Properties

Label 187.2.m.a.10.10
Level $187$
Weight $2$
Character 187.10
Analytic conductor $1.493$
Analytic rank $0$
Dimension $128$
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] = [187,2,Mod(10,187)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(187, base_ring=CyclotomicField(16))
 
chi = DirichletCharacter(H, H._module([8, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("187.10");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 187 = 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 187.m (of order \(16\), degree \(8\), 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: \(1.49320251780\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(16\) over \(\Q(\zeta_{16})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 10.10
Character \(\chi\) \(=\) 187.10
Dual form 187.2.m.a.131.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.821699 + 0.340359i) q^{2} +(-1.10085 - 0.735567i) q^{3} +(-0.854868 - 0.854868i) q^{4} +(-1.20971 + 0.240627i) q^{5} +(-0.654214 - 0.979100i) q^{6} +(0.644166 - 3.23844i) q^{7} +(-1.09220 - 2.63681i) q^{8} +(-0.477230 - 1.15214i) q^{9} +O(q^{10})\) \(q+(0.821699 + 0.340359i) q^{2} +(-1.10085 - 0.735567i) q^{3} +(-0.854868 - 0.854868i) q^{4} +(-1.20971 + 0.240627i) q^{5} +(-0.654214 - 0.979100i) q^{6} +(0.644166 - 3.23844i) q^{7} +(-1.09220 - 2.63681i) q^{8} +(-0.477230 - 1.15214i) q^{9} +(-1.07592 - 0.214014i) q^{10} +(1.65273 + 2.87549i) q^{11} +(0.312272 + 1.56990i) q^{12} +(-1.63055 - 1.63055i) q^{13} +(1.63154 - 2.44178i) q^{14} +(1.50872 + 0.624931i) q^{15} -0.120470i q^{16} +(3.82367 - 1.54259i) q^{17} -1.10914i q^{18} +(0.142777 + 0.0591403i) q^{19} +(1.23985 + 0.828442i) q^{20} +(-3.09122 + 3.09122i) q^{21} +(0.379351 + 2.92532i) q^{22} +(-3.92070 + 2.61973i) q^{23} +(-0.737194 + 3.70612i) q^{24} +(-3.21389 + 1.33124i) q^{25} +(-0.784847 - 1.89479i) q^{26} +(-1.09700 + 5.51500i) q^{27} +(-3.31912 + 2.21776i) q^{28} +(10.4724 - 2.08309i) q^{29} +(1.02701 + 1.02701i) q^{30} +(4.58202 - 6.85748i) q^{31} +(-2.14340 + 5.17462i) q^{32} +(0.295700 - 4.38119i) q^{33} +(3.66694 + 0.0338745i) q^{34} +4.07260i q^{35} +(-0.576955 + 1.39289i) q^{36} +(3.24498 + 2.16822i) q^{37} +(0.0971910 + 0.0971910i) q^{38} +(0.595616 + 2.99437i) q^{39} +(1.95574 + 2.92697i) q^{40} +(1.14921 - 5.77744i) q^{41} +(-3.59218 + 1.48793i) q^{42} +(-2.89603 + 1.19958i) q^{43} +(1.04530 - 3.87104i) q^{44} +(0.854548 + 1.27892i) q^{45} +(-4.11329 + 0.818184i) q^{46} +(1.61330 - 1.61330i) q^{47} +(-0.0886138 + 0.132620i) q^{48} +(-3.60541 - 1.49341i) q^{49} -3.09395 q^{50} +(-5.34397 - 1.11440i) q^{51} +2.78780i q^{52} +(1.53381 - 3.70294i) q^{53} +(-2.77849 + 4.15830i) q^{54} +(-2.69126 - 3.08083i) q^{55} +(-9.24270 + 1.83849i) q^{56} +(-0.113675 - 0.170127i) q^{57} +(9.31417 + 1.85270i) q^{58} +(-8.26728 + 3.42442i) q^{59} +(-0.755520 - 1.82399i) q^{60} +(11.0781 + 2.20357i) q^{61} +(6.09905 - 4.07525i) q^{62} +(-4.03854 + 0.803316i) q^{63} +(-3.69283 + 3.69283i) q^{64} +(2.36485 + 1.58014i) q^{65} +(1.73416 - 3.49938i) q^{66} -8.67662i q^{67} +(-4.58744 - 1.95002i) q^{68} +6.24311 q^{69} +(-1.38614 + 3.34645i) q^{70} +(8.51952 + 5.69256i) q^{71} +(-2.51673 + 2.51673i) q^{72} +(-2.45632 - 12.3487i) q^{73} +(1.92842 + 2.88608i) q^{74} +(4.51724 + 0.898534i) q^{75} +(-0.0714986 - 0.172613i) q^{76} +(10.3768 - 3.49999i) q^{77} +(-0.529742 + 2.66319i) q^{78} +(-11.6242 + 7.76701i) q^{79} +(0.0289884 + 0.145734i) q^{80} +(2.61887 - 2.61887i) q^{81} +(2.91071 - 4.35618i) q^{82} +(4.49667 - 10.8559i) q^{83} +5.28518 q^{84} +(-4.25435 + 2.78617i) q^{85} -2.78795 q^{86} +(-13.0608 - 5.40998i) q^{87} +(5.77700 - 7.49856i) q^{88} +(-1.93717 - 1.93717i) q^{89} +(0.266889 + 1.34174i) q^{90} +(-6.33077 + 4.23009i) q^{91} +(5.59121 + 1.11216i) q^{92} +(-10.0883 + 4.17870i) q^{93} +(1.87475 - 0.776546i) q^{94} +(-0.186950 - 0.0371868i) q^{95} +(6.16585 - 4.11989i) q^{96} +(2.36816 + 11.9056i) q^{97} +(-2.45427 - 2.45427i) q^{98} +(2.52423 - 3.27645i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 128 q - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{9} - 64 q^{12} + 16 q^{14} - 16 q^{15} - 16 q^{20} + 8 q^{22} - 32 q^{23} + 16 q^{26} + 32 q^{27} - 80 q^{31} - 16 q^{34} + 16 q^{36} + 16 q^{37} + 80 q^{38} - 112 q^{42} - 72 q^{44} - 16 q^{45} - 16 q^{47} + 32 q^{48} + 48 q^{49} - 16 q^{53} - 8 q^{55} - 16 q^{56} - 128 q^{58} + 48 q^{59} + 112 q^{60} + 48 q^{64} + 72 q^{66} - 192 q^{69} + 128 q^{70} - 16 q^{71} + 48 q^{75} + 8 q^{77} - 16 q^{78} + 112 q^{80} - 16 q^{82} + 32 q^{86} - 168 q^{88} - 16 q^{89} + 144 q^{91} - 176 q^{92} + 48 q^{93} + 48 q^{97} - 112 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/187\mathbb{Z}\right)^\times\).

\(n\) \(35\) \(122\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{16}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.821699 + 0.340359i 0.581029 + 0.240670i 0.653786 0.756680i \(-0.273180\pi\)
−0.0727567 + 0.997350i \(0.523180\pi\)
\(3\) −1.10085 0.735567i −0.635578 0.424680i 0.195602 0.980683i \(-0.437334\pi\)
−0.831180 + 0.556004i \(0.812334\pi\)
\(4\) −0.854868 0.854868i −0.427434 0.427434i
\(5\) −1.20971 + 0.240627i −0.541001 + 0.107612i −0.458024 0.888940i \(-0.651443\pi\)
−0.0829766 + 0.996551i \(0.526443\pi\)
\(6\) −0.654214 0.979100i −0.267082 0.399716i
\(7\) 0.644166 3.23844i 0.243472 1.22402i −0.644675 0.764457i \(-0.723007\pi\)
0.888147 0.459560i \(-0.151993\pi\)
\(8\) −1.09220 2.63681i −0.386151 0.932251i
\(9\) −0.477230 1.15214i −0.159077 0.384045i
\(10\) −1.07592 0.214014i −0.340236 0.0676772i
\(11\) 1.65273 + 2.87549i 0.498318 + 0.866994i
\(12\) 0.312272 + 1.56990i 0.0901451 + 0.453190i
\(13\) −1.63055 1.63055i −0.452232 0.452232i 0.443863 0.896095i \(-0.353608\pi\)
−0.896095 + 0.443863i \(0.853608\pi\)
\(14\) 1.63154 2.44178i 0.436049 0.652593i
\(15\) 1.50872 + 0.624931i 0.389549 + 0.161356i
\(16\) 0.120470i 0.0301175i
\(17\) 3.82367 1.54259i 0.927375 0.374133i
\(18\) 1.10914i 0.261427i
\(19\) 0.142777 + 0.0591403i 0.0327553 + 0.0135677i 0.399001 0.916951i \(-0.369357\pi\)
−0.366246 + 0.930518i \(0.619357\pi\)
\(20\) 1.23985 + 0.828442i 0.277239 + 0.185245i
\(21\) −3.09122 + 3.09122i −0.674560 + 0.674560i
\(22\) 0.379351 + 2.92532i 0.0808778 + 0.623679i
\(23\) −3.92070 + 2.61973i −0.817523 + 0.546252i −0.892560 0.450929i \(-0.851093\pi\)
0.0750364 + 0.997181i \(0.476093\pi\)
\(24\) −0.737194 + 3.70612i −0.150479 + 0.756509i
\(25\) −3.21389 + 1.33124i −0.642778 + 0.266247i
\(26\) −0.784847 1.89479i −0.153921 0.371599i
\(27\) −1.09700 + 5.51500i −0.211118 + 1.06136i
\(28\) −3.31912 + 2.21776i −0.627254 + 0.419118i
\(29\) 10.4724 2.08309i 1.94468 0.386820i 0.946789 0.321854i \(-0.104306\pi\)
0.997887 0.0649660i \(-0.0206939\pi\)
\(30\) 1.02701 + 1.02701i 0.187506 + 0.187506i
\(31\) 4.58202 6.85748i 0.822955 1.23164i −0.147188 0.989108i \(-0.547022\pi\)
0.970144 0.242531i \(-0.0779776\pi\)
\(32\) −2.14340 + 5.17462i −0.378903 + 0.914752i
\(33\) 0.295700 4.38119i 0.0514747 0.762668i
\(34\) 3.66694 + 0.0338745i 0.628875 + 0.00580943i
\(35\) 4.07260i 0.688394i
\(36\) −0.576955 + 1.39289i −0.0961592 + 0.232149i
\(37\) 3.24498 + 2.16822i 0.533471 + 0.356454i 0.792942 0.609297i \(-0.208548\pi\)
−0.259471 + 0.965751i \(0.583548\pi\)
\(38\) 0.0971910 + 0.0971910i 0.0157665 + 0.0157665i
\(39\) 0.595616 + 2.99437i 0.0953750 + 0.479482i
\(40\) 1.95574 + 2.92697i 0.309229 + 0.462794i
\(41\) 1.14921 5.77744i 0.179476 0.902285i −0.781130 0.624369i \(-0.785356\pi\)
0.960605 0.277916i \(-0.0896438\pi\)
\(42\) −3.59218 + 1.48793i −0.554286 + 0.229593i
\(43\) −2.89603 + 1.19958i −0.441641 + 0.182933i −0.592412 0.805635i \(-0.701824\pi\)
0.150772 + 0.988569i \(0.451824\pi\)
\(44\) 1.04530 3.87104i 0.157585 0.583581i
\(45\) 0.854548 + 1.27892i 0.127388 + 0.190650i
\(46\) −4.11329 + 0.818184i −0.606471 + 0.120635i
\(47\) 1.61330 1.61330i 0.235324 0.235324i −0.579587 0.814911i \(-0.696786\pi\)
0.814911 + 0.579587i \(0.196786\pi\)
\(48\) −0.0886138 + 0.132620i −0.0127903 + 0.0191420i
\(49\) −3.60541 1.49341i −0.515058 0.213344i
\(50\) −3.09395 −0.437551
\(51\) −5.34397 1.11440i −0.748306 0.156047i
\(52\) 2.78780i 0.386599i
\(53\) 1.53381 3.70294i 0.210684 0.508637i −0.782844 0.622218i \(-0.786232\pi\)
0.993529 + 0.113580i \(0.0362319\pi\)
\(54\) −2.77849 + 4.15830i −0.378104 + 0.565873i
\(55\) −2.69126 3.08083i −0.362889 0.415420i
\(56\) −9.24270 + 1.83849i −1.23511 + 0.245678i
\(57\) −0.113675 0.170127i −0.0150566 0.0225339i
\(58\) 9.31417 + 1.85270i 1.22301 + 0.243272i
\(59\) −8.26728 + 3.42442i −1.07631 + 0.445822i −0.849213 0.528051i \(-0.822923\pi\)
−0.227096 + 0.973872i \(0.572923\pi\)
\(60\) −0.755520 1.82399i −0.0975372 0.235476i
\(61\) 11.0781 + 2.20357i 1.41841 + 0.282139i 0.843961 0.536404i \(-0.180218\pi\)
0.574446 + 0.818543i \(0.305218\pi\)
\(62\) 6.09905 4.07525i 0.774580 0.517558i
\(63\) −4.03854 + 0.803316i −0.508809 + 0.101208i
\(64\) −3.69283 + 3.69283i −0.461604 + 0.461604i
\(65\) 2.36485 + 1.58014i 0.293323 + 0.195992i
\(66\) 1.73416 3.49938i 0.213460 0.430744i
\(67\) 8.67662i 1.06002i −0.847992 0.530009i \(-0.822189\pi\)
0.847992 0.530009i \(-0.177811\pi\)
\(68\) −4.58744 1.95002i −0.556309 0.236475i
\(69\) 6.24311 0.751582
\(70\) −1.38614 + 3.34645i −0.165676 + 0.399977i
\(71\) 8.51952 + 5.69256i 1.01108 + 0.675583i 0.946625 0.322338i \(-0.104469\pi\)
0.0644562 + 0.997921i \(0.479469\pi\)
\(72\) −2.51673 + 2.51673i −0.296599 + 0.296599i
\(73\) −2.45632 12.3487i −0.287490 1.44531i −0.806851 0.590755i \(-0.798830\pi\)
0.519361 0.854555i \(-0.326170\pi\)
\(74\) 1.92842 + 2.88608i 0.224174 + 0.335500i
\(75\) 4.51724 + 0.898534i 0.521605 + 0.103754i
\(76\) −0.0714986 0.172613i −0.00820145 0.0198000i
\(77\) 10.3768 3.49999i 1.18254 0.398861i
\(78\) −0.529742 + 2.66319i −0.0599815 + 0.301547i
\(79\) −11.6242 + 7.76701i −1.30782 + 0.873857i −0.997060 0.0766310i \(-0.975584\pi\)
−0.310760 + 0.950488i \(0.600584\pi\)
\(80\) 0.0289884 + 0.145734i 0.00324100 + 0.0162936i
\(81\) 2.61887 2.61887i 0.290986 0.290986i
\(82\) 2.91071 4.35618i 0.321434 0.481060i
\(83\) 4.49667 10.8559i 0.493574 1.19159i −0.459315 0.888273i \(-0.651905\pi\)
0.952889 0.303319i \(-0.0980949\pi\)
\(84\) 5.28518 0.576660
\(85\) −4.25435 + 2.78617i −0.461450 + 0.302203i
\(86\) −2.78795 −0.300633
\(87\) −13.0608 5.40998i −1.40027 0.580010i
\(88\) 5.77700 7.49856i 0.615830 0.799349i
\(89\) −1.93717 1.93717i −0.205340 0.205340i 0.596943 0.802283i \(-0.296382\pi\)
−0.802283 + 0.596943i \(0.796382\pi\)
\(90\) 0.266889 + 1.34174i 0.0281326 + 0.141432i
\(91\) −6.33077 + 4.23009i −0.663645 + 0.443433i
\(92\) 5.59121 + 1.11216i 0.582924 + 0.115951i
\(93\) −10.0883 + 4.17870i −1.04610 + 0.433311i
\(94\) 1.87475 0.776546i 0.193365 0.0800946i
\(95\) −0.186950 0.0371868i −0.0191807 0.00381528i
\(96\) 6.16585 4.11989i 0.629299 0.420484i
\(97\) 2.36816 + 11.9056i 0.240451 + 1.20883i 0.892640 + 0.450771i \(0.148851\pi\)
−0.652189 + 0.758056i \(0.726149\pi\)
\(98\) −2.45427 2.45427i −0.247918 0.247918i
\(99\) 2.52423 3.27645i 0.253694 0.329295i
\(100\) 3.88548 + 1.60942i 0.388548 + 0.160942i
\(101\) 6.27550 0.624435 0.312218 0.950011i \(-0.398928\pi\)
0.312218 + 0.950011i \(0.398928\pi\)
\(102\) −4.01184 2.73457i −0.397232 0.270763i
\(103\) −2.34754 −0.231310 −0.115655 0.993289i \(-0.536897\pi\)
−0.115655 + 0.993289i \(0.536897\pi\)
\(104\) −2.51855 + 6.08031i −0.246964 + 0.596224i
\(105\) 2.99567 4.48333i 0.292347 0.437528i
\(106\) 2.52066 2.52066i 0.244828 0.244828i
\(107\) 1.11784 + 5.61975i 0.108065 + 0.543281i 0.996450 + 0.0841822i \(0.0268278\pi\)
−0.888385 + 0.459099i \(0.848172\pi\)
\(108\) 5.65239 3.77681i 0.543902 0.363423i
\(109\) −1.45208 + 7.30009i −0.139084 + 0.699222i 0.846816 + 0.531886i \(0.178516\pi\)
−0.985900 + 0.167336i \(0.946484\pi\)
\(110\) −1.16282 3.44751i −0.110870 0.328708i
\(111\) −1.97737 4.77379i −0.187684 0.453108i
\(112\) −0.390136 0.0776028i −0.0368644 0.00733278i
\(113\) −1.44349 2.16033i −0.135792 0.203227i 0.757341 0.653019i \(-0.226498\pi\)
−0.893133 + 0.449792i \(0.851498\pi\)
\(114\) −0.0355026 0.178484i −0.00332512 0.0167165i
\(115\) 4.11255 4.11255i 0.383498 0.383498i
\(116\) −10.7333 7.17176i −0.996561 0.665881i
\(117\) −1.10046 + 2.65676i −0.101738 + 0.245617i
\(118\) −7.95876 −0.732663
\(119\) −2.53251 13.3764i −0.232155 1.22621i
\(120\) 4.66074i 0.425465i
\(121\) −5.53694 + 9.50486i −0.503358 + 0.864078i
\(122\) 8.35287 + 5.58121i 0.756233 + 0.505299i
\(123\) −5.51480 + 5.51480i −0.497253 + 0.497253i
\(124\) −9.77926 + 1.94522i −0.878204 + 0.174686i
\(125\) 8.69529 5.81001i 0.777730 0.519663i
\(126\) −3.59188 0.714470i −0.319991 0.0636501i
\(127\) −3.34365 8.07229i −0.296701 0.716300i −0.999985 0.00539138i \(-0.998284\pi\)
0.703284 0.710909i \(-0.251716\pi\)
\(128\) 6.05796 2.50929i 0.535453 0.221792i
\(129\) 4.07047 + 0.809667i 0.358385 + 0.0712872i
\(130\) 1.40538 + 2.10330i 0.123260 + 0.184471i
\(131\) −1.50320 + 0.299005i −0.131335 + 0.0261242i −0.260320 0.965522i \(-0.583828\pi\)
0.128985 + 0.991647i \(0.458828\pi\)
\(132\) −3.99813 + 3.49256i −0.347992 + 0.303988i
\(133\) 0.283495 0.424280i 0.0245821 0.0367897i
\(134\) 2.95317 7.12958i 0.255115 0.615902i
\(135\) 6.93555i 0.596917i
\(136\) −8.24372 8.39745i −0.706893 0.720075i
\(137\) 9.97809 0.852486 0.426243 0.904609i \(-0.359837\pi\)
0.426243 + 0.904609i \(0.359837\pi\)
\(138\) 5.12996 + 2.12490i 0.436691 + 0.180883i
\(139\) −2.04787 + 3.06486i −0.173698 + 0.259958i −0.908096 0.418761i \(-0.862465\pi\)
0.734398 + 0.678719i \(0.237465\pi\)
\(140\) 3.48153 3.48153i 0.294243 0.294243i
\(141\) −2.96269 + 0.589316i −0.249504 + 0.0496294i
\(142\) 5.06297 + 7.57727i 0.424875 + 0.635870i
\(143\) 1.99377 7.38348i 0.166727 0.617438i
\(144\) −0.138798 + 0.0574920i −0.0115665 + 0.00479100i
\(145\) −12.1674 + 5.03989i −1.01045 + 0.418540i
\(146\) 2.18465 10.9830i 0.180803 0.908957i
\(147\) 2.87052 + 4.29604i 0.236757 + 0.354332i
\(148\) −0.920481 4.62757i −0.0756631 0.380384i
\(149\) 13.6015 + 13.6015i 1.11428 + 1.11428i 0.992565 + 0.121712i \(0.0388386\pi\)
0.121712 + 0.992565i \(0.461161\pi\)
\(150\) 3.40599 + 2.27581i 0.278098 + 0.185819i
\(151\) −6.08169 + 14.6825i −0.494921 + 1.19484i 0.457267 + 0.889330i \(0.348828\pi\)
−0.952187 + 0.305515i \(0.901172\pi\)
\(152\) 0.441069i 0.0357754i
\(153\) −3.60204 3.66921i −0.291208 0.296638i
\(154\) 9.71783 + 0.655885i 0.783085 + 0.0528527i
\(155\) −3.89284 + 9.39815i −0.312681 + 0.754878i
\(156\) 2.05061 3.06896i 0.164181 0.245714i
\(157\) −8.01536 8.01536i −0.639695 0.639695i 0.310785 0.950480i \(-0.399408\pi\)
−0.950480 + 0.310785i \(0.899408\pi\)
\(158\) −12.1951 + 2.42576i −0.970193 + 0.192983i
\(159\) −4.41225 + 2.94817i −0.349914 + 0.233805i
\(160\) 1.34775 6.77557i 0.106549 0.535656i
\(161\) 5.95826 + 14.3845i 0.469577 + 1.13366i
\(162\) 3.04328 1.26057i 0.239103 0.0990396i
\(163\) −2.79301 + 14.0414i −0.218766 + 1.09981i 0.702741 + 0.711446i \(0.251959\pi\)
−0.921506 + 0.388363i \(0.873041\pi\)
\(164\) −5.92137 + 3.95653i −0.462381 + 0.308953i
\(165\) 0.696523 + 5.37115i 0.0542242 + 0.418143i
\(166\) 7.38983 7.38983i 0.573562 0.573562i
\(167\) −5.35109 3.57548i −0.414080 0.276679i 0.331031 0.943620i \(-0.392603\pi\)
−0.745111 + 0.666941i \(0.767603\pi\)
\(168\) 11.5272 + 4.77472i 0.889342 + 0.368378i
\(169\) 7.68264i 0.590973i
\(170\) −4.44410 + 0.841386i −0.340847 + 0.0645314i
\(171\) 0.192722i 0.0147378i
\(172\) 3.50120 + 1.45025i 0.266964 + 0.110580i
\(173\) −12.2307 + 18.3046i −0.929885 + 1.39167i −0.00979980 + 0.999952i \(0.503119\pi\)
−0.920085 + 0.391719i \(0.871881\pi\)
\(174\) −8.89075 8.89075i −0.674006 0.674006i
\(175\) 2.24085 + 11.2655i 0.169393 + 0.851595i
\(176\) 0.346411 0.199105i 0.0261117 0.0150081i
\(177\) 11.6200 + 2.31135i 0.873410 + 0.173732i
\(178\) −0.932440 2.25111i −0.0698893 0.168728i
\(179\) 4.04519 + 9.76595i 0.302352 + 0.729941i 0.999910 + 0.0134135i \(0.00426977\pi\)
−0.697558 + 0.716528i \(0.745730\pi\)
\(180\) 0.362783 1.82383i 0.0270403 0.135941i
\(181\) −1.91603 2.86754i −0.142417 0.213142i 0.753403 0.657559i \(-0.228411\pi\)
−0.895820 + 0.444417i \(0.853411\pi\)
\(182\) −6.64174 + 1.32112i −0.492318 + 0.0979282i
\(183\) −10.5745 10.5745i −0.781690 0.781690i
\(184\) 11.1899 + 7.47686i 0.824931 + 0.551202i
\(185\) −4.44723 1.84210i −0.326967 0.135434i
\(186\) −9.71178 −0.712102
\(187\) 10.7552 + 8.44544i 0.786499 + 0.617592i
\(188\) −2.75831 −0.201171
\(189\) 17.1534 + 7.10516i 1.24772 + 0.516824i
\(190\) −0.140960 0.0941866i −0.0102263 0.00683301i
\(191\) 12.1017 + 12.1017i 0.875650 + 0.875650i 0.993081 0.117431i \(-0.0374660\pi\)
−0.117431 + 0.993081i \(0.537466\pi\)
\(192\) 6.78158 1.34894i 0.489419 0.0973514i
\(193\) 0.108594 + 0.162522i 0.00781674 + 0.0116986i 0.835357 0.549707i \(-0.185261\pi\)
−0.827541 + 0.561406i \(0.810261\pi\)
\(194\) −2.10625 + 10.5888i −0.151220 + 0.760233i
\(195\) −1.44105 3.47901i −0.103196 0.249137i
\(196\) 1.80548 + 4.35881i 0.128963 + 0.311344i
\(197\) −3.06068 0.608807i −0.218064 0.0433757i 0.0848490 0.996394i \(-0.472959\pi\)
−0.302913 + 0.953018i \(0.597959\pi\)
\(198\) 3.18932 1.83311i 0.226655 0.130274i
\(199\) 2.58233 + 12.9823i 0.183057 + 0.920288i 0.957673 + 0.287857i \(0.0929427\pi\)
−0.774617 + 0.632431i \(0.782057\pi\)
\(200\) 7.02042 + 7.02042i 0.496419 + 0.496419i
\(201\) −6.38224 + 9.55169i −0.450168 + 0.673724i
\(202\) 5.15657 + 2.13592i 0.362815 + 0.150283i
\(203\) 35.2561i 2.47450i
\(204\) 3.61573 + 5.52105i 0.253152 + 0.386551i
\(205\) 7.26559i 0.507451i
\(206\) −1.92897 0.799005i −0.134398 0.0556693i
\(207\) 4.88937 + 3.26697i 0.339834 + 0.227070i
\(208\) −0.196432 + 0.196432i −0.0136201 + 0.0136201i
\(209\) 0.0659154 + 0.508298i 0.00455946 + 0.0351597i
\(210\) 3.98748 2.66435i 0.275162 0.183858i
\(211\) 0.540621 2.71788i 0.0372179 0.187107i −0.957704 0.287754i \(-0.907091\pi\)
0.994922 + 0.100647i \(0.0320914\pi\)
\(212\) −4.47672 + 1.85432i −0.307463 + 0.127355i
\(213\) −5.19148 12.5334i −0.355715 0.858771i
\(214\) −0.994206 + 4.99821i −0.0679625 + 0.341671i
\(215\) 3.21472 2.14801i 0.219242 0.146493i
\(216\) 15.7401 3.13091i 1.07098 0.213031i
\(217\) −19.2560 19.2560i −1.30718 1.30718i
\(218\) −3.67782 + 5.50425i −0.249094 + 0.372795i
\(219\) −6.37927 + 15.4009i −0.431071 + 1.04070i
\(220\) −0.333035 + 4.93438i −0.0224532 + 0.332676i
\(221\) −8.74992 3.71940i −0.588583 0.250194i
\(222\) 4.59564i 0.308439i
\(223\) −8.02853 + 19.3826i −0.537630 + 1.29795i 0.388742 + 0.921347i \(0.372910\pi\)
−0.926373 + 0.376608i \(0.877090\pi\)
\(224\) 15.3770 + 10.2746i 1.02742 + 0.686500i
\(225\) 3.06753 + 3.06753i 0.204502 + 0.204502i
\(226\) −0.450825 2.26645i −0.0299884 0.150762i
\(227\) −3.88526 5.81470i −0.257873 0.385935i 0.679831 0.733369i \(-0.262053\pi\)
−0.937704 + 0.347434i \(0.887053\pi\)
\(228\) −0.0482588 + 0.242613i −0.00319602 + 0.0160675i
\(229\) 0.503243 0.208450i 0.0332552 0.0137748i −0.365994 0.930617i \(-0.619271\pi\)
0.399249 + 0.916843i \(0.369271\pi\)
\(230\) 4.77903 1.97954i 0.315120 0.130527i
\(231\) −13.9978 3.77982i −0.920986 0.248694i
\(232\) −16.9307 25.3385i −1.11155 1.66356i
\(233\) 2.16472 0.430589i 0.141815 0.0282088i −0.123672 0.992323i \(-0.539467\pi\)
0.265488 + 0.964114i \(0.414467\pi\)
\(234\) −1.80850 + 1.80850i −0.118225 + 0.118225i
\(235\) −1.56343 + 2.33983i −0.101987 + 0.152634i
\(236\) 9.99486 + 4.14001i 0.650610 + 0.269492i
\(237\) 18.5097 1.20233
\(238\) 2.47182 11.8533i 0.160224 0.768339i
\(239\) 7.40380i 0.478912i −0.970907 0.239456i \(-0.923031\pi\)
0.970907 0.239456i \(-0.0769691\pi\)
\(240\) 0.0752855 0.181755i 0.00485966 0.0117322i
\(241\) 15.7787 23.6145i 1.01639 1.52114i 0.172229 0.985057i \(-0.444903\pi\)
0.844165 0.536084i \(-0.180097\pi\)
\(242\) −7.78476 + 5.92559i −0.500423 + 0.380911i
\(243\) 11.7357 2.33437i 0.752843 0.149750i
\(244\) −7.58656 11.3541i −0.485680 0.726871i
\(245\) 4.72087 + 0.939039i 0.301605 + 0.0599930i
\(246\) −6.40852 + 2.65450i −0.408593 + 0.169245i
\(247\) −0.136374 0.329236i −0.00867726 0.0209488i
\(248\) −23.0863 4.59215i −1.46598 0.291602i
\(249\) −12.9354 + 8.64318i −0.819750 + 0.547739i
\(250\) 9.12240 1.81456i 0.576951 0.114763i
\(251\) −10.4073 + 10.4073i −0.656900 + 0.656900i −0.954645 0.297745i \(-0.903765\pi\)
0.297745 + 0.954645i \(0.403765\pi\)
\(252\) 4.13915 + 2.76569i 0.260742 + 0.174222i
\(253\) −14.0129 6.94424i −0.880984 0.436581i
\(254\) 7.77104i 0.487598i
\(255\) 6.73284 + 0.0621967i 0.421627 + 0.00389491i
\(256\) 16.2768 1.01730
\(257\) 4.74982 11.4671i 0.296286 0.715297i −0.703703 0.710494i \(-0.748471\pi\)
0.999988 0.00480222i \(-0.00152860\pi\)
\(258\) 3.06913 + 2.05073i 0.191076 + 0.127673i
\(259\) 9.11197 9.11197i 0.566190 0.566190i
\(260\) −0.670821 3.37244i −0.0416025 0.209150i
\(261\) −7.39775 11.0715i −0.457909 0.685310i
\(262\) −1.33695 0.265936i −0.0825970 0.0164296i
\(263\) 3.60966 + 8.71449i 0.222581 + 0.537359i 0.995239 0.0974642i \(-0.0310731\pi\)
−0.772658 + 0.634823i \(0.781073\pi\)
\(264\) −11.8753 + 4.00544i −0.730875 + 0.246518i
\(265\) −0.964441 + 4.84857i −0.0592451 + 0.297845i
\(266\) 0.377355 0.252140i 0.0231371 0.0154597i
\(267\) 0.707624 + 3.55747i 0.0433059 + 0.217713i
\(268\) −7.41737 + 7.41737i −0.453088 + 0.453088i
\(269\) 2.24398 3.35836i 0.136818 0.204763i −0.756733 0.653724i \(-0.773206\pi\)
0.893551 + 0.448961i \(0.148206\pi\)
\(270\) 2.36058 5.69894i 0.143660 0.346826i
\(271\) −19.0447 −1.15688 −0.578441 0.815724i \(-0.696339\pi\)
−0.578441 + 0.815724i \(0.696339\pi\)
\(272\) −0.185836 0.460638i −0.0112680 0.0279303i
\(273\) 10.0808 0.610115
\(274\) 8.19899 + 3.39613i 0.495319 + 0.205168i
\(275\) −9.13967 7.04134i −0.551143 0.424609i
\(276\) −5.33703 5.33703i −0.321252 0.321252i
\(277\) −3.06680 15.4179i −0.184266 0.926370i −0.956656 0.291220i \(-0.905939\pi\)
0.772390 0.635149i \(-0.219061\pi\)
\(278\) −2.72589 + 1.82138i −0.163488 + 0.109239i
\(279\) −10.0874 2.00651i −0.603919 0.120127i
\(280\) 10.7386 4.44809i 0.641757 0.265824i
\(281\) −17.8139 + 7.37876i −1.06269 + 0.440180i −0.844405 0.535705i \(-0.820046\pi\)
−0.218284 + 0.975885i \(0.570046\pi\)
\(282\) −2.63502 0.524139i −0.156913 0.0312120i
\(283\) 24.1529 16.1385i 1.43574 0.959331i 0.437551 0.899194i \(-0.355846\pi\)
0.998190 0.0601378i \(-0.0191540\pi\)
\(284\) −2.41668 12.1495i −0.143403 0.720937i
\(285\) 0.178452 + 0.178452i 0.0105706 + 0.0105706i
\(286\) 4.15131 5.38841i 0.245472 0.318623i
\(287\) −17.9696 7.44327i −1.06071 0.439362i
\(288\) 6.98476 0.411581
\(289\) 12.2408 11.7967i 0.720049 0.693923i
\(290\) −11.7133 −0.687828
\(291\) 6.15034 14.8482i 0.360539 0.870418i
\(292\) −8.45671 + 12.6564i −0.494891 + 0.740657i
\(293\) 11.1082 11.1082i 0.648946 0.648946i −0.303792 0.952738i \(-0.598253\pi\)
0.952738 + 0.303792i \(0.0982528\pi\)
\(294\) 0.896511 + 4.50706i 0.0522856 + 0.262857i
\(295\) 9.17705 6.13191i 0.534308 0.357013i
\(296\) 2.17302 10.9245i 0.126304 0.634974i
\(297\) −17.6714 + 5.96041i −1.02540 + 0.345858i
\(298\) 6.54695 + 15.8057i 0.379255 + 0.915601i
\(299\) 10.6645 + 2.12130i 0.616743 + 0.122678i
\(300\) −3.09351 4.62977i −0.178604 0.267300i
\(301\) 2.01923 + 10.1514i 0.116387 + 0.585114i
\(302\) −9.99464 + 9.99464i −0.575127 + 0.575127i
\(303\) −6.90840 4.61605i −0.396877 0.265185i
\(304\) 0.00712464 0.0172004i 0.000408626 0.000986510i
\(305\) −13.9316 −0.797721
\(306\) −1.71095 4.24098i −0.0978083 0.242441i
\(307\) 10.9661i 0.625871i −0.949774 0.312935i \(-0.898688\pi\)
0.949774 0.312935i \(-0.101312\pi\)
\(308\) −11.8628 5.87873i −0.675945 0.334972i
\(309\) 2.58429 + 1.72677i 0.147015 + 0.0982325i
\(310\) −6.39749 + 6.39749i −0.363353 + 0.363353i
\(311\) 2.68260 0.533603i 0.152117 0.0302579i −0.118445 0.992961i \(-0.537791\pi\)
0.270561 + 0.962703i \(0.412791\pi\)
\(312\) 7.24503 4.84097i 0.410169 0.274066i
\(313\) −1.96778 0.391416i −0.111225 0.0221241i 0.139164 0.990269i \(-0.455559\pi\)
−0.250389 + 0.968145i \(0.580559\pi\)
\(314\) −3.85812 9.31432i −0.217726 0.525637i
\(315\) 4.69218 1.94357i 0.264375 0.109508i
\(316\) 16.5769 + 3.29735i 0.932523 + 0.185490i
\(317\) 15.2798 + 22.8679i 0.858201 + 1.28439i 0.957237 + 0.289305i \(0.0934241\pi\)
−0.0990360 + 0.995084i \(0.531576\pi\)
\(318\) −4.62898 + 0.920762i −0.259580 + 0.0516338i
\(319\) 23.2980 + 26.6705i 1.30444 + 1.49326i
\(320\) 3.57867 5.35586i 0.200054 0.299402i
\(321\) 2.90312 7.00876i 0.162037 0.391191i
\(322\) 13.8477i 0.771702i
\(323\) 0.637162 + 0.00588598i 0.0354526 + 0.000327505i
\(324\) −4.47758 −0.248754
\(325\) 7.41103 + 3.06975i 0.411090 + 0.170279i
\(326\) −7.07414 + 10.5872i −0.391800 + 0.586371i
\(327\) 6.96823 6.96823i 0.385344 0.385344i
\(328\) −16.4892 + 3.27990i −0.910462 + 0.181102i
\(329\) −4.18534 6.26381i −0.230745 0.345335i
\(330\) −1.25579 + 4.65054i −0.0691288 + 0.256004i
\(331\) 14.2988 5.92275i 0.785932 0.325544i 0.0466255 0.998912i \(-0.485153\pi\)
0.739307 + 0.673369i \(0.235153\pi\)
\(332\) −13.1244 + 5.43632i −0.720297 + 0.298357i
\(333\) 0.949487 4.77340i 0.0520316 0.261580i
\(334\) −3.18004 4.75927i −0.174004 0.260415i
\(335\) 2.08783 + 10.4962i 0.114070 + 0.573471i
\(336\) 0.372400 + 0.372400i 0.0203161 + 0.0203161i
\(337\) −1.92476 1.28608i −0.104848 0.0700574i 0.502041 0.864844i \(-0.332583\pi\)
−0.606889 + 0.794787i \(0.707583\pi\)
\(338\) 2.61486 6.31282i 0.142230 0.343372i
\(339\) 3.43999i 0.186835i
\(340\) 6.01872 + 1.25510i 0.326411 + 0.0680676i
\(341\) 27.2915 + 1.84198i 1.47792 + 0.0997490i
\(342\) 0.0655948 0.158360i 0.00354696 0.00856312i
\(343\) 5.68221 8.50403i 0.306811 0.459175i
\(344\) 6.32609 + 6.32609i 0.341080 + 0.341080i
\(345\) −7.55238 + 1.50226i −0.406606 + 0.0808790i
\(346\) −16.2801 + 10.8780i −0.875224 + 0.584806i
\(347\) −2.24128 + 11.2677i −0.120318 + 0.604879i 0.872831 + 0.488023i \(0.162282\pi\)
−0.993149 + 0.116856i \(0.962718\pi\)
\(348\) 6.54047 + 15.7901i 0.350606 + 0.846438i
\(349\) 4.86403 2.01475i 0.260366 0.107847i −0.248682 0.968585i \(-0.579998\pi\)
0.509048 + 0.860738i \(0.329998\pi\)
\(350\) −1.99302 + 10.0196i −0.106531 + 0.535569i
\(351\) 10.7812 7.20375i 0.575457 0.384508i
\(352\) −18.4221 + 2.38895i −0.981899 + 0.127331i
\(353\) 9.67239 9.67239i 0.514809 0.514809i −0.401187 0.915996i \(-0.631402\pi\)
0.915996 + 0.401187i \(0.131402\pi\)
\(354\) 8.76142 + 5.85420i 0.465664 + 0.311147i
\(355\) −11.6760 4.83635i −0.619696 0.256687i
\(356\) 3.31206i 0.175539i
\(357\) −7.05132 + 16.5883i −0.373195 + 0.877946i
\(358\) 9.40149i 0.496884i
\(359\) −15.2768 6.32786i −0.806279 0.333972i −0.0588105 0.998269i \(-0.518731\pi\)
−0.747468 + 0.664298i \(0.768731\pi\)
\(360\) 2.43893 3.65011i 0.128543 0.192378i
\(361\) −13.4181 13.4181i −0.706218 0.706218i
\(362\) −0.598406 3.00839i −0.0314515 0.158118i
\(363\) 13.0868 6.39067i 0.686880 0.335423i
\(364\) 9.02814 + 1.79581i 0.473203 + 0.0941259i
\(365\) 5.94288 + 14.3474i 0.311065 + 0.750976i
\(366\) −5.08993 12.2882i −0.266055 0.642314i
\(367\) 3.36107 16.8972i 0.175446 0.882029i −0.788317 0.615270i \(-0.789047\pi\)
0.963763 0.266759i \(-0.0859529\pi\)
\(368\) 0.315599 + 0.472328i 0.0164518 + 0.0246218i
\(369\) −7.20484 + 1.43313i −0.375069 + 0.0746058i
\(370\) −3.02731 3.02731i −0.157382 0.157382i
\(371\) −11.0037 7.35245i −0.571285 0.381720i
\(372\) 12.1964 + 5.05190i 0.632352 + 0.261929i
\(373\) 22.6574 1.17316 0.586578 0.809892i \(-0.300475\pi\)
0.586578 + 0.809892i \(0.300475\pi\)
\(374\) 5.96307 + 10.6002i 0.308343 + 0.548126i
\(375\) −13.8459 −0.714999
\(376\) −6.01600 2.49191i −0.310251 0.128510i
\(377\) −20.4723 13.6792i −1.05438 0.704512i
\(378\) 11.6766 + 11.6766i 0.600580 + 0.600580i
\(379\) 23.9695 4.76782i 1.23123 0.244907i 0.463741 0.885971i \(-0.346507\pi\)
0.767487 + 0.641064i \(0.221507\pi\)
\(380\) 0.128028 + 0.191608i 0.00656771 + 0.00982927i
\(381\) −2.25684 + 11.3459i −0.115621 + 0.581268i
\(382\) 5.82505 + 14.0629i 0.298035 + 0.719521i
\(383\) 2.39429 + 5.78034i 0.122343 + 0.295361i 0.973171 0.230082i \(-0.0738995\pi\)
−0.850829 + 0.525443i \(0.823899\pi\)
\(384\) −8.51467 1.69367i −0.434513 0.0864299i
\(385\) −11.7107 + 6.73092i −0.596834 + 0.343039i
\(386\) 0.0339155 + 0.170505i 0.00172626 + 0.00867847i
\(387\) 2.76415 + 2.76415i 0.140510 + 0.140510i
\(388\) 8.15322 12.2022i 0.413917 0.619470i
\(389\) 10.3435 + 4.28441i 0.524435 + 0.217228i 0.629164 0.777273i \(-0.283397\pi\)
−0.104729 + 0.994501i \(0.533397\pi\)
\(390\) 3.34917i 0.169592i
\(391\) −10.9503 + 16.0650i −0.553780 + 0.812442i
\(392\) 11.1379i 0.562547i
\(393\) 1.87474 + 0.776544i 0.0945683 + 0.0391715i
\(394\) −2.30774 1.54199i −0.116262 0.0776841i
\(395\) 12.1930 12.1930i 0.613494 0.613494i
\(396\) −4.95881 + 0.643051i −0.249190 + 0.0323145i
\(397\) −26.2443 + 17.5358i −1.31716 + 0.880099i −0.997719 0.0675067i \(-0.978496\pi\)
−0.319442 + 0.947606i \(0.603496\pi\)
\(398\) −2.29673 + 11.5464i −0.115125 + 0.578770i
\(399\) −0.624172 + 0.258541i −0.0312477 + 0.0129432i
\(400\) 0.160374 + 0.387178i 0.00801871 + 0.0193589i
\(401\) −4.04536 + 20.3374i −0.202016 + 1.01560i 0.738086 + 0.674707i \(0.235730\pi\)
−0.940102 + 0.340894i \(0.889270\pi\)
\(402\) −8.49528 + 5.67637i −0.423706 + 0.283111i
\(403\) −18.6526 + 3.71024i −0.929153 + 0.184820i
\(404\) −5.36472 5.36472i −0.266905 0.266905i
\(405\) −2.53792 + 3.79826i −0.126110 + 0.188737i
\(406\) 11.9997 28.9700i 0.595537 1.43775i
\(407\) −0.871631 + 12.9144i −0.0432051 + 0.640143i
\(408\) 2.89824 + 15.3082i 0.143484 + 0.757867i
\(409\) 11.9701i 0.591882i −0.955206 0.295941i \(-0.904367\pi\)
0.955206 0.295941i \(-0.0956331\pi\)
\(410\) −2.47291 + 5.97013i −0.122128 + 0.294844i
\(411\) −10.9844 7.33955i −0.541821 0.362033i
\(412\) 2.00683 + 2.00683i 0.0988696 + 0.0988696i
\(413\) 5.76429 + 28.9790i 0.283642 + 1.42596i
\(414\) 2.90565 + 4.34861i 0.142805 + 0.213722i
\(415\) −2.82746 + 14.2146i −0.138794 + 0.697767i
\(416\) 11.9324 4.94255i 0.585032 0.242328i
\(417\) 4.50882 1.86761i 0.220798 0.0914574i
\(418\) −0.118841 + 0.440103i −0.00581272 + 0.0215262i
\(419\) 2.08874 + 3.12603i 0.102042 + 0.152716i 0.878977 0.476864i \(-0.158227\pi\)
−0.776935 + 0.629581i \(0.783227\pi\)
\(420\) −6.39355 + 1.27176i −0.311974 + 0.0620554i
\(421\) 14.2049 14.2049i 0.692304 0.692304i −0.270435 0.962738i \(-0.587167\pi\)
0.962738 + 0.270435i \(0.0871674\pi\)
\(422\) 1.36928 2.04928i 0.0666557 0.0997573i
\(423\) −2.62865 1.08882i −0.127810 0.0529404i
\(424\) −11.4391 −0.555534
\(425\) −10.2353 + 10.0479i −0.496484 + 0.487396i
\(426\) 12.0656i 0.584581i
\(427\) 14.2723 34.4564i 0.690685 1.66746i
\(428\) 3.84854 5.75974i 0.186026 0.278408i
\(429\) −7.62589 + 6.66158i −0.368181 + 0.321624i
\(430\) 3.37263 0.670857i 0.162643 0.0323516i
\(431\) 7.74330 + 11.5887i 0.372981 + 0.558206i 0.969717 0.244232i \(-0.0785358\pi\)
−0.596735 + 0.802438i \(0.703536\pi\)
\(432\) 0.664393 + 0.132156i 0.0319656 + 0.00635836i
\(433\) 7.24287 3.00009i 0.348070 0.144175i −0.201797 0.979427i \(-0.564678\pi\)
0.549867 + 0.835252i \(0.314678\pi\)
\(434\) −9.26868 22.3766i −0.444911 1.07411i
\(435\) 17.1017 + 3.40173i 0.819962 + 0.163101i
\(436\) 7.48195 4.99928i 0.358320 0.239422i
\(437\) −0.714719 + 0.142166i −0.0341896 + 0.00680074i
\(438\) −10.4837 + 10.4837i −0.500930 + 0.500930i
\(439\) 18.5256 + 12.3784i 0.884180 + 0.590790i 0.912622 0.408806i \(-0.134055\pi\)
−0.0284420 + 0.999595i \(0.509055\pi\)
\(440\) −5.18417 + 10.4612i −0.247145 + 0.498719i
\(441\) 4.86662i 0.231744i
\(442\) −5.92387 6.03434i −0.281770 0.287024i
\(443\) −8.14266 −0.386870 −0.193435 0.981113i \(-0.561963\pi\)
−0.193435 + 0.981113i \(0.561963\pi\)
\(444\) −2.39057 + 5.77135i −0.113452 + 0.273896i
\(445\) 2.80956 + 1.87729i 0.133186 + 0.0889921i
\(446\) −13.1941 + 13.1941i −0.624758 + 0.624758i
\(447\) −4.96845 24.9781i −0.234999 1.18142i
\(448\) 9.58022 + 14.3378i 0.452623 + 0.677398i
\(449\) −36.0248 7.16578i −1.70012 0.338174i −0.752745 0.658312i \(-0.771271\pi\)
−0.947371 + 0.320138i \(0.896271\pi\)
\(450\) 1.47653 + 3.56465i 0.0696041 + 0.168039i
\(451\) 18.5123 6.24405i 0.871712 0.294021i
\(452\) −0.612808 + 3.08079i −0.0288241 + 0.144908i
\(453\) 17.4950 11.6898i 0.821987 0.549234i
\(454\) −1.21343 6.10031i −0.0569490 0.286302i
\(455\) 6.64055 6.64055i 0.311314 0.311314i
\(456\) −0.324436 + 0.485552i −0.0151931 + 0.0227381i
\(457\) 1.75502 4.23699i 0.0820963 0.198198i −0.877501 0.479575i \(-0.840791\pi\)
0.959597 + 0.281377i \(0.0907910\pi\)
\(458\) 0.484462 0.0226374
\(459\) 4.31281 + 22.7798i 0.201305 + 1.06327i
\(460\) −7.03138 −0.327840
\(461\) −3.07200 1.27246i −0.143077 0.0592646i 0.309996 0.950738i \(-0.399672\pi\)
−0.453073 + 0.891473i \(0.649672\pi\)
\(462\) −10.2155 7.87015i −0.475266 0.366152i
\(463\) 13.2111 + 13.2111i 0.613973 + 0.613973i 0.943979 0.330006i \(-0.107051\pi\)
−0.330006 + 0.943979i \(0.607051\pi\)
\(464\) −0.250950 1.26161i −0.0116501 0.0585689i
\(465\) 11.1984 7.48254i 0.519314 0.346995i
\(466\) 1.92530 + 0.382967i 0.0891879 + 0.0177406i
\(467\) −9.80387 + 4.06090i −0.453669 + 0.187916i −0.597804 0.801642i \(-0.703960\pi\)
0.144135 + 0.989558i \(0.453960\pi\)
\(468\) 3.21193 1.33042i 0.148471 0.0614989i
\(469\) −28.0988 5.58919i −1.29748 0.258085i
\(470\) −2.08105 + 1.39051i −0.0959917 + 0.0641396i
\(471\) 2.92790 + 14.7196i 0.134911 + 0.678242i
\(472\) 18.0591 + 18.0591i 0.831236 + 0.831236i
\(473\) −8.23574 6.34494i −0.378680 0.291741i
\(474\) 15.2094 + 6.29993i 0.698589 + 0.289365i
\(475\) −0.537600 −0.0246668
\(476\) −9.27010 + 13.6000i −0.424894 + 0.623356i
\(477\) −4.99827 −0.228855
\(478\) 2.51995 6.08370i 0.115260 0.278262i
\(479\) −1.18281 + 1.77020i −0.0540438 + 0.0808823i −0.857507 0.514472i \(-0.827988\pi\)
0.803464 + 0.595354i \(0.202988\pi\)
\(480\) −6.46756 + 6.46756i −0.295202 + 0.295202i
\(481\) −1.75569 8.82646i −0.0800527 0.402452i
\(482\) 21.0027 14.0336i 0.956648 0.639212i
\(483\) 4.02160 20.2180i 0.182989 0.919949i
\(484\) 12.8587 3.39205i 0.584489 0.154184i
\(485\) −5.72960 13.8325i −0.260168 0.628101i
\(486\) 10.4377 + 2.07619i 0.473464 + 0.0941779i
\(487\) −12.9454 19.3742i −0.586613 0.877928i 0.412847 0.910800i \(-0.364534\pi\)
−0.999460 + 0.0328726i \(0.989534\pi\)
\(488\) −6.28913 31.6176i −0.284695 1.43126i
\(489\) 13.4031 13.4031i 0.606109 0.606109i
\(490\) 3.55952 + 2.37840i 0.160803 + 0.107445i
\(491\) −10.2791 + 24.8159i −0.463888 + 1.11992i 0.502900 + 0.864344i \(0.332266\pi\)
−0.966788 + 0.255579i \(0.917734\pi\)
\(492\) 9.42886 0.425086
\(493\) 36.8296 24.1197i 1.65872 1.08629i
\(494\) 0.316949i 0.0142602i
\(495\) −2.26519 + 4.57096i −0.101813 + 0.205450i
\(496\) −0.826121 0.551997i −0.0370939 0.0247854i
\(497\) 23.9230 23.9230i 1.07309 1.07309i
\(498\) −13.5708 + 2.69941i −0.608123 + 0.120963i
\(499\) −23.0909 + 15.4289i −1.03369 + 0.690691i −0.952041 0.305970i \(-0.901019\pi\)
−0.0816511 + 0.996661i \(0.526019\pi\)
\(500\) −12.4001 2.46654i −0.554550 0.110307i
\(501\) 3.26076 + 7.87217i 0.145680 + 0.351703i
\(502\) −12.0938 + 5.00943i −0.539774 + 0.223582i
\(503\) 1.48979 + 0.296337i 0.0664264 + 0.0132130i 0.228192 0.973616i \(-0.426719\pi\)
−0.161765 + 0.986829i \(0.551719\pi\)
\(504\) 6.52909 + 9.77147i 0.290829 + 0.435256i
\(505\) −7.59156 + 1.51006i −0.337820 + 0.0671966i
\(506\) −9.15086 10.4755i −0.406805 0.465693i
\(507\) −5.65110 + 8.45747i −0.250974 + 0.375609i
\(508\) −4.04236 + 9.75913i −0.179351 + 0.432991i
\(509\) 38.3986i 1.70199i 0.525174 + 0.850995i \(0.324000\pi\)
−0.525174 + 0.850995i \(0.676000\pi\)
\(510\) 5.51120 + 2.34269i 0.244040 + 0.103736i
\(511\) −41.5729 −1.83908
\(512\) 1.25870 + 0.521371i 0.0556272 + 0.0230415i
\(513\) −0.482786 + 0.722540i −0.0213155 + 0.0319009i
\(514\) 7.80585 7.80585i 0.344301 0.344301i
\(515\) 2.83985 0.564881i 0.125139 0.0248916i
\(516\) −2.78756 4.17188i −0.122715 0.183657i
\(517\) 7.30538 + 1.97268i 0.321290 + 0.0867582i
\(518\) 10.5886 4.38596i 0.465238 0.192708i
\(519\) 26.9285 11.1541i 1.18203 0.489612i
\(520\) 1.58364 7.96147i 0.0694470 0.349134i
\(521\) 20.9561 + 31.3631i 0.918105 + 1.37404i 0.927394 + 0.374085i \(0.122043\pi\)
−0.00928892 + 0.999957i \(0.502957\pi\)
\(522\) −2.31044 11.6154i −0.101125 0.508390i
\(523\) −26.6724 26.6724i −1.16630 1.16630i −0.983070 0.183232i \(-0.941344\pi\)
−0.183232 0.983070i \(-0.558656\pi\)
\(524\) 1.54065 + 1.02943i 0.0673036 + 0.0449708i
\(525\) 5.81970 14.0500i 0.253993 0.613192i
\(526\) 8.38927i 0.365790i
\(527\) 6.94184 33.2889i 0.302391 1.45009i
\(528\) −0.527803 0.0356230i −0.0229697 0.00155029i
\(529\) −0.292787 + 0.706851i −0.0127299 + 0.0307326i
\(530\) −2.44274 + 3.65581i −0.106106 + 0.158798i
\(531\) 7.89080 + 7.89080i 0.342432 + 0.342432i
\(532\) −0.605054 + 0.120353i −0.0262324 + 0.00521795i
\(533\) −11.2942 + 7.54655i −0.489207 + 0.326878i
\(534\) −0.629361 + 3.16401i −0.0272351 + 0.136920i
\(535\) −2.70453 6.52931i −0.116927 0.282287i
\(536\) −22.8786 + 9.47661i −0.988203 + 0.409327i
\(537\) 2.73035 13.7264i 0.117823 0.592337i
\(538\) 2.98693 1.99580i 0.128776 0.0860451i
\(539\) −1.66449 12.8355i −0.0716948 0.552866i
\(540\) −5.92898 + 5.92898i −0.255143 + 0.255143i
\(541\) −20.5525 13.7327i −0.883621 0.590416i 0.0288387 0.999584i \(-0.490819\pi\)
−0.912459 + 0.409168i \(0.865819\pi\)
\(542\) −15.6490 6.48203i −0.672182 0.278427i
\(543\) 4.56610i 0.195950i
\(544\) −0.213323 + 23.0924i −0.00914617 + 0.990079i
\(545\) 9.18044i 0.393247i
\(546\) 8.28336 + 3.43108i 0.354495 + 0.146837i
\(547\) −12.7326 + 19.0557i −0.544407 + 0.814762i −0.997036 0.0769365i \(-0.975486\pi\)
0.452629 + 0.891699i \(0.350486\pi\)
\(548\) −8.52995 8.52995i −0.364381 0.364381i
\(549\) −2.74800 13.8151i −0.117282 0.589614i
\(550\) −5.11348 8.89664i −0.218039 0.379354i
\(551\) 1.61842 + 0.321923i 0.0689468 + 0.0137144i
\(552\) −6.81873 16.4619i −0.290224 0.700663i
\(553\) 17.6651 + 42.6474i 0.751198 + 1.81355i
\(554\) 2.72762 13.7127i 0.115885 0.582595i
\(555\) 3.54076 + 5.29912i 0.150297 + 0.224935i
\(556\) 4.37071 0.869388i 0.185359 0.0368703i
\(557\) 15.0182 + 15.0182i 0.636342 + 0.636342i 0.949651 0.313309i \(-0.101438\pi\)
−0.313309 + 0.949651i \(0.601438\pi\)
\(558\) −7.60590 5.08210i −0.321983 0.215142i
\(559\) 6.67807 + 2.76615i 0.282452 + 0.116996i
\(560\) 0.490626 0.0207327
\(561\) −5.62773 17.2084i −0.237603 0.726538i
\(562\) −17.1491 −0.723391
\(563\) 4.02715 + 1.66810i 0.169724 + 0.0703021i 0.465928 0.884823i \(-0.345721\pi\)
−0.296204 + 0.955125i \(0.595721\pi\)
\(564\) 3.03650 + 2.02892i 0.127860 + 0.0854331i
\(565\) 2.26605 + 2.26605i 0.0953332 + 0.0953332i
\(566\) 25.3393 5.04030i 1.06509 0.211860i
\(567\) −6.79408 10.1681i −0.285324 0.427018i
\(568\) 5.70515 28.6817i 0.239383 1.20346i
\(569\) −18.1872 43.9077i −0.762445 1.84071i −0.461873 0.886946i \(-0.652823\pi\)
−0.300572 0.953759i \(-0.597177\pi\)
\(570\) 0.0858960 + 0.207371i 0.00359779 + 0.00868583i
\(571\) −9.23567 1.83709i −0.386501 0.0768798i −0.00198449 0.999998i \(-0.500632\pi\)
−0.384516 + 0.923118i \(0.625632\pi\)
\(572\) −8.01631 + 4.60750i −0.335179 + 0.192649i
\(573\) −4.42060 22.2238i −0.184673 0.928414i
\(574\) −12.2323 12.2323i −0.510565 0.510565i
\(575\) 9.11323 13.6389i 0.380048 0.568782i
\(576\) 6.01697 + 2.49231i 0.250707 + 0.103846i
\(577\) 17.5337i 0.729938i 0.931020 + 0.364969i \(0.118920\pi\)
−0.931020 + 0.364969i \(0.881080\pi\)
\(578\) 14.0734 5.52705i 0.585376 0.229895i
\(579\) 0.258791i 0.0107550i
\(580\) 14.7099 + 6.09306i 0.610797 + 0.253000i
\(581\) −32.2597 21.5552i −1.33836 0.894262i
\(582\) 10.1075 10.1075i 0.418967 0.418967i
\(583\) 13.1827 1.70952i 0.545974 0.0708010i
\(584\) −29.8784 + 19.9641i −1.23638 + 0.826121i
\(585\) 0.691960 3.47872i 0.0286090 0.143827i
\(586\) 12.9083 5.34681i 0.533239 0.220875i
\(587\) 2.37577 + 5.73561i 0.0980585 + 0.236734i 0.965295 0.261163i \(-0.0841059\pi\)
−0.867236 + 0.497897i \(0.834106\pi\)
\(588\) 1.21863 6.12647i 0.0502555 0.252651i
\(589\) 1.05976 0.708110i 0.0436667 0.0291772i
\(590\) 9.62782 1.91509i 0.396371 0.0788431i
\(591\) 2.92154 + 2.92154i 0.120176 + 0.120176i
\(592\) 0.261206 0.390923i 0.0107355 0.0160668i
\(593\) −13.4916 + 32.5715i −0.554032 + 1.33755i 0.360394 + 0.932800i \(0.382642\pi\)
−0.914426 + 0.404752i \(0.867358\pi\)
\(594\) −16.5493 1.11696i −0.679025 0.0458294i
\(595\) 6.28234 + 15.5722i 0.257551 + 0.638400i
\(596\) 23.2550i 0.952560i
\(597\) 6.70655 16.1910i 0.274481 0.662655i
\(598\) 8.04099 + 5.37282i 0.328821 + 0.219711i
\(599\) 20.5367 + 20.5367i 0.839108 + 0.839108i 0.988742 0.149633i \(-0.0478093\pi\)
−0.149633 + 0.988742i \(0.547809\pi\)
\(600\) −2.56447 12.8924i −0.104694 0.526332i
\(601\) 5.96895 + 8.93316i 0.243478 + 0.364391i 0.933001 0.359873i \(-0.117180\pi\)
−0.689523 + 0.724264i \(0.742180\pi\)
\(602\) −1.79591 + 9.02863i −0.0731956 + 0.367979i
\(603\) −9.99665 + 4.14075i −0.407095 + 0.168624i
\(604\) 17.7506 7.35255i 0.722263 0.299171i
\(605\) 4.41099 12.8305i 0.179332 0.521634i
\(606\) −4.10552 6.14434i −0.166775 0.249597i
\(607\) 22.7234 4.51997i 0.922315 0.183460i 0.288978 0.957336i \(-0.406685\pi\)
0.633337 + 0.773876i \(0.281685\pi\)
\(608\) −0.612057 + 0.612057i −0.0248222 + 0.0248222i
\(609\) −25.9332 + 38.8119i −1.05087 + 1.57274i
\(610\) −11.4476 4.74174i −0.463499 0.191988i
\(611\) −5.26111 −0.212842
\(612\) −0.0574219 + 6.21596i −0.00232114 + 0.251265i
\(613\) 25.7690i 1.04080i 0.853923 + 0.520400i \(0.174217\pi\)
−0.853923 + 0.520400i \(0.825783\pi\)
\(614\) 3.73243 9.01088i 0.150628 0.363649i
\(615\) 5.34433 7.99835i 0.215504 0.322525i
\(616\) −20.5623 23.5388i −0.828479 0.948406i
\(617\) 9.85233 1.95975i 0.396640 0.0788966i 0.00725951 0.999974i \(-0.497689\pi\)
0.389380 + 0.921077i \(0.372689\pi\)
\(618\) 1.53579 + 2.29847i 0.0617786 + 0.0924581i
\(619\) 31.3305 + 6.23202i 1.25928 + 0.250486i 0.779220 0.626750i \(-0.215615\pi\)
0.480059 + 0.877236i \(0.340615\pi\)
\(620\) 11.3620 4.70631i 0.456311 0.189010i
\(621\) −10.1468 24.4965i −0.407177 0.983013i
\(622\) 2.38591 + 0.474587i 0.0956663 + 0.0190292i
\(623\) −7.52129 + 5.02557i −0.301334 + 0.201345i
\(624\) 0.360732 0.0717540i 0.0144408 0.00287246i
\(625\) 3.17825 3.17825i 0.127130 0.127130i
\(626\) −1.48370 0.991378i −0.0593006 0.0396234i
\(627\) 0.301324 0.608047i 0.0120337 0.0242831i
\(628\) 13.7042i 0.546855i
\(629\) 15.7524 + 3.28490i 0.628088 + 0.130977i
\(630\) 4.51708 0.179965
\(631\) 1.71853 4.14891i 0.0684138 0.165165i −0.885974 0.463734i \(-0.846509\pi\)
0.954388 + 0.298569i \(0.0965092\pi\)
\(632\) 33.1760 + 22.1675i 1.31967 + 0.881776i
\(633\) −2.59433 + 2.59433i −0.103115 + 0.103115i
\(634\) 4.77214 + 23.9912i 0.189526 + 0.952811i
\(635\) 5.98728 + 8.96060i 0.237598 + 0.355590i
\(636\) 6.29219 + 1.25159i 0.249502 + 0.0496290i
\(637\) 3.44371 + 8.31385i 0.136445 + 0.329407i
\(638\) 10.0664 + 29.8449i 0.398533 + 1.18157i
\(639\) 2.49283 12.5323i 0.0986149 0.495770i
\(640\) −6.72460 + 4.49323i −0.265813 + 0.177611i
\(641\) −2.28873 11.5062i −0.0903994 0.454468i −0.999298 0.0374522i \(-0.988076\pi\)
0.908899 0.417016i \(-0.136924\pi\)
\(642\) 4.77099 4.77099i 0.188296 0.188296i
\(643\) −16.9758 + 25.4060i −0.669459 + 1.00192i 0.328884 + 0.944370i \(0.393327\pi\)
−0.998343 + 0.0575454i \(0.981673\pi\)
\(644\) 7.20334 17.3904i 0.283851 0.685277i
\(645\) −5.11894 −0.201558
\(646\) 0.521552 + 0.221700i 0.0205202 + 0.00872268i
\(647\) −24.2027 −0.951507 −0.475754 0.879579i \(-0.657825\pi\)
−0.475754 + 0.879579i \(0.657825\pi\)
\(648\) −9.76579 4.04512i −0.383636 0.158907i
\(649\) −23.5105 18.1129i −0.922869 0.710992i
\(650\) 5.04483 + 5.04483i 0.197874 + 0.197874i
\(651\) 7.03395 + 35.3621i 0.275682 + 1.38595i
\(652\) 14.3912 9.61590i 0.563604 0.376588i
\(653\) −34.2112 6.80503i −1.33879 0.266301i −0.526806 0.849985i \(-0.676611\pi\)
−0.811981 + 0.583684i \(0.801611\pi\)
\(654\) 8.09749 3.35409i 0.316637 0.131155i
\(655\) 1.74650 0.723423i 0.0682413 0.0282665i
\(656\) −0.696010 0.138445i −0.0271746 0.00540537i
\(657\) −13.0552 + 8.72320i −0.509332 + 0.340324i
\(658\) −1.30715 6.57149i −0.0509580 0.256183i
\(659\) 0.763993 + 0.763993i 0.0297610 + 0.0297610i 0.721831 0.692070i \(-0.243301\pi\)
−0.692070 + 0.721831i \(0.743301\pi\)
\(660\) 3.99619 5.18706i 0.155551 0.201906i
\(661\) −6.43294 2.66461i −0.250212 0.103641i 0.254052 0.967190i \(-0.418236\pi\)
−0.504265 + 0.863549i \(0.668236\pi\)
\(662\) 13.7652 0.534998
\(663\) 6.89652 + 10.5307i 0.267838 + 0.408977i
\(664\) −33.5362 −1.30146
\(665\) −0.240854 + 0.581474i −0.00933993 + 0.0225486i
\(666\) 2.40486 3.59913i 0.0931865 0.139463i
\(667\) −35.6021 + 35.6021i −1.37852 + 1.37852i
\(668\) 1.51791 + 7.63104i 0.0587296 + 0.295254i
\(669\) 23.0954 15.4319i 0.892921 0.596631i
\(670\) −1.85692 + 9.33536i −0.0717391 + 0.360657i
\(671\) 11.9728 + 35.4970i 0.462205 + 1.37035i
\(672\) −9.37019 22.6216i −0.361463 0.872649i
\(673\) −16.2166 3.22569i −0.625106 0.124341i −0.127634 0.991821i \(-0.540738\pi\)
−0.497472 + 0.867480i \(0.665738\pi\)
\(674\) −1.14384 1.71188i −0.0440592 0.0659393i
\(675\) −3.81613 19.1850i −0.146883 0.738430i
\(676\) −6.56765 + 6.56765i −0.252602 + 0.252602i
\(677\) 8.62991 + 5.76632i 0.331674 + 0.221618i 0.710245 0.703955i \(-0.248584\pi\)
−0.378570 + 0.925572i \(0.623584\pi\)
\(678\) −1.17083 + 2.82664i −0.0449656 + 0.108557i
\(679\) 40.0810 1.53817
\(680\) 11.9932 + 8.17485i 0.459918 + 0.313491i
\(681\) 9.25899i 0.354805i
\(682\) 21.7985 + 10.8025i 0.834707 + 0.413648i
\(683\) −9.23884 6.17319i −0.353514 0.236211i 0.366114 0.930570i \(-0.380688\pi\)
−0.719629 + 0.694359i \(0.755688\pi\)
\(684\) −0.164752 + 0.164752i −0.00629946 + 0.00629946i
\(685\) −12.0706 + 2.40100i −0.461195 + 0.0917375i
\(686\) 7.56350 5.05377i 0.288776 0.192954i
\(687\) −0.707326 0.140696i −0.0269862 0.00536788i
\(688\) 0.144513 + 0.348885i 0.00550951 + 0.0133011i
\(689\) −8.53874 + 3.53686i −0.325300 + 0.134744i
\(690\) −6.71709 1.33611i −0.255715 0.0508649i
\(691\) 8.21047 + 12.2878i 0.312341 + 0.467451i 0.954114 0.299443i \(-0.0968009\pi\)
−0.641773 + 0.766895i \(0.721801\pi\)
\(692\) 26.1036 5.19234i 0.992312 0.197383i
\(693\) −8.98457 10.2851i −0.341296 0.390700i
\(694\) −5.67670 + 8.49578i −0.215485 + 0.322496i
\(695\) 1.73985 4.20038i 0.0659964 0.159329i
\(696\) 40.3477i 1.52937i
\(697\) −4.51805 23.8638i −0.171133 0.903905i
\(698\) 4.68251 0.177236
\(699\) −2.69977 1.11828i −0.102115 0.0422972i
\(700\) 7.71491 11.5462i 0.291596 0.436405i
\(701\) −17.4384 + 17.4384i −0.658640 + 0.658640i −0.955058 0.296419i \(-0.904208\pi\)
0.296419 + 0.955058i \(0.404208\pi\)
\(702\) 11.3107 2.24985i 0.426897 0.0849150i
\(703\) 0.335079 + 0.501482i 0.0126378 + 0.0189137i
\(704\) −16.7220 4.51544i −0.630233 0.170182i
\(705\) 3.44221 1.42581i 0.129641 0.0536991i
\(706\) 11.2399 4.65571i 0.423018 0.175220i
\(707\) 4.04247 20.3228i 0.152033 0.764319i
\(708\) −7.95763 11.9094i −0.299066 0.447584i
\(709\) −1.32471 6.65974i −0.0497504 0.250112i 0.947905 0.318554i \(-0.103197\pi\)
−0.997655 + 0.0684420i \(0.978197\pi\)
\(710\) −7.94804 7.94804i −0.298285 0.298285i
\(711\) 14.4961 + 9.68596i 0.543645 + 0.363252i
\(712\) −2.99217 + 7.22373i −0.112136 + 0.270721i
\(713\) 38.8898i 1.45643i
\(714\) −11.4400 + 11.2306i −0.428133 + 0.420295i
\(715\) −0.635220 + 9.41166i −0.0237559 + 0.351976i
\(716\) 4.89050 11.8067i 0.182766 0.441237i
\(717\) −5.44599 + 8.15050i −0.203384 + 0.304386i
\(718\) −10.3992 10.3992i −0.388095 0.388095i
\(719\) 39.4388 7.84487i 1.47082 0.292564i 0.606329 0.795214i \(-0.292641\pi\)
0.864490 + 0.502649i \(0.167641\pi\)
\(720\) 0.154072 0.102948i 0.00574192 0.00383663i
\(721\) −1.51220 + 7.60236i −0.0563174 + 0.283127i
\(722\) −6.45869 15.5927i −0.240368 0.580299i
\(723\) −34.7400 + 14.3898i −1.29200 + 0.535162i
\(724\) −0.813416 + 4.08932i −0.0302304 + 0.151978i
\(725\) −30.8841 + 20.6361i −1.14701 + 0.766405i
\(726\) 12.9285 0.796994i 0.479823 0.0295792i
\(727\) 22.8927 22.8927i 0.849044 0.849044i −0.140970 0.990014i \(-0.545022\pi\)
0.990014 + 0.140970i \(0.0450221\pi\)
\(728\) 18.0684 + 12.0729i 0.669659 + 0.447452i
\(729\) −24.9015 10.3145i −0.922277 0.382020i
\(730\) 13.8120i 0.511203i
\(731\) −9.22300 + 9.05416i −0.341125 + 0.334880i
\(732\) 18.0796i 0.668241i
\(733\) −14.0746 5.82989i −0.519858 0.215332i 0.107297 0.994227i \(-0.465780\pi\)
−0.627154 + 0.778895i \(0.715780\pi\)
\(734\) 8.51292 12.7405i 0.314218 0.470260i
\(735\) −4.50626 4.50626i −0.166216 0.166216i
\(736\) −5.15248 25.9033i −0.189923 0.954808i
\(737\) 24.9496 14.3402i 0.919030 0.528226i
\(738\) −6.40799 1.27463i −0.235881 0.0469197i
\(739\) −12.0566 29.1073i −0.443511 1.07073i −0.974708 0.223481i \(-0.928258\pi\)
0.531198 0.847248i \(-0.321742\pi\)
\(740\) 2.22704 + 5.37655i 0.0818675 + 0.197646i
\(741\) −0.0920471 + 0.462752i −0.00338144 + 0.0169996i
\(742\) −6.53928 9.78672i −0.240064 0.359282i
\(743\) 12.2976 2.44614i 0.451153 0.0897400i 0.0357165 0.999362i \(-0.488629\pi\)
0.415437 + 0.909622i \(0.363629\pi\)
\(744\) 22.0368 + 22.0368i 0.807909 + 0.807909i
\(745\) −19.7268 13.1810i −0.722735 0.482916i
\(746\) 18.6176 + 7.71166i 0.681638 + 0.282344i
\(747\) −14.6535 −0.536142
\(748\) −1.97455 16.4140i −0.0721967 0.600156i
\(749\) 18.9193 0.691296
\(750\) −11.3772 4.71257i −0.415435 0.172079i
\(751\) −33.4450 22.3472i −1.22043 0.815463i −0.232836 0.972516i \(-0.574801\pi\)
−0.987590 + 0.157053i \(0.949801\pi\)
\(752\) −0.194354 0.194354i −0.00708737 0.00708737i
\(753\) 19.1121 3.80163i 0.696483 0.138539i
\(754\) −12.1663 18.2081i −0.443069 0.663099i
\(755\) 3.82410 19.2250i 0.139173 0.699671i
\(756\) −8.58990 20.7378i −0.312411 0.754228i
\(757\) 13.3453 + 32.2184i 0.485043 + 1.17100i 0.957185 + 0.289475i \(0.0934808\pi\)
−0.472142 + 0.881522i \(0.656519\pi\)
\(758\) 21.3185 + 4.24051i 0.774321 + 0.154022i
\(759\) 10.3182 + 17.9520i 0.374527 + 0.651617i
\(760\) 0.106133 + 0.533567i 0.00384985 + 0.0193545i
\(761\) 2.27965 + 2.27965i 0.0826372 + 0.0826372i 0.747217 0.664580i \(-0.231389\pi\)
−0.664580 + 0.747217i \(0.731389\pi\)
\(762\) −5.71612 + 8.55478i −0.207073 + 0.309907i
\(763\) 22.7056 + 9.40495i 0.821996 + 0.340482i
\(764\) 20.6907i 0.748565i
\(765\) 5.24036 + 3.57195i 0.189465 + 0.129144i
\(766\) 5.56462i 0.201058i
\(767\) 19.0639 + 7.89651i 0.688356 + 0.285126i
\(768\) −17.9183 11.9727i −0.646573 0.432026i
\(769\) −36.9587 + 36.9587i −1.33277 + 1.33277i −0.429880 + 0.902886i \(0.641444\pi\)
−0.902886 + 0.429880i \(0.858556\pi\)
\(770\) −11.9136 + 1.54494i −0.429337 + 0.0556758i
\(771\) −13.6637 + 9.12976i −0.492084 + 0.328800i
\(772\) 0.0461015 0.231768i 0.00165923 0.00834151i
\(773\) 5.10723 2.11548i 0.183694 0.0760887i −0.288940 0.957347i \(-0.593303\pi\)
0.472635 + 0.881258i \(0.343303\pi\)
\(774\) 1.33050 + 3.21210i 0.0478237 + 0.115457i
\(775\) −5.59718 + 28.1389i −0.201057 + 1.01078i
\(776\) 28.8061 19.2476i 1.03408 0.690950i
\(777\) −16.7334 + 3.32848i −0.600308 + 0.119409i
\(778\) 7.04099 + 7.04099i 0.252432 + 0.252432i
\(779\) 0.505760 0.756923i 0.0181207 0.0271196i
\(780\) −1.74218 + 4.20600i −0.0623801 + 0.150599i
\(781\) −2.28842 + 33.9061i −0.0818862 + 1.21326i
\(782\) −14.4657 + 9.47358i −0.517293 + 0.338774i
\(783\) 60.0405i 2.14567i
\(784\) −0.179911 + 0.434344i −0.00642540 + 0.0155123i
\(785\) 11.6250 + 7.76759i 0.414914 + 0.277237i
\(786\) 1.27617 + 1.27617i 0.0455195 + 0.0455195i
\(787\) −1.04404 5.24873i −0.0372159 0.187097i 0.957706 0.287749i \(-0.0929070\pi\)
−0.994922 + 0.100652i \(0.967907\pi\)
\(788\) 2.09603 + 3.13692i 0.0746678 + 0.111748i
\(789\) 2.43638 12.2485i 0.0867375 0.436059i
\(790\) 14.1689 5.86896i 0.504108 0.208808i
\(791\) −7.92597 + 3.28304i −0.281815 + 0.116732i
\(792\) −11.3963 3.07735i −0.404951 0.109349i
\(793\) −14.4703 21.6564i −0.513857 0.769041i
\(794\) −27.5334 + 5.47673i −0.977123 + 0.194362i
\(795\) 4.62816 4.62816i 0.164144 0.164144i
\(796\) 8.89056 13.3057i 0.315118 0.471607i
\(797\) −28.7473 11.9075i −1.01828 0.421786i −0.189813 0.981820i \(-0.560788\pi\)
−0.828470 + 0.560034i \(0.810788\pi\)
\(798\) −0.600879 −0.0212709
\(799\) 3.68006 8.65737i 0.130191 0.306276i
\(800\) 19.4840i 0.688864i
\(801\) −1.30741 + 3.15637i −0.0461951 + 0.111525i
\(802\) −10.2461 + 15.3343i −0.361802 + 0.541475i
\(803\) 31.4491 27.4723i 1.10981 0.969476i
\(804\) 13.6214 2.70947i 0.480390 0.0955555i
\(805\) −10.6691 15.9674i −0.376037 0.562778i
\(806\) −16.5897 3.29989i −0.584346 0.116234i
\(807\) −4.94060 + 2.04646i −0.173917 + 0.0720389i
\(808\) −6.85410 16.5473i −0.241127 0.582131i
\(809\) 38.1207 + 7.58268i 1.34025 + 0.266593i 0.812577 0.582853i \(-0.198064\pi\)
0.527675 + 0.849446i \(0.323064\pi\)
\(810\) −3.37818 + 2.25722i −0.118697 + 0.0793108i
\(811\) 24.9045 4.95381i 0.874514 0.173952i 0.262628 0.964897i \(-0.415411\pi\)
0.611887 + 0.790946i \(0.290411\pi\)
\(812\) −30.1393 + 30.1393i −1.05768 + 1.05768i
\(813\) 20.9654 + 14.0086i 0.735289 + 0.491304i
\(814\) −5.11175 + 10.3151i −0.179167 + 0.361544i
\(815\) 17.6582i 0.618539i
\(816\) −0.134252 + 0.643789i −0.00469974 + 0.0225371i
\(817\) −0.484430 −0.0169481
\(818\) 4.07412 9.83579i 0.142448 0.343900i
\(819\) 7.89487 + 5.27518i 0.275869 + 0.184330i
\(820\) 6.21112 6.21112i 0.216902 0.216902i
\(821\) 6.82518 + 34.3125i 0.238201 + 1.19752i 0.895907 + 0.444241i \(0.146527\pi\)
−0.657707 + 0.753274i \(0.728473\pi\)
\(822\) −6.52780 9.76955i −0.227683 0.340752i
\(823\) −33.2573 6.61529i −1.15928 0.230594i −0.422263 0.906473i \(-0.638764\pi\)
−0.737013 + 0.675879i \(0.763764\pi\)
\(824\) 2.56398 + 6.18999i 0.0893205 + 0.215639i
\(825\) 4.88206 + 14.4743i 0.169972 + 0.503931i
\(826\) −5.12676 + 25.7740i −0.178383 + 0.896791i
\(827\) 9.17260 6.12894i 0.318963 0.213124i −0.385774 0.922594i \(-0.626065\pi\)
0.704736 + 0.709470i \(0.251065\pi\)
\(828\) −1.38693 6.97259i −0.0481993 0.242314i
\(829\) −4.52231 + 4.52231i −0.157066 + 0.157066i −0.781265 0.624199i \(-0.785425\pi\)
0.624199 + 0.781265i \(0.285425\pi\)
\(830\) −7.16139 + 10.7178i −0.248575 + 0.372019i
\(831\) −7.96477 + 19.2286i −0.276295 + 0.667034i
\(832\) 12.0426 0.417504
\(833\) −16.0896 0.148633i −0.557471 0.00514982i
\(834\) 4.34055 0.150301
\(835\) 7.33365 + 3.03770i 0.253791 + 0.105124i
\(836\) 0.378179 0.490877i 0.0130796 0.0169773i
\(837\) 32.7925 + 32.7925i 1.13348 + 1.13348i
\(838\) 0.652348 + 3.27958i 0.0225350 + 0.113291i
\(839\) 7.42306 4.95993i 0.256272 0.171236i −0.420797 0.907155i \(-0.638250\pi\)
0.677070 + 0.735919i \(0.263250\pi\)
\(840\) −15.0935 3.00229i −0.520777 0.103589i
\(841\) 78.5395 32.5321i 2.70826 1.12180i
\(842\) 16.5069 6.83738i 0.568865 0.235632i
\(843\) 25.0381 + 4.98038i 0.862357 + 0.171534i
\(844\) −2.78559 + 1.86127i −0.0958840 + 0.0640676i
\(845\) 1.84865 + 9.29381i 0.0635956 + 0.319717i
\(846\) −1.78937 1.78937i −0.0615199 0.0615199i
\(847\) 27.2142 + 24.0538i 0.935092 + 0.826497i
\(848\) −0.446093 0.184778i −0.0153189 0.00634530i
\(849\) −38.4597 −1.31993
\(850\) −11.8302 + 4.77269i −0.405774 + 0.163702i
\(851\) −18.4027 −0.630838
\(852\) −6.27633 + 15.1524i −0.215023 + 0.519112i
\(853\) −21.9343 + 32.8270i −0.751016 + 1.12398i 0.237282 + 0.971441i \(0.423744\pi\)
−0.988298 + 0.152535i \(0.951256\pi\)
\(854\) 23.4551 23.4551i 0.802616 0.802616i
\(855\) 0.0463742 + 0.233139i 0.00158597 + 0.00797319i
\(856\) 13.5973 9.08541i 0.464745 0.310533i
\(857\) −0.180413 + 0.906999i −0.00616280 + 0.0309825i −0.983744 0.179575i \(-0.942528\pi\)
0.977582 + 0.210557i \(0.0675278\pi\)
\(858\) −8.53352 + 2.87828i −0.291329 + 0.0982629i
\(859\) 4.95487 + 11.9621i 0.169058 + 0.408142i 0.985589 0.169160i \(-0.0541056\pi\)
−0.816531 + 0.577302i \(0.804106\pi\)
\(860\) −4.58442 0.911898i −0.156328 0.0310955i
\(861\) 14.3069 + 21.4118i 0.487579 + 0.729713i
\(862\) 2.41836 + 12.1579i 0.0823695 + 0.414100i
\(863\) 29.9456 29.9456i 1.01936 1.01936i 0.0195529 0.999809i \(-0.493776\pi\)
0.999809 0.0195529i \(-0.00622429\pi\)
\(864\) −26.1867 17.4974i −0.890891 0.595274i
\(865\) 10.3911 25.0864i 0.353308 0.852962i
\(866\) 6.97257 0.236937
\(867\) −22.1526 + 3.98247i −0.752342 + 0.135252i
\(868\) 32.9226i 1.11747i
\(869\) −41.5457 20.5884i −1.40934 0.698413i
\(870\) 12.8946 + 8.61591i 0.437169 + 0.292107i
\(871\) −14.1476 + 14.1476i −0.479374 + 0.479374i
\(872\) 20.8349 4.14432i 0.705558 0.140344i
\(873\) 12.5867 8.41014i 0.425994 0.284640i
\(874\) −0.635672 0.126443i −0.0215019 0.00427700i
\(875\) −13.2142 31.9018i −0.446720 1.07848i
\(876\) 18.6192 7.71232i 0.629084 0.260575i
\(877\) 36.7992 + 7.31981i 1.24262 + 0.247173i 0.772263 0.635303i \(-0.219125\pi\)
0.470358 + 0.882476i \(0.344125\pi\)
\(878\) 11.0094 + 16.4767i 0.371549 + 0.556062i
\(879\) −20.3993 + 4.05767i −0.688051 + 0.136862i
\(880\) −0.371149 + 0.324216i −0.0125114 + 0.0109293i
\(881\) −11.3162 + 16.9359i −0.381252 + 0.570584i −0.971619 0.236551i \(-0.923983\pi\)
0.590367 + 0.807135i \(0.298983\pi\)
\(882\) −1.65640 + 3.99890i −0.0557738 + 0.134650i
\(883\) 33.5810i 1.13009i −0.825060 0.565046i \(-0.808859\pi\)
0.825060 0.565046i \(-0.191141\pi\)
\(884\) 4.30043 + 10.6596i 0.144639 + 0.358522i
\(885\) −14.6130 −0.491211
\(886\) −6.69082 2.77143i −0.224783 0.0931080i
\(887\) 28.9052 43.2597i 0.970541 1.45252i 0.0804374 0.996760i \(-0.474368\pi\)
0.890104 0.455758i \(-0.150632\pi\)
\(888\) −10.4279 + 10.4279i −0.349937 + 0.349937i
\(889\) −28.2955 + 5.62833i −0.949002 + 0.188768i
\(890\) 1.66966 + 2.49883i 0.0559673 + 0.0837609i
\(891\) 11.8589 + 3.20225i 0.397286 + 0.107279i
\(892\) 23.4329 9.70622i 0.784591 0.324988i
\(893\) 0.325753 0.134931i 0.0109009 0.00451531i
\(894\) 4.41894 22.2155i 0.147791 0.742998i
\(895\) −7.24348 10.8406i −0.242123 0.362362i
\(896\) −4.22386 21.2348i −0.141109 0.709403i
\(897\) −10.1797 10.1797i −0.339889 0.339889i
\(898\) −27.1626 18.1495i −0.906429 0.605656i
\(899\) 33.7000 81.3591i 1.12396 2.71348i
\(900\) 5.24467i 0.174822i
\(901\) 0.152653 16.5248i 0.00508562 0.550522i
\(902\) 17.3368 + 1.17011i 0.577252 + 0.0389604i
\(903\) 5.24412 12.6604i 0.174514 0.421313i
\(904\) −4.11980 + 6.16572i −0.137023 + 0.205069i
\(905\) 3.00785 + 3.00785i 0.0999844 + 0.0999844i
\(906\) 18.3544 3.65091i 0.609783 0.121293i
\(907\) −45.0785 + 30.1205i −1.49681 + 1.00013i −0.506346 + 0.862330i \(0.669004\pi\)
−0.990460 + 0.137803i \(0.955996\pi\)
\(908\) −1.64942 + 8.29218i −0.0547378 + 0.275186i
\(909\) −2.99486 7.23023i −0.0993332 0.239812i
\(910\) 7.71671 3.19637i 0.255806 0.105958i
\(911\) 4.62200 23.2364i 0.153134 0.769855i −0.825525 0.564365i \(-0.809121\pi\)
0.978659 0.205490i \(-0.0658789\pi\)
\(912\) −0.0204952 + 0.0136945i −0.000678665 + 0.000453469i
\(913\) 38.6480 5.01181i 1.27906 0.165867i
\(914\) 2.88419 2.88419i 0.0954007 0.0954007i
\(915\) 15.3366 + 10.2476i 0.507014 + 0.338776i
\(916\) −0.608403 0.252009i −0.0201022 0.00832661i
\(917\) 5.06064i 0.167117i
\(918\) −4.20946 + 20.1860i −0.138933 + 0.666238i
\(919\) 52.5704i 1.73414i −0.498188 0.867069i \(-0.666001\pi\)
0.498188 0.867069i \(-0.333999\pi\)
\(920\) −15.3357 6.35227i −0.505604 0.209428i
\(921\) −8.06633 + 12.0721i −0.265795 + 0.397790i
\(922\) −2.09117 2.09117i −0.0688689 0.0688689i
\(923\) −4.60948 23.1734i −0.151723 0.762763i
\(924\) 8.73499 + 15.1975i 0.287360 + 0.499961i
\(925\) −13.3154 2.64860i −0.437808 0.0870854i
\(926\) 6.35905 + 15.3521i 0.208971 + 0.504502i
\(927\) 1.12032 + 2.70468i 0.0367960 + 0.0888334i
\(928\) −11.6673 + 58.6556i −0.382999 + 1.92546i
\(929\) −27.7455 41.5241i −0.910301 1.36236i −0.931947 0.362596i \(-0.881891\pi\)
0.0216457 0.999766i \(-0.493109\pi\)
\(930\) 11.7485 2.33692i 0.385248 0.0766306i
\(931\) −0.426450 0.426450i −0.0139763 0.0139763i
\(932\) −2.21865 1.48245i −0.0726742 0.0485593i
\(933\) −3.34565 1.38582i −0.109532 0.0453696i
\(934\) −9.43800 −0.308821
\(935\) −15.0429 7.62857i −0.491957 0.249481i
\(936\) 8.20728 0.268263
\(937\) −54.7629 22.6835i −1.78903 0.741038i −0.990231 0.139433i \(-0.955472\pi\)
−0.798794 0.601605i \(-0.794528\pi\)
\(938\) −21.1864 14.1563i −0.691760 0.462219i
\(939\) 1.87832 + 1.87832i 0.0612968 + 0.0612968i
\(940\) 3.33677 0.663725i 0.108834 0.0216483i
\(941\) 30.8058 + 46.1042i 1.00424 + 1.50295i 0.857965 + 0.513709i \(0.171729\pi\)
0.146276 + 0.989244i \(0.453271\pi\)
\(942\) −2.60408 + 13.0916i −0.0848456 + 0.426547i
\(943\) 10.6297 + 25.6623i 0.346149 + 0.835678i
\(944\) 0.412541 + 0.995961i 0.0134271 + 0.0324158i
\(945\) −22.4604 4.46765i −0.730636 0.145333i
\(946\) −4.60775 8.01674i −0.149811 0.260647i
\(947\) −4.13571 20.7916i −0.134393 0.675637i −0.987967 0.154666i \(-0.950570\pi\)
0.853574 0.520971i \(-0.174430\pi\)
\(948\) −15.8233 15.8233i −0.513917 0.513917i
\(949\) −16.1300 + 24.1403i −0.523603 + 0.783627i
\(950\) −0.441746 0.182977i −0.0143321 0.00593656i
\(951\) 36.4135i 1.18079i
\(952\) −32.5050 + 21.2875i −1.05349 + 0.689930i
\(953\) 54.2500i 1.75733i −0.477439 0.878665i \(-0.658435\pi\)
0.477439 0.878665i \(-0.341565\pi\)
\(954\) −4.10707 1.70120i −0.132971 0.0550785i
\(955\) −17.5516 11.7276i −0.567957 0.379497i
\(956\) −6.32927 + 6.32927i −0.204703 + 0.204703i
\(957\) −6.02974 46.4976i −0.194914 1.50305i
\(958\) −1.57441 + 1.05199i −0.0508670 + 0.0339882i
\(959\) 6.42755 32.3135i 0.207556 1.04346i
\(960\) −7.87919 + 3.26367i −0.254300 + 0.105334i
\(961\) −14.1669 34.2019i −0.456997 1.10329i
\(962\) 1.56152 7.85027i 0.0503453 0.253103i
\(963\) 5.94125 3.96982i 0.191454 0.127926i
\(964\) −33.6759 + 6.69856i −1.08463 + 0.215746i
\(965\) −0.170474 0.170474i −0.00548777 0.00548777i
\(966\) 10.1859 15.2443i 0.327726 0.490477i
\(967\) −0.737952 + 1.78157i −0.0237309 + 0.0572915i −0.935301 0.353854i \(-0.884871\pi\)
0.911570 + 0.411145i \(0.134871\pi\)
\(968\) 31.1099 + 4.21861i 0.999910 + 0.135591i
\(969\) −0.697092 0.475154i −0.0223938 0.0152642i
\(970\) 13.3163i 0.427560i
\(971\) −17.5533 + 42.3774i −0.563312 + 1.35996i 0.343790 + 0.939047i \(0.388289\pi\)
−0.907102 + 0.420910i \(0.861711\pi\)
\(972\) −12.0280 8.03686i −0.385799 0.257783i
\(973\) 8.60620 + 8.60620i 0.275902 + 0.275902i
\(974\) −4.04306 20.3258i −0.129548 0.651282i
\(975\) −5.90046 8.83066i −0.188966 0.282807i
\(976\) 0.265465 1.33458i 0.00849732 0.0427189i
\(977\) −19.8042 + 8.20317i −0.633593 + 0.262443i −0.676279 0.736646i \(-0.736408\pi\)
0.0426860 + 0.999089i \(0.486408\pi\)
\(978\) 15.5752 6.45145i 0.498040 0.206295i
\(979\) 2.36870 8.77197i 0.0757039 0.280353i
\(980\) −3.23296 4.83847i −0.103273 0.154559i
\(981\) 9.10367 1.81083i 0.290658 0.0578155i
\(982\) −16.8926 + 16.8926i −0.539065 + 0.539065i
\(983\) −4.51996 + 6.76460i −0.144164 + 0.215757i −0.896524 0.442996i \(-0.853916\pi\)
0.752359 + 0.658753i \(0.228916\pi\)
\(984\) 20.5647 + 8.51819i 0.655580 + 0.271550i
\(985\) 3.84904 0.122641
\(986\) 38.4722 7.28382i 1.22521 0.231964i
\(987\) 9.97413i 0.317480i
\(988\) −0.164871 + 0.398035i −0.00524526 + 0.0126632i
\(989\) 8.21191 12.2900i 0.261124 0.390799i
\(990\) −3.41707 + 2.98498i −0.108602 + 0.0948689i
\(991\) 46.5232 9.25404i 1.47786 0.293964i 0.610646 0.791904i \(-0.290910\pi\)
0.867212 + 0.497940i \(0.165910\pi\)
\(992\) 25.6638 + 38.4085i 0.814825 + 1.21947i
\(993\) −20.0974 3.99763i −0.637773 0.126861i
\(994\) 27.8000 11.5151i 0.881761 0.365237i
\(995\) −6.24777 15.0834i −0.198067 0.478177i
\(996\) 18.4469 + 3.66931i 0.584511 + 0.116267i
\(997\) 12.3302 8.23875i 0.390500 0.260924i −0.344785 0.938682i \(-0.612048\pi\)
0.735285 + 0.677758i \(0.237048\pi\)
\(998\) −24.2252 + 4.81868i −0.766834 + 0.152533i
\(999\) −15.5175 + 15.5175i −0.490952 + 0.490952i
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 187.2.m.a.10.10 yes 128
11.10 odd 2 inner 187.2.m.a.10.7 128
17.12 odd 16 inner 187.2.m.a.131.7 yes 128
187.131 even 16 inner 187.2.m.a.131.10 yes 128
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
187.2.m.a.10.7 128 11.10 odd 2 inner
187.2.m.a.10.10 yes 128 1.1 even 1 trivial
187.2.m.a.131.7 yes 128 17.12 odd 16 inner
187.2.m.a.131.10 yes 128 187.131 even 16 inner