Properties

Label 38.6.e.b.25.5
Level $38$
Weight $6$
Character 38.25
Analytic conductor $6.095$
Analytic rank $0$
Dimension $30$
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] = [38,6,Mod(5,38)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(38, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("38.5");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 38.e (of order \(9\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.09458515289\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(5\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 25.5
Character \(\chi\) \(=\) 38.25
Dual form 38.6.e.b.35.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.06418 - 2.57115i) q^{2} +(25.6880 + 9.34967i) q^{3} +(2.77837 - 15.7569i) q^{4} +(-15.8279 - 89.7646i) q^{5} +(102.752 - 37.3987i) q^{6} +(-22.7823 + 39.4602i) q^{7} +(-32.0000 - 55.4256i) q^{8} +(386.309 + 324.152i) q^{9} +O(q^{10})\) \(q+(3.06418 - 2.57115i) q^{2} +(25.6880 + 9.34967i) q^{3} +(2.77837 - 15.7569i) q^{4} +(-15.8279 - 89.7646i) q^{5} +(102.752 - 37.3987i) q^{6} +(-22.7823 + 39.4602i) q^{7} +(-32.0000 - 55.4256i) q^{8} +(386.309 + 324.152i) q^{9} +(-279.298 - 234.359i) q^{10} +(203.862 + 353.099i) q^{11} +(218.693 - 378.787i) q^{12} +(-395.824 + 144.068i) q^{13} +(31.6489 + 179.490i) q^{14} +(432.682 - 2453.86i) q^{15} +(-240.561 - 87.5572i) q^{16} +(-646.820 + 542.747i) q^{17} +2017.16 q^{18} +(1163.24 - 1059.70i) q^{19} -1458.39 q^{20} +(-954.172 + 800.646i) q^{21} +(1532.54 + 557.799i) q^{22} +(-809.743 + 4592.28i) q^{23} +(-303.805 - 1722.96i) q^{24} +(-4870.62 + 1772.76i) q^{25} +(-842.455 + 1459.17i) q^{26} +(3571.40 + 6185.84i) q^{27} +(558.473 + 468.614i) q^{28} +(-3060.04 - 2567.68i) q^{29} +(-4983.43 - 8631.55i) q^{30} +(3731.62 - 6463.36i) q^{31} +(-962.245 + 350.229i) q^{32} +(1935.45 + 10976.5i) q^{33} +(-586.489 + 3326.14i) q^{34} +(3902.72 + 1420.47i) q^{35} +(6180.94 - 5186.43i) q^{36} -12556.5 q^{37} +(839.717 - 6237.99i) q^{38} -11514.9 q^{39} +(-4468.77 + 3749.74i) q^{40} +(5873.19 + 2137.66i) q^{41} +(-865.173 + 4906.64i) q^{42} +(182.346 + 1034.14i) q^{43} +(6130.16 - 2231.20i) q^{44} +(22982.9 - 39807.5i) q^{45} +(9326.24 + 16153.5i) q^{46} +(-4079.56 - 3423.16i) q^{47} +(-5360.91 - 4498.34i) q^{48} +(7365.43 + 12757.3i) q^{49} +(-10366.4 + 17955.2i) q^{50} +(-21690.0 + 7894.52i) q^{51} +(1170.33 + 6637.25i) q^{52} +(879.321 - 4986.88i) q^{53} +(26848.1 + 9771.92i) q^{54} +(28469.1 - 23888.4i) q^{55} +2916.14 q^{56} +(39789.2 - 16345.8i) q^{57} -15978.4 q^{58} +(5503.27 - 4617.79i) q^{59} +(-37463.1 - 13635.5i) q^{60} +(8084.99 - 45852.3i) q^{61} +(-5183.92 - 29399.5i) q^{62} +(-21592.1 + 7858.88i) q^{63} +(-2048.00 + 3547.24i) q^{64} +(19197.3 + 33250.7i) q^{65} +(34152.7 + 28657.5i) q^{66} +(-30001.1 - 25173.9i) q^{67} +(6754.91 + 11699.8i) q^{68} +(-63737.0 + 110396. i) q^{69} +(15610.9 - 5681.90i) q^{70} +(-3784.11 - 21460.8i) q^{71} +(5604.42 - 31784.3i) q^{72} +(13216.5 + 4810.40i) q^{73} +(-38475.3 + 32284.6i) q^{74} -141691. q^{75} +(-13465.8 - 21273.3i) q^{76} -18577.8 q^{77} +(-35283.8 + 29606.6i) q^{78} +(89140.7 + 32444.6i) q^{79} +(-4051.95 + 22979.7i) q^{80} +(12627.2 + 71612.5i) q^{81} +(23492.7 - 8550.66i) q^{82} +(-12207.9 + 21144.6i) q^{83} +(9964.67 + 17259.3i) q^{84} +(58957.2 + 49471.0i) q^{85} +(3217.66 + 2699.94i) q^{86} +(-54599.5 - 94569.1i) q^{87} +(13047.2 - 22598.3i) q^{88} +(47985.0 - 17465.1i) q^{89} +(-31927.5 - 181070. i) q^{90} +(3332.85 - 18901.5i) q^{91} +(70110.4 + 25518.1i) q^{92} +(156288. - 131141. i) q^{93} -21301.9 q^{94} +(-113536. - 87644.9i) q^{95} -27992.7 q^{96} +(99852.9 - 83786.5i) q^{97} +(55369.9 + 20153.0i) q^{98} +(-35704.0 + 202487. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q + 15 q^{3} + 60 q^{6} - 84 q^{7} - 960 q^{8} - 345 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q + 15 q^{3} + 60 q^{6} - 84 q^{7} - 960 q^{8} - 345 q^{9} - 126 q^{11} - 2610 q^{13} - 864 q^{14} - 5160 q^{15} + 1902 q^{17} + 17016 q^{18} - 2400 q^{19} + 3456 q^{20} - 6426 q^{21} + 216 q^{22} - 3306 q^{23} + 960 q^{24} - 18060 q^{25} + 456 q^{26} + 13017 q^{27} + 6048 q^{28} + 5988 q^{29} - 6840 q^{31} + 51867 q^{33} - 10752 q^{34} + 24408 q^{35} - 5520 q^{36} - 8556 q^{37} + 2772 q^{38} + 9912 q^{39} - 40527 q^{41} + 27432 q^{42} + 3678 q^{43} + 864 q^{44} - 31770 q^{45} - 15744 q^{46} - 133740 q^{47} - 7680 q^{48} - 63777 q^{49} - 107580 q^{50} + 45657 q^{51} + 5760 q^{52} - 64626 q^{53} + 1476 q^{54} + 142056 q^{55} + 10752 q^{56} + 232824 q^{57} + 117264 q^{58} + 169041 q^{59} - 56640 q^{60} + 61698 q^{61} - 101616 q^{62} - 188064 q^{63} - 61440 q^{64} - 80646 q^{65} - 173772 q^{66} - 72129 q^{67} - 65904 q^{68} - 124224 q^{69} + 97632 q^{70} + 417828 q^{71} + 44160 q^{72} + 239082 q^{73} - 116112 q^{74} - 174960 q^{75} + 6912 q^{76} + 242436 q^{77} + 336624 q^{78} - 145740 q^{79} + 14781 q^{81} - 162108 q^{82} - 201630 q^{83} - 54528 q^{84} - 46512 q^{85} - 75720 q^{86} - 376512 q^{87} - 8064 q^{88} + 416928 q^{89} + 560640 q^{90} - 380316 q^{91} + 269376 q^{92} - 205146 q^{93} + 5616 q^{94} + 708168 q^{95} + 858363 q^{97} + 308328 q^{98} - 1068531 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).

\(n\) \(21\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.06418 2.57115i 0.541675 0.454519i
\(3\) 25.6880 + 9.34967i 1.64789 + 0.599782i 0.988392 0.151927i \(-0.0485479\pi\)
0.659495 + 0.751709i \(0.270770\pi\)
\(4\) 2.77837 15.7569i 0.0868241 0.492404i
\(5\) −15.8279 89.7646i −0.283138 1.60576i −0.711860 0.702321i \(-0.752147\pi\)
0.428722 0.903437i \(-0.358964\pi\)
\(6\) 102.752 37.3987i 1.16523 0.424110i
\(7\) −22.7823 + 39.4602i −0.175733 + 0.304378i −0.940415 0.340030i \(-0.889563\pi\)
0.764682 + 0.644408i \(0.222896\pi\)
\(8\) −32.0000 55.4256i −0.176777 0.306186i
\(9\) 386.309 + 324.152i 1.58975 + 1.33396i
\(10\) −279.298 234.359i −0.883217 0.741107i
\(11\) 203.862 + 353.099i 0.507989 + 0.879863i 0.999957 + 0.00924962i \(0.00294429\pi\)
−0.491968 + 0.870613i \(0.663722\pi\)
\(12\) 218.693 378.787i 0.438411 0.759350i
\(13\) −395.824 + 144.068i −0.649597 + 0.236434i −0.645739 0.763559i \(-0.723450\pi\)
−0.00385856 + 0.999993i \(0.501228\pi\)
\(14\) 31.6489 + 179.490i 0.0431557 + 0.244748i
\(15\) 432.682 2453.86i 0.496524 2.81593i
\(16\) −240.561 87.5572i −0.234923 0.0855050i
\(17\) −646.820 + 542.747i −0.542827 + 0.455486i −0.872503 0.488608i \(-0.837505\pi\)
0.329677 + 0.944094i \(0.393060\pi\)
\(18\) 2017.16 1.46744
\(19\) 1163.24 1059.70i 0.739240 0.673442i
\(20\) −1458.39 −0.815265
\(21\) −954.172 + 800.646i −0.472149 + 0.396180i
\(22\) 1532.54 + 557.799i 0.675080 + 0.245709i
\(23\) −809.743 + 4592.28i −0.319174 + 1.81013i 0.228624 + 0.973515i \(0.426577\pi\)
−0.547798 + 0.836611i \(0.684534\pi\)
\(24\) −303.805 1722.96i −0.107663 0.610588i
\(25\) −4870.62 + 1772.76i −1.55860 + 0.567284i
\(26\) −842.455 + 1459.17i −0.244407 + 0.423325i
\(27\) 3571.40 + 6185.84i 0.942820 + 1.63301i
\(28\) 558.473 + 468.614i 0.134619 + 0.112959i
\(29\) −3060.04 2567.68i −0.675667 0.566952i 0.239070 0.971002i \(-0.423158\pi\)
−0.914737 + 0.404051i \(0.867602\pi\)
\(30\) −4983.43 8631.55i −1.01094 1.75100i
\(31\) 3731.62 6463.36i 0.697419 1.20796i −0.271940 0.962314i \(-0.587665\pi\)
0.969358 0.245650i \(-0.0790015\pi\)
\(32\) −962.245 + 350.229i −0.166116 + 0.0604612i
\(33\) 1935.45 + 10976.5i 0.309383 + 1.75460i
\(34\) −586.489 + 3326.14i −0.0870087 + 0.493451i
\(35\) 3902.72 + 1420.47i 0.538515 + 0.196003i
\(36\) 6180.94 5186.43i 0.794874 0.666979i
\(37\) −12556.5 −1.50787 −0.753934 0.656950i \(-0.771846\pi\)
−0.753934 + 0.656950i \(0.771846\pi\)
\(38\) 839.717 6237.99i 0.0943352 0.700786i
\(39\) −11514.9 −1.21227
\(40\) −4468.77 + 3749.74i −0.441609 + 0.370554i
\(41\) 5873.19 + 2137.66i 0.545650 + 0.198600i 0.600113 0.799915i \(-0.295122\pi\)
−0.0544628 + 0.998516i \(0.517345\pi\)
\(42\) −865.173 + 4906.64i −0.0756798 + 0.429201i
\(43\) 182.346 + 1034.14i 0.0150392 + 0.0852917i 0.991404 0.130839i \(-0.0417672\pi\)
−0.976364 + 0.216131i \(0.930656\pi\)
\(44\) 6130.16 2231.20i 0.477354 0.173742i
\(45\) 22982.9 39807.5i 1.69189 2.93045i
\(46\) 9326.24 + 16153.5i 0.649849 + 1.12557i
\(47\) −4079.56 3423.16i −0.269382 0.226038i 0.498083 0.867130i \(-0.334038\pi\)
−0.767465 + 0.641091i \(0.778482\pi\)
\(48\) −5360.91 4498.34i −0.335842 0.281805i
\(49\) 7365.43 + 12757.3i 0.438236 + 0.759047i
\(50\) −10366.4 + 17955.2i −0.586413 + 1.01570i
\(51\) −21690.0 + 7894.52i −1.16771 + 0.425011i
\(52\) 1170.33 + 6637.25i 0.0600204 + 0.340392i
\(53\) 879.321 4986.88i 0.0429989 0.243859i −0.955731 0.294242i \(-0.904933\pi\)
0.998730 + 0.0503826i \(0.0160441\pi\)
\(54\) 26848.1 + 9771.92i 1.25294 + 0.456032i
\(55\) 28469.1 23888.4i 1.26902 1.06483i
\(56\) 2916.14 0.124262
\(57\) 39789.2 16345.8i 1.62210 0.666374i
\(58\) −15978.4 −0.623683
\(59\) 5503.27 4617.79i 0.205822 0.172705i −0.534050 0.845453i \(-0.679331\pi\)
0.739872 + 0.672748i \(0.234886\pi\)
\(60\) −37463.1 13635.5i −1.34346 0.488981i
\(61\) 8084.99 45852.3i 0.278199 1.57774i −0.450416 0.892819i \(-0.648724\pi\)
0.728615 0.684924i \(-0.240165\pi\)
\(62\) −5183.92 29399.5i −0.171269 0.971315i
\(63\) −21592.1 + 7858.88i −0.685399 + 0.249465i
\(64\) −2048.00 + 3547.24i −0.0625000 + 0.108253i
\(65\) 19197.3 + 33250.7i 0.563582 + 0.976152i
\(66\) 34152.7 + 28657.5i 0.965083 + 0.809801i
\(67\) −30001.1 25173.9i −0.816489 0.685116i 0.135658 0.990756i \(-0.456685\pi\)
−0.952147 + 0.305640i \(0.901130\pi\)
\(68\) 6754.91 + 11699.8i 0.177152 + 0.306837i
\(69\) −63737.0 + 110396.i −1.61164 + 2.79145i
\(70\) 15610.9 5681.90i 0.380787 0.138595i
\(71\) −3784.11 21460.8i −0.0890877 0.505242i −0.996399 0.0847830i \(-0.972980\pi\)
0.907312 0.420459i \(-0.138131\pi\)
\(72\) 5604.42 31784.3i 0.127409 0.722572i
\(73\) 13216.5 + 4810.40i 0.290274 + 0.105651i 0.483053 0.875591i \(-0.339528\pi\)
−0.192779 + 0.981242i \(0.561750\pi\)
\(74\) −38475.3 + 32284.6i −0.816775 + 0.685356i
\(75\) −141691. −2.90864
\(76\) −13465.8 21273.3i −0.267422 0.422476i
\(77\) −18577.8 −0.357082
\(78\) −35283.8 + 29606.6i −0.656657 + 0.551001i
\(79\) 89140.7 + 32444.6i 1.60697 + 0.584890i 0.980838 0.194826i \(-0.0624141\pi\)
0.626134 + 0.779716i \(0.284636\pi\)
\(80\) −4051.95 + 22979.7i −0.0707846 + 0.401440i
\(81\) 12627.2 + 71612.5i 0.213843 + 1.21276i
\(82\) 23492.7 8550.66i 0.385833 0.140432i
\(83\) −12207.9 + 21144.6i −0.194511 + 0.336903i −0.946740 0.321999i \(-0.895645\pi\)
0.752229 + 0.658902i \(0.228979\pi\)
\(84\) 9964.67 + 17259.3i 0.154087 + 0.266886i
\(85\) 58957.2 + 49471.0i 0.885095 + 0.742683i
\(86\) 3217.66 + 2699.94i 0.0469131 + 0.0393648i
\(87\) −54599.5 94569.1i −0.773375 1.33953i
\(88\) 13047.2 22598.3i 0.179601 0.311078i
\(89\) 47985.0 17465.1i 0.642141 0.233720i −0.000366096 1.00000i \(-0.500117\pi\)
0.642507 + 0.766280i \(0.277894\pi\)
\(90\) −31927.5 181070.i −0.415488 2.35635i
\(91\) 3332.85 18901.5i 0.0421902 0.239273i
\(92\) 70110.4 + 25518.1i 0.863601 + 0.314325i
\(93\) 156288. 131141.i 1.87378 1.57229i
\(94\) −21301.9 −0.248656
\(95\) −113536. 87644.9i −1.29069 0.996363i
\(96\) −27992.7 −0.310003
\(97\) 99852.9 83786.5i 1.07754 0.904159i 0.0818212 0.996647i \(-0.473926\pi\)
0.995714 + 0.0924878i \(0.0294819\pi\)
\(98\) 55369.9 + 20153.0i 0.582383 + 0.211970i
\(99\) −35704.0 + 202487.i −0.366125 + 2.07640i
\(100\) 14400.9 + 81671.4i 0.144009 + 0.816714i
\(101\) −23974.3 + 8725.91i −0.233852 + 0.0851153i −0.456288 0.889832i \(-0.650821\pi\)
0.222436 + 0.974947i \(0.428599\pi\)
\(102\) −46164.1 + 79958.5i −0.439343 + 0.760965i
\(103\) 19591.6 + 33933.6i 0.181960 + 0.315165i 0.942548 0.334071i \(-0.108422\pi\)
−0.760588 + 0.649235i \(0.775089\pi\)
\(104\) 20651.5 + 17328.6i 0.187226 + 0.157102i
\(105\) 86972.2 + 72978.4i 0.769852 + 0.645983i
\(106\) −10127.6 17541.5i −0.0875472 0.151636i
\(107\) −21463.4 + 37175.7i −0.181234 + 0.313906i −0.942301 0.334767i \(-0.891342\pi\)
0.761067 + 0.648673i \(0.224676\pi\)
\(108\) 107392. 39087.7i 0.885961 0.322463i
\(109\) 17214.9 + 97630.8i 0.138784 + 0.787083i 0.972150 + 0.234361i \(0.0752998\pi\)
−0.833366 + 0.552722i \(0.813589\pi\)
\(110\) 25813.7 146397.i 0.203408 1.15358i
\(111\) −322551. 117399.i −2.48480 0.904392i
\(112\) 8935.57 7497.83i 0.0673096 0.0564795i
\(113\) −168649. −1.24248 −0.621238 0.783622i \(-0.713370\pi\)
−0.621238 + 0.783622i \(0.713370\pi\)
\(114\) 79893.8 152390.i 0.575772 1.09824i
\(115\) 425041. 2.99699
\(116\) −48960.7 + 41082.9i −0.337833 + 0.283476i
\(117\) −199610. 72652.2i −1.34809 0.490664i
\(118\) 4989.96 28299.5i 0.0329907 0.187100i
\(119\) −6680.79 37888.7i −0.0432475 0.245269i
\(120\) −149853. + 54541.9i −0.949973 + 0.345762i
\(121\) −2593.84 + 4492.66i −0.0161057 + 0.0278959i
\(122\) −93119.2 161287.i −0.566422 0.981071i
\(123\) 130884. + 109825.i 0.780052 + 0.654542i
\(124\) −91474.9 76756.5i −0.534254 0.448292i
\(125\) 93802.2 + 162470.i 0.536955 + 0.930033i
\(126\) −45955.6 + 79597.5i −0.257877 + 0.446656i
\(127\) 9722.65 3538.75i 0.0534903 0.0194689i −0.315136 0.949046i \(-0.602050\pi\)
0.368627 + 0.929577i \(0.379828\pi\)
\(128\) 2845.05 + 16135.1i 0.0153485 + 0.0870455i
\(129\) −4984.73 + 28269.8i −0.0263735 + 0.149571i
\(130\) 144317. + 52526.9i 0.748959 + 0.272599i
\(131\) −171444. + 143858.i −0.872858 + 0.732415i −0.964698 0.263359i \(-0.915170\pi\)
0.0918401 + 0.995774i \(0.470725\pi\)
\(132\) 178333. 0.890832
\(133\) 15314.7 + 70044.2i 0.0750725 + 0.343355i
\(134\) −156655. −0.753671
\(135\) 498742. 418494.i 2.35527 1.97631i
\(136\) 50780.3 + 18482.5i 0.235423 + 0.0856868i
\(137\) 52594.2 298276.i 0.239407 1.35774i −0.593725 0.804668i \(-0.702343\pi\)
0.833132 0.553074i \(-0.186545\pi\)
\(138\) 88542.5 + 502149.i 0.395780 + 2.24458i
\(139\) −273068. + 99388.5i −1.19876 + 0.436314i −0.862792 0.505559i \(-0.831286\pi\)
−0.335970 + 0.941873i \(0.609064\pi\)
\(140\) 33225.5 57548.3i 0.143269 0.248149i
\(141\) −72790.4 126077.i −0.308337 0.534056i
\(142\) −66774.0 56030.0i −0.277899 0.233185i
\(143\) −131564. 110395.i −0.538018 0.451451i
\(144\) −64549.2 111802.i −0.259409 0.449309i
\(145\) −182053. + 315325.i −0.719080 + 1.24548i
\(146\) 52865.9 19241.6i 0.205255 0.0747067i
\(147\) 69926.7 + 396574.i 0.266901 + 1.51367i
\(148\) −34886.5 + 197851.i −0.130919 + 0.742480i
\(149\) 50157.0 + 18255.7i 0.185083 + 0.0673646i 0.432899 0.901442i \(-0.357491\pi\)
−0.247816 + 0.968807i \(0.579713\pi\)
\(150\) −434167. + 364310.i −1.57554 + 1.32203i
\(151\) 270164. 0.964241 0.482120 0.876105i \(-0.339867\pi\)
0.482120 + 0.876105i \(0.339867\pi\)
\(152\) −95958.4 30562.8i −0.336879 0.107296i
\(153\) −425804. −1.47056
\(154\) −56925.7 + 47766.3i −0.193422 + 0.162301i
\(155\) −639245. 232666.i −2.13717 0.777865i
\(156\) −31992.8 + 181440.i −0.105254 + 0.596927i
\(157\) −60964.1 345744.i −0.197390 1.11945i −0.908974 0.416853i \(-0.863133\pi\)
0.711584 0.702601i \(-0.247978\pi\)
\(158\) 356563. 129778.i 1.13630 0.413580i
\(159\) 69213.7 119882.i 0.217120 0.376062i
\(160\) 46668.5 + 80832.2i 0.144120 + 0.249623i
\(161\) −162764. 136575.i −0.494874 0.415248i
\(162\) 222818. + 186967.i 0.667058 + 0.559728i
\(163\) −224025. 388022.i −0.660430 1.14390i −0.980503 0.196506i \(-0.937041\pi\)
0.320073 0.947393i \(-0.396293\pi\)
\(164\) 50000.9 86604.1i 0.145167 0.251437i
\(165\) 954663. 347469.i 2.72986 0.993588i
\(166\) 16959.0 + 96179.1i 0.0477672 + 0.270901i
\(167\) −119756. + 679171.i −0.332282 + 1.88446i 0.120296 + 0.992738i \(0.461616\pi\)
−0.452577 + 0.891725i \(0.649495\pi\)
\(168\) 74909.8 + 27264.9i 0.204770 + 0.0745300i
\(169\) −148506. + 124611.i −0.399969 + 0.335614i
\(170\) 307853. 0.816998
\(171\) 792874. 32306.7i 2.07355 0.0844895i
\(172\) 16801.4 0.0433037
\(173\) −92158.5 + 77330.1i −0.234110 + 0.196442i −0.752294 0.658828i \(-0.771053\pi\)
0.518184 + 0.855269i \(0.326608\pi\)
\(174\) −410454. 149393.i −1.02776 0.374074i
\(175\) 41010.7 232583.i 0.101228 0.574094i
\(176\) −18124.9 102792.i −0.0441057 0.250136i
\(177\) 184543. 67168.1i 0.442756 0.161150i
\(178\) 102129. 176893.i 0.241601 0.418466i
\(179\) −2927.25 5070.15i −0.00682854 0.0118274i 0.862591 0.505902i \(-0.168840\pi\)
−0.869419 + 0.494075i \(0.835507\pi\)
\(180\) −563389. 472739.i −1.29607 1.08753i
\(181\) 68249.8 + 57268.4i 0.154848 + 0.129933i 0.716920 0.697155i \(-0.245551\pi\)
−0.562072 + 0.827088i \(0.689996\pi\)
\(182\) −38386.2 66486.8i −0.0859006 0.148784i
\(183\) 636391. 1.10226e6i 1.40474 2.43308i
\(184\) 280442. 102072.i 0.610658 0.222261i
\(185\) 198743. + 1.12713e6i 0.426936 + 2.42127i
\(186\) 141711. 803682.i 0.300345 1.70334i
\(187\) −323505. 117746.i −0.676515 0.246231i
\(188\) −65272.9 + 54770.5i −0.134691 + 0.113019i
\(189\) −325459. −0.662738
\(190\) −573241. + 23357.5i −1.15200 + 0.0469399i
\(191\) 214632. 0.425707 0.212854 0.977084i \(-0.431724\pi\)
0.212854 + 0.977084i \(0.431724\pi\)
\(192\) −85774.6 + 71973.4i −0.167921 + 0.140903i
\(193\) 258131. + 93951.9i 0.498823 + 0.181557i 0.579165 0.815211i \(-0.303379\pi\)
−0.0803416 + 0.996767i \(0.525601\pi\)
\(194\) 90539.3 513474.i 0.172716 0.979521i
\(195\) 182257. + 1.03363e6i 0.343241 + 1.94661i
\(196\) 221480. 80612.0i 0.411807 0.149886i
\(197\) −374230. + 648185.i −0.687026 + 1.18996i 0.285770 + 0.958298i \(0.407751\pi\)
−0.972796 + 0.231665i \(0.925583\pi\)
\(198\) 411222. + 712258.i 0.745442 + 1.29114i
\(199\) 125533. + 105335.i 0.224711 + 0.188555i 0.748192 0.663482i \(-0.230922\pi\)
−0.523481 + 0.852038i \(0.675367\pi\)
\(200\) 254116. + 213229.i 0.449218 + 0.376939i
\(201\) −535301. 927169.i −0.934562 1.61871i
\(202\) −51025.7 + 88379.2i −0.0879854 + 0.152395i
\(203\) 171036. 62252.0i 0.291305 0.106026i
\(204\) 64130.5 + 363702.i 0.107892 + 0.611886i
\(205\) 98926.3 561039.i 0.164410 0.932413i
\(206\) 147281. + 53605.8i 0.241812 + 0.0880123i
\(207\) −1.80141e6 + 1.51156e6i −2.92204 + 2.45188i
\(208\) 107834. 0.172822
\(209\) 611321. + 194706.i 0.968063 + 0.308328i
\(210\) 454137. 0.710621
\(211\) 245769. 206224.i 0.380032 0.318885i −0.432683 0.901546i \(-0.642433\pi\)
0.812715 + 0.582661i \(0.197989\pi\)
\(212\) −76134.7 27710.8i −0.116344 0.0423457i
\(213\) 103445. 586664.i 0.156228 0.886014i
\(214\) 29816.6 + 169098.i 0.0445066 + 0.252409i
\(215\) 89942.7 32736.5i 0.132700 0.0482987i
\(216\) 228569. 395894.i 0.333337 0.577357i
\(217\) 170030. + 294501.i 0.245119 + 0.424558i
\(218\) 303773. + 254896.i 0.432921 + 0.363263i
\(219\) 294529. + 247139.i 0.414971 + 0.348202i
\(220\) −297310. 514956.i −0.414146 0.717321i
\(221\) 177835. 308019.i 0.244926 0.424225i
\(222\) −1.29020e6 + 469596.i −1.75702 + 0.639502i
\(223\) −83074.5 471139.i −0.111868 0.634434i −0.988253 0.152824i \(-0.951163\pi\)
0.876386 0.481610i \(-0.159948\pi\)
\(224\) 8102.11 45949.4i 0.0107889 0.0611871i
\(225\) −2.45621e6 893986.i −3.23451 1.17727i
\(226\) −516771. + 433623.i −0.673019 + 0.564730i
\(227\) −218041. −0.280849 −0.140425 0.990091i \(-0.544847\pi\)
−0.140425 + 0.990091i \(0.544847\pi\)
\(228\) −147010. 672370.i −0.187288 0.856587i
\(229\) −464565. −0.585407 −0.292703 0.956203i \(-0.594555\pi\)
−0.292703 + 0.956203i \(0.594555\pi\)
\(230\) 1.30240e6 1.09284e6i 1.62340 1.36219i
\(231\) −477227. 173696.i −0.588430 0.214171i
\(232\) −44394.0 + 251771.i −0.0541507 + 0.307104i
\(233\) 15563.2 + 88263.2i 0.0187806 + 0.106510i 0.992757 0.120139i \(-0.0383341\pi\)
−0.973976 + 0.226649i \(0.927223\pi\)
\(234\) −798442. + 290609.i −0.953243 + 0.346952i
\(235\) −242707. + 420381.i −0.286690 + 0.496562i
\(236\) −57472.1 99544.5i −0.0671702 0.116342i
\(237\) 1.98650e6 + 1.66687e6i 2.29730 + 1.92766i
\(238\) −117889. 98920.3i −0.134905 0.113199i
\(239\) 376740. + 652532.i 0.426625 + 0.738937i 0.996571 0.0827460i \(-0.0263690\pi\)
−0.569945 + 0.821683i \(0.693036\pi\)
\(240\) −318940. + 552419.i −0.357421 + 0.619072i
\(241\) 261371. 95131.4i 0.289878 0.105507i −0.192988 0.981201i \(-0.561818\pi\)
0.482866 + 0.875694i \(0.339596\pi\)
\(242\) 3603.32 + 20435.4i 0.00395516 + 0.0224308i
\(243\) −43784.2 + 248312.i −0.0475665 + 0.269763i
\(244\) −700028. 254789.i −0.752732 0.273972i
\(245\) 1.02857e6 863077.i 1.09476 0.918616i
\(246\) 683428. 0.720037
\(247\) −307769. + 587043.i −0.320983 + 0.612248i
\(248\) −477648. −0.493150
\(249\) −511291. + 429024.i −0.522600 + 0.438514i
\(250\) 705162. + 256658.i 0.713573 + 0.259720i
\(251\) 211349. 1.19862e6i 0.211746 1.20087i −0.674717 0.738076i \(-0.735734\pi\)
0.886464 0.462798i \(-0.153154\pi\)
\(252\) 63840.9 + 362060.i 0.0633283 + 0.359153i
\(253\) −1.78661e6 + 650271.i −1.75480 + 0.638694i
\(254\) 20693.2 35841.8i 0.0201254 0.0348582i
\(255\) 1.05196e6 + 1.82204e6i 1.01309 + 1.75472i
\(256\) 50203.5 + 42125.7i 0.0478778 + 0.0401742i
\(257\) 299064. + 250945.i 0.282444 + 0.236998i 0.772992 0.634415i \(-0.218759\pi\)
−0.490549 + 0.871414i \(0.663204\pi\)
\(258\) 57411.8 + 99440.2i 0.0536972 + 0.0930063i
\(259\) 286066. 495481.i 0.264982 0.458962i
\(260\) 577266. 210108.i 0.529594 0.192756i
\(261\) −349804. 1.98384e6i −0.317851 1.80262i
\(262\) −155453. + 881615.i −0.139909 + 0.793462i
\(263\) 771692. + 280873.i 0.687946 + 0.250392i 0.662256 0.749278i \(-0.269599\pi\)
0.0256907 + 0.999670i \(0.491821\pi\)
\(264\) 546443. 458520.i 0.482542 0.404901i
\(265\) −461563. −0.403753
\(266\) 227021. + 175251.i 0.196726 + 0.151865i
\(267\) 1.39593e6 1.19836
\(268\) −480018. + 402783.i −0.408245 + 0.342558i
\(269\) −554028. 201650.i −0.466821 0.169909i 0.0978905 0.995197i \(-0.468791\pi\)
−0.564712 + 0.825288i \(0.691013\pi\)
\(270\) 452222. 2.56468e6i 0.377522 2.14103i
\(271\) 70451.3 + 399549.i 0.0582728 + 0.330481i 0.999982 0.00594560i \(-0.00189256\pi\)
−0.941710 + 0.336427i \(0.890781\pi\)
\(272\) 203121. 73930.1i 0.166469 0.0605897i
\(273\) 262337. 454381.i 0.213036 0.368989i
\(274\) −605755. 1.04920e6i −0.487440 0.844270i
\(275\) −1.61889e6 1.35841e6i −1.29088 1.08318i
\(276\) 1.56241e6 + 1.31102e6i 1.23459 + 1.03594i
\(277\) −149595. 259106.i −0.117143 0.202898i 0.801491 0.598006i \(-0.204040\pi\)
−0.918634 + 0.395109i \(0.870707\pi\)
\(278\) −581185. + 1.00664e6i −0.451027 + 0.781201i
\(279\) 3.53667e6 1.28724e6i 2.72009 0.990033i
\(280\) −46156.4 261766.i −0.0351833 0.199535i
\(281\) 77455.6 439272.i 0.0585176 0.331870i −0.941469 0.337100i \(-0.890554\pi\)
0.999986 + 0.00523044i \(0.00166491\pi\)
\(282\) −547205. 199166.i −0.409757 0.149140i
\(283\) 1.34352e6 1.12735e6i 0.997189 0.836741i 0.0105968 0.999944i \(-0.496627\pi\)
0.986593 + 0.163203i \(0.0521824\pi\)
\(284\) −348669. −0.256518
\(285\) −2.09705e6 3.31294e6i −1.52932 2.41603i
\(286\) −686978. −0.496624
\(287\) −218157. + 183056.i −0.156338 + 0.131183i
\(288\) −485251. 176617.i −0.344735 0.125473i
\(289\) −122753. + 696167.i −0.0864545 + 0.490308i
\(290\) 252905. + 1.43430e6i 0.176589 + 1.00148i
\(291\) 3.34840e6 1.21872e6i 2.31795 0.843666i
\(292\) 112517. 194886.i 0.0772258 0.133759i
\(293\) 1.34994e6 + 2.33817e6i 0.918641 + 1.59113i 0.801481 + 0.598021i \(0.204046\pi\)
0.117161 + 0.993113i \(0.462621\pi\)
\(294\) 1.23392e6 + 1.03538e6i 0.832566 + 0.698605i
\(295\) −501620. 420909.i −0.335598 0.281600i
\(296\) 401807. + 695951.i 0.266556 + 0.461689i
\(297\) −1.45614e6 + 2.52211e6i −0.957884 + 1.65910i
\(298\) 200628. 73022.6i 0.130873 0.0476340i
\(299\) −341086. 1.93439e6i −0.220641 1.25132i
\(300\) −393671. + 2.23262e6i −0.252540 + 1.43223i
\(301\) −44961.5 16364.6i −0.0286038 0.0104109i
\(302\) 827831. 694633.i 0.522305 0.438266i
\(303\) −697435. −0.436413
\(304\) −372615. + 153074.i −0.231247 + 0.0949985i
\(305\) −4.24388e6 −2.61224
\(306\) −1.30474e6 + 1.09481e6i −0.796564 + 0.668396i
\(307\) −2.50836e6 912968.i −1.51895 0.552853i −0.558065 0.829797i \(-0.688456\pi\)
−0.960886 + 0.276944i \(0.910678\pi\)
\(308\) −51616.0 + 292729.i −0.0310033 + 0.175828i
\(309\) 186001. + 1.05486e6i 0.110820 + 0.628492i
\(310\) −2.55698e6 + 930665.i −1.51120 + 0.550033i
\(311\) −14473.3 + 25068.5i −0.00848529 + 0.0146969i −0.870237 0.492634i \(-0.836034\pi\)
0.861752 + 0.507330i \(0.169368\pi\)
\(312\) 368478. + 638222.i 0.214301 + 0.371181i
\(313\) 1.42867e6 + 1.19880e6i 0.824274 + 0.691648i 0.953969 0.299906i \(-0.0969552\pi\)
−0.129695 + 0.991554i \(0.541400\pi\)
\(314\) −1.07577e6 902675.i −0.615735 0.516663i
\(315\) 1.04721e6 + 1.81382e6i 0.594643 + 1.02995i
\(316\) 758892. 1.31444e6i 0.427526 0.740497i
\(317\) 1.15806e6 421499.i 0.647266 0.235585i 0.00253679 0.999997i \(-0.499193\pi\)
0.644729 + 0.764411i \(0.276970\pi\)
\(318\) −96150.6 545297.i −0.0533193 0.302389i
\(319\) 282820. 1.60395e6i 0.155608 0.882500i
\(320\) 350832. + 127692.i 0.191525 + 0.0697092i
\(321\) −898932. + 754294.i −0.486928 + 0.408581i
\(322\) −849894. −0.456799
\(323\) −177257. + 1.31678e6i −0.0945358 + 0.702276i
\(324\) 1.16348e6 0.615736
\(325\) 1.67251e6 1.40340e6i 0.878336 0.737012i
\(326\) −1.68411e6 612968.i −0.877663 0.319443i
\(327\) −470598. + 2.66890e6i −0.243378 + 1.38026i
\(328\) −69460.5 393930.i −0.0356495 0.202178i
\(329\) 228020. 82992.5i 0.116140 0.0422717i
\(330\) 2.03186e6 3.51929e6i 1.02709 1.77898i
\(331\) 1.06876e6 + 1.85115e6i 0.536179 + 0.928690i 0.999105 + 0.0422927i \(0.0134662\pi\)
−0.462926 + 0.886397i \(0.653200\pi\)
\(332\) 299256. + 251106.i 0.149004 + 0.125029i
\(333\) −4.85068e6 4.07020e6i −2.39713 2.01143i
\(334\) 1.37930e6 + 2.38901e6i 0.676536 + 1.17180i
\(335\) −1.78487e6 + 3.09149e6i −0.868951 + 1.50507i
\(336\) 299639. 109060.i 0.144794 0.0527007i
\(337\) 97903.8 + 555240.i 0.0469597 + 0.266321i 0.999243 0.0388927i \(-0.0123831\pi\)
−0.952284 + 0.305214i \(0.901272\pi\)
\(338\) −134654. + 763661.i −0.0641103 + 0.363587i
\(339\) −4.33226e6 1.57682e6i −2.04746 0.745215i
\(340\) 943316. 791536.i 0.442548 0.371341i
\(341\) 3.04294e6 1.41712
\(342\) 2.34644e6 2.13759e6i 1.08479 0.988234i
\(343\) −1.43701e6 −0.659516
\(344\) 51482.6 43199.0i 0.0234566 0.0196824i
\(345\) 1.09184e7 + 3.97399e6i 4.93871 + 1.79754i
\(346\) −83562.5 + 473907.i −0.0375251 + 0.212815i
\(347\) −52940.9 300243.i −0.0236030 0.133859i 0.970729 0.240176i \(-0.0772053\pi\)
−0.994332 + 0.106317i \(0.966094\pi\)
\(348\) −1.64181e6 + 597572.i −0.726735 + 0.264510i
\(349\) −840224. + 1.45531e6i −0.369259 + 0.639576i −0.989450 0.144875i \(-0.953722\pi\)
0.620191 + 0.784451i \(0.287055\pi\)
\(350\) −472342. 818121.i −0.206104 0.356983i
\(351\) −2.30483e6 1.93398e6i −0.998553 0.837885i
\(352\) −319831. 268370.i −0.137583 0.115445i
\(353\) 284313. + 492445.i 0.121440 + 0.210340i 0.920336 0.391130i \(-0.127916\pi\)
−0.798896 + 0.601469i \(0.794582\pi\)
\(354\) 392773. 680303.i 0.166584 0.288532i
\(355\) −1.86652e6 + 679358.i −0.786072 + 0.286107i
\(356\) −141876. 804620.i −0.0593314 0.336485i
\(357\) 182630. 1.03575e6i 0.0758407 0.430114i
\(358\) −22005.7 8009.44i −0.00907462 0.00330289i
\(359\) −1.91630e6 + 1.60797e6i −0.784744 + 0.658478i −0.944439 0.328688i \(-0.893393\pi\)
0.159695 + 0.987166i \(0.448949\pi\)
\(360\) −2.94181e6 −1.19635
\(361\) 230156. 2.46538e6i 0.0929509 0.995671i
\(362\) 356375. 0.142934
\(363\) −108635. + 91155.9i −0.0432718 + 0.0363093i
\(364\) −288570. 105031.i −0.114156 0.0415492i
\(365\) 222615. 1.26251e6i 0.0874624 0.496024i
\(366\) −884065. 5.01378e6i −0.344970 1.95642i
\(367\) −1.49962e6 + 545818.i −0.581188 + 0.211535i −0.615849 0.787864i \(-0.711187\pi\)
0.0346614 + 0.999399i \(0.488965\pi\)
\(368\) 596880. 1.03383e6i 0.229756 0.397949i
\(369\) 1.57594e6 + 2.72960e6i 0.602522 + 1.04360i
\(370\) 3.50700e6 + 2.94272e6i 1.33178 + 1.11749i
\(371\) 176750. + 148311.i 0.0666691 + 0.0559420i
\(372\) −1.63216e6 2.82698e6i −0.611512 1.05917i
\(373\) 1.02464e6 1.77474e6i 0.381330 0.660483i −0.609922 0.792461i \(-0.708799\pi\)
0.991253 + 0.131978i \(0.0421327\pi\)
\(374\) −1.29402e6 + 470985.i −0.478368 + 0.174112i
\(375\) 890549. + 5.05055e6i 0.327024 + 1.85465i
\(376\) −59184.7 + 335653.i −0.0215894 + 0.122439i
\(377\) 1.58116e6 + 575496.i 0.572958 + 0.208540i
\(378\) −997264. + 836804.i −0.358989 + 0.301227i
\(379\) 1.56118e6 0.558284 0.279142 0.960250i \(-0.409950\pi\)
0.279142 + 0.960250i \(0.409950\pi\)
\(380\) −1.69646e6 + 1.54546e6i −0.602676 + 0.549034i
\(381\) 282842. 0.0998231
\(382\) 657670. 551851.i 0.230595 0.193492i
\(383\) −1.56104e6 568171.i −0.543772 0.197917i 0.0555055 0.998458i \(-0.482323\pi\)
−0.599277 + 0.800542i \(0.704545\pi\)
\(384\) −77774.1 + 441079.i −0.0269158 + 0.152647i
\(385\) 294048. + 1.66763e6i 0.101104 + 0.573387i
\(386\) 1.03252e6 375808.i 0.352721 0.128380i
\(387\) −264775. + 458604.i −0.0898669 + 0.155654i
\(388\) −1.04279e6 1.80616e6i −0.351656 0.609085i
\(389\) −365255. 306485.i −0.122383 0.102692i 0.579542 0.814942i \(-0.303231\pi\)
−0.701925 + 0.712251i \(0.747676\pi\)
\(390\) 3.21610e6 + 2.69863e6i 1.07070 + 0.898423i
\(391\) −1.96869e6 3.40986e6i −0.651230 1.12796i
\(392\) 471388. 816467.i 0.154940 0.268364i
\(393\) −5.74908e6 + 2.09249e6i −1.87766 + 0.683412i
\(394\) 519875. + 2.94836e6i 0.168717 + 0.956840i
\(395\) 1.50146e6 8.51521e6i 0.484196 2.74601i
\(396\) 3.09138e6 + 1.12517e6i 0.990637 + 0.360562i
\(397\) 4.69391e6 3.93866e6i 1.49472 1.25422i 0.606248 0.795276i \(-0.292674\pi\)
0.888468 0.458939i \(-0.151771\pi\)
\(398\) 655486. 0.207423
\(399\) −261484. + 1.94248e6i −0.0822268 + 0.610837i
\(400\) 1.32690e6 0.414657
\(401\) −1.53721e6 + 1.28987e6i −0.477389 + 0.400577i −0.849481 0.527619i \(-0.823085\pi\)
0.372092 + 0.928196i \(0.378640\pi\)
\(402\) −4.02415e6 1.46467e6i −1.24196 0.452038i
\(403\) −545902. + 3.09596e6i −0.167437 + 0.949584i
\(404\) 70884.2 + 402004.i 0.0216071 + 0.122540i
\(405\) 6.22840e6 2.26695e6i 1.88686 0.686760i
\(406\) 364026. 630511.i 0.109602 0.189836i
\(407\) −2.55979e6 4.43368e6i −0.765981 1.32672i
\(408\) 1.13164e6 + 949558.i 0.336556 + 0.282404i
\(409\) 3.28179e6 + 2.75375e6i 0.970068 + 0.813983i 0.982561 0.185939i \(-0.0595325\pi\)
−0.0124938 + 0.999922i \(0.503977\pi\)
\(410\) −1.13939e6 1.97348e6i −0.334743 0.579792i
\(411\) 4.13982e6 7.17039e6i 1.20886 2.09381i
\(412\) 589122. 214423.i 0.170987 0.0622341i
\(413\) 56841.5 + 322364.i 0.0163980 + 0.0929975i
\(414\) −1.63338e6 + 9.26337e6i −0.468368 + 2.65624i
\(415\) 2.09126e6 + 761158.i 0.596058 + 0.216947i
\(416\) 330423. 277258.i 0.0936132 0.0785508i
\(417\) −7.94381e6 −2.23712
\(418\) 2.37381e6 975184.i 0.664517 0.272989i
\(419\) −2.21461e6 −0.616257 −0.308128 0.951345i \(-0.599703\pi\)
−0.308128 + 0.951345i \(0.599703\pi\)
\(420\) 1.39156e6 1.16765e6i 0.384926 0.322991i
\(421\) 1.73504e6 + 631503.i 0.477094 + 0.173648i 0.569363 0.822086i \(-0.307190\pi\)
−0.0922692 + 0.995734i \(0.529412\pi\)
\(422\) 222845. 1.26382e6i 0.0609146 0.345464i
\(423\) −466348. 2.64479e6i −0.126724 0.718688i
\(424\) −304539. + 110843.i −0.0822675 + 0.0299429i
\(425\) 2.18826e6 3.79017e6i 0.587660 1.01786i
\(426\) −1.19143e6 2.06362e6i −0.318086 0.550941i
\(427\) 1.62514e6 + 1.36366e6i 0.431342 + 0.361939i
\(428\) 526141. + 441485.i 0.138833 + 0.116495i
\(429\) −2.34746e6 4.06591e6i −0.615821 1.06663i
\(430\) 191430. 331567.i 0.0499274 0.0864768i
\(431\) 5.97922e6 2.17626e6i 1.55043 0.564309i 0.581909 0.813254i \(-0.302306\pi\)
0.968518 + 0.248945i \(0.0800839\pi\)
\(432\) −317525. 1.80078e6i −0.0818595 0.464248i
\(433\) −402579. + 2.28314e6i −0.103188 + 0.585211i 0.888740 + 0.458412i \(0.151581\pi\)
−0.991928 + 0.126799i \(0.959530\pi\)
\(434\) 1.27821e6 + 465230.i 0.325745 + 0.118561i
\(435\) −7.62476e6 + 6.39793e6i −1.93198 + 1.62112i
\(436\) 1.58619e6 0.399613
\(437\) 3.92453e6 + 6.20001e6i 0.983069 + 1.55306i
\(438\) 1.53792e6 0.383044
\(439\) −1.06499e6 + 893631.i −0.263744 + 0.221308i −0.765064 0.643954i \(-0.777293\pi\)
0.501319 + 0.865262i \(0.332848\pi\)
\(440\) −2.23504e6 813488.i −0.550369 0.200318i
\(441\) −1.28997e6 + 7.31577e6i −0.315851 + 1.79128i
\(442\) −247045. 1.40106e6i −0.0601480 0.341116i
\(443\) −578433. + 210532.i −0.140037 + 0.0509694i −0.411088 0.911596i \(-0.634851\pi\)
0.271051 + 0.962565i \(0.412629\pi\)
\(444\) −2.74601e6 + 4.75623e6i −0.661066 + 1.14500i
\(445\) −2.32725e6 4.03092e6i −0.557113 0.964948i
\(446\) −1.46592e6 1.23006e6i −0.348959 0.292811i
\(447\) 1.11775e6 + 937903.i 0.264591 + 0.222019i
\(448\) −93316.4 161629.i −0.0219666 0.0380473i
\(449\) −3.13258e6 + 5.42579e6i −0.733309 + 1.27013i 0.222153 + 0.975012i \(0.428692\pi\)
−0.955461 + 0.295116i \(0.904642\pi\)
\(450\) −9.82483e6 + 3.57595e6i −2.28715 + 0.832453i
\(451\) 442511. + 2.50961e6i 0.102443 + 0.580984i
\(452\) −468570. + 2.65739e6i −0.107877 + 0.611800i
\(453\) 6.93998e6 + 2.52595e6i 1.58896 + 0.578334i
\(454\) −668116. + 560616.i −0.152129 + 0.127651i
\(455\) −1.74944e6 −0.396160
\(456\) −2.17923e6 1.68228e6i −0.490784 0.378866i
\(457\) 1.16914e6 0.261863 0.130932 0.991391i \(-0.458203\pi\)
0.130932 + 0.991391i \(0.458203\pi\)
\(458\) −1.42351e6 + 1.19447e6i −0.317100 + 0.266079i
\(459\) −5.66739e6 2.06276e6i −1.25560 0.457001i
\(460\) 1.18092e6 6.69733e6i 0.260211 1.47573i
\(461\) 1.23937e6 + 7.02880e6i 0.271611 + 1.54038i 0.749525 + 0.661976i \(0.230282\pi\)
−0.477914 + 0.878407i \(0.658607\pi\)
\(462\) −1.90891e6 + 694785.i −0.416083 + 0.151442i
\(463\) −2.60014e6 + 4.50357e6i −0.563694 + 0.976347i 0.433476 + 0.901165i \(0.357287\pi\)
−0.997170 + 0.0751818i \(0.976046\pi\)
\(464\) 511309. + 885614.i 0.110253 + 0.190963i
\(465\) −1.42456e7 1.19535e7i −3.05526 2.56367i
\(466\) 274626. + 230439.i 0.0585838 + 0.0491576i
\(467\) 3.80544e6 + 6.59122e6i 0.807445 + 1.39854i 0.914628 + 0.404296i \(0.132483\pi\)
−0.107183 + 0.994239i \(0.534183\pi\)
\(468\) −1.69937e6 + 2.94339e6i −0.358652 + 0.621203i
\(469\) 1.67686e6 610328.i 0.352019 0.128124i
\(470\) 337165. + 1.91216e6i 0.0704042 + 0.399282i
\(471\) 1.66655e6 9.45148e6i 0.346152 1.96312i
\(472\) −432049. 157253.i −0.0892643 0.0324895i
\(473\) −327979. + 275207.i −0.0674052 + 0.0565597i
\(474\) 1.03728e7 2.12055
\(475\) −3.78710e6 + 7.22356e6i −0.770146 + 1.46899i
\(476\) −615570. −0.124526
\(477\) 1.95619e6 1.64144e6i 0.393655 0.330316i
\(478\) 2.83216e6 + 1.03082e6i 0.566953 + 0.206354i
\(479\) 1.32980e6 7.54168e6i 0.264818 1.50186i −0.504734 0.863275i \(-0.668409\pi\)
0.769552 0.638584i \(-0.220479\pi\)
\(480\) 443066. + 2.51275e6i 0.0877739 + 0.497791i
\(481\) 4.97016e6 1.80899e6i 0.979507 0.356511i
\(482\) 556291. 963525.i 0.109065 0.188906i
\(483\) −2.90415e6 5.03014e6i −0.566437 0.981098i
\(484\) 63583.8 + 53353.2i 0.0123377 + 0.0103525i
\(485\) −9.10153e6 7.63709e6i −1.75695 1.47426i
\(486\) 504286. + 873449.i 0.0968471 + 0.167744i
\(487\) 2.07459e6 3.59329e6i 0.396377 0.686546i −0.596898 0.802317i \(-0.703600\pi\)
0.993276 + 0.115771i \(0.0369338\pi\)
\(488\) −2.80011e6 + 1.01916e6i −0.532262 + 0.193728i
\(489\) −2.12687e6 1.20621e7i −0.402225 2.28113i
\(490\) 932636. 5.28924e6i 0.175478 0.995183i
\(491\) 7.94139e6 + 2.89043e6i 1.48660 + 0.541077i 0.952551 0.304379i \(-0.0984489\pi\)
0.534045 + 0.845456i \(0.320671\pi\)
\(492\) 2.09414e6 1.75720e6i 0.390026 0.327271i
\(493\) 3.37290e6 0.625009
\(494\) 566315. + 2.59012e6i 0.104410 + 0.477533i
\(495\) 1.87413e7 3.43785
\(496\) −1.46360e6 + 1.22810e6i −0.267127 + 0.224146i
\(497\) 933056. + 339604.i 0.169440 + 0.0616712i
\(498\) −463601. + 2.62921e6i −0.0837666 + 0.475064i
\(499\) −1.88309e6 1.06795e7i −0.338547 1.92000i −0.388928 0.921268i \(-0.627155\pi\)
0.0503809 0.998730i \(-0.483956\pi\)
\(500\) 2.82065e6 1.02663e6i 0.504573 0.183649i
\(501\) −9.42632e6 + 1.63269e7i −1.67783 + 2.90609i
\(502\) −2.43422e6 4.21620e6i −0.431123 0.746727i
\(503\) −664251. 557373.i −0.117061 0.0982259i 0.582378 0.812918i \(-0.302122\pi\)
−0.699439 + 0.714692i \(0.746567\pi\)
\(504\) 1.12653e6 + 945271.i 0.197545 + 0.165760i
\(505\) 1.16274e6 + 2.01393e6i 0.202887 + 0.351411i
\(506\) −3.80253e6 + 6.58618e6i −0.660232 + 1.14356i
\(507\) −4.97989e6 + 1.81253e6i −0.860399 + 0.313159i
\(508\) −28746.8 163031.i −0.00494231 0.0280292i
\(509\) −1.23264e6 + 6.99064e6i −0.210883 + 1.19598i 0.677027 + 0.735958i \(0.263268\pi\)
−0.887910 + 0.460017i \(0.847843\pi\)
\(510\) 7.90813e6 + 2.87832e6i 1.34632 + 0.490020i
\(511\) −490921. + 411932.i −0.0831687 + 0.0697868i
\(512\) 262144. 0.0441942
\(513\) 1.07095e7 + 3.41099e6i 1.79671 + 0.572252i
\(514\) 1.56160e6 0.260713
\(515\) 2.73595e6 2.29573e6i 0.454558 0.381419i
\(516\) 431596. + 157088.i 0.0713597 + 0.0259728i
\(517\) 377047. 2.13834e6i 0.0620396 0.351844i
\(518\) −397398. 2.25376e6i −0.0650731 0.369048i
\(519\) −3.09038e6 + 1.12481e6i −0.503609 + 0.183299i
\(520\) 1.22863e6 2.12805e6i 0.199256 0.345122i
\(521\) −3.06342e6 5.30600e6i −0.494438 0.856392i 0.505541 0.862802i \(-0.331293\pi\)
−0.999979 + 0.00641026i \(0.997960\pi\)
\(522\) −6.17260e6 5.17943e6i −0.991499 0.831966i
\(523\) 8.62375e6 + 7.23619e6i 1.37861 + 1.15679i 0.969723 + 0.244209i \(0.0785284\pi\)
0.408890 + 0.912584i \(0.365916\pi\)
\(524\) 1.79043e6 + 3.10112e6i 0.284859 + 0.493390i
\(525\) 3.22806e6 5.59116e6i 0.511144 0.885327i
\(526\) 3.08677e6 1.12349e6i 0.486452 0.177054i
\(527\) 1.09428e6 + 6.20596e6i 0.171633 + 0.973380i
\(528\) 495474. 2.80997e6i 0.0773457 0.438649i
\(529\) −1.43852e7 5.23577e6i −2.23499 0.813469i
\(530\) −1.41431e6 + 1.18675e6i −0.218703 + 0.183514i
\(531\) 3.62283e6 0.557585
\(532\) 1.14623e6 46704.7i 0.175587 0.00715454i
\(533\) −2.63272e6 −0.401409
\(534\) 4.27738e6 3.58915e6i 0.649120 0.544677i
\(535\) 3.67678e6 + 1.33824e6i 0.555371 + 0.202139i
\(536\) −435245. + 2.46840e6i −0.0654368 + 0.371110i
\(537\) −27791.1 157611.i −0.00415881 0.0235858i
\(538\) −2.21611e6 + 806598.i −0.330093 + 0.120144i
\(539\) −3.00306e6 + 5.20145e6i −0.445238 + 0.771175i
\(540\) −5.20849e6 9.02137e6i −0.768648 1.33134i
\(541\) −2.91093e6 2.44256e6i −0.427601 0.358800i 0.403445 0.915004i \(-0.367813\pi\)
−0.831046 + 0.556204i \(0.812257\pi\)
\(542\) 1.24318e6 + 1.04315e6i 0.181775 + 0.152527i
\(543\) 1.21776e6 + 2.10922e6i 0.177240 + 0.306989i
\(544\) 432314. 748790.i 0.0626329 0.108483i
\(545\) 8.49131e6 3.09059e6i 1.22457 0.445707i
\(546\) −364435. 2.06681e6i −0.0523164 0.296701i
\(547\) −40862.9 + 231745.i −0.00583931 + 0.0331164i −0.987588 0.157065i \(-0.949797\pi\)
0.981749 + 0.190182i \(0.0609077\pi\)
\(548\) −4.55379e6 1.65744e6i −0.647771 0.235769i
\(549\) 1.79864e7 1.50924e7i 2.54691 2.13711i
\(550\) −8.45327e6 −1.19157
\(551\) −6.28055e6 + 255909.i −0.881289 + 0.0359093i
\(552\) 8.15833e6 1.13960
\(553\) −3.31110e6 + 2.77834e6i −0.460426 + 0.386343i
\(554\) −1.12458e6 409315.i −0.155675 0.0566609i
\(555\) −5.43296e6 + 3.08118e7i −0.748693 + 4.24605i
\(556\) 807374. + 4.57884e6i 0.110761 + 0.628158i
\(557\) −5.38847e6 + 1.96124e6i −0.735915 + 0.267851i −0.682666 0.730730i \(-0.739180\pi\)
−0.0532483 + 0.998581i \(0.516957\pi\)
\(558\) 7.52729e6 1.30376e7i 1.02342 1.77261i
\(559\) −221163. 383066.i −0.0299353 0.0518495i
\(560\) −814471. 683423.i −0.109750 0.0920914i
\(561\) −7.20932e6 6.04934e6i −0.967135 0.811523i
\(562\) −892098. 1.54516e6i −0.119144 0.206363i
\(563\) 849812. 1.47192e6i 0.112993 0.195710i −0.803983 0.594653i \(-0.797290\pi\)
0.916976 + 0.398943i \(0.130623\pi\)
\(564\) −2.18882e6 + 796665.i −0.289742 + 0.105458i
\(565\) 2.66937e6 + 1.51387e7i 0.351793 + 1.99512i
\(566\) 1.21820e6 6.90878e6i 0.159838 0.906484i
\(567\) −3.11352e6 1.13323e6i −0.406718 0.148033i
\(568\) −1.06838e6 + 896481.i −0.138949 + 0.116592i
\(569\) 2.92415e6 0.378633 0.189317 0.981916i \(-0.439373\pi\)
0.189317 + 0.981916i \(0.439373\pi\)
\(570\) −1.49438e7 4.75961e6i −1.92652 0.613598i
\(571\) −3.29435e6 −0.422844 −0.211422 0.977395i \(-0.567809\pi\)
−0.211422 + 0.977395i \(0.567809\pi\)
\(572\) −2.10502e6 + 1.76632e6i −0.269009 + 0.225725i
\(573\) 5.51347e6 + 2.00674e6i 0.701517 + 0.255331i
\(574\) −197809. + 1.12183e6i −0.0250592 + 0.142118i
\(575\) −4.19706e6 2.38027e7i −0.529390 3.00232i
\(576\) −1.94100e6 + 706468.i −0.243764 + 0.0887230i
\(577\) −5.78523e6 + 1.00203e7i −0.723405 + 1.25297i 0.236223 + 0.971699i \(0.424091\pi\)
−0.959627 + 0.281275i \(0.909243\pi\)
\(578\) 1.41381e6 + 2.44880e6i 0.176024 + 0.304883i
\(579\) 5.75245e6 + 4.82687e6i 0.713109 + 0.598370i
\(580\) 4.46274e6 + 3.74468e6i 0.550847 + 0.462216i
\(581\) −556247. 963448.i −0.0683640 0.118410i
\(582\) 7.12658e6 1.23436e7i 0.872115 1.51055i
\(583\) 1.94012e6 706147.i 0.236406 0.0860446i
\(584\) −156308. 886464.i −0.0189648 0.107555i
\(585\) −3.36218e6 + 1.90679e7i −0.406192 + 2.30363i
\(586\) 1.01482e7 + 3.69366e6i 1.22081 + 0.444337i
\(587\) 4.95748e6 4.15982e6i 0.593835 0.498287i −0.295622 0.955305i \(-0.595527\pi\)
0.889457 + 0.457018i \(0.151083\pi\)
\(588\) 6.44307e6 0.768510
\(589\) −2.50847e6 1.14729e7i −0.297935 1.36265i
\(590\) −2.61927e6 −0.309778
\(591\) −1.56735e7 + 1.31517e7i −1.84586 + 1.54886i
\(592\) 3.02060e6 + 1.09941e6i 0.354233 + 0.128930i
\(593\) 661171. 3.74969e6i 0.0772106 0.437883i −0.921557 0.388244i \(-0.873082\pi\)
0.998767 0.0496391i \(-0.0158071\pi\)
\(594\) 2.02285e6 + 1.14722e7i 0.235233 + 1.33407i
\(595\) −3.29532e6 + 1.19940e6i −0.381597 + 0.138890i
\(596\) 427008. 739599.i 0.0492402 0.0852866i
\(597\) 2.23985e6 + 3.87953e6i 0.257207 + 0.445495i
\(598\) −6.01877e6 5.05034e6i −0.688263 0.577521i
\(599\) −1.88973e6 1.58567e6i −0.215195 0.180570i 0.528818 0.848735i \(-0.322635\pi\)
−0.744013 + 0.668165i \(0.767080\pi\)
\(600\) 4.53412e6 + 7.85333e6i 0.514180 + 0.890586i
\(601\) −5.45631e6 + 9.45061e6i −0.616188 + 1.06727i 0.373987 + 0.927434i \(0.377990\pi\)
−0.990175 + 0.139835i \(0.955343\pi\)
\(602\) −179846. + 65458.6i −0.0202260 + 0.00736165i
\(603\) −3.42953e6 1.94498e7i −0.384097 2.17832i
\(604\) 750616. 4.25696e6i 0.0837193 0.474796i
\(605\) 444337. + 161725.i 0.0493542 + 0.0179634i
\(606\) −2.13707e6 + 1.79321e6i −0.236394 + 0.198358i
\(607\) −8.96624e6 −0.987731 −0.493865 0.869538i \(-0.664416\pi\)
−0.493865 + 0.869538i \(0.664416\pi\)
\(608\) −748184. + 1.42709e6i −0.0820823 + 0.156565i
\(609\) 4.97561e6 0.543630
\(610\) −1.30040e7 + 1.09117e7i −1.41499 + 1.18731i
\(611\) 2.10796e6 + 767234.i 0.228433 + 0.0831428i
\(612\) −1.18304e6 + 6.70937e6i −0.127680 + 0.724108i
\(613\) −3.00432e6 1.70383e7i −0.322920 1.83137i −0.523905 0.851777i \(-0.675525\pi\)
0.200985 0.979594i \(-0.435586\pi\)
\(614\) −1.00334e7 + 3.65187e6i −1.07406 + 0.390926i
\(615\) 7.78675e6 1.34870e7i 0.830173 1.43790i
\(616\) 594490. + 1.02969e6i 0.0631237 + 0.109333i
\(617\) 1.18698e7 + 9.95993e6i 1.25525 + 1.05328i 0.996171 + 0.0874226i \(0.0278630\pi\)
0.259078 + 0.965856i \(0.416581\pi\)
\(618\) 3.28215e6 + 2.75405e6i 0.345690 + 0.290069i
\(619\) 468168. + 810891.i 0.0491106 + 0.0850620i 0.889536 0.456866i \(-0.151028\pi\)
−0.840425 + 0.541928i \(0.817695\pi\)
\(620\) −5.44216e6 + 9.42610e6i −0.568581 + 0.984811i
\(621\) −3.12990e7 + 1.13919e7i −3.25688 + 1.18541i
\(622\) 20106.1 + 114027.i 0.00208378 + 0.0118177i
\(623\) −404034. + 2.29139e6i −0.0417059 + 0.236526i
\(624\) 2.77005e6 + 1.00821e6i 0.284791 + 0.103655i
\(625\) 691351. 580112.i 0.0707943 0.0594035i
\(626\) 7.46000e6 0.760857
\(627\) 1.38832e7 + 1.07173e7i 1.41033 + 1.08872i
\(628\) −5.61725e6 −0.568361
\(629\) 8.12178e6 6.81498e6i 0.818511 0.686813i
\(630\) 7.87242e6 + 2.86533e6i 0.790236 + 0.287622i
\(631\) −74089.5 + 420183.i −0.00740770 + 0.0420112i −0.988288 0.152603i \(-0.951234\pi\)
0.980880 + 0.194614i \(0.0623455\pi\)
\(632\) −1.05424e6 5.97890e6i −0.104990 0.595428i
\(633\) 8.24144e6 2.99964e6i 0.817511 0.297550i
\(634\) 2.46476e6 4.26909e6i 0.243530 0.421806i
\(635\) −471544. 816738.i −0.0464075 0.0803801i
\(636\) −1.69666e6 1.42367e6i −0.166323 0.139562i
\(637\) −4.75334e6 3.98853e6i −0.464141 0.389461i
\(638\) −3.25739e6 5.64196e6i −0.316824 0.548755i
\(639\) 5.49470e6 9.51710e6i 0.532344 0.922046i
\(640\) 1.40333e6 510770.i 0.135428 0.0492919i
\(641\) −2.12084e6 1.20279e7i −0.203875 1.15623i −0.899201 0.437537i \(-0.855851\pi\)
0.695326 0.718695i \(-0.255260\pi\)
\(642\) −815086. + 4.62258e6i −0.0780487 + 0.442636i
\(643\) 1.05234e7 + 3.83020e6i 1.00376 + 0.365337i 0.791032 0.611775i \(-0.209544\pi\)
0.212724 + 0.977112i \(0.431767\pi\)
\(644\) −2.60423e6 + 2.18521e6i −0.247437 + 0.207624i
\(645\) 2.61652e6 0.247643
\(646\) 2.84250e6 + 4.49061e6i 0.267990 + 0.423374i
\(647\) −3.69266e6 −0.346799 −0.173400 0.984852i \(-0.555475\pi\)
−0.173400 + 0.984852i \(0.555475\pi\)
\(648\) 3.56509e6 2.99147e6i 0.333529 0.279864i
\(649\) 2.75245e6 + 1.00181e6i 0.256512 + 0.0933626i
\(650\) 1.51651e6 8.60056e6i 0.140787 0.798442i
\(651\) 1.61425e6 + 9.15487e6i 0.149286 + 0.846642i
\(652\) −6.73646e6 + 2.45187e6i −0.620601 + 0.225880i
\(653\) 3.61843e6 6.26730e6i 0.332076 0.575172i −0.650843 0.759212i \(-0.725584\pi\)
0.982919 + 0.184040i \(0.0589177\pi\)
\(654\) 5.42014e6 + 9.38795e6i 0.495525 + 0.858275i
\(655\) 1.56270e7 + 1.31126e7i 1.42322 + 1.19422i
\(656\) −1.22569e6 1.02848e6i −0.111204 0.0933116i
\(657\) 3.54634e6 + 6.14244e6i 0.320529 + 0.555172i
\(658\) 485308. 840578.i 0.0436971 0.0756856i
\(659\) −2.32948e6 + 847860.i −0.208951 + 0.0760520i −0.444375 0.895841i \(-0.646574\pi\)
0.235424 + 0.971893i \(0.424352\pi\)
\(660\) −2.82263e6 1.60080e7i −0.252229 1.43046i
\(661\) 1.99551e6 1.13171e7i 0.177644 1.00747i −0.757404 0.652946i \(-0.773533\pi\)
0.935048 0.354521i \(-0.115356\pi\)
\(662\) 8.03444e6 + 2.92430e6i 0.712542 + 0.259344i
\(663\) 7.44809e6 6.24969e6i 0.658053 0.552172i
\(664\) 1.56261e6 0.137540
\(665\) 6.04509e6 2.48338e6i 0.530088 0.217765i
\(666\) −2.53284e7 −2.21270
\(667\) 1.42694e7 1.19734e7i 1.24191 1.04209i
\(668\) 1.03689e7 + 3.77398e6i 0.899067 + 0.327234i
\(669\) 2.27097e6 1.28793e7i 0.196176 1.11257i
\(670\) 2.47952e6 + 1.40621e7i 0.213393 + 1.21021i
\(671\) 1.78386e7 6.49273e6i 1.52952 0.556699i
\(672\) 637739. 1.10460e6i 0.0544778 0.0943583i
\(673\) −3.96497e6 6.86754e6i −0.337445 0.584471i 0.646507 0.762908i \(-0.276229\pi\)
−0.983951 + 0.178437i \(0.942896\pi\)
\(674\) 1.72760e6 + 1.44963e6i 0.146485 + 0.122916i
\(675\) −2.83609e7 2.37977e7i −2.39586 2.01036i
\(676\) 1.55088e6 + 2.68621e6i 0.130531 + 0.226086i
\(677\) −2.41310e6 + 4.17962e6i −0.202351 + 0.350482i −0.949285 0.314416i \(-0.898191\pi\)
0.746935 + 0.664897i \(0.231525\pi\)
\(678\) −1.73291e7 + 6.30726e6i −1.44777 + 0.526947i
\(679\) 1.03135e6 + 5.84906e6i 0.0858481 + 0.486869i
\(680\) 855329. 4.85081e6i 0.0709351 0.402293i
\(681\) −5.60103e6 2.03861e6i −0.462807 0.168448i
\(682\) 9.32412e6 7.82387e6i 0.767621 0.644111i
\(683\) −2.02601e7 −1.66184 −0.830920 0.556392i \(-0.812185\pi\)
−0.830920 + 0.556392i \(0.812185\pi\)
\(684\) 1.69384e6 1.25830e7i 0.138431 1.02836i
\(685\) −2.76071e7 −2.24799
\(686\) −4.40326e6 + 3.69477e6i −0.357243 + 0.299763i
\(687\) −1.19338e7 4.34353e6i −0.964684 0.351116i
\(688\) 46680.6 264739.i 0.00375981 0.0213229i
\(689\) 370394. + 2.10061e6i 0.0297246 + 0.168577i
\(690\) 4.36738e7 1.58960e7i 3.49219 1.27105i
\(691\) 1.18937e7 2.06006e7i 0.947597 1.64129i 0.197131 0.980377i \(-0.436838\pi\)
0.750466 0.660909i \(-0.229829\pi\)
\(692\) 962435. + 1.66699e6i 0.0764022 + 0.132333i
\(693\) −7.17677e6 6.02202e6i −0.567670 0.476331i
\(694\) −934189. 783878.i −0.0736269 0.0617803i
\(695\) 1.32437e7 + 2.29387e7i 1.04003 + 1.80139i
\(696\) −3.49437e6 + 6.05242e6i −0.273429 + 0.473594i
\(697\) −4.95910e6 + 1.80497e6i −0.386653 + 0.140730i
\(698\) 1.16723e6 + 6.61967e6i 0.0906810 + 0.514278i
\(699\) −425445. + 2.41282e6i −0.0329344 + 0.186780i
\(700\) −3.55085e6 1.29240e6i −0.273897 0.0996904i
\(701\) −3.16272e6 + 2.65384e6i −0.243089 + 0.203976i −0.756190 0.654352i \(-0.772941\pi\)
0.513100 + 0.858329i \(0.328497\pi\)
\(702\) −1.20350e7 −0.921726
\(703\) −1.46062e7 + 1.33061e7i −1.11468 + 1.01546i
\(704\) −1.67004e6 −0.126997
\(705\) −1.01651e7 + 8.52953e6i −0.770262 + 0.646327i
\(706\) 2.13734e6 + 777927.i 0.161384 + 0.0587391i
\(707\) 201863. 1.14482e6i 0.0151883 0.0861371i
\(708\) −545634. 3.09445e6i −0.0409090 0.232006i
\(709\) 6.35459e6 2.31288e6i 0.474757 0.172798i −0.0935488 0.995615i \(-0.529821\pi\)
0.568306 + 0.822817i \(0.307599\pi\)
\(710\) −3.97262e6 + 6.88078e6i −0.295754 + 0.512262i
\(711\) 2.39189e7 + 4.14287e7i 1.77446 + 3.07346i
\(712\) −2.50353e6 2.10071e6i −0.185077 0.155298i
\(713\) 2.66599e7 + 2.23703e7i 1.96397 + 1.64797i
\(714\) −2.10345e6 3.64328e6i −0.154414 0.267453i
\(715\) −7.82720e6 + 1.35571e7i −0.572587 + 0.991749i
\(716\) −88023.0 + 32037.8i −0.00641673 + 0.00233550i
\(717\) 3.57673e6 + 2.02846e7i 0.259829 + 1.47357i
\(718\) −1.73756e6 + 9.85420e6i −0.125785 + 0.713363i
\(719\) −826283. 300742.i −0.0596083 0.0216956i 0.312044 0.950068i \(-0.398986\pi\)
−0.371652 + 0.928372i \(0.621209\pi\)
\(720\) −9.01422e6 + 7.56383e6i −0.648033 + 0.543764i
\(721\) −1.78537e6 −0.127906
\(722\) −5.63362e6 8.14612e6i −0.402203 0.581578i
\(723\) 7.60356e6 0.540968
\(724\) 1.09200e6 916294.i 0.0774239 0.0649664i
\(725\) 1.94562e7 + 7.08148e6i 1.37472 + 0.500356i
\(726\) −98502.6 + 558636.i −0.00693595 + 0.0393357i
\(727\) −2.77831e6 1.57566e7i −0.194959 1.10567i −0.912477 0.409129i \(-0.865833\pi\)
0.717517 0.696540i \(-0.245278\pi\)
\(728\) −1.15428e6 + 420123.i −0.0807202 + 0.0293798i
\(729\) 5.38877e6 9.33362e6i 0.375553 0.650476i
\(730\) −2.56397e6 4.44093e6i −0.178076 0.308437i
\(731\) −679219. 569933.i −0.0470129 0.0394485i
\(732\) −1.56001e7 1.30901e7i −1.07609 0.902950i
\(733\) −1.41988e7 2.45931e7i −0.976096 1.69065i −0.676270 0.736654i \(-0.736405\pi\)
−0.299826 0.953994i \(-0.596929\pi\)
\(734\) −3.19173e6 + 5.52823e6i −0.218668 + 0.378744i
\(735\) 3.44915e7 1.25539e7i 2.35502 0.857156i
\(736\) −829176. 4.70249e6i −0.0564225 0.319988i
\(737\) 2.77281e6 1.57254e7i 0.188040 1.06643i
\(738\) 1.18472e7 + 4.31201e6i 0.800707 + 0.291433i
\(739\) 1.00382e7 8.42301e6i 0.676150 0.567357i −0.238729 0.971086i \(-0.576731\pi\)
0.914878 + 0.403729i \(0.132286\pi\)
\(740\) 1.83122e7 1.22931
\(741\) −1.33946e7 + 1.22024e7i −0.896159 + 0.816395i
\(742\) 922923. 0.0615397
\(743\) −1.45754e7 + 1.22302e7i −0.968607 + 0.812758i −0.982332 0.187148i \(-0.940076\pi\)
0.0137245 + 0.999906i \(0.495631\pi\)
\(744\) −1.22698e7 4.46585e6i −0.812655 0.295782i
\(745\) 844831. 4.79127e6i 0.0557672 0.316272i
\(746\) −1.42342e6 8.07263e6i −0.0936454 0.531090i
\(747\) −1.15701e7 + 4.21116e6i −0.758638 + 0.276122i
\(748\) −2.75414e6 + 4.77031e6i −0.179983 + 0.311740i
\(749\) −977972. 1.69390e6i −0.0636974 0.110327i
\(750\) 1.57145e7 + 1.31861e7i 1.02011 + 0.855977i
\(751\) −1.05860e6 888270.i −0.0684907 0.0574705i 0.607900 0.794014i \(-0.292012\pi\)
−0.676390 + 0.736543i \(0.736457\pi\)
\(752\) 681662. + 1.18067e6i 0.0439566 + 0.0761351i
\(753\) 1.66358e7 2.88141e7i 1.06920 1.85190i
\(754\) 6.32465e6 2.30198e6i 0.405143 0.147460i
\(755\) −4.27614e6 2.42512e7i −0.273014 1.54834i
\(756\) −904246. + 5.12823e6i −0.0575416 + 0.326335i
\(757\) −1.92877e7 7.02014e6i −1.22332 0.445252i −0.352015 0.935994i \(-0.614503\pi\)
−0.871305 + 0.490743i \(0.836726\pi\)
\(758\) 4.78374e6 4.01403e6i 0.302409 0.253751i
\(759\) −5.19742e7 −3.27479
\(760\) −1.22463e6 + 9.09741e6i −0.0769082 + 0.571326i
\(761\) −2.00812e7 −1.25698 −0.628490 0.777818i \(-0.716327\pi\)
−0.628490 + 0.777818i \(0.716327\pi\)
\(762\) 866677. 727228.i 0.0540717 0.0453715i
\(763\) −4.24472e6 1.54495e6i −0.263960 0.0960736i
\(764\) 596327. 3.38194e6i 0.0369616 0.209620i
\(765\) 6.73960e6 + 3.82222e7i 0.416371 + 2.36136i
\(766\) −6.24415e6 + 2.27269e6i −0.384505 + 0.139948i
\(767\) −1.51305e6 + 2.62068e6i −0.0928678 + 0.160852i
\(768\) 895766. + 1.55151e6i 0.0548014 + 0.0949188i
\(769\) 269480. + 226121.i 0.0164328 + 0.0137887i 0.650967 0.759106i \(-0.274364\pi\)
−0.634534 + 0.772895i \(0.718808\pi\)
\(770\) 5.18874e6 + 4.35387e6i 0.315381 + 0.264636i
\(771\) 5.33612e6 + 9.24243e6i 0.323288 + 0.559951i
\(772\) 2.19758e6 3.80631e6i 0.132709 0.229859i
\(773\) −1.80843e7 + 6.58214e6i −1.08856 + 0.396203i −0.823087 0.567915i \(-0.807750\pi\)
−0.265472 + 0.964118i \(0.585528\pi\)
\(774\) 367822. + 2.08602e6i 0.0220691 + 0.125160i
\(775\) −6.71733e6 + 3.80959e7i −0.401738 + 2.27837i
\(776\) −7.83921e6 2.85324e6i −0.467324 0.170092i
\(777\) 1.19810e7 1.00533e7i 0.711938 0.597387i
\(778\) −1.90723e6 −0.112967
\(779\) 9.09721e6 3.73722e6i 0.537112 0.220650i
\(780\) 1.67933e7 0.988322
\(781\) 6.80634e6 5.71120e6i 0.399288 0.335042i
\(782\) −1.47997e7 5.38664e6i −0.865437 0.314993i
\(783\) 4.95464e6 2.80992e7i 0.288807 1.63791i
\(784\) −654845. 3.71381e6i −0.0380494 0.215789i
\(785\) −3.00707e7 + 1.09448e7i −1.74168 + 0.633921i
\(786\) −1.22361e7 + 2.11935e7i −0.706458 + 1.22362i
\(787\) 9.08008e6 + 1.57272e7i 0.522580 + 0.905135i 0.999655 + 0.0262723i \(0.00836369\pi\)
−0.477075 + 0.878863i \(0.658303\pi\)
\(788\) 9.17366e6 + 7.69761e6i 0.526292 + 0.441612i
\(789\) 1.71972e7 + 1.44301e7i 0.983477 + 0.825235i
\(790\) −1.72931e7 2.99526e7i −0.985839 1.70752i
\(791\) 3.84222e6 6.65493e6i 0.218344 0.378183i
\(792\) 1.23655e7 4.50068e6i 0.700486 0.254956i
\(793\) 3.40562e6 + 1.93142e7i 0.192315 + 1.09067i
\(794\) 4.25609e6 2.41375e7i 0.239585 1.35875i
\(795\) −1.18566e7 4.31546e6i −0.665340 0.242164i
\(796\) 2.00853e6 1.68535e6i 0.112356 0.0942776i
\(797\) 2.32589e7 1.29701 0.648506 0.761210i \(-0.275394\pi\)
0.648506 + 0.761210i \(0.275394\pi\)
\(798\) 4.19318e6 + 6.62443e6i 0.233097 + 0.368249i
\(799\) 4.49665e6 0.249185
\(800\) 4.06586e6 3.41166e6i 0.224609 0.188470i
\(801\) 2.41984e7 + 8.80749e6i 1.33262 + 0.485032i
\(802\) −1.39383e6 + 7.90479e6i −0.0765197 + 0.433965i
\(803\) 995786. + 5.64738e6i 0.0544976 + 0.309071i
\(804\) −1.60966e7 + 5.85868e6i −0.878201 + 0.319639i
\(805\) −9.68342e6 + 1.67722e7i −0.526670 + 0.912220i
\(806\) 6.28745e6 + 1.08902e7i 0.340908 + 0.590470i
\(807\) −1.23465e7 1.03600e7i −0.667361 0.559982i
\(808\) 1.25082e6 + 1.04956e6i 0.0674008 + 0.0565560i
\(809\) −4.55852e6 7.89560e6i −0.244880 0.424144i 0.717218 0.696849i \(-0.245415\pi\)
−0.962098 + 0.272705i \(0.912082\pi\)
\(810\) 1.32563e7 2.29605e7i 0.709918 1.22961i
\(811\) −1.27314e7 + 4.63384e6i −0.679708 + 0.247394i −0.658722 0.752386i \(-0.728903\pi\)
−0.0209861 + 0.999780i \(0.506681\pi\)
\(812\) −505699. 2.86796e6i −0.0269155 0.152645i
\(813\) −1.92590e6 + 1.09223e7i −0.102190 + 0.579547i
\(814\) −1.92433e7 7.00399e6i −1.01793 0.370497i
\(815\) −3.12848e7 + 2.62511e7i −1.64983 + 1.38437i
\(816\) 5.90900e6 0.310662
\(817\) 1.30799e6 + 1.00972e6i 0.0685566 + 0.0529230i
\(818\) 1.71363e7 0.895433
\(819\) 7.41446e6 6.22147e6i 0.386251 0.324103i
\(820\) −8.56539e6 3.11755e6i −0.444849 0.161912i
\(821\) −4.86172e6 + 2.75722e7i −0.251728 + 1.42762i 0.552605 + 0.833443i \(0.313634\pi\)
−0.804333 + 0.594178i \(0.797477\pi\)
\(822\) −5.75098e6 3.26155e7i −0.296867 1.68362i
\(823\) −4.49487e6 + 1.63600e6i −0.231322 + 0.0841944i −0.455081 0.890450i \(-0.650390\pi\)
0.223758 + 0.974645i \(0.428167\pi\)
\(824\) 1.25386e6 2.17175e6i 0.0643327 0.111427i
\(825\) −2.88855e7 5.00311e7i −1.47756 2.55921i
\(826\) 1.00302e6 + 841633.i 0.0511516 + 0.0429213i
\(827\) 6.35869e6 + 5.33558e6i 0.323299 + 0.271280i 0.789963 0.613155i \(-0.210100\pi\)
−0.466664 + 0.884435i \(0.654544\pi\)
\(828\) 1.88125e7 + 3.25843e7i 0.953612 + 1.65170i
\(829\) −7.16735e6 + 1.24142e7i −0.362220 + 0.627383i −0.988326 0.152355i \(-0.951314\pi\)
0.626106 + 0.779738i \(0.284648\pi\)
\(830\) 8.36506e6 3.04463e6i 0.421477 0.153405i
\(831\) −1.42024e6 8.05457e6i −0.0713442 0.404613i
\(832\) 299604. 1.69914e6i 0.0150051 0.0850981i
\(833\) −1.16881e7 4.25412e6i −0.583621 0.212421i
\(834\) −2.43413e7 + 2.04247e7i −1.21179 + 1.01681i
\(835\) 6.28610e7 3.12007
\(836\) 4.76644e6 9.09157e6i 0.235873 0.449907i
\(837\) 5.33084e7 2.63016
\(838\) −6.78595e6 + 5.69409e6i −0.333811 + 0.280101i
\(839\) −3.03453e6 1.10448e6i −0.148829 0.0541692i 0.266532 0.963826i \(-0.414122\pi\)
−0.415360 + 0.909657i \(0.636345\pi\)
\(840\) 1.26176e6 7.15580e6i 0.0616991 0.349913i
\(841\) −790844. 4.48510e6i −0.0385568 0.218666i
\(842\) 6.94016e6 2.52601e6i 0.337356 0.122788i
\(843\) 6.09673e6 1.05598e7i 0.295480 0.511786i
\(844\) −2.56663e6 4.44553e6i −0.124024 0.214816i
\(845\) 1.35362e7 + 1.13582e7i 0.652161 + 0.547228i
\(846\) −8.22913e6 6.90506e6i −0.395301 0.331697i
\(847\) −118187. 204706.i −0.00566060 0.00980444i
\(848\) −648167. + 1.12266e6i −0.0309526 + 0.0536115i
\(849\) 4.50526e7 1.63978e7i 2.14512 0.780759i
\(850\) −3.03989e6 1.72401e7i −0.144315 0.818450i
\(851\) 1.01675e7 5.76628e7i 0.481272 2.72943i
\(852\) −8.95662e6 3.25994e6i −0.422712 0.153855i
\(853\) −1.35699e7 + 1.13865e7i −0.638563 + 0.535818i −0.903577 0.428427i \(-0.859068\pi\)
0.265013 + 0.964245i \(0.414624\pi\)
\(854\) 8.48589e6 0.398156
\(855\) −1.54496e7 7.06607e7i −0.722771 3.30569i
\(856\) 2.74731e6 0.128152
\(857\) 2.29879e7 1.92892e7i 1.06917 0.897143i 0.0741961 0.997244i \(-0.476361\pi\)
0.994977 + 0.100101i \(0.0319165\pi\)
\(858\) −1.76471e7 6.42302e6i −0.818380 0.297866i
\(859\) 1.53009e6 8.67760e6i 0.0707514 0.401251i −0.928780 0.370632i \(-0.879141\pi\)
0.999531 0.0306191i \(-0.00974788\pi\)
\(860\) −265932. 1.50817e6i −0.0122610 0.0695353i
\(861\) −7.31554e6 + 2.66264e6i −0.336309 + 0.122407i
\(862\) 1.27259e7 2.20419e7i 0.583338 1.01037i
\(863\) −1.36378e7 2.36213e7i −0.623328 1.07963i −0.988862 0.148837i \(-0.952447\pi\)
0.365534 0.930798i \(-0.380886\pi\)
\(864\) −5.60302e6 4.70149e6i −0.255351 0.214265i
\(865\) 8.40019e6 + 7.04859e6i 0.381723 + 0.320304i
\(866\) 4.63672e6 + 8.03103e6i 0.210095 + 0.363895i
\(867\) −9.66222e6 + 1.67355e7i −0.436545 + 0.756118i
\(868\) 5.11284e6 1.86092e6i 0.230336 0.0838356i
\(869\) 6.71624e6 + 3.80897e7i 0.301701 + 1.71103i
\(870\) −6.91357e6 + 3.92088e7i −0.309674 + 1.75625i
\(871\) 1.55019e7 + 5.64225e6i 0.692374 + 0.252004i
\(872\) 4.86037e6 4.07834e6i 0.216460 0.181632i
\(873\) 6.57336e7 2.91912
\(874\) 2.79666e7 + 8.90738e6i 1.23840 + 0.394431i
\(875\) −8.54813e6 −0.377443
\(876\) 4.71247e6 3.95423e6i 0.207486 0.174101i
\(877\) 845943. + 307898.i 0.0371400 + 0.0135179i 0.360523 0.932750i \(-0.382598\pi\)
−0.323383 + 0.946268i \(0.604820\pi\)
\(878\) −965652. + 5.47649e6i −0.0422751 + 0.239754i
\(879\) 1.28162e7 + 7.26844e7i 0.559484 + 3.17299i
\(880\) −8.94016e6 + 3.25395e6i −0.389170 + 0.141646i
\(881\) −1.47779e7 + 2.55960e7i −0.641464 + 1.11105i 0.343642 + 0.939101i \(0.388339\pi\)
−0.985106 + 0.171947i \(0.944994\pi\)
\(882\) 1.48573e7 + 2.57335e7i 0.643083 + 1.11385i
\(883\) −2.60686e7 2.18742e7i −1.12516 0.944125i −0.126311 0.991991i \(-0.540314\pi\)
−0.998854 + 0.0478657i \(0.984758\pi\)
\(884\) −4.35933e6 3.65792e6i −0.187625 0.157436i
\(885\) −8.95025e6 1.55023e7i −0.384129 0.665331i
\(886\) −1.23111e6 + 2.13235e6i −0.0526881 + 0.0912585i
\(887\) −1.37448e7 + 5.00271e6i −0.586584 + 0.213499i −0.618226 0.786000i \(-0.712148\pi\)
0.0316424 + 0.999499i \(0.489926\pi\)
\(888\) 3.81472e6 + 2.16344e7i 0.162342 + 0.920686i
\(889\) −81864.8 + 464278.i −0.00347410 + 0.0197026i
\(890\) −1.74952e7 6.36773e6i −0.740362 0.269470i
\(891\) −2.27121e7 + 1.90577e7i −0.958435 + 0.804223i
\(892\) −7.65451e6 −0.322111
\(893\) −8.37304e6 + 341171.i −0.351362 + 0.0143167i
\(894\) 5.83647e6 0.244234
\(895\) −408788. + 343014.i −0.0170585 + 0.0143138i
\(896\) −701510. 255329.i −0.0291920 0.0106250i
\(897\) 9.32413e6 5.28798e7i 0.386925 2.19436i
\(898\) 4.35174e6 + 2.46799e7i 0.180083 + 1.02130i
\(899\) −2.80148e7 + 1.01965e7i −1.15608 + 0.420779i
\(900\) −2.09107e7 + 3.62185e7i −0.860524 + 1.49047i
\(901\) 2.13785e6 + 3.70286e6i 0.0877334 + 0.151959i
\(902\) 7.80850e6 + 6.55211e6i 0.319559 + 0.268142i
\(903\) −1.00197e6 840750.i −0.0408916 0.0343121i
\(904\) 5.39678e6 + 9.34749e6i 0.219641 + 0.380429i
\(905\) 4.06042e6 7.03286e6i 0.164797 0.285437i
\(906\) 2.77599e7 1.01038e7i 1.12356 0.408944i
\(907\) −6.58613e6 3.73518e7i −0.265835 1.50762i −0.766647 0.642069i \(-0.778076\pi\)
0.500812 0.865556i \(-0.333035\pi\)
\(908\) −605798. + 3.43565e6i −0.0243845 + 0.138291i
\(909\) −1.20900e7 4.40039e6i −0.485306 0.176637i
\(910\) −5.36059e6 + 4.49807e6i −0.214590 + 0.180062i
\(911\) −4.47251e6 −0.178548 −0.0892740 0.996007i \(-0.528455\pi\)
−0.0892740 + 0.996007i \(0.528455\pi\)
\(912\) −1.10029e7 + 448329.i −0.438048 + 0.0178488i
\(913\) −9.95487e6 −0.395238
\(914\) 3.58244e6 3.00603e6i 0.141845 0.119022i
\(915\) −1.09017e8 3.96789e7i −4.30468 1.56678i
\(916\) −1.29073e6 + 7.32012e6i −0.0508274 + 0.288257i
\(917\) −1.77079e6 1.00426e7i −0.0695413 0.394388i
\(918\) −2.26696e7 + 8.25105e6i −0.887844 + 0.323149i
\(919\) −6.85042e6 + 1.18653e7i −0.267564 + 0.463435i −0.968232 0.250052i \(-0.919552\pi\)
0.700668 + 0.713488i \(0.252885\pi\)
\(920\) −1.36013e7 2.35581e7i −0.529799 0.917638i
\(921\) −5.58988e7 4.69047e7i −2.17147 1.82208i
\(922\) 2.18697e7 + 1.83509e7i 0.847259 + 0.710935i
\(923\) 4.58966e6 + 7.94952e6i 0.177327 + 0.307140i
\(924\) −4.06283e6 + 7.03703e6i −0.156549 + 0.271150i
\(925\) 6.11579e7 2.22596e7i 2.35016 0.855389i
\(926\) 3.61207e6 + 2.04851e7i 0.138430 + 0.785073i
\(927\) −3.43124e6 + 1.94595e7i −0.131145 + 0.743760i
\(928\) 3.84379e6 + 1.39902e6i 0.146518 + 0.0533280i
\(929\) −2.90387e7 + 2.43664e7i −1.10392 + 0.926301i −0.997683 0.0680399i \(-0.978325\pi\)
−0.106240 + 0.994341i \(0.533881\pi\)
\(930\) −7.43851e7 −2.82019
\(931\) 2.20867e7 + 7.03463e6i 0.835136 + 0.265991i
\(932\) 1.43400e6 0.0540765
\(933\) −606172. + 508639.i −0.0227977 + 0.0191296i
\(934\) 2.86076e7 + 1.04123e7i 1.07303 + 0.390553i
\(935\) −5.44903e6 + 3.09030e7i −0.203841 + 1.15604i
\(936\) 2.36074e6 + 1.33884e7i 0.0880761 + 0.499504i
\(937\) 3.96747e7 1.44404e7i 1.47626 0.537316i 0.526471 0.850193i \(-0.323515\pi\)
0.949794 + 0.312877i \(0.101293\pi\)
\(938\) 3.56896e6 6.18162e6i 0.132445 0.229401i
\(939\) 2.54914e7 + 4.41524e7i 0.943473 + 1.63414i
\(940\) 5.94959e6 + 4.99230e6i 0.219618 + 0.184281i
\(941\) 3.55324e7 + 2.98152e7i 1.30813 + 1.09765i 0.988679 + 0.150046i \(0.0479421\pi\)
0.319449 + 0.947604i \(0.396502\pi\)
\(942\) −1.91946e7 3.32460e7i −0.704776 1.22071i
\(943\) −1.45725e7 + 2.52403e7i −0.533649 + 0.924307i
\(944\) −1.72819e6 + 629011.i −0.0631194 + 0.0229736i
\(945\) 5.15134e6 + 2.92147e7i 0.187647 + 1.06420i
\(946\) −297388. + 1.68657e6i −0.0108043 + 0.0612740i
\(947\) −1.76506e7 6.42430e6i −0.639566 0.232783i 0.00182363 0.999998i \(-0.499420\pi\)
−0.641390 + 0.767215i \(0.721642\pi\)
\(948\) 3.17840e7 2.66700e7i 1.14865 0.963832i
\(949\) −5.92443e6 −0.213541
\(950\) 6.96852e6 + 3.18715e7i 0.250514 + 1.14576i
\(951\) 3.36891e7 1.20792
\(952\) −1.88622e6 + 1.58272e6i −0.0674527 + 0.0565995i
\(953\) −3.48718e7 1.26923e7i −1.24378 0.452697i −0.365481 0.930819i \(-0.619096\pi\)
−0.878294 + 0.478122i \(0.841318\pi\)
\(954\) 1.77373e6 1.00593e7i 0.0630982 0.357848i
\(955\) −3.39718e6 1.92663e7i −0.120534 0.683582i
\(956\) 1.13286e7 4.12328e6i 0.400897 0.145914i
\(957\) 2.22615e7 3.85580e7i 0.785732 1.36093i
\(958\) −1.53160e7 2.65282e7i −0.539179 0.933885i
\(959\) 1.05718e7 + 8.87080e6i 0.371196 + 0.311470i
\(960\) 7.81830e6 + 6.56033e6i 0.273800 + 0.229746i
\(961\) −1.35355e7 2.34441e7i −0.472786 0.818889i
\(962\) 1.05783e7 1.83221e7i 0.368533 0.638318i
\(963\) −2.03421e7 + 7.40390e6i −0.706853 + 0.257273i
\(964\) −772792. 4.38272e6i −0.0267837 0.151898i
\(965\) 4.34788e6 2.46581e7i 0.150300 0.852395i
\(966\) −2.18321e7 7.94623e6i −0.752753 0.273980i
\(967\) 3.93857e6 3.30485e6i 0.135448 0.113654i −0.572547 0.819872i \(-0.694044\pi\)
0.707995 + 0.706218i \(0.249600\pi\)
\(968\) 332011. 0.0113884
\(969\) −1.68649e7 + 3.21682e7i −0.576996 + 1.10057i
\(970\) −4.75248e7 −1.62178
\(971\) 3.13880e6 2.63376e6i 0.106835 0.0896455i −0.587805 0.809002i \(-0.700008\pi\)
0.694641 + 0.719357i \(0.255563\pi\)
\(972\) 3.79099e6 + 1.37981e6i 0.128703 + 0.0468439i
\(973\) 2.29923e6 1.30396e7i 0.0778575 0.441552i
\(974\) −2.88198e6 1.63445e7i −0.0973406 0.552046i
\(975\) 5.60849e7 2.04132e7i 1.88945 0.687702i
\(976\) −5.95963e6 + 1.03224e7i −0.200260 + 0.346861i
\(977\) 2.17088e7 + 3.76008e7i 0.727612 + 1.26026i 0.957890 + 0.287136i \(0.0927030\pi\)
−0.230278 + 0.973125i \(0.573964\pi\)
\(978\) −3.75305e7 3.14918e7i −1.25469 1.05281i
\(979\) 1.59492e7 + 1.33830e7i 0.531842 + 0.446269i
\(980\) −1.07417e7 1.86051e7i −0.357278 0.618824i
\(981\) −2.49969e7 + 4.32959e7i −0.829304 + 1.43640i
\(982\) 3.17656e7 1.15617e7i 1.05118 0.382599i
\(983\) 164879. + 935072.i 0.00544227 + 0.0308647i 0.987408 0.158195i \(-0.0505673\pi\)
−0.981966 + 0.189059i \(0.939456\pi\)
\(984\) 1.89882e6 1.07687e7i 0.0625166 0.354549i
\(985\) 6.41074e7 + 2.33332e7i 2.10532 + 0.766273i
\(986\) 1.03352e7 8.67223e6i 0.338552 0.284079i
\(987\) 6.63334e6 0.216740
\(988\) 8.39489e6 + 6.48052e6i 0.273604 + 0.211211i
\(989\) −4.89670e6 −0.159189
\(990\) 5.74268e7 4.81868e7i 1.86220 1.56257i
\(991\) 3.71071e7 + 1.35059e7i 1.20025 + 0.436856i 0.863312 0.504670i \(-0.168386\pi\)
0.336940 + 0.941526i \(0.390608\pi\)
\(992\) −1.32708e6 + 7.52626e6i −0.0428173 + 0.242829i
\(993\) 1.01467e7 + 5.75448e7i 0.326552 + 1.85197i
\(994\) 3.73222e6 1.35842e6i 0.119812 0.0436081i
\(995\) 7.46840e6 1.29356e7i 0.239150 0.414219i
\(996\) 5.33954e6 + 9.24836e6i 0.170552 + 0.295404i
\(997\) −1.49656e7 1.25576e7i −0.476822 0.400101i 0.372454 0.928051i \(-0.378517\pi\)
−0.849276 + 0.527950i \(0.822961\pi\)
\(998\) −3.32288e7 2.78823e7i −1.05606 0.886139i
\(999\) −4.48442e7 7.76723e7i −1.42165 2.46237i
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 38.6.e.b.25.5 30
19.4 even 9 722.6.a.r.1.3 15
19.15 odd 18 722.6.a.q.1.13 15
19.16 even 9 inner 38.6.e.b.35.5 yes 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.6.e.b.25.5 30 1.1 even 1 trivial
38.6.e.b.35.5 yes 30 19.16 even 9 inner
722.6.a.q.1.13 15 19.15 odd 18
722.6.a.r.1.3 15 19.4 even 9