Properties

Label 17.4.c.a.13.4
Level $17$
Weight $4$
Character 17.13
Analytic conductor $1.003$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [17,4,Mod(4,17)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(17, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("17.4");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 17.c (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: \(1.00303247010\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 46x^{6} + 561x^{4} + 836x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 13.4
Root \(4.93651i\) of defining polynomial
Character \(\chi\) \(=\) 17.13
Dual form 17.4.c.a.4.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.93651i q^{2} +(-0.299807 - 0.299807i) q^{3} -7.49613 q^{4} +(1.37942 + 1.37942i) q^{5} +(1.18019 - 1.18019i) q^{6} +(17.9849 - 17.9849i) q^{7} +1.98349i q^{8} -26.8202i q^{9} +O(q^{10})\) \(q+3.93651i q^{2} +(-0.299807 - 0.299807i) q^{3} -7.49613 q^{4} +(1.37942 + 1.37942i) q^{5} +(1.18019 - 1.18019i) q^{6} +(17.9849 - 17.9849i) q^{7} +1.98349i q^{8} -26.8202i q^{9} +(-5.43011 + 5.43011i) q^{10} +(-22.9317 + 22.9317i) q^{11} +(2.24739 + 2.24739i) q^{12} -54.6855 q^{13} +(70.7978 + 70.7978i) q^{14} -0.827121i q^{15} -67.7771 q^{16} +(58.5003 - 38.6098i) q^{17} +105.578 q^{18} +46.1336i q^{19} +(-10.3403 - 10.3403i) q^{20} -10.7840 q^{21} +(-90.2708 - 90.2708i) q^{22} +(-53.2436 + 53.2436i) q^{23} +(0.594665 - 0.594665i) q^{24} -121.194i q^{25} -215.270i q^{26} +(-16.1357 + 16.1357i) q^{27} +(-134.817 + 134.817i) q^{28} +(111.044 + 111.044i) q^{29} +3.25597 q^{30} +(178.619 + 178.619i) q^{31} -250.937i q^{32} +13.7502 q^{33} +(151.988 + 230.287i) q^{34} +49.6175 q^{35} +201.048i q^{36} +(-159.957 - 159.957i) q^{37} -181.606 q^{38} +(16.3951 + 16.3951i) q^{39} +(-2.73608 + 2.73608i) q^{40} +(-163.457 + 163.457i) q^{41} -42.4513i q^{42} +119.642i q^{43} +(171.899 - 171.899i) q^{44} +(36.9964 - 36.9964i) q^{45} +(-209.594 - 209.594i) q^{46} -188.319 q^{47} +(20.3200 + 20.3200i) q^{48} -303.913i q^{49} +477.083 q^{50} +(-29.1143 - 5.96329i) q^{51} +409.930 q^{52} -468.212i q^{53} +(-63.5183 - 63.5183i) q^{54} -63.2650 q^{55} +(35.6729 + 35.6729i) q^{56} +(13.8312 - 13.8312i) q^{57} +(-437.125 + 437.125i) q^{58} +751.217i q^{59} +6.20021i q^{60} +(341.681 - 341.681i) q^{61} +(-703.136 + 703.136i) q^{62} +(-482.359 - 482.359i) q^{63} +445.601 q^{64} +(-75.4344 - 75.4344i) q^{65} +54.1277i q^{66} +533.879 q^{67} +(-438.526 + 289.424i) q^{68} +31.9256 q^{69} +195.320i q^{70} +(55.2619 + 55.2619i) q^{71} +53.1977 q^{72} +(270.831 + 270.831i) q^{73} +(629.674 - 629.674i) q^{74} +(-36.3349 + 36.3349i) q^{75} -345.824i q^{76} +824.848i q^{77} +(-64.5395 + 64.5395i) q^{78} +(904.285 - 904.285i) q^{79} +(-93.4932 - 93.4932i) q^{80} -714.471 q^{81} +(-643.449 - 643.449i) q^{82} -591.376i q^{83} +80.8382 q^{84} +(133.956 + 27.4373i) q^{85} -470.973 q^{86} -66.5834i q^{87} +(-45.4848 - 45.4848i) q^{88} -609.729 q^{89} +(145.637 + 145.637i) q^{90} +(-983.513 + 983.513i) q^{91} +(399.121 - 399.121i) q^{92} -107.103i q^{93} -741.321i q^{94} +(-63.6378 + 63.6378i) q^{95} +(-75.2328 + 75.2328i) q^{96} +(1125.76 + 1125.76i) q^{97} +1196.36 q^{98} +(615.033 + 615.033i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 36 q^{4} + 14 q^{5} + 22 q^{6} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 36 q^{4} + 14 q^{5} + 22 q^{6} + 2 q^{7} + 78 q^{10} - 108 q^{11} - 174 q^{12} - 88 q^{13} + 108 q^{14} + 420 q^{16} - 10 q^{17} + 428 q^{18} - 306 q^{20} - 260 q^{21} + 30 q^{22} - 22 q^{23} - 862 q^{24} + 540 q^{27} - 764 q^{28} + 46 q^{29} - 120 q^{30} + 610 q^{31} + 816 q^{33} + 1002 q^{34} + 1172 q^{35} - 574 q^{37} - 768 q^{38} - 844 q^{39} - 342 q^{40} - 968 q^{41} + 550 q^{44} - 1154 q^{45} - 944 q^{46} - 368 q^{47} + 2494 q^{48} + 468 q^{50} + 296 q^{51} + 2564 q^{52} - 1592 q^{54} - 1996 q^{55} + 684 q^{56} - 300 q^{57} + 266 q^{58} + 1258 q^{61} - 2516 q^{62} + 122 q^{63} - 3044 q^{64} + 628 q^{65} + 764 q^{67} + 1914 q^{68} + 1812 q^{69} + 1266 q^{71} + 1404 q^{72} - 1732 q^{73} + 1538 q^{74} + 1292 q^{75} - 2836 q^{78} + 914 q^{79} + 498 q^{80} + 280 q^{81} - 280 q^{82} - 2952 q^{84} - 2498 q^{85} - 4244 q^{86} + 442 q^{88} - 2156 q^{89} + 2478 q^{90} - 1632 q^{91} - 1768 q^{92} + 1484 q^{95} + 3998 q^{96} + 1836 q^{97} + 6728 q^{98} - 2088 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.93651i 1.39177i 0.718155 + 0.695884i \(0.244987\pi\)
−0.718155 + 0.695884i \(0.755013\pi\)
\(3\) −0.299807 0.299807i −0.0576979 0.0576979i 0.677669 0.735367i \(-0.262990\pi\)
−0.735367 + 0.677669i \(0.762990\pi\)
\(4\) −7.49613 −0.937016
\(5\) 1.37942 + 1.37942i 0.123379 + 0.123379i 0.766100 0.642721i \(-0.222195\pi\)
−0.642721 + 0.766100i \(0.722195\pi\)
\(6\) 1.18019 1.18019i 0.0803021 0.0803021i
\(7\) 17.9849 17.9849i 0.971093 0.971093i −0.0285007 0.999594i \(-0.509073\pi\)
0.999594 + 0.0285007i \(0.00907327\pi\)
\(8\) 1.98349i 0.0876588i
\(9\) 26.8202i 0.993342i
\(10\) −5.43011 + 5.43011i −0.171715 + 0.171715i
\(11\) −22.9317 + 22.9317i −0.628560 + 0.628560i −0.947706 0.319146i \(-0.896604\pi\)
0.319146 + 0.947706i \(0.396604\pi\)
\(12\) 2.24739 + 2.24739i 0.0540639 + 0.0540639i
\(13\) −54.6855 −1.16669 −0.583347 0.812223i \(-0.698257\pi\)
−0.583347 + 0.812223i \(0.698257\pi\)
\(14\) 70.7978 + 70.7978i 1.35154 + 1.35154i
\(15\) 0.827121i 0.0142375i
\(16\) −67.7771 −1.05902
\(17\) 58.5003 38.6098i 0.834612 0.550839i
\(18\) 105.578 1.38250
\(19\) 46.1336i 0.557041i 0.960430 + 0.278521i \(0.0898441\pi\)
−0.960430 + 0.278521i \(0.910156\pi\)
\(20\) −10.3403 10.3403i −0.115608 0.115608i
\(21\) −10.7840 −0.112060
\(22\) −90.2708 90.2708i −0.874809 0.874809i
\(23\) −53.2436 + 53.2436i −0.482698 + 0.482698i −0.905992 0.423294i \(-0.860874\pi\)
0.423294 + 0.905992i \(0.360874\pi\)
\(24\) 0.594665 0.594665i 0.00505773 0.00505773i
\(25\) 121.194i 0.969555i
\(26\) 215.270i 1.62377i
\(27\) −16.1357 + 16.1357i −0.115012 + 0.115012i
\(28\) −134.817 + 134.817i −0.909930 + 0.909930i
\(29\) 111.044 + 111.044i 0.711045 + 0.711045i 0.966754 0.255709i \(-0.0823088\pi\)
−0.255709 + 0.966754i \(0.582309\pi\)
\(30\) 3.25597 0.0198152
\(31\) 178.619 + 178.619i 1.03487 + 1.03487i 0.999370 + 0.0354994i \(0.0113022\pi\)
0.0354994 + 0.999370i \(0.488698\pi\)
\(32\) 250.937i 1.38625i
\(33\) 13.7502 0.0725332
\(34\) 151.988 + 230.287i 0.766639 + 1.16159i
\(35\) 49.6175 0.239626
\(36\) 201.048i 0.930777i
\(37\) −159.957 159.957i −0.710725 0.710725i 0.255962 0.966687i \(-0.417608\pi\)
−0.966687 + 0.255962i \(0.917608\pi\)
\(38\) −181.606 −0.775272
\(39\) 16.3951 + 16.3951i 0.0673158 + 0.0673158i
\(40\) −2.73608 + 2.73608i −0.0108153 + 0.0108153i
\(41\) −163.457 + 163.457i −0.622626 + 0.622626i −0.946202 0.323576i \(-0.895115\pi\)
0.323576 + 0.946202i \(0.395115\pi\)
\(42\) 42.4513i 0.155962i
\(43\) 119.642i 0.424309i 0.977236 + 0.212154i \(0.0680480\pi\)
−0.977236 + 0.212154i \(0.931952\pi\)
\(44\) 171.899 171.899i 0.588971 0.588971i
\(45\) 36.9964 36.9964i 0.122558 0.122558i
\(46\) −209.594 209.594i −0.671803 0.671803i
\(47\) −188.319 −0.584451 −0.292225 0.956349i \(-0.594396\pi\)
−0.292225 + 0.956349i \(0.594396\pi\)
\(48\) 20.3200 + 20.3200i 0.0611031 + 0.0611031i
\(49\) 303.913i 0.886044i
\(50\) 477.083 1.34940
\(51\) −29.1143 5.96329i −0.0799376 0.0163731i
\(52\) 409.930 1.09321
\(53\) 468.212i 1.21347i −0.794905 0.606734i \(-0.792479\pi\)
0.794905 0.606734i \(-0.207521\pi\)
\(54\) −63.5183 63.5183i −0.160069 0.160069i
\(55\) −63.2650 −0.155103
\(56\) 35.6729 + 35.6729i 0.0851249 + 0.0851249i
\(57\) 13.8312 13.8312i 0.0321401 0.0321401i
\(58\) −437.125 + 437.125i −0.989609 + 0.989609i
\(59\) 751.217i 1.65763i 0.559523 + 0.828815i \(0.310984\pi\)
−0.559523 + 0.828815i \(0.689016\pi\)
\(60\) 6.20021i 0.0133407i
\(61\) 341.681 341.681i 0.717177 0.717177i −0.250849 0.968026i \(-0.580710\pi\)
0.968026 + 0.250849i \(0.0807099\pi\)
\(62\) −703.136 + 703.136i −1.44030 + 1.44030i
\(63\) −482.359 482.359i −0.964627 0.964627i
\(64\) 445.601 0.870315
\(65\) −75.4344 75.4344i −0.143946 0.143946i
\(66\) 54.1277i 0.100949i
\(67\) 533.879 0.973487 0.486744 0.873545i \(-0.338185\pi\)
0.486744 + 0.873545i \(0.338185\pi\)
\(68\) −438.526 + 289.424i −0.782045 + 0.516145i
\(69\) 31.9256 0.0557013
\(70\) 195.320i 0.333503i
\(71\) 55.2619 + 55.2619i 0.0923715 + 0.0923715i 0.751783 0.659411i \(-0.229194\pi\)
−0.659411 + 0.751783i \(0.729194\pi\)
\(72\) 53.1977 0.0870752
\(73\) 270.831 + 270.831i 0.434224 + 0.434224i 0.890062 0.455839i \(-0.150661\pi\)
−0.455839 + 0.890062i \(0.650661\pi\)
\(74\) 629.674 629.674i 0.989164 0.989164i
\(75\) −36.3349 + 36.3349i −0.0559413 + 0.0559413i
\(76\) 345.824i 0.521957i
\(77\) 824.848i 1.22078i
\(78\) −64.5395 + 64.5395i −0.0936880 + 0.0936880i
\(79\) 904.285 904.285i 1.28785 1.28785i 0.351757 0.936091i \(-0.385584\pi\)
0.936091 0.351757i \(-0.114416\pi\)
\(80\) −93.4932 93.4932i −0.130661 0.130661i
\(81\) −714.471 −0.980070
\(82\) −643.449 643.449i −0.866550 0.866550i
\(83\) 591.376i 0.782071i −0.920376 0.391036i \(-0.872117\pi\)
0.920376 0.391036i \(-0.127883\pi\)
\(84\) 80.8382 0.105002
\(85\) 133.956 + 27.4373i 0.170936 + 0.0350117i
\(86\) −470.973 −0.590539
\(87\) 66.5834i 0.0820516i
\(88\) −45.4848 45.4848i −0.0550989 0.0550989i
\(89\) −609.729 −0.726192 −0.363096 0.931752i \(-0.618280\pi\)
−0.363096 + 0.931752i \(0.618280\pi\)
\(90\) 145.637 + 145.637i 0.170572 + 0.170572i
\(91\) −983.513 + 983.513i −1.13297 + 1.13297i
\(92\) 399.121 399.121i 0.452296 0.452296i
\(93\) 107.103i 0.119420i
\(94\) 741.321i 0.813420i
\(95\) −63.6378 + 63.6378i −0.0687274 + 0.0687274i
\(96\) −75.2328 + 75.2328i −0.0799835 + 0.0799835i
\(97\) 1125.76 + 1125.76i 1.17838 + 1.17838i 0.980156 + 0.198226i \(0.0635182\pi\)
0.198226 + 0.980156i \(0.436482\pi\)
\(98\) 1196.36 1.23317
\(99\) 615.033 + 615.033i 0.624375 + 0.624375i
\(100\) 908.489i 0.908489i
\(101\) −666.897 −0.657017 −0.328508 0.944501i \(-0.606546\pi\)
−0.328508 + 0.944501i \(0.606546\pi\)
\(102\) 23.4746 114.609i 0.0227875 0.111255i
\(103\) −872.373 −0.834538 −0.417269 0.908783i \(-0.637013\pi\)
−0.417269 + 0.908783i \(0.637013\pi\)
\(104\) 108.468i 0.102271i
\(105\) −14.8757 14.8757i −0.0138259 0.0138259i
\(106\) 1843.12 1.68887
\(107\) −244.890 244.890i −0.221256 0.221256i 0.587771 0.809027i \(-0.300006\pi\)
−0.809027 + 0.587771i \(0.800006\pi\)
\(108\) 120.955 120.955i 0.107768 0.107768i
\(109\) −96.0400 + 96.0400i −0.0843942 + 0.0843942i −0.748044 0.663649i \(-0.769007\pi\)
0.663649 + 0.748044i \(0.269007\pi\)
\(110\) 249.043i 0.215867i
\(111\) 95.9128i 0.0820147i
\(112\) −1218.96 + 1218.96i −1.02840 + 1.02840i
\(113\) 626.459 626.459i 0.521525 0.521525i −0.396507 0.918032i \(-0.629778\pi\)
0.918032 + 0.396507i \(0.129778\pi\)
\(114\) 54.4467 + 54.4467i 0.0447316 + 0.0447316i
\(115\) −146.891 −0.119110
\(116\) −832.398 832.398i −0.666261 0.666261i
\(117\) 1466.68i 1.15893i
\(118\) −2957.18 −2.30703
\(119\) 357.727 1746.51i 0.275570 1.34540i
\(120\) 1.64059 0.00124804
\(121\) 279.276i 0.209824i
\(122\) 1345.03 + 1345.03i 0.998143 + 0.998143i
\(123\) 98.0110 0.0718484
\(124\) −1338.95 1338.95i −0.969689 0.969689i
\(125\) 339.606 339.606i 0.243002 0.243002i
\(126\) 1898.81 1898.81i 1.34254 1.34254i
\(127\) 1971.07i 1.37720i −0.725144 0.688598i \(-0.758227\pi\)
0.725144 0.688598i \(-0.241773\pi\)
\(128\) 253.384i 0.174970i
\(129\) 35.8696 35.8696i 0.0244817 0.0244817i
\(130\) 296.949 296.949i 0.200339 0.200339i
\(131\) 177.333 + 177.333i 0.118272 + 0.118272i 0.763766 0.645493i \(-0.223348\pi\)
−0.645493 + 0.763766i \(0.723348\pi\)
\(132\) −103.073 −0.0679648
\(133\) 829.709 + 829.709i 0.540939 + 0.540939i
\(134\) 2101.62i 1.35487i
\(135\) −44.5159 −0.0283801
\(136\) 76.5823 + 116.035i 0.0482859 + 0.0731611i
\(137\) 436.372 0.272130 0.136065 0.990700i \(-0.456554\pi\)
0.136065 + 0.990700i \(0.456554\pi\)
\(138\) 125.676i 0.0775233i
\(139\) −59.2009 59.2009i −0.0361249 0.0361249i 0.688814 0.724938i \(-0.258132\pi\)
−0.724938 + 0.688814i \(0.758132\pi\)
\(140\) −371.940 −0.224533
\(141\) 56.4595 + 56.4595i 0.0337216 + 0.0337216i
\(142\) −217.539 + 217.539i −0.128560 + 0.128560i
\(143\) 1254.03 1254.03i 0.733338 0.733338i
\(144\) 1817.80i 1.05197i
\(145\) 306.353i 0.175457i
\(146\) −1066.13 + 1066.13i −0.604339 + 0.604339i
\(147\) −91.1153 + 91.1153i −0.0511229 + 0.0511229i
\(148\) 1199.06 + 1199.06i 0.665961 + 0.665961i
\(149\) −2357.45 −1.29617 −0.648085 0.761568i \(-0.724430\pi\)
−0.648085 + 0.761568i \(0.724430\pi\)
\(150\) −143.033 143.033i −0.0778573 0.0778573i
\(151\) 149.746i 0.0807031i −0.999186 0.0403515i \(-0.987152\pi\)
0.999186 0.0403515i \(-0.0128478\pi\)
\(152\) −91.5058 −0.0488296
\(153\) −1035.52 1568.99i −0.547171 0.829055i
\(154\) −3247.02 −1.69904
\(155\) 492.783i 0.255363i
\(156\) −122.900 122.900i −0.0630760 0.0630760i
\(157\) −119.280 −0.0606343 −0.0303172 0.999540i \(-0.509652\pi\)
−0.0303172 + 0.999540i \(0.509652\pi\)
\(158\) 3559.73 + 3559.73i 1.79238 + 1.79238i
\(159\) −140.373 + 140.373i −0.0700146 + 0.0700146i
\(160\) 346.149 346.149i 0.171034 0.171034i
\(161\) 1915.16i 0.937489i
\(162\) 2812.52i 1.36403i
\(163\) 107.923 107.923i 0.0518600 0.0518600i −0.680701 0.732561i \(-0.738325\pi\)
0.732561 + 0.680701i \(0.238325\pi\)
\(164\) 1225.29 1225.29i 0.583410 0.583410i
\(165\) 18.9673 + 18.9673i 0.00894910 + 0.00894910i
\(166\) 2327.96 1.08846
\(167\) −1785.49 1785.49i −0.827339 0.827339i 0.159809 0.987148i \(-0.448912\pi\)
−0.987148 + 0.159809i \(0.948912\pi\)
\(168\) 21.3900i 0.00982306i
\(169\) 793.506 0.361177
\(170\) −108.007 + 527.319i −0.0487281 + 0.237903i
\(171\) 1237.31 0.553332
\(172\) 896.854i 0.397584i
\(173\) 232.125 + 232.125i 0.102012 + 0.102012i 0.756271 0.654259i \(-0.227019\pi\)
−0.654259 + 0.756271i \(0.727019\pi\)
\(174\) 262.106 0.114197
\(175\) −2179.67 2179.67i −0.941528 0.941528i
\(176\) 1554.24 1554.24i 0.665656 0.665656i
\(177\) 225.220 225.220i 0.0956417 0.0956417i
\(178\) 2400.20i 1.01069i
\(179\) 4155.11i 1.73501i 0.497427 + 0.867506i \(0.334278\pi\)
−0.497427 + 0.867506i \(0.665722\pi\)
\(180\) −277.330 + 277.330i −0.114839 + 0.114839i
\(181\) 675.588 675.588i 0.277437 0.277437i −0.554648 0.832085i \(-0.687147\pi\)
0.832085 + 0.554648i \(0.187147\pi\)
\(182\) −3871.61 3871.61i −1.57683 1.57683i
\(183\) −204.877 −0.0827592
\(184\) −105.608 105.608i −0.0423128 0.0423128i
\(185\) 441.298i 0.175378i
\(186\) 421.611 0.166204
\(187\) −456.121 + 2226.90i −0.178368 + 0.870839i
\(188\) 1411.67 0.547640
\(189\) 580.397i 0.223374i
\(190\) −250.511 250.511i −0.0956525 0.0956525i
\(191\) −889.758 −0.337072 −0.168536 0.985696i \(-0.553904\pi\)
−0.168536 + 0.985696i \(0.553904\pi\)
\(192\) −133.594 133.594i −0.0502154 0.0502154i
\(193\) −1224.76 + 1224.76i −0.456789 + 0.456789i −0.897600 0.440811i \(-0.854691\pi\)
0.440811 + 0.897600i \(0.354691\pi\)
\(194\) −4431.55 + 4431.55i −1.64003 + 1.64003i
\(195\) 45.2316i 0.0166108i
\(196\) 2278.17i 0.830237i
\(197\) 3142.32 3142.32i 1.13645 1.13645i 0.147369 0.989082i \(-0.452919\pi\)
0.989082 0.147369i \(-0.0470805\pi\)
\(198\) −2421.08 + 2421.08i −0.868985 + 0.868985i
\(199\) 2205.02 + 2205.02i 0.785478 + 0.785478i 0.980749 0.195272i \(-0.0625588\pi\)
−0.195272 + 0.980749i \(0.562559\pi\)
\(200\) 240.388 0.0849901
\(201\) −160.061 160.061i −0.0561682 0.0561682i
\(202\) 2625.25i 0.914415i
\(203\) 3994.22 1.38098
\(204\) 218.245 + 44.7016i 0.0749028 + 0.0153419i
\(205\) −450.952 −0.153638
\(206\) 3434.11i 1.16148i
\(207\) 1428.01 + 1428.01i 0.479484 + 0.479484i
\(208\) 3706.42 1.23555
\(209\) −1057.92 1057.92i −0.350134 0.350134i
\(210\) 58.5583 58.5583i 0.0192424 0.0192424i
\(211\) −3204.98 + 3204.98i −1.04569 + 1.04569i −0.0467829 + 0.998905i \(0.514897\pi\)
−0.998905 + 0.0467829i \(0.985103\pi\)
\(212\) 3509.78i 1.13704i
\(213\) 33.1358i 0.0106593i
\(214\) 964.014 964.014i 0.307937 0.307937i
\(215\) −165.037 + 165.037i −0.0523509 + 0.0523509i
\(216\) −32.0050 32.0050i −0.0100818 0.0100818i
\(217\) 6424.89 2.00991
\(218\) −378.063 378.063i −0.117457 0.117457i
\(219\) 162.394i 0.0501076i
\(220\) 474.242 0.145334
\(221\) −3199.12 + 2111.40i −0.973737 + 0.642661i
\(222\) −377.562 −0.114145
\(223\) 123.574i 0.0371082i −0.999828 0.0185541i \(-0.994094\pi\)
0.999828 0.0185541i \(-0.00590629\pi\)
\(224\) −4513.08 4513.08i −1.34617 1.34617i
\(225\) −3250.46 −0.963100
\(226\) 2466.06 + 2466.06i 0.725841 + 0.725841i
\(227\) 551.638 551.638i 0.161293 0.161293i −0.621846 0.783139i \(-0.713617\pi\)
0.783139 + 0.621846i \(0.213617\pi\)
\(228\) −103.680 + 103.680i −0.0301158 + 0.0301158i
\(229\) 2776.64i 0.801247i −0.916243 0.400624i \(-0.868794\pi\)
0.916243 0.400624i \(-0.131206\pi\)
\(230\) 578.237i 0.165773i
\(231\) 247.295 247.295i 0.0704365 0.0704365i
\(232\) −220.255 + 220.255i −0.0623294 + 0.0623294i
\(233\) −3569.19 3569.19i −1.00354 1.00354i −0.999994 0.00354906i \(-0.998870\pi\)
−0.00354906 0.999994i \(-0.501130\pi\)
\(234\) −5773.60 −1.61296
\(235\) −259.772 259.772i −0.0721091 0.0721091i
\(236\) 5631.22i 1.55323i
\(237\) −542.222 −0.148612
\(238\) 6875.18 + 1408.20i 1.87249 + 0.383529i
\(239\) 2254.20 0.610092 0.305046 0.952338i \(-0.401328\pi\)
0.305046 + 0.952338i \(0.401328\pi\)
\(240\) 56.0599i 0.0150777i
\(241\) −1222.67 1222.67i −0.326802 0.326802i 0.524567 0.851369i \(-0.324227\pi\)
−0.851369 + 0.524567i \(0.824227\pi\)
\(242\) −1099.37 −0.292027
\(243\) 649.867 + 649.867i 0.171560 + 0.171560i
\(244\) −2561.29 + 2561.29i −0.672006 + 0.672006i
\(245\) 419.224 419.224i 0.109319 0.109319i
\(246\) 385.821i 0.0999962i
\(247\) 2522.84i 0.649897i
\(248\) −354.290 + 354.290i −0.0907154 + 0.0907154i
\(249\) −177.299 + 177.299i −0.0451239 + 0.0451239i
\(250\) 1336.86 + 1336.86i 0.338203 + 0.338203i
\(251\) −1314.25 −0.330496 −0.165248 0.986252i \(-0.552842\pi\)
−0.165248 + 0.986252i \(0.552842\pi\)
\(252\) 3615.83 + 3615.83i 0.903872 + 0.903872i
\(253\) 2441.93i 0.606809i
\(254\) 7759.13 1.91674
\(255\) −31.9350 48.3868i −0.00784254 0.0118827i
\(256\) 4562.26 1.11383
\(257\) 6039.96i 1.46600i 0.680228 + 0.733001i \(0.261881\pi\)
−0.680228 + 0.733001i \(0.738119\pi\)
\(258\) 141.201 + 141.201i 0.0340729 + 0.0340729i
\(259\) −5753.64 −1.38036
\(260\) 565.466 + 565.466i 0.134880 + 0.134880i
\(261\) 2978.22 2978.22i 0.706311 0.706311i
\(262\) −698.074 + 698.074i −0.164608 + 0.164608i
\(263\) 990.368i 0.232201i 0.993237 + 0.116100i \(0.0370394\pi\)
−0.993237 + 0.116100i \(0.962961\pi\)
\(264\) 27.2733i 0.00635818i
\(265\) 645.862 645.862i 0.149717 0.149717i
\(266\) −3266.16 + 3266.16i −0.752861 + 0.752861i
\(267\) 182.801 + 182.801i 0.0418998 + 0.0418998i
\(268\) −4002.02 −0.912173
\(269\) 2397.48 + 2397.48i 0.543409 + 0.543409i 0.924527 0.381117i \(-0.124461\pi\)
−0.381117 + 0.924527i \(0.624461\pi\)
\(270\) 175.237i 0.0394985i
\(271\) −3706.24 −0.830767 −0.415383 0.909646i \(-0.636353\pi\)
−0.415383 + 0.909646i \(0.636353\pi\)
\(272\) −3964.98 + 2616.86i −0.883868 + 0.583348i
\(273\) 589.729 0.130740
\(274\) 1717.79i 0.378742i
\(275\) 2779.19 + 2779.19i 0.609424 + 0.609424i
\(276\) −239.318 −0.0521930
\(277\) −5410.66 5410.66i −1.17363 1.17363i −0.981338 0.192290i \(-0.938409\pi\)
−0.192290 0.981338i \(-0.561591\pi\)
\(278\) 233.045 233.045i 0.0502774 0.0502774i
\(279\) 4790.61 4790.61i 1.02798 1.02798i
\(280\) 98.4161i 0.0210053i
\(281\) 3194.87i 0.678256i −0.940740 0.339128i \(-0.889868\pi\)
0.940740 0.339128i \(-0.110132\pi\)
\(282\) −222.253 + 222.253i −0.0469326 + 0.0469326i
\(283\) −4235.43 + 4235.43i −0.889648 + 0.889648i −0.994489 0.104841i \(-0.966567\pi\)
0.104841 + 0.994489i \(0.466567\pi\)
\(284\) −414.250 414.250i −0.0865536 0.0865536i
\(285\) 38.1581 0.00793085
\(286\) 4936.51 + 4936.51i 1.02064 + 1.02064i
\(287\) 5879.50i 1.20925i
\(288\) −6730.20 −1.37702
\(289\) 1931.56 4517.37i 0.393153 0.919473i
\(290\) −1205.96 −0.244195
\(291\) 675.019i 0.135980i
\(292\) −2030.18 2030.18i −0.406875 0.406875i
\(293\) 5372.44 1.07120 0.535600 0.844472i \(-0.320086\pi\)
0.535600 + 0.844472i \(0.320086\pi\)
\(294\) −358.676 358.676i −0.0711511 0.0711511i
\(295\) −1036.25 + 1036.25i −0.204517 + 0.204517i
\(296\) 317.275 317.275i 0.0623014 0.0623014i
\(297\) 740.037i 0.144583i
\(298\) 9280.11i 1.80397i
\(299\) 2911.65 2911.65i 0.563161 0.563161i
\(300\) 272.371 272.371i 0.0524179 0.0524179i
\(301\) 2151.75 + 2151.75i 0.412043 + 0.412043i
\(302\) 589.477 0.112320
\(303\) 199.940 + 199.940i 0.0379085 + 0.0379085i
\(304\) 3126.80i 0.589916i
\(305\) 942.645 0.176970
\(306\) 6176.35 4076.36i 1.15385 0.761535i
\(307\) 7020.91 1.30523 0.652613 0.757692i \(-0.273673\pi\)
0.652613 + 0.757692i \(0.273673\pi\)
\(308\) 6183.16i 1.14389i
\(309\) 261.544 + 261.544i 0.0481511 + 0.0481511i
\(310\) −1939.84 −0.355406
\(311\) −725.496 725.496i −0.132280 0.132280i 0.637867 0.770147i \(-0.279817\pi\)
−0.770147 + 0.637867i \(0.779817\pi\)
\(312\) −32.5196 + 32.5196i −0.00590083 + 0.00590083i
\(313\) −1761.31 + 1761.31i −0.318067 + 0.318067i −0.848024 0.529957i \(-0.822208\pi\)
0.529957 + 0.848024i \(0.322208\pi\)
\(314\) 469.548i 0.0843889i
\(315\) 1330.75i 0.238030i
\(316\) −6778.64 + 6778.64i −1.20673 + 1.20673i
\(317\) −1962.35 + 1962.35i −0.347686 + 0.347686i −0.859247 0.511561i \(-0.829067\pi\)
0.511561 + 0.859247i \(0.329067\pi\)
\(318\) −552.581 552.581i −0.0974440 0.0974440i
\(319\) −5092.84 −0.893869
\(320\) 614.673 + 614.673i 0.107379 + 0.107379i
\(321\) 146.840i 0.0255321i
\(322\) −7539.05 −1.30477
\(323\) 1781.21 + 2698.83i 0.306840 + 0.464913i
\(324\) 5355.77 0.918341
\(325\) 6627.58i 1.13117i
\(326\) 424.840 + 424.840i 0.0721770 + 0.0721770i
\(327\) 57.5870 0.00973873
\(328\) −324.215 324.215i −0.0545786 0.0545786i
\(329\) −3386.90 + 3386.90i −0.567556 + 0.567556i
\(330\) −74.6649 + 74.6649i −0.0124551 + 0.0124551i
\(331\) 6017.90i 0.999317i −0.866222 0.499659i \(-0.833459\pi\)
0.866222 0.499659i \(-0.166541\pi\)
\(332\) 4433.03i 0.732813i
\(333\) −4290.10 + 4290.10i −0.705993 + 0.705993i
\(334\) 7028.61 7028.61i 1.15146 1.15146i
\(335\) 736.444 + 736.444i 0.120108 + 0.120108i
\(336\) 730.908 0.118674
\(337\) 335.433 + 335.433i 0.0542202 + 0.0542202i 0.733697 0.679477i \(-0.237793\pi\)
−0.679477 + 0.733697i \(0.737793\pi\)
\(338\) 3123.64i 0.502674i
\(339\) −375.634 −0.0601818
\(340\) −1004.15 205.674i −0.160170 0.0328065i
\(341\) −8192.07 −1.30095
\(342\) 4870.71i 0.770110i
\(343\) 702.976 + 702.976i 0.110662 + 0.110662i
\(344\) −237.310 −0.0371944
\(345\) 44.0389 + 44.0389i 0.00687239 + 0.00687239i
\(346\) −913.762 + 913.762i −0.141977 + 0.141977i
\(347\) 1043.30 1043.30i 0.161405 0.161405i −0.621784 0.783189i \(-0.713592\pi\)
0.783189 + 0.621784i \(0.213592\pi\)
\(348\) 499.118i 0.0768837i
\(349\) 6855.25i 1.05144i 0.850657 + 0.525721i \(0.176204\pi\)
−0.850657 + 0.525721i \(0.823796\pi\)
\(350\) 8580.29 8580.29i 1.31039 1.31039i
\(351\) 882.388 882.388i 0.134183 0.134183i
\(352\) 5754.41 + 5754.41i 0.871339 + 0.871339i
\(353\) 7485.74 1.12868 0.564342 0.825541i \(-0.309130\pi\)
0.564342 + 0.825541i \(0.309130\pi\)
\(354\) 886.582 + 886.582i 0.133111 + 0.133111i
\(355\) 152.459i 0.0227935i
\(356\) 4570.60 0.680454
\(357\) −630.867 + 416.368i −0.0935266 + 0.0617270i
\(358\) −16356.6 −2.41473
\(359\) 7169.54i 1.05402i −0.849859 0.527011i \(-0.823313\pi\)
0.849859 0.527011i \(-0.176687\pi\)
\(360\) 73.3822 + 73.3822i 0.0107433 + 0.0107433i
\(361\) 4730.69 0.689705
\(362\) 2659.46 + 2659.46i 0.386127 + 0.386127i
\(363\) 83.7290 83.7290i 0.0121064 0.0121064i
\(364\) 7372.54 7372.54i 1.06161 1.06161i
\(365\) 747.180i 0.107149i
\(366\) 806.500i 0.115182i
\(367\) −4673.13 + 4673.13i −0.664674 + 0.664674i −0.956478 0.291804i \(-0.905744\pi\)
0.291804 + 0.956478i \(0.405744\pi\)
\(368\) 3608.69 3608.69i 0.511185 0.511185i
\(369\) 4383.95 + 4383.95i 0.618480 + 0.618480i
\(370\) 1737.17 0.244085
\(371\) −8420.74 8420.74i −1.17839 1.17839i
\(372\) 802.855i 0.111898i
\(373\) −1602.91 −0.222508 −0.111254 0.993792i \(-0.535487\pi\)
−0.111254 + 0.993792i \(0.535487\pi\)
\(374\) −8766.21 1795.53i −1.21200 0.248247i
\(375\) −203.633 −0.0280415
\(376\) 373.530i 0.0512323i
\(377\) −6072.49 6072.49i −0.829573 0.829573i
\(378\) −2284.74 −0.310885
\(379\) 1232.54 + 1232.54i 0.167049 + 0.167049i 0.785681 0.618632i \(-0.212313\pi\)
−0.618632 + 0.785681i \(0.712313\pi\)
\(380\) 477.037 477.037i 0.0643986 0.0643986i
\(381\) −590.940 + 590.940i −0.0794613 + 0.0794613i
\(382\) 3502.55i 0.469125i
\(383\) 1155.24i 0.154125i −0.997026 0.0770627i \(-0.975446\pi\)
0.997026 0.0770627i \(-0.0245542\pi\)
\(384\) −75.9662 + 75.9662i −0.0100954 + 0.0100954i
\(385\) −1137.81 + 1137.81i −0.150619 + 0.150619i
\(386\) −4821.29 4821.29i −0.635744 0.635744i
\(387\) 3208.83 0.421484
\(388\) −8438.81 8438.81i −1.10416 1.10416i
\(389\) 3698.95i 0.482119i −0.970510 0.241060i \(-0.922505\pi\)
0.970510 0.241060i \(-0.0774949\pi\)
\(390\) −178.055 −0.0231183
\(391\) −1059.04 + 5170.49i −0.136977 + 0.668754i
\(392\) 602.809 0.0776696
\(393\) 106.332i 0.0136481i
\(394\) 12369.8 + 12369.8i 1.58167 + 1.58167i
\(395\) 2494.78 0.317788
\(396\) −4610.37 4610.37i −0.585050 0.585050i
\(397\) 9608.12 9608.12i 1.21465 1.21465i 0.245176 0.969479i \(-0.421154\pi\)
0.969479 0.245176i \(-0.0788458\pi\)
\(398\) −8680.11 + 8680.11i −1.09320 + 1.09320i
\(399\) 497.505i 0.0624221i
\(400\) 8214.20i 1.02678i
\(401\) −1883.98 + 1883.98i −0.234617 + 0.234617i −0.814617 0.580000i \(-0.803053\pi\)
0.580000 + 0.814617i \(0.303053\pi\)
\(402\) 630.081 630.081i 0.0781730 0.0781730i
\(403\) −9767.88 9767.88i −1.20738 1.20738i
\(404\) 4999.14 0.615635
\(405\) −985.558 985.558i −0.120920 0.120920i
\(406\) 15723.3i 1.92201i
\(407\) 7336.19 0.893467
\(408\) 11.8282 57.7480i 0.00143525 0.00700724i
\(409\) 4145.86 0.501222 0.250611 0.968088i \(-0.419368\pi\)
0.250611 + 0.968088i \(0.419368\pi\)
\(410\) 1775.18i 0.213829i
\(411\) −130.828 130.828i −0.0157013 0.0157013i
\(412\) 6539.42 0.781976
\(413\) 13510.6 + 13510.6i 1.60971 + 1.60971i
\(414\) −5621.36 + 5621.36i −0.667330 + 0.667330i
\(415\) 815.757 815.757i 0.0964914 0.0964914i
\(416\) 13722.6i 1.61733i
\(417\) 35.4977i 0.00416866i
\(418\) 4164.52 4164.52i 0.487305 0.487305i
\(419\) 10074.5 10074.5i 1.17463 1.17463i 0.193542 0.981092i \(-0.438003\pi\)
0.981092 0.193542i \(-0.0619975\pi\)
\(420\) 111.510 + 111.510i 0.0129551 + 0.0129551i
\(421\) −3191.61 −0.369477 −0.184738 0.982788i \(-0.559144\pi\)
−0.184738 + 0.982788i \(0.559144\pi\)
\(422\) −12616.5 12616.5i −1.45535 1.45535i
\(423\) 5050.77i 0.580560i
\(424\) 928.695 0.106371
\(425\) −4679.29 7089.90i −0.534069 0.809202i
\(426\) 130.439 0.0148352
\(427\) 12290.2i 1.39289i
\(428\) 1835.73 + 1835.73i 0.207321 + 0.207321i
\(429\) −751.935 −0.0846241
\(430\) −649.671 649.671i −0.0728603 0.0728603i
\(431\) −1159.24 + 1159.24i −0.129556 + 0.129556i −0.768911 0.639355i \(-0.779201\pi\)
0.639355 + 0.768911i \(0.279201\pi\)
\(432\) 1093.63 1093.63i 0.121799 0.121799i
\(433\) 16579.9i 1.84013i 0.391764 + 0.920066i \(0.371865\pi\)
−0.391764 + 0.920066i \(0.628135\pi\)
\(434\) 25291.7i 2.79732i
\(435\) 91.8467 91.8467i 0.0101235 0.0101235i
\(436\) 719.928 719.928i 0.0790787 0.0790787i
\(437\) −2456.32 2456.32i −0.268883 0.268883i
\(438\) 639.266 0.0697382
\(439\) 5195.18 + 5195.18i 0.564812 + 0.564812i 0.930670 0.365859i \(-0.119225\pi\)
−0.365859 + 0.930670i \(0.619225\pi\)
\(440\) 125.486i 0.0135961i
\(441\) −8151.02 −0.880144
\(442\) −8311.55 12593.4i −0.894434 1.35522i
\(443\) −13325.5 −1.42915 −0.714575 0.699559i \(-0.753380\pi\)
−0.714575 + 0.699559i \(0.753380\pi\)
\(444\) 718.974i 0.0768491i
\(445\) −841.074 841.074i −0.0895971 0.0895971i
\(446\) 486.451 0.0516460
\(447\) 706.779 + 706.779i 0.0747863 + 0.0747863i
\(448\) 8014.09 8014.09i 0.845157 0.845157i
\(449\) −6849.28 + 6849.28i −0.719906 + 0.719906i −0.968586 0.248680i \(-0.920003\pi\)
0.248680 + 0.968586i \(0.420003\pi\)
\(450\) 12795.5i 1.34041i
\(451\) 7496.67i 0.782715i
\(452\) −4696.02 + 4696.02i −0.488677 + 0.488677i
\(453\) −44.8949 + 44.8949i −0.00465640 + 0.00465640i
\(454\) 2171.53 + 2171.53i 0.224482 + 0.224482i
\(455\) −2713.36 −0.279570
\(456\) 27.4341 + 27.4341i 0.00281736 + 0.00281736i
\(457\) 698.065i 0.0714532i −0.999362 0.0357266i \(-0.988625\pi\)
0.999362 0.0357266i \(-0.0113745\pi\)
\(458\) 10930.3 1.11515
\(459\) −320.946 + 1566.94i −0.0326372 + 0.159343i
\(460\) 1101.11 0.111608
\(461\) 6505.58i 0.657256i −0.944459 0.328628i \(-0.893414\pi\)
0.944459 0.328628i \(-0.106586\pi\)
\(462\) 973.481 + 973.481i 0.0980312 + 0.0980312i
\(463\) 1181.74 0.118618 0.0593089 0.998240i \(-0.481110\pi\)
0.0593089 + 0.998240i \(0.481110\pi\)
\(464\) −7526.22 7526.22i −0.753009 0.753009i
\(465\) 147.740 147.740i 0.0147339 0.0147339i
\(466\) 14050.2 14050.2i 1.39670 1.39670i
\(467\) 2950.96i 0.292407i 0.989255 + 0.146204i \(0.0467054\pi\)
−0.989255 + 0.146204i \(0.953295\pi\)
\(468\) 10994.4i 1.08593i
\(469\) 9601.75 9601.75i 0.945347 0.945347i
\(470\) 1022.60 1022.60i 0.100359 0.100359i
\(471\) 35.7610 + 35.7610i 0.00349847 + 0.00349847i
\(472\) −1490.03 −0.145306
\(473\) −2743.60 2743.60i −0.266704 0.266704i
\(474\) 2134.46i 0.206834i
\(475\) 5591.14 0.540082
\(476\) −2681.57 + 13092.1i −0.258213 + 1.26066i
\(477\) −12557.5 −1.20539
\(478\) 8873.69i 0.849107i
\(479\) 6286.33 + 6286.33i 0.599644 + 0.599644i 0.940218 0.340573i \(-0.110621\pi\)
−0.340573 + 0.940218i \(0.610621\pi\)
\(480\) −207.556 −0.0197366
\(481\) 8747.36 + 8747.36i 0.829200 + 0.829200i
\(482\) 4813.07 4813.07i 0.454832 0.454832i
\(483\) 574.179 574.179i 0.0540912 0.0540912i
\(484\) 2093.49i 0.196609i
\(485\) 3105.78i 0.290776i
\(486\) −2558.21 + 2558.21i −0.238771 + 0.238771i
\(487\) −5023.62 + 5023.62i −0.467437 + 0.467437i −0.901083 0.433646i \(-0.857227\pi\)
0.433646 + 0.901083i \(0.357227\pi\)
\(488\) 677.722 + 677.722i 0.0628669 + 0.0628669i
\(489\) −64.7121 −0.00598442
\(490\) 1650.28 + 1650.28i 0.152147 + 0.152147i
\(491\) 7638.33i 0.702063i −0.936364 0.351031i \(-0.885831\pi\)
0.936364 0.351031i \(-0.114169\pi\)
\(492\) −734.703 −0.0673231
\(493\) 10783.5 + 2208.71i 0.985118 + 0.201775i
\(494\) 9931.20 0.904505
\(495\) 1696.78i 0.154070i
\(496\) −12106.3 12106.3i −1.09594 1.09594i
\(497\) 1987.76 0.179403
\(498\) −697.938 697.938i −0.0628019 0.0628019i
\(499\) −14285.4 + 14285.4i −1.28156 + 1.28156i −0.341787 + 0.939778i \(0.611032\pi\)
−0.939778 + 0.341787i \(0.888968\pi\)
\(500\) −2545.73 + 2545.73i −0.227697 + 0.227697i
\(501\) 1070.61i 0.0954714i
\(502\) 5173.54i 0.459973i
\(503\) −14474.1 + 14474.1i −1.28304 + 1.28304i −0.344107 + 0.938931i \(0.611818\pi\)
−0.938931 + 0.344107i \(0.888182\pi\)
\(504\) 956.756 956.756i 0.0845581 0.0845581i
\(505\) −919.932 919.932i −0.0810623 0.0810623i
\(506\) 9612.68 0.844537
\(507\) −237.899 237.899i −0.0208391 0.0208391i
\(508\) 14775.4i 1.29045i
\(509\) −19503.1 −1.69835 −0.849173 0.528116i \(-0.822899\pi\)
−0.849173 + 0.528116i \(0.822899\pi\)
\(510\) 190.475 125.713i 0.0165380 0.0109150i
\(511\) 9741.73 0.843344
\(512\) 15932.3i 1.37523i
\(513\) −744.398 744.398i −0.0640662 0.0640662i
\(514\) −23776.4 −2.04033
\(515\) −1203.37 1203.37i −0.102965 0.102965i
\(516\) −268.883 + 268.883i −0.0229398 + 0.0229398i
\(517\) 4318.48 4318.48i 0.367362 0.367362i
\(518\) 22649.3i 1.92114i
\(519\) 139.185i 0.0117718i
\(520\) 149.624 149.624i 0.0126181 0.0126181i
\(521\) 4923.95 4923.95i 0.414054 0.414054i −0.469094 0.883148i \(-0.655420\pi\)
0.883148 + 0.469094i \(0.155420\pi\)
\(522\) 11723.8 + 11723.8i 0.983020 + 0.983020i
\(523\) −2507.22 −0.209623 −0.104812 0.994492i \(-0.533424\pi\)
−0.104812 + 0.994492i \(0.533424\pi\)
\(524\) −1329.31 1329.31i −0.110823 0.110823i
\(525\) 1306.96i 0.108648i
\(526\) −3898.60 −0.323169
\(527\) 17345.7 + 3552.81i 1.43376 + 0.293668i
\(528\) −931.946 −0.0768139
\(529\) 6497.24i 0.534005i
\(530\) 2542.44 + 2542.44i 0.208371 + 0.208371i
\(531\) 20147.8 1.64659
\(532\) −6219.60 6219.60i −0.506868 0.506868i
\(533\) 8938.71 8938.71i 0.726414 0.726414i
\(534\) −719.598 + 719.598i −0.0583147 + 0.0583147i
\(535\) 675.614i 0.0545969i
\(536\) 1058.94i 0.0853348i
\(537\) 1245.73 1245.73i 0.100107 0.100107i
\(538\) −9437.72 + 9437.72i −0.756299 + 0.756299i
\(539\) 6969.23 + 6969.23i 0.556932 + 0.556932i
\(540\) 333.697 0.0265926
\(541\) 13701.0 + 13701.0i 1.08882 + 1.08882i 0.995650 + 0.0931705i \(0.0297002\pi\)
0.0931705 + 0.995650i \(0.470300\pi\)
\(542\) 14589.6i 1.15623i
\(543\) −405.092 −0.0320150
\(544\) −9688.65 14679.9i −0.763598 1.15698i
\(545\) −264.960 −0.0208250
\(546\) 2321.47i 0.181960i
\(547\) −2090.43 2090.43i −0.163401 0.163401i 0.620671 0.784071i \(-0.286860\pi\)
−0.784071 + 0.620671i \(0.786860\pi\)
\(548\) −3271.10 −0.254990
\(549\) −9163.97 9163.97i −0.712402 0.712402i
\(550\) −10940.3 + 10940.3i −0.848176 + 0.848176i
\(551\) −5122.85 + 5122.85i −0.396081 + 0.396081i
\(552\) 63.3242i 0.00488271i
\(553\) 32526.9i 2.50124i
\(554\) 21299.1 21299.1i 1.63342 1.63342i
\(555\) −132.304 + 132.304i −0.0101189 + 0.0101189i
\(556\) 443.778 + 443.778i 0.0338496 + 0.0338496i
\(557\) −3920.00 −0.298197 −0.149099 0.988822i \(-0.547637\pi\)
−0.149099 + 0.988822i \(0.547637\pi\)
\(558\) 18858.3 + 18858.3i 1.43071 + 1.43071i
\(559\) 6542.70i 0.495039i
\(560\) −3362.93 −0.253768
\(561\) 804.388 530.891i 0.0605371 0.0399541i
\(562\) 12576.6 0.943975
\(563\) 20821.5i 1.55865i −0.626618 0.779326i \(-0.715561\pi\)
0.626618 0.779326i \(-0.284439\pi\)
\(564\) −423.227 423.227i −0.0315977 0.0315977i
\(565\) 1728.30 0.128691
\(566\) −16672.8 16672.8i −1.23818 1.23818i
\(567\) −12849.7 + 12849.7i −0.951739 + 0.951739i
\(568\) −109.612 + 109.612i −0.00809718 + 0.00809718i
\(569\) 7849.66i 0.578339i −0.957278 0.289170i \(-0.906621\pi\)
0.957278 0.289170i \(-0.0933791\pi\)
\(570\) 150.210i 0.0110379i
\(571\) −17349.3 + 17349.3i −1.27154 + 1.27154i −0.326254 + 0.945282i \(0.605786\pi\)
−0.945282 + 0.326254i \(0.894214\pi\)
\(572\) −9400.38 + 9400.38i −0.687149 + 0.687149i
\(573\) 266.756 + 266.756i 0.0194483 + 0.0194483i
\(574\) −23144.7 −1.68300
\(575\) 6452.82 + 6452.82i 0.468002 + 0.468002i
\(576\) 11951.1i 0.864521i
\(577\) −7549.37 −0.544687 −0.272343 0.962200i \(-0.587799\pi\)
−0.272343 + 0.962200i \(0.587799\pi\)
\(578\) 17782.7 + 7603.62i 1.27969 + 0.547178i
\(579\) 734.384 0.0527115
\(580\) 2296.46i 0.164406i
\(581\) −10635.8 10635.8i −0.759464 0.759464i
\(582\) 2657.22 0.189253
\(583\) 10736.9 + 10736.9i 0.762738 + 0.762738i
\(584\) −537.191 + 537.191i −0.0380636 + 0.0380636i
\(585\) −2023.17 + 2023.17i −0.142988 + 0.142988i
\(586\) 21148.7i 1.49086i
\(587\) 6451.77i 0.453651i 0.973935 + 0.226826i \(0.0728347\pi\)
−0.973935 + 0.226826i \(0.927165\pi\)
\(588\) 683.012 683.012i 0.0479029 0.0479029i
\(589\) −8240.35 + 8240.35i −0.576465 + 0.576465i
\(590\) −4079.19 4079.19i −0.284640 0.284640i
\(591\) −1884.18 −0.131142
\(592\) 10841.4 + 10841.4i 0.752670 + 0.752670i
\(593\) 176.420i 0.0122170i −0.999981 0.00610850i \(-0.998056\pi\)
0.999981 0.00610850i \(-0.00194441\pi\)
\(594\) 2913.16 0.201227
\(595\) 2902.64 1915.72i 0.199994 0.131995i
\(596\) 17671.7 1.21453
\(597\) 1322.16i 0.0906408i
\(598\) 11461.8 + 11461.8i 0.783789 + 0.783789i
\(599\) −11248.7 −0.767292 −0.383646 0.923480i \(-0.625332\pi\)
−0.383646 + 0.923480i \(0.625332\pi\)
\(600\) −72.0701 72.0701i −0.00490375 0.00490375i
\(601\) 17973.6 17973.6i 1.21990 1.21990i 0.252228 0.967668i \(-0.418837\pi\)
0.967668 0.252228i \(-0.0811632\pi\)
\(602\) −8470.41 + 8470.41i −0.573469 + 0.573469i
\(603\) 14318.7i 0.967006i
\(604\) 1122.52i 0.0756201i
\(605\) −385.240 + 385.240i −0.0258880 + 0.0258880i
\(606\) −787.068 + 787.068i −0.0527598 + 0.0527598i
\(607\) −13916.2 13916.2i −0.930542 0.930542i 0.0671975 0.997740i \(-0.478594\pi\)
−0.997740 + 0.0671975i \(0.978594\pi\)
\(608\) 11576.7 0.772196
\(609\) −1197.50 1197.50i −0.0796798 0.0796798i
\(610\) 3710.74i 0.246300i
\(611\) 10298.3 0.681876
\(612\) 7762.43 + 11761.4i 0.512708 + 0.776838i
\(613\) 3619.34 0.238473 0.119236 0.992866i \(-0.461955\pi\)
0.119236 + 0.992866i \(0.461955\pi\)
\(614\) 27637.9i 1.81657i
\(615\) 135.199 + 135.199i 0.00886460 + 0.00886460i
\(616\) −1636.08 −0.107012
\(617\) 13961.7 + 13961.7i 0.910985 + 0.910985i 0.996350 0.0853644i \(-0.0272055\pi\)
−0.0853644 + 0.996350i \(0.527205\pi\)
\(618\) −1029.57 + 1029.57i −0.0670151 + 0.0670151i
\(619\) 13220.0 13220.0i 0.858409 0.858409i −0.132741 0.991151i \(-0.542378\pi\)
0.991151 + 0.132741i \(0.0423780\pi\)
\(620\) 3693.96i 0.239279i
\(621\) 1718.24i 0.111032i
\(622\) 2855.93 2855.93i 0.184103 0.184103i
\(623\) −10965.9 + 10965.9i −0.705200 + 0.705200i
\(624\) −1111.21 1111.21i −0.0712886 0.0712886i
\(625\) −14212.4 −0.909592
\(626\) −6933.41 6933.41i −0.442676 0.442676i
\(627\) 634.345i 0.0404040i
\(628\) 894.139 0.0568153
\(629\) −15533.5 3181.62i −0.984675 0.201685i
\(630\) 5238.53 0.331283
\(631\) 10087.2i 0.636394i 0.948025 + 0.318197i \(0.103077\pi\)
−0.948025 + 0.318197i \(0.896923\pi\)
\(632\) 1793.64 + 1793.64i 0.112891 + 0.112891i
\(633\) 1921.75 0.120668
\(634\) −7724.81 7724.81i −0.483898 0.483898i
\(635\) 2718.93 2718.93i 0.169917 0.169917i
\(636\) 1052.26 1052.26i 0.0656048 0.0656048i
\(637\) 16619.6i 1.03374i
\(638\) 20048.0i 1.24406i
\(639\) 1482.14 1482.14i 0.0917565 0.0917565i
\(640\) 349.523 349.523i 0.0215877 0.0215877i
\(641\) 7258.52 + 7258.52i 0.447261 + 0.447261i 0.894443 0.447182i \(-0.147572\pi\)
−0.447182 + 0.894443i \(0.647572\pi\)
\(642\) −578.036 −0.0355347
\(643\) −5500.06 5500.06i −0.337327 0.337327i 0.518034 0.855360i \(-0.326664\pi\)
−0.855360 + 0.518034i \(0.826664\pi\)
\(644\) 14356.3i 0.878443i
\(645\) 98.9587 0.00604108
\(646\) −10624.0 + 7011.76i −0.647051 + 0.427050i
\(647\) 5015.28 0.304746 0.152373 0.988323i \(-0.451308\pi\)
0.152373 + 0.988323i \(0.451308\pi\)
\(648\) 1417.15i 0.0859118i
\(649\) −17226.7 17226.7i −1.04192 1.04192i
\(650\) −26089.5 −1.57433
\(651\) −1926.23 1926.23i −0.115968 0.115968i
\(652\) −809.004 + 809.004i −0.0485936 + 0.0485936i
\(653\) −10298.2 + 10298.2i −0.617151 + 0.617151i −0.944800 0.327649i \(-0.893744\pi\)
0.327649 + 0.944800i \(0.393744\pi\)
\(654\) 226.692i 0.0135541i
\(655\) 489.235i 0.0291847i
\(656\) 11078.6 11078.6i 0.659371 0.659371i
\(657\) 7263.75 7263.75i 0.431333 0.431333i
\(658\) −13332.6 13332.6i −0.789906 0.789906i
\(659\) 6199.21 0.366445 0.183222 0.983072i \(-0.441347\pi\)
0.183222 + 0.983072i \(0.441347\pi\)
\(660\) −142.181 142.181i −0.00838545 0.00838545i
\(661\) 15131.8i 0.890406i −0.895430 0.445203i \(-0.853132\pi\)
0.895430 0.445203i \(-0.146868\pi\)
\(662\) 23689.6 1.39082
\(663\) 1592.13 + 326.106i 0.0932628 + 0.0191024i
\(664\) 1172.99 0.0685554
\(665\) 2289.04i 0.133481i
\(666\) −16888.0 16888.0i −0.982578 0.982578i
\(667\) −11824.7 −0.686440
\(668\) 13384.3 + 13384.3i 0.775230 + 0.775230i
\(669\) −37.0484 + 37.0484i −0.00214107 + 0.00214107i
\(670\) −2899.02 + 2899.02i −0.167163 + 0.167163i
\(671\) 15670.6i 0.901577i
\(672\) 2706.11i 0.155343i
\(673\) 19122.8 19122.8i 1.09529 1.09529i 0.100337 0.994953i \(-0.468008\pi\)
0.994953 0.100337i \(-0.0319922\pi\)
\(674\) −1320.44 + 1320.44i −0.0754619 + 0.0754619i
\(675\) 1955.55 + 1955.55i 0.111510 + 0.111510i
\(676\) −5948.22 −0.338429
\(677\) 1889.00 + 1889.00i 0.107238 + 0.107238i 0.758690 0.651452i \(-0.225840\pi\)
−0.651452 + 0.758690i \(0.725840\pi\)
\(678\) 1478.69i 0.0837591i
\(679\) 40493.2 2.28864
\(680\) −54.4217 + 265.701i −0.00306909 + 0.0149840i
\(681\) −330.770 −0.0186125
\(682\) 32248.2i 1.81063i
\(683\) 10455.7 + 10455.7i 0.585763 + 0.585763i 0.936481 0.350718i \(-0.114063\pi\)
−0.350718 + 0.936481i \(0.614063\pi\)
\(684\) −9275.07 −0.518481
\(685\) 601.942 + 601.942i 0.0335752 + 0.0335752i
\(686\) −2767.27 + 2767.27i −0.154016 + 0.154016i
\(687\) −832.457 + 832.457i −0.0462303 + 0.0462303i
\(688\) 8109.01i 0.449350i
\(689\) 25604.4i 1.41575i
\(690\) −173.360 + 173.360i −0.00956477 + 0.00956477i
\(691\) −13201.7 + 13201.7i −0.726798 + 0.726798i −0.969981 0.243182i \(-0.921809\pi\)
0.243182 + 0.969981i \(0.421809\pi\)
\(692\) −1740.04 1740.04i −0.0955871 0.0955871i
\(693\) 22122.6 1.21265
\(694\) 4106.98 + 4106.98i 0.224638 + 0.224638i
\(695\) 163.326i 0.00891413i
\(696\) 132.068 0.00719255
\(697\) −3251.23 + 15873.3i −0.176684 + 0.862617i
\(698\) −26985.8 −1.46336
\(699\) 2140.14i 0.115805i
\(700\) 16339.1 + 16339.1i 0.882227 + 0.882227i
\(701\) 27668.5 1.49076 0.745381 0.666638i \(-0.232267\pi\)
0.745381 + 0.666638i \(0.232267\pi\)
\(702\) 3473.53 + 3473.53i 0.186752 + 0.186752i
\(703\) 7379.42 7379.42i 0.395903 0.395903i
\(704\) −10218.4 + 10218.4i −0.547045 + 0.547045i
\(705\) 155.763i 0.00832109i
\(706\) 29467.7i 1.57087i
\(707\) −11994.1 + 11994.1i −0.638025 + 0.638025i
\(708\) −1688.28 + 1688.28i −0.0896178 + 0.0896178i
\(709\) −7382.12 7382.12i −0.391032 0.391032i 0.484023 0.875055i \(-0.339175\pi\)
−0.875055 + 0.484023i \(0.839175\pi\)
\(710\) −600.157 −0.0317232
\(711\) −24253.1 24253.1i −1.27927 1.27927i
\(712\) 1209.39i 0.0636572i
\(713\) −19020.6 −0.999059
\(714\) −1639.04 2483.41i −0.0859097 0.130167i
\(715\) 3459.68 0.180957
\(716\) 31147.2i 1.62573i
\(717\) −675.825 675.825i −0.0352010 0.0352010i
\(718\) 28223.0 1.46695
\(719\) −12597.2 12597.2i −0.653402 0.653402i 0.300409 0.953811i \(-0.402877\pi\)
−0.953811 + 0.300409i \(0.902877\pi\)
\(720\) −2507.51 + 2507.51i −0.129791 + 0.129791i
\(721\) −15689.5 + 15689.5i −0.810414 + 0.810414i
\(722\) 18622.4i 0.959909i
\(723\) 733.132i 0.0377116i
\(724\) −5064.29 + 5064.29i −0.259963 + 0.259963i
\(725\) 13457.9 13457.9i 0.689397 0.689397i
\(726\) 329.600 + 329.600i 0.0168493 + 0.0168493i
\(727\) −4296.42 −0.219182 −0.109591 0.993977i \(-0.534954\pi\)
−0.109591 + 0.993977i \(0.534954\pi\)
\(728\) −1950.79 1950.79i −0.0993148 0.0993148i
\(729\) 18901.0i 0.960273i
\(730\) −2941.28 −0.149126
\(731\) 4619.37 + 6999.11i 0.233726 + 0.354133i
\(732\) 1535.78 0.0775467
\(733\) 28559.1i 1.43909i 0.694445 + 0.719546i \(0.255650\pi\)
−0.694445 + 0.719546i \(0.744350\pi\)
\(734\) −18395.8 18395.8i −0.925071 0.925071i
\(735\) −251.373 −0.0126150
\(736\) 13360.8 + 13360.8i 0.669138 + 0.669138i
\(737\) −12242.7 + 12242.7i −0.611895 + 0.611895i
\(738\) −17257.5 + 17257.5i −0.860780 + 0.860780i
\(739\) 10646.9i 0.529974i −0.964252 0.264987i \(-0.914632\pi\)
0.964252 0.264987i \(-0.0853677\pi\)
\(740\) 3308.03i 0.164332i
\(741\) −756.366 + 756.366i −0.0374977 + 0.0374977i
\(742\) 33148.3 33148.3i 1.64005 1.64005i
\(743\) −9874.51 9874.51i −0.487565 0.487565i 0.419972 0.907537i \(-0.362040\pi\)
−0.907537 + 0.419972i \(0.862040\pi\)
\(744\) 212.437 0.0104682
\(745\) −3251.91 3251.91i −0.159921 0.159921i
\(746\) 6309.87i 0.309679i
\(747\) −15860.8 −0.776864
\(748\) 3419.14 16693.1i 0.167134 0.815990i
\(749\) −8808.65 −0.429721
\(750\) 801.602i 0.0390272i
\(751\) 18922.9 + 18922.9i 0.919449 + 0.919449i 0.996989 0.0775401i \(-0.0247066\pi\)
−0.0775401 + 0.996989i \(0.524707\pi\)
\(752\) 12763.7 0.618943
\(753\) 394.020 + 394.020i 0.0190689 + 0.0190689i
\(754\) 23904.4 23904.4i 1.15457 1.15457i
\(755\) 206.563 206.563i 0.00995709 0.00995709i
\(756\) 4350.73i 0.209305i
\(757\) 1399.40i 0.0671889i −0.999436 0.0335945i \(-0.989305\pi\)
0.999436 0.0335945i \(-0.0106955\pi\)
\(758\) −4851.93 + 4851.93i −0.232493 + 0.232493i
\(759\) −732.108 + 732.108i −0.0350116 + 0.0350116i
\(760\) −126.225 126.225i −0.00602456 0.00602456i
\(761\) 29282.9 1.39488 0.697440 0.716644i \(-0.254323\pi\)
0.697440 + 0.716644i \(0.254323\pi\)
\(762\) −2326.24 2326.24i −0.110592 0.110592i
\(763\) 3454.54i 0.163909i
\(764\) 6669.74 0.315841
\(765\) 735.875 3592.73i 0.0347786 0.169798i
\(766\) 4547.62 0.214507
\(767\) 41080.7i 1.93395i
\(768\) −1367.80 1367.80i −0.0642658 0.0642658i
\(769\) −11804.9 −0.553571 −0.276786 0.960932i \(-0.589269\pi\)
−0.276786 + 0.960932i \(0.589269\pi\)
\(770\) −4479.02 4479.02i −0.209627 0.209627i
\(771\) 1810.82 1810.82i 0.0845852 0.0845852i
\(772\) 9180.97 9180.97i 0.428019 0.428019i
\(773\) 18421.7i 0.857155i −0.903505 0.428578i \(-0.859015\pi\)
0.903505 0.428578i \(-0.140985\pi\)
\(774\) 12631.6i 0.586607i
\(775\) 21647.6 21647.6i 1.00336 1.00336i
\(776\) −2232.93 + 2232.93i −0.103296 + 0.103296i
\(777\) 1724.98 + 1724.98i 0.0796439 + 0.0796439i
\(778\) 14561.0 0.670998
\(779\) −7540.85 7540.85i −0.346828 0.346828i
\(780\) 339.062i 0.0155646i
\(781\) −2534.49 −0.116122
\(782\) −20353.7 4168.92i −0.930750 0.190640i
\(783\) −3583.53 −0.163557
\(784\) 20598.3i 0.938335i
\(785\) −164.538 164.538i −0.00748102 0.00748102i
\(786\) 418.575 0.0189950
\(787\) −15833.2 15833.2i −0.717143 0.717143i 0.250876 0.968019i \(-0.419281\pi\)
−0.968019 + 0.250876i \(0.919281\pi\)
\(788\) −23555.2 + 23555.2i −1.06487 + 1.06487i
\(789\) 296.919 296.919i 0.0133975 0.0133975i
\(790\) 9820.74i 0.442286i
\(791\) 22533.6i 1.01290i
\(792\) −1219.91 + 1219.91i −0.0547320 + 0.0547320i
\(793\) −18685.0 + 18685.0i −0.836727 + 0.836727i
\(794\) 37822.5 + 37822.5i 1.69052 + 1.69052i
\(795\) −387.268 −0.0172767
\(796\) −16529.2 16529.2i −0.736005 0.736005i
\(797\) 13676.1i 0.607818i 0.952701 + 0.303909i \(0.0982919\pi\)
−0.952701 + 0.303909i \(0.901708\pi\)
\(798\) 1958.43 0.0868770
\(799\) −11016.7 + 7270.98i −0.487790 + 0.321938i
\(800\) −30412.2 −1.34404
\(801\) 16353.1i 0.721357i
\(802\) −7416.29 7416.29i −0.326532 0.326532i
\(803\) −12421.2 −0.545872
\(804\) 1199.83 + 1199.83i 0.0526305 + 0.0526305i
\(805\) −2641.82 + 2641.82i −0.115667 + 0.115667i
\(806\) 38451.4 38451.4i 1.68039 1.68039i
\(807\) 1437.56i 0.0627071i
\(808\) 1322.79i 0.0575933i
\(809\) −71.3327 + 71.3327i −0.00310003 + 0.00310003i −0.708655 0.705555i \(-0.750698\pi\)
0.705555 + 0.708655i \(0.250698\pi\)
\(810\) 3879.66 3879.66i 0.168293 0.168293i
\(811\) 11822.5 + 11822.5i 0.511893 + 0.511893i 0.915106 0.403213i \(-0.132107\pi\)
−0.403213 + 0.915106i \(0.632107\pi\)
\(812\) −29941.2 −1.29400
\(813\) 1111.16 + 1111.16i 0.0479335 + 0.0479335i
\(814\) 28879.0i 1.24350i
\(815\) 297.743 0.0127969
\(816\) 1973.28 + 404.175i 0.0846552 + 0.0173394i
\(817\) −5519.54 −0.236358
\(818\) 16320.2i 0.697584i
\(819\) 26378.1 + 26378.1i 1.12543 + 1.12543i
\(820\) 3380.39 0.143962
\(821\) −3487.82 3487.82i −0.148265 0.148265i 0.629077 0.777343i \(-0.283433\pi\)
−0.777343 + 0.629077i \(0.783433\pi\)
\(822\) 515.004 515.004i 0.0218526 0.0218526i
\(823\) 18792.3 18792.3i 0.795939 0.795939i −0.186513 0.982452i \(-0.559719\pi\)
0.982452 + 0.186513i \(0.0597187\pi\)
\(824\) 1730.35i 0.0731547i
\(825\) 1666.44i 0.0703249i
\(826\) −53184.5 + 53184.5i −2.24034 + 2.24034i
\(827\) 22017.0 22017.0i 0.925762 0.925762i −0.0716667 0.997429i \(-0.522832\pi\)
0.997429 + 0.0716667i \(0.0228318\pi\)
\(828\) −10704.5 10704.5i −0.449284 0.449284i
\(829\) 17274.9 0.723742 0.361871 0.932228i \(-0.382138\pi\)
0.361871 + 0.932228i \(0.382138\pi\)
\(830\) 3211.24 + 3211.24i 0.134294 + 0.134294i
\(831\) 3244.31i 0.135432i
\(832\) −24367.9 −1.01539
\(833\) −11734.0 17779.0i −0.488067 0.739502i
\(834\) −139.737 −0.00580180
\(835\) 4925.90i 0.204153i
\(836\) 7930.32 + 7930.32i 0.328081 + 0.328081i
\(837\) −5764.28 −0.238044
\(838\) 39658.4 + 39658.4i 1.63482 + 1.63482i
\(839\) 3970.01 3970.01i 0.163361 0.163361i −0.620693 0.784054i \(-0.713149\pi\)
0.784054 + 0.620693i \(0.213149\pi\)
\(840\) 29.5058 29.5058i 0.00121196 0.00121196i
\(841\) 272.434i 0.0111704i
\(842\) 12563.8i 0.514226i
\(843\) −957.845 + 957.845i −0.0391340 + 0.0391340i
\(844\) 24025.0 24025.0i 0.979827 0.979827i
\(845\) 1094.58 + 1094.58i 0.0445618 + 0.0445618i
\(846\) −19882.4 −0.808004
\(847\) 5022.76 + 5022.76i 0.203759 + 0.203759i
\(848\) 31734.0i 1.28508i
\(849\) 2539.63 0.102662
\(850\) 27909.5 18420.1i 1.12622 0.743299i
\(851\) 17033.4 0.686132
\(852\) 248.390i 0.00998792i
\(853\) 2686.89 + 2686.89i 0.107851 + 0.107851i 0.758973 0.651122i \(-0.225701\pi\)
−0.651122 + 0.758973i \(0.725701\pi\)
\(854\) 48380.5 1.93858
\(855\) 1706.78 + 1706.78i 0.0682698 + 0.0682698i
\(856\) 485.738 485.738i 0.0193951 0.0193951i
\(857\) 29847.2 29847.2i 1.18969 1.18969i 0.212532 0.977154i \(-0.431829\pi\)
0.977154 0.212532i \(-0.0681710\pi\)
\(858\) 2960.00i 0.117777i
\(859\) 3132.98i 0.124442i 0.998062 + 0.0622212i \(0.0198184\pi\)
−0.998062 + 0.0622212i \(0.980182\pi\)
\(860\) 1237.14 1237.14i 0.0490537 0.0490537i
\(861\) 1762.72 1762.72i 0.0697715 0.0697715i
\(862\) −4563.37 4563.37i −0.180312 0.180312i
\(863\) −31934.9 −1.25965 −0.629824 0.776738i \(-0.716873\pi\)
−0.629824 + 0.776738i \(0.716873\pi\)
\(864\) 4049.05 + 4049.05i 0.159434 + 0.159434i
\(865\) 640.396i 0.0251724i
\(866\) −65266.8 −2.56104
\(867\) −1933.44 + 775.244i −0.0757358 + 0.0303675i
\(868\) −48161.8 −1.88332
\(869\) 41473.5i 1.61898i
\(870\) 361.556 + 361.556i 0.0140895 + 0.0140895i
\(871\) −29195.4 −1.13576
\(872\) −190.495 190.495i −0.00739790 0.00739790i
\(873\) 30193.0 30193.0i 1.17054 1.17054i
\(874\) 9669.33 9669.33i 0.374222 0.374222i
\(875\) 12215.6i 0.471956i
\(876\) 1217.33i 0.0469517i
\(877\) −10847.5 + 10847.5i −0.417667 + 0.417667i −0.884399 0.466732i \(-0.845431\pi\)
0.466732 + 0.884399i \(0.345431\pi\)
\(878\) −20450.9 + 20450.9i −0.786086 + 0.786086i
\(879\) −1610.70 1610.70i −0.0618060 0.0618060i
\(880\) 4287.91 0.164256
\(881\) 32730.5 + 32730.5i 1.25167 + 1.25167i 0.954972 + 0.296695i \(0.0958845\pi\)
0.296695 + 0.954972i \(0.404116\pi\)
\(882\) 32086.6i 1.22496i
\(883\) −26455.9 −1.00828 −0.504140 0.863622i \(-0.668190\pi\)
−0.504140 + 0.863622i \(0.668190\pi\)
\(884\) 23981.0 15827.3i 0.912407 0.602184i
\(885\) 621.348 0.0236004
\(886\) 52456.0i 1.98904i
\(887\) −12749.8 12749.8i −0.482633 0.482633i 0.423339 0.905972i \(-0.360858\pi\)
−0.905972 + 0.423339i \(0.860858\pi\)
\(888\) −190.242 −0.00718932
\(889\) −35449.4 35449.4i −1.33739 1.33739i
\(890\) 3310.90 3310.90i 0.124698 0.124698i
\(891\) 16384.0 16384.0i 0.616033 0.616033i
\(892\) 926.327i 0.0347710i
\(893\) 8687.85i 0.325563i
\(894\) −2782.24 + 2782.24i −0.104085 + 0.104085i
\(895\) −5731.65 + 5731.65i −0.214065 + 0.214065i
\(896\) −4557.08 4557.08i −0.169912 0.169912i
\(897\) −1745.87 −0.0649864
\(898\) −26962.3 26962.3i −1.00194 1.00194i
\(899\) 39669.1i 1.47168i
\(900\) 24365.9 0.902440
\(901\) −18077.6 27390.5i −0.668425 1.01277i
\(902\) 29510.7 1.08936
\(903\) 1290.22i 0.0475481i
\(904\) 1242.58 + 1242.58i 0.0457163 + 0.0457163i
\(905\) 1863.84 0.0684599
\(906\) −176.729 176.729i −0.00648062 0.00648062i
\(907\) −32345.3 + 32345.3i −1.18413 + 1.18413i −0.205467 + 0.978664i \(0.565871\pi\)
−0.978664 + 0.205467i \(0.934129\pi\)
\(908\) −4135.15 + 4135.15i −0.151134 + 0.151134i
\(909\) 17886.3i 0.652642i
\(910\) 10681.2i 0.389096i
\(911\) −1203.07 + 1203.07i −0.0437534 + 0.0437534i −0.728645 0.684892i \(-0.759850\pi\)
0.684892 + 0.728645i \(0.259850\pi\)
\(912\) −937.438 + 937.438i −0.0340369 + 0.0340369i
\(913\) 13561.2 + 13561.2i 0.491579 + 0.491579i
\(914\) 2747.94 0.0994462
\(915\) −282.612 282.612i −0.0102108 0.0102108i
\(916\) 20814.1i 0.750782i
\(917\) 6378.64 0.229707
\(918\) −6168.27 1263.41i −0.221768 0.0454234i
\(919\) 30814.5 1.10607 0.553035 0.833158i \(-0.313470\pi\)
0.553035 + 0.833158i \(0.313470\pi\)
\(920\) 291.357i 0.0104410i
\(921\) −2104.92 2104.92i −0.0753088 0.0753088i
\(922\) 25609.3 0.914747
\(923\) −3022.02 3022.02i −0.107769 0.107769i
\(924\) −1853.76 + 1853.76i −0.0660001 + 0.0660001i
\(925\) −19385.9 + 19385.9i −0.689087 + 0.689087i
\(926\) 4651.93i 0.165088i
\(927\) 23397.2i 0.828982i
\(928\) 27865.0 27865.0i 0.985684 0.985684i
\(929\) 2894.34 2894.34i 0.102218 0.102218i −0.654149 0.756366i \(-0.726973\pi\)
0.756366 + 0.654149i \(0.226973\pi\)
\(930\) 581.579 + 581.579i 0.0205062 + 0.0205062i
\(931\) 14020.6 0.493563
\(932\) 26755.1 + 26755.1i 0.940336 + 0.940336i
\(933\) 435.018i 0.0152646i
\(934\) −11616.5 −0.406963
\(935\) −3701.02 + 2442.65i −0.129450 + 0.0854365i
\(936\) −2909.15 −0.101590
\(937\) 16517.3i 0.575877i 0.957649 + 0.287939i \(0.0929699\pi\)
−0.957649 + 0.287939i \(0.907030\pi\)
\(938\) 37797.4 + 37797.4i 1.31570 + 1.31570i
\(939\) 1056.11 0.0367036
\(940\) 1947.28 + 1947.28i 0.0675674 + 0.0675674i
\(941\) −4851.27 + 4851.27i −0.168063 + 0.168063i −0.786127 0.618065i \(-0.787917\pi\)
0.618065 + 0.786127i \(0.287917\pi\)
\(942\) −140.774 + 140.774i −0.00486906 + 0.00486906i
\(943\) 17406.0i 0.601080i
\(944\) 50915.3i 1.75546i
\(945\) −800.613 + 800.613i −0.0275597 + 0.0275597i
\(946\) 10800.2 10800.2i 0.371189 0.371189i
\(947\) 23545.8 + 23545.8i 0.807957 + 0.807957i 0.984324 0.176367i \(-0.0564347\pi\)
−0.176367 + 0.984324i \(0.556435\pi\)
\(948\) 4064.57 0.139252
\(949\) −14810.5 14810.5i −0.506607 0.506607i
\(950\) 22009.6i 0.751669i
\(951\) 1176.65 0.0401215
\(952\) 3464.20 + 709.550i 0.117936 + 0.0241561i
\(953\) −24857.5 −0.844925 −0.422462 0.906380i \(-0.638834\pi\)
−0.422462 + 0.906380i \(0.638834\pi\)
\(954\) 49432.9i 1.67762i
\(955\) −1227.35 1227.35i −0.0415877 0.0415877i
\(956\) −16897.8 −0.571666
\(957\) 1526.87 + 1526.87i 0.0515744 + 0.0515744i
\(958\) −24746.2 + 24746.2i −0.834565 + 0.834565i
\(959\) 7848.11 7848.11i 0.264264 0.264264i
\(960\) 368.566i 0.0123911i
\(961\) 34018.6i 1.14191i
\(962\) −34434.1 + 34434.1i −1.15405 + 1.15405i
\(963\) −6568.01 + 6568.01i −0.219783 + 0.219783i
\(964\) 9165.31 + 9165.31i 0.306219 + 0.306219i
\(965\) −3378.93 −0.112717
\(966\) 2260.26 + 2260.26i 0.0752823 + 0.0752823i
\(967\) 15832.2i 0.526504i −0.964727 0.263252i \(-0.915205\pi\)
0.964727 0.263252i \(-0.0847951\pi\)
\(968\) −553.943 −0.0183930
\(969\) 275.108 1343.15i 0.00912049 0.0445285i
\(970\) −12226.0 −0.404693
\(971\) 39521.9i 1.30620i 0.757273 + 0.653098i \(0.226531\pi\)
−0.757273 + 0.653098i \(0.773469\pi\)
\(972\) −4871.49 4871.49i −0.160754 0.160754i
\(973\) −2129.45 −0.0701612
\(974\) −19775.5 19775.5i −0.650564 0.650564i
\(975\) 1986.99 1986.99i 0.0652664 0.0652664i
\(976\) −23158.2 + 23158.2i −0.759502 + 0.759502i
\(977\) 11587.3i 0.379438i −0.981838 0.189719i \(-0.939242\pi\)
0.981838 0.189719i \(-0.0607577\pi\)
\(978\) 254.740i 0.00832893i
\(979\) 13982.1 13982.1i 0.456455 0.456455i
\(980\) −3142.56 + 3142.56i −0.102434 + 0.102434i
\(981\) 2575.82 + 2575.82i 0.0838323 + 0.0838323i
\(982\) 30068.4 0.977108
\(983\) −22711.9 22711.9i −0.736925 0.736925i 0.235057 0.971982i \(-0.424472\pi\)
−0.971982 + 0.235057i \(0.924472\pi\)
\(984\) 194.404i 0.00629815i
\(985\) 8669.17 0.280429
\(986\) −8694.61 + 42449.3i −0.280824 + 1.37105i
\(987\) 2030.83 0.0654936
\(988\) 18911.5i 0.608964i
\(989\) −6370.19 6370.19i −0.204813 0.204813i
\(990\) −6679.40 −0.214429
\(991\) −13235.2 13235.2i −0.424247 0.424247i 0.462416 0.886663i \(-0.346983\pi\)
−0.886663 + 0.462416i \(0.846983\pi\)
\(992\) 44822.2 44822.2i 1.43458 1.43458i
\(993\) −1804.21 + 1804.21i −0.0576585 + 0.0576585i
\(994\) 7824.83i 0.249687i
\(995\) 6083.32i 0.193823i
\(996\) 1329.05 1329.05i 0.0422818 0.0422818i
\(997\) −8210.42 + 8210.42i −0.260809 + 0.260809i −0.825383 0.564574i \(-0.809041\pi\)
0.564574 + 0.825383i \(0.309041\pi\)
\(998\) −56234.5 56234.5i −1.78364 1.78364i
\(999\) 5162.05 0.163483
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 17.4.c.a.13.4 yes 8
3.2 odd 2 153.4.f.a.64.1 8
4.3 odd 2 272.4.o.e.81.3 8
17.2 even 8 289.4.a.f.1.1 8
17.4 even 4 inner 17.4.c.a.4.1 8
17.8 even 8 289.4.b.c.288.8 8
17.9 even 8 289.4.b.c.288.7 8
17.15 even 8 289.4.a.f.1.2 8
51.38 odd 4 153.4.f.a.55.4 8
68.55 odd 4 272.4.o.e.225.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.4.c.a.4.1 8 17.4 even 4 inner
17.4.c.a.13.4 yes 8 1.1 even 1 trivial
153.4.f.a.55.4 8 51.38 odd 4
153.4.f.a.64.1 8 3.2 odd 2
272.4.o.e.81.3 8 4.3 odd 2
272.4.o.e.225.3 8 68.55 odd 4
289.4.a.f.1.1 8 17.2 even 8
289.4.a.f.1.2 8 17.15 even 8
289.4.b.c.288.7 8 17.9 even 8
289.4.b.c.288.8 8 17.8 even 8