Properties

Label 847.2.f.j.729.1
Level $847$
Weight $2$
Character 847.729
Analytic conductor $6.763$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [847,2,Mod(148,847)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(847, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("847.148");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.f (of order \(5\), 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: \(6.76332905120\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 729.1
Root \(0.809017 + 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 847.729
Dual form 847.2.f.j.323.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.309017 + 0.224514i) q^{2} +(-0.500000 - 1.53884i) q^{3} +(-0.572949 + 1.76336i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.500000 + 0.363271i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.454915 - 1.40008i) q^{8} +(0.309017 - 0.224514i) q^{9} +O(q^{10})\) \(q+(-0.309017 + 0.224514i) q^{2} +(-0.500000 - 1.53884i) q^{3} +(-0.572949 + 1.76336i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.500000 + 0.363271i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.454915 - 1.40008i) q^{8} +(0.309017 - 0.224514i) q^{9} +0.381966 q^{10} +3.00000 q^{12} +(-1.00000 + 0.726543i) q^{13} +(-0.118034 - 0.363271i) q^{14} +(-0.500000 + 1.53884i) q^{15} +(-2.54508 - 1.84911i) q^{16} +(2.50000 + 1.81636i) q^{17} +(-0.0450850 + 0.138757i) q^{18} +(0.545085 + 1.67760i) q^{19} +(1.50000 - 1.08981i) q^{20} +1.61803 q^{21} +5.09017 q^{23} +(-1.92705 + 1.40008i) q^{24} +(-1.23607 - 3.80423i) q^{25} +(0.145898 - 0.449028i) q^{26} +(-4.42705 - 3.21644i) q^{27} +(-1.50000 - 1.08981i) q^{28} +(1.42705 - 4.39201i) q^{29} +(-0.190983 - 0.587785i) q^{30} +(3.42705 - 2.48990i) q^{31} +4.14590 q^{32} -1.18034 q^{34} +(0.809017 - 0.587785i) q^{35} +(0.218847 + 0.673542i) q^{36} +(2.00000 - 6.15537i) q^{37} +(-0.545085 - 0.396027i) q^{38} +(1.61803 + 1.17557i) q^{39} +(-0.454915 + 1.40008i) q^{40} +(3.45492 + 10.6331i) q^{41} +(-0.500000 + 0.363271i) q^{42} +12.5623 q^{43} -0.381966 q^{45} +(-1.57295 + 1.14281i) q^{46} +(-2.04508 - 6.29412i) q^{47} +(-1.57295 + 4.84104i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(1.23607 + 0.898056i) q^{50} +(1.54508 - 4.75528i) q^{51} +(-0.708204 - 2.17963i) q^{52} +(1.92705 - 1.40008i) q^{53} +2.09017 q^{54} +1.47214 q^{56} +(2.30902 - 1.67760i) q^{57} +(0.545085 + 1.67760i) q^{58} +(3.42705 - 10.5474i) q^{59} +(-2.42705 - 1.76336i) q^{60} +(-6.16312 - 4.47777i) q^{61} +(-0.500000 + 1.53884i) q^{62} +(0.118034 + 0.363271i) q^{63} +(3.80902 - 2.76741i) q^{64} +1.23607 q^{65} -8.32624 q^{67} +(-4.63525 + 3.36771i) q^{68} +(-2.54508 - 7.83297i) q^{69} +(-0.118034 + 0.363271i) q^{70} +(13.0172 + 9.45756i) q^{71} +(-0.454915 - 0.330515i) q^{72} +(4.39919 - 13.5393i) q^{73} +(0.763932 + 2.35114i) q^{74} +(-5.23607 + 3.80423i) q^{75} -3.27051 q^{76} -0.763932 q^{78} +(5.16312 - 3.75123i) q^{79} +(0.972136 + 2.99193i) q^{80} +(-2.38197 + 7.33094i) q^{81} +(-3.45492 - 2.51014i) q^{82} +(2.19098 + 1.59184i) q^{83} +(-0.927051 + 2.85317i) q^{84} +(-0.954915 - 2.93893i) q^{85} +(-3.88197 + 2.82041i) q^{86} -7.47214 q^{87} +6.85410 q^{89} +(0.118034 - 0.0857567i) q^{90} +(-0.381966 - 1.17557i) q^{91} +(-2.91641 + 8.97578i) q^{92} +(-5.54508 - 4.02874i) q^{93} +(2.04508 + 1.48584i) q^{94} +(0.545085 - 1.67760i) q^{95} +(-2.07295 - 6.37988i) q^{96} +(-5.66312 + 4.11450i) q^{97} +0.381966 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} - 2 q^{3} - 9 q^{4} - q^{5} + 2 q^{6} + q^{7} - 13 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{2} - 2 q^{3} - 9 q^{4} - q^{5} + 2 q^{6} + q^{7} - 13 q^{8} - q^{9} + 6 q^{10} + 12 q^{12} - 4 q^{13} + 4 q^{14} - 2 q^{15} + q^{16} + 10 q^{17} + 11 q^{18} - 9 q^{19} + 6 q^{20} + 2 q^{21} - 2 q^{23} - q^{24} + 4 q^{25} + 14 q^{26} - 11 q^{27} - 6 q^{28} - q^{29} - 3 q^{30} + 7 q^{31} + 30 q^{32} + 40 q^{34} + q^{35} + 21 q^{36} + 8 q^{37} + 9 q^{38} + 2 q^{39} - 13 q^{40} + 25 q^{41} - 2 q^{42} + 10 q^{43} - 6 q^{45} - 13 q^{46} + 3 q^{47} - 13 q^{48} - q^{49} - 4 q^{50} - 5 q^{51} + 24 q^{52} + q^{53} - 14 q^{54} - 12 q^{56} + 7 q^{57} - 9 q^{58} + 7 q^{59} - 3 q^{60} - 9 q^{61} - 2 q^{62} - 4 q^{63} + 13 q^{64} - 4 q^{65} - 2 q^{67} + 15 q^{68} + q^{69} + 4 q^{70} + 23 q^{71} - 13 q^{72} - 7 q^{73} + 12 q^{74} - 12 q^{75} + 54 q^{76} - 12 q^{78} + 5 q^{79} - 14 q^{80} - 14 q^{81} - 25 q^{82} + 11 q^{83} + 3 q^{84} - 15 q^{85} - 20 q^{86} - 12 q^{87} + 14 q^{89} - 4 q^{90} - 6 q^{91} + 42 q^{92} - 11 q^{93} - 3 q^{94} - 9 q^{95} - 15 q^{96} - 7 q^{97} + 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(365\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 + 0.224514i −0.218508 + 0.158755i −0.691655 0.722228i \(-0.743118\pi\)
0.473147 + 0.880984i \(0.343118\pi\)
\(3\) −0.500000 1.53884i −0.288675 0.888451i −0.985273 0.170989i \(-0.945304\pi\)
0.696598 0.717462i \(-0.254696\pi\)
\(4\) −0.572949 + 1.76336i −0.286475 + 0.881678i
\(5\) −0.809017 0.587785i −0.361803 0.262866i 0.392000 0.919965i \(-0.371783\pi\)
−0.753804 + 0.657099i \(0.771783\pi\)
\(6\) 0.500000 + 0.363271i 0.204124 + 0.148305i
\(7\) −0.309017 + 0.951057i −0.116797 + 0.359466i
\(8\) −0.454915 1.40008i −0.160837 0.495005i
\(9\) 0.309017 0.224514i 0.103006 0.0748380i
\(10\) 0.381966 0.120788
\(11\) 0 0
\(12\) 3.00000 0.866025
\(13\) −1.00000 + 0.726543i −0.277350 + 0.201507i −0.717761 0.696290i \(-0.754833\pi\)
0.440411 + 0.897796i \(0.354833\pi\)
\(14\) −0.118034 0.363271i −0.0315459 0.0970883i
\(15\) −0.500000 + 1.53884i −0.129099 + 0.397327i
\(16\) −2.54508 1.84911i −0.636271 0.462278i
\(17\) 2.50000 + 1.81636i 0.606339 + 0.440531i 0.848123 0.529799i \(-0.177733\pi\)
−0.241784 + 0.970330i \(0.577733\pi\)
\(18\) −0.0450850 + 0.138757i −0.0106266 + 0.0327054i
\(19\) 0.545085 + 1.67760i 0.125051 + 0.384868i 0.993910 0.110191i \(-0.0351464\pi\)
−0.868859 + 0.495059i \(0.835146\pi\)
\(20\) 1.50000 1.08981i 0.335410 0.243690i
\(21\) 1.61803 0.353084
\(22\) 0 0
\(23\) 5.09017 1.06137 0.530687 0.847568i \(-0.321934\pi\)
0.530687 + 0.847568i \(0.321934\pi\)
\(24\) −1.92705 + 1.40008i −0.393358 + 0.285791i
\(25\) −1.23607 3.80423i −0.247214 0.760845i
\(26\) 0.145898 0.449028i 0.0286130 0.0880616i
\(27\) −4.42705 3.21644i −0.851986 0.619004i
\(28\) −1.50000 1.08981i −0.283473 0.205955i
\(29\) 1.42705 4.39201i 0.264997 0.815576i −0.726697 0.686958i \(-0.758946\pi\)
0.991694 0.128618i \(-0.0410542\pi\)
\(30\) −0.190983 0.587785i −0.0348686 0.107314i
\(31\) 3.42705 2.48990i 0.615517 0.447199i −0.235836 0.971793i \(-0.575783\pi\)
0.851353 + 0.524594i \(0.175783\pi\)
\(32\) 4.14590 0.732898
\(33\) 0 0
\(34\) −1.18034 −0.202427
\(35\) 0.809017 0.587785i 0.136749 0.0993538i
\(36\) 0.218847 + 0.673542i 0.0364745 + 0.112257i
\(37\) 2.00000 6.15537i 0.328798 1.01194i −0.640899 0.767625i \(-0.721438\pi\)
0.969697 0.244311i \(-0.0785617\pi\)
\(38\) −0.545085 0.396027i −0.0884245 0.0642441i
\(39\) 1.61803 + 1.17557i 0.259093 + 0.188242i
\(40\) −0.454915 + 1.40008i −0.0719284 + 0.221373i
\(41\) 3.45492 + 10.6331i 0.539567 + 1.66062i 0.733569 + 0.679615i \(0.237853\pi\)
−0.194001 + 0.981001i \(0.562147\pi\)
\(42\) −0.500000 + 0.363271i −0.0771517 + 0.0560540i
\(43\) 12.5623 1.91573 0.957867 0.287213i \(-0.0927286\pi\)
0.957867 + 0.287213i \(0.0927286\pi\)
\(44\) 0 0
\(45\) −0.381966 −0.0569401
\(46\) −1.57295 + 1.14281i −0.231919 + 0.168499i
\(47\) −2.04508 6.29412i −0.298306 0.918092i −0.982091 0.188408i \(-0.939667\pi\)
0.683784 0.729684i \(-0.260333\pi\)
\(48\) −1.57295 + 4.84104i −0.227036 + 0.698744i
\(49\) −0.809017 0.587785i −0.115574 0.0839693i
\(50\) 1.23607 + 0.898056i 0.174806 + 0.127004i
\(51\) 1.54508 4.75528i 0.216355 0.665873i
\(52\) −0.708204 2.17963i −0.0982102 0.302260i
\(53\) 1.92705 1.40008i 0.264701 0.192316i −0.447516 0.894276i \(-0.647691\pi\)
0.712217 + 0.701960i \(0.247691\pi\)
\(54\) 2.09017 0.284436
\(55\) 0 0
\(56\) 1.47214 0.196722
\(57\) 2.30902 1.67760i 0.305837 0.222203i
\(58\) 0.545085 + 1.67760i 0.0715732 + 0.220280i
\(59\) 3.42705 10.5474i 0.446164 1.37315i −0.435038 0.900412i \(-0.643265\pi\)
0.881202 0.472740i \(-0.156735\pi\)
\(60\) −2.42705 1.76336i −0.313331 0.227648i
\(61\) −6.16312 4.47777i −0.789107 0.573319i 0.118592 0.992943i \(-0.462162\pi\)
−0.907698 + 0.419624i \(0.862162\pi\)
\(62\) −0.500000 + 1.53884i −0.0635001 + 0.195433i
\(63\) 0.118034 + 0.363271i 0.0148709 + 0.0457679i
\(64\) 3.80902 2.76741i 0.476127 0.345927i
\(65\) 1.23607 0.153315
\(66\) 0 0
\(67\) −8.32624 −1.01721 −0.508606 0.860999i \(-0.669839\pi\)
−0.508606 + 0.860999i \(0.669839\pi\)
\(68\) −4.63525 + 3.36771i −0.562107 + 0.408395i
\(69\) −2.54508 7.83297i −0.306392 0.942978i
\(70\) −0.118034 + 0.363271i −0.0141078 + 0.0434192i
\(71\) 13.0172 + 9.45756i 1.54486 + 1.12241i 0.947194 + 0.320661i \(0.103905\pi\)
0.597666 + 0.801745i \(0.296095\pi\)
\(72\) −0.454915 0.330515i −0.0536123 0.0389516i
\(73\) 4.39919 13.5393i 0.514886 1.58466i −0.268604 0.963251i \(-0.586562\pi\)
0.783490 0.621405i \(-0.213438\pi\)
\(74\) 0.763932 + 2.35114i 0.0888053 + 0.273315i
\(75\) −5.23607 + 3.80423i −0.604609 + 0.439274i
\(76\) −3.27051 −0.375153
\(77\) 0 0
\(78\) −0.763932 −0.0864983
\(79\) 5.16312 3.75123i 0.580896 0.422046i −0.258151 0.966105i \(-0.583113\pi\)
0.839047 + 0.544059i \(0.183113\pi\)
\(80\) 0.972136 + 2.99193i 0.108688 + 0.334508i
\(81\) −2.38197 + 7.33094i −0.264663 + 0.814549i
\(82\) −3.45492 2.51014i −0.381532 0.277199i
\(83\) 2.19098 + 1.59184i 0.240492 + 0.174727i 0.701502 0.712667i \(-0.252513\pi\)
−0.461011 + 0.887395i \(0.652513\pi\)
\(84\) −0.927051 + 2.85317i −0.101150 + 0.311306i
\(85\) −0.954915 2.93893i −0.103575 0.318771i
\(86\) −3.88197 + 2.82041i −0.418603 + 0.304133i
\(87\) −7.47214 −0.801097
\(88\) 0 0
\(89\) 6.85410 0.726533 0.363267 0.931685i \(-0.381661\pi\)
0.363267 + 0.931685i \(0.381661\pi\)
\(90\) 0.118034 0.0857567i 0.0124419 0.00903955i
\(91\) −0.381966 1.17557i −0.0400409 0.123233i
\(92\) −2.91641 + 8.97578i −0.304057 + 0.935790i
\(93\) −5.54508 4.02874i −0.574999 0.417761i
\(94\) 2.04508 + 1.48584i 0.210934 + 0.153253i
\(95\) 0.545085 1.67760i 0.0559245 0.172118i
\(96\) −2.07295 6.37988i −0.211569 0.651144i
\(97\) −5.66312 + 4.11450i −0.575003 + 0.417764i −0.836919 0.547327i \(-0.815646\pi\)
0.261916 + 0.965091i \(0.415646\pi\)
\(98\) 0.381966 0.0385844
\(99\) 0 0
\(100\) 7.41641 0.741641
\(101\) −11.9721 + 8.69827i −1.19127 + 0.865510i −0.993398 0.114718i \(-0.963404\pi\)
−0.197874 + 0.980227i \(0.563404\pi\)
\(102\) 0.590170 + 1.81636i 0.0584355 + 0.179846i
\(103\) 2.73607 8.42075i 0.269593 0.829721i −0.721007 0.692928i \(-0.756320\pi\)
0.990600 0.136793i \(-0.0436796\pi\)
\(104\) 1.47214 + 1.06957i 0.144355 + 0.104880i
\(105\) −1.30902 0.951057i −0.127747 0.0928136i
\(106\) −0.281153 + 0.865300i −0.0273080 + 0.0840453i
\(107\) −0.836881 2.57565i −0.0809043 0.248998i 0.902420 0.430857i \(-0.141789\pi\)
−0.983325 + 0.181859i \(0.941789\pi\)
\(108\) 8.20820 5.96361i 0.789835 0.573849i
\(109\) 1.52786 0.146343 0.0731714 0.997319i \(-0.476688\pi\)
0.0731714 + 0.997319i \(0.476688\pi\)
\(110\) 0 0
\(111\) −10.4721 −0.993971
\(112\) 2.54508 1.84911i 0.240488 0.174725i
\(113\) 0.0450850 + 0.138757i 0.00424124 + 0.0130532i 0.953155 0.302483i \(-0.0978156\pi\)
−0.948914 + 0.315536i \(0.897816\pi\)
\(114\) −0.336881 + 1.03681i −0.0315518 + 0.0971065i
\(115\) −4.11803 2.99193i −0.384009 0.278999i
\(116\) 6.92705 + 5.03280i 0.643161 + 0.467283i
\(117\) −0.145898 + 0.449028i −0.0134883 + 0.0415127i
\(118\) 1.30902 + 4.02874i 0.120505 + 0.370876i
\(119\) −2.50000 + 1.81636i −0.229175 + 0.166505i
\(120\) 2.38197 0.217443
\(121\) 0 0
\(122\) 2.90983 0.263444
\(123\) 14.6353 10.6331i 1.31962 0.958758i
\(124\) 2.42705 + 7.46969i 0.217956 + 0.670798i
\(125\) −2.78115 + 8.55951i −0.248754 + 0.765586i
\(126\) −0.118034 0.0857567i −0.0105153 0.00763982i
\(127\) 2.38197 + 1.73060i 0.211365 + 0.153566i 0.688431 0.725302i \(-0.258300\pi\)
−0.477066 + 0.878868i \(0.658300\pi\)
\(128\) −3.11803 + 9.59632i −0.275598 + 0.848203i
\(129\) −6.28115 19.3314i −0.553025 1.70203i
\(130\) −0.381966 + 0.277515i −0.0335006 + 0.0243396i
\(131\) −18.9443 −1.65517 −0.827584 0.561341i \(-0.810285\pi\)
−0.827584 + 0.561341i \(0.810285\pi\)
\(132\) 0 0
\(133\) −1.76393 −0.152952
\(134\) 2.57295 1.86936i 0.222269 0.161488i
\(135\) 1.69098 + 5.20431i 0.145537 + 0.447916i
\(136\) 1.40576 4.32650i 0.120543 0.370994i
\(137\) 12.3992 + 9.00854i 1.05933 + 0.769651i 0.973965 0.226698i \(-0.0727931\pi\)
0.0853690 + 0.996349i \(0.472793\pi\)
\(138\) 2.54508 + 1.84911i 0.216652 + 0.157407i
\(139\) −3.69098 + 11.3597i −0.313065 + 0.963515i 0.663478 + 0.748195i \(0.269079\pi\)
−0.976544 + 0.215320i \(0.930921\pi\)
\(140\) 0.572949 + 1.76336i 0.0484230 + 0.149031i
\(141\) −8.66312 + 6.29412i −0.729566 + 0.530061i
\(142\) −6.14590 −0.515752
\(143\) 0 0
\(144\) −1.20163 −0.100136
\(145\) −3.73607 + 2.71441i −0.310264 + 0.225420i
\(146\) 1.68034 + 5.17155i 0.139066 + 0.428001i
\(147\) −0.500000 + 1.53884i −0.0412393 + 0.126922i
\(148\) 9.70820 + 7.05342i 0.798009 + 0.579788i
\(149\) −7.16312 5.20431i −0.586826 0.426354i 0.254353 0.967112i \(-0.418138\pi\)
−0.841178 + 0.540758i \(0.818138\pi\)
\(150\) 0.763932 2.35114i 0.0623748 0.191970i
\(151\) −0.0172209 0.0530006i −0.00140142 0.00431312i 0.950353 0.311173i \(-0.100722\pi\)
−0.951755 + 0.306860i \(0.900722\pi\)
\(152\) 2.10081 1.52633i 0.170398 0.123802i
\(153\) 1.18034 0.0954248
\(154\) 0 0
\(155\) −4.23607 −0.340249
\(156\) −3.00000 + 2.17963i −0.240192 + 0.174510i
\(157\) 6.14590 + 18.9151i 0.490496 + 1.50959i 0.823860 + 0.566793i \(0.191816\pi\)
−0.333364 + 0.942798i \(0.608184\pi\)
\(158\) −0.753289 + 2.31838i −0.0599284 + 0.184441i
\(159\) −3.11803 2.26538i −0.247276 0.179657i
\(160\) −3.35410 2.43690i −0.265165 0.192654i
\(161\) −1.57295 + 4.84104i −0.123966 + 0.381527i
\(162\) −0.909830 2.80017i −0.0714830 0.220002i
\(163\) 7.04508 5.11855i 0.551814 0.400916i −0.276640 0.960974i \(-0.589221\pi\)
0.828454 + 0.560058i \(0.189221\pi\)
\(164\) −20.7295 −1.61870
\(165\) 0 0
\(166\) −1.03444 −0.0802883
\(167\) 5.23607 3.80423i 0.405179 0.294380i −0.366468 0.930431i \(-0.619433\pi\)
0.771647 + 0.636051i \(0.219433\pi\)
\(168\) −0.736068 2.26538i −0.0567889 0.174778i
\(169\) −3.54508 + 10.9106i −0.272699 + 0.839281i
\(170\) 0.954915 + 0.693786i 0.0732386 + 0.0532110i
\(171\) 0.545085 + 0.396027i 0.0416837 + 0.0302850i
\(172\) −7.19756 + 22.1518i −0.548809 + 1.68906i
\(173\) 4.75329 + 14.6291i 0.361386 + 1.11223i 0.952213 + 0.305433i \(0.0988014\pi\)
−0.590828 + 0.806798i \(0.701199\pi\)
\(174\) 2.30902 1.67760i 0.175046 0.127178i
\(175\) 4.00000 0.302372
\(176\) 0 0
\(177\) −17.9443 −1.34877
\(178\) −2.11803 + 1.53884i −0.158753 + 0.115341i
\(179\) −1.16312 3.57971i −0.0869356 0.267560i 0.898133 0.439725i \(-0.144924\pi\)
−0.985068 + 0.172164i \(0.944924\pi\)
\(180\) 0.218847 0.673542i 0.0163119 0.0502029i
\(181\) 6.00000 + 4.35926i 0.445976 + 0.324021i 0.788005 0.615669i \(-0.211114\pi\)
−0.342029 + 0.939690i \(0.611114\pi\)
\(182\) 0.381966 + 0.277515i 0.0283132 + 0.0205707i
\(183\) −3.80902 + 11.7229i −0.281571 + 0.866585i
\(184\) −2.31559 7.12667i −0.170708 0.525385i
\(185\) −5.23607 + 3.80423i −0.384963 + 0.279692i
\(186\) 2.61803 0.191964
\(187\) 0 0
\(188\) 12.2705 0.894919
\(189\) 4.42705 3.21644i 0.322021 0.233962i
\(190\) 0.208204 + 0.640786i 0.0151047 + 0.0464875i
\(191\) 4.87132 14.9924i 0.352477 1.08481i −0.604982 0.796239i \(-0.706820\pi\)
0.957458 0.288572i \(-0.0931804\pi\)
\(192\) −6.16312 4.47777i −0.444785 0.323155i
\(193\) −12.3992 9.00854i −0.892513 0.648449i 0.0440190 0.999031i \(-0.485984\pi\)
−0.936532 + 0.350582i \(0.885984\pi\)
\(194\) 0.826238 2.54290i 0.0593204 0.182569i
\(195\) −0.618034 1.90211i −0.0442583 0.136213i
\(196\) 1.50000 1.08981i 0.107143 0.0778438i
\(197\) 4.29180 0.305778 0.152889 0.988243i \(-0.451142\pi\)
0.152889 + 0.988243i \(0.451142\pi\)
\(198\) 0 0
\(199\) −8.23607 −0.583839 −0.291920 0.956443i \(-0.594294\pi\)
−0.291920 + 0.956443i \(0.594294\pi\)
\(200\) −4.76393 + 3.46120i −0.336861 + 0.244744i
\(201\) 4.16312 + 12.8128i 0.293644 + 0.903743i
\(202\) 1.74671 5.37582i 0.122898 0.378242i
\(203\) 3.73607 + 2.71441i 0.262221 + 0.190514i
\(204\) 7.50000 + 5.44907i 0.525105 + 0.381511i
\(205\) 3.45492 10.6331i 0.241302 0.742650i
\(206\) 1.04508 + 3.21644i 0.0728145 + 0.224100i
\(207\) 1.57295 1.14281i 0.109328 0.0794311i
\(208\) 3.88854 0.269622
\(209\) 0 0
\(210\) 0.618034 0.0426484
\(211\) 12.6353 9.18005i 0.869847 0.631981i −0.0606990 0.998156i \(-0.519333\pi\)
0.930546 + 0.366175i \(0.119333\pi\)
\(212\) 1.36475 + 4.20025i 0.0937311 + 0.288475i
\(213\) 8.04508 24.7602i 0.551240 1.69654i
\(214\) 0.836881 + 0.608030i 0.0572080 + 0.0415641i
\(215\) −10.1631 7.38394i −0.693119 0.503580i
\(216\) −2.48936 + 7.66145i −0.169379 + 0.521296i
\(217\) 1.30902 + 4.02874i 0.0888619 + 0.273489i
\(218\) −0.472136 + 0.343027i −0.0319771 + 0.0232327i
\(219\) −23.0344 −1.55652
\(220\) 0 0
\(221\) −3.81966 −0.256938
\(222\) 3.23607 2.35114i 0.217191 0.157798i
\(223\) 0.628677 + 1.93487i 0.0420993 + 0.129568i 0.969897 0.243515i \(-0.0783005\pi\)
−0.927798 + 0.373083i \(0.878301\pi\)
\(224\) −1.28115 + 3.94298i −0.0856006 + 0.263452i
\(225\) −1.23607 0.898056i −0.0824045 0.0598704i
\(226\) −0.0450850 0.0327561i −0.00299901 0.00217891i
\(227\) 4.95492 15.2497i 0.328869 1.01216i −0.640794 0.767713i \(-0.721395\pi\)
0.969664 0.244443i \(-0.0786051\pi\)
\(228\) 1.63525 + 5.03280i 0.108297 + 0.333305i
\(229\) −5.47214 + 3.97574i −0.361609 + 0.262724i −0.753723 0.657192i \(-0.771744\pi\)
0.392114 + 0.919917i \(0.371744\pi\)
\(230\) 1.94427 0.128201
\(231\) 0 0
\(232\) −6.79837 −0.446335
\(233\) −23.7984 + 17.2905i −1.55908 + 1.13274i −0.622327 + 0.782757i \(0.713813\pi\)
−0.936756 + 0.349983i \(0.886187\pi\)
\(234\) −0.0557281 0.171513i −0.00364306 0.0112122i
\(235\) −2.04508 + 6.29412i −0.133407 + 0.410583i
\(236\) 16.6353 + 12.0862i 1.08286 + 0.786746i
\(237\) −8.35410 6.06961i −0.542657 0.394264i
\(238\) 0.364745 1.12257i 0.0236429 0.0727654i
\(239\) 5.28115 + 16.2537i 0.341609 + 1.05137i 0.963374 + 0.268161i \(0.0864161\pi\)
−0.621765 + 0.783204i \(0.713584\pi\)
\(240\) 4.11803 2.99193i 0.265818 0.193128i
\(241\) −16.2705 −1.04808 −0.524038 0.851695i \(-0.675575\pi\)
−0.524038 + 0.851695i \(0.675575\pi\)
\(242\) 0 0
\(243\) −3.94427 −0.253025
\(244\) 11.4271 8.30224i 0.731542 0.531496i
\(245\) 0.309017 + 0.951057i 0.0197424 + 0.0607608i
\(246\) −2.13525 + 6.57164i −0.136139 + 0.418992i
\(247\) −1.76393 1.28157i −0.112236 0.0815445i
\(248\) −5.04508 3.66547i −0.320363 0.232758i
\(249\) 1.35410 4.16750i 0.0858127 0.264104i
\(250\) −1.06231 3.26944i −0.0671861 0.206778i
\(251\) −18.6074 + 13.5191i −1.17449 + 0.853316i −0.991539 0.129807i \(-0.958564\pi\)
−0.182949 + 0.983122i \(0.558564\pi\)
\(252\) −0.708204 −0.0446127
\(253\) 0 0
\(254\) −1.12461 −0.0705644
\(255\) −4.04508 + 2.93893i −0.253313 + 0.184043i
\(256\) 1.71885 + 5.29007i 0.107428 + 0.330629i
\(257\) −2.64590 + 8.14324i −0.165047 + 0.507961i −0.999040 0.0438137i \(-0.986049\pi\)
0.833993 + 0.551775i \(0.186049\pi\)
\(258\) 6.28115 + 4.56352i 0.391048 + 0.284113i
\(259\) 5.23607 + 3.80423i 0.325353 + 0.236383i
\(260\) −0.708204 + 2.17963i −0.0439209 + 0.135175i
\(261\) −0.545085 1.67760i −0.0337399 0.103841i
\(262\) 5.85410 4.25325i 0.361668 0.262767i
\(263\) 17.1246 1.05595 0.527974 0.849260i \(-0.322952\pi\)
0.527974 + 0.849260i \(0.322952\pi\)
\(264\) 0 0
\(265\) −2.38197 −0.146323
\(266\) 0.545085 0.396027i 0.0334213 0.0242820i
\(267\) −3.42705 10.5474i −0.209732 0.645489i
\(268\) 4.77051 14.6821i 0.291405 0.896853i
\(269\) −13.6353 9.90659i −0.831356 0.604016i 0.0885865 0.996068i \(-0.471765\pi\)
−0.919943 + 0.392053i \(0.871765\pi\)
\(270\) −1.69098 1.22857i −0.102910 0.0747685i
\(271\) 1.48278 4.56352i 0.0900724 0.277214i −0.895866 0.444325i \(-0.853444\pi\)
0.985938 + 0.167110i \(0.0534436\pi\)
\(272\) −3.00407 9.24556i −0.182148 0.560595i
\(273\) −1.61803 + 1.17557i −0.0979279 + 0.0711488i
\(274\) −5.85410 −0.353659
\(275\) 0 0
\(276\) 15.2705 0.919177
\(277\) 18.6353 13.5393i 1.11968 0.813498i 0.135523 0.990774i \(-0.456729\pi\)
0.984161 + 0.177276i \(0.0567286\pi\)
\(278\) −1.40983 4.33901i −0.0845560 0.260237i
\(279\) 0.500000 1.53884i 0.0299342 0.0921280i
\(280\) −1.19098 0.865300i −0.0711748 0.0517116i
\(281\) −20.3713 14.8006i −1.21525 0.882932i −0.219554 0.975600i \(-0.570460\pi\)
−0.995697 + 0.0926686i \(0.970460\pi\)
\(282\) 1.26393 3.88998i 0.0752661 0.231645i
\(283\) −3.69098 11.3597i −0.219406 0.675263i −0.998811 0.0487426i \(-0.984479\pi\)
0.779405 0.626520i \(-0.215521\pi\)
\(284\) −24.1353 + 17.5353i −1.43216 + 1.04053i
\(285\) −2.85410 −0.169062
\(286\) 0 0
\(287\) −11.1803 −0.659955
\(288\) 1.28115 0.930812i 0.0754927 0.0548486i
\(289\) −2.30244 7.08618i −0.135438 0.416834i
\(290\) 0.545085 1.67760i 0.0320085 0.0985120i
\(291\) 9.16312 + 6.65740i 0.537152 + 0.390263i
\(292\) 21.3541 + 15.5147i 1.24965 + 0.907927i
\(293\) 3.39919 10.4616i 0.198583 0.611174i −0.801333 0.598218i \(-0.795876\pi\)
0.999916 0.0129565i \(-0.00412430\pi\)
\(294\) −0.190983 0.587785i −0.0111384 0.0342803i
\(295\) −8.97214 + 6.51864i −0.522378 + 0.379530i
\(296\) −9.52786 −0.553796
\(297\) 0 0
\(298\) 3.38197 0.195912
\(299\) −5.09017 + 3.69822i −0.294372 + 0.213874i
\(300\) −3.70820 11.4127i −0.214093 0.658911i
\(301\) −3.88197 + 11.9475i −0.223753 + 0.688640i
\(302\) 0.0172209 + 0.0125117i 0.000990953 + 0.000719969i
\(303\) 19.3713 + 14.0741i 1.11285 + 0.808535i
\(304\) 1.71478 5.27756i 0.0983495 0.302689i
\(305\) 2.35410 + 7.24518i 0.134795 + 0.414858i
\(306\) −0.364745 + 0.265003i −0.0208511 + 0.0151492i
\(307\) 23.1803 1.32297 0.661486 0.749958i \(-0.269926\pi\)
0.661486 + 0.749958i \(0.269926\pi\)
\(308\) 0 0
\(309\) −14.3262 −0.814991
\(310\) 1.30902 0.951057i 0.0743472 0.0540164i
\(311\) 2.78115 + 8.55951i 0.157705 + 0.485365i 0.998425 0.0561046i \(-0.0178680\pi\)
−0.840720 + 0.541470i \(0.817868\pi\)
\(312\) 0.909830 2.80017i 0.0515090 0.158528i
\(313\) −14.8262 10.7719i −0.838029 0.608863i 0.0837907 0.996483i \(-0.473297\pi\)
−0.921819 + 0.387620i \(0.873297\pi\)
\(314\) −6.14590 4.46526i −0.346833 0.251989i
\(315\) 0.118034 0.363271i 0.00665046 0.0204680i
\(316\) 3.65654 + 11.2537i 0.205697 + 0.633069i
\(317\) 3.59017 2.60841i 0.201644 0.146503i −0.482381 0.875962i \(-0.660228\pi\)
0.684025 + 0.729459i \(0.260228\pi\)
\(318\) 1.47214 0.0825533
\(319\) 0 0
\(320\) −4.70820 −0.263197
\(321\) −3.54508 + 2.57565i −0.197867 + 0.143759i
\(322\) −0.600813 1.84911i −0.0334820 0.103047i
\(323\) −1.68441 + 5.18407i −0.0937228 + 0.288449i
\(324\) −11.5623 8.40051i −0.642350 0.466695i
\(325\) 4.00000 + 2.90617i 0.221880 + 0.161205i
\(326\) −1.02786 + 3.16344i −0.0569281 + 0.175207i
\(327\) −0.763932 2.35114i −0.0422455 0.130018i
\(328\) 13.3156 9.67435i 0.735231 0.534176i
\(329\) 6.61803 0.364864
\(330\) 0 0
\(331\) 6.18034 0.339702 0.169851 0.985470i \(-0.445671\pi\)
0.169851 + 0.985470i \(0.445671\pi\)
\(332\) −4.06231 + 2.95144i −0.222948 + 0.161981i
\(333\) −0.763932 2.35114i −0.0418632 0.128842i
\(334\) −0.763932 + 2.35114i −0.0418005 + 0.128649i
\(335\) 6.73607 + 4.89404i 0.368031 + 0.267390i
\(336\) −4.11803 2.99193i −0.224657 0.163223i
\(337\) −8.01722 + 24.6745i −0.436726 + 1.34410i 0.454582 + 0.890705i \(0.349789\pi\)
−0.891308 + 0.453399i \(0.850211\pi\)
\(338\) −1.35410 4.16750i −0.0736534 0.226682i
\(339\) 0.190983 0.138757i 0.0103728 0.00753626i
\(340\) 5.72949 0.310725
\(341\) 0 0
\(342\) −0.257354 −0.0139161
\(343\) 0.809017 0.587785i 0.0436828 0.0317374i
\(344\) −5.71478 17.5883i −0.308120 0.948297i
\(345\) −2.54508 + 7.83297i −0.137023 + 0.421713i
\(346\) −4.75329 3.45347i −0.255538 0.185660i
\(347\) 1.89919 + 1.37984i 0.101954 + 0.0740737i 0.637594 0.770373i \(-0.279930\pi\)
−0.535640 + 0.844446i \(0.679930\pi\)
\(348\) 4.28115 13.1760i 0.229494 0.706310i
\(349\) −10.1353 31.1931i −0.542528 1.66973i −0.726797 0.686853i \(-0.758992\pi\)
0.184269 0.982876i \(-0.441008\pi\)
\(350\) −1.23607 + 0.898056i −0.0660706 + 0.0480031i
\(351\) 6.76393 0.361032
\(352\) 0 0
\(353\) 24.0902 1.28219 0.641095 0.767461i \(-0.278480\pi\)
0.641095 + 0.767461i \(0.278480\pi\)
\(354\) 5.54508 4.02874i 0.294718 0.214125i
\(355\) −4.97214 15.3027i −0.263894 0.812181i
\(356\) −3.92705 + 12.0862i −0.208133 + 0.640568i
\(357\) 4.04508 + 2.93893i 0.214089 + 0.155544i
\(358\) 1.16312 + 0.845055i 0.0614727 + 0.0446626i
\(359\) 4.82624 14.8536i 0.254719 0.783945i −0.739166 0.673524i \(-0.764780\pi\)
0.993885 0.110421i \(-0.0352200\pi\)
\(360\) 0.173762 + 0.534785i 0.00915807 + 0.0281856i
\(361\) 12.8541 9.33905i 0.676532 0.491529i
\(362\) −2.83282 −0.148889
\(363\) 0 0
\(364\) 2.29180 0.120123
\(365\) −11.5172 + 8.36775i −0.602839 + 0.437988i
\(366\) −1.45492 4.47777i −0.0760496 0.234057i
\(367\) 10.1459 31.2259i 0.529612 1.62998i −0.225401 0.974266i \(-0.572369\pi\)
0.755012 0.655711i \(-0.227631\pi\)
\(368\) −12.9549 9.41230i −0.675322 0.490650i
\(369\) 3.45492 + 2.51014i 0.179856 + 0.130673i
\(370\) 0.763932 2.35114i 0.0397149 0.122230i
\(371\) 0.736068 + 2.26538i 0.0382147 + 0.117613i
\(372\) 10.2812 7.46969i 0.533053 0.387286i
\(373\) 15.4377 0.799334 0.399667 0.916661i \(-0.369126\pi\)
0.399667 + 0.916661i \(0.369126\pi\)
\(374\) 0 0
\(375\) 14.5623 0.751994
\(376\) −7.88197 + 5.72658i −0.406481 + 0.295326i
\(377\) 1.76393 + 5.42882i 0.0908471 + 0.279599i
\(378\) −0.645898 + 1.98787i −0.0332214 + 0.102245i
\(379\) −25.9443 18.8496i −1.33267 0.968240i −0.999680 0.0253087i \(-0.991943\pi\)
−0.332988 0.942931i \(-0.608057\pi\)
\(380\) 2.64590 + 1.92236i 0.135732 + 0.0986149i
\(381\) 1.47214 4.53077i 0.0754198 0.232118i
\(382\) 1.86068 + 5.72658i 0.0952007 + 0.292998i
\(383\) 27.9894 20.3355i 1.43019 1.03909i 0.440208 0.897896i \(-0.354905\pi\)
0.989981 0.141197i \(-0.0450953\pi\)
\(384\) 16.3262 0.833145
\(385\) 0 0
\(386\) 5.85410 0.297966
\(387\) 3.88197 2.82041i 0.197331 0.143370i
\(388\) −4.01064 12.3435i −0.203610 0.626646i
\(389\) −10.5623 + 32.5074i −0.535530 + 1.64819i 0.206971 + 0.978347i \(0.433640\pi\)
−0.742501 + 0.669845i \(0.766360\pi\)
\(390\) 0.618034 + 0.449028i 0.0312954 + 0.0227374i
\(391\) 12.7254 + 9.24556i 0.643552 + 0.467568i
\(392\) −0.454915 + 1.40008i −0.0229767 + 0.0707149i
\(393\) 9.47214 + 29.1522i 0.477806 + 1.47054i
\(394\) −1.32624 + 0.963568i −0.0668149 + 0.0485439i
\(395\) −6.38197 −0.321112
\(396\) 0 0
\(397\) −0.819660 −0.0411376 −0.0205688 0.999788i \(-0.506548\pi\)
−0.0205688 + 0.999788i \(0.506548\pi\)
\(398\) 2.54508 1.84911i 0.127574 0.0926876i
\(399\) 0.881966 + 2.71441i 0.0441535 + 0.135891i
\(400\) −3.88854 + 11.9677i −0.194427 + 0.598385i
\(401\) 14.1803 + 10.3026i 0.708132 + 0.514488i 0.882571 0.470180i \(-0.155811\pi\)
−0.174438 + 0.984668i \(0.555811\pi\)
\(402\) −4.16312 3.02468i −0.207638 0.150857i
\(403\) −1.61803 + 4.97980i −0.0806000 + 0.248061i
\(404\) −8.47871 26.0948i −0.421832 1.29826i
\(405\) 6.23607 4.53077i 0.309873 0.225136i
\(406\) −1.76393 −0.0875425
\(407\) 0 0
\(408\) −7.36068 −0.364408
\(409\) −14.3262 + 10.4086i −0.708387 + 0.514673i −0.882653 0.470025i \(-0.844245\pi\)
0.174266 + 0.984699i \(0.444245\pi\)
\(410\) 1.31966 + 4.06150i 0.0651734 + 0.200583i
\(411\) 7.66312 23.5847i 0.377994 1.16335i
\(412\) 13.2812 + 9.64932i 0.654315 + 0.475388i
\(413\) 8.97214 + 6.51864i 0.441490 + 0.320761i
\(414\) −0.229490 + 0.706298i −0.0112788 + 0.0347127i
\(415\) −0.836881 2.57565i −0.0410809 0.126434i
\(416\) −4.14590 + 3.01217i −0.203269 + 0.147684i
\(417\) 19.3262 0.946410
\(418\) 0 0
\(419\) 29.8885 1.46015 0.730075 0.683367i \(-0.239485\pi\)
0.730075 + 0.683367i \(0.239485\pi\)
\(420\) 2.42705 1.76336i 0.118428 0.0860430i
\(421\) 0.236068 + 0.726543i 0.0115052 + 0.0354095i 0.956644 0.291259i \(-0.0940740\pi\)
−0.945139 + 0.326668i \(0.894074\pi\)
\(422\) −1.84346 + 5.67358i −0.0897382 + 0.276186i
\(423\) −2.04508 1.48584i −0.0994354 0.0722441i
\(424\) −2.83688 2.06111i −0.137771 0.100097i
\(425\) 3.81966 11.7557i 0.185281 0.570235i
\(426\) 3.07295 + 9.45756i 0.148885 + 0.458221i
\(427\) 6.16312 4.47777i 0.298254 0.216694i
\(428\) 5.02129 0.242713
\(429\) 0 0
\(430\) 4.79837 0.231398
\(431\) −11.2082 + 8.14324i −0.539880 + 0.392246i −0.824041 0.566531i \(-0.808285\pi\)
0.284160 + 0.958777i \(0.408285\pi\)
\(432\) 5.31966 + 16.3722i 0.255942 + 0.787709i
\(433\) −2.77051 + 8.52675i −0.133142 + 0.409770i −0.995296 0.0968764i \(-0.969115\pi\)
0.862154 + 0.506646i \(0.169115\pi\)
\(434\) −1.30902 0.951057i −0.0628348 0.0456522i
\(435\) 6.04508 + 4.39201i 0.289840 + 0.210581i
\(436\) −0.875388 + 2.69417i −0.0419235 + 0.129027i
\(437\) 2.77458 + 8.53926i 0.132726 + 0.408488i
\(438\) 7.11803 5.17155i 0.340113 0.247106i
\(439\) −3.38197 −0.161412 −0.0807062 0.996738i \(-0.525718\pi\)
−0.0807062 + 0.996738i \(0.525718\pi\)
\(440\) 0 0
\(441\) −0.381966 −0.0181889
\(442\) 1.18034 0.857567i 0.0561430 0.0407903i
\(443\) 0.954915 + 2.93893i 0.0453694 + 0.139633i 0.971175 0.238367i \(-0.0766121\pi\)
−0.925806 + 0.378000i \(0.876612\pi\)
\(444\) 6.00000 18.4661i 0.284747 0.876362i
\(445\) −5.54508 4.02874i −0.262862 0.190981i
\(446\) −0.628677 0.456761i −0.0297687 0.0216282i
\(447\) −4.42705 + 13.6251i −0.209392 + 0.644443i
\(448\) 1.45492 + 4.47777i 0.0687383 + 0.211555i
\(449\) −9.97214 + 7.24518i −0.470614 + 0.341921i −0.797681 0.603080i \(-0.793940\pi\)
0.327066 + 0.945001i \(0.393940\pi\)
\(450\) 0.583592 0.0275108
\(451\) 0 0
\(452\) −0.270510 −0.0127237
\(453\) −0.0729490 + 0.0530006i −0.00342744 + 0.00249018i
\(454\) 1.89261 + 5.82485i 0.0888245 + 0.273374i
\(455\) −0.381966 + 1.17557i −0.0179068 + 0.0551116i
\(456\) −3.39919 2.46965i −0.159182 0.115652i
\(457\) −0.118034 0.0857567i −0.00552140 0.00401153i 0.585021 0.811018i \(-0.301086\pi\)
−0.590543 + 0.807007i \(0.701086\pi\)
\(458\) 0.798374 2.45714i 0.0373056 0.114815i
\(459\) −5.22542 16.0822i −0.243902 0.750653i
\(460\) 7.63525 5.54734i 0.355996 0.258646i
\(461\) 18.5066 0.861937 0.430969 0.902367i \(-0.358172\pi\)
0.430969 + 0.902367i \(0.358172\pi\)
\(462\) 0 0
\(463\) 22.2361 1.03340 0.516699 0.856167i \(-0.327161\pi\)
0.516699 + 0.856167i \(0.327161\pi\)
\(464\) −11.7533 + 8.53926i −0.545633 + 0.396425i
\(465\) 2.11803 + 6.51864i 0.0982215 + 0.302295i
\(466\) 3.47214 10.6861i 0.160844 0.495026i
\(467\) 3.64590 + 2.64890i 0.168712 + 0.122576i 0.668937 0.743319i \(-0.266749\pi\)
−0.500225 + 0.865895i \(0.666749\pi\)
\(468\) −0.708204 0.514540i −0.0327367 0.0237846i
\(469\) 2.57295 7.91872i 0.118808 0.365653i
\(470\) −0.781153 2.40414i −0.0360319 0.110895i
\(471\) 26.0344 18.9151i 1.19960 0.871563i
\(472\) −16.3262 −0.751476
\(473\) 0 0
\(474\) 3.94427 0.181166
\(475\) 5.70820 4.14725i 0.261910 0.190289i
\(476\) −1.77051 5.44907i −0.0811512 0.249758i
\(477\) 0.281153 0.865300i 0.0128731 0.0396194i
\(478\) −5.28115 3.83698i −0.241554 0.175499i
\(479\) 17.6074 + 12.7925i 0.804502 + 0.584505i 0.912231 0.409675i \(-0.134358\pi\)
−0.107729 + 0.994180i \(0.534358\pi\)
\(480\) −2.07295 + 6.37988i −0.0946167 + 0.291200i
\(481\) 2.47214 + 7.60845i 0.112720 + 0.346916i
\(482\) 5.02786 3.65296i 0.229013 0.166388i
\(483\) 8.23607 0.374754
\(484\) 0 0
\(485\) 7.00000 0.317854
\(486\) 1.21885 0.885544i 0.0552880 0.0401691i
\(487\) −10.0729 31.0013i −0.456449 1.40481i −0.869426 0.494064i \(-0.835511\pi\)
0.412977 0.910742i \(-0.364489\pi\)
\(488\) −3.46556 + 10.6659i −0.156878 + 0.482822i
\(489\) −11.3992 8.28199i −0.515489 0.374525i
\(490\) −0.309017 0.224514i −0.0139600 0.0101425i
\(491\) −6.84346 + 21.0620i −0.308841 + 0.950515i 0.669375 + 0.742925i \(0.266562\pi\)
−0.978216 + 0.207590i \(0.933438\pi\)
\(492\) 10.3647 + 31.8994i 0.467279 + 1.43814i
\(493\) 11.5451 8.38800i 0.519964 0.377776i
\(494\) 0.832816 0.0374702
\(495\) 0 0
\(496\) −13.3262 −0.598366
\(497\) −13.0172 + 9.45756i −0.583902 + 0.424230i
\(498\) 0.517221 + 1.59184i 0.0231772 + 0.0713322i
\(499\) −3.11803 + 9.59632i −0.139582 + 0.429590i −0.996275 0.0862375i \(-0.972516\pi\)
0.856692 + 0.515828i \(0.172516\pi\)
\(500\) −13.5000 9.80832i −0.603738 0.438642i
\(501\) −8.47214 6.15537i −0.378507 0.275002i
\(502\) 2.71478 8.35524i 0.121167 0.372913i
\(503\) 10.7639 + 33.1280i 0.479940 + 1.47710i 0.839178 + 0.543857i \(0.183037\pi\)
−0.359238 + 0.933246i \(0.616963\pi\)
\(504\) 0.454915 0.330515i 0.0202635 0.0147223i
\(505\) 14.7984 0.658519
\(506\) 0 0
\(507\) 18.5623 0.824381
\(508\) −4.41641 + 3.20871i −0.195946 + 0.142363i
\(509\) −3.31966 10.2169i −0.147141 0.452855i 0.850139 0.526559i \(-0.176518\pi\)
−0.997280 + 0.0737042i \(0.976518\pi\)
\(510\) 0.590170 1.81636i 0.0261332 0.0804296i
\(511\) 11.5172 + 8.36775i 0.509492 + 0.370168i
\(512\) −18.0451 13.1105i −0.797488 0.579409i
\(513\) 2.98278 9.18005i 0.131693 0.405309i
\(514\) −1.01064 3.11044i −0.0445776 0.137196i
\(515\) −7.16312 + 5.20431i −0.315645 + 0.229329i
\(516\) 37.6869 1.65907
\(517\) 0 0
\(518\) −2.47214 −0.108619
\(519\) 20.1353 14.6291i 0.883840 0.642147i
\(520\) −0.562306 1.73060i −0.0246587 0.0758918i
\(521\) −3.78115 + 11.6372i −0.165655 + 0.509835i −0.999084 0.0427924i \(-0.986375\pi\)
0.833429 + 0.552627i \(0.186375\pi\)
\(522\) 0.545085 + 0.396027i 0.0238577 + 0.0173336i
\(523\) 13.3992 + 9.73508i 0.585906 + 0.425685i 0.840848 0.541271i \(-0.182057\pi\)
−0.254943 + 0.966956i \(0.582057\pi\)
\(524\) 10.8541 33.4055i 0.474164 1.45933i
\(525\) −2.00000 6.15537i −0.0872872 0.268642i
\(526\) −5.29180 + 3.84471i −0.230733 + 0.167638i
\(527\) 13.0902 0.570217
\(528\) 0 0
\(529\) 2.90983 0.126514
\(530\) 0.736068 0.534785i 0.0319727 0.0232296i
\(531\) −1.30902 4.02874i −0.0568065 0.174832i
\(532\) 1.01064 3.11044i 0.0438169 0.134855i
\(533\) −11.1803 8.12299i −0.484274 0.351846i
\(534\) 3.42705 + 2.48990i 0.148303 + 0.107748i
\(535\) −0.836881 + 2.57565i −0.0361815 + 0.111355i
\(536\) 3.78773 + 11.6574i 0.163605 + 0.503525i
\(537\) −4.92705 + 3.57971i −0.212618 + 0.154476i
\(538\) 6.43769 0.277549
\(539\) 0 0
\(540\) −10.1459 −0.436610
\(541\) 0.572949 0.416272i 0.0246330 0.0178969i −0.575401 0.817872i \(-0.695154\pi\)
0.600034 + 0.799975i \(0.295154\pi\)
\(542\) 0.566371 + 1.74311i 0.0243277 + 0.0748730i
\(543\) 3.70820 11.4127i 0.159134 0.489765i
\(544\) 10.3647 + 7.53043i 0.444385 + 0.322864i
\(545\) −1.23607 0.898056i −0.0529473 0.0384685i
\(546\) 0.236068 0.726543i 0.0101028 0.0310931i
\(547\) 0.534442 + 1.64484i 0.0228511 + 0.0703284i 0.961832 0.273641i \(-0.0882282\pi\)
−0.938981 + 0.343970i \(0.888228\pi\)
\(548\) −22.9894 + 16.7027i −0.982057 + 0.713506i
\(549\) −2.90983 −0.124189
\(550\) 0 0
\(551\) 8.14590 0.347027
\(552\) −9.80902 + 7.12667i −0.417499 + 0.303331i
\(553\) 1.97214 + 6.06961i 0.0838638 + 0.258106i
\(554\) −2.71885 + 8.36775i −0.115513 + 0.355512i
\(555\) 8.47214 + 6.15537i 0.359622 + 0.261281i
\(556\) −17.9164 13.0170i −0.759825 0.552045i
\(557\) 3.01722 9.28605i 0.127844 0.393463i −0.866565 0.499065i \(-0.833677\pi\)
0.994408 + 0.105602i \(0.0336770\pi\)
\(558\) 0.190983 + 0.587785i 0.00808496 + 0.0248829i
\(559\) −12.5623 + 9.12705i −0.531329 + 0.386033i
\(560\) −3.14590 −0.132938
\(561\) 0 0
\(562\) 9.61803 0.405712
\(563\) −25.8713 + 18.7966i −1.09035 + 0.792183i −0.979458 0.201650i \(-0.935370\pi\)
−0.110889 + 0.993833i \(0.535370\pi\)
\(564\) −6.13525 18.8824i −0.258341 0.795091i
\(565\) 0.0450850 0.138757i 0.00189674 0.00583756i
\(566\) 3.69098 + 2.68166i 0.155144 + 0.112718i
\(567\) −6.23607 4.53077i −0.261890 0.190274i
\(568\) 7.31966 22.5276i 0.307126 0.945237i
\(569\) −11.5279 35.4791i −0.483273 1.48736i −0.834466 0.551059i \(-0.814224\pi\)
0.351193 0.936303i \(-0.385776\pi\)
\(570\) 0.881966 0.640786i 0.0369415 0.0268396i
\(571\) −34.3050 −1.43562 −0.717809 0.696240i \(-0.754855\pi\)
−0.717809 + 0.696240i \(0.754855\pi\)
\(572\) 0 0
\(573\) −25.5066 −1.06555
\(574\) 3.45492 2.51014i 0.144205 0.104771i
\(575\) −6.29180 19.3642i −0.262386 0.807541i
\(576\) 0.555728 1.71036i 0.0231553 0.0712648i
\(577\) −7.80902 5.67358i −0.325094 0.236194i 0.413252 0.910617i \(-0.364393\pi\)
−0.738346 + 0.674422i \(0.764393\pi\)
\(578\) 2.30244 + 1.67282i 0.0957688 + 0.0695801i
\(579\) −7.66312 + 23.5847i −0.318468 + 0.980145i
\(580\) −2.64590 8.14324i −0.109865 0.338130i
\(581\) −2.19098 + 1.59184i −0.0908973 + 0.0660407i
\(582\) −4.32624 −0.179328
\(583\) 0 0
\(584\) −20.9574 −0.867225
\(585\) 0.381966 0.277515i 0.0157924 0.0114738i
\(586\) 1.29837 + 3.99598i 0.0536353 + 0.165073i
\(587\) 0.309017 0.951057i 0.0127545 0.0392543i −0.944477 0.328578i \(-0.893431\pi\)
0.957231 + 0.289324i \(0.0934305\pi\)
\(588\) −2.42705 1.76336i −0.100090 0.0727196i
\(589\) 6.04508 + 4.39201i 0.249083 + 0.180970i
\(590\) 1.30902 4.02874i 0.0538914 0.165861i
\(591\) −2.14590 6.60440i −0.0882705 0.271669i
\(592\) −16.4721 + 11.9677i −0.677001 + 0.491870i
\(593\) −11.1246 −0.456833 −0.228417 0.973564i \(-0.573355\pi\)
−0.228417 + 0.973564i \(0.573355\pi\)
\(594\) 0 0
\(595\) 3.09017 0.126685
\(596\) 13.2812 9.64932i 0.544017 0.395252i
\(597\) 4.11803 + 12.6740i 0.168540 + 0.518713i
\(598\) 0.742646 2.28563i 0.0303690 0.0934663i
\(599\) 12.9443 + 9.40456i 0.528889 + 0.384260i 0.819942 0.572447i \(-0.194006\pi\)
−0.291053 + 0.956707i \(0.594006\pi\)
\(600\) 7.70820 + 5.60034i 0.314686 + 0.228633i
\(601\) −4.23607 + 13.0373i −0.172793 + 0.531802i −0.999526 0.0307929i \(-0.990197\pi\)
0.826733 + 0.562595i \(0.190197\pi\)
\(602\) −1.48278 4.56352i −0.0604336 0.185995i
\(603\) −2.57295 + 1.86936i −0.104779 + 0.0761261i
\(604\) 0.103326 0.00420426
\(605\) 0 0
\(606\) −9.14590 −0.371527
\(607\) 16.3435 11.8742i 0.663361 0.481960i −0.204436 0.978880i \(-0.565536\pi\)
0.867796 + 0.496920i \(0.165536\pi\)
\(608\) 2.25987 + 6.95515i 0.0916497 + 0.282069i
\(609\) 2.30902 7.10642i 0.0935661 0.287967i
\(610\) −2.35410 1.71036i −0.0953148 0.0692503i
\(611\) 6.61803 + 4.80828i 0.267737 + 0.194522i
\(612\) −0.676275 + 2.08136i −0.0273368 + 0.0841340i
\(613\) 0.274575 + 0.845055i 0.0110900 + 0.0341315i 0.956448 0.291902i \(-0.0942879\pi\)
−0.945358 + 0.326033i \(0.894288\pi\)
\(614\) −7.16312 + 5.20431i −0.289080 + 0.210029i
\(615\) −18.0902 −0.729466
\(616\) 0 0
\(617\) 9.41641 0.379090 0.189545 0.981872i \(-0.439299\pi\)
0.189545 + 0.981872i \(0.439299\pi\)
\(618\) 4.42705 3.21644i 0.178082 0.129384i
\(619\) −12.2705 37.7647i −0.493193 1.51789i −0.819753 0.572717i \(-0.805889\pi\)
0.326560 0.945177i \(-0.394111\pi\)
\(620\) 2.42705 7.46969i 0.0974727 0.299990i
\(621\) −22.5344 16.3722i −0.904276 0.656995i
\(622\) −2.78115 2.02063i −0.111514 0.0810197i
\(623\) −2.11803 + 6.51864i −0.0848572 + 0.261164i
\(624\) −1.94427 5.98385i −0.0778332 0.239546i
\(625\) −8.89919 + 6.46564i −0.355967 + 0.258626i
\(626\) 7.00000 0.279776
\(627\) 0 0
\(628\) −36.8754 −1.47149
\(629\) 16.1803 11.7557i 0.645152 0.468731i
\(630\) 0.0450850 + 0.138757i 0.00179623 + 0.00552822i
\(631\) 5.51064 16.9600i 0.219375 0.675168i −0.779439 0.626478i \(-0.784496\pi\)
0.998814 0.0486891i \(-0.0155044\pi\)
\(632\) −7.60081 5.52231i −0.302344 0.219666i
\(633\) −20.4443 14.8536i −0.812587 0.590379i
\(634\) −0.523799 + 1.61209i −0.0208027 + 0.0640241i
\(635\) −0.909830 2.80017i −0.0361055 0.111121i
\(636\) 5.78115 4.20025i 0.229238 0.166551i
\(637\) 1.23607 0.0489748
\(638\) 0 0
\(639\) 6.14590 0.243128
\(640\) 8.16312 5.93085i 0.322676 0.234438i
\(641\) 9.78115 + 30.1033i 0.386332 + 1.18901i 0.935509 + 0.353302i \(0.114941\pi\)
−0.549177 + 0.835706i \(0.685059\pi\)
\(642\) 0.517221 1.59184i 0.0204131 0.0628250i
\(643\) −1.28115 0.930812i −0.0505237 0.0367076i 0.562237 0.826976i \(-0.309941\pi\)
−0.612760 + 0.790269i \(0.709941\pi\)
\(644\) −7.63525 5.54734i −0.300871 0.218596i
\(645\) −6.28115 + 19.3314i −0.247320 + 0.761173i
\(646\) −0.643386 1.98014i −0.0253137 0.0779075i
\(647\) −5.00000 + 3.63271i −0.196570 + 0.142817i −0.681717 0.731616i \(-0.738766\pi\)
0.485146 + 0.874433i \(0.338766\pi\)
\(648\) 11.3475 0.445773
\(649\) 0 0
\(650\) −1.88854 −0.0740748
\(651\) 5.54508 4.02874i 0.217329 0.157899i
\(652\) 4.98936 + 15.3557i 0.195398 + 0.601374i
\(653\) 5.63525 17.3435i 0.220525 0.678705i −0.778191 0.628028i \(-0.783862\pi\)
0.998715 0.0506766i \(-0.0161378\pi\)
\(654\) 0.763932 + 0.555029i 0.0298721 + 0.0217034i
\(655\) 15.3262 + 11.1352i 0.598846 + 0.435087i
\(656\) 10.8688 33.4508i 0.424356 1.30603i
\(657\) −1.68034 5.17155i −0.0655563 0.201762i
\(658\) −2.04508 + 1.48584i −0.0797257 + 0.0579241i
\(659\) −31.4721 −1.22598 −0.612990 0.790091i \(-0.710033\pi\)
−0.612990 + 0.790091i \(0.710033\pi\)
\(660\) 0 0
\(661\) −34.5623 −1.34432 −0.672159 0.740407i \(-0.734633\pi\)
−0.672159 + 0.740407i \(0.734633\pi\)
\(662\) −1.90983 + 1.38757i −0.0742277 + 0.0539295i
\(663\) 1.90983 + 5.87785i 0.0741717 + 0.228277i
\(664\) 1.23200 3.79171i 0.0478110 0.147147i
\(665\) 1.42705 + 1.03681i 0.0553387 + 0.0402059i
\(666\) 0.763932 + 0.555029i 0.0296018 + 0.0215069i
\(667\) 7.26393 22.3561i 0.281261 0.865631i
\(668\) 3.70820 + 11.4127i 0.143475 + 0.441570i
\(669\) 2.66312 1.93487i 0.102962 0.0748064i
\(670\) −3.18034 −0.122867
\(671\) 0 0
\(672\) 6.70820 0.258775
\(673\) −5.32624 + 3.86974i −0.205311 + 0.149167i −0.685690 0.727894i \(-0.740499\pi\)
0.480378 + 0.877061i \(0.340499\pi\)
\(674\) −3.06231 9.42481i −0.117956 0.363030i
\(675\) −6.76393 + 20.8172i −0.260344 + 0.801256i
\(676\) −17.2082 12.5025i −0.661854 0.480865i
\(677\) −29.3435 21.3193i −1.12776 0.819366i −0.142393 0.989810i \(-0.545480\pi\)
−0.985367 + 0.170444i \(0.945480\pi\)
\(678\) −0.0278640 + 0.0857567i −0.00107011 + 0.00329347i
\(679\) −2.16312 6.65740i −0.0830129 0.255487i
\(680\) −3.68034 + 2.67392i −0.141135 + 0.102540i
\(681\) −25.9443 −0.994187
\(682\) 0 0
\(683\) 0.493422 0.0188803 0.00944014 0.999955i \(-0.496995\pi\)
0.00944014 + 0.999955i \(0.496995\pi\)
\(684\) −1.01064 + 0.734275i −0.0386429 + 0.0280757i
\(685\) −4.73607 14.5761i −0.180956 0.556925i
\(686\) −0.118034 + 0.363271i −0.00450656 + 0.0138698i
\(687\) 8.85410 + 6.43288i 0.337805 + 0.245430i
\(688\) −31.9721 23.2291i −1.21893 0.885602i
\(689\) −0.909830 + 2.80017i −0.0346618 + 0.106678i
\(690\) −0.972136 2.99193i −0.0370086 0.113901i
\(691\) −15.0000 + 10.8981i −0.570627 + 0.414585i −0.835333 0.549744i \(-0.814725\pi\)
0.264706 + 0.964329i \(0.414725\pi\)
\(692\) −28.5197 −1.08416
\(693\) 0 0
\(694\) −0.896674 −0.0340373
\(695\) 9.66312 7.02067i 0.366543 0.266309i
\(696\) 3.39919 + 10.4616i 0.128846 + 0.396547i
\(697\) −10.6763 + 32.8582i −0.404393 + 1.24459i
\(698\) 10.1353 + 7.36369i 0.383625 + 0.278720i
\(699\) 38.5066 + 27.9767i 1.45645 + 1.05817i
\(700\) −2.29180 + 7.05342i −0.0866217 + 0.266594i
\(701\) −5.71885 17.6008i −0.215998 0.664773i −0.999081 0.0428564i \(-0.986354\pi\)
0.783083 0.621917i \(-0.213646\pi\)
\(702\) −2.09017 + 1.51860i −0.0788884 + 0.0573158i
\(703\) 11.4164 0.430578
\(704\) 0 0
\(705\) 10.7082 0.403294
\(706\) −7.44427 + 5.40858i −0.280169 + 0.203555i
\(707\) −4.57295 14.0741i −0.171983 0.529311i
\(708\) 10.2812 31.6421i 0.386389 1.18918i
\(709\) 5.69098 + 4.13474i 0.213729 + 0.155283i 0.689499 0.724286i \(-0.257831\pi\)
−0.475770 + 0.879570i \(0.657831\pi\)
\(710\) 4.97214 + 3.61247i 0.186601 + 0.135574i
\(711\) 0.753289 2.31838i 0.0282505 0.0869462i
\(712\) −3.11803 9.59632i −0.116853 0.359637i
\(713\) 17.4443 12.6740i 0.653293 0.474645i
\(714\) −1.90983 −0.0714736
\(715\) 0 0
\(716\) 6.97871 0.260807
\(717\) 22.3713 16.2537i 0.835472 0.607006i
\(718\) 1.84346 + 5.67358i 0.0687973 + 0.211736i
\(719\) −0.892609 + 2.74717i −0.0332887 + 0.102452i −0.966320 0.257342i \(-0.917153\pi\)
0.933032 + 0.359794i \(0.117153\pi\)
\(720\) 0.972136 + 0.706298i 0.0362294 + 0.0263222i
\(721\) 7.16312 + 5.20431i 0.266768 + 0.193819i
\(722\) −1.87539 + 5.77185i −0.0697947 + 0.214806i
\(723\) 8.13525 + 25.0377i 0.302553 + 0.931164i
\(724\) −11.1246 + 8.08250i −0.413443 + 0.300384i
\(725\) −18.4721 −0.686038
\(726\) 0 0
\(727\) −12.4508 −0.461776 −0.230888 0.972980i \(-0.574163\pi\)
−0.230888 + 0.972980i \(0.574163\pi\)
\(728\) −1.47214 + 1.06957i −0.0545610 + 0.0396409i
\(729\) 9.11803 + 28.0624i 0.337705 + 1.03935i
\(730\) 1.68034 5.17155i 0.0621922 0.191408i
\(731\) 31.4058 + 22.8176i 1.16158 + 0.843940i
\(732\) −18.4894 13.4333i −0.683386 0.496509i
\(733\) −16.3607 + 50.3530i −0.604295 + 1.85983i −0.102733 + 0.994709i \(0.532759\pi\)
−0.501563 + 0.865121i \(0.667241\pi\)
\(734\) 3.87539 + 11.9272i 0.143043 + 0.440242i
\(735\) 1.30902 0.951057i 0.0482838 0.0350802i
\(736\) 21.1033 0.777879
\(737\) 0 0
\(738\) −1.63119 −0.0600449
\(739\) −9.20820 + 6.69015i −0.338729 + 0.246101i −0.744125 0.668040i \(-0.767134\pi\)
0.405396 + 0.914141i \(0.367134\pi\)
\(740\) −3.70820 11.4127i −0.136316 0.419538i
\(741\) −1.09017 + 3.35520i −0.0400484 + 0.123256i
\(742\) −0.736068 0.534785i −0.0270219 0.0196326i
\(743\) −12.0623 8.76378i −0.442523 0.321512i 0.344114 0.938928i \(-0.388179\pi\)
−0.786637 + 0.617416i \(0.788179\pi\)
\(744\) −3.11803 + 9.59632i −0.114313 + 0.351818i
\(745\) 2.73607 + 8.42075i 0.100242 + 0.308512i
\(746\) −4.77051 + 3.46598i −0.174661 + 0.126898i
\(747\) 1.03444 0.0378482
\(748\) 0 0
\(749\) 2.70820 0.0989556
\(750\) −4.50000 + 3.26944i −0.164317 + 0.119383i
\(751\) 12.7639 + 39.2833i 0.465762 + 1.43347i 0.858021 + 0.513615i \(0.171694\pi\)
−0.392259 + 0.919855i \(0.628306\pi\)
\(752\) −6.43363 + 19.8007i −0.234610 + 0.722056i
\(753\) 30.1074 + 21.8743i 1.09717 + 0.797144i
\(754\) −1.76393 1.28157i −0.0642386 0.0466721i
\(755\) −0.0172209 + 0.0530006i −0.000626734 + 0.00192889i
\(756\) 3.13525 + 9.64932i 0.114028 + 0.350942i
\(757\) 11.9443 8.67802i 0.434122 0.315408i −0.349173 0.937058i \(-0.613537\pi\)
0.783295 + 0.621650i \(0.213537\pi\)
\(758\) 12.2492 0.444912
\(759\) 0 0
\(760\) −2.59675 −0.0941939
\(761\) 12.3820 8.99602i 0.448846 0.326106i −0.340294 0.940319i \(-0.610527\pi\)
0.789140 + 0.614213i \(0.210527\pi\)
\(762\) 0.562306 + 1.73060i 0.0203702 + 0.0626930i
\(763\) −0.472136 + 1.45309i −0.0170925 + 0.0526052i
\(764\) 23.6459 + 17.1798i 0.855479 + 0.621542i
\(765\) −0.954915 0.693786i −0.0345250 0.0250839i
\(766\) −4.08359 + 12.5680i −0.147546 + 0.454100i
\(767\) 4.23607 + 13.0373i 0.152956 + 0.470749i
\(768\) 7.28115 5.29007i 0.262736 0.190889i
\(769\) −48.5623 −1.75120 −0.875601 0.483035i \(-0.839534\pi\)
−0.875601 + 0.483035i \(0.839534\pi\)
\(770\) 0 0
\(771\) 13.8541 0.498943
\(772\) 22.9894 16.7027i 0.827405 0.601145i
\(773\) 12.4336 + 38.2668i 0.447207 + 1.37636i 0.880046 + 0.474889i \(0.157512\pi\)
−0.432839 + 0.901471i \(0.642488\pi\)
\(774\) −0.566371 + 1.74311i −0.0203578 + 0.0626548i
\(775\) −13.7082 9.95959i −0.492413 0.357759i
\(776\) 8.33688 + 6.05710i 0.299277 + 0.217437i
\(777\) 3.23607 9.95959i 0.116093 0.357298i
\(778\) −4.03444 12.4167i −0.144642 0.445162i
\(779\) −15.9549 + 11.5919i −0.571644 + 0.415324i
\(780\) 3.70820 0.132775
\(781\) 0 0
\(782\) −6.00813 −0.214850
\(783\) −20.4443 + 14.8536i −0.730619 + 0.530826i
\(784\) 0.972136 + 2.99193i 0.0347191 + 0.106855i
\(785\) 6.14590 18.9151i 0.219357 0.675110i
\(786\) −9.47214 6.88191i −0.337860 0.245470i
\(787\) 16.6353 + 12.0862i 0.592983 + 0.430827i 0.843381 0.537316i \(-0.180562\pi\)
−0.250398 + 0.968143i \(0.580562\pi\)
\(788\) −2.45898 + 7.56796i −0.0875975 + 0.269598i
\(789\) −8.56231 26.3521i −0.304826 0.938158i
\(790\) 1.97214 1.43284i 0.0701654 0.0509782i
\(791\) −0.145898 −0.00518754
\(792\) 0 0
\(793\) 9.41641 0.334386
\(794\) 0.253289 0.184025i 0.00898889 0.00653081i
\(795\) 1.19098 + 3.66547i 0.0422398 + 0.130001i
\(796\) 4.71885 14.5231i 0.167255 0.514758i
\(797\) −26.0795 18.9479i −0.923784 0.671169i 0.0206788 0.999786i \(-0.493417\pi\)
−0.944463 + 0.328618i \(0.893417\pi\)
\(798\) −0.881966 0.640786i −0.0312213 0.0226836i
\(799\) 6.31966 19.4499i 0.223574 0.688088i
\(800\) −5.12461 15.7719i −0.181182 0.557622i
\(801\) 2.11803 1.53884i 0.0748371 0.0543723i
\(802\) −6.69505 −0.236410
\(803\) 0 0
\(804\) −24.9787 −0.880931
\(805\) 4.11803 2.99193i 0.145142 0.105452i
\(806\) −0.618034 1.90211i −0.0217693 0.0669991i
\(807\) −8.42705 + 25.9358i −0.296646 + 0.912983i
\(808\) 17.6246 + 12.8050i 0.620032 + 0.450479i
\(809\) 26.2984 + 19.1069i 0.924602 + 0.671762i 0.944665 0.328036i \(-0.106387\pi\)
−0.0200635 + 0.999799i \(0.506387\pi\)
\(810\) −0.909830 + 2.80017i −0.0319682 + 0.0983879i
\(811\) −0.360680 1.11006i −0.0126652 0.0389794i 0.944524 0.328442i \(-0.106523\pi\)
−0.957189 + 0.289462i \(0.906523\pi\)
\(812\) −6.92705 + 5.03280i −0.243092 + 0.176617i
\(813\) −7.76393 −0.272293
\(814\) 0 0
\(815\) −8.70820 −0.305035
\(816\) −12.7254 + 9.24556i −0.445479 + 0.323659i
\(817\) 6.84752 + 21.0745i 0.239565 + 0.737304i
\(818\) 2.09017 6.43288i 0.0730811 0.224920i
\(819\) −0.381966 0.277515i −0.0133470 0.00969714i
\(820\) 16.7705 + 12.1845i 0.585652 + 0.425501i
\(821\) −17.5106 + 53.8922i −0.611126 + 1.88085i −0.163760 + 0.986500i \(0.552362\pi\)
−0.447366 + 0.894351i \(0.647638\pi\)
\(822\) 2.92705 + 9.00854i 0.102093 + 0.314209i
\(823\) 25.7984 18.7436i 0.899275 0.653361i −0.0390048 0.999239i \(-0.512419\pi\)
0.938280 + 0.345878i \(0.112419\pi\)
\(824\) −13.0344 −0.454076
\(825\) 0 0
\(826\) −4.23607 −0.147392
\(827\) −15.8541 + 11.5187i −0.551301 + 0.400544i −0.828265 0.560337i \(-0.810672\pi\)
0.276964 + 0.960880i \(0.410672\pi\)
\(828\) 1.11397 + 3.42844i 0.0387131 + 0.119147i
\(829\) −14.8262 + 45.6305i −0.514937 + 1.58481i 0.268461 + 0.963291i \(0.413485\pi\)
−0.783397 + 0.621521i \(0.786515\pi\)
\(830\) 0.836881 + 0.608030i 0.0290486 + 0.0211050i
\(831\) −30.1525 21.9071i −1.04598 0.759947i
\(832\) −1.79837 + 5.53483i −0.0623474 + 0.191886i
\(833\) −0.954915 2.93893i −0.0330858 0.101828i
\(834\) −5.97214 + 4.33901i −0.206798 + 0.150248i
\(835\) −6.47214 −0.223978
\(836\) 0 0
\(837\) −23.1803 −0.801230
\(838\) −9.23607 + 6.71040i −0.319055 + 0.231807i
\(839\) 9.45492 + 29.0992i 0.326420 + 1.00462i 0.970796 + 0.239908i \(0.0771173\pi\)
−0.644376 + 0.764709i \(0.722883\pi\)
\(840\) −0.736068 + 2.26538i −0.0253968 + 0.0781632i
\(841\) 6.20820 + 4.51052i 0.214076 + 0.155535i
\(842\) −0.236068 0.171513i −0.00813544 0.00591074i
\(843\) −12.5902 + 38.7486i −0.433628 + 1.33457i
\(844\) 8.94834 + 27.5402i 0.308014 + 0.947971i
\(845\) 9.28115 6.74315i 0.319281 0.231971i
\(846\) 0.965558 0.0331966
\(847\) 0 0
\(848\) −7.49342 −0.257325
\(849\) −15.6353 + 11.3597i −0.536601 + 0.389863i
\(850\) 1.45898 + 4.49028i 0.0500426 + 0.154015i
\(851\) 10.1803 31.3319i 0.348978 1.07404i
\(852\) 39.0517 + 28.3727i 1.33789 + 0.972032i
\(853\) −28.2426 20.5195i −0.967010 0.702574i −0.0122416 0.999925i \(-0.503897\pi\)
−0.954768 + 0.297351i \(0.903897\pi\)
\(854\) −0.899187 + 2.76741i −0.0307695 + 0.0946989i
\(855\) −0.208204 0.640786i −0.00712042 0.0219144i
\(856\) −3.22542 + 2.34341i −0.110243 + 0.0800960i
\(857\) 15.0902 0.515470 0.257735 0.966216i \(-0.417024\pi\)
0.257735 + 0.966216i \(0.417024\pi\)
\(858\) 0 0
\(859\) 21.5623 0.735696 0.367848 0.929886i \(-0.380095\pi\)
0.367848 + 0.929886i \(0.380095\pi\)
\(860\) 18.8435 13.6906i 0.642557 0.466845i
\(861\) 5.59017 + 17.2048i 0.190512 + 0.586337i
\(862\) 1.63525 5.03280i 0.0556970 0.171418i
\(863\) 38.7877 + 28.1809i 1.32035 + 0.959290i 0.999928 + 0.0120153i \(0.00382467\pi\)
0.320422 + 0.947275i \(0.396175\pi\)
\(864\) −18.3541 13.3350i −0.624419 0.453667i
\(865\) 4.75329 14.6291i 0.161617 0.497405i
\(866\) −1.05824 3.25693i −0.0359605 0.110675i
\(867\) −9.75329 + 7.08618i −0.331239 + 0.240659i
\(868\) −7.85410 −0.266586
\(869\) 0 0
\(870\) −2.85410 −0.0967631
\(871\) 8.32624 6.04937i 0.282124 0.204975i
\(872\) −0.695048 2.13914i −0.0235373 0.0724404i
\(873\) −0.826238 + 2.54290i −0.0279639 + 0.0860641i
\(874\) −2.77458 2.01585i −0.0938514 0.0681870i
\(875\) −7.28115 5.29007i −0.246148 0.178837i
\(876\) 13.1976 40.6179i 0.445904 1.37235i
\(877\) −4.01722 12.3637i −0.135652 0.417494i 0.860039 0.510228i \(-0.170439\pi\)
−0.995691 + 0.0927348i \(0.970439\pi\)
\(878\) 1.04508 0.759299i 0.0352699 0.0256251i
\(879\) −17.7984 −0.600324
\(880\) 0 0
\(881\) 14.1459 0.476587 0.238294 0.971193i \(-0.423412\pi\)
0.238294 + 0.971193i \(0.423412\pi\)
\(882\) 0.118034 0.0857567i 0.00397441 0.00288758i
\(883\) 9.77458 + 30.0830i 0.328941 + 1.01238i 0.969630 + 0.244575i \(0.0786485\pi\)
−0.640690 + 0.767800i \(0.721351\pi\)
\(884\) 2.18847 6.73542i 0.0736062 0.226537i
\(885\) 14.5172 + 10.5474i 0.487991 + 0.354546i
\(886\) −0.954915 0.693786i −0.0320810 0.0233082i
\(887\) −17.6803 + 54.4145i −0.593648 + 1.82706i −0.0323024 + 0.999478i \(0.510284\pi\)
−0.561345 + 0.827582i \(0.689716\pi\)
\(888\) 4.76393 + 14.6619i 0.159867 + 0.492020i
\(889\) −2.38197 + 1.73060i −0.0798886 + 0.0580424i
\(890\) 2.61803 0.0877567
\(891\) 0 0
\(892\) −3.77206 −0.126298
\(893\) 9.44427 6.86167i 0.316041 0.229617i
\(894\) −1.69098 5.20431i −0.0565549 0.174058i
\(895\) −1.16312 + 3.57971i −0.0388788 + 0.119657i
\(896\) −8.16312 5.93085i −0.272711 0.198136i
\(897\) 8.23607 + 5.98385i 0.274994 + 0.199795i
\(898\) 1.45492 4.47777i 0.0485511 0.149425i
\(899\) −6.04508 18.6049i −0.201615 0.620507i
\(900\) 2.29180 1.66509i 0.0763932 0.0555029i
\(901\) 7.36068 0.245220
\(902\) 0 0
\(903\) 20.3262 0.676415
\(904\) 0.173762 0.126246i 0.00577924 0.00419886i
\(905\) −2.29180 7.05342i −0.0761819 0.234464i
\(906\) 0.0106431 0.0327561i 0.000353594 0.00108825i
\(907\) 12.7533 + 9.26581i 0.423466 + 0.307666i 0.779031 0.626986i \(-0.215711\pi\)
−0.355565 + 0.934652i \(0.615711\pi\)
\(908\) 24.0517 + 17.4746i 0.798182 + 0.579914i
\(909\) −1.74671 + 5.37582i −0.0579348 + 0.178305i
\(910\) −0.145898 0.449028i −0.00483647 0.0148851i
\(911\) 36.5517 26.5563i 1.21101 0.879851i 0.215688 0.976462i \(-0.430800\pi\)
0.995322 + 0.0966115i \(0.0308004\pi\)
\(912\) −8.97871 −0.297315
\(913\) 0 0
\(914\) 0.0557281 0.00184332
\(915\) 9.97214 7.24518i 0.329669 0.239518i
\(916\) −3.87539 11.9272i −0.128046 0.394086i
\(917\) 5.85410 18.0171i 0.193319 0.594976i
\(918\) 5.22542 + 3.79649i 0.172465 + 0.125303i
\(919\) −12.0451 8.75127i −0.397331 0.288678i 0.371122 0.928584i \(-0.378973\pi\)
−0.768453 + 0.639906i \(0.778973\pi\)
\(920\) −2.31559 + 7.12667i −0.0763429 + 0.234959i
\(921\) −11.5902 35.6709i −0.381909 1.17540i
\(922\) −5.71885 + 4.15499i −0.188340 + 0.136837i
\(923\) −19.8885 −0.654639
\(924\) 0 0
\(925\) −25.8885 −0.851210
\(926\) −6.87132 + 4.99231i −0.225806 + 0.164057i
\(927\) −1.04508 3.21644i −0.0343251 0.105642i
\(928\) 5.91641 18.2088i 0.194216 0.597734i
\(929\) −19.4164 14.1068i −0.637032 0.462831i 0.221797 0.975093i \(-0.428808\pi\)
−0.858829 + 0.512262i \(0.828808\pi\)
\(930\) −2.11803 1.53884i −0.0694531 0.0504606i
\(931\) 0.545085 1.67760i 0.0178644 0.0549811i
\(932\) −16.8541 51.8716i −0.552074 1.69911i
\(933\) 11.7812 8.55951i 0.385698 0.280226i
\(934\) −1.72136 −0.0563246
\(935\) 0 0
\(936\) 0.695048 0.0227184
\(937\) −41.8435 + 30.4011i −1.36697 + 0.993159i −0.368999 + 0.929430i \(0.620299\pi\)
−0.997967 + 0.0637293i \(0.979701\pi\)
\(938\) 0.982779 + 3.02468i 0.0320889 + 0.0987594i
\(939\) −9.16312 + 28.2012i −0.299027 + 0.920311i
\(940\) −9.92705 7.21242i −0.323785 0.235243i
\(941\) 21.8992 + 15.9107i 0.713893 + 0.518674i 0.884427 0.466678i \(-0.154549\pi\)
−0.170534 + 0.985352i \(0.554549\pi\)
\(942\) −3.79837 + 11.6902i −0.123758 + 0.380887i
\(943\) 17.5861 + 54.1245i 0.572682 + 1.76254i
\(944\) −28.2254 + 20.5070i −0.918659 + 0.667445i
\(945\) −5.47214 −0.178009
\(946\) 0 0
\(947\) 6.29180 0.204456 0.102228 0.994761i \(-0.467403\pi\)
0.102228 + 0.994761i \(0.467403\pi\)
\(948\) 15.4894 11.2537i 0.503071 0.365502i
\(949\) 5.43769 + 16.7355i 0.176515 + 0.543257i
\(950\) −0.832816 + 2.56314i −0.0270201 + 0.0831593i
\(951\) −5.80902 4.22050i −0.188370 0.136859i
\(952\) 3.68034 + 2.67392i 0.119281 + 0.0866624i
\(953\) 1.92705 5.93085i 0.0624233 0.192119i −0.914981 0.403496i \(-0.867795\pi\)
0.977405 + 0.211377i \(0.0677948\pi\)
\(954\) 0.107391 + 0.330515i 0.00347691 + 0.0107008i
\(955\) −12.7533 + 9.26581i −0.412687 + 0.299834i
\(956\) −31.6869 −1.02483
\(957\) 0 0
\(958\) −8.31308 −0.268583
\(959\) −12.3992 + 9.00854i −0.400391 + 0.290901i
\(960\) 2.35410 + 7.24518i 0.0759783 + 0.233837i
\(961\) −4.03444 + 12.4167i −0.130143 + 0.400540i
\(962\) −2.47214 1.79611i −0.0797049 0.0579090i
\(963\) −0.836881 0.608030i −0.0269681 0.0195935i
\(964\) 9.32217 28.6907i 0.300247 0.924065i
\(965\) 4.73607 + 14.5761i 0.152459 + 0.469222i
\(966\) −2.54508 + 1.84911i −0.0818868 + 0.0594942i
\(967\) −27.4508 −0.882760 −0.441380 0.897320i \(-0.645511\pi\)
−0.441380 + 0.897320i \(0.645511\pi\)
\(968\) 0 0
\(969\) 8.81966 0.283328
\(970\) −2.16312 + 1.57160i −0.0694536 + 0.0504610i
\(971\) −8.72949 26.8666i −0.280143 0.862190i −0.987813 0.155647i \(-0.950254\pi\)
0.707670 0.706543i \(-0.249746\pi\)
\(972\) 2.25987 6.95515i 0.0724853 0.223087i
\(973\) −9.66312 7.02067i −0.309785 0.225072i
\(974\) 10.0729 + 7.31843i 0.322758 + 0.234497i
\(975\) 2.47214 7.60845i 0.0791717 0.243665i
\(976\) 7.40576 + 22.7926i 0.237053 + 0.729573i
\(977\) 8.75329 6.35964i 0.280043 0.203463i −0.438893 0.898539i \(-0.644629\pi\)
0.718936 + 0.695076i \(0.244629\pi\)
\(978\) 5.38197 0.172096
\(979\) 0 0
\(980\) −1.85410 −0.0592271
\(981\) 0.472136 0.343027i 0.0150741 0.0109520i
\(982\) −2.61397 8.04497i −0.0834151 0.256725i
\(983\) −3.82624 + 11.7759i −0.122038 + 0.375594i −0.993350 0.115135i \(-0.963270\pi\)
0.871312 + 0.490730i \(0.163270\pi\)
\(984\) −21.5451 15.6534i −0.686832 0.499013i
\(985\) −3.47214 2.52265i −0.110631 0.0803785i
\(986\) −1.68441 + 5.18407i −0.0536424 + 0.165094i
\(987\) −3.30902 10.1841i −0.105327 0.324164i
\(988\) 3.27051 2.37616i 0.104049 0.0755959i
\(989\) 63.9443 2.03331
\(990\) 0 0
\(991\) −0.729490 −0.0231730 −0.0115865 0.999933i \(-0.503688\pi\)
−0.0115865 + 0.999933i \(0.503688\pi\)
\(992\) 14.2082 10.3229i 0.451111 0.327751i
\(993\) −3.09017 9.51057i −0.0980636 0.301809i
\(994\) 1.89919 5.84510i 0.0602386 0.185395i
\(995\) 6.66312 + 4.84104i 0.211235 + 0.153471i
\(996\) 6.57295 + 4.77553i 0.208272 + 0.151318i
\(997\) 17.2639 53.1329i 0.546754 1.68274i −0.170028 0.985439i \(-0.554386\pi\)
0.716782 0.697297i \(-0.245614\pi\)
\(998\) −1.19098 3.66547i −0.0376999 0.116028i
\(999\) −28.6525 + 20.8172i −0.906524 + 0.658628i
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 847.2.f.j.729.1 4
11.2 odd 10 847.2.a.d.1.2 2
11.3 even 5 847.2.f.c.148.1 4
11.4 even 5 inner 847.2.f.j.323.1 4
11.5 even 5 847.2.f.c.372.1 4
11.6 odd 10 847.2.f.l.372.1 4
11.7 odd 10 847.2.f.d.323.1 4
11.8 odd 10 847.2.f.l.148.1 4
11.9 even 5 847.2.a.h.1.1 yes 2
11.10 odd 2 847.2.f.d.729.1 4
33.2 even 10 7623.2.a.bx.1.1 2
33.20 odd 10 7623.2.a.t.1.2 2
77.13 even 10 5929.2.a.i.1.2 2
77.20 odd 10 5929.2.a.s.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
847.2.a.d.1.2 2 11.2 odd 10
847.2.a.h.1.1 yes 2 11.9 even 5
847.2.f.c.148.1 4 11.3 even 5
847.2.f.c.372.1 4 11.5 even 5
847.2.f.d.323.1 4 11.7 odd 10
847.2.f.d.729.1 4 11.10 odd 2
847.2.f.j.323.1 4 11.4 even 5 inner
847.2.f.j.729.1 4 1.1 even 1 trivial
847.2.f.l.148.1 4 11.8 odd 10
847.2.f.l.372.1 4 11.6 odd 10
5929.2.a.i.1.2 2 77.13 even 10
5929.2.a.s.1.1 2 77.20 odd 10
7623.2.a.t.1.2 2 33.20 odd 10
7623.2.a.bx.1.1 2 33.2 even 10