Properties

Label 10.5.c.b.3.1
Level $10$
Weight $5$
Character 10.3
Analytic conductor $1.034$
Analytic rank $0$
Dimension $2$
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] = [10,5,Mod(3,10)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(10, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("10.3");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 10.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: \(1.03369963084\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 3.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 10.3
Dual form 10.5.c.b.7.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.00000 - 2.00000i) q^{2} +(1.00000 + 1.00000i) q^{3} -8.00000i q^{4} +(-15.0000 + 20.0000i) q^{5} +4.00000 q^{6} +(-19.0000 + 19.0000i) q^{7} +(-16.0000 - 16.0000i) q^{8} -79.0000i q^{9} +O(q^{10})\) \(q+(2.00000 - 2.00000i) q^{2} +(1.00000 + 1.00000i) q^{3} -8.00000i q^{4} +(-15.0000 + 20.0000i) q^{5} +4.00000 q^{6} +(-19.0000 + 19.0000i) q^{7} +(-16.0000 - 16.0000i) q^{8} -79.0000i q^{9} +(10.0000 + 70.0000i) q^{10} +202.000 q^{11} +(8.00000 - 8.00000i) q^{12} +(-99.0000 - 99.0000i) q^{13} +76.0000i q^{14} +(-35.0000 + 5.00000i) q^{15} -64.0000 q^{16} +(-239.000 + 239.000i) q^{17} +(-158.000 - 158.000i) q^{18} -40.0000i q^{19} +(160.000 + 120.000i) q^{20} -38.0000 q^{21} +(404.000 - 404.000i) q^{22} +(541.000 + 541.000i) q^{23} -32.0000i q^{24} +(-175.000 - 600.000i) q^{25} -396.000 q^{26} +(160.000 - 160.000i) q^{27} +(152.000 + 152.000i) q^{28} +200.000i q^{29} +(-60.0000 + 80.0000i) q^{30} -758.000 q^{31} +(-128.000 + 128.000i) q^{32} +(202.000 + 202.000i) q^{33} +956.000i q^{34} +(-95.0000 - 665.000i) q^{35} -632.000 q^{36} +(141.000 - 141.000i) q^{37} +(-80.0000 - 80.0000i) q^{38} -198.000i q^{39} +(560.000 - 80.0000i) q^{40} +1042.00 q^{41} +(-76.0000 + 76.0000i) q^{42} +(-759.000 - 759.000i) q^{43} -1616.00i q^{44} +(1580.00 + 1185.00i) q^{45} +2164.00 q^{46} +(-459.000 + 459.000i) q^{47} +(-64.0000 - 64.0000i) q^{48} +1679.00i q^{49} +(-1550.00 - 850.000i) q^{50} -478.000 q^{51} +(-792.000 + 792.000i) q^{52} +(-1819.00 - 1819.00i) q^{53} -640.000i q^{54} +(-3030.00 + 4040.00i) q^{55} +608.000 q^{56} +(40.0000 - 40.0000i) q^{57} +(400.000 + 400.000i) q^{58} -4600.00i q^{59} +(40.0000 + 280.000i) q^{60} +2082.00 q^{61} +(-1516.00 + 1516.00i) q^{62} +(1501.00 + 1501.00i) q^{63} +512.000i q^{64} +(3465.00 - 495.000i) q^{65} +808.000 q^{66} +(5081.00 - 5081.00i) q^{67} +(1912.00 + 1912.00i) q^{68} +1082.00i q^{69} +(-1520.00 - 1140.00i) q^{70} -3478.00 q^{71} +(-1264.00 + 1264.00i) q^{72} +(-3479.00 - 3479.00i) q^{73} -564.000i q^{74} +(425.000 - 775.000i) q^{75} -320.000 q^{76} +(-3838.00 + 3838.00i) q^{77} +(-396.000 - 396.000i) q^{78} +7680.00i q^{79} +(960.000 - 1280.00i) q^{80} -6079.00 q^{81} +(2084.00 - 2084.00i) q^{82} +(6081.00 + 6081.00i) q^{83} +304.000i q^{84} +(-1195.00 - 8365.00i) q^{85} -3036.00 q^{86} +(-200.000 + 200.000i) q^{87} +(-3232.00 - 3232.00i) q^{88} +5680.00i q^{89} +(5530.00 - 790.000i) q^{90} +3762.00 q^{91} +(4328.00 - 4328.00i) q^{92} +(-758.000 - 758.000i) q^{93} +1836.00i q^{94} +(800.000 + 600.000i) q^{95} -256.000 q^{96} +(561.000 - 561.000i) q^{97} +(3358.00 + 3358.00i) q^{98} -15958.0i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 4 q^{2} + 2 q^{3} - 30 q^{5} + 8 q^{6} - 38 q^{7} - 32 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 4 q^{2} + 2 q^{3} - 30 q^{5} + 8 q^{6} - 38 q^{7} - 32 q^{8} + 20 q^{10} + 404 q^{11} + 16 q^{12} - 198 q^{13} - 70 q^{15} - 128 q^{16} - 478 q^{17} - 316 q^{18} + 320 q^{20} - 76 q^{21} + 808 q^{22} + 1082 q^{23} - 350 q^{25} - 792 q^{26} + 320 q^{27} + 304 q^{28} - 120 q^{30} - 1516 q^{31} - 256 q^{32} + 404 q^{33} - 190 q^{35} - 1264 q^{36} + 282 q^{37} - 160 q^{38} + 1120 q^{40} + 2084 q^{41} - 152 q^{42} - 1518 q^{43} + 3160 q^{45} + 4328 q^{46} - 918 q^{47} - 128 q^{48} - 3100 q^{50} - 956 q^{51} - 1584 q^{52} - 3638 q^{53} - 6060 q^{55} + 1216 q^{56} + 80 q^{57} + 800 q^{58} + 80 q^{60} + 4164 q^{61} - 3032 q^{62} + 3002 q^{63} + 6930 q^{65} + 1616 q^{66} + 10162 q^{67} + 3824 q^{68} - 3040 q^{70} - 6956 q^{71} - 2528 q^{72} - 6958 q^{73} + 850 q^{75} - 640 q^{76} - 7676 q^{77} - 792 q^{78} + 1920 q^{80} - 12158 q^{81} + 4168 q^{82} + 12162 q^{83} - 2390 q^{85} - 6072 q^{86} - 400 q^{87} - 6464 q^{88} + 11060 q^{90} + 7524 q^{91} + 8656 q^{92} - 1516 q^{93} + 1600 q^{95} - 512 q^{96} + 1122 q^{97} + 6716 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/10\mathbb{Z}\right)^\times\).

\(n\) \(7\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 2.00000i 0.500000 0.500000i
\(3\) 1.00000 + 1.00000i 0.111111 + 0.111111i 0.760477 0.649365i \(-0.224965\pi\)
−0.649365 + 0.760477i \(0.724965\pi\)
\(4\) 8.00000i 0.500000i
\(5\) −15.0000 + 20.0000i −0.600000 + 0.800000i
\(6\) 4.00000 0.111111
\(7\) −19.0000 + 19.0000i −0.387755 + 0.387755i −0.873886 0.486131i \(-0.838408\pi\)
0.486131 + 0.873886i \(0.338408\pi\)
\(8\) −16.0000 16.0000i −0.250000 0.250000i
\(9\) 79.0000i 0.975309i
\(10\) 10.0000 + 70.0000i 0.100000 + 0.700000i
\(11\) 202.000 1.66942 0.834711 0.550689i \(-0.185635\pi\)
0.834711 + 0.550689i \(0.185635\pi\)
\(12\) 8.00000 8.00000i 0.0555556 0.0555556i
\(13\) −99.0000 99.0000i −0.585799 0.585799i 0.350692 0.936491i \(-0.385946\pi\)
−0.936491 + 0.350692i \(0.885946\pi\)
\(14\) 76.0000i 0.387755i
\(15\) −35.0000 + 5.00000i −0.155556 + 0.0222222i
\(16\) −64.0000 −0.250000
\(17\) −239.000 + 239.000i −0.826990 + 0.826990i −0.987099 0.160110i \(-0.948815\pi\)
0.160110 + 0.987099i \(0.448815\pi\)
\(18\) −158.000 158.000i −0.487654 0.487654i
\(19\) 40.0000i 0.110803i −0.998464 0.0554017i \(-0.982356\pi\)
0.998464 0.0554017i \(-0.0176439\pi\)
\(20\) 160.000 + 120.000i 0.400000 + 0.300000i
\(21\) −38.0000 −0.0861678
\(22\) 404.000 404.000i 0.834711 0.834711i
\(23\) 541.000 + 541.000i 1.02268 + 1.02268i 0.999737 + 0.0229476i \(0.00730510\pi\)
0.0229476 + 0.999737i \(0.492695\pi\)
\(24\) 32.0000i 0.0555556i
\(25\) −175.000 600.000i −0.280000 0.960000i
\(26\) −396.000 −0.585799
\(27\) 160.000 160.000i 0.219479 0.219479i
\(28\) 152.000 + 152.000i 0.193878 + 0.193878i
\(29\) 200.000i 0.237812i 0.992906 + 0.118906i \(0.0379387\pi\)
−0.992906 + 0.118906i \(0.962061\pi\)
\(30\) −60.0000 + 80.0000i −0.0666667 + 0.0888889i
\(31\) −758.000 −0.788762 −0.394381 0.918947i \(-0.629041\pi\)
−0.394381 + 0.918947i \(0.629041\pi\)
\(32\) −128.000 + 128.000i −0.125000 + 0.125000i
\(33\) 202.000 + 202.000i 0.185491 + 0.185491i
\(34\) 956.000i 0.826990i
\(35\) −95.0000 665.000i −0.0775510 0.542857i
\(36\) −632.000 −0.487654
\(37\) 141.000 141.000i 0.102995 0.102995i −0.653732 0.756726i \(-0.726797\pi\)
0.756726 + 0.653732i \(0.226797\pi\)
\(38\) −80.0000 80.0000i −0.0554017 0.0554017i
\(39\) 198.000i 0.130178i
\(40\) 560.000 80.0000i 0.350000 0.0500000i
\(41\) 1042.00 0.619869 0.309935 0.950758i \(-0.399693\pi\)
0.309935 + 0.950758i \(0.399693\pi\)
\(42\) −76.0000 + 76.0000i −0.0430839 + 0.0430839i
\(43\) −759.000 759.000i −0.410492 0.410492i 0.471418 0.881910i \(-0.343742\pi\)
−0.881910 + 0.471418i \(0.843742\pi\)
\(44\) 1616.00i 0.834711i
\(45\) 1580.00 + 1185.00i 0.780247 + 0.585185i
\(46\) 2164.00 1.02268
\(47\) −459.000 + 459.000i −0.207786 + 0.207786i −0.803326 0.595540i \(-0.796938\pi\)
0.595540 + 0.803326i \(0.296938\pi\)
\(48\) −64.0000 64.0000i −0.0277778 0.0277778i
\(49\) 1679.00i 0.699292i
\(50\) −1550.00 850.000i −0.620000 0.340000i
\(51\) −478.000 −0.183775
\(52\) −792.000 + 792.000i −0.292899 + 0.292899i
\(53\) −1819.00 1819.00i −0.647561 0.647561i 0.304842 0.952403i \(-0.401396\pi\)
−0.952403 + 0.304842i \(0.901396\pi\)
\(54\) 640.000i 0.219479i
\(55\) −3030.00 + 4040.00i −1.00165 + 1.33554i
\(56\) 608.000 0.193878
\(57\) 40.0000 40.0000i 0.0123115 0.0123115i
\(58\) 400.000 + 400.000i 0.118906 + 0.118906i
\(59\) 4600.00i 1.32146i −0.750624 0.660730i \(-0.770247\pi\)
0.750624 0.660730i \(-0.229753\pi\)
\(60\) 40.0000 + 280.000i 0.0111111 + 0.0777778i
\(61\) 2082.00 0.559527 0.279764 0.960069i \(-0.409744\pi\)
0.279764 + 0.960069i \(0.409744\pi\)
\(62\) −1516.00 + 1516.00i −0.394381 + 0.394381i
\(63\) 1501.00 + 1501.00i 0.378181 + 0.378181i
\(64\) 512.000i 0.125000i
\(65\) 3465.00 495.000i 0.820118 0.117160i
\(66\) 808.000 0.185491
\(67\) 5081.00 5081.00i 1.13188 1.13188i 0.142013 0.989865i \(-0.454642\pi\)
0.989865 0.142013i \(-0.0453575\pi\)
\(68\) 1912.00 + 1912.00i 0.413495 + 0.413495i
\(69\) 1082.00i 0.227263i
\(70\) −1520.00 1140.00i −0.310204 0.232653i
\(71\) −3478.00 −0.689942 −0.344971 0.938613i \(-0.612111\pi\)
−0.344971 + 0.938613i \(0.612111\pi\)
\(72\) −1264.00 + 1264.00i −0.243827 + 0.243827i
\(73\) −3479.00 3479.00i −0.652843 0.652843i 0.300834 0.953677i \(-0.402735\pi\)
−0.953677 + 0.300834i \(0.902735\pi\)
\(74\) 564.000i 0.102995i
\(75\) 425.000 775.000i 0.0755556 0.137778i
\(76\) −320.000 −0.0554017
\(77\) −3838.00 + 3838.00i −0.647327 + 0.647327i
\(78\) −396.000 396.000i −0.0650888 0.0650888i
\(79\) 7680.00i 1.23057i 0.788304 + 0.615286i \(0.210959\pi\)
−0.788304 + 0.615286i \(0.789041\pi\)
\(80\) 960.000 1280.00i 0.150000 0.200000i
\(81\) −6079.00 −0.926536
\(82\) 2084.00 2084.00i 0.309935 0.309935i
\(83\) 6081.00 + 6081.00i 0.882712 + 0.882712i 0.993809 0.111098i \(-0.0354367\pi\)
−0.111098 + 0.993809i \(0.535437\pi\)
\(84\) 304.000i 0.0430839i
\(85\) −1195.00 8365.00i −0.165398 1.15779i
\(86\) −3036.00 −0.410492
\(87\) −200.000 + 200.000i −0.0264236 + 0.0264236i
\(88\) −3232.00 3232.00i −0.417355 0.417355i
\(89\) 5680.00i 0.717081i 0.933514 + 0.358541i \(0.116726\pi\)
−0.933514 + 0.358541i \(0.883274\pi\)
\(90\) 5530.00 790.000i 0.682716 0.0975309i
\(91\) 3762.00 0.454293
\(92\) 4328.00 4328.00i 0.511342 0.511342i
\(93\) −758.000 758.000i −0.0876402 0.0876402i
\(94\) 1836.00i 0.207786i
\(95\) 800.000 + 600.000i 0.0886427 + 0.0664820i
\(96\) −256.000 −0.0277778
\(97\) 561.000 561.000i 0.0596238 0.0596238i −0.676666 0.736290i \(-0.736576\pi\)
0.736290 + 0.676666i \(0.236576\pi\)
\(98\) 3358.00 + 3358.00i 0.349646 + 0.349646i
\(99\) 15958.0i 1.62820i
\(100\) −4800.00 + 1400.00i −0.480000 + 0.140000i
\(101\) 1682.00 0.164886 0.0824429 0.996596i \(-0.473728\pi\)
0.0824429 + 0.996596i \(0.473728\pi\)
\(102\) −956.000 + 956.000i −0.0918877 + 0.0918877i
\(103\) 7021.00 + 7021.00i 0.661797 + 0.661797i 0.955803 0.294007i \(-0.0949888\pi\)
−0.294007 + 0.955803i \(0.594989\pi\)
\(104\) 3168.00i 0.292899i
\(105\) 570.000 760.000i 0.0517007 0.0689342i
\(106\) −7276.00 −0.647561
\(107\) −2159.00 + 2159.00i −0.188575 + 0.188575i −0.795080 0.606505i \(-0.792571\pi\)
0.606505 + 0.795080i \(0.292571\pi\)
\(108\) −1280.00 1280.00i −0.109739 0.109739i
\(109\) 280.000i 0.0235670i 0.999931 + 0.0117835i \(0.00375090\pi\)
−0.999931 + 0.0117835i \(0.996249\pi\)
\(110\) 2020.00 + 14140.0i 0.166942 + 1.16860i
\(111\) 282.000 0.0228878
\(112\) 1216.00 1216.00i 0.0969388 0.0969388i
\(113\) −8479.00 8479.00i −0.664030 0.664030i 0.292297 0.956327i \(-0.405580\pi\)
−0.956327 + 0.292297i \(0.905580\pi\)
\(114\) 160.000i 0.0123115i
\(115\) −18935.0 + 2705.00i −1.43176 + 0.204537i
\(116\) 1600.00 0.118906
\(117\) −7821.00 + 7821.00i −0.571335 + 0.571335i
\(118\) −9200.00 9200.00i −0.660730 0.660730i
\(119\) 9082.00i 0.641339i
\(120\) 640.000 + 480.000i 0.0444444 + 0.0333333i
\(121\) 26163.0 1.78697
\(122\) 4164.00 4164.00i 0.279764 0.279764i
\(123\) 1042.00 + 1042.00i 0.0688743 + 0.0688743i
\(124\) 6064.00i 0.394381i
\(125\) 14625.0 + 5500.00i 0.936000 + 0.352000i
\(126\) 6004.00 0.378181
\(127\) 821.000 821.000i 0.0509021 0.0509021i −0.681198 0.732100i \(-0.738541\pi\)
0.732100 + 0.681198i \(0.238541\pi\)
\(128\) 1024.00 + 1024.00i 0.0625000 + 0.0625000i
\(129\) 1518.00i 0.0912205i
\(130\) 5940.00 7920.00i 0.351479 0.468639i
\(131\) −2198.00 −0.128081 −0.0640406 0.997947i \(-0.520399\pi\)
−0.0640406 + 0.997947i \(0.520399\pi\)
\(132\) 1616.00 1616.00i 0.0927456 0.0927456i
\(133\) 760.000 + 760.000i 0.0429646 + 0.0429646i
\(134\) 20324.0i 1.13188i
\(135\) 800.000 + 5600.00i 0.0438957 + 0.307270i
\(136\) 7648.00 0.413495
\(137\) −9399.00 + 9399.00i −0.500773 + 0.500773i −0.911678 0.410905i \(-0.865213\pi\)
0.410905 + 0.911678i \(0.365213\pi\)
\(138\) 2164.00 + 2164.00i 0.113632 + 0.113632i
\(139\) 13960.0i 0.722530i 0.932463 + 0.361265i \(0.117655\pi\)
−0.932463 + 0.361265i \(0.882345\pi\)
\(140\) −5320.00 + 760.000i −0.271429 + 0.0387755i
\(141\) −918.000 −0.0461747
\(142\) −6956.00 + 6956.00i −0.344971 + 0.344971i
\(143\) −19998.0 19998.0i −0.977945 0.977945i
\(144\) 5056.00i 0.243827i
\(145\) −4000.00 3000.00i −0.190250 0.142687i
\(146\) −13916.0 −0.652843
\(147\) −1679.00 + 1679.00i −0.0776991 + 0.0776991i
\(148\) −1128.00 1128.00i −0.0514974 0.0514974i
\(149\) 9000.00i 0.405387i 0.979242 + 0.202694i \(0.0649695\pi\)
−0.979242 + 0.202694i \(0.935030\pi\)
\(150\) −700.000 2400.00i −0.0311111 0.106667i
\(151\) −23798.0 −1.04373 −0.521863 0.853029i \(-0.674763\pi\)
−0.521863 + 0.853029i \(0.674763\pi\)
\(152\) −640.000 + 640.000i −0.0277008 + 0.0277008i
\(153\) 18881.0 + 18881.0i 0.806570 + 0.806570i
\(154\) 15352.0i 0.647327i
\(155\) 11370.0 15160.0i 0.473257 0.631009i
\(156\) −1584.00 −0.0650888
\(157\) 29781.0 29781.0i 1.20820 1.20820i 0.236595 0.971608i \(-0.423969\pi\)
0.971608 0.236595i \(-0.0760314\pi\)
\(158\) 15360.0 + 15360.0i 0.615286 + 0.615286i
\(159\) 3638.00i 0.143903i
\(160\) −640.000 4480.00i −0.0250000 0.175000i
\(161\) −20558.0 −0.793102
\(162\) −12158.0 + 12158.0i −0.463268 + 0.463268i
\(163\) 12641.0 + 12641.0i 0.475780 + 0.475780i 0.903779 0.427999i \(-0.140781\pi\)
−0.427999 + 0.903779i \(0.640781\pi\)
\(164\) 8336.00i 0.309935i
\(165\) −7070.00 + 1010.00i −0.259688 + 0.0370983i
\(166\) 24324.0 0.882712
\(167\) 29981.0 29981.0i 1.07501 1.07501i 0.0780632 0.996948i \(-0.475126\pi\)
0.996948 0.0780632i \(-0.0248736\pi\)
\(168\) 608.000 + 608.000i 0.0215420 + 0.0215420i
\(169\) 8959.00i 0.313679i
\(170\) −19120.0 14340.0i −0.661592 0.496194i
\(171\) −3160.00 −0.108067
\(172\) −6072.00 + 6072.00i −0.205246 + 0.205246i
\(173\) −4739.00 4739.00i −0.158341 0.158341i 0.623490 0.781831i \(-0.285714\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(174\) 800.000i 0.0264236i
\(175\) 14725.0 + 8075.00i 0.480816 + 0.263673i
\(176\) −12928.0 −0.417355
\(177\) 4600.00 4600.00i 0.146829 0.146829i
\(178\) 11360.0 + 11360.0i 0.358541 + 0.358541i
\(179\) 32920.0i 1.02743i 0.857960 + 0.513717i \(0.171732\pi\)
−0.857960 + 0.513717i \(0.828268\pi\)
\(180\) 9480.00 12640.0i 0.292593 0.390123i
\(181\) −40558.0 −1.23800 −0.618998 0.785392i \(-0.712461\pi\)
−0.618998 + 0.785392i \(0.712461\pi\)
\(182\) 7524.00 7524.00i 0.227146 0.227146i
\(183\) 2082.00 + 2082.00i 0.0621697 + 0.0621697i
\(184\) 17312.0i 0.511342i
\(185\) 705.000 + 4935.00i 0.0205990 + 0.144193i
\(186\) −3032.00 −0.0876402
\(187\) −48278.0 + 48278.0i −1.38059 + 1.38059i
\(188\) 3672.00 + 3672.00i 0.103893 + 0.103893i
\(189\) 6080.00i 0.170208i
\(190\) 2800.00 400.000i 0.0775623 0.0110803i
\(191\) 33002.0 0.904635 0.452318 0.891857i \(-0.350597\pi\)
0.452318 + 0.891857i \(0.350597\pi\)
\(192\) −512.000 + 512.000i −0.0138889 + 0.0138889i
\(193\) −23199.0 23199.0i −0.622809 0.622809i 0.323440 0.946249i \(-0.395161\pi\)
−0.946249 + 0.323440i \(0.895161\pi\)
\(194\) 2244.00i 0.0596238i
\(195\) 3960.00 + 2970.00i 0.104142 + 0.0781065i
\(196\) 13432.0 0.349646
\(197\) −16899.0 + 16899.0i −0.435440 + 0.435440i −0.890474 0.455034i \(-0.849627\pi\)
0.455034 + 0.890474i \(0.349627\pi\)
\(198\) −31916.0 31916.0i −0.814101 0.814101i
\(199\) 14160.0i 0.357567i −0.983888 0.178783i \(-0.942784\pi\)
0.983888 0.178783i \(-0.0572161\pi\)
\(200\) −6800.00 + 12400.0i −0.170000 + 0.310000i
\(201\) 10162.0 0.251528
\(202\) 3364.00 3364.00i 0.0824429 0.0824429i
\(203\) −3800.00 3800.00i −0.0922129 0.0922129i
\(204\) 3824.00i 0.0918877i
\(205\) −15630.0 + 20840.0i −0.371921 + 0.495895i
\(206\) 28084.0 0.661797
\(207\) 42739.0 42739.0i 0.997433 0.997433i
\(208\) 6336.00 + 6336.00i 0.146450 + 0.146450i
\(209\) 8080.00i 0.184977i
\(210\) −380.000 2660.00i −0.00861678 0.0603175i
\(211\) 48842.0 1.09706 0.548528 0.836132i \(-0.315189\pi\)
0.548528 + 0.836132i \(0.315189\pi\)
\(212\) −14552.0 + 14552.0i −0.323781 + 0.323781i
\(213\) −3478.00 3478.00i −0.0766603 0.0766603i
\(214\) 8636.00i 0.188575i
\(215\) 26565.0 3795.00i 0.574689 0.0820984i
\(216\) −5120.00 −0.109739
\(217\) 14402.0 14402.0i 0.305846 0.305846i
\(218\) 560.000 + 560.000i 0.0117835 + 0.0117835i
\(219\) 6958.00i 0.145076i
\(220\) 32320.0 + 24240.0i 0.667769 + 0.500826i
\(221\) 47322.0 0.968899
\(222\) 564.000 564.000i 0.0114439 0.0114439i
\(223\) −35019.0 35019.0i −0.704197 0.704197i 0.261112 0.965309i \(-0.415911\pi\)
−0.965309 + 0.261112i \(0.915911\pi\)
\(224\) 4864.00i 0.0969388i
\(225\) −47400.0 + 13825.0i −0.936296 + 0.273086i
\(226\) −33916.0 −0.664030
\(227\) −68599.0 + 68599.0i −1.33127 + 1.33127i −0.427034 + 0.904235i \(0.640442\pi\)
−0.904235 + 0.427034i \(0.859558\pi\)
\(228\) −320.000 320.000i −0.00615574 0.00615574i
\(229\) 98760.0i 1.88326i −0.336651 0.941630i \(-0.609294\pi\)
0.336651 0.941630i \(-0.390706\pi\)
\(230\) −32460.0 + 43280.0i −0.613611 + 0.818147i
\(231\) −7676.00 −0.143850
\(232\) 3200.00 3200.00i 0.0594530 0.0594530i
\(233\) 53721.0 + 53721.0i 0.989537 + 0.989537i 0.999946 0.0104084i \(-0.00331314\pi\)
−0.0104084 + 0.999946i \(0.503313\pi\)
\(234\) 31284.0i 0.571335i
\(235\) −2295.00 16065.0i −0.0415573 0.290901i
\(236\) −36800.0 −0.660730
\(237\) −7680.00 + 7680.00i −0.136730 + 0.136730i
\(238\) −18164.0 18164.0i −0.320669 0.320669i
\(239\) 45600.0i 0.798305i 0.916884 + 0.399153i \(0.130696\pi\)
−0.916884 + 0.399153i \(0.869304\pi\)
\(240\) 2240.00 320.000i 0.0388889 0.00555556i
\(241\) −57038.0 −0.982042 −0.491021 0.871148i \(-0.663376\pi\)
−0.491021 + 0.871148i \(0.663376\pi\)
\(242\) 52326.0 52326.0i 0.893484 0.893484i
\(243\) −19039.0 19039.0i −0.322427 0.322427i
\(244\) 16656.0i 0.279764i
\(245\) −33580.0 25185.0i −0.559434 0.419575i
\(246\) 4168.00 0.0688743
\(247\) −3960.00 + 3960.00i −0.0649085 + 0.0649085i
\(248\) 12128.0 + 12128.0i 0.197190 + 0.197190i
\(249\) 12162.0i 0.196158i
\(250\) 40250.0 18250.0i 0.644000 0.292000i
\(251\) 39402.0 0.625419 0.312709 0.949849i \(-0.398763\pi\)
0.312709 + 0.949849i \(0.398763\pi\)
\(252\) 12008.0 12008.0i 0.189090 0.189090i
\(253\) 109282. + 109282.i 1.70729 + 1.70729i
\(254\) 3284.00i 0.0509021i
\(255\) 7170.00 9560.00i 0.110265 0.147020i
\(256\) 4096.00 0.0625000
\(257\) 31121.0 31121.0i 0.471180 0.471180i −0.431116 0.902297i \(-0.641880\pi\)
0.902297 + 0.431116i \(0.141880\pi\)
\(258\) −3036.00 3036.00i −0.0456102 0.0456102i
\(259\) 5358.00i 0.0798736i
\(260\) −3960.00 27720.0i −0.0585799 0.410059i
\(261\) 15800.0 0.231940
\(262\) −4396.00 + 4396.00i −0.0640406 + 0.0640406i
\(263\) −60739.0 60739.0i −0.878125 0.878125i 0.115216 0.993340i \(-0.463244\pi\)
−0.993340 + 0.115216i \(0.963244\pi\)
\(264\) 6464.00i 0.0927456i
\(265\) 63665.0 9095.00i 0.906586 0.129512i
\(266\) 3040.00 0.0429646
\(267\) −5680.00 + 5680.00i −0.0796757 + 0.0796757i
\(268\) −40648.0 40648.0i −0.565939 0.565939i
\(269\) 63800.0i 0.881690i 0.897583 + 0.440845i \(0.145321\pi\)
−0.897583 + 0.440845i \(0.854679\pi\)
\(270\) 12800.0 + 9600.00i 0.175583 + 0.131687i
\(271\) −113238. −1.54189 −0.770945 0.636901i \(-0.780216\pi\)
−0.770945 + 0.636901i \(0.780216\pi\)
\(272\) 15296.0 15296.0i 0.206747 0.206747i
\(273\) 3762.00 + 3762.00i 0.0504770 + 0.0504770i
\(274\) 37596.0i 0.500773i
\(275\) −35350.0 121200.i −0.467438 1.60264i
\(276\) 8656.00 0.113632
\(277\) −14739.0 + 14739.0i −0.192092 + 0.192092i −0.796599 0.604508i \(-0.793370\pi\)
0.604508 + 0.796599i \(0.293370\pi\)
\(278\) 27920.0 + 27920.0i 0.361265 + 0.361265i
\(279\) 59882.0i 0.769286i
\(280\) −9120.00 + 12160.0i −0.116327 + 0.155102i
\(281\) −7278.00 −0.0921721 −0.0460860 0.998937i \(-0.514675\pi\)
−0.0460860 + 0.998937i \(0.514675\pi\)
\(282\) −1836.00 + 1836.00i −0.0230874 + 0.0230874i
\(283\) 58601.0 + 58601.0i 0.731698 + 0.731698i 0.970956 0.239258i \(-0.0769041\pi\)
−0.239258 + 0.970956i \(0.576904\pi\)
\(284\) 27824.0i 0.344971i
\(285\) 200.000 + 1400.00i 0.00246230 + 0.0172361i
\(286\) −79992.0 −0.977945
\(287\) −19798.0 + 19798.0i −0.240357 + 0.240357i
\(288\) 10112.0 + 10112.0i 0.121914 + 0.121914i
\(289\) 30721.0i 0.367824i
\(290\) −14000.0 + 2000.00i −0.166468 + 0.0237812i
\(291\) 1122.00 0.0132497
\(292\) −27832.0 + 27832.0i −0.326421 + 0.326421i
\(293\) −95499.0 95499.0i −1.11241 1.11241i −0.992824 0.119582i \(-0.961844\pi\)
−0.119582 0.992824i \(-0.538156\pi\)
\(294\) 6716.00i 0.0776991i
\(295\) 92000.0 + 69000.0i 1.05717 + 0.792876i
\(296\) −4512.00 −0.0514974
\(297\) 32320.0 32320.0i 0.366403 0.366403i
\(298\) 18000.0 + 18000.0i 0.202694 + 0.202694i
\(299\) 107118.i 1.19817i
\(300\) −6200.00 3400.00i −0.0688889 0.0377778i
\(301\) 28842.0 0.318341
\(302\) −47596.0 + 47596.0i −0.521863 + 0.521863i
\(303\) 1682.00 + 1682.00i 0.0183206 + 0.0183206i
\(304\) 2560.00i 0.0277008i
\(305\) −31230.0 + 41640.0i −0.335716 + 0.447622i
\(306\) 75524.0 0.806570
\(307\) 38601.0 38601.0i 0.409564 0.409564i −0.472022 0.881587i \(-0.656476\pi\)
0.881587 + 0.472022i \(0.156476\pi\)
\(308\) 30704.0 + 30704.0i 0.323663 + 0.323663i
\(309\) 14042.0i 0.147066i
\(310\) −7580.00 53060.0i −0.0788762 0.552133i
\(311\) 29162.0 0.301506 0.150753 0.988571i \(-0.451830\pi\)
0.150753 + 0.988571i \(0.451830\pi\)
\(312\) −3168.00 + 3168.00i −0.0325444 + 0.0325444i
\(313\) 1881.00 + 1881.00i 0.0192000 + 0.0192000i 0.716642 0.697442i \(-0.245678\pi\)
−0.697442 + 0.716642i \(0.745678\pi\)
\(314\) 119124.i 1.20820i
\(315\) −52535.0 + 7505.00i −0.529453 + 0.0756362i
\(316\) 61440.0 0.615286
\(317\) 83781.0 83781.0i 0.833733 0.833733i −0.154292 0.988025i \(-0.549310\pi\)
0.988025 + 0.154292i \(0.0493097\pi\)
\(318\) −7276.00 7276.00i −0.0719513 0.0719513i
\(319\) 40400.0i 0.397009i
\(320\) −10240.0 7680.00i −0.100000 0.0750000i
\(321\) −4318.00 −0.0419056
\(322\) −41116.0 + 41116.0i −0.396551 + 0.396551i
\(323\) 9560.00 + 9560.00i 0.0916332 + 0.0916332i
\(324\) 48632.0i 0.463268i
\(325\) −42075.0 + 76725.0i −0.398343 + 0.726391i
\(326\) 50564.0 0.475780
\(327\) −280.000 + 280.000i −0.00261856 + 0.00261856i
\(328\) −16672.0 16672.0i −0.154967 0.154967i
\(329\) 17442.0i 0.161140i
\(330\) −12120.0 + 16160.0i −0.111295 + 0.148393i
\(331\) 106282. 0.970071 0.485036 0.874494i \(-0.338807\pi\)
0.485036 + 0.874494i \(0.338807\pi\)
\(332\) 48648.0 48648.0i 0.441356 0.441356i
\(333\) −11139.0 11139.0i −0.100452 0.100452i
\(334\) 119924.i 1.07501i
\(335\) 25405.0 + 177835.i 0.226376 + 1.58463i
\(336\) 2432.00 0.0215420
\(337\) −142479. + 142479.i −1.25456 + 1.25456i −0.300905 + 0.953654i \(0.597289\pi\)
−0.953654 + 0.300905i \(0.902711\pi\)
\(338\) −17918.0 17918.0i −0.156840 0.156840i
\(339\) 16958.0i 0.147562i
\(340\) −66920.0 + 9560.00i −0.578893 + 0.0826990i
\(341\) −153116. −1.31678
\(342\) −6320.00 + 6320.00i −0.0540337 + 0.0540337i
\(343\) −77520.0 77520.0i −0.658909 0.658909i
\(344\) 24288.0i 0.205246i
\(345\) −21640.0 16230.0i −0.181811 0.136358i
\(346\) −18956.0 −0.158341
\(347\) −6479.00 + 6479.00i −0.0538083 + 0.0538083i −0.733499 0.679691i \(-0.762114\pi\)
0.679691 + 0.733499i \(0.262114\pi\)
\(348\) 1600.00 + 1600.00i 0.0132118 + 0.0132118i
\(349\) 32920.0i 0.270277i −0.990827 0.135138i \(-0.956852\pi\)
0.990827 0.135138i \(-0.0431479\pi\)
\(350\) 45600.0 13300.0i 0.372245 0.108571i
\(351\) −31680.0 −0.257141
\(352\) −25856.0 + 25856.0i −0.208678 + 0.208678i
\(353\) −53919.0 53919.0i −0.432706 0.432706i 0.456842 0.889548i \(-0.348980\pi\)
−0.889548 + 0.456842i \(0.848980\pi\)
\(354\) 18400.0i 0.146829i
\(355\) 52170.0 69560.0i 0.413965 0.551954i
\(356\) 45440.0 0.358541
\(357\) 9082.00 9082.00i 0.0712599 0.0712599i
\(358\) 65840.0 + 65840.0i 0.513717 + 0.513717i
\(359\) 171760.i 1.33270i 0.745638 + 0.666351i \(0.232145\pi\)
−0.745638 + 0.666351i \(0.767855\pi\)
\(360\) −6320.00 44240.0i −0.0487654 0.341358i
\(361\) 128721. 0.987723
\(362\) −81116.0 + 81116.0i −0.618998 + 0.618998i
\(363\) 26163.0 + 26163.0i 0.198552 + 0.198552i
\(364\) 30096.0i 0.227146i
\(365\) 121765. 17395.0i 0.913980 0.130569i
\(366\) 8328.00 0.0621697
\(367\) 152261. 152261.i 1.13046 1.13046i 0.140363 0.990100i \(-0.455173\pi\)
0.990100 0.140363i \(-0.0448271\pi\)
\(368\) −34624.0 34624.0i −0.255671 0.255671i
\(369\) 82318.0i 0.604564i
\(370\) 11280.0 + 8460.00i 0.0823959 + 0.0617969i
\(371\) 69122.0 0.502190
\(372\) −6064.00 + 6064.00i −0.0438201 + 0.0438201i
\(373\) −71339.0 71339.0i −0.512754 0.512754i 0.402615 0.915369i \(-0.368101\pi\)
−0.915369 + 0.402615i \(0.868101\pi\)
\(374\) 193112.i 1.38059i
\(375\) 9125.00 + 20125.0i 0.0648889 + 0.143111i
\(376\) 14688.0 0.103893
\(377\) 19800.0 19800.0i 0.139310 0.139310i
\(378\) 12160.0 + 12160.0i 0.0851040 + 0.0851040i
\(379\) 172600.i 1.20161i −0.799397 0.600803i \(-0.794847\pi\)
0.799397 0.600803i \(-0.205153\pi\)
\(380\) 4800.00 6400.00i 0.0332410 0.0443213i
\(381\) 1642.00 0.0113116
\(382\) 66004.0 66004.0i 0.452318 0.452318i
\(383\) 158421. + 158421.i 1.07998 + 1.07998i 0.996510 + 0.0834683i \(0.0265997\pi\)
0.0834683 + 0.996510i \(0.473400\pi\)
\(384\) 2048.00i 0.0138889i
\(385\) −19190.0 134330.i −0.129465 0.906257i
\(386\) −92796.0 −0.622809
\(387\) −59961.0 + 59961.0i −0.400357 + 0.400357i
\(388\) −4488.00 4488.00i −0.0298119 0.0298119i
\(389\) 146760.i 0.969859i 0.874553 + 0.484929i \(0.161155\pi\)
−0.874553 + 0.484929i \(0.838845\pi\)
\(390\) 13860.0 1980.00i 0.0911243 0.0130178i
\(391\) −258598. −1.69150
\(392\) 26864.0 26864.0i 0.174823 0.174823i
\(393\) −2198.00 2198.00i −0.0142312 0.0142312i
\(394\) 67596.0i 0.435440i
\(395\) −153600. 115200.i −0.984458 0.738343i
\(396\) −127664. −0.814101
\(397\) −83579.0 + 83579.0i −0.530293 + 0.530293i −0.920660 0.390366i \(-0.872348\pi\)
0.390366 + 0.920660i \(0.372348\pi\)
\(398\) −28320.0 28320.0i −0.178783 0.178783i
\(399\) 1520.00i 0.00954768i
\(400\) 11200.0 + 38400.0i 0.0700000 + 0.240000i
\(401\) −42078.0 −0.261677 −0.130839 0.991404i \(-0.541767\pi\)
−0.130839 + 0.991404i \(0.541767\pi\)
\(402\) 20324.0 20324.0i 0.125764 0.125764i
\(403\) 75042.0 + 75042.0i 0.462056 + 0.462056i
\(404\) 13456.0i 0.0824429i
\(405\) 91185.0 121580.i 0.555921 0.741228i
\(406\) −15200.0 −0.0922129
\(407\) 28482.0 28482.0i 0.171942 0.171942i
\(408\) 7648.00 + 7648.00i 0.0459439 + 0.0459439i
\(409\) 300960.i 1.79913i 0.436789 + 0.899564i \(0.356116\pi\)
−0.436789 + 0.899564i \(0.643884\pi\)
\(410\) 10420.0 + 72940.0i 0.0619869 + 0.433908i
\(411\) −18798.0 −0.111283
\(412\) 56168.0 56168.0i 0.330898 0.330898i
\(413\) 87400.0 + 87400.0i 0.512403 + 0.512403i
\(414\) 170956.i 0.997433i
\(415\) −212835. + 30405.0i −1.23580 + 0.176542i
\(416\) 25344.0 0.146450
\(417\) −13960.0 + 13960.0i −0.0802811 + 0.0802811i
\(418\) −16160.0 16160.0i −0.0924887 0.0924887i
\(419\) 208680.i 1.18865i −0.804226 0.594323i \(-0.797420\pi\)
0.804226 0.594323i \(-0.202580\pi\)
\(420\) −6080.00 4560.00i −0.0344671 0.0258503i
\(421\) 86882.0 0.490191 0.245096 0.969499i \(-0.421181\pi\)
0.245096 + 0.969499i \(0.421181\pi\)
\(422\) 97684.0 97684.0i 0.548528 0.548528i
\(423\) 36261.0 + 36261.0i 0.202656 + 0.202656i
\(424\) 58208.0i 0.323781i
\(425\) 185225. + 101575.i 1.02547 + 0.562353i
\(426\) −13912.0 −0.0766603
\(427\) −39558.0 + 39558.0i −0.216959 + 0.216959i
\(428\) 17272.0 + 17272.0i 0.0942877 + 0.0942877i
\(429\) 39996.0i 0.217321i
\(430\) 45540.0 60720.0i 0.246295 0.328394i
\(431\) −125078. −0.673328 −0.336664 0.941625i \(-0.609299\pi\)
−0.336664 + 0.941625i \(0.609299\pi\)
\(432\) −10240.0 + 10240.0i −0.0548697 + 0.0548697i
\(433\) 5921.00 + 5921.00i 0.0315805 + 0.0315805i 0.722721 0.691140i \(-0.242891\pi\)
−0.691140 + 0.722721i \(0.742891\pi\)
\(434\) 57608.0i 0.305846i
\(435\) −1000.00 7000.00i −0.00528471 0.0369930i
\(436\) 2240.00 0.0117835
\(437\) 21640.0 21640.0i 0.113317 0.113317i
\(438\) −13916.0 13916.0i −0.0725381 0.0725381i
\(439\) 55280.0i 0.286840i −0.989662 0.143420i \(-0.954190\pi\)
0.989662 0.143420i \(-0.0458099\pi\)
\(440\) 113120. 16160.0i 0.584298 0.0834711i
\(441\) 132641. 0.682025
\(442\) 94644.0 94644.0i 0.484450 0.484450i
\(443\) 63561.0 + 63561.0i 0.323879 + 0.323879i 0.850253 0.526374i \(-0.176449\pi\)
−0.526374 + 0.850253i \(0.676449\pi\)
\(444\) 2256.00i 0.0114439i
\(445\) −113600. 85200.0i −0.573665 0.430249i
\(446\) −140076. −0.704197
\(447\) −9000.00 + 9000.00i −0.0450430 + 0.0450430i
\(448\) −9728.00 9728.00i −0.0484694 0.0484694i
\(449\) 204880.i 1.01626i −0.861279 0.508132i \(-0.830336\pi\)
0.861279 0.508132i \(-0.169664\pi\)
\(450\) −67150.0 + 122450.i −0.331605 + 0.604691i
\(451\) 210484. 1.03482
\(452\) −67832.0 + 67832.0i −0.332015 + 0.332015i
\(453\) −23798.0 23798.0i −0.115970 0.115970i
\(454\) 274396.i 1.33127i
\(455\) −56430.0 + 75240.0i −0.272576 + 0.363434i
\(456\) −1280.00 −0.00615574
\(457\) −10599.0 + 10599.0i −0.0507496 + 0.0507496i −0.732026 0.681277i \(-0.761425\pi\)
0.681277 + 0.732026i \(0.261425\pi\)
\(458\) −197520. 197520.i −0.941630 0.941630i
\(459\) 76480.0i 0.363013i
\(460\) 21640.0 + 151480.i 0.102268 + 0.715879i
\(461\) 224242. 1.05515 0.527576 0.849508i \(-0.323101\pi\)
0.527576 + 0.849508i \(0.323101\pi\)
\(462\) −15352.0 + 15352.0i −0.0719252 + 0.0719252i
\(463\) −243499. 243499.i −1.13589 1.13589i −0.989180 0.146707i \(-0.953132\pi\)
−0.146707 0.989180i \(-0.546868\pi\)
\(464\) 12800.0i 0.0594530i
\(465\) 26530.0 3790.00i 0.122696 0.0175280i
\(466\) 214884. 0.989537
\(467\) −226919. + 226919.i −1.04049 + 1.04049i −0.0413430 + 0.999145i \(0.513164\pi\)
−0.999145 + 0.0413430i \(0.986836\pi\)
\(468\) 62568.0 + 62568.0i 0.285667 + 0.285667i
\(469\) 193078.i 0.877783i
\(470\) −36720.0 27540.0i −0.166229 0.124672i
\(471\) 59562.0 0.268490
\(472\) −73600.0 + 73600.0i −0.330365 + 0.330365i
\(473\) −153318. 153318.i −0.685284 0.685284i
\(474\) 30720.0i 0.136730i
\(475\) −24000.0 + 7000.00i −0.106371 + 0.0310249i
\(476\) −72656.0 −0.320669
\(477\) −143701. + 143701.i −0.631572 + 0.631572i
\(478\) 91200.0 + 91200.0i 0.399153 + 0.399153i
\(479\) 334240.i 1.45676i −0.685174 0.728379i \(-0.740274\pi\)
0.685174 0.728379i \(-0.259726\pi\)
\(480\) 3840.00 5120.00i 0.0166667 0.0222222i
\(481\) −27918.0 −0.120669
\(482\) −114076. + 114076.i −0.491021 + 0.491021i
\(483\) −20558.0 20558.0i −0.0881225 0.0881225i
\(484\) 209304.i 0.893484i
\(485\) 2805.00 + 19635.0i 0.0119248 + 0.0834733i
\(486\) −76156.0 −0.322427
\(487\) 278541. 278541.i 1.17444 1.17444i 0.193302 0.981139i \(-0.438080\pi\)
0.981139 0.193302i \(-0.0619196\pi\)
\(488\) −33312.0 33312.0i −0.139882 0.139882i
\(489\) 25282.0i 0.105729i
\(490\) −117530. + 16790.0i −0.489504 + 0.0699292i
\(491\) −84118.0 −0.348920 −0.174460 0.984664i \(-0.555818\pi\)
−0.174460 + 0.984664i \(0.555818\pi\)
\(492\) 8336.00 8336.00i 0.0344372 0.0344372i
\(493\) −47800.0 47800.0i −0.196668 0.196668i
\(494\) 15840.0i 0.0649085i
\(495\) 319160. + 239370.i 1.30256 + 0.976921i
\(496\) 48512.0 0.197190
\(497\) 66082.0 66082.0i 0.267529 0.267529i
\(498\) 24324.0 + 24324.0i 0.0980791 + 0.0980791i
\(499\) 166840.i 0.670037i 0.942211 + 0.335019i \(0.108743\pi\)
−0.942211 + 0.335019i \(0.891257\pi\)
\(500\) 44000.0 117000.i 0.176000 0.468000i
\(501\) 59962.0 0.238891
\(502\) 78804.0 78804.0i 0.312709 0.312709i
\(503\) 190461. + 190461.i 0.752783 + 0.752783i 0.974998 0.222214i \(-0.0713285\pi\)
−0.222214 + 0.974998i \(0.571328\pi\)
\(504\) 48032.0i 0.189090i
\(505\) −25230.0 + 33640.0i −0.0989315 + 0.131909i
\(506\) 437128. 1.70729
\(507\) 8959.00 8959.00i 0.0348533 0.0348533i
\(508\) −6568.00 6568.00i −0.0254511 0.0254511i
\(509\) 223960.i 0.864440i −0.901768 0.432220i \(-0.857730\pi\)
0.901768 0.432220i \(-0.142270\pi\)
\(510\) −4780.00 33460.0i −0.0183775 0.128643i
\(511\) 132202. 0.506286
\(512\) 8192.00 8192.00i 0.0312500 0.0312500i
\(513\) −6400.00 6400.00i −0.0243190 0.0243190i
\(514\) 124484.i 0.471180i
\(515\) −245735. + 35105.0i −0.926515 + 0.132359i
\(516\) −12144.0 −0.0456102
\(517\) −92718.0 + 92718.0i −0.346883 + 0.346883i
\(518\) 10716.0 + 10716.0i 0.0399368 + 0.0399368i
\(519\) 9478.00i 0.0351870i
\(520\) −63360.0 47520.0i −0.234320 0.175740i
\(521\) −297918. −1.09754 −0.548771 0.835973i \(-0.684904\pi\)
−0.548771 + 0.835973i \(0.684904\pi\)
\(522\) 31600.0 31600.0i 0.115970 0.115970i
\(523\) 200601. + 200601.i 0.733381 + 0.733381i 0.971288 0.237907i \(-0.0764613\pi\)
−0.237907 + 0.971288i \(0.576461\pi\)
\(524\) 17584.0i 0.0640406i
\(525\) 6650.00 + 22800.0i 0.0241270 + 0.0827211i
\(526\) −242956. −0.878125
\(527\) 181162. 181162.i 0.652298 0.652298i
\(528\) −12928.0 12928.0i −0.0463728 0.0463728i
\(529\) 305521.i 1.09177i
\(530\) 109140. 145520.i 0.388537 0.518049i
\(531\) −363400. −1.28883
\(532\) 6080.00 6080.00i 0.0214823 0.0214823i
\(533\) −103158. 103158.i −0.363119 0.363119i
\(534\) 22720.0i 0.0796757i
\(535\) −10795.0 75565.0i −0.0377151 0.264006i
\(536\) −162592. −0.565939
\(537\) −32920.0 + 32920.0i −0.114159 + 0.114159i
\(538\) 127600. + 127600.i 0.440845 + 0.440845i
\(539\) 339158.i 1.16741i
\(540\) 44800.0 6400.00i 0.153635 0.0219479i
\(541\) −288398. −0.985366 −0.492683 0.870209i \(-0.663984\pi\)
−0.492683 + 0.870209i \(0.663984\pi\)
\(542\) −226476. + 226476.i −0.770945 + 0.770945i
\(543\) −40558.0 40558.0i −0.137555 0.137555i
\(544\) 61184.0i 0.206747i
\(545\) −5600.00 4200.00i −0.0188536 0.0141402i
\(546\) 15048.0 0.0504770
\(547\) 123081. 123081.i 0.411355 0.411355i −0.470856 0.882210i \(-0.656055\pi\)
0.882210 + 0.470856i \(0.156055\pi\)
\(548\) 75192.0 + 75192.0i 0.250386 + 0.250386i
\(549\) 164478.i 0.545712i
\(550\) −313100. 171700.i −1.03504 0.567603i
\(551\) 8000.00 0.0263504
\(552\) 17312.0 17312.0i 0.0568158 0.0568158i
\(553\) −145920. 145920.i −0.477161 0.477161i
\(554\) 58956.0i 0.192092i
\(555\) −4230.00 + 5640.00i −0.0137327 + 0.0183102i
\(556\) 111680. 0.361265
\(557\) 162261. 162261.i 0.523002 0.523002i −0.395474 0.918477i \(-0.629420\pi\)
0.918477 + 0.395474i \(0.129420\pi\)
\(558\) 119764. + 119764.i 0.384643 + 0.384643i
\(559\) 150282.i 0.480932i
\(560\) 6080.00 + 42560.0i 0.0193878 + 0.135714i
\(561\) −96556.0 −0.306799
\(562\) −14556.0 + 14556.0i −0.0460860 + 0.0460860i
\(563\) 264081. + 264081.i 0.833145 + 0.833145i 0.987946 0.154801i \(-0.0494737\pi\)
−0.154801 + 0.987946i \(0.549474\pi\)
\(564\) 7344.00i 0.0230874i
\(565\) 296765. 42395.0i 0.929642 0.132806i
\(566\) 234404. 0.731698
\(567\) 115501. 115501.i 0.359269 0.359269i
\(568\) 55648.0 + 55648.0i 0.172486 + 0.172486i
\(569\) 8320.00i 0.0256980i 0.999917 + 0.0128490i \(0.00409007\pi\)
−0.999917 + 0.0128490i \(0.995910\pi\)
\(570\) 3200.00 + 2400.00i 0.00984918 + 0.00738689i
\(571\) 283082. 0.868240 0.434120 0.900855i \(-0.357059\pi\)
0.434120 + 0.900855i \(0.357059\pi\)
\(572\) −159984. + 159984.i −0.488973 + 0.488973i
\(573\) 33002.0 + 33002.0i 0.100515 + 0.100515i
\(574\) 79192.0i 0.240357i
\(575\) 229925. 419275.i 0.695425 1.26813i
\(576\) 40448.0 0.121914
\(577\) 260401. 260401.i 0.782152 0.782152i −0.198042 0.980194i \(-0.563458\pi\)
0.980194 + 0.198042i \(0.0634582\pi\)
\(578\) −61442.0 61442.0i −0.183912 0.183912i
\(579\) 46398.0i 0.138402i
\(580\) −24000.0 + 32000.0i −0.0713436 + 0.0951249i
\(581\) −231078. −0.684552
\(582\) 2244.00 2244.00i 0.00662486 0.00662486i
\(583\) −367438. 367438.i −1.08105 1.08105i
\(584\) 111328.i 0.326421i
\(585\) −39105.0 273735.i −0.114267 0.799869i
\(586\) −381996. −1.11241
\(587\) −281439. + 281439.i −0.816786 + 0.816786i −0.985641 0.168855i \(-0.945993\pi\)
0.168855 + 0.985641i \(0.445993\pi\)
\(588\) 13432.0 + 13432.0i 0.0388496 + 0.0388496i
\(589\) 30320.0i 0.0873974i
\(590\) 322000. 46000.0i 0.925022 0.132146i
\(591\) −33798.0 −0.0967645
\(592\) −9024.00 + 9024.00i −0.0257487 + 0.0257487i
\(593\) 419761. + 419761.i 1.19369 + 1.19369i 0.976022 + 0.217671i \(0.0698460\pi\)
0.217671 + 0.976022i \(0.430154\pi\)
\(594\) 129280.i 0.366403i
\(595\) 181640. + 136230.i 0.513071 + 0.384803i
\(596\) 72000.0 0.202694
\(597\) 14160.0 14160.0i 0.0397296 0.0397296i
\(598\) −214236. 214236.i −0.599087 0.599087i
\(599\) 136240.i 0.379709i −0.981812 0.189855i \(-0.939198\pi\)
0.981812 0.189855i \(-0.0608016\pi\)
\(600\) −19200.0 + 5600.00i −0.0533333 + 0.0155556i
\(601\) 234962. 0.650502 0.325251 0.945628i \(-0.394551\pi\)
0.325251 + 0.945628i \(0.394551\pi\)
\(602\) 57684.0 57684.0i 0.159170 0.159170i
\(603\) −401399. 401399.i −1.10393 1.10393i
\(604\) 190384.i 0.521863i
\(605\) −392445. + 523260.i −1.07218 + 1.42957i
\(606\) 6728.00 0.0183206
\(607\) −406779. + 406779.i −1.10403 + 1.10403i −0.110111 + 0.993919i \(0.535121\pi\)
−0.993919 + 0.110111i \(0.964879\pi\)
\(608\) 5120.00 + 5120.00i 0.0138504 + 0.0138504i
\(609\) 7600.00i 0.0204917i
\(610\) 20820.0 + 145740.i 0.0559527 + 0.391669i
\(611\) 90882.0 0.243442
\(612\) 151048. 151048.i 0.403285 0.403285i
\(613\) 135621. + 135621.i 0.360916 + 0.360916i 0.864150 0.503234i \(-0.167857\pi\)
−0.503234 + 0.864150i \(0.667857\pi\)
\(614\) 154404.i 0.409564i
\(615\) −36470.0 + 5210.00i −0.0964241 + 0.0137749i
\(616\) 122816. 0.323663
\(617\) −151959. + 151959.i −0.399168 + 0.399168i −0.877940 0.478771i \(-0.841082\pi\)
0.478771 + 0.877940i \(0.341082\pi\)
\(618\) 28084.0 + 28084.0i 0.0735330 + 0.0735330i
\(619\) 22440.0i 0.0585655i 0.999571 + 0.0292827i \(0.00932231\pi\)
−0.999571 + 0.0292827i \(0.990678\pi\)
\(620\) −121280. 90960.0i −0.315505 0.236629i
\(621\) 173120. 0.448915
\(622\) 58324.0 58324.0i 0.150753 0.150753i
\(623\) −107920. 107920.i −0.278052 0.278052i
\(624\) 12672.0i 0.0325444i
\(625\) −329375. + 210000.i −0.843200 + 0.537600i
\(626\) 7524.00 0.0192000
\(627\) 8080.00 8080.00i 0.0205531 0.0205531i
\(628\) −238248. 238248.i −0.604102 0.604102i
\(629\) 67398.0i 0.170351i
\(630\) −90060.0 + 120080.i −0.226909 + 0.302545i
\(631\) −199958. −0.502204 −0.251102 0.967961i \(-0.580793\pi\)
−0.251102 + 0.967961i \(0.580793\pi\)
\(632\) 122880. 122880.i 0.307643 0.307643i
\(633\) 48842.0 + 48842.0i 0.121895 + 0.121895i
\(634\) 335124.i 0.833733i
\(635\) 4105.00 + 28735.0i 0.0101804 + 0.0712629i
\(636\) −29104.0 −0.0719513
\(637\) 166221. 166221.i 0.409644 0.409644i
\(638\) 80800.0 + 80800.0i 0.198504 + 0.198504i
\(639\) 274762.i 0.672907i
\(640\) −35840.0 + 5120.00i −0.0875000 + 0.0125000i
\(641\) 448562. 1.09171 0.545854 0.837880i \(-0.316205\pi\)
0.545854 + 0.837880i \(0.316205\pi\)
\(642\) −8636.00 + 8636.00i −0.0209528 + 0.0209528i
\(643\) 73041.0 + 73041.0i 0.176663 + 0.176663i 0.789899 0.613237i \(-0.210133\pi\)
−0.613237 + 0.789899i \(0.710133\pi\)
\(644\) 164464.i 0.396551i
\(645\) 30360.0 + 22770.0i 0.0729764 + 0.0547323i
\(646\) 38240.0 0.0916332
\(647\) −90259.0 + 90259.0i −0.215616 + 0.215616i −0.806648 0.591032i \(-0.798721\pi\)
0.591032 + 0.806648i \(0.298721\pi\)
\(648\) 97264.0 + 97264.0i 0.231634 + 0.231634i
\(649\) 929200.i 2.20607i
\(650\) 69300.0 + 237600.i 0.164024 + 0.562367i
\(651\) 28804.0 0.0679659
\(652\) 101128. 101128.i 0.237890 0.237890i
\(653\) −56019.0 56019.0i −0.131374 0.131374i 0.638362 0.769736i \(-0.279612\pi\)
−0.769736 + 0.638362i \(0.779612\pi\)
\(654\) 1120.00i 0.00261856i
\(655\) 32970.0 43960.0i 0.0768487 0.102465i
\(656\) −66688.0 −0.154967
\(657\) −274841. + 274841.i −0.636723 + 0.636723i
\(658\) −34884.0 34884.0i −0.0805702 0.0805702i
\(659\) 438920.i 1.01068i −0.862920 0.505341i \(-0.831367\pi\)
0.862920 0.505341i \(-0.168633\pi\)
\(660\) 8080.00 + 56560.0i 0.0185491 + 0.129844i
\(661\) 593762. 1.35897 0.679484 0.733690i \(-0.262204\pi\)
0.679484 + 0.733690i \(0.262204\pi\)
\(662\) 212564. 212564.i 0.485036 0.485036i
\(663\) 47322.0 + 47322.0i 0.107655 + 0.107655i
\(664\) 194592.i 0.441356i
\(665\) −26600.0 + 3800.00i −0.0601504 + 0.00859291i
\(666\) −44556.0 −0.100452
\(667\) −108200. + 108200.i −0.243207 + 0.243207i
\(668\) −239848. 239848.i −0.537506 0.537506i
\(669\) 70038.0i 0.156488i
\(670\) 406480. + 304860.i 0.905502 + 0.679127i
\(671\) 420564. 0.934086
\(672\) 4864.00 4864.00i 0.0107710 0.0107710i
\(673\) 424561. + 424561.i 0.937368 + 0.937368i 0.998151 0.0607833i \(-0.0193599\pi\)
−0.0607833 + 0.998151i \(0.519360\pi\)
\(674\) 569916.i 1.25456i
\(675\) −124000. 68000.0i −0.272154 0.149246i
\(676\) −71672.0 −0.156840
\(677\) 229021. 229021.i 0.499687 0.499687i −0.411654 0.911340i \(-0.635049\pi\)
0.911340 + 0.411654i \(0.135049\pi\)
\(678\) −33916.0 33916.0i −0.0737811 0.0737811i
\(679\) 21318.0i 0.0462388i
\(680\) −114720. + 152960.i −0.248097 + 0.330796i
\(681\) −137198. −0.295838
\(682\) −306232. + 306232.i −0.658388 + 0.658388i
\(683\) −450999. 450999.i −0.966795 0.966795i 0.0326716 0.999466i \(-0.489598\pi\)
−0.999466 + 0.0326716i \(0.989598\pi\)
\(684\) 25280.0i 0.0540337i
\(685\) −46995.0 328965.i −0.100155 0.701082i
\(686\) −310080. −0.658909
\(687\) 98760.0 98760.0i 0.209251 0.209251i
\(688\) 48576.0 + 48576.0i 0.102623 + 0.102623i
\(689\) 360162.i 0.758681i
\(690\) −75740.0 + 10820.0i −0.159084 + 0.0227263i
\(691\) −432438. −0.905665 −0.452833 0.891596i \(-0.649587\pi\)
−0.452833 + 0.891596i \(0.649587\pi\)
\(692\) −37912.0 + 37912.0i −0.0791707 + 0.0791707i
\(693\) 303202. + 303202.i 0.631343 + 0.631343i
\(694\) 25916.0i 0.0538083i
\(695\) −279200. 209400.i −0.578024 0.433518i
\(696\) 6400.00 0.0132118
\(697\) −249038. + 249038.i −0.512625 + 0.512625i
\(698\) −65840.0 65840.0i −0.135138 0.135138i
\(699\) 107442.i 0.219897i
\(700\) 64600.0 117800.i 0.131837 0.240408i
\(701\) −895838. −1.82303 −0.911514 0.411269i \(-0.865086\pi\)
−0.911514 + 0.411269i \(0.865086\pi\)
\(702\) −63360.0 + 63360.0i −0.128570 + 0.128570i
\(703\) −5640.00 5640.00i −0.0114122 0.0114122i
\(704\) 103424.i 0.208678i
\(705\) 13770.0 18360.0i 0.0277048 0.0369398i
\(706\) −215676. −0.432706
\(707\) −31958.0 + 31958.0i −0.0639353 + 0.0639353i
\(708\) −36800.0 36800.0i −0.0734144 0.0734144i
\(709\) 64360.0i 0.128033i −0.997949 0.0640167i \(-0.979609\pi\)
0.997949 0.0640167i \(-0.0203911\pi\)
\(710\) −34780.0 243460.i −0.0689942 0.482960i
\(711\) 606720. 1.20019
\(712\) 90880.0 90880.0i 0.179270 0.179270i
\(713\) −410078. 410078.i −0.806654 0.806654i
\(714\) 36328.0i 0.0712599i
\(715\) 699930. 99990.0i 1.36912 0.195589i
\(716\) 263360. 0.513717
\(717\) −45600.0 + 45600.0i −0.0887006 + 0.0887006i
\(718\) 343520. + 343520.i 0.666351 + 0.666351i
\(719\) 239840.i 0.463942i 0.972723 + 0.231971i \(0.0745175\pi\)
−0.972723 + 0.231971i \(0.925483\pi\)
\(720\) −101120. 75840.0i −0.195062 0.146296i
\(721\) −266798. −0.513230
\(722\) 257442. 257442.i 0.493861 0.493861i
\(723\) −57038.0 57038.0i −0.109116 0.109116i
\(724\) 324464.i 0.618998i
\(725\) 120000. 35000.0i 0.228300 0.0665874i
\(726\) 104652. 0.198552
\(727\) −438339. + 438339.i −0.829357 + 0.829357i −0.987428 0.158071i \(-0.949472\pi\)
0.158071 + 0.987428i \(0.449472\pi\)
\(728\) −60192.0 60192.0i −0.113573 0.113573i
\(729\) 454321.i 0.854885i
\(730\) 208740. 278320.i 0.391706 0.522274i
\(731\) 362802. 0.678946
\(732\) 16656.0 16656.0i 0.0310848 0.0310848i
\(733\) 145261. + 145261.i 0.270359 + 0.270359i 0.829245 0.558886i \(-0.188771\pi\)
−0.558886 + 0.829245i \(0.688771\pi\)
\(734\) 609044.i 1.13046i
\(735\) −8395.00 58765.0i −0.0155398 0.108779i
\(736\) −138496. −0.255671
\(737\) 1.02636e6 1.02636e6i 1.88958 1.88958i
\(738\) −164636. 164636.i −0.302282 0.302282i
\(739\) 738040.i 1.35142i 0.737167 + 0.675711i \(0.236163\pi\)
−0.737167 + 0.675711i \(0.763837\pi\)
\(740\) 39480.0 5640.00i 0.0720964 0.0102995i
\(741\) −7920.00 −0.0144241
\(742\) 138244. 138244.i 0.251095 0.251095i
\(743\) 579101. + 579101.i 1.04900 + 1.04900i 0.998736 + 0.0502671i \(0.0160073\pi\)
0.0502671 + 0.998736i \(0.483993\pi\)
\(744\) 24256.0i 0.0438201i
\(745\) −180000. 135000.i −0.324310 0.243232i
\(746\) −285356. −0.512754
\(747\) 480399. 480399.i 0.860916 0.860916i
\(748\) 386224. + 386224.i 0.690297 + 0.690297i
\(749\) 82042.0i 0.146242i
\(750\) 58500.0 + 22000.0i 0.104000 + 0.0391111i
\(751\) −495318. −0.878222 −0.439111 0.898433i \(-0.644706\pi\)
−0.439111 + 0.898433i \(0.644706\pi\)
\(752\) 29376.0 29376.0i 0.0519466 0.0519466i
\(753\) 39402.0 + 39402.0i 0.0694910 + 0.0694910i
\(754\) 79200.0i 0.139310i
\(755\) 356970. 475960.i 0.626236 0.834981i
\(756\) 48640.0 0.0851040
\(757\) −536979. + 536979.i −0.937056 + 0.937056i −0.998133 0.0610771i \(-0.980546\pi\)
0.0610771 + 0.998133i \(0.480546\pi\)
\(758\) −345200. 345200.i −0.600803 0.600803i
\(759\) 218564.i 0.379398i
\(760\) −3200.00 22400.0i −0.00554017 0.0387812i
\(761\) −908798. −1.56927 −0.784636 0.619957i \(-0.787150\pi\)
−0.784636 + 0.619957i \(0.787150\pi\)
\(762\) 3284.00 3284.00i 0.00565579 0.00565579i
\(763\) −5320.00 5320.00i −0.00913824 0.00913824i
\(764\) 264016.i 0.452318i
\(765\) −660835. + 94405.0i −1.12920 + 0.161314i
\(766\) 633684. 1.07998
\(767\) −455400. + 455400.i −0.774109 + 0.774109i
\(768\) 4096.00 + 4096.00i 0.00694444 + 0.00694444i
\(769\) 1.02704e6i 1.73674i −0.495917 0.868370i \(-0.665168\pi\)
0.495917 0.868370i \(-0.334832\pi\)
\(770\) −307040. 230280.i −0.517861 0.388396i
\(771\) 62242.0 0.104707
\(772\) −185592. + 185592.i −0.311404 + 0.311404i
\(773\) 161061. + 161061.i 0.269545 + 0.269545i 0.828917 0.559372i \(-0.188958\pi\)
−0.559372 + 0.828917i \(0.688958\pi\)
\(774\) 239844.i 0.400357i
\(775\) 132650. + 454800.i 0.220853 + 0.757211i
\(776\) −17952.0 −0.0298119
\(777\) −5358.00 + 5358.00i −0.00887484 + 0.00887484i
\(778\) 293520. + 293520.i 0.484929 + 0.484929i
\(779\) 41680.0i 0.0686836i
\(780\) 23760.0 31680.0i 0.0390533 0.0520710i
\(781\) −702556. −1.15180
\(782\) −517196. + 517196.i −0.845749 + 0.845749i
\(783\) 32000.0 + 32000.0i 0.0521947 + 0.0521947i
\(784\) 107456.i 0.174823i
\(785\) 148905. + 1.04234e6i 0.241641 + 1.69148i
\(786\) −8792.00 −0.0142312
\(787\) 772201. 772201.i 1.24675 1.24675i 0.289609 0.957145i \(-0.406475\pi\)
0.957145 0.289609i \(-0.0935254\pi\)
\(788\) 135192. + 135192.i 0.217720 + 0.217720i
\(789\) 121478.i 0.195139i
\(790\) −537600. + 76800.0i −0.861400 + 0.123057i
\(791\) 322202. 0.514962
\(792\) −255328. + 255328.i −0.407050 + 0.407050i
\(793\) −206118. 206118.i −0.327770 0.327770i
\(794\) 334316.i 0.530293i
\(795\) 72760.0 + 54570.0i 0.115122 + 0.0863415i
\(796\) −113280. −0.178783
\(797\) 299781. 299781.i 0.471941 0.471941i −0.430601 0.902542i \(-0.641699\pi\)
0.902542 + 0.430601i \(0.141699\pi\)
\(798\) 3040.00 + 3040.00i 0.00477384 + 0.00477384i
\(799\) 219402.i 0.343674i
\(800\) 99200.0 + 54400.0i 0.155000 + 0.0850000i
\(801\) 448720. 0.699375
\(802\) −84156.0 + 84156.0i −0.130839 + 0.130839i
\(803\) −702758. 702758.i −1.08987 1.08987i
\(804\) 81296.0i 0.125764i
\(805\) 308370. 411160.i 0.475861 0.634482i
\(806\) 300168. 0.462056
\(807\) −63800.0 + 63800.0i −0.0979656 + 0.0979656i
\(808\) −26912.0 26912.0i −0.0412214 0.0412214i
\(809\) 897040.i 1.37061i 0.728255 + 0.685306i \(0.240332\pi\)
−0.728255 + 0.685306i \(0.759668\pi\)
\(810\) −60790.0 425530.i −0.0926536 0.648575i
\(811\) −115798. −0.176059 −0.0880297 0.996118i \(-0.528057\pi\)
−0.0880297 + 0.996118i \(0.528057\pi\)
\(812\) −30400.0 + 30400.0i −0.0461064 + 0.0461064i
\(813\) −113238. 113238.i −0.171321 0.171321i
\(814\) 113928.i 0.171942i
\(815\) −442435. + 63205.0i −0.666092 + 0.0951560i
\(816\) 30592.0 0.0459439
\(817\) −30360.0 + 30360.0i −0.0454839 + 0.0454839i
\(818\) 601920. + 601920.i 0.899564 + 0.899564i
\(819\) 297198.i 0.443076i
\(820\) 166720. + 125040.i 0.247948 + 0.185961i
\(821\) 1.24160e6 1.84203 0.921014 0.389530i \(-0.127363\pi\)
0.921014 + 0.389530i \(0.127363\pi\)
\(822\) −37596.0 + 37596.0i −0.0556414 + 0.0556414i
\(823\) −13219.0 13219.0i −0.0195164 0.0195164i 0.697281 0.716798i \(-0.254393\pi\)
−0.716798 + 0.697281i \(0.754393\pi\)
\(824\) 224672.i 0.330898i
\(825\) 85850.0 156550.i 0.126134 0.230009i
\(826\) 349600. 0.512403
\(827\) 394641. 394641.i 0.577020 0.577020i −0.357061 0.934081i \(-0.616221\pi\)
0.934081 + 0.357061i \(0.116221\pi\)
\(828\) −341912. 341912.i −0.498716 0.498716i
\(829\) 694760.i 1.01094i −0.862844 0.505470i \(-0.831319\pi\)
0.862844 0.505470i \(-0.168681\pi\)
\(830\) −364860. + 486480.i −0.529627 + 0.706169i
\(831\) −29478.0 −0.0426870
\(832\) 50688.0 50688.0i 0.0732249 0.0732249i
\(833\) −401281. 401281.i −0.578307 0.578307i
\(834\) 55840.0i 0.0802811i
\(835\) 149905. + 1.04934e6i 0.215002 + 1.50502i
\(836\) −64640.0 −0.0924887
\(837\) −121280. + 121280.i −0.173116 + 0.173116i
\(838\) −417360. 417360.i −0.594323 0.594323i
\(839\) 124400.i 0.176724i −0.996088 0.0883622i \(-0.971837\pi\)
0.996088 0.0883622i \(-0.0281633\pi\)
\(840\) −21280.0 + 3040.00i −0.0301587 + 0.00430839i
\(841\) 667281. 0.943445
\(842\) 173764. 173764.i 0.245096 0.245096i
\(843\) −7278.00 7278.00i −0.0102413 0.0102413i
\(844\) 390736.i 0.548528i
\(845\) 179180. + 134385.i 0.250944 + 0.188208i
\(846\) 145044. 0.202656
\(847\) −497097. + 497097.i −0.692906 + 0.692906i
\(848\) 116416. + 116416.i 0.161890 + 0.161890i
\(849\) 117202.i 0.162600i
\(850\) 573600. 167300.i 0.793910 0.231557i
\(851\) 152562. 0.210663
\(852\) −27824.0 + 27824.0i −0.0383301 + 0.0383301i
\(853\) −432299. 432299.i −0.594136 0.594136i 0.344610 0.938746i \(-0.388011\pi\)
−0.938746 + 0.344610i \(0.888011\pi\)
\(854\) 158232.i 0.216959i
\(855\) 47400.0 63200.0i 0.0648405 0.0864540i
\(856\) 69088.0 0.0942877
\(857\) −669159. + 669159.i −0.911103 + 0.911103i −0.996359 0.0852557i \(-0.972829\pi\)
0.0852557 + 0.996359i \(0.472829\pi\)
\(858\) −79992.0 79992.0i −0.108661 0.108661i
\(859\) 370040.i 0.501490i −0.968053 0.250745i \(-0.919324\pi\)
0.968053 0.250745i \(-0.0806756\pi\)
\(860\) −30360.0 212520.i −0.0410492 0.287345i
\(861\) −39596.0 −0.0534128
\(862\) −250156. + 250156.i −0.336664 + 0.336664i
\(863\) 490981. + 490981.i 0.659239 + 0.659239i 0.955200 0.295961i \(-0.0956398\pi\)
−0.295961 + 0.955200i \(0.595640\pi\)
\(864\) 40960.0i 0.0548697i
\(865\) 165865. 23695.0i 0.221678 0.0316683i
\(866\) 23684.0 0.0315805
\(867\) 30721.0 30721.0i 0.0408693 0.0408693i
\(868\) −115216. 115216.i −0.152923 0.152923i
\(869\) 1.55136e6i 2.05434i
\(870\) −16000.0 12000.0i −0.0211389 0.0158541i
\(871\) −1.00604e6 −1.32611
\(872\) 4480.00 4480.00i 0.00589176 0.00589176i
\(873\) −44319.0 44319.0i −0.0581516 0.0581516i
\(874\) 86560.0i 0.113317i
\(875\) −382375. + 173375.i −0.499429 + 0.226449i
\(876\) −55664.0 −0.0725381
\(877\) 206181. 206181.i 0.268071 0.268071i −0.560252 0.828322i \(-0.689296\pi\)
0.828322 + 0.560252i \(0.189296\pi\)
\(878\) −110560. 110560.i −0.143420 0.143420i
\(879\) 190998.i 0.247201i
\(880\) 193920. 258560.i 0.250413 0.333884i
\(881\) −118478. −0.152646 −0.0763231 0.997083i \(-0.524318\pi\)
−0.0763231 + 0.997083i \(0.524318\pi\)
\(882\) 265282. 265282.i 0.341013 0.341013i
\(883\) −204719. 204719.i −0.262565 0.262565i 0.563530 0.826095i \(-0.309443\pi\)
−0.826095 + 0.563530i \(0.809443\pi\)
\(884\) 378576.i 0.484450i
\(885\) 23000.0 + 161000.i 0.0293658 + 0.205560i
\(886\) 254244. 0.323879
\(887\) −562179. + 562179.i −0.714541 + 0.714541i −0.967482 0.252940i \(-0.918602\pi\)
0.252940 + 0.967482i \(0.418602\pi\)
\(888\) −4512.00 4512.00i −0.00572194 0.00572194i
\(889\) 31198.0i 0.0394751i
\(890\) −397600. + 56800.0i −0.501957 + 0.0717081i
\(891\) −1.22796e6 −1.54678
\(892\) −280152. + 280152.i −0.352098 + 0.352098i
\(893\) 18360.0 + 18360.0i 0.0230234 + 0.0230234i
\(894\) 36000.0i 0.0450430i
\(895\) −658400. 493800.i −0.821947 0.616460i
\(896\) −38912.0 −0.0484694
\(897\) 107118. 107118.i 0.133131 0.133131i
\(898\) −409760. 409760.i −0.508132 0.508132i
\(899\) 151600.i 0.187577i
\(900\) 110600. + 379200.i 0.136543 + 0.468148i
\(901\) 869482. 1.07105
\(902\) 420968. 420968.i 0.517411 0.517411i
\(903\) 28842.0 + 28842.0i 0.0353712 + 0.0353712i
\(904\) 271328.i 0.332015i
\(905\) 608370. 811160.i 0.742798 0.990397i
\(906\) −95192.0 −0.115970
\(907\) 492241. 492241.i 0.598361 0.598361i −0.341515 0.939876i \(-0.610940\pi\)
0.939876 + 0.341515i \(0.110940\pi\)
\(908\) 548792. + 548792.i 0.665635 + 0.665635i
\(909\) 132878.i 0.160815i
\(910\) 37620.0 + 263340.i 0.0454293 + 0.318005i
\(911\) 1.15284e6 1.38910 0.694549 0.719445i \(-0.255604\pi\)
0.694549 + 0.719445i \(0.255604\pi\)
\(912\) −2560.00 + 2560.00i −0.00307787 + 0.00307787i
\(913\) 1.22836e6 + 1.22836e6i 1.47362 + 1.47362i
\(914\) 42396.0i 0.0507496i
\(915\) −72870.0 + 10410.0i −0.0870375 + 0.0124339i
\(916\) −790080. −0.941630
\(917\) 41762.0 41762.0i 0.0496641 0.0496641i
\(918\) 152960. + 152960.i 0.181507 + 0.181507i
\(919\) 337520.i 0.399640i −0.979833 0.199820i \(-0.935964\pi\)
0.979833 0.199820i \(-0.0640357\pi\)
\(920\) 346240. + 259680.i 0.409074 + 0.306805i
\(921\) 77202.0 0.0910142
\(922\) 448484. 448484.i 0.527576 0.527576i
\(923\) 344322. + 344322.i 0.404167 + 0.404167i
\(924\) 61408.0i 0.0719252i
\(925\) −109275. 59925.0i −0.127714 0.0700365i
\(926\) −973996. −1.13589
\(927\) 554659. 554659.i 0.645456 0.645456i
\(928\) −25600.0 25600.0i −0.0297265 0.0297265i
\(929\) 760240.i 0.880885i −0.897781 0.440443i \(-0.854822\pi\)
0.897781 0.440443i \(-0.145178\pi\)
\(930\) 45480.0 60640.0i 0.0525841 0.0701122i
\(931\) 67160.0 0.0774839
\(932\) 429768. 429768.i 0.494769 0.494769i
\(933\) 29162.0 + 29162.0i 0.0335007 + 0.0335007i
\(934\) 907676.i 1.04049i
\(935\) −241390. 1.68973e6i −0.276119 1.93283i
\(936\) 250272. 0.285667
\(937\) 75721.0 75721.0i 0.0862456 0.0862456i −0.662668 0.748913i \(-0.730576\pi\)
0.748913 + 0.662668i \(0.230576\pi\)
\(938\) 386156. + 386156.i 0.438891 + 0.438891i
\(939\) 3762.00i 0.00426666i
\(940\) −128520. + 18360.0i −0.145450 + 0.0207786i
\(941\) −1.16552e6 −1.31625 −0.658127 0.752907i \(-0.728651\pi\)
−0.658127 + 0.752907i \(0.728651\pi\)
\(942\) 119124. 119124.i 0.134245 0.134245i
\(943\) 563722. + 563722.i 0.633930 + 0.633930i
\(944\) 294400.i 0.330365i
\(945\) −121600. 91200.0i −0.136166 0.102125i
\(946\) −613272. −0.685284
\(947\) −331639. + 331639.i −0.369799 + 0.369799i −0.867404 0.497605i \(-0.834213\pi\)
0.497605 + 0.867404i \(0.334213\pi\)
\(948\) 61440.0 + 61440.0i 0.0683651 + 0.0683651i
\(949\) 688842.i 0.764869i
\(950\) −34000.0 + 62000.0i −0.0376731 + 0.0686981i
\(951\) 167562. 0.185274
\(952\) −145312. + 145312.i −0.160335 + 0.160335i
\(953\) −573639. 573639.i −0.631616 0.631616i 0.316858 0.948473i \(-0.397372\pi\)
−0.948473 + 0.316858i \(0.897372\pi\)
\(954\) 574804.i 0.631572i
\(955\) −495030. + 660040.i −0.542781 + 0.723708i
\(956\) 364800. 0.399153
\(957\) −40400.0 + 40400.0i −0.0441121 + 0.0441121i
\(958\) −668480. 668480.i −0.728379 0.728379i
\(959\) 357162.i 0.388354i
\(960\) −2560.00 17920.0i −0.00277778 0.0194444i
\(961\) −348957. −0.377855
\(962\) −55836.0 + 55836.0i −0.0603343 + 0.0603343i
\(963\) 170561. + 170561.i 0.183919 + 0.183919i
\(964\) 456304.i 0.491021i
\(965\) 811965. 115995.i 0.871932 0.124562i
\(966\) −82232.0 −0.0881225
\(967\) −49859.0 + 49859.0i −0.0533201 + 0.0533201i −0.733264 0.679944i \(-0.762004\pi\)
0.679944 + 0.733264i \(0.262004\pi\)
\(968\) −418608. 418608.i −0.446742 0.446742i
\(969\) 19120.0i 0.0203629i
\(970\) 44880.0 + 33660.0i 0.0476990 + 0.0357743i
\(971\) −1.41132e6 −1.49688 −0.748439 0.663204i \(-0.769196\pi\)
−0.748439 + 0.663204i \(0.769196\pi\)
\(972\) −152312. + 152312.i −0.161214 + 0.161214i
\(973\) −265240. 265240.i −0.280165 0.280165i
\(974\) 1.11416e6i 1.17444i
\(975\) −118800. + 34650.0i −0.124970 + 0.0364497i
\(976\) −133248. −0.139882
\(977\) −708639. + 708639.i −0.742397 + 0.742397i −0.973039 0.230642i \(-0.925917\pi\)
0.230642 + 0.973039i \(0.425917\pi\)
\(978\) 50564.0 + 50564.0i 0.0528644 + 0.0528644i
\(979\) 1.14736e6i 1.19711i
\(980\) −201480. + 268640.i −0.209788 + 0.279717i
\(981\) 22120.0 0.0229851
\(982\) −168236. + 168236.i −0.174460 + 0.174460i
\(983\) 234221. + 234221.i 0.242392 + 0.242392i 0.817839 0.575447i \(-0.195172\pi\)
−0.575447 + 0.817839i \(0.695172\pi\)
\(984\) 33344.0i 0.0344372i
\(985\) −84495.0 591465.i −0.0870880 0.609616i
\(986\) −191200. −0.196668
\(987\) 17442.0 17442.0i 0.0179045 0.0179045i
\(988\) 31680.0 + 31680.0i 0.0324542 + 0.0324542i
\(989\) 821238.i 0.839608i
\(990\) 1.11706e6 159580.i 1.13974 0.162820i
\(991\) 898762. 0.915161 0.457580 0.889168i \(-0.348716\pi\)
0.457580 + 0.889168i \(0.348716\pi\)
\(992\) 97024.0 97024.0i 0.0985952 0.0985952i
\(993\) 106282. + 106282.i 0.107786 + 0.107786i
\(994\) 264328.i 0.267529i
\(995\) 283200. + 212400.i 0.286053 + 0.214540i
\(996\) 97296.0 0.0980791
\(997\) −223379. + 223379.i −0.224725 + 0.224725i −0.810485 0.585760i \(-0.800796\pi\)
0.585760 + 0.810485i \(0.300796\pi\)
\(998\) 333680. + 333680.i 0.335019 + 0.335019i
\(999\) 45120.0i 0.0452104i
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 10.5.c.b.3.1 2
3.2 odd 2 90.5.g.a.73.1 2
4.3 odd 2 80.5.p.c.33.1 2
5.2 odd 4 inner 10.5.c.b.7.1 yes 2
5.3 odd 4 50.5.c.a.7.1 2
5.4 even 2 50.5.c.a.43.1 2
8.3 odd 2 320.5.p.g.193.1 2
8.5 even 2 320.5.p.d.193.1 2
15.2 even 4 90.5.g.a.37.1 2
15.8 even 4 450.5.g.b.307.1 2
15.14 odd 2 450.5.g.b.343.1 2
20.3 even 4 400.5.p.b.257.1 2
20.7 even 4 80.5.p.c.17.1 2
20.19 odd 2 400.5.p.b.193.1 2
40.27 even 4 320.5.p.g.257.1 2
40.37 odd 4 320.5.p.d.257.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
10.5.c.b.3.1 2 1.1 even 1 trivial
10.5.c.b.7.1 yes 2 5.2 odd 4 inner
50.5.c.a.7.1 2 5.3 odd 4
50.5.c.a.43.1 2 5.4 even 2
80.5.p.c.17.1 2 20.7 even 4
80.5.p.c.33.1 2 4.3 odd 2
90.5.g.a.37.1 2 15.2 even 4
90.5.g.a.73.1 2 3.2 odd 2
320.5.p.d.193.1 2 8.5 even 2
320.5.p.d.257.1 2 40.37 odd 4
320.5.p.g.193.1 2 8.3 odd 2
320.5.p.g.257.1 2 40.27 even 4
400.5.p.b.193.1 2 20.19 odd 2
400.5.p.b.257.1 2 20.3 even 4
450.5.g.b.307.1 2 15.8 even 4
450.5.g.b.343.1 2 15.14 odd 2