Properties

Label 429.2.j.a.122.6
Level $429$
Weight $2$
Character 429.122
Analytic conductor $3.426$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [429,2,Mod(122,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.122");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.j (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: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(48\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 122.6
Character \(\chi\) \(=\) 429.122
Dual form 429.2.j.a.320.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.70776 - 1.70776i) q^{2} +(0.636556 - 1.61084i) q^{3} +3.83287i q^{4} +(0.490801 + 0.490801i) q^{5} +(-3.83800 + 1.66383i) q^{6} +(-0.206749 - 0.206749i) q^{7} +(3.13009 - 3.13009i) q^{8} +(-2.18959 - 2.05078i) q^{9} +O(q^{10})\) \(q+(-1.70776 - 1.70776i) q^{2} +(0.636556 - 1.61084i) q^{3} +3.83287i q^{4} +(0.490801 + 0.490801i) q^{5} +(-3.83800 + 1.66383i) q^{6} +(-0.206749 - 0.206749i) q^{7} +(3.13009 - 3.13009i) q^{8} +(-2.18959 - 2.05078i) q^{9} -1.67634i q^{10} +(-0.707107 + 0.707107i) q^{11} +(6.17412 + 2.43984i) q^{12} +(-3.34311 - 1.35040i) q^{13} +0.706154i q^{14} +(1.10302 - 0.478178i) q^{15} -3.02513 q^{16} -7.70465 q^{17} +(0.237061 + 7.24152i) q^{18} +(-2.28456 + 2.28456i) q^{19} +(-1.88117 + 1.88117i) q^{20} +(-0.464646 + 0.201432i) q^{21} +2.41513 q^{22} -5.93163 q^{23} +(-3.04958 - 7.03454i) q^{24} -4.51823i q^{25} +(3.40306 + 8.01539i) q^{26} +(-4.69727 + 2.22164i) q^{27} +(0.792441 - 0.792441i) q^{28} -3.81466i q^{29} +(-2.70031 - 1.06708i) q^{30} +(0.609361 - 0.609361i) q^{31} +(-1.09400 - 1.09400i) q^{32} +(0.688920 + 1.58915i) q^{33} +(13.1577 + 13.1577i) q^{34} -0.202945i q^{35} +(7.86035 - 8.39241i) q^{36} +(2.18188 + 2.18188i) q^{37} +7.80293 q^{38} +(-4.30336 + 4.52560i) q^{39} +3.07250 q^{40} +(5.44677 + 5.44677i) q^{41} +(1.13750 + 0.449507i) q^{42} -5.00836i q^{43} +(-2.71025 - 2.71025i) q^{44} +(-0.0681301 - 2.08118i) q^{45} +(10.1298 + 10.1298i) q^{46} +(6.31754 - 6.31754i) q^{47} +(-1.92566 + 4.87298i) q^{48} -6.91451i q^{49} +(-7.71603 + 7.71603i) q^{50} +(-4.90445 + 12.4109i) q^{51} +(5.17592 - 12.8137i) q^{52} +7.19003i q^{53} +(11.8158 + 4.22777i) q^{54} -0.694098 q^{55} -1.29429 q^{56} +(2.22580 + 5.13430i) q^{57} +(-6.51451 + 6.51451i) q^{58} +(0.134466 - 0.134466i) q^{59} +(1.83279 + 4.22774i) q^{60} +2.61118 q^{61} -2.08128 q^{62} +(0.0286997 + 0.876692i) q^{63} +9.78681i q^{64} +(-0.978024 - 2.30358i) q^{65} +(1.53737 - 3.89038i) q^{66} +(2.48830 - 2.48830i) q^{67} -29.5309i q^{68} +(-3.77582 + 9.55488i) q^{69} +(-0.346581 + 0.346581i) q^{70} +(5.16561 + 5.16561i) q^{71} +(-13.2727 + 0.434501i) q^{72} +(0.488464 + 0.488464i) q^{73} -7.45225i q^{74} +(-7.27813 - 2.87611i) q^{75} +(-8.75640 - 8.75640i) q^{76} +0.292387 q^{77} +(15.0777 - 0.379533i) q^{78} -4.88091 q^{79} +(-1.48474 - 1.48474i) q^{80} +(0.588623 + 8.98073i) q^{81} -18.6035i q^{82} +(-12.2258 - 12.2258i) q^{83} +(-0.772060 - 1.78093i) q^{84} +(-3.78145 - 3.78145i) q^{85} +(-8.55306 + 8.55306i) q^{86} +(-6.14479 - 2.42824i) q^{87} +4.42661i q^{88} +(5.33030 - 5.33030i) q^{89} +(-3.43780 + 3.67049i) q^{90} +(0.411991 + 0.970380i) q^{91} -22.7351i q^{92} +(-0.593688 - 1.36947i) q^{93} -21.5776 q^{94} -2.24253 q^{95} +(-2.45864 + 1.06586i) q^{96} +(-3.91936 + 3.91936i) q^{97} +(-11.8083 + 11.8083i) q^{98} +(2.99839 - 0.0981564i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q + 12 q^{6} - 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 96 q + 12 q^{6} - 16 q^{7} + 16 q^{13} - 16 q^{15} - 120 q^{16} - 28 q^{18} - 24 q^{19} + 24 q^{24} - 24 q^{27} + 56 q^{28} + 48 q^{31} - 16 q^{34} - 16 q^{37} + 80 q^{40} + 52 q^{42} + 4 q^{45} - 56 q^{46} + 28 q^{48} + 4 q^{54} + 4 q^{57} + 48 q^{58} + 4 q^{60} - 96 q^{61} - 36 q^{63} + 20 q^{66} - 16 q^{67} + 48 q^{70} - 16 q^{72} - 16 q^{73} - 88 q^{76} + 80 q^{78} + 16 q^{79} + 32 q^{81} + 52 q^{84} - 8 q^{85} - 48 q^{87} - 16 q^{91} - 36 q^{93} - 16 q^{94} - 108 q^{96} - 48 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.70776 1.70776i −1.20757 1.20757i −0.971813 0.235753i \(-0.924244\pi\)
−0.235753 0.971813i \(-0.575756\pi\)
\(3\) 0.636556 1.61084i 0.367516 0.930017i
\(4\) 3.83287i 1.91643i
\(5\) 0.490801 + 0.490801i 0.219493 + 0.219493i 0.808285 0.588792i \(-0.200396\pi\)
−0.588792 + 0.808285i \(0.700396\pi\)
\(6\) −3.83800 + 1.66383i −1.56686 + 0.679257i
\(7\) −0.206749 0.206749i −0.0781438 0.0781438i 0.666955 0.745098i \(-0.267597\pi\)
−0.745098 + 0.666955i \(0.767597\pi\)
\(8\) 3.13009 3.13009i 1.10665 1.10665i
\(9\) −2.18959 2.05078i −0.729864 0.683592i
\(10\) 1.67634i 0.530104i
\(11\) −0.707107 + 0.707107i −0.213201 + 0.213201i
\(12\) 6.17412 + 2.43984i 1.78232 + 0.704320i
\(13\) −3.34311 1.35040i −0.927213 0.374535i
\(14\) 0.706154i 0.188728i
\(15\) 1.10302 0.478178i 0.284799 0.123465i
\(16\) −3.02513 −0.756281
\(17\) −7.70465 −1.86865 −0.934326 0.356419i \(-0.883998\pi\)
−0.934326 + 0.356419i \(0.883998\pi\)
\(18\) 0.237061 + 7.24152i 0.0558758 + 1.70684i
\(19\) −2.28456 + 2.28456i −0.524113 + 0.524113i −0.918811 0.394698i \(-0.870849\pi\)
0.394698 + 0.918811i \(0.370849\pi\)
\(20\) −1.88117 + 1.88117i −0.420643 + 0.420643i
\(21\) −0.464646 + 0.201432i −0.101394 + 0.0439560i
\(22\) 2.41513 0.514908
\(23\) −5.93163 −1.23683 −0.618415 0.785852i \(-0.712225\pi\)
−0.618415 + 0.785852i \(0.712225\pi\)
\(24\) −3.04958 7.03454i −0.622494 1.43592i
\(25\) 4.51823i 0.903646i
\(26\) 3.40306 + 8.01539i 0.667395 + 1.57195i
\(27\) −4.69727 + 2.22164i −0.903989 + 0.427555i
\(28\) 0.792441 0.792441i 0.149757 0.149757i
\(29\) 3.81466i 0.708364i −0.935176 0.354182i \(-0.884759\pi\)
0.935176 0.354182i \(-0.115241\pi\)
\(30\) −2.70031 1.06708i −0.493006 0.194822i
\(31\) 0.609361 0.609361i 0.109444 0.109444i −0.650264 0.759708i \(-0.725342\pi\)
0.759708 + 0.650264i \(0.225342\pi\)
\(32\) −1.09400 1.09400i −0.193393 0.193393i
\(33\) 0.688920 + 1.58915i 0.119926 + 0.276635i
\(34\) 13.1577 + 13.1577i 2.25652 + 2.25652i
\(35\) 0.202945i 0.0343040i
\(36\) 7.86035 8.39241i 1.31006 1.39873i
\(37\) 2.18188 + 2.18188i 0.358699 + 0.358699i 0.863333 0.504634i \(-0.168373\pi\)
−0.504634 + 0.863333i \(0.668373\pi\)
\(38\) 7.80293 1.26580
\(39\) −4.30336 + 4.52560i −0.689089 + 0.724676i
\(40\) 3.07250 0.485805
\(41\) 5.44677 + 5.44677i 0.850643 + 0.850643i 0.990212 0.139570i \(-0.0445719\pi\)
−0.139570 + 0.990212i \(0.544572\pi\)
\(42\) 1.13750 + 0.449507i 0.175520 + 0.0693604i
\(43\) 5.00836i 0.763768i −0.924210 0.381884i \(-0.875275\pi\)
0.924210 0.381884i \(-0.124725\pi\)
\(44\) −2.71025 2.71025i −0.408585 0.408585i
\(45\) −0.0681301 2.08118i −0.0101562 0.310244i
\(46\) 10.1298 + 10.1298i 1.49355 + 1.49355i
\(47\) 6.31754 6.31754i 0.921508 0.921508i −0.0756279 0.997136i \(-0.524096\pi\)
0.997136 + 0.0756279i \(0.0240961\pi\)
\(48\) −1.92566 + 4.87298i −0.277946 + 0.703355i
\(49\) 6.91451i 0.987787i
\(50\) −7.71603 + 7.71603i −1.09121 + 1.09121i
\(51\) −4.90445 + 12.4109i −0.686760 + 1.73788i
\(52\) 5.17592 12.8137i 0.717771 1.77694i
\(53\) 7.19003i 0.987627i 0.869568 + 0.493813i \(0.164397\pi\)
−0.869568 + 0.493813i \(0.835603\pi\)
\(54\) 11.8158 + 4.22777i 1.60793 + 0.575327i
\(55\) −0.694098 −0.0935921
\(56\) −1.29429 −0.172956
\(57\) 2.22580 + 5.13430i 0.294814 + 0.680054i
\(58\) −6.51451 + 6.51451i −0.855397 + 0.855397i
\(59\) 0.134466 0.134466i 0.0175060 0.0175060i −0.698300 0.715806i \(-0.746060\pi\)
0.715806 + 0.698300i \(0.246060\pi\)
\(60\) 1.83279 + 4.22774i 0.236612 + 0.545799i
\(61\) 2.61118 0.334327 0.167163 0.985929i \(-0.446539\pi\)
0.167163 + 0.985929i \(0.446539\pi\)
\(62\) −2.08128 −0.264323
\(63\) 0.0286997 + 0.876692i 0.00361582 + 0.110453i
\(64\) 9.78681i 1.22335i
\(65\) −0.978024 2.30358i −0.121309 0.285724i
\(66\) 1.53737 3.89038i 0.189237 0.478873i
\(67\) 2.48830 2.48830i 0.303994 0.303994i −0.538580 0.842574i \(-0.681039\pi\)
0.842574 + 0.538580i \(0.181039\pi\)
\(68\) 29.5309i 3.58115i
\(69\) −3.77582 + 9.55488i −0.454555 + 1.15027i
\(70\) −0.346581 + 0.346581i −0.0414244 + 0.0414244i
\(71\) 5.16561 + 5.16561i 0.613045 + 0.613045i 0.943738 0.330693i \(-0.107283\pi\)
−0.330693 + 0.943738i \(0.607283\pi\)
\(72\) −13.2727 + 0.434501i −1.56421 + 0.0512064i
\(73\) 0.488464 + 0.488464i 0.0571704 + 0.0571704i 0.735114 0.677944i \(-0.237129\pi\)
−0.677944 + 0.735114i \(0.737129\pi\)
\(74\) 7.45225i 0.866307i
\(75\) −7.27813 2.87611i −0.840406 0.332104i
\(76\) −8.75640 8.75640i −1.00443 1.00443i
\(77\) 0.292387 0.0333206
\(78\) 15.0777 0.379533i 1.70722 0.0429736i
\(79\) −4.88091 −0.549145 −0.274573 0.961566i \(-0.588536\pi\)
−0.274573 + 0.961566i \(0.588536\pi\)
\(80\) −1.48474 1.48474i −0.165998 0.165998i
\(81\) 0.588623 + 8.98073i 0.0654026 + 0.997859i
\(82\) 18.6035i 2.05441i
\(83\) −12.2258 12.2258i −1.34195 1.34195i −0.894115 0.447837i \(-0.852195\pi\)
−0.447837 0.894115i \(-0.647805\pi\)
\(84\) −0.772060 1.78093i −0.0842387 0.194315i
\(85\) −3.78145 3.78145i −0.410156 0.410156i
\(86\) −8.55306 + 8.55306i −0.922300 + 0.922300i
\(87\) −6.14479 2.42824i −0.658791 0.260335i
\(88\) 4.42661i 0.471879i
\(89\) 5.33030 5.33030i 0.565010 0.565010i −0.365716 0.930726i \(-0.619176\pi\)
0.930726 + 0.365716i \(0.119176\pi\)
\(90\) −3.43780 + 3.67049i −0.362375 + 0.386904i
\(91\) 0.411991 + 0.970380i 0.0431884 + 0.101724i
\(92\) 22.7351i 2.37030i
\(93\) −0.593688 1.36947i −0.0615626 0.142008i
\(94\) −21.5776 −2.22556
\(95\) −2.24253 −0.230078
\(96\) −2.45864 + 1.06586i −0.250934 + 0.108784i
\(97\) −3.91936 + 3.91936i −0.397951 + 0.397951i −0.877510 0.479559i \(-0.840797\pi\)
0.479559 + 0.877510i \(0.340797\pi\)
\(98\) −11.8083 + 11.8083i −1.19282 + 1.19282i
\(99\) 2.99839 0.0981564i 0.301350 0.00986509i
\(100\) 17.3178 1.73178
\(101\) 7.48913 0.745196 0.372598 0.927993i \(-0.378467\pi\)
0.372598 + 0.927993i \(0.378467\pi\)
\(102\) 29.5705 12.8193i 2.92791 1.26930i
\(103\) 13.1275i 1.29349i −0.762706 0.646745i \(-0.776130\pi\)
0.762706 0.646745i \(-0.223870\pi\)
\(104\) −14.6911 + 6.23735i −1.44058 + 0.611623i
\(105\) −0.326912 0.129186i −0.0319033 0.0126073i
\(106\) 12.2788 12.2788i 1.19262 1.19262i
\(107\) 13.1793i 1.27409i −0.770828 0.637043i \(-0.780157\pi\)
0.770828 0.637043i \(-0.219843\pi\)
\(108\) −8.51525 18.0040i −0.819380 1.73243i
\(109\) −9.34026 + 9.34026i −0.894634 + 0.894634i −0.994955 0.100321i \(-0.968013\pi\)
0.100321 + 0.994955i \(0.468013\pi\)
\(110\) 1.18535 + 1.18535i 0.113019 + 0.113019i
\(111\) 4.90355 2.12577i 0.465424 0.201769i
\(112\) 0.625442 + 0.625442i 0.0590987 + 0.0590987i
\(113\) 12.4461i 1.17083i 0.810733 + 0.585416i \(0.199069\pi\)
−0.810733 + 0.585416i \(0.800931\pi\)
\(114\) 4.96701 12.5693i 0.465203 1.17722i
\(115\) −2.91125 2.91125i −0.271475 0.271475i
\(116\) 14.6211 1.35753
\(117\) 4.55067 + 9.81282i 0.420710 + 0.907195i
\(118\) −0.459271 −0.0422793
\(119\) 1.59293 + 1.59293i 0.146024 + 0.146024i
\(120\) 1.95582 4.94930i 0.178541 0.451807i
\(121\) 1.00000i 0.0909091i
\(122\) −4.45925 4.45925i −0.403722 0.403722i
\(123\) 12.2410 5.30668i 1.10374 0.478487i
\(124\) 2.33560 + 2.33560i 0.209743 + 0.209743i
\(125\) 4.67156 4.67156i 0.417837 0.417837i
\(126\) 1.44817 1.54619i 0.129013 0.137745i
\(127\) 15.3653i 1.36345i −0.731607 0.681727i \(-0.761229\pi\)
0.731607 0.681727i \(-0.238771\pi\)
\(128\) 14.5255 14.5255i 1.28388 1.28388i
\(129\) −8.06765 3.18810i −0.710317 0.280697i
\(130\) −2.26373 + 5.60419i −0.198543 + 0.491520i
\(131\) 5.15162i 0.450099i 0.974347 + 0.225050i \(0.0722544\pi\)
−0.974347 + 0.225050i \(0.927746\pi\)
\(132\) −6.09099 + 2.64054i −0.530152 + 0.229829i
\(133\) 0.944660 0.0819124
\(134\) −8.49881 −0.734186
\(135\) −3.39581 1.21504i −0.292265 0.104574i
\(136\) −24.1162 + 24.1162i −2.06795 + 2.06795i
\(137\) −6.36931 + 6.36931i −0.544167 + 0.544167i −0.924748 0.380581i \(-0.875724\pi\)
0.380581 + 0.924748i \(0.375724\pi\)
\(138\) 22.7656 9.86924i 1.93794 0.840126i
\(139\) −3.12234 −0.264833 −0.132417 0.991194i \(-0.542274\pi\)
−0.132417 + 0.991194i \(0.542274\pi\)
\(140\) 0.777862 0.0657413
\(141\) −6.15506 14.1980i −0.518349 1.19569i
\(142\) 17.6432i 1.48059i
\(143\) 3.31882 1.40906i 0.277534 0.117831i
\(144\) 6.62379 + 6.20386i 0.551983 + 0.516988i
\(145\) 1.87224 1.87224i 0.155481 0.155481i
\(146\) 1.66835i 0.138074i
\(147\) −11.1381 4.40148i −0.918659 0.363028i
\(148\) −8.36286 + 8.36286i −0.687423 + 0.687423i
\(149\) 1.16939 + 1.16939i 0.0958001 + 0.0958001i 0.753383 0.657582i \(-0.228421\pi\)
−0.657582 + 0.753383i \(0.728421\pi\)
\(150\) 7.51758 + 17.3410i 0.613808 + 1.41588i
\(151\) −2.50991 2.50991i −0.204253 0.204253i 0.597566 0.801819i \(-0.296134\pi\)
−0.801819 + 0.597566i \(0.796134\pi\)
\(152\) 14.3017i 1.16002i
\(153\) 16.8700 + 15.8005i 1.36386 + 1.27740i
\(154\) −0.499326 0.499326i −0.0402369 0.0402369i
\(155\) 0.598150 0.0480445
\(156\) −17.3460 16.4942i −1.38879 1.32059i
\(157\) −14.5015 −1.15734 −0.578672 0.815560i \(-0.696429\pi\)
−0.578672 + 0.815560i \(0.696429\pi\)
\(158\) 8.33541 + 8.33541i 0.663129 + 0.663129i
\(159\) 11.5820 + 4.57686i 0.918510 + 0.362969i
\(160\) 1.07387i 0.0848969i
\(161\) 1.22636 + 1.22636i 0.0966506 + 0.0966506i
\(162\) 14.3317 16.3421i 1.12600 1.28396i
\(163\) 14.9820 + 14.9820i 1.17348 + 1.17348i 0.981375 + 0.192103i \(0.0615307\pi\)
0.192103 + 0.981375i \(0.438469\pi\)
\(164\) −20.8767 + 20.8767i −1.63020 + 1.63020i
\(165\) −0.441832 + 1.11808i −0.0343966 + 0.0870423i
\(166\) 41.7573i 3.24099i
\(167\) −2.44130 + 2.44130i −0.188914 + 0.188914i −0.795226 0.606313i \(-0.792648\pi\)
0.606313 + 0.795226i \(0.292648\pi\)
\(168\) −0.823886 + 2.08488i −0.0635642 + 0.160852i
\(169\) 9.35282 + 9.02911i 0.719447 + 0.694547i
\(170\) 12.9156i 0.990581i
\(171\) 9.68736 0.317129i 0.740811 0.0242514i
\(172\) 19.1964 1.46371
\(173\) 11.4929 0.873787 0.436893 0.899513i \(-0.356079\pi\)
0.436893 + 0.899513i \(0.356079\pi\)
\(174\) 6.34696 + 14.6407i 0.481162 + 1.10991i
\(175\) −0.934140 + 0.934140i −0.0706143 + 0.0706143i
\(176\) 2.13909 2.13909i 0.161240 0.161240i
\(177\) −0.131008 0.302199i −0.00984715 0.0227146i
\(178\) −18.2057 −1.36457
\(179\) −24.7845 −1.85248 −0.926241 0.376932i \(-0.876979\pi\)
−0.926241 + 0.376932i \(0.876979\pi\)
\(180\) 7.97687 0.261134i 0.594561 0.0194638i
\(181\) 18.5500i 1.37881i −0.724377 0.689404i \(-0.757873\pi\)
0.724377 0.689404i \(-0.242127\pi\)
\(182\) 0.953594 2.36075i 0.0706851 0.174991i
\(183\) 1.66216 4.20618i 0.122870 0.310930i
\(184\) −18.5665 + 18.5665i −1.36874 + 1.36874i
\(185\) 2.14174i 0.157464i
\(186\) −1.32485 + 3.35260i −0.0971428 + 0.245825i
\(187\) 5.44801 5.44801i 0.398398 0.398398i
\(188\) 24.2143 + 24.2143i 1.76601 + 1.76601i
\(189\) 1.43048 + 0.511834i 0.104052 + 0.0372304i
\(190\) 3.82969 + 3.82969i 0.277835 + 0.277835i
\(191\) 12.5407i 0.907413i −0.891151 0.453707i \(-0.850101\pi\)
0.891151 0.453707i \(-0.149899\pi\)
\(192\) 15.7650 + 6.22986i 1.13774 + 0.449601i
\(193\) −10.9222 10.9222i −0.786200 0.786200i 0.194669 0.980869i \(-0.437637\pi\)
−0.980869 + 0.194669i \(0.937637\pi\)
\(194\) 13.3866 0.961103
\(195\) −4.33327 + 0.109076i −0.310312 + 0.00781108i
\(196\) 26.5024 1.89303
\(197\) 8.01738 + 8.01738i 0.571215 + 0.571215i 0.932468 0.361253i \(-0.117651\pi\)
−0.361253 + 0.932468i \(0.617651\pi\)
\(198\) −5.28815 4.95290i −0.375813 0.351987i
\(199\) 7.96039i 0.564297i −0.959371 0.282149i \(-0.908953\pi\)
0.959371 0.282149i \(-0.0910471\pi\)
\(200\) −14.1425 14.1425i −1.00002 1.00002i
\(201\) −2.42430 5.59218i −0.170997 0.394442i
\(202\) −12.7896 12.7896i −0.899874 0.899874i
\(203\) −0.788677 + 0.788677i −0.0553543 + 0.0553543i
\(204\) −47.5695 18.7981i −3.33053 1.31613i
\(205\) 5.34656i 0.373420i
\(206\) −22.4186 + 22.4186i −1.56198 + 1.56198i
\(207\) 12.9878 + 12.1644i 0.902717 + 0.845488i
\(208\) 10.1133 + 4.08514i 0.701234 + 0.283254i
\(209\) 3.23085i 0.223483i
\(210\) 0.337667 + 0.778904i 0.0233013 + 0.0537495i
\(211\) 3.06592 0.211067 0.105533 0.994416i \(-0.466345\pi\)
0.105533 + 0.994416i \(0.466345\pi\)
\(212\) −27.5584 −1.89272
\(213\) 11.6092 5.03275i 0.795446 0.344839i
\(214\) −22.5070 + 22.5070i −1.53854 + 1.53854i
\(215\) 2.45811 2.45811i 0.167642 0.167642i
\(216\) −7.74893 + 21.6568i −0.527248 + 1.47356i
\(217\) −0.251969 −0.0171048
\(218\) 31.9018 2.16066
\(219\) 1.09777 0.475901i 0.0741804 0.0321584i
\(220\) 2.66038i 0.179363i
\(221\) 25.7575 + 10.4044i 1.73264 + 0.699875i
\(222\) −12.0044 4.74378i −0.805680 0.318382i
\(223\) −10.6166 + 10.6166i −0.710937 + 0.710937i −0.966731 0.255794i \(-0.917663\pi\)
0.255794 + 0.966731i \(0.417663\pi\)
\(224\) 0.452366i 0.0302250i
\(225\) −9.26588 + 9.89308i −0.617725 + 0.659538i
\(226\) 21.2550 21.2550i 1.41386 1.41386i
\(227\) 14.5721 + 14.5721i 0.967185 + 0.967185i 0.999478 0.0322931i \(-0.0102810\pi\)
−0.0322931 + 0.999478i \(0.510281\pi\)
\(228\) −19.6791 + 8.53119i −1.30328 + 0.564992i
\(229\) −15.2204 15.2204i −1.00579 1.00579i −0.999983 0.00580798i \(-0.998151\pi\)
−0.00580798 0.999983i \(-0.501849\pi\)
\(230\) 9.94341i 0.655649i
\(231\) 0.186121 0.470988i 0.0122459 0.0309888i
\(232\) −11.9402 11.9402i −0.783913 0.783913i
\(233\) 13.0759 0.856632 0.428316 0.903629i \(-0.359107\pi\)
0.428316 + 0.903629i \(0.359107\pi\)
\(234\) 8.98646 24.5293i 0.587463 1.60353i
\(235\) 6.20131 0.404529
\(236\) 0.515391 + 0.515391i 0.0335491 + 0.0335491i
\(237\) −3.10698 + 7.86235i −0.201820 + 0.510715i
\(238\) 5.44067i 0.352666i
\(239\) −12.6577 12.6577i −0.818758 0.818758i 0.167170 0.985928i \(-0.446537\pi\)
−0.985928 + 0.167170i \(0.946537\pi\)
\(240\) −3.33678 + 1.44655i −0.215388 + 0.0933743i
\(241\) 11.0145 + 11.0145i 0.709507 + 0.709507i 0.966432 0.256924i \(-0.0827091\pi\)
−0.256924 + 0.966432i \(0.582709\pi\)
\(242\) −1.70776 + 1.70776i −0.109779 + 0.109779i
\(243\) 14.8412 + 4.76857i 0.952062 + 0.305904i
\(244\) 10.0083i 0.640715i
\(245\) 3.39365 3.39365i 0.216812 0.216812i
\(246\) −29.9672 11.8422i −1.91064 0.755030i
\(247\) 10.7226 4.55246i 0.682263 0.289666i
\(248\) 3.81470i 0.242234i
\(249\) −27.4761 + 11.9113i −1.74123 + 0.754850i
\(250\) −15.9558 −1.00913
\(251\) 1.23189 0.0777564 0.0388782 0.999244i \(-0.487622\pi\)
0.0388782 + 0.999244i \(0.487622\pi\)
\(252\) −3.36024 + 0.110002i −0.211675 + 0.00692948i
\(253\) 4.19429 4.19429i 0.263693 0.263693i
\(254\) −26.2403 + 26.2403i −1.64646 + 1.64646i
\(255\) −8.49841 + 3.68419i −0.532191 + 0.230713i
\(256\) −30.0384 −1.87740
\(257\) −3.07858 −0.192036 −0.0960182 0.995380i \(-0.530611\pi\)
−0.0960182 + 0.995380i \(0.530611\pi\)
\(258\) 8.33308 + 19.2221i 0.518795 + 1.19672i
\(259\) 0.902205i 0.0560603i
\(260\) 8.82933 3.74863i 0.547572 0.232480i
\(261\) −7.82301 + 8.35254i −0.484232 + 0.517009i
\(262\) 8.79771 8.79771i 0.543524 0.543524i
\(263\) 0.738856i 0.0455598i 0.999741 + 0.0227799i \(0.00725170\pi\)
−0.999741 + 0.0227799i \(0.992748\pi\)
\(264\) 7.13055 + 2.81779i 0.438855 + 0.173423i
\(265\) −3.52887 + 3.52887i −0.216777 + 0.216777i
\(266\) −1.61325 1.61325i −0.0989146 0.0989146i
\(267\) −5.19320 11.9793i −0.317819 0.733120i
\(268\) 9.53731 + 9.53731i 0.582584 + 0.582584i
\(269\) 32.4101i 1.97608i −0.154210 0.988038i \(-0.549283\pi\)
0.154210 0.988038i \(-0.450717\pi\)
\(270\) 3.72422 + 7.87421i 0.226649 + 0.479209i
\(271\) −12.1407 12.1407i −0.737497 0.737497i 0.234596 0.972093i \(-0.424623\pi\)
−0.972093 + 0.234596i \(0.924623\pi\)
\(272\) 23.3075 1.41323
\(273\) 1.82538 0.0459480i 0.110477 0.00278090i
\(274\) 21.7545 1.31423
\(275\) 3.19487 + 3.19487i 0.192658 + 0.192658i
\(276\) −36.6226 14.4722i −2.20442 0.871124i
\(277\) 28.1478i 1.69124i 0.533786 + 0.845620i \(0.320769\pi\)
−0.533786 + 0.845620i \(0.679231\pi\)
\(278\) 5.33219 + 5.33219i 0.319803 + 0.319803i
\(279\) −2.58391 + 0.0845879i −0.154695 + 0.00506414i
\(280\) −0.635237 0.635237i −0.0379627 0.0379627i
\(281\) 13.0914 13.0914i 0.780965 0.780965i −0.199029 0.979994i \(-0.563779\pi\)
0.979994 + 0.199029i \(0.0637788\pi\)
\(282\) −13.7354 + 34.7581i −0.817931 + 2.06981i
\(283\) 18.4563i 1.09711i 0.836113 + 0.548557i \(0.184823\pi\)
−0.836113 + 0.548557i \(0.815177\pi\)
\(284\) −19.7991 + 19.7991i −1.17486 + 1.17486i
\(285\) −1.42749 + 3.61234i −0.0845574 + 0.213977i
\(286\) −8.07406 3.26141i −0.477429 0.192851i
\(287\) 2.25223i 0.132945i
\(288\) 0.151862 + 4.63895i 0.00894857 + 0.273353i
\(289\) 42.3617 2.49186
\(290\) −6.39465 −0.375507
\(291\) 3.81856 + 8.80834i 0.223848 + 0.516354i
\(292\) −1.87222 + 1.87222i −0.109563 + 0.109563i
\(293\) 17.5261 17.5261i 1.02389 1.02389i 0.0241777 0.999708i \(-0.492303\pi\)
0.999708 0.0241777i \(-0.00769675\pi\)
\(294\) 11.5046 + 26.5379i 0.670962 + 1.54772i
\(295\) 0.131992 0.00768489
\(296\) 13.6590 0.793912
\(297\) 1.75053 4.89241i 0.101576 0.283886i
\(298\) 3.99406i 0.231370i
\(299\) 19.8301 + 8.01009i 1.14680 + 0.463236i
\(300\) 11.0237 27.8961i 0.636456 1.61058i
\(301\) −1.03547 + 1.03547i −0.0596837 + 0.0596837i
\(302\) 8.57261i 0.493299i
\(303\) 4.76725 12.0638i 0.273872 0.693045i
\(304\) 6.91107 6.91107i 0.396377 0.396377i
\(305\) 1.28157 + 1.28157i 0.0733824 + 0.0733824i
\(306\) −1.82647 55.7934i −0.104412 3.18949i
\(307\) −13.7811 13.7811i −0.786529 0.786529i 0.194395 0.980923i \(-0.437726\pi\)
−0.980923 + 0.194395i \(0.937726\pi\)
\(308\) 1.12068i 0.0638567i
\(309\) −21.1463 8.35639i −1.20297 0.475379i
\(310\) −1.02149 1.02149i −0.0580170 0.0580170i
\(311\) −12.7746 −0.724383 −0.362192 0.932104i \(-0.617971\pi\)
−0.362192 + 0.932104i \(0.617971\pi\)
\(312\) 0.695632 + 27.6354i 0.0393824 + 1.56455i
\(313\) 5.00198 0.282728 0.141364 0.989958i \(-0.454851\pi\)
0.141364 + 0.989958i \(0.454851\pi\)
\(314\) 24.7650 + 24.7650i 1.39757 + 1.39757i
\(315\) −0.416196 + 0.444367i −0.0234500 + 0.0250373i
\(316\) 18.7079i 1.05240i
\(317\) −4.15600 4.15600i −0.233424 0.233424i 0.580696 0.814120i \(-0.302780\pi\)
−0.814120 + 0.580696i \(0.802780\pi\)
\(318\) −11.9630 27.5953i −0.670853 1.54747i
\(319\) 2.69737 + 2.69737i 0.151024 + 0.151024i
\(320\) −4.80338 + 4.80338i −0.268517 + 0.268517i
\(321\) −21.2296 8.38934i −1.18492 0.468247i
\(322\) 4.18864i 0.233424i
\(323\) 17.6017 17.6017i 0.979385 0.979385i
\(324\) −34.4219 + 2.25611i −1.91233 + 0.125340i
\(325\) −6.10144 + 15.1050i −0.338447 + 0.837872i
\(326\) 51.1711i 2.83410i
\(327\) 9.10003 + 20.9912i 0.503233 + 1.16082i
\(328\) 34.0977 1.88273
\(329\) −2.61229 −0.144020
\(330\) 2.66395 1.15486i 0.146645 0.0635731i
\(331\) 17.3835 17.3835i 0.955486 0.955486i −0.0435644 0.999051i \(-0.513871\pi\)
0.999051 + 0.0435644i \(0.0138714\pi\)
\(332\) 46.8597 46.8597i 2.57176 2.57176i
\(333\) −0.302876 9.25199i −0.0165975 0.507006i
\(334\) 8.33830 0.456251
\(335\) 2.44252 0.133449
\(336\) 1.40561 0.609356i 0.0766825 0.0332431i
\(337\) 16.8962i 0.920397i 0.887816 + 0.460199i \(0.152222\pi\)
−0.887816 + 0.460199i \(0.847778\pi\)
\(338\) −0.552811 31.3919i −0.0300690 1.70749i
\(339\) 20.0487 + 7.92266i 1.08889 + 0.430300i
\(340\) 14.4938 14.4938i 0.786036 0.786036i
\(341\) 0.861766i 0.0466672i
\(342\) −17.0852 16.0021i −0.923864 0.865293i
\(343\) −2.87681 + 2.87681i −0.155333 + 0.155333i
\(344\) −15.6766 15.6766i −0.845226 0.845226i
\(345\) −6.54272 + 2.83637i −0.352248 + 0.152705i
\(346\) −19.6270 19.6270i −1.05516 1.05516i
\(347\) 16.2445i 0.872051i −0.899934 0.436025i \(-0.856386\pi\)
0.899934 0.436025i \(-0.143614\pi\)
\(348\) 9.30714 23.5522i 0.498915 1.26253i
\(349\) 16.4776 + 16.4776i 0.882027 + 0.882027i 0.993740 0.111713i \(-0.0356338\pi\)
−0.111713 + 0.993740i \(0.535634\pi\)
\(350\) 3.19057 0.170543
\(351\) 18.7036 1.08398i 0.998325 0.0578588i
\(352\) 1.54715 0.0824631
\(353\) −7.48343 7.48343i −0.398303 0.398303i 0.479331 0.877634i \(-0.340879\pi\)
−0.877634 + 0.479331i \(0.840879\pi\)
\(354\) −0.292352 + 0.739811i −0.0155383 + 0.0393205i
\(355\) 5.07057i 0.269118i
\(356\) 20.4303 + 20.4303i 1.08280 + 1.08280i
\(357\) 3.57994 1.55196i 0.189470 0.0821384i
\(358\) 42.3259 + 42.3259i 2.23699 + 2.23699i
\(359\) 3.64309 3.64309i 0.192275 0.192275i −0.604404 0.796678i \(-0.706589\pi\)
0.796678 + 0.604404i \(0.206589\pi\)
\(360\) −6.72752 6.30102i −0.354572 0.332093i
\(361\) 8.56161i 0.450611i
\(362\) −31.6788 + 31.6788i −1.66500 + 1.66500i
\(363\) −1.61084 0.636556i −0.0845470 0.0334106i
\(364\) −3.71934 + 1.57911i −0.194946 + 0.0827676i
\(365\) 0.479477i 0.0250970i
\(366\) −10.0217 + 4.34456i −0.523842 + 0.227094i
\(367\) 7.14984 0.373219 0.186609 0.982434i \(-0.440250\pi\)
0.186609 + 0.982434i \(0.440250\pi\)
\(368\) 17.9439 0.935391
\(369\) −0.756089 23.0963i −0.0393604 1.20235i
\(370\) 3.65757 3.65757i 0.190148 0.190148i
\(371\) 1.48653 1.48653i 0.0771769 0.0771769i
\(372\) 5.24901 2.27553i 0.272148 0.117981i
\(373\) −3.35659 −0.173798 −0.0868988 0.996217i \(-0.527696\pi\)
−0.0868988 + 0.996217i \(0.527696\pi\)
\(374\) −18.6078 −0.962184
\(375\) −4.55141 10.4988i −0.235034 0.542157i
\(376\) 39.5489i 2.03958i
\(377\) −5.15133 + 12.7528i −0.265307 + 0.656804i
\(378\) −1.56882 3.31699i −0.0806914 0.170608i
\(379\) 2.65048 2.65048i 0.136146 0.136146i −0.635749 0.771896i \(-0.719309\pi\)
0.771896 + 0.635749i \(0.219309\pi\)
\(380\) 8.59530i 0.440929i
\(381\) −24.7511 9.78091i −1.26804 0.501091i
\(382\) −21.4165 + 21.4165i −1.09576 + 1.09576i
\(383\) −20.2101 20.2101i −1.03269 1.03269i −0.999447 0.0332396i \(-0.989418\pi\)
−0.0332396 0.999447i \(-0.510582\pi\)
\(384\) −14.1519 32.6445i −0.722187 1.66588i
\(385\) 0.143504 + 0.143504i 0.00731364 + 0.00731364i
\(386\) 37.3051i 1.89878i
\(387\) −10.2710 + 10.9663i −0.522106 + 0.557447i
\(388\) −15.0224 15.0224i −0.762646 0.762646i
\(389\) −38.1102 −1.93226 −0.966132 0.258049i \(-0.916920\pi\)
−0.966132 + 0.258049i \(0.916920\pi\)
\(390\) 7.58644 + 7.21389i 0.384154 + 0.365289i
\(391\) 45.7011 2.31120
\(392\) −21.6430 21.6430i −1.09314 1.09314i
\(393\) 8.29842 + 3.27930i 0.418600 + 0.165419i
\(394\) 27.3835i 1.37956i
\(395\) −2.39556 2.39556i −0.120534 0.120534i
\(396\) 0.376220 + 11.4924i 0.0189058 + 0.577517i
\(397\) −24.4808 24.4808i −1.22866 1.22866i −0.964472 0.264183i \(-0.914898\pi\)
−0.264183 0.964472i \(-0.585102\pi\)
\(398\) −13.5944 + 13.5944i −0.681426 + 0.681426i
\(399\) 0.601329 1.52169i 0.0301041 0.0761799i
\(400\) 13.6682i 0.683411i
\(401\) −22.1907 + 22.1907i −1.10815 + 1.10815i −0.114756 + 0.993394i \(0.536609\pi\)
−0.993394 + 0.114756i \(0.963391\pi\)
\(402\) −5.40998 + 13.6902i −0.269825 + 0.682805i
\(403\) −2.86004 + 1.21428i −0.142469 + 0.0604875i
\(404\) 28.7048i 1.42812i
\(405\) −4.11886 + 4.69665i −0.204668 + 0.233378i
\(406\) 2.69374 0.133688
\(407\) −3.08565 −0.152950
\(408\) 23.4960 + 54.1987i 1.16322 + 2.68323i
\(409\) −25.4319 + 25.4319i −1.25753 + 1.25753i −0.305256 + 0.952270i \(0.598742\pi\)
−0.952270 + 0.305256i \(0.901258\pi\)
\(410\) 9.13063 9.13063i 0.450929 0.450929i
\(411\) 6.20549 + 14.3143i 0.306094 + 0.706074i
\(412\) 50.3159 2.47889
\(413\) −0.0556015 −0.00273597
\(414\) −1.40616 42.9540i −0.0691088 2.11107i
\(415\) 12.0008i 0.589098i
\(416\) 2.18002 + 5.13469i 0.106884 + 0.251749i
\(417\) −1.98754 + 5.02957i −0.0973304 + 0.246299i
\(418\) −5.51751 + 5.51751i −0.269870 + 0.269870i
\(419\) 0.526677i 0.0257298i 0.999917 + 0.0128649i \(0.00409514\pi\)
−0.999917 + 0.0128649i \(0.995905\pi\)
\(420\) 0.495153 1.25301i 0.0241610 0.0611406i
\(421\) −15.4532 + 15.4532i −0.753144 + 0.753144i −0.975065 0.221921i \(-0.928767\pi\)
0.221921 + 0.975065i \(0.428767\pi\)
\(422\) −5.23584 5.23584i −0.254877 0.254877i
\(423\) −26.7887 + 0.876964i −1.30251 + 0.0426395i
\(424\) 22.5054 + 22.5054i 1.09296 + 1.09296i
\(425\) 34.8114i 1.68860i
\(426\) −28.4203 11.2309i −1.37697 0.544139i
\(427\) −0.539858 0.539858i −0.0261256 0.0261256i
\(428\) 50.5143 2.44170
\(429\) −0.157148 6.24302i −0.00758716 0.301416i
\(430\) −8.39570 −0.404877
\(431\) −10.0651 10.0651i −0.484817 0.484817i 0.421849 0.906666i \(-0.361381\pi\)
−0.906666 + 0.421849i \(0.861381\pi\)
\(432\) 14.2098 6.72074i 0.683671 0.323352i
\(433\) 11.4494i 0.550224i 0.961412 + 0.275112i \(0.0887150\pi\)
−0.961412 + 0.275112i \(0.911285\pi\)
\(434\) 0.430302 + 0.430302i 0.0206552 + 0.0206552i
\(435\) −1.82408 4.20766i −0.0874582 0.201742i
\(436\) −35.7999 35.7999i −1.71451 1.71451i
\(437\) 13.5511 13.5511i 0.648239 0.648239i
\(438\) −2.68745 1.06200i −0.128411 0.0507444i
\(439\) 3.61495i 0.172532i 0.996272 + 0.0862661i \(0.0274935\pi\)
−0.996272 + 0.0862661i \(0.972506\pi\)
\(440\) −2.17259 + 2.17259i −0.103574 + 0.103574i
\(441\) −14.1801 + 15.1400i −0.675244 + 0.720950i
\(442\) −26.2194 61.7558i −1.24713 2.93742i
\(443\) 10.0361i 0.476830i 0.971163 + 0.238415i \(0.0766278\pi\)
−0.971163 + 0.238415i \(0.923372\pi\)
\(444\) 8.14778 + 18.7946i 0.386676 + 0.891955i
\(445\) 5.23223 0.248032
\(446\) 36.2610 1.71701
\(447\) 2.62808 1.13931i 0.124304 0.0538877i
\(448\) 2.02341 2.02341i 0.0955973 0.0955973i
\(449\) −14.0855 + 14.0855i −0.664737 + 0.664737i −0.956493 0.291755i \(-0.905761\pi\)
0.291755 + 0.956493i \(0.405761\pi\)
\(450\) 32.7188 1.07109i 1.54238 0.0504919i
\(451\) −7.70290 −0.362715
\(452\) −47.7043 −2.24382
\(453\) −5.64074 + 2.44535i −0.265025 + 0.114893i
\(454\) 49.7713i 2.33588i
\(455\) −0.274058 + 0.678469i −0.0128480 + 0.0318071i
\(456\) 23.0377 + 9.10385i 1.07884 + 0.426327i
\(457\) 5.29636 5.29636i 0.247753 0.247753i −0.572295 0.820048i \(-0.693947\pi\)
0.820048 + 0.572295i \(0.193947\pi\)
\(458\) 51.9854i 2.42912i
\(459\) 36.1908 17.1170i 1.68924 0.798951i
\(460\) 11.1584 11.1584i 0.520264 0.520264i
\(461\) 18.5585 + 18.5585i 0.864354 + 0.864354i 0.991840 0.127486i \(-0.0406908\pi\)
−0.127486 + 0.991840i \(0.540691\pi\)
\(462\) −1.12218 + 0.486484i −0.0522087 + 0.0226333i
\(463\) −7.18404 7.18404i −0.333871 0.333871i 0.520184 0.854054i \(-0.325863\pi\)
−0.854054 + 0.520184i \(0.825863\pi\)
\(464\) 11.5398i 0.535723i
\(465\) 0.380756 0.963522i 0.0176571 0.0446822i
\(466\) −22.3305 22.3305i −1.03444 1.03444i
\(467\) 8.04940 0.372482 0.186241 0.982504i \(-0.440370\pi\)
0.186241 + 0.982504i \(0.440370\pi\)
\(468\) −37.6112 + 17.4421i −1.73858 + 0.806262i
\(469\) −1.02891 −0.0475105
\(470\) −10.5903 10.5903i −0.488496 0.488496i
\(471\) −9.23102 + 23.3595i −0.425343 + 1.07635i
\(472\) 0.841782i 0.0387462i
\(473\) 3.54145 + 3.54145i 0.162836 + 0.162836i
\(474\) 18.7329 8.12103i 0.860433 0.373011i
\(475\) 10.3221 + 10.3221i 0.473613 + 0.473613i
\(476\) −6.10548 + 6.10548i −0.279844 + 0.279844i
\(477\) 14.7452 15.7432i 0.675134 0.720833i
\(478\) 43.2325i 1.97741i
\(479\) −29.7250 + 29.7250i −1.35817 + 1.35817i −0.481999 + 0.876172i \(0.660089\pi\)
−0.876172 + 0.481999i \(0.839911\pi\)
\(480\) −1.72983 0.683579i −0.0789555 0.0312010i
\(481\) −4.34786 10.2407i −0.198245 0.466936i
\(482\) 37.6202i 1.71355i
\(483\) 2.75611 1.19482i 0.125407 0.0543661i
\(484\) 3.83287 0.174221
\(485\) −3.84725 −0.174695
\(486\) −17.2016 33.4887i −0.780280 1.51908i
\(487\) −6.16106 + 6.16106i −0.279184 + 0.279184i −0.832783 0.553599i \(-0.813254\pi\)
0.553599 + 0.832783i \(0.313254\pi\)
\(488\) 8.17321 8.17321i 0.369984 0.369984i
\(489\) 33.6704 14.5966i 1.52263 0.660082i
\(490\) −11.5911 −0.523630
\(491\) −24.6292 −1.11150 −0.555750 0.831349i \(-0.687569\pi\)
−0.555750 + 0.831349i \(0.687569\pi\)
\(492\) 20.3398 + 46.9182i 0.916989 + 2.11524i
\(493\) 29.3906i 1.32369i
\(494\) −26.0861 10.5371i −1.17367 0.474087i
\(495\) 1.51979 + 1.42344i 0.0683095 + 0.0639789i
\(496\) −1.84339 + 1.84339i −0.0827708 + 0.0827708i
\(497\) 2.13597i 0.0958114i
\(498\) 67.2641 + 26.5809i 3.01418 + 1.19112i
\(499\) 23.1951 23.1951i 1.03835 1.03835i 0.0391187 0.999235i \(-0.487545\pi\)
0.999235 0.0391187i \(-0.0124551\pi\)
\(500\) 17.9054 + 17.9054i 0.800756 + 0.800756i
\(501\) 2.37851 + 5.48656i 0.106264 + 0.245122i
\(502\) −2.10377 2.10377i −0.0938960 0.0938960i
\(503\) 5.48591i 0.244605i −0.992493 0.122302i \(-0.960972\pi\)
0.992493 0.122302i \(-0.0390277\pi\)
\(504\) 2.83396 + 2.65429i 0.126234 + 0.118232i
\(505\) 3.67567 + 3.67567i 0.163565 + 0.163565i
\(506\) −14.3257 −0.636853
\(507\) 20.4980 9.31832i 0.910349 0.413841i
\(508\) 58.8933 2.61297
\(509\) −4.06978 4.06978i −0.180390 0.180390i 0.611136 0.791526i \(-0.290713\pi\)
−0.791526 + 0.611136i \(0.790713\pi\)
\(510\) 20.8049 + 8.22151i 0.921257 + 0.364054i
\(511\) 0.201979i 0.00893502i
\(512\) 22.2473 + 22.2473i 0.983201 + 0.983201i
\(513\) 5.65571 15.8066i 0.249706 0.697880i
\(514\) 5.25746 + 5.25746i 0.231897 + 0.231897i
\(515\) 6.44299 6.44299i 0.283912 0.283912i
\(516\) 12.2196 30.9222i 0.537937 1.36128i
\(517\) 8.93435i 0.392932i
\(518\) −1.54075 + 1.54075i −0.0676965 + 0.0676965i
\(519\) 7.31586 18.5131i 0.321131 0.812637i
\(520\) −10.2717 4.14912i −0.450445 0.181951i
\(521\) 28.4799i 1.24773i 0.781534 + 0.623863i \(0.214438\pi\)
−0.781534 + 0.623863i \(0.785562\pi\)
\(522\) 27.6239 0.904306i 1.20907 0.0395804i
\(523\) 36.3221 1.58826 0.794128 0.607751i \(-0.207928\pi\)
0.794128 + 0.607751i \(0.207928\pi\)
\(524\) −19.7455 −0.862585
\(525\) 0.910114 + 2.09938i 0.0397206 + 0.0916244i
\(526\) 1.26179 1.26179i 0.0550165 0.0550165i
\(527\) −4.69491 + 4.69491i −0.204514 + 0.204514i
\(528\) −2.08407 4.80737i −0.0906975 0.209214i
\(529\) 12.1842 0.529748
\(530\) 12.0529 0.523545
\(531\) −0.570187 + 0.0186658i −0.0247440 + 0.000810028i
\(532\) 3.62075i 0.156980i
\(533\) −10.8538 25.5645i −0.470132 1.10732i
\(534\) −11.5890 + 29.3264i −0.501503 + 1.26908i
\(535\) 6.46839 6.46839i 0.279653 0.279653i
\(536\) 15.5772i 0.672832i
\(537\) −15.7767 + 39.9238i −0.680817 + 1.72284i
\(538\) −55.3485 + 55.3485i −2.38624 + 2.38624i
\(539\) 4.88930 + 4.88930i 0.210597 + 0.210597i
\(540\) 4.65709 13.0157i 0.200409 0.560105i
\(541\) 12.3828 + 12.3828i 0.532377 + 0.532377i 0.921279 0.388902i \(-0.127146\pi\)
−0.388902 + 0.921279i \(0.627146\pi\)
\(542\) 41.4668i 1.78115i
\(543\) −29.8810 11.8081i −1.28231 0.506734i
\(544\) 8.42886 + 8.42886i 0.361385 + 0.361385i
\(545\) −9.16842 −0.392732
\(546\) −3.19577 3.03884i −0.136766 0.130050i
\(547\) 6.37191 0.272443 0.136222 0.990678i \(-0.456504\pi\)
0.136222 + 0.990678i \(0.456504\pi\)
\(548\) −24.4127 24.4127i −1.04286 1.04286i
\(549\) −5.71741 5.35494i −0.244013 0.228543i
\(550\) 10.9121i 0.465294i
\(551\) 8.71480 + 8.71480i 0.371263 + 0.371263i
\(552\) 18.0890 + 41.7263i 0.769919 + 1.77599i
\(553\) 1.00912 + 1.00912i 0.0429123 + 0.0429123i
\(554\) 48.0697 48.0697i 2.04228 2.04228i
\(555\) 3.45000 + 1.36334i 0.146444 + 0.0578705i
\(556\) 11.9675i 0.507535i
\(557\) 12.9428 12.9428i 0.548405 0.548405i −0.377574 0.925979i \(-0.623242\pi\)
0.925979 + 0.377574i \(0.123242\pi\)
\(558\) 4.55715 + 4.26824i 0.192920 + 0.180689i
\(559\) −6.76331 + 16.7435i −0.286058 + 0.708175i
\(560\) 0.613935i 0.0259435i
\(561\) −5.30789 12.2438i −0.224099 0.516935i
\(562\) −44.7137 −1.88613
\(563\) 20.5332 0.865372 0.432686 0.901545i \(-0.357566\pi\)
0.432686 + 0.901545i \(0.357566\pi\)
\(564\) 54.4190 23.5915i 2.29145 0.993382i
\(565\) −6.10857 + 6.10857i −0.256990 + 0.256990i
\(566\) 31.5189 31.5189i 1.32484 1.32484i
\(567\) 1.73506 1.97845i 0.0728657 0.0830873i
\(568\) 32.3376 1.35686
\(569\) 19.1130 0.801257 0.400629 0.916241i \(-0.368792\pi\)
0.400629 + 0.916241i \(0.368792\pi\)
\(570\) 8.60681 3.73119i 0.360500 0.156282i
\(571\) 45.6854i 1.91188i 0.293569 + 0.955938i \(0.405157\pi\)
−0.293569 + 0.955938i \(0.594843\pi\)
\(572\) 5.40073 + 12.7206i 0.225816 + 0.531874i
\(573\) −20.2010 7.98286i −0.843910 0.333489i
\(574\) −3.84626 + 3.84626i −0.160540 + 0.160540i
\(575\) 26.8004i 1.11766i
\(576\) 20.0706 21.4291i 0.836274 0.892880i
\(577\) −25.0351 + 25.0351i −1.04222 + 1.04222i −0.0431553 + 0.999068i \(0.513741\pi\)
−0.999068 + 0.0431553i \(0.986259\pi\)
\(578\) −72.3434 72.3434i −3.00909 3.00909i
\(579\) −24.5466 + 10.6413i −1.02012 + 0.442238i
\(580\) 7.17604 + 7.17604i 0.297969 + 0.297969i
\(581\) 5.05533i 0.209730i
\(582\) 8.52134 21.5637i 0.353221 0.893843i
\(583\) −5.08412 5.08412i −0.210563 0.210563i
\(584\) 3.05787 0.126536
\(585\) −2.58266 + 7.04962i −0.106780 + 0.291466i
\(586\) −59.8606 −2.47282
\(587\) −27.2706 27.2706i −1.12558 1.12558i −0.990887 0.134692i \(-0.956995\pi\)
−0.134692 0.990887i \(-0.543005\pi\)
\(588\) 16.8703 42.6910i 0.695718 1.76055i
\(589\) 2.78424i 0.114722i
\(590\) −0.225411 0.225411i −0.00928002 0.00928002i
\(591\) 18.0182 7.81118i 0.741170 0.321309i
\(592\) −6.60047 6.60047i −0.271278 0.271278i
\(593\) 12.9483 12.9483i 0.531722 0.531722i −0.389363 0.921084i \(-0.627305\pi\)
0.921084 + 0.389363i \(0.127305\pi\)
\(594\) −11.3445 + 5.36555i −0.465471 + 0.220151i
\(595\) 1.56362i 0.0641023i
\(596\) −4.48211 + 4.48211i −0.183594 + 0.183594i
\(597\) −12.8229 5.06724i −0.524806 0.207388i
\(598\) −20.1857 47.5443i −0.825454 1.94423i
\(599\) 28.2602i 1.15468i −0.816504 0.577340i \(-0.804091\pi\)
0.816504 0.577340i \(-0.195909\pi\)
\(600\) −31.7837 + 13.7787i −1.29756 + 0.562514i
\(601\) −13.5389 −0.552264 −0.276132 0.961120i \(-0.589053\pi\)
−0.276132 + 0.961120i \(0.589053\pi\)
\(602\) 3.53668 0.144144
\(603\) −10.5513 + 0.345411i −0.429682 + 0.0140662i
\(604\) 9.62013 9.62013i 0.391437 0.391437i
\(605\) 0.490801 0.490801i 0.0199539 0.0199539i
\(606\) −28.7433 + 12.4607i −1.16762 + 0.506180i
\(607\) −34.4697 −1.39908 −0.699542 0.714592i \(-0.746612\pi\)
−0.699542 + 0.714592i \(0.746612\pi\)
\(608\) 4.99859 0.202720
\(609\) 0.768392 + 1.77247i 0.0311368 + 0.0718240i
\(610\) 4.37721i 0.177228i
\(611\) −29.6515 + 12.5890i −1.19957 + 0.509297i
\(612\) −60.5613 + 64.6606i −2.44804 + 2.61375i
\(613\) 21.9672 21.9672i 0.887246 0.887246i −0.107011 0.994258i \(-0.534128\pi\)
0.994258 + 0.107011i \(0.0341281\pi\)
\(614\) 47.0695i 1.89957i
\(615\) 8.61244 + 3.40339i 0.347287 + 0.137238i
\(616\) 0.915198 0.915198i 0.0368744 0.0368744i
\(617\) 30.7830 + 30.7830i 1.23928 + 1.23928i 0.960297 + 0.278979i \(0.0899960\pi\)
0.278979 + 0.960297i \(0.410004\pi\)
\(618\) 21.8420 + 50.3833i 0.878613 + 2.02672i
\(619\) −3.05526 3.05526i −0.122801 0.122801i 0.643035 0.765836i \(-0.277675\pi\)
−0.765836 + 0.643035i \(0.777675\pi\)
\(620\) 2.29263i 0.0920741i
\(621\) 27.8624 13.1779i 1.11808 0.528812i
\(622\) 21.8160 + 21.8160i 0.874741 + 0.874741i
\(623\) −2.20407 −0.0883041
\(624\) 13.0182 13.6905i 0.521146 0.548059i
\(625\) −18.0055 −0.720221
\(626\) −8.54216 8.54216i −0.341413 0.341413i
\(627\) −5.20437 2.05662i −0.207843 0.0821334i
\(628\) 55.5822i 2.21797i
\(629\) −16.8106 16.8106i −0.670284 0.670284i
\(630\) 1.46963 0.0481104i 0.0585516 0.00191676i
\(631\) 17.2385 + 17.2385i 0.686256 + 0.686256i 0.961402 0.275147i \(-0.0887264\pi\)
−0.275147 + 0.961402i \(0.588726\pi\)
\(632\) −15.2777 + 15.2777i −0.607714 + 0.607714i
\(633\) 1.95163 4.93870i 0.0775704 0.196296i
\(634\) 14.1949i 0.563750i
\(635\) 7.54133 7.54133i 0.299268 0.299268i
\(636\) −17.5425 + 44.3921i −0.695605 + 1.76026i
\(637\) −9.33738 + 23.1160i −0.369961 + 0.915889i
\(638\) 9.21290i 0.364742i
\(639\) −0.717060 21.9041i −0.0283665 0.866513i
\(640\) 14.2583 0.563607
\(641\) 7.92897 0.313175 0.156588 0.987664i \(-0.449951\pi\)
0.156588 + 0.987664i \(0.449951\pi\)
\(642\) 21.9281 + 50.5820i 0.865433 + 1.99631i
\(643\) −17.1643 + 17.1643i −0.676894 + 0.676894i −0.959296 0.282402i \(-0.908869\pi\)
0.282402 + 0.959296i \(0.408869\pi\)
\(644\) −4.70047 + 4.70047i −0.185224 + 0.185224i
\(645\) −2.39489 5.52434i −0.0942986 0.217521i
\(646\) −60.1189 −2.36535
\(647\) 16.6296 0.653777 0.326889 0.945063i \(-0.394000\pi\)
0.326889 + 0.945063i \(0.394000\pi\)
\(648\) 29.9529 + 26.2680i 1.17666 + 1.03191i
\(649\) 0.190164i 0.00746459i
\(650\) 36.2153 15.3758i 1.42048 0.603089i
\(651\) −0.160393 + 0.405882i −0.00628629 + 0.0159078i
\(652\) −57.4238 + 57.4238i −2.24889 + 2.24889i
\(653\) 23.9169i 0.935942i 0.883744 + 0.467971i \(0.155015\pi\)
−0.883744 + 0.467971i \(0.844985\pi\)
\(654\) 20.3073 51.3886i 0.794077 2.00945i
\(655\) −2.52842 + 2.52842i −0.0987936 + 0.0987936i
\(656\) −16.4772 16.4772i −0.643325 0.643325i
\(657\) −0.0678057 2.07127i −0.00264535 0.0808078i
\(658\) 4.46116 + 4.46116i 0.173914 + 0.173914i
\(659\) 46.0117i 1.79236i −0.443690 0.896180i \(-0.646331\pi\)
0.443690 0.896180i \(-0.353669\pi\)
\(660\) −4.28544 1.69348i −0.166811 0.0659188i
\(661\) −2.99437 2.99437i −0.116468 0.116468i 0.646471 0.762939i \(-0.276244\pi\)
−0.762939 + 0.646471i \(0.776244\pi\)
\(662\) −59.3737 −2.30763
\(663\) 33.1559 34.8682i 1.28767 1.35417i
\(664\) −76.5354 −2.97015
\(665\) 0.463640 + 0.463640i 0.0179792 + 0.0179792i
\(666\) −15.2829 + 16.3174i −0.592201 + 0.632286i
\(667\) 22.6271i 0.876126i
\(668\) −9.35718 9.35718i −0.362040 0.362040i
\(669\) 10.3435 + 23.8596i 0.399903 + 0.922465i
\(670\) −4.17123 4.17123i −0.161149 0.161149i
\(671\) −1.84638 + 1.84638i −0.0712787 + 0.0712787i
\(672\) 0.728687 + 0.287956i 0.0281097 + 0.0111082i
\(673\) 36.5964i 1.41069i −0.708865 0.705344i \(-0.750792\pi\)
0.708865 0.705344i \(-0.249208\pi\)
\(674\) 28.8547 28.8547i 1.11144 1.11144i
\(675\) 10.0379 + 21.2233i 0.386358 + 0.816886i
\(676\) −34.6074 + 35.8481i −1.33105 + 1.37877i
\(677\) 33.1807i 1.27524i −0.770352 0.637619i \(-0.779919\pi\)
0.770352 0.637619i \(-0.220081\pi\)
\(678\) −20.7083 47.7682i −0.795297 1.83453i
\(679\) 1.62065 0.0621947
\(680\) −23.6725 −0.907801
\(681\) 32.7493 14.1973i 1.25496 0.544043i
\(682\) 1.47169 1.47169i 0.0563538 0.0563538i
\(683\) −2.90156 + 2.90156i −0.111025 + 0.111025i −0.760437 0.649412i \(-0.775015\pi\)
0.649412 + 0.760437i \(0.275015\pi\)
\(684\) 1.21551 + 37.1304i 0.0464763 + 1.41971i
\(685\) −6.25213 −0.238881
\(686\) 9.82579 0.375150
\(687\) −34.2062 + 14.8289i −1.30505 + 0.565759i
\(688\) 15.1509i 0.577624i
\(689\) 9.70945 24.0371i 0.369901 0.915740i
\(690\) 16.0172 + 6.32954i 0.609765 + 0.240962i
\(691\) 10.6714 10.6714i 0.405960 0.405960i −0.474367 0.880327i \(-0.657323\pi\)
0.880327 + 0.474367i \(0.157323\pi\)
\(692\) 44.0506i 1.67455i
\(693\) −0.640209 0.599621i −0.0243195 0.0227777i
\(694\) −27.7417 + 27.7417i −1.05306 + 1.05306i
\(695\) −1.53245 1.53245i −0.0581290 0.0581290i
\(696\) −26.8344 + 11.6331i −1.01715 + 0.440952i
\(697\) −41.9655 41.9655i −1.58956 1.58956i
\(698\) 56.2796i 2.13021i
\(699\) 8.32356 21.0632i 0.314826 0.796682i
\(700\) −3.58043 3.58043i −0.135328 0.135328i
\(701\) 39.1347 1.47810 0.739049 0.673651i \(-0.235275\pi\)
0.739049 + 0.673651i \(0.235275\pi\)
\(702\) −33.7924 30.0900i −1.27541 1.13568i
\(703\) −9.96927 −0.375998
\(704\) −6.92032 6.92032i −0.260819 0.260819i
\(705\) 3.94749 9.98930i 0.148671 0.376219i
\(706\) 25.5598i 0.961954i
\(707\) −1.54837 1.54837i −0.0582325 0.0582325i
\(708\) 1.15829 0.502135i 0.0435311 0.0188714i
\(709\) 2.37210 + 2.37210i 0.0890862 + 0.0890862i 0.750246 0.661159i \(-0.229935\pi\)
−0.661159 + 0.750246i \(0.729935\pi\)
\(710\) 8.65931 8.65931i 0.324978 0.324978i
\(711\) 10.6872 + 10.0097i 0.400801 + 0.375392i
\(712\) 33.3686i 1.25054i
\(713\) −3.61450 + 3.61450i −0.135364 + 0.135364i
\(714\) −8.76404 3.46329i −0.327986 0.129611i
\(715\) 2.32045 + 0.937312i 0.0867798 + 0.0350535i
\(716\) 94.9957i 3.55016i
\(717\) −28.4468 + 12.3321i −1.06237 + 0.460552i
\(718\) −12.4430 −0.464369
\(719\) 4.95664 0.184851 0.0924257 0.995720i \(-0.470538\pi\)
0.0924257 + 0.995720i \(0.470538\pi\)
\(720\) 0.206102 + 6.29582i 0.00768098 + 0.234632i
\(721\) −2.71410 + 2.71410i −0.101078 + 0.101078i
\(722\) 14.6211 14.6211i 0.544142 0.544142i
\(723\) 24.7540 10.7312i 0.920609 0.399099i
\(724\) 71.0995 2.64239
\(725\) −17.2355 −0.640110
\(726\) 1.66383 + 3.83800i 0.0617507 + 0.142442i
\(727\) 25.3584i 0.940491i −0.882536 0.470245i \(-0.844165\pi\)
0.882536 0.470245i \(-0.155835\pi\)
\(728\) 4.32694 + 1.74781i 0.160367 + 0.0647781i
\(729\) 17.1286 20.8713i 0.634394 0.773010i
\(730\) 0.818830 0.818830i 0.0303063 0.0303063i
\(731\) 38.5877i 1.42722i
\(732\) 16.1217 + 6.37084i 0.595876 + 0.235473i
\(733\) 12.4432 12.4432i 0.459599 0.459599i −0.438925 0.898524i \(-0.644641\pi\)
0.898524 + 0.438925i \(0.144641\pi\)
\(734\) −12.2102 12.2102i −0.450686 0.450686i
\(735\) −3.30637 7.62686i −0.121957 0.281321i
\(736\) 6.48918 + 6.48918i 0.239194 + 0.239194i
\(737\) 3.51898i 0.129623i
\(738\) −38.1517 + 40.7341i −1.40438 + 1.49944i
\(739\) 9.98888 + 9.98888i 0.367447 + 0.367447i 0.866545 0.499098i \(-0.166335\pi\)
−0.499098 + 0.866545i \(0.666335\pi\)
\(740\) −8.20901 −0.301769
\(741\) −0.507721 20.1703i −0.0186516 0.740973i
\(742\) −5.07727 −0.186392
\(743\) 23.8013 + 23.8013i 0.873184 + 0.873184i 0.992818 0.119634i \(-0.0381720\pi\)
−0.119634 + 0.992818i \(0.538172\pi\)
\(744\) −6.14487 2.42827i −0.225282 0.0890249i
\(745\) 1.14788i 0.0420549i
\(746\) 5.73224 + 5.73224i 0.209872 + 0.209872i
\(747\) 1.69711 + 51.8418i 0.0620940 + 1.89679i
\(748\) 20.8815 + 20.8815i 0.763503 + 0.763503i
\(749\) −2.72480 + 2.72480i −0.0995620 + 0.0995620i
\(750\) −10.1567 + 25.7021i −0.370872 + 0.938509i
\(751\) 44.5125i 1.62428i −0.583459 0.812142i \(-0.698301\pi\)
0.583459 0.812142i \(-0.301699\pi\)
\(752\) −19.1114 + 19.1114i −0.696920 + 0.696920i
\(753\) 0.784169 1.98438i 0.0285767 0.0723148i
\(754\) 30.5760 12.9815i 1.11351 0.472759i
\(755\) 2.46373i 0.0896643i
\(756\) −1.96179 + 5.48283i −0.0713496 + 0.199409i
\(757\) −7.13372 −0.259280 −0.129640 0.991561i \(-0.541382\pi\)
−0.129640 + 0.991561i \(0.541382\pi\)
\(758\) −9.05277 −0.328811
\(759\) −4.08642 9.42623i −0.148328 0.342150i
\(760\) −7.01930 + 7.01930i −0.254617 + 0.254617i
\(761\) −15.8503 + 15.8503i −0.574571 + 0.574571i −0.933403 0.358831i \(-0.883175\pi\)
0.358831 + 0.933403i \(0.383175\pi\)
\(762\) 25.5654 + 58.9722i 0.926136 + 2.13634i
\(763\) 3.86218 0.139820
\(764\) 48.0668 1.73900
\(765\) 0.524919 + 16.0347i 0.0189785 + 0.579738i
\(766\) 69.0278i 2.49408i
\(767\) −0.631120 + 0.267952i −0.0227884 + 0.00967519i
\(768\) −19.1211 + 48.3870i −0.689975 + 1.74602i
\(769\) 25.8917 25.8917i 0.933680 0.933680i −0.0642540 0.997934i \(-0.520467\pi\)
0.997934 + 0.0642540i \(0.0204668\pi\)
\(770\) 0.490140i 0.0176634i
\(771\) −1.95969 + 4.95909i −0.0705765 + 0.178597i
\(772\) 41.8635 41.8635i 1.50670 1.50670i
\(773\) 13.5883 + 13.5883i 0.488739 + 0.488739i 0.907908 0.419169i \(-0.137679\pi\)
−0.419169 + 0.907908i \(0.637679\pi\)
\(774\) 36.2681 1.18729i 1.30363 0.0426761i
\(775\) −2.75323 2.75323i −0.0988989 0.0988989i
\(776\) 24.5359i 0.880787i
\(777\) −1.45330 0.574304i −0.0521370 0.0206030i
\(778\) 65.0829 + 65.0829i 2.33334 + 2.33334i
\(779\) −24.8869 −0.891666
\(780\) −0.418073 16.6088i −0.0149694 0.594691i
\(781\) −7.30528 −0.261403
\(782\) −78.0464 78.0464i −2.79093 2.79093i
\(783\) 8.47479 + 17.9185i 0.302864 + 0.640354i
\(784\) 20.9173i 0.747045i
\(785\) −7.11735 7.11735i −0.254029 0.254029i
\(786\) −8.57144 19.7719i −0.305733 0.705241i
\(787\) −10.0432 10.0432i −0.358003 0.358003i 0.505073 0.863076i \(-0.331465\pi\)
−0.863076 + 0.505073i \(0.831465\pi\)
\(788\) −30.7295 + 30.7295i −1.09469 + 1.09469i
\(789\) 1.19018 + 0.470324i 0.0423714 + 0.0167440i
\(790\) 8.18205i 0.291104i
\(791\) 2.57322 2.57322i 0.0914933 0.0914933i
\(792\) 9.07800 9.69247i 0.322573 0.344407i
\(793\) −8.72946 3.52614i −0.309992 0.125217i
\(794\) 83.6145i 2.96737i
\(795\) 3.43811 + 7.93077i 0.121937 + 0.281275i
\(796\) 30.5111 1.08144
\(797\) 9.35059 0.331215 0.165608 0.986192i \(-0.447042\pi\)
0.165608 + 0.986192i \(0.447042\pi\)
\(798\) −3.62560 + 1.57176i −0.128345 + 0.0556396i
\(799\) −48.6745 + 48.6745i −1.72198 + 1.72198i
\(800\) −4.94293 + 4.94293i −0.174759 + 0.174759i
\(801\) −22.6024 + 0.739921i −0.798617 + 0.0261438i
\(802\) 75.7926 2.67633
\(803\) −0.690792 −0.0243775
\(804\) 21.4341 9.29202i 0.755922 0.327704i
\(805\) 1.20380i 0.0424282i
\(806\) 6.95795 + 2.81057i 0.245083 + 0.0989980i
\(807\) −52.2073 20.6308i −1.83778 0.726240i
\(808\) 23.4416 23.4416i 0.824674 0.824674i
\(809\) 8.55554i 0.300797i −0.988625 0.150398i \(-0.951944\pi\)
0.988625 0.150398i \(-0.0480556\pi\)
\(810\) 15.0547 0.986731i 0.528970 0.0346702i
\(811\) 28.7824 28.7824i 1.01069 1.01069i 0.0107441 0.999942i \(-0.496580\pi\)
0.999942 0.0107441i \(-0.00342003\pi\)
\(812\) −3.02289 3.02289i −0.106083 0.106083i
\(813\) −27.2850 + 11.8285i −0.956927 + 0.414843i
\(814\) 5.26954 + 5.26954i 0.184697 + 0.184697i
\(815\) 14.7063i 0.515140i
\(816\) 14.8366 37.5446i 0.519384 1.31433i
\(817\) 11.4419 + 11.4419i 0.400301 + 0.400301i
\(818\) 86.8630 3.03709
\(819\) 1.08794 2.96964i 0.0380158 0.103768i
\(820\) −20.4927 −0.715634
\(821\) 28.8221 + 28.8221i 1.00590 + 1.00590i 0.999982 + 0.00591632i \(0.00188323\pi\)
0.00591632 + 0.999982i \(0.498117\pi\)
\(822\) 13.8479 35.0429i 0.483002 1.22226i
\(823\) 35.9860i 1.25439i −0.778861 0.627197i \(-0.784202\pi\)
0.778861 0.627197i \(-0.215798\pi\)
\(824\) −41.0902 41.0902i −1.43145 1.43145i
\(825\) 7.18013 3.11270i 0.249980 0.108370i
\(826\) 0.0949539 + 0.0949539i 0.00330387 + 0.00330387i
\(827\) 21.6443 21.6443i 0.752647 0.752647i −0.222326 0.974972i \(-0.571365\pi\)
0.974972 + 0.222326i \(0.0713648\pi\)
\(828\) −46.6247 + 49.7806i −1.62032 + 1.73000i
\(829\) 16.5762i 0.575714i −0.957673 0.287857i \(-0.907057\pi\)
0.957673 0.287857i \(-0.0929428\pi\)
\(830\) −20.4945 + 20.4945i −0.711375 + 0.711375i
\(831\) 45.3416 + 17.9177i 1.57288 + 0.621558i
\(832\) 13.2162 32.7184i 0.458188 1.13431i
\(833\) 53.2739i 1.84583i
\(834\) 11.9835 5.19505i 0.414956 0.179890i
\(835\) −2.39639 −0.0829304
\(836\) 12.3834 0.428289
\(837\) −1.50855 + 4.21611i −0.0521431 + 0.145730i
\(838\) 0.899436 0.899436i 0.0310705 0.0310705i
\(839\) 19.9818 19.9818i 0.689847 0.689847i −0.272351 0.962198i \(-0.587801\pi\)
0.962198 + 0.272351i \(0.0878012\pi\)
\(840\) −1.42763 + 0.618899i −0.0492578 + 0.0213540i
\(841\) 14.4484 0.498220
\(842\) 52.7807 1.81894
\(843\) −12.7546 29.4214i −0.439293 1.01333i
\(844\) 11.7513i 0.404495i
\(845\) 0.158875 + 9.02187i 0.00546548 + 0.310362i
\(846\) 47.2462 + 44.2510i 1.62436 + 1.52138i
\(847\) −0.206749 + 0.206749i −0.00710398 + 0.00710398i
\(848\) 21.7507i 0.746924i
\(849\) 29.7301 + 11.7485i 1.02034 + 0.403207i
\(850\) 59.4494 59.4494i 2.03910 2.03910i
\(851\) −12.9421 12.9421i −0.443650 0.443650i
\(852\) 19.2899 + 44.4963i 0.660860 + 1.52442i
\(853\) −1.18725 1.18725i −0.0406508 0.0406508i 0.686489 0.727140i \(-0.259151\pi\)
−0.727140 + 0.686489i \(0.759151\pi\)
\(854\) 1.84389i 0.0630967i
\(855\) 4.91021 + 4.59892i 0.167926 + 0.157280i
\(856\) −41.2522 41.2522i −1.40997 1.40997i
\(857\) −43.2926 −1.47885 −0.739424 0.673240i \(-0.764902\pi\)
−0.739424 + 0.673240i \(0.764902\pi\)
\(858\) −10.3932 + 10.9299i −0.354818 + 0.373142i
\(859\) 25.3908 0.866322 0.433161 0.901317i \(-0.357398\pi\)
0.433161 + 0.901317i \(0.357398\pi\)
\(860\) 9.42160 + 9.42160i 0.321274 + 0.321274i
\(861\) −3.62797 1.43367i −0.123641 0.0488594i
\(862\) 34.3774i 1.17090i
\(863\) −24.3693 24.3693i −0.829539 0.829539i 0.157914 0.987453i \(-0.449523\pi\)
−0.987453 + 0.157914i \(0.949523\pi\)
\(864\) 7.56926 + 2.70833i 0.257512 + 0.0921392i
\(865\) 5.64071 + 5.64071i 0.191790 + 0.191790i
\(866\) 19.5528 19.5528i 0.664432 0.664432i
\(867\) 26.9656 68.2377i 0.915799 2.31747i
\(868\) 0.965765i 0.0327802i
\(869\) 3.45133 3.45133i 0.117078 0.117078i
\(870\) −4.07056 + 10.3007i −0.138005 + 0.349228i
\(871\) −11.6789 + 4.95845i −0.395723 + 0.168011i
\(872\) 58.4717i 1.98010i
\(873\) 16.6195 0.544063i 0.562486 0.0184137i
\(874\) −46.2841 −1.56558
\(875\) −1.93168 −0.0653027
\(876\) 1.82406 + 4.20761i 0.0616294 + 0.142162i
\(877\) −15.7593 + 15.7593i −0.532155 + 0.532155i −0.921213 0.389058i \(-0.872801\pi\)
0.389058 + 0.921213i \(0.372801\pi\)
\(878\) 6.17346 6.17346i 0.208344 0.208344i
\(879\) −17.0753 39.3880i −0.575937 1.32853i
\(880\) 2.09973 0.0707820
\(881\) 14.4374 0.486409 0.243205 0.969975i \(-0.421801\pi\)
0.243205 + 0.969975i \(0.421801\pi\)
\(882\) 50.0715 1.63916i 1.68600 0.0551934i
\(883\) 25.0665i 0.843555i 0.906699 + 0.421778i \(0.138594\pi\)
−0.906699 + 0.421778i \(0.861406\pi\)
\(884\) −39.8786 + 98.7251i −1.34126 + 3.32049i
\(885\) 0.0840206 0.212618i 0.00282432 0.00714708i
\(886\) 17.1392 17.1392i 0.575804 0.575804i
\(887\) 36.6379i 1.23018i 0.788457 + 0.615091i \(0.210881\pi\)
−0.788457 + 0.615091i \(0.789119\pi\)
\(888\) 8.69471 22.0024i 0.291775 0.738351i
\(889\) −3.17677 + 3.17677i −0.106545 + 0.106545i
\(890\) −8.93538 8.93538i −0.299514 0.299514i
\(891\) −6.76656 5.93412i −0.226688 0.198800i
\(892\) −40.6918 40.6918i −1.36246 1.36246i
\(893\) 28.8656i 0.965949i
\(894\) −6.43379 2.54245i −0.215178 0.0850322i
\(895\) −12.1643 12.1643i −0.406607 0.406607i
\(896\) −6.00627 −0.200655
\(897\) 25.5259 26.8442i 0.852286 0.896301i
\(898\) 48.1093 1.60543
\(899\) −2.32450 2.32450i −0.0775265 0.0775265i
\(900\) −37.9188 35.5149i −1.26396 1.18383i
\(901\) 55.3967i 1.84553i
\(902\) 13.1547 + 13.1547i 0.438003 + 0.438003i
\(903\) 1.00884 + 2.32712i 0.0335722 + 0.0774416i
\(904\) 38.9575 + 38.9575i 1.29571 + 1.29571i
\(905\) 9.10434 9.10434i 0.302638 0.302638i
\(906\) 13.8091 + 5.45695i 0.458776 + 0.181295i
\(907\) 3.87488i 0.128663i 0.997929 + 0.0643317i \(0.0204916\pi\)
−0.997929 + 0.0643317i \(0.979508\pi\)
\(908\) −55.8530 + 55.8530i −1.85355 + 1.85355i
\(909\) −16.3981 15.3585i −0.543892 0.509411i
\(910\) 1.62669 0.690636i 0.0539241 0.0228943i
\(911\) 1.41239i 0.0467945i −0.999726 0.0233973i \(-0.992552\pi\)
0.999726 0.0233973i \(-0.00744826\pi\)
\(912\) −6.73332 15.5319i −0.222963 0.514312i
\(913\) 17.2898 0.572210
\(914\) −18.0898 −0.598357
\(915\) 2.88019 1.24861i 0.0952161 0.0412777i
\(916\) 58.3377 58.3377i 1.92753 1.92753i
\(917\) 1.06509 1.06509i 0.0351725 0.0351725i
\(918\) −91.0367 32.5735i −3.00466 1.07509i
\(919\) −58.2892 −1.92278 −0.961391 0.275186i \(-0.911261\pi\)
−0.961391 + 0.275186i \(0.911261\pi\)
\(920\) −18.2249 −0.600858
\(921\) −30.9716 + 13.4267i −1.02055 + 0.442423i
\(922\) 63.3867i 2.08753i
\(923\) −10.2936 24.2449i −0.338817 0.798030i
\(924\) 1.80523 + 0.713377i 0.0593879 + 0.0234684i
\(925\) 9.85825 9.85825i 0.324137 0.324137i
\(926\) 24.5372i 0.806342i
\(927\) −26.9216 + 28.7439i −0.884220 + 0.944072i
\(928\) −4.17322 + 4.17322i −0.136993 + 0.136993i
\(929\) −22.0972 22.0972i −0.724986 0.724986i 0.244630 0.969616i \(-0.421333\pi\)
−0.969616 + 0.244630i \(0.921333\pi\)
\(930\) −2.29570 + 0.995222i −0.0752789 + 0.0326346i
\(931\) 15.7966 + 15.7966i 0.517712 + 0.517712i
\(932\) 50.1182i 1.64168i
\(933\) −8.13178 + 20.5779i −0.266223 + 0.673689i
\(934\) −13.7464 13.7464i −0.449796 0.449796i
\(935\) 5.34778 0.174891
\(936\) 44.9590 + 16.4710i 1.46953 + 0.538370i
\(937\) −19.6838 −0.643042 −0.321521 0.946902i \(-0.604194\pi\)
−0.321521 + 0.946902i \(0.604194\pi\)
\(938\) 1.75712 + 1.75712i 0.0573721 + 0.0573721i
\(939\) 3.18404 8.05737i 0.103907 0.262942i
\(940\) 23.7688i 0.775253i
\(941\) −15.1802 15.1802i −0.494860 0.494860i 0.414974 0.909833i \(-0.363791\pi\)
−0.909833 + 0.414974i \(0.863791\pi\)
\(942\) 55.6567 24.1281i 1.81339 0.786135i
\(943\) −32.3082 32.3082i −1.05210 1.05210i
\(944\) −0.406777 + 0.406777i −0.0132395 + 0.0132395i
\(945\) 0.450871 + 0.953288i 0.0146668 + 0.0310105i
\(946\) 12.0959i 0.393270i
\(947\) 37.5296 37.5296i 1.21955 1.21955i 0.251759 0.967790i \(-0.418991\pi\)
0.967790 0.251759i \(-0.0810092\pi\)
\(948\) −30.1353 11.9086i −0.978750 0.386774i
\(949\) −0.973366 2.29261i −0.0315968 0.0744214i
\(950\) 35.2554i 1.14384i
\(951\) −9.34016 + 4.04911i −0.302875 + 0.131301i
\(952\) 9.97202 0.323195
\(953\) −32.6456 −1.05749 −0.528747 0.848780i \(-0.677338\pi\)
−0.528747 + 0.848780i \(0.677338\pi\)
\(954\) −52.0667 + 1.70447i −1.68572 + 0.0551844i
\(955\) 6.15499 6.15499i 0.199171 0.199171i
\(956\) 48.5152 48.5152i 1.56910 1.56910i
\(957\) 6.06205 2.62800i 0.195958 0.0849510i
\(958\) 101.526 3.28016
\(959\) 2.63370 0.0850465
\(960\) 4.67984 + 10.7951i 0.151041 + 0.348410i
\(961\) 30.2574i 0.976044i
\(962\) −10.0636 + 24.9137i −0.324462 + 0.803251i
\(963\) −27.0277 + 28.8572i −0.870956 + 0.929910i
\(964\) −42.2172 + 42.2172i −1.35972 + 1.35972i
\(965\) 10.7213i 0.345131i
\(966\) −6.74722 2.66631i −0.217088 0.0857870i
\(967\) 2.99860 2.99860i 0.0964286 0.0964286i −0.657247 0.753675i \(-0.728279\pi\)
0.753675 + 0.657247i \(0.228279\pi\)
\(968\) −3.13009 3.13009i −0.100605 0.100605i
\(969\) −17.1490 39.5580i −0.550905 1.27078i
\(970\) 6.57017 + 6.57017i 0.210955 + 0.210955i
\(971\) 11.5308i 0.370042i 0.982735 + 0.185021i \(0.0592353\pi\)
−0.982735 + 0.185021i \(0.940765\pi\)
\(972\) −18.2773 + 56.8843i −0.586244 + 1.82456i
\(973\) 0.645540 + 0.645540i 0.0206951 + 0.0206951i
\(974\) 21.0432 0.674267
\(975\) 20.4477 + 19.4436i 0.654851 + 0.622693i
\(976\) −7.89914 −0.252845
\(977\) −0.512393 0.512393i −0.0163929 0.0163929i 0.698863 0.715256i \(-0.253690\pi\)
−0.715256 + 0.698863i \(0.753690\pi\)
\(978\) −82.4283 32.5733i −2.63577 1.04158i
\(979\) 7.53818i 0.240921i
\(980\) 13.0074 + 13.0074i 0.415506 + 0.415506i
\(981\) 39.6061 1.29656i 1.26453 0.0413960i
\(982\) 42.0607 + 42.0607i 1.34221 + 1.34221i
\(983\) −29.5660 + 29.5660i −0.943009 + 0.943009i −0.998461 0.0554528i \(-0.982340\pi\)
0.0554528 + 0.998461i \(0.482340\pi\)
\(984\) 21.7051 54.9259i 0.691935 1.75097i
\(985\) 7.86988i 0.250755i
\(986\) 50.1920 50.1920i 1.59844 1.59844i
\(987\) −1.66287 + 4.20798i −0.0529298 + 0.133941i
\(988\) 17.4490 + 41.0983i 0.555125 + 1.30751i
\(989\) 29.7077i 0.944651i
\(990\) −0.164543 5.02632i −0.00522953 0.159747i
\(991\) 19.5779 0.621913 0.310956 0.950424i \(-0.399351\pi\)
0.310956 + 0.950424i \(0.399351\pi\)
\(992\) −1.33328 −0.0423316
\(993\) −16.9365 39.0677i −0.537462 1.23978i
\(994\) −3.64772 + 3.64772i −0.115699 + 0.115699i
\(995\) 3.90697 3.90697i 0.123859 0.123859i
\(996\) −45.6545 105.312i −1.44662 3.33695i
\(997\) 44.3850 1.40569 0.702843 0.711345i \(-0.251914\pi\)
0.702843 + 0.711345i \(0.251914\pi\)
\(998\) −79.2230 −2.50776
\(999\) −15.0962 5.40153i −0.477624 0.170897i
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 429.2.j.a.122.6 96
3.2 odd 2 inner 429.2.j.a.122.43 yes 96
13.8 odd 4 inner 429.2.j.a.320.43 yes 96
39.8 even 4 inner 429.2.j.a.320.6 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.j.a.122.6 96 1.1 even 1 trivial
429.2.j.a.122.43 yes 96 3.2 odd 2 inner
429.2.j.a.320.6 yes 96 39.8 even 4 inner
429.2.j.a.320.43 yes 96 13.8 odd 4 inner