Properties

Label 315.2.bq.a.164.5
Level $315$
Weight $2$
Character 315.164
Analytic conductor $2.515$
Analytic rank $0$
Dimension $88$
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] = [315,2,Mod(164,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.164");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.bq (of order \(6\), degree \(2\), 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: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(44\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 164.5
Character \(\chi\) \(=\) 315.164
Dual form 315.2.bq.a.194.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.29795 q^{2} +(0.238210 + 1.71559i) q^{3} +3.28056 q^{4} +(-0.0571900 - 2.23534i) q^{5} +(-0.547395 - 3.94234i) q^{6} +(-0.338914 - 2.62395i) q^{7} -2.94267 q^{8} +(-2.88651 + 0.817344i) q^{9} +O(q^{10})\) \(q-2.29795 q^{2} +(0.238210 + 1.71559i) q^{3} +3.28056 q^{4} +(-0.0571900 - 2.23534i) q^{5} +(-0.547395 - 3.94234i) q^{6} +(-0.338914 - 2.62395i) q^{7} -2.94267 q^{8} +(-2.88651 + 0.817344i) q^{9} +(0.131420 + 5.13669i) q^{10} +(-4.36132 + 2.51801i) q^{11} +(0.781465 + 5.62811i) q^{12} +(1.81474 + 3.14323i) q^{13} +(0.778808 + 6.02971i) q^{14} +(3.82130 - 0.630595i) q^{15} +0.200971 q^{16} +(-5.20593 - 3.00564i) q^{17} +(6.63305 - 1.87821i) q^{18} +(-2.26155 + 1.30571i) q^{19} +(-0.187615 - 7.33316i) q^{20} +(4.42090 - 1.20649i) q^{21} +(10.0221 - 5.78625i) q^{22} +(-1.33854 + 2.31842i) q^{23} +(-0.700974 - 5.04842i) q^{24} +(-4.99346 + 0.255678i) q^{25} +(-4.17019 - 7.22298i) q^{26} +(-2.08983 - 4.75738i) q^{27} +(-1.11183 - 8.60805i) q^{28} +(-1.65943 - 0.958073i) q^{29} +(-8.78115 + 1.44907i) q^{30} -1.46018i q^{31} +5.42352 q^{32} +(-5.35879 - 6.88243i) q^{33} +(11.9630 + 6.90681i) q^{34} +(-5.84604 + 0.907652i) q^{35} +(-9.46939 + 2.68135i) q^{36} +(-3.39771 + 1.96167i) q^{37} +(5.19693 - 3.00045i) q^{38} +(-4.96021 + 3.86211i) q^{39} +(0.168291 + 6.57785i) q^{40} +(-0.294240 - 0.509638i) q^{41} +(-10.1590 + 2.77246i) q^{42} +(-4.96969 - 2.86925i) q^{43} +(-14.3076 + 8.26049i) q^{44} +(1.99212 + 6.40558i) q^{45} +(3.07590 - 5.32761i) q^{46} +4.60984i q^{47} +(0.0478734 + 0.344784i) q^{48} +(-6.77027 + 1.77859i) q^{49} +(11.4747 - 0.587534i) q^{50} +(3.91635 - 9.64723i) q^{51} +(5.95338 + 10.3116i) q^{52} +(5.84795 - 10.1290i) q^{53} +(4.80231 + 10.9322i) q^{54} +(5.87802 + 9.60501i) q^{55} +(0.997313 + 7.72143i) q^{56} +(-2.77879 - 3.56887i) q^{57} +(3.81329 + 2.20160i) q^{58} +2.90947 q^{59} +(12.5360 - 2.06871i) q^{60} -13.0521i q^{61} +3.35542i q^{62} +(3.12295 + 7.29707i) q^{63} -12.8649 q^{64} +(6.92239 - 4.23633i) q^{65} +(12.3142 + 15.8155i) q^{66} -4.76136i q^{67} +(-17.0784 - 9.86021i) q^{68} +(-4.29632 - 1.74412i) q^{69} +(13.4339 - 2.08574i) q^{70} +12.6849i q^{71} +(8.49405 - 2.40517i) q^{72} +(-2.88859 + 5.00318i) q^{73} +(7.80775 - 4.50781i) q^{74} +(-1.62813 - 8.50583i) q^{75} +(-7.41917 + 4.28346i) q^{76} +(8.08525 + 10.5905i) q^{77} +(11.3983 - 8.87493i) q^{78} +0.152914 q^{79} +(-0.0114935 - 0.449238i) q^{80} +(7.66390 - 4.71855i) q^{81} +(0.676147 + 1.17112i) q^{82} +(2.74097 + 1.58250i) q^{83} +(14.5031 - 3.95797i) q^{84} +(-6.42090 + 11.8089i) q^{85} +(11.4201 + 6.59340i) q^{86} +(1.24837 - 3.07513i) q^{87} +(12.8339 - 7.40966i) q^{88} +(2.51793 + 4.36117i) q^{89} +(-4.57778 - 14.7197i) q^{90} +(7.63265 - 5.82709i) q^{91} +(-4.39117 + 7.60573i) q^{92} +(2.50508 - 0.347831i) q^{93} -10.5932i q^{94} +(3.04804 + 4.98066i) q^{95} +(1.29194 + 9.30454i) q^{96} +(-4.18757 + 7.25308i) q^{97} +(15.5577 - 4.08711i) q^{98} +(10.5309 - 10.8330i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q + 76 q^{4} - 3 q^{5} - 12 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 88 q + 76 q^{4} - 3 q^{5} - 12 q^{6} - 6 q^{10} - 12 q^{11} - 12 q^{14} - 6 q^{15} + 52 q^{16} - 12 q^{19} - 6 q^{20} - 12 q^{21} - 48 q^{24} + q^{25} - 12 q^{26} + 6 q^{29} + 33 q^{30} - 12 q^{34} - 36 q^{36} + 12 q^{39} - 30 q^{40} + 6 q^{41} - 84 q^{44} + 21 q^{45} - 18 q^{46} - 8 q^{49} + 30 q^{50} - 24 q^{51} - 60 q^{54} - 78 q^{56} - 12 q^{59} - 45 q^{60} - 8 q^{64} - 24 q^{66} + 60 q^{69} + 15 q^{70} - 30 q^{74} - 48 q^{75} - 48 q^{76} - 16 q^{79} - 69 q^{80} + 36 q^{81} - 90 q^{84} - 7 q^{85} - 12 q^{86} + 72 q^{89} + 33 q^{90} + 20 q^{91} - 60 q^{96} + 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.29795 −1.62489 −0.812447 0.583035i \(-0.801865\pi\)
−0.812447 + 0.583035i \(0.801865\pi\)
\(3\) 0.238210 + 1.71559i 0.137531 + 0.990497i
\(4\) 3.28056 1.64028
\(5\) −0.0571900 2.23534i −0.0255761 0.999673i
\(6\) −0.547395 3.94234i −0.223473 1.60945i
\(7\) −0.338914 2.62395i −0.128098 0.991762i
\(8\) −2.94267 −1.04039
\(9\) −2.88651 + 0.817344i −0.962171 + 0.272448i
\(10\) 0.131420 + 5.13669i 0.0415585 + 1.62436i
\(11\) −4.36132 + 2.51801i −1.31499 + 0.759208i −0.982917 0.184047i \(-0.941080\pi\)
−0.332069 + 0.943255i \(0.607747\pi\)
\(12\) 0.781465 + 5.62811i 0.225589 + 1.62470i
\(13\) 1.81474 + 3.14323i 0.503320 + 0.871775i 0.999993 + 0.00383730i \(0.00122145\pi\)
−0.496673 + 0.867938i \(0.665445\pi\)
\(14\) 0.778808 + 6.02971i 0.208145 + 1.61151i
\(15\) 3.82130 0.630595i 0.986656 0.162819i
\(16\) 0.200971 0.0502428
\(17\) −5.20593 3.00564i −1.26262 0.728976i −0.289042 0.957316i \(-0.593337\pi\)
−0.973581 + 0.228340i \(0.926670\pi\)
\(18\) 6.63305 1.87821i 1.56343 0.442699i
\(19\) −2.26155 + 1.30571i −0.518836 + 0.299550i −0.736458 0.676483i \(-0.763503\pi\)
0.217622 + 0.976033i \(0.430170\pi\)
\(20\) −0.187615 7.33316i −0.0419521 1.63975i
\(21\) 4.42090 1.20649i 0.964720 0.263278i
\(22\) 10.0221 5.78625i 2.13671 1.23363i
\(23\) −1.33854 + 2.31842i −0.279105 + 0.483424i −0.971163 0.238418i \(-0.923371\pi\)
0.692057 + 0.721842i \(0.256704\pi\)
\(24\) −0.700974 5.04842i −0.143086 1.03050i
\(25\) −4.99346 + 0.255678i −0.998692 + 0.0511355i
\(26\) −4.17019 7.22298i −0.817841 1.41654i
\(27\) −2.08983 4.75738i −0.402187 0.915557i
\(28\) −1.11183 8.60805i −0.210116 1.62677i
\(29\) −1.65943 0.958073i −0.308149 0.177910i 0.337949 0.941164i \(-0.390267\pi\)
−0.646098 + 0.763255i \(0.723600\pi\)
\(30\) −8.78115 + 1.44907i −1.60321 + 0.264564i
\(31\) 1.46018i 0.262257i −0.991365 0.131128i \(-0.958140\pi\)
0.991365 0.131128i \(-0.0418600\pi\)
\(32\) 5.42352 0.958751
\(33\) −5.35879 6.88243i −0.932845 1.19808i
\(34\) 11.9630 + 6.90681i 2.05163 + 1.18451i
\(35\) −5.84604 + 0.907652i −0.988161 + 0.153421i
\(36\) −9.46939 + 2.68135i −1.57823 + 0.446891i
\(37\) −3.39771 + 1.96167i −0.558579 + 0.322496i −0.752575 0.658506i \(-0.771189\pi\)
0.193996 + 0.981002i \(0.437855\pi\)
\(38\) 5.19693 3.00045i 0.843053 0.486737i
\(39\) −4.96021 + 3.86211i −0.794269 + 0.618433i
\(40\) 0.168291 + 6.57785i 0.0266092 + 1.04005i
\(41\) −0.294240 0.509638i −0.0459525 0.0795921i 0.842134 0.539268i \(-0.181299\pi\)
−0.888087 + 0.459676i \(0.847966\pi\)
\(42\) −10.1590 + 2.77246i −1.56757 + 0.427799i
\(43\) −4.96969 2.86925i −0.757871 0.437557i 0.0706596 0.997500i \(-0.477490\pi\)
−0.828531 + 0.559943i \(0.810823\pi\)
\(44\) −14.3076 + 8.26049i −2.15695 + 1.24532i
\(45\) 1.99212 + 6.40558i 0.296967 + 0.954888i
\(46\) 3.07590 5.32761i 0.453516 0.785513i
\(47\) 4.60984i 0.672415i 0.941788 + 0.336207i \(0.109144\pi\)
−0.941788 + 0.336207i \(0.890856\pi\)
\(48\) 0.0478734 + 0.344784i 0.00690993 + 0.0497653i
\(49\) −6.77027 + 1.77859i −0.967182 + 0.254085i
\(50\) 11.4747 0.587534i 1.62277 0.0830899i
\(51\) 3.91635 9.64723i 0.548399 1.35088i
\(52\) 5.95338 + 10.3116i 0.825586 + 1.42996i
\(53\) 5.84795 10.1290i 0.803278 1.39132i −0.114169 0.993461i \(-0.536420\pi\)
0.917447 0.397858i \(-0.130246\pi\)
\(54\) 4.80231 + 10.9322i 0.653512 + 1.48768i
\(55\) 5.87802 + 9.60501i 0.792592 + 1.29514i
\(56\) 0.997313 + 7.72143i 0.133272 + 1.03182i
\(57\) −2.77879 3.56887i −0.368059 0.472708i
\(58\) 3.81329 + 2.20160i 0.500709 + 0.289085i
\(59\) 2.90947 0.378780 0.189390 0.981902i \(-0.439349\pi\)
0.189390 + 0.981902i \(0.439349\pi\)
\(60\) 12.5360 2.06871i 1.61839 0.267069i
\(61\) 13.0521i 1.67115i −0.549379 0.835573i \(-0.685136\pi\)
0.549379 0.835573i \(-0.314864\pi\)
\(62\) 3.35542i 0.426139i
\(63\) 3.12295 + 7.29707i 0.393455 + 0.919344i
\(64\) −12.8649 −1.60811
\(65\) 6.92239 4.23633i 0.858617 0.525452i
\(66\) 12.3142 + 15.8155i 1.51577 + 1.94675i
\(67\) 4.76136i 0.581693i −0.956770 0.290846i \(-0.906063\pi\)
0.956770 0.290846i \(-0.0939368\pi\)
\(68\) −17.0784 9.86021i −2.07106 1.19573i
\(69\) −4.29632 1.74412i −0.517216 0.209967i
\(70\) 13.4339 2.08574i 1.60566 0.249293i
\(71\) 12.6849i 1.50543i 0.658349 + 0.752713i \(0.271255\pi\)
−0.658349 + 0.752713i \(0.728745\pi\)
\(72\) 8.49405 2.40517i 1.00103 0.283452i
\(73\) −2.88859 + 5.00318i −0.338083 + 0.585578i −0.984072 0.177769i \(-0.943112\pi\)
0.645989 + 0.763347i \(0.276445\pi\)
\(74\) 7.80775 4.50781i 0.907633 0.524022i
\(75\) −1.62813 8.50583i −0.188001 0.982169i
\(76\) −7.41917 + 4.28346i −0.851037 + 0.491346i
\(77\) 8.08525 + 10.5905i 0.921400 + 1.20690i
\(78\) 11.3983 8.87493i 1.29060 1.00489i
\(79\) 0.152914 0.0172042 0.00860211 0.999963i \(-0.497262\pi\)
0.00860211 + 0.999963i \(0.497262\pi\)
\(80\) −0.0114935 0.449238i −0.00128502 0.0502263i
\(81\) 7.66390 4.71855i 0.851544 0.524283i
\(82\) 0.676147 + 1.17112i 0.0746680 + 0.129329i
\(83\) 2.74097 + 1.58250i 0.300860 + 0.173702i 0.642829 0.766009i \(-0.277760\pi\)
−0.341969 + 0.939711i \(0.611094\pi\)
\(84\) 14.5031 3.95797i 1.58241 0.431850i
\(85\) −6.42090 + 11.8089i −0.696444 + 1.28085i
\(86\) 11.4201 + 6.59340i 1.23146 + 0.710984i
\(87\) 1.24837 3.07513i 0.133839 0.329689i
\(88\) 12.8339 7.40966i 1.36810 0.789873i
\(89\) 2.51793 + 4.36117i 0.266900 + 0.462284i 0.968060 0.250720i \(-0.0806675\pi\)
−0.701160 + 0.713004i \(0.747334\pi\)
\(90\) −4.57778 14.7197i −0.482541 1.55159i
\(91\) 7.63265 5.82709i 0.800119 0.610845i
\(92\) −4.39117 + 7.60573i −0.457811 + 0.792952i
\(93\) 2.50508 0.347831i 0.259764 0.0360684i
\(94\) 10.5932i 1.09260i
\(95\) 3.04804 + 4.98066i 0.312722 + 0.511005i
\(96\) 1.29194 + 9.30454i 0.131858 + 0.949641i
\(97\) −4.18757 + 7.25308i −0.425183 + 0.736438i −0.996437 0.0843346i \(-0.973124\pi\)
0.571255 + 0.820773i \(0.306457\pi\)
\(98\) 15.5577 4.08711i 1.57157 0.412861i
\(99\) 10.5309 10.8330i 1.05840 1.08875i
\(100\) −16.3814 + 0.838767i −1.63814 + 0.0838767i
\(101\) −3.44460 5.96622i −0.342751 0.593661i 0.642192 0.766544i \(-0.278025\pi\)
−0.984942 + 0.172883i \(0.944692\pi\)
\(102\) −8.99958 + 22.1688i −0.891091 + 2.19504i
\(103\) −7.87687 + 13.6431i −0.776131 + 1.34430i 0.158026 + 0.987435i \(0.449487\pi\)
−0.934157 + 0.356863i \(0.883846\pi\)
\(104\) −5.34019 9.24948i −0.523649 0.906986i
\(105\) −2.94975 9.81320i −0.287866 0.957671i
\(106\) −13.4383 + 23.2758i −1.30524 + 2.26075i
\(107\) 6.46598 + 11.1994i 0.625090 + 1.08269i 0.988524 + 0.151067i \(0.0482710\pi\)
−0.363434 + 0.931620i \(0.618396\pi\)
\(108\) −6.85581 15.6069i −0.659700 1.50177i
\(109\) 8.39688 14.5438i 0.804276 1.39305i −0.112503 0.993651i \(-0.535887\pi\)
0.916779 0.399395i \(-0.130780\pi\)
\(110\) −13.5074 22.0718i −1.28788 2.10446i
\(111\) −4.17479 5.36179i −0.396253 0.508918i
\(112\) −0.0681120 0.527339i −0.00643598 0.0498289i
\(113\) −4.83169 8.36874i −0.454528 0.787265i 0.544133 0.838999i \(-0.316859\pi\)
−0.998661 + 0.0517339i \(0.983525\pi\)
\(114\) 6.38551 + 8.20107i 0.598058 + 0.768101i
\(115\) 5.25900 + 2.85950i 0.490405 + 0.266650i
\(116\) −5.44387 3.14302i −0.505451 0.291822i
\(117\) −7.80738 7.58970i −0.721793 0.701668i
\(118\) −6.68580 −0.615478
\(119\) −6.12231 + 14.6788i −0.561231 + 1.34560i
\(120\) −11.2448 + 1.85563i −1.02651 + 0.169395i
\(121\) 7.18073 12.4374i 0.652793 1.13067i
\(122\) 29.9930i 2.71544i
\(123\) 0.804240 0.626196i 0.0725159 0.0564622i
\(124\) 4.79022i 0.430175i
\(125\) 0.857102 + 11.1474i 0.0766615 + 0.997057i
\(126\) −7.17638 16.7683i −0.639323 1.49384i
\(127\) 11.0818i 0.983347i −0.870780 0.491674i \(-0.836385\pi\)
0.870780 0.491674i \(-0.163615\pi\)
\(128\) 18.7158 1.65426
\(129\) 3.73864 9.20946i 0.329169 0.810847i
\(130\) −15.9073 + 9.73485i −1.39516 + 0.853803i
\(131\) −5.74409 + 9.94906i −0.501864 + 0.869253i 0.498134 + 0.867100i \(0.334019\pi\)
−0.999998 + 0.00215316i \(0.999315\pi\)
\(132\) −17.5798 22.5782i −1.53013 1.96518i
\(133\) 4.19259 + 5.49169i 0.363544 + 0.476190i
\(134\) 10.9414i 0.945189i
\(135\) −10.5148 + 4.94354i −0.904972 + 0.425472i
\(136\) 15.3193 + 8.84462i 1.31362 + 0.758420i
\(137\) −2.86212 4.95734i −0.244527 0.423534i 0.717471 0.696588i \(-0.245299\pi\)
−0.961999 + 0.273054i \(0.911966\pi\)
\(138\) 9.87272 + 4.00789i 0.840422 + 0.341175i
\(139\) −5.25854 + 3.03602i −0.446024 + 0.257512i −0.706149 0.708063i \(-0.749569\pi\)
0.260126 + 0.965575i \(0.416236\pi\)
\(140\) −19.1783 + 2.97761i −1.62086 + 0.251654i
\(141\) −7.90861 + 1.09811i −0.666025 + 0.0924778i
\(142\) 29.1493i 2.44616i
\(143\) −15.8294 9.13908i −1.32372 0.764248i
\(144\) −0.580105 + 0.164263i −0.0483421 + 0.0136885i
\(145\) −2.04671 + 3.76418i −0.169970 + 0.312598i
\(146\) 6.63782 11.4970i 0.549350 0.951502i
\(147\) −4.66409 11.1913i −0.384687 0.923047i
\(148\) −11.1464 + 6.43537i −0.916228 + 0.528984i
\(149\) −13.8193 7.97859i −1.13212 0.653631i −0.187655 0.982235i \(-0.560089\pi\)
−0.944468 + 0.328604i \(0.893422\pi\)
\(150\) 3.74136 + 19.5460i 0.305481 + 1.59592i
\(151\) 7.27090 + 12.5936i 0.591698 + 1.02485i 0.994004 + 0.109345i \(0.0348754\pi\)
−0.402306 + 0.915505i \(0.631791\pi\)
\(152\) 6.65500 3.84227i 0.539792 0.311649i
\(153\) 17.4836 + 4.42079i 1.41347 + 0.357400i
\(154\) −18.5795 24.3364i −1.49718 1.96109i
\(155\) −3.26400 + 0.0835078i −0.262171 + 0.00670751i
\(156\) −16.2723 + 12.6699i −1.30282 + 1.01440i
\(157\) 1.06714 0.0851671 0.0425835 0.999093i \(-0.486441\pi\)
0.0425835 + 0.999093i \(0.486441\pi\)
\(158\) −0.351389 −0.0279550
\(159\) 18.7702 + 7.61988i 1.48857 + 0.604296i
\(160\) −0.310171 12.1234i −0.0245212 0.958438i
\(161\) 6.53708 + 2.72652i 0.515194 + 0.214880i
\(162\) −17.6112 + 10.8430i −1.38367 + 0.851904i
\(163\) −2.51831 + 1.45395i −0.197249 + 0.113882i −0.595372 0.803450i \(-0.702995\pi\)
0.398123 + 0.917332i \(0.369662\pi\)
\(164\) −0.965272 1.67190i −0.0753751 0.130553i
\(165\) −15.0781 + 12.3723i −1.17383 + 0.963182i
\(166\) −6.29860 3.63650i −0.488866 0.282247i
\(167\) 21.4761 12.3993i 1.66187 0.959483i 0.690053 0.723759i \(-0.257587\pi\)
0.971820 0.235724i \(-0.0757463\pi\)
\(168\) −13.0093 + 3.55031i −1.00369 + 0.273912i
\(169\) −0.0865940 + 0.149985i −0.00666108 + 0.0115373i
\(170\) 14.7549 27.1362i 1.13165 2.08125i
\(171\) 5.46079 5.61741i 0.417597 0.429574i
\(172\) −16.3034 9.41277i −1.24312 0.717717i
\(173\) 3.40664i 0.259002i −0.991579 0.129501i \(-0.958662\pi\)
0.991579 0.129501i \(-0.0413375\pi\)
\(174\) −2.86869 + 7.06649i −0.217475 + 0.535709i
\(175\) 2.36324 + 13.0160i 0.178644 + 0.983914i
\(176\) −0.876499 + 0.506047i −0.0660686 + 0.0381447i
\(177\) 0.693065 + 4.99146i 0.0520940 + 0.375181i
\(178\) −5.78606 10.0218i −0.433684 0.751162i
\(179\) −0.604912 0.349246i −0.0452133 0.0261039i 0.477223 0.878782i \(-0.341643\pi\)
−0.522436 + 0.852678i \(0.674977\pi\)
\(180\) 6.53527 + 21.0139i 0.487110 + 1.56628i
\(181\) 17.8235i 1.32481i 0.749147 + 0.662403i \(0.230463\pi\)
−0.749147 + 0.662403i \(0.769537\pi\)
\(182\) −17.5394 + 13.3904i −1.30011 + 0.992559i
\(183\) 22.3920 3.10914i 1.65527 0.229834i
\(184\) 3.93888 6.82235i 0.290378 0.502950i
\(185\) 4.57930 + 7.48283i 0.336677 + 0.550149i
\(186\) −5.75654 + 0.799297i −0.422090 + 0.0586073i
\(187\) 30.2730 2.21378
\(188\) 15.1229i 1.10295i
\(189\) −11.7749 + 7.09595i −0.856495 + 0.516155i
\(190\) −7.00423 11.4453i −0.508140 0.830329i
\(191\) 12.1781i 0.881176i −0.897709 0.440588i \(-0.854770\pi\)
0.897709 0.440588i \(-0.145230\pi\)
\(192\) −3.06455 22.0709i −0.221165 1.59283i
\(193\) 0.773008i 0.0556423i 0.999613 + 0.0278212i \(0.00885689\pi\)
−0.999613 + 0.0278212i \(0.991143\pi\)
\(194\) 9.62281 16.6672i 0.690877 1.19663i
\(195\) 8.91679 + 10.8669i 0.638545 + 0.778192i
\(196\) −22.2103 + 5.83478i −1.58645 + 0.416770i
\(197\) −0.319064 −0.0227323 −0.0113662 0.999935i \(-0.503618\pi\)
−0.0113662 + 0.999935i \(0.503618\pi\)
\(198\) −24.1995 + 24.8936i −1.71978 + 1.76911i
\(199\) 7.49062 + 4.32471i 0.530996 + 0.306571i 0.741422 0.671039i \(-0.234152\pi\)
−0.210426 + 0.977610i \(0.567485\pi\)
\(200\) 14.6941 0.752375i 1.03903 0.0532009i
\(201\) 8.16855 1.13421i 0.576165 0.0800007i
\(202\) 7.91551 + 13.7101i 0.556933 + 0.964637i
\(203\) −1.95154 + 4.67898i −0.136971 + 0.328400i
\(204\) 12.8478 31.6483i 0.899529 2.21583i
\(205\) −1.12238 + 0.686871i −0.0783908 + 0.0479731i
\(206\) 18.1006 31.3512i 1.26113 2.18434i
\(207\) 1.96877 7.78620i 0.136839 0.541178i
\(208\) 0.364711 + 0.631698i 0.0252882 + 0.0438004i
\(209\) 6.57557 11.3892i 0.454841 0.787808i
\(210\) 6.77837 + 22.5502i 0.467752 + 1.55611i
\(211\) −9.40901 16.2969i −0.647743 1.12192i −0.983661 0.180032i \(-0.942380\pi\)
0.335918 0.941891i \(-0.390954\pi\)
\(212\) 19.1846 33.2287i 1.31760 2.28216i
\(213\) −21.7622 + 3.02169i −1.49112 + 0.207043i
\(214\) −14.8585 25.7356i −1.01570 1.75925i
\(215\) −6.12953 + 11.2730i −0.418031 + 0.768814i
\(216\) 6.14967 + 13.9994i 0.418432 + 0.952537i
\(217\) −3.83145 + 0.494877i −0.260096 + 0.0335944i
\(218\) −19.2956 + 33.4210i −1.30686 + 2.26355i
\(219\) −9.27150 3.76382i −0.626510 0.254336i
\(220\) 19.2832 + 31.5098i 1.30007 + 2.12439i
\(221\) 21.8179i 1.46763i
\(222\) 9.59345 + 12.3211i 0.643870 + 0.826939i
\(223\) −9.51294 + 16.4769i −0.637034 + 1.10338i 0.349046 + 0.937105i \(0.386506\pi\)
−0.986080 + 0.166270i \(0.946828\pi\)
\(224\) −1.83811 14.2311i −0.122814 0.950853i
\(225\) 14.2047 4.81939i 0.946980 0.321293i
\(226\) 11.1030 + 19.2309i 0.738559 + 1.27922i
\(227\) 10.7207 6.18962i 0.711560 0.410819i −0.100078 0.994980i \(-0.531909\pi\)
0.811638 + 0.584160i \(0.198576\pi\)
\(228\) −9.11599 11.7079i −0.603721 0.775375i
\(229\) 0.982839 + 0.567442i 0.0649478 + 0.0374976i 0.532122 0.846668i \(-0.321395\pi\)
−0.467174 + 0.884165i \(0.654728\pi\)
\(230\) −12.0849 6.57098i −0.796856 0.433278i
\(231\) −16.2430 + 16.3938i −1.06871 + 1.07863i
\(232\) 4.88316 + 2.81929i 0.320595 + 0.185096i
\(233\) −1.96907 3.41053i −0.128998 0.223431i 0.794291 0.607538i \(-0.207843\pi\)
−0.923289 + 0.384107i \(0.874509\pi\)
\(234\) 17.9410 + 17.4407i 1.17284 + 1.14014i
\(235\) 10.3046 0.263637i 0.672195 0.0171978i
\(236\) 9.54469 0.621306
\(237\) 0.0364258 + 0.262339i 0.00236611 + 0.0170407i
\(238\) 14.0688 33.7311i 0.911942 2.18646i
\(239\) 2.56257 1.47950i 0.165759 0.0957008i −0.414826 0.909901i \(-0.636157\pi\)
0.580584 + 0.814200i \(0.302824\pi\)
\(240\) 0.767971 0.126731i 0.0495723 0.00818048i
\(241\) −10.5820 + 6.10951i −0.681646 + 0.393548i −0.800475 0.599366i \(-0.795419\pi\)
0.118829 + 0.992915i \(0.462086\pi\)
\(242\) −16.5009 + 28.5805i −1.06072 + 1.83722i
\(243\) 9.92072 + 12.0241i 0.636414 + 0.771347i
\(244\) 42.8181i 2.74115i
\(245\) 4.36294 + 15.0321i 0.278738 + 0.960367i
\(246\) −1.84810 + 1.43897i −0.117831 + 0.0917451i
\(247\) −8.20828 4.73905i −0.522280 0.301539i
\(248\) 4.29683i 0.272849i
\(249\) −2.06199 + 5.07935i −0.130674 + 0.321891i
\(250\) −1.96957 25.6162i −0.124567 1.62011i
\(251\) 19.3025 1.21836 0.609182 0.793030i \(-0.291498\pi\)
0.609182 + 0.793030i \(0.291498\pi\)
\(252\) 10.2450 + 23.9385i 0.645377 + 1.50798i
\(253\) 13.4818i 0.847595i
\(254\) 25.4653i 1.59784i
\(255\) −21.7888 8.20264i −1.36447 0.513669i
\(256\) −17.2782 −1.07989
\(257\) −3.24550 1.87379i −0.202449 0.116884i 0.395348 0.918531i \(-0.370624\pi\)
−0.597797 + 0.801647i \(0.703957\pi\)
\(258\) −8.59119 + 21.1628i −0.534864 + 1.31754i
\(259\) 6.29886 + 8.25059i 0.391392 + 0.512667i
\(260\) 22.7093 13.8975i 1.40837 0.861889i
\(261\) 5.57304 + 1.40916i 0.344963 + 0.0872250i
\(262\) 13.1996 22.8624i 0.815475 1.41244i
\(263\) −12.3518 21.3940i −0.761647 1.31921i −0.942001 0.335609i \(-0.891058\pi\)
0.180355 0.983602i \(-0.442275\pi\)
\(264\) 15.7691 + 20.2527i 0.970523 + 1.24647i
\(265\) −22.9761 12.4929i −1.41141 0.767431i
\(266\) −9.63436 12.6196i −0.590720 0.773758i
\(267\) −6.88220 + 5.35861i −0.421184 + 0.327942i
\(268\) 15.6199i 0.954140i
\(269\) −9.85276 + 17.0655i −0.600733 + 1.04050i 0.391977 + 0.919975i \(0.371791\pi\)
−0.992710 + 0.120525i \(0.961542\pi\)
\(270\) 24.1625 11.3600i 1.47048 0.691347i
\(271\) 17.0234 9.82848i 1.03410 0.597038i 0.115943 0.993256i \(-0.463011\pi\)
0.918156 + 0.396218i \(0.129678\pi\)
\(272\) −1.04624 0.604048i −0.0634377 0.0366258i
\(273\) 11.8151 + 11.7064i 0.715082 + 0.708506i
\(274\) 6.57700 + 11.3917i 0.397331 + 0.688198i
\(275\) 21.1343 13.6887i 1.27444 0.825457i
\(276\) −14.0944 5.72169i −0.848380 0.344405i
\(277\) 5.68157 3.28026i 0.341372 0.197091i −0.319506 0.947584i \(-0.603517\pi\)
0.660879 + 0.750493i \(0.270184\pi\)
\(278\) 12.0839 6.97662i 0.724741 0.418430i
\(279\) 1.19347 + 4.21483i 0.0714513 + 0.252336i
\(280\) 17.2030 2.67092i 1.02807 0.159618i
\(281\) 13.6397 + 7.87486i 0.813674 + 0.469775i 0.848230 0.529628i \(-0.177668\pi\)
−0.0345563 + 0.999403i \(0.511002\pi\)
\(282\) 18.1736 2.52341i 1.08222 0.150267i
\(283\) 16.1994 0.962955 0.481477 0.876458i \(-0.340100\pi\)
0.481477 + 0.876458i \(0.340100\pi\)
\(284\) 41.6138i 2.46932i
\(285\) −7.81870 + 6.41563i −0.463140 + 0.380029i
\(286\) 36.3750 + 21.0011i 2.15090 + 1.24182i
\(287\) −1.23754 + 0.944795i −0.0730500 + 0.0557695i
\(288\) −15.6550 + 4.43288i −0.922482 + 0.261210i
\(289\) 9.56780 + 16.5719i 0.562812 + 0.974819i
\(290\) 4.70324 8.64989i 0.276184 0.507939i
\(291\) −13.4408 5.45640i −0.787916 0.319860i
\(292\) −9.47619 + 16.4132i −0.554552 + 0.960512i
\(293\) −15.3284 + 8.84983i −0.895492 + 0.517013i −0.875735 0.482792i \(-0.839623\pi\)
−0.0197572 + 0.999805i \(0.506289\pi\)
\(294\) 10.7178 + 25.7171i 0.625077 + 1.49985i
\(295\) −0.166392 6.50363i −0.00968773 0.378656i
\(296\) 9.99832 5.77253i 0.581141 0.335522i
\(297\) 21.0935 + 15.4862i 1.22397 + 0.898602i
\(298\) 31.7561 + 18.3344i 1.83958 + 1.06208i
\(299\) −9.71644 −0.561916
\(300\) −5.34119 27.9039i −0.308374 1.61103i
\(301\) −5.84449 + 14.0127i −0.336871 + 0.807678i
\(302\) −16.7082 28.9394i −0.961446 1.66527i
\(303\) 9.41506 7.33074i 0.540881 0.421140i
\(304\) −0.454507 + 0.262410i −0.0260677 + 0.0150502i
\(305\) −29.1758 + 0.746448i −1.67060 + 0.0427415i
\(306\) −40.1764 10.1588i −2.29673 0.580737i
\(307\) 6.36015 0.362993 0.181497 0.983392i \(-0.441906\pi\)
0.181497 + 0.983392i \(0.441906\pi\)
\(308\) 26.5242 + 34.7428i 1.51136 + 1.97966i
\(309\) −25.2824 10.2636i −1.43827 0.583873i
\(310\) 7.50050 0.191897i 0.426000 0.0108990i
\(311\) −26.9639 −1.52899 −0.764493 0.644633i \(-0.777010\pi\)
−0.764493 + 0.644633i \(0.777010\pi\)
\(312\) 14.5962 11.3649i 0.826350 0.643411i
\(313\) −9.97596 −0.563875 −0.281937 0.959433i \(-0.590977\pi\)
−0.281937 + 0.959433i \(0.590977\pi\)
\(314\) −2.45223 −0.138388
\(315\) 16.1328 7.39817i 0.908980 0.416840i
\(316\) 0.501645 0.0282198
\(317\) −28.5140 −1.60151 −0.800753 0.598995i \(-0.795567\pi\)
−0.800753 + 0.598995i \(0.795567\pi\)
\(318\) −43.1329 17.5101i −2.41877 0.981917i
\(319\) 9.64975 0.540282
\(320\) 0.735743 + 28.7574i 0.0411293 + 1.60759i
\(321\) −17.6733 + 13.7608i −0.986430 + 0.768053i
\(322\) −15.0219 6.26541i −0.837136 0.349158i
\(323\) 15.6980 0.873459
\(324\) 25.1419 15.4795i 1.39677 0.859972i
\(325\) −9.86550 15.2316i −0.547240 0.844897i
\(326\) 5.78694 3.34109i 0.320509 0.185046i
\(327\) 26.9515 + 10.9411i 1.49042 + 0.605046i
\(328\) 0.865850 + 1.49970i 0.0478086 + 0.0828069i
\(329\) 12.0960 1.56234i 0.666875 0.0861347i
\(330\) 34.6486 28.4309i 1.90734 1.56507i
\(331\) −25.0896 −1.37905 −0.689525 0.724262i \(-0.742181\pi\)
−0.689525 + 0.724262i \(0.742181\pi\)
\(332\) 8.99192 + 5.19149i 0.493496 + 0.284920i
\(333\) 8.20416 8.43947i 0.449585 0.462480i
\(334\) −49.3510 + 28.4928i −2.70037 + 1.55906i
\(335\) −10.6432 + 0.272302i −0.581502 + 0.0148774i
\(336\) 0.888474 0.242470i 0.0484702 0.0132278i
\(337\) 30.3670 17.5324i 1.65420 0.955051i 0.678879 0.734250i \(-0.262466\pi\)
0.975319 0.220801i \(-0.0708671\pi\)
\(338\) 0.198989 0.344658i 0.0108236 0.0187469i
\(339\) 13.2064 10.2827i 0.717272 0.558482i
\(340\) −21.0642 + 38.7398i −1.14237 + 2.10096i
\(341\) 3.67675 + 6.36832i 0.199107 + 0.344864i
\(342\) −12.5486 + 12.9085i −0.678551 + 0.698012i
\(343\) 6.96149 + 17.1621i 0.375885 + 0.926666i
\(344\) 14.6242 + 8.44327i 0.788482 + 0.455230i
\(345\) −3.65299 + 9.70347i −0.196670 + 0.522417i
\(346\) 7.82827i 0.420851i
\(347\) −30.8081 −1.65387 −0.826933 0.562300i \(-0.809917\pi\)
−0.826933 + 0.562300i \(0.809917\pi\)
\(348\) 4.09535 10.0882i 0.219534 0.540782i
\(349\) −5.17646 2.98863i −0.277089 0.159978i 0.355016 0.934860i \(-0.384476\pi\)
−0.632105 + 0.774883i \(0.717809\pi\)
\(350\) −5.43061 29.9100i −0.290278 1.59876i
\(351\) 11.1610 15.2022i 0.595731 0.811435i
\(352\) −23.6537 + 13.6565i −1.26075 + 0.727892i
\(353\) −0.986963 + 0.569823i −0.0525307 + 0.0303286i −0.526035 0.850463i \(-0.676322\pi\)
0.473505 + 0.880791i \(0.342989\pi\)
\(354\) −1.59263 11.4701i −0.0846472 0.609629i
\(355\) 28.3551 0.725452i 1.50493 0.0385030i
\(356\) 8.26021 + 14.3071i 0.437790 + 0.758275i
\(357\) −26.6412 7.00675i −1.41000 0.370836i
\(358\) 1.39006 + 0.802550i 0.0734668 + 0.0424161i
\(359\) −4.46715 + 2.57911i −0.235767 + 0.136120i −0.613230 0.789905i \(-0.710130\pi\)
0.377463 + 0.926025i \(0.376797\pi\)
\(360\) −5.86214 18.8495i −0.308962 0.993456i
\(361\) −6.09025 + 10.5486i −0.320540 + 0.555191i
\(362\) 40.9574i 2.15267i
\(363\) 23.0480 + 9.35648i 1.20971 + 0.491088i
\(364\) 25.0394 19.1161i 1.31242 1.00196i
\(365\) 11.3490 + 6.17083i 0.594033 + 0.322996i
\(366\) −51.4557 + 7.14464i −2.68963 + 0.373456i
\(367\) −4.24201 7.34738i −0.221431 0.383530i 0.733811 0.679353i \(-0.237740\pi\)
−0.955243 + 0.295823i \(0.904406\pi\)
\(368\) −0.269008 + 0.465936i −0.0140230 + 0.0242886i
\(369\) 1.26588 + 1.23058i 0.0658989 + 0.0640615i
\(370\) −10.5230 17.1952i −0.547064 0.893933i
\(371\) −28.5599 11.9119i −1.48275 0.618436i
\(372\) 8.21807 1.14108i 0.426087 0.0591623i
\(373\) −13.0687 7.54521i −0.676671 0.390676i 0.121929 0.992539i \(-0.461092\pi\)
−0.798600 + 0.601863i \(0.794425\pi\)
\(374\) −69.5657 −3.59715
\(375\) −18.9203 + 4.12587i −0.977039 + 0.213059i
\(376\) 13.5652i 0.699574i
\(377\) 6.95463i 0.358182i
\(378\) 27.0580 16.3061i 1.39171 0.838697i
\(379\) 4.62607 0.237625 0.118813 0.992917i \(-0.462091\pi\)
0.118813 + 0.992917i \(0.462091\pi\)
\(380\) 9.99927 + 16.3394i 0.512952 + 0.838192i
\(381\) 19.0118 2.63979i 0.974003 0.135241i
\(382\) 27.9846i 1.43182i
\(383\) 2.03184 + 1.17308i 0.103822 + 0.0599418i 0.551012 0.834497i \(-0.314242\pi\)
−0.447190 + 0.894439i \(0.647575\pi\)
\(384\) 4.45831 + 32.1087i 0.227512 + 1.63854i
\(385\) 23.2110 18.6789i 1.18294 0.951966i
\(386\) 1.77633i 0.0904129i
\(387\) 16.6902 + 4.22019i 0.848413 + 0.214524i
\(388\) −13.7376 + 23.7942i −0.697420 + 1.20797i
\(389\) −11.0970 + 6.40683i −0.562638 + 0.324839i −0.754204 0.656640i \(-0.771977\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(390\) −20.4903 24.9715i −1.03757 1.26448i
\(391\) 13.9367 8.04636i 0.704809 0.406922i
\(392\) 19.9227 5.23381i 1.00625 0.264347i
\(393\) −18.4368 7.48455i −0.930015 0.377545i
\(394\) 0.733191 0.0369376
\(395\) −0.00874517 0.341815i −0.000440017 0.0171986i
\(396\) 34.5473 35.5382i 1.73607 1.78586i
\(397\) 2.38016 + 4.12255i 0.119457 + 0.206905i 0.919552 0.392967i \(-0.128551\pi\)
−0.800096 + 0.599872i \(0.795218\pi\)
\(398\) −17.2131 9.93797i −0.862813 0.498145i
\(399\) −8.42278 + 8.50095i −0.421666 + 0.425580i
\(400\) −1.00354 + 0.0513838i −0.0501770 + 0.00256919i
\(401\) 20.0840 + 11.5955i 1.00295 + 0.579052i 0.909119 0.416536i \(-0.136756\pi\)
0.0938285 + 0.995588i \(0.470089\pi\)
\(402\) −18.7709 + 2.60634i −0.936207 + 0.129993i
\(403\) 4.58969 2.64986i 0.228629 0.131999i
\(404\) −11.3002 19.5726i −0.562207 0.973772i
\(405\) −10.9858 16.8615i −0.545891 0.837857i
\(406\) 4.48453 10.7520i 0.222563 0.533615i
\(407\) 9.87898 17.1109i 0.489683 0.848156i
\(408\) −11.5245 + 28.3886i −0.570549 + 1.40544i
\(409\) 10.9626i 0.542066i −0.962570 0.271033i \(-0.912635\pi\)
0.962570 0.271033i \(-0.0873652\pi\)
\(410\) 2.57918 1.57839i 0.127377 0.0779513i
\(411\) 7.82298 6.09112i 0.385879 0.300453i
\(412\) −25.8406 + 44.7572i −1.27307 + 2.20503i
\(413\) −0.986060 7.63430i −0.0485208 0.375660i
\(414\) −4.52412 + 17.8923i −0.222349 + 0.879358i
\(415\) 3.38066 6.21749i 0.165950 0.305205i
\(416\) 9.84230 + 17.0474i 0.482558 + 0.835815i
\(417\) −6.46121 8.29830i −0.316407 0.406370i
\(418\) −15.1103 + 26.1718i −0.739069 + 1.28011i
\(419\) 1.39994 + 2.42477i 0.0683915 + 0.118458i 0.898193 0.439601i \(-0.144880\pi\)
−0.829802 + 0.558058i \(0.811547\pi\)
\(420\) −9.67683 32.1928i −0.472181 1.57085i
\(421\) 8.97588 15.5467i 0.437457 0.757699i −0.560035 0.828469i \(-0.689212\pi\)
0.997493 + 0.0707703i \(0.0225457\pi\)
\(422\) 21.6214 + 37.4494i 1.05251 + 1.82301i
\(423\) −3.76783 13.3064i −0.183198 0.646978i
\(424\) −17.2086 + 29.8062i −0.835723 + 1.44751i
\(425\) 26.7641 + 13.6775i 1.29825 + 0.663457i
\(426\) 50.0084 6.94368i 2.42291 0.336422i
\(427\) −34.2480 + 4.42353i −1.65738 + 0.214070i
\(428\) 21.2121 + 36.7404i 1.02532 + 1.77591i
\(429\) 11.9082 29.3337i 0.574934 1.41625i
\(430\) 14.0853 25.9048i 0.679256 1.24924i
\(431\) −17.8638 10.3136i −0.860467 0.496791i 0.00370165 0.999993i \(-0.498822\pi\)
−0.864169 + 0.503202i \(0.832155\pi\)
\(432\) −0.419995 0.956095i −0.0202070 0.0460001i
\(433\) −13.0171 −0.625560 −0.312780 0.949826i \(-0.601260\pi\)
−0.312780 + 0.949826i \(0.601260\pi\)
\(434\) 8.80448 1.13720i 0.422628 0.0545874i
\(435\) −6.94535 2.61466i −0.333004 0.125363i
\(436\) 27.5465 47.7120i 1.31924 2.28499i
\(437\) 6.99098i 0.334424i
\(438\) 21.3054 + 8.64907i 1.01801 + 0.413269i
\(439\) 25.9894i 1.24040i 0.784442 + 0.620202i \(0.212949\pi\)
−0.784442 + 0.620202i \(0.787051\pi\)
\(440\) −17.2971 28.2644i −0.824605 1.34745i
\(441\) 18.0888 10.6676i 0.861369 0.507979i
\(442\) 50.1364i 2.38475i
\(443\) −12.5578 −0.596641 −0.298321 0.954466i \(-0.596426\pi\)
−0.298321 + 0.954466i \(0.596426\pi\)
\(444\) −13.6957 17.5897i −0.649967 0.834770i
\(445\) 9.60469 5.87783i 0.455306 0.278636i
\(446\) 21.8602 37.8631i 1.03511 1.79287i
\(447\) 10.3961 25.6089i 0.491718 1.21126i
\(448\) 4.36010 + 33.7569i 0.205995 + 1.59486i
\(449\) 27.6483i 1.30480i 0.757874 + 0.652401i \(0.226238\pi\)
−0.757874 + 0.652401i \(0.773762\pi\)
\(450\) −32.6417 + 11.0747i −1.53874 + 0.522067i
\(451\) 2.56655 + 1.48180i 0.120854 + 0.0697750i
\(452\) −15.8507 27.4542i −0.745553 1.29134i
\(453\) −19.8734 + 15.4738i −0.933735 + 0.727024i
\(454\) −24.6357 + 14.2234i −1.15621 + 0.667538i
\(455\) −13.4620 16.7283i −0.631109 0.784234i
\(456\) 8.17705 + 10.5020i 0.382926 + 0.491801i
\(457\) 4.63917i 0.217011i −0.994096 0.108506i \(-0.965393\pi\)
0.994096 0.108506i \(-0.0346066\pi\)
\(458\) −2.25851 1.30395i −0.105533 0.0609297i
\(459\) −3.41950 + 31.0478i −0.159608 + 1.44919i
\(460\) 17.2525 + 9.38077i 0.804402 + 0.437381i
\(461\) −4.85128 + 8.40266i −0.225947 + 0.391351i −0.956603 0.291394i \(-0.905881\pi\)
0.730656 + 0.682745i \(0.239214\pi\)
\(462\) 37.3256 37.6720i 1.73654 1.75266i
\(463\) −13.1716 + 7.60465i −0.612138 + 0.353418i −0.773802 0.633428i \(-0.781647\pi\)
0.161664 + 0.986846i \(0.448314\pi\)
\(464\) −0.333498 0.192545i −0.0154822 0.00893868i
\(465\) −0.920784 5.57980i −0.0427003 0.258757i
\(466\) 4.52482 + 7.83722i 0.209608 + 0.363052i
\(467\) 0.943117 0.544509i 0.0436423 0.0251969i −0.478020 0.878349i \(-0.658645\pi\)
0.521662 + 0.853152i \(0.325312\pi\)
\(468\) −25.6126 24.8985i −1.18394 1.15093i
\(469\) −12.4936 + 1.61369i −0.576900 + 0.0745134i
\(470\) −23.6793 + 0.605824i −1.09225 + 0.0279446i
\(471\) 0.254204 + 1.83078i 0.0117131 + 0.0843578i
\(472\) −8.56159 −0.394079
\(473\) 28.8992 1.32879
\(474\) −0.0837046 0.602841i −0.00384468 0.0276894i
\(475\) 10.9591 7.09823i 0.502839 0.325689i
\(476\) −20.0846 + 48.1547i −0.920578 + 2.20717i
\(477\) −8.60135 + 34.0171i −0.393829 + 1.55754i
\(478\) −5.88864 + 3.39981i −0.269340 + 0.155504i
\(479\) 12.2449 + 21.2088i 0.559484 + 0.969055i 0.997539 + 0.0701067i \(0.0223340\pi\)
−0.438056 + 0.898948i \(0.644333\pi\)
\(480\) 20.7249 3.42004i 0.945958 0.156103i
\(481\) −12.3319 7.11985i −0.562288 0.324637i
\(482\) 24.3169 14.0393i 1.10760 0.639474i
\(483\) −3.12040 + 11.8645i −0.141983 + 0.539851i
\(484\) 23.5568 40.8016i 1.07077 1.85462i
\(485\) 16.4526 + 8.94581i 0.747072 + 0.406209i
\(486\) −22.7973 27.6308i −1.03411 1.25336i
\(487\) 19.5953 + 11.3134i 0.887949 + 0.512657i 0.873271 0.487235i \(-0.161994\pi\)
0.0146777 + 0.999892i \(0.495328\pi\)
\(488\) 38.4079i 1.73864i
\(489\) −3.09426 3.97404i −0.139927 0.179712i
\(490\) −10.0258 34.5430i −0.452920 1.56050i
\(491\) −10.0195 + 5.78479i −0.452176 + 0.261064i −0.708749 0.705461i \(-0.750740\pi\)
0.256573 + 0.966525i \(0.417407\pi\)
\(492\) 2.63836 2.05428i 0.118946 0.0926140i
\(493\) 5.75926 + 9.97533i 0.259384 + 0.449266i
\(494\) 18.8622 + 10.8901i 0.848650 + 0.489969i
\(495\) −24.8176 22.9206i −1.11547 1.03020i
\(496\) 0.293455i 0.0131765i
\(497\) 33.2847 4.29911i 1.49302 0.192842i
\(498\) 4.73836 11.6721i 0.212331 0.523038i
\(499\) 7.77544 13.4675i 0.348077 0.602886i −0.637831 0.770176i \(-0.720168\pi\)
0.985908 + 0.167290i \(0.0535016\pi\)
\(500\) 2.81178 + 36.5699i 0.125746 + 1.63545i
\(501\) 26.3879 + 33.8907i 1.17892 + 1.51412i
\(502\) −44.3562 −1.97971
\(503\) 7.19412i 0.320770i −0.987055 0.160385i \(-0.948726\pi\)
0.987055 0.160385i \(-0.0512736\pi\)
\(504\) −9.18982 21.4728i −0.409347 0.956477i
\(505\) −13.1395 + 8.04105i −0.584701 + 0.357822i
\(506\) 30.9805i 1.37725i
\(507\) −0.277941 0.112832i −0.0123438 0.00501104i
\(508\) 36.3544i 1.61297i
\(509\) 20.8063 36.0375i 0.922221 1.59733i 0.126250 0.991998i \(-0.459706\pi\)
0.795971 0.605335i \(-0.206961\pi\)
\(510\) 50.0695 + 18.8492i 2.21711 + 0.834659i
\(511\) 14.1071 + 5.88387i 0.624061 + 0.260287i
\(512\) 2.27275 0.100442
\(513\) 10.9380 + 8.03035i 0.482924 + 0.354549i
\(514\) 7.45800 + 4.30588i 0.328958 + 0.189924i
\(515\) 30.9475 + 16.8272i 1.36371 + 0.741495i
\(516\) 12.2648 30.2122i 0.539929 1.33002i
\(517\) −11.6076 20.1050i −0.510503 0.884217i
\(518\) −14.4744 18.9594i −0.635970 0.833029i
\(519\) 5.84440 0.811496i 0.256541 0.0356207i
\(520\) −20.3703 + 12.4661i −0.893297 + 0.546675i
\(521\) −5.95581 + 10.3158i −0.260929 + 0.451942i −0.966489 0.256708i \(-0.917362\pi\)
0.705560 + 0.708650i \(0.250695\pi\)
\(522\) −12.8066 3.23818i −0.560528 0.141731i
\(523\) −14.7582 25.5619i −0.645330 1.11775i −0.984225 0.176921i \(-0.943386\pi\)
0.338895 0.940824i \(-0.389947\pi\)
\(524\) −18.8439 + 32.6385i −0.823198 + 1.42582i
\(525\) −21.7671 + 7.15490i −0.949995 + 0.312265i
\(526\) 28.3839 + 49.1623i 1.23760 + 2.14358i
\(527\) −4.38879 + 7.60161i −0.191179 + 0.331131i
\(528\) −1.07696 1.38317i −0.0468687 0.0601947i
\(529\) 7.91661 + 13.7120i 0.344201 + 0.596173i
\(530\) 52.7978 + 28.7080i 2.29339 + 1.24699i
\(531\) −8.39821 + 2.37803i −0.364451 + 0.103198i
\(532\) 13.7541 + 18.0158i 0.596314 + 0.781085i
\(533\) 1.06794 1.84973i 0.0462576 0.0801205i
\(534\) 15.8149 12.3138i 0.684379 0.532870i
\(535\) 24.6646 15.0941i 1.06635 0.652576i
\(536\) 14.0111i 0.605187i
\(537\) 0.455068 1.12098i 0.0196376 0.0483737i
\(538\) 22.6411 39.2156i 0.976128 1.69070i
\(539\) 25.0488 24.8046i 1.07893 1.06841i
\(540\) −34.4945 + 16.2176i −1.48441 + 0.697894i
\(541\) −0.448564 0.776935i −0.0192853 0.0334030i 0.856222 0.516609i \(-0.172806\pi\)
−0.875507 + 0.483205i \(0.839472\pi\)
\(542\) −39.1190 + 22.5853i −1.68030 + 0.970123i
\(543\) −30.5778 + 4.24573i −1.31222 + 0.182202i
\(544\) −28.2344 16.3012i −1.21054 0.698907i
\(545\) −32.9906 17.9381i −1.41316 0.768384i
\(546\) −27.1505 26.9008i −1.16193 1.15125i
\(547\) 5.58675 + 3.22551i 0.238872 + 0.137913i 0.614658 0.788794i \(-0.289294\pi\)
−0.375786 + 0.926706i \(0.622627\pi\)
\(548\) −9.38937 16.2629i −0.401094 0.694715i
\(549\) 10.6680 + 37.6750i 0.455300 + 1.60793i
\(550\) −48.5654 + 31.4558i −2.07084 + 1.34128i
\(551\) 5.00386 0.213171
\(552\) 12.6426 + 5.13236i 0.538107 + 0.218448i
\(553\) −0.0518249 0.401240i −0.00220382 0.0170625i
\(554\) −13.0559 + 7.53786i −0.554694 + 0.320253i
\(555\) −11.7466 + 9.63870i −0.498617 + 0.409140i
\(556\) −17.2510 + 9.95986i −0.731605 + 0.422392i
\(557\) −1.69987 + 2.94426i −0.0720258 + 0.124752i −0.899789 0.436325i \(-0.856280\pi\)
0.827763 + 0.561078i \(0.189613\pi\)
\(558\) −2.74254 9.68547i −0.116101 0.410019i
\(559\) 20.8279i 0.880924i
\(560\) −1.17488 + 0.182412i −0.0496479 + 0.00770830i
\(561\) 7.21133 + 51.9360i 0.304463 + 2.19274i
\(562\) −31.3432 18.0960i −1.32213 0.763334i
\(563\) 24.6855i 1.04037i 0.854054 + 0.520184i \(0.174137\pi\)
−0.854054 + 0.520184i \(0.825863\pi\)
\(564\) −25.9447 + 3.60243i −1.09247 + 0.151690i
\(565\) −18.4306 + 11.2791i −0.775382 + 0.474514i
\(566\) −37.2254 −1.56470
\(567\) −14.9787 18.5105i −0.629044 0.777369i
\(568\) 37.3276i 1.56623i
\(569\) 39.9610i 1.67525i −0.546245 0.837626i \(-0.683943\pi\)
0.546245 0.837626i \(-0.316057\pi\)
\(570\) 17.9670 14.7428i 0.752554 0.617507i
\(571\) −16.5448 −0.692376 −0.346188 0.938165i \(-0.612524\pi\)
−0.346188 + 0.938165i \(0.612524\pi\)
\(572\) −51.9292 29.9813i −2.17127 1.25358i
\(573\) 20.8926 2.90095i 0.872802 0.121189i
\(574\) 2.84381 2.17109i 0.118698 0.0906195i
\(575\) 6.09118 11.9192i 0.254020 0.497064i
\(576\) 37.1347 10.5150i 1.54728 0.438127i
\(577\) 10.2849 17.8139i 0.428164 0.741602i −0.568546 0.822651i \(-0.692494\pi\)
0.996710 + 0.0810497i \(0.0258273\pi\)
\(578\) −21.9863 38.0814i −0.914510 1.58398i
\(579\) −1.32617 + 0.184139i −0.0551136 + 0.00765254i
\(580\) −6.71437 + 12.3486i −0.278799 + 0.512749i
\(581\) 3.22345 7.72851i 0.133731 0.320632i
\(582\) 30.8864 + 12.5385i 1.28028 + 0.519738i
\(583\) 58.9008i 2.43942i
\(584\) 8.50015 14.7227i 0.351739 0.609229i
\(585\) −16.5190 + 17.8862i −0.682978 + 0.739502i
\(586\) 35.2238 20.3364i 1.45508 0.840091i
\(587\) −19.8410 11.4552i −0.818924 0.472806i 0.0311213 0.999516i \(-0.490092\pi\)
−0.850045 + 0.526710i \(0.823426\pi\)
\(588\) −15.3008 36.7139i −0.630996 1.51406i
\(589\) 1.90657 + 3.30228i 0.0785589 + 0.136068i
\(590\) 0.382361 + 14.9450i 0.0157415 + 0.615276i
\(591\) −0.0760043 0.547383i −0.00312640 0.0225163i
\(592\) −0.682841 + 0.394238i −0.0280646 + 0.0162031i
\(593\) −30.9777 + 17.8850i −1.27210 + 0.734448i −0.975383 0.220518i \(-0.929225\pi\)
−0.296718 + 0.954965i \(0.595892\pi\)
\(594\) −48.4718 35.5865i −1.98882 1.46013i
\(595\) 33.1621 + 12.8459i 1.35952 + 0.526632i
\(596\) −45.3352 26.1743i −1.85700 1.07214i
\(597\) −5.63510 + 13.8810i −0.230629 + 0.568113i
\(598\) 22.3279 0.913055
\(599\) 6.82479i 0.278853i 0.990232 + 0.139427i \(0.0445260\pi\)
−0.990232 + 0.139427i \(0.955474\pi\)
\(600\) 4.79106 + 25.0298i 0.195594 + 1.02184i
\(601\) −23.1815 13.3839i −0.945595 0.545940i −0.0538853 0.998547i \(-0.517161\pi\)
−0.891710 + 0.452608i \(0.850494\pi\)
\(602\) 13.4303 32.2004i 0.547380 1.31239i
\(603\) 3.89167 + 13.7437i 0.158481 + 0.559687i
\(604\) 23.8527 + 41.3140i 0.970551 + 1.68104i
\(605\) −28.2124 15.3401i −1.14700 0.623662i
\(606\) −21.6353 + 16.8457i −0.878875 + 0.684308i
\(607\) −9.30933 + 16.1242i −0.377854 + 0.654463i −0.990750 0.135701i \(-0.956671\pi\)
0.612896 + 0.790164i \(0.290005\pi\)
\(608\) −12.2656 + 7.08153i −0.497434 + 0.287194i
\(609\) −8.49209 2.23346i −0.344117 0.0905043i
\(610\) 67.0444 1.71530i 2.71455 0.0694504i
\(611\) −14.4898 + 8.36569i −0.586194 + 0.338440i
\(612\) 57.3561 + 14.5027i 2.31848 + 0.586237i
\(613\) −14.3042 8.25853i −0.577741 0.333559i 0.182494 0.983207i \(-0.441583\pi\)
−0.760235 + 0.649648i \(0.774916\pi\)
\(614\) −14.6153 −0.589825
\(615\) −1.44575 1.76193i −0.0582984 0.0710481i
\(616\) −23.7922 31.1644i −0.958616 1.25565i
\(617\) −18.5590 32.1451i −0.747156 1.29411i −0.949181 0.314731i \(-0.898086\pi\)
0.202025 0.979380i \(-0.435248\pi\)
\(618\) 58.0977 + 23.5851i 2.33703 + 0.948732i
\(619\) −36.0085 + 20.7895i −1.44730 + 0.835600i −0.998320 0.0579408i \(-0.981547\pi\)
−0.448982 + 0.893541i \(0.648213\pi\)
\(620\) −10.7078 + 0.273953i −0.430034 + 0.0110022i
\(621\) 13.8269 + 1.52285i 0.554855 + 0.0611097i
\(622\) 61.9617 2.48444
\(623\) 10.5902 8.08499i 0.424286 0.323918i
\(624\) −0.996858 + 0.776173i −0.0399063 + 0.0310718i
\(625\) 24.8693 2.55343i 0.994770 0.102137i
\(626\) 22.9242 0.916237
\(627\) 21.1056 + 8.56796i 0.842877 + 0.342171i
\(628\) 3.50082 0.139698
\(629\) 23.5843 0.940367
\(630\) −37.0723 + 17.0006i −1.47700 + 0.677321i
\(631\) −13.2963 −0.529317 −0.264658 0.964342i \(-0.585259\pi\)
−0.264658 + 0.964342i \(0.585259\pi\)
\(632\) −0.449976 −0.0178991
\(633\) 25.7175 20.0241i 1.02218 0.795887i
\(634\) 65.5237 2.60228
\(635\) −24.7715 + 0.633766i −0.983026 + 0.0251502i
\(636\) 61.5768 + 24.9975i 2.44168 + 0.991216i
\(637\) −17.8768 18.0528i −0.708306 0.715279i
\(638\) −22.1746 −0.877901
\(639\) −10.3680 36.6153i −0.410150 1.44848i
\(640\) −1.07036 41.8362i −0.0423096 1.65372i
\(641\) −21.2639 + 12.2767i −0.839873 + 0.484901i −0.857221 0.514948i \(-0.827811\pi\)
0.0173479 + 0.999850i \(0.494478\pi\)
\(642\) 40.6124 31.6216i 1.60284 1.24800i
\(643\) 9.11132 + 15.7813i 0.359316 + 0.622353i 0.987847 0.155432i \(-0.0496769\pi\)
−0.628531 + 0.777784i \(0.716344\pi\)
\(644\) 21.4453 + 8.94454i 0.845064 + 0.352464i
\(645\) −20.8000 7.83042i −0.819001 0.308323i
\(646\) −36.0731 −1.41928
\(647\) −14.3597 8.29061i −0.564540 0.325937i 0.190426 0.981702i \(-0.439013\pi\)
−0.754966 + 0.655764i \(0.772347\pi\)
\(648\) −22.5523 + 13.8851i −0.885938 + 0.545459i
\(649\) −12.6891 + 7.32606i −0.498091 + 0.287573i
\(650\) 22.6704 + 35.0014i 0.889207 + 1.37287i
\(651\) −1.76170 6.45533i −0.0690464 0.253004i
\(652\) −8.26147 + 4.76976i −0.323544 + 0.186798i
\(653\) 14.9733 25.9346i 0.585952 1.01490i −0.408805 0.912622i \(-0.634054\pi\)
0.994756 0.102276i \(-0.0326125\pi\)
\(654\) −61.9331 25.1422i −2.42178 0.983136i
\(655\) 22.5680 + 12.2710i 0.881805 + 0.479467i
\(656\) −0.0591337 0.102423i −0.00230878 0.00399893i
\(657\) 4.24862 16.8027i 0.165754 0.655536i
\(658\) −27.7960 + 3.59018i −1.08360 + 0.139960i
\(659\) −26.8528 15.5035i −1.04604 0.603929i −0.124499 0.992220i \(-0.539732\pi\)
−0.921537 + 0.388291i \(0.873066\pi\)
\(660\) −49.4646 + 40.5881i −1.92541 + 1.57989i
\(661\) 43.8123i 1.70410i −0.523459 0.852051i \(-0.675359\pi\)
0.523459 0.852051i \(-0.324641\pi\)
\(662\) 57.6546 2.24081
\(663\) 37.4306 5.19725i 1.45369 0.201845i
\(664\) −8.06576 4.65677i −0.313012 0.180718i
\(665\) 12.0360 9.68592i 0.466736 0.375604i
\(666\) −18.8527 + 19.3935i −0.730529 + 0.751481i
\(667\) 4.44244 2.56484i 0.172012 0.0993111i
\(668\) 70.4538 40.6765i 2.72594 1.57382i
\(669\) −30.5337 12.3954i −1.18050 0.479232i
\(670\) 24.4576 0.625736i 0.944880 0.0241743i
\(671\) 32.8652 + 56.9242i 1.26875 + 2.19754i
\(672\) 23.9768 6.54343i 0.924926 0.252418i
\(673\) −8.68818 5.01613i −0.334905 0.193357i 0.323112 0.946361i \(-0.395271\pi\)
−0.658017 + 0.753003i \(0.728604\pi\)
\(674\) −69.7819 + 40.2886i −2.68790 + 1.55186i
\(675\) 11.6518 + 23.2214i 0.448479 + 0.893794i
\(676\) −0.284077 + 0.492036i −0.0109260 + 0.0189245i
\(677\) 27.6141i 1.06130i 0.847592 + 0.530649i \(0.178052\pi\)
−0.847592 + 0.530649i \(0.821948\pi\)
\(678\) −30.3476 + 23.6292i −1.16549 + 0.907474i
\(679\) 20.4510 + 8.52981i 0.784836 + 0.327344i
\(680\) 18.8946 34.7497i 0.724574 1.33259i
\(681\) 13.1726 + 16.9180i 0.504777 + 0.648298i
\(682\) −8.44898 14.6341i −0.323528 0.560367i
\(683\) −3.99993 + 6.92808i −0.153053 + 0.265096i −0.932348 0.361561i \(-0.882244\pi\)
0.779295 + 0.626657i \(0.215577\pi\)
\(684\) 17.9145 18.4283i 0.684976 0.704622i
\(685\) −10.9176 + 6.68131i −0.417141 + 0.255280i
\(686\) −15.9971 39.4376i −0.610773 1.50573i
\(687\) −0.739377 + 1.82132i −0.0282090 + 0.0694877i
\(688\) −0.998765 0.576637i −0.0380776 0.0219841i
\(689\) 42.4502 1.61722
\(690\) 8.39437 22.2981i 0.319568 0.848873i
\(691\) 2.74942i 0.104593i 0.998632 + 0.0522965i \(0.0166541\pi\)
−0.998632 + 0.0522965i \(0.983346\pi\)
\(692\) 11.1757i 0.424836i
\(693\) −31.9943 23.9612i −1.21536 0.910211i
\(694\) 70.7955 2.68736
\(695\) 7.08726 + 11.5810i 0.268835 + 0.439292i
\(696\) −3.67354 + 9.04909i −0.139245 + 0.343005i
\(697\) 3.53752i 0.133993i
\(698\) 11.8952 + 6.86771i 0.450241 + 0.259947i
\(699\) 5.38203 4.19055i 0.203567 0.158501i
\(700\) 7.75277 + 42.6997i 0.293027 + 1.61390i
\(701\) 23.6035i 0.891491i −0.895160 0.445745i \(-0.852939\pi\)
0.895160 0.445745i \(-0.147061\pi\)
\(702\) −25.6475 + 34.9339i −0.968001 + 1.31850i
\(703\) 5.12273 8.87283i 0.193207 0.334645i
\(704\) 56.1079 32.3939i 2.11465 1.22089i
\(705\) 2.90695 + 17.6156i 0.109482 + 0.663442i
\(706\) 2.26799 1.30942i 0.0853569 0.0492808i
\(707\) −14.4877 + 11.0605i −0.544865 + 0.415973i
\(708\) 2.27364 + 16.3748i 0.0854488 + 0.615402i
\(709\) 43.5908 1.63709 0.818544 0.574445i \(-0.194782\pi\)
0.818544 + 0.574445i \(0.194782\pi\)
\(710\) −65.1586 + 1.66705i −2.44536 + 0.0625633i
\(711\) −0.441389 + 0.124984i −0.0165534 + 0.00468725i
\(712\) −7.40942 12.8335i −0.277680 0.480955i
\(713\) 3.38532 + 1.95451i 0.126781 + 0.0731972i
\(714\) 61.2201 + 16.1011i 2.29110 + 0.602570i
\(715\) −19.5236 + 35.9066i −0.730143 + 1.34283i
\(716\) −1.98445 1.14572i −0.0741625 0.0428177i
\(717\) 3.14865 + 4.04389i 0.117588 + 0.151022i
\(718\) 10.2653 5.92666i 0.383097 0.221181i
\(719\) −20.3284 35.2098i −0.758121 1.31310i −0.943808 0.330496i \(-0.892784\pi\)
0.185686 0.982609i \(-0.440549\pi\)
\(720\) 0.400358 + 1.28734i 0.0149205 + 0.0479762i
\(721\) 38.4686 + 16.0447i 1.43264 + 0.597536i
\(722\) 13.9951 24.2402i 0.520843 0.902127i
\(723\) −13.0022 16.6990i −0.483556 0.621043i
\(724\) 58.4710i 2.17306i
\(725\) 8.53126 + 4.35982i 0.316843 + 0.161920i
\(726\) −52.9631 21.5007i −1.96565 0.797966i
\(727\) −19.7944 + 34.2849i −0.734134 + 1.27156i 0.220969 + 0.975281i \(0.429078\pi\)
−0.955102 + 0.296276i \(0.904255\pi\)
\(728\) −22.4604 + 17.1472i −0.832436 + 0.635518i
\(729\) −18.2653 + 19.8842i −0.676491 + 0.736451i
\(730\) −26.0794 14.1802i −0.965241 0.524834i
\(731\) 17.2479 + 29.8743i 0.637937 + 1.10494i
\(732\) 73.4585 10.1997i 2.71510 0.376993i
\(733\) 18.5351 32.1038i 0.684611 1.18578i −0.288948 0.957345i \(-0.593306\pi\)
0.973559 0.228436i \(-0.0733610\pi\)
\(734\) 9.74793 + 16.8839i 0.359803 + 0.623196i
\(735\) −24.7497 + 11.0658i −0.912906 + 0.408170i
\(736\) −7.25960 + 12.5740i −0.267592 + 0.463484i
\(737\) 11.9891 + 20.7658i 0.441626 + 0.764918i
\(738\) −2.90892 2.82781i −0.107079 0.104093i
\(739\) 22.0824 38.2479i 0.812315 1.40697i −0.0989252 0.995095i \(-0.531540\pi\)
0.911240 0.411876i \(-0.135126\pi\)
\(740\) 15.0227 + 24.5479i 0.552245 + 0.902399i
\(741\) 6.17498 15.2110i 0.226844 0.558788i
\(742\) 65.6291 + 27.3730i 2.40932 + 1.00489i
\(743\) 8.00062 + 13.8575i 0.293514 + 0.508382i 0.974638 0.223786i \(-0.0718418\pi\)
−0.681124 + 0.732168i \(0.738508\pi\)
\(744\) −7.37161 + 1.02355i −0.270256 + 0.0375252i
\(745\) −17.0445 + 31.3471i −0.624462 + 1.14847i
\(746\) 30.0312 + 17.3385i 1.09952 + 0.634808i
\(747\) −9.20528 2.32759i −0.336804 0.0851620i
\(748\) 99.3123 3.63122
\(749\) 27.1953 20.7621i 0.993695 0.758630i
\(750\) 43.4778 9.48104i 1.58759 0.346199i
\(751\) −16.7868 + 29.0756i −0.612559 + 1.06098i 0.378249 + 0.925704i \(0.376526\pi\)
−0.990808 + 0.135279i \(0.956807\pi\)
\(752\) 0.926445i 0.0337840i
\(753\) 4.59806 + 33.1152i 0.167563 + 1.20679i
\(754\) 15.9814i 0.582008i
\(755\) 27.7351 16.9731i 1.00938 0.617716i
\(756\) −38.6282 + 23.2787i −1.40489 + 0.846639i
\(757\) 18.4257i 0.669692i 0.942273 + 0.334846i \(0.108684\pi\)
−0.942273 + 0.334846i \(0.891316\pi\)
\(758\) −10.6305 −0.386116
\(759\) 23.1293 3.21151i 0.839541 0.116571i
\(760\) −8.96936 14.6564i −0.325353 0.531644i
\(761\) −13.8388 + 23.9696i −0.501658 + 0.868897i 0.498340 + 0.866982i \(0.333943\pi\)
−0.999998 + 0.00191544i \(0.999390\pi\)
\(762\) −43.6881 + 6.06610i −1.58265 + 0.219752i
\(763\) −41.0082 17.1039i −1.48460 0.619204i
\(764\) 39.9510i 1.44538i
\(765\) 8.88207 39.3346i 0.321132 1.42215i
\(766\) −4.66907 2.69569i −0.168700 0.0973991i
\(767\) 5.27994 + 9.14512i 0.190647 + 0.330211i
\(768\) −4.11585 29.6424i −0.148518 1.06963i
\(769\) −23.5650 + 13.6052i −0.849775 + 0.490618i −0.860575 0.509324i \(-0.829895\pi\)
0.0108001 + 0.999942i \(0.496562\pi\)
\(770\) −53.3376 + 42.9232i −1.92215 + 1.54684i
\(771\) 2.44155 6.01432i 0.0879303 0.216600i
\(772\) 2.53590i 0.0912691i
\(773\) −22.1087 12.7645i −0.795195 0.459106i 0.0465934 0.998914i \(-0.485163\pi\)
−0.841788 + 0.539808i \(0.818497\pi\)
\(774\) −38.3533 9.69777i −1.37858 0.348579i
\(775\) 0.373336 + 7.29136i 0.0134106 + 0.261913i
\(776\) 12.3226 21.3434i 0.442356 0.766183i
\(777\) −12.6542 + 12.7716i −0.453967 + 0.458180i
\(778\) 25.5002 14.7226i 0.914228 0.527830i
\(779\) 1.33088 + 0.768382i 0.0476836 + 0.0275301i
\(780\) 29.2521 + 35.6494i 1.04739 + 1.27645i
\(781\) −31.9408 55.3231i −1.14293 1.97962i
\(782\) −32.0258 + 18.4901i −1.14524 + 0.661205i
\(783\) −1.08999 + 9.89675i −0.0389531 + 0.353681i
\(784\) −1.36063 + 0.357446i −0.0485939 + 0.0127659i
\(785\) −0.0610298 2.38542i −0.00217825 0.0851392i
\(786\) 42.3669 + 17.1991i 1.51118 + 0.613471i
\(787\) −31.8685 −1.13599 −0.567995 0.823032i \(-0.692281\pi\)
−0.567995 + 0.823032i \(0.692281\pi\)
\(788\) −1.04671 −0.0372874
\(789\) 33.7610 26.2870i 1.20193 0.935841i
\(790\) 0.0200959 + 0.785473i 0.000714982 + 0.0279459i
\(791\) −20.3217 + 15.5144i −0.722555 + 0.551630i
\(792\) −30.9890 + 31.8778i −1.10115 + 1.13273i
\(793\) 41.0257 23.6862i 1.45686 0.841121i
\(794\) −5.46947 9.47341i −0.194104 0.336199i
\(795\) 15.9595 42.3935i 0.566026 1.50354i
\(796\) 24.5735 + 14.1875i 0.870984 + 0.502863i
\(797\) −8.87275 + 5.12268i −0.314289 + 0.181455i −0.648844 0.760921i \(-0.724747\pi\)
0.334555 + 0.942376i \(0.391414\pi\)
\(798\) 19.3551 19.5347i 0.685163 0.691523i
\(799\) 13.8556 23.9985i 0.490174 0.849007i
\(800\) −27.0821 + 1.38667i −0.957497 + 0.0490263i
\(801\) −10.8326 10.5306i −0.382751 0.372079i
\(802\) −46.1520 26.6459i −1.62968 0.940898i
\(803\) 29.0939i 1.02670i
\(804\) 26.7974 3.72083i 0.945073 0.131224i
\(805\) 5.72085 14.7685i 0.201633 0.520522i
\(806\) −10.5469 + 6.08924i −0.371498 + 0.214484i
\(807\) −31.6244 12.8381i −1.11323 0.451924i
\(808\) 10.1363 + 17.5566i 0.356594 + 0.617640i
\(809\) −5.79707 3.34694i −0.203814 0.117672i 0.394619 0.918845i \(-0.370877\pi\)
−0.598433 + 0.801173i \(0.704210\pi\)
\(810\) 25.2449 + 38.7469i 0.887014 + 1.36143i
\(811\) 3.93422i 0.138149i −0.997611 0.0690746i \(-0.977995\pi\)
0.997611 0.0690746i \(-0.0220046\pi\)
\(812\) −6.40214 + 15.3497i −0.224671 + 0.538668i
\(813\) 20.9168 + 26.8640i 0.733585 + 0.942162i
\(814\) −22.7014 + 39.3200i −0.795683 + 1.37816i
\(815\) 3.39408 + 5.54611i 0.118889 + 0.194272i
\(816\) 0.787074 1.93881i 0.0275531 0.0678721i
\(817\) 14.9856 0.524281
\(818\) 25.1915i 0.880799i
\(819\) −17.2690 + 23.0585i −0.603427 + 0.805728i
\(820\) −3.68206 + 2.25332i −0.128583 + 0.0786895i
\(821\) 23.6393i 0.825017i −0.910954 0.412508i \(-0.864653\pi\)
0.910954 0.412508i \(-0.135347\pi\)
\(822\) −17.9768 + 13.9971i −0.627013 + 0.488204i
\(823\) 26.5103i 0.924092i 0.886856 + 0.462046i \(0.152884\pi\)
−0.886856 + 0.462046i \(0.847116\pi\)
\(824\) 23.1790 40.1472i 0.807479 1.39860i
\(825\) 28.5186 + 32.9970i 0.992889 + 1.14881i
\(826\) 2.26591 + 17.5432i 0.0788412 + 0.610407i
\(827\) 19.6354 0.682789 0.341395 0.939920i \(-0.389101\pi\)
0.341395 + 0.939920i \(0.389101\pi\)
\(828\) 6.45867 25.5431i 0.224454 0.887685i
\(829\) −6.83587 3.94669i −0.237420 0.137074i 0.376571 0.926388i \(-0.377103\pi\)
−0.613990 + 0.789314i \(0.710437\pi\)
\(830\) −7.76858 + 14.2875i −0.269651 + 0.495925i
\(831\) 6.98099 + 8.96586i 0.242168 + 0.311022i
\(832\) −23.3465 40.4373i −0.809394 1.40191i
\(833\) 40.5914 + 11.0898i 1.40641 + 0.384239i
\(834\) 14.8475 + 19.0691i 0.514128 + 0.660308i
\(835\) −28.9447 47.2973i −1.00167 1.63679i
\(836\) 21.5716 37.3630i 0.746068 1.29223i
\(837\) −6.94664 + 3.05153i −0.240111 + 0.105476i
\(838\) −3.21699 5.57198i −0.111129 0.192481i
\(839\) 1.57247 2.72360i 0.0542876 0.0940290i −0.837604 0.546277i \(-0.816045\pi\)
0.891892 + 0.452248i \(0.149378\pi\)
\(840\) 8.68013 + 28.8770i 0.299493 + 0.996351i
\(841\) −12.6642 21.9350i −0.436696 0.756380i
\(842\) −20.6261 + 35.7254i −0.710822 + 1.23118i
\(843\) −10.2609 + 25.2760i −0.353405 + 0.870550i
\(844\) −30.8669 53.4630i −1.06248 1.84027i
\(845\) 0.340220 + 0.184989i 0.0117039 + 0.00636382i
\(846\) 8.65827 + 30.5773i 0.297678 + 1.05127i
\(847\) −35.0688 14.6267i −1.20498 0.502579i
\(848\) 1.17527 2.03563i 0.0403589 0.0699037i
\(849\) 3.85887 + 27.7916i 0.132436 + 0.953804i
\(850\) −61.5024 31.4302i −2.10952 1.07805i
\(851\) 10.5031i 0.360041i
\(852\) −71.3923 + 9.91284i −2.44586 + 0.339608i
\(853\) 9.31488 16.1338i 0.318935 0.552412i −0.661331 0.750094i \(-0.730008\pi\)
0.980266 + 0.197682i \(0.0633414\pi\)
\(854\) 78.7002 10.1651i 2.69307 0.347841i
\(855\) −12.8691 11.8854i −0.440114 0.406473i
\(856\) −19.0272 32.9561i −0.650337 1.12642i
\(857\) 7.10839 4.10403i 0.242818 0.140191i −0.373653 0.927568i \(-0.621895\pi\)
0.616471 + 0.787377i \(0.288562\pi\)
\(858\) −27.3645 + 67.4074i −0.934207 + 2.30125i
\(859\) −42.9187 24.7791i −1.46437 0.845453i −0.465159 0.885227i \(-0.654003\pi\)
−0.999209 + 0.0397741i \(0.987336\pi\)
\(860\) −20.1083 + 36.9819i −0.685688 + 1.26107i
\(861\) −1.91568 1.89806i −0.0652862 0.0646858i
\(862\) 41.0500 + 23.7002i 1.39817 + 0.807233i
\(863\) −5.35093 9.26808i −0.182148 0.315489i 0.760464 0.649380i \(-0.224972\pi\)
−0.942612 + 0.333891i \(0.891638\pi\)
\(864\) −11.3342 25.8017i −0.385597 0.877792i
\(865\) −7.61498 + 0.194825i −0.258917 + 0.00662427i
\(866\) 29.9125 1.01647
\(867\) −26.1515 + 20.3621i −0.888152 + 0.691531i
\(868\) −12.5693 + 1.62348i −0.426631 + 0.0551043i
\(869\) −0.666908 + 0.385040i −0.0226233 + 0.0130616i
\(870\) 15.9600 + 6.00835i 0.541096 + 0.203702i
\(871\) 14.9660 8.64065i 0.507105 0.292777i
\(872\) −24.7092 + 42.7977i −0.836761 + 1.44931i
\(873\) 6.15920 24.3588i 0.208457 0.824419i
\(874\) 16.0649i 0.543403i
\(875\) 28.9599 6.02702i 0.979023 0.203751i
\(876\) −30.4158 12.3475i −1.02765 0.417182i
\(877\) 21.2470 + 12.2669i 0.717459 + 0.414225i 0.813817 0.581121i \(-0.197386\pi\)
−0.0963575 + 0.995347i \(0.530719\pi\)
\(878\) 59.7222i 2.01553i
\(879\) −18.8341 24.1891i −0.635258 0.815878i
\(880\) 1.18131 + 1.93033i 0.0398220 + 0.0650714i
\(881\) −32.5316 −1.09602 −0.548008 0.836473i \(-0.684614\pi\)
−0.548008 + 0.836473i \(0.684614\pi\)
\(882\) −41.5670 + 24.5135i −1.39963 + 0.825413i
\(883\) 17.6949i 0.595481i −0.954647 0.297741i \(-0.903767\pi\)
0.954647 0.297741i \(-0.0962330\pi\)
\(884\) 71.5750i 2.40733i
\(885\) 11.1179 1.83469i 0.373726 0.0616726i
\(886\) 28.8573 0.969479
\(887\) 47.6387 + 27.5042i 1.59955 + 0.923501i 0.991573 + 0.129547i \(0.0413522\pi\)
0.607977 + 0.793954i \(0.291981\pi\)
\(888\) 12.2850 + 15.7780i 0.412258 + 0.529474i
\(889\) −29.0780 + 3.75577i −0.975246 + 0.125964i
\(890\) −22.0711 + 13.5069i −0.739824 + 0.452754i
\(891\) −21.5434 + 39.8768i −0.721730 + 1.33592i
\(892\) −31.2078 + 54.0535i −1.04492 + 1.80985i
\(893\) −6.01911 10.4254i −0.201422 0.348873i
\(894\) −23.8897 + 58.8479i −0.798990 + 1.96817i
\(895\) −0.746088 + 1.37216i −0.0249390 + 0.0458661i
\(896\) −6.34306 49.1095i −0.211907 1.64063i
\(897\) −2.31456 16.6694i −0.0772808 0.556577i
\(898\) 63.5343i 2.12017i
\(899\) −1.39896 + 2.42307i −0.0466580 + 0.0808140i
\(900\) 46.5994 15.8103i 1.55331 0.527011i
\(901\) −60.8881 + 35.1538i −2.02848 + 1.17114i
\(902\) −5.89779 3.40509i −0.196375 0.113377i
\(903\) −25.4323 6.68880i −0.846333 0.222589i
\(904\) 14.2181 + 24.6264i 0.472886 + 0.819063i
\(905\) 39.8414 1.01932i 1.32437 0.0338834i
\(906\) 45.6681 35.5580i 1.51722 1.18134i
\(907\) −0.453563 + 0.261865i −0.0150603 + 0.00869507i −0.507511 0.861645i \(-0.669434\pi\)
0.492451 + 0.870340i \(0.336101\pi\)
\(908\) 35.1700 20.3054i 1.16716 0.673860i
\(909\) 14.8193 + 14.4061i 0.491526 + 0.477822i
\(910\) 30.9350 + 38.4407i 1.02549 + 1.27430i
\(911\) −3.34141 1.92916i −0.110706 0.0639160i 0.443625 0.896213i \(-0.353692\pi\)
−0.554331 + 0.832297i \(0.687026\pi\)
\(912\) −0.558456 0.717239i −0.0184923 0.0237502i
\(913\) −15.9390 −0.527503
\(914\) 10.6606i 0.352621i
\(915\) −8.23057 49.8759i −0.272094 1.64885i
\(916\) 3.22427 + 1.86153i 0.106533 + 0.0615067i
\(917\) 28.0526 + 11.7004i 0.926379 + 0.386380i
\(918\) 7.85782 71.3463i 0.259347 2.35478i
\(919\) −7.77655 13.4694i −0.256525 0.444314i 0.708784 0.705426i \(-0.249244\pi\)
−0.965309 + 0.261112i \(0.915911\pi\)
\(920\) −15.4755 8.41456i −0.510212 0.277420i
\(921\) 1.51505 + 10.9114i 0.0499227 + 0.359544i
\(922\) 11.1480 19.3089i 0.367139 0.635904i
\(923\) −39.8717 + 23.0199i −1.31239 + 0.757711i
\(924\) −53.2862 + 53.7808i −1.75299 + 1.76926i
\(925\) 16.4648 10.6642i 0.541358 0.350637i
\(926\) 30.2677 17.4751i 0.994659 0.574267i
\(927\) 11.5855 45.8192i 0.380519 1.50490i
\(928\) −8.99996 5.19613i −0.295438 0.170571i
\(929\) 30.2451 0.992309 0.496154 0.868234i \(-0.334745\pi\)
0.496154 + 0.868234i \(0.334745\pi\)
\(930\) 2.11591 + 12.8221i 0.0693836 + 0.420453i
\(931\) 12.9890 12.8624i 0.425698 0.421547i
\(932\) −6.45967 11.1885i −0.211593 0.366490i
\(933\) −6.42309 46.2591i −0.210283 1.51446i
\(934\) −2.16723 + 1.25125i −0.0709141 + 0.0409423i
\(935\) −1.73131 67.6702i −0.0566199 2.21305i
\(936\) 22.9745 + 22.3340i 0.750946 + 0.730008i
\(937\) 34.6840 1.13308 0.566539 0.824035i \(-0.308282\pi\)
0.566539 + 0.824035i \(0.308282\pi\)
\(938\) 28.7096 3.70818i 0.937402 0.121076i
\(939\) −2.37638 17.1147i −0.0775502 0.558516i
\(940\) 33.8047 0.864878i 1.10259 0.0282092i
\(941\) −42.7800 −1.39459 −0.697295 0.716785i \(-0.745613\pi\)
−0.697295 + 0.716785i \(0.745613\pi\)
\(942\) −0.584148 4.20703i −0.0190326 0.137073i
\(943\) 1.57541 0.0513023
\(944\) 0.584718 0.0190310
\(945\) 16.5352 + 25.9150i 0.537892 + 0.843014i
\(946\) −66.4089 −2.15914
\(947\) −8.08106 −0.262599 −0.131300 0.991343i \(-0.541915\pi\)
−0.131300 + 0.991343i \(0.541915\pi\)
\(948\) 0.119497 + 0.860619i 0.00388109 + 0.0279516i
\(949\) −20.9682 −0.680656
\(950\) −25.1835 + 16.3114i −0.817061 + 0.529210i
\(951\) −6.79233 48.9184i −0.220256 1.58629i
\(952\) 18.0159 43.1948i 0.583900 1.39995i
\(953\) 44.3390 1.43628 0.718141 0.695897i \(-0.244993\pi\)
0.718141 + 0.695897i \(0.244993\pi\)
\(954\) 19.7655 78.1696i 0.639930 2.53083i
\(955\) −27.2221 + 0.696465i −0.880888 + 0.0225371i
\(956\) 8.40666 4.85359i 0.271891 0.156976i
\(957\) 2.29867 + 16.5550i 0.0743055 + 0.535148i
\(958\) −28.1381 48.7367i −0.909102 1.57461i
\(959\) −12.0378 + 9.19019i −0.388721 + 0.296767i
\(960\) −49.1607 + 8.11254i −1.58665 + 0.261831i
\(961\) 28.8679 0.931221
\(962\) 28.3381 + 16.3610i 0.913659 + 0.527501i
\(963\) −27.8179 27.0423i −0.896419 0.871425i
\(964\) −34.7149 + 20.0426i −1.11809 + 0.645530i
\(965\) 1.72793 0.0442083i 0.0556241 0.00142312i
\(966\) 7.17052 27.2639i 0.230708 0.877201i
\(967\) −10.7988 + 6.23472i −0.347267 + 0.200495i −0.663481 0.748193i \(-0.730922\pi\)
0.316214 + 0.948688i \(0.397588\pi\)
\(968\) −21.1305 + 36.5991i −0.679160 + 1.17634i
\(969\) 3.73942 + 26.9313i 0.120128 + 0.865159i
\(970\) −37.8071 20.5570i −1.21391 0.660046i
\(971\) 0.187323 + 0.324453i 0.00601148 + 0.0104122i 0.869015 0.494785i \(-0.164753\pi\)
−0.863004 + 0.505197i \(0.831420\pi\)
\(972\) 32.5456 + 39.4459i 1.04390 + 1.26523i
\(973\) 9.74858 + 12.7692i 0.312525 + 0.409363i
\(974\) −45.0290 25.9975i −1.44282 0.833014i
\(975\) 23.7811 20.5535i 0.761606 0.658239i
\(976\) 2.62309i 0.0839630i
\(977\) 56.1534 1.79650 0.898252 0.439480i \(-0.144837\pi\)
0.898252 + 0.439480i \(0.144837\pi\)
\(978\) 7.11046 + 9.13214i 0.227367 + 0.292014i
\(979\) −21.9629 12.6803i −0.701939 0.405265i
\(980\) 14.3129 + 49.3138i 0.457209 + 1.57527i
\(981\) −12.3504 + 48.8441i −0.394318 + 1.55947i
\(982\) 23.0244 13.2931i 0.734738 0.424201i
\(983\) 10.5677 6.10125i 0.337057 0.194600i −0.321913 0.946769i \(-0.604326\pi\)
0.658970 + 0.752169i \(0.270993\pi\)
\(984\) −2.36661 + 1.84269i −0.0754448 + 0.0587428i
\(985\) 0.0182472 + 0.713214i 0.000581405 + 0.0227249i
\(986\) −13.2345 22.9228i −0.421471 0.730010i
\(987\) 5.56174 + 20.3797i 0.177032 + 0.648692i
\(988\) −26.9278 15.5468i −0.856687 0.494608i
\(989\) 13.3043 7.68123i 0.423052 0.244249i
\(990\) 57.0295 + 52.6703i 1.81252 + 1.67397i
\(991\) −8.67105 + 15.0187i −0.275445 + 0.477085i −0.970247 0.242116i \(-0.922158\pi\)
0.694802 + 0.719201i \(0.255492\pi\)
\(992\) 7.91932i 0.251439i
\(993\) −5.97661 43.0436i −0.189662 1.36595i
\(994\) −76.4866 + 9.87913i −2.42601 + 0.313347i
\(995\) 9.23880 16.9914i 0.292890 0.538663i
\(996\) −6.76450 + 16.6631i −0.214342 + 0.527992i
\(997\) 6.03037 + 10.4449i 0.190984 + 0.330793i 0.945577 0.325400i \(-0.105499\pi\)
−0.754593 + 0.656193i \(0.772166\pi\)
\(998\) −17.8676 + 30.9475i −0.565588 + 0.979627i
\(999\) 16.4330 + 12.0646i 0.519917 + 0.381708i
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 315.2.bq.a.164.5 yes 88
3.2 odd 2 945.2.bq.a.899.40 88
5.4 even 2 inner 315.2.bq.a.164.40 yes 88
7.5 odd 6 315.2.u.a.299.40 yes 88
9.4 even 3 945.2.u.a.584.40 88
9.5 odd 6 315.2.u.a.59.5 88
15.14 odd 2 945.2.bq.a.899.5 88
21.5 even 6 945.2.u.a.89.5 88
35.19 odd 6 315.2.u.a.299.5 yes 88
45.4 even 6 945.2.u.a.584.5 88
45.14 odd 6 315.2.u.a.59.40 yes 88
63.5 even 6 inner 315.2.bq.a.194.40 yes 88
63.40 odd 6 945.2.bq.a.719.5 88
105.89 even 6 945.2.u.a.89.40 88
315.194 even 6 inner 315.2.bq.a.194.5 yes 88
315.229 odd 6 945.2.bq.a.719.40 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.u.a.59.5 88 9.5 odd 6
315.2.u.a.59.40 yes 88 45.14 odd 6
315.2.u.a.299.5 yes 88 35.19 odd 6
315.2.u.a.299.40 yes 88 7.5 odd 6
315.2.bq.a.164.5 yes 88 1.1 even 1 trivial
315.2.bq.a.164.40 yes 88 5.4 even 2 inner
315.2.bq.a.194.5 yes 88 315.194 even 6 inner
315.2.bq.a.194.40 yes 88 63.5 even 6 inner
945.2.u.a.89.5 88 21.5 even 6
945.2.u.a.89.40 88 105.89 even 6
945.2.u.a.584.5 88 45.4 even 6
945.2.u.a.584.40 88 9.4 even 3
945.2.bq.a.719.5 88 63.40 odd 6
945.2.bq.a.719.40 88 315.229 odd 6
945.2.bq.a.899.5 88 15.14 odd 2
945.2.bq.a.899.40 88 3.2 odd 2