Properties

Label 315.2.bq.a.164.3
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 164.3
Character \(\chi\) \(=\) 315.164
Dual form 315.2.bq.a.194.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.53172 q^{2} +(1.70470 - 0.306605i) q^{3} +4.40959 q^{4} +(-1.09270 - 1.95090i) q^{5} +(-4.31581 + 0.776236i) q^{6} +(2.57916 + 0.589845i) q^{7} -6.10041 q^{8} +(2.81199 - 1.04534i) q^{9} +O(q^{10})\) \(q-2.53172 q^{2} +(1.70470 - 0.306605i) q^{3} +4.40959 q^{4} +(-1.09270 - 1.95090i) q^{5} +(-4.31581 + 0.776236i) q^{6} +(2.57916 + 0.589845i) q^{7} -6.10041 q^{8} +(2.81199 - 1.04534i) q^{9} +(2.76640 + 4.93913i) q^{10} +(1.23377 - 0.712319i) q^{11} +(7.51702 - 1.35200i) q^{12} +(-2.08746 - 3.61559i) q^{13} +(-6.52971 - 1.49332i) q^{14} +(-2.46088 - 2.99067i) q^{15} +6.62532 q^{16} +(4.27416 + 2.46769i) q^{17} +(-7.11916 + 2.64650i) q^{18} +(-4.54377 + 2.62335i) q^{19} +(-4.81835 - 8.60267i) q^{20} +(4.57754 + 0.214725i) q^{21} +(-3.12356 + 1.80339i) q^{22} +(0.238847 - 0.413696i) q^{23} +(-10.3993 + 1.87041i) q^{24} +(-2.61202 + 4.26349i) q^{25} +(5.28486 + 9.15364i) q^{26} +(4.47308 - 2.64415i) q^{27} +(11.3731 + 2.60098i) q^{28} +(-1.74963 - 1.01015i) q^{29} +(6.23024 + 7.57152i) q^{30} -10.6444i q^{31} -4.57262 q^{32} +(1.88481 - 1.59257i) q^{33} +(-10.8210 - 6.24749i) q^{34} +(-1.66752 - 5.67621i) q^{35} +(12.3997 - 4.60951i) q^{36} +(7.03282 - 4.06040i) q^{37} +(11.5035 - 6.64157i) q^{38} +(-4.66704 - 5.52345i) q^{39} +(6.66590 + 11.9013i) q^{40} +(0.421048 + 0.729276i) q^{41} +(-11.5890 - 0.543622i) q^{42} +(3.70789 + 2.14075i) q^{43} +(5.44044 - 3.14104i) q^{44} +(-5.11200 - 4.34367i) q^{45} +(-0.604694 + 1.04736i) q^{46} -4.94304i q^{47} +(11.2942 - 2.03135i) q^{48} +(6.30416 + 3.04261i) q^{49} +(6.61290 - 10.7940i) q^{50} +(8.04276 + 2.89618i) q^{51} +(-9.20484 - 15.9433i) q^{52} +(-2.33122 + 4.03778i) q^{53} +(-11.3246 + 6.69424i) q^{54} +(-2.73781 - 1.62862i) q^{55} +(-15.7339 - 3.59830i) q^{56} +(-6.94142 + 5.86515i) q^{57} +(4.42958 + 2.55742i) q^{58} +0.202459 q^{59} +(-10.8515 - 13.1876i) q^{60} +1.78370i q^{61} +26.9486i q^{62} +(7.86916 - 1.03745i) q^{63} -1.67406 q^{64} +(-4.77268 + 8.02317i) q^{65} +(-4.77180 + 4.03193i) q^{66} -2.38316i q^{67} +(18.8473 + 10.8815i) q^{68} +(0.280322 - 0.778458i) q^{69} +(4.22169 + 14.3706i) q^{70} +11.7260i q^{71} +(-17.1543 + 6.37697i) q^{72} +(-4.52420 + 7.83614i) q^{73} +(-17.8051 + 10.2798i) q^{74} +(-3.14550 + 8.06882i) q^{75} +(-20.0362 + 11.5679i) q^{76} +(3.60226 - 1.10945i) q^{77} +(11.8156 + 13.9838i) q^{78} +0.452236 q^{79} +(-7.23947 - 12.9253i) q^{80} +(6.81454 - 5.87894i) q^{81} +(-1.06597 - 1.84632i) q^{82} +(-10.6524 - 6.15019i) q^{83} +(20.1851 + 0.946848i) q^{84} +(0.143843 - 11.0349i) q^{85} +(-9.38732 - 5.41977i) q^{86} +(-3.29231 - 1.18556i) q^{87} +(-7.52652 + 4.34544i) q^{88} +(-1.33067 - 2.30479i) q^{89} +(12.9421 + 10.9969i) q^{90} +(-3.25126 - 10.5565i) q^{91} +(1.05322 - 1.82423i) q^{92} +(-3.26363 - 18.1455i) q^{93} +12.5144i q^{94} +(10.0829 + 5.99791i) q^{95} +(-7.79493 + 1.40199i) q^{96} +(-4.69437 + 8.13089i) q^{97} +(-15.9604 - 7.70304i) q^{98} +(2.72474 - 3.29274i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.53172 −1.79019 −0.895097 0.445871i \(-0.852894\pi\)
−0.895097 + 0.445871i \(0.852894\pi\)
\(3\) 1.70470 0.306605i 0.984208 0.177018i
\(4\) 4.40959 2.20480
\(5\) −1.09270 1.95090i −0.488670 0.872469i
\(6\) −4.31581 + 0.776236i −1.76192 + 0.316897i
\(7\) 2.57916 + 0.589845i 0.974832 + 0.222941i
\(8\) −6.10041 −2.15682
\(9\) 2.81199 1.04534i 0.937329 0.348445i
\(10\) 2.76640 + 4.93913i 0.874814 + 1.56189i
\(11\) 1.23377 0.712319i 0.371997 0.214772i −0.302334 0.953202i \(-0.597766\pi\)
0.674330 + 0.738430i \(0.264432\pi\)
\(12\) 7.51702 1.35200i 2.16998 0.390289i
\(13\) −2.08746 3.61559i −0.578957 1.00278i −0.995599 0.0937125i \(-0.970127\pi\)
0.416642 0.909071i \(-0.363207\pi\)
\(14\) −6.52971 1.49332i −1.74514 0.399107i
\(15\) −2.46088 2.99067i −0.635395 0.772187i
\(16\) 6.62532 1.65633
\(17\) 4.27416 + 2.46769i 1.03664 + 0.598502i 0.918879 0.394540i \(-0.129096\pi\)
0.117758 + 0.993042i \(0.462429\pi\)
\(18\) −7.11916 + 2.64650i −1.67800 + 0.623785i
\(19\) −4.54377 + 2.62335i −1.04241 + 0.601837i −0.920515 0.390706i \(-0.872231\pi\)
−0.121896 + 0.992543i \(0.538898\pi\)
\(20\) −4.81835 8.60267i −1.07742 1.92362i
\(21\) 4.57754 + 0.214725i 0.998902 + 0.0468568i
\(22\) −3.12356 + 1.80339i −0.665946 + 0.384484i
\(23\) 0.238847 0.413696i 0.0498031 0.0862616i −0.840049 0.542510i \(-0.817474\pi\)
0.889852 + 0.456249i \(0.150807\pi\)
\(24\) −10.3993 + 1.87041i −2.12276 + 0.381796i
\(25\) −2.61202 + 4.26349i −0.522404 + 0.852698i
\(26\) 5.28486 + 9.15364i 1.03645 + 1.79518i
\(27\) 4.47308 2.64415i 0.860845 0.508867i
\(28\) 11.3731 + 2.60098i 2.14931 + 0.491539i
\(29\) −1.74963 1.01015i −0.324899 0.187580i 0.328675 0.944443i \(-0.393398\pi\)
−0.653574 + 0.756863i \(0.726731\pi\)
\(30\) 6.23024 + 7.57152i 1.13748 + 1.38236i
\(31\) 10.6444i 1.91179i −0.293703 0.955897i \(-0.594888\pi\)
0.293703 0.955897i \(-0.405112\pi\)
\(32\) −4.57262 −0.808333
\(33\) 1.88481 1.59257i 0.328103 0.277231i
\(34\) −10.8210 6.24749i −1.85578 1.07144i
\(35\) −1.66752 5.67621i −0.281862 0.959455i
\(36\) 12.3997 4.60951i 2.06662 0.768251i
\(37\) 7.03282 4.06040i 1.15619 0.667526i 0.205801 0.978594i \(-0.434020\pi\)
0.950388 + 0.311068i \(0.100687\pi\)
\(38\) 11.5035 6.64157i 1.86612 1.07740i
\(39\) −4.66704 5.52345i −0.747325 0.884461i
\(40\) 6.66590 + 11.9013i 1.05397 + 1.88176i
\(41\) 0.421048 + 0.729276i 0.0657566 + 0.113894i 0.897029 0.441971i \(-0.145721\pi\)
−0.831273 + 0.555865i \(0.812387\pi\)
\(42\) −11.5890 0.543622i −1.78823 0.0838827i
\(43\) 3.70789 + 2.14075i 0.565447 + 0.326461i 0.755329 0.655346i \(-0.227477\pi\)
−0.189882 + 0.981807i \(0.560810\pi\)
\(44\) 5.44044 3.14104i 0.820176 0.473529i
\(45\) −5.11200 4.34367i −0.762052 0.647516i
\(46\) −0.604694 + 1.04736i −0.0891573 + 0.154425i
\(47\) 4.94304i 0.721016i −0.932756 0.360508i \(-0.882603\pi\)
0.932756 0.360508i \(-0.117397\pi\)
\(48\) 11.2942 2.03135i 1.63017 0.293201i
\(49\) 6.30416 + 3.04261i 0.900595 + 0.434659i
\(50\) 6.61290 10.7940i 0.935205 1.52650i
\(51\) 8.04276 + 2.89618i 1.12621 + 0.405547i
\(52\) −9.20484 15.9433i −1.27648 2.21093i
\(53\) −2.33122 + 4.03778i −0.320217 + 0.554632i −0.980533 0.196356i \(-0.937089\pi\)
0.660316 + 0.750988i \(0.270423\pi\)
\(54\) −11.3246 + 6.69424i −1.54108 + 0.910971i
\(55\) −2.73781 1.62862i −0.369166 0.219603i
\(56\) −15.7339 3.59830i −2.10254 0.480843i
\(57\) −6.94142 + 5.86515i −0.919413 + 0.776858i
\(58\) 4.42958 + 2.55742i 0.581632 + 0.335805i
\(59\) 0.202459 0.0263579 0.0131790 0.999913i \(-0.495805\pi\)
0.0131790 + 0.999913i \(0.495805\pi\)
\(60\) −10.8515 13.1876i −1.40092 1.70251i
\(61\) 1.78370i 0.228379i 0.993459 + 0.114189i \(0.0364271\pi\)
−0.993459 + 0.114189i \(0.963573\pi\)
\(62\) 26.9486i 3.42248i
\(63\) 7.86916 1.03745i 0.991421 0.130707i
\(64\) −1.67406 −0.209257
\(65\) −4.77268 + 8.02317i −0.591978 + 0.995152i
\(66\) −4.77180 + 4.03193i −0.587368 + 0.496297i
\(67\) 2.38316i 0.291150i −0.989347 0.145575i \(-0.953497\pi\)
0.989347 0.145575i \(-0.0465032\pi\)
\(68\) 18.8473 + 10.8815i 2.28557 + 1.31958i
\(69\) 0.280322 0.778458i 0.0337468 0.0937154i
\(70\) 4.22169 + 14.3706i 0.504588 + 1.71761i
\(71\) 11.7260i 1.39162i 0.718223 + 0.695812i \(0.244956\pi\)
−0.718223 + 0.695812i \(0.755044\pi\)
\(72\) −17.1543 + 6.37697i −2.02165 + 0.751534i
\(73\) −4.52420 + 7.83614i −0.529517 + 0.917150i 0.469890 + 0.882725i \(0.344293\pi\)
−0.999407 + 0.0344256i \(0.989040\pi\)
\(74\) −17.8051 + 10.2798i −2.06980 + 1.19500i
\(75\) −3.14550 + 8.06882i −0.363211 + 0.931707i
\(76\) −20.0362 + 11.5679i −2.29831 + 1.32693i
\(77\) 3.60226 1.10945i 0.410516 0.126434i
\(78\) 11.8156 + 13.9838i 1.33786 + 1.58336i
\(79\) 0.452236 0.0508806 0.0254403 0.999676i \(-0.491901\pi\)
0.0254403 + 0.999676i \(0.491901\pi\)
\(80\) −7.23947 12.9253i −0.809398 1.44510i
\(81\) 6.81454 5.87894i 0.757172 0.653216i
\(82\) −1.06597 1.84632i −0.117717 0.203892i
\(83\) −10.6524 6.15019i −1.16926 0.675071i −0.215752 0.976448i \(-0.569220\pi\)
−0.953505 + 0.301378i \(0.902553\pi\)
\(84\) 20.1851 + 0.946848i 2.20237 + 0.103310i
\(85\) 0.143843 11.0349i 0.0156019 1.19690i
\(86\) −9.38732 5.41977i −1.01226 0.584429i
\(87\) −3.29231 1.18556i −0.352973 0.127105i
\(88\) −7.52652 + 4.34544i −0.802329 + 0.463225i
\(89\) −1.33067 2.30479i −0.141051 0.244307i 0.786842 0.617155i \(-0.211715\pi\)
−0.927893 + 0.372848i \(0.878381\pi\)
\(90\) 12.9421 + 10.9969i 1.36422 + 1.15918i
\(91\) −3.25126 10.5565i −0.340825 1.10662i
\(92\) 1.05322 1.82423i 0.109806 0.190189i
\(93\) −3.26363 18.1455i −0.338422 1.88160i
\(94\) 12.5144i 1.29076i
\(95\) 10.0829 + 5.99791i 1.03448 + 0.615372i
\(96\) −7.79493 + 1.40199i −0.795567 + 0.143090i
\(97\) −4.69437 + 8.13089i −0.476641 + 0.825567i −0.999642 0.0267656i \(-0.991479\pi\)
0.523001 + 0.852332i \(0.324813\pi\)
\(98\) −15.9604 7.70304i −1.61224 0.778125i
\(99\) 2.72474 3.29274i 0.273847 0.330933i
\(100\) −11.5179 + 18.8003i −1.15179 + 1.88003i
\(101\) 9.22577 + 15.9795i 0.917998 + 1.59002i 0.802452 + 0.596717i \(0.203529\pi\)
0.115546 + 0.993302i \(0.463138\pi\)
\(102\) −20.3620 7.33232i −2.01614 0.726008i
\(103\) −9.34498 + 16.1860i −0.920789 + 1.59485i −0.122591 + 0.992457i \(0.539120\pi\)
−0.798198 + 0.602396i \(0.794213\pi\)
\(104\) 12.7343 + 22.0565i 1.24871 + 2.16282i
\(105\) −4.58297 9.16496i −0.447252 0.894408i
\(106\) 5.90198 10.2225i 0.573251 0.992900i
\(107\) 0.440832 + 0.763543i 0.0426168 + 0.0738145i 0.886547 0.462639i \(-0.153097\pi\)
−0.843930 + 0.536453i \(0.819764\pi\)
\(108\) 19.7245 11.6596i 1.89799 1.12195i
\(109\) 2.17023 3.75895i 0.207870 0.360042i −0.743173 0.669099i \(-0.766680\pi\)
0.951043 + 0.309057i \(0.100013\pi\)
\(110\) 6.93135 + 4.12320i 0.660878 + 0.393132i
\(111\) 10.7439 9.07805i 1.01977 0.861650i
\(112\) 17.0878 + 3.90791i 1.61464 + 0.369263i
\(113\) −4.60460 7.97540i −0.433164 0.750262i 0.563980 0.825789i \(-0.309270\pi\)
−0.997144 + 0.0755263i \(0.975936\pi\)
\(114\) 17.5737 14.8489i 1.64593 1.39073i
\(115\) −1.06807 0.0139225i −0.0995978 0.00129828i
\(116\) −7.71517 4.45436i −0.716336 0.413577i
\(117\) −9.64941 7.98488i −0.892088 0.738203i
\(118\) −0.512569 −0.0471858
\(119\) 9.56821 + 8.88566i 0.877116 + 0.814548i
\(120\) 15.0123 + 18.2443i 1.37043 + 1.66547i
\(121\) −4.48520 + 7.76860i −0.407746 + 0.706236i
\(122\) 4.51581i 0.408843i
\(123\) 0.941358 + 1.11410i 0.0848794 + 0.100455i
\(124\) 46.9375i 4.21511i
\(125\) 11.1718 + 0.437080i 0.999236 + 0.0390936i
\(126\) −19.9225 + 2.62654i −1.77484 + 0.233991i
\(127\) 8.82849i 0.783401i 0.920093 + 0.391701i \(0.128113\pi\)
−0.920093 + 0.391701i \(0.871887\pi\)
\(128\) 13.3835 1.18294
\(129\) 6.97719 + 2.51247i 0.614307 + 0.221211i
\(130\) 12.0831 20.3124i 1.05976 1.78151i
\(131\) −1.10536 + 1.91453i −0.0965753 + 0.167273i −0.910265 0.414026i \(-0.864122\pi\)
0.813690 + 0.581300i \(0.197456\pi\)
\(132\) 8.31124 7.02258i 0.723401 0.611237i
\(133\) −13.2665 + 4.08591i −1.15035 + 0.354294i
\(134\) 6.03350i 0.521215i
\(135\) −10.0462 5.83728i −0.864639 0.502393i
\(136\) −26.0741 15.0539i −2.23584 1.29086i
\(137\) 2.41786 + 4.18786i 0.206572 + 0.357793i 0.950632 0.310319i \(-0.100436\pi\)
−0.744061 + 0.668112i \(0.767103\pi\)
\(138\) −0.709695 + 1.97084i −0.0604133 + 0.167769i
\(139\) 1.08200 0.624695i 0.0917743 0.0529859i −0.453410 0.891302i \(-0.649793\pi\)
0.545185 + 0.838316i \(0.316459\pi\)
\(140\) −7.35308 25.0298i −0.621448 2.11540i
\(141\) −1.51556 8.42638i −0.127633 0.709630i
\(142\) 29.6870i 2.49128i
\(143\) −5.15090 2.97387i −0.430740 0.248688i
\(144\) 18.6303 6.92568i 1.55253 0.577140i
\(145\) −0.0588822 + 4.51715i −0.00488990 + 0.375129i
\(146\) 11.4540 19.8389i 0.947938 1.64188i
\(147\) 11.6796 + 3.25385i 0.963315 + 0.268373i
\(148\) 31.0119 17.9047i 2.54916 1.47176i
\(149\) 2.98242 + 1.72190i 0.244329 + 0.141063i 0.617165 0.786834i \(-0.288281\pi\)
−0.372836 + 0.927897i \(0.621615\pi\)
\(150\) 7.96351 20.4280i 0.650218 1.66794i
\(151\) 8.51168 + 14.7427i 0.692671 + 1.19974i 0.970960 + 0.239244i \(0.0768995\pi\)
−0.278288 + 0.960498i \(0.589767\pi\)
\(152\) 27.7188 16.0035i 2.24829 1.29805i
\(153\) 14.5985 + 2.47117i 1.18021 + 0.199782i
\(154\) −9.11990 + 2.80882i −0.734903 + 0.226341i
\(155\) −20.7662 + 11.6311i −1.66798 + 0.934235i
\(156\) −20.5797 24.3562i −1.64770 1.95006i
\(157\) 4.68164 0.373636 0.186818 0.982395i \(-0.440183\pi\)
0.186818 + 0.982395i \(0.440183\pi\)
\(158\) −1.14493 −0.0910861
\(159\) −2.73601 + 7.59796i −0.216980 + 0.602558i
\(160\) 4.99649 + 8.92072i 0.395008 + 0.705245i
\(161\) 0.860043 0.926106i 0.0677809 0.0729874i
\(162\) −17.2525 + 14.8838i −1.35548 + 1.16938i
\(163\) −13.9563 + 8.05767i −1.09314 + 0.631125i −0.934411 0.356197i \(-0.884073\pi\)
−0.158730 + 0.987322i \(0.550740\pi\)
\(164\) 1.85665 + 3.21581i 0.144980 + 0.251112i
\(165\) −5.16647 1.93688i −0.402209 0.150786i
\(166\) 26.9689 + 15.5705i 2.09320 + 1.20851i
\(167\) −9.83837 + 5.68018i −0.761316 + 0.439546i −0.829768 0.558108i \(-0.811527\pi\)
0.0684521 + 0.997654i \(0.478194\pi\)
\(168\) −27.9249 1.30991i −2.15445 0.101062i
\(169\) −2.21497 + 3.83644i −0.170382 + 0.295111i
\(170\) −0.364169 + 27.9372i −0.0279305 + 2.14269i
\(171\) −10.0347 + 12.1266i −0.767376 + 0.927343i
\(172\) 16.3503 + 9.43983i 1.24670 + 0.719780i
\(173\) 13.5586i 1.03084i −0.856938 0.515420i \(-0.827636\pi\)
0.856938 0.515420i \(-0.172364\pi\)
\(174\) 8.33521 + 3.00149i 0.631890 + 0.227543i
\(175\) −9.25163 + 9.45555i −0.699357 + 0.714772i
\(176\) 8.17414 4.71934i 0.616149 0.355734i
\(177\) 0.345132 0.0620749i 0.0259417 0.00466584i
\(178\) 3.36888 + 5.83507i 0.252508 + 0.437357i
\(179\) −0.777342 0.448799i −0.0581013 0.0335448i 0.470668 0.882310i \(-0.344013\pi\)
−0.528769 + 0.848766i \(0.677346\pi\)
\(180\) −22.5418 19.1538i −1.68017 1.42764i
\(181\) 13.4784i 1.00184i −0.865493 0.500921i \(-0.832995\pi\)
0.865493 0.500921i \(-0.167005\pi\)
\(182\) 8.23127 + 26.7260i 0.610143 + 1.98106i
\(183\) 0.546889 + 3.04066i 0.0404272 + 0.224772i
\(184\) −1.45707 + 2.52371i −0.107416 + 0.186051i
\(185\) −15.6062 9.28353i −1.14739 0.682539i
\(186\) 8.26258 + 45.9393i 0.605842 + 3.36843i
\(187\) 7.03113 0.514167
\(188\) 21.7968i 1.58969i
\(189\) 13.0964 4.18127i 0.952627 0.304142i
\(190\) −25.5269 15.1850i −1.85192 1.10164i
\(191\) 1.97538i 0.142934i 0.997443 + 0.0714668i \(0.0227680\pi\)
−0.997443 + 0.0714668i \(0.977232\pi\)
\(192\) −2.85376 + 0.513273i −0.205952 + 0.0370423i
\(193\) 16.5768i 1.19322i 0.802531 + 0.596611i \(0.203486\pi\)
−0.802531 + 0.596611i \(0.796514\pi\)
\(194\) 11.8848 20.5851i 0.853280 1.47792i
\(195\) −5.67604 + 15.1404i −0.406470 + 1.08423i
\(196\) 27.7988 + 13.4167i 1.98563 + 0.958335i
\(197\) 24.5924 1.75214 0.876069 0.482186i \(-0.160157\pi\)
0.876069 + 0.482186i \(0.160157\pi\)
\(198\) −6.89827 + 8.33629i −0.490239 + 0.592434i
\(199\) 0.627348 + 0.362200i 0.0444715 + 0.0256757i 0.522071 0.852902i \(-0.325160\pi\)
−0.477599 + 0.878578i \(0.658493\pi\)
\(200\) 15.9344 26.0090i 1.12673 1.83912i
\(201\) −0.730689 4.06257i −0.0515388 0.286552i
\(202\) −23.3570 40.4556i −1.64339 2.84644i
\(203\) −3.91676 3.63736i −0.274902 0.255293i
\(204\) 35.4653 + 12.7710i 2.48307 + 0.894148i
\(205\) 0.962666 1.61830i 0.0672355 0.113027i
\(206\) 23.6589 40.9783i 1.64839 2.85510i
\(207\) 0.239185 1.41298i 0.0166245 0.0982092i
\(208\) −13.8301 23.9544i −0.958944 1.66094i
\(209\) −3.73732 + 6.47322i −0.258516 + 0.447762i
\(210\) 11.6028 + 23.2031i 0.800668 + 1.60116i
\(211\) 5.83962 + 10.1145i 0.402016 + 0.696312i 0.993969 0.109660i \(-0.0349763\pi\)
−0.591953 + 0.805972i \(0.701643\pi\)
\(212\) −10.2797 + 17.8050i −0.706013 + 1.22285i
\(213\) 3.59526 + 19.9894i 0.246343 + 1.36965i
\(214\) −1.11606 1.93307i −0.0762924 0.132142i
\(215\) 0.124785 9.57291i 0.00851029 0.652867i
\(216\) −27.2876 + 16.1304i −1.85669 + 1.09753i
\(217\) 6.27856 27.4537i 0.426216 1.86368i
\(218\) −5.49441 + 9.51659i −0.372128 + 0.644545i
\(219\) −5.30979 + 14.7454i −0.358802 + 0.996401i
\(220\) −12.0726 7.18154i −0.813935 0.484179i
\(221\) 20.6048i 1.38603i
\(222\) −27.2005 + 22.9831i −1.82558 + 1.54252i
\(223\) 13.2349 22.9235i 0.886275 1.53507i 0.0420295 0.999116i \(-0.486618\pi\)
0.844245 0.535957i \(-0.180049\pi\)
\(224\) −11.7935 2.69714i −0.787989 0.180210i
\(225\) −2.88819 + 14.7193i −0.192546 + 0.981288i
\(226\) 11.6575 + 20.1915i 0.775448 + 1.34312i
\(227\) −6.71384 + 3.87624i −0.445613 + 0.257275i −0.705976 0.708236i \(-0.749491\pi\)
0.260363 + 0.965511i \(0.416158\pi\)
\(228\) −30.6088 + 25.8629i −2.02712 + 1.71281i
\(229\) −16.0456 9.26392i −1.06032 0.612177i −0.134800 0.990873i \(-0.543039\pi\)
−0.925521 + 0.378696i \(0.876373\pi\)
\(230\) 2.70405 + 0.0352479i 0.178299 + 0.00232418i
\(231\) 5.80060 2.99575i 0.381651 0.197106i
\(232\) 10.6735 + 6.16233i 0.700748 + 0.404577i
\(233\) 4.75564 + 8.23700i 0.311552 + 0.539624i 0.978699 0.205302i \(-0.0658178\pi\)
−0.667146 + 0.744927i \(0.732484\pi\)
\(234\) 24.4296 + 20.2155i 1.59701 + 1.32153i
\(235\) −9.64337 + 5.40125i −0.629064 + 0.352339i
\(236\) 0.892762 0.0581139
\(237\) 0.770926 0.138658i 0.0500770 0.00900679i
\(238\) −24.2240 22.4960i −1.57021 1.45820i
\(239\) −17.6506 + 10.1906i −1.14173 + 0.659175i −0.946857 0.321654i \(-0.895761\pi\)
−0.194868 + 0.980829i \(0.562428\pi\)
\(240\) −16.3041 19.8141i −1.05242 1.27900i
\(241\) −7.82942 + 4.52032i −0.504337 + 0.291179i −0.730503 0.682910i \(-0.760714\pi\)
0.226166 + 0.974089i \(0.427381\pi\)
\(242\) 11.3553 19.6679i 0.729944 1.26430i
\(243\) 9.81423 12.1112i 0.629583 0.776933i
\(244\) 7.86537i 0.503529i
\(245\) −0.952715 15.6235i −0.0608667 0.998146i
\(246\) −2.38325 2.82058i −0.151951 0.179834i
\(247\) 18.9699 + 10.9523i 1.20702 + 0.696875i
\(248\) 64.9352i 4.12339i
\(249\) −20.0449 7.21812i −1.27029 0.457430i
\(250\) −28.2838 1.10656i −1.78883 0.0699852i
\(251\) −4.81421 −0.303871 −0.151935 0.988390i \(-0.548551\pi\)
−0.151935 + 0.988390i \(0.548551\pi\)
\(252\) 34.6998 4.57475i 2.18588 0.288182i
\(253\) 0.680543i 0.0427853i
\(254\) 22.3512i 1.40244i
\(255\) −3.13814 18.8553i −0.196518 1.18076i
\(256\) −30.5351 −1.90844
\(257\) −0.228355 0.131841i −0.0142444 0.00822401i 0.492861 0.870108i \(-0.335951\pi\)
−0.507105 + 0.861884i \(0.669284\pi\)
\(258\) −17.6643 6.36088i −1.09973 0.396011i
\(259\) 20.5338 6.32416i 1.27591 0.392964i
\(260\) −21.0456 + 35.3789i −1.30519 + 2.19411i
\(261\) −5.97589 1.01158i −0.369899 0.0626151i
\(262\) 2.79845 4.84705i 0.172889 0.299452i
\(263\) 4.69057 + 8.12431i 0.289233 + 0.500966i 0.973627 0.228146i \(-0.0732664\pi\)
−0.684394 + 0.729113i \(0.739933\pi\)
\(264\) −11.4981 + 9.71532i −0.707659 + 0.597936i
\(265\) 10.4246 + 0.135888i 0.640380 + 0.00834752i
\(266\) 33.5870 10.3444i 2.05935 0.634255i
\(267\) −2.97505 3.52097i −0.182070 0.215480i
\(268\) 10.5088i 0.641926i
\(269\) 5.85382 10.1391i 0.356914 0.618192i −0.630530 0.776165i \(-0.717162\pi\)
0.987444 + 0.157972i \(0.0504957\pi\)
\(270\) 25.4341 + 14.7783i 1.54787 + 0.899381i
\(271\) 9.67252 5.58443i 0.587564 0.339230i −0.176570 0.984288i \(-0.556500\pi\)
0.764134 + 0.645058i \(0.223167\pi\)
\(272\) 28.3177 + 16.3492i 1.71701 + 0.991317i
\(273\) −8.77908 16.9987i −0.531334 1.02881i
\(274\) −6.12134 10.6025i −0.369804 0.640519i
\(275\) −0.185674 + 7.12077i −0.0111966 + 0.429399i
\(276\) 1.23610 3.43268i 0.0744047 0.206623i
\(277\) −8.68920 + 5.01671i −0.522083 + 0.301425i −0.737787 0.675034i \(-0.764129\pi\)
0.215703 + 0.976459i \(0.430796\pi\)
\(278\) −2.73933 + 1.58155i −0.164294 + 0.0948551i
\(279\) −11.1270 29.9320i −0.666156 1.79198i
\(280\) 10.1725 + 34.6272i 0.607925 + 2.06937i
\(281\) −11.3034 6.52601i −0.674303 0.389309i 0.123402 0.992357i \(-0.460620\pi\)
−0.797705 + 0.603048i \(0.793953\pi\)
\(282\) 3.83696 + 21.3332i 0.228488 + 1.27037i
\(283\) 13.3399 0.792974 0.396487 0.918040i \(-0.370229\pi\)
0.396487 + 0.918040i \(0.370229\pi\)
\(284\) 51.7071i 3.06825i
\(285\) 19.0272 + 7.13317i 1.12707 + 0.422533i
\(286\) 13.0406 + 7.52901i 0.771108 + 0.445200i
\(287\) 0.655790 + 2.12927i 0.0387101 + 0.125687i
\(288\) −12.8581 + 4.77993i −0.757674 + 0.281660i
\(289\) 3.67897 + 6.37216i 0.216410 + 0.374833i
\(290\) 0.149073 11.4361i 0.00875388 0.671554i
\(291\) −5.50951 + 15.3000i −0.322973 + 0.896903i
\(292\) −19.9499 + 34.5542i −1.16748 + 2.02213i
\(293\) 3.97741 2.29636i 0.232363 0.134155i −0.379299 0.925274i \(-0.623835\pi\)
0.611662 + 0.791120i \(0.290501\pi\)
\(294\) −29.5694 8.23783i −1.72452 0.480440i
\(295\) −0.221227 0.394978i −0.0128803 0.0229965i
\(296\) −42.9031 + 24.7701i −2.49369 + 1.43973i
\(297\) 3.63529 6.44854i 0.210941 0.374182i
\(298\) −7.55063 4.35936i −0.437396 0.252531i
\(299\) −1.99434 −0.115336
\(300\) −13.8704 + 35.5802i −0.800806 + 2.05422i
\(301\) 8.30053 + 7.70842i 0.478435 + 0.444306i
\(302\) −21.5492 37.3243i −1.24002 2.14777i
\(303\) 20.6265 + 24.4115i 1.18496 + 1.40241i
\(304\) −30.1039 + 17.3805i −1.72658 + 0.996840i
\(305\) 3.47981 1.94904i 0.199253 0.111602i
\(306\) −36.9592 6.25631i −2.11281 0.357649i
\(307\) −20.6137 −1.17649 −0.588244 0.808683i \(-0.700181\pi\)
−0.588244 + 0.808683i \(0.700181\pi\)
\(308\) 15.8845 4.89223i 0.905103 0.278761i
\(309\) −10.9677 + 30.4574i −0.623929 + 1.73266i
\(310\) 52.5741 29.4467i 2.98601 1.67246i
\(311\) −11.5614 −0.655584 −0.327792 0.944750i \(-0.606305\pi\)
−0.327792 + 0.944750i \(0.606305\pi\)
\(312\) 28.4708 + 33.6953i 1.61184 + 1.90762i
\(313\) 29.0404 1.64146 0.820731 0.571315i \(-0.193566\pi\)
0.820731 + 0.571315i \(0.193566\pi\)
\(314\) −11.8526 −0.668881
\(315\) −10.6226 14.2183i −0.598515 0.801111i
\(316\) 1.99418 0.112181
\(317\) −21.6855 −1.21798 −0.608988 0.793179i \(-0.708424\pi\)
−0.608988 + 0.793179i \(0.708424\pi\)
\(318\) 6.92682 19.2359i 0.388437 1.07870i
\(319\) −2.87820 −0.161148
\(320\) 1.82924 + 3.26591i 0.102257 + 0.182570i
\(321\) 0.985590 + 1.16645i 0.0550103 + 0.0651048i
\(322\) −2.17739 + 2.34464i −0.121341 + 0.130662i
\(323\) −25.8944 −1.44080
\(324\) 30.0494 25.9237i 1.66941 1.44021i
\(325\) 20.8675 + 0.544119i 1.15752 + 0.0301823i
\(326\) 35.3334 20.3997i 1.95693 1.12984i
\(327\) 2.54707 7.07327i 0.140854 0.391153i
\(328\) −2.56856 4.44888i −0.141825 0.245648i
\(329\) 2.91563 12.7489i 0.160744 0.702870i
\(330\) 13.0800 + 4.90362i 0.720033 + 0.269936i
\(331\) 5.95239 0.327173 0.163587 0.986529i \(-0.447694\pi\)
0.163587 + 0.986529i \(0.447694\pi\)
\(332\) −46.9729 27.1198i −2.57797 1.48839i
\(333\) 15.5317 18.7695i 0.851133 1.02856i
\(334\) 24.9080 14.3806i 1.36290 0.786873i
\(335\) −4.64931 + 2.60408i −0.254019 + 0.142276i
\(336\) 30.3277 + 1.42262i 1.65451 + 0.0776102i
\(337\) 2.43132 1.40373i 0.132443 0.0764658i −0.432315 0.901723i \(-0.642303\pi\)
0.564757 + 0.825257i \(0.308970\pi\)
\(338\) 5.60768 9.71279i 0.305018 0.528306i
\(339\) −10.2947 12.1839i −0.559134 0.661736i
\(340\) 0.634288 48.6594i 0.0343991 2.63893i
\(341\) −7.58222 13.1328i −0.410600 0.711181i
\(342\) 25.4051 30.7011i 1.37375 1.66012i
\(343\) 14.4648 + 11.5659i 0.781026 + 0.624499i
\(344\) −22.6196 13.0594i −1.21957 0.704118i
\(345\) −1.82500 + 0.303741i −0.0982548 + 0.0163529i
\(346\) 34.3265i 1.84540i
\(347\) 9.89128 0.530992 0.265496 0.964112i \(-0.414464\pi\)
0.265496 + 0.964112i \(0.414464\pi\)
\(348\) −14.5178 5.22782i −0.778233 0.280241i
\(349\) 0.279669 + 0.161467i 0.0149703 + 0.00864312i 0.507466 0.861671i \(-0.330582\pi\)
−0.492496 + 0.870315i \(0.663915\pi\)
\(350\) 23.4225 23.9388i 1.25199 1.27958i
\(351\) −18.8975 10.6533i −1.00868 0.568629i
\(352\) −5.64157 + 3.25716i −0.300697 + 0.173607i
\(353\) 14.7971 8.54312i 0.787571 0.454704i −0.0515356 0.998671i \(-0.516412\pi\)
0.839107 + 0.543967i \(0.183078\pi\)
\(354\) −0.873776 + 0.157156i −0.0464407 + 0.00835275i
\(355\) 22.8763 12.8130i 1.21415 0.680045i
\(356\) −5.86771 10.1632i −0.310988 0.538647i
\(357\) 19.0353 + 12.2137i 1.00745 + 0.646418i
\(358\) 1.96801 + 1.13623i 0.104013 + 0.0600517i
\(359\) −17.2188 + 9.94126i −0.908772 + 0.524680i −0.880036 0.474907i \(-0.842482\pi\)
−0.0287362 + 0.999587i \(0.509148\pi\)
\(360\) 31.1853 + 26.4981i 1.64361 + 1.39657i
\(361\) 4.26388 7.38525i 0.224415 0.388698i
\(362\) 34.1235i 1.79349i
\(363\) −5.26403 + 14.6183i −0.276290 + 0.767262i
\(364\) −14.3367 46.5497i −0.751449 2.43987i
\(365\) 20.2311 + 0.263718i 1.05894 + 0.0138036i
\(366\) −1.38457 7.69810i −0.0723726 0.402386i
\(367\) 15.6841 + 27.1656i 0.818702 + 1.41803i 0.906639 + 0.421907i \(0.138639\pi\)
−0.0879374 + 0.996126i \(0.528028\pi\)
\(368\) 1.58244 2.74087i 0.0824904 0.142878i
\(369\) 1.94632 + 1.61058i 0.101321 + 0.0838433i
\(370\) 39.5104 + 23.5033i 2.05405 + 1.22188i
\(371\) −8.39425 + 9.03905i −0.435808 + 0.469284i
\(372\) −14.3913 80.0143i −0.746152 4.14855i
\(373\) −22.1887 12.8107i −1.14889 0.663312i −0.200273 0.979740i \(-0.564183\pi\)
−0.948616 + 0.316428i \(0.897516\pi\)
\(374\) −17.8008 −0.920459
\(375\) 19.1785 2.68023i 0.990375 0.138407i
\(376\) 30.1545i 1.55510i
\(377\) 8.43460i 0.434404i
\(378\) −33.1565 + 10.5858i −1.70539 + 0.544474i
\(379\) −5.00587 −0.257134 −0.128567 0.991701i \(-0.541038\pi\)
−0.128567 + 0.991701i \(0.541038\pi\)
\(380\) 44.4613 + 26.4483i 2.28081 + 1.35677i
\(381\) 2.70685 + 15.0499i 0.138676 + 0.771030i
\(382\) 5.00111i 0.255879i
\(383\) −19.9749 11.5325i −1.02067 0.589284i −0.106372 0.994326i \(-0.533923\pi\)
−0.914298 + 0.405043i \(0.867257\pi\)
\(384\) 22.8148 4.10343i 1.16426 0.209403i
\(385\) −6.10061 5.81535i −0.310916 0.296378i
\(386\) 41.9677i 2.13610i
\(387\) 12.6643 + 2.14377i 0.643764 + 0.108974i
\(388\) −20.7003 + 35.8539i −1.05090 + 1.82021i
\(389\) 14.5687 8.41123i 0.738661 0.426466i −0.0829213 0.996556i \(-0.526425\pi\)
0.821582 + 0.570090i \(0.193092\pi\)
\(390\) 14.3701 38.3312i 0.727659 1.94098i
\(391\) 2.04175 1.17880i 0.103256 0.0596146i
\(392\) −38.4580 18.5612i −1.94242 0.937481i
\(393\) −1.29729 + 3.60260i −0.0654397 + 0.181727i
\(394\) −62.2611 −3.13667
\(395\) −0.494158 0.882268i −0.0248638 0.0443917i
\(396\) 12.0150 14.5196i 0.603776 0.729639i
\(397\) −13.0997 22.6893i −0.657453 1.13874i −0.981273 0.192623i \(-0.938301\pi\)
0.323820 0.946119i \(-0.395033\pi\)
\(398\) −1.58827 0.916987i −0.0796127 0.0459644i
\(399\) −21.3626 + 11.0328i −1.06947 + 0.552332i
\(400\) −17.3055 + 28.2470i −0.865273 + 1.41235i
\(401\) 31.4306 + 18.1465i 1.56957 + 0.906192i 0.996219 + 0.0868828i \(0.0276906\pi\)
0.573352 + 0.819309i \(0.305643\pi\)
\(402\) 1.84990 + 10.2853i 0.0922645 + 0.512983i
\(403\) −38.4858 + 22.2198i −1.91711 + 1.10685i
\(404\) 40.6819 + 70.4631i 2.02400 + 3.50567i
\(405\) −18.9155 6.87058i −0.939917 0.341402i
\(406\) 9.91612 + 9.20876i 0.492129 + 0.457023i
\(407\) 5.78460 10.0192i 0.286732 0.496634i
\(408\) −49.0641 17.6679i −2.42903 0.874691i
\(409\) 2.42575i 0.119945i 0.998200 + 0.0599727i \(0.0191014\pi\)
−0.998200 + 0.0599727i \(0.980899\pi\)
\(410\) −2.43720 + 4.09708i −0.120365 + 0.202340i
\(411\) 5.40574 + 6.39770i 0.266645 + 0.315575i
\(412\) −41.2076 + 71.3736i −2.03015 + 3.51633i
\(413\) 0.522175 + 0.119420i 0.0256946 + 0.00587626i
\(414\) −0.605548 + 3.57728i −0.0297611 + 0.175813i
\(415\) −0.358497 + 27.5021i −0.0175979 + 1.35003i
\(416\) 9.54516 + 16.5327i 0.467990 + 0.810582i
\(417\) 1.65295 1.39666i 0.0809455 0.0683949i
\(418\) 9.46183 16.3884i 0.462793 0.801582i
\(419\) 7.51552 + 13.0173i 0.367157 + 0.635935i 0.989120 0.147112i \(-0.0469978\pi\)
−0.621963 + 0.783047i \(0.713664\pi\)
\(420\) −20.2090 40.4137i −0.986099 1.97199i
\(421\) 11.1388 19.2929i 0.542871 0.940281i −0.455866 0.890048i \(-0.650671\pi\)
0.998738 0.0502323i \(-0.0159962\pi\)
\(422\) −14.7843 25.6071i −0.719687 1.24653i
\(423\) −5.16714 13.8998i −0.251235 0.675829i
\(424\) 14.2214 24.6321i 0.690650 1.19624i
\(425\) −21.6852 + 11.7772i −1.05188 + 0.571278i
\(426\) −9.10218 50.6074i −0.441002 2.45194i
\(427\) −1.05210 + 4.60044i −0.0509149 + 0.222631i
\(428\) 1.94389 + 3.36691i 0.0939614 + 0.162746i
\(429\) −9.69253 3.49027i −0.467960 0.168512i
\(430\) −0.315921 + 24.2359i −0.0152351 + 1.16876i
\(431\) 16.8829 + 9.74735i 0.813221 + 0.469514i 0.848073 0.529879i \(-0.177763\pi\)
−0.0348520 + 0.999392i \(0.511096\pi\)
\(432\) 29.6356 17.5183i 1.42584 0.842851i
\(433\) 16.9416 0.814161 0.407080 0.913392i \(-0.366547\pi\)
0.407080 + 0.913392i \(0.366547\pi\)
\(434\) −15.8955 + 69.5050i −0.763010 + 3.33634i
\(435\) 1.28460 + 7.71843i 0.0615920 + 0.370070i
\(436\) 9.56983 16.5754i 0.458312 0.793819i
\(437\) 2.50632i 0.119893i
\(438\) 13.4429 37.3311i 0.642326 1.78375i
\(439\) 1.65776i 0.0791207i −0.999217 0.0395604i \(-0.987404\pi\)
0.999217 0.0395604i \(-0.0125957\pi\)
\(440\) 16.7017 + 9.93523i 0.796223 + 0.473643i
\(441\) 20.9078 + 1.96582i 0.995609 + 0.0936106i
\(442\) 52.1655i 2.48126i
\(443\) −36.0899 −1.71468 −0.857341 0.514749i \(-0.827885\pi\)
−0.857341 + 0.514749i \(0.827885\pi\)
\(444\) 47.3762 40.0305i 2.24837 1.89976i
\(445\) −3.04239 + 5.11444i −0.144223 + 0.242448i
\(446\) −33.5070 + 58.0359i −1.58660 + 2.74808i
\(447\) 5.61206 + 2.02089i 0.265441 + 0.0955850i
\(448\) −4.31766 0.987434i −0.203990 0.0466519i
\(449\) 26.4059i 1.24617i −0.782154 0.623086i \(-0.785879\pi\)
0.782154 0.623086i \(-0.214121\pi\)
\(450\) 7.31207 37.2652i 0.344694 1.75670i
\(451\) 1.03895 + 0.599840i 0.0489224 + 0.0282454i
\(452\) −20.3044 35.1683i −0.955039 1.65418i
\(453\) 19.0300 + 22.5221i 0.894108 + 1.05818i
\(454\) 16.9975 9.81354i 0.797734 0.460572i
\(455\) −17.0420 + 17.8779i −0.798939 + 0.838130i
\(456\) 42.3455 35.7798i 1.98301 1.67554i
\(457\) 31.7898i 1.48706i −0.668700 0.743532i \(-0.733149\pi\)
0.668700 0.743532i \(-0.266851\pi\)
\(458\) 40.6229 + 23.4536i 1.89818 + 1.09592i
\(459\) 25.6436 0.263351i 1.19694 0.0122922i
\(460\) −4.70974 0.0613927i −0.219593 0.00286245i
\(461\) −5.79487 + 10.0370i −0.269894 + 0.467470i −0.968834 0.247710i \(-0.920322\pi\)
0.698940 + 0.715180i \(0.253655\pi\)
\(462\) −14.6855 + 7.58439i −0.683230 + 0.352858i
\(463\) −25.9642 + 14.9904i −1.20666 + 0.696664i −0.962028 0.272952i \(-0.912000\pi\)
−0.244630 + 0.969616i \(0.578667\pi\)
\(464\) −11.5919 6.69257i −0.538139 0.310695i
\(465\) −31.8339 + 26.1946i −1.47626 + 1.21474i
\(466\) −12.0399 20.8538i −0.557739 0.966032i
\(467\) 2.17113 1.25350i 0.100468 0.0580052i −0.448924 0.893570i \(-0.648193\pi\)
0.549392 + 0.835565i \(0.314859\pi\)
\(468\) −42.5500 35.2101i −1.96687 1.62759i
\(469\) 1.40570 6.14657i 0.0649091 0.283822i
\(470\) 24.4143 13.6744i 1.12615 0.630755i
\(471\) 7.98079 1.43541i 0.367735 0.0661404i
\(472\) −1.23508 −0.0568493
\(473\) 6.09959 0.280459
\(474\) −1.95177 + 0.351042i −0.0896476 + 0.0161239i
\(475\) 0.683804 26.2245i 0.0313751 1.20326i
\(476\) 42.1919 + 39.1822i 1.93386 + 1.79591i
\(477\) −2.33451 + 13.7911i −0.106890 + 0.631451i
\(478\) 44.6864 25.7997i 2.04391 1.18005i
\(479\) −17.7777 30.7920i −0.812286 1.40692i −0.911261 0.411830i \(-0.864890\pi\)
0.0989748 0.995090i \(-0.468444\pi\)
\(480\) 11.2526 + 13.6752i 0.513611 + 0.624184i
\(481\) −29.3614 16.9518i −1.33877 0.772937i
\(482\) 19.8219 11.4442i 0.902862 0.521267i
\(483\) 1.18217 1.84242i 0.0537904 0.0838332i
\(484\) −19.7779 + 34.2564i −0.898996 + 1.55711i
\(485\) 20.9921 + 0.273637i 0.953201 + 0.0124252i
\(486\) −24.8468 + 30.6621i −1.12708 + 1.39086i
\(487\) 15.4460 + 8.91776i 0.699926 + 0.404102i 0.807320 0.590114i \(-0.200917\pi\)
−0.107394 + 0.994217i \(0.534251\pi\)
\(488\) 10.8813i 0.492572i
\(489\) −21.3207 + 18.0149i −0.964157 + 0.814664i
\(490\) 2.41200 + 39.5542i 0.108963 + 1.78688i
\(491\) −6.13294 + 3.54085i −0.276776 + 0.159796i −0.631963 0.774999i \(-0.717750\pi\)
0.355187 + 0.934795i \(0.384417\pi\)
\(492\) 4.15100 + 4.91272i 0.187142 + 0.221483i
\(493\) −4.98548 8.63510i −0.224535 0.388905i
\(494\) −48.0263 27.7280i −2.16081 1.24754i
\(495\) −9.40113 1.71772i −0.422549 0.0772060i
\(496\) 70.5226i 3.16656i
\(497\) −6.91655 + 30.2434i −0.310250 + 1.35660i
\(498\) 50.7479 + 18.2742i 2.27407 + 0.818888i
\(499\) −11.4852 + 19.8930i −0.514149 + 0.890533i 0.485716 + 0.874117i \(0.338559\pi\)
−0.999865 + 0.0164161i \(0.994774\pi\)
\(500\) 49.2630 + 1.92734i 2.20311 + 0.0861934i
\(501\) −15.0299 + 12.6995i −0.671485 + 0.567371i
\(502\) 12.1882 0.543987
\(503\) 5.23692i 0.233503i −0.993161 0.116751i \(-0.962752\pi\)
0.993161 0.116751i \(-0.0372481\pi\)
\(504\) −48.0051 + 6.32890i −2.13832 + 0.281911i
\(505\) 21.0934 35.4593i 0.938645 1.57792i
\(506\) 1.72294i 0.0765941i
\(507\) −2.59959 + 7.21910i −0.115452 + 0.320611i
\(508\) 38.9300i 1.72724i
\(509\) −4.85855 + 8.41525i −0.215351 + 0.373000i −0.953381 0.301769i \(-0.902423\pi\)
0.738030 + 0.674768i \(0.235756\pi\)
\(510\) 7.94489 + 47.7362i 0.351806 + 2.11379i
\(511\) −16.2907 + 17.5421i −0.720660 + 0.776017i
\(512\) 50.5392 2.23354
\(513\) −13.3881 + 23.7488i −0.591100 + 1.04854i
\(514\) 0.578131 + 0.333784i 0.0255003 + 0.0147226i
\(515\) 41.7885 + 0.544724i 1.84142 + 0.0240034i
\(516\) 30.7666 + 11.0790i 1.35442 + 0.487725i
\(517\) −3.52102 6.09859i −0.154854 0.268216i
\(518\) −51.9858 + 16.0110i −2.28412 + 0.703482i
\(519\) −4.15712 23.1133i −0.182477 1.01456i
\(520\) 29.1153 48.9446i 1.27679 2.14636i
\(521\) 2.77492 4.80630i 0.121571 0.210568i −0.798816 0.601575i \(-0.794540\pi\)
0.920387 + 0.391007i \(0.127873\pi\)
\(522\) 15.1293 + 2.56103i 0.662190 + 0.112093i
\(523\) −3.79740 6.57728i −0.166049 0.287605i 0.770979 0.636861i \(-0.219768\pi\)
−0.937027 + 0.349257i \(0.886434\pi\)
\(524\) −4.87417 + 8.44230i −0.212929 + 0.368804i
\(525\) −12.8721 + 18.9554i −0.561785 + 0.827283i
\(526\) −11.8752 20.5685i −0.517784 0.896827i
\(527\) 26.2671 45.4959i 1.14421 1.98183i
\(528\) 12.4875 10.5513i 0.543447 0.459185i
\(529\) 11.3859 + 19.7210i 0.495039 + 0.857433i
\(530\) −26.3922 0.344029i −1.14640 0.0149437i
\(531\) 0.569313 0.211638i 0.0247061 0.00918430i
\(532\) −58.4998 + 18.0172i −2.53629 + 0.781145i
\(533\) 1.75784 3.04467i 0.0761405 0.131879i
\(534\) 7.53198 + 8.91411i 0.325940 + 0.385751i
\(535\) 1.00790 1.69434i 0.0435753 0.0732527i
\(536\) 14.5383i 0.627957i
\(537\) −1.46274 0.526729i −0.0631218 0.0227301i
\(538\) −14.8202 + 25.6694i −0.638945 + 1.10668i
\(539\) 9.94522 0.736681i 0.428371 0.0317311i
\(540\) −44.2997 25.7400i −1.90635 1.10767i
\(541\) −16.8986 29.2693i −0.726530 1.25839i −0.958341 0.285626i \(-0.907799\pi\)
0.231812 0.972761i \(-0.425535\pi\)
\(542\) −24.4881 + 14.1382i −1.05185 + 0.607288i
\(543\) −4.13254 22.9766i −0.177344 0.986021i
\(544\) −19.5441 11.2838i −0.837947 0.483789i
\(545\) −9.70474 0.126504i −0.415705 0.00541883i
\(546\) 22.2261 + 43.0360i 0.951191 + 1.84177i
\(547\) 14.5277 + 8.38754i 0.621158 + 0.358626i 0.777320 0.629106i \(-0.216579\pi\)
−0.156162 + 0.987731i \(0.549912\pi\)
\(548\) 10.6618 + 18.4667i 0.455449 + 0.788860i
\(549\) 1.86456 + 5.01573i 0.0795776 + 0.214066i
\(550\) 0.470074 18.0278i 0.0200440 0.768707i
\(551\) 10.5999 0.451571
\(552\) −1.71008 + 4.74891i −0.0727857 + 0.202127i
\(553\) 1.16639 + 0.266749i 0.0496000 + 0.0113433i
\(554\) 21.9986 12.7009i 0.934631 0.539609i
\(555\) −29.4502 11.0407i −1.25009 0.468651i
\(556\) 4.77119 2.75465i 0.202344 0.116823i
\(557\) −3.36711 + 5.83201i −0.142669 + 0.247110i −0.928501 0.371330i \(-0.878902\pi\)
0.785832 + 0.618440i \(0.212235\pi\)
\(558\) 28.1704 + 75.7793i 1.19255 + 3.20799i
\(559\) 17.8749i 0.756028i
\(560\) −11.0478 37.6067i −0.466856 1.58917i
\(561\) 11.9859 2.15578i 0.506047 0.0910169i
\(562\) 28.6170 + 16.5220i 1.20713 + 0.696939i
\(563\) 45.8890i 1.93399i −0.254795 0.966995i \(-0.582008\pi\)
0.254795 0.966995i \(-0.417992\pi\)
\(564\) −6.68299 37.1569i −0.281405 1.56459i
\(565\) −10.5278 + 17.6978i −0.442906 + 0.744553i
\(566\) −33.7728 −1.41958
\(567\) 21.0435 11.1432i 0.883744 0.467972i
\(568\) 71.5336i 3.00148i
\(569\) 25.9763i 1.08898i −0.838767 0.544491i \(-0.816723\pi\)
0.838767 0.544491i \(-0.183277\pi\)
\(570\) −48.1715 18.0592i −2.01768 0.756416i
\(571\) −27.1543 −1.13637 −0.568187 0.822900i \(-0.692355\pi\)
−0.568187 + 0.822900i \(0.692355\pi\)
\(572\) −22.7134 13.1136i −0.949694 0.548306i
\(573\) 0.605661 + 3.36743i 0.0253019 + 0.140676i
\(574\) −1.66028 5.39072i −0.0692986 0.225004i
\(575\) 1.13991 + 2.09891i 0.0475377 + 0.0875304i
\(576\) −4.70742 + 1.74995i −0.196143 + 0.0729146i
\(577\) −6.23651 + 10.8020i −0.259629 + 0.449691i −0.966143 0.258008i \(-0.916934\pi\)
0.706513 + 0.707700i \(0.250267\pi\)
\(578\) −9.31411 16.1325i −0.387416 0.671024i
\(579\) 5.08251 + 28.2584i 0.211222 + 1.17438i
\(580\) −0.259647 + 19.9188i −0.0107812 + 0.827083i
\(581\) −23.8467 22.1456i −0.989328 0.918755i
\(582\) 13.9485 38.7353i 0.578185 1.60563i
\(583\) 6.64228i 0.275095i
\(584\) 27.5994 47.8036i 1.14207 1.97813i
\(585\) −5.03381 + 27.5501i −0.208122 + 1.13906i
\(586\) −10.0697 + 5.81373i −0.415974 + 0.240163i
\(587\) 14.4358 + 8.33452i 0.595830 + 0.344002i 0.767399 0.641170i \(-0.221550\pi\)
−0.171569 + 0.985172i \(0.554884\pi\)
\(588\) 51.5022 + 14.3482i 2.12391 + 0.591708i
\(589\) 27.9240 + 48.3657i 1.15059 + 1.99288i
\(590\) 0.560084 + 0.999972i 0.0230583 + 0.0411682i
\(591\) 41.9227 7.54015i 1.72447 0.310160i
\(592\) 46.5947 26.9014i 1.91503 1.10564i
\(593\) 0.329806 0.190413i 0.0135435 0.00781934i −0.493213 0.869909i \(-0.664178\pi\)
0.506756 + 0.862089i \(0.330844\pi\)
\(594\) −9.20353 + 16.3259i −0.377625 + 0.669859i
\(595\) 6.87988 28.3760i 0.282048 1.16330i
\(596\) 13.1512 + 7.59287i 0.538696 + 0.311016i
\(597\) 1.18049 + 0.425093i 0.0483143 + 0.0173979i
\(598\) 5.04910 0.206473
\(599\) 21.0025i 0.858137i −0.903272 0.429069i \(-0.858842\pi\)
0.903272 0.429069i \(-0.141158\pi\)
\(600\) 19.1888 49.2231i 0.783380 2.00952i
\(601\) −3.49714 2.01907i −0.142651 0.0823597i 0.426976 0.904263i \(-0.359579\pi\)
−0.569627 + 0.821903i \(0.692912\pi\)
\(602\) −21.0146 19.5155i −0.856491 0.795394i
\(603\) −2.49121 6.70143i −0.101450 0.272903i
\(604\) 37.5331 + 65.0092i 1.52720 + 2.64519i
\(605\) 20.0567 + 0.261445i 0.815422 + 0.0106292i
\(606\) −52.2205 61.8031i −2.12131 2.51058i
\(607\) 8.88367 15.3870i 0.360577 0.624538i −0.627479 0.778634i \(-0.715913\pi\)
0.988056 + 0.154096i \(0.0492465\pi\)
\(608\) 20.7769 11.9956i 0.842615 0.486484i
\(609\) −7.79212 4.99970i −0.315753 0.202598i
\(610\) −8.80990 + 4.93442i −0.356702 + 0.199789i
\(611\) −17.8720 + 10.3184i −0.723023 + 0.417437i
\(612\) 64.3732 + 10.8969i 2.60213 + 0.440480i
\(613\) 12.3044 + 7.10394i 0.496969 + 0.286925i 0.727461 0.686149i \(-0.240700\pi\)
−0.230492 + 0.973074i \(0.574034\pi\)
\(614\) 52.1881 2.10614
\(615\) 1.14488 3.05387i 0.0461659 0.123144i
\(616\) −21.9752 + 6.76811i −0.885408 + 0.272695i
\(617\) 16.5509 + 28.6670i 0.666314 + 1.15409i 0.978927 + 0.204209i \(0.0654622\pi\)
−0.312614 + 0.949880i \(0.601205\pi\)
\(618\) 27.7670 77.1096i 1.11695 3.10180i
\(619\) 35.6504 20.5828i 1.43291 0.827291i 0.435569 0.900155i \(-0.356547\pi\)
0.997342 + 0.0728641i \(0.0232139\pi\)
\(620\) −91.5704 + 51.2886i −3.67756 + 2.05980i
\(621\) −0.0254898 2.48205i −0.00102287 0.0996010i
\(622\) 29.2701 1.17362
\(623\) −2.07254 6.72931i −0.0830348 0.269604i
\(624\) −30.9206 36.5946i −1.23782 1.46496i
\(625\) −11.3547 22.2726i −0.454188 0.890906i
\(626\) −73.5222 −2.93854
\(627\) −4.38628 + 12.1808i −0.175171 + 0.486453i
\(628\) 20.6441 0.823791
\(629\) 40.0792 1.59806
\(630\) 26.8934 + 35.9968i 1.07146 + 1.43415i
\(631\) 10.0626 0.400586 0.200293 0.979736i \(-0.435811\pi\)
0.200293 + 0.979736i \(0.435811\pi\)
\(632\) −2.75882 −0.109740
\(633\) 13.0559 + 15.4517i 0.518927 + 0.614151i
\(634\) 54.9015 2.18042
\(635\) 17.2235 9.64687i 0.683493 0.382824i
\(636\) −12.0647 + 33.5039i −0.478397 + 1.32852i
\(637\) −2.15885 29.1446i −0.0855369 1.15475i
\(638\) 7.28679 0.288487
\(639\) 12.2577 + 32.9735i 0.484905 + 1.30441i
\(640\) −14.6241 26.1098i −0.578068 1.03208i
\(641\) −33.9181 + 19.5826i −1.33968 + 0.773466i −0.986760 0.162186i \(-0.948145\pi\)
−0.352923 + 0.935652i \(0.614812\pi\)
\(642\) −2.49524 2.95312i −0.0984791 0.116550i
\(643\) 7.40682 + 12.8290i 0.292097 + 0.505926i 0.974305 0.225231i \(-0.0723138\pi\)
−0.682209 + 0.731157i \(0.738980\pi\)
\(644\) 3.79244 4.08375i 0.149443 0.160922i
\(645\) −2.72238 16.3572i −0.107193 0.644063i
\(646\) 65.5573 2.57932
\(647\) −23.0628 13.3153i −0.906691 0.523478i −0.0273261 0.999627i \(-0.508699\pi\)
−0.879365 + 0.476148i \(0.842033\pi\)
\(648\) −41.5715 + 35.8639i −1.63308 + 1.40887i
\(649\) 0.249789 0.144216i 0.00980506 0.00566096i
\(650\) −52.8306 1.37756i −2.07219 0.0540322i
\(651\) 2.28562 48.7253i 0.0895804 1.90969i
\(652\) −61.5415 + 35.5310i −2.41015 + 1.39150i
\(653\) 10.6651 18.4725i 0.417358 0.722885i −0.578315 0.815814i \(-0.696289\pi\)
0.995673 + 0.0929286i \(0.0296228\pi\)
\(654\) −6.44847 + 17.9075i −0.252155 + 0.700240i
\(655\) 4.94288 + 0.0644317i 0.193134 + 0.00251756i
\(656\) 2.78957 + 4.83168i 0.108915 + 0.188646i
\(657\) −4.53058 + 26.7644i −0.176755 + 1.04418i
\(658\) −7.38155 + 32.2766i −0.287763 + 1.25827i
\(659\) −3.91124 2.25816i −0.152360 0.0879653i 0.421882 0.906651i \(-0.361370\pi\)
−0.574242 + 0.818686i \(0.694703\pi\)
\(660\) −22.7820 8.54083i −0.886789 0.332452i
\(661\) 33.8778i 1.31770i −0.752276 0.658848i \(-0.771044\pi\)
0.752276 0.658848i \(-0.228956\pi\)
\(662\) −15.0698 −0.585703
\(663\) −6.31752 35.1249i −0.245352 1.36414i
\(664\) 64.9842 + 37.5186i 2.52187 + 1.45601i
\(665\) 22.4675 + 21.4169i 0.871251 + 0.830512i
\(666\) −39.3219 + 47.5190i −1.52369 + 1.84132i
\(667\) −0.835791 + 0.482544i −0.0323620 + 0.0186842i
\(668\) −43.3832 + 25.0473i −1.67855 + 0.969109i
\(669\) 15.5331 43.1356i 0.600543 1.66772i
\(670\) 11.7707 6.59279i 0.454744 0.254702i
\(671\) 1.27056 + 2.20068i 0.0490495 + 0.0849561i
\(672\) −20.9314 0.981854i −0.807445 0.0378758i
\(673\) −0.00944408 0.00545254i −0.000364043 0.000210180i 0.499818 0.866130i \(-0.333400\pi\)
−0.500182 + 0.865920i \(0.666734\pi\)
\(674\) −6.15542 + 3.55384i −0.237098 + 0.136889i
\(675\) −0.410472 + 25.9775i −0.0157991 + 0.999875i
\(676\) −9.76712 + 16.9172i −0.375659 + 0.650660i
\(677\) 35.1941i 1.35262i −0.736618 0.676309i \(-0.763578\pi\)
0.736618 0.676309i \(-0.236422\pi\)
\(678\) 26.0634 + 30.8461i 1.00096 + 1.18464i
\(679\) −16.9035 + 18.2019i −0.648697 + 0.698526i
\(680\) −0.877499 + 67.3174i −0.0336506 + 2.58150i
\(681\) −10.2566 + 8.66631i −0.393034 + 0.332094i
\(682\) 19.1960 + 33.2485i 0.735054 + 1.27315i
\(683\) −13.2893 + 23.0177i −0.508499 + 0.880746i 0.491452 + 0.870904i \(0.336466\pi\)
−0.999952 + 0.00984199i \(0.996867\pi\)
\(684\) −44.2491 + 53.4733i −1.69191 + 2.04460i
\(685\) 5.52810 9.29307i 0.211218 0.355070i
\(686\) −36.6208 29.2815i −1.39819 1.11797i
\(687\) −30.1932 10.8725i −1.15194 0.414813i
\(688\) 24.5659 + 14.1831i 0.936567 + 0.540727i
\(689\) 19.4653 0.741568
\(690\) 4.62039 0.768986i 0.175895 0.0292748i
\(691\) 3.28870i 0.125108i −0.998042 0.0625540i \(-0.980075\pi\)
0.998042 0.0625540i \(-0.0199246\pi\)
\(692\) 59.7878i 2.27279i
\(693\) 8.96976 6.88534i 0.340733 0.261552i
\(694\) −25.0419 −0.950578
\(695\) −2.40102 1.42828i −0.0910759 0.0541776i
\(696\) 20.0844 + 7.23238i 0.761299 + 0.274143i
\(697\) 4.15606i 0.157422i
\(698\) −0.708042 0.408788i −0.0267998 0.0154729i
\(699\) 10.6324 + 12.5835i 0.402155 + 0.475952i
\(700\) −40.7959 + 41.6951i −1.54194 + 1.57593i
\(701\) 39.7933i 1.50297i 0.659749 + 0.751486i \(0.270663\pi\)
−0.659749 + 0.751486i \(0.729337\pi\)
\(702\) 47.8432 + 26.9710i 1.80573 + 1.01796i
\(703\) −21.3037 + 36.8990i −0.803483 + 1.39167i
\(704\) −2.06540 + 1.19246i −0.0778428 + 0.0449426i
\(705\) −14.7830 + 12.1642i −0.556759 + 0.458130i
\(706\) −37.4621 + 21.6288i −1.40991 + 0.814009i
\(707\) 14.3693 + 46.6555i 0.540414 + 1.75466i
\(708\) 1.52189 0.273725i 0.0571961 0.0102872i
\(709\) −3.08929 −0.116021 −0.0580103 0.998316i \(-0.518476\pi\)
−0.0580103 + 0.998316i \(0.518476\pi\)
\(710\) −57.9164 + 32.4390i −2.17356 + 1.21741i
\(711\) 1.27168 0.472739i 0.0476918 0.0177291i
\(712\) 8.11762 + 14.0601i 0.304221 + 0.526926i
\(713\) −4.40355 2.54239i −0.164914 0.0952133i
\(714\) −48.1919 30.9217i −1.80354 1.15721i
\(715\) −0.173349 + 13.2984i −0.00648287 + 0.497333i
\(716\) −3.42776 1.97902i −0.128101 0.0739594i
\(717\) −26.9645 + 22.7837i −1.00701 + 0.850872i
\(718\) 43.5931 25.1685i 1.62688 0.939279i
\(719\) 10.5791 + 18.3235i 0.394532 + 0.683350i 0.993041 0.117766i \(-0.0375734\pi\)
−0.598509 + 0.801116i \(0.704240\pi\)
\(720\) −33.8686 28.7782i −1.26221 1.07250i
\(721\) −33.6495 + 36.2342i −1.25317 + 1.34943i
\(722\) −10.7949 + 18.6974i −0.401746 + 0.695844i
\(723\) −11.9608 + 10.1063i −0.444829 + 0.375858i
\(724\) 59.4343i 2.20886i
\(725\) 8.87685 4.82101i 0.329678 0.179048i
\(726\) 13.3270 37.0094i 0.494612 1.37355i
\(727\) 4.31669 7.47672i 0.160097 0.277296i −0.774806 0.632199i \(-0.782153\pi\)
0.934903 + 0.354903i \(0.115486\pi\)
\(728\) 19.8340 + 64.3987i 0.735097 + 2.38677i
\(729\) 13.0169 23.6550i 0.482109 0.876111i
\(730\) −51.2194 0.667659i −1.89572 0.0247112i
\(731\) 10.5654 + 18.2998i 0.390776 + 0.676843i
\(732\) 2.41156 + 13.4081i 0.0891338 + 0.495577i
\(733\) −2.57990 + 4.46851i −0.0952907 + 0.165048i −0.909730 0.415201i \(-0.863711\pi\)
0.814439 + 0.580249i \(0.197045\pi\)
\(734\) −39.7076 68.7756i −1.46564 2.53855i
\(735\) −6.41431 26.3412i −0.236596 0.971608i
\(736\) −1.09216 + 1.89167i −0.0402575 + 0.0697280i
\(737\) −1.69757 2.94028i −0.0625309 0.108307i
\(738\) −4.92753 4.07753i −0.181385 0.150096i
\(739\) −7.92896 + 13.7334i −0.291671 + 0.505190i −0.974205 0.225664i \(-0.927545\pi\)
0.682534 + 0.730854i \(0.260878\pi\)
\(740\) −68.8169 40.9366i −2.52976 1.50486i
\(741\) 35.6959 + 12.8540i 1.31132 + 0.472205i
\(742\) 21.2519 22.8843i 0.780181 0.840110i
\(743\) −14.5897 25.2701i −0.535243 0.927069i −0.999152 0.0411854i \(-0.986887\pi\)
0.463908 0.885883i \(-0.346447\pi\)
\(744\) 19.9094 + 110.695i 0.729916 + 4.05827i
\(745\) 0.100370 7.69991i 0.00367729 0.282103i
\(746\) 56.1756 + 32.4330i 2.05674 + 1.18746i
\(747\) −36.3835 6.15887i −1.33120 0.225341i
\(748\) 31.0044 1.13363
\(749\) 0.686605 + 2.22932i 0.0250880 + 0.0814577i
\(750\) −48.5546 + 6.78560i −1.77296 + 0.247775i
\(751\) 13.9911 24.2333i 0.510543 0.884287i −0.489382 0.872069i \(-0.662778\pi\)
0.999925 0.0122173i \(-0.00388898\pi\)
\(752\) 32.7492i 1.19424i
\(753\) −8.20678 + 1.47606i −0.299072 + 0.0537906i
\(754\) 21.3540i 0.777668i
\(755\) 19.4608 32.7147i 0.708250 1.19061i
\(756\) 57.7500 18.4377i 2.10035 0.670572i
\(757\) 12.4434i 0.452263i 0.974097 + 0.226132i \(0.0726079\pi\)
−0.974097 + 0.226132i \(0.927392\pi\)
\(758\) 12.6734 0.460320
\(759\) −0.208657 1.16012i −0.00757379 0.0421097i
\(760\) −61.5095 36.5897i −2.23118 1.32725i
\(761\) −10.5154 + 18.2131i −0.381181 + 0.660225i −0.991231 0.132138i \(-0.957816\pi\)
0.610050 + 0.792363i \(0.291149\pi\)
\(762\) −6.85299 38.1021i −0.248258 1.38029i
\(763\) 7.81457 8.41484i 0.282907 0.304638i
\(764\) 8.71063i 0.315140i
\(765\) −11.1307 31.1804i −0.402431 1.12733i
\(766\) 50.5708 + 29.1971i 1.82720 + 1.05493i
\(767\) −0.422625 0.732009i −0.0152601 0.0264313i
\(768\) −52.0530 + 9.36219i −1.87830 + 0.337829i
\(769\) −11.8574 + 6.84585i −0.427588 + 0.246868i −0.698318 0.715787i \(-0.746068\pi\)
0.270731 + 0.962655i \(0.412735\pi\)
\(770\) 15.4450 + 14.7228i 0.556600 + 0.530574i
\(771\) −0.429700 0.154734i −0.0154753 0.00557262i
\(772\) 73.0967i 2.63081i
\(773\) 0.308779 + 0.178273i 0.0111060 + 0.00641205i 0.505543 0.862802i \(-0.331292\pi\)
−0.494437 + 0.869214i \(0.664626\pi\)
\(774\) −32.0625 5.42742i −1.15246 0.195085i
\(775\) 45.3824 + 27.8034i 1.63018 + 0.998729i
\(776\) 28.6376 49.6017i 1.02803 1.78060i
\(777\) 33.0649 17.0765i 1.18620 0.612617i
\(778\) −36.8838 + 21.2948i −1.32235 + 0.763457i
\(779\) −3.82628 2.20911i −0.137091 0.0791494i
\(780\) −25.0290 + 66.7630i −0.896182 + 2.39050i
\(781\) 8.35268 + 14.4673i 0.298882 + 0.517680i
\(782\) −5.16912 + 2.98439i −0.184847 + 0.106722i
\(783\) −10.4972 + 0.107803i −0.375141 + 0.00385257i
\(784\) 41.7671 + 20.1583i 1.49168 + 0.719939i
\(785\) −5.11562 9.13342i −0.182584 0.325986i
\(786\) 3.28438 9.12077i 0.117150 0.325327i
\(787\) 10.5853 0.377324 0.188662 0.982042i \(-0.439585\pi\)
0.188662 + 0.982042i \(0.439585\pi\)
\(788\) 108.443 3.86311
\(789\) 10.4870 + 12.4113i 0.373346 + 0.441855i
\(790\) 1.25107 + 2.23365i 0.0445110 + 0.0794698i
\(791\) −7.17176 23.2859i −0.254998 0.827950i
\(792\) −16.6220 + 20.0870i −0.590638 + 0.713762i
\(793\) 6.44910 3.72339i 0.229014 0.132222i
\(794\) 33.1646 + 57.4428i 1.17697 + 2.03857i
\(795\) 17.8125 2.96459i 0.631744 0.105143i
\(796\) 2.76635 + 1.59715i 0.0980507 + 0.0566096i
\(797\) −32.2113 + 18.5972i −1.14098 + 0.658747i −0.946674 0.322193i \(-0.895580\pi\)
−0.194309 + 0.980940i \(0.562247\pi\)
\(798\) 54.0840 27.9320i 1.91455 0.988781i
\(799\) 12.1979 21.1273i 0.431530 0.747432i
\(800\) 11.9438 19.4953i 0.422276 0.689264i
\(801\) −6.15110 5.09003i −0.217338 0.179847i
\(802\) −79.5735 45.9418i −2.80984 1.62226i
\(803\) 12.8907i 0.454902i
\(804\) −3.22204 17.9143i −0.113633 0.631788i
\(805\) −2.74651 0.665903i −0.0968017 0.0234700i
\(806\) 97.4351 56.2542i 3.43201 1.98147i
\(807\) 6.87029 19.0789i 0.241846 0.671610i
\(808\) −56.2809 97.4814i −1.97996 3.42938i
\(809\) −27.2837 15.7522i −0.959243 0.553819i −0.0633032 0.997994i \(-0.520164\pi\)
−0.895940 + 0.444175i \(0.853497\pi\)
\(810\) 47.8886 + 17.3944i 1.68263 + 0.611176i
\(811\) 1.59210i 0.0559062i −0.999609 0.0279531i \(-0.991101\pi\)
0.999609 0.0279531i \(-0.00889891\pi\)
\(812\) −17.2713 16.0393i −0.606104 0.562868i
\(813\) 14.7765 12.4854i 0.518235 0.437882i
\(814\) −14.6450 + 25.3658i −0.513306 + 0.889072i
\(815\) 30.9697 + 18.4227i 1.08482 + 0.645320i
\(816\) 53.2858 + 19.1881i 1.86538 + 0.671719i
\(817\) −22.4637 −0.785905
\(818\) 6.14130i 0.214726i
\(819\) −20.1776 26.2860i −0.705061 0.918506i
\(820\) 4.24496 7.13604i 0.148241 0.249201i
\(821\) 25.4155i 0.887006i −0.896273 0.443503i \(-0.853736\pi\)
0.896273 0.443503i \(-0.146264\pi\)
\(822\) −13.6858 16.1972i −0.477347 0.564941i
\(823\) 19.7366i 0.687973i −0.938975 0.343986i \(-0.888223\pi\)
0.938975 0.343986i \(-0.111777\pi\)
\(824\) 57.0082 98.7411i 1.98597 3.43981i
\(825\) 1.86674 + 12.1957i 0.0649917 + 0.424599i
\(826\) −1.32200 0.302337i −0.0459983 0.0105196i
\(827\) −11.0429 −0.383998 −0.191999 0.981395i \(-0.561497\pi\)
−0.191999 + 0.981395i \(0.561497\pi\)
\(828\) 1.05471 6.23068i 0.0366536 0.216531i
\(829\) −18.4118 10.6300i −0.639467 0.369196i 0.144942 0.989440i \(-0.453700\pi\)
−0.784409 + 0.620244i \(0.787034\pi\)
\(830\) 0.907614 69.6276i 0.0315037 2.41681i
\(831\) −13.2743 + 11.2161i −0.460481 + 0.389083i
\(832\) 3.49452 + 6.05269i 0.121151 + 0.209839i
\(833\) 19.4368 + 28.5613i 0.673445 + 0.989592i
\(834\) −4.18481 + 3.53596i −0.144908 + 0.122440i
\(835\) 21.8318 + 12.9869i 0.755522 + 0.449432i
\(836\) −16.4800 + 28.5443i −0.569974 + 0.987225i
\(837\) −28.1454 47.6133i −0.972848 1.64576i
\(838\) −19.0272 32.9560i −0.657283 1.13845i
\(839\) −17.8301 + 30.8827i −0.615564 + 1.06619i 0.374721 + 0.927137i \(0.377738\pi\)
−0.990285 + 0.139051i \(0.955595\pi\)
\(840\) 27.9580 + 55.9099i 0.964641 + 1.92908i
\(841\) −12.4592 21.5799i −0.429627 0.744136i
\(842\) −28.2003 + 48.8443i −0.971845 + 1.68328i
\(843\) −21.2698 7.65921i −0.732569 0.263797i
\(844\) 25.7503 + 44.6009i 0.886363 + 1.53523i
\(845\) 9.90481 + 0.129112i 0.340736 + 0.00444158i
\(846\) 13.0817 + 35.1903i 0.449759 + 1.20987i
\(847\) −16.1503 + 17.3909i −0.554932 + 0.597559i
\(848\) −15.4450 + 26.7516i −0.530385 + 0.918654i
\(849\) 22.7405 4.09007i 0.780451 0.140371i
\(850\) 54.9007 29.8165i 1.88308 1.02270i
\(851\) 3.87927i 0.132980i
\(852\) 15.8536 + 88.1449i 0.543136 + 3.01979i
\(853\) 12.0777 20.9192i 0.413534 0.716261i −0.581740 0.813375i \(-0.697628\pi\)
0.995273 + 0.0971139i \(0.0309611\pi\)
\(854\) 2.66363 11.6470i 0.0911476 0.398553i
\(855\) 34.6227 + 6.32607i 1.18407 + 0.216347i
\(856\) −2.68925 4.65792i −0.0919167 0.159204i
\(857\) 46.6132 26.9122i 1.59228 0.919302i 0.599362 0.800478i \(-0.295421\pi\)
0.992915 0.118824i \(-0.0379123\pi\)
\(858\) 24.5388 + 8.83637i 0.837739 + 0.301669i
\(859\) −14.8971 8.60083i −0.508282 0.293457i 0.223845 0.974625i \(-0.428139\pi\)
−0.732127 + 0.681168i \(0.761472\pi\)
\(860\) 0.550253 42.2126i 0.0187635 1.43944i
\(861\) 1.77077 + 3.42870i 0.0603477 + 0.116850i
\(862\) −42.7428 24.6775i −1.45582 0.840521i
\(863\) 14.6092 + 25.3039i 0.497304 + 0.861356i 0.999995 0.00310991i \(-0.000989916\pi\)
−0.502691 + 0.864466i \(0.667657\pi\)
\(864\) −20.4537 + 12.0907i −0.695849 + 0.411334i
\(865\) −26.4514 + 14.8154i −0.899375 + 0.503740i
\(866\) −42.8913 −1.45751
\(867\) 8.22527 + 9.73462i 0.279345 + 0.330605i
\(868\) 27.6859 121.060i 0.939720 4.10903i
\(869\) 0.557957 0.322137i 0.0189274 0.0109277i
\(870\) −3.25225 19.5409i −0.110262 0.662498i
\(871\) −8.61653 + 4.97476i −0.291960 + 0.168563i
\(872\) −13.2393 + 22.9311i −0.448339 + 0.776545i
\(873\) −4.70100 + 27.7712i −0.159105 + 0.939911i
\(874\) 6.34529i 0.214633i
\(875\) 28.5561 + 7.71693i 0.965371 + 0.260880i
\(876\) −23.4140 + 65.0211i −0.791086 + 2.19686i
\(877\) −28.2956 16.3364i −0.955473 0.551643i −0.0606963 0.998156i \(-0.519332\pi\)
−0.894777 + 0.446514i \(0.852665\pi\)
\(878\) 4.19699i 0.141641i
\(879\) 6.07621 5.13409i 0.204945 0.173168i
\(880\) −18.1388 10.7901i −0.611460 0.363734i
\(881\) −51.6741 −1.74094 −0.870472 0.492217i \(-0.836186\pi\)
−0.870472 + 0.492217i \(0.836186\pi\)
\(882\) −52.9326 4.97691i −1.78233 0.167581i
\(883\) 18.8576i 0.634610i −0.948324 0.317305i \(-0.897222\pi\)
0.948324 0.317305i \(-0.102778\pi\)
\(884\) 90.8587i 3.05591i
\(885\) −0.498227 0.605488i −0.0167477 0.0203533i
\(886\) 91.3693 3.06961
\(887\) −33.3082 19.2305i −1.11838 0.645697i −0.177393 0.984140i \(-0.556766\pi\)
−0.940987 + 0.338443i \(0.890100\pi\)
\(888\) −65.5421 + 55.3798i −2.19945 + 1.85842i
\(889\) −5.20744 + 22.7701i −0.174652 + 0.763685i
\(890\) 7.70246 12.9483i 0.258187 0.434028i
\(891\) 4.21992 12.1074i 0.141373 0.405614i
\(892\) 58.3605 101.083i 1.95406 3.38452i
\(893\) 12.9673 + 22.4600i 0.433934 + 0.751596i
\(894\) −14.2081 5.11633i −0.475192 0.171116i
\(895\) −0.0261607 + 2.00692i −0.000874456 + 0.0670839i
\(896\) 34.5182 + 7.89418i 1.15317 + 0.263726i
\(897\) −3.39974 + 0.611473i −0.113514 + 0.0204165i
\(898\) 66.8523i 2.23089i
\(899\) −10.7525 + 18.6238i −0.358615 + 0.621139i
\(900\) −12.7357 + 64.9062i −0.424524 + 2.16354i
\(901\) −19.9280 + 11.5054i −0.663897 + 0.383301i
\(902\) −2.63034 1.51863i −0.0875807 0.0505647i
\(903\) 16.5133 + 10.5955i 0.549529 + 0.352598i
\(904\) 28.0899 + 48.6532i 0.934257 + 1.61818i
\(905\) −26.2950 + 14.7278i −0.874076 + 0.489570i
\(906\) −48.1786 57.0195i −1.60063 1.89435i
\(907\) 5.68017 3.27945i 0.188607 0.108892i −0.402723 0.915322i \(-0.631936\pi\)
0.591330 + 0.806430i \(0.298603\pi\)
\(908\) −29.6053 + 17.0926i −0.982486 + 0.567239i
\(909\) 42.6467 + 35.2901i 1.41450 + 1.17050i
\(910\) 43.1454 45.2618i 1.43026 1.50042i
\(911\) 40.3423 + 23.2916i 1.33660 + 0.771686i 0.986302 0.164952i \(-0.0527469\pi\)
0.350298 + 0.936638i \(0.386080\pi\)
\(912\) −45.9891 + 38.8585i −1.52285 + 1.28673i
\(913\) −17.5236 −0.579946
\(914\) 80.4828i 2.66213i
\(915\) 5.33444 4.38945i 0.176351 0.145111i
\(916\) −70.7544 40.8501i −2.33779 1.34972i
\(917\) −3.98017 + 4.28590i −0.131437 + 0.141533i
\(918\) −64.9224 + 0.666731i −2.14276 + 0.0220054i
\(919\) −25.8448 44.7644i −0.852540 1.47664i −0.878909 0.476990i \(-0.841728\pi\)
0.0263686 0.999652i \(-0.491606\pi\)
\(920\) 6.51565 + 0.0849332i 0.214814 + 0.00280016i
\(921\) −35.1402 + 6.32027i −1.15791 + 0.208260i
\(922\) 14.6710 25.4109i 0.483163 0.836863i
\(923\) 42.3965 24.4776i 1.39550 0.805691i
\(924\) 25.5783 13.2100i 0.841464 0.434578i
\(925\) −1.05839 + 40.5902i −0.0347996 + 1.33460i
\(926\) 65.7340 37.9515i 2.16015 1.24716i
\(927\) −9.35818 + 55.2834i −0.307363 + 1.81575i
\(928\) 8.00041 + 4.61904i 0.262626 + 0.151627i
\(929\) 45.2591 1.48490 0.742452 0.669899i \(-0.233663\pi\)
0.742452 + 0.669899i \(0.233663\pi\)
\(930\) 80.5945 66.3173i 2.64280 2.17463i
\(931\) −36.6265 + 2.71307i −1.20038 + 0.0889172i
\(932\) 20.9704 + 36.3218i 0.686909 + 1.18976i
\(933\) −19.7086 + 3.54476i −0.645231 + 0.116050i
\(934\) −5.49669 + 3.17352i −0.179857 + 0.103841i
\(935\) −7.68290 13.7170i −0.251258 0.448595i
\(936\) 58.8653 + 48.7110i 1.92407 + 1.59217i
\(937\) 16.0761 0.525184 0.262592 0.964907i \(-0.415423\pi\)
0.262592 + 0.964907i \(0.415423\pi\)
\(938\) −3.55883 + 15.5614i −0.116200 + 0.508097i
\(939\) 49.5052 8.90393i 1.61554 0.290569i
\(940\) −42.5233 + 23.8173i −1.38696 + 0.776835i
\(941\) −23.6483 −0.770912 −0.385456 0.922726i \(-0.625956\pi\)
−0.385456 + 0.922726i \(0.625956\pi\)
\(942\) −20.2051 + 3.63406i −0.658318 + 0.118404i
\(943\) 0.402265 0.0130995
\(944\) 1.34136 0.0436574
\(945\) −22.4677 20.9810i −0.730875 0.682512i
\(946\) −15.4424 −0.502077
\(947\) 28.5396 0.927413 0.463707 0.885989i \(-0.346519\pi\)
0.463707 + 0.885989i \(0.346519\pi\)
\(948\) 3.39947 0.611424i 0.110410 0.0198581i
\(949\) 37.7763 1.22627
\(950\) −1.73120 + 66.3931i −0.0561675 + 2.15408i
\(951\) −36.9672 + 6.64886i −1.19874 + 0.215604i
\(952\) −58.3699 54.2062i −1.89178 1.75683i
\(953\) 60.3601 1.95525 0.977627 0.210346i \(-0.0674590\pi\)
0.977627 + 0.210346i \(0.0674590\pi\)
\(954\) 5.91031 34.9152i 0.191353 1.13042i
\(955\) 3.85377 2.15850i 0.124705 0.0698473i
\(956\) −77.8321 + 44.9364i −2.51727 + 1.45335i
\(957\) −4.90646 + 0.882470i −0.158603 + 0.0285262i
\(958\) 45.0082 + 77.9565i 1.45415 + 2.51866i
\(959\) 3.76587 + 12.2273i 0.121606 + 0.394841i
\(960\) 4.11964 + 5.00654i 0.132961 + 0.161585i
\(961\) −82.3036 −2.65495
\(962\) 74.3349 + 42.9173i 2.39665 + 1.38371i
\(963\) 2.03777 + 1.68626i 0.0656663 + 0.0543388i
\(964\) −34.5245 + 19.9328i −1.11196 + 0.641991i
\(965\) 32.3396 18.1134i 1.04105 0.583091i
\(966\) −2.99291 + 4.66450i −0.0962952 + 0.150078i
\(967\) 20.6715 11.9347i 0.664752 0.383795i −0.129333 0.991601i \(-0.541284\pi\)
0.794085 + 0.607807i \(0.207950\pi\)
\(968\) 27.3616 47.3916i 0.879434 1.52322i
\(969\) −44.1421 + 7.93934i −1.41805 + 0.255048i
\(970\) −53.1460 0.692772i −1.70642 0.0222436i
\(971\) −21.2234 36.7601i −0.681092 1.17969i −0.974648 0.223745i \(-0.928172\pi\)
0.293555 0.955942i \(-0.405161\pi\)
\(972\) 43.2767 53.4054i 1.38810 1.71298i
\(973\) 3.15914 0.972975i 0.101277 0.0311922i
\(974\) −39.1049 22.5772i −1.25300 0.723422i
\(975\) 35.7396 5.47051i 1.14458 0.175197i
\(976\) 11.8176i 0.378271i
\(977\) 7.00412 0.224082 0.112041 0.993704i \(-0.464261\pi\)
0.112041 + 0.993704i \(0.464261\pi\)
\(978\) 53.9781 45.6087i 1.72603 1.45841i
\(979\) −3.28349 1.89572i −0.104941 0.0605875i
\(980\) −4.20108 68.8931i −0.134199 2.20071i
\(981\) 2.17329 12.8387i 0.0693879 0.409909i
\(982\) 15.5269 8.96444i 0.495482 0.286067i
\(983\) 24.7050 14.2634i 0.787967 0.454933i −0.0512794 0.998684i \(-0.516330\pi\)
0.839246 + 0.543751i \(0.182997\pi\)
\(984\) −5.74267 6.79646i −0.183069 0.216663i
\(985\) −26.8721 47.9774i −0.856217 1.52869i
\(986\) 12.6218 + 21.8616i 0.401961 + 0.696216i
\(987\) 1.06139 22.6270i 0.0337845 0.720224i
\(988\) 83.6493 + 48.2950i 2.66124 + 1.53647i
\(989\) 1.77124 1.02263i 0.0563221 0.0325176i
\(990\) 23.8010 + 4.34879i 0.756445 + 0.138214i
\(991\) 28.9247 50.0991i 0.918824 1.59145i 0.117620 0.993059i \(-0.462474\pi\)
0.801204 0.598391i \(-0.204193\pi\)
\(992\) 48.6729i 1.54536i
\(993\) 10.1470 1.82503i 0.322006 0.0579156i
\(994\) 17.5108 76.5677i 0.555407 2.42858i
\(995\) 0.0211128 1.61967i 0.000669321 0.0513469i
\(996\) −88.3896 31.8290i −2.80073 1.00854i
\(997\) −1.10662 1.91671i −0.0350469 0.0607030i 0.847970 0.530044i \(-0.177825\pi\)
−0.883017 + 0.469341i \(0.844491\pi\)
\(998\) 29.0773 50.3634i 0.920427 1.59423i
\(999\) 20.7221 36.7583i 0.655617 1.16298i
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.164.3 yes 88
3.2 odd 2 945.2.bq.a.899.42 88
5.4 even 2 inner 315.2.bq.a.164.42 yes 88
7.5 odd 6 315.2.u.a.299.42 yes 88
9.4 even 3 945.2.u.a.584.42 88
9.5 odd 6 315.2.u.a.59.3 88
15.14 odd 2 945.2.bq.a.899.3 88
21.5 even 6 945.2.u.a.89.3 88
35.19 odd 6 315.2.u.a.299.3 yes 88
45.4 even 6 945.2.u.a.584.3 88
45.14 odd 6 315.2.u.a.59.42 yes 88
63.5 even 6 inner 315.2.bq.a.194.42 yes 88
63.40 odd 6 945.2.bq.a.719.3 88
105.89 even 6 945.2.u.a.89.42 88
315.194 even 6 inner 315.2.bq.a.194.3 yes 88
315.229 odd 6 945.2.bq.a.719.42 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.u.a.59.3 88 9.5 odd 6
315.2.u.a.59.42 yes 88 45.14 odd 6
315.2.u.a.299.3 yes 88 35.19 odd 6
315.2.u.a.299.42 yes 88 7.5 odd 6
315.2.bq.a.164.3 yes 88 1.1 even 1 trivial
315.2.bq.a.164.42 yes 88 5.4 even 2 inner
315.2.bq.a.194.3 yes 88 315.194 even 6 inner
315.2.bq.a.194.42 yes 88 63.5 even 6 inner
945.2.u.a.89.3 88 21.5 even 6
945.2.u.a.89.42 88 105.89 even 6
945.2.u.a.584.3 88 45.4 even 6
945.2.u.a.584.42 88 9.4 even 3
945.2.bq.a.719.3 88 63.40 odd 6
945.2.bq.a.719.42 88 315.229 odd 6
945.2.bq.a.899.3 88 15.14 odd 2
945.2.bq.a.899.42 88 3.2 odd 2