Properties

Label 361.3.f.d.307.1
Level $361$
Weight $3$
Character 361.307
Analytic conductor $9.837$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $12$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [361,3,Mod(116,361)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(361, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("361.116");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 361 = 19^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 361.f (of order \(18\), degree \(6\), not 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: \(9.83653754341\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{18})\)
Coefficient field: 12.0.7659539263855005696.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2197x^{6} + 4826809 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 19)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 307.1
Root \(-2.31760 + 2.76201i\) of defining polynomial
Character \(\chi\) \(=\) 361.307
Dual form 361.3.f.d.127.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.31760 + 2.76201i) q^{2} +(1.23317 + 3.38811i) q^{3} +(-1.56283 - 8.86327i) q^{4} +(0.694593 - 3.93923i) q^{5} +(-12.2160 - 4.44626i) q^{6} +(2.50000 + 4.33013i) q^{7} +(15.6125 + 9.01388i) q^{8} +(-3.06418 + 2.57115i) q^{9} +O(q^{10})\) \(q+(-2.31760 + 2.76201i) q^{2} +(1.23317 + 3.38811i) q^{3} +(-1.56283 - 8.86327i) q^{4} +(0.694593 - 3.93923i) q^{5} +(-12.2160 - 4.44626i) q^{6} +(2.50000 + 4.33013i) q^{7} +(15.6125 + 9.01388i) q^{8} +(-3.06418 + 2.57115i) q^{9} +(9.27041 + 11.0481i) q^{10} +(5.00000 - 8.66025i) q^{11} +(28.1025 - 16.2250i) q^{12} +(1.23317 - 3.38811i) q^{13} +(-17.7539 - 3.13049i) q^{14} +(14.2031 - 2.50439i) q^{15} +(-27.2511 + 9.91858i) q^{16} +(11.4907 + 9.64181i) q^{17} -14.4222i q^{18} -36.0000 q^{20} +(-11.5880 + 13.8101i) q^{21} +(12.3317 + 33.8811i) q^{22} +(6.07769 + 34.4683i) q^{23} +(-11.2871 + 64.0125i) q^{24} +(8.45723 + 3.07818i) q^{25} +(6.50000 + 11.2583i) q^{26} +(15.6125 + 9.01388i) q^{27} +(34.4720 - 28.9254i) q^{28} +(11.5880 + 13.8101i) q^{29} +(-26.0000 + 45.0333i) q^{30} +(-31.2250 + 18.0278i) q^{31} +(11.0985 - 30.4930i) q^{32} +(35.5077 + 6.26097i) q^{33} +(-53.2616 + 9.39146i) q^{34} +(18.7939 - 6.84040i) q^{35} +(27.5776 + 23.1404i) q^{36} -21.6333i q^{37} +13.0000 q^{39} +(46.3521 - 55.2403i) q^{40} +(-12.3317 - 33.8811i) q^{41} +(-11.2871 - 64.0125i) q^{42} +(-3.47296 + 19.6962i) q^{43} +(-84.5723 - 30.7818i) q^{44} +(8.00000 + 13.8564i) q^{45} +(-109.287 - 63.0971i) q^{46} +(7.66044 - 6.42788i) q^{47} +(-67.2105 - 80.0984i) q^{48} +(12.0000 - 20.7846i) q^{49} +(-28.1025 + 16.2250i) q^{50} +(-18.4976 + 50.8216i) q^{51} +(-31.9570 - 5.63488i) q^{52} +(74.5663 - 13.1480i) q^{53} +(-61.0800 + 22.2313i) q^{54} +(-30.6418 - 25.7115i) q^{55} +90.1388i q^{56} -65.0000 q^{58} +(-11.5880 + 13.8101i) q^{59} +(-44.3942 - 121.972i) q^{60} +(-6.94593 - 39.3923i) q^{61} +(22.5743 - 128.025i) q^{62} +(-18.7939 - 6.84040i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-12.4900 - 7.21110i) q^{65} +(-99.5858 + 83.5624i) q^{66} +(25.4936 + 30.3821i) q^{67} +(67.5000 - 116.913i) q^{68} +(-109.287 + 63.0971i) q^{69} +(-24.6634 + 67.7622i) q^{70} +(106.523 + 18.7829i) q^{71} +(-71.0155 + 12.5219i) q^{72} +(-98.6677 + 35.9121i) q^{73} +(59.7515 + 50.1374i) q^{74} +32.4500i q^{75} +50.0000 q^{77} +(-30.1288 + 35.9062i) q^{78} +(12.3317 + 33.8811i) q^{79} +(20.1432 + 114.238i) q^{80} +(-17.5385 + 99.4656i) q^{81} +(122.160 + 44.4626i) q^{82} +(20.0000 + 34.6410i) q^{83} +(140.512 + 81.1249i) q^{84} +(45.9627 - 38.5673i) q^{85} +(-46.3521 - 55.2403i) q^{86} +(-32.5000 + 56.2917i) q^{87} +(156.125 - 90.1388i) q^{88} +(-56.8124 - 10.0176i) q^{90} +(17.7539 - 3.13049i) q^{91} +(296.003 - 107.736i) q^{92} +(-99.5858 - 83.5624i) q^{93} +36.0555i q^{94} +117.000 q^{96} +(-78.7985 + 93.9084i) q^{97} +(29.5961 + 81.3146i) q^{98} +(6.94593 + 39.3923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 30 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 30 q^{7} + 60 q^{11} - 432 q^{20} + 78 q^{26} - 312 q^{30} + 156 q^{39} + 96 q^{45} + 144 q^{49} - 780 q^{58} + 6 q^{64} + 810 q^{68} + 600 q^{77} + 240 q^{83} - 390 q^{87} + 1404 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/361\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.31760 + 2.76201i −1.15880 + 1.38101i −0.247694 + 0.968838i \(0.579673\pi\)
−0.911108 + 0.412168i \(0.864772\pi\)
\(3\) 1.23317 + 3.38811i 0.411057 + 1.12937i 0.956630 + 0.291306i \(0.0940899\pi\)
−0.545573 + 0.838063i \(0.683688\pi\)
\(4\) −1.56283 8.86327i −0.390708 2.21582i
\(5\) 0.694593 3.93923i 0.138919 0.787846i −0.833132 0.553074i \(-0.813455\pi\)
0.972050 0.234772i \(-0.0754343\pi\)
\(6\) −12.2160 4.44626i −2.03600 0.741044i
\(7\) 2.50000 + 4.33013i 0.357143 + 0.618590i 0.987482 0.157730i \(-0.0504176\pi\)
−0.630339 + 0.776320i \(0.717084\pi\)
\(8\) 15.6125 + 9.01388i 1.95156 + 1.12673i
\(9\) −3.06418 + 2.57115i −0.340464 + 0.285683i
\(10\) 9.27041 + 11.0481i 0.927041 + 1.10481i
\(11\) 5.00000 8.66025i 0.454545 0.787296i −0.544116 0.839010i \(-0.683135\pi\)
0.998662 + 0.0517139i \(0.0164684\pi\)
\(12\) 28.1025 16.2250i 2.34187 1.35208i
\(13\) 1.23317 3.38811i 0.0948593 0.260624i −0.883184 0.469027i \(-0.844605\pi\)
0.978043 + 0.208404i \(0.0668268\pi\)
\(14\) −17.7539 3.13049i −1.26813 0.223606i
\(15\) 14.2031 2.50439i 0.946873 0.166959i
\(16\) −27.2511 + 9.91858i −1.70319 + 0.619912i
\(17\) 11.4907 + 9.64181i 0.675922 + 0.567166i 0.914811 0.403881i \(-0.132339\pi\)
−0.238890 + 0.971047i \(0.576784\pi\)
\(18\) 14.4222i 0.801234i
\(19\) 0 0
\(20\) −36.0000 −1.80000
\(21\) −11.5880 + 13.8101i −0.551810 + 0.657622i
\(22\) 12.3317 + 33.8811i 0.560532 + 1.54005i
\(23\) 6.07769 + 34.4683i 0.264247 + 1.49862i 0.771170 + 0.636629i \(0.219672\pi\)
−0.506923 + 0.861991i \(0.669217\pi\)
\(24\) −11.2871 + 64.0125i −0.470297 + 2.66719i
\(25\) 8.45723 + 3.07818i 0.338289 + 0.123127i
\(26\) 6.50000 + 11.2583i 0.250000 + 0.433013i
\(27\) 15.6125 + 9.01388i 0.578241 + 0.333847i
\(28\) 34.4720 28.9254i 1.23114 1.03305i
\(29\) 11.5880 + 13.8101i 0.399587 + 0.476209i 0.927894 0.372844i \(-0.121617\pi\)
−0.528307 + 0.849053i \(0.677173\pi\)
\(30\) −26.0000 + 45.0333i −0.866667 + 1.50111i
\(31\) −31.2250 + 18.0278i −1.00726 + 0.581541i −0.910388 0.413756i \(-0.864216\pi\)
−0.0968702 + 0.995297i \(0.530883\pi\)
\(32\) 11.0985 30.4930i 0.346829 0.952906i
\(33\) 35.5077 + 6.26097i 1.07599 + 0.189726i
\(34\) −53.2616 + 9.39146i −1.56652 + 0.276219i
\(35\) 18.7939 6.84040i 0.536967 0.195440i
\(36\) 27.5776 + 23.1404i 0.766044 + 0.642788i
\(37\) 21.6333i 0.584684i −0.956314 0.292342i \(-0.905565\pi\)
0.956314 0.292342i \(-0.0944346\pi\)
\(38\) 0 0
\(39\) 13.0000 0.333333
\(40\) 46.3521 55.2403i 1.15880 1.38101i
\(41\) −12.3317 33.8811i −0.300773 0.826368i −0.994366 0.106001i \(-0.966195\pi\)
0.693593 0.720367i \(-0.256027\pi\)
\(42\) −11.2871 64.0125i −0.268741 1.52411i
\(43\) −3.47296 + 19.6962i −0.0807666 + 0.458050i 0.917423 + 0.397912i \(0.130265\pi\)
−0.998190 + 0.0601379i \(0.980846\pi\)
\(44\) −84.5723 30.7818i −1.92210 0.699587i
\(45\) 8.00000 + 13.8564i 0.177778 + 0.307920i
\(46\) −109.287 63.0971i −2.37581 1.37168i
\(47\) 7.66044 6.42788i 0.162988 0.136763i −0.557646 0.830079i \(-0.688295\pi\)
0.720634 + 0.693316i \(0.243851\pi\)
\(48\) −67.2105 80.0984i −1.40022 1.66872i
\(49\) 12.0000 20.7846i 0.244898 0.424176i
\(50\) −28.1025 + 16.2250i −0.562050 + 0.324500i
\(51\) −18.4976 + 50.8216i −0.362697 + 0.996503i
\(52\) −31.9570 5.63488i −0.614557 0.108363i
\(53\) 74.5663 13.1480i 1.40691 0.248076i 0.581931 0.813238i \(-0.302297\pi\)
0.824980 + 0.565162i \(0.191186\pi\)
\(54\) −61.0800 + 22.2313i −1.13111 + 0.411691i
\(55\) −30.6418 25.7115i −0.557123 0.467482i
\(56\) 90.1388i 1.60962i
\(57\) 0 0
\(58\) −65.0000 −1.12069
\(59\) −11.5880 + 13.8101i −0.196407 + 0.234069i −0.855255 0.518207i \(-0.826600\pi\)
0.658848 + 0.752276i \(0.271044\pi\)
\(60\) −44.3942 121.972i −0.739903 2.03287i
\(61\) −6.94593 39.3923i −0.113868 0.645776i −0.987305 0.158838i \(-0.949225\pi\)
0.873437 0.486937i \(-0.161886\pi\)
\(62\) 22.5743 128.025i 0.364101 2.06492i
\(63\) −18.7939 6.84040i −0.298315 0.108578i
\(64\) 0.500000 + 0.866025i 0.00781250 + 0.0135316i
\(65\) −12.4900 7.21110i −0.192154 0.110940i
\(66\) −99.5858 + 83.5624i −1.50888 + 1.26610i
\(67\) 25.4936 + 30.3821i 0.380502 + 0.453465i 0.921973 0.387255i \(-0.126577\pi\)
−0.541471 + 0.840720i \(0.682132\pi\)
\(68\) 67.5000 116.913i 0.992647 1.71932i
\(69\) −109.287 + 63.0971i −1.58388 + 0.914451i
\(70\) −24.6634 + 67.7622i −0.352335 + 0.968031i
\(71\) 106.523 + 18.7829i 1.50033 + 0.264548i 0.862668 0.505770i \(-0.168792\pi\)
0.637659 + 0.770319i \(0.279903\pi\)
\(72\) −71.0155 + 12.5219i −0.986326 + 0.173916i
\(73\) −98.6677 + 35.9121i −1.35161 + 0.491947i −0.913451 0.406949i \(-0.866593\pi\)
−0.438162 + 0.898896i \(0.644370\pi\)
\(74\) 59.7515 + 50.1374i 0.807452 + 0.677533i
\(75\) 32.4500i 0.432666i
\(76\) 0 0
\(77\) 50.0000 0.649351
\(78\) −30.1288 + 35.9062i −0.386267 + 0.460335i
\(79\) 12.3317 + 33.8811i 0.156098 + 0.428875i 0.992947 0.118558i \(-0.0378273\pi\)
−0.836849 + 0.547433i \(0.815605\pi\)
\(80\) 20.1432 + 114.238i 0.251790 + 1.42797i
\(81\) −17.5385 + 99.4656i −0.216524 + 1.22797i
\(82\) 122.160 + 44.4626i 1.48976 + 0.542227i
\(83\) 20.0000 + 34.6410i 0.240964 + 0.417362i 0.960989 0.276586i \(-0.0892031\pi\)
−0.720025 + 0.693948i \(0.755870\pi\)
\(84\) 140.512 + 81.1249i 1.67277 + 0.965773i
\(85\) 45.9627 38.5673i 0.540737 0.453732i
\(86\) −46.3521 55.2403i −0.538978 0.642328i
\(87\) −32.5000 + 56.2917i −0.373563 + 0.647030i
\(88\) 156.125 90.1388i 1.77415 1.02430i
\(89\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(90\) −56.8124 10.0176i −0.631249 0.111306i
\(91\) 17.7539 3.13049i 0.195098 0.0344010i
\(92\) 296.003 107.736i 3.21743 1.17105i
\(93\) −99.5858 83.5624i −1.07081 0.898520i
\(94\) 36.0555i 0.383569i
\(95\) 0 0
\(96\) 117.000 1.21875
\(97\) −78.7985 + 93.9084i −0.812356 + 0.968128i −0.999900 0.0141281i \(-0.995503\pi\)
0.187544 + 0.982256i \(0.439947\pi\)
\(98\) 29.5961 + 81.3146i 0.302001 + 0.829741i
\(99\) 6.94593 + 39.3923i 0.0701609 + 0.397902i
\(100\) 14.0655 79.7694i 0.140655 0.797694i
\(101\) 46.9846 + 17.1010i 0.465194 + 0.169317i 0.563974 0.825792i \(-0.309272\pi\)
−0.0987798 + 0.995109i \(0.531494\pi\)
\(102\) −97.5000 168.875i −0.955882 1.65564i
\(103\) −49.9600 28.8444i −0.485048 0.280043i 0.237470 0.971395i \(-0.423682\pi\)
−0.722518 + 0.691352i \(0.757015\pi\)
\(104\) 49.7929 41.7812i 0.478778 0.401742i
\(105\) 46.3521 + 55.2403i 0.441448 + 0.526098i
\(106\) −136.500 + 236.425i −1.28774 + 2.23042i
\(107\) 65.5725 37.8583i 0.612827 0.353816i −0.161244 0.986915i \(-0.551551\pi\)
0.774071 + 0.633099i \(0.218217\pi\)
\(108\) 55.4927 152.465i 0.513821 1.41171i
\(109\) −195.293 34.4354i −1.79168 0.315921i −0.823711 0.567009i \(-0.808100\pi\)
−0.967964 + 0.251089i \(0.919211\pi\)
\(110\) 142.031 25.0439i 1.29119 0.227672i
\(111\) 73.2960 26.6776i 0.660325 0.240338i
\(112\) −111.076 93.2042i −0.991754 0.832180i
\(113\) 122.589i 1.08486i −0.840102 0.542428i \(-0.817505\pi\)
0.840102 0.542428i \(-0.182495\pi\)
\(114\) 0 0
\(115\) 140.000 1.21739
\(116\) 104.292 124.291i 0.899070 1.07147i
\(117\) 4.93268 + 13.5524i 0.0421597 + 0.115833i
\(118\) −11.2871 64.0125i −0.0956537 0.542479i
\(119\) −13.0236 + 73.8606i −0.109442 + 0.620677i
\(120\) 244.320 + 88.9252i 2.03600 + 0.741044i
\(121\) 10.5000 + 18.1865i 0.0867769 + 0.150302i
\(122\) 124.900 + 72.1110i 1.02377 + 0.591074i
\(123\) 99.5858 83.5624i 0.809640 0.679369i
\(124\) 208.584 + 248.581i 1.68213 + 2.00469i
\(125\) 68.0000 117.779i 0.544000 0.942236i
\(126\) 62.4500 36.0555i 0.495635 0.286155i
\(127\) −44.3942 + 121.972i −0.349560 + 0.960409i 0.632949 + 0.774194i \(0.281844\pi\)
−0.982509 + 0.186215i \(0.940378\pi\)
\(128\) 124.277 + 21.9134i 0.970915 + 0.171199i
\(129\) −71.0155 + 12.5219i −0.550508 + 0.0970694i
\(130\) 48.8640 17.7850i 0.375877 0.136808i
\(131\) 85.7970 + 71.9922i 0.654939 + 0.549559i 0.908565 0.417743i \(-0.137179\pi\)
−0.253626 + 0.967302i \(0.581623\pi\)
\(132\) 324.500i 2.45833i
\(133\) 0 0
\(134\) −143.000 −1.06716
\(135\) 46.3521 55.2403i 0.343349 0.409187i
\(136\) 92.4878 + 254.108i 0.680058 + 1.86844i
\(137\) 21.7060 + 123.101i 0.158438 + 0.898547i 0.955575 + 0.294748i \(0.0952358\pi\)
−0.797137 + 0.603799i \(0.793653\pi\)
\(138\) 79.0099 448.088i 0.572536 3.24701i
\(139\) −46.9846 17.1010i −0.338019 0.123029i 0.167433 0.985883i \(-0.446452\pi\)
−0.505452 + 0.862855i \(0.668674\pi\)
\(140\) −90.0000 155.885i −0.642857 1.11346i
\(141\) 31.2250 + 18.0278i 0.221454 + 0.127856i
\(142\) −298.757 + 250.687i −2.10392 + 1.76540i
\(143\) −23.1760 27.6201i −0.162070 0.193148i
\(144\) 58.0000 100.459i 0.402778 0.697632i
\(145\) 62.4500 36.0555i 0.430690 0.248659i
\(146\) 129.483 355.752i 0.886870 2.43665i
\(147\) 85.2186 + 15.0263i 0.579718 + 0.102220i
\(148\) −191.742 + 33.8093i −1.29555 + 0.228441i
\(149\) −65.7785 + 23.9414i −0.441466 + 0.160681i −0.553183 0.833059i \(-0.686587\pi\)
0.111717 + 0.993740i \(0.464365\pi\)
\(150\) −89.6272 75.2062i −0.597515 0.501374i
\(151\) 36.0555i 0.238778i 0.992848 + 0.119389i \(0.0380936\pi\)
−0.992848 + 0.119389i \(0.961906\pi\)
\(152\) 0 0
\(153\) −60.0000 −0.392157
\(154\) −115.880 + 138.101i −0.752469 + 0.896757i
\(155\) 49.3268 + 135.524i 0.318238 + 0.874351i
\(156\) −20.3168 115.223i −0.130236 0.738606i
\(157\) 1.73648 9.84808i 0.0110604 0.0627266i −0.978778 0.204923i \(-0.934305\pi\)
0.989838 + 0.142197i \(0.0454166\pi\)
\(158\) −122.160 44.4626i −0.773165 0.281409i
\(159\) 136.500 + 236.425i 0.858491 + 1.48695i
\(160\) −112.410 64.8999i −0.702562 0.405625i
\(161\) −134.058 + 112.488i −0.832657 + 0.698682i
\(162\) −234.078 278.963i −1.44493 1.72200i
\(163\) 135.000 233.827i 0.828221 1.43452i −0.0712118 0.997461i \(-0.522687\pi\)
0.899433 0.437059i \(-0.143980\pi\)
\(164\) −281.025 + 162.250i −1.71357 + 0.989328i
\(165\) 49.3268 135.524i 0.298951 0.821360i
\(166\) −142.031 25.0439i −0.855608 0.150867i
\(167\) −120.726 + 21.2873i −0.722912 + 0.127469i −0.522985 0.852342i \(-0.675182\pi\)
−0.199927 + 0.979811i \(0.564071\pi\)
\(168\) −305.400 + 111.157i −1.81786 + 0.661646i
\(169\) 119.503 + 100.275i 0.707118 + 0.593342i
\(170\) 216.333i 1.27255i
\(171\) 0 0
\(172\) 180.000 1.04651
\(173\) 78.7985 93.9084i 0.455483 0.542823i −0.488610 0.872502i \(-0.662496\pi\)
0.944093 + 0.329679i \(0.106940\pi\)
\(174\) −80.1561 220.227i −0.460667 1.26567i
\(175\) 7.81417 + 44.3163i 0.0446524 + 0.253236i
\(176\) −50.3580 + 285.594i −0.286125 + 1.62269i
\(177\) −61.0800 22.2313i −0.345085 0.125601i
\(178\) 0 0
\(179\) −31.2250 18.0278i −0.174441 0.100714i 0.410237 0.911979i \(-0.365446\pi\)
−0.584678 + 0.811265i \(0.698779\pi\)
\(180\) 110.310 92.5614i 0.612836 0.514230i
\(181\) 69.5281 + 82.8604i 0.384133 + 0.457792i 0.923114 0.384526i \(-0.125635\pi\)
−0.538981 + 0.842318i \(0.681191\pi\)
\(182\) −32.5000 + 56.2917i −0.178571 + 0.309295i
\(183\) 124.900 72.1110i 0.682513 0.394049i
\(184\) −215.805 + 592.919i −1.17285 + 3.22239i
\(185\) −85.2186 15.0263i −0.460641 0.0812234i
\(186\) 461.601 81.3927i 2.48172 0.437595i
\(187\) 140.954 51.3030i 0.753764 0.274348i
\(188\) −68.9440 57.8509i −0.366723 0.307717i
\(189\) 90.1388i 0.476925i
\(190\) 0 0
\(191\) 193.000 1.01047 0.505236 0.862981i \(-0.331406\pi\)
0.505236 + 0.862981i \(0.331406\pi\)
\(192\) −2.31760 + 2.76201i −0.0120709 + 0.0143855i
\(193\) −91.2547 250.720i −0.472822 1.29907i −0.915475 0.402375i \(-0.868185\pi\)
0.442653 0.896693i \(-0.354037\pi\)
\(194\) −76.7525 435.285i −0.395631 2.24374i
\(195\) 9.02971 51.2100i 0.0463062 0.262615i
\(196\) −202.974 73.8764i −1.03558 0.376920i
\(197\) −45.0000 77.9423i −0.228426 0.395646i 0.728916 0.684604i \(-0.240025\pi\)
−0.957342 + 0.288958i \(0.906691\pi\)
\(198\) −124.900 72.1110i −0.630808 0.364197i
\(199\) 94.2235 79.0629i 0.473485 0.397301i −0.374579 0.927195i \(-0.622213\pi\)
0.848064 + 0.529894i \(0.177768\pi\)
\(200\) 104.292 + 124.291i 0.521461 + 0.621453i
\(201\) −71.5000 + 123.842i −0.355721 + 0.616128i
\(202\) −156.125 + 90.1388i −0.772896 + 0.446232i
\(203\) −30.8293 + 84.7027i −0.151868 + 0.417255i
\(204\) 479.355 + 84.5232i 2.34978 + 0.414329i
\(205\) −142.031 + 25.0439i −0.692834 + 0.122165i
\(206\) 195.456 71.1402i 0.948816 0.345341i
\(207\) −107.246 89.9903i −0.518098 0.434736i
\(208\) 104.561i 0.502697i
\(209\) 0 0
\(210\) −260.000 −1.23810
\(211\) 150.644 179.531i 0.713954 0.850857i −0.280075 0.959978i \(-0.590359\pi\)
0.994028 + 0.109121i \(0.0348037\pi\)
\(212\) −233.069 640.353i −1.09938 3.02053i
\(213\) 67.7228 + 384.075i 0.317947 + 1.80317i
\(214\) −47.4060 + 268.853i −0.221523 + 1.25632i
\(215\) 75.1754 + 27.3616i 0.349653 + 0.127263i
\(216\) 162.500 + 281.458i 0.752315 + 1.30305i
\(217\) −156.125 90.1388i −0.719470 0.415386i
\(218\) 547.722 459.593i 2.51249 2.10823i
\(219\) −243.348 290.011i −1.11118 1.32425i
\(220\) −180.000 + 311.769i −0.818182 + 1.41713i
\(221\) 46.8375 27.0416i 0.211934 0.122360i
\(222\) −96.1874 + 264.273i −0.433276 + 1.19042i
\(223\) −198.843 35.0615i −0.891674 0.157226i −0.291003 0.956722i \(-0.593989\pi\)
−0.600672 + 0.799496i \(0.705100\pi\)
\(224\) 159.785 28.1744i 0.713325 0.125778i
\(225\) −33.8289 + 12.3127i −0.150351 + 0.0547232i
\(226\) 338.592 + 284.112i 1.49819 + 1.25713i
\(227\) 255.994i 1.12773i 0.825868 + 0.563864i \(0.190686\pi\)
−0.825868 + 0.563864i \(0.809314\pi\)
\(228\) 0 0
\(229\) −160.000 −0.698690 −0.349345 0.936994i \(-0.613596\pi\)
−0.349345 + 0.936994i \(0.613596\pi\)
\(230\) −324.465 + 386.682i −1.41072 + 1.68123i
\(231\) 61.6586 + 169.405i 0.266920 + 0.733357i
\(232\) 56.4357 + 320.063i 0.243257 + 1.37958i
\(233\) −46.8850 + 265.898i −0.201223 + 1.14119i 0.702050 + 0.712128i \(0.252268\pi\)
−0.903273 + 0.429066i \(0.858843\pi\)
\(234\) −48.8640 17.7850i −0.208821 0.0760045i
\(235\) −20.0000 34.6410i −0.0851064 0.147409i
\(236\) 140.512 + 81.1249i 0.595392 + 0.343750i
\(237\) −99.5858 + 83.5624i −0.420193 + 0.352584i
\(238\) −173.820 207.151i −0.730337 0.870382i
\(239\) −98.5000 + 170.607i −0.412134 + 0.713837i −0.995123 0.0986432i \(-0.968550\pi\)
0.582989 + 0.812480i \(0.301883\pi\)
\(240\) −362.210 + 209.122i −1.50921 + 0.871342i
\(241\) 135.649 372.692i 0.562858 1.54644i −0.252568 0.967579i \(-0.581275\pi\)
0.815426 0.578861i \(-0.196503\pi\)
\(242\) −74.5663 13.1480i −0.308125 0.0543308i
\(243\) −198.843 + 35.0615i −0.818286 + 0.144286i
\(244\) −338.289 + 123.127i −1.38643 + 0.504620i
\(245\) −73.5403 61.7076i −0.300164 0.251868i
\(246\) 468.722i 1.90537i
\(247\) 0 0
\(248\) −650.000 −2.62097
\(249\) −92.7041 + 110.481i −0.372306 + 0.443697i
\(250\) 167.711 + 460.783i 0.670845 + 1.84313i
\(251\) −69.8066 395.893i −0.278114 1.57726i −0.728894 0.684627i \(-0.759965\pi\)
0.450780 0.892635i \(-0.351146\pi\)
\(252\) −31.2567 + 177.265i −0.124034 + 0.703434i
\(253\) 328.892 + 119.707i 1.29997 + 0.473150i
\(254\) −234.000 405.300i −0.921260 1.59567i
\(255\) 187.350 + 108.167i 0.734706 + 0.424183i
\(256\) −351.614 + 295.040i −1.37349 + 1.15250i
\(257\) −268.842 320.393i −1.04608 1.24667i −0.968325 0.249694i \(-0.919670\pi\)
−0.0777533 0.996973i \(-0.524775\pi\)
\(258\) 130.000 225.167i 0.503876 0.872739i
\(259\) 93.6750 54.0833i 0.361679 0.208816i
\(260\) −44.3942 + 121.972i −0.170747 + 0.469123i
\(261\) −71.0155 12.5219i −0.272090 0.0479768i
\(262\) −397.687 + 70.1229i −1.51789 + 0.267645i
\(263\) −291.305 + 106.026i −1.10762 + 0.403142i −0.830121 0.557584i \(-0.811729\pi\)
−0.277502 + 0.960725i \(0.589506\pi\)
\(264\) 497.929 + 417.812i 1.88609 + 1.58262i
\(265\) 302.866i 1.14289i
\(266\) 0 0
\(267\) 0 0
\(268\) 229.443 273.439i 0.856130 1.02030i
\(269\) −36.9951 101.643i −0.137528 0.377856i 0.851740 0.523964i \(-0.175547\pi\)
−0.989269 + 0.146108i \(0.953325\pi\)
\(270\) 45.1485 + 256.050i 0.167217 + 0.948333i
\(271\) 18.2331 103.405i 0.0672807 0.381568i −0.932511 0.361142i \(-0.882387\pi\)
0.999791 0.0204253i \(-0.00650202\pi\)
\(272\) −408.766 148.779i −1.50282 0.546981i
\(273\) 32.5000 + 56.2917i 0.119048 + 0.206197i
\(274\) −390.312 225.347i −1.42450 0.822434i
\(275\) 68.9440 57.8509i 0.250705 0.210367i
\(276\) 730.045 + 870.034i 2.64509 + 3.15230i
\(277\) 25.0000 43.3013i 0.0902527 0.156322i −0.817365 0.576121i \(-0.804566\pi\)
0.907617 + 0.419798i \(0.137899\pi\)
\(278\) 156.125 90.1388i 0.561601 0.324240i
\(279\) 49.3268 135.524i 0.176799 0.485751i
\(280\) 355.077 + 62.6097i 1.26813 + 0.223606i
\(281\) 284.062 50.0878i 1.01090 0.178248i 0.356416 0.934327i \(-0.383999\pi\)
0.654480 + 0.756079i \(0.272887\pi\)
\(282\) −122.160 + 44.4626i −0.433192 + 0.157669i
\(283\) −245.134 205.692i −0.866199 0.726827i 0.0970955 0.995275i \(-0.469045\pi\)
−0.963294 + 0.268448i \(0.913489\pi\)
\(284\) 973.499i 3.42781i
\(285\) 0 0
\(286\) 130.000 0.454545
\(287\) 115.880 138.101i 0.403764 0.481187i
\(288\) 44.3942 + 121.972i 0.154146 + 0.423514i
\(289\) −11.1135 63.0277i −0.0384550 0.218089i
\(290\) −45.1485 + 256.050i −0.155685 + 0.882931i
\(291\) −415.344 151.173i −1.42730 0.519495i
\(292\) 472.500 + 818.394i 1.61815 + 2.80272i
\(293\) 190.472 + 109.969i 0.650077 + 0.375322i 0.788486 0.615053i \(-0.210866\pi\)
−0.138409 + 0.990375i \(0.544199\pi\)
\(294\) −239.006 + 200.550i −0.812945 + 0.682142i
\(295\) 46.3521 + 55.2403i 0.157126 + 0.187255i
\(296\) 195.000 337.750i 0.658784 1.14105i
\(297\) 156.125 90.1388i 0.525673 0.303498i
\(298\) 86.3220 237.168i 0.289671 0.795865i
\(299\) 124.277 + 21.9134i 0.415643 + 0.0732890i
\(300\) 287.613 50.7139i 0.958709 0.169046i
\(301\) −93.9693 + 34.2020i −0.312190 + 0.113628i
\(302\) −99.5858 83.5624i −0.329754 0.276697i
\(303\) 180.278i 0.594975i
\(304\) 0 0
\(305\) −160.000 −0.524590
\(306\) 139.056 165.721i 0.454432 0.541571i
\(307\) −81.3893 223.615i −0.265112 0.728388i −0.998803 0.0489059i \(-0.984427\pi\)
0.733692 0.679483i \(-0.237796\pi\)
\(308\) −78.1417 443.163i −0.253707 1.43884i
\(309\) 36.1188 204.840i 0.116889 0.662913i
\(310\) −488.640 177.850i −1.57626 0.573711i
\(311\) −197.500 342.080i −0.635048 1.09994i −0.986505 0.163732i \(-0.947647\pi\)
0.351457 0.936204i \(-0.385686\pi\)
\(312\) 202.962 + 117.180i 0.650521 + 0.375578i
\(313\) 95.7556 80.3485i 0.305928 0.256704i −0.476878 0.878969i \(-0.658232\pi\)
0.782807 + 0.622265i \(0.213787\pi\)
\(314\) 23.1760 + 27.6201i 0.0738090 + 0.0879622i
\(315\) −40.0000 + 69.2820i −0.126984 + 0.219943i
\(316\) 281.025 162.250i 0.889319 0.513449i
\(317\) 1.23317 3.38811i 0.00389013 0.0106880i −0.937732 0.347359i \(-0.887079\pi\)
0.941622 + 0.336671i \(0.109301\pi\)
\(318\) −969.362 170.925i −3.04831 0.537499i
\(319\) 177.539 31.3049i 0.556548 0.0981344i
\(320\) 3.75877 1.36808i 0.0117462 0.00427525i
\(321\) 209.130 + 175.481i 0.651496 + 0.546670i
\(322\) 630.971i 1.95954i
\(323\) 0 0
\(324\) 909.000 2.80556
\(325\) 20.8584 24.8581i 0.0641798 0.0764865i
\(326\) 332.956 + 914.790i 1.02134 + 2.80610i
\(327\) −124.158 704.138i −0.379689 2.15333i
\(328\) 112.871 640.125i 0.344120 1.95160i
\(329\) 46.9846 + 17.1010i 0.142810 + 0.0519787i
\(330\) 260.000 + 450.333i 0.787879 + 1.36465i
\(331\) 171.737 + 99.1527i 0.518844 + 0.299555i 0.736462 0.676479i \(-0.236495\pi\)
−0.217617 + 0.976034i \(0.569829\pi\)
\(332\) 275.776 231.404i 0.830651 0.696999i
\(333\) 55.6225 + 66.2883i 0.167034 + 0.199064i
\(334\) 221.000 382.783i 0.661677 1.14606i
\(335\) 137.390 79.3221i 0.410119 0.236782i
\(336\) 178.810 491.276i 0.532172 1.46213i
\(337\) 56.8124 + 10.0176i 0.168583 + 0.0297257i 0.257302 0.966331i \(-0.417166\pi\)
−0.0887195 + 0.996057i \(0.528277\pi\)
\(338\) −553.921 + 97.6712i −1.63882 + 0.288968i
\(339\) 415.344 151.173i 1.22520 0.445938i
\(340\) −413.664 347.105i −1.21666 1.02090i
\(341\) 360.555i 1.05735i
\(342\) 0 0
\(343\) 365.000 1.06414
\(344\) −231.760 + 276.201i −0.673722 + 0.802911i
\(345\) 172.644 + 474.335i 0.500417 + 1.37489i
\(346\) 76.7525 + 435.285i 0.221828 + 1.25805i
\(347\) −6.94593 + 39.3923i −0.0200171 + 0.113523i −0.993179 0.116598i \(-0.962801\pi\)
0.973162 + 0.230121i \(0.0739121\pi\)
\(348\) 549.720 + 200.082i 1.57966 + 0.574948i
\(349\) −49.0000 84.8705i −0.140401 0.243182i 0.787247 0.616638i \(-0.211506\pi\)
−0.927648 + 0.373456i \(0.878173\pi\)
\(350\) −140.512 81.1249i −0.401464 0.231785i
\(351\) 49.7929 41.7812i 0.141860 0.119035i
\(352\) −208.584 248.581i −0.592569 0.706196i
\(353\) 92.5000 160.215i 0.262040 0.453866i −0.704744 0.709462i \(-0.748938\pi\)
0.966784 + 0.255596i \(0.0822715\pi\)
\(354\) 202.962 117.180i 0.573340 0.331018i
\(355\) 147.981 406.573i 0.416847 1.14528i
\(356\) 0 0
\(357\) −266.308 + 46.9573i −0.745961 + 0.131533i
\(358\) 122.160 44.4626i 0.341229 0.124197i
\(359\) −172.360 144.627i −0.480111 0.402861i 0.370355 0.928890i \(-0.379236\pi\)
−0.850467 + 0.526029i \(0.823680\pi\)
\(360\) 288.444i 0.801234i
\(361\) 0 0
\(362\) −390.000 −1.07735
\(363\) −48.6697 + 58.0023i −0.134076 + 0.159786i
\(364\) −55.4927 152.465i −0.152452 0.418860i
\(365\) 72.9322 + 413.619i 0.199814 + 1.13320i
\(366\) −90.2971 + 512.100i −0.246713 + 1.39918i
\(367\) −46.9846 17.1010i −0.128024 0.0465967i 0.277214 0.960808i \(-0.410589\pi\)
−0.405237 + 0.914211i \(0.632811\pi\)
\(368\) −507.500 879.016i −1.37908 2.38863i
\(369\) 124.900 + 72.1110i 0.338482 + 0.195423i
\(370\) 239.006 200.550i 0.645962 0.542026i
\(371\) 243.348 + 290.011i 0.655926 + 0.781702i
\(372\) −585.000 + 1013.25i −1.57258 + 2.72379i
\(373\) −377.822 + 218.136i −1.01293 + 0.584815i −0.912048 0.410084i \(-0.865499\pi\)
−0.100881 + 0.994899i \(0.532166\pi\)
\(374\) −184.976 + 508.216i −0.494587 + 1.35887i
\(375\) 482.905 + 85.1492i 1.28775 + 0.227065i
\(376\) 177.539 31.3049i 0.472178 0.0832576i
\(377\) 61.0800 22.2313i 0.162016 0.0589690i
\(378\) −248.964 208.906i −0.658636 0.552661i
\(379\) 486.749i 1.28430i −0.766579 0.642150i \(-0.778043\pi\)
0.766579 0.642150i \(-0.221957\pi\)
\(380\) 0 0
\(381\) −468.000 −1.22835
\(382\) −447.298 + 533.068i −1.17094 + 1.39547i
\(383\) −69.0576 189.734i −0.180307 0.495389i 0.816306 0.577619i \(-0.196018\pi\)
−0.996613 + 0.0822297i \(0.973796\pi\)
\(384\) 79.0099 + 448.088i 0.205755 + 1.16689i
\(385\) 34.7296 196.962i 0.0902068 0.511588i
\(386\) 903.984 + 329.023i 2.34193 + 0.852392i
\(387\) −40.0000 69.2820i −0.103359 0.179023i
\(388\) 955.485 + 551.649i 2.46259 + 1.42178i
\(389\) −366.169 + 307.252i −0.941309 + 0.789852i −0.977813 0.209481i \(-0.932822\pi\)
0.0365035 + 0.999334i \(0.488378\pi\)
\(390\) 120.515 + 143.625i 0.309014 + 0.368268i
\(391\) −262.500 + 454.663i −0.671355 + 1.16282i
\(392\) 374.700 216.333i 0.955867 0.551870i
\(393\) −138.115 + 379.468i −0.351438 + 0.965568i
\(394\) 319.570 + 56.3488i 0.811091 + 0.143017i
\(395\) 142.031 25.0439i 0.359572 0.0634023i
\(396\) 338.289 123.127i 0.854266 0.310927i
\(397\) 574.533 + 482.091i 1.44719 + 1.21433i 0.934601 + 0.355699i \(0.115757\pi\)
0.512587 + 0.858636i \(0.328687\pi\)
\(398\) 443.483i 1.11428i
\(399\) 0 0
\(400\) −261.000 −0.652500
\(401\) 185.408 220.961i 0.462365 0.551025i −0.483602 0.875288i \(-0.660672\pi\)
0.945967 + 0.324263i \(0.105116\pi\)
\(402\) −176.343 484.500i −0.438665 1.20522i
\(403\) 22.5743 + 128.025i 0.0560155 + 0.317680i
\(404\) 78.1417 443.163i 0.193420 1.09694i
\(405\) 379.636 + 138.176i 0.937372 + 0.341176i
\(406\) −162.500 281.458i −0.400246 0.693247i
\(407\) −187.350 108.167i −0.460319 0.265765i
\(408\) −746.893 + 626.718i −1.83062 + 1.53607i
\(409\) −23.1760 27.6201i −0.0566651 0.0675309i 0.736967 0.675928i \(-0.236257\pi\)
−0.793632 + 0.608397i \(0.791813\pi\)
\(410\) 260.000 450.333i 0.634146 1.09837i
\(411\) −390.312 + 225.347i −0.949665 + 0.548289i
\(412\) −177.577 + 487.888i −0.431011 + 1.18419i
\(413\) −88.7694 15.6524i −0.214938 0.0378994i
\(414\) 497.108 87.6536i 1.20075 0.211724i
\(415\) 150.351 54.7232i 0.362291 0.131863i
\(416\) −89.6272 75.2062i −0.215450 0.180784i
\(417\) 180.278i 0.432320i
\(418\) 0 0
\(419\) 112.000 0.267303 0.133652 0.991028i \(-0.457330\pi\)
0.133652 + 0.991028i \(0.457330\pi\)
\(420\) 417.169 497.162i 0.993259 1.18372i
\(421\) −215.805 592.919i −0.512601 1.40836i −0.878517 0.477711i \(-0.841466\pi\)
0.365916 0.930648i \(-0.380756\pi\)
\(422\) 146.733 + 832.163i 0.347708 + 1.97195i
\(423\) −6.94593 + 39.3923i −0.0164206 + 0.0931260i
\(424\) 1282.68 + 466.857i 3.02519 + 1.10108i
\(425\) 67.5000 + 116.913i 0.158824 + 0.275090i
\(426\) −1217.77 703.082i −2.85863 1.65043i
\(427\) 153.209 128.558i 0.358803 0.301071i
\(428\) −438.027 522.020i −1.02343 1.21967i
\(429\) 65.0000 112.583i 0.151515 0.262432i
\(430\) −249.800 + 144.222i −0.580930 + 0.335400i
\(431\) −147.981 + 406.573i −0.343342 + 0.943325i 0.641075 + 0.767478i \(0.278489\pi\)
−0.984417 + 0.175847i \(0.943734\pi\)
\(432\) −514.862 90.7841i −1.19181 0.210148i
\(433\) 724.358 127.724i 1.67288 0.294974i 0.744783 0.667307i \(-0.232553\pi\)
0.928099 + 0.372332i \(0.121442\pi\)
\(434\) 610.800 222.313i 1.40737 0.512242i
\(435\) 199.172 + 167.125i 0.457866 + 0.384195i
\(436\) 1784.75i 4.09346i
\(437\) 0 0
\(438\) 1365.00 3.11644
\(439\) −509.873 + 607.643i −1.16144 + 1.38415i −0.252308 + 0.967647i \(0.581190\pi\)
−0.909133 + 0.416505i \(0.863255\pi\)
\(440\) −246.634 677.622i −0.560532 1.54005i
\(441\) 16.6702 + 94.5415i 0.0378010 + 0.214380i
\(442\) −33.8614 + 192.038i −0.0766095 + 0.434474i
\(443\) −629.594 229.153i −1.42121 0.517277i −0.486808 0.873509i \(-0.661839\pi\)
−0.934397 + 0.356232i \(0.884061\pi\)
\(444\) −351.000 607.950i −0.790541 1.36926i
\(445\) 0 0
\(446\) 557.680 467.949i 1.25040 1.04921i
\(447\) −162.232 193.341i −0.362936 0.432530i
\(448\) −2.50000 + 4.33013i −0.00558036 + 0.00966546i
\(449\) −31.2250 + 18.0278i −0.0695434 + 0.0401509i −0.534369 0.845252i \(-0.679451\pi\)
0.464825 + 0.885403i \(0.346117\pi\)
\(450\) 44.3942 121.972i 0.0986537 0.271049i
\(451\) −355.077 62.6097i −0.787311 0.138824i
\(452\) −1086.54 + 191.586i −2.40384 + 0.423862i
\(453\) −122.160 + 44.4626i −0.269669 + 0.0981515i
\(454\) −707.059 593.293i −1.55740 1.30681i
\(455\) 72.1110i 0.158486i
\(456\) 0 0
\(457\) −755.000 −1.65208 −0.826039 0.563612i \(-0.809411\pi\)
−0.826039 + 0.563612i \(0.809411\pi\)
\(458\) 370.817 441.922i 0.809643 0.964895i
\(459\) 92.4878 + 254.108i 0.201499 + 0.553613i
\(460\) −218.797 1240.86i −0.475645 2.69752i
\(461\) 134.056 760.272i 0.290795 1.64918i −0.393025 0.919528i \(-0.628571\pi\)
0.683819 0.729651i \(-0.260318\pi\)
\(462\) −610.800 222.313i −1.32208 0.481197i
\(463\) 175.000 + 303.109i 0.377970 + 0.654663i 0.990767 0.135578i \(-0.0432890\pi\)
−0.612797 + 0.790240i \(0.709956\pi\)
\(464\) −452.762 261.402i −0.975781 0.563367i
\(465\) −398.343 + 334.250i −0.856652 + 0.718816i
\(466\) −625.753 745.743i −1.34282 1.60031i
\(467\) −35.0000 + 60.6218i −0.0749465 + 0.129811i −0.901063 0.433688i \(-0.857212\pi\)
0.826117 + 0.563499i \(0.190545\pi\)
\(468\) 112.410 64.8999i 0.240192 0.138675i
\(469\) −67.8244 + 186.346i −0.144615 + 0.397326i
\(470\) 142.031 + 25.0439i 0.302194 + 0.0532849i
\(471\) 35.5077 6.26097i 0.0753880 0.0132929i
\(472\) −305.400 + 111.157i −0.647034 + 0.235501i
\(473\) 153.209 + 128.558i 0.323909 + 0.271792i
\(474\) 468.722i 0.988864i
\(475\) 0 0
\(476\) 675.000 1.41807
\(477\) −194.679 + 232.009i −0.408131 + 0.486392i
\(478\) −242.935 667.458i −0.508232 1.39635i
\(479\) −64.2498 364.379i −0.134133 0.760707i −0.975459 0.220180i \(-0.929336\pi\)
0.841326 0.540528i \(-0.181775\pi\)
\(480\) 81.2673 460.890i 0.169307 0.960188i
\(481\) −73.2960 26.6776i −0.152383 0.0554627i
\(482\) 715.000 + 1238.42i 1.48340 + 2.56933i
\(483\) −546.437 315.486i −1.13134 0.653180i
\(484\) 144.782 121.487i 0.299137 0.251006i
\(485\) 315.194 + 375.634i 0.649885 + 0.774502i
\(486\) 364.000 630.466i 0.748971 1.29726i
\(487\) −449.640 + 259.600i −0.923285 + 0.533059i −0.884682 0.466196i \(-0.845624\pi\)
−0.0386035 + 0.999255i \(0.512291\pi\)
\(488\) 246.634 677.622i 0.505398 1.38857i
\(489\) 958.709 + 169.046i 1.96055 + 0.345698i
\(490\) 340.874 60.1054i 0.695662 0.122664i
\(491\) 593.886 216.157i 1.20954 0.440238i 0.342998 0.939336i \(-0.388558\pi\)
0.866545 + 0.499098i \(0.166335\pi\)
\(492\) −896.272 752.062i −1.82169 1.52858i
\(493\) 270.416i 0.548512i
\(494\) 0 0
\(495\) 160.000 0.323232
\(496\) 672.105 800.984i 1.35505 1.61489i
\(497\) 184.976 + 508.216i 0.372184 + 1.02257i
\(498\) −90.2971 512.100i −0.181319 1.02831i
\(499\) 65.9863 374.227i 0.132237 0.749954i −0.844507 0.535545i \(-0.820106\pi\)
0.976744 0.214409i \(-0.0687826\pi\)
\(500\) −1150.18 418.633i −2.30037 0.837265i
\(501\) −221.000 382.783i −0.441118 0.764038i
\(502\) 1255.24 + 724.716i 2.50049 + 1.44366i
\(503\) −34.4720 + 28.9254i −0.0685328 + 0.0575058i −0.676411 0.736525i \(-0.736465\pi\)
0.607878 + 0.794031i \(0.292021\pi\)
\(504\) −231.760 276.201i −0.459842 0.548018i
\(505\) 100.000 173.205i 0.198020 0.342980i
\(506\) −1092.87 + 630.971i −2.15983 + 1.24698i
\(507\) −192.375 + 528.545i −0.379437 + 1.04250i
\(508\) 1150.45 + 202.856i 2.26467 + 0.399322i
\(509\) −816.678 + 144.002i −1.60448 + 0.282912i −0.902955 0.429736i \(-0.858607\pi\)
−0.701521 + 0.712648i \(0.747495\pi\)
\(510\) −732.960 + 266.776i −1.43718 + 0.523090i
\(511\) −402.173 337.463i −0.787032 0.660398i
\(512\) 1150.17i 2.24643i
\(513\) 0 0
\(514\) 1508.00 2.93385
\(515\) −148.327 + 176.769i −0.288013 + 0.343240i
\(516\) 221.971 + 609.860i 0.430176 + 1.18190i
\(517\) −17.3648 98.4808i −0.0335877 0.190485i
\(518\) −67.7228 + 384.075i −0.130739 + 0.741458i
\(519\) 415.344 + 151.173i 0.800278 + 0.291277i
\(520\) −130.000 225.167i −0.250000 0.433013i
\(521\) −530.825 306.472i −1.01886 0.588238i −0.105085 0.994463i \(-0.533511\pi\)
−0.913773 + 0.406226i \(0.866845\pi\)
\(522\) 199.172 167.125i 0.381555 0.320162i
\(523\) 298.971 + 356.300i 0.571646 + 0.681261i 0.971968 0.235113i \(-0.0755461\pi\)
−0.400322 + 0.916375i \(0.631102\pi\)
\(524\) 504.000 872.954i 0.961832 1.66594i
\(525\) −140.512 + 81.1249i −0.267643 + 0.154524i
\(526\) 382.283 1050.31i 0.726774 1.99679i
\(527\) −532.616 93.9146i −1.01066 0.178206i
\(528\) −1029.72 + 181.568i −1.95024 + 0.343879i
\(529\) −654.026 + 238.046i −1.23634 + 0.449992i
\(530\) 836.521 + 701.924i 1.57834 + 1.32439i
\(531\) 72.1110i 0.135802i
\(532\) 0 0
\(533\) −130.000 −0.243902
\(534\) 0 0
\(535\) −103.586 284.601i −0.193619 0.531965i
\(536\) 124.158 + 704.138i 0.231639 + 1.31369i
\(537\) 22.5743 128.025i 0.0420377 0.238408i
\(538\) 366.480 + 133.388i 0.681190 + 0.247933i
\(539\) −120.000 207.846i −0.222635 0.385614i
\(540\) −562.050 324.500i −1.04083 0.600925i
\(541\) −459.627 + 385.673i −0.849587 + 0.712888i −0.959699 0.281031i \(-0.909324\pi\)
0.110112 + 0.993919i \(0.464879\pi\)
\(542\) 243.348 + 290.011i 0.448982 + 0.535076i
\(543\) −195.000 + 337.750i −0.359116 + 0.622007i
\(544\) 421.537 243.375i 0.774885 0.447380i
\(545\) −271.298 + 745.384i −0.497794 + 1.36768i
\(546\) −230.800 40.6963i −0.422711 0.0745354i
\(547\) 589.429 103.932i 1.07757 0.190004i 0.393427 0.919356i \(-0.371289\pi\)
0.684139 + 0.729352i \(0.260178\pi\)
\(548\) 1057.15 384.773i 1.92911 0.702140i
\(549\) 122.567 + 102.846i 0.223255 + 0.187333i
\(550\) 324.500i 0.589999i
\(551\) 0 0
\(552\) −2275.00 −4.12138
\(553\) −115.880 + 138.101i −0.209548 + 0.249730i
\(554\) 61.6586 + 169.405i 0.111297 + 0.305786i
\(555\) −54.1782 307.260i −0.0976184 0.553622i
\(556\) −78.1417 + 443.163i −0.140543 + 0.797057i
\(557\) −357.083 129.968i −0.641083 0.233335i 0.000965080 1.00000i \(-0.499693\pi\)
−0.642048 + 0.766664i \(0.721915\pi\)
\(558\) 260.000 + 450.333i 0.465950 + 0.807049i
\(559\) 62.4500 + 36.0555i 0.111717 + 0.0645000i
\(560\) −444.306 + 372.817i −0.793403 + 0.665744i
\(561\) 347.641 + 414.302i 0.619680 + 0.738506i
\(562\) −520.000 + 900.666i −0.925267 + 1.60261i
\(563\) 106.165 61.2944i 0.188570 0.108871i −0.402743 0.915313i \(-0.631943\pi\)
0.591313 + 0.806442i \(0.298610\pi\)
\(564\) 110.985 304.930i 0.196783 0.540656i
\(565\) −482.905 85.1492i −0.854700 0.150707i
\(566\) 1136.25 200.351i 2.00751 0.353977i
\(567\) −474.545 + 172.720i −0.836940 + 0.304621i
\(568\) 1493.79 + 1253.44i 2.62991 + 2.20675i
\(569\) 36.0555i 0.0633665i 0.999498 + 0.0316832i \(0.0100868\pi\)
−0.999498 + 0.0316832i \(0.989913\pi\)
\(570\) 0 0
\(571\) −790.000 −1.38354 −0.691769 0.722119i \(-0.743168\pi\)
−0.691769 + 0.722119i \(0.743168\pi\)
\(572\) −208.584 + 248.581i −0.364658 + 0.434582i
\(573\) 238.002 + 653.905i 0.415361 + 1.14120i
\(574\) 112.871 + 640.125i 0.196640 + 1.11520i
\(575\) −54.6992 + 310.214i −0.0951290 + 0.539503i
\(576\) −3.75877 1.36808i −0.00652564 0.00237514i
\(577\) −337.500 584.567i −0.584922 1.01311i −0.994885 0.101013i \(-0.967792\pi\)
0.409963 0.912102i \(-0.365542\pi\)
\(578\) 199.840 + 115.378i 0.345744 + 0.199615i
\(579\) 736.935 618.362i 1.27277 1.06798i
\(580\) −417.169 497.162i −0.719256 0.857176i
\(581\) −100.000 + 173.205i −0.172117 + 0.298115i
\(582\) 1380.14 796.827i 2.37138 1.36912i
\(583\) 258.966 711.503i 0.444195 1.22042i
\(584\) −1864.16 328.701i −3.19205 0.562844i
\(585\) 56.8124 10.0176i 0.0971152 0.0171240i
\(586\) −745.176 + 271.222i −1.27163 + 0.462836i
\(587\) −214.492 179.981i −0.365405 0.306611i 0.441536 0.897244i \(-0.354434\pi\)
−0.806940 + 0.590633i \(0.798878\pi\)
\(588\) 778.799i 1.32449i
\(589\) 0 0
\(590\) −260.000 −0.440678
\(591\) 208.584 248.581i 0.352935 0.420611i
\(592\) 214.572 + 589.531i 0.362452 + 0.995830i
\(593\) 130.236 + 738.606i 0.219622 + 1.24554i 0.872703 + 0.488252i \(0.162365\pi\)
−0.653080 + 0.757289i \(0.726524\pi\)
\(594\) −112.871 + 640.125i −0.190019 + 1.07765i
\(595\) 281.908 + 102.606i 0.473795 + 0.172447i
\(596\) 315.000 + 545.596i 0.528523 + 0.915430i
\(597\) 384.067 + 221.741i 0.643329 + 0.371426i
\(598\) −348.550 + 292.468i −0.582860 + 0.489078i
\(599\) 324.465 + 386.682i 0.541677 + 0.645545i 0.965563 0.260170i \(-0.0837787\pi\)
−0.423886 + 0.905716i \(0.639334\pi\)
\(600\) −292.500 + 506.625i −0.487500 + 0.844375i
\(601\) 530.825 306.472i 0.883236 0.509937i 0.0115120 0.999934i \(-0.496336\pi\)
0.871724 + 0.489997i \(0.163002\pi\)
\(602\) 123.317 338.811i 0.204846 0.562809i
\(603\) −156.234 27.5483i −0.259095 0.0456854i
\(604\) 319.570 56.3488i 0.529089 0.0932927i
\(605\) 78.9342 28.7297i 0.130470 0.0474871i
\(606\) −497.929 417.812i −0.821665 0.689459i
\(607\) 987.921i 1.62755i −0.581182 0.813774i \(-0.697410\pi\)
0.581182 0.813774i \(-0.302590\pi\)
\(608\) 0 0
\(609\) −325.000 −0.533662
\(610\) 370.817 441.922i 0.607896 0.724462i
\(611\) −12.3317 33.8811i −0.0201828 0.0554519i
\(612\) 93.7700 + 531.796i 0.153219 + 0.868948i
\(613\) −208.378 + 1181.77i −0.339931 + 1.92785i 0.0317749 + 0.999495i \(0.489884\pi\)
−0.371706 + 0.928350i \(0.621227\pi\)
\(614\) 806.256 + 293.453i 1.31312 + 0.477937i
\(615\) −260.000 450.333i −0.422764 0.732249i
\(616\) 780.625 + 450.694i 1.26725 + 0.731646i
\(617\) −268.116 + 224.976i −0.434547 + 0.364628i −0.833664 0.552272i \(-0.813761\pi\)
0.399117 + 0.916900i \(0.369317\pi\)
\(618\) 482.062 + 574.499i 0.780035 + 0.929609i
\(619\) −280.000 + 484.974i −0.452342 + 0.783480i −0.998531 0.0541821i \(-0.982745\pi\)
0.546189 + 0.837662i \(0.316078\pi\)
\(620\) 1124.10 648.999i 1.81306 1.04677i
\(621\) −215.805 + 592.919i −0.347512 + 0.954781i
\(622\) 1402.56 + 247.308i 2.25491 + 0.397602i
\(623\) 0 0
\(624\) −354.264 + 128.942i −0.567731 + 0.206637i
\(625\) −244.368 205.049i −0.390989 0.328079i
\(626\) 450.694i 0.719958i
\(627\) 0 0
\(628\) −90.0000 −0.143312
\(629\) 208.584 248.581i 0.331613 0.395201i
\(630\) −98.6537 271.049i −0.156593 0.430236i
\(631\) −182.331 1034.05i −0.288955 1.63875i −0.690806 0.723040i \(-0.742744\pi\)
0.401851 0.915705i \(-0.368367\pi\)
\(632\) −112.871 + 640.125i −0.178594 + 1.01286i
\(633\) 794.040 + 289.007i 1.25441 + 0.456567i
\(634\) 6.50000 + 11.2583i 0.0102524 + 0.0177576i
\(635\) 449.640 + 259.600i 0.708094 + 0.408818i
\(636\) 1882.17 1579.33i 2.95939 2.48322i
\(637\) −55.6225 66.2883i −0.0873194 0.104063i
\(638\) −325.000 + 562.917i −0.509404 + 0.882314i
\(639\) −374.700 + 216.333i −0.586385 + 0.338549i
\(640\) 172.644 474.335i 0.269756 0.741149i
\(641\) 1207.26 + 212.873i 1.88341 + 0.332095i 0.992515 0.122121i \(-0.0389698\pi\)
0.890891 + 0.454217i \(0.150081\pi\)
\(642\) −969.362 + 170.925i −1.50991 + 0.266238i
\(643\) 967.883 352.281i 1.50526 0.547871i 0.547845 0.836580i \(-0.315448\pi\)
0.957417 + 0.288709i \(0.0932261\pi\)
\(644\) 1206.52 + 1012.39i 1.87348 + 1.57203i
\(645\) 288.444i 0.447200i
\(646\) 0 0
\(647\) 555.000 0.857805 0.428903 0.903351i \(-0.358900\pi\)
0.428903 + 0.903351i \(0.358900\pi\)
\(648\) −1170.39 + 1394.82i −1.80616 + 2.15249i
\(649\) 61.6586 + 169.405i 0.0950055 + 0.261025i
\(650\) 20.3168 + 115.223i 0.0312567 + 0.177265i
\(651\) 112.871 640.125i 0.173381 0.983295i
\(652\) −2283.45 831.109i −3.50223 1.27471i
\(653\) −25.0000 43.3013i −0.0382848 0.0663113i 0.846248 0.532789i \(-0.178856\pi\)
−0.884533 + 0.466478i \(0.845523\pi\)
\(654\) 2232.59 + 1288.98i 3.41374 + 1.97092i
\(655\) 343.188 287.969i 0.523951 0.439647i
\(656\) 672.105 + 800.984i 1.02455 + 1.22101i
\(657\) 210.000 363.731i 0.319635 0.553624i
\(658\) −156.125 + 90.1388i −0.237272 + 0.136989i
\(659\) 67.8244 186.346i 0.102920 0.282771i −0.877535 0.479512i \(-0.840814\pi\)
0.980455 + 0.196741i \(0.0630359\pi\)
\(660\) −1278.28 225.395i −1.93679 0.341508i
\(661\) −195.293 + 34.4354i −0.295450 + 0.0520959i −0.319409 0.947617i \(-0.603484\pi\)
0.0239583 + 0.999713i \(0.492373\pi\)
\(662\) −671.880 + 244.544i −1.01492 + 0.369402i
\(663\) 149.379 + 125.344i 0.225307 + 0.189055i
\(664\) 721.110i 1.08601i
\(665\) 0 0
\(666\) −312.000 −0.468468
\(667\) −405.581 + 483.352i −0.608067 + 0.724666i
\(668\) 377.350 + 1036.76i 0.564896 + 1.55204i
\(669\) −126.416 716.940i −0.188962 1.07166i
\(670\) −99.3268 + 563.310i −0.148249 + 0.840761i
\(671\) −375.877 136.808i −0.560174 0.203887i
\(672\) 292.500 + 506.625i 0.435268 + 0.753906i
\(673\) −518.335 299.261i −0.770185 0.444667i 0.0627553 0.998029i \(-0.480011\pi\)
−0.832941 + 0.553362i \(0.813345\pi\)
\(674\) −159.337 + 133.700i −0.236405 + 0.198368i
\(675\) 104.292 + 124.291i 0.154507 + 0.184134i
\(676\) 702.000 1215.90i 1.03846 1.79867i
\(677\) 59.3275 34.2527i 0.0876329 0.0505949i −0.455543 0.890214i \(-0.650555\pi\)
0.543176 + 0.839619i \(0.317222\pi\)
\(678\) −545.062 + 1497.54i −0.803926 + 2.20877i
\(679\) −603.632 106.437i −0.889001 0.156755i
\(680\) 1065.23 187.829i 1.56652 0.276219i
\(681\) −867.336 + 315.685i −1.27362 + 0.463560i
\(682\) −995.858 835.624i −1.46020 1.22525i
\(683\) 237.966i 0.348413i −0.984709 0.174207i \(-0.944264\pi\)
0.984709 0.174207i \(-0.0557361\pi\)
\(684\) 0 0
\(685\) 500.000 0.729927
\(686\) −845.925 + 1008.13i −1.23313 + 1.46958i
\(687\) −197.307 542.098i −0.287201 0.789079i
\(688\) −100.716 571.188i −0.146389 0.830216i
\(689\) 47.4060 268.853i 0.0688040 0.390207i
\(690\) −1710.24 622.477i −2.47861 0.902140i
\(691\) 410.000 + 710.141i 0.593343 + 1.02770i 0.993778 + 0.111375i \(0.0355255\pi\)
−0.400435 + 0.916325i \(0.631141\pi\)
\(692\) −955.485 551.649i −1.38076 0.797181i
\(693\) −153.209 + 128.558i −0.221081 + 0.185509i
\(694\) −92.7041 110.481i −0.133579 0.159194i
\(695\) −100.000 + 173.205i −0.143885 + 0.249216i
\(696\) −1014.81 + 585.902i −1.45806 + 0.841813i
\(697\) 184.976 508.216i 0.265388 0.729148i
\(698\) 347.976 + 61.3575i 0.498533 + 0.0879048i
\(699\) −958.709 + 169.046i −1.37154 + 0.241840i
\(700\) 380.576 138.518i 0.543679 0.197883i
\(701\) −413.664 347.105i −0.590106 0.495157i 0.298143 0.954521i \(-0.403633\pi\)
−0.888248 + 0.459364i \(0.848077\pi\)
\(702\) 234.361i 0.333847i
\(703\) 0 0
\(704\) 10.0000 0.0142045
\(705\) 92.7041 110.481i 0.131495 0.156710i
\(706\) 228.137 + 626.800i 0.323140 + 0.887819i
\(707\) 43.4120 + 246.202i 0.0614032 + 0.348235i
\(708\) −101.584 + 576.113i −0.143480 + 0.813718i
\(709\) −251.838 91.6614i −0.355201 0.129283i 0.158255 0.987398i \(-0.449413\pi\)
−0.513457 + 0.858116i \(0.671635\pi\)
\(710\) 780.000 + 1351.00i 1.09859 + 1.90282i
\(711\) −124.900 72.1110i −0.175668 0.101422i
\(712\) 0 0
\(713\) −811.161 966.704i −1.13767 1.35583i
\(714\) 487.500 844.375i 0.682773 1.18260i
\(715\) −124.900 + 72.1110i −0.174685 + 0.100855i
\(716\) −110.985 + 304.930i −0.155008 + 0.425880i
\(717\) −699.503 123.341i −0.975596 0.172024i
\(718\) 798.924 140.872i 1.11271 0.196200i
\(719\) −98.6677 + 35.9121i −0.137229 + 0.0499473i −0.409722 0.912211i \(-0.634374\pi\)
0.272493 + 0.962158i \(0.412152\pi\)
\(720\) −355.445 298.253i −0.493673 0.414241i
\(721\) 288.444i 0.400061i
\(722\) 0 0
\(723\) 1430.00 1.97787
\(724\) 625.753 745.743i 0.864300 1.03003i
\(725\) 55.4927 + 152.465i 0.0765417 + 0.210296i
\(726\) −47.4060 268.853i −0.0652975 0.370320i
\(727\) 120.685 684.441i 0.166005 0.941460i −0.782018 0.623256i \(-0.785809\pi\)
0.948022 0.318204i \(-0.103080\pi\)
\(728\) 305.400 + 111.157i 0.419506 + 0.152688i
\(729\) 90.5000 + 156.751i 0.124143 + 0.215021i
\(730\) −1311.45 757.166i −1.79651 1.03721i
\(731\) −229.813 + 192.836i −0.314382 + 0.263798i
\(732\) −834.337 994.325i −1.13981 1.35837i
\(733\) −80.0000 + 138.564i −0.109141 + 0.189037i −0.915422 0.402495i \(-0.868143\pi\)
0.806282 + 0.591532i \(0.201477\pi\)
\(734\) 156.125 90.1388i 0.212704 0.122805i
\(735\) 118.384 325.259i 0.161067 0.442529i
\(736\) 1118.49 + 197.221i 1.51969 + 0.267963i
\(737\) 390.585 68.8707i 0.529966 0.0934474i
\(738\) −488.640 + 177.850i −0.662114 + 0.240990i
\(739\) 787.494 + 660.786i 1.06562 + 0.894162i 0.994649 0.103316i \(-0.0329454\pi\)
0.0709721 + 0.997478i \(0.477390\pi\)
\(740\) 778.799i 1.05243i
\(741\) 0 0
\(742\) −1365.00 −1.83962
\(743\) 338.370 403.254i 0.455411 0.542737i −0.488663 0.872473i \(-0.662515\pi\)
0.944073 + 0.329735i \(0.106960\pi\)
\(744\) −801.561 2202.27i −1.07737 2.96004i
\(745\) 48.6215 + 275.746i 0.0652637 + 0.370129i
\(746\) 273.149 1549.10i 0.366151 2.07655i
\(747\) −150.351 54.7232i −0.201273 0.0732573i
\(748\) −675.000 1169.13i −0.902406 1.56301i
\(749\) 327.862 + 189.291i 0.437734 + 0.252726i
\(750\) −1354.37 + 1136.45i −1.80582 + 1.51526i
\(751\) 23.1760 + 27.6201i 0.0308602 + 0.0367778i 0.781254 0.624213i \(-0.214580\pi\)
−0.750394 + 0.660991i \(0.770136\pi\)
\(752\) −145.000 + 251.147i −0.192819 + 0.333973i
\(753\) 1255.24 724.716i 1.66699 0.962438i
\(754\) −80.1561 + 220.227i −0.106308 + 0.292078i
\(755\) 142.031 + 25.0439i 0.188121 + 0.0331707i
\(756\) 798.924 140.872i 1.05678 0.186339i
\(757\) −56.3816 + 20.5212i −0.0744803 + 0.0271086i −0.378992 0.925400i \(-0.623729\pi\)
0.304511 + 0.952509i \(0.401507\pi\)
\(758\) 1344.41 + 1128.09i 1.77363 + 1.48825i
\(759\) 1261.94i 1.66264i
\(760\) 0 0
\(761\) −655.000 −0.860710 −0.430355 0.902660i \(-0.641612\pi\)
−0.430355 + 0.902660i \(0.641612\pi\)
\(762\) 1084.64 1292.62i 1.42341 1.69635i
\(763\) −339.122 931.730i −0.444459 1.22114i
\(764\) −301.627 1710.61i −0.394800 2.23902i
\(765\) −41.6756 + 236.354i −0.0544779 + 0.308959i
\(766\) 684.096 + 248.991i 0.893076 + 0.325053i
\(767\) 32.5000 + 56.2917i 0.0423729 + 0.0733920i
\(768\) −1433.23 827.474i −1.86618 1.07744i
\(769\) −141.718 + 118.916i −0.184289 + 0.154637i −0.730265 0.683164i \(-0.760603\pi\)
0.545976 + 0.837801i \(0.316159\pi\)
\(770\) 463.521 + 552.403i 0.601975 + 0.717406i
\(771\) 754.000 1305.97i 0.977951 1.69386i
\(772\) −2079.58 + 1200.65i −2.69376 + 1.55524i
\(773\) −109.752 + 301.542i −0.141982 + 0.390093i −0.990219 0.139525i \(-0.955442\pi\)
0.848236 + 0.529618i \(0.177665\pi\)
\(774\) 284.062 + 50.0878i 0.367005 + 0.0647129i
\(775\) −319.570 + 56.3488i −0.412348 + 0.0727081i
\(776\) −2076.72 + 755.865i −2.67619 + 0.974052i
\(777\) 298.757 + 250.687i 0.384501 + 0.322635i
\(778\) 1723.45i 2.21524i
\(779\) 0 0
\(780\) −468.000 −0.600000
\(781\) 695.281 828.604i 0.890245 1.06095i
\(782\) −647.415 1778.76i −0.827896 2.27463i
\(783\) 56.4357 + 320.063i 0.0720762 + 0.408764i
\(784\) −120.859 + 685.426i −0.154157 + 0.874268i
\(785\) −37.5877 13.6808i −0.0478824 0.0174278i
\(786\) −728.000 1260.93i −0.926209 1.60424i
\(787\) −59.3275 34.2527i −0.0753843 0.0435232i 0.461834 0.886966i \(-0.347192\pi\)
−0.537218 + 0.843443i \(0.680525\pi\)
\(788\) −620.496 + 520.658i −0.787431 + 0.660733i
\(789\) −718.457 856.224i −0.910592 1.08520i
\(790\) −260.000 + 450.333i −0.329114 + 0.570042i
\(791\) 530.825 306.472i 0.671081 0.387449i
\(792\) −246.634 + 677.622i −0.311407 + 0.855583i
\(793\) −142.031 25.0439i −0.179106 0.0315812i
\(794\) −2663.08 + 469.573i −3.35401 + 0.591402i
\(795\) 1026.14 373.486i 1.29075 0.469794i
\(796\) −848.011 711.566i −1.06534 0.893927i
\(797\) 1258.34i 1.57884i 0.613852 + 0.789421i \(0.289619\pi\)
−0.613852 + 0.789421i \(0.710381\pi\)
\(798\) 0 0
\(799\) 150.000 0.187735
\(800\) 187.726 223.723i 0.234657 0.279654i
\(801\) 0 0
\(802\) 180.594 + 1024.20i 0.225180 + 1.27706i
\(803\) −182.331 + 1034.05i −0.227062 + 1.28773i
\(804\) 1209.38 + 440.180i 1.50421 + 0.547487i
\(805\) 350.000 + 606.218i 0.434783 + 0.753066i
\(806\) −405.925 234.361i −0.503629 0.290770i
\(807\) 298.757 250.687i 0.370207 0.310641i
\(808\) 579.401 + 690.503i 0.717080 + 0.854583i
\(809\) 3.50000 6.06218i 0.00432633 0.00749342i −0.863854 0.503742i \(-0.831956\pi\)
0.868180 + 0.496249i \(0.165290\pi\)
\(810\) −1261.49 + 728.321i −1.55739 + 0.899162i
\(811\) 351.454 965.611i 0.433359 1.19064i −0.510380 0.859949i \(-0.670495\pi\)
0.943738 0.330694i \(-0.107283\pi\)
\(812\) 798.924 + 140.872i 0.983897 + 0.173488i
\(813\) 372.831 65.7402i 0.458587 0.0808613i
\(814\) 732.960 266.776i 0.900443 0.327734i
\(815\) −827.328 694.211i −1.01513 0.851792i
\(816\) 1568.41i 1.92208i
\(817\) 0 0
\(818\) 130.000 0.158924
\(819\) −46.3521 + 55.2403i −0.0565959 + 0.0674484i
\(820\) 443.942 + 1219.72i 0.541392 + 1.48746i
\(821\) 146.212 + 829.208i 0.178090 + 1.01000i 0.934517 + 0.355919i \(0.115832\pi\)
−0.756427 + 0.654078i \(0.773057\pi\)
\(822\) 282.178 1600.31i 0.343283 1.94685i
\(823\) −728.262 265.066i −0.884887 0.322072i −0.140707 0.990051i \(-0.544937\pi\)
−0.744180 + 0.667979i \(0.767160\pi\)
\(824\) −520.000 900.666i −0.631068 1.09304i
\(825\) 281.025 + 162.250i 0.340636 + 0.196666i
\(826\) 248.964 208.906i 0.301410 0.252913i
\(827\) −813.479 969.466i −0.983650 1.17227i −0.985050 0.172270i \(-0.944890\pi\)
0.00139937 0.999999i \(-0.499555\pi\)
\(828\) −630.000 + 1091.19i −0.760870 + 1.31786i
\(829\) −1358.29 + 784.207i −1.63846 + 0.945968i −0.657102 + 0.753802i \(0.728218\pi\)
−0.981362 + 0.192166i \(0.938449\pi\)
\(830\) −197.307 + 542.098i −0.237720 + 0.653130i
\(831\) 177.539 + 31.3049i 0.213645 + 0.0376713i
\(832\) 3.55077 0.626097i 0.00426776 0.000752521i
\(833\) 338.289 123.127i 0.406110 0.147812i
\(834\) 497.929 + 417.812i 0.597037 + 0.500974i
\(835\) 490.355i 0.587251i
\(836\) 0 0
\(837\) −650.000 −0.776583
\(838\) −259.572 + 309.345i −0.309751 + 0.369147i
\(839\) 394.615 + 1084.20i 0.470339 + 1.29225i 0.917480 + 0.397783i \(0.130220\pi\)
−0.447140 + 0.894464i \(0.647557\pi\)
\(840\) 225.743 + 1280.25i 0.268741 + 1.52411i
\(841\) 89.6025 508.161i 0.106543 0.604234i
\(842\) 2137.80 + 778.096i 2.53896 + 0.924104i
\(843\) 520.000 + 900.666i 0.616845 + 1.06841i
\(844\) −1826.66 1054.62i −2.16429 1.24955i
\(845\) 478.012 401.099i 0.565694 0.474674i
\(846\) −92.7041 110.481i −0.109579 0.130592i
\(847\) −52.5000 + 90.9327i −0.0619835 + 0.107359i
\(848\) −1901.60 + 1097.89i −2.24246 + 1.29468i
\(849\) 394.615 1084.20i 0.464799 1.27703i
\(850\) −479.355 84.5232i −0.563947 0.0994390i
\(851\) 745.663 131.480i 0.876219 0.154501i
\(852\) 3298.32 1200.49i 3.87127 1.40903i
\(853\) 306.418 + 257.115i 0.359224 + 0.301424i 0.804481 0.593978i \(-0.202443\pi\)
−0.445258 + 0.895403i \(0.646888\pi\)
\(854\) 721.110i 0.844391i
\(855\) 0 0
\(856\) 1365.00 1.59463
\(857\) −101.975 + 121.529i −0.118990 + 0.141807i −0.822251 0.569125i \(-0.807282\pi\)
0.703261 + 0.710932i \(0.251727\pi\)
\(858\) 160.312 + 440.454i 0.186844 + 0.513350i
\(859\) 248.664 + 1410.24i 0.289481 + 1.64173i 0.688825 + 0.724927i \(0.258127\pi\)
−0.399344 + 0.916801i \(0.630762\pi\)
\(860\) 125.027 709.062i 0.145380 0.824490i
\(861\) 610.800 + 222.313i 0.709408 + 0.258203i
\(862\) −780.000 1351.00i −0.904872 1.56728i
\(863\) 112.410 + 64.8999i 0.130255 + 0.0752027i 0.563712 0.825972i \(-0.309373\pi\)
−0.433457 + 0.901174i \(0.642706\pi\)
\(864\) 448.136 376.031i 0.518676 0.435221i
\(865\) −315.194 375.634i −0.364386 0.434259i
\(866\) −1326.00 + 2296.70i −1.53118 + 2.65208i
\(867\) 199.840 115.378i 0.230496 0.133077i
\(868\) −554.927 + 1524.65i −0.639317 + 1.75651i
\(869\) 355.077 + 62.6097i 0.408605 + 0.0720480i
\(870\) −923.201 + 162.785i −1.06115 + 0.187110i
\(871\) 134.376 48.9089i 0.154278 0.0561526i
\(872\) −2738.61 2297.97i −3.14061 2.63528i
\(873\) 490.355i 0.561690i
\(874\) 0 0
\(875\) 680.000 0.777143
\(876\) −2190.14 + 2610.10i −2.50015 + 2.97957i
\(877\) −134.416 369.304i −0.153268 0.421099i 0.839167 0.543874i \(-0.183043\pi\)
−0.992435 + 0.122775i \(0.960821\pi\)
\(878\) −496.634 2816.55i −0.565642 3.20792i
\(879\) −137.703 + 780.953i −0.156659 + 0.888456i
\(880\) 1090.04 + 396.743i 1.23869 + 0.450845i
\(881\) −375.000 649.519i −0.425653 0.737252i 0.570828 0.821069i \(-0.306622\pi\)
−0.996481 + 0.0838173i \(0.973289\pi\)
\(882\) −299.760 173.066i −0.339864 0.196220i
\(883\) 91.9253 77.1345i 0.104106 0.0873551i −0.589249 0.807951i \(-0.700576\pi\)
0.693355 + 0.720596i \(0.256132\pi\)
\(884\) −312.876 372.872i −0.353933 0.421801i
\(885\) −130.000 + 225.167i −0.146893 + 0.254426i
\(886\) 2092.07 1207.86i 2.36126 1.36327i
\(887\) 291.028 799.594i 0.328104 0.901459i −0.660487 0.750837i \(-0.729650\pi\)
0.988591 0.150622i \(-0.0481275\pi\)
\(888\) 1384.80 + 244.178i 1.55946 + 0.274975i
\(889\) −639.139 + 112.698i −0.718942 + 0.126769i
\(890\) 0 0
\(891\) 773.705 + 649.215i 0.868356 + 0.728637i
\(892\) 1817.20i 2.03722i
\(893\) 0 0
\(894\) 910.000 1.01790
\(895\) −92.7041 + 110.481i −0.103580 + 0.123442i
\(896\) 215.805 + 592.919i 0.240854 + 0.661740i
\(897\) 79.0099 + 448.088i 0.0880824 + 0.499540i
\(898\) 22.5743 128.025i 0.0251384 0.142567i
\(899\) −610.800 222.313i −0.679422 0.247289i
\(900\) 162.000 + 280.592i 0.180000 + 0.311769i
\(901\) 983.587 + 567.874i 1.09166 + 0.630271i
\(902\) 995.858 835.624i 1.10406 0.926412i
\(903\) −231.760 276.201i −0.256656 0.305871i
\(904\) 1105.00 1913.92i 1.22235 2.11716i
\(905\) 374.700 216.333i 0.414033 0.239042i
\(906\) 160.312 440.454i 0.176945 0.486153i
\(907\) −635.589 112.071i −0.700759 0.123563i −0.188094 0.982151i \(-0.560231\pi\)
−0.512666 + 0.858588i \(0.671342\pi\)
\(908\) 2268.95 400.076i 2.49884 0.440613i
\(909\) −187.939 + 68.4040i −0.206753 + 0.0752520i
\(910\) 199.172 + 167.125i 0.218870 + 0.183654i
\(911\) 1225.89i 1.34565i −0.739802 0.672825i \(-0.765081\pi\)
0.739802 0.672825i \(-0.234919\pi\)
\(912\) 0 0
\(913\) 400.000 0.438116
\(914\) 1749.79 2085.32i 1.91443 2.28153i
\(915\) −197.307 542.098i −0.215636 0.592456i
\(916\) 250.053 + 1418.12i 0.272984 + 1.54817i
\(917\) −97.2430 + 551.492i −0.106045 + 0.601409i
\(918\) −916.200 333.470i −0.998040 0.363257i
\(919\) 256.500 + 444.271i 0.279108 + 0.483429i 0.971163 0.238416i \(-0.0766280\pi\)
−0.692056 + 0.721844i \(0.743295\pi\)
\(920\) 2185.75 + 1261.94i 2.37581 + 1.37168i
\(921\) 657.266 551.512i 0.713644 0.598818i
\(922\) 1789.19 + 2132.27i 1.94055 + 2.31266i
\(923\) 195.000 337.750i 0.211268 0.365926i
\(924\) 1405.12 811.249i 1.52070 0.877975i
\(925\) 66.5912 182.958i 0.0719905 0.197792i
\(926\) −1242.77 219.134i −1.34209 0.236646i
\(927\) 227.250 40.0702i 0.245145 0.0432257i
\(928\) 549.720 200.082i 0.592371 0.215605i
\(929\) −932.276 782.273i −1.00353 0.842059i −0.0160574 0.999871i \(-0.505111\pi\)
−0.987469 + 0.157812i \(0.949556\pi\)
\(930\) 1874.89i 2.01601i
\(931\) 0 0
\(932\) 2430.00 2.60730
\(933\) 915.453 1090.99i 0.981193 1.16934i
\(934\) −86.3220 237.168i −0.0924218 0.253927i
\(935\) −104.189 590.885i −0.111432 0.631962i
\(936\) −45.1485 + 256.050i −0.0482356 + 0.273558i
\(937\) 1028.96 + 374.512i 1.09815 + 0.399693i 0.826633 0.562742i \(-0.190253\pi\)
0.271514 + 0.962435i \(0.412476\pi\)
\(938\) −357.500 619.208i −0.381130 0.660137i
\(939\) 390.312 + 225.347i 0.415668 + 0.239986i
\(940\) −275.776 + 231.404i −0.293379 + 0.246174i
\(941\) 706.869 + 842.414i 0.751189 + 0.895233i 0.997257 0.0740202i \(-0.0235829\pi\)
−0.246067 + 0.969253i \(0.579138\pi\)
\(942\) −65.0000 + 112.583i −0.0690021 + 0.119515i
\(943\) 1092.87 630.971i 1.15893 0.669111i
\(944\) 178.810 491.276i 0.189417 0.520419i
\(945\) 355.077 + 62.6097i 0.375743 + 0.0662537i
\(946\) −710.155 + 125.219i −0.750692 + 0.132367i
\(947\) −601.403 + 218.893i −0.635062 + 0.231143i −0.639433 0.768847i \(-0.720831\pi\)
0.00437131 + 0.999990i \(0.498609\pi\)
\(948\) 896.272 + 752.062i 0.945435 + 0.793314i
\(949\) 378.583i 0.398928i
\(950\) 0 0
\(951\) 13.0000 0.0136698
\(952\) −869.101 + 1035.75i −0.912922 + 1.08798i
\(953\) −399.547 1097.75i −0.419252 1.15189i −0.952130 0.305694i \(-0.901112\pi\)
0.532878 0.846192i \(-0.321111\pi\)
\(954\) −189.624 1075.41i −0.198767 1.12726i
\(955\) 134.056 760.272i 0.140373 0.796096i
\(956\) 1666.08 + 606.402i 1.74276 + 0.634311i
\(957\) 325.000 + 562.917i 0.339603 + 0.588210i
\(958\) 1155.32 + 667.027i 1.20598 + 0.696270i
\(959\) −478.778 + 401.742i −0.499247 + 0.418918i
\(960\) 9.27041 + 11.0481i 0.00965668 + 0.0115084i
\(961\) 169.500 293.583i 0.176379 0.305497i
\(962\) 243.555 140.616i 0.253176 0.146171i
\(963\) −103.586 + 284.601i −0.107566 + 0.295536i
\(964\) −3515.27 619.836i −3.64654 0.642984i
\(965\) −1051.03 + 185.325i −1.08915 + 0.192046i
\(966\) 2137.80 778.096i 2.21304 0.805482i
\(967\) −773.705 649.215i −0.800108 0.671371i 0.148117 0.988970i \(-0.452679\pi\)
−0.948225 + 0.317599i \(0.897123\pi\)
\(968\) 378.583i 0.391098i
\(969\) 0 0
\(970\) −1768.00 −1.82268
\(971\) 486.697 580.023i 0.501233 0.597346i −0.454805 0.890591i \(-0.650291\pi\)
0.956037 + 0.293246i \(0.0947354\pi\)
\(972\) 621.518 + 1707.61i 0.639422 + 1.75680i
\(973\) −43.4120 246.202i −0.0446167 0.253034i
\(974\) 325.069 1843.56i 0.333747 1.89277i
\(975\) 109.944 + 40.0164i 0.112763 + 0.0410424i
\(976\) 580.000 + 1004.59i 0.594262 + 1.02929i
\(977\) −518.335 299.261i −0.530537 0.306306i 0.210698 0.977551i \(-0.432426\pi\)
−0.741235 + 0.671245i \(0.765760\pi\)
\(978\) −2688.82 + 2256.18i −2.74930 + 2.30694i
\(979\) 0 0
\(980\) −432.000 + 748.246i −0.440816 + 0.763516i
\(981\) 686.950 396.611i 0.700255 0.404292i
\(982\) −779.364 + 2141.29i −0.793650 + 2.18054i
\(983\) 56.8124 + 10.0176i 0.0577949 + 0.0101908i 0.202471 0.979288i \(-0.435103\pi\)
−0.144676 + 0.989479i \(0.546214\pi\)
\(984\) 2308.00 406.963i 2.34553 0.413581i
\(985\) −338.289 + 123.127i −0.343441 + 0.125002i
\(986\) −746.893 626.718i −0.757498 0.635617i
\(987\) 180.278i 0.182652i
\(988\) 0 0
\(989\) −700.000 −0.707786
\(990\) −370.817 + 441.922i −0.374562 + 0.446386i
\(991\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(992\) 203.168 + 1152.23i 0.204807 + 1.16152i
\(993\) −124.158 + 704.138i −0.125034 + 0.709101i
\(994\) −1832.40 666.939i −1.84346 0.670965i
\(995\) −246.000 426.084i −0.247236 0.428226i
\(996\) 1124.10 + 648.999i 1.12861 + 0.651606i
\(997\) −130.228 + 109.274i −0.130619 + 0.109603i −0.705757 0.708454i \(-0.749393\pi\)
0.575138 + 0.818057i \(0.304949\pi\)
\(998\) 880.689 + 1049.56i 0.882454 + 1.05167i
\(999\) 195.000 337.750i 0.195195 0.338088i
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 361.3.f.d.307.1 12
19.2 odd 18 361.3.d.b.69.1 4
19.3 odd 18 361.3.d.b.293.2 4
19.4 even 9 inner 361.3.f.d.333.1 12
19.5 even 9 19.3.b.b.18.2 yes 2
19.6 even 9 inner 361.3.f.d.127.2 12
19.7 even 3 inner 361.3.f.d.299.1 12
19.8 odd 6 inner 361.3.f.d.116.1 12
19.9 even 9 inner 361.3.f.d.262.2 12
19.10 odd 18 inner 361.3.f.d.262.1 12
19.11 even 3 inner 361.3.f.d.116.2 12
19.12 odd 6 inner 361.3.f.d.299.2 12
19.13 odd 18 inner 361.3.f.d.127.1 12
19.14 odd 18 19.3.b.b.18.1 2
19.15 odd 18 inner 361.3.f.d.333.2 12
19.16 even 9 361.3.d.b.293.1 4
19.17 even 9 361.3.d.b.69.2 4
19.18 odd 2 inner 361.3.f.d.307.2 12
57.5 odd 18 171.3.c.b.37.1 2
57.14 even 18 171.3.c.b.37.2 2
76.43 odd 18 304.3.e.d.113.2 2
76.71 even 18 304.3.e.d.113.1 2
95.14 odd 18 475.3.c.b.151.2 2
95.24 even 18 475.3.c.b.151.1 2
95.33 even 36 475.3.d.b.474.2 4
95.43 odd 36 475.3.d.b.474.4 4
95.52 even 36 475.3.d.b.474.3 4
95.62 odd 36 475.3.d.b.474.1 4
152.5 even 18 1216.3.e.g.1025.2 2
152.43 odd 18 1216.3.e.h.1025.1 2
152.109 odd 18 1216.3.e.g.1025.1 2
152.147 even 18 1216.3.e.h.1025.2 2
228.71 odd 18 2736.3.o.d.721.1 2
228.119 even 18 2736.3.o.d.721.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
19.3.b.b.18.1 2 19.14 odd 18
19.3.b.b.18.2 yes 2 19.5 even 9
171.3.c.b.37.1 2 57.5 odd 18
171.3.c.b.37.2 2 57.14 even 18
304.3.e.d.113.1 2 76.71 even 18
304.3.e.d.113.2 2 76.43 odd 18
361.3.d.b.69.1 4 19.2 odd 18
361.3.d.b.69.2 4 19.17 even 9
361.3.d.b.293.1 4 19.16 even 9
361.3.d.b.293.2 4 19.3 odd 18
361.3.f.d.116.1 12 19.8 odd 6 inner
361.3.f.d.116.2 12 19.11 even 3 inner
361.3.f.d.127.1 12 19.13 odd 18 inner
361.3.f.d.127.2 12 19.6 even 9 inner
361.3.f.d.262.1 12 19.10 odd 18 inner
361.3.f.d.262.2 12 19.9 even 9 inner
361.3.f.d.299.1 12 19.7 even 3 inner
361.3.f.d.299.2 12 19.12 odd 6 inner
361.3.f.d.307.1 12 1.1 even 1 trivial
361.3.f.d.307.2 12 19.18 odd 2 inner
361.3.f.d.333.1 12 19.4 even 9 inner
361.3.f.d.333.2 12 19.15 odd 18 inner
475.3.c.b.151.1 2 95.24 even 18
475.3.c.b.151.2 2 95.14 odd 18
475.3.d.b.474.1 4 95.62 odd 36
475.3.d.b.474.2 4 95.33 even 36
475.3.d.b.474.3 4 95.52 even 36
475.3.d.b.474.4 4 95.43 odd 36
1216.3.e.g.1025.1 2 152.109 odd 18
1216.3.e.g.1025.2 2 152.5 even 18
1216.3.e.h.1025.1 2 152.43 odd 18
1216.3.e.h.1025.2 2 152.147 even 18
2736.3.o.d.721.1 2 228.71 odd 18
2736.3.o.d.721.2 2 228.119 even 18