Properties

Label 325.2.e.c.276.2
Level $325$
Weight $2$
Character 325.276
Analytic conductor $2.595$
Analytic rank $0$
Dimension $10$
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] = [325,2,Mod(126,325)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(325, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("325.126");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 325.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.59513806569\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} + 8x^{8} - 2x^{7} + 52x^{6} - 5x^{5} + 97x^{4} + 60x^{3} + 141x^{2} + 36x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 276.2
Root \(-0.547998 - 0.949161i\) of defining polynomial
Character \(\chi\) \(=\) 325.276
Dual form 325.2.e.c.126.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.547998 - 0.949161i) q^{2} +(-1.68234 - 2.91389i) q^{3} +(0.399395 - 0.691773i) q^{4} +(-1.84383 + 3.19362i) q^{6} +(-0.795836 + 1.37843i) q^{7} -3.06747 q^{8} +(-4.16051 + 7.20621i) q^{9} +O(q^{10})\) \(q+(-0.547998 - 0.949161i) q^{2} +(-1.68234 - 2.91389i) q^{3} +(0.399395 - 0.691773i) q^{4} +(-1.84383 + 3.19362i) q^{6} +(-0.795836 + 1.37843i) q^{7} -3.06747 q^{8} +(-4.16051 + 7.20621i) q^{9} +(-1.84383 - 3.19362i) q^{11} -2.68767 q^{12} +(3.21311 - 1.63582i) q^{13} +1.74447 q^{14} +(0.882175 + 1.52797i) q^{16} +(-1.49244 + 2.58498i) q^{17} +9.11981 q^{18} +(1.39940 - 2.42382i) q^{19} +5.35546 q^{21} +(-2.02084 + 3.50019i) q^{22} +(-0.335546 - 0.581184i) q^{23} +(5.16051 + 8.93826i) q^{24} +(-3.31344 - 2.15334i) q^{26} +17.9035 q^{27} +(0.635707 + 1.10108i) q^{28} +(-1.37894 - 2.38839i) q^{29} -6.43214 q^{31} +(-2.10060 + 3.63835i) q^{32} +(-6.20390 + 10.7455i) q^{33} +3.27141 q^{34} +(3.32338 + 5.75626i) q^{36} +(-0.479163 - 0.829935i) q^{37} -3.06747 q^{38} +(-10.1721 - 6.61067i) q^{39} +(-1.42722 - 2.47202i) q^{41} +(-2.93478 - 5.08319i) q^{42} +(2.44279 - 4.23103i) q^{43} -2.94568 q^{44} +(-0.367758 + 0.636975i) q^{46} -3.83323 q^{47} +(2.96823 - 5.14113i) q^{48} +(2.23329 + 3.86817i) q^{49} +10.0431 q^{51} +(0.151689 - 2.87608i) q^{52} -2.70355 q^{53} +(-9.81108 - 16.9933i) q^{54} +(2.44120 - 4.22828i) q^{56} -9.41701 q^{57} +(-1.51131 + 2.61767i) q^{58} +(5.17839 - 8.96924i) q^{59} +(-3.71607 + 6.43642i) q^{61} +(3.52480 + 6.10513i) q^{62} +(-6.62217 - 11.4699i) q^{63} +8.13321 q^{64} +13.5989 q^{66} +(-5.76308 - 9.98194i) q^{67} +(1.19215 + 2.06486i) q^{68} +(-1.12900 + 1.95549i) q^{69} +(-4.28885 + 7.42851i) q^{71} +(12.7622 - 22.1048i) q^{72} -3.72859 q^{73} +(-0.525161 + 0.909606i) q^{74} +(-1.11782 - 1.93613i) q^{76} +5.86956 q^{77} +(-0.700282 + 13.2776i) q^{78} +4.33442 q^{79} +(-17.6381 - 30.5501i) q^{81} +(-1.56423 + 2.70932i) q^{82} -15.6619 q^{83} +(2.13895 - 3.70476i) q^{84} -5.35457 q^{86} +(-4.63967 + 8.03615i) q^{87} +(5.65590 + 9.79631i) q^{88} +(-0.826615 - 1.43174i) q^{89} +(-0.302256 + 5.73089i) q^{91} -0.536063 q^{92} +(10.8210 + 18.7426i) q^{93} +(2.10060 + 3.63835i) q^{94} +14.1357 q^{96} +(-1.12863 + 1.95484i) q^{97} +(2.44768 - 4.23950i) q^{98} +30.6852 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 3 q^{3} - 6 q^{4} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 3 q^{3} - 6 q^{4} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 4 q^{9} - 3 q^{11} + 4 q^{12} + 10 q^{13} - 16 q^{14} - 4 q^{16} - 4 q^{17} - 4 q^{18} + 4 q^{19} - 16 q^{21} - 8 q^{22} - 15 q^{23} + 14 q^{24} - 9 q^{26} + 42 q^{27} + 17 q^{28} + q^{29} - 31 q^{32} + 2 q^{33} + 54 q^{34} + 13 q^{36} - 17 q^{37} + 6 q^{38} - 10 q^{39} - 6 q^{41} - 32 q^{42} - 12 q^{43} - 16 q^{44} + 7 q^{46} - 24 q^{47} + 2 q^{48} - 7 q^{49} + 23 q^{52} + 16 q^{53} - 19 q^{54} + 17 q^{56} - 8 q^{57} - 38 q^{58} + 12 q^{59} - 5 q^{61} - 13 q^{62} - 26 q^{63} - 10 q^{64} + 86 q^{66} + 16 q^{67} - 25 q^{68} - 20 q^{69} - 19 q^{71} + 45 q^{72} - 16 q^{73} - 2 q^{74} - 24 q^{76} + 64 q^{77} + 42 q^{78} - 28 q^{79} - 29 q^{81} + 23 q^{82} - 14 q^{83} + 34 q^{84} - 84 q^{86} - 21 q^{87} - 2 q^{88} + 10 q^{89} + 17 q^{91} + 142 q^{92} + 33 q^{93} + 31 q^{94} + 34 q^{96} - 37 q^{97} + 21 q^{98} + 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(301\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.547998 0.949161i −0.387493 0.671158i 0.604618 0.796515i \(-0.293326\pi\)
−0.992112 + 0.125357i \(0.959992\pi\)
\(3\) −1.68234 2.91389i −0.971297 1.68234i −0.691650 0.722233i \(-0.743116\pi\)
−0.279647 0.960103i \(-0.590218\pi\)
\(4\) 0.399395 0.691773i 0.199698 0.345887i
\(5\) 0 0
\(6\) −1.84383 + 3.19362i −0.752742 + 1.30379i
\(7\) −0.795836 + 1.37843i −0.300798 + 0.520997i −0.976317 0.216345i \(-0.930586\pi\)
0.675519 + 0.737343i \(0.263920\pi\)
\(8\) −3.06747 −1.08451
\(9\) −4.16051 + 7.20621i −1.38684 + 2.40207i
\(10\) 0 0
\(11\) −1.84383 3.19362i −0.555937 0.962911i −0.997830 0.0658435i \(-0.979026\pi\)
0.441893 0.897068i \(-0.354307\pi\)
\(12\) −2.68767 −0.775863
\(13\) 3.21311 1.63582i 0.891158 0.453694i
\(14\) 1.74447 0.466229
\(15\) 0 0
\(16\) 0.882175 + 1.52797i 0.220544 + 0.381993i
\(17\) −1.49244 + 2.58498i −0.361969 + 0.626949i −0.988285 0.152620i \(-0.951229\pi\)
0.626316 + 0.779570i \(0.284562\pi\)
\(18\) 9.11981 2.14956
\(19\) 1.39940 2.42382i 0.321043 0.556063i −0.659660 0.751564i \(-0.729300\pi\)
0.980704 + 0.195501i \(0.0626331\pi\)
\(20\) 0 0
\(21\) 5.35546 1.16866
\(22\) −2.02084 + 3.50019i −0.430844 + 0.746244i
\(23\) −0.335546 0.581184i −0.0699663 0.121185i 0.828920 0.559367i \(-0.188956\pi\)
−0.898886 + 0.438182i \(0.855623\pi\)
\(24\) 5.16051 + 8.93826i 1.05338 + 1.82452i
\(25\) 0 0
\(26\) −3.31344 2.15334i −0.649818 0.422304i
\(27\) 17.9035 3.44553
\(28\) 0.635707 + 1.10108i 0.120137 + 0.208084i
\(29\) −1.37894 2.38839i −0.256062 0.443513i 0.709121 0.705087i \(-0.249092\pi\)
−0.965183 + 0.261574i \(0.915759\pi\)
\(30\) 0 0
\(31\) −6.43214 −1.15525 −0.577623 0.816304i \(-0.696020\pi\)
−0.577623 + 0.816304i \(0.696020\pi\)
\(32\) −2.10060 + 3.63835i −0.371338 + 0.643176i
\(33\) −6.20390 + 10.7455i −1.07996 + 1.87055i
\(34\) 3.27141 0.561043
\(35\) 0 0
\(36\) 3.32338 + 5.75626i 0.553896 + 0.959376i
\(37\) −0.479163 0.829935i −0.0787739 0.136440i 0.823947 0.566666i \(-0.191767\pi\)
−0.902721 + 0.430226i \(0.858434\pi\)
\(38\) −3.06747 −0.497609
\(39\) −10.1721 6.61067i −1.62884 1.05855i
\(40\) 0 0
\(41\) −1.42722 2.47202i −0.222894 0.386064i 0.732791 0.680453i \(-0.238217\pi\)
−0.955686 + 0.294389i \(0.904884\pi\)
\(42\) −2.93478 5.08319i −0.452847 0.784353i
\(43\) 2.44279 4.23103i 0.372521 0.645226i −0.617431 0.786625i \(-0.711827\pi\)
0.989953 + 0.141399i \(0.0451600\pi\)
\(44\) −2.94568 −0.444078
\(45\) 0 0
\(46\) −0.367758 + 0.636975i −0.0542229 + 0.0939169i
\(47\) −3.83323 −0.559134 −0.279567 0.960126i \(-0.590191\pi\)
−0.279567 + 0.960126i \(0.590191\pi\)
\(48\) 2.96823 5.14113i 0.428427 0.742058i
\(49\) 2.23329 + 3.86817i 0.319041 + 0.552596i
\(50\) 0 0
\(51\) 10.0431 1.40632
\(52\) 0.151689 2.87608i 0.0210355 0.398841i
\(53\) −2.70355 −0.371361 −0.185681 0.982610i \(-0.559449\pi\)
−0.185681 + 0.982610i \(0.559449\pi\)
\(54\) −9.81108 16.9933i −1.33512 2.31249i
\(55\) 0 0
\(56\) 2.44120 4.22828i 0.326219 0.565028i
\(57\) −9.41701 −1.24731
\(58\) −1.51131 + 2.61767i −0.198445 + 0.343717i
\(59\) 5.17839 8.96924i 0.674169 1.16770i −0.302542 0.953136i \(-0.597835\pi\)
0.976711 0.214559i \(-0.0688314\pi\)
\(60\) 0 0
\(61\) −3.71607 + 6.43642i −0.475794 + 0.824099i −0.999615 0.0277288i \(-0.991173\pi\)
0.523822 + 0.851828i \(0.324506\pi\)
\(62\) 3.52480 + 6.10513i 0.447650 + 0.775353i
\(63\) −6.62217 11.4699i −0.834315 1.44508i
\(64\) 8.13321 1.01665
\(65\) 0 0
\(66\) 13.5989 1.67391
\(67\) −5.76308 9.98194i −0.704072 1.21949i −0.967025 0.254680i \(-0.918030\pi\)
0.262954 0.964808i \(-0.415303\pi\)
\(68\) 1.19215 + 2.06486i 0.144569 + 0.250401i
\(69\) −1.12900 + 1.95549i −0.135916 + 0.235414i
\(70\) 0 0
\(71\) −4.28885 + 7.42851i −0.508993 + 0.881601i 0.490953 + 0.871186i \(0.336649\pi\)
−0.999946 + 0.0104153i \(0.996685\pi\)
\(72\) 12.7622 22.1048i 1.50404 2.60508i
\(73\) −3.72859 −0.436398 −0.218199 0.975904i \(-0.570018\pi\)
−0.218199 + 0.975904i \(0.570018\pi\)
\(74\) −0.525161 + 0.909606i −0.0610487 + 0.105740i
\(75\) 0 0
\(76\) −1.11782 1.93613i −0.128223 0.222089i
\(77\) 5.86956 0.668899
\(78\) −0.700282 + 13.2776i −0.0792913 + 1.50340i
\(79\) 4.33442 0.487661 0.243830 0.969818i \(-0.421596\pi\)
0.243830 + 0.969818i \(0.421596\pi\)
\(80\) 0 0
\(81\) −17.6381 30.5501i −1.95979 3.39446i
\(82\) −1.56423 + 2.70932i −0.172740 + 0.299195i
\(83\) −15.6619 −1.71912 −0.859559 0.511036i \(-0.829262\pi\)
−0.859559 + 0.511036i \(0.829262\pi\)
\(84\) 2.13895 3.70476i 0.233378 0.404223i
\(85\) 0 0
\(86\) −5.35457 −0.577398
\(87\) −4.63967 + 8.03615i −0.497425 + 0.861565i
\(88\) 5.65590 + 9.79631i 0.602921 + 1.04429i
\(89\) −0.826615 1.43174i −0.0876210 0.151764i 0.818884 0.573959i \(-0.194593\pi\)
−0.906505 + 0.422195i \(0.861260\pi\)
\(90\) 0 0
\(91\) −0.302256 + 5.73089i −0.0316850 + 0.600761i
\(92\) −0.536063 −0.0558884
\(93\) 10.8210 + 18.7426i 1.12209 + 1.94351i
\(94\) 2.10060 + 3.63835i 0.216661 + 0.375268i
\(95\) 0 0
\(96\) 14.1357 1.44272
\(97\) −1.12863 + 1.95484i −0.114595 + 0.198484i −0.917618 0.397464i \(-0.869890\pi\)
0.803023 + 0.595948i \(0.203224\pi\)
\(98\) 2.44768 4.23950i 0.247253 0.428254i
\(99\) 30.6852 3.08397
\(100\) 0 0
\(101\) −5.64329 9.77446i −0.561528 0.972595i −0.997363 0.0725688i \(-0.976880\pi\)
0.435835 0.900026i \(-0.356453\pi\)
\(102\) −5.50362 9.53254i −0.544939 0.943863i
\(103\) 19.5998 1.93122 0.965612 0.259986i \(-0.0837179\pi\)
0.965612 + 0.259986i \(0.0837179\pi\)
\(104\) −9.85612 + 5.01781i −0.966472 + 0.492037i
\(105\) 0 0
\(106\) 1.48154 + 2.56611i 0.143900 + 0.249242i
\(107\) −0.880787 1.52557i −0.0851489 0.147482i 0.820306 0.571925i \(-0.193803\pi\)
−0.905455 + 0.424443i \(0.860470\pi\)
\(108\) 7.15057 12.3851i 0.688064 1.19176i
\(109\) −9.33442 −0.894076 −0.447038 0.894515i \(-0.647521\pi\)
−0.447038 + 0.894515i \(0.647521\pi\)
\(110\) 0 0
\(111\) −1.61223 + 2.79246i −0.153026 + 0.265048i
\(112\) −2.80827 −0.265357
\(113\) 5.66946 9.81979i 0.533338 0.923768i −0.465904 0.884835i \(-0.654271\pi\)
0.999242 0.0389329i \(-0.0123959\pi\)
\(114\) 5.16051 + 8.93826i 0.483326 + 0.837145i
\(115\) 0 0
\(116\) −2.20297 −0.204540
\(117\) −1.58015 + 29.9602i −0.146085 + 2.76982i
\(118\) −11.3510 −1.04494
\(119\) −2.37547 4.11444i −0.217759 0.377170i
\(120\) 0 0
\(121\) −1.29945 + 2.25072i −0.118132 + 0.204611i
\(122\) 8.14560 0.737468
\(123\) −4.80212 + 8.31752i −0.432993 + 0.749966i
\(124\) −2.56897 + 4.44958i −0.230700 + 0.399584i
\(125\) 0 0
\(126\) −7.25787 + 12.5710i −0.646583 + 1.11991i
\(127\) −5.09996 8.83339i −0.452548 0.783837i 0.545995 0.837788i \(-0.316152\pi\)
−0.998544 + 0.0539516i \(0.982818\pi\)
\(128\) −0.255779 0.443022i −0.0226079 0.0391580i
\(129\) −16.4383 −1.44732
\(130\) 0 0
\(131\) −10.7666 −0.940679 −0.470339 0.882486i \(-0.655868\pi\)
−0.470339 + 0.882486i \(0.655868\pi\)
\(132\) 4.95562 + 8.58338i 0.431331 + 0.747088i
\(133\) 2.22738 + 3.85793i 0.193138 + 0.334525i
\(134\) −6.31631 + 10.9402i −0.545646 + 0.945087i
\(135\) 0 0
\(136\) 4.57800 7.92933i 0.392560 0.679935i
\(137\) 6.37230 11.0371i 0.544422 0.942967i −0.454221 0.890889i \(-0.650082\pi\)
0.998643 0.0520777i \(-0.0165844\pi\)
\(138\) 2.47477 0.210666
\(139\) 1.95172 3.38047i 0.165543 0.286728i −0.771305 0.636465i \(-0.780396\pi\)
0.936848 + 0.349737i \(0.113729\pi\)
\(140\) 0 0
\(141\) 6.44878 + 11.1696i 0.543085 + 0.940652i
\(142\) 9.40113 0.788925
\(143\) −11.1486 7.24528i −0.932295 0.605880i
\(144\) −14.6812 −1.22343
\(145\) 0 0
\(146\) 2.04326 + 3.53903i 0.169101 + 0.292892i
\(147\) 7.51428 13.0151i 0.619768 1.07347i
\(148\) −0.765502 −0.0629239
\(149\) 0.727708 1.26043i 0.0596162 0.103258i −0.834677 0.550740i \(-0.814346\pi\)
0.894293 + 0.447482i \(0.147679\pi\)
\(150\) 0 0
\(151\) 18.4701 1.50308 0.751538 0.659690i \(-0.229312\pi\)
0.751538 + 0.659690i \(0.229312\pi\)
\(152\) −4.29260 + 7.43500i −0.348176 + 0.603058i
\(153\) −12.4186 21.5096i −1.00398 1.73895i
\(154\) −3.21651 5.57116i −0.259194 0.448937i
\(155\) 0 0
\(156\) −8.63579 + 4.39654i −0.691417 + 0.352005i
\(157\) 11.2891 0.900972 0.450486 0.892784i \(-0.351251\pi\)
0.450486 + 0.892784i \(0.351251\pi\)
\(158\) −2.37526 4.11407i −0.188965 0.327297i
\(159\) 4.54828 + 7.87786i 0.360702 + 0.624755i
\(160\) 0 0
\(161\) 1.06816 0.0841828
\(162\) −19.3313 + 33.4829i −1.51881 + 2.63066i
\(163\) 6.24224 10.8119i 0.488930 0.846851i −0.510989 0.859587i \(-0.670721\pi\)
0.999919 + 0.0127358i \(0.00405403\pi\)
\(164\) −2.28010 −0.178046
\(165\) 0 0
\(166\) 8.58270 + 14.8657i 0.666147 + 1.15380i
\(167\) 6.28642 + 10.8884i 0.486458 + 0.842570i 0.999879 0.0155669i \(-0.00495529\pi\)
−0.513421 + 0.858137i \(0.671622\pi\)
\(168\) −16.4277 −1.26742
\(169\) 7.64821 10.5121i 0.588324 0.808626i
\(170\) 0 0
\(171\) 11.6444 + 20.1687i 0.890469 + 1.54234i
\(172\) −1.95128 3.37971i −0.148783 0.257700i
\(173\) −1.34902 + 2.33657i −0.102564 + 0.177646i −0.912740 0.408540i \(-0.866038\pi\)
0.810176 + 0.586186i \(0.199371\pi\)
\(174\) 10.1701 0.770996
\(175\) 0 0
\(176\) 3.25317 5.63466i 0.245217 0.424728i
\(177\) −34.8472 −2.61927
\(178\) −0.905967 + 1.56918i −0.0679051 + 0.117615i
\(179\) 1.15559 + 2.00154i 0.0863728 + 0.149602i 0.905975 0.423330i \(-0.139139\pi\)
−0.819603 + 0.572933i \(0.805806\pi\)
\(180\) 0 0
\(181\) 4.80127 0.356875 0.178438 0.983951i \(-0.442896\pi\)
0.178438 + 0.983951i \(0.442896\pi\)
\(182\) 5.60518 2.85363i 0.415483 0.211525i
\(183\) 25.0067 1.84855
\(184\) 1.02928 + 1.78276i 0.0758793 + 0.131427i
\(185\) 0 0
\(186\) 11.8598 20.5418i 0.869603 1.50620i
\(187\) 11.0072 0.804929
\(188\) −1.53098 + 2.65173i −0.111658 + 0.193397i
\(189\) −14.2482 + 24.6787i −1.03641 + 1.79511i
\(190\) 0 0
\(191\) 8.91168 15.4355i 0.644826 1.11687i −0.339515 0.940601i \(-0.610263\pi\)
0.984342 0.176272i \(-0.0564037\pi\)
\(192\) −13.6828 23.6993i −0.987471 1.71035i
\(193\) 1.25888 + 2.18045i 0.0906165 + 0.156952i 0.907771 0.419467i \(-0.137783\pi\)
−0.817154 + 0.576419i \(0.804450\pi\)
\(194\) 2.47394 0.177618
\(195\) 0 0
\(196\) 3.56786 0.254847
\(197\) 9.25781 + 16.0350i 0.659591 + 1.14245i 0.980721 + 0.195411i \(0.0626040\pi\)
−0.321130 + 0.947035i \(0.604063\pi\)
\(198\) −16.8154 29.1252i −1.19502 2.06983i
\(199\) −6.60105 + 11.4333i −0.467936 + 0.810489i −0.999329 0.0366369i \(-0.988335\pi\)
0.531393 + 0.847126i \(0.321669\pi\)
\(200\) 0 0
\(201\) −19.3909 + 33.5860i −1.36773 + 2.36897i
\(202\) −6.18503 + 10.7128i −0.435177 + 0.753748i
\(203\) 4.38963 0.308092
\(204\) 4.01118 6.94757i 0.280839 0.486427i
\(205\) 0 0
\(206\) −10.7407 18.6034i −0.748337 1.29616i
\(207\) 5.58418 0.388127
\(208\) 5.33401 + 3.46647i 0.369847 + 0.240357i
\(209\) −10.3210 −0.713920
\(210\) 0 0
\(211\) 3.96666 + 6.87046i 0.273076 + 0.472982i 0.969648 0.244505i \(-0.0786255\pi\)
−0.696572 + 0.717487i \(0.745292\pi\)
\(212\) −1.07979 + 1.87024i −0.0741600 + 0.128449i
\(213\) 28.8611 1.97753
\(214\) −0.965340 + 1.67202i −0.0659893 + 0.114297i
\(215\) 0 0
\(216\) −54.9183 −3.73672
\(217\) 5.11893 8.86625i 0.347496 0.601880i
\(218\) 5.11525 + 8.85987i 0.346448 + 0.600066i
\(219\) 6.27273 + 10.8647i 0.423872 + 0.734168i
\(220\) 0 0
\(221\) −0.566823 + 10.7472i −0.0381286 + 0.722934i
\(222\) 3.53399 0.237186
\(223\) −1.87499 3.24758i −0.125559 0.217474i 0.796392 0.604780i \(-0.206739\pi\)
−0.921951 + 0.387306i \(0.873406\pi\)
\(224\) −3.34347 5.79107i −0.223395 0.386932i
\(225\) 0 0
\(226\) −12.4274 −0.826660
\(227\) 6.46171 11.1920i 0.428879 0.742840i −0.567895 0.823101i \(-0.692242\pi\)
0.996774 + 0.0802612i \(0.0255754\pi\)
\(228\) −3.76111 + 6.51444i −0.249086 + 0.431429i
\(229\) −24.5322 −1.62114 −0.810568 0.585645i \(-0.800841\pi\)
−0.810568 + 0.585645i \(0.800841\pi\)
\(230\) 0 0
\(231\) −9.87458 17.1033i −0.649699 1.12531i
\(232\) 4.22984 + 7.32630i 0.277703 + 0.480995i
\(233\) 8.82732 0.578297 0.289149 0.957284i \(-0.406628\pi\)
0.289149 + 0.957284i \(0.406628\pi\)
\(234\) 29.3030 14.9183i 1.91560 0.975242i
\(235\) 0 0
\(236\) −4.13645 7.16454i −0.269260 0.466372i
\(237\) −7.29195 12.6300i −0.473663 0.820409i
\(238\) −2.60351 + 4.50941i −0.168760 + 0.292302i
\(239\) 4.23582 0.273993 0.136996 0.990572i \(-0.456255\pi\)
0.136996 + 0.990572i \(0.456255\pi\)
\(240\) 0 0
\(241\) 9.06784 15.7060i 0.584111 1.01171i −0.410874 0.911692i \(-0.634777\pi\)
0.994986 0.100018i \(-0.0318902\pi\)
\(242\) 2.84839 0.183102
\(243\) −32.4913 + 56.2766i −2.08432 + 3.61015i
\(244\) 2.96836 + 5.14135i 0.190030 + 0.329141i
\(245\) 0 0
\(246\) 10.5262 0.671128
\(247\) 0.531485 10.0772i 0.0338176 0.641196i
\(248\) 19.7304 1.25288
\(249\) 26.3486 + 45.6371i 1.66977 + 2.89213i
\(250\) 0 0
\(251\) 0.540917 0.936895i 0.0341424 0.0591363i −0.848449 0.529277i \(-0.822463\pi\)
0.882592 + 0.470140i \(0.155797\pi\)
\(252\) −10.5795 −0.666443
\(253\) −1.23738 + 2.14321i −0.0777937 + 0.134743i
\(254\) −5.58954 + 9.68137i −0.350719 + 0.607463i
\(255\) 0 0
\(256\) 7.85288 13.6016i 0.490805 0.850099i
\(257\) 4.07280 + 7.05430i 0.254054 + 0.440035i 0.964638 0.263578i \(-0.0849025\pi\)
−0.710584 + 0.703612i \(0.751569\pi\)
\(258\) 9.00819 + 15.6026i 0.560825 + 0.971378i
\(259\) 1.52534 0.0947801
\(260\) 0 0
\(261\) 22.9483 1.42047
\(262\) 5.90006 + 10.2192i 0.364507 + 0.631344i
\(263\) −8.63198 14.9510i −0.532271 0.921920i −0.999290 0.0376726i \(-0.988006\pi\)
0.467020 0.884247i \(-0.345328\pi\)
\(264\) 19.0302 32.9614i 1.17123 2.02863i
\(265\) 0 0
\(266\) 2.44120 4.22828i 0.149680 0.259253i
\(267\) −2.78129 + 4.81733i −0.170212 + 0.294816i
\(268\) −9.20699 −0.562406
\(269\) 9.47829 16.4169i 0.577901 1.00095i −0.417818 0.908531i \(-0.637205\pi\)
0.995720 0.0924239i \(-0.0294615\pi\)
\(270\) 0 0
\(271\) −11.6797 20.2299i −0.709492 1.22888i −0.965046 0.262081i \(-0.915591\pi\)
0.255554 0.966795i \(-0.417742\pi\)
\(272\) −5.26637 −0.319320
\(273\) 17.2077 8.76055i 1.04146 0.530212i
\(274\) −13.9680 −0.843840
\(275\) 0 0
\(276\) 0.901838 + 1.56203i 0.0542843 + 0.0940231i
\(277\) 3.00362 5.20242i 0.180470 0.312583i −0.761571 0.648082i \(-0.775572\pi\)
0.942041 + 0.335499i \(0.108905\pi\)
\(278\) −4.27815 −0.256587
\(279\) 26.7610 46.3513i 1.60214 2.77498i
\(280\) 0 0
\(281\) 18.1001 1.07976 0.539881 0.841742i \(-0.318469\pi\)
0.539881 + 0.841742i \(0.318469\pi\)
\(282\) 7.06784 12.2419i 0.420884 0.728993i
\(283\) −1.19566 2.07094i −0.0710743 0.123104i 0.828298 0.560288i \(-0.189309\pi\)
−0.899372 + 0.437183i \(0.855976\pi\)
\(284\) 3.42589 + 5.93382i 0.203289 + 0.352108i
\(285\) 0 0
\(286\) −0.767507 + 14.5522i −0.0453836 + 0.860492i
\(287\) 4.54333 0.268184
\(288\) −17.4792 30.2748i −1.02997 1.78396i
\(289\) 4.04526 + 7.00660i 0.237956 + 0.412153i
\(290\) 0 0
\(291\) 7.59491 0.445221
\(292\) −1.48918 + 2.57934i −0.0871477 + 0.150944i
\(293\) 7.38780 12.7960i 0.431600 0.747553i −0.565411 0.824809i \(-0.691283\pi\)
0.997011 + 0.0772560i \(0.0246159\pi\)
\(294\) −16.4713 −0.960624
\(295\) 0 0
\(296\) 1.46982 + 2.54580i 0.0854313 + 0.147971i
\(297\) −33.0110 57.1768i −1.91550 3.31774i
\(298\) −1.59513 −0.0924035
\(299\) −2.02886 1.31852i −0.117332 0.0762518i
\(300\) 0 0
\(301\) 3.88812 + 6.73441i 0.224107 + 0.388165i
\(302\) −10.1216 17.5311i −0.582432 1.00880i
\(303\) −18.9878 + 32.8879i −1.09082 + 1.88936i
\(304\) 4.93805 0.283217
\(305\) 0 0
\(306\) −13.6107 + 23.5745i −0.778074 + 1.34766i
\(307\) −14.6966 −0.838781 −0.419390 0.907806i \(-0.637756\pi\)
−0.419390 + 0.907806i \(0.637756\pi\)
\(308\) 2.34428 4.06041i 0.133578 0.231363i
\(309\) −32.9734 57.1117i −1.87579 3.24897i
\(310\) 0 0
\(311\) −14.2032 −0.805392 −0.402696 0.915334i \(-0.631927\pi\)
−0.402696 + 0.915334i \(0.631927\pi\)
\(312\) 31.2027 + 20.2780i 1.76650 + 1.14802i
\(313\) −21.0319 −1.18879 −0.594397 0.804171i \(-0.702609\pi\)
−0.594397 + 0.804171i \(0.702609\pi\)
\(314\) −6.18643 10.7152i −0.349121 0.604694i
\(315\) 0 0
\(316\) 1.73115 2.99844i 0.0973847 0.168675i
\(317\) 22.4641 1.26171 0.630854 0.775902i \(-0.282705\pi\)
0.630854 + 0.775902i \(0.282705\pi\)
\(318\) 4.98490 8.63410i 0.279539 0.484177i
\(319\) −5.08506 + 8.80759i −0.284709 + 0.493130i
\(320\) 0 0
\(321\) −2.96356 + 5.13304i −0.165410 + 0.286498i
\(322\) −0.585350 1.01386i −0.0326203 0.0565000i
\(323\) 4.17702 + 7.23481i 0.232416 + 0.402556i
\(324\) −28.1784 −1.56546
\(325\) 0 0
\(326\) −13.6829 −0.757828
\(327\) 15.7036 + 27.1995i 0.868413 + 1.50414i
\(328\) 4.37795 + 7.58283i 0.241732 + 0.418692i
\(329\) 3.05062 5.28384i 0.168186 0.291307i
\(330\) 0 0
\(331\) 4.66419 8.07861i 0.256367 0.444041i −0.708899 0.705310i \(-0.750808\pi\)
0.965266 + 0.261269i \(0.0841411\pi\)
\(332\) −6.25530 + 10.8345i −0.343304 + 0.594620i
\(333\) 7.97425 0.436986
\(334\) 6.88990 11.9337i 0.376999 0.652981i
\(335\) 0 0
\(336\) 4.72445 + 8.18299i 0.257740 + 0.446419i
\(337\) −27.6999 −1.50891 −0.754455 0.656352i \(-0.772099\pi\)
−0.754455 + 0.656352i \(0.772099\pi\)
\(338\) −14.1689 1.49875i −0.770687 0.0815212i
\(339\) −38.1517 −2.07212
\(340\) 0 0
\(341\) 11.8598 + 20.5418i 0.642244 + 1.11240i
\(342\) 12.7622 22.1048i 0.690102 1.19529i
\(343\) −18.2510 −0.985464
\(344\) −7.49316 + 12.9785i −0.404004 + 0.699756i
\(345\) 0 0
\(346\) 2.95704 0.158971
\(347\) 0.156978 0.271894i 0.00842702 0.0145960i −0.861781 0.507280i \(-0.830651\pi\)
0.870208 + 0.492684i \(0.163984\pi\)
\(348\) 3.70613 + 6.41920i 0.198669 + 0.344105i
\(349\) −12.3713 21.4278i −0.662223 1.14700i −0.980030 0.198848i \(-0.936280\pi\)
0.317808 0.948155i \(-0.397053\pi\)
\(350\) 0 0
\(351\) 57.5259 29.2868i 3.07051 1.56321i
\(352\) 15.4927 0.825762
\(353\) −3.12287 5.40898i −0.166214 0.287891i 0.770872 0.636990i \(-0.219821\pi\)
−0.937086 + 0.349099i \(0.886488\pi\)
\(354\) 19.0962 + 33.0756i 1.01495 + 1.75795i
\(355\) 0 0
\(356\) −1.32058 −0.0699909
\(357\) −7.99268 + 13.8437i −0.423018 + 0.732688i
\(358\) 1.26652 2.19368i 0.0669378 0.115940i
\(359\) 16.3025 0.860411 0.430205 0.902731i \(-0.358441\pi\)
0.430205 + 0.902731i \(0.358441\pi\)
\(360\) 0 0
\(361\) 5.58338 + 9.67071i 0.293862 + 0.508985i
\(362\) −2.63109 4.55718i −0.138287 0.239520i
\(363\) 8.74447 0.458966
\(364\) 3.84376 + 2.49799i 0.201468 + 0.130930i
\(365\) 0 0
\(366\) −13.7036 23.7354i −0.716300 1.24067i
\(367\) −1.98854 3.44425i −0.103801 0.179788i 0.809447 0.587193i \(-0.199767\pi\)
−0.913248 + 0.407405i \(0.866434\pi\)
\(368\) 0.592022 1.02541i 0.0308613 0.0534533i
\(369\) 23.7518 1.23647
\(370\) 0 0
\(371\) 2.15158 3.72665i 0.111705 0.193478i
\(372\) 17.2875 0.896313
\(373\) 15.1191 26.1870i 0.782837 1.35591i −0.147445 0.989070i \(-0.547105\pi\)
0.930283 0.366844i \(-0.119562\pi\)
\(374\) −6.03195 10.4476i −0.311905 0.540235i
\(375\) 0 0
\(376\) 11.7583 0.606388
\(377\) −8.33765 5.41848i −0.429411 0.279066i
\(378\) 31.2320 1.60640
\(379\) 4.46836 + 7.73943i 0.229524 + 0.397548i 0.957667 0.287878i \(-0.0929496\pi\)
−0.728143 + 0.685425i \(0.759616\pi\)
\(380\) 0 0
\(381\) −17.1597 + 29.7215i −0.879118 + 1.52268i
\(382\) −19.5343 −0.999464
\(383\) −13.4674 + 23.3261i −0.688150 + 1.19191i 0.284286 + 0.958739i \(0.408243\pi\)
−0.972436 + 0.233171i \(0.925090\pi\)
\(384\) −0.860612 + 1.49062i −0.0439179 + 0.0760681i
\(385\) 0 0
\(386\) 1.37973 2.38977i 0.0702266 0.121636i
\(387\) 20.3265 + 35.2065i 1.03325 + 1.78965i
\(388\) 0.901536 + 1.56151i 0.0457685 + 0.0792734i
\(389\) 29.5512 1.49831 0.749153 0.662397i \(-0.230461\pi\)
0.749153 + 0.662397i \(0.230461\pi\)
\(390\) 0 0
\(391\) 2.00313 0.101303
\(392\) −6.85054 11.8655i −0.346004 0.599297i
\(393\) 18.1130 + 31.3726i 0.913679 + 1.58254i
\(394\) 10.1465 17.5743i 0.511175 0.885380i
\(395\) 0 0
\(396\) 12.2555 21.2272i 0.615863 1.06671i
\(397\) −10.1450 + 17.5717i −0.509165 + 0.881899i 0.490779 + 0.871284i \(0.336712\pi\)
−0.999944 + 0.0106149i \(0.996621\pi\)
\(398\) 14.4695 0.725288
\(399\) 7.49440 12.9807i 0.375189 0.649847i
\(400\) 0 0
\(401\) −5.92420 10.2610i −0.295840 0.512410i 0.679340 0.733824i \(-0.262266\pi\)
−0.975180 + 0.221414i \(0.928933\pi\)
\(402\) 42.5046 2.11994
\(403\) −20.6672 + 10.5218i −1.02951 + 0.524128i
\(404\) −9.01562 −0.448544
\(405\) 0 0
\(406\) −2.40551 4.16647i −0.119384 0.206778i
\(407\) −1.76699 + 3.06052i −0.0875867 + 0.151705i
\(408\) −30.8069 −1.52517
\(409\) −14.2989 + 24.7664i −0.707033 + 1.22462i 0.258920 + 0.965899i \(0.416634\pi\)
−0.965953 + 0.258718i \(0.916700\pi\)
\(410\) 0 0
\(411\) −42.8814 −2.11518
\(412\) 7.82807 13.5586i 0.385661 0.667985i
\(413\) 8.24230 + 14.2761i 0.405577 + 0.702480i
\(414\) −3.06012 5.30028i −0.150397 0.260495i
\(415\) 0 0
\(416\) −0.797802 + 15.1267i −0.0391155 + 0.741645i
\(417\) −13.1338 −0.643164
\(418\) 5.65590 + 9.79631i 0.276639 + 0.479153i
\(419\) 7.46032 + 12.9217i 0.364461 + 0.631264i 0.988689 0.149977i \(-0.0479201\pi\)
−0.624229 + 0.781242i \(0.714587\pi\)
\(420\) 0 0
\(421\) −31.6984 −1.54489 −0.772443 0.635085i \(-0.780965\pi\)
−0.772443 + 0.635085i \(0.780965\pi\)
\(422\) 4.34745 7.53001i 0.211631 0.366555i
\(423\) 15.9482 27.6231i 0.775427 1.34308i
\(424\) 8.29305 0.402746
\(425\) 0 0
\(426\) −15.8159 27.3939i −0.766281 1.32724i
\(427\) −5.91477 10.2447i −0.286236 0.495775i
\(428\) −1.40713 −0.0680162
\(429\) −2.35622 + 44.6749i −0.113759 + 2.15692i
\(430\) 0 0
\(431\) 20.1828 + 34.9577i 0.972172 + 1.68385i 0.688968 + 0.724792i \(0.258064\pi\)
0.283204 + 0.959060i \(0.408603\pi\)
\(432\) 15.7940 + 27.3560i 0.759889 + 1.31617i
\(433\) 0.559489 0.969063i 0.0268873 0.0465702i −0.852269 0.523104i \(-0.824774\pi\)
0.879156 + 0.476534i \(0.158107\pi\)
\(434\) −11.2207 −0.538609
\(435\) 0 0
\(436\) −3.72813 + 6.45730i −0.178545 + 0.309249i
\(437\) −1.87825 −0.0898488
\(438\) 6.87490 11.9077i 0.328495 0.568971i
\(439\) 17.8611 + 30.9364i 0.852465 + 1.47651i 0.878977 + 0.476864i \(0.158226\pi\)
−0.0265125 + 0.999648i \(0.508440\pi\)
\(440\) 0 0
\(441\) −37.1665 −1.76983
\(442\) 10.5114 5.35143i 0.499978 0.254542i
\(443\) 26.4988 1.25899 0.629497 0.777003i \(-0.283261\pi\)
0.629497 + 0.777003i \(0.283261\pi\)
\(444\) 1.28783 + 2.23059i 0.0611178 + 0.105859i
\(445\) 0 0
\(446\) −2.05499 + 3.55934i −0.0973064 + 0.168540i
\(447\) −4.89700 −0.231620
\(448\) −6.47271 + 11.2111i −0.305807 + 0.529673i
\(449\) 17.5306 30.3639i 0.827321 1.43296i −0.0728122 0.997346i \(-0.523197\pi\)
0.900133 0.435616i \(-0.143469\pi\)
\(450\) 0 0
\(451\) −5.26311 + 9.11598i −0.247830 + 0.429255i
\(452\) −4.52871 7.84396i −0.213013 0.368949i
\(453\) −31.0729 53.8199i −1.45993 2.52868i
\(454\) −14.1640 −0.664751
\(455\) 0 0
\(456\) 28.8864 1.35273
\(457\) 5.86670 + 10.1614i 0.274433 + 0.475332i 0.969992 0.243137i \(-0.0781766\pi\)
−0.695559 + 0.718469i \(0.744843\pi\)
\(458\) 13.4436 + 23.2850i 0.628179 + 1.08804i
\(459\) −26.7198 + 46.2801i −1.24717 + 2.16017i
\(460\) 0 0
\(461\) −10.3514 + 17.9292i −0.482114 + 0.835045i −0.999789 0.0205318i \(-0.993464\pi\)
0.517676 + 0.855577i \(0.326797\pi\)
\(462\) −10.8225 + 18.7451i −0.503508 + 0.872102i
\(463\) −10.1342 −0.470976 −0.235488 0.971877i \(-0.575669\pi\)
−0.235488 + 0.971877i \(0.575669\pi\)
\(464\) 2.43293 4.21396i 0.112946 0.195628i
\(465\) 0 0
\(466\) −4.83736 8.37855i −0.224086 0.388129i
\(467\) −23.3950 −1.08259 −0.541296 0.840832i \(-0.682066\pi\)
−0.541296 + 0.840832i \(0.682066\pi\)
\(468\) 20.0946 + 13.0591i 0.928872 + 0.603656i
\(469\) 18.3459 0.847133
\(470\) 0 0
\(471\) −18.9921 32.8953i −0.875111 1.51574i
\(472\) −15.8845 + 27.5128i −0.731145 + 1.26638i
\(473\) −18.0164 −0.828394
\(474\) −7.99196 + 13.8425i −0.367083 + 0.635806i
\(475\) 0 0
\(476\) −3.79501 −0.173944
\(477\) 11.2481 19.4824i 0.515017 0.892036i
\(478\) −2.32122 4.02048i −0.106170 0.183892i
\(479\) 13.9714 + 24.1993i 0.638372 + 1.10569i 0.985790 + 0.167982i \(0.0537251\pi\)
−0.347418 + 0.937710i \(0.612942\pi\)
\(480\) 0 0
\(481\) −2.89723 1.88285i −0.132102 0.0858507i
\(482\) −19.8767 −0.905357
\(483\) −1.79700 3.11250i −0.0817665 0.141624i
\(484\) 1.03799 + 1.79785i 0.0471814 + 0.0817206i
\(485\) 0 0
\(486\) 71.2208 3.23064
\(487\) −3.69829 + 6.40563i −0.167586 + 0.290267i −0.937570 0.347795i \(-0.886930\pi\)
0.769985 + 0.638062i \(0.220264\pi\)
\(488\) 11.3989 19.7435i 0.516005 0.893746i
\(489\) −42.0062 −1.89958
\(490\) 0 0
\(491\) 4.73425 + 8.19997i 0.213654 + 0.370059i 0.952855 0.303425i \(-0.0981302\pi\)
−0.739201 + 0.673484i \(0.764797\pi\)
\(492\) 3.83589 + 6.64396i 0.172935 + 0.299533i
\(493\) 8.23191 0.370747
\(494\) −9.85612 + 5.01781i −0.443448 + 0.225762i
\(495\) 0 0
\(496\) −5.67427 9.82813i −0.254782 0.441296i
\(497\) −6.82645 11.8237i −0.306208 0.530368i
\(498\) 28.8780 50.0181i 1.29405 2.24137i
\(499\) −30.6022 −1.36994 −0.684971 0.728571i \(-0.740185\pi\)
−0.684971 + 0.728571i \(0.740185\pi\)
\(500\) 0 0
\(501\) 21.1518 36.6359i 0.944991 1.63677i
\(502\) −1.18569 −0.0529197
\(503\) −11.9604 + 20.7161i −0.533290 + 0.923685i 0.465954 + 0.884809i \(0.345711\pi\)
−0.999244 + 0.0388762i \(0.987622\pi\)
\(504\) 20.3133 + 35.1836i 0.904825 + 1.56720i
\(505\) 0 0
\(506\) 2.71234 0.120578
\(507\) −43.4981 4.60110i −1.93182 0.204342i
\(508\) −8.14761 −0.361492
\(509\) −1.72122 2.98124i −0.0762918 0.132141i 0.825356 0.564613i \(-0.190975\pi\)
−0.901647 + 0.432472i \(0.857641\pi\)
\(510\) 0 0
\(511\) 2.96734 5.13959i 0.131268 0.227362i
\(512\) −18.2366 −0.805951
\(513\) 25.0540 43.3949i 1.10616 1.91593i
\(514\) 4.46378 7.73149i 0.196889 0.341021i
\(515\) 0 0
\(516\) −6.56540 + 11.3716i −0.289026 + 0.500607i
\(517\) 7.06784 + 12.2419i 0.310843 + 0.538397i
\(518\) −0.835885 1.44779i −0.0367267 0.0636124i
\(519\) 9.07801 0.398480
\(520\) 0 0
\(521\) −5.33204 −0.233601 −0.116800 0.993155i \(-0.537264\pi\)
−0.116800 + 0.993155i \(0.537264\pi\)
\(522\) −12.5756 21.7817i −0.550421 0.953357i
\(523\) 1.57545 + 2.72876i 0.0688897 + 0.119320i 0.898413 0.439152i \(-0.144721\pi\)
−0.829523 + 0.558472i \(0.811388\pi\)
\(524\) −4.30012 + 7.44802i −0.187851 + 0.325368i
\(525\) 0 0
\(526\) −9.46062 + 16.3863i −0.412503 + 0.714475i
\(527\) 9.59956 16.6269i 0.418164 0.724281i
\(528\) −21.8917 −0.952714
\(529\) 11.2748 19.5286i 0.490209 0.849068i
\(530\) 0 0
\(531\) 43.0895 + 74.6332i 1.86992 + 3.23880i
\(532\) 3.55842 0.154277
\(533\) −8.62958 5.60820i −0.373789 0.242918i
\(534\) 6.09656 0.263824
\(535\) 0 0
\(536\) 17.6780 + 30.6193i 0.763575 + 1.32255i
\(537\) 3.88818 6.73453i 0.167787 0.290616i
\(538\) −20.7763 −0.895732
\(539\) 8.23563 14.2645i 0.354734 0.614417i
\(540\) 0 0
\(541\) 3.22739 0.138757 0.0693783 0.997590i \(-0.477898\pi\)
0.0693783 + 0.997590i \(0.477898\pi\)
\(542\) −12.8009 + 22.1719i −0.549847 + 0.952363i
\(543\) −8.07734 13.9904i −0.346632 0.600384i
\(544\) −6.27004 10.8600i −0.268826 0.465620i
\(545\) 0 0
\(546\) −17.7450 11.5321i −0.759414 0.493529i
\(547\) −7.09772 −0.303476 −0.151738 0.988421i \(-0.548487\pi\)
−0.151738 + 0.988421i \(0.548487\pi\)
\(548\) −5.09013 8.81637i −0.217440 0.376617i
\(549\) −30.9215 53.5576i −1.31970 2.28578i
\(550\) 0 0
\(551\) −7.71871 −0.328828
\(552\) 3.46318 5.99841i 0.147403 0.255309i
\(553\) −3.44949 + 5.97469i −0.146687 + 0.254070i
\(554\) −6.58391 −0.279724
\(555\) 0 0
\(556\) −1.55901 2.70029i −0.0661170 0.114518i
\(557\) 19.2037 + 33.2617i 0.813685 + 1.40934i 0.910268 + 0.414019i \(0.135875\pi\)
−0.0965835 + 0.995325i \(0.530791\pi\)
\(558\) −58.6599 −2.48327
\(559\) 0.927762 17.5907i 0.0392401 0.744009i
\(560\) 0 0
\(561\) −18.5179 32.0739i −0.781825 1.35416i
\(562\) −9.91882 17.1799i −0.418400 0.724691i
\(563\) −14.1990 + 24.5934i −0.598416 + 1.03649i 0.394639 + 0.918836i \(0.370870\pi\)
−0.993055 + 0.117650i \(0.962464\pi\)
\(564\) 10.3025 0.433812
\(565\) 0 0
\(566\) −1.31043 + 2.26974i −0.0550817 + 0.0954042i
\(567\) 56.1483 2.35801
\(568\) 13.1559 22.7867i 0.552009 0.956108i
\(569\) 12.2675 + 21.2479i 0.514279 + 0.890757i 0.999863 + 0.0165666i \(0.00527356\pi\)
−0.485584 + 0.874190i \(0.661393\pi\)
\(570\) 0 0
\(571\) −35.1010 −1.46893 −0.734465 0.678646i \(-0.762567\pi\)
−0.734465 + 0.678646i \(0.762567\pi\)
\(572\) −9.46480 + 4.81859i −0.395743 + 0.201475i
\(573\) −59.9698 −2.50527
\(574\) −2.48974 4.31235i −0.103920 0.179994i
\(575\) 0 0
\(576\) −33.8383 + 58.6097i −1.40993 + 2.44207i
\(577\) 42.0461 1.75040 0.875202 0.483758i \(-0.160729\pi\)
0.875202 + 0.483758i \(0.160729\pi\)
\(578\) 4.43359 7.67921i 0.184413 0.319413i
\(579\) 4.23573 7.33650i 0.176031 0.304895i
\(580\) 0 0
\(581\) 12.4643 21.5888i 0.517107 0.895656i
\(582\) −4.16200 7.20879i −0.172520 0.298814i
\(583\) 4.98490 + 8.63410i 0.206454 + 0.357588i
\(584\) 11.4373 0.473279
\(585\) 0 0
\(586\) −16.1940 −0.668969
\(587\) −20.2428 35.0615i −0.835509 1.44714i −0.893615 0.448834i \(-0.851839\pi\)
0.0581057 0.998310i \(-0.481494\pi\)
\(588\) −6.00234 10.3964i −0.247532 0.428739i
\(589\) −9.00110 + 15.5904i −0.370884 + 0.642390i
\(590\) 0 0
\(591\) 31.1495 53.9525i 1.28132 2.21931i
\(592\) 0.845412 1.46430i 0.0347462 0.0601822i
\(593\) 3.00502 0.123402 0.0617008 0.998095i \(-0.480348\pi\)
0.0617008 + 0.998095i \(0.480348\pi\)
\(594\) −36.1800 + 62.6656i −1.48448 + 2.57120i
\(595\) 0 0
\(596\) −0.581287 1.00682i −0.0238104 0.0412409i
\(597\) 44.4207 1.81802
\(598\) −0.139673 + 2.64826i −0.00571166 + 0.108295i
\(599\) 20.3595 0.831865 0.415932 0.909396i \(-0.363455\pi\)
0.415932 + 0.909396i \(0.363455\pi\)
\(600\) 0 0
\(601\) 19.6123 + 33.9695i 0.800003 + 1.38565i 0.919613 + 0.392825i \(0.128502\pi\)
−0.119611 + 0.992821i \(0.538165\pi\)
\(602\) 4.26136 7.38090i 0.173680 0.300823i
\(603\) 95.9093 3.90573
\(604\) 7.37688 12.7771i 0.300161 0.519894i
\(605\) 0 0
\(606\) 41.6212 1.69074
\(607\) −7.72213 + 13.3751i −0.313432 + 0.542880i −0.979103 0.203366i \(-0.934812\pi\)
0.665671 + 0.746245i \(0.268145\pi\)
\(608\) 5.87915 + 10.1830i 0.238431 + 0.412975i
\(609\) −7.38484 12.7909i −0.299249 0.518314i
\(610\) 0 0
\(611\) −12.3166 + 6.27046i −0.498277 + 0.253676i
\(612\) −19.8397 −0.801974
\(613\) 13.5792 + 23.5198i 0.548457 + 0.949955i 0.998381 + 0.0568882i \(0.0181179\pi\)
−0.449924 + 0.893067i \(0.648549\pi\)
\(614\) 8.05373 + 13.9495i 0.325022 + 0.562954i
\(615\) 0 0
\(616\) −18.0047 −0.725429
\(617\) −13.4870 + 23.3601i −0.542964 + 0.940442i 0.455768 + 0.890099i \(0.349365\pi\)
−0.998732 + 0.0503430i \(0.983969\pi\)
\(618\) −36.1388 + 62.5942i −1.45371 + 2.51791i
\(619\) 38.2116 1.53586 0.767928 0.640537i \(-0.221288\pi\)
0.767928 + 0.640537i \(0.221288\pi\)
\(620\) 0 0
\(621\) −6.00745 10.4052i −0.241071 0.417546i
\(622\) 7.78336 + 13.4812i 0.312084 + 0.540546i
\(623\) 2.63140 0.105425
\(624\) 1.12732 21.3745i 0.0451291 0.855665i
\(625\) 0 0
\(626\) 11.5255 + 19.9627i 0.460650 + 0.797870i
\(627\) 17.3634 + 30.0743i 0.693428 + 1.20105i
\(628\) 4.50883 7.80953i 0.179922 0.311634i
\(629\) 2.86048 0.114055
\(630\) 0 0
\(631\) 5.94887 10.3037i 0.236821 0.410186i −0.722980 0.690869i \(-0.757228\pi\)
0.959800 + 0.280684i \(0.0905613\pi\)
\(632\) −13.2957 −0.528874
\(633\) 13.3465 23.1169i 0.530477 0.918813i
\(634\) −12.3103 21.3220i −0.488903 0.846806i
\(635\) 0 0
\(636\) 7.26625 0.288126
\(637\) 13.5034 + 8.77562i 0.535025 + 0.347703i
\(638\) 11.1464 0.441291
\(639\) −35.6876 61.8127i −1.41178 2.44527i
\(640\) 0 0
\(641\) 23.9587 41.4977i 0.946312 1.63906i 0.193209 0.981158i \(-0.438110\pi\)
0.753103 0.657903i \(-0.228556\pi\)
\(642\) 6.49610 0.256381
\(643\) 15.3849 26.6475i 0.606722 1.05087i −0.385054 0.922894i \(-0.625817\pi\)
0.991777 0.127980i \(-0.0408494\pi\)
\(644\) 0.426618 0.738925i 0.0168111 0.0291177i
\(645\) 0 0
\(646\) 4.57800 7.92933i 0.180119 0.311975i
\(647\) −17.1725 29.7436i −0.675121 1.16934i −0.976434 0.215818i \(-0.930758\pi\)
0.301313 0.953525i \(-0.402575\pi\)
\(648\) 54.1044 + 93.7115i 2.12542 + 3.68134i
\(649\) −38.1924 −1.49918
\(650\) 0 0
\(651\) −34.4470 −1.35009
\(652\) −4.98624 8.63643i −0.195276 0.338229i
\(653\) 11.7346 + 20.3250i 0.459211 + 0.795377i 0.998919 0.0464749i \(-0.0147988\pi\)
−0.539708 + 0.841852i \(0.681465\pi\)
\(654\) 17.2111 29.8106i 0.673009 1.16569i
\(655\) 0 0
\(656\) 2.51812 4.36150i 0.0983159 0.170288i
\(657\) 15.5128 26.8690i 0.605212 1.04826i
\(658\) −6.68695 −0.260684
\(659\) −24.4179 + 42.2931i −0.951187 + 1.64750i −0.208325 + 0.978060i \(0.566801\pi\)
−0.742862 + 0.669445i \(0.766532\pi\)
\(660\) 0 0
\(661\) −11.9416 20.6835i −0.464476 0.804495i 0.534702 0.845041i \(-0.320424\pi\)
−0.999178 + 0.0405453i \(0.987090\pi\)
\(662\) −10.2239 −0.397362
\(663\) 32.2697 16.4287i 1.25325 0.638038i
\(664\) 48.0424 1.86441
\(665\) 0 0
\(666\) −4.36987 7.56884i −0.169329 0.293287i
\(667\) −0.925395 + 1.60283i −0.0358314 + 0.0620619i
\(668\) 10.0431 0.388578
\(669\) −6.30873 + 10.9270i −0.243910 + 0.422464i
\(670\) 0 0
\(671\) 27.4073 1.05805
\(672\) −11.2497 + 19.4850i −0.433966 + 0.751652i
\(673\) −14.4017 24.9444i −0.555143 0.961536i −0.997892 0.0648907i \(-0.979330\pi\)
0.442749 0.896646i \(-0.354003\pi\)
\(674\) 15.1795 + 26.2917i 0.584692 + 1.01272i
\(675\) 0 0
\(676\) −4.21735 9.48932i −0.162206 0.364974i
\(677\) 6.71561 0.258102 0.129051 0.991638i \(-0.458807\pi\)
0.129051 + 0.991638i \(0.458807\pi\)
\(678\) 20.9071 + 36.2121i 0.802932 + 1.39072i
\(679\) −1.79640 3.11146i −0.0689396 0.119407i
\(680\) 0 0
\(681\) −43.4831 −1.66627
\(682\) 12.9983 22.5137i 0.497731 0.862095i
\(683\) −2.66564 + 4.61703i −0.101998 + 0.176666i −0.912508 0.409059i \(-0.865857\pi\)
0.810510 + 0.585725i \(0.199190\pi\)
\(684\) 18.6029 0.711299
\(685\) 0 0
\(686\) 10.0015 + 17.3232i 0.381861 + 0.661402i
\(687\) 41.2715 + 71.4843i 1.57460 + 2.72729i
\(688\) 8.61986 0.328629
\(689\) −8.68682 + 4.42252i −0.330942 + 0.168484i
\(690\) 0 0
\(691\) −22.1827 38.4216i −0.843871 1.46163i −0.886598 0.462541i \(-0.846938\pi\)
0.0427272 0.999087i \(-0.486395\pi\)
\(692\) 1.07758 + 1.86643i 0.0409636 + 0.0709510i
\(693\) −24.4204 + 42.2973i −0.927653 + 1.60674i
\(694\) −0.344095 −0.0130617
\(695\) 0 0
\(696\) 14.2320 24.6506i 0.539464 0.934379i
\(697\) 8.52014 0.322723
\(698\) −13.5589 + 23.4848i −0.513214 + 0.888912i
\(699\) −14.8505 25.7219i −0.561698 0.972890i
\(700\) 0 0
\(701\) 40.0973 1.51445 0.757227 0.653151i \(-0.226553\pi\)
0.757227 + 0.653151i \(0.226553\pi\)
\(702\) −59.3220 38.5522i −2.23896 1.45506i
\(703\) −2.68215 −0.101159
\(704\) −14.9963 25.9744i −0.565194 0.978945i
\(705\) 0 0
\(706\) −3.42266 + 5.92822i −0.128814 + 0.223112i
\(707\) 17.9645 0.675626
\(708\) −13.9178 + 24.1063i −0.523063 + 0.905972i
\(709\) 0.800778 1.38699i 0.0300739 0.0520894i −0.850597 0.525819i \(-0.823759\pi\)
0.880671 + 0.473729i \(0.157092\pi\)
\(710\) 0 0
\(711\) −18.0334 + 31.2348i −0.676305 + 1.17140i
\(712\) 2.53561 + 4.39181i 0.0950261 + 0.164590i
\(713\) 2.15828 + 3.73825i 0.0808283 + 0.139999i
\(714\) 17.5199 0.655666
\(715\) 0 0
\(716\) 1.84615 0.0689938
\(717\) −7.12608 12.3427i −0.266128 0.460948i
\(718\) −8.93372 15.4737i −0.333404 0.577472i
\(719\) 0.826615 1.43174i 0.0308275 0.0533948i −0.850200 0.526460i \(-0.823519\pi\)
0.881028 + 0.473065i \(0.156852\pi\)
\(720\) 0 0
\(721\) −15.5982 + 27.0169i −0.580908 + 1.00616i
\(722\) 6.11937 10.5991i 0.227739 0.394456i
\(723\) −61.0206 −2.26938
\(724\) 1.91760 3.32139i 0.0712672 0.123438i
\(725\) 0 0
\(726\) −4.79195 8.29991i −0.177846 0.308039i
\(727\) −5.56875 −0.206533 −0.103267 0.994654i \(-0.532930\pi\)
−0.103267 + 0.994654i \(0.532930\pi\)
\(728\) 0.927159 17.5793i 0.0343628 0.651533i
\(729\) 112.816 4.17839
\(730\) 0 0
\(731\) 7.29141 + 12.6291i 0.269683 + 0.467104i
\(732\) 9.98757 17.2990i 0.369151 0.639388i
\(733\) 36.1927 1.33681 0.668403 0.743799i \(-0.266978\pi\)
0.668403 + 0.743799i \(0.266978\pi\)
\(734\) −2.17943 + 3.77488i −0.0804442 + 0.139334i
\(735\) 0 0
\(736\) 2.81940 0.103925
\(737\) −21.2523 + 36.8101i −0.782839 + 1.35592i
\(738\) −13.0160 22.5443i −0.479124 0.829868i
\(739\) −13.6967 23.7234i −0.503842 0.872680i −0.999990 0.00444240i \(-0.998586\pi\)
0.496148 0.868238i \(-0.334747\pi\)
\(740\) 0 0
\(741\) −30.2579 + 15.4045i −1.11155 + 0.565899i
\(742\) −4.71626 −0.173139
\(743\) −15.0123 26.0020i −0.550746 0.953920i −0.998221 0.0596237i \(-0.981010\pi\)
0.447475 0.894297i \(-0.352323\pi\)
\(744\) −33.1931 57.4921i −1.21692 2.10776i
\(745\) 0 0
\(746\) −33.1410 −1.21338
\(747\) 65.1615 112.863i 2.38414 4.12944i
\(748\) 4.39624 7.61451i 0.160742 0.278414i
\(749\) 2.80385 0.102450
\(750\) 0 0
\(751\) −13.2453 22.9415i −0.483328 0.837148i 0.516489 0.856294i \(-0.327239\pi\)
−0.999817 + 0.0191455i \(0.993905\pi\)
\(752\) −3.38158 5.85707i −0.123314 0.213585i
\(753\) −3.64001 −0.132649
\(754\) −0.573990 + 10.8831i −0.0209035 + 0.396339i
\(755\) 0 0
\(756\) 11.3814 + 19.7131i 0.413936 + 0.716958i
\(757\) −5.52919 9.57685i −0.200962 0.348076i 0.747877 0.663838i \(-0.231073\pi\)
−0.948839 + 0.315761i \(0.897740\pi\)
\(758\) 4.89731 8.48239i 0.177878 0.308094i
\(759\) 8.32679 0.302243
\(760\) 0 0
\(761\) 5.01890 8.69300i 0.181935 0.315121i −0.760604 0.649216i \(-0.775097\pi\)
0.942539 + 0.334095i \(0.108431\pi\)
\(762\) 37.6139 1.36261
\(763\) 7.42867 12.8668i 0.268936 0.465811i
\(764\) −7.11857 12.3297i −0.257541 0.446074i
\(765\) 0 0
\(766\) 29.5204 1.06661
\(767\) 1.96673 37.2901i 0.0710147 1.34647i
\(768\) −52.8447 −1.90687
\(769\) 2.59941 + 4.50232i 0.0937372 + 0.162358i 0.909081 0.416620i \(-0.136785\pi\)
−0.815344 + 0.578977i \(0.803452\pi\)
\(770\) 0 0
\(771\) 13.7036 23.7354i 0.493524 0.854809i
\(772\) 2.01117 0.0723836
\(773\) −1.27337 + 2.20553i −0.0457998 + 0.0793275i −0.888017 0.459812i \(-0.847917\pi\)
0.842217 + 0.539139i \(0.181250\pi\)
\(774\) 22.2777 38.5862i 0.800757 1.38695i
\(775\) 0 0
\(776\) 3.46202 5.99639i 0.124279 0.215258i
\(777\) −2.56614 4.44468i −0.0920596 0.159452i
\(778\) −16.1940 28.0489i −0.580584 1.00560i
\(779\) −7.98898 −0.286235
\(780\) 0 0
\(781\) 31.6317 1.13187
\(782\) −1.09771 1.90129i −0.0392541 0.0679901i
\(783\) −24.6878 42.7605i −0.882269 1.52813i
\(784\) −3.94031 + 6.82481i −0.140725 + 0.243743i
\(785\) 0 0
\(786\) 19.8518 34.3843i 0.708089 1.22645i
\(787\) −20.3917 + 35.3195i −0.726886 + 1.25900i 0.231307 + 0.972881i \(0.425700\pi\)
−0.958193 + 0.286123i \(0.907633\pi\)
\(788\) 14.7901 0.526876
\(789\) −29.0438 + 50.3053i −1.03399 + 1.79092i
\(790\) 0 0
\(791\) 9.02392 + 15.6299i 0.320854 + 0.555735i
\(792\) −94.1257 −3.34461
\(793\) −1.41135 + 26.7598i −0.0501185 + 0.950267i
\(794\) 22.2378 0.789192
\(795\) 0 0
\(796\) 5.27286 + 9.13286i 0.186891 + 0.323705i
\(797\) −8.86862 + 15.3609i −0.314143 + 0.544111i −0.979255 0.202632i \(-0.935050\pi\)
0.665112 + 0.746743i \(0.268384\pi\)
\(798\) −16.4277 −0.581534
\(799\) 5.72086 9.90882i 0.202389 0.350549i
\(800\) 0 0
\(801\) 13.7565 0.486064
\(802\) −6.49290 + 11.2460i −0.229272 + 0.397111i
\(803\) 6.87490 + 11.9077i 0.242610 + 0.420213i
\(804\) 15.4892 + 26.8282i 0.546264 + 0.946156i
\(805\) 0 0
\(806\) 21.3125 + 13.8506i 0.750700 + 0.487865i
\(807\) −63.7826 −2.24526
\(808\) 17.3106 + 29.9828i 0.608985 + 1.05479i
\(809\) −17.0104 29.4629i −0.598054 1.03586i −0.993108 0.117202i \(-0.962607\pi\)
0.395054 0.918658i \(-0.370726\pi\)
\(810\) 0 0
\(811\) −2.94630 −0.103459 −0.0517294 0.998661i \(-0.516473\pi\)
−0.0517294 + 0.998661i \(0.516473\pi\)
\(812\) 1.75320 3.03663i 0.0615253 0.106565i
\(813\) −39.2984 + 68.0668i −1.37825 + 2.38721i
\(814\) 3.87324 0.135757
\(815\) 0 0
\(816\) 8.85980 + 15.3456i 0.310155 + 0.537204i
\(817\) −6.83685 11.8418i −0.239191 0.414291i
\(818\) 31.3430 1.09588
\(819\) −40.0405 26.0215i −1.39913 0.909266i
\(820\) 0 0
\(821\) 4.25553 + 7.37080i 0.148519 + 0.257243i 0.930680 0.365833i \(-0.119216\pi\)
−0.782161 + 0.623076i \(0.785883\pi\)
\(822\) 23.4989 + 40.7013i 0.819619 + 1.41962i
\(823\) 18.3511 31.7850i 0.639678 1.10796i −0.345825 0.938299i \(-0.612401\pi\)
0.985503 0.169657i \(-0.0542658\pi\)
\(824\) −60.1217 −2.09444
\(825\) 0 0
\(826\) 9.03354 15.6465i 0.314317 0.544413i
\(827\) 3.32022 0.115455 0.0577277 0.998332i \(-0.481614\pi\)
0.0577277 + 0.998332i \(0.481614\pi\)
\(828\) 2.23029 3.86298i 0.0775081 0.134248i
\(829\) 18.0712 + 31.3002i 0.627637 + 1.08710i 0.988025 + 0.154297i \(0.0493112\pi\)
−0.360387 + 0.932803i \(0.617355\pi\)
\(830\) 0 0
\(831\) −20.2124 −0.701159
\(832\) 26.1329 13.3044i 0.905997 0.461249i
\(833\) −13.3322 −0.461933
\(834\) 7.19729 + 12.4661i 0.249222 + 0.431665i
\(835\) 0 0
\(836\) −4.12217 + 7.13980i −0.142568 + 0.246935i
\(837\) −115.158 −3.98043
\(838\) 8.17649 14.1621i 0.282452 0.489221i
\(839\) 10.8414 18.7778i 0.374286 0.648283i −0.615934 0.787798i \(-0.711221\pi\)
0.990220 + 0.139515i \(0.0445544\pi\)
\(840\) 0 0
\(841\) 10.6971 18.5279i 0.368864 0.638892i
\(842\) 17.3707 + 30.0869i 0.598633 + 1.03686i
\(843\) −30.4504 52.7417i −1.04877 1.81652i
\(844\) 6.33707 0.218131
\(845\) 0 0
\(846\) −34.9583 −1.20189
\(847\) −2.06830 3.58241i −0.0710678 0.123093i
\(848\) −2.38501 4.13095i −0.0819015 0.141858i
\(849\) −4.02299 + 6.96802i −0.138069 + 0.239142i
\(850\) 0 0
\(851\) −0.321563 + 0.556963i −0.0110230 + 0.0190925i
\(852\) 11.5270 19.9654i 0.394909 0.684002i
\(853\) 12.0199 0.411553 0.205776 0.978599i \(-0.434028\pi\)
0.205776 + 0.978599i \(0.434028\pi\)
\(854\) −6.48256 + 11.2281i −0.221829 + 0.384219i
\(855\) 0 0
\(856\) 2.70178 + 4.67963i 0.0923451 + 0.159946i
\(857\) 47.3024 1.61582 0.807910 0.589306i \(-0.200599\pi\)
0.807910 + 0.589306i \(0.200599\pi\)
\(858\) 43.6948 22.2453i 1.49172 0.759443i
\(859\) −19.5027 −0.665423 −0.332712 0.943029i \(-0.607964\pi\)
−0.332712 + 0.943029i \(0.607964\pi\)
\(860\) 0 0
\(861\) −7.64341 13.2388i −0.260487 0.451176i
\(862\) 22.1203 38.3135i 0.753420 1.30496i
\(863\) −31.5568 −1.07420 −0.537102 0.843517i \(-0.680481\pi\)
−0.537102 + 0.843517i \(0.680481\pi\)
\(864\) −37.6081 + 65.1392i −1.27945 + 2.21608i
\(865\) 0 0
\(866\) −1.22640 −0.0416746
\(867\) 13.6110 23.5749i 0.462253 0.800645i
\(868\) −4.08895 7.08228i −0.138788 0.240388i
\(869\) −7.99196 13.8425i −0.271109 0.469574i
\(870\) 0 0
\(871\) −34.8461 22.6458i −1.18071 0.767323i
\(872\) 28.6330 0.969637
\(873\) −9.39131 16.2662i −0.317848 0.550528i
\(874\) 1.02928 + 1.78276i 0.0348158 + 0.0603028i
\(875\) 0 0
\(876\) 10.0212 0.338585
\(877\) 5.20428 9.01408i 0.175736 0.304384i −0.764680 0.644411i \(-0.777103\pi\)
0.940416 + 0.340027i \(0.110436\pi\)
\(878\) 19.5757 33.9062i 0.660649 1.14428i
\(879\) −49.7151 −1.67685
\(880\) 0 0
\(881\) 3.00838 + 5.21067i 0.101355 + 0.175552i 0.912243 0.409649i \(-0.134349\pi\)
−0.810888 + 0.585201i \(0.801016\pi\)
\(882\) 20.3672 + 35.2770i 0.685798 + 1.18784i
\(883\) −18.0630 −0.607869 −0.303934 0.952693i \(-0.598300\pi\)
−0.303934 + 0.952693i \(0.598300\pi\)
\(884\) 7.20823 + 4.68449i 0.242439 + 0.157556i
\(885\) 0 0
\(886\) −14.5213 25.1516i −0.487852 0.844985i
\(887\) −6.89386 11.9405i −0.231473 0.400924i 0.726769 0.686882i \(-0.241021\pi\)
−0.958242 + 0.285959i \(0.907688\pi\)
\(888\) 4.94545 8.56577i 0.165958 0.287448i
\(889\) 16.2349 0.544502
\(890\) 0 0
\(891\) −65.0436 + 112.659i −2.17904 + 3.77421i
\(892\) −2.99545 −0.100295
\(893\) −5.36421 + 9.29108i −0.179506 + 0.310914i
\(894\) 2.68355 + 4.64804i 0.0897512 + 0.155454i
\(895\) 0 0
\(896\) 0.814233 0.0272016
\(897\) −0.428792 + 8.13006i −0.0143169 + 0.271455i
\(898\) −38.4270 −1.28233
\(899\) 8.86951 + 15.3624i 0.295815 + 0.512366i
\(900\) 0 0
\(901\) 4.03488 6.98862i 0.134421 0.232825i
\(902\) 11.5367 0.384130
\(903\) 13.0822 22.6591i 0.435350 0.754047i
\(904\) −17.3909 + 30.1219i −0.578412 + 1.00184i
\(905\) 0 0
\(906\) −34.0558 + 58.9864i −1.13143 + 1.95969i
\(907\) 7.81727 + 13.5399i 0.259568 + 0.449585i 0.966126 0.258070i \(-0.0830865\pi\)
−0.706558 + 0.707655i \(0.749753\pi\)
\(908\) −5.16156 8.94008i −0.171292 0.296687i
\(909\) 93.9158 3.11499
\(910\) 0 0
\(911\) −34.5627 −1.14511 −0.572557 0.819865i \(-0.694048\pi\)
−0.572557 + 0.819865i \(0.694048\pi\)
\(912\) −8.30746 14.3889i −0.275087 0.476465i
\(913\) 28.8780 + 50.0181i 0.955722 + 1.65536i
\(914\) 6.42989 11.1369i 0.212682 0.368376i
\(915\) 0 0
\(916\) −9.79806 + 16.9707i −0.323737 + 0.560729i
\(917\) 8.56842 14.8409i 0.282954 0.490091i
\(918\) 58.5697 1.93309
\(919\) 14.7356 25.5229i 0.486084 0.841922i −0.513788 0.857917i \(-0.671758\pi\)
0.999872 + 0.0159954i \(0.00509170\pi\)
\(920\) 0 0
\(921\) 24.7247 + 42.8244i 0.814705 + 1.41111i
\(922\) 22.6902 0.747263
\(923\) −1.62889 + 30.8844i −0.0536156 + 1.01657i
\(924\) −15.7754 −0.518974
\(925\) 0 0
\(926\) 5.55352 + 9.61898i 0.182500 + 0.316099i
\(927\) −81.5451 + 141.240i −2.67829 + 4.63894i
\(928\) 11.5864 0.380342
\(929\) −14.2382 + 24.6613i −0.467140 + 0.809110i −0.999295 0.0375367i \(-0.988049\pi\)
0.532155 + 0.846647i \(0.321382\pi\)
\(930\) 0 0
\(931\) 12.5010 0.409704
\(932\) 3.52559 6.10651i 0.115485 0.200025i
\(933\) 23.8946 + 41.3867i 0.782275 + 1.35494i
\(934\) 12.8204 + 22.2056i 0.419497 + 0.726591i
\(935\) 0 0
\(936\) 4.84704 91.9019i 0.158431 3.00391i
\(937\) 36.3202 1.18653 0.593264 0.805008i \(-0.297839\pi\)
0.593264 + 0.805008i \(0.297839\pi\)
\(938\) −10.0535 17.4132i −0.328259 0.568560i
\(939\) 35.3828 + 61.2848i 1.15467 + 1.99995i
\(940\) 0 0
\(941\) 46.7007 1.52240 0.761200 0.648517i \(-0.224610\pi\)
0.761200 + 0.648517i \(0.224610\pi\)
\(942\) −20.8153 + 36.0532i −0.678200 + 1.17468i
\(943\) −0.957797 + 1.65895i −0.0311902 + 0.0540229i
\(944\) 18.2730 0.594735
\(945\) 0 0
\(946\) 9.87295 + 17.1004i 0.320997 + 0.555983i
\(947\) −7.48133 12.9580i −0.243110 0.421080i 0.718488 0.695539i \(-0.244834\pi\)
−0.961599 + 0.274459i \(0.911501\pi\)
\(948\) −11.6495 −0.378358
\(949\) −11.9804 + 6.09928i −0.388899 + 0.197991i
\(950\) 0 0
\(951\) −37.7921 65.4578i −1.22549 2.12262i
\(952\) 7.28668 + 12.6209i 0.236163 + 0.409046i
\(953\) −14.9792 + 25.9447i −0.485224 + 0.840432i −0.999856 0.0169791i \(-0.994595\pi\)
0.514632 + 0.857411i \(0.327928\pi\)
\(954\) −24.6559 −0.798263
\(955\) 0 0
\(956\) 1.69177 2.93023i 0.0547157 0.0947704i
\(957\) 34.2191 1.10615
\(958\) 15.3127 26.5223i 0.494730 0.856897i
\(959\) 10.1426 + 17.5675i 0.327522 + 0.567285i
\(960\) 0 0
\(961\) 10.3724 0.334593
\(962\) −0.199454 + 3.78173i −0.00643067 + 0.121928i
\(963\) 14.6581 0.472350
\(964\) −7.24331 12.5458i −0.233291 0.404073i
\(965\) 0 0
\(966\) −1.96951 + 3.41129i −0.0633680 + 0.109757i
\(967\) −13.5633 −0.436166 −0.218083 0.975930i \(-0.569980\pi\)
−0.218083 + 0.975930i \(0.569980\pi\)
\(968\) 3.98603 6.90400i 0.128116 0.221903i
\(969\) 14.0543 24.3428i 0.451489 0.782002i
\(970\) 0 0
\(971\) 18.1715 31.4739i 0.583150 1.01005i −0.411953 0.911205i \(-0.635153\pi\)
0.995103 0.0988405i \(-0.0315134\pi\)
\(972\) 25.9538 + 44.9532i 0.832468 + 1.44188i
\(973\) 3.10650 + 5.38061i 0.0995897 + 0.172494i
\(974\) 8.10663 0.259753
\(975\) 0 0
\(976\) −13.1129 −0.419734
\(977\) 1.38358 + 2.39642i 0.0442645 + 0.0766684i 0.887309 0.461176i \(-0.152572\pi\)
−0.843044 + 0.537844i \(0.819239\pi\)
\(978\) 23.0193 + 39.8706i 0.736077 + 1.27492i
\(979\) −3.04828 + 5.27978i −0.0974235 + 0.168742i
\(980\) 0 0
\(981\) 38.8359 67.2658i 1.23994 2.14763i
\(982\) 5.18873 8.98714i 0.165579 0.286791i
\(983\) 52.2816 1.66752 0.833762 0.552124i \(-0.186183\pi\)
0.833762 + 0.552124i \(0.186183\pi\)
\(984\) 14.7304 25.5137i 0.469587 0.813348i
\(985\) 0 0
\(986\) −4.51107 7.81341i −0.143662 0.248830i
\(987\) −20.5287 −0.653436
\(988\) −6.75885 4.39245i −0.215028 0.139742i
\(989\) −3.27867 −0.104256
\(990\) 0 0
\(991\) 1.29643 + 2.24548i 0.0411825 + 0.0713302i 0.885882 0.463911i \(-0.153554\pi\)
−0.844699 + 0.535241i \(0.820221\pi\)
\(992\) 13.5114 23.4024i 0.428987 0.743027i
\(993\) −31.3869 −0.996034
\(994\) −7.48176 + 12.9588i −0.237307 + 0.411028i
\(995\) 0 0
\(996\) 42.0941 1.33380
\(997\) 8.58746 14.8739i 0.271968 0.471062i −0.697398 0.716684i \(-0.745659\pi\)
0.969366 + 0.245622i \(0.0789923\pi\)
\(998\) 16.7699 + 29.0464i 0.530843 + 0.919447i
\(999\) −8.57868 14.8587i −0.271417 0.470109i
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 325.2.e.c.276.2 yes 10
5.2 odd 4 325.2.o.c.224.7 20
5.3 odd 4 325.2.o.c.224.4 20
5.4 even 2 325.2.e.d.276.4 yes 10
13.3 even 3 4225.2.a.bp.1.4 5
13.9 even 3 inner 325.2.e.c.126.2 10
13.10 even 6 4225.2.a.bo.1.2 5
65.9 even 6 325.2.e.d.126.4 yes 10
65.22 odd 12 325.2.o.c.74.4 20
65.29 even 6 4225.2.a.bn.1.2 5
65.48 odd 12 325.2.o.c.74.7 20
65.49 even 6 4225.2.a.bm.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
325.2.e.c.126.2 10 13.9 even 3 inner
325.2.e.c.276.2 yes 10 1.1 even 1 trivial
325.2.e.d.126.4 yes 10 65.9 even 6
325.2.e.d.276.4 yes 10 5.4 even 2
325.2.o.c.74.4 20 65.22 odd 12
325.2.o.c.74.7 20 65.48 odd 12
325.2.o.c.224.4 20 5.3 odd 4
325.2.o.c.224.7 20 5.2 odd 4
4225.2.a.bm.1.4 5 65.49 even 6
4225.2.a.bn.1.2 5 65.29 even 6
4225.2.a.bo.1.2 5 13.10 even 6
4225.2.a.bp.1.4 5 13.3 even 3