Properties

Label 950.2.q.g.293.2
Level $950$
Weight $2$
Character 950.293
Analytic conductor $7.586$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(107,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([3, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.107");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.q (of order \(12\), degree \(4\), 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: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 293.2
Character \(\chi\) \(=\) 950.293
Dual form 950.2.q.g.107.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.965926 + 0.258819i) q^{2} +(0.186170 + 0.694795i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.359652 - 0.622936i) q^{6} +(-1.01416 + 1.01416i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.15000 - 1.24130i) q^{9} +O(q^{10})\) \(q+(-0.965926 + 0.258819i) q^{2} +(0.186170 + 0.694795i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.359652 - 0.622936i) q^{6} +(-1.01416 + 1.01416i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.15000 - 1.24130i) q^{9} +2.38827 q^{11} +(0.508625 + 0.508625i) q^{12} +(2.90425 + 0.778192i) q^{13} +(0.717117 - 1.24208i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.22959 - 4.58888i) q^{17} +(-1.75546 + 1.75546i) q^{18} +(-3.35250 + 2.78581i) q^{19} +(-0.893436 - 0.515825i) q^{21} +(-2.30689 + 0.618129i) q^{22} +(1.35931 - 5.07300i) q^{23} +(-0.622936 - 0.359652i) q^{24} -3.00670 q^{26} +(2.78859 + 2.78859i) q^{27} +(-0.371207 + 1.38536i) q^{28} +(4.88449 + 8.46019i) q^{29} -10.0965i q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.444623 + 1.65935i) q^{33} +(2.37538 + 4.11428i) q^{34} +(1.24130 - 2.15000i) q^{36} +(2.87570 + 2.87570i) q^{37} +(2.51725 - 3.55857i) q^{38} +2.16273i q^{39} +(6.97985 + 4.02982i) q^{41} +(0.996498 + 0.267011i) q^{42} +(-1.76075 + 0.471793i) q^{43} +(2.06830 - 1.19413i) q^{44} +5.25195i q^{46} +(0.349235 + 0.0935773i) q^{47} +(0.694795 + 0.186170i) q^{48} +4.94297i q^{49} +(2.95942 - 1.70862i) q^{51} +(2.90425 - 0.778192i) q^{52} +(7.08396 + 1.89814i) q^{53} +(-3.41531 - 1.97183i) q^{54} -1.43423i q^{56} +(-2.55970 - 1.81067i) q^{57} +(-6.90772 - 6.90772i) q^{58} +(1.29825 - 2.24864i) q^{59} +(-0.310205 - 0.537291i) q^{61} +(2.61317 + 9.75248i) q^{62} +(-0.921559 + 3.43931i) q^{63} -1.00000i q^{64} +(-0.858945 - 1.48774i) q^{66} +(0.368486 - 1.37521i) q^{67} +(-3.35930 - 3.35930i) q^{68} +3.77775 q^{69} +(-5.38910 - 3.11140i) q^{71} +(-0.642545 + 2.39801i) q^{72} +(-3.21735 + 0.862086i) q^{73} +(-3.52199 - 2.03342i) q^{74} +(-1.51045 + 4.08883i) q^{76} +(-2.42208 + 2.42208i) q^{77} +(-0.559756 - 2.08904i) q^{78} +(-0.0163335 + 0.0282904i) q^{79} +(2.30556 - 3.99334i) q^{81} +(-7.78501 - 2.08599i) q^{82} +(12.0016 + 12.0016i) q^{83} -1.03165 q^{84} +(1.57865 - 0.911434i) q^{86} +(-4.96875 + 4.96875i) q^{87} +(-1.68876 + 1.68876i) q^{88} +(1.11103 + 1.92436i) q^{89} +(-3.73457 + 2.15616i) q^{91} +(-1.35931 - 5.07300i) q^{92} +(7.01500 - 1.87966i) q^{93} -0.361555 q^{94} -0.719304 q^{96} +(9.85916 - 2.64175i) q^{97} +(-1.27934 - 4.77454i) q^{98} +(5.13476 - 2.96456i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 12 q^{3} - 24 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 12 q^{3} - 24 q^{7} - 16 q^{11} - 24 q^{13} + 16 q^{16} + 8 q^{17} + 12 q^{22} - 4 q^{23} - 16 q^{26} + 12 q^{28} + 24 q^{33} - 8 q^{36} - 16 q^{38} + 24 q^{41} - 20 q^{42} + 24 q^{43} + 36 q^{47} + 12 q^{48} + 24 q^{51} - 24 q^{52} + 72 q^{53} + 24 q^{57} - 24 q^{58} - 48 q^{61} + 4 q^{62} - 16 q^{63} + 32 q^{66} - 36 q^{67} - 16 q^{68} + 24 q^{71} - 8 q^{73} + 24 q^{77} + 24 q^{78} + 56 q^{81} - 8 q^{82} - 24 q^{83} - 104 q^{87} - 24 q^{91} + 4 q^{92} - 52 q^{93} + 24 q^{97} - 72 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.965926 + 0.258819i −0.683013 + 0.183013i
\(3\) 0.186170 + 0.694795i 0.107485 + 0.401140i 0.998615 0.0526080i \(-0.0167534\pi\)
−0.891130 + 0.453748i \(0.850087\pi\)
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) 0 0
\(6\) −0.359652 0.622936i −0.146827 0.254312i
\(7\) −1.01416 + 1.01416i −0.383315 + 0.383315i −0.872295 0.488980i \(-0.837369\pi\)
0.488980 + 0.872295i \(0.337369\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 2.15000 1.24130i 0.716665 0.413767i
\(10\) 0 0
\(11\) 2.38827 0.720089 0.360045 0.932935i \(-0.382761\pi\)
0.360045 + 0.932935i \(0.382761\pi\)
\(12\) 0.508625 + 0.508625i 0.146827 + 0.146827i
\(13\) 2.90425 + 0.778192i 0.805494 + 0.215831i 0.637995 0.770041i \(-0.279764\pi\)
0.167499 + 0.985872i \(0.446431\pi\)
\(14\) 0.717117 1.24208i 0.191658 0.331961i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −1.22959 4.58888i −0.298219 1.11297i −0.938627 0.344933i \(-0.887902\pi\)
0.640408 0.768035i \(-0.278765\pi\)
\(18\) −1.75546 + 1.75546i −0.413767 + 0.413767i
\(19\) −3.35250 + 2.78581i −0.769117 + 0.639108i
\(20\) 0 0
\(21\) −0.893436 0.515825i −0.194964 0.112562i
\(22\) −2.30689 + 0.618129i −0.491830 + 0.131785i
\(23\) 1.35931 5.07300i 0.283435 1.05779i −0.666541 0.745469i \(-0.732226\pi\)
0.949975 0.312325i \(-0.101108\pi\)
\(24\) −0.622936 0.359652i −0.127156 0.0734137i
\(25\) 0 0
\(26\) −3.00670 −0.589663
\(27\) 2.78859 + 2.78859i 0.536664 + 0.536664i
\(28\) −0.371207 + 1.38536i −0.0701516 + 0.261809i
\(29\) 4.88449 + 8.46019i 0.907027 + 1.57102i 0.818172 + 0.574973i \(0.194988\pi\)
0.0888552 + 0.996045i \(0.471679\pi\)
\(30\) 0 0
\(31\) 10.0965i 1.81339i −0.421791 0.906693i \(-0.638598\pi\)
0.421791 0.906693i \(-0.361402\pi\)
\(32\) −0.258819 + 0.965926i −0.0457532 + 0.170753i
\(33\) 0.444623 + 1.65935i 0.0773988 + 0.288856i
\(34\) 2.37538 + 4.11428i 0.407374 + 0.705593i
\(35\) 0 0
\(36\) 1.24130 2.15000i 0.206883 0.358333i
\(37\) 2.87570 + 2.87570i 0.472762 + 0.472762i 0.902807 0.430046i \(-0.141503\pi\)
−0.430046 + 0.902807i \(0.641503\pi\)
\(38\) 2.51725 3.55857i 0.408352 0.577277i
\(39\) 2.16273i 0.346314i
\(40\) 0 0
\(41\) 6.97985 + 4.02982i 1.09007 + 0.629352i 0.933595 0.358330i \(-0.116654\pi\)
0.156475 + 0.987682i \(0.449987\pi\)
\(42\) 0.996498 + 0.267011i 0.153763 + 0.0412007i
\(43\) −1.76075 + 0.471793i −0.268513 + 0.0719477i −0.390563 0.920576i \(-0.627720\pi\)
0.122051 + 0.992524i \(0.461053\pi\)
\(44\) 2.06830 1.19413i 0.311808 0.180022i
\(45\) 0 0
\(46\) 5.25195i 0.774358i
\(47\) 0.349235 + 0.0935773i 0.0509412 + 0.0136496i 0.284200 0.958765i \(-0.408272\pi\)
−0.233258 + 0.972415i \(0.574939\pi\)
\(48\) 0.694795 + 0.186170i 0.100285 + 0.0268713i
\(49\) 4.94297i 0.706139i
\(50\) 0 0
\(51\) 2.95942 1.70862i 0.414402 0.239255i
\(52\) 2.90425 0.778192i 0.402747 0.107916i
\(53\) 7.08396 + 1.89814i 0.973056 + 0.260730i 0.710118 0.704083i \(-0.248642\pi\)
0.262939 + 0.964813i \(0.415308\pi\)
\(54\) −3.41531 1.97183i −0.464765 0.268332i
\(55\) 0 0
\(56\) 1.43423i 0.191658i
\(57\) −2.55970 1.81067i −0.339040 0.239829i
\(58\) −6.90772 6.90772i −0.907027 0.907027i
\(59\) 1.29825 2.24864i 0.169018 0.292748i −0.769057 0.639180i \(-0.779274\pi\)
0.938075 + 0.346433i \(0.112607\pi\)
\(60\) 0 0
\(61\) −0.310205 0.537291i −0.0397177 0.0687931i 0.845483 0.534002i \(-0.179313\pi\)
−0.885201 + 0.465209i \(0.845979\pi\)
\(62\) 2.61317 + 9.75248i 0.331873 + 1.23857i
\(63\) −0.921559 + 3.43931i −0.116106 + 0.433312i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) −0.858945 1.48774i −0.105729 0.183128i
\(67\) 0.368486 1.37521i 0.0450177 0.168008i −0.939757 0.341843i \(-0.888949\pi\)
0.984775 + 0.173834i \(0.0556157\pi\)
\(68\) −3.35930 3.35930i −0.407374 0.407374i
\(69\) 3.77775 0.454788
\(70\) 0 0
\(71\) −5.38910 3.11140i −0.639568 0.369255i 0.144880 0.989449i \(-0.453720\pi\)
−0.784448 + 0.620194i \(0.787054\pi\)
\(72\) −0.642545 + 2.39801i −0.0757246 + 0.282608i
\(73\) −3.21735 + 0.862086i −0.376562 + 0.100900i −0.442136 0.896948i \(-0.645779\pi\)
0.0655734 + 0.997848i \(0.479112\pi\)
\(74\) −3.52199 2.03342i −0.409424 0.236381i
\(75\) 0 0
\(76\) −1.51045 + 4.08883i −0.173261 + 0.469021i
\(77\) −2.42208 + 2.42208i −0.276021 + 0.276021i
\(78\) −0.559756 2.08904i −0.0633799 0.236537i
\(79\) −0.0163335 + 0.0282904i −0.00183766 + 0.00318292i −0.866943 0.498408i \(-0.833918\pi\)
0.865105 + 0.501591i \(0.167252\pi\)
\(80\) 0 0
\(81\) 2.30556 3.99334i 0.256173 0.443705i
\(82\) −7.78501 2.08599i −0.859711 0.230359i
\(83\) 12.0016 + 12.0016i 1.31735 + 1.31735i 0.915865 + 0.401485i \(0.131506\pi\)
0.401485 + 0.915865i \(0.368494\pi\)
\(84\) −1.03165 −0.112562
\(85\) 0 0
\(86\) 1.57865 0.911434i 0.170230 0.0982824i
\(87\) −4.96875 + 4.96875i −0.532706 + 0.532706i
\(88\) −1.68876 + 1.68876i −0.180022 + 0.180022i
\(89\) 1.11103 + 1.92436i 0.117769 + 0.203981i 0.918883 0.394530i \(-0.129093\pi\)
−0.801114 + 0.598511i \(0.795759\pi\)
\(90\) 0 0
\(91\) −3.73457 + 2.15616i −0.391490 + 0.226027i
\(92\) −1.35931 5.07300i −0.141717 0.528897i
\(93\) 7.01500 1.87966i 0.727421 0.194912i
\(94\) −0.361555 −0.0372915
\(95\) 0 0
\(96\) −0.719304 −0.0734137
\(97\) 9.85916 2.64175i 1.00105 0.268229i 0.279162 0.960244i \(-0.409943\pi\)
0.721883 + 0.692015i \(0.243277\pi\)
\(98\) −1.27934 4.77454i −0.129232 0.482302i
\(99\) 5.13476 2.96456i 0.516063 0.297949i
\(100\) 0 0
\(101\) 8.56678 + 14.8381i 0.852427 + 1.47645i 0.879012 + 0.476800i \(0.158203\pi\)
−0.0265848 + 0.999647i \(0.508463\pi\)
\(102\) −2.41636 + 2.41636i −0.239255 + 0.239255i
\(103\) −1.78051 + 1.78051i −0.175438 + 0.175438i −0.789364 0.613926i \(-0.789590\pi\)
0.613926 + 0.789364i \(0.289590\pi\)
\(104\) −2.60388 + 1.50335i −0.255331 + 0.147416i
\(105\) 0 0
\(106\) −7.33385 −0.712327
\(107\) 4.96199 + 4.96199i 0.479694 + 0.479694i 0.905034 0.425340i \(-0.139845\pi\)
−0.425340 + 0.905034i \(0.639845\pi\)
\(108\) 3.80928 + 1.02069i 0.366548 + 0.0982163i
\(109\) 4.61026 7.98521i 0.441583 0.764844i −0.556224 0.831032i \(-0.687750\pi\)
0.997807 + 0.0661882i \(0.0210838\pi\)
\(110\) 0 0
\(111\) −1.46265 + 2.53339i −0.138829 + 0.240458i
\(112\) 0.371207 + 1.38536i 0.0350758 + 0.130905i
\(113\) 0.471659 0.471659i 0.0443699 0.0443699i −0.684574 0.728944i \(-0.740012\pi\)
0.728944 + 0.684574i \(0.240012\pi\)
\(114\) 2.94111 + 1.08647i 0.275461 + 0.101758i
\(115\) 0 0
\(116\) 8.46019 + 4.88449i 0.785509 + 0.453514i
\(117\) 7.21010 1.93194i 0.666574 0.178608i
\(118\) −0.672024 + 2.50803i −0.0618648 + 0.230883i
\(119\) 5.90084 + 3.40685i 0.540929 + 0.312306i
\(120\) 0 0
\(121\) −5.29619 −0.481472
\(122\) 0.438696 + 0.438696i 0.0397177 + 0.0397177i
\(123\) −1.50046 + 5.59979i −0.135292 + 0.504916i
\(124\) −5.04825 8.74383i −0.453347 0.785219i
\(125\) 0 0
\(126\) 3.56063i 0.317206i
\(127\) −2.58532 + 9.64853i −0.229410 + 0.856169i 0.751180 + 0.660097i \(0.229485\pi\)
−0.980590 + 0.196071i \(0.937182\pi\)
\(128\) 0.258819 + 0.965926i 0.0228766 + 0.0853766i
\(129\) −0.655598 1.13553i −0.0577222 0.0999778i
\(130\) 0 0
\(131\) −3.29085 + 5.69992i −0.287523 + 0.498004i −0.973218 0.229885i \(-0.926165\pi\)
0.685695 + 0.727889i \(0.259498\pi\)
\(132\) 1.21473 + 1.21473i 0.105729 + 0.105729i
\(133\) 0.574720 6.22521i 0.0498345 0.539794i
\(134\) 1.42372i 0.122991i
\(135\) 0 0
\(136\) 4.11428 + 2.37538i 0.352797 + 0.203687i
\(137\) −8.71025 2.33391i −0.744167 0.199399i −0.133238 0.991084i \(-0.542537\pi\)
−0.610929 + 0.791685i \(0.709204\pi\)
\(138\) −3.64903 + 0.977755i −0.310626 + 0.0832320i
\(139\) −4.69540 + 2.71089i −0.398259 + 0.229935i −0.685732 0.727854i \(-0.740518\pi\)
0.287474 + 0.957789i \(0.407185\pi\)
\(140\) 0 0
\(141\) 0.260068i 0.0219017i
\(142\) 6.01076 + 1.61058i 0.504412 + 0.135157i
\(143\) 6.93612 + 1.85853i 0.580028 + 0.155418i
\(144\) 2.48260i 0.206883i
\(145\) 0 0
\(146\) 2.88460 1.66542i 0.238731 0.137831i
\(147\) −3.43435 + 0.920231i −0.283260 + 0.0758994i
\(148\) 3.92827 + 1.05258i 0.322902 + 0.0865214i
\(149\) −5.72771 3.30689i −0.469232 0.270911i 0.246686 0.969095i \(-0.420658\pi\)
−0.715918 + 0.698184i \(0.753992\pi\)
\(150\) 0 0
\(151\) 17.2548i 1.40418i −0.712091 0.702088i \(-0.752251\pi\)
0.712091 0.702088i \(-0.247749\pi\)
\(152\) 0.400715 4.34044i 0.0325023 0.352056i
\(153\) −8.33979 8.33979i −0.674232 0.674232i
\(154\) 1.71267 2.96642i 0.138011 0.239041i
\(155\) 0 0
\(156\) 1.08137 + 1.87298i 0.0865786 + 0.149959i
\(157\) −0.838326 3.12868i −0.0669057 0.249696i 0.924371 0.381496i \(-0.124591\pi\)
−0.991276 + 0.131800i \(0.957924\pi\)
\(158\) 0.00845484 0.0315539i 0.000672631 0.00251029i
\(159\) 5.27527i 0.418356i
\(160\) 0 0
\(161\) 3.76627 + 6.52336i 0.296823 + 0.514113i
\(162\) −1.19344 + 4.45399i −0.0937658 + 0.349939i
\(163\) −13.0605 13.0605i −1.02297 1.02297i −0.999730 0.0232448i \(-0.992600\pi\)
−0.0232448 0.999730i \(-0.507400\pi\)
\(164\) 8.05964 0.629352
\(165\) 0 0
\(166\) −14.6989 8.48644i −1.14086 0.658675i
\(167\) 5.62051 20.9760i 0.434928 1.62317i −0.306309 0.951932i \(-0.599094\pi\)
0.741238 0.671243i \(-0.234239\pi\)
\(168\) 0.996498 0.267011i 0.0768815 0.0206003i
\(169\) −3.42924 1.97987i −0.263788 0.152298i
\(170\) 0 0
\(171\) −3.74985 + 10.1509i −0.286758 + 0.776262i
\(172\) −1.28896 + 1.28896i −0.0982824 + 0.0982824i
\(173\) 1.72920 + 6.45347i 0.131469 + 0.490649i 0.999987 0.00500806i \(-0.00159412\pi\)
−0.868519 + 0.495657i \(0.834927\pi\)
\(174\) 3.51344 6.08545i 0.266353 0.461337i
\(175\) 0 0
\(176\) 1.19413 2.06830i 0.0900111 0.155904i
\(177\) 1.80404 + 0.483390i 0.135600 + 0.0363338i
\(178\) −1.57123 1.57123i −0.117769 0.117769i
\(179\) −11.9857 −0.895851 −0.447925 0.894071i \(-0.647837\pi\)
−0.447925 + 0.894071i \(0.647837\pi\)
\(180\) 0 0
\(181\) −20.6699 + 11.9338i −1.53638 + 0.887031i −0.537337 + 0.843368i \(0.680570\pi\)
−0.999046 + 0.0436636i \(0.986097\pi\)
\(182\) 3.04927 3.04927i 0.226027 0.226027i
\(183\) 0.315556 0.315556i 0.0233266 0.0233266i
\(184\) 2.62598 + 4.54833i 0.193590 + 0.335307i
\(185\) 0 0
\(186\) −6.28948 + 3.63123i −0.461167 + 0.266255i
\(187\) −2.93658 10.9595i −0.214744 0.801436i
\(188\) 0.349235 0.0935773i 0.0254706 0.00682482i
\(189\) −5.65613 −0.411423
\(190\) 0 0
\(191\) 16.5623 1.19840 0.599201 0.800598i \(-0.295485\pi\)
0.599201 + 0.800598i \(0.295485\pi\)
\(192\) 0.694795 0.186170i 0.0501425 0.0134356i
\(193\) −2.74324 10.2379i −0.197463 0.736941i −0.991616 0.129223i \(-0.958752\pi\)
0.794153 0.607718i \(-0.207915\pi\)
\(194\) −8.83948 + 5.10347i −0.634637 + 0.366408i
\(195\) 0 0
\(196\) 2.47149 + 4.28074i 0.176535 + 0.305767i
\(197\) 17.3356 17.3356i 1.23511 1.23511i 0.273139 0.961975i \(-0.411938\pi\)
0.961975 0.273139i \(-0.0880618\pi\)
\(198\) −4.19251 + 4.19251i −0.297949 + 0.297949i
\(199\) −9.91254 + 5.72301i −0.702682 + 0.405693i −0.808345 0.588709i \(-0.799637\pi\)
0.105664 + 0.994402i \(0.466303\pi\)
\(200\) 0 0
\(201\) 1.02409 0.0722336
\(202\) −12.1153 12.1153i −0.852427 0.852427i
\(203\) −13.5336 3.62632i −0.949872 0.254518i
\(204\) 1.70862 2.95942i 0.119627 0.207201i
\(205\) 0 0
\(206\) 1.25901 2.18067i 0.0877192 0.151934i
\(207\) −3.37461 12.5942i −0.234552 0.875360i
\(208\) 2.12606 2.12606i 0.147416 0.147416i
\(209\) −8.00667 + 6.65325i −0.553833 + 0.460215i
\(210\) 0 0
\(211\) −6.74675 3.89524i −0.464465 0.268159i 0.249455 0.968387i \(-0.419749\pi\)
−0.713920 + 0.700227i \(0.753082\pi\)
\(212\) 7.08396 1.89814i 0.486528 0.130365i
\(213\) 1.15850 4.32356i 0.0793788 0.296246i
\(214\) −6.07718 3.50866i −0.415427 0.239847i
\(215\) 0 0
\(216\) −3.94366 −0.268332
\(217\) 10.2394 + 10.2394i 0.695099 + 0.695099i
\(218\) −2.38645 + 8.90634i −0.161631 + 0.603213i
\(219\) −1.19795 2.07490i −0.0809497 0.140209i
\(220\) 0 0
\(221\) 14.2841i 0.960854i
\(222\) 0.757124 2.82562i 0.0508148 0.189643i
\(223\) 3.10249 + 11.5787i 0.207758 + 0.775365i 0.988591 + 0.150625i \(0.0481285\pi\)
−0.780833 + 0.624740i \(0.785205\pi\)
\(224\) −0.717117 1.24208i −0.0479144 0.0829902i
\(225\) 0 0
\(226\) −0.333513 + 0.577661i −0.0221850 + 0.0384255i
\(227\) −15.2621 15.2621i −1.01298 1.01298i −0.999915 0.0130664i \(-0.995841\pi\)
−0.0130664 0.999915i \(-0.504159\pi\)
\(228\) −3.12210 0.288236i −0.206766 0.0190889i
\(229\) 14.2432i 0.941219i −0.882342 0.470609i \(-0.844034\pi\)
0.882342 0.470609i \(-0.155966\pi\)
\(230\) 0 0
\(231\) −2.13376 1.23193i −0.140391 0.0810549i
\(232\) −9.43611 2.52840i −0.619511 0.165998i
\(233\) −15.7624 + 4.22353i −1.03263 + 0.276693i −0.735056 0.678006i \(-0.762844\pi\)
−0.297575 + 0.954699i \(0.596178\pi\)
\(234\) −6.46440 + 3.73222i −0.422591 + 0.243983i
\(235\) 0 0
\(236\) 2.59650i 0.169018i
\(237\) −0.0226968 0.00608160i −0.00147432 0.000395042i
\(238\) −6.58153 1.76352i −0.426617 0.114312i
\(239\) 11.7603i 0.760711i −0.924840 0.380355i \(-0.875802\pi\)
0.924840 0.380355i \(-0.124198\pi\)
\(240\) 0 0
\(241\) 11.5318 6.65790i 0.742829 0.428873i −0.0802677 0.996773i \(-0.525578\pi\)
0.823097 + 0.567901i \(0.192244\pi\)
\(242\) 5.11572 1.37075i 0.328851 0.0881154i
\(243\) 14.6316 + 3.92053i 0.938619 + 0.251502i
\(244\) −0.537291 0.310205i −0.0343965 0.0198589i
\(245\) 0 0
\(246\) 5.79733i 0.369624i
\(247\) −11.9044 + 5.48179i −0.757459 + 0.348798i
\(248\) 7.13931 + 7.13931i 0.453347 + 0.453347i
\(249\) −6.10433 + 10.5730i −0.386846 + 0.670037i
\(250\) 0 0
\(251\) −12.9058 22.3535i −0.814606 1.41094i −0.909610 0.415463i \(-0.863620\pi\)
0.0950040 0.995477i \(-0.469714\pi\)
\(252\) 0.921559 + 3.43931i 0.0580528 + 0.216656i
\(253\) 3.24638 12.1157i 0.204098 0.761706i
\(254\) 9.98889i 0.626759i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −1.83587 + 6.85158i −0.114519 + 0.427390i −0.999250 0.0387109i \(-0.987675\pi\)
0.884732 + 0.466101i \(0.154342\pi\)
\(258\) 0.927156 + 0.927156i 0.0577222 + 0.0577222i
\(259\) −5.83281 −0.362433
\(260\) 0 0
\(261\) 21.0033 + 12.1262i 1.30007 + 0.750596i
\(262\) 1.70347 6.35743i 0.105241 0.392764i
\(263\) 20.1313 5.39416i 1.24135 0.332618i 0.422359 0.906429i \(-0.361202\pi\)
0.818988 + 0.573811i \(0.194535\pi\)
\(264\) −1.48774 0.858945i −0.0915638 0.0528644i
\(265\) 0 0
\(266\) 1.05607 + 6.16184i 0.0647516 + 0.377807i
\(267\) −1.13019 + 1.13019i −0.0691667 + 0.0691667i
\(268\) −0.368486 1.37521i −0.0225088 0.0840042i
\(269\) 10.3374 17.9049i 0.630282 1.09168i −0.357212 0.934023i \(-0.616272\pi\)
0.987494 0.157657i \(-0.0503942\pi\)
\(270\) 0 0
\(271\) −12.5983 + 21.8210i −0.765295 + 1.32553i 0.174796 + 0.984605i \(0.444073\pi\)
−0.940091 + 0.340925i \(0.889260\pi\)
\(272\) −4.58888 1.22959i −0.278242 0.0745547i
\(273\) −2.19335 2.19335i −0.132748 0.132748i
\(274\) 9.01752 0.544768
\(275\) 0 0
\(276\) 3.27163 1.88888i 0.196929 0.113697i
\(277\) −16.2232 + 16.2232i −0.974760 + 0.974760i −0.999689 0.0249288i \(-0.992064\pi\)
0.0249288 + 0.999689i \(0.492064\pi\)
\(278\) 3.83378 3.83378i 0.229935 0.229935i
\(279\) −12.5328 21.7074i −0.750319 1.29959i
\(280\) 0 0
\(281\) −4.62150 + 2.66822i −0.275695 + 0.159173i −0.631473 0.775398i \(-0.717549\pi\)
0.355778 + 0.934571i \(0.384216\pi\)
\(282\) −0.0673105 0.251206i −0.00400828 0.0149591i
\(283\) −31.6725 + 8.48662i −1.88274 + 0.504477i −0.883377 + 0.468664i \(0.844736\pi\)
−0.999358 + 0.0358135i \(0.988598\pi\)
\(284\) −6.22280 −0.369255
\(285\) 0 0
\(286\) −7.18080 −0.424610
\(287\) −11.1655 + 2.99179i −0.659080 + 0.176600i
\(288\) 0.642545 + 2.39801i 0.0378623 + 0.141304i
\(289\) −4.82354 + 2.78487i −0.283737 + 0.163816i
\(290\) 0 0
\(291\) 3.67095 + 6.35827i 0.215195 + 0.372729i
\(292\) −2.35526 + 2.35526i −0.137831 + 0.137831i
\(293\) −13.1650 + 13.1650i −0.769106 + 0.769106i −0.977949 0.208844i \(-0.933030\pi\)
0.208844 + 0.977949i \(0.433030\pi\)
\(294\) 3.07915 1.77775i 0.179580 0.103681i
\(295\) 0 0
\(296\) −4.06685 −0.236381
\(297\) 6.65989 + 6.65989i 0.386446 + 0.386446i
\(298\) 6.38843 + 1.71177i 0.370072 + 0.0991604i
\(299\) 7.89553 13.6755i 0.456610 0.790872i
\(300\) 0 0
\(301\) 1.30721 2.26415i 0.0753463 0.130504i
\(302\) 4.46587 + 16.6669i 0.256982 + 0.959070i
\(303\) −8.71456 + 8.71456i −0.500638 + 0.500638i
\(304\) 0.736327 + 4.29626i 0.0422313 + 0.246407i
\(305\) 0 0
\(306\) 10.2141 + 5.89712i 0.583902 + 0.337116i
\(307\) −18.1679 + 4.86806i −1.03689 + 0.277835i −0.736826 0.676083i \(-0.763676\pi\)
−0.300069 + 0.953918i \(0.597010\pi\)
\(308\) −0.886541 + 3.30862i −0.0505154 + 0.188526i
\(309\) −1.56856 0.905610i −0.0892324 0.0515183i
\(310\) 0 0
\(311\) −4.47649 −0.253838 −0.126919 0.991913i \(-0.540509\pi\)
−0.126919 + 0.991913i \(0.540509\pi\)
\(312\) −1.52928 1.52928i −0.0865786 0.0865786i
\(313\) −3.22806 + 12.0473i −0.182461 + 0.680953i 0.812699 + 0.582684i \(0.197997\pi\)
−0.995160 + 0.0982696i \(0.968669\pi\)
\(314\) 1.61952 + 2.80509i 0.0913949 + 0.158301i
\(315\) 0 0
\(316\) 0.0326670i 0.00183766i
\(317\) 1.46541 5.46899i 0.0823058 0.307169i −0.912485 0.409111i \(-0.865839\pi\)
0.994790 + 0.101942i \(0.0325055\pi\)
\(318\) −1.36534 5.09552i −0.0765645 0.285743i
\(319\) 11.6655 + 20.2052i 0.653141 + 1.13127i
\(320\) 0 0
\(321\) −2.52379 + 4.37134i −0.140864 + 0.243984i
\(322\) −5.32631 5.32631i −0.296823 0.296823i
\(323\) 16.9059 + 11.9589i 0.940672 + 0.665409i
\(324\) 4.61111i 0.256173i
\(325\) 0 0
\(326\) 15.9957 + 9.23514i 0.885922 + 0.511487i
\(327\) 6.40637 + 1.71658i 0.354273 + 0.0949272i
\(328\) −7.78501 + 2.08599i −0.429855 + 0.115179i
\(329\) −0.449081 + 0.259277i −0.0247586 + 0.0142944i
\(330\) 0 0
\(331\) 13.4811i 0.740988i 0.928835 + 0.370494i \(0.120812\pi\)
−0.928835 + 0.370494i \(0.879188\pi\)
\(332\) 16.3945 + 4.39290i 0.899767 + 0.241092i
\(333\) 9.75234 + 2.61313i 0.534425 + 0.143199i
\(334\) 21.7160i 1.18825i
\(335\) 0 0
\(336\) −0.893436 + 0.515825i −0.0487409 + 0.0281406i
\(337\) 30.9819 8.30158i 1.68769 0.452216i 0.717900 0.696147i \(-0.245104\pi\)
0.969793 + 0.243931i \(0.0784370\pi\)
\(338\) 3.82482 + 1.02486i 0.208043 + 0.0557449i
\(339\) 0.415514 + 0.239897i 0.0225676 + 0.0130294i
\(340\) 0 0
\(341\) 24.1131i 1.30580i
\(342\) 0.994816 10.7756i 0.0537935 0.582677i
\(343\) −12.1120 12.1120i −0.653989 0.653989i
\(344\) 0.911434 1.57865i 0.0491412 0.0851151i
\(345\) 0 0
\(346\) −3.34056 5.78603i −0.179590 0.311059i
\(347\) −0.973759 3.63412i −0.0522741 0.195090i 0.934851 0.355041i \(-0.115533\pi\)
−0.987125 + 0.159951i \(0.948866\pi\)
\(348\) −1.81869 + 6.78744i −0.0974919 + 0.363845i
\(349\) 31.2369i 1.67207i −0.548673 0.836037i \(-0.684867\pi\)
0.548673 0.836037i \(-0.315133\pi\)
\(350\) 0 0
\(351\) 5.92870 + 10.2688i 0.316451 + 0.548109i
\(352\) −0.618129 + 2.30689i −0.0329464 + 0.122958i
\(353\) −17.2688 17.2688i −0.919124 0.919124i 0.0778415 0.996966i \(-0.475197\pi\)
−0.996966 + 0.0778415i \(0.975197\pi\)
\(354\) −1.86767 −0.0992658
\(355\) 0 0
\(356\) 1.92436 + 1.11103i 0.101991 + 0.0588843i
\(357\) −1.26851 + 4.73413i −0.0671364 + 0.250556i
\(358\) 11.5773 3.10212i 0.611878 0.163952i
\(359\) 11.6435 + 6.72238i 0.614521 + 0.354794i 0.774733 0.632289i \(-0.217884\pi\)
−0.160212 + 0.987083i \(0.551218\pi\)
\(360\) 0 0
\(361\) 3.47856 18.6789i 0.183082 0.983098i
\(362\) 16.8769 16.8769i 0.887031 0.887031i
\(363\) −0.985989 3.67976i −0.0517510 0.193137i
\(364\) −2.15616 + 3.73457i −0.113013 + 0.195745i
\(365\) 0 0
\(366\) −0.223132 + 0.386476i −0.0116633 + 0.0202014i
\(367\) 1.20298 + 0.322337i 0.0627950 + 0.0168259i 0.290080 0.957002i \(-0.406318\pi\)
−0.227285 + 0.973828i \(0.572985\pi\)
\(368\) −3.71369 3.71369i −0.193590 0.193590i
\(369\) 20.0089 1.04162
\(370\) 0 0
\(371\) −9.10926 + 5.25923i −0.472929 + 0.273046i
\(372\) 5.13534 5.13534i 0.266255 0.266255i
\(373\) 20.2015 20.2015i 1.04599 1.04599i 0.0471036 0.998890i \(-0.485001\pi\)
0.998890 0.0471036i \(-0.0149991\pi\)
\(374\) 5.67304 + 9.82599i 0.293346 + 0.508090i
\(375\) 0 0
\(376\) −0.313116 + 0.180777i −0.0161477 + 0.00932288i
\(377\) 7.60214 + 28.3716i 0.391530 + 1.46121i
\(378\) 5.46340 1.46391i 0.281007 0.0752956i
\(379\) −6.67007 −0.342618 −0.171309 0.985217i \(-0.554800\pi\)
−0.171309 + 0.985217i \(0.554800\pi\)
\(380\) 0 0
\(381\) −7.18505 −0.368101
\(382\) −15.9979 + 4.28663i −0.818524 + 0.219323i
\(383\) 6.20447 + 23.1554i 0.317033 + 1.18319i 0.922081 + 0.386996i \(0.126487\pi\)
−0.605048 + 0.796189i \(0.706846\pi\)
\(384\) −0.622936 + 0.359652i −0.0317891 + 0.0183534i
\(385\) 0 0
\(386\) 5.29953 + 9.17906i 0.269739 + 0.467202i
\(387\) −3.19998 + 3.19998i −0.162664 + 0.162664i
\(388\) 7.21740 7.21740i 0.366408 0.366408i
\(389\) −0.912264 + 0.526696i −0.0462536 + 0.0267045i −0.522948 0.852364i \(-0.675168\pi\)
0.476695 + 0.879069i \(0.341835\pi\)
\(390\) 0 0
\(391\) −24.9508 −1.26182
\(392\) −3.49521 3.49521i −0.176535 0.176535i
\(393\) −4.57293 1.22531i −0.230674 0.0618089i
\(394\) −12.2582 + 21.2317i −0.617557 + 1.06964i
\(395\) 0 0
\(396\) 2.96456 5.13476i 0.148975 0.258031i
\(397\) −3.38776 12.6433i −0.170027 0.634548i −0.997345 0.0728155i \(-0.976802\pi\)
0.827319 0.561733i \(-0.189865\pi\)
\(398\) 8.09356 8.09356i 0.405693 0.405693i
\(399\) 4.43224 0.759633i 0.221889 0.0380292i
\(400\) 0 0
\(401\) 0.812592 + 0.469150i 0.0405789 + 0.0234282i 0.520152 0.854074i \(-0.325875\pi\)
−0.479573 + 0.877502i \(0.659209\pi\)
\(402\) −0.989193 + 0.265053i −0.0493364 + 0.0132197i
\(403\) 7.85702 29.3228i 0.391386 1.46067i
\(404\) 14.8381 + 8.56678i 0.738223 + 0.426213i
\(405\) 0 0
\(406\) 14.0110 0.695355
\(407\) 6.86793 + 6.86793i 0.340430 + 0.340430i
\(408\) −0.884448 + 3.30080i −0.0437867 + 0.163414i
\(409\) 6.72826 + 11.6537i 0.332691 + 0.576238i 0.983039 0.183399i \(-0.0587100\pi\)
−0.650347 + 0.759637i \(0.725377\pi\)
\(410\) 0 0
\(411\) 6.48634i 0.319947i
\(412\) −0.651710 + 2.43222i −0.0321075 + 0.119827i
\(413\) 0.963840 + 3.59710i 0.0474275 + 0.177002i
\(414\) 6.51926 + 11.2917i 0.320404 + 0.554956i
\(415\) 0 0
\(416\) −1.50335 + 2.60388i −0.0737078 + 0.127666i
\(417\) −2.75765 2.75765i −0.135043 0.135043i
\(418\) 6.01186 8.49882i 0.294050 0.415691i
\(419\) 31.4227i 1.53510i 0.640989 + 0.767550i \(0.278524\pi\)
−0.640989 + 0.767550i \(0.721476\pi\)
\(420\) 0 0
\(421\) −13.8219 7.98005i −0.673636 0.388924i 0.123817 0.992305i \(-0.460486\pi\)
−0.797453 + 0.603381i \(0.793820\pi\)
\(422\) 7.52502 + 2.01632i 0.366312 + 0.0981531i
\(423\) 0.867011 0.232315i 0.0421555 0.0112955i
\(424\) −6.35130 + 3.66693i −0.308447 + 0.178082i
\(425\) 0 0
\(426\) 4.47608i 0.216867i
\(427\) 0.859494 + 0.230301i 0.0415938 + 0.0111450i
\(428\) 6.77821 + 1.81622i 0.327637 + 0.0877901i
\(429\) 5.16518i 0.249377i
\(430\) 0 0
\(431\) 16.0614 9.27303i 0.773648 0.446666i −0.0605263 0.998167i \(-0.519278\pi\)
0.834174 + 0.551501i \(0.185945\pi\)
\(432\) 3.80928 1.02069i 0.183274 0.0491082i
\(433\) −4.93514 1.32237i −0.237168 0.0635489i 0.138277 0.990394i \(-0.455843\pi\)
−0.375445 + 0.926845i \(0.622510\pi\)
\(434\) −12.5407 7.24038i −0.601973 0.347549i
\(435\) 0 0
\(436\) 9.22052i 0.441583i
\(437\) 9.57532 + 20.7940i 0.458049 + 0.994712i
\(438\) 1.69415 + 1.69415i 0.0809497 + 0.0809497i
\(439\) −6.25946 + 10.8417i −0.298748 + 0.517446i −0.975850 0.218443i \(-0.929902\pi\)
0.677102 + 0.735889i \(0.263236\pi\)
\(440\) 0 0
\(441\) 6.13572 + 10.6274i 0.292177 + 0.506065i
\(442\) 3.69700 + 13.7974i 0.175848 + 0.656276i
\(443\) −10.0467 + 37.4948i −0.477333 + 1.78143i 0.135017 + 0.990843i \(0.456891\pi\)
−0.612350 + 0.790587i \(0.709776\pi\)
\(444\) 2.92530i 0.138829i
\(445\) 0 0
\(446\) −5.99356 10.3811i −0.283803 0.491562i
\(447\) 1.23129 4.59522i 0.0582379 0.217347i
\(448\) 1.01416 + 1.01416i 0.0479144 + 0.0479144i
\(449\) −10.8951 −0.514169 −0.257085 0.966389i \(-0.582762\pi\)
−0.257085 + 0.966389i \(0.582762\pi\)
\(450\) 0 0
\(451\) 16.6697 + 9.62428i 0.784947 + 0.453189i
\(452\) 0.172639 0.644298i 0.00812026 0.0303052i
\(453\) 11.9885 3.21232i 0.563271 0.150928i
\(454\) 18.6922 + 10.7919i 0.877267 + 0.506491i
\(455\) 0 0
\(456\) 3.09032 0.529643i 0.144717 0.0248028i
\(457\) −10.9672 + 10.9672i −0.513025 + 0.513025i −0.915452 0.402427i \(-0.868167\pi\)
0.402427 + 0.915452i \(0.368167\pi\)
\(458\) 3.68642 + 13.7579i 0.172255 + 0.642864i
\(459\) 9.36769 16.2253i 0.437246 0.757333i
\(460\) 0 0
\(461\) 1.58025 2.73707i 0.0735995 0.127478i −0.826877 0.562383i \(-0.809885\pi\)
0.900476 + 0.434905i \(0.143218\pi\)
\(462\) 2.37990 + 0.637693i 0.110723 + 0.0296682i
\(463\) −25.6630 25.6630i −1.19266 1.19266i −0.976317 0.216344i \(-0.930587\pi\)
−0.216344 0.976317i \(-0.569413\pi\)
\(464\) 9.76898 0.453514
\(465\) 0 0
\(466\) 14.1322 8.15923i 0.654662 0.377969i
\(467\) −15.1541 + 15.1541i −0.701248 + 0.701248i −0.964678 0.263431i \(-0.915146\pi\)
0.263431 + 0.964678i \(0.415146\pi\)
\(468\) 5.27816 5.27816i 0.243983 0.243983i
\(469\) 1.02097 + 1.76838i 0.0471442 + 0.0816561i
\(470\) 0 0
\(471\) 2.01772 1.16493i 0.0929715 0.0536771i
\(472\) 0.672024 + 2.50803i 0.0309324 + 0.115441i
\(473\) −4.20515 + 1.12677i −0.193353 + 0.0518088i
\(474\) 0.0234975 0.00107928
\(475\) 0 0
\(476\) 6.81371 0.312306
\(477\) 17.5866 4.71233i 0.805237 0.215763i
\(478\) 3.04379 + 11.3596i 0.139220 + 0.519575i
\(479\) 8.65416 4.99648i 0.395418 0.228295i −0.289087 0.957303i \(-0.593352\pi\)
0.684505 + 0.729008i \(0.260018\pi\)
\(480\) 0 0
\(481\) 6.11390 + 10.5896i 0.278770 + 0.482843i
\(482\) −9.41569 + 9.41569i −0.428873 + 0.428873i
\(483\) −3.83123 + 3.83123i −0.174327 + 0.174327i
\(484\) −4.58663 + 2.64809i −0.208483 + 0.120368i
\(485\) 0 0
\(486\) −15.1478 −0.687117
\(487\) 3.95427 + 3.95427i 0.179185 + 0.179185i 0.791001 0.611815i \(-0.209560\pi\)
−0.611815 + 0.791001i \(0.709560\pi\)
\(488\) 0.599271 + 0.160574i 0.0271277 + 0.00726885i
\(489\) 6.64288 11.5058i 0.300401 0.520310i
\(490\) 0 0
\(491\) 15.2803 26.4663i 0.689592 1.19441i −0.282378 0.959303i \(-0.591123\pi\)
0.971970 0.235105i \(-0.0755435\pi\)
\(492\) 1.50046 + 5.59979i 0.0676459 + 0.252458i
\(493\) 32.8169 32.8169i 1.47800 1.47800i
\(494\) 10.0800 8.37609i 0.453520 0.376858i
\(495\) 0 0
\(496\) −8.74383 5.04825i −0.392610 0.226673i
\(497\) 8.62084 2.30995i 0.386697 0.103615i
\(498\) 3.15983 11.7927i 0.141596 0.528442i
\(499\) 23.2626 + 13.4307i 1.04138 + 0.601239i 0.920223 0.391394i \(-0.128007\pi\)
0.121154 + 0.992634i \(0.461340\pi\)
\(500\) 0 0
\(501\) 15.6204 0.697868
\(502\) 18.2515 + 18.2515i 0.814606 + 0.814606i
\(503\) 6.03190 22.5113i 0.268949 1.00373i −0.690840 0.723008i \(-0.742759\pi\)
0.959789 0.280723i \(-0.0905744\pi\)
\(504\) −1.78032 3.08360i −0.0793016 0.137354i
\(505\) 0 0
\(506\) 12.5431i 0.557607i
\(507\) 0.737185 2.75121i 0.0327395 0.122186i
\(508\) 2.58532 + 9.64853i 0.114705 + 0.428084i
\(509\) 4.75131 + 8.22951i 0.210598 + 0.364767i 0.951902 0.306403i \(-0.0991255\pi\)
−0.741304 + 0.671170i \(0.765792\pi\)
\(510\) 0 0
\(511\) 2.38861 4.13719i 0.105666 0.183018i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) −17.1172 1.58028i −0.755744 0.0697713i
\(514\) 7.09327i 0.312871i
\(515\) 0 0
\(516\) −1.13553 0.655598i −0.0499889 0.0288611i
\(517\) 0.834066 + 0.223487i 0.0366822 + 0.00982896i
\(518\) 5.63406 1.50964i 0.247547 0.0663299i
\(519\) −4.16191 + 2.40288i −0.182688 + 0.105475i
\(520\) 0 0
\(521\) 23.0578i 1.01018i 0.863067 + 0.505090i \(0.168541\pi\)
−0.863067 + 0.505090i \(0.831459\pi\)
\(522\) −23.4261 6.27701i −1.02533 0.274737i
\(523\) 32.3420 + 8.66602i 1.41422 + 0.378939i 0.883429 0.468565i \(-0.155229\pi\)
0.530789 + 0.847504i \(0.321896\pi\)
\(524\) 6.58170i 0.287523i
\(525\) 0 0
\(526\) −18.0492 + 10.4207i −0.786983 + 0.454365i
\(527\) −46.3317 + 12.4145i −2.01824 + 0.540786i
\(528\) 1.65935 + 0.444623i 0.0722141 + 0.0193497i
\(529\) −3.96902 2.29151i −0.172566 0.0996311i
\(530\) 0 0
\(531\) 6.44608i 0.279736i
\(532\) −2.61488 5.67855i −0.113370 0.246196i
\(533\) 17.1353 + 17.1353i 0.742211 + 0.742211i
\(534\) 0.799167 1.38420i 0.0345833 0.0599001i
\(535\) 0 0
\(536\) 0.711860 + 1.23298i 0.0307477 + 0.0532565i
\(537\) −2.23137 8.32758i −0.0962906 0.359361i
\(538\) −5.35103 + 19.9703i −0.230699 + 0.860982i
\(539\) 11.8051i 0.508483i
\(540\) 0 0
\(541\) 6.15206 + 10.6557i 0.264498 + 0.458124i 0.967432 0.253131i \(-0.0814605\pi\)
−0.702934 + 0.711255i \(0.748127\pi\)
\(542\) 6.52138 24.3381i 0.280117 1.04541i
\(543\) −12.1396 12.1396i −0.520962 0.520962i
\(544\) 4.75076 0.203687
\(545\) 0 0
\(546\) 2.68629 + 1.55093i 0.114963 + 0.0663738i
\(547\) −9.47712 + 35.3691i −0.405212 + 1.51227i 0.398451 + 0.917189i \(0.369548\pi\)
−0.803664 + 0.595084i \(0.797119\pi\)
\(548\) −8.71025 + 2.33391i −0.372084 + 0.0996995i
\(549\) −1.33388 0.770116i −0.0569286 0.0328677i
\(550\) 0 0
\(551\) −39.9437 14.7556i −1.70166 0.628608i
\(552\) −2.67127 + 2.67127i −0.113697 + 0.113697i
\(553\) −0.0121262 0.0452557i −0.000515659 0.00192447i
\(554\) 11.4716 19.8693i 0.487380 0.844167i
\(555\) 0 0
\(556\) −2.71089 + 4.69540i −0.114967 + 0.199129i
\(557\) 15.9320 + 4.26897i 0.675061 + 0.180882i 0.580033 0.814593i \(-0.303040\pi\)
0.0950272 + 0.995475i \(0.469706\pi\)
\(558\) 17.7241 + 17.7241i 0.750319 + 0.750319i
\(559\) −5.48082 −0.231814
\(560\) 0 0
\(561\) 7.06788 4.08064i 0.298406 0.172285i
\(562\) 3.77344 3.77344i 0.159173 0.159173i
\(563\) −3.10059 + 3.10059i −0.130674 + 0.130674i −0.769419 0.638745i \(-0.779454\pi\)
0.638745 + 0.769419i \(0.279454\pi\)
\(564\) 0.130034 + 0.225225i 0.00547542 + 0.00948370i
\(565\) 0 0
\(566\) 28.3968 16.3949i 1.19361 0.689129i
\(567\) 1.71168 + 6.38807i 0.0718837 + 0.268274i
\(568\) 6.01076 1.61058i 0.252206 0.0675784i
\(569\) −16.6846 −0.699455 −0.349727 0.936851i \(-0.613726\pi\)
−0.349727 + 0.936851i \(0.613726\pi\)
\(570\) 0 0
\(571\) −7.93391 −0.332024 −0.166012 0.986124i \(-0.553089\pi\)
−0.166012 + 0.986124i \(0.553089\pi\)
\(572\) 6.93612 1.85853i 0.290014 0.0777090i
\(573\) 3.08339 + 11.5074i 0.128810 + 0.480727i
\(574\) 10.0107 5.77970i 0.417840 0.241240i
\(575\) 0 0
\(576\) −1.24130 2.15000i −0.0517209 0.0895832i
\(577\) −12.2981 + 12.2981i −0.511976 + 0.511976i −0.915131 0.403156i \(-0.867913\pi\)
0.403156 + 0.915131i \(0.367913\pi\)
\(578\) 3.93840 3.93840i 0.163816 0.163816i
\(579\) 6.60254 3.81198i 0.274392 0.158420i
\(580\) 0 0
\(581\) −24.3431 −1.00992
\(582\) −5.19151 5.19151i −0.215195 0.215195i
\(583\) 16.9184 + 4.53326i 0.700687 + 0.187749i
\(584\) 1.66542 2.88460i 0.0689157 0.119365i
\(585\) 0 0
\(586\) 9.30904 16.1237i 0.384553 0.666065i
\(587\) −0.106964 0.399196i −0.00441488 0.0164766i 0.963683 0.267048i \(-0.0860482\pi\)
−0.968098 + 0.250571i \(0.919382\pi\)
\(588\) −2.51412 + 2.51412i −0.103681 + 0.103681i
\(589\) 28.1269 + 33.8486i 1.15895 + 1.39471i
\(590\) 0 0
\(591\) 15.2721 + 8.81734i 0.628209 + 0.362697i
\(592\) 3.92827 1.05258i 0.161451 0.0432607i
\(593\) −0.915527 + 3.41679i −0.0375962 + 0.140311i −0.982173 0.187980i \(-0.939806\pi\)
0.944577 + 0.328291i \(0.106473\pi\)
\(594\) −8.15666 4.70925i −0.334672 0.193223i
\(595\) 0 0
\(596\) −6.61379 −0.270911
\(597\) −5.82173 5.82173i −0.238268 0.238268i
\(598\) −4.08703 + 15.2530i −0.167131 + 0.623741i
\(599\) −6.17905 10.7024i −0.252469 0.437290i 0.711736 0.702447i \(-0.247909\pi\)
−0.964205 + 0.265158i \(0.914576\pi\)
\(600\) 0 0
\(601\) 19.5516i 0.797528i 0.917054 + 0.398764i \(0.130561\pi\)
−0.917054 + 0.398764i \(0.869439\pi\)
\(602\) −0.676661 + 2.52533i −0.0275787 + 0.102925i
\(603\) −0.914803 3.41409i −0.0372537 0.139033i
\(604\) −8.62740 14.9431i −0.351044 0.608026i
\(605\) 0 0
\(606\) 6.16212 10.6731i 0.250319 0.433566i
\(607\) −11.0587 11.0587i −0.448860 0.448860i 0.446115 0.894975i \(-0.352807\pi\)
−0.894975 + 0.446115i \(0.852807\pi\)
\(608\) −1.82319 3.95929i −0.0739402 0.160570i
\(609\) 10.0782i 0.408388i
\(610\) 0 0
\(611\) 0.941445 + 0.543544i 0.0380868 + 0.0219894i
\(612\) −11.3924 3.05258i −0.460509 0.123393i
\(613\) 3.06788 0.822036i 0.123911 0.0332017i −0.196331 0.980538i \(-0.562903\pi\)
0.320241 + 0.947336i \(0.396236\pi\)
\(614\) 16.2889 9.40438i 0.657365 0.379530i
\(615\) 0 0
\(616\) 3.42533i 0.138011i
\(617\) 35.6742 + 9.55886i 1.43619 + 0.384825i 0.891197 0.453617i \(-0.149867\pi\)
0.544990 + 0.838442i \(0.316533\pi\)
\(618\) 1.74950 + 0.468778i 0.0703753 + 0.0188570i
\(619\) 18.5959i 0.747433i 0.927543 + 0.373716i \(0.121917\pi\)
−0.927543 + 0.373716i \(0.878083\pi\)
\(620\) 0 0
\(621\) 17.9370 10.3560i 0.719789 0.415570i
\(622\) 4.32396 1.15860i 0.173375 0.0464556i
\(623\) −3.07835 0.824843i −0.123332 0.0330466i
\(624\) 1.87298 + 1.08137i 0.0749793 + 0.0432893i
\(625\) 0 0
\(626\) 12.4723i 0.498492i
\(627\) −6.11324 4.32436i −0.244139 0.172698i
\(628\) −2.29035 2.29035i −0.0913949 0.0913949i
\(629\) 9.66032 16.7322i 0.385182 0.667155i
\(630\) 0 0
\(631\) −18.8281 32.6113i −0.749536 1.29823i −0.948045 0.318136i \(-0.896943\pi\)
0.198509 0.980099i \(-0.436390\pi\)
\(632\) −0.00845484 0.0315539i −0.000336315 0.00125515i
\(633\) 1.45035 5.41278i 0.0576462 0.215139i
\(634\) 5.66192i 0.224864i
\(635\) 0 0
\(636\) 2.63764 + 4.56852i 0.104589 + 0.181154i
\(637\) −3.84658 + 14.3556i −0.152407 + 0.568791i
\(638\) −16.4975 16.4975i −0.653141 0.653141i
\(639\) −15.4487 −0.611142
\(640\) 0 0
\(641\) 29.8628 + 17.2413i 1.17951 + 0.680990i 0.955901 0.293689i \(-0.0948829\pi\)
0.223609 + 0.974679i \(0.428216\pi\)
\(642\) 1.30641 4.87560i 0.0515600 0.192424i
\(643\) −29.4620 + 7.89433i −1.16187 + 0.311322i −0.787712 0.616044i \(-0.788734\pi\)
−0.374157 + 0.927365i \(0.622068\pi\)
\(644\) 6.52336 + 3.76627i 0.257057 + 0.148412i
\(645\) 0 0
\(646\) −19.4251 7.17579i −0.764269 0.282328i
\(647\) −9.95134 + 9.95134i −0.391227 + 0.391227i −0.875125 0.483897i \(-0.839221\pi\)
0.483897 + 0.875125i \(0.339221\pi\)
\(648\) 1.19344 + 4.45399i 0.0468829 + 0.174969i
\(649\) 3.10057 5.37034i 0.121708 0.210804i
\(650\) 0 0
\(651\) −5.20803 + 9.02058i −0.204119 + 0.353544i
\(652\) −17.8409 4.78046i −0.698705 0.187217i
\(653\) −25.1527 25.1527i −0.984302 0.984302i 0.0155764 0.999879i \(-0.495042\pi\)
−0.999879 + 0.0155764i \(0.995042\pi\)
\(654\) −6.63236 −0.259346
\(655\) 0 0
\(656\) 6.97985 4.02982i 0.272517 0.157338i
\(657\) −5.84718 + 5.84718i −0.228120 + 0.228120i
\(658\) 0.366673 0.366673i 0.0142944 0.0142944i
\(659\) −5.83576 10.1078i −0.227329 0.393745i 0.729687 0.683782i \(-0.239666\pi\)
−0.957016 + 0.290036i \(0.906333\pi\)
\(660\) 0 0
\(661\) −3.70480 + 2.13897i −0.144100 + 0.0831963i −0.570317 0.821425i \(-0.693180\pi\)
0.426217 + 0.904621i \(0.359846\pi\)
\(662\) −3.48916 13.0217i −0.135610 0.506104i
\(663\) 9.92453 2.65927i 0.385437 0.103277i
\(664\) −16.9729 −0.658675
\(665\) 0 0
\(666\) −10.0964 −0.391226
\(667\) 49.5580 13.2790i 1.91890 0.514166i
\(668\) −5.62051 20.9760i −0.217464 0.811587i
\(669\) −7.46721 + 4.31119i −0.288699 + 0.166680i
\(670\) 0 0
\(671\) −0.740853 1.28319i −0.0286003 0.0495372i
\(672\) 0.729487 0.729487i 0.0281406 0.0281406i
\(673\) −28.2136 + 28.2136i −1.08756 + 1.08756i −0.0917757 + 0.995780i \(0.529254\pi\)
−0.995780 + 0.0917757i \(0.970746\pi\)
\(674\) −27.7776 + 16.0374i −1.06995 + 0.617738i
\(675\) 0 0
\(676\) −3.95975 −0.152298
\(677\) −28.7454 28.7454i −1.10477 1.10477i −0.993826 0.110948i \(-0.964611\pi\)
−0.110948 0.993826i \(-0.535389\pi\)
\(678\) −0.463446 0.124180i −0.0177985 0.00476910i
\(679\) −7.31958 + 12.6779i −0.280900 + 0.486532i
\(680\) 0 0
\(681\) 7.76268 13.4454i 0.297467 0.515227i
\(682\) 6.24094 + 23.2915i 0.238978 + 0.891878i
\(683\) 26.4931 26.4931i 1.01373 1.01373i 0.0138253 0.999904i \(-0.495599\pi\)
0.999904 0.0138253i \(-0.00440088\pi\)
\(684\) 1.82801 + 10.6659i 0.0698956 + 0.407821i
\(685\) 0 0
\(686\) 14.8342 + 8.56451i 0.566371 + 0.326994i
\(687\) 9.89611 2.65166i 0.377560 0.101167i
\(688\) −0.471793 + 1.76075i −0.0179869 + 0.0671281i
\(689\) 19.0965 + 11.0254i 0.727518 + 0.420032i
\(690\) 0 0
\(691\) 14.6142 0.555951 0.277975 0.960588i \(-0.410337\pi\)
0.277975 + 0.960588i \(0.410337\pi\)
\(692\) 4.72427 + 4.72427i 0.179590 + 0.179590i
\(693\) −2.20093 + 8.21398i −0.0836064 + 0.312023i
\(694\) 1.88116 + 3.25826i 0.0714078 + 0.123682i
\(695\) 0 0
\(696\) 7.02687i 0.266353i
\(697\) 9.91003 36.9847i 0.375369 1.40090i
\(698\) 8.08471 + 30.1725i 0.306011 + 1.14205i
\(699\) −5.86897 10.1654i −0.221985 0.384489i
\(700\) 0 0
\(701\) −8.12955 + 14.0808i −0.307049 + 0.531824i −0.977715 0.209935i \(-0.932675\pi\)
0.670666 + 0.741759i \(0.266008\pi\)
\(702\) −8.38445 8.38445i −0.316451 0.316451i
\(703\) −17.6519 1.62965i −0.665755 0.0614634i
\(704\) 2.38827i 0.0900111i
\(705\) 0 0
\(706\) 21.1498 + 12.2109i 0.795985 + 0.459562i
\(707\) −23.7362 6.36010i −0.892693 0.239196i
\(708\) 1.80404 0.483390i 0.0677998 0.0181669i
\(709\) 5.92229 3.41924i 0.222416 0.128412i −0.384652 0.923062i \(-0.625679\pi\)
0.607069 + 0.794649i \(0.292345\pi\)
\(710\) 0 0
\(711\) 0.0810991i 0.00304145i
\(712\) −2.14634 0.575110i −0.0804375 0.0215532i
\(713\) −51.2196 13.7242i −1.91819 0.513977i
\(714\) 4.90113i 0.183420i
\(715\) 0 0
\(716\) −10.3799 + 5.99283i −0.387915 + 0.223963i
\(717\) 8.17099 2.18941i 0.305151 0.0817651i
\(718\) −12.9866 3.47976i −0.484657 0.129864i
\(719\) −38.3648 22.1499i −1.43077 0.826054i −0.433588 0.901111i \(-0.642752\pi\)
−0.997179 + 0.0750579i \(0.976086\pi\)
\(720\) 0 0
\(721\) 3.61142i 0.134496i
\(722\) 1.47441 + 18.9427i 0.0548719 + 0.704975i
\(723\) 6.77274 + 6.77274i 0.251881 + 0.251881i
\(724\) −11.9338 + 20.6699i −0.443516 + 0.768192i
\(725\) 0 0
\(726\) 1.90479 + 3.29918i 0.0706932 + 0.122444i
\(727\) 2.48623 + 9.27872i 0.0922090 + 0.344129i 0.996582 0.0826152i \(-0.0263272\pi\)
−0.904373 + 0.426744i \(0.859661\pi\)
\(728\) 1.11611 4.16538i 0.0413657 0.154379i
\(729\) 2.93749i 0.108796i
\(730\) 0 0
\(731\) 4.33000 + 7.49979i 0.160151 + 0.277390i
\(732\) 0.115502 0.431058i 0.00426906 0.0159324i
\(733\) 13.8225 + 13.8225i 0.510547 + 0.510547i 0.914694 0.404147i \(-0.132432\pi\)
−0.404147 + 0.914694i \(0.632432\pi\)
\(734\) −1.24542 −0.0459691
\(735\) 0 0
\(736\) 4.54833 + 2.62598i 0.167654 + 0.0967948i
\(737\) 0.880042 3.28436i 0.0324168 0.120981i
\(738\) −19.3271 + 5.17868i −0.711440 + 0.190630i
\(739\) 2.25750 + 1.30337i 0.0830433 + 0.0479451i 0.540947 0.841057i \(-0.318066\pi\)
−0.457903 + 0.889002i \(0.651399\pi\)
\(740\) 0 0
\(741\) −6.02496 7.25057i −0.221332 0.266356i
\(742\) 7.43768 7.43768i 0.273046 0.273046i
\(743\) 7.64152 + 28.5185i 0.280340 + 1.04624i 0.952178 + 0.305545i \(0.0988386\pi\)
−0.671838 + 0.740698i \(0.734495\pi\)
\(744\) −3.63123 + 6.28948i −0.133127 + 0.230583i
\(745\) 0 0
\(746\) −14.2846 + 24.7417i −0.522997 + 0.905857i
\(747\) 40.7011 + 10.9058i 1.48918 + 0.399023i
\(748\) −8.02289 8.02289i −0.293346 0.293346i
\(749\) −10.0645 −0.367748
\(750\) 0 0
\(751\) 23.6406 13.6489i 0.862659 0.498056i −0.00224314 0.999997i \(-0.500714\pi\)
0.864902 + 0.501941i \(0.167381\pi\)
\(752\) 0.255658 0.255658i 0.00932288 0.00932288i
\(753\) 13.1284 13.1284i 0.478426 0.478426i
\(754\) −14.6862 25.4373i −0.534840 0.926370i
\(755\) 0 0
\(756\) −4.89835 + 2.82806i −0.178151 + 0.102856i
\(757\) −9.93389 37.0738i −0.361053 1.34747i −0.872693 0.488270i \(-0.837628\pi\)
0.511639 0.859200i \(-0.329038\pi\)
\(758\) 6.44279 1.72634i 0.234013 0.0627035i
\(759\) 9.02228 0.327488
\(760\) 0 0
\(761\) −37.8413 −1.37175 −0.685873 0.727721i \(-0.740580\pi\)
−0.685873 + 0.727721i \(0.740580\pi\)
\(762\) 6.94023 1.85963i 0.251418 0.0673672i
\(763\) 3.42272 + 12.7738i 0.123911 + 0.462442i
\(764\) 14.3433 8.28113i 0.518924 0.299601i
\(765\) 0 0
\(766\) −11.9861 20.7606i −0.433076 0.750109i
\(767\) 5.52032 5.52032i 0.199327 0.199327i
\(768\) 0.508625 0.508625i 0.0183534 0.0183534i
\(769\) 3.75568 2.16834i 0.135433 0.0781925i −0.430752 0.902470i \(-0.641752\pi\)
0.566186 + 0.824278i \(0.308418\pi\)
\(770\) 0 0
\(771\) −5.10222 −0.183752
\(772\) −7.49467 7.49467i −0.269739 0.269739i
\(773\) 15.7765 + 4.22729i 0.567440 + 0.152045i 0.531122 0.847295i \(-0.321770\pi\)
0.0363177 + 0.999340i \(0.488437\pi\)
\(774\) 2.26273 3.91916i 0.0813320 0.140871i
\(775\) 0 0
\(776\) −5.10347 + 8.83948i −0.183204 + 0.317319i
\(777\) −1.08589 4.05261i −0.0389562 0.145386i
\(778\) 0.744860 0.744860i 0.0267045 0.0267045i
\(779\) −34.6263 + 5.93453i −1.24061 + 0.212627i
\(780\) 0 0
\(781\) −12.8706 7.43084i −0.460546 0.265897i
\(782\) 24.1006 6.45774i 0.861836 0.230928i
\(783\) −9.97114 + 37.2128i −0.356340 + 1.32988i
\(784\) 4.28074 + 2.47149i 0.152884 + 0.0882674i
\(785\) 0 0
\(786\) 4.73425 0.168865
\(787\) −20.1032 20.1032i −0.716600 0.716600i 0.251307 0.967907i \(-0.419140\pi\)
−0.967907 + 0.251307i \(0.919140\pi\)
\(788\) 6.34529 23.6809i 0.226041 0.843598i
\(789\) 7.49566 + 12.9829i 0.266853 + 0.462202i
\(790\) 0 0
\(791\) 0.956671i 0.0340153i
\(792\) −1.53457 + 5.72708i −0.0545285 + 0.203503i
\(793\) −0.482798 1.80183i −0.0171447 0.0639848i
\(794\) 6.54465 + 11.3357i 0.232261 + 0.402287i
\(795\) 0 0
\(796\) −5.72301 + 9.91254i −0.202847 + 0.351341i
\(797\) −15.3795 15.3795i −0.544770 0.544770i 0.380154 0.924923i \(-0.375871\pi\)
−0.924923 + 0.380154i \(0.875871\pi\)
\(798\) −4.08460 + 1.88090i −0.144593 + 0.0665830i
\(799\) 1.71766i 0.0607665i
\(800\) 0 0
\(801\) 4.77741 + 2.75824i 0.168801 + 0.0974576i
\(802\) −0.906329 0.242850i −0.0320036 0.00857533i
\(803\) −7.68389 + 2.05889i −0.271158 + 0.0726567i
\(804\) 0.886886 0.512044i 0.0312780 0.0180584i
\(805\) 0 0
\(806\) 30.3572i 1.06929i
\(807\) 14.3647 + 3.84902i 0.505663 + 0.135492i
\(808\) −16.5498 4.43449i −0.582218 0.156005i
\(809\) 33.7129i 1.18528i −0.805466 0.592642i \(-0.798085\pi\)
0.805466 0.592642i \(-0.201915\pi\)
\(810\) 0 0
\(811\) −3.19078 + 1.84220i −0.112043 + 0.0646883i −0.554974 0.831867i \(-0.687272\pi\)
0.442931 + 0.896556i \(0.353939\pi\)
\(812\) −13.5336 + 3.62632i −0.474936 + 0.127259i
\(813\) −17.5065 4.69086i −0.613980 0.164516i
\(814\) −8.41146 4.85636i −0.294821 0.170215i
\(815\) 0 0
\(816\) 3.41724i 0.119627i
\(817\) 4.58861 6.48681i 0.160535 0.226945i
\(818\) −9.51520 9.51520i −0.332691 0.332691i
\(819\) −5.35288 + 9.27146i −0.187045 + 0.323971i
\(820\) 0 0
\(821\) 10.9004 + 18.8801i 0.380427 + 0.658919i 0.991123 0.132946i \(-0.0424437\pi\)
−0.610696 + 0.791865i \(0.709110\pi\)
\(822\) 1.67879 + 6.26532i 0.0585545 + 0.218528i
\(823\) −12.7952 + 47.7524i −0.446014 + 1.66455i 0.267232 + 0.963632i \(0.413891\pi\)
−0.713246 + 0.700914i \(0.752776\pi\)
\(824\) 2.51802i 0.0877192i
\(825\) 0 0
\(826\) −1.86200 3.22507i −0.0647871 0.112215i
\(827\) −0.389735 + 1.45451i −0.0135524 + 0.0505783i −0.972371 0.233441i \(-0.925001\pi\)
0.958819 + 0.284019i \(0.0916680\pi\)
\(828\) −9.21962 9.21962i −0.320404 0.320404i
\(829\) 14.5438 0.505127 0.252563 0.967580i \(-0.418726\pi\)
0.252563 + 0.967580i \(0.418726\pi\)
\(830\) 0 0
\(831\) −14.2921 8.25155i −0.495787 0.286243i
\(832\) 0.778192 2.90425i 0.0269789 0.100687i
\(833\) 22.6827 6.07782i 0.785910 0.210584i
\(834\) 3.37742 + 1.94996i 0.116951 + 0.0675215i
\(835\) 0 0
\(836\) −3.60736 + 9.76521i −0.124763 + 0.337737i
\(837\) 28.1550 28.1550i 0.973179 0.973179i
\(838\) −8.13280 30.3520i −0.280943 1.04849i
\(839\) −27.6955 + 47.9700i −0.956155 + 1.65611i −0.224454 + 0.974485i \(0.572060\pi\)
−0.731702 + 0.681625i \(0.761274\pi\)
\(840\) 0 0
\(841\) −33.2165 + 57.5327i −1.14540 + 1.98389i
\(842\) 15.4163 + 4.13078i 0.531280 + 0.142356i
\(843\) −2.71425 2.71425i −0.0934837 0.0934837i
\(844\) −7.79048 −0.268159
\(845\) 0 0
\(846\) −0.777341 + 0.448798i −0.0267255 + 0.0154300i
\(847\) 5.37116 5.37116i 0.184555 0.184555i
\(848\) 5.18582 5.18582i 0.178082 0.178082i
\(849\) −11.7929 20.4259i −0.404732 0.701016i
\(850\) 0 0
\(851\) 18.4974 10.6795i 0.634081 0.366087i
\(852\) −1.15850 4.32356i −0.0396894 0.148123i
\(853\) −3.24887 + 0.870532i −0.111239 + 0.0298064i −0.314009 0.949420i \(-0.601672\pi\)
0.202770 + 0.979226i \(0.435006\pi\)
\(854\) −0.889814 −0.0304488
\(855\) 0 0
\(856\) −7.01732 −0.239847
\(857\) −54.1712 + 14.5151i −1.85045 + 0.495827i −0.999564 0.0295186i \(-0.990603\pi\)
−0.850889 + 0.525346i \(0.823936\pi\)
\(858\) −1.33685 4.98918i −0.0456392 0.170328i
\(859\) −9.38131 + 5.41630i −0.320086 + 0.184802i −0.651431 0.758708i \(-0.725831\pi\)
0.331345 + 0.943510i \(0.392498\pi\)
\(860\) 0 0
\(861\) −4.15737 7.20077i −0.141683 0.245402i
\(862\) −13.1140 + 13.1140i −0.446666 + 0.446666i
\(863\) 14.3014 14.3014i 0.486824 0.486824i −0.420479 0.907302i \(-0.638138\pi\)
0.907302 + 0.420479i \(0.138138\pi\)
\(864\) −3.41531 + 1.97183i −0.116191 + 0.0670830i
\(865\) 0 0
\(866\) 5.10923 0.173619
\(867\) −2.83291 2.83291i −0.0962106 0.0962106i
\(868\) 13.9873 + 3.74790i 0.474761 + 0.127212i
\(869\) −0.0390087 + 0.0675651i −0.00132328 + 0.00229199i
\(870\) 0 0
\(871\) 2.14035 3.70719i 0.0725230 0.125613i
\(872\) 2.38645 + 8.90634i 0.0808153 + 0.301607i
\(873\) 17.9179 17.9179i 0.606430 0.606430i
\(874\) −14.6309 17.6072i −0.494899 0.595572i
\(875\) 0 0
\(876\) −2.07490 1.19795i −0.0701045 0.0404748i
\(877\) −38.7696 + 10.3883i −1.30916 + 0.350787i −0.844905 0.534917i \(-0.820343\pi\)
−0.464251 + 0.885704i \(0.653676\pi\)
\(878\) 3.24013 12.0923i 0.109349 0.408097i
\(879\) −11.5979 6.69603i −0.391186 0.225851i
\(880\) 0 0
\(881\) 22.6745 0.763922 0.381961 0.924178i \(-0.375249\pi\)
0.381961 + 0.924178i \(0.375249\pi\)
\(882\) −8.67721 8.67721i −0.292177 0.292177i
\(883\) 2.64511 9.87168i 0.0890150 0.332209i −0.907029 0.421068i \(-0.861655\pi\)
0.996044 + 0.0888592i \(0.0283221\pi\)
\(884\) −7.14206 12.3704i −0.240214 0.416062i
\(885\) 0 0
\(886\) 38.8174i 1.30410i
\(887\) 8.93508 33.3462i 0.300011 1.11966i −0.637145 0.770744i \(-0.719885\pi\)
0.937156 0.348911i \(-0.113449\pi\)
\(888\) −0.757124 2.82562i −0.0254074 0.0948217i
\(889\) −7.16321 12.4070i −0.240246 0.416119i
\(890\) 0 0
\(891\) 5.50628 9.53716i 0.184467 0.319507i
\(892\) 8.47617 + 8.47617i 0.283803 + 0.283803i
\(893\) −1.43150 + 0.659183i −0.0479033 + 0.0220587i
\(894\) 4.75733i 0.159109i
\(895\) 0 0
\(896\) −1.24208 0.717117i −0.0414951 0.0239572i
\(897\) 10.9715 + 2.93982i 0.366329 + 0.0981576i
\(898\) 10.5238 2.81985i 0.351184 0.0940995i
\(899\) 85.4184 49.3163i 2.84886 1.64479i
\(900\) 0 0
\(901\) 34.8414i 1.16074i
\(902\) −18.5927 4.98189i −0.619068 0.165879i
\(903\) 1.81648 + 0.486725i 0.0604488 + 0.0161972i
\(904\) 0.667026i 0.0221850i
\(905\) 0 0
\(906\) −10.7486 + 6.20572i −0.357099 + 0.206171i
\(907\) 17.7271 4.74996i 0.588618 0.157720i 0.0477964 0.998857i \(-0.484780\pi\)
0.540821 + 0.841137i \(0.318113\pi\)
\(908\) −20.8484 5.58632i −0.691879 0.185388i
\(909\) 36.8371 + 21.2679i 1.22181 + 0.705412i
\(910\) 0 0
\(911\) 17.9694i 0.595351i 0.954667 + 0.297676i \(0.0962114\pi\)
−0.954667 + 0.297676i \(0.903789\pi\)
\(912\) −2.84793 + 1.31143i −0.0943045 + 0.0434257i
\(913\) 28.6631 + 28.6631i 0.948610 + 0.948610i
\(914\) 7.75500 13.4321i 0.256513 0.444293i
\(915\) 0 0
\(916\) −7.12161 12.3350i −0.235305 0.407560i
\(917\) −2.44317 9.11805i −0.0806807 0.301105i
\(918\) −4.84907 + 18.0970i −0.160043 + 0.597290i
\(919\) 37.9480i 1.25179i −0.779908 0.625895i \(-0.784734\pi\)
0.779908 0.625895i \(-0.215266\pi\)
\(920\) 0 0
\(921\) −6.76461 11.7166i −0.222901 0.386077i
\(922\) −0.817997 + 3.05281i −0.0269393 + 0.100539i
\(923\) −13.2300 13.2300i −0.435472 0.435472i
\(924\) −2.46386 −0.0810549
\(925\) 0 0
\(926\) 31.4306 + 18.1465i 1.03287 + 0.596331i
\(927\) −1.61794 + 6.03822i −0.0531400 + 0.198321i
\(928\) −9.43611 + 2.52840i −0.309756 + 0.0829988i
\(929\) −48.7534 28.1478i −1.59955 0.923498i −0.991574 0.129540i \(-0.958650\pi\)
−0.607972 0.793958i \(-0.708017\pi\)
\(930\) 0 0
\(931\) −13.7702 16.5713i −0.451299 0.543104i
\(932\) −11.5389 + 11.5389i −0.377969 + 0.377969i
\(933\) −0.833386 3.11024i −0.0272838 0.101825i
\(934\) 10.7156 18.5599i 0.350624 0.607298i
\(935\) 0 0
\(936\) −3.73222 + 6.46440i −0.121991 + 0.211295i
\(937\) 38.7515 + 10.3834i 1.26596 + 0.339212i 0.828481 0.560017i \(-0.189206\pi\)
0.437477 + 0.899230i \(0.355872\pi\)
\(938\) −1.44387 1.44387i −0.0471442 0.0471442i
\(939\) −8.97136 −0.292769
\(940\) 0 0
\(941\) 6.03359 3.48349i 0.196689 0.113559i −0.398421 0.917203i \(-0.630442\pi\)
0.595110 + 0.803644i \(0.297108\pi\)
\(942\) −1.64746 + 1.64746i −0.0536771 + 0.0536771i
\(943\) 29.9310 29.9310i 0.974688 0.974688i
\(944\) −1.29825 2.24864i −0.0422545 0.0731869i
\(945\) 0 0
\(946\) 3.77023 2.17675i 0.122581 0.0707721i
\(947\) 4.33802 + 16.1897i 0.140967 + 0.526095i 0.999902 + 0.0140106i \(0.00445985\pi\)
−0.858935 + 0.512084i \(0.828873\pi\)
\(948\) −0.0226968 + 0.00608160i −0.000737159 + 0.000197521i
\(949\) −10.0149 −0.325096
\(950\) 0 0
\(951\) 4.07264 0.132064
\(952\) −6.58153 + 1.76352i −0.213309 + 0.0571559i
\(953\) 6.50740 + 24.2860i 0.210795 + 0.786699i 0.987604 + 0.156963i \(0.0501704\pi\)
−0.776809 + 0.629736i \(0.783163\pi\)
\(954\) −15.7678 + 9.10352i −0.510500 + 0.294737i
\(955\) 0 0
\(956\) −5.88015 10.1847i −0.190178 0.329397i
\(957\) −11.8667 + 11.8667i −0.383596 + 0.383596i
\(958\) −7.06609 + 7.06609i −0.228295 + 0.228295i
\(959\) 11.2005 6.46662i 0.361683 0.208818i
\(960\) 0 0
\(961\) −70.9395 −2.28837
\(962\) −8.64636 8.64636i −0.278770 0.278770i
\(963\) 16.8276 + 4.50894i 0.542262 + 0.145299i
\(964\) 6.65790 11.5318i 0.214436 0.371415i
\(965\) 0 0
\(966\) 2.70909 4.69228i 0.0871636 0.150972i
\(967\) −6.83495 25.5084i −0.219797 0.820295i −0.984422 0.175819i \(-0.943743\pi\)
0.764625 0.644475i \(-0.222924\pi\)
\(968\) 3.74497 3.74497i 0.120368 0.120368i
\(969\) −5.16158 + 13.9725i −0.165814 + 0.448862i
\(970\) 0 0
\(971\) −6.03518 3.48441i −0.193678 0.111820i 0.400025 0.916504i \(-0.369001\pi\)
−0.593703 + 0.804684i \(0.702335\pi\)
\(972\) 14.6316 3.92053i 0.469309 0.125751i
\(973\) 2.01260 7.51114i 0.0645211 0.240796i
\(974\) −4.84298 2.79609i −0.155179 0.0895926i
\(975\) 0 0
\(976\) −0.620411 −0.0198589
\(977\) −8.36612 8.36612i −0.267656 0.267656i 0.560499 0.828155i \(-0.310609\pi\)
−0.828155 + 0.560499i \(0.810609\pi\)
\(978\) −3.43861 + 12.8331i −0.109955 + 0.410356i
\(979\) 2.65343 + 4.59587i 0.0848039 + 0.146885i
\(980\) 0 0
\(981\) 22.8909i 0.730850i
\(982\) −7.90969 + 29.5194i −0.252408 + 0.942000i
\(983\) 1.60946 + 6.00658i 0.0513338 + 0.191580i 0.986831 0.161753i \(-0.0517148\pi\)
−0.935497 + 0.353333i \(0.885048\pi\)
\(984\) −2.89867 5.02064i −0.0924061 0.160052i
\(985\) 0 0
\(986\) −23.2051 + 40.1923i −0.739000 + 1.27999i
\(987\) −0.263750 0.263750i −0.00839524 0.00839524i
\(988\) −7.56862 + 10.6996i −0.240790 + 0.340399i
\(989\) 9.57362i 0.304423i
\(990\) 0 0
\(991\) 45.1901 + 26.0905i 1.43551 + 0.828793i 0.997533 0.0701930i \(-0.0223615\pi\)
0.437978 + 0.898986i \(0.355695\pi\)
\(992\) 9.75248 + 2.61317i 0.309641 + 0.0829682i
\(993\) −9.36659 + 2.50977i −0.297240 + 0.0796451i
\(994\) −7.72923 + 4.46247i −0.245156 + 0.141541i
\(995\) 0 0
\(996\) 12.2087i 0.386846i
\(997\) −27.0771 7.25528i −0.857539 0.229777i −0.196847 0.980434i \(-0.563070\pi\)
−0.660692 + 0.750657i \(0.729737\pi\)
\(998\) −25.9461 6.95223i −0.821308 0.220069i
\(999\) 16.0383i 0.507428i
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 950.2.q.g.293.2 32
5.2 odd 4 inner 950.2.q.g.407.2 32
5.3 odd 4 190.2.m.b.27.7 32
5.4 even 2 190.2.m.b.103.7 yes 32
19.12 odd 6 inner 950.2.q.g.943.2 32
95.12 even 12 inner 950.2.q.g.107.2 32
95.69 odd 6 190.2.m.b.183.7 yes 32
95.88 even 12 190.2.m.b.107.7 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.m.b.27.7 32 5.3 odd 4
190.2.m.b.103.7 yes 32 5.4 even 2
190.2.m.b.107.7 yes 32 95.88 even 12
190.2.m.b.183.7 yes 32 95.69 odd 6
950.2.q.g.107.2 32 95.12 even 12 inner
950.2.q.g.293.2 32 1.1 even 1 trivial
950.2.q.g.407.2 32 5.2 odd 4 inner
950.2.q.g.943.2 32 19.12 odd 6 inner