Properties

Label 25.3.c.a.7.1
Level $25$
Weight $3$
Character 25.7
Analytic conductor $0.681$
Analytic rank $0$
Dimension $4$
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] = [25,3,Mod(7,25)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(25, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("25.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 25.c (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.681200660901\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 7.1
Root \(-1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 25.7
Dual form 25.3.c.a.18.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.22474 - 1.22474i) q^{2} +(1.22474 - 1.22474i) q^{3} -1.00000i q^{4} -3.00000 q^{6} +(4.89898 + 4.89898i) q^{7} +(-6.12372 + 6.12372i) q^{8} +6.00000i q^{9} +O(q^{10})\) \(q+(-1.22474 - 1.22474i) q^{2} +(1.22474 - 1.22474i) q^{3} -1.00000i q^{4} -3.00000 q^{6} +(4.89898 + 4.89898i) q^{7} +(-6.12372 + 6.12372i) q^{8} +6.00000i q^{9} -3.00000 q^{11} +(-1.22474 - 1.22474i) q^{12} +(7.34847 - 7.34847i) q^{13} -12.0000i q^{14} +11.0000 q^{16} +(-13.4722 - 13.4722i) q^{17} +(7.34847 - 7.34847i) q^{18} +5.00000i q^{19} +12.0000 q^{21} +(3.67423 + 3.67423i) q^{22} +(-17.1464 + 17.1464i) q^{23} +15.0000i q^{24} -18.0000 q^{26} +(18.3712 + 18.3712i) q^{27} +(4.89898 - 4.89898i) q^{28} -30.0000i q^{29} -38.0000 q^{31} +(11.0227 + 11.0227i) q^{32} +(-3.67423 + 3.67423i) q^{33} +33.0000i q^{34} +6.00000 q^{36} +(-19.5959 - 19.5959i) q^{37} +(6.12372 - 6.12372i) q^{38} -18.0000i q^{39} +57.0000 q^{41} +(-14.6969 - 14.6969i) q^{42} +(-4.89898 + 4.89898i) q^{43} +3.00000i q^{44} +42.0000 q^{46} +(-7.34847 - 7.34847i) q^{47} +(13.4722 - 13.4722i) q^{48} -1.00000i q^{49} -33.0000 q^{51} +(-7.34847 - 7.34847i) q^{52} +(31.8434 - 31.8434i) q^{53} -45.0000i q^{54} -60.0000 q^{56} +(6.12372 + 6.12372i) q^{57} +(-36.7423 + 36.7423i) q^{58} +90.0000i q^{59} -28.0000 q^{61} +(46.5403 + 46.5403i) q^{62} +(-29.3939 + 29.3939i) q^{63} -71.0000i q^{64} +9.00000 q^{66} +(47.7650 + 47.7650i) q^{67} +(-13.4722 + 13.4722i) q^{68} +42.0000i q^{69} +42.0000 q^{71} +(-36.7423 - 36.7423i) q^{72} +(13.4722 - 13.4722i) q^{73} +48.0000i q^{74} +5.00000 q^{76} +(-14.6969 - 14.6969i) q^{77} +(-22.0454 + 22.0454i) q^{78} -80.0000i q^{79} -9.00000 q^{81} +(-69.8105 - 69.8105i) q^{82} +(111.452 - 111.452i) q^{83} -12.0000i q^{84} +12.0000 q^{86} +(-36.7423 - 36.7423i) q^{87} +(18.3712 - 18.3712i) q^{88} -15.0000i q^{89} +72.0000 q^{91} +(17.1464 + 17.1464i) q^{92} +(-46.5403 + 46.5403i) q^{93} +18.0000i q^{94} +27.0000 q^{96} +(53.8888 + 53.8888i) q^{97} +(-1.22474 + 1.22474i) q^{98} -18.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 12 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 12 q^{6} - 12 q^{11} + 44 q^{16} + 48 q^{21} - 72 q^{26} - 152 q^{31} + 24 q^{36} + 228 q^{41} + 168 q^{46} - 132 q^{51} - 240 q^{56} - 112 q^{61} + 36 q^{66} + 168 q^{71} + 20 q^{76} - 36 q^{81} + 48 q^{86} + 288 q^{91} + 108 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 1.22474i −0.612372 0.612372i 0.331191 0.943564i \(-0.392549\pi\)
−0.943564 + 0.331191i \(0.892549\pi\)
\(3\) 1.22474 1.22474i 0.408248 0.408248i −0.472879 0.881127i \(-0.656785\pi\)
0.881127 + 0.472879i \(0.156785\pi\)
\(4\) 1.00000i 0.250000i
\(5\) 0 0
\(6\) −3.00000 −0.500000
\(7\) 4.89898 + 4.89898i 0.699854 + 0.699854i 0.964379 0.264525i \(-0.0852151\pi\)
−0.264525 + 0.964379i \(0.585215\pi\)
\(8\) −6.12372 + 6.12372i −0.765466 + 0.765466i
\(9\) 6.00000i 0.666667i
\(10\) 0 0
\(11\) −3.00000 −0.272727 −0.136364 0.990659i \(-0.543542\pi\)
−0.136364 + 0.990659i \(0.543542\pi\)
\(12\) −1.22474 1.22474i −0.102062 0.102062i
\(13\) 7.34847 7.34847i 0.565267 0.565267i −0.365532 0.930799i \(-0.619113\pi\)
0.930799 + 0.365532i \(0.119113\pi\)
\(14\) 12.0000i 0.857143i
\(15\) 0 0
\(16\) 11.0000 0.687500
\(17\) −13.4722 13.4722i −0.792482 0.792482i 0.189415 0.981897i \(-0.439341\pi\)
−0.981897 + 0.189415i \(0.939341\pi\)
\(18\) 7.34847 7.34847i 0.408248 0.408248i
\(19\) 5.00000i 0.263158i 0.991306 + 0.131579i \(0.0420047\pi\)
−0.991306 + 0.131579i \(0.957995\pi\)
\(20\) 0 0
\(21\) 12.0000 0.571429
\(22\) 3.67423 + 3.67423i 0.167011 + 0.167011i
\(23\) −17.1464 + 17.1464i −0.745497 + 0.745497i −0.973630 0.228133i \(-0.926738\pi\)
0.228133 + 0.973630i \(0.426738\pi\)
\(24\) 15.0000i 0.625000i
\(25\) 0 0
\(26\) −18.0000 −0.692308
\(27\) 18.3712 + 18.3712i 0.680414 + 0.680414i
\(28\) 4.89898 4.89898i 0.174964 0.174964i
\(29\) 30.0000i 1.03448i −0.855840 0.517241i \(-0.826959\pi\)
0.855840 0.517241i \(-0.173041\pi\)
\(30\) 0 0
\(31\) −38.0000 −1.22581 −0.612903 0.790158i \(-0.709998\pi\)
−0.612903 + 0.790158i \(0.709998\pi\)
\(32\) 11.0227 + 11.0227i 0.344459 + 0.344459i
\(33\) −3.67423 + 3.67423i −0.111340 + 0.111340i
\(34\) 33.0000i 0.970588i
\(35\) 0 0
\(36\) 6.00000 0.166667
\(37\) −19.5959 19.5959i −0.529619 0.529619i 0.390839 0.920459i \(-0.372185\pi\)
−0.920459 + 0.390839i \(0.872185\pi\)
\(38\) 6.12372 6.12372i 0.161151 0.161151i
\(39\) 18.0000i 0.461538i
\(40\) 0 0
\(41\) 57.0000 1.39024 0.695122 0.718892i \(-0.255350\pi\)
0.695122 + 0.718892i \(0.255350\pi\)
\(42\) −14.6969 14.6969i −0.349927 0.349927i
\(43\) −4.89898 + 4.89898i −0.113930 + 0.113930i −0.761773 0.647844i \(-0.775671\pi\)
0.647844 + 0.761773i \(0.275671\pi\)
\(44\) 3.00000i 0.0681818i
\(45\) 0 0
\(46\) 42.0000 0.913043
\(47\) −7.34847 7.34847i −0.156350 0.156350i 0.624597 0.780947i \(-0.285263\pi\)
−0.780947 + 0.624597i \(0.785263\pi\)
\(48\) 13.4722 13.4722i 0.280671 0.280671i
\(49\) 1.00000i 0.0204082i
\(50\) 0 0
\(51\) −33.0000 −0.647059
\(52\) −7.34847 7.34847i −0.141317 0.141317i
\(53\) 31.8434 31.8434i 0.600818 0.600818i −0.339711 0.940530i \(-0.610329\pi\)
0.940530 + 0.339711i \(0.110329\pi\)
\(54\) 45.0000i 0.833333i
\(55\) 0 0
\(56\) −60.0000 −1.07143
\(57\) 6.12372 + 6.12372i 0.107434 + 0.107434i
\(58\) −36.7423 + 36.7423i −0.633489 + 0.633489i
\(59\) 90.0000i 1.52542i 0.646738 + 0.762712i \(0.276133\pi\)
−0.646738 + 0.762712i \(0.723867\pi\)
\(60\) 0 0
\(61\) −28.0000 −0.459016 −0.229508 0.973307i \(-0.573712\pi\)
−0.229508 + 0.973307i \(0.573712\pi\)
\(62\) 46.5403 + 46.5403i 0.750650 + 0.750650i
\(63\) −29.3939 + 29.3939i −0.466569 + 0.466569i
\(64\) 71.0000i 1.10938i
\(65\) 0 0
\(66\) 9.00000 0.136364
\(67\) 47.7650 + 47.7650i 0.712911 + 0.712911i 0.967143 0.254232i \(-0.0818227\pi\)
−0.254232 + 0.967143i \(0.581823\pi\)
\(68\) −13.4722 + 13.4722i −0.198120 + 0.198120i
\(69\) 42.0000i 0.608696i
\(70\) 0 0
\(71\) 42.0000 0.591549 0.295775 0.955258i \(-0.404422\pi\)
0.295775 + 0.955258i \(0.404422\pi\)
\(72\) −36.7423 36.7423i −0.510310 0.510310i
\(73\) 13.4722 13.4722i 0.184551 0.184551i −0.608785 0.793335i \(-0.708343\pi\)
0.793335 + 0.608785i \(0.208343\pi\)
\(74\) 48.0000i 0.648649i
\(75\) 0 0
\(76\) 5.00000 0.0657895
\(77\) −14.6969 14.6969i −0.190869 0.190869i
\(78\) −22.0454 + 22.0454i −0.282633 + 0.282633i
\(79\) 80.0000i 1.01266i −0.862340 0.506329i \(-0.831002\pi\)
0.862340 0.506329i \(-0.168998\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) −69.8105 69.8105i −0.851347 0.851347i
\(83\) 111.452 111.452i 1.34279 1.34279i 0.449525 0.893268i \(-0.351593\pi\)
0.893268 0.449525i \(-0.148407\pi\)
\(84\) 12.0000i 0.142857i
\(85\) 0 0
\(86\) 12.0000 0.139535
\(87\) −36.7423 36.7423i −0.422326 0.422326i
\(88\) 18.3712 18.3712i 0.208763 0.208763i
\(89\) 15.0000i 0.168539i −0.996443 0.0842697i \(-0.973144\pi\)
0.996443 0.0842697i \(-0.0268557\pi\)
\(90\) 0 0
\(91\) 72.0000 0.791209
\(92\) 17.1464 + 17.1464i 0.186374 + 0.186374i
\(93\) −46.5403 + 46.5403i −0.500433 + 0.500433i
\(94\) 18.0000i 0.191489i
\(95\) 0 0
\(96\) 27.0000 0.281250
\(97\) 53.8888 + 53.8888i 0.555554 + 0.555554i 0.928039 0.372484i \(-0.121494\pi\)
−0.372484 + 0.928039i \(0.621494\pi\)
\(98\) −1.22474 + 1.22474i −0.0124974 + 0.0124974i
\(99\) 18.0000i 0.181818i
\(100\) 0 0
\(101\) −48.0000 −0.475248 −0.237624 0.971357i \(-0.576369\pi\)
−0.237624 + 0.971357i \(0.576369\pi\)
\(102\) 40.4166 + 40.4166i 0.396241 + 0.396241i
\(103\) −90.6311 + 90.6311i −0.879914 + 0.879914i −0.993525 0.113611i \(-0.963758\pi\)
0.113611 + 0.993525i \(0.463758\pi\)
\(104\) 90.0000i 0.865385i
\(105\) 0 0
\(106\) −78.0000 −0.735849
\(107\) −25.7196 25.7196i −0.240370 0.240370i 0.576633 0.817003i \(-0.304366\pi\)
−0.817003 + 0.576633i \(0.804366\pi\)
\(108\) 18.3712 18.3712i 0.170103 0.170103i
\(109\) 40.0000i 0.366972i 0.983022 + 0.183486i \(0.0587383\pi\)
−0.983022 + 0.183486i \(0.941262\pi\)
\(110\) 0 0
\(111\) −48.0000 −0.432432
\(112\) 53.8888 + 53.8888i 0.481150 + 0.481150i
\(113\) −84.5074 + 84.5074i −0.747853 + 0.747853i −0.974076 0.226223i \(-0.927362\pi\)
0.226223 + 0.974076i \(0.427362\pi\)
\(114\) 15.0000i 0.131579i
\(115\) 0 0
\(116\) −30.0000 −0.258621
\(117\) 44.0908 + 44.0908i 0.376845 + 0.376845i
\(118\) 110.227 110.227i 0.934127 0.934127i
\(119\) 132.000i 1.10924i
\(120\) 0 0
\(121\) −112.000 −0.925620
\(122\) 34.2929 + 34.2929i 0.281089 + 0.281089i
\(123\) 69.8105 69.8105i 0.567565 0.567565i
\(124\) 38.0000i 0.306452i
\(125\) 0 0
\(126\) 72.0000 0.571429
\(127\) −154.318 154.318i −1.21510 1.21510i −0.969327 0.245774i \(-0.920958\pi\)
−0.245774 0.969327i \(-0.579042\pi\)
\(128\) −42.8661 + 42.8661i −0.334891 + 0.334891i
\(129\) 12.0000i 0.0930233i
\(130\) 0 0
\(131\) 162.000 1.23664 0.618321 0.785926i \(-0.287813\pi\)
0.618321 + 0.785926i \(0.287813\pi\)
\(132\) 3.67423 + 3.67423i 0.0278351 + 0.0278351i
\(133\) −24.4949 + 24.4949i −0.184172 + 0.184172i
\(134\) 117.000i 0.873134i
\(135\) 0 0
\(136\) 165.000 1.21324
\(137\) −50.2145 50.2145i −0.366529 0.366529i 0.499680 0.866210i \(-0.333451\pi\)
−0.866210 + 0.499680i \(0.833451\pi\)
\(138\) 51.4393 51.4393i 0.372748 0.372748i
\(139\) 185.000i 1.33094i 0.746427 + 0.665468i \(0.231768\pi\)
−0.746427 + 0.665468i \(0.768232\pi\)
\(140\) 0 0
\(141\) −18.0000 −0.127660
\(142\) −51.4393 51.4393i −0.362248 0.362248i
\(143\) −22.0454 + 22.0454i −0.154164 + 0.154164i
\(144\) 66.0000i 0.458333i
\(145\) 0 0
\(146\) −33.0000 −0.226027
\(147\) −1.22474 1.22474i −0.00833160 0.00833160i
\(148\) −19.5959 + 19.5959i −0.132405 + 0.132405i
\(149\) 150.000i 1.00671i −0.864079 0.503356i \(-0.832099\pi\)
0.864079 0.503356i \(-0.167901\pi\)
\(150\) 0 0
\(151\) 52.0000 0.344371 0.172185 0.985065i \(-0.444917\pi\)
0.172185 + 0.985065i \(0.444917\pi\)
\(152\) −30.6186 30.6186i −0.201438 0.201438i
\(153\) 80.8332 80.8332i 0.528321 0.528321i
\(154\) 36.0000i 0.233766i
\(155\) 0 0
\(156\) −18.0000 −0.115385
\(157\) 188.611 + 188.611i 1.20134 + 1.20134i 0.973759 + 0.227584i \(0.0730825\pi\)
0.227584 + 0.973759i \(0.426918\pi\)
\(158\) −97.9796 + 97.9796i −0.620124 + 0.620124i
\(159\) 78.0000i 0.490566i
\(160\) 0 0
\(161\) −168.000 −1.04348
\(162\) 11.0227 + 11.0227i 0.0680414 + 0.0680414i
\(163\) 99.2043 99.2043i 0.608616 0.608616i −0.333969 0.942584i \(-0.608388\pi\)
0.942584 + 0.333969i \(0.108388\pi\)
\(164\) 57.0000i 0.347561i
\(165\) 0 0
\(166\) −273.000 −1.64458
\(167\) 17.1464 + 17.1464i 0.102673 + 0.102673i 0.756577 0.653904i \(-0.226870\pi\)
−0.653904 + 0.756577i \(0.726870\pi\)
\(168\) −73.4847 + 73.4847i −0.437409 + 0.437409i
\(169\) 61.0000i 0.360947i
\(170\) 0 0
\(171\) −30.0000 −0.175439
\(172\) 4.89898 + 4.89898i 0.0284824 + 0.0284824i
\(173\) −78.3837 + 78.3837i −0.453085 + 0.453085i −0.896377 0.443292i \(-0.853810\pi\)
0.443292 + 0.896377i \(0.353810\pi\)
\(174\) 90.0000i 0.517241i
\(175\) 0 0
\(176\) −33.0000 −0.187500
\(177\) 110.227 + 110.227i 0.622752 + 0.622752i
\(178\) −18.3712 + 18.3712i −0.103209 + 0.103209i
\(179\) 195.000i 1.08939i 0.838636 + 0.544693i \(0.183354\pi\)
−0.838636 + 0.544693i \(0.816646\pi\)
\(180\) 0 0
\(181\) 262.000 1.44751 0.723757 0.690055i \(-0.242414\pi\)
0.723757 + 0.690055i \(0.242414\pi\)
\(182\) −88.1816 88.1816i −0.484514 0.484514i
\(183\) −34.2929 + 34.2929i −0.187393 + 0.187393i
\(184\) 210.000i 1.14130i
\(185\) 0 0
\(186\) 114.000 0.612903
\(187\) 40.4166 + 40.4166i 0.216131 + 0.216131i
\(188\) −7.34847 + 7.34847i −0.0390876 + 0.0390876i
\(189\) 180.000i 0.952381i
\(190\) 0 0
\(191\) −18.0000 −0.0942408 −0.0471204 0.998889i \(-0.515004\pi\)
−0.0471204 + 0.998889i \(0.515004\pi\)
\(192\) −86.9569 86.9569i −0.452900 0.452900i
\(193\) 86.9569 86.9569i 0.450554 0.450554i −0.444984 0.895538i \(-0.646791\pi\)
0.895538 + 0.444984i \(0.146791\pi\)
\(194\) 132.000i 0.680412i
\(195\) 0 0
\(196\) −1.00000 −0.00510204
\(197\) −129.823 129.823i −0.659000 0.659000i 0.296144 0.955143i \(-0.404299\pi\)
−0.955143 + 0.296144i \(0.904299\pi\)
\(198\) −22.0454 + 22.0454i −0.111340 + 0.111340i
\(199\) 200.000i 1.00503i −0.864570 0.502513i \(-0.832409\pi\)
0.864570 0.502513i \(-0.167591\pi\)
\(200\) 0 0
\(201\) 117.000 0.582090
\(202\) 58.7878 + 58.7878i 0.291028 + 0.291028i
\(203\) 146.969 146.969i 0.723987 0.723987i
\(204\) 33.0000i 0.161765i
\(205\) 0 0
\(206\) 222.000 1.07767
\(207\) −102.879 102.879i −0.496998 0.496998i
\(208\) 80.8332 80.8332i 0.388621 0.388621i
\(209\) 15.0000i 0.0717703i
\(210\) 0 0
\(211\) −103.000 −0.488152 −0.244076 0.969756i \(-0.578485\pi\)
−0.244076 + 0.969756i \(0.578485\pi\)
\(212\) −31.8434 31.8434i −0.150205 0.150205i
\(213\) 51.4393 51.4393i 0.241499 0.241499i
\(214\) 63.0000i 0.294393i
\(215\) 0 0
\(216\) −225.000 −1.04167
\(217\) −186.161 186.161i −0.857886 0.857886i
\(218\) 48.9898 48.9898i 0.224724 0.224724i
\(219\) 33.0000i 0.150685i
\(220\) 0 0
\(221\) −198.000 −0.895928
\(222\) 58.7878 + 58.7878i 0.264810 + 0.264810i
\(223\) −200.858 + 200.858i −0.900709 + 0.900709i −0.995497 0.0947882i \(-0.969783\pi\)
0.0947882 + 0.995497i \(0.469783\pi\)
\(224\) 108.000i 0.482143i
\(225\) 0 0
\(226\) 207.000 0.915929
\(227\) 274.343 + 274.343i 1.20856 + 1.20856i 0.971494 + 0.237065i \(0.0761854\pi\)
0.237065 + 0.971494i \(0.423815\pi\)
\(228\) 6.12372 6.12372i 0.0268584 0.0268584i
\(229\) 20.0000i 0.0873362i 0.999046 + 0.0436681i \(0.0139044\pi\)
−0.999046 + 0.0436681i \(0.986096\pi\)
\(230\) 0 0
\(231\) −36.0000 −0.155844
\(232\) 183.712 + 183.712i 0.791861 + 0.791861i
\(233\) −102.879 + 102.879i −0.441539 + 0.441539i −0.892529 0.450990i \(-0.851071\pi\)
0.450990 + 0.892529i \(0.351071\pi\)
\(234\) 108.000i 0.461538i
\(235\) 0 0
\(236\) 90.0000 0.381356
\(237\) −97.9796 97.9796i −0.413416 0.413416i
\(238\) −161.666 + 161.666i −0.679270 + 0.679270i
\(239\) 210.000i 0.878661i 0.898325 + 0.439331i \(0.144784\pi\)
−0.898325 + 0.439331i \(0.855216\pi\)
\(240\) 0 0
\(241\) −43.0000 −0.178423 −0.0892116 0.996013i \(-0.528435\pi\)
−0.0892116 + 0.996013i \(0.528435\pi\)
\(242\) 137.171 + 137.171i 0.566824 + 0.566824i
\(243\) −176.363 + 176.363i −0.725775 + 0.725775i
\(244\) 28.0000i 0.114754i
\(245\) 0 0
\(246\) −171.000 −0.695122
\(247\) 36.7423 + 36.7423i 0.148754 + 0.148754i
\(248\) 232.702 232.702i 0.938313 0.938313i
\(249\) 273.000i 1.09639i
\(250\) 0 0
\(251\) −123.000 −0.490040 −0.245020 0.969518i \(-0.578795\pi\)
−0.245020 + 0.969518i \(0.578795\pi\)
\(252\) 29.3939 + 29.3939i 0.116642 + 0.116642i
\(253\) 51.4393 51.4393i 0.203317 0.203317i
\(254\) 378.000i 1.48819i
\(255\) 0 0
\(256\) −179.000 −0.699219
\(257\) 4.89898 + 4.89898i 0.0190622 + 0.0190622i 0.716574 0.697511i \(-0.245709\pi\)
−0.697511 + 0.716574i \(0.745709\pi\)
\(258\) 14.6969 14.6969i 0.0569649 0.0569649i
\(259\) 192.000i 0.741313i
\(260\) 0 0
\(261\) 180.000 0.689655
\(262\) −198.409 198.409i −0.757285 0.757285i
\(263\) 7.34847 7.34847i 0.0279409 0.0279409i −0.692998 0.720939i \(-0.743711\pi\)
0.720939 + 0.692998i \(0.243711\pi\)
\(264\) 45.0000i 0.170455i
\(265\) 0 0
\(266\) 60.0000 0.225564
\(267\) −18.3712 18.3712i −0.0688059 0.0688059i
\(268\) 47.7650 47.7650i 0.178228 0.178228i
\(269\) 120.000i 0.446097i −0.974807 0.223048i \(-0.928399\pi\)
0.974807 0.223048i \(-0.0716008\pi\)
\(270\) 0 0
\(271\) −58.0000 −0.214022 −0.107011 0.994258i \(-0.534128\pi\)
−0.107011 + 0.994258i \(0.534128\pi\)
\(272\) −148.194 148.194i −0.544831 0.544831i
\(273\) 88.1816 88.1816i 0.323010 0.323010i
\(274\) 123.000i 0.448905i
\(275\) 0 0
\(276\) 42.0000 0.152174
\(277\) −276.792 276.792i −0.999250 0.999250i 0.000749391 1.00000i \(-0.499761\pi\)
−1.00000 0.000749391i \(0.999761\pi\)
\(278\) 226.578 226.578i 0.815028 0.815028i
\(279\) 228.000i 0.817204i
\(280\) 0 0
\(281\) 462.000 1.64413 0.822064 0.569395i \(-0.192822\pi\)
0.822064 + 0.569395i \(0.192822\pi\)
\(282\) 22.0454 + 22.0454i 0.0781752 + 0.0781752i
\(283\) −72.2599 + 72.2599i −0.255336 + 0.255336i −0.823154 0.567818i \(-0.807788\pi\)
0.567818 + 0.823154i \(0.307788\pi\)
\(284\) 42.0000i 0.147887i
\(285\) 0 0
\(286\) 54.0000 0.188811
\(287\) 279.242 + 279.242i 0.972968 + 0.972968i
\(288\) −66.1362 + 66.1362i −0.229640 + 0.229640i
\(289\) 74.0000i 0.256055i
\(290\) 0 0
\(291\) 132.000 0.453608
\(292\) −13.4722 13.4722i −0.0461376 0.0461376i
\(293\) −4.89898 + 4.89898i −0.0167201 + 0.0167201i −0.715417 0.698697i \(-0.753763\pi\)
0.698697 + 0.715417i \(0.253763\pi\)
\(294\) 3.00000i 0.0102041i
\(295\) 0 0
\(296\) 240.000 0.810811
\(297\) −55.1135 55.1135i −0.185567 0.185567i
\(298\) −183.712 + 183.712i −0.616482 + 0.616482i
\(299\) 252.000i 0.842809i
\(300\) 0 0
\(301\) −48.0000 −0.159468
\(302\) −63.6867 63.6867i −0.210883 0.210883i
\(303\) −58.7878 + 58.7878i −0.194019 + 0.194019i
\(304\) 55.0000i 0.180921i
\(305\) 0 0
\(306\) −198.000 −0.647059
\(307\) −86.9569 86.9569i −0.283247 0.283247i 0.551155 0.834403i \(-0.314187\pi\)
−0.834403 + 0.551155i \(0.814187\pi\)
\(308\) −14.6969 + 14.6969i −0.0477173 + 0.0477173i
\(309\) 222.000i 0.718447i
\(310\) 0 0
\(311\) −528.000 −1.69775 −0.848875 0.528594i \(-0.822719\pi\)
−0.848875 + 0.528594i \(0.822719\pi\)
\(312\) 110.227 + 110.227i 0.353292 + 0.353292i
\(313\) 191.060 191.060i 0.610416 0.610416i −0.332638 0.943054i \(-0.607939\pi\)
0.943054 + 0.332638i \(0.107939\pi\)
\(314\) 462.000i 1.47134i
\(315\) 0 0
\(316\) −80.0000 −0.253165
\(317\) 200.858 + 200.858i 0.633622 + 0.633622i 0.948975 0.315353i \(-0.102123\pi\)
−0.315353 + 0.948975i \(0.602123\pi\)
\(318\) −95.5301 + 95.5301i −0.300409 + 0.300409i
\(319\) 90.0000i 0.282132i
\(320\) 0 0
\(321\) −63.0000 −0.196262
\(322\) 205.757 + 205.757i 0.638997 + 0.638997i
\(323\) 67.3610 67.3610i 0.208548 0.208548i
\(324\) 9.00000i 0.0277778i
\(325\) 0 0
\(326\) −243.000 −0.745399
\(327\) 48.9898 + 48.9898i 0.149816 + 0.149816i
\(328\) −349.052 + 349.052i −1.06418 + 1.06418i
\(329\) 72.0000i 0.218845i
\(330\) 0 0
\(331\) −313.000 −0.945619 −0.472810 0.881165i \(-0.656760\pi\)
−0.472810 + 0.881165i \(0.656760\pi\)
\(332\) −111.452 111.452i −0.335698 0.335698i
\(333\) 117.576 117.576i 0.353080 0.353080i
\(334\) 42.0000i 0.125749i
\(335\) 0 0
\(336\) 132.000 0.392857
\(337\) 194.734 + 194.734i 0.577847 + 0.577847i 0.934310 0.356463i \(-0.116017\pi\)
−0.356463 + 0.934310i \(0.616017\pi\)
\(338\) 74.7094 74.7094i 0.221034 0.221034i
\(339\) 207.000i 0.610619i
\(340\) 0 0
\(341\) 114.000 0.334311
\(342\) 36.7423 + 36.7423i 0.107434 + 0.107434i
\(343\) 244.949 244.949i 0.714137 0.714137i
\(344\) 60.0000i 0.174419i
\(345\) 0 0
\(346\) 192.000 0.554913
\(347\) −99.2043 99.2043i −0.285891 0.285891i 0.549562 0.835453i \(-0.314795\pi\)
−0.835453 + 0.549562i \(0.814795\pi\)
\(348\) −36.7423 + 36.7423i −0.105581 + 0.105581i
\(349\) 100.000i 0.286533i −0.989684 0.143266i \(-0.954239\pi\)
0.989684 0.143266i \(-0.0457606\pi\)
\(350\) 0 0
\(351\) 270.000 0.769231
\(352\) −33.0681 33.0681i −0.0939435 0.0939435i
\(353\) −396.817 + 396.817i −1.12413 + 1.12413i −0.133014 + 0.991114i \(0.542466\pi\)
−0.991114 + 0.133014i \(0.957534\pi\)
\(354\) 270.000i 0.762712i
\(355\) 0 0
\(356\) −15.0000 −0.0421348
\(357\) −161.666 161.666i −0.452847 0.452847i
\(358\) 238.825 238.825i 0.667110 0.667110i
\(359\) 540.000i 1.50418i 0.659061 + 0.752089i \(0.270954\pi\)
−0.659061 + 0.752089i \(0.729046\pi\)
\(360\) 0 0
\(361\) 336.000 0.930748
\(362\) −320.883 320.883i −0.886418 0.886418i
\(363\) −137.171 + 137.171i −0.377883 + 0.377883i
\(364\) 72.0000i 0.197802i
\(365\) 0 0
\(366\) 84.0000 0.229508
\(367\) −44.0908 44.0908i −0.120138 0.120138i 0.644481 0.764620i \(-0.277073\pi\)
−0.764620 + 0.644481i \(0.777073\pi\)
\(368\) −188.611 + 188.611i −0.512529 + 0.512529i
\(369\) 342.000i 0.926829i
\(370\) 0 0
\(371\) 312.000 0.840970
\(372\) 46.5403 + 46.5403i 0.125108 + 0.125108i
\(373\) 350.277 350.277i 0.939081 0.939081i −0.0591675 0.998248i \(-0.518845\pi\)
0.998248 + 0.0591675i \(0.0188446\pi\)
\(374\) 99.0000i 0.264706i
\(375\) 0 0
\(376\) 90.0000 0.239362
\(377\) −220.454 220.454i −0.584759 0.584759i
\(378\) 220.454 220.454i 0.583212 0.583212i
\(379\) 505.000i 1.33245i −0.745749 0.666227i \(-0.767908\pi\)
0.745749 0.666227i \(-0.232092\pi\)
\(380\) 0 0
\(381\) −378.000 −0.992126
\(382\) 22.0454 + 22.0454i 0.0577105 + 0.0577105i
\(383\) 142.070 142.070i 0.370941 0.370941i −0.496879 0.867820i \(-0.665521\pi\)
0.867820 + 0.496879i \(0.165521\pi\)
\(384\) 105.000i 0.273438i
\(385\) 0 0
\(386\) −213.000 −0.551813
\(387\) −29.3939 29.3939i −0.0759532 0.0759532i
\(388\) 53.8888 53.8888i 0.138889 0.138889i
\(389\) 690.000i 1.77378i −0.461982 0.886889i \(-0.652861\pi\)
0.461982 0.886889i \(-0.347139\pi\)
\(390\) 0 0
\(391\) 462.000 1.18159
\(392\) 6.12372 + 6.12372i 0.0156217 + 0.0156217i
\(393\) 198.409 198.409i 0.504857 0.504857i
\(394\) 318.000i 0.807107i
\(395\) 0 0
\(396\) −18.0000 −0.0454545
\(397\) 421.312 + 421.312i 1.06124 + 1.06124i 0.997998 + 0.0632416i \(0.0201439\pi\)
0.0632416 + 0.997998i \(0.479856\pi\)
\(398\) −244.949 + 244.949i −0.615450 + 0.615450i
\(399\) 60.0000i 0.150376i
\(400\) 0 0
\(401\) −573.000 −1.42893 −0.714464 0.699672i \(-0.753329\pi\)
−0.714464 + 0.699672i \(0.753329\pi\)
\(402\) −143.295 143.295i −0.356456 0.356456i
\(403\) −279.242 + 279.242i −0.692908 + 0.692908i
\(404\) 48.0000i 0.118812i
\(405\) 0 0
\(406\) −360.000 −0.886700
\(407\) 58.7878 + 58.7878i 0.144442 + 0.144442i
\(408\) 202.083 202.083i 0.495301 0.495301i
\(409\) 365.000i 0.892421i 0.894928 + 0.446210i \(0.147227\pi\)
−0.894928 + 0.446210i \(0.852773\pi\)
\(410\) 0 0
\(411\) −123.000 −0.299270
\(412\) 90.6311 + 90.6311i 0.219978 + 0.219978i
\(413\) −440.908 + 440.908i −1.06757 + 1.06757i
\(414\) 252.000i 0.608696i
\(415\) 0 0
\(416\) 162.000 0.389423
\(417\) 226.578 + 226.578i 0.543352 + 0.543352i
\(418\) −18.3712 + 18.3712i −0.0439502 + 0.0439502i
\(419\) 645.000i 1.53938i −0.638418 0.769690i \(-0.720411\pi\)
0.638418 0.769690i \(-0.279589\pi\)
\(420\) 0 0
\(421\) −8.00000 −0.0190024 −0.00950119 0.999955i \(-0.503024\pi\)
−0.00950119 + 0.999955i \(0.503024\pi\)
\(422\) 126.149 + 126.149i 0.298931 + 0.298931i
\(423\) 44.0908 44.0908i 0.104234 0.104234i
\(424\) 390.000i 0.919811i
\(425\) 0 0
\(426\) −126.000 −0.295775
\(427\) −137.171 137.171i −0.321245 0.321245i
\(428\) −25.7196 + 25.7196i −0.0600926 + 0.0600926i
\(429\) 54.0000i 0.125874i
\(430\) 0 0
\(431\) 12.0000 0.0278422 0.0139211 0.999903i \(-0.495569\pi\)
0.0139211 + 0.999903i \(0.495569\pi\)
\(432\) 202.083 + 202.083i 0.467784 + 0.467784i
\(433\) −439.683 + 439.683i −1.01544 + 1.01544i −0.0155561 + 0.999879i \(0.504952\pi\)
−0.999879 + 0.0155561i \(0.995048\pi\)
\(434\) 456.000i 1.05069i
\(435\) 0 0
\(436\) 40.0000 0.0917431
\(437\) −85.7321 85.7321i −0.196183 0.196183i
\(438\) −40.4166 + 40.4166i −0.0922753 + 0.0922753i
\(439\) 10.0000i 0.0227790i 0.999935 + 0.0113895i \(0.00362548\pi\)
−0.999935 + 0.0113895i \(0.996375\pi\)
\(440\) 0 0
\(441\) 6.00000 0.0136054
\(442\) 242.499 + 242.499i 0.548641 + 0.548641i
\(443\) 86.9569 86.9569i 0.196291 0.196291i −0.602117 0.798408i \(-0.705676\pi\)
0.798408 + 0.602117i \(0.205676\pi\)
\(444\) 48.0000i 0.108108i
\(445\) 0 0
\(446\) 492.000 1.10314
\(447\) −183.712 183.712i −0.410988 0.410988i
\(448\) 347.828 347.828i 0.776401 0.776401i
\(449\) 75.0000i 0.167038i −0.996506 0.0835189i \(-0.973384\pi\)
0.996506 0.0835189i \(-0.0266159\pi\)
\(450\) 0 0
\(451\) −171.000 −0.379157
\(452\) 84.5074 + 84.5074i 0.186963 + 0.186963i
\(453\) 63.6867 63.6867i 0.140589 0.140589i
\(454\) 672.000i 1.48018i
\(455\) 0 0
\(456\) −75.0000 −0.164474
\(457\) −209.431 209.431i −0.458274 0.458274i 0.439814 0.898089i \(-0.355044\pi\)
−0.898089 + 0.439814i \(0.855044\pi\)
\(458\) 24.4949 24.4949i 0.0534823 0.0534823i
\(459\) 495.000i 1.07843i
\(460\) 0 0
\(461\) −228.000 −0.494577 −0.247289 0.968942i \(-0.579540\pi\)
−0.247289 + 0.968942i \(0.579540\pi\)
\(462\) 44.0908 + 44.0908i 0.0954347 + 0.0954347i
\(463\) 436.009 436.009i 0.941704 0.941704i −0.0566875 0.998392i \(-0.518054\pi\)
0.998392 + 0.0566875i \(0.0180539\pi\)
\(464\) 330.000i 0.711207i
\(465\) 0 0
\(466\) 252.000 0.540773
\(467\) −533.989 533.989i −1.14344 1.14344i −0.987816 0.155629i \(-0.950259\pi\)
−0.155629 0.987816i \(-0.549741\pi\)
\(468\) 44.0908 44.0908i 0.0942111 0.0942111i
\(469\) 468.000i 0.997868i
\(470\) 0 0
\(471\) 462.000 0.980892
\(472\) −551.135 551.135i −1.16766 1.16766i
\(473\) 14.6969 14.6969i 0.0310718 0.0310718i
\(474\) 240.000i 0.506329i
\(475\) 0 0
\(476\) −132.000 −0.277311
\(477\) 191.060 + 191.060i 0.400545 + 0.400545i
\(478\) 257.196 257.196i 0.538068 0.538068i
\(479\) 270.000i 0.563674i 0.959462 + 0.281837i \(0.0909438\pi\)
−0.959462 + 0.281837i \(0.909056\pi\)
\(480\) 0 0
\(481\) −288.000 −0.598753
\(482\) 52.6640 + 52.6640i 0.109261 + 0.109261i
\(483\) −205.757 + 205.757i −0.425998 + 0.425998i
\(484\) 112.000i 0.231405i
\(485\) 0 0
\(486\) 432.000 0.888889
\(487\) −80.8332 80.8332i −0.165982 0.165982i 0.619229 0.785211i \(-0.287445\pi\)
−0.785211 + 0.619229i \(0.787445\pi\)
\(488\) 171.464 171.464i 0.351361 0.351361i
\(489\) 243.000i 0.496933i
\(490\) 0 0
\(491\) 582.000 1.18534 0.592668 0.805447i \(-0.298075\pi\)
0.592668 + 0.805447i \(0.298075\pi\)
\(492\) −69.8105 69.8105i −0.141891 0.141891i
\(493\) −404.166 + 404.166i −0.819809 + 0.819809i
\(494\) 90.0000i 0.182186i
\(495\) 0 0
\(496\) −418.000 −0.842742
\(497\) 205.757 + 205.757i 0.413998 + 0.413998i
\(498\) −334.355 + 334.355i −0.671396 + 0.671396i
\(499\) 250.000i 0.501002i 0.968116 + 0.250501i \(0.0805953\pi\)
−0.968116 + 0.250501i \(0.919405\pi\)
\(500\) 0 0
\(501\) 42.0000 0.0838323
\(502\) 150.644 + 150.644i 0.300087 + 0.300087i
\(503\) 460.504 460.504i 0.915515 0.915515i −0.0811841 0.996699i \(-0.525870\pi\)
0.996699 + 0.0811841i \(0.0258702\pi\)
\(504\) 360.000i 0.714286i
\(505\) 0 0
\(506\) −126.000 −0.249012
\(507\) 74.7094 + 74.7094i 0.147356 + 0.147356i
\(508\) −154.318 + 154.318i −0.303775 + 0.303775i
\(509\) 390.000i 0.766208i 0.923705 + 0.383104i \(0.125145\pi\)
−0.923705 + 0.383104i \(0.874855\pi\)
\(510\) 0 0
\(511\) 132.000 0.258317
\(512\) 390.694 + 390.694i 0.763073 + 0.763073i
\(513\) −91.8559 + 91.8559i −0.179056 + 0.179056i
\(514\) 12.0000i 0.0233463i
\(515\) 0 0
\(516\) 12.0000 0.0232558
\(517\) 22.0454 + 22.0454i 0.0426410 + 0.0426410i
\(518\) −235.151 + 235.151i −0.453959 + 0.453959i
\(519\) 192.000i 0.369942i
\(520\) 0 0
\(521\) −183.000 −0.351248 −0.175624 0.984457i \(-0.556194\pi\)
−0.175624 + 0.984457i \(0.556194\pi\)
\(522\) −220.454 220.454i −0.422326 0.422326i
\(523\) −476.426 + 476.426i −0.910948 + 0.910948i −0.996347 0.0853989i \(-0.972784\pi\)
0.0853989 + 0.996347i \(0.472784\pi\)
\(524\) 162.000i 0.309160i
\(525\) 0 0
\(526\) −18.0000 −0.0342205
\(527\) 511.943 + 511.943i 0.971430 + 0.971430i
\(528\) −40.4166 + 40.4166i −0.0765466 + 0.0765466i
\(529\) 59.0000i 0.111531i
\(530\) 0 0
\(531\) −540.000 −1.01695
\(532\) 24.4949 + 24.4949i 0.0460430 + 0.0460430i
\(533\) 418.863 418.863i 0.785859 0.785859i
\(534\) 45.0000i 0.0842697i
\(535\) 0 0
\(536\) −585.000 −1.09142
\(537\) 238.825 + 238.825i 0.444740 + 0.444740i
\(538\) −146.969 + 146.969i −0.273177 + 0.273177i
\(539\) 3.00000i 0.00556586i
\(540\) 0 0
\(541\) −568.000 −1.04991 −0.524954 0.851131i \(-0.675917\pi\)
−0.524954 + 0.851131i \(0.675917\pi\)
\(542\) 71.0352 + 71.0352i 0.131061 + 0.131061i
\(543\) 320.883 320.883i 0.590945 0.590945i
\(544\) 297.000i 0.545956i
\(545\) 0 0
\(546\) −216.000 −0.395604
\(547\) −160.442 160.442i −0.293312 0.293312i 0.545075 0.838387i \(-0.316501\pi\)
−0.838387 + 0.545075i \(0.816501\pi\)
\(548\) −50.2145 + 50.2145i −0.0916324 + 0.0916324i
\(549\) 168.000i 0.306011i
\(550\) 0 0
\(551\) 150.000 0.272232
\(552\) −257.196 257.196i −0.465936 0.465936i
\(553\) 391.918 391.918i 0.708713 0.708713i
\(554\) 678.000i 1.22383i
\(555\) 0 0
\(556\) 185.000 0.332734
\(557\) 66.1362 + 66.1362i 0.118736 + 0.118736i 0.763978 0.645242i \(-0.223243\pi\)
−0.645242 + 0.763978i \(0.723243\pi\)
\(558\) −279.242 + 279.242i −0.500433 + 0.500433i
\(559\) 72.0000i 0.128801i
\(560\) 0 0
\(561\) 99.0000 0.176471
\(562\) −565.832 565.832i −1.00682 1.00682i
\(563\) 191.060 191.060i 0.339361 0.339361i −0.516766 0.856127i \(-0.672864\pi\)
0.856127 + 0.516766i \(0.172864\pi\)
\(564\) 18.0000i 0.0319149i
\(565\) 0 0
\(566\) 177.000 0.312721
\(567\) −44.0908 44.0908i −0.0777616 0.0777616i
\(568\) −257.196 + 257.196i −0.452811 + 0.452811i
\(569\) 45.0000i 0.0790861i −0.999218 0.0395431i \(-0.987410\pi\)
0.999218 0.0395431i \(-0.0125902\pi\)
\(570\) 0 0
\(571\) 542.000 0.949212 0.474606 0.880198i \(-0.342591\pi\)
0.474606 + 0.880198i \(0.342591\pi\)
\(572\) 22.0454 + 22.0454i 0.0385409 + 0.0385409i
\(573\) −22.0454 + 22.0454i −0.0384737 + 0.0384737i
\(574\) 684.000i 1.19164i
\(575\) 0 0
\(576\) 426.000 0.739583
\(577\) 549.910 + 549.910i 0.953051 + 0.953051i 0.998946 0.0458952i \(-0.0146140\pi\)
−0.0458952 + 0.998946i \(0.514614\pi\)
\(578\) 90.6311 90.6311i 0.156801 0.156801i
\(579\) 213.000i 0.367876i
\(580\) 0 0
\(581\) 1092.00 1.87952
\(582\) −161.666 161.666i −0.277777 0.277777i
\(583\) −95.5301 + 95.5301i −0.163860 + 0.163860i
\(584\) 165.000i 0.282534i
\(585\) 0 0
\(586\) 12.0000 0.0204778
\(587\) −417.638 417.638i −0.711479 0.711479i 0.255366 0.966845i \(-0.417804\pi\)
−0.966845 + 0.255366i \(0.917804\pi\)
\(588\) −1.22474 + 1.22474i −0.00208290 + 0.00208290i
\(589\) 190.000i 0.322581i
\(590\) 0 0
\(591\) −318.000 −0.538071
\(592\) −215.555 215.555i −0.364113 0.364113i
\(593\) 331.906 331.906i 0.559706 0.559706i −0.369517 0.929224i \(-0.620477\pi\)
0.929224 + 0.369517i \(0.120477\pi\)
\(594\) 135.000i 0.227273i
\(595\) 0 0
\(596\) −150.000 −0.251678
\(597\) −244.949 244.949i −0.410300 0.410300i
\(598\) 308.636 308.636i 0.516113 0.516113i
\(599\) 900.000i 1.50250i 0.660015 + 0.751252i \(0.270550\pi\)
−0.660015 + 0.751252i \(0.729450\pi\)
\(600\) 0 0
\(601\) 577.000 0.960067 0.480033 0.877250i \(-0.340625\pi\)
0.480033 + 0.877250i \(0.340625\pi\)
\(602\) 58.7878 + 58.7878i 0.0976541 + 0.0976541i
\(603\) −286.590 + 286.590i −0.475274 + 0.475274i
\(604\) 52.0000i 0.0860927i
\(605\) 0 0
\(606\) 144.000 0.237624
\(607\) 127.373 + 127.373i 0.209841 + 0.209841i 0.804200 0.594359i \(-0.202594\pi\)
−0.594359 + 0.804200i \(0.702594\pi\)
\(608\) −55.1135 + 55.1135i −0.0906472 + 0.0906472i
\(609\) 360.000i 0.591133i
\(610\) 0 0
\(611\) −108.000 −0.176759
\(612\) −80.8332 80.8332i −0.132080 0.132080i
\(613\) −237.601 + 237.601i −0.387603 + 0.387603i −0.873832 0.486229i \(-0.838372\pi\)
0.486229 + 0.873832i \(0.338372\pi\)
\(614\) 213.000i 0.346906i
\(615\) 0 0
\(616\) 180.000 0.292208
\(617\) −656.463 656.463i −1.06396 1.06396i −0.997810 0.0661502i \(-0.978928\pi\)
−0.0661502 0.997810i \(-0.521072\pi\)
\(618\) 271.893 271.893i 0.439957 0.439957i
\(619\) 470.000i 0.759289i −0.925132 0.379645i \(-0.876046\pi\)
0.925132 0.379645i \(-0.123954\pi\)
\(620\) 0 0
\(621\) −630.000 −1.01449
\(622\) 646.665 + 646.665i 1.03965 + 1.03965i
\(623\) 73.4847 73.4847i 0.117953 0.117953i
\(624\) 198.000i 0.317308i
\(625\) 0 0
\(626\) −468.000 −0.747604
\(627\) −18.3712 18.3712i −0.0293001 0.0293001i
\(628\) 188.611 188.611i 0.300336 0.300336i
\(629\) 528.000i 0.839428i
\(630\) 0 0
\(631\) −838.000 −1.32805 −0.664025 0.747710i \(-0.731153\pi\)
−0.664025 + 0.747710i \(0.731153\pi\)
\(632\) 489.898 + 489.898i 0.775155 + 0.775155i
\(633\) −126.149 + 126.149i −0.199287 + 0.199287i
\(634\) 492.000i 0.776025i
\(635\) 0 0
\(636\) −78.0000 −0.122642
\(637\) −7.34847 7.34847i −0.0115361 0.0115361i
\(638\) 110.227 110.227i 0.172770 0.172770i
\(639\) 252.000i 0.394366i
\(640\) 0 0
\(641\) −618.000 −0.964119 −0.482059 0.876139i \(-0.660111\pi\)
−0.482059 + 0.876139i \(0.660111\pi\)
\(642\) 77.1589 + 77.1589i 0.120185 + 0.120185i
\(643\) −249.848 + 249.848i −0.388566 + 0.388566i −0.874176 0.485610i \(-0.838598\pi\)
0.485610 + 0.874176i \(0.338598\pi\)
\(644\) 168.000i 0.260870i
\(645\) 0 0
\(646\) −165.000 −0.255418
\(647\) 421.312 + 421.312i 0.651178 + 0.651178i 0.953277 0.302099i \(-0.0976872\pi\)
−0.302099 + 0.953277i \(0.597687\pi\)
\(648\) 55.1135 55.1135i 0.0850517 0.0850517i
\(649\) 270.000i 0.416025i
\(650\) 0 0
\(651\) −456.000 −0.700461
\(652\) −99.2043 99.2043i −0.152154 0.152154i
\(653\) −519.292 + 519.292i −0.795240 + 0.795240i −0.982341 0.187101i \(-0.940091\pi\)
0.187101 + 0.982341i \(0.440091\pi\)
\(654\) 120.000i 0.183486i
\(655\) 0 0
\(656\) 627.000 0.955793
\(657\) 80.8332 + 80.8332i 0.123034 + 0.123034i
\(658\) −88.1816 + 88.1816i −0.134015 + 0.134015i
\(659\) 885.000i 1.34294i −0.741030 0.671472i \(-0.765662\pi\)
0.741030 0.671472i \(-0.234338\pi\)
\(660\) 0 0
\(661\) 922.000 1.39486 0.697428 0.716655i \(-0.254328\pi\)
0.697428 + 0.716655i \(0.254328\pi\)
\(662\) 383.345 + 383.345i 0.579071 + 0.579071i
\(663\) −242.499 + 242.499i −0.365761 + 0.365761i
\(664\) 1365.00i 2.05572i
\(665\) 0 0
\(666\) −288.000 −0.432432
\(667\) 514.393 + 514.393i 0.771204 + 0.771204i
\(668\) 17.1464 17.1464i 0.0256683 0.0256683i
\(669\) 492.000i 0.735426i
\(670\) 0 0
\(671\) 84.0000 0.125186
\(672\) 132.272 + 132.272i 0.196834 + 0.196834i
\(673\) −78.3837 + 78.3837i −0.116469 + 0.116469i −0.762939 0.646470i \(-0.776244\pi\)
0.646470 + 0.762939i \(0.276244\pi\)
\(674\) 477.000i 0.707715i
\(675\) 0 0
\(676\) 61.0000 0.0902367
\(677\) −705.453 705.453i −1.04203 1.04203i −0.999077 0.0429510i \(-0.986324\pi\)
−0.0429510 0.999077i \(-0.513676\pi\)
\(678\) 253.522 253.522i 0.373927 0.373927i
\(679\) 528.000i 0.777614i
\(680\) 0 0
\(681\) 672.000 0.986784
\(682\) −139.621 139.621i −0.204723 0.204723i
\(683\) −133.497 + 133.497i −0.195457 + 0.195457i −0.798049 0.602592i \(-0.794135\pi\)
0.602592 + 0.798049i \(0.294135\pi\)
\(684\) 30.0000i 0.0438596i
\(685\) 0 0
\(686\) −600.000 −0.874636
\(687\) 24.4949 + 24.4949i 0.0356549 + 0.0356549i
\(688\) −53.8888 + 53.8888i −0.0783267 + 0.0783267i
\(689\) 468.000i 0.679245i
\(690\) 0 0
\(691\) −893.000 −1.29233 −0.646165 0.763198i \(-0.723628\pi\)
−0.646165 + 0.763198i \(0.723628\pi\)
\(692\) 78.3837 + 78.3837i 0.113271 + 0.113271i
\(693\) 88.1816 88.1816i 0.127246 0.127246i
\(694\) 243.000i 0.350144i
\(695\) 0 0
\(696\) 450.000 0.646552
\(697\) −767.915 767.915i −1.10174 1.10174i
\(698\) −122.474 + 122.474i −0.175465 + 0.175465i
\(699\) 252.000i 0.360515i
\(700\) 0 0
\(701\) 402.000 0.573466 0.286733 0.958010i \(-0.407431\pi\)
0.286733 + 0.958010i \(0.407431\pi\)
\(702\) −330.681 330.681i −0.471056 0.471056i
\(703\) 97.9796 97.9796i 0.139374 0.139374i
\(704\) 213.000i 0.302557i
\(705\) 0 0
\(706\) 972.000 1.37677
\(707\) −235.151 235.151i −0.332604 0.332604i
\(708\) 110.227 110.227i 0.155688 0.155688i
\(709\) 1060.00i 1.49506i −0.664226 0.747532i \(-0.731239\pi\)
0.664226 0.747532i \(-0.268761\pi\)
\(710\) 0 0
\(711\) 480.000 0.675105
\(712\) 91.8559 + 91.8559i 0.129011 + 0.129011i
\(713\) 651.564 651.564i 0.913835 0.913835i
\(714\) 396.000i 0.554622i
\(715\) 0 0
\(716\) 195.000 0.272346
\(717\) 257.196 + 257.196i 0.358712 + 0.358712i
\(718\) 661.362 661.362i 0.921117 0.921117i
\(719\) 1320.00i 1.83588i −0.396716 0.917942i \(-0.629850\pi\)
0.396716 0.917942i \(-0.370150\pi\)
\(720\) 0 0
\(721\) −888.000 −1.23162
\(722\) −411.514 411.514i −0.569964 0.569964i
\(723\) −52.6640 + 52.6640i −0.0728410 + 0.0728410i
\(724\) 262.000i 0.361878i
\(725\) 0 0
\(726\) 336.000 0.462810
\(727\) −31.8434 31.8434i −0.0438011 0.0438011i 0.684867 0.728668i \(-0.259860\pi\)
−0.728668 + 0.684867i \(0.759860\pi\)
\(728\) −440.908 + 440.908i −0.605643 + 0.605643i
\(729\) 351.000i 0.481481i
\(730\) 0 0
\(731\) 132.000 0.180575
\(732\) 34.2929 + 34.2929i 0.0468482 + 0.0468482i
\(733\) 815.680 815.680i 1.11280 1.11280i 0.120026 0.992771i \(-0.461702\pi\)
0.992771 0.120026i \(-0.0382978\pi\)
\(734\) 108.000i 0.147139i
\(735\) 0 0
\(736\) −378.000 −0.513587
\(737\) −143.295 143.295i −0.194430 0.194430i
\(738\) 418.863 418.863i 0.567565 0.567565i
\(739\) 710.000i 0.960758i 0.877061 + 0.480379i \(0.159501\pi\)
−0.877061 + 0.480379i \(0.840499\pi\)
\(740\) 0 0
\(741\) 90.0000 0.121457
\(742\) −382.120 382.120i −0.514987 0.514987i
\(743\) −800.983 + 800.983i −1.07804 + 1.07804i −0.0813540 + 0.996685i \(0.525924\pi\)
−0.996685 + 0.0813540i \(0.974076\pi\)
\(744\) 570.000i 0.766129i
\(745\) 0 0
\(746\) −858.000 −1.15013
\(747\) 668.711 + 668.711i 0.895195 + 0.895195i
\(748\) 40.4166 40.4166i 0.0540329 0.0540329i
\(749\) 252.000i 0.336449i
\(750\) 0 0
\(751\) 502.000 0.668442 0.334221 0.942495i \(-0.391527\pi\)
0.334221 + 0.942495i \(0.391527\pi\)
\(752\) −80.8332 80.8332i −0.107491 0.107491i
\(753\) −150.644 + 150.644i −0.200058 + 0.200058i
\(754\) 540.000i 0.716180i
\(755\) 0 0
\(756\) 180.000 0.238095
\(757\) 4.89898 + 4.89898i 0.00647157 + 0.00647157i 0.710335 0.703864i \(-0.248543\pi\)
−0.703864 + 0.710335i \(0.748543\pi\)
\(758\) −618.496 + 618.496i −0.815958 + 0.815958i
\(759\) 126.000i 0.166008i
\(760\) 0 0
\(761\) 747.000 0.981603 0.490802 0.871271i \(-0.336704\pi\)
0.490802 + 0.871271i \(0.336704\pi\)
\(762\) 462.954 + 462.954i 0.607551 + 0.607551i
\(763\) −195.959 + 195.959i −0.256827 + 0.256827i
\(764\) 18.0000i 0.0235602i
\(765\) 0 0
\(766\) −348.000 −0.454308
\(767\) 661.362 + 661.362i 0.862271 + 0.862271i
\(768\) −219.229 + 219.229i −0.285455 + 0.285455i
\(769\) 1255.00i 1.63199i 0.578059 + 0.815995i \(0.303810\pi\)
−0.578059 + 0.815995i \(0.696190\pi\)
\(770\) 0 0
\(771\) 12.0000 0.0155642
\(772\) −86.9569 86.9569i −0.112638 0.112638i
\(773\) −17.1464 + 17.1464i −0.0221817 + 0.0221817i −0.718111 0.695929i \(-0.754993\pi\)
0.695929 + 0.718111i \(0.254993\pi\)
\(774\) 72.0000i 0.0930233i
\(775\) 0 0
\(776\) −660.000 −0.850515
\(777\) −235.151 235.151i −0.302640 0.302640i
\(778\) −845.074 + 845.074i −1.08621 + 1.08621i
\(779\) 285.000i 0.365854i
\(780\) 0 0
\(781\) −126.000 −0.161332
\(782\) −565.832 565.832i −0.723570 0.723570i
\(783\) 551.135 551.135i 0.703876 0.703876i
\(784\) 11.0000i 0.0140306i
\(785\) 0 0
\(786\) −486.000 −0.618321
\(787\) 592.777 + 592.777i 0.753210 + 0.753210i 0.975077 0.221867i \(-0.0712150\pi\)
−0.221867 + 0.975077i \(0.571215\pi\)
\(788\) −129.823 + 129.823i −0.164750 + 0.164750i
\(789\) 18.0000i 0.0228137i
\(790\) 0 0
\(791\) −828.000 −1.04678
\(792\) 110.227 + 110.227i 0.139176 + 0.139176i
\(793\) −205.757 + 205.757i −0.259467 + 0.259467i
\(794\) 1032.00i 1.29975i
\(795\) 0 0
\(796\) −200.000 −0.251256
\(797\) 605.024 + 605.024i 0.759127 + 0.759127i 0.976163 0.217037i \(-0.0696391\pi\)
−0.217037 + 0.976163i \(0.569639\pi\)
\(798\) 73.4847 73.4847i 0.0920861 0.0920861i
\(799\) 198.000i 0.247810i
\(800\) 0 0
\(801\) 90.0000 0.112360
\(802\) 701.779 + 701.779i 0.875036 + 0.875036i
\(803\) −40.4166 + 40.4166i −0.0503320 + 0.0503320i
\(804\) 117.000i 0.145522i
\(805\) 0 0
\(806\) 684.000 0.848635
\(807\) −146.969 146.969i −0.182118 0.182118i
\(808\) 293.939 293.939i 0.363786 0.363786i
\(809\) 90.0000i 0.111248i 0.998452 + 0.0556242i \(0.0177149\pi\)
−0.998452 + 0.0556242i \(0.982285\pi\)
\(810\) 0 0
\(811\) −278.000 −0.342787 −0.171393 0.985203i \(-0.554827\pi\)
−0.171393 + 0.985203i \(0.554827\pi\)
\(812\) −146.969 146.969i −0.180997 0.180997i
\(813\) −71.0352 + 71.0352i −0.0873742 + 0.0873742i
\(814\) 144.000i 0.176904i
\(815\) 0 0
\(816\) −363.000 −0.444853
\(817\) −24.4949 24.4949i −0.0299815 0.0299815i
\(818\) 447.032 447.032i 0.546494 0.546494i
\(819\) 432.000i 0.527473i
\(820\) 0 0
\(821\) 42.0000 0.0511571 0.0255786 0.999673i \(-0.491857\pi\)
0.0255786 + 0.999673i \(0.491857\pi\)
\(822\) 150.644 + 150.644i 0.183265 + 0.183265i
\(823\) 778.938 778.938i 0.946461 0.946461i −0.0521765 0.998638i \(-0.516616\pi\)
0.998638 + 0.0521765i \(0.0166158\pi\)
\(824\) 1110.00i 1.34709i
\(825\) 0 0
\(826\) 1080.00 1.30751
\(827\) −674.834 674.834i −0.816003 0.816003i 0.169523 0.985526i \(-0.445777\pi\)
−0.985526 + 0.169523i \(0.945777\pi\)
\(828\) −102.879 + 102.879i −0.124249 + 0.124249i
\(829\) 170.000i 0.205066i 0.994730 + 0.102533i \(0.0326948\pi\)
−0.994730 + 0.102533i \(0.967305\pi\)
\(830\) 0 0
\(831\) −678.000 −0.815884
\(832\) −521.741 521.741i −0.627093 0.627093i
\(833\) −13.4722 + 13.4722i −0.0161731 + 0.0161731i
\(834\) 555.000i 0.665468i
\(835\) 0 0
\(836\) −15.0000 −0.0179426
\(837\) −698.105 698.105i −0.834056 0.834056i
\(838\) −789.960 + 789.960i −0.942674 + 0.942674i
\(839\) 360.000i 0.429082i 0.976715 + 0.214541i \(0.0688256\pi\)
−0.976715 + 0.214541i \(0.931174\pi\)
\(840\) 0 0
\(841\) −59.0000 −0.0701546
\(842\) 9.79796 + 9.79796i 0.0116365 + 0.0116365i
\(843\) 565.832 565.832i 0.671212 0.671212i
\(844\) 103.000i 0.122038i
\(845\) 0 0
\(846\) −108.000 −0.127660
\(847\) −548.686 548.686i −0.647799 0.647799i
\(848\) 350.277 350.277i 0.413063 0.413063i
\(849\) 177.000i 0.208481i
\(850\) 0 0
\(851\) 672.000 0.789659
\(852\) −51.4393 51.4393i −0.0603747 0.0603747i
\(853\) 521.741 521.741i 0.611655 0.611655i −0.331722 0.943377i \(-0.607630\pi\)
0.943377 + 0.331722i \(0.107630\pi\)
\(854\) 336.000i 0.393443i
\(855\) 0 0
\(856\) 315.000 0.367991
\(857\) 280.467 + 280.467i 0.327266 + 0.327266i 0.851546 0.524280i \(-0.175666\pi\)
−0.524280 + 0.851546i \(0.675666\pi\)
\(858\) 66.1362 66.1362i 0.0770818 0.0770818i
\(859\) 335.000i 0.389988i −0.980804 0.194994i \(-0.937531\pi\)
0.980804 0.194994i \(-0.0624688\pi\)
\(860\) 0 0
\(861\) 684.000 0.794425
\(862\) −14.6969 14.6969i −0.0170498 0.0170498i
\(863\) −849.973 + 849.973i −0.984905 + 0.984905i −0.999888 0.0149828i \(-0.995231\pi\)
0.0149828 + 0.999888i \(0.495231\pi\)
\(864\) 405.000i 0.468750i
\(865\) 0 0
\(866\) 1077.00 1.24365
\(867\) 90.6311 + 90.6311i 0.104534 + 0.104534i
\(868\) −186.161 + 186.161i −0.214471 + 0.214471i
\(869\) 240.000i 0.276180i
\(870\) 0 0
\(871\) 702.000 0.805970
\(872\) −244.949 244.949i −0.280905 0.280905i
\(873\) −323.333 + 323.333i −0.370370 + 0.370370i
\(874\) 210.000i 0.240275i
\(875\) 0 0
\(876\) −33.0000 −0.0376712
\(877\) 151.868 + 151.868i 0.173168 + 0.173168i 0.788370 0.615202i \(-0.210925\pi\)
−0.615202 + 0.788370i \(0.710925\pi\)
\(878\) 12.2474 12.2474i 0.0139493 0.0139493i
\(879\) 12.0000i 0.0136519i
\(880\) 0 0
\(881\) 162.000 0.183882 0.0919410 0.995764i \(-0.470693\pi\)
0.0919410 + 0.995764i \(0.470693\pi\)
\(882\) −7.34847 7.34847i −0.00833160 0.00833160i
\(883\) 295.164 295.164i 0.334274 0.334274i −0.519933 0.854207i \(-0.674043\pi\)
0.854207 + 0.519933i \(0.174043\pi\)
\(884\) 198.000i 0.223982i
\(885\) 0 0
\(886\) −213.000 −0.240406
\(887\) −509.494 509.494i −0.574401 0.574401i 0.358954 0.933355i \(-0.383133\pi\)
−0.933355 + 0.358954i \(0.883133\pi\)
\(888\) 293.939 293.939i 0.331012 0.331012i
\(889\) 1512.00i 1.70079i
\(890\) 0 0
\(891\) 27.0000 0.0303030
\(892\) 200.858 + 200.858i 0.225177 + 0.225177i
\(893\) 36.7423 36.7423i 0.0411448 0.0411448i
\(894\) 450.000i 0.503356i
\(895\) 0 0
\(896\) −420.000 −0.468750
\(897\) 308.636 + 308.636i 0.344075 + 0.344075i
\(898\) −91.8559 + 91.8559i −0.102289 + 0.102289i
\(899\) 1140.00i 1.26808i
\(900\) 0 0
\(901\) −858.000 −0.952275
\(902\) 209.431 + 209.431i 0.232186 + 0.232186i
\(903\) −58.7878 + 58.7878i −0.0651027 + 0.0651027i
\(904\) 1035.00i 1.14491i
\(905\) 0 0
\(906\) −156.000 −0.172185
\(907\) 494.797 + 494.797i 0.545531 + 0.545531i 0.925145 0.379614i \(-0.123943\pi\)
−0.379614 + 0.925145i \(0.623943\pi\)
\(908\) 274.343 274.343i 0.302140 0.302140i
\(909\) 288.000i 0.316832i
\(910\) 0 0
\(911\) −828.000 −0.908891 −0.454446 0.890774i \(-0.650163\pi\)
−0.454446 + 0.890774i \(0.650163\pi\)
\(912\) 67.3610 + 67.3610i 0.0738607 + 0.0738607i
\(913\) −334.355 + 334.355i −0.366216 + 0.366216i
\(914\) 513.000i 0.561269i
\(915\) 0 0
\(916\) 20.0000 0.0218341
\(917\) 793.635 + 793.635i 0.865469 + 0.865469i
\(918\) −606.249 + 606.249i −0.660402 + 0.660402i
\(919\) 1270.00i 1.38194i −0.722885 0.690968i \(-0.757184\pi\)
0.722885 0.690968i \(-0.242816\pi\)
\(920\) 0 0
\(921\) −213.000 −0.231270
\(922\) 279.242 + 279.242i 0.302865 + 0.302865i
\(923\) 308.636 308.636i 0.334383 0.334383i
\(924\) 36.0000i 0.0389610i
\(925\) 0 0
\(926\) −1068.00 −1.15335
\(927\) −543.787 543.787i −0.586609 0.586609i
\(928\) 330.681 330.681i 0.356337 0.356337i
\(929\) 570.000i 0.613563i 0.951780 + 0.306781i \(0.0992521\pi\)
−0.951780 + 0.306781i \(0.900748\pi\)
\(930\) 0 0
\(931\) 5.00000 0.00537057
\(932\) 102.879 + 102.879i 0.110385 + 0.110385i
\(933\) −646.665 + 646.665i −0.693103 + 0.693103i
\(934\) 1308.00i 1.40043i
\(935\) 0 0
\(936\) −540.000 −0.576923
\(937\) 317.209 + 317.209i 0.338537 + 0.338537i 0.855816 0.517280i \(-0.173055\pi\)
−0.517280 + 0.855816i \(0.673055\pi\)
\(938\) 573.181 573.181i 0.611067 0.611067i
\(939\) 468.000i 0.498403i
\(940\) 0 0
\(941\) −1518.00 −1.61318 −0.806589 0.591113i \(-0.798689\pi\)
−0.806589 + 0.591113i \(0.798689\pi\)
\(942\) −565.832 565.832i −0.600671 0.600671i
\(943\) −977.346 + 977.346i −1.03642 + 1.03642i
\(944\) 990.000i 1.04873i
\(945\) 0 0
\(946\) −36.0000 −0.0380550
\(947\) −436.009 436.009i −0.460411 0.460411i 0.438379 0.898790i \(-0.355553\pi\)
−0.898790 + 0.438379i \(0.855553\pi\)
\(948\) −97.9796 + 97.9796i −0.103354 + 0.103354i
\(949\) 198.000i 0.208641i
\(950\) 0 0
\(951\) 492.000 0.517350
\(952\) 808.332 + 808.332i 0.849088 + 0.849088i
\(953\) 429.885 429.885i 0.451087 0.451087i −0.444629 0.895715i \(-0.646664\pi\)
0.895715 + 0.444629i \(0.146664\pi\)
\(954\) 468.000i 0.490566i
\(955\) 0 0
\(956\) 210.000 0.219665
\(957\) 110.227 + 110.227i 0.115180 + 0.115180i
\(958\) 330.681 330.681i 0.345179 0.345179i
\(959\) 492.000i 0.513034i
\(960\) 0 0
\(961\) 483.000 0.502601
\(962\) 352.727 + 352.727i 0.366660 + 0.366660i
\(963\) 154.318 154.318i 0.160247 0.160247i
\(964\) 43.0000i 0.0446058i
\(965\) 0 0
\(966\) 504.000 0.521739
\(967\) −533.989 533.989i −0.552212 0.552212i 0.374867 0.927079i \(-0.377688\pi\)
−0.927079 + 0.374867i \(0.877688\pi\)
\(968\) 685.857 685.857i 0.708530 0.708530i
\(969\) 165.000i 0.170279i
\(970\) 0 0
\(971\) 1467.00 1.51081 0.755407 0.655256i \(-0.227439\pi\)
0.755407 + 0.655256i \(0.227439\pi\)
\(972\) 176.363 + 176.363i 0.181444 + 0.181444i
\(973\) −906.311 + 906.311i −0.931461 + 0.931461i
\(974\) 198.000i 0.203285i
\(975\) 0 0
\(976\) −308.000 −0.315574
\(977\) 1039.81 + 1039.81i 1.06429 + 1.06429i 0.997786 + 0.0665006i \(0.0211834\pi\)
0.0665006 + 0.997786i \(0.478817\pi\)
\(978\) −297.613 + 297.613i −0.304308 + 0.304308i
\(979\) 45.0000i 0.0459653i
\(980\) 0 0
\(981\) −240.000 −0.244648
\(982\) −712.802 712.802i −0.725867 0.725867i
\(983\) −715.251 + 715.251i −0.727621 + 0.727621i −0.970145 0.242525i \(-0.922024\pi\)
0.242525 + 0.970145i \(0.422024\pi\)
\(984\) 855.000i 0.868902i
\(985\) 0 0
\(986\) 990.000 1.00406
\(987\) −88.1816 88.1816i −0.0893431 0.0893431i
\(988\) 36.7423 36.7423i 0.0371886 0.0371886i
\(989\) 168.000i 0.169869i
\(990\) 0 0
\(991\) 1832.00 1.84864 0.924319 0.381621i \(-0.124634\pi\)
0.924319 + 0.381621i \(0.124634\pi\)
\(992\) −418.863 418.863i −0.422241 0.422241i
\(993\) −383.345 + 383.345i −0.386047 + 0.386047i
\(994\) 504.000i 0.507042i
\(995\) 0 0
\(996\) −273.000 −0.274096
\(997\) −1293.33 1293.33i −1.29722 1.29722i −0.930220 0.367002i \(-0.880384\pi\)
−0.367002 0.930220i \(-0.619616\pi\)
\(998\) 306.186 306.186i 0.306800 0.306800i
\(999\) 720.000i 0.720721i
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 25.3.c.a.7.1 4
3.2 odd 2 225.3.g.e.82.2 4
4.3 odd 2 400.3.p.j.257.1 4
5.2 odd 4 inner 25.3.c.a.18.2 yes 4
5.3 odd 4 inner 25.3.c.a.18.1 yes 4
5.4 even 2 inner 25.3.c.a.7.2 yes 4
15.2 even 4 225.3.g.e.118.1 4
15.8 even 4 225.3.g.e.118.2 4
15.14 odd 2 225.3.g.e.82.1 4
20.3 even 4 400.3.p.j.193.1 4
20.7 even 4 400.3.p.j.193.2 4
20.19 odd 2 400.3.p.j.257.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
25.3.c.a.7.1 4 1.1 even 1 trivial
25.3.c.a.7.2 yes 4 5.4 even 2 inner
25.3.c.a.18.1 yes 4 5.3 odd 4 inner
25.3.c.a.18.2 yes 4 5.2 odd 4 inner
225.3.g.e.82.1 4 15.14 odd 2
225.3.g.e.82.2 4 3.2 odd 2
225.3.g.e.118.1 4 15.2 even 4
225.3.g.e.118.2 4 15.8 even 4
400.3.p.j.193.1 4 20.3 even 4
400.3.p.j.193.2 4 20.7 even 4
400.3.p.j.257.1 4 4.3 odd 2
400.3.p.j.257.2 4 20.19 odd 2