Properties

Label 390.2.p.d.281.2
Level $390$
Weight $2$
Character 390.281
Analytic conductor $3.114$
Analytic rank $0$
Dimension $4$
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [390,2,Mod(161,390)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(390, 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("390.161");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.p (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: \(3.11416567883\)
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 281.2
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 390.281
Dual form 390.2.p.d.161.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(1.00000 - 1.41421i) q^{3} -1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.292893 - 1.70711i) q^{6} +(-0.707107 - 0.707107i) q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(1.00000 - 1.41421i) q^{3} -1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.292893 - 1.70711i) q^{6} +(-0.707107 - 0.707107i) q^{8} +(-1.00000 - 2.82843i) q^{9} -1.00000i q^{10} +(-1.41421 - 1.41421i) q^{11} +(-1.41421 - 1.00000i) q^{12} +(-3.00000 + 2.00000i) q^{13} +(-0.292893 - 1.70711i) q^{15} -1.00000 q^{16} +4.24264 q^{17} +(-2.70711 - 1.29289i) q^{18} +(6.00000 + 6.00000i) q^{19} +(-0.707107 - 0.707107i) q^{20} -2.00000 q^{22} +1.41421 q^{23} +(-1.70711 + 0.292893i) q^{24} -1.00000i q^{25} +(-0.707107 + 3.53553i) q^{26} +(-5.00000 - 1.41421i) q^{27} -1.41421i q^{29} +(-1.41421 - 1.00000i) q^{30} +(-3.00000 - 3.00000i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-3.41421 + 0.585786i) q^{33} +(3.00000 - 3.00000i) q^{34} +(-2.82843 + 1.00000i) q^{36} +(5.00000 - 5.00000i) q^{37} +8.48528 q^{38} +(-0.171573 + 6.24264i) q^{39} -1.00000 q^{40} +(-7.07107 + 7.07107i) q^{41} +4.00000i q^{43} +(-1.41421 + 1.41421i) q^{44} +(-2.70711 - 1.29289i) q^{45} +(1.00000 - 1.00000i) q^{46} +(4.24264 + 4.24264i) q^{47} +(-1.00000 + 1.41421i) q^{48} +7.00000i q^{49} +(-0.707107 - 0.707107i) q^{50} +(4.24264 - 6.00000i) q^{51} +(2.00000 + 3.00000i) q^{52} -11.3137i q^{53} +(-4.53553 + 2.53553i) q^{54} -2.00000 q^{55} +(14.4853 - 2.48528i) q^{57} +(-1.00000 - 1.00000i) q^{58} +(2.82843 + 2.82843i) q^{59} +(-1.70711 + 0.292893i) q^{60} +2.00000 q^{61} -4.24264 q^{62} +1.00000i q^{64} +(-0.707107 + 3.53553i) q^{65} +(-2.00000 + 2.82843i) q^{66} +(5.00000 + 5.00000i) q^{67} -4.24264i q^{68} +(1.41421 - 2.00000i) q^{69} +(-5.65685 + 5.65685i) q^{71} +(-1.29289 + 2.70711i) q^{72} +(6.00000 - 6.00000i) q^{73} -7.07107i q^{74} +(-1.41421 - 1.00000i) q^{75} +(6.00000 - 6.00000i) q^{76} +(4.29289 + 4.53553i) q^{78} +8.00000 q^{79} +(-0.707107 + 0.707107i) q^{80} +(-7.00000 + 5.65685i) q^{81} +10.0000i q^{82} +(-5.65685 + 5.65685i) q^{83} +(3.00000 - 3.00000i) q^{85} +(2.82843 + 2.82843i) q^{86} +(-2.00000 - 1.41421i) q^{87} +2.00000i q^{88} +(-4.24264 - 4.24264i) q^{89} +(-2.82843 + 1.00000i) q^{90} -1.41421i q^{92} +(-7.24264 + 1.24264i) q^{93} +6.00000 q^{94} +8.48528 q^{95} +(0.292893 + 1.70711i) q^{96} +(10.0000 + 10.0000i) q^{97} +(4.94975 + 4.94975i) q^{98} +(-2.58579 + 5.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{3} - 4 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{3} - 4 q^{6} - 4 q^{9} - 12 q^{13} - 4 q^{15} - 4 q^{16} - 8 q^{18} + 24 q^{19} - 8 q^{22} - 4 q^{24} - 20 q^{27} - 12 q^{31} - 8 q^{33} + 12 q^{34} + 20 q^{37} - 12 q^{39} - 4 q^{40} - 8 q^{45} + 4 q^{46} - 4 q^{48} + 8 q^{52} - 4 q^{54} - 8 q^{55} + 24 q^{57} - 4 q^{58} - 4 q^{60} + 8 q^{61} - 8 q^{66} + 20 q^{67} - 8 q^{72} + 24 q^{73} + 24 q^{76} + 20 q^{78} + 32 q^{79} - 28 q^{81} + 12 q^{85} - 8 q^{87} - 12 q^{93} + 24 q^{94} + 4 q^{96} + 40 q^{97} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) 1.00000 1.41421i 0.577350 0.816497i
\(4\) 1.00000i 0.500000i
\(5\) 0.707107 0.707107i 0.316228 0.316228i
\(6\) −0.292893 1.70711i −0.119573 0.696923i
\(7\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) −1.00000 2.82843i −0.333333 0.942809i
\(10\) 1.00000i 0.316228i
\(11\) −1.41421 1.41421i −0.426401 0.426401i 0.460999 0.887401i \(-0.347491\pi\)
−0.887401 + 0.460999i \(0.847491\pi\)
\(12\) −1.41421 1.00000i −0.408248 0.288675i
\(13\) −3.00000 + 2.00000i −0.832050 + 0.554700i
\(14\) 0 0
\(15\) −0.292893 1.70711i −0.0756247 0.440773i
\(16\) −1.00000 −0.250000
\(17\) 4.24264 1.02899 0.514496 0.857493i \(-0.327979\pi\)
0.514496 + 0.857493i \(0.327979\pi\)
\(18\) −2.70711 1.29289i −0.638071 0.304738i
\(19\) 6.00000 + 6.00000i 1.37649 + 1.37649i 0.850469 + 0.526026i \(0.176318\pi\)
0.526026 + 0.850469i \(0.323682\pi\)
\(20\) −0.707107 0.707107i −0.158114 0.158114i
\(21\) 0 0
\(22\) −2.00000 −0.426401
\(23\) 1.41421 0.294884 0.147442 0.989071i \(-0.452896\pi\)
0.147442 + 0.989071i \(0.452896\pi\)
\(24\) −1.70711 + 0.292893i −0.348462 + 0.0597866i
\(25\) 1.00000i 0.200000i
\(26\) −0.707107 + 3.53553i −0.138675 + 0.693375i
\(27\) −5.00000 1.41421i −0.962250 0.272166i
\(28\) 0 0
\(29\) 1.41421i 0.262613i −0.991342 0.131306i \(-0.958083\pi\)
0.991342 0.131306i \(-0.0419172\pi\)
\(30\) −1.41421 1.00000i −0.258199 0.182574i
\(31\) −3.00000 3.00000i −0.538816 0.538816i 0.384365 0.923181i \(-0.374420\pi\)
−0.923181 + 0.384365i \(0.874420\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −3.41421 + 0.585786i −0.594338 + 0.101972i
\(34\) 3.00000 3.00000i 0.514496 0.514496i
\(35\) 0 0
\(36\) −2.82843 + 1.00000i −0.471405 + 0.166667i
\(37\) 5.00000 5.00000i 0.821995 0.821995i −0.164399 0.986394i \(-0.552568\pi\)
0.986394 + 0.164399i \(0.0525685\pi\)
\(38\) 8.48528 1.37649
\(39\) −0.171573 + 6.24264i −0.0274736 + 0.999623i
\(40\) −1.00000 −0.158114
\(41\) −7.07107 + 7.07107i −1.10432 + 1.10432i −0.110432 + 0.993884i \(0.535223\pi\)
−0.993884 + 0.110432i \(0.964777\pi\)
\(42\) 0 0
\(43\) 4.00000i 0.609994i 0.952353 + 0.304997i \(0.0986555\pi\)
−0.952353 + 0.304997i \(0.901344\pi\)
\(44\) −1.41421 + 1.41421i −0.213201 + 0.213201i
\(45\) −2.70711 1.29289i −0.403552 0.192733i
\(46\) 1.00000 1.00000i 0.147442 0.147442i
\(47\) 4.24264 + 4.24264i 0.618853 + 0.618853i 0.945237 0.326384i \(-0.105830\pi\)
−0.326384 + 0.945237i \(0.605830\pi\)
\(48\) −1.00000 + 1.41421i −0.144338 + 0.204124i
\(49\) 7.00000i 1.00000i
\(50\) −0.707107 0.707107i −0.100000 0.100000i
\(51\) 4.24264 6.00000i 0.594089 0.840168i
\(52\) 2.00000 + 3.00000i 0.277350 + 0.416025i
\(53\) 11.3137i 1.55406i −0.629465 0.777029i \(-0.716726\pi\)
0.629465 0.777029i \(-0.283274\pi\)
\(54\) −4.53553 + 2.53553i −0.617208 + 0.345042i
\(55\) −2.00000 −0.269680
\(56\) 0 0
\(57\) 14.4853 2.48528i 1.91862 0.329184i
\(58\) −1.00000 1.00000i −0.131306 0.131306i
\(59\) 2.82843 + 2.82843i 0.368230 + 0.368230i 0.866831 0.498601i \(-0.166153\pi\)
−0.498601 + 0.866831i \(0.666153\pi\)
\(60\) −1.70711 + 0.292893i −0.220387 + 0.0378124i
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) −4.24264 −0.538816
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) −0.707107 + 3.53553i −0.0877058 + 0.438529i
\(66\) −2.00000 + 2.82843i −0.246183 + 0.348155i
\(67\) 5.00000 + 5.00000i 0.610847 + 0.610847i 0.943167 0.332320i \(-0.107831\pi\)
−0.332320 + 0.943167i \(0.607831\pi\)
\(68\) 4.24264i 0.514496i
\(69\) 1.41421 2.00000i 0.170251 0.240772i
\(70\) 0 0
\(71\) −5.65685 + 5.65685i −0.671345 + 0.671345i −0.958026 0.286681i \(-0.907448\pi\)
0.286681 + 0.958026i \(0.407448\pi\)
\(72\) −1.29289 + 2.70711i −0.152369 + 0.319036i
\(73\) 6.00000 6.00000i 0.702247 0.702247i −0.262646 0.964892i \(-0.584595\pi\)
0.964892 + 0.262646i \(0.0845950\pi\)
\(74\) 7.07107i 0.821995i
\(75\) −1.41421 1.00000i −0.163299 0.115470i
\(76\) 6.00000 6.00000i 0.688247 0.688247i
\(77\) 0 0
\(78\) 4.29289 + 4.53553i 0.486074 + 0.513548i
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) −0.707107 + 0.707107i −0.0790569 + 0.0790569i
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) 10.0000i 1.10432i
\(83\) −5.65685 + 5.65685i −0.620920 + 0.620920i −0.945767 0.324846i \(-0.894687\pi\)
0.324846 + 0.945767i \(0.394687\pi\)
\(84\) 0 0
\(85\) 3.00000 3.00000i 0.325396 0.325396i
\(86\) 2.82843 + 2.82843i 0.304997 + 0.304997i
\(87\) −2.00000 1.41421i −0.214423 0.151620i
\(88\) 2.00000i 0.213201i
\(89\) −4.24264 4.24264i −0.449719 0.449719i 0.445542 0.895261i \(-0.353011\pi\)
−0.895261 + 0.445542i \(0.853011\pi\)
\(90\) −2.82843 + 1.00000i −0.298142 + 0.105409i
\(91\) 0 0
\(92\) 1.41421i 0.147442i
\(93\) −7.24264 + 1.24264i −0.751027 + 0.128856i
\(94\) 6.00000 0.618853
\(95\) 8.48528 0.870572
\(96\) 0.292893 + 1.70711i 0.0298933 + 0.174231i
\(97\) 10.0000 + 10.0000i 1.01535 + 1.01535i 0.999880 + 0.0154658i \(0.00492310\pi\)
0.0154658 + 0.999880i \(0.495077\pi\)
\(98\) 4.94975 + 4.94975i 0.500000 + 0.500000i
\(99\) −2.58579 + 5.41421i −0.259881 + 0.544149i
\(100\) −1.00000 −0.100000
\(101\) −15.5563 −1.54791 −0.773957 0.633238i \(-0.781726\pi\)
−0.773957 + 0.633238i \(0.781726\pi\)
\(102\) −1.24264 7.24264i −0.123040 0.717128i
\(103\) 8.00000i 0.788263i −0.919054 0.394132i \(-0.871045\pi\)
0.919054 0.394132i \(-0.128955\pi\)
\(104\) 3.53553 + 0.707107i 0.346688 + 0.0693375i
\(105\) 0 0
\(106\) −8.00000 8.00000i −0.777029 0.777029i
\(107\) 11.3137i 1.09374i 0.837218 + 0.546869i \(0.184180\pi\)
−0.837218 + 0.546869i \(0.815820\pi\)
\(108\) −1.41421 + 5.00000i −0.136083 + 0.481125i
\(109\) 2.00000 + 2.00000i 0.191565 + 0.191565i 0.796372 0.604807i \(-0.206750\pi\)
−0.604807 + 0.796372i \(0.706750\pi\)
\(110\) −1.41421 + 1.41421i −0.134840 + 0.134840i
\(111\) −2.07107 12.0711i −0.196577 1.14574i
\(112\) 0 0
\(113\) 7.07107i 0.665190i −0.943070 0.332595i \(-0.892076\pi\)
0.943070 0.332595i \(-0.107924\pi\)
\(114\) 8.48528 12.0000i 0.794719 1.12390i
\(115\) 1.00000 1.00000i 0.0932505 0.0932505i
\(116\) −1.41421 −0.131306
\(117\) 8.65685 + 6.48528i 0.800326 + 0.599564i
\(118\) 4.00000 0.368230
\(119\) 0 0
\(120\) −1.00000 + 1.41421i −0.0912871 + 0.129099i
\(121\) 7.00000i 0.636364i
\(122\) 1.41421 1.41421i 0.128037 0.128037i
\(123\) 2.92893 + 17.0711i 0.264093 + 1.53925i
\(124\) −3.00000 + 3.00000i −0.269408 + 0.269408i
\(125\) −0.707107 0.707107i −0.0632456 0.0632456i
\(126\) 0 0
\(127\) 4.00000i 0.354943i −0.984126 0.177471i \(-0.943208\pi\)
0.984126 0.177471i \(-0.0567917\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 5.65685 + 4.00000i 0.498058 + 0.352180i
\(130\) 2.00000 + 3.00000i 0.175412 + 0.263117i
\(131\) 7.07107i 0.617802i 0.951094 + 0.308901i \(0.0999612\pi\)
−0.951094 + 0.308901i \(0.900039\pi\)
\(132\) 0.585786 + 3.41421i 0.0509862 + 0.297169i
\(133\) 0 0
\(134\) 7.07107 0.610847
\(135\) −4.53553 + 2.53553i −0.390357 + 0.218224i
\(136\) −3.00000 3.00000i −0.257248 0.257248i
\(137\) −14.1421 14.1421i −1.20824 1.20824i −0.971595 0.236649i \(-0.923951\pi\)
−0.236649 0.971595i \(-0.576049\pi\)
\(138\) −0.414214 2.41421i −0.0352602 0.205512i
\(139\) −16.0000 −1.35710 −0.678551 0.734553i \(-0.737392\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) 0 0
\(141\) 10.2426 1.75736i 0.862586 0.147996i
\(142\) 8.00000i 0.671345i
\(143\) 7.07107 + 1.41421i 0.591312 + 0.118262i
\(144\) 1.00000 + 2.82843i 0.0833333 + 0.235702i
\(145\) −1.00000 1.00000i −0.0830455 0.0830455i
\(146\) 8.48528i 0.702247i
\(147\) 9.89949 + 7.00000i 0.816497 + 0.577350i
\(148\) −5.00000 5.00000i −0.410997 0.410997i
\(149\) −7.07107 + 7.07107i −0.579284 + 0.579284i −0.934706 0.355422i \(-0.884337\pi\)
0.355422 + 0.934706i \(0.384337\pi\)
\(150\) −1.70711 + 0.292893i −0.139385 + 0.0239146i
\(151\) −13.0000 + 13.0000i −1.05792 + 1.05792i −0.0597092 + 0.998216i \(0.519017\pi\)
−0.998216 + 0.0597092i \(0.980983\pi\)
\(152\) 8.48528i 0.688247i
\(153\) −4.24264 12.0000i −0.342997 0.970143i
\(154\) 0 0
\(155\) −4.24264 −0.340777
\(156\) 6.24264 + 0.171573i 0.499811 + 0.0137368i
\(157\) −6.00000 −0.478852 −0.239426 0.970915i \(-0.576959\pi\)
−0.239426 + 0.970915i \(0.576959\pi\)
\(158\) 5.65685 5.65685i 0.450035 0.450035i
\(159\) −16.0000 11.3137i −1.26888 0.897235i
\(160\) 1.00000i 0.0790569i
\(161\) 0 0
\(162\) −0.949747 + 8.94975i −0.0746192 + 0.703159i
\(163\) −11.0000 + 11.0000i −0.861586 + 0.861586i −0.991522 0.129936i \(-0.958523\pi\)
0.129936 + 0.991522i \(0.458523\pi\)
\(164\) 7.07107 + 7.07107i 0.552158 + 0.552158i
\(165\) −2.00000 + 2.82843i −0.155700 + 0.220193i
\(166\) 8.00000i 0.620920i
\(167\) 11.3137 + 11.3137i 0.875481 + 0.875481i 0.993063 0.117582i \(-0.0375143\pi\)
−0.117582 + 0.993063i \(0.537514\pi\)
\(168\) 0 0
\(169\) 5.00000 12.0000i 0.384615 0.923077i
\(170\) 4.24264i 0.325396i
\(171\) 10.9706 22.9706i 0.838940 1.75660i
\(172\) 4.00000 0.304997
\(173\) 2.82843 0.215041 0.107521 0.994203i \(-0.465709\pi\)
0.107521 + 0.994203i \(0.465709\pi\)
\(174\) −2.41421 + 0.414214i −0.183021 + 0.0314014i
\(175\) 0 0
\(176\) 1.41421 + 1.41421i 0.106600 + 0.106600i
\(177\) 6.82843 1.17157i 0.513256 0.0880608i
\(178\) −6.00000 −0.449719
\(179\) −18.3848 −1.37414 −0.687071 0.726590i \(-0.741104\pi\)
−0.687071 + 0.726590i \(0.741104\pi\)
\(180\) −1.29289 + 2.70711i −0.0963666 + 0.201776i
\(181\) 18.0000i 1.33793i −0.743294 0.668965i \(-0.766738\pi\)
0.743294 0.668965i \(-0.233262\pi\)
\(182\) 0 0
\(183\) 2.00000 2.82843i 0.147844 0.209083i
\(184\) −1.00000 1.00000i −0.0737210 0.0737210i
\(185\) 7.07107i 0.519875i
\(186\) −4.24264 + 6.00000i −0.311086 + 0.439941i
\(187\) −6.00000 6.00000i −0.438763 0.438763i
\(188\) 4.24264 4.24264i 0.309426 0.309426i
\(189\) 0 0
\(190\) 6.00000 6.00000i 0.435286 0.435286i
\(191\) 19.7990i 1.43260i −0.697790 0.716302i \(-0.745833\pi\)
0.697790 0.716302i \(-0.254167\pi\)
\(192\) 1.41421 + 1.00000i 0.102062 + 0.0721688i
\(193\) −6.00000 + 6.00000i −0.431889 + 0.431889i −0.889271 0.457381i \(-0.848787\pi\)
0.457381 + 0.889271i \(0.348787\pi\)
\(194\) 14.1421 1.01535
\(195\) 4.29289 + 4.53553i 0.307420 + 0.324796i
\(196\) 7.00000 0.500000
\(197\) 9.89949 9.89949i 0.705310 0.705310i −0.260235 0.965545i \(-0.583800\pi\)
0.965545 + 0.260235i \(0.0838002\pi\)
\(198\) 2.00000 + 5.65685i 0.142134 + 0.402015i
\(199\) 2.00000i 0.141776i −0.997484 0.0708881i \(-0.977417\pi\)
0.997484 0.0708881i \(-0.0225833\pi\)
\(200\) −0.707107 + 0.707107i −0.0500000 + 0.0500000i
\(201\) 12.0711 2.07107i 0.851427 0.146082i
\(202\) −11.0000 + 11.0000i −0.773957 + 0.773957i
\(203\) 0 0
\(204\) −6.00000 4.24264i −0.420084 0.297044i
\(205\) 10.0000i 0.698430i
\(206\) −5.65685 5.65685i −0.394132 0.394132i
\(207\) −1.41421 4.00000i −0.0982946 0.278019i
\(208\) 3.00000 2.00000i 0.208013 0.138675i
\(209\) 16.9706i 1.17388i
\(210\) 0 0
\(211\) −24.0000 −1.65223 −0.826114 0.563503i \(-0.809453\pi\)
−0.826114 + 0.563503i \(0.809453\pi\)
\(212\) −11.3137 −0.777029
\(213\) 2.34315 + 13.6569i 0.160550 + 0.935752i
\(214\) 8.00000 + 8.00000i 0.546869 + 0.546869i
\(215\) 2.82843 + 2.82843i 0.192897 + 0.192897i
\(216\) 2.53553 + 4.53553i 0.172521 + 0.308604i
\(217\) 0 0
\(218\) 2.82843 0.191565
\(219\) −2.48528 14.4853i −0.167940 0.978825i
\(220\) 2.00000i 0.134840i
\(221\) −12.7279 + 8.48528i −0.856173 + 0.570782i
\(222\) −10.0000 7.07107i −0.671156 0.474579i
\(223\) −10.0000 10.0000i −0.669650 0.669650i 0.287985 0.957635i \(-0.407015\pi\)
−0.957635 + 0.287985i \(0.907015\pi\)
\(224\) 0 0
\(225\) −2.82843 + 1.00000i −0.188562 + 0.0666667i
\(226\) −5.00000 5.00000i −0.332595 0.332595i
\(227\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(228\) −2.48528 14.4853i −0.164592 0.959311i
\(229\) 6.00000 6.00000i 0.396491 0.396491i −0.480502 0.876993i \(-0.659546\pi\)
0.876993 + 0.480502i \(0.159546\pi\)
\(230\) 1.41421i 0.0932505i
\(231\) 0 0
\(232\) −1.00000 + 1.00000i −0.0656532 + 0.0656532i
\(233\) 18.3848 1.20443 0.602213 0.798335i \(-0.294286\pi\)
0.602213 + 0.798335i \(0.294286\pi\)
\(234\) 10.7071 1.53553i 0.699945 0.100381i
\(235\) 6.00000 0.391397
\(236\) 2.82843 2.82843i 0.184115 0.184115i
\(237\) 8.00000 11.3137i 0.519656 0.734904i
\(238\) 0 0
\(239\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(240\) 0.292893 + 1.70711i 0.0189062 + 0.110193i
\(241\) −1.00000 + 1.00000i −0.0644157 + 0.0644157i −0.738581 0.674165i \(-0.764504\pi\)
0.674165 + 0.738581i \(0.264504\pi\)
\(242\) −4.94975 4.94975i −0.318182 0.318182i
\(243\) 1.00000 + 15.5563i 0.0641500 + 0.997940i
\(244\) 2.00000i 0.128037i
\(245\) 4.94975 + 4.94975i 0.316228 + 0.316228i
\(246\) 14.1421 + 10.0000i 0.901670 + 0.637577i
\(247\) −30.0000 6.00000i −1.90885 0.381771i
\(248\) 4.24264i 0.269408i
\(249\) 2.34315 + 13.6569i 0.148491 + 0.865468i
\(250\) −1.00000 −0.0632456
\(251\) −4.24264 −0.267793 −0.133897 0.990995i \(-0.542749\pi\)
−0.133897 + 0.990995i \(0.542749\pi\)
\(252\) 0 0
\(253\) −2.00000 2.00000i −0.125739 0.125739i
\(254\) −2.82843 2.82843i −0.177471 0.177471i
\(255\) −1.24264 7.24264i −0.0778172 0.453552i
\(256\) 1.00000 0.0625000
\(257\) 1.41421 0.0882162 0.0441081 0.999027i \(-0.485955\pi\)
0.0441081 + 0.999027i \(0.485955\pi\)
\(258\) 6.82843 1.17157i 0.425119 0.0729389i
\(259\) 0 0
\(260\) 3.53553 + 0.707107i 0.219265 + 0.0438529i
\(261\) −4.00000 + 1.41421i −0.247594 + 0.0875376i
\(262\) 5.00000 + 5.00000i 0.308901 + 0.308901i
\(263\) 4.24264i 0.261612i 0.991408 + 0.130806i \(0.0417566\pi\)
−0.991408 + 0.130806i \(0.958243\pi\)
\(264\) 2.82843 + 2.00000i 0.174078 + 0.123091i
\(265\) −8.00000 8.00000i −0.491436 0.491436i
\(266\) 0 0
\(267\) −10.2426 + 1.75736i −0.626839 + 0.107549i
\(268\) 5.00000 5.00000i 0.305424 0.305424i
\(269\) 1.41421i 0.0862261i −0.999070 0.0431131i \(-0.986272\pi\)
0.999070 0.0431131i \(-0.0137276\pi\)
\(270\) −1.41421 + 5.00000i −0.0860663 + 0.304290i
\(271\) −3.00000 + 3.00000i −0.182237 + 0.182237i −0.792330 0.610093i \(-0.791132\pi\)
0.610093 + 0.792330i \(0.291132\pi\)
\(272\) −4.24264 −0.257248
\(273\) 0 0
\(274\) −20.0000 −1.20824
\(275\) −1.41421 + 1.41421i −0.0852803 + 0.0852803i
\(276\) −2.00000 1.41421i −0.120386 0.0851257i
\(277\) 28.0000i 1.68236i −0.540758 0.841178i \(-0.681862\pi\)
0.540758 0.841178i \(-0.318138\pi\)
\(278\) −11.3137 + 11.3137i −0.678551 + 0.678551i
\(279\) −5.48528 + 11.4853i −0.328395 + 0.687606i
\(280\) 0 0
\(281\) 12.7279 + 12.7279i 0.759284 + 0.759284i 0.976192 0.216908i \(-0.0695971\pi\)
−0.216908 + 0.976192i \(0.569597\pi\)
\(282\) 6.00000 8.48528i 0.357295 0.505291i
\(283\) 6.00000i 0.356663i 0.983970 + 0.178331i \(0.0570699\pi\)
−0.983970 + 0.178331i \(0.942930\pi\)
\(284\) 5.65685 + 5.65685i 0.335673 + 0.335673i
\(285\) 8.48528 12.0000i 0.502625 0.710819i
\(286\) 6.00000 4.00000i 0.354787 0.236525i
\(287\) 0 0
\(288\) 2.70711 + 1.29289i 0.159518 + 0.0761845i
\(289\) 1.00000 0.0588235
\(290\) −1.41421 −0.0830455
\(291\) 24.1421 4.14214i 1.41524 0.242816i
\(292\) −6.00000 6.00000i −0.351123 0.351123i
\(293\) −9.89949 9.89949i −0.578335 0.578335i 0.356110 0.934444i \(-0.384103\pi\)
−0.934444 + 0.356110i \(0.884103\pi\)
\(294\) 11.9497 2.05025i 0.696923 0.119573i
\(295\) 4.00000 0.232889
\(296\) −7.07107 −0.410997
\(297\) 5.07107 + 9.07107i 0.294253 + 0.526357i
\(298\) 10.0000i 0.579284i
\(299\) −4.24264 + 2.82843i −0.245358 + 0.163572i
\(300\) −1.00000 + 1.41421i −0.0577350 + 0.0816497i
\(301\) 0 0
\(302\) 18.3848i 1.05792i
\(303\) −15.5563 + 22.0000i −0.893689 + 1.26387i
\(304\) −6.00000 6.00000i −0.344124 0.344124i
\(305\) 1.41421 1.41421i 0.0809776 0.0809776i
\(306\) −11.4853 5.48528i −0.656570 0.313573i
\(307\) 23.0000 23.0000i 1.31268 1.31268i 0.393246 0.919433i \(-0.371352\pi\)
0.919433 0.393246i \(-0.128648\pi\)
\(308\) 0 0
\(309\) −11.3137 8.00000i −0.643614 0.455104i
\(310\) −3.00000 + 3.00000i −0.170389 + 0.170389i
\(311\) 2.82843 0.160385 0.0801927 0.996779i \(-0.474446\pi\)
0.0801927 + 0.996779i \(0.474446\pi\)
\(312\) 4.53553 4.29289i 0.256774 0.243037i
\(313\) 26.0000 1.46961 0.734803 0.678280i \(-0.237274\pi\)
0.734803 + 0.678280i \(0.237274\pi\)
\(314\) −4.24264 + 4.24264i −0.239426 + 0.239426i
\(315\) 0 0
\(316\) 8.00000i 0.450035i
\(317\) −18.3848 + 18.3848i −1.03259 + 1.03259i −0.0331412 + 0.999451i \(0.510551\pi\)
−0.999451 + 0.0331412i \(0.989449\pi\)
\(318\) −19.3137 + 3.31371i −1.08306 + 0.185824i
\(319\) −2.00000 + 2.00000i −0.111979 + 0.111979i
\(320\) 0.707107 + 0.707107i 0.0395285 + 0.0395285i
\(321\) 16.0000 + 11.3137i 0.893033 + 0.631470i
\(322\) 0 0
\(323\) 25.4558 + 25.4558i 1.41640 + 1.41640i
\(324\) 5.65685 + 7.00000i 0.314270 + 0.388889i
\(325\) 2.00000 + 3.00000i 0.110940 + 0.166410i
\(326\) 15.5563i 0.861586i
\(327\) 4.82843 0.828427i 0.267013 0.0458121i
\(328\) 10.0000 0.552158
\(329\) 0 0
\(330\) 0.585786 + 3.41421i 0.0322465 + 0.187946i
\(331\) 24.0000 + 24.0000i 1.31916 + 1.31916i 0.914442 + 0.404718i \(0.132630\pi\)
0.404718 + 0.914442i \(0.367370\pi\)
\(332\) 5.65685 + 5.65685i 0.310460 + 0.310460i
\(333\) −19.1421 9.14214i −1.04898 0.500986i
\(334\) 16.0000 0.875481
\(335\) 7.07107 0.386334
\(336\) 0 0
\(337\) 14.0000i 0.762629i −0.924445 0.381314i \(-0.875472\pi\)
0.924445 0.381314i \(-0.124528\pi\)
\(338\) −4.94975 12.0208i −0.269231 0.653846i
\(339\) −10.0000 7.07107i −0.543125 0.384048i
\(340\) −3.00000 3.00000i −0.162698 0.162698i
\(341\) 8.48528i 0.459504i
\(342\) −8.48528 24.0000i −0.458831 1.29777i
\(343\) 0 0
\(344\) 2.82843 2.82843i 0.152499 0.152499i
\(345\) −0.414214 2.41421i −0.0223005 0.129977i
\(346\) 2.00000 2.00000i 0.107521 0.107521i
\(347\) 11.3137i 0.607352i −0.952775 0.303676i \(-0.901786\pi\)
0.952775 0.303676i \(-0.0982140\pi\)
\(348\) −1.41421 + 2.00000i −0.0758098 + 0.107211i
\(349\) −12.0000 + 12.0000i −0.642345 + 0.642345i −0.951131 0.308786i \(-0.900077\pi\)
0.308786 + 0.951131i \(0.400077\pi\)
\(350\) 0 0
\(351\) 17.8284 5.75736i 0.951611 0.307305i
\(352\) 2.00000 0.106600
\(353\) 25.4558 25.4558i 1.35488 1.35488i 0.474766 0.880112i \(-0.342533\pi\)
0.880112 0.474766i \(-0.157467\pi\)
\(354\) 4.00000 5.65685i 0.212598 0.300658i
\(355\) 8.00000i 0.424596i
\(356\) −4.24264 + 4.24264i −0.224860 + 0.224860i
\(357\) 0 0
\(358\) −13.0000 + 13.0000i −0.687071 + 0.687071i
\(359\) 16.9706 + 16.9706i 0.895672 + 0.895672i 0.995050 0.0993777i \(-0.0316852\pi\)
−0.0993777 + 0.995050i \(0.531685\pi\)
\(360\) 1.00000 + 2.82843i 0.0527046 + 0.149071i
\(361\) 53.0000i 2.78947i
\(362\) −12.7279 12.7279i −0.668965 0.668965i
\(363\) −9.89949 7.00000i −0.519589 0.367405i
\(364\) 0 0
\(365\) 8.48528i 0.444140i
\(366\) −0.585786 3.41421i −0.0306195 0.178464i
\(367\) −8.00000 −0.417597 −0.208798 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) −1.41421 −0.0737210
\(369\) 27.0711 + 12.9289i 1.40926 + 0.673053i
\(370\) −5.00000 5.00000i −0.259938 0.259938i
\(371\) 0 0
\(372\) 1.24264 + 7.24264i 0.0644279 + 0.375513i
\(373\) −32.0000 −1.65690 −0.828449 0.560065i \(-0.810776\pi\)
−0.828449 + 0.560065i \(0.810776\pi\)
\(374\) −8.48528 −0.438763
\(375\) −1.70711 + 0.292893i −0.0881546 + 0.0151249i
\(376\) 6.00000i 0.309426i
\(377\) 2.82843 + 4.24264i 0.145671 + 0.218507i
\(378\) 0 0
\(379\) 16.0000 + 16.0000i 0.821865 + 0.821865i 0.986375 0.164511i \(-0.0526045\pi\)
−0.164511 + 0.986375i \(0.552604\pi\)
\(380\) 8.48528i 0.435286i
\(381\) −5.65685 4.00000i −0.289809 0.204926i
\(382\) −14.0000 14.0000i −0.716302 0.716302i
\(383\) −16.9706 + 16.9706i −0.867155 + 0.867155i −0.992157 0.125001i \(-0.960106\pi\)
0.125001 + 0.992157i \(0.460106\pi\)
\(384\) 1.70711 0.292893i 0.0871154 0.0149466i
\(385\) 0 0
\(386\) 8.48528i 0.431889i
\(387\) 11.3137 4.00000i 0.575108 0.203331i
\(388\) 10.0000 10.0000i 0.507673 0.507673i
\(389\) −26.8701 −1.36237 −0.681183 0.732113i \(-0.738534\pi\)
−0.681183 + 0.732113i \(0.738534\pi\)
\(390\) 6.24264 + 0.171573i 0.316108 + 0.00868793i
\(391\) 6.00000 0.303433
\(392\) 4.94975 4.94975i 0.250000 0.250000i
\(393\) 10.0000 + 7.07107i 0.504433 + 0.356688i
\(394\) 14.0000i 0.705310i
\(395\) 5.65685 5.65685i 0.284627 0.284627i
\(396\) 5.41421 + 2.58579i 0.272074 + 0.129941i
\(397\) 3.00000 3.00000i 0.150566 0.150566i −0.627805 0.778371i \(-0.716046\pi\)
0.778371 + 0.627805i \(0.216046\pi\)
\(398\) −1.41421 1.41421i −0.0708881 0.0708881i
\(399\) 0 0
\(400\) 1.00000i 0.0500000i
\(401\) 4.24264 + 4.24264i 0.211867 + 0.211867i 0.805060 0.593193i \(-0.202133\pi\)
−0.593193 + 0.805060i \(0.702133\pi\)
\(402\) 7.07107 10.0000i 0.352673 0.498755i
\(403\) 15.0000 + 3.00000i 0.747203 + 0.149441i
\(404\) 15.5563i 0.773957i
\(405\) −0.949747 + 8.94975i −0.0471933 + 0.444717i
\(406\) 0 0
\(407\) −14.1421 −0.701000
\(408\) −7.24264 + 1.24264i −0.358564 + 0.0615199i
\(409\) −3.00000 3.00000i −0.148340 0.148340i 0.629036 0.777376i \(-0.283450\pi\)
−0.777376 + 0.629036i \(0.783450\pi\)
\(410\) 7.07107 + 7.07107i 0.349215 + 0.349215i
\(411\) −34.1421 + 5.85786i −1.68411 + 0.288947i
\(412\) −8.00000 −0.394132
\(413\) 0 0
\(414\) −3.82843 1.82843i −0.188157 0.0898623i
\(415\) 8.00000i 0.392705i
\(416\) 0.707107 3.53553i 0.0346688 0.173344i
\(417\) −16.0000 + 22.6274i −0.783523 + 1.10807i
\(418\) −12.0000 12.0000i −0.586939 0.586939i
\(419\) 15.5563i 0.759977i 0.924991 + 0.379989i \(0.124072\pi\)
−0.924991 + 0.379989i \(0.875928\pi\)
\(420\) 0 0
\(421\) 12.0000 + 12.0000i 0.584844 + 0.584844i 0.936231 0.351386i \(-0.114290\pi\)
−0.351386 + 0.936231i \(0.614290\pi\)
\(422\) −16.9706 + 16.9706i −0.826114 + 0.826114i
\(423\) 7.75736 16.2426i 0.377176 0.789744i
\(424\) −8.00000 + 8.00000i −0.388514 + 0.388514i
\(425\) 4.24264i 0.205798i
\(426\) 11.3137 + 8.00000i 0.548151 + 0.387601i
\(427\) 0 0
\(428\) 11.3137 0.546869
\(429\) 9.07107 8.58579i 0.437955 0.414526i
\(430\) 4.00000 0.192897
\(431\) 25.4558 25.4558i 1.22616 1.22616i 0.260762 0.965403i \(-0.416026\pi\)
0.965403 0.260762i \(-0.0839737\pi\)
\(432\) 5.00000 + 1.41421i 0.240563 + 0.0680414i
\(433\) 14.0000i 0.672797i 0.941720 + 0.336399i \(0.109209\pi\)
−0.941720 + 0.336399i \(0.890791\pi\)
\(434\) 0 0
\(435\) −2.41421 + 0.414214i −0.115753 + 0.0198600i
\(436\) 2.00000 2.00000i 0.0957826 0.0957826i
\(437\) 8.48528 + 8.48528i 0.405906 + 0.405906i
\(438\) −12.0000 8.48528i −0.573382 0.405442i
\(439\) 6.00000i 0.286364i −0.989696 0.143182i \(-0.954267\pi\)
0.989696 0.143182i \(-0.0457335\pi\)
\(440\) 1.41421 + 1.41421i 0.0674200 + 0.0674200i
\(441\) 19.7990 7.00000i 0.942809 0.333333i
\(442\) −3.00000 + 15.0000i −0.142695 + 0.713477i
\(443\) 8.48528i 0.403148i −0.979473 0.201574i \(-0.935394\pi\)
0.979473 0.201574i \(-0.0646056\pi\)
\(444\) −12.0711 + 2.07107i −0.572868 + 0.0982885i
\(445\) −6.00000 −0.284427
\(446\) −14.1421 −0.669650
\(447\) 2.92893 + 17.0711i 0.138534 + 0.807434i
\(448\) 0 0
\(449\) −12.7279 12.7279i −0.600668 0.600668i 0.339822 0.940490i \(-0.389633\pi\)
−0.940490 + 0.339822i \(0.889633\pi\)
\(450\) −1.29289 + 2.70711i −0.0609476 + 0.127614i
\(451\) 20.0000 0.941763
\(452\) −7.07107 −0.332595
\(453\) 5.38478 + 31.3848i 0.252999 + 1.47459i
\(454\) 0 0
\(455\) 0 0
\(456\) −12.0000 8.48528i −0.561951 0.397360i
\(457\) 6.00000 + 6.00000i 0.280668 + 0.280668i 0.833375 0.552707i \(-0.186405\pi\)
−0.552707 + 0.833375i \(0.686405\pi\)
\(458\) 8.48528i 0.396491i
\(459\) −21.2132 6.00000i −0.990148 0.280056i
\(460\) −1.00000 1.00000i −0.0466252 0.0466252i
\(461\) −2.82843 + 2.82843i −0.131733 + 0.131733i −0.769899 0.638166i \(-0.779693\pi\)
0.638166 + 0.769899i \(0.279693\pi\)
\(462\) 0 0
\(463\) 22.0000 22.0000i 1.02243 1.02243i 0.0226840 0.999743i \(-0.492779\pi\)
0.999743 0.0226840i \(-0.00722117\pi\)
\(464\) 1.41421i 0.0656532i
\(465\) −4.24264 + 6.00000i −0.196748 + 0.278243i
\(466\) 13.0000 13.0000i 0.602213 0.602213i
\(467\) 2.82843 0.130884 0.0654420 0.997856i \(-0.479154\pi\)
0.0654420 + 0.997856i \(0.479154\pi\)
\(468\) 6.48528 8.65685i 0.299782 0.400163i
\(469\) 0 0
\(470\) 4.24264 4.24264i 0.195698 0.195698i
\(471\) −6.00000 + 8.48528i −0.276465 + 0.390981i
\(472\) 4.00000i 0.184115i
\(473\) 5.65685 5.65685i 0.260102 0.260102i
\(474\) −2.34315 13.6569i −0.107624 0.627280i
\(475\) 6.00000 6.00000i 0.275299 0.275299i
\(476\) 0 0
\(477\) −32.0000 + 11.3137i −1.46518 + 0.518019i
\(478\) 0 0
\(479\) 14.1421 + 14.1421i 0.646171 + 0.646171i 0.952065 0.305895i \(-0.0989555\pi\)
−0.305895 + 0.952065i \(0.598956\pi\)
\(480\) 1.41421 + 1.00000i 0.0645497 + 0.0456435i
\(481\) −5.00000 + 25.0000i −0.227980 + 1.13990i
\(482\) 1.41421i 0.0644157i
\(483\) 0 0
\(484\) −7.00000 −0.318182
\(485\) 14.1421 0.642161
\(486\) 11.7071 + 10.2929i 0.531045 + 0.466895i
\(487\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(488\) −1.41421 1.41421i −0.0640184 0.0640184i
\(489\) 4.55635 + 26.5563i 0.206045 + 1.20092i
\(490\) 7.00000 0.316228
\(491\) 15.5563 0.702048 0.351024 0.936366i \(-0.385834\pi\)
0.351024 + 0.936366i \(0.385834\pi\)
\(492\) 17.0711 2.92893i 0.769623 0.132046i
\(493\) 6.00000i 0.270226i
\(494\) −25.4558 + 16.9706i −1.14531 + 0.763542i
\(495\) 2.00000 + 5.65685i 0.0898933 + 0.254257i
\(496\) 3.00000 + 3.00000i 0.134704 + 0.134704i
\(497\) 0 0
\(498\) 11.3137 + 8.00000i 0.506979 + 0.358489i
\(499\) −18.0000 18.0000i −0.805791 0.805791i 0.178203 0.983994i \(-0.442972\pi\)
−0.983994 + 0.178203i \(0.942972\pi\)
\(500\) −0.707107 + 0.707107i −0.0316228 + 0.0316228i
\(501\) 27.3137 4.68629i 1.22029 0.209368i
\(502\) −3.00000 + 3.00000i −0.133897 + 0.133897i
\(503\) 9.89949i 0.441397i −0.975342 0.220698i \(-0.929166\pi\)
0.975342 0.220698i \(-0.0708336\pi\)
\(504\) 0 0
\(505\) −11.0000 + 11.0000i −0.489494 + 0.489494i
\(506\) −2.82843 −0.125739
\(507\) −11.9706 19.0711i −0.531631 0.846976i
\(508\) −4.00000 −0.177471
\(509\) −14.1421 + 14.1421i −0.626839 + 0.626839i −0.947271 0.320432i \(-0.896172\pi\)
0.320432 + 0.947271i \(0.396172\pi\)
\(510\) −6.00000 4.24264i −0.265684 0.187867i
\(511\) 0 0
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −21.5147 38.4853i −0.949898 1.69917i
\(514\) 1.00000 1.00000i 0.0441081 0.0441081i
\(515\) −5.65685 5.65685i −0.249271 0.249271i
\(516\) 4.00000 5.65685i 0.176090 0.249029i
\(517\) 12.0000i 0.527759i
\(518\) 0 0
\(519\) 2.82843 4.00000i 0.124154 0.175581i
\(520\) 3.00000 2.00000i 0.131559 0.0877058i
\(521\) 5.65685i 0.247831i −0.992293 0.123916i \(-0.960455\pi\)
0.992293 0.123916i \(-0.0395452\pi\)
\(522\) −1.82843 + 3.82843i −0.0800281 + 0.167566i
\(523\) 20.0000 0.874539 0.437269 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) 7.07107 0.308901
\(525\) 0 0
\(526\) 3.00000 + 3.00000i 0.130806 + 0.130806i
\(527\) −12.7279 12.7279i −0.554437 0.554437i
\(528\) 3.41421 0.585786i 0.148585 0.0254931i
\(529\) −21.0000 −0.913043
\(530\) −11.3137 −0.491436
\(531\) 5.17157 10.8284i 0.224427 0.469914i
\(532\) 0 0
\(533\) 7.07107 35.3553i 0.306282 1.53141i
\(534\) −6.00000 + 8.48528i −0.259645 + 0.367194i
\(535\) 8.00000 + 8.00000i 0.345870 + 0.345870i
\(536\) 7.07107i 0.305424i
\(537\) −18.3848 + 26.0000i −0.793362 + 1.12198i
\(538\) −1.00000 1.00000i −0.0431131 0.0431131i
\(539\) 9.89949 9.89949i 0.426401 0.426401i
\(540\) 2.53553 + 4.53553i 0.109112 + 0.195178i
\(541\) −8.00000 + 8.00000i −0.343947 + 0.343947i −0.857849 0.513902i \(-0.828199\pi\)
0.513902 + 0.857849i \(0.328199\pi\)
\(542\) 4.24264i 0.182237i
\(543\) −25.4558 18.0000i −1.09241 0.772454i
\(544\) −3.00000 + 3.00000i −0.128624 + 0.128624i
\(545\) 2.82843 0.121157
\(546\) 0 0
\(547\) −12.0000 −0.513083 −0.256541 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) −14.1421 + 14.1421i −0.604122 + 0.604122i
\(549\) −2.00000 5.65685i −0.0853579 0.241429i
\(550\) 2.00000i 0.0852803i
\(551\) 8.48528 8.48528i 0.361485 0.361485i
\(552\) −2.41421 + 0.414214i −0.102756 + 0.0176301i
\(553\) 0 0
\(554\) −19.7990 19.7990i −0.841178 0.841178i
\(555\) −10.0000 7.07107i −0.424476 0.300150i
\(556\) 16.0000i 0.678551i
\(557\) −18.3848 18.3848i −0.778988 0.778988i 0.200671 0.979659i \(-0.435688\pi\)
−0.979659 + 0.200671i \(0.935688\pi\)
\(558\) 4.24264 + 12.0000i 0.179605 + 0.508001i
\(559\) −8.00000 12.0000i −0.338364 0.507546i
\(560\) 0 0
\(561\) −14.4853 + 2.48528i −0.611569 + 0.104929i
\(562\) 18.0000 0.759284
\(563\) 19.7990 0.834428 0.417214 0.908808i \(-0.363007\pi\)
0.417214 + 0.908808i \(0.363007\pi\)
\(564\) −1.75736 10.2426i −0.0739982 0.431293i
\(565\) −5.00000 5.00000i −0.210352 0.210352i
\(566\) 4.24264 + 4.24264i 0.178331 + 0.178331i
\(567\) 0 0
\(568\) 8.00000 0.335673
\(569\) 45.2548 1.89718 0.948591 0.316506i \(-0.102510\pi\)
0.948591 + 0.316506i \(0.102510\pi\)
\(570\) −2.48528 14.4853i −0.104097 0.606722i
\(571\) 12.0000i 0.502184i −0.967963 0.251092i \(-0.919210\pi\)
0.967963 0.251092i \(-0.0807897\pi\)
\(572\) 1.41421 7.07107i 0.0591312 0.295656i
\(573\) −28.0000 19.7990i −1.16972 0.827115i
\(574\) 0 0
\(575\) 1.41421i 0.0589768i
\(576\) 2.82843 1.00000i 0.117851 0.0416667i
\(577\) 26.0000 + 26.0000i 1.08239 + 1.08239i 0.996286 + 0.0861084i \(0.0274431\pi\)
0.0861084 + 0.996286i \(0.472557\pi\)
\(578\) 0.707107 0.707107i 0.0294118 0.0294118i
\(579\) 2.48528 + 14.4853i 0.103285 + 0.601988i
\(580\) −1.00000 + 1.00000i −0.0415227 + 0.0415227i
\(581\) 0 0
\(582\) 14.1421 20.0000i 0.586210 0.829027i
\(583\) −16.0000 + 16.0000i −0.662652 + 0.662652i
\(584\) −8.48528 −0.351123
\(585\) 10.7071 1.53553i 0.442684 0.0634865i
\(586\) −14.0000 −0.578335
\(587\) −19.7990 + 19.7990i −0.817192 + 0.817192i −0.985700 0.168508i \(-0.946105\pi\)
0.168508 + 0.985700i \(0.446105\pi\)
\(588\) 7.00000 9.89949i 0.288675 0.408248i
\(589\) 36.0000i 1.48335i
\(590\) 2.82843 2.82843i 0.116445 0.116445i
\(591\) −4.10051 23.8995i −0.168672 0.983094i
\(592\) −5.00000 + 5.00000i −0.205499 + 0.205499i
\(593\) −25.4558 25.4558i −1.04535 1.04535i −0.998922 0.0464244i \(-0.985217\pi\)
−0.0464244 0.998922i \(-0.514783\pi\)
\(594\) 10.0000 + 2.82843i 0.410305 + 0.116052i
\(595\) 0 0
\(596\) 7.07107 + 7.07107i 0.289642 + 0.289642i
\(597\) −2.82843 2.00000i −0.115760 0.0818546i
\(598\) −1.00000 + 5.00000i −0.0408930 + 0.204465i
\(599\) 45.2548i 1.84906i −0.381106 0.924531i \(-0.624457\pi\)
0.381106 0.924531i \(-0.375543\pi\)
\(600\) 0.292893 + 1.70711i 0.0119573 + 0.0696923i
\(601\) 38.0000 1.55005 0.775026 0.631929i \(-0.217737\pi\)
0.775026 + 0.631929i \(0.217737\pi\)
\(602\) 0 0
\(603\) 9.14214 19.1421i 0.372297 0.779528i
\(604\) 13.0000 + 13.0000i 0.528962 + 0.528962i
\(605\) −4.94975 4.94975i −0.201236 0.201236i
\(606\) 4.55635 + 26.5563i 0.185089 + 1.07878i
\(607\) 36.0000 1.46119 0.730597 0.682808i \(-0.239242\pi\)
0.730597 + 0.682808i \(0.239242\pi\)
\(608\) −8.48528 −0.344124
\(609\) 0 0
\(610\) 2.00000i 0.0809776i
\(611\) −21.2132 4.24264i −0.858194 0.171639i
\(612\) −12.0000 + 4.24264i −0.485071 + 0.171499i
\(613\) −9.00000 9.00000i −0.363507 0.363507i 0.501596 0.865102i \(-0.332747\pi\)
−0.865102 + 0.501596i \(0.832747\pi\)
\(614\) 32.5269i 1.31268i
\(615\) 14.1421 + 10.0000i 0.570266 + 0.403239i
\(616\) 0 0
\(617\) 7.07107 7.07107i 0.284670 0.284670i −0.550298 0.834968i \(-0.685486\pi\)
0.834968 + 0.550298i \(0.185486\pi\)
\(618\) −13.6569 + 2.34315i −0.549359 + 0.0942551i
\(619\) 32.0000 32.0000i 1.28619 1.28619i 0.349105 0.937084i \(-0.386486\pi\)
0.937084 0.349105i \(-0.113514\pi\)
\(620\) 4.24264i 0.170389i
\(621\) −7.07107 2.00000i −0.283752 0.0802572i
\(622\) 2.00000 2.00000i 0.0801927 0.0801927i
\(623\) 0 0
\(624\) 0.171573 6.24264i 0.00686841 0.249906i
\(625\) −1.00000 −0.0400000
\(626\) 18.3848 18.3848i 0.734803 0.734803i
\(627\) −24.0000 16.9706i −0.958468 0.677739i
\(628\) 6.00000i 0.239426i
\(629\) 21.2132 21.2132i 0.845826 0.845826i
\(630\) 0 0
\(631\) 9.00000 9.00000i 0.358284 0.358284i −0.504896 0.863180i \(-0.668469\pi\)
0.863180 + 0.504896i \(0.168469\pi\)
\(632\) −5.65685 5.65685i −0.225018 0.225018i
\(633\) −24.0000 + 33.9411i −0.953914 + 1.34904i
\(634\) 26.0000i 1.03259i
\(635\) −2.82843 2.82843i −0.112243 0.112243i
\(636\) −11.3137 + 16.0000i −0.448618 + 0.634441i
\(637\) −14.0000 21.0000i −0.554700 0.832050i
\(638\) 2.82843i 0.111979i
\(639\) 21.6569 + 10.3431i 0.856732 + 0.409169i
\(640\) 1.00000 0.0395285
\(641\) −39.5980 −1.56403 −0.782013 0.623262i \(-0.785807\pi\)
−0.782013 + 0.623262i \(0.785807\pi\)
\(642\) 19.3137 3.31371i 0.762251 0.130782i
\(643\) −21.0000 21.0000i −0.828159 0.828159i 0.159103 0.987262i \(-0.449140\pi\)
−0.987262 + 0.159103i \(0.949140\pi\)
\(644\) 0 0
\(645\) 6.82843 1.17157i 0.268869 0.0461306i
\(646\) 36.0000 1.41640
\(647\) 7.07107 0.277992 0.138996 0.990293i \(-0.455612\pi\)
0.138996 + 0.990293i \(0.455612\pi\)
\(648\) 8.94975 + 0.949747i 0.351579 + 0.0373096i
\(649\) 8.00000i 0.314027i
\(650\) 3.53553 + 0.707107i 0.138675 + 0.0277350i
\(651\) 0 0
\(652\) 11.0000 + 11.0000i 0.430793 + 0.430793i
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 2.82843 4.00000i 0.110600 0.156412i
\(655\) 5.00000 + 5.00000i 0.195366 + 0.195366i
\(656\) 7.07107 7.07107i 0.276079 0.276079i
\(657\) −22.9706 10.9706i −0.896167 0.428002i
\(658\) 0 0
\(659\) 9.89949i 0.385630i −0.981235 0.192815i \(-0.938238\pi\)
0.981235 0.192815i \(-0.0617617\pi\)
\(660\) 2.82843 + 2.00000i 0.110096 + 0.0778499i
\(661\) −22.0000 + 22.0000i −0.855701 + 0.855701i −0.990828 0.135127i \(-0.956856\pi\)
0.135127 + 0.990828i \(0.456856\pi\)
\(662\) 33.9411 1.31916
\(663\) −0.727922 + 26.4853i −0.0282702 + 1.02860i
\(664\) 8.00000 0.310460
\(665\) 0 0
\(666\) −20.0000 + 7.07107i −0.774984 + 0.273998i
\(667\) 2.00000i 0.0774403i
\(668\) 11.3137 11.3137i 0.437741 0.437741i
\(669\) −24.1421 + 4.14214i −0.933389 + 0.160144i
\(670\) 5.00000 5.00000i 0.193167 0.193167i
\(671\) −2.82843 2.82843i −0.109190 0.109190i
\(672\) 0 0
\(673\) 6.00000i 0.231283i 0.993291 + 0.115642i \(0.0368924\pi\)
−0.993291 + 0.115642i \(0.963108\pi\)
\(674\) −9.89949 9.89949i −0.381314 0.381314i
\(675\) −1.41421 + 5.00000i −0.0544331 + 0.192450i
\(676\) −12.0000 5.00000i −0.461538 0.192308i
\(677\) 36.7696i 1.41317i 0.707629 + 0.706584i \(0.249765\pi\)
−0.707629 + 0.706584i \(0.750235\pi\)
\(678\) −12.0711 + 2.07107i −0.463587 + 0.0795389i
\(679\) 0 0
\(680\) −4.24264 −0.162698
\(681\) 0 0
\(682\) 6.00000 + 6.00000i 0.229752 + 0.229752i
\(683\) 16.9706 + 16.9706i 0.649361 + 0.649361i 0.952838 0.303478i \(-0.0981479\pi\)
−0.303478 + 0.952838i \(0.598148\pi\)
\(684\) −22.9706 10.9706i −0.878301 0.419470i
\(685\) −20.0000 −0.764161
\(686\) 0 0
\(687\) −2.48528 14.4853i −0.0948194 0.552648i
\(688\) 4.00000i 0.152499i
\(689\) 22.6274 + 33.9411i 0.862036 + 1.29305i
\(690\) −2.00000 1.41421i −0.0761387 0.0538382i
\(691\) −16.0000 16.0000i −0.608669 0.608669i 0.333929 0.942598i \(-0.391625\pi\)
−0.942598 + 0.333929i \(0.891625\pi\)
\(692\) 2.82843i 0.107521i
\(693\) 0 0
\(694\) −8.00000 8.00000i −0.303676 0.303676i
\(695\) −11.3137 + 11.3137i −0.429153 + 0.429153i
\(696\) 0.414214 + 2.41421i 0.0157007 + 0.0915105i
\(697\) −30.0000 + 30.0000i −1.13633 + 1.13633i
\(698\) 16.9706i 0.642345i
\(699\) 18.3848 26.0000i 0.695376 0.983410i
\(700\) 0 0
\(701\) 1.41421 0.0534141 0.0267071 0.999643i \(-0.491498\pi\)
0.0267071 + 0.999643i \(0.491498\pi\)
\(702\) 8.53553 16.6777i 0.322153 0.629458i
\(703\) 60.0000 2.26294
\(704\) 1.41421 1.41421i 0.0533002 0.0533002i
\(705\) 6.00000 8.48528i 0.225973 0.319574i
\(706\) 36.0000i 1.35488i
\(707\) 0 0
\(708\) −1.17157 6.82843i −0.0440304 0.256628i
\(709\) −18.0000 + 18.0000i −0.676004 + 0.676004i −0.959094 0.283089i \(-0.908641\pi\)
0.283089 + 0.959094i \(0.408641\pi\)
\(710\) 5.65685 + 5.65685i 0.212298 + 0.212298i
\(711\) −8.00000 22.6274i −0.300023 0.848594i
\(712\) 6.00000i 0.224860i
\(713\) −4.24264 4.24264i −0.158888 0.158888i
\(714\) 0 0
\(715\) 6.00000 4.00000i 0.224387 0.149592i
\(716\) 18.3848i 0.687071i
\(717\) 0 0
\(718\) 24.0000 0.895672
\(719\) 45.2548 1.68772 0.843860 0.536563i \(-0.180278\pi\)
0.843860 + 0.536563i \(0.180278\pi\)
\(720\) 2.70711 + 1.29289i 0.100888 + 0.0481833i
\(721\) 0 0
\(722\) 37.4767 + 37.4767i 1.39474 + 1.39474i
\(723\) 0.414214 + 2.41421i 0.0154048 + 0.0897856i
\(724\) −18.0000 −0.668965
\(725\) −1.41421 −0.0525226
\(726\) −11.9497 + 2.05025i −0.443497 + 0.0760920i
\(727\) 8.00000i 0.296704i 0.988935 + 0.148352i \(0.0473968\pi\)
−0.988935 + 0.148352i \(0.952603\pi\)
\(728\) 0 0
\(729\) 23.0000 + 14.1421i 0.851852 + 0.523783i
\(730\) −6.00000 6.00000i −0.222070 0.222070i
\(731\) 16.9706i 0.627679i
\(732\) −2.82843 2.00000i −0.104542 0.0739221i
\(733\) −9.00000 9.00000i −0.332423 0.332423i 0.521083 0.853506i \(-0.325528\pi\)
−0.853506 + 0.521083i \(0.825528\pi\)
\(734\) −5.65685 + 5.65685i −0.208798 + 0.208798i
\(735\) 11.9497 2.05025i 0.440773 0.0756247i
\(736\) −1.00000 + 1.00000i −0.0368605 + 0.0368605i
\(737\) 14.1421i 0.520932i
\(738\) 28.2843 10.0000i 1.04116 0.368105i
\(739\) −12.0000 + 12.0000i −0.441427 + 0.441427i −0.892491 0.451064i \(-0.851045\pi\)
0.451064 + 0.892491i \(0.351045\pi\)
\(740\) −7.07107 −0.259938
\(741\) −38.4853 + 36.4264i −1.41379 + 1.33816i
\(742\) 0 0
\(743\) −18.3848 + 18.3848i −0.674472 + 0.674472i −0.958744 0.284272i \(-0.908248\pi\)
0.284272 + 0.958744i \(0.408248\pi\)
\(744\) 6.00000 + 4.24264i 0.219971 + 0.155543i
\(745\) 10.0000i 0.366372i
\(746\) −22.6274 + 22.6274i −0.828449 + 0.828449i
\(747\) 21.6569 + 10.3431i 0.792383 + 0.378436i
\(748\) −6.00000 + 6.00000i −0.219382 + 0.219382i
\(749\) 0 0
\(750\) −1.00000 + 1.41421i −0.0365148 + 0.0516398i
\(751\) 10.0000i 0.364905i −0.983215 0.182453i \(-0.941596\pi\)
0.983215 0.182453i \(-0.0584036\pi\)
\(752\) −4.24264 4.24264i −0.154713 0.154713i
\(753\) −4.24264 + 6.00000i −0.154610 + 0.218652i
\(754\) 5.00000 + 1.00000i 0.182089 + 0.0364179i
\(755\) 18.3848i 0.669091i
\(756\) 0 0
\(757\) 42.0000 1.52652 0.763258 0.646094i \(-0.223599\pi\)
0.763258 + 0.646094i \(0.223599\pi\)
\(758\) 22.6274 0.821865
\(759\) −4.82843 + 0.828427i −0.175261 + 0.0300700i
\(760\) −6.00000 6.00000i −0.217643 0.217643i
\(761\) 9.89949 + 9.89949i 0.358856 + 0.358856i 0.863391 0.504535i \(-0.168336\pi\)
−0.504535 + 0.863391i \(0.668336\pi\)
\(762\) −6.82843 + 1.17157i −0.247368 + 0.0424416i
\(763\) 0 0
\(764\) −19.7990 −0.716302
\(765\) −11.4853 5.48528i −0.415251 0.198321i
\(766\) 24.0000i 0.867155i
\(767\) −14.1421 2.82843i −0.510643 0.102129i
\(768\) 1.00000 1.41421i 0.0360844 0.0510310i
\(769\) −21.0000 21.0000i −0.757279 0.757279i 0.218547 0.975826i \(-0.429868\pi\)
−0.975826 + 0.218547i \(0.929868\pi\)
\(770\) 0 0
\(771\) 1.41421 2.00000i 0.0509317 0.0720282i
\(772\) 6.00000 + 6.00000i 0.215945 + 0.215945i
\(773\) −4.24264 + 4.24264i −0.152597 + 0.152597i −0.779277 0.626680i \(-0.784413\pi\)
0.626680 + 0.779277i \(0.284413\pi\)
\(774\) 5.17157 10.8284i 0.185888 0.389220i