530 0.875879i \(-0.339718\pi\)
\(212\) −98667.3 + 56965.6i −2.19534 + 1.26748i
\(213\) 17183.2 2151.92i 0.378743 0.0474315i
\(214\) −37456.4 + 64876.4i −0.817896 + 1.41664i
\(215\) 30727.6i 0.664739i
\(216\) 48629.1 19071.9i 1.04229 0.408777i
\(217\) 81622.8 1.73337
\(218\) 27127.2 + 15661.9i 0.570810 + 0.329558i
\(219\) −1061.95 8479.75i −0.0221420 0.176805i
\(220\) 19831.6 + 34349.3i 0.409743 + 0.709696i
\(221\) −498.171 + 287.619i −0.0101998 + 0.00588888i
\(222\) 39387.0 93415.9i 0.799185 1.89546i
\(223\) −10955.5 + 18975.6i −0.220305 + 0.381579i −0.954901 0.296926i \(-0.904039\pi\)
0.734596 + 0.678505i \(0.237372\pi\)
\(224\) 47620.1i 0.949062i
\(225\) 10671.6 37905.5i 0.210797 0.748750i
\(226\) −29429.8 −0.576197
\(227\) 43115.6 + 24892.8i 0.836726 + 0.483084i 0.856150 0.516727i \(-0.172850\pi\)
−0.0194241 + 0.999811i \(0.506183\pi\)
\(228\) −10460.8 + 7922.41i −0.201231 + 0.152401i
\(229\) −14260.5 24699.9i −0.271934 0.471003i 0.697423 0.716660i \(-0.254330\pi\)
−0.969357 + 0.245656i \(0.920996\pi\)
\(230\) −26742.6 + 15439.9i −0.505531 + 0.291869i
\(231\) −36175.0 47765.6i −0.677929 0.895141i
\(232\) −19369.8 + 33549.5i −0.359873 + 0.623318i
\(233\) 44050.2i 0.811403i −0.914006 0.405701i \(-0.867027\pi\)
0.914006 0.405701i \(-0.132973\pi\)
\(234\) 9765.30 + 38376.7i 0.178342 + 0.700868i
\(235\) −9426.80 −0.170698
\(236\) −77752.1 44890.2i −1.39601 0.805986i
\(237\) −1973.57 832.119i −0.0351363 0.0148146i
\(238\) −1345.65 2330.73i −0.0237562 0.0411470i
\(239\) 17818.6 10287.6i 0.311945 0.180102i −0.335851 0.941915i \(-0.609024\pi\)
0.647797 + 0.761813i \(0.275691\pi\)
\(240\) 4055.84 507.930i 0.0704140 0.00881823i
\(241\) 28958.8 50158.0i 0.498593 0.863588i −0.501406 0.865212i \(-0.667184\pi\)
0.999999 + 0.00162435i \(0.000517045\pi\)
\(242\) 6400.56i 0.109292i
\(243\) −34450.1 47958.1i −0.583415 0.812174i
\(244\) 404.483 0.00679392
\(245\) −4459.27 2574.56i −0.0742902 0.0428915i
\(246\) 9230.75 + 73708.0i 0.152534 + 1.21799i
\(247\) −2019.36 3497.63i −0.0330993 0.0573297i
\(248\) 95076.5 54892.4i 1.54586 0.892502i
\(249\) −46035.7 + 109185.i −0.742499 + 1.76102i
\(250\) 42895.3 74296.9i 0.686325 1.18875i
\(251\) 54140.4i 0.859357i 0.902982 + 0.429679i \(0.141373\pi\)
−0.902982 + 0.429679i \(0.858627\pi\)
\(252\) −112639. + 28662.0i −1.77373 + 0.451341i
\(253\) 49982.8 0.780871
\(254\) −76728.4 44299.2i −1.18929 0.686639i
\(255\) 651.784 493.624i 0.0100236 0.00759130i
\(256\) 40330.8 + 69855.0i 0.615399 + 1.06590i
\(257\) 98522.7 56882.1i 1.49166 0.861211i 0.491706 0.870761i \(-0.336373\pi\)
0.999954 + 0.00955057i \(0.00304009\pi\)
\(258\) 92847.8 + 122597.i 1.39487 + 1.84179i
\(259\) −45790.8 + 79311.9i −0.682619 + 1.18233i
\(260\) 23679.7i 0.350292i
\(261\) 42154.2 + 11867.7i 0.618813 + 0.174215i
\(262\) −22258.6 −0.324262
\(263\) 38420.1 + 22181.8i 0.555452 + 0.320691i 0.751318 0.659940i \(-0.229418\pi\)
−0.195866 + 0.980631i \(0.562752\pi\)
\(264\) −74260.6 31310.6i −1.06549 0.449245i
\(265\) 24919.9 + 43162.6i 0.354859 + 0.614633i
\(266\) 16363.9 9447.71i 0.231272 0.133525i
\(267\) 5143.15 644.097i 0.0721451 0.00903502i
\(268\) 69794.6 120888.i 0.971745 1.68311i
\(269\) 4429.77i 0.0612176i 0.999531 + 0.0306088i \(0.00974461\pi\)
−0.999531 + 0.0306088i \(0.990255\pi\)
\(270\) −20550.4 52399.0i −0.281898 0.718779i
\(271\) −86111.9 −1.17253 −0.586266 0.810119i \(-0.699403\pi\)
−0.586266 + 0.810119i \(0.699403\pi\)
\(272\) −257.360 148.587i −0.00347859 0.00200836i
\(273\) −4445.20 35495.1i −0.0596439 0.476259i
\(274\) −12525.7 21695.2i −0.166841 0.288977i
\(275\) −52616.4 + 30378.1i −0.695754 + 0.401693i
\(276\) 37668.3 89339.5i 0.494490 1.17280i
\(277\) −35306.7 + 61153.0i −0.460148 + 0.797000i −0.998968 0.0454210i \(-0.985537\pi\)
0.538820 + 0.842421i \(0.318870\pi\)
\(278\) 22780.6i 0.294765i
\(279\) −86640.6 88857.0i −1.11305 1.14152i
\(280\) −44977.8 −0.573697
\(281\) −129258. 74627.2i −1.63699 0.945114i −0.981863 0.189592i \(-0.939283\pi\)
−0.655123 0.755522i \(-0.727383\pi\)
\(282\) 37611.0 28484.5i 0.472952 0.358187i
\(283\) 41963.4 + 72682.7i 0.523959 + 0.907524i 0.999611 + 0.0278902i \(0.00887887\pi\)
−0.475652 + 0.879634i \(0.657788\pi\)
\(284\) −44884.1 + 25913.8i −0.556488 + 0.321288i
\(285\) 3465.71 + 4576.14i 0.0426680 + 0.0563390i
\(286\) 30548.3 52911.2i 0.373469 0.646867i
\(287\) 67104.2i 0.814678i
\(288\) 51840.7 50547.6i 0.625008 0.609418i
\(289\) 83461.6 0.999288
\(290\) 36150.3 + 20871.4i 0.429849 + 0.248174i
\(291\) 125418. + 52880.3i 1.48107 + 0.624464i
\(292\) 12788.2 + 22149.9i 0.149984 + 0.259780i
\(293\) −31092.9 + 17951.5i −0.362182 + 0.209106i −0.670037 0.742327i \(-0.733722\pi\)
0.307856 + 0.951433i \(0.400389\pi\)
\(294\) 25571.0 3202.36i 0.295837 0.0370489i
\(295\) −19637.5 + 34013.1i −0.225653 + 0.390843i
\(296\) 123180.i 1.40590i
\(297\) −13600.2 + 90083.2i −0.154182 + 1.02125i
\(298\) −58389.0 −0.657504
\(299\) 25842.8 + 14920.4i 0.289067 + 0.166893i
\(300\) 14644.9 + 116940.i 0.162721 + 1.29934i
\(301\) −69462.2 120312.i −0.766682 1.32793i
\(302\) −56265.8 + 32485.1i −0.616923 + 0.356181i
\(303\) 38674.9 91727.0i 0.421254 0.999106i
\(304\) 1043.22 1806.91i 0.0112883 0.0195519i
\(305\) 176.944i 0.00190211i
\(306\) −1108.93 + 3938.92i −0.0118430 + 0.0420663i
\(307\) 7054.30 0.0748475 0.0374238 0.999299i \(-0.488085\pi\)
0.0374238 + 0.999299i \(0.488085\pi\)
\(308\) 155299. + 89661.8i 1.63707 + 0.945161i
\(309\) 25562.6 19359.7i 0.267725 0.202760i
\(310\) −59147.8 102447.i −0.615482 1.06605i
\(311\) 74184.9 42830.7i 0.766999 0.442827i −0.0648038 0.997898i \(-0.520642\pi\)
0.831803 + 0.555071i \(0.187309\pi\)
\(312\) −29048.8 38356.2i −0.298414 0.394028i
\(313\) −36721.2 + 63603.1i −0.374825 + 0.649216i −0.990301 0.138940i \(-0.955631\pi\)
0.615476 + 0.788156i \(0.288964\pi\)
\(314\) 37001.5i 0.375284i
\(315\) 12538.4 + 49274.6i 0.126363 + 0.496595i
\(316\) 6410.07 0.0641931
\(317\) 42642.8 + 24619.8i 0.424353 + 0.245000i 0.696938 0.717132i \(-0.254545\pi\)
−0.272585 + 0.962132i \(0.587879\pi\)
\(318\) −229848. 96910.8i −2.27293 0.958336i
\(319\) −33783.0 58513.9i −0.331984 0.575013i
\(320\) 66062.5 38141.2i 0.645141 0.372473i
\(321\) −102097. + 12786.0i −0.990836 + 0.124086i
\(322\) −69806.1 + 120908.i −0.673258 + 1.16612i
\(323\) 417.341i 0.00400024i
\(324\) 150766. + 92198.1i 1.43619 + 0.878277i
\(325\) −36272.7 −0.343410
\(326\) 12220.6 + 7055.58i 0.114990 + 0.0663893i
\(327\) 5346.29 + 42690.4i 0.0499985 + 0.399241i
\(328\) −45128.5 78164.8i −0.419472 0.726547i
\(329\) −36910.1 + 21310.0i −0.340999 + 0.196876i
\(330\) −33737.8 + 80017.5i −0.309806 + 0.734779i
\(331\) 41005.6 71023.7i 0.374271 0.648257i −0.615946 0.787788i \(-0.711226\pi\)
0.990218 + 0.139531i \(0.0445595\pi\)
\(332\) 354627.i 3.21733i
\(333\) 134947. 34338.5i 1.21696 0.309665i
\(334\) 242575. 2.17447
\(335\) −52883.1 30532.1i −0.471224 0.272061i
\(336\) 14732.2 11157.3i 0.130494 0.0988284i
\(337\) 23491.4 + 40688.3i 0.206847 + 0.358270i 0.950720 0.310052i \(-0.100346\pi\)
−0.743873 + 0.668322i \(0.767013\pi\)
\(338\) −130484. + 75335.0i −1.14215 + 0.659422i
\(339\) −24404.7 32224.1i −0.212360 0.280402i
\(340\) −1223.48 + 2119.12i −0.0105837 + 0.0183315i
\(341\) 191477.i 1.64667i
\(342\) −27654.9 7785.72i −0.236440 0.0665651i
\(343\) 104628. 0.889324
\(344\) −161823. 93428.4i −1.36749 0.789518i
\(345\) −39082.1 16478.2i −0.328352 0.138443i
\(346\) 159178. + 275705.i 1.32963 + 2.30299i
\(347\) 38382.0 22159.8i 0.318763 0.184038i −0.332078 0.943252i \(-0.607750\pi\)
0.650841 + 0.759214i \(0.274416\pi\)
\(348\) −130048. + 16286.4i −1.07385 + 0.134483i
\(349\) 93231.7 161482.i 0.765442 1.32579i −0.174570 0.984645i \(-0.555853\pi\)
0.940012 0.341140i \(-0.110813\pi\)
\(350\) 169704.i 1.38534i
\(351\) −33922.6 + 42516.4i −0.275343 + 0.345097i
\(352\) −111711. −0.901591
\(353\) −146959. 84847.1i −1.17936 0.680907i −0.223497 0.974705i \(-0.571747\pi\)
−0.955868 + 0.293798i \(0.905081\pi\)
\(354\) −24426.0 195043.i −0.194916 1.55641i
\(355\) 11336.2 + 19634.8i 0.0899517 + 0.155801i
\(356\) −13434.4 + 7756.35i −0.106003 + 0.0612008i
\(357\) 1436.14 3406.17i 0.0112684 0.0267257i
\(358\) −156336. + 270782.i −1.21981 + 2.11278i
\(359\) 69656.7i 0.540473i 0.962794 + 0.270236i \(0.0871019\pi\)
−0.962794 + 0.270236i \(0.912898\pi\)
\(360\) 47742.8 + 48964.2i 0.368386 + 0.377810i
\(361\) −127391. −0.977516
\(362\) 259712. + 149945.i 1.98187 + 1.14423i
\(363\) 7008.27 5307.66i 0.0531860 0.0402801i
\(364\) 53529.9 + 92716.6i 0.404012 + 0.699769i
\(365\) 9689.60 5594.30i 0.0727311 0.0419913i
\(366\) 534.661 + 705.969i 0.00399132 + 0.00527016i
\(367\) 88084.2 152566.i 0.653982 1.13273i −0.328166 0.944620i \(-0.606431\pi\)
0.982148 0.188110i \(-0.0602361\pi\)
\(368\) 15416.0i 0.113835i
\(369\) −73051.6 + 71229.5i −0.536509 + 0.523127i
\(370\) 132729. 0.969531
\(371\) 195145. + 112667.i 1.41778 + 0.818558i
\(372\) 342246. + 144302.i 2.47316 + 1.04276i
\(373\) −33593.6 58185.7i −0.241456 0.418214i 0.719673 0.694313i \(-0.244292\pi\)
−0.961129 + 0.276099i \(0.910958\pi\)
\(374\) 5467.59 3156.71i 0.0390888 0.0225679i
\(375\) 116922. 14642.6i 0.831445 0.104125i
\(376\) −28662.6 + 49645.0i −0.202740 + 0.351156i
\(377\) 40338.3i 0.283815i
\(378\) −198916. 158709.i −1.39215 1.11076i
\(379\) 43976.9 0.306158 0.153079 0.988214i \(-0.451081\pi\)
0.153079 + 0.988214i \(0.451081\pi\)
\(380\) −14878.2 8589.95i −0.103035 0.0594872i
\(381\) −15121.8 120749.i −0.104173 0.831825i
\(382\) −153065. 265116.i −1.04893 1.81681i
\(383\) −160336. + 92569.8i −1.09303 + 0.631062i −0.934382 0.356273i \(-0.884047\pi\)
−0.158649 + 0.987335i \(0.550714\pi\)
\(384\) −98317.7 + 233184.i −0.666759 + 1.58138i
\(385\) 39223.1 67936.4i 0.264619 0.458333i
\(386\) 178279.i 1.19654i
\(387\) −57242.8 + 203327.i −0.382207 + 1.35760i
\(388\) −407353. −2.70587
\(389\) −26364.0 15221.3i −0.174226 0.100589i 0.410351 0.911928i \(-0.365406\pi\)
−0.584577 + 0.811338i \(0.698740\pi\)
\(390\) −41329.7 + 31300.8i −0.271727 + 0.205791i
\(391\) 1541.80 + 2670.48i 0.0100850 + 0.0174677i
\(392\) −27117.2 + 15656.1i −0.176471 + 0.101885i
\(393\) −18458.0 24372.0i −0.119508 0.157800i
\(394\) 211860. 366951.i 1.36476 2.36383i
\(395\) 2804.12i 0.0179723i
\(396\) −67237.3 264236.i −0.428766 1.68501i
\(397\) −235724. −1.49563 −0.747813 0.663910i \(-0.768896\pi\)
−0.747813 + 0.663910i \(0.768896\pi\)
\(398\) 146640. + 84662.7i 0.925734 + 0.534473i
\(399\) 23914.5 + 10083.1i 0.150216 + 0.0633355i
\(400\) −9369.41 16228.3i −0.0585588 0.101427i
\(401\) 202830. 117104.i 1.26137 0.728254i 0.288032 0.957621i \(-0.406999\pi\)
0.973340 + 0.229367i \(0.0736656\pi\)
\(402\) 303250. 37977.2i 1.87650 0.235002i
\(403\) −57157.8 + 99000.1i −0.351937 + 0.609573i
\(404\) 297925.i 1.82534i
\(405\) 40332.6 65953.4i 0.245893 0.402093i
\(406\) 188726. 1.14493
\(407\) −186056. 107419.i −1.12319 0.648475i
\(408\) −617.832 4933.42i −0.00371150 0.0296365i
\(409\) 148893. + 257890.i 0.890076 + 1.54166i 0.839783 + 0.542922i \(0.182682\pi\)
0.0502930 + 0.998735i \(0.483984\pi\)
\(410\) −84224.3 + 48626.9i −0.501037 + 0.289274i
\(411\) 13368.1 31705.7i 0.0791382 0.187696i
\(412\) −47984.1 + 83110.9i −0.282685 + 0.489625i
\(413\) 177569.i 1.04104i
\(414\) 205721. 52347.5i 1.20027 0.305419i
\(415\) −155134. −0.900763
\(416\) −57758.3 33346.8i −0.333755 0.192694i
\(417\) −24943.5 + 18890.8i −0.143445 + 0.108637i
\(418\) 22163.1 + 38387.6i 0.126846 + 0.219704i
\(419\) −31934.0 + 18437.1i −0.181897 + 0.105018i −0.588184 0.808727i \(-0.700157\pi\)
0.406287 + 0.913746i \(0.366823\pi\)
\(420\) −91870.4 121306.i −0.520807 0.687676i
\(421\) −120305. + 208374.i −0.678764 + 1.17565i 0.296589 + 0.955005i \(0.404151\pi\)
−0.975353 + 0.220649i \(0.929183\pi\)
\(422\) 301799.i 1.69470i
\(423\) 62377.9 + 17561.3i 0.348618 + 0.0981468i
\(424\) 303080. 1.68588
\(425\) −3246.08 1874.12i −0.0179714 0.0103758i
\(426\) −104559. 44085.1i −0.576156 0.242925i
\(427\) −399.995 692.812i −0.00219381 0.00379979i
\(428\) 266686. 153971.i 1.45584 0.840529i
\(429\) 83267.0 10427.9i 0.452437 0.0566605i
\(430\) −100671. + 174368.i −0.544463 + 0.943038i
\(431\) 162758.i 0.876169i −0.898934 0.438084i \(-0.855657\pi\)
0.898934 0.438084i \(-0.144343\pi\)
\(432\) −27784.1 4194.67i −0.148877 0.0224766i
\(433\) 266637. 1.42215 0.711073 0.703118i \(-0.248209\pi\)
0.711073 + 0.703118i \(0.248209\pi\)
\(434\) −463180. 267417.i −2.45906 1.41974i
\(435\) 7124.59 + 56890.2i 0.0376514 + 0.300649i
\(436\) −64381.1 111511.i −0.338677 0.586605i
\(437\) −18749.3 + 10824.9i −0.0981796 + 0.0566840i
\(438\) −21755.6 + 51598.7i −0.113402 + 0.268962i
\(439\) 18408.7 31884.8i 0.0955201 0.165446i −0.814305 0.580437i \(-0.802882\pi\)
0.909826 + 0.414991i \(0.136215\pi\)
\(440\) 105512.i 0.545001i
\(441\) 24711.1 + 25343.3i 0.127062 + 0.130312i
\(442\) 3769.25 0.0192935
\(443\) −119117. 68772.0i −0.606967 0.350432i 0.164811 0.986325i \(-0.447299\pi\)
−0.771777 + 0.635893i \(0.780632\pi\)
\(444\) −332218. + 251603.i −1.68522 + 1.27629i
\(445\) 3393.06 + 5876.95i 0.0171345 + 0.0296778i
\(446\) 124337. 71786.2i 0.625075 0.360887i
\(447\) −48419.0 63932.7i −0.242326 0.319969i
\(448\) 172442. 298679.i 0.859188 1.48816i
\(449\) 174405.i 0.865101i −0.901610 0.432550i \(-0.857614\pi\)
0.901610 0.432550i \(-0.142386\pi\)
\(450\) −184745. + 180137.i −0.912322 + 0.889565i
\(451\) 157418. 0.773929
\(452\) 104769. + 60488.4i 0.512809 + 0.296070i
\(453\) −82227.8 34669.8i −0.400703 0.168949i
\(454\) −163110. 282515.i −0.791352 1.37066i
\(455\) 40559.4 23417.0i 0.195916 0.113112i
\(456\) 34637.2 4337.76i 0.166576 0.0208610i
\(457\) −57654.7 + 99860.9i −0.276059 + 0.478149i −0.970402 0.241496i \(-0.922362\pi\)
0.694342 + 0.719645i \(0.255695\pi\)
\(458\) 186884.i 0.890923i
\(459\) −5232.48 + 2052.13i −0.0248360 + 0.00974047i
\(460\) 126937. 0.599890
\(461\) 351141. + 202731.i 1.65226 + 0.953936i 0.976138 + 0.217150i \(0.0696762\pi\)
0.676127 + 0.736785i \(0.263657\pi\)
\(462\) 48787.5 + 389571.i 0.228573 + 1.82517i
\(463\) −36293.4 62861.9i −0.169303 0.293242i 0.768872 0.639403i \(-0.220818\pi\)
−0.938175 + 0.346161i \(0.887485\pi\)
\(464\) 18047.3 10419.6i 0.0838253 0.0483966i
\(465\) 63125.6 149718.i 0.291944 0.692417i
\(466\) −144320. + 249969.i −0.664590 + 1.15110i
\(467\) 358806.i 1.64523i −0.568602 0.822613i \(-0.692515\pi\)
0.568602 0.822613i \(-0.307485\pi\)
\(468\) 44113.3 156691.i 0.201408 0.715404i
\(469\) −276081. −1.25514
\(470\) 53493.6 + 30884.6i 0.242162 + 0.139812i
\(471\) −40514.7 + 30683.5i −0.182629 + 0.138313i
\(472\) 119417. + 206837.i 0.536022 + 0.928418i
\(473\) 282236. 162949.i 1.26151 0.728333i
\(474\) 8473.07 + 11187.9i 0.0377124 + 0.0497956i
\(475\) 13158.1 22790.5i 0.0583185 0.101011i
\(476\) 11063.1i 0.0488271i
\(477\) −84489.0 332034.i −0.371333 1.45930i
\(478\) −134819. −0.590058
\(479\) −22169.8 12799.8i −0.0966255 0.0557867i 0.450909 0.892570i \(-0.351100\pi\)
−0.547534 + 0.836783i \(0.684433\pi\)
\(480\) 87347.9 + 36828.5i 0.379114 + 0.159846i
\(481\) −64131.5 111079.i −0.277192 0.480111i
\(482\) −328661. + 189752.i −1.41466 + 0.816757i
\(483\) −190274. + 23828.8i −0.815615 + 0.102143i
\(484\) −13155.4 + 22785.7i −0.0561580 + 0.0972685i
\(485\) 178199.i 0.757569i
\(486\) 38368.8 + 385012.i 0.162445 + 1.63005i
\(487\) 247261. 1.04255 0.521277 0.853388i \(-0.325456\pi\)
0.521277 + 0.853388i \(0.325456\pi\)
\(488\) −931.850 538.004i −0.00391297 0.00225915i
\(489\) 2408.47 + 19231.8i 0.0100722 + 0.0804269i
\(490\) 16869.8 + 29219.4i 0.0702616 + 0.121697i
\(491\) −296403. + 171128.i −1.22947 + 0.709837i −0.966920 0.255081i \(-0.917898\pi\)
−0.262554 + 0.964917i \(0.584565\pi\)
\(492\) 118634. 281370.i 0.490094 1.16238i
\(493\) 2084.19 3609.92i 0.00857517 0.0148526i
\(494\) 26463.7i 0.108442i
\(495\) −115592. + 29413.4i −0.471755 + 0.120042i
\(496\) −59056.5 −0.240052
\(497\) 88772.2 + 51252.7i 0.359389 + 0.207493i
\(498\) 618953. 468760.i 2.49574 1.89013i
\(499\) 98919.1 + 171333.i 0.397264 + 0.688081i 0.993387 0.114812i \(-0.0366265\pi\)
−0.596124 + 0.802893i \(0.703293\pi\)
\(500\) −305411. + 176329.i −1.22164 + 0.705317i
\(501\) 201155. + 265606.i 0.801411 + 1.05819i
\(502\) 177377. 307227.i 0.703867 1.21913i
\(503\) 187051.i 0.739305i 0.929170 + 0.369652i \(0.120523\pi\)
−0.929170 + 0.369652i \(0.879477\pi\)
\(504\) 297622. + 83789.7i 1.17167 + 0.329860i
\(505\) 130329. 0.511044
\(506\) −283634. 163756.i −1.10779 0.639582i
\(507\) −190692. 80401.5i −0.741850 0.312787i
\(508\) 182100. + 315406.i 0.705639 + 1.22220i
\(509\) −25011.5 + 14440.4i −0.0965393 + 0.0557370i −0.547492 0.836811i \(-0.684417\pi\)
0.450953 + 0.892548i \(0.351084\pi\)
\(510\) −5315.87 + 665.728i −0.0204378 + 0.00255951i
\(511\) 25292.7 43808.3i 0.0968620 0.167770i
\(512\) 78644.0i 0.300003i
\(513\) −14407.9 36736.9i −0.0547477 0.139595i
\(514\) −745440. −2.82154
\(515\) 36357.4 + 20990.9i 0.137081 + 0.0791439i
\(516\) −78556.0 627274.i −0.295039 2.35590i
\(517\) −49990.6 86586.3i −0.187028 0.323943i
\(518\) 519692. 300044.i 1.93681 1.11822i
\(519\) −169883. + 402919.i −0.630689 + 1.49583i
\(520\) 31496.5 54553.5i 0.116481 0.201751i
\(521\) 269661.i 0.993443i 0.867910 + 0.496721i \(0.165463\pi\)
−0.867910 + 0.496721i \(0.834537\pi\)
\(522\) −200328. 205453.i −0.735191 0.753998i
\(523\) −187282. −0.684689 −0.342344 0.939575i \(-0.611221\pi\)
−0.342344 + 0.939575i \(0.611221\pi\)
\(524\) 79239.8 + 45749.1i 0.288590 + 0.166617i
\(525\) 185817. 140727.i 0.674166 0.510575i
\(526\) −145347. 251748.i −0.525331 0.909901i
\(527\) −10230.2 + 5906.41i −0.0368352 + 0.0212668i
\(528\) 26173.7 + 34559.9i 0.0938851 + 0.123966i
\(529\) −59938.8 + 103817.i −0.214189 + 0.370986i
\(530\) 326576.i 1.16261i
\(531\) 193306. 188485.i 0.685578 0.668478i
\(532\) −77673.1 −0.274440
\(533\) 81390.6 + 46990.9i 0.286497 + 0.165409i
\(534\) −31295.7 13195.2i −0.109749 0.0462737i
\(535\) −67355.7 116664.i −0.235324 0.407594i
\(536\) −321586. + 185668.i −1.11936 + 0.646260i
\(537\) −426133. + 53366.3i −1.47773 + 0.185063i
\(538\) 14513.0 25137.3i 0.0501411 0.0868469i
\(539\) 54611.9i 0.187979i
\(540\) −34539.3 + 228776.i −0.118447 + 0.784555i
\(541\) −25587.9 −0.0874259 −0.0437129 0.999044i \(-0.513919\pi\)
−0.0437129 + 0.999044i \(0.513919\pi\)
\(542\) 488653. + 282124.i 1.66342 + 0.960377i
\(543\) 51184.7 + 408713.i 0.173596 + 1.38618i
\(544\) −3445.90 5968.47i −0.0116441 0.0201681i
\(545\) −48781.3 + 28163.9i −0.164233 + 0.0948200i
\(546\) −91066.0 + 215985.i −0.305472 + 0.724501i
\(547\) 138424. 239758.i 0.462634 0.801306i −0.536457 0.843928i \(-0.680238\pi\)
0.999091 + 0.0426215i \(0.0135710\pi\)
\(548\) 102979.i 0.342915i
\(549\) −329.630 + 1170.85i −0.00109366 + 0.00388469i
\(550\) 398105. 1.31605
\(551\) 25345.0 + 14633.0i 0.0834813 + 0.0481980i
\(552\) −205611. + 155718.i −0.674790 + 0.511047i
\(553\) −6338.95 10979.4i −0.0207285 0.0359027i
\(554\) 400705. 231347.i 1.30559 0.753780i
\(555\) 110065. + 145331.i 0.357326 + 0.471815i
\(556\) 46821.9 81098.0i 0.151461 0.262338i
\(557\) 461786.i 1.48844i −0.667936 0.744219i \(-0.732822\pi\)
0.667936 0.744219i \(-0.267178\pi\)
\(558\) 200536. + 788087.i 0.644056 + 2.53108i
\(559\) 194568. 0.622656
\(560\) 20953.4 + 12097.4i 0.0668157 + 0.0385761i
\(561\) 7990.43 + 3369.01i 0.0253889 + 0.0107047i
\(562\) 488995. + 846964.i 1.54822 + 2.68159i
\(563\) −154104. + 88972.1i −0.486181 + 0.280697i −0.722989 0.690860i \(-0.757232\pi\)
0.236808 + 0.971556i \(0.423899\pi\)
\(564\) −192439. + 24099.9i −0.604971 + 0.0757630i
\(565\) 26461.0 45831.8i 0.0828914 0.143572i
\(566\) 549930.i 1.71662i
\(567\) 8826.98 349412.i 0.0274566 1.08685i
\(568\) 137872. 0.427347
\(569\) −5111.83 2951.31i −0.0157889 0.00911572i 0.492085 0.870547i \(-0.336235\pi\)
−0.507874 + 0.861432i \(0.669568\pi\)
\(570\) −4674.04 37322.4i −0.0143861 0.114874i
\(571\) −238346. 412828.i −0.731031 1.26618i −0.956443 0.291920i \(-0.905706\pi\)
0.225411 0.974264i \(-0.427627\pi\)
\(572\) −217501. + 125574.i −0.664767 + 0.383803i
\(573\) 163359. 387445.i 0.497545 1.18005i
\(574\) −219850. + 380792.i −0.667272 + 1.15575i
\(575\) 194442.i 0.588105i
\(576\) −508194. + 129315.i −1.53174 + 0.389765i
\(577\) 209901. 0.630468 0.315234 0.949014i \(-0.397917\pi\)
0.315234 + 0.949014i \(0.397917\pi\)
\(578\) −473614. 273441.i −1.41765 0.818480i
\(579\) 195206. 147838.i 0.582285 0.440990i
\(580\) −85795.7 148603.i −0.255041 0.441744i
\(581\) −607417. + 350693.i −1.79943 + 1.03890i
\(582\) −538455. 710978.i −1.58966 2.09899i
\(583\) −264302. + 457785.i −0.777614 + 1.34687i
\(584\) 68038.7i 0.199494i
\(585\) −68545.2 19297.6i −0.200293 0.0563887i
\(586\) 235255. 0.685083
\(587\) −156552. 90385.1i −0.454340 0.262313i 0.255321 0.966856i \(-0.417819\pi\)
−0.709661 + 0.704543i \(0.751152\pi\)
\(588\) −97613.6 41156.9i −0.282329 0.119039i
\(589\) −41468.6 71825.7i −0.119533 0.207038i
\(590\) 222871. 128675.i 0.640250 0.369649i
\(591\) 577476. 72319.7i 1.65333 0.207053i
\(592\) 33131.0 57384.5i 0.0945346 0.163739i
\(593\) 468097.i 1.33115i −0.746332 0.665574i \(-0.768187\pi\)
0.746332 0.665574i \(-0.231813\pi\)
\(594\) 372311. 466631.i 1.05520 1.32252i
\(595\) 4839.60 0.0136702
\(596\) 207862. + 120009.i 0.585171 + 0.337849i
\(597\) 28900.2 + 230769.i 0.0810871 + 0.647485i
\(598\) −97765.8 169335.i −0.273391 0.473527i
\(599\) 558557. 322483.i 1.55673 0.898780i 0.559167 0.829055i \(-0.311121\pi\)
0.997566 0.0697251i \(-0.0222122\pi\)
\(600\) 121804. 288887.i 0.338344 0.802465i
\(601\) −127517. + 220865.i −0.353035 + 0.611474i −0.986780 0.162068i \(-0.948184\pi\)
0.633745 + 0.773542i \(0.281517\pi\)
\(602\) 910302.i 2.51184i
\(603\) 293053. + 300550.i 0.805956 + 0.826574i
\(604\) 267072. 0.732073
\(605\) 9967.76 + 5754.89i 0.0272325 + 0.0157227i
\(606\) −519986. + 393808.i −1.41595 + 1.07236i
\(607\) 176351. + 305449.i 0.478631 + 0.829013i 0.999700 0.0245019i \(-0.00779999\pi\)
−0.521069 + 0.853514i \(0.674467\pi\)
\(608\) 41904.3 24193.5i 0.113358 0.0654472i
\(609\) 156501. + 206645.i 0.421971 + 0.557172i
\(610\) −579.711 + 1004.09i −0.00155795 + 0.00269844i
\(611\) 59690.9i 0.159892i
\(612\) 12043.6 11743.2i 0.0321553 0.0313532i
\(613\) −37013.8 −0.0985015 −0.0492508 0.998786i \(-0.515683\pi\)
−0.0492508 + 0.998786i \(0.515683\pi\)
\(614\) −40030.6 23111.7i −0.106183 0.0613048i
\(615\) −123087. 51897.2i −0.325433 0.137212i
\(616\) −238519. 413127.i −0.628581 1.08873i
\(617\) −493797. + 285094.i −1.29711 + 0.748888i −0.979904 0.199467i \(-0.936079\pi\)
−0.317208 + 0.948356i \(0.602745\pi\)
\(618\) −208486. + 26109.5i −0.545883 + 0.0683631i
\(619\) 220407. 381756.i 0.575233 0.996333i −0.420783 0.907161i \(-0.638245\pi\)
0.996016 0.0891715i \(-0.0284219\pi\)
\(620\) 486276.i 1.26503i
\(621\) 227912. + 181844.i 0.590995 + 0.471537i
\(622\) −561296. −1.45081
\(623\) 26570.7 + 15340.6i 0.0684583 + 0.0395244i
\(624\) 3216.23 + 25681.8i 0.00825996 + 0.0659562i
\(625\) −74789.0 129538.i −0.191460 0.331618i
\(626\) 416759. 240616.i 1.06350 0.614011i
\(627\) −23653.6 + 56100.3i −0.0601676 + 0.142702i
\(628\) 76050.9 131724.i 0.192835 0.333999i
\(629\) 13254.1i 0.0335003i
\(630\) 90285.3 320694.i 0.227476 0.807997i
\(631\) −80926.3 −0.203250 −0.101625 0.994823i \(-0.532404\pi\)
−0.101625 + 0.994823i \(0.532404\pi\)
\(632\) −14767.6 8526.05i −0.0369721 0.0213459i
\(633\) −330454. + 250267.i −0.824714 + 0.624592i
\(634\) −161321. 279417.i −0.401341 0.695143i
\(635\) 137976. 79660.7i 0.342182 0.197559i
\(636\) 619063. + 817414.i 1.53046 + 2.02082i
\(637\) 16302.2 28236.3i 0.0401761 0.0695870i
\(638\) 442727.i 1.08766i
\(639\) −38434.3 151043.i −0.0941278 0.369913i
\(640\) −331317. −0.808879
\(641\) −131917. 76162.1i −0.321058 0.185363i 0.330806 0.943699i \(-0.392679\pi\)
−0.651864 + 0.758336i \(0.726013\pi\)
\(642\) 621252. + 261939.i 1.50729 + 0.635521i
\(643\) −58437.1 101216.i −0.141340 0.244809i 0.786661 0.617385i \(-0.211808\pi\)
−0.928002 + 0.372576i \(0.878475\pi\)
\(644\) 497013. 286951.i 1.19838 0.691888i
\(645\) −274405. + 34364.8i −0.659587 + 0.0826027i
\(646\) −1367.31 + 2368.26i −0.00327645 + 0.00567498i
\(647\) 481407.i 1.15002i 0.818148 + 0.575008i \(0.195001\pi\)
−0.818148 + 0.575008i \(0.804999\pi\)
\(648\) −224702. 412940.i −0.535127 0.983416i
\(649\) −416553. −0.988965
\(650\) 205834. + 118838.i 0.487181 + 0.281274i
\(651\) −91284.6 728912.i −0.215395 1.71994i
\(652\) −29003.3 50235.2i −0.0682263 0.118171i
\(653\) 399091. 230415.i 0.935935 0.540363i 0.0472516 0.998883i \(-0.484954\pi\)
0.888684 + 0.458520i \(0.151620\pi\)
\(654\) 109526. 259768.i 0.256072 0.607338i
\(655\) 20013.2 34663.9i 0.0466482 0.0807970i
\(656\) 48551.9i 0.112823i
\(657\) −74538.5 + 18967.0i −0.172683 + 0.0439408i
\(658\) 279268. 0.645015
\(659\) 142960. + 82538.2i 0.329189 + 0.190057i 0.655481 0.755212i \(-0.272466\pi\)
−0.326292 + 0.945269i \(0.605799\pi\)
\(660\) 284569. 215516.i 0.653280 0.494757i
\(661\) 140878. + 244008.i 0.322434 + 0.558472i 0.980990 0.194060i \(-0.0621657\pi\)
−0.658556 + 0.752532i \(0.728832\pi\)
\(662\) −465383. + 268689.i −1.06193 + 0.613104i
\(663\) 3125.65 + 4127.12i 0.00711071 + 0.00938902i
\(664\) −471691. + 816992.i −1.06985 + 1.85303i
\(665\) 33978.6i 0.0768355i
\(666\) −878276. 247262.i −1.98008 0.557454i
\(667\) −216236. −0.486046
\(668\) −863556. 498574.i −1.93525 1.11732i
\(669\) 181709. + 76614.0i 0.405998 + 0.171181i
\(670\) 200061. + 346517.i 0.445670 + 0.771924i
\(671\) 1625.25 938.337i 0.00360973 0.00208408i
\(672\) 425259. 53256.9i 0.941706 0.117934i
\(673\) 378387. 655386.i 0.835423 1.44699i −0.0582627 0.998301i \(-0.518556\pi\)
0.893686 0.448694i \(-0.148111\pi\)
\(674\) 307855.i 0.677683i
\(675\) −350440. 52907.4i −0.769141 0.116120i
\(676\) 619357. 1.35534
\(677\) −59053.2 34094.4i −0.128845 0.0743885i 0.434192 0.900820i \(-0.357034\pi\)
−0.563037 + 0.826432i \(0.690367\pi\)
\(678\) 32913.4 + 262815.i 0.0716002 + 0.571731i
\(679\) 402833. + 697728.i 0.873747 + 1.51337i
\(680\) 5637.30 3254.70i 0.0121914 0.00703870i
\(681\) 174080. 412873.i 0.375365 0.890270i
\(682\) 627326. 1.08656e6i 1.34873 2.33606i
\(683\) 31351.1i 0.0672066i 0.999435 + 0.0336033i \(0.0106983\pi\)
−0.999435 + 0.0336033i \(0.989302\pi\)
\(684\) 82448.1 + 84557.2i 0.176225 + 0.180733i
\(685\) 45048.7 0.0960065
\(686\) −593726. 342788.i −1.26165 0.728412i
\(687\) −204627. + 154973.i −0.433561 + 0.328355i
\(688\) 50257.9 + 87049.3i 0.106176 + 0.183903i
\(689\) −273307. + 157794.i −0.575722 + 0.332393i
\(690\) 167790. + 221551.i 0.352426 + 0.465345i
\(691\) −187442. + 324659.i −0.392565 + 0.679942i −0.992787 0.119891i \(-0.961745\pi\)
0.600222 + 0.799833i \(0.295079\pi\)
\(692\) 1.30866e6i 2.73285i
\(693\) −386102. + 376471.i −0.803962 + 0.783908i
\(694\) −290405. −0.602955
\(695\) −35476.8 20482.5i −0.0734471 0.0424047i
\(696\) 321268. + 135456.i 0.663206 + 0.279628i
\(697\) 4855.81 + 8410.52i 0.00999531 + 0.0173124i
\(698\) −1.05811e6 + 610901.i −2.17180 + 1.25389i
\(699\) −393379. + 49264.5i −0.805114 + 0.100828i
\(700\) −348801. + 604140.i −0.711838 + 1.23294i
\(701\) 97448.5i 0.198308i 0.995072 + 0.0991538i \(0.0316136\pi\)
−0.995072 + 0.0991538i \(0.968386\pi\)
\(702\) 331792. 130126.i 0.673274 0.264052i
\(703\) 93056.2 0.188293
\(704\) 700663. + 404528.i 1.41372 + 0.816212i
\(705\) 10542.7 + 84183.6i 0.0212115 + 0.169375i
\(706\) 555961. + 962952.i 1.11541 + 1.93195i
\(707\) 510295. 294619.i 1.02090 0.589416i
\(708\) −313925. + 744549.i −0.626266 + 1.48534i
\(709\) 146263. 253334.i 0.290965 0.503967i −0.683073 0.730350i \(-0.739357\pi\)
0.974038 + 0.226383i \(0.0726902\pi\)
\(710\) 148561.i 0.294704i
\(711\) −5223.84 + 18555.1i −0.0103336 + 0.0367049i
\(712\) 41267.0 0.0814034
\(713\) 530697. + 306398.i 1.04392 + 0.602708i
\(714\) −19309.0 + 14623.6i −0.0378760 + 0.0286851i
\(715\) 54933.3 + 95147.2i 0.107454 + 0.186116i
\(716\) 1.11310e6 642648.i 2.17124 1.25357i
\(717\) −111798. 147619.i −0.217469 0.287147i
\(718\) 228213. 395276.i 0.442681 0.766746i
\(719\) 655579.i 1.26814i 0.773276 + 0.634070i \(0.218617\pi\)
−0.773276 + 0.634070i \(0.781383\pi\)
\(720\) −9071.87 35651.6i −0.0174998 0.0687724i
\(721\) 189807. 0.365125
\(722\) 722896. + 417364.i 1.38676 + 0.800647i
\(723\) −480310. 202513.i −0.918851 0.387416i
\(724\) −616376. 1.06760e6i −1.17590 2.03671i
\(725\) 227630. 131422.i 0.433065 0.250030i
\(726\) −57158.6 + 7158.20i −0.108445 + 0.0135810i
\(727\) −129630. + 224526.i −0.245266 + 0.424814i −0.962206 0.272321i \(-0.912209\pi\)
0.716940 + 0.697135i \(0.245542\pi\)
\(728\) 284801.i 0.537377i
\(729\) −389749. + 361282.i −0.733382 + 0.679817i
\(730\) −73313.3 −0.137574
\(731\) 17412.1 + 10052.9i 0.0325849 + 0.0188129i
\(732\) −452.362 3612.13i −0.000844236 0.00674126i
\(733\) −41254.4 71454.8i −0.0767826 0.132991i 0.825077 0.565020i \(-0.191131\pi\)
−0.901860 + 0.432028i \(0.857798\pi\)
\(734\) −999691. + 577172.i −1.85555 + 1.07130i
\(735\) −18004.3 + 42701.7i −0.0333275 + 0.0790442i
\(736\) −178758. + 309618.i −0.329996 + 0.571571i
\(737\) 647650.i 1.19235i
\(738\) 647907. 164866.i 1.18960 0.302703i
\(739\) −730583. −1.33777 −0.668884 0.743367i \(-0.733228\pi\)
−0.668884 + 0.743367i \(0.733228\pi\)
\(740\) −472509. 272803.i −0.862872 0.498179i
\(741\) −28976.3 + 21945.0i −0.0527723 + 0.0399667i
\(742\) −738251. 1.27869e6i −1.34090 2.32251i
\(743\) 391257. 225892.i 0.708735 0.409189i −0.101857 0.994799i \(-0.532479\pi\)
0.810593 + 0.585611i \(0.199145\pi\)
\(744\) −596533. 787666.i −1.07768 1.42297i
\(745\) 52498.8 90930.6i 0.0945882 0.163832i
\(746\) 440244.i 0.791071i
\(747\) 1.02653e6 + 289001.i 1.83963 + 0.517914i
\(748\) −25952.5 −0.0463849
\(749\) −527455. 304526.i −0.940203 0.542826i
\(750\) −711462. 299974.i −1.26482 0.533287i
\(751\) −290081. 502435.i −0.514327 0.890840i −0.999862 0.0166228i \(-0.994709\pi\)
0.485535 0.874217i \(-0.338625\pi\)
\(752\) 26705.5 15418.4i 0.0472243 0.0272650i
\(753\) 483487. 60549.0i 0.852696 0.106787i
\(754\) −132158. + 228905.i −0.232462 + 0.402636i
\(755\) 116832.i 0.204960i
\(756\) 381931. + 973838.i 0.668253 + 1.70390i
\(757\) 1.00242e6 1.74928 0.874641 0.484771i \(-0.161097\pi\)
0.874641 + 0.484771i \(0.161097\pi\)
\(758\) −249553. 144079.i −0.434334 0.250763i
\(759\) −55899.3 446358.i −0.0970337 0.774819i
\(760\) 22851.0 + 39579.2i 0.0395620 + 0.0685235i
\(761\) −73367.2 + 42358.6i −0.126687 + 0.0731429i −0.562004 0.827134i \(-0.689970\pi\)
0.435317 + 0.900277i \(0.356636\pi\)
\(762\) −309792. + 734746.i −0.533531 + 1.26540i
\(763\) −127334. + 220548.i −0.218723 + 0.378839i
\(764\) 1.25840e6i 2.15592i
\(765\) −5137.12 5268.53i −0.00877802 0.00900258i
\(766\) 1.21313e6 2.06752
\(767\) −215373. 124345.i −0.366100 0.211368i
\(768\) 578717. 438288.i 0.981170 0.743082i
\(769\) 341763. + 591950.i 0.577926 + 1.00100i 0.995717 + 0.0924535i \(0.0294710\pi\)
−0.417791 + 0.908543i \(0.637196\pi\)
\(770\) −445153. + 257009.i −0.750807 + 0.433478i
\(771\) −618156. 816216.i −1.03989 1.37308i
\(772\) −366425. + 634666.i −0.614823 + 1.06490i
\(773\) 235888.i 0.394772i −0.980326 0.197386i \(-0.936755\pi\)
0.980326 0.197386i \(-0.0632453\pi\)
\(774\) 990981. 966263.i 1.65418 1.61292i
\(775\) −744879. −1.24017
\(776\) 938462. + 541821.i 1.55845 + 0.899773i
\(777\) 759486. + 320223.i 1.25799 + 0.530408i
\(778\) 99737.5 + 172750.i 0.164778 + 0.285404i
\(779\) −59049.7 + 34092.4i −0.0973068 + 0.0561801i
\(780\) 211466. 26482.7i 0.347577 0.0435284i
\(781\) −120232. + 208248.i −0.197114 + 0.341412i
\(782\) 20205.3i 0.0330409i
\(783\) 58837.6 389720.i 0.0959690 0.635665i
\(784\) 16843.8 0.0274036
\(785\) −57623.5 33268.9i −0.0935104 0.0539883i
\(786\) 24893.4 + 198775.i 0.0402939 + 0.321749i
\(787\) 228728. + 396169.i 0.369292 + 0.639633i 0.989455 0.144840i \(-0.0462668\pi\)
−0.620163 + 0.784473i \(0.712933\pi\)
\(788\) −1.50842e6 + 870888.i −2.42924 + 1.40252i
\(789\) 155121. 367908.i 0.249183 0.590997i
\(790\) −9187.01 + 15912.4i −0.0147204 + 0.0254965i
\(791\) 239269.i 0.382414i
\(792\) −196560. + 698182.i −0.313361 + 1.11306i
\(793\) 1120.41 0.00178169
\(794\) 1.33765e6 + 772291.i 2.12178 + 1.22501i
\(795\) 357583. 270813.i 0.565773 0.428484i
\(796\) −348022. 602791.i −0.549263 0.951351i
\(797\) −148023. + 85461.0i −0.233030 + 0.134540i −0.611969 0.790882i \(-0.709622\pi\)
0.378939 + 0.925422i \(0.376289\pi\)
\(798\) −102671. 135568.i −0.161229 0.212888i
\(799\) 3084.09 5341.79i 0.00483095 0.00836746i
\(800\) 434575.i 0.679023i
\(801\) −11503.9 45209.2i −0.0179300 0.0704632i
\(802\) −1.53465e6 −2.38594
\(803\) 102769. + 59333.5i 0.159378 + 0.0920171i
\(804\) −1.15761e6 488085.i −1.79082 0.755064i
\(805\) −125528. 217422.i −0.193709 0.335514i
\(806\) 648699. 374526.i 0.998557 0.576517i
\(807\) 39558.9 4954.12i 0.0607432 0.00760711i
\(808\) 396271. 686361.i 0.606973 1.05131i
\(809\) 252280.i 0.385465i 0.981251 + 0.192733i \(0.0617350\pi\)
−0.981251 + 0.192733i \(0.938265\pi\)
\(810\) −444952. + 242121.i −0.678178 + 0.369031i
\(811\) 166784. 0.253579 0.126789 0.991930i \(-0.459533\pi\)
0.126789 + 0.991930i \(0.459533\pi\)
\(812\) −671856. 387896.i −1.01898 0.588307i
\(813\) 96305.0 + 769000.i 0.145703 + 1.16344i
\(814\) 703865. + 1.21913e6i 1.06228 + 1.83993i
\(815\) −21975.7 + 12687.7i −0.0330847 + 0.0191015i
\(816\) −1039.09 + 2464.46i −0.00156054 + 0.00370119i
\(817\) −70580.7 + 122249.i −0.105741 + 0.183148i
\(818\) 1.95124e6i 2.91611i
\(819\) −312009. + 79393.4i −0.465156 + 0.118363i
\(820\) 399780. 0.594557
\(821\) −235829. 136156.i −0.349873 0.201999i 0.314756 0.949173i \(-0.398077\pi\)
−0.664629 + 0.747173i \(0.731411\pi\)
\(822\) −179735. + 136121.i −0.266005 + 0.201457i
\(823\) −482314. 835392.i −0.712082 1.23336i −0.964074 0.265633i \(-0.914419\pi\)
0.251992 0.967729i \(-0.418914\pi\)
\(824\) 221092. 127648.i 0.325626 0.188000i
\(825\) 330128. + 435903.i 0.485037 + 0.640445i
\(826\) 581759. 1.00764e6i 0.852674 1.47687i
\(827\) 430905.i 0.630043i 0.949085 + 0.315021i \(0.102012\pi\)
−0.949085 + 0.315021i \(0.897988\pi\)
\(828\) −839950. 236472.i −1.22516 0.344921i
\(829\) 462870. 0.673520 0.336760 0.941591i \(-0.390669\pi\)
0.336760 + 0.941591i \(0.390669\pi\)
\(830\) 880328. + 508257.i 1.27787 + 0.737781i
\(831\) 585597. + 246906.i 0.848002 + 0.357544i
\(832\) 241511. + 418310.i 0.348892 + 0.604299i
\(833\) 2917.80 1684.59i 0.00420500 0.00242776i
\(834\) 203436. 25477.2i 0.292480 0.0366285i
\(835\) −218104. + 377768.i −0.312818 + 0.541816i
\(836\) 182211.i 0.260713i
\(837\) −696618. + 873097.i −0.994361 + 1.24627i
\(838\) 241618. 0.344066
\(839\) −696889. 402349.i −0.990010 0.571583i −0.0847327 0.996404i \(-0.527004\pi\)
−0.905277 + 0.424821i \(0.860337\pi\)
\(840\) 50301.9 + 401663.i 0.0712895 + 0.569250i
\(841\) −207488. 359379.i −0.293360 0.508114i
\(842\) 1.36537e6 788297.i 1.92587 1.11190i
\(843\) −521880. + 1.23777e6i −0.734372 + 1.74174i
\(844\) 620301. 1.07439e6i 0.870799 1.50827i
\(845\) 270942.i 0.379457i
\(846\) −296436. 304019.i −0.414181 0.424777i
\(847\) 52037.6 0.0725354
\(848\) −141193. 81518.0i −0.196346 0.113360i
\(849\) 602143. 456029.i 0.835381 0.632670i
\(850\) 12280.2 + 21269.9i 0.0169968 + 0.0294393i
\(851\) −595447. + 343781.i −0.822212 + 0.474704i
\(852\) 281614. + 371845.i 0.387949 + 0.512250i
\(853\) −105790. + 183234.i −0.145394 + 0.251830i −0.929520 0.368772i \(-0.879778\pi\)
0.784126 + 0.620602i \(0.213112\pi\)
\(854\) 5241.94i 0.00718747i
\(855\) 36990.1 36067.4i 0.0506003 0.0493381i
\(856\) −819191. −1.11799
\(857\) −245348. 141652.i −0.334057 0.192868i 0.323584 0.946199i \(-0.395112\pi\)
−0.657641 + 0.753332i \(0.728446\pi\)
\(858\) −506674. 213629.i −0.688262 0.290192i
\(859\) 15498.6 + 26844.3i 0.0210042 + 0.0363803i 0.876336 0.481700i \(-0.159980\pi\)
−0.855332 + 0.518080i \(0.826647\pi\)
\(860\) 716771. 413828.i 0.969133 0.559529i
\(861\) −599257. + 75047.4i −0.808364 + 0.101235i
\(862\) −533236. + 923592.i −0.717637 + 1.24298i
\(863\) 1.35611e6i 1.82085i 0.413677 + 0.910424i \(0.364244\pi\)
−0.413677 + 0.910424i \(0.635756\pi\)
\(864\) −509379. 406419.i −0.682360 0.544435i
\(865\) −572482. −0.765120
\(866\) −1.51307e6 873569.i −2.01754 1.16483i
\(867\) −93340.9 745332.i −0.124175 0.991543i
\(868\) 1.09927e6 + 1.90399e6i 1.45903 + 2.52711i
\(869\) 25756.2 14870.4i 0.0341069 0.0196916i
\(870\) 145957. 346173.i 0.192835 0.457356i
\(871\) 193330. 334858.i 0.254838 0.441392i
\(872\) 342534.i 0.450475i
\(873\) 331969. 1.17916e6i 0.435582 1.54719i
\(874\) 141860. 0.185711
\(875\) 604045. + 348746.i 0.788957 + 0.455504i
\(876\) 183502. 138974.i 0.239129 0.181103i
\(877\) 226465. + 392249.i 0.294443 + 0.509991i 0.974855 0.222839i \(-0.0715324\pi\)
−0.680412 + 0.732830i \(0.738199\pi\)
\(878\) −208926. + 120623.i −0.271021 + 0.156474i
\(879\) 195085. + 257591.i 0.252491 + 0.333390i
\(880\) −28379.1 + 49154.0i −0.0366465 + 0.0634736i
\(881\) 1.13788e6i 1.46603i 0.680211 + 0.733016i \(0.261888\pi\)
−0.680211 + 0.733016i \(0.738112\pi\)
\(882\) −57195.7 224774.i −0.0735235 0.288941i
\(883\) 970367. 1.24456 0.622279 0.782796i \(-0.286207\pi\)
0.622279 + 0.782796i \(0.286207\pi\)
\(884\) −13418.4 7747.09i −0.0171710 0.00991367i
\(885\) 325708. + 137328.i 0.415854 + 0.175337i
\(886\) 450629. + 780512.i 0.574052 + 0.994287i
\(887\) 1.12349e6 648647.i 1.42798 0.824444i 0.431017 0.902344i \(-0.358155\pi\)
0.996961 + 0.0779001i \(0.0248215\pi\)
\(888\) 1.10002e6 137760.i 1.39501 0.174702i
\(889\) 360159. 623814.i 0.455712 0.789317i
\(890\) 44466.1i 0.0561369i
\(891\) 819675. + 20707.0i 1.03249 + 0.0260832i
\(892\) −590181. −0.741747
\(893\) 37504.4 + 21653.2i 0.0470305 + 0.0271531i
\(894\) 65300.5 + 521428.i 0.0817036 + 0.652407i
\(895\) −281130. 486932.i −0.350963 0.607886i
\(896\) −1.29725e6 + 748968.i −1.61588 + 0.932927i
\(897\) 104341. 247469.i 0.129679 0.307565i
\(898\) −571395. + 989685.i −0.708572 + 1.22728i
\(899\) 828370.i 1.02496i
\(900\) 1.02793e6 261565.i 1.26905 0.322920i
\(901\) −32611.4 −0.0401716
\(902\) −893289. 515740.i −1.09794 0.633896i
\(903\) −996731. + 754867.i −1.22237 + 0.925753i
\(904\) −160912. 278707.i −0.196902 0.341044i
\(905\) −467026. + 269638.i −0.570222 + 0.329218i
\(906\) 353026. + 466137.i 0.430081 + 0.567881i
\(907\) −76984.1 + 133340.i −0.0935807 + 0.162087i −0.909015 0.416763i \(-0.863165\pi\)
0.815435 + 0.578849i \(0.196498\pi\)
\(908\) 1.34099e6i 1.62650i
\(909\) −862397. 242792.i −1.04371 0.293837i
\(910\) −306880. −0.370583
\(911\) −927466. 535473.i −1.11753 0.645209i −0.176764 0.984253i \(-0.556563\pi\)
−0.940770 + 0.339044i \(0.889896\pi\)
\(912\) −17302.8 7295.41i −0.0208031 0.00877122i
\(913\) −822680. 1.42492e6i −0.986937 1.70942i
\(914\) 654339. 377783.i 0.783268 0.452220i
\(915\) −1580.15 + 197.888i −0.00188736 + 0.000236362i
\(916\) 384110. 665298.i 0.457788 0.792912i
\(917\) 180966.i 0.215208i
\(918\) 36415.7 + 5497.83i 0.0432119 + 0.00652388i
\(919\) 747688. 0.885298 0.442649 0.896695i \(-0.354039\pi\)
0.442649 + 0.896695i \(0.354039\pi\)
\(920\) −292438. 168839.i −0.345508 0.199479i
\(921\) −7889.33 62996.6i −0.00930081 0.0742674i
\(922\) −1.32840e6 2.30085e6i −1.56267 2.70662i
\(923\) −124328. + 71781.1i −0.145938 + 0.0842571i
\(924\) 627020. 1.48713e6i 0.734408 1.74183i
\(925\) 417881. 723790.i 0.488392 0.845920i
\(926\) 475625.i 0.554680i
\(927\) −201475. 206629.i −0.234457 0.240454i
\(928\) 483285. 0.561187
\(929\) 1.28522e6 + 742020.i 1.48917 + 0.859774i 0.999923 0.0123702i \(-0.00393765\pi\)
0.489249 + 0.872144i \(0.337271\pi\)
\(930\) −848728. + 642778.i −0.981302 + 0.743182i
\(931\) 11827.4 + 20485.7i 0.0136456 + 0.0236348i
\(932\) 1.02754e6 593253.i 1.18296 0.682980i
\(933\) −465455. 614589.i −0.534705 0.706027i
\(934\) −1.17554e6 + 2.03609e6i −1.34754 + 2.33401i
\(935\) 11353.1i 0.0129865i
\(936\) −310043. + 302309.i −0.353892 + 0.345064i
\(937\) −650560. −0.740983 −0.370491 0.928836i \(-0.620811\pi\)
−0.370491 + 0.928836i \(0.620811\pi\)
\(938\) 1.56666e6 + 904510.i 1.78061 + 1.02803i
\(939\) 609059. + 256798.i 0.690761 + 0.291246i
\(940\) −126957. 219895.i −0.143681 0.248863i
\(941\) −352436. + 203479.i −0.398017 + 0.229795i −0.685628 0.727952i \(-0.740472\pi\)
0.287611 + 0.957747i \(0.407139\pi\)
\(942\) 330433. 41381.4i 0.372376 0.0466341i
\(943\) 251898. 436300.i 0.283270 0.490638i
\(944\) 128476.i 0.144171i
\(945\) 426012. 167078.i 0.477043 0.187092i
\(946\) −2.13545e6 −2.38620
\(947\) 718809. + 415005.i 0.801519 + 0.462757i 0.844002 0.536340i \(-0.180194\pi\)
−0.0424832 + 0.999097i \(0.513527\pi\)
\(948\) −7168.83 57243.5i −0.00797685 0.0636956i
\(949\) 35423.3 + 61355.0i 0.0393330 + 0.0681267i
\(950\) −149335. + 86218.5i −0.165468 + 0.0955330i
\(951\) 172170. 408344.i 0.190370 0.451508i
\(952\) 14715.0 25487.1i 0.0162363 0.0281221i
\(953\) 927863.i 1.02164i −0.859688 0.510820i \(-0.829342\pi\)
0.859688 0.510820i \(-0.170658\pi\)
\(954\) −608382. + 2.16098e6i −0.668467 + 2.37440i
\(955\) 550496. 0.603597
\(956\) 479949. + 277099.i 0.525145 + 0.303193i
\(957\) −484762. + 367131.i −0.529303 + 0.400864i
\(958\) 83870.5 + 145268.i 0.0913857 + 0.158285i
\(959\) 176385. 101836.i 0.191790 0.110730i
\(960\) −414492. 547298.i −0.449753 0.593856i
\(961\) −712006. + 1.23323e6i −0.770968 + 1.33536i
\(962\) 840444.i 0.908152i
\(963\) 228364. + 897450.i 0.246249 + 0.967737i
\(964\) 1.56002e6 1.67872
\(965\) 277639. + 160295.i 0.298143 + 0.172133i
\(966\) 1.15780e6 + 488166.i 1.24074 + 0.523134i
\(967\) 556238. + 963433.i 0.594851 + 1.03031i 0.993568 + 0.113238i \(0.0361222\pi\)
−0.398717 + 0.917074i \(0.630544\pi\)
\(968\) 60614.8 34995.9i 0.0646886 0.0373480i
\(969\) −3726.96 + 466.742i −0.00396924 + 0.000497084i
\(970\) 583825. 1.01121e6i 0.620496 1.07473i
\(971\) 68160.6i 0.0722927i 0.999347 + 0.0361464i \(0.0115083\pi\)
−0.999347 + 0.0361464i \(0.988492\pi\)
\(972\) 654739. 1.44949e6i 0.693004 1.53420i
\(973\) −185210. −0.195631
\(974\) −1.40312e6 810090.i −1.47903 0.853917i
\(975\) 40566.3 + 323924.i 0.0426733 + 0.340748i
\(976\) 289.408 + 501.270i 0.000303817 + 0.000526226i
\(977\) −685124. + 395556.i −0.717761 + 0.414399i −0.813928 0.580966i \(-0.802675\pi\)
0.0961671 + 0.995365i \(0.469342\pi\)
\(978\) 49340.9 117024.i 0.0515857 0.122348i
\(979\) −35987.0 + 62331.4i −0.0375475 + 0.0650341i
\(980\) 138693.i 0.144412i
\(981\) 375257. 95487.4i 0.389933 0.0992220i
\(982\) 2.24263e6 2.32560
\(983\) −948495. 547614.i −0.981585 0.566718i −0.0788368 0.996888i \(-0.525121\pi\)
−0.902748 + 0.430169i \(0.858454\pi\)
\(984\) −647560. + 490425.i −0.668790 + 0.506504i
\(985\) 380975. + 659868.i 0.392667 + 0.680119i
\(986\) −23654.0 + 13656.6i −0.0243305 + 0.0140472i
\(987\) 231583. + 305783.i 0.237724 + 0.313892i
\(988\) 54391.9 94209.5i 0.0557212 0.0965119i
\(989\) 1.04300e6i 1.06633i
\(990\) 752307. + 211798.i 0.767582 + 0.216098i
\(991\) 278492. 0.283573 0.141787 0.989897i \(-0.454715\pi\)
0.141787 + 0.989897i \(0.454715\pi\)
\(992\) −1.18610e6 684795.i −1.20531 0.695884i
\(993\) −680118. 286759.i −0.689741 0.290816i
\(994\) −335833. 581680.i −0.339900 0.588723i
\(995\) −263695. + 152244.i −0.266351 + 0.153778i
\(996\) −3.16691e6 + 396605.i −3.19240 + 0.399797i
\(997\) −665723. + 1.15307e6i −0.669736 + 1.16002i 0.308242 + 0.951308i \(0.400259\pi\)
−0.977978 + 0.208708i \(0.933074\pi\)
\(998\) 1.29633e6i 1.30154i
\(999\) −457572. 1.16671e6i −0.458488 1.16904i
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 9.5.d.a.2.1 6
3.2 odd 2 27.5.d.a.8.3 6
4.3 odd 2 144.5.q.a.65.2 6
9.2 odd 6 81.5.b.a.80.1 6
9.4 even 3 27.5.d.a.17.3 6
9.5 odd 6 inner 9.5.d.a.5.1 yes 6
9.7 even 3 81.5.b.a.80.6 6
12.11 even 2 432.5.q.a.305.2 6
36.7 odd 6 1296.5.e.c.161.4 6
36.11 even 6 1296.5.e.c.161.3 6
36.23 even 6 144.5.q.a.113.2 6
36.31 odd 6 432.5.q.a.17.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9.5.d.a.2.1 6 1.1 even 1 trivial
9.5.d.a.5.1 yes 6 9.5 odd 6 inner
27.5.d.a.8.3 6 3.2 odd 2
27.5.d.a.17.3 6 9.4 even 3
81.5.b.a.80.1 6 9.2 odd 6
81.5.b.a.80.6 6 9.7 even 3
144.5.q.a.65.2 6 4.3 odd 2
144.5.q.a.113.2 6 36.23 even 6
432.5.q.a.17.2 6 36.31 odd 6
432.5.q.a.305.2 6 12.11 even 2
1296.5.e.c.161.3 6 36.11 even 6
1296.5.e.c.161.4 6 36.7 odd 6