Properties

Label 210.2.m.b.13.4
Level $210$
Weight $2$
Character 210.13
Analytic conductor $1.677$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [210,2,Mod(13,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.m (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: \(1.67685844245\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.1698758656.6
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 13.4
Root \(-0.692297i\) of defining polynomial
Character \(\chi\) \(=\) 210.13
Dual form 210.2.m.b.97.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(1.19663 + 1.88893i) q^{5} +1.00000i q^{6} +(0.510472 + 2.59604i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(1.19663 + 1.88893i) q^{5} +1.00000i q^{6} +(0.510472 + 2.59604i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +(2.18183 + 0.489528i) q^{10} +4.79881 q^{11} +(0.707107 + 0.707107i) q^{12} +(0.585786 - 0.585786i) q^{13} +(2.19663 + 1.47472i) q^{14} +(-2.18183 - 0.489528i) q^{15} -1.00000 q^{16} +(-4.10651 - 4.10651i) q^{17} +(-0.707107 - 0.707107i) q^{18} -2.36365 q^{19} +(1.88893 - 1.19663i) q^{20} +(-2.19663 - 1.47472i) q^{21} +(3.39327 - 3.39327i) q^{22} +(2.97906 + 2.97906i) q^{23} +1.00000 q^{24} +(-2.13613 + 4.52072i) q^{25} -0.828427i q^{26} +(0.707107 + 0.707107i) q^{27} +(2.59604 - 0.510472i) q^{28} -9.94900i q^{29} +(-1.88893 + 1.19663i) q^{30} +3.02094i q^{31} +(-0.707107 + 0.707107i) q^{32} +(-3.39327 + 3.39327i) q^{33} -5.80748 q^{34} +(-4.29289 + 4.07076i) q^{35} -1.00000 q^{36} +(-6.10651 + 6.10651i) q^{37} +(-1.67135 + 1.67135i) q^{38} +0.828427i q^{39} +(0.489528 - 2.18183i) q^{40} -10.9996i q^{41} +(-2.59604 + 0.510472i) q^{42} +(-5.74825 - 5.74825i) q^{43} -4.79881i q^{44} +(1.88893 - 1.19663i) q^{45} +4.21302 q^{46} +(0.363651 + 0.363651i) q^{47} +(0.707107 - 0.707107i) q^{48} +(-6.47884 + 2.65041i) q^{49} +(1.68616 + 4.70711i) q^{50} +5.80748 q^{51} +(-0.585786 - 0.585786i) q^{52} +(2.36365 + 2.36365i) q^{53} +1.00000 q^{54} +(5.74242 + 9.06462i) q^{55} +(1.47472 - 2.19663i) q^{56} +(1.67135 - 1.67135i) q^{57} +(-7.03500 - 7.03500i) q^{58} -2.07912 q^{59} +(-0.489528 + 2.18183i) q^{60} -5.55573i q^{61} +(2.13613 + 2.13613i) q^{62} +(2.59604 - 0.510472i) q^{63} +1.00000i q^{64} +(1.80748 + 0.405538i) q^{65} +4.79881i q^{66} +(-0.979056 + 0.979056i) q^{67} +(-4.10651 + 4.10651i) q^{68} -4.21302 q^{69} +(-0.157074 + 5.91399i) q^{70} +5.25132 q^{71} +(-0.707107 + 0.707107i) q^{72} +(6.11519 - 6.11519i) q^{73} +8.63591i q^{74} +(-1.68616 - 4.70711i) q^{75} +2.36365i q^{76} +(2.44966 + 12.4579i) q^{77} +(0.585786 + 0.585786i) q^{78} -5.10069i q^{79} +(-1.19663 - 1.88893i) q^{80} -1.00000 q^{81} +(-7.77786 - 7.77786i) q^{82} +(-3.22170 + 3.22170i) q^{83} +(-1.47472 + 2.19663i) q^{84} +(2.84293 - 12.6709i) q^{85} -8.12925 q^{86} +(7.03500 + 7.03500i) q^{87} +(-3.39327 - 3.39327i) q^{88} +11.8989 q^{89} +(0.489528 - 2.18183i) q^{90} +(1.81975 + 1.22170i) q^{91} +(2.97906 - 2.97906i) q^{92} +(-2.13613 - 2.13613i) q^{93} +0.514280 q^{94} +(-2.82843 - 4.46478i) q^{95} -1.00000i q^{96} +(8.05595 + 8.05595i) q^{97} +(-2.70711 + 6.45535i) q^{98} -4.79881i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{7} + 4 q^{10} + 8 q^{11} + 16 q^{13} + 8 q^{14} - 4 q^{15} - 8 q^{16} - 12 q^{17} + 8 q^{19} - 4 q^{20} - 8 q^{21} + 8 q^{22} + 16 q^{23} + 8 q^{24} - 4 q^{25} - 4 q^{28} + 4 q^{30} - 8 q^{33} - 16 q^{34} - 40 q^{35} - 8 q^{36} - 28 q^{37} + 4 q^{38} + 4 q^{42} - 4 q^{45} - 8 q^{46} - 24 q^{47} - 4 q^{49} + 16 q^{51} - 16 q^{52} - 8 q^{53} + 8 q^{54} - 28 q^{55} + 4 q^{56} - 4 q^{57} - 12 q^{58} - 8 q^{59} + 4 q^{62} - 4 q^{63} - 16 q^{65} - 12 q^{68} + 8 q^{69} + 4 q^{70} + 8 q^{71} + 28 q^{73} + 44 q^{77} + 16 q^{78} - 8 q^{81} - 24 q^{82} + 16 q^{83} - 4 q^{84} + 28 q^{85} + 8 q^{86} + 12 q^{87} - 8 q^{88} + 64 q^{89} - 8 q^{91} + 16 q^{92} - 4 q^{93} - 8 q^{94} + 28 q^{97} - 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) −0.707107 + 0.707107i −0.408248 + 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) 1.19663 + 1.88893i 0.535151 + 0.844756i
\(6\) 1.00000i 0.408248i
\(7\) 0.510472 + 2.59604i 0.192940 + 0.981211i
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) 2.18183 + 0.489528i 0.689954 + 0.154802i
\(11\) 4.79881 1.44690 0.723448 0.690379i \(-0.242556\pi\)
0.723448 + 0.690379i \(0.242556\pi\)
\(12\) 0.707107 + 0.707107i 0.204124 + 0.204124i
\(13\) 0.585786 0.585786i 0.162468 0.162468i −0.621191 0.783659i \(-0.713351\pi\)
0.783659 + 0.621191i \(0.213351\pi\)
\(14\) 2.19663 + 1.47472i 0.587075 + 0.394135i
\(15\) −2.18183 0.489528i −0.563345 0.126396i
\(16\) −1.00000 −0.250000
\(17\) −4.10651 4.10651i −0.995975 0.995975i 0.00401675 0.999992i \(-0.498721\pi\)
−0.999992 + 0.00401675i \(0.998721\pi\)
\(18\) −0.707107 0.707107i −0.166667 0.166667i
\(19\) −2.36365 −0.542259 −0.271129 0.962543i \(-0.587397\pi\)
−0.271129 + 0.962543i \(0.587397\pi\)
\(20\) 1.88893 1.19663i 0.422378 0.267576i
\(21\) −2.19663 1.47472i −0.479345 0.321810i
\(22\) 3.39327 3.39327i 0.723448 0.723448i
\(23\) 2.97906 + 2.97906i 0.621176 + 0.621176i 0.945832 0.324656i \(-0.105249\pi\)
−0.324656 + 0.945832i \(0.605249\pi\)
\(24\) 1.00000 0.204124
\(25\) −2.13613 + 4.52072i −0.427226 + 0.904145i
\(26\) 0.828427i 0.162468i
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) 2.59604 0.510472i 0.490605 0.0964701i
\(29\) 9.94900i 1.84748i −0.383017 0.923741i \(-0.625115\pi\)
0.383017 0.923741i \(-0.374885\pi\)
\(30\) −1.88893 + 1.19663i −0.344870 + 0.218475i
\(31\) 3.02094i 0.542578i 0.962498 + 0.271289i \(0.0874498\pi\)
−0.962498 + 0.271289i \(0.912550\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −3.39327 + 3.39327i −0.590692 + 0.590692i
\(34\) −5.80748 −0.995975
\(35\) −4.29289 + 4.07076i −0.725631 + 0.688084i
\(36\) −1.00000 −0.166667
\(37\) −6.10651 + 6.10651i −1.00390 + 1.00390i −0.00391185 + 0.999992i \(0.501245\pi\)
−0.999992 + 0.00391185i \(0.998755\pi\)
\(38\) −1.67135 + 1.67135i −0.271129 + 0.271129i
\(39\) 0.828427i 0.132655i
\(40\) 0.489528 2.18183i 0.0774012 0.344977i
\(41\) 10.9996i 1.71784i −0.512107 0.858921i \(-0.671135\pi\)
0.512107 0.858921i \(-0.328865\pi\)
\(42\) −2.59604 + 0.510472i −0.400578 + 0.0787675i
\(43\) −5.74825 5.74825i −0.876599 0.876599i 0.116582 0.993181i \(-0.462806\pi\)
−0.993181 + 0.116582i \(0.962806\pi\)
\(44\) 4.79881i 0.723448i
\(45\) 1.88893 1.19663i 0.281585 0.178384i
\(46\) 4.21302 0.621176
\(47\) 0.363651 + 0.363651i 0.0530439 + 0.0530439i 0.733131 0.680087i \(-0.238058\pi\)
−0.680087 + 0.733131i \(0.738058\pi\)
\(48\) 0.707107 0.707107i 0.102062 0.102062i
\(49\) −6.47884 + 2.65041i −0.925548 + 0.378630i
\(50\) 1.68616 + 4.70711i 0.238459 + 0.665685i
\(51\) 5.80748 0.813210
\(52\) −0.585786 0.585786i −0.0812340 0.0812340i
\(53\) 2.36365 + 2.36365i 0.324672 + 0.324672i 0.850556 0.525884i \(-0.176265\pi\)
−0.525884 + 0.850556i \(0.676265\pi\)
\(54\) 1.00000 0.136083
\(55\) 5.74242 + 9.06462i 0.774308 + 1.22227i
\(56\) 1.47472 2.19663i 0.197068 0.293538i
\(57\) 1.67135 1.67135i 0.221376 0.221376i
\(58\) −7.03500 7.03500i −0.923741 0.923741i
\(59\) −2.07912 −0.270679 −0.135339 0.990799i \(-0.543212\pi\)
−0.135339 + 0.990799i \(0.543212\pi\)
\(60\) −0.489528 + 2.18183i −0.0631978 + 0.281672i
\(61\) 5.55573i 0.711338i −0.934612 0.355669i \(-0.884253\pi\)
0.934612 0.355669i \(-0.115747\pi\)
\(62\) 2.13613 + 2.13613i 0.271289 + 0.271289i
\(63\) 2.59604 0.510472i 0.327070 0.0643134i
\(64\) 1.00000i 0.125000i
\(65\) 1.80748 + 0.405538i 0.224191 + 0.0503008i
\(66\) 4.79881i 0.590692i
\(67\) −0.979056 + 0.979056i −0.119611 + 0.119611i −0.764379 0.644768i \(-0.776954\pi\)
0.644768 + 0.764379i \(0.276954\pi\)
\(68\) −4.10651 + 4.10651i −0.497988 + 0.497988i
\(69\) −4.21302 −0.507188
\(70\) −0.157074 + 5.91399i −0.0187739 + 0.706858i
\(71\) 5.25132 0.623217 0.311608 0.950211i \(-0.399132\pi\)
0.311608 + 0.950211i \(0.399132\pi\)
\(72\) −0.707107 + 0.707107i −0.0833333 + 0.0833333i
\(73\) 6.11519 6.11519i 0.715728 0.715728i −0.251999 0.967727i \(-0.581088\pi\)
0.967727 + 0.251999i \(0.0810880\pi\)
\(74\) 8.63591i 1.00390i
\(75\) −1.68616 4.70711i −0.194701 0.543530i
\(76\) 2.36365i 0.271129i
\(77\) 2.44966 + 12.4579i 0.279164 + 1.41971i
\(78\) 0.585786 + 0.585786i 0.0663273 + 0.0663273i
\(79\) 5.10069i 0.573872i −0.957950 0.286936i \(-0.907363\pi\)
0.957950 0.286936i \(-0.0926367\pi\)
\(80\) −1.19663 1.88893i −0.133788 0.211189i
\(81\) −1.00000 −0.111111
\(82\) −7.77786 7.77786i −0.858921 0.858921i
\(83\) −3.22170 + 3.22170i −0.353627 + 0.353627i −0.861457 0.507830i \(-0.830448\pi\)
0.507830 + 0.861457i \(0.330448\pi\)
\(84\) −1.47472 + 2.19663i −0.160905 + 0.239673i
\(85\) 2.84293 12.6709i 0.308359 1.37435i
\(86\) −8.12925 −0.876599
\(87\) 7.03500 + 7.03500i 0.754232 + 0.754232i
\(88\) −3.39327 3.39327i −0.361724 0.361724i
\(89\) 11.8989 1.26128 0.630639 0.776076i \(-0.282793\pi\)
0.630639 + 0.776076i \(0.282793\pi\)
\(90\) 0.489528 2.18183i 0.0516008 0.229985i
\(91\) 1.81975 + 1.22170i 0.190762 + 0.128069i
\(92\) 2.97906 2.97906i 0.310588 0.310588i
\(93\) −2.13613 2.13613i −0.221506 0.221506i
\(94\) 0.514280 0.0530439
\(95\) −2.82843 4.46478i −0.290191 0.458076i
\(96\) 1.00000i 0.102062i
\(97\) 8.05595 + 8.05595i 0.817958 + 0.817958i 0.985812 0.167854i \(-0.0536838\pi\)
−0.167854 + 0.985812i \(0.553684\pi\)
\(98\) −2.70711 + 6.45535i −0.273459 + 0.652089i
\(99\) 4.79881i 0.482298i
\(100\) 4.52072 + 2.13613i 0.452072 + 0.213613i
\(101\) 4.89020i 0.486593i −0.969952 0.243297i \(-0.921771\pi\)
0.969952 0.243297i \(-0.0782288\pi\)
\(102\) 4.10651 4.10651i 0.406605 0.406605i
\(103\) 1.06462 1.06462i 0.104900 0.104900i −0.652709 0.757609i \(-0.726367\pi\)
0.757609 + 0.652709i \(0.226367\pi\)
\(104\) −0.828427 −0.0812340
\(105\) 0.157074 5.91399i 0.0153288 0.577147i
\(106\) 3.34271 0.324672
\(107\) 2.15063 2.15063i 0.207909 0.207909i −0.595469 0.803378i \(-0.703034\pi\)
0.803378 + 0.595469i \(0.203034\pi\)
\(108\) 0.707107 0.707107i 0.0680414 0.0680414i
\(109\) 12.8984i 1.23545i 0.786396 + 0.617723i \(0.211945\pi\)
−0.786396 + 0.617723i \(0.788055\pi\)
\(110\) 10.4702 + 2.34915i 0.998291 + 0.223983i
\(111\) 8.63591i 0.819684i
\(112\) −0.510472 2.59604i −0.0482351 0.245303i
\(113\) −11.5853 11.5853i −1.08986 1.08986i −0.995542 0.0943155i \(-0.969934\pi\)
−0.0943155 0.995542i \(-0.530066\pi\)
\(114\) 2.36365i 0.221376i
\(115\) −2.06239 + 9.19208i −0.192319 + 0.857166i
\(116\) −9.94900 −0.923741
\(117\) −0.585786 0.585786i −0.0541560 0.0541560i
\(118\) −1.47016 + 1.47016i −0.135339 + 0.135339i
\(119\) 8.56440 12.7569i 0.785098 1.16943i
\(120\) 1.19663 + 1.88893i 0.109237 + 0.172435i
\(121\) 12.0286 1.09351
\(122\) −3.92849 3.92849i −0.355669 0.355669i
\(123\) 7.77786 + 7.77786i 0.701306 + 0.701306i
\(124\) 3.02094 0.271289
\(125\) −11.0955 + 1.37465i −0.992413 + 0.122953i
\(126\) 1.47472 2.19663i 0.131378 0.195692i
\(127\) 0.399714 0.399714i 0.0354689 0.0354689i −0.689150 0.724619i \(-0.742016\pi\)
0.724619 + 0.689150i \(0.242016\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 8.12925 0.715740
\(130\) 1.56484 0.991325i 0.137246 0.0869449i
\(131\) 22.2039i 1.93996i 0.243176 + 0.969982i \(0.421811\pi\)
−0.243176 + 0.969982i \(0.578189\pi\)
\(132\) 3.39327 + 3.39327i 0.295346 + 0.295346i
\(133\) −1.20658 6.13613i −0.104624 0.532070i
\(134\) 1.38459i 0.119611i
\(135\) −0.489528 + 2.18183i −0.0421319 + 0.187782i
\(136\) 5.80748i 0.497988i
\(137\) −5.92849 + 5.92849i −0.506505 + 0.506505i −0.913452 0.406947i \(-0.866594\pi\)
0.406947 + 0.913452i \(0.366594\pi\)
\(138\) −2.97906 + 2.97906i −0.253594 + 0.253594i
\(139\) −8.46478 −0.717973 −0.358986 0.933343i \(-0.616878\pi\)
−0.358986 + 0.933343i \(0.616878\pi\)
\(140\) 4.07076 + 4.29289i 0.344042 + 0.362816i
\(141\) −0.514280 −0.0433102
\(142\) 3.71324 3.71324i 0.311608 0.311608i
\(143\) 2.81108 2.81108i 0.235074 0.235074i
\(144\) 1.00000i 0.0833333i
\(145\) 18.7930 11.9053i 1.56067 0.988683i
\(146\) 8.64818i 0.715728i
\(147\) 2.70711 6.45535i 0.223278 0.532428i
\(148\) 6.10651 + 6.10651i 0.501952 + 0.501952i
\(149\) 4.43516i 0.363342i 0.983359 + 0.181671i \(0.0581506\pi\)
−0.983359 + 0.181671i \(0.941849\pi\)
\(150\) −4.52072 2.13613i −0.369116 0.174414i
\(151\) 7.61497 0.619697 0.309849 0.950786i \(-0.399722\pi\)
0.309849 + 0.950786i \(0.399722\pi\)
\(152\) 1.67135 + 1.67135i 0.135565 + 0.135565i
\(153\) −4.10651 + 4.10651i −0.331992 + 0.331992i
\(154\) 10.5412 + 7.07689i 0.849436 + 0.570272i
\(155\) −5.70636 + 3.61497i −0.458346 + 0.290361i
\(156\) 0.828427 0.0663273
\(157\) −6.30188 6.30188i −0.502945 0.502945i 0.409407 0.912352i \(-0.365736\pi\)
−0.912352 + 0.409407i \(0.865736\pi\)
\(158\) −3.60673 3.60673i −0.286936 0.286936i
\(159\) −3.34271 −0.265094
\(160\) −2.18183 0.489528i −0.172488 0.0387006i
\(161\) −6.21302 + 9.25447i −0.489655 + 0.729354i
\(162\) −0.707107 + 0.707107i −0.0555556 + 0.0555556i
\(163\) 10.8489 + 10.8489i 0.849754 + 0.849754i 0.990102 0.140348i \(-0.0448222\pi\)
−0.140348 + 0.990102i \(0.544822\pi\)
\(164\) −10.9996 −0.858921
\(165\) −10.4702 2.34915i −0.815101 0.182881i
\(166\) 4.55617i 0.353627i
\(167\) 5.63635 + 5.63635i 0.436154 + 0.436154i 0.890715 0.454562i \(-0.150204\pi\)
−0.454562 + 0.890715i \(0.650204\pi\)
\(168\) 0.510472 + 2.59604i 0.0393838 + 0.200289i
\(169\) 12.3137i 0.947208i
\(170\) −6.94944 10.9699i −0.532998 0.841356i
\(171\) 2.36365i 0.180753i
\(172\) −5.74825 + 5.74825i −0.438300 + 0.438300i
\(173\) −12.6923 + 12.6923i −0.964977 + 0.964977i −0.999407 0.0344296i \(-0.989039\pi\)
0.0344296 + 0.999407i \(0.489039\pi\)
\(174\) 9.94900 0.754232
\(175\) −12.8264 3.23777i −0.969586 0.244753i
\(176\) −4.79881 −0.361724
\(177\) 1.47016 1.47016i 0.110504 0.110504i
\(178\) 8.41377 8.41377i 0.630639 0.630639i
\(179\) 5.72836i 0.428158i 0.976816 + 0.214079i \(0.0686750\pi\)
−0.976816 + 0.214079i \(0.931325\pi\)
\(180\) −1.19663 1.88893i −0.0891919 0.140793i
\(181\) 8.91220i 0.662439i −0.943554 0.331219i \(-0.892540\pi\)
0.943554 0.331219i \(-0.107460\pi\)
\(182\) 2.15063 0.422889i 0.159415 0.0313466i
\(183\) 3.92849 + 3.92849i 0.290403 + 0.290403i
\(184\) 4.21302i 0.310588i
\(185\) −18.8420 4.22752i −1.38530 0.310814i
\(186\) −3.02094 −0.221506
\(187\) −19.7064 19.7064i −1.44107 1.44107i
\(188\) 0.363651 0.363651i 0.0265220 0.0265220i
\(189\) −1.47472 + 2.19663i −0.107270 + 0.159782i
\(190\) −5.15707 1.15707i −0.374133 0.0839429i
\(191\) −7.67824 −0.555578 −0.277789 0.960642i \(-0.589602\pi\)
−0.277789 + 0.960642i \(0.589602\pi\)
\(192\) −0.707107 0.707107i −0.0510310 0.0510310i
\(193\) −4.59762 4.59762i −0.330944 0.330944i 0.522001 0.852945i \(-0.325186\pi\)
−0.852945 + 0.522001i \(0.825186\pi\)
\(194\) 11.3928 0.817958
\(195\) −1.56484 + 0.991325i −0.112061 + 0.0709902i
\(196\) 2.65041 + 6.47884i 0.189315 + 0.462774i
\(197\) −5.25132 + 5.25132i −0.374141 + 0.374141i −0.868983 0.494842i \(-0.835226\pi\)
0.494842 + 0.868983i \(0.335226\pi\)
\(198\) −3.39327 3.39327i −0.241149 0.241149i
\(199\) 4.12163 0.292175 0.146087 0.989272i \(-0.453332\pi\)
0.146087 + 0.989272i \(0.453332\pi\)
\(200\) 4.70711 1.68616i 0.332843 0.119230i
\(201\) 1.38459i 0.0976618i
\(202\) −3.45789 3.45789i −0.243297 0.243297i
\(203\) 25.8280 5.07868i 1.81277 0.356454i
\(204\) 5.80748i 0.406605i
\(205\) 20.7774 13.1625i 1.45116 0.919306i
\(206\) 1.50560i 0.104900i
\(207\) 2.97906 2.97906i 0.207059 0.207059i
\(208\) −0.585786 + 0.585786i −0.0406170 + 0.0406170i
\(209\) −11.3427 −0.784591
\(210\) −4.07076 4.29289i −0.280909 0.296238i
\(211\) −27.6560 −1.90392 −0.951958 0.306229i \(-0.900933\pi\)
−0.951958 + 0.306229i \(0.900933\pi\)
\(212\) 2.36365 2.36365i 0.162336 0.162336i
\(213\) −3.71324 + 3.71324i −0.254427 + 0.254427i
\(214\) 3.04145i 0.207909i
\(215\) 3.97949 17.7366i 0.271399 1.20963i
\(216\) 1.00000i 0.0680414i
\(217\) −7.84249 + 1.54211i −0.532383 + 0.104685i
\(218\) 9.12057 + 9.12057i 0.617723 + 0.617723i
\(219\) 8.64818i 0.584390i
\(220\) 9.06462 5.74242i 0.611137 0.387154i
\(221\) −4.81108 −0.323628
\(222\) −6.10651 6.10651i −0.409842 0.409842i
\(223\) 15.3271 15.3271i 1.02638 1.02638i 0.0267394 0.999642i \(-0.491488\pi\)
0.999642 0.0267394i \(-0.00851242\pi\)
\(224\) −2.19663 1.47472i −0.146769 0.0985338i
\(225\) 4.52072 + 2.13613i 0.301382 + 0.142409i
\(226\) −16.3842 −1.08986
\(227\) −18.8984 18.8984i −1.25433 1.25433i −0.953758 0.300575i \(-0.902821\pi\)
−0.300575 0.953758i \(-0.597179\pi\)
\(228\) −1.67135 1.67135i −0.110688 0.110688i
\(229\) −13.3137 −0.879795 −0.439897 0.898048i \(-0.644985\pi\)
−0.439897 + 0.898048i \(0.644985\pi\)
\(230\) 5.04145 + 7.95811i 0.332423 + 0.524742i
\(231\) −10.5412 7.07689i −0.693562 0.465625i
\(232\) −7.03500 + 7.03500i −0.461871 + 0.461871i
\(233\) 7.35498 + 7.35498i 0.481840 + 0.481840i 0.905719 0.423879i \(-0.139332\pi\)
−0.423879 + 0.905719i \(0.639332\pi\)
\(234\) −0.828427 −0.0541560
\(235\) −0.251755 + 1.12207i −0.0164227 + 0.0731957i
\(236\) 2.07912i 0.135339i
\(237\) 3.60673 + 3.60673i 0.234282 + 0.234282i
\(238\) −2.96456 15.0765i −0.192164 0.977261i
\(239\) 13.0491i 0.844074i 0.906579 + 0.422037i \(0.138685\pi\)
−0.906579 + 0.422037i \(0.861315\pi\)
\(240\) 2.18183 + 0.489528i 0.140836 + 0.0315989i
\(241\) 24.4542i 1.57523i 0.616167 + 0.787616i \(0.288685\pi\)
−0.616167 + 0.787616i \(0.711315\pi\)
\(242\) 8.50548 8.50548i 0.546753 0.546753i
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) −5.55573 −0.355669
\(245\) −12.7592 9.06651i −0.815158 0.579238i
\(246\) 10.9996 0.701306
\(247\) −1.38459 + 1.38459i −0.0880996 + 0.0880996i
\(248\) 2.13613 2.13613i 0.135644 0.135644i
\(249\) 4.55617i 0.288735i
\(250\) −6.87368 + 8.81774i −0.434730 + 0.557683i
\(251\) 4.32326i 0.272882i −0.990648 0.136441i \(-0.956434\pi\)
0.990648 0.136441i \(-0.0435664\pi\)
\(252\) −0.510472 2.59604i −0.0321567 0.163535i
\(253\) 14.2959 + 14.2959i 0.898777 + 0.898777i
\(254\) 0.565281i 0.0354689i
\(255\) 6.94944 + 10.9699i 0.435191 + 0.686964i
\(256\) 1.00000 0.0625000
\(257\) 5.06418 + 5.06418i 0.315895 + 0.315895i 0.847188 0.531293i \(-0.178294\pi\)
−0.531293 + 0.847188i \(0.678294\pi\)
\(258\) 5.74825 5.74825i 0.357870 0.357870i
\(259\) −18.9699 12.7355i −1.17873 0.791348i
\(260\) 0.405538 1.80748i 0.0251504 0.112095i
\(261\) −9.94900 −0.615828
\(262\) 15.7005 + 15.7005i 0.969982 + 0.969982i
\(263\) −4.17113 4.17113i −0.257203 0.257203i 0.566712 0.823916i \(-0.308215\pi\)
−0.823916 + 0.566712i \(0.808215\pi\)
\(264\) 4.79881 0.295346
\(265\) −1.63635 + 7.29320i −0.100520 + 0.448018i
\(266\) −5.19208 3.48572i −0.318347 0.213723i
\(267\) −8.41377 + 8.41377i −0.514915 + 0.514915i
\(268\) 0.979056 + 0.979056i 0.0598054 + 0.0598054i
\(269\) 24.7484 1.50894 0.754469 0.656336i \(-0.227894\pi\)
0.754469 + 0.656336i \(0.227894\pi\)
\(270\) 1.19663 + 1.88893i 0.0728249 + 0.114957i
\(271\) 21.9960i 1.33616i 0.744089 + 0.668080i \(0.232884\pi\)
−0.744089 + 0.668080i \(0.767116\pi\)
\(272\) 4.10651 + 4.10651i 0.248994 + 0.248994i
\(273\) −2.15063 + 0.422889i −0.130162 + 0.0255944i
\(274\) 8.38416i 0.506505i
\(275\) −10.2509 + 21.6941i −0.618151 + 1.30820i
\(276\) 4.21302i 0.253594i
\(277\) 12.0646 12.0646i 0.724893 0.724893i −0.244705 0.969598i \(-0.578691\pi\)
0.969598 + 0.244705i \(0.0786910\pi\)
\(278\) −5.98550 + 5.98550i −0.358986 + 0.358986i
\(279\) 3.02094 0.180859
\(280\) 5.91399 + 0.157074i 0.353429 + 0.00938694i
\(281\) 14.3668 0.857052 0.428526 0.903530i \(-0.359033\pi\)
0.428526 + 0.903530i \(0.359033\pi\)
\(282\) −0.363651 + 0.363651i −0.0216551 + 0.0216551i
\(283\) −11.0833 + 11.0833i −0.658836 + 0.658836i −0.955105 0.296269i \(-0.904258\pi\)
0.296269 + 0.955105i \(0.404258\pi\)
\(284\) 5.25132i 0.311608i
\(285\) 5.15707 + 1.15707i 0.305479 + 0.0685391i
\(286\) 3.97546i 0.235074i
\(287\) 28.5553 5.61497i 1.68557 0.331441i
\(288\) 0.707107 + 0.707107i 0.0416667 + 0.0416667i
\(289\) 16.7269i 0.983933i
\(290\) 4.87031 21.7070i 0.285995 1.27468i
\(291\) −11.3928 −0.667860
\(292\) −6.11519 6.11519i −0.357864 0.357864i
\(293\) 6.35827 6.35827i 0.371454 0.371454i −0.496553 0.868007i \(-0.665401\pi\)
0.868007 + 0.496553i \(0.165401\pi\)
\(294\) −2.65041 6.47884i −0.154575 0.377853i
\(295\) −2.48795 3.92732i −0.144854 0.228658i
\(296\) 8.63591 0.501952
\(297\) 3.39327 + 3.39327i 0.196897 + 0.196897i
\(298\) 3.13613 + 3.13613i 0.181671 + 0.181671i
\(299\) 3.49018 0.201842
\(300\) −4.70711 + 1.68616i −0.271765 + 0.0973507i
\(301\) 11.9884 17.8570i 0.690997 1.02926i
\(302\) 5.38459 5.38459i 0.309849 0.309849i
\(303\) 3.45789 + 3.45789i 0.198651 + 0.198651i
\(304\) 2.36365 0.135565
\(305\) 10.4944 6.64818i 0.600907 0.380674i
\(306\) 5.80748i 0.331992i
\(307\) 16.8663 + 16.8663i 0.962610 + 0.962610i 0.999326 0.0367161i \(-0.0116897\pi\)
−0.0367161 + 0.999326i \(0.511690\pi\)
\(308\) 12.4579 2.44966i 0.709854 0.139582i
\(309\) 1.50560i 0.0856509i
\(310\) −1.47884 + 6.59117i −0.0839923 + 0.374353i
\(311\) 0.0592379i 0.00335907i −0.999999 0.00167954i \(-0.999465\pi\)
0.999999 0.00167954i \(-0.000534613\pi\)
\(312\) 0.585786 0.585786i 0.0331636 0.0331636i
\(313\) −0.458332 + 0.458332i −0.0259064 + 0.0259064i −0.719941 0.694035i \(-0.755831\pi\)
0.694035 + 0.719941i \(0.255831\pi\)
\(314\) −8.91220 −0.502945
\(315\) 4.07076 + 4.29289i 0.229361 + 0.241877i
\(316\) −5.10069 −0.286936
\(317\) 13.1130 13.1130i 0.736497 0.736497i −0.235401 0.971898i \(-0.575640\pi\)
0.971898 + 0.235401i \(0.0756404\pi\)
\(318\) −2.36365 + 2.36365i −0.132547 + 0.132547i
\(319\) 47.7433i 2.67311i
\(320\) −1.88893 + 1.19663i −0.105595 + 0.0668939i
\(321\) 3.04145i 0.169757i
\(322\) 2.15063 + 10.9372i 0.119850 + 0.609505i
\(323\) 9.70636 + 9.70636i 0.540076 + 0.540076i
\(324\) 1.00000i 0.0555556i
\(325\) 1.39686 + 3.89949i 0.0774840 + 0.216305i
\(326\) 15.3427 0.849754
\(327\) −9.12057 9.12057i −0.504369 0.504369i
\(328\) −7.77786 + 7.77786i −0.429461 + 0.429461i
\(329\) −0.758418 + 1.12969i −0.0418130 + 0.0622816i
\(330\) −9.06462 + 5.74242i −0.498991 + 0.316110i
\(331\) −25.1288 −1.38120 −0.690602 0.723235i \(-0.742654\pi\)
−0.690602 + 0.723235i \(0.742654\pi\)
\(332\) 3.22170 + 3.22170i 0.176814 + 0.176814i
\(333\) 6.10651 + 6.10651i 0.334635 + 0.334635i
\(334\) 7.97100 0.436154
\(335\) −3.02094 0.677798i −0.165052 0.0370321i
\(336\) 2.19663 + 1.47472i 0.119836 + 0.0804525i
\(337\) 16.5976 16.5976i 0.904130 0.904130i −0.0916605 0.995790i \(-0.529217\pi\)
0.995790 + 0.0916605i \(0.0292175\pi\)
\(338\) 8.70711 + 8.70711i 0.473604 + 0.473604i
\(339\) 16.3842 0.889865
\(340\) −12.6709 2.84293i −0.687177 0.154179i
\(341\) 14.4969i 0.785053i
\(342\) 1.67135 + 1.67135i 0.0903764 + 0.0903764i
\(343\) −10.1878 15.4664i −0.550091 0.835105i
\(344\) 8.12925i 0.438300i
\(345\) −5.04145 7.95811i −0.271422 0.428450i
\(346\) 17.9496i 0.964977i
\(347\) 14.4214 14.4214i 0.774181 0.774181i −0.204654 0.978834i \(-0.565607\pi\)
0.978834 + 0.204654i \(0.0656068\pi\)
\(348\) 7.03500 7.03500i 0.377116 0.377116i
\(349\) 28.6672 1.53452 0.767260 0.641337i \(-0.221620\pi\)
0.767260 + 0.641337i \(0.221620\pi\)
\(350\) −11.3591 + 6.78019i −0.607169 + 0.362416i
\(351\) 0.828427 0.0442182
\(352\) −3.39327 + 3.39327i −0.180862 + 0.180862i
\(353\) −5.06506 + 5.06506i −0.269586 + 0.269586i −0.828933 0.559347i \(-0.811052\pi\)
0.559347 + 0.828933i \(0.311052\pi\)
\(354\) 2.07912i 0.110504i
\(355\) 6.28391 + 9.91938i 0.333515 + 0.526466i
\(356\) 11.8989i 0.630639i
\(357\) 2.96456 + 15.0765i 0.156901 + 0.797931i
\(358\) 4.05056 + 4.05056i 0.214079 + 0.214079i
\(359\) 8.46478i 0.446754i −0.974732 0.223377i \(-0.928292\pi\)
0.974732 0.223377i \(-0.0717081\pi\)
\(360\) −2.18183 0.489528i −0.114992 0.0258004i
\(361\) −13.4132 −0.705956
\(362\) −6.30188 6.30188i −0.331219 0.331219i
\(363\) −8.50548 + 8.50548i −0.446422 + 0.446422i
\(364\) 1.22170 1.81975i 0.0640343 0.0953809i
\(365\) 18.8688 + 4.23353i 0.987639 + 0.221593i
\(366\) 5.55573 0.290403
\(367\) −18.1685 18.1685i −0.948386 0.948386i 0.0503457 0.998732i \(-0.483968\pi\)
−0.998732 + 0.0503457i \(0.983968\pi\)
\(368\) −2.97906 2.97906i −0.155294 0.155294i
\(369\) −10.9996 −0.572614
\(370\) −16.3126 + 10.3340i −0.848054 + 0.537241i
\(371\) −4.92955 + 7.34271i −0.255930 + 0.381214i
\(372\) −2.13613 + 2.13613i −0.110753 + 0.110753i
\(373\) −15.4492 15.4492i −0.799930 0.799930i 0.183154 0.983084i \(-0.441369\pi\)
−0.983084 + 0.183154i \(0.941369\pi\)
\(374\) −27.8690 −1.44107
\(375\) 6.87368 8.81774i 0.354956 0.455346i
\(376\) 0.514280i 0.0265220i
\(377\) −5.82799 5.82799i −0.300157 0.300157i
\(378\) 0.510472 + 2.59604i 0.0262558 + 0.133526i
\(379\) 32.3833i 1.66342i 0.555212 + 0.831709i \(0.312637\pi\)
−0.555212 + 0.831709i \(0.687363\pi\)
\(380\) −4.46478 + 2.82843i −0.229038 + 0.145095i
\(381\) 0.565281i 0.0289602i
\(382\) −5.42933 + 5.42933i −0.277789 + 0.277789i
\(383\) 16.1916 16.1916i 0.827354 0.827354i −0.159796 0.987150i \(-0.551084\pi\)
0.987150 + 0.159796i \(0.0510836\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −20.6008 + 19.5348i −1.04991 + 0.995585i
\(386\) −6.50201 −0.330944
\(387\) −5.74825 + 5.74825i −0.292200 + 0.292200i
\(388\) 8.05595 8.05595i 0.408979 0.408979i
\(389\) 12.0091i 0.608886i 0.952531 + 0.304443i \(0.0984704\pi\)
−0.952531 + 0.304443i \(0.901530\pi\)
\(390\) −0.405538 + 1.80748i −0.0205352 + 0.0915255i
\(391\) 24.4671i 1.23735i
\(392\) 6.45535 + 2.70711i 0.326045 + 0.136730i
\(393\) −15.7005 15.7005i −0.791987 0.791987i
\(394\) 7.42648i 0.374141i
\(395\) 9.63485 6.10366i 0.484782 0.307108i
\(396\) −4.79881 −0.241149
\(397\) 2.62680 + 2.62680i 0.131835 + 0.131835i 0.769945 0.638110i \(-0.220284\pi\)
−0.638110 + 0.769945i \(0.720284\pi\)
\(398\) 2.91443 2.91443i 0.146087 0.146087i
\(399\) 5.19208 + 3.48572i 0.259929 + 0.174504i
\(400\) 2.13613 4.52072i 0.106806 0.226036i
\(401\) 19.7571 0.986623 0.493311 0.869853i \(-0.335786\pi\)
0.493311 + 0.869853i \(0.335786\pi\)
\(402\) −0.979056 0.979056i −0.0488309 0.0488309i
\(403\) 1.76963 + 1.76963i 0.0881514 + 0.0881514i
\(404\) −4.89020 −0.243297
\(405\) −1.19663 1.88893i −0.0594613 0.0938618i
\(406\) 14.6720 21.8543i 0.728158 1.08461i
\(407\) −29.3040 + 29.3040i −1.45254 + 1.45254i
\(408\) −4.10651 4.10651i −0.203303 0.203303i
\(409\) 15.3846 0.760719 0.380360 0.924839i \(-0.375800\pi\)
0.380360 + 0.924839i \(0.375800\pi\)
\(410\) 5.38459 23.9991i 0.265926 1.18523i
\(411\) 8.38416i 0.413560i
\(412\) −1.06462 1.06462i −0.0524502 0.0524502i
\(413\) −1.06133 5.39748i −0.0522248 0.265593i
\(414\) 4.21302i 0.207059i
\(415\) −9.94076 2.23037i −0.487973 0.109485i
\(416\) 0.828427i 0.0406170i
\(417\) 5.98550 5.98550i 0.293111 0.293111i
\(418\) −8.02051 + 8.02051i −0.392296 + 0.392296i
\(419\) −28.0782 −1.37171 −0.685856 0.727737i \(-0.740572\pi\)
−0.685856 + 0.727737i \(0.740572\pi\)
\(420\) −5.91399 0.157074i −0.288573 0.00766441i
\(421\) 11.4836 0.559677 0.279838 0.960047i \(-0.409719\pi\)
0.279838 + 0.960047i \(0.409719\pi\)
\(422\) −19.5557 + 19.5557i −0.951958 + 0.951958i
\(423\) 0.363651 0.363651i 0.0176813 0.0176813i
\(424\) 3.34271i 0.162336i
\(425\) 27.3364 9.79236i 1.32601 0.474999i
\(426\) 5.25132i 0.254427i
\(427\) 14.4229 2.83604i 0.697973 0.137246i
\(428\) −2.15063 2.15063i −0.103955 0.103955i
\(429\) 3.97546i 0.191937i
\(430\) −9.72774 15.3556i −0.469113 0.740513i
\(431\) 11.3330 0.545890 0.272945 0.962030i \(-0.412002\pi\)
0.272945 + 0.962030i \(0.412002\pi\)
\(432\) −0.707107 0.707107i −0.0340207 0.0340207i
\(433\) −4.91337 + 4.91337i −0.236122 + 0.236122i −0.815242 0.579120i \(-0.803396\pi\)
0.579120 + 0.815242i \(0.303396\pi\)
\(434\) −4.45504 + 6.63591i −0.213849 + 0.318534i
\(435\) −4.87031 + 21.7070i −0.233514 + 1.04077i
\(436\) 12.8984 0.617723
\(437\) −7.04145 7.04145i −0.336838 0.336838i
\(438\) 6.11519 + 6.11519i 0.292195 + 0.292195i
\(439\) 22.7723 1.08686 0.543432 0.839453i \(-0.317124\pi\)
0.543432 + 0.839453i \(0.317124\pi\)
\(440\) 2.34915 10.4702i 0.111991 0.499145i
\(441\) 2.65041 + 6.47884i 0.126210 + 0.308516i
\(442\) −3.40194 + 3.40194i −0.161814 + 0.161814i
\(443\) −25.8189 25.8189i −1.22669 1.22669i −0.965208 0.261484i \(-0.915788\pi\)
−0.261484 0.965208i \(-0.584212\pi\)
\(444\) −8.63591 −0.409842
\(445\) 14.2386 + 22.4762i 0.674975 + 1.06547i
\(446\) 21.6759i 1.02638i
\(447\) −3.13613 3.13613i −0.148334 0.148334i
\(448\) −2.59604 + 0.510472i −0.122651 + 0.0241175i
\(449\) 9.55573i 0.450963i −0.974247 0.225481i \(-0.927605\pi\)
0.974247 0.225481i \(-0.0723955\pi\)
\(450\) 4.70711 1.68616i 0.221895 0.0794865i
\(451\) 52.7848i 2.48554i
\(452\) −11.5853 + 11.5853i −0.544929 + 0.544929i
\(453\) −5.38459 + 5.38459i −0.252990 + 0.252990i
\(454\) −26.7264 −1.25433
\(455\) −0.130124 + 4.89931i −0.00610031 + 0.229683i
\(456\) −2.36365 −0.110688
\(457\) −16.6569 + 16.6569i −0.779175 + 0.779175i −0.979690 0.200516i \(-0.935738\pi\)
0.200516 + 0.979690i \(0.435738\pi\)
\(458\) −9.41421 + 9.41421i −0.439897 + 0.439897i
\(459\) 5.80748i 0.271070i
\(460\) 9.19208 + 2.06239i 0.428583 + 0.0961596i
\(461\) 24.4762i 1.13997i 0.821656 + 0.569984i \(0.193051\pi\)
−0.821656 + 0.569984i \(0.806949\pi\)
\(462\) −12.4579 + 2.44966i −0.579594 + 0.113968i
\(463\) 6.83022 + 6.83022i 0.317427 + 0.317427i 0.847778 0.530351i \(-0.177940\pi\)
−0.530351 + 0.847778i \(0.677940\pi\)
\(464\) 9.94900i 0.461871i
\(465\) 1.47884 6.59117i 0.0685794 0.305658i
\(466\) 10.4015 0.481840
\(467\) −20.2503 20.2503i −0.937070 0.937070i 0.0610637 0.998134i \(-0.480551\pi\)
−0.998134 + 0.0610637i \(0.980551\pi\)
\(468\) −0.585786 + 0.585786i −0.0270780 + 0.0270780i
\(469\) −3.04145 2.04189i −0.140441 0.0942856i
\(470\) 0.615405 + 0.971440i 0.0283865 + 0.0448092i
\(471\) 8.91220 0.410653
\(472\) 1.47016 + 1.47016i 0.0676697 + 0.0676697i
\(473\) −27.5847 27.5847i −1.26835 1.26835i
\(474\) 5.10069 0.234282
\(475\) 5.04907 10.6854i 0.231667 0.490280i
\(476\) −12.7569 8.56440i −0.584713 0.392549i
\(477\) 2.36365 2.36365i 0.108224 0.108224i
\(478\) 9.22708 + 9.22708i 0.422037 + 0.422037i
\(479\) 6.82843 0.311999 0.155999 0.987757i \(-0.450140\pi\)
0.155999 + 0.987757i \(0.450140\pi\)
\(480\) 1.88893 1.19663i 0.0862176 0.0546187i
\(481\) 7.15422i 0.326204i
\(482\) 17.2917 + 17.2917i 0.787616 + 0.787616i
\(483\) −2.15063 10.9372i −0.0978570 0.497658i
\(484\) 12.0286i 0.546753i
\(485\) −5.57711 + 24.8572i −0.253244 + 1.12871i
\(486\) 1.00000i 0.0453609i
\(487\) 0.327587 0.327587i 0.0148444 0.0148444i −0.699646 0.714490i \(-0.746659\pi\)
0.714490 + 0.699646i \(0.246659\pi\)
\(488\) −3.92849 + 3.92849i −0.177835 + 0.177835i
\(489\) −15.3427 −0.693821
\(490\) −15.4331 + 2.61116i −0.697198 + 0.117960i
\(491\) 3.38521 0.152773 0.0763863 0.997078i \(-0.475662\pi\)
0.0763863 + 0.997078i \(0.475662\pi\)
\(492\) 7.77786 7.77786i 0.350653 0.350653i
\(493\) −40.8557 + 40.8557i −1.84005 + 1.84005i
\(494\) 1.95811i 0.0880996i
\(495\) 9.06462 5.74242i 0.407425 0.258103i
\(496\) 3.02094i 0.135644i
\(497\) 2.68065 + 13.6326i 0.120244 + 0.611507i
\(498\) −3.22170 3.22170i −0.144368 0.144368i
\(499\) 4.17771i 0.187020i 0.995618 + 0.0935101i \(0.0298087\pi\)
−0.995618 + 0.0935101i \(0.970191\pi\)
\(500\) 1.37465 + 11.0955i 0.0614763 + 0.496206i
\(501\) −7.97100 −0.356118
\(502\) −3.05701 3.05701i −0.136441 0.136441i
\(503\) 8.57667 8.57667i 0.382415 0.382415i −0.489557 0.871972i \(-0.662841\pi\)
0.871972 + 0.489557i \(0.162841\pi\)
\(504\) −2.19663 1.47472i −0.0978459 0.0656892i
\(505\) 9.23726 5.85178i 0.411052 0.260401i
\(506\) 20.2175 0.898777
\(507\) −8.70711 8.70711i −0.386696 0.386696i
\(508\) −0.399714 0.399714i −0.0177345 0.0177345i
\(509\) −3.29829 −0.146194 −0.0730970 0.997325i \(-0.523288\pi\)
−0.0730970 + 0.997325i \(0.523288\pi\)
\(510\) 12.6709 + 2.84293i 0.561078 + 0.125887i
\(511\) 18.9969 + 12.7536i 0.840373 + 0.564187i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −1.67135 1.67135i −0.0737921 0.0737921i
\(514\) 7.16184 0.315895
\(515\) 3.28497 + 0.737036i 0.144753 + 0.0324777i
\(516\) 8.12925i 0.357870i
\(517\) 1.74509 + 1.74509i 0.0767490 + 0.0767490i
\(518\) −22.4192 + 4.40839i −0.985041 + 0.193694i
\(519\) 17.9496i 0.787901i
\(520\) −0.991325 1.56484i −0.0434725 0.0686229i
\(521\) 15.6386i 0.685141i −0.939492 0.342570i \(-0.888702\pi\)
0.939492 0.342570i \(-0.111298\pi\)
\(522\) −7.03500 + 7.03500i −0.307914 + 0.307914i
\(523\) −25.2794 + 25.2794i −1.10539 + 1.10539i −0.111644 + 0.993748i \(0.535612\pi\)
−0.993748 + 0.111644i \(0.964388\pi\)
\(524\) 22.2039 0.969982
\(525\) 11.3591 6.78019i 0.495752 0.295912i
\(526\) −5.89887 −0.257203
\(527\) 12.4055 12.4055i 0.540394 0.540394i
\(528\) 3.39327 3.39327i 0.147673 0.147673i
\(529\) 5.25045i 0.228280i
\(530\) 4.00000 + 6.31415i 0.173749 + 0.274269i
\(531\) 2.07912i 0.0902262i
\(532\) −6.13613 + 1.20658i −0.266035 + 0.0523118i
\(533\) −6.44339 6.44339i −0.279094 0.279094i
\(534\) 11.8989i 0.514915i
\(535\) 6.63591 + 1.48887i 0.286895 + 0.0643697i
\(536\) 1.38459 0.0598054
\(537\) −4.05056 4.05056i −0.174795 0.174795i
\(538\) 17.4998 17.4998i 0.754469 0.754469i
\(539\) −31.0907 + 12.7188i −1.33917 + 0.547838i
\(540\) 2.18183 + 0.489528i 0.0938908 + 0.0210659i
\(541\) −2.70276 −0.116201 −0.0581005 0.998311i \(-0.518504\pi\)
−0.0581005 + 0.998311i \(0.518504\pi\)
\(542\) 15.5535 + 15.5535i 0.668080 + 0.668080i
\(543\) 6.30188 + 6.30188i 0.270439 + 0.270439i
\(544\) 5.80748 0.248994
\(545\) −24.3643 + 15.4347i −1.04365 + 0.661151i
\(546\) −1.22170 + 1.81975i −0.0522838 + 0.0778782i
\(547\) 1.65370 1.65370i 0.0707071 0.0707071i −0.670869 0.741576i \(-0.734079\pi\)
0.741576 + 0.670869i \(0.234079\pi\)
\(548\) 5.92849 + 5.92849i 0.253253 + 0.253253i
\(549\) −5.55573 −0.237113
\(550\) 8.09157 + 22.5885i 0.345026 + 0.963177i
\(551\) 23.5160i 1.00181i
\(552\) 2.97906 + 2.97906i 0.126797 + 0.126797i
\(553\) 13.2416 2.60376i 0.563089 0.110723i
\(554\) 17.0620i 0.724893i
\(555\) 16.3126 10.3340i 0.692433 0.438655i
\(556\) 8.46478i 0.358986i
\(557\) −27.6462 + 27.6462i −1.17141 + 1.17141i −0.189535 + 0.981874i \(0.560698\pi\)
−0.981874 + 0.189535i \(0.939302\pi\)
\(558\) 2.13613 2.13613i 0.0904296 0.0904296i
\(559\) −6.73449 −0.284839
\(560\) 4.29289 4.07076i 0.181408 0.172021i
\(561\) 27.8690 1.17663
\(562\) 10.1589 10.1589i 0.428526 0.428526i
\(563\) −3.25447 + 3.25447i −0.137160 + 0.137160i −0.772353 0.635193i \(-0.780920\pi\)
0.635193 + 0.772353i \(0.280920\pi\)
\(564\) 0.514280i 0.0216551i
\(565\) 8.02051 35.7474i 0.337425 1.50390i
\(566\) 15.6742i 0.658836i
\(567\) −0.510472 2.59604i −0.0214378 0.109023i
\(568\) −3.71324 3.71324i −0.155804 0.155804i
\(569\) 24.2411i 1.01624i −0.861286 0.508121i \(-0.830340\pi\)
0.861286 0.508121i \(-0.169660\pi\)
\(570\) 4.46478 2.82843i 0.187009 0.118470i
\(571\) 17.3801 0.727336 0.363668 0.931529i \(-0.381524\pi\)
0.363668 + 0.931529i \(0.381524\pi\)
\(572\) −2.81108 2.81108i −0.117537 0.117537i
\(573\) 5.42933 5.42933i 0.226814 0.226814i
\(574\) 16.2213 24.1620i 0.677062 1.00850i
\(575\) −19.8311 + 7.10384i −0.827016 + 0.296251i
\(576\) 1.00000 0.0416667
\(577\) 22.7961 + 22.7961i 0.949016 + 0.949016i 0.998762 0.0497462i \(-0.0158413\pi\)
−0.0497462 + 0.998762i \(0.515841\pi\)
\(578\) 11.8277 + 11.8277i 0.491967 + 0.491967i
\(579\) 6.50201 0.270214
\(580\) −11.9053 18.7930i −0.494341 0.780336i
\(581\) −10.0082 6.71907i −0.415212 0.278754i
\(582\) −8.05595 + 8.05595i −0.333930 + 0.333930i
\(583\) 11.3427 + 11.3427i 0.469767 + 0.469767i
\(584\) −8.64818 −0.357864
\(585\) 0.405538 1.80748i 0.0167669 0.0747302i
\(586\) 8.99195i 0.371454i
\(587\) 0.690067 + 0.690067i 0.0284821 + 0.0284821i 0.721204 0.692722i \(-0.243589\pi\)
−0.692722 + 0.721204i \(0.743589\pi\)
\(588\) −6.45535 2.70711i −0.266214 0.111639i
\(589\) 7.14046i 0.294217i
\(590\) −4.53628 1.01779i −0.186756 0.0419017i
\(591\) 7.42648i 0.305485i
\(592\) 6.10651 6.10651i 0.250976 0.250976i
\(593\) −16.0464 + 16.0464i −0.658946 + 0.658946i −0.955131 0.296184i \(-0.904286\pi\)
0.296184 + 0.955131i \(0.404286\pi\)
\(594\) 4.79881 0.196897
\(595\) 34.3454 + 0.912202i 1.40803 + 0.0373966i
\(596\) 4.43516 0.181671
\(597\) −2.91443 + 2.91443i −0.119280 + 0.119280i
\(598\) 2.46793 2.46793i 0.100921 0.100921i
\(599\) 0.262525i 0.0107265i 0.999986 + 0.00536325i \(0.00170718\pi\)
−0.999986 + 0.00536325i \(0.998293\pi\)
\(600\) −2.13613 + 4.52072i −0.0872071 + 0.184558i
\(601\) 6.35838i 0.259364i −0.991556 0.129682i \(-0.958604\pi\)
0.991556 0.129682i \(-0.0413956\pi\)
\(602\) −4.14975 21.1038i −0.169131 0.860128i
\(603\) 0.979056 + 0.979056i 0.0398703 + 0.0398703i
\(604\) 7.61497i 0.309849i
\(605\) 14.3938 + 22.7211i 0.585191 + 0.923745i
\(606\) 4.89020 0.198651
\(607\) 22.5571 + 22.5571i 0.915564 + 0.915564i 0.996703 0.0811391i \(-0.0258558\pi\)
−0.0811391 + 0.996703i \(0.525856\pi\)
\(608\) 1.67135 1.67135i 0.0677823 0.0677823i
\(609\) −14.6720 + 21.8543i −0.594538 + 0.885582i
\(610\) 2.71969 12.1216i 0.110117 0.490790i
\(611\) 0.426043 0.0172359
\(612\) 4.10651 + 4.10651i 0.165996 + 0.165996i
\(613\) −4.17864 4.17864i −0.168774 0.168774i 0.617667 0.786440i \(-0.288078\pi\)
−0.786440 + 0.617667i \(0.788078\pi\)
\(614\) 23.8525 0.962610
\(615\) −5.38459 + 23.9991i −0.217128 + 0.967738i
\(616\) 7.07689 10.5412i 0.285136 0.424718i
\(617\) 10.9152 10.9152i 0.439428 0.439428i −0.452391 0.891819i \(-0.649429\pi\)
0.891819 + 0.452391i \(0.149429\pi\)
\(618\) 1.06462 + 1.06462i 0.0428254 + 0.0428254i
\(619\) −2.48720 −0.0999688 −0.0499844 0.998750i \(-0.515917\pi\)
−0.0499844 + 0.998750i \(0.515917\pi\)
\(620\) 3.61497 + 5.70636i 0.145181 + 0.229173i
\(621\) 4.21302i 0.169063i
\(622\) −0.0418875 0.0418875i −0.00167954 0.00167954i
\(623\) 6.07404 + 30.8899i 0.243351 + 1.23758i
\(624\) 0.828427i 0.0331636i
\(625\) −15.8739 19.3137i −0.634956 0.772548i
\(626\) 0.648179i 0.0259064i
\(627\) 8.02051 8.02051i 0.320308 0.320308i
\(628\) −6.30188 + 6.30188i −0.251472 + 0.251472i
\(629\) 50.1529 1.99973
\(630\) 5.91399 + 0.157074i 0.235619 + 0.00625796i
\(631\) −34.6801 −1.38059 −0.690296 0.723527i \(-0.742520\pi\)
−0.690296 + 0.723527i \(0.742520\pi\)
\(632\) −3.60673 + 3.60673i −0.143468 + 0.143468i
\(633\) 19.5557 19.5557i 0.777270 0.777270i
\(634\) 18.5445i 0.736497i
\(635\) 1.23335 + 0.276721i 0.0489438 + 0.0109813i
\(636\) 3.34271i 0.132547i
\(637\) −2.24264 + 5.34779i −0.0888567 + 0.211887i
\(638\) −33.7596 33.7596i −1.33656 1.33656i
\(639\) 5.25132i 0.207739i
\(640\) −0.489528 + 2.18183i −0.0193503 + 0.0862442i
\(641\) −17.9572 −0.709268 −0.354634 0.935005i \(-0.615395\pi\)
−0.354634 + 0.935005i \(0.615395\pi\)
\(642\) 2.15063 + 2.15063i 0.0848786 + 0.0848786i
\(643\) −3.76560 + 3.76560i −0.148501 + 0.148501i −0.777448 0.628947i \(-0.783486\pi\)
0.628947 + 0.777448i \(0.283486\pi\)
\(644\) 9.25447 + 6.21302i 0.364677 + 0.244827i
\(645\) 9.72774 + 15.3556i 0.383029 + 0.604626i
\(646\) 13.7269 0.540076
\(647\) 24.7759 + 24.7759i 0.974042 + 0.974042i 0.999672 0.0256293i \(-0.00815894\pi\)
−0.0256293 + 0.999672i \(0.508159\pi\)
\(648\) 0.707107 + 0.707107i 0.0277778 + 0.0277778i
\(649\) −9.97731 −0.391644
\(650\) 3.74509 + 1.76963i 0.146895 + 0.0694105i
\(651\) 4.45504 6.63591i 0.174607 0.260082i
\(652\) 10.8489 10.8489i 0.424877 0.424877i
\(653\) −15.9566 15.9566i −0.624431 0.624431i 0.322231 0.946661i \(-0.395567\pi\)
−0.946661 + 0.322231i \(0.895567\pi\)
\(654\) −12.8984 −0.504369
\(655\) −41.9417 + 26.5700i −1.63880 + 1.03817i
\(656\) 10.9996i 0.429461i
\(657\) −6.11519 6.11519i −0.238576 0.238576i
\(658\) 0.262525 + 1.33509i 0.0102343 + 0.0520473i
\(659\) 15.8705i 0.618227i −0.951025 0.309113i \(-0.899968\pi\)
0.951025 0.309113i \(-0.100032\pi\)
\(660\) −2.34915 + 10.4702i −0.0914406 + 0.407550i
\(661\) 15.8409i 0.616139i −0.951364 0.308069i \(-0.900317\pi\)
0.951364 0.308069i \(-0.0996829\pi\)
\(662\) −17.7688 + 17.7688i −0.690602 + 0.690602i
\(663\) 3.40194 3.40194i 0.132121 0.132121i
\(664\) 4.55617 0.176814
\(665\) 10.1469 9.62185i 0.393480 0.373119i
\(666\) 8.63591 0.334635
\(667\) 29.6386 29.6386i 1.14761 1.14761i
\(668\) 5.63635 5.63635i 0.218077 0.218077i
\(669\) 21.6759i 0.838037i
\(670\) −2.61541 + 1.65685i −0.101042 + 0.0640099i
\(671\) 26.6609i 1.02923i
\(672\) 2.59604 0.510472i 0.100144 0.0196919i
\(673\) 4.25535 + 4.25535i 0.164032 + 0.164032i 0.784350 0.620318i \(-0.212997\pi\)
−0.620318 + 0.784350i \(0.712997\pi\)
\(674\) 23.4726i 0.904130i
\(675\) −4.70711 + 1.68616i −0.181177 + 0.0649004i
\(676\) 12.3137 0.473604
\(677\) −34.7614 34.7614i −1.33599 1.33599i −0.899906 0.436085i \(-0.856365\pi\)
−0.436085 0.899906i \(-0.643635\pi\)
\(678\) 11.5853 11.5853i 0.444933 0.444933i
\(679\) −16.8012 + 25.0259i −0.644772 + 0.960406i
\(680\) −10.9699 + 6.94944i −0.420678 + 0.266499i
\(681\) 26.7264 1.02416
\(682\) 10.2509 + 10.2509i 0.392526 + 0.392526i
\(683\) 8.10025 + 8.10025i 0.309947 + 0.309947i 0.844889 0.534942i \(-0.179666\pi\)
−0.534942 + 0.844889i \(0.679666\pi\)
\(684\) 2.36365 0.0903764
\(685\) −18.2928 4.10428i −0.698931 0.156816i
\(686\) −18.1402 3.73248i −0.692598 0.142507i
\(687\) 9.41421 9.41421i 0.359175 0.359175i
\(688\) 5.74825 + 5.74825i 0.219150 + 0.219150i
\(689\) 2.76919 0.105498
\(690\) −9.19208 2.06239i −0.349936 0.0785139i
\(691\) 39.2567i 1.49340i 0.665163 + 0.746699i \(0.268362\pi\)
−0.665163 + 0.746699i \(0.731638\pi\)
\(692\) 12.6923 + 12.6923i 0.482489 + 0.482489i
\(693\) 12.4579 2.44966i 0.473236 0.0930548i
\(694\) 20.3949i 0.774181i
\(695\) −10.1292 15.9894i −0.384224 0.606512i
\(696\) 9.94900i 0.377116i
\(697\) −45.1698 + 45.1698i −1.71093 + 1.71093i
\(698\) 20.2708 20.2708i 0.767260 0.767260i
\(699\) −10.4015 −0.393421
\(700\) −3.23777 + 12.8264i −0.122376 + 0.484793i
\(701\) 27.9663 1.05627 0.528137 0.849159i \(-0.322891\pi\)
0.528137 + 0.849159i \(0.322891\pi\)
\(702\) 0.585786 0.585786i 0.0221091 0.0221091i
\(703\) 14.4337 14.4337i 0.544376 0.544376i
\(704\) 4.79881i 0.180862i
\(705\) −0.615405 0.971440i −0.0231775 0.0365865i
\(706\) 7.16308i 0.269586i
\(707\) 12.6951 2.49631i 0.477450 0.0938834i
\(708\) −1.47016 1.47016i −0.0552521 0.0552521i
\(709\) 23.3998i 0.878799i −0.898292 0.439399i \(-0.855191\pi\)
0.898292 0.439399i \(-0.144809\pi\)
\(710\) 11.4575 + 2.57067i 0.429991 + 0.0964754i
\(711\) −5.10069 −0.191291
\(712\) −8.41377 8.41377i −0.315320 0.315320i
\(713\) −8.99956 + 8.99956i −0.337036 + 0.337036i
\(714\) 12.7569 + 8.56440i 0.477416 + 0.320515i
\(715\) 8.67377 + 1.94610i 0.324380 + 0.0727800i
\(716\) 5.72836 0.214079
\(717\) −9.22708 9.22708i −0.344592 0.344592i
\(718\) −5.98550 5.98550i −0.223377 0.223377i
\(719\) −50.8254 −1.89547 −0.947734 0.319060i \(-0.896633\pi\)
−0.947734 + 0.319060i \(0.896633\pi\)
\(720\) −1.88893 + 1.19663i −0.0703963 + 0.0445959i
\(721\) 3.30726 + 2.22034i 0.123169 + 0.0826899i
\(722\) −9.48453 + 9.48453i −0.352978 + 0.352978i
\(723\) −17.2917 17.2917i −0.643085 0.643085i
\(724\) −8.91220 −0.331219
\(725\) 44.9767 + 21.2524i 1.67039 + 0.789293i
\(726\) 12.0286i 0.446422i
\(727\) −5.10248 5.10248i −0.189240 0.189240i 0.606127 0.795368i \(-0.292722\pi\)
−0.795368 + 0.606127i \(0.792722\pi\)
\(728\) −0.422889 2.15063i −0.0156733 0.0797076i
\(729\) 1.00000i 0.0370370i
\(730\) 16.3358 10.3487i 0.604616 0.383023i
\(731\) 47.2105i 1.74614i
\(732\) 3.92849 3.92849i 0.145201 0.145201i
\(733\) −1.79925 + 1.79925i −0.0664567 + 0.0664567i −0.739554 0.673097i \(-0.764964\pi\)
0.673097 + 0.739554i \(0.264964\pi\)
\(734\) −25.6941 −0.948386
\(735\) 15.4331 2.61116i 0.569260 0.0963140i
\(736\) −4.21302 −0.155294
\(737\) −4.69830 + 4.69830i −0.173064 + 0.173064i
\(738\) −7.77786 + 7.77786i −0.286307 + 0.286307i
\(739\) 10.9122i 0.401412i −0.979652 0.200706i \(-0.935676\pi\)
0.979652 0.200706i \(-0.0643236\pi\)
\(740\) −4.22752 + 18.8420i −0.155407 + 0.692648i
\(741\) 1.95811i 0.0719331i
\(742\) 1.70636 + 8.67780i 0.0626424 + 0.318572i
\(743\) −12.3076 12.3076i −0.451521 0.451521i 0.444338 0.895859i \(-0.353439\pi\)
−0.895859 + 0.444338i \(0.853439\pi\)
\(744\) 3.02094i 0.110753i
\(745\) −8.37771 + 5.30726i −0.306936 + 0.194443i
\(746\) −21.8485 −0.799930
\(747\) 3.22170 + 3.22170i 0.117876 + 0.117876i
\(748\) −19.7064 + 19.7064i −0.720536 + 0.720536i
\(749\) 6.68095 + 4.48528i 0.244117 + 0.163889i
\(750\) −1.37465 11.0955i −0.0501952 0.405151i
\(751\) −12.4787 −0.455354 −0.227677 0.973737i \(-0.573113\pi\)
−0.227677 + 0.973737i \(0.573113\pi\)
\(752\) −0.363651 0.363651i −0.0132610 0.0132610i
\(753\) 3.05701 + 3.05701i 0.111404 + 0.111404i
\(754\) −8.24202 −0.300157
\(755\) 9.11233 + 14.3842i 0.331632 + 0.523493i
\(756\) 2.19663 + 1.47472i 0.0798908 + 0.0536350i
\(757\) 30.1930 30.1930i 1.09738 1.09738i 0.102667 0.994716i \(-0.467262\pi\)
0.994716 0.102667i \(-0.0327377\pi\)
\(758\) 22.8984 + 22.8984i 0.831709 + 0.831709i
\(759\) −20.2175 −0.733848
\(760\) −1.15707 + 5.15707i −0.0419715 + 0.187067i
\(761\) 33.4920i 1.21409i −0.794669 0.607043i \(-0.792356\pi\)
0.794669 0.607043i \(-0.207644\pi\)
\(762\) 0.399714 + 0.399714i 0.0144801 + 0.0144801i
\(763\) −33.4848 + 6.58429i −1.21223 + 0.238367i
\(764\) 7.67824i 0.277789i
\(765\) −12.6709 2.84293i −0.458118 0.102786i
\(766\) 22.8984i 0.827354i
\(767\) −1.21792 + 1.21792i −0.0439766 + 0.0439766i
\(768\) −0.707107 + 0.707107i −0.0255155 + 0.0255155i
\(769\) 31.8992 1.15032 0.575158 0.818042i \(-0.304941\pi\)
0.575158 + 0.818042i \(0.304941\pi\)
\(770\) −0.753766 + 28.3801i −0.0271638 + 1.02275i
\(771\) −7.16184 −0.257927
\(772\) −4.59762 + 4.59762i −0.165472 + 0.165472i
\(773\) 11.0809 11.0809i 0.398553 0.398553i −0.479170 0.877722i \(-0.659062\pi\)
0.877722 + 0.479170i \(0.159062\pi\)
\(774\) 8.12925i 0.292200i
\(775\) −13.6569 6.45313i −0.490569 0.231803i
\(776\) 11.3928i 0.408979i
\(777\) 22.4192 4.40839i 0.804283 0.158150i
\(778\) 8.49173 + 8.49173i 0.304443 + 0.304443i
\(779\) 25.9991i 0.931515i
\(780\) 0.991325 + 1.56484i 0.0354951 + 0.0560304i
\(781\) 25.2001 0.901729
\(782\) −17.3008 17.3008i −0.618676 0.618676i
\(783\) 7.03500 7.03500i 0.251411 0.251411i
\(784\) 6.47884 2.65041i 0.231387 0.0946575i
\(785\) 4.36277 19.4449i 0.155714 0.694017i
\(786\) −22.2039 −0.791987
\(787\) −27.9894 27.9894i −0.997714 0.997714i 0.00228344 0.999997i \(-0.499273\pi\)
−0.999997 + 0.00228344i \(0.999273\pi\)
\(788\) 5.25132 + 5.25132i 0.187070 + 0.187070i
\(789\) 5.89887 0.210005
\(790\) 2.49693 11.1288i 0.0888368 0.395945i
\(791\) 24.1620 35.9900i 0.859103 1.27966i
\(792\) −3.39327 + 3.39327i −0.120575 + 0.120575i
\(793\) −3.25447 3.25447i −0.115570 0.115570i
\(794\) 3.71485 0.131835
\(795\) −4.00000 6.31415i −0.141865 0.223940i
\(796\) 4.12163i 0.146087i
\(797\) −6.43293 6.43293i −0.227866 0.227866i 0.583935 0.811801i \(-0.301512\pi\)
−0.811801 + 0.583935i \(0.801512\pi\)
\(798\) 6.13613 1.20658i 0.217217 0.0427124i
\(799\) 2.98667i 0.105661i
\(800\) −1.68616 4.70711i −0.0596149 0.166421i
\(801\) 11.8989i 0.420426i
\(802\) 13.9704 13.9704i 0.493311 0.493311i
\(803\) 29.3456 29.3456i 1.03558 1.03558i
\(804\) −1.38459 −0.0488309
\(805\) −24.9158 0.661754i −0.878166 0.0233238i
\(806\) 2.50263 0.0881514
\(807\) −17.4998 + 17.4998i −0.616021 + 0.616021i
\(808\) −3.45789 + 3.45789i −0.121648 + 0.121648i
\(809\) 36.3842i 1.27920i 0.768708 + 0.639599i \(0.220900\pi\)
−0.768708 + 0.639599i \(0.779100\pi\)
\(810\) −2.18183 0.489528i −0.0766615 0.0172003i
\(811\) 26.5629i 0.932750i 0.884587 + 0.466375i \(0.154440\pi\)
−0.884587 + 0.466375i \(0.845560\pi\)
\(812\) −5.07868 25.8280i −0.178227 0.906385i
\(813\) −15.5535 15.5535i −0.545485 0.545485i
\(814\) 41.4421i 1.45254i
\(815\) −7.51069 + 33.4751i −0.263088 + 1.17258i
\(816\) −5.80748 −0.203303
\(817\) 13.5868 + 13.5868i 0.475344 + 0.475344i
\(818\) 10.8786 10.8786i 0.380360 0.380360i
\(819\) 1.22170 1.81975i 0.0426895 0.0635873i
\(820\) −13.1625 20.7774i −0.459653 0.725579i
\(821\) −45.9655 −1.60421 −0.802103 0.597186i \(-0.796286\pi\)
−0.802103 + 0.597186i \(0.796286\pi\)
\(822\) −5.92849 5.92849i −0.206780 0.206780i
\(823\) 36.5397 + 36.5397i 1.27369 + 1.27369i 0.944134 + 0.329561i \(0.106901\pi\)
0.329561 + 0.944134i \(0.393099\pi\)
\(824\) −1.50560 −0.0524502
\(825\) −8.09157 22.5885i −0.281712 0.786431i
\(826\) −4.56707 3.06612i −0.158909 0.106684i
\(827\) 15.7275 15.7275i 0.546898 0.546898i −0.378644 0.925542i \(-0.623610\pi\)
0.925542 + 0.378644i \(0.123610\pi\)
\(828\) −2.97906 2.97906i −0.103529 0.103529i
\(829\) −29.2892 −1.01725 −0.508627 0.860987i \(-0.669847\pi\)
−0.508627 + 0.860987i \(0.669847\pi\)
\(830\) −8.60629 + 5.45207i −0.298729 + 0.189244i
\(831\) 17.0620i 0.591873i
\(832\) 0.585786 + 0.585786i 0.0203085 + 0.0203085i
\(833\) 37.4894 + 15.7215i 1.29893 + 0.544717i
\(834\) 8.46478i 0.293111i
\(835\) −3.90203 + 17.3913i −0.135035 + 0.601852i
\(836\) 11.3427i 0.392296i
\(837\) −2.13613 + 2.13613i −0.0738354 + 0.0738354i
\(838\) −19.8543 + 19.8543i −0.685856 + 0.685856i
\(839\) 2.41886 0.0835082 0.0417541 0.999128i \(-0.486705\pi\)
0.0417541 + 0.999128i \(0.486705\pi\)
\(840\) −4.29289 + 4.07076i −0.148119 + 0.140454i
\(841\) −69.9826 −2.41319
\(842\) 8.12013 8.12013i 0.279838 0.279838i
\(843\) −10.1589 + 10.1589i −0.349890 + 0.349890i
\(844\) 27.6560i 0.951958i
\(845\) −23.2598 + 14.7350i −0.800160 + 0.506900i
\(846\) 0.514280i 0.0176813i
\(847\) 6.14024 + 31.2266i 0.210981 + 1.07296i
\(848\) −2.36365 2.36365i −0.0811681 0.0811681i
\(849\) 15.6742i 0.537937i
\(850\) 12.4055 26.2540i 0.425506 0.900506i
\(851\) −36.3833 −1.24720
\(852\) 3.71324 + 3.71324i 0.127214 + 0.127214i
\(853\) 28.0222 28.0222i 0.959461 0.959461i −0.0397491 0.999210i \(-0.512656\pi\)
0.999210 + 0.0397491i \(0.0126559\pi\)
\(854\) 8.19314 12.2039i 0.280363 0.417609i
\(855\) −4.46478 + 2.82843i −0.152692 + 0.0967302i
\(856\) −3.04145 −0.103955
\(857\) −19.1782 19.1782i −0.655115 0.655115i 0.299105 0.954220i \(-0.403312\pi\)
−0.954220 + 0.299105i \(0.903312\pi\)
\(858\) 2.81108 + 2.81108i 0.0959686 + 0.0959686i
\(859\) 45.5754 1.55501 0.777506 0.628876i \(-0.216485\pi\)
0.777506 + 0.628876i \(0.216485\pi\)
\(860\) −17.7366 3.97949i −0.604813 0.135700i
\(861\) −16.2213 + 24.1620i −0.552819 + 0.823439i
\(862\) 8.01362 8.01362i 0.272945 0.272945i
\(863\) 4.69515 + 4.69515i 0.159825 + 0.159825i 0.782489 0.622664i \(-0.213950\pi\)
−0.622664 + 0.782489i \(0.713950\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −39.1629 8.78684i −1.33158 0.298762i
\(866\) 6.94856i 0.236122i
\(867\) −11.8277 11.8277i −0.401689 0.401689i
\(868\) 1.54211 + 7.84249i 0.0523425 + 0.266191i
\(869\) 24.4772i 0.830333i
\(870\) 11.9053 + 18.7930i 0.403628 + 0.637142i
\(871\) 1.14704i 0.0388658i
\(872\) 9.12057 9.12057i 0.308862 0.308862i
\(873\) 8.05595 8.05595i 0.272653 0.272653i
\(874\) −9.95811 −0.336838
\(875\) −9.23260 28.1027i −0.312119 0.950043i
\(876\) 8.64818 0.292195
\(877\) 17.5321 17.5321i 0.592017 0.592017i −0.346159 0.938176i \(-0.612514\pi\)
0.938176 + 0.346159i \(0.112514\pi\)
\(878\) 16.1025 16.1025i 0.543432 0.543432i
\(879\) 8.99195i 0.303291i
\(880\) −5.74242 9.06462i −0.193577 0.305568i
\(881\) 3.93358i 0.132526i 0.997802 + 0.0662628i \(0.0211076\pi\)
−0.997802 + 0.0662628i \(0.978892\pi\)
\(882\) 6.45535 + 2.70711i 0.217363 + 0.0911530i
\(883\) 34.7362 + 34.7362i 1.16896 + 1.16896i 0.982453 + 0.186512i \(0.0597184\pi\)
0.186512 + 0.982453i \(0.440282\pi\)
\(884\) 4.81108i 0.161814i
\(885\) 4.53628 + 1.01779i 0.152485 + 0.0342126i
\(886\) −36.5134 −1.22669
\(887\) 33.3213 + 33.3213i 1.11882 + 1.11882i 0.991915 + 0.126906i \(0.0405046\pi\)
0.126906 + 0.991915i \(0.459495\pi\)
\(888\) −6.10651 + 6.10651i −0.204921 + 0.204921i
\(889\) 1.24172 + 0.833631i 0.0416458 + 0.0279591i
\(890\) 25.9613 + 5.82483i 0.870224 + 0.195249i
\(891\) −4.79881 −0.160766
\(892\) −15.3271 15.3271i −0.513191 0.513191i
\(893\) −0.859544 0.859544i −0.0287635 0.0287635i
\(894\) −4.43516 −0.148334
\(895\) −10.8205 + 6.85476i −0.361689 + 0.229129i
\(896\) −1.47472 + 2.19663i −0.0492669 + 0.0733844i
\(897\) −2.46793 + 2.46793i −0.0824018 + 0.0824018i
\(898\) −6.75692 6.75692i −0.225481 0.225481i
\(899\) 30.0554 1.00240
\(900\) 2.13613 4.52072i 0.0712043 0.150691i
\(901\) 19.4127i 0.646731i
\(902\) −37.3245 37.3245i −1.24277 1.24277i
\(903\) 4.14975 + 21.1038i 0.138095 + 0.702292i
\(904\) 16.3842i 0.544929i
\(905\) 16.8345 10.6647i 0.559599 0.354505i
\(906\) 7.61497i 0.252990i
\(907\) −0.932707 + 0.932707i −0.0309700 + 0.0309700i −0.722422 0.691452i \(-0.756971\pi\)
0.691452 + 0.722422i \(0.256971\pi\)
\(908\) −18.8984 + 18.8984i −0.627167 + 0.627167i
\(909\) −4.89020 −0.162198
\(910\) 3.37233 + 3.55635i 0.111792 + 0.117892i
\(911\) 45.5690 1.50977 0.754885 0.655857i \(-0.227693\pi\)
0.754885 + 0.655857i \(0.227693\pi\)
\(912\) −1.67135 + 1.67135i −0.0553440 + 0.0553440i
\(913\) −15.4603 + 15.4603i −0.511661 + 0.511661i
\(914\) 23.5563i 0.779175i
\(915\) −2.71969 + 12.1216i −0.0899100 + 0.400729i
\(916\) 13.3137i 0.439897i
\(917\) −57.6422 + 11.3345i −1.90351 + 0.374297i
\(918\) −4.10651 4.10651i −0.135535 0.135535i
\(919\) 20.8574i 0.688023i −0.938965 0.344011i \(-0.888214\pi\)
0.938965 0.344011i \(-0.111786\pi\)
\(920\) 7.95811 5.04145i 0.262371 0.166212i
\(921\) −23.8525 −0.785967
\(922\) 17.3073 + 17.3073i 0.569984 + 0.569984i
\(923\) 3.07615 3.07615i 0.101253 0.101253i
\(924\) −7.07689 + 10.5412i −0.232813 + 0.346781i
\(925\) −14.5616 40.6502i −0.478781 1.33657i
\(926\) 9.65939 0.317427
\(927\) −1.06462 1.06462i −0.0349668 0.0349668i
\(928\) 7.03500 + 7.03500i 0.230935 + 0.230935i
\(929\) −9.10069 −0.298584 −0.149292 0.988793i \(-0.547699\pi\)
−0.149292 + 0.988793i \(0.547699\pi\)
\(930\) −3.61497 5.70636i −0.118539 0.187119i
\(931\) 15.3137 6.26464i 0.501887 0.205315i
\(932\) 7.35498 7.35498i 0.240920 0.240920i
\(933\) 0.0418875 + 0.0418875i 0.00137134 + 0.00137134i
\(934\) −28.6382 −0.937070
\(935\) 13.6427 60.8053i 0.446163 1.98855i
\(936\) 0.828427i 0.0270780i
\(937\) −3.34154 3.34154i −0.109163 0.109163i 0.650415 0.759579i \(-0.274595\pi\)
−0.759579 + 0.650415i \(0.774595\pi\)
\(938\) −3.59446 + 0.706797i −0.117363 + 0.0230777i
\(939\) 0.648179i 0.0211525i
\(940\) 1.12207 + 0.251755i 0.0365979 + 0.00821133i
\(941\) 42.2862i 1.37849i −0.724528 0.689245i \(-0.757942\pi\)
0.724528 0.689245i \(-0.242058\pi\)
\(942\) 6.30188 6.30188i 0.205326 0.205326i
\(943\) 32.7683 32.7683i 1.06708 1.06708i
\(944\) 2.07912 0.0676697
\(945\) −5.91399 0.157074i −0.192382 0.00510960i
\(946\) −39.0107 −1.26835
\(947\) −0.00253441 + 0.00253441i −8.23572e−5 + 8.23572e-5i −0.707148 0.707066i \(-0.750019\pi\)
0.707066 + 0.707148i \(0.250019\pi\)
\(948\) 3.60673 3.60673i 0.117141 0.117141i
\(949\) 7.16439i 0.232566i
\(950\) −3.98550 11.1260i −0.129307 0.360974i
\(951\) 18.5445i 0.601347i
\(952\) −15.0765 + 2.96456i −0.488631 + 0.0960818i
\(953\) 14.4673 + 14.4673i 0.468642 + 0.468642i 0.901474 0.432832i \(-0.142486\pi\)
−0.432832 + 0.901474i \(0.642486\pi\)
\(954\) 3.34271i 0.108224i
\(955\) −9.18805 14.5037i −0.297318 0.469328i
\(956\) 13.0491 0.422037
\(957\) 33.7596 + 33.7596i 1.09129 + 1.09129i
\(958\) 4.82843 4.82843i 0.155999 0.155999i
\(959\) −18.4169 12.3643i −0.594714 0.399263i
\(960\) 0.489528 2.18183i 0.0157995 0.0704181i
\(961\) 21.8739 0.705610
\(962\) 5.05880 + 5.05880i 0.163102 + 0.163102i
\(963\) −2.15063 2.15063i −0.0693031 0.0693031i
\(964\) 24.4542 0.787616
\(965\) 3.18292 14.1863i 0.102462 0.456672i
\(966\) −9.25447 6.21302i −0.297758 0.199901i
\(967\) −4.38595 + 4.38595i −0.141043 + 0.141043i −0.774103 0.633060i \(-0.781799\pi\)
0.633060 + 0.774103i \(0.281799\pi\)
\(968\) −8.50548 8.50548i −0.273376 0.273376i
\(969\) −13.7269 −0.440970
\(970\) 13.6331 + 21.5203i 0.437731 + 0.690975i
\(971\) 24.3630i 0.781847i −0.920423 0.390923i \(-0.872156\pi\)
0.920423 0.390923i \(-0.127844\pi\)
\(972\) −0.707107 0.707107i −0.0226805 0.0226805i
\(973\) −4.32103 21.9749i −0.138526 0.704483i
\(974\) 0.463279i 0.0148444i
\(975\) −3.74509 1.76963i −0.119939 0.0566734i
\(976\) 5.55573i 0.177835i
\(977\) 38.9763 38.9763i 1.24696 1.24696i 0.289905 0.957055i \(-0.406376\pi\)
0.957055 0.289905i \(-0.0936239\pi\)
\(978\) −10.8489 + 10.8489i −0.346911 + 0.346911i
\(979\) 57.1004 1.82494
\(980\) −9.06651 + 12.7592i −0.289619 + 0.407579i
\(981\) 12.8984 0.411815
\(982\) 2.39371 2.39371i 0.0763863 0.0763863i
\(983\) −14.5896 + 14.5896i −0.465335 + 0.465335i −0.900399 0.435065i \(-0.856726\pi\)
0.435065 + 0.900399i \(0.356726\pi\)
\(984\) 10.9996i 0.350653i
\(985\) −16.2033 3.63547i −0.516280 0.115836i
\(986\) 57.7786i 1.84005i
\(987\) −0.262525 1.33509i −0.00835628 0.0424964i
\(988\) 1.38459 + 1.38459i 0.0440498 + 0.0440498i
\(989\) 34.2487i 1.08905i
\(990\) 2.34915 10.4702i 0.0746609 0.332764i
\(991\) 47.6560 1.51384 0.756921 0.653506i \(-0.226703\pi\)
0.756921 + 0.653506i \(0.226703\pi\)
\(992\) −2.13613 2.13613i −0.0678222 0.0678222i
\(993\) 17.7688 17.7688i 0.563874 0.563874i
\(994\) 11.5352 + 7.74421i 0.365875 + 0.245632i
\(995\) 4.93209 + 7.78548i 0.156358 + 0.246816i
\(996\) −4.55617 −0.144368
\(997\) 0.631258 + 0.631258i 0.0199921 + 0.0199921i 0.717032 0.697040i \(-0.245500\pi\)
−0.697040 + 0.717032i \(0.745500\pi\)
\(998\) 2.95409 + 2.95409i 0.0935101 + 0.0935101i
\(999\) −8.63591 −0.273228
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 210.2.m.b.13.4 yes 8
3.2 odd 2 630.2.p.c.433.1 8
4.3 odd 2 1680.2.cz.a.433.4 8
5.2 odd 4 210.2.m.a.97.3 yes 8
5.3 odd 4 1050.2.m.b.307.2 8
5.4 even 2 1050.2.m.a.643.2 8
7.6 odd 2 210.2.m.a.13.3 8
15.2 even 4 630.2.p.b.307.2 8
20.7 even 4 1680.2.cz.b.97.1 8
21.20 even 2 630.2.p.b.433.2 8
28.27 even 2 1680.2.cz.b.433.1 8
35.13 even 4 1050.2.m.a.307.2 8
35.27 even 4 inner 210.2.m.b.97.4 yes 8
35.34 odd 2 1050.2.m.b.643.2 8
105.62 odd 4 630.2.p.c.307.1 8
140.27 odd 4 1680.2.cz.a.97.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.m.a.13.3 8 7.6 odd 2
210.2.m.a.97.3 yes 8 5.2 odd 4
210.2.m.b.13.4 yes 8 1.1 even 1 trivial
210.2.m.b.97.4 yes 8 35.27 even 4 inner
630.2.p.b.307.2 8 15.2 even 4
630.2.p.b.433.2 8 21.20 even 2
630.2.p.c.307.1 8 105.62 odd 4
630.2.p.c.433.1 8 3.2 odd 2
1050.2.m.a.307.2 8 35.13 even 4
1050.2.m.a.643.2 8 5.4 even 2
1050.2.m.b.307.2 8 5.3 odd 4
1050.2.m.b.643.2 8 35.34 odd 2
1680.2.cz.a.97.4 8 140.27 odd 4
1680.2.cz.a.433.4 8 4.3 odd 2
1680.2.cz.b.97.1 8 20.7 even 4
1680.2.cz.b.433.1 8 28.27 even 2