Properties

Label 360.2.w.a.163.2
Level $360$
Weight $2$
Character 360.163
Analytic conductor $2.875$
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] = [360,2,Mod(163,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 2, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.163");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.w (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: \(2.87461447277\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 163.2
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 360.163
Dual form 360.2.w.a.307.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.41421i q^{2} -2.00000 q^{4} +(2.12132 - 0.707107i) q^{5} +(1.00000 + 1.00000i) q^{7} -2.82843i q^{8} +O(q^{10})\) \(q+1.41421i q^{2} -2.00000 q^{4} +(2.12132 - 0.707107i) q^{5} +(1.00000 + 1.00000i) q^{7} -2.82843i q^{8} +(1.00000 + 3.00000i) q^{10} +4.24264 q^{11} +(-2.00000 + 2.00000i) q^{13} +(-1.41421 + 1.41421i) q^{14} +4.00000 q^{16} +(2.82843 - 2.82843i) q^{17} +6.00000i q^{19} +(-4.24264 + 1.41421i) q^{20} +6.00000i q^{22} +(-1.41421 + 1.41421i) q^{23} +(4.00000 - 3.00000i) q^{25} +(-2.82843 - 2.82843i) q^{26} +(-2.00000 - 2.00000i) q^{28} -4.24264 q^{29} +6.00000i q^{31} +5.65685i q^{32} +(4.00000 + 4.00000i) q^{34} +(2.82843 + 1.41421i) q^{35} +(-8.00000 - 8.00000i) q^{37} -8.48528 q^{38} +(-2.00000 - 6.00000i) q^{40} +8.48528 q^{41} +(-2.00000 - 2.00000i) q^{43} -8.48528 q^{44} +(-2.00000 - 2.00000i) q^{46} +(1.41421 + 1.41421i) q^{47} -5.00000i q^{49} +(4.24264 + 5.65685i) q^{50} +(4.00000 - 4.00000i) q^{52} +(-1.41421 + 1.41421i) q^{53} +(9.00000 - 3.00000i) q^{55} +(2.82843 - 2.82843i) q^{56} -6.00000i q^{58} -9.89949i q^{59} -8.48528 q^{62} -8.00000 q^{64} +(-2.82843 + 5.65685i) q^{65} +(-8.00000 + 8.00000i) q^{67} +(-5.65685 + 5.65685i) q^{68} +(-2.00000 + 4.00000i) q^{70} -14.1421i q^{71} +(-5.00000 - 5.00000i) q^{73} +(11.3137 - 11.3137i) q^{74} -12.0000i q^{76} +(4.24264 + 4.24264i) q^{77} +14.0000 q^{79} +(8.48528 - 2.82843i) q^{80} +12.0000i q^{82} +(1.41421 + 1.41421i) q^{83} +(4.00000 - 8.00000i) q^{85} +(2.82843 - 2.82843i) q^{86} -12.0000i q^{88} +2.82843i q^{89} -4.00000 q^{91} +(2.82843 - 2.82843i) q^{92} +(-2.00000 + 2.00000i) q^{94} +(4.24264 + 12.7279i) q^{95} +(7.00000 - 7.00000i) q^{97} +7.07107 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 8 q^{4} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 8 q^{4} + 4 q^{7} + 4 q^{10} - 8 q^{13} + 16 q^{16} + 16 q^{25} - 8 q^{28} + 16 q^{34} - 32 q^{37} - 8 q^{40} - 8 q^{43} - 8 q^{46} + 16 q^{52} + 36 q^{55} - 32 q^{64} - 32 q^{67} - 8 q^{70} - 20 q^{73} + 56 q^{79} + 16 q^{85} - 16 q^{91} - 8 q^{94} + 28 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 1.00000i
\(3\) 0 0
\(4\) −2.00000 −1.00000
\(5\) 2.12132 0.707107i 0.948683 0.316228i
\(6\) 0 0
\(7\) 1.00000 + 1.00000i 0.377964 + 0.377964i 0.870367 0.492403i \(-0.163881\pi\)
−0.492403 + 0.870367i \(0.663881\pi\)
\(8\) 2.82843i 1.00000i
\(9\) 0 0
\(10\) 1.00000 + 3.00000i 0.316228 + 0.948683i
\(11\) 4.24264 1.27920 0.639602 0.768706i \(-0.279099\pi\)
0.639602 + 0.768706i \(0.279099\pi\)
\(12\) 0 0
\(13\) −2.00000 + 2.00000i −0.554700 + 0.554700i −0.927794 0.373094i \(-0.878297\pi\)
0.373094 + 0.927794i \(0.378297\pi\)
\(14\) −1.41421 + 1.41421i −0.377964 + 0.377964i
\(15\) 0 0
\(16\) 4.00000 1.00000
\(17\) 2.82843 2.82843i 0.685994 0.685994i −0.275350 0.961344i \(-0.588794\pi\)
0.961344 + 0.275350i \(0.0887937\pi\)
\(18\) 0 0
\(19\) 6.00000i 1.37649i 0.725476 + 0.688247i \(0.241620\pi\)
−0.725476 + 0.688247i \(0.758380\pi\)
\(20\) −4.24264 + 1.41421i −0.948683 + 0.316228i
\(21\) 0 0
\(22\) 6.00000i 1.27920i
\(23\) −1.41421 + 1.41421i −0.294884 + 0.294884i −0.839006 0.544122i \(-0.816863\pi\)
0.544122 + 0.839006i \(0.316863\pi\)
\(24\) 0 0
\(25\) 4.00000 3.00000i 0.800000 0.600000i
\(26\) −2.82843 2.82843i −0.554700 0.554700i
\(27\) 0 0
\(28\) −2.00000 2.00000i −0.377964 0.377964i
\(29\) −4.24264 −0.787839 −0.393919 0.919145i \(-0.628881\pi\)
−0.393919 + 0.919145i \(0.628881\pi\)
\(30\) 0 0
\(31\) 6.00000i 1.07763i 0.842424 + 0.538816i \(0.181128\pi\)
−0.842424 + 0.538816i \(0.818872\pi\)
\(32\) 5.65685i 1.00000i
\(33\) 0 0
\(34\) 4.00000 + 4.00000i 0.685994 + 0.685994i
\(35\) 2.82843 + 1.41421i 0.478091 + 0.239046i
\(36\) 0 0
\(37\) −8.00000 8.00000i −1.31519 1.31519i −0.917534 0.397658i \(-0.869823\pi\)
−0.397658 0.917534i \(-0.630177\pi\)
\(38\) −8.48528 −1.37649
\(39\) 0 0
\(40\) −2.00000 6.00000i −0.316228 0.948683i
\(41\) 8.48528 1.32518 0.662589 0.748983i \(-0.269458\pi\)
0.662589 + 0.748983i \(0.269458\pi\)
\(42\) 0 0
\(43\) −2.00000 2.00000i −0.304997 0.304997i 0.537968 0.842965i \(-0.319192\pi\)
−0.842965 + 0.537968i \(0.819192\pi\)
\(44\) −8.48528 −1.27920
\(45\) 0 0
\(46\) −2.00000 2.00000i −0.294884 0.294884i
\(47\) 1.41421 + 1.41421i 0.206284 + 0.206284i 0.802686 0.596402i \(-0.203403\pi\)
−0.596402 + 0.802686i \(0.703403\pi\)
\(48\) 0 0
\(49\) 5.00000i 0.714286i
\(50\) 4.24264 + 5.65685i 0.600000 + 0.800000i
\(51\) 0 0
\(52\) 4.00000 4.00000i 0.554700 0.554700i
\(53\) −1.41421 + 1.41421i −0.194257 + 0.194257i −0.797533 0.603276i \(-0.793862\pi\)
0.603276 + 0.797533i \(0.293862\pi\)
\(54\) 0 0
\(55\) 9.00000 3.00000i 1.21356 0.404520i
\(56\) 2.82843 2.82843i 0.377964 0.377964i
\(57\) 0 0
\(58\) 6.00000i 0.787839i
\(59\) 9.89949i 1.28880i −0.764687 0.644402i \(-0.777106\pi\)
0.764687 0.644402i \(-0.222894\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) −8.48528 −1.07763
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) −2.82843 + 5.65685i −0.350823 + 0.701646i
\(66\) 0 0
\(67\) −8.00000 + 8.00000i −0.977356 + 0.977356i −0.999749 0.0223937i \(-0.992871\pi\)
0.0223937 + 0.999749i \(0.492871\pi\)
\(68\) −5.65685 + 5.65685i −0.685994 + 0.685994i
\(69\) 0 0
\(70\) −2.00000 + 4.00000i −0.239046 + 0.478091i
\(71\) 14.1421i 1.67836i −0.543852 0.839181i \(-0.683035\pi\)
0.543852 0.839181i \(-0.316965\pi\)
\(72\) 0 0
\(73\) −5.00000 5.00000i −0.585206 0.585206i 0.351123 0.936329i \(-0.385800\pi\)
−0.936329 + 0.351123i \(0.885800\pi\)
\(74\) 11.3137 11.3137i 1.31519 1.31519i
\(75\) 0 0
\(76\) 12.0000i 1.37649i
\(77\) 4.24264 + 4.24264i 0.483494 + 0.483494i
\(78\) 0 0
\(79\) 14.0000 1.57512 0.787562 0.616236i \(-0.211343\pi\)
0.787562 + 0.616236i \(0.211343\pi\)
\(80\) 8.48528 2.82843i 0.948683 0.316228i
\(81\) 0 0
\(82\) 12.0000i 1.32518i
\(83\) 1.41421 + 1.41421i 0.155230 + 0.155230i 0.780449 0.625219i \(-0.214990\pi\)
−0.625219 + 0.780449i \(0.714990\pi\)
\(84\) 0 0
\(85\) 4.00000 8.00000i 0.433861 0.867722i
\(86\) 2.82843 2.82843i 0.304997 0.304997i
\(87\) 0 0
\(88\) 12.0000i 1.27920i
\(89\) 2.82843i 0.299813i 0.988700 + 0.149906i \(0.0478972\pi\)
−0.988700 + 0.149906i \(0.952103\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) 2.82843 2.82843i 0.294884 0.294884i
\(93\) 0 0
\(94\) −2.00000 + 2.00000i −0.206284 + 0.206284i
\(95\) 4.24264 + 12.7279i 0.435286 + 1.30586i
\(96\) 0 0
\(97\) 7.00000 7.00000i 0.710742 0.710742i −0.255948 0.966691i \(-0.582388\pi\)
0.966691 + 0.255948i \(0.0823876\pi\)
\(98\) 7.07107 0.714286
\(99\) 0 0
\(100\) −8.00000 + 6.00000i −0.800000 + 0.600000i
\(101\) 1.41421i 0.140720i −0.997522 0.0703598i \(-0.977585\pi\)
0.997522 0.0703598i \(-0.0224147\pi\)
\(102\) 0 0
\(103\) −5.00000 + 5.00000i −0.492665 + 0.492665i −0.909145 0.416480i \(-0.863264\pi\)
0.416480 + 0.909145i \(0.363264\pi\)
\(104\) 5.65685 + 5.65685i 0.554700 + 0.554700i
\(105\) 0 0
\(106\) −2.00000 2.00000i −0.194257 0.194257i
\(107\) −9.89949 + 9.89949i −0.957020 + 0.957020i −0.999114 0.0420934i \(-0.986597\pi\)
0.0420934 + 0.999114i \(0.486597\pi\)
\(108\) 0 0
\(109\) −4.00000 −0.383131 −0.191565 0.981480i \(-0.561356\pi\)
−0.191565 + 0.981480i \(0.561356\pi\)
\(110\) 4.24264 + 12.7279i 0.404520 + 1.21356i
\(111\) 0 0
\(112\) 4.00000 + 4.00000i 0.377964 + 0.377964i
\(113\) −11.3137 11.3137i −1.06430 1.06430i −0.997785 0.0665190i \(-0.978811\pi\)
−0.0665190 0.997785i \(-0.521189\pi\)
\(114\) 0 0
\(115\) −2.00000 + 4.00000i −0.186501 + 0.373002i
\(116\) 8.48528 0.787839
\(117\) 0 0
\(118\) 14.0000 1.28880
\(119\) 5.65685 0.518563
\(120\) 0 0
\(121\) 7.00000 0.636364
\(122\) 0 0
\(123\) 0 0
\(124\) 12.0000i 1.07763i
\(125\) 6.36396 9.19239i 0.569210 0.822192i
\(126\) 0 0
\(127\) −11.0000 11.0000i −0.976092 0.976092i 0.0236286 0.999721i \(-0.492478\pi\)
−0.999721 + 0.0236286i \(0.992478\pi\)
\(128\) 11.3137i 1.00000i
\(129\) 0 0
\(130\) −8.00000 4.00000i −0.701646 0.350823i
\(131\) −12.7279 −1.11204 −0.556022 0.831168i \(-0.687673\pi\)
−0.556022 + 0.831168i \(0.687673\pi\)
\(132\) 0 0
\(133\) −6.00000 + 6.00000i −0.520266 + 0.520266i
\(134\) −11.3137 11.3137i −0.977356 0.977356i
\(135\) 0 0
\(136\) −8.00000 8.00000i −0.685994 0.685994i
\(137\) −5.65685 + 5.65685i −0.483298 + 0.483298i −0.906183 0.422885i \(-0.861017\pi\)
0.422885 + 0.906183i \(0.361017\pi\)
\(138\) 0 0
\(139\) 6.00000i 0.508913i −0.967084 0.254457i \(-0.918103\pi\)
0.967084 0.254457i \(-0.0818966\pi\)
\(140\) −5.65685 2.82843i −0.478091 0.239046i
\(141\) 0 0
\(142\) 20.0000 1.67836
\(143\) −8.48528 + 8.48528i −0.709575 + 0.709575i
\(144\) 0 0
\(145\) −9.00000 + 3.00000i −0.747409 + 0.249136i
\(146\) 7.07107 7.07107i 0.585206 0.585206i
\(147\) 0 0
\(148\) 16.0000 + 16.0000i 1.31519 + 1.31519i
\(149\) −12.7279 −1.04271 −0.521356 0.853339i \(-0.674574\pi\)
−0.521356 + 0.853339i \(0.674574\pi\)
\(150\) 0 0
\(151\) 12.0000i 0.976546i 0.872691 + 0.488273i \(0.162373\pi\)
−0.872691 + 0.488273i \(0.837627\pi\)
\(152\) 16.9706 1.37649
\(153\) 0 0
\(154\) −6.00000 + 6.00000i −0.483494 + 0.483494i
\(155\) 4.24264 + 12.7279i 0.340777 + 1.02233i
\(156\) 0 0
\(157\) −8.00000 8.00000i −0.638470 0.638470i 0.311708 0.950178i \(-0.399099\pi\)
−0.950178 + 0.311708i \(0.899099\pi\)
\(158\) 19.7990i 1.57512i
\(159\) 0 0
\(160\) 4.00000 + 12.0000i 0.316228 + 0.948683i
\(161\) −2.82843 −0.222911
\(162\) 0 0
\(163\) 10.0000 + 10.0000i 0.783260 + 0.783260i 0.980380 0.197119i \(-0.0631586\pi\)
−0.197119 + 0.980380i \(0.563159\pi\)
\(164\) −16.9706 −1.32518
\(165\) 0 0
\(166\) −2.00000 + 2.00000i −0.155230 + 0.155230i
\(167\) −15.5563 15.5563i −1.20379 1.20379i −0.973006 0.230781i \(-0.925872\pi\)
−0.230781 0.973006i \(-0.574128\pi\)
\(168\) 0 0
\(169\) 5.00000i 0.384615i
\(170\) 11.3137 + 5.65685i 0.867722 + 0.433861i
\(171\) 0 0
\(172\) 4.00000 + 4.00000i 0.304997 + 0.304997i
\(173\) 2.82843 2.82843i 0.215041 0.215041i −0.591364 0.806405i \(-0.701410\pi\)
0.806405 + 0.591364i \(0.201410\pi\)
\(174\) 0 0
\(175\) 7.00000 + 1.00000i 0.529150 + 0.0755929i
\(176\) 16.9706 1.27920
\(177\) 0 0
\(178\) −4.00000 −0.299813
\(179\) 9.89949i 0.739923i −0.929047 0.369961i \(-0.879371\pi\)
0.929047 0.369961i \(-0.120629\pi\)
\(180\) 0 0
\(181\) 24.0000i 1.78391i 0.452128 + 0.891953i \(0.350665\pi\)
−0.452128 + 0.891953i \(0.649335\pi\)
\(182\) 5.65685i 0.419314i
\(183\) 0 0
\(184\) 4.00000 + 4.00000i 0.294884 + 0.294884i
\(185\) −22.6274 11.3137i −1.66360 0.831800i
\(186\) 0 0
\(187\) 12.0000 12.0000i 0.877527 0.877527i
\(188\) −2.82843 2.82843i −0.206284 0.206284i
\(189\) 0 0
\(190\) −18.0000 + 6.00000i −1.30586 + 0.435286i
\(191\) 11.3137i 0.818631i 0.912393 + 0.409316i \(0.134232\pi\)
−0.912393 + 0.409316i \(0.865768\pi\)
\(192\) 0 0
\(193\) 13.0000 + 13.0000i 0.935760 + 0.935760i 0.998058 0.0622972i \(-0.0198427\pi\)
−0.0622972 + 0.998058i \(0.519843\pi\)
\(194\) 9.89949 + 9.89949i 0.710742 + 0.710742i
\(195\) 0 0
\(196\) 10.0000i 0.714286i
\(197\) 9.89949 + 9.89949i 0.705310 + 0.705310i 0.965545 0.260235i \(-0.0838002\pi\)
−0.260235 + 0.965545i \(0.583800\pi\)
\(198\) 0 0
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) −8.48528 11.3137i −0.600000 0.800000i
\(201\) 0 0
\(202\) 2.00000 0.140720
\(203\) −4.24264 4.24264i −0.297775 0.297775i
\(204\) 0 0
\(205\) 18.0000 6.00000i 1.25717 0.419058i
\(206\) −7.07107 7.07107i −0.492665 0.492665i
\(207\) 0 0
\(208\) −8.00000 + 8.00000i −0.554700 + 0.554700i
\(209\) 25.4558i 1.76082i
\(210\) 0 0
\(211\) 2.00000 0.137686 0.0688428 0.997628i \(-0.478069\pi\)
0.0688428 + 0.997628i \(0.478069\pi\)
\(212\) 2.82843 2.82843i 0.194257 0.194257i
\(213\) 0 0
\(214\) −14.0000 14.0000i −0.957020 0.957020i
\(215\) −5.65685 2.82843i −0.385794 0.192897i
\(216\) 0 0
\(217\) −6.00000 + 6.00000i −0.407307 + 0.407307i
\(218\) 5.65685i 0.383131i
\(219\) 0 0
\(220\) −18.0000 + 6.00000i −1.21356 + 0.404520i
\(221\) 11.3137i 0.761042i
\(222\) 0 0
\(223\) −11.0000 + 11.0000i −0.736614 + 0.736614i −0.971921 0.235307i \(-0.924391\pi\)
0.235307 + 0.971921i \(0.424391\pi\)
\(224\) −5.65685 + 5.65685i −0.377964 + 0.377964i
\(225\) 0 0
\(226\) 16.0000 16.0000i 1.06430 1.06430i
\(227\) −5.65685 + 5.65685i −0.375459 + 0.375459i −0.869461 0.494002i \(-0.835534\pi\)
0.494002 + 0.869461i \(0.335534\pi\)
\(228\) 0 0
\(229\) 20.0000 1.32164 0.660819 0.750546i \(-0.270209\pi\)
0.660819 + 0.750546i \(0.270209\pi\)
\(230\) −5.65685 2.82843i −0.373002 0.186501i
\(231\) 0 0
\(232\) 12.0000i 0.787839i
\(233\) 5.65685 + 5.65685i 0.370593 + 0.370593i 0.867693 0.497100i \(-0.165602\pi\)
−0.497100 + 0.867693i \(0.665602\pi\)
\(234\) 0 0
\(235\) 4.00000 + 2.00000i 0.260931 + 0.130466i
\(236\) 19.7990i 1.28880i
\(237\) 0 0
\(238\) 8.00000i 0.518563i
\(239\) 25.4558 1.64660 0.823301 0.567605i \(-0.192130\pi\)
0.823301 + 0.567605i \(0.192130\pi\)
\(240\) 0 0
\(241\) −16.0000 −1.03065 −0.515325 0.856995i \(-0.672329\pi\)
−0.515325 + 0.856995i \(0.672329\pi\)
\(242\) 9.89949i 0.636364i
\(243\) 0 0
\(244\) 0 0
\(245\) −3.53553 10.6066i −0.225877 0.677631i
\(246\) 0 0
\(247\) −12.0000 12.0000i −0.763542 0.763542i
\(248\) 16.9706 1.07763
\(249\) 0 0
\(250\) 13.0000 + 9.00000i 0.822192 + 0.569210i
\(251\) −12.7279 −0.803379 −0.401690 0.915776i \(-0.631577\pi\)
−0.401690 + 0.915776i \(0.631577\pi\)
\(252\) 0 0
\(253\) −6.00000 + 6.00000i −0.377217 + 0.377217i
\(254\) 15.5563 15.5563i 0.976092 0.976092i
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) 19.7990 19.7990i 1.23503 1.23503i 0.273018 0.962009i \(-0.411978\pi\)
0.962009 0.273018i \(-0.0880219\pi\)
\(258\) 0 0
\(259\) 16.0000i 0.994192i
\(260\) 5.65685 11.3137i 0.350823 0.701646i
\(261\) 0 0
\(262\) 18.0000i 1.11204i
\(263\) 7.07107 7.07107i 0.436021 0.436021i −0.454650 0.890670i \(-0.650236\pi\)
0.890670 + 0.454650i \(0.150236\pi\)
\(264\) 0 0
\(265\) −2.00000 + 4.00000i −0.122859 + 0.245718i
\(266\) −8.48528 8.48528i −0.520266 0.520266i
\(267\) 0 0
\(268\) 16.0000 16.0000i 0.977356 0.977356i
\(269\) −21.2132 −1.29339 −0.646696 0.762748i \(-0.723850\pi\)
−0.646696 + 0.762748i \(0.723850\pi\)
\(270\) 0 0
\(271\) 12.0000i 0.728948i −0.931214 0.364474i \(-0.881249\pi\)
0.931214 0.364474i \(-0.118751\pi\)
\(272\) 11.3137 11.3137i 0.685994 0.685994i
\(273\) 0 0
\(274\) −8.00000 8.00000i −0.483298 0.483298i
\(275\) 16.9706 12.7279i 1.02336 0.767523i
\(276\) 0 0
\(277\) 4.00000 + 4.00000i 0.240337 + 0.240337i 0.816989 0.576653i \(-0.195641\pi\)
−0.576653 + 0.816989i \(0.695641\pi\)
\(278\) 8.48528 0.508913
\(279\) 0 0
\(280\) 4.00000 8.00000i 0.239046 0.478091i
\(281\) 16.9706 1.01238 0.506189 0.862422i \(-0.331054\pi\)
0.506189 + 0.862422i \(0.331054\pi\)
\(282\) 0 0
\(283\) −8.00000 8.00000i −0.475551 0.475551i 0.428155 0.903705i \(-0.359164\pi\)
−0.903705 + 0.428155i \(0.859164\pi\)
\(284\) 28.2843i 1.67836i
\(285\) 0 0
\(286\) −12.0000 12.0000i −0.709575 0.709575i
\(287\) 8.48528 + 8.48528i 0.500870 + 0.500870i
\(288\) 0 0
\(289\) 1.00000i 0.0588235i
\(290\) −4.24264 12.7279i −0.249136 0.747409i
\(291\) 0 0
\(292\) 10.0000 + 10.0000i 0.585206 + 0.585206i
\(293\) 15.5563 15.5563i 0.908812 0.908812i −0.0873648 0.996176i \(-0.527845\pi\)
0.996176 + 0.0873648i \(0.0278446\pi\)
\(294\) 0 0
\(295\) −7.00000 21.0000i −0.407556 1.22267i
\(296\) −22.6274 + 22.6274i −1.31519 + 1.31519i
\(297\) 0 0
\(298\) 18.0000i 1.04271i
\(299\) 5.65685i 0.327144i
\(300\) 0 0
\(301\) 4.00000i 0.230556i
\(302\) −16.9706 −0.976546
\(303\) 0 0
\(304\) 24.0000i 1.37649i
\(305\) 0 0
\(306\) 0 0
\(307\) 10.0000 10.0000i 0.570730 0.570730i −0.361602 0.932332i \(-0.617770\pi\)
0.932332 + 0.361602i \(0.117770\pi\)
\(308\) −8.48528 8.48528i −0.483494 0.483494i
\(309\) 0 0
\(310\) −18.0000 + 6.00000i −1.02233 + 0.340777i
\(311\) 31.1127i 1.76424i −0.471025 0.882120i \(-0.656116\pi\)
0.471025 0.882120i \(-0.343884\pi\)
\(312\) 0 0
\(313\) 1.00000 + 1.00000i 0.0565233 + 0.0565233i 0.734803 0.678280i \(-0.237274\pi\)
−0.678280 + 0.734803i \(0.737274\pi\)
\(314\) 11.3137 11.3137i 0.638470 0.638470i
\(315\) 0 0
\(316\) −28.0000 −1.57512
\(317\) 5.65685 + 5.65685i 0.317721 + 0.317721i 0.847891 0.530170i \(-0.177872\pi\)
−0.530170 + 0.847891i \(0.677872\pi\)
\(318\) 0 0
\(319\) −18.0000 −1.00781
\(320\) −16.9706 + 5.65685i −0.948683 + 0.316228i
\(321\) 0 0
\(322\) 4.00000i 0.222911i
\(323\) 16.9706 + 16.9706i 0.944267 + 0.944267i
\(324\) 0 0
\(325\) −2.00000 + 14.0000i −0.110940 + 0.776580i
\(326\) −14.1421 + 14.1421i −0.783260 + 0.783260i
\(327\) 0 0
\(328\) 24.0000i 1.32518i
\(329\) 2.82843i 0.155936i
\(330\) 0 0
\(331\) 2.00000 0.109930 0.0549650 0.998488i \(-0.482495\pi\)
0.0549650 + 0.998488i \(0.482495\pi\)
\(332\) −2.82843 2.82843i −0.155230 0.155230i
\(333\) 0 0
\(334\) 22.0000 22.0000i 1.20379 1.20379i
\(335\) −11.3137 + 22.6274i −0.618134 + 1.23627i
\(336\) 0 0
\(337\) −17.0000 + 17.0000i −0.926049 + 0.926049i −0.997448 0.0713988i \(-0.977254\pi\)
0.0713988 + 0.997448i \(0.477254\pi\)
\(338\) −7.07107 −0.384615
\(339\) 0 0
\(340\) −8.00000 + 16.0000i −0.433861 + 0.867722i
\(341\) 25.4558i 1.37851i
\(342\) 0 0
\(343\) 12.0000 12.0000i 0.647939 0.647939i
\(344\) −5.65685 + 5.65685i −0.304997 + 0.304997i
\(345\) 0 0
\(346\) 4.00000 + 4.00000i 0.215041 + 0.215041i
\(347\) 11.3137 11.3137i 0.607352 0.607352i −0.334901 0.942253i \(-0.608703\pi\)
0.942253 + 0.334901i \(0.108703\pi\)
\(348\) 0 0
\(349\) 20.0000 1.07058 0.535288 0.844670i \(-0.320203\pi\)
0.535288 + 0.844670i \(0.320203\pi\)
\(350\) −1.41421 + 9.89949i −0.0755929 + 0.529150i
\(351\) 0 0
\(352\) 24.0000i 1.27920i
\(353\) 5.65685 + 5.65685i 0.301084 + 0.301084i 0.841438 0.540354i \(-0.181710\pi\)
−0.540354 + 0.841438i \(0.681710\pi\)
\(354\) 0 0
\(355\) −10.0000 30.0000i −0.530745 1.59223i
\(356\) 5.65685i 0.299813i
\(357\) 0 0
\(358\) 14.0000 0.739923
\(359\) 8.48528 0.447836 0.223918 0.974608i \(-0.428115\pi\)
0.223918 + 0.974608i \(0.428115\pi\)
\(360\) 0 0
\(361\) −17.0000 −0.894737
\(362\) −33.9411 −1.78391
\(363\) 0 0
\(364\) 8.00000 0.419314
\(365\) −14.1421 7.07107i −0.740233 0.370117i
\(366\) 0 0
\(367\) −5.00000 5.00000i −0.260998 0.260998i 0.564462 0.825459i \(-0.309084\pi\)
−0.825459 + 0.564462i \(0.809084\pi\)
\(368\) −5.65685 + 5.65685i −0.294884 + 0.294884i
\(369\) 0 0
\(370\) 16.0000 32.0000i 0.831800 1.66360i
\(371\) −2.82843 −0.146845
\(372\) 0 0
\(373\) 16.0000 16.0000i 0.828449 0.828449i −0.158854 0.987302i \(-0.550780\pi\)
0.987302 + 0.158854i \(0.0507798\pi\)
\(374\) 16.9706 + 16.9706i 0.877527 + 0.877527i
\(375\) 0 0
\(376\) 4.00000 4.00000i 0.206284 0.206284i
\(377\) 8.48528 8.48528i 0.437014 0.437014i
\(378\) 0 0
\(379\) 18.0000i 0.924598i 0.886724 + 0.462299i \(0.152975\pi\)
−0.886724 + 0.462299i \(0.847025\pi\)
\(380\) −8.48528 25.4558i −0.435286 1.30586i
\(381\) 0 0
\(382\) −16.0000 −0.818631
\(383\) −18.3848 + 18.3848i −0.939418 + 0.939418i −0.998267 0.0588487i \(-0.981257\pi\)
0.0588487 + 0.998267i \(0.481257\pi\)
\(384\) 0 0
\(385\) 12.0000 + 6.00000i 0.611577 + 0.305788i
\(386\) −18.3848 + 18.3848i −0.935760 + 0.935760i
\(387\) 0 0
\(388\) −14.0000 + 14.0000i −0.710742 + 0.710742i
\(389\) 4.24264 0.215110 0.107555 0.994199i \(-0.465698\pi\)
0.107555 + 0.994199i \(0.465698\pi\)
\(390\) 0 0
\(391\) 8.00000i 0.404577i
\(392\) −14.1421 −0.714286
\(393\) 0 0
\(394\) −14.0000 + 14.0000i −0.705310 + 0.705310i
\(395\) 29.6985 9.89949i 1.49429 0.498098i
\(396\) 0 0
\(397\) 10.0000 + 10.0000i 0.501886 + 0.501886i 0.912024 0.410138i \(-0.134519\pi\)
−0.410138 + 0.912024i \(0.634519\pi\)
\(398\) 5.65685i 0.283552i
\(399\) 0 0
\(400\) 16.0000 12.0000i 0.800000 0.600000i
\(401\) 8.48528 0.423735 0.211867 0.977298i \(-0.432046\pi\)
0.211867 + 0.977298i \(0.432046\pi\)
\(402\) 0 0
\(403\) −12.0000 12.0000i −0.597763 0.597763i
\(404\) 2.82843i 0.140720i
\(405\) 0 0
\(406\) 6.00000 6.00000i 0.297775 0.297775i
\(407\) −33.9411 33.9411i −1.68240 1.68240i
\(408\) 0 0
\(409\) 12.0000i 0.593362i 0.954977 + 0.296681i \(0.0958798\pi\)
−0.954977 + 0.296681i \(0.904120\pi\)
\(410\) 8.48528 + 25.4558i 0.419058 + 1.25717i
\(411\) 0 0
\(412\) 10.0000 10.0000i 0.492665 0.492665i
\(413\) 9.89949 9.89949i 0.487122 0.487122i
\(414\) 0 0
\(415\) 4.00000 + 2.00000i 0.196352 + 0.0981761i
\(416\) −11.3137 11.3137i −0.554700 0.554700i
\(417\) 0 0
\(418\) −36.0000 −1.76082
\(419\) 9.89949i 0.483622i −0.970323 0.241811i \(-0.922259\pi\)
0.970323 0.241811i \(-0.0777414\pi\)
\(420\) 0 0
\(421\) 12.0000i 0.584844i −0.956289 0.292422i \(-0.905539\pi\)
0.956289 0.292422i \(-0.0944612\pi\)
\(422\) 2.82843i 0.137686i
\(423\) 0 0
\(424\) 4.00000 + 4.00000i 0.194257 + 0.194257i
\(425\) 2.82843 19.7990i 0.137199 0.960392i
\(426\) 0 0
\(427\) 0 0
\(428\) 19.7990 19.7990i 0.957020 0.957020i
\(429\) 0 0
\(430\) 4.00000 8.00000i 0.192897 0.385794i
\(431\) 36.7696i 1.77113i 0.464518 + 0.885564i \(0.346227\pi\)
−0.464518 + 0.885564i \(0.653773\pi\)
\(432\) 0 0
\(433\) −23.0000 23.0000i −1.10531 1.10531i −0.993759 0.111551i \(-0.964418\pi\)
−0.111551 0.993759i \(-0.535582\pi\)
\(434\) −8.48528 8.48528i −0.407307 0.407307i
\(435\) 0 0
\(436\) 8.00000 0.383131
\(437\) −8.48528 8.48528i −0.405906 0.405906i
\(438\) 0 0
\(439\) −4.00000 −0.190910 −0.0954548 0.995434i \(-0.530431\pi\)
−0.0954548 + 0.995434i \(0.530431\pi\)
\(440\) −8.48528 25.4558i −0.404520 1.21356i
\(441\) 0 0
\(442\) −16.0000 −0.761042
\(443\) 22.6274 + 22.6274i 1.07506 + 1.07506i 0.996944 + 0.0781168i \(0.0248907\pi\)
0.0781168 + 0.996944i \(0.475109\pi\)
\(444\) 0 0
\(445\) 2.00000 + 6.00000i 0.0948091 + 0.284427i
\(446\) −15.5563 15.5563i −0.736614 0.736614i
\(447\) 0 0
\(448\) −8.00000 8.00000i −0.377964 0.377964i
\(449\) 11.3137i 0.533927i 0.963707 + 0.266963i \(0.0860203\pi\)
−0.963707 + 0.266963i \(0.913980\pi\)
\(450\) 0 0
\(451\) 36.0000 1.69517
\(452\) 22.6274 + 22.6274i 1.06430 + 1.06430i
\(453\) 0 0
\(454\) −8.00000 8.00000i −0.375459 0.375459i
\(455\) −8.48528 + 2.82843i −0.397796 + 0.132599i
\(456\) 0 0
\(457\) 1.00000 1.00000i 0.0467780 0.0467780i −0.683331 0.730109i \(-0.739469\pi\)
0.730109 + 0.683331i \(0.239469\pi\)
\(458\) 28.2843i 1.32164i
\(459\) 0 0
\(460\) 4.00000 8.00000i 0.186501 0.373002i
\(461\) 7.07107i 0.329332i 0.986349 + 0.164666i \(0.0526547\pi\)
−0.986349 + 0.164666i \(0.947345\pi\)
\(462\) 0 0
\(463\) −5.00000 + 5.00000i −0.232370 + 0.232370i −0.813681 0.581311i \(-0.802540\pi\)
0.581311 + 0.813681i \(0.302540\pi\)
\(464\) −16.9706 −0.787839
\(465\) 0 0
\(466\) −8.00000 + 8.00000i −0.370593 + 0.370593i
\(467\) −9.89949 + 9.89949i −0.458094 + 0.458094i −0.898029 0.439935i \(-0.855001\pi\)
0.439935 + 0.898029i \(0.355001\pi\)
\(468\) 0 0
\(469\) −16.0000 −0.738811
\(470\) −2.82843 + 5.65685i −0.130466 + 0.260931i
\(471\) 0 0
\(472\) −28.0000 −1.28880
\(473\) −8.48528 8.48528i −0.390154 0.390154i
\(474\) 0 0
\(475\) 18.0000 + 24.0000i 0.825897 + 1.10120i
\(476\) −11.3137 −0.518563
\(477\) 0 0
\(478\) 36.0000i 1.64660i
\(479\) 25.4558 1.16311 0.581554 0.813508i \(-0.302445\pi\)
0.581554 + 0.813508i \(0.302445\pi\)
\(480\) 0 0
\(481\) 32.0000 1.45907
\(482\) 22.6274i 1.03065i
\(483\) 0 0
\(484\) −14.0000 −0.636364
\(485\) 9.89949 19.7990i 0.449513 0.899026i
\(486\) 0 0
\(487\) 7.00000 + 7.00000i 0.317200 + 0.317200i 0.847691 0.530491i \(-0.177992\pi\)
−0.530491 + 0.847691i \(0.677992\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 15.0000 5.00000i 0.677631 0.225877i
\(491\) −12.7279 −0.574403 −0.287202 0.957870i \(-0.592725\pi\)
−0.287202 + 0.957870i \(0.592725\pi\)
\(492\) 0 0
\(493\) −12.0000 + 12.0000i −0.540453 + 0.540453i
\(494\) 16.9706 16.9706i 0.763542 0.763542i
\(495\) 0 0
\(496\) 24.0000i 1.07763i
\(497\) 14.1421 14.1421i 0.634361 0.634361i
\(498\) 0 0
\(499\) 18.0000i 0.805791i −0.915246 0.402895i \(-0.868004\pi\)
0.915246 0.402895i \(-0.131996\pi\)
\(500\) −12.7279 + 18.3848i −0.569210 + 0.822192i
\(501\) 0 0
\(502\) 18.0000i 0.803379i
\(503\) 24.0416 24.0416i 1.07196 1.07196i 0.0747619 0.997201i \(-0.476180\pi\)
0.997201 0.0747619i \(-0.0238197\pi\)
\(504\) 0 0
\(505\) −1.00000 3.00000i −0.0444994 0.133498i
\(506\) −8.48528 8.48528i −0.377217 0.377217i
\(507\) 0 0
\(508\) 22.0000 + 22.0000i 0.976092 + 0.976092i
\(509\) 21.2132 0.940259 0.470129 0.882598i \(-0.344207\pi\)
0.470129 + 0.882598i \(0.344207\pi\)
\(510\) 0 0
\(511\) 10.0000i 0.442374i
\(512\) 22.6274i 1.00000i
\(513\) 0 0
\(514\) 28.0000 + 28.0000i 1.23503 + 1.23503i
\(515\) −7.07107 + 14.1421i −0.311588 + 0.623177i
\(516\) 0 0
\(517\) 6.00000 + 6.00000i 0.263880 + 0.263880i
\(518\) 22.6274 0.994192
\(519\) 0 0
\(520\) 16.0000 + 8.00000i 0.701646 + 0.350823i
\(521\) −16.9706 −0.743494 −0.371747 0.928334i \(-0.621241\pi\)
−0.371747 + 0.928334i \(0.621241\pi\)
\(522\) 0 0
\(523\) 4.00000 + 4.00000i 0.174908 + 0.174908i 0.789132 0.614224i \(-0.210531\pi\)
−0.614224 + 0.789132i \(0.710531\pi\)
\(524\) 25.4558 1.11204
\(525\) 0 0
\(526\) 10.0000 + 10.0000i 0.436021 + 0.436021i
\(527\) 16.9706 + 16.9706i 0.739249 + 0.739249i
\(528\) 0 0
\(529\) 19.0000i 0.826087i
\(530\) −5.65685 2.82843i −0.245718 0.122859i
\(531\) 0 0
\(532\) 12.0000 12.0000i 0.520266 0.520266i
\(533\) −16.9706 + 16.9706i −0.735077 + 0.735077i
\(534\) 0 0
\(535\) −14.0000 + 28.0000i −0.605273 + 1.21055i
\(536\) 22.6274 + 22.6274i 0.977356 + 0.977356i
\(537\) 0 0
\(538\) 30.0000i 1.29339i
\(539\) 21.2132i 0.913717i
\(540\) 0 0
\(541\) 12.0000i 0.515920i 0.966156 + 0.257960i \(0.0830503\pi\)
−0.966156 + 0.257960i \(0.916950\pi\)
\(542\) 16.9706 0.728948
\(543\) 0 0
\(544\) 16.0000 + 16.0000i 0.685994 + 0.685994i
\(545\) −8.48528 + 2.82843i −0.363470 + 0.121157i
\(546\) 0 0
\(547\) −26.0000 + 26.0000i −1.11168 + 1.11168i −0.118756 + 0.992923i \(0.537891\pi\)
−0.992923 + 0.118756i \(0.962109\pi\)
\(548\) 11.3137 11.3137i 0.483298 0.483298i
\(549\) 0 0
\(550\) 18.0000 + 24.0000i 0.767523 + 1.02336i
\(551\) 25.4558i 1.08446i
\(552\) 0 0
\(553\) 14.0000 + 14.0000i 0.595341 + 0.595341i
\(554\) −5.65685 + 5.65685i −0.240337 + 0.240337i
\(555\) 0 0
\(556\) 12.0000i 0.508913i
\(557\) 1.41421 + 1.41421i 0.0599222 + 0.0599222i 0.736433 0.676511i \(-0.236509\pi\)
−0.676511 + 0.736433i \(0.736509\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 11.3137 + 5.65685i 0.478091 + 0.239046i
\(561\) 0 0
\(562\) 24.0000i 1.01238i
\(563\) −11.3137 11.3137i −0.476816 0.476816i 0.427296 0.904112i \(-0.359466\pi\)
−0.904112 + 0.427296i \(0.859466\pi\)
\(564\) 0 0
\(565\) −32.0000 16.0000i −1.34625 0.673125i
\(566\) 11.3137 11.3137i 0.475551 0.475551i
\(567\) 0 0
\(568\) −40.0000 −1.67836
\(569\) 36.7696i 1.54146i 0.637162 + 0.770730i \(0.280108\pi\)
−0.637162 + 0.770730i \(0.719892\pi\)
\(570\) 0 0
\(571\) −34.0000 −1.42286 −0.711428 0.702759i \(-0.751951\pi\)
−0.711428 + 0.702759i \(0.751951\pi\)
\(572\) 16.9706 16.9706i 0.709575 0.709575i
\(573\) 0 0
\(574\) −12.0000 + 12.0000i −0.500870 + 0.500870i
\(575\) −1.41421 + 9.89949i −0.0589768 + 0.412837i
\(576\) 0 0
\(577\) 7.00000 7.00000i 0.291414 0.291414i −0.546225 0.837639i \(-0.683936\pi\)
0.837639 + 0.546225i \(0.183936\pi\)
\(578\) −1.41421 −0.0588235
\(579\) 0 0
\(580\) 18.0000 6.00000i 0.747409 0.249136i
\(581\) 2.82843i 0.117343i
\(582\) 0 0
\(583\) −6.00000 + 6.00000i −0.248495 + 0.248495i
\(584\) −14.1421 + 14.1421i −0.585206 + 0.585206i
\(585\) 0 0
\(586\) 22.0000 + 22.0000i 0.908812 + 0.908812i
\(587\) −18.3848 + 18.3848i −0.758821 + 0.758821i −0.976108 0.217287i \(-0.930279\pi\)
0.217287 + 0.976108i \(0.430279\pi\)
\(588\) 0 0
\(589\) −36.0000 −1.48335
\(590\) 29.6985 9.89949i 1.22267 0.407556i
\(591\) 0 0
\(592\) −32.0000 32.0000i −1.31519 1.31519i
\(593\) −2.82843 2.82843i −0.116150 0.116150i 0.646643 0.762793i \(-0.276172\pi\)
−0.762793 + 0.646643i \(0.776172\pi\)
\(594\) 0 0
\(595\) 12.0000 4.00000i 0.491952 0.163984i
\(596\) 25.4558 1.04271
\(597\) 0 0
\(598\) 8.00000 0.327144
\(599\) −8.48528 −0.346699 −0.173350 0.984860i \(-0.555459\pi\)
−0.173350 + 0.984860i \(0.555459\pi\)
\(600\) 0 0
\(601\) 14.0000 0.571072 0.285536 0.958368i \(-0.407828\pi\)
0.285536 + 0.958368i \(0.407828\pi\)
\(602\) 5.65685 0.230556
\(603\) 0 0
\(604\) 24.0000i 0.976546i
\(605\) 14.8492 4.94975i 0.603708 0.201236i
\(606\) 0 0
\(607\) 31.0000 + 31.0000i 1.25825 + 1.25825i 0.951927 + 0.306324i \(0.0990990\pi\)
0.306324 + 0.951927i \(0.400901\pi\)
\(608\) −33.9411 −1.37649
\(609\) 0 0
\(610\) 0 0
\(611\) −5.65685 −0.228852
\(612\) 0 0
\(613\) 10.0000 10.0000i 0.403896 0.403896i −0.475707 0.879604i \(-0.657808\pi\)
0.879604 + 0.475707i \(0.157808\pi\)
\(614\) 14.1421 + 14.1421i 0.570730 + 0.570730i
\(615\) 0 0
\(616\) 12.0000 12.0000i 0.483494 0.483494i
\(617\) −5.65685 + 5.65685i −0.227736 + 0.227736i −0.811746 0.584010i \(-0.801483\pi\)
0.584010 + 0.811746i \(0.301483\pi\)
\(618\) 0 0
\(619\) 30.0000i 1.20580i 0.797816 + 0.602901i \(0.205989\pi\)
−0.797816 + 0.602901i \(0.794011\pi\)
\(620\) −8.48528 25.4558i −0.340777 1.02233i
\(621\) 0 0
\(622\) 44.0000 1.76424
\(623\) −2.82843 + 2.82843i −0.113319 + 0.113319i
\(624\) 0 0
\(625\) 7.00000 24.0000i 0.280000 0.960000i
\(626\) −1.41421 + 1.41421i −0.0565233 + 0.0565233i
\(627\) 0 0
\(628\) 16.0000 + 16.0000i 0.638470 + 0.638470i
\(629\) −45.2548 −1.80443
\(630\) 0 0
\(631\) 30.0000i 1.19428i −0.802137 0.597141i \(-0.796303\pi\)
0.802137 0.597141i \(-0.203697\pi\)
\(632\) 39.5980i 1.57512i
\(633\) 0 0
\(634\) −8.00000 + 8.00000i −0.317721 + 0.317721i
\(635\) −31.1127 15.5563i −1.23467 0.617335i
\(636\) 0 0
\(637\) 10.0000 + 10.0000i 0.396214 + 0.396214i
\(638\) 25.4558i 1.00781i
\(639\) 0 0
\(640\) −8.00000 24.0000i −0.316228 0.948683i
\(641\) −16.9706 −0.670297 −0.335148 0.942165i \(-0.608786\pi\)
−0.335148 + 0.942165i \(0.608786\pi\)
\(642\) 0 0
\(643\) 10.0000 + 10.0000i 0.394362 + 0.394362i 0.876239 0.481877i \(-0.160045\pi\)
−0.481877 + 0.876239i \(0.660045\pi\)
\(644\) 5.65685 0.222911
\(645\) 0 0
\(646\) −24.0000 + 24.0000i −0.944267 + 0.944267i
\(647\) −7.07107 7.07107i −0.277992 0.277992i 0.554315 0.832307i \(-0.312980\pi\)
−0.832307 + 0.554315i \(0.812980\pi\)
\(648\) 0 0
\(649\) 42.0000i 1.64864i
\(650\) −19.7990 2.82843i −0.776580 0.110940i
\(651\) 0 0
\(652\) −20.0000 20.0000i −0.783260 0.783260i
\(653\) −5.65685 + 5.65685i −0.221370 + 0.221370i −0.809075 0.587705i \(-0.800031\pi\)
0.587705 + 0.809075i \(0.300031\pi\)
\(654\) 0 0
\(655\) −27.0000 + 9.00000i −1.05498 + 0.351659i
\(656\) 33.9411 1.32518
\(657\) 0 0
\(658\) −4.00000 −0.155936
\(659\) 1.41421i 0.0550899i −0.999621 0.0275450i \(-0.991231\pi\)
0.999621 0.0275450i \(-0.00876895\pi\)
\(660\) 0 0
\(661\) 24.0000i 0.933492i −0.884391 0.466746i \(-0.845426\pi\)
0.884391 0.466746i \(-0.154574\pi\)
\(662\) 2.82843i 0.109930i
\(663\) 0 0
\(664\) 4.00000 4.00000i 0.155230 0.155230i
\(665\) −8.48528 + 16.9706i −0.329045 + 0.658090i
\(666\) 0 0
\(667\) 6.00000 6.00000i 0.232321 0.232321i
\(668\) 31.1127 + 31.1127i 1.20379 + 1.20379i
\(669\) 0 0
\(670\) −32.0000 16.0000i −1.23627 0.618134i
\(671\) 0 0
\(672\) 0 0
\(673\) −5.00000 5.00000i −0.192736 0.192736i 0.604141 0.796877i \(-0.293516\pi\)
−0.796877 + 0.604141i \(0.793516\pi\)
\(674\) −24.0416 24.0416i −0.926049 0.926049i
\(675\) 0 0
\(676\) 10.0000i 0.384615i
\(677\) 22.6274 + 22.6274i 0.869642 + 0.869642i 0.992433 0.122790i \(-0.0391843\pi\)
−0.122790 + 0.992433i \(0.539184\pi\)
\(678\) 0 0
\(679\) 14.0000 0.537271
\(680\) −22.6274 11.3137i −0.867722 0.433861i
\(681\) 0 0
\(682\) −36.0000 −1.37851
\(683\) −15.5563 15.5563i −0.595247 0.595247i 0.343797 0.939044i \(-0.388287\pi\)
−0.939044 + 0.343797i \(0.888287\pi\)
\(684\) 0 0
\(685\) −8.00000 + 16.0000i −0.305664 + 0.611329i
\(686\) 16.9706 + 16.9706i 0.647939 + 0.647939i
\(687\) 0 0
\(688\) −8.00000 8.00000i −0.304997 0.304997i
\(689\) 5.65685i 0.215509i
\(690\) 0 0
\(691\) −22.0000 −0.836919 −0.418460 0.908235i \(-0.637430\pi\)
−0.418460 + 0.908235i \(0.637430\pi\)
\(692\) −5.65685 + 5.65685i −0.215041 + 0.215041i
\(693\) 0 0
\(694\) 16.0000 + 16.0000i 0.607352 + 0.607352i
\(695\) −4.24264 12.7279i −0.160933 0.482798i
\(696\) 0 0
\(697\) 24.0000 24.0000i 0.909065 0.909065i
\(698\) 28.2843i 1.07058i
\(699\) 0 0
\(700\) −14.0000 2.00000i −0.529150 0.0755929i
\(701\) 1.41421i 0.0534141i −0.999643 0.0267071i \(-0.991498\pi\)
0.999643 0.0267071i \(-0.00850213\pi\)
\(702\) 0 0
\(703\) 48.0000 48.0000i 1.81035 1.81035i
\(704\) −33.9411 −1.27920
\(705\) 0 0
\(706\) −8.00000 + 8.00000i −0.301084 + 0.301084i
\(707\) 1.41421 1.41421i 0.0531870 0.0531870i
\(708\) 0 0
\(709\) −16.0000 −0.600893 −0.300446 0.953799i \(-0.597136\pi\)
−0.300446 + 0.953799i \(0.597136\pi\)
\(710\) 42.4264 14.1421i 1.59223 0.530745i
\(711\) 0 0
\(712\) 8.00000 0.299813
\(713\) −8.48528 8.48528i −0.317776 0.317776i
\(714\) 0 0
\(715\) −12.0000 + 24.0000i −0.448775 + 0.897549i
\(716\) 19.7990i 0.739923i
\(717\) 0 0
\(718\) 12.0000i 0.447836i
\(719\) −16.9706 −0.632895 −0.316448 0.948610i \(-0.602490\pi\)
−0.316448 + 0.948610i \(0.602490\pi\)
\(720\) 0 0
\(721\) −10.0000 −0.372419
\(722\) 24.0416i 0.894737i
\(723\) 0 0
\(724\) 48.0000i 1.78391i
\(725\) −16.9706 + 12.7279i −0.630271 + 0.472703i
\(726\) 0 0
\(727\) 31.0000 + 31.0000i 1.14973 + 1.14973i 0.986606 + 0.163120i \(0.0521558\pi\)
0.163120 + 0.986606i \(0.447844\pi\)
\(728\) 11.3137i 0.419314i
\(729\) 0 0
\(730\) 10.0000 20.0000i 0.370117 0.740233i
\(731\) −11.3137 −0.418453
\(732\) 0 0
\(733\) 28.0000 28.0000i 1.03420 1.03420i 0.0348096 0.999394i \(-0.488918\pi\)
0.999394 0.0348096i \(-0.0110825\pi\)
\(734\) 7.07107 7.07107i 0.260998 0.260998i
\(735\) 0 0
\(736\) −8.00000 8.00000i −0.294884 0.294884i
\(737\) −33.9411 + 33.9411i −1.25024 + 1.25024i
\(738\) 0 0
\(739\) 6.00000i 0.220714i −0.993892 0.110357i \(-0.964801\pi\)
0.993892 0.110357i \(-0.0351994\pi\)
\(740\) 45.2548 + 22.6274i 1.66360 + 0.831800i
\(741\) 0 0
\(742\) 4.00000i 0.146845i
\(743\) −9.89949 + 9.89949i −0.363177 + 0.363177i −0.864981 0.501804i \(-0.832670\pi\)
0.501804 + 0.864981i \(0.332670\pi\)
\(744\) 0 0
\(745\) −27.0000 + 9.00000i −0.989203 + 0.329734i
\(746\) 22.6274 + 22.6274i 0.828449 + 0.828449i
\(747\) 0 0
\(748\) −24.0000 + 24.0000i −0.877527 + 0.877527i
\(749\) −19.7990 −0.723439
\(750\) 0 0
\(751\) 18.0000i 0.656829i 0.944534 + 0.328415i \(0.106514\pi\)
−0.944534 + 0.328415i \(0.893486\pi\)
\(752\) 5.65685 + 5.65685i 0.206284 + 0.206284i
\(753\) 0 0
\(754\) 12.0000 + 12.0000i 0.437014 + 0.437014i
\(755\) 8.48528 + 25.4558i 0.308811 + 0.926433i
\(756\) 0 0
\(757\) −8.00000 8.00000i −0.290765 0.290765i 0.546617 0.837382i \(-0.315915\pi\)
−0.837382 + 0.546617i \(0.815915\pi\)
\(758\) −25.4558 −0.924598
\(759\) 0 0
\(760\) 36.0000 12.0000i 1.30586 0.435286i
\(761\) 16.9706 0.615182 0.307591 0.951519i \(-0.400477\pi\)
0.307591 + 0.951519i \(0.400477\pi\)
\(762\) 0 0
\(763\) −4.00000 4.00000i −0.144810 0.144810i
\(764\) 22.6274i 0.818631i
\(765\) 0 0
\(766\) −26.0000 26.0000i −0.939418 0.939418i
\(767\) 19.7990 + 19.7990i 0.714900 + 0.714900i
\(768\) 0 0
\(769\) 6.00000i 0.216366i −0.994131 0.108183i \(-0.965497\pi\)
0.994131 0.108183i \(-0.0345032\pi\)
\(770\) −8.48528 + 16.9706i −0.305788 + 0.611577i
\(771\) 0 0
\(772\) −26.0000 26.0000i −0.935760 0.935760i
\(773\) 28.2843 28.2843i 1.01731 1.01731i 0.0174671 0.999847i \(-0.494440\pi\)
0.999847 0.0174671i \(-0.00556023\pi\)
\(774\) 0 0
\(775\) 18.0000 + 24.0000i 0.646579 + 0.862105i
\(776\) −19.7990 19.7990i −0.710742 0.710742i
\(777\) 0 0
\(778\) 6.00000i 0.215110i
\(779\) 50.9117i 1.82410i
\(780\) 0 0
\(781\) 60.0000i 2.14697i
\(782\) −11.3137 −0.404577
\(783\) 0 0
\(784\) 20.0000i 0.714286i
\(785\) −22.6274 11.3137i −0.807607 0.403804i
\(786\) 0 0
\(787\) −20.0000 + 20.0000i −0.712923 + 0.712923i −0.967146 0.254223i \(-0.918180\pi\)
0.254223 + 0.967146i \(0.418180\pi\)
\(788\) −19.7990 19.7990i −0.705310 0.705310i
\(789\) 0 0
\(790\) 14.0000 + 42.0000i 0.498098 + 1.49429i
\(791\) 22.6274i 0.804538i
\(792\) 0 0
\(793\) 0 0
\(794\) −14.1421 + 14.1421i −0.501886 + 0.501886i
\(795\) 0 0
\(796\) 8.00000 0.283552
\(797\) −11.3137 11.3137i −0.400752 0.400752i 0.477746 0.878498i \(-0.341454\pi\)
−0.878498 + 0.477746i \(0.841454\pi\)
\(798\) 0 0
\(799\) 8.00000 0.283020
\(800\) 16.9706 + 22.6274i 0.600000 + 0.800000i
\(801\) 0 0
\(802\) 12.0000i 0.423735i
\(803\) −21.2132 21.2132i −0.748598 0.748598i
\(804\) 0 0
\(805\) −6.00000 + 2.00000i −0.211472 + 0.0704907i
\(806\) 16.9706 16.9706i 0.597763 0.597763i
\(807\) 0 0
\(808\) −4.00000 −0.140720
\(809\) 39.5980i 1.39219i −0.717949 0.696095i \(-0.754919\pi\)
0.717949 0.696095i \(-0.245081\pi\)
\(810\) 0 0
\(811\) −22.0000 −0.772524 −0.386262 0.922389i \(-0.626234\pi\)
−0.386262 + 0.922389i \(0.626234\pi\)
\(812\) 8.48528 + 8.48528i 0.297775 + 0.297775i
\(813\) 0 0
\(814\) 48.0000 48.0000i 1.68240 1.68240i
\(815\) 28.2843 + 14.1421i 0.990755 + 0.495377i
\(816\) 0 0
\(817\) 12.0000 12.0000i 0.419827 0.419827i
\(818\) −16.9706 −0.593362
\(819\) 0 0
\(820\) −36.0000 + 12.0000i −1.25717 + 0.419058i
\(821\) 26.8701i 0.937771i −0.883259 0.468886i \(-0.844656\pi\)
0.883259 0.468886i \(-0.155344\pi\)
\(822\) 0 0
\(823\) −5.00000 + 5.00000i −0.174289 + 0.174289i −0.788861 0.614572i \(-0.789329\pi\)
0.614572 + 0.788861i \(0.289329\pi\)
\(824\) 14.1421 + 14.1421i 0.492665 + 0.492665i
\(825\) 0 0
\(826\) 14.0000 + 14.0000i 0.487122 + 0.487122i
\(827\) −5.65685 + 5.65685i −0.196708 + 0.196708i −0.798587 0.601879i \(-0.794419\pi\)
0.601879 + 0.798587i \(0.294419\pi\)
\(828\) 0 0
\(829\) −28.0000 −0.972480 −0.486240 0.873825i \(-0.661632\pi\)
−0.486240 + 0.873825i \(0.661632\pi\)
\(830\) −2.82843 + 5.65685i −0.0981761 + 0.196352i
\(831\) 0 0
\(832\) 16.0000 16.0000i 0.554700 0.554700i
\(833\) −14.1421 14.1421i −0.489996 0.489996i
\(834\) 0 0
\(835\) −44.0000 22.0000i −1.52268 0.761341i
\(836\) 50.9117i 1.76082i
\(837\) 0 0
\(838\) 14.0000 0.483622
\(839\) −8.48528 −0.292944 −0.146472 0.989215i \(-0.546792\pi\)
−0.146472 + 0.989215i \(0.546792\pi\)
\(840\) 0 0
\(841\) −11.0000 −0.379310
\(842\) 16.9706 0.584844
\(843\) 0 0
\(844\) −4.00000 −0.137686
\(845\) 3.53553 + 10.6066i 0.121626 + 0.364878i
\(846\) 0 0
\(847\) 7.00000 + 7.00000i 0.240523 + 0.240523i
\(848\) −5.65685 + 5.65685i −0.194257 + 0.194257i
\(849\) 0 0
\(850\) 28.0000 + 4.00000i 0.960392 + 0.137199i
\(851\) 22.6274 0.775658
\(852\) 0 0
\(853\) −14.0000 + 14.0000i −0.479351 + 0.479351i −0.904924 0.425573i \(-0.860073\pi\)
0.425573 + 0.904924i \(0.360073\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 28.0000 + 28.0000i 0.957020 + 0.957020i
\(857\) 19.7990 19.7990i 0.676321 0.676321i −0.282845 0.959166i \(-0.591278\pi\)
0.959166 + 0.282845i \(0.0912782\pi\)
\(858\) 0 0
\(859\) 6.00000i 0.204717i 0.994748 + 0.102359i \(0.0326389\pi\)
−0.994748 + 0.102359i \(0.967361\pi\)
\(860\) 11.3137 + 5.65685i 0.385794 + 0.192897i
\(861\) 0 0
\(862\) −52.0000 −1.77113
\(863\) −18.3848 + 18.3848i −0.625825 + 0.625825i −0.947015 0.321190i \(-0.895917\pi\)
0.321190 + 0.947015i \(0.395917\pi\)
\(864\) 0 0
\(865\) 4.00000 8.00000i 0.136004 0.272008i
\(866\) 32.5269 32.5269i 1.10531 1.10531i
\(867\) 0 0
\(868\) 12.0000 12.0000i 0.407307 0.407307i
\(869\) 59.3970 2.01490
\(870\) 0 0
\(871\) 32.0000i 1.08428i
\(872\) 11.3137i 0.383131i
\(873\) 0 0
\(874\) 12.0000 12.0000i 0.405906 0.405906i
\(875\) 15.5563 2.82843i 0.525901 0.0956183i
\(876\) 0 0
\(877\) 4.00000 + 4.00000i 0.135070 + 0.135070i 0.771409 0.636339i \(-0.219552\pi\)
−0.636339 + 0.771409i \(0.719552\pi\)
\(878\) 5.65685i 0.190910i
\(879\) 0 0
\(880\) 36.0000 12.0000i 1.21356 0.404520i
\(881\) 25.4558 0.857629 0.428815 0.903393i \(-0.358931\pi\)
0.428815 + 0.903393i \(0.358931\pi\)
\(882\) 0 0
\(883\) 34.0000 + 34.0000i 1.14419 + 1.14419i 0.987675 + 0.156516i \(0.0500262\pi\)
0.156516 + 0.987675i \(0.449974\pi\)
\(884\) 22.6274i 0.761042i
\(885\) 0 0
\(886\) −32.0000 + 32.0000i −1.07506 + 1.07506i
\(887\) 1.41421 + 1.41421i 0.0474846 + 0.0474846i 0.730450 0.682966i \(-0.239310\pi\)
−0.682966 + 0.730450i \(0.739310\pi\)
\(888\) 0 0
\(889\) 22.0000i 0.737856i
\(890\) −8.48528 + 2.82843i −0.284427 + 0.0948091i
\(891\) 0 0
\(892\) 22.0000 22.0000i 0.736614 0.736614i
\(893\) −8.48528 + 8.48528i −0.283949 + 0.283949i
\(894\) 0 0
\(895\) −7.00000 21.0000i −0.233984 0.701953i
\(896\) 11.3137 11.3137i 0.377964 0.377964i
\(897\) 0 0
\(898\) −16.0000 −0.533927
\(899\) 25.4558i 0.849000i
\(900\) 0 0
\(901\) 8.00000i 0.266519i
\(902\) 50.9117i 1.69517i
\(903\) 0 0
\(904\) −32.0000 + 32.0000i −1.06430 + 1.06430i
\(905\) 16.9706 + 50.9117i 0.564121 + 1.69236i
\(906\) 0 0
\(907\) 28.0000 28.0000i 0.929725 0.929725i −0.0679631 0.997688i \(-0.521650\pi\)
0.997688 + 0.0679631i \(0.0216500\pi\)
\(908\) 11.3137 11.3137i 0.375459 0.375459i
\(909\) 0 0
\(910\) −4.00000 12.0000i −0.132599 0.397796i
\(911\) 19.7990i 0.655970i 0.944683 + 0.327985i \(0.106370\pi\)
−0.944683 + 0.327985i \(0.893630\pi\)
\(912\) 0 0
\(913\) 6.00000 + 6.00000i 0.198571 + 0.198571i
\(914\) 1.41421 + 1.41421i 0.0467780 + 0.0467780i
\(915\) 0 0
\(916\) −40.0000 −1.32164
\(917\) −12.7279 12.7279i −0.420313 0.420313i
\(918\) 0 0
\(919\) −10.0000 −0.329870 −0.164935 0.986304i \(-0.552741\pi\)
−0.164935 + 0.986304i \(0.552741\pi\)
\(920\) 11.3137 + 5.65685i 0.373002 + 0.186501i
\(921\) 0 0
\(922\) −10.0000 −0.329332
\(923\) 28.2843 + 28.2843i 0.930988 + 0.930988i
\(924\) 0 0
\(925\) −56.0000 8.00000i −1.84127 0.263038i
\(926\) −7.07107 7.07107i −0.232370 0.232370i
\(927\) 0 0
\(928\) 24.0000i 0.787839i
\(929\) 39.5980i 1.29917i −0.760290 0.649584i \(-0.774943\pi\)
0.760290 0.649584i \(-0.225057\pi\)
\(930\) 0 0
\(931\) 30.0000 0.983210
\(932\) −11.3137 11.3137i −0.370593 0.370593i
\(933\) 0 0
\(934\) −14.0000 14.0000i −0.458094 0.458094i
\(935\) 16.9706 33.9411i 0.554997 1.10999i
\(936\) 0 0
\(937\) 7.00000 7.00000i 0.228680 0.228680i −0.583461 0.812141i \(-0.698302\pi\)
0.812141 + 0.583461i \(0.198302\pi\)
\(938\) 22.6274i 0.738811i
\(939\) 0 0
\(940\) −8.00000 4.00000i −0.260931 0.130466i
\(941\) 9.89949i 0.322714i −0.986896 0.161357i \(-0.948413\pi\)
0.986896 0.161357i \(-0.0515871\pi\)
\(942\) 0 0
\(943\) −12.0000 + 12.0000i −0.390774 + 0.390774i
\(944\) 39.5980i 1.28880i
\(945\) 0 0
\(946\) 12.0000 12.0000i 0.390154 0.390154i
\(947\) 11.3137 11.3137i 0.367646 0.367646i −0.498972 0.866618i \(-0.666289\pi\)
0.866618 + 0.498972i \(0.166289\pi\)
\(948\) 0 0
\(949\) 20.0000 0.649227
\(950\) −33.9411 + 25.4558i −1.10120 + 0.825897i
\(951\) 0 0
\(952\) 16.0000i 0.518563i
\(953\) 14.1421 + 14.1421i 0.458109 + 0.458109i 0.898034 0.439926i \(-0.144995\pi\)
−0.439926 + 0.898034i \(0.644995\pi\)
\(954\) 0 0
\(955\) 8.00000 + 24.0000i 0.258874 + 0.776622i
\(956\) −50.9117 −1.64660
\(957\) 0 0
\(958\) 36.0000i 1.16311i
\(959\) −11.3137 −0.365339
\(960\) 0 0
\(961\) −5.00000 −0.161290
\(962\) 45.2548i 1.45907i
\(963\) 0 0
\(964\) 32.0000 1.03065
\(965\) 36.7696 + 18.3848i 1.18365 + 0.591827i
\(966\) 0 0
\(967\) 7.00000 + 7.00000i 0.225105 + 0.225105i 0.810644 0.585539i \(-0.199117\pi\)
−0.585539 + 0.810644i \(0.699117\pi\)
\(968\) 19.7990i 0.636364i
\(969\) 0 0
\(970\) 28.0000 + 14.0000i 0.899026 + 0.449513i
\(971\) 29.6985 0.953070 0.476535 0.879156i \(-0.341893\pi\)
0.476535 + 0.879156i \(0.341893\pi\)
\(972\) 0 0
\(973\) 6.00000 6.00000i 0.192351 0.192351i
\(974\) −9.89949 + 9.89949i −0.317200 + 0.317200i
\(975\) 0 0
\(976\) 0 0
\(977\) −22.6274 + 22.6274i −0.723915 + 0.723915i −0.969400 0.245485i \(-0.921053\pi\)
0.245485 + 0.969400i \(0.421053\pi\)
\(978\) 0 0
\(979\) 12.0000i 0.383522i
\(980\) 7.07107 + 21.2132i 0.225877 + 0.677631i
\(981\) 0 0
\(982\) 18.0000i 0.574403i
\(983\) −9.89949 + 9.89949i −0.315745 + 0.315745i −0.847130 0.531385i \(-0.821672\pi\)
0.531385 + 0.847130i \(0.321672\pi\)
\(984\) 0 0
\(985\) 28.0000 + 14.0000i 0.892154 + 0.446077i
\(986\) −16.9706 16.9706i −0.540453 0.540453i
\(987\) 0 0
\(988\) 24.0000 + 24.0000i 0.763542 + 0.763542i
\(989\) 5.65685 0.179878
\(990\) 0 0
\(991\) 36.0000i 1.14358i 0.820401 + 0.571789i \(0.193750\pi\)
−0.820401 + 0.571789i \(0.806250\pi\)
\(992\) −33.9411 −1.07763
\(993\) 0 0
\(994\) 20.0000 + 20.0000i 0.634361 + 0.634361i
\(995\) −8.48528 + 2.82843i −0.269002 + 0.0896672i
\(996\) 0 0
\(997\) 22.0000 + 22.0000i 0.696747 + 0.696747i 0.963707 0.266960i \(-0.0860193\pi\)
−0.266960 + 0.963707i \(0.586019\pi\)
\(998\) 25.4558 0.805791
\(999\) 0 0
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 360.2.w.a.163.2 yes 4
3.2 odd 2 inner 360.2.w.a.163.1 4
4.3 odd 2 1440.2.bi.a.1423.2 4
5.2 odd 4 360.2.w.b.307.1 yes 4
8.3 odd 2 360.2.w.b.163.1 yes 4
8.5 even 2 1440.2.bi.b.1423.1 4
12.11 even 2 1440.2.bi.a.1423.1 4
15.2 even 4 360.2.w.b.307.2 yes 4
20.7 even 4 1440.2.bi.b.847.1 4
24.5 odd 2 1440.2.bi.b.1423.2 4
24.11 even 2 360.2.w.b.163.2 yes 4
40.27 even 4 inner 360.2.w.a.307.1 yes 4
40.37 odd 4 1440.2.bi.a.847.2 4
60.47 odd 4 1440.2.bi.b.847.2 4
120.77 even 4 1440.2.bi.a.847.1 4
120.107 odd 4 inner 360.2.w.a.307.2 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.w.a.163.1 4 3.2 odd 2 inner
360.2.w.a.163.2 yes 4 1.1 even 1 trivial
360.2.w.a.307.1 yes 4 40.27 even 4 inner
360.2.w.a.307.2 yes 4 120.107 odd 4 inner
360.2.w.b.163.1 yes 4 8.3 odd 2
360.2.w.b.163.2 yes 4 24.11 even 2
360.2.w.b.307.1 yes 4 5.2 odd 4
360.2.w.b.307.2 yes 4 15.2 even 4
1440.2.bi.a.847.1 4 120.77 even 4
1440.2.bi.a.847.2 4 40.37 odd 4
1440.2.bi.a.1423.1 4 12.11 even 2
1440.2.bi.a.1423.2 4 4.3 odd 2
1440.2.bi.b.847.1 4 20.7 even 4
1440.2.bi.b.847.2 4 60.47 odd 4
1440.2.bi.b.1423.1 4 8.5 even 2
1440.2.bi.b.1423.2 4 24.5 odd 2