Properties

Label 1110.2.u.c.191.2
Level $1110$
Weight $2$
Character 1110.191
Analytic conductor $8.863$
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] = [1110,2,Mod(191,1110)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([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("1110.191");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.u (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: \(8.86339462436\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 191.2
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1110.191
Dual form 1110.2.u.c.401.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(1.41421 + 1.00000i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.292893 + 1.70711i) q^{6} -4.00000 q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(1.41421 + 1.00000i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.292893 + 1.70711i) q^{6} -4.00000 q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} -1.00000 q^{10} -1.41421 q^{11} +(-1.00000 + 1.41421i) q^{12} +(-3.00000 - 3.00000i) q^{13} +(-2.82843 - 2.82843i) q^{14} +(-1.70711 + 0.292893i) q^{15} -1.00000 q^{16} +(-1.41421 + 1.41421i) q^{17} +(-1.29289 + 2.70711i) q^{18} +(4.00000 + 4.00000i) q^{19} +(-0.707107 - 0.707107i) q^{20} +(-5.65685 - 4.00000i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(-1.41421 + 1.41421i) q^{23} +(-1.70711 + 0.292893i) q^{24} -1.00000i q^{25} -4.24264i q^{26} +(-1.41421 + 5.00000i) q^{27} -4.00000i q^{28} +(-2.82843 - 2.82843i) q^{29} +(-1.41421 - 1.00000i) q^{30} +(-3.00000 + 3.00000i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.00000 - 1.41421i) q^{33} -2.00000 q^{34} +(2.82843 - 2.82843i) q^{35} +(-2.82843 + 1.00000i) q^{36} +(-6.00000 + 1.00000i) q^{37} +5.65685i q^{38} +(-1.24264 - 7.24264i) q^{39} -1.00000i q^{40} +5.65685 q^{41} +(-1.17157 - 6.82843i) q^{42} +(3.00000 + 3.00000i) q^{43} -1.41421i q^{44} +(-2.70711 - 1.29289i) q^{45} -2.00000 q^{46} -1.41421i q^{47} +(-1.41421 - 1.00000i) q^{48} +9.00000 q^{49} +(0.707107 - 0.707107i) q^{50} +(-3.41421 + 0.585786i) q^{51} +(3.00000 - 3.00000i) q^{52} +2.82843i q^{53} +(-4.53553 + 2.53553i) q^{54} +(1.00000 - 1.00000i) q^{55} +(2.82843 - 2.82843i) q^{56} +(1.65685 + 9.65685i) q^{57} -4.00000i q^{58} +(8.48528 - 8.48528i) q^{59} +(-0.292893 - 1.70711i) q^{60} +(-6.00000 + 6.00000i) q^{61} -4.24264 q^{62} +(-4.00000 - 11.3137i) q^{63} -1.00000i q^{64} +4.24264 q^{65} +(-0.414214 - 2.41421i) q^{66} +6.00000i q^{67} +(-1.41421 - 1.41421i) q^{68} +(-3.41421 + 0.585786i) q^{69} +4.00000 q^{70} +2.82843i q^{71} +(-2.70711 - 1.29289i) q^{72} +10.0000i q^{73} +(-4.94975 - 3.53553i) q^{74} +(1.00000 - 1.41421i) q^{75} +(-4.00000 + 4.00000i) q^{76} +5.65685 q^{77} +(4.24264 - 6.00000i) q^{78} +(5.00000 + 5.00000i) q^{79} +(0.707107 - 0.707107i) q^{80} +(-7.00000 + 5.65685i) q^{81} +(4.00000 + 4.00000i) q^{82} -2.82843i q^{83} +(4.00000 - 5.65685i) q^{84} -2.00000i q^{85} +4.24264i q^{86} +(-1.17157 - 6.82843i) q^{87} +(1.00000 - 1.00000i) q^{88} +(1.41421 + 1.41421i) q^{89} +(-1.00000 - 2.82843i) q^{90} +(12.0000 + 12.0000i) q^{91} +(-1.41421 - 1.41421i) q^{92} +(-7.24264 + 1.24264i) q^{93} +(1.00000 - 1.00000i) q^{94} -5.65685 q^{95} +(-0.292893 - 1.70711i) q^{96} +(6.00000 + 6.00000i) q^{97} +(6.36396 + 6.36396i) q^{98} +(-1.41421 - 4.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{6} - 16 q^{7} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{6} - 16 q^{7} + 4 q^{9} - 4 q^{10} - 4 q^{12} - 12 q^{13} - 4 q^{15} - 4 q^{16} - 8 q^{18} + 16 q^{19} - 4 q^{22} - 4 q^{24} - 12 q^{31} - 8 q^{33} - 8 q^{34} - 24 q^{37} + 12 q^{39} - 16 q^{42} + 12 q^{43} - 8 q^{45} - 8 q^{46} + 36 q^{49} - 8 q^{51} + 12 q^{52} - 4 q^{54} + 4 q^{55} - 16 q^{57} - 4 q^{60} - 24 q^{61} - 16 q^{63} + 4 q^{66} - 8 q^{69} + 16 q^{70} - 8 q^{72} + 4 q^{75} - 16 q^{76} + 20 q^{79} - 28 q^{81} + 16 q^{82} + 16 q^{84} - 16 q^{87} + 4 q^{88} - 4 q^{90} + 48 q^{91} - 12 q^{93} + 4 q^{94} - 4 q^{96} + 24 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) 1.41421 + 1.00000i 0.816497 + 0.577350i
\(4\) 1.00000i 0.500000i
\(5\) −0.707107 + 0.707107i −0.316228 + 0.316228i
\(6\) 0.292893 + 1.70711i 0.119573 + 0.696923i
\(7\) −4.00000 −1.51186 −0.755929 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 1.00000 + 2.82843i 0.333333 + 0.942809i
\(10\) −1.00000 −0.316228
\(11\) −1.41421 −0.426401 −0.213201 0.977008i \(-0.568389\pi\)
−0.213201 + 0.977008i \(0.568389\pi\)
\(12\) −1.00000 + 1.41421i −0.288675 + 0.408248i
\(13\) −3.00000 3.00000i −0.832050 0.832050i 0.155747 0.987797i \(-0.450222\pi\)
−0.987797 + 0.155747i \(0.950222\pi\)
\(14\) −2.82843 2.82843i −0.755929 0.755929i
\(15\) −1.70711 + 0.292893i −0.440773 + 0.0756247i
\(16\) −1.00000 −0.250000
\(17\) −1.41421 + 1.41421i −0.342997 + 0.342997i −0.857493 0.514496i \(-0.827979\pi\)
0.514496 + 0.857493i \(0.327979\pi\)
\(18\) −1.29289 + 2.70711i −0.304738 + 0.638071i
\(19\) 4.00000 + 4.00000i 0.917663 + 0.917663i 0.996859 0.0791961i \(-0.0252353\pi\)
−0.0791961 + 0.996859i \(0.525235\pi\)
\(20\) −0.707107 0.707107i −0.158114 0.158114i
\(21\) −5.65685 4.00000i −1.23443 0.872872i
\(22\) −1.00000 1.00000i −0.213201 0.213201i
\(23\) −1.41421 + 1.41421i −0.294884 + 0.294884i −0.839006 0.544122i \(-0.816863\pi\)
0.544122 + 0.839006i \(0.316863\pi\)
\(24\) −1.70711 + 0.292893i −0.348462 + 0.0597866i
\(25\) 1.00000i 0.200000i
\(26\) 4.24264i 0.832050i
\(27\) −1.41421 + 5.00000i −0.272166 + 0.962250i
\(28\) 4.00000i 0.755929i
\(29\) −2.82843 2.82843i −0.525226 0.525226i 0.393919 0.919145i \(-0.371119\pi\)
−0.919145 + 0.393919i \(0.871119\pi\)
\(30\) −1.41421 1.00000i −0.258199 0.182574i
\(31\) −3.00000 + 3.00000i −0.538816 + 0.538816i −0.923181 0.384365i \(-0.874420\pi\)
0.384365 + 0.923181i \(0.374420\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) −2.00000 1.41421i −0.348155 0.246183i
\(34\) −2.00000 −0.342997
\(35\) 2.82843 2.82843i 0.478091 0.478091i
\(36\) −2.82843 + 1.00000i −0.471405 + 0.166667i
\(37\) −6.00000 + 1.00000i −0.986394 + 0.164399i
\(38\) 5.65685i 0.917663i
\(39\) −1.24264 7.24264i −0.198982 1.15975i
\(40\) 1.00000i 0.158114i
\(41\) 5.65685 0.883452 0.441726 0.897150i \(-0.354366\pi\)
0.441726 + 0.897150i \(0.354366\pi\)
\(42\) −1.17157 6.82843i −0.180778 1.05365i
\(43\) 3.00000 + 3.00000i 0.457496 + 0.457496i 0.897833 0.440337i \(-0.145141\pi\)
−0.440337 + 0.897833i \(0.645141\pi\)
\(44\) 1.41421i 0.213201i
\(45\) −2.70711 1.29289i −0.403552 0.192733i
\(46\) −2.00000 −0.294884
\(47\) 1.41421i 0.206284i −0.994667 0.103142i \(-0.967110\pi\)
0.994667 0.103142i \(-0.0328896\pi\)
\(48\) −1.41421 1.00000i −0.204124 0.144338i
\(49\) 9.00000 1.28571
\(50\) 0.707107 0.707107i 0.100000 0.100000i
\(51\) −3.41421 + 0.585786i −0.478086 + 0.0820265i
\(52\) 3.00000 3.00000i 0.416025 0.416025i
\(53\) 2.82843i 0.388514i 0.980951 + 0.194257i \(0.0622296\pi\)
−0.980951 + 0.194257i \(0.937770\pi\)
\(54\) −4.53553 + 2.53553i −0.617208 + 0.345042i
\(55\) 1.00000 1.00000i 0.134840 0.134840i
\(56\) 2.82843 2.82843i 0.377964 0.377964i
\(57\) 1.65685 + 9.65685i 0.219456 + 1.27908i
\(58\) 4.00000i 0.525226i
\(59\) 8.48528 8.48528i 1.10469 1.10469i 0.110853 0.993837i \(-0.464642\pi\)
0.993837 0.110853i \(-0.0353582\pi\)
\(60\) −0.292893 1.70711i −0.0378124 0.220387i
\(61\) −6.00000 + 6.00000i −0.768221 + 0.768221i −0.977793 0.209572i \(-0.932793\pi\)
0.209572 + 0.977793i \(0.432793\pi\)
\(62\) −4.24264 −0.538816
\(63\) −4.00000 11.3137i −0.503953 1.42539i
\(64\) 1.00000i 0.125000i
\(65\) 4.24264 0.526235
\(66\) −0.414214 2.41421i −0.0509862 0.297169i
\(67\) 6.00000i 0.733017i 0.930415 + 0.366508i \(0.119447\pi\)
−0.930415 + 0.366508i \(0.880553\pi\)
\(68\) −1.41421 1.41421i −0.171499 0.171499i
\(69\) −3.41421 + 0.585786i −0.411023 + 0.0705204i
\(70\) 4.00000 0.478091
\(71\) 2.82843i 0.335673i 0.985815 + 0.167836i \(0.0536780\pi\)
−0.985815 + 0.167836i \(0.946322\pi\)
\(72\) −2.70711 1.29289i −0.319036 0.152369i
\(73\) 10.0000i 1.17041i 0.810885 + 0.585206i \(0.198986\pi\)
−0.810885 + 0.585206i \(0.801014\pi\)
\(74\) −4.94975 3.53553i −0.575396 0.410997i
\(75\) 1.00000 1.41421i 0.115470 0.163299i
\(76\) −4.00000 + 4.00000i −0.458831 + 0.458831i
\(77\) 5.65685 0.644658
\(78\) 4.24264 6.00000i 0.480384 0.679366i
\(79\) 5.00000 + 5.00000i 0.562544 + 0.562544i 0.930029 0.367485i \(-0.119781\pi\)
−0.367485 + 0.930029i \(0.619781\pi\)
\(80\) 0.707107 0.707107i 0.0790569 0.0790569i
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) 4.00000 + 4.00000i 0.441726 + 0.441726i
\(83\) 2.82843i 0.310460i −0.987878 0.155230i \(-0.950388\pi\)
0.987878 0.155230i \(-0.0496119\pi\)
\(84\) 4.00000 5.65685i 0.436436 0.617213i
\(85\) 2.00000i 0.216930i
\(86\) 4.24264i 0.457496i
\(87\) −1.17157 6.82843i −0.125606 0.732084i
\(88\) 1.00000 1.00000i 0.106600 0.106600i
\(89\) 1.41421 + 1.41421i 0.149906 + 0.149906i 0.778076 0.628170i \(-0.216196\pi\)
−0.628170 + 0.778076i \(0.716196\pi\)
\(90\) −1.00000 2.82843i −0.105409 0.298142i
\(91\) 12.0000 + 12.0000i 1.25794 + 1.25794i
\(92\) −1.41421 1.41421i −0.147442 0.147442i
\(93\) −7.24264 + 1.24264i −0.751027 + 0.128856i
\(94\) 1.00000 1.00000i 0.103142 0.103142i
\(95\) −5.65685 −0.580381
\(96\) −0.292893 1.70711i −0.0298933 0.174231i
\(97\) 6.00000 + 6.00000i 0.609208 + 0.609208i 0.942739 0.333531i \(-0.108240\pi\)
−0.333531 + 0.942739i \(0.608240\pi\)
\(98\) 6.36396 + 6.36396i 0.642857 + 0.642857i
\(99\) −1.41421 4.00000i −0.142134 0.402015i
\(100\) 1.00000 0.100000
\(101\) −1.41421 −0.140720 −0.0703598 0.997522i \(-0.522415\pi\)
−0.0703598 + 0.997522i \(0.522415\pi\)
\(102\) −2.82843 2.00000i −0.280056 0.198030i
\(103\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(104\) 4.24264 0.416025
\(105\) 6.82843 1.17157i 0.666386 0.114334i
\(106\) −2.00000 + 2.00000i −0.194257 + 0.194257i
\(107\) 8.48528i 0.820303i −0.912017 0.410152i \(-0.865476\pi\)
0.912017 0.410152i \(-0.134524\pi\)
\(108\) −5.00000 1.41421i −0.481125 0.136083i
\(109\) 14.0000 + 14.0000i 1.34096 + 1.34096i 0.895109 + 0.445848i \(0.147098\pi\)
0.445848 + 0.895109i \(0.352902\pi\)
\(110\) 1.41421 0.134840
\(111\) −9.48528 4.58579i −0.900303 0.435264i
\(112\) 4.00000 0.377964
\(113\) −1.41421 1.41421i −0.133038 0.133038i 0.637452 0.770490i \(-0.279988\pi\)
−0.770490 + 0.637452i \(0.779988\pi\)
\(114\) −5.65685 + 8.00000i −0.529813 + 0.749269i
\(115\) 2.00000i 0.186501i
\(116\) 2.82843 2.82843i 0.262613 0.262613i
\(117\) 5.48528 11.4853i 0.507114 1.06181i
\(118\) 12.0000 1.10469
\(119\) 5.65685 5.65685i 0.518563 0.518563i
\(120\) 1.00000 1.41421i 0.0912871 0.129099i
\(121\) −9.00000 −0.818182
\(122\) −8.48528 −0.768221
\(123\) 8.00000 + 5.65685i 0.721336 + 0.510061i
\(124\) −3.00000 3.00000i −0.269408 0.269408i
\(125\) 0.707107 + 0.707107i 0.0632456 + 0.0632456i
\(126\) 5.17157 10.8284i 0.460720 0.964673i
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 1.24264 + 7.24264i 0.109408 + 0.637679i
\(130\) 3.00000 + 3.00000i 0.263117 + 0.263117i
\(131\) 2.82843 + 2.82843i 0.247121 + 0.247121i 0.819788 0.572667i \(-0.194091\pi\)
−0.572667 + 0.819788i \(0.694091\pi\)
\(132\) 1.41421 2.00000i 0.123091 0.174078i
\(133\) −16.0000 16.0000i −1.38738 1.38738i
\(134\) −4.24264 + 4.24264i −0.366508 + 0.366508i
\(135\) −2.53553 4.53553i −0.218224 0.390357i
\(136\) 2.00000i 0.171499i
\(137\) 21.2132i 1.81237i −0.422885 0.906183i \(-0.638983\pi\)
0.422885 0.906183i \(-0.361017\pi\)
\(138\) −2.82843 2.00000i −0.240772 0.170251i
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 2.82843 + 2.82843i 0.239046 + 0.239046i
\(141\) 1.41421 2.00000i 0.119098 0.168430i
\(142\) −2.00000 + 2.00000i −0.167836 + 0.167836i
\(143\) 4.24264 + 4.24264i 0.354787 + 0.354787i
\(144\) −1.00000 2.82843i −0.0833333 0.235702i
\(145\) 4.00000 0.332182
\(146\) −7.07107 + 7.07107i −0.585206 + 0.585206i
\(147\) 12.7279 + 9.00000i 1.04978 + 0.742307i
\(148\) −1.00000 6.00000i −0.0821995 0.493197i
\(149\) 18.3848i 1.50614i 0.657941 + 0.753070i \(0.271428\pi\)
−0.657941 + 0.753070i \(0.728572\pi\)
\(150\) 1.70711 0.292893i 0.139385 0.0239146i
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) −5.65685 −0.458831
\(153\) −5.41421 2.58579i −0.437713 0.209048i
\(154\) 4.00000 + 4.00000i 0.322329 + 0.322329i
\(155\) 4.24264i 0.340777i
\(156\) 7.24264 1.24264i 0.579875 0.0994909i
\(157\) −14.0000 −1.11732 −0.558661 0.829396i \(-0.688685\pi\)
−0.558661 + 0.829396i \(0.688685\pi\)
\(158\) 7.07107i 0.562544i
\(159\) −2.82843 + 4.00000i −0.224309 + 0.317221i
\(160\) 1.00000 0.0790569
\(161\) 5.65685 5.65685i 0.445823 0.445823i
\(162\) −8.94975 0.949747i −0.703159 0.0746192i
\(163\) −15.0000 + 15.0000i −1.17489 + 1.17489i −0.193862 + 0.981029i \(0.562101\pi\)
−0.981029 + 0.193862i \(0.937899\pi\)
\(164\) 5.65685i 0.441726i
\(165\) 2.41421 0.414214i 0.187946 0.0322465i
\(166\) 2.00000 2.00000i 0.155230 0.155230i
\(167\) 1.41421 1.41421i 0.109435 0.109435i −0.650269 0.759704i \(-0.725344\pi\)
0.759704 + 0.650269i \(0.225344\pi\)
\(168\) 6.82843 1.17157i 0.526825 0.0903888i
\(169\) 5.00000i 0.384615i
\(170\) 1.41421 1.41421i 0.108465 0.108465i
\(171\) −7.31371 + 15.3137i −0.559293 + 1.17107i
\(172\) −3.00000 + 3.00000i −0.228748 + 0.228748i
\(173\) −19.7990 −1.50529 −0.752645 0.658427i \(-0.771222\pi\)
−0.752645 + 0.658427i \(0.771222\pi\)
\(174\) 4.00000 5.65685i 0.303239 0.428845i
\(175\) 4.00000i 0.302372i
\(176\) 1.41421 0.106600
\(177\) 20.4853 3.51472i 1.53977 0.264182i
\(178\) 2.00000i 0.149906i
\(179\) −7.07107 7.07107i −0.528516 0.528516i 0.391613 0.920130i \(-0.371917\pi\)
−0.920130 + 0.391613i \(0.871917\pi\)
\(180\) 1.29289 2.70711i 0.0963666 0.201776i
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 16.9706i 1.25794i
\(183\) −14.4853 + 2.48528i −1.07078 + 0.183717i
\(184\) 2.00000i 0.147442i
\(185\) 3.53553 4.94975i 0.259938 0.363913i
\(186\) −6.00000 4.24264i −0.439941 0.311086i
\(187\) 2.00000 2.00000i 0.146254 0.146254i
\(188\) 1.41421 0.103142
\(189\) 5.65685 20.0000i 0.411476 1.45479i
\(190\) −4.00000 4.00000i −0.290191 0.290191i
\(191\) −16.9706 + 16.9706i −1.22795 + 1.22795i −0.263208 + 0.964739i \(0.584780\pi\)
−0.964739 + 0.263208i \(0.915220\pi\)
\(192\) 1.00000 1.41421i 0.0721688 0.102062i
\(193\) −12.0000 12.0000i −0.863779 0.863779i 0.127996 0.991775i \(-0.459146\pi\)
−0.991775 + 0.127996i \(0.959146\pi\)
\(194\) 8.48528i 0.609208i
\(195\) 6.00000 + 4.24264i 0.429669 + 0.303822i
\(196\) 9.00000i 0.642857i
\(197\) 2.82843i 0.201517i 0.994911 + 0.100759i \(0.0321270\pi\)
−0.994911 + 0.100759i \(0.967873\pi\)
\(198\) 1.82843 3.82843i 0.129941 0.272074i
\(199\) 1.00000 1.00000i 0.0708881 0.0708881i −0.670774 0.741662i \(-0.734038\pi\)
0.741662 + 0.670774i \(0.234038\pi\)
\(200\) 0.707107 + 0.707107i 0.0500000 + 0.0500000i
\(201\) −6.00000 + 8.48528i −0.423207 + 0.598506i
\(202\) −1.00000 1.00000i −0.0703598 0.0703598i
\(203\) 11.3137 + 11.3137i 0.794067 + 0.794067i
\(204\) −0.585786 3.41421i −0.0410133 0.239043i
\(205\) −4.00000 + 4.00000i −0.279372 + 0.279372i
\(206\) 0 0
\(207\) −5.41421 2.58579i −0.376314 0.179725i
\(208\) 3.00000 + 3.00000i 0.208013 + 0.208013i
\(209\) −5.65685 5.65685i −0.391293 0.391293i
\(210\) 5.65685 + 4.00000i 0.390360 + 0.276026i
\(211\) 8.00000 0.550743 0.275371 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) −2.82843 −0.194257
\(213\) −2.82843 + 4.00000i −0.193801 + 0.274075i
\(214\) 6.00000 6.00000i 0.410152 0.410152i
\(215\) −4.24264 −0.289346
\(216\) −2.53553 4.53553i −0.172521 0.308604i
\(217\) 12.0000 12.0000i 0.814613 0.814613i
\(218\) 19.7990i 1.34096i
\(219\) −10.0000 + 14.1421i −0.675737 + 0.955637i
\(220\) 1.00000 + 1.00000i 0.0674200 + 0.0674200i
\(221\) 8.48528 0.570782
\(222\) −3.46447 9.94975i −0.232520 0.667783i
\(223\) 8.00000 0.535720 0.267860 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) 2.82843 + 2.82843i 0.188982 + 0.188982i
\(225\) 2.82843 1.00000i 0.188562 0.0666667i
\(226\) 2.00000i 0.133038i
\(227\) 16.9706 16.9706i 1.12638 1.12638i 0.135614 0.990762i \(-0.456699\pi\)
0.990762 0.135614i \(-0.0433007\pi\)
\(228\) −9.65685 + 1.65685i −0.639541 + 0.109728i
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 1.41421 1.41421i 0.0932505 0.0932505i
\(231\) 8.00000 + 5.65685i 0.526361 + 0.372194i
\(232\) 4.00000 0.262613
\(233\) 12.7279 0.833834 0.416917 0.908945i \(-0.363111\pi\)
0.416917 + 0.908945i \(0.363111\pi\)
\(234\) 12.0000 4.24264i 0.784465 0.277350i
\(235\) 1.00000 + 1.00000i 0.0652328 + 0.0652328i
\(236\) 8.48528 + 8.48528i 0.552345 + 0.552345i
\(237\) 2.07107 + 12.0711i 0.134530 + 0.784100i
\(238\) 8.00000 0.518563
\(239\) 14.1421 14.1421i 0.914779 0.914779i −0.0818647 0.996643i \(-0.526088\pi\)
0.996643 + 0.0818647i \(0.0260876\pi\)
\(240\) 1.70711 0.292893i 0.110193 0.0189062i
\(241\) −13.0000 13.0000i −0.837404 0.837404i 0.151113 0.988517i \(-0.451714\pi\)
−0.988517 + 0.151113i \(0.951714\pi\)
\(242\) −6.36396 6.36396i −0.409091 0.409091i
\(243\) −15.5563 + 1.00000i −0.997940 + 0.0641500i
\(244\) −6.00000 6.00000i −0.384111 0.384111i
\(245\) −6.36396 + 6.36396i −0.406579 + 0.406579i
\(246\) 1.65685 + 9.65685i 0.105637 + 0.615699i
\(247\) 24.0000i 1.52708i
\(248\) 4.24264i 0.269408i
\(249\) 2.82843 4.00000i 0.179244 0.253490i
\(250\) 1.00000i 0.0632456i
\(251\) 8.48528 + 8.48528i 0.535586 + 0.535586i 0.922229 0.386643i \(-0.126365\pi\)
−0.386643 + 0.922229i \(0.626365\pi\)
\(252\) 11.3137 4.00000i 0.712697 0.251976i
\(253\) 2.00000 2.00000i 0.125739 0.125739i
\(254\) 11.3137 + 11.3137i 0.709885 + 0.709885i
\(255\) 2.00000 2.82843i 0.125245 0.177123i
\(256\) 1.00000 0.0625000
\(257\) −16.9706 + 16.9706i −1.05859 + 1.05859i −0.0604217 + 0.998173i \(0.519245\pi\)
−0.998173 + 0.0604217i \(0.980755\pi\)
\(258\) −4.24264 + 6.00000i −0.264135 + 0.373544i
\(259\) 24.0000 4.00000i 1.49129 0.248548i
\(260\) 4.24264i 0.263117i
\(261\) 5.17157 10.8284i 0.320112 0.670263i
\(262\) 4.00000i 0.247121i
\(263\) 26.8701 1.65688 0.828439 0.560079i \(-0.189229\pi\)
0.828439 + 0.560079i \(0.189229\pi\)
\(264\) 2.41421 0.414214i 0.148585 0.0254931i
\(265\) −2.00000 2.00000i −0.122859 0.122859i
\(266\) 22.6274i 1.38738i
\(267\) 0.585786 + 3.41421i 0.0358495 + 0.208946i
\(268\) −6.00000 −0.366508
\(269\) 7.07107i 0.431131i 0.976489 + 0.215565i \(0.0691594\pi\)
−0.976489 + 0.215565i \(0.930841\pi\)
\(270\) 1.41421 5.00000i 0.0860663 0.304290i
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 1.41421 1.41421i 0.0857493 0.0857493i
\(273\) 4.97056 + 28.9706i 0.300832 + 1.75338i
\(274\) 15.0000 15.0000i 0.906183 0.906183i
\(275\) 1.41421i 0.0852803i
\(276\) −0.585786 3.41421i −0.0352602 0.205512i
\(277\) 15.0000 15.0000i 0.901263 0.901263i −0.0942828 0.995545i \(-0.530056\pi\)
0.995545 + 0.0942828i \(0.0300558\pi\)
\(278\) 0 0
\(279\) −11.4853 5.48528i −0.687606 0.328395i
\(280\) 4.00000i 0.239046i
\(281\) 4.24264 4.24264i 0.253095 0.253095i −0.569143 0.822238i \(-0.692725\pi\)
0.822238 + 0.569143i \(0.192725\pi\)
\(282\) 2.41421 0.414214i 0.143764 0.0246661i
\(283\) −21.0000 + 21.0000i −1.24832 + 1.24832i −0.291859 + 0.956461i \(0.594274\pi\)
−0.956461 + 0.291859i \(0.905726\pi\)
\(284\) −2.82843 −0.167836
\(285\) −8.00000 5.65685i −0.473879 0.335083i
\(286\) 6.00000i 0.354787i
\(287\) −22.6274 −1.33565
\(288\) 1.29289 2.70711i 0.0761845 0.159518i
\(289\) 13.0000i 0.764706i
\(290\) 2.82843 + 2.82843i 0.166091 + 0.166091i
\(291\) 2.48528 + 14.4853i 0.145690 + 0.849142i
\(292\) −10.0000 −0.585206
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 2.63604 + 15.3640i 0.153737 + 0.896044i
\(295\) 12.0000i 0.698667i
\(296\) 3.53553 4.94975i 0.205499 0.287698i
\(297\) 2.00000 7.07107i 0.116052 0.410305i
\(298\) −13.0000 + 13.0000i −0.753070 + 0.753070i
\(299\) 8.48528 0.490716
\(300\) 1.41421 + 1.00000i 0.0816497 + 0.0577350i
\(301\) −12.0000 12.0000i −0.691669 0.691669i
\(302\) 0 0
\(303\) −2.00000 1.41421i −0.114897 0.0812444i
\(304\) −4.00000 4.00000i −0.229416 0.229416i
\(305\) 8.48528i 0.485866i
\(306\) −2.00000 5.65685i −0.114332 0.323381i
\(307\) 28.0000i 1.59804i −0.601302 0.799022i \(-0.705351\pi\)
0.601302 0.799022i \(-0.294649\pi\)
\(308\) 5.65685i 0.322329i
\(309\) 0 0
\(310\) 3.00000 3.00000i 0.170389 0.170389i
\(311\) 14.1421 + 14.1421i 0.801927 + 0.801927i 0.983397 0.181470i \(-0.0580854\pi\)
−0.181470 + 0.983397i \(0.558085\pi\)
\(312\) 6.00000 + 4.24264i 0.339683 + 0.240192i
\(313\) 24.0000 + 24.0000i 1.35656 + 1.35656i 0.878120 + 0.478440i \(0.158798\pi\)
0.478440 + 0.878120i \(0.341202\pi\)
\(314\) −9.89949 9.89949i −0.558661 0.558661i
\(315\) 10.8284 + 5.17157i 0.610113 + 0.291385i
\(316\) −5.00000 + 5.00000i −0.281272 + 0.281272i
\(317\) −25.4558 −1.42974 −0.714871 0.699256i \(-0.753515\pi\)
−0.714871 + 0.699256i \(0.753515\pi\)
\(318\) −4.82843 + 0.828427i −0.270765 + 0.0464559i
\(319\) 4.00000 + 4.00000i 0.223957 + 0.223957i
\(320\) 0.707107 + 0.707107i 0.0395285 + 0.0395285i
\(321\) 8.48528 12.0000i 0.473602 0.669775i
\(322\) 8.00000 0.445823
\(323\) −11.3137 −0.629512
\(324\) −5.65685 7.00000i −0.314270 0.388889i
\(325\) −3.00000 + 3.00000i −0.166410 + 0.166410i
\(326\) −21.2132 −1.17489
\(327\) 5.79899 + 33.7990i 0.320685 + 1.86909i
\(328\) −4.00000 + 4.00000i −0.220863 + 0.220863i
\(329\) 5.65685i 0.311872i
\(330\) 2.00000 + 1.41421i 0.110096 + 0.0778499i
\(331\) −2.00000 2.00000i −0.109930 0.109930i 0.650002 0.759932i \(-0.274768\pi\)
−0.759932 + 0.650002i \(0.774768\pi\)
\(332\) 2.82843 0.155230
\(333\) −8.82843 15.9706i −0.483795 0.875181i
\(334\) 2.00000 0.109435
\(335\) −4.24264 4.24264i −0.231800 0.231800i
\(336\) 5.65685 + 4.00000i 0.308607 + 0.218218i
\(337\) 26.0000i 1.41631i 0.706057 + 0.708155i \(0.250472\pi\)
−0.706057 + 0.708155i \(0.749528\pi\)
\(338\) −3.53553 + 3.53553i −0.192308 + 0.192308i
\(339\) −0.585786 3.41421i −0.0318156 0.185435i
\(340\) 2.00000 0.108465
\(341\) 4.24264 4.24264i 0.229752 0.229752i
\(342\) −16.0000 + 5.65685i −0.865181 + 0.305888i
\(343\) −8.00000 −0.431959
\(344\) −4.24264 −0.228748
\(345\) 2.00000 2.82843i 0.107676 0.152277i
\(346\) −14.0000 14.0000i −0.752645 0.752645i
\(347\) 22.6274 + 22.6274i 1.21470 + 1.21470i 0.969462 + 0.245241i \(0.0788672\pi\)
0.245241 + 0.969462i \(0.421133\pi\)
\(348\) 6.82843 1.17157i 0.366042 0.0628029i
\(349\) 6.00000 0.321173 0.160586 0.987022i \(-0.448662\pi\)
0.160586 + 0.987022i \(0.448662\pi\)
\(350\) −2.82843 + 2.82843i −0.151186 + 0.151186i
\(351\) 19.2426 10.7574i 1.02710 0.574185i
\(352\) 1.00000 + 1.00000i 0.0533002 + 0.0533002i
\(353\) −18.3848 18.3848i −0.978523 0.978523i 0.0212513 0.999774i \(-0.493235\pi\)
−0.999774 + 0.0212513i \(0.993235\pi\)
\(354\) 16.9706 + 12.0000i 0.901975 + 0.637793i
\(355\) −2.00000 2.00000i −0.106149 0.106149i
\(356\) −1.41421 + 1.41421i −0.0749532 + 0.0749532i
\(357\) 13.6569 2.34315i 0.722797 0.124012i
\(358\) 10.0000i 0.528516i
\(359\) 22.6274i 1.19423i −0.802156 0.597115i \(-0.796314\pi\)
0.802156 0.597115i \(-0.203686\pi\)
\(360\) 2.82843 1.00000i 0.149071 0.0527046i
\(361\) 13.0000i 0.684211i
\(362\) 7.07107 + 7.07107i 0.371647 + 0.371647i
\(363\) −12.7279 9.00000i −0.668043 0.472377i
\(364\) −12.0000 + 12.0000i −0.628971 + 0.628971i
\(365\) −7.07107 7.07107i −0.370117 0.370117i
\(366\) −12.0000 8.48528i −0.627250 0.443533i
\(367\) −12.0000 −0.626395 −0.313197 0.949688i \(-0.601400\pi\)
−0.313197 + 0.949688i \(0.601400\pi\)
\(368\) 1.41421 1.41421i 0.0737210 0.0737210i
\(369\) 5.65685 + 16.0000i 0.294484 + 0.832927i
\(370\) 6.00000 1.00000i 0.311925 0.0519875i
\(371\) 11.3137i 0.587378i
\(372\) −1.24264 7.24264i −0.0644279 0.375513i
\(373\) 22.0000i 1.13912i −0.821951 0.569558i \(-0.807114\pi\)
0.821951 0.569558i \(-0.192886\pi\)
\(374\) 2.82843 0.146254
\(375\) 0.292893 + 1.70711i 0.0151249 + 0.0881546i
\(376\) 1.00000 + 1.00000i 0.0515711 + 0.0515711i
\(377\) 16.9706i 0.874028i
\(378\) 18.1421 10.1421i 0.933131 0.521655i
\(379\) 28.0000 1.43826 0.719132 0.694874i \(-0.244540\pi\)
0.719132 + 0.694874i \(0.244540\pi\)
\(380\) 5.65685i 0.290191i
\(381\) 22.6274 + 16.0000i 1.15924 + 0.819705i
\(382\) −24.0000 −1.22795
\(383\) 16.9706 16.9706i 0.867155 0.867155i −0.125001 0.992157i \(-0.539894\pi\)
0.992157 + 0.125001i \(0.0398935\pi\)
\(384\) 1.70711 0.292893i 0.0871154 0.0149466i
\(385\) −4.00000 + 4.00000i −0.203859 + 0.203859i
\(386\) 16.9706i 0.863779i
\(387\) −5.48528 + 11.4853i −0.278833 + 0.583830i
\(388\) −6.00000 + 6.00000i −0.304604 + 0.304604i
\(389\) 16.9706 16.9706i 0.860442 0.860442i −0.130948 0.991389i \(-0.541802\pi\)
0.991389 + 0.130948i \(0.0418020\pi\)
\(390\) 1.24264 + 7.24264i 0.0629236 + 0.366745i
\(391\) 4.00000i 0.202289i
\(392\) −6.36396 + 6.36396i −0.321429 + 0.321429i
\(393\) 1.17157 + 6.82843i 0.0590980 + 0.344449i
\(394\) −2.00000 + 2.00000i −0.100759 + 0.100759i
\(395\) −7.07107 −0.355784
\(396\) 4.00000 1.41421i 0.201008 0.0710669i
\(397\) 22.0000i 1.10415i 0.833795 + 0.552074i \(0.186163\pi\)
−0.833795 + 0.552074i \(0.813837\pi\)
\(398\) 1.41421 0.0708881
\(399\) −6.62742 38.6274i −0.331786 1.93379i
\(400\) 1.00000i 0.0500000i
\(401\) −4.24264 4.24264i −0.211867 0.211867i 0.593193 0.805060i \(-0.297867\pi\)
−0.805060 + 0.593193i \(0.797867\pi\)
\(402\) −10.2426 + 1.75736i −0.510856 + 0.0876491i
\(403\) 18.0000 0.896644
\(404\) 1.41421i 0.0703598i
\(405\) 0.949747 8.94975i 0.0471933 0.444717i
\(406\) 16.0000i 0.794067i
\(407\) 8.48528 1.41421i 0.420600 0.0701000i
\(408\) 2.00000 2.82843i 0.0990148 0.140028i
\(409\) −3.00000 + 3.00000i −0.148340 + 0.148340i −0.777376 0.629036i \(-0.783450\pi\)
0.629036 + 0.777376i \(0.283450\pi\)
\(410\) −5.65685 −0.279372
\(411\) 21.2132 30.0000i 1.04637 1.47979i
\(412\) 0 0
\(413\) −33.9411 + 33.9411i −1.67013 + 1.67013i
\(414\) −2.00000 5.65685i −0.0982946 0.278019i
\(415\) 2.00000 + 2.00000i 0.0981761 + 0.0981761i
\(416\) 4.24264i 0.208013i
\(417\) 0 0
\(418\) 8.00000i 0.391293i
\(419\) 32.5269i 1.58904i −0.607236 0.794522i \(-0.707722\pi\)
0.607236 0.794522i \(-0.292278\pi\)
\(420\) 1.17157 + 6.82843i 0.0571669 + 0.333193i
\(421\) 20.0000 20.0000i 0.974740 0.974740i −0.0249484 0.999689i \(-0.507942\pi\)
0.999689 + 0.0249484i \(0.00794214\pi\)
\(422\) 5.65685 + 5.65685i 0.275371 + 0.275371i
\(423\) 4.00000 1.41421i 0.194487 0.0687614i
\(424\) −2.00000 2.00000i −0.0971286 0.0971286i
\(425\) 1.41421 + 1.41421i 0.0685994 + 0.0685994i
\(426\) −4.82843 + 0.828427i −0.233938 + 0.0401374i
\(427\) 24.0000 24.0000i 1.16144 1.16144i
\(428\) 8.48528 0.410152
\(429\) 1.75736 + 10.2426i 0.0848461 + 0.494519i
\(430\) −3.00000 3.00000i −0.144673 0.144673i
\(431\) 8.48528 + 8.48528i 0.408722 + 0.408722i 0.881293 0.472571i \(-0.156674\pi\)
−0.472571 + 0.881293i \(0.656674\pi\)
\(432\) 1.41421 5.00000i 0.0680414 0.240563i
\(433\) −34.0000 −1.63394 −0.816968 0.576683i \(-0.804347\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) 16.9706 0.814613
\(435\) 5.65685 + 4.00000i 0.271225 + 0.191785i
\(436\) −14.0000 + 14.0000i −0.670478 + 0.670478i
\(437\) −11.3137 −0.541208
\(438\) −17.0711 + 2.92893i −0.815687 + 0.139950i
\(439\) 9.00000 9.00000i 0.429547 0.429547i −0.458927 0.888474i \(-0.651766\pi\)
0.888474 + 0.458927i \(0.151766\pi\)
\(440\) 1.41421i 0.0674200i
\(441\) 9.00000 + 25.4558i 0.428571 + 1.21218i
\(442\) 6.00000 + 6.00000i 0.285391 + 0.285391i
\(443\) −14.1421 −0.671913 −0.335957 0.941877i \(-0.609060\pi\)
−0.335957 + 0.941877i \(0.609060\pi\)
\(444\) 4.58579 9.48528i 0.217632 0.450152i
\(445\) −2.00000 −0.0948091
\(446\) 5.65685 + 5.65685i 0.267860 + 0.267860i
\(447\) −18.3848 + 26.0000i −0.869570 + 1.22976i
\(448\) 4.00000i 0.188982i
\(449\) −15.5563 + 15.5563i −0.734150 + 0.734150i −0.971439 0.237289i \(-0.923741\pi\)
0.237289 + 0.971439i \(0.423741\pi\)
\(450\) 2.70711 + 1.29289i 0.127614 + 0.0609476i
\(451\) −8.00000 −0.376705
\(452\) 1.41421 1.41421i 0.0665190 0.0665190i
\(453\) 0 0
\(454\) 24.0000 1.12638
\(455\) −16.9706 −0.795592
\(456\) −8.00000 5.65685i −0.374634 0.264906i
\(457\) −30.0000 30.0000i −1.40334 1.40334i −0.789184 0.614157i \(-0.789496\pi\)
−0.614157 0.789184i \(-0.710504\pi\)
\(458\) 7.07107 + 7.07107i 0.330409 + 0.330409i
\(459\) −5.07107 9.07107i −0.236697 0.423401i
\(460\) 2.00000 0.0932505
\(461\) −4.24264 + 4.24264i −0.197599 + 0.197599i −0.798970 0.601371i \(-0.794622\pi\)
0.601371 + 0.798970i \(0.294622\pi\)
\(462\) 1.65685 + 9.65685i 0.0770838 + 0.449278i
\(463\) −4.00000 4.00000i −0.185896 0.185896i 0.608023 0.793919i \(-0.291963\pi\)
−0.793919 + 0.608023i \(0.791963\pi\)
\(464\) 2.82843 + 2.82843i 0.131306 + 0.131306i
\(465\) 4.24264 6.00000i 0.196748 0.278243i
\(466\) 9.00000 + 9.00000i 0.416917 + 0.416917i
\(467\) −22.6274 + 22.6274i −1.04707 + 1.04707i −0.0482360 + 0.998836i \(0.515360\pi\)
−0.998836 + 0.0482360i \(0.984640\pi\)
\(468\) 11.4853 + 5.48528i 0.530907 + 0.253557i
\(469\) 24.0000i 1.10822i
\(470\) 1.41421i 0.0652328i
\(471\) −19.7990 14.0000i −0.912289 0.645086i
\(472\) 12.0000i 0.552345i
\(473\) −4.24264 4.24264i −0.195077 0.195077i
\(474\) −7.07107 + 10.0000i −0.324785 + 0.459315i
\(475\) 4.00000 4.00000i 0.183533 0.183533i
\(476\) 5.65685 + 5.65685i 0.259281 + 0.259281i
\(477\) −8.00000 + 2.82843i −0.366295 + 0.129505i
\(478\) 20.0000 0.914779
\(479\) 11.3137 11.3137i 0.516937 0.516937i −0.399707 0.916643i \(-0.630888\pi\)
0.916643 + 0.399707i \(0.130888\pi\)
\(480\) 1.41421 + 1.00000i 0.0645497 + 0.0456435i
\(481\) 21.0000 + 15.0000i 0.957518 + 0.683941i
\(482\) 18.3848i 0.837404i
\(483\) 13.6569 2.34315i 0.621408 0.106617i
\(484\) 9.00000i 0.409091i
\(485\) −8.48528 −0.385297
\(486\) −11.7071 10.2929i −0.531045 0.466895i
\(487\) 8.00000 + 8.00000i 0.362515 + 0.362515i 0.864738 0.502223i \(-0.167484\pi\)
−0.502223 + 0.864738i \(0.667484\pi\)
\(488\) 8.48528i 0.384111i
\(489\) −36.2132 + 6.21320i −1.63762 + 0.280971i
\(490\) −9.00000 −0.406579
\(491\) 12.7279i 0.574403i −0.957870 0.287202i \(-0.907275\pi\)
0.957870 0.287202i \(-0.0927249\pi\)
\(492\) −5.65685 + 8.00000i −0.255031 + 0.360668i
\(493\) 8.00000 0.360302
\(494\) 16.9706 16.9706i 0.763542 0.763542i
\(495\) 3.82843 + 1.82843i 0.172075 + 0.0821817i
\(496\) 3.00000 3.00000i 0.134704 0.134704i
\(497\) 11.3137i 0.507489i
\(498\) 4.82843 0.828427i 0.216367 0.0371227i
\(499\) 6.00000 6.00000i 0.268597 0.268597i −0.559938 0.828535i \(-0.689175\pi\)
0.828535 + 0.559938i \(0.189175\pi\)
\(500\) −0.707107 + 0.707107i −0.0316228 + 0.0316228i
\(501\) 3.41421 0.585786i 0.152536 0.0261710i
\(502\) 12.0000i 0.535586i
\(503\) −7.07107 + 7.07107i −0.315283 + 0.315283i −0.846952 0.531669i \(-0.821565\pi\)
0.531669 + 0.846952i \(0.321565\pi\)
\(504\) 10.8284 + 5.17157i 0.482336 + 0.230360i
\(505\) 1.00000 1.00000i 0.0444994 0.0444994i
\(506\) 2.82843 0.125739
\(507\) −5.00000 + 7.07107i −0.222058 + 0.314037i
\(508\) 16.0000i 0.709885i
\(509\) −1.41421 −0.0626839 −0.0313420 0.999509i \(-0.509978\pi\)
−0.0313420 + 0.999509i \(0.509978\pi\)
\(510\) 3.41421 0.585786i 0.151184 0.0259391i
\(511\) 40.0000i 1.76950i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) −25.6569 + 14.3431i −1.13278 + 0.633265i
\(514\) −24.0000 −1.05859
\(515\) 0 0
\(516\) −7.24264 + 1.24264i −0.318839 + 0.0547042i
\(517\) 2.00000i 0.0879599i
\(518\) 19.7990 + 14.1421i 0.869918 + 0.621370i
\(519\) −28.0000 19.7990i −1.22906 0.869079i
\(520\) −3.00000 + 3.00000i −0.131559 + 0.131559i
\(521\) −31.1127 −1.36307 −0.681536 0.731785i \(-0.738688\pi\)
−0.681536 + 0.731785i \(0.738688\pi\)
\(522\) 11.3137 4.00000i 0.495188 0.175075i
\(523\) 21.0000 + 21.0000i 0.918266 + 0.918266i 0.996903 0.0786374i \(-0.0250569\pi\)
−0.0786374 + 0.996903i \(0.525057\pi\)
\(524\) −2.82843 + 2.82843i −0.123560 + 0.123560i
\(525\) −4.00000 + 5.65685i −0.174574 + 0.246885i
\(526\) 19.0000 + 19.0000i 0.828439 + 0.828439i
\(527\) 8.48528i 0.369625i
\(528\) 2.00000 + 1.41421i 0.0870388 + 0.0615457i
\(529\) 19.0000i 0.826087i
\(530\) 2.82843i 0.122859i
\(531\) 32.4853 + 15.5147i 1.40974 + 0.673281i
\(532\) 16.0000 16.0000i 0.693688 0.693688i
\(533\) −16.9706 16.9706i −0.735077 0.735077i
\(534\) −2.00000 + 2.82843i −0.0865485 + 0.122398i
\(535\) 6.00000 + 6.00000i 0.259403 + 0.259403i
\(536\) −4.24264 4.24264i −0.183254 0.183254i
\(537\) −2.92893 17.0711i −0.126393 0.736671i
\(538\) −5.00000 + 5.00000i −0.215565 + 0.215565i
\(539\) −12.7279 −0.548230
\(540\) 4.53553 2.53553i 0.195178 0.109112i
\(541\) −12.0000 12.0000i −0.515920 0.515920i 0.400414 0.916334i \(-0.368866\pi\)
−0.916334 + 0.400414i \(0.868866\pi\)
\(542\) −11.3137 11.3137i −0.485965 0.485965i
\(543\) 14.1421 + 10.0000i 0.606897 + 0.429141i
\(544\) 2.00000 0.0857493
\(545\) −19.7990 −0.848096
\(546\) −16.9706 + 24.0000i −0.726273 + 1.02711i
\(547\) −3.00000 + 3.00000i −0.128271 + 0.128271i −0.768328 0.640057i \(-0.778911\pi\)
0.640057 + 0.768328i \(0.278911\pi\)
\(548\) 21.2132 0.906183
\(549\) −22.9706 10.9706i −0.980360 0.468212i
\(550\) −1.00000 + 1.00000i −0.0426401 + 0.0426401i
\(551\) 22.6274i 0.963960i
\(552\) 2.00000 2.82843i 0.0851257 0.120386i
\(553\) −20.0000 20.0000i −0.850487 0.850487i
\(554\) 21.2132 0.901263
\(555\) 9.94975 3.46447i 0.422343 0.147058i
\(556\) 0 0
\(557\) −1.41421 1.41421i −0.0599222 0.0599222i 0.676511 0.736433i \(-0.263491\pi\)
−0.736433 + 0.676511i \(0.763491\pi\)
\(558\) −4.24264 12.0000i −0.179605 0.508001i
\(559\) 18.0000i 0.761319i
\(560\) −2.82843 + 2.82843i −0.119523 + 0.119523i
\(561\) 4.82843 0.828427i 0.203856 0.0349762i
\(562\) 6.00000 0.253095
\(563\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(564\) 2.00000 + 1.41421i 0.0842152 + 0.0595491i
\(565\) 2.00000 0.0841406
\(566\) −29.6985 −1.24832
\(567\) 28.0000 22.6274i 1.17589 0.950262i
\(568\) −2.00000 2.00000i −0.0839181 0.0839181i
\(569\) 29.6985 + 29.6985i 1.24503 + 1.24503i 0.957890 + 0.287135i \(0.0927029\pi\)
0.287135 + 0.957890i \(0.407297\pi\)
\(570\) −1.65685 9.65685i −0.0693980 0.404481i
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) −4.24264 + 4.24264i −0.177394 + 0.177394i
\(573\) −40.9706 + 7.02944i −1.71157 + 0.293659i
\(574\) −16.0000 16.0000i −0.667827 0.667827i
\(575\) 1.41421 + 1.41421i 0.0589768 + 0.0589768i
\(576\) 2.82843 1.00000i 0.117851 0.0416667i
\(577\) 10.0000 + 10.0000i 0.416305 + 0.416305i 0.883928 0.467623i \(-0.154889\pi\)
−0.467623 + 0.883928i \(0.654889\pi\)
\(578\) −9.19239 + 9.19239i −0.382353 + 0.382353i
\(579\) −4.97056 28.9706i −0.206570 1.20398i
\(580\) 4.00000i 0.166091i
\(581\) 11.3137i 0.469372i
\(582\) −8.48528 + 12.0000i −0.351726 + 0.497416i
\(583\) 4.00000i 0.165663i
\(584\) −7.07107 7.07107i −0.292603 0.292603i
\(585\) 4.24264 + 12.0000i 0.175412 + 0.496139i
\(586\) 0 0
\(587\) −28.2843 28.2843i −1.16742 1.16742i −0.982813 0.184604i \(-0.940900\pi\)
−0.184604 0.982813i \(-0.559100\pi\)
\(588\) −9.00000 + 12.7279i −0.371154 + 0.524891i
\(589\) −24.0000 −0.988903
\(590\) −8.48528 + 8.48528i −0.349334 + 0.349334i
\(591\) −2.82843 + 4.00000i −0.116346 + 0.164538i
\(592\) 6.00000 1.00000i 0.246598 0.0410997i
\(593\) 24.0416i 0.987271i −0.869669 0.493636i \(-0.835668\pi\)
0.869669 0.493636i \(-0.164332\pi\)
\(594\) 6.41421 3.58579i 0.263178 0.147127i
\(595\) 8.00000i 0.327968i
\(596\) −18.3848 −0.753070
\(597\) 2.41421 0.414214i 0.0988072 0.0169526i
\(598\) 6.00000 + 6.00000i 0.245358 + 0.245358i
\(599\) 22.6274i 0.924531i −0.886742 0.462266i \(-0.847037\pi\)
0.886742 0.462266i \(-0.152963\pi\)
\(600\) 0.292893 + 1.70711i 0.0119573 + 0.0696923i
\(601\) −42.0000 −1.71322 −0.856608 0.515968i \(-0.827432\pi\)
−0.856608 + 0.515968i \(0.827432\pi\)
\(602\) 16.9706i 0.691669i
\(603\) −16.9706 + 6.00000i −0.691095 + 0.244339i
\(604\) 0 0
\(605\) 6.36396 6.36396i 0.258732 0.258732i
\(606\) −0.414214 2.41421i −0.0168263 0.0980707i
\(607\) −8.00000 + 8.00000i −0.324710 + 0.324710i −0.850571 0.525861i \(-0.823743\pi\)
0.525861 + 0.850571i \(0.323743\pi\)
\(608\) 5.65685i 0.229416i
\(609\) 4.68629 + 27.3137i 0.189898 + 1.10681i
\(610\) 6.00000 6.00000i 0.242933 0.242933i
\(611\) −4.24264 + 4.24264i −0.171639 + 0.171639i
\(612\) 2.58579 5.41421i 0.104524 0.218857i
\(613\) 16.0000i 0.646234i 0.946359 + 0.323117i \(0.104731\pi\)
−0.946359 + 0.323117i \(0.895269\pi\)
\(614\) 19.7990 19.7990i 0.799022 0.799022i
\(615\) −9.65685 + 1.65685i −0.389402 + 0.0668108i
\(616\) −4.00000 + 4.00000i −0.161165 + 0.161165i
\(617\) −35.3553 −1.42335 −0.711676 0.702508i \(-0.752064\pi\)
−0.711676 + 0.702508i \(0.752064\pi\)
\(618\) 0 0
\(619\) 20.0000i 0.803868i −0.915669 0.401934i \(-0.868338\pi\)
0.915669 0.401934i \(-0.131662\pi\)
\(620\) 4.24264 0.170389
\(621\) −5.07107 9.07107i −0.203495 0.364009i
\(622\) 20.0000i 0.801927i
\(623\) −5.65685 5.65685i −0.226637 0.226637i
\(624\) 1.24264 + 7.24264i 0.0497454 + 0.289938i
\(625\) −1.00000 −0.0400000
\(626\) 33.9411i 1.35656i
\(627\) −2.34315 13.6569i −0.0935762 0.545402i
\(628\) 14.0000i 0.558661i
\(629\) 7.07107 9.89949i 0.281942 0.394719i
\(630\) 4.00000 + 11.3137i 0.159364 + 0.450749i
\(631\) −11.0000 + 11.0000i −0.437903 + 0.437903i −0.891306 0.453403i \(-0.850210\pi\)
0.453403 + 0.891306i \(0.350210\pi\)
\(632\) −7.07107 −0.281272
\(633\) 11.3137 + 8.00000i 0.449680 + 0.317971i
\(634\) −18.0000 18.0000i −0.714871 0.714871i
\(635\) −11.3137 + 11.3137i −0.448971 + 0.448971i
\(636\) −4.00000 2.82843i −0.158610 0.112154i
\(637\) −27.0000 27.0000i −1.06978 1.06978i
\(638\) 5.65685i 0.223957i
\(639\) −8.00000 + 2.82843i −0.316475 + 0.111891i
\(640\) 1.00000i 0.0395285i
\(641\) 11.3137i 0.446865i 0.974719 + 0.223432i \(0.0717262\pi\)
−0.974719 + 0.223432i \(0.928274\pi\)
\(642\) 14.4853 2.48528i 0.571688 0.0980862i
\(643\) −25.0000 + 25.0000i −0.985904 + 0.985904i −0.999902 0.0139983i \(-0.995544\pi\)
0.0139983 + 0.999902i \(0.495544\pi\)
\(644\) 5.65685 + 5.65685i 0.222911 + 0.222911i
\(645\) −6.00000 4.24264i −0.236250 0.167054i
\(646\) −8.00000 8.00000i −0.314756 0.314756i
\(647\) 5.65685 + 5.65685i 0.222394 + 0.222394i 0.809506 0.587112i \(-0.199735\pi\)
−0.587112 + 0.809506i \(0.699735\pi\)
\(648\) 0.949747 8.94975i 0.0373096 0.351579i
\(649\) −12.0000 + 12.0000i −0.471041 + 0.471041i
\(650\) −4.24264 −0.166410
\(651\) 28.9706 4.97056i 1.13545 0.194812i
\(652\) −15.0000 15.0000i −0.587445 0.587445i
\(653\) 12.7279 + 12.7279i 0.498082 + 0.498082i 0.910841 0.412758i \(-0.135435\pi\)
−0.412758 + 0.910841i \(0.635435\pi\)
\(654\) −19.7990 + 28.0000i −0.774202 + 1.09489i
\(655\) −4.00000 −0.156293
\(656\) −5.65685 −0.220863
\(657\) −28.2843 + 10.0000i −1.10347 + 0.390137i
\(658\) −4.00000 + 4.00000i −0.155936 + 0.155936i
\(659\) 26.8701 1.04671 0.523354 0.852115i \(-0.324680\pi\)
0.523354 + 0.852115i \(0.324680\pi\)
\(660\) 0.414214 + 2.41421i 0.0161232 + 0.0939731i
\(661\) −28.0000 + 28.0000i −1.08907 + 1.08907i −0.0934498 + 0.995624i \(0.529789\pi\)
−0.995624 + 0.0934498i \(0.970211\pi\)
\(662\) 2.82843i 0.109930i
\(663\) 12.0000 + 8.48528i 0.466041 + 0.329541i
\(664\) 2.00000 + 2.00000i 0.0776151 + 0.0776151i
\(665\) 22.6274 0.877454
\(666\) 5.05025 17.5355i 0.195693 0.679488i
\(667\) 8.00000 0.309761
\(668\) 1.41421 + 1.41421i 0.0547176 + 0.0547176i
\(669\) 11.3137 + 8.00000i 0.437413 + 0.309298i
\(670\) 6.00000i 0.231800i
\(671\) 8.48528 8.48528i 0.327571 0.327571i
\(672\) 1.17157 + 6.82843i 0.0451944 + 0.263412i
\(673\) 14.0000 0.539660 0.269830 0.962908i \(-0.413032\pi\)
0.269830 + 0.962908i \(0.413032\pi\)
\(674\) −18.3848 + 18.3848i −0.708155 + 0.708155i
\(675\) 5.00000 + 1.41421i 0.192450 + 0.0544331i
\(676\) −5.00000 −0.192308
\(677\) 45.2548 1.73928 0.869642 0.493682i \(-0.164349\pi\)
0.869642 + 0.493682i \(0.164349\pi\)
\(678\) 2.00000 2.82843i 0.0768095 0.108625i
\(679\) −24.0000 24.0000i −0.921035 0.921035i
\(680\) 1.41421 + 1.41421i 0.0542326 + 0.0542326i
\(681\) 40.9706 7.02944i 1.57000 0.269369i
\(682\) 6.00000 0.229752
\(683\) 33.9411 33.9411i 1.29872 1.29872i 0.369484 0.929237i \(-0.379534\pi\)
0.929237 0.369484i \(-0.120466\pi\)
\(684\) −15.3137 7.31371i −0.585534 0.279647i
\(685\) 15.0000 + 15.0000i 0.573121 + 0.573121i
\(686\) −5.65685 5.65685i −0.215980 0.215980i
\(687\) 14.1421 + 10.0000i 0.539556 + 0.381524i
\(688\) −3.00000 3.00000i −0.114374 0.114374i
\(689\) 8.48528 8.48528i 0.323263 0.323263i
\(690\) 3.41421 0.585786i 0.129977 0.0223005i
\(691\) 12.0000i 0.456502i −0.973602 0.228251i \(-0.926699\pi\)
0.973602 0.228251i \(-0.0733006\pi\)
\(692\) 19.7990i 0.752645i
\(693\) 5.65685 + 16.0000i 0.214886 + 0.607790i
\(694\) 32.0000i 1.21470i
\(695\) 0 0
\(696\) 5.65685 + 4.00000i 0.214423 + 0.151620i
\(697\) −8.00000 + 8.00000i −0.303022 + 0.303022i
\(698\) 4.24264 + 4.24264i 0.160586 + 0.160586i
\(699\) 18.0000 + 12.7279i 0.680823 + 0.481414i
\(700\) −4.00000 −0.151186
\(701\) −21.2132 + 21.2132i −0.801212 + 0.801212i −0.983285 0.182073i \(-0.941719\pi\)
0.182073 + 0.983285i \(0.441719\pi\)
\(702\) 21.2132 + 6.00000i 0.800641 + 0.226455i
\(703\) −28.0000 20.0000i −1.05604 0.754314i
\(704\) 1.41421i 0.0533002i
\(705\) 0.414214 + 2.41421i 0.0156002 + 0.0909245i
\(706\) 26.0000i 0.978523i
\(707\) 5.65685 0.212748
\(708\) 3.51472 + 20.4853i 0.132091 + 0.769884i
\(709\) −14.0000 14.0000i −0.525781 0.525781i 0.393531 0.919312i \(-0.371254\pi\)
−0.919312 + 0.393531i \(0.871254\pi\)
\(710\) 2.82843i 0.106149i
\(711\) −9.14214 + 19.1421i −0.342857 + 0.717886i
\(712\) −2.00000 −0.0749532
\(713\) 8.48528i 0.317776i
\(714\) 11.3137 + 8.00000i 0.423405 + 0.299392i
\(715\) −6.00000 −0.224387
\(716\) 7.07107 7.07107i 0.264258 0.264258i
\(717\) 34.1421 5.85786i 1.27506 0.218766i
\(718\) 16.0000 16.0000i 0.597115 0.597115i
\(719\) 14.1421i 0.527413i 0.964603 + 0.263706i \(0.0849450\pi\)
−0.964603 + 0.263706i \(0.915055\pi\)
\(720\) 2.70711 + 1.29289i 0.100888 + 0.0481833i
\(721\) 0 0
\(722\) −9.19239 + 9.19239i −0.342105 + 0.342105i
\(723\) −5.38478 31.3848i −0.200262 1.16721i
\(724\) 10.0000i 0.371647i
\(725\) −2.82843 + 2.82843i −0.105045 + 0.105045i
\(726\) −2.63604 15.3640i −0.0978326 0.570210i
\(727\) −22.0000 + 22.0000i −0.815935 + 0.815935i −0.985516 0.169581i \(-0.945758\pi\)
0.169581 + 0.985516i \(0.445758\pi\)
\(728\) −16.9706 −0.628971
\(729\) −23.0000 14.1421i −0.851852 0.523783i
\(730\) 10.0000i 0.370117i
\(731\) −8.48528 −0.313839
\(732\) −2.48528 14.4853i −0.0918586 0.535391i
\(733\) 40.0000i 1.47743i −0.674016 0.738717i \(-0.735432\pi\)
0.674016 0.738717i \(-0.264568\pi\)
\(734\) −8.48528 8.48528i −0.313197 0.313197i
\(735\) −15.3640 + 2.63604i −0.566708 + 0.0972318i
\(736\) 2.00000 0.0737210
\(737\) 8.48528i 0.312559i
\(738\) −7.31371 + 15.3137i −0.269221 + 0.563705i
\(739\) 4.00000i 0.147142i −0.997290 0.0735712i \(-0.976560\pi\)
0.997290 0.0735712i \(-0.0234396\pi\)
\(740\) 4.94975 + 3.53553i 0.181956 + 0.129969i
\(741\) 24.0000 33.9411i 0.881662 1.24686i
\(742\) 8.00000 8.00000i 0.293689 0.293689i
\(743\) 41.0122 1.50459 0.752296 0.658826i \(-0.228946\pi\)
0.752296 + 0.658826i \(0.228946\pi\)
\(744\) 4.24264 6.00000i 0.155543 0.219971i
\(745\) −13.0000 13.0000i −0.476283 0.476283i
\(746\) 15.5563 15.5563i 0.569558 0.569558i
\(747\) 8.00000 2.82843i 0.292705 0.103487i
\(748\) 2.00000 + 2.00000i 0.0731272 + 0.0731272i
\(749\) 33.9411i 1.24018i
\(750\) −1.00000 + 1.41421i −0.0365148 + 0.0516398i
\(751\) 2.00000i 0.0729810i −0.999334 0.0364905i \(-0.988382\pi\)
0.999334 0.0364905i \(-0.0116179\pi\)
\(752\) 1.41421i 0.0515711i
\(753\) 3.51472 + 20.4853i 0.128083 + 0.746525i
\(754\) −12.0000 + 12.0000i −0.437014 + 0.437014i
\(755\) 0 0
\(756\) 20.0000 + 5.65685i 0.727393 + 0.205738i
\(757\) 5.00000 + 5.00000i 0.181728 + 0.181728i 0.792108 0.610380i \(-0.208983\pi\)
−0.610380 + 0.792108i \(0.708983\pi\)
\(758\) 19.7990 + 19.7990i 0.719132 + 0.719132i
\(759\) 4.82843 0.828427i 0.175261 0.0300700i
\(760\) 4.00000 4.00000i 0.145095 0.145095i
\(761\) 5.65685 0.205061 0.102530 0.994730i \(-0.467306\pi\)
0.102530 + 0.994730i \(0.467306\pi\)
\(762\) 4.68629 + 27.3137i 0.169766 + 0.989471i
\(763\) −56.0000 56.0000i −2.02734 2.02734i
\(764\) −16.9706 16.9706i −0.613973 0.613973i
\(765\) 5.65685 2.00000i 0.204524 0.0723102i
\(766\) 24.0000 0.867155
\(767\) −50.9117 −1.83831
\(768\) 1.41421 + 1.00000i 0.0510310 + 0.0360844i
\(769\) −5.00000 + 5.00000i −0.180305 + 0.180305i −0.791489 0.611184i \(-0.790694\pi\)
0.611184 + 0.791489i \(0.290694\pi\)
\(770\) −5.65685 −0.203859
\(771\) −40.9706 + 7.02944i −1.47552 + 0.253159i
\(772\) 12.0000 12.0000i 0.431889 0.431889i
\(773\) 28.2843i 1.01731i −0.860969 0.508657i \(-0.830142\pi\)
0.860969 0.508657i \(-0.169858\pi\)
\(774\) −12.0000 + 4.24264i −0.431331 + 0.152499i
\(775\) 3.00000 + 3.00000i 0.107763 + 0.107763i
\(776\) −8.48528 −0.304604
\(777\) 37.9411 + 18.3431i 1.36113 + 0.658057i
\(778\) 24.0000 0.860442
\(779\) 22.6274 + 22.6274i 0.810711 + 0.810711i
\(780\) −4.24264 + 6.00000i −0.151911 + 0.214834i
\(781\) 4.00000i 0.143131i
\(782\) 2.82843 2.82843i 0.101144 0.101144i
\(783\) 18.1421 10.1421i 0.648347 0.362450i
\(784\) −9.00000 −0.321429
\(785\) 9.89949 9.89949i 0.353328 0.353328i
\(786\) −4.00000 + 5.65685i −0.142675 + 0.201773i
\(787\) 50.0000 1.78231 0.891154 0.453701i \(-0.149897\pi\)
0.891154 + 0.453701i \(0.149897\pi\)
\(788\) −2.82843 −0.100759
\(789\) 38.0000 + 26.8701i 1.35284 + 0.956599i
\(790\) −5.00000 5.00000i −0.177892 0.177892i
\(791\) 5.65685 + 5.65685i 0.201135 + 0.201135i
\(792\) 3.82843 + 1.82843i 0.136037 + 0.0649703i
\(793\) 36.0000 1.27840
\(794\) −15.5563 + 15.5563i −0.552074 + 0.552074i
\(795\) −0.828427 4.82843i −0.0293813 0.171247i
\(796\) 1.00000 + 1.00000i 0.0354441 + 0.0354441i
\(797\) 29.6985 + 29.6985i 1.05197 + 1.05197i 0.998573 + 0.0534012i \(0.0170062\pi\)
0.0534012 + 0.998573i \(0.482994\pi\)
\(798\) 22.6274 32.0000i 0.801002 1.13279i
\(799\) 2.00000 + 2.00000i 0.0707549 + 0.0707549i
\(800\) −0.707107 + 0.707107i −0.0250000 + 0.0250000i
\(801\) −2.58579 + 5.41421i −0.0913643 + 0.191302i
\(802\) 6.00000i 0.211867i
\(803\) 14.1421i 0.499065i
\(804\) −8.48528 6.00000i −0.299253 0.211604i
\(805\) 8.00000i 0.281963i
\(806\) 12.7279 + 12.7279i 0.448322 + 0.448322i
\(807\) −7.07107 + 10.0000i −0.248913 + 0.352017i
\(808\) 1.00000 1.00000i 0.0351799 0.0351799i
\(809\) 7.07107 + 7.07107i 0.248606 + 0.248606i 0.820398 0.571793i \(-0.193752\pi\)
−0.571793 + 0.820398i \(0.693752\pi\)
\(810\) 7.00000 5.65685i 0.245955 0.198762i
\(811\) 20.0000 0.702295 0.351147 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) −11.3137 + 11.3137i −0.397033 + 0.397033i
\(813\) −22.6274 16.0000i −0.793578 0.561144i
\(814\) 7.00000 + 5.00000i 0.245350 + 0.175250i
\(815\) 21.2132i 0.743066i
\(816\) 3.41421 0.585786i 0.119521 0.0205066i
\(817\) 24.0000i 0.839654i
\(818\) −4.24264 −0.148340
\(819\) −21.9411 + 45.9411i −0.766685 + 1.60531i
\(820\) −4.00000 4.00000i −0.139686 0.139686i
\(821\) 7.07107i 0.246782i 0.992358 + 0.123391i \(0.0393769\pi\)
−0.992358 + 0.123391i \(0.960623\pi\)
\(822\) 36.2132 6.21320i 1.26308 0.216710i
\(823\) −24.0000 −0.836587 −0.418294 0.908312i \(-0.637372\pi\)
−0.418294 + 0.908312i \(0.637372\pi\)
\(824\) 0 0
\(825\) −1.41421 + 2.00000i −0.0492366 + 0.0696311i
\(826\) −48.0000 −1.67013
\(827\) −36.7696 + 36.7696i −1.27860 + 1.27860i −0.337153 + 0.941450i \(0.609464\pi\)
−0.941450 + 0.337153i \(0.890536\pi\)
\(828\) 2.58579 5.41421i 0.0898623 0.188157i
\(829\) −30.0000 + 30.0000i −1.04194 + 1.04194i −0.0428621 + 0.999081i \(0.513648\pi\)
−0.999081 + 0.0428621i \(0.986352\pi\)
\(830\) 2.82843i 0.0981761i
\(831\) 36.2132 6.21320i 1.25622 0.215534i
\(832\) −3.00000 + 3.00000i −0.104006 + 0.104006i
\(833\) −12.7279 + 12.7279i −0.440996 + 0.440996i
\(834\) 0 0
\(835\) 2.00000i 0.0692129i
\(836\) 5.65685 5.65685i 0.195646 0.195646i
\(837\) −10.7574 19.2426i −0.371829 0.665123i
\(838\) 23.0000 23.0000i 0.794522 0.794522i
\(839\) 25.4558 0.878833 0.439417 0.898283i \(-0.355185\pi\)
0.439417 + 0.898283i \(0.355185\pi\)
\(840\) −4.00000 + 5.65685i −0.138013 + 0.195180i
\(841\) 13.0000i 0.448276i
\(842\) 28.2843 0.974740
\(843\) 10.2426 1.75736i 0.352775 0.0605267i
\(844\) 8.00000i 0.275371i
\(845\) −3.53553 3.53553i −0.121626 0.121626i
\(846\) 3.82843 + 1.82843i 0.131624 + 0.0628626i
\(847\) 36.0000 1.23697
\(848\) 2.82843i 0.0971286i
\(849\) −50.6985 + 8.69848i −1.73997 + 0.298531i
\(850\) 2.00000i 0.0685994i
\(851\) 7.07107 9.89949i 0.242393 0.339350i
\(852\) −4.00000 2.82843i −0.137038 0.0969003i
\(853\) 11.0000 11.0000i 0.376633 0.376633i −0.493253 0.869886i \(-0.664192\pi\)
0.869886 + 0.493253i \(0.164192\pi\)
\(854\) 33.9411 1.16144
\(855\) −5.65685 16.0000i −0.193460 0.547188i
\(856\) 6.00000 + 6.00000i 0.205076 + 0.205076i
\(857\) −15.5563 + 15.5563i −0.531395 + 0.531395i −0.920987 0.389593i \(-0.872616\pi\)
0.389593 + 0.920987i \(0.372616\pi\)
\(858\) −6.00000 + 8.48528i −0.204837 + 0.289683i
\(859\) −16.0000 16.0000i −0.545913 0.545913i 0.379343 0.925256i \(-0.376150\pi\)
−0.925256 + 0.379343i \(0.876150\pi\)
\(860\) 4.24264i 0.144673i
\(861\) −32.0000 22.6274i −1.09056 0.771140i
\(862\) 12.0000i 0.408722i
\(863\) 21.2132i 0.722106i 0.932545 + 0.361053i \(0.117583\pi\)
−0.932545 + 0.361053i \(0.882417\pi\)
\(864\) 4.53553 2.53553i 0.154302 0.0862606i
\(865\) 14.0000 14.0000i 0.476014 0.476014i
\(866\) −24.0416 24.0416i −0.816968 0.816968i
\(867\) −13.0000 + 18.3848i −0.441503 + 0.624380i
\(868\) 12.0000 + 12.0000i 0.407307 + 0.407307i
\(869\) −7.07107 7.07107i −0.239870 0.239870i
\(870\) 1.17157 + 6.82843i 0.0397200 + 0.231505i
\(871\) 18.0000 18.0000i 0.609907 0.609907i
\(872\) −19.7990 −0.670478
\(873\) −10.9706 + 22.9706i −0.371297 + 0.777436i
\(874\) −8.00000 8.00000i −0.270604 0.270604i
\(875\) −2.82843 2.82843i −0.0956183 0.0956183i
\(876\) −14.1421 10.0000i −0.477818 0.337869i
\(877\) −36.0000 −1.21563 −0.607817 0.794077i \(-0.707955\pi\)
−0.607817 + 0.794077i \(0.707955\pi\)
\(878\) 12.7279 0.429547
\(879\) 0 0
\(880\) −1.00000 + 1.00000i −0.0337100 + 0.0337100i
\(881\) 33.9411 1.14351 0.571753 0.820426i \(-0.306264\pi\)
0.571753 + 0.820426i \(0.306264\pi\)
\(882\) −11.6360 + 24.3640i −0.391806 + 0.820377i
\(883\) 21.0000 21.0000i 0.706706 0.706706i −0.259135 0.965841i \(-0.583437\pi\)
0.965841 + 0.259135i \(0.0834374\pi\)
\(884\) 8.48528i 0.285391i
\(885\) −12.0000 + 16.9706i −0.403376 + 0.570459i
\(886\) −10.0000 10.0000i −0.335957 0.335957i
\(887\) 49.4975 1.66196 0.830981 0.556300i \(-0.187780\pi\)
0.830981 + 0.556300i \(0.187780\pi\)
\(888\) 9.94975 3.46447i 0.333892 0.116260i
\(889\) −64.0000 −2.14649
\(890\) −1.41421 1.41421i −0.0474045 0.0474045i
\(891\) 9.89949 8.00000i 0.331646 0.268010i
\(892\) 8.00000i 0.267860i
\(893\) 5.65685 5.65685i 0.189299 0.189299i
\(894\) −31.3848 + 5.38478i −1.04966 + 0.180094i
\(895\) 10.0000 0.334263
\(896\) −2.82843 + 2.82843i −0.0944911 + 0.0944911i
\(897\) 12.0000 + 8.48528i 0.400668 + 0.283315i
\(898\) −22.0000 −0.734150
\(899\) 16.9706 0.566000
\(900\) 1.00000 + 2.82843i 0.0333333 + 0.0942809i
\(901\) −4.00000 4.00000i −0.133259 0.133259i
\(902\) −5.65685 5.65685i −0.188353 0.188353i
\(903\) −4.97056 28.9706i −0.165410 0.964080i
\(904\) 2.00000 0.0665190
\(905\) −7.07107 + 7.07107i −0.235050 + 0.235050i
\(906\) 0 0
\(907\) 39.0000 + 39.0000i 1.29497 + 1.29497i 0.931671 + 0.363303i \(0.118351\pi\)
0.363303 + 0.931671i \(0.381649\pi\)
\(908\) 16.9706 + 16.9706i 0.563188 + 0.563188i
\(909\) −1.41421 4.00000i −0.0469065 0.132672i
\(910\) −12.0000 12.0000i −0.397796 0.397796i
\(911\) −8.48528 + 8.48528i −0.281130 + 0.281130i −0.833560 0.552430i \(-0.813701\pi\)
0.552430 + 0.833560i \(0.313701\pi\)
\(912\) −1.65685 9.65685i −0.0548639 0.319770i
\(913\) 4.00000i 0.132381i
\(914\) 42.4264i 1.40334i
\(915\) 8.48528 12.0000i 0.280515 0.396708i
\(916\) 10.0000i 0.330409i
\(917\) −11.3137 11.3137i −0.373612 0.373612i
\(918\) 2.82843 10.0000i 0.0933520 0.330049i
\(919\) −33.0000 + 33.0000i −1.08857 + 1.08857i −0.0928935 + 0.995676i \(0.529612\pi\)
−0.995676 + 0.0928935i \(0.970388\pi\)
\(920\) 1.41421 + 1.41421i 0.0466252 + 0.0466252i
\(921\) 28.0000 39.5980i 0.922631 1.30480i
\(922\) −6.00000 −0.197599
\(923\) 8.48528 8.48528i 0.279296 0.279296i
\(924\) −5.65685 + 8.00000i −0.186097 + 0.263181i
\(925\) 1.00000 + 6.00000i 0.0328798 + 0.197279i
\(926\) 5.65685i 0.185896i
\(927\) 0 0
\(928\) 4.00000i 0.131306i
\(929\) 59.3970 1.94875 0.974376 0.224927i \(-0.0722143\pi\)
0.974376 + 0.224927i \(0.0722143\pi\)
\(930\) 7.24264 1.24264i 0.237496 0.0407478i
\(931\) 36.0000 + 36.0000i 1.17985 + 1.17985i
\(932\) 12.7279i 0.416917i
\(933\) 5.85786 + 34.1421i 0.191778 + 1.11776i
\(934\) −32.0000 −1.04707
\(935\) 2.82843i 0.0924995i
\(936\) 4.24264 + 12.0000i 0.138675 + 0.392232i
\(937\) −22.0000 −0.718709 −0.359354 0.933201i \(-0.617003\pi\)
−0.359354 + 0.933201i \(0.617003\pi\)
\(938\) 16.9706 16.9706i 0.554109 0.554109i
\(939\) 9.94113 + 57.9411i 0.324416 + 1.89084i
\(940\) −1.00000 + 1.00000i −0.0326164 + 0.0326164i
\(941\) 21.2132i 0.691531i −0.938321 0.345765i \(-0.887619\pi\)
0.938321 0.345765i \(-0.112381\pi\)
\(942\) −4.10051 23.8995i −0.133602 0.778688i
\(943\) −8.00000 + 8.00000i −0.260516 + 0.260516i
\(944\) −8.48528 + 8.48528i −0.276172 + 0.276172i
\(945\) 10.1421 + 18.1421i 0.329924 + 0.590164i
\(946\) 6.00000i 0.195077i
\(947\) −36.7696 + 36.7696i −1.19485 + 1.19485i −0.219161 + 0.975689i \(0.570332\pi\)
−0.975689 + 0.219161i \(0.929668\pi\)
\(948\) −12.0711 + 2.07107i −0.392050 + 0.0672652i
\(949\) 30.0000 30.0000i 0.973841 0.973841i
\(950\) 5.65685 0.183533
\(951\) −36.0000 25.4558i −1.16738 0.825462i
\(952\) 8.00000i 0.259281i
\(953\) 35.3553 1.14527 0.572636 0.819810i \(-0.305921\pi\)
0.572636 + 0.819810i \(0.305921\pi\)
\(954\) −7.65685 3.65685i −0.247900 0.118395i
\(955\) 24.0000i 0.776622i
\(956\) 14.1421 + 14.1421i 0.457389 + 0.457389i
\(957\) 1.65685 + 9.65685i 0.0535585 + 0.312162i
\(958\) 16.0000 0.516937
\(959\) 84.8528i 2.74004i
\(960\) 0.292893 + 1.70711i 0.00945309 + 0.0550966i
\(961\) 13.0000i 0.419355i
\(962\) 4.24264 + 25.4558i 0.136788 + 0.820729i
\(963\) 24.0000 8.48528i 0.773389 0.273434i
\(964\) 13.0000 13.0000i 0.418702 0.418702i
\(965\) 16.9706 0.546302
\(966\) 11.3137 + 8.00000i 0.364013 + 0.257396i
\(967\) 10.0000 + 10.0000i 0.321578 + 0.321578i 0.849372 0.527794i \(-0.176981\pi\)
−0.527794 + 0.849372i \(0.676981\pi\)
\(968\) 6.36396 6.36396i 0.204545 0.204545i
\(969\) −16.0000 11.3137i −0.513994 0.363449i
\(970\) −6.00000 6.00000i −0.192648 0.192648i
\(971\) 29.6985i 0.953070i −0.879156 0.476535i \(-0.841893\pi\)
0.879156 0.476535i \(-0.158107\pi\)
\(972\) −1.00000 15.5563i −0.0320750 0.498970i
\(973\) 0 0
\(974\) 11.3137i 0.362515i
\(975\) −7.24264 + 1.24264i −0.231950 + 0.0397964i
\(976\) 6.00000 6.00000i 0.192055 0.192055i
\(977\) −42.4264 42.4264i −1.35734 1.35734i −0.877181 0.480160i \(-0.840579\pi\)
−0.480160 0.877181i \(-0.659421\pi\)
\(978\) −30.0000 21.2132i −0.959294 0.678323i
\(979\) −2.00000 2.00000i −0.0639203 0.0639203i
\(980\) −6.36396 6.36396i −0.203289 0.203289i
\(981\) −25.5980 + 53.5980i −0.817281 + 1.71125i
\(982\) 9.00000 9.00000i 0.287202 0.287202i
\(983\) −43.8406 −1.39830 −0.699149 0.714976i \(-0.746438\pi\)
−0.699149 + 0.714976i \(0.746438\pi\)
\(984\) −9.65685 + 1.65685i −0.307849 + 0.0528186i
\(985\) −2.00000 2.00000i −0.0637253 0.0637253i
\(986\) 5.65685 + 5.65685i 0.180151 + 0.180151i
\(987\) −5.65685 + 8.00000i −0.180060 + 0.254643i
\(988\) 24.0000 0.763542
\(989\) −8.48528 −0.269816
\(990\) 1.41421 + 4.00000i 0.0449467 + 0.127128i
\(991\) −21.0000 + 21.0000i −0.667087 + 0.667087i −0.957041 0.289954i \(-0.906360\pi\)
0.289954 + 0.957041i \(0.406360\pi\)
\(992\) 4.24264 0.134704
\(993\) −0.828427 4.82843i −0.0262893 0.153226i
\(994\) 8.00000 8.00000i 0.253745 0.253745i
\(995\) 1.41421i 0.0448336i
\(996\) 4.00000 + 2.82843i 0.126745 + 0.0896221i
\(997\) −23.0000 23.0000i −0.728417 0.728417i 0.241887 0.970304i \(-0.422234\pi\)
−0.970304 + 0.241887i \(0.922234\pi\)
\(998\) 8.48528 0.268597
\(999\) 3.48528 31.4142i 0.110269 0.993902i
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 1110.2.u.c.191.2 yes 4
3.2 odd 2 inner 1110.2.u.c.191.1 4
37.31 odd 4 inner 1110.2.u.c.401.1 yes 4
111.68 even 4 inner 1110.2.u.c.401.2 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1110.2.u.c.191.1 4 3.2 odd 2 inner
1110.2.u.c.191.2 yes 4 1.1 even 1 trivial
1110.2.u.c.401.1 yes 4 37.31 odd 4 inner
1110.2.u.c.401.2 yes 4 111.68 even 4 inner