Properties

Label 175.2.n.a.169.9
Level $175$
Weight $2$
Character 175.169
Analytic conductor $1.397$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [175,2,Mod(29,175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(175, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("175.29");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.n (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.39738203537\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 169.9
Character \(\chi\) \(=\) 175.169
Dual form 175.2.n.a.29.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.03051 - 0.334833i) q^{2} +(-1.58321 - 2.17910i) q^{3} +(-0.668196 + 0.485473i) q^{4} +(-2.00240 - 0.995194i) q^{5} +(-2.36115 - 1.71547i) q^{6} -1.00000i q^{7} +(-1.79981 + 2.47723i) q^{8} +(-1.31487 + 4.04676i) q^{9} +O(q^{10})\) \(q+(1.03051 - 0.334833i) q^{2} +(-1.58321 - 2.17910i) q^{3} +(-0.668196 + 0.485473i) q^{4} +(-2.00240 - 0.995194i) q^{5} +(-2.36115 - 1.71547i) q^{6} -1.00000i q^{7} +(-1.79981 + 2.47723i) q^{8} +(-1.31487 + 4.04676i) q^{9} +(-2.39671 - 0.355089i) q^{10} +(-1.20073 - 3.69547i) q^{11} +(2.11579 + 0.687461i) q^{12} +(2.12541 + 0.690588i) q^{13} +(-0.334833 - 1.03051i) q^{14} +(1.00158 + 5.93902i) q^{15} +(-0.514809 + 1.58442i) q^{16} +(4.12875 - 5.68273i) q^{17} +4.61049i q^{18} +(-5.15646 - 3.74639i) q^{19} +(1.82113 - 0.307124i) q^{20} +(-2.17910 + 1.58321i) q^{21} +(-2.47473 - 3.40618i) q^{22} +(4.94286 - 1.60603i) q^{23} +8.24760 q^{24} +(3.01918 + 3.98554i) q^{25} +2.42149 q^{26} +(3.21497 - 1.04461i) q^{27} +(0.485473 + 0.668196i) q^{28} +(-4.72713 + 3.43446i) q^{29} +(3.02072 + 5.78485i) q^{30} +(0.520209 + 0.377954i) q^{31} -4.31891i q^{32} +(-6.15179 + 8.46722i) q^{33} +(2.35195 - 7.23856i) q^{34} +(-0.995194 + 2.00240i) q^{35} +(-1.08600 - 3.34237i) q^{36} +(6.79092 + 2.20650i) q^{37} +(-6.56820 - 2.13414i) q^{38} +(-1.86011 - 5.72482i) q^{39} +(6.06926 - 3.16923i) q^{40} +(-0.201628 + 0.620549i) q^{41} +(-1.71547 + 2.36115i) q^{42} -0.957977i q^{43} +(2.59638 + 1.88638i) q^{44} +(6.66021 - 6.79467i) q^{45} +(4.55591 - 3.31006i) q^{46} +(1.01412 + 1.39581i) q^{47} +(4.26766 - 1.38665i) q^{48} -1.00000 q^{49} +(4.44578 + 3.09622i) q^{50} -18.9199 q^{51} +(-1.75545 + 0.570381i) q^{52} +(-5.94778 - 8.18641i) q^{53} +(2.96329 - 2.15295i) q^{54} +(-1.27337 + 8.59476i) q^{55} +(2.47723 + 1.79981i) q^{56} +17.1678i q^{57} +(-3.72139 + 5.12205i) q^{58} +(-0.235963 + 0.726220i) q^{59} +(-3.55249 - 3.48219i) q^{60} +(3.07593 + 9.46675i) q^{61} +(0.662631 + 0.215302i) q^{62} +(4.04676 + 1.31487i) q^{63} +(-2.47573 - 7.61952i) q^{64} +(-3.56864 - 3.49803i) q^{65} +(-3.50438 + 10.7854i) q^{66} +(-1.61593 + 2.22413i) q^{67} +5.80158i q^{68} +(-11.3253 - 8.22830i) q^{69} +(-0.355089 + 2.39671i) q^{70} +(10.3133 - 7.49305i) q^{71} +(-7.65823 - 10.5407i) q^{72} +(-9.69099 + 3.14879i) q^{73} +7.73692 q^{74} +(3.90491 - 12.8890i) q^{75} +5.26430 q^{76} +(-3.69547 + 1.20073i) q^{77} +(-3.83372 - 5.27666i) q^{78} +(3.52524 - 2.56124i) q^{79} +(2.60766 - 2.66030i) q^{80} +(2.96089 + 2.15121i) q^{81} +0.706994i q^{82} +(6.22474 - 8.56762i) q^{83} +(0.687461 - 2.11579i) q^{84} +(-13.9228 + 7.27018i) q^{85} +(-0.320762 - 0.987205i) q^{86} +(14.9681 + 4.86342i) q^{87} +(11.3156 + 3.67667i) q^{88} +(-0.431368 - 1.32762i) q^{89} +(4.58834 - 9.23203i) q^{90} +(0.690588 - 2.12541i) q^{91} +(-2.52311 + 3.47277i) q^{92} -1.73197i q^{93} +(1.51242 + 1.09884i) q^{94} +(6.59690 + 12.6334i) q^{95} +(-9.41133 + 6.83773i) q^{96} +(-6.50724 - 8.95645i) q^{97} +(-1.03051 + 0.334833i) q^{98} +16.5335 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9} - 4 q^{10} + 8 q^{11} - 40 q^{12} - 4 q^{14} - 18 q^{15} - 32 q^{16} + 12 q^{19} + 12 q^{20} + 4 q^{21} - 30 q^{22} + 10 q^{23} - 28 q^{24} + 4 q^{25} + 12 q^{26} + 30 q^{27} - 2 q^{29} + 28 q^{30} + 12 q^{31} + 20 q^{33} + 2 q^{35} - 14 q^{36} - 70 q^{37} - 70 q^{38} - 4 q^{39} - 30 q^{40} + 4 q^{41} + 50 q^{42} + 22 q^{44} - 52 q^{45} - 4 q^{46} - 10 q^{47} + 30 q^{48} - 56 q^{49} - 54 q^{50} - 44 q^{51} - 20 q^{53} + 54 q^{54} - 2 q^{55} + 12 q^{56} + 10 q^{58} - 6 q^{59} + 16 q^{60} - 4 q^{61} + 50 q^{62} + 20 q^{63} + 24 q^{64} - 18 q^{65} - 74 q^{66} + 10 q^{67} - 78 q^{69} + 8 q^{70} - 8 q^{71} + 140 q^{72} + 40 q^{73} + 60 q^{74} - 8 q^{75} + 52 q^{76} - 20 q^{77} - 90 q^{78} + 124 q^{80} - 72 q^{81} - 30 q^{83} - 12 q^{84} + 96 q^{85} - 20 q^{86} + 30 q^{87} + 140 q^{88} + 38 q^{89} - 8 q^{90} + 8 q^{91} + 80 q^{92} + 88 q^{94} - 70 q^{95} - 28 q^{96} - 30 q^{97} + 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{9}{10}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.03051 0.334833i 0.728681 0.236763i 0.0788979 0.996883i \(-0.474860\pi\)
0.649783 + 0.760120i \(0.274860\pi\)
\(3\) −1.58321 2.17910i −0.914066 1.25810i −0.965759 0.259440i \(-0.916462\pi\)
0.0516935 0.998663i \(-0.483538\pi\)
\(4\) −0.668196 + 0.485473i −0.334098 + 0.242737i
\(5\) −2.00240 0.995194i −0.895499 0.445064i
\(6\) −2.36115 1.71547i −0.963934 0.700339i
\(7\) 1.00000i 0.377964i
\(8\) −1.79981 + 2.47723i −0.636329 + 0.875832i
\(9\) −1.31487 + 4.04676i −0.438291 + 1.34892i
\(10\) −2.39671 0.355089i −0.757907 0.112289i
\(11\) −1.20073 3.69547i −0.362034 1.11423i −0.951817 0.306665i \(-0.900787\pi\)
0.589783 0.807562i \(-0.299213\pi\)
\(12\) 2.11579 + 0.687461i 0.610775 + 0.198453i
\(13\) 2.12541 + 0.690588i 0.589483 + 0.191535i 0.588544 0.808465i \(-0.299701\pi\)
0.000938449 1.00000i \(0.499701\pi\)
\(14\) −0.334833 1.03051i −0.0894879 0.275415i
\(15\) 1.00158 + 5.93902i 0.258608 + 1.53345i
\(16\) −0.514809 + 1.58442i −0.128702 + 0.396105i
\(17\) 4.12875 5.68273i 1.00137 1.37827i 0.0768864 0.997040i \(-0.475502\pi\)
0.924482 0.381226i \(-0.124498\pi\)
\(18\) 4.61049i 1.08670i
\(19\) −5.15646 3.74639i −1.18297 0.859481i −0.190470 0.981693i \(-0.561001\pi\)
−0.992504 + 0.122212i \(0.961001\pi\)
\(20\) 1.82113 0.307124i 0.407218 0.0686750i
\(21\) −2.17910 + 1.58321i −0.475518 + 0.345484i
\(22\) −2.47473 3.40618i −0.527615 0.726199i
\(23\) 4.94286 1.60603i 1.03066 0.334881i 0.255607 0.966781i \(-0.417725\pi\)
0.775050 + 0.631900i \(0.217725\pi\)
\(24\) 8.24760 1.68353
\(25\) 3.01918 + 3.98554i 0.603835 + 0.797109i
\(26\) 2.42149 0.474893
\(27\) 3.21497 1.04461i 0.618720 0.201034i
\(28\) 0.485473 + 0.668196i 0.0917458 + 0.126277i
\(29\) −4.72713 + 3.43446i −0.877807 + 0.637764i −0.932670 0.360730i \(-0.882528\pi\)
0.0548634 + 0.998494i \(0.482528\pi\)
\(30\) 3.02072 + 5.78485i 0.551505 + 1.05617i
\(31\) 0.520209 + 0.377954i 0.0934322 + 0.0678825i 0.633521 0.773726i \(-0.281609\pi\)
−0.540088 + 0.841608i \(0.681609\pi\)
\(32\) 4.31891i 0.763482i
\(33\) −6.15179 + 8.46722i −1.07089 + 1.47395i
\(34\) 2.35195 7.23856i 0.403356 1.24140i
\(35\) −0.995194 + 2.00240i −0.168219 + 0.338467i
\(36\) −1.08600 3.34237i −0.181000 0.557061i
\(37\) 6.79092 + 2.20650i 1.11642 + 0.362747i 0.808401 0.588633i \(-0.200334\pi\)
0.308020 + 0.951380i \(0.400334\pi\)
\(38\) −6.56820 2.13414i −1.06550 0.346203i
\(39\) −1.86011 5.72482i −0.297856 0.916705i
\(40\) 6.06926 3.16923i 0.959634 0.501099i
\(41\) −0.201628 + 0.620549i −0.0314891 + 0.0969134i −0.965566 0.260159i \(-0.916225\pi\)
0.934077 + 0.357072i \(0.116225\pi\)
\(42\) −1.71547 + 2.36115i −0.264703 + 0.364333i
\(43\) 0.957977i 0.146090i −0.997329 0.0730450i \(-0.976728\pi\)
0.997329 0.0730450i \(-0.0232717\pi\)
\(44\) 2.59638 + 1.88638i 0.391419 + 0.284382i
\(45\) 6.66021 6.79467i 0.992846 1.01289i
\(46\) 4.55591 3.31006i 0.671733 0.488042i
\(47\) 1.01412 + 1.39581i 0.147924 + 0.203600i 0.876549 0.481313i \(-0.159840\pi\)
−0.728624 + 0.684914i \(0.759840\pi\)
\(48\) 4.26766 1.38665i 0.615983 0.200145i
\(49\) −1.00000 −0.142857
\(50\) 4.44578 + 3.09622i 0.628729 + 0.437872i
\(51\) −18.9199 −2.64932
\(52\) −1.75545 + 0.570381i −0.243437 + 0.0790976i
\(53\) −5.94778 8.18641i −0.816990 1.12449i −0.990207 0.139606i \(-0.955416\pi\)
0.173217 0.984884i \(-0.444584\pi\)
\(54\) 2.96329 2.15295i 0.403252 0.292980i
\(55\) −1.27337 + 8.59476i −0.171701 + 1.15892i
\(56\) 2.47723 + 1.79981i 0.331033 + 0.240510i
\(57\) 17.1678i 2.27393i
\(58\) −3.72139 + 5.12205i −0.488642 + 0.672558i
\(59\) −0.235963 + 0.726220i −0.0307198 + 0.0945458i −0.965241 0.261362i \(-0.915828\pi\)
0.934521 + 0.355908i \(0.115828\pi\)
\(60\) −3.55249 3.48219i −0.458624 0.449549i
\(61\) 3.07593 + 9.46675i 0.393833 + 1.21209i 0.929867 + 0.367897i \(0.119922\pi\)
−0.536034 + 0.844197i \(0.680078\pi\)
\(62\) 0.662631 + 0.215302i 0.0841543 + 0.0273434i
\(63\) 4.04676 + 1.31487i 0.509844 + 0.165658i
\(64\) −2.47573 7.61952i −0.309466 0.952440i
\(65\) −3.56864 3.49803i −0.442636 0.433877i
\(66\) −3.50438 + 10.7854i −0.431359 + 1.32759i
\(67\) −1.61593 + 2.22413i −0.197417 + 0.271721i −0.896236 0.443577i \(-0.853709\pi\)
0.698819 + 0.715298i \(0.253709\pi\)
\(68\) 5.80158i 0.703545i
\(69\) −11.3253 8.22830i −1.36340 0.990570i
\(70\) −0.355089 + 2.39671i −0.0424413 + 0.286462i
\(71\) 10.3133 7.49305i 1.22396 0.889261i 0.227541 0.973769i \(-0.426932\pi\)
0.996423 + 0.0845072i \(0.0269316\pi\)
\(72\) −7.65823 10.5407i −0.902531 1.24223i
\(73\) −9.69099 + 3.14879i −1.13424 + 0.368538i −0.815187 0.579197i \(-0.803366\pi\)
−0.319057 + 0.947736i \(0.603366\pi\)
\(74\) 7.73692 0.899399
\(75\) 3.90491 12.8890i 0.450900 1.48830i
\(76\) 5.26430 0.603857
\(77\) −3.69547 + 1.20073i −0.421138 + 0.136836i
\(78\) −3.83372 5.27666i −0.434083 0.597464i
\(79\) 3.52524 2.56124i 0.396620 0.288162i −0.371543 0.928416i \(-0.621171\pi\)
0.768163 + 0.640254i \(0.221171\pi\)
\(80\) 2.60766 2.66030i 0.291545 0.297431i
\(81\) 2.96089 + 2.15121i 0.328988 + 0.239024i
\(82\) 0.706994i 0.0780744i
\(83\) 6.22474 8.56762i 0.683254 0.940419i −0.316713 0.948521i \(-0.602579\pi\)
0.999967 + 0.00810282i \(0.00257924\pi\)
\(84\) 0.687461 2.11579i 0.0750082 0.230851i
\(85\) −13.9228 + 7.27018i −1.51014 + 0.788561i
\(86\) −0.320762 0.987205i −0.0345887 0.106453i
\(87\) 14.9681 + 4.86342i 1.60475 + 0.521414i
\(88\) 11.3156 + 3.67667i 1.20625 + 0.391934i
\(89\) −0.431368 1.32762i −0.0457249 0.140727i 0.925588 0.378534i \(-0.123572\pi\)
−0.971313 + 0.237807i \(0.923572\pi\)
\(90\) 4.58834 9.23203i 0.483653 0.973142i
\(91\) 0.690588 2.12541i 0.0723932 0.222804i
\(92\) −2.52311 + 3.47277i −0.263053 + 0.362061i
\(93\) 1.73197i 0.179596i
\(94\) 1.51242 + 1.09884i 0.155995 + 0.113337i
\(95\) 6.59690 + 12.6334i 0.676827 + 1.29616i
\(96\) −9.41133 + 6.83773i −0.960539 + 0.697873i
\(97\) −6.50724 8.95645i −0.660710 0.909389i 0.338795 0.940860i \(-0.389981\pi\)
−0.999505 + 0.0314709i \(0.989981\pi\)
\(98\) −1.03051 + 0.334833i −0.104097 + 0.0338232i
\(99\) 16.5335 1.66168
\(100\) −3.95228 1.19740i −0.395228 0.119740i
\(101\) −8.27731 −0.823623 −0.411811 0.911269i \(-0.635104\pi\)
−0.411811 + 0.911269i \(0.635104\pi\)
\(102\) −19.4972 + 6.33501i −1.93051 + 0.627259i
\(103\) −4.05337 5.57898i −0.399390 0.549713i 0.561201 0.827680i \(-0.310340\pi\)
−0.960591 + 0.277966i \(0.910340\pi\)
\(104\) −5.53608 + 4.02220i −0.542857 + 0.394409i
\(105\) 5.93902 1.00158i 0.579589 0.0977445i
\(106\) −8.87032 6.44467i −0.861562 0.625961i
\(107\) 12.0065i 1.16071i −0.814362 0.580357i \(-0.802913\pi\)
0.814362 0.580357i \(-0.197087\pi\)
\(108\) −1.64110 + 2.25878i −0.157915 + 0.217351i
\(109\) 0.360059 1.10815i 0.0344874 0.106141i −0.932331 0.361606i \(-0.882229\pi\)
0.966818 + 0.255465i \(0.0822285\pi\)
\(110\) 1.56559 + 9.28335i 0.149273 + 0.885133i
\(111\) −5.94325 18.2914i −0.564108 1.73615i
\(112\) 1.58442 + 0.514809i 0.149714 + 0.0486449i
\(113\) 18.4253 + 5.98673i 1.73330 + 0.563184i 0.993920 0.110102i \(-0.0351179\pi\)
0.739382 + 0.673286i \(0.235118\pi\)
\(114\) 5.74833 + 17.6915i 0.538381 + 1.65697i
\(115\) −11.4959 1.70319i −1.07200 0.158823i
\(116\) 1.49131 4.58979i 0.138465 0.426152i
\(117\) −5.58929 + 7.69300i −0.516730 + 0.711218i
\(118\) 0.827386i 0.0761670i
\(119\) −5.68273 4.12875i −0.520935 0.378482i
\(120\) −16.5150 8.20796i −1.50760 0.749281i
\(121\) −3.31558 + 2.40891i −0.301416 + 0.218992i
\(122\) 6.33956 + 8.72566i 0.573957 + 0.789984i
\(123\) 1.67146 0.543089i 0.150710 0.0489687i
\(124\) −0.531088 −0.0476931
\(125\) −2.07920 10.9853i −0.185969 0.982556i
\(126\) 4.61049 0.410735
\(127\) −0.752993 + 0.244662i −0.0668173 + 0.0217103i −0.342235 0.939614i \(-0.611184\pi\)
0.275418 + 0.961325i \(0.411184\pi\)
\(128\) −0.0253510 0.0348927i −0.00224073 0.00308410i
\(129\) −2.08753 + 1.51668i −0.183796 + 0.133536i
\(130\) −4.84878 2.40985i −0.425266 0.211358i
\(131\) 1.66351 + 1.20861i 0.145342 + 0.105597i 0.658080 0.752948i \(-0.271369\pi\)
−0.512738 + 0.858545i \(0.671369\pi\)
\(132\) 8.64429i 0.752389i
\(133\) −3.74639 + 5.15646i −0.324853 + 0.447122i
\(134\) −0.920516 + 2.83306i −0.0795204 + 0.244739i
\(135\) −7.47722 1.10780i −0.643536 0.0953443i
\(136\) 6.64646 + 20.4557i 0.569929 + 1.75406i
\(137\) 7.56640 + 2.45847i 0.646441 + 0.210041i 0.613844 0.789427i \(-0.289622\pi\)
0.0325968 + 0.999469i \(0.489622\pi\)
\(138\) −14.4259 4.68726i −1.22802 0.399006i
\(139\) 4.66431 + 14.3553i 0.395622 + 1.21760i 0.928476 + 0.371392i \(0.121119\pi\)
−0.532854 + 0.846207i \(0.678881\pi\)
\(140\) −0.307124 1.82113i −0.0259567 0.153914i
\(141\) 1.43606 4.41973i 0.120938 0.372208i
\(142\) 8.11904 11.1749i 0.681334 0.937776i
\(143\) 8.68361i 0.726160i
\(144\) −5.73486 4.16662i −0.477905 0.347219i
\(145\) 12.8836 2.17274i 1.06992 0.180436i
\(146\) −8.93234 + 6.48972i −0.739246 + 0.537093i
\(147\) 1.58321 + 2.17910i 0.130581 + 0.179729i
\(148\) −5.60887 + 1.82243i −0.461046 + 0.149803i
\(149\) −3.74915 −0.307143 −0.153571 0.988138i \(-0.549077\pi\)
−0.153571 + 0.988138i \(0.549077\pi\)
\(150\) −0.291624 14.5898i −0.0238110 1.19125i
\(151\) 0.172096 0.0140050 0.00700248 0.999975i \(-0.497771\pi\)
0.00700248 + 0.999975i \(0.497771\pi\)
\(152\) 18.5613 6.03094i 1.50552 0.489174i
\(153\) 17.5679 + 24.1801i 1.42028 + 1.95485i
\(154\) −3.40618 + 2.47473i −0.274478 + 0.199420i
\(155\) −0.665526 1.27452i −0.0534563 0.102372i
\(156\) 4.02216 + 2.92227i 0.322031 + 0.233969i
\(157\) 6.90269i 0.550895i 0.961316 + 0.275447i \(0.0888259\pi\)
−0.961316 + 0.275447i \(0.911174\pi\)
\(158\) 2.77521 3.81975i 0.220784 0.303883i
\(159\) −8.42243 + 25.9216i −0.667942 + 2.05572i
\(160\) −4.29815 + 8.64816i −0.339799 + 0.683697i
\(161\) −1.60603 4.94286i −0.126573 0.389552i
\(162\) 3.77153 + 1.22544i 0.296319 + 0.0962799i
\(163\) 9.52841 + 3.09597i 0.746323 + 0.242495i 0.657398 0.753543i \(-0.271657\pi\)
0.0889246 + 0.996038i \(0.471657\pi\)
\(164\) −0.166532 0.512534i −0.0130040 0.0400221i
\(165\) 20.7448 10.8325i 1.61498 0.843308i
\(166\) 3.54594 10.9133i 0.275218 0.847034i
\(167\) 4.61709 6.35488i 0.357281 0.491755i −0.592108 0.805859i \(-0.701704\pi\)
0.949389 + 0.314104i \(0.101704\pi\)
\(168\) 8.24760i 0.636316i
\(169\) −6.47676 4.70564i −0.498213 0.361973i
\(170\) −11.9133 + 12.1538i −0.913708 + 0.932154i
\(171\) 21.9409 15.9410i 1.67786 1.21904i
\(172\) 0.465072 + 0.640116i 0.0354614 + 0.0488084i
\(173\) 19.5169 6.34143i 1.48384 0.482130i 0.548585 0.836095i \(-0.315167\pi\)
0.935259 + 0.353965i \(0.115167\pi\)
\(174\) 17.0532 1.29280
\(175\) 3.98554 3.01918i 0.301279 0.228228i
\(176\) 6.47333 0.487945
\(177\) 1.95608 0.635571i 0.147028 0.0477724i
\(178\) −0.889059 1.22368i −0.0666378 0.0917190i
\(179\) 0.138259 0.100451i 0.0103340 0.00750805i −0.582606 0.812755i \(-0.697967\pi\)
0.592940 + 0.805246i \(0.297967\pi\)
\(180\) −1.15170 + 7.77353i −0.0858427 + 0.579405i
\(181\) 16.5075 + 11.9934i 1.22700 + 0.891465i 0.996661 0.0816467i \(-0.0260179\pi\)
0.230335 + 0.973111i \(0.426018\pi\)
\(182\) 2.42149i 0.179493i
\(183\) 15.7591 21.6906i 1.16495 1.60342i
\(184\) −4.91771 + 15.1351i −0.362538 + 1.11578i
\(185\) −11.4022 11.1766i −0.838307 0.821719i
\(186\) −0.579919 1.78481i −0.0425217 0.130868i
\(187\) −25.9579 8.43424i −1.89823 0.616772i
\(188\) −1.35526 0.440351i −0.0988426 0.0321159i
\(189\) −1.04461 3.21497i −0.0759839 0.233854i
\(190\) 11.0283 + 10.8100i 0.800074 + 0.784242i
\(191\) −0.182058 + 0.560317i −0.0131733 + 0.0405431i −0.957427 0.288675i \(-0.906785\pi\)
0.944254 + 0.329218i \(0.106785\pi\)
\(192\) −12.6841 + 17.4581i −0.915395 + 1.25993i
\(193\) 9.74725i 0.701623i 0.936446 + 0.350811i \(0.114094\pi\)
−0.936446 + 0.350811i \(0.885906\pi\)
\(194\) −9.70469 7.05087i −0.696756 0.506223i
\(195\) −1.97264 + 13.3145i −0.141264 + 0.953473i
\(196\) 0.668196 0.485473i 0.0477283 0.0346766i
\(197\) −2.12986 2.93151i −0.151746 0.208861i 0.726375 0.687298i \(-0.241203\pi\)
−0.878122 + 0.478437i \(0.841203\pi\)
\(198\) 17.0380 5.53597i 1.21083 0.393424i
\(199\) 3.85851 0.273522 0.136761 0.990604i \(-0.456331\pi\)
0.136761 + 0.990604i \(0.456331\pi\)
\(200\) −15.3070 + 0.305961i −1.08237 + 0.0216347i
\(201\) 7.40495 0.522305
\(202\) −8.52985 + 2.77152i −0.600158 + 0.195003i
\(203\) 3.43446 + 4.72713i 0.241052 + 0.331780i
\(204\) 12.6422 9.18510i 0.885132 0.643086i
\(205\) 1.02131 1.04192i 0.0713311 0.0727712i
\(206\) −6.04506 4.39200i −0.421180 0.306005i
\(207\) 22.1143i 1.53705i
\(208\) −2.18836 + 3.01202i −0.151736 + 0.208846i
\(209\) −7.65315 + 23.5540i −0.529380 + 1.62926i
\(210\) 5.78485 3.02072i 0.399193 0.208449i
\(211\) 3.22549 + 9.92705i 0.222052 + 0.683406i 0.998577 + 0.0533203i \(0.0169804\pi\)
−0.776525 + 0.630086i \(0.783020\pi\)
\(212\) 7.94856 + 2.58265i 0.545910 + 0.177377i
\(213\) −32.6562 10.6106i −2.23757 0.727029i
\(214\) −4.02018 12.3728i −0.274814 0.845789i
\(215\) −0.953373 + 1.91825i −0.0650195 + 0.130823i
\(216\) −3.19860 + 9.84429i −0.217637 + 0.669819i
\(217\) 0.377954 0.520209i 0.0256572 0.0353141i
\(218\) 1.26252i 0.0855084i
\(219\) 22.2044 + 16.1324i 1.50043 + 1.09013i
\(220\) −3.32166 6.36118i −0.223946 0.428870i
\(221\) 12.6997 9.22688i 0.854275 0.620667i
\(222\) −12.2492 16.8595i −0.822110 1.13154i
\(223\) −9.58256 + 3.11356i −0.641696 + 0.208500i −0.611749 0.791052i \(-0.709534\pi\)
−0.0299467 + 0.999551i \(0.509534\pi\)
\(224\) −4.31891 −0.288569
\(225\) −20.0984 + 6.97741i −1.33989 + 0.465161i
\(226\) 20.9920 1.39636
\(227\) −17.9785 + 5.84157i −1.19328 + 0.387719i −0.837283 0.546770i \(-0.815857\pi\)
−0.355993 + 0.934489i \(0.615857\pi\)
\(228\) −8.33449 11.4714i −0.551965 0.759714i
\(229\) 12.7540 9.26633i 0.842809 0.612337i −0.0803449 0.996767i \(-0.525602\pi\)
0.923154 + 0.384431i \(0.125602\pi\)
\(230\) −12.4169 + 2.09404i −0.818746 + 0.138077i
\(231\) 8.46722 + 6.15179i 0.557102 + 0.404758i
\(232\) 17.8916i 1.17464i
\(233\) −0.136891 + 0.188414i −0.00896801 + 0.0123434i −0.813477 0.581596i \(-0.802428\pi\)
0.804509 + 0.593940i \(0.202428\pi\)
\(234\) −3.18395 + 9.79919i −0.208141 + 0.640593i
\(235\) −0.641560 3.80422i −0.0418508 0.248160i
\(236\) −0.194891 0.599812i −0.0126863 0.0390444i
\(237\) −11.1624 3.62688i −0.725074 0.235591i
\(238\) −7.23856 2.35195i −0.469206 0.152454i
\(239\) 7.28392 + 22.4176i 0.471158 + 1.45007i 0.851070 + 0.525052i \(0.175954\pi\)
−0.379912 + 0.925023i \(0.624046\pi\)
\(240\) −9.92552 1.47053i −0.640690 0.0949225i
\(241\) 0.907156 2.79194i 0.0584351 0.179845i −0.917578 0.397555i \(-0.869859\pi\)
0.976013 + 0.217710i \(0.0698588\pi\)
\(242\) −2.61015 + 3.59257i −0.167787 + 0.230939i
\(243\) 19.9991i 1.28295i
\(244\) −6.65118 4.83237i −0.425798 0.309361i
\(245\) 2.00240 + 0.995194i 0.127928 + 0.0635806i
\(246\) 1.54061 1.11932i 0.0982256 0.0713651i
\(247\) −8.37239 11.5236i −0.532722 0.733229i
\(248\) −1.87255 + 0.608430i −0.118907 + 0.0386353i
\(249\) −28.5248 −1.80768
\(250\) −5.82088 10.6243i −0.368145 0.671939i
\(251\) −11.1248 −0.702191 −0.351096 0.936340i \(-0.614191\pi\)
−0.351096 + 0.936340i \(0.614191\pi\)
\(252\) −3.34237 + 1.08600i −0.210549 + 0.0684117i
\(253\) −11.8701 16.3378i −0.746267 1.02715i
\(254\) −0.694046 + 0.504254i −0.0435483 + 0.0316397i
\(255\) 37.8851 + 18.8290i 2.37246 + 1.17912i
\(256\) 12.9253 + 9.39077i 0.807830 + 0.586923i
\(257\) 23.1468i 1.44386i 0.691966 + 0.721930i \(0.256745\pi\)
−0.691966 + 0.721930i \(0.743255\pi\)
\(258\) −1.64338 + 2.26192i −0.102313 + 0.140821i
\(259\) 2.20650 6.79092i 0.137106 0.421967i
\(260\) 4.08275 + 0.604887i 0.253201 + 0.0375135i
\(261\) −7.68289 23.6455i −0.475559 1.46362i
\(262\) 2.11895 + 0.688488i 0.130909 + 0.0425349i
\(263\) −27.5402 8.94835i −1.69820 0.551779i −0.709901 0.704301i \(-0.751260\pi\)
−0.988300 + 0.152522i \(0.951260\pi\)
\(264\) −9.90316 30.4788i −0.609497 1.87584i
\(265\) 3.76273 + 22.3116i 0.231143 + 1.37059i
\(266\) −2.13414 + 6.56820i −0.130852 + 0.402722i
\(267\) −2.21006 + 3.04189i −0.135253 + 0.186160i
\(268\) 2.27065i 0.138702i
\(269\) −7.60170 5.52296i −0.463484 0.336741i 0.331412 0.943486i \(-0.392475\pi\)
−0.794896 + 0.606745i \(0.792475\pi\)
\(270\) −8.07628 + 1.36202i −0.491507 + 0.0828899i
\(271\) −11.6500 + 8.46422i −0.707687 + 0.514165i −0.882427 0.470450i \(-0.844092\pi\)
0.174740 + 0.984615i \(0.444092\pi\)
\(272\) 6.87832 + 9.46719i 0.417059 + 0.574033i
\(273\) −5.72482 + 1.86011i −0.346482 + 0.112579i
\(274\) 8.62043 0.520779
\(275\) 11.1033 15.9429i 0.669551 0.961391i
\(276\) 11.5621 0.695958
\(277\) 2.72923 0.886780i 0.163984 0.0532815i −0.225875 0.974156i \(-0.572524\pi\)
0.389858 + 0.920875i \(0.372524\pi\)
\(278\) 9.61324 + 13.2315i 0.576564 + 0.793572i
\(279\) −2.21350 + 1.60820i −0.132519 + 0.0962804i
\(280\) −3.16923 6.06926i −0.189398 0.362707i
\(281\) −21.2310 15.4252i −1.26653 0.920191i −0.267476 0.963565i \(-0.586190\pi\)
−0.999059 + 0.0433733i \(0.986190\pi\)
\(282\) 5.03542i 0.299855i
\(283\) 12.6986 17.4781i 0.754854 1.03897i −0.242770 0.970084i \(-0.578056\pi\)
0.997625 0.0688841i \(-0.0219439\pi\)
\(284\) −3.25363 + 10.0137i −0.193068 + 0.594201i
\(285\) 17.0853 34.3767i 1.01204 2.03630i
\(286\) −2.90756 8.94854i −0.171927 0.529138i
\(287\) 0.620549 + 0.201628i 0.0366298 + 0.0119018i
\(288\) 17.4776 + 5.67882i 1.02988 + 0.334627i
\(289\) −9.99362 30.7572i −0.587860 1.80925i
\(290\) 12.5491 6.55287i 0.736910 0.384798i
\(291\) −9.21467 + 28.3598i −0.540174 + 1.66248i
\(292\) 4.94683 6.80872i 0.289491 0.398450i
\(293\) 25.5957i 1.49532i −0.664084 0.747658i \(-0.731178\pi\)
0.664084 0.747658i \(-0.268822\pi\)
\(294\) 2.36115 + 1.71547i 0.137705 + 0.100048i
\(295\) 1.19522 1.21935i 0.0695885 0.0709934i
\(296\) −17.6884 + 12.8514i −1.02812 + 0.746971i
\(297\) −7.72062 10.6265i −0.447996 0.616614i
\(298\) −3.86354 + 1.25534i −0.223809 + 0.0727199i
\(299\) 11.6147 0.671696
\(300\) 3.64803 + 10.5081i 0.210619 + 0.606687i
\(301\) −0.957977 −0.0552169
\(302\) 0.177346 0.0576233i 0.0102051 0.00331585i
\(303\) 13.1047 + 18.0371i 0.752845 + 1.03620i
\(304\) 8.59045 6.24133i 0.492696 0.357965i
\(305\) 3.26202 22.0173i 0.186783 1.26071i
\(306\) 26.2002 + 19.0356i 1.49777 + 1.08819i
\(307\) 13.8294i 0.789286i 0.918834 + 0.394643i \(0.129132\pi\)
−0.918834 + 0.394643i \(0.870868\pi\)
\(308\) 1.88638 2.59638i 0.107486 0.147942i
\(309\) −5.73983 + 17.6654i −0.326528 + 1.00495i
\(310\) −1.11258 1.09057i −0.0631905 0.0619400i
\(311\) 3.66490 + 11.2794i 0.207818 + 0.639597i 0.999586 + 0.0287752i \(0.00916069\pi\)
−0.791768 + 0.610821i \(0.790839\pi\)
\(312\) 17.5295 + 5.69569i 0.992414 + 0.322455i
\(313\) 2.49543 + 0.810816i 0.141050 + 0.0458300i 0.378691 0.925523i \(-0.376374\pi\)
−0.237641 + 0.971353i \(0.576374\pi\)
\(314\) 2.31125 + 7.11329i 0.130431 + 0.401426i
\(315\) −6.79467 6.66021i −0.382836 0.375261i
\(316\) −1.11214 + 3.42282i −0.0625628 + 0.192549i
\(317\) 12.6997 17.4796i 0.713285 0.981753i −0.286435 0.958100i \(-0.592470\pi\)
0.999720 0.0236532i \(-0.00752976\pi\)
\(318\) 29.5326i 1.65610i
\(319\) 18.3680 + 13.3451i 1.02841 + 0.747184i
\(320\) −2.62550 + 17.7211i −0.146770 + 0.990641i
\(321\) −26.1634 + 19.0088i −1.46030 + 1.06097i
\(322\) −3.31006 4.55591i −0.184463 0.253891i
\(323\) −42.5795 + 13.8349i −2.36919 + 0.769795i
\(324\) −3.02281 −0.167934
\(325\) 3.66462 + 10.5559i 0.203277 + 0.585537i
\(326\) 10.8558 0.601245
\(327\) −2.98481 + 0.969824i −0.165060 + 0.0536314i
\(328\) −1.17435 1.61635i −0.0648425 0.0892480i
\(329\) 1.39581 1.01412i 0.0769538 0.0559102i
\(330\) 17.7507 18.1090i 0.977144 0.996870i
\(331\) −23.0393 16.7390i −1.26636 0.920061i −0.267304 0.963612i \(-0.586133\pi\)
−0.999051 + 0.0435513i \(0.986133\pi\)
\(332\) 8.74680i 0.480043i
\(333\) −17.8584 + 24.5800i −0.978635 + 1.34698i
\(334\) 2.63013 8.09472i 0.143915 0.442923i
\(335\) 5.44917 2.84543i 0.297720 0.155463i
\(336\) −1.38665 4.26766i −0.0756477 0.232820i
\(337\) −6.24267 2.02836i −0.340060 0.110492i 0.134009 0.990980i \(-0.457215\pi\)
−0.474068 + 0.880488i \(0.657215\pi\)
\(338\) −8.24998 2.68058i −0.448740 0.145804i
\(339\) −16.1253 49.6287i −0.875808 2.69546i
\(340\) 5.77370 11.6171i 0.313123 0.630023i
\(341\) 0.772086 2.37624i 0.0418108 0.128680i
\(342\) 17.2727 23.7738i 0.934001 1.28554i
\(343\) 1.00000i 0.0539949i
\(344\) 2.37313 + 1.72418i 0.127950 + 0.0929614i
\(345\) 14.4889 + 27.7472i 0.780058 + 1.49386i
\(346\) 17.9891 13.0698i 0.967098 0.702637i
\(347\) 8.09221 + 11.1380i 0.434413 + 0.597918i 0.968959 0.247221i \(-0.0795175\pi\)
−0.534546 + 0.845139i \(0.679517\pi\)
\(348\) −12.3627 + 4.01688i −0.662709 + 0.215327i
\(349\) 14.7554 0.789836 0.394918 0.918716i \(-0.370773\pi\)
0.394918 + 0.918716i \(0.370773\pi\)
\(350\) 3.09622 4.44578i 0.165500 0.237637i
\(351\) 7.55451 0.403230
\(352\) −15.9604 + 5.18585i −0.850692 + 0.276407i
\(353\) 18.8654 + 25.9660i 1.00411 + 1.38203i 0.922773 + 0.385345i \(0.125918\pi\)
0.0813325 + 0.996687i \(0.474082\pi\)
\(354\) 1.80296 1.30992i 0.0958260 0.0696217i
\(355\) −28.1083 + 4.74032i −1.49184 + 0.251590i
\(356\) 0.932760 + 0.677690i 0.0494362 + 0.0359175i
\(357\) 18.9199i 1.00135i
\(358\) 0.108843 0.149809i 0.00575252 0.00791767i
\(359\) −0.329224 + 1.01325i −0.0173758 + 0.0534772i −0.959368 0.282156i \(-0.908950\pi\)
0.941993 + 0.335633i \(0.108950\pi\)
\(360\) 4.84482 + 28.7280i 0.255344 + 1.51410i
\(361\) 6.68236 + 20.5662i 0.351703 + 1.08243i
\(362\) 21.0270 + 6.83208i 1.10515 + 0.359086i
\(363\) 10.4985 + 3.41117i 0.551028 + 0.179040i
\(364\) 0.570381 + 1.75545i 0.0298961 + 0.0920107i
\(365\) 22.5389 + 3.33928i 1.17974 + 0.174786i
\(366\) 8.97723 27.6291i 0.469247 1.44419i
\(367\) 3.56817 4.91117i 0.186257 0.256361i −0.705669 0.708541i \(-0.749354\pi\)
0.891927 + 0.452180i \(0.149354\pi\)
\(368\) 8.65836i 0.451348i
\(369\) −2.24610 1.63189i −0.116927 0.0849526i
\(370\) −15.4924 7.69974i −0.805411 0.400290i
\(371\) −8.18641 + 5.94778i −0.425017 + 0.308793i
\(372\) 0.840822 + 1.15729i 0.0435946 + 0.0600028i
\(373\) 36.0268 11.7058i 1.86540 0.606104i 0.872274 0.489017i \(-0.162644\pi\)
0.993122 0.117087i \(-0.0373557\pi\)
\(374\) −29.5739 −1.52923
\(375\) −20.6463 + 21.9228i −1.06617 + 1.13209i
\(376\) −5.28297 −0.272448
\(377\) −12.4189 + 4.03514i −0.639606 + 0.207821i
\(378\) −2.15295 2.96329i −0.110736 0.152415i
\(379\) −0.378625 + 0.275087i −0.0194486 + 0.0141303i −0.597467 0.801893i \(-0.703826\pi\)
0.578018 + 0.816024i \(0.303826\pi\)
\(380\) −10.5412 5.23900i −0.540753 0.268755i
\(381\) 1.72529 + 1.25350i 0.0883892 + 0.0642185i
\(382\) 0.638371i 0.0326619i
\(383\) 1.01849 1.40183i 0.0520425 0.0716303i −0.782203 0.623024i \(-0.785904\pi\)
0.834245 + 0.551394i \(0.185904\pi\)
\(384\) −0.0358986 + 0.110485i −0.00183194 + 0.00563815i
\(385\) 8.59476 + 1.27337i 0.438030 + 0.0648971i
\(386\) 3.26370 + 10.0446i 0.166118 + 0.511259i
\(387\) 3.87671 + 1.25962i 0.197064 + 0.0640300i
\(388\) 8.69623 + 2.82558i 0.441484 + 0.143447i
\(389\) 1.42480 + 4.38509i 0.0722403 + 0.222333i 0.980657 0.195732i \(-0.0627084\pi\)
−0.908417 + 0.418065i \(0.862708\pi\)
\(390\) 2.42532 + 14.3813i 0.122811 + 0.728223i
\(391\) 11.2812 34.7199i 0.570513 1.75586i
\(392\) 1.79981 2.47723i 0.0909042 0.125119i
\(393\) 5.53844i 0.279377i
\(394\) −3.17641 2.30780i −0.160025 0.116265i
\(395\) −9.60785 + 1.62031i −0.483423 + 0.0815267i
\(396\) −11.0476 + 8.02658i −0.555165 + 0.403351i
\(397\) 18.8369 + 25.9268i 0.945398 + 1.30123i 0.953541 + 0.301262i \(0.0974078\pi\)
−0.00814343 + 0.999967i \(0.502592\pi\)
\(398\) 3.97623 1.29196i 0.199310 0.0647599i
\(399\) 17.1678 0.859463
\(400\) −7.86908 + 2.73185i −0.393454 + 0.136592i
\(401\) −36.7072 −1.83307 −0.916535 0.399956i \(-0.869026\pi\)
−0.916535 + 0.399956i \(0.869026\pi\)
\(402\) 7.63088 2.47942i 0.380593 0.123662i
\(403\) 0.844646 + 1.16256i 0.0420748 + 0.0579110i
\(404\) 5.53087 4.01841i 0.275171 0.199923i
\(405\) −3.78800 7.25425i −0.188227 0.360466i
\(406\) 5.12205 + 3.72139i 0.254203 + 0.184689i
\(407\) 27.7451i 1.37527i
\(408\) 34.0523 46.8689i 1.68584 2.32036i
\(409\) 5.85545 18.0212i 0.289533 0.891091i −0.695470 0.718555i \(-0.744804\pi\)
0.985003 0.172536i \(-0.0551962\pi\)
\(410\) 0.703596 1.41568i 0.0347481 0.0699155i
\(411\) −6.62193 20.3802i −0.326636 1.00528i
\(412\) 5.41689 + 1.76005i 0.266871 + 0.0867117i
\(413\) 0.726220 + 0.235963i 0.0357350 + 0.0116110i
\(414\) 7.40460 + 22.7890i 0.363916 + 1.12002i
\(415\) −20.9908 + 10.9609i −1.03040 + 0.538051i
\(416\) 2.98258 9.17945i 0.146233 0.450059i
\(417\) 23.8970 32.8914i 1.17024 1.61070i
\(418\) 26.8351i 1.31255i
\(419\) 22.8721 + 16.6176i 1.11738 + 0.811821i 0.983809 0.179219i \(-0.0573571\pi\)
0.133566 + 0.991040i \(0.457357\pi\)
\(420\) −3.48219 + 3.55249i −0.169913 + 0.173344i
\(421\) 19.1053 13.8808i 0.931134 0.676509i −0.0151360 0.999885i \(-0.504818\pi\)
0.946270 + 0.323377i \(0.104818\pi\)
\(422\) 6.64781 + 9.14992i 0.323610 + 0.445411i
\(423\) −6.98197 + 2.26858i −0.339475 + 0.110302i
\(424\) 30.9845 1.50474
\(425\) 35.1142 0.701872i 1.70329 0.0340458i
\(426\) −37.2053 −1.80260
\(427\) 9.46675 3.07593i 0.458128 0.148855i
\(428\) 5.82884 + 8.02271i 0.281747 + 0.387792i
\(429\) −18.9224 + 13.7480i −0.913584 + 0.663758i
\(430\) −0.340167 + 2.29599i −0.0164043 + 0.110723i
\(431\) −26.7969 19.4691i −1.29076 0.937792i −0.290939 0.956742i \(-0.593968\pi\)
−0.999820 + 0.0189497i \(0.993968\pi\)
\(432\) 5.63163i 0.270952i
\(433\) −14.3451 + 19.7443i −0.689381 + 0.948851i −0.999999 0.00168384i \(-0.999464\pi\)
0.310618 + 0.950535i \(0.399464\pi\)
\(434\) 0.215302 0.662631i 0.0103348 0.0318073i
\(435\) −25.1320 24.6346i −1.20499 1.18114i
\(436\) 0.297386 + 0.915259i 0.0142422 + 0.0438329i
\(437\) −31.5045 10.2364i −1.50706 0.489675i
\(438\) 28.2835 + 9.18987i 1.35144 + 0.439109i
\(439\) −3.83788 11.8118i −0.183172 0.563745i 0.816740 0.577006i \(-0.195779\pi\)
−0.999912 + 0.0132604i \(0.995779\pi\)
\(440\) −18.9993 18.6234i −0.905758 0.887835i
\(441\) 1.31487 4.04676i 0.0626130 0.192703i
\(442\) 9.99771 13.7607i 0.475543 0.654528i
\(443\) 7.55360i 0.358882i 0.983769 + 0.179441i \(0.0574289\pi\)
−0.983769 + 0.179441i \(0.942571\pi\)
\(444\) 12.8513 + 9.33699i 0.609894 + 0.443114i
\(445\) −0.457465 + 3.08771i −0.0216859 + 0.146371i
\(446\) −8.83240 + 6.41711i −0.418226 + 0.303859i
\(447\) 5.93569 + 8.16978i 0.280749 + 0.386417i
\(448\) −7.61952 + 2.47573i −0.359988 + 0.116967i
\(449\) −5.46297 −0.257813 −0.128907 0.991657i \(-0.541147\pi\)
−0.128907 + 0.991657i \(0.541147\pi\)
\(450\) −18.3753 + 13.9199i −0.866221 + 0.656190i
\(451\) 2.53532 0.119384
\(452\) −15.2181 + 4.94465i −0.715798 + 0.232577i
\(453\) −0.272463 0.375014i −0.0128014 0.0176197i
\(454\) −16.5711 + 12.0396i −0.777720 + 0.565046i
\(455\) −3.49803 + 3.56864i −0.163990 + 0.167301i
\(456\) −42.5284 30.8987i −1.99158 1.44697i
\(457\) 0.354917i 0.0166023i 0.999966 + 0.00830116i \(0.00264237\pi\)
−0.999966 + 0.00830116i \(0.997358\pi\)
\(458\) 10.0405 13.8195i 0.469160 0.645743i
\(459\) 7.33757 22.5827i 0.342488 1.05407i
\(460\) 8.50835 4.44287i 0.396704 0.207150i
\(461\) 6.46313 + 19.8915i 0.301018 + 0.926438i 0.981133 + 0.193333i \(0.0619296\pi\)
−0.680115 + 0.733105i \(0.738070\pi\)
\(462\) 10.7854 + 3.50438i 0.501781 + 0.163039i
\(463\) 8.89199 + 2.88918i 0.413246 + 0.134272i 0.508259 0.861204i \(-0.330289\pi\)
−0.0950132 + 0.995476i \(0.530289\pi\)
\(464\) −3.00806 9.25786i −0.139646 0.429785i
\(465\) −1.72364 + 3.46808i −0.0799320 + 0.160828i
\(466\) −0.0779800 + 0.239998i −0.00361236 + 0.0111177i
\(467\) −12.0224 + 16.5474i −0.556329 + 0.765721i −0.990854 0.134939i \(-0.956916\pi\)
0.434525 + 0.900660i \(0.356916\pi\)
\(468\) 7.85388i 0.363046i
\(469\) 2.22413 + 1.61593i 0.102701 + 0.0746165i
\(470\) −1.93491 3.70547i −0.0892508 0.170921i
\(471\) 15.0416 10.9284i 0.693082 0.503554i
\(472\) −1.37432 1.89159i −0.0632584 0.0870677i
\(473\) −3.54018 + 1.15027i −0.162778 + 0.0528896i
\(474\) −12.7173 −0.584127
\(475\) −0.636873 31.8623i −0.0292217 1.46194i
\(476\) 5.80158 0.265915
\(477\) 40.9491 13.3052i 1.87493 0.609201i
\(478\) 15.0123 + 20.6627i 0.686647 + 0.945089i
\(479\) 7.76930 5.64473i 0.354988 0.257914i −0.395970 0.918263i \(-0.629592\pi\)
0.750959 + 0.660349i \(0.229592\pi\)
\(480\) 25.6501 4.32574i 1.17076 0.197442i
\(481\) 12.9097 + 9.37945i 0.588632 + 0.427666i
\(482\) 3.18087i 0.144885i
\(483\) −8.22830 + 11.3253i −0.374400 + 0.515318i
\(484\) 1.04600 3.21925i 0.0475453 0.146329i
\(485\) 4.11667 + 24.4103i 0.186928 + 1.10842i
\(486\) −6.69637 20.6093i −0.303754 0.934858i
\(487\) −9.00420 2.92564i −0.408019 0.132574i 0.0978141 0.995205i \(-0.468815\pi\)
−0.505833 + 0.862631i \(0.668815\pi\)
\(488\) −28.9874 9.41858i −1.31220 0.426359i
\(489\) −8.33904 25.6649i −0.377104 1.16061i
\(490\) 2.39671 + 0.355089i 0.108272 + 0.0160413i
\(491\) −12.8195 + 39.4544i −0.578536 + 1.78055i 0.0452724 + 0.998975i \(0.485584\pi\)
−0.623809 + 0.781577i \(0.714416\pi\)
\(492\) −0.853206 + 1.17434i −0.0384655 + 0.0529432i
\(493\) 41.0431i 1.84849i
\(494\) −12.4863 9.07184i −0.561786 0.408161i
\(495\) −33.1066 16.4541i −1.48803 0.739555i
\(496\) −0.866645 + 0.629655i −0.0389135 + 0.0282723i
\(497\) −7.49305 10.3133i −0.336109 0.462615i
\(498\) −29.3950 + 9.55103i −1.31722 + 0.427992i
\(499\) 23.6709 1.05965 0.529827 0.848106i \(-0.322257\pi\)
0.529827 + 0.848106i \(0.322257\pi\)
\(500\) 6.72238 + 6.33095i 0.300634 + 0.283129i
\(501\) −21.1577 −0.945257
\(502\) −11.4642 + 3.72495i −0.511673 + 0.166253i
\(503\) 10.3206 + 14.2051i 0.460175 + 0.633376i 0.974545 0.224192i \(-0.0719743\pi\)
−0.514370 + 0.857568i \(0.671974\pi\)
\(504\) −10.5407 + 7.65823i −0.469518 + 0.341125i
\(505\) 16.5744 + 8.23753i 0.737553 + 0.366565i
\(506\) −17.7027 12.8618i −0.786980 0.571775i
\(507\) 21.5635i 0.957670i
\(508\) 0.384370 0.529040i 0.0170537 0.0234724i
\(509\) −4.63196 + 14.2557i −0.205308 + 0.631873i 0.794392 + 0.607405i \(0.207789\pi\)
−0.999701 + 0.0244686i \(0.992211\pi\)
\(510\) 45.3456 + 6.71826i 2.00794 + 0.297489i
\(511\) 3.14879 + 9.69099i 0.139294 + 0.428704i
\(512\) 16.5460 + 5.37613i 0.731237 + 0.237593i
\(513\) −20.4914 6.65804i −0.904715 0.293960i
\(514\) 7.75032 + 23.8530i 0.341852 + 1.05211i
\(515\) 2.56428 + 15.2052i 0.112996 + 0.670022i
\(516\) 0.658572 2.02688i 0.0289920 0.0892282i
\(517\) 3.94051 5.42365i 0.173303 0.238532i
\(518\) 7.73692i 0.339941i
\(519\) −44.7179 32.4895i −1.96290 1.42613i
\(520\) 15.0883 2.54456i 0.661665 0.111586i
\(521\) 11.2778 8.19378i 0.494088 0.358976i −0.312666 0.949863i \(-0.601222\pi\)
0.806754 + 0.590887i \(0.201222\pi\)
\(522\) −15.8346 21.7944i −0.693061 0.953916i
\(523\) −3.89819 + 1.26660i −0.170456 + 0.0553845i −0.393002 0.919538i \(-0.628563\pi\)
0.222546 + 0.974922i \(0.428563\pi\)
\(524\) −1.69830 −0.0741906
\(525\) −12.8890 3.90491i −0.562524 0.170424i
\(526\) −31.3767 −1.36809
\(527\) 4.29562 1.39573i 0.187120 0.0607990i
\(528\) −10.2486 14.1060i −0.446014 0.613886i
\(529\) 3.24513 2.35772i 0.141092 0.102510i
\(530\) 11.3482 + 21.7325i 0.492934 + 0.943998i
\(531\) −2.62858 1.90978i −0.114071 0.0828772i
\(532\) 5.26430i 0.228236i
\(533\) −0.857086 + 1.17968i −0.0371245 + 0.0510975i
\(534\) −1.25896 + 3.87469i −0.0544807 + 0.167674i
\(535\) −11.9488 + 24.0418i −0.516592 + 1.03942i
\(536\) −2.60132 8.00603i −0.112360 0.345808i
\(537\) −0.437785 0.142245i −0.0188918 0.00613832i
\(538\) −9.68290 3.14616i −0.417459 0.135641i
\(539\) 1.20073 + 3.69547i 0.0517192 + 0.159175i
\(540\) 5.53406 2.88976i 0.238148 0.124355i
\(541\) 0.708335 2.18003i 0.0304537 0.0937269i −0.934674 0.355505i \(-0.884309\pi\)
0.965128 + 0.261778i \(0.0843089\pi\)
\(542\) −9.17134 + 12.6233i −0.393943 + 0.542216i
\(543\) 54.9597i 2.35855i
\(544\) −24.5432 17.8317i −1.05228 0.764527i
\(545\) −1.82380 + 1.86062i −0.0781231 + 0.0797002i
\(546\) −5.27666 + 3.83372i −0.225820 + 0.164068i
\(547\) 6.30500 + 8.67808i 0.269582 + 0.371048i 0.922249 0.386597i \(-0.126350\pi\)
−0.652666 + 0.757645i \(0.726350\pi\)
\(548\) −6.24936 + 2.03054i −0.266960 + 0.0867404i
\(549\) −42.3542 −1.80763
\(550\) 6.10382 20.1470i 0.260268 0.859071i
\(551\) 37.2421 1.58657
\(552\) 40.7667 13.2459i 1.73515 0.563783i
\(553\) −2.56124 3.52524i −0.108915 0.149908i
\(554\) 2.51557 1.82767i 0.106877 0.0776503i
\(555\) −6.30280 + 42.5414i −0.267539 + 1.80578i
\(556\) −10.0858 7.32775i −0.427732 0.310766i
\(557\) 16.7497i 0.709709i −0.934922 0.354854i \(-0.884530\pi\)
0.934922 0.354854i \(-0.115470\pi\)
\(558\) −1.74255 + 2.39842i −0.0737682 + 0.101533i
\(559\) 0.661567 2.03609i 0.0279813 0.0861176i
\(560\) −2.66030 2.60766i −0.112418 0.110194i
\(561\) 22.7177 + 69.9180i 0.959144 + 2.95194i
\(562\) −27.0436 8.78700i −1.14077 0.370657i
\(563\) 17.8470 + 5.79885i 0.752162 + 0.244392i 0.659911 0.751343i \(-0.270594\pi\)
0.0922510 + 0.995736i \(0.470594\pi\)
\(564\) 1.18609 + 3.65041i 0.0499435 + 0.153710i
\(565\) −30.9367 30.3245i −1.30152 1.27576i
\(566\) 7.23379 22.2633i 0.304059 0.935797i
\(567\) 2.15121 2.96089i 0.0903425 0.124346i
\(568\) 39.0345i 1.63785i
\(569\) 19.2376 + 13.9770i 0.806483 + 0.585944i 0.912809 0.408387i \(-0.133909\pi\)
−0.106326 + 0.994331i \(0.533909\pi\)
\(570\) 6.09609 41.1462i 0.255337 1.72342i
\(571\) −22.4615 + 16.3193i −0.939986 + 0.682940i −0.948417 0.317024i \(-0.897316\pi\)
0.00843096 + 0.999964i \(0.497316\pi\)
\(572\) 4.21566 + 5.80235i 0.176265 + 0.242609i
\(573\) 1.50922 0.490376i 0.0630486 0.0204857i
\(574\) 0.706994 0.0295093
\(575\) 21.3243 + 14.8511i 0.889284 + 0.619333i
\(576\) 34.0897 1.42040
\(577\) −20.4243 + 6.63627i −0.850277 + 0.276272i −0.701562 0.712609i \(-0.747514\pi\)
−0.148715 + 0.988880i \(0.547514\pi\)
\(578\) −20.5970 28.3494i −0.856724 1.17918i
\(579\) 21.2402 15.4319i 0.882714 0.641329i
\(580\) −7.55394 + 7.70644i −0.313660 + 0.319992i
\(581\) −8.56762 6.22474i −0.355445 0.258246i
\(582\) 32.3105i 1.33931i
\(583\) −23.1110 + 31.8095i −0.957159 + 1.31742i
\(584\) 9.64167 29.6740i 0.398975 1.22792i
\(585\) 18.8480 9.84200i 0.779269 0.406917i
\(586\) −8.57028 26.3766i −0.354035 1.08961i
\(587\) 0.826003 + 0.268385i 0.0340928 + 0.0110774i 0.326014 0.945365i \(-0.394294\pi\)
−0.291921 + 0.956442i \(0.594294\pi\)
\(588\) −2.11579 0.687461i −0.0872536 0.0283504i
\(589\) −1.26647 3.89781i −0.0521842 0.160606i
\(590\) 0.823409 1.65675i 0.0338992 0.0682075i
\(591\) −3.01602 + 9.28237i −0.124063 + 0.381826i
\(592\) −6.99206 + 9.62374i −0.287372 + 0.395533i
\(593\) 1.48792i 0.0611015i −0.999533 0.0305507i \(-0.990274\pi\)
0.999533 0.0305507i \(-0.00972611\pi\)
\(594\) −11.5143 8.36562i −0.472437 0.343246i
\(595\) 7.27018 + 13.9228i 0.298048 + 0.570780i
\(596\) 2.50517 1.82011i 0.102616 0.0745548i
\(597\) −6.10882 8.40807i −0.250017 0.344119i
\(598\) 11.9691 3.88899i 0.489452 0.159033i
\(599\) −18.2242 −0.744622 −0.372311 0.928108i \(-0.621435\pi\)
−0.372311 + 0.928108i \(0.621435\pi\)
\(600\) 24.9010 + 32.8712i 1.01658 + 1.34196i
\(601\) 39.6429 1.61707 0.808534 0.588450i \(-0.200262\pi\)
0.808534 + 0.588450i \(0.200262\pi\)
\(602\) −0.987205 + 0.320762i −0.0402355 + 0.0130733i
\(603\) −6.87580 9.46373i −0.280004 0.385393i
\(604\) −0.114994 + 0.0835479i −0.00467903 + 0.00339951i
\(605\) 9.03643 1.52394i 0.367383 0.0619571i
\(606\) 19.5439 + 14.1995i 0.793918 + 0.576815i
\(607\) 37.1742i 1.50885i −0.656385 0.754426i \(-0.727915\pi\)
0.656385 0.754426i \(-0.272085\pi\)
\(608\) −16.1803 + 22.2703i −0.656198 + 0.903180i
\(609\) 4.86342 14.9681i 0.197076 0.606537i
\(610\) −4.01059 23.7813i −0.162384 0.962877i
\(611\) 1.19149 + 3.66702i 0.0482024 + 0.148352i
\(612\) −23.4776 7.62834i −0.949026 0.308357i
\(613\) 25.4549 + 8.27079i 1.02811 + 0.334054i 0.774044 0.633132i \(-0.218231\pi\)
0.254069 + 0.967186i \(0.418231\pi\)
\(614\) 4.63054 + 14.2514i 0.186874 + 0.575138i
\(615\) −3.88740 0.575944i −0.156755 0.0232243i
\(616\) 3.67667 11.3156i 0.148137 0.455919i
\(617\) 3.54694 4.88195i 0.142794 0.196540i −0.731629 0.681703i \(-0.761240\pi\)
0.874424 + 0.485163i \(0.161240\pi\)
\(618\) 20.1262i 0.809596i
\(619\) −16.4516 11.9528i −0.661246 0.480424i 0.205837 0.978586i \(-0.434008\pi\)
−0.867084 + 0.498163i \(0.834008\pi\)
\(620\) 1.06345 + 0.528535i 0.0427091 + 0.0212265i
\(621\) 14.2135 10.3267i 0.570366 0.414395i
\(622\) 7.55344 + 10.3964i 0.302865 + 0.416858i
\(623\) −1.32762 + 0.431368i −0.0531898 + 0.0172824i
\(624\) 10.0281 0.401446
\(625\) −6.76914 + 24.0661i −0.270765 + 0.962645i
\(626\) 2.84306 0.113631
\(627\) 63.4430 20.6139i 2.53367 0.823239i
\(628\) −3.35107 4.61235i −0.133722 0.184053i
\(629\) 40.5770 29.4809i 1.61791 1.17548i
\(630\) −9.23203 4.58834i −0.367813 0.182804i
\(631\) 14.5049 + 10.5384i 0.577432 + 0.419529i 0.837797 0.545981i \(-0.183843\pi\)
−0.260366 + 0.965510i \(0.583843\pi\)
\(632\) 13.3426i 0.530739i
\(633\) 16.5254 22.7453i 0.656826 0.904043i
\(634\) 7.23440 22.2652i 0.287315 0.884264i
\(635\) 1.75128 + 0.259464i 0.0694973 + 0.0102965i
\(636\) −6.95639 21.4096i −0.275839 0.848945i
\(637\) −2.12541 0.690588i −0.0842118 0.0273621i
\(638\) 23.3968 + 7.60208i 0.926288 + 0.300969i
\(639\) 16.7619 + 51.5879i 0.663092 + 2.04079i
\(640\) 0.0160378 + 0.0950981i 0.000633948 + 0.00375908i
\(641\) 0.606586 1.86688i 0.0239587 0.0737373i −0.938362 0.345653i \(-0.887657\pi\)
0.962321 + 0.271916i \(0.0876573\pi\)
\(642\) −20.5968 + 28.3491i −0.812893 + 1.11885i
\(643\) 44.6024i 1.75895i −0.475948 0.879474i \(-0.657895\pi\)
0.475948 0.879474i \(-0.342105\pi\)
\(644\) 3.47277 + 2.52311i 0.136846 + 0.0994247i
\(645\) 5.68944 0.959493i 0.224022 0.0377800i
\(646\) −39.2462 + 28.5140i −1.54412 + 1.12187i
\(647\) 12.3281 + 16.9682i 0.484668 + 0.667088i 0.979394 0.201961i \(-0.0647314\pi\)
−0.494726 + 0.869049i \(0.664731\pi\)
\(648\) −10.6581 + 3.46302i −0.418689 + 0.136040i
\(649\) 2.96706 0.116467
\(650\) 7.31090 + 9.65095i 0.286757 + 0.378541i
\(651\) −1.73197 −0.0678811
\(652\) −7.86986 + 2.55707i −0.308207 + 0.100143i
\(653\) −14.5892 20.0803i −0.570920 0.785805i 0.421743 0.906715i \(-0.361418\pi\)
−0.992663 + 0.120911i \(0.961418\pi\)
\(654\) −2.75115 + 1.99883i −0.107578 + 0.0781603i
\(655\) −2.12820 4.07563i −0.0831558 0.159248i
\(656\) −0.879409 0.638928i −0.0343352 0.0249460i
\(657\) 43.3574i 1.69153i
\(658\) 1.09884 1.51242i 0.0428373 0.0589604i
\(659\) 4.63827 14.2751i 0.180681 0.556080i −0.819166 0.573557i \(-0.805563\pi\)
0.999847 + 0.0174764i \(0.00556321\pi\)
\(660\) −8.60275 + 17.3093i −0.334862 + 0.673763i
\(661\) 6.93189 + 21.3342i 0.269619 + 0.829803i 0.990593 + 0.136841i \(0.0436949\pi\)
−0.720974 + 0.692963i \(0.756305\pi\)
\(662\) −29.3470 9.53543i −1.14060 0.370605i
\(663\) −40.2126 13.0659i −1.56173 0.507436i
\(664\) 10.0206 + 30.8402i 0.388874 + 1.19683i
\(665\) 12.6334 6.59690i 0.489904 0.255817i
\(666\) −10.1731 + 31.3095i −0.394199 + 1.21322i
\(667\) −17.8497 + 24.5680i −0.691143 + 0.951277i
\(668\) 6.48778i 0.251020i
\(669\) 21.9559 + 15.9519i 0.848866 + 0.616737i
\(670\) 4.66268 4.75681i 0.180135 0.183771i
\(671\) 31.2908 22.7341i 1.20797 0.877639i
\(672\) 6.83773 + 9.41133i 0.263771 + 0.363050i
\(673\) 35.4813 11.5286i 1.36770 0.444394i 0.469096 0.883147i \(-0.344580\pi\)
0.898607 + 0.438754i \(0.144580\pi\)
\(674\) −7.11229 −0.273955
\(675\) 13.8699 + 9.65954i 0.533852 + 0.371796i
\(676\) 6.61221 0.254316
\(677\) −27.9149 + 9.07011i −1.07286 + 0.348592i −0.791600 0.611040i \(-0.790751\pi\)
−0.281257 + 0.959632i \(0.590751\pi\)
\(678\) −33.2346 45.7436i −1.27637 1.75677i
\(679\) −8.95645 + 6.50724i −0.343717 + 0.249725i
\(680\) 7.04855 47.5749i 0.270299 1.82441i
\(681\) 41.1931 + 29.9285i 1.57852 + 1.14686i
\(682\) 2.70726i 0.103666i
\(683\) −4.07402 + 5.60741i −0.155888 + 0.214562i −0.879816 0.475314i \(-0.842335\pi\)
0.723928 + 0.689875i \(0.242335\pi\)
\(684\) −6.92189 + 21.3034i −0.264665 + 0.814555i
\(685\) −12.7043 12.4529i −0.485405 0.475800i
\(686\) 0.334833 + 1.03051i 0.0127840 + 0.0393451i
\(687\) −40.3845 13.1217i −1.54077 0.500625i
\(688\) 1.51784 + 0.493175i 0.0578670 + 0.0188021i
\(689\) −6.98803 21.5069i −0.266223 0.819349i
\(690\) 24.2217 + 23.7423i 0.922103 + 0.903856i
\(691\) 4.66411 14.3546i 0.177431 0.546077i −0.822305 0.569047i \(-0.807312\pi\)
0.999736 + 0.0229703i \(0.00731231\pi\)
\(692\) −9.96254 + 13.7123i −0.378719 + 0.521262i
\(693\) 16.5335i 0.628056i
\(694\) 12.0685 + 8.76825i 0.458113 + 0.332838i
\(695\) 4.94649 33.3868i 0.187631 1.26644i
\(696\) −38.9875 + 28.3261i −1.47782 + 1.07370i
\(697\) 2.69394 + 3.70789i 0.102040 + 0.140446i
\(698\) 15.2055 4.94058i 0.575538 0.187004i
\(699\) 0.627299 0.0237266
\(700\) −1.19740 + 3.95228i −0.0452574 + 0.149382i
\(701\) −22.7749 −0.860195 −0.430098 0.902782i \(-0.641521\pi\)
−0.430098 + 0.902782i \(0.641521\pi\)
\(702\) 7.78500 2.52950i 0.293826 0.0954698i
\(703\) −26.7507 36.8192i −1.00892 1.38866i
\(704\) −25.1850 + 18.2980i −0.949196 + 0.689632i
\(705\) −7.27404 + 7.42089i −0.273956 + 0.279487i
\(706\) 28.1353 + 20.4415i 1.05889 + 0.769325i
\(707\) 8.27731i 0.311300i
\(708\) −0.998496 + 1.37431i −0.0375258 + 0.0516498i
\(709\) 8.80251 27.0913i 0.330585 1.01744i −0.638271 0.769812i \(-0.720350\pi\)
0.968856 0.247625i \(-0.0796499\pi\)
\(710\) −27.3787 + 14.2965i −1.02750 + 0.536540i
\(711\) 5.72948 + 17.6335i 0.214872 + 0.661309i
\(712\) 4.06519 + 1.32086i 0.152349 + 0.0495013i
\(713\) 3.17832 + 1.03270i 0.119029 + 0.0386749i
\(714\) 6.33501 + 19.4972i 0.237082 + 0.729663i
\(715\) −8.64187 + 17.3880i −0.323188 + 0.650275i
\(716\) −0.0436178 + 0.134242i −0.00163007 + 0.00501685i
\(717\) 37.3182 51.3641i 1.39367 1.91823i
\(718\) 1.15440i 0.0430817i
\(719\) −8.44303 6.13422i −0.314872 0.228768i 0.419112 0.907934i \(-0.362341\pi\)
−0.733984 + 0.679167i \(0.762341\pi\)
\(720\) 7.33687 + 14.0505i 0.273429 + 0.523632i
\(721\) −5.57898 + 4.05337i −0.207772 + 0.150955i
\(722\) 13.7725 + 18.9562i 0.512558 + 0.705476i
\(723\) −7.52013 + 2.44344i −0.279677 + 0.0908725i
\(724\) −16.8528 −0.626328
\(725\) −27.9603 8.47095i −1.03842 0.314603i
\(726\) 11.9610 0.443913
\(727\) −24.0315 + 7.80830i −0.891279 + 0.289594i −0.718633 0.695390i \(-0.755232\pi\)
−0.172646 + 0.984984i \(0.555232\pi\)
\(728\) 4.02220 + 5.53608i 0.149073 + 0.205181i
\(729\) −34.6974 + 25.2092i −1.28509 + 0.933673i
\(730\) 24.3446 4.10559i 0.901035 0.151955i
\(731\) −5.44393 3.95524i −0.201351 0.146290i
\(732\) 22.1442i 0.818474i
\(733\) −15.9868 + 22.0040i −0.590488 + 0.812736i −0.994796 0.101886i \(-0.967512\pi\)
0.404308 + 0.914623i \(0.367512\pi\)
\(734\) 2.03262 6.25575i 0.0750253 0.230904i
\(735\) −1.00158 5.93902i −0.0369439 0.219064i
\(736\) −6.93630 21.3477i −0.255676 0.786888i
\(737\) 10.1595 + 3.30103i 0.374230 + 0.121595i
\(738\) −2.86104 0.929607i −0.105316 0.0342193i
\(739\) 15.5929 + 47.9900i 0.573594 + 1.76534i 0.640917 + 0.767610i \(0.278554\pi\)
−0.0673231 + 0.997731i \(0.521446\pi\)
\(740\) 13.0448 + 1.93268i 0.479538 + 0.0710468i
\(741\) −11.8558 + 36.4885i −0.435535 + 1.34044i
\(742\) −6.44467 + 8.87032i −0.236591 + 0.325640i
\(743\) 12.4526i 0.456841i −0.973563 0.228421i \(-0.926644\pi\)
0.973563 0.228421i \(-0.0733562\pi\)
\(744\) 4.29047 + 3.11721i 0.157296 + 0.114282i
\(745\) 7.50729 + 3.73114i 0.275046 + 0.136698i
\(746\) 33.2065 24.1259i 1.21578 0.883312i
\(747\) 26.4864 + 36.4554i 0.969087 + 1.33383i
\(748\) 21.4396 6.96614i 0.783908 0.254707i
\(749\) −12.0065 −0.438708
\(750\) −13.9357 + 29.5047i −0.508860 + 1.07736i
\(751\) 25.4002 0.926868 0.463434 0.886131i \(-0.346617\pi\)
0.463434 + 0.886131i \(0.346617\pi\)
\(752\) −2.73363 + 0.888212i −0.0996854 + 0.0323897i
\(753\) 17.6129 + 24.2420i 0.641849 + 0.883429i
\(754\) −11.4467 + 8.31651i −0.416864 + 0.302870i
\(755\) −0.344604 0.171269i −0.0125414 0.00623311i
\(756\) 2.25878 + 1.64110i 0.0821511 + 0.0596862i
\(757\) 49.1681i 1.78705i −0.449018 0.893523i \(-0.648226\pi\)
0.449018 0.893523i \(-0.351774\pi\)
\(758\) −0.298068 + 0.410256i −0.0108263 + 0.0149012i
\(759\) −16.8088 + 51.7322i −0.610122 + 1.87776i
\(760\) −43.1691 6.39579i −1.56591 0.232000i
\(761\) 1.49278 + 4.59430i 0.0541131 + 0.166543i 0.974461 0.224559i \(-0.0720940\pi\)
−0.920347 + 0.391102i \(0.872094\pi\)
\(762\) 2.19764 + 0.714056i 0.0796120 + 0.0258675i
\(763\) −1.10815 0.360059i −0.0401176 0.0130350i
\(764\) −0.150368 0.462786i −0.00544013 0.0167430i
\(765\) −11.1140 65.9017i −0.401826 2.38268i
\(766\) 0.580186 1.78563i 0.0209630 0.0645173i
\(767\) −1.00304 + 1.38056i −0.0362176 + 0.0498492i
\(768\) 43.0330i 1.55282i
\(769\) 15.6362 + 11.3604i 0.563856 + 0.409665i 0.832868 0.553471i \(-0.186697\pi\)
−0.269012 + 0.963137i \(0.586697\pi\)
\(770\) 9.28335 1.56559i 0.334549 0.0564198i
\(771\) 50.4392 36.6463i 1.81652 1.31978i
\(772\) −4.73203 6.51308i −0.170309 0.234411i
\(773\) 42.0704 13.6695i 1.51317 0.491658i 0.569341 0.822101i \(-0.307198\pi\)
0.943826 + 0.330443i \(0.107198\pi\)
\(774\) 4.41675 0.158757
\(775\) 0.0642507 + 3.21442i 0.00230795 + 0.115466i
\(776\) 33.8990 1.21690
\(777\) −18.2914 + 5.94325i −0.656202 + 0.213213i
\(778\) 2.93654 + 4.04181i 0.105280 + 0.144906i
\(779\) 3.36451 2.44446i 0.120546 0.0875818i
\(780\) −5.14573 9.85438i −0.184247 0.352843i
\(781\) −40.0739 29.1154i −1.43396 1.04183i
\(782\) 39.5565i 1.41454i
\(783\) −11.6099 + 15.9797i −0.414904 + 0.571067i
\(784\) 0.514809 1.58442i 0.0183860 0.0565864i
\(785\) 6.86952 13.8219i 0.245184 0.493325i
\(786\) −1.85445 5.70741i −0.0661461 0.203577i
\(787\) 49.0264 + 15.9296i 1.74760 + 0.567830i 0.995800 0.0915580i \(-0.0291847\pi\)
0.751802 + 0.659388i \(0.229185\pi\)
\(788\) 2.84633 + 0.924830i 0.101396 + 0.0329457i
\(789\) 24.1025 + 74.1799i 0.858072 + 2.64088i
\(790\) −9.35845 + 4.88677i −0.332959 + 0.173864i
\(791\) 5.98673 18.4253i 0.212864 0.655127i
\(792\) −29.7572 + 40.9573i −1.05738 + 1.45535i
\(793\) 22.2449i 0.789941i
\(794\) 28.0928 + 20.4106i 0.996976 + 0.724345i
\(795\) 42.6621 43.5233i 1.51307 1.54361i
\(796\) −2.57824 + 1.87320i −0.0913833 + 0.0663939i
\(797\) −1.21019 1.66569i −0.0428672 0.0590017i 0.787045 0.616895i \(-0.211610\pi\)
−0.829913 + 0.557893i \(0.811610\pi\)
\(798\) 17.6915 5.74833i 0.626274 0.203489i
\(799\) 12.1191 0.428742
\(800\) 17.2132 13.0395i 0.608578 0.461018i
\(801\) 5.93974 0.209870
\(802\) −37.8271 + 12.2908i −1.33572 + 0.434002i
\(803\) 23.2726 + 32.0319i 0.821271 + 1.13038i
\(804\) −4.94796 + 3.59490i −0.174501 + 0.126782i
\(805\) −1.70319 + 11.4959i −0.0600296 + 0.405176i
\(806\) 1.25968 + 0.915210i 0.0443703 + 0.0322369i
\(807\) 25.3089i 0.890914i
\(808\) 14.8976 20.5048i 0.524095 0.721355i
\(809\) 14.1045 43.4092i 0.495888 1.52619i −0.319681 0.947525i \(-0.603576\pi\)
0.815569 0.578660i \(-0.196424\pi\)
\(810\) −6.33254 6.20722i −0.222503 0.218100i
\(811\) −14.5558 44.7982i −0.511123 1.57308i −0.790227 0.612815i \(-0.790037\pi\)
0.279103 0.960261i \(-0.409963\pi\)
\(812\) −4.58979 1.49131i −0.161070 0.0523349i
\(813\) 36.8887 + 11.9859i 1.29374 + 0.420363i
\(814\) −9.28997 28.5916i −0.325613 1.00213i
\(815\) −15.9986 15.6820i −0.560405 0.549316i
\(816\) 9.74014 29.9771i 0.340973 1.04941i
\(817\) −3.58895 + 4.93977i −0.125562 + 0.172821i
\(818\) 20.5316i 0.717872i
\(819\) 7.69300 + 5.58929i 0.268815 + 0.195306i
\(820\) −0.176607 + 1.19203i −0.00616738 + 0.0416274i
\(821\) −15.0760 + 10.9534i −0.526157 + 0.382276i −0.818918 0.573910i \(-0.805426\pi\)
0.292761 + 0.956186i \(0.405426\pi\)
\(822\) −13.6479 18.7848i −0.476026 0.655194i
\(823\) −20.6075 + 6.69579i −0.718334 + 0.233401i −0.645301 0.763929i \(-0.723268\pi\)
−0.0730330 + 0.997330i \(0.523268\pi\)
\(824\) 21.1157 0.735600
\(825\) −52.3198 + 1.04578i −1.82154 + 0.0364095i
\(826\) 0.827386 0.0287884
\(827\) −10.5250 + 3.41978i −0.365990 + 0.118917i −0.486238 0.873827i \(-0.661631\pi\)
0.120248 + 0.992744i \(0.461631\pi\)
\(828\) −10.7359 14.7767i −0.373098 0.513526i
\(829\) 23.5312 17.0964i 0.817272 0.593783i −0.0986576 0.995121i \(-0.531455\pi\)
0.915930 + 0.401338i \(0.131455\pi\)
\(830\) −17.9612 + 18.3238i −0.623442 + 0.636028i
\(831\) −6.25332 4.54330i −0.216925 0.157605i
\(832\) 17.9043i 0.620720i
\(833\) −4.12875 + 5.68273i −0.143053 + 0.196895i
\(834\) 13.6130 41.8964i 0.471379 1.45075i
\(835\) −15.5696 + 8.13008i −0.538807 + 0.281353i
\(836\) −6.32102 19.4541i −0.218617 0.672834i
\(837\) 2.06726 + 0.671695i 0.0714551 + 0.0232172i
\(838\) 29.1340 + 9.46622i 1.00642 + 0.327005i
\(839\) −5.14999 15.8500i −0.177797 0.547204i 0.821953 0.569556i \(-0.192885\pi\)
−0.999750 + 0.0223515i \(0.992885\pi\)
\(840\) −8.20796 + 16.5150i −0.283202 + 0.569820i
\(841\) 1.58877 4.88972i 0.0547850 0.168611i
\(842\) 15.0404 20.7014i 0.518327 0.713417i
\(843\) 70.6858i 2.43455i
\(844\) −6.97458 5.06733i −0.240075 0.174425i
\(845\) 8.28602 + 15.8682i 0.285048 + 0.545883i
\(846\) −6.43540 + 4.67559i −0.221253 + 0.160750i
\(847\) 2.40891 + 3.31558i 0.0827710 + 0.113925i
\(848\) 16.0327 5.20933i 0.550565 0.178889i
\(849\) −58.1912 −1.99712
\(850\) 35.9505 12.4807i 1.23309 0.428084i
\(851\) 37.1103 1.27212
\(852\) 26.9719 8.76371i 0.924043 0.300240i
\(853\) −15.2772 21.0273i −0.523083 0.719962i 0.462974 0.886372i \(-0.346782\pi\)
−0.986057 + 0.166410i \(0.946782\pi\)
\(854\) 8.72566 6.33956i 0.298586 0.216935i
\(855\) −59.7986 + 10.0847i −2.04507 + 0.344890i
\(856\) 29.7429 + 21.6094i 1.01659 + 0.738596i
\(857\) 6.76094i 0.230949i −0.993310 0.115475i \(-0.963161\pi\)
0.993310 0.115475i \(-0.0368389\pi\)
\(858\) −14.8965 + 20.5033i −0.508558 + 0.699970i
\(859\) 2.69769 8.30264i 0.0920440 0.283282i −0.894428 0.447212i \(-0.852417\pi\)
0.986472 + 0.163930i \(0.0524170\pi\)
\(860\) −0.294218 1.74460i −0.0100327 0.0594905i
\(861\) −0.543089 1.67146i −0.0185084 0.0569631i
\(862\) −34.1333 11.0906i −1.16259 0.377747i
\(863\) −37.8185 12.2880i −1.28736 0.418288i −0.416191 0.909277i \(-0.636635\pi\)
−0.871166 + 0.490989i \(0.836635\pi\)
\(864\) −4.51155 13.8851i −0.153486 0.472382i
\(865\) −45.3915 6.72507i −1.54336 0.228659i
\(866\) −8.17170 + 25.1499i −0.277686 + 0.854629i
\(867\) −51.2010 + 70.4721i −1.73888 + 2.39336i
\(868\) 0.531088i 0.0180263i
\(869\) −13.6978 9.95207i −0.464668 0.337601i
\(870\) −34.1472 16.9712i −1.15770 0.575379i
\(871\) −4.97046 + 3.61125i −0.168418 + 0.122363i
\(872\) 2.09709 + 2.88640i 0.0710166 + 0.0977459i
\(873\) 44.8008 14.5567i 1.51628 0.492669i
\(874\) −35.8932 −1.21411
\(875\) −10.9853 + 2.07920i −0.371371 + 0.0702897i
\(876\) −22.6687 −0.765906
\(877\) 37.8198 12.2884i 1.27708 0.414950i 0.409532 0.912296i \(-0.365692\pi\)
0.867552 + 0.497346i \(0.165692\pi\)
\(878\) −7.90995 10.8871i −0.266948 0.367422i
\(879\) −55.7756 + 40.5233i −1.88126 + 1.36682i
\(880\) −12.9622 6.44222i −0.436954 0.217167i
\(881\) −26.7746 19.4529i −0.902058 0.655384i 0.0369355 0.999318i \(-0.488240\pi\)
−0.938994 + 0.343934i \(0.888240\pi\)
\(882\) 4.61049i 0.155243i
\(883\) −26.3380 + 36.2512i −0.886345 + 1.21995i 0.0882779 + 0.996096i \(0.471864\pi\)
−0.974623 + 0.223853i \(0.928136\pi\)
\(884\) −4.00650 + 12.3307i −0.134753 + 0.414727i
\(885\) −4.54937 0.674020i −0.152925 0.0226570i
\(886\) 2.52919 + 7.78406i 0.0849699 + 0.261511i
\(887\) −27.1205 8.81200i −0.910618 0.295878i −0.184006 0.982925i \(-0.558906\pi\)
−0.726613 + 0.687047i \(0.758906\pi\)
\(888\) 56.0088 + 18.1984i 1.87953 + 0.610697i
\(889\) 0.244662 + 0.752993i 0.00820571 + 0.0252546i
\(890\) 0.562444 + 3.33509i 0.0188532 + 0.111792i
\(891\) 4.39452 13.5249i 0.147222 0.453102i
\(892\) 4.89148 6.73255i 0.163779 0.225422i
\(893\) 10.9968i 0.367992i
\(894\) 8.85230 + 6.43157i 0.296065 + 0.215104i
\(895\) −0.376817 + 0.0635481i −0.0125956 + 0.00212418i
\(896\) −0.0348927 + 0.0253510i −0.00116568 + 0.000846917i
\(897\) −18.3885 25.3096i −0.613974 0.845063i
\(898\) −5.62964 + 1.82918i −0.187864 + 0.0610406i
\(899\) −3.75716 −0.125308
\(900\) 10.0423 14.4195i 0.334744 0.480650i
\(901\) −71.0781 −2.36795
\(902\) 2.61268 0.848910i 0.0869926 0.0282656i
\(903\) 1.51668 + 2.08753i 0.0504718 + 0.0694685i
\(904\) −47.9925 + 34.8686i −1.59621 + 1.15971i
\(905\) −21.1188 40.4438i −0.702014 1.34440i
\(906\) −0.406343 0.295226i −0.0134999 0.00980822i
\(907\) 36.1881i 1.20161i 0.799396 + 0.600804i \(0.205153\pi\)
−0.799396 + 0.600804i \(0.794847\pi\)
\(908\) 9.17725 12.6314i 0.304558 0.419188i
\(909\) 10.8836 33.4963i 0.360987 1.11100i
\(910\) −2.40985 + 4.84878i −0.0798858 + 0.160735i
\(911\) 10.1760 + 31.3186i 0.337147 + 1.03763i 0.965655 + 0.259828i \(0.0836658\pi\)
−0.628508 + 0.777803i \(0.716334\pi\)
\(912\) −27.2009 8.83812i −0.900713 0.292659i
\(913\) −39.1357 12.7159i −1.29520 0.420836i
\(914\) 0.118838 + 0.365745i 0.00393081 + 0.0120978i
\(915\) −53.1424 + 27.7498i −1.75683 + 0.917379i
\(916\) −4.02363 + 12.3835i −0.132944 + 0.409161i
\(917\) 1.20861 1.66351i 0.0399119 0.0549340i
\(918\) 25.7286i 0.849169i
\(919\) 5.51905 + 4.00983i 0.182057 + 0.132272i 0.675081 0.737744i \(-0.264109\pi\)
−0.493024 + 0.870016i \(0.664109\pi\)
\(920\) 24.9096 25.4125i 0.821245 0.837824i
\(921\) 30.1357 21.8948i 0.993004 0.721460i
\(922\) 13.3206 + 18.3343i 0.438692 + 0.603807i
\(923\) 27.0946 8.80357i 0.891829 0.289773i
\(924\) −8.64429 −0.284376
\(925\) 11.7089 + 33.7274i 0.384986 + 1.10895i
\(926\) 10.1307 0.332915
\(927\) 27.9065 9.06737i 0.916570 0.297811i
\(928\) 14.8331 + 20.4161i 0.486921 + 0.670190i
\(929\) 7.76195 5.63939i 0.254661 0.185022i −0.453129 0.891445i \(-0.649692\pi\)
0.707790 + 0.706423i \(0.249692\pi\)
\(930\) −0.615002 + 4.15102i −0.0201667 + 0.136117i
\(931\) 5.15646 + 3.74639i 0.168996 + 0.122783i
\(932\) 0.192354i 0.00630077i
\(933\) 18.7766 25.8438i 0.614720 0.846089i
\(934\) −6.84856 + 21.0777i −0.224092 + 0.689684i
\(935\) 43.5843 + 42.7218i 1.42536 + 1.39715i
\(936\) −8.99764 27.6919i −0.294097 0.905138i
\(937\) −4.64554 1.50943i −0.151763 0.0493108i 0.232150 0.972680i \(-0.425424\pi\)
−0.383913 + 0.923369i \(0.625424\pi\)
\(938\) 2.83306 + 0.920516i 0.0925025 + 0.0300559i
\(939\) −2.18394 6.72149i −0.0712703 0.219347i
\(940\) 2.27553 + 2.23050i 0.0742197 + 0.0727510i
\(941\) −11.4243 + 35.1605i −0.372423 + 1.14620i 0.572778 + 0.819711i \(0.305866\pi\)
−0.945201 + 0.326490i \(0.894134\pi\)
\(942\) 11.8414 16.2983i 0.385813 0.531026i
\(943\) 3.39111i 0.110430i
\(944\) −1.02916 0.747730i −0.0334964 0.0243365i
\(945\) −1.10780 + 7.47722i −0.0360368 + 0.243234i
\(946\) −3.26304 + 2.37074i −0.106091 + 0.0770793i
\(947\) −20.4890 28.2007i −0.665804 0.916400i 0.333852 0.942625i \(-0.391651\pi\)
−0.999656 + 0.0262251i \(0.991651\pi\)
\(948\) 9.21941 2.99557i 0.299432 0.0972915i
\(949\) −22.7718 −0.739205
\(950\) −11.3249 32.6212i −0.367427 1.05837i
\(951\) −58.1960 −1.88714
\(952\) 20.4557 6.64646i 0.662973 0.215413i
\(953\) −10.1623 13.9872i −0.329189 0.453090i 0.612056 0.790814i \(-0.290343\pi\)
−0.941245 + 0.337725i \(0.890343\pi\)
\(954\) 37.7434 27.4222i 1.22199 0.887826i
\(955\) 0.922176 0.940793i 0.0298409 0.0304433i
\(956\) −15.7502 11.4432i −0.509399 0.370100i
\(957\) 61.1538i 1.97682i
\(958\) 6.11630 8.41837i 0.197609 0.271985i
\(959\) 2.45847 7.56640i 0.0793882 0.244332i
\(960\) 42.7728 22.3350i 1.38049 0.720859i
\(961\) −9.45176 29.0895i −0.304895 0.938372i
\(962\) 16.4441 + 5.34302i 0.530180 + 0.172266i
\(963\) 48.5875 + 15.7870i 1.56571 + 0.508730i
\(964\) 0.749253 + 2.30596i 0.0241318 + 0.0742701i
\(965\) 9.70041 19.5179i 0.312267 0.628302i
\(966\) −4.68726 + 14.4259i −0.150810 + 0.464146i
\(967\) 22.9780 31.6265i 0.738922 1.01704i −0.259758 0.965674i \(-0.583643\pi\)
0.998680 0.0513647i \(-0.0163571\pi\)
\(968\) 12.5490i 0.403341i
\(969\) 97.5598 + 70.8814i 3.13407 + 2.27704i
\(970\) 12.4156 + 23.7767i 0.398642 + 0.763423i
\(971\) −24.0642 + 17.4837i −0.772258 + 0.561078i −0.902646 0.430385i \(-0.858378\pi\)
0.130387 + 0.991463i \(0.458378\pi\)
\(972\) 9.70904 + 13.3634i 0.311418 + 0.428630i
\(973\) 14.3553 4.66431i 0.460209 0.149531i
\(974\) −10.2585 −0.328704
\(975\) 17.2005 24.6978i 0.550858 0.790963i
\(976\) −16.5828 −0.530803
\(977\) −23.4027 + 7.60399i −0.748717 + 0.243273i −0.658429 0.752643i \(-0.728779\pi\)
−0.0902882 + 0.995916i \(0.528779\pi\)
\(978\) −17.1869 23.6558i −0.549577 0.756428i
\(979\) −4.38821 + 3.18822i −0.140248 + 0.101896i
\(980\) −1.82113 + 0.307124i −0.0581740 + 0.00981072i
\(981\) 4.01098 + 2.91415i 0.128061 + 0.0930416i
\(982\) 44.9505i 1.43443i
\(983\) −2.58100 + 3.55244i −0.0823212 + 0.113305i −0.848192 0.529690i \(-0.822308\pi\)
0.765870 + 0.642995i \(0.222308\pi\)
\(984\) −1.66295 + 5.11804i −0.0530129 + 0.163157i
\(985\) 1.34741 + 7.98966i 0.0429321 + 0.254572i
\(986\) 13.7426 + 42.2953i 0.437653 + 1.34696i
\(987\) −4.41973 1.43606i −0.140682 0.0457102i
\(988\) 11.1888 + 3.63546i 0.355963 + 0.115659i
\(989\) −1.53854 4.73514i −0.0489228 0.150569i
\(990\) −39.6261 5.87088i −1.25940 0.186589i
\(991\) 7.11743 21.9052i 0.226093 0.695842i −0.772086 0.635518i \(-0.780787\pi\)
0.998179 0.0603238i \(-0.0192133\pi\)
\(992\) 1.63235 2.24673i 0.0518271 0.0713338i
\(993\) 76.7063i 2.43420i
\(994\) −11.1749 8.11904i −0.354446 0.257520i
\(995\) −7.72626 3.83996i −0.244939 0.121735i
\(996\) 19.0601 13.8480i 0.603943 0.438791i
\(997\) −20.3652 28.0303i −0.644972 0.887728i 0.353897 0.935285i \(-0.384856\pi\)
−0.998869 + 0.0475568i \(0.984856\pi\)
\(998\) 24.3931 7.92579i 0.772149 0.250886i
\(999\) 24.1375 0.763677
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 175.2.n.a.169.9 yes 56
5.2 odd 4 875.2.h.e.526.10 56
5.3 odd 4 875.2.h.d.526.5 56
5.4 even 2 875.2.n.c.99.6 56
25.2 odd 20 4375.2.a.o.1.21 28
25.3 odd 20 875.2.h.d.351.5 56
25.4 even 10 inner 175.2.n.a.29.9 56
25.21 even 5 875.2.n.c.274.6 56
25.22 odd 20 875.2.h.e.351.10 56
25.23 odd 20 4375.2.a.p.1.8 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
175.2.n.a.29.9 56 25.4 even 10 inner
175.2.n.a.169.9 yes 56 1.1 even 1 trivial
875.2.h.d.351.5 56 25.3 odd 20
875.2.h.d.526.5 56 5.3 odd 4
875.2.h.e.351.10 56 25.22 odd 20
875.2.h.e.526.10 56 5.2 odd 4
875.2.n.c.99.6 56 5.4 even 2
875.2.n.c.274.6 56 25.21 even 5
4375.2.a.o.1.21 28 25.2 odd 20
4375.2.a.p.1.8 28 25.23 odd 20