Properties

Label 294.4.e.o.67.2
Level $294$
Weight $4$
Character 294.67
Analytic conductor $17.347$
Analytic rank $0$
Dimension $4$
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] = [294,4,Mod(67,294)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(294, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("294.67");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 294.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(17.3465615417\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.2
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 294.67
Dual form 294.4.e.o.79.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(1.94975 + 3.37706i) q^{5} +6.00000 q^{6} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(1.94975 + 3.37706i) q^{5} +6.00000 q^{6} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-3.89949 + 6.75412i) q^{10} +(30.6985 - 53.1713i) q^{11} +(6.00000 + 10.3923i) q^{12} +53.6985 q^{13} +11.6985 q^{15} +(-8.00000 - 13.8564i) q^{16} +(-16.0503 + 27.7999i) q^{17} +(9.00000 - 15.5885i) q^{18} +(27.8995 + 48.3233i) q^{19} -15.5980 q^{20} +122.794 q^{22} +(47.3015 + 81.9286i) q^{23} +(-12.0000 + 20.7846i) q^{24} +(54.8970 - 95.0843i) q^{25} +(53.6985 + 93.0085i) q^{26} -27.0000 q^{27} +138.191 q^{29} +(11.6985 + 20.2624i) q^{30} +(-66.3015 + 114.838i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-92.0955 - 159.514i) q^{33} -64.2010 q^{34} +36.0000 q^{36} +(-74.6030 - 129.216i) q^{37} +(-55.7990 + 96.6467i) q^{38} +(80.5477 - 139.513i) q^{39} +(-15.5980 - 27.0165i) q^{40} +427.497 q^{41} +437.588 q^{43} +(122.794 + 212.685i) q^{44} +(17.5477 - 30.3936i) q^{45} +(-94.6030 + 163.857i) q^{46} +(-28.5025 - 49.3678i) q^{47} -48.0000 q^{48} +219.588 q^{50} +(48.1508 + 83.3996i) q^{51} +(-107.397 + 186.017i) q^{52} +(131.794 - 228.274i) q^{53} +(-27.0000 - 46.7654i) q^{54} +239.417 q^{55} +167.397 q^{57} +(138.191 + 239.354i) q^{58} +(-225.899 + 391.269i) q^{59} +(-23.3970 + 40.5247i) q^{60} +(-289.653 - 501.694i) q^{61} -265.206 q^{62} +64.0000 q^{64} +(104.698 + 181.343i) q^{65} +(184.191 - 319.028i) q^{66} +(-154.794 + 268.111i) q^{67} +(-64.2010 - 111.199i) q^{68} +283.809 q^{69} -1058.98 q^{71} +(36.0000 + 62.3538i) q^{72} +(-596.829 + 1033.74i) q^{73} +(149.206 - 258.432i) q^{74} +(-164.691 - 285.253i) q^{75} -223.196 q^{76} +322.191 q^{78} +(-659.779 - 1142.77i) q^{79} +(31.1960 - 54.0330i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(427.497 + 740.447i) q^{82} +1190.33 q^{83} -125.176 q^{85} +(437.588 + 757.924i) q^{86} +(207.286 - 359.031i) q^{87} +(-245.588 + 425.371i) q^{88} +(116.543 + 201.858i) q^{89} +70.1909 q^{90} -378.412 q^{92} +(198.905 + 344.513i) q^{93} +(57.0051 - 98.7356i) q^{94} +(-108.794 + 188.437i) q^{95} +(-48.0000 - 83.1384i) q^{96} -1609.44 q^{97} -552.573 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 6 q^{3} - 8 q^{4} - 12 q^{5} + 24 q^{6} - 32 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{2} + 6 q^{3} - 8 q^{4} - 12 q^{5} + 24 q^{6} - 32 q^{8} - 18 q^{9} + 24 q^{10} + 4 q^{11} + 24 q^{12} + 96 q^{13} - 72 q^{15} - 32 q^{16} - 84 q^{17} + 36 q^{18} + 72 q^{19} + 96 q^{20} + 16 q^{22} + 308 q^{23} - 48 q^{24} - 18 q^{25} + 96 q^{26} - 108 q^{27} - 160 q^{29} - 72 q^{30} - 384 q^{31} + 64 q^{32} - 12 q^{33} - 336 q^{34} + 144 q^{36} - 536 q^{37} - 144 q^{38} + 144 q^{39} + 96 q^{40} + 1512 q^{41} + 800 q^{43} + 16 q^{44} - 108 q^{45} - 616 q^{46} - 312 q^{47} - 192 q^{48} - 72 q^{50} + 252 q^{51} - 192 q^{52} + 52 q^{53} - 108 q^{54} + 2304 q^{55} + 432 q^{57} - 160 q^{58} - 864 q^{59} + 144 q^{60} - 1416 q^{61} - 1536 q^{62} + 256 q^{64} + 300 q^{65} + 24 q^{66} - 144 q^{67} - 336 q^{68} + 1848 q^{69} - 3048 q^{71} + 144 q^{72} - 744 q^{73} + 1072 q^{74} + 54 q^{75} - 576 q^{76} + 576 q^{78} - 976 q^{79} - 192 q^{80} - 162 q^{81} + 1512 q^{82} - 624 q^{83} + 1400 q^{85} + 800 q^{86} - 240 q^{87} - 32 q^{88} - 108 q^{89} - 432 q^{90} - 2464 q^{92} + 1152 q^{93} + 624 q^{94} + 40 q^{95} - 192 q^{96} - 1488 q^{97} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(199\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.353553 + 0.612372i
\(3\) 1.50000 2.59808i 0.288675 0.500000i
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) 1.94975 + 3.37706i 0.174391 + 0.302054i 0.939950 0.341311i \(-0.110871\pi\)
−0.765560 + 0.643365i \(0.777538\pi\)
\(6\) 6.00000 0.408248
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) −3.89949 + 6.75412i −0.123313 + 0.213584i
\(11\) 30.6985 53.1713i 0.841449 1.45743i −0.0472203 0.998885i \(-0.515036\pi\)
0.888669 0.458548i \(-0.151630\pi\)
\(12\) 6.00000 + 10.3923i 0.144338 + 0.250000i
\(13\) 53.6985 1.14564 0.572818 0.819682i \(-0.305850\pi\)
0.572818 + 0.819682i \(0.305850\pi\)
\(14\) 0 0
\(15\) 11.6985 0.201369
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −16.0503 + 27.7999i −0.228986 + 0.396615i −0.957508 0.288407i \(-0.906874\pi\)
0.728522 + 0.685022i \(0.240208\pi\)
\(18\) 9.00000 15.5885i 0.117851 0.204124i
\(19\) 27.8995 + 48.3233i 0.336873 + 0.583481i 0.983843 0.179035i \(-0.0572974\pi\)
−0.646970 + 0.762515i \(0.723964\pi\)
\(20\) −15.5980 −0.174391
\(21\) 0 0
\(22\) 122.794 1.18999
\(23\) 47.3015 + 81.9286i 0.428828 + 0.742752i 0.996769 0.0803170i \(-0.0255932\pi\)
−0.567941 + 0.823069i \(0.692260\pi\)
\(24\) −12.0000 + 20.7846i −0.102062 + 0.176777i
\(25\) 54.8970 95.0843i 0.439176 0.760675i
\(26\) 53.6985 + 93.0085i 0.405044 + 0.701556i
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) 138.191 0.884876 0.442438 0.896799i \(-0.354114\pi\)
0.442438 + 0.896799i \(0.354114\pi\)
\(30\) 11.6985 + 20.2624i 0.0711947 + 0.123313i
\(31\) −66.3015 + 114.838i −0.384132 + 0.665337i −0.991648 0.128971i \(-0.958833\pi\)
0.607516 + 0.794307i \(0.292166\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) −92.0955 159.514i −0.485811 0.841449i
\(34\) −64.2010 −0.323835
\(35\) 0 0
\(36\) 36.0000 0.166667
\(37\) −74.6030 129.216i −0.331477 0.574136i 0.651324 0.758799i \(-0.274214\pi\)
−0.982802 + 0.184664i \(0.940880\pi\)
\(38\) −55.7990 + 96.6467i −0.238205 + 0.412583i
\(39\) 80.5477 139.513i 0.330717 0.572818i
\(40\) −15.5980 27.0165i −0.0616564 0.106792i
\(41\) 427.497 1.62839 0.814194 0.580593i \(-0.197179\pi\)
0.814194 + 0.580593i \(0.197179\pi\)
\(42\) 0 0
\(43\) 437.588 1.55190 0.775948 0.630797i \(-0.217272\pi\)
0.775948 + 0.630797i \(0.217272\pi\)
\(44\) 122.794 + 212.685i 0.420725 + 0.728716i
\(45\) 17.5477 30.3936i 0.0581302 0.100685i
\(46\) −94.6030 + 163.857i −0.303227 + 0.525205i
\(47\) −28.5025 49.3678i −0.0884579 0.153214i 0.818402 0.574647i \(-0.194861\pi\)
−0.906859 + 0.421433i \(0.861527\pi\)
\(48\) −48.0000 −0.144338
\(49\) 0 0
\(50\) 219.588 0.621088
\(51\) 48.1508 + 83.3996i 0.132205 + 0.228986i
\(52\) −107.397 + 186.017i −0.286409 + 0.496075i
\(53\) 131.794 228.274i 0.341572 0.591619i −0.643153 0.765737i \(-0.722374\pi\)
0.984725 + 0.174118i \(0.0557075\pi\)
\(54\) −27.0000 46.7654i −0.0680414 0.117851i
\(55\) 239.417 0.586964
\(56\) 0 0
\(57\) 167.397 0.388987
\(58\) 138.191 + 239.354i 0.312851 + 0.541874i
\(59\) −225.899 + 391.269i −0.498468 + 0.863372i −0.999998 0.00176815i \(-0.999437\pi\)
0.501530 + 0.865140i \(0.332771\pi\)
\(60\) −23.3970 + 40.5247i −0.0503423 + 0.0871954i
\(61\) −289.653 501.694i −0.607972 1.05304i −0.991574 0.129540i \(-0.958650\pi\)
0.383602 0.923499i \(-0.374683\pi\)
\(62\) −265.206 −0.543245
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 104.698 + 181.343i 0.199788 + 0.346044i
\(66\) 184.191 319.028i 0.343520 0.594994i
\(67\) −154.794 + 268.111i −0.282255 + 0.488880i −0.971940 0.235230i \(-0.924416\pi\)
0.689685 + 0.724110i \(0.257749\pi\)
\(68\) −64.2010 111.199i −0.114493 0.198307i
\(69\) 283.809 0.495168
\(70\) 0 0
\(71\) −1058.98 −1.77012 −0.885059 0.465479i \(-0.845882\pi\)
−0.885059 + 0.465479i \(0.845882\pi\)
\(72\) 36.0000 + 62.3538i 0.0589256 + 0.102062i
\(73\) −596.829 + 1033.74i −0.956898 + 1.65740i −0.226934 + 0.973910i \(0.572870\pi\)
−0.729964 + 0.683486i \(0.760463\pi\)
\(74\) 149.206 258.432i 0.234390 0.405975i
\(75\) −164.691 285.253i −0.253558 0.439176i
\(76\) −223.196 −0.336873
\(77\) 0 0
\(78\) 322.191 0.467704
\(79\) −659.779 1142.77i −0.939632 1.62749i −0.766159 0.642651i \(-0.777834\pi\)
−0.173473 0.984839i \(-0.555499\pi\)
\(80\) 31.1960 54.0330i 0.0435977 0.0755134i
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 427.497 + 740.447i 0.575722 + 0.997180i
\(83\) 1190.33 1.57417 0.787083 0.616847i \(-0.211590\pi\)
0.787083 + 0.616847i \(0.211590\pi\)
\(84\) 0 0
\(85\) −125.176 −0.159732
\(86\) 437.588 + 757.924i 0.548678 + 0.950338i
\(87\) 207.286 359.031i 0.255442 0.442438i
\(88\) −245.588 + 425.371i −0.297497 + 0.515280i
\(89\) 116.543 + 201.858i 0.138803 + 0.240414i 0.927044 0.374953i \(-0.122341\pi\)
−0.788241 + 0.615367i \(0.789008\pi\)
\(90\) 70.1909 0.0822086
\(91\) 0 0
\(92\) −378.412 −0.428828
\(93\) 198.905 + 344.513i 0.221779 + 0.384132i
\(94\) 57.0051 98.7356i 0.0625492 0.108338i
\(95\) −108.794 + 188.437i −0.117495 + 0.203507i
\(96\) −48.0000 83.1384i −0.0510310 0.0883883i
\(97\) −1609.44 −1.68468 −0.842338 0.538950i \(-0.818821\pi\)
−0.842338 + 0.538950i \(0.818821\pi\)
\(98\) 0 0
\(99\) −552.573 −0.560966
\(100\) 219.588 + 380.337i 0.219588 + 0.380337i
\(101\) 739.628 1281.07i 0.728671 1.26209i −0.228774 0.973479i \(-0.573472\pi\)
0.957445 0.288615i \(-0.0931948\pi\)
\(102\) −96.3015 + 166.799i −0.0934830 + 0.161917i
\(103\) 572.673 + 991.899i 0.547837 + 0.948881i 0.998422 + 0.0561477i \(0.0178818\pi\)
−0.450586 + 0.892733i \(0.648785\pi\)
\(104\) −429.588 −0.405044
\(105\) 0 0
\(106\) 527.176 0.483055
\(107\) −218.477 378.414i −0.197392 0.341894i 0.750290 0.661109i \(-0.229914\pi\)
−0.947682 + 0.319215i \(0.896581\pi\)
\(108\) 54.0000 93.5307i 0.0481125 0.0833333i
\(109\) 83.1758 144.065i 0.0730898 0.126595i −0.827164 0.561960i \(-0.810047\pi\)
0.900254 + 0.435365i \(0.143381\pi\)
\(110\) 239.417 + 414.683i 0.207523 + 0.359440i
\(111\) −447.618 −0.382757
\(112\) 0 0
\(113\) 490.824 0.408609 0.204305 0.978907i \(-0.434507\pi\)
0.204305 + 0.978907i \(0.434507\pi\)
\(114\) 167.397 + 289.940i 0.137528 + 0.238205i
\(115\) −184.452 + 319.480i −0.149567 + 0.259058i
\(116\) −276.382 + 478.707i −0.221219 + 0.383163i
\(117\) −241.643 418.538i −0.190939 0.330717i
\(118\) −903.598 −0.704940
\(119\) 0 0
\(120\) −93.5879 −0.0711947
\(121\) −1219.29 2111.88i −0.916074 1.58669i
\(122\) 579.307 1003.39i 0.429901 0.744611i
\(123\) 641.246 1110.67i 0.470075 0.814194i
\(124\) −265.206 459.350i −0.192066 0.332668i
\(125\) 915.578 0.655134
\(126\) 0 0
\(127\) −2616.70 −1.82831 −0.914153 0.405369i \(-0.867143\pi\)
−0.914153 + 0.405369i \(0.867143\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) 656.382 1136.89i 0.447994 0.775948i
\(130\) −209.397 + 362.686i −0.141272 + 0.244690i
\(131\) −88.7939 153.796i −0.0592211 0.102574i 0.834895 0.550409i \(-0.185528\pi\)
−0.894116 + 0.447835i \(0.852195\pi\)
\(132\) 736.764 0.485811
\(133\) 0 0
\(134\) −619.176 −0.399169
\(135\) −52.6432 91.1807i −0.0335615 0.0581302i
\(136\) 128.402 222.399i 0.0809587 0.140225i
\(137\) −13.5076 + 23.3958i −0.00842358 + 0.0145901i −0.870206 0.492687i \(-0.836015\pi\)
0.861783 + 0.507277i \(0.169348\pi\)
\(138\) 283.809 + 491.572i 0.175068 + 0.303227i
\(139\) −922.754 −0.563071 −0.281536 0.959551i \(-0.590844\pi\)
−0.281536 + 0.959551i \(0.590844\pi\)
\(140\) 0 0
\(141\) −171.015 −0.102142
\(142\) −1058.98 1834.22i −0.625831 1.08397i
\(143\) 1648.46 2855.22i 0.963995 1.66969i
\(144\) −72.0000 + 124.708i −0.0416667 + 0.0721688i
\(145\) 269.437 + 466.679i 0.154314 + 0.267280i
\(146\) −2387.32 −1.35326
\(147\) 0 0
\(148\) 596.824 0.331477
\(149\) −373.352 646.664i −0.205276 0.355549i 0.744945 0.667126i \(-0.232476\pi\)
−0.950221 + 0.311578i \(0.899143\pi\)
\(150\) 329.382 570.506i 0.179293 0.310544i
\(151\) −1036.57 + 1795.40i −0.558643 + 0.967598i 0.438967 + 0.898503i \(0.355344\pi\)
−0.997610 + 0.0690949i \(0.977989\pi\)
\(152\) −223.196 386.587i −0.119103 0.206292i
\(153\) 288.905 0.152657
\(154\) 0 0
\(155\) −517.085 −0.267956
\(156\) 322.191 + 558.051i 0.165358 + 0.286409i
\(157\) −783.110 + 1356.39i −0.398083 + 0.689500i −0.993489 0.113925i \(-0.963658\pi\)
0.595407 + 0.803425i \(0.296991\pi\)
\(158\) 1319.56 2285.54i 0.664420 1.15081i
\(159\) −395.382 684.821i −0.197206 0.341572i
\(160\) 124.784 0.0616564
\(161\) 0 0
\(162\) −162.000 −0.0785674
\(163\) −49.3667 85.5056i −0.0237221 0.0410878i 0.853921 0.520403i \(-0.174218\pi\)
−0.877643 + 0.479315i \(0.840885\pi\)
\(164\) −854.995 + 1480.89i −0.407097 + 0.705112i
\(165\) 359.126 622.024i 0.169442 0.293482i
\(166\) 1190.33 + 2061.71i 0.556552 + 0.963976i
\(167\) −2231.36 −1.03394 −0.516969 0.856004i \(-0.672940\pi\)
−0.516969 + 0.856004i \(0.672940\pi\)
\(168\) 0 0
\(169\) 686.527 0.312484
\(170\) −125.176 216.811i −0.0564738 0.0978155i
\(171\) 251.095 434.910i 0.112291 0.194494i
\(172\) −875.176 + 1515.85i −0.387974 + 0.671991i
\(173\) −1050.42 1819.38i −0.461631 0.799568i 0.537412 0.843320i \(-0.319402\pi\)
−0.999042 + 0.0437522i \(0.986069\pi\)
\(174\) 829.145 0.361249
\(175\) 0 0
\(176\) −982.352 −0.420725
\(177\) 677.698 + 1173.81i 0.287791 + 0.498468i
\(178\) −233.085 + 403.716i −0.0981488 + 0.169999i
\(179\) −861.271 + 1491.77i −0.359634 + 0.622904i −0.987900 0.155095i \(-0.950432\pi\)
0.628266 + 0.777999i \(0.283765\pi\)
\(180\) 70.1909 + 121.574i 0.0290651 + 0.0503423i
\(181\) 1655.00 0.679644 0.339822 0.940490i \(-0.389633\pi\)
0.339822 + 0.940490i \(0.389633\pi\)
\(182\) 0 0
\(183\) −1737.92 −0.702026
\(184\) −378.412 655.429i −0.151614 0.262603i
\(185\) 290.914 503.878i 0.115613 0.200248i
\(186\) −397.809 + 689.026i −0.156821 + 0.271623i
\(187\) 985.437 + 1706.83i 0.385360 + 0.667463i
\(188\) 228.020 0.0884579
\(189\) 0 0
\(190\) −435.176 −0.166163
\(191\) 503.844 + 872.683i 0.190874 + 0.330603i 0.945540 0.325506i \(-0.105535\pi\)
−0.754666 + 0.656109i \(0.772201\pi\)
\(192\) 96.0000 166.277i 0.0360844 0.0625000i
\(193\) 3.82424 6.62378i 0.00142630 0.00247042i −0.865311 0.501235i \(-0.832879\pi\)
0.866738 + 0.498764i \(0.166213\pi\)
\(194\) −1609.44 2787.63i −0.595623 1.03165i
\(195\) 628.191 0.230696
\(196\) 0 0
\(197\) 2689.88 0.972822 0.486411 0.873730i \(-0.338306\pi\)
0.486411 + 0.873730i \(0.338306\pi\)
\(198\) −552.573 957.084i −0.198331 0.343520i
\(199\) −433.748 + 751.274i −0.154511 + 0.267620i −0.932881 0.360185i \(-0.882713\pi\)
0.778370 + 0.627806i \(0.216047\pi\)
\(200\) −439.176 + 760.675i −0.155272 + 0.268939i
\(201\) 464.382 + 804.333i 0.162960 + 0.282255i
\(202\) 2958.51 1.03050
\(203\) 0 0
\(204\) −385.206 −0.132205
\(205\) 833.512 + 1443.69i 0.283976 + 0.491860i
\(206\) −1145.35 + 1983.80i −0.387379 + 0.670960i
\(207\) 425.714 737.358i 0.142943 0.247584i
\(208\) −429.588 744.068i −0.143205 0.248038i
\(209\) 3425.89 1.13385
\(210\) 0 0
\(211\) 162.030 0.0528655 0.0264328 0.999651i \(-0.491585\pi\)
0.0264328 + 0.999651i \(0.491585\pi\)
\(212\) 527.176 + 913.095i 0.170786 + 0.295810i
\(213\) −1588.48 + 2751.32i −0.510989 + 0.885059i
\(214\) 436.955 756.827i 0.139578 0.241755i
\(215\) 853.186 + 1477.76i 0.270636 + 0.468756i
\(216\) 216.000 0.0680414
\(217\) 0 0
\(218\) 332.703 0.103365
\(219\) 1790.49 + 3101.21i 0.552465 + 0.956898i
\(220\) −478.834 + 829.365i −0.146741 + 0.254163i
\(221\) −861.874 + 1492.81i −0.262335 + 0.454377i
\(222\) −447.618 775.297i −0.135325 0.234390i
\(223\) −4577.85 −1.37469 −0.687344 0.726332i \(-0.741223\pi\)
−0.687344 + 0.726332i \(0.741223\pi\)
\(224\) 0 0
\(225\) −988.145 −0.292784
\(226\) 490.824 + 850.133i 0.144465 + 0.250221i
\(227\) 1109.10 1921.01i 0.324287 0.561682i −0.657080 0.753820i \(-0.728209\pi\)
0.981368 + 0.192138i \(0.0615422\pi\)
\(228\) −334.794 + 579.880i −0.0972468 + 0.168436i
\(229\) −392.608 680.018i −0.113294 0.196231i 0.803803 0.594896i \(-0.202807\pi\)
−0.917096 + 0.398665i \(0.869473\pi\)
\(230\) −737.808 −0.211520
\(231\) 0 0
\(232\) −1105.53 −0.312851
\(233\) 2684.56 + 4649.80i 0.754813 + 1.30738i 0.945467 + 0.325718i \(0.105606\pi\)
−0.190654 + 0.981657i \(0.561061\pi\)
\(234\) 483.286 837.077i 0.135015 0.233852i
\(235\) 111.145 192.510i 0.0308525 0.0534380i
\(236\) −903.598 1565.08i −0.249234 0.431686i
\(237\) −3958.67 −1.08499
\(238\) 0 0
\(239\) 3713.28 1.00499 0.502493 0.864581i \(-0.332416\pi\)
0.502493 + 0.864581i \(0.332416\pi\)
\(240\) −93.5879 162.099i −0.0251711 0.0435977i
\(241\) −3499.31 + 6060.99i −0.935313 + 1.62001i −0.161238 + 0.986915i \(0.551549\pi\)
−0.774075 + 0.633094i \(0.781785\pi\)
\(242\) 2438.59 4223.76i 0.647762 1.12196i
\(243\) 121.500 + 210.444i 0.0320750 + 0.0555556i
\(244\) 2317.23 0.607972
\(245\) 0 0
\(246\) 2564.98 0.664786
\(247\) 1498.16 + 2594.89i 0.385934 + 0.668457i
\(248\) 530.412 918.701i 0.135811 0.235232i
\(249\) 1785.50 3092.57i 0.454423 0.787083i
\(250\) 915.578 + 1585.83i 0.231625 + 0.401186i
\(251\) 3722.75 0.936168 0.468084 0.883684i \(-0.344945\pi\)
0.468084 + 0.883684i \(0.344945\pi\)
\(252\) 0 0
\(253\) 5808.34 1.44335
\(254\) −2616.70 4532.26i −0.646404 1.11960i
\(255\) −187.764 + 325.216i −0.0461106 + 0.0798660i
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −615.075 1065.34i −0.149289 0.258576i 0.781676 0.623685i \(-0.214365\pi\)
−0.930965 + 0.365109i \(0.881032\pi\)
\(258\) 2625.53 0.633559
\(259\) 0 0
\(260\) −837.588 −0.199788
\(261\) −621.859 1077.09i −0.147479 0.255442i
\(262\) 177.588 307.591i 0.0418756 0.0725307i
\(263\) −1194.32 + 2068.62i −0.280018 + 0.485005i −0.971389 0.237495i \(-0.923674\pi\)
0.691371 + 0.722500i \(0.257007\pi\)
\(264\) 736.764 + 1276.11i 0.171760 + 0.297497i
\(265\) 1027.86 0.238268
\(266\) 0 0
\(267\) 699.256 0.160276
\(268\) −619.176 1072.44i −0.141128 0.244440i
\(269\) −3351.16 + 5804.37i −0.759567 + 1.31561i 0.183504 + 0.983019i \(0.441256\pi\)
−0.943071 + 0.332590i \(0.892077\pi\)
\(270\) 105.286 182.361i 0.0237316 0.0411043i
\(271\) −2475.19 4287.15i −0.554822 0.960980i −0.997917 0.0645056i \(-0.979453\pi\)
0.443095 0.896475i \(-0.353880\pi\)
\(272\) 513.608 0.114493
\(273\) 0 0
\(274\) −54.0303 −0.0119127
\(275\) −3370.51 5837.89i −0.739088 1.28014i
\(276\) −567.618 + 983.144i −0.123792 + 0.214414i
\(277\) 1852.59 3208.78i 0.401846 0.696017i −0.592103 0.805862i \(-0.701702\pi\)
0.993949 + 0.109845i \(0.0350355\pi\)
\(278\) −922.754 1598.26i −0.199076 0.344809i
\(279\) 1193.43 0.256088
\(280\) 0 0
\(281\) 9324.74 1.97960 0.989800 0.142465i \(-0.0455029\pi\)
0.989800 + 0.142465i \(0.0455029\pi\)
\(282\) −171.015 296.207i −0.0361128 0.0625492i
\(283\) 2784.74 4823.32i 0.584932 1.01313i −0.409952 0.912107i \(-0.634454\pi\)
0.994884 0.101025i \(-0.0322122\pi\)
\(284\) 2117.97 3668.43i 0.442530 0.766484i
\(285\) 326.382 + 565.310i 0.0678358 + 0.117495i
\(286\) 6593.85 1.36330
\(287\) 0 0
\(288\) −288.000 −0.0589256
\(289\) 1941.28 + 3362.39i 0.395131 + 0.684387i
\(290\) −538.875 + 933.358i −0.109117 + 0.188996i
\(291\) −2414.16 + 4181.44i −0.486324 + 0.842338i
\(292\) −2387.32 4134.95i −0.478449 0.828698i
\(293\) −1665.31 −0.332042 −0.166021 0.986122i \(-0.553092\pi\)
−0.166021 + 0.986122i \(0.553092\pi\)
\(294\) 0 0
\(295\) −1761.79 −0.347713
\(296\) 596.824 + 1033.73i 0.117195 + 0.202988i
\(297\) −828.859 + 1435.63i −0.161937 + 0.280483i
\(298\) 746.703 1293.33i 0.145152 0.251411i
\(299\) 2540.02 + 4399.44i 0.491281 + 0.850924i
\(300\) 1317.53 0.253558
\(301\) 0 0
\(302\) −4146.29 −0.790040
\(303\) −2218.88 3843.22i −0.420698 0.728671i
\(304\) 446.392 773.173i 0.0842182 0.145870i
\(305\) 1129.50 1956.35i 0.212049 0.367280i
\(306\) 288.905 + 500.397i 0.0539725 + 0.0934830i
\(307\) −5303.32 −0.985916 −0.492958 0.870053i \(-0.664084\pi\)
−0.492958 + 0.870053i \(0.664084\pi\)
\(308\) 0 0
\(309\) 3436.04 0.632587
\(310\) −517.085 895.617i −0.0947369 0.164089i
\(311\) −562.994 + 975.135i −0.102651 + 0.177797i −0.912776 0.408460i \(-0.866066\pi\)
0.810125 + 0.586257i \(0.199399\pi\)
\(312\) −644.382 + 1116.10i −0.116926 + 0.202522i
\(313\) 4149.75 + 7187.58i 0.749386 + 1.29798i 0.948117 + 0.317921i \(0.102985\pi\)
−0.198731 + 0.980054i \(0.563682\pi\)
\(314\) −3132.44 −0.562974
\(315\) 0 0
\(316\) 5278.23 0.939632
\(317\) 2139.38 + 3705.52i 0.379053 + 0.656538i 0.990925 0.134418i \(-0.0429166\pi\)
−0.611872 + 0.790957i \(0.709583\pi\)
\(318\) 790.764 1369.64i 0.139446 0.241528i
\(319\) 4242.25 7347.80i 0.744578 1.28965i
\(320\) 124.784 + 216.132i 0.0217988 + 0.0377567i
\(321\) −1310.86 −0.227929
\(322\) 0 0
\(323\) −1791.18 −0.308556
\(324\) −162.000 280.592i −0.0277778 0.0481125i
\(325\) 2947.88 5105.89i 0.503136 0.871457i
\(326\) 98.7333 171.011i 0.0167740 0.0290535i
\(327\) −249.527 432.194i −0.0421984 0.0730898i
\(328\) −3419.98 −0.575722
\(329\) 0 0
\(330\) 1436.50 0.239627
\(331\) 853.558 + 1478.41i 0.141739 + 0.245500i 0.928152 0.372202i \(-0.121397\pi\)
−0.786412 + 0.617702i \(0.788064\pi\)
\(332\) −2380.66 + 4123.43i −0.393542 + 0.681634i
\(333\) −671.427 + 1162.95i −0.110492 + 0.191379i
\(334\) −2231.36 3864.82i −0.365552 0.633155i
\(335\) −1207.24 −0.196891
\(336\) 0 0
\(337\) 1710.67 0.276517 0.138259 0.990396i \(-0.455849\pi\)
0.138259 + 0.990396i \(0.455849\pi\)
\(338\) 686.527 + 1189.10i 0.110480 + 0.191357i
\(339\) 736.236 1275.20i 0.117955 0.204305i
\(340\) 250.352 433.622i 0.0399330 0.0691660i
\(341\) 4070.71 + 7050.68i 0.646456 + 1.11969i
\(342\) 1004.38 0.158803
\(343\) 0 0
\(344\) −3500.70 −0.548678
\(345\) 553.356 + 958.441i 0.0863527 + 0.149567i
\(346\) 2100.84 3638.77i 0.326422 0.565380i
\(347\) −4455.15 + 7716.55i −0.689236 + 1.19379i 0.282849 + 0.959164i \(0.408720\pi\)
−0.972085 + 0.234628i \(0.924613\pi\)
\(348\) 829.145 + 1436.12i 0.127721 + 0.221219i
\(349\) 5378.68 0.824969 0.412485 0.910965i \(-0.364661\pi\)
0.412485 + 0.910965i \(0.364661\pi\)
\(350\) 0 0
\(351\) −1449.86 −0.220478
\(352\) −982.352 1701.48i −0.148749 0.257640i
\(353\) 2126.28 3682.83i 0.320596 0.555289i −0.660015 0.751253i \(-0.729450\pi\)
0.980611 + 0.195963i \(0.0627833\pi\)
\(354\) −1355.40 + 2347.62i −0.203499 + 0.352470i
\(355\) −2064.75 3576.26i −0.308692 0.534670i
\(356\) −932.341 −0.138803
\(357\) 0 0
\(358\) −3445.08 −0.508599
\(359\) −2451.94 4246.89i −0.360470 0.624352i 0.627568 0.778561i \(-0.284050\pi\)
−0.988038 + 0.154209i \(0.950717\pi\)
\(360\) −140.382 + 243.148i −0.0205521 + 0.0355974i
\(361\) 1872.74 3243.67i 0.273033 0.472908i
\(362\) 1655.00 + 2866.55i 0.240290 + 0.416195i
\(363\) −7315.76 −1.05779
\(364\) 0 0
\(365\) −4654.66 −0.667497
\(366\) −1737.92 3010.17i −0.248204 0.429901i
\(367\) 2020.78 3500.10i 0.287423 0.497830i −0.685771 0.727817i \(-0.740535\pi\)
0.973194 + 0.229987i \(0.0738683\pi\)
\(368\) 756.824 1310.86i 0.107207 0.185688i
\(369\) −1923.74 3332.01i −0.271398 0.470075i
\(370\) 1163.66 0.163502
\(371\) 0 0
\(372\) −1591.24 −0.221779
\(373\) 3725.67 + 6453.05i 0.517180 + 0.895781i 0.999801 + 0.0199523i \(0.00635144\pi\)
−0.482621 + 0.875829i \(0.660315\pi\)
\(374\) −1970.87 + 3413.65i −0.272491 + 0.471967i
\(375\) 1373.37 2378.74i 0.189121 0.327567i
\(376\) 228.020 + 394.943i 0.0312746 + 0.0541692i
\(377\) 7420.64 1.01375
\(378\) 0 0
\(379\) −12564.4 −1.70288 −0.851438 0.524456i \(-0.824269\pi\)
−0.851438 + 0.524456i \(0.824269\pi\)
\(380\) −435.176 753.747i −0.0587475 0.101754i
\(381\) −3925.05 + 6798.39i −0.527786 + 0.914153i
\(382\) −1007.69 + 1745.37i −0.134968 + 0.233772i
\(383\) 2144.96 + 3715.19i 0.286169 + 0.495659i 0.972892 0.231260i \(-0.0742849\pi\)
−0.686723 + 0.726919i \(0.740952\pi\)
\(384\) 384.000 0.0510310
\(385\) 0 0
\(386\) 15.2970 0.00201709
\(387\) −1969.15 3410.66i −0.258649 0.447994i
\(388\) 3218.87 5575.25i 0.421169 0.729486i
\(389\) −2831.39 + 4904.11i −0.369041 + 0.639198i −0.989416 0.145108i \(-0.953647\pi\)
0.620375 + 0.784306i \(0.286981\pi\)
\(390\) 628.191 + 1088.06i 0.0815633 + 0.141272i
\(391\) −3036.81 −0.392782
\(392\) 0 0
\(393\) −532.764 −0.0683826
\(394\) 2689.88 + 4659.01i 0.343945 + 0.595729i
\(395\) 2572.80 4456.23i 0.327726 0.567638i
\(396\) 1105.15 1914.17i 0.140242 0.242905i
\(397\) −7280.69 12610.5i −0.920421 1.59422i −0.798764 0.601644i \(-0.794513\pi\)
−0.121657 0.992572i \(-0.538821\pi\)
\(398\) −1734.99 −0.218511
\(399\) 0 0
\(400\) −1756.70 −0.219588
\(401\) 1871.10 + 3240.83i 0.233013 + 0.403590i 0.958693 0.284442i \(-0.0918083\pi\)
−0.725681 + 0.688032i \(0.758475\pi\)
\(402\) −928.764 + 1608.67i −0.115230 + 0.199584i
\(403\) −3560.29 + 6166.60i −0.440076 + 0.762234i
\(404\) 2958.51 + 5124.29i 0.364335 + 0.631047i
\(405\) −315.859 −0.0387535
\(406\) 0 0
\(407\) −9160.80 −1.11569
\(408\) −385.206 667.196i −0.0467415 0.0809587i
\(409\) 1758.59 3045.96i 0.212608 0.368247i −0.739922 0.672692i \(-0.765138\pi\)
0.952530 + 0.304445i \(0.0984710\pi\)
\(410\) −1667.02 + 2887.37i −0.200801 + 0.347798i
\(411\) 40.5227 + 70.1874i 0.00486335 + 0.00842358i
\(412\) −4581.39 −0.547837
\(413\) 0 0
\(414\) 1702.85 0.202152
\(415\) 2320.85 + 4019.82i 0.274520 + 0.475483i
\(416\) 859.176 1488.14i 0.101261 0.175389i
\(417\) −1384.13 + 2397.38i −0.162545 + 0.281536i
\(418\) 3425.89 + 5933.81i 0.400875 + 0.694336i
\(419\) −7579.52 −0.883732 −0.441866 0.897081i \(-0.645683\pi\)
−0.441866 + 0.897081i \(0.645683\pi\)
\(420\) 0 0
\(421\) −4980.87 −0.576610 −0.288305 0.957539i \(-0.593092\pi\)
−0.288305 + 0.957539i \(0.593092\pi\)
\(422\) 162.030 + 280.645i 0.0186908 + 0.0323734i
\(423\) −256.523 + 444.310i −0.0294860 + 0.0510712i
\(424\) −1054.35 + 1826.19i −0.120764 + 0.209169i
\(425\) 1762.22 + 3052.26i 0.201130 + 0.348367i
\(426\) −6353.91 −0.722648
\(427\) 0 0
\(428\) 1747.82 0.197392
\(429\) −4945.39 8565.66i −0.556563 0.963995i
\(430\) −1706.37 + 2955.52i −0.191369 + 0.331460i
\(431\) −7101.66 + 12300.4i −0.793678 + 1.37469i 0.129998 + 0.991514i \(0.458503\pi\)
−0.923676 + 0.383176i \(0.874830\pi\)
\(432\) 216.000 + 374.123i 0.0240563 + 0.0416667i
\(433\) 3874.82 0.430051 0.215026 0.976608i \(-0.431017\pi\)
0.215026 + 0.976608i \(0.431017\pi\)
\(434\) 0 0
\(435\) 1616.62 0.178187
\(436\) 332.703 + 576.259i 0.0365449 + 0.0632977i
\(437\) −2639.38 + 4571.53i −0.288921 + 0.500426i
\(438\) −3580.97 + 6202.43i −0.390652 + 0.676629i
\(439\) −3881.91 6723.66i −0.422035 0.730986i 0.574103 0.818783i \(-0.305351\pi\)
−0.996138 + 0.0877966i \(0.972017\pi\)
\(440\) −1915.34 −0.207523
\(441\) 0 0
\(442\) −3447.50 −0.370997
\(443\) −4831.12 8367.74i −0.518134 0.897435i −0.999778 0.0210676i \(-0.993293\pi\)
0.481644 0.876367i \(-0.340040\pi\)
\(444\) 895.236 1550.59i 0.0956893 0.165739i
\(445\) −454.458 + 787.144i −0.0484120 + 0.0838521i
\(446\) −4577.85 7929.07i −0.486026 0.841821i
\(447\) −2240.11 −0.237032
\(448\) 0 0
\(449\) −10942.6 −1.15014 −0.575069 0.818105i \(-0.695025\pi\)
−0.575069 + 0.818105i \(0.695025\pi\)
\(450\) −988.145 1711.52i −0.103515 0.179293i
\(451\) 13123.5 22730.6i 1.37021 2.37327i
\(452\) −981.648 + 1700.27i −0.102152 + 0.176933i
\(453\) 3109.72 + 5386.19i 0.322533 + 0.558643i
\(454\) 4436.38 0.458612
\(455\) 0 0
\(456\) −1339.18 −0.137528
\(457\) −6809.17 11793.8i −0.696979 1.20720i −0.969509 0.245056i \(-0.921194\pi\)
0.272530 0.962147i \(-0.412140\pi\)
\(458\) 785.217 1360.04i 0.0801108 0.138756i
\(459\) 433.357 750.596i 0.0440683 0.0763286i
\(460\) −737.808 1277.92i −0.0747836 0.129529i
\(461\) 11955.8 1.20789 0.603947 0.797025i \(-0.293594\pi\)
0.603947 + 0.797025i \(0.293594\pi\)
\(462\) 0 0
\(463\) 648.503 0.0650939 0.0325470 0.999470i \(-0.489638\pi\)
0.0325470 + 0.999470i \(0.489638\pi\)
\(464\) −1105.53 1914.83i −0.110610 0.191581i
\(465\) −775.627 + 1343.43i −0.0773524 + 0.133978i
\(466\) −5369.12 + 9299.60i −0.533734 + 0.924454i
\(467\) −1392.37 2411.66i −0.137969 0.238969i 0.788759 0.614703i \(-0.210724\pi\)
−0.926728 + 0.375734i \(0.877391\pi\)
\(468\) 1933.15 0.190939
\(469\) 0 0
\(470\) 444.582 0.0436320
\(471\) 2349.33 + 4069.16i 0.229833 + 0.398083i
\(472\) 1807.20 3130.16i 0.176235 0.305248i
\(473\) 13433.3 23267.1i 1.30584 2.26178i
\(474\) −3958.67 6856.62i −0.383603 0.664420i
\(475\) 6126.39 0.591785
\(476\) 0 0
\(477\) −2372.29 −0.227714
\(478\) 3713.28 + 6431.58i 0.355316 + 0.615426i
\(479\) −5556.70 + 9624.49i −0.530046 + 0.918067i 0.469339 + 0.883018i \(0.344492\pi\)
−0.999386 + 0.0350493i \(0.988841\pi\)
\(480\) 187.176 324.198i 0.0177987 0.0308282i
\(481\) −4006.07 6938.72i −0.379753 0.657751i
\(482\) −13997.2 −1.32273
\(483\) 0 0
\(484\) 9754.35 0.916074
\(485\) −3138.00 5435.17i −0.293792 0.508862i
\(486\) −243.000 + 420.888i −0.0226805 + 0.0392837i
\(487\) 1893.14 3279.01i 0.176152 0.305105i −0.764407 0.644734i \(-0.776968\pi\)
0.940559 + 0.339629i \(0.110302\pi\)
\(488\) 2317.23 + 4013.55i 0.214951 + 0.372305i
\(489\) −296.200 −0.0273919
\(490\) 0 0
\(491\) −9582.12 −0.880723 −0.440361 0.897821i \(-0.645150\pi\)
−0.440361 + 0.897821i \(0.645150\pi\)
\(492\) 2564.98 + 4442.68i 0.235037 + 0.407097i
\(493\) −2218.00 + 3841.69i −0.202624 + 0.350955i
\(494\) −2996.32 + 5189.78i −0.272896 + 0.472671i
\(495\) −1077.38 1866.07i −0.0978273 0.169442i
\(496\) 2121.65 0.192066
\(497\) 0 0
\(498\) 7141.99 0.642651
\(499\) −2790.77 4833.76i −0.250365 0.433645i 0.713261 0.700898i \(-0.247217\pi\)
−0.963626 + 0.267253i \(0.913884\pi\)
\(500\) −1831.16 + 3171.65i −0.163784 + 0.283681i
\(501\) −3347.03 + 5797.23i −0.298472 + 0.516969i
\(502\) 3722.75 + 6448.00i 0.330985 + 0.573283i
\(503\) −14116.3 −1.25132 −0.625661 0.780095i \(-0.715171\pi\)
−0.625661 + 0.780095i \(0.715171\pi\)
\(504\) 0 0
\(505\) 5768.35 0.508294
\(506\) 5808.34 + 10060.3i 0.510301 + 0.883867i
\(507\) 1029.79 1783.65i 0.0902064 0.156242i
\(508\) 5233.41 9064.53i 0.457076 0.791680i
\(509\) −8393.81 14538.5i −0.730941 1.26603i −0.956481 0.291793i \(-0.905748\pi\)
0.225540 0.974234i \(-0.427585\pi\)
\(510\) −751.055 −0.0652103
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) −753.286 1304.73i −0.0648312 0.112291i
\(514\) 1230.15 2130.68i 0.105563 0.182841i
\(515\) −2233.14 + 3867.91i −0.191075 + 0.330952i
\(516\) 2625.53 + 4547.55i 0.223997 + 0.387974i
\(517\) −3499.94 −0.297731
\(518\) 0 0
\(519\) −6302.53 −0.533045
\(520\) −837.588 1450.74i −0.0706359 0.122345i
\(521\) 2799.31 4848.54i 0.235393 0.407713i −0.723994 0.689807i \(-0.757696\pi\)
0.959387 + 0.282094i \(0.0910289\pi\)
\(522\) 1243.72 2154.18i 0.104284 0.180625i
\(523\) 6635.37 + 11492.8i 0.554769 + 0.960889i 0.997921 + 0.0644422i \(0.0205268\pi\)
−0.443152 + 0.896446i \(0.646140\pi\)
\(524\) 710.352 0.0592211
\(525\) 0 0
\(526\) −4777.27 −0.396005
\(527\) −2128.31 3686.34i −0.175922 0.304705i
\(528\) −1473.53 + 2552.22i −0.121453 + 0.210362i
\(529\) 1608.63 2786.23i 0.132213 0.228999i
\(530\) 1027.86 + 1780.31i 0.0842403 + 0.145909i
\(531\) 4066.19 0.332312
\(532\) 0 0
\(533\) 22956.0 1.86554
\(534\) 699.256 + 1211.15i 0.0566662 + 0.0981488i
\(535\) 851.951 1475.62i 0.0688468 0.119246i
\(536\) 1238.35 2144.89i 0.0997922 0.172845i
\(537\) 2583.81 + 4475.30i 0.207635 + 0.359634i
\(538\) −13404.6 −1.07419
\(539\) 0 0
\(540\) 421.145 0.0335615
\(541\) 11508.8 + 19933.8i 0.914603 + 1.58414i 0.807482 + 0.589893i \(0.200830\pi\)
0.107121 + 0.994246i \(0.465837\pi\)
\(542\) 4950.37 8574.29i 0.392319 0.679516i
\(543\) 2482.51 4299.83i 0.196196 0.339822i
\(544\) 513.608 + 889.595i 0.0404793 + 0.0701123i
\(545\) 648.687 0.0509848
\(546\) 0 0
\(547\) 4475.84 0.349859 0.174930 0.984581i \(-0.444030\pi\)
0.174930 + 0.984581i \(0.444030\pi\)
\(548\) −54.0303 93.5832i −0.00421179 0.00729503i
\(549\) −2606.88 + 4515.25i −0.202657 + 0.351013i
\(550\) 6741.02 11675.8i 0.522614 0.905194i
\(551\) 3855.46 + 6677.85i 0.298091 + 0.516308i
\(552\) −2270.47 −0.175068
\(553\) 0 0
\(554\) 7410.35 0.568295
\(555\) −872.742 1511.63i −0.0667493 0.115613i
\(556\) 1845.51 3196.51i 0.140768 0.243817i
\(557\) −770.848 + 1335.15i −0.0586390 + 0.101566i −0.893855 0.448357i \(-0.852009\pi\)
0.835216 + 0.549922i \(0.185343\pi\)
\(558\) 1193.43 + 2067.08i 0.0905409 + 0.156821i
\(559\) 23497.8 1.77791
\(560\) 0 0
\(561\) 5912.62 0.444975
\(562\) 9324.74 + 16150.9i 0.699894 + 1.21225i
\(563\) −6539.83 + 11327.3i −0.489557 + 0.847938i −0.999928 0.0120164i \(-0.996175\pi\)
0.510370 + 0.859955i \(0.329508\pi\)
\(564\) 342.030 592.414i 0.0255356 0.0442289i
\(565\) 956.983 + 1657.54i 0.0712577 + 0.123422i
\(566\) 11139.0 0.827219
\(567\) 0 0
\(568\) 8471.88 0.625831
\(569\) −5705.59 9882.37i −0.420370 0.728102i 0.575605 0.817728i \(-0.304766\pi\)
−0.995976 + 0.0896251i \(0.971433\pi\)
\(570\) −652.764 + 1130.62i −0.0479671 + 0.0830815i
\(571\) −1155.87 + 2002.03i −0.0847139 + 0.146729i −0.905269 0.424838i \(-0.860331\pi\)
0.820555 + 0.571567i \(0.193664\pi\)
\(572\) 6593.85 + 11420.9i 0.481998 + 0.834844i
\(573\) 3023.06 0.220402
\(574\) 0 0
\(575\) 10386.8 0.753324
\(576\) −288.000 498.831i −0.0208333 0.0360844i
\(577\) −12548.5 + 21734.6i −0.905373 + 1.56815i −0.0849578 + 0.996385i \(0.527076\pi\)
−0.820415 + 0.571768i \(0.806258\pi\)
\(578\) −3882.56 + 6724.79i −0.279400 + 0.483935i
\(579\) −11.4727 19.8713i −0.000823472 0.00142630i
\(580\) −2155.50 −0.154314
\(581\) 0 0
\(582\) −9656.62 −0.687766
\(583\) −8091.75 14015.3i −0.574830 0.995635i
\(584\) 4774.63 8269.91i 0.338315 0.585978i
\(585\) 942.286 1632.09i 0.0665961 0.115348i
\(586\) −1665.31 2884.40i −0.117395 0.203333i
\(587\) 19789.1 1.39145 0.695726 0.718307i \(-0.255083\pi\)
0.695726 + 0.718307i \(0.255083\pi\)
\(588\) 0 0
\(589\) −7399.12 −0.517615
\(590\) −1761.79 3051.51i −0.122935 0.212930i
\(591\) 4034.82 6988.51i 0.280830 0.486411i
\(592\) −1193.65 + 2067.46i −0.0828693 + 0.143534i
\(593\) 1387.07 + 2402.47i 0.0960540 + 0.166370i 0.910048 0.414503i \(-0.136045\pi\)
−0.813994 + 0.580873i \(0.802711\pi\)
\(594\) −3315.44 −0.229013
\(595\) 0 0
\(596\) 2986.81 0.205276
\(597\) 1301.25 + 2253.82i 0.0892068 + 0.154511i
\(598\) −5080.04 + 8798.89i −0.347388 + 0.601694i
\(599\) 13095.2 22681.5i 0.893245 1.54715i 0.0572831 0.998358i \(-0.481756\pi\)
0.835962 0.548788i \(-0.184910\pi\)
\(600\) 1317.53 + 2282.02i 0.0896464 + 0.155272i
\(601\) −11038.6 −0.749211 −0.374605 0.927184i \(-0.622222\pi\)
−0.374605 + 0.927184i \(0.622222\pi\)
\(602\) 0 0
\(603\) 2786.29 0.188170
\(604\) −4146.29 7181.59i −0.279321 0.483799i
\(605\) 4754.63 8235.26i 0.319509 0.553407i
\(606\) 4437.77 7686.44i 0.297479 0.515248i
\(607\) 927.197 + 1605.95i 0.0619996 + 0.107386i 0.895359 0.445345i \(-0.146919\pi\)
−0.833360 + 0.552731i \(0.813586\pi\)
\(608\) 1785.57 0.119103
\(609\) 0 0
\(610\) 4518.01 0.299883
\(611\) −1530.54 2650.98i −0.101341 0.175527i
\(612\) −577.809 + 1000.79i −0.0381643 + 0.0661025i
\(613\) 7428.42 12866.4i 0.489447 0.847747i −0.510479 0.859890i \(-0.670532\pi\)
0.999926 + 0.0121428i \(0.00386527\pi\)
\(614\) −5303.32 9185.61i −0.348574 0.603748i
\(615\) 5001.07 0.327907
\(616\) 0 0
\(617\) 7600.00 0.495890 0.247945 0.968774i \(-0.420245\pi\)
0.247945 + 0.968774i \(0.420245\pi\)
\(618\) 3436.04 + 5951.39i 0.223653 + 0.387379i
\(619\) −11342.6 + 19646.0i −0.736509 + 1.27567i 0.217549 + 0.976049i \(0.430194\pi\)
−0.954058 + 0.299622i \(0.903139\pi\)
\(620\) 1034.17 1791.23i 0.0669891 0.116029i
\(621\) −1277.14 2212.07i −0.0825280 0.142943i
\(622\) −2251.98 −0.145171
\(623\) 0 0
\(624\) −2577.53 −0.165358
\(625\) −5076.98 8793.58i −0.324926 0.562789i
\(626\) −8299.51 + 14375.2i −0.529896 + 0.917807i
\(627\) 5138.83 8900.72i 0.327313 0.566923i
\(628\) −3132.44 5425.55i −0.199041 0.344750i
\(629\) 4789.59 0.303614
\(630\) 0 0
\(631\) −12024.1 −0.758595 −0.379297 0.925275i \(-0.623834\pi\)
−0.379297 + 0.925275i \(0.623834\pi\)
\(632\) 5278.23 + 9142.16i 0.332210 + 0.575405i
\(633\) 243.045 420.967i 0.0152610 0.0264328i
\(634\) −4278.76 + 7411.04i −0.268031 + 0.464243i
\(635\) −5101.91 8836.77i −0.318840 0.552246i
\(636\) 3163.05 0.197206
\(637\) 0 0
\(638\) 16969.0 1.05299
\(639\) 4765.43 + 8253.97i 0.295020 + 0.510989i
\(640\) −249.568 + 432.264i −0.0154141 + 0.0266980i
\(641\) −5660.28 + 9803.89i −0.348779 + 0.604104i −0.986033 0.166551i \(-0.946737\pi\)
0.637253 + 0.770654i \(0.280070\pi\)
\(642\) −1310.86 2270.48i −0.0805851 0.139578i
\(643\) 16843.6 1.03304 0.516521 0.856275i \(-0.327227\pi\)
0.516521 + 0.856275i \(0.327227\pi\)
\(644\) 0 0
\(645\) 5119.12 0.312504
\(646\) −1791.18 3102.41i −0.109091 0.188951i
\(647\) −3859.66 + 6685.13i −0.234527 + 0.406212i −0.959135 0.282949i \(-0.908687\pi\)
0.724608 + 0.689161i \(0.242021\pi\)
\(648\) 324.000 561.184i 0.0196419 0.0340207i
\(649\) 13869.5 + 24022.8i 0.838871 + 1.45297i
\(650\) 11791.5 0.711542
\(651\) 0 0
\(652\) 394.933 0.0237221
\(653\) 15401.6 + 26676.3i 0.922987 + 1.59866i 0.794768 + 0.606914i \(0.207593\pi\)
0.128219 + 0.991746i \(0.459074\pi\)
\(654\) 499.055 864.388i 0.0298388 0.0516823i
\(655\) 346.252 599.725i 0.0206552 0.0357759i
\(656\) −3419.98 5923.58i −0.203548 0.352556i
\(657\) 10742.9 0.637932
\(658\) 0 0
\(659\) 9760.68 0.576968 0.288484 0.957485i \(-0.406849\pi\)
0.288484 + 0.957485i \(0.406849\pi\)
\(660\) 1436.50 + 2488.10i 0.0847209 + 0.146741i
\(661\) −9035.53 + 15650.0i −0.531682 + 0.920899i 0.467635 + 0.883922i \(0.345106\pi\)
−0.999316 + 0.0369775i \(0.988227\pi\)
\(662\) −1707.12 + 2956.81i −0.100225 + 0.173595i
\(663\) 2585.62 + 4478.43i 0.151459 + 0.262335i
\(664\) −9522.65 −0.556552
\(665\) 0 0
\(666\) −2685.71 −0.156260
\(667\) 6536.64 + 11321.8i 0.379460 + 0.657244i
\(668\) 4462.71 7729.65i 0.258484 0.447708i
\(669\) −6866.77 + 11893.6i −0.396838 + 0.687344i
\(670\) −1207.24 2090.99i −0.0696114 0.120570i
\(671\) −35567.7 −2.04631
\(672\) 0 0
\(673\) 26591.1 1.52305 0.761524 0.648137i \(-0.224451\pi\)
0.761524 + 0.648137i \(0.224451\pi\)
\(674\) 1710.67 + 2962.97i 0.0977636 + 0.169331i
\(675\) −1482.22 + 2567.28i −0.0845194 + 0.146392i
\(676\) −1373.05 + 2378.20i −0.0781210 + 0.135310i
\(677\) −16540.1 28648.3i −0.938979 1.62636i −0.767380 0.641192i \(-0.778440\pi\)
−0.171599 0.985167i \(-0.554893\pi\)
\(678\) 2944.95 0.166814
\(679\) 0 0
\(680\) 1001.41 0.0564738
\(681\) −3327.29 5763.03i −0.187227 0.324287i
\(682\) −8141.42 + 14101.4i −0.457113 + 0.791743i
\(683\) 5233.04 9063.89i 0.293172 0.507789i −0.681386 0.731924i \(-0.738622\pi\)
0.974558 + 0.224135i \(0.0719557\pi\)
\(684\) 1004.38 + 1739.64i 0.0561455 + 0.0972468i
\(685\) −105.345 −0.00587597
\(686\) 0 0
\(687\) −2355.65 −0.130820
\(688\) −3500.70 6063.40i −0.193987 0.335995i
\(689\) 7077.13 12258.0i 0.391317 0.677781i
\(690\) −1106.71 + 1916.88i −0.0610606 + 0.105760i
\(691\) −6634.95 11492.1i −0.365275 0.632675i 0.623545 0.781787i \(-0.285692\pi\)
−0.988820 + 0.149112i \(0.952358\pi\)
\(692\) 8403.38 0.461631
\(693\) 0 0
\(694\) −17820.6 −0.974727
\(695\) −1799.14 3116.20i −0.0981944 0.170078i
\(696\) −1658.29 + 2872.24i −0.0903123 + 0.156425i
\(697\) −6861.44 + 11884.4i −0.372878 + 0.645843i
\(698\) 5378.68 + 9316.15i 0.291671 + 0.505189i
\(699\) 16107.4 0.871583
\(700\) 0 0
\(701\) −15169.9 −0.817344 −0.408672 0.912681i \(-0.634008\pi\)
−0.408672 + 0.912681i \(0.634008\pi\)
\(702\) −1449.86 2511.23i −0.0779507 0.135015i
\(703\) 4162.77 7210.14i 0.223331 0.386821i
\(704\) 1964.70 3402.97i 0.105181 0.182179i
\(705\) −333.436 577.529i −0.0178127 0.0308525i
\(706\) 8505.13 0.453392
\(707\) 0 0
\(708\) −5421.59 −0.287791
\(709\) −13158.9 22791.8i −0.697026 1.20728i −0.969493 0.245119i \(-0.921173\pi\)
0.272467 0.962165i \(-0.412160\pi\)
\(710\) 4129.51 7152.51i 0.218278 0.378069i
\(711\) −5938.01 + 10284.9i −0.313211 + 0.542497i
\(712\) −932.341 1614.86i −0.0490744 0.0849994i
\(713\) −12544.6 −0.658907
\(714\) 0 0
\(715\) 12856.3 0.672447
\(716\) −3445.08 5967.06i −0.179817 0.311452i
\(717\) 5569.91 9647.37i 0.290115 0.502493i
\(718\) 4903.89 8493.78i 0.254891 0.441484i
\(719\) −11506.5 19929.9i −0.596831 1.03374i −0.993286 0.115687i \(-0.963093\pi\)
0.396455 0.918054i \(-0.370240\pi\)
\(720\) −561.527 −0.0290651
\(721\) 0 0
\(722\) 7490.95 0.386128
\(723\) 10497.9 + 18183.0i 0.540003 + 0.935313i
\(724\) −3310.01 + 5733.10i −0.169911 + 0.294294i
\(725\) 7586.26 13139.8i 0.388616 0.673103i
\(726\) −7315.76 12671.3i −0.373985 0.647762i
\(727\) −16265.4 −0.829780 −0.414890 0.909872i \(-0.636180\pi\)
−0.414890 + 0.909872i \(0.636180\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) −4654.66 8062.11i −0.235996 0.408756i
\(731\) −7023.40 + 12164.9i −0.355362 + 0.615505i
\(732\) 3475.84 6020.33i 0.175506 0.303986i
\(733\) 433.222 + 750.362i 0.0218300 + 0.0378107i 0.876734 0.480975i \(-0.159717\pi\)
−0.854904 + 0.518786i \(0.826384\pi\)
\(734\) 8083.14 0.406477
\(735\) 0 0
\(736\) 3027.30 0.151614
\(737\) 9503.88 + 16461.2i 0.475007 + 0.822736i
\(738\) 3847.48 6664.03i 0.191907 0.332393i
\(739\) −5495.03 + 9517.68i −0.273529 + 0.473766i −0.969763 0.244049i \(-0.921524\pi\)
0.696234 + 0.717815i \(0.254858\pi\)
\(740\) 1163.66 + 2015.51i 0.0578066 + 0.100124i
\(741\) 8988.96 0.445638
\(742\) 0 0
\(743\) −22416.4 −1.10683 −0.553417 0.832905i \(-0.686676\pi\)
−0.553417 + 0.832905i \(0.686676\pi\)
\(744\) −1591.24 2756.10i −0.0784107 0.135811i
\(745\) 1455.88 2521.66i 0.0715965 0.124009i
\(746\) −7451.35 + 12906.1i −0.365701 + 0.633413i
\(747\) −5356.49 9277.71i −0.262361 0.454423i
\(748\) −7883.49 −0.385360
\(749\) 0 0
\(750\) 5493.47 0.267457
\(751\) 9858.97 + 17076.2i 0.479040 + 0.829722i 0.999711 0.0240358i \(-0.00765155\pi\)
−0.520671 + 0.853757i \(0.674318\pi\)
\(752\) −456.040 + 789.885i −0.0221145 + 0.0383034i
\(753\) 5584.13 9671.99i 0.270248 0.468084i
\(754\) 7420.64 + 12852.9i 0.358414 + 0.620791i
\(755\) −8084.22 −0.389689
\(756\) 0 0
\(757\) 839.321 0.0402981 0.0201490 0.999797i \(-0.493586\pi\)
0.0201490 + 0.999797i \(0.493586\pi\)
\(758\) −12564.4 21762.2i −0.602057 1.04279i
\(759\) 8712.51 15090.5i 0.416659 0.721674i
\(760\) 870.352 1507.49i 0.0415407 0.0719507i
\(761\) −9182.25 15904.1i −0.437393 0.757587i 0.560094 0.828429i \(-0.310765\pi\)
−0.997488 + 0.0708415i \(0.977432\pi\)
\(762\) −15700.2 −0.746403
\(763\) 0 0
\(764\) −4030.75 −0.190874
\(765\) 563.291 + 975.648i 0.0266220 + 0.0461106i
\(766\) −4289.93 + 7430.38i −0.202352 + 0.350484i
\(767\) −12130.5 + 21010.6i −0.571063 + 0.989111i
\(768\) 384.000 + 665.108i 0.0180422 + 0.0312500i
\(769\) −14890.8 −0.698277 −0.349138 0.937071i \(-0.613526\pi\)
−0.349138 + 0.937071i \(0.613526\pi\)
\(770\) 0 0
\(771\) −3690.45 −0.172384
\(772\) 15.2970 + 26.4951i 0.000713148 + 0.00123521i
\(773\) 8303.10 14381.4i 0.386341 0.669163i −0.605613 0.795759i \(-0.707072\pi\)
0.991954 + 0.126597i \(0.0404053\pi\)
\(774\) 3938.29 6821.32i 0.182893 0.316779i
\(775\) 7279.50 + 12608.5i 0.337403 + 0.584400i
\(776\) 12875.5 0.595623
\(777\) 0 0
\(778\) −11325.5 −0.521903
\(779\) 11927.0 + 20658.1i 0.548559 + 0.950133i
\(780\) −1256.38 + 2176.12i −0.0576740 + 0.0998942i
\(781\) −32509.2 + 56307.6i −1.48946 + 2.57983i
\(782\) −3036.81 5259.90i −0.138869 0.240529i
\(783\) −3731.15 −0.170294
\(784\) 0 0
\(785\) −6107.47 −0.277688
\(786\) −532.764 922.774i −0.0241769 0.0418756i
\(787\) −1578.10 + 2733.35i −0.0714781 + 0.123804i −0.899549 0.436819i \(-0.856105\pi\)
0.828071 + 0.560623i \(0.189438\pi\)
\(788\) −5379.76 + 9318.01i −0.243205 + 0.421244i
\(789\) 3582.95 + 6205.85i 0.161668 + 0.280018i
\(790\) 10291.2 0.463475
\(791\) 0 0
\(792\) 4420.58 0.198331
\(793\) −15553.9 26940.2i −0.696515 1.20640i
\(794\) 14561.4 25221.0i 0.650836 1.12728i
\(795\) 1541.79 2670.46i 0.0687819 0.119134i
\(796\) −1734.99 3005.10i −0.0772553 0.133810i
\(797\) −13514.8 −0.600652 −0.300326 0.953837i \(-0.597096\pi\)
−0.300326 + 0.953837i \(0.597096\pi\)
\(798\) 0 0
\(799\) 1829.89 0.0810224
\(800\) −1756.70 3042.70i −0.0776360 0.134470i
\(801\) 1048.88 1816.72i 0.0462678 0.0801382i
\(802\) −3742.19 + 6481.66i −0.164765 + 0.285381i
\(803\) 36643.5 + 63468.4i 1.61036 + 2.78923i
\(804\) −3715.05 −0.162960
\(805\) 0 0
\(806\) −14241.2 −0.622362
\(807\) 10053.5 + 17413.1i 0.438536 + 0.759567i
\(808\) −5917.02 + 10248.6i −0.257624 + 0.446218i
\(809\) 13379.1 23173.2i 0.581437 1.00708i −0.413872 0.910335i \(-0.635824\pi\)
0.995309 0.0967438i \(-0.0308427\pi\)
\(810\) −315.859 547.084i −0.0137014 0.0237316i
\(811\) −15920.7 −0.689338 −0.344669 0.938724i \(-0.612009\pi\)
−0.344669 + 0.938724i \(0.612009\pi\)
\(812\) 0 0
\(813\) −14851.1 −0.640653
\(814\) −9160.80 15867.0i −0.394454 0.683215i
\(815\) 192.505 333.429i 0.00827381 0.0143307i
\(816\) 770.412 1334.39i 0.0330512 0.0572464i
\(817\) 12208.5 + 21145.7i 0.522792 + 0.905501i
\(818\) 7034.35 0.300673
\(819\) 0 0
\(820\) −6668.10 −0.283976
\(821\) 9653.11 + 16719.7i 0.410348 + 0.710744i 0.994928 0.100593i \(-0.0320739\pi\)
−0.584580 + 0.811336i \(0.698741\pi\)
\(822\) −81.0455 + 140.375i −0.00343891 + 0.00595637i
\(823\) −395.500 + 685.026i −0.0167512 + 0.0290140i −0.874280 0.485423i \(-0.838666\pi\)
0.857528 + 0.514437i \(0.171999\pi\)
\(824\) −4581.39 7935.19i −0.193689 0.335480i
\(825\) −20223.0 −0.853426
\(826\) 0 0
\(827\) 29537.6 1.24199 0.620993 0.783816i \(-0.286730\pi\)
0.620993 + 0.783816i \(0.286730\pi\)
\(828\) 1702.85 + 2949.43i 0.0714714 + 0.123792i
\(829\) 2883.26 4993.96i 0.120796 0.209225i −0.799286 0.600951i \(-0.794789\pi\)
0.920082 + 0.391726i \(0.128122\pi\)
\(830\) −4641.69 + 8039.64i −0.194115 + 0.336217i
\(831\) −5557.76 9626.33i −0.232006 0.401846i
\(832\) 3436.70 0.143205
\(833\) 0 0
\(834\) −5536.52 −0.229873
\(835\) −4350.58 7535.43i −0.180309 0.312305i
\(836\) −6851.78 + 11867.6i −0.283461 + 0.490969i
\(837\) 1790.14 3100.62i 0.0739263 0.128044i
\(838\) −7579.52 13128.1i −0.312446 0.541173i
\(839\) 29726.4 1.22321 0.611603 0.791165i \(-0.290525\pi\)
0.611603 + 0.791165i \(0.290525\pi\)
\(840\) 0 0
\(841\) −5292.27 −0.216994
\(842\) −4980.87 8627.12i −0.203862 0.353100i
\(843\) 13987.1 24226.4i 0.571461 0.989800i
\(844\) −324.061 + 561.289i −0.0132164 + 0.0228914i
\(845\) 1338.55 + 2318.44i 0.0544943 + 0.0943869i
\(846\) −1026.09 −0.0416994
\(847\) 0 0
\(848\) −4217.41 −0.170786
\(849\) −8354.23 14469.9i −0.337711 0.584932i
\(850\) −3524.44 + 6104.51i −0.142220 + 0.246333i
\(851\) 7057.67 12224.2i 0.284294 0.492411i
\(852\) −6353.91 11005.3i −0.255495 0.442530i
\(853\) −17829.6 −0.715677 −0.357838 0.933784i \(-0.616486\pi\)
−0.357838 + 0.933784i \(0.616486\pi\)
\(854\) 0 0
\(855\) 1958.29 0.0783300
\(856\) 1747.82 + 3027.31i 0.0697888 + 0.120878i
\(857\) 19841.2 34366.0i 0.790856 1.36980i −0.134582 0.990902i \(-0.542969\pi\)
0.925438 0.378900i \(-0.123697\pi\)
\(858\) 9890.77 17131.3i 0.393549 0.681648i
\(859\) 1097.57 + 1901.04i 0.0435955 + 0.0755096i 0.887000 0.461770i \(-0.152785\pi\)
−0.843404 + 0.537279i \(0.819452\pi\)
\(860\) −6825.49 −0.270636
\(861\) 0 0
\(862\) −28406.6 −1.12243
\(863\) −15958.5 27641.0i −0.629472 1.09028i −0.987658 0.156627i \(-0.949938\pi\)
0.358186 0.933650i \(-0.383396\pi\)
\(864\) −432.000 + 748.246i −0.0170103 + 0.0294628i
\(865\) 4096.12 7094.68i 0.161008 0.278874i
\(866\) 3874.82 + 6711.39i 0.152046 + 0.263351i
\(867\) 11647.7 0.456258
\(868\) 0 0
\(869\) −81016.8 −3.16261
\(870\) 1616.62 + 2800.08i 0.0629985 + 0.109117i
\(871\) −8312.20 + 14397.2i −0.323362 + 0.560079i
\(872\) −665.406 + 1152.52i −0.0258412 + 0.0447582i
\(873\) 7242.47 + 12544.3i 0.280779 + 0.486324i
\(874\) −10557.5 −0.408596
\(875\) 0 0
\(876\) −14323.9 −0.552465
\(877\) −14421.4 24978.6i −0.555276 0.961766i −0.997882 0.0650500i \(-0.979279\pi\)
0.442606 0.896716i \(-0.354054\pi\)
\(878\) 7763.82 13447.3i 0.298424 0.516885i
\(879\) −2497.96 + 4326.59i −0.0958522 + 0.166021i
\(880\) −1915.34 3317.46i −0.0733705 0.127081i
\(881\) −15350.2 −0.587015 −0.293508 0.955957i \(-0.594823\pi\)
−0.293508 + 0.955957i \(0.594823\pi\)
\(882\) 0 0
\(883\) 6089.64 0.232087 0.116043 0.993244i \(-0.462979\pi\)
0.116043 + 0.993244i \(0.462979\pi\)
\(884\) −3447.50 5971.24i −0.131167 0.227188i
\(885\) −2642.68 + 4577.26i −0.100376 + 0.173856i
\(886\) 9662.24 16735.5i 0.366376 0.634582i
\(887\) 192.221 + 332.936i 0.00727637 + 0.0126030i 0.869641 0.493685i \(-0.164351\pi\)
−0.862364 + 0.506288i \(0.831017\pi\)
\(888\) 3580.95 0.135325
\(889\) 0 0
\(890\) −1817.83 −0.0684650
\(891\) 2486.58 + 4306.88i 0.0934944 + 0.161937i
\(892\) 9155.70 15858.1i 0.343672 0.595257i
\(893\) 1590.41 2754.67i 0.0595981 0.103227i
\(894\) −2240.11 3879.98i −0.0838036 0.145152i
\(895\) −6717.05 −0.250867
\(896\) 0 0
\(897\) 15240.1 0.567283
\(898\) −10942.6 18953.1i −0.406636 0.704313i
\(899\) −9162.27 + 15869.5i −0.339910 + 0.588741i
\(900\) 1976.29 3423.04i 0.0731960 0.126779i
\(901\) 4230.65 + 7327.70i 0.156430 + 0.270945i
\(902\) 52494.1 1.93776
\(903\) 0 0
\(904\) −3926.59 −0.144465
\(905\) 3226.84 + 5589.05i 0.118524 + 0.205289i
\(906\) −6219.44 + 10772.4i −0.228065 + 0.395020i
\(907\) 3633.97 6294.21i 0.133036 0.230426i −0.791809 0.610768i \(-0.790861\pi\)
0.924846 + 0.380343i \(0.124194\pi\)
\(908\) 4436.38 + 7684.04i 0.162144 + 0.280841i
\(909\) −13313.3 −0.485780
\(910\) 0 0
\(911\) −8535.12 −0.310408 −0.155204 0.987882i \(-0.549603\pi\)
−0.155204 + 0.987882i \(0.549603\pi\)
\(912\) −1339.18 2319.52i −0.0486234 0.0842182i
\(913\) 36541.4 63291.5i 1.32458 2.29424i
\(914\) 13618.3 23587.7i 0.492839 0.853622i
\(915\) −3388.50 5869.06i −0.122427 0.212049i
\(916\) 3140.87 0.113294
\(917\) 0 0
\(918\) 1733.43 0.0623220
\(919\) 5425.86 + 9397.87i 0.194758 + 0.337331i 0.946821 0.321760i \(-0.104275\pi\)
−0.752063 + 0.659091i \(0.770941\pi\)
\(920\) 1475.62 2555.84i 0.0528800 0.0915909i
\(921\) −7954.97 + 13778.4i −0.284609 + 0.492958i
\(922\) 11955.8 + 20708.1i 0.427055 + 0.739681i
\(923\) −56865.9 −2.02791
\(924\) 0 0
\(925\) −16381.9 −0.582307
\(926\) 648.503 + 1123.24i 0.0230142 + 0.0398617i
\(927\) 5154.06 8927.09i 0.182612 0.316294i
\(928\) 2211.05 3829.66i 0.0782127 0.135468i
\(929\) 780.319 + 1351.55i 0.0275581 + 0.0477320i 0.879476 0.475944i \(-0.157894\pi\)
−0.851917 + 0.523676i \(0.824560\pi\)
\(930\) −3102.51 −0.109393
\(931\) 0 0
\(932\) −21476.5 −0.754813
\(933\) 1688.98 + 2925.40i 0.0592656 + 0.102651i
\(934\) 2784.74 4823.32i 0.0975585 0.168976i
\(935\) −3842.71 + 6655.76i −0.134406 + 0.232799i
\(936\) 1933.15 + 3348.31i 0.0675073 + 0.116926i
\(937\) 11978.4 0.417627 0.208813 0.977956i \(-0.433040\pi\)
0.208813 + 0.977956i \(0.433040\pi\)
\(938\) 0 0
\(939\) 24898.5 0.865317
\(940\) 444.582 + 770.038i 0.0154262 + 0.0267190i
\(941\) −12298.8 + 21302.2i −0.426068 + 0.737972i −0.996520 0.0833594i \(-0.973435\pi\)
0.570451 + 0.821332i \(0.306768\pi\)
\(942\) −4698.66 + 8138.32i −0.162517 + 0.281487i
\(943\) 20221.3 + 35024.3i 0.698298 + 1.20949i
\(944\) 7228.78 0.249234
\(945\) 0 0
\(946\) 53733.1 1.84674
\(947\) 5417.32 + 9383.07i 0.185891 + 0.321973i 0.943877 0.330298i \(-0.107149\pi\)
−0.757985 + 0.652272i \(0.773816\pi\)
\(948\) 7917.35 13713.2i 0.271248 0.469816i
\(949\) −32048.8 + 55510.2i −1.09626 + 1.89877i
\(950\) 6126.39 + 10611.2i 0.209228 + 0.362393i
\(951\) 12836.3 0.437692
\(952\) 0 0
\(953\) 701.418 0.0238417 0.0119209 0.999929i \(-0.496205\pi\)
0.0119209 + 0.999929i \(0.496205\pi\)
\(954\) −2372.29 4108.93i −0.0805092 0.139446i
\(955\) −1964.74 + 3403.02i −0.0665732 + 0.115308i
\(956\) −7426.55 + 12863.2i −0.251247 + 0.435172i
\(957\) −12726.8 22043.4i −0.429882 0.744578i
\(958\) −22226.8 −0.749599
\(959\) 0 0
\(960\) 748.703 0.0251711
\(961\) 6103.72 + 10571.9i 0.204885 + 0.354871i
\(962\) 8012.14 13877.4i 0.268526 0.465100i
\(963\) −1966.30 + 3405.72i −0.0657975 + 0.113965i
\(964\) −13997.2 24243.9i −0.467657 0.810005i
\(965\) 29.8252 0.000994931
\(966\) 0 0
\(967\) 42402.5 1.41011 0.705053 0.709154i \(-0.250923\pi\)
0.705053 + 0.709154i \(0.250923\pi\)
\(968\) 9754.35 + 16895.0i 0.323881 + 0.560978i
\(969\) −2686.76 + 4653.61i −0.0890725 + 0.154278i
\(970\) 6275.99 10870.3i 0.207742 0.359820i
\(971\) −7731.69 13391.7i −0.255532 0.442595i 0.709508 0.704698i \(-0.248917\pi\)
−0.965040 + 0.262103i \(0.915584\pi\)
\(972\) −972.000 −0.0320750
\(973\) 0 0
\(974\) 7572.55 0.249117
\(975\) −8843.65 15317.7i −0.290486 0.503136i
\(976\) −4634.45 + 8027.11i −0.151993 + 0.263260i
\(977\) 17242.1 29864.1i 0.564609 0.977931i −0.432477 0.901645i \(-0.642360\pi\)
0.997086 0.0762860i \(-0.0243062\pi\)
\(978\) −296.200 513.033i −0.00968449 0.0167740i
\(979\) 14310.7 0.467184
\(980\) 0 0
\(981\) −1497.16 −0.0487266
\(982\) −9582.12 16596.7i −0.311383 0.539330i
\(983\) −3667.68 + 6352.61i −0.119004 + 0.206121i −0.919373 0.393386i \(-0.871303\pi\)
0.800369 + 0.599507i \(0.204637\pi\)
\(984\) −5129.97 + 8885.37i −0.166197 + 0.287861i
\(985\) 5244.58 + 9083.89i 0.169651 + 0.293844i
\(986\) −8872.00 −0.286554
\(987\) 0 0
\(988\) −11985.3 −0.385934
\(989\) 20698.6 + 35851.0i 0.665497 + 1.15267i
\(990\) 2154.75 3732.14i 0.0691743 0.119813i
\(991\) 5061.48 8766.74i 0.162243 0.281014i −0.773430 0.633882i \(-0.781460\pi\)
0.935673 + 0.352869i \(0.114794\pi\)
\(992\) 2121.65 + 3674.80i 0.0679057 + 0.117616i
\(993\) 5121.35 0.163667
\(994\) 0 0
\(995\) −3382.80 −0.107781
\(996\) 7141.99 + 12370.3i 0.227211 + 0.393542i
\(997\) −28334.6 + 49076.9i −0.900066 + 1.55896i −0.0726582 + 0.997357i \(0.523148\pi\)
−0.827407 + 0.561602i \(0.810185\pi\)
\(998\) 5581.55 9667.52i 0.177035 0.306633i
\(999\) 2014.28 + 3488.84i 0.0637928 + 0.110492i
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 294.4.e.o.67.2 4
3.2 odd 2 882.4.g.bd.361.1 4
7.2 even 3 inner 294.4.e.o.79.2 4
7.3 odd 6 294.4.a.k.1.2 yes 2
7.4 even 3 294.4.a.j.1.1 2
7.5 odd 6 294.4.e.n.79.1 4
7.6 odd 2 294.4.e.n.67.1 4
21.2 odd 6 882.4.g.bd.667.1 4
21.5 even 6 882.4.g.y.667.2 4
21.11 odd 6 882.4.a.bc.1.2 2
21.17 even 6 882.4.a.bi.1.1 2
21.20 even 2 882.4.g.y.361.2 4
28.3 even 6 2352.4.a.bn.1.2 2
28.11 odd 6 2352.4.a.cd.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
294.4.a.j.1.1 2 7.4 even 3
294.4.a.k.1.2 yes 2 7.3 odd 6
294.4.e.n.67.1 4 7.6 odd 2
294.4.e.n.79.1 4 7.5 odd 6
294.4.e.o.67.2 4 1.1 even 1 trivial
294.4.e.o.79.2 4 7.2 even 3 inner
882.4.a.bc.1.2 2 21.11 odd 6
882.4.a.bi.1.1 2 21.17 even 6
882.4.g.y.361.2 4 21.20 even 2
882.4.g.y.667.2 4 21.5 even 6
882.4.g.bd.361.1 4 3.2 odd 2
882.4.g.bd.667.1 4 21.2 odd 6
2352.4.a.bn.1.2 2 28.3 even 6
2352.4.a.cd.1.1 2 28.11 odd 6