Properties

Label 450.2.l.a.379.1
Level $450$
Weight $2$
Character 450.379
Analytic conductor $3.593$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [450,2,Mod(19,450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(450, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("450.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.l (of order \(10\), 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: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{20})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 150)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 379.1
Root \(-0.951057 - 0.309017i\) of defining polynomial
Character \(\chi\) \(=\) 450.379
Dual form 450.2.l.a.19.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.951057 - 0.309017i) q^{2} +(0.809017 + 0.587785i) q^{4} +(0.166977 + 2.22982i) q^{5} +2.07768i q^{7} +(-0.587785 - 0.809017i) q^{8} +O(q^{10})\) \(q+(-0.951057 - 0.309017i) q^{2} +(0.809017 + 0.587785i) q^{4} +(0.166977 + 2.22982i) q^{5} +2.07768i q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.530249 - 2.17229i) q^{10} +(-0.160734 + 0.494689i) q^{11} +(-2.07919 + 0.675571i) q^{13} +(0.642040 - 1.97599i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-1.58450 - 2.18088i) q^{17} +(-5.55899 + 4.03884i) q^{19} +(-1.17557 + 1.90211i) q^{20} +(0.305735 - 0.420808i) q^{22} +(-3.67171 - 1.19301i) q^{23} +(-4.94424 + 0.744661i) q^{25} +2.18619 q^{26} +(-1.22123 + 1.68088i) q^{28} +(7.30844 + 5.30989i) q^{29} +(5.99083 - 4.35259i) q^{31} -1.00000i q^{32} +(0.833023 + 2.56378i) q^{34} +(-4.63287 + 0.346926i) q^{35} +(-5.04743 + 1.64001i) q^{37} +(6.53498 - 2.12334i) q^{38} +(1.70582 - 1.44575i) q^{40} +(0.996141 + 3.06581i) q^{41} +9.53920i q^{43} +(-0.420808 + 0.305735i) q^{44} +(3.12334 + 2.26924i) q^{46} +(-5.44627 + 7.49614i) q^{47} +2.68323 q^{49} +(4.93236 + 0.819639i) q^{50} +(-2.07919 - 0.675571i) q^{52} +(1.43326 - 1.97271i) q^{53} +(-1.12991 - 0.275807i) q^{55} +(1.68088 - 1.22123i) q^{56} +(-5.30989 - 7.30844i) q^{58} +(2.67261 + 8.22545i) q^{59} +(3.88998 - 11.9721i) q^{61} +(-7.04264 + 2.28829i) q^{62} +(-0.309017 + 0.951057i) q^{64} +(-1.85358 - 4.52343i) q^{65} +(3.93455 + 5.41544i) q^{67} -2.69572i q^{68} +(4.51333 + 1.10169i) q^{70} +(-6.60886 - 4.80162i) q^{71} +(3.65537 + 1.18770i) q^{73} +5.30719 q^{74} -6.87129 q^{76} +(-1.02781 - 0.333955i) q^{77} +(2.84162 + 2.06455i) q^{79} +(-2.06909 + 0.847859i) q^{80} -3.22358i q^{82} +(-7.71827 - 10.6233i) q^{83} +(4.59841 - 3.89732i) q^{85} +(2.94777 - 9.07232i) q^{86} +(0.494689 - 0.160734i) q^{88} +(-3.04654 + 9.37628i) q^{89} +(-1.40362 - 4.31990i) q^{91} +(-2.26924 - 3.12334i) q^{92} +(7.49614 - 5.44627i) q^{94} +(-9.93414 - 11.7212i) q^{95} +(6.32443 - 8.70483i) q^{97} +(-2.55190 - 0.829164i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{4} - 10 q^{11} - 20 q^{13} + 2 q^{14} - 2 q^{16} - 10 q^{17} - 8 q^{19} + 10 q^{23} - 10 q^{25} - 4 q^{26} - 10 q^{28} + 22 q^{29} + 24 q^{31} + 8 q^{34} - 10 q^{35} - 20 q^{37} + 10 q^{38} - 22 q^{41} + 10 q^{46} - 10 q^{47} + 8 q^{49} + 20 q^{50} - 20 q^{52} + 30 q^{53} + 10 q^{55} - 2 q^{56} + 30 q^{58} + 20 q^{59} - 10 q^{62} + 2 q^{64} - 20 q^{65} + 10 q^{67} - 10 q^{70} - 20 q^{71} - 20 q^{73} + 4 q^{74} - 12 q^{76} + 20 q^{77} + 16 q^{79} - 70 q^{83} + 20 q^{85} + 18 q^{86} + 10 q^{88} + 34 q^{89} - 24 q^{91} - 30 q^{92} + 30 q^{94} - 30 q^{95} + 60 q^{97} - 20 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.951057 0.309017i −0.672499 0.218508i
\(3\) 0 0
\(4\) 0.809017 + 0.587785i 0.404508 + 0.293893i
\(5\) 0.166977 + 2.22982i 0.0746746 + 0.997208i
\(6\) 0 0
\(7\) 2.07768i 0.785291i 0.919690 + 0.392645i \(0.128440\pi\)
−0.919690 + 0.392645i \(0.871560\pi\)
\(8\) −0.587785 0.809017i −0.207813 0.286031i
\(9\) 0 0
\(10\) 0.530249 2.17229i 0.167679 0.686938i
\(11\) −0.160734 + 0.494689i −0.0484632 + 0.149154i −0.972360 0.233488i \(-0.924986\pi\)
0.923896 + 0.382643i \(0.124986\pi\)
\(12\) 0 0
\(13\) −2.07919 + 0.675571i −0.576664 + 0.187370i −0.582806 0.812612i \(-0.698045\pi\)
0.00614146 + 0.999981i \(0.498045\pi\)
\(14\) 0.642040 1.97599i 0.171592 0.528107i
\(15\) 0 0
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) −1.58450 2.18088i −0.384298 0.528941i 0.572418 0.819962i \(-0.306005\pi\)
−0.956717 + 0.291020i \(0.906005\pi\)
\(18\) 0 0
\(19\) −5.55899 + 4.03884i −1.27532 + 0.926574i −0.999401 0.0346072i \(-0.988982\pi\)
−0.275919 + 0.961181i \(0.588982\pi\)
\(20\) −1.17557 + 1.90211i −0.262866 + 0.425325i
\(21\) 0 0
\(22\) 0.305735 0.420808i 0.0651829 0.0897165i
\(23\) −3.67171 1.19301i −0.765605 0.248760i −0.0999224 0.994995i \(-0.531859\pi\)
−0.665682 + 0.746235i \(0.731859\pi\)
\(24\) 0 0
\(25\) −4.94424 + 0.744661i −0.988847 + 0.148932i
\(26\) 2.18619 0.428748
\(27\) 0 0
\(28\) −1.22123 + 1.68088i −0.230791 + 0.317657i
\(29\) 7.30844 + 5.30989i 1.35714 + 0.986022i 0.998621 + 0.0525013i \(0.0167194\pi\)
0.358523 + 0.933521i \(0.383281\pi\)
\(30\) 0 0
\(31\) 5.99083 4.35259i 1.07598 0.781749i 0.0990065 0.995087i \(-0.468434\pi\)
0.976978 + 0.213338i \(0.0684335\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 0.833023 + 2.56378i 0.142862 + 0.439685i
\(35\) −4.63287 + 0.346926i −0.783098 + 0.0586413i
\(36\) 0 0
\(37\) −5.04743 + 1.64001i −0.829793 + 0.269616i −0.692958 0.720978i \(-0.743693\pi\)
−0.136835 + 0.990594i \(0.543693\pi\)
\(38\) 6.53498 2.12334i 1.06011 0.344452i
\(39\) 0 0
\(40\) 1.70582 1.44575i 0.269714 0.228592i
\(41\) 0.996141 + 3.06581i 0.155571 + 0.478799i 0.998218 0.0596673i \(-0.0190040\pi\)
−0.842647 + 0.538466i \(0.819004\pi\)
\(42\) 0 0
\(43\) 9.53920i 1.45471i 0.686259 + 0.727357i \(0.259252\pi\)
−0.686259 + 0.727357i \(0.740748\pi\)
\(44\) −0.420808 + 0.305735i −0.0634392 + 0.0460912i
\(45\) 0 0
\(46\) 3.12334 + 2.26924i 0.460512 + 0.334582i
\(47\) −5.44627 + 7.49614i −0.794419 + 1.09342i 0.199124 + 0.979974i \(0.436190\pi\)
−0.993544 + 0.113450i \(0.963810\pi\)
\(48\) 0 0
\(49\) 2.68323 0.383319
\(50\) 4.93236 + 0.819639i 0.697541 + 0.115914i
\(51\) 0 0
\(52\) −2.07919 0.675571i −0.288332 0.0936848i
\(53\) 1.43326 1.97271i 0.196873 0.270973i −0.699155 0.714970i \(-0.746440\pi\)
0.896028 + 0.443998i \(0.146440\pi\)
\(54\) 0 0
\(55\) −1.12991 0.275807i −0.152357 0.0371898i
\(56\) 1.68088 1.22123i 0.224617 0.163194i
\(57\) 0 0
\(58\) −5.30989 7.30844i −0.697223 0.959645i
\(59\) 2.67261 + 8.22545i 0.347944 + 1.07086i 0.959989 + 0.280039i \(0.0903473\pi\)
−0.612045 + 0.790823i \(0.709653\pi\)
\(60\) 0 0
\(61\) 3.88998 11.9721i 0.498061 1.53287i −0.314070 0.949400i \(-0.601693\pi\)
0.812131 0.583475i \(-0.198307\pi\)
\(62\) −7.04264 + 2.28829i −0.894417 + 0.290614i
\(63\) 0 0
\(64\) −0.309017 + 0.951057i −0.0386271 + 0.118882i
\(65\) −1.85358 4.52343i −0.229909 0.561062i
\(66\) 0 0
\(67\) 3.93455 + 5.41544i 0.480682 + 0.661601i 0.978636 0.205602i \(-0.0659152\pi\)
−0.497954 + 0.867203i \(0.665915\pi\)
\(68\) 2.69572i 0.326904i
\(69\) 0 0
\(70\) 4.51333 + 1.10169i 0.539446 + 0.131677i
\(71\) −6.60886 4.80162i −0.784328 0.569848i 0.121947 0.992537i \(-0.461086\pi\)
−0.906275 + 0.422689i \(0.861086\pi\)
\(72\) 0 0
\(73\) 3.65537 + 1.18770i 0.427828 + 0.139010i 0.515013 0.857182i \(-0.327787\pi\)
−0.0871848 + 0.996192i \(0.527787\pi\)
\(74\) 5.30719 0.616948
\(75\) 0 0
\(76\) −6.87129 −0.788191
\(77\) −1.02781 0.333955i −0.117130 0.0380577i
\(78\) 0 0
\(79\) 2.84162 + 2.06455i 0.319707 + 0.232281i 0.736050 0.676927i \(-0.236689\pi\)
−0.416344 + 0.909207i \(0.636689\pi\)
\(80\) −2.06909 + 0.847859i −0.231331 + 0.0947935i
\(81\) 0 0
\(82\) 3.22358i 0.355985i
\(83\) −7.71827 10.6233i −0.847190 1.16606i −0.984475 0.175526i \(-0.943837\pi\)
0.137285 0.990532i \(-0.456163\pi\)
\(84\) 0 0
\(85\) 4.59841 3.89732i 0.498767 0.422724i
\(86\) 2.94777 9.07232i 0.317867 0.978293i
\(87\) 0 0
\(88\) 0.494689 0.160734i 0.0527340 0.0171343i
\(89\) −3.04654 + 9.37628i −0.322932 + 0.993883i 0.649433 + 0.760419i \(0.275006\pi\)
−0.972365 + 0.233465i \(0.924994\pi\)
\(90\) 0 0
\(91\) −1.40362 4.31990i −0.147140 0.452849i
\(92\) −2.26924 3.12334i −0.236585 0.325631i
\(93\) 0 0
\(94\) 7.49614 5.44627i 0.773168 0.561739i
\(95\) −9.93414 11.7212i −1.01922 1.20257i
\(96\) 0 0
\(97\) 6.32443 8.70483i 0.642149 0.883842i −0.356579 0.934265i \(-0.616057\pi\)
0.998728 + 0.0504234i \(0.0160571\pi\)
\(98\) −2.55190 0.829164i −0.257781 0.0837582i
\(99\) 0 0
\(100\) −4.43767 2.30371i −0.443767 0.230371i
\(101\) 17.6400 1.75524 0.877622 0.479353i \(-0.159129\pi\)
0.877622 + 0.479353i \(0.159129\pi\)
\(102\) 0 0
\(103\) 5.11231 7.03649i 0.503731 0.693326i −0.479116 0.877752i \(-0.659043\pi\)
0.982846 + 0.184426i \(0.0590425\pi\)
\(104\) 1.76867 + 1.28501i 0.173432 + 0.126006i
\(105\) 0 0
\(106\) −1.97271 + 1.43326i −0.191607 + 0.139210i
\(107\) 5.40977i 0.522983i 0.965206 + 0.261491i \(0.0842143\pi\)
−0.965206 + 0.261491i \(0.915786\pi\)
\(108\) 0 0
\(109\) −0.891135 2.74263i −0.0853553 0.262697i 0.899265 0.437404i \(-0.144102\pi\)
−0.984620 + 0.174707i \(0.944102\pi\)
\(110\) 0.989378 + 0.611469i 0.0943335 + 0.0583013i
\(111\) 0 0
\(112\) −1.97599 + 0.642040i −0.186714 + 0.0606670i
\(113\) 6.05780 1.96830i 0.569870 0.185162i −0.00988741 0.999951i \(-0.503147\pi\)
0.579757 + 0.814789i \(0.303147\pi\)
\(114\) 0 0
\(115\) 2.04711 8.38648i 0.190894 0.782043i
\(116\) 2.79158 + 8.59159i 0.259191 + 0.797709i
\(117\) 0 0
\(118\) 8.64875i 0.796182i
\(119\) 4.53118 3.29210i 0.415373 0.301786i
\(120\) 0 0
\(121\) 8.68031 + 6.30661i 0.789119 + 0.573328i
\(122\) −7.39919 + 10.1841i −0.669891 + 0.922026i
\(123\) 0 0
\(124\) 7.40507 0.664995
\(125\) −2.48604 10.9004i −0.222358 0.974965i
\(126\) 0 0
\(127\) −14.2348 4.62515i −1.26313 0.410416i −0.400522 0.916287i \(-0.631171\pi\)
−0.862609 + 0.505871i \(0.831171\pi\)
\(128\) 0.587785 0.809017i 0.0519534 0.0715077i
\(129\) 0 0
\(130\) 0.365045 + 4.87483i 0.0320165 + 0.427550i
\(131\) 11.2090 8.14385i 0.979339 0.711531i 0.0217781 0.999763i \(-0.493067\pi\)
0.957561 + 0.288232i \(0.0930673\pi\)
\(132\) 0 0
\(133\) −8.39144 11.5498i −0.727630 1.00150i
\(134\) −2.06851 6.36623i −0.178692 0.549959i
\(135\) 0 0
\(136\) −0.833023 + 2.56378i −0.0714311 + 0.219842i
\(137\) 18.9202 6.14755i 1.61646 0.525221i 0.645359 0.763879i \(-0.276708\pi\)
0.971103 + 0.238659i \(0.0767077\pi\)
\(138\) 0 0
\(139\) −1.74398 + 5.36743i −0.147923 + 0.455259i −0.997375 0.0724056i \(-0.976932\pi\)
0.849453 + 0.527665i \(0.176932\pi\)
\(140\) −3.95199 2.44246i −0.334004 0.206426i
\(141\) 0 0
\(142\) 4.80162 + 6.60886i 0.402943 + 0.554604i
\(143\) 1.13714i 0.0950925i
\(144\) 0 0
\(145\) −10.6198 + 17.1832i −0.881925 + 1.42698i
\(146\) −3.10944 2.25914i −0.257339 0.186968i
\(147\) 0 0
\(148\) −5.04743 1.64001i −0.414897 0.134808i
\(149\) −15.0956 −1.23668 −0.618339 0.785911i \(-0.712194\pi\)
−0.618339 + 0.785911i \(0.712194\pi\)
\(150\) 0 0
\(151\) −20.9353 −1.70369 −0.851847 0.523791i \(-0.824517\pi\)
−0.851847 + 0.523791i \(0.824517\pi\)
\(152\) 6.53498 + 2.12334i 0.530057 + 0.172226i
\(153\) 0 0
\(154\) 0.874305 + 0.635220i 0.0704535 + 0.0511875i
\(155\) 10.7059 + 12.6317i 0.859915 + 1.01460i
\(156\) 0 0
\(157\) 5.71998i 0.456504i 0.973602 + 0.228252i \(0.0733010\pi\)
−0.973602 + 0.228252i \(0.926699\pi\)
\(158\) −2.06455 2.84162i −0.164247 0.226067i
\(159\) 0 0
\(160\) 2.22982 0.166977i 0.176283 0.0132007i
\(161\) 2.47870 7.62866i 0.195349 0.601222i
\(162\) 0 0
\(163\) 11.3129 3.67577i 0.886091 0.287908i 0.169607 0.985512i \(-0.445750\pi\)
0.716484 + 0.697603i \(0.245750\pi\)
\(164\) −0.996141 + 3.06581i −0.0777856 + 0.239399i
\(165\) 0 0
\(166\) 4.05774 + 12.4884i 0.314941 + 0.969290i
\(167\) 5.25731 + 7.23607i 0.406823 + 0.559944i 0.962440 0.271495i \(-0.0875179\pi\)
−0.555617 + 0.831438i \(0.687518\pi\)
\(168\) 0 0
\(169\) −6.65058 + 4.83193i −0.511583 + 0.371687i
\(170\) −5.57768 + 2.28559i −0.427789 + 0.175297i
\(171\) 0 0
\(172\) −5.60700 + 7.71737i −0.427530 + 0.588444i
\(173\) 15.5394 + 5.04904i 1.18144 + 0.383872i 0.832900 0.553424i \(-0.186679\pi\)
0.348536 + 0.937295i \(0.386679\pi\)
\(174\) 0 0
\(175\) −1.54717 10.2726i −0.116955 0.776533i
\(176\) −0.520147 −0.0392076
\(177\) 0 0
\(178\) 5.79486 7.97594i 0.434343 0.597822i
\(179\) −2.97599 2.16219i −0.222436 0.161609i 0.470986 0.882140i \(-0.343898\pi\)
−0.693423 + 0.720531i \(0.743898\pi\)
\(180\) 0 0
\(181\) 18.6472 13.5480i 1.38604 1.00702i 0.389751 0.920920i \(-0.372561\pi\)
0.996287 0.0860956i \(-0.0274391\pi\)
\(182\) 4.54222i 0.336691i
\(183\) 0 0
\(184\) 1.19301 + 3.67171i 0.0879500 + 0.270682i
\(185\) −4.49975 10.9811i −0.330828 0.807343i
\(186\) 0 0
\(187\) 1.33354 0.433294i 0.0975183 0.0316856i
\(188\) −8.81224 + 2.86327i −0.642699 + 0.208826i
\(189\) 0 0
\(190\) 5.82588 + 14.2173i 0.422654 + 1.03143i
\(191\) 0.552424 + 1.70019i 0.0399720 + 0.123021i 0.969051 0.246859i \(-0.0793986\pi\)
−0.929079 + 0.369881i \(0.879399\pi\)
\(192\) 0 0
\(193\) 6.60138i 0.475178i 0.971366 + 0.237589i \(0.0763571\pi\)
−0.971366 + 0.237589i \(0.923643\pi\)
\(194\) −8.70483 + 6.32443i −0.624970 + 0.454068i
\(195\) 0 0
\(196\) 2.17078 + 1.57716i 0.155056 + 0.112655i
\(197\) −7.43989 + 10.2401i −0.530070 + 0.729579i −0.987141 0.159851i \(-0.948899\pi\)
0.457071 + 0.889430i \(0.348899\pi\)
\(198\) 0 0
\(199\) −6.24148 −0.442447 −0.221223 0.975223i \(-0.571005\pi\)
−0.221223 + 0.975223i \(0.571005\pi\)
\(200\) 3.50859 + 3.56227i 0.248095 + 0.251891i
\(201\) 0 0
\(202\) −16.7766 5.45106i −1.18040 0.383535i
\(203\) −11.0323 + 15.1846i −0.774314 + 1.06575i
\(204\) 0 0
\(205\) −6.66988 + 2.73314i −0.465845 + 0.190891i
\(206\) −7.03649 + 5.11231i −0.490256 + 0.356192i
\(207\) 0 0
\(208\) −1.28501 1.76867i −0.0890995 0.122635i
\(209\) −1.10445 3.39915i −0.0763965 0.235124i
\(210\) 0 0
\(211\) −6.94607 + 21.3778i −0.478187 + 1.47171i 0.363424 + 0.931624i \(0.381608\pi\)
−0.841611 + 0.540084i \(0.818392\pi\)
\(212\) 2.31906 0.753509i 0.159274 0.0517512i
\(213\) 0 0
\(214\) 1.67171 5.14500i 0.114276 0.351705i
\(215\) −21.2707 + 1.59283i −1.45065 + 0.108630i
\(216\) 0 0
\(217\) 9.04331 + 12.4471i 0.613900 + 0.844961i
\(218\) 2.88377i 0.195314i
\(219\) 0 0
\(220\) −0.752000 0.887277i −0.0506999 0.0598202i
\(221\) 4.76783 + 3.46403i 0.320719 + 0.233016i
\(222\) 0 0
\(223\) 17.0524 + 5.54065i 1.14191 + 0.371029i 0.818091 0.575089i \(-0.195033\pi\)
0.323820 + 0.946119i \(0.395033\pi\)
\(224\) 2.07768 0.138821
\(225\) 0 0
\(226\) −6.36955 −0.423696
\(227\) 8.42412 + 2.73716i 0.559129 + 0.181672i 0.574929 0.818203i \(-0.305030\pi\)
−0.0158003 + 0.999875i \(0.505030\pi\)
\(228\) 0 0
\(229\) 17.8490 + 12.9681i 1.17950 + 0.856953i 0.992115 0.125334i \(-0.0400003\pi\)
0.187380 + 0.982287i \(0.440000\pi\)
\(230\) −4.53849 + 7.34342i −0.299259 + 0.484211i
\(231\) 0 0
\(232\) 9.03373i 0.593093i
\(233\) −6.78466 9.33828i −0.444478 0.611771i 0.526722 0.850037i \(-0.323421\pi\)
−0.971200 + 0.238267i \(0.923421\pi\)
\(234\) 0 0
\(235\) −17.6245 10.8925i −1.14969 0.710550i
\(236\) −2.67261 + 8.22545i −0.173972 + 0.535431i
\(237\) 0 0
\(238\) −5.32672 + 1.73076i −0.345280 + 0.112188i
\(239\) −0.273457 + 0.841616i −0.0176885 + 0.0544396i −0.959511 0.281671i \(-0.909111\pi\)
0.941823 + 0.336110i \(0.109111\pi\)
\(240\) 0 0
\(241\) 3.91637 + 12.0534i 0.252276 + 0.776425i 0.994354 + 0.106112i \(0.0338402\pi\)
−0.742078 + 0.670313i \(0.766160\pi\)
\(242\) −6.30661 8.68031i −0.405404 0.557991i
\(243\) 0 0
\(244\) 10.1841 7.39919i 0.651971 0.473684i
\(245\) 0.448039 + 5.98314i 0.0286242 + 0.382248i
\(246\) 0 0
\(247\) 8.82968 12.1530i 0.561819 0.773278i
\(248\) −7.04264 2.28829i −0.447208 0.145307i
\(249\) 0 0
\(250\) −1.00406 + 11.1352i −0.0635021 + 0.704250i
\(251\) −18.0966 −1.14225 −0.571124 0.820864i \(-0.693493\pi\)
−0.571124 + 0.820864i \(0.693493\pi\)
\(252\) 0 0
\(253\) 1.18034 1.62460i 0.0742073 0.102138i
\(254\) 12.1088 + 8.79756i 0.759774 + 0.552008i
\(255\) 0 0
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) 1.28053i 0.0798774i −0.999202 0.0399387i \(-0.987284\pi\)
0.999202 0.0399387i \(-0.0127163\pi\)
\(258\) 0 0
\(259\) −3.40742 10.4870i −0.211727 0.651629i
\(260\) 1.15923 4.74904i 0.0718921 0.294523i
\(261\) 0 0
\(262\) −13.1770 + 4.28147i −0.814079 + 0.264510i
\(263\) 6.76605 2.19842i 0.417213 0.135561i −0.0928855 0.995677i \(-0.529609\pi\)
0.510098 + 0.860116i \(0.329609\pi\)
\(264\) 0 0
\(265\) 4.63812 + 2.86652i 0.284918 + 0.176089i
\(266\) 4.41164 + 13.5776i 0.270495 + 0.832498i
\(267\) 0 0
\(268\) 6.69385i 0.408892i
\(269\) 7.62892 5.54274i 0.465143 0.337947i −0.330402 0.943840i \(-0.607184\pi\)
0.795546 + 0.605894i \(0.207184\pi\)
\(270\) 0 0
\(271\) −1.11231 0.808141i −0.0675681 0.0490911i 0.553488 0.832857i \(-0.313296\pi\)
−0.621057 + 0.783766i \(0.713296\pi\)
\(272\) 1.58450 2.18088i 0.0960746 0.132235i
\(273\) 0 0
\(274\) −19.8939 −1.20183
\(275\) 0.426333 2.56555i 0.0257088 0.154709i
\(276\) 0 0
\(277\) 18.6375 + 6.05571i 1.11982 + 0.363852i 0.809700 0.586845i \(-0.199630\pi\)
0.310122 + 0.950697i \(0.399630\pi\)
\(278\) 3.31725 4.56581i 0.198956 0.273839i
\(279\) 0 0
\(280\) 3.00380 + 3.54415i 0.179512 + 0.211804i
\(281\) −2.29605 + 1.66817i −0.136971 + 0.0995150i −0.654161 0.756356i \(-0.726978\pi\)
0.517190 + 0.855871i \(0.326978\pi\)
\(282\) 0 0
\(283\) −1.31285 1.80699i −0.0780411 0.107414i 0.768212 0.640196i \(-0.221147\pi\)
−0.846253 + 0.532781i \(0.821147\pi\)
\(284\) −2.52436 7.76919i −0.149793 0.461016i
\(285\) 0 0
\(286\) −0.351396 + 1.08149i −0.0207785 + 0.0639496i
\(287\) −6.36978 + 2.06967i −0.375996 + 0.122169i
\(288\) 0 0
\(289\) 3.00770 9.25673i 0.176923 0.544514i
\(290\) 15.4099 13.0605i 0.904901 0.766938i
\(291\) 0 0
\(292\) 2.25914 + 3.10944i 0.132206 + 0.181966i
\(293\) 24.0260i 1.40361i 0.712367 + 0.701807i \(0.247623\pi\)
−0.712367 + 0.701807i \(0.752377\pi\)
\(294\) 0 0
\(295\) −17.8950 + 7.33292i −1.04189 + 0.426939i
\(296\) 4.29360 + 3.11949i 0.249561 + 0.181316i
\(297\) 0 0
\(298\) 14.3568 + 4.66479i 0.831664 + 0.270224i
\(299\) 8.44016 0.488107
\(300\) 0 0
\(301\) −19.8194 −1.14237
\(302\) 19.9107 + 6.46937i 1.14573 + 0.372271i
\(303\) 0 0
\(304\) −5.55899 4.03884i −0.318830 0.231643i
\(305\) 27.3453 + 6.67490i 1.56579 + 0.382204i
\(306\) 0 0
\(307\) 17.1204i 0.977111i 0.872533 + 0.488556i \(0.162476\pi\)
−0.872533 + 0.488556i \(0.837524\pi\)
\(308\) −0.635220 0.874305i −0.0361950 0.0498182i
\(309\) 0 0
\(310\) −6.27846 15.3218i −0.356592 0.870218i
\(311\) 6.22754 19.1664i 0.353131 1.08683i −0.603954 0.797020i \(-0.706409\pi\)
0.957085 0.289807i \(-0.0935912\pi\)
\(312\) 0 0
\(313\) −24.2560 + 7.88127i −1.37103 + 0.445476i −0.899711 0.436486i \(-0.856223\pi\)
−0.471322 + 0.881961i \(0.656223\pi\)
\(314\) 1.76757 5.44002i 0.0997498 0.306998i
\(315\) 0 0
\(316\) 1.08540 + 3.34052i 0.0610586 + 0.187919i
\(317\) −18.5260 25.4988i −1.04052 1.43215i −0.896747 0.442544i \(-0.854076\pi\)
−0.143775 0.989610i \(-0.545924\pi\)
\(318\) 0 0
\(319\) −3.80146 + 2.76193i −0.212841 + 0.154638i
\(320\) −2.17229 0.530249i −0.121435 0.0296418i
\(321\) 0 0
\(322\) −4.71477 + 6.48932i −0.262744 + 0.361636i
\(323\) 17.6165 + 5.72394i 0.980207 + 0.318488i
\(324\) 0 0
\(325\) 9.77695 4.88847i 0.542328 0.271164i
\(326\) −11.8950 −0.658805
\(327\) 0 0
\(328\) 1.89477 2.60793i 0.104621 0.143999i
\(329\) −15.5746 11.3156i −0.858656 0.623850i
\(330\) 0 0
\(331\) 5.90633 4.29120i 0.324641 0.235866i −0.413512 0.910499i \(-0.635698\pi\)
0.738153 + 0.674633i \(0.235698\pi\)
\(332\) 13.1311i 0.720663i
\(333\) 0 0
\(334\) −2.76393 8.50651i −0.151236 0.465455i
\(335\) −11.4185 + 9.67761i −0.623859 + 0.528744i
\(336\) 0 0
\(337\) 25.4358 8.26459i 1.38558 0.450201i 0.481077 0.876678i \(-0.340246\pi\)
0.904498 + 0.426477i \(0.140246\pi\)
\(338\) 7.81822 2.54029i 0.425255 0.138174i
\(339\) 0 0
\(340\) 6.01098 0.450124i 0.325991 0.0244114i
\(341\) 1.19025 + 3.66321i 0.0644556 + 0.198374i
\(342\) 0 0
\(343\) 20.1187i 1.08631i
\(344\) 7.71737 5.60700i 0.416093 0.302309i
\(345\) 0 0
\(346\) −13.2186 9.60385i −0.710635 0.516306i
\(347\) 2.86327 3.94095i 0.153708 0.211562i −0.725217 0.688520i \(-0.758261\pi\)
0.878926 + 0.476958i \(0.158261\pi\)
\(348\) 0 0
\(349\) −16.7173 −0.894855 −0.447428 0.894320i \(-0.647660\pi\)
−0.447428 + 0.894320i \(0.647660\pi\)
\(350\) −1.70295 + 10.2479i −0.0910265 + 0.547773i
\(351\) 0 0
\(352\) 0.494689 + 0.160734i 0.0263670 + 0.00856717i
\(353\) 15.9175 21.9086i 0.847203 1.16608i −0.137269 0.990534i \(-0.543832\pi\)
0.984472 0.175541i \(-0.0561676\pi\)
\(354\) 0 0
\(355\) 9.60324 15.5384i 0.509687 0.824691i
\(356\) −7.97594 + 5.79486i −0.422724 + 0.307127i
\(357\) 0 0
\(358\) 2.16219 + 2.97599i 0.114275 + 0.157286i
\(359\) −2.62299 8.07273i −0.138436 0.426062i 0.857673 0.514196i \(-0.171910\pi\)
−0.996109 + 0.0881339i \(0.971910\pi\)
\(360\) 0 0
\(361\) 8.71879 26.8337i 0.458884 1.41230i
\(362\) −21.9211 + 7.12261i −1.15215 + 0.374356i
\(363\) 0 0
\(364\) 1.40362 4.31990i 0.0735698 0.226424i
\(365\) −2.03800 + 8.34915i −0.106674 + 0.437014i
\(366\) 0 0
\(367\) −7.49289 10.3131i −0.391126 0.538339i 0.567363 0.823468i \(-0.307964\pi\)
−0.958489 + 0.285129i \(0.907964\pi\)
\(368\) 3.86067i 0.201251i
\(369\) 0 0
\(370\) 0.886181 + 11.8341i 0.0460703 + 0.615225i
\(371\) 4.09867 + 2.97786i 0.212792 + 0.154603i
\(372\) 0 0
\(373\) −10.4051 3.38081i −0.538754 0.175052i 0.0269853 0.999636i \(-0.491409\pi\)
−0.565740 + 0.824584i \(0.691409\pi\)
\(374\) −1.40217 −0.0725045
\(375\) 0 0
\(376\) 9.26574 0.477844
\(377\) −18.7829 6.10292i −0.967367 0.314316i
\(378\) 0 0
\(379\) −11.5124 8.36427i −0.591354 0.429644i 0.251446 0.967871i \(-0.419094\pi\)
−0.842799 + 0.538228i \(0.819094\pi\)
\(380\) −1.14735 15.3218i −0.0588578 0.785990i
\(381\) 0 0
\(382\) 1.78768i 0.0914658i
\(383\) 4.21101 + 5.79595i 0.215172 + 0.296159i 0.902936 0.429776i \(-0.141407\pi\)
−0.687763 + 0.725935i \(0.741407\pi\)
\(384\) 0 0
\(385\) 0.573040 2.34759i 0.0292048 0.119644i
\(386\) 2.03994 6.27828i 0.103830 0.319556i
\(387\) 0 0
\(388\) 10.2331 3.32495i 0.519509 0.168799i
\(389\) −0.283978 + 0.873994i −0.0143982 + 0.0443133i −0.957998 0.286776i \(-0.907416\pi\)
0.943599 + 0.331090i \(0.107416\pi\)
\(390\) 0 0
\(391\) 3.21602 + 9.89790i 0.162641 + 0.500558i
\(392\) −1.57716 2.17078i −0.0796588 0.109641i
\(393\) 0 0
\(394\) 10.2401 7.43989i 0.515891 0.374816i
\(395\) −4.12911 + 6.68104i −0.207758 + 0.336160i
\(396\) 0 0
\(397\) 12.8148 17.6381i 0.643159 0.885232i −0.355620 0.934630i \(-0.615730\pi\)
0.998779 + 0.0493984i \(0.0157304\pi\)
\(398\) 5.93600 + 1.92872i 0.297545 + 0.0966782i
\(399\) 0 0
\(400\) −2.23607 4.47214i −0.111803 0.223607i
\(401\) −22.8035 −1.13875 −0.569375 0.822078i \(-0.692815\pi\)
−0.569375 + 0.822078i \(0.692815\pi\)
\(402\) 0 0
\(403\) −9.51560 + 13.0971i −0.474006 + 0.652413i
\(404\) 14.2711 + 10.3685i 0.710011 + 0.515853i
\(405\) 0 0
\(406\) 15.1846 11.0323i 0.753600 0.547523i
\(407\) 2.76052i 0.136834i
\(408\) 0 0
\(409\) −1.54554 4.75668i −0.0764220 0.235203i 0.905547 0.424247i \(-0.139461\pi\)
−0.981969 + 0.189044i \(0.939461\pi\)
\(410\) 7.18802 0.538266i 0.354991 0.0265830i
\(411\) 0 0
\(412\) 8.27189 2.68770i 0.407527 0.132414i
\(413\) −17.0899 + 5.55284i −0.840938 + 0.273237i
\(414\) 0 0
\(415\) 22.3993 18.9842i 1.09954 0.931900i
\(416\) 0.675571 + 2.07919i 0.0331226 + 0.101941i
\(417\) 0 0
\(418\) 3.57408i 0.174814i
\(419\) 18.4661 13.4164i 0.902128 0.655434i −0.0368836 0.999320i \(-0.511743\pi\)
0.939012 + 0.343885i \(0.111743\pi\)
\(420\) 0 0
\(421\) −12.7124 9.23612i −0.619566 0.450141i 0.233204 0.972428i \(-0.425079\pi\)
−0.852770 + 0.522287i \(0.825079\pi\)
\(422\) 13.2122 18.1850i 0.643160 0.885234i
\(423\) 0 0
\(424\) −2.43841 −0.118419
\(425\) 9.45818 + 9.60288i 0.458789 + 0.465808i
\(426\) 0 0
\(427\) 24.8743 + 8.08215i 1.20375 + 0.391123i
\(428\) −3.17979 + 4.37660i −0.153701 + 0.211551i
\(429\) 0 0
\(430\) 20.7219 + 5.05815i 0.999298 + 0.243926i
\(431\) −7.73154 + 5.61729i −0.372415 + 0.270576i −0.758212 0.652008i \(-0.773927\pi\)
0.385796 + 0.922584i \(0.373927\pi\)
\(432\) 0 0
\(433\) 4.77408 + 6.57096i 0.229428 + 0.315780i 0.908174 0.418593i \(-0.137476\pi\)
−0.678747 + 0.734373i \(0.737476\pi\)
\(434\) −4.75435 14.6324i −0.228216 0.702377i
\(435\) 0 0
\(436\) 0.891135 2.74263i 0.0426776 0.131348i
\(437\) 25.2294 8.19753i 1.20689 0.392141i
\(438\) 0 0
\(439\) −2.84899 + 8.76829i −0.135975 + 0.418488i −0.995740 0.0922014i \(-0.970610\pi\)
0.859766 + 0.510689i \(0.170610\pi\)
\(440\) 0.441011 + 1.07623i 0.0210244 + 0.0513073i
\(441\) 0 0
\(442\) −3.46403 4.76783i −0.164767 0.226782i
\(443\) 9.63232i 0.457645i 0.973468 + 0.228823i \(0.0734876\pi\)
−0.973468 + 0.228823i \(0.926512\pi\)
\(444\) 0 0
\(445\) −21.4162 5.22762i −1.01522 0.247813i
\(446\) −14.5056 10.5389i −0.686861 0.499033i
\(447\) 0 0
\(448\) −1.97599 0.642040i −0.0933570 0.0303335i
\(449\) −21.3096 −1.00566 −0.502831 0.864385i \(-0.667708\pi\)
−0.502831 + 0.864385i \(0.667708\pi\)
\(450\) 0 0
\(451\) −1.67674 −0.0789544
\(452\) 6.05780 + 1.96830i 0.284935 + 0.0925810i
\(453\) 0 0
\(454\) −7.16599 5.20640i −0.336317 0.244348i
\(455\) 9.39825 3.85116i 0.440597 0.180545i
\(456\) 0 0
\(457\) 13.4662i 0.629923i −0.949104 0.314961i \(-0.898008\pi\)
0.949104 0.314961i \(-0.101992\pi\)
\(458\) −12.9681 17.8490i −0.605958 0.834029i
\(459\) 0 0
\(460\) 6.58560 5.58154i 0.307055 0.260241i
\(461\) −10.1468 + 31.2286i −0.472582 + 1.45446i 0.376608 + 0.926373i \(0.377090\pi\)
−0.849191 + 0.528086i \(0.822910\pi\)
\(462\) 0 0
\(463\) −21.8083 + 7.08596i −1.01352 + 0.329312i −0.768255 0.640144i \(-0.778875\pi\)
−0.245264 + 0.969456i \(0.578875\pi\)
\(464\) −2.79158 + 8.59159i −0.129596 + 0.398854i
\(465\) 0 0
\(466\) 3.56690 + 10.9778i 0.165234 + 0.508537i
\(467\) 12.2459 + 16.8551i 0.566674 + 0.779960i 0.992156 0.125007i \(-0.0398954\pi\)
−0.425482 + 0.904967i \(0.639895\pi\)
\(468\) 0 0
\(469\) −11.2516 + 8.17475i −0.519549 + 0.377475i
\(470\) 13.3959 + 15.8057i 0.617907 + 0.729062i
\(471\) 0 0
\(472\) 5.08361 6.99698i 0.233992 0.322062i
\(473\) −4.71894 1.53328i −0.216977 0.0705001i
\(474\) 0 0
\(475\) 24.4774 24.1086i 1.12310 1.10618i
\(476\) 5.60085 0.256714
\(477\) 0 0
\(478\) 0.520147 0.715921i 0.0237910 0.0327455i
\(479\) −10.9401 7.94842i −0.499864 0.363172i 0.309101 0.951029i \(-0.399972\pi\)
−0.808965 + 0.587857i \(0.799972\pi\)
\(480\) 0 0
\(481\) 9.38664 6.81980i 0.427994 0.310956i
\(482\) 12.6736i 0.577269i
\(483\) 0 0
\(484\) 3.31558 + 10.2043i 0.150708 + 0.463832i
\(485\) 20.4663 + 12.6489i 0.929326 + 0.574355i
\(486\) 0 0
\(487\) −25.3198 + 8.22690i −1.14735 + 0.372796i −0.820144 0.572157i \(-0.806107\pi\)
−0.327205 + 0.944953i \(0.606107\pi\)
\(488\) −11.9721 + 3.88998i −0.541953 + 0.176091i
\(489\) 0 0
\(490\) 1.42278 5.82875i 0.0642746 0.263316i
\(491\) 3.71521 + 11.4342i 0.167665 + 0.516020i 0.999223 0.0394184i \(-0.0125505\pi\)
−0.831558 + 0.555438i \(0.812551\pi\)
\(492\) 0 0
\(493\) 24.3524i 1.09678i
\(494\) −12.1530 + 8.82968i −0.546790 + 0.397266i
\(495\) 0 0
\(496\) 5.99083 + 4.35259i 0.268996 + 0.195437i
\(497\) 9.97625 13.7311i 0.447496 0.615925i
\(498\) 0 0
\(499\) 27.3600 1.22480 0.612400 0.790548i \(-0.290204\pi\)
0.612400 + 0.790548i \(0.290204\pi\)
\(500\) 4.39587 10.2799i 0.196589 0.459731i
\(501\) 0 0
\(502\) 17.2109 + 5.59216i 0.768161 + 0.249590i
\(503\) −5.38563 + 7.41268i −0.240133 + 0.330515i −0.912025 0.410134i \(-0.865482\pi\)
0.671892 + 0.740649i \(0.265482\pi\)
\(504\) 0 0
\(505\) 2.94548 + 39.3341i 0.131072 + 1.75034i
\(506\) −1.62460 + 1.18034i −0.0722222 + 0.0524725i
\(507\) 0 0
\(508\) −8.79756 12.1088i −0.390329 0.537241i
\(509\) −0.725667 2.23337i −0.0321646 0.0989925i 0.933685 0.358094i \(-0.116573\pi\)
−0.965850 + 0.259102i \(0.916573\pi\)
\(510\) 0 0
\(511\) −2.46767 + 7.59470i −0.109163 + 0.335970i
\(512\) 0.951057 0.309017i 0.0420312 0.0136568i
\(513\) 0 0
\(514\) −0.395706 + 1.21786i −0.0174538 + 0.0537174i
\(515\) 16.5438 + 10.2246i 0.729006 + 0.450551i
\(516\) 0 0
\(517\) −2.83286 3.89910i −0.124589 0.171482i
\(518\) 11.0267i 0.484483i
\(519\) 0 0
\(520\) −2.57002 + 4.15838i −0.112703 + 0.182357i
\(521\) −1.24129 0.901848i −0.0543818 0.0395107i 0.560262 0.828315i \(-0.310700\pi\)
−0.614644 + 0.788805i \(0.710700\pi\)
\(522\) 0 0
\(523\) 39.5506 + 12.8508i 1.72943 + 0.561926i 0.993367 0.114988i \(-0.0366830\pi\)
0.736062 + 0.676914i \(0.236683\pi\)
\(524\) 13.8551 0.605265
\(525\) 0 0
\(526\) −7.11425 −0.310196
\(527\) −18.9850 6.16859i −0.826999 0.268708i
\(528\) 0 0
\(529\) −6.54920 4.75827i −0.284748 0.206881i
\(530\) −3.52532 4.15948i −0.153130 0.180676i
\(531\) 0 0
\(532\) 14.2764i 0.618959i
\(533\) −4.14234 5.70144i −0.179425 0.246957i
\(534\) 0 0
\(535\) −12.0628 + 0.903310i −0.521522 + 0.0390535i
\(536\) 2.06851 6.36623i 0.0893462 0.274979i
\(537\) 0 0
\(538\) −8.96833 + 2.91399i −0.386652 + 0.125631i
\(539\) −0.431287 + 1.32737i −0.0185769 + 0.0571737i
\(540\) 0 0
\(541\) 5.88428 + 18.1100i 0.252985 + 0.778608i 0.994220 + 0.107362i \(0.0342404\pi\)
−0.741235 + 0.671246i \(0.765760\pi\)
\(542\) 0.808141 + 1.11231i 0.0347126 + 0.0477778i
\(543\) 0 0
\(544\) −2.18088 + 1.58450i −0.0935045 + 0.0679350i
\(545\) 5.96679 2.44503i 0.255589 0.104734i
\(546\) 0 0
\(547\) −16.0588 + 22.1030i −0.686624 + 0.945057i −0.999990 0.00457542i \(-0.998544\pi\)
0.313365 + 0.949633i \(0.398544\pi\)
\(548\) 18.9202 + 6.14755i 0.808231 + 0.262610i
\(549\) 0 0
\(550\) −1.19827 + 2.30824i −0.0510942 + 0.0984238i
\(551\) −62.0734 −2.64441
\(552\) 0 0
\(553\) −4.28949 + 5.90398i −0.182408 + 0.251063i
\(554\) −15.8540 11.5186i −0.673574 0.489380i
\(555\) 0 0
\(556\) −4.56581 + 3.31725i −0.193633 + 0.140683i
\(557\) 9.89921i 0.419443i −0.977761 0.209721i \(-0.932744\pi\)
0.977761 0.209721i \(-0.0672557\pi\)
\(558\) 0 0
\(559\) −6.44440 19.8338i −0.272569 0.838881i
\(560\) −1.76158 4.29892i −0.0744404 0.181662i
\(561\) 0 0
\(562\) 2.69916 0.877011i 0.113857 0.0369945i
\(563\) 1.91338 0.621694i 0.0806392 0.0262013i −0.268420 0.963302i \(-0.586501\pi\)
0.349059 + 0.937101i \(0.386501\pi\)
\(564\) 0 0
\(565\) 5.40048 + 13.1792i 0.227200 + 0.554452i
\(566\) 0.690208 + 2.12424i 0.0290116 + 0.0892886i
\(567\) 0 0
\(568\) 8.16901i 0.342764i
\(569\) −19.0969 + 13.8747i −0.800585 + 0.581659i −0.911086 0.412217i \(-0.864755\pi\)
0.110501 + 0.993876i \(0.464755\pi\)
\(570\) 0 0
\(571\) −17.1782 12.4807i −0.718886 0.522301i 0.167142 0.985933i \(-0.446546\pi\)
−0.886028 + 0.463631i \(0.846546\pi\)
\(572\) 0.668395 0.919967i 0.0279470 0.0384657i
\(573\) 0 0
\(574\) 6.69758 0.279552
\(575\) 19.0422 + 3.16435i 0.794115 + 0.131963i
\(576\) 0 0
\(577\) −43.1167 14.0095i −1.79497 0.583222i −0.795238 0.606297i \(-0.792654\pi\)
−0.999734 + 0.0230749i \(0.992654\pi\)
\(578\) −5.72098 + 7.87425i −0.237961 + 0.327526i
\(579\) 0 0
\(580\) −18.6916 + 7.65933i −0.776127 + 0.318036i
\(581\) 22.0718 16.0361i 0.915694 0.665291i
\(582\) 0 0
\(583\) 0.745506 + 1.02610i 0.0308757 + 0.0424967i
\(584\) −1.18770 3.65537i −0.0491474 0.151260i
\(585\) 0 0
\(586\) 7.42445 22.8501i 0.306701 0.943929i
\(587\) 15.5245 5.04421i 0.640764 0.208197i 0.0294265 0.999567i \(-0.490632\pi\)
0.611337 + 0.791370i \(0.290632\pi\)
\(588\) 0 0
\(589\) −15.7235 + 48.3920i −0.647877 + 1.99396i
\(590\) 19.2852 1.44415i 0.793959 0.0594545i
\(591\) 0 0
\(592\) −3.11949 4.29360i −0.128210 0.176466i
\(593\) 32.8357i 1.34840i 0.738549 + 0.674199i \(0.235511\pi\)
−0.738549 + 0.674199i \(0.764489\pi\)
\(594\) 0 0
\(595\) 8.09740 + 9.55403i 0.331961 + 0.391677i
\(596\) −12.2126 8.87296i −0.500247 0.363451i
\(597\) 0 0
\(598\) −8.02707 2.60815i −0.328251 0.106655i
\(599\) −13.1905 −0.538947 −0.269474 0.963008i \(-0.586850\pi\)
−0.269474 + 0.963008i \(0.586850\pi\)
\(600\) 0 0
\(601\) −19.1992 −0.783152 −0.391576 0.920146i \(-0.628070\pi\)
−0.391576 + 0.920146i \(0.628070\pi\)
\(602\) 18.8494 + 6.12454i 0.768244 + 0.249618i
\(603\) 0 0
\(604\) −16.9370 12.3055i −0.689158 0.500703i
\(605\) −12.6132 + 20.4086i −0.512800 + 0.829728i
\(606\) 0 0
\(607\) 6.54268i 0.265559i −0.991146 0.132779i \(-0.957610\pi\)
0.991146 0.132779i \(-0.0423902\pi\)
\(608\) 4.03884 + 5.55899i 0.163797 + 0.225447i
\(609\) 0 0
\(610\) −23.9443 14.7984i −0.969475 0.599169i
\(611\) 6.25966 19.2653i 0.253239 0.779389i
\(612\) 0 0
\(613\) 8.87528 2.88375i 0.358469 0.116474i −0.124245 0.992252i \(-0.539651\pi\)
0.482714 + 0.875778i \(0.339651\pi\)
\(614\) 5.29049 16.2824i 0.213507 0.657106i
\(615\) 0 0
\(616\) 0.333955 + 1.02781i 0.0134554 + 0.0414115i
\(617\) 19.3979 + 26.6989i 0.780929 + 1.07486i 0.995179 + 0.0980778i \(0.0312694\pi\)
−0.214250 + 0.976779i \(0.568731\pi\)
\(618\) 0 0
\(619\) 22.7569 16.5339i 0.914678 0.664553i −0.0275155 0.999621i \(-0.508760\pi\)
0.942194 + 0.335069i \(0.108760\pi\)
\(620\) 1.23648 + 16.5120i 0.0496583 + 0.663139i
\(621\) 0 0
\(622\) −11.8455 + 16.3039i −0.474961 + 0.653727i
\(623\) −19.4809 6.32974i −0.780487 0.253596i
\(624\) 0 0
\(625\) 23.8910 7.36356i 0.955638 0.294542i
\(626\) 25.5043 1.01936
\(627\) 0 0
\(628\) −3.36212 + 4.62756i −0.134163 + 0.184660i
\(629\) 11.5743 + 8.40925i 0.461499 + 0.335299i
\(630\) 0 0
\(631\) 1.93909 1.40883i 0.0771940 0.0560847i −0.548519 0.836138i \(-0.684808\pi\)
0.625713 + 0.780053i \(0.284808\pi\)
\(632\) 3.51243i 0.139717i
\(633\) 0 0
\(634\) 9.73967 + 29.9756i 0.386812 + 1.19048i
\(635\) 7.93640 32.5133i 0.314946 1.29025i
\(636\) 0 0
\(637\) −5.57895 + 1.81271i −0.221046 + 0.0718223i
\(638\) 4.46889 1.45203i 0.176925 0.0574864i
\(639\) 0 0
\(640\) 1.90211 + 1.17557i 0.0751876 + 0.0464685i
\(641\) −3.76246 11.5797i −0.148608 0.457370i 0.848849 0.528635i \(-0.177296\pi\)
−0.997457 + 0.0712658i \(0.977296\pi\)
\(642\) 0 0
\(643\) 27.0249i 1.06576i 0.846192 + 0.532878i \(0.178890\pi\)
−0.846192 + 0.532878i \(0.821110\pi\)
\(644\) 6.48932 4.71477i 0.255715 0.185788i
\(645\) 0 0
\(646\) −14.9855 10.8876i −0.589595 0.428366i
\(647\) 19.9375 27.4417i 0.783826 1.07884i −0.211024 0.977481i \(-0.567680\pi\)
0.994850 0.101363i \(-0.0323203\pi\)
\(648\) 0 0
\(649\) −4.49862 −0.176586
\(650\) −10.8091 + 1.62797i −0.423966 + 0.0638543i
\(651\) 0 0
\(652\) 11.3129 + 3.67577i 0.443046 + 0.143954i
\(653\) −8.73039 + 12.0163i −0.341646 + 0.470236i −0.944921 0.327297i \(-0.893862\pi\)
0.603275 + 0.797533i \(0.293862\pi\)
\(654\) 0 0
\(655\) 20.0310 + 23.6344i 0.782676 + 0.923471i
\(656\) −2.60793 + 1.89477i −0.101823 + 0.0739785i
\(657\) 0 0
\(658\) 11.3156 + 15.5746i 0.441129 + 0.607162i
\(659\) 1.45835 + 4.48835i 0.0568094 + 0.174841i 0.975435 0.220288i \(-0.0706997\pi\)
−0.918625 + 0.395129i \(0.870700\pi\)
\(660\) 0 0
\(661\) 1.08059 3.32571i 0.0420300 0.129355i −0.927840 0.372979i \(-0.878336\pi\)
0.969870 + 0.243624i \(0.0783363\pi\)
\(662\) −6.94330 + 2.25602i −0.269859 + 0.0876826i
\(663\) 0 0
\(664\) −4.05774 + 12.4884i −0.157471 + 0.484645i
\(665\) 24.3529 20.6400i 0.944365 0.800384i
\(666\) 0 0
\(667\) −20.4997 28.2155i −0.793753 1.09251i
\(668\) 8.94427i 0.346064i
\(669\) 0 0
\(670\) 13.8502 5.67544i 0.535079 0.219261i
\(671\) 5.29723 + 3.84867i 0.204497 + 0.148576i
\(672\) 0 0
\(673\) −23.4287 7.61244i −0.903110 0.293438i −0.179590 0.983742i \(-0.557477\pi\)
−0.723520 + 0.690303i \(0.757477\pi\)
\(674\) −26.7448 −1.03017
\(675\) 0 0
\(676\) −8.22056 −0.316176
\(677\) −28.3655 9.21651i −1.09017 0.354219i −0.291861 0.956461i \(-0.594274\pi\)
−0.798314 + 0.602242i \(0.794274\pi\)
\(678\) 0 0
\(679\) 18.0859 + 13.1402i 0.694072 + 0.504273i
\(680\) −5.85588 1.42940i −0.224563 0.0548150i
\(681\) 0 0
\(682\) 3.85173i 0.147490i
\(683\) 15.3138 + 21.0776i 0.585964 + 0.806511i 0.994333 0.106306i \(-0.0339023\pi\)
−0.408369 + 0.912817i \(0.633902\pi\)
\(684\) 0 0
\(685\) 16.8672 + 41.1623i 0.644463 + 1.57273i
\(686\) 6.21702 19.1340i 0.237367 0.730540i
\(687\) 0 0
\(688\) −9.07232 + 2.94777i −0.345879 + 0.112383i
\(689\) −1.64732 + 5.06992i −0.0627577 + 0.193148i
\(690\) 0 0
\(691\) 10.6313 + 32.7197i 0.404432 + 1.24471i 0.921368 + 0.388690i \(0.127072\pi\)
−0.516936 + 0.856024i \(0.672928\pi\)
\(692\) 9.60385 + 13.2186i 0.365084 + 0.502495i
\(693\) 0 0
\(694\) −3.94095 + 2.86327i −0.149597 + 0.108688i
\(695\) −12.2596 2.99254i −0.465034 0.113513i
\(696\) 0 0
\(697\) 5.10777 7.03025i 0.193471 0.266290i
\(698\) 15.8991 + 5.16592i 0.601789 + 0.195533i
\(699\) 0 0
\(700\) 4.78637 9.22008i 0.180908 0.348486i
\(701\) −13.2937 −0.502095 −0.251047 0.967975i \(-0.580775\pi\)
−0.251047 + 0.967975i \(0.580775\pi\)
\(702\) 0 0
\(703\) 21.4349 29.5026i 0.808432 1.11271i
\(704\) −0.420808 0.305735i −0.0158598 0.0115228i
\(705\) 0 0
\(706\) −21.9086 + 15.9175i −0.824540 + 0.599063i
\(707\) 36.6503i 1.37838i
\(708\) 0 0
\(709\) 2.24820 + 6.91924i 0.0844329 + 0.259858i 0.984356 0.176191i \(-0.0563776\pi\)
−0.899923 + 0.436049i \(0.856378\pi\)
\(710\) −13.9348 + 11.8103i −0.522966 + 0.443233i
\(711\) 0 0
\(712\) 9.37628 3.04654i 0.351391 0.114174i
\(713\) −27.1893 + 8.83434i −1.01825 + 0.330849i
\(714\) 0 0
\(715\) 2.53563 0.189877i 0.0948270 0.00710100i
\(716\) −1.13673 3.49849i −0.0424815 0.130745i
\(717\) 0 0
\(718\) 8.48817i 0.316776i
\(719\) 26.0071 18.8953i 0.969902 0.704675i 0.0144727 0.999895i \(-0.495393\pi\)
0.955429 + 0.295220i \(0.0953930\pi\)
\(720\) 0 0
\(721\) 14.6196 + 10.6218i 0.544462 + 0.395575i
\(722\) −16.5841 + 22.8261i −0.617197 + 0.849499i
\(723\) 0 0
\(724\) 23.0493 0.856619
\(725\) −40.0887 20.8111i −1.48886 0.772903i
\(726\) 0 0
\(727\) 2.97260 + 0.965858i 0.110248 + 0.0358217i 0.363621 0.931547i \(-0.381540\pi\)
−0.253374 + 0.967369i \(0.581540\pi\)
\(728\) −2.66985 + 3.67473i −0.0989511 + 0.136195i
\(729\) 0 0
\(730\) 4.51828 7.31073i 0.167229 0.270582i
\(731\) 20.8039 15.1149i 0.769458 0.559044i
\(732\) 0 0
\(733\) −27.2488 37.5047i −1.00646 1.38527i −0.921279 0.388902i \(-0.872854\pi\)
−0.0851773 0.996366i \(-0.527146\pi\)
\(734\) 3.93925 + 12.1238i 0.145400 + 0.447496i
\(735\) 0 0
\(736\) −1.19301 + 3.67171i −0.0439750 + 0.135341i
\(737\) −3.31138 + 1.07593i −0.121976 + 0.0396324i
\(738\) 0 0
\(739\) 14.8417 45.6779i 0.545959 1.68029i −0.172739 0.984968i \(-0.555262\pi\)
0.718698 0.695322i \(-0.244738\pi\)
\(740\) 2.81413 11.5287i 0.103449 0.423805i
\(741\) 0 0
\(742\) −2.97786 4.09867i −0.109321 0.150467i
\(743\) 2.88963i 0.106010i −0.998594 0.0530051i \(-0.983120\pi\)
0.998594 0.0530051i \(-0.0168799\pi\)
\(744\) 0 0
\(745\) −2.52062 33.6605i −0.0923484 1.23323i
\(746\) 8.85108 + 6.43069i 0.324061 + 0.235444i
\(747\) 0 0
\(748\) 1.33354 + 0.433294i 0.0487591 + 0.0158428i
\(749\) −11.2398 −0.410693
\(750\) 0 0
\(751\) −39.4965 −1.44125 −0.720624 0.693326i \(-0.756144\pi\)
−0.720624 + 0.693326i \(0.756144\pi\)
\(752\) −8.81224 2.86327i −0.321349 0.104413i
\(753\) 0 0
\(754\) 15.9777 + 11.6084i 0.581872 + 0.422755i
\(755\) −3.49573 46.6821i −0.127223 1.69894i
\(756\) 0 0
\(757\) 25.4654i 0.925555i 0.886475 + 0.462777i \(0.153147\pi\)
−0.886475 + 0.462777i \(0.846853\pi\)
\(758\) 8.36427 + 11.5124i 0.303804 + 0.418150i
\(759\) 0 0
\(760\) −3.64349 + 14.9264i −0.132163 + 0.541438i
\(761\) −12.8769 + 39.6310i −0.466787 + 1.43662i 0.389934 + 0.920843i \(0.372498\pi\)
−0.856721 + 0.515780i \(0.827502\pi\)
\(762\) 0 0
\(763\) 5.69832 1.85150i 0.206293 0.0670287i
\(764\) −0.552424 + 1.70019i −0.0199860 + 0.0615106i
\(765\) 0 0
\(766\) −2.21386 6.81355i −0.0799899 0.246184i
\(767\) −11.1137 15.2967i −0.401294 0.552334i
\(768\) 0 0
\(769\) 1.67667 1.21817i 0.0604621 0.0439283i −0.557144 0.830416i \(-0.688103\pi\)
0.617606 + 0.786488i \(0.288103\pi\)
\(770\) −1.27044 + 2.05562i −0.0457835 + 0.0740792i
\(771\) 0 0
\(772\) −3.88019 + 5.34063i −0.139651 + 0.192213i
\(773\) −7.59855 2.46892i −0.273301 0.0888009i 0.169160 0.985589i \(-0.445895\pi\)
−0.442461 + 0.896788i \(0.645895\pi\)
\(774\) 0 0
\(775\) −26.3789 + 25.9814i −0.947557 + 0.933279i
\(776\) −10.7598 −0.386253
\(777\) 0 0
\(778\) 0.540158 0.743464i 0.0193656 0.0266545i
\(779\) −17.9199 13.0195i −0.642045 0.466473i
\(780\) 0 0
\(781\) 3.43758 2.49755i 0.123006 0.0893693i
\(782\) 10.4073i 0.372163i
\(783\) 0 0
\(784\) 0.829164 + 2.55190i 0.0296130 + 0.0911394i
\(785\) −12.7545 + 0.955107i −0.455229 + 0.0340892i
\(786\) 0 0
\(787\) 17.0337 5.53459i 0.607186 0.197287i 0.0107432 0.999942i \(-0.496580\pi\)
0.596443 + 0.802656i \(0.296580\pi\)
\(788\) −12.0380 + 3.91138i −0.428836 + 0.139337i
\(789\) 0 0
\(790\) 5.99157 5.07808i 0.213171 0.180670i
\(791\) 4.08950 + 12.5862i 0.145406 + 0.447514i
\(792\) 0 0
\(793\) 27.5203i 0.977276i
\(794\) −17.6381 + 12.8148i −0.625954 + 0.454782i
\(795\) 0 0
\(796\) −5.04946 3.66865i −0.178973 0.130032i
\(797\) 15.4319 21.2401i 0.546625 0.752364i −0.442925 0.896559i \(-0.646059\pi\)
0.989549 + 0.144195i \(0.0460591\pi\)
\(798\) 0 0
\(799\) 24.9778 0.883652
\(800\) 0.744661 + 4.94424i 0.0263277 + 0.174805i
\(801\) 0 0
\(802\) 21.6874 + 7.04666i 0.765808 + 0.248826i
\(803\) −1.17509 + 1.61737i −0.0414679 + 0.0570756i
\(804\) 0 0
\(805\) 17.4245 + 4.25325i 0.614131 + 0.149908i
\(806\) 13.0971 9.51560i 0.461326 0.335173i
\(807\) 0 0
\(808\) −10.3685 14.2711i −0.364763 0.502054i
\(809\) 9.12577 + 28.0862i 0.320845 + 0.987459i 0.973281 + 0.229616i \(0.0737470\pi\)
−0.652436 + 0.757844i \(0.726253\pi\)
\(810\) 0 0
\(811\) 9.10810 28.0318i 0.319829 0.984331i −0.653893 0.756587i \(-0.726865\pi\)
0.973721 0.227744i \(-0.0731348\pi\)
\(812\) −17.8506 + 5.80001i −0.626433 + 0.203540i
\(813\) 0 0
\(814\) −0.853047 + 2.62541i −0.0298993 + 0.0920205i
\(815\) 10.0853 + 24.6119i 0.353273 + 0.862118i
\(816\) 0 0
\(817\) −38.5273 53.0283i −1.34790 1.85523i
\(818\) 5.00147i 0.174872i
\(819\) 0 0
\(820\) −7.00255 1.70930i −0.244540 0.0596913i
\(821\) 36.2580 + 26.3430i 1.26541 + 0.919377i 0.999010 0.0444846i \(-0.0141646\pi\)
0.266404 + 0.963862i \(0.414165\pi\)
\(822\) 0 0
\(823\) 20.6983 + 6.72529i 0.721498 + 0.234429i 0.646673 0.762768i \(-0.276160\pi\)
0.0748255 + 0.997197i \(0.476160\pi\)
\(824\) −8.69758 −0.302995
\(825\) 0 0
\(826\) 17.9694 0.625234
\(827\) −18.1721 5.90446i −0.631905 0.205318i −0.0244861 0.999700i \(-0.507795\pi\)
−0.607419 + 0.794382i \(0.707795\pi\)
\(828\) 0 0
\(829\) −29.3862 21.3503i −1.02063 0.741528i −0.0542146 0.998529i \(-0.517265\pi\)
−0.966411 + 0.257001i \(0.917265\pi\)
\(830\) −27.1694 + 11.1333i −0.943065 + 0.386443i
\(831\) 0 0
\(832\) 2.18619i 0.0757926i
\(833\) −4.25159 5.85181i −0.147309 0.202753i
\(834\) 0 0
\(835\) −15.2573 + 12.9311i −0.528001 + 0.447501i
\(836\) 1.10445 3.39915i 0.0381983 0.117562i
\(837\) 0 0
\(838\) −21.7082 + 7.05342i −0.749897 + 0.243656i
\(839\) 6.13673 18.8869i 0.211863 0.652049i −0.787498 0.616317i \(-0.788624\pi\)
0.999361 0.0357313i \(-0.0113761\pi\)
\(840\) 0 0
\(841\) 16.2568 + 50.0334i 0.560581 + 1.72529i
\(842\) 9.23612 + 12.7124i 0.318298 + 0.438099i
\(843\) 0 0
\(844\) −18.1850 + 13.2122i −0.625955 + 0.454783i
\(845\) −11.8848 14.0228i −0.408851 0.482399i
\(846\) 0 0
\(847\) −13.1031 + 18.0349i −0.450229 + 0.619687i
\(848\) 2.31906 + 0.753509i 0.0796369 + 0.0258756i
\(849\) 0 0
\(850\) −6.02781 12.0556i −0.206752 0.413504i
\(851\) 20.4893 0.702363
\(852\) 0 0
\(853\) 15.3025 21.0621i 0.523948 0.721153i −0.462245 0.886752i \(-0.652956\pi\)
0.986193 + 0.165600i \(0.0529559\pi\)
\(854\) −21.1594 15.3732i −0.724058 0.526059i
\(855\) 0 0
\(856\) 4.37660 3.17979i 0.149589 0.108683i
\(857\) 34.8614i 1.19084i 0.803414 + 0.595421i \(0.203015\pi\)
−0.803414 + 0.595421i \(0.796985\pi\)
\(858\) 0 0
\(859\) 4.67229 + 14.3798i 0.159417 + 0.490634i 0.998582 0.0532431i \(-0.0169558\pi\)
−0.839165 + 0.543877i \(0.816956\pi\)
\(860\) −18.1446 11.2140i −0.618727 0.382394i
\(861\) 0 0
\(862\) 9.08897 2.95319i 0.309572 0.100586i
\(863\) 21.7819 7.07738i 0.741466 0.240917i 0.0861610 0.996281i \(-0.472540\pi\)
0.655305 + 0.755364i \(0.272540\pi\)
\(864\) 0 0
\(865\) −8.66376 + 35.4931i −0.294577 + 1.20680i
\(866\) −2.50988 7.72462i −0.0852892 0.262493i
\(867\) 0 0
\(868\) 15.3854i 0.522215i
\(869\) −1.47806 + 1.07387i −0.0501397 + 0.0364286i
\(870\) 0 0
\(871\) −11.8392 8.60168i −0.401156 0.291457i
\(872\) −1.69504 + 2.33302i −0.0574013 + 0.0790061i
\(873\) 0 0
\(874\) −26.5278 −0.897315
\(875\) 22.6477 5.16520i 0.765631 0.174616i
\(876\) 0 0
\(877\) 15.6806 + 5.09493i 0.529495 + 0.172043i 0.561550 0.827443i \(-0.310205\pi\)
−0.0320550 + 0.999486i \(0.510205\pi\)
\(878\) 5.41910 7.45875i 0.182886 0.251721i
\(879\) 0 0
\(880\) −0.0868528 1.15984i −0.00292781 0.0390981i
\(881\) 18.7621 13.6315i 0.632112 0.459257i −0.225019 0.974354i \(-0.572244\pi\)
0.857131 + 0.515098i \(0.172244\pi\)
\(882\) 0 0
\(883\) −14.3841 19.7980i −0.484062 0.666254i 0.495217 0.868769i \(-0.335089\pi\)
−0.979279 + 0.202515i \(0.935089\pi\)
\(884\) 1.82115 + 5.60491i 0.0612518 + 0.188514i
\(885\) 0 0
\(886\) 2.97655 9.16088i 0.0999991 0.307766i
\(887\) −3.75624 + 1.22048i −0.126122 + 0.0409796i −0.371398 0.928474i \(-0.621121\pi\)
0.245276 + 0.969453i \(0.421121\pi\)
\(888\) 0 0
\(889\) 9.60960 29.5753i 0.322296 0.991924i
\(890\) 18.7526 + 11.5897i 0.628587 + 0.388488i
\(891\) 0 0
\(892\) 10.5389 + 14.5056i 0.352870 + 0.485684i
\(893\) 63.6676i 2.13055i
\(894\) 0 0
\(895\) 4.32437 6.99698i 0.144548 0.233883i
\(896\) 1.68088 + 1.22123i 0.0561543 + 0.0407985i
\(897\) 0 0
\(898\) 20.2666 + 6.58502i 0.676306 + 0.219745i
\(899\) 66.8954 2.23109
\(900\) 0 0
\(901\) −6.57325 −0.218987
\(902\) 1.59467 + 0.518140i 0.0530967 + 0.0172522i
\(903\) 0 0
\(904\) −5.15307 3.74393i −0.171389 0.124521i
\(905\) 33.3234 + 39.3179i 1.10771 + 1.30697i
\(906\) 0 0
\(907\) 52.8637i 1.75531i 0.479291 + 0.877656i \(0.340894\pi\)
−0.479291 + 0.877656i \(0.659106\pi\)
\(908\) 5.20640 + 7.16599i 0.172780 + 0.237812i
\(909\) 0 0
\(910\) −10.1283 + 0.758448i −0.335751 + 0.0251423i
\(911\) −3.55654 + 10.9459i −0.117833 + 0.362654i −0.992527 0.122021i \(-0.961062\pi\)
0.874694 + 0.484676i \(0.161062\pi\)
\(912\) 0 0
\(913\) 6.49582 2.11062i 0.214980 0.0698513i
\(914\) −4.16129 + 12.8071i −0.137643 + 0.423622i
\(915\) 0 0
\(916\) 6.81771 + 20.9828i 0.225264 + 0.693290i
\(917\) 16.9203 + 23.2888i 0.558759 + 0.769066i
\(918\) 0 0
\(919\) 25.1008 18.2368i 0.828000 0.601577i −0.0909927 0.995852i \(-0.529004\pi\)
0.918993 + 0.394274i \(0.129004\pi\)
\(920\) −7.98807 + 3.27330i −0.263359 + 0.107918i
\(921\) 0 0
\(922\) 19.3003 26.5646i 0.635622 0.874858i
\(923\) 16.9849 + 5.51874i 0.559066 + 0.181652i
\(924\) 0 0
\(925\) 23.7345 11.8672i 0.780384 0.390192i
\(926\) 22.9306 0.753547
\(927\) 0 0
\(928\) 5.30989 7.30844i 0.174306 0.239911i
\(929\) 9.67177 + 7.02695i 0.317320 + 0.230547i 0.735031 0.678033i \(-0.237167\pi\)
−0.417711 + 0.908580i \(0.637167\pi\)
\(930\) 0 0
\(931\) −14.9161 + 10.8371i −0.488854 + 0.355173i
\(932\) 11.5427i 0.378095i
\(933\) 0 0
\(934\) −6.43806 19.8143i −0.210660 0.648344i
\(935\) 1.18884 + 2.90122i 0.0388793 + 0.0948799i
\(936\) 0 0
\(937\) −13.9740 + 4.54042i −0.456510 + 0.148329i −0.528240 0.849095i \(-0.677148\pi\)
0.0717304 + 0.997424i \(0.477148\pi\)
\(938\) 13.2270 4.29772i 0.431877 0.140325i
\(939\) 0 0
\(940\) −7.85604 19.1717i −0.256236 0.625310i
\(941\) −15.6185 48.0688i −0.509149 1.56700i −0.793682 0.608333i \(-0.791838\pi\)
0.284533 0.958666i \(-0.408162\pi\)
\(942\) 0 0
\(943\) 12.4452i 0.405271i
\(944\) −6.99698 + 5.08361i −0.227732 + 0.165457i
\(945\) 0 0
\(946\) 4.01417 + 2.91646i 0.130512 + 0.0948224i
\(947\) 23.3247 32.1037i 0.757952 1.04323i −0.239430 0.970914i \(-0.576960\pi\)
0.997382 0.0723177i \(-0.0230395\pi\)
\(948\) 0 0
\(949\) −8.40259 −0.272759
\(950\) −30.7293 + 15.3647i −0.996991 + 0.498496i
\(951\) 0 0
\(952\) −5.32672 1.73076i −0.172640 0.0560942i
\(953\) 29.7563 40.9560i 0.963901 1.32670i 0.0188330 0.999823i \(-0.494005\pi\)
0.945068 0.326873i \(-0.105995\pi\)
\(954\) 0 0
\(955\) −3.69888 + 1.51570i −0.119693 + 0.0490470i
\(956\) −0.715921 + 0.520147i −0.0231545 + 0.0168228i
\(957\) 0 0
\(958\) 7.94842 + 10.9401i 0.256802 + 0.353457i
\(959\) 12.7727 + 39.3102i 0.412451 + 1.26939i
\(960\) 0 0
\(961\) 7.36546 22.6685i 0.237595 0.731243i
\(962\) −11.0347 + 3.58538i −0.355772 + 0.115597i
\(963\) 0 0
\(964\) −3.91637 + 12.0534i −0.126138 + 0.388212i
\(965\) −14.7199 + 1.10228i −0.473851 + 0.0354837i
\(966\) 0 0
\(967\) 6.49628 + 8.94137i 0.208906 + 0.287535i 0.900594 0.434662i \(-0.143132\pi\)
−0.691687 + 0.722197i \(0.743132\pi\)
\(968\) 10.7294i 0.344857i
\(969\) 0 0
\(970\) −15.5559 18.3542i −0.499469 0.589318i
\(971\) 19.9495 + 14.4942i 0.640211 + 0.465140i 0.859923 0.510424i \(-0.170512\pi\)
−0.219712 + 0.975565i \(0.570512\pi\)
\(972\) 0 0
\(973\) −11.1518 3.62345i −0.357511 0.116162i
\(974\) 26.6228 0.853050
\(975\) 0 0
\(976\) 12.5882 0.402940
\(977\) −7.71967 2.50827i −0.246974 0.0802467i 0.182914 0.983129i \(-0.441447\pi\)
−0.429888 + 0.902882i \(0.641447\pi\)
\(978\) 0 0
\(979\) −4.14866 3.01418i −0.132592 0.0963336i
\(980\) −3.15433 + 5.10381i −0.100761 + 0.163035i
\(981\) 0 0
\(982\) 12.0227i 0.383659i
\(983\) −15.6954 21.6028i −0.500605 0.689023i 0.481695 0.876339i \(-0.340021\pi\)
−0.982300 + 0.187316i \(0.940021\pi\)
\(984\) 0 0
\(985\) −24.0760 14.8798i −0.767125 0.474109i
\(986\) −7.52530 + 23.1605i −0.239654 + 0.737580i
\(987\) 0 0
\(988\) 14.2867 4.64204i 0.454521 0.147683i
\(989\) 11.3804 35.0252i 0.361875 1.11374i
\(990\) 0 0
\(991\) −16.3515 50.3248i −0.519423 1.59862i −0.775088 0.631854i \(-0.782294\pi\)
0.255665 0.966765i \(-0.417706\pi\)
\(992\) −4.35259 5.99083i −0.138195 0.190209i
\(993\) 0 0
\(994\) −13.7311 + 9.97625i −0.435525 + 0.316427i
\(995\) −1.04219 13.9174i −0.0330395 0.441211i
\(996\) 0 0
\(997\) −16.6169 + 22.8712i −0.526262 + 0.724337i −0.986555 0.163430i \(-0.947744\pi\)
0.460293 + 0.887767i \(0.347744\pi\)
\(998\) −26.0209 8.45469i −0.823676 0.267629i
\(999\) 0 0
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 450.2.l.a.379.1 8
3.2 odd 2 150.2.h.a.79.2 yes 8
15.2 even 4 750.2.g.e.601.1 8
15.8 even 4 750.2.g.c.601.2 8
15.14 odd 2 750.2.h.c.649.1 8
25.19 even 10 inner 450.2.l.a.19.1 8
75.8 even 20 750.2.g.c.151.2 8
75.17 even 20 750.2.g.e.151.1 8
75.38 even 20 3750.2.a.o.1.4 4
75.41 odd 10 3750.2.c.e.1249.8 8
75.44 odd 10 150.2.h.a.19.2 8
75.56 odd 10 750.2.h.c.349.1 8
75.59 odd 10 3750.2.c.e.1249.1 8
75.62 even 20 3750.2.a.m.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.2.h.a.19.2 8 75.44 odd 10
150.2.h.a.79.2 yes 8 3.2 odd 2
450.2.l.a.19.1 8 25.19 even 10 inner
450.2.l.a.379.1 8 1.1 even 1 trivial
750.2.g.c.151.2 8 75.8 even 20
750.2.g.c.601.2 8 15.8 even 4
750.2.g.e.151.1 8 75.17 even 20
750.2.g.e.601.1 8 15.2 even 4
750.2.h.c.349.1 8 75.56 odd 10
750.2.h.c.649.1 8 15.14 odd 2
3750.2.a.m.1.1 4 75.62 even 20
3750.2.a.o.1.4 4 75.38 even 20
3750.2.c.e.1249.1 8 75.59 odd 10
3750.2.c.e.1249.8 8 75.41 odd 10