Properties

Label 370.2.h.d.117.1
Level $370$
Weight $2$
Character 370.117
Analytic conductor $2.954$
Analytic rank $0$
Dimension $10$
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] = [370,2,Mod(117,370)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(370, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("370.117");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.h (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} + 3x^{8} - 8x^{7} - 26x^{6} + 12x^{5} + 24x^{4} + 166x^{3} + 113x^{2} - 152x + 160 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 117.1
Root \(-0.287871 + 2.59703i\) of defining polynomial
Character \(\chi\) \(=\) 370.117
Dual form 370.2.h.d.253.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-1.70160 - 1.70160i) q^{3} +1.00000 q^{4} +(1.73245 - 1.41373i) q^{5} +(-1.70160 - 1.70160i) q^{6} +(2.82745 + 2.82745i) q^{7} +1.00000 q^{8} +2.79087i q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(-1.70160 - 1.70160i) q^{3} +1.00000 q^{4} +(1.73245 - 1.41373i) q^{5} +(-1.70160 - 1.70160i) q^{6} +(2.82745 + 2.82745i) q^{7} +1.00000 q^{8} +2.79087i q^{9} +(1.73245 - 1.41373i) q^{10} -2.94236i q^{11} +(-1.70160 - 1.70160i) q^{12} -0.738730 q^{13} +(2.82745 + 2.82745i) q^{14} +(-5.35353 - 0.542335i) q^{15} +1.00000 q^{16} -6.61833i q^{17} +2.79087i q^{18} +(-5.03108 + 5.03108i) q^{19} +(1.73245 - 1.41373i) q^{20} -9.62238i q^{21} -2.94236i q^{22} +6.39364 q^{23} +(-1.70160 - 1.70160i) q^{24} +(1.00275 - 4.89842i) q^{25} -0.738730 q^{26} +(-0.355853 + 0.355853i) q^{27} +(2.82745 + 2.82745i) q^{28} +(-2.49797 - 2.49797i) q^{29} +(-5.35353 - 0.542335i) q^{30} +(-1.48171 + 1.48171i) q^{31} +1.00000 q^{32} +(-5.00671 + 5.00671i) q^{33} -6.61833i q^{34} +(8.89567 + 0.901168i) q^{35} +2.79087i q^{36} +(-6.07917 + 0.209128i) q^{37} +(-5.03108 + 5.03108i) q^{38} +(1.25702 + 1.25702i) q^{39} +(1.73245 - 1.41373i) q^{40} +7.39769i q^{41} -9.62238i q^{42} +6.98494 q^{43} -2.94236i q^{44} +(3.94553 + 4.83504i) q^{45} +6.39364 q^{46} +(7.56618 + 7.56618i) q^{47} +(-1.70160 - 1.70160i) q^{48} +8.98899i q^{49} +(1.00275 - 4.89842i) q^{50} +(-11.2617 + 11.2617i) q^{51} -0.738730 q^{52} +(1.94236 - 1.94236i) q^{53} +(-0.355853 + 0.355853i) q^{54} +(-4.15969 - 5.09748i) q^{55} +(2.82745 + 2.82745i) q^{56} +17.1218 q^{57} +(-2.49797 - 2.49797i) q^{58} +(-8.34044 + 8.34044i) q^{59} +(-5.35353 - 0.542335i) q^{60} +(-2.31872 + 2.31872i) q^{61} +(-1.48171 + 1.48171i) q^{62} +(-7.89106 + 7.89106i) q^{63} +1.00000 q^{64} +(-1.27981 + 1.04436i) q^{65} +(-5.00671 + 5.00671i) q^{66} +(2.10003 - 2.10003i) q^{67} -6.61833i q^{68} +(-10.8794 - 10.8794i) q^{69} +(8.89567 + 0.901168i) q^{70} -2.52254 q^{71} +2.79087i q^{72} +(7.18876 + 7.18876i) q^{73} +(-6.07917 + 0.209128i) q^{74} +(-10.0414 + 6.62886i) q^{75} +(-5.03108 + 5.03108i) q^{76} +(8.31937 - 8.31937i) q^{77} +(1.25702 + 1.25702i) q^{78} +(-5.69610 + 5.69610i) q^{79} +(1.73245 - 1.41373i) q^{80} +9.58365 q^{81} +7.39769i q^{82} +(-2.72617 + 2.72617i) q^{83} -9.62238i q^{84} +(-9.35651 - 11.4659i) q^{85} +6.98494 q^{86} +8.50109i q^{87} -2.94236i q^{88} +(-4.25577 - 4.25577i) q^{89} +(3.94553 + 4.83504i) q^{90} +(-2.08872 - 2.08872i) q^{91} +6.39364 q^{92} +5.04255 q^{93} +(7.56618 + 7.56618i) q^{94} +(-1.60351 + 15.8287i) q^{95} +(-1.70160 - 1.70160i) q^{96} +3.40320i q^{97} +8.98899i q^{98} +8.21174 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 10 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 10 q^{8} + 2 q^{10} + 2 q^{12} - 12 q^{13} - 4 q^{14} - 14 q^{15} + 10 q^{16} + 8 q^{19} + 2 q^{20} + 4 q^{23} + 2 q^{24} + 28 q^{25} - 12 q^{26} - 28 q^{27} - 4 q^{28} - 32 q^{29} - 14 q^{30} - 26 q^{31} + 10 q^{32} - 24 q^{33} + 22 q^{35} - 2 q^{37} + 8 q^{38} + 6 q^{39} + 2 q^{40} + 12 q^{43} - 10 q^{45} + 4 q^{46} + 48 q^{47} + 2 q^{48} + 28 q^{50} + 16 q^{51} - 12 q^{52} - 2 q^{53} - 28 q^{54} + 12 q^{55} - 4 q^{56} + 76 q^{57} - 32 q^{58} - 20 q^{59} - 14 q^{60} - 24 q^{61} - 26 q^{62} + 20 q^{63} + 10 q^{64} + 28 q^{65} - 24 q^{66} - 10 q^{67} - 46 q^{69} + 22 q^{70} - 16 q^{71} + 4 q^{73} - 2 q^{74} - 48 q^{75} + 8 q^{76} - 24 q^{77} + 6 q^{78} - 2 q^{79} + 2 q^{80} + 2 q^{81} + 8 q^{83} - 10 q^{85} + 12 q^{86} - 2 q^{89} - 10 q^{90} + 16 q^{91} + 4 q^{92} - 60 q^{93} + 48 q^{94} - 28 q^{95} + 2 q^{96} + 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.70160 1.70160i −0.982418 0.982418i 0.0174300 0.999848i \(-0.494452\pi\)
−0.999848 + 0.0174300i \(0.994452\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.73245 1.41373i 0.774774 0.632238i
\(6\) −1.70160 1.70160i −0.694674 0.694674i
\(7\) 2.82745 + 2.82745i 1.06868 + 1.06868i 0.997461 + 0.0712163i \(0.0226881\pi\)
0.0712163 + 0.997461i \(0.477312\pi\)
\(8\) 1.00000 0.353553
\(9\) 2.79087i 0.930291i
\(10\) 1.73245 1.41373i 0.547848 0.447060i
\(11\) 2.94236i 0.887153i −0.896236 0.443577i \(-0.853709\pi\)
0.896236 0.443577i \(-0.146291\pi\)
\(12\) −1.70160 1.70160i −0.491209 0.491209i
\(13\) −0.738730 −0.204887 −0.102443 0.994739i \(-0.532666\pi\)
−0.102443 + 0.994739i \(0.532666\pi\)
\(14\) 2.82745 + 2.82745i 0.755669 + 0.755669i
\(15\) −5.35353 0.542335i −1.38227 0.140030i
\(16\) 1.00000 0.250000
\(17\) 6.61833i 1.60518i −0.596531 0.802590i \(-0.703455\pi\)
0.596531 0.802590i \(-0.296545\pi\)
\(18\) 2.79087i 0.657815i
\(19\) −5.03108 + 5.03108i −1.15421 + 1.15421i −0.168509 + 0.985700i \(0.553895\pi\)
−0.985700 + 0.168509i \(0.946105\pi\)
\(20\) 1.73245 1.41373i 0.387387 0.316119i
\(21\) 9.62238i 2.09978i
\(22\) 2.94236i 0.627312i
\(23\) 6.39364 1.33317 0.666583 0.745431i \(-0.267756\pi\)
0.666583 + 0.745431i \(0.267756\pi\)
\(24\) −1.70160 1.70160i −0.347337 0.347337i
\(25\) 1.00275 4.89842i 0.200550 0.979683i
\(26\) −0.738730 −0.144877
\(27\) −0.355853 + 0.355853i −0.0684839 + 0.0684839i
\(28\) 2.82745 + 2.82745i 0.534339 + 0.534339i
\(29\) −2.49797 2.49797i −0.463862 0.463862i 0.436057 0.899919i \(-0.356375\pi\)
−0.899919 + 0.436057i \(0.856375\pi\)
\(30\) −5.35353 0.542335i −0.977415 0.0990163i
\(31\) −1.48171 + 1.48171i −0.266123 + 0.266123i −0.827536 0.561413i \(-0.810258\pi\)
0.561413 + 0.827536i \(0.310258\pi\)
\(32\) 1.00000 0.176777
\(33\) −5.00671 + 5.00671i −0.871556 + 0.871556i
\(34\) 6.61833i 1.13503i
\(35\) 8.89567 + 0.901168i 1.50364 + 0.152325i
\(36\) 2.79087i 0.465145i
\(37\) −6.07917 + 0.209128i −0.999409 + 0.0343805i
\(38\) −5.03108 + 5.03108i −0.816149 + 0.816149i
\(39\) 1.25702 + 1.25702i 0.201284 + 0.201284i
\(40\) 1.73245 1.41373i 0.273924 0.223530i
\(41\) 7.39769i 1.15533i 0.816276 + 0.577663i \(0.196035\pi\)
−0.816276 + 0.577663i \(0.803965\pi\)
\(42\) 9.62238i 1.48477i
\(43\) 6.98494 1.06519 0.532597 0.846369i \(-0.321216\pi\)
0.532597 + 0.846369i \(0.321216\pi\)
\(44\) 2.94236i 0.443577i
\(45\) 3.94553 + 4.83504i 0.588165 + 0.720765i
\(46\) 6.39364 0.942691
\(47\) 7.56618 + 7.56618i 1.10364 + 1.10364i 0.993968 + 0.109674i \(0.0349806\pi\)
0.109674 + 0.993968i \(0.465019\pi\)
\(48\) −1.70160 1.70160i −0.245605 0.245605i
\(49\) 8.98899i 1.28414i
\(50\) 1.00275 4.89842i 0.141810 0.692741i
\(51\) −11.2617 + 11.2617i −1.57696 + 1.57696i
\(52\) −0.738730 −0.102443
\(53\) 1.94236 1.94236i 0.266803 0.266803i −0.561008 0.827811i \(-0.689586\pi\)
0.827811 + 0.561008i \(0.189586\pi\)
\(54\) −0.355853 + 0.355853i −0.0484254 + 0.0484254i
\(55\) −4.15969 5.09748i −0.560892 0.687344i
\(56\) 2.82745 + 2.82745i 0.377834 + 0.377834i
\(57\) 17.1218 2.26783
\(58\) −2.49797 2.49797i −0.328000 0.328000i
\(59\) −8.34044 + 8.34044i −1.08583 + 1.08583i −0.0898798 + 0.995953i \(0.528648\pi\)
−0.995953 + 0.0898798i \(0.971352\pi\)
\(60\) −5.35353 0.542335i −0.691137 0.0700151i
\(61\) −2.31872 + 2.31872i −0.296882 + 0.296882i −0.839791 0.542909i \(-0.817323\pi\)
0.542909 + 0.839791i \(0.317323\pi\)
\(62\) −1.48171 + 1.48171i −0.188177 + 0.188177i
\(63\) −7.89106 + 7.89106i −0.994180 + 0.994180i
\(64\) 1.00000 0.125000
\(65\) −1.27981 + 1.04436i −0.158741 + 0.129537i
\(66\) −5.00671 + 5.00671i −0.616283 + 0.616283i
\(67\) 2.10003 2.10003i 0.256560 0.256560i −0.567093 0.823653i \(-0.691932\pi\)
0.823653 + 0.567093i \(0.191932\pi\)
\(68\) 6.61833i 0.802590i
\(69\) −10.8794 10.8794i −1.30973 1.30973i
\(70\) 8.89567 + 0.901168i 1.06324 + 0.107710i
\(71\) −2.52254 −0.299370 −0.149685 0.988734i \(-0.547826\pi\)
−0.149685 + 0.988734i \(0.547826\pi\)
\(72\) 2.79087i 0.328907i
\(73\) 7.18876 + 7.18876i 0.841381 + 0.841381i 0.989038 0.147658i \(-0.0471735\pi\)
−0.147658 + 0.989038i \(0.547173\pi\)
\(74\) −6.07917 + 0.209128i −0.706689 + 0.0243107i
\(75\) −10.0414 + 6.62886i −1.15948 + 0.765434i
\(76\) −5.03108 + 5.03108i −0.577104 + 0.577104i
\(77\) 8.31937 8.31937i 0.948081 0.948081i
\(78\) 1.25702 + 1.25702i 0.142330 + 0.142330i
\(79\) −5.69610 + 5.69610i −0.640861 + 0.640861i −0.950767 0.309906i \(-0.899702\pi\)
0.309906 + 0.950767i \(0.399702\pi\)
\(80\) 1.73245 1.41373i 0.193694 0.158059i
\(81\) 9.58365 1.06485
\(82\) 7.39769i 0.816939i
\(83\) −2.72617 + 2.72617i −0.299236 + 0.299236i −0.840714 0.541479i \(-0.817865\pi\)
0.541479 + 0.840714i \(0.317865\pi\)
\(84\) 9.62238i 1.04989i
\(85\) −9.35651 11.4659i −1.01486 1.24365i
\(86\) 6.98494 0.753205
\(87\) 8.50109i 0.911413i
\(88\) 2.94236i 0.313656i
\(89\) −4.25577 4.25577i −0.451110 0.451110i 0.444613 0.895723i \(-0.353341\pi\)
−0.895723 + 0.444613i \(0.853341\pi\)
\(90\) 3.94553 + 4.83504i 0.415895 + 0.509658i
\(91\) −2.08872 2.08872i −0.218958 0.218958i
\(92\) 6.39364 0.666583
\(93\) 5.04255 0.522888
\(94\) 7.56618 + 7.56618i 0.780392 + 0.780392i
\(95\) −1.60351 + 15.8287i −0.164517 + 1.62399i
\(96\) −1.70160 1.70160i −0.173669 0.173669i
\(97\) 3.40320i 0.345542i 0.984962 + 0.172771i \(0.0552721\pi\)
−0.984962 + 0.172771i \(0.944728\pi\)
\(98\) 8.98899i 0.908026i
\(99\) 8.21174 0.825310
\(100\) 1.00275 4.89842i 0.100275 0.489842i
\(101\) 4.21918i 0.419825i 0.977720 + 0.209912i \(0.0673178\pi\)
−0.977720 + 0.209912i \(0.932682\pi\)
\(102\) −11.2617 + 11.2617i −1.11508 + 1.11508i
\(103\) 8.10234i 0.798347i −0.916875 0.399174i \(-0.869297\pi\)
0.916875 0.399174i \(-0.130703\pi\)
\(104\) −0.738730 −0.0724384
\(105\) −13.6034 16.6703i −1.32756 1.62685i
\(106\) 1.94236 1.94236i 0.188658 0.188658i
\(107\) −11.7919 11.7919i −1.13996 1.13996i −0.988456 0.151508i \(-0.951587\pi\)
−0.151508 0.988456i \(-0.548413\pi\)
\(108\) −0.355853 + 0.355853i −0.0342419 + 0.0342419i
\(109\) 9.81489 9.81489i 0.940096 0.940096i −0.0582084 0.998304i \(-0.518539\pi\)
0.998304 + 0.0582084i \(0.0185388\pi\)
\(110\) −4.15969 5.09748i −0.396611 0.486025i
\(111\) 10.7002 + 9.98845i 1.01561 + 0.948061i
\(112\) 2.82745 + 2.82745i 0.267169 + 0.267169i
\(113\) 5.85257i 0.550564i 0.961364 + 0.275282i \(0.0887712\pi\)
−0.961364 + 0.275282i \(0.911229\pi\)
\(114\) 17.1218 1.60360
\(115\) 11.0766 9.03886i 1.03290 0.842878i
\(116\) −2.49797 2.49797i −0.231931 0.231931i
\(117\) 2.06170i 0.190604i
\(118\) −8.34044 + 8.34044i −0.767799 + 0.767799i
\(119\) 18.7130 18.7130i 1.71542 1.71542i
\(120\) −5.35353 0.542335i −0.488708 0.0495082i
\(121\) 2.34255 0.212959
\(122\) −2.31872 + 2.31872i −0.209927 + 0.209927i
\(123\) 12.5879 12.5879i 1.13501 1.13501i
\(124\) −1.48171 + 1.48171i −0.133061 + 0.133061i
\(125\) −5.18781 9.90387i −0.464012 0.885829i
\(126\) −7.89106 + 7.89106i −0.702992 + 0.702992i
\(127\) 1.49192 + 1.49192i 0.132387 + 0.132387i 0.770195 0.637808i \(-0.220159\pi\)
−0.637808 + 0.770195i \(0.720159\pi\)
\(128\) 1.00000 0.0883883
\(129\) −11.8856 11.8856i −1.04647 1.04647i
\(130\) −1.27981 + 1.04436i −0.112247 + 0.0915966i
\(131\) −11.9137 + 11.9137i −1.04090 + 1.04090i −0.0417762 + 0.999127i \(0.513302\pi\)
−0.999127 + 0.0417762i \(0.986698\pi\)
\(132\) −5.00671 + 5.00671i −0.435778 + 0.435778i
\(133\) −28.4503 −2.46695
\(134\) 2.10003 2.10003i 0.181415 0.181415i
\(135\) −0.113418 + 1.11957i −0.00976143 + 0.0963576i
\(136\) 6.61833i 0.567517i
\(137\) 5.09297 + 5.09297i 0.435122 + 0.435122i 0.890367 0.455244i \(-0.150448\pi\)
−0.455244 + 0.890367i \(0.650448\pi\)
\(138\) −10.8794 10.8794i −0.926116 0.926116i
\(139\) 1.23936 0.105121 0.0525606 0.998618i \(-0.483262\pi\)
0.0525606 + 0.998618i \(0.483262\pi\)
\(140\) 8.89567 + 0.901168i 0.751821 + 0.0761626i
\(141\) 25.7492i 2.16847i
\(142\) −2.52254 −0.211687
\(143\) 2.17361i 0.181766i
\(144\) 2.79087i 0.232573i
\(145\) −7.85906 0.796156i −0.652659 0.0661171i
\(146\) 7.18876 + 7.18876i 0.594946 + 0.594946i
\(147\) 15.2957 15.2957i 1.26156 1.26156i
\(148\) −6.07917 + 0.209128i −0.499704 + 0.0171903i
\(149\) 0.292738i 0.0239821i 0.999928 + 0.0119910i \(0.00381696\pi\)
−0.999928 + 0.0119910i \(0.996183\pi\)
\(150\) −10.0414 + 6.62886i −0.819878 + 0.541244i
\(151\) 16.1449i 1.31386i −0.753954 0.656928i \(-0.771856\pi\)
0.753954 0.656928i \(-0.228144\pi\)
\(152\) −5.03108 + 5.03108i −0.408074 + 0.408074i
\(153\) 18.4709 1.49328
\(154\) 8.31937 8.31937i 0.670394 0.670394i
\(155\) −0.472251 + 4.66171i −0.0379321 + 0.374438i
\(156\) 1.25702 + 1.25702i 0.100642 + 0.100642i
\(157\) −3.24426 3.24426i −0.258920 0.258920i 0.565695 0.824615i \(-0.308608\pi\)
−0.824615 + 0.565695i \(0.808608\pi\)
\(158\) −5.69610 + 5.69610i −0.453157 + 0.453157i
\(159\) −6.61022 −0.524224
\(160\) 1.73245 1.41373i 0.136962 0.111765i
\(161\) 18.0777 + 18.0777i 1.42472 + 1.42472i
\(162\) 9.58365 0.752963
\(163\) 23.5099i 1.84144i 0.390228 + 0.920718i \(0.372396\pi\)
−0.390228 + 0.920718i \(0.627604\pi\)
\(164\) 7.39769i 0.577663i
\(165\) −1.59574 + 15.7520i −0.124228 + 1.22629i
\(166\) −2.72617 + 2.72617i −0.211592 + 0.211592i
\(167\) 11.4543i 0.886359i 0.896433 + 0.443179i \(0.146150\pi\)
−0.896433 + 0.443179i \(0.853850\pi\)
\(168\) 9.62238i 0.742383i
\(169\) −12.4543 −0.958021
\(170\) −9.35651 11.4659i −0.717611 0.879395i
\(171\) −14.0411 14.0411i −1.07375 1.07375i
\(172\) 6.98494 0.532597
\(173\) 2.14087 + 2.14087i 0.162767 + 0.162767i 0.783791 0.621024i \(-0.213283\pi\)
−0.621024 + 0.783791i \(0.713283\pi\)
\(174\) 8.50109i 0.644466i
\(175\) 16.6853 11.0148i 1.26129 0.832642i
\(176\) 2.94236i 0.221788i
\(177\) 28.3841 2.13348
\(178\) −4.25577 4.25577i −0.318983 0.318983i
\(179\) 14.9428 + 14.9428i 1.11688 + 1.11688i 0.992197 + 0.124682i \(0.0397909\pi\)
0.124682 + 0.992197i \(0.460209\pi\)
\(180\) 3.94553 + 4.83504i 0.294082 + 0.360383i
\(181\) 12.0625 0.896602 0.448301 0.893883i \(-0.352029\pi\)
0.448301 + 0.893883i \(0.352029\pi\)
\(182\) −2.08872 2.08872i −0.154827 0.154827i
\(183\) 7.89106 0.583324
\(184\) 6.39364 0.471345
\(185\) −10.2362 + 8.95659i −0.752580 + 0.658501i
\(186\) 5.04255 0.369737
\(187\) −19.4735 −1.42404
\(188\) 7.56618 + 7.56618i 0.551821 + 0.551821i
\(189\) −2.01231 −0.146374
\(190\) −1.60351 + 15.8287i −0.116331 + 1.14833i
\(191\) −10.7383 10.7383i −0.776998 0.776998i 0.202321 0.979319i \(-0.435151\pi\)
−0.979319 + 0.202321i \(0.935151\pi\)
\(192\) −1.70160 1.70160i −0.122802 0.122802i
\(193\) −9.09024 −0.654330 −0.327165 0.944967i \(-0.606093\pi\)
−0.327165 + 0.944967i \(0.606093\pi\)
\(194\) 3.40320i 0.244335i
\(195\) 3.95481 + 0.400639i 0.283210 + 0.0286903i
\(196\) 8.98899i 0.642071i
\(197\) −7.91262 7.91262i −0.563751 0.563751i 0.366620 0.930371i \(-0.380515\pi\)
−0.930371 + 0.366620i \(0.880515\pi\)
\(198\) 8.21174 0.583583
\(199\) −9.14683 9.14683i −0.648402 0.648402i 0.304205 0.952607i \(-0.401609\pi\)
−0.952607 + 0.304205i \(0.901609\pi\)
\(200\) 1.00275 4.89842i 0.0709052 0.346370i
\(201\) −7.14683 −0.504098
\(202\) 4.21918i 0.296861i
\(203\) 14.1258i 0.991437i
\(204\) −11.2617 + 11.2617i −0.788479 + 0.788479i
\(205\) 10.4583 + 12.8161i 0.730441 + 0.895117i
\(206\) 8.10234i 0.564517i
\(207\) 17.8438i 1.24023i
\(208\) −0.738730 −0.0512217
\(209\) 14.8032 + 14.8032i 1.02396 + 1.02396i
\(210\) −13.6034 16.6703i −0.938725 1.15036i
\(211\) −12.2667 −0.844473 −0.422237 0.906486i \(-0.638755\pi\)
−0.422237 + 0.906486i \(0.638755\pi\)
\(212\) 1.94236 1.94236i 0.133402 0.133402i
\(213\) 4.29235 + 4.29235i 0.294107 + 0.294107i
\(214\) −11.7919 11.7919i −0.806076 0.806076i
\(215\) 12.1010 9.87480i 0.825284 0.673456i
\(216\) −0.355853 + 0.355853i −0.0242127 + 0.0242127i
\(217\) −8.37893 −0.568799
\(218\) 9.81489 9.81489i 0.664748 0.664748i
\(219\) 24.4648i 1.65317i
\(220\) −4.15969 5.09748i −0.280446 0.343672i
\(221\) 4.88915i 0.328880i
\(222\) 10.7002 + 9.98845i 0.718147 + 0.670381i
\(223\) −8.70510 + 8.70510i −0.582937 + 0.582937i −0.935709 0.352772i \(-0.885239\pi\)
0.352772 + 0.935709i \(0.385239\pi\)
\(224\) 2.82745 + 2.82745i 0.188917 + 0.188917i
\(225\) 13.6709 + 2.79855i 0.911390 + 0.186570i
\(226\) 5.85257i 0.389307i
\(227\) 22.3785i 1.48532i −0.669671 0.742658i \(-0.733565\pi\)
0.669671 0.742658i \(-0.266435\pi\)
\(228\) 17.1218 1.13392
\(229\) 6.97332i 0.460810i −0.973095 0.230405i \(-0.925995\pi\)
0.973095 0.230405i \(-0.0740051\pi\)
\(230\) 11.0766 9.03886i 0.730372 0.596005i
\(231\) −28.3125 −1.86282
\(232\) −2.49797 2.49797i −0.164000 0.164000i
\(233\) 15.1891 + 15.1891i 0.995069 + 0.995069i 0.999988 0.00491851i \(-0.00156562\pi\)
−0.00491851 + 0.999988i \(0.501566\pi\)
\(234\) 2.06170i 0.134778i
\(235\) 23.8045 + 2.41150i 1.55284 + 0.157309i
\(236\) −8.34044 + 8.34044i −0.542916 + 0.542916i
\(237\) 19.3849 1.25919
\(238\) 18.7130 18.7130i 1.21298 1.21298i
\(239\) 1.35831 1.35831i 0.0878617 0.0878617i −0.661810 0.749672i \(-0.730211\pi\)
0.749672 + 0.661810i \(0.230211\pi\)
\(240\) −5.35353 0.542335i −0.345569 0.0350076i
\(241\) −9.55663 9.55663i −0.615596 0.615596i 0.328802 0.944399i \(-0.393355\pi\)
−0.944399 + 0.328802i \(0.893355\pi\)
\(242\) 2.34255 0.150585
\(243\) −15.2400 15.2400i −0.977644 0.977644i
\(244\) −2.31872 + 2.31872i −0.148441 + 0.148441i
\(245\) 12.7080 + 15.5730i 0.811883 + 0.994920i
\(246\) 12.5879 12.5879i 0.802575 0.802575i
\(247\) 3.71661 3.71661i 0.236482 0.236482i
\(248\) −1.48171 + 1.48171i −0.0940886 + 0.0940886i
\(249\) 9.27768 0.587949
\(250\) −5.18781 9.90387i −0.328106 0.626376i
\(251\) 11.4900 11.4900i 0.725241 0.725241i −0.244427 0.969668i \(-0.578600\pi\)
0.969668 + 0.244427i \(0.0785998\pi\)
\(252\) −7.89106 + 7.89106i −0.497090 + 0.497090i
\(253\) 18.8124i 1.18272i
\(254\) 1.49192 + 1.49192i 0.0936114 + 0.0936114i
\(255\) −3.58935 + 35.4314i −0.224774 + 2.21880i
\(256\) 1.00000 0.0625000
\(257\) 31.7662i 1.98152i −0.135622 0.990761i \(-0.543303\pi\)
0.135622 0.990761i \(-0.456697\pi\)
\(258\) −11.8856 11.8856i −0.739963 0.739963i
\(259\) −17.7799 16.5973i −1.10479 1.03130i
\(260\) −1.27981 + 1.04436i −0.0793705 + 0.0647686i
\(261\) 6.97152 6.97152i 0.431526 0.431526i
\(262\) −11.9137 + 11.9137i −0.736030 + 0.736030i
\(263\) −18.8716 18.8716i −1.16367 1.16367i −0.983665 0.180007i \(-0.942388\pi\)
−0.180007 0.983665i \(-0.557612\pi\)
\(264\) −5.00671 + 5.00671i −0.308141 + 0.308141i
\(265\) 0.619069 6.11099i 0.0380291 0.375395i
\(266\) −28.4503 −1.74440
\(267\) 14.4832i 0.886358i
\(268\) 2.10003 2.10003i 0.128280 0.128280i
\(269\) 5.87409i 0.358150i 0.983835 + 0.179075i \(0.0573104\pi\)
−0.983835 + 0.179075i \(0.942690\pi\)
\(270\) −0.113418 + 1.11957i −0.00690238 + 0.0681351i
\(271\) 2.68158 0.162895 0.0814473 0.996678i \(-0.474046\pi\)
0.0814473 + 0.996678i \(0.474046\pi\)
\(272\) 6.61833i 0.401295i
\(273\) 7.10834i 0.430216i
\(274\) 5.09297 + 5.09297i 0.307678 + 0.307678i
\(275\) −14.4129 2.95045i −0.869130 0.177919i
\(276\) −10.8794 10.8794i −0.654863 0.654863i
\(277\) −8.90912 −0.535297 −0.267649 0.963517i \(-0.586247\pi\)
−0.267649 + 0.963517i \(0.586247\pi\)
\(278\) 1.23936 0.0743319
\(279\) −4.13526 4.13526i −0.247571 0.247571i
\(280\) 8.89567 + 0.901168i 0.531618 + 0.0538551i
\(281\) −3.03708 3.03708i −0.181177 0.181177i 0.610692 0.791869i \(-0.290892\pi\)
−0.791869 + 0.610692i \(0.790892\pi\)
\(282\) 25.7492i 1.53334i
\(283\) 5.36256i 0.318771i 0.987216 + 0.159386i \(0.0509513\pi\)
−0.987216 + 0.159386i \(0.949049\pi\)
\(284\) −2.52254 −0.149685
\(285\) 29.6625 24.2055i 1.75706 1.43381i
\(286\) 2.17361i 0.128528i
\(287\) −20.9166 + 20.9166i −1.23467 + 1.23467i
\(288\) 2.79087i 0.164454i
\(289\) −26.8022 −1.57660
\(290\) −7.85906 0.796156i −0.461500 0.0467519i
\(291\) 5.79087 5.79087i 0.339467 0.339467i
\(292\) 7.18876 + 7.18876i 0.420690 + 0.420690i
\(293\) 13.2752 13.2752i 0.775544 0.775544i −0.203525 0.979070i \(-0.565240\pi\)
0.979070 + 0.203525i \(0.0652399\pi\)
\(294\) 15.2957 15.2957i 0.892061 0.892061i
\(295\) −2.65827 + 26.2405i −0.154771 + 1.52778i
\(296\) −6.07917 + 0.209128i −0.353344 + 0.0121553i
\(297\) 1.04704 + 1.04704i 0.0607557 + 0.0607557i
\(298\) 0.292738i 0.0169579i
\(299\) −4.72317 −0.273148
\(300\) −10.0414 + 6.62886i −0.579741 + 0.382717i
\(301\) 19.7496 + 19.7496i 1.13835 + 1.13835i
\(302\) 16.1449i 0.929036i
\(303\) 7.17936 7.17936i 0.412443 0.412443i
\(304\) −5.03108 + 5.03108i −0.288552 + 0.288552i
\(305\) −0.739025 + 7.29510i −0.0423164 + 0.417716i
\(306\) 18.4709 1.05591
\(307\) 3.46389 3.46389i 0.197694 0.197694i −0.601316 0.799011i \(-0.705357\pi\)
0.799011 + 0.601316i \(0.205357\pi\)
\(308\) 8.31937 8.31937i 0.474040 0.474040i
\(309\) −13.7869 + 13.7869i −0.784311 + 0.784311i
\(310\) −0.472251 + 4.66171i −0.0268221 + 0.264768i
\(311\) 10.6674 10.6674i 0.604894 0.604894i −0.336713 0.941607i \(-0.609315\pi\)
0.941607 + 0.336713i \(0.109315\pi\)
\(312\) 1.25702 + 1.25702i 0.0711648 + 0.0711648i
\(313\) −23.2451 −1.31389 −0.656947 0.753937i \(-0.728152\pi\)
−0.656947 + 0.753937i \(0.728152\pi\)
\(314\) −3.24426 3.24426i −0.183084 0.183084i
\(315\) −2.51505 + 24.8267i −0.141707 + 1.39882i
\(316\) −5.69610 + 5.69610i −0.320430 + 0.320430i
\(317\) 7.42086 7.42086i 0.416797 0.416797i −0.467301 0.884098i \(-0.654774\pi\)
0.884098 + 0.467301i \(0.154774\pi\)
\(318\) −6.61022 −0.370682
\(319\) −7.34992 + 7.34992i −0.411517 + 0.411517i
\(320\) 1.73245 1.41373i 0.0968468 0.0790297i
\(321\) 40.1301i 2.23984i
\(322\) 18.0777 + 18.0777i 1.00743 + 1.00743i
\(323\) 33.2973 + 33.2973i 1.85271 + 1.85271i
\(324\) 9.58365 0.532425
\(325\) −0.740762 + 3.61861i −0.0410901 + 0.200724i
\(326\) 23.5099i 1.30209i
\(327\) −33.4020 −1.84713
\(328\) 7.39769i 0.408469i
\(329\) 42.7861i 2.35887i
\(330\) −1.59574 + 15.7520i −0.0878427 + 0.867118i
\(331\) 13.2492 + 13.2492i 0.728243 + 0.728243i 0.970270 0.242027i \(-0.0778122\pi\)
−0.242027 + 0.970270i \(0.577812\pi\)
\(332\) −2.72617 + 2.72617i −0.149618 + 0.149618i
\(333\) −0.583651 16.9662i −0.0319839 0.929741i
\(334\) 11.4543i 0.626750i
\(335\) 0.669325 6.60708i 0.0365691 0.360983i
\(336\) 9.62238i 0.524944i
\(337\) 3.84828 3.84828i 0.209629 0.209629i −0.594481 0.804110i \(-0.702642\pi\)
0.804110 + 0.594481i \(0.202642\pi\)
\(338\) −12.4543 −0.677423
\(339\) 9.95872 9.95872i 0.540884 0.540884i
\(340\) −9.35651 11.4659i −0.507428 0.621826i
\(341\) 4.35971 + 4.35971i 0.236092 + 0.236092i
\(342\) −14.0411 14.0411i −0.759256 0.759256i
\(343\) −5.62379 + 5.62379i −0.303656 + 0.303656i
\(344\) 6.98494 0.376603
\(345\) −34.2285 3.46749i −1.84280 0.186683i
\(346\) 2.14087 + 2.14087i 0.115094 + 0.115094i
\(347\) 20.7126 1.11191 0.555956 0.831212i \(-0.312352\pi\)
0.555956 + 0.831212i \(0.312352\pi\)
\(348\) 8.50109i 0.455706i
\(349\) 29.0891i 1.55711i 0.627579 + 0.778553i \(0.284046\pi\)
−0.627579 + 0.778553i \(0.715954\pi\)
\(350\) 16.6853 11.0148i 0.891866 0.588767i
\(351\) 0.262879 0.262879i 0.0140314 0.0140314i
\(352\) 2.94236i 0.156828i
\(353\) 22.8767i 1.21760i −0.793323 0.608801i \(-0.791651\pi\)
0.793323 0.608801i \(-0.208349\pi\)
\(354\) 28.3841 1.50860
\(355\) −4.37017 + 3.56618i −0.231945 + 0.189273i
\(356\) −4.25577 4.25577i −0.225555 0.225555i
\(357\) −63.6841 −3.37052
\(358\) 14.9428 + 14.9428i 0.789752 + 0.789752i
\(359\) 25.7577i 1.35944i 0.733472 + 0.679720i \(0.237899\pi\)
−0.733472 + 0.679720i \(0.762101\pi\)
\(360\) 3.94553 + 4.83504i 0.207948 + 0.254829i
\(361\) 31.6235i 1.66440i
\(362\) 12.0625 0.633993
\(363\) −3.98607 3.98607i −0.209214 0.209214i
\(364\) −2.08872 2.08872i −0.109479 0.109479i
\(365\) 22.6171 + 2.29121i 1.18383 + 0.119927i
\(366\) 7.89106 0.412472
\(367\) −17.7447 17.7447i −0.926265 0.926265i 0.0711974 0.997462i \(-0.477318\pi\)
−0.997462 + 0.0711974i \(0.977318\pi\)
\(368\) 6.39364 0.333291
\(369\) −20.6460 −1.07479
\(370\) −10.2362 + 8.95659i −0.532154 + 0.465631i
\(371\) 10.9838 0.570253
\(372\) 5.04255 0.261444
\(373\) 22.7050 + 22.7050i 1.17562 + 1.17562i 0.980848 + 0.194773i \(0.0623969\pi\)
0.194773 + 0.980848i \(0.437603\pi\)
\(374\) −19.4735 −1.00695
\(375\) −8.02484 + 25.6800i −0.414401 + 1.32611i
\(376\) 7.56618 + 7.56618i 0.390196 + 0.390196i
\(377\) 1.84533 + 1.84533i 0.0950392 + 0.0950392i
\(378\) −2.01231 −0.103502
\(379\) 27.5341i 1.41433i −0.707047 0.707166i \(-0.749973\pi\)
0.707047 0.707166i \(-0.250027\pi\)
\(380\) −1.60351 + 15.8287i −0.0822583 + 0.811993i
\(381\) 5.07730i 0.260118i
\(382\) −10.7383 10.7383i −0.549420 0.549420i
\(383\) 4.93269 0.252049 0.126024 0.992027i \(-0.459778\pi\)
0.126024 + 0.992027i \(0.459778\pi\)
\(384\) −1.70160 1.70160i −0.0868343 0.0868343i
\(385\) 2.65156 26.1742i 0.135136 1.33396i
\(386\) −9.09024 −0.462681
\(387\) 19.4941i 0.990939i
\(388\) 3.40320i 0.172771i
\(389\) −4.25176 + 4.25176i −0.215573 + 0.215573i −0.806630 0.591057i \(-0.798711\pi\)
0.591057 + 0.806630i \(0.298711\pi\)
\(390\) 3.95481 + 0.400639i 0.200259 + 0.0202871i
\(391\) 42.3152i 2.13997i
\(392\) 8.98899i 0.454013i
\(393\) 40.5446 2.04520
\(394\) −7.91262 7.91262i −0.398632 0.398632i
\(395\) −1.81546 + 17.9209i −0.0913459 + 0.901699i
\(396\) 8.21174 0.412655
\(397\) −6.85748 + 6.85748i −0.344167 + 0.344167i −0.857931 0.513764i \(-0.828251\pi\)
0.513764 + 0.857931i \(0.328251\pi\)
\(398\) −9.14683 9.14683i −0.458489 0.458489i
\(399\) 48.4110 + 48.4110i 2.42358 + 2.42358i
\(400\) 1.00275 4.89842i 0.0501376 0.244921i
\(401\) 4.52089 4.52089i 0.225763 0.225763i −0.585157 0.810920i \(-0.698967\pi\)
0.810920 + 0.585157i \(0.198967\pi\)
\(402\) −7.14683 −0.356451
\(403\) 1.09458 1.09458i 0.0545250 0.0545250i
\(404\) 4.21918i 0.209912i
\(405\) 16.6032 13.5487i 0.825018 0.673239i
\(406\) 14.1258i 0.701052i
\(407\) 0.615330 + 17.8871i 0.0305008 + 0.886629i
\(408\) −11.2617 + 11.2617i −0.557539 + 0.557539i
\(409\) 12.6409 + 12.6409i 0.625053 + 0.625053i 0.946819 0.321766i \(-0.104277\pi\)
−0.321766 + 0.946819i \(0.604277\pi\)
\(410\) 10.4583 + 12.8161i 0.516500 + 0.632943i
\(411\) 17.3324i 0.854944i
\(412\) 8.10234i 0.399174i
\(413\) −47.1644 −2.32081
\(414\) 17.8438i 0.876976i
\(415\) −0.868886 + 8.57700i −0.0426519 + 0.421028i
\(416\) −0.738730 −0.0362192
\(417\) −2.10889 2.10889i −0.103273 0.103273i
\(418\) 14.8032 + 14.8032i 0.724049 + 0.724049i
\(419\) 18.0818i 0.883353i −0.897174 0.441676i \(-0.854384\pi\)
0.897174 0.441676i \(-0.145616\pi\)
\(420\) −13.6034 16.6703i −0.663779 0.813426i
\(421\) −2.11385 + 2.11385i −0.103023 + 0.103023i −0.756739 0.653717i \(-0.773209\pi\)
0.653717 + 0.756739i \(0.273209\pi\)
\(422\) −12.2667 −0.597133
\(423\) −21.1162 + 21.1162i −1.02671 + 1.02671i
\(424\) 1.94236 1.94236i 0.0943291 0.0943291i
\(425\) −32.4193 6.63654i −1.57257 0.321919i
\(426\) 4.29235 + 4.29235i 0.207965 + 0.207965i
\(427\) −13.1122 −0.634542
\(428\) −11.7919 11.7919i −0.569982 0.569982i
\(429\) 3.69860 3.69860i 0.178570 0.178570i
\(430\) 12.1010 9.87480i 0.583564 0.476205i
\(431\) −2.69254 + 2.69254i −0.129695 + 0.129695i −0.768975 0.639279i \(-0.779233\pi\)
0.639279 + 0.768975i \(0.279233\pi\)
\(432\) −0.355853 + 0.355853i −0.0171210 + 0.0171210i
\(433\) −13.9527 + 13.9527i −0.670524 + 0.670524i −0.957837 0.287312i \(-0.907238\pi\)
0.287312 + 0.957837i \(0.407238\pi\)
\(434\) −8.37893 −0.402201
\(435\) 12.0182 + 14.7277i 0.576230 + 0.706139i
\(436\) 9.81489 9.81489i 0.470048 0.470048i
\(437\) −32.1669 + 32.1669i −1.53875 + 1.53875i
\(438\) 24.4648i 1.16897i
\(439\) −22.9884 22.9884i −1.09718 1.09718i −0.994739 0.102437i \(-0.967336\pi\)
−0.102437 0.994739i \(-0.532664\pi\)
\(440\) −4.15969 5.09748i −0.198305 0.243013i
\(441\) −25.0871 −1.19463
\(442\) 4.88915i 0.232553i
\(443\) −7.06197 7.06197i −0.335524 0.335524i 0.519156 0.854680i \(-0.326247\pi\)
−0.854680 + 0.519156i \(0.826247\pi\)
\(444\) 10.7002 + 9.98845i 0.507807 + 0.474031i
\(445\) −13.3894 1.35640i −0.634718 0.0642996i
\(446\) −8.70510 + 8.70510i −0.412199 + 0.412199i
\(447\) 0.498123 0.498123i 0.0235604 0.0235604i
\(448\) 2.82745 + 2.82745i 0.133585 + 0.133585i
\(449\) 2.65135 2.65135i 0.125125 0.125125i −0.641771 0.766896i \(-0.721800\pi\)
0.766896 + 0.641771i \(0.221800\pi\)
\(450\) 13.6709 + 2.79855i 0.644450 + 0.131925i
\(451\) 21.7666 1.02495
\(452\) 5.85257i 0.275282i
\(453\) −27.4722 + 27.4722i −1.29075 + 1.29075i
\(454\) 22.3785i 1.05028i
\(455\) −6.57149 0.665720i −0.308076 0.0312094i
\(456\) 17.1218 0.801799
\(457\) 6.35811i 0.297420i −0.988881 0.148710i \(-0.952488\pi\)
0.988881 0.148710i \(-0.0475121\pi\)
\(458\) 6.97332i 0.325842i
\(459\) 2.35515 + 2.35515i 0.109929 + 0.109929i
\(460\) 11.0766 9.03886i 0.516451 0.421439i
\(461\) 13.5522 + 13.5522i 0.631188 + 0.631188i 0.948366 0.317178i \(-0.102735\pi\)
−0.317178 + 0.948366i \(0.602735\pi\)
\(462\) −28.3125 −1.31721
\(463\) 6.65144 0.309119 0.154559 0.987983i \(-0.450604\pi\)
0.154559 + 0.987983i \(0.450604\pi\)
\(464\) −2.49797 2.49797i −0.115965 0.115965i
\(465\) 8.73595 7.12878i 0.405120 0.330589i
\(466\) 15.1891 + 15.1891i 0.703620 + 0.703620i
\(467\) 18.5636i 0.859019i −0.903062 0.429510i \(-0.858686\pi\)
0.903062 0.429510i \(-0.141314\pi\)
\(468\) 2.06170i 0.0953021i
\(469\) 11.8755 0.548360
\(470\) 23.8045 + 2.41150i 1.09802 + 0.111234i
\(471\) 11.0409i 0.508736i
\(472\) −8.34044 + 8.34044i −0.383900 + 0.383900i
\(473\) 20.5522i 0.944990i
\(474\) 19.3849 0.890379
\(475\) 19.5994 + 29.6892i 0.899282 + 1.36224i
\(476\) 18.7130 18.7130i 0.857710 0.857710i
\(477\) 5.42086 + 5.42086i 0.248204 + 0.248204i
\(478\) 1.35831 1.35831i 0.0621276 0.0621276i
\(479\) −3.71611 + 3.71611i −0.169793 + 0.169793i −0.786889 0.617095i \(-0.788309\pi\)
0.617095 + 0.786889i \(0.288309\pi\)
\(480\) −5.35353 0.542335i −0.244354 0.0247541i
\(481\) 4.49086 0.154489i 0.204766 0.00704411i
\(482\) −9.55663 9.55663i −0.435292 0.435292i
\(483\) 61.5220i 2.79935i
\(484\) 2.34255 0.106479
\(485\) 4.81119 + 5.89586i 0.218465 + 0.267717i
\(486\) −15.2400 15.2400i −0.691299 0.691299i
\(487\) 0.818395i 0.0370850i 0.999828 + 0.0185425i \(0.00590260\pi\)
−0.999828 + 0.0185425i \(0.994097\pi\)
\(488\) −2.31872 + 2.31872i −0.104964 + 0.104964i
\(489\) 40.0044 40.0044i 1.80906 1.80906i
\(490\) 12.7080 + 15.5730i 0.574088 + 0.703515i
\(491\) 5.21815 0.235492 0.117746 0.993044i \(-0.462433\pi\)
0.117746 + 0.993044i \(0.462433\pi\)
\(492\) 12.5879 12.5879i 0.567506 0.567506i
\(493\) −16.5324 + 16.5324i −0.744582 + 0.744582i
\(494\) 3.71661 3.71661i 0.167218 0.167218i
\(495\) 14.2264 11.6092i 0.639429 0.521793i
\(496\) −1.48171 + 1.48171i −0.0665307 + 0.0665307i
\(497\) −7.13237 7.13237i −0.319930 0.319930i
\(498\) 9.27768 0.415743
\(499\) −17.1758 17.1758i −0.768894 0.768894i 0.209018 0.977912i \(-0.432973\pi\)
−0.977912 + 0.209018i \(0.932973\pi\)
\(500\) −5.18781 9.90387i −0.232006 0.442914i
\(501\) 19.4906 19.4906i 0.870775 0.870775i
\(502\) 11.4900 11.4900i 0.512823 0.512823i
\(503\) 26.2211 1.16914 0.584569 0.811344i \(-0.301263\pi\)
0.584569 + 0.811344i \(0.301263\pi\)
\(504\) −7.89106 + 7.89106i −0.351496 + 0.351496i
\(505\) 5.96478 + 7.30952i 0.265429 + 0.325269i
\(506\) 18.8124i 0.836311i
\(507\) 21.1922 + 21.1922i 0.941178 + 0.941178i
\(508\) 1.49192 + 1.49192i 0.0661933 + 0.0661933i
\(509\) −5.42333 −0.240385 −0.120192 0.992751i \(-0.538351\pi\)
−0.120192 + 0.992751i \(0.538351\pi\)
\(510\) −3.58935 + 35.4314i −0.158939 + 1.56893i
\(511\) 40.6518i 1.79833i
\(512\) 1.00000 0.0441942
\(513\) 3.58064i 0.158089i
\(514\) 31.7662i 1.40115i
\(515\) −11.4545 14.0369i −0.504745 0.618539i
\(516\) −11.8856 11.8856i −0.523233 0.523233i
\(517\) 22.2624 22.2624i 0.979099 0.979099i
\(518\) −17.7799 16.5973i −0.781202 0.729242i
\(519\) 7.28579i 0.319811i
\(520\) −1.27981 + 1.04436i −0.0561234 + 0.0457983i
\(521\) 20.3630i 0.892120i −0.895003 0.446060i \(-0.852827\pi\)
0.895003 0.446060i \(-0.147173\pi\)
\(522\) 6.97152 6.97152i 0.305135 0.305135i
\(523\) −3.41343 −0.149259 −0.0746293 0.997211i \(-0.523777\pi\)
−0.0746293 + 0.997211i \(0.523777\pi\)
\(524\) −11.9137 + 11.9137i −0.520452 + 0.520452i
\(525\) −47.1344 9.64886i −2.05712 0.421111i
\(526\) −18.8716 18.8716i −0.822841 0.822841i
\(527\) 9.80643 + 9.80643i 0.427175 + 0.427175i
\(528\) −5.00671 + 5.00671i −0.217889 + 0.217889i
\(529\) 17.8786 0.777331
\(530\) 0.619069 6.11099i 0.0268906 0.265444i
\(531\) −23.2771 23.2771i −1.01014 1.01014i
\(532\) −28.4503 −1.23348
\(533\) 5.46490i 0.236711i
\(534\) 14.4832i 0.626750i
\(535\) −37.0993 3.75832i −1.60394 0.162486i
\(536\) 2.10003 2.10003i 0.0907077 0.0907077i
\(537\) 50.8533i 2.19448i
\(538\) 5.87409i 0.253250i
\(539\) 26.4488 1.13923
\(540\) −0.113418 + 1.11957i −0.00488072 + 0.0481788i
\(541\) 1.72146 + 1.72146i 0.0740112 + 0.0740112i 0.743143 0.669132i \(-0.233334\pi\)
−0.669132 + 0.743143i \(0.733334\pi\)
\(542\) 2.68158 0.115184
\(543\) −20.5256 20.5256i −0.880838 0.880838i
\(544\) 6.61833i 0.283758i
\(545\) 3.12821 30.8794i 0.133998 1.32273i
\(546\) 7.10834i 0.304209i
\(547\) 38.3283 1.63880 0.819400 0.573223i \(-0.194307\pi\)
0.819400 + 0.573223i \(0.194307\pi\)
\(548\) 5.09297 + 5.09297i 0.217561 + 0.217561i
\(549\) −6.47125 6.47125i −0.276186 0.276186i
\(550\) −14.4129 2.95045i −0.614567 0.125808i
\(551\) 25.1350 1.07079
\(552\) −10.8794 10.8794i −0.463058 0.463058i
\(553\) −32.2109 −1.36975
\(554\) −8.90912 −0.378512
\(555\) 32.6584 + 2.17737i 1.38627 + 0.0924242i
\(556\) 1.23936 0.0525606
\(557\) −14.2458 −0.603613 −0.301806 0.953369i \(-0.597590\pi\)
−0.301806 + 0.953369i \(0.597590\pi\)
\(558\) −4.13526 4.13526i −0.175059 0.175059i
\(559\) −5.15998 −0.218244
\(560\) 8.89567 + 0.901168i 0.375910 + 0.0380813i
\(561\) 33.1360 + 33.1360i 1.39900 + 1.39900i
\(562\) −3.03708 3.03708i −0.128112 0.128112i
\(563\) −4.87106 −0.205291 −0.102645 0.994718i \(-0.532731\pi\)
−0.102645 + 0.994718i \(0.532731\pi\)
\(564\) 25.7492i 1.08424i
\(565\) 8.27394 + 10.1393i 0.348087 + 0.426563i
\(566\) 5.36256i 0.225405i
\(567\) 27.0973 + 27.0973i 1.13798 + 1.13798i
\(568\) −2.52254 −0.105843
\(569\) 15.2311 + 15.2311i 0.638521 + 0.638521i 0.950191 0.311669i \(-0.100888\pi\)
−0.311669 + 0.950191i \(0.600888\pi\)
\(570\) 29.6625 24.2055i 1.24243 1.01386i
\(571\) 10.5691 0.442302 0.221151 0.975240i \(-0.429019\pi\)
0.221151 + 0.975240i \(0.429019\pi\)
\(572\) 2.17361i 0.0908830i
\(573\) 36.5446i 1.52667i
\(574\) −20.9166 + 20.9166i −0.873044 + 0.873044i
\(575\) 6.41123 31.3187i 0.267367 1.30608i
\(576\) 2.79087i 0.116286i
\(577\) 27.8591i 1.15979i 0.814691 + 0.579895i \(0.196906\pi\)
−0.814691 + 0.579895i \(0.803094\pi\)
\(578\) −26.8022 −1.11483
\(579\) 15.4679 + 15.4679i 0.642826 + 0.642826i
\(580\) −7.85906 0.796156i −0.326330 0.0330586i
\(581\) −15.4162 −0.639573
\(582\) 5.79087 5.79087i 0.240039 0.240039i
\(583\) −5.71510 5.71510i −0.236695 0.236695i
\(584\) 7.18876 + 7.18876i 0.297473 + 0.297473i
\(585\) −2.91468 3.57179i −0.120507 0.147675i
\(586\) 13.2752 13.2752i 0.548393 0.548393i
\(587\) −1.53471 −0.0633441 −0.0316720 0.999498i \(-0.510083\pi\)
−0.0316720 + 0.999498i \(0.510083\pi\)
\(588\) 15.2957 15.2957i 0.630782 0.630782i
\(589\) 14.9092i 0.614322i
\(590\) −2.65827 + 26.2405i −0.109439 + 1.08030i
\(591\) 26.9282i 1.10768i
\(592\) −6.07917 + 0.209128i −0.249852 + 0.00859513i
\(593\) 33.9424 33.9424i 1.39385 1.39385i 0.577353 0.816495i \(-0.304086\pi\)
0.816495 0.577353i \(-0.195914\pi\)
\(594\) 1.04704 + 1.04704i 0.0429608 + 0.0429608i
\(595\) 5.96423 58.8744i 0.244509 2.41362i
\(596\) 0.292738i 0.0119910i
\(597\) 31.1285i 1.27400i
\(598\) −4.72317 −0.193145
\(599\) 3.02066i 0.123421i −0.998094 0.0617105i \(-0.980344\pi\)
0.998094 0.0617105i \(-0.0196555\pi\)
\(600\) −10.0414 + 6.62886i −0.409939 + 0.270622i
\(601\) 19.6569 0.801820 0.400910 0.916117i \(-0.368694\pi\)
0.400910 + 0.916117i \(0.368694\pi\)
\(602\) 19.7496 + 19.7496i 0.804933 + 0.804933i
\(603\) 5.86093 + 5.86093i 0.238675 + 0.238675i
\(604\) 16.1449i 0.656928i
\(605\) 4.05834 3.31172i 0.164995 0.134641i
\(606\) 7.17936 7.17936i 0.291641 0.291641i
\(607\) −2.50292 −0.101590 −0.0507951 0.998709i \(-0.516176\pi\)
−0.0507951 + 0.998709i \(0.516176\pi\)
\(608\) −5.03108 + 5.03108i −0.204037 + 0.204037i
\(609\) −24.0364 + 24.0364i −0.974006 + 0.974006i
\(610\) −0.739025 + 7.29510i −0.0299222 + 0.295370i
\(611\) −5.58936 5.58936i −0.226122 0.226122i
\(612\) 18.4709 0.746642
\(613\) 26.8961 + 26.8961i 1.08632 + 1.08632i 0.995904 + 0.0904205i \(0.0288211\pi\)
0.0904205 + 0.995904i \(0.471179\pi\)
\(614\) 3.46389 3.46389i 0.139791 0.139791i
\(615\) 4.01203 39.6037i 0.161780 1.59698i
\(616\) 8.31937 8.31937i 0.335197 0.335197i
\(617\) −4.81845 + 4.81845i −0.193983 + 0.193983i −0.797415 0.603432i \(-0.793800\pi\)
0.603432 + 0.797415i \(0.293800\pi\)
\(618\) −13.7869 + 13.7869i −0.554591 + 0.554591i
\(619\) −10.4774 −0.421121 −0.210560 0.977581i \(-0.567529\pi\)
−0.210560 + 0.977581i \(0.567529\pi\)
\(620\) −0.472251 + 4.66171i −0.0189661 + 0.187219i
\(621\) −2.27519 + 2.27519i −0.0913003 + 0.0913003i
\(622\) 10.6674 10.6674i 0.427725 0.427725i
\(623\) 24.0660i 0.964183i
\(624\) 1.25702 + 1.25702i 0.0503211 + 0.0503211i
\(625\) −22.9890 9.82379i −0.919559 0.392952i
\(626\) −23.2451 −0.929063
\(627\) 50.3783i 2.01191i
\(628\) −3.24426 3.24426i −0.129460 0.129460i
\(629\) 1.38408 + 40.2339i 0.0551869 + 1.60423i
\(630\) −2.51505 + 24.8267i −0.100202 + 0.989118i
\(631\) −20.7491 + 20.7491i −0.826008 + 0.826008i −0.986962 0.160954i \(-0.948543\pi\)
0.160954 + 0.986962i \(0.448543\pi\)
\(632\) −5.69610 + 5.69610i −0.226578 + 0.226578i
\(633\) 20.8730 + 20.8730i 0.829626 + 0.829626i
\(634\) 7.42086 7.42086i 0.294720 0.294720i
\(635\) 4.69384 + 0.475506i 0.186269 + 0.0188699i
\(636\) −6.61022 −0.262112
\(637\) 6.64044i 0.263104i
\(638\) −7.34992 + 7.34992i −0.290986 + 0.290986i
\(639\) 7.04009i 0.278502i
\(640\) 1.73245 1.41373i 0.0684810 0.0558825i
\(641\) −31.3975 −1.24013 −0.620064 0.784552i \(-0.712893\pi\)
−0.620064 + 0.784552i \(0.712893\pi\)
\(642\) 40.1301i 1.58381i
\(643\) 39.2482i 1.54780i −0.633309 0.773899i \(-0.718304\pi\)
0.633309 0.773899i \(-0.281696\pi\)
\(644\) 18.0777 + 18.0777i 0.712362 + 0.712362i
\(645\) −37.3940 3.78817i −1.47239 0.149159i
\(646\) 33.2973 + 33.2973i 1.31007 + 1.31007i
\(647\) 33.5881 1.32048 0.660242 0.751053i \(-0.270454\pi\)
0.660242 + 0.751053i \(0.270454\pi\)
\(648\) 9.58365 0.376481
\(649\) 24.5405 + 24.5405i 0.963300 + 0.963300i
\(650\) −0.740762 + 3.61861i −0.0290551 + 0.141933i
\(651\) 14.2576 + 14.2576i 0.558798 + 0.558798i
\(652\) 23.5099i 0.920718i
\(653\) 32.2571i 1.26232i −0.775653 0.631159i \(-0.782579\pi\)
0.775653 0.631159i \(-0.217421\pi\)
\(654\) −33.4020 −1.30612
\(655\) −3.79714 + 37.4825i −0.148366 + 1.46456i
\(656\) 7.39769i 0.288831i
\(657\) −20.0629 + 20.0629i −0.782728 + 0.782728i
\(658\) 42.7861i 1.66797i
\(659\) 28.7104 1.11840 0.559199 0.829033i \(-0.311109\pi\)
0.559199 + 0.829033i \(0.311109\pi\)
\(660\) −1.59574 + 15.7520i −0.0621141 + 0.613145i
\(661\) 5.46781 5.46781i 0.212673 0.212673i −0.592729 0.805402i \(-0.701949\pi\)
0.805402 + 0.592729i \(0.201949\pi\)
\(662\) 13.2492 + 13.2492i 0.514945 + 0.514945i
\(663\) 8.31937 8.31937i 0.323098 0.323098i
\(664\) −2.72617 + 2.72617i −0.105796 + 0.105796i
\(665\) −49.2887 + 40.2210i −1.91133 + 1.55970i
\(666\) −0.583651 16.9662i −0.0226160 0.657426i
\(667\) −15.9711 15.9711i −0.618405 0.618405i
\(668\) 11.4543i 0.443179i
\(669\) 29.6252 1.14538
\(670\) 0.669325 6.60708i 0.0258583 0.255254i
\(671\) 6.82250 + 6.82250i 0.263380 + 0.263380i
\(672\) 9.62238i 0.371191i
\(673\) 15.3921 15.3921i 0.593323 0.593323i −0.345204 0.938528i \(-0.612190\pi\)
0.938528 + 0.345204i \(0.112190\pi\)
\(674\) 3.84828 3.84828i 0.148230 0.148230i
\(675\) 1.38628 + 2.09995i 0.0533580 + 0.0808269i
\(676\) −12.4543 −0.479011
\(677\) 8.46595 8.46595i 0.325373 0.325373i −0.525451 0.850824i \(-0.676103\pi\)
0.850824 + 0.525451i \(0.176103\pi\)
\(678\) 9.95872 9.95872i 0.382462 0.382462i
\(679\) −9.62238 + 9.62238i −0.369273 + 0.369273i
\(680\) −9.35651 11.4659i −0.358806 0.439697i
\(681\) −38.0793 + 38.0793i −1.45920 + 1.45920i
\(682\) 4.35971 + 4.35971i 0.166942 + 0.166942i
\(683\) −42.2105 −1.61514 −0.807570 0.589772i \(-0.799218\pi\)
−0.807570 + 0.589772i \(0.799218\pi\)
\(684\) −14.0411 14.0411i −0.536875 0.536875i
\(685\) 16.0234 + 1.62324i 0.612222 + 0.0620207i
\(686\) −5.62379 + 5.62379i −0.214717 + 0.214717i
\(687\) −11.8658 + 11.8658i −0.452708 + 0.452708i
\(688\) 6.98494 0.266298
\(689\) −1.43488 + 1.43488i −0.0546644 + 0.0546644i
\(690\) −34.2285 3.46749i −1.30306 0.132005i
\(691\) 7.77112i 0.295627i 0.989015 + 0.147814i \(0.0472236\pi\)
−0.989015 + 0.147814i \(0.952776\pi\)
\(692\) 2.14087 + 2.14087i 0.0813835 + 0.0813835i
\(693\) 23.2183 + 23.2183i 0.881991 + 0.881991i
\(694\) 20.7126 0.786240
\(695\) 2.14713 1.75212i 0.0814452 0.0664616i
\(696\) 8.50109i 0.322233i
\(697\) 48.9603 1.85451
\(698\) 29.0891i 1.10104i
\(699\) 51.6914i 1.95515i
\(700\) 16.6853 11.0148i 0.630644 0.416321i
\(701\) −36.6175 36.6175i −1.38302 1.38302i −0.839197 0.543828i \(-0.816974\pi\)
−0.543828 0.839197i \(-0.683026\pi\)
\(702\) 0.262879 0.262879i 0.00992172 0.00992172i
\(703\) 29.5326 31.6369i 1.11384 1.19321i
\(704\) 2.94236i 0.110894i
\(705\) −36.4024 44.6092i −1.37099 1.68008i
\(706\) 22.8767i 0.860975i
\(707\) −11.9296 + 11.9296i −0.448657 + 0.448657i
\(708\) 28.3841 1.06674
\(709\) 33.4953 33.4953i 1.25794 1.25794i 0.305869 0.952074i \(-0.401053\pi\)
0.952074 0.305869i \(-0.0989469\pi\)
\(710\) −4.37017 + 3.56618i −0.164010 + 0.133836i
\(711\) −15.8971 15.8971i −0.596187 0.596187i
\(712\) −4.25577 4.25577i −0.159492 0.159492i
\(713\) −9.47351 + 9.47351i −0.354786 + 0.354786i
\(714\) −63.6841 −2.38332
\(715\) 3.07288 + 3.76566i 0.114919 + 0.140828i
\(716\) 14.9428 + 14.9428i 0.558439 + 0.558439i
\(717\) −4.62259 −0.172634
\(718\) 25.7577i 0.961269i
\(719\) 7.36568i 0.274693i 0.990523 + 0.137347i \(0.0438574\pi\)
−0.990523 + 0.137347i \(0.956143\pi\)
\(720\) 3.94553 + 4.83504i 0.147041 + 0.180191i
\(721\) 22.9090 22.9090i 0.853175 0.853175i
\(722\) 31.6235i 1.17691i
\(723\) 32.5231i 1.20955i
\(724\) 12.0625 0.448301
\(725\) −14.7410 + 9.73127i −0.547465 + 0.361410i
\(726\) −3.98607 3.98607i −0.147937 0.147937i
\(727\) −49.6628 −1.84189 −0.920945 0.389692i \(-0.872581\pi\)
−0.920945 + 0.389692i \(0.872581\pi\)
\(728\) −2.08872 2.08872i −0.0774133 0.0774133i
\(729\) 23.1136i 0.856060i
\(730\) 22.6171 + 2.29121i 0.837096 + 0.0848014i
\(731\) 46.2286i 1.70983i
\(732\) 7.89106 0.291662
\(733\) −1.72578 1.72578i −0.0637431 0.0637431i 0.674517 0.738260i \(-0.264352\pi\)
−0.738260 + 0.674517i \(0.764352\pi\)
\(734\) −17.7447 17.7447i −0.654968 0.654968i
\(735\) 4.87504 48.1228i 0.179819 1.77504i
\(736\) 6.39364 0.235673
\(737\) −6.17905 6.17905i −0.227608 0.227608i
\(738\) −20.6460 −0.759990
\(739\) −34.0153 −1.25127 −0.625636 0.780115i \(-0.715160\pi\)
−0.625636 + 0.780115i \(0.715160\pi\)
\(740\) −10.2362 + 8.95659i −0.376290 + 0.329251i
\(741\) −12.6483 −0.464649
\(742\) 10.9838 0.403229
\(743\) 11.8640 + 11.8640i 0.435249 + 0.435249i 0.890410 0.455160i \(-0.150418\pi\)
−0.455160 + 0.890410i \(0.650418\pi\)
\(744\) 5.04255 0.184869
\(745\) 0.413852 + 0.507154i 0.0151624 + 0.0185807i
\(746\) 22.7050 + 22.7050i 0.831290 + 0.831290i
\(747\) −7.60838 7.60838i −0.278376 0.278376i
\(748\) −19.4735 −0.712020
\(749\) 66.6820i 2.43651i
\(750\) −8.02484 + 25.6800i −0.293026 + 0.937700i
\(751\) 18.1038i 0.660617i 0.943873 + 0.330308i \(0.107153\pi\)
−0.943873 + 0.330308i \(0.892847\pi\)
\(752\) 7.56618 + 7.56618i 0.275910 + 0.275910i
\(753\) −39.1026 −1.42498
\(754\) 1.84533 + 1.84533i 0.0672028 + 0.0672028i
\(755\) −22.8245 27.9702i −0.830669 1.01794i
\(756\) −2.01231 −0.0731871
\(757\) 25.2565i 0.917964i −0.888445 0.458982i \(-0.848214\pi\)
0.888445 0.458982i \(-0.151786\pi\)
\(758\) 27.5341i 1.00008i
\(759\) −32.0111 + 32.0111i −1.16193 + 1.16193i
\(760\) −1.60351 + 15.8287i −0.0581654 + 0.574166i
\(761\) 45.4777i 1.64856i 0.566179 + 0.824282i \(0.308421\pi\)
−0.566179 + 0.824282i \(0.691579\pi\)
\(762\) 5.07730i 0.183931i
\(763\) 55.5023 2.00932
\(764\) −10.7383 10.7383i −0.388499 0.388499i
\(765\) 31.9999 26.1128i 1.15696 0.944111i
\(766\) 4.93269 0.178225
\(767\) 6.16133 6.16133i 0.222473 0.222473i
\(768\) −1.70160 1.70160i −0.0614011 0.0614011i
\(769\) 5.30402 + 5.30402i 0.191268 + 0.191268i 0.796244 0.604976i \(-0.206817\pi\)
−0.604976 + 0.796244i \(0.706817\pi\)
\(770\) 2.65156 26.1742i 0.0955555 0.943253i
\(771\) −54.0533 + 54.0533i −1.94668 + 1.94668i
\(772\) −9.09024 −0.327165
\(773\) −21.8164 + 21.8164i −0.784681 + 0.784681i −0.980617 0.195935i \(-0.937226\pi\)
0.195935 + 0.980617i \(0.437226\pi\)
\(774\) 19.4941i 0.700700i
\(775\) 5.77224 + 8.74381i 0.207345 + 0.314087i
\(776\) 3.40320i 0.122168i
\(777\) 2.01231 + 58.4961i 0.0721913 + 2.09853i
\(778\) −4.25176 + 4.25176i −0.152433 + 0.152433i
\(779\) −37.2184 37.2184i −1.33349 1.33349i
\(780\) 3.95481 + 0.400639i 0.141605 + 0.0143452i
\(781\) 7.42221i 0.265588i
\(782\) 42.3152i 1.51319i
\(783\) 1.77782 0.0635341
\(784\) 8.98899i 0.321036i
\(785\) −10.2070 1.03401i −0.364304 0.0369055i
\(786\) 40.5446 1.44618
\(787\) −29.6710 29.6710i −1.05766 1.05766i −0.998233 0.0594240i \(-0.981074\pi\)
−0.0594240 0.998233i \(-0.518926\pi\)
\(788\) −7.91262 7.91262i −0.281875 0.281875i
\(789\) 64.2237i 2.28643i
\(790\) −1.81546 + 17.9209i −0.0645913 + 0.637597i
\(791\) −16.5479 + 16.5479i −0.588375 + 0.588375i
\(792\) 8.21174 0.291791
\(793\) 1.71291 1.71291i 0.0608271 0.0608271i
\(794\) −6.85748 + 6.85748i −0.243363 + 0.243363i
\(795\) −11.4519 + 9.34504i −0.406155 + 0.331434i
\(796\) −9.14683 9.14683i −0.324201 0.324201i
\(797\) −12.5492 −0.444515 −0.222257 0.974988i \(-0.571343\pi\)
−0.222257 + 0.974988i \(0.571343\pi\)
\(798\) 48.4110 + 48.4110i 1.71373 + 1.71373i
\(799\) 50.0755 50.0755i 1.77154 1.77154i
\(800\) 1.00275 4.89842i 0.0354526 0.173185i
\(801\) 11.8773 11.8773i 0.419664 0.419664i
\(802\) 4.52089 4.52089i 0.159638 0.159638i
\(803\) 21.1519 21.1519i 0.746434 0.746434i
\(804\) −7.14683 −0.252049
\(805\) 56.8757 + 5.76175i 2.00460 + 0.203075i
\(806\) 1.09458 1.09458i 0.0385550 0.0385550i
\(807\) 9.99535 9.99535i 0.351853 0.351853i
\(808\) 4.21918i 0.148430i
\(809\) −19.1078 19.1078i −0.671796 0.671796i 0.286334 0.958130i \(-0.407563\pi\)
−0.958130 + 0.286334i \(0.907563\pi\)
\(810\) 16.6032 13.5487i 0.583376 0.476052i
\(811\) 9.22121 0.323801 0.161900 0.986807i \(-0.448238\pi\)
0.161900 + 0.986807i \(0.448238\pi\)
\(812\) 14.1258i 0.495719i
\(813\) −4.56298 4.56298i −0.160031 0.160031i
\(814\) 0.615330 + 17.8871i 0.0215673 + 0.626941i
\(815\) 33.2366 + 40.7297i 1.16423 + 1.42670i
\(816\) −11.2617 + 11.2617i −0.394239 + 0.394239i
\(817\) −35.1418 + 35.1418i −1.22946 + 1.22946i
\(818\) 12.6409 + 12.6409i 0.441979 + 0.441979i
\(819\) 5.82936 5.82936i 0.203694 0.203694i
\(820\) 10.4583 + 12.8161i 0.365220 + 0.447558i
\(821\) 1.92924 0.0673310 0.0336655 0.999433i \(-0.489282\pi\)
0.0336655 + 0.999433i \(0.489282\pi\)
\(822\) 17.3324i 0.604536i
\(823\) −14.9775 + 14.9775i −0.522084 + 0.522084i −0.918200 0.396116i \(-0.870358\pi\)
0.396116 + 0.918200i \(0.370358\pi\)
\(824\) 8.10234i 0.282258i
\(825\) 19.5045 + 29.5454i 0.679058 + 1.02864i
\(826\) −47.1644 −1.64106
\(827\) 46.1448i 1.60461i 0.596913 + 0.802306i \(0.296394\pi\)
−0.596913 + 0.802306i \(0.703606\pi\)
\(828\) 17.8438i 0.620116i
\(829\) −10.2967 10.2967i −0.357619 0.357619i 0.505315 0.862935i \(-0.331376\pi\)
−0.862935 + 0.505315i \(0.831376\pi\)
\(830\) −0.868886 + 8.57700i −0.0301595 + 0.297712i
\(831\) 15.1597 + 15.1597i 0.525885 + 0.525885i
\(832\) −0.738730 −0.0256108
\(833\) 59.4921 2.06128
\(834\) −2.10889 2.10889i −0.0730250 0.0730250i
\(835\) 16.1932 + 19.8439i 0.560390 + 0.686728i
\(836\) 14.8032 + 14.8032i 0.511980 + 0.511980i
\(837\) 1.05454i 0.0364502i
\(838\) 18.0818i 0.624625i
\(839\) 32.5351 1.12324 0.561619 0.827396i \(-0.310179\pi\)
0.561619 + 0.827396i \(0.310179\pi\)
\(840\) −13.6034 16.6703i −0.469363 0.575179i
\(841\) 16.5203i 0.569664i
\(842\) −2.11385 + 2.11385i −0.0728482 + 0.0728482i
\(843\) 10.3358i 0.355983i
\(844\) −12.2667 −0.422237
\(845\) −21.5764 + 17.6070i −0.742250 + 0.605698i
\(846\) −21.1162 + 21.1162i −0.725992 + 0.725992i
\(847\) 6.62344 + 6.62344i 0.227584 + 0.227584i
\(848\) 1.94236 1.94236i 0.0667008 0.0667008i
\(849\) 9.12492 9.12492i 0.313166 0.313166i
\(850\) −32.4193 6.63654i −1.11197 0.227631i
\(851\) −38.8680 + 1.33709i −1.33238 + 0.0458349i
\(852\) 4.29235 + 4.29235i 0.147053 + 0.147053i
\(853\) 42.8714i 1.46789i 0.679209 + 0.733945i \(0.262323\pi\)
−0.679209 + 0.733945i \(0.737677\pi\)
\(854\) −13.1122 −0.448689
\(855\) −44.1757 4.47519i −1.51078 0.153048i
\(856\) −11.7919 11.7919i −0.403038 0.403038i
\(857\) 3.29400i 0.112521i −0.998416 0.0562604i \(-0.982082\pi\)
0.998416 0.0562604i \(-0.0179177\pi\)
\(858\) 3.69860 3.69860i 0.126268 0.126268i
\(859\) −18.0550 + 18.0550i −0.616030 + 0.616030i −0.944511 0.328481i \(-0.893463\pi\)
0.328481 + 0.944511i \(0.393463\pi\)
\(860\) 12.1010 9.87480i 0.412642 0.336728i
\(861\) 71.1834 2.42592
\(862\) −2.69254 + 2.69254i −0.0917083 + 0.0917083i
\(863\) −18.6224 + 18.6224i −0.633913 + 0.633913i −0.949047 0.315134i \(-0.897950\pi\)
0.315134 + 0.949047i \(0.397950\pi\)
\(864\) −0.355853 + 0.355853i −0.0121063 + 0.0121063i
\(865\) 6.73554 + 0.682339i 0.229015 + 0.0232002i
\(866\) −13.9527 + 13.9527i −0.474132 + 0.474132i
\(867\) 45.6066 + 45.6066i 1.54888 + 1.54888i
\(868\) −8.37893 −0.284399
\(869\) 16.7599 + 16.7599i 0.568542 + 0.568542i
\(870\) 12.0182 + 14.7277i 0.407456 + 0.499316i
\(871\) −1.55136 + 1.55136i −0.0525658 + 0.0525658i
\(872\) 9.81489 9.81489i 0.332374 0.332374i
\(873\) −9.49788 −0.321455
\(874\) −32.1669 + 32.1669i −1.08806 + 1.08806i
\(875\) 13.3344 42.6710i 0.450786 1.44254i
\(876\) 24.4648i 0.826587i
\(877\) 25.3664 + 25.3664i 0.856561 + 0.856561i 0.990931 0.134370i \(-0.0429011\pi\)
−0.134370 + 0.990931i \(0.542901\pi\)
\(878\) −22.9884 22.9884i −0.775821 0.775821i
\(879\) −45.1780 −1.52382
\(880\) −4.15969 5.09748i −0.140223 0.171836i
\(881\) 28.4586i 0.958796i −0.877598 0.479398i \(-0.840855\pi\)
0.877598 0.479398i \(-0.159145\pi\)
\(882\) −25.0871 −0.844728
\(883\) 17.5471i 0.590508i 0.955419 + 0.295254i \(0.0954042\pi\)
−0.955419 + 0.295254i \(0.904596\pi\)
\(884\) 4.88915i 0.164440i
\(885\) 49.1740 40.1274i 1.65297 1.34887i
\(886\) −7.06197 7.06197i −0.237251 0.237251i
\(887\) 25.1122 25.1122i 0.843184 0.843184i −0.146088 0.989272i \(-0.546668\pi\)
0.989272 + 0.146088i \(0.0466683\pi\)
\(888\) 10.7002 + 9.98845i 0.359074 + 0.335190i
\(889\) 8.43667i 0.282957i
\(890\) −13.3894 1.35640i −0.448813 0.0454667i
\(891\) 28.1985i 0.944685i
\(892\) −8.70510 + 8.70510i −0.291468 + 0.291468i
\(893\) −76.1321 −2.54767
\(894\) 0.498123 0.498123i 0.0166597 0.0166597i
\(895\) 47.0127 + 4.76259i 1.57146 + 0.159196i
\(896\) 2.82745 + 2.82745i 0.0944586 + 0.0944586i
\(897\) 8.03694 + 8.03694i 0.268346 + 0.268346i
\(898\) 2.65135 2.65135i 0.0884768 0.0884768i
\(899\) 7.40254 0.246888
\(900\) 13.6709 + 2.79855i 0.455695 + 0.0932850i
\(901\) −12.8551 12.8551i −0.428267 0.428267i
\(902\) 21.7666 0.724750
\(903\) 67.2117i 2.23667i
\(904\) 5.85257i 0.194654i
\(905\) 20.8977 17.0532i 0.694664 0.566866i
\(906\) −27.4722 + 27.4722i −0.912702 + 0.912702i
\(907\) 57.0816i 1.89536i 0.319215 + 0.947682i \(0.396581\pi\)
−0.319215 + 0.947682i \(0.603419\pi\)
\(908\) 22.3785i 0.742658i
\(909\) −11.7752 −0.390559
\(910\) −6.57149 0.665720i −0.217843 0.0220684i
\(911\) −22.4319 22.4319i −0.743203 0.743203i 0.229990 0.973193i \(-0.426131\pi\)
−0.973193 + 0.229990i \(0.926131\pi\)
\(912\) 17.1218 0.566958
\(913\) 8.02135 + 8.02135i 0.265468 + 0.265468i
\(914\) 6.35811i 0.210308i
\(915\) 13.6709 11.1558i 0.451944 0.368800i
\(916\) 6.97332i 0.230405i
\(917\) −67.3708 −2.22478
\(918\) 2.35515 + 2.35515i 0.0777315 + 0.0777315i
\(919\) 33.5651 + 33.5651i 1.10721 + 1.10721i 0.993516 + 0.113694i \(0.0362684\pi\)
0.113694 + 0.993516i \(0.463732\pi\)
\(920\) 11.0766 9.03886i 0.365186 0.298002i
\(921\) −11.7883 −0.388437
\(922\) 13.5522 + 13.5522i 0.446317 + 0.446317i
\(923\) 1.86348 0.0613370
\(924\) −28.3125 −0.931412
\(925\) −5.07149 + 29.9880i −0.166750 + 0.985999i
\(926\) 6.65144 0.218580
\(927\) 22.6126 0.742695
\(928\) −2.49797 2.49797i −0.0820000 0.0820000i
\(929\) −58.2060 −1.90968 −0.954838 0.297127i \(-0.903972\pi\)
−0.954838 + 0.297127i \(0.903972\pi\)
\(930\) 8.73595 7.12878i 0.286463 0.233762i
\(931\) −45.2243 45.2243i −1.48217 1.48217i
\(932\) 15.1891 + 15.1891i 0.497535 + 0.497535i
\(933\) −36.3033 −1.18852
\(934\) 18.5636i 0.607418i
\(935\) −33.7368 + 27.5302i −1.10331 + 0.900333i
\(936\) 2.06170i 0.0673888i
\(937\) 23.5283 + 23.5283i 0.768637 + 0.768637i 0.977867 0.209229i \(-0.0670955\pi\)
−0.209229 + 0.977867i \(0.567095\pi\)
\(938\) 11.8755 0.387749
\(939\) 39.5539 + 39.5539i 1.29079 + 1.29079i
\(940\) 23.8045 + 2.41150i 0.776418 + 0.0786545i
\(941\) 23.9226 0.779853 0.389926 0.920846i \(-0.372500\pi\)
0.389926 + 0.920846i \(0.372500\pi\)
\(942\) 11.0409i 0.359731i
\(943\) 47.2982i 1.54024i
\(944\) −8.34044 + 8.34044i −0.271458 + 0.271458i
\(945\) −3.48623 + 2.84486i −0.113407 + 0.0925434i
\(946\) 20.5522i 0.668209i
\(947\) 44.9073i 1.45929i −0.683826 0.729645i \(-0.739685\pi\)
0.683826 0.729645i \(-0.260315\pi\)
\(948\) 19.3849 0.629593
\(949\) −5.31055 5.31055i −0.172388 0.172388i
\(950\) 19.5994 + 29.6892i 0.635889 + 0.963246i
\(951\) −25.2547 −0.818938
\(952\) 18.7130 18.7130i 0.606492 0.606492i
\(953\) −6.57978 6.57978i −0.213140 0.213140i 0.592460 0.805600i \(-0.298157\pi\)
−0.805600 + 0.592460i \(0.798157\pi\)
\(954\) 5.42086 + 5.42086i 0.175507 + 0.175507i
\(955\) −33.7846 3.42253i −1.09325 0.110750i
\(956\) 1.35831 1.35831i 0.0439309 0.0439309i
\(957\) 25.0132 0.808563
\(958\) −3.71611 + 3.71611i −0.120062 + 0.120062i
\(959\) 28.8003i 0.930010i
\(960\) −5.35353 0.542335i −0.172784 0.0175038i
\(961\) 26.6091i 0.858357i
\(962\) 4.49086 0.154489i 0.144791 0.00498094i
\(963\) 32.9096 32.9096i 1.06050 1.06050i
\(964\) −9.55663 9.55663i −0.307798 0.307798i
\(965\) −15.7484 + 12.8511i −0.506958 + 0.413692i
\(966\) 61.5220i 1.97944i
\(967\) 37.1279i 1.19395i −0.802259 0.596977i \(-0.796369\pi\)
0.802259 0.596977i \(-0.203631\pi\)
\(968\) 2.34255 0.0752923
\(969\) 113.317i 3.64028i
\(970\) 4.81119 + 5.89586i 0.154478 + 0.189305i
\(971\) −12.7942 −0.410586 −0.205293 0.978701i \(-0.565815\pi\)
−0.205293 + 0.978701i \(0.565815\pi\)
\(972\) −15.2400 15.2400i −0.488822 0.488822i
\(973\) 3.50423 + 3.50423i 0.112341 + 0.112341i
\(974\) 0.818395i 0.0262231i
\(975\) 7.41789 4.89693i 0.237563 0.156827i
\(976\) −2.31872 + 2.31872i −0.0742204 + 0.0742204i
\(977\) −27.6004 −0.883015 −0.441507 0.897258i \(-0.645556\pi\)
−0.441507 + 0.897258i \(0.645556\pi\)
\(978\) 40.0044 40.0044i 1.27920 1.27920i
\(979\) −12.5220 + 12.5220i −0.400204 + 0.400204i
\(980\) 12.7080 + 15.5730i 0.405942 + 0.497460i
\(981\) 27.3921 + 27.3921i 0.874562 + 0.874562i
\(982\) 5.21815 0.166518
\(983\) −3.23105 3.23105i −0.103054 0.103054i 0.653700 0.756754i \(-0.273216\pi\)
−0.756754 + 0.653700i \(0.773216\pi\)
\(984\) 12.5879 12.5879i 0.401288 0.401288i
\(985\) −24.8945 2.52192i −0.793205 0.0803550i
\(986\) −16.5324 + 16.5324i −0.526499 + 0.526499i
\(987\) 72.8047 72.8047i 2.31740 2.31740i
\(988\) 3.71661 3.71661i 0.118241 0.118241i
\(989\) 44.6592 1.42008
\(990\) 14.2264 11.6092i 0.452145 0.368963i
\(991\) −19.0174 + 19.0174i −0.604108 + 0.604108i −0.941400 0.337292i \(-0.890489\pi\)
0.337292 + 0.941400i \(0.390489\pi\)
\(992\) −1.48171 + 1.48171i −0.0470443 + 0.0470443i
\(993\) 45.0897i 1.43088i
\(994\) −7.13237 7.13237i −0.226225 0.226225i
\(995\) −28.7775 2.91528i −0.912309 0.0924207i
\(996\) 9.27768 0.293974
\(997\) 28.6699i 0.907984i −0.891006 0.453992i \(-0.849999\pi\)
0.891006 0.453992i \(-0.150001\pi\)
\(998\) −17.1758 17.1758i −0.543690 0.543690i
\(999\) 2.08887 2.23771i 0.0660889 0.0707979i
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 370.2.h.d.117.1 yes 10
5.3 odd 4 370.2.g.d.43.5 10
37.31 odd 4 370.2.g.d.327.5 yes 10
185.68 even 4 inner 370.2.h.d.253.1 yes 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
370.2.g.d.43.5 10 5.3 odd 4
370.2.g.d.327.5 yes 10 37.31 odd 4
370.2.h.d.117.1 yes 10 1.1 even 1 trivial
370.2.h.d.253.1 yes 10 185.68 even 4 inner