Properties

Label 605.2.j.h.9.4
Level $605$
Weight $2$
Character 605.9
Analytic conductor $4.831$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [605,2,Mod(9,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("605.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.j (of order \(10\), degree \(4\), not 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: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 7x^{14} + 25x^{12} - 57x^{10} + 194x^{8} - 303x^{6} + 235x^{4} - 33x^{2} + 121 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 55)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 9.4
Root \(1.92464 - 0.625353i\) of defining polynomial
Character \(\chi\) \(=\) 605.9
Dual form 605.2.j.h.269.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.92464 + 0.625353i) q^{2} +(1.54035 + 2.12011i) q^{3} +(1.69513 + 1.23158i) q^{4} +(2.01689 - 0.965471i) q^{5} +(1.63880 + 5.04369i) q^{6} +(-0.567697 + 0.781367i) q^{7} +(0.113351 + 0.156015i) q^{8} +(-1.19513 + 3.67823i) q^{9} +O(q^{10})\) \(q+(1.92464 + 0.625353i) q^{2} +(1.54035 + 2.12011i) q^{3} +(1.69513 + 1.23158i) q^{4} +(2.01689 - 0.965471i) q^{5} +(1.63880 + 5.04369i) q^{6} +(-0.567697 + 0.781367i) q^{7} +(0.113351 + 0.156015i) q^{8} +(-1.19513 + 3.67823i) q^{9} +(4.48555 - 0.596911i) q^{10} +5.49092i q^{12} +(-4.30362 - 1.39833i) q^{13} +(-1.58124 + 1.14884i) q^{14} +(5.15362 + 2.78887i) q^{15} +(-1.17437 - 3.61433i) q^{16} +(-3.17338 + 1.03109i) q^{17} +(-4.60038 + 6.33188i) q^{18} +(2.65163 - 1.92652i) q^{19} +(4.60795 + 0.847376i) q^{20} -2.53103 q^{21} -3.36643i q^{23} +(-0.156167 + 0.480634i) q^{24} +(3.13573 - 3.89451i) q^{25} +(-7.40846 - 5.38256i) q^{26} +(-2.16214 + 0.702522i) q^{27} +(-1.92464 + 0.625353i) q^{28} +(3.97470 + 2.88779i) q^{29} +(8.17482 + 8.59039i) q^{30} +(-0.129282 + 0.397889i) q^{31} -8.07636i q^{32} -6.75241 q^{34} +(-0.390597 + 2.12403i) q^{35} +(-6.55594 + 4.76317i) q^{36} +(-3.72512 + 5.12719i) q^{37} +(6.30817 - 2.04965i) q^{38} +(-3.66446 - 11.2780i) q^{39} +(0.379246 + 0.205228i) q^{40} +(-4.68068 + 3.40071i) q^{41} +(-4.87132 - 1.58279i) q^{42} -2.26205i q^{43} +(1.14077 + 8.57246i) q^{45} +(2.10520 - 6.47915i) q^{46} +(2.54173 + 3.49838i) q^{47} +(5.85383 - 8.05710i) q^{48} +(1.87486 + 5.77024i) q^{49} +(8.47058 - 5.53458i) q^{50} +(-7.07414 - 5.13966i) q^{51} +(-5.57303 - 7.67061i) q^{52} +(-2.53047 - 0.822201i) q^{53} -4.60066 q^{54} -0.186254 q^{56} +(8.16885 + 2.65422i) q^{57} +(5.84397 + 8.04353i) q^{58} +(-8.19153 - 5.95150i) q^{59} +(5.30132 + 11.0746i) q^{60} +(-0.763537 - 2.34993i) q^{61} +(-0.497642 + 0.684945i) q^{62} +(-2.19558 - 3.02195i) q^{63} +(2.70184 - 8.31540i) q^{64} +(-10.0300 + 1.33473i) q^{65} +9.60059i q^{67} +(-6.64917 - 2.16045i) q^{68} +(7.13718 - 5.18546i) q^{69} +(-2.08002 + 3.84373i) q^{70} +(-1.68510 - 5.18621i) q^{71} +(-0.709327 + 0.230474i) q^{72} +(0.843791 - 1.16138i) q^{73} +(-10.3758 + 7.53847i) q^{74} +(13.0869 + 0.649186i) q^{75} +6.86752 q^{76} -23.9977i q^{78} +(-0.310240 + 0.954820i) q^{79} +(-5.85811 - 6.15591i) q^{80} +(4.56679 + 3.31797i) q^{81} +(-11.1353 + 3.61806i) q^{82} +(-7.03346 + 2.28531i) q^{83} +(-4.29042 - 3.11717i) q^{84} +(-5.40489 + 5.14342i) q^{85} +(1.41458 - 4.35363i) q^{86} +12.8750i q^{87} +12.1964 q^{89} +(-3.16523 + 17.2123i) q^{90} +(3.53576 - 2.56888i) q^{91} +(4.14603 - 5.70652i) q^{92} +(-1.04271 + 0.338796i) q^{93} +(2.70418 + 8.32259i) q^{94} +(3.48805 - 6.44566i) q^{95} +(17.1227 - 12.4404i) q^{96} +(2.87147 + 0.932997i) q^{97} +12.2781i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 6 q^{4} - 2 q^{5} + 12 q^{6} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 6 q^{4} - 2 q^{5} + 12 q^{6} + 2 q^{9} + 8 q^{14} + 24 q^{15} + 6 q^{16} + 6 q^{19} + 12 q^{20} + 8 q^{21} - 4 q^{24} + 24 q^{25} - 50 q^{26} + 22 q^{29} - 4 q^{30} - 22 q^{31} - 16 q^{34} - 8 q^{35} - 30 q^{36} + 12 q^{40} + 18 q^{41} + 12 q^{45} + 38 q^{46} - 20 q^{49} - 12 q^{50} - 12 q^{51} - 40 q^{54} - 20 q^{56} - 8 q^{59} - 2 q^{60} + 20 q^{61} + 22 q^{64} - 40 q^{65} + 6 q^{69} + 26 q^{70} + 6 q^{71} - 52 q^{74} + 40 q^{75} + 56 q^{76} - 22 q^{79} - 6 q^{80} - 32 q^{81} - 18 q^{84} - 62 q^{85} - 68 q^{86} + 24 q^{89} - 32 q^{90} - 56 q^{94} - 22 q^{95} + 94 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.92464 + 0.625353i 1.36092 + 0.442191i 0.896352 0.443344i \(-0.146208\pi\)
0.464572 + 0.885535i \(0.346208\pi\)
\(3\) 1.54035 + 2.12011i 0.889320 + 1.22404i 0.973751 + 0.227614i \(0.0730925\pi\)
−0.0844316 + 0.996429i \(0.526907\pi\)
\(4\) 1.69513 + 1.23158i 0.847564 + 0.615791i
\(5\) 2.01689 0.965471i 0.901983 0.431772i
\(6\) 1.63880 + 5.04369i 0.669035 + 2.05908i
\(7\) −0.567697 + 0.781367i −0.214569 + 0.295329i −0.902711 0.430247i \(-0.858427\pi\)
0.688142 + 0.725576i \(0.258427\pi\)
\(8\) 0.113351 + 0.156015i 0.0400758 + 0.0551595i
\(9\) −1.19513 + 3.67823i −0.398376 + 1.22608i
\(10\) 4.48555 0.596911i 1.41846 0.188760i
\(11\) 0 0
\(12\) 5.49092i 1.58509i
\(13\) −4.30362 1.39833i −1.19361 0.387827i −0.356203 0.934408i \(-0.615929\pi\)
−0.837406 + 0.546581i \(0.815929\pi\)
\(14\) −1.58124 + 1.14884i −0.422604 + 0.307040i
\(15\) 5.15362 + 2.78887i 1.33066 + 0.720083i
\(16\) −1.17437 3.61433i −0.293592 0.903582i
\(17\) −3.17338 + 1.03109i −0.769658 + 0.250077i −0.667419 0.744683i \(-0.732601\pi\)
−0.102239 + 0.994760i \(0.532601\pi\)
\(18\) −4.60038 + 6.33188i −1.08432 + 1.49244i
\(19\) 2.65163 1.92652i 0.608325 0.441974i −0.240499 0.970649i \(-0.577311\pi\)
0.848824 + 0.528675i \(0.177311\pi\)
\(20\) 4.60795 + 0.847376i 1.03037 + 0.189479i
\(21\) −2.53103 −0.552316
\(22\) 0 0
\(23\) 3.36643i 0.701948i −0.936385 0.350974i \(-0.885851\pi\)
0.936385 0.350974i \(-0.114149\pi\)
\(24\) −0.156167 + 0.480634i −0.0318775 + 0.0981089i
\(25\) 3.13573 3.89451i 0.627146 0.778902i
\(26\) −7.40846 5.38256i −1.45292 1.05561i
\(27\) −2.16214 + 0.702522i −0.416104 + 0.135200i
\(28\) −1.92464 + 0.625353i −0.363722 + 0.118181i
\(29\) 3.97470 + 2.88779i 0.738083 + 0.536249i 0.892110 0.451818i \(-0.149224\pi\)
−0.154027 + 0.988067i \(0.549224\pi\)
\(30\) 8.17482 + 8.59039i 1.49251 + 1.56838i
\(31\) −0.129282 + 0.397889i −0.0232197 + 0.0714629i −0.961995 0.273067i \(-0.911962\pi\)
0.938775 + 0.344530i \(0.111962\pi\)
\(32\) 8.07636i 1.42771i
\(33\) 0 0
\(34\) −6.75241 −1.15803
\(35\) −0.390597 + 2.12403i −0.0660229 + 0.359027i
\(36\) −6.55594 + 4.76317i −1.09266 + 0.793861i
\(37\) −3.72512 + 5.12719i −0.612406 + 0.842905i −0.996773 0.0802758i \(-0.974420\pi\)
0.384367 + 0.923181i \(0.374420\pi\)
\(38\) 6.30817 2.04965i 1.02332 0.332497i
\(39\) −3.66446 11.2780i −0.586783 1.80593i
\(40\) 0.379246 + 0.205228i 0.0599640 + 0.0324494i
\(41\) −4.68068 + 3.40071i −0.730999 + 0.531102i −0.889879 0.456196i \(-0.849212\pi\)
0.158880 + 0.987298i \(0.449212\pi\)
\(42\) −4.87132 1.58279i −0.751660 0.244229i
\(43\) 2.26205i 0.344960i −0.985013 0.172480i \(-0.944822\pi\)
0.985013 0.172480i \(-0.0551780\pi\)
\(44\) 0 0
\(45\) 1.14077 + 8.57246i 0.170057 + 1.27791i
\(46\) 2.10520 6.47915i 0.310395 0.955298i
\(47\) 2.54173 + 3.49838i 0.370749 + 0.510292i 0.953104 0.302642i \(-0.0978688\pi\)
−0.582355 + 0.812934i \(0.697869\pi\)
\(48\) 5.85383 8.05710i 0.844927 1.16294i
\(49\) 1.87486 + 5.77024i 0.267838 + 0.824320i
\(50\) 8.47058 5.53458i 1.19792 0.782708i
\(51\) −7.07414 5.13966i −0.990577 0.719697i
\(52\) −5.57303 7.67061i −0.772840 1.06372i
\(53\) −2.53047 0.822201i −0.347587 0.112938i 0.130020 0.991511i \(-0.458496\pi\)
−0.477607 + 0.878573i \(0.658496\pi\)
\(54\) −4.60066 −0.626071
\(55\) 0 0
\(56\) −0.186254 −0.0248892
\(57\) 8.16885 + 2.65422i 1.08199 + 0.351560i
\(58\) 5.84397 + 8.04353i 0.767350 + 1.05617i
\(59\) −8.19153 5.95150i −1.06645 0.774819i −0.0911765 0.995835i \(-0.529063\pi\)
−0.975270 + 0.221016i \(0.929063\pi\)
\(60\) 5.30132 + 11.0746i 0.684398 + 1.42972i
\(61\) −0.763537 2.34993i −0.0977609 0.300877i 0.890202 0.455565i \(-0.150563\pi\)
−0.987963 + 0.154688i \(0.950563\pi\)
\(62\) −0.497642 + 0.684945i −0.0632005 + 0.0869881i
\(63\) −2.19558 3.02195i −0.276617 0.380730i
\(64\) 2.70184 8.31540i 0.337729 1.03942i
\(65\) −10.0300 + 1.33473i −1.24407 + 0.165553i
\(66\) 0 0
\(67\) 9.60059i 1.17290i 0.809986 + 0.586449i \(0.199475\pi\)
−0.809986 + 0.586449i \(0.800525\pi\)
\(68\) −6.64917 2.16045i −0.806330 0.261992i
\(69\) 7.13718 5.18546i 0.859215 0.624256i
\(70\) −2.08002 + 3.84373i −0.248611 + 0.459413i
\(71\) −1.68510 5.18621i −0.199985 0.615490i −0.999882 0.0153533i \(-0.995113\pi\)
0.799897 0.600137i \(-0.204887\pi\)
\(72\) −0.709327 + 0.230474i −0.0835950 + 0.0271617i
\(73\) 0.843791 1.16138i 0.0987582 0.135929i −0.756778 0.653672i \(-0.773228\pi\)
0.855536 + 0.517743i \(0.173228\pi\)
\(74\) −10.3758 + 7.53847i −1.20616 + 0.876329i
\(75\) 13.0869 + 0.649186i 1.51114 + 0.0749616i
\(76\) 6.86752 0.787758
\(77\) 0 0
\(78\) 23.9977i 2.71721i
\(79\) −0.310240 + 0.954820i −0.0349047 + 0.107426i −0.966991 0.254811i \(-0.917987\pi\)
0.932086 + 0.362237i \(0.117987\pi\)
\(80\) −5.85811 6.15591i −0.654956 0.688251i
\(81\) 4.56679 + 3.31797i 0.507421 + 0.368663i
\(82\) −11.1353 + 3.61806i −1.22968 + 0.399548i
\(83\) −7.03346 + 2.28531i −0.772022 + 0.250845i −0.668430 0.743775i \(-0.733034\pi\)
−0.103592 + 0.994620i \(0.533034\pi\)
\(84\) −4.29042 3.11717i −0.468123 0.340112i
\(85\) −5.40489 + 5.14342i −0.586242 + 0.557882i
\(86\) 1.41458 4.35363i 0.152538 0.469464i
\(87\) 12.8750i 1.38034i
\(88\) 0 0
\(89\) 12.1964 1.29282 0.646410 0.762991i \(-0.276270\pi\)
0.646410 + 0.762991i \(0.276270\pi\)
\(90\) −3.16523 + 17.2123i −0.333645 + 1.81433i
\(91\) 3.53576 2.56888i 0.370648 0.269292i
\(92\) 4.14603 5.70652i 0.432254 0.594946i
\(93\) −1.04271 + 0.338796i −0.108124 + 0.0351315i
\(94\) 2.70418 + 8.32259i 0.278914 + 0.858410i
\(95\) 3.48805 6.44566i 0.357867 0.661310i
\(96\) 17.1227 12.4404i 1.74758 1.26969i
\(97\) 2.87147 + 0.932997i 0.291553 + 0.0947315i 0.451142 0.892452i \(-0.351017\pi\)
−0.159589 + 0.987184i \(0.551017\pi\)
\(98\) 12.2781i 1.24027i
\(99\) 0 0
\(100\) 10.1119 2.73978i 1.01119 0.273978i
\(101\) 4.69588 14.4524i 0.467258 1.43807i −0.388863 0.921296i \(-0.627132\pi\)
0.856120 0.516776i \(-0.172868\pi\)
\(102\) −10.4010 14.3158i −1.02986 1.41748i
\(103\) −5.72909 + 7.88542i −0.564504 + 0.776974i −0.991890 0.127096i \(-0.959435\pi\)
0.427386 + 0.904069i \(0.359435\pi\)
\(104\) −0.269661 0.829931i −0.0264424 0.0813814i
\(105\) −5.10482 + 2.44364i −0.498180 + 0.238475i
\(106\) −4.35608 3.16488i −0.423100 0.307400i
\(107\) 4.49173 + 6.18234i 0.434232 + 0.597669i 0.968918 0.247382i \(-0.0795701\pi\)
−0.534686 + 0.845051i \(0.679570\pi\)
\(108\) −4.53032 1.47199i −0.435930 0.141642i
\(109\) 9.85576 0.944010 0.472005 0.881596i \(-0.343530\pi\)
0.472005 + 0.881596i \(0.343530\pi\)
\(110\) 0 0
\(111\) −16.6082 −1.57638
\(112\) 3.49080 + 1.13423i 0.329850 + 0.107175i
\(113\) −2.94987 4.06014i −0.277500 0.381946i 0.647404 0.762147i \(-0.275855\pi\)
−0.924904 + 0.380201i \(0.875855\pi\)
\(114\) 14.0623 + 10.2168i 1.31705 + 0.956893i
\(115\) −3.25019 6.78973i −0.303081 0.633145i
\(116\) 3.18107 + 9.79034i 0.295355 + 0.909010i
\(117\) 10.2868 14.1585i 0.951011 1.30895i
\(118\) −12.0439 16.5771i −1.10873 1.52604i
\(119\) 0.995855 3.06493i 0.0912898 0.280961i
\(120\) 0.149065 + 1.12016i 0.0136077 + 0.102256i
\(121\) 0 0
\(122\) 5.00023i 0.452700i
\(123\) −14.4197 4.68526i −1.30018 0.422455i
\(124\) −0.709183 + 0.515251i −0.0636865 + 0.0462709i
\(125\) 2.56440 10.8823i 0.229367 0.973340i
\(126\) −2.33590 7.18917i −0.208099 0.640462i
\(127\) 6.74338 2.19106i 0.598378 0.194425i 0.00586102 0.999983i \(-0.498134\pi\)
0.592517 + 0.805558i \(0.298134\pi\)
\(128\) 0.905782 1.24670i 0.0800605 0.110194i
\(129\) 4.79579 3.48435i 0.422246 0.306780i
\(130\) −20.1388 3.70340i −1.76629 0.324810i
\(131\) 7.21704 0.630556 0.315278 0.948999i \(-0.397902\pi\)
0.315278 + 0.948999i \(0.397902\pi\)
\(132\) 0 0
\(133\) 3.16557i 0.274490i
\(134\) −6.00375 + 18.4776i −0.518645 + 1.59623i
\(135\) −3.68255 + 3.50440i −0.316943 + 0.301611i
\(136\) −0.520573 0.378218i −0.0446388 0.0324320i
\(137\) 8.07522 2.62380i 0.689913 0.224166i 0.0569827 0.998375i \(-0.481852\pi\)
0.632930 + 0.774209i \(0.281852\pi\)
\(138\) 16.9792 5.51688i 1.44537 0.469628i
\(139\) 6.26192 + 4.54955i 0.531129 + 0.385888i 0.820780 0.571245i \(-0.193539\pi\)
−0.289651 + 0.957132i \(0.593539\pi\)
\(140\) −3.27803 + 3.11945i −0.277044 + 0.263642i
\(141\) −3.50181 + 10.7775i −0.294905 + 0.907625i
\(142\) 11.0354i 0.926067i
\(143\) 0 0
\(144\) 14.6978 1.22482
\(145\) 10.8046 + 1.98691i 0.897275 + 0.165004i
\(146\) 2.35026 1.70756i 0.194509 0.141319i
\(147\) −9.34557 + 12.8631i −0.770810 + 1.06093i
\(148\) −12.6291 + 4.10345i −1.03811 + 0.337301i
\(149\) 5.21723 + 16.0570i 0.427412 + 1.31544i 0.900666 + 0.434513i \(0.143079\pi\)
−0.473254 + 0.880926i \(0.656921\pi\)
\(150\) 24.7815 + 9.43336i 2.02340 + 0.770231i
\(151\) 9.93687 7.21956i 0.808651 0.587519i −0.104788 0.994495i \(-0.533416\pi\)
0.913439 + 0.406975i \(0.133416\pi\)
\(152\) 0.601131 + 0.195319i 0.0487582 + 0.0158425i
\(153\) 12.9047i 1.04328i
\(154\) 0 0
\(155\) 0.123402 + 0.927318i 0.00991190 + 0.0744840i
\(156\) 7.67812 23.6308i 0.614741 1.89198i
\(157\) 2.47441 + 3.40573i 0.197479 + 0.271807i 0.896260 0.443529i \(-0.146274\pi\)
−0.698781 + 0.715336i \(0.746274\pi\)
\(158\) −1.19420 + 1.64367i −0.0950053 + 0.130764i
\(159\) −2.15466 6.63135i −0.170875 0.525900i
\(160\) −7.79749 16.2892i −0.616446 1.28777i
\(161\) 2.63041 + 1.91111i 0.207306 + 0.150616i
\(162\) 6.71452 + 9.24174i 0.527542 + 0.726100i
\(163\) −15.7624 5.12151i −1.23461 0.401148i −0.382225 0.924069i \(-0.624842\pi\)
−0.852381 + 0.522922i \(0.824842\pi\)
\(164\) −12.1226 −0.946617
\(165\) 0 0
\(166\) −14.9660 −1.16159
\(167\) −8.71813 2.83269i −0.674629 0.219200i −0.0483867 0.998829i \(-0.515408\pi\)
−0.626242 + 0.779628i \(0.715408\pi\)
\(168\) −0.286896 0.394878i −0.0221345 0.0304655i
\(169\) 6.04859 + 4.39456i 0.465276 + 0.338043i
\(170\) −13.6189 + 6.51925i −1.04452 + 0.500004i
\(171\) 3.91714 + 12.0557i 0.299551 + 0.921924i
\(172\) 2.78591 3.83447i 0.212423 0.292376i
\(173\) 2.41560 + 3.32479i 0.183655 + 0.252779i 0.890911 0.454178i \(-0.150067\pi\)
−0.707256 + 0.706958i \(0.750067\pi\)
\(174\) −8.05140 + 24.7797i −0.610375 + 1.87854i
\(175\) 1.26290 + 4.66106i 0.0954661 + 0.352343i
\(176\) 0 0
\(177\) 26.5343i 1.99444i
\(178\) 23.4737 + 7.62707i 1.75943 + 0.571673i
\(179\) −13.1838 + 9.57858i −0.985403 + 0.715937i −0.958910 0.283712i \(-0.908434\pi\)
−0.0264932 + 0.999649i \(0.508434\pi\)
\(180\) −8.62394 + 15.9364i −0.642790 + 1.18783i
\(181\) −1.71408 5.27541i −0.127407 0.392118i 0.866925 0.498438i \(-0.166093\pi\)
−0.994332 + 0.106321i \(0.966093\pi\)
\(182\) 8.41151 2.73307i 0.623503 0.202588i
\(183\) 3.80598 5.23848i 0.281346 0.387240i
\(184\) 0.525212 0.381589i 0.0387191 0.0281311i
\(185\) −2.56302 + 13.9375i −0.188437 + 1.02471i
\(186\) −2.21870 −0.162683
\(187\) 0 0
\(188\) 9.06056i 0.660809i
\(189\) 0.678512 2.08825i 0.0493545 0.151898i
\(190\) 10.7440 10.2243i 0.779455 0.741748i
\(191\) −17.6496 12.8232i −1.27708 0.927854i −0.277621 0.960691i \(-0.589546\pi\)
−0.999461 + 0.0328370i \(0.989546\pi\)
\(192\) 21.7913 7.08042i 1.57265 0.510985i
\(193\) −21.3787 + 6.94637i −1.53887 + 0.500010i −0.951065 0.308990i \(-0.900009\pi\)
−0.587808 + 0.809000i \(0.700009\pi\)
\(194\) 4.94308 + 3.59136i 0.354893 + 0.257845i
\(195\) −18.2795 19.2087i −1.30902 1.37556i
\(196\) −3.92839 + 12.0903i −0.280599 + 0.863596i
\(197\) 25.7479i 1.83446i 0.398358 + 0.917230i \(0.369580\pi\)
−0.398358 + 0.917230i \(0.630420\pi\)
\(198\) 0 0
\(199\) −16.9671 −1.20277 −0.601385 0.798960i \(-0.705384\pi\)
−0.601385 + 0.798960i \(0.705384\pi\)
\(200\) 0.963040 + 0.0477725i 0.0680972 + 0.00337802i
\(201\) −20.3543 + 14.7882i −1.43568 + 1.04308i
\(202\) 18.0757 24.8791i 1.27181 1.75049i
\(203\) −4.51284 + 1.46631i −0.316740 + 0.102915i
\(204\) −5.66165 17.4248i −0.396395 1.21998i
\(205\) −6.15715 + 11.3779i −0.430034 + 0.794670i
\(206\) −15.9576 + 11.5939i −1.11182 + 0.807783i
\(207\) 12.3825 + 4.02331i 0.860642 + 0.279639i
\(208\) 17.1969i 1.19239i
\(209\) 0 0
\(210\) −11.3531 + 1.51080i −0.783436 + 0.104255i
\(211\) −1.80045 + 5.54121i −0.123948 + 0.381472i −0.993708 0.112002i \(-0.964274\pi\)
0.869760 + 0.493475i \(0.164274\pi\)
\(212\) −3.27687 4.51023i −0.225056 0.309764i
\(213\) 8.39968 11.5612i 0.575537 0.792158i
\(214\) 4.77881 + 14.7077i 0.326673 + 1.00540i
\(215\) −2.18395 4.56232i −0.148944 0.311148i
\(216\) −0.354686 0.257694i −0.0241333 0.0175339i
\(217\) −0.237504 0.326897i −0.0161229 0.0221912i
\(218\) 18.9688 + 6.16332i 1.28473 + 0.417433i
\(219\) 3.76197 0.254211
\(220\) 0 0
\(221\) 15.0988 1.01566
\(222\) −31.9647 10.3860i −2.14533 0.697060i
\(223\) −11.1810 15.3893i −0.748736 1.03055i −0.998068 0.0621285i \(-0.980211\pi\)
0.249332 0.968418i \(-0.419789\pi\)
\(224\) 6.31060 + 4.58492i 0.421645 + 0.306343i
\(225\) 10.5773 + 16.1884i 0.705152 + 1.07922i
\(226\) −3.13840 9.65900i −0.208763 0.642507i
\(227\) −16.7319 + 23.0294i −1.11053 + 1.52852i −0.289902 + 0.957056i \(0.593623\pi\)
−0.820630 + 0.571460i \(0.806377\pi\)
\(228\) 10.5784 + 14.5599i 0.700569 + 0.964250i
\(229\) 7.84636 24.1486i 0.518502 1.59579i −0.258316 0.966060i \(-0.583168\pi\)
0.776818 0.629725i \(-0.216832\pi\)
\(230\) −2.00946 15.1003i −0.132500 0.995682i
\(231\) 0 0
\(232\) 0.947446i 0.0622029i
\(233\) 11.9048 + 3.86810i 0.779908 + 0.253407i 0.671801 0.740732i \(-0.265521\pi\)
0.108107 + 0.994139i \(0.465521\pi\)
\(234\) 28.6523 20.8171i 1.87306 1.36086i
\(235\) 8.50398 + 4.60191i 0.554739 + 0.300196i
\(236\) −6.55594 20.1771i −0.426755 1.31342i
\(237\) −2.50220 + 0.813013i −0.162535 + 0.0528108i
\(238\) 3.83332 5.27611i 0.248477 0.341999i
\(239\) 16.4939 11.9835i 1.06690 0.775149i 0.0915488 0.995801i \(-0.470818\pi\)
0.975353 + 0.220651i \(0.0708183\pi\)
\(240\) 4.02766 21.9020i 0.259984 1.41377i
\(241\) −22.7935 −1.46826 −0.734129 0.679010i \(-0.762409\pi\)
−0.734129 + 0.679010i \(0.762409\pi\)
\(242\) 0 0
\(243\) 21.6131i 1.38648i
\(244\) 1.59983 4.92378i 0.102419 0.315213i
\(245\) 9.35240 + 9.82783i 0.597503 + 0.627877i
\(246\) −24.8228 18.0348i −1.58265 1.14986i
\(247\) −14.1055 + 4.58316i −0.897512 + 0.291619i
\(248\) −0.0767308 + 0.0249314i −0.00487241 + 0.00158314i
\(249\) −15.6791 11.3915i −0.993620 0.721907i
\(250\) 11.7408 19.3408i 0.742554 1.22322i
\(251\) 5.23870 16.1231i 0.330664 1.01768i −0.638155 0.769908i \(-0.720302\pi\)
0.968819 0.247771i \(-0.0796980\pi\)
\(252\) 7.82663i 0.493031i
\(253\) 0 0
\(254\) 14.3487 0.900320
\(255\) −19.2300 3.53628i −1.20423 0.221451i
\(256\) −11.6241 + 8.44538i −0.726504 + 0.527836i
\(257\) −2.78366 + 3.83138i −0.173640 + 0.238995i −0.886963 0.461841i \(-0.847189\pi\)
0.713323 + 0.700835i \(0.247189\pi\)
\(258\) 11.4091 3.70704i 0.710300 0.230790i
\(259\) −1.89148 5.82138i −0.117531 0.361723i
\(260\) −18.6460 10.0902i −1.15637 0.625769i
\(261\) −15.3722 + 11.1686i −0.951516 + 0.691317i
\(262\) 13.8902 + 4.51319i 0.858138 + 0.278826i
\(263\) 18.1037i 1.11632i −0.829732 0.558162i \(-0.811507\pi\)
0.829732 0.558162i \(-0.188493\pi\)
\(264\) 0 0
\(265\) −5.89751 + 0.784807i −0.362281 + 0.0482103i
\(266\) −1.97960 + 6.09258i −0.121377 + 0.373560i
\(267\) 18.7867 + 25.8577i 1.14973 + 1.58247i
\(268\) −11.8239 + 16.2742i −0.722261 + 0.994107i
\(269\) 0.710127 + 2.18555i 0.0432972 + 0.133255i 0.970368 0.241630i \(-0.0776821\pi\)
−0.927071 + 0.374885i \(0.877682\pi\)
\(270\) −9.27905 + 4.44181i −0.564705 + 0.270320i
\(271\) −0.651815 0.473572i −0.0395950 0.0287674i 0.567812 0.823158i \(-0.307790\pi\)
−0.607407 + 0.794391i \(0.707790\pi\)
\(272\) 7.45343 + 10.2588i 0.451930 + 0.622029i
\(273\) 10.8926 + 3.53922i 0.659250 + 0.214203i
\(274\) 17.1827 1.03804
\(275\) 0 0
\(276\) 18.4848 1.11265
\(277\) 11.2538 + 3.65657i 0.676173 + 0.219702i 0.626919 0.779084i \(-0.284316\pi\)
0.0492539 + 0.998786i \(0.484316\pi\)
\(278\) 9.20685 + 12.6721i 0.552190 + 0.760025i
\(279\) −1.30902 0.951057i −0.0783688 0.0569383i
\(280\) −0.375655 + 0.179823i −0.0224497 + 0.0107465i
\(281\) 1.92496 + 5.92441i 0.114833 + 0.353420i 0.991912 0.126926i \(-0.0405110\pi\)
−0.877079 + 0.480346i \(0.840511\pi\)
\(282\) −13.4794 + 18.5528i −0.802687 + 1.10480i
\(283\) 5.08178 + 6.99448i 0.302081 + 0.415778i 0.932891 0.360159i \(-0.117277\pi\)
−0.630810 + 0.775937i \(0.717277\pi\)
\(284\) 3.53079 10.8666i 0.209514 0.644817i
\(285\) 19.0383 2.53351i 1.12773 0.150072i
\(286\) 0 0
\(287\) 5.58790i 0.329843i
\(288\) 29.7067 + 9.65228i 1.75048 + 0.568766i
\(289\) −4.74609 + 3.44824i −0.279182 + 0.202838i
\(290\) 19.5525 + 10.5808i 1.14816 + 0.621324i
\(291\) 2.44501 + 7.52496i 0.143329 + 0.441121i
\(292\) 2.86067 0.929487i 0.167408 0.0543941i
\(293\) 3.41532 4.70078i 0.199525 0.274622i −0.697517 0.716568i \(-0.745712\pi\)
0.897042 + 0.441946i \(0.145712\pi\)
\(294\) −26.0308 + 18.9125i −1.51815 + 1.10300i
\(295\) −22.2675 4.09485i −1.29646 0.238412i
\(296\) −1.22216 −0.0710369
\(297\) 0 0
\(298\) 34.1665i 1.97921i
\(299\) −4.70738 + 14.4878i −0.272235 + 0.837852i
\(300\) 21.3844 + 17.2180i 1.23463 + 0.994084i
\(301\) 1.76749 + 1.28416i 0.101877 + 0.0740177i
\(302\) 23.6396 7.68098i 1.36031 0.441991i
\(303\) 37.8740 12.3060i 2.17580 0.706962i
\(304\) −10.0771 7.32141i −0.577959 0.419912i
\(305\) −3.80876 4.00238i −0.218089 0.229176i
\(306\) 8.06999 24.8369i 0.461331 1.41983i
\(307\) 18.4721i 1.05426i −0.849785 0.527130i \(-0.823268\pi\)
0.849785 0.527130i \(-0.176732\pi\)
\(308\) 0 0
\(309\) −25.5427 −1.45307
\(310\) −0.342396 + 1.86192i −0.0194468 + 0.105750i
\(311\) 9.16726 6.66041i 0.519828 0.377677i −0.296711 0.954967i \(-0.595890\pi\)
0.816539 + 0.577290i \(0.195890\pi\)
\(312\) 1.34417 1.85009i 0.0760986 0.104741i
\(313\) 4.86464 1.58062i 0.274966 0.0893418i −0.168288 0.985738i \(-0.553824\pi\)
0.443254 + 0.896396i \(0.353824\pi\)
\(314\) 2.63256 + 8.10217i 0.148564 + 0.457232i
\(315\) −7.34585 3.97519i −0.413892 0.223977i
\(316\) −1.70184 + 1.23646i −0.0957357 + 0.0695561i
\(317\) −11.2351 3.65051i −0.631027 0.205033i −0.0239968 0.999712i \(-0.507639\pi\)
−0.607030 + 0.794679i \(0.707639\pi\)
\(318\) 14.1104i 0.791270i
\(319\) 0 0
\(320\) −2.57896 19.3798i −0.144168 1.08337i
\(321\) −6.18839 + 19.0459i −0.345402 + 1.06304i
\(322\) 3.86748 + 5.32313i 0.215526 + 0.296646i
\(323\) −6.42820 + 8.84766i −0.357675 + 0.492297i
\(324\) 3.65494 + 11.2488i 0.203052 + 0.624931i
\(325\) −18.9408 + 12.3757i −1.05065 + 0.686480i
\(326\) −27.1341 19.7141i −1.50282 1.09186i
\(327\) 15.1813 + 20.8952i 0.839527 + 1.15551i
\(328\) −1.06112 0.344780i −0.0585907 0.0190373i
\(329\) −4.17645 −0.230255
\(330\) 0 0
\(331\) 29.2692 1.60878 0.804391 0.594100i \(-0.202492\pi\)
0.804391 + 0.594100i \(0.202492\pi\)
\(332\) −14.7372 4.78839i −0.808807 0.262797i
\(333\) −14.4070 19.8295i −0.789497 1.08665i
\(334\) −15.0078 10.9038i −0.821191 0.596630i
\(335\) 9.26909 + 19.3634i 0.506424 + 1.05793i
\(336\) 2.97236 + 9.14798i 0.162155 + 0.499063i
\(337\) 15.6610 21.5555i 0.853109 1.17420i −0.130060 0.991506i \(-0.541517\pi\)
0.983169 0.182698i \(-0.0584830\pi\)
\(338\) 8.89320 + 12.2404i 0.483726 + 0.665792i
\(339\) 4.06411 12.5081i 0.220732 0.679344i
\(340\) −15.4965 + 2.06219i −0.840417 + 0.111838i
\(341\) 0 0
\(342\) 25.6525i 1.38713i
\(343\) −12.0029 3.89998i −0.648095 0.210579i
\(344\) 0.352914 0.256407i 0.0190278 0.0138245i
\(345\) 9.38852 17.3493i 0.505461 0.934054i
\(346\) 2.56999 + 7.90962i 0.138164 + 0.425224i
\(347\) 4.10028 1.33226i 0.220114 0.0715195i −0.196884 0.980427i \(-0.563082\pi\)
0.416998 + 0.908907i \(0.363082\pi\)
\(348\) −15.8566 + 21.8247i −0.850003 + 1.16993i
\(349\) −10.6543 + 7.74083i −0.570314 + 0.414357i −0.835219 0.549917i \(-0.814659\pi\)
0.264905 + 0.964274i \(0.414659\pi\)
\(350\) −0.484183 + 9.76060i −0.0258807 + 0.521726i
\(351\) 10.2874 0.549100
\(352\) 0 0
\(353\) 25.4904i 1.35672i 0.734732 + 0.678358i \(0.237308\pi\)
−0.734732 + 0.678358i \(0.762692\pi\)
\(354\) 16.5933 51.0689i 0.881923 2.71428i
\(355\) −8.40582 8.83313i −0.446134 0.468814i
\(356\) 20.6745 + 15.0209i 1.09575 + 0.796107i
\(357\) 8.03193 2.60973i 0.425095 0.138122i
\(358\) −31.3640 + 10.1908i −1.65764 + 0.538600i
\(359\) 21.2562 + 15.4435i 1.12186 + 0.815079i 0.984490 0.175441i \(-0.0561351\pi\)
0.137370 + 0.990520i \(0.456135\pi\)
\(360\) −1.20812 + 1.14968i −0.0636736 + 0.0605933i
\(361\) −2.55168 + 7.85325i −0.134299 + 0.413329i
\(362\) 11.2252i 0.589981i
\(363\) 0 0
\(364\) 9.15736 0.479976
\(365\) 0.580560 3.15703i 0.0303879 0.165247i
\(366\) 10.6010 7.70209i 0.554124 0.402595i
\(367\) −1.18658 + 1.63319i −0.0619391 + 0.0852518i −0.838863 0.544343i \(-0.816779\pi\)
0.776924 + 0.629595i \(0.216779\pi\)
\(368\) −12.1674 + 3.95342i −0.634268 + 0.206086i
\(369\) −6.91458 21.2809i −0.359959 1.10784i
\(370\) −13.6487 + 25.2218i −0.709564 + 1.31122i
\(371\) 2.07898 1.51047i 0.107935 0.0784197i
\(372\) −2.18477 0.709876i −0.113275 0.0368054i
\(373\) 8.87153i 0.459351i −0.973267 0.229675i \(-0.926234\pi\)
0.973267 0.229675i \(-0.0737664\pi\)
\(374\) 0 0
\(375\) 27.0216 11.3257i 1.39539 0.584855i
\(376\) −0.257692 + 0.793093i −0.0132894 + 0.0409007i
\(377\) −13.0675 17.9859i −0.673011 0.926320i
\(378\) 2.61178 3.59481i 0.134335 0.184897i
\(379\) −6.50916 20.0331i −0.334353 1.02903i −0.967040 0.254625i \(-0.918048\pi\)
0.632686 0.774408i \(-0.281952\pi\)
\(380\) 13.8511 6.63039i 0.710544 0.340132i
\(381\) 15.0324 + 10.9217i 0.770134 + 0.559535i
\(382\) −25.9501 35.7172i −1.32772 1.82745i
\(383\) 24.7080 + 8.02812i 1.26252 + 0.410218i 0.862392 0.506241i \(-0.168965\pi\)
0.400129 + 0.916459i \(0.368965\pi\)
\(384\) 4.03836 0.206082
\(385\) 0 0
\(386\) −45.4902 −2.31539
\(387\) 8.32034 + 2.70344i 0.422947 + 0.137424i
\(388\) 3.71845 + 5.11800i 0.188775 + 0.259827i
\(389\) −1.32987 0.966206i −0.0674270 0.0489886i 0.553561 0.832809i \(-0.313269\pi\)
−0.620988 + 0.783820i \(0.713269\pi\)
\(390\) −23.1691 48.4009i −1.17321 2.45087i
\(391\) 3.47110 + 10.6830i 0.175541 + 0.540260i
\(392\) −0.687724 + 0.946571i −0.0347353 + 0.0478090i
\(393\) 11.1167 + 15.3009i 0.560766 + 0.771828i
\(394\) −16.1015 + 49.5553i −0.811182 + 2.49656i
\(395\) 0.296130 + 2.22530i 0.0148999 + 0.111967i
\(396\) 0 0
\(397\) 16.7088i 0.838588i −0.907850 0.419294i \(-0.862278\pi\)
0.907850 0.419294i \(-0.137722\pi\)
\(398\) −32.6556 10.6104i −1.63688 0.531854i
\(399\) −6.71135 + 4.87608i −0.335988 + 0.244109i
\(400\) −17.7585 6.75998i −0.887927 0.337999i
\(401\) 8.58819 + 26.4317i 0.428874 + 1.31994i 0.899236 + 0.437464i \(0.144123\pi\)
−0.470362 + 0.882474i \(0.655877\pi\)
\(402\) −48.4224 + 15.7334i −2.41509 + 0.784711i
\(403\) 1.11276 1.53158i 0.0554305 0.0762936i
\(404\) 25.7595 18.7154i 1.28158 0.931125i
\(405\) 12.4141 + 2.28289i 0.616864 + 0.113438i
\(406\) −9.60255 −0.476567
\(407\) 0 0
\(408\) 1.68626i 0.0834822i
\(409\) −12.1855 + 37.5030i −0.602532 + 1.85440i −0.0895906 + 0.995979i \(0.528556\pi\)
−0.512941 + 0.858424i \(0.671444\pi\)
\(410\) −18.9655 + 18.0480i −0.936639 + 0.891328i
\(411\) 18.0014 + 13.0788i 0.887942 + 0.645128i
\(412\) −19.4231 + 6.31095i −0.956908 + 0.310918i
\(413\) 9.30061 3.02195i 0.457653 0.148700i
\(414\) 21.3158 + 15.4868i 1.04761 + 0.761136i
\(415\) −11.9793 + 11.3998i −0.588043 + 0.559596i
\(416\) −11.2934 + 34.7576i −0.553705 + 1.70413i
\(417\) 20.2838i 0.993303i
\(418\) 0 0
\(419\) −14.7812 −0.722111 −0.361055 0.932544i \(-0.617583\pi\)
−0.361055 + 0.932544i \(0.617583\pi\)
\(420\) −11.6629 2.14473i −0.569090 0.104652i
\(421\) 8.71900 6.33473i 0.424938 0.308736i −0.354684 0.934986i \(-0.615411\pi\)
0.779622 + 0.626251i \(0.215411\pi\)
\(422\) −6.93042 + 9.53890i −0.337367 + 0.464346i
\(423\) −15.9055 + 5.16802i −0.773354 + 0.251278i
\(424\) −0.158557 0.487989i −0.00770022 0.0236988i
\(425\) −5.93526 + 15.5920i −0.287903 + 0.756323i
\(426\) 23.3961 16.9983i 1.13355 0.823570i
\(427\) 2.26961 + 0.737442i 0.109834 + 0.0356873i
\(428\) 16.0118i 0.773960i
\(429\) 0 0
\(430\) −1.35025 10.1466i −0.0651146 0.489310i
\(431\) 9.94774 30.6160i 0.479166 1.47472i −0.361090 0.932531i \(-0.617595\pi\)
0.840256 0.542190i \(-0.182405\pi\)
\(432\) 5.07829 + 6.98967i 0.244330 + 0.336291i
\(433\) 0.224905 0.309555i 0.0108082 0.0148763i −0.803579 0.595199i \(-0.797073\pi\)
0.814387 + 0.580322i \(0.197073\pi\)
\(434\) −0.252684 0.777682i −0.0121292 0.0373299i
\(435\) 12.4304 + 25.9675i 0.595993 + 1.24504i
\(436\) 16.7068 + 12.1382i 0.800109 + 0.581314i
\(437\) −6.48548 8.92650i −0.310243 0.427013i
\(438\) 7.24044 + 2.35256i 0.345961 + 0.112410i
\(439\) −26.5331 −1.26635 −0.633177 0.774007i \(-0.718249\pi\)
−0.633177 + 0.774007i \(0.718249\pi\)
\(440\) 0 0
\(441\) −23.4649 −1.11738
\(442\) 29.0598 + 9.44210i 1.38223 + 0.449115i
\(443\) 8.52347 + 11.7316i 0.404962 + 0.557383i 0.961981 0.273117i \(-0.0880547\pi\)
−0.557018 + 0.830500i \(0.688055\pi\)
\(444\) −28.1530 20.4543i −1.33608 0.970720i
\(445\) 24.5989 11.7753i 1.16610 0.558203i
\(446\) −11.8956 36.6110i −0.563274 1.73358i
\(447\) −26.0062 + 35.7944i −1.23005 + 1.69302i
\(448\) 4.96356 + 6.83175i 0.234506 + 0.322770i
\(449\) −3.12540 + 9.61898i −0.147497 + 0.453948i −0.997324 0.0731139i \(-0.976706\pi\)
0.849827 + 0.527062i \(0.176706\pi\)
\(450\) 10.2340 + 37.7713i 0.482435 + 1.78055i
\(451\) 0 0
\(452\) 10.5155i 0.494606i
\(453\) 30.6125 + 9.94659i 1.43830 + 0.467332i
\(454\) −46.6043 + 33.8600i −2.18725 + 1.58913i
\(455\) 4.65108 8.59484i 0.218046 0.402932i
\(456\) 0.511853 + 1.57532i 0.0239697 + 0.0737712i
\(457\) 37.1756 12.0791i 1.73900 0.565036i 0.744301 0.667845i \(-0.232783\pi\)
0.994701 + 0.102809i \(0.0327830\pi\)
\(458\) 30.2028 41.5706i 1.41128 1.94247i
\(459\) 6.13693 4.45874i 0.286448 0.208116i
\(460\) 2.85263 15.5123i 0.133004 0.723266i
\(461\) 39.1322 1.82257 0.911285 0.411776i \(-0.135092\pi\)
0.911285 + 0.411776i \(0.135092\pi\)
\(462\) 0 0
\(463\) 12.9189i 0.600392i −0.953878 0.300196i \(-0.902948\pi\)
0.953878 0.300196i \(-0.0970521\pi\)
\(464\) 5.76966 17.7572i 0.267850 0.824357i
\(465\) −1.77593 + 1.69002i −0.0823568 + 0.0783727i
\(466\) 20.4934 + 14.8894i 0.949341 + 0.689736i
\(467\) −10.6985 + 3.47616i −0.495069 + 0.160858i −0.545901 0.837850i \(-0.683813\pi\)
0.0508323 + 0.998707i \(0.483813\pi\)
\(468\) 34.8747 11.3315i 1.61209 0.523798i
\(469\) −7.50158 5.45022i −0.346391 0.251668i
\(470\) 13.4893 + 14.1750i 0.622213 + 0.653844i
\(471\) −3.40906 + 10.4920i −0.157081 + 0.483446i
\(472\) 1.95261i 0.0898762i
\(473\) 0 0
\(474\) −5.32424 −0.244550
\(475\) 0.811941 16.3678i 0.0372544 0.751008i
\(476\) 5.46281 3.96896i 0.250388 0.181917i
\(477\) 6.04848 8.32503i 0.276941 0.381177i
\(478\) 39.2387 12.7494i 1.79474 0.583145i
\(479\) −6.47894 19.9401i −0.296030 0.911087i −0.982873 0.184282i \(-0.941004\pi\)
0.686843 0.726806i \(-0.258996\pi\)
\(480\) 22.5239 41.6225i 1.02807 1.89980i
\(481\) 23.2010 16.8565i 1.05788 0.768591i
\(482\) −43.8692 14.2540i −1.99819 0.649250i
\(483\) 8.52053i 0.387697i
\(484\) 0 0
\(485\) 6.69223 0.890564i 0.303879 0.0404384i
\(486\) −13.5158 + 41.5974i −0.613090 + 1.88690i
\(487\) 13.2658 + 18.2588i 0.601130 + 0.827385i 0.995811 0.0914336i \(-0.0291449\pi\)
−0.394681 + 0.918818i \(0.629145\pi\)
\(488\) 0.280075 0.385490i 0.0126784 0.0174503i
\(489\) −13.4214 41.3068i −0.606937 1.86796i
\(490\) 11.8541 + 24.7636i 0.535514 + 1.11870i
\(491\) 16.2420 + 11.8005i 0.732991 + 0.532549i 0.890508 0.454967i \(-0.150349\pi\)
−0.157518 + 0.987516i \(0.550349\pi\)
\(492\) −18.6730 25.7012i −0.841845 1.15870i
\(493\) −15.5908 5.06576i −0.702175 0.228150i
\(494\) −30.0141 −1.35040
\(495\) 0 0
\(496\) 1.58993 0.0713898
\(497\) 5.00897 + 1.62751i 0.224683 + 0.0730039i
\(498\) −23.0528 31.7295i −1.03302 1.42183i
\(499\) 3.76342 + 2.73429i 0.168474 + 0.122403i 0.668827 0.743418i \(-0.266797\pi\)
−0.500353 + 0.865821i \(0.666797\pi\)
\(500\) 17.7494 15.2886i 0.793778 0.683726i
\(501\) −7.42334 22.8467i −0.331650 1.02071i
\(502\) 20.1652 27.7550i 0.900017 1.23877i
\(503\) −7.63957 10.5150i −0.340632 0.468839i 0.603994 0.796989i \(-0.293575\pi\)
−0.944626 + 0.328149i \(0.893575\pi\)
\(504\) 0.222597 0.685085i 0.00991528 0.0305161i
\(505\) −4.48232 33.6828i −0.199460 1.49887i
\(506\) 0 0
\(507\) 19.5928i 0.870147i
\(508\) 14.1294 + 4.59091i 0.626889 + 0.203689i
\(509\) 23.9020 17.3658i 1.05944 0.769727i 0.0854540 0.996342i \(-0.472766\pi\)
0.973984 + 0.226615i \(0.0727659\pi\)
\(510\) −34.7993 18.8316i −1.54094 0.833876i
\(511\) 0.428446 + 1.31862i 0.0189533 + 0.0583323i
\(512\) −30.5846 + 9.93755i −1.35166 + 0.439182i
\(513\) −4.37977 + 6.02824i −0.193372 + 0.266153i
\(514\) −7.75350 + 5.63324i −0.341992 + 0.248472i
\(515\) −3.94183 + 21.4353i −0.173698 + 0.944554i
\(516\) 12.4207 0.546793
\(517\) 0 0
\(518\) 12.3869i 0.544248i
\(519\) −3.32804 + 10.2427i −0.146085 + 0.449603i
\(520\) −1.34515 1.41353i −0.0589888 0.0619875i
\(521\) 25.4446 + 18.4866i 1.11475 + 0.809911i 0.983405 0.181426i \(-0.0580712\pi\)
0.131343 + 0.991337i \(0.458071\pi\)
\(522\) −36.5702 + 11.8824i −1.60064 + 0.520078i
\(523\) −8.57873 + 2.78740i −0.375121 + 0.121884i −0.490509 0.871436i \(-0.663189\pi\)
0.115387 + 0.993321i \(0.463189\pi\)
\(524\) 12.2338 + 8.88838i 0.534437 + 0.388291i
\(525\) −7.93663 + 9.85712i −0.346383 + 0.430200i
\(526\) 11.3212 34.8431i 0.493628 1.51923i
\(527\) 1.39595i 0.0608088i
\(528\) 0 0
\(529\) 11.6672 0.507269
\(530\) −11.8414 2.17756i −0.514356 0.0945870i
\(531\) 31.6809 23.0175i 1.37483 0.998875i
\(532\) −3.89867 + 5.36605i −0.169029 + 0.232648i
\(533\) 24.8992 8.09024i 1.07850 0.350427i
\(534\) 19.9875 + 61.5151i 0.864942 + 2.66202i
\(535\) 15.0282 + 8.13249i 0.649727 + 0.351598i
\(536\) −1.49783 + 1.08824i −0.0646965 + 0.0470048i
\(537\) −40.6152 13.1967i −1.75268 0.569479i
\(538\) 4.65046i 0.200496i
\(539\) 0 0
\(540\) −10.5583 + 1.40504i −0.454359 + 0.0604635i
\(541\) −2.64213 + 8.13165i −0.113594 + 0.349607i −0.991651 0.128949i \(-0.958840\pi\)
0.878057 + 0.478556i \(0.158840\pi\)
\(542\) −0.958359 1.31907i −0.0411650 0.0566588i
\(543\) 8.54414 11.7600i 0.366664 0.504670i
\(544\) 8.32748 + 25.6294i 0.357038 + 1.09885i
\(545\) 19.8780 9.51545i 0.851481 0.407597i
\(546\) 18.7510 + 13.6234i 0.802470 + 0.583029i
\(547\) −19.9435 27.4499i −0.852725 1.17367i −0.983256 0.182230i \(-0.941668\pi\)
0.130531 0.991444i \(-0.458332\pi\)
\(548\) 16.9200 + 5.49763i 0.722785 + 0.234847i
\(549\) 9.55608 0.407844
\(550\) 0 0
\(551\) 16.1028 0.686002
\(552\) 1.61802 + 0.525726i 0.0688674 + 0.0223764i
\(553\) −0.569943 0.784459i −0.0242364 0.0333586i
\(554\) 19.3728 + 14.0751i 0.823070 + 0.597995i
\(555\) −33.4969 + 16.0347i −1.42187 + 0.680635i
\(556\) 5.01161 + 15.4241i 0.212540 + 0.654129i
\(557\) 13.4842 18.5594i 0.571342 0.786385i −0.421371 0.906888i \(-0.638451\pi\)
0.992713 + 0.120503i \(0.0384509\pi\)
\(558\) −1.92464 2.64904i −0.0814764 0.112143i
\(559\) −3.16310 + 9.73501i −0.133785 + 0.411747i
\(560\) 8.13565 1.08265i 0.343794 0.0457501i
\(561\) 0 0
\(562\) 12.6061i 0.531757i
\(563\) 8.82830 + 2.86849i 0.372068 + 0.120892i 0.489082 0.872238i \(-0.337332\pi\)
−0.117013 + 0.993130i \(0.537332\pi\)
\(564\) −19.2093 + 13.9564i −0.808859 + 0.587670i
\(565\) −9.86952 5.34087i −0.415214 0.224692i
\(566\) 5.40658 + 16.6397i 0.227255 + 0.699420i
\(567\) −5.18510 + 1.68474i −0.217754 + 0.0707525i
\(568\) 0.618117 0.850765i 0.0259356 0.0356973i
\(569\) 25.0206 18.1785i 1.04892 0.762083i 0.0769109 0.997038i \(-0.475494\pi\)
0.972006 + 0.234955i \(0.0754943\pi\)
\(570\) 38.2261 + 7.02956i 1.60112 + 0.294436i
\(571\) −2.63736 −0.110370 −0.0551851 0.998476i \(-0.517575\pi\)
−0.0551851 + 0.998476i \(0.517575\pi\)
\(572\) 0 0
\(573\) 57.1712i 2.38836i
\(574\) 3.49441 10.7547i 0.145854 0.448892i
\(575\) −13.1106 10.5562i −0.546749 0.440224i
\(576\) 27.3569 + 19.8759i 1.13987 + 0.828164i
\(577\) −34.8377 + 11.3194i −1.45031 + 0.471235i −0.925096 0.379734i \(-0.876015\pi\)
−0.525216 + 0.850969i \(0.676015\pi\)
\(578\) −11.2909 + 3.66863i −0.469638 + 0.152595i
\(579\) −47.6577 34.6253i −1.98058 1.43898i
\(580\) 15.8682 + 16.6749i 0.658891 + 0.692386i
\(581\) 2.20720 6.79308i 0.0915703 0.281824i
\(582\) 16.0118i 0.663710i
\(583\) 0 0
\(584\) 0.276837 0.0114556
\(585\) 7.07768 38.4878i 0.292626 1.59127i
\(586\) 9.51289 6.91152i 0.392974 0.285512i
\(587\) −8.08348 + 11.1259i −0.333641 + 0.459217i −0.942571 0.334007i \(-0.891599\pi\)
0.608930 + 0.793224i \(0.291599\pi\)
\(588\) −31.6839 + 10.2947i −1.30662 + 0.424547i
\(589\) 0.423733 + 1.30412i 0.0174596 + 0.0537352i
\(590\) −40.2961 21.8061i −1.65896 0.897744i
\(591\) −54.5882 + 39.6607i −2.24546 + 1.63142i
\(592\) 22.9060 + 7.44261i 0.941431 + 0.305890i
\(593\) 20.1550i 0.827668i 0.910352 + 0.413834i \(0.135811\pi\)
−0.910352 + 0.413834i \(0.864189\pi\)
\(594\) 0 0
\(595\) −0.950563 7.14310i −0.0389693 0.292839i
\(596\) −10.9316 + 33.6441i −0.447777 + 1.37812i
\(597\) −26.1353 35.9721i −1.06965 1.47224i
\(598\) −18.1200 + 24.9400i −0.740981 + 1.01987i
\(599\) −1.33594 4.11159i −0.0545849 0.167995i 0.920047 0.391807i \(-0.128150\pi\)
−0.974632 + 0.223812i \(0.928150\pi\)
\(600\) 1.38213 + 2.11533i 0.0564253 + 0.0863581i
\(601\) −29.1161 21.1541i −1.18767 0.862894i −0.194655 0.980872i \(-0.562359\pi\)
−0.993016 + 0.117978i \(0.962359\pi\)
\(602\) 2.59873 + 3.57685i 0.105916 + 0.145781i
\(603\) −35.3131 11.4739i −1.43806 0.467255i
\(604\) 25.7358 1.04717
\(605\) 0 0
\(606\) 80.5893 3.27372
\(607\) −37.7092 12.2525i −1.53057 0.497313i −0.581815 0.813321i \(-0.697657\pi\)
−0.948756 + 0.316009i \(0.897657\pi\)
\(608\) −15.5593 21.4155i −0.631011 0.868513i
\(609\) −10.0601 7.30908i −0.407655 0.296179i
\(610\) −4.82758 10.0849i −0.195463 0.408327i
\(611\) −6.04672 18.6099i −0.244624 0.752875i
\(612\) 15.8932 21.8751i 0.642445 0.884250i
\(613\) 2.24234 + 3.08631i 0.0905671 + 0.124655i 0.851896 0.523711i \(-0.175453\pi\)
−0.761329 + 0.648366i \(0.775453\pi\)
\(614\) 11.5516 35.5521i 0.466184 1.43477i
\(615\) −33.6066 + 4.47217i −1.35515 + 0.180335i
\(616\) 0 0
\(617\) 28.4055i 1.14356i −0.820407 0.571781i \(-0.806253\pi\)
0.820407 0.571781i \(-0.193747\pi\)
\(618\) −49.1605 15.9732i −1.97752 0.642537i
\(619\) 19.4737 14.1485i 0.782715 0.568676i −0.123077 0.992397i \(-0.539276\pi\)
0.905793 + 0.423721i \(0.139276\pi\)
\(620\) −0.932886 + 1.72390i −0.0374656 + 0.0692336i
\(621\) 2.36499 + 7.27869i 0.0949037 + 0.292084i
\(622\) 21.8088 7.08610i 0.874452 0.284127i
\(623\) −6.92387 + 9.52989i −0.277399 + 0.381807i
\(624\) −36.4591 + 26.4891i −1.45953 + 1.06041i
\(625\) −5.33439 24.4243i −0.213376 0.976970i
\(626\) 10.3511 0.413714
\(627\) 0 0
\(628\) 8.82059i 0.351980i
\(629\) 6.53462 20.1115i 0.260552 0.801897i
\(630\) −11.6522 12.2446i −0.464235 0.487835i
\(631\) −15.4697 11.2394i −0.615838 0.447432i 0.235627 0.971843i \(-0.424286\pi\)
−0.851465 + 0.524411i \(0.824286\pi\)
\(632\) −0.184132 + 0.0598281i −0.00732438 + 0.00237984i
\(633\) −14.5213 + 4.71824i −0.577168 + 0.187533i
\(634\) −19.3407 14.0518i −0.768115 0.558069i
\(635\) 11.4853 10.9297i 0.455779 0.433731i
\(636\) 4.51464 13.8946i 0.179017 0.550958i
\(637\) 27.4546i 1.08779i
\(638\) 0 0
\(639\) 21.0900 0.834307
\(640\) 0.623212 3.38897i 0.0246346 0.133961i
\(641\) −9.69123 + 7.04109i −0.382780 + 0.278106i −0.762491 0.646999i \(-0.776024\pi\)
0.379710 + 0.925105i \(0.376024\pi\)
\(642\) −23.8208 + 32.7865i −0.940132 + 1.29398i
\(643\) −24.4810 + 7.95435i −0.965435 + 0.313689i −0.748972 0.662602i \(-0.769452\pi\)
−0.216463 + 0.976291i \(0.569452\pi\)
\(644\) 2.10520 + 6.47915i 0.0829566 + 0.255314i
\(645\) 6.30857 11.6578i 0.248400 0.459024i
\(646\) −17.9049 + 13.0086i −0.704457 + 0.511818i
\(647\) 8.84699 + 2.87456i 0.347811 + 0.113011i 0.477712 0.878516i \(-0.341466\pi\)
−0.129901 + 0.991527i \(0.541466\pi\)
\(648\) 1.08858i 0.0427636i
\(649\) 0 0
\(650\) −44.1933 + 11.9740i −1.73341 + 0.469661i
\(651\) 0.327217 1.00707i 0.0128246 0.0394701i
\(652\) −20.4117 28.0943i −0.799384 1.10026i
\(653\) 22.0129 30.2982i 0.861432 1.18566i −0.119794 0.992799i \(-0.538223\pi\)
0.981226 0.192861i \(-0.0617766\pi\)
\(654\) 16.1516 + 49.7094i 0.631576 + 1.94379i
\(655\) 14.5560 6.96785i 0.568750 0.272256i
\(656\) 17.7881 + 12.9238i 0.694510 + 0.504591i
\(657\) 3.26337 + 4.49165i 0.127316 + 0.175236i
\(658\) −8.03815 2.61175i −0.313360 0.101817i
\(659\) 4.93753 0.192339 0.0961693 0.995365i \(-0.469341\pi\)
0.0961693 + 0.995365i \(0.469341\pi\)
\(660\) 0 0
\(661\) −4.82155 −0.187537 −0.0937683 0.995594i \(-0.529891\pi\)
−0.0937683 + 0.995594i \(0.529891\pi\)
\(662\) 56.3327 + 18.3036i 2.18943 + 0.711389i
\(663\) 23.2574 + 32.0111i 0.903244 + 1.24321i
\(664\) −1.15379 0.838280i −0.0447759 0.0325316i
\(665\) 3.05627 + 6.38463i 0.118517 + 0.247585i
\(666\) −15.3278 47.1740i −0.593939 1.82796i
\(667\) 9.72152 13.3805i 0.376419 0.518096i
\(668\) −11.2897 15.5389i −0.436810 0.601217i
\(669\) 15.4044 47.4098i 0.595568 1.83297i
\(670\) 5.73070 + 43.0639i 0.221396 + 1.66370i
\(671\) 0 0
\(672\) 20.4415i 0.788548i
\(673\) −31.3031 10.1710i −1.20665 0.392063i −0.364445 0.931225i \(-0.618741\pi\)
−0.842202 + 0.539162i \(0.818741\pi\)
\(674\) 43.6215 31.6929i 1.68024 1.22077i
\(675\) −4.04391 + 10.6234i −0.155650 + 0.408895i
\(676\) 4.84088 + 14.8987i 0.186188 + 0.573026i
\(677\) −16.3035 + 5.29734i −0.626596 + 0.203593i −0.605067 0.796175i \(-0.706854\pi\)
−0.0215294 + 0.999768i \(0.506854\pi\)
\(678\) 15.6439 21.5320i 0.600800 0.826930i
\(679\) −2.35914 + 1.71401i −0.0905353 + 0.0657778i
\(680\) −1.41510 0.260229i −0.0542666 0.00997931i
\(681\) −74.5977 −2.85859
\(682\) 0 0
\(683\) 19.3586i 0.740737i −0.928885 0.370368i \(-0.879231\pi\)
0.928885 0.370368i \(-0.120769\pi\)
\(684\) −8.20756 + 25.2603i −0.313824 + 0.965851i
\(685\) 13.7537 13.0883i 0.525501 0.500079i
\(686\) −20.6624 15.0121i −0.788892 0.573164i
\(687\) 63.2837 20.5621i 2.41442 0.784494i
\(688\) −8.17580 + 2.65648i −0.311700 + 0.101277i
\(689\) 9.74049 + 7.07688i 0.371083 + 0.269608i
\(690\) 28.9189 27.5199i 1.10092 1.04767i
\(691\) −2.82486 + 8.69404i −0.107463 + 0.330737i −0.990301 0.138941i \(-0.955630\pi\)
0.882838 + 0.469678i \(0.155630\pi\)
\(692\) 8.61097i 0.327340i
\(693\) 0 0
\(694\) 8.72467 0.331184
\(695\) 17.0221 + 3.13026i 0.645685 + 0.118738i
\(696\) −2.00869 + 1.45940i −0.0761390 + 0.0553183i
\(697\) 11.3471 15.6180i 0.429803 0.591573i
\(698\) −25.3465 + 8.23558i −0.959379 + 0.311721i
\(699\) 10.1367 + 31.1976i 0.383406 + 1.18000i
\(700\) −3.59970 + 9.45645i −0.136056 + 0.357420i
\(701\) 12.3727 8.98928i 0.467310 0.339520i −0.329082 0.944301i \(-0.606739\pi\)
0.796392 + 0.604781i \(0.206739\pi\)
\(702\) 19.7995 + 6.43325i 0.747284 + 0.242807i
\(703\) 20.7719i 0.783428i
\(704\) 0 0
\(705\) 3.34254 + 25.1179i 0.125887 + 0.945994i
\(706\) −15.9405 + 49.0597i −0.599927 + 1.84639i
\(707\) 8.62683 + 11.8738i 0.324445 + 0.446561i
\(708\) 32.6792 44.9790i 1.22816 1.69042i
\(709\) −13.2608 40.8126i −0.498020 1.53275i −0.812197 0.583383i \(-0.801729\pi\)
0.314177 0.949364i \(-0.398271\pi\)
\(710\) −10.6543 22.2572i −0.399850 0.835297i
\(711\) −3.14127 2.28226i −0.117807 0.0855916i
\(712\) 1.38248 + 1.90282i 0.0518107 + 0.0713113i
\(713\) 1.33946 + 0.435218i 0.0501633 + 0.0162990i
\(714\) 17.0905 0.639598
\(715\) 0 0
\(716\) −34.1450 −1.27606
\(717\) 50.8126 + 16.5100i 1.89763 + 0.616578i
\(718\) 31.2528 + 43.0158i 1.16635 + 1.60534i
\(719\) 3.89401 + 2.82916i 0.145222 + 0.105510i 0.658024 0.752997i \(-0.271393\pi\)
−0.512802 + 0.858507i \(0.671393\pi\)
\(720\) 29.6440 14.1903i 1.10477 0.528843i
\(721\) −2.90902 8.95305i −0.108338 0.333429i
\(722\) −9.82210 + 13.5190i −0.365541 + 0.503124i
\(723\) −35.1099 48.3246i −1.30575 1.79721i
\(724\) 3.59151 11.0535i 0.133477 0.410801i
\(725\) 23.7101 6.42417i 0.880571 0.238588i
\(726\) 0 0
\(727\) 21.8922i 0.811937i 0.913887 + 0.405969i \(0.133066\pi\)
−0.913887 + 0.405969i \(0.866934\pi\)
\(728\) 0.801566 + 0.260445i 0.0297080 + 0.00965272i
\(729\) −32.1218 + 23.3378i −1.18969 + 0.864364i
\(730\) 3.09163 5.71309i 0.114426 0.211451i
\(731\) 2.33239 + 7.17836i 0.0862665 + 0.265501i
\(732\) 12.9032 4.19252i 0.476918 0.154960i
\(733\) −28.2310 + 38.8567i −1.04274 + 1.43520i −0.147797 + 0.989018i \(0.547218\pi\)
−0.894940 + 0.446187i \(0.852782\pi\)
\(734\) −3.30506 + 2.40127i −0.121992 + 0.0886324i
\(735\) −6.43011 + 34.9664i −0.237178 + 1.28975i
\(736\) −27.1885 −1.00218
\(737\) 0 0
\(738\) 45.2820i 1.66685i
\(739\) 10.5398 32.4380i 0.387711 1.19325i −0.546783 0.837274i \(-0.684148\pi\)
0.934494 0.355978i \(-0.115852\pi\)
\(740\) −21.5098 + 20.4693i −0.790718 + 0.752466i
\(741\) −31.4441 22.8455i −1.15513 0.839251i
\(742\) 4.94586 1.60701i 0.181568 0.0589951i
\(743\) 25.1461 8.17046i 0.922521 0.299745i 0.191020 0.981586i \(-0.438820\pi\)
0.731501 + 0.681841i \(0.238820\pi\)
\(744\) −0.171049 0.124274i −0.00627097 0.00455612i
\(745\) 26.0252 + 27.3482i 0.953488 + 1.00196i
\(746\) 5.54784 17.0745i 0.203121 0.625141i
\(747\) 28.6019i 1.04649i
\(748\) 0 0
\(749\) −7.38062 −0.269682
\(750\) 59.0894 4.89975i 2.15764 0.178914i
\(751\) −37.1665 + 27.0030i −1.35622 + 0.985355i −0.357549 + 0.933894i \(0.616388\pi\)
−0.998675 + 0.0514603i \(0.983612\pi\)
\(752\) 9.65940 13.2950i 0.352242 0.484819i
\(753\) 42.2520 13.7285i 1.53975 0.500295i
\(754\) −13.9027 42.7881i −0.506306 1.55825i
\(755\) 13.0713 24.1549i 0.475715 0.879085i
\(756\) 3.72201 2.70420i 0.135368 0.0983509i
\(757\) 29.3455 + 9.53493i 1.06658 + 0.346553i 0.789155 0.614194i \(-0.210519\pi\)
0.277426 + 0.960747i \(0.410519\pi\)
\(758\) 42.6271i 1.54828i
\(759\) 0 0
\(760\) 1.40099 0.186436i 0.0508194 0.00676275i
\(761\) −4.38726 + 13.5026i −0.159038 + 0.489469i −0.998548 0.0538760i \(-0.982842\pi\)
0.839510 + 0.543345i \(0.182842\pi\)
\(762\) 22.1020 + 30.4208i 0.800672 + 1.10203i
\(763\) −5.59508 + 7.70097i −0.202555 + 0.278794i
\(764\) −14.1255 43.4739i −0.511044 1.57283i
\(765\) −12.4591 26.0274i −0.450461 0.941024i
\(766\) 42.5336 + 30.9024i 1.53680 + 1.11655i
\(767\) 26.9311 + 37.0674i 0.972425 + 1.33843i
\(768\) −35.8102 11.6354i −1.29219 0.419858i
\(769\) 30.0208 1.08258 0.541290 0.840836i \(-0.317936\pi\)
0.541290 + 0.840836i \(0.317936\pi\)
\(770\) 0 0
\(771\) −12.4107 −0.446961
\(772\) −44.7947 14.5547i −1.61220 0.523834i
\(773\) 17.8859 + 24.6179i 0.643313 + 0.885444i 0.998787 0.0492422i \(-0.0156806\pi\)
−0.355474 + 0.934686i \(0.615681\pi\)
\(774\) 14.3230 + 10.4063i 0.514831 + 0.374047i
\(775\) 1.14419 + 1.75116i 0.0411004 + 0.0629036i
\(776\) 0.179924 + 0.553748i 0.00645888 + 0.0198784i
\(777\) 9.42840 12.9771i 0.338242 0.465550i
\(778\) −1.95530 2.69123i −0.0701007 0.0964854i
\(779\) −5.85988 + 18.0348i −0.209952 + 0.646165i
\(780\) −7.32892 55.0739i −0.262417 1.97196i
\(781\) 0 0
\(782\) 22.7315i 0.812876i
\(783\) −10.6226 3.45149i −0.379621 0.123346i
\(784\) 18.6538 13.5527i 0.666206 0.484027i
\(785\) 8.27875 + 4.48003i 0.295481 + 0.159899i
\(786\) 11.8273 + 36.4005i 0.421864 + 1.29836i
\(787\) 28.9737 9.41413i 1.03280 0.335577i 0.256904 0.966437i \(-0.417298\pi\)
0.775897 + 0.630859i \(0.217298\pi\)
\(788\) −31.7106 + 43.6460i −1.12964 + 1.55482i
\(789\) 38.3818 27.8860i 1.36643 0.992768i
\(790\) −0.821653 + 4.46808i −0.0292331 + 0.158967i
\(791\) 4.84709 0.172343
\(792\) 0 0
\(793\) 11.1809i 0.397044i
\(794\) 10.4489 32.1583i 0.370816 1.14126i
\(795\) −10.7481 11.2945i −0.381196 0.400574i
\(796\) −28.7615 20.8964i −1.01942 0.740655i
\(797\) −31.4278 + 10.2115i −1.11323 + 0.361711i −0.807180 0.590305i \(-0.799008\pi\)
−0.306050 + 0.952015i \(0.599008\pi\)
\(798\) −15.9662 + 5.18773i −0.565197 + 0.183644i
\(799\) −11.6730 8.48095i −0.412962 0.300034i
\(800\) −31.4534 25.3253i −1.11205 0.895384i
\(801\) −14.5763 + 44.8613i −0.515028 + 1.58509i
\(802\) 56.2421i 1.98598i
\(803\) 0 0
\(804\) −52.7160 −1.85915
\(805\) 7.15039 + 1.31491i 0.252018 + 0.0463447i
\(806\) 3.09944 2.25187i 0.109173 0.0793189i
\(807\) −3.53975 + 4.87204i −0.124605 + 0.171504i
\(808\) 2.78708 0.905577i 0.0980491 0.0318581i
\(809\) −3.39595 10.4517i −0.119395 0.367461i 0.873443 0.486926i \(-0.161882\pi\)
−0.992838 + 0.119465i \(0.961882\pi\)
\(810\) 22.4651 + 12.1569i 0.789343 + 0.427151i
\(811\) −32.9745 + 23.9573i −1.15789 + 0.841256i −0.989510 0.144466i \(-0.953854\pi\)
−0.168380 + 0.985722i \(0.553854\pi\)
\(812\) −9.45574 3.07235i −0.331831 0.107819i
\(813\) 2.11138i 0.0740494i
\(814\) 0 0
\(815\) −36.7358 + 4.88858i −1.28680 + 0.171240i
\(816\) −10.2688 + 31.6041i −0.359480 + 1.10637i
\(817\) −4.35789 5.99812i −0.152463 0.209848i
\(818\) −46.9052 + 64.5594i −1.64000 + 2.25727i
\(819\) 5.22324 + 16.0755i 0.182515 + 0.561722i
\(820\) −24.4500 + 11.7040i −0.853832 + 0.408723i
\(821\) −12.2223 8.88003i −0.426562 0.309915i 0.353711 0.935355i \(-0.384920\pi\)
−0.780273 + 0.625439i \(0.784920\pi\)
\(822\) 26.4673 + 36.4291i 0.923152 + 1.27061i
\(823\) 34.6482 + 11.2579i 1.20776 + 0.392425i 0.842610 0.538524i \(-0.181018\pi\)
0.365150 + 0.930949i \(0.381018\pi\)
\(824\) −1.87964 −0.0654805
\(825\) 0 0
\(826\) 19.7901 0.688585
\(827\) −3.61727 1.17532i −0.125785 0.0408700i 0.245448 0.969410i \(-0.421065\pi\)
−0.371233 + 0.928540i \(0.621065\pi\)
\(828\) 16.0348 + 22.0701i 0.557250 + 0.766988i
\(829\) −22.0912 16.0502i −0.767261 0.557447i 0.133868 0.990999i \(-0.457260\pi\)
−0.901129 + 0.433552i \(0.857260\pi\)
\(830\) −30.1848 + 14.4492i −1.04773 + 0.501540i
\(831\) 9.58238 + 29.4915i 0.332409 + 1.02305i
\(832\) −23.2553 + 32.0082i −0.806234 + 1.10969i
\(833\) −11.8993 16.3780i −0.412287 0.567464i
\(834\) −12.6845 + 39.0390i −0.439230 + 1.35181i
\(835\) −20.3184 + 2.70386i −0.703148 + 0.0935710i
\(836\) 0 0
\(837\) 0.951115i 0.0328754i
\(838\) −28.4485 9.24348i −0.982738 0.319311i
\(839\) 22.9154 16.6490i 0.791128 0.574788i −0.117170 0.993112i \(-0.537382\pi\)
0.908298 + 0.418324i \(0.137382\pi\)
\(840\) −0.959882 0.519438i −0.0331191 0.0179223i
\(841\) −1.50258 4.62448i −0.0518132 0.159465i
\(842\) 20.7424 6.73960i 0.714829 0.232262i
\(843\) −9.59527 + 13.2068i −0.330479 + 0.454865i
\(844\) −9.87645 + 7.17566i −0.339961 + 0.246996i
\(845\) 16.4422 + 3.02362i 0.565629 + 0.104016i
\(846\) −33.8442 −1.16359
\(847\) 0 0
\(848\) 10.1115i 0.347232i
\(849\) −7.00132 + 21.5478i −0.240285 + 0.739520i
\(850\) −21.1737 + 26.2973i −0.726253 + 0.901990i
\(851\) 17.2603 + 12.5403i 0.591676 + 0.429877i
\(852\) 28.4771 9.25276i 0.975608 0.316994i
\(853\) −7.93484 + 2.57818i −0.271684 + 0.0882754i −0.441690 0.897168i \(-0.645621\pi\)
0.170007 + 0.985443i \(0.445621\pi\)
\(854\) 3.90702 + 2.83862i 0.133695 + 0.0971354i
\(855\) 19.5399 + 20.5332i 0.668251 + 0.702222i
\(856\) −0.455392 + 1.40155i −0.0155650 + 0.0479041i
\(857\) 8.59547i 0.293616i 0.989165 + 0.146808i \(0.0468999\pi\)
−0.989165 + 0.146808i \(0.953100\pi\)
\(858\) 0 0
\(859\) −9.40807 −0.320999 −0.160500 0.987036i \(-0.551311\pi\)
−0.160500 + 0.987036i \(0.551311\pi\)
\(860\) 1.91681 10.4234i 0.0653626 0.355436i
\(861\) 11.8469 8.60731i 0.403743 0.293336i
\(862\) 38.2916 52.7039i 1.30422 1.79510i
\(863\) 9.82067 3.19093i 0.334299 0.108620i −0.137057 0.990563i \(-0.543764\pi\)
0.471357 + 0.881943i \(0.343764\pi\)
\(864\) 5.67382 + 17.4622i 0.193027 + 0.594077i
\(865\) 8.08201 + 4.37356i 0.274797 + 0.148706i
\(866\) 0.626441 0.455136i 0.0212873 0.0154662i
\(867\) −14.6213 4.75074i −0.496564 0.161343i
\(868\) 0.846638i 0.0287368i
\(869\) 0 0
\(870\) 7.68522 + 57.7514i 0.260553 + 1.95795i
\(871\) 13.4248 41.3173i 0.454882 1.39998i
\(872\) 1.11716 + 1.53764i 0.0378319 + 0.0520712i
\(873\) −6.86355 + 9.44686i −0.232296 + 0.319728i
\(874\) −6.89999 21.2360i −0.233396 0.718318i
\(875\) 7.04725 + 8.18157i 0.238240 + 0.276588i
\(876\) 6.37703 + 4.63318i 0.215460 + 0.156541i
\(877\) 17.5179 + 24.1113i 0.591536 + 0.814180i 0.994901 0.100859i \(-0.0321593\pi\)
−0.403364 + 0.915039i \(0.632159\pi\)
\(878\) −51.0665 16.5925i −1.72341 0.559970i
\(879\) 15.2269 0.513591
\(880\) 0 0
\(881\) 30.1175 1.01469 0.507343 0.861744i \(-0.330628\pi\)
0.507343 + 0.861744i \(0.330628\pi\)
\(882\) −45.1615 14.6739i −1.52067 0.494095i
\(883\) −29.6020 40.7436i −0.996185 1.37113i −0.927637 0.373484i \(-0.878163\pi\)
−0.0685488 0.997648i \(-0.521837\pi\)
\(884\) 25.5945 + 18.5955i 0.860835 + 0.625433i
\(885\) −25.6181 53.5169i −0.861143 1.79895i
\(886\) 9.06824 + 27.9092i 0.304653 + 0.937627i
\(887\) −24.3375 + 33.4977i −0.817173 + 1.12474i 0.173003 + 0.984921i \(0.444653\pi\)
−0.990177 + 0.139821i \(0.955347\pi\)
\(888\) −1.88256 2.59112i −0.0631745 0.0869522i
\(889\) −2.11617 + 6.51291i −0.0709741 + 0.218436i
\(890\) 54.7077 7.28019i 1.83381 0.244033i
\(891\) 0 0
\(892\) 39.8572i 1.33452i
\(893\) 13.4794 + 4.37973i 0.451071 + 0.146562i
\(894\) −72.4365 + 52.6282i −2.42264 + 1.76015i
\(895\) −17.3425 + 32.0476i −0.579695 + 1.07123i
\(896\) 0.459923 + 1.41550i 0.0153649 + 0.0472884i
\(897\) −37.9667 + 12.3361i −1.26767 + 0.411891i
\(898\) −12.0305 + 16.5586i −0.401463 + 0.552567i
\(899\) −1.66287 + 1.20815i −0.0554600 + 0.0402940i
\(900\) −2.00746 + 40.4682i −0.0669153 + 1.34894i
\(901\) 8.87793 0.295767
\(902\) 0 0
\(903\) 5.72532i 0.190527i
\(904\) 0.299071 0.920445i 0.00994694 0.0306135i
\(905\) −8.55038 8.98504i −0.284224 0.298673i
\(906\) 52.6977 + 38.2872i 1.75077 + 1.27201i
\(907\) −4.40544 + 1.43142i −0.146280 + 0.0475294i −0.381242 0.924475i \(-0.624504\pi\)
0.234962 + 0.972005i \(0.424504\pi\)
\(908\) −56.7253 + 18.4312i −1.88249 + 0.611660i
\(909\) 47.5472 + 34.5451i 1.57704 + 1.14579i
\(910\) 14.3264 13.6334i 0.474917 0.451942i
\(911\) 2.15649 6.63699i 0.0714477 0.219893i −0.908956 0.416892i \(-0.863119\pi\)
0.980404 + 0.196998i \(0.0631194\pi\)
\(912\) 32.6419i 1.08088i
\(913\) 0 0
\(914\) 79.1032 2.61650
\(915\) 2.61866 14.2400i 0.0865701 0.470761i
\(916\) 43.0416 31.2716i 1.42213 1.03324i
\(917\) −4.09709 + 5.63916i −0.135298 + 0.186221i
\(918\) 14.5997 4.74372i 0.481860 0.156566i
\(919\) 7.23738 + 22.2744i 0.238739 + 0.734763i 0.996603 + 0.0823512i \(0.0262429\pi\)
−0.757864 + 0.652412i \(0.773757\pi\)
\(920\) 0.690884 1.27670i 0.0227778 0.0420916i
\(921\) 39.1628 28.4535i 1.29046 0.937574i
\(922\) 75.3154 + 24.4714i 2.48038 + 0.805924i
\(923\) 24.6758i 0.812215i
\(924\) 0 0
\(925\) 8.28691 + 30.5850i 0.272472 + 1.00563i
\(926\) 8.07887 24.8642i 0.265488 0.817088i
\(927\) −22.1574 30.4970i −0.727744 1.00165i
\(928\) 23.3228 32.1011i 0.765608 1.05377i
\(929\) 5.59027 + 17.2051i 0.183411 + 0.564480i 0.999917 0.0128560i \(-0.00409231\pi\)
−0.816507 + 0.577336i \(0.804092\pi\)
\(930\) −4.47488 + 2.14209i −0.146737 + 0.0702418i
\(931\) 16.0879 + 11.6886i 0.527260 + 0.383077i
\(932\) 15.4162 + 21.2186i 0.504976 + 0.695039i
\(933\) 28.2415 + 9.17623i 0.924586 + 0.300416i
\(934\) −22.7646 −0.744881
\(935\) 0 0
\(936\) 3.37495 0.110314
\(937\) −10.4708 3.40215i −0.342065 0.111144i 0.132947 0.991123i \(-0.457556\pi\)
−0.475011 + 0.879980i \(0.657556\pi\)
\(938\) −11.0295 15.1808i −0.360127 0.495672i
\(939\) 10.8443 + 7.87885i 0.353891 + 0.257117i
\(940\) 8.74771 + 18.2742i 0.285319 + 0.596038i
\(941\) 10.4388 + 32.1275i 0.340297 + 1.04733i 0.964054 + 0.265707i \(0.0856055\pi\)
−0.623757 + 0.781618i \(0.714395\pi\)
\(942\) −13.1224 + 18.0615i −0.427551 + 0.588474i
\(943\) 11.4482 + 15.7572i 0.372806 + 0.513124i
\(944\) −11.8908 + 36.5961i −0.387013 + 1.19110i
\(945\) −0.647654 4.86686i −0.0210682 0.158319i
\(946\) 0 0
\(947\) 46.9853i 1.52682i 0.645915 + 0.763409i \(0.276476\pi\)
−0.645915 + 0.763409i \(0.723524\pi\)
\(948\) −5.24284 1.70350i −0.170279 0.0553271i
\(949\) −5.25534 + 3.81823i −0.170596 + 0.123945i
\(950\) 11.7984 30.9944i 0.382789 1.00559i
\(951\) −9.56650 29.4427i −0.310215 0.954744i
\(952\) 0.591055 0.192045i 0.0191562 0.00622423i
\(953\) 24.9754 34.3757i 0.809032 1.11354i −0.182440 0.983217i \(-0.558400\pi\)
0.991472 0.130320i \(-0.0416005\pi\)
\(954\) 16.8472 12.2402i 0.545449 0.396292i
\(955\) −47.9778 8.82284i −1.55253 0.285500i
\(956\) 42.7180 1.38160
\(957\) 0 0
\(958\) 42.4291i 1.37082i
\(959\) −2.53413 + 7.79924i −0.0818312 + 0.251850i
\(960\) 37.1148 35.3193i 1.19787 1.13993i
\(961\) 24.9379 + 18.1185i 0.804449 + 0.584467i
\(962\) 55.1948 17.9339i 1.77955 0.578211i
\(963\) −28.1082 + 9.13292i −0.905776 + 0.294304i
\(964\) −38.6379 28.0721i −1.24444 0.904140i
\(965\) −36.4121 + 34.6506i −1.17215 + 1.11544i
\(966\) −5.32833 + 16.3989i −0.171436 + 0.527627i
\(967\) 54.1642i 1.74180i −0.491458 0.870901i \(-0.663536\pi\)
0.491458 0.870901i \(-0.336464\pi\)
\(968\) 0 0
\(969\) −28.6596 −0.920680
\(970\) 13.4370 + 2.47099i 0.431437 + 0.0793388i
\(971\) −4.23802 + 3.07910i −0.136004 + 0.0988130i −0.653707 0.756747i \(-0.726787\pi\)
0.517703 + 0.855560i \(0.326787\pi\)
\(972\) −26.6184 + 36.6370i −0.853784 + 1.17513i
\(973\) −7.10974 + 2.31009i −0.227928 + 0.0740582i
\(974\) 14.1136 + 43.4373i 0.452230 + 1.39182i
\(975\) −55.4132 21.0936i −1.77464 0.675537i
\(976\) −7.59673 + 5.51935i −0.243165 + 0.176670i
\(977\) 7.40057 + 2.40459i 0.236765 + 0.0769297i 0.424996 0.905195i \(-0.360275\pi\)
−0.188231 + 0.982125i \(0.560275\pi\)
\(978\) 87.8938i 2.81053i
\(979\) 0 0
\(980\) 3.74973 + 28.1777i 0.119781 + 0.900104i
\(981\) −11.7789 + 36.2517i −0.376071 + 1.15743i
\(982\) 23.8805 + 32.8686i 0.762056 + 1.04888i
\(983\) 30.2789 41.6754i 0.965748 1.32924i 0.0215828 0.999767i \(-0.493129\pi\)
0.944166 0.329471i \(-0.106871\pi\)
\(984\) −0.903528 2.78077i −0.0288034 0.0886478i
\(985\) 24.8588 + 51.9308i 0.792068 + 1.65465i
\(986\) −26.8388 19.4995i −0.854721 0.620991i
\(987\) −6.43318 8.85452i −0.204771 0.281842i
\(988\) −29.5552 9.60306i −0.940276 0.305514i
\(989\) −7.61503 −0.242144
\(990\) 0 0
\(991\) −22.3382 −0.709596 −0.354798 0.934943i \(-0.615450\pi\)
−0.354798 + 0.934943i \(0.615450\pi\)
\(992\) 3.21349 + 1.04413i 0.102028 + 0.0331511i
\(993\) 45.0848 + 62.0539i 1.43072 + 1.96922i
\(994\) 8.62267 + 6.26474i 0.273495 + 0.198705i
\(995\) −34.2209 + 16.3813i −1.08488 + 0.519322i
\(996\) −12.5484 38.6201i −0.397613 1.22373i
\(997\) −0.108473 + 0.149301i −0.00343539 + 0.00472840i −0.810731 0.585419i \(-0.800930\pi\)
0.807296 + 0.590147i \(0.200930\pi\)
\(998\) 5.53333 + 7.61597i 0.175154 + 0.241079i
\(999\) 4.45227 13.7027i 0.140864 0.433534i
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 605.2.j.h.9.4 16
5.4 even 2 inner 605.2.j.h.9.1 16
11.2 odd 10 605.2.j.d.124.4 16
11.3 even 5 55.2.j.a.4.4 yes 16
11.4 even 5 605.2.b.g.364.8 8
11.5 even 5 inner 605.2.j.h.269.1 16
11.6 odd 10 605.2.j.g.269.4 16
11.7 odd 10 605.2.b.f.364.1 8
11.8 odd 10 605.2.j.d.444.1 16
11.9 even 5 55.2.j.a.14.1 yes 16
11.10 odd 2 605.2.j.g.9.1 16
33.14 odd 10 495.2.ba.a.334.1 16
33.20 odd 10 495.2.ba.a.289.4 16
44.3 odd 10 880.2.cd.c.609.4 16
44.31 odd 10 880.2.cd.c.289.1 16
55.3 odd 20 275.2.h.d.26.1 16
55.4 even 10 605.2.b.g.364.1 8
55.7 even 20 3025.2.a.bk.1.8 8
55.9 even 10 55.2.j.a.14.4 yes 16
55.14 even 10 55.2.j.a.4.1 16
55.18 even 20 3025.2.a.bk.1.1 8
55.19 odd 10 605.2.j.d.444.4 16
55.24 odd 10 605.2.j.d.124.1 16
55.29 odd 10 605.2.b.f.364.8 8
55.37 odd 20 3025.2.a.bl.1.1 8
55.39 odd 10 605.2.j.g.269.1 16
55.42 odd 20 275.2.h.d.201.4 16
55.47 odd 20 275.2.h.d.26.4 16
55.48 odd 20 3025.2.a.bl.1.8 8
55.49 even 10 inner 605.2.j.h.269.4 16
55.53 odd 20 275.2.h.d.201.1 16
55.54 odd 2 605.2.j.g.9.4 16
165.14 odd 10 495.2.ba.a.334.4 16
165.119 odd 10 495.2.ba.a.289.1 16
220.119 odd 10 880.2.cd.c.289.4 16
220.179 odd 10 880.2.cd.c.609.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.j.a.4.1 16 55.14 even 10
55.2.j.a.4.4 yes 16 11.3 even 5
55.2.j.a.14.1 yes 16 11.9 even 5
55.2.j.a.14.4 yes 16 55.9 even 10
275.2.h.d.26.1 16 55.3 odd 20
275.2.h.d.26.4 16 55.47 odd 20
275.2.h.d.201.1 16 55.53 odd 20
275.2.h.d.201.4 16 55.42 odd 20
495.2.ba.a.289.1 16 165.119 odd 10
495.2.ba.a.289.4 16 33.20 odd 10
495.2.ba.a.334.1 16 33.14 odd 10
495.2.ba.a.334.4 16 165.14 odd 10
605.2.b.f.364.1 8 11.7 odd 10
605.2.b.f.364.8 8 55.29 odd 10
605.2.b.g.364.1 8 55.4 even 10
605.2.b.g.364.8 8 11.4 even 5
605.2.j.d.124.1 16 55.24 odd 10
605.2.j.d.124.4 16 11.2 odd 10
605.2.j.d.444.1 16 11.8 odd 10
605.2.j.d.444.4 16 55.19 odd 10
605.2.j.g.9.1 16 11.10 odd 2
605.2.j.g.9.4 16 55.54 odd 2
605.2.j.g.269.1 16 55.39 odd 10
605.2.j.g.269.4 16 11.6 odd 10
605.2.j.h.9.1 16 5.4 even 2 inner
605.2.j.h.9.4 16 1.1 even 1 trivial
605.2.j.h.269.1 16 11.5 even 5 inner
605.2.j.h.269.4 16 55.49 even 10 inner
880.2.cd.c.289.1 16 44.31 odd 10
880.2.cd.c.289.4 16 220.119 odd 10
880.2.cd.c.609.1 16 220.179 odd 10
880.2.cd.c.609.4 16 44.3 odd 10
3025.2.a.bk.1.1 8 55.18 even 20
3025.2.a.bk.1.8 8 55.7 even 20
3025.2.a.bl.1.1 8 55.37 odd 20
3025.2.a.bl.1.8 8 55.48 odd 20