Properties

Label 605.2.g.l.511.1
Level $605$
Weight $2$
Character 605.511
Analytic conductor $4.831$
Analytic rank $0$
Dimension $8$
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(81,605)]
 
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([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("605.81");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.g (of order \(5\), 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: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.64000000.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 55)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 511.1
Root \(1.14412 + 0.831254i\) of defining polynomial
Character \(\chi\) \(=\) 605.511
Dual form 605.2.g.l.251.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.746033 - 2.29605i) q^{2} +(2.28825 + 1.66251i) q^{3} +(-3.09726 + 2.25029i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(2.11010 - 6.49422i) q^{6} +(-1.61803 + 1.17557i) q^{7} +(3.57117 + 2.59461i) q^{8} +(1.54508 + 4.75528i) q^{9} +O(q^{10})\) \(q+(-0.746033 - 2.29605i) q^{2} +(2.28825 + 1.66251i) q^{3} +(-3.09726 + 2.25029i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(2.11010 - 6.49422i) q^{6} +(-1.61803 + 1.17557i) q^{7} +(3.57117 + 2.59461i) q^{8} +(1.54508 + 4.75528i) q^{9} +2.41421 q^{10} -10.8284 q^{12} +(0.362036 + 1.11423i) q^{13} +(3.90628 + 2.83808i) q^{14} +(-2.28825 + 1.66251i) q^{15} +(0.927051 - 2.85317i) q^{16} +(-2.11010 + 6.49422i) q^{17} +(9.76570 - 7.09520i) q^{18} +(-1.18305 - 3.64105i) q^{20} -5.65685 q^{21} -2.82843 q^{23} +(3.85816 + 11.8742i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(2.28825 - 1.66251i) q^{26} +(-1.74806 + 5.37999i) q^{27} +(2.36610 - 7.28210i) q^{28} +(-2.95846 + 2.14944i) q^{29} +(5.52431 + 4.01365i) q^{30} +1.58579 q^{32} +16.4853 q^{34} +(-0.618034 - 1.90211i) q^{35} +(-15.4863 - 11.2515i) q^{36} +(6.19453 - 4.50059i) q^{37} +(-1.02399 + 3.15152i) q^{39} +(-3.57117 + 2.59461i) q^{40} +(4.85410 + 3.52671i) q^{41} +(4.22020 + 12.9884i) q^{42} +6.00000 q^{43} -5.00000 q^{45} +(2.11010 + 6.49422i) q^{46} +(-2.28825 - 1.66251i) q^{47} +(6.86474 - 4.98752i) q^{48} +(-0.927051 + 2.85317i) q^{49} +(-0.746033 + 2.29605i) q^{50} +(-15.6251 + 11.3523i) q^{51} +(-3.62867 - 2.63638i) q^{52} +(3.60217 + 11.0863i) q^{53} +13.6569 q^{54} -8.82843 q^{56} +(7.14235 + 5.18922i) q^{58} +(-1.34042 + 0.973874i) q^{59} +(3.34617 - 10.2984i) q^{60} +(2.87809 - 8.85786i) q^{61} +(-8.09017 - 5.87785i) q^{63} +(-3.03715 - 9.34739i) q^{64} -1.17157 q^{65} +12.4853 q^{67} +(-8.07836 - 24.8626i) q^{68} +(-6.47214 - 4.70228i) q^{69} +(-3.90628 + 2.83808i) q^{70} +(3.49613 - 10.7600i) q^{71} +(-6.82034 + 20.9908i) q^{72} +(-0.947822 + 0.688633i) q^{73} +(-14.9549 - 10.8654i) q^{74} +(-0.874032 - 2.68999i) q^{75} +8.00000 q^{78} +(-1.23607 - 3.80423i) q^{79} +(2.42705 + 1.76336i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(4.47620 - 13.7763i) q^{82} +(1.85410 - 5.70634i) q^{83} +(17.5208 - 12.7296i) q^{84} +(-5.52431 - 4.01365i) q^{85} +(-4.47620 - 13.7763i) q^{86} -10.3431 q^{87} -13.3137 q^{89} +(3.73017 + 11.4803i) q^{90} +(-1.89564 - 1.37727i) q^{91} +(8.76038 - 6.36479i) q^{92} +(-2.11010 + 6.49422i) q^{94} +(3.62867 + 2.63638i) q^{96} +(1.13003 + 3.47788i) q^{97} +7.24264 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{8} - 10 q^{9} + 8 q^{10} - 64 q^{12} - 8 q^{13} + 4 q^{14} - 6 q^{16} + 8 q^{17} + 10 q^{18} + 2 q^{20} - 8 q^{24} - 2 q^{25} - 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{32} + 64 q^{34} + 4 q^{35} - 10 q^{36} + 4 q^{37} - 16 q^{39} - 6 q^{40} + 12 q^{41} - 16 q^{42} + 48 q^{43} - 40 q^{45} - 8 q^{46} + 6 q^{49} + 2 q^{50} - 16 q^{51} + 8 q^{52} - 12 q^{53} + 64 q^{54} - 48 q^{56} + 12 q^{58} + 8 q^{59} - 16 q^{60} + 4 q^{61} - 20 q^{63} + 14 q^{64} - 32 q^{65} + 32 q^{67} + 24 q^{68} - 16 q^{69} - 4 q^{70} + 30 q^{72} - 8 q^{73} - 20 q^{74} + 64 q^{78} + 8 q^{79} + 6 q^{80} - 2 q^{81} - 12 q^{82} - 12 q^{83} + 32 q^{84} - 8 q^{85} + 12 q^{86} - 128 q^{87} - 16 q^{89} - 10 q^{90} - 16 q^{91} + 16 q^{92} + 8 q^{94} - 8 q^{96} + 4 q^{97} + 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(122\) \(486\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.746033 2.29605i −0.527525 1.62356i −0.759268 0.650778i \(-0.774443\pi\)
0.231743 0.972777i \(-0.425557\pi\)
\(3\) 2.28825 + 1.66251i 1.32112 + 0.959849i 0.999918 + 0.0128385i \(0.00408672\pi\)
0.321202 + 0.947011i \(0.395913\pi\)
\(4\) −3.09726 + 2.25029i −1.54863 + 1.12515i
\(5\) −0.309017 + 0.951057i −0.138197 + 0.425325i
\(6\) 2.11010 6.49422i 0.861445 2.65125i
\(7\) −1.61803 + 1.17557i −0.611559 + 0.444324i −0.849963 0.526842i \(-0.823376\pi\)
0.238404 + 0.971166i \(0.423376\pi\)
\(8\) 3.57117 + 2.59461i 1.26260 + 0.917333i
\(9\) 1.54508 + 4.75528i 0.515028 + 1.58509i
\(10\) 2.41421 0.763441
\(11\) 0 0
\(12\) −10.8284 −3.12590
\(13\) 0.362036 + 1.11423i 0.100411 + 0.309032i 0.988626 0.150395i \(-0.0480546\pi\)
−0.888215 + 0.459428i \(0.848055\pi\)
\(14\) 3.90628 + 2.83808i 1.04400 + 0.758508i
\(15\) −2.28825 + 1.66251i −0.590822 + 0.429258i
\(16\) 0.927051 2.85317i 0.231763 0.713292i
\(17\) −2.11010 + 6.49422i −0.511774 + 1.57508i 0.277301 + 0.960783i \(0.410560\pi\)
−0.789075 + 0.614297i \(0.789440\pi\)
\(18\) 9.76570 7.09520i 2.30180 1.67235i
\(19\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(20\) −1.18305 3.64105i −0.264538 0.814164i
\(21\) −5.65685 −1.23443
\(22\) 0 0
\(23\) −2.82843 −0.589768 −0.294884 0.955533i \(-0.595281\pi\)
−0.294884 + 0.955533i \(0.595281\pi\)
\(24\) 3.85816 + 11.8742i 0.787544 + 2.42381i
\(25\) −0.809017 0.587785i −0.161803 0.117557i
\(26\) 2.28825 1.66251i 0.448762 0.326045i
\(27\) −1.74806 + 5.37999i −0.336415 + 1.03538i
\(28\) 2.36610 7.28210i 0.447151 1.37619i
\(29\) −2.95846 + 2.14944i −0.549372 + 0.399142i −0.827554 0.561386i \(-0.810268\pi\)
0.278182 + 0.960528i \(0.410268\pi\)
\(30\) 5.52431 + 4.01365i 1.00860 + 0.732789i
\(31\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(32\) 1.58579 0.280330
\(33\) 0 0
\(34\) 16.4853 2.82720
\(35\) −0.618034 1.90211i −0.104467 0.321516i
\(36\) −15.4863 11.2515i −2.58105 1.87524i
\(37\) 6.19453 4.50059i 1.01837 0.739892i 0.0524248 0.998625i \(-0.483305\pi\)
0.965949 + 0.258733i \(0.0833050\pi\)
\(38\) 0 0
\(39\) −1.02399 + 3.15152i −0.163970 + 0.504648i
\(40\) −3.57117 + 2.59461i −0.564652 + 0.410244i
\(41\) 4.85410 + 3.52671i 0.758083 + 0.550780i 0.898322 0.439338i \(-0.144787\pi\)
−0.140238 + 0.990118i \(0.544787\pi\)
\(42\) 4.22020 + 12.9884i 0.651191 + 2.00416i
\(43\) 6.00000 0.914991 0.457496 0.889212i \(-0.348747\pi\)
0.457496 + 0.889212i \(0.348747\pi\)
\(44\) 0 0
\(45\) −5.00000 −0.745356
\(46\) 2.11010 + 6.49422i 0.311117 + 0.957521i
\(47\) −2.28825 1.66251i −0.333775 0.242502i 0.408256 0.912868i \(-0.366137\pi\)
−0.742031 + 0.670366i \(0.766137\pi\)
\(48\) 6.86474 4.98752i 0.990839 0.719887i
\(49\) −0.927051 + 2.85317i −0.132436 + 0.407596i
\(50\) −0.746033 + 2.29605i −0.105505 + 0.324711i
\(51\) −15.6251 + 11.3523i −2.18795 + 1.58964i
\(52\) −3.62867 2.63638i −0.503206 0.365600i
\(53\) 3.60217 + 11.0863i 0.494796 + 1.52282i 0.817275 + 0.576248i \(0.195484\pi\)
−0.322480 + 0.946576i \(0.604516\pi\)
\(54\) 13.6569 1.85846
\(55\) 0 0
\(56\) −8.82843 −1.17975
\(57\) 0 0
\(58\) 7.14235 + 5.18922i 0.937836 + 0.681378i
\(59\) −1.34042 + 0.973874i −0.174508 + 0.126788i −0.671611 0.740904i \(-0.734397\pi\)
0.497103 + 0.867692i \(0.334397\pi\)
\(60\) 3.34617 10.2984i 0.431988 1.32952i
\(61\) 2.87809 8.85786i 0.368502 1.13413i −0.579257 0.815145i \(-0.696657\pi\)
0.947759 0.318988i \(-0.103343\pi\)
\(62\) 0 0
\(63\) −8.09017 5.87785i −1.01927 0.740540i
\(64\) −3.03715 9.34739i −0.379644 1.16842i
\(65\) −1.17157 −0.145316
\(66\) 0 0
\(67\) 12.4853 1.52532 0.762660 0.646800i \(-0.223893\pi\)
0.762660 + 0.646800i \(0.223893\pi\)
\(68\) −8.07836 24.8626i −0.979646 3.01504i
\(69\) −6.47214 4.70228i −0.779154 0.566088i
\(70\) −3.90628 + 2.83808i −0.466890 + 0.339215i
\(71\) 3.49613 10.7600i 0.414914 1.27697i −0.497414 0.867513i \(-0.665717\pi\)
0.912328 0.409461i \(-0.134283\pi\)
\(72\) −6.82034 + 20.9908i −0.803784 + 2.47379i
\(73\) −0.947822 + 0.688633i −0.110934 + 0.0805984i −0.641869 0.766814i \(-0.721841\pi\)
0.530935 + 0.847413i \(0.321841\pi\)
\(74\) −14.9549 10.8654i −1.73847 1.26307i
\(75\) −0.874032 2.68999i −0.100925 0.310614i
\(76\) 0 0
\(77\) 0 0
\(78\) 8.00000 0.905822
\(79\) −1.23607 3.80423i −0.139069 0.428009i 0.857132 0.515097i \(-0.172244\pi\)
−0.996201 + 0.0870877i \(0.972244\pi\)
\(80\) 2.42705 + 1.76336i 0.271353 + 0.197149i
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) 4.47620 13.7763i 0.494313 1.52134i
\(83\) 1.85410 5.70634i 0.203514 0.626352i −0.796257 0.604959i \(-0.793190\pi\)
0.999771 0.0213936i \(-0.00681031\pi\)
\(84\) 17.5208 12.7296i 1.91167 1.38891i
\(85\) −5.52431 4.01365i −0.599196 0.435341i
\(86\) −4.47620 13.7763i −0.482681 1.48554i
\(87\) −10.3431 −1.10890
\(88\) 0 0
\(89\) −13.3137 −1.41125 −0.705625 0.708585i \(-0.749334\pi\)
−0.705625 + 0.708585i \(0.749334\pi\)
\(90\) 3.73017 + 11.4803i 0.393194 + 1.21013i
\(91\) −1.89564 1.37727i −0.198718 0.144377i
\(92\) 8.76038 6.36479i 0.913333 0.663575i
\(93\) 0 0
\(94\) −2.11010 + 6.49422i −0.217640 + 0.669828i
\(95\) 0 0
\(96\) 3.62867 + 2.63638i 0.370349 + 0.269075i
\(97\) 1.13003 + 3.47788i 0.114737 + 0.353125i 0.991892 0.127083i \(-0.0405614\pi\)
−0.877155 + 0.480207i \(0.840561\pi\)
\(98\) 7.24264 0.731617
\(99\) 0 0
\(100\) 3.82843 0.382843
\(101\) −2.87809 8.85786i −0.286381 0.881390i −0.985981 0.166856i \(-0.946639\pi\)
0.699600 0.714534i \(-0.253361\pi\)
\(102\) 37.7224 + 27.4069i 3.73507 + 2.71369i
\(103\) −5.52431 + 4.01365i −0.544327 + 0.395477i −0.825689 0.564125i \(-0.809214\pi\)
0.281363 + 0.959602i \(0.409214\pi\)
\(104\) −1.59810 + 4.91846i −0.156707 + 0.482294i
\(105\) 1.74806 5.37999i 0.170594 0.525033i
\(106\) 22.7675 16.5415i 2.21137 1.60666i
\(107\) 6.19453 + 4.50059i 0.598847 + 0.435088i 0.845470 0.534024i \(-0.179321\pi\)
−0.246622 + 0.969112i \(0.579321\pi\)
\(108\) −6.69234 20.5969i −0.643970 1.98194i
\(109\) 7.65685 0.733394 0.366697 0.930341i \(-0.380489\pi\)
0.366697 + 0.930341i \(0.380489\pi\)
\(110\) 0 0
\(111\) 21.6569 2.05558
\(112\) 1.85410 + 5.70634i 0.175196 + 0.539198i
\(113\) −15.9027 11.5540i −1.49600 1.08691i −0.971940 0.235230i \(-0.924416\pi\)
−0.524063 0.851679i \(-0.675584\pi\)
\(114\) 0 0
\(115\) 0.874032 2.68999i 0.0815039 0.250843i
\(116\) 4.32624 13.3148i 0.401681 1.23625i
\(117\) −4.73911 + 3.44317i −0.438131 + 0.318321i
\(118\) 3.23607 + 2.35114i 0.297904 + 0.216440i
\(119\) −4.22020 12.9884i −0.386865 1.19065i
\(120\) −12.4853 −1.13975
\(121\) 0 0
\(122\) −22.4853 −2.03572
\(123\) 5.24419 + 16.1400i 0.472853 + 1.45529i
\(124\) 0 0
\(125\) 0.809017 0.587785i 0.0723607 0.0525731i
\(126\) −7.46033 + 22.9605i −0.664619 + 2.04549i
\(127\) −1.34211 + 4.13058i −0.119093 + 0.366529i −0.992779 0.119961i \(-0.961723\pi\)
0.873686 + 0.486490i \(0.161723\pi\)
\(128\) −16.6304 + 12.0827i −1.46994 + 1.06797i
\(129\) 13.7295 + 9.97505i 1.20881 + 0.878254i
\(130\) 0.874032 + 2.68999i 0.0766577 + 0.235928i
\(131\) 11.3137 0.988483 0.494242 0.869325i \(-0.335446\pi\)
0.494242 + 0.869325i \(0.335446\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −9.31443 28.6669i −0.804644 2.47644i
\(135\) −4.57649 3.32502i −0.393882 0.286172i
\(136\) −24.3855 + 17.7171i −2.09104 + 1.51923i
\(137\) −3.39009 + 10.4336i −0.289635 + 0.891405i 0.695336 + 0.718685i \(0.255256\pi\)
−0.984971 + 0.172720i \(0.944744\pi\)
\(138\) −5.96826 + 18.3684i −0.508052 + 1.56362i
\(139\) −3.23607 + 2.35114i −0.274480 + 0.199421i −0.716506 0.697581i \(-0.754260\pi\)
0.442026 + 0.897002i \(0.354260\pi\)
\(140\) 6.19453 + 4.50059i 0.523533 + 0.380369i
\(141\) −2.47214 7.60845i −0.208191 0.640747i
\(142\) −27.3137 −2.29212
\(143\) 0 0
\(144\) 15.0000 1.25000
\(145\) −1.13003 3.47788i −0.0938439 0.288822i
\(146\) 2.28825 + 1.66251i 0.189377 + 0.137590i
\(147\) −6.86474 + 4.98752i −0.566194 + 0.411364i
\(148\) −9.05843 + 27.8790i −0.744599 + 2.29164i
\(149\) −0.106038 + 0.326351i −0.00868696 + 0.0267357i −0.955306 0.295619i \(-0.904474\pi\)
0.946619 + 0.322354i \(0.104474\pi\)
\(150\) −5.52431 + 4.01365i −0.451058 + 0.327713i
\(151\) −9.70820 7.05342i −0.790042 0.573999i 0.117934 0.993021i \(-0.462373\pi\)
−0.907976 + 0.419022i \(0.862373\pi\)
\(152\) 0 0
\(153\) −34.1421 −2.76023
\(154\) 0 0
\(155\) 0 0
\(156\) −3.92028 12.0654i −0.313874 0.966004i
\(157\) 11.3262 + 8.22899i 0.903932 + 0.656745i 0.939473 0.342623i \(-0.111315\pi\)
−0.0355408 + 0.999368i \(0.511315\pi\)
\(158\) −7.81256 + 5.67616i −0.621534 + 0.451571i
\(159\) −10.1885 + 31.3569i −0.807998 + 2.48676i
\(160\) −0.490035 + 1.50817i −0.0387407 + 0.119232i
\(161\) 4.57649 3.32502i 0.360678 0.262048i
\(162\) 1.95314 + 1.41904i 0.153453 + 0.111490i
\(163\) 5.09423 + 15.6784i 0.399011 + 1.22803i 0.925794 + 0.378030i \(0.123398\pi\)
−0.526782 + 0.850000i \(0.676602\pi\)
\(164\) −22.9706 −1.79370
\(165\) 0 0
\(166\) −14.4853 −1.12428
\(167\) 7.09829 + 21.8463i 0.549283 + 1.69052i 0.710584 + 0.703613i \(0.248431\pi\)
−0.161301 + 0.986905i \(0.551569\pi\)
\(168\) −20.2016 14.6773i −1.55859 1.13238i
\(169\) 9.40678 6.83442i 0.723598 0.525725i
\(170\) −5.09423 + 15.6784i −0.390710 + 1.20248i
\(171\) 0 0
\(172\) −18.5836 + 13.5018i −1.41698 + 1.02950i
\(173\) −17.9134 13.0148i −1.36193 0.989499i −0.998320 0.0579465i \(-0.981545\pi\)
−0.363608 0.931552i \(-0.618455\pi\)
\(174\) 7.71633 + 23.7484i 0.584973 + 1.80036i
\(175\) 2.00000 0.151186
\(176\) 0 0
\(177\) −4.68629 −0.352243
\(178\) 9.93247 + 30.5690i 0.744470 + 2.29124i
\(179\) −7.81256 5.67616i −0.583938 0.424256i 0.256204 0.966623i \(-0.417528\pi\)
−0.840142 + 0.542367i \(0.817528\pi\)
\(180\) 15.4863 11.2515i 1.15428 0.838635i
\(181\) 6.58630 20.2705i 0.489556 1.50670i −0.335717 0.941963i \(-0.608979\pi\)
0.825273 0.564735i \(-0.191021\pi\)
\(182\) −1.74806 + 5.37999i −0.129575 + 0.398791i
\(183\) 21.3121 15.4841i 1.57543 1.14462i
\(184\) −10.1008 7.33866i −0.744641 0.541014i
\(185\) 2.36610 + 7.28210i 0.173959 + 0.535391i
\(186\) 0 0
\(187\) 0 0
\(188\) 10.8284 0.789744
\(189\) −3.49613 10.7600i −0.254306 0.782673i
\(190\) 0 0
\(191\) −2.68085 + 1.94775i −0.193979 + 0.140934i −0.680536 0.732715i \(-0.738253\pi\)
0.486556 + 0.873649i \(0.338253\pi\)
\(192\) 8.59036 26.4384i 0.619956 1.90803i
\(193\) 0.362036 1.11423i 0.0260599 0.0802042i −0.937181 0.348844i \(-0.886574\pi\)
0.963241 + 0.268640i \(0.0865742\pi\)
\(194\) 7.14235 5.18922i 0.512791 0.372564i
\(195\) −2.68085 1.94775i −0.191979 0.139481i
\(196\) −3.54915 10.9232i −0.253511 0.780225i
\(197\) 10.8284 0.771493 0.385747 0.922605i \(-0.373944\pi\)
0.385747 + 0.922605i \(0.373944\pi\)
\(198\) 0 0
\(199\) 10.3431 0.733206 0.366603 0.930377i \(-0.380521\pi\)
0.366603 + 0.930377i \(0.380521\pi\)
\(200\) −1.36407 4.19817i −0.0964541 0.296855i
\(201\) 28.5694 + 20.7569i 2.01513 + 1.46408i
\(202\) −18.1910 + 13.2165i −1.27991 + 0.929911i
\(203\) 2.26006 6.95575i 0.158625 0.488198i
\(204\) 22.8491 70.3222i 1.59975 4.92354i
\(205\) −4.85410 + 3.52671i −0.339025 + 0.246316i
\(206\) 13.3369 + 9.68981i 0.929224 + 0.675121i
\(207\) −4.37016 13.4500i −0.303747 0.934838i
\(208\) 3.51472 0.243702
\(209\) 0 0
\(210\) −13.6569 −0.942412
\(211\) 4.94427 + 15.2169i 0.340378 + 1.04757i 0.964012 + 0.265859i \(0.0856555\pi\)
−0.623634 + 0.781716i \(0.714345\pi\)
\(212\) −36.1043 26.2313i −2.47966 1.80158i
\(213\) 25.8885 18.8091i 1.77385 1.28878i
\(214\) 5.71227 17.5805i 0.390482 1.20178i
\(215\) −1.85410 + 5.70634i −0.126449 + 0.389169i
\(216\) −20.2016 + 14.6773i −1.37455 + 0.998666i
\(217\) 0 0
\(218\) −5.71227 17.5805i −0.386883 1.19070i
\(219\) −3.31371 −0.223920
\(220\) 0 0
\(221\) −8.00000 −0.538138
\(222\) −16.1567 49.7253i −1.08437 3.33734i
\(223\) 8.76038 + 6.36479i 0.586639 + 0.426218i 0.841111 0.540862i \(-0.181902\pi\)
−0.254473 + 0.967080i \(0.581902\pi\)
\(224\) −2.56586 + 1.86420i −0.171438 + 0.124557i
\(225\) 1.54508 4.75528i 0.103006 0.317019i
\(226\) −14.6647 + 45.1332i −0.975479 + 3.00222i
\(227\) 20.4792 14.8790i 1.35925 0.987556i 0.360762 0.932658i \(-0.382517\pi\)
0.998492 0.0548975i \(-0.0174832\pi\)
\(228\) 0 0
\(229\) 0.405958 + 1.24941i 0.0268265 + 0.0825634i 0.963573 0.267444i \(-0.0861791\pi\)
−0.936747 + 0.350007i \(0.886179\pi\)
\(230\) −6.82843 −0.450253
\(231\) 0 0
\(232\) −16.1421 −1.05978
\(233\) 1.89802 + 5.84152i 0.124344 + 0.382691i 0.993781 0.111353i \(-0.0355184\pi\)
−0.869437 + 0.494043i \(0.835518\pi\)
\(234\) 11.4412 + 8.31254i 0.747936 + 0.543408i
\(235\) 2.28825 1.66251i 0.149269 0.108450i
\(236\) 1.96014 6.03269i 0.127594 0.392695i
\(237\) 3.49613 10.7600i 0.227098 0.698936i
\(238\) −26.6737 + 19.3796i −1.72900 + 1.25619i
\(239\) −18.8612 13.7035i −1.22003 0.886403i −0.223926 0.974606i \(-0.571887\pi\)
−0.996102 + 0.0882033i \(0.971887\pi\)
\(240\) 2.62210 + 8.06998i 0.169256 + 0.520915i
\(241\) −6.00000 −0.386494 −0.193247 0.981150i \(-0.561902\pi\)
−0.193247 + 0.981150i \(0.561902\pi\)
\(242\) 0 0
\(243\) 14.1421 0.907218
\(244\) 11.0186 + 33.9117i 0.705392 + 2.17097i
\(245\) −2.42705 1.76336i −0.155059 0.112657i
\(246\) 33.1459 24.0819i 2.11330 1.53541i
\(247\) 0 0
\(248\) 0 0
\(249\) 13.7295 9.97505i 0.870070 0.632143i
\(250\) −1.95314 1.41904i −0.123527 0.0897479i
\(251\) 3.70820 + 11.4127i 0.234060 + 0.720362i 0.997245 + 0.0741818i \(0.0236345\pi\)
−0.763185 + 0.646180i \(0.776365\pi\)
\(252\) 38.2843 2.41168
\(253\) 0 0
\(254\) 10.4853 0.657905
\(255\) −5.96826 18.3684i −0.373747 1.15028i
\(256\) 24.2467 + 17.6163i 1.51542 + 1.10102i
\(257\) 7.53495 5.47446i 0.470017 0.341487i −0.327431 0.944875i \(-0.606183\pi\)
0.797448 + 0.603388i \(0.206183\pi\)
\(258\) 12.6606 38.9653i 0.788215 2.42587i
\(259\) −4.73220 + 14.5642i −0.294044 + 0.904975i
\(260\) 3.62867 2.63638i 0.225040 0.163501i
\(261\) −14.7923 10.7472i −0.915620 0.665237i
\(262\) −8.44040 25.9769i −0.521450 1.60486i
\(263\) 10.9706 0.676474 0.338237 0.941061i \(-0.390169\pi\)
0.338237 + 0.941061i \(0.390169\pi\)
\(264\) 0 0
\(265\) −11.6569 −0.716075
\(266\) 0 0
\(267\) −30.4650 22.1341i −1.86443 1.35459i
\(268\) −38.6702 + 28.0955i −2.36216 + 1.71621i
\(269\) 5.35023 16.4663i 0.326209 1.00397i −0.644683 0.764450i \(-0.723010\pi\)
0.970892 0.239519i \(-0.0769896\pi\)
\(270\) −4.22020 + 12.9884i −0.256833 + 0.790451i
\(271\) 5.91691 4.29889i 0.359427 0.261139i −0.393386 0.919373i \(-0.628696\pi\)
0.752813 + 0.658234i \(0.228696\pi\)
\(272\) 16.5729 + 12.0409i 1.00488 + 0.730090i
\(273\) −2.04798 6.30305i −0.123950 0.381478i
\(274\) 26.4853 1.60003
\(275\) 0 0
\(276\) 30.6274 1.84355
\(277\) −2.11010 6.49422i −0.126784 0.390200i 0.867438 0.497545i \(-0.165765\pi\)
−0.994222 + 0.107345i \(0.965765\pi\)
\(278\) 7.81256 + 5.67616i 0.468566 + 0.340433i
\(279\) 0 0
\(280\) 2.72813 8.39633i 0.163037 0.501777i
\(281\) −5.35023 + 16.4663i −0.319168 + 0.982298i 0.654837 + 0.755770i \(0.272737\pi\)
−0.974005 + 0.226528i \(0.927263\pi\)
\(282\) −15.6251 + 11.3523i −0.930462 + 0.676020i
\(283\) 26.3961 + 19.1779i 1.56909 + 1.14001i 0.928024 + 0.372521i \(0.121507\pi\)
0.641064 + 0.767488i \(0.278493\pi\)
\(284\) 13.3847 + 41.1938i 0.794234 + 2.44440i
\(285\) 0 0
\(286\) 0 0
\(287\) −12.0000 −0.708338
\(288\) 2.45017 + 7.54086i 0.144378 + 0.444350i
\(289\) −23.9691 17.4146i −1.40995 1.02439i
\(290\) −7.14235 + 5.18922i −0.419413 + 0.304721i
\(291\) −3.19621 + 9.83692i −0.187365 + 0.576650i
\(292\) 1.38603 4.26576i 0.0811112 0.249634i
\(293\) −7.41996 + 5.39092i −0.433479 + 0.314941i −0.783038 0.621973i \(-0.786331\pi\)
0.349560 + 0.936914i \(0.386331\pi\)
\(294\) 16.5729 + 12.0409i 0.966554 + 0.702242i
\(295\) −0.511996 1.57576i −0.0298096 0.0917444i
\(296\) 33.7990 1.96453
\(297\) 0 0
\(298\) 0.828427 0.0479895
\(299\) −1.02399 3.15152i −0.0592190 0.182257i
\(300\) 8.76038 + 6.36479i 0.505781 + 0.367471i
\(301\) −9.70820 + 7.05342i −0.559572 + 0.406553i
\(302\) −8.95240 + 27.5526i −0.515153 + 1.58548i
\(303\) 8.14048 25.0538i 0.467658 1.43930i
\(304\) 0 0
\(305\) 7.53495 + 5.47446i 0.431450 + 0.313467i
\(306\) 25.4712 + 78.3922i 1.45609 + 4.48138i
\(307\) 16.3431 0.932753 0.466376 0.884586i \(-0.345559\pi\)
0.466376 + 0.884586i \(0.345559\pi\)
\(308\) 0 0
\(309\) −19.3137 −1.09872
\(310\) 0 0
\(311\) −3.79129 2.75453i −0.214984 0.156195i 0.475082 0.879942i \(-0.342419\pi\)
−0.690066 + 0.723746i \(0.742419\pi\)
\(312\) −11.8338 + 8.59778i −0.669959 + 0.486753i
\(313\) −0.405958 + 1.24941i −0.0229461 + 0.0706209i −0.961874 0.273493i \(-0.911821\pi\)
0.938928 + 0.344114i \(0.111821\pi\)
\(314\) 10.4445 32.1447i 0.589415 1.81403i
\(315\) 8.09017 5.87785i 0.455829 0.331179i
\(316\) 12.3891 + 9.00117i 0.696939 + 0.506355i
\(317\) −0.405958 1.24941i −0.0228009 0.0701739i 0.939009 0.343894i \(-0.111746\pi\)
−0.961810 + 0.273720i \(0.911746\pi\)
\(318\) 79.5980 4.46363
\(319\) 0 0
\(320\) 9.82843 0.549426
\(321\) 6.69234 + 20.5969i 0.373530 + 1.14961i
\(322\) −11.0486 8.02730i −0.615716 0.447344i
\(323\) 0 0
\(324\) 1.18305 3.64105i 0.0657249 0.202281i
\(325\) 0.362036 1.11423i 0.0200821 0.0618065i
\(326\) 32.1981 23.3933i 1.78329 1.29563i
\(327\) 17.5208 + 12.7296i 0.968900 + 0.703947i
\(328\) 8.18440 + 25.1890i 0.451908 + 1.39083i
\(329\) 5.65685 0.311872
\(330\) 0 0
\(331\) −7.31371 −0.401998 −0.200999 0.979591i \(-0.564419\pi\)
−0.200999 + 0.979591i \(0.564419\pi\)
\(332\) 7.09829 + 21.8463i 0.389570 + 1.19897i
\(333\) 30.9726 + 22.5029i 1.69729 + 1.23315i
\(334\) 44.8647 32.5961i 2.45489 1.78358i
\(335\) −3.85816 + 11.8742i −0.210794 + 0.648757i
\(336\) −5.24419 + 16.1400i −0.286094 + 0.880507i
\(337\) −16.5729 + 12.0409i −0.902786 + 0.655912i −0.939180 0.343425i \(-0.888413\pi\)
0.0363944 + 0.999338i \(0.488413\pi\)
\(338\) −22.7100 16.4998i −1.23526 0.897469i
\(339\) −17.1807 52.8768i −0.933129 2.87187i
\(340\) 26.1421 1.41776
\(341\) 0 0
\(342\) 0 0
\(343\) −6.18034 19.0211i −0.333707 1.02704i
\(344\) 21.4270 + 15.5677i 1.15527 + 0.839352i
\(345\) 6.47214 4.70228i 0.348448 0.253162i
\(346\) −16.5188 + 50.8395i −0.888054 + 2.73315i
\(347\) −3.39009 + 10.4336i −0.181990 + 0.560106i −0.999884 0.0152627i \(-0.995142\pi\)
0.817894 + 0.575369i \(0.195142\pi\)
\(348\) 32.0354 23.2751i 1.71728 1.24768i
\(349\) 21.8196 + 15.8529i 1.16798 + 0.848586i 0.990766 0.135586i \(-0.0432918\pi\)
0.177213 + 0.984172i \(0.443292\pi\)
\(350\) −1.49207 4.59211i −0.0797543 0.245458i
\(351\) −6.62742 −0.353745
\(352\) 0 0
\(353\) 21.3137 1.13441 0.567207 0.823575i \(-0.308024\pi\)
0.567207 + 0.823575i \(0.308024\pi\)
\(354\) 3.49613 + 10.7600i 0.185817 + 0.571886i
\(355\) 9.15298 + 6.65003i 0.485790 + 0.352947i
\(356\) 41.2361 29.9597i 2.18551 1.58786i
\(357\) 11.9365 36.7369i 0.631748 1.94432i
\(358\) −7.20433 + 22.1727i −0.380761 + 1.17186i
\(359\) 0.555221 0.403392i 0.0293035 0.0212902i −0.573037 0.819529i \(-0.694235\pi\)
0.602341 + 0.798239i \(0.294235\pi\)
\(360\) −17.8559 12.9730i −0.941087 0.683740i
\(361\) −5.87132 18.0701i −0.309017 0.951057i
\(362\) −51.4558 −2.70446
\(363\) 0 0
\(364\) 8.97056 0.470185
\(365\) −0.362036 1.11423i −0.0189498 0.0583216i
\(366\) −51.4518 37.3820i −2.68943 1.95399i
\(367\) 6.86474 4.98752i 0.358336 0.260347i −0.394022 0.919101i \(-0.628916\pi\)
0.752358 + 0.658755i \(0.228916\pi\)
\(368\) −2.62210 + 8.06998i −0.136686 + 0.420677i
\(369\) −9.27051 + 28.5317i −0.482603 + 1.48530i
\(370\) 14.9549 10.8654i 0.777469 0.564864i
\(371\) −18.8612 13.7035i −0.979224 0.711448i
\(372\) 0 0
\(373\) −35.7990 −1.85360 −0.926801 0.375554i \(-0.877453\pi\)
−0.926801 + 0.375554i \(0.877453\pi\)
\(374\) 0 0
\(375\) 2.82843 0.146059
\(376\) −3.85816 11.8742i −0.198970 0.612366i
\(377\) −3.46605 2.51823i −0.178511 0.129696i
\(378\) −22.0973 + 16.0546i −1.13656 + 0.825759i
\(379\) 10.4005 32.0096i 0.534240 1.64422i −0.211046 0.977476i \(-0.567687\pi\)
0.745286 0.666745i \(-0.232313\pi\)
\(380\) 0 0
\(381\) −9.93818 + 7.22051i −0.509149 + 0.369918i
\(382\) 6.47214 + 4.70228i 0.331143 + 0.240590i
\(383\) −1.81018 5.57116i −0.0924959 0.284673i 0.894097 0.447873i \(-0.147818\pi\)
−0.986593 + 0.163200i \(0.947818\pi\)
\(384\) −58.1421 −2.96705
\(385\) 0 0
\(386\) −2.82843 −0.143963
\(387\) 9.27051 + 28.5317i 0.471246 + 1.45035i
\(388\) −11.3262 8.22899i −0.575003 0.417764i
\(389\) −16.6879 + 12.1245i −0.846112 + 0.614736i −0.924071 0.382220i \(-0.875160\pi\)
0.0779595 + 0.996957i \(0.475160\pi\)
\(390\) −2.47214 + 7.60845i −0.125181 + 0.385269i
\(391\) 5.96826 18.3684i 0.301828 0.928931i
\(392\) −10.7135 + 7.78383i −0.541115 + 0.393143i
\(393\) 25.8885 + 18.8091i 1.30590 + 0.948795i
\(394\) −8.07836 24.8626i −0.406982 1.25256i
\(395\) 4.00000 0.201262
\(396\) 0 0
\(397\) −9.31371 −0.467442 −0.233721 0.972304i \(-0.575090\pi\)
−0.233721 + 0.972304i \(0.575090\pi\)
\(398\) −7.71633 23.7484i −0.386785 1.19040i
\(399\) 0 0
\(400\) −2.42705 + 1.76336i −0.121353 + 0.0881678i
\(401\) −1.64203 + 5.05364i −0.0819989 + 0.252367i −0.983648 0.180102i \(-0.942357\pi\)
0.901649 + 0.432468i \(0.142357\pi\)
\(402\) 26.3452 81.0822i 1.31398 4.04401i
\(403\) 0 0
\(404\) 28.8470 + 20.9586i 1.43519 + 1.04273i
\(405\) −0.309017 0.951057i −0.0153552 0.0472584i
\(406\) −17.6569 −0.876295
\(407\) 0 0
\(408\) −85.2548 −4.22074
\(409\) −0.318114 0.979053i −0.0157297 0.0484111i 0.942884 0.333122i \(-0.108102\pi\)
−0.958613 + 0.284711i \(0.908102\pi\)
\(410\) 11.7188 + 8.51423i 0.578752 + 0.420488i
\(411\) −25.1033 + 18.2386i −1.23826 + 0.899646i
\(412\) 8.07836 24.8626i 0.397992 1.22489i
\(413\) 1.02399 3.15152i 0.0503874 0.155076i
\(414\) −27.6216 + 20.0682i −1.35753 + 0.986300i
\(415\) 4.85410 + 3.52671i 0.238278 + 0.173119i
\(416\) 0.574112 + 1.76693i 0.0281481 + 0.0866311i
\(417\) −11.3137 −0.554035
\(418\) 0 0
\(419\) −25.6569 −1.25342 −0.626710 0.779253i \(-0.715599\pi\)
−0.626710 + 0.779253i \(0.715599\pi\)
\(420\) 6.69234 + 20.5969i 0.326553 + 1.00503i
\(421\) 4.85410 + 3.52671i 0.236574 + 0.171881i 0.699756 0.714382i \(-0.253292\pi\)
−0.463181 + 0.886264i \(0.653292\pi\)
\(422\) 31.2502 22.7046i 1.52124 1.10524i
\(423\) 4.37016 13.4500i 0.212484 0.653960i
\(424\) −15.9007 + 48.9374i −0.772208 + 2.37661i
\(425\) 5.52431 4.01365i 0.267969 0.194691i
\(426\) −62.5005 45.4093i −3.02816 2.20009i
\(427\) 5.75619 + 17.7157i 0.278561 + 0.857324i
\(428\) −29.3137 −1.41693
\(429\) 0 0
\(430\) 14.4853 0.698542
\(431\) 3.49613 + 10.7600i 0.168403 + 0.518290i 0.999271 0.0381792i \(-0.0121558\pi\)
−0.830868 + 0.556469i \(0.812156\pi\)
\(432\) 13.7295 + 9.97505i 0.660560 + 0.479925i
\(433\) 6.19453 4.50059i 0.297690 0.216284i −0.428907 0.903349i \(-0.641101\pi\)
0.726596 + 0.687065i \(0.241101\pi\)
\(434\) 0 0
\(435\) 3.19621 9.83692i 0.153246 0.471644i
\(436\) −23.7153 + 17.2302i −1.13576 + 0.825175i
\(437\) 0 0
\(438\) 2.47214 + 7.60845i 0.118123 + 0.363546i
\(439\) 16.0000 0.763638 0.381819 0.924237i \(-0.375298\pi\)
0.381819 + 0.924237i \(0.375298\pi\)
\(440\) 0 0
\(441\) −15.0000 −0.714286
\(442\) 5.96826 + 18.3684i 0.283881 + 0.873697i
\(443\) 21.7047 + 15.7694i 1.03122 + 0.749225i 0.968552 0.248810i \(-0.0800394\pi\)
0.0626669 + 0.998035i \(0.480039\pi\)
\(444\) −67.0770 + 48.7343i −3.18333 + 2.31283i
\(445\) 4.11416 12.6621i 0.195030 0.600241i
\(446\) 8.07836 24.8626i 0.382522 1.17728i
\(447\) −0.785202 + 0.570482i −0.0371388 + 0.0269829i
\(448\) 15.9027 + 11.5540i 0.751333 + 0.545876i
\(449\) 8.84636 + 27.2263i 0.417485 + 1.28489i 0.910009 + 0.414589i \(0.136075\pi\)
−0.492523 + 0.870299i \(0.663925\pi\)
\(450\) −12.0711 −0.569036
\(451\) 0 0
\(452\) 75.2548 3.53969
\(453\) −10.4884 32.2799i −0.492787 1.51664i
\(454\) −49.4412 35.9211i −2.32039 1.68586i
\(455\) 1.89564 1.37727i 0.0888692 0.0645673i
\(456\) 0 0
\(457\) −0.149960 + 0.461530i −0.00701484 + 0.0215895i −0.954503 0.298202i \(-0.903613\pi\)
0.947488 + 0.319792i \(0.103613\pi\)
\(458\) 2.56586 1.86420i 0.119895 0.0871085i
\(459\) −31.2502 22.7046i −1.45864 1.05976i
\(460\) 3.34617 + 10.2984i 0.156016 + 0.480168i
\(461\) −12.6274 −0.588117 −0.294059 0.955787i \(-0.595006\pi\)
−0.294059 + 0.955787i \(0.595006\pi\)
\(462\) 0 0
\(463\) −6.14214 −0.285449 −0.142725 0.989762i \(-0.545586\pi\)
−0.142725 + 0.989762i \(0.545586\pi\)
\(464\) 3.39009 + 10.4336i 0.157381 + 0.484369i
\(465\) 0 0
\(466\) 11.9964 8.71593i 0.555725 0.403758i
\(467\) −4.58224 + 14.1027i −0.212041 + 0.652594i 0.787310 + 0.616557i \(0.211473\pi\)
−0.999350 + 0.0360364i \(0.988527\pi\)
\(468\) 6.93014 21.3288i 0.320346 0.985923i
\(469\) −20.2016 + 14.6773i −0.932824 + 0.677736i
\(470\) −5.52431 4.01365i −0.254818 0.185136i
\(471\) 12.2364 + 37.6599i 0.563826 + 1.73528i
\(472\) −7.31371 −0.336641
\(473\) 0 0
\(474\) −27.3137 −1.25456
\(475\) 0 0
\(476\) 42.2989 + 30.7319i 1.93877 + 1.40860i
\(477\) −47.1530 + 34.2586i −2.15899 + 1.56860i
\(478\) −17.3928 + 53.5295i −0.795528 + 2.44838i
\(479\) 11.1246 34.2380i 0.508296 1.56438i −0.286861 0.957972i \(-0.592612\pi\)
0.795157 0.606403i \(-0.207388\pi\)
\(480\) −3.62867 + 2.63638i −0.165625 + 0.120334i
\(481\) 7.25734 + 5.27276i 0.330906 + 0.240417i
\(482\) 4.47620 + 13.7763i 0.203885 + 0.627494i
\(483\) 16.0000 0.728025
\(484\) 0 0
\(485\) −3.65685 −0.166049
\(486\) −10.5505 32.4711i −0.478580 1.47292i
\(487\) 19.8090 + 14.3921i 0.897632 + 0.652168i 0.937857 0.347023i \(-0.112807\pi\)
−0.0402248 + 0.999191i \(0.512807\pi\)
\(488\) 33.2609 24.1654i 1.50565 1.09392i
\(489\) −14.4087 + 44.3453i −0.651582 + 2.00536i
\(490\) −2.23810 + 6.88816i −0.101107 + 0.311175i
\(491\) −0.555221 + 0.403392i −0.0250568 + 0.0182048i −0.600243 0.799818i \(-0.704930\pi\)
0.575186 + 0.818022i \(0.304930\pi\)
\(492\) −52.5623 38.1887i −2.36969 1.72168i
\(493\) −7.71633 23.7484i −0.347526 1.06957i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 6.99226 + 21.5200i 0.313646 + 0.965302i
\(498\) −33.1459 24.0819i −1.48530 1.07914i
\(499\) −7.81256 + 5.67616i −0.349738 + 0.254100i −0.748759 0.662842i \(-0.769350\pi\)
0.399021 + 0.916942i \(0.369350\pi\)
\(500\) −1.18305 + 3.64105i −0.0529076 + 0.162833i
\(501\) −20.0770 + 61.7907i −0.896975 + 2.76060i
\(502\) 23.4377 17.0285i 1.04607 0.760018i
\(503\) 13.4519 + 9.77335i 0.599789 + 0.435772i 0.845804 0.533494i \(-0.179121\pi\)
−0.246015 + 0.969266i \(0.579121\pi\)
\(504\) −13.6407 41.9817i −0.607604 1.87001i
\(505\) 9.31371 0.414455
\(506\) 0 0
\(507\) 32.8873 1.46058
\(508\) −5.13815 15.8136i −0.227969 0.701616i
\(509\) 10.7710 + 7.82560i 0.477417 + 0.346864i 0.800325 0.599567i \(-0.204660\pi\)
−0.322908 + 0.946430i \(0.604660\pi\)
\(510\) −37.7224 + 27.4069i −1.67037 + 1.21360i
\(511\) 0.724072 2.22846i 0.0320311 0.0985814i
\(512\) 9.65451 29.7135i 0.426673 1.31316i
\(513\) 0 0
\(514\) −18.1910 13.2165i −0.802369 0.582956i
\(515\) −2.11010 6.49422i −0.0929821 0.286170i
\(516\) −64.9706 −2.86017
\(517\) 0 0
\(518\) 36.9706 1.62439
\(519\) −19.3529 59.5622i −0.849500 2.61449i
\(520\) −4.18389 3.03977i −0.183476 0.133303i
\(521\) −20.4792 + 14.8790i −0.897211 + 0.651862i −0.937748 0.347316i \(-0.887093\pi\)
0.0405372 + 0.999178i \(0.487093\pi\)
\(522\) −13.6407 + 41.9817i −0.597036 + 1.83749i
\(523\) 12.8545 39.5620i 0.562087 1.72993i −0.114364 0.993439i \(-0.536483\pi\)
0.676451 0.736488i \(-0.263517\pi\)
\(524\) −35.0415 + 25.4592i −1.53080 + 1.11219i
\(525\) 4.57649 + 3.32502i 0.199734 + 0.145116i
\(526\) −8.18440 25.1890i −0.356857 1.09829i
\(527\) 0 0
\(528\) 0 0
\(529\) −15.0000 −0.652174
\(530\) 8.69640 + 26.7648i 0.377747 + 1.16259i
\(531\) −6.70212 4.86937i −0.290847 0.211313i
\(532\) 0 0
\(533\) −2.17222 + 6.68539i −0.0940891 + 0.289576i
\(534\) −28.0933 + 86.4622i −1.21571 + 3.74158i
\(535\) −6.19453 + 4.50059i −0.267813 + 0.194577i
\(536\) 44.5871 + 32.3944i 1.92587 + 1.39923i
\(537\) −8.44040 25.9769i −0.364230 1.12099i
\(538\) −41.7990 −1.80208
\(539\) 0 0
\(540\) 21.6569 0.931963
\(541\) −1.85410 5.70634i −0.0797141 0.245335i 0.903255 0.429103i \(-0.141170\pi\)
−0.982970 + 0.183768i \(0.941170\pi\)
\(542\) −14.2847 10.3784i −0.613580 0.445792i
\(543\) 48.7710 35.4342i 2.09296 1.52063i
\(544\) −3.34617 + 10.2984i −0.143466 + 0.441542i
\(545\) −2.36610 + 7.28210i −0.101353 + 0.311931i
\(546\) −12.9443 + 9.40456i −0.553964 + 0.402478i
\(547\) −27.5066 19.9847i −1.17610 0.854484i −0.184370 0.982857i \(-0.559025\pi\)
−0.991726 + 0.128373i \(0.959025\pi\)
\(548\) −12.9787 39.9444i −0.554423 1.70634i
\(549\) 46.5685 1.98750
\(550\) 0 0
\(551\) 0 0
\(552\) −10.9125 33.5853i −0.464468 1.42949i
\(553\) 6.47214 + 4.70228i 0.275223 + 0.199961i
\(554\) −13.3369 + 9.68981i −0.566629 + 0.411680i
\(555\) −6.69234 + 20.5969i −0.284074 + 0.874289i
\(556\) 4.73220 14.5642i 0.200690 0.617660i
\(557\) 7.97518 5.79431i 0.337919 0.245513i −0.405864 0.913933i \(-0.633029\pi\)
0.743783 + 0.668421i \(0.233029\pi\)
\(558\) 0 0
\(559\) 2.17222 + 6.68539i 0.0918749 + 0.282762i
\(560\) −6.00000 −0.253546
\(561\) 0 0
\(562\) 41.7990 1.76318
\(563\) −0.106038 0.326351i −0.00446896 0.0137541i 0.948797 0.315886i \(-0.102302\pi\)
−0.953266 + 0.302132i \(0.902302\pi\)
\(564\) 24.7781 + 18.0023i 1.04335 + 0.758035i
\(565\) 15.9027 11.5540i 0.669033 0.486081i
\(566\) 24.3411 74.9143i 1.02313 3.14888i
\(567\) 0.618034 1.90211i 0.0259550 0.0798812i
\(568\) 40.4032 29.3547i 1.69528 1.23169i
\(569\) 25.6109 + 18.6074i 1.07367 + 0.780064i 0.976568 0.215211i \(-0.0690438\pi\)
0.0970985 + 0.995275i \(0.469044\pi\)
\(570\) 0 0
\(571\) 21.9411 0.918208 0.459104 0.888383i \(-0.348171\pi\)
0.459104 + 0.888383i \(0.348171\pi\)
\(572\) 0 0
\(573\) −9.37258 −0.391545
\(574\) 8.95240 + 27.5526i 0.373666 + 1.15003i
\(575\) 2.28825 + 1.66251i 0.0954264 + 0.0693314i
\(576\) 39.7568 28.8850i 1.65653 1.20354i
\(577\) −8.33436 + 25.6505i −0.346964 + 1.06785i 0.613560 + 0.789648i \(0.289737\pi\)
−0.960524 + 0.278197i \(0.910263\pi\)
\(578\) −22.1030 + 68.0261i −0.919365 + 2.82951i
\(579\) 2.68085 1.94775i 0.111412 0.0809457i
\(580\) 11.3262 + 8.22899i 0.470296 + 0.341690i
\(581\) 3.70820 + 11.4127i 0.153842 + 0.473478i
\(582\) 24.9706 1.03506
\(583\) 0 0
\(584\) −5.17157 −0.214001
\(585\) −1.81018 5.57116i −0.0748417 0.230339i
\(586\) 17.9134 + 13.0148i 0.739994 + 0.537637i
\(587\) 1.73302 1.25912i 0.0715296 0.0519693i −0.551446 0.834211i \(-0.685924\pi\)
0.622975 + 0.782241i \(0.285924\pi\)
\(588\) 10.0385 30.8953i 0.413981 1.27410i
\(589\) 0 0
\(590\) −3.23607 + 2.35114i −0.133227 + 0.0967949i
\(591\) 24.7781 + 18.0023i 1.01923 + 0.740517i
\(592\) −7.09829 21.8463i −0.291738 0.897878i
\(593\) −3.51472 −0.144332 −0.0721661 0.997393i \(-0.522991\pi\)
−0.0721661 + 0.997393i \(0.522991\pi\)
\(594\) 0 0
\(595\) 13.6569 0.559876
\(596\) −0.405958 1.24941i −0.0166287 0.0511779i
\(597\) 23.6677 + 17.1956i 0.968653 + 0.703767i
\(598\) −6.47214 + 4.70228i −0.264665 + 0.192291i
\(599\) −1.74806 + 5.37999i −0.0714240 + 0.219820i −0.980396 0.197036i \(-0.936868\pi\)
0.908972 + 0.416857i \(0.136868\pi\)
\(600\) 3.85816 11.8742i 0.157509 0.484763i
\(601\) 19.3688 14.0722i 0.790069 0.574019i −0.117915 0.993024i \(-0.537621\pi\)
0.907984 + 0.419005i \(0.137621\pi\)
\(602\) 23.4377 + 17.0285i 0.955248 + 0.694029i
\(603\) 19.2908 + 59.3710i 0.785583 + 2.41778i
\(604\) 45.9411 1.86932
\(605\) 0 0
\(606\) −63.5980 −2.58349
\(607\) −11.8305 36.4105i −0.480185 1.47786i −0.838835 0.544385i \(-0.816763\pi\)
0.358651 0.933472i \(-0.383237\pi\)
\(608\) 0 0
\(609\) 16.7356 12.1591i 0.678159 0.492711i
\(610\) 6.94833 21.3848i 0.281330 0.865844i
\(611\) 1.02399 3.15152i 0.0414263 0.127497i
\(612\) 105.747 76.8298i 4.27458 3.10566i
\(613\) −20.5942 14.9626i −0.831792 0.604333i 0.0882735 0.996096i \(-0.471865\pi\)
−0.920066 + 0.391764i \(0.871865\pi\)
\(614\) −12.1925 37.5247i −0.492050 1.51438i
\(615\) −16.9706 −0.684319
\(616\) 0 0
\(617\) 0.343146 0.0138145 0.00690726 0.999976i \(-0.497801\pi\)
0.00690726 + 0.999976i \(0.497801\pi\)
\(618\) 14.4087 + 44.3453i 0.579601 + 1.78383i
\(619\) 11.6038 + 8.43069i 0.466398 + 0.338858i 0.796036 0.605249i \(-0.206927\pi\)
−0.329638 + 0.944107i \(0.606927\pi\)
\(620\) 0 0
\(621\) 4.94427 15.2169i 0.198407 0.610633i
\(622\) −3.49613 + 10.7600i −0.140182 + 0.431436i
\(623\) 21.5420 15.6512i 0.863063 0.627052i
\(624\) 8.04254 + 5.84325i 0.321959 + 0.233917i
\(625\) 0.309017 + 0.951057i 0.0123607 + 0.0380423i
\(626\) 3.17157 0.126762
\(627\) 0 0
\(628\) −53.5980 −2.13879
\(629\) 16.1567 + 49.7253i 0.644211 + 1.98268i
\(630\) −19.5314 14.1904i −0.778150 0.565359i
\(631\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(632\) 5.45627 16.7927i 0.217039 0.667976i
\(633\) −13.9845 + 43.0399i −0.555834 + 1.71068i
\(634\) −2.56586 + 1.86420i −0.101903 + 0.0740370i
\(635\) −3.51368 2.55284i −0.139436 0.101306i
\(636\) −39.0058 120.047i −1.54668 4.76019i
\(637\) −3.51472 −0.139258
\(638\) 0 0
\(639\) 56.5685 2.23782
\(640\) −6.35226 19.5502i −0.251095 0.772791i
\(641\) −24.2705 17.6336i −0.958628 0.696484i −0.00579592 0.999983i \(-0.501845\pi\)
−0.952832 + 0.303500i \(0.901845\pi\)
\(642\) 42.2989 30.7319i 1.66940 1.21289i
\(643\) −0.449881 + 1.38459i −0.0177416 + 0.0546029i −0.959535 0.281588i \(-0.909139\pi\)
0.941794 + 0.336191i \(0.109139\pi\)
\(644\) −6.69234 + 20.5969i −0.263715 + 0.811631i
\(645\) −13.7295 + 9.97505i −0.540597 + 0.392767i
\(646\) 0 0
\(647\) 8.37828 + 25.7857i 0.329384 + 1.01374i 0.969422 + 0.245398i \(0.0789185\pi\)
−0.640038 + 0.768343i \(0.721081\pi\)
\(648\) −4.41421 −0.173407
\(649\) 0 0
\(650\) −2.82843 −0.110940
\(651\) 0 0
\(652\) −51.0592 37.0967i −1.99963 1.45282i
\(653\) −9.43059 + 6.85173i −0.369048 + 0.268129i −0.756816 0.653628i \(-0.773246\pi\)
0.387768 + 0.921757i \(0.373246\pi\)
\(654\) 16.1567 49.7253i 0.631778 1.94441i
\(655\) −3.49613 + 10.7600i −0.136605 + 0.420427i
\(656\) 14.5623 10.5801i 0.568563 0.413085i
\(657\) −4.73911 3.44317i −0.184890 0.134331i
\(658\) −4.22020 12.9884i −0.164521 0.506342i
\(659\) −45.9411 −1.78961 −0.894806 0.446455i \(-0.852686\pi\)
−0.894806 + 0.446455i \(0.852686\pi\)
\(660\) 0 0
\(661\) 44.6274 1.73581 0.867903 0.496734i \(-0.165468\pi\)
0.867903 + 0.496734i \(0.165468\pi\)
\(662\) 5.45627 + 16.7927i 0.212064 + 0.652666i
\(663\) −18.3060 13.3001i −0.710945 0.516532i
\(664\) 21.4270 15.5677i 0.831531 0.604142i
\(665\) 0 0
\(666\) 28.5613 87.9027i 1.10673 3.40616i
\(667\) 8.36778 6.07955i 0.324002 0.235401i
\(668\) −71.1459 51.6905i −2.75272 1.99997i
\(669\) 9.46439 + 29.1284i 0.365915 + 1.12617i
\(670\) 30.1421 1.16449
\(671\) 0 0
\(672\) −8.97056 −0.346047
\(673\) 3.85816 + 11.8742i 0.148721 + 0.457717i 0.997471 0.0710781i \(-0.0226440\pi\)
−0.848749 + 0.528795i \(0.822644\pi\)
\(674\) 40.0106 + 29.0694i 1.54115 + 1.11971i
\(675\) 4.57649 3.32502i 0.176149 0.127980i
\(676\) −13.7558 + 42.3360i −0.529069 + 1.62831i
\(677\) −7.05437 + 21.7111i −0.271122 + 0.834426i 0.719098 + 0.694909i \(0.244555\pi\)
−0.990220 + 0.139518i \(0.955445\pi\)
\(678\) −108.591 + 78.8957i −4.17040 + 3.02997i
\(679\) −5.91691 4.29889i −0.227070 0.164976i
\(680\) −9.31443 28.6669i −0.357192 1.09932i
\(681\) 71.5980 2.74364
\(682\) 0 0
\(683\) −7.79899 −0.298420 −0.149210 0.988806i \(-0.547673\pi\)
−0.149210 + 0.988806i \(0.547673\pi\)
\(684\) 0 0
\(685\) −8.87537 6.44833i −0.339111 0.246378i
\(686\) −39.0628 + 28.3808i −1.49142 + 1.08358i
\(687\) −1.14822 + 3.53387i −0.0438075 + 0.134825i
\(688\) 5.56231 17.1190i 0.212061 0.652656i
\(689\) −11.0486 + 8.02730i −0.420919 + 0.305816i
\(690\) −15.6251 11.3523i −0.594838 0.432175i
\(691\) −12.1486 37.3896i −0.462155 1.42237i −0.862526 0.506013i \(-0.831119\pi\)
0.400371 0.916353i \(-0.368881\pi\)
\(692\) 84.7696 3.22245
\(693\) 0 0
\(694\) 26.4853 1.00537
\(695\) −1.23607 3.80423i −0.0468867 0.144303i
\(696\) −36.9372 26.8364i −1.40010 1.01723i
\(697\) −33.1459 + 24.0819i −1.25549 + 0.912167i
\(698\) 20.1209 61.9259i 0.761588 2.34393i
\(699\) −5.36842 + 16.5223i −0.203052 + 0.624931i
\(700\) −6.19453 + 4.50059i −0.234131 + 0.170106i
\(701\) −10.2158 7.42221i −0.385845 0.280333i 0.377906 0.925844i \(-0.376644\pi\)
−0.763751 + 0.645511i \(0.776644\pi\)
\(702\) 4.94427 + 15.2169i 0.186610 + 0.574325i
\(703\) 0 0
\(704\) 0 0
\(705\) 8.00000 0.301297
\(706\) −15.9007 48.9374i −0.598432 1.84178i
\(707\) 15.0699 + 10.9489i 0.566762 + 0.411777i
\(708\) 14.5147 10.5455i 0.545495 0.396325i
\(709\) 7.61029 23.4221i 0.285810 0.879634i −0.700344 0.713805i \(-0.746970\pi\)
0.986155 0.165829i \(-0.0530299\pi\)
\(710\) 8.44040 25.9769i 0.316763 0.974895i
\(711\) 16.1803 11.7557i 0.606810 0.440873i
\(712\) −47.5456 34.5439i −1.78185 1.29459i
\(713\) 0 0
\(714\) −93.2548 −3.48997
\(715\) 0 0
\(716\) 36.9706 1.38165
\(717\) −20.3769 62.7137i −0.760990 2.34209i
\(718\) −1.34042 0.973874i −0.0500242 0.0363447i
\(719\) −14.8399 + 10.7818i −0.553436 + 0.402094i −0.829051 0.559174i \(-0.811118\pi\)
0.275615 + 0.961268i \(0.411118\pi\)
\(720\) −4.63525 + 14.2658i −0.172746 + 0.531657i
\(721\) 4.22020 12.9884i 0.157168 0.483715i
\(722\) −37.1097 + 26.9617i −1.38108 + 1.00341i
\(723\) −13.7295 9.97505i −0.510605 0.370976i
\(724\) 25.2152 + 77.6043i 0.937114 + 2.88414i
\(725\) 3.65685 0.135812
\(726\) 0 0
\(727\) −19.5147 −0.723761 −0.361880 0.932225i \(-0.617865\pi\)
−0.361880 + 0.932225i \(0.617865\pi\)
\(728\) −3.19621 9.83692i −0.118459 0.364580i
\(729\) 34.7877 + 25.2748i 1.28843 + 0.936102i
\(730\) −2.28825 + 1.66251i −0.0846918 + 0.0615322i
\(731\) −12.6606 + 38.9653i −0.468269 + 1.44118i
\(732\) −31.1652 + 95.9167i −1.15190 + 3.54518i
\(733\) −14.1221 + 10.2603i −0.521611 + 0.378972i −0.817210 0.576340i \(-0.804481\pi\)
0.295600 + 0.955312i \(0.404481\pi\)
\(734\) −16.5729 12.0409i −0.611718 0.444439i
\(735\) −2.62210 8.06998i −0.0967175 0.297666i
\(736\) −4.48528 −0.165330
\(737\) 0 0
\(738\) 72.4264 2.66605
\(739\) −9.25232 28.4757i −0.340352 1.04750i −0.964025 0.265811i \(-0.914360\pi\)
0.623673 0.781685i \(-0.285640\pi\)
\(740\) −23.7153 17.2302i −0.871791 0.633393i
\(741\) 0 0
\(742\) −17.3928 + 53.5295i −0.638510 + 1.96513i
\(743\) 15.3266 47.1705i 0.562279 1.73052i −0.113621 0.993524i \(-0.536245\pi\)
0.675900 0.736993i \(-0.263755\pi\)
\(744\) 0 0
\(745\) −0.277611 0.201696i −0.0101709 0.00738957i
\(746\) 26.7072 + 82.1964i 0.977821 + 3.00942i
\(747\) 30.0000 1.09764
\(748\) 0 0
\(749\) −15.3137 −0.559551
\(750\) −2.11010 6.49422i −0.0770500 0.237135i
\(751\) 12.9443 + 9.40456i 0.472343 + 0.343177i 0.798354 0.602189i \(-0.205705\pi\)
−0.326011 + 0.945366i \(0.605705\pi\)
\(752\) −6.86474 + 4.98752i −0.250331 + 0.181876i
\(753\) −10.4884 + 32.2799i −0.382218 + 1.17635i
\(754\) −3.19621 + 9.83692i −0.116399 + 0.358239i
\(755\) 9.70820 7.05342i 0.353318 0.256700i
\(756\) 35.0415 + 25.4592i 1.27445 + 0.925941i
\(757\) 4.11416 + 12.6621i 0.149532 + 0.460211i 0.997566 0.0697302i \(-0.0222138\pi\)
−0.848034 + 0.529942i \(0.822214\pi\)
\(758\) −81.2548 −2.95131
\(759\) 0 0
\(760\) 0 0
\(761\) 9.27051 + 28.5317i 0.336056 + 1.03427i 0.966200 + 0.257795i \(0.0829959\pi\)
−0.630144 + 0.776478i \(0.717004\pi\)
\(762\) 23.9929 + 17.4319i 0.869171 + 0.631490i
\(763\) −12.3891 + 9.00117i −0.448514 + 0.325864i
\(764\) 3.92028 12.0654i 0.141831 0.436510i
\(765\) 10.5505 32.4711i 0.381454 1.17400i
\(766\) −11.4412 + 8.31254i −0.413388 + 0.300344i
\(767\) −1.57040 1.14096i −0.0567040 0.0411979i
\(768\) 26.1952 + 80.6206i 0.945239 + 2.90915i
\(769\) 18.9706 0.684096 0.342048 0.939682i \(-0.388879\pi\)
0.342048 + 0.939682i \(0.388879\pi\)
\(770\) 0 0
\(771\) 26.3431 0.948725
\(772\) 1.38603 + 4.26576i 0.0498842 + 0.153528i
\(773\) −21.2644 15.4495i −0.764828 0.555680i 0.135559 0.990769i \(-0.456717\pi\)
−0.900387 + 0.435089i \(0.856717\pi\)
\(774\) 58.5942 42.5712i 2.10612 1.53019i
\(775\) 0 0
\(776\) −4.98819 + 15.3521i −0.179066 + 0.551108i
\(777\) −35.0415 + 25.4592i −1.25711 + 0.913342i
\(778\) 40.2882 + 29.2711i 1.44440 + 1.04942i
\(779\) 0 0
\(780\) 12.6863 0.454242
\(781\) 0 0
\(782\) −46.6274 −1.66739
\(783\) −6.39242 19.6738i −0.228446 0.703085i
\(784\) 7.28115 + 5.29007i 0.260041 + 0.188931i
\(785\) −11.3262 + 8.22899i −0.404251 + 0.293705i
\(786\) 23.8731 73.4737i 0.851524 2.62072i
\(787\) 4.62616 14.2379i 0.164905 0.507525i −0.834125 0.551576i \(-0.814027\pi\)
0.999029 + 0.0440516i \(0.0140266\pi\)
\(788\) −33.5385 + 24.3671i −1.19476 + 0.868043i
\(789\) 25.1033 + 18.2386i 0.893703 + 0.649313i
\(790\) −2.98413 9.18421i −0.106171 0.326760i
\(791\) 39.3137 1.39783
\(792\) 0 0
\(793\) 10.9117 0.387485
\(794\) 6.94833 + 21.3848i 0.246587 + 0.758917i
\(795\) −26.6737 19.3796i −0.946020 0.687324i
\(796\) −32.0354 + 23.2751i −1.13547 + 0.824964i
\(797\) 10.0824 31.0305i 0.357138 1.09916i −0.597622 0.801778i \(-0.703887\pi\)
0.954759 0.297379i \(-0.0961125\pi\)
\(798\) 0 0
\(799\) 15.6251 11.3523i 0.552777 0.401616i
\(800\) −1.28293 0.932102i −0.0453584 0.0329548i
\(801\) −20.5708 63.3104i −0.726834 2.23696i
\(802\) 12.8284 0.452988
\(803\) 0 0
\(804\) −135.196 −4.76799
\(805\) 1.74806 + 5.37999i 0.0616112 + 0.189620i
\(806\) 0 0
\(807\) 39.6180 28.7842i 1.39462 1.01325i
\(808\) 12.7045 39.1005i 0.446944 1.37555i
\(809\) 3.39009 10.4336i 0.119189 0.366827i −0.873608 0.486629i \(-0.838226\pi\)
0.992798 + 0.119803i \(0.0382262\pi\)
\(810\) −1.95314 + 1.41904i −0.0686263 + 0.0498600i
\(811\) 43.6393 + 31.7058i 1.53238 + 1.11334i 0.954896 + 0.296941i \(0.0959665\pi\)
0.577487 + 0.816400i \(0.304033\pi\)
\(812\) 8.65248 + 26.6296i 0.303642 + 0.934515i
\(813\) 20.6863 0.725500
\(814\) 0 0
\(815\) −16.4853 −0.577454
\(816\) 17.9048 + 55.1053i 0.626793 + 1.92907i
\(817\) 0 0
\(818\) −2.01063 + 1.46081i −0.0703002 + 0.0510761i
\(819\) 3.62036 11.1423i 0.126506 0.389344i
\(820\) 7.09829 21.8463i 0.247883 0.762906i
\(821\) −33.4235 + 24.2836i −1.16649 + 0.847503i −0.990584 0.136904i \(-0.956285\pi\)
−0.175904 + 0.984407i \(0.556285\pi\)
\(822\) 60.6048 + 44.0320i 2.11384 + 1.53579i
\(823\) 6.03038 + 18.5596i 0.210206 + 0.646947i 0.999459 + 0.0328795i \(0.0104678\pi\)
−0.789254 + 0.614068i \(0.789532\pi\)
\(824\) −30.1421 −1.05005
\(825\) 0 0
\(826\) −8.00000 −0.278356
\(827\) −6.88622 21.1936i −0.239457 0.736974i −0.996499 0.0836070i \(-0.973356\pi\)
0.757042 0.653367i \(-0.226644\pi\)
\(828\) 43.8019 + 31.8239i 1.52222 + 1.10596i
\(829\) −14.5623 + 10.5801i −0.505770 + 0.367463i −0.811217 0.584746i \(-0.801194\pi\)
0.305447 + 0.952209i \(0.401194\pi\)
\(830\) 4.47620 13.7763i 0.155371 0.478183i
\(831\) 5.96826 18.3684i 0.207037 0.637194i
\(832\) 9.31560 6.76818i 0.322960 0.234644i
\(833\) −16.5729 12.0409i −0.574218 0.417194i
\(834\) 8.44040 + 25.9769i 0.292267 + 0.899506i
\(835\) −22.9706 −0.794929
\(836\) 0 0
\(837\) 0 0
\(838\) 19.1409 + 58.9095i 0.661210 + 2.03500i
\(839\) −21.3121 15.4841i −0.735774 0.534571i 0.155611 0.987818i \(-0.450265\pi\)
−0.891385 + 0.453247i \(0.850265\pi\)
\(840\) 20.2016 14.6773i 0.697022 0.506416i
\(841\) −4.82914 + 14.8626i −0.166522 + 0.512502i
\(842\) 4.47620 13.7763i 0.154260 0.474763i
\(843\) −39.6180 + 28.7842i −1.36452 + 0.991380i
\(844\) −49.5562 36.0047i −1.70579 1.23933i
\(845\) 3.59307 + 11.0583i 0.123605 + 0.380418i
\(846\) −34.1421 −1.17383
\(847\) 0 0
\(848\) 34.9706 1.20089
\(849\) 28.5174 + 87.7676i 0.978715 + 3.01217i
\(850\) −13.3369 9.68981i −0.457451 0.332358i
\(851\) −17.5208 + 12.7296i −0.600604 + 0.436364i
\(852\) −37.8576 + 116.514i −1.29698 + 3.99169i
\(853\) 4.79431 14.7554i 0.164154 0.505214i −0.834819 0.550525i \(-0.814428\pi\)
0.998973 + 0.0453103i \(0.0144277\pi\)
\(854\) 36.3819 26.4330i 1.24496 0.904520i
\(855\) 0 0
\(856\) 10.4445 + 32.1447i 0.356984 + 1.09868i
\(857\) −24.7696 −0.846112 −0.423056 0.906104i \(-0.639043\pi\)
−0.423056 + 0.906104i \(0.639043\pi\)
\(858\) 0 0
\(859\) 24.2843 0.828569 0.414284 0.910148i \(-0.364032\pi\)
0.414284 + 0.910148i \(0.364032\pi\)
\(860\) −7.09829 21.8463i −0.242050 0.744953i
\(861\) −27.4589 19.9501i −0.935798 0.679897i
\(862\) 22.0973 16.0546i 0.752635 0.546822i
\(863\) −2.83417 + 8.72268i −0.0964763 + 0.296924i −0.987636 0.156767i \(-0.949893\pi\)
0.891159 + 0.453691i \(0.149893\pi\)
\(864\) −2.77206 + 8.53151i −0.0943073 + 0.290248i
\(865\) 17.9134 13.0148i 0.609073 0.442517i
\(866\) −14.9549 10.8654i −0.508188 0.369220i
\(867\) −25.8953 79.6976i −0.879451 2.70667i
\(868\) 0 0
\(869\) 0 0
\(870\) −24.9706 −0.846581
\(871\) 4.52012 + 13.9115i 0.153158 + 0.471373i
\(872\) 27.3440 + 19.8665i 0.925983 + 0.672766i
\(873\) −14.7923 + 10.7472i −0.500643 + 0.363738i
\(874\) 0 0
\(875\) −0.618034 + 1.90211i −0.0208934 + 0.0643032i
\(876\) 10.2634 7.45682i 0.346769 0.251942i
\(877\) −40.0106 29.0694i −1.35106 0.981604i −0.998958 0.0456438i \(-0.985466\pi\)
−0.352105 0.935961i \(-0.614534\pi\)
\(878\) −11.9365 36.7369i −0.402838 1.23981i
\(879\) −25.9411 −0.874972
\(880\) 0 0
\(881\) −7.37258 −0.248389 −0.124194 0.992258i \(-0.539635\pi\)
−0.124194 + 0.992258i \(0.539635\pi\)
\(882\) 11.1905 + 34.4408i 0.376804 + 1.15968i
\(883\) −30.0724 21.8489i −1.01202 0.735274i −0.0473866 0.998877i \(-0.515089\pi\)
−0.964631 + 0.263603i \(0.915089\pi\)
\(884\) 24.7781 18.0023i 0.833378 0.605484i
\(885\) 1.44814 4.45693i 0.0486788 0.149818i
\(886\) 20.0149 61.5995i 0.672413 2.06948i
\(887\) 30.9726 22.5029i 1.03996 0.755574i 0.0696815 0.997569i \(-0.477802\pi\)
0.970278 + 0.241995i \(0.0778017\pi\)
\(888\) 77.3404 + 56.1911i 2.59537 + 1.88565i
\(889\) −2.68421 8.26115i −0.0900256 0.277070i
\(890\) −32.1421 −1.07741
\(891\) 0 0
\(892\) −41.4558 −1.38804
\(893\) 0 0
\(894\) 1.89564 + 1.37727i 0.0633998 + 0.0460627i
\(895\) 7.81256 5.67616i 0.261145 0.189733i
\(896\) 12.7045 39.1005i 0.424428 1.30626i
\(897\) 2.89629 8.91386i 0.0967042 0.297625i
\(898\) 55.9133 40.6234i 1.86585 1.35562i
\(899\) 0 0
\(900\) 5.91525 + 18.2053i 0.197175 + 0.606842i
\(901\) −79.5980 −2.65179
\(902\) 0 0
\(903\) −33.9411 −1.12949
\(904\) −26.8133 82.5227i −0.891796 2.74467i
\(905\) 17.2432 + 12.5279i 0.573182 + 0.416441i
\(906\) −66.2918 + 48.1638i −2.20240 + 1.60013i
\(907\) −8.50252 + 26.1681i −0.282321 + 0.868896i 0.704867 + 0.709339i \(0.251007\pi\)
−0.987189 + 0.159557i \(0.948993\pi\)
\(908\) −29.9474 + 92.1685i −0.993838 + 3.05872i
\(909\) 37.6747 27.3723i 1.24959 0.907882i
\(910\) −4.57649 3.32502i −0.151709 0.110223i
\(911\) −3.07198 9.45457i −0.101779 0.313244i 0.887182 0.461420i \(-0.152660\pi\)
−0.988961 + 0.148176i \(0.952660\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 1.17157 0.0387522
\(915\) 8.14048 + 25.0538i 0.269116 + 0.828254i
\(916\) −4.06890 2.95623i −0.134440 0.0976766i
\(917\) −18.3060 + 13.3001i −0.604516 + 0.439207i
\(918\) −28.8173 + 88.6906i −0.951114 + 2.92723i
\(919\) 9.88854 30.4338i 0.326193 1.00392i −0.644706 0.764430i \(-0.723020\pi\)
0.970899 0.239488i \(-0.0769797\pi\)
\(920\) 10.1008 7.33866i 0.333014 0.241949i
\(921\) 37.3971 + 27.1706i 1.23228 + 0.895302i
\(922\) 9.42047 + 28.9932i 0.310247 + 0.954841i
\(923\) 13.2548 0.436288
\(924\) 0 0
\(925\) −7.65685 −0.251756
\(926\) 4.58224 + 14.1027i 0.150582 + 0.463443i
\(927\) −27.6216 20.0682i −0.907211 0.659128i
\(928\) −4.69148 + 3.40856i −0.154005 + 0.111891i
\(929\) 1.64203 5.05364i 0.0538731 0.165804i −0.920500 0.390743i \(-0.872218\pi\)
0.974373 + 0.224939i \(0.0722181\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −19.0238 13.8216i −0.623146 0.452742i
\(933\) −4.09597 12.6061i −0.134096 0.412705i
\(934\) 35.7990 1.17138
\(935\) 0 0
\(936\) −25.8579 −0.845191
\(937\) 0.449881 + 1.38459i 0.0146970 + 0.0452326i 0.958136 0.286313i \(-0.0924298\pi\)
−0.943439 + 0.331546i \(0.892430\pi\)
\(938\) 48.7710 + 35.4342i 1.59243 + 1.15697i
\(939\) −3.00609 + 2.18405i −0.0981000 + 0.0712738i
\(940\) −3.34617 + 10.2984i −0.109140 + 0.335898i
\(941\) 2.06618 6.35904i 0.0673555 0.207299i −0.911714 0.410826i \(-0.865240\pi\)
0.979069 + 0.203527i \(0.0652405\pi\)
\(942\) 77.3404 56.1911i 2.51989 1.83080i
\(943\) −13.7295 9.97505i −0.447093 0.324832i
\(944\) 1.53599 + 4.72729i 0.0499922 + 0.153860i
\(945\) 11.3137 0.368035
\(946\) 0 0
\(947\) 41.1716 1.33790 0.668948 0.743309i \(-0.266745\pi\)
0.668948 + 0.743309i \(0.266745\pi\)
\(948\) 13.3847 + 41.1938i 0.434714 + 1.33791i
\(949\) −1.11044 0.806784i −0.0360465 0.0261893i
\(950\) 0 0
\(951\) 1.14822 3.53387i 0.0372337 0.114594i
\(952\) 18.6289 57.3337i 0.603765 1.85820i
\(953\) 43.0167 31.2535i 1.39345 1.01240i 0.397971 0.917398i \(-0.369715\pi\)
0.995477 0.0950009i \(-0.0302854\pi\)
\(954\) 113.837 + 82.7077i 3.68562 + 2.67776i
\(955\) −1.02399 3.15152i −0.0331356 0.101981i
\(956\) 89.2548 2.88671
\(957\) 0 0
\(958\) −86.9117 −2.80799
\(959\) −6.78018 20.8673i −0.218943 0.673839i
\(960\) 22.4899 + 16.3398i 0.725857 + 0.527366i
\(961\) 25.0795 18.2213i 0.809017 0.587785i
\(962\) 6.69234 20.5969i 0.215770 0.664070i
\(963\) −11.8305 + 36.4105i −0.381232 + 1.17331i
\(964\) 18.5836 13.5018i 0.598537 0.434862i
\(965\) 0.947822 + 0.688633i 0.0305115 + 0.0221679i
\(966\) −11.9365 36.7369i −0.384052 1.18199i
\(967\) 14.9706 0.481421 0.240710 0.970597i \(-0.422620\pi\)
0.240710 + 0.970597i \(0.422620\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 2.72813 + 8.39633i 0.0875951 + 0.269590i
\(971\) 7.02736 + 5.10567i 0.225519 + 0.163849i 0.694807 0.719196i \(-0.255490\pi\)
−0.469289 + 0.883045i \(0.655490\pi\)
\(972\) −43.8019 + 31.8239i −1.40495 + 1.02075i
\(973\) 2.47214 7.60845i 0.0792530 0.243916i
\(974\) 18.2668 56.2195i 0.585307 1.80139i
\(975\) 2.68085 1.94775i 0.0858558 0.0623779i
\(976\) −22.6048 16.4234i −0.723563 0.525700i
\(977\) 9.99458 + 30.7602i 0.319755 + 0.984105i 0.973753 + 0.227608i \(0.0730906\pi\)
−0.653998 + 0.756496i \(0.726909\pi\)
\(978\) 112.569 3.59955
\(979\) 0 0
\(980\) 11.4853 0.366884
\(981\) 11.8305 + 36.4105i 0.377718 + 1.16250i
\(982\) 1.34042 + 0.973874i 0.0427746 + 0.0310776i
\(983\) 17.6834 12.8477i 0.564012 0.409779i −0.268913 0.963165i \(-0.586664\pi\)
0.832925 + 0.553386i \(0.186664\pi\)
\(984\) −23.1490 + 71.2452i −0.737963 + 2.27122i
\(985\) −3.34617 + 10.2984i −0.106618 + 0.328136i
\(986\) −48.7710 + 35.4342i −1.55319 + 1.12845i
\(987\) 12.9443 + 9.40456i 0.412021 + 0.299351i
\(988\) 0 0
\(989\) −16.9706 −0.539633
\(990\) 0 0
\(991\) −57.9411 −1.84056 −0.920280 0.391260i \(-0.872039\pi\)
−0.920280 + 0.391260i \(0.872039\pi\)
\(992\) 0 0
\(993\) −16.7356 12.1591i −0.531087 0.385857i
\(994\) 44.1945 32.1092i 1.40176 1.01844i
\(995\) −3.19621 + 9.83692i −0.101327 + 0.311851i
\(996\) −20.0770 + 61.7907i −0.636164 + 1.95791i
\(997\) −33.5385 + 24.3671i −1.06217 + 0.771715i −0.974489 0.224433i \(-0.927947\pi\)
−0.0876850 + 0.996148i \(0.527947\pi\)
\(998\) 18.8612 + 13.7035i 0.597040 + 0.433775i
\(999\) 13.3847 + 41.1938i 0.423472 + 1.30331i
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.g.l.511.1 8
11.2 odd 10 605.2.g.f.251.2 8
11.3 even 5 605.2.a.d.1.1 2
11.4 even 5 inner 605.2.g.l.366.2 8
11.5 even 5 inner 605.2.g.l.81.2 8
11.6 odd 10 605.2.g.f.81.1 8
11.7 odd 10 605.2.g.f.366.1 8
11.8 odd 10 55.2.a.b.1.2 2
11.9 even 5 inner 605.2.g.l.251.1 8
11.10 odd 2 605.2.g.f.511.2 8
33.8 even 10 495.2.a.b.1.1 2
33.14 odd 10 5445.2.a.y.1.2 2
44.3 odd 10 9680.2.a.bn.1.2 2
44.19 even 10 880.2.a.m.1.2 2
55.8 even 20 275.2.b.d.199.1 4
55.14 even 10 3025.2.a.o.1.2 2
55.19 odd 10 275.2.a.c.1.1 2
55.52 even 20 275.2.b.d.199.4 4
77.41 even 10 2695.2.a.f.1.2 2
88.19 even 10 3520.2.a.bo.1.1 2
88.85 odd 10 3520.2.a.bn.1.2 2
132.107 odd 10 7920.2.a.ch.1.2 2
143.129 odd 10 9295.2.a.g.1.1 2
165.8 odd 20 2475.2.c.l.199.4 4
165.74 even 10 2475.2.a.x.1.2 2
165.107 odd 20 2475.2.c.l.199.1 4
220.19 even 10 4400.2.a.bn.1.1 2
220.63 odd 20 4400.2.b.q.4049.3 4
220.107 odd 20 4400.2.b.q.4049.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.a.b.1.2 2 11.8 odd 10
275.2.a.c.1.1 2 55.19 odd 10
275.2.b.d.199.1 4 55.8 even 20
275.2.b.d.199.4 4 55.52 even 20
495.2.a.b.1.1 2 33.8 even 10
605.2.a.d.1.1 2 11.3 even 5
605.2.g.f.81.1 8 11.6 odd 10
605.2.g.f.251.2 8 11.2 odd 10
605.2.g.f.366.1 8 11.7 odd 10
605.2.g.f.511.2 8 11.10 odd 2
605.2.g.l.81.2 8 11.5 even 5 inner
605.2.g.l.251.1 8 11.9 even 5 inner
605.2.g.l.366.2 8 11.4 even 5 inner
605.2.g.l.511.1 8 1.1 even 1 trivial
880.2.a.m.1.2 2 44.19 even 10
2475.2.a.x.1.2 2 165.74 even 10
2475.2.c.l.199.1 4 165.107 odd 20
2475.2.c.l.199.4 4 165.8 odd 20
2695.2.a.f.1.2 2 77.41 even 10
3025.2.a.o.1.2 2 55.14 even 10
3520.2.a.bn.1.2 2 88.85 odd 10
3520.2.a.bo.1.1 2 88.19 even 10
4400.2.a.bn.1.1 2 220.19 even 10
4400.2.b.q.4049.2 4 220.107 odd 20
4400.2.b.q.4049.3 4 220.63 odd 20
5445.2.a.y.1.2 2 33.14 odd 10
7920.2.a.ch.1.2 2 132.107 odd 10
9295.2.a.g.1.1 2 143.129 odd 10
9680.2.a.bn.1.2 2 44.3 odd 10