Properties

Label 825.2.bx.b.724.2
Level $825$
Weight $2$
Character 825.724
Analytic conductor $6.588$
Analytic rank $0$
Dimension $8$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [825,2,Mod(49,825)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(825, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 5, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("825.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.bx (of order \(10\), degree \(4\), 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: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{20})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 724.2
Root \(0.587785 - 0.809017i\) of defining polynomial
Character \(\chi\) \(=\) 825.724
Dual form 825.2.bx.b.49.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.587785 + 0.190983i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-1.30902 - 0.951057i) q^{4} +(-0.190983 - 0.587785i) q^{6} +(-1.76336 + 2.42705i) q^{7} +(-1.31433 - 1.80902i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(1.69098 + 2.85317i) q^{11} +1.61803i q^{12} +(1.67760 + 0.545085i) q^{13} +(-1.50000 + 1.08981i) q^{14} +(0.572949 + 1.76336i) q^{16} +(1.53884 - 0.500000i) q^{17} +(-0.363271 + 0.500000i) q^{18} +(4.73607 - 3.44095i) q^{19} +3.00000 q^{21} +(0.449028 + 2.00000i) q^{22} +3.47214i q^{23} +(-0.690983 + 2.12663i) q^{24} +(0.881966 + 0.640786i) q^{26} +(0.951057 - 0.309017i) q^{27} +(4.61653 - 1.50000i) q^{28} +(3.61803 + 2.62866i) q^{29} +(0.881966 - 2.71441i) q^{31} +5.61803i q^{32} +(1.31433 - 3.04508i) q^{33} +1.00000 q^{34} +(1.30902 - 0.951057i) q^{36} +(-0.138757 + 0.190983i) q^{37} +(3.44095 - 1.11803i) q^{38} +(-0.545085 - 1.67760i) q^{39} +(9.66312 - 7.02067i) q^{41} +(1.76336 + 0.572949i) q^{42} +6.23607i q^{43} +(0.500000 - 5.34307i) q^{44} +(-0.663119 + 2.04087i) q^{46} +(0.951057 + 1.30902i) q^{47} +(1.08981 - 1.50000i) q^{48} +(-0.618034 - 1.90211i) q^{49} +(-1.30902 - 0.951057i) q^{51} +(-1.67760 - 2.30902i) q^{52} +(-9.14729 - 2.97214i) q^{53} +0.618034 q^{54} +6.70820 q^{56} +(-5.56758 - 1.80902i) q^{57} +(1.62460 + 2.23607i) q^{58} +(8.35410 + 6.06961i) q^{59} +(2.42705 + 7.46969i) q^{61} +(1.03681 - 1.42705i) q^{62} +(-1.76336 - 2.42705i) q^{63} +(0.0729490 - 0.224514i) q^{64} +(1.35410 - 1.53884i) q^{66} +9.56231i q^{67} +(-2.48990 - 0.809017i) q^{68} +(2.80902 - 2.04087i) q^{69} +(-1.71885 - 5.29007i) q^{71} +(2.12663 - 0.690983i) q^{72} +(-1.90211 + 2.61803i) q^{73} +(-0.118034 + 0.0857567i) q^{74} -9.47214 q^{76} +(-9.90659 - 0.927051i) q^{77} -1.09017i q^{78} +(-2.92705 + 9.00854i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(7.02067 - 2.28115i) q^{82} +(-0.673542 + 0.218847i) q^{83} +(-3.92705 - 2.85317i) q^{84} +(-1.19098 + 3.66547i) q^{86} -4.47214i q^{87} +(2.93893 - 6.80902i) q^{88} -0.527864 q^{89} +(-4.28115 + 3.11044i) q^{91} +(3.30220 - 4.54508i) q^{92} +(-2.71441 + 0.881966i) q^{93} +(0.309017 + 0.951057i) q^{94} +(4.54508 - 3.30220i) q^{96} +(13.3475 + 4.33688i) q^{97} -1.23607i q^{98} +(-3.23607 + 0.726543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 6 q^{4} - 6 q^{6} + 2 q^{9} + 18 q^{11} - 12 q^{14} + 18 q^{16} + 20 q^{19} + 24 q^{21} - 10 q^{24} + 16 q^{26} + 20 q^{29} + 16 q^{31} + 8 q^{34} + 6 q^{36} + 18 q^{39} + 46 q^{41} + 4 q^{44} + 26 q^{46}+ \cdots - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.587785 + 0.190983i 0.415627 + 0.135045i 0.509363 0.860552i \(-0.329881\pi\)
−0.0937362 + 0.995597i \(0.529881\pi\)
\(3\) −0.587785 0.809017i −0.339358 0.467086i
\(4\) −1.30902 0.951057i −0.654508 0.475528i
\(5\) 0 0
\(6\) −0.190983 0.587785i −0.0779685 0.239962i
\(7\) −1.76336 + 2.42705i −0.666486 + 0.917339i −0.999674 0.0255212i \(-0.991875\pi\)
0.333188 + 0.942860i \(0.391875\pi\)
\(8\) −1.31433 1.80902i −0.464685 0.639584i
\(9\) −0.309017 + 0.951057i −0.103006 + 0.317019i
\(10\) 0 0
\(11\) 1.69098 + 2.85317i 0.509851 + 0.860263i
\(12\) 1.61803i 0.467086i
\(13\) 1.67760 + 0.545085i 0.465282 + 0.151179i 0.532270 0.846574i \(-0.321339\pi\)
−0.0669881 + 0.997754i \(0.521339\pi\)
\(14\) −1.50000 + 1.08981i −0.400892 + 0.291265i
\(15\) 0 0
\(16\) 0.572949 + 1.76336i 0.143237 + 0.440839i
\(17\) 1.53884 0.500000i 0.373224 0.121268i −0.116398 0.993203i \(-0.537135\pi\)
0.489622 + 0.871935i \(0.337135\pi\)
\(18\) −0.363271 + 0.500000i −0.0856239 + 0.117851i
\(19\) 4.73607 3.44095i 1.08653 0.789409i 0.107719 0.994181i \(-0.465645\pi\)
0.978810 + 0.204772i \(0.0656454\pi\)
\(20\) 0 0
\(21\) 3.00000 0.654654
\(22\) 0.449028 + 2.00000i 0.0957331 + 0.426401i
\(23\) 3.47214i 0.723990i 0.932180 + 0.361995i \(0.117904\pi\)
−0.932180 + 0.361995i \(0.882096\pi\)
\(24\) −0.690983 + 2.12663i −0.141046 + 0.434096i
\(25\) 0 0
\(26\) 0.881966 + 0.640786i 0.172968 + 0.125668i
\(27\) 0.951057 0.309017i 0.183031 0.0594703i
\(28\) 4.61653 1.50000i 0.872441 0.283473i
\(29\) 3.61803 + 2.62866i 0.671852 + 0.488129i 0.870645 0.491912i \(-0.163702\pi\)
−0.198793 + 0.980042i \(0.563702\pi\)
\(30\) 0 0
\(31\) 0.881966 2.71441i 0.158406 0.487523i −0.840084 0.542456i \(-0.817495\pi\)
0.998490 + 0.0549331i \(0.0174946\pi\)
\(32\) 5.61803i 0.993137i
\(33\) 1.31433 3.04508i 0.228795 0.530081i
\(34\) 1.00000 0.171499
\(35\) 0 0
\(36\) 1.30902 0.951057i 0.218169 0.158509i
\(37\) −0.138757 + 0.190983i −0.0228116 + 0.0313974i −0.820270 0.571976i \(-0.806177\pi\)
0.797459 + 0.603373i \(0.206177\pi\)
\(38\) 3.44095 1.11803i 0.558197 0.181369i
\(39\) −0.545085 1.67760i −0.0872835 0.268631i
\(40\) 0 0
\(41\) 9.66312 7.02067i 1.50913 1.09644i 0.542562 0.840015i \(-0.317454\pi\)
0.966563 0.256428i \(-0.0825458\pi\)
\(42\) 1.76336 + 0.572949i 0.272092 + 0.0884080i
\(43\) 6.23607i 0.950991i 0.879718 + 0.475496i \(0.157731\pi\)
−0.879718 + 0.475496i \(0.842269\pi\)
\(44\) 0.500000 5.34307i 0.0753778 0.805498i
\(45\) 0 0
\(46\) −0.663119 + 2.04087i −0.0977716 + 0.300910i
\(47\) 0.951057 + 1.30902i 0.138726 + 0.190940i 0.872727 0.488208i \(-0.162349\pi\)
−0.734001 + 0.679148i \(0.762349\pi\)
\(48\) 1.08981 1.50000i 0.157301 0.216506i
\(49\) −0.618034 1.90211i −0.0882906 0.271730i
\(50\) 0 0
\(51\) −1.30902 0.951057i −0.183299 0.133175i
\(52\) −1.67760 2.30902i −0.232641 0.320203i
\(53\) −9.14729 2.97214i −1.25648 0.408254i −0.396240 0.918147i \(-0.629685\pi\)
−0.860238 + 0.509893i \(0.829685\pi\)
\(54\) 0.618034 0.0841038
\(55\) 0 0
\(56\) 6.70820 0.896421
\(57\) −5.56758 1.80902i −0.737444 0.239610i
\(58\) 1.62460 + 2.23607i 0.213320 + 0.293610i
\(59\) 8.35410 + 6.06961i 1.08761 + 0.790196i 0.978994 0.203888i \(-0.0653577\pi\)
0.108617 + 0.994084i \(0.465358\pi\)
\(60\) 0 0
\(61\) 2.42705 + 7.46969i 0.310752 + 0.956396i 0.977468 + 0.211084i \(0.0676995\pi\)
−0.666716 + 0.745312i \(0.732301\pi\)
\(62\) 1.03681 1.42705i 0.131675 0.181236i
\(63\) −1.76336 2.42705i −0.222162 0.305780i
\(64\) 0.0729490 0.224514i 0.00911863 0.0280642i
\(65\) 0 0
\(66\) 1.35410 1.53884i 0.166678 0.189418i
\(67\) 9.56231i 1.16822i 0.811674 + 0.584111i \(0.198557\pi\)
−0.811674 + 0.584111i \(0.801443\pi\)
\(68\) −2.48990 0.809017i −0.301945 0.0981077i
\(69\) 2.80902 2.04087i 0.338166 0.245692i
\(70\) 0 0
\(71\) −1.71885 5.29007i −0.203990 0.627815i −0.999753 0.0222083i \(-0.992930\pi\)
0.795764 0.605607i \(-0.207070\pi\)
\(72\) 2.12663 0.690983i 0.250625 0.0814331i
\(73\) −1.90211 + 2.61803i −0.222625 + 0.306418i −0.905690 0.423940i \(-0.860647\pi\)
0.683065 + 0.730358i \(0.260647\pi\)
\(74\) −0.118034 + 0.0857567i −0.0137212 + 0.00996902i
\(75\) 0 0
\(76\) −9.47214 −1.08653
\(77\) −9.90659 0.927051i −1.12896 0.105647i
\(78\) 1.09017i 0.123437i
\(79\) −2.92705 + 9.00854i −0.329319 + 1.01354i 0.640134 + 0.768263i \(0.278879\pi\)
−0.969453 + 0.245276i \(0.921121\pi\)
\(80\) 0 0
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) 7.02067 2.28115i 0.775303 0.251911i
\(83\) −0.673542 + 0.218847i −0.0739308 + 0.0240216i −0.345749 0.938327i \(-0.612375\pi\)
0.271818 + 0.962349i \(0.412375\pi\)
\(84\) −3.92705 2.85317i −0.428476 0.311306i
\(85\) 0 0
\(86\) −1.19098 + 3.66547i −0.128427 + 0.395258i
\(87\) 4.47214i 0.479463i
\(88\) 2.93893 6.80902i 0.313291 0.725844i
\(89\) −0.527864 −0.0559535 −0.0279767 0.999609i \(-0.508906\pi\)
−0.0279767 + 0.999609i \(0.508906\pi\)
\(90\) 0 0
\(91\) −4.28115 + 3.11044i −0.448787 + 0.326063i
\(92\) 3.30220 4.54508i 0.344278 0.473858i
\(93\) −2.71441 + 0.881966i −0.281471 + 0.0914556i
\(94\) 0.309017 + 0.951057i 0.0318727 + 0.0980940i
\(95\) 0 0
\(96\) 4.54508 3.30220i 0.463881 0.337029i
\(97\) 13.3475 + 4.33688i 1.35524 + 0.440344i 0.894451 0.447167i \(-0.147567\pi\)
0.460788 + 0.887510i \(0.347567\pi\)
\(98\) 1.23607i 0.124862i
\(99\) −3.23607 + 0.726543i −0.325237 + 0.0730203i
\(100\) 0 0
\(101\) −0.927051 + 2.85317i −0.0922450 + 0.283901i −0.986526 0.163605i \(-0.947688\pi\)
0.894281 + 0.447506i \(0.147688\pi\)
\(102\) −0.587785 0.809017i −0.0581994 0.0801046i
\(103\) −3.52671 + 4.85410i −0.347497 + 0.478289i −0.946612 0.322374i \(-0.895519\pi\)
0.599115 + 0.800663i \(0.295519\pi\)
\(104\) −1.21885 3.75123i −0.119518 0.367838i
\(105\) 0 0
\(106\) −4.80902 3.49396i −0.467093 0.339363i
\(107\) −2.48990 3.42705i −0.240708 0.331306i 0.671522 0.740984i \(-0.265641\pi\)
−0.912230 + 0.409679i \(0.865641\pi\)
\(108\) −1.53884 0.500000i −0.148075 0.0481125i
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0.236068 0.0224066
\(112\) −5.29007 1.71885i −0.499864 0.162416i
\(113\) −0.416272 0.572949i −0.0391596 0.0538985i 0.788988 0.614408i \(-0.210605\pi\)
−0.828148 + 0.560510i \(0.810605\pi\)
\(114\) −2.92705 2.12663i −0.274143 0.199177i
\(115\) 0 0
\(116\) −2.23607 6.88191i −0.207614 0.638969i
\(117\) −1.03681 + 1.42705i −0.0958534 + 0.131931i
\(118\) 3.75123 + 5.16312i 0.345328 + 0.475304i
\(119\) −1.50000 + 4.61653i −0.137505 + 0.423196i
\(120\) 0 0
\(121\) −5.28115 + 9.64932i −0.480105 + 0.877211i
\(122\) 4.85410i 0.439470i
\(123\) −11.3597 3.69098i −1.02427 0.332805i
\(124\) −3.73607 + 2.71441i −0.335509 + 0.243761i
\(125\) 0 0
\(126\) −0.572949 1.76336i −0.0510424 0.157092i
\(127\) −3.52671 + 1.14590i −0.312945 + 0.101682i −0.461279 0.887255i \(-0.652609\pi\)
0.148333 + 0.988937i \(0.452609\pi\)
\(128\) 6.69015 9.20820i 0.591331 0.813898i
\(129\) 5.04508 3.66547i 0.444195 0.322727i
\(130\) 0 0
\(131\) −7.14590 −0.624340 −0.312170 0.950026i \(-0.601056\pi\)
−0.312170 + 0.950026i \(0.601056\pi\)
\(132\) −4.61653 + 2.73607i −0.401817 + 0.238144i
\(133\) 17.5623i 1.52285i
\(134\) −1.82624 + 5.62058i −0.157763 + 0.485544i
\(135\) 0 0
\(136\) −2.92705 2.12663i −0.250993 0.182357i
\(137\) 7.10642 2.30902i 0.607143 0.197273i 0.0107192 0.999943i \(-0.496588\pi\)
0.596424 + 0.802670i \(0.296588\pi\)
\(138\) 2.04087 0.663119i 0.173730 0.0564484i
\(139\) −0.690983 0.502029i −0.0586084 0.0425815i 0.558095 0.829777i \(-0.311532\pi\)
−0.616704 + 0.787195i \(0.711532\pi\)
\(140\) 0 0
\(141\) 0.500000 1.53884i 0.0421076 0.129594i
\(142\) 3.43769i 0.288485i
\(143\) 1.28157 + 5.70820i 0.107170 + 0.477344i
\(144\) −1.85410 −0.154508
\(145\) 0 0
\(146\) −1.61803 + 1.17557i −0.133909 + 0.0972909i
\(147\) −1.17557 + 1.61803i −0.0969594 + 0.133453i
\(148\) 0.363271 0.118034i 0.0298607 0.00970233i
\(149\) −4.63525 14.2658i −0.379735 1.16870i −0.940228 0.340545i \(-0.889388\pi\)
0.560493 0.828159i \(-0.310612\pi\)
\(150\) 0 0
\(151\) −1.61803 + 1.17557i −0.131674 + 0.0956666i −0.651673 0.758500i \(-0.725932\pi\)
0.519999 + 0.854167i \(0.325932\pi\)
\(152\) −12.4495 4.04508i −1.00979 0.328100i
\(153\) 1.61803i 0.130810i
\(154\) −5.64590 2.43690i −0.454959 0.196371i
\(155\) 0 0
\(156\) −0.881966 + 2.71441i −0.0706138 + 0.217327i
\(157\) −2.17963 3.00000i −0.173953 0.239426i 0.713134 0.701028i \(-0.247275\pi\)
−0.887087 + 0.461601i \(0.847275\pi\)
\(158\) −3.44095 + 4.73607i −0.273748 + 0.376781i
\(159\) 2.97214 + 9.14729i 0.235706 + 0.725428i
\(160\) 0 0
\(161\) −8.42705 6.12261i −0.664145 0.482529i
\(162\) −0.363271 0.500000i −0.0285413 0.0392837i
\(163\) 17.3763 + 5.64590i 1.36102 + 0.442221i 0.896382 0.443282i \(-0.146186\pi\)
0.464634 + 0.885503i \(0.346186\pi\)
\(164\) −19.3262 −1.50913
\(165\) 0 0
\(166\) −0.437694 −0.0339717
\(167\) −9.54332 3.10081i −0.738484 0.239948i −0.0844656 0.996426i \(-0.526918\pi\)
−0.654019 + 0.756478i \(0.726918\pi\)
\(168\) −3.94298 5.42705i −0.304208 0.418706i
\(169\) −8.00000 5.81234i −0.615385 0.447103i
\(170\) 0 0
\(171\) 1.80902 + 5.56758i 0.138339 + 0.425764i
\(172\) 5.93085 8.16312i 0.452223 0.622432i
\(173\) −9.04129 12.4443i −0.687397 0.946120i 0.312596 0.949886i \(-0.398801\pi\)
−0.999993 + 0.00376565i \(0.998801\pi\)
\(174\) 0.854102 2.62866i 0.0647493 0.199278i
\(175\) 0 0
\(176\) −4.06231 + 4.61653i −0.306208 + 0.347984i
\(177\) 10.3262i 0.776168i
\(178\) −0.310271 0.100813i −0.0232558 0.00755626i
\(179\) −1.80902 + 1.31433i −0.135212 + 0.0982375i −0.653335 0.757069i \(-0.726631\pi\)
0.518123 + 0.855306i \(0.326631\pi\)
\(180\) 0 0
\(181\) −5.39919 16.6170i −0.401318 1.23513i −0.923930 0.382560i \(-0.875042\pi\)
0.522612 0.852571i \(-0.324958\pi\)
\(182\) −3.11044 + 1.01064i −0.230561 + 0.0749139i
\(183\) 4.61653 6.35410i 0.341263 0.469709i
\(184\) 6.28115 4.56352i 0.463053 0.336428i
\(185\) 0 0
\(186\) −1.76393 −0.129338
\(187\) 4.02874 + 3.54508i 0.294611 + 0.259242i
\(188\) 2.61803i 0.190940i
\(189\) −0.927051 + 2.85317i −0.0674330 + 0.207538i
\(190\) 0 0
\(191\) 6.04508 + 4.39201i 0.437407 + 0.317795i 0.784604 0.619998i \(-0.212866\pi\)
−0.347197 + 0.937792i \(0.612866\pi\)
\(192\) −0.224514 + 0.0729490i −0.0162029 + 0.00526464i
\(193\) 17.6538 5.73607i 1.27075 0.412891i 0.405436 0.914124i \(-0.367120\pi\)
0.865313 + 0.501232i \(0.167120\pi\)
\(194\) 7.01722 + 5.09831i 0.503807 + 0.366037i
\(195\) 0 0
\(196\) −1.00000 + 3.07768i −0.0714286 + 0.219835i
\(197\) 24.3820i 1.73714i −0.495564 0.868572i \(-0.665039\pi\)
0.495564 0.868572i \(-0.334961\pi\)
\(198\) −2.04087 0.190983i −0.145038 0.0135726i
\(199\) 16.7082 1.18441 0.592207 0.805786i \(-0.298257\pi\)
0.592207 + 0.805786i \(0.298257\pi\)
\(200\) 0 0
\(201\) 7.73607 5.62058i 0.545660 0.396445i
\(202\) −1.08981 + 1.50000i −0.0766790 + 0.105540i
\(203\) −12.7598 + 4.14590i −0.895560 + 0.290985i
\(204\) 0.809017 + 2.48990i 0.0566425 + 0.174328i
\(205\) 0 0
\(206\) −3.00000 + 2.17963i −0.209020 + 0.151862i
\(207\) −3.30220 1.07295i −0.229519 0.0745751i
\(208\) 3.27051i 0.226769i
\(209\) 17.8262 + 7.69421i 1.23307 + 0.532220i
\(210\) 0 0
\(211\) −6.88197 + 21.1805i −0.473774 + 1.45813i 0.373830 + 0.927497i \(0.378044\pi\)
−0.847604 + 0.530629i \(0.821956\pi\)
\(212\) 9.14729 + 12.5902i 0.628239 + 0.864696i
\(213\) −3.26944 + 4.50000i −0.224018 + 0.308335i
\(214\) −0.809017 2.48990i −0.0553033 0.170206i
\(215\) 0 0
\(216\) −1.80902 1.31433i −0.123088 0.0894287i
\(217\) 5.03280 + 6.92705i 0.341649 + 0.470239i
\(218\) 0 0
\(219\) 3.23607 0.218673
\(220\) 0 0
\(221\) 2.85410 0.191988
\(222\) 0.138757 + 0.0450850i 0.00931278 + 0.00302591i
\(223\) −0.416272 0.572949i −0.0278756 0.0383675i 0.794852 0.606804i \(-0.207549\pi\)
−0.822727 + 0.568436i \(0.807549\pi\)
\(224\) −13.6353 9.90659i −0.911044 0.661912i
\(225\) 0 0
\(226\) −0.135255 0.416272i −0.00899702 0.0276900i
\(227\) 14.6291 20.1353i 0.970969 1.33642i 0.0294127 0.999567i \(-0.490636\pi\)
0.941556 0.336856i \(-0.109364\pi\)
\(228\) 5.56758 + 7.66312i 0.368722 + 0.507502i
\(229\) −3.09017 + 9.51057i −0.204204 + 0.628476i 0.795541 + 0.605900i \(0.207187\pi\)
−0.999745 + 0.0225760i \(0.992813\pi\)
\(230\) 0 0
\(231\) 5.07295 + 8.55951i 0.333776 + 0.563174i
\(232\) 10.0000i 0.656532i
\(233\) 23.1356 + 7.51722i 1.51567 + 0.492470i 0.944541 0.328394i \(-0.106507\pi\)
0.571124 + 0.820863i \(0.306507\pi\)
\(234\) −0.881966 + 0.640786i −0.0576559 + 0.0418895i
\(235\) 0 0
\(236\) −5.16312 15.8904i −0.336090 1.03438i
\(237\) 9.00854 2.92705i 0.585167 0.190132i
\(238\) −1.76336 + 2.42705i −0.114301 + 0.157322i
\(239\) 2.07295 1.50609i 0.134088 0.0974206i −0.518719 0.854945i \(-0.673591\pi\)
0.652807 + 0.757524i \(0.273591\pi\)
\(240\) 0 0
\(241\) −23.1246 −1.48959 −0.744794 0.667295i \(-0.767452\pi\)
−0.744794 + 0.667295i \(0.767452\pi\)
\(242\) −4.94704 + 4.66312i −0.318008 + 0.299757i
\(243\) 1.00000i 0.0641500i
\(244\) 3.92705 12.0862i 0.251404 0.773741i
\(245\) 0 0
\(246\) −5.97214 4.33901i −0.380769 0.276645i
\(247\) 9.82084 3.19098i 0.624885 0.203037i
\(248\) −6.06961 + 1.97214i −0.385421 + 0.125231i
\(249\) 0.572949 + 0.416272i 0.0363092 + 0.0263802i
\(250\) 0 0
\(251\) −2.40983 + 7.41669i −0.152107 + 0.468138i −0.997856 0.0654431i \(-0.979154\pi\)
0.845749 + 0.533581i \(0.179154\pi\)
\(252\) 4.85410i 0.305780i
\(253\) −9.90659 + 5.87132i −0.622822 + 0.369127i
\(254\) −2.29180 −0.143800
\(255\) 0 0
\(256\) 5.30902 3.85723i 0.331814 0.241077i
\(257\) 6.86167 9.44427i 0.428019 0.589117i −0.539478 0.842000i \(-0.681378\pi\)
0.967497 + 0.252882i \(0.0813785\pi\)
\(258\) 3.66547 1.19098i 0.228202 0.0741474i
\(259\) −0.218847 0.673542i −0.0135985 0.0418519i
\(260\) 0 0
\(261\) −3.61803 + 2.62866i −0.223951 + 0.162710i
\(262\) −4.20025 1.36475i −0.259493 0.0843142i
\(263\) 16.3262i 1.00672i −0.864077 0.503359i \(-0.832097\pi\)
0.864077 0.503359i \(-0.167903\pi\)
\(264\) −7.23607 + 1.62460i −0.445349 + 0.0999871i
\(265\) 0 0
\(266\) −3.35410 + 10.3229i −0.205653 + 0.632935i
\(267\) 0.310271 + 0.427051i 0.0189883 + 0.0261351i
\(268\) 9.09429 12.5172i 0.555522 0.764611i
\(269\) −4.79837 14.7679i −0.292562 0.900413i −0.984029 0.178006i \(-0.943035\pi\)
0.691467 0.722408i \(-0.256965\pi\)
\(270\) 0 0
\(271\) 22.0623 + 16.0292i 1.34019 + 0.973705i 0.999437 + 0.0335518i \(0.0106819\pi\)
0.340753 + 0.940153i \(0.389318\pi\)
\(272\) 1.76336 + 2.42705i 0.106919 + 0.147162i
\(273\) 5.03280 + 1.63525i 0.304599 + 0.0989701i
\(274\) 4.61803 0.278986
\(275\) 0 0
\(276\) −5.61803 −0.338166
\(277\) −29.0665 9.44427i −1.74644 0.567451i −0.750779 0.660554i \(-0.770322\pi\)
−0.995657 + 0.0931022i \(0.970322\pi\)
\(278\) −0.310271 0.427051i −0.0186088 0.0256128i
\(279\) 2.30902 + 1.67760i 0.138237 + 0.100435i
\(280\) 0 0
\(281\) −0.236068 0.726543i −0.0140826 0.0433419i 0.943768 0.330608i \(-0.107254\pi\)
−0.957851 + 0.287266i \(0.907254\pi\)
\(282\) 0.587785 0.809017i 0.0350021 0.0481763i
\(283\) −0.106001 0.145898i −0.00630111 0.00867274i 0.805855 0.592113i \(-0.201706\pi\)
−0.812156 + 0.583440i \(0.801706\pi\)
\(284\) −2.78115 + 8.55951i −0.165031 + 0.507913i
\(285\) 0 0
\(286\) −0.336881 + 3.59996i −0.0199202 + 0.212870i
\(287\) 35.8328i 2.11514i
\(288\) −5.34307 1.73607i −0.314843 0.102299i
\(289\) −11.6353 + 8.45351i −0.684427 + 0.497265i
\(290\) 0 0
\(291\) −4.33688 13.3475i −0.254232 0.782447i
\(292\) 4.97980 1.61803i 0.291421 0.0946883i
\(293\) 0.0327561 0.0450850i 0.00191363 0.00263389i −0.808059 0.589101i \(-0.799482\pi\)
0.809973 + 0.586468i \(0.199482\pi\)
\(294\) −1.00000 + 0.726543i −0.0583212 + 0.0423728i
\(295\) 0 0
\(296\) 0.527864 0.0306815
\(297\) 2.48990 + 2.19098i 0.144479 + 0.127134i
\(298\) 9.27051i 0.537026i
\(299\) −1.89261 + 5.82485i −0.109452 + 0.336860i
\(300\) 0 0
\(301\) −15.1353 10.9964i −0.872382 0.633822i
\(302\) −1.17557 + 0.381966i −0.0676465 + 0.0219797i
\(303\) 2.85317 0.927051i 0.163910 0.0532577i
\(304\) 8.78115 + 6.37988i 0.503634 + 0.365911i
\(305\) 0 0
\(306\) −0.309017 + 0.951057i −0.0176653 + 0.0543683i
\(307\) 0.562306i 0.0320925i −0.999871 0.0160462i \(-0.994892\pi\)
0.999871 0.0160462i \(-0.00510790\pi\)
\(308\) 12.0862 + 10.6353i 0.688676 + 0.606000i
\(309\) 6.00000 0.341328
\(310\) 0 0
\(311\) −2.04508 + 1.48584i −0.115966 + 0.0842543i −0.644257 0.764809i \(-0.722833\pi\)
0.528291 + 0.849064i \(0.322833\pi\)
\(312\) −2.31838 + 3.19098i −0.131253 + 0.180654i
\(313\) −24.5685 + 7.98278i −1.38869 + 0.451213i −0.905517 0.424310i \(-0.860517\pi\)
−0.483175 + 0.875524i \(0.660517\pi\)
\(314\) −0.708204 2.17963i −0.0399663 0.123004i
\(315\) 0 0
\(316\) 12.3992 9.00854i 0.697509 0.506770i
\(317\) 18.4131 + 5.98278i 1.03418 + 0.336026i 0.776443 0.630188i \(-0.217022\pi\)
0.257740 + 0.966214i \(0.417022\pi\)
\(318\) 5.94427i 0.333338i
\(319\) −1.38197 + 14.7679i −0.0773752 + 0.826842i
\(320\) 0 0
\(321\) −1.30902 + 4.02874i −0.0730622 + 0.224862i
\(322\) −3.78398 5.20820i −0.210873 0.290242i
\(323\) 5.56758 7.66312i 0.309789 0.426387i
\(324\) 0.500000 + 1.53884i 0.0277778 + 0.0854912i
\(325\) 0 0
\(326\) 9.13525 + 6.63715i 0.505955 + 0.367598i
\(327\) 0 0
\(328\) −25.4010 8.25329i −1.40254 0.455712i
\(329\) −4.85410 −0.267615
\(330\) 0 0
\(331\) 26.5967 1.46189 0.730945 0.682437i \(-0.239080\pi\)
0.730945 + 0.682437i \(0.239080\pi\)
\(332\) 1.08981 + 0.354102i 0.0598113 + 0.0194339i
\(333\) −0.138757 0.190983i −0.00760385 0.0104658i
\(334\) −5.01722 3.64522i −0.274530 0.199458i
\(335\) 0 0
\(336\) 1.71885 + 5.29007i 0.0937708 + 0.288597i
\(337\) 0.171513 0.236068i 0.00934293 0.0128594i −0.804320 0.594196i \(-0.797470\pi\)
0.813663 + 0.581337i \(0.197470\pi\)
\(338\) −3.59222 4.94427i −0.195391 0.268933i
\(339\) −0.218847 + 0.673542i −0.0118861 + 0.0365818i
\(340\) 0 0
\(341\) 9.23607 2.07363i 0.500161 0.112293i
\(342\) 3.61803i 0.195641i
\(343\) −14.2658 4.63525i −0.770283 0.250280i
\(344\) 11.2812 8.19624i 0.608239 0.441912i
\(345\) 0 0
\(346\) −2.93769 9.04129i −0.157931 0.486063i
\(347\) −19.9192 + 6.47214i −1.06932 + 0.347442i −0.790222 0.612821i \(-0.790035\pi\)
−0.279096 + 0.960263i \(0.590035\pi\)
\(348\) −4.25325 + 5.85410i −0.227998 + 0.313813i
\(349\) −8.19098 + 5.95110i −0.438453 + 0.318555i −0.785020 0.619470i \(-0.787347\pi\)
0.346567 + 0.938025i \(0.387347\pi\)
\(350\) 0 0
\(351\) 1.76393 0.0941517
\(352\) −16.0292 + 9.50000i −0.854359 + 0.506352i
\(353\) 10.4721i 0.557376i −0.960382 0.278688i \(-0.910101\pi\)
0.960382 0.278688i \(-0.0898995\pi\)
\(354\) 1.97214 6.06961i 0.104818 0.322596i
\(355\) 0 0
\(356\) 0.690983 + 0.502029i 0.0366220 + 0.0266075i
\(357\) 4.61653 1.50000i 0.244332 0.0793884i
\(358\) −1.31433 + 0.427051i −0.0694644 + 0.0225703i
\(359\) −10.3262 7.50245i −0.544998 0.395964i 0.280940 0.959725i \(-0.409354\pi\)
−0.825938 + 0.563761i \(0.809354\pi\)
\(360\) 0 0
\(361\) 4.71885 14.5231i 0.248360 0.764375i
\(362\) 10.7984i 0.567550i
\(363\) 10.9106 1.39919i 0.572661 0.0734383i
\(364\) 8.56231 0.448787
\(365\) 0 0
\(366\) 3.92705 2.85317i 0.205270 0.149138i
\(367\) −3.26944 + 4.50000i −0.170663 + 0.234898i −0.885778 0.464109i \(-0.846375\pi\)
0.715115 + 0.699007i \(0.246375\pi\)
\(368\) −6.12261 + 1.98936i −0.319163 + 0.103702i
\(369\) 3.69098 + 11.3597i 0.192145 + 0.591361i
\(370\) 0 0
\(371\) 23.3435 16.9600i 1.21193 0.880520i
\(372\) 4.39201 + 1.42705i 0.227715 + 0.0739891i
\(373\) 4.41641i 0.228673i −0.993442 0.114336i \(-0.963526\pi\)
0.993442 0.114336i \(-0.0364742\pi\)
\(374\) 1.69098 + 2.85317i 0.0874386 + 0.147534i
\(375\) 0 0
\(376\) 1.11803 3.44095i 0.0576582 0.177454i
\(377\) 4.63677 + 6.38197i 0.238806 + 0.328688i
\(378\) −1.08981 + 1.50000i −0.0560540 + 0.0771517i
\(379\) −0.489357 1.50609i −0.0251366 0.0773624i 0.937701 0.347443i \(-0.112950\pi\)
−0.962838 + 0.270080i \(0.912950\pi\)
\(380\) 0 0
\(381\) 3.00000 + 2.17963i 0.153695 + 0.111666i
\(382\) 2.71441 + 3.73607i 0.138881 + 0.191154i
\(383\) 25.5725 + 8.30902i 1.30669 + 0.424571i 0.877906 0.478834i \(-0.158940\pi\)
0.428789 + 0.903405i \(0.358940\pi\)
\(384\) −11.3820 −0.580834
\(385\) 0 0
\(386\) 11.4721 0.583916
\(387\) −5.93085 1.92705i −0.301482 0.0979575i
\(388\) −13.3475 18.3713i −0.677619 0.932663i
\(389\) 19.6353 + 14.2658i 0.995547 + 0.723307i 0.961129 0.276100i \(-0.0890422\pi\)
0.0344181 + 0.999408i \(0.489042\pi\)
\(390\) 0 0
\(391\) 1.73607 + 5.34307i 0.0877967 + 0.270211i
\(392\) −2.62866 + 3.61803i −0.132767 + 0.182738i
\(393\) 4.20025 + 5.78115i 0.211875 + 0.291621i
\(394\) 4.65654 14.3314i 0.234593 0.722003i
\(395\) 0 0
\(396\) 4.92705 + 2.12663i 0.247594 + 0.106867i
\(397\) 38.7082i 1.94271i 0.237635 + 0.971355i \(0.423628\pi\)
−0.237635 + 0.971355i \(0.576372\pi\)
\(398\) 9.82084 + 3.19098i 0.492274 + 0.159950i
\(399\) 14.2082 10.3229i 0.711300 0.516790i
\(400\) 0 0
\(401\) −8.06231 24.8132i −0.402612 1.23911i −0.922873 0.385106i \(-0.874165\pi\)
0.520260 0.854008i \(-0.325835\pi\)
\(402\) 5.62058 1.82624i 0.280329 0.0910845i
\(403\) 2.95917 4.07295i 0.147407 0.202888i
\(404\) 3.92705 2.85317i 0.195378 0.141950i
\(405\) 0 0
\(406\) −8.29180 −0.411515
\(407\) −0.779543 0.0729490i −0.0386405 0.00361595i
\(408\) 3.61803i 0.179119i
\(409\) 3.41641 10.5146i 0.168930 0.519915i −0.830374 0.557207i \(-0.811873\pi\)
0.999304 + 0.0372920i \(0.0118732\pi\)
\(410\) 0 0
\(411\) −6.04508 4.39201i −0.298182 0.216642i
\(412\) 9.23305 3.00000i 0.454880 0.147799i
\(413\) −29.4625 + 9.57295i −1.44976 + 0.471054i
\(414\) −1.73607 1.26133i −0.0853231 0.0619909i
\(415\) 0 0
\(416\) −3.06231 + 9.42481i −0.150142 + 0.462089i
\(417\) 0.854102i 0.0418256i
\(418\) 9.00854 + 7.92705i 0.440622 + 0.387725i
\(419\) −16.5066 −0.806399 −0.403200 0.915112i \(-0.632102\pi\)
−0.403200 + 0.915112i \(0.632102\pi\)
\(420\) 0 0
\(421\) 30.1525 21.9071i 1.46954 1.06768i 0.488795 0.872398i \(-0.337436\pi\)
0.980746 0.195286i \(-0.0625636\pi\)
\(422\) −8.09024 + 11.1353i −0.393827 + 0.542056i
\(423\) −1.53884 + 0.500000i −0.0748210 + 0.0243108i
\(424\) 6.64590 + 20.4540i 0.322753 + 0.993333i
\(425\) 0 0
\(426\) −2.78115 + 2.02063i −0.134747 + 0.0978996i
\(427\) −22.4091 7.28115i −1.08445 0.352360i
\(428\) 6.85410i 0.331306i
\(429\) 3.86475 4.39201i 0.186592 0.212048i
\(430\) 0 0
\(431\) −12.2082 + 37.5730i −0.588048 + 1.80983i −0.00138127 + 0.999999i \(0.500440\pi\)
−0.586667 + 0.809828i \(0.699560\pi\)
\(432\) 1.08981 + 1.50000i 0.0524337 + 0.0721688i
\(433\) −3.52671 + 4.85410i −0.169483 + 0.233273i −0.885307 0.465008i \(-0.846051\pi\)
0.715824 + 0.698281i \(0.246051\pi\)
\(434\) 1.63525 + 5.03280i 0.0784947 + 0.241582i
\(435\) 0 0
\(436\) 0 0
\(437\) 11.9475 + 16.4443i 0.571525 + 0.786636i
\(438\) 1.90211 + 0.618034i 0.0908865 + 0.0295308i
\(439\) −3.29180 −0.157109 −0.0785544 0.996910i \(-0.525030\pi\)
−0.0785544 + 0.996910i \(0.525030\pi\)
\(440\) 0 0
\(441\) 2.00000 0.0952381
\(442\) 1.67760 + 0.545085i 0.0797952 + 0.0259270i
\(443\) 24.1724 + 33.2705i 1.14847 + 1.58073i 0.746953 + 0.664877i \(0.231516\pi\)
0.401514 + 0.915853i \(0.368484\pi\)
\(444\) −0.309017 0.224514i −0.0146653 0.0106550i
\(445\) 0 0
\(446\) −0.135255 0.416272i −0.00640451 0.0197110i
\(447\) −8.81678 + 12.1353i −0.417019 + 0.573978i
\(448\) 0.416272 + 0.572949i 0.0196670 + 0.0270693i
\(449\) 7.56231 23.2744i 0.356887 1.09839i −0.598020 0.801481i \(-0.704046\pi\)
0.954907 0.296905i \(-0.0959544\pi\)
\(450\) 0 0
\(451\) 36.3713 + 15.6987i 1.71266 + 0.739222i
\(452\) 1.14590i 0.0538985i
\(453\) 1.90211 + 0.618034i 0.0893691 + 0.0290378i
\(454\) 12.4443 9.04129i 0.584039 0.424329i
\(455\) 0 0
\(456\) 4.04508 + 12.4495i 0.189428 + 0.583001i
\(457\) 7.80021 2.53444i 0.364878 0.118556i −0.120839 0.992672i \(-0.538558\pi\)
0.485717 + 0.874116i \(0.338558\pi\)
\(458\) −3.63271 + 5.00000i −0.169746 + 0.233635i
\(459\) 1.30902 0.951057i 0.0610997 0.0443915i
\(460\) 0 0
\(461\) −21.0902 −0.982267 −0.491134 0.871084i \(-0.663417\pi\)
−0.491134 + 0.871084i \(0.663417\pi\)
\(462\) 1.34708 + 6.00000i 0.0626720 + 0.279145i
\(463\) 15.7984i 0.734213i −0.930179 0.367106i \(-0.880349\pi\)
0.930179 0.367106i \(-0.119651\pi\)
\(464\) −2.56231 + 7.88597i −0.118952 + 0.366097i
\(465\) 0 0
\(466\) 12.1631 + 8.83702i 0.563446 + 0.409367i
\(467\) −9.28605 + 3.01722i −0.429707 + 0.139620i −0.515882 0.856660i \(-0.672536\pi\)
0.0861747 + 0.996280i \(0.472536\pi\)
\(468\) 2.71441 0.881966i 0.125474 0.0407689i
\(469\) −23.2082 16.8617i −1.07166 0.778603i
\(470\) 0 0
\(471\) −1.14590 + 3.52671i −0.0528002 + 0.162502i
\(472\) 23.0902i 1.06281i
\(473\) −17.7926 + 10.5451i −0.818103 + 0.484864i
\(474\) 5.85410 0.268888
\(475\) 0 0
\(476\) 6.35410 4.61653i 0.291240 0.211598i
\(477\) 5.65334 7.78115i 0.258849 0.356275i
\(478\) 1.50609 0.489357i 0.0688868 0.0223827i
\(479\) 8.68034 + 26.7153i 0.396615 + 1.22066i 0.927697 + 0.373335i \(0.121786\pi\)
−0.531082 + 0.847320i \(0.678214\pi\)
\(480\) 0 0
\(481\) −0.336881 + 0.244758i −0.0153605 + 0.0111600i
\(482\) −13.5923 4.41641i −0.619113 0.201162i
\(483\) 10.4164i 0.473963i
\(484\) 16.0902 7.60845i 0.731371 0.345839i
\(485\) 0 0
\(486\) −0.190983 + 0.587785i −0.00866317 + 0.0266625i
\(487\) 9.88635 + 13.6074i 0.447993 + 0.616610i 0.971965 0.235126i \(-0.0755503\pi\)
−0.523972 + 0.851736i \(0.675550\pi\)
\(488\) 10.3229 14.2082i 0.467294 0.643175i
\(489\) −5.64590 17.3763i −0.255316 0.785783i
\(490\) 0 0
\(491\) −20.3992 14.8209i −0.920602 0.668857i 0.0230715 0.999734i \(-0.492655\pi\)
−0.943674 + 0.330877i \(0.892655\pi\)
\(492\) 11.3597 + 15.6353i 0.512134 + 0.704892i
\(493\) 6.88191 + 2.23607i 0.309946 + 0.100707i
\(494\) 6.38197 0.287138
\(495\) 0 0
\(496\) 5.29180 0.237609
\(497\) 15.8702 + 5.15654i 0.711876 + 0.231302i
\(498\) 0.257270 + 0.354102i 0.0115286 + 0.0158677i
\(499\) −14.2082 10.3229i −0.636047 0.462115i 0.222443 0.974946i \(-0.428597\pi\)
−0.858490 + 0.512831i \(0.828597\pi\)
\(500\) 0 0
\(501\) 3.10081 + 9.54332i 0.138534 + 0.426364i
\(502\) −2.83293 + 3.89919i −0.126440 + 0.174029i
\(503\) −16.4985 22.7082i −0.735631 1.01251i −0.998858 0.0477750i \(-0.984787\pi\)
0.263227 0.964734i \(-0.415213\pi\)
\(504\) −2.07295 + 6.37988i −0.0923365 + 0.284182i
\(505\) 0 0
\(506\) −6.94427 + 1.55909i −0.308711 + 0.0693098i
\(507\) 9.88854i 0.439166i
\(508\) 5.70634 + 1.85410i 0.253178 + 0.0822625i
\(509\) 19.1074 13.8823i 0.846920 0.615324i −0.0773749 0.997002i \(-0.524654\pi\)
0.924295 + 0.381679i \(0.124654\pi\)
\(510\) 0 0
\(511\) −3.00000 9.23305i −0.132712 0.408446i
\(512\) −17.7926 + 5.78115i −0.786327 + 0.255493i
\(513\) 3.44095 4.73607i 0.151922 0.209103i
\(514\) 5.83688 4.24074i 0.257454 0.187051i
\(515\) 0 0
\(516\) −10.0902 −0.444195
\(517\) −2.12663 + 4.92705i −0.0935289 + 0.216691i
\(518\) 0.437694i 0.0192312i
\(519\) −4.75329 + 14.6291i −0.208646 + 0.642147i
\(520\) 0 0
\(521\) 12.0000 + 8.71851i 0.525730 + 0.381965i 0.818758 0.574139i \(-0.194663\pi\)
−0.293028 + 0.956104i \(0.594663\pi\)
\(522\) −2.62866 + 0.854102i −0.115053 + 0.0373830i
\(523\) 11.3924 3.70163i 0.498156 0.161861i −0.0491529 0.998791i \(-0.515652\pi\)
0.547309 + 0.836930i \(0.315652\pi\)
\(524\) 9.35410 + 6.79615i 0.408636 + 0.296891i
\(525\) 0 0
\(526\) 3.11803 9.59632i 0.135953 0.418420i
\(527\) 4.61803i 0.201165i
\(528\) 6.12261 + 0.572949i 0.266452 + 0.0249344i
\(529\) 10.9443 0.475838
\(530\) 0 0
\(531\) −8.35410 + 6.06961i −0.362537 + 0.263399i
\(532\) 16.7027 22.9894i 0.724156 0.996715i
\(533\) 20.0377 6.51064i 0.867929 0.282007i
\(534\) 0.100813 + 0.310271i 0.00436261 + 0.0134267i
\(535\) 0 0
\(536\) 17.2984 12.5680i 0.747176 0.542855i
\(537\) 2.12663 + 0.690983i 0.0917707 + 0.0298181i
\(538\) 9.59675i 0.413745i
\(539\) 4.38197 4.97980i 0.188745 0.214495i
\(540\) 0 0
\(541\) 6.04508 18.6049i 0.259899 0.799885i −0.732926 0.680308i \(-0.761846\pi\)
0.992825 0.119577i \(-0.0381540\pi\)
\(542\) 9.90659 + 13.6353i 0.425525 + 0.585684i
\(543\) −10.2699 + 14.1353i −0.440722 + 0.606602i
\(544\) 2.80902 + 8.64527i 0.120436 + 0.370663i
\(545\) 0 0
\(546\) 2.64590 + 1.92236i 0.113234 + 0.0822693i
\(547\) 12.7068 + 17.4894i 0.543302 + 0.747791i 0.989084 0.147350i \(-0.0470745\pi\)
−0.445782 + 0.895141i \(0.647075\pi\)
\(548\) −11.4984 3.73607i −0.491189 0.159597i
\(549\) −7.85410 −0.335205
\(550\) 0 0
\(551\) 26.1803 1.11532
\(552\) −7.38394 2.39919i −0.314281 0.102116i
\(553\) −16.7027 22.9894i −0.710273 0.977607i
\(554\) −15.2812 11.1024i −0.649234 0.471696i
\(555\) 0 0
\(556\) 0.427051 + 1.31433i 0.0181110 + 0.0557399i
\(557\) −8.76378 + 12.0623i −0.371333 + 0.511096i −0.953263 0.302143i \(-0.902298\pi\)
0.581929 + 0.813239i \(0.302298\pi\)
\(558\) 1.03681 + 1.42705i 0.0438918 + 0.0604119i
\(559\) −3.39919 + 10.4616i −0.143770 + 0.442479i
\(560\) 0 0
\(561\) 0.500000 5.34307i 0.0211100 0.225585i
\(562\) 0.472136i 0.0199159i
\(563\) −8.45351 2.74671i −0.356273 0.115760i 0.125412 0.992105i \(-0.459975\pi\)
−0.481684 + 0.876345i \(0.659975\pi\)
\(564\) −2.11803 + 1.53884i −0.0891853 + 0.0647969i
\(565\) 0 0
\(566\) −0.0344419 0.106001i −0.00144770 0.00445556i
\(567\) 2.85317 0.927051i 0.119822 0.0389325i
\(568\) −7.31069 + 10.0623i −0.306750 + 0.422205i
\(569\) −19.4721 + 14.1473i −0.816314 + 0.593087i −0.915654 0.401966i \(-0.868327\pi\)
0.0993400 + 0.995054i \(0.468327\pi\)
\(570\) 0 0
\(571\) 34.6869 1.45160 0.725801 0.687905i \(-0.241469\pi\)
0.725801 + 0.687905i \(0.241469\pi\)
\(572\) 3.75123 8.69098i 0.156847 0.363388i
\(573\) 7.47214i 0.312153i
\(574\) −6.84346 + 21.0620i −0.285640 + 0.879111i
\(575\) 0 0
\(576\) 0.190983 + 0.138757i 0.00795763 + 0.00578155i
\(577\) 10.2371 3.32624i 0.426176 0.138473i −0.0880726 0.996114i \(-0.528071\pi\)
0.514249 + 0.857641i \(0.328071\pi\)
\(578\) −8.45351 + 2.74671i −0.351620 + 0.114248i
\(579\) −15.0172 10.9106i −0.624094 0.453431i
\(580\) 0 0
\(581\) 0.656541 2.02063i 0.0272379 0.0838297i
\(582\) 8.67376i 0.359539i
\(583\) −6.98791 31.1246i −0.289410 1.28905i
\(584\) 7.23607 0.299431
\(585\) 0 0
\(586\) 0.0278640 0.0202444i 0.00115105 0.000836289i
\(587\) 22.5151 30.9894i 0.929297 1.27907i −0.0308361 0.999524i \(-0.509817\pi\)
0.960133 0.279543i \(-0.0901830\pi\)
\(588\) 3.07768 1.00000i 0.126922 0.0412393i
\(589\) −5.16312 15.8904i −0.212743 0.654754i
\(590\) 0 0
\(591\) −19.7254 + 14.3314i −0.811396 + 0.589513i
\(592\) −0.416272 0.135255i −0.0171087 0.00555894i
\(593\) 22.2148i 0.912252i 0.889915 + 0.456126i \(0.150763\pi\)
−0.889915 + 0.456126i \(0.849237\pi\)
\(594\) 1.04508 + 1.76336i 0.0428804 + 0.0723514i
\(595\) 0 0
\(596\) −7.50000 + 23.0826i −0.307212 + 0.945501i
\(597\) −9.82084 13.5172i −0.401940 0.553223i
\(598\) −2.22490 + 3.06231i −0.0909827 + 0.125227i
\(599\) 2.56231 + 7.88597i 0.104693 + 0.322212i 0.989658 0.143445i \(-0.0458181\pi\)
−0.884965 + 0.465657i \(0.845818\pi\)
\(600\) 0 0
\(601\) −27.3713 19.8864i −1.11650 0.811184i −0.132825 0.991140i \(-0.542405\pi\)
−0.983675 + 0.179955i \(0.942405\pi\)
\(602\) −6.79615 9.35410i −0.276991 0.381245i
\(603\) −9.09429 2.95492i −0.370348 0.120333i
\(604\) 3.23607 0.131674
\(605\) 0 0
\(606\) 1.85410 0.0753177
\(607\) −12.6740 4.11803i −0.514422 0.167146i 0.0402904 0.999188i \(-0.487172\pi\)
−0.554712 + 0.832042i \(0.687172\pi\)
\(608\) 19.3314 + 26.6074i 0.783992 + 1.07907i
\(609\) 10.8541 + 7.88597i 0.439830 + 0.319555i
\(610\) 0 0
\(611\) 0.881966 + 2.71441i 0.0356805 + 0.109813i
\(612\) 1.53884 2.11803i 0.0622040 0.0856164i
\(613\) −20.3682 28.0344i −0.822664 1.13230i −0.989244 0.146272i \(-0.953272\pi\)
0.166580 0.986028i \(-0.446728\pi\)
\(614\) 0.107391 0.330515i 0.00433394 0.0133385i
\(615\) 0 0
\(616\) 11.3435 + 19.1396i 0.457041 + 0.771158i
\(617\) 19.5836i 0.788406i −0.919023 0.394203i \(-0.871021\pi\)
0.919023 0.394203i \(-0.128979\pi\)
\(618\) 3.52671 + 1.14590i 0.141865 + 0.0460948i
\(619\) −7.13525 + 5.18407i −0.286790 + 0.208365i −0.721874 0.692025i \(-0.756719\pi\)
0.435084 + 0.900390i \(0.356719\pi\)
\(620\) 0 0
\(621\) 1.07295 + 3.30220i 0.0430560 + 0.132513i
\(622\) −1.48584 + 0.482779i −0.0595768 + 0.0193577i
\(623\) 0.930812 1.28115i 0.0372922 0.0513283i
\(624\) 2.64590 1.92236i 0.105921 0.0769559i
\(625\) 0 0
\(626\) −15.9656 −0.638112
\(627\) −4.25325 18.9443i −0.169859 0.756561i
\(628\) 6.00000i 0.239426i
\(629\) −0.118034 + 0.363271i −0.00470632 + 0.0144846i
\(630\) 0 0
\(631\) −37.4336 27.1971i −1.49021 1.08270i −0.974084 0.226187i \(-0.927374\pi\)
−0.516125 0.856513i \(-0.672626\pi\)
\(632\) 20.1437 6.54508i 0.801273 0.260350i
\(633\) 21.1805 6.88197i 0.841850 0.273534i
\(634\) 9.68034 + 7.03318i 0.384455 + 0.279323i
\(635\) 0 0
\(636\) 4.80902 14.8006i 0.190690 0.586883i
\(637\) 3.52786i 0.139779i
\(638\) −3.63271 + 8.41641i −0.143820 + 0.333209i
\(639\) 5.56231 0.220041
\(640\) 0 0
\(641\) −28.9164 + 21.0090i −1.14213 + 0.829806i −0.987415 0.158154i \(-0.949446\pi\)
−0.154715 + 0.987959i \(0.549446\pi\)
\(642\) −1.53884 + 2.11803i −0.0607332 + 0.0835921i
\(643\) 36.6749 11.9164i 1.44632 0.469937i 0.522457 0.852666i \(-0.325015\pi\)
0.923861 + 0.382728i \(0.125015\pi\)
\(644\) 5.20820 + 16.0292i 0.205232 + 0.631639i
\(645\) 0 0
\(646\) 4.73607 3.44095i 0.186338 0.135383i
\(647\) −26.4378 8.59017i −1.03938 0.337714i −0.260887 0.965369i \(-0.584015\pi\)
−0.778492 + 0.627655i \(0.784015\pi\)
\(648\) 2.23607i 0.0878410i
\(649\) −3.19098 + 34.0993i −0.125257 + 1.33851i
\(650\) 0 0
\(651\) 2.64590 8.14324i 0.103701 0.319159i
\(652\) −17.3763 23.9164i −0.680508 0.936639i
\(653\) 29.9973 41.2877i 1.17388 1.61571i 0.543632 0.839323i \(-0.317049\pi\)
0.630252 0.776390i \(-0.282951\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 17.9164 + 13.0170i 0.699518 + 0.508230i
\(657\) −1.90211 2.61803i −0.0742085 0.102139i
\(658\) −2.85317 0.927051i −0.111228 0.0361402i
\(659\) 10.6525 0.414962 0.207481 0.978239i \(-0.433474\pi\)
0.207481 + 0.978239i \(0.433474\pi\)
\(660\) 0 0
\(661\) −9.90983 −0.385448 −0.192724 0.981253i \(-0.561732\pi\)
−0.192724 + 0.981253i \(0.561732\pi\)
\(662\) 15.6332 + 5.07953i 0.607601 + 0.197421i
\(663\) −1.67760 2.30902i −0.0651525 0.0896748i
\(664\) 1.28115 + 0.930812i 0.0497184 + 0.0361225i
\(665\) 0 0
\(666\) −0.0450850 0.138757i −0.00174701 0.00537674i
\(667\) −9.12705 + 12.5623i −0.353401 + 0.486414i
\(668\) 9.54332 + 13.1353i 0.369242 + 0.508218i
\(669\) −0.218847 + 0.673542i −0.00846112 + 0.0260406i
\(670\) 0 0
\(671\) −17.2082 + 19.5559i −0.664315 + 0.754948i
\(672\) 16.8541i 0.650161i
\(673\) 11.8087 + 3.83688i 0.455192 + 0.147901i 0.527634 0.849472i \(-0.323079\pi\)
−0.0724420 + 0.997373i \(0.523079\pi\)
\(674\) 0.145898 0.106001i 0.00561978 0.00408301i
\(675\) 0 0
\(676\) 4.94427 + 15.2169i 0.190164 + 0.585266i
\(677\) 12.8658 4.18034i 0.494471 0.160664i −0.0511572 0.998691i \(-0.516291\pi\)
0.545629 + 0.838027i \(0.316291\pi\)
\(678\) −0.257270 + 0.354102i −0.00988040 + 0.0135992i
\(679\) −34.0623 + 24.7477i −1.30719 + 0.949730i
\(680\) 0 0
\(681\) −24.8885 −0.953731
\(682\) 5.82485 + 0.545085i 0.223045 + 0.0208724i
\(683\) 3.11146i 0.119057i −0.998227 0.0595283i \(-0.981040\pi\)
0.998227 0.0595283i \(-0.0189596\pi\)
\(684\) 2.92705 9.00854i 0.111919 0.344450i
\(685\) 0 0
\(686\) −7.50000 5.44907i −0.286351 0.208046i
\(687\) 9.51057 3.09017i 0.362851 0.117897i
\(688\) −10.9964 + 3.57295i −0.419234 + 0.136217i
\(689\) −13.7254 9.97210i −0.522897 0.379907i
\(690\) 0 0
\(691\) −8.12461 + 25.0050i −0.309075 + 0.951234i 0.669050 + 0.743217i \(0.266701\pi\)
−0.978125 + 0.208017i \(0.933299\pi\)
\(692\) 24.8885i 0.946120i
\(693\) 3.94298 9.13525i 0.149782 0.347020i
\(694\) −12.9443 −0.491358
\(695\) 0 0
\(696\) −8.09017 + 5.87785i −0.306657 + 0.222799i
\(697\) 11.3597 15.6353i 0.430278 0.592228i
\(698\) −5.95110 + 1.93363i −0.225252 + 0.0731889i
\(699\) −7.51722 23.1356i −0.284327 0.875070i
\(700\) 0 0
\(701\) 8.64590 6.28161i 0.326551 0.237253i −0.412415 0.910996i \(-0.635315\pi\)
0.738966 + 0.673743i \(0.235315\pi\)
\(702\) 1.03681 + 0.336881i 0.0391320 + 0.0127148i
\(703\) 1.38197i 0.0521218i
\(704\) 0.763932 0.171513i 0.0287918 0.00646416i
\(705\) 0 0
\(706\) 2.00000 6.15537i 0.0752710 0.231660i
\(707\) −5.29007 7.28115i −0.198953 0.273836i
\(708\) −9.82084 + 13.5172i −0.369090 + 0.508008i
\(709\) −15.0623 46.3570i −0.565677 1.74097i −0.665932 0.746012i \(-0.731966\pi\)
0.100255 0.994962i \(-0.468034\pi\)
\(710\) 0 0
\(711\) −7.66312 5.56758i −0.287389 0.208801i
\(712\) 0.693786 + 0.954915i 0.0260007 + 0.0357870i
\(713\) 9.42481 + 3.06231i 0.352962 + 0.114684i
\(714\) 3.00000 0.112272
\(715\) 0 0
\(716\) 3.61803 0.135212
\(717\) −2.43690 0.791796i −0.0910076 0.0295702i
\(718\) −4.63677 6.38197i −0.173043 0.238173i
\(719\) −1.28115 0.930812i −0.0477789 0.0347134i 0.563639 0.826021i \(-0.309401\pi\)
−0.611418 + 0.791307i \(0.709401\pi\)
\(720\) 0 0
\(721\) −5.56231 17.1190i −0.207151 0.637546i
\(722\) 5.54734 7.63525i 0.206451 0.284155i
\(723\) 13.5923 + 18.7082i 0.505503 + 0.695766i
\(724\) −8.73607 + 26.8869i −0.324673 + 0.999242i
\(725\) 0 0
\(726\) 6.68034 + 1.26133i 0.247931 + 0.0468122i
\(727\) 38.8541i 1.44102i −0.693445 0.720509i \(-0.743908\pi\)
0.693445 0.720509i \(-0.256092\pi\)
\(728\) 11.2537 + 3.65654i 0.417089 + 0.135520i
\(729\) 0.809017 0.587785i 0.0299636 0.0217698i
\(730\) 0 0
\(731\) 3.11803 + 9.59632i 0.115325 + 0.354933i
\(732\) −12.0862 + 3.92705i −0.446720 + 0.145148i
\(733\) −22.1643 + 30.5066i −0.818658 + 1.12679i 0.171271 + 0.985224i \(0.445213\pi\)
−0.989929 + 0.141562i \(0.954787\pi\)
\(734\) −2.78115 + 2.02063i −0.102654 + 0.0745827i
\(735\) 0 0
\(736\) −19.5066 −0.719022
\(737\) −27.2829 + 16.1697i −1.00498 + 0.595618i
\(738\) 7.38197i 0.271734i
\(739\) 7.72542 23.7764i 0.284184 0.874629i −0.702458 0.711726i \(-0.747914\pi\)
0.986642 0.162904i \(-0.0520860\pi\)
\(740\) 0 0
\(741\) −8.35410 6.06961i −0.306896 0.222973i
\(742\) 16.9600 5.51064i 0.622622 0.202302i
\(743\) −33.4585 + 10.8713i −1.22747 + 0.398830i −0.849798 0.527108i \(-0.823276\pi\)
−0.377675 + 0.925938i \(0.623276\pi\)
\(744\) 5.16312 + 3.75123i 0.189289 + 0.137527i
\(745\) 0 0
\(746\) 0.843459 2.59590i 0.0308812 0.0950426i
\(747\) 0.708204i 0.0259118i
\(748\) −1.90211 8.47214i −0.0695481 0.309772i
\(749\) 12.7082 0.464348
\(750\) 0 0
\(751\) −9.64590 + 7.00816i −0.351984 + 0.255731i −0.749701 0.661777i \(-0.769803\pi\)
0.397717 + 0.917508i \(0.369803\pi\)
\(752\) −1.76336 + 2.42705i −0.0643030 + 0.0885054i
\(753\) 7.41669 2.40983i 0.270279 0.0878191i
\(754\) 1.50658 + 4.63677i 0.0548663 + 0.168861i
\(755\) 0 0
\(756\) 3.92705 2.85317i 0.142825 0.103769i
\(757\) −1.84911 0.600813i −0.0672071 0.0218369i 0.275220 0.961381i \(-0.411249\pi\)
−0.342428 + 0.939544i \(0.611249\pi\)
\(758\) 0.978714i 0.0355485i
\(759\) 10.5729 + 4.56352i 0.383774 + 0.165645i
\(760\) 0 0
\(761\) −9.54508 + 29.3768i −0.346009 + 1.06491i 0.615032 + 0.788502i \(0.289143\pi\)
−0.961041 + 0.276404i \(0.910857\pi\)
\(762\) 1.34708 + 1.85410i 0.0487997 + 0.0671670i
\(763\) 0 0
\(764\) −3.73607 11.4984i −0.135166 0.415999i
\(765\) 0 0
\(766\) 13.4443 + 9.76784i 0.485761 + 0.352926i
\(767\) 10.7064 + 14.7361i 0.386585 + 0.532089i
\(768\) −6.24112 2.02786i −0.225207 0.0731742i
\(769\) −12.6869 −0.457502 −0.228751 0.973485i \(-0.573464\pi\)
−0.228751 + 0.973485i \(0.573464\pi\)
\(770\) 0 0
\(771\) −11.6738 −0.420420
\(772\) −28.5645 9.28115i −1.02806 0.334036i
\(773\) 18.3678 + 25.2812i 0.660645 + 0.909300i 0.999503 0.0315378i \(-0.0100405\pi\)
−0.338858 + 0.940838i \(0.610040\pi\)
\(774\) −3.11803 2.26538i −0.112075 0.0814276i
\(775\) 0 0
\(776\) −9.69756 29.8460i −0.348122 1.07141i
\(777\) −0.416272 + 0.572949i −0.0149337 + 0.0205544i
\(778\) 8.81678 + 12.1353i 0.316097 + 0.435070i
\(779\) 21.6074 66.5007i 0.774165 2.38264i
\(780\) 0 0
\(781\) 12.1869 13.8496i 0.436082 0.495577i
\(782\) 3.47214i 0.124163i
\(783\) 4.25325 + 1.38197i 0.151999 + 0.0493874i
\(784\) 3.00000 2.17963i 0.107143 0.0778438i
\(785\) 0 0
\(786\) 1.36475 + 4.20025i 0.0486788 + 0.149818i
\(787\) −9.78808 + 3.18034i −0.348907 + 0.113367i −0.478227 0.878236i \(-0.658721\pi\)
0.129320 + 0.991603i \(0.458721\pi\)
\(788\) −23.1886 + 31.9164i −0.826061 + 1.13697i
\(789\) −13.2082 + 9.59632i −0.470225 + 0.341638i
\(790\) 0 0
\(791\) 2.12461 0.0755425
\(792\) 5.56758 + 4.89919i 0.197835 + 0.174085i
\(793\) 13.8541i 0.491974i
\(794\) −7.39261 + 22.7521i −0.262354 + 0.807442i
\(795\) 0 0
\(796\) −21.8713 15.8904i −0.775208 0.563222i
\(797\) 10.2371 3.32624i 0.362617 0.117821i −0.122041 0.992525i \(-0.538944\pi\)
0.484658 + 0.874704i \(0.338944\pi\)
\(798\) 10.3229 3.35410i 0.365425 0.118734i
\(799\) 2.11803 + 1.53884i 0.0749307 + 0.0544403i
\(800\) 0 0
\(801\) 0.163119 0.502029i 0.00576353 0.0177383i
\(802\) 16.1246i 0.569380i
\(803\) −10.6861 1.00000i −0.377106 0.0352892i
\(804\) −15.4721 −0.545660
\(805\) 0 0
\(806\) 2.51722 1.82887i 0.0886653 0.0644191i
\(807\) −9.12705 + 12.5623i −0.321287 + 0.442214i
\(808\) 6.37988 2.07295i 0.224443 0.0729261i
\(809\) −2.98936 9.20029i −0.105100 0.323465i 0.884654 0.466249i \(-0.154395\pi\)
−0.989754 + 0.142783i \(0.954395\pi\)
\(810\) 0 0
\(811\) −2.63525 + 1.91462i −0.0925363 + 0.0672316i −0.633091 0.774077i \(-0.718214\pi\)
0.540555 + 0.841309i \(0.318214\pi\)
\(812\) 20.6457 + 6.70820i 0.724523 + 0.235412i
\(813\) 27.2705i 0.956419i
\(814\) −0.444272 0.191758i −0.0155717 0.00672111i
\(815\) 0 0
\(816\) 0.927051 2.85317i 0.0324533 0.0998809i
\(817\) 21.4580 + 29.5344i 0.750721 + 1.03328i
\(818\) 4.01623 5.52786i 0.140424 0.193277i
\(819\) −1.63525 5.03280i −0.0571404 0.175860i
\(820\) 0 0
\(821\) −32.6976 23.7562i −1.14115 0.829096i −0.153873 0.988091i \(-0.549175\pi\)
−0.987279 + 0.158995i \(0.949175\pi\)
\(822\) −2.71441 3.73607i −0.0946760 0.130310i
\(823\) −33.7360 10.9615i −1.17596 0.382094i −0.345098 0.938567i \(-0.612154\pi\)
−0.830866 + 0.556473i \(0.812154\pi\)
\(824\) 13.4164 0.467383
\(825\) 0 0
\(826\) −19.1459 −0.666171
\(827\) −50.5245 16.4164i −1.75691 0.570854i −0.760037 0.649880i \(-0.774819\pi\)
−0.996873 + 0.0790257i \(0.974819\pi\)
\(828\) 3.30220 + 4.54508i 0.114759 + 0.157953i
\(829\) 14.3090 + 10.3961i 0.496973 + 0.361072i 0.807859 0.589375i \(-0.200626\pi\)
−0.310887 + 0.950447i \(0.600626\pi\)
\(830\) 0 0
\(831\) 9.44427 + 29.0665i 0.327618 + 1.00831i
\(832\) 0.244758 0.336881i 0.00848547 0.0116792i
\(833\) −1.90211 2.61803i −0.0659043 0.0907095i
\(834\) −0.163119 + 0.502029i −0.00564835 + 0.0173838i
\(835\) 0 0
\(836\) −16.0172 27.0256i −0.553967 0.934700i
\(837\) 2.85410i 0.0986522i
\(838\) −9.70232 3.15248i −0.335161 0.108900i
\(839\) −29.6976 + 21.5765i −1.02527 + 0.744905i −0.967357 0.253417i \(-0.918446\pi\)
−0.0579164 + 0.998321i \(0.518446\pi\)
\(840\) 0 0
\(841\) −2.78115 8.55951i −0.0959018 0.295155i
\(842\) 21.9071 7.11803i 0.754967 0.245304i
\(843\) −0.449028 + 0.618034i −0.0154653 + 0.0212862i
\(844\) 29.1525 21.1805i 1.00347 0.729063i
\(845\) 0 0
\(846\) −1.00000 −0.0343807
\(847\) −14.1068 29.8328i −0.484717 1.02507i
\(848\) 17.8328i 0.612381i
\(849\) −0.0557281 + 0.171513i −0.00191258 + 0.00588633i
\(850\) 0 0
\(851\) −0.663119 0.481784i −0.0227314 0.0165153i
\(852\) 8.55951 2.78115i 0.293244 0.0952807i
\(853\) 9.45756 3.07295i 0.323821 0.105216i −0.142596 0.989781i \(-0.545545\pi\)
0.466416 + 0.884565i \(0.345545\pi\)
\(854\) −11.7812 8.55951i −0.403143 0.292900i
\(855\) 0 0
\(856\) −2.92705 + 9.00854i −0.100045 + 0.307905i
\(857\) 47.7214i 1.63013i −0.579369 0.815065i \(-0.696701\pi\)
0.579369 0.815065i \(-0.303299\pi\)
\(858\) 3.11044 1.84346i 0.106189 0.0629346i
\(859\) −7.11146 −0.242640 −0.121320 0.992613i \(-0.538713\pi\)
−0.121320 + 0.992613i \(0.538713\pi\)
\(860\) 0 0
\(861\) 28.9894 21.0620i 0.987955 0.717791i
\(862\) −14.3516 + 19.7533i −0.488818 + 0.672800i
\(863\) −11.3067 + 3.67376i −0.384884 + 0.125056i −0.495067 0.868855i \(-0.664856\pi\)
0.110183 + 0.993911i \(0.464856\pi\)
\(864\) 1.73607 + 5.34307i 0.0590622 + 0.181775i
\(865\) 0 0
\(866\) −3.00000 + 2.17963i −0.101944 + 0.0740668i
\(867\) 13.6781 + 4.44427i 0.464531 + 0.150935i
\(868\) 13.8541i 0.470239i
\(869\) −30.6525 + 6.88191i −1.03981 + 0.233453i
\(870\) 0 0
\(871\) −5.21227 + 16.0417i −0.176611 + 0.543553i
\(872\) 0 0
\(873\) −8.24924 + 11.3541i −0.279194 + 0.384278i
\(874\) 3.88197 + 11.9475i 0.131309 + 0.404129i
\(875\) 0 0
\(876\) −4.23607 3.07768i −0.143123 0.103985i
\(877\) 3.77147 + 5.19098i 0.127353 + 0.175287i 0.867932 0.496682i \(-0.165449\pi\)
−0.740579 + 0.671969i \(0.765449\pi\)
\(878\) −1.93487 0.628677i −0.0652987 0.0212168i
\(879\) −0.0557281 −0.00187966
\(880\) 0 0
\(881\) 13.9098 0.468634 0.234317 0.972160i \(-0.424715\pi\)
0.234317 + 0.972160i \(0.424715\pi\)
\(882\) 1.17557 + 0.381966i 0.0395835 + 0.0128615i
\(883\) −6.22088 8.56231i −0.209349 0.288145i 0.691411 0.722462i \(-0.256990\pi\)
−0.900760 + 0.434318i \(0.856990\pi\)
\(884\) −3.73607 2.71441i −0.125658 0.0912956i
\(885\) 0 0
\(886\) 7.85410 + 24.1724i 0.263864 + 0.812089i
\(887\) −1.76336 + 2.42705i −0.0592077 + 0.0814924i −0.837594 0.546293i \(-0.816038\pi\)
0.778386 + 0.627785i \(0.216038\pi\)
\(888\) −0.310271 0.427051i −0.0104120 0.0143309i
\(889\) 3.43769 10.5801i 0.115297 0.354846i
\(890\) 0 0
\(891\) 0.309017 3.30220i 0.0103525 0.110628i
\(892\) 1.14590i 0.0383675i
\(893\) 9.00854 + 2.92705i 0.301459 + 0.0979500i
\(894\) −7.50000 + 5.44907i −0.250838 + 0.182244i
\(895\) 0 0
\(896\) 10.5517 + 32.4747i 0.352506 + 1.08490i
\(897\) 5.82485 1.89261i 0.194486 0.0631924i
\(898\) 8.89002 12.2361i 0.296664 0.408323i
\(899\) 10.3262 7.50245i 0.344399 0.250221i
\(900\) 0 0
\(901\) −15.5623 −0.518456
\(902\) 18.3803 + 16.1738i 0.611999 + 0.538527i
\(903\) 18.7082i 0.622570i
\(904\) −0.489357 + 1.50609i −0.0162758 + 0.0500917i
\(905\) 0 0
\(906\) 1.00000 + 0.726543i 0.0332228 + 0.0241378i
\(907\) −40.8752 + 13.2812i −1.35724 + 0.440993i −0.895120 0.445825i \(-0.852910\pi\)
−0.462118 + 0.886818i \(0.652910\pi\)
\(908\) −38.2995 + 12.4443i −1.27101 + 0.412978i
\(909\) −2.42705 1.76336i −0.0805002 0.0584868i
\(910\) 0 0
\(911\) 5.57953 17.1720i 0.184858 0.568934i −0.815088 0.579337i \(-0.803311\pi\)
0.999946 + 0.0104029i \(0.00331142\pi\)
\(912\) 10.8541i 0.359415i
\(913\) −1.76336 1.55166i −0.0583586 0.0513525i
\(914\) 5.06888 0.167664
\(915\) 0 0
\(916\) 13.0902 9.51057i 0.432511 0.314238i
\(917\) 12.6008 17.3435i 0.416114 0.572731i
\(918\) 0.951057 0.309017i 0.0313895 0.0101991i
\(919\) −14.5106 44.6592i −0.478662 1.47317i −0.840955 0.541106i \(-0.818006\pi\)
0.362293 0.932064i \(-0.381994\pi\)
\(920\) 0 0
\(921\) −0.454915 + 0.330515i −0.0149900 + 0.0108908i
\(922\) −12.3965 4.02786i −0.408257 0.132651i
\(923\) 9.81153i 0.322950i
\(924\) 1.50000 16.0292i 0.0493464 0.527322i
\(925\) 0 0
\(926\) 3.01722 9.28605i 0.0991520 0.305159i
\(927\) −3.52671 4.85410i −0.115832 0.159430i
\(928\) −14.7679 + 20.3262i −0.484779 + 0.667241i
\(929\) 10.1631 + 31.2789i 0.333441 + 1.02623i 0.967485 + 0.252929i \(0.0813939\pi\)
−0.634044 + 0.773297i \(0.718606\pi\)
\(930\) 0 0
\(931\) −9.47214 6.88191i −0.310437 0.225545i
\(932\) −23.1356 31.8435i −0.757833 1.04307i
\(933\) 2.40414 + 0.781153i 0.0787081 + 0.0255738i
\(934\) −6.03444 −0.197453
\(935\) 0 0
\(936\) 3.94427 0.128923
\(937\) 15.7844 + 5.12868i 0.515655 + 0.167547i 0.555273 0.831668i \(-0.312614\pi\)
−0.0396173 + 0.999215i \(0.512614\pi\)
\(938\) −10.4211 14.3435i −0.340262 0.468331i
\(939\) 20.8992 + 15.1841i 0.682019 + 0.495516i
\(940\) 0 0
\(941\) −13.7918 42.4468i −0.449600 1.38373i −0.877360 0.479833i \(-0.840697\pi\)
0.427760 0.903892i \(-0.359303\pi\)
\(942\) −1.34708 + 1.85410i −0.0438904 + 0.0604099i
\(943\) 24.3767 + 33.5517i 0.793815 + 1.09259i
\(944\) −5.91641 + 18.2088i −0.192563 + 0.592647i
\(945\) 0 0
\(946\) −12.4721 + 2.80017i −0.405504 + 0.0910413i
\(947\) 18.3262i 0.595523i −0.954640 0.297761i \(-0.903760\pi\)
0.954640 0.297761i \(-0.0962400\pi\)
\(948\) −14.5761 4.73607i −0.473410 0.153820i
\(949\) −4.61803 + 3.35520i −0.149908 + 0.108914i
\(950\) 0 0
\(951\) −5.98278 18.4131i −0.194005 0.597086i
\(952\) 10.3229 3.35410i 0.334566 0.108707i
\(953\) 22.2298 30.5967i 0.720095 0.991126i −0.279426 0.960167i \(-0.590144\pi\)
0.999521 0.0309585i \(-0.00985598\pi\)
\(954\) 4.80902 3.49396i 0.155698 0.113121i
\(955\) 0 0
\(956\) −4.14590 −0.134088
\(957\) 12.7598 7.56231i 0.412465 0.244455i
\(958\) 17.3607i 0.560898i
\(959\) −6.92705 + 21.3193i −0.223686 + 0.688435i
\(960\) 0 0
\(961\) 18.4894 + 13.4333i 0.596431 + 0.433332i
\(962\) −0.244758 + 0.0795268i −0.00789133 + 0.00256405i
\(963\) 4.02874 1.30902i 0.129824 0.0421825i
\(964\) 30.2705 + 21.9928i 0.974947 + 0.708341i
\(965\) 0 0
\(966\) −1.98936 + 6.12261i −0.0640065 + 0.196992i
\(967\) 34.6869i 1.11546i 0.830024 + 0.557728i \(0.188327\pi\)
−0.830024 + 0.557728i \(0.811673\pi\)
\(968\) 24.3970 3.12868i 0.784148 0.100559i
\(969\) −9.47214 −0.304289
\(970\) 0 0
\(971\) −30.5623 + 22.2048i −0.980791 + 0.712586i −0.957885 0.287151i \(-0.907292\pi\)
−0.0229058 + 0.999738i \(0.507292\pi\)
\(972\) 0.951057 1.30902i 0.0305052 0.0419867i
\(973\) 2.43690 0.791796i 0.0781234 0.0253838i
\(974\) 3.21227 + 9.88635i 0.102928 + 0.316779i
\(975\) 0 0
\(976\) −11.7812 + 8.55951i −0.377106 + 0.273983i
\(977\) 4.41226 + 1.43363i 0.141161 + 0.0458658i 0.378745 0.925501i \(-0.376356\pi\)
−0.237585 + 0.971367i \(0.576356\pi\)
\(978\) 11.2918i 0.361072i
\(979\) −0.892609 1.50609i −0.0285279 0.0481347i
\(980\) 0 0
\(981\) 0 0
\(982\) −9.15981 12.6074i −0.292301 0.402318i
\(983\) −16.0494 + 22.0902i −0.511898 + 0.704567i −0.984238 0.176849i \(-0.943409\pi\)
0.472340 + 0.881416i \(0.343409\pi\)
\(984\) 8.25329 + 25.4010i 0.263105 + 0.809755i
\(985\) 0 0
\(986\) 3.61803 + 2.62866i 0.115222 + 0.0837134i
\(987\) 2.85317 + 3.92705i 0.0908174 + 0.124999i
\(988\) −15.8904 5.16312i −0.505542 0.164261i
\(989\) −21.6525 −0.688509
\(990\) 0 0
\(991\) 21.2705 0.675680 0.337840 0.941204i \(-0.390304\pi\)
0.337840 + 0.941204i \(0.390304\pi\)
\(992\) 15.2497 + 4.95492i 0.484177 + 0.157319i
\(993\) −15.6332 21.5172i −0.496104 0.682828i
\(994\) 8.34346 + 6.06188i 0.264638 + 0.192271i
\(995\) 0 0
\(996\) −0.354102 1.08981i −0.0112202 0.0345321i
\(997\) 7.62870 10.5000i 0.241603 0.332538i −0.670945 0.741507i \(-0.734111\pi\)
0.912548 + 0.408969i \(0.134111\pi\)
\(998\) −6.37988 8.78115i −0.201952 0.277963i
\(999\) −0.0729490 + 0.224514i −0.00230800 + 0.00710331i
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 825.2.bx.b.724.2 8
5.2 odd 4 33.2.e.a.31.1 yes 4
5.3 odd 4 825.2.n.f.526.1 4
5.4 even 2 inner 825.2.bx.b.724.1 8
11.5 even 5 inner 825.2.bx.b.49.1 8
15.2 even 4 99.2.f.b.64.1 4
20.7 even 4 528.2.y.f.97.1 4
45.2 even 12 891.2.n.a.757.1 8
45.7 odd 12 891.2.n.d.757.1 8
45.22 odd 12 891.2.n.d.460.1 8
45.32 even 12 891.2.n.a.460.1 8
55.2 even 20 363.2.e.c.124.1 4
55.7 even 20 363.2.a.e.1.2 2
55.17 even 20 363.2.e.j.148.1 4
55.18 even 20 9075.2.a.bv.1.1 2
55.27 odd 20 33.2.e.a.16.1 4
55.32 even 4 363.2.e.j.130.1 4
55.37 odd 20 363.2.a.h.1.1 2
55.38 odd 20 825.2.n.f.676.1 4
55.42 odd 20 363.2.e.h.124.1 4
55.47 odd 20 363.2.e.h.202.1 4
55.48 odd 20 9075.2.a.x.1.2 2
55.49 even 10 inner 825.2.bx.b.49.2 8
55.52 even 20 363.2.e.c.202.1 4
165.62 odd 20 1089.2.a.s.1.1 2
165.92 even 20 1089.2.a.m.1.2 2
165.137 even 20 99.2.f.b.82.1 4
220.7 odd 20 5808.2.a.bm.1.1 2
220.27 even 20 528.2.y.f.49.1 4
220.147 even 20 5808.2.a.bl.1.1 2
495.137 even 60 891.2.n.a.676.1 8
495.247 odd 60 891.2.n.d.379.1 8
495.302 even 60 891.2.n.a.379.1 8
495.412 odd 60 891.2.n.d.676.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.2.e.a.16.1 4 55.27 odd 20
33.2.e.a.31.1 yes 4 5.2 odd 4
99.2.f.b.64.1 4 15.2 even 4
99.2.f.b.82.1 4 165.137 even 20
363.2.a.e.1.2 2 55.7 even 20
363.2.a.h.1.1 2 55.37 odd 20
363.2.e.c.124.1 4 55.2 even 20
363.2.e.c.202.1 4 55.52 even 20
363.2.e.h.124.1 4 55.42 odd 20
363.2.e.h.202.1 4 55.47 odd 20
363.2.e.j.130.1 4 55.32 even 4
363.2.e.j.148.1 4 55.17 even 20
528.2.y.f.49.1 4 220.27 even 20
528.2.y.f.97.1 4 20.7 even 4
825.2.n.f.526.1 4 5.3 odd 4
825.2.n.f.676.1 4 55.38 odd 20
825.2.bx.b.49.1 8 11.5 even 5 inner
825.2.bx.b.49.2 8 55.49 even 10 inner
825.2.bx.b.724.1 8 5.4 even 2 inner
825.2.bx.b.724.2 8 1.1 even 1 trivial
891.2.n.a.379.1 8 495.302 even 60
891.2.n.a.460.1 8 45.32 even 12
891.2.n.a.676.1 8 495.137 even 60
891.2.n.a.757.1 8 45.2 even 12
891.2.n.d.379.1 8 495.247 odd 60
891.2.n.d.460.1 8 45.22 odd 12
891.2.n.d.676.1 8 495.412 odd 60
891.2.n.d.757.1 8 45.7 odd 12
1089.2.a.m.1.2 2 165.92 even 20
1089.2.a.s.1.1 2 165.62 odd 20
5808.2.a.bl.1.1 2 220.147 even 20
5808.2.a.bm.1.1 2 220.7 odd 20
9075.2.a.x.1.2 2 55.48 odd 20
9075.2.a.bv.1.1 2 55.18 even 20