Properties

Label 847.2.f.r.729.2
Level $847$
Weight $2$
Character 847.729
Analytic conductor $6.763$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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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: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.446265625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 4x^{6} - 7x^{5} + 19x^{4} + 21x^{3} + 36x^{2} + 27x + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 729.2
Root \(-0.711597 + 2.19007i\) of defining polynomial
Character \(\chi\) \(=\) 847.729
Dual form 847.2.f.r.323.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.86298 - 1.35354i) q^{2} +(-0.711597 - 2.19007i) q^{3} +(1.02061 - 3.14113i) q^{4} +(-2.91695 - 2.11929i) q^{5} +(-4.29004 - 3.11689i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.927051 - 2.85317i) q^{8} +(-1.86298 + 1.35354i) q^{9} +O(q^{10})\) \(q+(1.86298 - 1.35354i) q^{2} +(-0.711597 - 2.19007i) q^{3} +(1.02061 - 3.14113i) q^{4} +(-2.91695 - 2.11929i) q^{5} +(-4.29004 - 3.11689i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.927051 - 2.85317i) q^{8} +(-1.86298 + 1.35354i) q^{9} -8.30278 q^{10} -7.60555 q^{12} +(5.34400 - 3.88265i) q^{13} +(-0.711597 - 2.19007i) q^{14} +(-2.56570 + 7.89641i) q^{15} +(-0.244951 - 0.177967i) q^{16} +(2.18210 + 1.58539i) q^{17} +(-1.63865 + 5.04324i) q^{18} +(0.927051 + 2.85317i) q^{19} +(-9.63404 + 6.99954i) q^{20} -2.30278 q^{21} -2.69722 q^{23} +(-5.58895 + 4.06061i) q^{24} +(2.47214 + 7.60845i) q^{25} +(4.70049 - 14.4666i) q^{26} +(-1.29892 - 0.943719i) q^{27} +(-2.67200 - 1.94132i) q^{28} +(-1.45152 + 4.46733i) q^{29} +(5.90823 + 18.1837i) q^{30} +(-0.809017 + 0.587785i) q^{31} +5.30278 q^{32} +6.21110 q^{34} +(-2.91695 + 2.11929i) q^{35} +(2.35024 + 7.23331i) q^{36} +(-1.61032 + 4.95605i) q^{37} +(5.58895 + 4.06061i) q^{38} +(-12.3060 - 8.94086i) q^{39} +(-3.34253 + 10.2872i) q^{40} +(-2.16312 - 6.65740i) q^{41} +(-4.29004 + 3.11689i) q^{42} -1.69722 q^{43} +8.30278 q^{45} +(-5.02489 + 3.65079i) q^{46} +(-0.589705 - 1.81493i) q^{47} +(-0.215454 + 0.663100i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(14.9039 + 10.8283i) q^{50} +(1.91934 - 5.90711i) q^{51} +(-6.74172 - 20.7489i) q^{52} +(10.4431 - 7.58732i) q^{53} -3.69722 q^{54} -3.00000 q^{56} +(5.58895 - 4.06061i) q^{57} +(3.34253 + 10.2872i) q^{58} +(2.06956 - 6.36944i) q^{59} +(22.1850 + 16.1184i) q^{60} +(-3.48102 - 2.52911i) q^{61} +(-0.711597 + 2.19007i) q^{62} +(0.711597 + 2.19007i) q^{63} +(10.3689 - 7.53344i) q^{64} -23.8167 q^{65} +8.51388 q^{67} +(7.20699 - 5.23618i) q^{68} +(1.91934 + 5.90711i) q^{69} +(-2.56570 + 7.89641i) q^{70} +(3.48102 + 2.52911i) q^{71} +(5.58895 + 4.06061i) q^{72} +(1.54508 - 4.75528i) q^{73} +(3.70820 + 11.4127i) q^{74} +(14.9039 - 10.8283i) q^{75} +9.90833 q^{76} -35.0278 q^{78} +(-6.71709 + 4.88025i) q^{79} +(0.337346 + 1.03824i) q^{80} +(-3.27730 + 10.0865i) q^{81} +(-13.0409 - 9.47476i) q^{82} +(2.42705 + 1.76336i) q^{83} +(-2.35024 + 7.23331i) q^{84} +(-3.00518 - 9.24901i) q^{85} +(-3.16190 + 2.29726i) q^{86} +10.8167 q^{87} -14.7250 q^{89} +(15.4679 - 11.2381i) q^{90} +(-2.04123 - 6.28225i) q^{91} +(-2.75282 + 8.47232i) q^{92} +(1.86298 + 1.35354i) q^{93} +(-3.55518 - 2.58299i) q^{94} +(3.34253 - 10.2872i) q^{95} +(-3.77344 - 11.6134i) q^{96} +(2.91695 - 2.11929i) q^{97} -2.30278 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{2} + q^{3} - 3 q^{4} - 7 q^{6} - 2 q^{7} + 6 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{2} + q^{3} - 3 q^{4} - 7 q^{6} - 2 q^{7} + 6 q^{8} - q^{9} - 52 q^{10} - 32 q^{12} + 6 q^{13} + q^{14} + 13 q^{15} + 3 q^{16} + 9 q^{17} + 7 q^{18} - 6 q^{19} - 13 q^{20} - 4 q^{21} - 36 q^{23} - 3 q^{24} - 16 q^{25} - 16 q^{26} + 4 q^{27} - 3 q^{28} + 13 q^{29} - 13 q^{30} - 2 q^{31} + 28 q^{32} - 8 q^{34} - 8 q^{36} - 4 q^{37} + 3 q^{38} - 16 q^{39} + 14 q^{41} - 7 q^{42} - 28 q^{43} + 52 q^{45} + 2 q^{46} - 7 q^{47} + 5 q^{48} - 2 q^{49} + 8 q^{50} + 2 q^{51} + 22 q^{52} + 15 q^{53} - 44 q^{54} - 24 q^{56} + 3 q^{57} - 17 q^{59} + 26 q^{60} - 5 q^{61} + q^{62} - q^{63} + 4 q^{64} - 104 q^{65} - 4 q^{67} + 7 q^{68} + 2 q^{69} + 13 q^{70} + 5 q^{71} + 3 q^{72} - 10 q^{73} - 24 q^{74} + 8 q^{75} + 36 q^{76} - 136 q^{78} - 13 q^{79} - 13 q^{80} + 14 q^{81} - 7 q^{82} + 6 q^{83} + 8 q^{84} - 13 q^{85} + 3 q^{86} + 12 q^{89} + 13 q^{90} + 6 q^{91} + 7 q^{92} + q^{93} - 16 q^{94} + 10 q^{96} - 4 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.86298 1.35354i 1.31733 0.957096i 0.317368 0.948303i \(-0.397201\pi\)
0.999961 0.00879304i \(-0.00279895\pi\)
\(3\) −0.711597 2.19007i −0.410841 1.26444i −0.915919 0.401364i \(-0.868536\pi\)
0.505078 0.863074i \(-0.331464\pi\)
\(4\) 1.02061 3.14113i 0.510307 1.57056i
\(5\) −2.91695 2.11929i −1.30450 0.947775i −0.304512 0.952509i \(-0.598493\pi\)
−0.999989 + 0.00473329i \(0.998493\pi\)
\(6\) −4.29004 3.11689i −1.75140 1.27247i
\(7\) 0.309017 0.951057i 0.116797 0.359466i
\(8\) −0.927051 2.85317i −0.327762 1.00875i
\(9\) −1.86298 + 1.35354i −0.620995 + 0.451179i
\(10\) −8.30278 −2.62557
\(11\) 0 0
\(12\) −7.60555 −2.19553
\(13\) 5.34400 3.88265i 1.48216 1.07685i 0.505307 0.862940i \(-0.331379\pi\)
0.976853 0.213912i \(-0.0686207\pi\)
\(14\) −0.711597 2.19007i −0.190182 0.585321i
\(15\) −2.56570 + 7.89641i −0.662461 + 2.03884i
\(16\) −0.244951 0.177967i −0.0612377 0.0444918i
\(17\) 2.18210 + 1.58539i 0.529237 + 0.384513i 0.820072 0.572260i \(-0.193933\pi\)
−0.290835 + 0.956773i \(0.593933\pi\)
\(18\) −1.63865 + 5.04324i −0.386233 + 1.18870i
\(19\) 0.927051 + 2.85317i 0.212680 + 0.654562i 0.999310 + 0.0371374i \(0.0118239\pi\)
−0.786630 + 0.617425i \(0.788176\pi\)
\(20\) −9.63404 + 6.99954i −2.15424 + 1.56514i
\(21\) −2.30278 −0.502507
\(22\) 0 0
\(23\) −2.69722 −0.562410 −0.281205 0.959648i \(-0.590734\pi\)
−0.281205 + 0.959648i \(0.590734\pi\)
\(24\) −5.58895 + 4.06061i −1.14084 + 0.828869i
\(25\) 2.47214 + 7.60845i 0.494427 + 1.52169i
\(26\) 4.70049 14.4666i 0.921842 2.83714i
\(27\) −1.29892 0.943719i −0.249977 0.181619i
\(28\) −2.67200 1.94132i −0.504961 0.366876i
\(29\) −1.45152 + 4.46733i −0.269541 + 0.829562i 0.721071 + 0.692861i \(0.243650\pi\)
−0.990612 + 0.136701i \(0.956350\pi\)
\(30\) 5.90823 + 18.1837i 1.07869 + 3.31987i
\(31\) −0.809017 + 0.587785i −0.145304 + 0.105569i −0.658062 0.752964i \(-0.728624\pi\)
0.512758 + 0.858533i \(0.328624\pi\)
\(32\) 5.30278 0.937407
\(33\) 0 0
\(34\) 6.21110 1.06520
\(35\) −2.91695 + 2.11929i −0.493055 + 0.358225i
\(36\) 2.35024 + 7.23331i 0.391707 + 1.20555i
\(37\) −1.61032 + 4.95605i −0.264735 + 0.814770i 0.727020 + 0.686617i \(0.240905\pi\)
−0.991754 + 0.128153i \(0.959095\pi\)
\(38\) 5.58895 + 4.06061i 0.906648 + 0.658718i
\(39\) −12.3060 8.94086i −1.97054 1.43168i
\(40\) −3.34253 + 10.2872i −0.528500 + 1.62656i
\(41\) −2.16312 6.65740i −0.337822 1.03971i −0.965315 0.261088i \(-0.915919\pi\)
0.627493 0.778623i \(-0.284081\pi\)
\(42\) −4.29004 + 3.11689i −0.661967 + 0.480947i
\(43\) −1.69722 −0.258824 −0.129412 0.991591i \(-0.541309\pi\)
−0.129412 + 0.991591i \(0.541309\pi\)
\(44\) 0 0
\(45\) 8.30278 1.23770
\(46\) −5.02489 + 3.65079i −0.740879 + 0.538280i
\(47\) −0.589705 1.81493i −0.0860174 0.264734i 0.898791 0.438377i \(-0.144446\pi\)
−0.984809 + 0.173642i \(0.944446\pi\)
\(48\) −0.215454 + 0.663100i −0.0310981 + 0.0957102i
\(49\) −0.809017 0.587785i −0.115574 0.0839693i
\(50\) 14.9039 + 10.8283i 2.10773 + 1.53135i
\(51\) 1.91934 5.90711i 0.268761 0.827161i
\(52\) −6.74172 20.7489i −0.934908 2.87735i
\(53\) 10.4431 7.58732i 1.43446 1.04220i 0.445301 0.895381i \(-0.353097\pi\)
0.989164 0.146818i \(-0.0469031\pi\)
\(54\) −3.69722 −0.503129
\(55\) 0 0
\(56\) −3.00000 −0.400892
\(57\) 5.58895 4.06061i 0.740275 0.537841i
\(58\) 3.34253 + 10.2872i 0.438896 + 1.35078i
\(59\) 2.06956 6.36944i 0.269433 0.829230i −0.721206 0.692721i \(-0.756412\pi\)
0.990639 0.136509i \(-0.0435883\pi\)
\(60\) 22.1850 + 16.1184i 2.86408 + 2.08087i
\(61\) −3.48102 2.52911i −0.445699 0.323819i 0.342196 0.939628i \(-0.388829\pi\)
−0.787895 + 0.615809i \(0.788829\pi\)
\(62\) −0.711597 + 2.19007i −0.0903729 + 0.278139i
\(63\) 0.711597 + 2.19007i 0.0896528 + 0.275923i
\(64\) 10.3689 7.53344i 1.29611 0.941680i
\(65\) −23.8167 −2.95409
\(66\) 0 0
\(67\) 8.51388 1.04014 0.520068 0.854125i \(-0.325907\pi\)
0.520068 + 0.854125i \(0.325907\pi\)
\(68\) 7.20699 5.23618i 0.873976 0.634980i
\(69\) 1.91934 + 5.90711i 0.231061 + 0.711132i
\(70\) −2.56570 + 7.89641i −0.306660 + 0.943801i
\(71\) 3.48102 + 2.52911i 0.413121 + 0.300150i 0.774864 0.632128i \(-0.217818\pi\)
−0.361743 + 0.932278i \(0.617818\pi\)
\(72\) 5.58895 + 4.06061i 0.658665 + 0.478548i
\(73\) 1.54508 4.75528i 0.180839 0.556564i −0.819013 0.573774i \(-0.805479\pi\)
0.999852 + 0.0172107i \(0.00547861\pi\)
\(74\) 3.70820 + 11.4127i 0.431070 + 1.32670i
\(75\) 14.9039 10.8283i 1.72095 1.25034i
\(76\) 9.90833 1.13656
\(77\) 0 0
\(78\) −35.0278 −3.96611
\(79\) −6.71709 + 4.88025i −0.755731 + 0.549071i −0.897598 0.440815i \(-0.854690\pi\)
0.141867 + 0.989886i \(0.454690\pi\)
\(80\) 0.337346 + 1.03824i 0.0377164 + 0.116079i
\(81\) −3.27730 + 10.0865i −0.364144 + 1.12072i
\(82\) −13.0409 9.47476i −1.44013 1.04631i
\(83\) 2.42705 + 1.76336i 0.266403 + 0.193553i 0.712965 0.701199i \(-0.247352\pi\)
−0.446562 + 0.894753i \(0.647352\pi\)
\(84\) −2.35024 + 7.23331i −0.256433 + 0.789219i
\(85\) −3.00518 9.24901i −0.325958 1.00320i
\(86\) −3.16190 + 2.29726i −0.340957 + 0.247720i
\(87\) 10.8167 1.15967
\(88\) 0 0
\(89\) −14.7250 −1.56084 −0.780422 0.625253i \(-0.784996\pi\)
−0.780422 + 0.625253i \(0.784996\pi\)
\(90\) 15.4679 11.2381i 1.63046 1.18460i
\(91\) −2.04123 6.28225i −0.213979 0.658559i
\(92\) −2.75282 + 8.47232i −0.287002 + 0.883301i
\(93\) 1.86298 + 1.35354i 0.193183 + 0.140355i
\(94\) −3.55518 2.58299i −0.366689 0.266415i
\(95\) 3.34253 10.2872i 0.342936 1.05545i
\(96\) −3.77344 11.6134i −0.385125 1.18529i
\(97\) 2.91695 2.11929i 0.296172 0.215181i −0.429769 0.902939i \(-0.641405\pi\)
0.725940 + 0.687758i \(0.241405\pi\)
\(98\) −2.30278 −0.232615
\(99\) 0 0
\(100\) 26.4222 2.64222
\(101\) −4.29004 + 3.11689i −0.426874 + 0.310142i −0.780398 0.625283i \(-0.784983\pi\)
0.353523 + 0.935426i \(0.384983\pi\)
\(102\) −4.41980 13.6027i −0.437625 1.34687i
\(103\) −4.41980 + 13.6027i −0.435496 + 1.34032i 0.457082 + 0.889425i \(0.348895\pi\)
−0.892578 + 0.450894i \(0.851105\pi\)
\(104\) −16.0320 11.6479i −1.57207 1.14217i
\(105\) 6.71709 + 4.88025i 0.655521 + 0.476264i
\(106\) 9.18552 28.2701i 0.892177 2.74584i
\(107\) −3.83010 11.7878i −0.370269 1.13957i −0.946615 0.322366i \(-0.895522\pi\)
0.576346 0.817206i \(-0.304478\pi\)
\(108\) −4.29004 + 3.11689i −0.412809 + 0.299923i
\(109\) 8.00000 0.766261 0.383131 0.923694i \(-0.374846\pi\)
0.383131 + 0.923694i \(0.374846\pi\)
\(110\) 0 0
\(111\) 12.0000 1.13899
\(112\) −0.244951 + 0.177967i −0.0231457 + 0.0168163i
\(113\) −3.30562 10.1737i −0.310967 0.957058i −0.977383 0.211478i \(-0.932172\pi\)
0.666416 0.745580i \(-0.267828\pi\)
\(114\) 4.91594 15.1297i 0.460420 1.41703i
\(115\) 7.86767 + 5.71620i 0.733664 + 0.533038i
\(116\) 12.5510 + 9.11883i 1.16533 + 0.846662i
\(117\) −4.70049 + 14.4666i −0.434560 + 1.33744i
\(118\) −4.76572 14.6674i −0.438720 1.35024i
\(119\) 2.18210 1.58539i 0.200033 0.145332i
\(120\) 24.9083 2.27381
\(121\) 0 0
\(122\) −9.90833 −0.897058
\(123\) −13.0409 + 9.47476i −1.17586 + 0.854311i
\(124\) 1.02061 + 3.14113i 0.0916538 + 0.282081i
\(125\) 3.34253 10.2872i 0.298965 0.920120i
\(126\) 4.29004 + 3.11689i 0.382187 + 0.277675i
\(127\) 1.61803 + 1.17557i 0.143577 + 0.104315i 0.657255 0.753668i \(-0.271717\pi\)
−0.513678 + 0.857983i \(0.671717\pi\)
\(128\) 5.84299 17.9829i 0.516453 1.58948i
\(129\) 1.20774 + 3.71704i 0.106336 + 0.327267i
\(130\) −44.3701 + 32.2367i −3.89151 + 2.82735i
\(131\) 6.00000 0.524222 0.262111 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) 0 0
\(133\) 3.00000 0.260133
\(134\) 15.8612 11.5239i 1.37020 0.995509i
\(135\) 1.78887 + 5.50557i 0.153961 + 0.473844i
\(136\) 2.50046 7.69564i 0.214413 0.659896i
\(137\) 8.18679 + 5.94805i 0.699445 + 0.508176i 0.879751 0.475434i \(-0.157709\pi\)
−0.180307 + 0.983610i \(0.557709\pi\)
\(138\) 11.5712 + 8.40696i 0.985005 + 0.715648i
\(139\) −6.67648 + 20.5481i −0.566292 + 1.74287i 0.0977898 + 0.995207i \(0.468823\pi\)
−0.664082 + 0.747660i \(0.731177\pi\)
\(140\) 3.67988 + 11.3255i 0.311006 + 0.957179i
\(141\) −3.55518 + 2.58299i −0.299400 + 0.217527i
\(142\) 9.90833 0.831488
\(143\) 0 0
\(144\) 0.697224 0.0581020
\(145\) 13.7016 9.95478i 1.13785 0.826699i
\(146\) −3.55798 10.9503i −0.294461 0.906257i
\(147\) −0.711597 + 2.19007i −0.0586915 + 0.180634i
\(148\) 13.9241 + 10.1164i 1.14455 + 0.831566i
\(149\) −3.97092 2.88504i −0.325310 0.236352i 0.413128 0.910673i \(-0.364436\pi\)
−0.738438 + 0.674321i \(0.764436\pi\)
\(150\) 13.1092 40.3459i 1.07036 3.29423i
\(151\) 0.0652343 + 0.200770i 0.00530869 + 0.0163385i 0.953676 0.300836i \(-0.0972658\pi\)
−0.948367 + 0.317175i \(0.897266\pi\)
\(152\) 7.28115 5.29007i 0.590579 0.429081i
\(153\) −6.21110 −0.502138
\(154\) 0 0
\(155\) 3.60555 0.289605
\(156\) −40.6441 + 29.5297i −3.25413 + 2.36426i
\(157\) 2.22835 + 6.85817i 0.177842 + 0.547341i 0.999752 0.0222763i \(-0.00709134\pi\)
−0.821910 + 0.569618i \(0.807091\pi\)
\(158\) −5.90823 + 18.1837i −0.470033 + 1.44661i
\(159\) −24.0480 17.4719i −1.90713 1.38561i
\(160\) −15.4679 11.2381i −1.22285 0.888451i
\(161\) −0.833488 + 2.56521i −0.0656881 + 0.202167i
\(162\) 7.54688 + 23.2269i 0.592939 + 1.82488i
\(163\) −2.27872 + 1.65559i −0.178483 + 0.129676i −0.673440 0.739242i \(-0.735184\pi\)
0.494957 + 0.868918i \(0.335184\pi\)
\(164\) −23.1194 −1.80532
\(165\) 0 0
\(166\) 6.90833 0.536190
\(167\) −4.21587 + 3.06301i −0.326234 + 0.237023i −0.738831 0.673891i \(-0.764622\pi\)
0.412597 + 0.910914i \(0.364622\pi\)
\(168\) 2.13479 + 6.57021i 0.164703 + 0.506903i
\(169\) 9.46621 29.1340i 0.728170 2.24108i
\(170\) −18.1175 13.1631i −1.38955 1.00957i
\(171\) −5.58895 4.06061i −0.427398 0.310523i
\(172\) −1.73221 + 5.33120i −0.132080 + 0.406500i
\(173\) 0.402580 + 1.23901i 0.0306076 + 0.0942004i 0.965193 0.261538i \(-0.0842295\pi\)
−0.934586 + 0.355738i \(0.884230\pi\)
\(174\) 20.1513 14.6407i 1.52766 1.10991i
\(175\) 8.00000 0.604743
\(176\) 0 0
\(177\) −15.4222 −1.15920
\(178\) −27.4324 + 19.9308i −2.05615 + 1.49388i
\(179\) −1.97599 6.08148i −0.147693 0.454551i 0.849655 0.527339i \(-0.176810\pi\)
−0.997347 + 0.0727880i \(0.976810\pi\)
\(180\) 8.47393 26.0801i 0.631609 1.94389i
\(181\) 20.3962 + 14.8187i 1.51604 + 1.10147i 0.963408 + 0.268040i \(0.0863760\pi\)
0.552631 + 0.833426i \(0.313624\pi\)
\(182\) −12.3060 8.94086i −0.912184 0.662741i
\(183\) −3.06184 + 9.42338i −0.226338 + 0.696596i
\(184\) 2.50046 + 7.69564i 0.184337 + 0.567330i
\(185\) 15.2005 11.0438i 1.11757 0.811959i
\(186\) 5.30278 0.388818
\(187\) 0 0
\(188\) −6.30278 −0.459677
\(189\) −1.29892 + 0.943719i −0.0944824 + 0.0686455i
\(190\) −7.69710 23.6892i −0.558406 1.71860i
\(191\) −8.28680 + 25.5042i −0.599612 + 1.84542i −0.0693311 + 0.997594i \(0.522086\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(192\) −23.8772 17.3478i −1.72319 1.25197i
\(193\) −1.71465 1.24577i −0.123424 0.0896724i 0.524361 0.851496i \(-0.324304\pi\)
−0.647784 + 0.761824i \(0.724304\pi\)
\(194\) 2.56570 7.89641i 0.184206 0.566929i
\(195\) 16.9479 + 52.1601i 1.21366 + 3.73526i
\(196\) −2.67200 + 1.94132i −0.190857 + 0.138666i
\(197\) 10.6056 0.755614 0.377807 0.925884i \(-0.376678\pi\)
0.377807 + 0.925884i \(0.376678\pi\)
\(198\) 0 0
\(199\) 19.4222 1.37680 0.688402 0.725330i \(-0.258313\pi\)
0.688402 + 0.725330i \(0.258313\pi\)
\(200\) 19.4164 14.1068i 1.37295 0.997505i
\(201\) −6.05845 18.6460i −0.427330 1.31519i
\(202\) −3.77344 + 11.6134i −0.265498 + 0.817119i
\(203\) 3.80013 + 2.76096i 0.266717 + 0.193781i
\(204\) −16.5961 12.0578i −1.16196 0.844212i
\(205\) −7.79924 + 24.0036i −0.544722 + 1.67648i
\(206\) 10.1778 + 31.3241i 0.709122 + 2.18245i
\(207\) 5.02489 3.65079i 0.349254 0.253748i
\(208\) −2.00000 −0.138675
\(209\) 0 0
\(210\) 19.1194 1.31937
\(211\) 12.5510 9.11883i 0.864046 0.627766i −0.0649368 0.997889i \(-0.520685\pi\)
0.928983 + 0.370123i \(0.120685\pi\)
\(212\) −13.1744 40.5467i −0.904823 2.78476i
\(213\) 3.06184 9.42338i 0.209794 0.645679i
\(214\) −23.0907 16.7764i −1.57845 1.14681i
\(215\) 4.95072 + 3.59691i 0.337636 + 0.245307i
\(216\) −1.48843 + 4.58091i −0.101275 + 0.311691i
\(217\) 0.309017 + 0.951057i 0.0209774 + 0.0645619i
\(218\) 14.9039 10.8283i 1.00942 0.733385i
\(219\) −11.5139 −0.778036
\(220\) 0 0
\(221\) 17.8167 1.19848
\(222\) 22.3558 16.2425i 1.50042 1.09012i
\(223\) 4.29791 + 13.2276i 0.287809 + 0.885786i 0.985543 + 0.169428i \(0.0541921\pi\)
−0.697733 + 0.716358i \(0.745808\pi\)
\(224\) 1.63865 5.04324i 0.109487 0.336966i
\(225\) −14.9039 10.8283i −0.993592 0.721887i
\(226\) −19.9288 14.4791i −1.32564 0.963135i
\(227\) −2.01290 + 6.19507i −0.133601 + 0.411181i −0.995370 0.0961200i \(-0.969357\pi\)
0.861769 + 0.507301i \(0.169357\pi\)
\(228\) −7.05073 21.6999i −0.466946 1.43711i
\(229\) 2.10794 1.53150i 0.139296 0.101205i −0.515955 0.856616i \(-0.672563\pi\)
0.655251 + 0.755411i \(0.272563\pi\)
\(230\) 22.3944 1.47665
\(231\) 0 0
\(232\) 14.0917 0.925164
\(233\) 14.5623 10.5801i 0.954008 0.693128i 0.00225687 0.999997i \(-0.499282\pi\)
0.951752 + 0.306870i \(0.0992816\pi\)
\(234\) 10.8242 + 33.3134i 0.707598 + 2.17776i
\(235\) −2.12621 + 6.54381i −0.138699 + 0.426871i
\(236\) −17.8950 13.0015i −1.16486 0.846324i
\(237\) 15.4679 + 11.2381i 1.00475 + 0.729994i
\(238\) 1.91934 5.90711i 0.124412 0.382901i
\(239\) −8.13658 25.0418i −0.526312 1.61982i −0.761707 0.647921i \(-0.775639\pi\)
0.235396 0.971900i \(-0.424361\pi\)
\(240\) 2.03377 1.47762i 0.131279 0.0953800i
\(241\) −0.486122 −0.0313139 −0.0156569 0.999877i \(-0.504984\pi\)
−0.0156569 + 0.999877i \(0.504984\pi\)
\(242\) 0 0
\(243\) 19.6056 1.25770
\(244\) −11.4970 + 8.35308i −0.736022 + 0.534751i
\(245\) 1.11418 + 3.42908i 0.0711821 + 0.219076i
\(246\) −11.4705 + 35.3027i −0.731335 + 2.25082i
\(247\) 16.0320 + 11.6479i 1.02009 + 0.741140i
\(248\) 2.42705 + 1.76336i 0.154118 + 0.111973i
\(249\) 2.13479 6.57021i 0.135287 0.416370i
\(250\) −7.69710 23.6892i −0.486807 1.49824i
\(251\) −3.55518 + 2.58299i −0.224401 + 0.163037i −0.694306 0.719680i \(-0.744288\pi\)
0.469904 + 0.882717i \(0.344288\pi\)
\(252\) 7.60555 0.479105
\(253\) 0 0
\(254\) 4.60555 0.288978
\(255\) −18.1175 + 13.1631i −1.13456 + 0.824307i
\(256\) −5.53398 17.0318i −0.345874 1.06449i
\(257\) 2.00432 6.16867i 0.125026 0.384791i −0.868880 0.495023i \(-0.835160\pi\)
0.993906 + 0.110232i \(0.0351595\pi\)
\(258\) 7.28115 + 5.29007i 0.453305 + 0.329345i
\(259\) 4.21587 + 3.06301i 0.261961 + 0.190326i
\(260\) −24.3076 + 74.8111i −1.50749 + 4.63959i
\(261\) −3.34253 10.2872i −0.206897 0.636765i
\(262\) 11.1779 8.12123i 0.690573 0.501731i
\(263\) −20.2389 −1.24798 −0.623991 0.781432i \(-0.714490\pi\)
−0.623991 + 0.781432i \(0.714490\pi\)
\(264\) 0 0
\(265\) −46.5416 −2.85903
\(266\) 5.58895 4.06061i 0.342681 0.248972i
\(267\) 10.4782 + 32.2487i 0.641258 + 1.97359i
\(268\) 8.68938 26.7432i 0.530788 1.63360i
\(269\) −13.0409 9.47476i −0.795117 0.577686i 0.114360 0.993439i \(-0.463518\pi\)
−0.909478 + 0.415753i \(0.863518\pi\)
\(270\) 10.7846 + 7.83549i 0.656331 + 0.476853i
\(271\) 8.81127 27.1183i 0.535247 1.64732i −0.207869 0.978157i \(-0.566653\pi\)
0.743115 0.669163i \(-0.233347\pi\)
\(272\) −0.252360 0.776684i −0.0153016 0.0470934i
\(273\) −12.3060 + 8.94086i −0.744795 + 0.541126i
\(274\) 23.3028 1.40777
\(275\) 0 0
\(276\) 20.5139 1.23479
\(277\) 24.2188 17.5960i 1.45517 1.05724i 0.470577 0.882359i \(-0.344046\pi\)
0.984589 0.174882i \(-0.0559543\pi\)
\(278\) 15.3744 + 47.3177i 0.922098 + 2.83792i
\(279\) 0.711597 2.19007i 0.0426022 0.131116i
\(280\) 8.75086 + 6.35787i 0.522964 + 0.379955i
\(281\) 5.17322 + 3.75856i 0.308608 + 0.224217i 0.731299 0.682057i \(-0.238914\pi\)
−0.422691 + 0.906274i \(0.638914\pi\)
\(282\) −3.12708 + 9.62415i −0.186215 + 0.573110i
\(283\) −1.35796 4.17937i −0.0807223 0.248438i 0.902548 0.430589i \(-0.141694\pi\)
−0.983271 + 0.182151i \(0.941694\pi\)
\(284\) 11.4970 8.35308i 0.682223 0.495664i
\(285\) −24.9083 −1.47544
\(286\) 0 0
\(287\) −7.00000 −0.413197
\(288\) −9.87899 + 7.17751i −0.582125 + 0.422939i
\(289\) −3.00518 9.24901i −0.176776 0.544059i
\(290\) 12.0517 37.0912i 0.707698 2.17807i
\(291\) −6.71709 4.88025i −0.393763 0.286085i
\(292\) −13.3600 9.70661i −0.781835 0.568037i
\(293\) −1.48843 + 4.58091i −0.0869549 + 0.267620i −0.985074 0.172133i \(-0.944934\pi\)
0.898119 + 0.439753i \(0.144934\pi\)
\(294\) 1.63865 + 5.04324i 0.0955679 + 0.294128i
\(295\) −19.5355 + 14.1934i −1.13740 + 0.826369i
\(296\) 15.6333 0.908668
\(297\) 0 0
\(298\) −11.3028 −0.654752
\(299\) −14.4140 + 10.4724i −0.833582 + 0.605633i
\(300\) −18.8020 57.8665i −1.08553 3.34092i
\(301\) −0.524471 + 1.61416i −0.0302300 + 0.0930384i
\(302\) 0.393281 + 0.285735i 0.0226308 + 0.0164422i
\(303\) 9.87899 + 7.17751i 0.567533 + 0.412337i
\(304\) 0.280688 0.863870i 0.0160986 0.0495464i
\(305\) 4.79405 + 14.7546i 0.274507 + 0.844845i
\(306\) −11.5712 + 8.40696i −0.661481 + 0.480594i
\(307\) 16.6333 0.949313 0.474657 0.880171i \(-0.342572\pi\)
0.474657 + 0.880171i \(0.342572\pi\)
\(308\) 0 0
\(309\) 32.9361 1.87367
\(310\) 6.71709 4.88025i 0.381505 0.277180i
\(311\) 1.97599 + 6.08148i 0.112048 + 0.344849i 0.991320 0.131471i \(-0.0419702\pi\)
−0.879272 + 0.476321i \(0.841970\pi\)
\(312\) −14.1015 + 43.3999i −0.798338 + 2.45703i
\(313\) −12.3802 8.99475i −0.699771 0.508413i 0.180087 0.983651i \(-0.442362\pi\)
−0.879857 + 0.475238i \(0.842362\pi\)
\(314\) 13.4342 + 9.76050i 0.758134 + 0.550817i
\(315\) 2.56570 7.89641i 0.144561 0.444912i
\(316\) 8.47393 + 26.0801i 0.476696 + 1.46712i
\(317\) −13.9982 + 10.1703i −0.786219 + 0.571222i −0.906839 0.421477i \(-0.861512\pi\)
0.120620 + 0.992699i \(0.461512\pi\)
\(318\) −68.4500 −3.83848
\(319\) 0 0
\(320\) −46.2111 −2.58328
\(321\) −23.0907 + 16.7764i −1.28880 + 0.936365i
\(322\) 1.91934 + 5.90711i 0.106960 + 0.329190i
\(323\) −2.50046 + 7.69564i −0.139130 + 0.428197i
\(324\) 28.3381 + 20.5888i 1.57434 + 1.14382i
\(325\) 42.7520 + 31.0612i 2.37146 + 1.72296i
\(326\) −2.00432 + 6.16867i −0.111009 + 0.341651i
\(327\) −5.69277 17.5206i −0.314811 0.968889i
\(328\) −16.9894 + 12.3435i −0.938080 + 0.681555i
\(329\) −1.90833 −0.105209
\(330\) 0 0
\(331\) 23.8167 1.30908 0.654541 0.756027i \(-0.272862\pi\)
0.654541 + 0.756027i \(0.272862\pi\)
\(332\) 8.01600 5.82397i 0.439935 0.319632i
\(333\) −3.70820 11.4127i −0.203208 0.625411i
\(334\) −3.70820 + 11.4127i −0.202904 + 0.624474i
\(335\) −24.8346 18.0434i −1.35686 0.985815i
\(336\) 0.564066 + 0.409818i 0.0307723 + 0.0223574i
\(337\) −3.64297 + 11.2119i −0.198445 + 0.610752i 0.801474 + 0.598030i \(0.204050\pi\)
−0.999919 + 0.0127217i \(0.995950\pi\)
\(338\) −21.7986 67.0891i −1.18569 3.64916i
\(339\) −19.9288 + 14.4791i −1.08238 + 0.786396i
\(340\) −32.1194 −1.74192
\(341\) 0 0
\(342\) −15.9083 −0.860224
\(343\) −0.809017 + 0.587785i −0.0436828 + 0.0317374i
\(344\) 1.57341 + 4.84247i 0.0848328 + 0.261088i
\(345\) 6.92027 21.2984i 0.372575 1.14667i
\(346\) 2.42705 + 1.76336i 0.130479 + 0.0947986i
\(347\) 7.77105 + 5.64600i 0.417172 + 0.303093i 0.776499 0.630119i \(-0.216994\pi\)
−0.359327 + 0.933212i \(0.616994\pi\)
\(348\) 11.0396 33.9765i 0.591786 1.82133i
\(349\) 1.45152 + 4.46733i 0.0776982 + 0.239130i 0.982360 0.187000i \(-0.0598764\pi\)
−0.904662 + 0.426130i \(0.859876\pi\)
\(350\) 14.9039 10.8283i 0.796646 0.578797i
\(351\) −10.6056 −0.566082
\(352\) 0 0
\(353\) 5.09167 0.271002 0.135501 0.990777i \(-0.456736\pi\)
0.135501 + 0.990777i \(0.456736\pi\)
\(354\) −28.7313 + 20.8745i −1.52705 + 1.10947i
\(355\) −4.79405 14.7546i −0.254442 0.783092i
\(356\) −15.0285 + 46.2530i −0.796510 + 2.45141i
\(357\) −5.02489 3.65079i −0.265945 0.193221i
\(358\) −11.9128 8.65513i −0.629609 0.457438i
\(359\) 10.4868 32.2751i 0.553474 1.70342i −0.146467 0.989216i \(-0.546790\pi\)
0.699941 0.714201i \(-0.253210\pi\)
\(360\) −7.69710 23.6892i −0.405673 1.24853i
\(361\) 8.09017 5.87785i 0.425798 0.309361i
\(362\) 58.0555 3.05133
\(363\) 0 0
\(364\) −21.8167 −1.14350
\(365\) −14.5848 + 10.5964i −0.763401 + 0.554644i
\(366\) 7.05073 + 21.6999i 0.368548 + 1.13427i
\(367\) −5.44899 + 16.7703i −0.284435 + 0.875401i 0.702132 + 0.712046i \(0.252231\pi\)
−0.986567 + 0.163355i \(0.947769\pi\)
\(368\) 0.660687 + 0.480017i 0.0344407 + 0.0250226i
\(369\) 13.0409 + 9.47476i 0.678882 + 0.493236i
\(370\) 13.3701 41.1490i 0.695079 2.13923i
\(371\) −3.98889 12.2765i −0.207093 0.637367i
\(372\) 6.15302 4.47043i 0.319019 0.231781i
\(373\) 20.1194 1.04174 0.520872 0.853635i \(-0.325607\pi\)
0.520872 + 0.853635i \(0.325607\pi\)
\(374\) 0 0
\(375\) −24.9083 −1.28626
\(376\) −4.63161 + 3.36506i −0.238857 + 0.173540i
\(377\) 9.58810 + 29.5091i 0.493812 + 1.51980i
\(378\) −1.14251 + 3.51627i −0.0587641 + 0.180857i
\(379\) 12.7959 + 9.29680i 0.657283 + 0.477544i 0.865744 0.500486i \(-0.166845\pi\)
−0.208461 + 0.978031i \(0.566845\pi\)
\(380\) −28.9021 20.9986i −1.48265 1.07721i
\(381\) 1.42319 4.38014i 0.0729124 0.224401i
\(382\) 19.0826 + 58.7303i 0.976353 + 3.00491i
\(383\) −31.2550 + 22.7081i −1.59706 + 1.16033i −0.704185 + 0.710016i \(0.748687\pi\)
−0.892871 + 0.450313i \(0.851313\pi\)
\(384\) −43.5416 −2.22197
\(385\) 0 0
\(386\) −4.88057 −0.248414
\(387\) 3.16190 2.29726i 0.160729 0.116776i
\(388\) −3.67988 11.3255i −0.186817 0.574965i
\(389\) −2.41548 + 7.43408i −0.122470 + 0.376923i −0.993432 0.114428i \(-0.963497\pi\)
0.870962 + 0.491350i \(0.163497\pi\)
\(390\) 102.174 + 74.2340i 5.17380 + 3.75898i
\(391\) −5.88561 4.27615i −0.297648 0.216254i
\(392\) −0.927051 + 2.85317i −0.0468231 + 0.144107i
\(393\) −4.26958 13.1404i −0.215372 0.662846i
\(394\) 19.7580 14.3550i 0.995393 0.723195i
\(395\) 29.9361 1.50625
\(396\) 0 0
\(397\) 30.2111 1.51625 0.758126 0.652108i \(-0.226115\pi\)
0.758126 + 0.652108i \(0.226115\pi\)
\(398\) 36.1833 26.2887i 1.81370 1.31773i
\(399\) −2.13479 6.57021i −0.106873 0.328922i
\(400\) 0.748503 2.30365i 0.0374251 0.115183i
\(401\) 17.1601 + 12.4676i 0.856937 + 0.622601i 0.927050 0.374938i \(-0.122336\pi\)
−0.0701132 + 0.997539i \(0.522336\pi\)
\(402\) −36.5248 26.5369i −1.82169 1.32354i
\(403\) −2.04123 + 6.28225i −0.101681 + 0.312941i
\(404\) 5.41209 + 16.6567i 0.269261 + 0.828701i
\(405\) 30.9359 22.4762i 1.53722 1.11685i
\(406\) 10.8167 0.536822
\(407\) 0 0
\(408\) −18.6333 −0.922486
\(409\) 16.6702 12.1116i 0.824290 0.598882i −0.0936478 0.995605i \(-0.529853\pi\)
0.917938 + 0.396723i \(0.129853\pi\)
\(410\) 17.9599 + 55.2749i 0.886976 + 2.72983i
\(411\) 7.20095 22.1623i 0.355197 1.09318i
\(412\) 38.2170 + 27.7663i 1.88282 + 1.36795i
\(413\) −5.41817 3.93653i −0.266611 0.193704i
\(414\) 4.41980 13.6027i 0.217221 0.668539i
\(415\) −3.34253 10.2872i −0.164078 0.504981i
\(416\) 28.3381 20.5888i 1.38939 1.00945i
\(417\) 49.7527 2.43640
\(418\) 0 0
\(419\) −38.4222 −1.87705 −0.938524 0.345215i \(-0.887806\pi\)
−0.938524 + 0.345215i \(0.887806\pi\)
\(420\) 22.1850 16.1184i 1.08252 0.786496i
\(421\) −6.74172 20.7489i −0.328571 1.01124i −0.969803 0.243891i \(-0.921576\pi\)
0.641232 0.767347i \(-0.278424\pi\)
\(422\) 11.0396 33.9765i 0.537401 1.65395i
\(423\) 3.55518 + 2.58299i 0.172859 + 0.125589i
\(424\) −31.3292 22.7620i −1.52148 1.10542i
\(425\) −6.66791 + 20.5217i −0.323441 + 0.995449i
\(426\) −7.05073 21.6999i −0.341609 1.05136i
\(427\) −3.48102 + 2.52911i −0.168458 + 0.122392i
\(428\) −40.9361 −1.97872
\(429\) 0 0
\(430\) 14.0917 0.679561
\(431\) −2.52367 + 1.83355i −0.121561 + 0.0883192i −0.646905 0.762571i \(-0.723937\pi\)
0.525344 + 0.850890i \(0.323937\pi\)
\(432\) 0.150220 + 0.462329i 0.00722746 + 0.0222438i
\(433\) 9.00698 27.7206i 0.432848 1.33217i −0.462429 0.886657i \(-0.653022\pi\)
0.895276 0.445511i \(-0.146978\pi\)
\(434\) 1.86298 + 1.35354i 0.0894261 + 0.0649719i
\(435\) −31.5517 22.9236i −1.51279 1.09910i
\(436\) 8.16491 25.1290i 0.391028 1.20346i
\(437\) −2.50046 7.69564i −0.119613 0.368132i
\(438\) −21.4502 + 15.5845i −1.02493 + 0.744655i
\(439\) −27.7250 −1.32324 −0.661621 0.749839i \(-0.730131\pi\)
−0.661621 + 0.749839i \(0.730131\pi\)
\(440\) 0 0
\(441\) 2.30278 0.109656
\(442\) 33.1922 24.1155i 1.57879 1.14706i
\(443\) 8.32371 + 25.6177i 0.395471 + 1.21714i 0.928594 + 0.371097i \(0.121018\pi\)
−0.533123 + 0.846038i \(0.678982\pi\)
\(444\) 12.2474 37.6935i 0.581234 1.78886i
\(445\) 42.9521 + 31.2065i 2.03612 + 1.47933i
\(446\) 25.9110 + 18.8254i 1.22692 + 0.891411i
\(447\) −3.49275 + 10.7496i −0.165201 + 0.508438i
\(448\) −3.96056 12.1894i −0.187119 0.575893i
\(449\) −32.6281 + 23.7057i −1.53981 + 1.11874i −0.589363 + 0.807868i \(0.700621\pi\)
−0.950452 + 0.310872i \(0.899379\pi\)
\(450\) −42.4222 −1.99980
\(451\) 0 0
\(452\) −35.3305 −1.66181
\(453\) 0.393281 0.285735i 0.0184779 0.0134250i
\(454\) 4.63525 + 14.2658i 0.217543 + 0.669529i
\(455\) −7.35975 + 22.6510i −0.345030 + 1.06189i
\(456\) −16.7669 12.1818i −0.785180 0.570467i
\(457\) 17.0860 + 12.4137i 0.799248 + 0.580688i 0.910694 0.413083i \(-0.135548\pi\)
−0.111445 + 0.993771i \(0.535548\pi\)
\(458\) 1.85410 5.70634i 0.0866365 0.266640i
\(459\) −1.33821 4.11858i −0.0624622 0.192239i
\(460\) 25.9852 18.8793i 1.21156 0.880253i
\(461\) −8.09167 −0.376867 −0.188433 0.982086i \(-0.560341\pi\)
−0.188433 + 0.982086i \(0.560341\pi\)
\(462\) 0 0
\(463\) −30.8167 −1.43217 −0.716086 0.698012i \(-0.754068\pi\)
−0.716086 + 0.698012i \(0.754068\pi\)
\(464\) 1.15059 0.835951i 0.0534147 0.0388081i
\(465\) −2.56570 7.89641i −0.118981 0.366187i
\(466\) 12.8087 39.4213i 0.593354 1.82615i
\(467\) 10.9554 + 7.95957i 0.506956 + 0.368325i 0.811668 0.584120i \(-0.198560\pi\)
−0.304712 + 0.952445i \(0.598560\pi\)
\(468\) 40.6441 + 29.5297i 1.87877 + 1.36501i
\(469\) 2.63093 8.09718i 0.121485 0.373893i
\(470\) 4.89619 + 15.0689i 0.225844 + 0.695078i
\(471\) 13.4342 9.76050i 0.619014 0.449740i
\(472\) −20.0917 −0.924794
\(473\) 0 0
\(474\) 44.0278 2.02226
\(475\) −19.4164 + 14.1068i −0.890886 + 0.647266i
\(476\) −2.75282 8.47232i −0.126175 0.388328i
\(477\) −9.18552 + 28.2701i −0.420576 + 1.29440i
\(478\) −49.0534 35.6394i −2.24365 1.63011i
\(479\) −23.1648 16.8302i −1.05843 0.768993i −0.0846313 0.996412i \(-0.526971\pi\)
−0.973797 + 0.227419i \(0.926971\pi\)
\(480\) −13.6053 + 41.8729i −0.620995 + 1.91123i
\(481\) 10.6370 + 32.7375i 0.485008 + 1.49270i
\(482\) −0.905637 + 0.657984i −0.0412507 + 0.0299704i
\(483\) 6.21110 0.282615
\(484\) 0 0
\(485\) −13.0000 −0.590300
\(486\) 36.5248 26.5369i 1.65680 1.20374i
\(487\) −0.870394 2.67880i −0.0394413 0.121388i 0.929397 0.369081i \(-0.120328\pi\)
−0.968839 + 0.247693i \(0.920328\pi\)
\(488\) −3.98889 + 12.2765i −0.180569 + 0.555733i
\(489\) 5.24738 + 3.81245i 0.237295 + 0.172405i
\(490\) 6.71709 + 4.88025i 0.303447 + 0.220467i
\(491\) 3.92366 12.0758i 0.177072 0.544972i −0.822650 0.568548i \(-0.807505\pi\)
0.999722 + 0.0235761i \(0.00750521\pi\)
\(492\) 16.4517 + 50.6332i 0.741700 + 2.28272i
\(493\) −10.2498 + 7.44693i −0.461628 + 0.335393i
\(494\) 45.6333 2.05314
\(495\) 0 0
\(496\) 0.302776 0.0135950
\(497\) 3.48102 2.52911i 0.156145 0.113446i
\(498\) −4.91594 15.1297i −0.220289 0.677979i
\(499\) 0.898722 2.76598i 0.0402323 0.123822i −0.928923 0.370273i \(-0.879264\pi\)
0.969155 + 0.246450i \(0.0792642\pi\)
\(500\) −28.9021 20.9986i −1.29254 0.939087i
\(501\) 9.70820 + 7.05342i 0.433731 + 0.315124i
\(502\) −3.12708 + 9.62415i −0.139568 + 0.429547i
\(503\) −1.72363 5.30480i −0.0768530 0.236529i 0.905248 0.424883i \(-0.139685\pi\)
−0.982101 + 0.188354i \(0.939685\pi\)
\(504\) 5.58895 4.06061i 0.248952 0.180874i
\(505\) 19.1194 0.850803
\(506\) 0 0
\(507\) −70.5416 −3.13286
\(508\) 5.34400 3.88265i 0.237102 0.172265i
\(509\) 6.89194 + 21.2112i 0.305480 + 0.940170i 0.979498 + 0.201455i \(0.0645670\pi\)
−0.674018 + 0.738715i \(0.735433\pi\)
\(510\) −15.9358 + 49.0454i −0.705650 + 2.17177i
\(511\) −4.04508 2.93893i −0.178944 0.130010i
\(512\) −2.76862 2.01152i −0.122357 0.0888975i
\(513\) 1.48843 4.58091i 0.0657157 0.202252i
\(514\) −4.61550 14.2051i −0.203581 0.626558i
\(515\) 41.7205 30.3117i 1.83843 1.33569i
\(516\) 12.9083 0.568257
\(517\) 0 0
\(518\) 12.0000 0.527250
\(519\) 2.42705 1.76336i 0.106536 0.0774027i
\(520\) 22.0793 + 67.9530i 0.968239 + 2.97993i
\(521\) 2.29359 7.05894i 0.100484 0.309258i −0.888160 0.459534i \(-0.848016\pi\)
0.988644 + 0.150277i \(0.0480164\pi\)
\(522\) −20.1513 14.6407i −0.881997 0.640808i
\(523\) −36.0349 26.1809i −1.57570 1.14481i −0.921427 0.388551i \(-0.872976\pi\)
−0.654271 0.756260i \(-0.727024\pi\)
\(524\) 6.12368 18.8468i 0.267514 0.823324i
\(525\) −5.69277 17.5206i −0.248453 0.764660i
\(526\) −37.7047 + 27.3941i −1.64400 + 1.19444i
\(527\) −2.69722 −0.117493
\(528\) 0 0
\(529\) −15.7250 −0.683695
\(530\) −86.7063 + 62.9959i −3.76628 + 2.73636i
\(531\) 4.76572 + 14.6674i 0.206815 + 0.636510i
\(532\) 3.06184 9.42338i 0.132748 0.408555i
\(533\) −37.4080 27.1785i −1.62032 1.17723i
\(534\) 63.1707 + 45.8962i 2.73366 + 1.98612i
\(535\) −13.8096 + 42.5016i −0.597041 + 1.83750i
\(536\) −7.89280 24.2915i −0.340917 1.04923i
\(537\) −11.9128 + 8.65513i −0.514074 + 0.373496i
\(538\) −37.1194 −1.60033
\(539\) 0 0
\(540\) 19.1194 0.822769
\(541\) −26.2077 + 19.0410i −1.12676 + 0.818636i −0.985219 0.171297i \(-0.945204\pi\)
−0.141536 + 0.989933i \(0.545204\pi\)
\(542\) −20.2904 62.4474i −0.871547 2.68234i
\(543\) 17.9401 55.2141i 0.769885 2.36946i
\(544\) 11.5712 + 8.40696i 0.496111 + 0.360445i
\(545\) −23.3356 16.9543i −0.999588 0.726243i
\(546\) −10.8242 + 33.3134i −0.463232 + 1.42568i
\(547\) 9.25076 + 28.4709i 0.395534 + 1.21733i 0.928545 + 0.371220i \(0.121060\pi\)
−0.533011 + 0.846108i \(0.678940\pi\)
\(548\) 27.0391 19.6451i 1.15505 0.839196i
\(549\) 9.90833 0.422877
\(550\) 0 0
\(551\) −14.0917 −0.600325
\(552\) 15.0747 10.9524i 0.641620 0.466164i
\(553\) 2.56570 + 7.89641i 0.109105 + 0.335789i
\(554\) 21.3024 65.5621i 0.905053 2.78547i
\(555\) −35.0034 25.4315i −1.48581 1.07951i
\(556\) 57.7301 + 41.9433i 2.44830 + 1.77879i
\(557\) −2.23693 + 6.88456i −0.0947818 + 0.291708i −0.987197 0.159507i \(-0.949009\pi\)
0.892415 + 0.451216i \(0.149009\pi\)
\(558\) −1.63865 5.04324i −0.0693695 0.213497i
\(559\) −9.06997 + 6.58972i −0.383619 + 0.278715i
\(560\) 1.09167 0.0461316
\(561\) 0 0
\(562\) 14.7250 0.621136
\(563\) −0.244951 + 0.177967i −0.0103234 + 0.00750042i −0.592935 0.805250i \(-0.702031\pi\)
0.582612 + 0.812751i \(0.302031\pi\)
\(564\) 4.48504 + 13.8035i 0.188854 + 0.581233i
\(565\) −11.9186 + 36.6817i −0.501419 + 1.54321i
\(566\) −8.18679 5.94805i −0.344116 0.250015i
\(567\) 8.58007 + 6.23379i 0.360329 + 0.261794i
\(568\) 3.98889 12.2765i 0.167370 0.515113i
\(569\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(570\) −46.4038 + 33.7144i −1.94364 + 1.41214i
\(571\) −25.8444 −1.08155 −0.540777 0.841166i \(-0.681870\pi\)
−0.540777 + 0.841166i \(0.681870\pi\)
\(572\) 0 0
\(573\) 61.7527 2.57976
\(574\) −13.0409 + 9.47476i −0.544316 + 0.395469i
\(575\) −6.66791 20.5217i −0.278071 0.855814i
\(576\) −9.12029 + 28.0694i −0.380012 + 1.16956i
\(577\) −1.78882 1.29965i −0.0744695 0.0541053i 0.549928 0.835212i \(-0.314655\pi\)
−0.624397 + 0.781107i \(0.714655\pi\)
\(578\) −18.1175 13.1631i −0.753588 0.547514i
\(579\) −1.50818 + 4.64170i −0.0626778 + 0.192902i
\(580\) −17.2852 53.1984i −0.717729 2.20894i
\(581\) 2.42705 1.76336i 0.100691 0.0731563i
\(582\) −19.1194 −0.792526
\(583\) 0 0
\(584\) −15.0000 −0.620704
\(585\) 44.3701 32.2367i 1.83448 1.33282i
\(586\) 3.42752 + 10.5488i 0.141589 + 0.435767i
\(587\) −4.20435 + 12.9396i −0.173532 + 0.534076i −0.999563 0.0295476i \(-0.990593\pi\)
0.826031 + 0.563624i \(0.190593\pi\)
\(588\) 6.15302 + 4.47043i 0.253746 + 0.184357i
\(589\) −2.42705 1.76336i −0.100005 0.0726578i
\(590\) −17.1831 + 52.8840i −0.707415 + 2.17720i
\(591\) −7.54688 23.2269i −0.310437 0.955427i
\(592\) 1.27646 0.927405i 0.0524623 0.0381161i
\(593\) −22.6056 −0.928299 −0.464149 0.885757i \(-0.653640\pi\)
−0.464149 + 0.885757i \(0.653640\pi\)
\(594\) 0 0
\(595\) −9.72498 −0.398685
\(596\) −13.1151 + 9.52865i −0.537214 + 0.390309i
\(597\) −13.8208 42.5360i −0.565647 1.74088i
\(598\) −12.6783 + 39.0197i −0.518453 + 1.59563i
\(599\) 11.9645 + 8.69270i 0.488855 + 0.355174i 0.804744 0.593622i \(-0.202303\pi\)
−0.315889 + 0.948796i \(0.602303\pi\)
\(600\) −44.7116 32.4849i −1.82534 1.32619i
\(601\) 1.79744 5.53197i 0.0733193 0.225654i −0.907681 0.419662i \(-0.862149\pi\)
0.981000 + 0.194008i \(0.0621488\pi\)
\(602\) 1.20774 + 3.71704i 0.0492238 + 0.151495i
\(603\) −15.8612 + 11.5239i −0.645919 + 0.469288i
\(604\) 0.697224 0.0283697
\(605\) 0 0
\(606\) 28.1194 1.14227
\(607\) −16.6185 + 12.0741i −0.674525 + 0.490071i −0.871537 0.490330i \(-0.836876\pi\)
0.197012 + 0.980401i \(0.436876\pi\)
\(608\) 4.91594 + 15.1297i 0.199368 + 0.613591i
\(609\) 3.34253 10.2872i 0.135446 0.416860i
\(610\) 28.9021 + 20.9986i 1.17021 + 0.850209i
\(611\) −10.1981 7.40936i −0.412571 0.299751i
\(612\) −6.33914 + 19.5099i −0.256244 + 0.788639i
\(613\) 10.2147 + 31.4377i 0.412568 + 1.26976i 0.914408 + 0.404794i \(0.132657\pi\)
−0.501839 + 0.864961i \(0.667343\pi\)
\(614\) 30.9876 22.5138i 1.25056 0.908583i
\(615\) 58.1194 2.34360
\(616\) 0 0
\(617\) 21.6333 0.870924 0.435462 0.900207i \(-0.356585\pi\)
0.435462 + 0.900207i \(0.356585\pi\)
\(618\) 61.3594 44.5802i 2.46824 1.79328i
\(619\) 12.3040 + 37.8679i 0.494540 + 1.52204i 0.817672 + 0.575685i \(0.195264\pi\)
−0.323131 + 0.946354i \(0.604736\pi\)
\(620\) 3.67988 11.3255i 0.147787 0.454843i
\(621\) 3.50347 + 2.54542i 0.140590 + 0.102144i
\(622\) 11.9128 + 8.65513i 0.477658 + 0.347039i
\(623\) −4.55027 + 14.0043i −0.182303 + 0.561070i
\(624\) 1.42319 + 4.38014i 0.0569733 + 0.175346i
\(625\) 0.809017 0.587785i 0.0323607 0.0235114i
\(626\) −35.2389 −1.40843
\(627\) 0 0
\(628\) 23.8167 0.950388
\(629\) −11.3711 + 8.26162i −0.453397 + 0.329412i
\(630\) −5.90823 18.1837i −0.235389 0.724454i
\(631\) −9.59668 + 29.5355i −0.382038 + 1.17579i 0.556569 + 0.830802i \(0.312118\pi\)
−0.938606 + 0.344990i \(0.887882\pi\)
\(632\) 20.1513 + 14.6407i 0.801574 + 0.582378i
\(633\) −28.9021 20.9986i −1.14876 0.834620i
\(634\) −12.3126 + 37.8943i −0.488996 + 1.50497i
\(635\) −2.22835 6.85817i −0.0884295 0.272158i
\(636\) −79.4252 + 57.7058i −3.14941 + 2.28818i
\(637\) −6.60555 −0.261721
\(638\) 0 0
\(639\) −9.90833 −0.391967
\(640\) −55.1547 + 40.0722i −2.18018 + 1.58399i
\(641\) −8.90484 27.4063i −0.351720 1.08248i −0.957887 0.287145i \(-0.907294\pi\)
0.606167 0.795337i \(-0.292706\pi\)
\(642\) −20.3101 + 62.5082i −0.801577 + 2.46700i
\(643\) 1.00226 + 0.728183i 0.0395252 + 0.0287167i 0.607372 0.794417i \(-0.292224\pi\)
−0.567847 + 0.823134i \(0.692224\pi\)
\(644\) 7.20699 + 5.23618i 0.283995 + 0.206335i
\(645\) 4.35457 13.4020i 0.171461 0.527702i
\(646\) 5.75801 + 17.7213i 0.226546 + 0.697236i
\(647\) −8.58007 + 6.23379i −0.337317 + 0.245075i −0.743529 0.668704i \(-0.766850\pi\)
0.406212 + 0.913779i \(0.366850\pi\)
\(648\) 31.8167 1.24988
\(649\) 0 0
\(650\) 121.689 4.77303
\(651\) 1.86298 1.35354i 0.0730161 0.0530493i
\(652\) 2.87472 + 8.84747i 0.112583 + 0.346493i
\(653\) −2.10646 + 6.48302i −0.0824322 + 0.253700i −0.983775 0.179406i \(-0.942582\pi\)
0.901343 + 0.433106i \(0.142582\pi\)
\(654\) −34.3203 24.9351i −1.34203 0.975041i
\(655\) −17.5017 12.7157i −0.683849 0.496845i
\(656\) −0.654940 + 2.01570i −0.0255711 + 0.0786998i
\(657\) 3.55798 + 10.9503i 0.138810 + 0.427214i
\(658\) −3.55518 + 2.58299i −0.138595 + 0.100696i
\(659\) −4.63331 −0.180488 −0.0902440 0.995920i \(-0.528765\pi\)
−0.0902440 + 0.995920i \(0.528765\pi\)
\(660\) 0 0
\(661\) −18.3028 −0.711895 −0.355948 0.934506i \(-0.615842\pi\)
−0.355948 + 0.934506i \(0.615842\pi\)
\(662\) 44.3701 32.2367i 1.72449 1.25292i
\(663\) −12.6783 39.0197i −0.492383 1.51540i
\(664\) 2.78115 8.55951i 0.107930 0.332173i
\(665\) −8.75086 6.35787i −0.339344 0.246548i
\(666\) −22.3558 16.2425i −0.866270 0.629382i
\(667\) 3.91508 12.0494i 0.151593 0.466554i
\(668\) 5.31852 + 16.3687i 0.205780 + 0.633325i
\(669\) 25.9110 18.8254i 1.00178 0.727834i
\(670\) −70.6888 −2.73095
\(671\) 0 0
\(672\) −12.2111 −0.471054
\(673\) −6.81371 + 4.95045i −0.262649 + 0.190826i −0.711314 0.702874i \(-0.751900\pi\)
0.448665 + 0.893700i \(0.351900\pi\)
\(674\) 8.38894 + 25.8185i 0.323130 + 0.994492i
\(675\) 3.96914 12.2158i 0.152772 0.470185i
\(676\) −81.8522 59.4691i −3.14816 2.28727i
\(677\) 8.33512 + 6.05582i 0.320345 + 0.232744i 0.736323 0.676631i \(-0.236561\pi\)
−0.415978 + 0.909375i \(0.636561\pi\)
\(678\) −17.5290 + 53.9487i −0.673197 + 2.07189i
\(679\) −1.11418 3.42908i −0.0427582 0.131596i
\(680\) −23.6030 + 17.1486i −0.905135 + 0.657619i
\(681\) 15.0000 0.574801
\(682\) 0 0
\(683\) 15.6972 0.600638 0.300319 0.953839i \(-0.402907\pi\)
0.300319 + 0.953839i \(0.402907\pi\)
\(684\) −18.4591 + 13.4113i −0.705800 + 0.512794i
\(685\) −11.2748 34.7004i −0.430789 1.32583i
\(686\) −0.711597 + 2.19007i −0.0271689 + 0.0836173i
\(687\) −4.85410 3.52671i −0.185196 0.134552i
\(688\) 0.415736 + 0.302050i 0.0158498 + 0.0115155i
\(689\) 26.3488 81.0934i 1.00381 3.08941i
\(690\) −15.9358 49.0454i −0.606666 1.86713i
\(691\) 13.7757 10.0087i 0.524054 0.380748i −0.294075 0.955782i \(-0.595012\pi\)
0.818129 + 0.575035i \(0.195012\pi\)
\(692\) 4.30278 0.163567
\(693\) 0 0
\(694\) 22.1194 0.839642
\(695\) 63.0224 45.7884i 2.39057 1.73685i
\(696\) −10.0276 30.8617i −0.380095 1.16981i
\(697\) 5.83442 17.9565i 0.220994 0.680151i
\(698\) 8.75086 + 6.35787i 0.331225 + 0.240649i
\(699\) −33.5337 24.3637i −1.26836 0.921519i
\(700\) 8.16491 25.1290i 0.308605 0.949787i
\(701\) 9.61643 + 29.5963i 0.363208 + 1.11784i 0.951096 + 0.308896i \(0.0999595\pi\)
−0.587888 + 0.808942i \(0.700040\pi\)
\(702\) −19.7580 + 14.3550i −0.745717 + 0.541795i
\(703\) −15.6333 −0.589621
\(704\) 0 0
\(705\) 15.8444 0.596735
\(706\) 9.48571 6.89177i 0.356999 0.259375i
\(707\) 1.63865 + 5.04324i 0.0616277 + 0.189671i
\(708\) −15.7401 + 48.4431i −0.591550 + 1.82060i
\(709\) −20.4928 14.8889i −0.769624 0.559165i 0.132223 0.991220i \(-0.457789\pi\)
−0.901847 + 0.432055i \(0.857789\pi\)
\(710\) −28.9021 20.9986i −1.08468 0.788064i
\(711\) 5.90823 18.1837i 0.221576 0.681940i
\(712\) 13.6508 + 42.0129i 0.511586 + 1.57450i
\(713\) 2.18210 1.58539i 0.0817203 0.0593733i
\(714\) −14.3028 −0.535268
\(715\) 0 0
\(716\) −21.1194 −0.789270
\(717\) −49.0534 + 35.6394i −1.83193 + 1.33098i
\(718\) −24.1488 74.3224i −0.901226 2.77369i
\(719\) 6.56317 20.1994i 0.244765 0.753309i −0.750910 0.660404i \(-0.770385\pi\)
0.995675 0.0929045i \(-0.0296151\pi\)
\(720\) −2.03377 1.47762i −0.0757941 0.0550677i
\(721\) 11.5712 + 8.40696i 0.430934 + 0.313092i
\(722\) 7.11597 21.9007i 0.264829 0.815060i
\(723\) 0.345923 + 1.06464i 0.0128650 + 0.0395944i
\(724\) 67.3641 48.9429i 2.50357 1.81895i
\(725\) −37.5778 −1.39560
\(726\) 0 0
\(727\) 24.1194 0.894540 0.447270 0.894399i \(-0.352396\pi\)
0.447270 + 0.894399i \(0.352396\pi\)
\(728\) −16.0320 + 11.6479i −0.594186 + 0.431701i
\(729\) −4.11936 12.6781i −0.152569 0.469559i
\(730\) −12.8285 + 39.4820i −0.474804 + 1.46130i
\(731\) −3.70351 2.69076i −0.136979 0.0995214i
\(732\) 26.4751 + 19.2353i 0.978547 + 0.710956i
\(733\) 2.09788 6.45663i 0.0774871 0.238481i −0.904808 0.425819i \(-0.859986\pi\)
0.982295 + 0.187338i \(0.0599860\pi\)
\(734\) 12.5478 + 38.6182i 0.463148 + 1.42542i
\(735\) 6.71709 4.88025i 0.247763 0.180011i
\(736\) −14.3028 −0.527207
\(737\) 0 0
\(738\) 37.1194 1.36639
\(739\) −34.8844 + 25.3450i −1.28324 + 0.932330i −0.999646 0.0266143i \(-0.991527\pi\)
−0.283596 + 0.958944i \(0.591527\pi\)
\(740\) −19.1762 59.0183i −0.704931 2.16956i
\(741\) 14.1015 43.3999i 0.518030 1.59433i
\(742\) −24.0480 17.4719i −0.882830 0.641414i
\(743\) 36.3541 + 26.4128i 1.33370 + 0.968990i 0.999651 + 0.0264352i \(0.00841558\pi\)
0.334050 + 0.942555i \(0.391584\pi\)
\(744\) 2.13479 6.57021i 0.0782652 0.240876i
\(745\) 5.46874 + 16.8311i 0.200359 + 0.616642i
\(746\) 37.4822 27.2324i 1.37232 0.997049i
\(747\) −6.90833 −0.252762
\(748\) 0 0
\(749\) −12.3944 −0.452883
\(750\) −46.4038 + 33.7144i −1.69443 + 1.23107i
\(751\) 2.35882 + 7.25971i 0.0860746 + 0.264910i 0.984825 0.173550i \(-0.0555239\pi\)
−0.898750 + 0.438461i \(0.855524\pi\)
\(752\) −0.178548 + 0.549516i −0.00651099 + 0.0200388i
\(753\) 8.18679 + 5.94805i 0.298343 + 0.216759i
\(754\) 57.8042 + 41.9972i 2.10511 + 1.52945i
\(755\) 0.235206 0.723888i 0.00856001 0.0263450i
\(756\) 1.63865 + 5.04324i 0.0595970 + 0.183421i
\(757\) 19.2681 13.9991i 0.700310 0.508805i −0.179723 0.983717i \(-0.557520\pi\)
0.880033 + 0.474912i \(0.157520\pi\)
\(758\) 36.4222 1.32291
\(759\) 0 0
\(760\) −32.4500 −1.17708
\(761\) 33.9787 24.6870i 1.23173 0.894902i 0.234709 0.972066i \(-0.424586\pi\)
0.997018 + 0.0771633i \(0.0245863\pi\)
\(762\) −3.27730 10.0865i −0.118724 0.365395i
\(763\) 2.47214 7.60845i 0.0894973 0.275444i
\(764\) 71.6541 + 52.0598i 2.59236 + 1.88346i
\(765\) 18.1175 + 13.1631i 0.655039 + 0.475914i
\(766\) −27.4913 + 84.6096i −0.993302 + 3.05707i
\(767\) −13.6706 42.0737i −0.493615 1.51919i
\(768\) −33.3629 + 24.2396i −1.20388 + 0.874671i
\(769\) 39.3305 1.41830 0.709148 0.705060i \(-0.249080\pi\)
0.709148 + 0.705060i \(0.249080\pi\)
\(770\) 0 0
\(771\) −14.9361 −0.537910
\(772\) −5.66312 + 4.11450i −0.203820 + 0.148084i
\(773\) 9.46621 + 29.1340i 0.340476 + 1.04788i 0.963961 + 0.266042i \(0.0857161\pi\)
−0.623485 + 0.781835i \(0.714284\pi\)
\(774\) 2.78115 8.55951i 0.0999665 0.307665i
\(775\) −6.47214 4.70228i −0.232486 0.168911i
\(776\) −8.75086 6.35787i −0.314137 0.228234i
\(777\) 3.70820 11.4127i 0.133031 0.409428i
\(778\) 5.56231 + 17.1190i 0.199418 + 0.613747i
\(779\) 16.9894 12.3435i 0.608707 0.442251i
\(780\) 181.139 6.48581
\(781\) 0 0
\(782\) −16.7527 −0.599077
\(783\) 6.10131 4.43286i 0.218043 0.158418i
\(784\) 0.0935628 + 0.287957i 0.00334153 + 0.0102842i
\(785\) 8.03444 24.7275i 0.286762 0.882561i
\(786\) −25.7402 18.7014i −0.918123 0.667055i
\(787\) −18.1917 13.2170i −0.648462 0.471136i 0.214285 0.976771i \(-0.431258\pi\)
−0.862747 + 0.505636i \(0.831258\pi\)
\(788\) 10.8242 33.3134i 0.385595 1.18674i
\(789\) 14.4019 + 44.3245i 0.512721 + 1.57799i
\(790\) 55.7705 40.5196i 1.98422 1.44162i
\(791\) −10.6972 −0.380350
\(792\) 0 0
\(793\) −28.4222 −1.00930
\(794\) 56.2828 40.8919i 1.99740 1.45120i
\(795\) 33.1189 + 101.929i 1.17461 + 3.61506i
\(796\) 19.8226 61.0076i 0.702592 2.16236i
\(797\) 23.1648 + 16.8302i 0.820540 + 0.596158i 0.916867 0.399192i \(-0.130709\pi\)
−0.0963268 + 0.995350i \(0.530709\pi\)
\(798\) −12.8701 9.35068i −0.455597 0.331010i
\(799\) 1.59057 4.89526i 0.0562702 0.173182i
\(800\) 13.1092 + 40.3459i 0.463480 + 1.42644i
\(801\) 27.4324 19.9308i 0.969277 0.704221i
\(802\) 48.8444 1.72476
\(803\) 0 0
\(804\) −64.7527 −2.28365
\(805\) 7.86767 5.71620i 0.277299 0.201470i
\(806\) 4.70049 + 14.4666i 0.165568 + 0.509565i
\(807\) −11.4705 + 35.3027i −0.403782 + 1.24271i
\(808\) 12.8701 + 9.35068i 0.452769 + 0.328956i
\(809\) 6.54630 + 4.75617i 0.230156 + 0.167218i 0.696886 0.717182i \(-0.254568\pi\)
−0.466731 + 0.884400i \(0.654568\pi\)
\(810\) 27.2106 83.7458i 0.956085 2.94253i
\(811\) 12.6216 + 38.8453i 0.443205 + 1.36404i 0.884440 + 0.466653i \(0.154540\pi\)
−0.441236 + 0.897391i \(0.645460\pi\)
\(812\) 12.5510 9.11883i 0.440453 0.320008i
\(813\) −65.6611 −2.30283
\(814\) 0 0
\(815\) 10.1556 0.355735
\(816\) −1.52141 + 1.10537i −0.0532601 + 0.0386957i
\(817\) −1.57341 4.84247i −0.0550468 0.169417i
\(818\) 14.6628 45.1276i 0.512674 1.57785i
\(819\) 12.3060 + 8.94086i 0.430008 + 0.312419i
\(820\) 67.4383 + 48.9968i 2.35505 + 1.71104i
\(821\) 8.47393 26.0801i 0.295742 0.910201i −0.687229 0.726441i \(-0.741173\pi\)
0.982971 0.183760i \(-0.0588269\pi\)
\(822\) −16.5822 51.0347i −0.578370 1.78004i
\(823\) −28.4864 + 20.6966i −0.992973 + 0.721437i −0.960570 0.278038i \(-0.910316\pi\)
−0.0324027 + 0.999475i \(0.510316\pi\)
\(824\) 42.9083 1.49478
\(825\) 0 0
\(826\) −15.4222 −0.536607
\(827\) −11.4746 + 8.33676i −0.399010 + 0.289898i −0.769138 0.639083i \(-0.779314\pi\)
0.370128 + 0.928981i \(0.379314\pi\)
\(828\) −6.33914 19.5099i −0.220300 0.678014i
\(829\) 4.10221 12.6253i 0.142476 0.438495i −0.854202 0.519941i \(-0.825954\pi\)
0.996678 + 0.0814464i \(0.0259539\pi\)
\(830\) −20.1513 14.6407i −0.699460 0.508188i
\(831\) −55.7705 40.5196i −1.93466 1.40561i
\(832\) 26.1617 80.5175i 0.906994 2.79144i
\(833\) −0.833488 2.56521i −0.0288787 0.0888794i
\(834\) 92.6886 67.3422i 3.20954 2.33187i
\(835\) 18.7889 0.650217
\(836\) 0 0
\(837\) 1.60555 0.0554960
\(838\) −71.5800 + 52.0059i −2.47269 + 1.79651i
\(839\) 13.0439 + 40.1451i 0.450327 + 1.38596i 0.876535 + 0.481339i \(0.159849\pi\)
−0.426208 + 0.904625i \(0.640151\pi\)
\(840\) 7.69710 23.6892i 0.265575 0.817356i
\(841\) 5.61141 + 4.07693i 0.193497 + 0.140584i
\(842\) −40.6441 29.5297i −1.40069 1.01766i
\(843\) 4.55027 14.0043i 0.156720 0.482333i
\(844\) −15.8337 48.7311i −0.545018 1.67739i
\(845\) −89.3559 + 64.9209i −3.07394 + 2.23335i
\(846\) 10.1194 0.347913
\(847\) 0 0
\(848\) −3.90833 −0.134212
\(849\) −8.18679 + 5.94805i −0.280970 + 0.204137i
\(850\) 15.3547 + 47.2569i 0.526662 + 1.62090i
\(851\) 4.34339 13.3676i 0.148890 0.458235i
\(852\) −26.4751 19.2353i −0.907021 0.658989i
\(853\) −36.9923 26.8765i −1.26659 0.920233i −0.267530 0.963549i \(-0.586208\pi\)
−0.999061 + 0.0433166i \(0.986208\pi\)
\(854\) −3.06184 + 9.42338i −0.104774 + 0.322461i
\(855\) 7.69710 + 23.6892i 0.263235 + 0.810154i
\(856\) −30.0820 + 21.8558i −1.02818 + 0.747017i
\(857\) −35.3583 −1.20782 −0.603908 0.797054i \(-0.706391\pi\)
−0.603908 + 0.797054i \(0.706391\pi\)
\(858\) 0 0
\(859\) −25.3028 −0.863320 −0.431660 0.902036i \(-0.642072\pi\)
−0.431660 + 0.902036i \(0.642072\pi\)
\(860\) 16.3511 11.8798i 0.557569 0.405097i
\(861\) 4.98118 + 15.3305i 0.169758 + 0.522462i
\(862\) −2.21978 + 6.83177i −0.0756059 + 0.232691i
\(863\) −25.4211 18.4695i −0.865344 0.628709i 0.0639894 0.997951i \(-0.479618\pi\)
−0.929334 + 0.369241i \(0.879618\pi\)
\(864\) −6.88787 5.00433i −0.234330 0.170251i
\(865\) 1.45152 4.46733i 0.0493532 0.151894i
\(866\) −20.7410 63.8344i −0.704809 2.16918i
\(867\) −18.1175 + 13.1631i −0.615302 + 0.447043i
\(868\) 3.30278 0.112104
\(869\) 0 0
\(870\) −89.8082 −3.04478
\(871\) 45.4982 33.0564i 1.54165 1.12007i
\(872\) −7.41641 22.8254i −0.251151 0.772964i
\(873\) −2.56570 + 7.89641i −0.0868357 + 0.267253i
\(874\) −15.0747 10.9524i −0.509908 0.370470i
\(875\) −8.75086 6.35787i −0.295833 0.214935i
\(876\) −11.7512 + 36.1665i −0.397037 + 1.22195i
\(877\) −14.5410 44.7525i −0.491013 1.51118i −0.823079 0.567927i \(-0.807746\pi\)
0.332066 0.943256i \(-0.392254\pi\)
\(878\) −51.6512 + 37.5268i −1.74314 + 1.26647i
\(879\) 11.0917 0.374113
\(880\) 0 0
\(881\) 34.3305 1.15663 0.578313 0.815815i \(-0.303711\pi\)
0.578313 + 0.815815i \(0.303711\pi\)
\(882\) 4.29004 3.11689i 0.144453 0.104951i
\(883\) −2.38715 7.34689i −0.0803340 0.247243i 0.902821 0.430017i \(-0.141492\pi\)
−0.983155 + 0.182774i \(0.941492\pi\)
\(884\) 18.1839 55.9644i 0.611592 1.88229i
\(885\) 44.9858 + 32.6841i 1.51218 + 1.09866i
\(886\) 50.1815 + 36.4590i 1.68588 + 1.22486i
\(887\) −13.6337 + 41.9601i −0.457773 + 1.40888i 0.410075 + 0.912052i \(0.365503\pi\)
−0.867848 + 0.496829i \(0.834497\pi\)
\(888\) −11.1246 34.2380i −0.373318 1.14895i
\(889\) 1.61803 1.17557i 0.0542671 0.0394274i
\(890\) 122.258 4.09810
\(891\) 0 0
\(892\) 45.9361 1.53805
\(893\) 4.63161 3.36506i 0.154991 0.112607i
\(894\) 8.04302 + 24.7539i 0.268999 + 0.827893i
\(895\) −7.12455 + 21.9271i −0.238147 + 0.732942i
\(896\) −15.2972 11.1140i −0.511042 0.371294i
\(897\) 33.1922 + 24.1155i 1.10825 + 0.805193i
\(898\) −28.6991 + 88.3267i −0.957701 + 2.94750i
\(899\) −1.45152 4.46733i −0.0484110 0.148994i
\(900\) −49.2242 + 35.7634i −1.64081 + 1.19211i
\(901\) 34.8167 1.15991
\(902\) 0 0
\(903\) 3.90833 0.130061
\(904\) −25.9627 + 18.8630i −0.863507 + 0.627374i
\(905\) −28.0896 86.4510i −0.933731 2.87373i
\(906\) 0.345923 1.06464i 0.0114925 0.0353703i
\(907\) −0.319116 0.231851i −0.0105961 0.00769849i 0.582475 0.812849i \(-0.302085\pi\)
−0.593071 + 0.805150i \(0.702085\pi\)
\(908\) 17.4051 + 12.6455i 0.577608 + 0.419657i
\(909\) 3.77344 11.6134i 0.125157 0.385194i
\(910\) 16.9479 + 52.1601i 0.561816 + 1.72909i
\(911\) 40.8149 29.6537i 1.35226 0.982472i 0.353362 0.935487i \(-0.385039\pi\)
0.998896 0.0469855i \(-0.0149615\pi\)
\(912\) −2.09167 −0.0692622
\(913\) 0 0
\(914\) 48.6333 1.60865
\(915\) 28.9021 20.9986i 0.955474 0.694193i
\(916\) −2.65926 8.18437i −0.0878645 0.270419i
\(917\) 1.85410 5.70634i 0.0612278 0.188440i
\(918\) −8.06771 5.86154i −0.266274 0.193460i
\(919\) 44.8824 + 32.6090i 1.48053 + 1.07567i 0.977384 + 0.211472i \(0.0678258\pi\)
0.503150 + 0.864199i \(0.332174\pi\)
\(920\) 9.01555 27.7470i 0.297234 0.914792i
\(921\) −11.8362 36.4281i −0.390016 1.20035i
\(922\) −15.0747 + 10.9524i −0.496458 + 0.360698i
\(923\) 28.4222 0.935528
\(924\) 0 0
\(925\) −41.6888 −1.37072
\(926\) −57.4110 + 41.7115i −1.88664 + 1.37072i
\(927\) −10.1778 31.3241i −0.334283 1.02882i
\(928\) −7.69710 + 23.6892i −0.252670 + 0.777637i
\(929\) 22.3558 + 16.2425i 0.733471 + 0.532898i 0.890659 0.454671i \(-0.150243\pi\)
−0.157189 + 0.987569i \(0.550243\pi\)
\(930\) −15.4679 11.2381i −0.507214 0.368512i
\(931\) 0.927051 2.85317i 0.0303829 0.0935089i
\(932\) −18.3710 56.5403i −0.601764 1.85204i
\(933\) 11.9128 8.65513i 0.390006 0.283356i
\(934\) 31.1833 1.02035
\(935\) 0 0
\(936\) 45.6333 1.49157
\(937\) 25.5694 18.5773i 0.835317 0.606893i −0.0857417 0.996317i \(-0.527326\pi\)
0.921059 + 0.389424i \(0.127326\pi\)
\(938\) −6.05845 18.6460i −0.197815 0.608813i
\(939\) −10.8894 + 33.5141i −0.355362 + 1.09369i
\(940\) 18.3849 + 13.3574i 0.599649 + 0.435671i
\(941\) 30.2752 + 21.9962i 0.986943 + 0.717056i 0.959250 0.282560i \(-0.0911837\pi\)
0.0276937 + 0.999616i \(0.491184\pi\)
\(942\) 11.8165 36.3673i 0.385001 1.18491i
\(943\) 5.83442 + 17.9565i 0.189995 + 0.584744i
\(944\) −1.64049 + 1.19189i −0.0533934 + 0.0387926i
\(945\) 5.78890 0.188313
\(946\) 0 0
\(947\) 46.6611 1.51628 0.758140 0.652091i \(-0.226108\pi\)
0.758140 + 0.652091i \(0.226108\pi\)
\(948\) 51.0871 37.1170i 1.65923 1.20550i
\(949\) −10.2061 31.4113i −0.331305 1.01965i
\(950\) −17.0783 + 52.5617i −0.554094 + 1.70533i
\(951\) 32.2348 + 23.4200i 1.04529 + 0.759444i
\(952\) −6.54630 4.75617i −0.212167 0.154148i
\(953\) 1.86268 5.73274i 0.0603381 0.185702i −0.916344 0.400392i \(-0.868874\pi\)
0.976682 + 0.214690i \(0.0688741\pi\)
\(954\) 21.1522 + 65.0998i 0.684828 + 2.10768i
\(955\) 78.2229 56.8323i 2.53123 1.83905i
\(956\) −86.9638 −2.81261
\(957\) 0 0
\(958\) −65.9361 −2.13030
\(959\) 8.18679 5.94805i 0.264365 0.192073i
\(960\) 32.8837 + 101.206i 1.06132 + 3.26639i
\(961\) −9.27051 + 28.5317i −0.299049 + 0.920377i
\(962\) 64.1280 + 46.5917i 2.06757 + 1.50218i
\(963\) 23.0907 + 16.7764i 0.744086 + 0.540610i
\(964\) −0.496143 + 1.52697i −0.0159797 + 0.0491804i
\(965\) 2.36142 + 7.26770i 0.0760168 + 0.233956i
\(966\) 11.5712 8.40696i 0.372297 0.270490i
\(967\) −40.5139 −1.30284 −0.651419 0.758718i \(-0.725826\pi\)
−0.651419 + 0.758718i \(0.725826\pi\)
\(968\) 0 0
\(969\) 18.6333 0.598588
\(970\) −24.2188 + 17.5960i −0.777619 + 0.564973i
\(971\) −1.96742 6.05508i −0.0631374 0.194317i 0.914512 0.404559i \(-0.132575\pi\)
−0.977649 + 0.210242i \(0.932575\pi\)
\(972\) 20.0097 61.5835i 0.641811 1.97529i
\(973\) 17.4793 + 12.6994i 0.560359 + 0.407125i
\(974\) −5.24738 3.81245i −0.168137 0.122159i
\(975\) 37.6039 115.733i 1.20429 3.70642i
\(976\) 0.402580 + 1.23901i 0.0128863 + 0.0396598i
\(977\) −32.3831 + 23.5277i −1.03603 + 0.752719i −0.969506 0.245066i \(-0.921190\pi\)
−0.0665220 + 0.997785i \(0.521190\pi\)
\(978\) 14.9361 0.477603
\(979\) 0 0
\(980\) 11.9083 0.380398
\(981\) −14.9039 + 10.8283i −0.475844 + 0.345721i
\(982\) −9.03530 27.8078i −0.288328 0.887383i
\(983\) −2.86614 + 8.82107i −0.0914156 + 0.281348i −0.986303 0.164944i \(-0.947256\pi\)
0.894887 + 0.446292i \(0.147256\pi\)
\(984\) 39.1227 + 28.4243i 1.24719 + 0.906133i
\(985\) −30.9359 22.4762i −0.985699 0.716152i
\(986\) −9.01555 + 27.7470i −0.287114 + 0.883645i
\(987\) 1.35796 + 4.17937i 0.0432243 + 0.133031i
\(988\) 52.9501 38.4705i 1.68457 1.22391i
\(989\) 4.57779 0.145565
\(990\) 0 0
\(991\) −43.7250 −1.38897 −0.694485 0.719507i \(-0.744368\pi\)
−0.694485 + 0.719507i \(0.744368\pi\)
\(992\) −4.29004 + 3.11689i −0.136209 + 0.0989615i
\(993\) −16.9479 52.1601i −0.537824 1.65525i
\(994\) 3.06184 9.42338i 0.0971157 0.298891i
\(995\) −56.6536 41.1613i −1.79604 1.30490i
\(996\) −18.4591 13.4113i −0.584898 0.424953i
\(997\) −14.1212 + 43.4606i −0.447223 + 1.37641i 0.432803 + 0.901488i \(0.357524\pi\)
−0.880027 + 0.474924i \(0.842476\pi\)
\(998\) −2.06956 6.36944i −0.0655107 0.201621i
\(999\) 6.76880 4.91782i 0.214155 0.155593i
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.r.729.2 8
11.2 odd 10 847.2.a.g.1.2 yes 2
11.3 even 5 inner 847.2.f.r.148.1 8
11.4 even 5 inner 847.2.f.r.323.2 8
11.5 even 5 inner 847.2.f.r.372.1 8
11.6 odd 10 847.2.f.o.372.2 8
11.7 odd 10 847.2.f.o.323.1 8
11.8 odd 10 847.2.f.o.148.2 8
11.9 even 5 847.2.a.e.1.1 2
11.10 odd 2 847.2.f.o.729.1 8
33.2 even 10 7623.2.a.bc.1.1 2
33.20 odd 10 7623.2.a.bs.1.2 2
77.13 even 10 5929.2.a.p.1.2 2
77.20 odd 10 5929.2.a.k.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
847.2.a.e.1.1 2 11.9 even 5
847.2.a.g.1.2 yes 2 11.2 odd 10
847.2.f.o.148.2 8 11.8 odd 10
847.2.f.o.323.1 8 11.7 odd 10
847.2.f.o.372.2 8 11.6 odd 10
847.2.f.o.729.1 8 11.10 odd 2
847.2.f.r.148.1 8 11.3 even 5 inner
847.2.f.r.323.2 8 11.4 even 5 inner
847.2.f.r.372.1 8 11.5 even 5 inner
847.2.f.r.729.2 8 1.1 even 1 trivial
5929.2.a.k.1.1 2 77.20 odd 10
5929.2.a.p.1.2 2 77.13 even 10
7623.2.a.bc.1.1 2 33.2 even 10
7623.2.a.bs.1.2 2 33.20 odd 10