Properties

Label 74.3.g.b.23.3
Level $74$
Weight $3$
Character 74.23
Analytic conductor $2.016$
Analytic rank $0$
Dimension $12$
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] = [74,3,Mod(23,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.23");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 74.g (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.01635395627\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(3\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 82x^{10} + 2505x^{8} + 34456x^{6} + 196096x^{4} + 262464x^{2} + 69696 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 23.3
Root \(5.23421i\) of defining polynomial
Character \(\chi\) \(=\) 74.23
Dual form 74.3.g.b.29.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.366025 + 1.36603i) q^{2} +(4.53296 - 2.61711i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-0.866025 + 3.23205i) q^{5} +(5.23421 + 5.23421i) q^{6} +(-0.548432 - 0.949912i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(9.19850 - 15.9323i) q^{9} +O(q^{10})\) \(q+(0.366025 + 1.36603i) q^{2} +(4.53296 - 2.61711i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-0.866025 + 3.23205i) q^{5} +(5.23421 + 5.23421i) q^{6} +(-0.548432 - 0.949912i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(9.19850 - 15.9323i) q^{9} -4.73205 q^{10} -7.96906i q^{11} +(-5.23421 + 9.06593i) q^{12} +(-5.69692 + 21.2612i) q^{13} +(1.09686 - 1.09686i) q^{14} +(4.53296 + 16.9172i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-27.3687 + 7.33343i) q^{17} +(25.1308 + 6.73377i) q^{18} +(5.66649 - 21.1476i) q^{19} +(-1.73205 - 6.46410i) q^{20} +(-4.97204 - 2.87061i) q^{21} +(10.8859 - 2.91688i) q^{22} +(-11.3461 - 11.3461i) q^{23} +(-14.3001 - 3.83171i) q^{24} +(11.9545 + 6.90192i) q^{25} -31.1285 q^{26} -49.1859i q^{27} +(1.89982 + 1.09686i) q^{28} +(6.59322 - 6.59322i) q^{29} +(-21.4502 + 12.3843i) q^{30} +(-17.7384 + 17.7384i) q^{31} +(5.46410 + 1.46410i) q^{32} +(-20.8559 - 36.1235i) q^{33} +(-20.0353 - 34.7022i) q^{34} +(3.54512 - 0.949912i) q^{35} +36.7940i q^{36} +(-5.38912 - 36.6054i) q^{37} +30.9623 q^{38} +(29.8189 + 111.286i) q^{39} +(8.19615 - 4.73205i) q^{40} +(-10.5120 + 6.06911i) q^{41} +(2.10143 - 7.84266i) q^{42} +(49.1668 + 49.1668i) q^{43} +(7.96906 + 13.8028i) q^{44} +(43.5278 + 43.5278i) q^{45} +(11.3461 - 19.6520i) q^{46} +37.1317 q^{47} -20.9369i q^{48} +(23.8984 - 41.3933i) q^{49} +(-5.05256 + 18.8564i) q^{50} +(-104.869 + 104.869i) q^{51} +(-11.3938 - 42.5224i) q^{52} +(-6.36524 + 11.0249i) q^{53} +(67.1892 - 18.0033i) q^{54} +(25.7564 + 6.90141i) q^{55} +(-0.802960 + 2.99669i) q^{56} +(-29.6596 - 110.691i) q^{57} +(11.4198 + 6.59322i) q^{58} +(-50.8363 + 13.6216i) q^{59} +(-24.7686 - 24.7686i) q^{60} +(105.650 + 28.3088i) q^{61} +(-30.7238 - 17.7384i) q^{62} -20.1790 q^{63} +8.00000i q^{64} +(-63.7836 - 36.8255i) q^{65} +(41.7118 - 41.7118i) q^{66} +(51.2985 - 29.6172i) q^{67} +(40.0706 - 40.0706i) q^{68} +(-81.1253 - 21.7375i) q^{69} +(2.59521 + 4.49503i) q^{70} +(27.3533 + 47.3773i) q^{71} +(-50.2616 + 13.4675i) q^{72} +61.1000i q^{73} +(48.0314 - 20.7602i) q^{74} +72.2523 q^{75} +(11.3330 + 42.2953i) q^{76} +(-7.56991 + 4.37049i) q^{77} +(-141.105 + 81.4667i) q^{78} +(28.3909 - 105.956i) q^{79} +(9.46410 + 9.46410i) q^{80} +(-45.9384 - 79.5676i) q^{81} +(-12.1382 - 12.1382i) q^{82} +(-54.2776 + 94.0115i) q^{83} +11.4824 q^{84} -94.8081i q^{85} +(-49.1668 + 85.1595i) q^{86} +(12.6317 - 47.1420i) q^{87} +(-15.9381 + 15.9381i) q^{88} +(6.28409 + 23.4525i) q^{89} +(-43.5278 + 75.3923i) q^{90} +(23.3206 - 6.24875i) q^{91} +(30.9981 + 8.30591i) q^{92} +(-33.9842 + 126.831i) q^{93} +(13.5911 + 50.7228i) q^{94} +(63.4429 + 36.6288i) q^{95} +(28.6003 - 7.66342i) q^{96} +(-41.9263 - 41.9263i) q^{97} +(65.2918 + 17.4949i) q^{98} +(-126.965 - 73.3034i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 6 q^{2} + 4 q^{6} - 8 q^{7} - 24 q^{8} + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 6 q^{2} + 4 q^{6} - 8 q^{7} - 24 q^{8} + 28 q^{9} - 36 q^{10} - 4 q^{12} + 16 q^{13} + 16 q^{14} + 24 q^{16} + 40 q^{17} + 28 q^{18} - 26 q^{19} + 66 q^{21} + 4 q^{22} - 80 q^{23} - 4 q^{24} - 54 q^{25} - 124 q^{26} - 12 q^{28} + 16 q^{29} - 6 q^{30} - 32 q^{31} + 24 q^{32} - 20 q^{33} - 10 q^{34} + 12 q^{35} - 148 q^{37} + 92 q^{38} + 216 q^{39} + 36 q^{40} + 66 q^{41} - 46 q^{42} + 152 q^{43} - 16 q^{44} + 84 q^{45} + 80 q^{46} - 112 q^{47} - 160 q^{49} + 168 q^{50} - 446 q^{51} + 32 q^{52} + 74 q^{53} + 230 q^{54} + 28 q^{56} + 50 q^{57} + 84 q^{58} - 114 q^{59} - 12 q^{60} + 448 q^{61} - 204 q^{62} - 784 q^{63} - 138 q^{65} + 40 q^{66} + 468 q^{67} + 20 q^{68} - 278 q^{69} + 18 q^{70} + 116 q^{71} - 56 q^{72} - 2 q^{74} + 76 q^{75} - 52 q^{76} + 60 q^{77} - 366 q^{78} + 114 q^{79} + 72 q^{80} + 14 q^{81} + 128 q^{82} - 20 q^{83} - 80 q^{84} - 152 q^{86} + 770 q^{87} + 32 q^{88} + 340 q^{89} - 84 q^{90} + 792 q^{91} + 68 q^{92} - 498 q^{93} + 20 q^{94} + 60 q^{95} + 8 q^{96} - 356 q^{97} - 160 q^{98} - 348 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{5}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.366025 + 1.36603i 0.183013 + 0.683013i
\(3\) 4.53296 2.61711i 1.51099 0.872369i 0.511070 0.859539i \(-0.329249\pi\)
0.999918 0.0128300i \(-0.00408404\pi\)
\(4\) −1.73205 + 1.00000i −0.433013 + 0.250000i
\(5\) −0.866025 + 3.23205i −0.173205 + 0.646410i 0.823645 + 0.567105i \(0.191937\pi\)
−0.996850 + 0.0793049i \(0.974730\pi\)
\(6\) 5.23421 + 5.23421i 0.872369 + 0.872369i
\(7\) −0.548432 0.949912i −0.0783474 0.135702i 0.824190 0.566314i \(-0.191631\pi\)
−0.902537 + 0.430612i \(0.858298\pi\)
\(8\) −2.00000 2.00000i −0.250000 0.250000i
\(9\) 9.19850 15.9323i 1.02206 1.77025i
\(10\) −4.73205 −0.473205
\(11\) 7.96906i 0.724460i −0.932089 0.362230i \(-0.882015\pi\)
0.932089 0.362230i \(-0.117985\pi\)
\(12\) −5.23421 + 9.06593i −0.436185 + 0.755494i
\(13\) −5.69692 + 21.2612i −0.438224 + 1.63548i 0.295006 + 0.955496i \(0.404678\pi\)
−0.733230 + 0.679981i \(0.761988\pi\)
\(14\) 1.09686 1.09686i 0.0783474 0.0783474i
\(15\) 4.53296 + 16.9172i 0.302198 + 1.12782i
\(16\) 2.00000 3.46410i 0.125000 0.216506i
\(17\) −27.3687 + 7.33343i −1.60993 + 0.431378i −0.948021 0.318209i \(-0.896919\pi\)
−0.661905 + 0.749587i \(0.730252\pi\)
\(18\) 25.1308 + 6.73377i 1.39615 + 0.374098i
\(19\) 5.66649 21.1476i 0.298237 1.11303i −0.640376 0.768061i \(-0.721222\pi\)
0.938613 0.344973i \(-0.112112\pi\)
\(20\) −1.73205 6.46410i −0.0866025 0.323205i
\(21\) −4.97204 2.87061i −0.236764 0.136696i
\(22\) 10.8859 2.91688i 0.494816 0.132585i
\(23\) −11.3461 11.3461i −0.493308 0.493308i 0.416039 0.909347i \(-0.363418\pi\)
−0.909347 + 0.416039i \(0.863418\pi\)
\(24\) −14.3001 3.83171i −0.595839 0.159655i
\(25\) 11.9545 + 6.90192i 0.478179 + 0.276077i
\(26\) −31.1285 −1.19725
\(27\) 49.1859i 1.82170i
\(28\) 1.89982 + 1.09686i 0.0678509 + 0.0391737i
\(29\) 6.59322 6.59322i 0.227352 0.227352i −0.584233 0.811586i \(-0.698605\pi\)
0.811586 + 0.584233i \(0.198605\pi\)
\(30\) −21.4502 + 12.3843i −0.715007 + 0.412810i
\(31\) −17.7384 + 17.7384i −0.572206 + 0.572206i −0.932744 0.360538i \(-0.882593\pi\)
0.360538 + 0.932744i \(0.382593\pi\)
\(32\) 5.46410 + 1.46410i 0.170753 + 0.0457532i
\(33\) −20.8559 36.1235i −0.631997 1.09465i
\(34\) −20.0353 34.7022i −0.589274 1.02065i
\(35\) 3.54512 0.949912i 0.101289 0.0271403i
\(36\) 36.7940i 1.02206i
\(37\) −5.38912 36.6054i −0.145652 0.989336i
\(38\) 30.9623 0.814797
\(39\) 29.8189 + 111.286i 0.764587 + 2.85348i
\(40\) 8.19615 4.73205i 0.204904 0.118301i
\(41\) −10.5120 + 6.06911i −0.256391 + 0.148027i −0.622687 0.782471i \(-0.713959\pi\)
0.366296 + 0.930498i \(0.380626\pi\)
\(42\) 2.10143 7.84266i 0.0500341 0.186730i
\(43\) 49.1668 + 49.1668i 1.14341 + 1.14341i 0.987821 + 0.155594i \(0.0497291\pi\)
0.155594 + 0.987821i \(0.450271\pi\)
\(44\) 7.96906 + 13.8028i 0.181115 + 0.313700i
\(45\) 43.5278 + 43.5278i 0.967284 + 0.967284i
\(46\) 11.3461 19.6520i 0.246654 0.427217i
\(47\) 37.1317 0.790036 0.395018 0.918673i \(-0.370738\pi\)
0.395018 + 0.918673i \(0.370738\pi\)
\(48\) 20.9369i 0.436185i
\(49\) 23.8984 41.3933i 0.487723 0.844762i
\(50\) −5.05256 + 18.8564i −0.101051 + 0.377128i
\(51\) −104.869 + 104.869i −2.05626 + 2.05626i
\(52\) −11.3938 42.5224i −0.219112 0.817738i
\(53\) −6.36524 + 11.0249i −0.120099 + 0.208017i −0.919806 0.392372i \(-0.871654\pi\)
0.799708 + 0.600390i \(0.204988\pi\)
\(54\) 67.1892 18.0033i 1.24425 0.333395i
\(55\) 25.7564 + 6.90141i 0.468298 + 0.125480i
\(56\) −0.802960 + 2.99669i −0.0143386 + 0.0535123i
\(57\) −29.6596 110.691i −0.520345 1.94195i
\(58\) 11.4198 + 6.59322i 0.196893 + 0.113676i
\(59\) −50.8363 + 13.6216i −0.861633 + 0.230874i −0.662466 0.749092i \(-0.730490\pi\)
−0.199167 + 0.979966i \(0.563823\pi\)
\(60\) −24.7686 24.7686i −0.412810 0.412810i
\(61\) 105.650 + 28.3088i 1.73196 + 0.464078i 0.980634 0.195849i \(-0.0627462\pi\)
0.751330 + 0.659927i \(0.229413\pi\)
\(62\) −30.7238 17.7384i −0.495545 0.286103i
\(63\) −20.1790 −0.320302
\(64\) 8.00000i 0.125000i
\(65\) −63.7836 36.8255i −0.981286 0.566546i
\(66\) 41.7118 41.7118i 0.631997 0.631997i
\(67\) 51.2985 29.6172i 0.765649 0.442048i −0.0656711 0.997841i \(-0.520919\pi\)
0.831320 + 0.555793i \(0.187585\pi\)
\(68\) 40.0706 40.0706i 0.589274 0.589274i
\(69\) −81.1253 21.7375i −1.17573 0.315036i
\(70\) 2.59521 + 4.49503i 0.0370744 + 0.0642148i
\(71\) 27.3533 + 47.3773i 0.385258 + 0.667286i 0.991805 0.127762i \(-0.0407792\pi\)
−0.606547 + 0.795048i \(0.707446\pi\)
\(72\) −50.2616 + 13.4675i −0.698077 + 0.187049i
\(73\) 61.1000i 0.836986i 0.908220 + 0.418493i \(0.137442\pi\)
−0.908220 + 0.418493i \(0.862558\pi\)
\(74\) 48.0314 20.7602i 0.649073 0.280543i
\(75\) 72.2523 0.963364
\(76\) 11.3330 + 42.2953i 0.149118 + 0.556517i
\(77\) −7.56991 + 4.37049i −0.0983105 + 0.0567596i
\(78\) −141.105 + 81.4667i −1.80903 + 1.04445i
\(79\) 28.3909 105.956i 0.359378 1.34122i −0.515507 0.856885i \(-0.672396\pi\)
0.874885 0.484331i \(-0.160937\pi\)
\(80\) 9.46410 + 9.46410i 0.118301 + 0.118301i
\(81\) −45.9384 79.5676i −0.567140 0.982316i
\(82\) −12.1382 12.1382i −0.148027 0.148027i
\(83\) −54.2776 + 94.0115i −0.653947 + 1.13267i 0.328210 + 0.944605i \(0.393555\pi\)
−0.982157 + 0.188064i \(0.939779\pi\)
\(84\) 11.4824 0.136696
\(85\) 94.8081i 1.11539i
\(86\) −49.1668 + 85.1595i −0.571707 + 0.990226i
\(87\) 12.6317 47.1420i 0.145191 0.541862i
\(88\) −15.9381 + 15.9381i −0.181115 + 0.181115i
\(89\) 6.28409 + 23.4525i 0.0706077 + 0.263512i 0.992202 0.124644i \(-0.0397789\pi\)
−0.921594 + 0.388156i \(0.873112\pi\)
\(90\) −43.5278 + 75.3923i −0.483642 + 0.837693i
\(91\) 23.3206 6.24875i 0.256271 0.0686675i
\(92\) 30.9981 + 8.30591i 0.336936 + 0.0902817i
\(93\) −33.9842 + 126.831i −0.365421 + 1.36377i
\(94\) 13.5911 + 50.7228i 0.144587 + 0.539605i
\(95\) 63.4429 + 36.6288i 0.667820 + 0.385566i
\(96\) 28.6003 7.66342i 0.297920 0.0798273i
\(97\) −41.9263 41.9263i −0.432230 0.432230i 0.457156 0.889386i \(-0.348868\pi\)
−0.889386 + 0.457156i \(0.848868\pi\)
\(98\) 65.2918 + 17.4949i 0.666242 + 0.178519i
\(99\) −126.965 73.3034i −1.28248 0.740439i
\(100\) −27.6077 −0.276077
\(101\) 115.721i 1.14575i −0.819642 0.572876i \(-0.805827\pi\)
0.819642 0.572876i \(-0.194173\pi\)
\(102\) −181.639 104.869i −1.78077 1.02813i
\(103\) 23.0389 23.0389i 0.223678 0.223678i −0.586367 0.810046i \(-0.699442\pi\)
0.810046 + 0.586367i \(0.199442\pi\)
\(104\) 53.9162 31.1285i 0.518425 0.299313i
\(105\) 13.5839 13.5839i 0.129370 0.129370i
\(106\) −17.3901 4.65968i −0.164058 0.0439592i
\(107\) −5.43971 9.42185i −0.0508384 0.0880547i 0.839486 0.543381i \(-0.182856\pi\)
−0.890325 + 0.455326i \(0.849523\pi\)
\(108\) 49.1859 + 85.1926i 0.455425 + 0.788820i
\(109\) −125.675 + 33.6745i −1.15298 + 0.308941i −0.784160 0.620559i \(-0.786906\pi\)
−0.368823 + 0.929500i \(0.620239\pi\)
\(110\) 37.7100i 0.342818i
\(111\) −120.229 151.827i −1.08314 1.36781i
\(112\) −4.38746 −0.0391737
\(113\) −55.7117 207.919i −0.493024 1.83999i −0.540830 0.841132i \(-0.681890\pi\)
0.0478062 0.998857i \(-0.484777\pi\)
\(114\) 140.351 81.0317i 1.23115 0.710804i
\(115\) 46.4971 26.8451i 0.404323 0.233436i
\(116\) −4.82657 + 18.0130i −0.0416084 + 0.155285i
\(117\) 286.336 + 286.336i 2.44732 + 2.44732i
\(118\) −37.2148 64.4579i −0.315379 0.546253i
\(119\) 21.9760 + 21.9760i 0.184672 + 0.184672i
\(120\) 24.7686 42.9004i 0.206405 0.357504i
\(121\) 57.4941 0.475157
\(122\) 154.682i 1.26789i
\(123\) −31.7670 + 55.0221i −0.258269 + 0.447334i
\(124\) 12.9854 48.4622i 0.104721 0.390824i
\(125\) −91.8109 + 91.8109i −0.734487 + 0.734487i
\(126\) −7.38603 27.5650i −0.0586193 0.218770i
\(127\) −85.3177 + 147.775i −0.671793 + 1.16358i 0.305603 + 0.952159i \(0.401142\pi\)
−0.977395 + 0.211420i \(0.932191\pi\)
\(128\) −10.9282 + 2.92820i −0.0853766 + 0.0228766i
\(129\) 351.546 + 94.1966i 2.72517 + 0.730206i
\(130\) 26.9581 100.609i 0.207370 0.773916i
\(131\) −29.5996 110.467i −0.225951 0.843260i −0.982021 0.188770i \(-0.939550\pi\)
0.756070 0.654490i \(-0.227117\pi\)
\(132\) 72.2469 + 41.7118i 0.547325 + 0.315998i
\(133\) −23.1961 + 6.21537i −0.174407 + 0.0467321i
\(134\) 59.2344 + 59.2344i 0.442048 + 0.442048i
\(135\) 158.971 + 42.5963i 1.17757 + 0.315528i
\(136\) 69.4043 + 40.0706i 0.510326 + 0.294637i
\(137\) 7.64504 0.0558032 0.0279016 0.999611i \(-0.491117\pi\)
0.0279016 + 0.999611i \(0.491117\pi\)
\(138\) 118.776i 0.860694i
\(139\) 8.95727 + 5.17148i 0.0644408 + 0.0372049i 0.531874 0.846823i \(-0.321488\pi\)
−0.467433 + 0.884028i \(0.654821\pi\)
\(140\) −5.19042 + 5.19042i −0.0370744 + 0.0370744i
\(141\) 168.317 97.1776i 1.19373 0.689203i
\(142\) −54.7066 + 54.7066i −0.385258 + 0.385258i
\(143\) 169.432 + 45.3991i 1.18484 + 0.317476i
\(144\) −36.7940 63.7291i −0.255514 0.442563i
\(145\) 15.5997 + 27.0195i 0.107584 + 0.186341i
\(146\) −83.4642 + 22.3642i −0.571672 + 0.153179i
\(147\) 250.179i 1.70190i
\(148\) 45.9397 + 58.0133i 0.310403 + 0.391982i
\(149\) −219.043 −1.47009 −0.735045 0.678018i \(-0.762839\pi\)
−0.735045 + 0.678018i \(0.762839\pi\)
\(150\) 26.4462 + 98.6985i 0.176308 + 0.657990i
\(151\) −117.627 + 67.9122i −0.778989 + 0.449750i −0.836072 0.548620i \(-0.815153\pi\)
0.0570827 + 0.998369i \(0.481820\pi\)
\(152\) −53.6283 + 30.9623i −0.352818 + 0.203699i
\(153\) −134.913 + 503.503i −0.881785 + 3.29087i
\(154\) −8.74098 8.74098i −0.0567596 0.0567596i
\(155\) −41.9695 72.6933i −0.270771 0.468989i
\(156\) −162.933 162.933i −1.04445 1.04445i
\(157\) −33.6256 + 58.2413i −0.214176 + 0.370964i −0.953017 0.302916i \(-0.902040\pi\)
0.738841 + 0.673879i \(0.235373\pi\)
\(158\) 155.131 0.981839
\(159\) 66.6340i 0.419082i
\(160\) −9.46410 + 16.3923i −0.0591506 + 0.102452i
\(161\) −4.55523 + 17.0003i −0.0282933 + 0.105592i
\(162\) 91.8767 91.8767i 0.567140 0.567140i
\(163\) −49.7651 185.726i −0.305307 1.13942i −0.932681 0.360703i \(-0.882537\pi\)
0.627373 0.778719i \(-0.284130\pi\)
\(164\) 12.1382 21.0240i 0.0740136 0.128195i
\(165\) 134.815 36.1235i 0.817058 0.218930i
\(166\) −148.289 39.7339i −0.893308 0.239361i
\(167\) 7.67484 28.6429i 0.0459571 0.171514i −0.939133 0.343554i \(-0.888369\pi\)
0.985090 + 0.172040i \(0.0550358\pi\)
\(168\) 4.20287 + 15.6853i 0.0250171 + 0.0933649i
\(169\) −273.225 157.747i −1.61672 0.933411i
\(170\) 129.510 34.7022i 0.761825 0.204130i
\(171\) −284.807 284.807i −1.66554 1.66554i
\(172\) −134.326 35.9926i −0.780967 0.209259i
\(173\) −79.5962 45.9549i −0.460094 0.265635i 0.251990 0.967730i \(-0.418915\pi\)
−0.712084 + 0.702095i \(0.752248\pi\)
\(174\) 69.0206 0.396670
\(175\) 15.1409i 0.0865197i
\(176\) −27.6056 15.9381i −0.156850 0.0905575i
\(177\) −194.790 + 194.790i −1.10051 + 1.10051i
\(178\) −29.7366 + 17.1684i −0.167060 + 0.0964520i
\(179\) 61.4177 61.4177i 0.343116 0.343116i −0.514422 0.857537i \(-0.671993\pi\)
0.857537 + 0.514422i \(0.171993\pi\)
\(180\) −118.920 31.8645i −0.660667 0.177025i
\(181\) 21.8239 + 37.8001i 0.120574 + 0.208841i 0.919994 0.391932i \(-0.128193\pi\)
−0.799420 + 0.600772i \(0.794860\pi\)
\(182\) 17.0719 + 29.5694i 0.0938016 + 0.162469i
\(183\) 552.994 148.174i 3.02182 0.809695i
\(184\) 45.3843i 0.246654i
\(185\) 122.978 + 14.2833i 0.664744 + 0.0772071i
\(186\) −185.693 −0.998350
\(187\) 58.4406 + 218.103i 0.312516 + 1.16633i
\(188\) −64.3140 + 37.1317i −0.342096 + 0.197509i
\(189\) −46.7223 + 26.9751i −0.247208 + 0.142726i
\(190\) −26.8141 + 100.072i −0.141127 + 0.526693i
\(191\) 61.8580 + 61.8580i 0.323864 + 0.323864i 0.850247 0.526383i \(-0.176452\pi\)
−0.526383 + 0.850247i \(0.676452\pi\)
\(192\) 20.9369 + 36.2637i 0.109046 + 0.188873i
\(193\) 265.059 + 265.059i 1.37336 + 1.37336i 0.855406 + 0.517957i \(0.173307\pi\)
0.517957 + 0.855406i \(0.326693\pi\)
\(194\) 41.9263 72.6186i 0.216115 0.374322i
\(195\) −385.505 −1.97695
\(196\) 95.5938i 0.487723i
\(197\) −57.3963 + 99.4133i −0.291352 + 0.504636i −0.974130 0.225990i \(-0.927438\pi\)
0.682778 + 0.730626i \(0.260772\pi\)
\(198\) 53.6618 200.269i 0.271019 1.01146i
\(199\) −72.0011 + 72.0011i −0.361815 + 0.361815i −0.864481 0.502666i \(-0.832353\pi\)
0.502666 + 0.864481i \(0.332353\pi\)
\(200\) −10.1051 37.7128i −0.0505256 0.188564i
\(201\) 155.023 268.507i 0.771258 1.33586i
\(202\) 158.078 42.3568i 0.782564 0.209687i
\(203\) −9.87891 2.64705i −0.0486646 0.0130396i
\(204\) 76.7695 286.508i 0.376321 1.40445i
\(205\) −10.5120 39.2314i −0.0512781 0.191373i
\(206\) 39.9045 + 23.0389i 0.193711 + 0.111839i
\(207\) −285.136 + 76.4020i −1.37747 + 0.369092i
\(208\) 62.2571 + 62.2571i 0.299313 + 0.299313i
\(209\) −168.527 45.1566i −0.806349 0.216060i
\(210\) 23.5280 + 13.5839i 0.112038 + 0.0646851i
\(211\) −244.211 −1.15740 −0.578700 0.815541i \(-0.696440\pi\)
−0.578700 + 0.815541i \(0.696440\pi\)
\(212\) 25.4609i 0.120099i
\(213\) 247.983 + 143.173i 1.16424 + 0.672174i
\(214\) 10.8794 10.8794i 0.0508384 0.0508384i
\(215\) −201.489 + 116.330i −0.937160 + 0.541070i
\(216\) −98.3719 + 98.3719i −0.455425 + 0.455425i
\(217\) 26.5782 + 7.12161i 0.122480 + 0.0328185i
\(218\) −92.0006 159.350i −0.422021 0.730962i
\(219\) 159.905 + 276.964i 0.730161 + 1.26468i
\(220\) −51.5128 + 13.8028i −0.234149 + 0.0627401i
\(221\) 623.670i 2.82204i
\(222\) 163.393 219.808i 0.736004 0.990128i
\(223\) −59.6793 −0.267620 −0.133810 0.991007i \(-0.542721\pi\)
−0.133810 + 0.991007i \(0.542721\pi\)
\(224\) −1.60592 5.99338i −0.00716929 0.0267561i
\(225\) 219.927 126.975i 0.977452 0.564332i
\(226\) 263.630 152.207i 1.16651 0.673483i
\(227\) 9.06348 33.8254i 0.0399272 0.149010i −0.943084 0.332553i \(-0.892090\pi\)
0.983012 + 0.183543i \(0.0587566\pi\)
\(228\) 162.063 + 162.063i 0.710804 + 0.710804i
\(229\) 31.4476 + 54.4688i 0.137326 + 0.237855i 0.926483 0.376335i \(-0.122816\pi\)
−0.789158 + 0.614191i \(0.789483\pi\)
\(230\) 53.6903 + 53.6903i 0.233436 + 0.233436i
\(231\) −22.8761 + 39.6225i −0.0990306 + 0.171526i
\(232\) −26.3729 −0.113676
\(233\) 224.895i 0.965216i 0.875836 + 0.482608i \(0.160310\pi\)
−0.875836 + 0.482608i \(0.839690\pi\)
\(234\) −286.336 + 495.948i −1.22366 + 2.11944i
\(235\) −32.1570 + 120.012i −0.136838 + 0.510687i
\(236\) 74.4295 74.4295i 0.315379 0.315379i
\(237\) −148.604 554.597i −0.627020 2.34007i
\(238\) −21.9760 + 38.0636i −0.0923362 + 0.159931i
\(239\) 106.846 28.6292i 0.447053 0.119788i −0.0282670 0.999600i \(-0.508999\pi\)
0.475320 + 0.879813i \(0.342332\pi\)
\(240\) 67.6690 + 18.1319i 0.281954 + 0.0755494i
\(241\) −0.837357 + 3.12506i −0.00347451 + 0.0129671i −0.967641 0.252330i \(-0.918803\pi\)
0.964167 + 0.265297i \(0.0854699\pi\)
\(242\) 21.0443 + 78.5383i 0.0869598 + 0.324539i
\(243\) −33.1074 19.1146i −0.136244 0.0786608i
\(244\) −211.300 + 56.6175i −0.865982 + 0.232039i
\(245\) 113.089 + 113.089i 0.461586 + 0.461586i
\(246\) −86.7892 23.2551i −0.352802 0.0945329i
\(247\) 417.342 + 240.953i 1.68965 + 0.975517i
\(248\) 70.9536 0.286103
\(249\) 568.201i 2.28193i
\(250\) −159.021 91.8109i −0.636084 0.367244i
\(251\) 246.179 246.179i 0.980791 0.980791i −0.0190278 0.999819i \(-0.506057\pi\)
0.999819 + 0.0190278i \(0.00605711\pi\)
\(252\) 34.9511 20.1790i 0.138695 0.0800755i
\(253\) −90.4177 + 90.4177i −0.357382 + 0.357382i
\(254\) −233.092 62.4569i −0.917686 0.245893i
\(255\) −248.123 429.762i −0.973031 1.68534i
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) 15.9581 4.27595i 0.0620936 0.0166379i −0.227639 0.973746i \(-0.573100\pi\)
0.289732 + 0.957108i \(0.406434\pi\)
\(258\) 514.700i 1.99496i
\(259\) −31.8164 + 25.1948i −0.122843 + 0.0972771i
\(260\) 147.302 0.566546
\(261\) −44.3972 165.693i −0.170104 0.634838i
\(262\) 140.067 80.8675i 0.534605 0.308655i
\(263\) 424.963 245.352i 1.61583 0.932899i 0.627845 0.778338i \(-0.283937\pi\)
0.987983 0.154561i \(-0.0493963\pi\)
\(264\) −30.5351 + 113.959i −0.115663 + 0.431662i
\(265\) −30.1206 30.1206i −0.113663 0.113663i
\(266\) −16.9807 29.4115i −0.0638373 0.110569i
\(267\) 89.8633 + 89.8633i 0.336567 + 0.336567i
\(268\) −59.2344 + 102.597i −0.221024 + 0.382825i
\(269\) −307.691 −1.14383 −0.571917 0.820311i \(-0.693800\pi\)
−0.571917 + 0.820311i \(0.693800\pi\)
\(270\) 232.750i 0.862038i
\(271\) −52.1193 + 90.2733i −0.192322 + 0.333112i −0.946019 0.324110i \(-0.894935\pi\)
0.753697 + 0.657222i \(0.228269\pi\)
\(272\) −29.3337 + 109.475i −0.107845 + 0.402481i
\(273\) 89.3579 89.3579i 0.327318 0.327318i
\(274\) 2.79828 + 10.4433i 0.0102127 + 0.0381143i
\(275\) 55.0019 95.2660i 0.200007 0.346422i
\(276\) 162.251 43.4749i 0.587865 0.157518i
\(277\) −111.247 29.8086i −0.401614 0.107612i 0.0523574 0.998628i \(-0.483327\pi\)
−0.453971 + 0.891016i \(0.649993\pi\)
\(278\) −3.78579 + 14.1287i −0.0136179 + 0.0508228i
\(279\) 119.446 + 445.780i 0.428123 + 1.59778i
\(280\) −8.99007 5.19042i −0.0321074 0.0185372i
\(281\) 290.413 77.8160i 1.03350 0.276925i 0.298082 0.954540i \(-0.403653\pi\)
0.735417 + 0.677615i \(0.236986\pi\)
\(282\) 194.355 + 194.355i 0.689203 + 0.689203i
\(283\) −110.565 29.6257i −0.390688 0.104685i 0.0581270 0.998309i \(-0.481487\pi\)
−0.448815 + 0.893625i \(0.648154\pi\)
\(284\) −94.7546 54.7066i −0.333643 0.192629i
\(285\) 383.446 1.34542
\(286\) 248.065i 0.867361i
\(287\) 11.5302 + 6.65699i 0.0401751 + 0.0231951i
\(288\) 73.5880 73.5880i 0.255514 0.255514i
\(289\) 444.987 256.914i 1.53975 0.888974i
\(290\) −31.1994 + 31.1994i −0.107584 + 0.107584i
\(291\) −299.776 80.3248i −1.03016 0.276030i
\(292\) −61.1000 105.828i −0.209247 0.362426i
\(293\) 56.1445 + 97.2451i 0.191619 + 0.331894i 0.945787 0.324787i \(-0.105293\pi\)
−0.754168 + 0.656682i \(0.771959\pi\)
\(294\) 341.751 91.5719i 1.16242 0.311469i
\(295\) 176.102i 0.596957i
\(296\) −62.4326 + 83.9891i −0.210921 + 0.283747i
\(297\) −391.966 −1.31975
\(298\) −80.1755 299.219i −0.269045 1.00409i
\(299\) 305.869 176.594i 1.02297 0.590614i
\(300\) −125.145 + 72.2523i −0.417149 + 0.240841i
\(301\) 19.7395 73.6688i 0.0655798 0.244747i
\(302\) −135.824 135.824i −0.449750 0.449750i
\(303\) −302.854 524.559i −0.999519 1.73122i
\(304\) −61.9246 61.9246i −0.203699 0.203699i
\(305\) −182.991 + 316.949i −0.599970 + 1.03918i
\(306\) −737.179 −2.40908
\(307\) 170.779i 0.556285i −0.960540 0.278142i \(-0.910281\pi\)
0.960540 0.278142i \(-0.0897187\pi\)
\(308\) 8.74098 15.1398i 0.0283798 0.0491553i
\(309\) 44.1392 164.730i 0.142845 0.533106i
\(310\) 83.9390 83.9390i 0.270771 0.270771i
\(311\) 24.7120 + 92.2264i 0.0794598 + 0.296548i 0.994208 0.107477i \(-0.0342774\pi\)
−0.914748 + 0.404026i \(0.867611\pi\)
\(312\) 162.933 282.209i 0.522223 0.904516i
\(313\) −190.739 + 51.1084i −0.609390 + 0.163286i −0.550300 0.834967i \(-0.685487\pi\)
−0.0590900 + 0.998253i \(0.518820\pi\)
\(314\) −91.8669 24.6157i −0.292570 0.0783938i
\(315\) 17.4755 65.2196i 0.0554779 0.207046i
\(316\) 56.7817 + 211.912i 0.179689 + 0.670608i
\(317\) −189.409 109.355i −0.597504 0.344969i 0.170555 0.985348i \(-0.445444\pi\)
−0.768059 + 0.640379i \(0.778777\pi\)
\(318\) −91.0238 + 24.3897i −0.286238 + 0.0766973i
\(319\) −52.5418 52.5418i −0.164708 0.164708i
\(320\) −25.8564 6.92820i −0.0808013 0.0216506i
\(321\) −49.3160 28.4726i −0.153632 0.0886997i
\(322\) −24.8902 −0.0772989
\(323\) 620.339i 1.92055i
\(324\) 159.135 + 91.8767i 0.491158 + 0.283570i
\(325\) −214.847 + 214.847i −0.661067 + 0.661067i
\(326\) 235.491 135.961i 0.722365 0.417057i
\(327\) −481.551 + 481.551i −1.47263 + 1.47263i
\(328\) 33.1623 + 8.88580i 0.101104 + 0.0270909i
\(329\) −20.3642 35.2719i −0.0618973 0.107209i
\(330\) 98.6911 + 170.938i 0.299064 + 0.517994i
\(331\) 43.2300 11.5834i 0.130604 0.0349953i −0.192925 0.981214i \(-0.561797\pi\)
0.323529 + 0.946218i \(0.395131\pi\)
\(332\) 217.110i 0.653947i
\(333\) −632.780 250.854i −1.90024 0.753316i
\(334\) 41.9361 0.125557
\(335\) 51.2985 + 191.449i 0.153130 + 0.571488i
\(336\) −19.8882 + 11.4824i −0.0591910 + 0.0341739i
\(337\) −11.1262 + 6.42373i −0.0330155 + 0.0190615i −0.516417 0.856337i \(-0.672735\pi\)
0.483401 + 0.875399i \(0.339401\pi\)
\(338\) 115.478 430.971i 0.341652 1.27506i
\(339\) −796.685 796.685i −2.35010 2.35010i
\(340\) 94.8081 + 164.212i 0.278847 + 0.482978i
\(341\) 141.358 + 141.358i 0.414541 + 0.414541i
\(342\) 284.807 493.300i 0.832768 1.44240i
\(343\) −106.173 −0.309542
\(344\) 196.667i 0.571707i
\(345\) 140.513 243.376i 0.407285 0.705438i
\(346\) 33.6413 125.551i 0.0972292 0.362864i
\(347\) −404.610 + 404.610i −1.16602 + 1.16602i −0.182890 + 0.983133i \(0.558545\pi\)
−0.983133 + 0.182890i \(0.941455\pi\)
\(348\) 25.2633 + 94.2839i 0.0725957 + 0.270931i
\(349\) −8.11863 + 14.0619i −0.0232625 + 0.0402919i −0.877422 0.479719i \(-0.840739\pi\)
0.854160 + 0.520011i \(0.174072\pi\)
\(350\) 20.6829 5.54197i 0.0590940 0.0158342i
\(351\) 1045.75 + 280.208i 2.97935 + 0.798314i
\(352\) 11.6675 43.5438i 0.0331464 0.123704i
\(353\) 173.137 + 646.154i 0.490472 + 1.83047i 0.554042 + 0.832489i \(0.313085\pi\)
−0.0635704 + 0.997977i \(0.520249\pi\)
\(354\) −337.386 194.790i −0.953069 0.550255i
\(355\) −176.815 + 47.3773i −0.498069 + 0.133457i
\(356\) −34.3369 34.3369i −0.0964520 0.0964520i
\(357\) 157.130 + 42.1029i 0.440140 + 0.117935i
\(358\) 106.379 + 61.4177i 0.297147 + 0.171558i
\(359\) 197.067 0.548934 0.274467 0.961597i \(-0.411499\pi\)
0.274467 + 0.961597i \(0.411499\pi\)
\(360\) 174.111i 0.483642i
\(361\) −102.478 59.1660i −0.283874 0.163895i
\(362\) −43.6478 + 43.6478i −0.120574 + 0.120574i
\(363\) 260.618 150.468i 0.717957 0.414513i
\(364\) −34.1438 + 34.1438i −0.0938016 + 0.0938016i
\(365\) −197.478 52.9142i −0.541037 0.144970i
\(366\) 404.819 + 701.168i 1.10606 + 1.91576i
\(367\) 18.2293 + 31.5741i 0.0496711 + 0.0860329i 0.889792 0.456366i \(-0.150849\pi\)
−0.840121 + 0.542399i \(0.817516\pi\)
\(368\) −61.9962 + 16.6118i −0.168468 + 0.0451408i
\(369\) 223.307i 0.605168i
\(370\) 25.5016 + 173.219i 0.0689232 + 0.468159i
\(371\) 13.9636 0.0376377
\(372\) −67.9684 253.661i −0.182711 0.681886i
\(373\) 302.762 174.800i 0.811695 0.468632i −0.0358490 0.999357i \(-0.511414\pi\)
0.847544 + 0.530725i \(0.178080\pi\)
\(374\) −276.544 + 159.663i −0.739422 + 0.426905i
\(375\) −175.896 + 656.454i −0.469057 + 1.75054i
\(376\) −74.2634 74.2634i −0.197509 0.197509i
\(377\) 102.619 + 177.741i 0.272198 + 0.471461i
\(378\) −53.9503 53.9503i −0.142726 0.142726i
\(379\) −121.998 + 211.307i −0.321894 + 0.557537i −0.980879 0.194619i \(-0.937653\pi\)
0.658985 + 0.752156i \(0.270986\pi\)
\(380\) −146.515 −0.385566
\(381\) 893.142i 2.34420i
\(382\) −61.8580 + 107.141i −0.161932 + 0.280474i
\(383\) 90.8995 339.241i 0.237335 0.885748i −0.739747 0.672885i \(-0.765055\pi\)
0.977082 0.212862i \(-0.0682786\pi\)
\(384\) −41.8737 + 41.8737i −0.109046 + 0.109046i
\(385\) −7.56991 28.2513i −0.0196621 0.0733800i
\(386\) −265.059 + 459.096i −0.686682 + 1.18937i
\(387\) 1235.60 331.078i 3.19277 0.855499i
\(388\) 114.545 + 30.6922i 0.295219 + 0.0791036i
\(389\) 79.0227 294.917i 0.203143 0.758141i −0.786864 0.617126i \(-0.788297\pi\)
0.990007 0.141015i \(-0.0450365\pi\)
\(390\) −141.105 526.609i −0.361806 1.35028i
\(391\) 393.734 + 227.322i 1.00699 + 0.581387i
\(392\) −130.584 + 34.9898i −0.333121 + 0.0892596i
\(393\) −423.278 423.278i −1.07704 1.07704i
\(394\) −156.810 42.0170i −0.397994 0.106642i
\(395\) 317.868 + 183.521i 0.804730 + 0.464611i
\(396\) 293.214 0.740439
\(397\) 331.348i 0.834631i −0.908762 0.417315i \(-0.862971\pi\)
0.908762 0.417315i \(-0.137029\pi\)
\(398\) −124.710 72.0011i −0.313341 0.180907i
\(399\) −88.8807 + 88.8807i −0.222759 + 0.222759i
\(400\) 47.8179 27.6077i 0.119545 0.0690192i
\(401\) −27.1067 + 27.1067i −0.0675979 + 0.0675979i −0.740097 0.672500i \(-0.765221\pi\)
0.672500 + 0.740097i \(0.265221\pi\)
\(402\) 423.530 + 113.485i 1.05356 + 0.282300i
\(403\) −276.085 478.193i −0.685075 1.18658i
\(404\) 115.721 + 200.435i 0.286438 + 0.496126i
\(405\) 296.950 79.5676i 0.733211 0.196463i
\(406\) 14.4637i 0.0356249i
\(407\) −291.711 + 42.9462i −0.716734 + 0.105519i
\(408\) 419.476 1.02813
\(409\) −9.14751 34.1390i −0.0223655 0.0834693i 0.953841 0.300312i \(-0.0970908\pi\)
−0.976207 + 0.216843i \(0.930424\pi\)
\(410\) 49.7434 28.7194i 0.121325 0.0700472i
\(411\) 34.6547 20.0079i 0.0843179 0.0486810i
\(412\) −16.8656 + 62.9434i −0.0409360 + 0.152775i
\(413\) 40.8195 + 40.8195i 0.0988367 + 0.0988367i
\(414\) −208.734 361.538i −0.504188 0.873280i
\(415\) −256.844 256.844i −0.618902 0.618902i
\(416\) −62.2571 + 107.832i −0.149656 + 0.259213i
\(417\) 54.1373 0.129826
\(418\) 246.740i 0.590288i
\(419\) 2.98377 5.16805i 0.00712118 0.0123342i −0.862443 0.506154i \(-0.831067\pi\)
0.869564 + 0.493820i \(0.164400\pi\)
\(420\) −9.94409 + 37.1118i −0.0236764 + 0.0883615i
\(421\) −44.7646 + 44.7646i −0.106329 + 0.106329i −0.758270 0.651941i \(-0.773955\pi\)
0.651941 + 0.758270i \(0.273955\pi\)
\(422\) −89.3875 333.599i −0.211819 0.790518i
\(423\) 341.556 591.592i 0.807461 1.39856i
\(424\) 34.7803 9.31935i 0.0820290 0.0219796i
\(425\) −377.794 101.230i −0.888927 0.238187i
\(426\) −104.810 + 391.156i −0.246033 + 0.918207i
\(427\) −31.0509 115.883i −0.0727187 0.271390i
\(428\) 18.8437 + 10.8794i 0.0440273 + 0.0254192i
\(429\) 886.842 237.629i 2.06723 0.553913i
\(430\) −232.660 232.660i −0.541070 0.541070i
\(431\) −43.6534 11.6969i −0.101284 0.0271389i 0.207821 0.978167i \(-0.433363\pi\)
−0.309105 + 0.951028i \(0.600029\pi\)
\(432\) −170.385 98.3719i −0.394410 0.227713i
\(433\) 308.294 0.711995 0.355997 0.934487i \(-0.384141\pi\)
0.355997 + 0.934487i \(0.384141\pi\)
\(434\) 38.9132i 0.0896618i
\(435\) 141.426 + 81.6523i 0.325117 + 0.187706i
\(436\) 184.001 184.001i 0.422021 0.422021i
\(437\) −304.236 + 175.650i −0.696191 + 0.401946i
\(438\) −319.811 + 319.811i −0.730161 + 0.730161i
\(439\) 519.254 + 139.134i 1.18281 + 0.316933i 0.796041 0.605243i \(-0.206924\pi\)
0.386770 + 0.922176i \(0.373591\pi\)
\(440\) −37.7100 65.3156i −0.0857046 0.148445i
\(441\) −439.660 761.513i −0.996961 1.72679i
\(442\) 851.949 228.279i 1.92749 0.516468i
\(443\) 563.760i 1.27260i 0.771443 + 0.636298i \(0.219535\pi\)
−0.771443 + 0.636298i \(0.780465\pi\)
\(444\) 360.070 + 142.743i 0.810968 + 0.321494i
\(445\) −81.2420 −0.182566
\(446\) −21.8441 81.5234i −0.0489779 0.182788i
\(447\) −992.916 + 573.260i −2.22129 + 1.28246i
\(448\) 7.59930 4.38746i 0.0169627 0.00979343i
\(449\) 34.5830 129.066i 0.0770224 0.287451i −0.916662 0.399664i \(-0.869127\pi\)
0.993684 + 0.112212i \(0.0357936\pi\)
\(450\) 253.949 + 253.949i 0.564332 + 0.564332i
\(451\) 48.3651 + 83.7709i 0.107240 + 0.185745i
\(452\) 304.414 + 304.414i 0.673483 + 0.673483i
\(453\) −355.467 + 615.687i −0.784695 + 1.35913i
\(454\) 49.5238 0.109083
\(455\) 80.7850i 0.177550i
\(456\) −162.063 + 280.702i −0.355402 + 0.615574i
\(457\) 107.541 401.347i 0.235319 0.878222i −0.742686 0.669640i \(-0.766448\pi\)
0.978005 0.208582i \(-0.0668848\pi\)
\(458\) −62.8952 + 62.8952i −0.137326 + 0.137326i
\(459\) 360.702 + 1346.16i 0.785843 + 2.93280i
\(460\) −53.6903 + 92.9943i −0.116718 + 0.202161i
\(461\) −802.672 + 215.075i −1.74115 + 0.466541i −0.982703 0.185188i \(-0.940710\pi\)
−0.758452 + 0.651729i \(0.774044\pi\)
\(462\) −62.4986 16.7465i −0.135278 0.0362477i
\(463\) 46.7162 174.347i 0.100899 0.376560i −0.896949 0.442135i \(-0.854221\pi\)
0.997848 + 0.0655746i \(0.0208880\pi\)
\(464\) −9.65314 36.0260i −0.0208042 0.0776423i
\(465\) −380.492 219.677i −0.818263 0.472424i
\(466\) −307.213 + 82.3174i −0.659255 + 0.176647i
\(467\) −111.727 111.727i −0.239245 0.239245i 0.577292 0.816537i \(-0.304109\pi\)
−0.816537 + 0.577292i \(0.804109\pi\)
\(468\) −782.284 209.612i −1.67155 0.447890i
\(469\) −56.2675 32.4860i −0.119973 0.0692666i
\(470\) −175.709 −0.373849
\(471\) 352.007i 0.747362i
\(472\) 128.916 + 74.4295i 0.273127 + 0.157690i
\(473\) 391.814 391.814i 0.828359 0.828359i
\(474\) 703.201 405.993i 1.48355 0.856526i
\(475\) 213.699 213.699i 0.449894 0.449894i
\(476\) −60.0396 16.0876i −0.126134 0.0337974i
\(477\) 117.101 + 202.825i 0.245495 + 0.425210i
\(478\) 78.2165 + 135.475i 0.163633 + 0.283420i
\(479\) −514.363 + 137.823i −1.07383 + 0.287731i −0.752065 0.659089i \(-0.770942\pi\)
−0.321763 + 0.946820i \(0.604275\pi\)
\(480\) 99.0743i 0.206405i
\(481\) 808.976 + 93.9590i 1.68186 + 0.195341i
\(482\) −4.57540 −0.00949254
\(483\) 23.8430 + 88.9834i 0.0493645 + 0.184231i
\(484\) −99.5826 + 57.4941i −0.205749 + 0.118789i
\(485\) 171.817 99.1988i 0.354263 0.204534i
\(486\) 13.9928 52.2220i 0.0287918 0.107453i
\(487\) −10.3553 10.3553i −0.0212634 0.0212634i 0.696395 0.717659i \(-0.254786\pi\)
−0.717659 + 0.696395i \(0.754786\pi\)
\(488\) −154.682 267.917i −0.316971 0.549010i
\(489\) −711.648 711.648i −1.45531 1.45531i
\(490\) −113.089 + 195.875i −0.230793 + 0.399745i
\(491\) 816.251 1.66243 0.831213 0.555954i \(-0.187647\pi\)
0.831213 + 0.555954i \(0.187647\pi\)
\(492\) 127.068i 0.258269i
\(493\) −132.097 + 228.799i −0.267945 + 0.464095i
\(494\) −176.390 + 658.295i −0.357064 + 1.33258i
\(495\) 346.876 346.876i 0.700759 0.700759i
\(496\) 25.9708 + 96.9244i 0.0523605 + 0.195412i
\(497\) 30.0029 51.9665i 0.0603679 0.104560i
\(498\) −776.177 + 207.976i −1.55859 + 0.417622i
\(499\) −868.763 232.784i −1.74101 0.466502i −0.758337 0.651863i \(-0.773988\pi\)
−0.982670 + 0.185361i \(0.940654\pi\)
\(500\) 67.2102 250.832i 0.134420 0.501664i
\(501\) −40.1718 149.923i −0.0801832 0.299248i
\(502\) 426.394 + 246.179i 0.849390 + 0.490396i
\(503\) 487.086 130.514i 0.968362 0.259472i 0.260226 0.965548i \(-0.416203\pi\)
0.708136 + 0.706076i \(0.249536\pi\)
\(504\) 40.3580 + 40.3580i 0.0800755 + 0.0800755i
\(505\) 374.016 + 100.217i 0.740626 + 0.198450i
\(506\) −156.608 90.4177i −0.309502 0.178691i
\(507\) −1651.36 −3.25712
\(508\) 341.271i 0.671793i
\(509\) −168.180 97.0988i −0.330413 0.190764i 0.325612 0.945504i \(-0.394430\pi\)
−0.656024 + 0.754740i \(0.727763\pi\)
\(510\) 496.246 496.246i 0.973031 0.973031i
\(511\) 58.0396 33.5092i 0.113581 0.0655757i
\(512\) 16.0000 16.0000i 0.0312500 0.0312500i
\(513\) −1040.17 278.712i −2.02762 0.543298i
\(514\) 11.6821 + 20.2340i 0.0227278 + 0.0393658i
\(515\) 54.5106 + 94.4151i 0.105846 + 0.183330i
\(516\) −703.093 + 188.393i −1.36258 + 0.365103i
\(517\) 295.905i 0.572350i
\(518\) −46.0623 34.2400i −0.0889234 0.0661005i
\(519\) −481.075 −0.926928
\(520\) 53.9162 + 201.218i 0.103685 + 0.386958i
\(521\) 315.017 181.875i 0.604638 0.349088i −0.166226 0.986088i \(-0.553158\pi\)
0.770864 + 0.637000i \(0.219825\pi\)
\(522\) 210.090 121.295i 0.402471 0.232367i
\(523\) 137.443 512.944i 0.262797 0.980772i −0.700788 0.713370i \(-0.747168\pi\)
0.963585 0.267402i \(-0.0861653\pi\)
\(524\) 161.735 + 161.735i 0.308655 + 0.308655i
\(525\) −39.6255 68.6333i −0.0754771 0.130730i
\(526\) 490.705 + 490.705i 0.932899 + 0.932899i
\(527\) 355.394 615.561i 0.674372 1.16805i
\(528\) −166.847 −0.315998
\(529\) 271.533i 0.513294i
\(530\) 30.1206 52.1704i 0.0568314 0.0984348i
\(531\) −250.596 + 935.236i −0.471932 + 1.76127i
\(532\) 33.9614 33.9614i 0.0638373 0.0638373i
\(533\) −69.1505 258.073i −0.129738 0.484190i
\(534\) −89.8633 + 155.648i −0.168283 + 0.291475i
\(535\) 35.1628 9.42185i 0.0657249 0.0176109i
\(536\) −161.831 43.3626i −0.301924 0.0809004i
\(537\) 117.667 439.141i 0.219120 0.817767i
\(538\) −112.623 420.314i −0.209336 0.781253i
\(539\) −329.866 190.448i −0.611996 0.353336i
\(540\) −317.943 + 85.1926i −0.588783 + 0.157764i
\(541\) −350.399 350.399i −0.647687 0.647687i 0.304747 0.952433i \(-0.401428\pi\)
−0.952433 + 0.304747i \(0.901428\pi\)
\(542\) −142.393 38.1540i −0.262717 0.0703948i
\(543\) 197.854 + 114.231i 0.364372 + 0.210370i
\(544\) −160.282 −0.294637
\(545\) 435.351i 0.798810i
\(546\) 154.772 + 89.3579i 0.283466 + 0.163659i
\(547\) −221.802 + 221.802i −0.405487 + 0.405487i −0.880162 0.474674i \(-0.842566\pi\)
0.474674 + 0.880162i \(0.342566\pi\)
\(548\) −13.2416 + 7.64504i −0.0241635 + 0.0139508i
\(549\) 1422.84 1422.84i 2.59170 2.59170i
\(550\) 150.268 + 40.2642i 0.273214 + 0.0732076i
\(551\) −102.071 176.791i −0.185246 0.320856i
\(552\) 118.776 + 205.726i 0.215173 + 0.372691i
\(553\) −116.219 + 31.1409i −0.210162 + 0.0563127i
\(554\) 162.877i 0.294002i
\(555\) 594.834 257.100i 1.07177 0.463244i
\(556\) −20.6859 −0.0372049
\(557\) 274.119 + 1023.02i 0.492134 + 1.83667i 0.545523 + 0.838096i \(0.316331\pi\)
−0.0533893 + 0.998574i \(0.517002\pi\)
\(558\) −565.226 + 326.333i −1.01295 + 0.584827i
\(559\) −1325.44 + 765.246i −2.37110 + 1.36896i
\(560\) 3.79965 14.1805i 0.00678509 0.0253223i
\(561\) 835.708 + 835.708i 1.48968 + 1.48968i
\(562\) 212.597 + 368.229i 0.378287 + 0.655212i
\(563\) 377.677 + 377.677i 0.670829 + 0.670829i 0.957907 0.287078i \(-0.0926838\pi\)
−0.287078 + 0.957907i \(0.592684\pi\)
\(564\) −194.355 + 336.633i −0.344602 + 0.596867i
\(565\) 720.252 1.27478
\(566\) 161.878i 0.286004i
\(567\) −50.3882 + 87.2748i −0.0888680 + 0.153924i
\(568\) 40.0480 149.461i 0.0705071 0.263136i
\(569\) −52.7742 + 52.7742i −0.0927490 + 0.0927490i −0.751959 0.659210i \(-0.770891\pi\)
0.659210 + 0.751959i \(0.270891\pi\)
\(570\) 140.351 + 523.797i 0.246230 + 0.918942i
\(571\) 356.707 617.834i 0.624705 1.08202i −0.363893 0.931441i \(-0.618553\pi\)
0.988598 0.150580i \(-0.0481142\pi\)
\(572\) −338.863 + 90.7982i −0.592419 + 0.158738i
\(573\) 442.289 + 118.511i 0.771883 + 0.206825i
\(574\) −4.87326 + 18.1872i −0.00848999 + 0.0316851i
\(575\) −57.3268 213.946i −0.0996987 0.372081i
\(576\) 127.458 + 73.5880i 0.221282 + 0.127757i
\(577\) 589.411 157.932i 1.02151 0.273712i 0.291078 0.956699i \(-0.405986\pi\)
0.730431 + 0.682987i \(0.239319\pi\)
\(578\) 513.827 + 513.827i 0.888974 + 0.888974i
\(579\) 1895.19 + 507.815i 3.27322 + 0.877056i
\(580\) −54.0390 31.1994i −0.0931707 0.0537921i
\(581\) 119.070 0.204940
\(582\) 438.903i 0.754129i
\(583\) 87.8582 + 50.7250i 0.150700 + 0.0870068i
\(584\) 122.200 122.200i 0.209247 0.209247i
\(585\) −1173.43 + 677.478i −2.00586 + 1.15808i
\(586\) −112.289 + 112.289i −0.191619 + 0.191619i
\(587\) 452.570 + 121.266i 0.770988 + 0.206586i 0.622808 0.782375i \(-0.285992\pi\)
0.148180 + 0.988960i \(0.452659\pi\)
\(588\) 250.179 + 433.323i 0.425475 + 0.736944i
\(589\) 274.611 + 475.640i 0.466232 + 0.807538i
\(590\) 240.560 64.4579i 0.407729 0.109251i
\(591\) 600.849i 1.01667i
\(592\) −137.583 54.5424i −0.232404 0.0921324i
\(593\) −329.159 −0.555074 −0.277537 0.960715i \(-0.589518\pi\)
−0.277537 + 0.960715i \(0.589518\pi\)
\(594\) −143.469 535.435i −0.241531 0.901406i
\(595\) −90.0594 + 51.9958i −0.151360 + 0.0873879i
\(596\) 379.394 219.043i 0.636568 0.367523i
\(597\) −137.944 + 514.813i −0.231061 + 0.862333i
\(598\) 353.187 + 353.187i 0.590614 + 0.590614i
\(599\) −386.007 668.584i −0.644419 1.11617i −0.984435 0.175747i \(-0.943766\pi\)
0.340016 0.940420i \(-0.389567\pi\)
\(600\) −144.505 144.505i −0.240841 0.240841i
\(601\) −307.381 + 532.400i −0.511450 + 0.885857i 0.488462 + 0.872585i \(0.337558\pi\)
−0.999912 + 0.0132720i \(0.995775\pi\)
\(602\) 107.859 0.179167
\(603\) 1089.74i 1.80719i
\(604\) 135.824 235.255i 0.224875 0.389495i
\(605\) −49.7913 + 185.824i −0.0822997 + 0.307147i
\(606\) 605.709 605.709i 0.999519 0.999519i
\(607\) −11.7934 44.0136i −0.0194290 0.0725100i 0.955531 0.294892i \(-0.0952836\pi\)
−0.974960 + 0.222382i \(0.928617\pi\)
\(608\) 61.9246 107.257i 0.101850 0.176409i
\(609\) −51.7083 + 13.8552i −0.0849069 + 0.0227507i
\(610\) −499.940 133.959i −0.819574 0.219604i
\(611\) −211.536 + 789.464i −0.346213 + 1.29209i
\(612\) −269.826 1007.01i −0.440893 1.64543i
\(613\) 373.812 + 215.821i 0.609808 + 0.352073i 0.772890 0.634540i \(-0.218810\pi\)
−0.163082 + 0.986612i \(0.552144\pi\)
\(614\) 233.289 62.5096i 0.379950 0.101807i
\(615\) −150.323 150.323i −0.244428 0.244428i
\(616\) 23.8808 + 6.39884i 0.0387675 + 0.0103877i
\(617\) −460.862 266.079i −0.746940 0.431246i 0.0776469 0.996981i \(-0.475259\pi\)
−0.824587 + 0.565735i \(0.808593\pi\)
\(618\) 241.181 0.390260
\(619\) 729.925i 1.17920i −0.807695 0.589600i \(-0.799285\pi\)
0.807695 0.589600i \(-0.200715\pi\)
\(620\) 145.387 + 83.9390i 0.234494 + 0.135385i
\(621\) −558.068 + 558.068i −0.898660 + 0.898660i
\(622\) −116.938 + 67.5144i −0.188004 + 0.108544i
\(623\) 18.8315 18.8315i 0.0302271 0.0302271i
\(624\) 445.143 + 119.276i 0.713369 + 0.191147i
\(625\) −44.6788 77.3860i −0.0714861 0.123818i
\(626\) −139.631 241.847i −0.223052 0.386338i
\(627\) −882.106 + 236.360i −1.40687 + 0.376969i
\(628\) 134.502i 0.214176i
\(629\) 415.937 + 962.324i 0.661267 + 1.52993i
\(630\) 95.4881 0.151568
\(631\) −139.954 522.316i −0.221797 0.827758i −0.983662 0.180023i \(-0.942383\pi\)
0.761865 0.647736i \(-0.224284\pi\)
\(632\) −268.694 + 155.131i −0.425149 + 0.245460i
\(633\) −1107.00 + 639.127i −1.74882 + 1.00968i
\(634\) 80.0536 298.764i 0.126268 0.471237i
\(635\) −403.727 403.727i −0.635791 0.635791i
\(636\) −66.6340 115.414i −0.104770 0.181468i
\(637\) 743.924 + 743.924i 1.16786 + 1.16786i
\(638\) 52.5418 91.0050i 0.0823538 0.142641i
\(639\) 1006.44 1.57502
\(640\) 37.8564i 0.0591506i
\(641\) 221.255 383.225i 0.345172 0.597855i −0.640213 0.768197i \(-0.721154\pi\)
0.985385 + 0.170342i \(0.0544874\pi\)
\(642\) 20.8434 77.7886i 0.0324663 0.121166i
\(643\) −628.036 + 628.036i −0.976728 + 0.976728i −0.999735 0.0230073i \(-0.992676\pi\)
0.0230073 + 0.999735i \(0.492676\pi\)
\(644\) −9.11046 34.0007i −0.0141467 0.0527961i
\(645\) −608.896 + 1054.64i −0.944025 + 1.63510i
\(646\) −847.399 + 227.060i −1.31176 + 0.351486i
\(647\) 925.141 + 247.891i 1.42989 + 0.383139i 0.888983 0.457941i \(-0.151413\pi\)
0.540911 + 0.841080i \(0.318080\pi\)
\(648\) −67.2584 + 251.012i −0.103794 + 0.387364i
\(649\) 108.551 + 405.118i 0.167259 + 0.624219i
\(650\) −372.126 214.847i −0.572501 0.330534i
\(651\) 139.116 37.2760i 0.213696 0.0572597i
\(652\) 271.921 + 271.921i 0.417057 + 0.417057i
\(653\) −879.488 235.658i −1.34684 0.360886i −0.487874 0.872914i \(-0.662228\pi\)
−0.858969 + 0.512028i \(0.828894\pi\)
\(654\) −834.070 481.551i −1.27534 0.736316i
\(655\) 382.669 0.584228
\(656\) 48.5529i 0.0740136i
\(657\) 973.462 + 562.029i 1.48168 + 0.855447i
\(658\) 40.7284 40.7284i 0.0618973 0.0618973i
\(659\) 752.287 434.333i 1.14156 0.659079i 0.194742 0.980855i \(-0.437613\pi\)
0.946816 + 0.321776i \(0.104280\pi\)
\(660\) −197.382 + 197.382i −0.299064 + 0.299064i
\(661\) −763.709 204.635i −1.15538 0.309584i −0.370263 0.928927i \(-0.620733\pi\)
−0.785121 + 0.619343i \(0.787399\pi\)
\(662\) 31.6465 + 54.8134i 0.0478044 + 0.0827997i
\(663\) −1632.21 2827.07i −2.46186 4.26406i
\(664\) 296.578 79.4679i 0.446654 0.119681i
\(665\) 80.3536i 0.120833i
\(666\) 111.060 956.212i 0.166756 1.43575i
\(667\) −149.614 −0.224309
\(668\) 15.3497 + 57.2858i 0.0229786 + 0.0857572i
\(669\) −270.524 + 156.187i −0.404371 + 0.233464i
\(670\) −242.747 + 140.150i −0.362309 + 0.209179i
\(671\) 225.594 841.930i 0.336206 1.25474i
\(672\) −22.9649 22.9649i −0.0341739 0.0341739i
\(673\) 408.357 + 707.295i 0.606771 + 1.05096i 0.991769 + 0.128041i \(0.0408689\pi\)
−0.384998 + 0.922918i \(0.625798\pi\)
\(674\) −12.8475 12.8475i −0.0190615 0.0190615i
\(675\) 339.478 587.992i 0.502930 0.871100i
\(676\) 630.986 0.933411
\(677\) 673.536i 0.994884i 0.867497 + 0.497442i \(0.165727\pi\)
−0.867497 + 0.497442i \(0.834273\pi\)
\(678\) 796.685 1379.90i 1.17505 2.03525i
\(679\) −16.8326 + 62.8201i −0.0247903 + 0.0925185i
\(680\) −189.616 + 189.616i −0.278847 + 0.278847i
\(681\) −47.4402 177.049i −0.0696626 0.259984i
\(682\) −141.358 + 244.840i −0.207270 + 0.359003i
\(683\) −266.637 + 71.4452i −0.390391 + 0.104605i −0.448675 0.893695i \(-0.648104\pi\)
0.0582838 + 0.998300i \(0.481437\pi\)
\(684\) 778.107 + 208.493i 1.13758 + 0.304814i
\(685\) −6.62080 + 24.7092i −0.00966540 + 0.0360718i
\(686\) −38.8620 145.035i −0.0566502 0.211421i
\(687\) 285.101 + 164.603i 0.414995 + 0.239597i
\(688\) 268.653 71.9852i 0.390483 0.104630i
\(689\) −198.141 198.141i −0.287577 0.287577i
\(690\) 383.889 + 102.863i 0.556361 + 0.149076i
\(691\) 952.431 + 549.886i 1.37834 + 0.795783i 0.991959 0.126558i \(-0.0403929\pi\)
0.386377 + 0.922341i \(0.373726\pi\)
\(692\) 183.820 0.265635
\(693\) 160.808i 0.232046i
\(694\) −700.805 404.610i −1.00981 0.583012i
\(695\) −24.4717 + 24.4717i −0.0352111 + 0.0352111i
\(696\) −119.547 + 69.0206i −0.171763 + 0.0991676i
\(697\) 243.193 243.193i 0.348914 0.348914i
\(698\) −22.1805 5.94325i −0.0317772 0.00851468i
\(699\) 588.575 + 1019.44i 0.842025 + 1.45843i
\(700\) 15.1409 + 26.2249i 0.0216299 + 0.0374641i
\(701\) −153.209 + 41.0521i −0.218557 + 0.0585622i −0.366436 0.930443i \(-0.619422\pi\)
0.147879 + 0.989005i \(0.452755\pi\)
\(702\) 1531.09i 2.18104i
\(703\) −804.656 93.4572i −1.14460 0.132941i
\(704\) 63.7525 0.0905575
\(705\) 168.317 + 628.166i 0.238747 + 0.891016i
\(706\) −819.291 + 473.018i −1.16047 + 0.669997i
\(707\) −109.925 + 63.4651i −0.155481 + 0.0897668i
\(708\) 142.596 532.176i 0.201407 0.751662i
\(709\) −638.923 638.923i −0.901160 0.901160i 0.0943763 0.995537i \(-0.469914\pi\)
−0.995537 + 0.0943763i \(0.969914\pi\)
\(710\) −129.437 224.192i −0.182306 0.315763i
\(711\) −1426.97 1426.97i −2.00699 2.00699i
\(712\) 34.3369 59.4733i 0.0482260 0.0835298i
\(713\) 402.523 0.564548
\(714\) 230.054i 0.322205i
\(715\) −293.464 + 508.295i −0.410440 + 0.710902i
\(716\) −44.9609 + 167.796i −0.0627945 + 0.234352i
\(717\) 409.402 409.402i 0.570993 0.570993i
\(718\) 72.1316 + 269.199i 0.100462 + 0.374929i
\(719\) −635.609 + 1100.91i −0.884018 + 1.53116i −0.0371834 + 0.999308i \(0.511839\pi\)
−0.846835 + 0.531856i \(0.821495\pi\)
\(720\) 237.840 63.7291i 0.330334 0.0885126i
\(721\) −34.5202 9.24965i −0.0478782 0.0128289i
\(722\) 43.3125 161.644i 0.0599896 0.223884i
\(723\) 4.38291 + 16.3572i 0.00606211 + 0.0226241i
\(724\) −75.6003 43.6478i −0.104420 0.0602871i
\(725\) 124.324 33.3126i 0.171482 0.0459484i
\(726\) 300.936 + 300.936i 0.414513 + 0.414513i
\(727\) −235.524 63.1084i −0.323967 0.0868066i 0.0931704 0.995650i \(-0.470300\pi\)
−0.417137 + 0.908844i \(0.636967\pi\)
\(728\) −59.1388 34.1438i −0.0812346 0.0469008i
\(729\) 626.791 0.859796
\(730\) 289.128i 0.396066i
\(731\) −1706.20 985.073i −2.33406 1.34757i
\(732\) −809.639 + 809.639i −1.10606 + 1.10606i
\(733\) −843.518 + 487.006i −1.15078 + 0.664400i −0.949076 0.315047i \(-0.897980\pi\)
−0.201699 + 0.979447i \(0.564646\pi\)
\(734\) −36.4586 + 36.4586i −0.0496711 + 0.0496711i
\(735\) 808.592 + 216.662i 1.10012 + 0.294778i
\(736\) −45.3843 78.6080i −0.0616635 0.106804i
\(737\) −236.021 408.801i −0.320246 0.554682i
\(738\) −305.043 + 81.7360i −0.413337 + 0.110753i
\(739\) 574.895i 0.777937i −0.921251 0.388969i \(-0.872831\pi\)
0.921251 0.388969i \(-0.127169\pi\)
\(740\) −227.287 + 98.2383i −0.307145 + 0.132754i
\(741\) 2522.40 3.40405
\(742\) 5.11103 + 19.0746i 0.00688818 + 0.0257070i
\(743\) 331.399 191.333i 0.446029 0.257515i −0.260123 0.965576i \(-0.583763\pi\)
0.706151 + 0.708061i \(0.250430\pi\)
\(744\) 321.630 185.693i 0.432298 0.249588i
\(745\) 189.697 707.960i 0.254627 0.950281i
\(746\) 349.600 + 349.600i 0.468632 + 0.468632i
\(747\) 998.545 + 1729.53i 1.33674 + 2.31530i
\(748\) −319.325 319.325i −0.426905 0.426905i
\(749\) −5.96662 + 10.3345i −0.00796611 + 0.0137977i
\(750\) −961.116 −1.28149
\(751\) 1233.34i 1.64227i −0.570735 0.821134i \(-0.693342\pi\)
0.570735 0.821134i \(-0.306658\pi\)
\(752\) 74.2634 128.628i 0.0987545 0.171048i
\(753\) 471.643 1760.19i 0.626351 2.33758i
\(754\) −205.237 + 205.237i −0.272198 + 0.272198i
\(755\) −117.627 438.991i −0.155798 0.581445i
\(756\) 53.9503 93.4446i 0.0713628 0.123604i
\(757\) −391.060 + 104.784i −0.516592 + 0.138420i −0.507690 0.861540i \(-0.669500\pi\)
−0.00890207 + 0.999960i \(0.502834\pi\)
\(758\) −333.305 89.3087i −0.439716 0.117821i
\(759\) −173.227 + 646.493i −0.228231 + 0.851769i
\(760\) −53.6283 200.143i −0.0705635 0.263347i
\(761\) 598.566 + 345.582i 0.786552 + 0.454116i 0.838747 0.544521i \(-0.183288\pi\)
−0.0521953 + 0.998637i \(0.516622\pi\)
\(762\) −1220.05 + 326.913i −1.60112 + 0.429019i
\(763\) 100.912 + 100.912i 0.132257 + 0.132257i
\(764\) −168.999 45.2832i −0.221203 0.0592712i
\(765\) −1510.51 872.092i −1.97452 1.13999i
\(766\) 496.684 0.648412
\(767\) 1158.44i 1.51035i
\(768\) −72.5274 41.8737i −0.0944367 0.0545231i
\(769\) −815.124 + 815.124i −1.05998 + 1.05998i −0.0618968 + 0.998083i \(0.519715\pi\)
−0.998083 + 0.0618968i \(0.980285\pi\)
\(770\) 35.8212 20.6814i 0.0465210 0.0268589i
\(771\) 61.1467 61.1467i 0.0793082 0.0793082i
\(772\) −724.155 194.037i −0.938025 0.251343i
\(773\) −25.7966 44.6811i −0.0333721 0.0578022i 0.848857 0.528623i \(-0.177291\pi\)
−0.882229 + 0.470820i \(0.843958\pi\)
\(774\) 904.523 + 1566.68i 1.16863 + 2.02413i
\(775\) −334.482 + 89.6243i −0.431590 + 0.115644i
\(776\) 167.705i 0.216115i
\(777\) −78.2850 + 197.474i −0.100753 + 0.254149i
\(778\) 431.788 0.554998
\(779\) 68.7812 + 256.695i 0.0882942 + 0.329518i
\(780\) 667.714 385.505i 0.856043 0.494237i
\(781\) 377.553 217.980i 0.483422 0.279104i
\(782\) −166.412 + 621.056i −0.212802 + 0.794189i
\(783\) −324.294 324.294i −0.414168 0.414168i
\(784\) −95.5938 165.573i −0.121931 0.211190i
\(785\) −159.118 159.118i −0.202698 0.202698i
\(786\) 423.278 733.139i 0.538522 0.932747i
\(787\) 583.361 0.741246 0.370623 0.928783i \(-0.379144\pi\)
0.370623 + 0.928783i \(0.379144\pi\)
\(788\) 229.585i 0.291352i
\(789\) 1284.23 2224.35i 1.62766 2.81920i
\(790\) −134.347 + 501.390i −0.170059 + 0.634671i
\(791\) −166.950 + 166.950i −0.211063 + 0.211063i
\(792\) 107.324 + 400.537i 0.135510 + 0.505729i
\(793\) −1203.76 + 2084.97i −1.51798 + 2.62921i
\(794\) 452.630 121.282i 0.570063 0.152748i
\(795\) −215.365 57.7068i −0.270899 0.0725871i
\(796\) 52.7085 196.711i 0.0662167 0.247124i
\(797\) 137.023 + 511.376i 0.171923 + 0.641626i 0.997055 + 0.0766860i \(0.0244339\pi\)
−0.825132 + 0.564940i \(0.808899\pi\)
\(798\) −153.946 88.8807i −0.192915 0.111379i
\(799\) −1016.25 + 272.303i −1.27190 + 0.340804i
\(800\) 55.2154 + 55.2154i 0.0690192 + 0.0690192i
\(801\) 431.456 + 115.608i 0.538647 + 0.144330i
\(802\) −46.9503 27.1067i −0.0585415 0.0337989i
\(803\) 486.910 0.606363
\(804\) 620.091i 0.771258i
\(805\) −51.0010 29.4455i −0.0633553 0.0365782i
\(806\) 552.170 552.170i 0.685075 0.685075i
\(807\) −1394.75 + 805.261i −1.72832 + 0.997846i
\(808\) −231.442 + 231.442i −0.286438 + 0.286438i
\(809\) 270.117 + 72.3776i 0.333890 + 0.0894655i 0.421869 0.906657i \(-0.361374\pi\)
−0.0879791 + 0.996122i \(0.528041\pi\)
\(810\) 217.383 + 376.518i 0.268374 + 0.464837i
\(811\) 679.349 + 1176.67i 0.837668 + 1.45088i 0.891840 + 0.452352i \(0.149415\pi\)
−0.0541715 + 0.998532i \(0.517252\pi\)
\(812\) 19.7578 5.29409i 0.0243323 0.00651982i
\(813\) 545.607i 0.671104i
\(814\) −165.439 382.765i −0.203242 0.470227i
\(815\) 643.373 0.789415
\(816\) 153.539 + 573.015i 0.188161 + 0.702225i
\(817\) 1318.37 761.159i 1.61367 0.931651i
\(818\) 43.2865 24.9914i 0.0529174 0.0305519i
\(819\) 114.958 429.030i 0.140364 0.523846i
\(820\) 57.4387 + 57.4387i 0.0700472 + 0.0700472i
\(821\) −615.011 1065.23i −0.749100 1.29748i −0.948255 0.317511i \(-0.897153\pi\)
0.199155 0.979968i \(-0.436180\pi\)
\(822\) 40.0158 + 40.0158i 0.0486810 + 0.0486810i
\(823\) −10.0892 + 17.4751i −0.0122591 + 0.0212334i −0.872090 0.489346i \(-0.837236\pi\)
0.859831 + 0.510579i \(0.170569\pi\)
\(824\) −92.1555 −0.111839
\(825\) 575.783i 0.697919i
\(826\) −40.8195 + 70.7015i −0.0494183 + 0.0855951i
\(827\) −196.114 + 731.909i −0.237140 + 0.885017i 0.740033 + 0.672570i \(0.234810\pi\)
−0.977173 + 0.212446i \(0.931857\pi\)
\(828\) 417.468 417.468i 0.504188 0.504188i
\(829\) 180.645 + 674.176i 0.217907 + 0.813240i 0.985123 + 0.171851i \(0.0549748\pi\)
−0.767216 + 0.641389i \(0.778359\pi\)
\(830\) 256.844 444.867i 0.309451 0.535985i
\(831\) −582.291 + 156.024i −0.700711 + 0.187755i
\(832\) −170.090 45.5753i −0.204435 0.0547781i
\(833\) −350.515 + 1308.14i −0.420787 + 1.57040i
\(834\) 19.8156 + 73.9529i 0.0237597 + 0.0886726i
\(835\) 85.9287 + 49.6110i 0.102909 + 0.0594143i
\(836\) 337.054 90.3133i 0.403174 0.108030i
\(837\) 872.480 + 872.480i 1.04239 + 1.04239i
\(838\) 8.15182 + 2.18427i 0.00972771 + 0.00260653i
\(839\) 1076.40 + 621.463i 1.28296 + 0.740718i 0.977389 0.211450i \(-0.0678187\pi\)
0.305573 + 0.952169i \(0.401152\pi\)
\(840\) −54.3355 −0.0646851
\(841\) 754.059i 0.896622i
\(842\) −77.5345 44.7646i −0.0920838 0.0531646i
\(843\) 1112.78 1112.78i 1.32002 1.32002i
\(844\) 422.986 244.211i 0.501169 0.289350i
\(845\) 746.464 746.464i 0.883390 0.883390i
\(846\) 933.148 + 250.036i 1.10301 + 0.295551i
\(847\) −31.5316 54.6143i −0.0372274 0.0644797i
\(848\) 25.4609 + 44.0997i 0.0300247 + 0.0520043i
\(849\) −578.720 + 155.067i −0.681649 + 0.182647i
\(850\) 553.129i 0.650740i
\(851\) −354.183 + 476.474i −0.416196 + 0.559899i
\(852\) −572.692 −0.672174
\(853\) −147.550 550.663i −0.172977 0.645560i −0.996887 0.0788394i \(-0.974879\pi\)
0.823910 0.566721i \(-0.191788\pi\)
\(854\) 146.934 84.8326i 0.172054 0.0993356i
\(855\) 1167.16 673.860i 1.36510 0.788140i
\(856\) −7.96428 + 29.7231i −0.00930407 + 0.0347233i
\(857\) 492.222 + 492.222i 0.574355 + 0.574355i 0.933342 0.358987i \(-0.116878\pi\)
−0.358987 + 0.933342i \(0.616878\pi\)
\(858\) 649.213 + 1124.47i 0.756659 + 1.31057i
\(859\) −181.096 181.096i −0.210822 0.210822i 0.593795 0.804617i \(-0.297629\pi\)
−0.804617 + 0.593795i \(0.797629\pi\)
\(860\) 232.660 402.979i 0.270535 0.468580i
\(861\) 69.6883 0.0809387
\(862\) 63.9129i 0.0741450i
\(863\) −497.794 + 862.205i −0.576819 + 0.999079i 0.419023 + 0.907976i \(0.362373\pi\)
−0.995841 + 0.0911034i \(0.970961\pi\)
\(864\) 72.0132 268.757i 0.0833486 0.311061i
\(865\) 217.461 217.461i 0.251400 0.251400i
\(866\) 112.843 + 421.137i 0.130304 + 0.486302i
\(867\) 1344.74 2329.16i 1.55103 2.68646i
\(868\) −53.1564 + 14.2432i −0.0612401 + 0.0164092i
\(869\) −844.371 226.248i −0.971658 0.260355i
\(870\) −59.7736 + 223.078i −0.0687053 + 0.256412i
\(871\) 337.454 + 1259.39i 0.387432 + 1.44592i
\(872\) 318.699 + 184.001i 0.365481 + 0.211010i
\(873\) −1053.64 + 282.322i −1.20692 + 0.323393i
\(874\) −351.301 351.301i −0.401946 0.401946i
\(875\) 137.564 + 36.8602i 0.157216 + 0.0421260i
\(876\) −553.928 319.811i −0.632338 0.365081i
\(877\) −1053.75 −1.20153 −0.600767 0.799424i \(-0.705138\pi\)
−0.600767 + 0.799424i \(0.705138\pi\)
\(878\) 760.241i 0.865878i
\(879\) 509.002 + 293.872i 0.579069 + 0.334326i
\(880\) 75.4200 75.4200i 0.0857046 0.0857046i
\(881\) −467.452 + 269.884i −0.530593 + 0.306338i −0.741258 0.671220i \(-0.765770\pi\)
0.210665 + 0.977558i \(0.432437\pi\)
\(882\) 879.320 879.320i 0.996961 0.996961i
\(883\) 375.206 + 100.536i 0.424922 + 0.113858i 0.464942 0.885341i \(-0.346075\pi\)
−0.0400195 + 0.999199i \(0.512742\pi\)
\(884\) 623.670 + 1080.23i 0.705509 + 1.22198i
\(885\) −460.878 798.265i −0.520766 0.901994i
\(886\) −770.111 + 206.351i −0.869200 + 0.232901i
\(887\) 1012.84i 1.14188i −0.820993 0.570938i \(-0.806580\pi\)
0.820993 0.570938i \(-0.193420\pi\)
\(888\) −63.1962 + 544.112i −0.0711669 + 0.612739i
\(889\) 187.164 0.210533
\(890\) −29.7366 110.979i −0.0334119 0.124695i
\(891\) −634.079 + 366.086i −0.711649 + 0.410871i
\(892\) 103.368 59.6793i 0.115883 0.0669050i
\(893\) 210.407 785.248i 0.235618 0.879337i
\(894\) −1146.52 1146.52i −1.28246 1.28246i
\(895\) 145.316 + 251.694i 0.162364 + 0.281223i
\(896\) 8.77491 + 8.77491i 0.00979343 + 0.00979343i
\(897\) 924.329 1600.98i 1.03047 1.78482i
\(898\) 188.965 0.210429
\(899\) 233.906i 0.260185i
\(900\) −253.949 + 439.853i −0.282166 + 0.488726i
\(901\) 93.3581 348.417i 0.103616 0.386700i
\(902\) −96.7303 + 96.7303i −0.107240 + 0.107240i
\(903\) −103.321 385.599i −0.114420 0.427019i
\(904\) −304.414 + 527.261i −0.336741 + 0.583253i
\(905\) −141.072 + 37.8001i −0.155881 + 0.0417681i
\(906\) −971.154 260.220i −1.07191 0.287218i
\(907\) 354.112 1321.56i 0.390421 1.45707i −0.439020 0.898478i \(-0.644674\pi\)
0.829441 0.558595i \(-0.188659\pi\)
\(908\) 18.1270 + 67.6508i 0.0199636 + 0.0745052i
\(909\) −1843.70 1064.46i −2.02827 1.17102i
\(910\) −110.354 + 29.5694i −0.121269 + 0.0324938i
\(911\) 882.939 + 882.939i 0.969197 + 0.969197i 0.999540 0.0303421i \(-0.00965968\pi\)
−0.0303421 + 0.999540i \(0.509660\pi\)
\(912\) −442.765 118.639i −0.485488 0.130086i
\(913\) 749.184 + 432.541i 0.820574 + 0.473758i
\(914\) 587.613 0.642903
\(915\) 1915.63i 2.09358i
\(916\) −108.938 62.8952i −0.118928 0.0686629i
\(917\) −88.7007 + 88.7007i −0.0967292 + 0.0967292i
\(918\) −1706.86 + 985.455i −1.85932 + 1.07348i
\(919\) −1243.71 + 1243.71i −1.35333 + 1.35333i −0.471427 + 0.881905i \(0.656261\pi\)
−0.881905 + 0.471427i \(0.843739\pi\)
\(920\) −146.685 39.3040i −0.159440 0.0427217i
\(921\) −446.948 774.137i −0.485286 0.840539i
\(922\) −587.597 1017.75i −0.637307 1.10385i
\(923\) −1163.13 + 311.659i −1.26016 + 0.337659i
\(924\) 91.5043i 0.0990306i
\(925\) 188.224 474.794i 0.203485 0.513291i
\(926\) 255.262 0.275661
\(927\) −155.139 578.985i −0.167356 0.624579i
\(928\) 45.6791 26.3729i 0.0492232 0.0284190i
\(929\) 808.546 466.814i 0.870340 0.502491i 0.00287910 0.999996i \(-0.499084\pi\)
0.867461 + 0.497505i \(0.165750\pi\)
\(930\) 160.815 600.170i 0.172919 0.645344i
\(931\) −739.951 739.951i −0.794791 0.794791i
\(932\) −224.895 389.530i −0.241304 0.417951i
\(933\) 353.385 + 353.385i 0.378762 + 0.378762i
\(934\) 111.727 193.518i 0.119622 0.207192i
\(935\) −755.532 −0.808055
\(936\) 1145.34i 1.22366i
\(937\) 590.350 1022.52i 0.630042 1.09127i −0.357500 0.933913i \(-0.616371\pi\)
0.987543 0.157352i \(-0.0502958\pi\)
\(938\) 23.7814 88.7535i 0.0253533 0.0946200i
\(939\) −730.857 + 730.857i −0.778335 + 0.778335i
\(940\) −64.3140 240.023i −0.0684191 0.255344i
\(941\) 840.243 1455.34i 0.892925 1.54659i 0.0565734 0.998398i \(-0.481982\pi\)
0.836352 0.548193i \(-0.184684\pi\)
\(942\) −480.851 + 128.844i −0.510458 + 0.136777i
\(943\) 188.131 + 50.4095i 0.199503 + 0.0534565i
\(944\) −54.4862 + 203.345i −0.0577184 + 0.215408i
\(945\) −46.7223 174.370i −0.0494416 0.184519i
\(946\) 678.641 + 391.814i 0.717380 + 0.414179i
\(947\) 659.754 176.781i 0.696678 0.186674i 0.106936 0.994266i \(-0.465896\pi\)
0.589742 + 0.807592i \(0.299229\pi\)
\(948\) 811.986 + 811.986i 0.856526 + 0.856526i
\(949\) −1299.06 348.082i −1.36887 0.366788i
\(950\) 370.138 + 213.699i 0.389619 + 0.224947i
\(951\) −1144.78 −1.20376
\(952\) 87.9040i 0.0923362i
\(953\) 674.715 + 389.547i 0.707990 + 0.408758i 0.810316 0.585993i \(-0.199295\pi\)
−0.102326 + 0.994751i \(0.532629\pi\)
\(954\) −234.203 + 234.203i −0.245495 + 0.245495i
\(955\) −253.499 + 146.358i −0.265444 + 0.153254i
\(956\) −156.433 + 156.433i −0.163633 + 0.163633i
\(957\) −375.677 100.662i −0.392557 0.105185i
\(958\) −376.540 652.187i −0.393048 0.680780i
\(959\) −4.19278 7.26211i −0.00437204 0.00757259i
\(960\) −135.338 + 36.2637i −0.140977 + 0.0377747i
\(961\) 331.699i 0.345160i
\(962\) 167.755 + 1139.47i 0.174382 + 1.18448i
\(963\) −200.149 −0.207839
\(964\) −1.67471 6.25012i −0.00173726 0.00648353i
\(965\) −1086.23 + 627.137i −1.12563 + 0.649883i
\(966\) −112.826 + 65.1404i −0.116798 + 0.0674331i
\(967\) −121.165 + 452.194i −0.125300 + 0.467626i −0.999850 0.0173092i \(-0.994490\pi\)
0.874550 + 0.484935i \(0.161157\pi\)
\(968\) −114.988 114.988i −0.118789 0.118789i
\(969\) 1623.49 + 2811.97i 1.67543 + 2.90193i
\(970\) 198.398 + 198.398i 0.204534 + 0.204534i
\(971\) −105.007 + 181.877i −0.108143 + 0.187309i −0.915018 0.403413i \(-0.867824\pi\)
0.806875 + 0.590722i \(0.201157\pi\)
\(972\) 76.4583 0.0786608
\(973\) 11.3448i 0.0116596i
\(974\) 10.3553 17.9359i 0.0106317 0.0184147i
\(975\) −411.615 + 1536.17i −0.422170 + 1.57556i
\(976\) 309.364 309.364i 0.316971 0.316971i
\(977\) −134.375 501.494i −0.137538 0.513300i −0.999975 0.00713434i \(-0.997729\pi\)
0.862436 0.506166i \(-0.168938\pi\)
\(978\) 711.648 1232.61i 0.727656 1.26034i
\(979\) 186.895 50.0783i 0.190904 0.0511525i
\(980\) −308.964 82.7866i −0.315269 0.0844762i
\(981\) −619.511 + 2312.05i −0.631509 + 2.35683i
\(982\) 298.769 + 1115.02i 0.304245 + 1.13546i
\(983\) 1522.82 + 879.202i 1.54916 + 0.894407i 0.998206 + 0.0598706i \(0.0190688\pi\)
0.550953 + 0.834537i \(0.314265\pi\)
\(984\) 173.578 46.5102i 0.176401 0.0472664i
\(985\) −271.602 271.602i −0.275738 0.275738i
\(986\) −360.896 96.7018i −0.366020 0.0980749i
\(987\) −184.620 106.591i −0.187052 0.107995i
\(988\) −963.811 −0.975517
\(989\) 1115.70i 1.12811i
\(990\) 600.806 + 346.876i 0.606875 + 0.350379i
\(991\) −620.013 + 620.013i −0.625643 + 0.625643i −0.946969 0.321325i \(-0.895872\pi\)
0.321325 + 0.946969i \(0.395872\pi\)
\(992\) −122.895 + 70.9536i −0.123886 + 0.0715258i
\(993\) 165.645 165.645i 0.166812 0.166812i
\(994\) 81.9693 + 21.9636i 0.0824641 + 0.0220962i
\(995\) −170.356 295.066i −0.171212 0.296549i
\(996\) −568.201 984.153i −0.570483 0.988105i
\(997\) 1551.59 415.747i 1.55626 0.416998i 0.624782 0.780799i \(-0.285188\pi\)
0.931477 + 0.363800i \(0.118521\pi\)
\(998\) 1271.96i 1.27451i
\(999\) −1800.47 + 265.069i −1.80227 + 0.265334i
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 74.3.g.b.23.3 12
37.29 odd 12 inner 74.3.g.b.29.3 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
74.3.g.b.23.3 12 1.1 even 1 trivial
74.3.g.b.29.3 yes 12 37.29 odd 12 inner