Properties

Label 128.5.l.a.3.13
Level $128$
Weight $5$
Character 128.3
Analytic conductor $13.231$
Analytic rank $0$
Dimension $1008$
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] = [128,5,Mod(3,128)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(128, base_ring=CyclotomicField(32))
 
chi = DirichletCharacter(H, H._module([16, 3]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("128.3");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 128.l (of order \(32\), degree \(16\), 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: \(13.2313552747\)
Analytic rank: \(0\)
Dimension: \(1008\)
Relative dimension: \(63\) over \(\Q(\zeta_{32})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label 3.13
Character \(\chi\) \(=\) 128.3
Dual form 128.5.l.a.43.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.25888 - 2.31942i) q^{2} +(5.81494 - 4.77220i) q^{3} +(5.24061 + 15.1174i) q^{4} +(-28.0812 - 8.51835i) q^{5} +(-30.0189 + 2.06475i) q^{6} +(-9.11012 - 45.7997i) q^{7} +(17.9850 - 61.4210i) q^{8} +(-4.76266 + 23.9435i) q^{9} +O(q^{10})\) \(q+(-3.25888 - 2.31942i) q^{2} +(5.81494 - 4.77220i) q^{3} +(5.24061 + 15.1174i) q^{4} +(-28.0812 - 8.51835i) q^{5} +(-30.0189 + 2.06475i) q^{6} +(-9.11012 - 45.7997i) q^{7} +(17.9850 - 61.4210i) q^{8} +(-4.76266 + 23.9435i) q^{9} +(71.7558 + 92.8924i) q^{10} +(10.5016 + 106.624i) q^{11} +(102.617 + 62.8976i) q^{12} +(-38.7544 - 127.756i) q^{13} +(-76.5398 + 170.386i) q^{14} +(-203.942 + 84.4756i) q^{15} +(-201.072 + 158.449i) q^{16} +(-6.00675 + 14.5016i) q^{17} +(71.0559 - 66.9824i) q^{18} +(-152.343 + 285.014i) q^{19} +(-18.3874 - 469.157i) q^{20} +(-271.540 - 222.847i) q^{21} +(213.083 - 371.834i) q^{22} +(-337.725 + 225.661i) q^{23} +(-188.531 - 442.988i) q^{24} +(196.325 + 131.180i) q^{25} +(-170.024 + 506.229i) q^{26} +(373.800 + 699.330i) q^{27} +(644.630 - 377.740i) q^{28} +(-41.6767 + 423.151i) q^{29} +(860.557 + 197.731i) q^{30} +(473.001 + 473.001i) q^{31} +(1022.78 - 49.9961i) q^{32} +(569.899 + 569.899i) q^{33} +(53.2105 - 33.3268i) q^{34} +(-134.314 + 1363.72i) q^{35} +(-386.923 + 53.4795i) q^{36} +(362.939 + 679.011i) q^{37} +(1157.54 - 575.480i) q^{38} +(-835.032 - 557.950i) q^{39} +(-1028.25 + 1571.57i) q^{40} +(-2612.46 + 1745.59i) q^{41} +(368.041 + 1356.05i) q^{42} +(656.216 + 538.542i) q^{43} +(-1556.85 + 717.534i) q^{44} +(337.700 - 631.793i) q^{45} +(1624.01 + 47.9240i) q^{46} +(-257.793 + 622.369i) q^{47} +(-413.072 + 1880.93i) q^{48} +(203.618 - 84.3415i) q^{49} +(-335.539 - 882.862i) q^{50} +(34.2755 + 112.991i) q^{51} +(1728.24 - 1255.39i) q^{52} +(-7.55794 - 76.7370i) q^{53} +(403.869 - 3146.03i) q^{54} +(613.367 - 3083.60i) q^{55} +(-2976.91 - 264.157i) q^{56} +(474.277 + 2384.35i) q^{57} +(1117.28 - 1282.33i) q^{58} +(-3068.41 - 930.793i) q^{59} +(-2345.83 - 2640.37i) q^{60} +(4084.19 - 3351.81i) q^{61} +(-444.367 - 2638.54i) q^{62} +1139.99 q^{63} +(-3449.08 - 2209.32i) q^{64} +3917.67i q^{65} +(-535.400 - 3179.07i) q^{66} +(-3060.68 - 3729.45i) q^{67} +(-250.705 - 14.8094i) q^{68} +(-886.954 + 2923.90i) q^{69} +(3600.74 - 4132.65i) q^{70} +(-4930.33 + 980.704i) q^{71} +(1384.98 + 723.152i) q^{72} +(-2587.62 - 514.709i) q^{73} +(392.135 - 3054.62i) q^{74} +(1767.64 - 174.097i) q^{75} +(-5107.05 - 809.387i) q^{76} +(4787.70 - 1452.33i) q^{77} +(1427.15 + 3755.08i) q^{78} +(-2880.93 - 6955.17i) q^{79} +(6996.08 - 2736.64i) q^{80} +(3684.07 + 1525.99i) q^{81} +(12562.4 + 370.714i) q^{82} +(-7599.60 - 4062.07i) q^{83} +(1945.84 - 5272.84i) q^{84} +(292.207 - 356.055i) q^{85} +(-889.425 - 3277.08i) q^{86} +(1777.01 + 2659.49i) q^{87} +(6737.85 + 1272.63i) q^{88} +(-7667.51 + 11475.2i) q^{89} +(-2565.92 + 1275.67i) q^{90} +(-5498.13 + 2938.81i) q^{91} +(-5181.29 - 3922.93i) q^{92} +(5007.72 + 493.218i) q^{93} +(2283.65 - 1430.29i) q^{94} +(6705.84 - 6705.84i) q^{95} +(5708.81 - 5171.63i) q^{96} +(-4107.13 + 4107.13i) q^{97} +(-859.191 - 197.417i) q^{98} +(-2602.98 - 256.371i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1008 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 1008 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} - 43072 q^{50} - 16 q^{51} - 17968 q^{52} - 16 q^{53} + 31088 q^{54} - 16 q^{55} + 49376 q^{56} - 16 q^{57} + 65504 q^{58} - 16 q^{59} + 63920 q^{60} - 16 q^{61} + 11792 q^{62} - 32 q^{63} - 24400 q^{64} - 70864 q^{66} - 16 q^{67} - 53296 q^{68} - 16 q^{69} - 122320 q^{70} - 16 q^{71} - 81664 q^{72} - 16 q^{73} - 33280 q^{74} - 16 q^{75} + 28272 q^{76} - 16 q^{77} + 99344 q^{78} - 16 q^{79} + 105248 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{32}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.25888 2.31942i −0.814720 0.579854i
\(3\) 5.81494 4.77220i 0.646105 0.530244i −0.253285 0.967392i \(-0.581511\pi\)
0.899390 + 0.437147i \(0.144011\pi\)
\(4\) 5.24061 + 15.1174i 0.327538 + 0.944838i
\(5\) −28.0812 8.51835i −1.12325 0.340734i −0.326592 0.945165i \(-0.605900\pi\)
−0.796657 + 0.604431i \(0.793400\pi\)
\(6\) −30.0189 + 2.06475i −0.833859 + 0.0573543i
\(7\) −9.11012 45.7997i −0.185921 0.934687i −0.955242 0.295825i \(-0.904405\pi\)
0.769321 0.638862i \(-0.220595\pi\)
\(8\) 17.9850 61.4210i 0.281016 0.959703i
\(9\) −4.76266 + 23.9435i −0.0587982 + 0.295599i
\(10\) 71.7558 + 92.8924i 0.717558 + 0.928924i
\(11\) 10.5016 + 106.624i 0.0867900 + 0.881194i 0.935733 + 0.352709i \(0.114740\pi\)
−0.848943 + 0.528485i \(0.822760\pi\)
\(12\) 102.617 + 62.8976i 0.712619 + 0.436789i
\(13\) −38.7544 127.756i −0.229316 0.755953i −0.993787 0.111295i \(-0.964500\pi\)
0.764472 0.644657i \(-0.223000\pi\)
\(14\) −76.5398 + 170.386i −0.390509 + 0.869316i
\(15\) −203.942 + 84.4756i −0.906409 + 0.375447i
\(16\) −201.072 + 158.449i −0.785438 + 0.618941i
\(17\) −6.00675 + 14.5016i −0.0207846 + 0.0501785i −0.933931 0.357453i \(-0.883645\pi\)
0.913146 + 0.407632i \(0.133645\pi\)
\(18\) 71.0559 66.9824i 0.219308 0.206736i
\(19\) −152.343 + 285.014i −0.422004 + 0.789513i −0.999641 0.0267801i \(-0.991475\pi\)
0.577638 + 0.816293i \(0.303975\pi\)
\(20\) −18.3874 469.157i −0.0459686 1.17289i
\(21\) −271.540 222.847i −0.615737 0.505322i
\(22\) 213.083 371.834i 0.440254 0.768252i
\(23\) −337.725 + 225.661i −0.638422 + 0.426580i −0.832208 0.554464i \(-0.812923\pi\)
0.193786 + 0.981044i \(0.437923\pi\)
\(24\) −188.531 442.988i −0.327311 0.769076i
\(25\) 196.325 + 131.180i 0.314121 + 0.209889i
\(26\) −170.024 + 506.229i −0.251514 + 0.748860i
\(27\) 373.800 + 699.330i 0.512757 + 0.959301i
\(28\) 644.630 377.740i 0.822232 0.481811i
\(29\) −41.6767 + 423.151i −0.0495561 + 0.503152i 0.938083 + 0.346410i \(0.112599\pi\)
−0.987640 + 0.156742i \(0.949901\pi\)
\(30\) 860.557 + 197.731i 0.956174 + 0.219701i
\(31\) 473.001 + 473.001i 0.492196 + 0.492196i 0.908998 0.416801i \(-0.136849\pi\)
−0.416801 + 0.908998i \(0.636849\pi\)
\(32\) 1022.78 49.9961i 0.998807 0.0488243i
\(33\) 569.899 + 569.899i 0.523323 + 0.523323i
\(34\) 53.2105 33.3268i 0.0460299 0.0288294i
\(35\) −134.314 + 1363.72i −0.109644 + 1.11324i
\(36\) −386.923 + 53.4795i −0.298552 + 0.0412650i
\(37\) 362.939 + 679.011i 0.265112 + 0.495990i 0.978892 0.204381i \(-0.0655180\pi\)
−0.713779 + 0.700371i \(0.753018\pi\)
\(38\) 1157.54 575.480i 0.801617 0.398532i
\(39\) −835.032 557.950i −0.549002 0.366831i
\(40\) −1028.25 + 1571.57i −0.642655 + 0.982234i
\(41\) −2612.46 + 1745.59i −1.55411 + 1.03842i −0.579374 + 0.815062i \(0.696703\pi\)
−0.974736 + 0.223361i \(0.928297\pi\)
\(42\) 368.041 + 1356.05i 0.208640 + 0.768734i
\(43\) 656.216 + 538.542i 0.354903 + 0.291261i 0.794903 0.606736i \(-0.207522\pi\)
−0.440000 + 0.897998i \(0.645022\pi\)
\(44\) −1556.85 + 717.534i −0.804158 + 0.370627i
\(45\) 337.700 631.793i 0.166766 0.311997i
\(46\) 1624.01 + 47.9240i 0.767490 + 0.0226484i
\(47\) −257.793 + 622.369i −0.116701 + 0.281742i −0.971427 0.237338i \(-0.923725\pi\)
0.854726 + 0.519080i \(0.173725\pi\)
\(48\) −413.072 + 1880.93i −0.179285 + 0.816374i
\(49\) 203.618 84.3415i 0.0848057 0.0351277i
\(50\) −335.539 882.862i −0.134216 0.353145i
\(51\) 34.2755 + 112.991i 0.0131778 + 0.0434415i
\(52\) 1728.24 1255.39i 0.639143 0.464270i
\(53\) −7.55794 76.7370i −0.00269062 0.0273183i 0.993746 0.111667i \(-0.0356190\pi\)
−0.996436 + 0.0843488i \(0.973119\pi\)
\(54\) 403.869 3146.03i 0.138501 1.07889i
\(55\) 613.367 3083.60i 0.202766 1.01937i
\(56\) −2976.91 264.157i −0.949269 0.0842337i
\(57\) 474.277 + 2384.35i 0.145976 + 0.733873i
\(58\) 1117.28 1282.33i 0.332129 0.381193i
\(59\) −3068.41 930.793i −0.881475 0.267392i −0.183074 0.983099i \(-0.558605\pi\)
−0.698401 + 0.715707i \(0.746105\pi\)
\(60\) −2345.83 2640.37i −0.651620 0.733437i
\(61\) 4084.19 3351.81i 1.09761 0.900782i 0.102033 0.994781i \(-0.467465\pi\)
0.995572 + 0.0939995i \(0.0299652\pi\)
\(62\) −444.367 2638.54i −0.115600 0.686404i
\(63\) 1139.99 0.287224
\(64\) −3449.08 2209.32i −0.842060 0.539385i
\(65\) 3917.67i 0.927259i
\(66\) −535.400 3179.07i −0.122911 0.729814i
\(67\) −3060.68 3729.45i −0.681817 0.830797i 0.311003 0.950409i \(-0.399335\pi\)
−0.992821 + 0.119612i \(0.961835\pi\)
\(68\) −250.705 14.8094i −0.0542183 0.00320272i
\(69\) −886.954 + 2923.90i −0.186296 + 0.614135i
\(70\) 3600.74 4132.65i 0.734844 0.843399i
\(71\) −4930.33 + 980.704i −0.978046 + 0.194546i −0.658133 0.752901i \(-0.728654\pi\)
−0.319913 + 0.947447i \(0.603654\pi\)
\(72\) 1384.98 + 723.152i 0.267164 + 0.139497i
\(73\) −2587.62 514.709i −0.485573 0.0965865i −0.0537680 0.998553i \(-0.517123\pi\)
−0.431805 + 0.901967i \(0.642123\pi\)
\(74\) 392.135 3054.62i 0.0716097 0.557820i
\(75\) 1767.64 174.097i 0.314247 0.0309506i
\(76\) −5107.05 809.387i −0.884184 0.140129i
\(77\) 4787.70 1452.33i 0.807505 0.244954i
\(78\) 1427.15 + 3755.08i 0.234574 + 0.617206i
\(79\) −2880.93 6955.17i −0.461613 1.11443i −0.967735 0.251970i \(-0.918922\pi\)
0.506122 0.862462i \(-0.331078\pi\)
\(80\) 6996.08 2736.64i 1.09314 0.427600i
\(81\) 3684.07 + 1525.99i 0.561510 + 0.232585i
\(82\) 12562.4 + 370.714i 1.86830 + 0.0551330i
\(83\) −7599.60 4062.07i −1.10315 0.589646i −0.183751 0.982973i \(-0.558824\pi\)
−0.919399 + 0.393327i \(0.871324\pi\)
\(84\) 1945.84 5272.84i 0.275770 0.747284i
\(85\) 292.207 356.055i 0.0404438 0.0492810i
\(86\) −889.425 3277.08i −0.120258 0.443089i
\(87\) 1777.01 + 2659.49i 0.234775 + 0.351366i
\(88\) 6737.85 + 1272.63i 0.870074 + 0.164337i
\(89\) −7667.51 + 11475.2i −0.967998 + 1.44871i −0.0757710 + 0.997125i \(0.524142\pi\)
−0.892227 + 0.451587i \(0.850858\pi\)
\(90\) −2565.92 + 1275.67i −0.316780 + 0.157490i
\(91\) −5498.13 + 2938.81i −0.663945 + 0.354886i
\(92\) −5181.29 3922.93i −0.612157 0.463484i
\(93\) 5007.72 + 493.218i 0.578995 + 0.0570260i
\(94\) 2283.65 1430.29i 0.258448 0.161871i
\(95\) 6705.84 6705.84i 0.743029 0.743029i
\(96\) 5708.81 5171.63i 0.619445 0.561158i
\(97\) −4107.13 + 4107.13i −0.436511 + 0.436511i −0.890836 0.454325i \(-0.849880\pi\)
0.454325 + 0.890836i \(0.349880\pi\)
\(98\) −859.191 197.417i −0.0894618 0.0205557i
\(99\) −2602.98 256.371i −0.265583 0.0261576i
\(100\) −954.243 + 3655.40i −0.0954243 + 0.365540i
\(101\) −14239.6 + 7611.21i −1.39590 + 0.746124i −0.986116 0.166059i \(-0.946896\pi\)
−0.409784 + 0.912183i \(0.634396\pi\)
\(102\) 150.374 447.724i 0.0144535 0.0430339i
\(103\) −2020.40 + 3023.74i −0.190442 + 0.285017i −0.914387 0.404841i \(-0.867327\pi\)
0.723945 + 0.689858i \(0.242327\pi\)
\(104\) −8543.90 + 82.6332i −0.789932 + 0.00763990i
\(105\) 5726.89 + 8570.90i 0.519446 + 0.777406i
\(106\) −153.355 + 267.607i −0.0136485 + 0.0238169i
\(107\) 10348.7 12609.9i 0.903895 1.10140i −0.0905243 0.995894i \(-0.528854\pi\)
0.994419 0.105504i \(-0.0336457\pi\)
\(108\) −8613.12 + 9315.80i −0.738436 + 0.798680i
\(109\) −4344.94 2322.42i −0.365705 0.195473i 0.278301 0.960494i \(-0.410229\pi\)
−0.644006 + 0.765021i \(0.722729\pi\)
\(110\) −9151.05 + 8626.44i −0.756285 + 0.712929i
\(111\) 5350.84 + 2216.39i 0.434286 + 0.179887i
\(112\) 9088.70 + 7765.55i 0.724545 + 0.619065i
\(113\) −4196.32 10130.8i −0.328633 0.793391i −0.998694 0.0510849i \(-0.983732\pi\)
0.670061 0.742306i \(-0.266268\pi\)
\(114\) 3984.70 8870.37i 0.306609 0.682546i
\(115\) 11406.0 3459.97i 0.862458 0.261624i
\(116\) −6615.35 + 1587.52i −0.491629 + 0.117979i
\(117\) 3243.50 319.457i 0.236942 0.0233368i
\(118\) 7840.70 + 10150.3i 0.563107 + 0.728977i
\(119\) 718.890 + 142.996i 0.0507655 + 0.0100979i
\(120\) 1520.66 + 14045.6i 0.105602 + 0.975390i
\(121\) 3101.19 616.864i 0.211815 0.0421327i
\(122\) −21084.1 + 1450.20i −1.41656 + 0.0974337i
\(123\) −6860.99 + 22617.7i −0.453499 + 1.49499i
\(124\) −4671.73 + 9629.36i −0.303833 + 0.626259i
\(125\) 7239.48 + 8821.33i 0.463327 + 0.564565i
\(126\) −3715.10 2644.12i −0.234007 0.166548i
\(127\) 14546.3i 0.901871i −0.892557 0.450936i \(-0.851090\pi\)
0.892557 0.450936i \(-0.148910\pi\)
\(128\) 6115.80 + 15199.8i 0.373279 + 0.927719i
\(129\) 6385.89 0.383744
\(130\) 9086.71 12767.2i 0.537675 0.755457i
\(131\) 13685.6 11231.5i 0.797485 0.654479i −0.144736 0.989470i \(-0.546233\pi\)
0.942221 + 0.334991i \(0.108733\pi\)
\(132\) −5628.78 + 11602.0i −0.323047 + 0.665864i
\(133\) 14441.4 + 4380.76i 0.816407 + 0.247654i
\(134\) 1324.24 + 19252.8i 0.0737493 + 1.07222i
\(135\) −4539.62 22822.2i −0.249088 1.25225i
\(136\) 782.670 + 629.752i 0.0423156 + 0.0340480i
\(137\) −853.944 + 4293.07i −0.0454976 + 0.228732i −0.996843 0.0793935i \(-0.974702\pi\)
0.951346 + 0.308125i \(0.0997016\pi\)
\(138\) 9672.21 7471.41i 0.507888 0.392324i
\(139\) −1216.12 12347.5i −0.0629431 0.639072i −0.973963 0.226709i \(-0.927203\pi\)
0.911020 0.412363i \(-0.135297\pi\)
\(140\) −21319.7 + 5116.22i −1.08774 + 0.261031i
\(141\) 1471.01 + 4849.28i 0.0739909 + 0.243915i
\(142\) 18342.0 + 8239.50i 0.909642 + 0.408624i
\(143\) 13214.9 5473.80i 0.646239 0.267681i
\(144\) −2836.18 5569.01i −0.136776 0.268567i
\(145\) 4774.88 11527.6i 0.227105 0.548280i
\(146\) 7238.91 + 7679.14i 0.339600 + 0.360253i
\(147\) 781.535 1462.15i 0.0361671 0.0676639i
\(148\) −8362.86 + 9045.12i −0.381796 + 0.412944i
\(149\) 25819.0 + 21189.1i 1.16297 + 0.954421i 0.999484 0.0321251i \(-0.0102275\pi\)
0.163482 + 0.986546i \(0.447728\pi\)
\(150\) −6164.33 3532.53i −0.273970 0.157001i
\(151\) −13979.4 + 9340.71i −0.613103 + 0.409662i −0.822984 0.568065i \(-0.807692\pi\)
0.209881 + 0.977727i \(0.432692\pi\)
\(152\) 14766.0 + 14483.1i 0.639108 + 0.626864i
\(153\) −318.611 212.889i −0.0136106 0.00909431i
\(154\) −18971.1 6371.69i −0.799928 0.268666i
\(155\) −9253.26 17311.6i −0.385151 0.720567i
\(156\) 4058.69 15547.5i 0.166777 0.638869i
\(157\) 3434.40 34870.1i 0.139332 1.41466i −0.630387 0.776281i \(-0.717104\pi\)
0.769719 0.638383i \(-0.220396\pi\)
\(158\) −6743.34 + 29348.1i −0.270123 + 1.17562i
\(159\) −410.153 410.153i −0.0162238 0.0162238i
\(160\) −29146.8 7308.44i −1.13855 0.285486i
\(161\) 13411.9 + 13411.9i 0.517415 + 0.517415i
\(162\) −8466.53 13517.9i −0.322608 0.515086i
\(163\) −3230.30 + 32797.8i −0.121581 + 1.23444i 0.719872 + 0.694107i \(0.244201\pi\)
−0.841453 + 0.540330i \(0.818299\pi\)
\(164\) −40079.6 30345.6i −1.49017 1.12826i
\(165\) −11148.9 20858.1i −0.409509 0.766137i
\(166\) 15344.6 + 30864.5i 0.556850 + 1.12006i
\(167\) −31859.3 21287.7i −1.14236 0.763300i −0.167446 0.985881i \(-0.553552\pi\)
−0.974914 + 0.222581i \(0.928552\pi\)
\(168\) −18571.2 + 12670.3i −0.657991 + 0.448921i
\(169\) 8927.90 5965.43i 0.312591 0.208866i
\(170\) −1778.11 + 482.591i −0.0615262 + 0.0166987i
\(171\) −6098.68 5005.06i −0.208566 0.171166i
\(172\) −4702.39 + 12742.6i −0.158951 + 0.430725i
\(173\) −10832.4 + 20266.0i −0.361937 + 0.677137i −0.995313 0.0967078i \(-0.969169\pi\)
0.633376 + 0.773844i \(0.281669\pi\)
\(174\) 377.387 12788.6i 0.0124649 0.422400i
\(175\) 4219.47 10186.7i 0.137779 0.332627i
\(176\) −19006.1 19775.2i −0.613575 0.638405i
\(177\) −22284.6 + 9230.57i −0.711308 + 0.294634i
\(178\) 51603.4 19612.3i 1.62869 0.618997i
\(179\) 7713.73 + 25428.8i 0.240746 + 0.793632i 0.991161 + 0.132665i \(0.0423535\pi\)
−0.750415 + 0.660967i \(0.770146\pi\)
\(180\) 11320.8 + 1794.17i 0.349408 + 0.0553758i
\(181\) 1430.69 + 14526.0i 0.0436705 + 0.443394i 0.992012 + 0.126143i \(0.0402597\pi\)
−0.948342 + 0.317251i \(0.897240\pi\)
\(182\) 24734.1 + 3175.22i 0.746712 + 0.0958585i
\(183\) 7753.83 38981.1i 0.231534 1.16400i
\(184\) 7786.30 + 24801.9i 0.229983 + 0.732572i
\(185\) −4407.72 22159.1i −0.128787 0.647454i
\(186\) −15175.6 13222.3i −0.438652 0.382193i
\(187\) −1609.30 488.177i −0.0460209 0.0139603i
\(188\) −10759.6 635.579i −0.304425 0.0179826i
\(189\) 28623.7 23490.9i 0.801314 0.657621i
\(190\) −37407.2 + 6299.89i −1.03621 + 0.174512i
\(191\) −14422.5 −0.395344 −0.197672 0.980268i \(-0.563338\pi\)
−0.197672 + 0.980268i \(0.563338\pi\)
\(192\) −30599.5 + 3612.62i −0.830064 + 0.0979985i
\(193\) 59617.2i 1.60050i 0.599664 + 0.800252i \(0.295301\pi\)
−0.599664 + 0.800252i \(0.704699\pi\)
\(194\) 22910.8 3858.50i 0.608747 0.102522i
\(195\) 18695.9 + 22781.0i 0.491674 + 0.599107i
\(196\) 2342.11 + 2636.18i 0.0609670 + 0.0686220i
\(197\) 10143.4 33438.3i 0.261367 0.861613i −0.723799 0.690011i \(-0.757606\pi\)
0.985166 0.171602i \(-0.0548943\pi\)
\(198\) 7888.16 + 6872.87i 0.201208 + 0.175311i
\(199\) −65421.0 + 13013.0i −1.65200 + 0.328604i −0.931193 0.364528i \(-0.881231\pi\)
−0.720811 + 0.693132i \(0.756231\pi\)
\(200\) 11588.1 9699.21i 0.289704 0.242480i
\(201\) −35595.3 7080.35i −0.881051 0.175252i
\(202\) 64058.6 + 8223.48i 1.56991 + 0.201536i
\(203\) 19759.8 1946.18i 0.479503 0.0472269i
\(204\) −1528.51 + 1110.30i −0.0367289 + 0.0266797i
\(205\) 88230.6 26764.5i 2.09948 0.636870i
\(206\) 13597.6 5167.87i 0.320425 0.121780i
\(207\) −3794.64 9161.07i −0.0885584 0.213799i
\(208\) 28035.2 + 19547.6i 0.648003 + 0.451821i
\(209\) −31989.3 13250.4i −0.732340 0.303345i
\(210\) 1216.23 41214.6i 0.0275789 0.934571i
\(211\) 71993.1 + 38481.1i 1.61706 + 0.864336i 0.996800 + 0.0799393i \(0.0254727\pi\)
0.620259 + 0.784397i \(0.287027\pi\)
\(212\) 1120.46 516.405i 0.0249301 0.0114900i
\(213\) −23989.5 + 29231.3i −0.528764 + 0.644300i
\(214\) −62972.8 + 17091.3i −1.37507 + 0.373205i
\(215\) −13839.9 20712.8i −0.299402 0.448087i
\(216\) 49676.4 10381.7i 1.06474 0.222515i
\(217\) 17354.2 25972.4i 0.368540 0.551559i
\(218\) 8772.99 + 17646.2i 0.184601 + 0.371312i
\(219\) −17503.1 + 9355.63i −0.364945 + 0.195067i
\(220\) 49830.5 6887.44i 1.02956 0.142303i
\(221\) 2085.45 + 205.399i 0.0426988 + 0.00420547i
\(222\) −12297.0 19633.8i −0.249513 0.398381i
\(223\) −21614.5 + 21614.5i −0.434646 + 0.434646i −0.890205 0.455559i \(-0.849439\pi\)
0.455559 + 0.890205i \(0.349439\pi\)
\(224\) −11607.4 46387.5i −0.231335 0.924495i
\(225\) −4075.95 + 4075.95i −0.0805125 + 0.0805125i
\(226\) −9822.27 + 42748.1i −0.192307 + 0.836951i
\(227\) 84957.5 + 8367.58i 1.64873 + 0.162386i 0.879276 0.476313i \(-0.158027\pi\)
0.769456 + 0.638699i \(0.220527\pi\)
\(228\) −33559.7 + 19665.3i −0.645578 + 0.378295i
\(229\) 17963.5 9601.70i 0.342547 0.183095i −0.291148 0.956678i \(-0.594037\pi\)
0.633695 + 0.773583i \(0.281537\pi\)
\(230\) −45195.9 15179.6i −0.854365 0.286950i
\(231\) 20909.4 31293.1i 0.391847 0.586441i
\(232\) 25240.8 + 10170.2i 0.468950 + 0.188953i
\(233\) −520.474 778.944i −0.00958709 0.0143481i 0.826645 0.562724i \(-0.190246\pi\)
−0.836232 + 0.548376i \(0.815246\pi\)
\(234\) −11311.1 6481.96i −0.206573 0.118379i
\(235\) 12540.7 15280.9i 0.227084 0.276703i
\(236\) −2009.18 51264.4i −0.0360740 0.920432i
\(237\) −49943.9 26695.5i −0.889171 0.475272i
\(238\) −2011.11 2133.41i −0.0355044 0.0376635i
\(239\) −58871.1 24385.2i −1.03064 0.426904i −0.197695 0.980264i \(-0.563346\pi\)
−0.832943 + 0.553359i \(0.813346\pi\)
\(240\) 27622.0 49300.1i 0.479548 0.855904i
\(241\) −33855.3 81733.8i −0.582897 1.40724i −0.890175 0.455618i \(-0.849418\pi\)
0.307278 0.951620i \(-0.400582\pi\)
\(242\) −11537.2 5182.66i −0.197001 0.0884956i
\(243\) −32759.2 + 9937.40i −0.554780 + 0.168291i
\(244\) 72074.3 + 44176.8i 1.21060 + 0.742019i
\(245\) −6436.31 + 633.921i −0.107227 + 0.0105610i
\(246\) 74819.0 57794.8i 1.23635 0.955033i
\(247\) 42316.2 + 8417.23i 0.693607 + 0.137967i
\(248\) 37559.1 20545.2i 0.610678 0.334047i
\(249\) −63576.3 + 12646.1i −1.02541 + 0.203966i
\(250\) −3132.26 45539.0i −0.0501161 0.728625i
\(251\) −24764.7 + 81638.2i −0.393084 + 1.29582i 0.507692 + 0.861539i \(0.330499\pi\)
−0.900776 + 0.434285i \(0.857001\pi\)
\(252\) 5974.26 + 17233.7i 0.0940769 + 0.271380i
\(253\) −27607.6 33640.0i −0.431308 0.525551i
\(254\) −33738.9 + 47404.6i −0.522954 + 0.734773i
\(255\) 3464.91i 0.0532858i
\(256\) 15323.9 63719.3i 0.233824 0.972279i
\(257\) −119889. −1.81515 −0.907575 0.419890i \(-0.862069\pi\)
−0.907575 + 0.419890i \(0.862069\pi\)
\(258\) −20810.8 14811.5i −0.312644 0.222516i
\(259\) 27792.1 22808.4i 0.414306 0.340012i
\(260\) −59225.0 + 20531.0i −0.876110 + 0.303713i
\(261\) −9933.22 3013.21i −0.145817 0.0442332i
\(262\) −70650.4 + 4859.46i −1.02923 + 0.0707922i
\(263\) −1640.88 8249.24i −0.0237227 0.119262i 0.967109 0.254360i \(-0.0818650\pi\)
−0.990832 + 0.135098i \(0.956865\pi\)
\(264\) 45253.4 24754.1i 0.649298 0.355173i
\(265\) −441.437 + 2219.25i −0.00628604 + 0.0316020i
\(266\) −36902.1 47772.1i −0.521540 0.675166i
\(267\) 10176.0 + 103319.i 0.142743 + 1.44929i
\(268\) 40339.8 65814.1i 0.561647 0.916325i
\(269\) −1551.44 5114.41i −0.0214403 0.0706791i 0.945567 0.325426i \(-0.105508\pi\)
−0.967008 + 0.254747i \(0.918008\pi\)
\(270\) −38140.1 + 84904.2i −0.523184 + 1.16467i
\(271\) −37789.9 + 15653.1i −0.514561 + 0.213138i −0.624826 0.780764i \(-0.714830\pi\)
0.110265 + 0.993902i \(0.464830\pi\)
\(272\) −1089.97 3867.63i −0.0147325 0.0522765i
\(273\) −17946.7 + 43327.2i −0.240802 + 0.581346i
\(274\) 12740.3 12009.9i 0.169699 0.159970i
\(275\) −11925.3 + 22310.7i −0.157690 + 0.295017i
\(276\) −48849.9 + 1914.55i −0.641277 + 0.0251332i
\(277\) 93415.5 + 76664.2i 1.21747 + 0.999155i 0.999732 + 0.0231485i \(0.00736905\pi\)
0.217742 + 0.976006i \(0.430131\pi\)
\(278\) −24675.8 + 43059.7i −0.319287 + 0.557162i
\(279\) −13578.0 + 9072.55i −0.174433 + 0.116552i
\(280\) 81345.1 + 32776.2i 1.03756 + 0.418064i
\(281\) 76815.4 + 51326.4i 0.972827 + 0.650023i 0.936998 0.349335i \(-0.113593\pi\)
0.0358297 + 0.999358i \(0.488593\pi\)
\(282\) 6453.64 19215.1i 0.0811534 0.241627i
\(283\) −22590.1 42263.1i −0.282063 0.527702i 0.700496 0.713657i \(-0.252962\pi\)
−0.982558 + 0.185954i \(0.940462\pi\)
\(284\) −40663.6 69394.3i −0.504161 0.860374i
\(285\) 6992.46 70995.7i 0.0860876 0.874062i
\(286\) −55761.9 12812.5i −0.681720 0.156639i
\(287\) 103747. + 103747.i 1.25954 + 1.25954i
\(288\) −3674.06 + 24727.0i −0.0442957 + 0.298117i
\(289\) 58884.1 + 58884.1i 0.705021 + 0.705021i
\(290\) −42298.0 + 26492.1i −0.502949 + 0.315007i
\(291\) −4282.68 + 43482.8i −0.0505743 + 0.513489i
\(292\) −5779.63 41815.5i −0.0677851 0.490424i
\(293\) −10112.2 18918.6i −0.117790 0.220370i 0.816116 0.577888i \(-0.196123\pi\)
−0.933906 + 0.357518i \(0.883623\pi\)
\(294\) −5938.26 + 2952.26i −0.0687012 + 0.0341555i
\(295\) 78236.0 + 52275.7i 0.899007 + 0.600697i
\(296\) 48233.0 10080.0i 0.550504 0.115048i
\(297\) −70640.2 + 47200.3i −0.800828 + 0.535096i
\(298\) −34994.7 128938.i −0.394066 1.45194i
\(299\) 41917.9 + 34401.1i 0.468875 + 0.384795i
\(300\) 11895.4 + 25809.7i 0.132171 + 0.286775i
\(301\) 18686.9 34960.7i 0.206254 0.385875i
\(302\) 67222.1 + 1983.71i 0.737052 + 0.0217502i
\(303\) −46480.1 + 112213.i −0.506269 + 1.22224i
\(304\) −14528.2 81447.0i −0.157204 0.881308i
\(305\) −143241. + 59332.4i −1.53981 + 0.637811i
\(306\) 544.536 + 1432.77i 0.00581546 + 0.0153015i
\(307\) −4320.02 14241.2i −0.0458363 0.151102i 0.931035 0.364930i \(-0.118907\pi\)
−0.976871 + 0.213828i \(0.931407\pi\)
\(308\) 47045.9 + 64766.4i 0.495930 + 0.682729i
\(309\) 2681.39 + 27224.6i 0.0280830 + 0.285131i
\(310\) −9997.62 + 77878.7i −0.104034 + 0.810393i
\(311\) 28564.6 143604.i 0.295330 1.48472i −0.493303 0.869858i \(-0.664210\pi\)
0.788632 0.614865i \(-0.210790\pi\)
\(312\) −49287.9 + 41253.7i −0.506327 + 0.423793i
\(313\) 22727.6 + 114260.i 0.231988 + 1.16628i 0.904591 + 0.426280i \(0.140176\pi\)
−0.672603 + 0.740003i \(0.734824\pi\)
\(314\) −92070.5 + 105672.i −0.933816 + 1.07176i
\(315\) −32012.4 9710.86i −0.322625 0.0978671i
\(316\) 90046.3 80001.4i 0.901762 0.801168i
\(317\) 17075.0 14013.1i 0.169919 0.139449i −0.545590 0.838052i \(-0.683695\pi\)
0.715510 + 0.698603i \(0.246195\pi\)
\(318\) 385.324 + 2287.96i 0.00381041 + 0.0226253i
\(319\) −45555.9 −0.447675
\(320\) 78034.6 + 91420.9i 0.762056 + 0.892782i
\(321\) 122712.i 1.19090i
\(322\) −12600.0 74815.6i −0.121523 0.721574i
\(323\) −3218.07 3921.23i −0.0308454 0.0375852i
\(324\) −3762.27 + 63690.7i −0.0358393 + 0.606717i
\(325\) 9150.62 30165.6i 0.0866331 0.285591i
\(326\) 86598.8 99391.6i 0.814849 0.935221i
\(327\) −36348.6 + 7230.19i −0.339932 + 0.0676168i
\(328\) 60230.6 + 191854.i 0.559847 + 1.78330i
\(329\) 30852.8 + 6137.01i 0.285038 + 0.0566976i
\(330\) −12045.7 + 93832.9i −0.110613 + 0.861643i
\(331\) −31925.6 + 3144.40i −0.291396 + 0.0287000i −0.242659 0.970112i \(-0.578020\pi\)
−0.0487370 + 0.998812i \(0.515520\pi\)
\(332\) 21581.4 136174.i 0.195796 1.23543i
\(333\) −17986.4 + 5456.13i −0.162202 + 0.0492035i
\(334\) 54450.6 + 143269.i 0.488101 + 1.28428i
\(335\) 54178.9 + 130799.i 0.482770 + 1.16551i
\(336\) 89909.0 + 1783.12i 0.796388 + 0.0157943i
\(337\) 48791.7 + 20210.2i 0.429621 + 0.177955i 0.587006 0.809582i \(-0.300306\pi\)
−0.157385 + 0.987537i \(0.550306\pi\)
\(338\) −42931.3 1266.89i −0.375786 0.0110893i
\(339\) −72747.6 38884.4i −0.633022 0.338358i
\(340\) 6913.97 + 2551.46i 0.0598094 + 0.0220715i
\(341\) −45466.2 + 55400.7i −0.391003 + 0.476438i
\(342\) 8266.05 + 30456.3i 0.0706718 + 0.260390i
\(343\) −68008.0 101781.i −0.578058 0.865125i
\(344\) 44879.9 30619.7i 0.379258 0.258752i
\(345\) 49813.6 74551.3i 0.418513 0.626350i
\(346\) 82306.9 40919.7i 0.687518 0.341806i
\(347\) −79378.6 + 42428.7i −0.659241 + 0.352372i −0.766854 0.641821i \(-0.778179\pi\)
0.107613 + 0.994193i \(0.465679\pi\)
\(348\) −30891.9 + 40801.1i −0.255086 + 0.336910i
\(349\) −59502.2 5860.46i −0.488520 0.0481150i −0.149241 0.988801i \(-0.547683\pi\)
−0.339279 + 0.940686i \(0.610183\pi\)
\(350\) −37378.0 + 23410.5i −0.305126 + 0.191107i
\(351\) 74857.3 74857.3i 0.607603 0.607603i
\(352\) 16071.6 + 108528.i 0.129710 + 0.875905i
\(353\) 89667.3 89667.3i 0.719589 0.719589i −0.248932 0.968521i \(-0.580080\pi\)
0.968521 + 0.248932i \(0.0800796\pi\)
\(354\) 94032.3 + 21605.9i 0.750362 + 0.172411i
\(355\) 146804. + 14458.9i 1.16488 + 0.114731i
\(356\) −213658. 55775.7i −1.68585 0.440093i
\(357\) 4862.71 2599.17i 0.0381542 0.0203938i
\(358\) 33841.8 100761.i 0.264051 0.786185i
\(359\) 42021.6 62889.8i 0.326050 0.487968i −0.631842 0.775097i \(-0.717701\pi\)
0.957892 + 0.287129i \(0.0927009\pi\)
\(360\) −32731.8 32104.7i −0.252560 0.247722i
\(361\) 14377.8 + 21518.0i 0.110326 + 0.165115i
\(362\) 29029.4 50656.9i 0.221524 0.386564i
\(363\) 15089.4 18386.5i 0.114514 0.139536i
\(364\) −73240.7 67716.3i −0.552777 0.511082i
\(365\) 68279.1 + 36495.9i 0.512509 + 0.273942i
\(366\) −115682. + 109051.i −0.863584 + 0.814077i
\(367\) −150869. 62491.8i −1.12012 0.463971i −0.255712 0.966753i \(-0.582310\pi\)
−0.864413 + 0.502782i \(0.832310\pi\)
\(368\) 32151.4 98886.3i 0.237413 0.730197i
\(369\) −29353.3 70865.0i −0.215578 0.520450i
\(370\) −37032.0 + 82437.2i −0.270504 + 0.602171i
\(371\) −3445.68 + 1045.24i −0.0250338 + 0.00759392i
\(372\) 18787.4 + 78288.6i 0.135762 + 0.565734i
\(373\) −151696. + 14940.8i −1.09033 + 0.107388i −0.627166 0.778886i \(-0.715785\pi\)
−0.463162 + 0.886274i \(0.653285\pi\)
\(374\) 4112.24 + 5323.56i 0.0293992 + 0.0380591i
\(375\) 84194.3 + 16747.3i 0.598715 + 0.119092i
\(376\) 33590.1 + 27027.3i 0.237594 + 0.191173i
\(377\) 55675.2 11074.5i 0.391723 0.0779186i
\(378\) −147767. + 10163.6i −1.03417 + 0.0711321i
\(379\) −50340.8 + 165951.i −0.350463 + 1.15532i 0.587687 + 0.809089i \(0.300039\pi\)
−0.938149 + 0.346231i \(0.887461\pi\)
\(380\) 136518. + 66232.2i 0.945413 + 0.458672i
\(381\) −69417.7 84585.8i −0.478212 0.582703i
\(382\) 47001.3 + 33451.9i 0.322095 + 0.229242i
\(383\) 164940.i 1.12442i 0.826994 + 0.562210i \(0.190049\pi\)
−0.826994 + 0.562210i \(0.809951\pi\)
\(384\) 108099. + 59199.9i 0.733095 + 0.401475i
\(385\) −146816. −0.990493
\(386\) 138277. 194285.i 0.928059 1.30396i
\(387\) −16019.9 + 13147.2i −0.106964 + 0.0877832i
\(388\) −83613.1 40565.3i −0.555406 0.269458i
\(389\) 157114. + 47660.1i 1.03828 + 0.314960i 0.762997 0.646402i \(-0.223727\pi\)
0.275287 + 0.961362i \(0.411227\pi\)
\(390\) −8089.03 117604.i −0.0531823 0.773204i
\(391\) −1243.81 6253.04i −0.00813579 0.0409014i
\(392\) −1518.25 14023.3i −0.00988034 0.0912597i
\(393\) 25982.2 130621.i 0.168225 0.845724i
\(394\) −110614. + 85444.7i −0.712551 + 0.550418i
\(395\) 21653.4 + 219851.i 0.138782 + 1.40907i
\(396\) −9765.53 40693.8i −0.0622738 0.259500i
\(397\) −30585.3 100826.i −0.194058 0.639724i −0.998929 0.0462736i \(-0.985265\pi\)
0.804871 0.593450i \(-0.202235\pi\)
\(398\) 243382. + 109331.i 1.53646 + 0.690201i
\(399\) 104882. 43443.5i 0.658802 0.272885i
\(400\) −60260.9 + 4730.82i −0.376631 + 0.0295676i
\(401\) 33610.1 81141.9i 0.209017 0.504611i −0.784252 0.620442i \(-0.786953\pi\)
0.993269 + 0.115831i \(0.0369532\pi\)
\(402\) 99578.7 + 105634.i 0.616189 + 0.653662i
\(403\) 42097.8 78759.5i 0.259209 0.484946i
\(404\) −189686. 175378.i −1.16218 1.07452i
\(405\) −90454.3 74233.9i −0.551466 0.452577i
\(406\) −68909.0 39489.0i −0.418046 0.239565i
\(407\) −68587.7 + 45828.8i −0.414054 + 0.276662i
\(408\) 7556.48 73.0833i 0.0453941 0.000439033i
\(409\) 173162. + 115703.i 1.03515 + 0.691668i 0.952384 0.304901i \(-0.0986234\pi\)
0.0827698 + 0.996569i \(0.473623\pi\)
\(410\) −349611. 117421.i −2.07978 0.698521i
\(411\) 15521.7 + 29039.1i 0.0918876 + 0.171910i
\(412\) −56299.3 14697.0i −0.331672 0.0865831i
\(413\) −14676.4 + 149012.i −0.0860438 + 0.873617i
\(414\) −8882.06 + 38656.2i −0.0518219 + 0.225537i
\(415\) 178804. + 178804.i 1.03820 + 1.03820i
\(416\) −46024.4 128729.i −0.265951 0.743855i
\(417\) −65996.4 65996.4i −0.379532 0.379532i
\(418\) 73516.2 + 117378.i 0.420756 + 0.671792i
\(419\) 27467.5 278882.i 0.156456 1.58852i −0.521391 0.853318i \(-0.674587\pi\)
0.677847 0.735203i \(-0.262913\pi\)
\(420\) −99557.3 + 131492.i −0.564384 + 0.745422i
\(421\) −118195. 221128.i −0.666863 1.24761i −0.956850 0.290582i \(-0.906151\pi\)
0.289987 0.957031i \(-0.406349\pi\)
\(422\) −145363. 292387.i −0.816262 1.64185i
\(423\) −13673.9 9136.61i −0.0764208 0.0510627i
\(424\) −4849.20 915.903i −0.0269735 0.00509469i
\(425\) −3081.60 + 2059.06i −0.0170608 + 0.0113996i
\(426\) 145978. 39619.6i 0.804395 0.218319i
\(427\) −190719. 156519.i −1.04602 0.858444i
\(428\) 244863. + 90361.7i 1.33670 + 0.493284i
\(429\) 50722.0 94894.1i 0.275602 0.515614i
\(430\) −2939.20 + 99601.0i −0.0158961 + 0.538675i
\(431\) 82201.3 198452.i 0.442511 1.06832i −0.532554 0.846396i \(-0.678768\pi\)
0.975065 0.221920i \(-0.0712325\pi\)
\(432\) −185969. 81387.6i −0.996489 0.436105i
\(433\) −196984. + 81593.5i −1.05064 + 0.435191i −0.840121 0.542398i \(-0.817516\pi\)
−0.210522 + 0.977589i \(0.567516\pi\)
\(434\) −116796. + 44389.3i −0.620081 + 0.235667i
\(435\) −27246.3 89818.9i −0.143989 0.474667i
\(436\) 12338.8 77855.2i 0.0649084 0.409557i
\(437\) −12866.4 130634.i −0.0673741 0.684061i
\(438\) 78740.3 + 10108.2i 0.410439 + 0.0526898i
\(439\) −1420.29 + 7140.30i −0.00736969 + 0.0370499i −0.984295 0.176531i \(-0.943513\pi\)
0.976925 + 0.213580i \(0.0685126\pi\)
\(440\) −178367. 93132.4i −0.921315 0.481056i
\(441\) 1049.67 + 5277.03i 0.00539727 + 0.0271339i
\(442\) −6319.84 5506.41i −0.0323490 0.0281854i
\(443\) −14.3623 4.35677i −7.31843e−5 2.22002e-5i 0.290248 0.956951i \(-0.406262\pi\)
−0.290321 + 0.956929i \(0.593762\pi\)
\(444\) −5464.42 + 92506.1i −0.0277190 + 0.469250i
\(445\) 313064. 256925.i 1.58093 1.29744i
\(446\) 120572. 20306.1i 0.606146 0.102084i
\(447\) 251255. 1.25747
\(448\) −69764.6 + 178094.i −0.347599 + 0.887345i
\(449\) 273652.i 1.35740i −0.734418 0.678698i \(-0.762545\pi\)
0.734418 0.678698i \(-0.237455\pi\)
\(450\) 22736.8 3829.21i 0.112281 0.0189097i
\(451\) −213557. 260220.i −1.04993 1.27935i
\(452\) 131160. 116529.i 0.641986 0.570371i
\(453\) −36713.4 + 121028.i −0.178908 + 0.589779i
\(454\) −257458. 224321.i −1.24910 1.08832i
\(455\) 179428. 35690.5i 0.866698 0.172397i
\(456\) 154979. + 13752.1i 0.745322 + 0.0661363i
\(457\) 163118. + 32446.3i 0.781035 + 0.155358i 0.569476 0.822008i \(-0.307146\pi\)
0.211559 + 0.977365i \(0.432146\pi\)
\(458\) −80811.3 10374.1i −0.385249 0.0494560i
\(459\) −12386.7 + 1219.99i −0.0587937 + 0.00579068i
\(460\) 112080. + 154297.i 0.529680 + 0.729191i
\(461\) 228718. 69380.7i 1.07621 0.326465i 0.298064 0.954546i \(-0.403659\pi\)
0.778148 + 0.628081i \(0.216159\pi\)
\(462\) −140723. + 53482.8i −0.659296 + 0.250571i
\(463\) −80308.4 193882.i −0.374627 0.904430i −0.992953 0.118508i \(-0.962189\pi\)
0.618326 0.785922i \(-0.287811\pi\)
\(464\) −58667.7 91687.4i −0.272498 0.425867i
\(465\) −136422. 56507.7i −0.630925 0.261338i
\(466\) −110.534 + 3745.68i −0.000509007 + 0.0172488i
\(467\) 295668. + 158038.i 1.35572 + 0.724647i 0.979417 0.201849i \(-0.0646951\pi\)
0.376303 + 0.926497i \(0.377195\pi\)
\(468\) 21827.3 + 47359.2i 0.0996570 + 0.216228i
\(469\) −142924. + 174154.i −0.649771 + 0.791749i
\(470\) −76311.5 + 20711.5i −0.345457 + 0.0937596i
\(471\) −146436. 219157.i −0.660094 0.987901i
\(472\) −112356. + 171725.i −0.504326 + 0.770812i
\(473\) −50530.5 + 75624.2i −0.225856 + 0.338017i
\(474\) 100843. + 202838.i 0.448837 + 0.902803i
\(475\) −67297.1 + 35971.1i −0.298270 + 0.159429i
\(476\) 1605.69 + 11617.1i 0.00708677 + 0.0512726i
\(477\) 1873.35 + 184.509i 0.00823345 + 0.000810924i
\(478\) 135294. + 216015.i 0.592139 + 0.945427i
\(479\) −317723. + 317723.i −1.38477 + 1.38477i −0.548847 + 0.835923i \(0.684933\pi\)
−0.835923 + 0.548847i \(0.815067\pi\)
\(480\) −204364. + 96596.1i −0.886997 + 0.419254i
\(481\) 72682.2 72682.2i 0.314151 0.314151i
\(482\) −79244.5 + 344885.i −0.341095 + 1.48450i
\(483\) 141994. + 13985.2i 0.608660 + 0.0599478i
\(484\) 25577.5 + 43649.2i 0.109186 + 0.186331i
\(485\) 150319. 80347.4i 0.639045 0.341577i
\(486\) 129807. + 43597.5i 0.549575 + 0.184582i
\(487\) 81097.2 121371.i 0.341938 0.511747i −0.620151 0.784483i \(-0.712929\pi\)
0.962089 + 0.272736i \(0.0879285\pi\)
\(488\) −132417. 311137.i −0.556038 1.30651i
\(489\) 137733. + 206133.i 0.575999 + 0.862043i
\(490\) 22445.5 + 12862.6i 0.0934839 + 0.0535719i
\(491\) 167113. 203627.i 0.693180 0.844642i −0.300859 0.953669i \(-0.597273\pi\)
0.994039 + 0.109027i \(0.0347733\pi\)
\(492\) −377876. + 14809.9i −1.56106 + 0.0611818i
\(493\) −5886.02 3146.14i −0.0242174 0.0129445i
\(494\) −118381. 125580.i −0.485095 0.514595i
\(495\) 70911.0 + 29372.3i 0.289403 + 0.119875i
\(496\) −170054. 20160.8i −0.691230 0.0819491i
\(497\) 89831.9 + 216873.i 0.363678 + 0.877997i
\(498\) 236519. + 106248.i 0.953690 + 0.428411i
\(499\) −119556. + 36266.8i −0.480142 + 0.145649i −0.521072 0.853513i \(-0.674468\pi\)
0.0409306 + 0.999162i \(0.486968\pi\)
\(500\) −95416.4 + 155671.i −0.381666 + 0.622685i
\(501\) −286849. + 28252.1i −1.14282 + 0.112558i
\(502\) 270058. 208609.i 1.07164 0.827802i
\(503\) −221632. 44085.4i −0.875985 0.174244i −0.263436 0.964677i \(-0.584856\pi\)
−0.612549 + 0.790433i \(0.709856\pi\)
\(504\) 20502.8 70019.5i 0.0807147 0.275650i
\(505\) 464700. 92434.6i 1.82217 0.362453i
\(506\) 11944.8 + 173662.i 0.0466528 + 0.678273i
\(507\) 23447.0 77294.4i 0.0912160 0.300699i
\(508\) 219902. 76231.4i 0.852122 0.295397i
\(509\) 216629. + 263963.i 0.836144 + 1.01884i 0.999479 + 0.0322742i \(0.0102750\pi\)
−0.163335 + 0.986571i \(0.552225\pi\)
\(510\) −8036.56 + 11291.7i −0.0308980 + 0.0434130i
\(511\) 123201.i 0.471816i
\(512\) −197730. + 172111.i −0.754281 + 0.656551i
\(513\) −256265. −0.973765
\(514\) 390704. + 278072.i 1.47884 + 1.05252i
\(515\) 82492.6 67700.0i 0.311029 0.255255i
\(516\) 33465.9 + 96538.1i 0.125691 + 0.362576i
\(517\) −69066.9 20951.2i −0.258398 0.0783842i
\(518\) −143473. + 9868.33i −0.534701 + 0.0367777i
\(519\) 33723.6 + 169540.i 0.125199 + 0.629416i
\(520\) 240627. + 70459.5i 0.889894 + 0.260575i
\(521\) 11469.4 57660.5i 0.0422537 0.212424i −0.953891 0.300155i \(-0.902962\pi\)
0.996144 + 0.0877312i \(0.0279617\pi\)
\(522\) 25382.3 + 32859.0i 0.0931515 + 0.120590i
\(523\) −4949.36 50251.7i −0.0180945 0.183716i 0.981889 0.189457i \(-0.0606727\pi\)
−0.999984 + 0.00574065i \(0.998173\pi\)
\(524\) 241512. + 148031.i 0.879583 + 0.539127i
\(525\) −24077.0 79371.3i −0.0873542 0.287968i
\(526\) −13786.0 + 30689.2i −0.0498273 + 0.110921i
\(527\) −9700.46 + 4018.06i −0.0349278 + 0.0144676i
\(528\) −204891. 24290.9i −0.734944 0.0871316i
\(529\) −43955.0 + 106117.i −0.157071 + 0.379203i
\(530\) 6585.96 6208.40i 0.0234459 0.0221018i
\(531\) 36900.2 69035.5i 0.130870 0.244841i
\(532\) 9456.16 + 241275.i 0.0334112 + 0.852489i
\(533\) 324254. + 266108.i 1.14138 + 0.936707i
\(534\) 206477. 360306.i 0.724084 1.26354i
\(535\) −398020. + 265948.i −1.39058 + 0.929158i
\(536\) −284113. + 120916.i −0.988920 + 0.420875i
\(537\) 166206. + 111055.i 0.576366 + 0.385115i
\(538\) −6806.49 + 20265.7i −0.0235158 + 0.0700159i
\(539\) 11131.2 + 20825.0i 0.0383146 + 0.0716815i
\(540\) 321222. 188230.i 1.10159 0.645506i
\(541\) −21798.0 + 221319.i −0.0744770 + 0.756178i 0.883327 + 0.468757i \(0.155298\pi\)
−0.957804 + 0.287421i \(0.907202\pi\)
\(542\) 159459. + 36639.0i 0.542812 + 0.124722i
\(543\) 77640.4 + 77640.4i 0.263323 + 0.263323i
\(544\) −5418.56 + 15132.2i −0.0183099 + 0.0511334i
\(545\) 102228. + 102228.i 0.344174 + 0.344174i
\(546\) 158980. 99572.2i 0.533282 0.334005i
\(547\) 23570.6 239316.i 0.0787764 0.799831i −0.871908 0.489670i \(-0.837117\pi\)
0.950684 0.310160i \(-0.100383\pi\)
\(548\) −69375.2 + 9588.87i −0.231017 + 0.0319305i
\(549\) 60802.4 + 113753.i 0.201733 + 0.377415i
\(550\) 90610.9 45048.1i 0.299540 0.148919i
\(551\) −114255. 76342.6i −0.376332 0.251457i
\(552\) 163637. + 107064.i 0.537035 + 0.351371i
\(553\) −292299. + 195308.i −0.955822 + 0.638660i
\(554\) −126614. 466509.i −0.412536 1.51999i
\(555\) −131378. 107819.i −0.426518 0.350034i
\(556\) 180289. 83093.1i 0.583203 0.268791i
\(557\) −277082. + 518384.i −0.893096 + 1.67086i −0.163992 + 0.986462i \(0.552437\pi\)
−0.729104 + 0.684403i \(0.760063\pi\)
\(558\) 65292.2 + 1926.76i 0.209697 + 0.00618811i
\(559\) 43370.8 104706.i 0.138795 0.335081i
\(560\) −189072. 295487.i −0.602909 0.942241i
\(561\) −11687.7 + 4841.20i −0.0371367 + 0.0153825i
\(562\) −131285. 345434.i −0.415664 1.09368i
\(563\) −81206.6 267702.i −0.256197 0.844570i −0.986825 0.161793i \(-0.948272\pi\)
0.730627 0.682776i \(-0.239228\pi\)
\(564\) −65599.5 + 47651.1i −0.206226 + 0.149801i
\(565\) 31540.0 + 320231.i 0.0988019 + 1.00315i
\(566\) −24407.3 + 190126.i −0.0761882 + 0.593485i
\(567\) 36327.6 182631.i 0.112998 0.568079i
\(568\) −28436.5 + 320464.i −0.0881412 + 0.993304i
\(569\) 106172. + 533761.i 0.327932 + 1.64863i 0.695423 + 0.718601i \(0.255217\pi\)
−0.367491 + 0.930027i \(0.619783\pi\)
\(570\) −187456. + 215148.i −0.576966 + 0.662197i
\(571\) −402582. 122122.i −1.23476 0.374560i −0.395587 0.918428i \(-0.629459\pi\)
−0.839170 + 0.543869i \(0.816959\pi\)
\(572\) 152004. + 171089.i 0.464583 + 0.522915i
\(573\) −83866.2 + 68827.2i −0.255433 + 0.209629i
\(574\) −97466.8 578733.i −0.295824 1.75653i
\(575\) −95906.3 −0.290076
\(576\) 69325.6 72060.7i 0.208953 0.217197i
\(577\) 59294.7i 0.178100i −0.996027 0.0890501i \(-0.971617\pi\)
0.996027 0.0890501i \(-0.0283831\pi\)
\(578\) −55319.4 328473.i −0.165585 0.983204i
\(579\) 284505. + 346670.i 0.848658 + 1.03409i
\(580\) 199290. + 11772.3i 0.592421 + 0.0349948i
\(581\) −116808. + 385065.i −0.346036 + 1.14073i
\(582\) 114811. 131772.i 0.338953 0.389024i
\(583\) 8102.68 1611.72i 0.0238392 0.00474191i
\(584\) −78152.4 + 149677.i −0.229148 + 0.438863i
\(585\) −93802.8 18658.5i −0.274097 0.0545212i
\(586\) −10925.6 + 85107.7i −0.0318165 + 0.247841i
\(587\) −511536. + 50381.9i −1.48457 + 0.146217i −0.807571 0.589770i \(-0.799218\pi\)
−0.676995 + 0.735987i \(0.736718\pi\)
\(588\) 26199.6 + 4152.23i 0.0757775 + 0.0120095i
\(589\) −206870. + 62753.4i −0.596304 + 0.180887i
\(590\) −133713. 351822.i −0.384122 1.01069i
\(591\) −100591. 242848.i −0.287995 0.695280i
\(592\) −180565. 79022.8i −0.515218 0.225481i
\(593\) −16286.9 6746.24i −0.0463157 0.0191846i 0.359405 0.933182i \(-0.382980\pi\)
−0.405721 + 0.913997i \(0.632980\pi\)
\(594\) 339685. + 10024.0i 0.962728 + 0.0284098i
\(595\) −18969.2 10139.3i −0.0535816 0.0286400i
\(596\) −185017. + 501360.i −0.520858 + 1.41142i
\(597\) −318318. + 387872.i −0.893127 + 1.08828i
\(598\) −56814.8 209334.i −0.158876 0.585380i
\(599\) 108926. + 163020.i 0.303585 + 0.454346i 0.951626 0.307259i \(-0.0994117\pi\)
−0.648042 + 0.761605i \(0.724412\pi\)
\(600\) 21097.8 111701.i 0.0586051 0.310281i
\(601\) 124770. 186732.i 0.345431 0.516974i −0.617554 0.786528i \(-0.711876\pi\)
0.962985 + 0.269554i \(0.0868764\pi\)
\(602\) −141987. + 70590.0i −0.391791 + 0.194783i
\(603\) 103873. 55521.3i 0.285672 0.152695i
\(604\) −214468. 162381.i −0.587879 0.445103i
\(605\) −92339.8 9094.68i −0.252277 0.0248472i
\(606\) 411741. 257882.i 1.12119 0.702223i
\(607\) −302650. + 302650.i −0.821416 + 0.821416i −0.986311 0.164895i \(-0.947271\pi\)
0.164895 + 0.986311i \(0.447271\pi\)
\(608\) −141564. + 299123.i −0.382953 + 0.809175i
\(609\) 105615. 105615.i 0.284767 0.284767i
\(610\) 604422. + 138879.i 1.62435 + 0.373229i
\(611\) 89502.0 + 8815.17i 0.239745 + 0.0236129i
\(612\) 1548.61 5932.23i 0.00413466 0.0158385i
\(613\) −433616. + 231772.i −1.15394 + 0.616795i −0.933490 0.358603i \(-0.883253\pi\)
−0.220452 + 0.975398i \(0.570753\pi\)
\(614\) −18952.9 + 56430.3i −0.0502734 + 0.149684i
\(615\) 385330. 576688.i 1.01879 1.52472i
\(616\) −3096.70 320185.i −0.00816090 0.843801i
\(617\) −72681.5 108776.i −0.190921 0.285733i 0.723643 0.690174i \(-0.242466\pi\)
−0.914564 + 0.404441i \(0.867466\pi\)
\(618\) 54406.9 94941.1i 0.142455 0.248586i
\(619\) 179964. 219287.i 0.469683 0.572311i −0.483253 0.875481i \(-0.660545\pi\)
0.952936 + 0.303170i \(0.0980450\pi\)
\(620\) 213214. 230609.i 0.554668 0.599919i
\(621\) −284053. 151829.i −0.736574 0.393707i
\(622\) −426166. + 401735.i −1.10153 + 1.03839i
\(623\) 595415. + 246629.i 1.53406 + 0.635430i
\(624\) 256308. 20121.6i 0.658253 0.0516766i
\(625\) −184625. 445723.i −0.472639 1.14105i
\(626\) 190949. 425073.i 0.487269 1.08471i
\(627\) −249250. + 75609.1i −0.634015 + 0.192326i
\(628\) 545143. 130821.i 1.38227 0.331710i
\(629\) −12026.8 + 1184.54i −0.0303983 + 0.00299397i
\(630\) 81801.1 + 105897.i 0.206100 + 0.266809i
\(631\) −218813. 43524.6i −0.549558 0.109314i −0.0875018 0.996164i \(-0.527888\pi\)
−0.462057 + 0.886850i \(0.652888\pi\)
\(632\) −479007. + 51860.2i −1.19924 + 0.129838i
\(633\) 602275. 119800.i 1.50310 0.298985i
\(634\) −88147.6 + 6062.95i −0.219297 + 0.0150836i
\(635\) −123910. + 408478.i −0.307298 + 1.01303i
\(636\) 4051.00 8349.91i 0.0100149 0.0206428i
\(637\) −18666.2 22744.9i −0.0460021 0.0560538i
\(638\) 148461. + 105663.i 0.364730 + 0.259586i
\(639\) 122720.i 0.300548i
\(640\) −42262.3 478924.i −0.103179 1.16925i
\(641\) 583222. 1.41944 0.709722 0.704482i \(-0.248821\pi\)
0.709722 + 0.704482i \(0.248821\pi\)
\(642\) −284620. + 399903.i −0.690551 + 0.970253i
\(643\) 93374.9 76630.8i 0.225844 0.185345i −0.514666 0.857391i \(-0.672084\pi\)
0.740510 + 0.672045i \(0.234584\pi\)
\(644\) −132467. + 273040.i −0.319400 + 0.658346i
\(645\) −179324. 54397.2i −0.431041 0.130755i
\(646\) 1392.34 + 20242.9i 0.00333642 + 0.0485073i
\(647\) −27615.1 138830.i −0.0659687 0.331647i 0.933681 0.358105i \(-0.116577\pi\)
−0.999650 + 0.0264582i \(0.991577\pi\)
\(648\) 159986. 198834.i 0.381006 0.473523i
\(649\) 67022.1 336943.i 0.159121 0.799957i
\(650\) −99787.3 + 77081.8i −0.236183 + 0.182442i
\(651\) −23031.8 233845.i −0.0543457 0.551781i
\(652\) −512746. + 123047.i −1.20617 + 0.289450i
\(653\) −199192. 656649.i −0.467139 1.53995i −0.801789 0.597608i \(-0.796118\pi\)
0.334650 0.942343i \(-0.391382\pi\)
\(654\) 135226. + 60745.3i 0.316158 + 0.142023i
\(655\) −479984. + 198816.i −1.11878 + 0.463413i
\(656\) 248706. 764930.i 0.577934 1.77752i
\(657\) 24647.9 59505.3i 0.0571017 0.137856i
\(658\) −86311.4 91560.3i −0.199350 0.211473i
\(659\) 134633. 251881.i 0.310014 0.579994i −0.677872 0.735180i \(-0.737098\pi\)
0.987885 + 0.155186i \(0.0495976\pi\)
\(660\) 256893. 277851.i 0.589746 0.637858i
\(661\) 184627. + 151520.i 0.422564 + 0.346789i 0.821519 0.570181i \(-0.193127\pi\)
−0.398955 + 0.916971i \(0.630627\pi\)
\(662\) 111335. + 63801.7i 0.254048 + 0.145585i
\(663\) 13107.0 8757.81i 0.0298178 0.0199236i
\(664\) −386176. + 393719.i −0.875888 + 0.892996i
\(665\) −368216. 246034.i −0.832645 0.556355i
\(666\) 71270.7 + 23937.2i 0.160680 + 0.0539666i
\(667\) −81413.3 152314.i −0.182997 0.342363i
\(668\) 154853. 593190.i 0.347029 1.32935i
\(669\) −22538.4 + 228836.i −0.0503582 + 0.511295i
\(670\) 126816. 551923.i 0.282504 1.22950i
\(671\) 400275. + 400275.i 0.889024 + 0.889024i
\(672\) −288867. 214347.i −0.639675 0.474657i
\(673\) 255206. + 255206.i 0.563456 + 0.563456i 0.930287 0.366831i \(-0.119557\pi\)
−0.366831 + 0.930287i \(0.619557\pi\)
\(674\) −112130. 179031.i −0.246833 0.394101i
\(675\) −18352.0 + 186331.i −0.0402788 + 0.408958i
\(676\) 136970. + 103704.i 0.299730 + 0.226936i
\(677\) 154623. + 289279.i 0.337362 + 0.631161i 0.992207 0.124603i \(-0.0397658\pi\)
−0.654844 + 0.755764i \(0.727266\pi\)
\(678\) 146887. + 295452.i 0.319538 + 0.642728i
\(679\) 225522. + 150689.i 0.489158 + 0.326845i
\(680\) −16613.9 24351.3i −0.0359297 0.0526628i
\(681\) 533955. 356777.i 1.15136 0.769312i
\(682\) 276666. 75089.3i 0.594822 0.161439i
\(683\) −239327. 196411.i −0.513039 0.421041i 0.341925 0.939727i \(-0.388921\pi\)
−0.854964 + 0.518687i \(0.826421\pi\)
\(684\) 43702.7 118426.i 0.0934105 0.253124i
\(685\) 60549.7 113280.i 0.129042 0.241420i
\(686\) −14443.0 + 489432.i −0.0306908 + 1.04002i
\(687\) 58635.6 141559.i 0.124236 0.299932i
\(688\) −217278. 4309.16i −0.459028 0.00910365i
\(689\) −9510.72 + 3939.47i −0.0200343 + 0.00829849i
\(690\) −335252. + 127415.i −0.704163 + 0.267623i
\(691\) −85485.5 281808.i −0.179034 0.590197i −0.999820 0.0189610i \(-0.993964\pi\)
0.820786 0.571236i \(-0.193536\pi\)
\(692\) −363138. 57551.7i −0.758333 0.120184i
\(693\) 11971.7 + 121551.i 0.0249282 + 0.253100i
\(694\) 357095. + 45841.8i 0.741421 + 0.0951794i
\(695\) −71030.1 + 357093.i −0.147053 + 0.739284i
\(696\) 195308. 61314.8i 0.403182 0.126575i
\(697\) −9621.41 48370.1i −0.0198049 0.0995661i
\(698\) 180318. + 157109.i 0.370107 + 0.322471i
\(699\) −6743.80 2045.71i −0.0138023 0.00418687i
\(700\) 176109. + 10402.9i 0.359407 + 0.0212305i
\(701\) 9867.13 8097.74i 0.0200796 0.0164789i −0.624300 0.781185i \(-0.714616\pi\)
0.644380 + 0.764706i \(0.277116\pi\)
\(702\) −417576. + 70325.7i −0.847347 + 0.142705i
\(703\) −248819. −0.503469
\(704\) 199347. 390957.i 0.402220 0.788831i
\(705\) 148704.i 0.299189i
\(706\) −500191. + 84239.2i −1.00352 + 0.169007i
\(707\) 478315. + 582829.i 0.956920 + 1.16601i
\(708\) −256327. 288511.i −0.511361 0.575567i
\(709\) 52409.4 172771.i 0.104260 0.343699i −0.889253 0.457415i \(-0.848775\pi\)
0.993513 + 0.113716i \(0.0362755\pi\)
\(710\) −444880. 387619.i −0.882523 0.768933i
\(711\) 180252. 35854.3i 0.356567 0.0709255i
\(712\) 566920. + 677329.i 1.11831 + 1.33610i
\(713\) −266482. 53006.6i −0.524190 0.104268i
\(714\) −21875.6 2808.26i −0.0429104 0.00550859i
\(715\) −417720. + 41141.8i −0.817095 + 0.0804769i
\(716\) −343992. + 249874.i −0.671000 + 0.487410i
\(717\) −458703. + 139146.i −0.892263 + 0.270665i
\(718\) −282811. + 107485.i −0.548589 + 0.208496i
\(719\) 381009. + 919836.i 0.737016 + 1.77931i 0.617633 + 0.786467i \(0.288092\pi\)
0.119384 + 0.992848i \(0.461908\pi\)
\(720\) 32204.8 + 180544.i 0.0621234 + 0.348272i
\(721\) 156893. + 64987.0i 0.301809 + 0.125013i
\(722\) 3053.45 103473.i 0.00585756 0.198496i
\(723\) −586916. 313713.i −1.12279 0.600145i
\(724\) −212098. + 97753.5i −0.404631 + 0.186490i
\(725\) −63691.3 + 77608.0i −0.121172 + 0.147649i
\(726\) −91820.6 + 24920.8i −0.174208 + 0.0472812i
\(727\) 400732. + 599737.i 0.758202 + 1.13473i 0.986916 + 0.161236i \(0.0515480\pi\)
−0.228714 + 0.973494i \(0.573452\pi\)
\(728\) 81620.6 + 390555.i 0.154006 + 0.736919i
\(729\) −322517. + 482680.i −0.606872 + 0.908248i
\(730\) −137864. 277303.i −0.258705 0.520367i
\(731\) −11751.4 + 6281.28i −0.0219916 + 0.0117547i
\(732\) 629928. 87067.1i 1.17563 0.162492i
\(733\) 802757. + 79064.7i 1.49409 + 0.147155i 0.811803 0.583931i \(-0.198486\pi\)
0.682285 + 0.731086i \(0.260986\pi\)
\(734\) 346718. + 553580.i 0.643553 + 1.02752i
\(735\) −34401.6 + 34401.6i −0.0636801 + 0.0636801i
\(736\) −334136. + 247686.i −0.616833 + 0.457242i
\(737\) 365508. 365508.i 0.672918 0.672918i
\(738\) −68706.8 + 299023.i −0.126150 + 0.549025i
\(739\) −55698.9 5485.87i −0.101990 0.0100451i 0.0468933 0.998900i \(-0.485068\pi\)
−0.148883 + 0.988855i \(0.547568\pi\)
\(740\) 311889. 182761.i 0.569556 0.333748i
\(741\) 286235. 152996.i 0.521299 0.278640i
\(742\) 13653.4 + 4585.67i 0.0247989 + 0.00832904i
\(743\) 195621. 292767.i 0.354354 0.530329i −0.610877 0.791725i \(-0.709183\pi\)
0.965231 + 0.261397i \(0.0841831\pi\)
\(744\) 120358. 298709.i 0.217435 0.539638i
\(745\) −544533. 814952.i −0.981097 1.46832i
\(746\) 529013. + 303156.i 0.950581 + 0.544740i
\(747\) 133455. 162615.i 0.239162 0.291420i
\(748\) −1053.76 26886.9i −0.00188339 0.0480548i
\(749\) −671808. 359089.i −1.19752 0.640086i
\(750\) −235535. 249859.i −0.418729 0.444194i
\(751\) 80836.4 + 33483.5i 0.143327 + 0.0593678i 0.453194 0.891412i \(-0.350285\pi\)
−0.309867 + 0.950780i \(0.600285\pi\)
\(752\) −46778.5 165988.i −0.0827201 0.293522i
\(753\) 245589. + 592903.i 0.433130 + 1.04567i
\(754\) −207125. 93043.6i −0.364326 0.163660i
\(755\) 472125. 143218.i 0.828254 0.251248i
\(756\) 505127. + 309610.i 0.883806 + 0.541716i
\(757\) 646443. 63669.0i 1.12808 0.111106i 0.483284 0.875464i \(-0.339444\pi\)
0.644792 + 0.764358i \(0.276944\pi\)
\(758\) 548965. 424054.i 0.955446 0.738045i
\(759\) −321073. 63865.4i −0.557341 0.110862i
\(760\) −291274. 532484.i −0.504284 0.921891i
\(761\) 667404. 132755.i 1.15244 0.229235i 0.418351 0.908285i \(-0.362608\pi\)
0.734092 + 0.679050i \(0.237608\pi\)
\(762\) 30034.5 + 436664.i 0.0517262 + 0.752033i
\(763\) −66783.1 + 220154.i −0.114714 + 0.378163i
\(764\) −75582.9 218031.i −0.129490 0.373536i
\(765\) 7133.52 + 8692.22i 0.0121894 + 0.0148528i
\(766\) 382565. 537520.i 0.652000 0.916088i
\(767\) 428081.i 0.727671i
\(768\) −214973. 443653.i −0.364470 0.752178i
\(769\) −58758.0 −0.0993606 −0.0496803 0.998765i \(-0.515820\pi\)
−0.0496803 + 0.998765i \(0.515820\pi\)
\(770\) 478456. + 340527.i 0.806975 + 0.574342i
\(771\) −697147. + 572134.i −1.17278 + 0.962473i
\(772\) −901257. + 312430.i −1.51222 + 0.524226i
\(773\) −600072. 182030.i −1.00426 0.304638i −0.255016 0.966937i \(-0.582081\pi\)
−0.749240 + 0.662299i \(0.769581\pi\)
\(774\) 82700.9 5688.31i 0.138047 0.00949514i
\(775\) 30813.6 + 154910.i 0.0513026 + 0.257915i
\(776\) 178397. + 326131.i 0.296254 + 0.541588i
\(777\) 52763.2 265258.i 0.0873955 0.439367i
\(778\) −401473. 519732.i −0.663280 0.858658i
\(779\) −99527.2 1.01052e6i −0.164009 1.66521i
\(780\) −246412. + 402020.i −0.405017 + 0.660783i
\(781\) −156343. 515395.i −0.256317 0.844964i
\(782\) −10450.0 + 23262.8i −0.0170884 + 0.0380407i
\(783\) −311501. + 129028.i −0.508084 + 0.210455i
\(784\) −27578.2 + 49221.8i −0.0448676 + 0.0800803i
\(785\) −393478. + 949939.i −0.638529 + 1.54155i
\(786\) −387638. + 365415.i −0.627453 + 0.591482i
\(787\) 86614.3 162044.i 0.139843 0.261628i −0.802244 0.596996i \(-0.796361\pi\)
0.942087 + 0.335368i \(0.108861\pi\)
\(788\) 558658. 21895.2i 0.899692 0.0352612i
\(789\) −48908.6 40138.3i −0.0785654 0.0644770i
\(790\) 439359. 766690.i 0.703988 1.22847i
\(791\) −425759. + 284483.i −0.680473 + 0.454677i
\(792\) −62561.2 + 155267.i −0.0997367 + 0.247530i
\(793\) −586494. 391883.i −0.932647 0.623175i
\(794\) −134184. + 399521.i −0.212843 + 0.633721i
\(795\) 8023.79 + 15011.4i 0.0126954 + 0.0237514i
\(796\) −539569. 920800.i −0.851572 1.45325i
\(797\) 100425. 1.01963e6i 0.158097 1.60519i −0.509368 0.860549i \(-0.670121\pi\)
0.667465 0.744641i \(-0.267379\pi\)
\(798\) −442561. 101688.i −0.694972 0.159684i
\(799\) −7476.83 7476.83i −0.0117118 0.0117118i
\(800\) 207356. + 124353.i 0.323994 + 0.194302i
\(801\) −238240. 238240.i −0.371321 0.371321i
\(802\) −297733. + 186476.i −0.462891 + 0.289918i
\(803\) 27706.5 281309.i 0.0429685 0.436267i
\(804\) −79504.7 575214.i −0.122993 0.889852i
\(805\) −262376. 490871.i −0.404885 0.757487i
\(806\) −319868. + 159025.i −0.492380 + 0.244792i
\(807\) −33428.5 22336.2i −0.0513298 0.0342975i
\(808\) 211389. + 1.01150e6i 0.323787 + 1.54932i
\(809\) −447025. + 298693.i −0.683023 + 0.456381i −0.848056 0.529907i \(-0.822227\pi\)
0.165033 + 0.986288i \(0.447227\pi\)
\(810\) 122600. + 451721.i 0.186862 + 0.688494i
\(811\) 288250. + 236560.i 0.438255 + 0.359667i 0.827498 0.561468i \(-0.189763\pi\)
−0.389243 + 0.921135i \(0.627263\pi\)
\(812\) 132975. + 288519.i 0.201677 + 0.437584i
\(813\) −145046. + 271363.i −0.219445 + 0.410553i
\(814\) 329815. + 9732.76i 0.497762 + 0.0146888i
\(815\) 370094. 893485.i 0.557181 1.34515i
\(816\) −24795.2 17288.5i −0.0372381 0.0259643i
\(817\) −253462. + 104988.i −0.379725 + 0.157287i
\(818\) −295950. 778696.i −0.442294 1.16375i
\(819\) −44179.7 145641.i −0.0658650 0.217128i
\(820\) 866991. + 1.19356e6i 1.28940 + 1.77507i
\(821\) −44662.9 453470.i −0.0662614 0.672764i −0.969742 0.244134i \(-0.921496\pi\)
0.903480 0.428630i \(-0.141004\pi\)
\(822\) 16770.4 130636.i 0.0248198 0.193340i
\(823\) 93140.4 468248.i 0.137511 0.691316i −0.849101 0.528231i \(-0.822856\pi\)
0.986612 0.163085i \(-0.0521444\pi\)
\(824\) 149384. + 178477.i 0.220014 + 0.262862i
\(825\) 37126.0 + 186645.i 0.0545470 + 0.274226i
\(826\) 393450. 451572.i 0.576672 0.661861i
\(827\) −14451.1 4383.69i −0.0211295 0.00640957i 0.279702 0.960087i \(-0.409764\pi\)
−0.300832 + 0.953677i \(0.597264\pi\)
\(828\) 118605. 105375.i 0.172999 0.153701i
\(829\) 852693. 699787.i 1.24075 1.01826i 0.241899 0.970302i \(-0.422230\pi\)
0.998850 0.0479540i \(-0.0152701\pi\)
\(830\) −167980. 997423.i −0.243838 1.44785i
\(831\) 909062. 1.31641
\(832\) −148587. + 526261.i −0.214652 + 0.760247i
\(833\) 3459.41i 0.00498554i
\(834\) 62001.3 + 368148.i 0.0891391 + 0.529286i
\(835\) 713312. + 869173.i 1.02307 + 1.24662i
\(836\) 32668.3 553036.i 0.0467428 0.791299i
\(837\) −153976. + 507591.i −0.219787 + 0.724541i
\(838\) −736358. + 845135.i −1.04858 + 1.20348i
\(839\) 422421. 84024.7i 0.600097 0.119367i 0.114312 0.993445i \(-0.463534\pi\)
0.485785 + 0.874078i \(0.338534\pi\)
\(840\) 629431. 197603.i 0.892051 0.280050i
\(841\) 516371. + 102713.i 0.730079 + 0.145222i
\(842\) −127703. + 994775.i −0.180127 + 1.40314i
\(843\) 691617. 68118.3i 0.973219 0.0958537i
\(844\) −204447. + 1.29001e6i −0.287009 + 1.81096i
\(845\) −301522. + 91465.8i −0.422285 + 0.128099i
\(846\) 23370.0 + 61490.6i 0.0326526 + 0.0859148i
\(847\) −56504.4 136414.i −0.0787617 0.190148i
\(848\) 13678.6 + 14232.1i 0.0190217 + 0.0197915i
\(849\) −333048. 137953.i −0.462053 0.191389i
\(850\) 14818.4 + 437.287i 0.0205099 + 0.000605241i
\(851\) −275800. 147418.i −0.380833 0.203560i
\(852\) −567620. 209469.i −0.781950 0.288563i
\(853\) −534296. + 651042.i −0.734318 + 0.894768i −0.997550 0.0699641i \(-0.977712\pi\)
0.263232 + 0.964733i \(0.415212\pi\)
\(854\) 258498. + 952435.i 0.354439 + 1.30593i
\(855\) 128624. + 192499.i 0.175950 + 0.263327i
\(856\) −588392. 862417.i −0.803006 1.17698i
\(857\) −551776. + 825791.i −0.751278 + 1.12437i 0.236971 + 0.971517i \(0.423845\pi\)
−0.988249 + 0.152851i \(0.951155\pi\)
\(858\) −385396. + 191603.i −0.523519 + 0.260273i
\(859\) −618829. + 330771.i −0.838657 + 0.448272i −0.834031 0.551718i \(-0.813973\pi\)
−0.00462614 + 0.999989i \(0.501473\pi\)
\(860\) 240595. 317771.i 0.325304 0.429652i
\(861\) 1.09839e6 + 108182.i 1.48166 + 0.145931i
\(862\) −728176. + 456071.i −0.979991 + 0.613787i
\(863\) 361390. 361390.i 0.485238 0.485238i −0.421562 0.906800i \(-0.638518\pi\)
0.906800 + 0.421562i \(0.138518\pi\)
\(864\) 417278. + 696571.i 0.558982 + 0.933121i
\(865\) 476821. 476821.i 0.637269 0.637269i
\(866\) 831197. + 190985.i 1.10833 + 0.254661i
\(867\) 623414. + 61400.9i 0.829351 + 0.0816839i
\(868\) 483581. + 126239.i 0.641845 + 0.167554i
\(869\) 711337. 380217.i 0.941967 0.503492i
\(870\) −119535. + 355905.i −0.157927 + 0.470213i
\(871\) −357845. + 535552.i −0.471692 + 0.705937i
\(872\) −220789. + 225102.i −0.290366 + 0.296037i
\(873\) −78778.2 117900.i −0.103366 0.154698i
\(874\) −261066. + 455564.i −0.341764 + 0.596385i
\(875\) 338062. 411929.i 0.441550 0.538030i
\(876\) −233160. 215573.i −0.303841 0.280922i
\(877\) 423336. + 226278.i 0.550410 + 0.294200i 0.723063 0.690783i \(-0.242734\pi\)
−0.172653 + 0.984983i \(0.555234\pi\)
\(878\) 21189.9 19975.1i 0.0274878 0.0259120i
\(879\) −149085. 61753.0i −0.192955 0.0799246i
\(880\) 365263. + 717214.i 0.471672 + 0.926154i
\(881\) 293815. + 709333.i 0.378550 + 0.913900i 0.992238 + 0.124352i \(0.0396851\pi\)
−0.613689 + 0.789548i \(0.710315\pi\)
\(882\) 8818.89 19631.8i 0.0113364 0.0252362i
\(883\) −665872. + 201990.i −0.854023 + 0.259065i −0.686793 0.726853i \(-0.740982\pi\)
−0.167230 + 0.985918i \(0.553482\pi\)
\(884\) 7823.94 + 32603.1i 0.0100120 + 0.0417209i
\(885\) 704408. 69378.1i 0.899368 0.0885801i
\(886\) 36.7000 + 47.5105i 4.67518e−5 + 6.05232e-5i
\(887\) 185204. + 36839.3i 0.235398 + 0.0468235i 0.311379 0.950286i \(-0.399209\pi\)
−0.0759817 + 0.997109i \(0.524209\pi\)
\(888\) 232368. 288792.i 0.294680 0.366235i
\(889\) −666215. + 132518.i −0.842967 + 0.167677i
\(890\) −1.61615e6 + 111162.i −2.04034 + 0.140338i
\(891\) −124019. + 408837.i −0.156219 + 0.514985i
\(892\) −440029. 213482.i −0.553033 0.268307i
\(893\) −138111. 168288.i −0.173191 0.211034i
\(894\) −818809. 582764.i −1.02449 0.729152i
\(895\) 779779.i 0.973477i
\(896\) 640428. 418573.i 0.797727 0.521381i
\(897\) 407919. 0.506978
\(898\) −634714. + 891800.i −0.787092 + 1.10590i
\(899\) −219864. + 180437.i −0.272041 + 0.223258i
\(900\) −82978.2 40257.3i −0.102442 0.0497004i
\(901\) 1158.21 + 351.338i 0.00142671 + 0.000432789i
\(902\) 92398.4 + 1.34336e6i 0.113567 + 1.65112i
\(903\) −58176.2 292472.i −0.0713461 0.358681i
\(904\) −697715. + 75538.9i −0.853771 + 0.0924345i
\(905\) 83562.2 420096.i 0.102026 0.512922i
\(906\) 400359. 309262.i 0.487746 0.376765i
\(907\) 3230.75 + 32802.4i 0.00392725 + 0.0398741i 0.996949 0.0780604i \(-0.0248727\pi\)
−0.993021 + 0.117935i \(0.962373\pi\)
\(908\) 318733. + 1.32819e6i 0.386594 + 1.61097i
\(909\) −114421. 377195.i −0.138477 0.456497i
\(910\) −667516. 299858.i −0.806081 0.362103i
\(911\) −306141. + 126808.i −0.368879 + 0.152795i −0.559420 0.828885i \(-0.688976\pi\)
0.190540 + 0.981679i \(0.438976\pi\)
\(912\) −473162. 404278.i −0.568879 0.486061i
\(913\) 353308. 852962.i 0.423850 1.02326i
\(914\) −456327. 484078.i −0.546240 0.579459i
\(915\) −549792. + 1.02859e6i −0.656684 + 1.22857i
\(916\) 239293. + 221243.i 0.285193 + 0.263681i
\(917\) −639078. 524477.i −0.760002 0.623718i
\(918\) 43196.5 + 24754.2i 0.0512582 + 0.0293740i
\(919\) −952895. + 636704.i −1.12827 + 0.753888i −0.972268 0.233869i \(-0.924861\pi\)
−0.156004 + 0.987756i \(0.549861\pi\)
\(920\) −7377.45 762796.i −0.00871627 0.901224i
\(921\) −93082.6 62195.8i −0.109736 0.0733232i
\(922\) −906286. 304388.i −1.06611 0.358068i
\(923\) 316363. + 591873.i 0.371349 + 0.694745i
\(924\) 582648. + 152100.i 0.682436 + 0.178150i
\(925\) −17818.8 + 180917.i −0.0208255 + 0.211445i
\(926\) −187977. + 818106.i −0.219221 + 0.954086i
\(927\) −62776.5 62776.5i −0.0730529 0.0730529i
\(928\) −21470.2 + 434873.i −0.0249310 + 0.504971i
\(929\) −487721. 487721.i −0.565119 0.565119i 0.365638 0.930757i \(-0.380851\pi\)
−0.930757 + 0.365638i \(0.880851\pi\)
\(930\) 313517. + 500571.i 0.362489 + 0.578761i
\(931\) −6981.37 + 70883.0i −0.00805455 + 0.0817792i
\(932\) 9048.01 11950.4i 0.0104165 0.0137578i
\(933\) −519205. 971364.i −0.596452 1.11588i
\(934\) −596990. 1.20080e6i −0.684343 1.37650i
\(935\) 41032.8 + 27417.2i 0.0469362 + 0.0313618i
\(936\) 38713.1 204964.i 0.0441883 0.233952i
\(937\) 741675. 495572.i 0.844762 0.564452i −0.0561653 0.998421i \(-0.517887\pi\)
0.900928 + 0.433969i \(0.142887\pi\)
\(938\) 869709. 236045.i 0.988481 0.268281i
\(939\) 677429. + 555952.i 0.768304 + 0.630531i
\(940\) 296729. + 109502.i 0.335818 + 0.123927i
\(941\) −418581. + 783111.i −0.472716 + 0.884390i 0.526694 + 0.850055i \(0.323431\pi\)
−0.999410 + 0.0343351i \(0.989069\pi\)
\(942\) −31098.9 + 1.05385e6i −0.0350464 + 1.18762i
\(943\) 488382. 1.17906e6i 0.549207 1.32590i
\(944\) 764455. 299030.i 0.857844 0.335561i
\(945\) −1.00389e6 + 415826.i −1.12415 + 0.465638i
\(946\) 340077. 129249.i 0.380010 0.144426i
\(947\) 70016.6 + 230814.i 0.0780731 + 0.257372i 0.987285 0.158962i \(-0.0508147\pi\)
−0.909212 + 0.416334i \(0.863315\pi\)
\(948\) 141831. 894923.i 0.157817 0.995792i
\(949\) 34524.3 + 350531.i 0.0383347 + 0.389219i
\(950\) 302745. + 38864.7i 0.335452 + 0.0430634i
\(951\) 32416.9 162971.i 0.0358435 0.180197i
\(952\) 21712.2 41583.2i 0.0239569 0.0458821i
\(953\) 244986. + 1.23163e6i 0.269746 + 1.35611i 0.843522 + 0.537094i \(0.180478\pi\)
−0.573776 + 0.819012i \(0.694522\pi\)
\(954\) −5677.07 4946.37i −0.00623774 0.00543488i
\(955\) 405003. + 122856.i 0.444070 + 0.134707i
\(956\) 60120.6 1.01777e6i 0.0657821 1.11361i
\(957\) −264905. + 217402.i −0.289245 + 0.237377i
\(958\) 1.77235e6 298489.i 1.93116 0.325235i
\(959\) 204401. 0.222252
\(960\) 890045. + 159210.i 0.965761 + 0.172754i
\(961\) 476062.i 0.515486i
\(962\) −405443. + 68282.3i −0.438107 + 0.0737833i
\(963\) 252638. + 307841.i 0.272425 + 0.331950i
\(964\) 1.05818e6 940139.i 1.13869 1.01167i
\(965\) 507840. 1.67412e6i 0.545346 1.79777i
\(966\) −430303. 374919.i −0.461127 0.401775i
\(967\) 633780. 126067.i 0.677775 0.134818i 0.155813 0.987787i \(-0.450200\pi\)
0.521962 + 0.852969i \(0.325200\pi\)
\(968\) 17886.6 201572.i 0.0190887 0.215120i
\(969\) −37425.8 7444.45i −0.0398587 0.00792839i
\(970\) −676232. 86810.8i −0.718708 0.0922635i
\(971\) 1.33025e6 131018.i 1.41089 0.138961i 0.636311 0.771433i \(-0.280460\pi\)
0.774583 + 0.632472i \(0.217960\pi\)
\(972\) −321906. 443157.i −0.340719 0.469056i
\(973\) −554433. + 168185.i −0.585630 + 0.177649i
\(974\) −545795. + 207434.i −0.575323 + 0.218656i
\(975\) −90745.7 219080.i −0.0954590 0.230458i
\(976\) −290126. + 1.32109e6i −0.304570 + 1.38686i
\(977\) 882533. + 365557.i 0.924575 + 0.382971i 0.793618 0.608417i \(-0.208195\pi\)
0.130957 + 0.991388i \(0.458195\pi\)
\(978\) 29250.7 991223.i 0.0305815 1.03632i
\(979\) −1.30406e6 697036.i −1.36061 0.727260i
\(980\) −43313.4 93978.2i −0.0450994 0.0978532i
\(981\) 76300.3 92972.2i 0.0792845 0.0966085i
\(982\) −1.01690e6 + 275993.i −1.05452 + 0.286204i
\(983\) 107236. + 160490.i 0.110977 + 0.166090i 0.882801 0.469747i \(-0.155655\pi\)
−0.771823 + 0.635837i \(0.780655\pi\)
\(984\) 1.26580e6 + 828189.i 1.30730 + 0.855341i
\(985\) −569679. + 852585.i −0.587162 + 0.878749i
\(986\) 11884.6 + 23905.0i 0.0122245 + 0.0245887i
\(987\) 208694. 111549.i 0.214228 0.114507i
\(988\) 94516.3 + 683823.i 0.0968262 + 0.700535i
\(989\) −343149. 33797.2i −0.350824 0.0345532i
\(990\) −162964. 260193.i −0.166273 0.265476i
\(991\) 38467.0 38467.0i 0.0391689 0.0391689i −0.687251 0.726420i \(-0.741183\pi\)
0.726420 + 0.687251i \(0.241183\pi\)
\(992\) 507423. + 460127.i 0.515641 + 0.467578i
\(993\) −170640. + 170640.i −0.173054 + 0.173054i
\(994\) 210268. 915122.i 0.212814 0.926203i
\(995\) 1.94795e6 + 191857.i 1.96758 + 0.193790i
\(996\) −524355. 894835.i −0.528575 0.902037i
\(997\) 1.43615e6 767637.i 1.44480 0.772264i 0.452000 0.892018i \(-0.350711\pi\)
0.992804 + 0.119754i \(0.0382107\pi\)
\(998\) 473736. + 159110.i 0.475636 + 0.159749i
\(999\) −339186. + 507628.i −0.339866 + 0.508645i
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 128.5.l.a.3.13 1008
128.43 odd 32 inner 128.5.l.a.43.13 yes 1008
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
128.5.l.a.3.13 1008 1.1 even 1 trivial
128.5.l.a.43.13 yes 1008 128.43 odd 32 inner