Properties

Label 275.2.h.c.126.1
Level $275$
Weight $2$
Character 275.126
Analytic conductor $2.196$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [275,2,Mod(26,275)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(275, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("275.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 275 = 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 275.h (of order \(5\), 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: \(2.19588605559\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4 x^{15} + 10 x^{14} - 13 x^{13} + 53 x^{12} - 12 x^{11} + 136 x^{10} + 8 x^{9} + 300 x^{8} - 256 x^{7} + 472 x^{6} - 48 x^{5} + 432 x^{4} + 88 x^{3} + 128 x^{2} + 64 x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 126.1
Root \(0.545543 - 1.67901i\) of defining polynomial
Character \(\chi\) \(=\) 275.126
Dual form 275.2.h.c.251.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.854560 - 2.63006i) q^{2} +(-1.32800 - 0.964848i) q^{3} +(-4.56893 + 3.31953i) q^{4} +(-1.40276 + 4.31724i) q^{6} +(-1.53545 + 1.11557i) q^{7} +(8.16046 + 5.92892i) q^{8} +(-0.0944009 - 0.290536i) q^{9} +O(q^{10})\) \(q+(-0.854560 - 2.63006i) q^{2} +(-1.32800 - 0.964848i) q^{3} +(-4.56893 + 3.31953i) q^{4} +(-1.40276 + 4.31724i) q^{6} +(-1.53545 + 1.11557i) q^{7} +(8.16046 + 5.92892i) q^{8} +(-0.0944009 - 0.290536i) q^{9} +(0.102720 + 3.31503i) q^{11} +9.27038 q^{12} +(-0.638270 - 1.96439i) q^{13} +(4.24616 + 3.08501i) q^{14} +(5.12949 - 15.7870i) q^{16} +(-1.12040 + 3.44822i) q^{17} +(-0.683457 + 0.496561i) q^{18} +(1.03575 + 0.752517i) q^{19} +3.11543 q^{21} +(8.63097 - 3.10305i) q^{22} -3.36725 q^{23} +(-5.11658 - 15.7472i) q^{24} +(-4.62104 + 3.35738i) q^{26} +(-1.67671 + 5.16038i) q^{27} +(3.31221 - 10.1939i) q^{28} +(-0.910336 + 0.661398i) q^{29} +(1.42251 + 4.37805i) q^{31} -25.7304 q^{32} +(3.06209 - 4.50147i) q^{33} +10.0265 q^{34} +(1.39575 + 1.01407i) q^{36} +(-1.45794 + 1.05926i) q^{37} +(1.09406 - 3.36716i) q^{38} +(-1.04772 + 3.22455i) q^{39} +(-3.73360 - 2.71262i) q^{41} +(-2.66232 - 8.19379i) q^{42} +0.0110430 q^{43} +(-11.4737 - 14.8052i) q^{44} +(2.87752 + 8.85610i) q^{46} +(7.46408 + 5.42297i) q^{47} +(-22.0440 + 16.0159i) q^{48} +(-1.05001 + 3.23159i) q^{49} +(4.81489 - 3.49822i) q^{51} +(9.43707 + 6.85643i) q^{52} +(2.02220 + 6.22368i) q^{53} +15.0050 q^{54} -19.1441 q^{56} +(-0.649412 - 1.99868i) q^{57} +(2.51746 + 1.82904i) q^{58} +(-4.43142 + 3.21961i) q^{59} +(2.27166 - 6.99144i) q^{61} +(10.2989 - 7.48261i) q^{62} +(0.469061 + 0.340793i) q^{63} +(11.7292 + 36.0987i) q^{64} +(-14.4559 - 4.20672i) q^{66} -7.01002 q^{67} +(-6.32745 - 19.4739i) q^{68} +(4.47171 + 3.24889i) q^{69} +(-3.68735 + 11.3485i) q^{71} +(0.952211 - 2.93060i) q^{72} +(-2.44810 + 1.77865i) q^{73} +(4.03181 + 2.92928i) q^{74} -7.23028 q^{76} +(-3.85587 - 4.97548i) q^{77} +9.37610 q^{78} +(-1.89180 - 5.82235i) q^{79} +(6.46422 - 4.69653i) q^{81} +(-3.94377 + 12.1377i) q^{82} +(-4.52716 + 13.9332i) q^{83} +(-14.2342 + 10.3418i) q^{84} +(-0.00943687 - 0.0290437i) q^{86} +1.84707 q^{87} +(-18.8163 + 27.6612i) q^{88} -13.8156 q^{89} +(3.17145 + 2.30419i) q^{91} +(15.3848 - 11.1777i) q^{92} +(2.33505 - 7.18656i) q^{93} +(7.88426 - 24.2653i) q^{94} +(34.1699 + 24.8259i) q^{96} +(-5.34722 - 16.4571i) q^{97} +9.39658 q^{98} +(0.953440 - 0.342786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{3} - 2 q^{4} - 3 q^{6} + 4 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{3} - 2 q^{4} - 3 q^{6} + 4 q^{7} + 16 q^{8} + 8 q^{9} - 5 q^{11} - 6 q^{12} + 7 q^{13} + 3 q^{14} - 4 q^{16} + 12 q^{17} + 16 q^{18} - 13 q^{19} + 10 q^{21} + 28 q^{22} - 4 q^{23} - 43 q^{24} - 34 q^{26} - 11 q^{27} + 47 q^{28} - 11 q^{29} - 10 q^{31} - 58 q^{32} - 34 q^{33} + 20 q^{34} + 3 q^{36} - 4 q^{37} - 36 q^{38} + 3 q^{39} + 25 q^{41} + 13 q^{42} - 28 q^{43} - q^{44} + 40 q^{46} + 8 q^{47} - 106 q^{48} + 16 q^{49} + 35 q^{51} + 39 q^{52} - 22 q^{53} + 60 q^{54} - 20 q^{56} + 29 q^{57} + 6 q^{58} + 14 q^{59} + 16 q^{61} - 10 q^{62} + 73 q^{63} + 40 q^{64} - 55 q^{66} - 14 q^{67} + 83 q^{68} + 35 q^{69} - 46 q^{71} + 28 q^{72} + 7 q^{73} - 7 q^{74} - 62 q^{76} - 51 q^{77} + 34 q^{78} - 39 q^{79} - 43 q^{81} - 51 q^{82} + 28 q^{83} - 54 q^{84} + 2 q^{86} - 50 q^{87} - 76 q^{88} - 22 q^{89} - 34 q^{91} + 4 q^{92} + 3 q^{93} - 40 q^{94} + 108 q^{96} - 39 q^{97} - 52 q^{98} - 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/275\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(177\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.854560 2.63006i −0.604265 1.85974i −0.501766 0.865004i \(-0.667316\pi\)
−0.102499 0.994733i \(-0.532684\pi\)
\(3\) −1.32800 0.964848i −0.766721 0.557055i 0.134244 0.990948i \(-0.457139\pi\)
−0.900964 + 0.433893i \(0.857139\pi\)
\(4\) −4.56893 + 3.31953i −2.28447 + 1.65976i
\(5\) 0 0
\(6\) −1.40276 + 4.31724i −0.572673 + 1.76251i
\(7\) −1.53545 + 1.11557i −0.580346 + 0.421646i −0.838849 0.544365i \(-0.816771\pi\)
0.258503 + 0.966010i \(0.416771\pi\)
\(8\) 8.16046 + 5.92892i 2.88516 + 2.09619i
\(9\) −0.0944009 0.290536i −0.0314670 0.0968453i
\(10\) 0 0
\(11\) 0.102720 + 3.31503i 0.0309712 + 0.999520i
\(12\) 9.27038 2.67613
\(13\) −0.638270 1.96439i −0.177024 0.544825i 0.822696 0.568482i \(-0.192469\pi\)
−0.999720 + 0.0236571i \(0.992469\pi\)
\(14\) 4.24616 + 3.08501i 1.13483 + 0.824504i
\(15\) 0 0
\(16\) 5.12949 15.7870i 1.28237 3.94674i
\(17\) −1.12040 + 3.44822i −0.271736 + 0.836317i 0.718329 + 0.695704i \(0.244907\pi\)
−0.990065 + 0.140613i \(0.955093\pi\)
\(18\) −0.683457 + 0.496561i −0.161092 + 0.117040i
\(19\) 1.03575 + 0.752517i 0.237618 + 0.172639i 0.700221 0.713926i \(-0.253085\pi\)
−0.462604 + 0.886565i \(0.653085\pi\)
\(20\) 0 0
\(21\) 3.11543 0.679843
\(22\) 8.63097 3.10305i 1.84013 0.661573i
\(23\) −3.36725 −0.702121 −0.351061 0.936353i \(-0.614179\pi\)
−0.351061 + 0.936353i \(0.614179\pi\)
\(24\) −5.11658 15.7472i −1.04442 3.21438i
\(25\) 0 0
\(26\) −4.62104 + 3.35738i −0.906261 + 0.658437i
\(27\) −1.67671 + 5.16038i −0.322683 + 0.993116i
\(28\) 3.31221 10.1939i 0.625949 1.92647i
\(29\) −0.910336 + 0.661398i −0.169045 + 0.122819i −0.669091 0.743180i \(-0.733316\pi\)
0.500046 + 0.865999i \(0.333316\pi\)
\(30\) 0 0
\(31\) 1.42251 + 4.37805i 0.255491 + 0.786321i 0.993732 + 0.111784i \(0.0356566\pi\)
−0.738241 + 0.674537i \(0.764343\pi\)
\(32\) −25.7304 −4.54853
\(33\) 3.06209 4.50147i 0.533042 0.783605i
\(34\) 10.0265 1.71953
\(35\) 0 0
\(36\) 1.39575 + 1.01407i 0.232625 + 0.169012i
\(37\) −1.45794 + 1.05926i −0.239684 + 0.174141i −0.701142 0.713021i \(-0.747326\pi\)
0.461459 + 0.887162i \(0.347326\pi\)
\(38\) 1.09406 3.36716i 0.177480 0.546226i
\(39\) −1.04772 + 3.22455i −0.167769 + 0.516341i
\(40\) 0 0
\(41\) −3.73360 2.71262i −0.583090 0.423639i 0.256747 0.966479i \(-0.417349\pi\)
−0.839837 + 0.542839i \(0.817349\pi\)
\(42\) −2.66232 8.19379i −0.410805 1.26433i
\(43\) 0.0110430 0.00168404 0.000842018 1.00000i \(-0.499732\pi\)
0.000842018 1.00000i \(0.499732\pi\)
\(44\) −11.4737 14.8052i −1.72972 2.23197i
\(45\) 0 0
\(46\) 2.87752 + 8.85610i 0.424267 + 1.30576i
\(47\) 7.46408 + 5.42297i 1.08875 + 0.791022i 0.979187 0.202958i \(-0.0650556\pi\)
0.109561 + 0.993980i \(0.465056\pi\)
\(48\) −22.0440 + 16.0159i −3.18177 + 2.31169i
\(49\) −1.05001 + 3.23159i −0.150001 + 0.461656i
\(50\) 0 0
\(51\) 4.81489 3.49822i 0.674220 0.489849i
\(52\) 9.43707 + 6.85643i 1.30869 + 0.950816i
\(53\) 2.02220 + 6.22368i 0.277770 + 0.854888i 0.988473 + 0.151396i \(0.0483769\pi\)
−0.710703 + 0.703492i \(0.751623\pi\)
\(54\) 15.0050 2.04192
\(55\) 0 0
\(56\) −19.1441 −2.55824
\(57\) −0.649412 1.99868i −0.0860167 0.264732i
\(58\) 2.51746 + 1.82904i 0.330558 + 0.240165i
\(59\) −4.43142 + 3.21961i −0.576921 + 0.419158i −0.837613 0.546264i \(-0.816049\pi\)
0.260692 + 0.965422i \(0.416049\pi\)
\(60\) 0 0
\(61\) 2.27166 6.99144i 0.290856 0.895162i −0.693726 0.720239i \(-0.744032\pi\)
0.984582 0.174923i \(-0.0559678\pi\)
\(62\) 10.2989 7.48261i 1.30797 0.950293i
\(63\) 0.469061 + 0.340793i 0.0590962 + 0.0429359i
\(64\) 11.7292 + 36.0987i 1.46615 + 4.51234i
\(65\) 0 0
\(66\) −14.4559 4.20672i −1.77940 0.517812i
\(67\) −7.01002 −0.856410 −0.428205 0.903682i \(-0.640854\pi\)
−0.428205 + 0.903682i \(0.640854\pi\)
\(68\) −6.32745 19.4739i −0.767316 2.36155i
\(69\) 4.47171 + 3.24889i 0.538331 + 0.391120i
\(70\) 0 0
\(71\) −3.68735 + 11.3485i −0.437607 + 1.34682i 0.452783 + 0.891621i \(0.350431\pi\)
−0.890391 + 0.455197i \(0.849569\pi\)
\(72\) 0.952211 2.93060i 0.112219 0.345375i
\(73\) −2.44810 + 1.77865i −0.286529 + 0.208175i −0.721760 0.692143i \(-0.756667\pi\)
0.435231 + 0.900319i \(0.356667\pi\)
\(74\) 4.03181 + 2.92928i 0.468688 + 0.340522i
\(75\) 0 0
\(76\) −7.23028 −0.829370
\(77\) −3.85587 4.97548i −0.439418 0.567009i
\(78\) 9.37610 1.06163
\(79\) −1.89180 5.82235i −0.212844 0.655066i −0.999300 0.0374192i \(-0.988086\pi\)
0.786456 0.617646i \(-0.211914\pi\)
\(80\) 0 0
\(81\) 6.46422 4.69653i 0.718247 0.521837i
\(82\) −3.94377 + 12.1377i −0.435517 + 1.34038i
\(83\) −4.52716 + 13.9332i −0.496921 + 1.52936i 0.317021 + 0.948418i \(0.397317\pi\)
−0.813942 + 0.580946i \(0.802683\pi\)
\(84\) −14.2342 + 10.3418i −1.55308 + 1.12838i
\(85\) 0 0
\(86\) −0.00943687 0.0290437i −0.00101760 0.00313186i
\(87\) 1.84707 0.198027
\(88\) −18.8163 + 27.6612i −2.00583 + 2.94870i
\(89\) −13.8156 −1.46445 −0.732227 0.681060i \(-0.761519\pi\)
−0.732227 + 0.681060i \(0.761519\pi\)
\(90\) 0 0
\(91\) 3.17145 + 2.30419i 0.332458 + 0.241545i
\(92\) 15.3848 11.1777i 1.60397 1.16535i
\(93\) 2.33505 7.18656i 0.242134 0.745211i
\(94\) 7.88426 24.2653i 0.813200 2.50277i
\(95\) 0 0
\(96\) 34.1699 + 24.8259i 3.48745 + 2.53378i
\(97\) −5.34722 16.4571i −0.542928 1.67096i −0.725866 0.687836i \(-0.758561\pi\)
0.182938 0.983124i \(-0.441439\pi\)
\(98\) 9.39658 0.949198
\(99\) 0.953440 0.342786i 0.0958243 0.0344513i
\(100\) 0 0
\(101\) −4.60266 14.1655i −0.457982 1.40952i −0.867599 0.497265i \(-0.834338\pi\)
0.409617 0.912258i \(-0.365662\pi\)
\(102\) −13.3152 9.67404i −1.31840 0.957873i
\(103\) −0.344090 + 0.249996i −0.0339042 + 0.0246329i −0.604608 0.796523i \(-0.706670\pi\)
0.570704 + 0.821156i \(0.306670\pi\)
\(104\) 6.43816 19.8146i 0.631313 1.94298i
\(105\) 0 0
\(106\) 14.6406 10.6370i 1.42202 1.03316i
\(107\) −6.82802 4.96085i −0.660090 0.479583i 0.206603 0.978425i \(-0.433759\pi\)
−0.866693 + 0.498841i \(0.833759\pi\)
\(108\) −9.46924 29.1433i −0.911178 2.80432i
\(109\) 0.922589 0.0883680 0.0441840 0.999023i \(-0.485931\pi\)
0.0441840 + 0.999023i \(0.485931\pi\)
\(110\) 0 0
\(111\) 2.95816 0.280776
\(112\) 9.73537 + 29.9624i 0.919906 + 2.83118i
\(113\) −2.19418 1.59417i −0.206411 0.149967i 0.479777 0.877390i \(-0.340718\pi\)
−0.686189 + 0.727424i \(0.740718\pi\)
\(114\) −4.70171 + 3.41599i −0.440355 + 0.319937i
\(115\) 0 0
\(116\) 1.96374 6.04377i 0.182329 0.561150i
\(117\) −0.510474 + 0.370881i −0.0471933 + 0.0342880i
\(118\) 12.2547 + 8.90356i 1.12814 + 0.819639i
\(119\) −2.12642 6.54445i −0.194929 0.599929i
\(120\) 0 0
\(121\) −10.9789 + 0.681040i −0.998082 + 0.0619127i
\(122\) −20.3292 −1.84052
\(123\) 2.34095 + 7.20470i 0.211076 + 0.649626i
\(124\) −21.0324 15.2809i −1.88877 1.37227i
\(125\) 0 0
\(126\) 0.495467 1.52489i 0.0441397 0.135848i
\(127\) −2.51456 + 7.73903i −0.223131 + 0.686728i 0.775345 + 0.631539i \(0.217576\pi\)
−0.998476 + 0.0551893i \(0.982424\pi\)
\(128\) 43.2860 31.4491i 3.82598 2.77973i
\(129\) −0.0146650 0.0106548i −0.00129118 0.000938101i
\(130\) 0 0
\(131\) 2.69256 0.235250 0.117625 0.993058i \(-0.462472\pi\)
0.117625 + 0.993058i \(0.462472\pi\)
\(132\) 0.952252 + 30.7316i 0.0828829 + 2.67484i
\(133\) −2.42983 −0.210693
\(134\) 5.99048 + 18.4368i 0.517498 + 1.59270i
\(135\) 0 0
\(136\) −29.5872 + 21.4963i −2.53708 + 1.84330i
\(137\) 2.62279 8.07211i 0.224080 0.689647i −0.774304 0.632814i \(-0.781900\pi\)
0.998384 0.0568330i \(-0.0181003\pi\)
\(138\) 4.72344 14.5373i 0.402086 1.23749i
\(139\) 17.8961 13.0023i 1.51793 1.10284i 0.555427 0.831565i \(-0.312555\pi\)
0.962502 0.271275i \(-0.0874452\pi\)
\(140\) 0 0
\(141\) −4.67995 14.4034i −0.394123 1.21299i
\(142\) 32.9983 2.76916
\(143\) 6.44647 2.31767i 0.539081 0.193813i
\(144\) −5.07091 −0.422575
\(145\) 0 0
\(146\) 6.77002 + 4.91871i 0.560291 + 0.407075i
\(147\) 4.51240 3.27845i 0.372176 0.270402i
\(148\) 3.14501 9.67934i 0.258518 0.795637i
\(149\) −4.96839 + 15.2911i −0.407026 + 1.25270i 0.512165 + 0.858887i \(0.328844\pi\)
−0.919191 + 0.393811i \(0.871156\pi\)
\(150\) 0 0
\(151\) −18.7865 13.6492i −1.52882 1.11075i −0.956889 0.290454i \(-0.906194\pi\)
−0.571933 0.820300i \(-0.693806\pi\)
\(152\) 3.99059 + 12.2818i 0.323680 + 0.996183i
\(153\) 1.10760 0.0895441
\(154\) −9.79076 + 14.3930i −0.788962 + 1.15982i
\(155\) 0 0
\(156\) −5.91700 18.2107i −0.473740 1.45802i
\(157\) 13.1364 + 9.54418i 1.04840 + 0.761709i 0.971908 0.235361i \(-0.0756274\pi\)
0.0764941 + 0.997070i \(0.475627\pi\)
\(158\) −13.6965 + 9.95109i −1.08964 + 0.791666i
\(159\) 3.31943 10.2162i 0.263248 0.810194i
\(160\) 0 0
\(161\) 5.17025 3.75641i 0.407473 0.296047i
\(162\) −17.8762 12.9878i −1.40449 1.02042i
\(163\) 3.78855 + 11.6599i 0.296742 + 0.913277i 0.982631 + 0.185571i \(0.0594136\pi\)
−0.685889 + 0.727706i \(0.740586\pi\)
\(164\) 26.0631 2.03519
\(165\) 0 0
\(166\) 40.5139 3.14449
\(167\) 1.95812 + 6.02648i 0.151524 + 0.466343i 0.997792 0.0664141i \(-0.0211558\pi\)
−0.846268 + 0.532757i \(0.821156\pi\)
\(168\) 25.4234 + 18.4712i 1.96146 + 1.42508i
\(169\) 7.06577 5.13358i 0.543521 0.394891i
\(170\) 0 0
\(171\) 0.120858 0.371961i 0.00924221 0.0284446i
\(172\) −0.0504546 + 0.0366574i −0.00384712 + 0.00279510i
\(173\) 1.70469 + 1.23853i 0.129605 + 0.0941637i 0.650699 0.759336i \(-0.274476\pi\)
−0.521094 + 0.853499i \(0.674476\pi\)
\(174\) −1.57844 4.85792i −0.119661 0.368278i
\(175\) 0 0
\(176\) 52.8612 + 15.3828i 3.98456 + 1.15952i
\(177\) 8.99135 0.675831
\(178\) 11.8063 + 36.3360i 0.884919 + 2.72350i
\(179\) 7.90157 + 5.74083i 0.590591 + 0.429090i 0.842527 0.538654i \(-0.181067\pi\)
−0.251936 + 0.967744i \(0.581067\pi\)
\(180\) 0 0
\(181\) −5.97245 + 18.3813i −0.443928 + 1.36627i 0.439726 + 0.898132i \(0.355076\pi\)
−0.883655 + 0.468139i \(0.844924\pi\)
\(182\) 3.34999 10.3102i 0.248317 0.764242i
\(183\) −9.76243 + 7.09282i −0.721660 + 0.524317i
\(184\) −27.4784 19.9642i −2.02573 1.47178i
\(185\) 0 0
\(186\) −20.8965 −1.53221
\(187\) −11.5461 3.35995i −0.844331 0.245704i
\(188\) −52.1046 −3.80012
\(189\) −3.18226 9.79400i −0.231476 0.712409i
\(190\) 0 0
\(191\) −11.7719 + 8.55279i −0.851785 + 0.618858i −0.925638 0.378411i \(-0.876471\pi\)
0.0738525 + 0.997269i \(0.476471\pi\)
\(192\) 19.2534 59.2559i 1.38950 4.27643i
\(193\) 6.86801 21.1376i 0.494370 1.52151i −0.323566 0.946206i \(-0.604882\pi\)
0.817936 0.575309i \(-0.195118\pi\)
\(194\) −38.7136 + 28.1271i −2.77947 + 2.01941i
\(195\) 0 0
\(196\) −5.92993 18.2504i −0.423566 1.30360i
\(197\) 9.00781 0.641780 0.320890 0.947116i \(-0.396018\pi\)
0.320890 + 0.947116i \(0.396018\pi\)
\(198\) −1.71632 2.21468i −0.121974 0.157390i
\(199\) 0.459925 0.0326032 0.0163016 0.999867i \(-0.494811\pi\)
0.0163016 + 0.999867i \(0.494811\pi\)
\(200\) 0 0
\(201\) 9.30929 + 6.76360i 0.656627 + 0.477067i
\(202\) −33.3230 + 24.2106i −2.34460 + 1.70345i
\(203\) 0.659941 2.03109i 0.0463187 0.142554i
\(204\) −10.3865 + 31.9663i −0.727199 + 2.23809i
\(205\) 0 0
\(206\) 0.951553 + 0.691343i 0.0662978 + 0.0481682i
\(207\) 0.317872 + 0.978309i 0.0220936 + 0.0679972i
\(208\) −34.2858 −2.37729
\(209\) −2.38823 + 3.51085i −0.165197 + 0.242850i
\(210\) 0 0
\(211\) 0.242564 + 0.746536i 0.0166988 + 0.0513936i 0.959059 0.283207i \(-0.0913985\pi\)
−0.942360 + 0.334601i \(0.891398\pi\)
\(212\) −29.8989 21.7229i −2.05347 1.49193i
\(213\) 15.8463 11.5130i 1.08577 0.788861i
\(214\) −7.21240 + 22.1975i −0.493029 + 1.51739i
\(215\) 0 0
\(216\) −44.2782 + 32.1700i −3.01275 + 2.18889i
\(217\) −7.06822 5.13536i −0.479822 0.348611i
\(218\) −0.788407 2.42647i −0.0533977 0.164341i
\(219\) 4.96721 0.335653
\(220\) 0 0
\(221\) 7.48878 0.503750
\(222\) −2.52793 7.78016i −0.169663 0.522170i
\(223\) −10.8039 7.84950i −0.723483 0.525641i 0.164012 0.986458i \(-0.447556\pi\)
−0.887495 + 0.460817i \(0.847556\pi\)
\(224\) 39.5077 28.7041i 2.63972 1.91787i
\(225\) 0 0
\(226\) −2.31770 + 7.13316i −0.154171 + 0.474491i
\(227\) 13.9787 10.1561i 0.927801 0.674087i −0.0176523 0.999844i \(-0.505619\pi\)
0.945453 + 0.325757i \(0.105619\pi\)
\(228\) 9.60180 + 6.97612i 0.635895 + 0.462005i
\(229\) 3.64367 + 11.2141i 0.240780 + 0.741045i 0.996302 + 0.0859217i \(0.0273835\pi\)
−0.755522 + 0.655124i \(0.772616\pi\)
\(230\) 0 0
\(231\) 0.320017 + 10.3278i 0.0210556 + 0.679517i
\(232\) −11.3501 −0.745173
\(233\) −0.780690 2.40272i −0.0511447 0.157407i 0.922222 0.386661i \(-0.126372\pi\)
−0.973367 + 0.229254i \(0.926372\pi\)
\(234\) 1.41167 + 1.02564i 0.0922838 + 0.0670481i
\(235\) 0 0
\(236\) 9.55927 29.4204i 0.622255 1.91510i
\(237\) −3.10538 + 9.55737i −0.201716 + 0.620818i
\(238\) −15.3952 + 11.1853i −0.997922 + 0.725032i
\(239\) −20.0190 14.5446i −1.29492 0.940815i −0.295028 0.955489i \(-0.595329\pi\)
−0.999892 + 0.0146739i \(0.995329\pi\)
\(240\) 0 0
\(241\) 18.8935 1.21704 0.608520 0.793539i \(-0.291764\pi\)
0.608520 + 0.793539i \(0.291764\pi\)
\(242\) 11.1733 + 28.2932i 0.718247 + 1.81876i
\(243\) 3.16193 0.202838
\(244\) 12.8292 + 39.4843i 0.821306 + 2.52772i
\(245\) 0 0
\(246\) 16.9484 12.3137i 1.08059 0.785093i
\(247\) 0.817151 2.51493i 0.0519941 0.160021i
\(248\) −14.3487 + 44.1609i −0.911146 + 2.80422i
\(249\) 19.4555 14.1352i 1.23294 0.895783i
\(250\) 0 0
\(251\) 1.11446 + 3.42996i 0.0703443 + 0.216497i 0.980048 0.198760i \(-0.0636915\pi\)
−0.909704 + 0.415258i \(0.863691\pi\)
\(252\) −3.27438 −0.206267
\(253\) −0.345884 11.1626i −0.0217455 0.701784i
\(254\) 22.5030 1.41196
\(255\) 0 0
\(256\) −58.2889 42.3493i −3.64305 2.64683i
\(257\) 10.6382 7.72911i 0.663593 0.482129i −0.204281 0.978912i \(-0.565486\pi\)
0.867874 + 0.496784i \(0.165486\pi\)
\(258\) −0.0154906 + 0.0476752i −0.000964402 + 0.00296813i
\(259\) 1.05692 3.25287i 0.0656739 0.202123i
\(260\) 0 0
\(261\) 0.278096 + 0.202049i 0.0172137 + 0.0125065i
\(262\) −2.30096 7.08162i −0.142154 0.437504i
\(263\) −6.24673 −0.385190 −0.192595 0.981278i \(-0.561690\pi\)
−0.192595 + 0.981278i \(0.561690\pi\)
\(264\) 51.6769 18.5792i 3.18050 1.14347i
\(265\) 0 0
\(266\) 2.07644 + 6.39061i 0.127314 + 0.391834i
\(267\) 18.3472 + 13.3300i 1.12283 + 0.815782i
\(268\) 32.0283 23.2699i 1.95644 1.42144i
\(269\) −6.92064 + 21.2995i −0.421959 + 1.29866i 0.483918 + 0.875114i \(0.339213\pi\)
−0.905876 + 0.423542i \(0.860787\pi\)
\(270\) 0 0
\(271\) 7.00497 5.08941i 0.425521 0.309159i −0.354334 0.935119i \(-0.615292\pi\)
0.779856 + 0.625959i \(0.215292\pi\)
\(272\) 48.6899 + 35.3752i 2.95226 + 2.14494i
\(273\) −1.98849 6.11994i −0.120349 0.370395i
\(274\) −23.4715 −1.41797
\(275\) 0 0
\(276\) −31.2157 −1.87897
\(277\) 0.804194 + 2.47505i 0.0483193 + 0.148712i 0.972305 0.233715i \(-0.0750884\pi\)
−0.923986 + 0.382427i \(0.875088\pi\)
\(278\) −49.4902 35.9567i −2.96822 2.15654i
\(279\) 1.13769 0.826583i 0.0681120 0.0494862i
\(280\) 0 0
\(281\) −6.39755 + 19.6896i −0.381646 + 1.17459i 0.557238 + 0.830353i \(0.311861\pi\)
−0.938884 + 0.344233i \(0.888139\pi\)
\(282\) −33.8826 + 24.6171i −2.01768 + 1.46593i
\(283\) 8.74594 + 6.35430i 0.519892 + 0.377724i 0.816563 0.577256i \(-0.195877\pi\)
−0.296671 + 0.954980i \(0.595877\pi\)
\(284\) −20.8243 64.0907i −1.23570 3.80308i
\(285\) 0 0
\(286\) −11.6045 14.9740i −0.686189 0.885434i
\(287\) 8.75886 0.517019
\(288\) 2.42897 + 7.47560i 0.143128 + 0.440504i
\(289\) 3.11834 + 2.26561i 0.183432 + 0.133271i
\(290\) 0 0
\(291\) −8.77745 + 27.0142i −0.514543 + 1.58360i
\(292\) 5.28095 16.2531i 0.309044 0.951140i
\(293\) 0.423178 0.307457i 0.0247223 0.0179618i −0.575355 0.817903i \(-0.695136\pi\)
0.600078 + 0.799942i \(0.295136\pi\)
\(294\) −12.4787 9.06627i −0.727770 0.528756i
\(295\) 0 0
\(296\) −18.1777 −1.05656
\(297\) −17.2791 5.02828i −1.00263 0.291770i
\(298\) 44.4624 2.57564
\(299\) 2.14922 + 6.61461i 0.124292 + 0.382533i
\(300\) 0 0
\(301\) −0.0169559 + 0.0123192i −0.000977323 + 0.000710067i
\(302\) −19.8440 + 61.0737i −1.14190 + 3.51440i
\(303\) −7.55525 + 23.2527i −0.434038 + 1.33583i
\(304\) 17.1928 12.4913i 0.986076 0.716426i
\(305\) 0 0
\(306\) −0.946510 2.91306i −0.0541083 0.166528i
\(307\) −20.0401 −1.14375 −0.571873 0.820342i \(-0.693783\pi\)
−0.571873 + 0.820342i \(0.693783\pi\)
\(308\) 34.1335 + 9.93297i 1.94493 + 0.565983i
\(309\) 0.698160 0.0397169
\(310\) 0 0
\(311\) 12.3892 + 9.00127i 0.702527 + 0.510415i 0.880754 0.473574i \(-0.157036\pi\)
−0.178227 + 0.983989i \(0.557036\pi\)
\(312\) −27.6679 + 20.1019i −1.56639 + 1.13805i
\(313\) 8.78365 27.0333i 0.496481 1.52801i −0.318154 0.948039i \(-0.603063\pi\)
0.814635 0.579974i \(-0.196937\pi\)
\(314\) 13.8759 42.7058i 0.783065 2.41003i
\(315\) 0 0
\(316\) 27.9709 + 20.3221i 1.57349 + 1.14321i
\(317\) 5.82421 + 17.9251i 0.327120 + 1.00677i 0.970474 + 0.241204i \(0.0775424\pi\)
−0.643354 + 0.765569i \(0.722458\pi\)
\(318\) −29.7058 −1.66582
\(319\) −2.28607 2.94986i −0.127995 0.165160i
\(320\) 0 0
\(321\) 4.28114 + 13.1760i 0.238950 + 0.735413i
\(322\) −14.2979 10.3880i −0.796790 0.578902i
\(323\) −3.75530 + 2.72838i −0.208950 + 0.151811i
\(324\) −13.9443 + 42.9163i −0.774686 + 2.38424i
\(325\) 0 0
\(326\) 27.4289 19.9282i 1.51914 1.10372i
\(327\) −1.22520 0.890158i −0.0677535 0.0492258i
\(328\) −14.3850 44.2724i −0.794277 2.44453i
\(329\) −17.5104 −0.965381
\(330\) 0 0
\(331\) −12.0888 −0.664461 −0.332230 0.943198i \(-0.607801\pi\)
−0.332230 + 0.943198i \(0.607801\pi\)
\(332\) −25.5672 78.6878i −1.40318 4.31855i
\(333\) 0.445383 + 0.323589i 0.0244068 + 0.0177326i
\(334\) 14.1767 10.3000i 0.775715 0.563590i
\(335\) 0 0
\(336\) 15.9806 49.1832i 0.871812 2.68316i
\(337\) 18.8783 13.7159i 1.02837 0.747151i 0.0603846 0.998175i \(-0.480767\pi\)
0.967981 + 0.251024i \(0.0807673\pi\)
\(338\) −19.5398 14.1965i −1.06282 0.772186i
\(339\) 1.37574 + 4.23411i 0.0747202 + 0.229965i
\(340\) 0 0
\(341\) −14.3673 + 5.16540i −0.778031 + 0.279722i
\(342\) −1.08156 −0.0584842
\(343\) −6.09826 18.7685i −0.329275 1.01340i
\(344\) 0.0901157 + 0.0654729i 0.00485871 + 0.00353006i
\(345\) 0 0
\(346\) 1.80065 5.54185i 0.0968038 0.297931i
\(347\) 6.37801 19.6295i 0.342389 1.05377i −0.620577 0.784145i \(-0.713102\pi\)
0.962967 0.269621i \(-0.0868983\pi\)
\(348\) −8.43916 + 6.13141i −0.452387 + 0.328678i
\(349\) 20.6326 + 14.9904i 1.10444 + 0.802419i 0.981778 0.190030i \(-0.0608585\pi\)
0.122657 + 0.992449i \(0.460859\pi\)
\(350\) 0 0
\(351\) 11.2072 0.598197
\(352\) −2.64302 85.2971i −0.140874 4.54635i
\(353\) −3.41010 −0.181501 −0.0907506 0.995874i \(-0.528927\pi\)
−0.0907506 + 0.995874i \(0.528927\pi\)
\(354\) −7.68365 23.6478i −0.408381 1.25687i
\(355\) 0 0
\(356\) 63.1227 45.8614i 3.34550 2.43065i
\(357\) −3.49052 + 10.7427i −0.184738 + 0.568564i
\(358\) 8.34638 25.6875i 0.441120 1.35763i
\(359\) −3.86662 + 2.80926i −0.204072 + 0.148267i −0.685128 0.728423i \(-0.740254\pi\)
0.481055 + 0.876690i \(0.340254\pi\)
\(360\) 0 0
\(361\) −5.36482 16.5112i −0.282359 0.869012i
\(362\) 53.4478 2.80916
\(363\) 15.2371 + 9.68854i 0.799738 + 0.508517i
\(364\) −22.1390 −1.16040
\(365\) 0 0
\(366\) 26.9972 + 19.6146i 1.41116 + 1.02527i
\(367\) −10.6250 + 7.71953i −0.554622 + 0.402956i −0.829487 0.558526i \(-0.811367\pi\)
0.274865 + 0.961483i \(0.411367\pi\)
\(368\) −17.2723 + 53.1587i −0.900381 + 2.77109i
\(369\) −0.435658 + 1.34082i −0.0226794 + 0.0698001i
\(370\) 0 0
\(371\) −10.0479 7.30025i −0.521663 0.379010i
\(372\) 13.1872 + 40.5862i 0.683727 + 2.10429i
\(373\) −24.9476 −1.29174 −0.645869 0.763448i \(-0.723505\pi\)
−0.645869 + 0.763448i \(0.723505\pi\)
\(374\) 1.02992 + 33.2382i 0.0532559 + 1.71870i
\(375\) 0 0
\(376\) 28.7580 + 88.5079i 1.48308 + 4.56445i
\(377\) 1.88029 + 1.36611i 0.0968397 + 0.0703582i
\(378\) −23.0394 + 16.7391i −1.18502 + 0.860968i
\(379\) −0.630173 + 1.93947i −0.0323698 + 0.0996240i −0.965936 0.258781i \(-0.916679\pi\)
0.933566 + 0.358405i \(0.116679\pi\)
\(380\) 0 0
\(381\) 10.8063 7.85125i 0.553625 0.402232i
\(382\) 32.5542 + 23.6520i 1.66562 + 1.21014i
\(383\) 9.94983 + 30.6224i 0.508413 + 1.56473i 0.794957 + 0.606666i \(0.207493\pi\)
−0.286544 + 0.958067i \(0.592507\pi\)
\(384\) −87.8273 −4.48192
\(385\) 0 0
\(386\) −61.4623 −3.12835
\(387\) −0.00104247 0.00320838i −5.29915e−5 0.000163091i
\(388\) 79.0607 + 57.4410i 4.01370 + 2.91612i
\(389\) −2.25775 + 1.64035i −0.114473 + 0.0831692i −0.643549 0.765405i \(-0.722539\pi\)
0.529076 + 0.848574i \(0.322539\pi\)
\(390\) 0 0
\(391\) 3.77266 11.6110i 0.190791 0.587196i
\(392\) −27.7284 + 20.1458i −1.40049 + 1.01752i
\(393\) −3.57572 2.59791i −0.180371 0.131047i
\(394\) −7.69772 23.6911i −0.387805 1.19354i
\(395\) 0 0
\(396\) −3.21832 + 4.73113i −0.161727 + 0.237748i
\(397\) 26.6387 1.33696 0.668480 0.743730i \(-0.266945\pi\)
0.668480 + 0.743730i \(0.266945\pi\)
\(398\) −0.393033 1.20963i −0.0197010 0.0606333i
\(399\) 3.22681 + 2.34442i 0.161543 + 0.117368i
\(400\) 0 0
\(401\) −5.62283 + 17.3053i −0.280791 + 0.864186i 0.706838 + 0.707376i \(0.250121\pi\)
−0.987629 + 0.156810i \(0.949879\pi\)
\(402\) 9.83335 30.2639i 0.490443 1.50943i
\(403\) 7.69226 5.58876i 0.383179 0.278396i
\(404\) 68.0521 + 49.4427i 3.38572 + 2.45987i
\(405\) 0 0
\(406\) −5.90585 −0.293103
\(407\) −3.66123 4.72431i −0.181480 0.234176i
\(408\) 60.0324 2.97205
\(409\) 2.34693 + 7.22312i 0.116048 + 0.357160i 0.992164 0.124940i \(-0.0398740\pi\)
−0.876116 + 0.482101i \(0.839874\pi\)
\(410\) 0 0
\(411\) −11.2714 + 8.18916i −0.555978 + 0.403942i
\(412\) 0.742258 2.28443i 0.0365684 0.112546i
\(413\) 3.21252 9.88711i 0.158078 0.486513i
\(414\) 2.30137 1.67205i 0.113106 0.0821766i
\(415\) 0 0
\(416\) 16.4229 + 50.5446i 0.805201 + 2.47815i
\(417\) −36.3113 −1.77817
\(418\) 11.2746 + 3.28096i 0.551461 + 0.160477i
\(419\) 29.8323 1.45740 0.728701 0.684832i \(-0.240125\pi\)
0.728701 + 0.684832i \(0.240125\pi\)
\(420\) 0 0
\(421\) −20.4942 14.8899i −0.998828 0.725691i −0.0369918 0.999316i \(-0.511778\pi\)
−0.961837 + 0.273624i \(0.911778\pi\)
\(422\) 1.75615 1.27592i 0.0854881 0.0621108i
\(423\) 0.870953 2.68052i 0.0423472 0.130331i
\(424\) −20.3977 + 62.7775i −0.990598 + 3.04875i
\(425\) 0 0
\(426\) −43.8217 31.8383i −2.12317 1.54257i
\(427\) 4.31143 + 13.2692i 0.208645 + 0.642142i
\(428\) 47.6644 2.30395
\(429\) −10.7971 3.14200i −0.521289 0.151697i
\(430\) 0 0
\(431\) −6.34030 19.5134i −0.305401 0.939929i −0.979527 0.201312i \(-0.935479\pi\)
0.674126 0.738617i \(-0.264521\pi\)
\(432\) 72.8660 + 52.9403i 3.50577 + 2.54709i
\(433\) −11.1286 + 8.08542i −0.534807 + 0.388560i −0.822153 0.569267i \(-0.807227\pi\)
0.287346 + 0.957827i \(0.407227\pi\)
\(434\) −7.46612 + 22.9784i −0.358385 + 1.10300i
\(435\) 0 0
\(436\) −4.21525 + 3.06256i −0.201874 + 0.146670i
\(437\) −3.48764 2.53392i −0.166836 0.121214i
\(438\) −4.24478 13.0641i −0.202823 0.624226i
\(439\) −24.1841 −1.15425 −0.577123 0.816657i \(-0.695825\pi\)
−0.577123 + 0.816657i \(0.695825\pi\)
\(440\) 0 0
\(441\) 1.03801 0.0494293
\(442\) −6.39961 19.6960i −0.304398 0.936842i
\(443\) −1.37342 0.997848i −0.0652532 0.0474092i 0.554680 0.832063i \(-0.312840\pi\)
−0.619934 + 0.784654i \(0.712840\pi\)
\(444\) −13.5157 + 9.81970i −0.641425 + 0.466022i
\(445\) 0 0
\(446\) −11.4121 + 35.1228i −0.540379 + 1.66311i
\(447\) 21.3516 15.5129i 1.00990 0.733733i
\(448\) −58.2802 42.3430i −2.75348 2.00052i
\(449\) 0.804184 + 2.47502i 0.0379518 + 0.116804i 0.968238 0.250032i \(-0.0804412\pi\)
−0.930286 + 0.366836i \(0.880441\pi\)
\(450\) 0 0
\(451\) 8.60890 12.6556i 0.405377 0.595931i
\(452\) 15.3170 0.720449
\(453\) 11.7790 + 36.2522i 0.553428 + 1.70328i
\(454\) −38.6570 28.0859i −1.81426 1.31814i
\(455\) 0 0
\(456\) 6.55054 20.1605i 0.306757 0.944102i
\(457\) −4.31421 + 13.2778i −0.201810 + 0.621108i 0.798019 + 0.602632i \(0.205881\pi\)
−0.999829 + 0.0184756i \(0.994119\pi\)
\(458\) 26.3800 19.1662i 1.23265 0.895576i
\(459\) −15.9156 11.5633i −0.742875 0.539730i
\(460\) 0 0
\(461\) 26.5365 1.23593 0.617963 0.786207i \(-0.287958\pi\)
0.617963 + 0.786207i \(0.287958\pi\)
\(462\) 26.8892 9.66736i 1.25100 0.449766i
\(463\) −23.6363 −1.09847 −0.549237 0.835667i \(-0.685081\pi\)
−0.549237 + 0.835667i \(0.685081\pi\)
\(464\) 5.77190 + 17.7641i 0.267954 + 0.824676i
\(465\) 0 0
\(466\) −5.65215 + 4.10653i −0.261831 + 0.190231i
\(467\) −3.12854 + 9.62866i −0.144772 + 0.445561i −0.996982 0.0776386i \(-0.975262\pi\)
0.852210 + 0.523200i \(0.175262\pi\)
\(468\) 1.10117 3.38906i 0.0509017 0.156659i
\(469\) 10.7635 7.82016i 0.497014 0.361102i
\(470\) 0 0
\(471\) −8.23650 25.3493i −0.379518 1.16804i
\(472\) −55.2512 −2.54314
\(473\) 0.00113433 + 0.0366078i 5.21566e−5 + 0.00168323i
\(474\) 27.7902 1.27645
\(475\) 0 0
\(476\) 31.4400 + 22.8425i 1.44105 + 1.04698i
\(477\) 1.61731 1.17504i 0.0740513 0.0538015i
\(478\) −21.1459 + 65.0805i −0.967192 + 2.97671i
\(479\) 0.210601 0.648162i 0.00962259 0.0296153i −0.946130 0.323787i \(-0.895044\pi\)
0.955753 + 0.294172i \(0.0950438\pi\)
\(480\) 0 0
\(481\) 3.01135 + 2.18788i 0.137306 + 0.0997586i
\(482\) −16.1457 49.6912i −0.735414 2.26337i
\(483\) −10.4905 −0.477332
\(484\) 47.9011 39.5564i 2.17732 1.79802i
\(485\) 0 0
\(486\) −2.70206 8.31608i −0.122568 0.377225i
\(487\) −8.59541 6.24493i −0.389495 0.282985i 0.375754 0.926720i \(-0.377384\pi\)
−0.765249 + 0.643735i \(0.777384\pi\)
\(488\) 59.9895 43.5849i 2.71560 1.97300i
\(489\) 6.21889 19.1398i 0.281228 0.865530i
\(490\) 0 0
\(491\) 9.34180 6.78722i 0.421590 0.306303i −0.356687 0.934224i \(-0.616094\pi\)
0.778277 + 0.627921i \(0.216094\pi\)
\(492\) −34.6118 25.1470i −1.56042 1.13371i
\(493\) −1.26071 3.88007i −0.0567796 0.174750i
\(494\) −7.31274 −0.329016
\(495\) 0 0
\(496\) 76.4128 3.43104
\(497\) −6.99829 21.5385i −0.313916 0.966135i
\(498\) −53.8024 39.0897i −2.41094 1.75165i
\(499\) 7.47146 5.42833i 0.334469 0.243006i −0.407856 0.913046i \(-0.633723\pi\)
0.742324 + 0.670041i \(0.233723\pi\)
\(500\) 0 0
\(501\) 3.21425 9.89246i 0.143602 0.441962i
\(502\) 8.06865 5.86222i 0.360122 0.261644i
\(503\) 15.6117 + 11.3426i 0.696092 + 0.505740i 0.878657 0.477453i \(-0.158440\pi\)
−0.182565 + 0.983194i \(0.558440\pi\)
\(504\) 1.80722 + 5.56205i 0.0805000 + 0.247754i
\(505\) 0 0
\(506\) −29.0627 + 10.4488i −1.29199 + 0.464505i
\(507\) −14.3365 −0.636704
\(508\) −14.2010 43.7063i −0.630069 1.93915i
\(509\) −2.62203 1.90502i −0.116219 0.0844384i 0.528157 0.849147i \(-0.322883\pi\)
−0.644377 + 0.764708i \(0.722883\pi\)
\(510\) 0 0
\(511\) 1.77473 5.46206i 0.0785095 0.241627i
\(512\) −28.5026 + 87.7221i −1.25965 + 3.87681i
\(513\) −5.61993 + 4.08312i −0.248126 + 0.180274i
\(514\) −29.4190 21.3742i −1.29762 0.942775i
\(515\) 0 0
\(516\) 0.102372 0.00450669
\(517\) −17.2106 + 25.3007i −0.756922 + 1.11272i
\(518\) −9.45846 −0.415581
\(519\) −1.06883 3.28953i −0.0469166 0.144395i
\(520\) 0 0
\(521\) 9.45689 6.87083i 0.414314 0.301017i −0.361032 0.932553i \(-0.617576\pi\)
0.775346 + 0.631537i \(0.217576\pi\)
\(522\) 0.293752 0.904075i 0.0128572 0.0395703i
\(523\) −3.39708 + 10.4551i −0.148544 + 0.457171i −0.997450 0.0713730i \(-0.977262\pi\)
0.848906 + 0.528544i \(0.177262\pi\)
\(524\) −12.3021 + 8.93803i −0.537422 + 0.390460i
\(525\) 0 0
\(526\) 5.33821 + 16.4293i 0.232757 + 0.716352i
\(527\) −16.6903 −0.727039
\(528\) −55.3575 71.4313i −2.40913 3.10865i
\(529\) −11.6616 −0.507026
\(530\) 0 0
\(531\) 1.35374 + 0.983552i 0.0587474 + 0.0426825i
\(532\) 11.1017 8.06588i 0.481321 0.349700i
\(533\) −2.94560 + 9.06563i −0.127588 + 0.392676i
\(534\) 19.3800 59.6455i 0.838654 2.58111i
\(535\) 0 0
\(536\) −57.2050 41.5618i −2.47088 1.79520i
\(537\) −4.95425 15.2476i −0.213792 0.657984i
\(538\) 61.9333 2.67013
\(539\) −10.8207 3.14886i −0.466080 0.135631i
\(540\) 0 0
\(541\) −6.93398 21.3406i −0.298115 0.917504i −0.982157 0.188061i \(-0.939780\pi\)
0.684042 0.729442i \(-0.260220\pi\)
\(542\) −19.3716 14.0743i −0.832083 0.604544i
\(543\) 25.6666 18.6478i 1.10146 0.800256i
\(544\) 28.8282 88.7241i 1.23600 3.80401i
\(545\) 0 0
\(546\) −14.3965 + 10.4597i −0.616115 + 0.447634i
\(547\) −21.6722 15.7458i −0.926638 0.673242i 0.0185290 0.999828i \(-0.494102\pi\)
−0.945167 + 0.326586i \(0.894102\pi\)
\(548\) 14.8122 + 45.5874i 0.632747 + 1.94740i
\(549\) −2.24571 −0.0958446
\(550\) 0 0
\(551\) −1.44060 −0.0613714
\(552\) 17.2288 + 53.0248i 0.733307 + 2.25689i
\(553\) 9.40000 + 6.82950i 0.399729 + 0.290420i
\(554\) 5.82232 4.23016i 0.247367 0.179722i
\(555\) 0 0
\(556\) −38.6048 + 118.813i −1.63721 + 5.03880i
\(557\) −4.99921 + 3.63214i −0.211824 + 0.153899i −0.688638 0.725105i \(-0.741791\pi\)
0.476815 + 0.879004i \(0.341791\pi\)
\(558\) −3.14620 2.28584i −0.133189 0.0967675i
\(559\) −0.00704839 0.0216927i −0.000298115 0.000917504i
\(560\) 0 0
\(561\) 12.0913 + 15.6022i 0.510496 + 0.658725i
\(562\) 57.2521 2.41503
\(563\) −9.10209 28.0133i −0.383607 1.18062i −0.937486 0.348024i \(-0.886853\pi\)
0.553878 0.832598i \(-0.313147\pi\)
\(564\) 69.1948 + 50.2730i 2.91363 + 2.11687i
\(565\) 0 0
\(566\) 9.23828 28.4325i 0.388314 1.19511i
\(567\) −4.68618 + 14.4226i −0.196801 + 0.605691i
\(568\) −97.3747 + 70.7469i −4.08575 + 2.96847i
\(569\) −31.0867 22.5858i −1.30322 0.946845i −0.303239 0.952915i \(-0.598068\pi\)
−0.999982 + 0.00606937i \(0.998068\pi\)
\(570\) 0 0
\(571\) 23.3745 0.978193 0.489096 0.872230i \(-0.337327\pi\)
0.489096 + 0.872230i \(0.337327\pi\)
\(572\) −21.7599 + 31.9885i −0.909828 + 1.33751i
\(573\) 23.8852 0.997819
\(574\) −7.48497 23.0364i −0.312417 0.961520i
\(575\) 0 0
\(576\) 9.38073 6.81550i 0.390864 0.283979i
\(577\) 5.77115 17.7618i 0.240256 0.739432i −0.756124 0.654428i \(-0.772910\pi\)
0.996381 0.0850044i \(-0.0270904\pi\)
\(578\) 3.29388 10.1375i 0.137007 0.421666i
\(579\) −29.5152 + 21.4441i −1.22661 + 0.891185i
\(580\) 0 0
\(581\) −8.59220 26.4441i −0.356464 1.09708i
\(582\) 78.5499 3.25600
\(583\) −20.4240 + 7.34294i −0.845875 + 0.304114i
\(584\) −30.5231 −1.26306
\(585\) 0 0
\(586\) −1.17026 0.850245i −0.0483431 0.0351233i
\(587\) −15.1091 + 10.9774i −0.623621 + 0.453087i −0.854184 0.519970i \(-0.825943\pi\)
0.230563 + 0.973057i \(0.425943\pi\)
\(588\) −9.73396 + 29.9581i −0.401422 + 1.23545i
\(589\) −1.82119 + 5.60504i −0.0750407 + 0.230951i
\(590\) 0 0
\(591\) −11.9624 8.69117i −0.492066 0.357507i
\(592\) 9.24392 + 28.4499i 0.379923 + 1.16928i
\(593\) −10.2335 −0.420240 −0.210120 0.977676i \(-0.567385\pi\)
−0.210120 + 0.977676i \(0.567385\pi\)
\(594\) 1.54131 + 49.7421i 0.0632408 + 2.04094i
\(595\) 0 0
\(596\) −28.0590 86.3569i −1.14934 3.53731i
\(597\) −0.610779 0.443757i −0.0249975 0.0181618i
\(598\) 15.5602 11.3052i 0.636305 0.462303i
\(599\) 6.79277 20.9060i 0.277545 0.854196i −0.710990 0.703203i \(-0.751753\pi\)
0.988535 0.150994i \(-0.0482473\pi\)
\(600\) 0 0
\(601\) −15.0923 + 10.9652i −0.615627 + 0.447279i −0.851391 0.524531i \(-0.824241\pi\)
0.235764 + 0.971810i \(0.424241\pi\)
\(602\) 0.0468901 + 0.0340677i 0.00191110 + 0.00138850i
\(603\) 0.661752 + 2.03666i 0.0269486 + 0.0829393i
\(604\) 131.143 5.33613
\(605\) 0 0
\(606\) 67.6124 2.74657
\(607\) 1.02449 + 3.15306i 0.0415829 + 0.127979i 0.969693 0.244327i \(-0.0785671\pi\)
−0.928110 + 0.372306i \(0.878567\pi\)
\(608\) −26.6503 19.3626i −1.08081 0.785256i
\(609\) −2.83609 + 2.06054i −0.114924 + 0.0834973i
\(610\) 0 0
\(611\) 5.88875 18.1237i 0.238233 0.733207i
\(612\) −5.06055 + 3.67670i −0.204560 + 0.148622i
\(613\) 18.0980 + 13.1489i 0.730970 + 0.531081i 0.889870 0.456214i \(-0.150795\pi\)
−0.158900 + 0.987295i \(0.550795\pi\)
\(614\) 17.1254 + 52.7066i 0.691126 + 2.12707i
\(615\) 0 0
\(616\) −1.96648 63.4634i −0.0792318 2.55701i
\(617\) −11.3963 −0.458798 −0.229399 0.973332i \(-0.573676\pi\)
−0.229399 + 0.973332i \(0.573676\pi\)
\(618\) −0.596620 1.83621i −0.0239996 0.0738631i
\(619\) 16.5704 + 12.0391i 0.666019 + 0.483891i 0.868690 0.495356i \(-0.164962\pi\)
−0.202671 + 0.979247i \(0.564962\pi\)
\(620\) 0 0
\(621\) 5.64591 17.3763i 0.226563 0.697288i
\(622\) 13.0866 40.2765i 0.524726 1.61494i
\(623\) 21.2132 15.4123i 0.849890 0.617481i
\(624\) 45.5315 + 33.0806i 1.82272 + 1.32428i
\(625\) 0 0
\(626\) −78.6055 −3.14171
\(627\) 6.55900 2.35813i 0.261941 0.0941745i
\(628\) −91.7017 −3.65930
\(629\) −2.01908 6.21409i −0.0805060 0.247772i
\(630\) 0 0
\(631\) −14.1408 + 10.2739i −0.562937 + 0.408998i −0.832533 0.553976i \(-0.813110\pi\)
0.269596 + 0.962974i \(0.413110\pi\)
\(632\) 19.0823 58.7294i 0.759054 2.33613i
\(633\) 0.398168 1.22544i 0.0158258 0.0487067i
\(634\) 42.1670 30.6361i 1.67467 1.21672i
\(635\) 0 0
\(636\) 18.7465 + 57.6959i 0.743348 + 2.28779i
\(637\) 7.01830 0.278075
\(638\) −5.80473 + 8.53333i −0.229812 + 0.337838i
\(639\) 3.64523 0.144203
\(640\) 0 0
\(641\) −4.17247 3.03148i −0.164803 0.119736i 0.502327 0.864678i \(-0.332477\pi\)
−0.667130 + 0.744942i \(0.732477\pi\)
\(642\) 30.9953 22.5194i 1.22328 0.888769i
\(643\) 5.82659 17.9324i 0.229778 0.707185i −0.767993 0.640458i \(-0.778744\pi\)
0.997771 0.0667267i \(-0.0212556\pi\)
\(644\) −11.1531 + 34.3256i −0.439492 + 1.35262i
\(645\) 0 0
\(646\) 10.3849 + 7.54511i 0.408590 + 0.296858i
\(647\) 7.59827 + 23.3851i 0.298719 + 0.919362i 0.981947 + 0.189157i \(0.0605754\pi\)
−0.683228 + 0.730205i \(0.739425\pi\)
\(648\) 80.5964 3.16612
\(649\) −11.1283 14.3596i −0.436825 0.563663i
\(650\) 0 0
\(651\) 4.43175 + 13.6395i 0.173694 + 0.534575i
\(652\) −56.0151 40.6974i −2.19372 1.59383i
\(653\) −33.4097 + 24.2736i −1.30742 + 0.949898i −0.999999 0.00167469i \(-0.999467\pi\)
−0.307424 + 0.951573i \(0.599467\pi\)
\(654\) −1.29417 + 3.98304i −0.0506060 + 0.155749i
\(655\) 0 0
\(656\) −61.9754 + 45.0277i −2.41973 + 1.75804i
\(657\) 0.747865 + 0.543356i 0.0291770 + 0.0211983i
\(658\) 14.9637 + 46.0536i 0.583346 + 1.79536i
\(659\) −4.73658 −0.184511 −0.0922555 0.995735i \(-0.529408\pi\)
−0.0922555 + 0.995735i \(0.529408\pi\)
\(660\) 0 0
\(661\) 10.7556 0.418344 0.209172 0.977879i \(-0.432923\pi\)
0.209172 + 0.977879i \(0.432923\pi\)
\(662\) 10.3306 + 31.7943i 0.401511 + 1.23572i
\(663\) −9.94509 7.22553i −0.386235 0.280616i
\(664\) −119.552 + 86.8599i −4.63953 + 3.37082i
\(665\) 0 0
\(666\) 0.470455 1.44791i 0.0182298 0.0561054i
\(667\) 3.06533 2.22710i 0.118690 0.0862335i
\(668\) −28.9516 21.0346i −1.12017 0.813852i
\(669\) 6.77401 + 20.8482i 0.261898 + 0.806040i
\(670\) 0 0
\(671\) 23.4102 + 6.81246i 0.903741 + 0.262992i
\(672\) −80.1613 −3.09229
\(673\) 11.6621 + 35.8921i 0.449539 + 1.38354i 0.877428 + 0.479708i \(0.159257\pi\)
−0.427889 + 0.903831i \(0.640743\pi\)
\(674\) −52.2063 37.9301i −2.01091 1.46101i
\(675\) 0 0
\(676\) −15.2420 + 46.9100i −0.586230 + 1.80423i
\(677\) −7.19149 + 22.1331i −0.276392 + 0.850646i 0.712456 + 0.701716i \(0.247583\pi\)
−0.988848 + 0.148929i \(0.952417\pi\)
\(678\) 9.96032 7.23659i 0.382524 0.277920i
\(679\) 26.5694 + 19.3038i 1.01964 + 0.740811i
\(680\) 0 0
\(681\) −28.3629 −1.08687
\(682\) 25.8630 + 33.3727i 0.990346 + 1.27791i
\(683\) 12.6153 0.482712 0.241356 0.970437i \(-0.422408\pi\)
0.241356 + 0.970437i \(0.422408\pi\)
\(684\) 0.682545 + 2.10066i 0.0260977 + 0.0803206i
\(685\) 0 0
\(686\) −44.1511 + 32.0776i −1.68570 + 1.22473i
\(687\) 5.98107 18.4078i 0.228192 0.702303i
\(688\) 0.0566448 0.174335i 0.00215956 0.00664645i
\(689\) 10.9350 7.94478i 0.416592 0.302672i
\(690\) 0 0
\(691\) 2.26469 + 6.97000i 0.0861529 + 0.265151i 0.984847 0.173424i \(-0.0554831\pi\)
−0.898694 + 0.438576i \(0.855483\pi\)
\(692\) −11.9000 −0.452368
\(693\) −1.08156 + 1.58996i −0.0410850 + 0.0603976i
\(694\) −57.0772 −2.16662
\(695\) 0 0
\(696\) 15.0730 + 10.9512i 0.571340 + 0.415103i
\(697\) 13.5368 9.83506i 0.512743 0.372530i
\(698\) 21.7940 67.0752i 0.824917 2.53883i
\(699\) −1.28150 + 3.94405i −0.0484708 + 0.149178i
\(700\) 0 0
\(701\) 29.7236 + 21.5954i 1.12264 + 0.815649i 0.984608 0.174778i \(-0.0559209\pi\)
0.138036 + 0.990427i \(0.455921\pi\)
\(702\) −9.57724 29.4757i −0.361470 1.11249i
\(703\) −2.30717 −0.0870166
\(704\) −118.464 + 42.5907i −4.46476 + 1.60520i
\(705\) 0 0
\(706\) 2.91413 + 8.96878i 0.109675 + 0.337545i
\(707\) 22.8698 + 16.6159i 0.860107 + 0.624904i
\(708\) −41.0809 + 29.8470i −1.54391 + 1.12172i
\(709\) −8.01840 + 24.6781i −0.301137 + 0.926806i 0.679953 + 0.733256i \(0.262000\pi\)
−0.981090 + 0.193550i \(0.938000\pi\)
\(710\) 0 0
\(711\) −1.51302 + 1.09927i −0.0567425 + 0.0412258i
\(712\) −112.742 81.9118i −4.22518 3.06978i
\(713\) −4.78997 14.7420i −0.179386 0.552093i
\(714\) 31.2369 1.16901
\(715\) 0 0
\(716\) −55.1586 −2.06137
\(717\) 12.5518 + 38.6305i 0.468756 + 1.44268i
\(718\) 10.6928 + 7.76877i 0.399052 + 0.289928i
\(719\) 2.19677 1.59605i 0.0819259 0.0595226i −0.546068 0.837741i \(-0.683876\pi\)
0.627994 + 0.778218i \(0.283876\pi\)
\(720\) 0 0
\(721\) 0.249445 0.767714i 0.00928983 0.0285912i
\(722\) −38.8410 + 28.2197i −1.44551 + 1.05023i
\(723\) −25.0906 18.2294i −0.933129 0.677958i
\(724\) −33.7295 103.809i −1.25355 3.85802i
\(725\) 0 0
\(726\) 12.4605 48.3539i 0.462453 1.79458i
\(727\) −18.6564 −0.691926 −0.345963 0.938248i \(-0.612448\pi\)
−0.345963 + 0.938248i \(0.612448\pi\)
\(728\) 12.2191 + 37.6066i 0.452871 + 1.39379i
\(729\) −23.5917 17.1404i −0.873767 0.634829i
\(730\) 0 0
\(731\) −0.0123725 + 0.0380786i −0.000457613 + 0.00140839i
\(732\) 21.0591 64.8133i 0.778367 2.39557i
\(733\) −27.1407 + 19.7188i −1.00246 + 0.728332i −0.962615 0.270874i \(-0.912687\pi\)
−0.0398480 + 0.999206i \(0.512687\pi\)
\(734\) 29.3826 + 21.3477i 1.08453 + 0.787958i
\(735\) 0 0
\(736\) 86.6408 3.19362
\(737\) −0.720068 23.2384i −0.0265240 0.855999i
\(738\) 3.89873 0.143514
\(739\) 13.7840 + 42.4228i 0.507053 + 1.56055i 0.797291 + 0.603595i \(0.206266\pi\)
−0.290238 + 0.956955i \(0.593734\pi\)
\(740\) 0 0
\(741\) −3.51170 + 2.55140i −0.129006 + 0.0937280i
\(742\) −10.6136 + 32.6652i −0.389637 + 1.19918i
\(743\) 4.17597 12.8523i 0.153202 0.471506i −0.844773 0.535125i \(-0.820264\pi\)
0.997974 + 0.0636194i \(0.0202644\pi\)
\(744\) 61.6636 44.8013i 2.26070 1.64249i
\(745\) 0 0
\(746\) 21.3192 + 65.6139i 0.780553 + 2.40229i
\(747\) 4.47546 0.163748
\(748\) 63.9066 22.9761i 2.33666 0.840088i
\(749\) 16.0183 0.585295
\(750\) 0 0
\(751\) 20.4965 + 14.8915i 0.747926 + 0.543400i 0.895183 0.445698i \(-0.147045\pi\)
−0.147257 + 0.989098i \(0.547045\pi\)
\(752\) 123.899 90.0180i 4.51814 3.28262i
\(753\) 1.82939 5.63028i 0.0666666 0.205179i
\(754\) 1.98614 6.11270i 0.0723308 0.222611i
\(755\) 0 0
\(756\) 47.0510 + 34.1845i 1.71123 + 1.24328i
\(757\) 5.48060 + 16.8676i 0.199196 + 0.613062i 0.999902 + 0.0140044i \(0.00445787\pi\)
−0.800706 + 0.599057i \(0.795542\pi\)
\(758\) 5.63946 0.204834
\(759\) −10.3108 + 15.1576i −0.374260 + 0.550186i
\(760\) 0 0
\(761\) 7.43998 + 22.8979i 0.269699 + 0.830048i 0.990573 + 0.136982i \(0.0437404\pi\)
−0.720875 + 0.693066i \(0.756260\pi\)
\(762\) −29.8840 21.7120i −1.08258 0.786541i
\(763\) −1.41659 + 1.02921i −0.0512840 + 0.0372600i
\(764\) 25.3939 78.1543i 0.918718 2.82752i
\(765\) 0 0
\(766\) 72.0362 52.3374i 2.60278 1.89103i
\(767\) 9.15303 + 6.65006i 0.330497 + 0.240120i
\(768\) 36.5469 + 112.480i 1.31877 + 4.05876i
\(769\) 25.1389 0.906532 0.453266 0.891375i \(-0.350259\pi\)
0.453266 + 0.891375i \(0.350259\pi\)
\(770\) 0 0
\(771\) −21.5849 −0.777363
\(772\) 38.7872 + 119.375i 1.39598 + 4.29639i
\(773\) 37.4614 + 27.2173i 1.34739 + 0.978937i 0.999137 + 0.0415374i \(0.0132256\pi\)
0.348255 + 0.937400i \(0.386774\pi\)
\(774\) −0.00754739 + 0.00548350i −0.000271285 + 0.000197100i
\(775\) 0 0
\(776\) 53.9368 166.000i 1.93622 5.95907i
\(777\) −4.54211 + 3.30004i −0.162947 + 0.118388i
\(778\) 6.24362 + 4.53625i 0.223845 + 0.162633i
\(779\) −1.82579 5.61919i −0.0654155 0.201328i
\(780\) 0 0
\(781\) −37.9994 11.0580i −1.35972 0.395685i
\(782\) −33.7618 −1.20732
\(783\) −1.88670 5.80666i −0.0674251 0.207513i
\(784\) 45.6309 + 33.1528i 1.62968 + 1.18403i
\(785\) 0 0
\(786\) −3.77701 + 11.6245i −0.134722 + 0.414630i
\(787\) −5.85893 + 18.0319i −0.208848 + 0.642769i 0.790685 + 0.612223i \(0.209724\pi\)
−0.999533 + 0.0305456i \(0.990276\pi\)
\(788\) −41.1561 + 29.9017i −1.46613 + 1.06520i
\(789\) 8.29565 + 6.02714i 0.295333 + 0.214572i
\(790\) 0 0
\(791\) 5.14747 0.183023
\(792\) 9.81286 + 2.85558i 0.348685 + 0.101469i
\(793\) −15.1839 −0.539195
\(794\) −22.7644 70.0616i −0.807878 2.48639i
\(795\) 0 0
\(796\) −2.10137 + 1.52673i −0.0744809 + 0.0541136i
\(797\) 3.66796 11.2888i 0.129926 0.399871i −0.864841 0.502047i \(-0.832581\pi\)
0.994766 + 0.102176i \(0.0325805\pi\)
\(798\) 3.40846 10.4902i 0.120658 0.371348i
\(799\) −27.0623 + 19.6619i −0.957396 + 0.695589i
\(800\) 0 0
\(801\) 1.30421 + 4.01394i 0.0460819 + 0.141826i
\(802\) 50.3191 1.77683
\(803\) −6.14776 7.93284i −0.216950 0.279944i
\(804\) −64.9855 −2.29186
\(805\) 0 0
\(806\) −21.2723 15.4552i −0.749285 0.544387i
\(807\) 29.7414 21.6084i 1.04695 0.760652i
\(808\) 46.4265 142.886i 1.63328 5.02671i
\(809\) −2.17500 + 6.69397i −0.0764690 + 0.235347i −0.981983 0.188969i \(-0.939486\pi\)
0.905514 + 0.424316i \(0.139486\pi\)
\(810\) 0 0
\(811\) 28.5326 + 20.7302i 1.00192 + 0.727935i 0.962498 0.271288i \(-0.0874496\pi\)
0.0394182 + 0.999223i \(0.487450\pi\)
\(812\) 3.72702 + 11.4706i 0.130793 + 0.402539i
\(813\) −14.2131 −0.498475
\(814\) −9.29651 + 13.6665i −0.325843 + 0.479010i
\(815\) 0 0
\(816\) −30.5283 93.9566i −1.06871 3.28914i
\(817\) 0.0114378 + 0.00831002i 0.000400157 + 0.000290731i
\(818\) 16.9917 12.3452i 0.594100 0.431639i
\(819\) 0.370064 1.13894i 0.0129311 0.0397977i
\(820\) 0 0
\(821\) −41.5952 + 30.2207i −1.45168 + 1.05471i −0.466246 + 0.884655i \(0.654394\pi\)
−0.985435 + 0.170053i \(0.945606\pi\)
\(822\) 31.1701 + 22.6464i 1.08718 + 0.789885i
\(823\) −11.9306 36.7186i −0.415875 1.27993i −0.911466 0.411376i \(-0.865048\pi\)
0.495591 0.868556i \(-0.334952\pi\)
\(824\) −4.29015 −0.149454
\(825\) 0 0
\(826\) −28.7490 −1.00031
\(827\) 5.45382 + 16.7851i 0.189648 + 0.583677i 0.999997 0.00227034i \(-0.000722673\pi\)
−0.810349 + 0.585947i \(0.800723\pi\)
\(828\) −4.69986 3.41464i −0.163331 0.118667i
\(829\) 20.5573 14.9357i 0.713984 0.518740i −0.170472 0.985362i \(-0.554529\pi\)
0.884457 + 0.466623i \(0.154529\pi\)
\(830\) 0 0
\(831\) 1.32008 4.06279i 0.0457931 0.140937i
\(832\) 63.4257 46.0814i 2.19889 1.59759i
\(833\) −9.96681 7.24131i −0.345330 0.250897i
\(834\) 31.0301 + 95.5010i 1.07449 + 3.30693i
\(835\) 0 0
\(836\) −0.742693 23.9686i −0.0256866 0.828972i
\(837\) −24.9776 −0.863351
\(838\) −25.4935 78.4608i −0.880657 2.71038i
\(839\) 44.0635 + 32.0140i 1.52124 + 1.10525i 0.960868 + 0.277005i \(0.0893419\pi\)
0.560372 + 0.828241i \(0.310658\pi\)
\(840\) 0 0
\(841\) −8.57023 + 26.3764i −0.295525 + 0.909533i
\(842\) −21.6480 + 66.6255i −0.746038 + 2.29607i
\(843\) 27.4934 19.9752i 0.946924 0.687981i
\(844\) −3.58640 2.60567i −0.123449 0.0896910i
\(845\) 0 0
\(846\) −7.79421 −0.267971
\(847\) 16.0978 13.2934i 0.553127 0.456768i
\(848\) 108.626 3.73022
\(849\) −5.48367 16.8770i −0.188199 0.579217i
\(850\) 0 0
\(851\) 4.90926 3.56678i 0.168287 0.122268i
\(852\) −34.1831 + 105.205i −1.17109 + 3.60425i
\(853\) 0.526298 1.61978i 0.0180201 0.0554601i −0.941642 0.336616i \(-0.890718\pi\)
0.959662 + 0.281156i \(0.0907177\pi\)
\(854\) 31.2145 22.6787i 1.06814 0.776048i
\(855\) 0 0
\(856\) −26.3073 80.9656i −0.899166 2.76735i
\(857\) −34.5112 −1.17888 −0.589440 0.807812i \(-0.700652\pi\)
−0.589440 + 0.807812i \(0.700652\pi\)
\(858\) 0.963112 + 31.0821i 0.0328801 + 1.06113i
\(859\) −41.1808 −1.40507 −0.702535 0.711650i \(-0.747948\pi\)
−0.702535 + 0.711650i \(0.747948\pi\)
\(860\) 0 0
\(861\) −11.6318 8.45097i −0.396409 0.288008i
\(862\) −45.9034 + 33.3508i −1.56348 + 1.13593i
\(863\) 5.64904 17.3860i 0.192296 0.591825i −0.807702 0.589591i \(-0.799289\pi\)
0.999998 0.00223395i \(-0.000711090\pi\)
\(864\) 43.1424 132.779i 1.46773 4.51722i
\(865\) 0 0
\(866\) 30.7752 + 22.3595i 1.04579 + 0.759808i
\(867\) −1.95519 6.01744i −0.0664016 0.204363i
\(868\) 49.3412 1.67475
\(869\) 19.1070 6.86944i 0.648159 0.233030i
\(870\) 0 0
\(871\) 4.47428 + 13.7704i 0.151605 + 0.466593i
\(872\) 7.52875 + 5.46996i 0.254956 + 0.185236i
\(873\) −4.27658 + 3.10712i −0.144740 + 0.105160i
\(874\) −3.68397 + 11.3381i −0.124612 + 0.383517i
\(875\) 0 0
\(876\) −22.6948 + 16.4888i −0.766788 + 0.557104i
\(877\) 33.5709 + 24.3907i 1.13361 + 0.823614i 0.986216 0.165464i \(-0.0529122\pi\)
0.147392 + 0.989078i \(0.452912\pi\)
\(878\) 20.6668 + 63.6059i 0.697471 + 2.14659i
\(879\) −0.858629 −0.0289608
\(880\) 0 0
\(881\) 49.7389 1.67575 0.837873 0.545866i \(-0.183799\pi\)
0.837873 + 0.545866i \(0.183799\pi\)
\(882\) −0.887046 2.73005i −0.0298684 0.0919254i
\(883\) −15.3859 11.1785i −0.517776 0.376186i 0.297990 0.954569i \(-0.403684\pi\)
−0.815765 + 0.578383i \(0.803684\pi\)
\(884\) −34.2157 + 24.8592i −1.15080 + 0.836105i
\(885\) 0 0
\(886\) −1.45074 + 4.46491i −0.0487384 + 0.150001i
\(887\) 2.73133 1.98443i 0.0917090 0.0666305i −0.540986 0.841032i \(-0.681949\pi\)
0.632695 + 0.774401i \(0.281949\pi\)
\(888\) 24.1400 + 17.5387i 0.810085 + 0.588561i
\(889\) −4.77244 14.6881i −0.160063 0.492622i
\(890\) 0 0
\(891\) 16.2332 + 20.9467i 0.543831 + 0.701740i
\(892\) 75.4189 2.52521
\(893\) 3.65005 + 11.2337i 0.122144 + 0.375921i
\(894\) −59.0461 42.8995i −1.97480 1.43477i
\(895\) 0 0
\(896\) −31.3798 + 96.5771i −1.04833 + 3.22641i
\(897\) 3.52794 10.8579i 0.117794 0.362534i
\(898\) 5.82225 4.23011i 0.194291 0.141161i
\(899\) −4.19060 3.04465i −0.139764 0.101545i
\(900\) 0 0
\(901\) −23.7263 −0.790437
\(902\) −40.6420 11.8270i −1.35323 0.393795i
\(903\) 0.0344036 0.00114488
\(904\) −8.45385 26.0183i −0.281171 0.865355i
\(905\) 0 0
\(906\) 85.2797 61.9593i 2.83323 2.05846i
\(907\) 10.3770 31.9372i 0.344563 1.06046i −0.617254 0.786764i \(-0.711755\pi\)
0.961817 0.273692i \(-0.0882449\pi\)
\(908\) −30.1543 + 92.8055i −1.00071 + 3.07986i
\(909\) −3.68110 + 2.67448i −0.122094 + 0.0887068i
\(910\) 0 0
\(911\) 14.7638 + 45.4384i 0.489147 + 1.50544i 0.825883 + 0.563841i \(0.190677\pi\)
−0.336736 + 0.941599i \(0.609323\pi\)
\(912\) −34.8843 −1.15513
\(913\) −46.6540 13.5765i −1.54402 0.449316i
\(914\) 38.6081 1.27704
\(915\) 0 0
\(916\) −53.8730 39.1410i −1.78001 1.29326i
\(917\) −4.13430 + 3.00374i −0.136527 + 0.0991923i
\(918\) −16.8115 + 51.7405i −0.554863 + 1.70769i
\(919\) 3.79764 11.6879i 0.125273 0.385550i −0.868678 0.495377i \(-0.835030\pi\)
0.993951 + 0.109827i \(0.0350298\pi\)
\(920\) 0 0
\(921\) 26.6132 + 19.3356i 0.876934 + 0.637130i
\(922\) −22.6770 69.7926i −0.746827 2.29850i
\(923\) 24.6464 0.811246
\(924\) −35.7454 46.1246i −1.17594 1.51739i
\(925\) 0 0
\(926\) 20.1987 + 62.1651i 0.663769 + 2.04287i
\(927\) 0.105115 + 0.0763708i 0.00345244 + 0.00250835i
\(928\) 23.4233 17.0180i 0.768908 0.558644i
\(929\) 16.3005 50.1679i 0.534804 1.64596i −0.209269 0.977858i \(-0.567109\pi\)
0.744073 0.668098i \(-0.232891\pi\)
\(930\) 0 0
\(931\) −3.51937 + 2.55697i −0.115343 + 0.0838014i
\(932\) 11.5428 + 8.38633i 0.378097 + 0.274703i
\(933\) −7.76797 23.9074i −0.254312 0.782692i
\(934\) 27.9975 0.916107
\(935\) 0 0
\(936\) −6.36462 −0.208034
\(937\) −12.5153 38.5181i −0.408857 1.25833i −0.917632 0.397432i \(-0.869901\pi\)
0.508775 0.860900i \(-0.330099\pi\)
\(938\) −29.7656 21.6260i −0.971882 0.706114i
\(939\) −37.7477 + 27.4253i −1.23185 + 0.894991i
\(940\) 0 0
\(941\) 2.10825 6.48852i 0.0687269 0.211520i −0.910794 0.412860i \(-0.864530\pi\)
0.979521 + 0.201341i \(0.0645298\pi\)
\(942\) −59.6318 + 43.3250i −1.94291 + 1.41161i
\(943\) 12.5720 + 9.13407i 0.409400 + 0.297446i
\(944\) 28.0969 + 86.4735i 0.914478 + 2.81447i
\(945\) 0 0
\(946\) 0.0953115 0.0342669i 0.00309884 0.00111411i
\(947\) −31.5841 −1.02634 −0.513172 0.858286i \(-0.671530\pi\)
−0.513172 + 0.858286i \(0.671530\pi\)
\(948\) −17.5377 53.9754i −0.569597 1.75304i
\(949\) 5.05652 + 3.67378i 0.164142 + 0.119256i
\(950\) 0 0
\(951\) 9.56043 29.4240i 0.310018 0.954138i
\(952\) 21.4490 66.0132i 0.695165 2.13950i
\(953\) −17.5279 + 12.7347i −0.567784 + 0.412519i −0.834299 0.551312i \(-0.814128\pi\)
0.266516 + 0.963831i \(0.414128\pi\)
\(954\) −4.47252 3.24948i −0.144803 0.105206i
\(955\) 0 0
\(956\) 139.747 4.51973
\(957\) 0.189731 + 6.12311i 0.00613314 + 0.197932i
\(958\) −1.88468 −0.0608912
\(959\) 4.97785 + 15.3202i 0.160743 + 0.494716i
\(960\) 0 0
\(961\) 7.93576 5.76566i 0.255992 0.185989i
\(962\) 3.18088 9.78973i 0.102556 0.315634i
\(963\) −0.796734 + 2.45209i −0.0256744 + 0.0790176i
\(964\) −86.3233 + 62.7175i −2.78029 + 2.02000i
\(965\) 0 0
\(966\) 8.96472 + 27.5906i 0.288435 + 0.887712i
\(967\) 9.03757 0.290629 0.145314 0.989386i \(-0.453581\pi\)
0.145314 + 0.989386i \(0.453581\pi\)
\(968\) −93.6307 59.5354i −3.00940 1.91354i
\(969\) 7.61950 0.244774
\(970\) 0 0
\(971\) −27.7379 20.1528i −0.890151 0.646733i 0.0457664 0.998952i \(-0.485427\pi\)
−0.935917 + 0.352220i \(0.885427\pi\)
\(972\) −14.4467 + 10.4961i −0.463377 + 0.336663i
\(973\) −12.9736 + 39.9288i −0.415916 + 1.28006i
\(974\) −9.07928 + 27.9431i −0.290919 + 0.895356i
\(975\) 0 0
\(976\) −98.7211 71.7251i −3.15998 2.29586i
\(977\) −5.30858 16.3381i −0.169837 0.522703i 0.829523 0.558472i \(-0.188612\pi\)
−0.999360 + 0.0357684i \(0.988612\pi\)
\(978\) −55.6532 −1.77959
\(979\) −1.41914 45.7993i −0.0453559 1.46375i
\(980\) 0 0
\(981\) −0.0870932 0.268045i −0.00278067 0.00855802i
\(982\) −25.8340 18.7695i −0.824395 0.598958i
\(983\) −3.12224 + 2.26844i −0.0995839 + 0.0723519i −0.636463 0.771307i \(-0.719603\pi\)
0.536879 + 0.843659i \(0.319603\pi\)
\(984\) −23.6129 + 72.6730i −0.752751 + 2.31673i
\(985\) 0 0
\(986\) −9.12748 + 6.63150i −0.290678 + 0.211190i
\(987\) 23.2538 + 16.8949i 0.740178 + 0.537771i
\(988\) 4.61487 + 14.2031i 0.146819 + 0.451861i
\(989\) −0.0371845 −0.00118240
\(990\) 0 0
\(991\) −31.5631 −1.00263 −0.501317 0.865264i \(-0.667151\pi\)
−0.501317 + 0.865264i \(0.667151\pi\)
\(992\) −36.6019 112.649i −1.16211 3.57661i
\(993\) 16.0539 + 11.6639i 0.509456 + 0.370141i
\(994\) −50.6673 + 36.8119i −1.60707 + 1.16760i
\(995\) 0 0
\(996\) −41.9685 + 129.166i −1.32982 + 4.09277i
\(997\) −7.49529 + 5.44564i −0.237378 + 0.172465i −0.700114 0.714031i \(-0.746868\pi\)
0.462736 + 0.886496i \(0.346868\pi\)
\(998\) −20.6617 15.0116i −0.654034 0.475184i
\(999\) −3.02162 9.29959i −0.0955999 0.294226i
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 275.2.h.c.126.1 16
5.2 odd 4 275.2.z.c.49.8 32
5.3 odd 4 275.2.z.c.49.1 32
5.4 even 2 275.2.h.e.126.4 yes 16
11.3 even 5 3025.2.a.bi.1.1 8
11.8 odd 10 3025.2.a.bm.1.8 8
11.9 even 5 inner 275.2.h.c.251.1 yes 16
55.9 even 10 275.2.h.e.251.4 yes 16
55.14 even 10 3025.2.a.bn.1.8 8
55.19 odd 10 3025.2.a.bj.1.1 8
55.42 odd 20 275.2.z.c.174.1 32
55.53 odd 20 275.2.z.c.174.8 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
275.2.h.c.126.1 16 1.1 even 1 trivial
275.2.h.c.251.1 yes 16 11.9 even 5 inner
275.2.h.e.126.4 yes 16 5.4 even 2
275.2.h.e.251.4 yes 16 55.9 even 10
275.2.z.c.49.1 32 5.3 odd 4
275.2.z.c.49.8 32 5.2 odd 4
275.2.z.c.174.1 32 55.42 odd 20
275.2.z.c.174.8 32 55.53 odd 20
3025.2.a.bi.1.1 8 11.3 even 5
3025.2.a.bj.1.1 8 55.19 odd 10
3025.2.a.bm.1.8 8 11.8 odd 10
3025.2.a.bn.1.8 8 55.14 even 10