Properties

Label 33.3.g.a.13.3
Level $33$
Weight $3$
Character 33.13
Analytic conductor $0.899$
Analytic rank $0$
Dimension $16$
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] = [33,3,Mod(7,33)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(33, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 7]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("33.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 33.g (of order \(10\), 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: \(0.899184872389\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 77 x^{12} + 88 x^{11} - 577 x^{10} + 578 x^{9} + 1520 x^{8} + 1868 x^{7} - 1619 x^{6} - 16804 x^{5} + 32427 x^{4} + 43316 x^{3} + \cdots + 83521 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 13.3
Root \(0.988132 + 0.846795i\) of defining polynomial
Character \(\chi\) \(=\) 33.13
Dual form 33.3.g.a.28.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.28981 + 0.419086i) q^{2} +(1.40126 - 1.01807i) q^{3} +(-1.74808 - 1.27006i) q^{4} +(0.708979 + 2.18201i) q^{5} +(2.23402 - 0.725878i) q^{6} +(-5.74346 + 7.90520i) q^{7} +(-4.91103 - 6.75946i) q^{8} +(0.927051 - 2.85317i) q^{9} +O(q^{10})\) \(q+(1.28981 + 0.419086i) q^{2} +(1.40126 - 1.01807i) q^{3} +(-1.74808 - 1.27006i) q^{4} +(0.708979 + 2.18201i) q^{5} +(2.23402 - 0.725878i) q^{6} +(-5.74346 + 7.90520i) q^{7} +(-4.91103 - 6.75946i) q^{8} +(0.927051 - 2.85317i) q^{9} +3.11151i q^{10} +(10.3340 - 3.76954i) q^{11} -3.74252 q^{12} +(-14.6363 - 4.75561i) q^{13} +(-10.7210 + 7.78923i) q^{14} +(3.21491 + 2.33577i) q^{15} +(-0.830695 - 2.55662i) q^{16} +(11.2386 - 3.65165i) q^{17} +(2.39145 - 3.29154i) q^{18} +(7.10329 + 9.77683i) q^{19} +(1.53192 - 4.71477i) q^{20} +16.9245i q^{21} +(14.9086 - 0.531195i) q^{22} +16.6610 q^{23} +(-13.7633 - 4.47195i) q^{24} +(15.9669 - 11.6006i) q^{25} +(-16.8850 - 12.2677i) q^{26} +(-1.60570 - 4.94183i) q^{27} +(20.0801 - 6.52441i) q^{28} +(-15.6013 + 21.4734i) q^{29} +(3.16775 + 4.36003i) q^{30} +(1.28594 - 3.95770i) q^{31} +29.7749i q^{32} +(10.6429 - 15.8028i) q^{33} +16.0261 q^{34} +(-21.3212 - 6.92769i) q^{35} +(-5.24424 + 3.81017i) q^{36} +(-54.4646 - 39.5709i) q^{37} +(5.06458 + 15.5872i) q^{38} +(-25.3507 + 8.23696i) q^{39} +(11.2674 - 15.5082i) q^{40} +(-10.6080 - 14.6006i) q^{41} +(-7.09282 + 21.8295i) q^{42} +46.3735i q^{43} +(-22.8521 - 6.53522i) q^{44} +6.88291 q^{45} +(21.4896 + 6.98238i) q^{46} +(-49.2812 + 35.8049i) q^{47} +(-3.76684 - 2.73677i) q^{48} +(-14.3630 - 44.2047i) q^{49} +(25.4560 - 8.27115i) q^{50} +(12.0306 - 16.5587i) q^{51} +(19.5455 + 26.9020i) q^{52} +(31.2773 - 96.2616i) q^{53} -7.04697i q^{54} +(15.5517 + 19.8763i) q^{55} +81.6412 q^{56} +(19.9071 + 6.46820i) q^{57} +(-29.1220 + 21.1584i) q^{58} +(78.7122 + 57.1878i) q^{59} +(-2.65337 - 8.16623i) q^{60} +(1.19706 - 0.388949i) q^{61} +(3.31724 - 4.56578i) q^{62} +(17.2304 + 23.7156i) q^{63} +(-15.8010 + 48.6305i) q^{64} -35.3081i q^{65} +(20.3501 - 15.9224i) q^{66} -55.1168 q^{67} +(-24.2838 - 7.89030i) q^{68} +(23.3463 - 16.9621i) q^{69} +(-24.5971 - 17.8709i) q^{70} +(-4.62167 - 14.2240i) q^{71} +(-23.8387 + 7.74565i) q^{72} +(-44.6021 + 61.3895i) q^{73} +(-53.6656 - 73.8644i) q^{74} +(10.5635 - 32.5110i) q^{75} -26.1123i q^{76} +(-29.5537 + 103.342i) q^{77} -36.1497 q^{78} +(27.7900 + 9.02950i) q^{79} +(4.98962 - 3.62517i) q^{80} +(-7.28115 - 5.29007i) q^{81} +(-7.56341 - 23.2778i) q^{82} +(-6.06044 + 1.96915i) q^{83} +(21.4951 - 29.5854i) q^{84} +(15.9359 + 21.9339i) q^{85} +(-19.4345 + 59.8133i) q^{86} +45.9731i q^{87} +(-76.2304 - 51.3395i) q^{88} -3.95503 q^{89} +(8.87767 + 2.88453i) q^{90} +(121.657 - 88.3889i) q^{91} +(-29.1247 - 21.1604i) q^{92} +(-2.22731 - 6.85494i) q^{93} +(-78.5689 + 25.5286i) q^{94} +(-16.2971 + 22.4310i) q^{95} +(30.3130 + 41.7223i) q^{96} +(-10.2392 + 31.5131i) q^{97} -63.0352i q^{98} +(-1.17504 - 32.9791i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 20 q^{4} - 4 q^{5} - 30 q^{7} - 40 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 20 q^{4} - 4 q^{5} - 30 q^{7} - 40 q^{8} - 12 q^{9} - 10 q^{11} - 24 q^{12} + 30 q^{13} - 2 q^{14} - 24 q^{15} + 16 q^{16} - 10 q^{17} - 30 q^{18} + 42 q^{20} + 42 q^{22} + 132 q^{23} + 90 q^{24} - 2 q^{25} + 46 q^{26} - 50 q^{28} + 160 q^{29} + 180 q^{30} + 10 q^{31} + 12 q^{33} - 368 q^{34} - 320 q^{35} + 60 q^{36} - 126 q^{37} - 130 q^{38} + 30 q^{40} - 120 q^{41} - 204 q^{42} - 206 q^{44} - 12 q^{45} + 50 q^{46} - 150 q^{47} - 96 q^{48} + 210 q^{49} + 330 q^{50} - 60 q^{51} + 110 q^{52} + 342 q^{53} + 244 q^{55} + 524 q^{56} + 60 q^{57} + 150 q^{58} + 110 q^{59} + 36 q^{60} - 90 q^{61} + 40 q^{62} + 90 q^{63} - 168 q^{64} + 48 q^{66} + 36 q^{67} + 80 q^{68} + 210 q^{69} + 340 q^{70} - 236 q^{71} - 150 q^{72} - 350 q^{73} - 730 q^{74} - 408 q^{75} - 390 q^{77} - 312 q^{78} + 210 q^{79} - 806 q^{80} - 36 q^{81} + 114 q^{82} - 190 q^{83} - 180 q^{84} + 110 q^{85} + 736 q^{86} + 144 q^{88} + 76 q^{89} + 60 q^{90} + 306 q^{91} - 150 q^{92} + 144 q^{93} - 350 q^{94} + 430 q^{95} + 450 q^{96} - 354 q^{97} + 180 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(e\left(\frac{1}{10}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.28981 + 0.419086i 0.644907 + 0.209543i 0.613167 0.789953i \(-0.289895\pi\)
0.0317398 + 0.999496i \(0.489895\pi\)
\(3\) 1.40126 1.01807i 0.467086 0.339358i
\(4\) −1.74808 1.27006i −0.437020 0.317514i
\(5\) 0.708979 + 2.18201i 0.141796 + 0.436402i 0.996585 0.0825729i \(-0.0263137\pi\)
−0.854789 + 0.518975i \(0.826314\pi\)
\(6\) 2.23402 0.725878i 0.372337 0.120980i
\(7\) −5.74346 + 7.90520i −0.820495 + 1.12931i 0.169123 + 0.985595i \(0.445906\pi\)
−0.989618 + 0.143720i \(0.954094\pi\)
\(8\) −4.91103 6.75946i −0.613879 0.844932i
\(9\) 0.927051 2.85317i 0.103006 0.317019i
\(10\) 3.11151i 0.311151i
\(11\) 10.3340 3.76954i 0.939450 0.342686i
\(12\) −3.74252 −0.311877
\(13\) −14.6363 4.75561i −1.12587 0.365816i −0.313862 0.949468i \(-0.601623\pi\)
−0.812004 + 0.583652i \(0.801623\pi\)
\(14\) −10.7210 + 7.78923i −0.765783 + 0.556374i
\(15\) 3.21491 + 2.33577i 0.214327 + 0.155718i
\(16\) −0.830695 2.55662i −0.0519184 0.159789i
\(17\) 11.2386 3.65165i 0.661096 0.214803i 0.0407956 0.999168i \(-0.487011\pi\)
0.620300 + 0.784364i \(0.287011\pi\)
\(18\) 2.39145 3.29154i 0.132858 0.182864i
\(19\) 7.10329 + 9.77683i 0.373857 + 0.514570i 0.953944 0.299984i \(-0.0969814\pi\)
−0.580087 + 0.814555i \(0.696981\pi\)
\(20\) 1.53192 4.71477i 0.0765962 0.235739i
\(21\) 16.9245i 0.805929i
\(22\) 14.9086 0.531195i 0.677665 0.0241452i
\(23\) 16.6610 0.724390 0.362195 0.932102i \(-0.382027\pi\)
0.362195 + 0.932102i \(0.382027\pi\)
\(24\) −13.7633 4.47195i −0.573469 0.186331i
\(25\) 15.9669 11.6006i 0.638676 0.464025i
\(26\) −16.8850 12.2677i −0.649425 0.471835i
\(27\) −1.60570 4.94183i −0.0594703 0.183031i
\(28\) 20.0801 6.52441i 0.717146 0.233015i
\(29\) −15.6013 + 21.4734i −0.537977 + 0.740462i −0.988320 0.152394i \(-0.951302\pi\)
0.450343 + 0.892856i \(0.351302\pi\)
\(30\) 3.16775 + 4.36003i 0.105592 + 0.145334i
\(31\) 1.28594 3.95770i 0.0414818 0.127668i −0.928171 0.372154i \(-0.878619\pi\)
0.969653 + 0.244486i \(0.0786193\pi\)
\(32\) 29.7749i 0.930466i
\(33\) 10.6429 15.8028i 0.322511 0.478874i
\(34\) 16.0261 0.471356
\(35\) −21.3212 6.92769i −0.609178 0.197934i
\(36\) −5.24424 + 3.81017i −0.145673 + 0.105838i
\(37\) −54.4646 39.5709i −1.47202 1.06948i −0.980023 0.198884i \(-0.936268\pi\)
−0.491994 0.870599i \(-0.663732\pi\)
\(38\) 5.06458 + 15.5872i 0.133279 + 0.410189i
\(39\) −25.3507 + 8.23696i −0.650019 + 0.211204i
\(40\) 11.2674 15.5082i 0.281685 0.387706i
\(41\) −10.6080 14.6006i −0.258731 0.356113i 0.659814 0.751429i \(-0.270635\pi\)
−0.918545 + 0.395316i \(0.870635\pi\)
\(42\) −7.09282 + 21.8295i −0.168877 + 0.519749i
\(43\) 46.3735i 1.07845i 0.842160 + 0.539227i \(0.181284\pi\)
−0.842160 + 0.539227i \(0.818716\pi\)
\(44\) −22.8521 6.53522i −0.519366 0.148528i
\(45\) 6.88291 0.152954
\(46\) 21.4896 + 6.98238i 0.467164 + 0.151791i
\(47\) −49.2812 + 35.8049i −1.04854 + 0.761806i −0.971934 0.235255i \(-0.924407\pi\)
−0.0766030 + 0.997062i \(0.524407\pi\)
\(48\) −3.76684 2.73677i −0.0784759 0.0570161i
\(49\) −14.3630 44.2047i −0.293122 0.902137i
\(50\) 25.4560 8.27115i 0.509120 0.165423i
\(51\) 12.0306 16.5587i 0.235894 0.324680i
\(52\) 19.5455 + 26.9020i 0.375875 + 0.517347i
\(53\) 31.2773 96.2616i 0.590138 1.81626i 0.0125594 0.999921i \(-0.496002\pi\)
0.577578 0.816335i \(-0.303998\pi\)
\(54\) 7.04697i 0.130500i
\(55\) 15.5517 + 19.8763i 0.282759 + 0.361387i
\(56\) 81.6412 1.45788
\(57\) 19.9071 + 6.46820i 0.349247 + 0.113477i
\(58\) −29.1220 + 21.1584i −0.502104 + 0.364800i
\(59\) 78.7122 + 57.1878i 1.33411 + 0.969284i 0.999639 + 0.0268769i \(0.00855621\pi\)
0.334467 + 0.942408i \(0.391444\pi\)
\(60\) −2.65337 8.16623i −0.0442228 0.136104i
\(61\) 1.19706 0.388949i 0.0196240 0.00637621i −0.299189 0.954194i \(-0.596716\pi\)
0.318813 + 0.947818i \(0.396716\pi\)
\(62\) 3.31724 4.56578i 0.0535038 0.0736416i
\(63\) 17.2304 + 23.7156i 0.273498 + 0.376438i
\(64\) −15.8010 + 48.6305i −0.246891 + 0.759852i
\(65\) 35.3081i 0.543202i
\(66\) 20.3501 15.9224i 0.308334 0.241249i
\(67\) −55.1168 −0.822638 −0.411319 0.911491i \(-0.634932\pi\)
−0.411319 + 0.911491i \(0.634932\pi\)
\(68\) −24.2838 7.89030i −0.357115 0.116034i
\(69\) 23.3463 16.9621i 0.338353 0.245828i
\(70\) −24.5971 17.8709i −0.351388 0.255298i
\(71\) −4.62167 14.2240i −0.0650939 0.200338i 0.913220 0.407467i \(-0.133588\pi\)
−0.978314 + 0.207129i \(0.933588\pi\)
\(72\) −23.8387 + 7.74565i −0.331092 + 0.107578i
\(73\) −44.6021 + 61.3895i −0.610987 + 0.840952i −0.996658 0.0816847i \(-0.973970\pi\)
0.385671 + 0.922636i \(0.373970\pi\)
\(74\) −53.6656 73.8644i −0.725211 0.998168i
\(75\) 10.5635 32.5110i 0.140846 0.433480i
\(76\) 26.1123i 0.343582i
\(77\) −29.5537 + 103.342i −0.383814 + 1.34211i
\(78\) −36.1497 −0.463458
\(79\) 27.7900 + 9.02950i 0.351772 + 0.114298i 0.479572 0.877502i \(-0.340792\pi\)
−0.127801 + 0.991800i \(0.540792\pi\)
\(80\) 4.98962 3.62517i 0.0623703 0.0453147i
\(81\) −7.28115 5.29007i −0.0898908 0.0653095i
\(82\) −7.56341 23.2778i −0.0922367 0.283875i
\(83\) −6.06044 + 1.96915i −0.0730173 + 0.0237248i −0.345298 0.938493i \(-0.612222\pi\)
0.272281 + 0.962218i \(0.412222\pi\)
\(84\) 21.4951 29.5854i 0.255893 0.352207i
\(85\) 15.9359 + 21.9339i 0.187481 + 0.258046i
\(86\) −19.4345 + 59.8133i −0.225983 + 0.695503i
\(87\) 45.9731i 0.528427i
\(88\) −76.2304 51.3395i −0.866255 0.583404i
\(89\) −3.95503 −0.0444385 −0.0222193 0.999753i \(-0.507073\pi\)
−0.0222193 + 0.999753i \(0.507073\pi\)
\(90\) 8.87767 + 2.88453i 0.0986408 + 0.0320503i
\(91\) 121.657 88.3889i 1.33689 0.971306i
\(92\) −29.1247 21.1604i −0.316573 0.230004i
\(93\) −2.22731 6.85494i −0.0239495 0.0737090i
\(94\) −78.5689 + 25.5286i −0.835840 + 0.271581i
\(95\) −16.2971 + 22.4310i −0.171548 + 0.236116i
\(96\) 30.3130 + 41.7223i 0.315761 + 0.434608i
\(97\) −10.2392 + 31.5131i −0.105559 + 0.324877i −0.989861 0.142038i \(-0.954635\pi\)
0.884302 + 0.466915i \(0.154635\pi\)
\(98\) 63.0352i 0.643216i
\(99\) −1.17504 32.9791i −0.0118691 0.333122i
\(100\) −42.6449 −0.426449
\(101\) 92.3279 + 29.9992i 0.914138 + 0.297021i 0.728060 0.685514i \(-0.240422\pi\)
0.186078 + 0.982535i \(0.440422\pi\)
\(102\) 22.4567 16.3158i 0.220164 0.159958i
\(103\) 150.522 + 109.361i 1.46138 + 1.06175i 0.983001 + 0.183602i \(0.0587757\pi\)
0.478380 + 0.878153i \(0.341224\pi\)
\(104\) 39.7338 + 122.288i 0.382056 + 1.17585i
\(105\) −36.9295 + 11.9991i −0.351709 + 0.114277i
\(106\) 80.6838 111.052i 0.761168 1.04766i
\(107\) −112.786 155.236i −1.05407 1.45081i −0.885224 0.465165i \(-0.845995\pi\)
−0.168849 0.985642i \(-0.554005\pi\)
\(108\) −3.46951 + 10.6781i −0.0321251 + 0.0988709i
\(109\) 113.760i 1.04367i −0.853047 0.521834i \(-0.825248\pi\)
0.853047 0.521834i \(-0.174752\pi\)
\(110\) 11.7290 + 32.1542i 0.106627 + 0.292311i
\(111\) −116.605 −1.05050
\(112\) 24.9816 + 8.11703i 0.223050 + 0.0724734i
\(113\) −13.2504 + 9.62696i −0.117260 + 0.0851944i −0.644870 0.764293i \(-0.723088\pi\)
0.527610 + 0.849487i \(0.323088\pi\)
\(114\) 22.9657 + 16.6856i 0.201453 + 0.146365i
\(115\) 11.8123 + 36.3544i 0.102715 + 0.316125i
\(116\) 54.5448 17.7227i 0.470214 0.152782i
\(117\) −27.1371 + 37.3510i −0.231941 + 0.319240i
\(118\) 77.5575 + 106.749i 0.657267 + 0.904651i
\(119\) −35.6816 + 109.817i −0.299846 + 0.922830i
\(120\) 33.2021i 0.276684i
\(121\) 92.5811 77.9085i 0.765133 0.643872i
\(122\) 1.70699 0.0139917
\(123\) −29.7291 9.65956i −0.241700 0.0785330i
\(124\) −7.27442 + 5.28518i −0.0586647 + 0.0426224i
\(125\) 83.0361 + 60.3293i 0.664289 + 0.482634i
\(126\) 12.2851 + 37.8097i 0.0975010 + 0.300077i
\(127\) 5.31423 1.72670i 0.0418443 0.0135960i −0.288020 0.957624i \(-0.592997\pi\)
0.329864 + 0.944028i \(0.392997\pi\)
\(128\) 29.2442 40.2512i 0.228471 0.314463i
\(129\) 47.2117 + 64.9813i 0.365982 + 0.503731i
\(130\) 14.7971 45.5409i 0.113824 0.350315i
\(131\) 225.713i 1.72300i −0.507758 0.861500i \(-0.669526\pi\)
0.507758 0.861500i \(-0.330474\pi\)
\(132\) −38.6751 + 14.1076i −0.292993 + 0.106876i
\(133\) −118.085 −0.887860
\(134\) −71.0904 23.0987i −0.530525 0.172378i
\(135\) 9.64473 7.00731i 0.0714425 0.0519060i
\(136\) −79.8765 58.0336i −0.587327 0.426718i
\(137\) 16.1770 + 49.7877i 0.118080 + 0.363414i 0.992577 0.121618i \(-0.0388081\pi\)
−0.874497 + 0.485031i \(0.838808\pi\)
\(138\) 37.2210 12.0938i 0.269717 0.0876365i
\(139\) 16.4968 22.7058i 0.118682 0.163351i −0.745543 0.666458i \(-0.767810\pi\)
0.864224 + 0.503106i \(0.167810\pi\)
\(140\) 28.4727 + 39.1893i 0.203376 + 0.279924i
\(141\) −32.6037 + 100.344i −0.231232 + 0.711659i
\(142\) 20.2832i 0.142840i
\(143\) −169.177 + 6.02777i −1.18305 + 0.0421523i
\(144\) −8.06456 −0.0560039
\(145\) −57.9162 18.8181i −0.399422 0.129780i
\(146\) −83.2558 + 60.4889i −0.570245 + 0.414308i
\(147\) −65.1299 47.3197i −0.443061 0.321902i
\(148\) 44.9514 + 138.346i 0.303726 + 0.934771i
\(149\) 10.6920 3.47406i 0.0717587 0.0233158i −0.272918 0.962037i \(-0.587989\pi\)
0.344676 + 0.938722i \(0.387989\pi\)
\(150\) 27.2498 37.5061i 0.181665 0.250041i
\(151\) −59.4636 81.8446i −0.393799 0.542018i 0.565375 0.824834i \(-0.308731\pi\)
−0.959174 + 0.282816i \(0.908731\pi\)
\(152\) 31.2016 96.0287i 0.205274 0.631768i
\(153\) 35.4510i 0.231706i
\(154\) −81.4280 + 120.907i −0.528753 + 0.785108i
\(155\) 9.54745 0.0615965
\(156\) 54.7765 + 17.7980i 0.351132 + 0.114090i
\(157\) −15.4295 + 11.2102i −0.0982772 + 0.0714025i −0.635839 0.771822i \(-0.719346\pi\)
0.537561 + 0.843225i \(0.319346\pi\)
\(158\) 32.0597 + 23.2928i 0.202910 + 0.147423i
\(159\) −54.1739 166.730i −0.340716 1.04862i
\(160\) −64.9692 + 21.1098i −0.406057 + 0.131936i
\(161\) −95.6917 + 131.708i −0.594358 + 0.818064i
\(162\) −7.17434 9.87463i −0.0442860 0.0609545i
\(163\) −4.46584 + 13.7444i −0.0273978 + 0.0843217i −0.963820 0.266552i \(-0.914115\pi\)
0.936423 + 0.350874i \(0.114115\pi\)
\(164\) 38.9958i 0.237779i
\(165\) 42.0275 + 12.0190i 0.254712 + 0.0728423i
\(166\) −8.64208 −0.0520607
\(167\) 125.427 + 40.7538i 0.751062 + 0.244035i 0.659438 0.751759i \(-0.270794\pi\)
0.0916237 + 0.995794i \(0.470794\pi\)
\(168\) 114.400 83.1168i 0.680955 0.494743i
\(169\) 54.8803 + 39.8729i 0.324736 + 0.235934i
\(170\) 11.3622 + 34.9691i 0.0668362 + 0.205701i
\(171\) 34.4801 11.2033i 0.201638 0.0655161i
\(172\) 58.8970 81.0647i 0.342424 0.471306i
\(173\) −20.6503 28.4227i −0.119366 0.164293i 0.745153 0.666894i \(-0.232377\pi\)
−0.864519 + 0.502601i \(0.832377\pi\)
\(174\) −19.2667 + 59.2968i −0.110728 + 0.340786i
\(175\) 192.849i 1.10200i
\(176\) −18.2216 23.2886i −0.103532 0.132322i
\(177\) 168.518 0.952077
\(178\) −5.10125 1.65750i −0.0286587 0.00931178i
\(179\) 146.405 106.370i 0.817907 0.594244i −0.0982054 0.995166i \(-0.531310\pi\)
0.916112 + 0.400922i \(0.131310\pi\)
\(180\) −12.0319 8.74167i −0.0668438 0.0485648i
\(181\) 6.29265 + 19.3668i 0.0347660 + 0.106999i 0.966934 0.255028i \(-0.0820848\pi\)
−0.932168 + 0.362027i \(0.882085\pi\)
\(182\) 193.957 63.0205i 1.06570 0.346267i
\(183\) 1.28141 1.76372i 0.00700226 0.00963779i
\(184\) −81.8226 112.619i −0.444688 0.612060i
\(185\) 47.7298 146.897i 0.257999 0.794040i
\(186\) 9.77503i 0.0525539i
\(187\) 102.374 80.1005i 0.547457 0.428345i
\(188\) 131.622 0.700116
\(189\) 48.2885 + 15.6899i 0.255495 + 0.0830152i
\(190\) −30.4207 + 22.1020i −0.160109 + 0.116326i
\(191\) −48.1778 35.0032i −0.252240 0.183263i 0.454479 0.890757i \(-0.349825\pi\)
−0.706719 + 0.707495i \(0.749825\pi\)
\(192\) 27.3682 + 84.2306i 0.142543 + 0.438701i
\(193\) −235.929 + 76.6578i −1.22243 + 0.397191i −0.847965 0.530051i \(-0.822173\pi\)
−0.374462 + 0.927242i \(0.622173\pi\)
\(194\) −26.4134 + 36.3549i −0.136151 + 0.187396i
\(195\) −35.9463 49.4758i −0.184340 0.253722i
\(196\) −31.0348 + 95.5152i −0.158341 + 0.487323i
\(197\) 166.342i 0.844374i 0.906509 + 0.422187i \(0.138737\pi\)
−0.906509 + 0.422187i \(0.861263\pi\)
\(198\) 12.3055 43.0293i 0.0621489 0.217320i
\(199\) 97.9933 0.492429 0.246214 0.969215i \(-0.420813\pi\)
0.246214 + 0.969215i \(0.420813\pi\)
\(200\) −156.828 50.9565i −0.784140 0.254782i
\(201\) −77.2328 + 56.1129i −0.384243 + 0.279169i
\(202\) 106.514 + 77.3866i 0.527295 + 0.383102i
\(203\) −80.1458 246.664i −0.394807 1.21509i
\(204\) −42.0608 + 13.6664i −0.206181 + 0.0669921i
\(205\) 24.3379 33.4983i 0.118722 0.163406i
\(206\) 148.314 + 204.137i 0.719971 + 0.990955i
\(207\) 15.4456 47.5366i 0.0746163 0.229645i
\(208\) 41.3698i 0.198893i
\(209\) 110.259 + 74.2572i 0.527556 + 0.355298i
\(210\) −52.6608 −0.250766
\(211\) −11.0358 3.58574i −0.0523023 0.0169940i 0.282749 0.959194i \(-0.408754\pi\)
−0.335051 + 0.942200i \(0.608754\pi\)
\(212\) −176.933 + 128.549i −0.834589 + 0.606364i
\(213\) −20.9573 15.2263i −0.0983909 0.0714852i
\(214\) −80.4153 247.493i −0.375773 1.15651i
\(215\) −101.188 + 32.8778i −0.470640 + 0.152920i
\(216\) −25.5185 + 35.1232i −0.118141 + 0.162607i
\(217\) 23.9007 + 32.8965i 0.110142 + 0.151597i
\(218\) 47.6751 146.729i 0.218693 0.673069i
\(219\) 131.431i 0.600140i
\(220\) −1.94172 54.4969i −0.00882602 0.247713i
\(221\) −181.857 −0.822884
\(222\) −150.399 48.8676i −0.677472 0.220124i
\(223\) −252.345 + 183.339i −1.13159 + 0.822149i −0.985926 0.167185i \(-0.946532\pi\)
−0.145666 + 0.989334i \(0.546532\pi\)
\(224\) −235.377 171.011i −1.05079 0.763442i
\(225\) −18.2964 56.3107i −0.0813175 0.250270i
\(226\) −21.1251 + 6.86395i −0.0934737 + 0.0303714i
\(227\) −5.60519 + 7.71488i −0.0246925 + 0.0339863i −0.821185 0.570662i \(-0.806686\pi\)
0.796492 + 0.604649i \(0.206686\pi\)
\(228\) −26.5842 36.5900i −0.116597 0.160483i
\(229\) 62.0564 190.990i 0.270989 0.834017i −0.719264 0.694737i \(-0.755521\pi\)
0.990253 0.139281i \(-0.0444791\pi\)
\(230\) 51.8408i 0.225395i
\(231\) 63.7976 + 174.897i 0.276180 + 0.757130i
\(232\) 221.767 0.955893
\(233\) 228.533 + 74.2548i 0.980827 + 0.318690i 0.755179 0.655519i \(-0.227550\pi\)
0.225648 + 0.974209i \(0.427550\pi\)
\(234\) −50.6551 + 36.8031i −0.216475 + 0.157278i
\(235\) −113.066 82.1473i −0.481132 0.349563i
\(236\) −64.9637 199.938i −0.275270 0.847194i
\(237\) 48.1336 15.6396i 0.203095 0.0659897i
\(238\) −92.0453 + 126.690i −0.386745 + 0.532309i
\(239\) 47.4322 + 65.2848i 0.198461 + 0.273158i 0.896636 0.442769i \(-0.146004\pi\)
−0.698174 + 0.715928i \(0.746004\pi\)
\(240\) 3.30106 10.1596i 0.0137544 0.0423317i
\(241\) 153.259i 0.635928i 0.948103 + 0.317964i \(0.102999\pi\)
−0.948103 + 0.317964i \(0.897001\pi\)
\(242\) 152.063 61.6881i 0.628359 0.254909i
\(243\) −15.5885 −0.0641500
\(244\) −2.58655 0.840420i −0.0106006 0.00344435i
\(245\) 86.2722 62.6804i 0.352131 0.255838i
\(246\) −34.2968 24.9181i −0.139418 0.101293i
\(247\) −57.4707 176.877i −0.232675 0.716100i
\(248\) −33.0672 + 10.7442i −0.133335 + 0.0433233i
\(249\) −6.48749 + 8.92927i −0.0260542 + 0.0358605i
\(250\) 81.8180 + 112.613i 0.327272 + 0.450451i
\(251\) −108.893 + 335.138i −0.433836 + 1.33521i 0.460439 + 0.887691i \(0.347692\pi\)
−0.894275 + 0.447518i \(0.852308\pi\)
\(252\) 63.3403i 0.251351i
\(253\) 172.174 62.8042i 0.680528 0.248238i
\(254\) 7.57800 0.0298347
\(255\) 44.6606 + 14.5111i 0.175140 + 0.0569063i
\(256\) 220.059 159.882i 0.859605 0.624539i
\(257\) −104.897 76.2121i −0.408159 0.296545i 0.364697 0.931126i \(-0.381173\pi\)
−0.772856 + 0.634581i \(0.781173\pi\)
\(258\) 33.6615 + 103.600i 0.130471 + 0.401549i
\(259\) 625.631 203.280i 2.41557 0.784865i
\(260\) −44.8432 + 61.7214i −0.172474 + 0.237390i
\(261\) 46.8040 + 64.4202i 0.179326 + 0.246821i
\(262\) 94.5931 291.128i 0.361042 1.11117i
\(263\) 180.174i 0.685072i 0.939505 + 0.342536i \(0.111286\pi\)
−0.939505 + 0.342536i \(0.888714\pi\)
\(264\) −159.086 + 5.66824i −0.602598 + 0.0214706i
\(265\) 232.219 0.876297
\(266\) −152.308 49.4879i −0.572587 0.186045i
\(267\) −5.54202 + 4.02651i −0.0207566 + 0.0150806i
\(268\) 96.3485 + 70.0013i 0.359509 + 0.261199i
\(269\) 103.985 + 320.033i 0.386561 + 1.18971i 0.935342 + 0.353746i \(0.115092\pi\)
−0.548781 + 0.835966i \(0.684908\pi\)
\(270\) 15.3766 4.99615i 0.0569503 0.0185043i
\(271\) −129.003 + 177.557i −0.476026 + 0.655193i −0.977735 0.209843i \(-0.932705\pi\)
0.501709 + 0.865036i \(0.332705\pi\)
\(272\) −18.6717 25.6995i −0.0686461 0.0944833i
\(273\) 80.4863 247.711i 0.294822 0.907368i
\(274\) 70.9964i 0.259111i
\(275\) 121.272 180.068i 0.440989 0.654794i
\(276\) −62.3541 −0.225921
\(277\) −232.844 75.6555i −0.840591 0.273125i −0.143091 0.989709i \(-0.545704\pi\)
−0.697500 + 0.716585i \(0.745704\pi\)
\(278\) 30.7934 22.3727i 0.110768 0.0804775i
\(279\) −10.0999 7.33798i −0.0362002 0.0263010i
\(280\) 57.8819 + 178.142i 0.206721 + 0.636222i
\(281\) −328.343 + 106.685i −1.16848 + 0.379662i −0.828075 0.560617i \(-0.810564\pi\)
−0.340404 + 0.940279i \(0.610564\pi\)
\(282\) −84.1054 + 115.761i −0.298246 + 0.410501i
\(283\) −136.711 188.166i −0.483077 0.664898i 0.496016 0.868313i \(-0.334796\pi\)
−0.979093 + 0.203415i \(0.934796\pi\)
\(284\) −9.98625 + 30.7345i −0.0351629 + 0.108220i
\(285\) 48.0233i 0.168503i
\(286\) −220.733 63.1249i −0.771793 0.220717i
\(287\) 176.348 0.614452
\(288\) 84.9528 + 27.6028i 0.294975 + 0.0958432i
\(289\) −120.834 + 87.7908i −0.418110 + 0.303774i
\(290\) −66.8148 48.5438i −0.230396 0.167392i
\(291\) 17.7349 + 54.5823i 0.0609445 + 0.187568i
\(292\) 155.936 50.6667i 0.534027 0.173516i
\(293\) 313.718 431.796i 1.07071 1.47371i 0.201355 0.979518i \(-0.435465\pi\)
0.869355 0.494188i \(-0.164535\pi\)
\(294\) −64.1745 88.3286i −0.218281 0.300437i
\(295\) −68.9791 + 212.296i −0.233828 + 0.719647i
\(296\) 562.485i 1.90029i
\(297\) −35.2217 45.0159i −0.118592 0.151569i
\(298\) 15.2467 0.0511633
\(299\) −243.854 79.2331i −0.815566 0.264993i
\(300\) −59.7565 + 43.4156i −0.199188 + 0.144719i
\(301\) −366.592 266.345i −1.21791 0.884867i
\(302\) −42.3971 130.485i −0.140388 0.432069i
\(303\) 159.917 51.9601i 0.527778 0.171485i
\(304\) 19.0950 26.2819i 0.0628123 0.0864538i
\(305\) 1.69738 + 2.33625i 0.00556519 + 0.00765982i
\(306\) 14.8570 45.7252i 0.0485523 0.149429i
\(307\) 142.846i 0.465296i −0.972561 0.232648i \(-0.925261\pi\)
0.972561 0.232648i \(-0.0747389\pi\)
\(308\) 182.913 143.116i 0.593872 0.464661i
\(309\) 322.258 1.04291
\(310\) 12.3144 + 4.00120i 0.0397240 + 0.0129071i
\(311\) 37.1343 26.9797i 0.119403 0.0867514i −0.526481 0.850187i \(-0.676489\pi\)
0.645884 + 0.763435i \(0.276489\pi\)
\(312\) 180.176 + 130.905i 0.577486 + 0.419568i
\(313\) 110.168 + 339.062i 0.351975 + 1.08327i 0.957743 + 0.287625i \(0.0928658\pi\)
−0.605768 + 0.795641i \(0.707134\pi\)
\(314\) −24.5992 + 7.99278i −0.0783415 + 0.0254547i
\(315\) −39.5317 + 54.4108i −0.125498 + 0.172733i
\(316\) −37.1111 51.0791i −0.117440 0.161643i
\(317\) −19.1154 + 58.8312i −0.0603010 + 0.185587i −0.976669 0.214749i \(-0.931107\pi\)
0.916368 + 0.400336i \(0.131107\pi\)
\(318\) 237.754i 0.747655i
\(319\) −80.2786 + 280.715i −0.251657 + 0.879985i
\(320\) −117.315 −0.366609
\(321\) −316.084 102.702i −0.984686 0.319944i
\(322\) −178.622 + 129.776i −0.554726 + 0.403032i
\(323\) 115.533 + 83.9395i 0.357687 + 0.259875i
\(324\) 6.00937 + 18.4949i 0.0185474 + 0.0570831i
\(325\) −288.864 + 93.8575i −0.888812 + 0.288792i
\(326\) −11.5202 + 15.8562i −0.0353380 + 0.0486386i
\(327\) −115.816 159.407i −0.354177 0.487483i
\(328\) −46.5962 + 143.408i −0.142062 + 0.437221i
\(329\) 595.222i 1.80919i
\(330\) 49.1707 + 33.1154i 0.149002 + 0.100350i
\(331\) −339.961 −1.02707 −0.513536 0.858068i \(-0.671665\pi\)
−0.513536 + 0.858068i \(0.671665\pi\)
\(332\) 13.0951 + 4.25485i 0.0394430 + 0.0128158i
\(333\) −163.394 + 118.713i −0.490672 + 0.356494i
\(334\) 144.699 + 105.130i 0.433229 + 0.314759i
\(335\) −39.0766 120.265i −0.116647 0.359001i
\(336\) 43.2695 14.0591i 0.128778 0.0418426i
\(337\) −175.877 + 242.074i −0.521890 + 0.718320i −0.985868 0.167527i \(-0.946422\pi\)
0.463977 + 0.885847i \(0.346422\pi\)
\(338\) 54.0753 + 74.4282i 0.159986 + 0.220202i
\(339\) −8.76625 + 26.9797i −0.0258591 + 0.0795862i
\(340\) 58.5817i 0.172299i
\(341\) −1.62993 45.7461i −0.00477986 0.134153i
\(342\) 49.1680 0.143766
\(343\) −23.4224 7.61041i −0.0682870 0.0221878i
\(344\) 313.460 227.742i 0.911221 0.662041i
\(345\) 53.5635 + 38.9162i 0.155257 + 0.112801i
\(346\) −14.7235 45.3143i −0.0425535 0.130966i
\(347\) 202.617 65.8344i 0.583912 0.189724i −0.00214053 0.999998i \(-0.500681\pi\)
0.586052 + 0.810273i \(0.300681\pi\)
\(348\) 58.3884 80.3647i 0.167783 0.230933i
\(349\) −44.0593 60.6425i −0.126245 0.173761i 0.741216 0.671266i \(-0.234249\pi\)
−0.867461 + 0.497506i \(0.834249\pi\)
\(350\) −80.8205 + 248.740i −0.230916 + 0.710685i
\(351\) 79.9660i 0.227823i
\(352\) 112.238 + 307.692i 0.318857 + 0.874126i
\(353\) −372.860 −1.05626 −0.528130 0.849164i \(-0.677107\pi\)
−0.528130 + 0.849164i \(0.677107\pi\)
\(354\) 217.356 + 70.6233i 0.614001 + 0.199501i
\(355\) 27.7603 20.1691i 0.0781981 0.0568142i
\(356\) 6.91371 + 5.02310i 0.0194205 + 0.0141098i
\(357\) 61.8024 + 190.208i 0.173116 + 0.532796i
\(358\) 233.414 75.8407i 0.651993 0.211846i
\(359\) 156.070 214.812i 0.434736 0.598363i −0.534296 0.845297i \(-0.679423\pi\)
0.969032 + 0.246934i \(0.0794232\pi\)
\(360\) −33.8022 46.5247i −0.0938950 0.129235i
\(361\) 66.4253 204.436i 0.184004 0.566305i
\(362\) 27.6167i 0.0762892i
\(363\) 50.4134 203.424i 0.138880 0.560398i
\(364\) −324.925 −0.892651
\(365\) −165.574 53.7984i −0.453629 0.147393i
\(366\) 2.39193 1.73784i 0.00653534 0.00474820i
\(367\) −80.4998 58.4866i −0.219346 0.159364i 0.472686 0.881231i \(-0.343284\pi\)
−0.692032 + 0.721867i \(0.743284\pi\)
\(368\) −13.8402 42.5957i −0.0376092 0.115749i
\(369\) −51.4923 + 16.7308i −0.139545 + 0.0453411i
\(370\) 123.125 169.467i 0.332771 0.458020i
\(371\) 581.327 + 800.128i 1.56692 + 2.15668i
\(372\) −4.81264 + 14.8118i −0.0129372 + 0.0398166i
\(373\) 469.949i 1.25992i −0.776629 0.629959i \(-0.783072\pi\)
0.776629 0.629959i \(-0.216928\pi\)
\(374\) 165.613 60.4111i 0.442815 0.161527i
\(375\) 177.775 0.474066
\(376\) 484.043 + 157.275i 1.28735 + 0.418285i
\(377\) 330.464 240.096i 0.876563 0.636861i
\(378\) 55.7077 + 40.4740i 0.147375 + 0.107074i
\(379\) 89.1943 + 274.512i 0.235341 + 0.724305i 0.997076 + 0.0764166i \(0.0243479\pi\)
−0.761735 + 0.647889i \(0.775652\pi\)
\(380\) 56.9773 18.5130i 0.149940 0.0487185i
\(381\) 5.68870 7.82983i 0.0149310 0.0205507i
\(382\) −47.4710 65.3382i −0.124270 0.171042i
\(383\) −60.7882 + 187.087i −0.158716 + 0.488477i −0.998518 0.0544147i \(-0.982671\pi\)
0.839803 + 0.542892i \(0.182671\pi\)
\(384\) 86.1752i 0.224414i
\(385\) −246.447 + 8.78090i −0.640122 + 0.0228075i
\(386\) −336.430 −0.871581
\(387\) 132.312 + 42.9906i 0.341890 + 0.111087i
\(388\) 57.9223 42.0830i 0.149284 0.108461i
\(389\) 363.076 + 263.790i 0.933358 + 0.678124i 0.946813 0.321785i \(-0.104283\pi\)
−0.0134546 + 0.999909i \(0.504283\pi\)
\(390\) −25.6294 78.8791i −0.0657164 0.202254i
\(391\) 187.247 60.8401i 0.478891 0.155601i
\(392\) −228.263 + 314.177i −0.582303 + 0.801471i
\(393\) −229.792 316.282i −0.584714 0.804789i
\(394\) −69.7115 + 214.550i −0.176933 + 0.544543i
\(395\) 67.0397i 0.169721i
\(396\) −39.8312 + 59.1425i −0.100584 + 0.149350i
\(397\) 608.594 1.53298 0.766491 0.642255i \(-0.222001\pi\)
0.766491 + 0.642255i \(0.222001\pi\)
\(398\) 126.393 + 41.0676i 0.317571 + 0.103185i
\(399\) −165.468 + 120.220i −0.414707 + 0.301302i
\(400\) −42.9220 31.1847i −0.107305 0.0779616i
\(401\) −80.0898 246.491i −0.199725 0.614691i −0.999889 0.0149093i \(-0.995254\pi\)
0.800164 0.599782i \(-0.204746\pi\)
\(402\) −123.132 + 40.0080i −0.306299 + 0.0995225i
\(403\) −37.6426 + 51.8105i −0.0934059 + 0.128562i
\(404\) −123.296 169.702i −0.305188 0.420056i
\(405\) 6.38081 19.6381i 0.0157551 0.0484891i
\(406\) 351.738i 0.866350i
\(407\) −711.999 203.617i −1.74938 0.500287i
\(408\) −171.010 −0.419142
\(409\) 249.341 + 81.0159i 0.609637 + 0.198083i 0.597534 0.801844i \(-0.296147\pi\)
0.0121029 + 0.999927i \(0.496147\pi\)
\(410\) 45.4301 33.0069i 0.110805 0.0805046i
\(411\) 73.3557 + 53.2961i 0.178481 + 0.129674i
\(412\) −124.231 382.343i −0.301531 0.928017i
\(413\) −904.162 + 293.780i −2.18925 + 0.711332i
\(414\) 39.8438 54.8403i 0.0962411 0.132465i
\(415\) −8.59344 11.8279i −0.0207071 0.0285008i
\(416\) 141.598 435.793i 0.340379 1.04758i
\(417\) 48.6117i 0.116575i
\(418\) 111.094 + 141.986i 0.265774 + 0.339680i
\(419\) −650.465 −1.55242 −0.776211 0.630473i \(-0.782861\pi\)
−0.776211 + 0.630473i \(0.782861\pi\)
\(420\) 79.7952 + 25.9270i 0.189989 + 0.0617310i
\(421\) 508.799 369.664i 1.20855 0.878062i 0.213450 0.976954i \(-0.431530\pi\)
0.995098 + 0.0988920i \(0.0315298\pi\)
\(422\) −12.7314 9.24988i −0.0301691 0.0219191i
\(423\) 56.4713 + 173.801i 0.133502 + 0.410876i
\(424\) −804.280 + 261.326i −1.89689 + 0.616336i
\(425\) 137.085 188.681i 0.322552 0.443955i
\(426\) −20.6498 28.4220i −0.0484738 0.0667184i
\(427\) −3.80056 + 11.6969i −0.00890062 + 0.0273933i
\(428\) 414.610i 0.968715i
\(429\) −230.924 + 180.681i −0.538284 + 0.421168i
\(430\) −144.292 −0.335562
\(431\) 560.194 + 182.018i 1.29975 + 0.422316i 0.875496 0.483225i \(-0.160535\pi\)
0.424258 + 0.905541i \(0.360535\pi\)
\(432\) −11.3005 + 8.21031i −0.0261586 + 0.0190054i
\(433\) 126.292 + 91.7565i 0.291668 + 0.211909i 0.723990 0.689810i \(-0.242306\pi\)
−0.432323 + 0.901719i \(0.642306\pi\)
\(434\) 17.0410 + 52.4468i 0.0392650 + 0.120845i
\(435\) −100.314 + 32.5940i −0.230607 + 0.0749286i
\(436\) −144.481 + 198.861i −0.331379 + 0.456104i
\(437\) 118.348 + 162.892i 0.270818 + 0.372750i
\(438\) −55.0808 + 169.521i −0.125755 + 0.387035i
\(439\) 209.017i 0.476121i 0.971250 + 0.238060i \(0.0765116\pi\)
−0.971250 + 0.238060i \(0.923488\pi\)
\(440\) 57.9777 202.734i 0.131768 0.460760i
\(441\) −139.439 −0.316188
\(442\) −234.562 76.2138i −0.530683 0.172430i
\(443\) −276.987 + 201.242i −0.625252 + 0.454272i −0.854752 0.519037i \(-0.826291\pi\)
0.229500 + 0.973309i \(0.426291\pi\)
\(444\) 203.835 + 148.095i 0.459088 + 0.333547i
\(445\) −2.80403 8.62992i −0.00630119 0.0193931i
\(446\) −402.313 + 130.719i −0.902047 + 0.293093i
\(447\) 11.4455 15.7533i 0.0256051 0.0352424i
\(448\) −293.682 404.218i −0.655539 0.902273i
\(449\) 17.7730 54.6996i 0.0395835 0.121825i −0.929312 0.369295i \(-0.879599\pi\)
0.968896 + 0.247470i \(0.0795991\pi\)
\(450\) 80.2981i 0.178440i
\(451\) −164.660 110.895i −0.365100 0.245887i
\(452\) 35.3895 0.0782954
\(453\) −166.648 54.1472i −0.367876 0.119530i
\(454\) −10.4629 + 7.60171i −0.0230459 + 0.0167438i
\(455\) 279.118 + 202.791i 0.613445 + 0.445694i
\(456\) −54.0428 166.327i −0.118515 0.364751i
\(457\) 608.260 197.636i 1.33098 0.432463i 0.444731 0.895664i \(-0.353299\pi\)
0.886253 + 0.463201i \(0.153299\pi\)
\(458\) 160.082 220.335i 0.349525 0.481080i
\(459\) −36.0917 49.6760i −0.0786312 0.108227i
\(460\) 25.5233 78.5527i 0.0554855 0.170767i
\(461\) 492.084i 1.06743i −0.845666 0.533713i \(-0.820796\pi\)
0.845666 0.533713i \(-0.179204\pi\)
\(462\) 8.99021 + 252.321i 0.0194593 + 0.546150i
\(463\) 366.054 0.790614 0.395307 0.918549i \(-0.370638\pi\)
0.395307 + 0.918549i \(0.370638\pi\)
\(464\) 67.8592 + 22.0488i 0.146248 + 0.0475190i
\(465\) 13.3784 9.72001i 0.0287709 0.0209033i
\(466\) 263.646 + 191.550i 0.565763 + 0.411051i
\(467\) 100.584 + 309.566i 0.215383 + 0.662882i 0.999126 + 0.0417963i \(0.0133080\pi\)
−0.783743 + 0.621086i \(0.786692\pi\)
\(468\) 94.8757 30.8270i 0.202726 0.0658697i
\(469\) 316.561 435.709i 0.674970 0.929017i
\(470\) −111.407 153.339i −0.237037 0.326253i
\(471\) −10.2079 + 31.4168i −0.0216729 + 0.0667023i
\(472\) 812.903i 1.72225i
\(473\) 174.807 + 479.222i 0.369571 + 1.01315i
\(474\) 68.6377 0.144805
\(475\) 226.835 + 73.7031i 0.477547 + 0.155165i
\(476\) 201.848 146.651i 0.424050 0.308090i
\(477\) −245.655 178.479i −0.515000 0.374169i
\(478\) 33.8188 + 104.083i 0.0707506 + 0.217748i
\(479\) 312.398 101.504i 0.652187 0.211908i 0.0358087 0.999359i \(-0.488599\pi\)
0.616378 + 0.787450i \(0.288599\pi\)
\(480\) −69.5473 + 95.7237i −0.144890 + 0.199424i
\(481\) 608.975 + 838.182i 1.26606 + 1.74258i
\(482\) −64.2285 + 197.675i −0.133254 + 0.410114i
\(483\) 281.979i 0.583807i
\(484\) −260.787 + 18.6073i −0.538817 + 0.0384449i
\(485\) −76.0213 −0.156745
\(486\) −20.1062 6.53290i −0.0413708 0.0134422i
\(487\) −260.740 + 189.439i −0.535400 + 0.388991i −0.822374 0.568947i \(-0.807351\pi\)
0.286974 + 0.957938i \(0.407351\pi\)
\(488\) −8.50789 6.18135i −0.0174342 0.0126667i
\(489\) 7.73506 + 23.8061i 0.0158181 + 0.0486831i
\(490\) 137.544 44.6906i 0.280701 0.0912053i
\(491\) 454.813 625.997i 0.926300 1.27494i −0.0349859 0.999388i \(-0.511139\pi\)
0.961286 0.275554i \(-0.0888614\pi\)
\(492\) 39.7006 + 54.6432i 0.0806924 + 0.111064i
\(493\) −96.9243 + 298.302i −0.196601 + 0.605076i
\(494\) 252.223i 0.510573i
\(495\) 71.1276 25.9454i 0.143692 0.0524150i
\(496\) −11.1865 −0.0225535
\(497\) 138.988 + 45.1600i 0.279654 + 0.0908652i
\(498\) −12.1098 + 8.79828i −0.0243168 + 0.0176672i
\(499\) 41.3425 + 30.0371i 0.0828507 + 0.0601946i 0.628440 0.777858i \(-0.283694\pi\)
−0.545589 + 0.838053i \(0.683694\pi\)
\(500\) −68.5324 210.921i −0.137065 0.421842i
\(501\) 217.246 70.5877i 0.433626 0.140894i
\(502\) −280.903 + 386.630i −0.559568 + 0.770179i
\(503\) −244.325 336.284i −0.485735 0.668557i 0.493859 0.869542i \(-0.335586\pi\)
−0.979594 + 0.200985i \(0.935586\pi\)
\(504\) 75.6856 232.936i 0.150170 0.462175i
\(505\) 222.729i 0.441048i
\(506\) 248.392 8.85022i 0.490894 0.0174906i
\(507\) 117.495 0.231746
\(508\) −11.4827 3.73096i −0.0226038 0.00734441i
\(509\) −270.522 + 196.546i −0.531478 + 0.386141i −0.820910 0.571057i \(-0.806533\pi\)
0.289433 + 0.957198i \(0.406533\pi\)
\(510\) 51.5225 + 37.4333i 0.101024 + 0.0733986i
\(511\) −229.126 705.177i −0.448387 1.37999i
\(512\) 161.567 52.4962i 0.315560 0.102532i
\(513\) 36.9098 50.8019i 0.0719488 0.0990291i
\(514\) −103.358 142.260i −0.201086 0.276771i
\(515\) −131.909 + 405.976i −0.256135 + 0.788302i
\(516\) 173.554i 0.336345i
\(517\) −374.302 + 555.774i −0.723988 + 1.07500i
\(518\) 892.140 1.72228
\(519\) −57.8729 18.8040i −0.111508 0.0362313i
\(520\) −238.664 + 173.399i −0.458968 + 0.333460i
\(521\) −700.990 509.299i −1.34547 0.977541i −0.999224 0.0393970i \(-0.987456\pi\)
−0.346246 0.938144i \(-0.612544\pi\)
\(522\) 33.3709 + 102.705i 0.0639289 + 0.196753i
\(523\) −415.392 + 134.969i −0.794248 + 0.258067i −0.677912 0.735143i \(-0.737115\pi\)
−0.116336 + 0.993210i \(0.537115\pi\)
\(524\) −286.668 + 394.564i −0.547076 + 0.752986i
\(525\) 196.335 + 270.232i 0.373971 + 0.514727i
\(526\) −75.5083 + 232.391i −0.143552 + 0.441808i
\(527\) 49.1749i 0.0933111i
\(528\) −49.2427 14.0824i −0.0932628 0.0266712i
\(529\) −251.412 −0.475259
\(530\) 299.519 + 97.3197i 0.565130 + 0.183622i
\(531\) 236.137 171.563i 0.444702 0.323095i
\(532\) 206.423 + 149.975i 0.388013 + 0.281908i
\(533\) 85.8263 + 264.146i 0.161025 + 0.495584i
\(534\) −8.83563 + 2.87087i −0.0165461 + 0.00537616i
\(535\) 258.765 356.159i 0.483672 0.665718i
\(536\) 270.680 + 372.559i 0.505000 + 0.695073i
\(537\) 96.8595 298.103i 0.180371 0.555126i
\(538\) 456.361i 0.848255i
\(539\) −315.058 402.668i −0.584523 0.747064i
\(540\) −25.7594 −0.0477027
\(541\) −738.226 239.864i −1.36456 0.443372i −0.466996 0.884259i \(-0.654664\pi\)
−0.897562 + 0.440888i \(0.854664\pi\)
\(542\) −240.802 + 174.953i −0.444283 + 0.322791i
\(543\) 28.5344 + 20.7315i 0.0525496 + 0.0381795i
\(544\) 108.728 + 334.629i 0.199867 + 0.615127i
\(545\) 248.225 80.6533i 0.455459 0.147988i
\(546\) 207.625 285.771i 0.380265 0.523390i
\(547\) −466.258 641.749i −0.852391 1.17322i −0.983331 0.181825i \(-0.941800\pi\)
0.130940 0.991390i \(-0.458200\pi\)
\(548\) 34.9544 107.579i 0.0637854 0.196311i
\(549\) 3.77600i 0.00687795i
\(550\) 231.883 181.431i 0.421605 0.329875i
\(551\) −320.763 −0.582147
\(552\) −229.309 74.5071i −0.415415 0.134977i
\(553\) −230.991 + 167.825i −0.417705 + 0.303480i
\(554\) −268.619 195.163i −0.484872 0.352280i
\(555\) −82.6705 254.434i −0.148956 0.458439i
\(556\) −57.6753 + 18.7399i −0.103733 + 0.0337048i
\(557\) −390.960 + 538.111i −0.701904 + 0.966088i 0.298030 + 0.954557i \(0.403671\pi\)
−0.999934 + 0.0115312i \(0.996329\pi\)
\(558\) −9.95171 13.6973i −0.0178346 0.0245472i
\(559\) 220.534 678.735i 0.394516 1.21420i
\(560\) 60.2650i 0.107616i
\(561\) 61.9048 216.466i 0.110347 0.385858i
\(562\) −468.211 −0.833116
\(563\) −375.847 122.120i −0.667579 0.216910i −0.0444299 0.999013i \(-0.514147\pi\)
−0.623149 + 0.782103i \(0.714147\pi\)
\(564\) 184.436 134.001i 0.327014 0.237590i
\(565\) −30.4004 22.0872i −0.0538060 0.0390923i
\(566\) −97.4736 299.993i −0.172215 0.530023i
\(567\) 83.6381 27.1757i 0.147510 0.0479289i
\(568\) −73.4495 + 101.095i −0.129313 + 0.177983i
\(569\) −31.1806 42.9165i −0.0547990 0.0754244i 0.780738 0.624858i \(-0.214843\pi\)
−0.835537 + 0.549434i \(0.814843\pi\)
\(570\) −20.1259 + 61.9411i −0.0353086 + 0.108669i
\(571\) 878.429i 1.53840i 0.639005 + 0.769202i \(0.279346\pi\)
−0.639005 + 0.769202i \(0.720654\pi\)
\(572\) 303.390 + 204.327i 0.530403 + 0.357215i
\(573\) −103.145 −0.180009
\(574\) 227.456 + 73.9048i 0.396264 + 0.128754i
\(575\) 266.024 193.278i 0.462651 0.336135i
\(576\) 124.103 + 90.1660i 0.215456 + 0.156538i
\(577\) 334.518 + 1029.54i 0.579755 + 1.78430i 0.619385 + 0.785087i \(0.287382\pi\)
−0.0396306 + 0.999214i \(0.512618\pi\)
\(578\) −192.645 + 62.5941i −0.333296 + 0.108294i
\(579\) −252.554 + 347.610i −0.436189 + 0.600363i
\(580\) 77.3422 + 106.452i 0.133349 + 0.183539i
\(581\) 19.2413 59.2187i 0.0331176 0.101926i
\(582\) 77.8334i 0.133734i
\(583\) −39.6442 1112.66i −0.0680004 1.90851i
\(584\) 634.002 1.08562
\(585\) −100.740 32.7324i −0.172205 0.0559528i
\(586\) 585.598 425.462i 0.999313 0.726044i
\(587\) −12.3428 8.96760i −0.0210270 0.0152770i 0.577222 0.816587i \(-0.304137\pi\)
−0.598249 + 0.801310i \(0.704137\pi\)
\(588\) 53.7538 + 165.437i 0.0914180 + 0.281356i
\(589\) 47.8282 15.5403i 0.0812023 0.0263842i
\(590\) −177.940 + 244.914i −0.301594 + 0.415109i
\(591\) 169.348 + 233.088i 0.286545 + 0.394396i
\(592\) −55.9240 + 172.116i −0.0944663 + 0.290737i
\(593\) 214.000i 0.360877i −0.983586 0.180439i \(-0.942248\pi\)
0.983586 0.180439i \(-0.0577517\pi\)
\(594\) −26.5639 72.8231i −0.0447203 0.122598i
\(595\) −264.919 −0.445242
\(596\) −23.1028 7.50655i −0.0387631 0.0125949i
\(597\) 137.314 99.7644i 0.230007 0.167110i
\(598\) −281.321 204.392i −0.470437 0.341792i
\(599\) 192.777 + 593.308i 0.321832 + 0.990498i 0.972850 + 0.231435i \(0.0743422\pi\)
−0.651018 + 0.759062i \(0.725658\pi\)
\(600\) −271.634 + 88.2592i −0.452723 + 0.147099i
\(601\) 237.449 326.821i 0.395090 0.543795i −0.564413 0.825493i \(-0.690897\pi\)
0.959503 + 0.281698i \(0.0908975\pi\)
\(602\) −361.214 497.169i −0.600024 0.825862i
\(603\) −51.0960 + 157.257i −0.0847364 + 0.260792i
\(604\) 218.593i 0.361909i
\(605\) 235.635 + 146.778i 0.389480 + 0.242607i
\(606\) 228.038 0.376301
\(607\) −349.561 113.579i −0.575882 0.187115i 0.00657281 0.999978i \(-0.497908\pi\)
−0.582455 + 0.812863i \(0.697908\pi\)
\(608\) −291.104 + 211.500i −0.478790 + 0.347861i
\(609\) −363.427 264.045i −0.596760 0.433571i
\(610\) 1.21022 + 3.72467i 0.00198397 + 0.00610602i
\(611\) 891.567 289.688i 1.45919 0.474120i
\(612\) −45.0247 + 61.9712i −0.0735698 + 0.101260i
\(613\) 286.364 + 394.147i 0.467152 + 0.642980i 0.975973 0.217893i \(-0.0699183\pi\)
−0.508820 + 0.860873i \(0.669918\pi\)
\(614\) 59.8646 184.244i 0.0974994 0.300072i
\(615\) 71.7176i 0.116614i
\(616\) 843.676 307.750i 1.36960 0.499594i
\(617\) 455.862 0.738836 0.369418 0.929263i \(-0.379557\pi\)
0.369418 + 0.929263i \(0.379557\pi\)
\(618\) 415.653 + 135.054i 0.672577 + 0.218534i
\(619\) −463.020 + 336.404i −0.748013 + 0.543463i −0.895210 0.445644i \(-0.852975\pi\)
0.147197 + 0.989107i \(0.452975\pi\)
\(620\) −16.6897 12.1258i −0.0269189 0.0195577i
\(621\) −26.7525 82.3358i −0.0430797 0.132586i
\(622\) 59.2032 19.2363i 0.0951820 0.0309265i
\(623\) 22.7156 31.2653i 0.0364616 0.0501851i
\(624\) 42.1175 + 57.9697i 0.0674959 + 0.0929002i
\(625\) 79.7020 245.297i 0.127523 0.392476i
\(626\) 483.497i 0.772360i
\(627\) 230.101 8.19850i 0.366987 0.0130758i
\(628\) 41.2096 0.0656204
\(629\) −756.607 245.836i −1.20287 0.390837i
\(630\) −73.7914 + 53.6126i −0.117129 + 0.0850993i
\(631\) −181.250 131.686i −0.287243 0.208694i 0.434828 0.900514i \(-0.356809\pi\)
−0.722070 + 0.691820i \(0.756809\pi\)
\(632\) −75.4428 232.189i −0.119372 0.367388i
\(633\) −19.1145 + 6.21069i −0.0301967 + 0.00981151i
\(634\) −49.3106 + 67.8703i −0.0777770 + 0.107051i
\(635\) 7.53535 + 10.3715i 0.0118667 + 0.0163331i
\(636\) −117.056 + 360.261i −0.184050 + 0.566449i
\(637\) 715.296i 1.12291i
\(638\) −221.188 + 328.427i −0.346690 + 0.514775i
\(639\) −44.8681 −0.0702161
\(640\) 108.562 + 35.2740i 0.169628 + 0.0551156i
\(641\) 383.601 278.702i 0.598441 0.434793i −0.246884 0.969045i \(-0.579407\pi\)
0.845325 + 0.534252i \(0.179407\pi\)
\(642\) −364.649 264.933i −0.567989 0.412668i
\(643\) −255.732 787.063i −0.397717 1.22405i −0.926825 0.375493i \(-0.877473\pi\)
0.529108 0.848554i \(-0.322527\pi\)
\(644\) 334.554 108.703i 0.519493 0.168794i
\(645\) −108.318 + 149.087i −0.167935 + 0.231142i
\(646\) 113.838 + 156.685i 0.176220 + 0.242546i
\(647\) 153.080 471.133i 0.236600 0.728181i −0.760305 0.649567i \(-0.774950\pi\)
0.996905 0.0786144i \(-0.0250496\pi\)
\(648\) 75.1963i 0.116044i
\(649\) 1028.98 + 294.267i 1.58549 + 0.453415i
\(650\) −411.915 −0.633715
\(651\) 66.9821 + 21.7638i 0.102891 + 0.0334314i
\(652\) 25.2628 18.3545i 0.0387467 0.0281511i
\(653\) 543.344 + 394.762i 0.832073 + 0.604536i 0.920145 0.391578i \(-0.128071\pi\)
−0.0880721 + 0.996114i \(0.528071\pi\)
\(654\) −82.5758 254.142i −0.126263 0.388596i
\(655\) 492.508 160.026i 0.751921 0.244314i
\(656\) −28.5162 + 39.2492i −0.0434699 + 0.0598312i
\(657\) 133.806 + 184.168i 0.203662 + 0.280317i
\(658\) 249.449 767.726i 0.379102 1.16676i
\(659\) 59.3106i 0.0900009i 0.998987 + 0.0450004i \(0.0143289\pi\)
−0.998987 + 0.0450004i \(0.985671\pi\)
\(660\) −58.2027 74.3874i −0.0881860 0.112708i
\(661\) 604.118 0.913946 0.456973 0.889481i \(-0.348934\pi\)
0.456973 + 0.889481i \(0.348934\pi\)
\(662\) −438.486 142.473i −0.662366 0.215216i
\(663\) −254.829 + 185.144i −0.384358 + 0.279252i
\(664\) 43.0734 + 31.2947i 0.0648696 + 0.0471305i
\(665\) −83.7200 257.664i −0.125895 0.387464i
\(666\) −260.499 + 84.6411i −0.391139 + 0.127089i
\(667\) −259.934 + 357.768i −0.389705 + 0.536384i
\(668\) −167.498 230.541i −0.250745 0.345121i
\(669\) −166.947 + 513.811i −0.249548 + 0.768029i
\(670\) 171.496i 0.255965i
\(671\) 10.9042 8.53176i 0.0162507 0.0127150i
\(672\) −503.925 −0.749889
\(673\) 96.0114 + 31.1960i 0.142662 + 0.0463536i 0.379477 0.925201i \(-0.376104\pi\)
−0.236816 + 0.971555i \(0.576104\pi\)
\(674\) −328.298 + 238.523i −0.487090 + 0.353891i
\(675\) −82.9665 60.2787i −0.122913 0.0893017i
\(676\) −45.2945 139.402i −0.0670037 0.206216i
\(677\) 191.488 62.2184i 0.282849 0.0919031i −0.164157 0.986434i \(-0.552490\pi\)
0.447006 + 0.894531i \(0.352490\pi\)
\(678\) −22.6137 + 31.1250i −0.0333535 + 0.0459071i
\(679\) −190.309 261.937i −0.280278 0.385769i
\(680\) 69.9994 215.436i 0.102940 0.316818i
\(681\) 16.5170i 0.0242541i
\(682\) 17.0692 59.6870i 0.0250282 0.0875176i
\(683\) 381.312 0.558290 0.279145 0.960249i \(-0.409949\pi\)
0.279145 + 0.960249i \(0.409949\pi\)
\(684\) −74.5027 24.2074i −0.108922 0.0353909i
\(685\) −97.1682 + 70.5968i −0.141851 + 0.103061i
\(686\) −27.0212 19.6320i −0.0393895 0.0286181i
\(687\) −107.485 330.804i −0.156455 0.481520i
\(688\) 118.559 38.5223i 0.172325 0.0559917i
\(689\) −915.565 + 1260.17i −1.32883 + 1.82898i
\(690\) 52.7778 + 72.6424i 0.0764895 + 0.105279i
\(691\) −353.424 + 1087.73i −0.511468 + 1.57414i 0.278150 + 0.960538i \(0.410279\pi\)
−0.789618 + 0.613598i \(0.789721\pi\)
\(692\) 75.9123i 0.109700i
\(693\) 267.455 + 180.125i 0.385938 + 0.259921i
\(694\) 288.929 0.416324
\(695\) 61.2403 + 19.8982i 0.0881155 + 0.0286305i
\(696\) 310.753 225.775i 0.446485 0.324390i
\(697\) −172.536 125.355i −0.247541 0.179849i
\(698\) −31.4139 96.6822i −0.0450056 0.138513i
\(699\) 395.830 128.613i 0.566281 0.183996i
\(700\) 244.929 337.116i 0.349899 0.481595i
\(701\) −302.844 416.829i −0.432017 0.594620i 0.536398 0.843965i \(-0.319785\pi\)
−0.968415 + 0.249345i \(0.919785\pi\)
\(702\) −33.5126 + 103.141i −0.0477388 + 0.146925i
\(703\) 813.575i 1.15729i
\(704\) 20.0279 + 562.108i 0.0284488 + 0.798449i
\(705\) −242.067 −0.343357
\(706\) −480.920 156.260i −0.681189 0.221332i
\(707\) −767.431 + 557.572i −1.08548 + 0.788644i
\(708\) −294.582 214.027i −0.416077 0.302297i
\(709\) −276.488 850.942i −0.389969 1.20020i −0.932811 0.360366i \(-0.882652\pi\)
0.542842 0.839835i \(-0.317348\pi\)
\(710\) 44.2582 14.3804i 0.0623355 0.0202540i
\(711\) 51.5254 70.9186i 0.0724689 0.0997449i
\(712\) 19.4233 + 26.7338i 0.0272799 + 0.0375475i
\(713\) 21.4249 65.9392i 0.0300490 0.0924813i
\(714\) 271.234i 0.379879i
\(715\) −133.095 364.872i −0.186147 0.510311i
\(716\) −391.024 −0.546122
\(717\) 132.930 + 43.1914i 0.185397 + 0.0602391i
\(718\) 291.326 211.661i 0.405747 0.294793i
\(719\) −126.704 92.0559i −0.176223 0.128033i 0.496177 0.868221i \(-0.334737\pi\)
−0.672400 + 0.740188i \(0.734737\pi\)
\(720\) −5.71760 17.5970i −0.00794111 0.0244402i
\(721\) −1729.04 + 561.798i −2.39811 + 0.779193i
\(722\) 171.353 235.847i 0.237330 0.326657i
\(723\) 156.029 + 214.755i 0.215807 + 0.297033i
\(724\) 13.5968 41.8467i 0.0187801 0.0577993i
\(725\) 523.849i 0.722551i
\(726\) 150.276 241.252i 0.206992 0.332303i
\(727\) 28.5853 0.0393195 0.0196598 0.999807i \(-0.493742\pi\)
0.0196598 + 0.999807i \(0.493742\pi\)
\(728\) −1194.92 388.254i −1.64138 0.533315i
\(729\) −21.8435 + 15.8702i −0.0299636 + 0.0217698i
\(730\) −191.014 138.780i −0.261663 0.190109i
\(731\) 169.340 + 521.175i 0.231655 + 0.712962i
\(732\) −4.48003 + 1.45565i −0.00612026 + 0.00198859i
\(733\) 317.269 436.684i 0.432837 0.595749i −0.535765 0.844367i \(-0.679977\pi\)
0.968601 + 0.248619i \(0.0799766\pi\)
\(734\) −79.3189 109.173i −0.108064 0.148737i
\(735\) 57.0763 175.663i 0.0776549 0.238997i
\(736\) 496.079i 0.674020i
\(737\) −569.574 + 207.765i −0.772827 + 0.281906i
\(738\) −73.4271 −0.0994947
\(739\) 337.414 + 109.632i 0.456582 + 0.148352i 0.528273 0.849074i \(-0.322840\pi\)
−0.0716913 + 0.997427i \(0.522840\pi\)
\(740\) −270.003 + 196.169i −0.364869 + 0.265093i
\(741\) −260.605 189.341i −0.351694 0.255520i
\(742\) 414.481 + 1275.64i 0.558600 + 1.71920i
\(743\) 820.225 266.507i 1.10394 0.358691i 0.300321 0.953838i \(-0.402906\pi\)
0.803617 + 0.595147i \(0.202906\pi\)
\(744\) −35.3973 + 48.7202i −0.0475770 + 0.0654842i
\(745\) 15.1609 + 20.8671i 0.0203501 + 0.0280096i
\(746\) 196.949 606.147i 0.264007 0.812529i
\(747\) 19.1170i 0.0255916i
\(748\) −280.691 + 10.0010i −0.375255 + 0.0133703i
\(749\) 1874.96 2.50328
\(750\) 229.296 + 74.5029i 0.305729 + 0.0993372i
\(751\) −15.0547 + 10.9379i −0.0200462 + 0.0145644i −0.597763 0.801673i \(-0.703944\pi\)
0.577717 + 0.816237i \(0.303944\pi\)
\(752\) 132.477 + 96.2502i 0.176166 + 0.127992i
\(753\) 188.608 + 580.475i 0.250475 + 0.770884i
\(754\) 526.859 171.187i 0.698752 0.227038i
\(755\) 136.428 187.776i 0.180699 0.248710i
\(756\) −64.4852 88.7562i −0.0852978 0.117402i
\(757\) 194.396 598.290i 0.256798 0.790343i −0.736672 0.676250i \(-0.763604\pi\)
0.993470 0.114093i \(-0.0363962\pi\)
\(758\) 391.449i 0.516424i
\(759\) 177.320 263.291i 0.233624 0.346891i
\(760\) 231.657 0.304812
\(761\) 897.680 + 291.674i 1.17961 + 0.383277i 0.832220 0.554445i \(-0.187070\pi\)
0.347385 + 0.937722i \(0.387070\pi\)
\(762\) 10.6187 7.71497i 0.0139354 0.0101246i
\(763\) 899.294 + 653.376i 1.17863 + 0.856324i
\(764\) 39.7626 + 122.377i 0.0520453 + 0.160179i
\(765\) 77.3545 25.1340i 0.101117 0.0328549i
\(766\) −156.811 + 215.832i −0.204714 + 0.281765i
\(767\) −880.090 1211.34i −1.14744 1.57932i
\(768\) 145.587 448.072i 0.189567 0.583427i
\(769\) 332.508i 0.432390i 0.976350 + 0.216195i \(0.0693646\pi\)
−0.976350 + 0.216195i \(0.930635\pi\)
\(770\) −321.550 91.9567i −0.417598 0.119424i
\(771\) −224.577 −0.291281
\(772\) 509.782 + 165.638i 0.660339 + 0.214557i
\(773\) 747.482 543.077i 0.966988 0.702558i 0.0122246 0.999925i \(-0.496109\pi\)
0.954763 + 0.297368i \(0.0961087\pi\)
\(774\) 152.641 + 110.900i 0.197210 + 0.143281i
\(775\) −25.3794 78.1099i −0.0327477 0.100787i
\(776\) 263.296 85.5502i 0.339300 0.110245i
\(777\) 669.717 921.787i 0.861927 1.18634i
\(778\) 357.750 + 492.401i 0.459833 + 0.632906i
\(779\) 67.3965 207.425i 0.0865167 0.266271i
\(780\) 132.141i 0.169412i
\(781\) −101.378 129.569i −0.129806 0.165901i
\(782\) 267.010 0.341445
\(783\) 131.169 + 42.6194i 0.167521 + 0.0544309i
\(784\) −101.083 + 73.4413i −0.128933 + 0.0936751i
\(785\) −35.4000 25.7196i −0.0450955 0.0327638i
\(786\) −163.840 504.248i −0.208448 0.641537i
\(787\) −1224.73 + 397.937i −1.55619 + 0.505638i −0.955788 0.294057i \(-0.904995\pi\)
−0.600407 + 0.799695i \(0.704995\pi\)
\(788\) 211.263 290.779i 0.268100 0.369009i
\(789\) 183.430 + 252.470i 0.232485 + 0.319988i
\(790\) −28.0954 + 86.4688i −0.0355638 + 0.109454i
\(791\) 160.039i 0.202325i
\(792\) −217.150 + 169.904i −0.274179 + 0.214525i
\(793\) −19.3702 −0.0244265
\(794\) 784.973 + 255.053i 0.988630 + 0.321225i
\(795\) 325.399 236.416i 0.409306 0.297379i
\(796\) −171.300 124.457i −0.215201 0.156353i
\(797\) −67.4452 207.575i −0.0846239 0.260445i 0.899787 0.436329i \(-0.143722\pi\)
−0.984411 + 0.175884i \(0.943722\pi\)
\(798\) −263.805 + 85.7156i −0.330583 + 0.107413i
\(799\) −423.106 + 582.356i −0.529545 + 0.728856i
\(800\) 345.408 + 475.413i 0.431760 + 0.594266i
\(801\) −3.66651 + 11.2844i −0.00457742 + 0.0140878i
\(802\) 351.492i 0.438270i
\(803\) −229.505 + 802.525i −0.285810 + 0.999409i
\(804\) 206.276 0.256562
\(805\) −355.232 115.422i −0.441283 0.143381i
\(806\) −70.2650 + 51.0505i −0.0871774 + 0.0633381i
\(807\) 471.526 + 342.584i 0.584295 + 0.424516i
\(808\) −250.647 771.413i −0.310207 0.954719i
\(809\) −733.095 + 238.197i −0.906174 + 0.294434i −0.724783 0.688977i \(-0.758060\pi\)
−0.181391 + 0.983411i \(0.558060\pi\)
\(810\) 16.4601 22.6554i 0.0203211 0.0279696i
\(811\) 929.155 + 1278.87i 1.14569 + 1.57691i 0.754088 + 0.656773i \(0.228079\pi\)
0.391602 + 0.920135i \(0.371921\pi\)
\(812\) −173.175 + 532.977i −0.213270 + 0.656376i
\(813\) 380.138i 0.467575i
\(814\) −833.013 561.016i −1.02336 0.689209i
\(815\) −33.1567 −0.0406831
\(816\) −52.3279 17.0024i −0.0641273 0.0208362i
\(817\) −453.387 + 329.405i −0.554941 + 0.403188i
\(818\) 287.651 + 208.991i 0.351652 + 0.255490i
\(819\) −139.406 429.049i −0.170215 0.523869i
\(820\) −85.0894 + 27.6472i −0.103768 + 0.0337161i
\(821\) 116.880 160.872i 0.142364 0.195947i −0.731881 0.681433i \(-0.761357\pi\)
0.874245 + 0.485486i \(0.161357\pi\)
\(822\) 72.2796 + 99.4844i 0.0879314 + 0.121027i
\(823\) 41.5286 127.812i 0.0504600 0.155300i −0.922651 0.385635i \(-0.873982\pi\)
0.973111 + 0.230335i \(0.0739823\pi\)
\(824\) 1554.52i 1.88656i
\(825\) −13.3893 375.786i −0.0162294 0.455498i
\(826\) −1289.32 −1.56092
\(827\) 1136.57 + 369.292i 1.37432 + 0.446545i 0.900799 0.434236i \(-0.142982\pi\)
0.473524 + 0.880781i \(0.342982\pi\)
\(828\) −87.3742 + 63.4811i −0.105524 + 0.0766679i
\(829\) −1155.60 839.591i −1.39397 1.01278i −0.995417 0.0956281i \(-0.969514\pi\)
−0.398549 0.917147i \(-0.630486\pi\)
\(830\) −6.12705 18.8571i −0.00738199 0.0227194i
\(831\) −403.297 + 131.039i −0.485316 + 0.157689i
\(832\) 462.536 636.626i 0.555932 0.765175i
\(833\) −322.841 444.352i −0.387564 0.533436i
\(834\) 20.3725 62.7000i 0.0244274 0.0751799i
\(835\) 302.577i 0.362368i
\(836\) −98.4313 269.843i −0.117741 0.322779i
\(837\) −21.6231 −0.0258341
\(838\) −838.979 272.601i −1.00117 0.325299i
\(839\) −771.245 + 560.342i −0.919243 + 0.667869i −0.943335 0.331841i \(-0.892330\pi\)
0.0240928 + 0.999710i \(0.492330\pi\)
\(840\) 262.469 + 190.695i 0.312463 + 0.227018i
\(841\) 42.1780 + 129.810i 0.0501522 + 0.154353i
\(842\) 811.177 263.567i 0.963393 0.313025i
\(843\) −351.480 + 483.770i −0.416939 + 0.573867i
\(844\) 14.7373 + 20.2842i 0.0174613 + 0.0240334i
\(845\) −48.0941 + 148.019i −0.0569162 + 0.175170i
\(846\) 247.837i 0.292951i
\(847\) 84.1464 + 1179.34i 0.0993464 + 1.39237i
\(848\) −272.086 −0.320856
\(849\) −383.134 124.488i −0.451277 0.146629i
\(850\) 255.887 185.913i 0.301044 0.218721i
\(851\) −907.434 659.289i −1.06631 0.774723i
\(852\) 17.2967 + 53.2338i 0.0203013 + 0.0624809i
\(853\) 926.904 301.170i 1.08664 0.353071i 0.289693 0.957120i \(-0.406447\pi\)
0.796947 + 0.604049i \(0.206447\pi\)
\(854\) −9.80404 + 13.4941i −0.0114801 + 0.0158011i
\(855\) 48.8913 + 67.2931i 0.0571828 + 0.0787053i
\(856\) −495.419 + 1524.74i −0.578760 + 1.78124i
\(857\) 1571.80i 1.83407i −0.398805 0.917036i \(-0.630575\pi\)
0.398805 0.917036i \(-0.369425\pi\)
\(858\) −373.570 + 136.268i −0.435396 + 0.158820i
\(859\) −740.779 −0.862373 −0.431187 0.902263i \(-0.641905\pi\)
−0.431187 + 0.902263i \(0.641905\pi\)
\(860\) 218.641 + 71.0407i 0.254234 + 0.0826055i
\(861\) 247.109 179.535i 0.287002 0.208519i
\(862\) 646.265 + 469.539i 0.749727 + 0.544709i
\(863\) 105.378 + 324.320i 0.122106 + 0.375805i 0.993363 0.115023i \(-0.0366943\pi\)
−0.871256 + 0.490828i \(0.836694\pi\)
\(864\) 147.143 47.8095i 0.170304 0.0553351i
\(865\) 47.3781 65.2103i 0.0547723 0.0753877i
\(866\) 124.439 + 171.276i 0.143694 + 0.197778i
\(867\) −79.9417 + 246.035i −0.0922049 + 0.283778i
\(868\) 87.8610i 0.101222i
\(869\) 321.217 11.4450i 0.369640 0.0131703i
\(870\) −143.046 −0.164421
\(871\) 806.703 + 262.114i 0.926180 + 0.300934i
\(872\) −768.955 + 558.678i −0.881829 + 0.640686i
\(873\) 80.4199 + 58.4285i 0.0921190 + 0.0669284i
\(874\) 84.3809 + 259.698i 0.0965456 + 0.297137i
\(875\) −953.830 + 309.918i −1.09009 + 0.354192i
\(876\) 166.924 229.752i 0.190553 0.262273i
\(877\) −601.554 827.969i −0.685923 0.944092i 0.314063 0.949402i \(-0.398310\pi\)
−0.999986 + 0.00531028i \(0.998310\pi\)
\(878\) −87.5961 + 269.593i −0.0997678 + 0.307054i
\(879\) 924.446i 1.05170i
\(880\) 37.8973 56.2709i 0.0430651 0.0639443i
\(881\) −1023.93 −1.16224 −0.581121 0.813817i \(-0.697386\pi\)
−0.581121 + 0.813817i \(0.697386\pi\)
\(882\) −179.850 58.4368i −0.203912 0.0662549i
\(883\) 1348.73 979.908i 1.52744 1.10975i 0.569795 0.821787i \(-0.307022\pi\)
0.957642 0.287961i \(-0.0929775\pi\)
\(884\) 317.901 + 230.969i 0.359617 + 0.261277i
\(885\) 119.475 + 367.707i 0.135000 + 0.415488i
\(886\) −441.599 + 143.484i −0.498419 + 0.161946i
\(887\) 408.038 561.617i 0.460021 0.633164i −0.514492 0.857495i \(-0.672020\pi\)
0.974513 + 0.224331i \(0.0720196\pi\)
\(888\) 572.651 + 788.187i 0.644878 + 0.887598i
\(889\) −16.8722 + 51.9273i −0.0189789 + 0.0584109i
\(890\) 12.3061i 0.0138271i
\(891\) −95.1842 27.2207i −0.106829 0.0305507i
\(892\) 673.970 0.755572
\(893\) −700.117 227.482i −0.784006 0.254739i
\(894\) 21.3645 15.5222i 0.0238977 0.0173627i
\(895\) 335.898 + 244.044i 0.375305 + 0.272675i
\(896\) 150.231 + 462.363i 0.167668 + 0.516030i
\(897\) −422.368 + 137.236i −0.470867 + 0.152994i
\(898\) 45.8477 63.1039i 0.0510553 0.0702717i
\(899\) 64.9230 + 89.3589i 0.0722169 + 0.0993981i
\(900\) −39.5340 + 121.673i −0.0439266 + 0.135192i
\(901\) 1196.06i 1.32748i
\(902\) −165.906 212.041i −0.183932 0.235078i
\(903\) −784.849 −0.869157
\(904\) 130.146 + 42.2870i 0.143967 + 0.0467777i
\(905\) −37.7972 + 27.4613i −0.0417648 + 0.0303439i
\(906\) −192.252 139.680i −0.212199 0.154172i
\(907\) −249.523 767.953i −0.275108 0.846696i −0.989191 0.146635i \(-0.953156\pi\)
0.714083 0.700062i \(-0.246844\pi\)
\(908\) 19.5967 6.36734i 0.0215822 0.00701249i
\(909\) 171.185 235.616i 0.188323 0.259204i
\(910\) 275.023 + 378.537i 0.302223 + 0.415974i
\(911\) −282.696 + 870.047i −0.310313 + 0.955046i 0.667327 + 0.744765i \(0.267438\pi\)
−0.977641 + 0.210282i \(0.932562\pi\)
\(912\) 56.2679i 0.0616972i
\(913\) −55.2054 + 43.1942i −0.0604660 + 0.0473102i
\(914\) 867.368 0.948981
\(915\) 4.75694 + 1.54562i 0.00519884 + 0.00168921i
\(916\) −351.047 + 255.051i −0.383240 + 0.278440i
\(917\) 1784.31 + 1296.37i 1.94581 + 1.41371i
\(918\) −25.7331 79.1983i −0.0280317 0.0862727i
\(919\) 960.986 312.243i 1.04569 0.339764i 0.264712 0.964327i \(-0.414723\pi\)
0.780974 + 0.624563i \(0.214723\pi\)
\(920\) 187.726 258.382i 0.204050 0.280850i
\(921\) −145.428 200.164i −0.157902 0.217333i
\(922\) 206.225 634.696i 0.223672 0.688391i
\(923\) 230.165i 0.249367i
\(924\) 110.605 386.761i 0.119703 0.418572i
\(925\) −1328.68 −1.43641
\(926\) 472.142 + 153.408i 0.509872 + 0.165668i
\(927\) 451.567 328.082i 0.487127 0.353918i
\(928\) −639.369 464.528i −0.688975 0.500569i
\(929\) −76.5132 235.483i −0.0823608 0.253480i 0.901393 0.433001i \(-0.142545\pi\)
−0.983754 + 0.179521i \(0.942545\pi\)
\(930\) 21.3292 6.93029i 0.0229347 0.00745192i
\(931\) 330.158 454.423i 0.354627 0.488102i
\(932\) −305.186 420.053i −0.327453 0.450700i
\(933\) 24.5675 75.6110i 0.0263317 0.0810407i
\(934\) 441.436i 0.472629i
\(935\) 247.361 + 166.593i 0.264558 + 0.178174i
\(936\) 385.744 0.412120
\(937\) 1221.51 + 396.891i 1.30363 + 0.423576i 0.876844 0.480774i \(-0.159644\pi\)
0.426790 + 0.904351i \(0.359644\pi\)
\(938\) 590.904 429.317i 0.629962 0.457694i
\(939\) 499.565 + 362.955i 0.532018 + 0.386533i
\(940\) 93.3170 + 287.200i 0.0992734 + 0.305532i
\(941\) −1665.76 + 541.238i −1.77020 + 0.575173i −0.998173 0.0604169i \(-0.980757\pi\)
−0.772027 + 0.635590i \(0.780757\pi\)
\(942\) −26.3327 + 36.2438i −0.0279540 + 0.0384754i
\(943\) −176.739 243.261i −0.187422 0.257965i
\(944\) 80.8214 248.743i 0.0856159 0.263498i
\(945\) 116.490i 0.123270i
\(946\) 24.6334 + 691.366i 0.0260395 + 0.730831i
\(947\) −87.2570 −0.0921405 −0.0460702 0.998938i \(-0.514670\pi\)
−0.0460702 + 0.998938i \(0.514670\pi\)
\(948\) −104.005 33.7931i −0.109709 0.0356468i
\(949\) 944.752 686.402i 0.995523 0.723290i
\(950\) 261.687 + 190.127i 0.275460 + 0.200133i
\(951\) 33.1089 + 101.899i 0.0348148 + 0.107149i
\(952\) 917.535 298.125i 0.963798 0.313157i
\(953\) −758.674 + 1044.23i −0.796090 + 1.09572i 0.197233 + 0.980357i \(0.436805\pi\)
−0.993323 + 0.115368i \(0.963195\pi\)
\(954\) −242.051 333.155i −0.253723 0.349219i
\(955\) 42.2204 129.941i 0.0442098 0.136064i
\(956\) 174.365i 0.182390i
\(957\) 173.298 + 475.084i 0.181084 + 0.496430i
\(958\) 445.474 0.465004
\(959\) −486.494 158.071i −0.507293 0.164829i
\(960\) −164.389 + 119.435i −0.171238 + 0.124412i
\(961\) 763.456 + 554.683i 0.794439 + 0.577193i
\(962\) 434.194 + 1336.31i 0.451345 + 1.38910i
\(963\) −547.474 + 177.885i −0.568509 + 0.184720i
\(964\) 194.647 267.908i 0.201916 0.277913i
\(965\) −334.536 460.450i −0.346670 0.477150i
\(966\) −118.173 + 363.700i −0.122333 + 0.376501i
\(967\) 321.693i 0.332671i −0.986069 0.166336i \(-0.946806\pi\)
0.986069 0.166336i \(-0.0531935\pi\)
\(968\) −981.288 243.187i −1.01373 0.251226i
\(969\) 247.348 0.255261
\(970\) −98.0533 31.8595i −0.101086 0.0328448i
\(971\) −101.171 + 73.5048i −0.104192 + 0.0757001i −0.638661 0.769488i \(-0.720512\pi\)
0.534469 + 0.845188i \(0.320512\pi\)
\(972\) 27.2499 + 19.7982i 0.0280349 + 0.0203685i
\(973\) 84.7457 + 260.820i 0.0870973 + 0.268058i
\(974\) −415.697 + 135.068i −0.426794 + 0.138674i
\(975\) −309.219 + 425.603i −0.317148 + 0.436516i
\(976\) −1.98879 2.73733i −0.00203769 0.00280464i
\(977\) 435.482 1340.28i 0.445734 1.37183i −0.435943 0.899974i \(-0.643585\pi\)
0.881677 0.471854i \(-0.156415\pi\)
\(978\) 33.9470i 0.0347107i
\(979\) −40.8711 + 14.9086i −0.0417478 + 0.0152284i
\(980\) −230.418 −0.235121
\(981\) −324.576 105.461i −0.330862 0.107504i
\(982\) 848.971 616.813i 0.864532 0.628119i
\(983\) −14.9478 10.8602i −0.0152063 0.0110480i 0.580156 0.814505i \(-0.302992\pi\)
−0.595362 + 0.803457i \(0.702992\pi\)
\(984\) 80.7070 + 248.391i 0.0820194 + 0.252430i
\(985\) −362.960 + 117.933i −0.368487 + 0.119729i
\(986\) −250.029 + 344.135i −0.253579 + 0.349021i
\(987\) −605.980 834.060i −0.613962 0.845046i
\(988\) −124.180 + 382.186i −0.125688 + 0.386828i
\(989\) 772.628i 0.781222i
\(990\) 102.615 3.65617i 0.103651 0.00369310i
\(991\) −212.736 −0.214668 −0.107334 0.994223i \(-0.534231\pi\)
−0.107334 + 0.994223i \(0.534231\pi\)
\(992\) 117.840 + 38.2886i 0.118791 + 0.0385974i
\(993\) −476.373 + 346.105i −0.479731 + 0.348545i
\(994\) 160.343 + 116.496i 0.161311 + 0.117199i
\(995\) 69.4751 + 213.822i 0.0698242 + 0.214897i
\(996\) 22.6813 7.36961i 0.0227724 0.00739920i
\(997\) −206.481 + 284.197i −0.207103 + 0.285052i −0.899915 0.436066i \(-0.856372\pi\)
0.692812 + 0.721118i \(0.256372\pi\)
\(998\) 40.7360 + 56.0683i 0.0408177 + 0.0561807i
\(999\) −108.099 + 332.694i −0.108207 + 0.333027i
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 33.3.g.a.13.3 16
3.2 odd 2 99.3.k.c.46.2 16
4.3 odd 2 528.3.bf.b.145.2 16
11.2 odd 10 363.3.g.a.118.3 16
11.3 even 5 363.3.g.a.40.3 16
11.4 even 5 363.3.c.e.241.11 16
11.5 even 5 363.3.g.f.94.2 16
11.6 odd 10 inner 33.3.g.a.28.3 yes 16
11.7 odd 10 363.3.c.e.241.6 16
11.8 odd 10 363.3.g.g.40.2 16
11.9 even 5 363.3.g.g.118.2 16
11.10 odd 2 363.3.g.f.112.2 16
33.17 even 10 99.3.k.c.28.2 16
33.26 odd 10 1089.3.c.m.604.6 16
33.29 even 10 1089.3.c.m.604.11 16
44.39 even 10 528.3.bf.b.193.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.3.g.a.13.3 16 1.1 even 1 trivial
33.3.g.a.28.3 yes 16 11.6 odd 10 inner
99.3.k.c.28.2 16 33.17 even 10
99.3.k.c.46.2 16 3.2 odd 2
363.3.c.e.241.6 16 11.7 odd 10
363.3.c.e.241.11 16 11.4 even 5
363.3.g.a.40.3 16 11.3 even 5
363.3.g.a.118.3 16 11.2 odd 10
363.3.g.f.94.2 16 11.5 even 5
363.3.g.f.112.2 16 11.10 odd 2
363.3.g.g.40.2 16 11.8 odd 10
363.3.g.g.118.2 16 11.9 even 5
528.3.bf.b.145.2 16 4.3 odd 2
528.3.bf.b.193.2 16 44.39 even 10
1089.3.c.m.604.6 16 33.26 odd 10
1089.3.c.m.604.11 16 33.29 even 10