Properties

Label 23.6.c.a.3.2
Level $23$
Weight $6$
Character 23.3
Analytic conductor $3.689$
Analytic rank $0$
Dimension $90$
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] = [23,6,Mod(2,23)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(23, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("23.2");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 23.c (of order \(11\), degree \(10\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.68882785570\)
Analytic rank: \(0\)
Dimension: \(90\)
Relative dimension: \(9\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 3.2
Character \(\chi\) \(=\) 23.3
Dual form 23.6.c.a.8.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.13164 - 7.87071i) q^{2} +(-6.81486 + 14.9225i) q^{3} +(-29.9637 + 8.79812i) q^{4} +(-54.8415 + 63.2904i) q^{5} +(125.162 + 36.7510i) q^{6} +(-3.45670 + 2.22148i) q^{7} +(-2.54800 - 5.57934i) q^{8} +(-17.1066 - 19.7421i) q^{9} +O(q^{10})\) \(q+(-1.13164 - 7.87071i) q^{2} +(-6.81486 + 14.9225i) q^{3} +(-29.9637 + 8.79812i) q^{4} +(-54.8415 + 63.2904i) q^{5} +(125.162 + 36.7510i) q^{6} +(-3.45670 + 2.22148i) q^{7} +(-2.54800 - 5.57934i) q^{8} +(-17.1066 - 19.7421i) q^{9} +(560.201 + 360.019i) q^{10} +(-64.8376 + 450.955i) q^{11} +(72.9085 - 507.090i) q^{12} +(-801.248 - 514.931i) q^{13} +(21.3964 + 24.6927i) q^{14} +(-570.713 - 1249.69i) q^{15} +(-881.708 + 566.640i) q^{16} +(278.854 + 81.8789i) q^{17} +(-136.026 + 156.982i) q^{18} +(-237.974 + 69.8756i) q^{19} +(1086.41 - 2378.92i) q^{20} +(-9.59312 - 66.7216i) q^{21} +3622.71 q^{22} +(2290.68 + 1090.46i) q^{23} +100.622 q^{24} +(-553.358 - 3848.69i) q^{25} +(-3146.15 + 6889.11i) q^{26} +(-3413.75 + 1002.37i) q^{27} +(84.0304 - 96.9763i) q^{28} +(6799.06 + 1996.39i) q^{29} +(-9190.08 + 5906.10i) q^{30} +(-2553.58 - 5591.56i) q^{31} +(5329.09 + 6150.10i) q^{32} +(-6287.51 - 4040.74i) q^{33} +(328.883 - 2287.43i) q^{34} +(48.9717 - 340.605i) q^{35} +(686.270 + 441.039i) q^{36} +(3120.58 + 3601.34i) q^{37} +(819.271 + 1793.95i) q^{38} +(13144.4 - 8447.42i) q^{39} +(492.855 + 144.715i) q^{40} +(-8161.16 + 9418.48i) q^{41} +(-514.290 + 151.009i) q^{42} +(2731.88 - 5981.99i) q^{43} +(-2024.79 - 14082.7i) q^{44} +2187.64 q^{45} +(5990.51 - 19263.3i) q^{46} +11655.7 q^{47} +(-2446.94 - 17018.8i) q^{48} +(-6974.87 + 15272.8i) q^{49} +(-29665.7 + 8710.64i) q^{50} +(-3122.19 + 3603.19i) q^{51} +(28538.8 + 8379.74i) q^{52} +(-18212.0 + 11704.1i) q^{53} +(11752.5 + 25734.3i) q^{54} +(-24985.4 - 28834.7i) q^{55} +(21.2021 + 13.6257i) q^{56} +(579.047 - 4027.36i) q^{57} +(8018.89 - 55772.6i) q^{58} +(-32099.6 - 20629.2i) q^{59} +(28095.5 + 32424.0i) q^{60} +(23152.4 + 50696.6i) q^{61} +(-41119.8 + 26426.1i) q^{62} +(102.989 + 30.2404i) q^{63} +(20411.8 - 23556.5i) q^{64} +(76531.9 - 22471.8i) q^{65} +(-24688.3 + 54059.8i) q^{66} +(4611.93 + 32076.7i) q^{67} -9075.86 q^{68} +(-31883.1 + 26751.3i) q^{69} -2736.22 q^{70} +(2544.22 + 17695.4i) q^{71} +(-66.5602 + 145.747i) q^{72} +(-7259.56 + 2131.60i) q^{73} +(24813.7 - 28636.6i) q^{74} +(61203.1 + 17970.8i) q^{75} +(6515.81 - 4187.46i) q^{76} +(-777.666 - 1702.85i) q^{77} +(-81361.9 - 93896.7i) q^{78} +(-33871.9 - 21768.1i) q^{79} +(12491.3 - 86879.1i) q^{80} +(9209.82 - 64055.7i) q^{81} +(83365.6 + 53575.8i) q^{82} +(-23301.6 - 26891.5i) q^{83} +(874.470 + 1914.82i) q^{84} +(-20474.9 + 13158.4i) q^{85} +(-50174.0 - 14732.4i) q^{86} +(-76125.7 + 87853.7i) q^{87} +(2681.24 - 787.282i) q^{88} +(-32495.6 + 71155.5i) q^{89} +(-2475.61 - 17218.3i) q^{90} +3913.59 q^{91} +(-78231.3 - 12520.6i) q^{92} +100842. q^{93} +(-13190.0 - 91738.8i) q^{94} +(8628.41 - 18893.6i) q^{95} +(-128092. + 37611.1i) q^{96} +(101421. - 117046. i) q^{97} +(128101. + 37613.8i) q^{98} +(10012.0 - 6434.29i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 90 q - 11 q^{2} - 7 q^{3} - 139 q^{4} + 5 q^{5} - 148 q^{6} - 29 q^{7} - 44 q^{8} - 894 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 90 q - 11 q^{2} - 7 q^{3} - 139 q^{4} + 5 q^{5} - 148 q^{6} - 29 q^{7} - 44 q^{8} - 894 q^{9} + 155 q^{10} - 89 q^{11} + 276 q^{12} + 313 q^{13} + 957 q^{14} - 4232 q^{15} + 5637 q^{16} + 5256 q^{17} + 11184 q^{18} - 3622 q^{19} - 2135 q^{20} - 6000 q^{21} - 10050 q^{22} - 11740 q^{23} - 20042 q^{24} - 3312 q^{25} + 432 q^{26} + 18236 q^{27} + 42219 q^{28} + 820 q^{29} + 39879 q^{30} - 10618 q^{31} - 44595 q^{32} - 52342 q^{33} - 48583 q^{34} - 12737 q^{35} + 62095 q^{36} + 37741 q^{37} + 93044 q^{38} + 51241 q^{39} + 54519 q^{40} + 27731 q^{41} - 74509 q^{42} - 24555 q^{43} - 93314 q^{44} - 97906 q^{45} - 178395 q^{46} - 72522 q^{47} - 84106 q^{48} - 60450 q^{49} + 100394 q^{50} + 92167 q^{51} + 289884 q^{52} + 37321 q^{53} + 74406 q^{54} + 24327 q^{55} + 73828 q^{56} + 210858 q^{57} - 46295 q^{58} + 12675 q^{59} + 40595 q^{60} + 169431 q^{61} + 126424 q^{62} + 48782 q^{63} - 152118 q^{64} - 204392 q^{65} - 289970 q^{66} - 68547 q^{67} - 619298 q^{68} - 269580 q^{69} - 616314 q^{70} - 116130 q^{71} - 90563 q^{72} - 41005 q^{73} - 39958 q^{74} - 89428 q^{75} - 54510 q^{76} + 473172 q^{77} + 749704 q^{78} + 562545 q^{79} + 1784628 q^{80} + 1038036 q^{81} + 361674 q^{82} + 235154 q^{83} + 314877 q^{84} - 216047 q^{85} - 896543 q^{86} - 516271 q^{87} - 213359 q^{88} - 497007 q^{89} - 1378102 q^{90} - 630132 q^{91} - 861506 q^{92} - 1401408 q^{93} - 497781 q^{94} - 605790 q^{95} - 1213923 q^{96} - 292308 q^{97} + 943825 q^{98} + 525394 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/23\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(e\left(\frac{8}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.13164 7.87071i −0.200047 1.39136i −0.804138 0.594442i \(-0.797373\pi\)
0.604091 0.796915i \(-0.293536\pi\)
\(3\) −6.81486 + 14.9225i −0.437174 + 0.957277i 0.554935 + 0.831894i \(0.312743\pi\)
−0.992108 + 0.125383i \(0.959984\pi\)
\(4\) −29.9637 + 8.79812i −0.936364 + 0.274941i
\(5\) −54.8415 + 63.2904i −0.981034 + 1.13217i 0.0101853 + 0.999948i \(0.496758\pi\)
−0.991220 + 0.132226i \(0.957788\pi\)
\(6\) 125.162 + 36.7510i 1.41937 + 0.416765i
\(7\) −3.45670 + 2.22148i −0.0266634 + 0.0171356i −0.553905 0.832580i \(-0.686863\pi\)
0.527241 + 0.849716i \(0.323226\pi\)
\(8\) −2.54800 5.57934i −0.0140758 0.0308218i
\(9\) −17.1066 19.7421i −0.0703976 0.0812432i
\(10\) 560.201 + 360.019i 1.77151 + 1.13848i
\(11\) −64.8376 + 450.955i −0.161564 + 1.12370i 0.734122 + 0.679017i \(0.237594\pi\)
−0.895686 + 0.444686i \(0.853315\pi\)
\(12\) 72.9085 507.090i 0.146159 1.01656i
\(13\) −801.248 514.931i −1.31495 0.845066i −0.320194 0.947352i \(-0.603748\pi\)
−0.994755 + 0.102286i \(0.967384\pi\)
\(14\) 21.3964 + 24.6927i 0.0291756 + 0.0336705i
\(15\) −570.713 1249.69i −0.654922 1.43408i
\(16\) −881.708 + 566.640i −0.861043 + 0.553359i
\(17\) 278.854 + 81.8789i 0.234021 + 0.0687147i 0.396640 0.917974i \(-0.370176\pi\)
−0.162619 + 0.986689i \(0.551994\pi\)
\(18\) −136.026 + 156.982i −0.0989555 + 0.114201i
\(19\) −237.974 + 69.8756i −0.151233 + 0.0444060i −0.356473 0.934306i \(-0.616021\pi\)
0.205240 + 0.978712i \(0.434203\pi\)
\(20\) 1086.41 2378.92i 0.607324 1.32985i
\(21\) −9.59312 66.7216i −0.00474692 0.0330155i
\(22\) 3622.71 1.59579
\(23\) 2290.68 + 1090.46i 0.902912 + 0.429825i
\(24\) 100.622 0.0356586
\(25\) −553.358 3848.69i −0.177075 1.23158i
\(26\) −3146.15 + 6889.11i −0.912738 + 1.99862i
\(27\) −3413.75 + 1002.37i −0.901201 + 0.264617i
\(28\) 84.0304 96.9763i 0.0202554 0.0233760i
\(29\) 6799.06 + 1996.39i 1.50125 + 0.440808i 0.926113 0.377247i \(-0.123129\pi\)
0.575141 + 0.818054i \(0.304947\pi\)
\(30\) −9190.08 + 5906.10i −1.86430 + 1.19811i
\(31\) −2553.58 5591.56i −0.477249 1.04503i −0.983211 0.182473i \(-0.941590\pi\)
0.505962 0.862556i \(-0.331138\pi\)
\(32\) 5329.09 + 6150.10i 0.919980 + 1.06171i
\(33\) −6287.51 4040.74i −1.00506 0.645915i
\(34\) 328.883 2287.43i 0.0487915 0.339353i
\(35\) 48.9717 340.605i 0.00675733 0.0469982i
\(36\) 686.270 + 441.039i 0.0882549 + 0.0567180i
\(37\) 3120.58 + 3601.34i 0.374740 + 0.432474i 0.911524 0.411246i \(-0.134906\pi\)
−0.536784 + 0.843720i \(0.680361\pi\)
\(38\) 819.271 + 1793.95i 0.0920383 + 0.201536i
\(39\) 13144.4 8447.42i 1.38382 0.889329i
\(40\) 492.855 + 144.715i 0.0487045 + 0.0143009i
\(41\) −8161.16 + 9418.48i −0.758215 + 0.875027i −0.995338 0.0964531i \(-0.969250\pi\)
0.237123 + 0.971480i \(0.423796\pi\)
\(42\) −514.290 + 151.009i −0.0449868 + 0.0132093i
\(43\) 2731.88 5981.99i 0.225315 0.493372i −0.762886 0.646533i \(-0.776218\pi\)
0.988201 + 0.153161i \(0.0489454\pi\)
\(44\) −2024.79 14082.7i −0.157670 1.09662i
\(45\) 2187.64 0.161044
\(46\) 5990.51 19263.3i 0.417416 1.34226i
\(47\) 11655.7 0.769652 0.384826 0.922989i \(-0.374261\pi\)
0.384826 + 0.922989i \(0.374261\pi\)
\(48\) −2446.94 17018.8i −0.153292 1.06617i
\(49\) −6974.87 + 15272.8i −0.414998 + 0.908718i
\(50\) −29665.7 + 8710.64i −1.67815 + 0.492748i
\(51\) −3122.19 + 3603.19i −0.168087 + 0.193982i
\(52\) 28538.8 + 8379.74i 1.46361 + 0.429756i
\(53\) −18212.0 + 11704.1i −0.890567 + 0.572333i −0.903979 0.427577i \(-0.859367\pi\)
0.0134115 + 0.999910i \(0.495731\pi\)
\(54\) 11752.5 + 25734.3i 0.548459 + 1.20096i
\(55\) −24985.4 28834.7i −1.11373 1.28531i
\(56\) 21.2021 + 13.6257i 0.000903459 + 0.000580618i
\(57\) 579.047 4027.36i 0.0236062 0.164185i
\(58\) 8018.89 55772.6i 0.313000 2.17696i
\(59\) −32099.6 20629.2i −1.20052 0.771528i −0.221474 0.975166i \(-0.571087\pi\)
−0.979046 + 0.203639i \(0.934723\pi\)
\(60\) 28095.5 + 32424.0i 1.00753 + 1.16275i
\(61\) 23152.4 + 50696.6i 0.796656 + 1.74443i 0.656531 + 0.754299i \(0.272023\pi\)
0.140125 + 0.990134i \(0.455249\pi\)
\(62\) −41119.8 + 26426.1i −1.35854 + 0.873079i
\(63\) 102.989 + 30.2404i 0.00326919 + 0.000959921i
\(64\) 20411.8 23556.5i 0.622918 0.718886i
\(65\) 76531.9 22471.8i 2.24677 0.659712i
\(66\) −24688.3 + 54059.8i −0.697639 + 1.52762i
\(67\) 4611.93 + 32076.7i 0.125515 + 0.872976i 0.951141 + 0.308758i \(0.0999132\pi\)
−0.825626 + 0.564218i \(0.809178\pi\)
\(68\) −9075.86 −0.238021
\(69\) −31883.1 + 26751.3i −0.806191 + 0.676429i
\(70\) −2736.22 −0.0667431
\(71\) 2544.22 + 17695.4i 0.0598975 + 0.416596i 0.997605 + 0.0691702i \(0.0220352\pi\)
−0.937707 + 0.347426i \(0.887056\pi\)
\(72\) −66.5602 + 145.747i −0.00151315 + 0.00331335i
\(73\) −7259.56 + 2131.60i −0.159442 + 0.0468164i −0.360479 0.932767i \(-0.617387\pi\)
0.201037 + 0.979584i \(0.435569\pi\)
\(74\) 24813.7 28636.6i 0.526760 0.607913i
\(75\) 61203.1 + 17970.8i 1.25638 + 0.368906i
\(76\) 6515.81 4187.46i 0.129400 0.0831603i
\(77\) −777.666 1702.85i −0.0149474 0.0327303i
\(78\) −81361.9 93896.7i −1.51420 1.74749i
\(79\) −33871.9 21768.1i −0.610621 0.392422i 0.198469 0.980107i \(-0.436403\pi\)
−0.809090 + 0.587685i \(0.800039\pi\)
\(80\) 12491.3 86879.1i 0.218214 1.51771i
\(81\) 9209.82 64055.7i 0.155969 1.08479i
\(82\) 83365.6 + 53575.8i 1.36915 + 0.879902i
\(83\) −23301.6 26891.5i −0.371271 0.428470i 0.539113 0.842233i \(-0.318760\pi\)
−0.910384 + 0.413763i \(0.864214\pi\)
\(84\) 874.470 + 1914.82i 0.0135222 + 0.0296094i
\(85\) −20474.9 + 13158.4i −0.307379 + 0.197541i
\(86\) −50174.0 14732.4i −0.731530 0.214797i
\(87\) −76125.7 + 87853.7i −1.07828 + 1.24441i
\(88\) 2681.24 787.282i 0.0369087 0.0108374i
\(89\) −32495.6 + 71155.5i −0.434861 + 0.952212i 0.557653 + 0.830074i \(0.311702\pi\)
−0.992513 + 0.122137i \(0.961025\pi\)
\(90\) −2475.61 17218.3i −0.0322164 0.224070i
\(91\) 3913.59 0.0495417
\(92\) −78231.3 12520.6i −0.963631 0.154225i
\(93\) 100842. 1.20902
\(94\) −13190.0 91738.8i −0.153967 1.07086i
\(95\) 8628.41 18893.6i 0.0980894 0.214786i
\(96\) −128092. + 37611.1i −1.41855 + 0.416522i
\(97\) 101421. 117046.i 1.09446 1.26307i 0.132112 0.991235i \(-0.457824\pi\)
0.962344 0.271835i \(-0.0876304\pi\)
\(98\) 128101. + 37613.8i 1.34737 + 0.395624i
\(99\) 10012.0 6434.29i 0.102667 0.0659801i
\(100\) 50441.9 + 110452.i 0.504419 + 1.10452i
\(101\) 73586.4 + 84923.2i 0.717784 + 0.828367i 0.991039 0.133575i \(-0.0426456\pi\)
−0.273255 + 0.961942i \(0.588100\pi\)
\(102\) 31892.9 + 20496.3i 0.303524 + 0.195063i
\(103\) 23609.7 164209.i 0.219279 1.52512i −0.521430 0.853294i \(-0.674601\pi\)
0.740709 0.671826i \(-0.234490\pi\)
\(104\) −831.395 + 5782.48i −0.00753745 + 0.0524241i
\(105\) 4748.94 + 3051.96i 0.0420362 + 0.0270150i
\(106\) 112729. + 130096.i 0.974475 + 1.12460i
\(107\) 11138.3 + 24389.6i 0.0940505 + 0.205942i 0.950810 0.309774i \(-0.100253\pi\)
−0.856760 + 0.515716i \(0.827526\pi\)
\(108\) 93469.4 60069.1i 0.771099 0.495555i
\(109\) 4085.39 + 1199.58i 0.0329357 + 0.00967081i 0.298159 0.954516i \(-0.403627\pi\)
−0.265223 + 0.964187i \(0.585446\pi\)
\(110\) −198675. + 229283.i −1.56553 + 1.80672i
\(111\) −75007.2 + 22024.1i −0.577824 + 0.169664i
\(112\) 1789.02 3917.40i 0.0134763 0.0295089i
\(113\) −19405.2 134966.i −0.142963 0.994328i −0.927387 0.374103i \(-0.877951\pi\)
0.784424 0.620225i \(-0.212959\pi\)
\(114\) −32353.4 −0.233162
\(115\) −194640. + 85175.7i −1.37242 + 0.600580i
\(116\) −221289. −1.52692
\(117\) 3540.84 + 24627.1i 0.0239134 + 0.166321i
\(118\) −126041. + 275991.i −0.833310 + 1.82469i
\(119\) −1145.81 + 336.439i −0.00741726 + 0.00217790i
\(120\) −5518.25 + 6368.40i −0.0349823 + 0.0403717i
\(121\) −44629.4 13104.4i −0.277113 0.0813678i
\(122\) 372818. 239596.i 2.26776 1.45740i
\(123\) −84929.8 185970.i −0.506171 1.10836i
\(124\) 125710. + 145077.i 0.734200 + 0.847312i
\(125\) 53773.1 + 34557.9i 0.307815 + 0.197821i
\(126\) 121.467 844.819i 0.000681602 0.00474064i
\(127\) 11445.5 79605.1i 0.0629687 0.437957i −0.933811 0.357767i \(-0.883538\pi\)
0.996780 0.0801900i \(-0.0255527\pi\)
\(128\) 10564.5 + 6789.37i 0.0569932 + 0.0366273i
\(129\) 70648.6 + 81532.9i 0.373792 + 0.431378i
\(130\) −263475. 576930.i −1.36735 2.99409i
\(131\) −200426. + 128806.i −1.02041 + 0.655778i −0.940067 0.340989i \(-0.889238\pi\)
−0.0803436 + 0.996767i \(0.525602\pi\)
\(132\) 223948. + 65756.9i 1.11869 + 0.328478i
\(133\) 667.378 770.195i 0.00327147 0.00377548i
\(134\) 247247. 72598.3i 1.18951 0.349272i
\(135\) 123775. 271029.i 0.584517 1.27991i
\(136\) −253.689 1764.45i −0.00117613 0.00818015i
\(137\) 4239.99 0.0193003 0.00965013 0.999953i \(-0.496928\pi\)
0.00965013 + 0.999953i \(0.496928\pi\)
\(138\) 246632. + 220670.i 1.10243 + 0.986383i
\(139\) −70681.4 −0.310290 −0.155145 0.987892i \(-0.549585\pi\)
−0.155145 + 0.987892i \(0.549585\pi\)
\(140\) 1529.32 + 10636.6i 0.00659444 + 0.0458653i
\(141\) −79432.2 + 173932.i −0.336472 + 0.736770i
\(142\) 136396. 40049.6i 0.567652 0.166678i
\(143\) 284162. 327940.i 1.16205 1.34108i
\(144\) 26269.7 + 7713.48i 0.105572 + 0.0309988i
\(145\) −499223. + 320831.i −1.97185 + 1.26723i
\(146\) 24992.4 + 54725.7i 0.0970343 + 0.212475i
\(147\) −180376. 208164.i −0.688469 0.794536i
\(148\) −125189. 80454.0i −0.469798 0.301921i
\(149\) −50852.1 + 353684.i −0.187648 + 1.30512i 0.650430 + 0.759566i \(0.274589\pi\)
−0.838077 + 0.545551i \(0.816320\pi\)
\(150\) 72183.6 502048.i 0.261945 1.82187i
\(151\) −38860.4 24974.1i −0.138696 0.0891348i 0.469453 0.882958i \(-0.344451\pi\)
−0.608149 + 0.793823i \(0.708088\pi\)
\(152\) 996.218 + 1149.70i 0.00349740 + 0.00403622i
\(153\) −3153.79 6905.83i −0.0108919 0.0238499i
\(154\) −12522.6 + 8047.79i −0.0425494 + 0.0273448i
\(155\) 493934. + 145032.i 1.65135 + 0.484881i
\(156\) −319534. + 368762.i −1.05125 + 1.21321i
\(157\) 53413.1 15683.5i 0.172941 0.0507802i −0.194115 0.980979i \(-0.562184\pi\)
0.367057 + 0.930199i \(0.380365\pi\)
\(158\) −133000. + 291229.i −0.423846 + 0.928094i
\(159\) −50542.3 351529.i −0.158548 1.10273i
\(160\) −681498. −2.10458
\(161\) −10340.7 + 1319.31i −0.0314400 + 0.00401127i
\(162\) −514586. −1.54053
\(163\) 46160.3 + 321052.i 0.136082 + 0.946468i 0.937406 + 0.348238i \(0.113220\pi\)
−0.801324 + 0.598230i \(0.795871\pi\)
\(164\) 161673. 354015.i 0.469384 1.02781i
\(165\) 600556. 176339.i 1.71729 0.504242i
\(166\) −185286. + 213832.i −0.521883 + 0.602285i
\(167\) −89343.0 26233.5i −0.247896 0.0727888i 0.155424 0.987848i \(-0.450326\pi\)
−0.403320 + 0.915059i \(0.632144\pi\)
\(168\) −347.819 + 223.530i −0.000950781 + 0.000611030i
\(169\) 222604. + 487435.i 0.599538 + 1.31281i
\(170\) 126736. + 146261.i 0.336340 + 0.388157i
\(171\) 5450.43 + 3502.78i 0.0142541 + 0.00916057i
\(172\) −29226.9 + 203278.i −0.0753289 + 0.523924i
\(173\) −74538.5 + 518427.i −0.189350 + 1.31696i 0.644346 + 0.764734i \(0.277130\pi\)
−0.833696 + 0.552224i \(0.813779\pi\)
\(174\) 777618. + 499745.i 1.94712 + 1.25134i
\(175\) 10462.6 + 12074.5i 0.0258253 + 0.0298039i
\(176\) −198361. 434350.i −0.482698 1.05696i
\(177\) 526592. 338420.i 1.26340 0.811939i
\(178\) 596818. + 175241.i 1.41186 + 0.414559i
\(179\) 342561. 395336.i 0.799107 0.922218i −0.199225 0.979954i \(-0.563842\pi\)
0.998332 + 0.0577353i \(0.0183879\pi\)
\(180\) −65549.7 + 19247.1i −0.150796 + 0.0442776i
\(181\) 116448. 254985.i 0.264201 0.578520i −0.730314 0.683112i \(-0.760626\pi\)
0.994515 + 0.104592i \(0.0333535\pi\)
\(182\) −4428.76 30802.7i −0.00991068 0.0689303i
\(183\) −914299. −2.01818
\(184\) 247.415 15559.0i 0.000538743 0.0338795i
\(185\) −399067. −0.857269
\(186\) −114117. 793699.i −0.241861 1.68218i
\(187\) −55003.9 + 120442.i −0.115024 + 0.251868i
\(188\) −349248. + 102548.i −0.720675 + 0.211609i
\(189\) 9573.55 11048.5i 0.0194948 0.0224982i
\(190\) −158470. 46531.0i −0.318466 0.0935101i
\(191\) 805490. 517657.i 1.59763 1.02674i 0.629270 0.777187i \(-0.283354\pi\)
0.968362 0.249549i \(-0.0802822\pi\)
\(192\) 212417. + 465128.i 0.415850 + 0.910584i
\(193\) 112996. + 130405.i 0.218359 + 0.251999i 0.854352 0.519696i \(-0.173955\pi\)
−0.635993 + 0.771695i \(0.719409\pi\)
\(194\) −1.03601e6 665801.i −1.97632 1.27011i
\(195\) −186220. + 1.29519e6i −0.350703 + 2.43919i
\(196\) 74620.3 518995.i 0.138745 0.964991i
\(197\) −144654. 92963.4i −0.265561 0.170666i 0.401083 0.916042i \(-0.368634\pi\)
−0.666645 + 0.745376i \(0.732270\pi\)
\(198\) −61972.3 71519.9i −0.112340 0.129647i
\(199\) 356140. + 779838.i 0.637511 + 1.39596i 0.902072 + 0.431586i \(0.142046\pi\)
−0.264560 + 0.964369i \(0.585227\pi\)
\(200\) −20063.2 + 12893.8i −0.0354671 + 0.0227933i
\(201\) −510093. 149777.i −0.890552 0.261490i
\(202\) 585133. 675279.i 1.00896 1.16441i
\(203\) −27937.2 + 8203.12i −0.0475821 + 0.0139714i
\(204\) 61850.7 135434.i 0.104057 0.227852i
\(205\) −148530. 1.03305e6i −0.246848 1.71686i
\(206\) −1.31916e6 −2.16585
\(207\) −17657.8 63877.1i −0.0286425 0.103614i
\(208\) 998248. 1.59985
\(209\) −16081.1 111846.i −0.0254653 0.177115i
\(210\) 18647.0 40831.2i 0.0291783 0.0638917i
\(211\) −216934. + 63697.6i −0.335445 + 0.0984957i −0.445118 0.895472i \(-0.646838\pi\)
0.109672 + 0.993968i \(0.465020\pi\)
\(212\) 442722. 510929.i 0.676537 0.780766i
\(213\) −281398. 82626.0i −0.424984 0.124786i
\(214\) 179359. 115267.i 0.267724 0.172056i
\(215\) 228782. + 500963.i 0.337541 + 0.739111i
\(216\) 14290.8 + 16492.4i 0.0208411 + 0.0240519i
\(217\) 21248.5 + 13655.6i 0.0306323 + 0.0196862i
\(218\) 4818.36 33512.4i 0.00686685 0.0477600i
\(219\) 17664.2 122857.i 0.0248876 0.173097i
\(220\) 1.00234e6 + 644167.i 1.39624 + 0.897309i
\(221\) −181269. 209196.i −0.249657 0.288119i
\(222\) 258226. + 565436.i 0.351656 + 0.770019i
\(223\) −749785. + 481858.i −1.00966 + 0.648868i −0.937305 0.348511i \(-0.886688\pi\)
−0.0723541 + 0.997379i \(0.523051\pi\)
\(224\) −32083.4 9420.54i −0.0427229 0.0125446i
\(225\) −66515.2 + 76762.6i −0.0875920 + 0.101087i
\(226\) −1.04032e6 + 305466.i −1.35487 + 0.397825i
\(227\) 216798. 474721.i 0.279248 0.611468i −0.717089 0.696982i \(-0.754526\pi\)
0.996337 + 0.0855137i \(0.0272531\pi\)
\(228\) 18082.8 + 125769.i 0.0230372 + 0.160227i
\(229\) 111582. 0.140606 0.0703031 0.997526i \(-0.477603\pi\)
0.0703031 + 0.997526i \(0.477603\pi\)
\(230\) 890655. + 1.43557e6i 1.11017 + 1.78939i
\(231\) 30710.4 0.0378666
\(232\) −6185.50 43021.1i −0.00754492 0.0524761i
\(233\) −70959.3 + 155379.i −0.0856287 + 0.187501i −0.947602 0.319452i \(-0.896501\pi\)
0.861974 + 0.506953i \(0.169228\pi\)
\(234\) 189825. 55737.8i 0.226629 0.0665442i
\(235\) −639217. + 737696.i −0.755055 + 0.871380i
\(236\) 1.14332e6 + 335709.i 1.33625 + 0.392358i
\(237\) 555666. 357105.i 0.642604 0.412976i
\(238\) 3944.65 + 8637.58i 0.00451405 + 0.00988438i
\(239\) −183560. 211839.i −0.207865 0.239890i 0.642238 0.766505i \(-0.278006\pi\)
−0.850103 + 0.526616i \(0.823461\pi\)
\(240\) 1.21132e6 + 778471.i 1.35748 + 0.872397i
\(241\) −6966.74 + 48454.7i −0.00772658 + 0.0537395i −0.993320 0.115393i \(-0.963187\pi\)
0.985593 + 0.169132i \(0.0540965\pi\)
\(242\) −52636.4 + 366094.i −0.0577760 + 0.401841i
\(243\) 165790. + 106547.i 0.180112 + 0.115751i
\(244\) −1.13976e6 1.31536e6i −1.22558 1.41439i
\(245\) −584112. 1.27903e6i −0.621700 1.36133i
\(246\) −1.36761e6 + 878909.i −1.44087 + 0.925989i
\(247\) 226658. + 66552.7i 0.236389 + 0.0694102i
\(248\) −24690.7 + 28494.6i −0.0254920 + 0.0294193i
\(249\) 560086. 164456.i 0.572474 0.168094i
\(250\) 211143. 462339.i 0.213662 0.467855i
\(251\) −12037.9 83725.7i −0.0120606 0.0838831i 0.982902 0.184129i \(-0.0589463\pi\)
−0.994963 + 0.100245i \(0.968037\pi\)
\(252\) −3351.99 −0.00332508
\(253\) −640273. + 962292.i −0.628874 + 0.945161i
\(254\) −639500. −0.621951
\(255\) −56822.5 395209.i −0.0547230 0.380607i
\(256\) 455829. 998126.i 0.434712 0.951888i
\(257\) −526395. + 154564.i −0.497141 + 0.145974i −0.520685 0.853749i \(-0.674323\pi\)
0.0235439 + 0.999723i \(0.492505\pi\)
\(258\) 561773. 648320.i 0.525426 0.606374i
\(259\) −18787.2 5516.42i −0.0174025 0.00510985i
\(260\) −2.09547e6 + 1.34667e6i −1.92241 + 1.23546i
\(261\) −76896.2 168379.i −0.0698721 0.152998i
\(262\) 1.24060e6 + 1.43173e6i 1.11655 + 1.28857i
\(263\) 839012. + 539200.i 0.747961 + 0.480685i 0.858261 0.513213i \(-0.171545\pi\)
−0.110300 + 0.993898i \(0.535181\pi\)
\(264\) −6524.07 + 45375.9i −0.00576115 + 0.0400697i
\(265\) 258012. 1.79451e6i 0.225697 1.56976i
\(266\) −6817.21 4381.16i −0.00590749 0.00379651i
\(267\) −840363. 969830.i −0.721421 0.832564i
\(268\) −420405. 920558.i −0.357545 0.782914i
\(269\) 1.12741e6 724540.i 0.949948 0.610494i 0.0287491 0.999587i \(-0.490848\pi\)
0.921199 + 0.389092i \(0.127211\pi\)
\(270\) −2.27326e6 667488.i −1.89775 0.557230i
\(271\) 70984.2 81920.1i 0.0587135 0.0677590i −0.725633 0.688082i \(-0.758453\pi\)
0.784347 + 0.620323i \(0.212998\pi\)
\(272\) −292263. + 85816.3i −0.239526 + 0.0703311i
\(273\) −26670.6 + 58400.4i −0.0216584 + 0.0474252i
\(274\) −4798.13 33371.7i −0.00386096 0.0268536i
\(275\) 1.77147e6 1.41254
\(276\) 719974. 1.08208e6i 0.568911 0.855039i
\(277\) 704707. 0.551835 0.275917 0.961181i \(-0.411018\pi\)
0.275917 + 0.961181i \(0.411018\pi\)
\(278\) 79985.7 + 556313.i 0.0620727 + 0.431725i
\(279\) −66705.9 + 146066.i −0.0513043 + 0.112341i
\(280\) −2025.13 + 594.633i −0.00154368 + 0.000453267i
\(281\) −677341. + 781693.i −0.511731 + 0.590569i −0.951541 0.307522i \(-0.900500\pi\)
0.439810 + 0.898091i \(0.355046\pi\)
\(282\) 1.45886e6 + 428359.i 1.09242 + 0.320764i
\(283\) 965157. 620269.i 0.716361 0.460377i −0.131008 0.991381i \(-0.541821\pi\)
0.847369 + 0.531004i \(0.178185\pi\)
\(284\) −231921. 507836.i −0.170625 0.373618i
\(285\) 223138. + 257514.i 0.162727 + 0.187797i
\(286\) −2.90269e6 1.86545e6i −2.09839 1.34855i
\(287\) 7287.65 50686.7i 0.00522255 0.0363237i
\(288\) 30253.1 210415.i 0.0214926 0.149484i
\(289\) −1.12340e6 721968.i −0.791210 0.508480i
\(290\) 3.09011e6 + 3.56617e6i 2.15764 + 2.49005i
\(291\) 1.05545e6 + 2.31110e6i 0.730640 + 1.59988i
\(292\) 198769. 127741.i 0.136424 0.0876744i
\(293\) 56981.7 + 16731.3i 0.0387763 + 0.0113857i 0.301063 0.953604i \(-0.402658\pi\)
−0.262287 + 0.964990i \(0.584477\pi\)
\(294\) −1.43428e6 + 1.65525e6i −0.967757 + 1.11685i
\(295\) 3.06602e6 900264.i 2.05126 0.602303i
\(296\) 12141.9 26587.0i 0.00805482 0.0176376i
\(297\) −230683. 1.60444e6i −0.151749 1.05544i
\(298\) 2.84129e6 1.85342
\(299\) −1.27389e6 2.05328e6i −0.824052 1.32822i
\(300\) −1.99198e6 −1.27785
\(301\) 3845.60 + 26746.8i 0.00244652 + 0.0170159i
\(302\) −152588. + 334121.i −0.0962726 + 0.210808i
\(303\) −1.76875e6 + 519350.i −1.10677 + 0.324978i
\(304\) 170230. 196456.i 0.105646 0.121922i
\(305\) −4.47832e6 1.31495e6i −2.75655 0.809396i
\(306\) −50784.8 + 32637.4i −0.0310049 + 0.0199256i
\(307\) 214697. + 470120.i 0.130011 + 0.284684i 0.963431 0.267955i \(-0.0863480\pi\)
−0.833421 + 0.552639i \(0.813621\pi\)
\(308\) 38283.6 + 44181.7i 0.0229951 + 0.0265378i
\(309\) 2.28951e6 + 1.47138e6i 1.36410 + 0.876653i
\(310\) 582551. 4.05173e6i 0.344294 2.39462i
\(311\) −338156. + 2.35193e6i −0.198251 + 1.37887i 0.611105 + 0.791550i \(0.290725\pi\)
−0.809356 + 0.587319i \(0.800184\pi\)
\(312\) −80623.1 51813.3i −0.0468892 0.0301339i
\(313\) 404361. + 466657.i 0.233296 + 0.269238i 0.860311 0.509769i \(-0.170269\pi\)
−0.627015 + 0.779007i \(0.715724\pi\)
\(314\) −183885. 402651.i −0.105250 0.230465i
\(315\) −7562.01 + 4859.81i −0.00429399 + 0.00275958i
\(316\) 1.20644e6 + 354244.i 0.679656 + 0.199565i
\(317\) −866189. + 999636.i −0.484133 + 0.558719i −0.944288 0.329119i \(-0.893248\pi\)
0.460155 + 0.887838i \(0.347794\pi\)
\(318\) −2.70959e6 + 795607.i −1.50257 + 0.441195i
\(319\) −1.34111e6 + 2.93663e6i −0.737886 + 1.61574i
\(320\) 371486. + 2.58374e6i 0.202800 + 1.41050i
\(321\) −439859. −0.238260
\(322\) 22085.8 + 79895.3i 0.0118706 + 0.0429419i
\(323\) −72081.4 −0.0384430
\(324\) 287610. + 2.00037e6i 0.152209 + 1.05864i
\(325\) −1.53843e6 + 3.36870e6i −0.807924 + 1.76911i
\(326\) 2.47467e6 726628.i 1.28965 0.378676i
\(327\) −45742.1 + 52789.2i −0.0236563 + 0.0273008i
\(328\) 73343.5 + 21535.6i 0.0376424 + 0.0110528i
\(329\) −40290.3 + 25893.0i −0.0205216 + 0.0131884i
\(330\) −2.06753e6 4.52725e6i −1.04512 2.28849i
\(331\) −958621. 1.10631e6i −0.480925 0.555017i 0.462493 0.886623i \(-0.346955\pi\)
−0.943418 + 0.331606i \(0.892410\pi\)
\(332\) 934797. + 600758.i 0.465449 + 0.299126i
\(333\) 17715.4 123213.i 0.00875469 0.0608902i
\(334\) −105372. + 732880.i −0.0516844 + 0.359473i
\(335\) −2.28307e6 1.46724e6i −1.11150 0.714315i
\(336\) 46265.4 + 53393.1i 0.0223567 + 0.0258010i
\(337\) 904371. + 1.98030e6i 0.433783 + 0.949851i 0.992698 + 0.120627i \(0.0384904\pi\)
−0.558915 + 0.829225i \(0.688782\pi\)
\(338\) 3.58455e6 2.30365e6i 1.70665 1.09679i
\(339\) 2.14628e6 + 630204.i 1.01435 + 0.297839i
\(340\) 497734. 574415.i 0.233507 0.269481i
\(341\) 2.68711e6 789006.i 1.25141 0.367447i
\(342\) 21401.4 46862.6i 0.00989413 0.0216651i
\(343\) −19646.6 136645.i −0.00901678 0.0627131i
\(344\) −40336.4 −0.0183781
\(345\) 55417.2 3.48498e6i 0.0250667 1.57635i
\(346\) 4.16473e6 1.87024
\(347\) 70754.9 + 492111.i 0.0315451 + 0.219401i 0.999496 0.0317375i \(-0.0101040\pi\)
−0.967951 + 0.251139i \(0.919195\pi\)
\(348\) 1.50806e6 3.30218e6i 0.667528 1.46168i
\(349\) 954134. 280159.i 0.419320 0.123123i −0.0652643 0.997868i \(-0.520789\pi\)
0.484584 + 0.874745i \(0.338971\pi\)
\(350\) 83194.9 96012.0i 0.0363017 0.0418944i
\(351\) 3.25141e6 + 954700.i 1.40865 + 0.413618i
\(352\) −3.11895e6 + 2.00442e6i −1.34169 + 0.862250i
\(353\) 92779.1 + 203158.i 0.0396290 + 0.0867755i 0.928411 0.371554i \(-0.121175\pi\)
−0.888782 + 0.458330i \(0.848448\pi\)
\(354\) −3.25952e6 3.76169e6i −1.38244 1.59542i
\(355\) −1.25948e6 809419.i −0.530421 0.340881i
\(356\) 347653. 2.41798e6i 0.145385 1.01118i
\(357\) 2788.01 19391.0i 0.00115777 0.00805250i
\(358\) −3.49923e6 2.24882e6i −1.44299 0.927356i
\(359\) 2.04930e6 + 2.36502e6i 0.839209 + 0.968499i 0.999829 0.0185176i \(-0.00589468\pi\)
−0.160620 + 0.987016i \(0.551349\pi\)
\(360\) −5574.10 12205.6i −0.00226683 0.00496366i
\(361\) −2.03128e6 + 1.30542e6i −0.820354 + 0.527210i
\(362\) −2.13869e6 627976.i −0.857781 0.251867i
\(363\) 499692. 576676.i 0.199038 0.229702i
\(364\) −117265. + 34432.2i −0.0463891 + 0.0136211i
\(365\) 263215. 576361.i 0.103414 0.226445i
\(366\) 1.03465e6 + 7.19618e6i 0.403731 + 2.80801i
\(367\) 193651. 0.0750509 0.0375254 0.999296i \(-0.488052\pi\)
0.0375254 + 0.999296i \(0.488052\pi\)
\(368\) −2.63761e6 + 336520.i −1.01529 + 0.129536i
\(369\) 325551. 0.124467
\(370\) 451599. + 3.14094e6i 0.171494 + 1.19277i
\(371\) 36952.7 80915.1i 0.0139384 0.0305207i
\(372\) −3.02160e6 + 887221.i −1.13209 + 0.332410i
\(373\) −171082. + 197439.i −0.0636697 + 0.0734787i −0.786691 0.617347i \(-0.788207\pi\)
0.723021 + 0.690826i \(0.242753\pi\)
\(374\) 1.01021e6 + 296623.i 0.373449 + 0.109654i
\(375\) −882145. + 566920.i −0.323938 + 0.208182i
\(376\) −29698.8 65031.2i −0.0108335 0.0237221i
\(377\) −4.41974e6 5.10065e6i −1.60156 1.84830i
\(378\) −97793.0 62847.7i −0.0352029 0.0226235i
\(379\) 331861. 2.30814e6i 0.118675 0.825401i −0.840343 0.542055i \(-0.817646\pi\)
0.959018 0.283346i \(-0.0914445\pi\)
\(380\) −92310.7 + 642035.i −0.0327939 + 0.228086i
\(381\) 1.10990e6 + 713293.i 0.391718 + 0.251742i
\(382\) −4.98585e6 5.75398e6i −1.74816 2.01748i
\(383\) −2.08232e6 4.55965e6i −0.725355 1.58831i −0.806244 0.591583i \(-0.798503\pi\)
0.0808887 0.996723i \(-0.474224\pi\)
\(384\) −173310. + 111379.i −0.0599784 + 0.0385458i
\(385\) 150423. + 44168.1i 0.0517203 + 0.0151865i
\(386\) 898506. 1.03693e6i 0.306939 0.354227i
\(387\) −164830. + 48398.5i −0.0559448 + 0.0164269i
\(388\) −2.00916e6 + 4.39944e6i −0.677539 + 1.48360i
\(389\) 698607. + 4.85892e6i 0.234077 + 1.62804i 0.680170 + 0.733055i \(0.261906\pi\)
−0.446093 + 0.894987i \(0.647185\pi\)
\(390\) 1.04048e7 3.46394
\(391\) 549480. + 491639.i 0.181765 + 0.162631i
\(392\) 102984. 0.0338498
\(393\) −556226. 3.86864e6i −0.181665 1.26350i
\(394\) −567992. + 1.24373e6i −0.184332 + 0.403632i
\(395\) 3.23530e6 949969.i 1.04333 0.306349i
\(396\) −243385. + 280881.i −0.0779931 + 0.0900088i
\(397\) 7202.53 + 2114.85i 0.00229355 + 0.000673448i 0.282879 0.959156i \(-0.408710\pi\)
−0.280586 + 0.959829i \(0.590529\pi\)
\(398\) 5.73485e6 3.68557e6i 1.81474 1.16626i
\(399\) 6945.13 + 15207.7i 0.00218398 + 0.00478224i
\(400\) 2.66872e6 + 3.07987e6i 0.833976 + 0.962459i
\(401\) 3.37649e6 + 2.16994e6i 1.04859 + 0.673887i 0.947096 0.320949i \(-0.104002\pi\)
0.101492 + 0.994836i \(0.467638\pi\)
\(402\) −601609. + 4.18428e6i −0.185673 + 1.29139i
\(403\) −833216. + 5.79514e6i −0.255561 + 1.77747i
\(404\) −2.95208e6 1.89719e6i −0.899860 0.578305i
\(405\) 3.54903e6 + 4.09580e6i 1.07516 + 1.24080i
\(406\) 96179.1 + 210603.i 0.0289578 + 0.0634088i
\(407\) −1.82637e6 + 1.17374e6i −0.546517 + 0.351225i
\(408\) 28058.8 + 8238.80i 0.00834484 + 0.00245027i
\(409\) 1.75496e6 2.02533e6i 0.518751 0.598671i −0.434567 0.900640i \(-0.643098\pi\)
0.953318 + 0.301969i \(0.0976439\pi\)
\(410\) −7.96273e6 + 2.33807e6i −2.33939 + 0.686906i
\(411\) −28894.9 + 63271.1i −0.00843757 + 0.0184757i
\(412\) 737298. + 5.12802e6i 0.213993 + 1.48836i
\(413\) 156786. 0.0452306
\(414\) −482776. + 211265.i −0.138435 + 0.0605796i
\(415\) 2.97987e6 0.849332
\(416\) −1.10305e6 7.67188e6i −0.312508 2.17354i
\(417\) 481684. 1.05474e6i 0.135651 0.297034i
\(418\) −862112. + 253139.i −0.241336 + 0.0708628i
\(419\) 814616. 940117.i 0.226682 0.261605i −0.631003 0.775781i \(-0.717356\pi\)
0.857685 + 0.514175i \(0.171902\pi\)
\(420\) −169147. 49666.1i −0.0467887 0.0137384i
\(421\) −3.73111e6 + 2.39784e6i −1.02597 + 0.659348i −0.941477 0.337077i \(-0.890562\pi\)
−0.0844881 + 0.996424i \(0.526926\pi\)
\(422\) 746836. + 1.63534e6i 0.204148 + 0.447021i
\(423\) −199390. 230108.i −0.0541817 0.0625290i
\(424\) 111705. + 71788.6i 0.0301758 + 0.0193928i
\(425\) 160820. 1.11853e6i 0.0431886 0.300383i
\(426\) −331884. + 2.30831e6i −0.0886059 + 0.616267i
\(427\) −192652. 123810.i −0.0511334 0.0328615i
\(428\) −548328. 632804.i −0.144688 0.166978i
\(429\) 2.95715e6 + 6.47527e6i 0.775766 + 1.69869i
\(430\) 3.68404e6 2.36759e6i 0.960844 0.617497i
\(431\) −6.01125e6 1.76506e6i −1.55873 0.457685i −0.615037 0.788499i \(-0.710859\pi\)
−0.943696 + 0.330813i \(0.892677\pi\)
\(432\) 2.44195e6 2.81816e6i 0.629545 0.726534i
\(433\) −1.50427e6 + 441694.i −0.385573 + 0.113214i −0.468774 0.883318i \(-0.655304\pi\)
0.0832005 + 0.996533i \(0.473486\pi\)
\(434\) 83433.5 182694.i 0.0212626 0.0465586i
\(435\) −1.38546e6 9.63606e6i −0.351051 2.44161i
\(436\) −132967. −0.0334988
\(437\) −621321. 99439.9i −0.155637 0.0249090i
\(438\) −986962. −0.245819
\(439\) 483683. + 3.36409e6i 0.119784 + 0.833118i 0.957793 + 0.287460i \(0.0928109\pi\)
−0.838008 + 0.545657i \(0.816280\pi\)
\(440\) −97215.6 + 212872.i −0.0239389 + 0.0524189i
\(441\) 420834. 123568.i 0.103042 0.0302559i
\(442\) −1.44139e6 + 1.66345e6i −0.350934 + 0.404999i
\(443\) −3.91180e6 1.14861e6i −0.947039 0.278076i −0.228485 0.973547i \(-0.573377\pi\)
−0.718553 + 0.695472i \(0.755195\pi\)
\(444\) 2.05372e6 1.31984e6i 0.494406 0.317735i
\(445\) −2.72136e6 5.95894e6i −0.651456 1.42649i
\(446\) 4.64104e6 + 5.35605e6i 1.10479 + 1.27499i
\(447\) −4.93129e6 3.16915e6i −1.16732 0.750194i
\(448\) −18227.1 + 126772.i −0.00429064 + 0.0298420i
\(449\) 172172. 1.19748e6i 0.0403039 0.280320i −0.959696 0.281041i \(-0.909320\pi\)
1.00000 0.000721050i \(0.000229517\pi\)
\(450\) 679447. + 436654.i 0.158170 + 0.101650i
\(451\) −3.71816e6 4.29099e6i −0.860770 0.993381i
\(452\) 1.76890e6 + 3.87336e6i 0.407247 + 0.891747i
\(453\) 637504. 409699.i 0.145961 0.0938035i
\(454\) −3.98173e6 1.16914e6i −0.906634 0.266212i
\(455\) −214627. + 247693.i −0.0486022 + 0.0560899i
\(456\) −23945.4 + 7031.01i −0.00539275 + 0.00158345i
\(457\) 2.29279e6 5.02052e6i 0.513540 1.12450i −0.458287 0.888804i \(-0.651537\pi\)
0.971828 0.235692i \(-0.0757358\pi\)
\(458\) −126270. 878227.i −0.0281279 0.195634i
\(459\) −1.03401e6 −0.229083
\(460\) 5.08275e6 4.26464e6i 1.11997 0.939698i
\(461\) 6.52844e6 1.43073 0.715364 0.698752i \(-0.246261\pi\)
0.715364 + 0.698752i \(0.246261\pi\)
\(462\) −34753.1 241713.i −0.00757510 0.0526860i
\(463\) 749138. 1.64038e6i 0.162409 0.355626i −0.810879 0.585214i \(-0.801011\pi\)
0.973288 + 0.229588i \(0.0737379\pi\)
\(464\) −7.12602e6 + 2.09239e6i −1.53657 + 0.451177i
\(465\) −5.53033e6 + 6.38234e6i −1.18609 + 1.36882i
\(466\) 1.30324e6 + 382667.i 0.278010 + 0.0816312i
\(467\) 1.73315e6 1.11383e6i 0.367743 0.236334i −0.343697 0.939080i \(-0.611679\pi\)
0.711440 + 0.702746i \(0.248043\pi\)
\(468\) −322768. 706764.i −0.0681203 0.149163i
\(469\) −87199.9 100634.i −0.0183056 0.0211258i
\(470\) 6.52955e6 + 4.19629e6i 1.36345 + 0.876235i
\(471\) −129966. + 903937.i −0.0269947 + 0.187753i
\(472\) −33307.3 + 231658.i −0.00688153 + 0.0478621i
\(473\) 2.52048e6 + 1.61981e6i 0.518001 + 0.332899i
\(474\) −3.43948e6 3.96937e6i −0.703149 0.811477i
\(475\) 400615. + 877224.i 0.0814691 + 0.178392i
\(476\) 31372.5 20161.9i 0.00634646 0.00407862i
\(477\) 542609. + 159324.i 0.109192 + 0.0320617i
\(478\) −1.45960e6 + 1.68447e6i −0.292189 + 0.337204i
\(479\) 6.71011e6 1.97027e6i 1.33626 0.392361i 0.465926 0.884824i \(-0.345721\pi\)
0.870334 + 0.492462i \(0.163903\pi\)
\(480\) 4.64432e6 1.01696e7i 0.920066 2.01466i
\(481\) −645917. 4.49245e6i −0.127296 0.885361i
\(482\) 389257. 0.0763166
\(483\) 50782.8 163299.i 0.00990486 0.0318505i
\(484\) 1.45255e6 0.281850
\(485\) 1.84582e6 + 1.28380e7i 0.356316 + 2.47823i
\(486\) 650986. 1.42546e6i 0.125020 0.273757i
\(487\) 5.29408e6 1.55448e6i 1.01151 0.297005i 0.266336 0.963880i \(-0.414187\pi\)
0.745169 + 0.666875i \(0.232369\pi\)
\(488\) 223861. 258350.i 0.0425529 0.0491087i
\(489\) −5.10546e6 1.49910e6i −0.965524 0.283503i
\(490\) −9.40584e6 + 6.04477e6i −1.76973 + 1.13734i
\(491\) −375309. 821812.i −0.0702563 0.153840i 0.871246 0.490847i \(-0.163313\pi\)
−0.941502 + 0.337007i \(0.890585\pi\)
\(492\) 4.18100e6 + 4.82513e6i 0.778695 + 0.898662i
\(493\) 1.73248e6 + 1.11340e6i 0.321034 + 0.206316i
\(494\) 267323. 1.85927e6i 0.0492854 0.342788i
\(495\) −141841. + 986527.i −0.0260189 + 0.180966i
\(496\) 5.41991e6 + 3.48316e6i 0.989208 + 0.635725i
\(497\) −48104.7 55515.8i −0.00873568 0.0100815i
\(498\) −1.92820e6 4.22217e6i −0.348400 0.762890i
\(499\) −5.20716e6 + 3.34644e6i −0.936160 + 0.601633i −0.917303 0.398189i \(-0.869639\pi\)
−0.0188562 + 0.999822i \(0.506002\pi\)
\(500\) −1.91528e6 562378.i −0.342616 0.100601i
\(501\) 1.00033e6 1.15444e6i 0.178053 0.205484i
\(502\) −645358. + 189494.i −0.114299 + 0.0335611i
\(503\) −3.72345e6 + 8.15323e6i −0.656184 + 1.43684i 0.229851 + 0.973226i \(0.426176\pi\)
−0.886035 + 0.463618i \(0.846551\pi\)
\(504\) −93.6952 651.664i −1.64301e−5 0.000114274i
\(505\) −9.41041e6 −1.64203
\(506\) 8.29848e6 + 3.95044e6i 1.44086 + 0.685913i
\(507\) −8.79076e6 −1.51882
\(508\) 357427. + 2.48596e6i 0.0614508 + 0.427400i
\(509\) 4.76567e6 1.04354e7i 0.815323 1.78531i 0.232734 0.972540i \(-0.425233\pi\)
0.582588 0.812767i \(-0.302040\pi\)
\(510\) −3.04627e6 + 894466.i −0.518613 + 0.152278i
\(511\) 20358.8 23495.3i 0.00344905 0.00398042i
\(512\) −7.98622e6 2.34496e6i −1.34638 0.395331i
\(513\) 742343. 477075.i 0.124541 0.0800375i
\(514\) 1.81221e6 + 3.96819e6i 0.302553 + 0.662499i
\(515\) 9.09807e6 + 1.04997e7i 1.51158 + 1.74446i
\(516\) −2.83423e6 1.82145e6i −0.468609 0.301157i
\(517\) −755729. + 5.25621e6i −0.124348 + 0.864861i
\(518\) −22157.8 + 154111.i −0.00362830 + 0.0252354i
\(519\) −7.22824e6 4.64531e6i −1.17792 0.757000i
\(520\) −320381. 369739.i −0.0519587 0.0599635i
\(521\) 1.62170e6 + 3.55103e6i 0.261744 + 0.573138i 0.994184 0.107692i \(-0.0343462\pi\)
−0.732441 + 0.680831i \(0.761619\pi\)
\(522\) −1.23824e6 + 795772.i −0.198898 + 0.127824i
\(523\) 5.27991e6 + 1.55032e6i 0.844058 + 0.247838i 0.675046 0.737776i \(-0.264124\pi\)
0.169013 + 0.985614i \(0.445942\pi\)
\(524\) 4.87224e6 5.62286e6i 0.775176 0.894600i
\(525\) −251482. + 73841.9i −0.0398208 + 0.0116924i
\(526\) 3.29443e6 7.21380e6i 0.519178 1.13684i
\(527\) −254245. 1.76831e6i −0.0398773 0.277352i
\(528\) 7.83339e6 1.22283
\(529\) 4.05812e6 + 4.99582e6i 0.630500 + 0.776189i
\(530\) −1.44161e7 −2.22924
\(531\) 141853. + 986609.i 0.0218324 + 0.151848i
\(532\) −13220.8 + 28949.5i −0.00202525 + 0.00443468i
\(533\) 1.13890e7 3.34411e6i 1.73647 0.509873i
\(534\) −6.68227e6 + 7.71175e6i −1.01408 + 1.17031i
\(535\) −2.15447e6 632610.i −0.325429 0.0955546i
\(536\) 167215. 107463.i 0.0251399 0.0161565i
\(537\) 3.56489e6 + 7.80601e6i 0.533470 + 1.16814i
\(538\) −6.97846e6 8.05357e6i −1.03945 1.19959i
\(539\) −6.43513e6 4.13560e6i −0.954081 0.613151i
\(540\) −1.32420e6 + 9.21000e6i −0.195420 + 1.35917i
\(541\) 1.82079e6 1.26639e7i 0.267464 1.86026i −0.204806 0.978803i \(-0.565656\pi\)
0.472271 0.881453i \(-0.343434\pi\)
\(542\) −725097. 465992.i −0.106023 0.0681365i
\(543\) 3.01143e6 + 3.47538e6i 0.438302 + 0.505828i
\(544\) 982475. + 2.15132e6i 0.142339 + 0.311679i
\(545\) −299971. + 192780.i −0.0432601 + 0.0278016i
\(546\) 489834. + 143828.i 0.0703181 + 0.0206472i
\(547\) 4.80906e6 5.54995e6i 0.687213 0.793086i −0.299753 0.954017i \(-0.596904\pi\)
0.986966 + 0.160931i \(0.0514496\pi\)
\(548\) −127046. + 37303.9i −0.0180721 + 0.00530644i
\(549\) 604799. 1.32432e6i 0.0856407 0.187527i
\(550\) −2.00466e6 1.39427e7i −0.282575 1.96535i
\(551\) −1.75750e6 −0.246613
\(552\) 230493. + 109725.i 0.0321966 + 0.0153270i
\(553\) 165442. 0.0230056
\(554\) −797472. 5.54654e6i −0.110393 0.767799i
\(555\) 2.71959e6 5.95507e6i 0.374775 0.820644i
\(556\) 2.11787e6 621864.i 0.290545 0.0853116i
\(557\) −3.23243e6 + 3.73042e6i −0.441460 + 0.509472i −0.932254 0.361804i \(-0.882161\pi\)
0.490795 + 0.871275i \(0.336707\pi\)
\(558\) 1.22513e6 + 359730.i 0.166570 + 0.0489092i
\(559\) −5.26923e6 + 3.38633e6i −0.713210 + 0.458352i
\(560\) 149822. + 328064.i 0.0201885 + 0.0442067i
\(561\) −1.42244e6 1.64159e6i −0.190822 0.220220i
\(562\) 6.91898e6 + 4.44656e6i 0.924062 + 0.593859i
\(563\) −1.67763e6 + 1.16682e7i −0.223062 + 1.55143i 0.503295 + 0.864114i \(0.332121\pi\)
−0.726358 + 0.687317i \(0.758788\pi\)
\(564\) 849801. 5.91050e6i 0.112491 0.782396i
\(565\) 9.60630e6 + 6.17359e6i 1.26600 + 0.813611i
\(566\) −5.97416e6 6.89455e6i −0.783855 0.904617i
\(567\) 110463. + 241881.i 0.0144298 + 0.0315968i
\(568\) 92246.2 59283.0i 0.0119971 0.00771009i
\(569\) −2.28222e6 670120.i −0.295513 0.0867705i 0.130615 0.991433i \(-0.458305\pi\)
−0.426129 + 0.904663i \(0.640123\pi\)
\(570\) 1.77431e6 2.04766e6i 0.228740 0.263980i
\(571\) 1.20499e7 3.53818e6i 1.54666 0.454139i 0.606557 0.795040i \(-0.292550\pi\)
0.940099 + 0.340901i \(0.110732\pi\)
\(572\) −5.62927e6 + 1.23264e7i −0.719386 + 1.57524i
\(573\) 2.23542e6 + 1.55477e7i 0.284428 + 1.97824i
\(574\) −407187. −0.0515840
\(575\) 2.92930e6 9.41955e6i 0.369482 1.18812i
\(576\) −814231. −0.102257
\(577\) −1.29254e6 8.98984e6i −0.161624 1.12412i −0.895573 0.444915i \(-0.853234\pi\)
0.733949 0.679204i \(-0.237675\pi\)
\(578\) −4.41111e6 + 9.65899e6i −0.549198 + 1.20258i
\(579\) −2.71601e6 + 797493.i −0.336694 + 0.0988623i
\(580\) 1.21358e7 1.40055e7i 1.49796 1.72874i
\(581\) 140286. + 41191.6i 0.0172414 + 0.00506254i
\(582\) 1.69956e7 1.09224e7i 2.07984 1.33663i
\(583\) −4.09721e6 8.97164e6i −0.499249 1.09320i
\(584\) 30390.3 + 35072.2i 0.00368725 + 0.00425531i
\(585\) −1.75284e6 1.12648e6i −0.211765 0.136093i
\(586\) 67204.8 467420.i 0.00808456 0.0562294i
\(587\) 31726.9 220666.i 0.00380043 0.0264326i −0.987833 0.155518i \(-0.950295\pi\)
0.991633 + 0.129086i \(0.0412043\pi\)
\(588\) 7.23617e6 + 4.65040e6i 0.863108 + 0.554686i
\(589\) 998399. + 1.15221e6i 0.118581 + 0.136850i
\(590\) −1.05553e7 2.31130e7i −1.24837 2.73354i
\(591\) 2.37304e6 1.52506e6i 0.279471 0.179605i
\(592\) −4.79210e6 1.40709e6i −0.561981 0.165012i
\(593\) −1.05927e7 + 1.22247e7i −1.23701 + 1.42758i −0.370186 + 0.928958i \(0.620706\pi\)
−0.866819 + 0.498622i \(0.833839\pi\)
\(594\) −1.23670e7 + 3.63128e6i −1.43813 + 0.422273i
\(595\) 41544.3 90969.4i 0.00481082 0.0105342i
\(596\) −1.58804e6 1.10451e7i −0.183124 1.27366i
\(597\) −1.40642e7 −1.61502
\(598\) −1.47192e7 + 1.23500e7i −1.68318 + 1.41226i
\(599\) 7.38005e6 0.840412 0.420206 0.907429i \(-0.361958\pi\)
0.420206 + 0.907429i \(0.361958\pi\)
\(600\) −55679.9 387262.i −0.00631423 0.0439164i
\(601\) −584497. + 1.27987e6i −0.0660079 + 0.144537i −0.939761 0.341833i \(-0.888952\pi\)
0.873753 + 0.486370i \(0.161679\pi\)
\(602\) 206164. 60535.2i 0.0231858 0.00680796i
\(603\) 554366. 639773.i 0.0620874 0.0716527i
\(604\) 1.38413e6 + 406416.i 0.154377 + 0.0453293i
\(605\) 3.27692e6 2.10595e6i 0.363980 0.233916i
\(606\) 6.08923e6 + 1.33336e7i 0.673567 + 1.47491i
\(607\) 874067. + 1.00873e6i 0.0962882 + 0.111122i 0.801849 0.597527i \(-0.203850\pi\)
−0.705560 + 0.708650i \(0.749305\pi\)
\(608\) −1.69793e6 1.09119e6i −0.186278 0.119713i
\(609\) 67977.8 472796.i 0.00742718 0.0516572i
\(610\) −5.28178e6 + 3.67356e7i −0.574720 + 3.99726i
\(611\) −9.33913e6 6.00189e6i −1.01205 0.650407i
\(612\) 155257. + 179176.i 0.0167561 + 0.0193376i
\(613\) 1.47660e6 + 3.23330e6i 0.158713 + 0.347532i 0.972237 0.233999i \(-0.0751812\pi\)
−0.813524 + 0.581531i \(0.802454\pi\)
\(614\) 3.45722e6 2.22182e6i 0.370089 0.237842i
\(615\) 1.64278e7 + 4.82364e6i 1.75143 + 0.514266i
\(616\) −7519.29 + 8677.73i −0.000798409 + 0.000921413i
\(617\) −1.60974e7 + 4.72662e6i −1.70233 + 0.499848i −0.981206 0.192963i \(-0.938190\pi\)
−0.721119 + 0.692811i \(0.756372\pi\)
\(618\) 8.98989e6 1.96851e7i 0.946854 2.07332i
\(619\) 1.04612e6 + 7.27595e6i 0.109738 + 0.763244i 0.968166 + 0.250310i \(0.0805324\pi\)
−0.858428 + 0.512934i \(0.828559\pi\)
\(620\) −1.60761e7 −1.67958
\(621\) −8.91286e6 1.42647e6i −0.927444 0.148434i
\(622\) 1.88940e7 1.95816
\(623\) −45743.3 318152.i −0.00472180 0.0328408i
\(624\) −6.80292e6 + 1.48963e7i −0.699414 + 1.53150i
\(625\) 6.52247e6 1.91517e6i 0.667901 0.196113i
\(626\) 3.21533e6 3.71069e6i 0.327937 0.378459i
\(627\) 1.77861e6 + 522248.i 0.180681 + 0.0530528i
\(628\) −1.46247e6 + 939870.i −0.147975 + 0.0950975i
\(629\) 575311. + 1.25976e6i 0.0579797 + 0.126958i
\(630\) 46807.6 + 54018.8i 0.00469856 + 0.00542243i
\(631\) −8.33491e6 5.35652e6i −0.833350 0.535562i 0.0529905 0.998595i \(-0.483125\pi\)
−0.886341 + 0.463033i \(0.846761\pi\)
\(632\) −35146.3 + 244448.i −0.00350015 + 0.0243441i
\(633\) 527851. 3.67129e6i 0.0523603 0.364174i
\(634\) 8.84805e6 + 5.68630e6i 0.874228 + 0.561832i
\(635\) 4.41055e6 + 5.09005e6i 0.434069 + 0.500942i
\(636\) 4.60723e6 + 1.00884e7i 0.451645 + 0.988964i
\(637\) 1.34531e7 8.64575e6i 1.31363 0.844217i
\(638\) 2.46310e7 + 7.23232e6i 2.39569 + 0.703438i
\(639\) 305822. 352937.i 0.0296290 0.0341937i
\(640\) −1.00907e6 + 296291.i −0.0973807 + 0.0285936i
\(641\) −5.33723e6 + 1.16869e7i −0.513063 + 1.12345i 0.458937 + 0.888469i \(0.348231\pi\)
−0.972000 + 0.234982i \(0.924497\pi\)
\(642\) 497761. + 3.46200e6i 0.0476632 + 0.331505i
\(643\) −1.47551e7 −1.40739 −0.703694 0.710503i \(-0.748467\pi\)
−0.703694 + 0.710503i \(0.748467\pi\)
\(644\) 298236. 130510.i 0.0283365 0.0124002i
\(645\) −9.03473e6 −0.855098
\(646\) 81570.0 + 567331.i 0.00769040 + 0.0534879i
\(647\) 4.25314e6 9.31308e6i 0.399438 0.874646i −0.597889 0.801579i \(-0.703994\pi\)
0.997327 0.0730677i \(-0.0232789\pi\)
\(648\) −380855. + 111829.i −0.0356305 + 0.0104621i
\(649\) 1.13841e7 1.31379e7i 1.06093 1.22438i
\(650\) 2.82550e7 + 8.29642e6i 2.62308 + 0.770207i
\(651\) −348581. + 224019.i −0.0322367 + 0.0207173i
\(652\) −4.20778e6 9.21376e6i −0.387645 0.848825i
\(653\) −6.62788e6 7.64898e6i −0.608263 0.701973i 0.365171 0.930940i \(-0.381011\pi\)
−0.973434 + 0.228967i \(0.926465\pi\)
\(654\) 467252. + 300284.i 0.0427176 + 0.0274529i
\(655\) 2.83947e6 1.97489e7i 0.258603 1.79862i
\(656\) 1.85888e6 1.29288e7i 0.168652 1.17300i
\(657\) 166269. + 106854.i 0.0150279 + 0.00965782i
\(658\) 249390. + 287812.i 0.0224551 + 0.0259146i
\(659\) −1.38131e6 3.02464e6i −0.123902 0.271306i 0.837509 0.546423i \(-0.184011\pi\)
−0.961411 + 0.275116i \(0.911284\pi\)
\(660\) −1.64434e7 + 1.05675e7i −1.46937 + 0.944308i
\(661\) −6.00222e6 1.76241e6i −0.534328 0.156893i 0.00342674 0.999994i \(-0.498909\pi\)
−0.537755 + 0.843101i \(0.680727\pi\)
\(662\) −7.62262e6 + 8.79697e6i −0.676019 + 0.780168i
\(663\) 4.35704e6 1.27934e6i 0.384953 0.113032i
\(664\) −90664.4 + 198527.i −0.00798025 + 0.0174743i
\(665\) 12146.0 + 84477.3i 0.00106507 + 0.00740774i
\(666\) −989825. −0.0864714
\(667\) 1.33975e7 + 1.19872e7i 1.16603 + 1.04329i
\(668\) 2.90785e6 0.252134
\(669\) −2.08082e6 1.44724e7i −0.179750 1.25019i
\(670\) −8.96462e6 + 1.96298e7i −0.771516 + 1.68938i
\(671\) −2.43630e7 + 7.15363e6i −2.08894 + 0.613367i
\(672\) 359222. 414564.i 0.0306860 0.0354135i
\(673\) −7.90569e6 2.32132e6i −0.672825 0.197559i −0.0725644 0.997364i \(-0.523118\pi\)
−0.600261 + 0.799804i \(0.704936\pi\)
\(674\) 1.45629e7 9.35902e6i 1.23481 0.793562i
\(675\) 5.74683e6 + 1.25838e7i 0.485477 + 1.06305i
\(676\) −1.09586e7 1.26468e7i −0.922331 1.06443i
\(677\) −988119. 635026.i −0.0828586 0.0532500i 0.498556 0.866858i \(-0.333864\pi\)
−0.581414 + 0.813608i \(0.697500\pi\)
\(678\) 2.53134e6 1.76059e7i 0.211484 1.47090i
\(679\) −90565.6 + 629898.i −0.00753857 + 0.0524319i
\(680\) 125585. + 80708.8i 0.0104152 + 0.00669343i
\(681\) 5.60656e6 + 6.47032e6i 0.463264 + 0.534636i
\(682\) −9.25087e6 2.02566e7i −0.761591 1.66765i
\(683\) −3.10602e6 + 1.99612e6i −0.254773 + 0.163733i −0.661793 0.749687i \(-0.730204\pi\)
0.407020 + 0.913419i \(0.366568\pi\)
\(684\) −194133. 57002.5i −0.0158657 0.00465858i
\(685\) −232527. + 268351.i −0.0189342 + 0.0218512i
\(686\) −1.05326e6 + 309265.i −0.0854525 + 0.0250911i
\(687\) −760415. + 1.66508e6i −0.0614693 + 0.134599i
\(688\) 980907. + 6.82236e6i 0.0790054 + 0.549495i
\(689\) 2.06191e7 1.65471
\(690\) −2.74920e7 + 3.50756e6i −2.19828 + 0.280467i
\(691\) −1.95646e7 −1.55875 −0.779373 0.626561i \(-0.784462\pi\)
−0.779373 + 0.626561i \(0.784462\pi\)
\(692\) −2.32774e6 1.61898e7i −0.184786 1.28521i
\(693\) −20314.6 + 44482.8i −0.00160685 + 0.00351851i
\(694\) 3.79319e6 1.11378e6i 0.298955 0.0877812i
\(695\) 3.87627e6 4.47346e6i 0.304405 0.351303i
\(696\) 684134. + 200880.i 0.0535326 + 0.0157186i
\(697\) −3.04694e6 + 1.95815e6i −0.237565 + 0.152674i
\(698\) −3.28478e6 7.19267e6i −0.255192 0.558794i
\(699\) −1.83506e6 2.11778e6i −0.142056 0.163941i
\(700\) −419731. 269745.i −0.0323762 0.0208069i
\(701\) −1.54259e6 + 1.07290e7i −0.118565 + 0.824636i 0.840573 + 0.541698i \(0.182218\pi\)
−0.959138 + 0.282938i \(0.908691\pi\)
\(702\) 3.83475e6 2.66713e7i 0.293693 2.04268i
\(703\) −994263. 638974.i −0.0758775 0.0487635i
\(704\) 9.29946e6 + 1.07321e7i 0.707173 + 0.816122i
\(705\) −6.65207e6 1.45660e7i −0.504062 1.10374i
\(706\) 1.49400e6 960138.i 0.112808 0.0724973i
\(707\) −443021. 130083.i −0.0333331 0.00978749i
\(708\) −1.28012e7 + 1.47733e7i −0.959769 + 1.10763i
\(709\) 1.14925e7 3.37449e6i 0.858614 0.252112i 0.177348 0.984148i \(-0.443248\pi\)
0.681265 + 0.732037i \(0.261430\pi\)
\(710\) −4.94543e6 + 1.08290e7i −0.368178 + 0.806198i
\(711\) 149685. + 1.04108e6i 0.0111046 + 0.0772344i
\(712\) 479800. 0.0354699
\(713\) 247957. 1.55931e7i 0.0182664 1.14870i
\(714\) −155776. −0.0114355
\(715\) 5.17163e6 + 3.59695e7i 0.378322 + 2.63129i
\(716\) −6.78615e6 + 1.48596e7i −0.494699 + 1.08324i
\(717\) 4.41210e6 1.29551e6i 0.320514 0.0941114i
\(718\) 1.62953e7 1.88058e7i 1.17965 1.36139i
\(719\) 1.83449e7 + 5.38655e6i 1.32341 + 0.388587i 0.865721 0.500526i \(-0.166860\pi\)
0.457686 + 0.889114i \(0.348678\pi\)
\(720\) −1.92886e6 + 1.23960e6i −0.138666 + 0.0891151i
\(721\) 283176. + 620070.i 0.0202870 + 0.0444224i
\(722\) 1.25733e7 + 1.45103e7i 0.897646 + 1.03594i
\(723\) −675587. 434174.i −0.0480657 0.0308900i
\(724\) −1.24581e6 + 8.66481e6i −0.0883295 + 0.614345i
\(725\) 3.92115e6 2.72722e7i 0.277057 1.92697i
\(726\) −5.10432e6 3.28035e6i −0.359415 0.230982i
\(727\) 6.78329e6 + 7.82833e6i 0.475997 + 0.549330i 0.942070 0.335417i \(-0.108877\pi\)
−0.466073 + 0.884746i \(0.654332\pi\)
\(728\) −9971.81 21835.2i −0.000697342 0.00152697i
\(729\) 1.05094e7 6.75400e6i 0.732420 0.470698i
\(730\) −4.83423e6 1.41946e6i −0.335753 0.0985860i
\(731\) 1.25159e6 1.44442e6i 0.0866303 0.0999767i
\(732\) 2.73957e7 8.04412e6i 1.88975 0.554882i
\(733\) −9.42910e6 + 2.06468e7i −0.648202 + 1.41936i 0.244917 + 0.969544i \(0.421239\pi\)
−0.893119 + 0.449820i \(0.851488\pi\)
\(734\) −219143. 1.52417e6i −0.0150137 0.104423i
\(735\) 2.30669e7 1.57496
\(736\) 5.50080e6 + 1.98991e7i 0.374310 + 1.35406i
\(737\) −1.47642e7 −1.00124
\(738\) −368405. 2.56231e6i −0.0248992 0.173177i
\(739\) 3.38997e6 7.42299e6i 0.228341 0.499997i −0.760433 0.649417i \(-0.775013\pi\)
0.988774 + 0.149419i \(0.0477404\pi\)
\(740\) 1.19575e7 3.51104e6i 0.802716 0.235699i
\(741\) −2.53777e6 + 2.92875e6i −0.169788 + 0.195946i
\(742\) −678676. 199277.i −0.0452536 0.0132877i
\(743\) 3.23062e6 2.07619e6i 0.214691 0.137973i −0.428876 0.903363i \(-0.641090\pi\)
0.643567 + 0.765390i \(0.277454\pi\)
\(744\) −256946. 562632.i −0.0170180 0.0372642i
\(745\) −1.95960e7 2.26150e7i −1.29353 1.49282i
\(746\) 1.74759e6 + 1.12311e6i 0.114972 + 0.0738881i
\(747\) −132283. + 920047.i −0.00867365 + 0.0603265i
\(748\) 588457. 4.09281e6i 0.0384557 0.267465i
\(749\) −92683.0 59563.7i −0.00603664 0.00387951i
\(750\) 5.46033e6 + 6.30156e6i 0.354459 + 0.409067i
\(751\) 8.58124e6 + 1.87903e7i 0.555201 + 1.21572i 0.954310 + 0.298817i \(0.0965920\pi\)
−0.399110 + 0.916903i \(0.630681\pi\)
\(752\) −1.02769e7 + 6.60459e6i −0.662704 + 0.425894i
\(753\) 1.33143e6 + 390943.i 0.0855719 + 0.0251262i
\(754\) −3.51442e7 + 4.05585e7i −2.25126 + 2.59809i
\(755\) 3.71179e6 1.08988e6i 0.236982 0.0695842i
\(756\) −189653. + 415282.i −0.0120685 + 0.0264264i
\(757\) −3.13439e6 2.18002e7i −0.198799 1.38268i −0.807776 0.589489i \(-0.799329\pi\)
0.608977 0.793188i \(-0.291580\pi\)
\(758\) −1.85423e7 −1.17217
\(759\) −9.99641e6 1.61123e7i −0.629853 1.01521i
\(760\) −127399. −0.00800077
\(761\) −92105.5 640608.i −0.00576533 0.0400987i 0.986736 0.162335i \(-0.0519025\pi\)
−0.992501 + 0.122236i \(0.960993\pi\)
\(762\) 4.35811e6 9.54293e6i 0.271901 0.595380i
\(763\) −16786.8 + 4929.05i −0.00104390 + 0.000306515i
\(764\) −1.95810e7 + 2.25977e7i −1.21367 + 1.40065i
\(765\) 610031. + 179121.i 0.0376876 + 0.0110661i
\(766\) −3.35312e7 + 2.15492e7i −2.06480 + 1.32696i
\(767\) 1.50972e7 + 3.30582e7i 0.926631 + 2.02904i
\(768\) 1.17881e7 + 1.36042e7i 0.721175 + 0.832281i
\(769\) 1.42719e7 + 9.17199e6i 0.870294 + 0.559304i 0.897843 0.440317i \(-0.145134\pi\)
−0.0275489 + 0.999620i \(0.508770\pi\)
\(770\) 177410. 1.23391e6i 0.0107833 0.0749995i
\(771\) 1.28084e6 8.90845e6i 0.0775996 0.539717i
\(772\) −4.53310e6 2.91324e6i −0.273748 0.175927i
\(773\) 1.23750e7 + 1.42815e7i 0.744895 + 0.859655i 0.994063 0.108806i \(-0.0347026\pi\)
−0.249168 + 0.968460i \(0.580157\pi\)
\(774\) 567459. + 1.24256e6i 0.0340472 + 0.0745531i
\(775\) −2.01071e7 + 1.29221e7i −1.20253 + 0.772819i
\(776\) −911460. 267629.i −0.0543354 0.0159543i
\(777\) 210351. 242758.i 0.0124995 0.0144252i
\(778\) 3.74525e7 1.09971e7i 2.21836 0.651370i
\(779\) 1.28403e6 2.81162e6i 0.0758106 0.166002i
\(780\) −5.81539e6 4.04469e7i −0.342249 2.38039i
\(781\) −8.14481e6 −0.477808
\(782\) 3.24773e6 4.88115e6i 0.189917 0.285434i
\(783\) −2.52114e7 −1.46958
\(784\) −2.50439e6 1.74184e7i −0.145516 1.01209i
\(785\) −1.93664e6 + 4.24065e6i −0.112169 + 0.245617i
\(786\) −2.98195e7 + 8.75579e6i −1.72165 + 0.505521i
\(787\) −9.00060e6 + 1.03873e7i −0.518006 + 0.597811i −0.953131 0.302559i \(-0.902159\pi\)
0.435124 + 0.900370i \(0.356704\pi\)
\(788\) 5.15226e6 + 1.51284e6i 0.295585 + 0.0867916i
\(789\) −1.37640e7 + 8.84556e6i −0.787138 + 0.505863i
\(790\) −1.11381e7 2.43891e7i −0.634956 1.39036i
\(791\) 366904. + 423430.i 0.0208502 + 0.0240625i
\(792\) −61409.5 39465.5i −0.00347875 0.00223566i
\(793\) 7.55446e6 5.25425e7i 0.426600 2.96707i
\(794\) 8494.74 59082.2i 0.000478188 0.00332587i
\(795\) 2.50203e7 + 1.60795e7i 1.40402 + 0.902310i
\(796\) −1.75324e7 2.02334e7i −0.980749 1.13184i
\(797\) 5.75233e6 + 1.25958e7i 0.320773 + 0.702395i 0.999488 0.0320069i \(-0.0101898\pi\)
−0.678714 + 0.734402i \(0.737463\pi\)
\(798\) 111836. 71872.7i 0.00621691 0.00399537i
\(799\) 3.25024e6 + 954357.i 0.180115 + 0.0528864i
\(800\) 2.07210e7 2.39133e7i 1.14468 1.32103i
\(801\) 1.96065e6 575699.i 0.107974 0.0317040i
\(802\) 1.32580e7 2.90310e7i 0.727851 1.59377i
\(803\) −490563. 3.41194e6i −0.0268476 0.186729i
\(804\) 1.66020e7 0.905775
\(805\) 483597. 726817.i 0.0263023 0.0395308i
\(806\) 4.65548e7 2.52422
\(807\) 3.12881e6 + 2.17613e7i 0.169120 + 1.17626i
\(808\) 286317. 626947.i 0.0154283 0.0337834i
\(809\) −9.97746e6 + 2.92965e6i −0.535980 + 0.157378i −0.538510 0.842619i \(-0.681013\pi\)
0.00253030 + 0.999997i \(0.499195\pi\)
\(810\) 2.82206e7 3.25684e7i 1.51131 1.74415i
\(811\) 7.75727e6 + 2.27774e6i 0.414149 + 0.121605i 0.482168 0.876079i \(-0.339850\pi\)
−0.0680185 + 0.997684i \(0.521668\pi\)
\(812\) 764930. 491591.i 0.0407129 0.0261646i
\(813\) 738703. + 1.61753e6i 0.0391961 + 0.0858276i
\(814\) 1.13049e7 + 1.30466e7i 0.598008 + 0.690139i
\(815\) −2.28510e7 1.46855e7i −1.20507 0.774450i
\(816\) 711145. 4.94612e6i 0.0373880 0.260039i
\(817\) −232123. + 1.61445e6i −0.0121664 + 0.0846194i
\(818\) −1.79268e7 1.15208e7i −0.936740 0.602006i
\(819\) −66948.2 77262.4i −0.00348762 0.00402493i
\(820\) 1.35394e7 + 2.96471e7i 0.703176 + 1.53974i
\(821\) 1.13365e7 7.28555e6i 0.586979 0.377229i −0.213183 0.977012i \(-0.568383\pi\)
0.800162 + 0.599784i \(0.204747\pi\)
\(822\) 530687. + 155824.i 0.0273942 + 0.00804366i
\(823\) −1.50492e7 + 1.73678e7i −0.774489 + 0.893808i −0.996699 0.0811911i \(-0.974128\pi\)
0.222210 + 0.974999i \(0.428673\pi\)
\(824\) −976335. + 286678.i −0.0500935 + 0.0147088i
\(825\) −1.20723e7 + 2.64347e7i −0.617526 + 1.35219i
\(826\) −177425. 1.23402e6i −0.00904824 0.0629319i
\(827\) −1.39765e7 −0.710616 −0.355308 0.934749i \(-0.615624\pi\)
−0.355308 + 0.934749i \(0.615624\pi\)
\(828\) 1.09109e6 + 1.75864e6i 0.0553076 + 0.0891456i
\(829\) 3.05110e6 0.154195 0.0770975 0.997024i \(-0.475435\pi\)
0.0770975 + 0.997024i \(0.475435\pi\)
\(830\) −3.37213e6 2.34537e7i −0.169906 1.18172i
\(831\) −4.80248e6 + 1.05160e7i −0.241248 + 0.528259i
\(832\) −2.84849e7 + 8.36391e6i −1.42661 + 0.418891i
\(833\) −3.19549e6 + 3.68779e6i −0.159560 + 0.184142i
\(834\) −8.84665e6 2.59761e6i −0.440417 0.129318i
\(835\) 6.56003e6 4.21588e6i 0.325604 0.209253i
\(836\) 1.46589e6 + 3.20984e6i 0.0725411 + 0.158843i
\(837\) 1.43221e7 + 1.65285e7i 0.706629 + 0.815494i
\(838\) −8.32123e6 5.34773e6i −0.409334 0.263063i
\(839\) 4.34715e6 3.02351e7i 0.213206 1.48288i −0.549150 0.835724i \(-0.685048\pi\)
0.762356 0.647158i \(-0.224043\pi\)
\(840\) 4927.62 34272.3i 0.000240957 0.00167589i
\(841\) 2.49866e7 + 1.60579e7i 1.21820 + 0.782888i
\(842\) 2.30949e7 + 2.66530e7i 1.12263 + 1.29558i
\(843\) −7.04880e6 1.54347e7i −0.341623 0.748049i
\(844\) 5.93972e6 3.81723e6i 0.287019 0.184456i
\(845\) −4.30580e7 1.26430e7i −2.07449 0.609126i
\(846\) −1.58548e6 + 1.82974e6i −0.0761613 + 0.0878949i
\(847\) 183381. 53845.6i 0.00878307 0.00257894i
\(848\) 9.42562e6 2.06392e7i 0.450112 0.985607i
\(849\) 2.67853e6 + 1.86296e7i 0.127534 + 0.887021i
\(850\) −8.98562e6 −0.426580
\(851\) 3.22112e6 + 1.16524e7i 0.152470 + 0.551559i
\(852\) 9.15867e6 0.432248
\(853\) 4.86269e6 + 3.38207e7i 0.228825 + 1.59151i 0.703070 + 0.711121i \(0.251812\pi\)
−0.474244 + 0.880393i \(0.657279\pi\)
\(854\) −756461. + 1.65642e6i −0.0354930 + 0.0777187i
\(855\) −520602. + 152863.i −0.0243551 + 0.00715131i
\(856\) 107697. 124289.i 0.00502366 0.00579761i
\(857\) −1.39089e7 4.08403e6i −0.646906 0.189949i −0.0582114 0.998304i \(-0.518540\pi\)
−0.588695 + 0.808356i \(0.700358\pi\)
\(858\) 4.76185e7 3.06025e7i 2.20830 1.41919i
\(859\) −8.22390e6 1.80078e7i −0.380273 0.832681i −0.998895 0.0469928i \(-0.985036\pi\)
0.618623 0.785688i \(-0.287691\pi\)
\(860\) −1.12627e7 1.29978e7i −0.519273 0.599273i
\(861\) 706707. + 454173.i 0.0324886 + 0.0208792i
\(862\) −7.08974e6 + 4.93102e7i −0.324984 + 2.26031i
\(863\) 3.24974e6 2.26024e7i 0.148532 1.03307i −0.770092 0.637933i \(-0.779790\pi\)
0.918624 0.395132i \(-0.129301\pi\)
\(864\) −2.43568e7 1.56532e7i −1.11003 0.713376i
\(865\) −2.87237e7 3.31489e7i −1.30527 1.50636i
\(866\) 5.17873e6 + 1.13398e7i 0.234655 + 0.513822i
\(867\) 1.84294e7 1.18439e7i 0.832652 0.535113i
\(868\) −756826. 222224.i −0.0340955 0.0100113i
\(869\) 1.20126e7 1.38633e7i 0.539620 0.622755i
\(870\) −7.42748e7 + 2.18090e7i −3.32693 + 0.976874i
\(871\) 1.28220e7 2.80762e7i 0.572677 1.25399i
\(872\) −3716.71 25850.3i −0.000165527 0.00115126i
\(873\) −4.04570e6 −0.179663
\(874\) −79552.6 + 5.00276e6i −0.00352270 + 0.221529i
\(875\) −262647. −0.0115972
\(876\) 551628. + 3.83666e6i 0.0242877 + 0.168925i
\(877\) 337709. 739479.i 0.0148267 0.0324659i −0.902074 0.431582i \(-0.857956\pi\)
0.916900 + 0.399116i \(0.130683\pi\)
\(878\) 2.59304e7 7.61386e6i 1.13520 0.333325i
\(879\) −637995. + 736286.i −0.0278513 + 0.0321421i
\(880\) 3.83687e7 + 1.12661e7i 1.67021 + 0.490417i
\(881\) −1.96313e7 + 1.26163e7i −0.852137 + 0.547635i −0.892241 0.451560i \(-0.850868\pi\)
0.0401038 + 0.999196i \(0.487231\pi\)
\(882\) −1.44880e6 3.17243e6i −0.0627100 0.137316i
\(883\) −7.89214e6 9.10802e6i −0.340638 0.393117i 0.559422 0.828883i \(-0.311023\pi\)
−0.900060 + 0.435766i \(0.856478\pi\)
\(884\) 7.27202e6 + 4.67344e6i 0.312986 + 0.201144i
\(885\) −7.46033e6 + 5.18877e7i −0.320184 + 2.22693i
\(886\) −4.61363e6 + 3.20885e7i −0.197450 + 1.37330i
\(887\) 2.67916e7 + 1.72179e7i 1.14338 + 0.734804i 0.968310 0.249753i \(-0.0803493\pi\)
0.175067 + 0.984556i \(0.443986\pi\)
\(888\) 313998. + 362373.i 0.0133627 + 0.0154214i
\(889\) 137278. + 300597.i 0.00582567 + 0.0127564i
\(890\) −4.38215e7 + 2.81623e7i −1.85444 + 1.19177i
\(891\) 2.82891e7 + 8.30643e6i 1.19378 + 0.350526i
\(892\) 1.82269e7 2.10349e7i 0.767008 0.885174i
\(893\) −2.77376e6 + 814450.i −0.116397 + 0.0341772i
\(894\) −1.93630e7 + 4.23991e7i −0.810268 + 1.77424i
\(895\) 6.23446e6 + 4.33616e7i 0.260160 + 1.80946i
\(896\) −51600.7 −0.00214726
\(897\) 3.93214e7 5.01681e6i 1.63173 0.208184i
\(898\) −9.61987e6 −0.398087
\(899\) −6.19904e6 4.31153e7i −0.255814 1.77923i
\(900\) 1.31767e6 2.88530e6i 0.0542251 0.118737i
\(901\) −6.03679e6 + 1.77256e6i −0.247739 + 0.0727427i
\(902\) −2.95655e7 + 3.41204e7i −1.20995 + 1.39636i
\(903\) −425335. 124890.i −0.0173585 0.00509691i
\(904\) −703579. + 452163.i −0.0286346 + 0.0184024i
\(905\) 9.75195e6 + 2.13538e7i 0.395795 + 0.866670i
\(906\) −3.94604e6 4.55398e6i −0.159713 0.184319i
\(907\) −1.48839e7 9.56533e6i −0.600758 0.386084i 0.204623 0.978841i \(-0.434403\pi\)
−0.805381 + 0.592757i \(0.798039\pi\)
\(908\) −2.31940e6 + 1.61318e7i −0.0933601 + 0.649334i
\(909\) 417748. 2.90550e6i 0.0167689 0.116630i
\(910\) 2.19240e6 + 1.40897e6i 0.0877638 + 0.0564024i
\(911\) −2.15559e7 2.48768e7i −0.860538 0.993114i −0.999996 0.00288591i \(-0.999081\pi\)
0.139458 0.990228i \(-0.455464\pi\)
\(912\) 1.77151e6 + 3.87907e6i 0.0705272 + 0.154433i
\(913\) 1.36377e7 8.76442e6i 0.541457 0.347973i
\(914\) −4.21096e7 1.23645e7i −1.66731 0.489566i
\(915\) 5.01415e7 5.78664e7i 1.97991 2.28493i
\(916\) −3.34340e6 + 981710.i −0.131659 + 0.0386585i
\(917\) 406671. 890485.i 0.0159705 0.0349706i
\(918\) 1.17012e6 + 8.13838e6i 0.0458273 + 0.318736i
\(919\) 2.83341e7 1.10668 0.553338 0.832957i \(-0.313354\pi\)
0.553338 + 0.832957i \(0.313354\pi\)
\(920\) 971168. + 868938.i 0.0378290 + 0.0338469i
\(921\) −8.47848e6 −0.329359
\(922\) −7.38782e6 5.13834e7i −0.286213 1.99065i
\(923\) 7.07338e6 1.54885e7i 0.273289 0.598420i
\(924\) −920197. + 270194.i −0.0354569 + 0.0104111i
\(925\) 1.21336e7 1.40030e7i 0.466269 0.538104i
\(926\) −1.37587e7 4.03993e6i −0.527292 0.154827i
\(927\) −3.64571e6 + 2.34296e6i −0.139342 + 0.0895499i
\(928\) 2.39549e7 + 5.24539e7i 0.913112 + 1.99944i
\(929\) 5.90126e6 + 6.81042e6i 0.224339 + 0.258901i 0.856750 0.515732i \(-0.172480\pi\)
−0.632411 + 0.774633i \(0.717934\pi\)
\(930\) 5.64919e7 + 3.63051e7i 2.14180 + 1.37645i
\(931\) 592642. 4.12191e6i 0.0224088 0.155856i
\(932\) 759155. 5.28004e6i 0.0286280 0.199112i
\(933\) −3.27921e7 2.10742e7i −1.23329 0.792587i
\(934\) −1.07279e7 1.23807e7i −0.402391 0.464384i
\(935\) −4.60632e6 1.00864e7i −0.172316 0.377319i
\(936\) 128381. 82505.3i 0.00478972 0.00307817i
\(937\) 4.69627e7 + 1.37895e7i 1.74745 + 0.513096i 0.990154 0.139981i \(-0.0447041\pi\)
0.757291 + 0.653077i \(0.226522\pi\)
\(938\) −693382. + 800206.i −0.0257315 + 0.0296958i
\(939\) −9.71934e6 + 2.85385e6i −0.359727 + 0.105625i
\(940\) 1.26629e7 2.77280e7i 0.467428 1.02353i
\(941\) −1.77055e6 1.23145e7i −0.0651831 0.453358i −0.996108 0.0881464i \(-0.971906\pi\)
0.930924 0.365212i \(-0.119003\pi\)
\(942\) 7.26170e6 0.266631
\(943\) −2.89652e7 + 1.26753e7i −1.06071 + 0.464172i
\(944\) 3.99918e7 1.46063
\(945\) 174235. + 1.21183e6i 0.00634680 + 0.0441430i
\(946\) 9.89681e6 2.16710e7i 0.359557 0.787320i
\(947\) −1.04335e6 + 306354.i −0.0378054 + 0.0111007i −0.300581 0.953756i \(-0.597180\pi\)
0.262775 + 0.964857i \(0.415362\pi\)
\(948\) −1.35079e7 + 1.55890e7i −0.488167 + 0.563375i
\(949\) 6.91433e6 + 2.03023e6i 0.249221 + 0.0731779i
\(950\) 6.45102e6 4.14582e6i 0.231910 0.149040i
\(951\) −9.01407e6 1.97381e7i −0.323199 0.707707i
\(952\) 4796.62 + 5535.59i 0.000171531 + 0.000197957i
\(953\) 1.42920e7 + 9.18494e6i 0.509756 + 0.327600i 0.770108 0.637914i \(-0.220202\pi\)
−0.260352 + 0.965514i \(0.583839\pi\)
\(954\) 639959. 4.45101e6i 0.0227657 0.158339i
\(955\) −1.14115e7 + 7.93689e7i −0.404888 + 2.81606i
\(956\) 7.36390e6 + 4.73249e6i 0.260593 + 0.167473i
\(957\) −3.46823e7 4.00255e7i −1.22413 1.41272i
\(958\) −2.31008e7 5.05837e7i −0.813230 1.78072i
\(959\) −14656.4 + 9419.07i −0.000514611 + 0.000330721i
\(960\) −4.10875e7 1.20644e7i −1.43890 0.422500i
\(961\) −5.99662e6 + 6.92047e6i −0.209459 + 0.241728i
\(962\) −3.46278e7 + 1.01676e7i −1.20639 + 0.354228i
\(963\) 290962. 637118.i 0.0101104 0.0221388i
\(964\) −217562. 1.51318e6i −0.00754033 0.0524441i
\(965\) −1.44502e7 −0.499525
\(966\) −1.34275e6 214901.i −0.0462968 0.00740962i
\(967\) 7.34745e6 0.252680 0.126340 0.991987i \(-0.459677\pi\)
0.126340 + 0.991987i \(0.459677\pi\)
\(968\) 40601.9 + 282392.i 0.00139270 + 0.00968644i
\(969\) 491225. 1.07563e6i 0.0168063 0.0368006i
\(970\) 9.89550e7 2.90558e7i 3.37682 0.991525i
\(971\) −3.49210e6 + 4.03010e6i −0.118861 + 0.137173i −0.812061 0.583572i \(-0.801655\pi\)
0.693201 + 0.720745i \(0.256200\pi\)
\(972\) −5.90510e6 1.73389e6i −0.200476 0.0588650i
\(973\) 244324. 157018.i 0.00827341 0.00531700i
\(974\) −1.82259e7 3.99091e7i −0.615589 1.34795i
\(975\) −3.97851e7 4.59145e7i −1.34032 1.54681i
\(976\) −4.91403e7 3.15806e7i −1.65125 1.06120i
\(977\) −7.02121e6 + 4.88336e7i −0.235329 + 1.63675i 0.439120 + 0.898429i \(0.355290\pi\)
−0.674449 + 0.738322i \(0.735619\pi\)
\(978\) −6.02144e6 + 4.18800e7i −0.201304 + 1.40010i
\(979\) −2.99810e7 1.92676e7i −0.999746 0.642498i
\(980\) 2.87552e7 + 3.31852e7i 0.956425 + 1.10377i
\(981\) −46205.1 101175.i −0.00153291 0.00335661i
\(982\) −6.04353e6 + 3.88394e6i −0.199992 + 0.128527i
\(983\) 1.67169e7 + 4.90852e6i 0.551787 + 0.162019i 0.545728 0.837962i \(-0.316253\pi\)
0.00605910 + 0.999982i \(0.498071\pi\)
\(984\) −821191. + 947705.i −0.0270369 + 0.0312022i
\(985\) 1.38167e7 4.05696e6i 0.453748 0.133232i
\(986\) 6.80270e6 1.48958e7i 0.222838 0.487947i
\(987\) −111815. 777688.i −0.00365347 0.0254105i
\(988\) −7.37703e6 −0.240430
\(989\) 1.27810e7 1.07238e7i 0.415504 0.348625i
\(990\) 7.92518e6 0.256993
\(991\) 6.13127e6 + 4.26439e7i 0.198320 + 1.37934i 0.809159 + 0.587590i \(0.199923\pi\)
−0.610839 + 0.791755i \(0.709168\pi\)
\(992\) 2.07804e7 4.55027e7i 0.670462 1.46811i
\(993\) 2.30417e7 6.76566e6i 0.741552 0.217739i
\(994\) −382512. + 441442.i −0.0122794 + 0.0141712i
\(995\) −6.88875e7 2.02272e7i −2.20588 0.647706i
\(996\) −1.53353e7 + 9.85540e6i −0.489829 + 0.314794i
\(997\) −1.33623e7 2.92593e7i −0.425738 0.932235i −0.993999 0.109387i \(-0.965111\pi\)
0.568262 0.822848i \(-0.307616\pi\)
\(998\) 3.22315e7 + 3.71971e7i 1.02436 + 1.18218i
\(999\) −1.42627e7 9.16609e6i −0.452156 0.290583i
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 23.6.c.a.3.2 90
23.8 even 11 inner 23.6.c.a.8.2 yes 90
23.10 odd 22 529.6.a.k.1.37 45
23.13 even 11 529.6.a.j.1.37 45
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
23.6.c.a.3.2 90 1.1 even 1 trivial
23.6.c.a.8.2 yes 90 23.8 even 11 inner
529.6.a.j.1.37 45 23.13 even 11
529.6.a.k.1.37 45 23.10 odd 22