Properties

Label 950.2.f.d.493.8
Level $950$
Weight $2$
Character 950.493
Analytic conductor $7.586$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(493,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.493");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.f (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: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 493.8
Character \(\chi\) \(=\) 950.493
Dual form 950.2.f.d.607.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(1.91489 - 1.91489i) q^{3} +1.00000i q^{4} -2.70806 q^{6} +(2.95447 - 2.95447i) q^{7} +(0.707107 - 0.707107i) q^{8} -4.33358i q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(1.91489 - 1.91489i) q^{3} +1.00000i q^{4} -2.70806 q^{6} +(2.95447 - 2.95447i) q^{7} +(0.707107 - 0.707107i) q^{8} -4.33358i q^{9} -3.90336 q^{11} +(1.91489 + 1.91489i) q^{12} +(-4.27208 + 4.27208i) q^{13} -4.17825 q^{14} -1.00000 q^{16} +(3.82166 - 3.82166i) q^{17} +(-3.06430 + 3.06430i) q^{18} +(-0.797842 - 4.28526i) q^{19} -11.3149i q^{21} +(2.76009 + 2.76009i) q^{22} +(-4.44500 - 4.44500i) q^{23} -2.70806i q^{24} +6.04164 q^{26} +(-2.55366 - 2.55366i) q^{27} +(2.95447 + 2.95447i) q^{28} +2.10793 q^{29} +3.46410i q^{31} +(0.707107 + 0.707107i) q^{32} +(-7.47449 + 7.47449i) q^{33} -5.40464 q^{34} +4.33358 q^{36} +(-1.05164 - 1.05164i) q^{37} +(-2.46598 + 3.59430i) q^{38} +16.3611i q^{39} -6.48808i q^{41} +(-8.00087 + 8.00087i) q^{42} +(6.63336 + 6.63336i) q^{43} -3.90336i q^{44} +6.28618i q^{46} +(2.35306 - 2.35306i) q^{47} +(-1.91489 + 1.91489i) q^{48} -10.4578i q^{49} -14.6361i q^{51} +(-4.27208 - 4.27208i) q^{52} +(3.83975 - 3.83975i) q^{53} +3.61142i q^{54} -4.17825i q^{56} +(-9.73356 - 6.67801i) q^{57} +(-1.49053 - 1.49053i) q^{58} +14.9154 q^{59} -2.00000 q^{61} +(2.44949 - 2.44949i) q^{62} +(-12.8034 - 12.8034i) q^{63} -1.00000i q^{64} +10.5705 q^{66} +(4.04760 + 4.04760i) q^{67} +(3.82166 + 3.82166i) q^{68} -17.0233 q^{69} +1.70103i q^{71} +(-3.06430 - 3.06430i) q^{72} +(5.04174 + 5.04174i) q^{73} +1.48724i q^{74} +(4.28526 - 0.797842i) q^{76} +(-11.5323 + 11.5323i) q^{77} +(11.5691 - 11.5691i) q^{78} -11.8206 q^{79} +3.22082 q^{81} +(-4.58776 + 4.58776i) q^{82} +(2.04560 + 2.04560i) q^{83} +11.3149 q^{84} -9.38099i q^{86} +(4.03645 - 4.03645i) q^{87} +(-2.76009 + 2.76009i) q^{88} -10.9767 q^{89} +25.2435i q^{91} +(4.44500 - 4.44500i) q^{92} +(6.63336 + 6.63336i) q^{93} -3.32773 q^{94} +2.70806 q^{96} +(-3.35802 - 3.35802i) q^{97} +(-7.39475 + 7.39475i) q^{98} +16.9155i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 8 q^{6} - 24 q^{11} - 32 q^{16} + 32 q^{26} + 56 q^{36} - 64 q^{61} + 72 q^{66} + 4 q^{76} - 32 q^{81} + 8 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i
\(3\) 1.91489 1.91489i 1.10556 1.10556i 0.111833 0.993727i \(-0.464328\pi\)
0.993727 0.111833i \(-0.0356723\pi\)
\(4\) 1.00000i 0.500000i
\(5\) 0 0
\(6\) −2.70806 −1.10556
\(7\) 2.95447 2.95447i 1.11668 1.11668i 0.124459 0.992225i \(-0.460280\pi\)
0.992225 0.124459i \(-0.0397195\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 4.33358i 1.44453i
\(10\) 0 0
\(11\) −3.90336 −1.17691 −0.588453 0.808531i \(-0.700263\pi\)
−0.588453 + 0.808531i \(0.700263\pi\)
\(12\) 1.91489 + 1.91489i 0.552780 + 0.552780i
\(13\) −4.27208 + 4.27208i −1.18486 + 1.18486i −0.206394 + 0.978469i \(0.566173\pi\)
−0.978469 + 0.206394i \(0.933827\pi\)
\(14\) −4.17825 −1.11668
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 3.82166 3.82166i 0.926888 0.926888i −0.0706153 0.997504i \(-0.522496\pi\)
0.997504 + 0.0706153i \(0.0224963\pi\)
\(18\) −3.06430 + 3.06430i −0.722263 + 0.722263i
\(19\) −0.797842 4.28526i −0.183037 0.983106i
\(20\) 0 0
\(21\) 11.3149i 2.46912i
\(22\) 2.76009 + 2.76009i 0.588453 + 0.588453i
\(23\) −4.44500 4.44500i −0.926846 0.926846i 0.0706544 0.997501i \(-0.477491\pi\)
−0.997501 + 0.0706544i \(0.977491\pi\)
\(24\) 2.70806i 0.552780i
\(25\) 0 0
\(26\) 6.04164 1.18486
\(27\) −2.55366 2.55366i −0.491451 0.491451i
\(28\) 2.95447 + 2.95447i 0.558342 + 0.558342i
\(29\) 2.10793 0.391433 0.195716 0.980661i \(-0.437297\pi\)
0.195716 + 0.980661i \(0.437297\pi\)
\(30\) 0 0
\(31\) 3.46410i 0.622171i 0.950382 + 0.311086i \(0.100693\pi\)
−0.950382 + 0.311086i \(0.899307\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) −7.47449 + 7.47449i −1.30114 + 1.30114i
\(34\) −5.40464 −0.926888
\(35\) 0 0
\(36\) 4.33358 0.722263
\(37\) −1.05164 1.05164i −0.172888 0.172888i 0.615359 0.788247i \(-0.289011\pi\)
−0.788247 + 0.615359i \(0.789011\pi\)
\(38\) −2.46598 + 3.59430i −0.400034 + 0.583072i
\(39\) 16.3611i 2.61987i
\(40\) 0 0
\(41\) 6.48808i 1.01327i −0.862161 0.506634i \(-0.830890\pi\)
0.862161 0.506634i \(-0.169110\pi\)
\(42\) −8.00087 + 8.00087i −1.23456 + 1.23456i
\(43\) 6.63336 + 6.63336i 1.01158 + 1.01158i 0.999932 + 0.0116460i \(0.00370711\pi\)
0.0116460 + 0.999932i \(0.496293\pi\)
\(44\) 3.90336i 0.588453i
\(45\) 0 0
\(46\) 6.28618i 0.926846i
\(47\) 2.35306 2.35306i 0.343230 0.343230i −0.514350 0.857580i \(-0.671967\pi\)
0.857580 + 0.514350i \(0.171967\pi\)
\(48\) −1.91489 + 1.91489i −0.276390 + 0.276390i
\(49\) 10.4578i 1.49397i
\(50\) 0 0
\(51\) 14.6361i 2.04946i
\(52\) −4.27208 4.27208i −0.592431 0.592431i
\(53\) 3.83975 3.83975i 0.527430 0.527430i −0.392375 0.919805i \(-0.628347\pi\)
0.919805 + 0.392375i \(0.128347\pi\)
\(54\) 3.61142i 0.491451i
\(55\) 0 0
\(56\) 4.17825i 0.558342i
\(57\) −9.73356 6.67801i −1.28924 0.884524i
\(58\) −1.49053 1.49053i −0.195716 0.195716i
\(59\) 14.9154 1.94182 0.970910 0.239443i \(-0.0769648\pi\)
0.970910 + 0.239443i \(0.0769648\pi\)
\(60\) 0 0
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 2.44949 2.44949i 0.311086 0.311086i
\(63\) −12.8034 12.8034i −1.61308 1.61308i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 10.5705 1.30114
\(67\) 4.04760 + 4.04760i 0.494494 + 0.494494i 0.909719 0.415225i \(-0.136297\pi\)
−0.415225 + 0.909719i \(0.636297\pi\)
\(68\) 3.82166 + 3.82166i 0.463444 + 0.463444i
\(69\) −17.0233 −2.04937
\(70\) 0 0
\(71\) 1.70103i 0.201875i 0.994893 + 0.100937i \(0.0321842\pi\)
−0.994893 + 0.100937i \(0.967816\pi\)
\(72\) −3.06430 3.06430i −0.361132 0.361132i
\(73\) 5.04174 + 5.04174i 0.590091 + 0.590091i 0.937656 0.347565i \(-0.112991\pi\)
−0.347565 + 0.937656i \(0.612991\pi\)
\(74\) 1.48724i 0.172888i
\(75\) 0 0
\(76\) 4.28526 0.797842i 0.491553 0.0915187i
\(77\) −11.5323 + 11.5323i −1.31423 + 1.31423i
\(78\) 11.5691 11.5691i 1.30994 1.30994i
\(79\) −11.8206 −1.32992 −0.664961 0.746878i \(-0.731552\pi\)
−0.664961 + 0.746878i \(0.731552\pi\)
\(80\) 0 0
\(81\) 3.22082 0.357869
\(82\) −4.58776 + 4.58776i −0.506634 + 0.506634i
\(83\) 2.04560 + 2.04560i 0.224534 + 0.224534i 0.810404 0.585871i \(-0.199247\pi\)
−0.585871 + 0.810404i \(0.699247\pi\)
\(84\) 11.3149 1.23456
\(85\) 0 0
\(86\) 9.38099i 1.01158i
\(87\) 4.03645 4.03645i 0.432753 0.432753i
\(88\) −2.76009 + 2.76009i −0.294227 + 0.294227i
\(89\) −10.9767 −1.16353 −0.581763 0.813359i \(-0.697637\pi\)
−0.581763 + 0.813359i \(0.697637\pi\)
\(90\) 0 0
\(91\) 25.2435i 2.64623i
\(92\) 4.44500 4.44500i 0.463423 0.463423i
\(93\) 6.63336 + 6.63336i 0.687848 + 0.687848i
\(94\) −3.32773 −0.343230
\(95\) 0 0
\(96\) 2.70806 0.276390
\(97\) −3.35802 3.35802i −0.340955 0.340955i 0.515771 0.856726i \(-0.327505\pi\)
−0.856726 + 0.515771i \(0.827505\pi\)
\(98\) −7.39475 + 7.39475i −0.746983 + 0.746983i
\(99\) 16.9155i 1.70007i
\(100\) 0 0
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) −10.3493 + 10.3493i −1.02473 + 1.02473i
\(103\) 0.884622 0.884622i 0.0871644 0.0871644i −0.662180 0.749345i \(-0.730369\pi\)
0.749345 + 0.662180i \(0.230369\pi\)
\(104\) 6.04164i 0.592431i
\(105\) 0 0
\(106\) −5.43022 −0.527430
\(107\) 4.87001 + 4.87001i 0.470802 + 0.470802i 0.902174 0.431372i \(-0.141970\pi\)
−0.431372 + 0.902174i \(0.641970\pi\)
\(108\) 2.55366 2.55366i 0.245726 0.245726i
\(109\) 0.310347 0.0297259 0.0148629 0.999890i \(-0.495269\pi\)
0.0148629 + 0.999890i \(0.495269\pi\)
\(110\) 0 0
\(111\) −4.02753 −0.382276
\(112\) −2.95447 + 2.95447i −0.279171 + 0.279171i
\(113\) −7.00273 + 7.00273i −0.658762 + 0.658762i −0.955087 0.296326i \(-0.904239\pi\)
0.296326 + 0.955087i \(0.404239\pi\)
\(114\) 2.16060 + 11.6047i 0.202359 + 1.08688i
\(115\) 0 0
\(116\) 2.10793i 0.195716i
\(117\) 18.5134 + 18.5134i 1.71157 + 1.71157i
\(118\) −10.5468 10.5468i −0.970910 0.970910i
\(119\) 22.5819i 2.07008i
\(120\) 0 0
\(121\) 4.23619 0.385109
\(122\) 1.41421 + 1.41421i 0.128037 + 0.128037i
\(123\) −12.4239 12.4239i −1.12023 1.12023i
\(124\) −3.46410 −0.311086
\(125\) 0 0
\(126\) 18.1068i 1.61308i
\(127\) 13.6515 + 13.6515i 1.21137 + 1.21137i 0.970575 + 0.240798i \(0.0774091\pi\)
0.240798 + 0.970575i \(0.422591\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) 25.4043 2.23672
\(130\) 0 0
\(131\) −0.667162 −0.0582902 −0.0291451 0.999575i \(-0.509278\pi\)
−0.0291451 + 0.999575i \(0.509278\pi\)
\(132\) −7.47449 7.47449i −0.650570 0.650570i
\(133\) −15.0179 10.3035i −1.30221 0.893423i
\(134\) 5.72418i 0.494494i
\(135\) 0 0
\(136\) 5.40464i 0.463444i
\(137\) 9.46015 9.46015i 0.808235 0.808235i −0.176132 0.984367i \(-0.556358\pi\)
0.984367 + 0.176132i \(0.0563585\pi\)
\(138\) 12.0373 + 12.0373i 1.02468 + 1.02468i
\(139\) 20.3772i 1.72837i 0.503171 + 0.864187i \(0.332167\pi\)
−0.503171 + 0.864187i \(0.667833\pi\)
\(140\) 0 0
\(141\) 9.01170i 0.758922i
\(142\) 1.20281 1.20281i 0.100937 0.100937i
\(143\) 16.6755 16.6755i 1.39447 1.39447i
\(144\) 4.33358i 0.361132i
\(145\) 0 0
\(146\) 7.13010i 0.590091i
\(147\) −20.0254 20.0254i −1.65167 1.65167i
\(148\) 1.05164 1.05164i 0.0864441 0.0864441i
\(149\) 1.80671i 0.148012i −0.997258 0.0740059i \(-0.976422\pi\)
0.997258 0.0740059i \(-0.0235784\pi\)
\(150\) 0 0
\(151\) 6.32069i 0.514370i 0.966362 + 0.257185i \(0.0827950\pi\)
−0.966362 + 0.257185i \(0.917205\pi\)
\(152\) −3.59430 2.46598i −0.291536 0.200017i
\(153\) −16.5615 16.5615i −1.33892 1.33892i
\(154\) 16.3092 1.31423
\(155\) 0 0
\(156\) −16.3611 −1.30994
\(157\) 10.8172 10.8172i 0.863309 0.863309i −0.128412 0.991721i \(-0.540988\pi\)
0.991721 + 0.128412i \(0.0409879\pi\)
\(158\) 8.35842 + 8.35842i 0.664961 + 0.664961i
\(159\) 14.7054i 1.16621i
\(160\) 0 0
\(161\) −26.2652 −2.06999
\(162\) −2.27746 2.27746i −0.178934 0.178934i
\(163\) 11.9456 + 11.9456i 0.935648 + 0.935648i 0.998051 0.0624032i \(-0.0198765\pi\)
−0.0624032 + 0.998051i \(0.519876\pi\)
\(164\) 6.48808 0.506634
\(165\) 0 0
\(166\) 2.89291i 0.224534i
\(167\) 7.71843 + 7.71843i 0.597270 + 0.597270i 0.939585 0.342315i \(-0.111211\pi\)
−0.342315 + 0.939585i \(0.611211\pi\)
\(168\) −8.00087 8.00087i −0.617281 0.617281i
\(169\) 23.5014i 1.80780i
\(170\) 0 0
\(171\) −18.5705 + 3.45751i −1.42012 + 0.264403i
\(172\) −6.63336 + 6.63336i −0.505789 + 0.505789i
\(173\) −2.36527 + 2.36527i −0.179828 + 0.179828i −0.791281 0.611453i \(-0.790585\pi\)
0.611453 + 0.791281i \(0.290585\pi\)
\(174\) −5.70840 −0.432753
\(175\) 0 0
\(176\) 3.90336 0.294227
\(177\) 28.5613 28.5613i 2.14680 2.14680i
\(178\) 7.76168 + 7.76168i 0.581763 + 0.581763i
\(179\) −9.68475 −0.723872 −0.361936 0.932203i \(-0.617884\pi\)
−0.361936 + 0.932203i \(0.617884\pi\)
\(180\) 0 0
\(181\) 14.1370i 1.05080i 0.850857 + 0.525398i \(0.176084\pi\)
−0.850857 + 0.525398i \(0.823916\pi\)
\(182\) 17.8498 17.8498i 1.32312 1.32312i
\(183\) −3.82977 + 3.82977i −0.283105 + 0.283105i
\(184\) −6.28618 −0.463423
\(185\) 0 0
\(186\) 9.38099i 0.687848i
\(187\) −14.9173 + 14.9173i −1.09086 + 1.09086i
\(188\) 2.35306 + 2.35306i 0.171615 + 0.171615i
\(189\) −15.0894 −1.09759
\(190\) 0 0
\(191\) −0.0275325 −0.00199218 −0.000996089 1.00000i \(-0.500317\pi\)
−0.000996089 1.00000i \(0.500317\pi\)
\(192\) −1.91489 1.91489i −0.138195 0.138195i
\(193\) 16.8244 16.8244i 1.21105 1.21105i 0.240368 0.970682i \(-0.422732\pi\)
0.970682 0.240368i \(-0.0772680\pi\)
\(194\) 4.74896i 0.340955i
\(195\) 0 0
\(196\) 10.4578 0.746983
\(197\) 12.3494 12.3494i 0.879861 0.879861i −0.113658 0.993520i \(-0.536257\pi\)
0.993520 + 0.113658i \(0.0362569\pi\)
\(198\) 11.9611 11.9611i 0.850037 0.850037i
\(199\) 5.01141i 0.355250i 0.984098 + 0.177625i \(0.0568414\pi\)
−0.984098 + 0.177625i \(0.943159\pi\)
\(200\) 0 0
\(201\) 15.5014 1.09339
\(202\) 4.24264 + 4.24264i 0.298511 + 0.298511i
\(203\) 6.22781 6.22781i 0.437107 0.437107i
\(204\) 14.6361 1.02473
\(205\) 0 0
\(206\) −1.25104 −0.0871644
\(207\) −19.2628 + 19.2628i −1.33885 + 1.33885i
\(208\) 4.27208 4.27208i 0.296216 0.296216i
\(209\) 3.11426 + 16.7269i 0.215418 + 1.15702i
\(210\) 0 0
\(211\) 19.5714i 1.34735i −0.739028 0.673675i \(-0.764715\pi\)
0.739028 0.673675i \(-0.235285\pi\)
\(212\) 3.83975 + 3.83975i 0.263715 + 0.263715i
\(213\) 3.25727 + 3.25727i 0.223185 + 0.223185i
\(214\) 6.88724i 0.470802i
\(215\) 0 0
\(216\) −3.61142 −0.245726
\(217\) 10.2346 + 10.2346i 0.694768 + 0.694768i
\(218\) −0.219449 0.219449i −0.0148629 0.0148629i
\(219\) 19.3087 1.30476
\(220\) 0 0
\(221\) 32.6529i 2.19647i
\(222\) 2.84790 + 2.84790i 0.191138 + 0.191138i
\(223\) 7.65955 7.65955i 0.512921 0.512921i −0.402499 0.915420i \(-0.631858\pi\)
0.915420 + 0.402499i \(0.131858\pi\)
\(224\) 4.17825 0.279171
\(225\) 0 0
\(226\) 9.90336 0.658762
\(227\) −17.0784 17.0784i −1.13353 1.13353i −0.989586 0.143945i \(-0.954021\pi\)
−0.143945 0.989586i \(-0.545979\pi\)
\(228\) 6.67801 9.73356i 0.442262 0.644621i
\(229\) 17.5812i 1.16180i 0.813976 + 0.580899i \(0.197299\pi\)
−0.813976 + 0.580899i \(0.802701\pi\)
\(230\) 0 0
\(231\) 44.1662i 2.90593i
\(232\) 1.49053 1.49053i 0.0978582 0.0978582i
\(233\) 10.7208 + 10.7208i 0.702343 + 0.702343i 0.964913 0.262570i \(-0.0845699\pi\)
−0.262570 + 0.964913i \(0.584570\pi\)
\(234\) 26.1819i 1.71157i
\(235\) 0 0
\(236\) 14.9154i 0.970910i
\(237\) −22.6351 + 22.6351i −1.47031 + 1.47031i
\(238\) −15.9678 + 15.9678i −1.03504 + 1.03504i
\(239\) 2.88649i 0.186712i −0.995633 0.0933559i \(-0.970241\pi\)
0.995633 0.0933559i \(-0.0297594\pi\)
\(240\) 0 0
\(241\) 2.89291i 0.186349i −0.995650 0.0931744i \(-0.970299\pi\)
0.995650 0.0931744i \(-0.0297014\pi\)
\(242\) −2.99544 2.99544i −0.192554 0.192554i
\(243\) 13.8285 13.8285i 0.887097 0.887097i
\(244\) 2.00000i 0.128037i
\(245\) 0 0
\(246\) 17.5701i 1.12023i
\(247\) 21.7154 + 14.8985i 1.38172 + 0.947972i
\(248\) 2.44949 + 2.44949i 0.155543 + 0.155543i
\(249\) 7.83417 0.496471
\(250\) 0 0
\(251\) 12.3772 0.781244 0.390622 0.920551i \(-0.372260\pi\)
0.390622 + 0.920551i \(0.372260\pi\)
\(252\) 12.8034 12.8034i 0.806540 0.806540i
\(253\) 17.3504 + 17.3504i 1.09081 + 1.09081i
\(254\) 19.3061i 1.21137i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −6.79772 6.79772i −0.424030 0.424030i 0.462559 0.886589i \(-0.346931\pi\)
−0.886589 + 0.462559i \(0.846931\pi\)
\(258\) −17.9635 17.9635i −1.11836 1.11836i
\(259\) −6.21406 −0.386123
\(260\) 0 0
\(261\) 9.13489i 0.565435i
\(262\) 0.471755 + 0.471755i 0.0291451 + 0.0291451i
\(263\) −14.2674 14.2674i −0.879763 0.879763i 0.113747 0.993510i \(-0.463715\pi\)
−0.993510 + 0.113747i \(0.963715\pi\)
\(264\) 10.5705i 0.650570i
\(265\) 0 0
\(266\) 3.33358 + 17.9049i 0.204395 + 1.09782i
\(267\) −21.0191 + 21.0191i −1.28635 + 1.28635i
\(268\) −4.04760 + 4.04760i −0.247247 + 0.247247i
\(269\) 20.4577 1.24733 0.623664 0.781692i \(-0.285643\pi\)
0.623664 + 0.781692i \(0.285643\pi\)
\(270\) 0 0
\(271\) −0.414105 −0.0251551 −0.0125775 0.999921i \(-0.504004\pi\)
−0.0125775 + 0.999921i \(0.504004\pi\)
\(272\) −3.82166 + 3.82166i −0.231722 + 0.231722i
\(273\) 48.3384 + 48.3384i 2.92557 + 2.92557i
\(274\) −13.3787 −0.808235
\(275\) 0 0
\(276\) 17.0233i 1.02468i
\(277\) 8.26575 8.26575i 0.496641 0.496641i −0.413750 0.910391i \(-0.635781\pi\)
0.910391 + 0.413750i \(0.135781\pi\)
\(278\) 14.4089 14.4089i 0.864187 0.864187i
\(279\) 15.0120 0.898743
\(280\) 0 0
\(281\) 23.6412i 1.41032i −0.709050 0.705158i \(-0.750876\pi\)
0.709050 0.705158i \(-0.249124\pi\)
\(282\) −6.37223 + 6.37223i −0.379461 + 0.379461i
\(283\) 17.0281 + 17.0281i 1.01221 + 1.01221i 0.999924 + 0.0122889i \(0.00391178\pi\)
0.0122889 + 0.999924i \(0.496088\pi\)
\(284\) −1.70103 −0.100937
\(285\) 0 0
\(286\) −23.5827 −1.39447
\(287\) −19.1688 19.1688i −1.13150 1.13150i
\(288\) 3.06430 3.06430i 0.180566 0.180566i
\(289\) 12.2101i 0.718244i
\(290\) 0 0
\(291\) −12.8604 −0.753893
\(292\) −5.04174 + 5.04174i −0.295046 + 0.295046i
\(293\) −15.7814 + 15.7814i −0.921957 + 0.921957i −0.997168 0.0752111i \(-0.976037\pi\)
0.0752111 + 0.997168i \(0.476037\pi\)
\(294\) 28.3202i 1.65167i
\(295\) 0 0
\(296\) −1.48724 −0.0864441
\(297\) 9.96783 + 9.96783i 0.578392 + 0.578392i
\(298\) −1.27754 + 1.27754i −0.0740059 + 0.0740059i
\(299\) 37.9788 2.19637
\(300\) 0 0
\(301\) 39.1961 2.25923
\(302\) 4.46940 4.46940i 0.257185 0.257185i
\(303\) −11.4893 + 11.4893i −0.660044 + 0.660044i
\(304\) 0.797842 + 4.28526i 0.0457594 + 0.245776i
\(305\) 0 0
\(306\) 23.4215i 1.33892i
\(307\) 0.784894 + 0.784894i 0.0447962 + 0.0447962i 0.729150 0.684354i \(-0.239916\pi\)
−0.684354 + 0.729150i \(0.739916\pi\)
\(308\) −11.5323 11.5323i −0.657116 0.657116i
\(309\) 3.38790i 0.192731i
\(310\) 0 0
\(311\) 15.6786 0.889050 0.444525 0.895766i \(-0.353372\pi\)
0.444525 + 0.895766i \(0.353372\pi\)
\(312\) 11.5691 + 11.5691i 0.654969 + 0.654969i
\(313\) −3.46164 3.46164i −0.195663 0.195663i 0.602475 0.798138i \(-0.294181\pi\)
−0.798138 + 0.602475i \(0.794181\pi\)
\(314\) −15.2979 −0.863309
\(315\) 0 0
\(316\) 11.8206i 0.664961i
\(317\) −12.7474 12.7474i −0.715965 0.715965i 0.251812 0.967776i \(-0.418974\pi\)
−0.967776 + 0.251812i \(0.918974\pi\)
\(318\) −10.3983 + 10.3983i −0.583106 + 0.583106i
\(319\) −8.22801 −0.460680
\(320\) 0 0
\(321\) 18.6510 1.04100
\(322\) 18.5723 + 18.5723i 1.03499 + 1.03499i
\(323\) −19.4259 13.3277i −1.08088 0.741574i
\(324\) 3.22082i 0.178934i
\(325\) 0 0
\(326\) 16.8936i 0.935648i
\(327\) 0.594280 0.594280i 0.0328638 0.0328638i
\(328\) −4.58776 4.58776i −0.253317 0.253317i
\(329\) 13.9041i 0.766558i
\(330\) 0 0
\(331\) 8.59601i 0.472479i −0.971695 0.236240i \(-0.924085\pi\)
0.971695 0.236240i \(-0.0759151\pi\)
\(332\) −2.04560 + 2.04560i −0.112267 + 0.112267i
\(333\) −4.55736 + 4.55736i −0.249742 + 0.249742i
\(334\) 10.9155i 0.597270i
\(335\) 0 0
\(336\) 11.3149i 0.617281i
\(337\) 2.01319 + 2.01319i 0.109666 + 0.109666i 0.759810 0.650145i \(-0.225292\pi\)
−0.650145 + 0.759810i \(0.725292\pi\)
\(338\) −16.6180 + 16.6180i −0.903900 + 0.903900i
\(339\) 26.8189i 1.45660i
\(340\) 0 0
\(341\) 13.5216i 0.732237i
\(342\) 15.5762 + 10.6865i 0.842263 + 0.577860i
\(343\) −10.2158 10.2158i −0.551603 0.551603i
\(344\) 9.38099 0.505789
\(345\) 0 0
\(346\) 3.34499 0.179828
\(347\) −4.87329 + 4.87329i −0.261612 + 0.261612i −0.825709 0.564097i \(-0.809225\pi\)
0.564097 + 0.825709i \(0.309225\pi\)
\(348\) 4.03645 + 4.03645i 0.216376 + 0.216376i
\(349\) 21.9692i 1.17599i −0.808866 0.587993i \(-0.799918\pi\)
0.808866 0.587993i \(-0.200082\pi\)
\(350\) 0 0
\(351\) 21.8189 1.16461
\(352\) −2.76009 2.76009i −0.147113 0.147113i
\(353\) 2.66894 + 2.66894i 0.142053 + 0.142053i 0.774557 0.632504i \(-0.217973\pi\)
−0.632504 + 0.774557i \(0.717973\pi\)
\(354\) −40.3918 −2.14680
\(355\) 0 0
\(356\) 10.9767i 0.581763i
\(357\) −43.2418 43.2418i −2.28860 2.28860i
\(358\) 6.84815 + 6.84815i 0.361936 + 0.361936i
\(359\) 3.01612i 0.159185i 0.996827 + 0.0795923i \(0.0253619\pi\)
−0.996827 + 0.0795923i \(0.974638\pi\)
\(360\) 0 0
\(361\) −17.7269 + 6.83792i −0.932995 + 0.359890i
\(362\) 9.99638 9.99638i 0.525398 0.525398i
\(363\) 8.11183 8.11183i 0.425761 0.425761i
\(364\) −25.2435 −1.32312
\(365\) 0 0
\(366\) 5.41612 0.283105
\(367\) −24.8917 + 24.8917i −1.29934 + 1.29934i −0.370510 + 0.928829i \(0.620817\pi\)
−0.928829 + 0.370510i \(0.879183\pi\)
\(368\) 4.44500 + 4.44500i 0.231712 + 0.231712i
\(369\) −28.1166 −1.46369
\(370\) 0 0
\(371\) 22.6888i 1.17795i
\(372\) −6.63336 + 6.63336i −0.343924 + 0.343924i
\(373\) −20.0368 + 20.0368i −1.03747 + 1.03747i −0.0381967 + 0.999270i \(0.512161\pi\)
−0.999270 + 0.0381967i \(0.987839\pi\)
\(374\) 21.0962 1.09086
\(375\) 0 0
\(376\) 3.32773i 0.171615i
\(377\) −9.00526 + 9.00526i −0.463794 + 0.463794i
\(378\) 10.6698 + 10.6698i 0.548796 + 0.548796i
\(379\) 7.82292 0.401836 0.200918 0.979608i \(-0.435607\pi\)
0.200918 + 0.979608i \(0.435607\pi\)
\(380\) 0 0
\(381\) 52.2821 2.67849
\(382\) 0.0194684 + 0.0194684i 0.000996089 + 0.000996089i
\(383\) −17.0323 + 17.0323i −0.870310 + 0.870310i −0.992506 0.122196i \(-0.961006\pi\)
0.122196 + 0.992506i \(0.461006\pi\)
\(384\) 2.70806i 0.138195i
\(385\) 0 0
\(386\) −23.7933 −1.21105
\(387\) 28.7462 28.7462i 1.46125 1.46125i
\(388\) 3.35802 3.35802i 0.170478 0.170478i
\(389\) 31.3894i 1.59151i 0.605622 + 0.795753i \(0.292924\pi\)
−0.605622 + 0.795753i \(0.707076\pi\)
\(390\) 0 0
\(391\) −33.9745 −1.71817
\(392\) −7.39475 7.39475i −0.373491 0.373491i
\(393\) −1.27754 + 1.27754i −0.0644433 + 0.0644433i
\(394\) −17.4648 −0.879861
\(395\) 0 0
\(396\) −16.9155 −0.850037
\(397\) −3.50332 + 3.50332i −0.175827 + 0.175827i −0.789534 0.613707i \(-0.789678\pi\)
0.613707 + 0.789534i \(0.289678\pi\)
\(398\) 3.54360 3.54360i 0.177625 0.177625i
\(399\) −48.4875 + 9.02753i −2.42741 + 0.451942i
\(400\) 0 0
\(401\) 2.27222i 0.113469i 0.998389 + 0.0567345i \(0.0180689\pi\)
−0.998389 + 0.0567345i \(0.981931\pi\)
\(402\) −10.9612 10.9612i −0.546693 0.546693i
\(403\) −14.7989 14.7989i −0.737187 0.737187i
\(404\) 6.00000i 0.298511i
\(405\) 0 0
\(406\) −8.80746 −0.437107
\(407\) 4.10492 + 4.10492i 0.203473 + 0.203473i
\(408\) −10.3493 10.3493i −0.512365 0.512365i
\(409\) −10.2870 −0.508657 −0.254329 0.967118i \(-0.581855\pi\)
−0.254329 + 0.967118i \(0.581855\pi\)
\(410\) 0 0
\(411\) 36.2302i 1.78710i
\(412\) 0.884622 + 0.884622i 0.0435822 + 0.0435822i
\(413\) 44.0671 44.0671i 2.16840 2.16840i
\(414\) 27.2417 1.33885
\(415\) 0 0
\(416\) −6.04164 −0.296216
\(417\) 39.0201 + 39.0201i 1.91082 + 1.91082i
\(418\) 9.62559 14.0298i 0.470803 0.686221i
\(419\) 35.2927i 1.72416i 0.506769 + 0.862082i \(0.330840\pi\)
−0.506769 + 0.862082i \(0.669160\pi\)
\(420\) 0 0
\(421\) 23.6067i 1.15052i 0.817971 + 0.575260i \(0.195099\pi\)
−0.817971 + 0.575260i \(0.804901\pi\)
\(422\) −13.8391 + 13.8391i −0.673675 + 0.673675i
\(423\) −10.1972 10.1972i −0.495804 0.495804i
\(424\) 5.43022i 0.263715i
\(425\) 0 0
\(426\) 4.60648i 0.223185i
\(427\) −5.90894 + 5.90894i −0.285953 + 0.285953i
\(428\) −4.87001 + 4.87001i −0.235401 + 0.235401i
\(429\) 63.8633i 3.08335i
\(430\) 0 0
\(431\) 7.05927i 0.340033i 0.985441 + 0.170016i \(0.0543821\pi\)
−0.985441 + 0.170016i \(0.945618\pi\)
\(432\) 2.55366 + 2.55366i 0.122863 + 0.122863i
\(433\) 12.8930 12.8930i 0.619600 0.619600i −0.325829 0.945429i \(-0.605643\pi\)
0.945429 + 0.325829i \(0.105643\pi\)
\(434\) 14.4739i 0.694768i
\(435\) 0 0
\(436\) 0.310347i 0.0148629i
\(437\) −15.5016 + 22.5944i −0.741541 + 1.08084i
\(438\) −13.6533 13.6533i −0.652382 0.652382i
\(439\) −31.1306 −1.48578 −0.742892 0.669412i \(-0.766546\pi\)
−0.742892 + 0.669412i \(0.766546\pi\)
\(440\) 0 0
\(441\) −45.3195 −2.15807
\(442\) 23.0891 23.0891i 1.09824 1.09824i
\(443\) −14.1929 14.1929i −0.674324 0.674324i 0.284386 0.958710i \(-0.408210\pi\)
−0.958710 + 0.284386i \(0.908210\pi\)
\(444\) 4.02753i 0.191138i
\(445\) 0 0
\(446\) −10.8322 −0.512921
\(447\) −3.45965 3.45965i −0.163636 0.163636i
\(448\) −2.95447 2.95447i −0.139585 0.139585i
\(449\) −8.10691 −0.382589 −0.191294 0.981533i \(-0.561269\pi\)
−0.191294 + 0.981533i \(0.561269\pi\)
\(450\) 0 0
\(451\) 25.3253i 1.19252i
\(452\) −7.00273 7.00273i −0.329381 0.329381i
\(453\) 12.1034 + 12.1034i 0.568667 + 0.568667i
\(454\) 24.1525i 1.13353i
\(455\) 0 0
\(456\) −11.6047 + 2.16060i −0.543441 + 0.101179i
\(457\) 8.09821 8.09821i 0.378818 0.378818i −0.491858 0.870676i \(-0.663682\pi\)
0.870676 + 0.491858i \(0.163682\pi\)
\(458\) 12.4318 12.4318i 0.580899 0.580899i
\(459\) −19.5184 −0.911041
\(460\) 0 0
\(461\) −29.4201 −1.37023 −0.685116 0.728434i \(-0.740249\pi\)
−0.685116 + 0.728434i \(0.740249\pi\)
\(462\) 31.2303 31.2303i 1.45296 1.45296i
\(463\) −16.1908 16.1908i −0.752452 0.752452i 0.222484 0.974936i \(-0.428583\pi\)
−0.974936 + 0.222484i \(0.928583\pi\)
\(464\) −2.10793 −0.0978582
\(465\) 0 0
\(466\) 15.1615i 0.702343i
\(467\) 26.2293 26.2293i 1.21375 1.21375i 0.243961 0.969785i \(-0.421553\pi\)
0.969785 0.243961i \(-0.0784470\pi\)
\(468\) −18.5134 + 18.5134i −0.855783 + 0.855783i
\(469\) 23.9170 1.10439
\(470\) 0 0
\(471\) 41.4275i 1.90888i
\(472\) 10.5468 10.5468i 0.485455 0.485455i
\(473\) −25.8924 25.8924i −1.19053 1.19053i
\(474\) 32.0109 1.47031
\(475\) 0 0
\(476\) 22.5819 1.03504
\(477\) −16.6399 16.6399i −0.761887 0.761887i
\(478\) −2.04106 + 2.04106i −0.0933559 + 0.0933559i
\(479\) 26.9048i 1.22931i 0.788795 + 0.614657i \(0.210705\pi\)
−0.788795 + 0.614657i \(0.789295\pi\)
\(480\) 0 0
\(481\) 8.98537 0.409697
\(482\) −2.04560 + 2.04560i −0.0931744 + 0.0931744i
\(483\) −50.2949 + 50.2949i −2.28850 + 2.28850i
\(484\) 4.23619i 0.192554i
\(485\) 0 0
\(486\) −19.5564 −0.887097
\(487\) 26.8151 + 26.8151i 1.21511 + 1.21511i 0.969325 + 0.245781i \(0.0790445\pi\)
0.245781 + 0.969325i \(0.420955\pi\)
\(488\) −1.41421 + 1.41421i −0.0640184 + 0.0640184i
\(489\) 45.7488 2.06883
\(490\) 0 0
\(491\) 10.8604 0.490125 0.245063 0.969507i \(-0.421191\pi\)
0.245063 + 0.969507i \(0.421191\pi\)
\(492\) 12.4239 12.4239i 0.560114 0.560114i
\(493\) 8.05579 8.05579i 0.362815 0.362815i
\(494\) −4.82027 25.8900i −0.216874 1.16485i
\(495\) 0 0
\(496\) 3.46410i 0.155543i
\(497\) 5.02563 + 5.02563i 0.225430 + 0.225430i
\(498\) −5.53960 5.53960i −0.248235 0.248235i
\(499\) 19.5827i 0.876641i −0.898819 0.438320i \(-0.855574\pi\)
0.898819 0.438320i \(-0.144426\pi\)
\(500\) 0 0
\(501\) 29.5598 1.32064
\(502\) −8.75203 8.75203i −0.390622 0.390622i
\(503\) −8.89712 8.89712i −0.396703 0.396703i 0.480365 0.877068i \(-0.340504\pi\)
−0.877068 + 0.480365i \(0.840504\pi\)
\(504\) −18.1068 −0.806540
\(505\) 0 0
\(506\) 24.5372i 1.09081i
\(507\) −45.0025 45.0025i −1.99863 1.99863i
\(508\) −13.6515 + 13.6515i −0.605687 + 0.605687i
\(509\) 37.2433 1.65078 0.825391 0.564561i \(-0.190955\pi\)
0.825391 + 0.564561i \(0.190955\pi\)
\(510\) 0 0
\(511\) 29.7913 1.31789
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −8.90567 + 12.9805i −0.393195 + 0.573103i
\(514\) 9.61343i 0.424030i
\(515\) 0 0
\(516\) 25.4043i 1.11836i
\(517\) −9.18485 + 9.18485i −0.403949 + 0.403949i
\(518\) 4.39400 + 4.39400i 0.193061 + 0.193061i
\(519\) 9.05844i 0.397621i
\(520\) 0 0
\(521\) 10.7039i 0.468948i −0.972122 0.234474i \(-0.924663\pi\)
0.972122 0.234474i \(-0.0753368\pi\)
\(522\) −6.45934 + 6.45934i −0.282718 + 0.282718i
\(523\) −28.4254 + 28.4254i −1.24295 + 1.24295i −0.284185 + 0.958769i \(0.591723\pi\)
−0.958769 + 0.284185i \(0.908277\pi\)
\(524\) 0.667162i 0.0291451i
\(525\) 0 0
\(526\) 20.1771i 0.879763i
\(527\) 13.2386 + 13.2386i 0.576683 + 0.576683i
\(528\) 7.47449 7.47449i 0.325285 0.325285i
\(529\) 16.5160i 0.718089i
\(530\) 0 0
\(531\) 64.6371i 2.80501i
\(532\) 10.3035 15.0179i 0.446712 0.651107i
\(533\) 27.7176 + 27.7176i 1.20058 + 1.20058i
\(534\) 29.7255 1.28635
\(535\) 0 0
\(536\) 5.72418 0.247247
\(537\) −18.5452 + 18.5452i −0.800284 + 0.800284i
\(538\) −14.4658 14.4658i −0.623664 0.623664i
\(539\) 40.8204i 1.75826i
\(540\) 0 0
\(541\) −14.2484 −0.612584 −0.306292 0.951938i \(-0.599088\pi\)
−0.306292 + 0.951938i \(0.599088\pi\)
\(542\) 0.292816 + 0.292816i 0.0125775 + 0.0125775i
\(543\) 27.0708 + 27.0708i 1.16172 + 1.16172i
\(544\) 5.40464 0.231722
\(545\) 0 0
\(546\) 68.3608i 2.92557i
\(547\) −12.9130 12.9130i −0.552119 0.552119i 0.374933 0.927052i \(-0.377666\pi\)
−0.927052 + 0.374933i \(0.877666\pi\)
\(548\) 9.46015 + 9.46015i 0.404117 + 0.404117i
\(549\) 8.66716i 0.369905i
\(550\) 0 0
\(551\) −1.68180 9.03303i −0.0716469 0.384820i
\(552\) −12.0373 + 12.0373i −0.512342 + 0.512342i
\(553\) −34.9236 + 34.9236i −1.48510 + 1.48510i
\(554\) −11.6895 −0.496641
\(555\) 0 0
\(556\) −20.3772 −0.864187
\(557\) −0.294848 + 0.294848i −0.0124931 + 0.0124931i −0.713326 0.700833i \(-0.752812\pi\)
0.700833 + 0.713326i \(0.252812\pi\)
\(558\) −10.6151 10.6151i −0.449371 0.449371i
\(559\) −56.6766 −2.39716
\(560\) 0 0
\(561\) 57.1299i 2.41202i
\(562\) −16.7168 + 16.7168i −0.705158 + 0.705158i
\(563\) 32.5972 32.5972i 1.37381 1.37381i 0.519091 0.854719i \(-0.326271\pi\)
0.854719 0.519091i \(-0.173729\pi\)
\(564\) 9.01170 0.379461
\(565\) 0 0
\(566\) 24.0813i 1.01221i
\(567\) 9.51580 9.51580i 0.399626 0.399626i
\(568\) 1.20281 + 1.20281i 0.0504687 + 0.0504687i
\(569\) −24.2387 −1.01614 −0.508070 0.861315i \(-0.669641\pi\)
−0.508070 + 0.861315i \(0.669641\pi\)
\(570\) 0 0
\(571\) −31.8082 −1.33113 −0.665566 0.746339i \(-0.731810\pi\)
−0.665566 + 0.746339i \(0.731810\pi\)
\(572\) 16.6755 + 16.6755i 0.697236 + 0.697236i
\(573\) −0.0527215 + 0.0527215i −0.00220247 + 0.00220247i
\(574\) 27.1088i 1.13150i
\(575\) 0 0
\(576\) −4.33358 −0.180566
\(577\) −20.9508 + 20.9508i −0.872194 + 0.872194i −0.992711 0.120518i \(-0.961545\pi\)
0.120518 + 0.992711i \(0.461545\pi\)
\(578\) −8.63388 + 8.63388i −0.359122 + 0.359122i
\(579\) 64.4338i 2.67778i
\(580\) 0 0
\(581\) 12.0873 0.501466
\(582\) 9.09371 + 9.09371i 0.376946 + 0.376946i
\(583\) −14.9879 + 14.9879i −0.620736 + 0.620736i
\(584\) 7.13010 0.295046
\(585\) 0 0
\(586\) 22.3182 0.921957
\(587\) −5.45185 + 5.45185i −0.225022 + 0.225022i −0.810609 0.585587i \(-0.800864\pi\)
0.585587 + 0.810609i \(0.300864\pi\)
\(588\) 20.0254 20.0254i 0.825834 0.825834i
\(589\) 14.8446 2.76381i 0.611660 0.113881i
\(590\) 0 0
\(591\) 47.2956i 1.94548i
\(592\) 1.05164 + 1.05164i 0.0432220 + 0.0432220i
\(593\) −5.88700 5.88700i −0.241750 0.241750i 0.575824 0.817574i \(-0.304681\pi\)
−0.817574 + 0.575824i \(0.804681\pi\)
\(594\) 14.0966i 0.578392i
\(595\) 0 0
\(596\) 1.80671 0.0740059
\(597\) 9.59629 + 9.59629i 0.392750 + 0.392750i
\(598\) −26.8551 26.8551i −1.09819 1.09819i
\(599\) −20.8668 −0.852595 −0.426297 0.904583i \(-0.640182\pi\)
−0.426297 + 0.904583i \(0.640182\pi\)
\(600\) 0 0
\(601\) 13.0125i 0.530790i 0.964140 + 0.265395i \(0.0855024\pi\)
−0.964140 + 0.265395i \(0.914498\pi\)
\(602\) −27.7158 27.7158i −1.12961 1.12961i
\(603\) 17.5406 17.5406i 0.714309 0.714309i
\(604\) −6.32069 −0.257185
\(605\) 0 0
\(606\) 16.2484 0.660044
\(607\) −31.0710 31.0710i −1.26113 1.26113i −0.950544 0.310589i \(-0.899474\pi\)
−0.310589 0.950544i \(-0.600526\pi\)
\(608\) 2.46598 3.59430i 0.100009 0.145768i
\(609\) 23.8511i 0.966496i
\(610\) 0 0
\(611\) 20.1050i 0.813360i
\(612\) 16.5615 16.5615i 0.669458 0.669458i
\(613\) 1.48834 + 1.48834i 0.0601134 + 0.0601134i 0.736524 0.676411i \(-0.236466\pi\)
−0.676411 + 0.736524i \(0.736466\pi\)
\(614\) 1.11001i 0.0447962i
\(615\) 0 0
\(616\) 16.3092i 0.657116i
\(617\) 22.9244 22.9244i 0.922901 0.922901i −0.0743326 0.997234i \(-0.523683\pi\)
0.997234 + 0.0743326i \(0.0236827\pi\)
\(618\) −2.39561 + 2.39561i −0.0963655 + 0.0963655i
\(619\) 4.72223i 0.189802i 0.995487 + 0.0949012i \(0.0302535\pi\)
−0.995487 + 0.0949012i \(0.969746\pi\)
\(620\) 0 0
\(621\) 22.7020i 0.911000i
\(622\) −11.0864 11.0864i −0.444525 0.444525i
\(623\) −32.4302 + 32.4302i −1.29929 + 1.29929i
\(624\) 16.3611i 0.654969i
\(625\) 0 0
\(626\) 4.89550i 0.195663i
\(627\) 37.9936 + 26.0667i 1.51732 + 1.04100i
\(628\) 10.8172 + 10.8172i 0.431655 + 0.431655i
\(629\) −8.03800 −0.320496
\(630\) 0 0
\(631\) 6.04291 0.240564 0.120282 0.992740i \(-0.461620\pi\)
0.120282 + 0.992740i \(0.461620\pi\)
\(632\) −8.35842 + 8.35842i −0.332480 + 0.332480i
\(633\) −37.4770 37.4770i −1.48958 1.48958i
\(634\) 18.0275i 0.715965i
\(635\) 0 0
\(636\) 14.7054 0.583106
\(637\) 44.6764 + 44.6764i 1.77014 + 1.77014i
\(638\) 5.81808 + 5.81808i 0.230340 + 0.230340i
\(639\) 7.37154 0.291614
\(640\) 0 0
\(641\) 13.5348i 0.534593i 0.963614 + 0.267296i \(0.0861302\pi\)
−0.963614 + 0.267296i \(0.913870\pi\)
\(642\) −13.1883 13.1883i −0.520500 0.520500i
\(643\) −5.37736 5.37736i −0.212062 0.212062i 0.593081 0.805143i \(-0.297912\pi\)
−0.805143 + 0.593081i \(0.797912\pi\)
\(644\) 26.2652i 1.03499i
\(645\) 0 0
\(646\) 4.31205 + 23.1603i 0.169655 + 0.911229i
\(647\) −25.3967 + 25.3967i −0.998448 + 0.998448i −0.999999 0.00155076i \(-0.999506\pi\)
0.00155076 + 0.999999i \(0.499506\pi\)
\(648\) 2.27746 2.27746i 0.0894672 0.0894672i
\(649\) −58.2202 −2.28534
\(650\) 0 0
\(651\) 39.1961 1.53622
\(652\) −11.9456 + 11.9456i −0.467824 + 0.467824i
\(653\) 18.9735 + 18.9735i 0.742490 + 0.742490i 0.973057 0.230567i \(-0.0740580\pi\)
−0.230567 + 0.973057i \(0.574058\pi\)
\(654\) −0.840439 −0.0328638
\(655\) 0 0
\(656\) 6.48808i 0.253317i
\(657\) 21.8488 21.8488i 0.852403 0.852403i
\(658\) −9.83168 + 9.83168i −0.383279 + 0.383279i
\(659\) −30.5839 −1.19138 −0.595689 0.803215i \(-0.703121\pi\)
−0.595689 + 0.803215i \(0.703121\pi\)
\(660\) 0 0
\(661\) 34.7263i 1.35070i −0.737499 0.675349i \(-0.763993\pi\)
0.737499 0.675349i \(-0.236007\pi\)
\(662\) −6.07830 + 6.07830i −0.236240 + 0.236240i
\(663\) 62.5266 + 62.5266i 2.42833 + 2.42833i
\(664\) 2.89291 0.112267
\(665\) 0 0
\(666\) 6.44507 0.249742
\(667\) −9.36975 9.36975i −0.362798 0.362798i
\(668\) −7.71843 + 7.71843i −0.298635 + 0.298635i
\(669\) 29.3343i 1.13413i
\(670\) 0 0
\(671\) 7.80671 0.301375
\(672\) 8.00087 8.00087i 0.308640 0.308640i
\(673\) 31.9784 31.9784i 1.23268 1.23268i 0.269746 0.962931i \(-0.413060\pi\)
0.962931 0.269746i \(-0.0869398\pi\)
\(674\) 2.84708i 0.109666i
\(675\) 0 0
\(676\) 23.5014 0.903900
\(677\) 8.41642 + 8.41642i 0.323469 + 0.323469i 0.850096 0.526627i \(-0.176544\pi\)
−0.526627 + 0.850096i \(0.676544\pi\)
\(678\) 18.9638 18.9638i 0.728301 0.728301i
\(679\) −19.8423 −0.761478
\(680\) 0 0
\(681\) −65.4063 −2.50637
\(682\) −9.56123 + 9.56123i −0.366119 + 0.366119i
\(683\) 7.28467 7.28467i 0.278740 0.278740i −0.553866 0.832606i \(-0.686848\pi\)
0.832606 + 0.553866i \(0.186848\pi\)
\(684\) −3.45751 18.5705i −0.132201 0.710062i
\(685\) 0 0
\(686\) 14.4474i 0.551603i
\(687\) 33.6660 + 33.6660i 1.28444 + 1.28444i
\(688\) −6.63336 6.63336i −0.252895 0.252895i
\(689\) 32.8075i 1.24986i
\(690\) 0 0
\(691\) 12.1517 0.462273 0.231136 0.972921i \(-0.425756\pi\)
0.231136 + 0.972921i \(0.425756\pi\)
\(692\) −2.36527 2.36527i −0.0899140 0.0899140i
\(693\) 49.9763 + 49.9763i 1.89844 + 1.89844i
\(694\) 6.89188 0.261612
\(695\) 0 0
\(696\) 5.70840i 0.216376i
\(697\) −24.7952 24.7952i −0.939186 0.939186i
\(698\) −15.5346 + 15.5346i −0.587993 + 0.587993i
\(699\) 41.0583 1.55297
\(700\) 0 0
\(701\) −16.2161 −0.612474 −0.306237 0.951955i \(-0.599070\pi\)
−0.306237 + 0.951955i \(0.599070\pi\)
\(702\) −15.4283 15.4283i −0.582303 0.582303i
\(703\) −3.66750 + 5.34558i −0.138322 + 0.201612i
\(704\) 3.90336i 0.147113i
\(705\) 0 0
\(706\) 3.77445i 0.142053i
\(707\) −17.7268 + 17.7268i −0.666685 + 0.666685i
\(708\) 28.5613 + 28.5613i 1.07340 + 1.07340i
\(709\) 22.0228i 0.827085i 0.910485 + 0.413542i \(0.135709\pi\)
−0.910485 + 0.413542i \(0.864291\pi\)
\(710\) 0 0
\(711\) 51.2255i 1.92111i
\(712\) −7.76168 + 7.76168i −0.290881 + 0.290881i
\(713\) 15.3979 15.3979i 0.576657 0.576657i
\(714\) 61.1532i 2.28860i
\(715\) 0 0
\(716\) 9.68475i 0.361936i
\(717\) −5.52731 5.52731i −0.206421 0.206421i
\(718\) 2.13272 2.13272i 0.0795923 0.0795923i
\(719\) 0.0275325i 0.00102679i −1.00000 0.000513394i \(-0.999837\pi\)
1.00000 0.000513394i \(-0.000163418\pi\)
\(720\) 0 0
\(721\) 5.22718i 0.194670i
\(722\) 17.3699 + 7.69967i 0.646443 + 0.286552i
\(723\) −5.53960 5.53960i −0.206020 0.206020i
\(724\) −14.1370 −0.525398
\(725\) 0 0
\(726\) −11.4719 −0.425761
\(727\) 23.0328 23.0328i 0.854239 0.854239i −0.136413 0.990652i \(-0.543558\pi\)
0.990652 + 0.136413i \(0.0435575\pi\)
\(728\) 17.8498 + 17.8498i 0.661559 + 0.661559i
\(729\) 43.2975i 1.60361i
\(730\) 0 0
\(731\) 50.7009 1.87524
\(732\) −3.82977 3.82977i −0.141552 0.141552i
\(733\) −2.78821 2.78821i −0.102985 0.102985i 0.653737 0.756722i \(-0.273200\pi\)
−0.756722 + 0.653737i \(0.773200\pi\)
\(734\) 35.2022 1.29934
\(735\) 0 0
\(736\) 6.28618i 0.231712i
\(737\) −15.7992 15.7992i −0.581973 0.581973i
\(738\) 19.8814 + 19.8814i 0.731846 + 0.731846i
\(739\) 26.4431i 0.972726i −0.873757 0.486363i \(-0.838323\pi\)
0.873757 0.486363i \(-0.161677\pi\)
\(740\) 0 0
\(741\) 70.1116 13.0536i 2.57561 0.479535i
\(742\) −16.0434 + 16.0434i −0.588973 + 0.588973i
\(743\) −17.9302 + 17.9302i −0.657796 + 0.657796i −0.954858 0.297062i \(-0.903993\pi\)
0.297062 + 0.954858i \(0.403993\pi\)
\(744\) 9.38099 0.343924
\(745\) 0 0
\(746\) 28.3363 1.03747
\(747\) 8.86476 8.86476i 0.324345 0.324345i
\(748\) −14.9173 14.9173i −0.545430 0.545430i
\(749\) 28.7766 1.05147
\(750\) 0 0
\(751\) 53.4720i 1.95122i 0.219508 + 0.975611i \(0.429555\pi\)
−0.219508 + 0.975611i \(0.570445\pi\)
\(752\) −2.35306 + 2.35306i −0.0858074 + 0.0858074i
\(753\) 23.7010 23.7010i 0.863712 0.863712i
\(754\) 12.7354 0.463794
\(755\) 0 0
\(756\) 15.0894i 0.548796i
\(757\) −8.12170 + 8.12170i −0.295188 + 0.295188i −0.839126 0.543938i \(-0.816933\pi\)
0.543938 + 0.839126i \(0.316933\pi\)
\(758\) −5.53164 5.53164i −0.200918 0.200918i
\(759\) 66.4482 2.41192
\(760\) 0 0
\(761\) −15.5881 −0.565069 −0.282535 0.959257i \(-0.591175\pi\)
−0.282535 + 0.959257i \(0.591175\pi\)
\(762\) −36.9690 36.9690i −1.33925 1.33925i
\(763\) 0.916911 0.916911i 0.0331944 0.0331944i
\(764\) 0.0275325i 0.000996089i
\(765\) 0 0
\(766\) 24.0873 0.870310
\(767\) −63.7199 + 63.7199i −2.30079 + 2.30079i
\(768\) 1.91489 1.91489i 0.0690975 0.0690975i
\(769\) 2.64037i 0.0952143i 0.998866 + 0.0476071i \(0.0151596\pi\)
−0.998866 + 0.0476071i \(0.984840\pi\)
\(770\) 0 0
\(771\) −26.0337 −0.937582
\(772\) 16.8244 + 16.8244i 0.605525 + 0.605525i
\(773\) 4.26211 4.26211i 0.153297 0.153297i −0.626292 0.779589i \(-0.715428\pi\)
0.779589 + 0.626292i \(0.215428\pi\)
\(774\) −40.6533 −1.46125
\(775\) 0 0
\(776\) −4.74896 −0.170478
\(777\) −11.8992 + 11.8992i −0.426882 + 0.426882i
\(778\) 22.1956 22.1956i 0.795753 0.795753i
\(779\) −27.8031 + 5.17646i −0.996149 + 0.185466i
\(780\) 0 0
\(781\) 6.63972i 0.237588i
\(782\) 24.0236 + 24.0236i 0.859083 + 0.859083i
\(783\) −5.38293 5.38293i −0.192370 0.192370i
\(784\) 10.4578i 0.373491i
\(785\) 0 0
\(786\) 1.80671 0.0644433
\(787\) 5.97579 + 5.97579i 0.213014 + 0.213014i 0.805546 0.592533i \(-0.201872\pi\)
−0.592533 + 0.805546i \(0.701872\pi\)
\(788\) 12.3494 + 12.3494i 0.439931 + 0.439931i
\(789\) −54.6408 −1.94526
\(790\) 0 0
\(791\) 41.3787i 1.47126i
\(792\) 11.9611 + 11.9611i 0.425018 + 0.425018i
\(793\) 8.54417 8.54417i 0.303412 0.303412i
\(794\) 4.95444 0.175827
\(795\) 0 0
\(796\) −5.01141 −0.177625
\(797\) 15.7814 + 15.7814i 0.559004 + 0.559004i 0.929024 0.370020i \(-0.120649\pi\)
−0.370020 + 0.929024i \(0.620649\pi\)
\(798\) 40.6692 + 27.9024i 1.43968 + 0.987733i
\(799\) 17.9852i 0.636271i
\(800\) 0 0
\(801\) 47.5683i 1.68074i
\(802\) 1.60670 1.60670i 0.0567345 0.0567345i
\(803\) −19.6797 19.6797i −0.694482 0.694482i
\(804\) 15.5014i 0.546693i
\(805\) 0 0
\(806\) 20.9289i 0.737187i
\(807\) 39.1742 39.1742i 1.37900 1.37900i
\(808\) −4.24264 + 4.24264i −0.149256 + 0.149256i
\(809\) 24.1847i 0.850288i 0.905126 + 0.425144i \(0.139777\pi\)
−0.905126 + 0.425144i \(0.860223\pi\)
\(810\) 0 0
\(811\) 7.38279i 0.259245i −0.991563 0.129622i \(-0.958623\pi\)
0.991563 0.129622i \(-0.0413765\pi\)
\(812\) 6.22781 + 6.22781i 0.218553 + 0.218553i
\(813\) −0.792964 + 0.792964i −0.0278105 + 0.0278105i
\(814\) 5.80523i 0.203473i
\(815\) 0 0
\(816\) 14.6361i 0.512365i
\(817\) 23.1333 33.7180i 0.809332 1.17965i
\(818\) 7.27398 + 7.27398i 0.254329 + 0.254329i
\(819\) 109.395 3.82256
\(820\) 0 0
\(821\) 31.9921 1.11653 0.558266 0.829662i \(-0.311467\pi\)
0.558266 + 0.829662i \(0.311467\pi\)
\(822\) −25.6186 + 25.6186i −0.893552 + 0.893552i
\(823\) 4.20827 + 4.20827i 0.146691 + 0.146691i 0.776638 0.629947i \(-0.216923\pi\)
−0.629947 + 0.776638i \(0.716923\pi\)
\(824\) 1.25104i 0.0435822i
\(825\) 0 0
\(826\) −62.3203 −2.16840
\(827\) −9.72213 9.72213i −0.338072 0.338072i 0.517569 0.855641i \(-0.326837\pi\)
−0.855641 + 0.517569i \(0.826837\pi\)
\(828\) −19.2628 19.2628i −0.669427 0.669427i
\(829\) −6.70058 −0.232721 −0.116360 0.993207i \(-0.537123\pi\)
−0.116360 + 0.993207i \(0.537123\pi\)
\(830\) 0 0
\(831\) 31.6559i 1.09813i
\(832\) 4.27208 + 4.27208i 0.148108 + 0.148108i
\(833\) −39.9660 39.9660i −1.38474 1.38474i
\(834\) 55.1827i 1.91082i
\(835\) 0 0
\(836\) −16.7269 + 3.11426i −0.578512 + 0.107709i
\(837\) 8.84612 8.84612i 0.305767 0.305767i
\(838\) 24.9557 24.9557i 0.862082 0.862082i
\(839\) −15.1405 −0.522707 −0.261353 0.965243i \(-0.584169\pi\)
−0.261353 + 0.965243i \(0.584169\pi\)
\(840\) 0 0
\(841\) −24.5566 −0.846780
\(842\) 16.6924 16.6924i 0.575260 0.575260i
\(843\) −45.2702 45.2702i −1.55919 1.55919i
\(844\) 19.5714 0.673675
\(845\) 0 0
\(846\) 14.4210i 0.495804i
\(847\) 12.5157 12.5157i 0.430045 0.430045i
\(848\) −3.83975 + 3.83975i −0.131857 + 0.131857i
\(849\) 65.2136 2.23813
\(850\) 0 0
\(851\) 9.34906i 0.320481i
\(852\) −3.25727 + 3.25727i −0.111592 + 0.111592i
\(853\) −36.0415 36.0415i −1.23404 1.23404i −0.962400 0.271637i \(-0.912435\pi\)
−0.271637 0.962400i \(-0.587565\pi\)
\(854\) 8.35650 0.285953
\(855\) 0 0
\(856\) 6.88724 0.235401
\(857\) −11.2682 11.2682i −0.384913 0.384913i 0.487955 0.872869i \(-0.337743\pi\)
−0.872869 + 0.487955i \(0.837743\pi\)
\(858\) −45.1581 + 45.1581i −1.54167 + 1.54167i
\(859\) 30.5383i 1.04195i −0.853571 0.520976i \(-0.825568\pi\)
0.853571 0.520976i \(-0.174432\pi\)
\(860\) 0 0
\(861\) −73.4122 −2.50188
\(862\) 4.99166 4.99166i 0.170016 0.170016i
\(863\) 31.6472 31.6472i 1.07728 1.07728i 0.0805325 0.996752i \(-0.474338\pi\)
0.996752 0.0805325i \(-0.0256621\pi\)
\(864\) 3.61142i 0.122863i
\(865\) 0 0
\(866\) −18.2335 −0.619600
\(867\) −23.3810 23.3810i −0.794062 0.794062i
\(868\) −10.2346 + 10.2346i −0.347384 + 0.347384i
\(869\) 46.1400 1.56519
\(870\) 0 0
\(871\) −34.5834 −1.17181
\(872\) 0.219449 0.219449i 0.00743147 0.00743147i
\(873\) −14.5522 + 14.5522i −0.492519 + 0.492519i
\(874\) 26.9379 5.01538i 0.911188 0.169648i
\(875\) 0 0
\(876\) 19.3087i 0.652382i
\(877\) −15.4991 15.4991i −0.523367 0.523367i 0.395220 0.918587i \(-0.370668\pi\)
−0.918587 + 0.395220i \(0.870668\pi\)
\(878\) 22.0127 + 22.0127i 0.742892 + 0.742892i
\(879\) 60.4390i 2.03856i
\(880\) 0 0
\(881\) −2.90484 −0.0978666 −0.0489333 0.998802i \(-0.515582\pi\)
−0.0489333 + 0.998802i \(0.515582\pi\)
\(882\) 32.0458 + 32.0458i 1.07904 + 1.07904i
\(883\) 34.0836 + 34.0836i 1.14701 + 1.14701i 0.987139 + 0.159867i \(0.0511066\pi\)
0.159867 + 0.987139i \(0.448893\pi\)
\(884\) −32.6529 −1.09824
\(885\) 0 0
\(886\) 20.0718i 0.674324i
\(887\) 18.7588 + 18.7588i 0.629859 + 0.629859i 0.948032 0.318174i \(-0.103070\pi\)
−0.318174 + 0.948032i \(0.603070\pi\)
\(888\) −2.84790 + 2.84790i −0.0955691 + 0.0955691i
\(889\) 80.6657 2.70544
\(890\) 0 0
\(891\) −12.5720 −0.421178
\(892\) 7.65955 + 7.65955i 0.256461 + 0.256461i
\(893\) −11.9609 8.20612i −0.400255 0.274607i
\(894\) 4.89269i 0.163636i
\(895\) 0 0
\(896\) 4.17825i 0.139585i
\(897\) 72.7251 72.7251i 2.42822 2.42822i
\(898\) 5.73245 + 5.73245i 0.191294 + 0.191294i
\(899\) 7.30209i 0.243538i
\(900\) 0 0
\(901\) 29.3484i 0.977737i
\(902\) 17.9077 17.9077i 0.596261 0.596261i
\(903\) 75.0561 75.0561i 2.49771 2.49771i
\(904\) 9.90336i 0.329381i
\(905\) 0 0
\(906\) 17.1168i 0.568667i
\(907\) 34.9725 + 34.9725i 1.16124 + 1.16124i 0.984204 + 0.177038i \(0.0566516\pi\)
0.177038 + 0.984204i \(0.443348\pi\)
\(908\) 17.0784 17.0784i 0.566765 0.566765i
\(909\) 26.0015i 0.862415i
\(910\) 0 0
\(911\) 3.12932i 0.103679i −0.998655 0.0518395i \(-0.983492\pi\)
0.998655 0.0518395i \(-0.0165084\pi\)
\(912\) 9.73356 + 6.67801i 0.322310 + 0.221131i
\(913\) −7.98470 7.98470i −0.264255 0.264255i
\(914\) −11.4526 −0.378818
\(915\) 0 0
\(916\) −17.5812 −0.580899
\(917\) −1.97111 + 1.97111i −0.0650917 + 0.0650917i
\(918\) 13.8016 + 13.8016i 0.455521 + 0.455521i
\(919\) 24.2860i 0.801120i 0.916271 + 0.400560i \(0.131184\pi\)
−0.916271 + 0.400560i \(0.868816\pi\)
\(920\) 0 0
\(921\) 3.00596 0.0990499
\(922\) 20.8032 + 20.8032i 0.685116 + 0.685116i
\(923\) −7.26693 7.26693i −0.239194 0.239194i
\(924\) −44.1662 −1.45296
\(925\) 0 0
\(926\) 22.8973i 0.752452i
\(927\) −3.83358 3.83358i −0.125911 0.125911i
\(928\) 1.49053 + 1.49053i 0.0489291 + 0.0489291i
\(929\) 19.3296i 0.634184i 0.948395 + 0.317092i \(0.102706\pi\)
−0.948395 + 0.317092i \(0.897294\pi\)
\(930\) 0 0
\(931\) −44.8142 + 8.34364i −1.46873 + 0.273452i
\(932\) −10.7208 + 10.7208i −0.351172 + 0.351172i
\(933\) 30.0227 30.0227i 0.982899 0.982899i
\(934\) −37.0938 −1.21375
\(935\) 0 0
\(936\) 26.1819 0.855783
\(937\) 7.03506 7.03506i 0.229825 0.229825i −0.582794 0.812620i \(-0.698041\pi\)
0.812620 + 0.582794i \(0.198041\pi\)
\(938\) −16.9119 16.9119i −0.552193 0.552193i
\(939\) −13.2573 −0.432636
\(940\) 0 0
\(941\) 15.3091i 0.499063i 0.968367 + 0.249532i \(0.0802767\pi\)
−0.968367 + 0.249532i \(0.919723\pi\)
\(942\) −29.2937 + 29.2937i −0.954440 + 0.954440i
\(943\) −28.8395 + 28.8395i −0.939143 + 0.939143i
\(944\) −14.9154 −0.485455
\(945\) 0 0
\(946\) 36.6174i 1.19053i
\(947\) 3.75429 3.75429i 0.121998 0.121998i −0.643472 0.765470i \(-0.722507\pi\)
0.765470 + 0.643472i \(0.222507\pi\)
\(948\) −22.6351 22.6351i −0.735154 0.735154i
\(949\) −43.0775 −1.39836
\(950\) 0 0
\(951\) −48.8196 −1.58308
\(952\) −15.9678 15.9678i −0.517521 0.517521i
\(953\) −24.3463 + 24.3463i −0.788653 + 0.788653i −0.981273 0.192621i \(-0.938301\pi\)
0.192621 + 0.981273i \(0.438301\pi\)
\(954\) 23.5323i 0.761887i
\(955\) 0 0
\(956\) 2.88649 0.0933559
\(957\) −15.7557 + 15.7557i −0.509309 + 0.509309i
\(958\) 19.0246 19.0246i 0.614657 0.614657i
\(959\) 55.8994i 1.80509i
\(960\) 0 0
\(961\) 19.0000 0.612903
\(962\) −6.35361 6.35361i −0.204849 0.204849i
\(963\) 21.1046 21.1046i 0.680086 0.680086i
\(964\) 2.89291 0.0931744
\(965\) 0 0
\(966\) 71.1277 2.28850
\(967\) 17.4994 17.4994i 0.562743 0.562743i −0.367343 0.930086i \(-0.619732\pi\)
0.930086 + 0.367343i \(0.119732\pi\)
\(968\) 2.99544 2.99544i 0.0962772 0.0962772i
\(969\) −62.7194 + 11.6773i −2.01484 + 0.375128i
\(970\) 0 0
\(971\) 9.33148i 0.299462i 0.988727 + 0.149731i \(0.0478407\pi\)
−0.988727 + 0.149731i \(0.952159\pi\)
\(972\) 13.8285 + 13.8285i 0.443548 + 0.443548i
\(973\) 60.2039 + 60.2039i 1.93005 + 1.93005i
\(974\) 37.9222i 1.21511i
\(975\) 0 0
\(976\) 2.00000 0.0640184
\(977\) −9.53501 9.53501i −0.305052 0.305052i 0.537935 0.842987i \(-0.319205\pi\)
−0.842987 + 0.537935i \(0.819205\pi\)
\(978\) −32.3493 32.3493i −1.03442 1.03442i
\(979\) 42.8459 1.36936
\(980\) 0 0
\(981\) 1.34492i 0.0429399i
\(982\) −7.67950 7.67950i −0.245063 0.245063i
\(983\) −17.6028 + 17.6028i −0.561443 + 0.561443i −0.929717 0.368274i \(-0.879949\pi\)
0.368274 + 0.929717i \(0.379949\pi\)
\(984\) −17.5701 −0.560114
\(985\) 0 0
\(986\) −11.3926 −0.362815
\(987\) −26.6248 26.6248i −0.847476 0.847476i
\(988\) −14.8985 + 21.7154i −0.473986 + 0.690860i
\(989\) 58.9706i 1.87516i
\(990\) 0 0
\(991\) 31.0484i 0.986286i −0.869948 0.493143i \(-0.835848\pi\)
0.869948 0.493143i \(-0.164152\pi\)
\(992\) −2.44949 + 2.44949i −0.0777714 + 0.0777714i
\(993\) −16.4604 16.4604i −0.522354 0.522354i
\(994\) 7.10731i 0.225430i
\(995\) 0 0
\(996\) 7.83417i 0.248235i
\(997\) −12.3889 + 12.3889i −0.392361 + 0.392361i −0.875528 0.483167i \(-0.839486\pi\)
0.483167 + 0.875528i \(0.339486\pi\)
\(998\) −13.8470 + 13.8470i −0.438320 + 0.438320i
\(999\) 5.37104i 0.169932i
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 950.2.f.d.493.8 yes 32
5.2 odd 4 inner 950.2.f.d.607.10 yes 32
5.3 odd 4 inner 950.2.f.d.607.7 yes 32
5.4 even 2 inner 950.2.f.d.493.9 yes 32
19.18 odd 2 inner 950.2.f.d.493.10 yes 32
95.18 even 4 inner 950.2.f.d.607.9 yes 32
95.37 even 4 inner 950.2.f.d.607.8 yes 32
95.94 odd 2 inner 950.2.f.d.493.7 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.f.d.493.7 32 95.94 odd 2 inner
950.2.f.d.493.8 yes 32 1.1 even 1 trivial
950.2.f.d.493.9 yes 32 5.4 even 2 inner
950.2.f.d.493.10 yes 32 19.18 odd 2 inner
950.2.f.d.607.7 yes 32 5.3 odd 4 inner
950.2.f.d.607.8 yes 32 95.37 even 4 inner
950.2.f.d.607.9 yes 32 95.18 even 4 inner
950.2.f.d.607.10 yes 32 5.2 odd 4 inner