Properties

Label 825.2.n.n.751.1
Level $825$
Weight $2$
Character 825.751
Analytic conductor $6.588$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [825,2,Mod(301,825)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(825, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("825.301");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.n (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 3 x^{15} + 9 x^{14} - 15 x^{13} + 44 x^{12} - 61 x^{11} + 208 x^{10} - 281 x^{9} + 851 x^{8} - 1252 x^{7} + 1929 x^{6} - 1320 x^{5} + 1261 x^{4} + 45 x^{3} + 640 x^{2} + \cdots + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 751.1
Root \(-0.624800 + 1.92294i\) of defining polynomial
Character \(\chi\) \(=\) 825.751
Dual form 825.2.n.n.301.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.63575 + 1.18844i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.645245 - 1.98586i) q^{4} +(1.63575 + 1.18844i) q^{6} +(-0.404805 + 1.24586i) q^{7} +(0.0550187 + 0.169330i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(-1.63575 + 1.18844i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.645245 - 1.98586i) q^{4} +(1.63575 + 1.18844i) q^{6} +(-0.404805 + 1.24586i) q^{7} +(0.0550187 + 0.169330i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(2.83030 - 1.72900i) q^{11} -2.08806 q^{12} +(-1.57642 + 1.14533i) q^{13} +(-0.818473 - 2.51900i) q^{14} +(3.08731 + 2.24306i) q^{16} +(-2.45542 - 1.78397i) q^{17} +(0.624800 - 1.92294i) q^{18} +(-0.322858 - 0.993654i) q^{19} +1.30998 q^{21} +(-2.57484 + 6.19184i) q^{22} +1.23786 q^{23} +(0.144041 - 0.104652i) q^{24} +(1.21746 - 3.74696i) q^{26} +(0.809017 + 0.587785i) q^{27} +(2.21291 + 1.60777i) q^{28} +(0.158207 - 0.486912i) q^{29} +(-1.02947 + 0.747953i) q^{31} -8.07190 q^{32} +(-2.51898 - 2.15748i) q^{33} +6.13658 q^{34} +(0.645245 + 1.98586i) q^{36} +(-0.679912 + 2.09255i) q^{37} +(1.70901 + 1.24167i) q^{38} +(1.57642 + 1.14533i) q^{39} +(-3.66786 - 11.2885i) q^{41} +(-2.14279 + 1.55683i) q^{42} +3.33759 q^{43} +(-1.60731 - 6.73620i) q^{44} +(-2.02482 + 1.47112i) q^{46} +(-4.02739 - 12.3950i) q^{47} +(1.17925 - 3.62935i) q^{48} +(4.27482 + 3.10583i) q^{49} +(-0.937887 + 2.88652i) q^{51} +(1.25730 + 3.86957i) q^{52} +(8.19681 - 5.95533i) q^{53} -2.02189 q^{54} -0.233234 q^{56} +(-0.845252 + 0.614112i) q^{57} +(0.319879 + 0.984486i) q^{58} +(0.989277 - 3.04468i) q^{59} +(-7.32395 - 5.32116i) q^{61} +(0.795054 - 2.44693i) q^{62} +(-0.404805 - 1.24586i) q^{63} +(7.02896 - 5.10684i) q^{64} +(6.68446 + 0.535438i) q^{66} +9.53414 q^{67} +(-5.12706 + 3.72503i) q^{68} +(-0.382520 - 1.17727i) q^{69} +(-3.37823 - 2.45443i) q^{71} +(-0.144041 - 0.104652i) q^{72} +(4.04828 - 12.4593i) q^{73} +(-1.37471 - 4.23093i) q^{74} -2.18158 q^{76} +(1.00837 + 4.22606i) q^{77} -3.93978 q^{78} +(-0.889024 + 0.645914i) q^{79} +(0.309017 - 0.951057i) q^{81} +(19.4154 + 14.1061i) q^{82} +(4.01823 + 2.91942i) q^{83} +(0.845256 - 2.60143i) q^{84} +(-5.45946 + 3.96653i) q^{86} -0.511970 q^{87} +(0.448490 + 0.384127i) q^{88} +7.38928 q^{89} +(-0.788787 - 2.42764i) q^{91} +(0.798723 - 2.45822i) q^{92} +(1.02947 + 0.747953i) q^{93} +(21.3185 + 15.4888i) q^{94} +(2.49435 + 7.67683i) q^{96} +(12.0147 - 8.72918i) q^{97} -10.6836 q^{98} +(-1.27348 + 3.06239i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 2 q^{2} + 4 q^{3} - 6 q^{4} - 2 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 2 q^{2} + 4 q^{3} - 6 q^{4} - 2 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 3 q^{11} - 14 q^{12} - 11 q^{13} + 4 q^{14} + 16 q^{16} - 17 q^{17} - 3 q^{18} + 8 q^{19} - 16 q^{21} - 23 q^{22} - 14 q^{23} - q^{24} + 33 q^{26} + 4 q^{27} + 7 q^{28} + 4 q^{29} - 5 q^{31} + 24 q^{32} + 12 q^{33} - 16 q^{34} - 6 q^{36} + 2 q^{37} - 3 q^{38} + 11 q^{39} + 2 q^{41} - 4 q^{42} + 22 q^{43} - 40 q^{46} - 20 q^{47} + 9 q^{48} - 26 q^{49} - 18 q^{51} - 43 q^{52} + 40 q^{53} - 2 q^{54} - 8 q^{56} + 2 q^{57} + 26 q^{58} + 6 q^{59} - 2 q^{61} + 26 q^{62} - 4 q^{63} + 4 q^{64} - 7 q^{66} - 12 q^{67} - 56 q^{68} + 4 q^{69} + 11 q^{71} + q^{72} - 21 q^{73} + 66 q^{74} - 10 q^{76} + 23 q^{77} + 2 q^{78} - 7 q^{79} - 4 q^{81} + 20 q^{82} + 13 q^{83} + 18 q^{84} + 37 q^{86} + 56 q^{87} + 26 q^{88} + 42 q^{89} + 2 q^{91} + 92 q^{92} + 5 q^{93} + 88 q^{94} + 11 q^{96} - 27 q^{97} - 54 q^{98} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.63575 + 1.18844i −1.15665 + 0.840354i −0.989351 0.145553i \(-0.953504\pi\)
−0.167297 + 0.985906i \(0.553504\pi\)
\(3\) −0.309017 0.951057i −0.178411 0.549093i
\(4\) 0.645245 1.98586i 0.322623 0.992931i
\(5\) 0 0
\(6\) 1.63575 + 1.18844i 0.667791 + 0.485179i
\(7\) −0.404805 + 1.24586i −0.153002 + 0.470891i −0.997953 0.0639522i \(-0.979629\pi\)
0.844951 + 0.534844i \(0.179629\pi\)
\(8\) 0.0550187 + 0.169330i 0.0194520 + 0.0598672i
\(9\) −0.809017 + 0.587785i −0.269672 + 0.195928i
\(10\) 0 0
\(11\) 2.83030 1.72900i 0.853366 0.521312i
\(12\) −2.08806 −0.602770
\(13\) −1.57642 + 1.14533i −0.437220 + 0.317659i −0.784529 0.620092i \(-0.787095\pi\)
0.347310 + 0.937751i \(0.387095\pi\)
\(14\) −0.818473 2.51900i −0.218746 0.673231i
\(15\) 0 0
\(16\) 3.08731 + 2.24306i 0.771828 + 0.560766i
\(17\) −2.45542 1.78397i −0.595527 0.432675i 0.248762 0.968565i \(-0.419976\pi\)
−0.844288 + 0.535889i \(0.819976\pi\)
\(18\) 0.624800 1.92294i 0.147267 0.453240i
\(19\) −0.322858 0.993654i −0.0740686 0.227960i 0.907168 0.420770i \(-0.138240\pi\)
−0.981236 + 0.192810i \(0.938240\pi\)
\(20\) 0 0
\(21\) 1.30998 0.285860
\(22\) −2.57484 + 6.19184i −0.548958 + 1.32010i
\(23\) 1.23786 0.258111 0.129056 0.991637i \(-0.458805\pi\)
0.129056 + 0.991637i \(0.458805\pi\)
\(24\) 0.144041 0.104652i 0.0294022 0.0213620i
\(25\) 0 0
\(26\) 1.21746 3.74696i 0.238764 0.734839i
\(27\) 0.809017 + 0.587785i 0.155695 + 0.113119i
\(28\) 2.21291 + 1.60777i 0.418201 + 0.303841i
\(29\) 0.158207 0.486912i 0.0293784 0.0904174i −0.935292 0.353876i \(-0.884863\pi\)
0.964671 + 0.263459i \(0.0848634\pi\)
\(30\) 0 0
\(31\) −1.02947 + 0.747953i −0.184898 + 0.134336i −0.676384 0.736549i \(-0.736454\pi\)
0.491486 + 0.870886i \(0.336454\pi\)
\(32\) −8.07190 −1.42692
\(33\) −2.51898 2.15748i −0.438498 0.375570i
\(34\) 6.13658 1.05242
\(35\) 0 0
\(36\) 0.645245 + 1.98586i 0.107541 + 0.330977i
\(37\) −0.679912 + 2.09255i −0.111777 + 0.344014i −0.991261 0.131914i \(-0.957888\pi\)
0.879484 + 0.475928i \(0.157888\pi\)
\(38\) 1.70901 + 1.24167i 0.277238 + 0.201425i
\(39\) 1.57642 + 1.14533i 0.252429 + 0.183400i
\(40\) 0 0
\(41\) −3.66786 11.2885i −0.572823 1.76297i −0.643476 0.765466i \(-0.722508\pi\)
0.0706535 0.997501i \(-0.477492\pi\)
\(42\) −2.14279 + 1.55683i −0.330640 + 0.240224i
\(43\) 3.33759 0.508978 0.254489 0.967076i \(-0.418093\pi\)
0.254489 + 0.967076i \(0.418093\pi\)
\(44\) −1.60731 6.73620i −0.242311 1.01552i
\(45\) 0 0
\(46\) −2.02482 + 1.47112i −0.298544 + 0.216905i
\(47\) −4.02739 12.3950i −0.587455 1.80800i −0.589179 0.808003i \(-0.700549\pi\)
0.00172330 0.999999i \(-0.499451\pi\)
\(48\) 1.17925 3.62935i 0.170210 0.523852i
\(49\) 4.27482 + 3.10583i 0.610688 + 0.443691i
\(50\) 0 0
\(51\) −0.937887 + 2.88652i −0.131330 + 0.404193i
\(52\) 1.25730 + 3.86957i 0.174356 + 0.536613i
\(53\) 8.19681 5.95533i 1.12592 0.818028i 0.140823 0.990035i \(-0.455025\pi\)
0.985096 + 0.172007i \(0.0550253\pi\)
\(54\) −2.02189 −0.275145
\(55\) 0 0
\(56\) −0.233234 −0.0311672
\(57\) −0.845252 + 0.614112i −0.111956 + 0.0813411i
\(58\) 0.319879 + 0.984486i 0.0420021 + 0.129269i
\(59\) 0.989277 3.04468i 0.128793 0.396384i −0.865780 0.500425i \(-0.833177\pi\)
0.994573 + 0.104041i \(0.0331772\pi\)
\(60\) 0 0
\(61\) −7.32395 5.32116i −0.937735 0.681305i 0.0101391 0.999949i \(-0.496773\pi\)
−0.947874 + 0.318644i \(0.896773\pi\)
\(62\) 0.795054 2.44693i 0.100972 0.310760i
\(63\) −0.404805 1.24586i −0.0510006 0.156964i
\(64\) 7.02896 5.10684i 0.878620 0.638355i
\(65\) 0 0
\(66\) 6.68446 + 0.535438i 0.822800 + 0.0659079i
\(67\) 9.53414 1.16478 0.582390 0.812909i \(-0.302118\pi\)
0.582390 + 0.812909i \(0.302118\pi\)
\(68\) −5.12706 + 3.72503i −0.621747 + 0.451726i
\(69\) −0.382520 1.17727i −0.0460499 0.141727i
\(70\) 0 0
\(71\) −3.37823 2.45443i −0.400922 0.291287i 0.368994 0.929432i \(-0.379702\pi\)
−0.769916 + 0.638145i \(0.779702\pi\)
\(72\) −0.144041 0.104652i −0.0169754 0.0123333i
\(73\) 4.04828 12.4593i 0.473815 1.45825i −0.373734 0.927536i \(-0.621923\pi\)
0.847549 0.530717i \(-0.178077\pi\)
\(74\) −1.37471 4.23093i −0.159807 0.491835i
\(75\) 0 0
\(76\) −2.18158 −0.250245
\(77\) 1.00837 + 4.22606i 0.114914 + 0.481605i
\(78\) −3.93978 −0.446093
\(79\) −0.889024 + 0.645914i −0.100023 + 0.0726710i −0.636673 0.771134i \(-0.719690\pi\)
0.536650 + 0.843805i \(0.319690\pi\)
\(80\) 0 0
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 19.4154 + 14.1061i 2.14407 + 1.55776i
\(83\) 4.01823 + 2.91942i 0.441058 + 0.320447i 0.786055 0.618156i \(-0.212120\pi\)
−0.344997 + 0.938604i \(0.612120\pi\)
\(84\) 0.845256 2.60143i 0.0922250 0.283839i
\(85\) 0 0
\(86\) −5.45946 + 3.96653i −0.588709 + 0.427722i
\(87\) −0.511970 −0.0548890
\(88\) 0.448490 + 0.384127i 0.0478092 + 0.0409481i
\(89\) 7.38928 0.783263 0.391631 0.920122i \(-0.371911\pi\)
0.391631 + 0.920122i \(0.371911\pi\)
\(90\) 0 0
\(91\) −0.788787 2.42764i −0.0826873 0.254485i
\(92\) 0.798723 2.45822i 0.0832726 0.256287i
\(93\) 1.02947 + 0.747953i 0.106751 + 0.0775592i
\(94\) 21.3185 + 15.4888i 2.19884 + 1.59755i
\(95\) 0 0
\(96\) 2.49435 + 7.67683i 0.254579 + 0.783514i
\(97\) 12.0147 8.72918i 1.21991 0.886314i 0.223814 0.974632i \(-0.428149\pi\)
0.996092 + 0.0883182i \(0.0281492\pi\)
\(98\) −10.6836 −1.07921
\(99\) −1.27348 + 3.06239i −0.127990 + 0.307782i
\(100\) 0 0
\(101\) 5.84831 4.24905i 0.581929 0.422796i −0.257490 0.966281i \(-0.582895\pi\)
0.839419 + 0.543485i \(0.182895\pi\)
\(102\) −1.89631 5.83624i −0.187762 0.577873i
\(103\) 2.73642 8.42184i 0.269628 0.829829i −0.720963 0.692973i \(-0.756300\pi\)
0.990591 0.136856i \(-0.0436996\pi\)
\(104\) −0.280672 0.203920i −0.0275222 0.0199960i
\(105\) 0 0
\(106\) −6.33035 + 19.4828i −0.614858 + 1.89234i
\(107\) −1.27605 3.92727i −0.123360 0.379663i 0.870239 0.492630i \(-0.163965\pi\)
−0.993599 + 0.112967i \(0.963965\pi\)
\(108\) 1.68927 1.22733i 0.162551 0.118100i
\(109\) −13.6437 −1.30683 −0.653414 0.757001i \(-0.726664\pi\)
−0.653414 + 0.757001i \(0.726664\pi\)
\(110\) 0 0
\(111\) 2.20024 0.208838
\(112\) −4.04431 + 2.93836i −0.382151 + 0.277649i
\(113\) 4.77495 + 14.6958i 0.449190 + 1.38246i 0.877823 + 0.478985i \(0.158995\pi\)
−0.428633 + 0.903479i \(0.641005\pi\)
\(114\) 0.652784 2.00906i 0.0611388 0.188166i
\(115\) 0 0
\(116\) −0.864858 0.628356i −0.0803001 0.0583414i
\(117\) 0.602138 1.85319i 0.0556677 0.171328i
\(118\) 2.00021 + 6.15603i 0.184135 + 0.566708i
\(119\) 3.21654 2.33695i 0.294860 0.214228i
\(120\) 0 0
\(121\) 5.02115 9.78714i 0.456468 0.889740i
\(122\) 18.3040 1.65717
\(123\) −9.60257 + 6.97667i −0.865835 + 0.629066i
\(124\) 0.821071 + 2.52700i 0.0737344 + 0.226931i
\(125\) 0 0
\(126\) 2.14279 + 1.55683i 0.190895 + 0.138693i
\(127\) 6.86545 + 4.98804i 0.609210 + 0.442617i 0.849136 0.528174i \(-0.177123\pi\)
−0.239926 + 0.970791i \(0.577123\pi\)
\(128\) −0.439723 + 1.35333i −0.0388664 + 0.119618i
\(129\) −1.03137 3.17424i −0.0908073 0.279476i
\(130\) 0 0
\(131\) −7.09703 −0.620070 −0.310035 0.950725i \(-0.600341\pi\)
−0.310035 + 0.950725i \(0.600341\pi\)
\(132\) −5.90982 + 3.61024i −0.514384 + 0.314231i
\(133\) 1.36865 0.118677
\(134\) −15.5954 + 11.3308i −1.34724 + 0.978828i
\(135\) 0 0
\(136\) 0.166985 0.513928i 0.0143189 0.0440690i
\(137\) −1.00875 0.732897i −0.0861831 0.0626157i 0.543859 0.839176i \(-0.316963\pi\)
−0.630042 + 0.776561i \(0.716963\pi\)
\(138\) 2.02482 + 1.47112i 0.172365 + 0.125230i
\(139\) −4.15401 + 12.7847i −0.352338 + 1.08439i 0.605198 + 0.796075i \(0.293094\pi\)
−0.957537 + 0.288311i \(0.906906\pi\)
\(140\) 0 0
\(141\) −10.5438 + 7.66055i −0.887952 + 0.645135i
\(142\) 8.44287 0.708510
\(143\) −2.48145 + 5.96726i −0.207509 + 0.499007i
\(144\) −3.81613 −0.318011
\(145\) 0 0
\(146\) 8.18519 + 25.1914i 0.677411 + 2.08486i
\(147\) 1.63283 5.02535i 0.134674 0.414484i
\(148\) 3.71681 + 2.70042i 0.305520 + 0.221973i
\(149\) 11.6912 + 8.49414i 0.957778 + 0.695867i 0.952634 0.304120i \(-0.0983624\pi\)
0.00514473 + 0.999987i \(0.498362\pi\)
\(150\) 0 0
\(151\) −5.97241 18.3812i −0.486028 1.49584i −0.830487 0.557039i \(-0.811937\pi\)
0.344459 0.938802i \(-0.388063\pi\)
\(152\) 0.150492 0.109339i 0.0122065 0.00886857i
\(153\) 3.03507 0.245370
\(154\) −6.67186 5.71438i −0.537634 0.460478i
\(155\) 0 0
\(156\) 3.29165 2.39153i 0.263543 0.191475i
\(157\) −6.91721 21.2890i −0.552053 1.69905i −0.703601 0.710595i \(-0.748426\pi\)
0.151548 0.988450i \(-0.451574\pi\)
\(158\) 0.686589 2.11310i 0.0546221 0.168109i
\(159\) −8.19681 5.95533i −0.650049 0.472288i
\(160\) 0 0
\(161\) −0.501092 + 1.54220i −0.0394915 + 0.121542i
\(162\) 0.624800 + 1.92294i 0.0490889 + 0.151080i
\(163\) −9.30657 + 6.76162i −0.728947 + 0.529611i −0.889230 0.457460i \(-0.848759\pi\)
0.160283 + 0.987071i \(0.448759\pi\)
\(164\) −24.7841 −1.93531
\(165\) 0 0
\(166\) −10.0424 −0.779438
\(167\) −12.5779 + 9.13840i −0.973310 + 0.707151i −0.956203 0.292703i \(-0.905445\pi\)
−0.0171062 + 0.999854i \(0.505445\pi\)
\(168\) 0.0720732 + 0.221818i 0.00556057 + 0.0171137i
\(169\) −2.84392 + 8.75268i −0.218763 + 0.673283i
\(170\) 0 0
\(171\) 0.845252 + 0.614112i 0.0646381 + 0.0469623i
\(172\) 2.15357 6.62800i 0.164208 0.505380i
\(173\) −4.19647 12.9154i −0.319052 0.981940i −0.974054 0.226314i \(-0.927333\pi\)
0.655003 0.755627i \(-0.272667\pi\)
\(174\) 0.837454 0.608446i 0.0634872 0.0461261i
\(175\) 0 0
\(176\) 12.6163 + 1.01059i 0.950986 + 0.0761759i
\(177\) −3.20137 −0.240630
\(178\) −12.0870 + 8.78172i −0.905959 + 0.658218i
\(179\) −7.59067 23.3617i −0.567353 1.74613i −0.660855 0.750514i \(-0.729806\pi\)
0.0935018 0.995619i \(-0.470194\pi\)
\(180\) 0 0
\(181\) −2.21301 1.60785i −0.164492 0.119510i 0.502494 0.864581i \(-0.332416\pi\)
−0.666986 + 0.745070i \(0.732416\pi\)
\(182\) 4.17535 + 3.03357i 0.309498 + 0.224863i
\(183\) −2.79750 + 8.60982i −0.206797 + 0.636456i
\(184\) 0.0681054 + 0.209607i 0.00502080 + 0.0154524i
\(185\) 0 0
\(186\) −2.57285 −0.188650
\(187\) −10.0340 0.803746i −0.733761 0.0587757i
\(188\) −27.2135 −1.98475
\(189\) −1.05979 + 0.769985i −0.0770886 + 0.0560082i
\(190\) 0 0
\(191\) −0.747926 + 2.30188i −0.0541181 + 0.166558i −0.974462 0.224551i \(-0.927909\pi\)
0.920344 + 0.391109i \(0.127909\pi\)
\(192\) −7.02896 5.10684i −0.507272 0.368554i
\(193\) 14.9746 + 10.8797i 1.07790 + 0.783137i 0.977315 0.211791i \(-0.0679298\pi\)
0.100581 + 0.994929i \(0.467930\pi\)
\(194\) −9.27888 + 28.5575i −0.666185 + 2.05031i
\(195\) 0 0
\(196\) 8.92606 6.48516i 0.637576 0.463226i
\(197\) −23.5986 −1.68133 −0.840664 0.541557i \(-0.817835\pi\)
−0.840664 + 0.541557i \(0.817835\pi\)
\(198\) −1.55638 6.52275i −0.110607 0.463552i
\(199\) −25.4697 −1.80550 −0.902751 0.430164i \(-0.858456\pi\)
−0.902751 + 0.430164i \(0.858456\pi\)
\(200\) 0 0
\(201\) −2.94621 9.06751i −0.207810 0.639573i
\(202\) −4.51662 + 13.9007i −0.317789 + 0.978053i
\(203\) 0.542582 + 0.394209i 0.0380818 + 0.0276681i
\(204\) 5.12706 + 3.72503i 0.358966 + 0.260804i
\(205\) 0 0
\(206\) 5.53276 + 17.0281i 0.385485 + 1.18640i
\(207\) −1.00145 + 0.727595i −0.0696055 + 0.0505714i
\(208\) −7.43596 −0.515591
\(209\) −2.63181 2.25412i −0.182046 0.155920i
\(210\) 0 0
\(211\) 3.84006 2.78996i 0.264360 0.192069i −0.447707 0.894180i \(-0.647759\pi\)
0.712067 + 0.702111i \(0.247759\pi\)
\(212\) −6.53751 20.1204i −0.448998 1.38187i
\(213\) −1.29037 + 3.97135i −0.0884146 + 0.272112i
\(214\) 6.75461 + 4.90751i 0.461736 + 0.335471i
\(215\) 0 0
\(216\) −0.0550187 + 0.169330i −0.00374355 + 0.0115215i
\(217\) −0.515112 1.58535i −0.0349681 0.107621i
\(218\) 22.3176 16.2147i 1.51154 1.09820i
\(219\) −13.1005 −0.885250
\(220\) 0 0
\(221\) 5.91401 0.397819
\(222\) −3.59904 + 2.61486i −0.241552 + 0.175498i
\(223\) −0.157853 0.485822i −0.0105706 0.0325331i 0.945632 0.325238i \(-0.105445\pi\)
−0.956203 + 0.292705i \(0.905445\pi\)
\(224\) 3.26755 10.0565i 0.218322 0.671926i
\(225\) 0 0
\(226\) −25.2757 18.3639i −1.68131 1.22155i
\(227\) 3.17203 9.76250i 0.210535 0.647960i −0.788906 0.614514i \(-0.789352\pi\)
0.999441 0.0334456i \(-0.0106481\pi\)
\(228\) 0.674146 + 2.07481i 0.0446464 + 0.137407i
\(229\) 17.7739 12.9135i 1.17453 0.853346i 0.182986 0.983116i \(-0.441424\pi\)
0.991544 + 0.129770i \(0.0414238\pi\)
\(230\) 0 0
\(231\) 3.70762 2.26494i 0.243944 0.149022i
\(232\) 0.0911533 0.00598451
\(233\) −6.52071 + 4.73757i −0.427186 + 0.310369i −0.780523 0.625128i \(-0.785047\pi\)
0.353337 + 0.935496i \(0.385047\pi\)
\(234\) 1.21746 + 3.74696i 0.0795878 + 0.244946i
\(235\) 0 0
\(236\) −5.40799 3.92914i −0.352030 0.255765i
\(237\) 0.889024 + 0.645914i 0.0577483 + 0.0419566i
\(238\) −2.48412 + 7.64533i −0.161022 + 0.495573i
\(239\) 4.57556 + 14.0821i 0.295969 + 0.910898i 0.982894 + 0.184170i \(0.0589598\pi\)
−0.686926 + 0.726728i \(0.741040\pi\)
\(240\) 0 0
\(241\) 17.7412 1.14281 0.571404 0.820669i \(-0.306399\pi\)
0.571404 + 0.820669i \(0.306399\pi\)
\(242\) 3.41809 + 21.9766i 0.219723 + 1.41271i
\(243\) −1.00000 −0.0641500
\(244\) −15.2928 + 11.1109i −0.979023 + 0.711302i
\(245\) 0 0
\(246\) 7.41602 22.8242i 0.472828 1.45521i
\(247\) 1.64702 + 1.19663i 0.104798 + 0.0761400i
\(248\) −0.183291 0.133169i −0.0116390 0.00845623i
\(249\) 1.53483 4.72371i 0.0972657 0.299353i
\(250\) 0 0
\(251\) −5.75951 + 4.18453i −0.363537 + 0.264125i −0.754526 0.656270i \(-0.772133\pi\)
0.390989 + 0.920395i \(0.372133\pi\)
\(252\) −2.73531 −0.172308
\(253\) 3.50351 2.14025i 0.220264 0.134557i
\(254\) −17.1581 −1.07660
\(255\) 0 0
\(256\) 4.48057 + 13.7898i 0.280036 + 0.861862i
\(257\) −6.04078 + 18.5916i −0.376813 + 1.15971i 0.565434 + 0.824794i \(0.308709\pi\)
−0.942247 + 0.334918i \(0.891291\pi\)
\(258\) 5.45946 + 3.96653i 0.339891 + 0.246945i
\(259\) −2.33180 1.69415i −0.144891 0.105270i
\(260\) 0 0
\(261\) 0.158207 + 0.486912i 0.00979280 + 0.0301391i
\(262\) 11.6089 8.43439i 0.717203 0.521078i
\(263\) −26.8455 −1.65537 −0.827683 0.561197i \(-0.810341\pi\)
−0.827683 + 0.561197i \(0.810341\pi\)
\(264\) 0.226736 0.545241i 0.0139546 0.0335573i
\(265\) 0 0
\(266\) −2.23876 + 1.62656i −0.137267 + 0.0997306i
\(267\) −2.28341 7.02763i −0.139743 0.430084i
\(268\) 6.15186 18.9335i 0.375785 1.15655i
\(269\) 14.8387 + 10.7810i 0.904734 + 0.657328i 0.939677 0.342062i \(-0.111125\pi\)
−0.0349437 + 0.999389i \(0.511125\pi\)
\(270\) 0 0
\(271\) −5.00793 + 15.4128i −0.304210 + 0.936262i 0.675761 + 0.737121i \(0.263815\pi\)
−0.979971 + 0.199141i \(0.936185\pi\)
\(272\) −3.57910 11.0153i −0.217015 0.667902i
\(273\) −2.06507 + 1.50036i −0.124984 + 0.0908060i
\(274\) 2.52106 0.152303
\(275\) 0 0
\(276\) −2.58472 −0.155582
\(277\) −15.2048 + 11.0469i −0.913566 + 0.663745i −0.941914 0.335853i \(-0.890975\pi\)
0.0283479 + 0.999598i \(0.490975\pi\)
\(278\) −8.39897 25.8494i −0.503737 1.55034i
\(279\) 0.393222 1.21021i 0.0235416 0.0724536i
\(280\) 0 0
\(281\) 24.9177 + 18.1038i 1.48647 + 1.07998i 0.975400 + 0.220441i \(0.0707495\pi\)
0.511067 + 0.859541i \(0.329250\pi\)
\(282\) 8.14296 25.0615i 0.484906 1.49239i
\(283\) 5.85955 + 18.0339i 0.348314 + 1.07200i 0.959785 + 0.280734i \(0.0905780\pi\)
−0.611471 + 0.791267i \(0.709422\pi\)
\(284\) −7.05394 + 5.12499i −0.418574 + 0.304112i
\(285\) 0 0
\(286\) −3.03270 12.7100i −0.179327 0.751557i
\(287\) 15.5487 0.917809
\(288\) 6.53030 4.74454i 0.384802 0.279575i
\(289\) −2.40674 7.40719i −0.141573 0.435717i
\(290\) 0 0
\(291\) −12.0147 8.72918i −0.704313 0.511713i
\(292\) −22.1303 16.0786i −1.29508 0.940931i
\(293\) −0.907237 + 2.79219i −0.0530013 + 0.163121i −0.974053 0.226318i \(-0.927331\pi\)
0.921052 + 0.389439i \(0.127331\pi\)
\(294\) 3.30142 + 10.1607i 0.192543 + 0.592585i
\(295\) 0 0
\(296\) −0.391740 −0.0227695
\(297\) 3.30604 + 0.264820i 0.191836 + 0.0153664i
\(298\) −29.2186 −1.69259
\(299\) −1.95138 + 1.41776i −0.112851 + 0.0819914i
\(300\) 0 0
\(301\) −1.35107 + 4.15818i −0.0778746 + 0.239674i
\(302\) 31.6143 + 22.9691i 1.81920 + 1.32172i
\(303\) −5.84831 4.24905i −0.335977 0.244102i
\(304\) 1.23207 3.79191i 0.0706639 0.217481i
\(305\) 0 0
\(306\) −4.96460 + 3.60699i −0.283807 + 0.206198i
\(307\) 18.4893 1.05524 0.527621 0.849480i \(-0.323084\pi\)
0.527621 + 0.849480i \(0.323084\pi\)
\(308\) 9.04302 + 0.724364i 0.515274 + 0.0412745i
\(309\) −8.85525 −0.503757
\(310\) 0 0
\(311\) 7.17840 + 22.0928i 0.407050 + 1.25277i 0.919171 + 0.393858i \(0.128860\pi\)
−0.512122 + 0.858913i \(0.671140\pi\)
\(312\) −0.107207 + 0.329950i −0.00606941 + 0.0186797i
\(313\) −1.81604 1.31943i −0.102649 0.0745785i 0.535277 0.844677i \(-0.320207\pi\)
−0.637926 + 0.770098i \(0.720207\pi\)
\(314\) 36.6155 + 26.6027i 2.06633 + 1.50128i
\(315\) 0 0
\(316\) 0.709057 + 2.18225i 0.0398875 + 0.122761i
\(317\) −5.16486 + 3.75249i −0.290088 + 0.210761i −0.723305 0.690528i \(-0.757378\pi\)
0.433218 + 0.901289i \(0.357378\pi\)
\(318\) 20.4855 1.14877
\(319\) −0.394095 1.65165i −0.0220651 0.0924744i
\(320\) 0 0
\(321\) −3.34073 + 2.42719i −0.186462 + 0.135472i
\(322\) −1.01315 3.11817i −0.0564609 0.173769i
\(323\) −0.979894 + 3.01580i −0.0545228 + 0.167804i
\(324\) −1.68927 1.22733i −0.0938486 0.0681850i
\(325\) 0 0
\(326\) 7.18742 22.1206i 0.398074 1.22515i
\(327\) 4.21613 + 12.9759i 0.233153 + 0.717570i
\(328\) 1.70968 1.24216i 0.0944014 0.0685866i
\(329\) 17.0728 0.941254
\(330\) 0 0
\(331\) −15.3804 −0.845383 −0.422691 0.906274i \(-0.638915\pi\)
−0.422691 + 0.906274i \(0.638915\pi\)
\(332\) 8.39030 6.09591i 0.460478 0.334556i
\(333\) −0.679912 2.09255i −0.0372590 0.114671i
\(334\) 9.71388 29.8962i 0.531520 1.63585i
\(335\) 0 0
\(336\) 4.04431 + 2.93836i 0.220635 + 0.160301i
\(337\) 3.34175 10.2848i 0.182037 0.560251i −0.817848 0.575434i \(-0.804833\pi\)
0.999885 + 0.0151830i \(0.00483309\pi\)
\(338\) −5.75010 17.6970i −0.312764 0.962590i
\(339\) 12.5010 9.08250i 0.678960 0.493294i
\(340\) 0 0
\(341\) −1.62050 + 3.89688i −0.0877548 + 0.211028i
\(342\) −2.11245 −0.114228
\(343\) −13.0185 + 9.45846i −0.702931 + 0.510709i
\(344\) 0.183630 + 0.565155i 0.00990067 + 0.0304711i
\(345\) 0 0
\(346\) 22.2136 + 16.1391i 1.19421 + 0.867643i
\(347\) 14.4919 + 10.5290i 0.777966 + 0.565226i 0.904368 0.426754i \(-0.140343\pi\)
−0.126402 + 0.991979i \(0.540343\pi\)
\(348\) −0.330346 + 1.01670i −0.0177084 + 0.0545009i
\(349\) 1.71595 + 5.28114i 0.0918525 + 0.282693i 0.986421 0.164239i \(-0.0525167\pi\)
−0.894568 + 0.446932i \(0.852517\pi\)
\(350\) 0 0
\(351\) −1.94856 −0.104006
\(352\) −22.8459 + 13.9563i −1.21769 + 0.743872i
\(353\) 28.1513 1.49834 0.749171 0.662376i \(-0.230452\pi\)
0.749171 + 0.662376i \(0.230452\pi\)
\(354\) 5.23663 3.80463i 0.278324 0.202214i
\(355\) 0 0
\(356\) 4.76790 14.6741i 0.252698 0.777725i
\(357\) −3.21654 2.33695i −0.170237 0.123685i
\(358\) 40.1803 + 29.1927i 2.12360 + 1.54288i
\(359\) 1.85030 5.69463i 0.0976549 0.300551i −0.890282 0.455411i \(-0.849493\pi\)
0.987936 + 0.154860i \(0.0494925\pi\)
\(360\) 0 0
\(361\) 14.4882 10.5263i 0.762537 0.554016i
\(362\) 5.53075 0.290690
\(363\) −10.8597 1.75101i −0.569989 0.0919041i
\(364\) −5.32991 −0.279363
\(365\) 0 0
\(366\) −5.65625 17.4081i −0.295657 0.909938i
\(367\) −5.45626 + 16.7926i −0.284814 + 0.876568i 0.701640 + 0.712532i \(0.252451\pi\)
−0.986454 + 0.164036i \(0.947549\pi\)
\(368\) 3.82166 + 2.77660i 0.199218 + 0.144740i
\(369\) 9.60257 + 6.97667i 0.499890 + 0.363191i
\(370\) 0 0
\(371\) 4.10141 + 12.6228i 0.212934 + 0.655345i
\(372\) 2.14959 1.56177i 0.111451 0.0809740i
\(373\) 3.01742 0.156236 0.0781179 0.996944i \(-0.475109\pi\)
0.0781179 + 0.996944i \(0.475109\pi\)
\(374\) 17.3683 10.6101i 0.898096 0.548636i
\(375\) 0 0
\(376\) 1.87727 1.36392i 0.0968129 0.0703387i
\(377\) 0.308277 + 0.948778i 0.0158771 + 0.0488646i
\(378\) 0.818473 2.51900i 0.0420977 0.129563i
\(379\) −19.0938 13.8724i −0.980781 0.712579i −0.0228981 0.999738i \(-0.507289\pi\)
−0.957883 + 0.287159i \(0.907289\pi\)
\(380\) 0 0
\(381\) 2.62237 8.07082i 0.134348 0.413480i
\(382\) −1.51223 4.65416i −0.0773723 0.238128i
\(383\) 6.71771 4.88071i 0.343259 0.249392i −0.402776 0.915298i \(-0.631955\pi\)
0.746036 + 0.665906i \(0.231955\pi\)
\(384\) 1.42297 0.0726158
\(385\) 0 0
\(386\) −37.4245 −1.90486
\(387\) −2.70017 + 1.96179i −0.137257 + 0.0997233i
\(388\) −9.58252 29.4920i −0.486479 1.49723i
\(389\) 9.22384 28.3881i 0.467667 1.43933i −0.387929 0.921689i \(-0.626809\pi\)
0.855597 0.517643i \(-0.173191\pi\)
\(390\) 0 0
\(391\) −3.03946 2.20830i −0.153712 0.111678i
\(392\) −0.290717 + 0.894734i −0.0146834 + 0.0451909i
\(393\) 2.19310 + 6.74967i 0.110627 + 0.340476i
\(394\) 38.6013 28.0455i 1.94471 1.41291i
\(395\) 0 0
\(396\) 5.25978 + 4.50495i 0.264314 + 0.226382i
\(397\) 10.4162 0.522772 0.261386 0.965234i \(-0.415820\pi\)
0.261386 + 0.965234i \(0.415820\pi\)
\(398\) 41.6621 30.2693i 2.08833 1.51726i
\(399\) −0.422936 1.30166i −0.0211733 0.0651647i
\(400\) 0 0
\(401\) −26.8199 19.4858i −1.33932 0.973075i −0.999469 0.0325971i \(-0.989622\pi\)
−0.339854 0.940478i \(-0.610378\pi\)
\(402\) 15.5954 + 11.3308i 0.777830 + 0.565127i
\(403\) 0.766217 2.35817i 0.0381680 0.117469i
\(404\) −4.66442 14.3556i −0.232064 0.714219i
\(405\) 0 0
\(406\) −1.35602 −0.0672982
\(407\) 1.69366 + 7.09811i 0.0839518 + 0.351840i
\(408\) −0.540376 −0.0267526
\(409\) 20.2486 14.7115i 1.00123 0.727436i 0.0388783 0.999244i \(-0.487622\pi\)
0.962352 + 0.271808i \(0.0876215\pi\)
\(410\) 0 0
\(411\) −0.385307 + 1.18585i −0.0190058 + 0.0584938i
\(412\) −14.9589 10.8683i −0.736974 0.535443i
\(413\) 3.39279 + 2.46501i 0.166948 + 0.121295i
\(414\) 0.773414 2.38032i 0.0380112 0.116987i
\(415\) 0 0
\(416\) 12.7247 9.24503i 0.623879 0.453275i
\(417\) 13.4427 0.658290
\(418\) 6.98385 + 0.559420i 0.341591 + 0.0273621i
\(419\) −4.38157 −0.214054 −0.107027 0.994256i \(-0.534133\pi\)
−0.107027 + 0.994256i \(0.534133\pi\)
\(420\) 0 0
\(421\) 9.97933 + 30.7132i 0.486363 + 1.49687i 0.829997 + 0.557768i \(0.188342\pi\)
−0.343634 + 0.939104i \(0.611658\pi\)
\(422\) −2.96566 + 9.12735i −0.144366 + 0.444313i
\(423\) 10.5438 + 7.66055i 0.512659 + 0.372469i
\(424\) 1.45939 + 1.06031i 0.0708745 + 0.0514933i
\(425\) 0 0
\(426\) −2.60899 8.02965i −0.126406 0.389038i
\(427\) 9.59420 6.97059i 0.464296 0.337331i
\(428\) −8.62237 −0.416778
\(429\) 6.44201 + 0.516018i 0.311023 + 0.0249136i
\(430\) 0 0
\(431\) −3.04370 + 2.21138i −0.146610 + 0.106518i −0.658672 0.752430i \(-0.728882\pi\)
0.512062 + 0.858948i \(0.328882\pi\)
\(432\) 1.17925 + 3.62935i 0.0567366 + 0.174617i
\(433\) 5.53863 17.0461i 0.266169 0.819185i −0.725252 0.688483i \(-0.758277\pi\)
0.991422 0.130702i \(-0.0417232\pi\)
\(434\) 2.72669 + 1.98106i 0.130885 + 0.0950937i
\(435\) 0 0
\(436\) −8.80352 + 27.0945i −0.421612 + 1.29759i
\(437\) −0.399652 1.23000i −0.0191180 0.0588390i
\(438\) 21.4291 15.5692i 1.02392 0.743923i
\(439\) 0.249655 0.0119154 0.00595768 0.999982i \(-0.498104\pi\)
0.00595768 + 0.999982i \(0.498104\pi\)
\(440\) 0 0
\(441\) −5.28396 −0.251617
\(442\) −9.67382 + 7.02844i −0.460137 + 0.334309i
\(443\) 7.50802 + 23.1073i 0.356717 + 1.09786i 0.955007 + 0.296582i \(0.0958468\pi\)
−0.598291 + 0.801279i \(0.704153\pi\)
\(444\) 1.41970 4.36938i 0.0673758 0.207361i
\(445\) 0 0
\(446\) 0.835578 + 0.607083i 0.0395658 + 0.0287462i
\(447\) 4.46563 13.7438i 0.211217 0.650060i
\(448\) 3.51706 + 10.8244i 0.166165 + 0.511404i
\(449\) 13.2783 9.64725i 0.626641 0.455282i −0.228594 0.973522i \(-0.573413\pi\)
0.855235 + 0.518240i \(0.173413\pi\)
\(450\) 0 0
\(451\) −29.8989 25.6081i −1.40788 1.20584i
\(452\) 32.2648 1.51761
\(453\) −15.6360 + 11.3602i −0.734642 + 0.533749i
\(454\) 6.41351 + 19.7388i 0.301001 + 0.926386i
\(455\) 0 0
\(456\) −0.150492 0.109339i −0.00704745 0.00512027i
\(457\) −11.5208 8.37034i −0.538920 0.391548i 0.284764 0.958598i \(-0.408085\pi\)
−0.823684 + 0.567050i \(0.808085\pi\)
\(458\) −13.7267 + 42.2463i −0.641405 + 1.97404i
\(459\) −0.937887 2.88652i −0.0437768 0.134731i
\(460\) 0 0
\(461\) −7.34050 −0.341881 −0.170940 0.985281i \(-0.554681\pi\)
−0.170940 + 0.985281i \(0.554681\pi\)
\(462\) −3.37298 + 8.11116i −0.156925 + 0.377365i
\(463\) 29.1159 1.35313 0.676566 0.736382i \(-0.263467\pi\)
0.676566 + 0.736382i \(0.263467\pi\)
\(464\) 1.58061 1.14838i 0.0733781 0.0533123i
\(465\) 0 0
\(466\) 5.03591 15.4989i 0.233284 0.717974i
\(467\) −13.8158 10.0377i −0.639317 0.464491i 0.220298 0.975433i \(-0.429297\pi\)
−0.859615 + 0.510942i \(0.829297\pi\)
\(468\) −3.29165 2.39153i −0.152157 0.110548i
\(469\) −3.85947 + 11.8782i −0.178214 + 0.548485i
\(470\) 0 0
\(471\) −18.1095 + 13.1573i −0.834441 + 0.606257i
\(472\) 0.569985 0.0262357
\(473\) 9.44638 5.77068i 0.434345 0.265336i
\(474\) −2.22185 −0.102053
\(475\) 0 0
\(476\) −2.56541 7.89551i −0.117585 0.361890i
\(477\) −3.13090 + 9.63593i −0.143354 + 0.441199i
\(478\) −24.2202 17.5970i −1.10781 0.804870i
\(479\) −0.898607 0.652876i −0.0410584 0.0298307i 0.567067 0.823672i \(-0.308078\pi\)
−0.608125 + 0.793841i \(0.708078\pi\)
\(480\) 0 0
\(481\) −1.32485 4.07747i −0.0604079 0.185917i
\(482\) −29.0200 + 21.0843i −1.32183 + 0.960363i
\(483\) 1.62157 0.0737838
\(484\) −16.1960 16.2864i −0.736183 0.740292i
\(485\) 0 0
\(486\) 1.63575 1.18844i 0.0741990 0.0539087i
\(487\) 8.27334 + 25.4627i 0.374901 + 1.15383i 0.943546 + 0.331243i \(0.107468\pi\)
−0.568645 + 0.822583i \(0.692532\pi\)
\(488\) 0.498079 1.53293i 0.0225470 0.0693924i
\(489\) 9.30657 + 6.76162i 0.420858 + 0.305771i
\(490\) 0 0
\(491\) 9.91454 30.5138i 0.447437 1.37707i −0.432352 0.901705i \(-0.642316\pi\)
0.879789 0.475364i \(-0.157684\pi\)
\(492\) 7.65869 + 23.5710i 0.345281 + 1.06266i
\(493\) −1.25710 + 0.913337i −0.0566170 + 0.0411347i
\(494\) −4.11624 −0.185199
\(495\) 0 0
\(496\) −4.85600 −0.218041
\(497\) 4.42540 3.21524i 0.198506 0.144223i
\(498\) 3.10326 + 9.55085i 0.139060 + 0.427984i
\(499\) −6.27290 + 19.3060i −0.280814 + 0.864255i 0.706809 + 0.707405i \(0.250134\pi\)
−0.987622 + 0.156851i \(0.949866\pi\)
\(500\) 0 0
\(501\) 12.5779 + 9.13840i 0.561941 + 0.408274i
\(502\) 4.44804 13.6897i 0.198526 0.611000i
\(503\) −6.52282 20.0752i −0.290838 0.895108i −0.984588 0.174892i \(-0.944042\pi\)
0.693749 0.720217i \(-0.255958\pi\)
\(504\) 0.188690 0.137091i 0.00840492 0.00610653i
\(505\) 0 0
\(506\) −3.18729 + 7.66462i −0.141692 + 0.340734i
\(507\) 9.20311 0.408725
\(508\) 14.3355 10.4153i 0.636033 0.462105i
\(509\) −2.83208 8.71625i −0.125530 0.386341i 0.868467 0.495746i \(-0.165105\pi\)
−0.993997 + 0.109405i \(0.965105\pi\)
\(510\) 0 0
\(511\) 13.8838 + 10.0872i 0.614184 + 0.446231i
\(512\) −26.0198 18.9045i −1.14993 0.835470i
\(513\) 0.322858 0.993654i 0.0142545 0.0438709i
\(514\) −12.2138 37.5903i −0.538728 1.65804i
\(515\) 0 0
\(516\) −6.96909 −0.306797
\(517\) −32.8297 28.1183i −1.44385 1.23664i
\(518\) 5.82764 0.256052
\(519\) −10.9865 + 7.98216i −0.482254 + 0.350378i
\(520\) 0 0
\(521\) −4.03826 + 12.4285i −0.176919 + 0.544502i −0.999716 0.0238341i \(-0.992413\pi\)
0.822796 + 0.568336i \(0.192413\pi\)
\(522\) −0.837454 0.608446i −0.0366543 0.0266309i
\(523\) −12.4336 9.03354i −0.543684 0.395009i 0.281768 0.959483i \(-0.409079\pi\)
−0.825451 + 0.564473i \(0.809079\pi\)
\(524\) −4.57932 + 14.0937i −0.200049 + 0.615687i
\(525\) 0 0
\(526\) 43.9125 31.9043i 1.91467 1.39109i
\(527\) 3.86210 0.168236
\(528\) −2.93751 12.3111i −0.127839 0.535770i
\(529\) −21.4677 −0.933378
\(530\) 0 0
\(531\) 0.989277 + 3.04468i 0.0429310 + 0.132128i
\(532\) 0.883115 2.71795i 0.0382879 0.117838i
\(533\) 18.7112 + 13.5945i 0.810471 + 0.588842i
\(534\) 12.0870 + 8.78172i 0.523056 + 0.380022i
\(535\) 0 0
\(536\) 0.524556 + 1.61442i 0.0226574 + 0.0697322i
\(537\) −19.8726 + 14.4383i −0.857567 + 0.623059i
\(538\) −37.0850 −1.59885
\(539\) 17.4690 + 1.39930i 0.752442 + 0.0602721i
\(540\) 0 0
\(541\) 17.7031 12.8621i 0.761116 0.552983i −0.138136 0.990413i \(-0.544111\pi\)
0.899252 + 0.437430i \(0.144111\pi\)
\(542\) −10.1255 31.1631i −0.434927 1.33857i
\(543\) −0.845294 + 2.60155i −0.0362750 + 0.111643i
\(544\) 19.8199 + 14.4000i 0.849771 + 0.617395i
\(545\) 0 0
\(546\) 1.59484 4.90842i 0.0682530 0.210061i
\(547\) 0.0925567 + 0.284860i 0.00395744 + 0.0121797i 0.953016 0.302921i \(-0.0979618\pi\)
−0.949058 + 0.315101i \(0.897962\pi\)
\(548\) −2.10632 + 1.53033i −0.0899776 + 0.0653726i
\(549\) 9.05290 0.386368
\(550\) 0 0
\(551\) −0.534901 −0.0227875
\(552\) 0.178302 0.129544i 0.00758905 0.00551377i
\(553\) −0.444838 1.36907i −0.0189164 0.0582188i
\(554\) 11.7426 36.1399i 0.498894 1.53544i
\(555\) 0 0
\(556\) 22.7083 + 16.4986i 0.963048 + 0.699695i
\(557\) −4.60835 + 14.1830i −0.195262 + 0.600954i 0.804712 + 0.593666i \(0.202320\pi\)
−0.999973 + 0.00728838i \(0.997680\pi\)
\(558\) 0.795054 + 2.44693i 0.0336573 + 0.103587i
\(559\) −5.26144 + 3.82266i −0.222535 + 0.161681i
\(560\) 0 0
\(561\) 2.33628 + 9.79130i 0.0986378 + 0.413389i
\(562\) −62.2744 −2.62689
\(563\) −25.4635 + 18.5003i −1.07316 + 0.779696i −0.976478 0.215619i \(-0.930823\pi\)
−0.0966820 + 0.995315i \(0.530823\pi\)
\(564\) 8.40943 + 25.8815i 0.354101 + 1.08981i
\(565\) 0 0
\(566\) −31.0169 22.5351i −1.30374 0.947221i
\(567\) 1.05979 + 0.769985i 0.0445071 + 0.0323363i
\(568\) 0.229743 0.707076i 0.00963979 0.0296682i
\(569\) 6.85188 + 21.0879i 0.287246 + 0.884052i 0.985717 + 0.168413i \(0.0538642\pi\)
−0.698471 + 0.715639i \(0.746136\pi\)
\(570\) 0 0
\(571\) 42.6015 1.78282 0.891409 0.453200i \(-0.149718\pi\)
0.891409 + 0.453200i \(0.149718\pi\)
\(572\) 10.2490 + 8.77816i 0.428532 + 0.367033i
\(573\) 2.42034 0.101111
\(574\) −25.4337 + 18.4787i −1.06158 + 0.771284i
\(575\) 0 0
\(576\) −2.68482 + 8.26304i −0.111868 + 0.344293i
\(577\) 5.07173 + 3.68483i 0.211139 + 0.153401i 0.688329 0.725399i \(-0.258345\pi\)
−0.477190 + 0.878800i \(0.658345\pi\)
\(578\) 12.7398 + 9.25602i 0.529907 + 0.385000i
\(579\) 5.71979 17.6037i 0.237706 0.731585i
\(580\) 0 0
\(581\) −5.26379 + 3.82437i −0.218379 + 0.158661i
\(582\) 30.0271 1.24466
\(583\) 12.9027 31.0276i 0.534374 1.28503i
\(584\) 2.33247 0.0965182
\(585\) 0 0
\(586\) −1.83434 5.64551i −0.0757758 0.233214i
\(587\) 0.230368 0.709000i 0.00950831 0.0292636i −0.946190 0.323612i \(-0.895103\pi\)
0.955698 + 0.294349i \(0.0951027\pi\)
\(588\) −8.92606 6.48516i −0.368105 0.267444i
\(589\) 1.07558 + 0.781454i 0.0443185 + 0.0321992i
\(590\) 0 0
\(591\) 7.29236 + 22.4436i 0.299968 + 0.923205i
\(592\) −6.79284 + 4.93529i −0.279184 + 0.202839i
\(593\) −31.7760 −1.30488 −0.652441 0.757840i \(-0.726255\pi\)
−0.652441 + 0.757840i \(0.726255\pi\)
\(594\) −5.72256 + 3.49585i −0.234800 + 0.143436i
\(595\) 0 0
\(596\) 24.4119 17.7363i 0.999949 0.726505i
\(597\) 7.87058 + 24.2232i 0.322121 + 0.991388i
\(598\) 1.50704 4.63820i 0.0616276 0.189670i
\(599\) −14.7282 10.7006i −0.601776 0.437216i 0.244733 0.969591i \(-0.421300\pi\)
−0.846509 + 0.532374i \(0.821300\pi\)
\(600\) 0 0
\(601\) −9.07978 + 27.9447i −0.370372 + 1.13989i 0.576176 + 0.817325i \(0.304544\pi\)
−0.946548 + 0.322562i \(0.895456\pi\)
\(602\) −2.73173 8.40740i −0.111337 0.342660i
\(603\) −7.71328 + 5.60403i −0.314109 + 0.228214i
\(604\) −40.3562 −1.64207
\(605\) 0 0
\(606\) 14.6161 0.593739
\(607\) 22.7962 16.5624i 0.925268 0.672247i −0.0195615 0.999809i \(-0.506227\pi\)
0.944830 + 0.327562i \(0.106227\pi\)
\(608\) 2.60608 + 8.02067i 0.105690 + 0.325281i
\(609\) 0.207248 0.637844i 0.00839811 0.0258467i
\(610\) 0 0
\(611\) 20.5453 + 14.9270i 0.831174 + 0.603884i
\(612\) 1.95836 6.02722i 0.0791621 0.243636i
\(613\) −13.1272 40.4013i −0.530201 1.63179i −0.753795 0.657110i \(-0.771779\pi\)
0.223593 0.974683i \(-0.428221\pi\)
\(614\) −30.2439 + 21.9735i −1.22054 + 0.886776i
\(615\) 0 0
\(616\) −0.660121 + 0.403260i −0.0265970 + 0.0162478i
\(617\) 1.38228 0.0556484 0.0278242 0.999613i \(-0.491142\pi\)
0.0278242 + 0.999613i \(0.491142\pi\)
\(618\) 14.4849 10.5239i 0.582670 0.423335i
\(619\) 11.5409 + 35.5193i 0.463868 + 1.42764i 0.860400 + 0.509619i \(0.170214\pi\)
−0.396532 + 0.918021i \(0.629786\pi\)
\(620\) 0 0
\(621\) 1.00145 + 0.727595i 0.0401868 + 0.0291974i
\(622\) −37.9981 27.6072i −1.52358 1.10695i
\(623\) −2.99122 + 9.20602i −0.119841 + 0.368832i
\(624\) 2.29784 + 7.07201i 0.0919871 + 0.283107i
\(625\) 0 0
\(626\) 4.53864 0.181401
\(627\) −1.33052 + 3.19956i −0.0531358 + 0.127778i
\(628\) −46.7402 −1.86514
\(629\) 5.40252 3.92516i 0.215412 0.156506i
\(630\) 0 0
\(631\) −11.6311 + 35.7967i −0.463025 + 1.42504i 0.398424 + 0.917201i \(0.369557\pi\)
−0.861449 + 0.507843i \(0.830443\pi\)
\(632\) −0.158286 0.115001i −0.00629626 0.00457450i
\(633\) −3.84006 2.78996i −0.152629 0.110891i
\(634\) 3.98880 12.2763i 0.158415 0.487552i
\(635\) 0 0
\(636\) −17.1154 + 12.4351i −0.678670 + 0.493083i
\(637\) −10.2961 −0.407947
\(638\) 2.60752 + 2.23332i 0.103233 + 0.0884179i
\(639\) 4.17572 0.165189
\(640\) 0 0
\(641\) −4.46046 13.7279i −0.176178 0.542219i 0.823508 0.567305i \(-0.192014\pi\)
−0.999685 + 0.0250860i \(0.992014\pi\)
\(642\) 2.58003 7.94052i 0.101826 0.313387i
\(643\) −22.4030 16.2767i −0.883488 0.641891i 0.0506841 0.998715i \(-0.483860\pi\)
−0.934172 + 0.356823i \(0.883860\pi\)
\(644\) 2.73927 + 1.99020i 0.107942 + 0.0784247i
\(645\) 0 0
\(646\) −1.98124 6.09764i −0.0779510 0.239908i
\(647\) −7.00966 + 5.09282i −0.275578 + 0.200219i −0.716986 0.697087i \(-0.754479\pi\)
0.441408 + 0.897306i \(0.354479\pi\)
\(648\) 0.178044 0.00699424
\(649\) −2.46429 10.3278i −0.0967320 0.405402i
\(650\) 0 0
\(651\) −1.34858 + 0.979801i −0.0528551 + 0.0384014i
\(652\) 7.42262 + 22.8445i 0.290692 + 0.894658i
\(653\) −0.669921 + 2.06180i −0.0262160 + 0.0806847i −0.963309 0.268397i \(-0.913506\pi\)
0.937092 + 0.349081i \(0.113506\pi\)
\(654\) −22.3176 16.2147i −0.872688 0.634045i
\(655\) 0 0
\(656\) 13.9970 43.0784i 0.546491 1.68193i
\(657\) 4.04828 + 12.4593i 0.157938 + 0.486084i
\(658\) −27.9268 + 20.2900i −1.08870 + 0.790987i
\(659\) −48.3550 −1.88364 −0.941822 0.336112i \(-0.890888\pi\)
−0.941822 + 0.336112i \(0.890888\pi\)
\(660\) 0 0
\(661\) 38.3261 1.49071 0.745356 0.666667i \(-0.232280\pi\)
0.745356 + 0.666667i \(0.232280\pi\)
\(662\) 25.1584 18.2787i 0.977810 0.710421i
\(663\) −1.82753 5.62455i −0.0709753 0.218440i
\(664\) −0.273267 + 0.841030i −0.0106048 + 0.0326383i
\(665\) 0 0
\(666\) 3.59904 + 2.61486i 0.139460 + 0.101324i
\(667\) 0.195839 0.602729i 0.00758290 0.0233378i
\(668\) 10.0317 + 30.8745i 0.388140 + 1.19457i
\(669\) −0.413265 + 0.300255i −0.0159777 + 0.0116085i
\(670\) 0 0
\(671\) −29.9292 2.39739i −1.15540 0.0925501i
\(672\) −10.5740 −0.407901
\(673\) 15.0694 10.9485i 0.580882 0.422035i −0.258160 0.966102i \(-0.583116\pi\)
0.839042 + 0.544067i \(0.183116\pi\)
\(674\) 6.75666 + 20.7949i 0.260257 + 0.800989i
\(675\) 0 0
\(676\) 15.5466 + 11.2953i 0.597946 + 0.434433i
\(677\) 2.98496 + 2.16870i 0.114721 + 0.0833498i 0.643667 0.765306i \(-0.277412\pi\)
−0.528945 + 0.848656i \(0.677412\pi\)
\(678\) −9.65445 + 29.7133i −0.370777 + 1.14113i
\(679\) 6.01174 + 18.5022i 0.230710 + 0.710051i
\(680\) 0 0
\(681\) −10.2649 −0.393352
\(682\) −1.98048 8.30017i −0.0758366 0.317830i
\(683\) −1.43352 −0.0548521 −0.0274260 0.999624i \(-0.508731\pi\)
−0.0274260 + 0.999624i \(0.508731\pi\)
\(684\) 1.76494 1.28230i 0.0674840 0.0490300i
\(685\) 0 0
\(686\) 10.0541 30.9433i 0.383867 1.18142i
\(687\) −17.7739 12.9135i −0.678115 0.492679i
\(688\) 10.3042 + 7.48644i 0.392844 + 0.285418i
\(689\) −6.10075 + 18.7762i −0.232420 + 0.715315i
\(690\) 0 0
\(691\) 17.0832 12.4117i 0.649876 0.472163i −0.213353 0.976975i \(-0.568438\pi\)
0.863229 + 0.504812i \(0.168438\pi\)
\(692\) −28.3560 −1.07793
\(693\) −3.29981 2.82625i −0.125349 0.107360i
\(694\) −36.2182 −1.37482
\(695\) 0 0
\(696\) −0.0281679 0.0866920i −0.00106770 0.00328605i
\(697\) −11.1322 + 34.2613i −0.421661 + 1.29774i
\(698\) −9.08317 6.59931i −0.343803 0.249788i
\(699\) 6.52071 + 4.73757i 0.246636 + 0.179191i
\(700\) 0 0
\(701\) −1.61516 4.97094i −0.0610036 0.187750i 0.915910 0.401383i \(-0.131470\pi\)
−0.976914 + 0.213633i \(0.931470\pi\)
\(702\) 3.18735 2.31575i 0.120299 0.0874022i
\(703\) 2.29879 0.0867005
\(704\) 11.0643 26.6069i 0.417003 1.00279i
\(705\) 0 0
\(706\) −46.0484 + 33.4561i −1.73305 + 1.25914i
\(707\) 2.92630 + 9.00623i 0.110055 + 0.338714i
\(708\) −2.06567 + 6.35747i −0.0776326 + 0.238929i
\(709\) −14.8032 10.7551i −0.555944 0.403917i 0.274028 0.961722i \(-0.411644\pi\)
−0.829972 + 0.557805i \(0.811644\pi\)
\(710\) 0 0
\(711\) 0.339577 1.04511i 0.0127351 0.0391947i
\(712\) 0.406549 + 1.25123i 0.0152361 + 0.0468918i
\(713\) −1.27434 + 0.925861i −0.0477243 + 0.0346738i
\(714\) 8.03878 0.300844
\(715\) 0 0
\(716\) −51.2909 −1.91683
\(717\) 11.9790 8.70324i 0.447363 0.325028i
\(718\) 3.74111 + 11.5139i 0.139617 + 0.429696i
\(719\) −6.11462 + 18.8189i −0.228037 + 0.701826i 0.769932 + 0.638126i \(0.220290\pi\)
−0.997969 + 0.0636999i \(0.979710\pi\)
\(720\) 0 0
\(721\) 9.38473 + 6.81841i 0.349506 + 0.253931i
\(722\) −11.1892 + 34.4367i −0.416418 + 1.28160i
\(723\) −5.48232 16.8728i −0.203890 0.627508i
\(724\) −4.62089 + 3.35727i −0.171734 + 0.124772i
\(725\) 0 0
\(726\) 19.8448 10.0419i 0.736508 0.372691i
\(727\) 7.17943 0.266270 0.133135 0.991098i \(-0.457496\pi\)
0.133135 + 0.991098i \(0.457496\pi\)
\(728\) 0.367674 0.267131i 0.0136269 0.00990052i
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) 0 0
\(731\) −8.19519 5.95416i −0.303110 0.220222i
\(732\) 15.2928 + 11.1109i 0.565239 + 0.410670i
\(733\) 6.22921 19.1715i 0.230081 0.708117i −0.767655 0.640864i \(-0.778576\pi\)
0.997736 0.0672534i \(-0.0214236\pi\)
\(734\) −11.0320 33.9529i −0.407198 1.25323i
\(735\) 0 0
\(736\) −9.99188 −0.368305
\(737\) 26.9844 16.4845i 0.993985 0.607214i
\(738\) −23.9987 −0.883406
\(739\) −14.7561 + 10.7210i −0.542813 + 0.394377i −0.825129 0.564945i \(-0.808897\pi\)
0.282316 + 0.959322i \(0.408897\pi\)
\(740\) 0 0
\(741\) 0.629108 1.93619i 0.0231108 0.0711279i
\(742\) −21.7103 15.7735i −0.797012 0.579063i
\(743\) 0.601874 + 0.437287i 0.0220806 + 0.0160425i 0.598771 0.800920i \(-0.295656\pi\)
−0.576690 + 0.816963i \(0.695656\pi\)
\(744\) −0.0700110 + 0.215472i −0.00256673 + 0.00789957i
\(745\) 0 0
\(746\) −4.93573 + 3.58602i −0.180710 + 0.131293i
\(747\) −4.96681 −0.181726
\(748\) −8.07054 + 19.4076i −0.295088 + 0.709612i
\(749\) 5.40938 0.197655
\(750\) 0 0
\(751\) −4.44667 13.6855i −0.162261 0.499389i 0.836563 0.547871i \(-0.184562\pi\)
−0.998824 + 0.0484819i \(0.984562\pi\)
\(752\) 15.3690 47.3011i 0.560451 1.72489i
\(753\) 5.75951 + 4.18453i 0.209888 + 0.152493i
\(754\) −1.63183 1.18559i −0.0594277 0.0431767i
\(755\) 0 0
\(756\) 0.845256 + 2.60143i 0.0307417 + 0.0946131i
\(757\) 16.8803 12.2643i 0.613525 0.445752i −0.237129 0.971478i \(-0.576206\pi\)
0.850654 + 0.525726i \(0.176206\pi\)
\(758\) 47.7191 1.73324
\(759\) −3.11814 2.67066i −0.113181 0.0969388i
\(760\) 0 0
\(761\) −3.33612 + 2.42384i −0.120934 + 0.0878640i −0.646608 0.762822i \(-0.723813\pi\)
0.525674 + 0.850686i \(0.323813\pi\)
\(762\) 5.30215 + 16.3183i 0.192077 + 0.591151i
\(763\) 5.52303 16.9981i 0.199947 0.615374i
\(764\) 4.08862 + 2.97056i 0.147921 + 0.107471i
\(765\) 0 0
\(766\) −5.18806 + 15.9672i −0.187452 + 0.576918i
\(767\) 1.92767 + 5.93275i 0.0696040 + 0.214219i
\(768\) 11.7303 8.52256i 0.423281 0.307531i
\(769\) 43.9189 1.58375 0.791877 0.610680i \(-0.209104\pi\)
0.791877 + 0.610680i \(0.209104\pi\)
\(770\) 0 0
\(771\) 19.5484 0.704017
\(772\) 31.2679 22.7174i 1.12535 0.817618i
\(773\) 7.91042 + 24.3458i 0.284518 + 0.875657i 0.986543 + 0.163504i \(0.0522797\pi\)
−0.702025 + 0.712153i \(0.747720\pi\)
\(774\) 2.08533 6.41798i 0.0749556 0.230690i
\(775\) 0 0
\(776\) 2.13915 + 1.55418i 0.0767908 + 0.0557918i
\(777\) −0.890669 + 2.74120i −0.0319526 + 0.0983399i
\(778\) 18.6496 + 57.3977i 0.668622 + 2.05781i
\(779\) −10.0327 + 7.28916i −0.359457 + 0.261161i
\(780\) 0 0
\(781\) −13.8051 1.10581i −0.493985 0.0395692i
\(782\) 7.59622 0.271640
\(783\) 0.414193 0.300928i 0.0148020 0.0107543i
\(784\) 6.23111 + 19.1774i 0.222540 + 0.684906i
\(785\) 0 0
\(786\) −11.6089 8.43439i −0.414077 0.300845i
\(787\) 1.55087 + 1.12677i 0.0552825 + 0.0401651i 0.615083 0.788462i \(-0.289122\pi\)
−0.559801 + 0.828627i \(0.689122\pi\)
\(788\) −15.2269 + 46.8635i −0.542435 + 1.66944i
\(789\) 8.29572 + 25.5316i 0.295335 + 0.908949i
\(790\) 0 0
\(791\) −20.2418 −0.719717
\(792\) −0.588621 0.0471497i −0.0209157 0.00167539i
\(793\) 17.6401 0.626419
\(794\) −17.0382 + 12.3790i −0.604663 + 0.439313i
\(795\) 0 0
\(796\) −16.4342 + 50.5794i −0.582496 + 1.79274i
\(797\) −20.7262 15.0585i −0.734161 0.533399i 0.156716 0.987644i \(-0.449909\pi\)
−0.890877 + 0.454244i \(0.849909\pi\)
\(798\) 2.23876 + 1.62656i 0.0792514 + 0.0575795i
\(799\) −12.2234 + 37.6197i −0.432433 + 1.33089i
\(800\) 0 0
\(801\) −5.97806 + 4.34331i −0.211224 + 0.153463i
\(802\) 67.0283 2.36685
\(803\) −10.0843 42.2630i −0.355866 1.49143i
\(804\) −19.9078 −0.702095
\(805\) 0 0
\(806\) 1.54921 + 4.76798i 0.0545686 + 0.167945i
\(807\) 5.66789 17.4440i 0.199519 0.614057i
\(808\) 1.04126 + 0.756519i 0.0366314 + 0.0266142i
\(809\) −5.42843 3.94399i −0.190853 0.138663i 0.488255 0.872701i \(-0.337634\pi\)
−0.679109 + 0.734038i \(0.737634\pi\)
\(810\) 0 0
\(811\) −7.45747 22.9517i −0.261867 0.805945i −0.992399 0.123065i \(-0.960728\pi\)
0.730531 0.682879i \(-0.239272\pi\)
\(812\) 1.13294 0.823132i 0.0397585 0.0288863i
\(813\) 16.2060 0.568369
\(814\) −11.2061 9.59790i −0.392773 0.336406i
\(815\) 0 0
\(816\) −9.37020 + 6.80785i −0.328023 + 0.238322i
\(817\) −1.07757 3.31641i −0.0376993 0.116027i
\(818\) −15.6379 + 48.1285i −0.546767 + 1.68277i
\(819\) 2.06507 + 1.50036i 0.0721594 + 0.0524269i
\(820\) 0 0
\(821\) 1.17008 3.60115i 0.0408362 0.125681i −0.928560 0.371182i \(-0.878953\pi\)
0.969396 + 0.245501i \(0.0789525\pi\)
\(822\) −0.779050 2.39767i −0.0271725 0.0836283i
\(823\) −33.1638 + 24.0949i −1.15602 + 0.839896i −0.989269 0.146104i \(-0.953327\pi\)
−0.166748 + 0.986000i \(0.553327\pi\)
\(824\) 1.57663 0.0549244
\(825\) 0 0
\(826\) −8.47925 −0.295031
\(827\) 36.6611 26.6358i 1.27483 0.926219i 0.275447 0.961316i \(-0.411174\pi\)
0.999384 + 0.0350975i \(0.0111742\pi\)
\(828\) 0.798723 + 2.45822i 0.0277575 + 0.0854289i
\(829\) 9.58044 29.4856i 0.332743 1.02408i −0.635081 0.772446i \(-0.719033\pi\)
0.967823 0.251630i \(-0.0809668\pi\)
\(830\) 0 0
\(831\) 15.2048 + 11.0469i 0.527448 + 0.383213i
\(832\) −5.23154 + 16.1010i −0.181371 + 0.558203i
\(833\) −4.95576 15.2523i −0.171707 0.528459i
\(834\) −21.9888 + 15.9758i −0.761409 + 0.553196i
\(835\) 0 0
\(836\) −6.17452 + 3.77194i −0.213550 + 0.130455i
\(837\) −1.27249 −0.0439838
\(838\) 7.16715 5.20724i 0.247585 0.179881i
\(839\) 0.696077 + 2.14230i 0.0240312 + 0.0739606i 0.962353 0.271803i \(-0.0876199\pi\)
−0.938322 + 0.345764i \(0.887620\pi\)
\(840\) 0 0
\(841\) 23.2494 + 16.8917i 0.801705 + 0.582473i
\(842\) −52.8245 38.3792i −1.82045 1.32264i
\(843\) 9.51773 29.2925i 0.327808 1.00889i
\(844\) −3.06270 9.42603i −0.105423 0.324457i
\(845\) 0 0
\(846\) −26.3512 −0.905972
\(847\) 10.1608 + 10.2175i 0.349130 + 0.351079i
\(848\) 38.6643 1.32774
\(849\) 15.3405 11.1455i 0.526485 0.382514i
\(850\) 0 0
\(851\) −0.841636 + 2.59029i −0.0288509 + 0.0887939i
\(852\) 7.05394 + 5.12499i 0.241664 + 0.175579i
\(853\) 3.95242 + 2.87160i 0.135328 + 0.0983218i 0.653390 0.757022i \(-0.273346\pi\)
−0.518062 + 0.855343i \(0.673346\pi\)
\(854\) −7.40955 + 22.8043i −0.253550 + 0.780345i
\(855\) 0 0
\(856\) 0.594799 0.432146i 0.0203298 0.0147705i
\(857\) 21.9877 0.751086 0.375543 0.926805i \(-0.377456\pi\)
0.375543 + 0.926805i \(0.377456\pi\)
\(858\) −11.1508 + 6.81186i −0.380680 + 0.232553i
\(859\) 3.07460 0.104904 0.0524520 0.998623i \(-0.483296\pi\)
0.0524520 + 0.998623i \(0.483296\pi\)
\(860\) 0 0
\(861\) −4.80480 14.7877i −0.163747 0.503962i
\(862\) 2.35064 7.23452i 0.0800630 0.246409i
\(863\) −23.0306 16.7327i −0.783971 0.569589i 0.122197 0.992506i \(-0.461006\pi\)
−0.906168 + 0.422917i \(0.861006\pi\)
\(864\) −6.53030 4.74454i −0.222165 0.161413i
\(865\) 0 0
\(866\) 11.1985 + 34.4655i 0.380541 + 1.17119i
\(867\) −6.30093 + 4.57790i −0.213991 + 0.155473i
\(868\) −3.48066 −0.118141
\(869\) −1.39942 + 3.36525i −0.0474721 + 0.114158i
\(870\) 0 0
\(871\) −15.0298 + 10.9198i −0.509265 + 0.370003i
\(872\) −0.750658 2.31029i −0.0254205 0.0782362i
\(873\) −4.58920 + 14.1241i −0.155321 + 0.478029i
\(874\) 2.11552 + 1.53701i 0.0715584 + 0.0519902i
\(875\) 0 0
\(876\) −8.45304 + 26.0158i −0.285602 + 0.878991i
\(877\) −1.20130 3.69721i −0.0405649 0.124846i 0.928723 0.370774i \(-0.120907\pi\)
−0.969288 + 0.245928i \(0.920907\pi\)
\(878\) −0.408372 + 0.296700i −0.0137819 + 0.0100131i
\(879\) 2.93588 0.0990248
\(880\) 0 0
\(881\) 3.09160 0.104159 0.0520793 0.998643i \(-0.483415\pi\)
0.0520793 + 0.998643i \(0.483415\pi\)
\(882\) 8.64323 6.27967i 0.291033 0.211448i
\(883\) 12.5339 + 38.5753i 0.421799 + 1.29816i 0.906026 + 0.423221i \(0.139101\pi\)
−0.484227 + 0.874942i \(0.660899\pi\)
\(884\) 3.81599 11.7444i 0.128345 0.395007i
\(885\) 0 0
\(886\) −39.7429 28.8749i −1.33519 0.970071i
\(887\) −4.82010 + 14.8348i −0.161843 + 0.498102i −0.998790 0.0491822i \(-0.984338\pi\)
0.836947 + 0.547285i \(0.184338\pi\)
\(888\) 0.121054 + 0.372567i 0.00406232 + 0.0125025i
\(889\) −8.99357 + 6.53421i −0.301635 + 0.219150i
\(890\) 0 0
\(891\) −0.769762 3.22606i −0.0257880 0.108077i
\(892\) −1.06663 −0.0357134
\(893\) −11.0161 + 8.00366i −0.368640 + 0.267832i
\(894\) 9.02904 + 27.7885i 0.301976 + 0.929387i
\(895\) 0 0
\(896\) −1.50806 1.09567i −0.0503807 0.0366037i
\(897\) 1.95138 + 1.41776i 0.0651548 + 0.0473377i
\(898\) −10.2548 + 31.5609i −0.342206 + 1.05320i
\(899\) 0.201318 + 0.619593i 0.00671433 + 0.0206646i
\(900\) 0 0
\(901\) −30.7507 −1.02445
\(902\) 79.3407 + 6.35534i 2.64176 + 0.211610i
\(903\) 4.37217 0.145497
\(904\) −2.22573 + 1.61709i −0.0740266 + 0.0537835i
\(905\) 0 0
\(906\) 12.0756 37.1648i 0.401185 1.23472i
\(907\) 7.61986 + 5.53615i 0.253013 + 0.183825i 0.707061 0.707152i \(-0.250021\pi\)
−0.454048 + 0.890977i \(0.650021\pi\)
\(908\) −17.3402 12.5984i −0.575456 0.418093i
\(909\) −2.23386 + 6.87511i −0.0740924 + 0.228033i
\(910\) 0 0
\(911\) −3.59196 + 2.60971i −0.119007 + 0.0864637i −0.645697 0.763594i \(-0.723433\pi\)
0.526690 + 0.850058i \(0.323433\pi\)
\(912\) −3.98705 −0.132024
\(913\) 16.4204 + 1.31531i 0.543437 + 0.0435304i
\(914\) 28.7927 0.952380
\(915\) 0 0
\(916\) −14.1758 43.6288i −0.468383 1.44154i
\(917\) 2.87291 8.84191i 0.0948719 0.291986i
\(918\) 4.96460 + 3.60699i 0.163856 + 0.119048i
\(919\) −24.8246 18.0361i −0.818888 0.594957i 0.0975057 0.995235i \(-0.468914\pi\)
−0.916394 + 0.400278i \(0.868914\pi\)
\(920\) 0 0
\(921\) −5.71352 17.5844i −0.188267 0.579425i
\(922\) 12.0072 8.72374i 0.395436 0.287301i
\(923\) 8.13664 0.267821
\(924\) −2.10554 8.82426i −0.0692671 0.290297i
\(925\) 0 0
\(926\) −47.6263 + 34.6025i −1.56510 + 1.13711i
\(927\) 2.73642 + 8.42184i 0.0898759 + 0.276610i
\(928\) −1.27703 + 3.93031i −0.0419207 + 0.129019i
\(929\) 16.7900 + 12.1986i 0.550861 + 0.400224i 0.828103 0.560576i \(-0.189420\pi\)
−0.277242 + 0.960800i \(0.589420\pi\)
\(930\) 0 0
\(931\) 1.70597 5.25043i 0.0559108 0.172076i
\(932\) 5.20070 + 16.0061i 0.170355 + 0.524298i
\(933\) 18.7933 13.6541i 0.615265 0.447016i
\(934\) 34.5283 1.12980
\(935\) 0 0
\(936\) 0.346930 0.0113398
\(937\) −4.95966 + 3.60340i −0.162025 + 0.117718i −0.665843 0.746092i \(-0.731928\pi\)
0.503818 + 0.863810i \(0.331928\pi\)
\(938\) −7.80344 24.0165i −0.254791 0.784167i
\(939\) −0.693665 + 2.13488i −0.0226369 + 0.0696692i
\(940\) 0 0
\(941\) 41.7733 + 30.3501i 1.36177 + 0.989385i 0.998330 + 0.0577680i \(0.0183984\pi\)
0.363442 + 0.931617i \(0.381602\pi\)
\(942\) 13.9859 43.0441i 0.455684 1.40245i
\(943\) −4.54029 13.9736i −0.147852 0.455042i
\(944\) 9.88363 7.18088i 0.321685 0.233718i
\(945\) 0 0
\(946\) −8.59378 + 20.6658i −0.279408 + 0.671904i
\(947\) 23.2475 0.755444 0.377722 0.925919i \(-0.376708\pi\)
0.377722 + 0.925919i \(0.376708\pi\)
\(948\) 1.85633 1.34871i 0.0602909 0.0438039i
\(949\) 7.88831 + 24.2777i 0.256065 + 0.788088i
\(950\) 0 0
\(951\) 5.16486 + 3.75249i 0.167482 + 0.121683i
\(952\) 0.572687 + 0.416081i 0.0185609 + 0.0134853i
\(953\) 6.43507 19.8051i 0.208453 0.641551i −0.791101 0.611685i \(-0.790492\pi\)
0.999554 0.0298658i \(-0.00950800\pi\)
\(954\) −6.33035 19.4828i −0.204953 0.630780i
\(955\) 0 0
\(956\) 30.9175 0.999945
\(957\) −1.44903 + 0.885194i −0.0468404 + 0.0286142i
\(958\) 2.24580 0.0725584
\(959\) 1.32143 0.960078i 0.0426713 0.0310025i
\(960\) 0 0
\(961\) −9.07915 + 27.9428i −0.292876 + 0.901379i
\(962\) 7.01294 + 5.09520i 0.226106 + 0.164276i
\(963\) 3.34073 + 2.42719i 0.107654 + 0.0782150i
\(964\) 11.4474 35.2315i 0.368696 1.13473i
\(965\) 0 0
\(966\) −2.65247 + 1.92713i −0.0853419 + 0.0620045i
\(967\) 26.7093 0.858913 0.429456 0.903088i \(-0.358705\pi\)
0.429456 + 0.903088i \(0.358705\pi\)
\(968\) 1.93351 + 0.311757i 0.0621455 + 0.0100203i
\(969\) 3.17100 0.101867
\(970\) 0 0
\(971\) −9.00422 27.7121i −0.288959 0.889324i −0.985184 0.171501i \(-0.945138\pi\)
0.696225 0.717824i \(-0.254862\pi\)
\(972\) −0.645245 + 1.98586i −0.0206963 + 0.0636965i
\(973\) −14.2464 10.3506i −0.456720 0.331826i
\(974\) −43.7940 31.8182i −1.40325 1.01952i
\(975\) 0 0
\(976\) −10.6756 32.8562i −0.341718 1.05170i
\(977\) −20.5646 + 14.9411i −0.657921 + 0.478008i −0.865960 0.500113i \(-0.833292\pi\)
0.208039 + 0.978121i \(0.433292\pi\)
\(978\) −23.2590 −0.743740
\(979\) 20.9139 12.7760i 0.668410 0.408324i
\(980\) 0 0
\(981\) 11.0380 8.01956i 0.352415 0.256045i
\(982\) 20.0462 + 61.6957i 0.639698 + 1.96879i
\(983\) 13.5014 41.5530i 0.430627 1.32534i −0.466874 0.884324i \(-0.654620\pi\)
0.897502 0.441011i \(-0.145380\pi\)
\(984\) −1.70968 1.24216i −0.0545027 0.0395985i
\(985\) 0 0
\(986\) 0.970853 2.98798i 0.0309183 0.0951566i
\(987\) −5.27579 16.2372i −0.167930 0.516836i
\(988\) 3.43908 2.49864i 0.109412 0.0794923i
\(989\) 4.13147 0.131373
\(990\) 0 0
\(991\) 54.9993 1.74711 0.873555 0.486725i \(-0.161809\pi\)
0.873555 + 0.486725i \(0.161809\pi\)
\(992\) 8.30978 6.03741i 0.263836 0.191688i
\(993\) 4.75280 + 14.6276i 0.150826 + 0.464193i
\(994\) −3.41772 + 10.5186i −0.108403 + 0.333631i
\(995\) 0 0
\(996\) −8.39030 6.09591i −0.265857 0.193156i
\(997\) −4.71321 + 14.5058i −0.149269 + 0.459402i −0.997535 0.0701677i \(-0.977647\pi\)
0.848266 + 0.529570i \(0.177647\pi\)
\(998\) −12.6831 39.0347i −0.401478 1.23562i
\(999\) −1.78003 + 1.29327i −0.0563178 + 0.0409172i
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 825.2.n.n.751.1 yes 16
5.2 odd 4 825.2.bx.j.124.2 32
5.3 odd 4 825.2.bx.j.124.7 32
5.4 even 2 825.2.n.m.751.4 yes 16
11.2 odd 10 9075.2.a.dt.1.2 8
11.4 even 5 inner 825.2.n.n.301.1 yes 16
11.9 even 5 9075.2.a.dv.1.7 8
55.4 even 10 825.2.n.m.301.4 16
55.9 even 10 9075.2.a.du.1.2 8
55.24 odd 10 9075.2.a.dw.1.7 8
55.37 odd 20 825.2.bx.j.499.7 32
55.48 odd 20 825.2.bx.j.499.2 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
825.2.n.m.301.4 16 55.4 even 10
825.2.n.m.751.4 yes 16 5.4 even 2
825.2.n.n.301.1 yes 16 11.4 even 5 inner
825.2.n.n.751.1 yes 16 1.1 even 1 trivial
825.2.bx.j.124.2 32 5.2 odd 4
825.2.bx.j.124.7 32 5.3 odd 4
825.2.bx.j.499.2 32 55.48 odd 20
825.2.bx.j.499.7 32 55.37 odd 20
9075.2.a.dt.1.2 8 11.2 odd 10
9075.2.a.du.1.2 8 55.9 even 10
9075.2.a.dv.1.7 8 11.9 even 5
9075.2.a.dw.1.7 8 55.24 odd 10