Properties

Label 625.2.d.q.126.2
Level $625$
Weight $2$
Character 625.126
Analytic conductor $4.991$
Analytic rank $0$
Dimension $16$
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] = [625,2,Mod(126,625)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(625, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("625.126");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 625 = 5^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 625.d (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: \(4.99065012633\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 126.2
Root \(0.0288455i\) of defining polynomial
Character \(\chi\) \(=\) 625.126
Dual form 625.2.d.q.501.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.326747 - 1.00562i) q^{2} +(-0.556121 + 0.404046i) q^{3} +(0.713519 - 0.518402i) q^{4} +(0.588029 + 0.427228i) q^{6} -1.01199 q^{7} +(-2.46533 - 1.79116i) q^{8} +(-0.781033 + 2.40377i) q^{9} +O(q^{10})\) \(q+(-0.326747 - 1.00562i) q^{2} +(-0.556121 + 0.404046i) q^{3} +(0.713519 - 0.518402i) q^{4} +(0.588029 + 0.427228i) q^{6} -1.01199 q^{7} +(-2.46533 - 1.79116i) q^{8} +(-0.781033 + 2.40377i) q^{9} +(1.58239 + 4.87011i) q^{11} +(-0.187345 + 0.576589i) q^{12} +(-1.88045 + 5.78744i) q^{13} +(0.330666 + 1.01769i) q^{14} +(-0.450619 + 1.38686i) q^{16} +(2.58335 + 1.87691i) q^{17} +2.67249 q^{18} +(-2.77389 - 2.01535i) q^{19} +(0.562792 - 0.408892i) q^{21} +(4.38045 - 3.18259i) q^{22} +(-0.902070 - 2.77629i) q^{23} +2.09473 q^{24} +6.43442 q^{26} +(-1.17414 - 3.61364i) q^{27} +(-0.722078 + 0.524620i) q^{28} +(1.25597 - 0.912514i) q^{29} +(6.46970 + 4.70051i) q^{31} -4.55272 q^{32} +(-2.84775 - 2.06901i) q^{33} +(1.04337 - 3.21115i) q^{34} +(0.688839 + 2.12003i) q^{36} +(-2.59799 + 7.99578i) q^{37} +(-1.12032 + 3.44799i) q^{38} +(-1.29263 - 3.97831i) q^{39} +(-0.575868 + 1.77234i) q^{41} +(-0.595082 - 0.432352i) q^{42} +5.22402 q^{43} +(3.65374 + 2.65460i) q^{44} +(-2.49715 + 1.81429i) q^{46} +(-3.88393 + 2.82184i) q^{47} +(-0.309757 - 0.953334i) q^{48} -5.97587 q^{49} -2.19501 q^{51} +(1.65848 + 5.10428i) q^{52} +(8.13057 - 5.90720i) q^{53} +(-3.25031 + 2.36149i) q^{54} +(2.49490 + 1.81265i) q^{56} +2.35691 q^{57} +(-1.32803 - 0.964869i) q^{58} +(0.894451 - 2.75284i) q^{59} +(-0.713724 - 2.19662i) q^{61} +(2.61299 - 8.04196i) q^{62} +(0.790401 - 2.43261i) q^{63} +(2.38882 + 7.35205i) q^{64} +(-1.15015 + 3.53981i) q^{66} +(3.76108 + 2.73258i) q^{67} +2.81626 q^{68} +(1.62341 + 1.17947i) q^{69} +(6.25945 - 4.54776i) q^{71} +(6.23105 - 4.52712i) q^{72} +(0.184032 + 0.566392i) q^{73} +8.88962 q^{74} -3.02398 q^{76} +(-1.60138 - 4.92853i) q^{77} +(-3.57832 + 2.59980i) q^{78} +(-8.94716 + 6.50050i) q^{79} +(-4.02127 - 2.92163i) q^{81} +1.97047 q^{82} +(11.5667 + 8.40373i) q^{83} +(0.189592 - 0.583505i) q^{84} +(-1.70693 - 5.25339i) q^{86} +(-0.329773 + 1.01494i) q^{87} +(4.82205 - 14.8407i) q^{88} +(-1.97562 - 6.08032i) q^{89} +(1.90301 - 5.85686i) q^{91} +(-2.08288 - 1.51330i) q^{92} -5.49716 q^{93} +(4.10677 + 2.98375i) q^{94} +(2.53186 - 1.83951i) q^{96} +(-11.3936 + 8.27794i) q^{97} +(1.95260 + 6.00947i) q^{98} -12.9425 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 5 q^{2} - 3 q^{4} + 7 q^{6} - 20 q^{7} + 5 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 5 q^{2} - 3 q^{4} + 7 q^{6} - 20 q^{7} + 5 q^{8} - 12 q^{9} - 3 q^{11} - 15 q^{12} + 5 q^{13} - q^{14} + q^{16} + 25 q^{17} + 10 q^{18} + 10 q^{19} + 7 q^{21} + 35 q^{22} + 15 q^{23} + 10 q^{24} + 22 q^{26} - 35 q^{28} - 8 q^{31} - 60 q^{32} - 6 q^{34} + q^{36} + 5 q^{37} + 35 q^{38} + q^{39} - 8 q^{41} + 10 q^{42} - 31 q^{44} + 42 q^{46} + 5 q^{47} + 25 q^{48} - 8 q^{49} - 28 q^{51} - 15 q^{52} + 10 q^{53} + 50 q^{54} + 35 q^{56} + 20 q^{57} - 35 q^{58} - 15 q^{59} + 17 q^{61} - 5 q^{62} - 10 q^{63} + 37 q^{64} + 44 q^{66} + 10 q^{67} - 80 q^{68} - 9 q^{69} - 13 q^{71} - 20 q^{72} - 40 q^{73} - 36 q^{74} - 20 q^{76} + 45 q^{77} - 5 q^{78} - 55 q^{79} - 19 q^{81} + 90 q^{82} + 15 q^{83} + 59 q^{84} + 7 q^{86} + 60 q^{87} - 40 q^{88} - 28 q^{91} - 45 q^{92} + 80 q^{93} + 4 q^{94} - 43 q^{96} - 40 q^{97} - 45 q^{98} - 44 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.326747 1.00562i −0.231045 0.711083i −0.997621 0.0689302i \(-0.978041\pi\)
0.766577 0.642153i \(-0.221959\pi\)
\(3\) −0.556121 + 0.404046i −0.321077 + 0.233276i −0.736635 0.676291i \(-0.763586\pi\)
0.415558 + 0.909567i \(0.363586\pi\)
\(4\) 0.713519 0.518402i 0.356760 0.259201i
\(5\) 0 0
\(6\) 0.588029 + 0.427228i 0.240062 + 0.174415i
\(7\) −1.01199 −0.382498 −0.191249 0.981542i \(-0.561254\pi\)
−0.191249 + 0.981542i \(0.561254\pi\)
\(8\) −2.46533 1.79116i −0.871624 0.633272i
\(9\) −0.781033 + 2.40377i −0.260344 + 0.801258i
\(10\) 0 0
\(11\) 1.58239 + 4.87011i 0.477110 + 1.46839i 0.843091 + 0.537771i \(0.180734\pi\)
−0.365981 + 0.930622i \(0.619266\pi\)
\(12\) −0.187345 + 0.576589i −0.0540819 + 0.166447i
\(13\) −1.88045 + 5.78744i −0.521544 + 1.60515i 0.249506 + 0.968373i \(0.419732\pi\)
−0.771050 + 0.636775i \(0.780268\pi\)
\(14\) 0.330666 + 1.01769i 0.0883742 + 0.271988i
\(15\) 0 0
\(16\) −0.450619 + 1.38686i −0.112655 + 0.346716i
\(17\) 2.58335 + 1.87691i 0.626554 + 0.455218i 0.855205 0.518290i \(-0.173431\pi\)
−0.228651 + 0.973509i \(0.573431\pi\)
\(18\) 2.67249 0.629912
\(19\) −2.77389 2.01535i −0.636374 0.462352i 0.222229 0.974995i \(-0.428667\pi\)
−0.858602 + 0.512642i \(0.828667\pi\)
\(20\) 0 0
\(21\) 0.562792 0.408892i 0.122811 0.0892276i
\(22\) 4.38045 3.18259i 0.933916 0.678530i
\(23\) −0.902070 2.77629i −0.188095 0.578896i 0.811893 0.583806i \(-0.198437\pi\)
−0.999988 + 0.00491011i \(0.998437\pi\)
\(24\) 2.09473 0.427585
\(25\) 0 0
\(26\) 6.43442 1.26189
\(27\) −1.17414 3.61364i −0.225964 0.695445i
\(28\) −0.722078 + 0.524620i −0.136460 + 0.0991439i
\(29\) 1.25597 0.912514i 0.233227 0.169450i −0.465033 0.885293i \(-0.653958\pi\)
0.698261 + 0.715844i \(0.253958\pi\)
\(30\) 0 0
\(31\) 6.46970 + 4.70051i 1.16199 + 0.844237i 0.990029 0.140866i \(-0.0449888\pi\)
0.171964 + 0.985103i \(0.444989\pi\)
\(32\) −4.55272 −0.804815
\(33\) −2.84775 2.06901i −0.495730 0.360169i
\(34\) 1.04337 3.21115i 0.178936 0.550708i
\(35\) 0 0
\(36\) 0.688839 + 2.12003i 0.114806 + 0.353338i
\(37\) −2.59799 + 7.99578i −0.427106 + 1.31450i 0.473857 + 0.880602i \(0.342861\pi\)
−0.900963 + 0.433896i \(0.857139\pi\)
\(38\) −1.12032 + 3.44799i −0.181740 + 0.559339i
\(39\) −1.29263 3.97831i −0.206987 0.637039i
\(40\) 0 0
\(41\) −0.575868 + 1.77234i −0.0899354 + 0.276793i −0.985901 0.167331i \(-0.946485\pi\)
0.895965 + 0.444124i \(0.146485\pi\)
\(42\) −0.595082 0.432352i −0.0918231 0.0667134i
\(43\) 5.22402 0.796655 0.398328 0.917243i \(-0.369591\pi\)
0.398328 + 0.917243i \(0.369591\pi\)
\(44\) 3.65374 + 2.65460i 0.550823 + 0.400196i
\(45\) 0 0
\(46\) −2.49715 + 1.81429i −0.368185 + 0.267502i
\(47\) −3.88393 + 2.82184i −0.566530 + 0.411608i −0.833843 0.552002i \(-0.813864\pi\)
0.267313 + 0.963610i \(0.413864\pi\)
\(48\) −0.309757 0.953334i −0.0447096 0.137602i
\(49\) −5.97587 −0.853695
\(50\) 0 0
\(51\) −2.19501 −0.307363
\(52\) 1.65848 + 5.10428i 0.229990 + 0.707837i
\(53\) 8.13057 5.90720i 1.11682 0.811417i 0.133095 0.991103i \(-0.457508\pi\)
0.983724 + 0.179686i \(0.0575083\pi\)
\(54\) −3.25031 + 2.36149i −0.442312 + 0.321358i
\(55\) 0 0
\(56\) 2.49490 + 1.81265i 0.333395 + 0.242225i
\(57\) 2.35691 0.312180
\(58\) −1.32803 0.964869i −0.174379 0.126694i
\(59\) 0.894451 2.75284i 0.116448 0.358389i −0.875799 0.482677i \(-0.839665\pi\)
0.992246 + 0.124288i \(0.0396646\pi\)
\(60\) 0 0
\(61\) −0.713724 2.19662i −0.0913830 0.281248i 0.894911 0.446244i \(-0.147239\pi\)
−0.986294 + 0.164996i \(0.947239\pi\)
\(62\) 2.61299 8.04196i 0.331850 1.02133i
\(63\) 0.790401 2.43261i 0.0995812 0.306479i
\(64\) 2.38882 + 7.35205i 0.298603 + 0.919006i
\(65\) 0 0
\(66\) −1.15015 + 3.53981i −0.141574 + 0.435720i
\(67\) 3.76108 + 2.73258i 0.459489 + 0.333838i 0.793331 0.608791i \(-0.208345\pi\)
−0.333842 + 0.942629i \(0.608345\pi\)
\(68\) 2.81626 0.341522
\(69\) 1.62341 + 1.17947i 0.195435 + 0.141992i
\(70\) 0 0
\(71\) 6.25945 4.54776i 0.742860 0.539720i −0.150745 0.988573i \(-0.548167\pi\)
0.893606 + 0.448853i \(0.148167\pi\)
\(72\) 6.23105 4.52712i 0.734337 0.533527i
\(73\) 0.184032 + 0.566392i 0.0215393 + 0.0662912i 0.961248 0.275684i \(-0.0889042\pi\)
−0.939709 + 0.341975i \(0.888904\pi\)
\(74\) 8.88962 1.03340
\(75\) 0 0
\(76\) −3.02398 −0.346875
\(77\) −1.60138 4.92853i −0.182494 0.561658i
\(78\) −3.57832 + 2.59980i −0.405165 + 0.294369i
\(79\) −8.94716 + 6.50050i −1.00663 + 0.731363i −0.963501 0.267706i \(-0.913734\pi\)
−0.0431341 + 0.999069i \(0.513734\pi\)
\(80\) 0 0
\(81\) −4.02127 2.92163i −0.446808 0.324625i
\(82\) 1.97047 0.217602
\(83\) 11.5667 + 8.40373i 1.26961 + 0.922429i 0.999187 0.0403114i \(-0.0128350\pi\)
0.270427 + 0.962740i \(0.412835\pi\)
\(84\) 0.189592 0.583505i 0.0206862 0.0636656i
\(85\) 0 0
\(86\) −1.70693 5.25339i −0.184063 0.566488i
\(87\) −0.329773 + 1.01494i −0.0353554 + 0.108813i
\(88\) 4.82205 14.8407i 0.514032 1.58203i
\(89\) −1.97562 6.08032i −0.209415 0.644513i −0.999503 0.0315198i \(-0.989965\pi\)
0.790088 0.612993i \(-0.210035\pi\)
\(90\) 0 0
\(91\) 1.90301 5.85686i 0.199490 0.613966i
\(92\) −2.08288 1.51330i −0.217155 0.157772i
\(93\) −5.49716 −0.570029
\(94\) 4.10677 + 2.98375i 0.423581 + 0.307750i
\(95\) 0 0
\(96\) 2.53186 1.83951i 0.258407 0.187744i
\(97\) −11.3936 + 8.27794i −1.15685 + 0.840498i −0.989376 0.145379i \(-0.953560\pi\)
−0.167470 + 0.985877i \(0.553560\pi\)
\(98\) 1.95260 + 6.00947i 0.197242 + 0.607048i
\(99\) −12.9425 −1.30077
\(100\) 0 0
\(101\) −10.5130 −1.04608 −0.523040 0.852308i \(-0.675202\pi\)
−0.523040 + 0.852308i \(0.675202\pi\)
\(102\) 0.717214 + 2.20736i 0.0710147 + 0.218561i
\(103\) −2.48991 + 1.80902i −0.245338 + 0.178248i −0.703658 0.710539i \(-0.748451\pi\)
0.458320 + 0.888787i \(0.348451\pi\)
\(104\) 15.0022 10.8997i 1.47109 1.06881i
\(105\) 0 0
\(106\) −8.59706 6.24613i −0.835020 0.606678i
\(107\) 5.24731 0.507277 0.253638 0.967299i \(-0.418373\pi\)
0.253638 + 0.967299i \(0.418373\pi\)
\(108\) −2.71109 1.96972i −0.260875 0.189537i
\(109\) −2.01450 + 6.19999i −0.192954 + 0.593852i 0.807040 + 0.590496i \(0.201068\pi\)
−0.999994 + 0.00335529i \(0.998932\pi\)
\(110\) 0 0
\(111\) −1.78586 5.49632i −0.169507 0.521688i
\(112\) 0.456024 1.40350i 0.0430902 0.132618i
\(113\) −0.119143 + 0.366684i −0.0112080 + 0.0344947i −0.956504 0.291719i \(-0.905773\pi\)
0.945296 + 0.326214i \(0.105773\pi\)
\(114\) −0.770113 2.37016i −0.0721277 0.221986i
\(115\) 0 0
\(116\) 0.423108 1.30219i 0.0392846 0.120906i
\(117\) −12.4430 9.04037i −1.15036 0.835782i
\(118\) −3.06058 −0.281749
\(119\) −2.61434 1.89943i −0.239656 0.174120i
\(120\) 0 0
\(121\) −12.3148 + 8.94724i −1.11953 + 0.813385i
\(122\) −1.97576 + 1.43548i −0.178877 + 0.129962i
\(123\) −0.395853 1.21831i −0.0356929 0.109851i
\(124\) 7.05301 0.633379
\(125\) 0 0
\(126\) −2.70455 −0.240940
\(127\) 1.43484 + 4.41598i 0.127321 + 0.391855i 0.994317 0.106461i \(-0.0339519\pi\)
−0.866995 + 0.498316i \(0.833952\pi\)
\(128\) −0.753609 + 0.547529i −0.0666103 + 0.0483952i
\(129\) −2.90519 + 2.11074i −0.255787 + 0.185840i
\(130\) 0 0
\(131\) −13.1233 9.53462i −1.14659 0.833044i −0.158563 0.987349i \(-0.550686\pi\)
−0.988023 + 0.154305i \(0.950686\pi\)
\(132\) −3.10450 −0.270212
\(133\) 2.80716 + 2.03952i 0.243412 + 0.176849i
\(134\) 1.51903 4.67509i 0.131224 0.403867i
\(135\) 0 0
\(136\) −3.00694 9.25440i −0.257843 0.793559i
\(137\) 5.92699 18.2414i 0.506377 1.55847i −0.292066 0.956398i \(-0.594343\pi\)
0.798443 0.602070i \(-0.205657\pi\)
\(138\) 0.655664 2.01792i 0.0558138 0.171777i
\(139\) 1.10864 + 3.41206i 0.0940340 + 0.289407i 0.987001 0.160716i \(-0.0513803\pi\)
−0.892967 + 0.450123i \(0.851380\pi\)
\(140\) 0 0
\(141\) 1.01978 3.13857i 0.0858813 0.264316i
\(142\) −6.61859 4.80869i −0.555420 0.403536i
\(143\) −31.1611 −2.60582
\(144\) −2.98175 2.16637i −0.248479 0.180531i
\(145\) 0 0
\(146\) 0.509445 0.370134i 0.0421620 0.0306325i
\(147\) 3.32331 2.41452i 0.274102 0.199147i
\(148\) 2.29131 + 7.05194i 0.188345 + 0.579666i
\(149\) 1.60192 0.131234 0.0656170 0.997845i \(-0.479098\pi\)
0.0656170 + 0.997845i \(0.479098\pi\)
\(150\) 0 0
\(151\) 6.74218 0.548671 0.274336 0.961634i \(-0.411542\pi\)
0.274336 + 0.961634i \(0.411542\pi\)
\(152\) 3.22872 + 9.93698i 0.261884 + 0.805995i
\(153\) −6.52935 + 4.74385i −0.527867 + 0.383518i
\(154\) −4.43300 + 3.22076i −0.357221 + 0.259536i
\(155\) 0 0
\(156\) −2.98468 2.16850i −0.238966 0.173619i
\(157\) 14.2612 1.13817 0.569083 0.822280i \(-0.307298\pi\)
0.569083 + 0.822280i \(0.307298\pi\)
\(158\) 9.46051 + 6.87346i 0.752638 + 0.546823i
\(159\) −2.13480 + 6.57024i −0.169301 + 0.521054i
\(160\) 0 0
\(161\) 0.912890 + 2.80959i 0.0719458 + 0.221426i
\(162\) −1.62412 + 4.99852i −0.127603 + 0.392721i
\(163\) 3.12542 9.61904i 0.244801 0.753421i −0.750868 0.660453i \(-0.770364\pi\)
0.995669 0.0929686i \(-0.0296356\pi\)
\(164\) 0.507891 + 1.56313i 0.0396596 + 0.122060i
\(165\) 0 0
\(166\) 4.67159 14.3777i 0.362586 1.11592i
\(167\) 13.5236 + 9.82548i 1.04649 + 0.760318i 0.971542 0.236869i \(-0.0761213\pi\)
0.0749467 + 0.997188i \(0.476121\pi\)
\(168\) −2.11986 −0.163551
\(169\) −19.4412 14.1248i −1.49547 1.08653i
\(170\) 0 0
\(171\) 7.01094 5.09374i 0.536140 0.389528i
\(172\) 3.72744 2.70814i 0.284214 0.206494i
\(173\) −1.99090 6.12735i −0.151365 0.465853i 0.846410 0.532533i \(-0.178760\pi\)
−0.997774 + 0.0666791i \(0.978760\pi\)
\(174\) 1.12840 0.0855435
\(175\) 0 0
\(176\) −7.46723 −0.562864
\(177\) 0.614849 + 1.89231i 0.0462149 + 0.142235i
\(178\) −5.46899 + 3.97345i −0.409918 + 0.297823i
\(179\) 12.4866 9.07201i 0.933289 0.678074i −0.0135069 0.999909i \(-0.504300\pi\)
0.946796 + 0.321835i \(0.104300\pi\)
\(180\) 0 0
\(181\) −1.03388 0.751154i −0.0768473 0.0558329i 0.548698 0.836020i \(-0.315124\pi\)
−0.625546 + 0.780188i \(0.715124\pi\)
\(182\) −6.51160 −0.482672
\(183\) 1.28445 + 0.933208i 0.0949493 + 0.0689847i
\(184\) −2.74889 + 8.46021i −0.202651 + 0.623695i
\(185\) 0 0
\(186\) 1.79618 + 5.52807i 0.131702 + 0.405338i
\(187\) −5.05290 + 15.5512i −0.369504 + 1.13722i
\(188\) −1.30841 + 4.02688i −0.0954258 + 0.293690i
\(189\) 1.18823 + 3.65699i 0.0864308 + 0.266007i
\(190\) 0 0
\(191\) 1.80346 5.55049i 0.130494 0.401619i −0.864368 0.502860i \(-0.832281\pi\)
0.994862 + 0.101241i \(0.0322812\pi\)
\(192\) −4.29904 3.12343i −0.310256 0.225414i
\(193\) 4.17773 0.300719 0.150360 0.988631i \(-0.451957\pi\)
0.150360 + 0.988631i \(0.451957\pi\)
\(194\) 12.0473 + 8.75289i 0.864947 + 0.628421i
\(195\) 0 0
\(196\) −4.26390 + 3.09790i −0.304564 + 0.221279i
\(197\) −14.1460 + 10.2777i −1.00786 + 0.732255i −0.963760 0.266772i \(-0.914043\pi\)
−0.0441025 + 0.999027i \(0.514043\pi\)
\(198\) 4.22893 + 13.0153i 0.300537 + 0.924959i
\(199\) 5.89046 0.417564 0.208782 0.977962i \(-0.433050\pi\)
0.208782 + 0.977962i \(0.433050\pi\)
\(200\) 0 0
\(201\) −3.19571 −0.225408
\(202\) 3.43508 + 10.5721i 0.241692 + 0.743850i
\(203\) −1.27103 + 0.923459i −0.0892090 + 0.0648141i
\(204\) −1.56618 + 1.13790i −0.109655 + 0.0796689i
\(205\) 0 0
\(206\) 2.63277 + 1.91282i 0.183434 + 0.133272i
\(207\) 7.37811 0.512814
\(208\) −7.17902 5.21586i −0.497775 0.361655i
\(209\) 5.42558 16.6982i 0.375295 1.15504i
\(210\) 0 0
\(211\) −3.70118 11.3911i −0.254800 0.784193i −0.993869 0.110564i \(-0.964734\pi\)
0.739069 0.673629i \(-0.235266\pi\)
\(212\) 2.73901 8.42981i 0.188116 0.578962i
\(213\) −1.64351 + 5.05821i −0.112612 + 0.346583i
\(214\) −1.71454 5.27682i −0.117204 0.360716i
\(215\) 0 0
\(216\) −3.57798 + 11.0119i −0.243451 + 0.749264i
\(217\) −6.54730 4.75689i −0.444460 0.322919i
\(218\) 6.89309 0.466859
\(219\) −0.331192 0.240625i −0.0223799 0.0162600i
\(220\) 0 0
\(221\) −15.7204 + 11.4215i −1.05747 + 0.768296i
\(222\) −4.94371 + 3.59181i −0.331800 + 0.241067i
\(223\) 0.394663 + 1.21465i 0.0264286 + 0.0813389i 0.963401 0.268065i \(-0.0863842\pi\)
−0.936972 + 0.349404i \(0.886384\pi\)
\(224\) 4.60733 0.307840
\(225\) 0 0
\(226\) 0.407676 0.0271182
\(227\) −8.69517 26.7610i −0.577119 1.77619i −0.628849 0.777527i \(-0.716474\pi\)
0.0517304 0.998661i \(-0.483526\pi\)
\(228\) 1.68170 1.22183i 0.111373 0.0809175i
\(229\) −9.12744 + 6.63147i −0.603158 + 0.438220i −0.846998 0.531595i \(-0.821593\pi\)
0.243840 + 0.969815i \(0.421593\pi\)
\(230\) 0 0
\(231\) 2.88191 + 2.09383i 0.189616 + 0.137764i
\(232\) −4.73083 −0.310594
\(233\) −10.8990 7.91861i −0.714019 0.518765i 0.170448 0.985367i \(-0.445478\pi\)
−0.884468 + 0.466601i \(0.845478\pi\)
\(234\) −5.02550 + 15.4669i −0.328527 + 1.01110i
\(235\) 0 0
\(236\) −0.788868 2.42789i −0.0513510 0.158042i
\(237\) 2.34921 7.23013i 0.152598 0.469647i
\(238\) −1.05588 + 3.24967i −0.0684426 + 0.210645i
\(239\) 0.587907 + 1.80939i 0.0380285 + 0.117040i 0.968269 0.249912i \(-0.0804015\pi\)
−0.930240 + 0.366951i \(0.880402\pi\)
\(240\) 0 0
\(241\) −6.04699 + 18.6107i −0.389521 + 1.19882i 0.543626 + 0.839327i \(0.317051\pi\)
−0.933147 + 0.359495i \(0.882949\pi\)
\(242\) 13.0214 + 9.46058i 0.837046 + 0.608149i
\(243\) 14.8156 0.950422
\(244\) −1.64799 1.19733i −0.105502 0.0766514i
\(245\) 0 0
\(246\) −1.09582 + 0.796159i −0.0698668 + 0.0507612i
\(247\) 16.8799 12.2639i 1.07404 0.780336i
\(248\) −7.53053 23.1766i −0.478189 1.47171i
\(249\) −9.82800 −0.622824
\(250\) 0 0
\(251\) 20.7096 1.30718 0.653590 0.756849i \(-0.273262\pi\)
0.653590 + 0.756849i \(0.273262\pi\)
\(252\) −0.697101 2.14546i −0.0439132 0.135151i
\(253\) 12.0934 8.78636i 0.760305 0.552394i
\(254\) 3.97199 2.88582i 0.249225 0.181072i
\(255\) 0 0
\(256\) 13.3049 + 9.66657i 0.831556 + 0.604161i
\(257\) −15.0730 −0.940225 −0.470113 0.882606i \(-0.655787\pi\)
−0.470113 + 0.882606i \(0.655787\pi\)
\(258\) 3.07187 + 2.23184i 0.191246 + 0.138949i
\(259\) 2.62915 8.09168i 0.163367 0.502793i
\(260\) 0 0
\(261\) 1.21252 + 3.73177i 0.0750534 + 0.230990i
\(262\) −5.30025 + 16.3125i −0.327450 + 1.00779i
\(263\) −1.54609 + 4.75839i −0.0953363 + 0.293415i −0.987341 0.158611i \(-0.949298\pi\)
0.892005 + 0.452026i \(0.149298\pi\)
\(264\) 3.31469 + 10.2016i 0.204005 + 0.627864i
\(265\) 0 0
\(266\) 1.13376 3.48935i 0.0695152 0.213946i
\(267\) 3.55541 + 2.58316i 0.217588 + 0.158087i
\(268\) 4.10018 0.250458
\(269\) 22.3939 + 16.2701i 1.36538 + 0.992007i 0.998082 + 0.0619045i \(0.0197174\pi\)
0.367299 + 0.930103i \(0.380283\pi\)
\(270\) 0 0
\(271\) 21.3522 15.5133i 1.29705 0.942365i 0.297132 0.954836i \(-0.403970\pi\)
0.999922 + 0.0124713i \(0.00396983\pi\)
\(272\) −3.76713 + 2.73698i −0.228416 + 0.165954i
\(273\) 1.30814 + 4.02603i 0.0791720 + 0.243666i
\(274\) −20.2806 −1.22520
\(275\) 0 0
\(276\) 1.76977 0.106528
\(277\) 2.20106 + 6.77415i 0.132249 + 0.407019i 0.995152 0.0983496i \(-0.0313563\pi\)
−0.862903 + 0.505369i \(0.831356\pi\)
\(278\) 3.06900 2.22976i 0.184066 0.133732i
\(279\) −16.3520 + 11.8804i −0.978970 + 0.711263i
\(280\) 0 0
\(281\) 8.35445 + 6.06986i 0.498385 + 0.362098i 0.808400 0.588634i \(-0.200334\pi\)
−0.310015 + 0.950732i \(0.600334\pi\)
\(282\) −3.48943 −0.207793
\(283\) 3.68901 + 2.68023i 0.219289 + 0.159323i 0.692007 0.721891i \(-0.256727\pi\)
−0.472717 + 0.881214i \(0.656727\pi\)
\(284\) 2.10867 6.48983i 0.125127 0.385100i
\(285\) 0 0
\(286\) 10.1818 + 31.3363i 0.602062 + 1.85296i
\(287\) 0.582775 1.79360i 0.0344001 0.105873i
\(288\) 3.55583 10.9437i 0.209529 0.644864i
\(289\) −2.10240 6.47052i −0.123670 0.380619i
\(290\) 0 0
\(291\) 2.99156 9.20708i 0.175368 0.539729i
\(292\) 0.424929 + 0.308729i 0.0248671 + 0.0180670i
\(293\) 20.8237 1.21653 0.608267 0.793733i \(-0.291865\pi\)
0.608267 + 0.793733i \(0.291865\pi\)
\(294\) −3.51398 2.55306i −0.204939 0.148897i
\(295\) 0 0
\(296\) 20.7266 15.0588i 1.20471 0.875274i
\(297\) 15.7409 11.4364i 0.913378 0.663608i
\(298\) −0.523421 1.61092i −0.0303210 0.0933183i
\(299\) 17.7639 1.02731
\(300\) 0 0
\(301\) −5.28668 −0.304719
\(302\) −2.20299 6.78010i −0.126768 0.390151i
\(303\) 5.84649 4.24772i 0.335872 0.244025i
\(304\) 4.04497 2.93885i 0.231995 0.168554i
\(305\) 0 0
\(306\) 6.90398 + 5.01603i 0.394674 + 0.286747i
\(307\) −9.44200 −0.538884 −0.269442 0.963017i \(-0.586839\pi\)
−0.269442 + 0.963017i \(0.586839\pi\)
\(308\) −3.69757 2.68644i −0.210689 0.153074i
\(309\) 0.653762 2.01207i 0.0371912 0.114463i
\(310\) 0 0
\(311\) 4.13477 + 12.7255i 0.234461 + 0.721597i 0.997192 + 0.0748814i \(0.0238578\pi\)
−0.762731 + 0.646715i \(0.776142\pi\)
\(312\) −3.93905 + 12.1231i −0.223005 + 0.686338i
\(313\) −7.41478 + 22.8203i −0.419108 + 1.28988i 0.489416 + 0.872050i \(0.337210\pi\)
−0.908524 + 0.417832i \(0.862790\pi\)
\(314\) −4.65979 14.3414i −0.262967 0.809330i
\(315\) 0 0
\(316\) −3.01410 + 9.27646i −0.169557 + 0.521841i
\(317\) 11.7806 + 8.55911i 0.661664 + 0.480727i 0.867225 0.497917i \(-0.165902\pi\)
−0.205560 + 0.978644i \(0.565902\pi\)
\(318\) 7.30473 0.409629
\(319\) 6.43148 + 4.67274i 0.360094 + 0.261623i
\(320\) 0 0
\(321\) −2.91814 + 2.12015i −0.162875 + 0.118335i
\(322\) 2.52710 1.83605i 0.140830 0.102319i
\(323\) −3.38329 10.4127i −0.188251 0.579378i
\(324\) −4.38383 −0.243546
\(325\) 0 0
\(326\) −10.6944 −0.592305
\(327\) −1.38477 4.26190i −0.0765782 0.235683i
\(328\) 4.59425 3.33792i 0.253675 0.184306i
\(329\) 3.93052 2.85569i 0.216697 0.157439i
\(330\) 0 0
\(331\) 19.7601 + 14.3566i 1.08611 + 0.789108i 0.978739 0.205111i \(-0.0657555\pi\)
0.107375 + 0.994219i \(0.465755\pi\)
\(332\) 12.6096 0.692042
\(333\) −17.1909 12.4899i −0.942056 0.684444i
\(334\) 5.46193 16.8101i 0.298864 0.919808i
\(335\) 0 0
\(336\) 0.313472 + 0.964769i 0.0171013 + 0.0526325i
\(337\) 2.64896 8.15266i 0.144298 0.444104i −0.852622 0.522528i \(-0.824989\pi\)
0.996920 + 0.0784246i \(0.0249890\pi\)
\(338\) −7.85192 + 24.1657i −0.427088 + 1.31444i
\(339\) −0.0818993 0.252060i −0.00444816 0.0136900i
\(340\) 0 0
\(341\) −12.6544 + 38.9462i −0.685274 + 2.10906i
\(342\) −7.41319 5.38600i −0.400859 0.291241i
\(343\) 13.1315 0.709035
\(344\) −12.8789 9.35707i −0.694384 0.504499i
\(345\) 0 0
\(346\) −5.51128 + 4.00418i −0.296288 + 0.215266i
\(347\) 8.74352 6.35254i 0.469377 0.341022i −0.327822 0.944740i \(-0.606314\pi\)
0.797198 + 0.603717i \(0.206314\pi\)
\(348\) 0.290846 + 0.895132i 0.0155910 + 0.0479841i
\(349\) −8.13956 −0.435701 −0.217850 0.975982i \(-0.569904\pi\)
−0.217850 + 0.975982i \(0.569904\pi\)
\(350\) 0 0
\(351\) 23.1217 1.23414
\(352\) −7.20420 22.1723i −0.383985 1.18179i
\(353\) 17.1237 12.4411i 0.911404 0.662174i −0.0299652 0.999551i \(-0.509540\pi\)
0.941370 + 0.337377i \(0.109540\pi\)
\(354\) 1.70205 1.23661i 0.0904630 0.0657252i
\(355\) 0 0
\(356\) −4.56169 3.31426i −0.241769 0.175656i
\(357\) 2.22134 0.117566
\(358\) −13.2030 9.59252i −0.697799 0.506980i
\(359\) −1.64578 + 5.06518i −0.0868608 + 0.267330i −0.985047 0.172285i \(-0.944885\pi\)
0.898186 + 0.439615i \(0.144885\pi\)
\(360\) 0 0
\(361\) −2.23849 6.88938i −0.117816 0.362599i
\(362\) −0.417563 + 1.28513i −0.0219466 + 0.0675447i
\(363\) 3.23344 9.95150i 0.169711 0.522318i
\(364\) −1.67838 5.16551i −0.0879708 0.270746i
\(365\) 0 0
\(366\) 0.518766 1.59660i 0.0271163 0.0834554i
\(367\) −13.7753 10.0083i −0.719064 0.522431i 0.167021 0.985953i \(-0.446585\pi\)
−0.886085 + 0.463523i \(0.846585\pi\)
\(368\) 4.25682 0.221902
\(369\) −3.81053 2.76851i −0.198368 0.144123i
\(370\) 0 0
\(371\) −8.22809 + 5.97806i −0.427181 + 0.310365i
\(372\) −3.92233 + 2.84974i −0.203363 + 0.147752i
\(373\) 2.11717 + 6.51599i 0.109623 + 0.337385i 0.990788 0.135425i \(-0.0432399\pi\)
−0.881165 + 0.472810i \(0.843240\pi\)
\(374\) 17.2897 0.894028
\(375\) 0 0
\(376\) 14.6295 0.754461
\(377\) 2.91933 + 8.98478i 0.150353 + 0.462740i
\(378\) 3.28930 2.38982i 0.169183 0.122919i
\(379\) 5.97714 4.34265i 0.307025 0.223067i −0.423594 0.905852i \(-0.639232\pi\)
0.730619 + 0.682785i \(0.239232\pi\)
\(380\) 0 0
\(381\) −2.58220 1.87608i −0.132290 0.0961145i
\(382\) −6.17097 −0.315734
\(383\) 16.3447 + 11.8751i 0.835175 + 0.606790i 0.921019 0.389518i \(-0.127359\pi\)
−0.0858436 + 0.996309i \(0.527359\pi\)
\(384\) 0.197871 0.608985i 0.0100976 0.0310771i
\(385\) 0 0
\(386\) −1.36506 4.20122i −0.0694797 0.213836i
\(387\) −4.08013 + 12.5573i −0.207405 + 0.638326i
\(388\) −3.83826 + 11.8129i −0.194858 + 0.599711i
\(389\) 2.71944 + 8.36957i 0.137881 + 0.424354i 0.996027 0.0890516i \(-0.0283836\pi\)
−0.858146 + 0.513406i \(0.828384\pi\)
\(390\) 0 0
\(391\) 2.88049 8.86522i 0.145672 0.448334i
\(392\) 14.7325 + 10.7038i 0.744102 + 0.540621i
\(393\) 11.1506 0.562471
\(394\) 14.9576 + 10.8674i 0.753555 + 0.547490i
\(395\) 0 0
\(396\) −9.23475 + 6.70944i −0.464064 + 0.337162i
\(397\) 4.92939 3.58141i 0.247399 0.179746i −0.457174 0.889377i \(-0.651138\pi\)
0.704573 + 0.709631i \(0.251138\pi\)
\(398\) −1.92469 5.92358i −0.0964759 0.296922i
\(399\) −2.38518 −0.119408
\(400\) 0 0
\(401\) −1.71924 −0.0858547 −0.0429274 0.999078i \(-0.513668\pi\)
−0.0429274 + 0.999078i \(0.513668\pi\)
\(402\) 1.04419 + 3.21368i 0.0520793 + 0.160284i
\(403\) −39.3699 + 28.6039i −1.96116 + 1.42486i
\(404\) −7.50121 + 5.44995i −0.373199 + 0.271145i
\(405\) 0 0
\(406\) 1.34396 + 0.976443i 0.0666995 + 0.0484600i
\(407\) −43.0514 −2.13398
\(408\) 5.41142 + 3.93163i 0.267905 + 0.194645i
\(409\) −8.57257 + 26.3837i −0.423886 + 1.30459i 0.480170 + 0.877175i \(0.340575\pi\)
−0.904056 + 0.427413i \(0.859425\pi\)
\(410\) 0 0
\(411\) 4.07423 + 12.5392i 0.200967 + 0.618513i
\(412\) −0.838796 + 2.58155i −0.0413245 + 0.127184i
\(413\) −0.905180 + 2.78586i −0.0445410 + 0.137083i
\(414\) −2.41077 7.41960i −0.118483 0.364653i
\(415\) 0 0
\(416\) 8.56118 26.3486i 0.419747 1.29185i
\(417\) −1.99517 1.44957i −0.0977037 0.0709859i
\(418\) −18.5649 −0.908039
\(419\) −13.2306 9.61263i −0.646359 0.469608i 0.215670 0.976466i \(-0.430807\pi\)
−0.862029 + 0.506859i \(0.830807\pi\)
\(420\) 0 0
\(421\) 8.04616 5.84588i 0.392146 0.284911i −0.374188 0.927353i \(-0.622079\pi\)
0.766334 + 0.642442i \(0.222079\pi\)
\(422\) −10.2458 + 7.44398i −0.498756 + 0.362367i
\(423\) −3.74959 11.5400i −0.182311 0.561096i
\(424\) −30.6253 −1.48729
\(425\) 0 0
\(426\) 5.62367 0.272467
\(427\) 0.722285 + 2.22296i 0.0349538 + 0.107577i
\(428\) 3.74406 2.72022i 0.180976 0.131487i
\(429\) 17.3294 12.5905i 0.836669 0.607876i
\(430\) 0 0
\(431\) 16.6093 + 12.0673i 0.800040 + 0.581263i 0.910926 0.412570i \(-0.135369\pi\)
−0.110886 + 0.993833i \(0.535369\pi\)
\(432\) 5.54071 0.266578
\(433\) −20.9914 15.2512i −1.00878 0.732925i −0.0448309 0.998995i \(-0.514275\pi\)
−0.963954 + 0.266070i \(0.914275\pi\)
\(434\) −2.64433 + 8.13842i −0.126932 + 0.390657i
\(435\) 0 0
\(436\) 1.77671 + 5.46814i 0.0850887 + 0.261876i
\(437\) −3.09294 + 9.51909i −0.147955 + 0.455360i
\(438\) −0.133762 + 0.411678i −0.00639141 + 0.0196708i
\(439\) 7.76509 + 23.8985i 0.370608 + 1.14061i 0.946395 + 0.323013i \(0.104696\pi\)
−0.575787 + 0.817600i \(0.695304\pi\)
\(440\) 0 0
\(441\) 4.66735 14.3646i 0.222255 0.684030i
\(442\) 16.6224 + 12.0768i 0.790645 + 0.574437i
\(443\) −27.0262 −1.28405 −0.642027 0.766682i \(-0.721906\pi\)
−0.642027 + 0.766682i \(0.721906\pi\)
\(444\) −4.12355 2.99594i −0.195695 0.142181i
\(445\) 0 0
\(446\) 1.09252 0.793765i 0.0517325 0.0375859i
\(447\) −0.890859 + 0.647247i −0.0421362 + 0.0306137i
\(448\) −2.41748 7.44023i −0.114215 0.351518i
\(449\) 37.9871 1.79272 0.896361 0.443325i \(-0.146201\pi\)
0.896361 + 0.443325i \(0.146201\pi\)
\(450\) 0 0
\(451\) −9.54273 −0.449350
\(452\) 0.105079 + 0.323400i 0.00494250 + 0.0152115i
\(453\) −3.74947 + 2.72415i −0.176166 + 0.127992i
\(454\) −24.0703 + 17.4881i −1.12968 + 0.820759i
\(455\) 0 0
\(456\) −5.81055 4.22161i −0.272104 0.197695i
\(457\) 29.9832 1.40256 0.701278 0.712888i \(-0.252613\pi\)
0.701278 + 0.712888i \(0.252613\pi\)
\(458\) 9.65113 + 7.01195i 0.450967 + 0.327647i
\(459\) 3.74927 11.5391i 0.175001 0.538597i
\(460\) 0 0
\(461\) −0.659330 2.02921i −0.0307081 0.0945097i 0.934528 0.355890i \(-0.115822\pi\)
−0.965236 + 0.261380i \(0.915822\pi\)
\(462\) 1.16395 3.58227i 0.0541518 0.166662i
\(463\) 6.79231 20.9046i 0.315665 0.971518i −0.659815 0.751428i \(-0.729365\pi\)
0.975480 0.220089i \(-0.0706348\pi\)
\(464\) 0.699568 + 2.15305i 0.0324766 + 0.0999528i
\(465\) 0 0
\(466\) −4.40192 + 13.5477i −0.203915 + 0.627585i
\(467\) 4.29663 + 3.12169i 0.198824 + 0.144454i 0.682743 0.730659i \(-0.260787\pi\)
−0.483918 + 0.875113i \(0.660787\pi\)
\(468\) −13.5649 −0.627036
\(469\) −3.80619 2.76536i −0.175754 0.127693i
\(470\) 0 0
\(471\) −7.93094 + 5.76216i −0.365438 + 0.265507i
\(472\) −7.13590 + 5.18453i −0.328456 + 0.238637i
\(473\) 8.26646 + 25.4415i 0.380092 + 1.16980i
\(474\) −8.03838 −0.369215
\(475\) 0 0
\(476\) −2.85005 −0.130632
\(477\) 7.84933 + 24.1578i 0.359396 + 1.10611i
\(478\) 1.62747 1.18243i 0.0744387 0.0540829i
\(479\) 17.0603 12.3950i 0.779506 0.566344i −0.125325 0.992116i \(-0.539997\pi\)
0.904831 + 0.425772i \(0.139997\pi\)
\(480\) 0 0
\(481\) −41.3897 30.0714i −1.88721 1.37114i
\(482\) 20.6912 0.942459
\(483\) −1.64288 1.19362i −0.0747536 0.0543116i
\(484\) −4.14859 + 12.7681i −0.188572 + 0.580366i
\(485\) 0 0
\(486\) −4.84095 14.8989i −0.219590 0.675829i
\(487\) 8.22358 25.3096i 0.372646 1.14689i −0.572407 0.819969i \(-0.693990\pi\)
0.945053 0.326917i \(-0.106010\pi\)
\(488\) −2.17494 + 6.69377i −0.0984549 + 0.303013i
\(489\) 2.14842 + 6.61216i 0.0971550 + 0.299012i
\(490\) 0 0
\(491\) 0.556442 1.71255i 0.0251119 0.0772865i −0.937715 0.347405i \(-0.887063\pi\)
0.962827 + 0.270119i \(0.0870629\pi\)
\(492\) −0.914024 0.664077i −0.0412074 0.0299389i
\(493\) 4.95731 0.223266
\(494\) −17.8484 12.9676i −0.803036 0.583440i
\(495\) 0 0
\(496\) −9.43433 + 6.85444i −0.423614 + 0.307774i
\(497\) −6.33453 + 4.60231i −0.284143 + 0.206442i
\(498\) 3.21127 + 9.88326i 0.143900 + 0.442880i
\(499\) 28.6962 1.28462 0.642309 0.766446i \(-0.277977\pi\)
0.642309 + 0.766446i \(0.277977\pi\)
\(500\) 0 0
\(501\) −11.4907 −0.513367
\(502\) −6.76681 20.8261i −0.302017 0.929514i
\(503\) −19.1597 + 13.9204i −0.854290 + 0.620678i −0.926326 0.376724i \(-0.877051\pi\)
0.0720355 + 0.997402i \(0.477051\pi\)
\(504\) −6.30579 + 4.58143i −0.280882 + 0.204073i
\(505\) 0 0
\(506\) −12.7872 9.29048i −0.568462 0.413012i
\(507\) 16.5187 0.733622
\(508\) 3.31304 + 2.40706i 0.146992 + 0.106796i
\(509\) 5.46826 16.8296i 0.242376 0.745958i −0.753681 0.657241i \(-0.771723\pi\)
0.996057 0.0887168i \(-0.0282766\pi\)
\(510\) 0 0
\(511\) −0.186239 0.573186i −0.00823874 0.0253562i
\(512\) 4.79789 14.7664i 0.212039 0.652589i
\(513\) −4.02580 + 12.3901i −0.177743 + 0.547038i
\(514\) 4.92504 + 15.1577i 0.217234 + 0.668578i
\(515\) 0 0
\(516\) −0.978694 + 3.01211i −0.0430846 + 0.132601i
\(517\) −19.8886 14.4499i −0.874700 0.635507i
\(518\) −8.99625 −0.395273
\(519\) 3.58291 + 2.60313i 0.157272 + 0.114265i
\(520\) 0 0
\(521\) −18.5876 + 13.5047i −0.814338 + 0.591651i −0.915085 0.403261i \(-0.867877\pi\)
0.100747 + 0.994912i \(0.467877\pi\)
\(522\) 3.35656 2.43868i 0.146913 0.106738i
\(523\) 8.95447 + 27.5590i 0.391552 + 1.20507i 0.931615 + 0.363447i \(0.118400\pi\)
−0.540063 + 0.841625i \(0.681600\pi\)
\(524\) −14.3065 −0.624982
\(525\) 0 0
\(526\) 5.29033 0.230669
\(527\) 7.89104 + 24.2861i 0.343739 + 1.05792i
\(528\) 4.15268 3.01710i 0.180722 0.131302i
\(529\) 11.7134 8.51025i 0.509276 0.370011i
\(530\) 0 0
\(531\) 5.91860 + 4.30011i 0.256845 + 0.186609i
\(532\) 3.06025 0.132679
\(533\) −9.17441 6.66560i −0.397388 0.288719i
\(534\) 1.43596 4.41944i 0.0621402 0.191248i
\(535\) 0 0
\(536\) −4.37778 13.4734i −0.189091 0.581963i
\(537\) −3.27853 + 10.0903i −0.141479 + 0.435428i
\(538\) 9.04448 27.8361i 0.389935 1.20010i
\(539\) −9.45618 29.1031i −0.407307 1.25356i
\(540\) 0 0
\(541\) 7.55563 23.2538i 0.324842 0.999760i −0.646670 0.762770i \(-0.723839\pi\)
0.971512 0.236990i \(-0.0761610\pi\)
\(542\) −22.5773 16.4034i −0.969778 0.704585i
\(543\) 0.878460 0.0376983
\(544\) −11.7613 8.54506i −0.504260 0.366367i
\(545\) 0 0
\(546\) 3.62124 2.63098i 0.154975 0.112596i
\(547\) −5.26131 + 3.82257i −0.224957 + 0.163441i −0.694555 0.719439i \(-0.744399\pi\)
0.469598 + 0.882880i \(0.344399\pi\)
\(548\) −5.22736 16.0882i −0.223302 0.687252i
\(549\) 5.83761 0.249143
\(550\) 0 0
\(551\) −5.32295 −0.226765
\(552\) −1.88959 5.81558i −0.0804265 0.247527i
\(553\) 9.05448 6.57847i 0.385036 0.279745i
\(554\) 6.09306 4.42687i 0.258869 0.188080i
\(555\) 0 0
\(556\) 2.55986 + 1.85984i 0.108562 + 0.0788749i
\(557\) −3.12305 −0.132328 −0.0661640 0.997809i \(-0.521076\pi\)
−0.0661640 + 0.997809i \(0.521076\pi\)
\(558\) 17.2902 + 12.5621i 0.731953 + 0.531795i
\(559\) −9.82352 + 30.2337i −0.415491 + 1.27875i
\(560\) 0 0
\(561\) −3.47338 10.6900i −0.146646 0.451330i
\(562\) 3.37421 10.3847i 0.142332 0.438054i
\(563\) 11.2869 34.7376i 0.475687 1.46401i −0.369342 0.929293i \(-0.620417\pi\)
0.845029 0.534720i \(-0.179583\pi\)
\(564\) −0.899407 2.76809i −0.0378719 0.116558i
\(565\) 0 0
\(566\) 1.48992 4.58551i 0.0626262 0.192744i
\(567\) 4.06951 + 2.95667i 0.170903 + 0.124168i
\(568\) −23.5774 −0.989285
\(569\) 30.5546 + 22.1992i 1.28092 + 0.930640i 0.999580 0.0289691i \(-0.00922244\pi\)
0.281336 + 0.959609i \(0.409222\pi\)
\(570\) 0 0
\(571\) 33.3614 24.2385i 1.39613 1.01435i 0.400971 0.916091i \(-0.368673\pi\)
0.995161 0.0982590i \(-0.0313274\pi\)
\(572\) −22.2340 + 16.1540i −0.929652 + 0.675432i
\(573\) 1.23971 + 3.81542i 0.0517895 + 0.159392i
\(574\) −1.99410 −0.0832322
\(575\) 0 0
\(576\) −19.5384 −0.814100
\(577\) 1.31928 + 4.06033i 0.0549224 + 0.169034i 0.974755 0.223277i \(-0.0716756\pi\)
−0.919833 + 0.392311i \(0.871676\pi\)
\(578\) −5.81995 + 4.22844i −0.242078 + 0.175880i
\(579\) −2.32332 + 1.68799i −0.0965540 + 0.0701506i
\(580\) 0 0
\(581\) −11.7055 8.50453i −0.485625 0.352827i
\(582\) −10.2363 −0.424310
\(583\) 41.6345 + 30.2492i 1.72432 + 1.25280i
\(584\) 0.560803 1.72597i 0.0232062 0.0714213i
\(585\) 0 0
\(586\) −6.80408 20.9408i −0.281074 0.865056i
\(587\) −3.53301 + 10.8735i −0.145823 + 0.448797i −0.997116 0.0758937i \(-0.975819\pi\)
0.851293 + 0.524691i \(0.175819\pi\)
\(588\) 1.11955 3.44562i 0.0461694 0.142095i
\(589\) −8.47306 26.0774i −0.349126 1.07450i
\(590\) 0 0
\(591\) 3.71425 11.4313i 0.152784 0.470220i
\(592\) −9.91834 7.20609i −0.407641 0.296169i
\(593\) −30.9375 −1.27045 −0.635225 0.772327i \(-0.719092\pi\)
−0.635225 + 0.772327i \(0.719092\pi\)
\(594\) −16.6440 12.0926i −0.682912 0.496164i
\(595\) 0 0
\(596\) 1.14300 0.830436i 0.0468190 0.0340160i
\(597\) −3.27581 + 2.38001i −0.134070 + 0.0974075i
\(598\) −5.80430 17.8638i −0.237355 0.730505i
\(599\) −46.1912 −1.88732 −0.943660 0.330916i \(-0.892642\pi\)
−0.943660 + 0.330916i \(0.892642\pi\)
\(600\) 0 0
\(601\) −38.0963 −1.55398 −0.776990 0.629513i \(-0.783254\pi\)
−0.776990 + 0.629513i \(0.783254\pi\)
\(602\) 1.72740 + 5.31641i 0.0704038 + 0.216681i
\(603\) −9.50604 + 6.90654i −0.387116 + 0.281256i
\(604\) 4.81068 3.49516i 0.195744 0.142216i
\(605\) 0 0
\(606\) −6.18193 4.49144i −0.251124 0.182452i
\(607\) −38.6361 −1.56819 −0.784095 0.620641i \(-0.786873\pi\)
−0.784095 + 0.620641i \(0.786873\pi\)
\(608\) 12.6287 + 9.17532i 0.512163 + 0.372108i
\(609\) 0.333728 1.02711i 0.0135234 0.0416206i
\(610\) 0 0
\(611\) −9.02770 27.7844i −0.365221 1.12404i
\(612\) −2.19960 + 6.76966i −0.0889134 + 0.273647i
\(613\) 3.32381 10.2296i 0.134247 0.413171i −0.861225 0.508224i \(-0.830302\pi\)
0.995472 + 0.0950531i \(0.0303021\pi\)
\(614\) 3.08515 + 9.49510i 0.124506 + 0.383191i
\(615\) 0 0
\(616\) −4.87989 + 15.0187i −0.196616 + 0.605123i
\(617\) −8.74322 6.35232i −0.351989 0.255735i 0.397714 0.917509i \(-0.369804\pi\)
−0.749703 + 0.661775i \(0.769804\pi\)
\(618\) −2.23700 −0.0899855
\(619\) 29.8477 + 21.6856i 1.19968 + 0.871619i 0.994253 0.107054i \(-0.0341417\pi\)
0.205427 + 0.978672i \(0.434142\pi\)
\(620\) 0 0
\(621\) −8.97334 + 6.51951i −0.360088 + 0.261619i
\(622\) 11.4460 8.31603i 0.458944 0.333443i
\(623\) 1.99931 + 6.15325i 0.0801008 + 0.246525i
\(624\) 6.09985 0.244189
\(625\) 0 0
\(626\) 25.3714 1.01405
\(627\) 3.72956 + 11.4784i 0.148944 + 0.458404i
\(628\) 10.1756 7.39302i 0.406051 0.295014i
\(629\) −21.7189 + 15.7797i −0.865988 + 0.629177i
\(630\) 0 0
\(631\) −31.7615 23.0761i −1.26440 0.918643i −0.265439 0.964128i \(-0.585517\pi\)
−0.998965 + 0.0454842i \(0.985517\pi\)
\(632\) 33.7011 1.34056
\(633\) 6.66081 + 4.83936i 0.264744 + 0.192347i
\(634\) 4.75796 14.6435i 0.188963 0.581568i
\(635\) 0 0
\(636\) 1.88281 + 5.79468i 0.0746581 + 0.229774i
\(637\) 11.2373 34.5850i 0.445240 1.37031i
\(638\) 2.59755 7.99445i 0.102838 0.316503i
\(639\) 6.04294 + 18.5983i 0.239055 + 0.735735i
\(640\) 0 0
\(641\) 2.57978 7.93973i 0.101895 0.313601i −0.887094 0.461589i \(-0.847280\pi\)
0.988989 + 0.147988i \(0.0472797\pi\)
\(642\) 3.08557 + 2.24180i 0.121778 + 0.0884767i
\(643\) 13.1408 0.518223 0.259112 0.965847i \(-0.416570\pi\)
0.259112 + 0.965847i \(0.416570\pi\)
\(644\) 2.10786 + 1.53145i 0.0830613 + 0.0603476i
\(645\) 0 0
\(646\) −9.36577 + 6.80463i −0.368491 + 0.267725i
\(647\) 21.0992 15.3295i 0.829496 0.602664i −0.0899210 0.995949i \(-0.528661\pi\)
0.919417 + 0.393285i \(0.128661\pi\)
\(648\) 4.68064 + 14.4055i 0.183873 + 0.565902i
\(649\) 14.8220 0.581814
\(650\) 0 0
\(651\) 5.56310 0.218035
\(652\) −2.75649 8.48359i −0.107952 0.332243i
\(653\) 18.6312 13.5364i 0.729097 0.529720i −0.160181 0.987088i \(-0.551208\pi\)
0.889278 + 0.457368i \(0.151208\pi\)
\(654\) −3.83339 + 2.78512i −0.149898 + 0.108907i
\(655\) 0 0
\(656\) −2.19849 1.59730i −0.0858367 0.0623640i
\(657\) −1.50521 −0.0587240
\(658\) −4.15603 3.01953i −0.162019 0.117714i
\(659\) 10.7408 33.0569i 0.418403 1.28771i −0.490768 0.871290i \(-0.663284\pi\)
0.909171 0.416422i \(-0.136716\pi\)
\(660\) 0 0
\(661\) 5.56334 + 17.1222i 0.216389 + 0.665976i 0.999052 + 0.0435308i \(0.0138607\pi\)
−0.782663 + 0.622445i \(0.786139\pi\)
\(662\) 7.98074 24.5622i 0.310180 0.954636i
\(663\) 4.12762 12.7035i 0.160304 0.493364i
\(664\) −13.4633 41.4359i −0.522478 1.60802i
\(665\) 0 0
\(666\) −6.94309 + 21.3686i −0.269039 + 0.828018i
\(667\) −3.66637 2.66377i −0.141962 0.103142i
\(668\) 14.7429 0.570420
\(669\) −0.710254 0.516030i −0.0274600 0.0199509i
\(670\) 0 0
\(671\) 9.56838 6.95183i 0.369383 0.268372i
\(672\) −2.56223 + 1.86157i −0.0988403 + 0.0718117i
\(673\) −4.59267 14.1348i −0.177034 0.544856i 0.822686 0.568496i \(-0.192474\pi\)
−0.999721 + 0.0236399i \(0.992474\pi\)
\(674\) −9.06404 −0.349134
\(675\) 0 0
\(676\) −21.1940 −0.815153
\(677\) 7.14565 + 21.9920i 0.274629 + 0.845223i 0.989317 + 0.145779i \(0.0465688\pi\)
−0.714688 + 0.699444i \(0.753431\pi\)
\(678\) −0.226717 + 0.164720i −0.00870702 + 0.00632602i
\(679\) 11.5303 8.37723i 0.442491 0.321489i
\(680\) 0 0
\(681\) 15.6482 + 11.3691i 0.599641 + 0.435665i
\(682\) 43.3000 1.65804
\(683\) −15.8848 11.5410i −0.607816 0.441604i 0.240828 0.970568i \(-0.422581\pi\)
−0.848645 + 0.528963i \(0.822581\pi\)
\(684\) 2.36183 7.26897i 0.0903069 0.277936i
\(685\) 0 0
\(686\) −4.29068 13.2054i −0.163819 0.504183i
\(687\) 2.39654 7.37580i 0.0914339 0.281404i
\(688\) −2.35404 + 7.24499i −0.0897469 + 0.276213i
\(689\) 18.8984 + 58.1634i 0.719973 + 2.21585i
\(690\) 0 0
\(691\) −1.81635 + 5.59014i −0.0690970 + 0.212659i −0.979642 0.200750i \(-0.935662\pi\)
0.910545 + 0.413409i \(0.135662\pi\)
\(692\) −4.59697 3.33989i −0.174751 0.126964i
\(693\) 13.0978 0.497544
\(694\) −9.24518 6.71702i −0.350942 0.254974i
\(695\) 0 0
\(696\) 2.63092 1.91147i 0.0997246 0.0724542i
\(697\) −4.81419 + 3.49771i −0.182351 + 0.132485i
\(698\) 2.65958 + 8.18533i 0.100666 + 0.309819i
\(699\) 9.26066 0.350270
\(700\) 0 0
\(701\) −50.0581 −1.89067 −0.945334 0.326103i \(-0.894264\pi\)
−0.945334 + 0.326103i \(0.894264\pi\)
\(702\) −7.55493 23.2517i −0.285142 0.877578i
\(703\) 23.3208 16.9435i 0.879560 0.639038i
\(704\) −32.0252 + 23.2677i −1.20700 + 0.876934i
\(705\) 0 0
\(706\) −18.1062 13.1549i −0.681436 0.495092i
\(707\) 10.6391 0.400124
\(708\) 1.41968 + 1.03146i 0.0533550 + 0.0387647i
\(709\) 4.24917 13.0776i 0.159581 0.491139i −0.839015 0.544108i \(-0.816868\pi\)
0.998596 + 0.0529685i \(0.0168683\pi\)
\(710\) 0 0
\(711\) −8.63768 26.5841i −0.323938 0.996980i
\(712\) −6.02032 + 18.5286i −0.225621 + 0.694390i
\(713\) 7.21384 22.2019i 0.270161 0.831469i
\(714\) −0.725816 2.23383i −0.0271630 0.0835991i
\(715\) 0 0
\(716\) 4.20645 12.9461i 0.157202 0.483819i
\(717\) −1.05802 0.768700i −0.0395126 0.0287076i
\(718\) 5.63142 0.210163
\(719\) 8.49464 + 6.17172i 0.316797 + 0.230166i 0.734807 0.678276i \(-0.237273\pi\)
−0.418011 + 0.908442i \(0.637273\pi\)
\(720\) 0 0
\(721\) 2.51977 1.83072i 0.0938413 0.0681797i
\(722\) −6.19670 + 4.50216i −0.230617 + 0.167553i
\(723\) −4.15672 12.7931i −0.154590 0.475780i
\(724\) −1.12709 −0.0418880
\(725\) 0 0
\(726\) −11.0640 −0.410623
\(727\) 1.87377 + 5.76688i 0.0694944 + 0.213882i 0.979772 0.200116i \(-0.0641320\pi\)
−0.910278 + 0.413998i \(0.864132\pi\)
\(728\) −15.1821 + 11.0305i −0.562687 + 0.408816i
\(729\) 3.82455 2.77870i 0.141650 0.102915i
\(730\) 0 0
\(731\) 13.4955 + 9.80503i 0.499148 + 0.362652i
\(732\) 1.40026 0.0517550
\(733\) 1.89367 + 1.37583i 0.0699442 + 0.0508174i 0.622208 0.782852i \(-0.286236\pi\)
−0.552264 + 0.833669i \(0.686236\pi\)
\(734\) −5.56358 + 17.1229i −0.205355 + 0.632019i
\(735\) 0 0
\(736\) 4.10687 + 12.6397i 0.151381 + 0.465904i
\(737\) −7.35648 + 22.6409i −0.270979 + 0.833988i
\(738\) −1.53900 + 4.73656i −0.0566514 + 0.174355i
\(739\) −12.8351 39.5024i −0.472147 1.45312i −0.849768 0.527158i \(-0.823258\pi\)
0.377621 0.925960i \(-0.376742\pi\)
\(740\) 0 0
\(741\) −4.43206 + 13.6405i −0.162816 + 0.501096i
\(742\) 8.70018 + 6.32105i 0.319394 + 0.232053i
\(743\) 0.813821 0.0298562 0.0149281 0.999889i \(-0.495248\pi\)
0.0149281 + 0.999889i \(0.495248\pi\)
\(744\) 13.5523 + 9.84631i 0.496851 + 0.360983i
\(745\) 0 0
\(746\) 5.86085 4.25815i 0.214581 0.155902i
\(747\) −29.2347 + 21.2402i −1.06964 + 0.777139i
\(748\) 4.45644 + 13.7155i 0.162944 + 0.501489i
\(749\) −5.31025 −0.194032
\(750\) 0 0
\(751\) 31.8919 1.16375 0.581877 0.813277i \(-0.302319\pi\)
0.581877 + 0.813277i \(0.302319\pi\)
\(752\) −2.16333 6.65806i −0.0788886 0.242794i
\(753\) −11.5171 + 8.36764i −0.419705 + 0.304934i
\(754\) 8.08142 5.87150i 0.294308 0.213827i
\(755\) 0 0
\(756\) 2.74361 + 1.99335i 0.0997842 + 0.0724974i
\(757\) −26.7040 −0.970572 −0.485286 0.874355i \(-0.661285\pi\)
−0.485286 + 0.874355i \(0.661285\pi\)
\(758\) −6.32008 4.59181i −0.229556 0.166782i
\(759\) −3.17530 + 9.77256i −0.115256 + 0.354722i
\(760\) 0 0
\(761\) 13.3076 + 40.9567i 0.482402 + 1.48468i 0.835709 + 0.549172i \(0.185057\pi\)
−0.353307 + 0.935507i \(0.614943\pi\)
\(762\) −1.04290 + 3.20973i −0.0377804 + 0.116276i
\(763\) 2.03866 6.27436i 0.0738046 0.227147i
\(764\) −1.59058 4.89530i −0.0575451 0.177106i
\(765\) 0 0
\(766\) 6.60132 20.3168i 0.238515 0.734075i
\(767\) 14.2499 + 10.3532i 0.514535 + 0.373831i
\(768\) −11.3049 −0.407929
\(769\) 0.852363 + 0.619278i 0.0307370 + 0.0223317i 0.603048 0.797705i \(-0.293953\pi\)
−0.572311 + 0.820037i \(0.693953\pi\)
\(770\) 0 0
\(771\) 8.38239 6.09016i 0.301884 0.219332i
\(772\) 2.98089 2.16574i 0.107285 0.0779468i
\(773\) 4.08825 + 12.5823i 0.147044 + 0.452556i 0.997268 0.0738656i \(-0.0235336\pi\)
−0.850224 + 0.526421i \(0.823534\pi\)
\(774\) 13.9611 0.501823
\(775\) 0 0
\(776\) 42.9161 1.54060
\(777\) 1.80728 + 5.56225i 0.0648360 + 0.199545i
\(778\) 7.52807 5.46946i 0.269894 0.196090i
\(779\) 5.16927 3.75569i 0.185208 0.134562i
\(780\) 0 0
\(781\) 32.0530 + 23.2879i 1.14695 + 0.833306i
\(782\) −9.85627 −0.352459
\(783\) −4.77218 3.46719i −0.170544 0.123907i
\(784\) 2.69284 8.28770i 0.0961728 0.295989i
\(785\) 0 0
\(786\) −3.64341 11.2133i −0.129956 0.399964i
\(787\) −10.3946 + 31.9914i −0.370529 + 1.14037i 0.575917 + 0.817508i \(0.304645\pi\)
−0.946446 + 0.322862i \(0.895355\pi\)
\(788\) −4.76548 + 14.6667i −0.169763 + 0.522478i
\(789\) −1.06279 3.27093i −0.0378364 0.116448i
\(790\) 0 0
\(791\) 0.120572 0.371082i 0.00428705 0.0131942i
\(792\) 31.9076 + 23.1822i 1.13379 + 0.823744i
\(793\) 14.0549 0.499105
\(794\) −5.21221 3.78689i −0.184974 0.134392i
\(795\) 0 0
\(796\) 4.20296 3.05363i 0.148970 0.108233i
\(797\) 5.58012 4.05419i 0.197658 0.143607i −0.484554 0.874761i \(-0.661018\pi\)
0.682212 + 0.731154i \(0.261018\pi\)
\(798\) 0.779350 + 2.39859i 0.0275887 + 0.0849093i
\(799\) −15.3299 −0.542333
\(800\) 0 0
\(801\) 16.1587 0.570941
\(802\) 0.561756 + 1.72891i 0.0198363 + 0.0610498i
\(803\) −2.46718 + 1.79251i −0.0870649 + 0.0632564i
\(804\) −2.28020 + 1.65666i −0.0804164 + 0.0584259i
\(805\) 0 0
\(806\) 41.6288 + 30.2451i 1.46631 + 1.06534i
\(807\) −19.0276 −0.669803
\(808\) 25.9179 + 18.8305i 0.911789 + 0.662454i
\(809\) −10.9185 + 33.6037i −0.383874 + 1.18144i 0.553420 + 0.832902i \(0.313322\pi\)
−0.937294 + 0.348540i \(0.886678\pi\)
\(810\) 0 0
\(811\) −1.22742 3.77760i −0.0431005 0.132650i 0.927191 0.374589i \(-0.122216\pi\)
−0.970291 + 0.241940i \(0.922216\pi\)
\(812\) −0.428183 + 1.31781i −0.0150263 + 0.0462461i
\(813\) −5.60634 + 17.2545i −0.196623 + 0.605143i
\(814\) 14.0669 + 43.2934i 0.493044 + 1.51743i
\(815\) 0 0
\(816\) 0.989114 3.04418i 0.0346259 0.106568i
\(817\) −14.4908 10.5282i −0.506970 0.368335i
\(818\) 29.3331 1.02561
\(819\) 12.5923 + 9.14881i 0.440009 + 0.319685i
\(820\) 0 0
\(821\) −19.7204 + 14.3277i −0.688247 + 0.500041i −0.876083 0.482160i \(-0.839853\pi\)
0.187836 + 0.982200i \(0.439853\pi\)
\(822\) 11.2785 8.19429i 0.393382 0.285809i
\(823\) −6.87883 21.1709i −0.239781 0.737970i −0.996451 0.0841731i \(-0.973175\pi\)
0.756670 0.653797i \(-0.226825\pi\)
\(824\) 9.37870 0.326722
\(825\) 0 0
\(826\) 3.09729 0.107768
\(827\) −8.22592 25.3168i −0.286043 0.880351i −0.986084 0.166248i \(-0.946835\pi\)
0.700041 0.714103i \(-0.253165\pi\)
\(828\) 5.26442 3.82483i 0.182951 0.132922i
\(829\) 6.33731 4.60432i 0.220104 0.159915i −0.472270 0.881454i \(-0.656565\pi\)
0.692373 + 0.721539i \(0.256565\pi\)
\(830\) 0 0
\(831\) −3.96112 2.87792i −0.137410 0.0998340i
\(832\) −47.0416 −1.63088
\(833\) −15.4378 11.2162i −0.534886 0.388618i
\(834\) −0.805810 + 2.48003i −0.0279029 + 0.0858764i
\(835\) 0 0
\(836\) −4.78513 14.7271i −0.165497 0.509348i
\(837\) 9.38961 28.8982i 0.324552 0.998870i
\(838\) −5.34361 + 16.4459i −0.184592 + 0.568116i
\(839\) 1.81517 + 5.58652i 0.0626666 + 0.192868i 0.977488 0.210990i \(-0.0676689\pi\)
−0.914822 + 0.403858i \(0.867669\pi\)
\(840\) 0 0
\(841\) −8.21672 + 25.2885i −0.283335 + 0.872016i
\(842\) −8.50781 6.18129i −0.293199 0.213021i
\(843\) −7.09859 −0.244488
\(844\) −8.54601 6.20904i −0.294166 0.213724i
\(845\) 0 0
\(846\) −10.3798 + 7.54135i −0.356864 + 0.259277i
\(847\) 12.4625 9.05456i 0.428218 0.311118i
\(848\) 4.52869 + 13.9379i 0.155516 + 0.478629i
\(849\) −3.13447 −0.107575
\(850\) 0 0
\(851\) 24.5421 0.841293
\(852\) 1.44951 + 4.46113i 0.0496594 + 0.152836i
\(853\) −22.7695 + 16.5430i −0.779613 + 0.566422i −0.904863 0.425703i \(-0.860027\pi\)
0.125250 + 0.992125i \(0.460027\pi\)
\(854\) 1.99946 1.45269i 0.0684201 0.0497101i
\(855\) 0 0
\(856\) −12.9363 9.39880i −0.442155 0.321244i
\(857\) 36.2976 1.23990 0.619951 0.784640i \(-0.287152\pi\)
0.619951 + 0.784640i \(0.287152\pi\)
\(858\) −18.3236 13.3129i −0.625558 0.454495i
\(859\) 1.18168 3.63684i 0.0403185 0.124087i −0.928871 0.370402i \(-0.879220\pi\)
0.969190 + 0.246315i \(0.0792198\pi\)
\(860\) 0 0
\(861\) 0.400602 + 1.23292i 0.0136525 + 0.0420180i
\(862\) 6.70817 20.6456i 0.228481 0.703192i
\(863\) −7.90944 + 24.3428i −0.269240 + 0.828637i 0.721446 + 0.692471i \(0.243478\pi\)
−0.990686 + 0.136166i \(0.956522\pi\)
\(864\) 5.34555 + 16.4519i 0.181859 + 0.559705i
\(865\) 0 0
\(866\) −8.47805 + 26.0928i −0.288096 + 0.886668i
\(867\) 3.78357 + 2.74893i 0.128497 + 0.0933584i
\(868\) −7.13761 −0.242266
\(869\) −45.8161 33.2873i −1.55420 1.12920i
\(870\) 0 0
\(871\) −22.8872 + 16.6285i −0.775504 + 0.563437i
\(872\) 16.0716 11.6767i 0.544253 0.395423i
\(873\) −10.9995 33.8530i −0.372277 1.14575i
\(874\) 10.5832 0.357983
\(875\) 0 0
\(876\) −0.361053 −0.0121988
\(877\) −4.59134 14.1307i −0.155038 0.477159i 0.843126 0.537716i \(-0.180713\pi\)
−0.998165 + 0.0605562i \(0.980713\pi\)
\(878\) 21.4957 15.6175i 0.725443 0.527066i
\(879\) −11.5805 + 8.41373i −0.390601 + 0.283788i
\(880\) 0 0
\(881\) −1.70995 1.24235i −0.0576098 0.0418560i 0.558608 0.829432i \(-0.311336\pi\)
−0.616217 + 0.787576i \(0.711336\pi\)
\(882\) −15.9704 −0.537753
\(883\) −41.3269 30.0257i −1.39076 1.01045i −0.995782 0.0917559i \(-0.970752\pi\)
−0.394978 0.918690i \(-0.629248\pi\)
\(884\) −5.29586 + 16.2990i −0.178119 + 0.548194i
\(885\) 0 0
\(886\) 8.83073 + 27.1782i 0.296674 + 0.913069i
\(887\) −14.0850 + 43.3491i −0.472927 + 1.45552i 0.375807 + 0.926698i \(0.377366\pi\)
−0.848733 + 0.528821i \(0.822634\pi\)
\(888\) −5.44208 + 16.7490i −0.182624 + 0.562060i
\(889\) −1.45205 4.46895i −0.0487002 0.149884i
\(890\) 0 0
\(891\) 7.86540 24.2072i 0.263501 0.810972i
\(892\) 0.911277 + 0.662081i 0.0305118 + 0.0221681i
\(893\) 16.4606 0.550833
\(894\) 0.941972 + 0.684383i 0.0315043 + 0.0228892i
\(895\) 0 0
\(896\) 0.762649 0.554097i 0.0254783 0.0185111i
\(897\) −9.87888 + 7.17743i −0.329846 + 0.239647i
\(898\) −12.4122 38.2007i −0.414199 1.27477i
\(899\) 12.4150 0.414064
\(900\) 0 0
\(901\) 32.0914 1.06912
\(902\) 3.11806 + 9.59639i 0.103820 + 0.319525i
\(903\) 2.94003 2.13606i 0.0978382 0.0710836i
\(904\) 0.950518 0.690592i 0.0316137 0.0229687i
\(905\) 0 0
\(906\) 3.96460 + 2.88045i 0.131715 + 0.0956965i
\(907\) 27.5215 0.913837 0.456919 0.889508i \(-0.348953\pi\)
0.456919 + 0.889508i \(0.348953\pi\)
\(908\) −20.0771 14.5869i −0.666283 0.484083i
\(909\) 8.21099 25.2708i 0.272341 0.838180i
\(910\) 0 0
\(911\) 15.5779 + 47.9437i 0.516118 + 1.58845i 0.781239 + 0.624232i \(0.214588\pi\)
−0.265121 + 0.964215i \(0.585412\pi\)
\(912\) −1.06207 + 3.26871i −0.0351686 + 0.108238i
\(913\) −22.6239 + 69.6293i −0.748743 + 2.30439i
\(914\) −9.79692 30.1518i −0.324053 0.997334i
\(915\) 0 0
\(916\) −3.07483 + 9.46337i −0.101595 + 0.312678i
\(917\) 13.2807 + 9.64899i 0.438567 + 0.318638i
\(918\) −12.8290 −0.423420
\(919\) −10.2376 7.43802i −0.337706 0.245358i 0.405988 0.913879i \(-0.366928\pi\)
−0.743693 + 0.668521i \(0.766928\pi\)
\(920\) 0 0
\(921\) 5.25090 3.81500i 0.173023 0.125709i
\(922\) −1.82519 + 1.32608i −0.0601093 + 0.0436720i
\(923\) 14.5493 + 44.7781i 0.478895 + 1.47389i
\(924\) 3.14174 0.103356
\(925\) 0 0
\(926\) −23.2415 −0.763763
\(927\) −2.40378 7.39808i −0.0789506 0.242985i
\(928\) −5.71807 + 4.15442i −0.187705 + 0.136376i
\(929\) 2.45910 1.78664i 0.0806805 0.0586178i −0.546714 0.837320i \(-0.684121\pi\)
0.627394 + 0.778702i \(0.284121\pi\)
\(930\) 0 0
\(931\) 16.5764 + 12.0434i 0.543269 + 0.394708i
\(932\) −11.8817 −0.389198
\(933\) −7.44111 5.40628i −0.243611 0.176994i
\(934\) 1.73533 5.34080i 0.0567817 0.174756i
\(935\) 0 0
\(936\) 14.4833 + 44.5749i 0.473400 + 1.45698i
\(937\) −0.0148559 + 0.0457219i −0.000485323 + 0.00149367i −0.951299 0.308270i \(-0.900250\pi\)
0.950814 + 0.309764i \(0.100250\pi\)
\(938\) −1.53725 + 4.73117i −0.0501930 + 0.154478i
\(939\) −5.09694 15.6868i −0.166332 0.511919i
\(940\) 0 0
\(941\) −0.387485 + 1.19256i −0.0126316 + 0.0388762i −0.957174 0.289514i \(-0.906506\pi\)
0.944542 + 0.328391i \(0.106506\pi\)
\(942\) 8.38598 + 6.09277i 0.273230 + 0.198513i
\(943\) 5.43999 0.177150
\(944\) 3.41475 + 2.48096i 0.111141 + 0.0807484i
\(945\) 0 0
\(946\) 22.8836 16.6259i 0.744009 0.540554i
\(947\) 36.0810 26.2143i 1.17247 0.851852i 0.181171 0.983452i \(-0.442011\pi\)
0.991303 + 0.131600i \(0.0420114\pi\)
\(948\) −2.07191 6.37667i −0.0672924 0.207105i
\(949\) −3.62403 −0.117641
\(950\) 0 0
\(951\) −10.0097 −0.324587
\(952\) 3.04301 + 9.36541i 0.0986244 + 0.303535i
\(953\) −33.8353 + 24.5828i −1.09603 + 0.796314i −0.980408 0.196980i \(-0.936887\pi\)
−0.115624 + 0.993293i \(0.536887\pi\)
\(954\) 21.7289 15.7869i 0.703498 0.511121i
\(955\) 0 0
\(956\) 1.35748 + 0.986264i 0.0439039 + 0.0318980i
\(957\) −5.46469 −0.176648
\(958\) −18.0392 13.1062i −0.582819 0.423443i
\(959\) −5.99808 + 18.4602i −0.193688 + 0.596111i
\(960\) 0 0
\(961\) 10.1827 + 31.3391i 0.328474 + 1.01094i
\(962\) −16.7165 + 51.4482i −0.538962 + 1.65876i
\(963\) −4.09833 + 12.6134i −0.132067 + 0.406460i
\(964\) 5.33319 + 16.4139i 0.171771 + 0.528656i
\(965\) 0 0
\(966\) −0.663528 + 2.04213i −0.0213487 + 0.0657044i
\(967\) 36.0001 + 26.1556i 1.15769 + 0.841109i 0.989484 0.144644i \(-0.0462037\pi\)
0.168203 + 0.985752i \(0.446204\pi\)
\(968\) 46.3860 1.49090
\(969\) 6.08872 + 4.42372i 0.195598 + 0.142110i
\(970\) 0 0
\(971\) −2.96504 + 2.15423i −0.0951526 + 0.0691324i −0.634344 0.773051i \(-0.718730\pi\)
0.539192 + 0.842183i \(0.318730\pi\)
\(972\) 10.5712 7.68044i 0.339072 0.246350i
\(973\) −1.12194 3.45298i −0.0359678 0.110698i
\(974\) −28.1389 −0.901629
\(975\) 0 0
\(976\) 3.36802 0.107808
\(977\) −4.86869 14.9843i −0.155763 0.479389i 0.842474 0.538736i \(-0.181098\pi\)
−0.998237 + 0.0593470i \(0.981098\pi\)
\(978\) 5.94735 4.32101i 0.190175 0.138171i
\(979\) 26.4856 19.2429i 0.846485 0.615007i
\(980\) 0 0
\(981\) −13.3300 9.68480i −0.425594 0.309212i
\(982\) −1.90400 −0.0607591
\(983\) 21.7641 + 15.8125i 0.694166 + 0.504341i 0.878027 0.478611i \(-0.158860\pi\)
−0.183861 + 0.982952i \(0.558860\pi\)
\(984\) −1.20629 + 3.71257i −0.0384551 + 0.118353i
\(985\) 0 0
\(986\) −1.61979 4.98519i −0.0515845 0.158761i
\(987\) −1.03202 + 3.17622i −0.0328494 + 0.101100i
\(988\) 5.68646 17.5011i 0.180910 0.556785i
\(989\) −4.71243 14.5034i −0.149847 0.461180i
\(990\) 0 0
\(991\) 4.34725 13.3795i 0.138095 0.425013i −0.857964 0.513710i \(-0.828271\pi\)
0.996059 + 0.0886979i \(0.0282706\pi\)
\(992\) −29.4547 21.4001i −0.935189 0.679455i
\(993\) −16.7897 −0.532806
\(994\) 6.69798 + 4.86636i 0.212447 + 0.154352i
\(995\) 0 0
\(996\) −7.01247 + 5.09485i −0.222198 + 0.161437i
\(997\) 0.500493 0.363630i 0.0158508 0.0115163i −0.579832 0.814736i \(-0.696882\pi\)
0.595682 + 0.803220i \(0.296882\pi\)
\(998\) −9.37639 28.8575i −0.296804 0.913470i
\(999\) 31.9443 1.01067
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 625.2.d.q.126.2 16
5.2 odd 4 625.2.e.j.499.6 32
5.3 odd 4 625.2.e.j.499.3 32
5.4 even 2 625.2.d.m.126.3 16
25.2 odd 20 625.2.b.d.624.6 16
25.3 odd 20 625.2.e.j.124.6 32
25.4 even 10 625.2.d.m.501.3 16
25.6 even 5 625.2.d.p.376.3 16
25.8 odd 20 625.2.e.k.249.6 32
25.9 even 10 625.2.d.n.251.2 16
25.11 even 5 625.2.a.e.1.4 8
25.12 odd 20 625.2.e.k.374.6 32
25.13 odd 20 625.2.e.k.374.3 32
25.14 even 10 625.2.a.g.1.5 yes 8
25.16 even 5 625.2.d.p.251.3 16
25.17 odd 20 625.2.e.k.249.3 32
25.19 even 10 625.2.d.n.376.2 16
25.21 even 5 inner 625.2.d.q.501.2 16
25.22 odd 20 625.2.e.j.124.3 32
25.23 odd 20 625.2.b.d.624.11 16
75.11 odd 10 5625.2.a.be.1.5 8
75.14 odd 10 5625.2.a.s.1.4 8
100.11 odd 10 10000.2.a.bn.1.3 8
100.39 odd 10 10000.2.a.be.1.6 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
625.2.a.e.1.4 8 25.11 even 5
625.2.a.g.1.5 yes 8 25.14 even 10
625.2.b.d.624.6 16 25.2 odd 20
625.2.b.d.624.11 16 25.23 odd 20
625.2.d.m.126.3 16 5.4 even 2
625.2.d.m.501.3 16 25.4 even 10
625.2.d.n.251.2 16 25.9 even 10
625.2.d.n.376.2 16 25.19 even 10
625.2.d.p.251.3 16 25.16 even 5
625.2.d.p.376.3 16 25.6 even 5
625.2.d.q.126.2 16 1.1 even 1 trivial
625.2.d.q.501.2 16 25.21 even 5 inner
625.2.e.j.124.3 32 25.22 odd 20
625.2.e.j.124.6 32 25.3 odd 20
625.2.e.j.499.3 32 5.3 odd 4
625.2.e.j.499.6 32 5.2 odd 4
625.2.e.k.249.3 32 25.17 odd 20
625.2.e.k.249.6 32 25.8 odd 20
625.2.e.k.374.3 32 25.13 odd 20
625.2.e.k.374.6 32 25.12 odd 20
5625.2.a.s.1.4 8 75.14 odd 10
5625.2.a.be.1.5 8 75.11 odd 10
10000.2.a.be.1.6 8 100.39 odd 10
10000.2.a.bn.1.3 8 100.11 odd 10