Properties

Label 13.3.f.a.7.1
Level $13$
Weight $3$
Character 13.7
Analytic conductor $0.354$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [13,3,Mod(2,13)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(13, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("13.2");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 13.f (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.354224343668\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 7.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 13.7
Dual form 13.3.f.a.2.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.133975i) q^{2} +(0.366025 - 0.633975i) q^{3} +(-3.23205 + 1.86603i) q^{4} +(-2.63397 - 2.63397i) q^{5} +(-0.0980762 + 0.366025i) q^{6} +(5.73205 + 1.53590i) q^{7} +(2.83013 - 2.83013i) q^{8} +(4.23205 + 7.33013i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.133975i) q^{2} +(0.366025 - 0.633975i) q^{3} +(-3.23205 + 1.86603i) q^{4} +(-2.63397 - 2.63397i) q^{5} +(-0.0980762 + 0.366025i) q^{6} +(5.73205 + 1.53590i) q^{7} +(2.83013 - 2.83013i) q^{8} +(4.23205 + 7.33013i) q^{9} +(1.66987 + 0.964102i) q^{10} +(-4.19615 - 15.6603i) q^{11} +2.73205i q^{12} +(-6.50000 + 11.2583i) q^{13} -3.07180 q^{14} +(-2.63397 + 0.705771i) q^{15} +(6.42820 - 11.1340i) q^{16} +(-15.9904 + 9.23205i) q^{17} +(-3.09808 - 3.09808i) q^{18} +(1.63397 - 6.09808i) q^{19} +(13.4282 + 3.59808i) q^{20} +(3.07180 - 3.07180i) q^{21} +(4.19615 + 7.26795i) q^{22} +(17.4904 + 10.0981i) q^{23} +(-0.758330 - 2.83013i) q^{24} -11.1244i q^{25} +(1.74167 - 6.50000i) q^{26} +12.7846 q^{27} +(-21.3923 + 5.73205i) q^{28} +(-4.69615 + 8.13397i) q^{29} +(1.22243 - 0.705771i) q^{30} +(-11.9282 - 11.9282i) q^{31} +(-5.86603 + 21.8923i) q^{32} +(-11.4641 - 3.07180i) q^{33} +(6.75833 - 6.75833i) q^{34} +(-11.0526 - 19.1436i) q^{35} +(-27.3564 - 15.7942i) q^{36} +(8.11474 + 30.2846i) q^{37} +3.26795i q^{38} +(4.75833 + 8.24167i) q^{39} -14.9090 q^{40} +(44.9186 - 12.0359i) q^{41} +(-1.12436 + 1.94744i) q^{42} +(45.0000 - 25.9808i) q^{43} +(42.7846 + 42.7846i) q^{44} +(8.16025 - 30.4545i) q^{45} +(-10.0981 - 2.70577i) q^{46} +(-34.3205 + 34.3205i) q^{47} +(-4.70577 - 8.15064i) q^{48} +(-11.9378 - 6.89230i) q^{49} +(1.49038 + 5.56218i) q^{50} +13.5167i q^{51} -48.5167i q^{52} -14.7654 q^{53} +(-6.39230 + 1.71281i) q^{54} +(-30.1962 + 52.3013i) q^{55} +(20.5692 - 11.8756i) q^{56} +(-3.26795 - 3.26795i) q^{57} +(1.25833 - 4.69615i) q^{58} +(-92.9615 - 24.9090i) q^{59} +(7.19615 - 7.19615i) q^{60} +(-12.8135 - 22.1936i) q^{61} +(7.56218 + 4.36603i) q^{62} +(13.0000 + 48.5167i) q^{63} +39.6936i q^{64} +(46.7750 - 12.5333i) q^{65} +6.14359 q^{66} +(39.0263 - 10.4571i) q^{67} +(34.4545 - 59.6769i) q^{68} +(12.8038 - 7.39230i) q^{69} +(8.09103 + 8.09103i) q^{70} +(-11.9737 + 44.6865i) q^{71} +(32.7224 + 8.76795i) q^{72} +(-19.2750 + 19.2750i) q^{73} +(-8.11474 - 14.0551i) q^{74} +(-7.05256 - 4.07180i) q^{75} +(6.09808 + 22.7583i) q^{76} -96.2102i q^{77} +(-3.48334 - 3.48334i) q^{78} +62.7461 q^{79} +(-46.2583 + 12.3949i) q^{80} +(-33.4090 + 57.8660i) q^{81} +(-20.8468 + 12.0359i) q^{82} +(-24.4833 - 24.4833i) q^{83} +(-4.19615 + 15.6603i) q^{84} +(66.4352 + 17.8013i) q^{85} +(-19.0192 + 19.0192i) q^{86} +(3.43782 + 5.95448i) q^{87} +(-56.1962 - 32.4449i) q^{88} +(-23.1699 - 86.4711i) q^{89} +16.3205i q^{90} +(-54.5500 + 54.5500i) q^{91} -75.3731 q^{92} +(-11.9282 + 3.19615i) q^{93} +(12.5622 - 21.7583i) q^{94} +(-20.3660 + 11.7583i) q^{95} +(11.7321 + 11.7321i) q^{96} +(14.1891 - 52.9545i) q^{97} +(6.89230 + 1.84679i) q^{98} +(97.0333 - 97.0333i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{3} - 6 q^{4} - 14 q^{5} + 10 q^{6} + 16 q^{7} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 2 q^{3} - 6 q^{4} - 14 q^{5} + 10 q^{6} + 16 q^{7} - 6 q^{8} + 10 q^{9} + 24 q^{10} + 4 q^{11} - 26 q^{13} - 40 q^{14} - 14 q^{15} - 2 q^{16} - 12 q^{17} - 2 q^{18} + 10 q^{19} + 26 q^{20} + 40 q^{21} - 4 q^{22} + 18 q^{23} + 42 q^{24} + 52 q^{26} - 32 q^{27} - 44 q^{28} + 2 q^{29} - 54 q^{30} - 20 q^{31} - 20 q^{32} - 32 q^{33} - 18 q^{34} + 32 q^{35} - 54 q^{36} - 68 q^{37} - 26 q^{39} + 72 q^{40} + 100 q^{41} + 44 q^{42} + 180 q^{43} + 88 q^{44} - 2 q^{45} - 30 q^{46} - 68 q^{47} - 50 q^{48} - 72 q^{49} - 46 q^{50} + 128 q^{53} + 16 q^{54} - 100 q^{55} - 84 q^{56} - 20 q^{57} - 40 q^{58} - 164 q^{59} + 8 q^{60} - 124 q^{61} + 6 q^{62} + 52 q^{63} + 52 q^{65} + 80 q^{66} + 118 q^{67} + 72 q^{68} + 72 q^{69} + 164 q^{70} - 86 q^{71} + 72 q^{72} + 58 q^{73} + 68 q^{74} + 48 q^{75} + 14 q^{76} - 104 q^{78} - 40 q^{79} - 140 q^{80} - 2 q^{81} + 24 q^{82} - 188 q^{83} + 4 q^{84} + 96 q^{85} - 180 q^{86} + 38 q^{87} - 204 q^{88} - 110 q^{89} + 52 q^{91} - 156 q^{92} - 20 q^{93} + 26 q^{94} - 78 q^{95} + 40 q^{96} + 178 q^{97} - 14 q^{98} + 208 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{11}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.133975i −0.250000 + 0.0669873i −0.381643 0.924310i \(-0.624642\pi\)
0.131643 + 0.991297i \(0.457975\pi\)
\(3\) 0.366025 0.633975i 0.122008 0.211325i −0.798551 0.601927i \(-0.794400\pi\)
0.920560 + 0.390602i \(0.127733\pi\)
\(4\) −3.23205 + 1.86603i −0.808013 + 0.466506i
\(5\) −2.63397 2.63397i −0.526795 0.526795i 0.392820 0.919615i \(-0.371499\pi\)
−0.919615 + 0.392820i \(0.871499\pi\)
\(6\) −0.0980762 + 0.366025i −0.0163460 + 0.0610042i
\(7\) 5.73205 + 1.53590i 0.818864 + 0.219414i 0.643850 0.765152i \(-0.277336\pi\)
0.175014 + 0.984566i \(0.444003\pi\)
\(8\) 2.83013 2.83013i 0.353766 0.353766i
\(9\) 4.23205 + 7.33013i 0.470228 + 0.814459i
\(10\) 1.66987 + 0.964102i 0.166987 + 0.0964102i
\(11\) −4.19615 15.6603i −0.381468 1.42366i −0.843659 0.536879i \(-0.819603\pi\)
0.462191 0.886780i \(-0.347063\pi\)
\(12\) 2.73205i 0.227671i
\(13\) −6.50000 + 11.2583i −0.500000 + 0.866025i
\(14\) −3.07180 −0.219414
\(15\) −2.63397 + 0.705771i −0.175598 + 0.0470514i
\(16\) 6.42820 11.1340i 0.401763 0.695873i
\(17\) −15.9904 + 9.23205i −0.940611 + 0.543062i −0.890152 0.455664i \(-0.849402\pi\)
−0.0504590 + 0.998726i \(0.516068\pi\)
\(18\) −3.09808 3.09808i −0.172115 0.172115i
\(19\) 1.63397 6.09808i 0.0859987 0.320951i −0.909503 0.415698i \(-0.863537\pi\)
0.995501 + 0.0947465i \(0.0302040\pi\)
\(20\) 13.4282 + 3.59808i 0.671410 + 0.179904i
\(21\) 3.07180 3.07180i 0.146276 0.146276i
\(22\) 4.19615 + 7.26795i 0.190734 + 0.330361i
\(23\) 17.4904 + 10.0981i 0.760451 + 0.439047i 0.829458 0.558569i \(-0.188650\pi\)
−0.0690064 + 0.997616i \(0.521983\pi\)
\(24\) −0.758330 2.83013i −0.0315971 0.117922i
\(25\) 11.1244i 0.444974i
\(26\) 1.74167 6.50000i 0.0669873 0.250000i
\(27\) 12.7846 0.473504
\(28\) −21.3923 + 5.73205i −0.764011 + 0.204716i
\(29\) −4.69615 + 8.13397i −0.161936 + 0.280482i −0.935563 0.353160i \(-0.885107\pi\)
0.773627 + 0.633642i \(0.218441\pi\)
\(30\) 1.22243 0.705771i 0.0407477 0.0235257i
\(31\) −11.9282 11.9282i −0.384781 0.384781i 0.488040 0.872821i \(-0.337712\pi\)
−0.872821 + 0.488040i \(0.837712\pi\)
\(32\) −5.86603 + 21.8923i −0.183313 + 0.684135i
\(33\) −11.4641 3.07180i −0.347397 0.0930848i
\(34\) 6.75833 6.75833i 0.198774 0.198774i
\(35\) −11.0526 19.1436i −0.315787 0.546960i
\(36\) −27.3564 15.7942i −0.759900 0.438729i
\(37\) 8.11474 + 30.2846i 0.219317 + 0.818503i 0.984602 + 0.174811i \(0.0559315\pi\)
−0.765285 + 0.643692i \(0.777402\pi\)
\(38\) 3.26795i 0.0859987i
\(39\) 4.75833 + 8.24167i 0.122008 + 0.211325i
\(40\) −14.9090 −0.372724
\(41\) 44.9186 12.0359i 1.09558 0.293558i 0.334614 0.942355i \(-0.391394\pi\)
0.760962 + 0.648797i \(0.224728\pi\)
\(42\) −1.12436 + 1.94744i −0.0267704 + 0.0463676i
\(43\) 45.0000 25.9808i 1.04651 0.604204i 0.124841 0.992177i \(-0.460158\pi\)
0.921671 + 0.387973i \(0.126825\pi\)
\(44\) 42.7846 + 42.7846i 0.972377 + 0.972377i
\(45\) 8.16025 30.4545i 0.181339 0.676766i
\(46\) −10.0981 2.70577i −0.219523 0.0588211i
\(47\) −34.3205 + 34.3205i −0.730224 + 0.730224i −0.970664 0.240440i \(-0.922708\pi\)
0.240440 + 0.970664i \(0.422708\pi\)
\(48\) −4.70577 8.15064i −0.0980369 0.169805i
\(49\) −11.9378 6.89230i −0.243629 0.140659i
\(50\) 1.49038 + 5.56218i 0.0298076 + 0.111244i
\(51\) 13.5167i 0.265033i
\(52\) 48.5167i 0.933013i
\(53\) −14.7654 −0.278592 −0.139296 0.990251i \(-0.544484\pi\)
−0.139296 + 0.990251i \(0.544484\pi\)
\(54\) −6.39230 + 1.71281i −0.118376 + 0.0317188i
\(55\) −30.1962 + 52.3013i −0.549021 + 0.950932i
\(56\) 20.5692 11.8756i 0.367307 0.212065i
\(57\) −3.26795 3.26795i −0.0573324 0.0573324i
\(58\) 1.25833 4.69615i 0.0216953 0.0809681i
\(59\) −92.9615 24.9090i −1.57562 0.422186i −0.638053 0.769993i \(-0.720260\pi\)
−0.937566 + 0.347807i \(0.886927\pi\)
\(60\) 7.19615 7.19615i 0.119936 0.119936i
\(61\) −12.8135 22.1936i −0.210057 0.363829i 0.741675 0.670759i \(-0.234032\pi\)
−0.951732 + 0.306930i \(0.900698\pi\)
\(62\) 7.56218 + 4.36603i 0.121971 + 0.0704198i
\(63\) 13.0000 + 48.5167i 0.206349 + 0.770106i
\(64\) 39.6936i 0.620212i
\(65\) 46.7750 12.5333i 0.719615 0.192820i
\(66\) 6.14359 0.0930848
\(67\) 39.0263 10.4571i 0.582482 0.156076i 0.0444669 0.999011i \(-0.485841\pi\)
0.538015 + 0.842935i \(0.319174\pi\)
\(68\) 34.4545 59.6769i 0.506684 0.877602i
\(69\) 12.8038 7.39230i 0.185563 0.107135i
\(70\) 8.09103 + 8.09103i 0.115586 + 0.115586i
\(71\) −11.9737 + 44.6865i −0.168644 + 0.629388i 0.828903 + 0.559392i \(0.188965\pi\)
−0.997547 + 0.0699959i \(0.977701\pi\)
\(72\) 32.7224 + 8.76795i 0.454478 + 0.121777i
\(73\) −19.2750 + 19.2750i −0.264041 + 0.264041i −0.826693 0.562653i \(-0.809781\pi\)
0.562653 + 0.826693i \(0.309781\pi\)
\(74\) −8.11474 14.0551i −0.109659 0.189934i
\(75\) −7.05256 4.07180i −0.0940341 0.0542906i
\(76\) 6.09808 + 22.7583i 0.0802378 + 0.299452i
\(77\) 96.2102i 1.24948i
\(78\) −3.48334 3.48334i −0.0446582 0.0446582i
\(79\) 62.7461 0.794255 0.397127 0.917763i \(-0.370007\pi\)
0.397127 + 0.917763i \(0.370007\pi\)
\(80\) −46.2583 + 12.3949i −0.578229 + 0.154936i
\(81\) −33.4090 + 57.8660i −0.412456 + 0.714395i
\(82\) −20.8468 + 12.0359i −0.254229 + 0.146779i
\(83\) −24.4833 24.4833i −0.294980 0.294980i 0.544064 0.839044i \(-0.316885\pi\)
−0.839044 + 0.544064i \(0.816885\pi\)
\(84\) −4.19615 + 15.6603i −0.0499542 + 0.186432i
\(85\) 66.4352 + 17.8013i 0.781591 + 0.209427i
\(86\) −19.0192 + 19.0192i −0.221154 + 0.221154i
\(87\) 3.43782 + 5.95448i 0.0395152 + 0.0684423i
\(88\) −56.1962 32.4449i −0.638593 0.368692i
\(89\) −23.1699 86.4711i −0.260336 0.971586i −0.965044 0.262089i \(-0.915589\pi\)
0.704708 0.709497i \(-0.251078\pi\)
\(90\) 16.3205i 0.181339i
\(91\) −54.5500 + 54.5500i −0.599450 + 0.599450i
\(92\) −75.3731 −0.819272
\(93\) −11.9282 + 3.19615i −0.128260 + 0.0343672i
\(94\) 12.5622 21.7583i 0.133640 0.231472i
\(95\) −20.3660 + 11.7583i −0.214379 + 0.123772i
\(96\) 11.7321 + 11.7321i 0.122209 + 0.122209i
\(97\) 14.1891 52.9545i 0.146279 0.545923i −0.853416 0.521231i \(-0.825473\pi\)
0.999695 0.0246915i \(-0.00786034\pi\)
\(98\) 6.89230 + 1.84679i 0.0703296 + 0.0188448i
\(99\) 97.0333 97.0333i 0.980135 0.980135i
\(100\) 20.7583 + 35.9545i 0.207583 + 0.359545i
\(101\) 138.560 + 79.9974i 1.37188 + 0.792054i 0.991164 0.132640i \(-0.0423453\pi\)
0.380713 + 0.924693i \(0.375679\pi\)
\(102\) −1.81089 6.75833i −0.0177538 0.0662581i
\(103\) 78.7705i 0.764762i 0.924005 + 0.382381i \(0.124896\pi\)
−0.924005 + 0.382381i \(0.875104\pi\)
\(104\) 13.4667 + 50.2583i 0.129487 + 0.483253i
\(105\) −16.1821 −0.154115
\(106\) 7.38269 1.97818i 0.0696480 0.0186621i
\(107\) 47.6673 82.5622i 0.445489 0.771609i −0.552597 0.833448i \(-0.686363\pi\)
0.998086 + 0.0618392i \(0.0196966\pi\)
\(108\) −41.3205 + 23.8564i −0.382597 + 0.220893i
\(109\) −51.9808 51.9808i −0.476888 0.476888i 0.427247 0.904135i \(-0.359483\pi\)
−0.904135 + 0.427247i \(0.859483\pi\)
\(110\) 8.09103 30.1962i 0.0735549 0.274510i
\(111\) 22.1699 + 5.94040i 0.199729 + 0.0535171i
\(112\) 53.9474 53.9474i 0.481674 0.481674i
\(113\) 71.9904 + 124.691i 0.637083 + 1.10346i 0.986070 + 0.166332i \(0.0531925\pi\)
−0.348987 + 0.937128i \(0.613474\pi\)
\(114\) 2.07180 + 1.19615i 0.0181737 + 0.0104926i
\(115\) −19.4711 72.6673i −0.169314 0.631890i
\(116\) 35.0526i 0.302177i
\(117\) −110.033 −0.940456
\(118\) 49.8179 0.422186
\(119\) −105.837 + 28.3590i −0.889388 + 0.238311i
\(120\) −5.45706 + 9.45191i −0.0454755 + 0.0787659i
\(121\) −122.847 + 70.9256i −1.01526 + 0.586162i
\(122\) 9.38011 + 9.38011i 0.0768861 + 0.0768861i
\(123\) 8.81089 32.8827i 0.0716332 0.267339i
\(124\) 60.8109 + 16.2942i 0.490410 + 0.131405i
\(125\) −95.1506 + 95.1506i −0.761205 + 0.761205i
\(126\) −13.0000 22.5167i −0.103175 0.178704i
\(127\) −24.6673 14.2417i −0.194231 0.112139i 0.399731 0.916633i \(-0.369104\pi\)
−0.593962 + 0.804493i \(0.702437\pi\)
\(128\) −28.7820 107.416i −0.224860 0.839188i
\(129\) 38.0385i 0.294872i
\(130\) −21.7083 + 12.5333i −0.166987 + 0.0964102i
\(131\) −2.98076 −0.0227539 −0.0113770 0.999935i \(-0.503621\pi\)
−0.0113770 + 0.999935i \(0.503621\pi\)
\(132\) 42.7846 11.4641i 0.324126 0.0868493i
\(133\) 18.7321 32.4449i 0.140842 0.243946i
\(134\) −18.1122 + 10.4571i −0.135165 + 0.0780378i
\(135\) −33.6743 33.6743i −0.249440 0.249440i
\(136\) −19.1269 + 71.3827i −0.140639 + 0.524873i
\(137\) 94.6051 + 25.3494i 0.690548 + 0.185032i 0.586993 0.809592i \(-0.300312\pi\)
0.103555 + 0.994624i \(0.466978\pi\)
\(138\) −5.41154 + 5.41154i −0.0392141 + 0.0392141i
\(139\) −16.2154 28.0859i −0.116657 0.202057i 0.801784 0.597614i \(-0.203885\pi\)
−0.918441 + 0.395558i \(0.870551\pi\)
\(140\) 71.4449 + 41.2487i 0.510320 + 0.294634i
\(141\) 9.19615 + 34.3205i 0.0652209 + 0.243408i
\(142\) 23.9474i 0.168644i
\(143\) 203.583 + 54.5500i 1.42366 + 0.381468i
\(144\) 108.818 0.755680
\(145\) 33.7942 9.05514i 0.233064 0.0624492i
\(146\) 7.05514 12.2199i 0.0483229 0.0836976i
\(147\) −8.73909 + 5.04552i −0.0594496 + 0.0343232i
\(148\) −82.7391 82.7391i −0.559048 0.559048i
\(149\) −33.0903 + 123.495i −0.222083 + 0.828824i 0.761469 + 0.648201i \(0.224478\pi\)
−0.983552 + 0.180624i \(0.942188\pi\)
\(150\) 4.07180 + 1.09103i 0.0271453 + 0.00727356i
\(151\) 127.995 127.995i 0.847648 0.847648i −0.142191 0.989839i \(-0.545415\pi\)
0.989839 + 0.142191i \(0.0454148\pi\)
\(152\) −12.6340 21.8827i −0.0831183 0.143965i
\(153\) −135.344 78.1410i −0.884603 0.510726i
\(154\) 12.8897 + 48.1051i 0.0836995 + 0.312371i
\(155\) 62.8372i 0.405401i
\(156\) −30.7583 17.7583i −0.197169 0.113835i
\(157\) −97.7461 −0.622587 −0.311293 0.950314i \(-0.600762\pi\)
−0.311293 + 0.950314i \(0.600762\pi\)
\(158\) −31.3731 + 8.40639i −0.198564 + 0.0532050i
\(159\) −5.40450 + 9.36087i −0.0339906 + 0.0588734i
\(160\) 73.1147 42.2128i 0.456967 0.263830i
\(161\) 84.7461 + 84.7461i 0.526374 + 0.526374i
\(162\) 8.95191 33.4090i 0.0552587 0.206228i
\(163\) −122.282 32.7654i −0.750197 0.201015i −0.136591 0.990627i \(-0.543615\pi\)
−0.613605 + 0.789613i \(0.710281\pi\)
\(164\) −122.720 + 122.720i −0.748292 + 0.748292i
\(165\) 22.1051 + 38.2872i 0.133970 + 0.232044i
\(166\) 15.5218 + 8.96152i 0.0935049 + 0.0539851i
\(167\) −13.5936 50.7321i −0.0813989 0.303785i 0.913209 0.407491i \(-0.133596\pi\)
−0.994608 + 0.103707i \(0.966930\pi\)
\(168\) 17.3872i 0.103495i
\(169\) −84.5000 146.358i −0.500000 0.866025i
\(170\) −35.6025 −0.209427
\(171\) 51.6147 13.8301i 0.301841 0.0808779i
\(172\) −96.9615 + 167.942i −0.563730 + 0.976409i
\(173\) 118.865 68.6269i 0.687083 0.396687i −0.115435 0.993315i \(-0.536826\pi\)
0.802518 + 0.596628i \(0.203493\pi\)
\(174\) −2.51666 2.51666i −0.0144636 0.0144636i
\(175\) 17.0859 63.7654i 0.0976336 0.364374i
\(176\) −201.335 53.9474i −1.14395 0.306520i
\(177\) −49.8179 + 49.8179i −0.281457 + 0.281457i
\(178\) 23.1699 + 40.1314i 0.130168 + 0.225457i
\(179\) 0.903811 + 0.521815i 0.00504922 + 0.00291517i 0.502522 0.864564i \(-0.332405\pi\)
−0.497473 + 0.867479i \(0.665739\pi\)
\(180\) 30.4545 + 113.658i 0.169192 + 0.631432i
\(181\) 23.0807i 0.127518i 0.997965 + 0.0637589i \(0.0203089\pi\)
−0.997965 + 0.0637589i \(0.979691\pi\)
\(182\) 19.9667 34.5833i 0.109707 0.190018i
\(183\) −18.7602 −0.102515
\(184\) 78.0788 20.9212i 0.424342 0.113702i
\(185\) 58.3949 101.143i 0.315648 0.546718i
\(186\) 5.53590 3.19615i 0.0297629 0.0171836i
\(187\) 211.674 + 211.674i 1.13195 + 1.13195i
\(188\) 46.8827 174.969i 0.249376 0.930684i
\(189\) 73.2820 + 19.6359i 0.387736 + 0.103893i
\(190\) 8.60770 8.60770i 0.0453037 0.0453037i
\(191\) −147.002 254.615i −0.769643 1.33306i −0.937756 0.347294i \(-0.887101\pi\)
0.168113 0.985768i \(-0.446233\pi\)
\(192\) 25.1647 + 14.5289i 0.131066 + 0.0756711i
\(193\) 85.5507 + 319.279i 0.443268 + 1.65430i 0.720470 + 0.693486i \(0.243926\pi\)
−0.277202 + 0.960812i \(0.589407\pi\)
\(194\) 28.3782i 0.146279i
\(195\) 9.17503 34.2417i 0.0470514 0.175598i
\(196\) 51.4449 0.262474
\(197\) 85.1122 22.8057i 0.432041 0.115765i −0.0362429 0.999343i \(-0.511539\pi\)
0.468284 + 0.883578i \(0.344872\pi\)
\(198\) −35.5167 + 61.5167i −0.179377 + 0.310690i
\(199\) 174.452 100.720i 0.876643 0.506130i 0.00709275 0.999975i \(-0.497742\pi\)
0.869550 + 0.493845i \(0.164409\pi\)
\(200\) −31.4833 31.4833i −0.157417 0.157417i
\(201\) 7.65510 28.5692i 0.0380851 0.142135i
\(202\) −79.9974 21.4352i −0.396027 0.106115i
\(203\) −39.4115 + 39.4115i −0.194146 + 0.194146i
\(204\) −25.2224 43.6865i −0.123639 0.214150i
\(205\) −150.017 86.6122i −0.731789 0.422498i
\(206\) −10.5532 39.3853i −0.0512294 0.191191i
\(207\) 170.942i 0.825808i
\(208\) 83.5666 + 144.742i 0.401763 + 0.695873i
\(209\) −102.354 −0.489731
\(210\) 8.09103 2.16799i 0.0385287 0.0103237i
\(211\) −36.6481 + 63.4763i −0.173687 + 0.300836i −0.939706 0.341983i \(-0.888902\pi\)
0.766019 + 0.642818i \(0.222235\pi\)
\(212\) 47.7224 27.5526i 0.225106 0.129965i
\(213\) 23.9474 + 23.9474i 0.112429 + 0.112429i
\(214\) −12.7724 + 47.6673i −0.0596842 + 0.222744i
\(215\) −186.962 50.0962i −0.869588 0.233006i
\(216\) 36.1821 36.1821i 0.167510 0.167510i
\(217\) −50.0526 86.6936i −0.230657 0.399510i
\(218\) 32.9545 + 19.0263i 0.151167 + 0.0872765i
\(219\) 5.16472 + 19.2750i 0.0235832 + 0.0880137i
\(220\) 225.387i 1.02449i
\(221\) 240.033i 1.08612i
\(222\) −11.8808 −0.0535171
\(223\) −367.533 + 98.4801i −1.64813 + 0.441615i −0.959088 0.283108i \(-0.908634\pi\)
−0.689040 + 0.724723i \(0.741968\pi\)
\(224\) −67.2487 + 116.478i −0.300217 + 0.519992i
\(225\) 81.5429 47.0788i 0.362413 0.209239i
\(226\) −52.7006 52.7006i −0.233189 0.233189i
\(227\) −108.280 + 404.107i −0.477005 + 1.78021i 0.136635 + 0.990621i \(0.456371\pi\)
−0.613640 + 0.789586i \(0.710296\pi\)
\(228\) 16.6603 + 4.46410i 0.0730713 + 0.0195794i
\(229\) −72.2679 + 72.2679i −0.315581 + 0.315581i −0.847067 0.531486i \(-0.821634\pi\)
0.531486 + 0.847067i \(0.321634\pi\)
\(230\) 19.4711 + 33.7250i 0.0846571 + 0.146630i
\(231\) −60.9948 35.2154i −0.264047 0.152448i
\(232\) 9.72947 + 36.3109i 0.0419374 + 0.156512i
\(233\) 256.592i 1.10125i −0.834751 0.550627i \(-0.814389\pi\)
0.834751 0.550627i \(-0.185611\pi\)
\(234\) 55.0167 14.7417i 0.235114 0.0629986i
\(235\) 180.799 0.769356
\(236\) 346.937 92.9615i 1.47007 0.393905i
\(237\) 22.9667 39.7795i 0.0969058 0.167846i
\(238\) 49.1192 28.3590i 0.206383 0.119155i
\(239\) 39.3449 + 39.3449i 0.164623 + 0.164623i 0.784611 0.619988i \(-0.212863\pi\)
−0.619988 + 0.784611i \(0.712863\pi\)
\(240\) −9.07368 + 33.8634i −0.0378070 + 0.141098i
\(241\) 233.351 + 62.5263i 0.968262 + 0.259445i 0.708094 0.706118i \(-0.249555\pi\)
0.260168 + 0.965563i \(0.416222\pi\)
\(242\) 51.9212 51.9212i 0.214550 0.214550i
\(243\) 81.9878 + 142.007i 0.337398 + 0.584391i
\(244\) 82.8275 + 47.8205i 0.339457 + 0.195986i
\(245\) 13.2898 + 49.5981i 0.0542439 + 0.202441i
\(246\) 17.6218i 0.0716332i
\(247\) 58.0333 + 58.0333i 0.234953 + 0.234953i
\(248\) −67.5167 −0.272245
\(249\) −24.4833 + 6.56029i −0.0983267 + 0.0263466i
\(250\) 34.8275 60.3231i 0.139310 0.241292i
\(251\) −221.375 + 127.811i −0.881972 + 0.509207i −0.871308 0.490736i \(-0.836728\pi\)
−0.0106638 + 0.999943i \(0.503394\pi\)
\(252\) −132.550 132.550i −0.525992 0.525992i
\(253\) 84.7461 316.277i 0.334965 1.25011i
\(254\) 14.2417 + 3.81604i 0.0560696 + 0.0150238i
\(255\) 35.6025 35.6025i 0.139618 0.139618i
\(256\) −50.6051 87.6506i −0.197676 0.342385i
\(257\) 85.7731 + 49.5211i 0.333747 + 0.192689i 0.657504 0.753451i \(-0.271612\pi\)
−0.323756 + 0.946141i \(0.604946\pi\)
\(258\) 5.09619 + 19.0192i 0.0197527 + 0.0737180i
\(259\) 186.056i 0.718364i
\(260\) −127.792 + 127.792i −0.491506 + 0.491506i
\(261\) −79.4974 −0.304588
\(262\) 1.49038 0.399346i 0.00568848 0.00152422i
\(263\) 127.669 221.130i 0.485434 0.840797i −0.514426 0.857535i \(-0.671995\pi\)
0.999860 + 0.0167383i \(0.00532822\pi\)
\(264\) −41.1384 + 23.7513i −0.155827 + 0.0899670i
\(265\) 38.8916 + 38.8916i 0.146761 + 0.146761i
\(266\) −5.01924 + 18.7321i −0.0188693 + 0.0704212i
\(267\) −63.3013 16.9615i −0.237083 0.0635263i
\(268\) −106.622 + 106.622i −0.397842 + 0.397842i
\(269\) 46.3538 + 80.2872i 0.172319 + 0.298465i 0.939230 0.343288i \(-0.111541\pi\)
−0.766911 + 0.641753i \(0.778207\pi\)
\(270\) 21.3487 + 12.3257i 0.0790692 + 0.0456506i
\(271\) −113.133 422.219i −0.417466 1.55800i −0.779845 0.625973i \(-0.784702\pi\)
0.362379 0.932031i \(-0.381965\pi\)
\(272\) 237.382i 0.872728i
\(273\) 14.6166 + 54.5500i 0.0535407 + 0.199817i
\(274\) −50.6987 −0.185032
\(275\) −174.210 + 46.6795i −0.633492 + 0.169744i
\(276\) −27.5885 + 47.7846i −0.0999582 + 0.173133i
\(277\) −302.110 + 174.423i −1.09065 + 0.629686i −0.933749 0.357929i \(-0.883483\pi\)
−0.156899 + 0.987615i \(0.550150\pi\)
\(278\) 11.8705 + 11.8705i 0.0426996 + 0.0426996i
\(279\) 36.9545 137.916i 0.132453 0.494323i
\(280\) −85.4589 22.8987i −0.305211 0.0817809i
\(281\) 91.9737 91.9737i 0.327309 0.327309i −0.524254 0.851562i \(-0.675656\pi\)
0.851562 + 0.524254i \(0.175656\pi\)
\(282\) −9.19615 15.9282i −0.0326105 0.0564830i
\(283\) −30.8038 17.7846i −0.108848 0.0628431i 0.444588 0.895735i \(-0.353350\pi\)
−0.553435 + 0.832892i \(0.686683\pi\)
\(284\) −44.6865 166.772i −0.157347 0.587227i
\(285\) 17.2154i 0.0604049i
\(286\) −109.100 −0.381468
\(287\) 275.962 0.961538
\(288\) −185.299 + 49.6506i −0.643398 + 0.172398i
\(289\) 25.9615 44.9667i 0.0898323 0.155594i
\(290\) −15.6840 + 9.05514i −0.0540826 + 0.0312246i
\(291\) −28.3782 28.3782i −0.0975197 0.0975197i
\(292\) 26.3301 98.2654i 0.0901717 0.336525i
\(293\) 386.758 + 103.631i 1.31999 + 0.353691i 0.848975 0.528433i \(-0.177220\pi\)
0.471017 + 0.882124i \(0.343887\pi\)
\(294\) 3.69358 3.69358i 0.0125632 0.0125632i
\(295\) 179.249 + 310.468i 0.607623 + 1.05243i
\(296\) 108.675 + 62.7436i 0.367145 + 0.211971i
\(297\) −53.6462 200.210i −0.180627 0.674109i
\(298\) 66.1807i 0.222083i
\(299\) −227.375 + 131.275i −0.760451 + 0.439047i
\(300\) 30.3923 0.101308
\(301\) 297.846 79.8076i 0.989522 0.265142i
\(302\) −46.8494 + 81.1455i −0.155130 + 0.268694i
\(303\) 101.433 58.5622i 0.334761 0.193275i
\(304\) −57.3923 57.3923i −0.188790 0.188790i
\(305\) −24.7070 + 92.2077i −0.0810065 + 0.302320i
\(306\) 78.1410 + 20.9378i 0.255363 + 0.0684243i
\(307\) 260.219 260.219i 0.847619 0.847619i −0.142216 0.989836i \(-0.545423\pi\)
0.989836 + 0.142216i \(0.0454228\pi\)
\(308\) 179.531 + 310.956i 0.582892 + 1.00960i
\(309\) 49.9385 + 28.8320i 0.161613 + 0.0933075i
\(310\) −8.41858 31.4186i −0.0271567 0.101350i
\(311\) 71.4782i 0.229833i 0.993375 + 0.114917i \(0.0366601\pi\)
−0.993375 + 0.114917i \(0.963340\pi\)
\(312\) 36.7917 + 9.85829i 0.117922 + 0.0315971i
\(313\) −394.315 −1.25979 −0.629897 0.776679i \(-0.716903\pi\)
−0.629897 + 0.776679i \(0.716903\pi\)
\(314\) 48.8731 13.0955i 0.155647 0.0417054i
\(315\) 93.5500 162.033i 0.296984 0.514391i
\(316\) −202.799 + 117.086i −0.641768 + 0.370525i
\(317\) −206.054 206.054i −0.650014 0.650014i 0.302982 0.952996i \(-0.402018\pi\)
−0.952996 + 0.302982i \(0.902018\pi\)
\(318\) 1.44813 5.40450i 0.00455387 0.0169953i
\(319\) 147.086 + 39.4115i 0.461084 + 0.123547i
\(320\) 104.552 104.552i 0.326725 0.326725i
\(321\) −34.8949 60.4397i −0.108707 0.188286i
\(322\) −53.7269 31.0192i −0.166854 0.0963330i
\(323\) 30.1699 + 112.595i 0.0934052 + 0.348593i
\(324\) 249.368i 0.769654i
\(325\) 125.242 + 72.3083i 0.385359 + 0.222487i
\(326\) 65.5307 0.201015
\(327\) −51.9808 + 13.9282i −0.158963 + 0.0425939i
\(328\) 93.0622 161.188i 0.283726 0.491428i
\(329\) −249.440 + 144.014i −0.758175 + 0.437733i
\(330\) −16.1821 16.1821i −0.0490366 0.0490366i
\(331\) −119.397 + 445.597i −0.360717 + 1.34622i 0.512417 + 0.858737i \(0.328750\pi\)
−0.873135 + 0.487479i \(0.837917\pi\)
\(332\) 124.818 + 33.4449i 0.375958 + 0.100738i
\(333\) −187.648 + 187.648i −0.563508 + 0.563508i
\(334\) 13.5936 + 23.5448i 0.0406994 + 0.0704935i
\(335\) −130.338 75.2506i −0.389068 0.224629i
\(336\) −14.4552 53.9474i −0.0430213 0.160558i
\(337\) 144.779i 0.429613i −0.976657 0.214806i \(-0.931088\pi\)
0.976657 0.214806i \(-0.0689120\pi\)
\(338\) 61.8583 + 61.8583i 0.183013 + 0.183013i
\(339\) 105.401 0.310918
\(340\) −247.940 + 66.4352i −0.729234 + 0.195398i
\(341\) −136.746 + 236.851i −0.401015 + 0.694578i
\(342\) −23.9545 + 13.8301i −0.0700423 + 0.0404390i
\(343\) −263.454 263.454i −0.768087 0.768087i
\(344\) 53.8269 200.885i 0.156473 0.583967i
\(345\) −53.1962 14.2539i −0.154192 0.0413156i
\(346\) −50.2384 + 50.2384i −0.145198 + 0.145198i
\(347\) −243.590 421.911i −0.701989 1.21588i −0.967767 0.251847i \(-0.918962\pi\)
0.265778 0.964034i \(-0.414371\pi\)
\(348\) −22.2224 12.8301i −0.0638576 0.0368682i
\(349\) −3.04036 11.3468i −0.00871164 0.0325123i 0.961433 0.275039i \(-0.0886906\pi\)
−0.970145 + 0.242526i \(0.922024\pi\)
\(350\) 34.1718i 0.0976336i
\(351\) −83.1000 + 143.933i −0.236752 + 0.410067i
\(352\) 367.454 1.04390
\(353\) −276.169 + 73.9993i −0.782349 + 0.209630i −0.627820 0.778358i \(-0.716053\pi\)
−0.154529 + 0.987988i \(0.549386\pi\)
\(354\) 18.2346 31.5833i 0.0515102 0.0892184i
\(355\) 149.242 86.1647i 0.420399 0.242718i
\(356\) 236.244 + 236.244i 0.663605 + 0.663605i
\(357\) −20.7602 + 77.4782i −0.0581519 + 0.217026i
\(358\) −0.521815 0.139820i −0.00145758 0.000390559i
\(359\) 92.0770 92.0770i 0.256482 0.256482i −0.567140 0.823622i \(-0.691950\pi\)
0.823622 + 0.567140i \(0.191950\pi\)
\(360\) −63.0955 109.285i −0.175265 0.303568i
\(361\) 278.119 + 160.572i 0.770411 + 0.444797i
\(362\) −3.09223 11.5404i −0.00854207 0.0318795i
\(363\) 103.842i 0.286067i
\(364\) 74.5167 278.100i 0.204716 0.764011i
\(365\) 101.540 0.278191
\(366\) 9.38011 2.51339i 0.0256287 0.00686719i
\(367\) −6.27499 + 10.8686i −0.0170981 + 0.0296147i −0.874448 0.485120i \(-0.838776\pi\)
0.857350 + 0.514734i \(0.172109\pi\)
\(368\) 224.863 129.825i 0.611042 0.352785i
\(369\) 278.322 + 278.322i 0.754261 + 0.754261i
\(370\) −15.6469 + 58.3949i −0.0422888 + 0.157824i
\(371\) −84.6359 22.6781i −0.228129 0.0611270i
\(372\) 32.5885 32.5885i 0.0876034 0.0876034i
\(373\) 155.638 + 269.574i 0.417261 + 0.722718i 0.995663 0.0930345i \(-0.0296567\pi\)
−0.578402 + 0.815752i \(0.696323\pi\)
\(374\) −134.196 77.4782i −0.358813 0.207161i
\(375\) 25.4955 + 95.1506i 0.0679881 + 0.253735i
\(376\) 194.263i 0.516656i
\(377\) −61.0500 105.742i −0.161936 0.280482i
\(378\) −39.2717 −0.103893
\(379\) 379.858 101.783i 1.00226 0.268556i 0.279871 0.960038i \(-0.409708\pi\)
0.722394 + 0.691482i \(0.243042\pi\)
\(380\) 43.8827 76.0070i 0.115481 0.200019i
\(381\) −18.0577 + 10.4256i −0.0473956 + 0.0273638i
\(382\) 107.613 + 107.613i 0.281709 + 0.281709i
\(383\) 191.061 713.051i 0.498855 1.86175i −0.00841386 0.999965i \(-0.502678\pi\)
0.507269 0.861788i \(-0.330655\pi\)
\(384\) −78.6340 21.0699i −0.204776 0.0548696i
\(385\) −253.415 + 253.415i −0.658222 + 0.658222i
\(386\) −85.5507 148.178i −0.221634 0.383881i
\(387\) 380.885 + 219.904i 0.984198 + 0.568227i
\(388\) 52.9545 + 197.629i 0.136481 + 0.509353i
\(389\) 344.478i 0.885548i −0.896633 0.442774i \(-0.853994\pi\)
0.896633 0.442774i \(-0.146006\pi\)
\(390\) 18.3501i 0.0470514i
\(391\) −372.904 −0.953718
\(392\) −53.2917 + 14.2795i −0.135948 + 0.0364272i
\(393\) −1.09103 + 1.88973i −0.00277617 + 0.00480847i
\(394\) −39.5007 + 22.8057i −0.100256 + 0.0578826i
\(395\) −165.272 165.272i −0.418409 0.418409i
\(396\) −132.550 + 494.683i −0.334722 + 1.24920i
\(397\) −678.422 181.783i −1.70887 0.457891i −0.733725 0.679447i \(-0.762220\pi\)
−0.975148 + 0.221556i \(0.928886\pi\)
\(398\) −73.7321 + 73.7321i −0.185256 + 0.185256i
\(399\) −13.7128 23.7513i −0.0343680 0.0595270i
\(400\) −123.858 71.5096i −0.309646 0.178774i
\(401\) 146.833 + 547.989i 0.366168 + 1.36656i 0.865831 + 0.500336i \(0.166790\pi\)
−0.499663 + 0.866220i \(0.666543\pi\)
\(402\) 15.3102i 0.0380851i
\(403\) 211.825 56.7583i 0.525620 0.140840i
\(404\) −597.109 −1.47799
\(405\) 240.416 64.4193i 0.593620 0.159060i
\(406\) 14.4256 24.9859i 0.0355311 0.0615417i
\(407\) 440.214 254.158i 1.08161 0.624466i
\(408\) 38.2539 + 38.2539i 0.0937595 + 0.0937595i
\(409\) 26.3212 98.2321i 0.0643550 0.240176i −0.926254 0.376899i \(-0.876990\pi\)
0.990609 + 0.136723i \(0.0436570\pi\)
\(410\) 86.6122 + 23.2077i 0.211249 + 0.0566040i
\(411\) 50.6987 50.6987i 0.123355 0.123355i
\(412\) −146.988 254.590i −0.356767 0.617938i
\(413\) −494.603 285.559i −1.19758 0.691426i
\(414\) −22.9019 85.4711i −0.0553187 0.206452i
\(415\) 128.977i 0.310788i
\(416\) −208.342 208.342i −0.500821 0.500821i
\(417\) −23.7410 −0.0569328
\(418\) 51.1769 13.7128i 0.122433 0.0328058i
\(419\) −322.279 + 558.203i −0.769162 + 1.33223i 0.168856 + 0.985641i \(0.445993\pi\)
−0.938018 + 0.346587i \(0.887341\pi\)
\(420\) 52.3013 30.1962i 0.124527 0.0718956i
\(421\) 346.619 + 346.619i 0.823322 + 0.823322i 0.986583 0.163261i \(-0.0522013\pi\)
−0.163261 + 0.986583i \(0.552201\pi\)
\(422\) 9.81982 36.6481i 0.0232697 0.0868437i
\(423\) −396.820 106.328i −0.938108 0.251365i
\(424\) −41.7879 + 41.7879i −0.0985563 + 0.0985563i
\(425\) 102.701 + 177.883i 0.241649 + 0.418547i
\(426\) −15.1821 8.76537i −0.0356387 0.0205760i
\(427\) −39.3604 146.895i −0.0921788 0.344016i
\(428\) 355.794i 0.831293i
\(429\) 109.100 109.100i 0.254312 0.254312i
\(430\) 100.192 0.233006
\(431\) 101.699 27.2501i 0.235960 0.0632253i −0.138901 0.990306i \(-0.544357\pi\)
0.374861 + 0.927081i \(0.377690\pi\)
\(432\) 82.1821 142.344i 0.190236 0.329499i
\(433\) 596.892 344.616i 1.37850 0.795880i 0.386525 0.922279i \(-0.373675\pi\)
0.991979 + 0.126399i \(0.0403421\pi\)
\(434\) 36.6410 + 36.6410i 0.0844263 + 0.0844263i
\(435\) 6.62882 24.7391i 0.0152387 0.0568715i
\(436\) 265.002 + 71.0070i 0.607802 + 0.162860i
\(437\) 90.1577 90.1577i 0.206310 0.206310i
\(438\) −5.16472 8.94555i −0.0117916 0.0204236i
\(439\) 78.0577 + 45.0666i 0.177808 + 0.102657i 0.586262 0.810121i \(-0.300599\pi\)
−0.408454 + 0.912779i \(0.633932\pi\)
\(440\) 62.5603 + 233.478i 0.142182 + 0.530632i
\(441\) 116.674i 0.264568i
\(442\) 32.1584 + 120.017i 0.0727565 + 0.271531i
\(443\) 642.277 1.44983 0.724917 0.688836i \(-0.241878\pi\)
0.724917 + 0.688836i \(0.241878\pi\)
\(444\) −82.7391 + 22.1699i −0.186349 + 0.0499321i
\(445\) −166.734 + 288.792i −0.374683 + 0.648970i
\(446\) 170.572 98.4801i 0.382450 0.220807i
\(447\) 66.1807 + 66.1807i 0.148055 + 0.148055i
\(448\) −60.9653 + 227.526i −0.136083 + 0.507870i
\(449\) 22.6007 + 6.05583i 0.0503355 + 0.0134874i 0.283899 0.958854i \(-0.408372\pi\)
−0.233563 + 0.972342i \(0.575039\pi\)
\(450\) −34.4641 + 34.4641i −0.0765869 + 0.0765869i
\(451\) −376.970 652.932i −0.835855 1.44774i
\(452\) −465.353 268.672i −1.02954 0.594407i
\(453\) −34.2961 127.995i −0.0757089 0.282549i
\(454\) 216.560i 0.477005i
\(455\) 287.367 0.631575
\(456\) −18.4974 −0.0405645
\(457\) 228.698 61.2795i 0.500433 0.134091i 0.000232237 1.00000i \(-0.499926\pi\)
0.500201 + 0.865909i \(0.333259\pi\)
\(458\) 26.4519 45.8160i 0.0577553 0.100035i
\(459\) −204.431 + 118.028i −0.445383 + 0.257142i
\(460\) 198.531 + 198.531i 0.431589 + 0.431589i
\(461\) −12.6032 + 47.0359i −0.0273389 + 0.102030i −0.978247 0.207443i \(-0.933486\pi\)
0.950908 + 0.309473i \(0.100153\pi\)
\(462\) 35.2154 + 9.43594i 0.0762238 + 0.0204241i
\(463\) −521.191 + 521.191i −1.12568 + 1.12568i −0.134811 + 0.990871i \(0.543043\pi\)
−0.990871 + 0.134811i \(0.956957\pi\)
\(464\) 60.3756 + 104.574i 0.130120 + 0.225374i
\(465\) 39.8372 + 23.0000i 0.0856713 + 0.0494624i
\(466\) 34.3768 + 128.296i 0.0737700 + 0.275314i
\(467\) 141.415i 0.302817i 0.988471 + 0.151408i \(0.0483808\pi\)
−0.988471 + 0.151408i \(0.951619\pi\)
\(468\) 355.633 205.325i 0.759900 0.438729i
\(469\) 239.762 0.511219
\(470\) −90.3993 + 24.2224i −0.192339 + 0.0515371i
\(471\) −35.7776 + 61.9686i −0.0759609 + 0.131568i
\(472\) −333.588 + 192.597i −0.706755 + 0.408045i
\(473\) −595.692 595.692i −1.25939 1.25939i
\(474\) −6.15390 + 22.9667i −0.0129829 + 0.0484529i
\(475\) −67.8372 18.1769i −0.142815 0.0382672i
\(476\) 289.153 289.153i 0.607463 0.607463i
\(477\) −62.4878 108.232i −0.131002 0.226902i
\(478\) −24.9437 14.4012i −0.0521834 0.0301281i
\(479\) 193.783 + 723.207i 0.404557 + 1.50983i 0.804872 + 0.593449i \(0.202234\pi\)
−0.400315 + 0.916378i \(0.631099\pi\)
\(480\) 61.8038i 0.128758i
\(481\) −393.700 105.492i −0.818503 0.219317i
\(482\) −125.053 −0.259445
\(483\) 84.7461 22.7077i 0.175458 0.0470138i
\(484\) 264.698 458.470i 0.546897 0.947253i
\(485\) −176.855 + 102.107i −0.364648 + 0.210530i
\(486\) −60.0192 60.0192i −0.123496 0.123496i
\(487\) −62.9371 + 234.885i −0.129234 + 0.482309i −0.999955 0.00946847i \(-0.996986\pi\)
0.870721 + 0.491778i \(0.163653\pi\)
\(488\) −99.0744 26.5469i −0.203021 0.0543994i
\(489\) −65.5307 + 65.5307i −0.134010 + 0.134010i
\(490\) −13.2898 23.0185i −0.0271220 0.0469766i
\(491\) −73.3191 42.3308i −0.149326 0.0862135i 0.423475 0.905908i \(-0.360810\pi\)
−0.572801 + 0.819694i \(0.694143\pi\)
\(492\) 32.8827 + 122.720i 0.0668347 + 0.249431i
\(493\) 173.420i 0.351766i
\(494\) −36.7917 21.2417i −0.0744770 0.0429993i
\(495\) −511.167 −1.03266
\(496\) −209.485 + 56.1314i −0.422349 + 0.113168i
\(497\) −137.268 + 237.755i −0.276193 + 0.478380i
\(498\) 11.3628 6.56029i 0.0228168 0.0131733i
\(499\) −134.397 134.397i −0.269334 0.269334i 0.559498 0.828832i \(-0.310994\pi\)
−0.828832 + 0.559498i \(0.810994\pi\)
\(500\) 129.978 485.085i 0.259956 0.970170i
\(501\) −37.1384 9.95121i −0.0741286 0.0198627i
\(502\) 93.5641 93.5641i 0.186383 0.186383i
\(503\) 398.200 + 689.703i 0.791650 + 1.37118i 0.924945 + 0.380102i \(0.124111\pi\)
−0.133295 + 0.991076i \(0.542556\pi\)
\(504\) 174.100 + 100.517i 0.345436 + 0.199438i
\(505\) −154.251 575.674i −0.305448 1.13995i
\(506\) 169.492i 0.334965i
\(507\) −123.717 −0.244017
\(508\) 106.301 0.209254
\(509\) 79.6051 21.3301i 0.156395 0.0419059i −0.179772 0.983708i \(-0.557536\pi\)
0.336167 + 0.941802i \(0.390869\pi\)
\(510\) −13.0314 + 22.5711i −0.0255518 + 0.0442571i
\(511\) −140.090 + 80.8808i −0.274148 + 0.158279i
\(512\) 351.581 + 351.581i 0.686682 + 0.686682i
\(513\) 20.8897 77.9615i 0.0407207 0.151972i
\(514\) −49.5211 13.2691i −0.0963446 0.0258155i
\(515\) 207.480 207.480i 0.402873 0.402873i
\(516\) 70.9808 + 122.942i 0.137560 + 0.238260i
\(517\) 681.482 + 393.454i 1.31815 + 0.761032i
\(518\) −24.9268 93.0282i −0.0481213 0.179591i
\(519\) 100.477i 0.193597i
\(520\) 96.9083 167.850i 0.186362 0.322789i
\(521\) 677.011 1.29945 0.649723 0.760171i \(-0.274885\pi\)
0.649723 + 0.760171i \(0.274885\pi\)
\(522\) 39.7487 10.6506i 0.0761470 0.0204035i
\(523\) 91.8269 159.049i 0.175577 0.304109i −0.764784 0.644287i \(-0.777154\pi\)
0.940361 + 0.340179i \(0.110488\pi\)
\(524\) 9.63397 5.56218i 0.0183854 0.0106148i
\(525\) −34.1718 34.1718i −0.0650891 0.0650891i
\(526\) −34.2089 + 127.669i −0.0650358 + 0.242717i
\(527\) 300.858 + 80.6147i 0.570889 + 0.152969i
\(528\) −107.895 + 107.895i −0.204346 + 0.204346i
\(529\) −60.5577 104.889i −0.114476 0.198278i
\(530\) −24.6563 14.2353i −0.0465213 0.0268591i
\(531\) −210.832 786.836i −0.397047 1.48180i
\(532\) 139.818i 0.262816i
\(533\) −156.467 + 583.942i −0.293558 + 1.09558i
\(534\) 33.9230 0.0635263
\(535\) −343.021 + 91.9122i −0.641161 + 0.171799i
\(536\) 80.8545 140.044i 0.150848 0.261276i
\(537\) 0.661635 0.381995i 0.00123210 0.000711351i
\(538\) −33.9334 33.9334i −0.0630732 0.0630732i
\(539\) −57.8423 + 215.870i −0.107314 + 0.400502i
\(540\) 171.674 + 46.0000i 0.317915 + 0.0851852i
\(541\) 317.629 317.629i 0.587114 0.587114i −0.349735 0.936849i \(-0.613728\pi\)
0.936849 + 0.349735i \(0.113728\pi\)
\(542\) 113.133 + 195.953i 0.208733 + 0.361536i
\(543\) 14.6326 + 8.44813i 0.0269477 + 0.0155583i
\(544\) −108.311 404.222i −0.199101 0.743055i
\(545\) 273.832i 0.502444i
\(546\) −14.6166 25.3167i −0.0267704 0.0463676i
\(547\) −724.904 −1.32524 −0.662618 0.748958i \(-0.730555\pi\)
−0.662618 + 0.748958i \(0.730555\pi\)
\(548\) −353.071 + 94.6051i −0.644290 + 0.172637i
\(549\) 108.454 187.849i 0.197549 0.342165i
\(550\) 80.8513 46.6795i 0.147002 0.0848718i
\(551\) 41.9282 + 41.9282i 0.0760947 + 0.0760947i
\(552\) 15.3154 57.1577i 0.0277452 0.103547i
\(553\) 359.664 + 96.3717i 0.650387 + 0.174271i
\(554\) 127.687 127.687i 0.230481 0.230481i
\(555\) −42.7480 74.0417i −0.0770235 0.133409i
\(556\) 104.818 + 60.5167i 0.188521 + 0.108843i
\(557\) −31.0641 115.933i −0.0557703 0.208138i 0.932418 0.361381i \(-0.117695\pi\)
−0.988188 + 0.153244i \(0.951028\pi\)
\(558\) 73.9090i 0.132453i
\(559\) 675.500i 1.20841i
\(560\) −284.192 −0.507486
\(561\) 211.674 56.7180i 0.377316 0.101102i
\(562\) −33.6647 + 58.3090i −0.0599016 + 0.103753i
\(563\) −534.888 + 308.818i −0.950068 + 0.548522i −0.893102 0.449854i \(-0.851476\pi\)
−0.0569660 + 0.998376i \(0.518143\pi\)
\(564\) −93.7654 93.7654i −0.166251 0.166251i
\(565\) 138.812 518.054i 0.245685 0.916909i
\(566\) 17.7846 + 4.76537i 0.0314216 + 0.00841938i
\(567\) −280.378 + 280.378i −0.494494 + 0.494494i
\(568\) 92.5814 + 160.356i 0.162995 + 0.282316i
\(569\) −381.315 220.153i −0.670150 0.386911i 0.125983 0.992032i \(-0.459791\pi\)
−0.796133 + 0.605121i \(0.793125\pi\)
\(570\) −2.30642 8.60770i −0.00404636 0.0151012i
\(571\) 618.249i 1.08275i −0.840782 0.541374i \(-0.817904\pi\)
0.840782 0.541374i \(-0.182096\pi\)
\(572\) −759.783 + 203.583i −1.32829 + 0.355915i
\(573\) −215.226 −0.375612
\(574\) −137.981 + 36.9718i −0.240385 + 0.0644109i
\(575\) 112.335 194.569i 0.195365 0.338381i
\(576\) −290.959 + 167.985i −0.505137 + 0.291641i
\(577\) −266.237 266.237i −0.461415 0.461415i 0.437704 0.899119i \(-0.355792\pi\)
−0.899119 + 0.437704i \(0.855792\pi\)
\(578\) −6.95637 + 25.9615i −0.0120352 + 0.0449161i
\(579\) 233.729 + 62.6274i 0.403677 + 0.108165i
\(580\) −92.3275 + 92.3275i −0.159185 + 0.159185i
\(581\) −102.736 177.944i −0.176826 0.306271i
\(582\) 17.9911 + 10.3872i 0.0309125 + 0.0178473i
\(583\) 61.9578 + 231.229i 0.106274 + 0.396620i
\(584\) 109.101i 0.186817i
\(585\) 289.825 + 289.825i 0.495427 + 0.495427i
\(586\) −207.263 −0.353691
\(587\) 465.123 124.629i 0.792373 0.212316i 0.160140 0.987094i \(-0.448805\pi\)
0.632233 + 0.774779i \(0.282139\pi\)
\(588\) 18.8301 32.6147i 0.0320240 0.0554672i
\(589\) −92.2295 + 53.2487i −0.156587 + 0.0904053i
\(590\) −131.219 131.219i −0.222405 0.222405i
\(591\) 16.6950 62.3064i 0.0282487 0.105425i
\(592\) 389.351 + 104.326i 0.657688 + 0.176227i
\(593\) 389.671 389.671i 0.657118 0.657118i −0.297579 0.954697i \(-0.596179\pi\)
0.954697 + 0.297579i \(0.0961792\pi\)
\(594\) 53.6462 + 92.9179i 0.0903134 + 0.156427i
\(595\) 353.469 + 204.076i 0.594066 + 0.342984i
\(596\) −123.495 460.889i −0.207206 0.773304i
\(597\) 147.464i 0.247009i
\(598\) 96.1000 96.1000i 0.160702 0.160702i
\(599\) 808.596 1.34991 0.674955 0.737859i \(-0.264163\pi\)
0.674955 + 0.737859i \(0.264163\pi\)
\(600\) −31.4833 + 8.43594i −0.0524722 + 0.0140599i
\(601\) 221.344 383.379i 0.368293 0.637903i −0.621006 0.783806i \(-0.713276\pi\)
0.989299 + 0.145904i \(0.0466089\pi\)
\(602\) −138.231 + 79.8076i −0.229619 + 0.132571i
\(603\) 241.813 + 241.813i 0.401016 + 0.401016i
\(604\) −174.844 + 652.527i −0.289477 + 1.08034i
\(605\) 510.392 + 136.759i 0.843623 + 0.226048i
\(606\) −42.8705 + 42.8705i −0.0707434 + 0.0707434i
\(607\) 471.398 + 816.485i 0.776603 + 1.34512i 0.933889 + 0.357563i \(0.116392\pi\)
−0.157286 + 0.987553i \(0.550275\pi\)
\(608\) 123.916 + 71.5429i 0.203809 + 0.117669i
\(609\) 10.5603 + 39.4115i 0.0173404 + 0.0647152i
\(610\) 49.4139i 0.0810065i
\(611\) −163.308 609.475i −0.267280 0.997504i
\(612\) 583.252 0.953027
\(613\) −973.161 + 260.758i −1.58754 + 0.425380i −0.941249 0.337713i \(-0.890347\pi\)
−0.646289 + 0.763093i \(0.723680\pi\)
\(614\) −95.2468 + 164.972i −0.155125 + 0.268685i
\(615\) −109.820 + 63.4045i −0.178569 + 0.103097i
\(616\) −272.287 272.287i −0.442025 0.442025i
\(617\) −71.9115 + 268.378i −0.116550 + 0.434972i −0.999398 0.0346873i \(-0.988956\pi\)
0.882848 + 0.469659i \(0.155623\pi\)
\(618\) −28.8320 7.72551i −0.0466537 0.0125008i
\(619\) 206.483 206.483i 0.333576 0.333576i −0.520367 0.853943i \(-0.674205\pi\)
0.853943 + 0.520367i \(0.174205\pi\)
\(620\) −117.256 203.093i −0.189122 0.327569i
\(621\) 223.608 + 129.100i 0.360077 + 0.207890i
\(622\) −9.57626 35.7391i −0.0153959 0.0574583i
\(623\) 531.244i 0.852718i
\(624\) 122.350 0.196074
\(625\) 223.140 0.357024
\(626\) 197.158 52.8282i 0.314948 0.0843902i
\(627\) −37.4641 + 64.8897i −0.0597514 + 0.103492i
\(628\) 315.920 182.397i 0.503058 0.290441i
\(629\) −409.347 409.347i −0.650790 0.650790i
\(630\) −25.0666 + 93.5500i −0.0397883 + 0.148492i
\(631\) −428.813 114.900i −0.679577 0.182092i −0.0975117 0.995234i \(-0.531088\pi\)
−0.582065 + 0.813142i \(0.697755\pi\)
\(632\) 177.580 177.580i 0.280980 0.280980i
\(633\) 26.8282 + 46.4679i 0.0423827 + 0.0734090i
\(634\) 130.633 + 75.4212i 0.206046 + 0.118961i
\(635\) 27.4608 + 102.485i 0.0432454 + 0.161394i
\(636\) 40.3397i 0.0634273i
\(637\) 155.192 89.6000i 0.243629 0.140659i
\(638\) −78.8231 −0.123547
\(639\) −378.231 + 101.347i −0.591911 + 0.158602i
\(640\) −207.120 + 358.742i −0.323625 + 0.560535i
\(641\) −471.717 + 272.346i −0.735908 + 0.424877i −0.820580 0.571532i \(-0.806349\pi\)
0.0846714 + 0.996409i \(0.473016\pi\)
\(642\) 25.5448 + 25.5448i 0.0397894 + 0.0397894i
\(643\) 100.073 373.478i 0.155635 0.580837i −0.843415 0.537262i \(-0.819459\pi\)
0.999050 0.0435749i \(-0.0138747\pi\)
\(644\) −432.042 115.765i −0.670873 0.179760i
\(645\) −100.192 + 100.192i −0.155337 + 0.155337i
\(646\) −30.1699 52.2558i −0.0467026 0.0808913i
\(647\) −436.056 251.757i −0.673966 0.389114i 0.123612 0.992331i \(-0.460552\pi\)
−0.797578 + 0.603216i \(0.793886\pi\)
\(648\) 69.2166 + 258.320i 0.106816 + 0.398642i
\(649\) 1560.32i 2.40420i
\(650\) −72.3083 19.3750i −0.111244 0.0298076i
\(651\) −73.2820 −0.112568
\(652\) 456.363 122.282i 0.699943 0.187549i
\(653\) −15.5692 + 26.9667i −0.0238426 + 0.0412966i −0.877701 0.479210i \(-0.840923\pi\)
0.853858 + 0.520506i \(0.174257\pi\)
\(654\) 24.1244 13.9282i 0.0368874 0.0212969i
\(655\) 7.85125 + 7.85125i 0.0119866 + 0.0119866i
\(656\) 154.738 577.492i 0.235882 0.880323i
\(657\) −222.861 59.7154i −0.339210 0.0908910i
\(658\) 105.426 105.426i 0.160221 0.160221i
\(659\) −379.488 657.293i −0.575855 0.997410i −0.995948 0.0899292i \(-0.971336\pi\)
0.420093 0.907481i \(-0.361997\pi\)
\(660\) −142.890 82.4974i −0.216500 0.124996i
\(661\) 67.8083 + 253.064i 0.102584 + 0.382850i 0.998060 0.0622605i \(-0.0198310\pi\)
−0.895475 + 0.445111i \(0.853164\pi\)
\(662\) 238.795i 0.360717i
\(663\) −152.175 87.8583i −0.229525 0.132516i
\(664\) −138.582 −0.208708
\(665\) −134.799 + 36.1192i −0.202705 + 0.0543146i
\(666\) 68.6840 118.964i 0.103129 0.178625i
\(667\) −164.275 + 94.8442i −0.246289 + 0.142195i
\(668\) 138.603 + 138.603i 0.207489 + 0.207489i
\(669\) −72.0924 + 269.053i −0.107761 + 0.402171i
\(670\) 75.2506 + 20.1633i 0.112314 + 0.0300945i
\(671\) −293.790 + 293.790i −0.437839 + 0.437839i
\(672\) 49.2295 + 85.2679i 0.0732581 + 0.126887i
\(673\) −272.210 157.160i −0.404472 0.233522i 0.283940 0.958842i \(-0.408358\pi\)
−0.688412 + 0.725320i \(0.741692\pi\)
\(674\) 19.3968 + 72.3897i 0.0287786 + 0.107403i
\(675\) 142.221i 0.210697i
\(676\) 546.217 + 315.358i 0.808013 + 0.466506i
\(677\) −547.384 −0.808544 −0.404272 0.914639i \(-0.632475\pi\)
−0.404272 + 0.914639i \(0.632475\pi\)
\(678\) −52.7006 + 14.1211i −0.0777295 + 0.0208276i
\(679\) 162.665 281.745i 0.239566 0.414941i
\(680\) 238.400 137.640i 0.350588 0.202412i
\(681\) 216.560 + 216.560i 0.318003 + 0.318003i
\(682\) 36.6410 136.746i 0.0537258 0.200508i
\(683\) 252.954 + 67.7789i 0.370358 + 0.0992371i 0.439197 0.898391i \(-0.355263\pi\)
−0.0688393 + 0.997628i \(0.521930\pi\)
\(684\) −141.014 + 141.014i −0.206161 + 0.206161i
\(685\) −182.418 315.957i −0.266303 0.461251i
\(686\) 167.023 + 96.4308i 0.243474 + 0.140570i
\(687\) 19.3641 + 72.2679i 0.0281865 + 0.105194i
\(688\) 668.038i 0.970986i
\(689\) 95.9749 166.233i 0.139296 0.241268i
\(690\) 28.5077 0.0413156
\(691\) 1062.75 284.764i 1.53799 0.412104i 0.612377 0.790566i \(-0.290214\pi\)
0.925617 + 0.378462i \(0.123547\pi\)
\(692\) −256.119 + 443.611i −0.370114 + 0.641057i
\(693\) 705.233 407.167i 1.01765 0.587542i
\(694\) 178.321 + 178.321i 0.256946 + 0.256946i
\(695\) −31.2666 + 116.688i −0.0449879 + 0.167897i
\(696\) 26.5814 + 7.12247i 0.0381917 + 0.0102334i
\(697\) −607.149 + 607.149i −0.871089 + 0.871089i
\(698\) 3.04036 + 5.26606i 0.00435582 + 0.00754450i
\(699\) −162.673 93.9193i −0.232722 0.134362i
\(700\) 63.7654 + 237.976i 0.0910934 + 0.339965i
\(701\) 638.323i 0.910589i 0.890341 + 0.455295i \(0.150466\pi\)
−0.890341 + 0.455295i \(0.849534\pi\)
\(702\) 22.2666 83.1000i 0.0317188 0.118376i
\(703\) 197.937 0.281561
\(704\) 621.611 166.560i 0.882971 0.236591i
\(705\) 66.1769 114.622i 0.0938680 0.162584i
\(706\) 128.171 73.9993i 0.181545 0.104815i
\(707\) 671.363 + 671.363i 0.949594 + 0.949594i
\(708\) 68.0526 253.976i 0.0961194 0.358723i
\(709\) −625.185 167.518i −0.881784 0.236273i −0.210608 0.977571i \(-0.567544\pi\)
−0.671177 + 0.741297i \(0.734211\pi\)
\(710\) −63.0770 + 63.0770i −0.0888408 + 0.0888408i
\(711\) 265.545 + 459.937i 0.373481 + 0.646888i
\(712\) −310.298 179.151i −0.435812 0.251616i
\(713\) −88.1769 329.081i −0.123670 0.461544i
\(714\) 41.5204i 0.0581519i
\(715\) −392.550 679.917i −0.549021 0.950932i
\(716\) −3.89488 −0.00543978
\(717\) 39.3449 10.5424i 0.0548743 0.0147035i
\(718\) −33.7025 + 58.3744i −0.0469394 + 0.0813015i
\(719\) 1058.38 611.056i 1.47202 0.849870i 0.472512 0.881324i \(-0.343347\pi\)
0.999505 + 0.0314543i \(0.0100139\pi\)
\(720\) −286.624 286.624i −0.398088 0.398088i
\(721\) −120.984 + 451.517i −0.167800 + 0.626237i
\(722\) −160.572 43.0251i −0.222399 0.0595915i
\(723\) 125.053 125.053i 0.172963 0.172963i
\(724\) −43.0692 74.5981i −0.0594879 0.103036i
\(725\) 90.4852 + 52.2417i 0.124807 + 0.0720575i
\(726\) −13.9122 51.9212i −0.0191629 0.0715168i
\(727\) 508.974i 0.700102i −0.936731 0.350051i \(-0.886164\pi\)
0.936731 0.350051i \(-0.113836\pi\)
\(728\) 308.767i 0.424130i
\(729\) −481.323 −0.660251
\(730\) −50.7698 + 13.6037i −0.0695477 + 0.0186353i
\(731\) −479.711 + 830.885i −0.656240 + 1.13664i
\(732\) 60.6340 35.0070i 0.0828333 0.0478238i
\(733\) 861.681 + 861.681i 1.17555 + 1.17555i 0.980865 + 0.194689i \(0.0623699\pi\)
0.194689 + 0.980865i \(0.437630\pi\)
\(734\) 1.68138 6.27499i 0.00229071 0.00854903i
\(735\) 36.3083 + 9.72878i 0.0493991 + 0.0132364i
\(736\) −323.669 + 323.669i −0.439768 + 0.439768i
\(737\) −327.520 567.282i −0.444397 0.769718i
\(738\) −176.449 101.873i −0.239091 0.138039i
\(739\) 40.4242 + 150.865i 0.0547013 + 0.204148i 0.987868 0.155296i \(-0.0496331\pi\)
−0.933167 + 0.359444i \(0.882966\pi\)
\(740\) 435.865i 0.589007i
\(741\) 58.0333 15.5500i 0.0783176 0.0209851i
\(742\) 45.3562 0.0611270
\(743\) −369.252 + 98.9409i −0.496975 + 0.133164i −0.498596 0.866835i \(-0.666151\pi\)
0.00162070 + 0.999999i \(0.499484\pi\)
\(744\) −24.7128 + 42.8038i −0.0332161 + 0.0575321i
\(745\) 412.441 238.123i 0.553613 0.319628i
\(746\) −113.935 113.935i −0.152728 0.152728i
\(747\) 75.8513 283.081i 0.101541 0.378957i
\(748\) −1079.13 289.153i −1.44269 0.386568i
\(749\) 400.038 400.038i 0.534097 0.534097i
\(750\) −25.4955 44.1596i −0.0339940 0.0588794i
\(751\) −906.415 523.319i −1.20694 0.696830i −0.244854 0.969560i \(-0.578740\pi\)
−0.962091 + 0.272730i \(0.912073\pi\)
\(752\) 161.504 + 602.743i 0.214767 + 0.801520i
\(753\) 187.128i 0.248510i
\(754\) 44.6917 + 44.6917i 0.0592728 + 0.0592728i
\(755\) −674.270 −0.893073
\(756\) −273.492 + 73.2820i −0.361762 + 0.0969339i
\(757\) 188.415 326.345i 0.248897 0.431103i −0.714323 0.699816i \(-0.753265\pi\)
0.963220 + 0.268713i \(0.0865985\pi\)
\(758\) −176.293 + 101.783i −0.232576 + 0.134278i
\(759\) −169.492 169.492i −0.223310 0.223310i
\(760\) −24.3609 + 90.9160i −0.0320538 + 0.119626i
\(761\) −742.044 198.830i −0.975091 0.261275i −0.264115 0.964491i \(-0.585080\pi\)
−0.710976 + 0.703216i \(0.751747\pi\)
\(762\) 7.63209 7.63209i 0.0100159 0.0100159i
\(763\) −218.119 377.794i −0.285871 0.495142i
\(764\) 950.235 + 548.619i 1.24376 + 0.718087i
\(765\) 150.672 + 562.315i 0.196957 + 0.735052i
\(766\) 382.123i 0.498855i
\(767\) 884.683 884.683i 1.15343 1.15343i
\(768\) −74.0910 −0.0964727
\(769\) −65.7006 + 17.6044i −0.0854364 + 0.0228926i −0.301284 0.953534i \(-0.597415\pi\)
0.215848 + 0.976427i \(0.430749\pi\)
\(770\) 92.7564 160.659i 0.120463 0.208648i
\(771\) 62.7903 36.2520i 0.0814400 0.0470194i
\(772\) −872.288 872.288i −1.12991 1.12991i
\(773\) −238.681 + 890.771i −0.308773 + 1.15236i 0.620876 + 0.783909i \(0.286777\pi\)
−0.929649 + 0.368447i \(0.879890\pi\)
\(774\) −219.904 58.9230i −0.284113 0.0761280i
\(775\) −132.694 + 132.694i −0.171218 + 0.171218i
\(776\) −109.711 190.025i −0.141380 0.244877i
\(777\) 117.955 + 68.1013i 0.151808 + 0.0876465i
\(778\) 46.1513 + 172.239i 0.0593205 + 0.221387i
\(779\) 293.583i 0.376872i
\(780\) 34.2417 + 127.792i 0.0438996 + 0.163835i
\(781\) 750.046 0.960366
\(782\) 186.452 49.9596i 0.238430 0.0638870i
\(783\) −60.0385 + 103.990i −0.0766775 + 0.132809i
\(784\) −153.477 + 88.6103i −0.195762 + 0.113023i
\(785\) 257.461 + 257.461i 0.327976 + 0.327976i
\(786\) 0.292342 1.09103i 0.000371936 0.00138808i
\(787\) 1188.62 + 318.489i 1.51031 + 0.404687i 0.916540 0.399944i \(-0.130970\pi\)
0.593774 + 0.804632i \(0.297637\pi\)
\(788\) −232.531 + 232.531i −0.295090 + 0.295090i
\(789\) −93.4603 161.878i −0.118454 0.205169i
\(790\) 104.778 + 60.4936i 0.132630 + 0.0765742i
\(791\) 221.140 + 825.305i 0.279570 + 1.04337i
\(792\) 549.233i 0.693476i
\(793\) 333.150 0.420114
\(794\) 363.565 0.457891
\(795\) 38.8916 10.4210i 0.0489203 0.0131081i
\(796\) −375.892 + 651.063i −0.472226 + 0.817919i
\(797\) −22.0615 + 12.7372i −0.0276807 + 0.0159814i −0.513776 0.857924i \(-0.671754\pi\)
0.486096 + 0.873906i \(0.338421\pi\)
\(798\) 10.0385 + 10.0385i 0.0125795 + 0.0125795i
\(799\) 231.949 865.647i 0.290300 1.08341i
\(800\) 243.538 + 65.2558i 0.304422 + 0.0815697i
\(801\) 535.788 535.788i 0.668899 0.668899i
\(802\) −146.833 254.323i −0.183084 0.317110i
\(803\) 382.732 + 220.970i 0.476628 + 0.275181i
\(804\) 28.5692 + 106.622i 0.0355339 + 0.132614i
\(805\) 446.438i 0.554582i
\(806\) −98.3083 + 56.7583i −0.121971 + 0.0704198i
\(807\) 67.8667 0.0840975
\(808\) 618.544 165.738i 0.765525 0.205122i
\(809\) 351.463 608.752i 0.434442 0.752475i −0.562808 0.826588i \(-0.690279\pi\)
0.997250 + 0.0741123i \(0.0236123\pi\)
\(810\) −111.577 + 64.4193i −0.137750 + 0.0795300i
\(811\) 506.292 + 506.292i 0.624282 + 0.624282i 0.946623 0.322342i \(-0.104470\pi\)
−0.322342 + 0.946623i \(0.604470\pi\)
\(812\) 53.8372 200.923i 0.0663019 0.247442i
\(813\) −309.086 82.8193i −0.380179 0.101869i
\(814\) −186.056 + 186.056i −0.228570 + 0.228570i
\(815\) 235.785 + 408.391i 0.289306 + 0.501093i
\(816\) 150.494 + 86.8878i 0.184429 + 0.106480i
\(817\) −84.9038 316.865i −0.103921 0.387840i
\(818\) 52.6424i 0.0643550i
\(819\) −630.717 169.000i −0.770106 0.206349i
\(820\) 646.482 0.788393
\(821\) −1090.79 + 292.276i −1.32861 + 0.356000i −0.852197 0.523220i \(-0.824730\pi\)
−0.476414 + 0.879221i \(0.658064\pi\)
\(822\) −18.5570 + 32.1417i −0.0225755 + 0.0391018i
\(823\) −449.858 + 259.726i −0.546607 + 0.315584i −0.747752 0.663978i \(-0.768867\pi\)
0.201145 + 0.979561i \(0.435534\pi\)
\(824\) 222.931 + 222.931i 0.270547 + 0.270547i
\(825\) −34.1718 + 127.531i −0.0414203 + 0.154583i
\(826\) 285.559 + 76.5153i 0.345713 + 0.0926335i
\(827\) −571.769 + 571.769i −0.691377 + 0.691377i −0.962535 0.271158i \(-0.912594\pi\)
0.271158 + 0.962535i \(0.412594\pi\)
\(828\) −318.983 552.494i −0.385245 0.667263i
\(829\) −848.094 489.647i −1.02303 0.590648i −0.108052 0.994145i \(-0.534461\pi\)
−0.914981 + 0.403497i \(0.867795\pi\)
\(830\) −17.2796 64.4885i −0.0208188 0.0776970i
\(831\) 255.373i 0.307308i
\(832\) −446.883 258.008i −0.537119 0.310106i
\(833\) 254.520 0.305547
\(834\) 11.8705 3.18069i 0.0142332 0.00381377i
\(835\) −97.8217 + 169.432i −0.117152 + 0.202913i
\(836\) 330.813 190.995i 0.395709 0.228463i
\(837\) −152.497 152.497i −0.182195 0.182195i
\(838\) 86.3543 322.279i 0.103048 0.384581i
\(839\) 513.757 + 137.661i 0.612344 + 0.164077i 0.551645 0.834079i \(-0.314000\pi\)
0.0606993 + 0.998156i \(0.480667\pi\)
\(840\) −45.7973 + 45.7973i −0.0545206 + 0.0545206i
\(841\) 376.392 + 651.931i 0.447553 + 0.775185i
\(842\) −219.747 126.871i −0.260983 0.150678i
\(843\) −24.6443 91.9737i −0.0292340 0.109103i
\(844\) 273.545i 0.324105i
\(845\) −162.933 + 608.075i −0.192820 + 0.719615i
\(846\) 212.655 0.251365
\(847\) −813.099 + 217.869i −0.959975 + 0.257224i
\(848\) −94.9148 + 164.397i −0.111928 + 0.193865i
\(849\) −22.5500 + 13.0192i −0.0265606 + 0.0153348i
\(850\) −75.1821 75.1821i −0.0884495 0.0884495i
\(851\) −163.886 + 611.633i −0.192581 + 0.718722i
\(852\) −122.086 32.7128i −0.143293 0.0383953i
\(853\) 713.043 713.043i 0.835924 0.835924i −0.152396 0.988320i \(-0.548699\pi\)
0.988320 + 0.152396i \(0.0486989\pi\)
\(854\) 39.3604 + 68.1742i 0.0460894 + 0.0798292i
\(855\) −172.380 99.5237i −0.201614 0.116402i
\(856\) −98.7569 368.566i −0.115370 0.430568i
\(857\) 311.663i 0.363667i −0.983329 0.181834i \(-0.941797\pi\)
0.983329 0.181834i \(-0.0582032\pi\)
\(858\) −39.9334 + 69.1666i −0.0465424 + 0.0806138i
\(859\) −1475.02 −1.71714 −0.858568 0.512700i \(-0.828645\pi\)
−0.858568 + 0.512700i \(0.828645\pi\)
\(860\) 697.750 186.962i 0.811337 0.217397i
\(861\) 101.009 174.953i 0.117316 0.203197i
\(862\) −47.1985 + 27.2501i −0.0547547 + 0.0316126i
\(863\) −700.396 700.396i −0.811583 0.811583i 0.173288 0.984871i \(-0.444561\pi\)
−0.984871 + 0.173288i \(0.944561\pi\)
\(864\) −74.9948 + 279.885i −0.0867996 + 0.323940i
\(865\) −493.850 132.327i −0.570925 0.152979i
\(866\) −252.276 + 252.276i −0.291312 + 0.291312i
\(867\) −19.0052 32.9179i −0.0219206 0.0379676i
\(868\) 323.545 + 186.799i 0.372747 + 0.215206i
\(869\) −263.292 982.620i −0.302983 1.13075i
\(870\) 13.2576i 0.0152387i
\(871\) −135.942 + 507.342i −0.156076 + 0.582482i
\(872\) −294.224 −0.337413
\(873\) 448.212 120.098i 0.513416 0.137569i
\(874\) −33.0000 + 57.1577i −0.0377574 + 0.0653978i
\(875\) −691.550 + 399.267i −0.790343 + 0.456305i
\(876\) −52.6603 52.6603i −0.0601144 0.0601144i
\(877\) −35.4498 + 132.301i −0.0404217 + 0.150856i −0.983187 0.182601i \(-0.941548\pi\)
0.942765 + 0.333457i \(0.108215\pi\)
\(878\) −45.0666 12.0756i −0.0513287 0.0137535i
\(879\) 207.263 207.263i 0.235794 0.235794i
\(880\) 388.214 + 672.406i 0.441152 + 0.764098i
\(881\) 383.677 + 221.516i 0.435502 + 0.251437i 0.701688 0.712485i \(-0.252430\pi\)
−0.266186 + 0.963922i \(0.585764\pi\)
\(882\) 15.6314 + 58.3372i 0.0177227 + 0.0661419i
\(883\) 1305.20i 1.47814i 0.673630 + 0.739069i \(0.264734\pi\)
−0.673630 + 0.739069i \(0.735266\pi\)
\(884\) 447.908 + 775.800i 0.506684 + 0.877602i
\(885\) 262.438 0.296540
\(886\) −321.138 + 86.0488i −0.362459 + 0.0971205i
\(887\) 861.377 1491.95i 0.971113 1.68202i 0.278904 0.960319i \(-0.410029\pi\)
0.692209 0.721697i \(-0.256638\pi\)
\(888\) 79.5556 45.9315i 0.0895897 0.0517246i
\(889\) −119.520 119.520i −0.134444 0.134444i
\(890\) 44.6762 166.734i 0.0501980 0.187342i
\(891\) 1046.39 + 280.378i 1.17439 + 0.314678i
\(892\) 1004.12 1004.12i 1.12569 1.12569i
\(893\) 153.210 + 265.368i 0.171568 + 0.297165i
\(894\) −41.9569 24.2238i −0.0469316 0.0270960i
\(895\) −1.00617 3.75506i −0.00112421 0.00419560i
\(896\) 659.920i 0.736518i
\(897\) 192.200i 0.214270i
\(898\) −12.1117 −0.0134874
\(899\) 153.040 41.0070i 0.170234 0.0456141i
\(900\) −175.701 + 304.322i −0.195223 + 0.338136i
\(901\) 236.104 136.315i 0.262047 0.151293i
\(902\) 275.962 + 275.962i 0.305944 + 0.305944i
\(903\) 58.4232 218.038i 0.0646990 0.241460i
\(904\) 556.633 + 149.149i 0.615745 + 0.164988i
\(905\) 60.7940 60.7940i 0.0671757 0.0671757i
\(906\) 34.2961 + 59.4026i 0.0378544 + 0.0655658i
\(907\) 758.800 + 438.093i 0.836604 + 0.483014i 0.856109 0.516796i \(-0.172875\pi\)
−0.0195043 + 0.999810i \(0.506209\pi\)
\(908\) −404.107 1508.15i −0.445052 1.66096i
\(909\) 1354.21i 1.48978i
\(910\) −143.683 + 38.4998i −0.157894 + 0.0423075i
\(911\) −1103.35 −1.21114 −0.605569 0.795793i \(-0.707054\pi\)
−0.605569 + 0.795793i \(0.707054\pi\)
\(912\) −57.3923 + 15.3782i −0.0629302 + 0.0168621i
\(913\) −280.679 + 486.151i −0.307426 + 0.532477i
\(914\) −106.139 + 61.2795i −0.116126 + 0.0670454i
\(915\) 49.4139 + 49.4139i 0.0540043 + 0.0540043i
\(916\) 98.7199 368.428i 0.107773 0.402213i
\(917\) −17.0859 4.57815i −0.0186324 0.00499253i
\(918\) 86.4026 86.4026i 0.0941205 0.0941205i
\(919\) 328.160 + 568.389i 0.357083 + 0.618486i 0.987472 0.157793i \(-0.0504379\pi\)
−0.630389 + 0.776279i \(0.717105\pi\)
\(920\) −260.763 150.552i −0.283439 0.163643i
\(921\) −69.7255 260.219i −0.0757063 0.282540i
\(922\) 25.2065i 0.0273389i
\(923\) −425.267 425.267i −0.460744 0.460744i
\(924\) 262.851 0.284471
\(925\) 336.897 90.2712i 0.364213 0.0975905i
\(926\) 190.769 330.422i 0.206014 0.356827i
\(927\) −577.398 + 333.361i −0.622867 + 0.359613i
\(928\) −150.524 150.524i −0.162202 0.162202i
\(929\) 219.574 819.460i 0.236355 0.882088i −0.741179 0.671308i \(-0.765733\pi\)
0.977533 0.210780i \(-0.0676005\pi\)
\(930\) −23.0000 6.16283i −0.0247312 0.00662670i
\(931\) −61.5359 + 61.5359i −0.0660966 + 0.0660966i
\(932\) 478.808 + 829.319i 0.513742 + 0.889827i
\(933\) 45.3154 + 26.1628i 0.0485695 + 0.0280416i
\(934\) −18.9461 70.7077i −0.0202849 0.0757041i
\(935\) 1115.09i 1.19261i
\(936\) −311.408 + 311.408i −0.332701 + 0.332701i
\(937\) 842.615 0.899269 0.449635 0.893213i \(-0.351554\pi\)
0.449635 + 0.893213i \(0.351554\pi\)
\(938\) −119.881 + 32.1220i −0.127805 + 0.0342452i
\(939\) −144.329 + 249.986i −0.153705 + 0.266226i
\(940\) −584.351 + 337.375i −0.621650 + 0.358910i
\(941\) −471.659 471.659i −0.501232 0.501232i 0.410589 0.911821i \(-0.365323\pi\)
−0.911821 + 0.410589i \(0.865323\pi\)
\(942\) 9.58657 35.7776i 0.0101768 0.0379804i
\(943\) 907.183 + 243.079i 0.962018 + 0.257772i
\(944\) −874.911 + 874.911i −0.926813 + 0.926813i
\(945\) −141.303 244.743i −0.149527 0.258988i
\(946\) 377.654 + 218.038i 0.399211 + 0.230485i
\(947\) −131.110 489.308i −0.138447 0.516693i −0.999960 0.00895652i \(-0.997149\pi\)
0.861512 0.507737i \(-0.169518\pi\)
\(948\) 171.426i 0.180829i
\(949\) −91.7168 342.292i −0.0966457 0.360687i
\(950\) 36.3538 0.0382672
\(951\) −206.054 + 55.2121i −0.216671 + 0.0580569i
\(952\) −219.273 + 379.792i −0.230329 + 0.398941i
\(953\) −770.092 + 444.613i −0.808071 + 0.466540i −0.846286 0.532729i \(-0.821166\pi\)
0.0382143 + 0.999270i \(0.487833\pi\)
\(954\) 45.7442 + 45.7442i 0.0479499 + 0.0479499i
\(955\) −283.450 + 1057.85i −0.296806 + 1.10769i
\(956\) −200.583 53.7461i −0.209815 0.0562198i
\(957\) 78.8231 78.8231i 0.0823648 0.0823648i
\(958\) −193.783 335.642i −0.202278 0.350356i
\(959\) 503.347 + 290.608i 0.524867 + 0.303032i
\(960\) −28.0146 104.552i −0.0291819 0.108908i
\(961\) 676.436i 0.703888i
\(962\) 210.983 0.219317
\(963\) 806.922 0.837925
\(964\) −870.879 + 233.351i −0.903401 + 0.242066i
\(965\) 615.636 1066.31i 0.637964 1.10499i
\(966\) −39.3308 + 22.7077i −0.0407151 + 0.0235069i
\(967\) −384.317 384.317i −0.397432 0.397432i 0.479894 0.877326i \(-0.340675\pi\)
−0.877326 + 0.479894i \(0.840675\pi\)
\(968\) −146.943 + 548.401i −0.151801 + 0.566529i
\(969\) 82.4256 + 22.0859i 0.0850626 + 0.0227924i
\(970\) 74.7475 74.7475i 0.0770593 0.0770593i
\(971\) 121.863 + 211.074i 0.125503 + 0.217378i 0.921929 0.387358i \(-0.126612\pi\)
−0.796426 + 0.604735i \(0.793279\pi\)
\(972\) −529.977 305.983i −0.545244 0.314797i
\(973\) −49.8104 185.895i −0.0511926 0.191053i
\(974\) 125.874i 0.129234i
\(975\) 91.6833 52.9334i 0.0940341 0.0542906i
\(976\) −329.470 −0.337572
\(977\) −1110.01 + 297.426i −1.13614 + 0.304428i −0.777398 0.629009i \(-0.783461\pi\)
−0.358742 + 0.933437i \(0.616794\pi\)
\(978\) 23.9859 41.5448i 0.0245255 0.0424794i
\(979\) −1256.94 + 725.692i −1.28390 + 0.741259i
\(980\) −135.504 135.504i −0.138270 0.138270i
\(981\) 161.040 601.011i 0.164159 0.612651i
\(982\) 42.3308 + 11.3425i 0.0431067 + 0.0115504i
\(983\) −774.213 + 774.213i −0.787602 + 0.787602i −0.981101 0.193499i \(-0.938016\pi\)
0.193499 + 0.981101i \(0.438016\pi\)
\(984\) −68.1262 117.998i −0.0692340 0.119917i
\(985\) −284.253 164.114i −0.288582 0.166613i
\(986\) 23.2339 + 86.7102i 0.0235638 + 0.0879414i
\(987\) 210.851i 0.213628i
\(988\) −295.858 79.2750i −0.299452 0.0802378i
\(989\) 1049.42 1.06109
\(990\) 255.583 68.4833i 0.258165 0.0691751i
\(991\) 391.733 678.501i 0.395290 0.684663i −0.597848 0.801609i \(-0.703977\pi\)
0.993138 + 0.116947i \(0.0373107\pi\)
\(992\) 331.107 191.165i 0.333777 0.192706i
\(993\) 238.795 + 238.795i 0.240478 + 0.240478i
\(994\) 36.7808 137.268i 0.0370029 0.138097i
\(995\) −724.795 194.208i −0.728438 0.195184i
\(996\) 66.8897 66.8897i 0.0671584 0.0671584i
\(997\) −250.817 434.428i −0.251572 0.435735i 0.712387 0.701787i \(-0.247614\pi\)
−0.963959 + 0.266052i \(0.914281\pi\)
\(998\) 85.2046 + 49.1929i 0.0853753 + 0.0492915i
\(999\) 103.744 + 387.177i 0.103848 + 0.387564i
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 13.3.f.a.7.1 yes 4
3.2 odd 2 117.3.bd.b.46.1 4
4.3 odd 2 208.3.bd.d.33.1 4
5.2 odd 4 325.3.w.a.124.1 4
5.3 odd 4 325.3.w.b.124.1 4
5.4 even 2 325.3.t.a.176.1 4
13.2 odd 12 inner 13.3.f.a.2.1 4
13.3 even 3 169.3.f.c.89.1 4
13.4 even 6 169.3.d.c.99.1 4
13.5 odd 4 169.3.f.c.19.1 4
13.6 odd 12 169.3.d.a.70.2 4
13.7 odd 12 169.3.d.c.70.1 4
13.8 odd 4 169.3.f.a.19.1 4
13.9 even 3 169.3.d.a.99.2 4
13.10 even 6 169.3.f.a.89.1 4
13.11 odd 12 169.3.f.b.80.1 4
13.12 even 2 169.3.f.b.150.1 4
39.2 even 12 117.3.bd.b.28.1 4
52.15 even 12 208.3.bd.d.145.1 4
65.2 even 12 325.3.w.b.249.1 4
65.28 even 12 325.3.w.a.249.1 4
65.54 odd 12 325.3.t.a.301.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
13.3.f.a.2.1 4 13.2 odd 12 inner
13.3.f.a.7.1 yes 4 1.1 even 1 trivial
117.3.bd.b.28.1 4 39.2 even 12
117.3.bd.b.46.1 4 3.2 odd 2
169.3.d.a.70.2 4 13.6 odd 12
169.3.d.a.99.2 4 13.9 even 3
169.3.d.c.70.1 4 13.7 odd 12
169.3.d.c.99.1 4 13.4 even 6
169.3.f.a.19.1 4 13.8 odd 4
169.3.f.a.89.1 4 13.10 even 6
169.3.f.b.80.1 4 13.11 odd 12
169.3.f.b.150.1 4 13.12 even 2
169.3.f.c.19.1 4 13.5 odd 4
169.3.f.c.89.1 4 13.3 even 3
208.3.bd.d.33.1 4 4.3 odd 2
208.3.bd.d.145.1 4 52.15 even 12
325.3.t.a.176.1 4 5.4 even 2
325.3.t.a.301.1 4 65.54 odd 12
325.3.w.a.124.1 4 5.2 odd 4
325.3.w.a.249.1 4 65.28 even 12
325.3.w.b.124.1 4 5.3 odd 4
325.3.w.b.249.1 4 65.2 even 12