Properties

Label 930.2.v.b.401.7
Level $930$
Weight $2$
Character 930.401
Analytic conductor $7.426$
Analytic rank $0$
Dimension $80$
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] = [930,2,Mod(401,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.401");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.v (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: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 401.7
Character \(\chi\) \(=\) 930.401
Dual form 930.2.v.b.821.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.587785 + 0.809017i) q^{2} +(0.305332 - 1.70493i) q^{3} +(-0.309017 - 0.951057i) q^{4} +1.00000i q^{5} +(1.19984 + 1.24915i) q^{6} +(0.0989466 + 0.304526i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-2.81354 - 1.04114i) q^{9} +O(q^{10})\) \(q+(-0.587785 + 0.809017i) q^{2} +(0.305332 - 1.70493i) q^{3} +(-0.309017 - 0.951057i) q^{4} +1.00000i q^{5} +(1.19984 + 1.24915i) q^{6} +(0.0989466 + 0.304526i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-2.81354 - 1.04114i) q^{9} +(-0.809017 - 0.587785i) q^{10} +(1.22254 + 3.76258i) q^{11} +(-1.71583 + 0.236463i) q^{12} +(1.08444 + 1.49261i) q^{13} +(-0.304526 - 0.0989466i) q^{14} +(1.70493 + 0.305332i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.39371 + 4.28941i) q^{17} +(2.49606 - 1.66424i) q^{18} +(-2.96328 - 2.15295i) q^{19} +(0.951057 - 0.309017i) q^{20} +(0.549406 - 0.0757150i) q^{21} +(-3.76258 - 1.22254i) q^{22} +(0.340963 - 1.04938i) q^{23} +(0.817239 - 1.52713i) q^{24} -1.00000 q^{25} -1.84496 q^{26} +(-2.63413 + 4.47899i) q^{27} +(0.259046 - 0.188208i) q^{28} +(6.99130 + 5.07948i) q^{29} +(-1.24915 + 1.19984i) q^{30} +(-3.36249 + 4.43776i) q^{31} -1.00000i q^{32} +(6.78819 - 0.935497i) q^{33} +(-2.65100 - 3.64879i) q^{34} +(-0.304526 + 0.0989466i) q^{35} +(-0.120747 + 2.99757i) q^{36} +3.30588i q^{37} +(3.48355 - 1.13187i) q^{38} +(2.87590 - 1.39315i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(3.17997 - 4.37686i) q^{41} +(-0.261678 + 0.488983i) q^{42} +(-3.41809 + 4.70460i) q^{43} +(3.20064 - 2.32540i) q^{44} +(1.04114 - 2.81354i) q^{45} +(0.648550 + 0.892653i) q^{46} +(1.10017 + 1.51425i) q^{47} +(0.755111 + 1.55878i) q^{48} +(5.58017 - 4.05423i) q^{49} +(0.587785 - 0.809017i) q^{50} +(6.88759 + 3.68588i) q^{51} +(1.08444 - 1.49261i) q^{52} +(0.284793 - 0.876502i) q^{53} +(-2.07528 - 4.76374i) q^{54} +(-3.76258 + 1.22254i) q^{55} +0.320198i q^{56} +(-4.57541 + 4.39481i) q^{57} +(-8.21877 + 2.67044i) q^{58} +(6.79254 + 9.34913i) q^{59} +(-0.236463 - 1.71583i) q^{60} -0.848964i q^{61} +(-1.61380 - 5.32876i) q^{62} +(0.0386629 - 0.959815i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-1.49261 + 1.08444i) q^{65} +(-3.23317 + 6.04163i) q^{66} -0.517067 q^{67} +4.51016 q^{68} +(-1.68500 - 0.901725i) q^{69} +(0.0989466 - 0.304526i) q^{70} +(7.22603 + 2.34788i) q^{71} +(-2.35411 - 1.85961i) q^{72} +(2.32363 - 0.754993i) q^{73} +(-2.67452 - 1.94315i) q^{74} +(-0.305332 + 1.70493i) q^{75} +(-1.13187 + 3.48355i) q^{76} +(-1.02484 + 0.744588i) q^{77} +(-0.563326 + 3.14553i) q^{78} +(-3.39328 - 1.10254i) q^{79} +(-0.587785 - 0.809017i) q^{80} +(6.83207 + 5.85857i) q^{81} +(1.67181 + 5.14530i) q^{82} +(5.91229 + 4.29553i) q^{83} +(-0.241785 - 0.499119i) q^{84} +(-4.28941 - 1.39371i) q^{85} +(-1.79700 - 5.53059i) q^{86} +(10.7948 - 10.3687i) q^{87} +3.95621i q^{88} +(1.06497 + 3.27764i) q^{89} +(1.66424 + 2.49606i) q^{90} +(-0.347236 + 0.477930i) q^{91} -1.10338 q^{92} +(6.53937 + 7.08778i) q^{93} -1.87171 q^{94} +(2.15295 - 2.96328i) q^{95} +(-1.70493 - 0.305332i) q^{96} +(2.64941 + 8.15403i) q^{97} +6.89747i q^{98} +(0.477700 - 11.8590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + 20 q^{4} + 12 q^{7} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q + 20 q^{4} + 12 q^{7} + 8 q^{9} - 20 q^{10} + 10 q^{13} - 20 q^{16} - 4 q^{18} - 12 q^{19} - 30 q^{21} - 10 q^{22} - 80 q^{25} + 60 q^{27} + 18 q^{28} + 8 q^{31} - 20 q^{33} + 10 q^{34} - 8 q^{36} - 46 q^{39} + 20 q^{40} + 50 q^{43} - 16 q^{45} - 10 q^{46} - 8 q^{49} - 20 q^{51} + 10 q^{52} - 10 q^{55} + 10 q^{58} + 44 q^{63} + 20 q^{64} - 10 q^{66} - 132 q^{67} - 16 q^{69} + 12 q^{70} + 4 q^{72} - 20 q^{73} - 18 q^{76} + 48 q^{78} - 120 q^{79} + 48 q^{81} - 20 q^{82} + 20 q^{84} - 136 q^{87} - 12 q^{90} - 110 q^{91} - 20 q^{93} - 28 q^{94} + 22 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.587785 + 0.809017i −0.415627 + 0.572061i
\(3\) 0.305332 1.70493i 0.176284 0.984339i
\(4\) −0.309017 0.951057i −0.154508 0.475528i
\(5\) 1.00000i 0.447214i
\(6\) 1.19984 + 1.24915i 0.489834 + 0.509963i
\(7\) 0.0989466 + 0.304526i 0.0373983 + 0.115100i 0.968013 0.250901i \(-0.0807267\pi\)
−0.930615 + 0.366001i \(0.880727\pi\)
\(8\) 0.951057 + 0.309017i 0.336249 + 0.109254i
\(9\) −2.81354 1.04114i −0.937848 0.347046i
\(10\) −0.809017 0.587785i −0.255834 0.185874i
\(11\) 1.22254 + 3.76258i 0.368608 + 1.13446i 0.947691 + 0.319190i \(0.103411\pi\)
−0.579082 + 0.815269i \(0.696589\pi\)
\(12\) −1.71583 + 0.236463i −0.495319 + 0.0682610i
\(13\) 1.08444 + 1.49261i 0.300770 + 0.413975i 0.932475 0.361234i \(-0.117645\pi\)
−0.631705 + 0.775209i \(0.717645\pi\)
\(14\) −0.304526 0.0989466i −0.0813881 0.0264446i
\(15\) 1.70493 + 0.305332i 0.440210 + 0.0788364i
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) −1.39371 + 4.28941i −0.338025 + 1.04034i 0.627187 + 0.778869i \(0.284206\pi\)
−0.965212 + 0.261467i \(0.915794\pi\)
\(18\) 2.49606 1.66424i 0.588326 0.392265i
\(19\) −2.96328 2.15295i −0.679824 0.493921i 0.193476 0.981105i \(-0.438024\pi\)
−0.873299 + 0.487184i \(0.838024\pi\)
\(20\) 0.951057 0.309017i 0.212663 0.0690983i
\(21\) 0.549406 0.0757150i 0.119890 0.0165224i
\(22\) −3.76258 1.22254i −0.802184 0.260645i
\(23\) 0.340963 1.04938i 0.0710957 0.218810i −0.909195 0.416371i \(-0.863302\pi\)
0.980291 + 0.197561i \(0.0633019\pi\)
\(24\) 0.817239 1.52713i 0.166818 0.311724i
\(25\) −1.00000 −0.200000
\(26\) −1.84496 −0.361827
\(27\) −2.63413 + 4.47899i −0.506938 + 0.861983i
\(28\) 0.259046 0.188208i 0.0489550 0.0355679i
\(29\) 6.99130 + 5.07948i 1.29825 + 0.943236i 0.999937 0.0112317i \(-0.00357525\pi\)
0.298315 + 0.954467i \(0.403575\pi\)
\(30\) −1.24915 + 1.19984i −0.228062 + 0.219061i
\(31\) −3.36249 + 4.43776i −0.603920 + 0.797045i
\(32\) 1.00000i 0.176777i
\(33\) 6.78819 0.935497i 1.18167 0.162849i
\(34\) −2.65100 3.64879i −0.454643 0.625763i
\(35\) −0.304526 + 0.0989466i −0.0514743 + 0.0167250i
\(36\) −0.120747 + 2.99757i −0.0201245 + 0.499595i
\(37\) 3.30588i 0.543484i 0.962370 + 0.271742i \(0.0875997\pi\)
−0.962370 + 0.271742i \(0.912400\pi\)
\(38\) 3.48355 1.13187i 0.565106 0.183614i
\(39\) 2.87590 1.39315i 0.460512 0.223083i
\(40\) −0.309017 + 0.951057i −0.0488599 + 0.150375i
\(41\) 3.17997 4.37686i 0.496628 0.683550i −0.484965 0.874534i \(-0.661168\pi\)
0.981593 + 0.190984i \(0.0611677\pi\)
\(42\) −0.261678 + 0.488983i −0.0403778 + 0.0754518i
\(43\) −3.41809 + 4.70460i −0.521254 + 0.717445i −0.985766 0.168122i \(-0.946230\pi\)
0.464512 + 0.885567i \(0.346230\pi\)
\(44\) 3.20064 2.32540i 0.482514 0.350567i
\(45\) 1.04114 2.81354i 0.155204 0.419418i
\(46\) 0.648550 + 0.892653i 0.0956235 + 0.131614i
\(47\) 1.10017 + 1.51425i 0.160476 + 0.220876i 0.881682 0.471845i \(-0.156412\pi\)
−0.721206 + 0.692721i \(0.756412\pi\)
\(48\) 0.755111 + 1.55878i 0.108991 + 0.224991i
\(49\) 5.58017 4.05423i 0.797168 0.579176i
\(50\) 0.587785 0.809017i 0.0831254 0.114412i
\(51\) 6.88759 + 3.68588i 0.964455 + 0.516126i
\(52\) 1.08444 1.49261i 0.150385 0.206987i
\(53\) 0.284793 0.876502i 0.0391193 0.120397i −0.929590 0.368596i \(-0.879839\pi\)
0.968709 + 0.248199i \(0.0798387\pi\)
\(54\) −2.07528 4.76374i −0.282410 0.648263i
\(55\) −3.76258 + 1.22254i −0.507346 + 0.164847i
\(56\) 0.320198i 0.0427882i
\(57\) −4.57541 + 4.39481i −0.606027 + 0.582107i
\(58\) −8.21877 + 2.67044i −1.07918 + 0.350646i
\(59\) 6.79254 + 9.34913i 0.884314 + 1.21715i 0.975207 + 0.221293i \(0.0710277\pi\)
−0.0908936 + 0.995861i \(0.528972\pi\)
\(60\) −0.236463 1.71583i −0.0305272 0.221513i
\(61\) 0.848964i 0.108699i −0.998522 0.0543493i \(-0.982692\pi\)
0.998522 0.0543493i \(-0.0173085\pi\)
\(62\) −1.61380 5.32876i −0.204953 0.676753i
\(63\) 0.0386629 0.959815i 0.00487107 0.120925i
\(64\) 0.809017 + 0.587785i 0.101127 + 0.0734732i
\(65\) −1.49261 + 1.08444i −0.185135 + 0.134509i
\(66\) −3.23317 + 6.04163i −0.397975 + 0.743674i
\(67\) −0.517067 −0.0631698 −0.0315849 0.999501i \(-0.510055\pi\)
−0.0315849 + 0.999501i \(0.510055\pi\)
\(68\) 4.51016 0.546937
\(69\) −1.68500 0.901725i −0.202850 0.108555i
\(70\) 0.0989466 0.304526i 0.0118264 0.0363979i
\(71\) 7.22603 + 2.34788i 0.857572 + 0.278642i 0.704614 0.709591i \(-0.251120\pi\)
0.152958 + 0.988233i \(0.451120\pi\)
\(72\) −2.35411 1.85961i −0.277435 0.219158i
\(73\) 2.32363 0.754993i 0.271960 0.0883653i −0.169862 0.985468i \(-0.554332\pi\)
0.441822 + 0.897103i \(0.354332\pi\)
\(74\) −2.67452 1.94315i −0.310906 0.225886i
\(75\) −0.305332 + 1.70493i −0.0352567 + 0.196868i
\(76\) −1.13187 + 3.48355i −0.129835 + 0.399590i
\(77\) −1.02484 + 0.744588i −0.116791 + 0.0848537i
\(78\) −0.563326 + 3.14553i −0.0637842 + 0.356161i
\(79\) −3.39328 1.10254i −0.381774 0.124046i 0.111842 0.993726i \(-0.464325\pi\)
−0.493616 + 0.869680i \(0.664325\pi\)
\(80\) −0.587785 0.809017i −0.0657164 0.0904508i
\(81\) 6.83207 + 5.85857i 0.759119 + 0.650952i
\(82\) 1.67181 + 5.14530i 0.184621 + 0.568204i
\(83\) 5.91229 + 4.29553i 0.648958 + 0.471496i 0.862916 0.505347i \(-0.168636\pi\)
−0.213958 + 0.976843i \(0.568636\pi\)
\(84\) −0.241785 0.499119i −0.0263809 0.0544584i
\(85\) −4.28941 1.39371i −0.465252 0.151170i
\(86\) −1.79700 5.53059i −0.193775 0.596379i
\(87\) 10.7948 10.3687i 1.15732 1.11164i
\(88\) 3.95621i 0.421733i
\(89\) 1.06497 + 3.27764i 0.112887 + 0.347430i 0.991500 0.130104i \(-0.0415310\pi\)
−0.878614 + 0.477533i \(0.841531\pi\)
\(90\) 1.66424 + 2.49606i 0.175426 + 0.263108i
\(91\) −0.347236 + 0.477930i −0.0364002 + 0.0501006i
\(92\) −1.10338 −0.115035
\(93\) 6.53937 + 7.08778i 0.678101 + 0.734968i
\(94\) −1.87171 −0.193053
\(95\) 2.15295 2.96328i 0.220888 0.304026i
\(96\) −1.70493 0.305332i −0.174008 0.0311628i
\(97\) 2.64941 + 8.15403i 0.269006 + 0.827917i 0.990743 + 0.135749i \(0.0433441\pi\)
−0.721737 + 0.692168i \(0.756656\pi\)
\(98\) 6.89747i 0.696750i
\(99\) 0.477700 11.8590i 0.0480107 1.19187i
\(100\) 0.309017 + 0.951057i 0.0309017 + 0.0951057i
\(101\) 13.5224 + 4.39369i 1.34553 + 0.437188i 0.891185 0.453640i \(-0.149875\pi\)
0.454341 + 0.890828i \(0.349875\pi\)
\(102\) −7.03036 + 3.40567i −0.696109 + 0.337212i
\(103\) −0.496147 0.360472i −0.0488868 0.0355183i 0.563074 0.826407i \(-0.309619\pi\)
−0.611960 + 0.790888i \(0.709619\pi\)
\(104\) 0.570125 + 1.75466i 0.0559054 + 0.172059i
\(105\) 0.0757150 + 0.549406i 0.00738903 + 0.0536166i
\(106\) 0.541708 + 0.745597i 0.0526153 + 0.0724188i
\(107\) −18.2962 5.94481i −1.76876 0.574707i −0.770718 0.637176i \(-0.780102\pi\)
−0.998047 + 0.0624698i \(0.980102\pi\)
\(108\) 5.07377 + 1.12112i 0.488223 + 0.107880i
\(109\) 1.34964 0.980573i 0.129272 0.0939219i −0.521270 0.853392i \(-0.674542\pi\)
0.650542 + 0.759470i \(0.274542\pi\)
\(110\) 1.22254 3.76258i 0.116564 0.358748i
\(111\) 5.63629 + 1.00939i 0.534973 + 0.0958072i
\(112\) −0.259046 0.188208i −0.0244775 0.0177839i
\(113\) −14.1916 + 4.61113i −1.33503 + 0.433779i −0.887632 0.460553i \(-0.847651\pi\)
−0.447403 + 0.894333i \(0.647651\pi\)
\(114\) −0.866121 6.28479i −0.0811197 0.588624i
\(115\) 1.04938 + 0.340963i 0.0978549 + 0.0317950i
\(116\) 2.67044 8.21877i 0.247944 0.763094i
\(117\) −1.49712 5.32857i −0.138409 0.492626i
\(118\) −11.5562 −1.06383
\(119\) −1.44414 −0.132384
\(120\) 1.52713 + 0.817239i 0.139407 + 0.0746034i
\(121\) −3.76320 + 2.73413i −0.342109 + 0.248557i
\(122\) 0.686826 + 0.499008i 0.0621823 + 0.0451781i
\(123\) −6.49127 6.75801i −0.585298 0.609349i
\(124\) 5.25962 + 1.82657i 0.472328 + 0.164031i
\(125\) 1.00000i 0.0894427i
\(126\) 0.753781 + 0.595444i 0.0671522 + 0.0530464i
\(127\) −9.27031 12.7595i −0.822607 1.13222i −0.989254 0.146205i \(-0.953294\pi\)
0.166647 0.986017i \(-0.446706\pi\)
\(128\) −0.951057 + 0.309017i −0.0840623 + 0.0273135i
\(129\) 6.97734 + 7.26406i 0.614321 + 0.639565i
\(130\) 1.84496i 0.161814i
\(131\) −13.1354 + 4.26796i −1.14765 + 0.372894i −0.820257 0.571995i \(-0.806170\pi\)
−0.327392 + 0.944889i \(0.606170\pi\)
\(132\) −2.98738 6.16687i −0.260018 0.536757i
\(133\) 0.362423 1.11542i 0.0314261 0.0967196i
\(134\) 0.303925 0.418316i 0.0262551 0.0361370i
\(135\) −4.47899 2.63413i −0.385490 0.226710i
\(136\) −2.65100 + 3.64879i −0.227322 + 0.312881i
\(137\) −13.2341 + 9.61513i −1.13066 + 0.821476i −0.985791 0.167974i \(-0.946277\pi\)
−0.144873 + 0.989450i \(0.546277\pi\)
\(138\) 1.71993 0.833175i 0.146410 0.0709245i
\(139\) −7.07192 9.73366i −0.599832 0.825599i 0.395860 0.918311i \(-0.370446\pi\)
−0.995693 + 0.0927121i \(0.970446\pi\)
\(140\) 0.188208 + 0.259046i 0.0159064 + 0.0218933i
\(141\) 2.91760 1.41335i 0.245706 0.119026i
\(142\) −6.14683 + 4.46593i −0.515830 + 0.374773i
\(143\) −4.29028 + 5.90506i −0.358771 + 0.493806i
\(144\) 2.88817 0.811463i 0.240681 0.0676219i
\(145\) −5.07948 + 6.99130i −0.421828 + 0.580596i
\(146\) −0.754993 + 2.32363i −0.0624837 + 0.192305i
\(147\) −5.20836 10.7517i −0.429578 0.886783i
\(148\) 3.14408 1.02157i 0.258442 0.0839729i
\(149\) 4.25628i 0.348688i 0.984685 + 0.174344i \(0.0557805\pi\)
−0.984685 + 0.174344i \(0.944219\pi\)
\(150\) −1.19984 1.24915i −0.0979669 0.101993i
\(151\) 5.51151 1.79080i 0.448520 0.145733i −0.0760432 0.997105i \(-0.524229\pi\)
0.524563 + 0.851372i \(0.324229\pi\)
\(152\) −2.15295 2.96328i −0.174627 0.240354i
\(153\) 8.38715 10.6174i 0.678060 0.858366i
\(154\) 1.26677i 0.102079i
\(155\) −4.43776 3.36249i −0.356449 0.270081i
\(156\) −2.21367 2.30463i −0.177235 0.184518i
\(157\) −1.87808 1.36450i −0.149887 0.108899i 0.510314 0.859988i \(-0.329529\pi\)
−0.660201 + 0.751089i \(0.729529\pi\)
\(158\) 2.88650 2.09716i 0.229637 0.166841i
\(159\) −1.40741 0.753175i −0.111615 0.0597306i
\(160\) 1.00000 0.0790569
\(161\) 0.353300 0.0278439
\(162\) −8.75547 + 2.08368i −0.687895 + 0.163709i
\(163\) 5.47956 16.8644i 0.429192 1.32092i −0.469730 0.882810i \(-0.655649\pi\)
0.898922 0.438108i \(-0.144351\pi\)
\(164\) −5.14530 1.67181i −0.401781 0.130546i
\(165\) 0.935497 + 6.78819i 0.0728283 + 0.528460i
\(166\) −6.95031 + 2.25829i −0.539449 + 0.175278i
\(167\) −4.78926 3.47960i −0.370604 0.269260i 0.386857 0.922140i \(-0.373561\pi\)
−0.757461 + 0.652880i \(0.773561\pi\)
\(168\) 0.545914 + 0.0977667i 0.0421182 + 0.00754286i
\(169\) 2.96536 9.12644i 0.228105 0.702034i
\(170\) 3.64879 2.65100i 0.279850 0.203323i
\(171\) 6.09581 + 9.14261i 0.466158 + 0.699153i
\(172\) 5.53059 + 1.79700i 0.421703 + 0.137020i
\(173\) −9.02889 12.4272i −0.686454 0.944823i 0.313535 0.949577i \(-0.398487\pi\)
−0.999989 + 0.00475374i \(0.998487\pi\)
\(174\) 2.04345 + 14.8278i 0.154913 + 1.12409i
\(175\) −0.0989466 0.304526i −0.00747966 0.0230200i
\(176\) −3.20064 2.32540i −0.241257 0.175284i
\(177\) 18.0136 8.72619i 1.35398 0.655901i
\(178\) −3.27764 1.06497i −0.245670 0.0798230i
\(179\) 0.978206 + 3.01061i 0.0731146 + 0.225023i 0.980935 0.194335i \(-0.0622550\pi\)
−0.907821 + 0.419359i \(0.862255\pi\)
\(180\) −2.99757 0.120747i −0.223426 0.00899995i
\(181\) 3.83839i 0.285305i −0.989773 0.142653i \(-0.954437\pi\)
0.989773 0.142653i \(-0.0455631\pi\)
\(182\) −0.182553 0.561840i −0.0135317 0.0416463i
\(183\) −1.44742 0.259216i −0.106996 0.0191618i
\(184\) 0.648550 0.892653i 0.0478118 0.0658072i
\(185\) −3.30588 −0.243053
\(186\) −9.57788 + 1.12437i −0.702284 + 0.0824429i
\(187\) −17.8431 −1.30482
\(188\) 1.10017 1.51425i 0.0802379 0.110438i
\(189\) −1.62461 0.358980i −0.118173 0.0261119i
\(190\) 1.13187 + 3.48355i 0.0821147 + 0.252723i
\(191\) 24.9007i 1.80175i −0.434077 0.900876i \(-0.642925\pi\)
0.434077 0.900876i \(-0.357075\pi\)
\(192\) 1.24915 1.19984i 0.0901496 0.0865913i
\(193\) 6.71504 + 20.6668i 0.483359 + 1.48763i 0.834343 + 0.551245i \(0.185847\pi\)
−0.350984 + 0.936381i \(0.614153\pi\)
\(194\) −8.15403 2.64941i −0.585426 0.190216i
\(195\) 1.39315 + 2.87590i 0.0997658 + 0.205947i
\(196\) −5.58017 4.05423i −0.398584 0.289588i
\(197\) 3.20208 + 9.85498i 0.228139 + 0.702138i 0.997958 + 0.0638763i \(0.0203463\pi\)
−0.769819 + 0.638262i \(0.779654\pi\)
\(198\) 9.31335 + 7.35701i 0.661871 + 0.522840i
\(199\) 1.63733 + 2.25359i 0.116067 + 0.159752i 0.863098 0.505037i \(-0.168521\pi\)
−0.747031 + 0.664790i \(0.768521\pi\)
\(200\) −0.951057 0.309017i −0.0672499 0.0218508i
\(201\) −0.157877 + 0.881561i −0.0111358 + 0.0621806i
\(202\) −11.5028 + 8.35729i −0.809335 + 0.588017i
\(203\) −0.855069 + 2.63163i −0.0600141 + 0.184704i
\(204\) 1.37709 7.68948i 0.0964159 0.538371i
\(205\) 4.37686 + 3.17997i 0.305693 + 0.222099i
\(206\) 0.583255 0.189511i 0.0406373 0.0132039i
\(207\) −2.05186 + 2.59748i −0.142614 + 0.180537i
\(208\) −1.75466 0.570125i −0.121664 0.0395311i
\(209\) 4.47792 13.7816i 0.309744 0.953295i
\(210\) −0.488983 0.261678i −0.0337430 0.0180575i
\(211\) 25.7865 1.77521 0.887607 0.460601i \(-0.152366\pi\)
0.887607 + 0.460601i \(0.152366\pi\)
\(212\) −0.921609 −0.0632964
\(213\) 6.20930 11.6030i 0.425454 0.795022i
\(214\) 15.5637 11.3077i 1.06391 0.772979i
\(215\) −4.70460 3.41809i −0.320851 0.233112i
\(216\) −3.88929 + 3.44579i −0.264633 + 0.234456i
\(217\) −1.68412 0.584864i −0.114326 0.0397032i
\(218\) 1.66825i 0.112988i
\(219\) −0.577729 4.19214i −0.0390393 0.283279i
\(220\) 2.32540 + 3.20064i 0.156778 + 0.215787i
\(221\) −7.91381 + 2.57135i −0.532341 + 0.172968i
\(222\) −4.12954 + 3.96654i −0.277157 + 0.266217i
\(223\) 14.7086i 0.984960i −0.870324 0.492480i \(-0.836090\pi\)
0.870324 0.492480i \(-0.163910\pi\)
\(224\) 0.304526 0.0989466i 0.0203470 0.00661115i
\(225\) 2.81354 + 1.04114i 0.187570 + 0.0694091i
\(226\) 4.61113 14.1916i 0.306728 0.944012i
\(227\) 11.5699 15.9246i 0.767920 1.05695i −0.228594 0.973522i \(-0.573413\pi\)
0.996514 0.0834288i \(-0.0265871\pi\)
\(228\) 5.59359 + 2.99340i 0.370445 + 0.198243i
\(229\) −1.77530 + 2.44349i −0.117315 + 0.161471i −0.863636 0.504116i \(-0.831818\pi\)
0.746321 + 0.665586i \(0.231818\pi\)
\(230\) −0.892653 + 0.648550i −0.0588598 + 0.0427641i
\(231\) 0.956552 + 1.97462i 0.0629365 + 0.129920i
\(232\) 5.07948 + 6.99130i 0.333484 + 0.459002i
\(233\) −3.17238 4.36641i −0.207830 0.286053i 0.692359 0.721553i \(-0.256571\pi\)
−0.900189 + 0.435500i \(0.856571\pi\)
\(234\) 5.19089 + 1.92086i 0.339339 + 0.125571i
\(235\) −1.51425 + 1.10017i −0.0987787 + 0.0717669i
\(236\) 6.79254 9.34913i 0.442157 0.608577i
\(237\) −2.91583 + 5.44865i −0.189404 + 0.353928i
\(238\) 0.848846 1.16834i 0.0550225 0.0757320i
\(239\) −8.10756 + 24.9525i −0.524435 + 1.61404i 0.240996 + 0.970526i \(0.422526\pi\)
−0.765431 + 0.643518i \(0.777474\pi\)
\(240\) −1.55878 + 0.755111i −0.100619 + 0.0487422i
\(241\) 20.9168 6.79629i 1.34737 0.437787i 0.455564 0.890203i \(-0.349438\pi\)
0.891807 + 0.452416i \(0.149438\pi\)
\(242\) 4.65157i 0.299014i
\(243\) 12.0745 9.85936i 0.774578 0.632478i
\(244\) −0.807412 + 0.262344i −0.0516893 + 0.0167949i
\(245\) 4.05423 + 5.58017i 0.259015 + 0.356504i
\(246\) 9.28282 1.27929i 0.591851 0.0815643i
\(247\) 6.75777i 0.429986i
\(248\) −4.56926 + 3.18149i −0.290148 + 0.202025i
\(249\) 9.12877 8.76845i 0.578512 0.555678i
\(250\) 0.809017 + 0.587785i 0.0511667 + 0.0371748i
\(251\) 3.47084 2.52172i 0.219078 0.159169i −0.472834 0.881152i \(-0.656769\pi\)
0.691911 + 0.721982i \(0.256769\pi\)
\(252\) −0.924786 + 0.259829i −0.0582561 + 0.0163677i
\(253\) 4.36520 0.274438
\(254\) 15.7716 0.989598
\(255\) −3.68588 + 6.88759i −0.230818 + 0.431317i
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) 11.4335 + 3.71498i 0.713205 + 0.231734i 0.643075 0.765803i \(-0.277658\pi\)
0.0701304 + 0.997538i \(0.477658\pi\)
\(258\) −9.97792 + 1.37508i −0.621198 + 0.0856088i
\(259\) −1.00673 + 0.327106i −0.0625551 + 0.0203254i
\(260\) 1.49261 + 1.08444i 0.0925676 + 0.0672543i
\(261\) −14.3819 21.5702i −0.890218 1.33516i
\(262\) 4.26796 13.1354i 0.263676 0.811510i
\(263\) 6.38149 4.63642i 0.393499 0.285894i −0.373389 0.927675i \(-0.621804\pi\)
0.766888 + 0.641781i \(0.221804\pi\)
\(264\) 6.74504 + 1.20796i 0.415128 + 0.0743446i
\(265\) 0.876502 + 0.284793i 0.0538431 + 0.0174947i
\(266\) 0.689370 + 0.948837i 0.0422680 + 0.0581769i
\(267\) 5.91331 0.814927i 0.361889 0.0498727i
\(268\) 0.159783 + 0.491760i 0.00976027 + 0.0300390i
\(269\) 21.0605 + 15.3014i 1.28408 + 0.932942i 0.999668 0.0257594i \(-0.00820038\pi\)
0.284416 + 0.958701i \(0.408200\pi\)
\(270\) 4.76374 2.07528i 0.289912 0.126298i
\(271\) −30.9428 10.0539i −1.87964 0.610732i −0.987181 0.159605i \(-0.948978\pi\)
−0.892459 0.451128i \(-0.851022\pi\)
\(272\) −1.39371 4.28941i −0.0845064 0.260084i
\(273\) 0.708812 + 0.737939i 0.0428993 + 0.0446621i
\(274\) 16.3582i 0.988237i
\(275\) −1.22254 3.76258i −0.0737216 0.226892i
\(276\) −0.336897 + 1.88118i −0.0202788 + 0.113234i
\(277\) −6.34752 + 8.73662i −0.381386 + 0.524932i −0.955951 0.293526i \(-0.905171\pi\)
0.574565 + 0.818459i \(0.305171\pi\)
\(278\) 12.0315 0.721600
\(279\) 14.0808 8.98502i 0.842997 0.537919i
\(280\) −0.320198 −0.0191355
\(281\) −3.12621 + 4.30285i −0.186494 + 0.256687i −0.892019 0.451998i \(-0.850711\pi\)
0.705525 + 0.708685i \(0.250711\pi\)
\(282\) −0.571494 + 3.19113i −0.0340320 + 0.190029i
\(283\) −0.337209 1.03782i −0.0200450 0.0616922i 0.940534 0.339701i \(-0.110326\pi\)
−0.960579 + 0.278008i \(0.910326\pi\)
\(284\) 7.59790i 0.450852i
\(285\) −4.39481 4.57541i −0.260326 0.271024i
\(286\) −2.25553 6.94182i −0.133372 0.410478i
\(287\) 1.64752 + 0.535310i 0.0972497 + 0.0315984i
\(288\) −1.04114 + 2.81354i −0.0613496 + 0.165790i
\(289\) −2.70333 1.96409i −0.159020 0.115534i
\(290\) −2.67044 8.21877i −0.156814 0.482623i
\(291\) 14.7110 2.02735i 0.862372 0.118846i
\(292\) −1.43608 1.97660i −0.0840404 0.115672i
\(293\) −27.1670 8.82708i −1.58711 0.515684i −0.623235 0.782035i \(-0.714182\pi\)
−0.963876 + 0.266351i \(0.914182\pi\)
\(294\) 11.7597 + 2.10602i 0.685839 + 0.122826i
\(295\) −9.34913 + 6.79254i −0.544328 + 0.395477i
\(296\) −1.02157 + 3.14408i −0.0593778 + 0.182746i
\(297\) −20.0729 4.43538i −1.16475 0.257367i
\(298\) −3.44341 2.50178i −0.199471 0.144924i
\(299\) 1.93606 0.629064i 0.111965 0.0363797i
\(300\) 1.71583 0.236463i 0.0990637 0.0136522i
\(301\) −1.77088 0.575395i −0.102072 0.0331652i
\(302\) −1.79080 + 5.51151i −0.103049 + 0.317151i
\(303\) 11.6197 21.7131i 0.667536 1.24739i
\(304\) 3.66282 0.210077
\(305\) 0.848964 0.0486115
\(306\) 3.65982 + 13.0261i 0.209218 + 0.744652i
\(307\) −9.74157 + 7.07767i −0.555981 + 0.403944i −0.829986 0.557785i \(-0.811652\pi\)
0.274005 + 0.961728i \(0.411652\pi\)
\(308\) 1.02484 + 0.744588i 0.0583956 + 0.0424269i
\(309\) −0.766067 + 0.735830i −0.0435800 + 0.0418599i
\(310\) 5.32876 1.61380i 0.302653 0.0916578i
\(311\) 33.9176i 1.92329i −0.274300 0.961644i \(-0.588446\pi\)
0.274300 0.961644i \(-0.411554\pi\)
\(312\) 3.16565 0.436266i 0.179220 0.0246987i
\(313\) 0.0384703 + 0.0529498i 0.00217447 + 0.00299290i 0.810103 0.586288i \(-0.199411\pi\)
−0.807928 + 0.589281i \(0.799411\pi\)
\(314\) 2.20781 0.717362i 0.124594 0.0404831i
\(315\) 0.959815 + 0.0386629i 0.0540795 + 0.00217841i
\(316\) 3.56791i 0.200710i
\(317\) −22.7178 + 7.38147i −1.27596 + 0.414584i −0.867155 0.498038i \(-0.834054\pi\)
−0.408804 + 0.912622i \(0.634054\pi\)
\(318\) 1.43659 0.695917i 0.0805599 0.0390251i
\(319\) −10.5648 + 32.5152i −0.591516 + 1.82050i
\(320\) −0.587785 + 0.809017i −0.0328582 + 0.0452254i
\(321\) −15.7219 + 29.3786i −0.877510 + 1.63975i
\(322\) −0.207664 + 0.285826i −0.0115727 + 0.0159284i
\(323\) 13.3649 9.71014i 0.743641 0.540287i
\(324\) 3.46061 8.30808i 0.192256 0.461560i
\(325\) −1.08444 1.49261i −0.0601540 0.0827949i
\(326\) 10.4227 + 14.3457i 0.577262 + 0.794533i
\(327\) −1.25972 2.60044i −0.0696624 0.143805i
\(328\) 4.37686 3.17997i 0.241671 0.175585i
\(329\) −0.352271 + 0.484859i −0.0194213 + 0.0267312i
\(330\) −6.04163 3.23317i −0.332581 0.177980i
\(331\) 2.57352 3.54215i 0.141454 0.194694i −0.732412 0.680862i \(-0.761606\pi\)
0.873866 + 0.486168i \(0.161606\pi\)
\(332\) 2.25829 6.95031i 0.123940 0.381448i
\(333\) 3.44188 9.30125i 0.188614 0.509705i
\(334\) 5.63011 1.82934i 0.308066 0.100097i
\(335\) 0.517067i 0.0282504i
\(336\) −0.399975 + 0.384188i −0.0218204 + 0.0209592i
\(337\) −9.80535 + 3.18595i −0.534131 + 0.173550i −0.563649 0.826015i \(-0.690603\pi\)
0.0295176 + 0.999564i \(0.490603\pi\)
\(338\) 5.64045 + 7.76342i 0.306800 + 0.422274i
\(339\) 3.52849 + 25.6036i 0.191641 + 1.39060i
\(340\) 4.51016i 0.244598i
\(341\) −20.8082 7.22630i −1.12682 0.391326i
\(342\) −10.9796 0.442274i −0.593706 0.0239155i
\(343\) 3.60008 + 2.61561i 0.194386 + 0.141230i
\(344\) −4.70460 + 3.41809i −0.253655 + 0.184291i
\(345\) 0.901725 1.68500i 0.0485472 0.0907175i
\(346\) 15.3609 0.825806
\(347\) −9.56534 −0.513494 −0.256747 0.966479i \(-0.582651\pi\)
−0.256747 + 0.966479i \(0.582651\pi\)
\(348\) −13.1970 7.06236i −0.707435 0.378582i
\(349\) 5.03182 15.4864i 0.269347 0.828966i −0.721313 0.692610i \(-0.756461\pi\)
0.990660 0.136356i \(-0.0435391\pi\)
\(350\) 0.304526 + 0.0989466i 0.0162776 + 0.00528892i
\(351\) −9.54193 + 0.925494i −0.509311 + 0.0493992i
\(352\) 3.76258 1.22254i 0.200546 0.0651613i
\(353\) 18.8876 + 13.7226i 1.00528 + 0.730382i 0.963215 0.268733i \(-0.0866049\pi\)
0.0420695 + 0.999115i \(0.486605\pi\)
\(354\) −3.52847 + 19.7024i −0.187536 + 1.04717i
\(355\) −2.34788 + 7.22603i −0.124613 + 0.383518i
\(356\) 2.78813 2.02570i 0.147771 0.107362i
\(357\) −0.440943 + 2.46216i −0.0233372 + 0.130311i
\(358\) −3.01061 0.978206i −0.159116 0.0516998i
\(359\) 0.989165 + 1.36147i 0.0522061 + 0.0718556i 0.834322 0.551278i \(-0.185859\pi\)
−0.782116 + 0.623133i \(0.785859\pi\)
\(360\) 1.85961 2.35411i 0.0980102 0.124073i
\(361\) −1.72548 5.31047i −0.0908146 0.279499i
\(362\) 3.10532 + 2.25615i 0.163212 + 0.118580i
\(363\) 3.51246 + 7.25079i 0.184356 + 0.380568i
\(364\) 0.561840 + 0.182553i 0.0294484 + 0.00956837i
\(365\) 0.754993 + 2.32363i 0.0395181 + 0.121624i
\(366\) 1.06048 1.01862i 0.0554323 0.0532443i
\(367\) 1.45574i 0.0759892i −0.999278 0.0379946i \(-0.987903\pi\)
0.999278 0.0379946i \(-0.0120970\pi\)
\(368\) 0.340963 + 1.04938i 0.0177739 + 0.0547025i
\(369\) −13.5039 + 9.00369i −0.702985 + 0.468714i
\(370\) 1.94315 2.67452i 0.101020 0.139041i
\(371\) 0.295097 0.0153207
\(372\) 4.72010 8.40956i 0.244726 0.436015i
\(373\) −22.0234 −1.14033 −0.570163 0.821531i \(-0.693120\pi\)
−0.570163 + 0.821531i \(0.693120\pi\)
\(374\) 10.4879 14.4354i 0.542317 0.746436i
\(375\) −1.70493 0.305332i −0.0880420 0.0157673i
\(376\) 0.578392 + 1.78011i 0.0298283 + 0.0918020i
\(377\) 15.9437i 0.821141i
\(378\) 1.24534 1.10333i 0.0640535 0.0567493i
\(379\) −3.38329 10.4127i −0.173788 0.534864i 0.825788 0.563980i \(-0.190731\pi\)
−0.999576 + 0.0291167i \(0.990731\pi\)
\(380\) −3.48355 1.13187i −0.178702 0.0580639i
\(381\) −24.5845 + 11.9093i −1.25950 + 0.610132i
\(382\) 20.1451 + 14.6363i 1.03071 + 0.748857i
\(383\) 0.252313 + 0.776540i 0.0128926 + 0.0396793i 0.957296 0.289110i \(-0.0933594\pi\)
−0.944403 + 0.328789i \(0.893359\pi\)
\(384\) 0.236463 + 1.71583i 0.0120670 + 0.0875608i
\(385\) −0.744588 1.02484i −0.0379477 0.0522306i
\(386\) −20.6668 6.71504i −1.05191 0.341786i
\(387\) 14.5151 9.67790i 0.737843 0.491955i
\(388\) 6.93624 5.03947i 0.352134 0.255840i
\(389\) −4.78596 + 14.7297i −0.242658 + 0.746823i 0.753355 + 0.657614i \(0.228434\pi\)
−0.996013 + 0.0892097i \(0.971566\pi\)
\(390\) −3.14553 0.563326i −0.159280 0.0285251i
\(391\) 4.02600 + 2.92506i 0.203604 + 0.147927i
\(392\) 6.55989 2.13144i 0.331324 0.107654i
\(393\) 3.26589 + 23.6981i 0.164742 + 1.19541i
\(394\) −9.85498 3.20208i −0.496487 0.161318i
\(395\) 1.10254 3.39328i 0.0554750 0.170734i
\(396\) −11.4262 + 3.21031i −0.574188 + 0.161324i
\(397\) 19.0079 0.953979 0.476989 0.878909i \(-0.341728\pi\)
0.476989 + 0.878909i \(0.341728\pi\)
\(398\) −2.78558 −0.139629
\(399\) −1.79106 0.958480i −0.0896650 0.0479840i
\(400\) 0.809017 0.587785i 0.0404508 0.0293893i
\(401\) −5.77489 4.19571i −0.288384 0.209524i 0.434182 0.900825i \(-0.357038\pi\)
−0.722566 + 0.691302i \(0.757038\pi\)
\(402\) −0.620400 0.645894i −0.0309428 0.0322143i
\(403\) −10.2702 0.206378i −0.511598 0.0102804i
\(404\) 14.2183i 0.707385i
\(405\) −5.85857 + 6.83207i −0.291115 + 0.339488i
\(406\) −1.62644 2.23860i −0.0807188 0.111100i
\(407\) −12.4386 + 4.04156i −0.616560 + 0.200333i
\(408\) 5.41148 + 5.63386i 0.267908 + 0.278917i
\(409\) 37.0809i 1.83353i 0.399424 + 0.916766i \(0.369210\pi\)
−0.399424 + 0.916766i \(0.630790\pi\)
\(410\) −5.14530 + 1.67181i −0.254108 + 0.0825648i
\(411\) 12.3523 + 25.4990i 0.609294 + 1.25777i
\(412\) −0.189511 + 0.583255i −0.00933655 + 0.0287349i
\(413\) −2.17496 + 2.99357i −0.107023 + 0.147304i
\(414\) −0.895351 3.18675i −0.0440041 0.156620i
\(415\) −4.29553 + 5.91229i −0.210859 + 0.290223i
\(416\) 1.49261 1.08444i 0.0731811 0.0531692i
\(417\) −18.7545 + 9.08510i −0.918410 + 0.444899i
\(418\) 8.51752 + 11.7234i 0.416605 + 0.573408i
\(419\) 13.6769 + 18.8246i 0.668160 + 0.919643i 0.999717 0.0237919i \(-0.00757390\pi\)
−0.331557 + 0.943435i \(0.607574\pi\)
\(420\) 0.499119 0.241785i 0.0243545 0.0117979i
\(421\) 10.4339 7.58068i 0.508517 0.369460i −0.303743 0.952754i \(-0.598237\pi\)
0.812261 + 0.583294i \(0.198237\pi\)
\(422\) −15.1569 + 20.8617i −0.737827 + 1.01553i
\(423\) −1.51883 5.40583i −0.0738479 0.262841i
\(424\) 0.541708 0.745597i 0.0263077 0.0362094i
\(425\) 1.39371 4.28941i 0.0676051 0.208067i
\(426\) 5.73726 + 11.8435i 0.277971 + 0.573819i
\(427\) 0.258532 0.0840021i 0.0125112 0.00406514i
\(428\) 19.2378i 0.929895i
\(429\) 8.75773 + 9.11761i 0.422827 + 0.440202i
\(430\) 5.53059 1.79700i 0.266709 0.0866589i
\(431\) −2.78641 3.83517i −0.134217 0.184734i 0.736618 0.676309i \(-0.236421\pi\)
−0.870835 + 0.491575i \(0.836421\pi\)
\(432\) −0.501633 5.17188i −0.0241348 0.248832i
\(433\) 23.5276i 1.13066i −0.824864 0.565331i \(-0.808748\pi\)
0.824864 0.565331i \(-0.191252\pi\)
\(434\) 1.46307 1.01871i 0.0702294 0.0488995i
\(435\) 10.3687 + 10.7948i 0.497142 + 0.517571i
\(436\) −1.34964 0.980573i −0.0646362 0.0469609i
\(437\) −3.26963 + 2.37552i −0.156407 + 0.113637i
\(438\) 3.73109 + 1.99669i 0.178279 + 0.0954053i
\(439\) 23.5350 1.12327 0.561633 0.827387i \(-0.310173\pi\)
0.561633 + 0.827387i \(0.310173\pi\)
\(440\) −3.95621 −0.188605
\(441\) −19.9211 + 5.59704i −0.948623 + 0.266526i
\(442\) 2.57135 7.91381i 0.122307 0.376422i
\(443\) 21.5630 + 7.00623i 1.02449 + 0.332876i 0.772609 0.634883i \(-0.218952\pi\)
0.251879 + 0.967759i \(0.418952\pi\)
\(444\) −0.781719 5.67234i −0.0370987 0.269198i
\(445\) −3.27764 + 1.06497i −0.155375 + 0.0504845i
\(446\) 11.8995 + 8.64549i 0.563458 + 0.409376i
\(447\) 7.25665 + 1.29958i 0.343228 + 0.0614680i
\(448\) −0.0989466 + 0.304526i −0.00467479 + 0.0143875i
\(449\) −6.57101 + 4.77412i −0.310105 + 0.225305i −0.731942 0.681367i \(-0.761386\pi\)
0.421836 + 0.906672i \(0.361386\pi\)
\(450\) −2.49606 + 1.66424i −0.117665 + 0.0784530i
\(451\) 20.3559 + 6.61403i 0.958521 + 0.311442i
\(452\) 8.77090 + 12.0721i 0.412548 + 0.567824i
\(453\) −1.37034 9.94350i −0.0643840 0.467186i
\(454\) 6.08264 + 18.7205i 0.285473 + 0.878594i
\(455\) −0.477930 0.347236i −0.0224057 0.0162787i
\(456\) −5.70954 + 2.76584i −0.267374 + 0.129522i
\(457\) 13.5772 + 4.41149i 0.635113 + 0.206361i 0.608839 0.793294i \(-0.291636\pi\)
0.0262744 + 0.999655i \(0.491636\pi\)
\(458\) −0.933332 2.87250i −0.0436117 0.134223i
\(459\) −15.5410 17.5413i −0.725393 0.818758i
\(460\) 1.10338i 0.0514453i
\(461\) −7.70348 23.7089i −0.358787 1.10423i −0.953781 0.300503i \(-0.902846\pi\)
0.594994 0.803730i \(-0.297154\pi\)
\(462\) −2.15975 0.386785i −0.100481 0.0179949i
\(463\) −9.46630 + 13.0292i −0.439936 + 0.605520i −0.970198 0.242314i \(-0.922094\pi\)
0.530262 + 0.847834i \(0.322094\pi\)
\(464\) −8.64173 −0.401182
\(465\) −7.08778 + 6.53937i −0.328688 + 0.303256i
\(466\) 5.39718 0.250019
\(467\) 3.90264 5.37152i 0.180593 0.248564i −0.709117 0.705090i \(-0.750906\pi\)
0.889710 + 0.456526i \(0.150906\pi\)
\(468\) −4.60514 + 3.07046i −0.212872 + 0.141932i
\(469\) −0.0511621 0.157461i −0.00236244 0.00727086i
\(470\) 1.87171i 0.0863358i
\(471\) −2.89981 + 2.78536i −0.133616 + 0.128342i
\(472\) 3.57105 + 10.9906i 0.164371 + 0.505882i
\(473\) −21.8801 7.10929i −1.00605 0.326886i
\(474\) −2.69417 5.56159i −0.123747 0.255453i
\(475\) 2.96328 + 2.15295i 0.135965 + 0.0987841i
\(476\) 0.446265 + 1.37346i 0.0204545 + 0.0629525i
\(477\) −1.71384 + 2.16957i −0.0784712 + 0.0993378i
\(478\) −15.4215 21.2259i −0.705363 0.970849i
\(479\) −16.3638 5.31692i −0.747681 0.242936i −0.0896979 0.995969i \(-0.528590\pi\)
−0.657983 + 0.753033i \(0.728590\pi\)
\(480\) 0.305332 1.70493i 0.0139364 0.0778189i
\(481\) −4.93438 + 3.58504i −0.224989 + 0.163464i
\(482\) −6.79629 + 20.9168i −0.309562 + 0.952735i
\(483\) 0.107874 0.602350i 0.00490843 0.0274079i
\(484\) 3.76320 + 2.73413i 0.171055 + 0.124278i
\(485\) −8.15403 + 2.64941i −0.370256 + 0.120303i
\(486\) 0.879189 + 15.5636i 0.0398808 + 0.705981i
\(487\) 14.3107 + 4.64982i 0.648478 + 0.210703i 0.614743 0.788727i \(-0.289260\pi\)
0.0337353 + 0.999431i \(0.489260\pi\)
\(488\) 0.262344 0.807412i 0.0118758 0.0365498i
\(489\) −27.0794 14.4915i −1.22457 0.655327i
\(490\) −6.89747 −0.311596
\(491\) 13.0454 0.588729 0.294364 0.955693i \(-0.404892\pi\)
0.294364 + 0.955693i \(0.404892\pi\)
\(492\) −4.42134 + 8.26190i −0.199329 + 0.372475i
\(493\) −31.5319 + 22.9092i −1.42012 + 1.03178i
\(494\) 5.46715 + 3.97212i 0.245979 + 0.178714i
\(495\) 11.8590 + 0.477700i 0.533023 + 0.0214710i
\(496\) 0.111860 5.56664i 0.00502267 0.249950i
\(497\) 2.43283i 0.109127i
\(498\) 1.72807 + 12.5393i 0.0774367 + 0.561899i
\(499\) 16.7942 + 23.1152i 0.751812 + 1.03478i 0.997851 + 0.0655200i \(0.0208706\pi\)
−0.246040 + 0.969260i \(0.579129\pi\)
\(500\) −0.951057 + 0.309017i −0.0425325 + 0.0138197i
\(501\) −7.39478 + 7.10290i −0.330374 + 0.317334i
\(502\) 4.29020i 0.191481i
\(503\) −24.0415 + 7.81155i −1.07196 + 0.348300i −0.791249 0.611494i \(-0.790569\pi\)
−0.280707 + 0.959793i \(0.590569\pi\)
\(504\) 0.333370 0.900891i 0.0148495 0.0401289i
\(505\) −4.39369 + 13.5224i −0.195516 + 0.601738i
\(506\) −2.56580 + 3.53152i −0.114064 + 0.156995i
\(507\) −14.6545 7.84232i −0.650829 0.348289i
\(508\) −9.27031 + 12.7595i −0.411303 + 0.566111i
\(509\) 21.2280 15.4230i 0.940914 0.683614i −0.00772660 0.999970i \(-0.502459\pi\)
0.948640 + 0.316356i \(0.102459\pi\)
\(510\) −3.40567 7.03036i −0.150806 0.311309i
\(511\) 0.459831 + 0.632902i 0.0203417 + 0.0279980i
\(512\) 0.587785 + 0.809017i 0.0259767 + 0.0357538i
\(513\) 17.4487 7.60138i 0.770379 0.335609i
\(514\) −9.72596 + 7.06632i −0.428994 + 0.311682i
\(515\) 0.360472 0.496147i 0.0158843 0.0218628i
\(516\) 4.75241 8.88056i 0.209213 0.390945i
\(517\) −4.35249 + 5.99068i −0.191422 + 0.263470i
\(518\) 0.327106 1.00673i 0.0143722 0.0442331i
\(519\) −23.9443 + 11.5992i −1.05104 + 0.509147i
\(520\) −1.75466 + 0.570125i −0.0769471 + 0.0250016i
\(521\) 2.89339i 0.126762i 0.997989 + 0.0633808i \(0.0201883\pi\)
−0.997989 + 0.0633808i \(0.979812\pi\)
\(522\) 25.9042 + 1.04346i 1.13379 + 0.0456711i
\(523\) 5.70023 1.85212i 0.249254 0.0809875i −0.181725 0.983349i \(-0.558168\pi\)
0.430979 + 0.902362i \(0.358168\pi\)
\(524\) 8.11815 + 11.1737i 0.354643 + 0.488124i
\(525\) −0.549406 + 0.0757150i −0.0239781 + 0.00330447i
\(526\) 7.88795i 0.343931i
\(527\) −14.3490 20.6081i −0.625053 0.897701i
\(528\) −4.94189 + 4.74683i −0.215068 + 0.206579i
\(529\) 17.6225 + 12.8035i 0.766194 + 0.556672i
\(530\) −0.745597 + 0.541708i −0.0323867 + 0.0235303i
\(531\) −9.37740 33.3762i −0.406944 1.44840i
\(532\) −1.17283 −0.0508485
\(533\) 9.98142 0.432343
\(534\) −2.81647 + 5.26297i −0.121880 + 0.227751i
\(535\) 5.94481 18.2962i 0.257017 0.791016i
\(536\) −0.491760 0.159783i −0.0212408 0.00690156i
\(537\) 5.43154 0.748534i 0.234388 0.0323016i
\(538\) −24.7582 + 8.04441i −1.06740 + 0.346819i
\(539\) 22.0763 + 16.0394i 0.950894 + 0.690865i
\(540\) −1.12112 + 5.07377i −0.0482453 + 0.218340i
\(541\) 8.94743 27.5374i 0.384680 1.18392i −0.552032 0.833823i \(-0.686147\pi\)
0.936712 0.350101i \(-0.113853\pi\)
\(542\) 26.3215 19.1237i 1.13061 0.821433i
\(543\) −6.54416 1.17198i −0.280837 0.0502946i
\(544\) 4.28941 + 1.39371i 0.183907 + 0.0597550i
\(545\) 0.980573 + 1.34964i 0.0420031 + 0.0578124i
\(546\) −1.01363 + 0.139691i −0.0433796 + 0.00597824i
\(547\) 3.04135 + 9.36030i 0.130039 + 0.400218i 0.994785 0.101990i \(-0.0325211\pi\)
−0.864747 + 0.502208i \(0.832521\pi\)
\(548\) 13.2341 + 9.61513i 0.565332 + 0.410738i
\(549\) −0.883887 + 2.38860i −0.0377234 + 0.101943i
\(550\) 3.76258 + 1.22254i 0.160437 + 0.0521291i
\(551\) −9.78134 30.1039i −0.416699 1.28247i
\(552\) −1.32388 1.37829i −0.0563482 0.0586637i
\(553\) 1.14244i 0.0485813i
\(554\) −3.33709 10.2705i −0.141779 0.436352i
\(555\) −1.00939 + 5.63629i −0.0428463 + 0.239247i
\(556\) −7.07192 + 9.73366i −0.299916 + 0.412799i
\(557\) 38.9217 1.64917 0.824583 0.565742i \(-0.191410\pi\)
0.824583 + 0.565742i \(0.191410\pi\)
\(558\) −1.00746 + 16.6729i −0.0426493 + 0.705819i
\(559\) −10.7288 −0.453782
\(560\) 0.188208 0.259046i 0.00795322 0.0109467i
\(561\) −5.44807 + 30.4212i −0.230018 + 1.28438i
\(562\) −1.64354 5.05831i −0.0693287 0.213372i
\(563\) 2.83753i 0.119588i −0.998211 0.0597939i \(-0.980956\pi\)
0.998211 0.0597939i \(-0.0190443\pi\)
\(564\) −2.24577 2.33805i −0.0945638 0.0984497i
\(565\) −4.61113 14.1916i −0.193992 0.597046i
\(566\) 1.03782 + 0.337209i 0.0436230 + 0.0141740i
\(567\) −1.10808 + 2.66023i −0.0465350 + 0.111719i
\(568\) 6.14683 + 4.46593i 0.257915 + 0.187386i
\(569\) 4.87430 + 15.0016i 0.204341 + 0.628898i 0.999740 + 0.0228111i \(0.00726163\pi\)
−0.795398 + 0.606087i \(0.792738\pi\)
\(570\) 6.28479 0.866121i 0.263241 0.0362778i
\(571\) −7.83338 10.7817i −0.327817 0.451201i 0.613017 0.790070i \(-0.289956\pi\)
−0.940834 + 0.338869i \(0.889956\pi\)
\(572\) 6.94182 + 2.25553i 0.290252 + 0.0943086i
\(573\) −42.4539 7.60298i −1.77354 0.317619i
\(574\) −1.40146 + 1.01822i −0.0584958 + 0.0424997i
\(575\) −0.340963 + 1.04938i −0.0142191 + 0.0437620i
\(576\) −1.66424 2.49606i −0.0693434 0.104002i
\(577\) −12.3943 9.00501i −0.515983 0.374884i 0.299106 0.954220i \(-0.403312\pi\)
−0.815089 + 0.579336i \(0.803312\pi\)
\(578\) 3.17796 1.03258i 0.132186 0.0429497i
\(579\) 37.2856 5.13842i 1.54954 0.213545i
\(580\) 8.21877 + 2.67044i 0.341266 + 0.110884i
\(581\) −0.723101 + 2.22548i −0.0299993 + 0.0923283i
\(582\) −7.00673 + 13.0931i −0.290438 + 0.542725i
\(583\) 3.64607 0.151005
\(584\) 2.44321 0.101101
\(585\) 5.32857 1.49712i 0.220309 0.0618982i
\(586\) 23.1096 16.7901i 0.954649 0.693593i
\(587\) 3.23454 + 2.35003i 0.133504 + 0.0969963i 0.652533 0.757760i \(-0.273706\pi\)
−0.519029 + 0.854757i \(0.673706\pi\)
\(588\) −8.61597 + 8.27589i −0.355317 + 0.341292i
\(589\) 19.5183 5.91106i 0.804236 0.243561i
\(590\) 11.5562i 0.475760i
\(591\) 17.7797 2.45026i 0.731359 0.100790i
\(592\) −1.94315 2.67452i −0.0798629 0.109922i
\(593\) 37.3148 12.1243i 1.53233 0.497885i 0.583085 0.812411i \(-0.301846\pi\)
0.949249 + 0.314526i \(0.101846\pi\)
\(594\) 15.3868 13.6322i 0.631329 0.559338i
\(595\) 1.44414i 0.0592041i
\(596\) 4.04797 1.31526i 0.165811 0.0538753i
\(597\) 4.34212 2.10343i 0.177711 0.0860875i
\(598\) −0.629064 + 1.93606i −0.0257244 + 0.0791714i
\(599\) −16.9392 + 23.3148i −0.692118 + 0.952619i 0.307881 + 0.951425i \(0.400380\pi\)
−0.999999 + 0.00119400i \(0.999620\pi\)
\(600\) −0.817239 + 1.52713i −0.0333636 + 0.0623447i
\(601\) −0.433825 + 0.597109i −0.0176961 + 0.0243566i −0.817773 0.575540i \(-0.804792\pi\)
0.800077 + 0.599897i \(0.204792\pi\)
\(602\) 1.50640 1.09447i 0.0613964 0.0446071i
\(603\) 1.45479 + 0.538338i 0.0592437 + 0.0219228i
\(604\) −3.40630 4.68837i −0.138600 0.190767i
\(605\) −2.73413 3.76320i −0.111158 0.152996i
\(606\) 10.7364 + 22.1632i 0.436135 + 0.900318i
\(607\) −30.9224 + 22.4664i −1.25510 + 0.911884i −0.998506 0.0546359i \(-0.982600\pi\)
−0.256594 + 0.966519i \(0.582600\pi\)
\(608\) −2.15295 + 2.96328i −0.0873137 + 0.120177i
\(609\) 4.22566 + 2.26135i 0.171232 + 0.0916346i
\(610\) −0.499008 + 0.686826i −0.0202043 + 0.0278088i
\(611\) −1.06711 + 3.28423i −0.0431707 + 0.132866i
\(612\) −12.6895 4.69569i −0.512944 0.189812i
\(613\) 28.8247 9.36571i 1.16422 0.378277i 0.337736 0.941241i \(-0.390339\pi\)
0.826482 + 0.562963i \(0.190339\pi\)
\(614\) 12.0412i 0.485945i
\(615\) 6.75801 6.49127i 0.272509 0.261753i
\(616\) −1.20477 + 0.391453i −0.0485415 + 0.0157721i
\(617\) 28.4933 + 39.2177i 1.14710 + 1.57884i 0.750527 + 0.660840i \(0.229800\pi\)
0.396570 + 0.918004i \(0.370200\pi\)
\(618\) −0.145016 1.05227i −0.00583340 0.0423286i
\(619\) 39.0743i 1.57053i −0.619160 0.785265i \(-0.712527\pi\)
0.619160 0.785265i \(-0.287473\pi\)
\(620\) −1.82657 + 5.25962i −0.0733569 + 0.211232i
\(621\) 3.80201 + 4.29136i 0.152569 + 0.172206i
\(622\) 27.4399 + 19.9362i 1.10024 + 0.799370i
\(623\) −0.892754 + 0.648624i −0.0357674 + 0.0259866i
\(624\) −1.50778 + 2.81750i −0.0603594 + 0.112790i
\(625\) 1.00000 0.0400000
\(626\) −0.0654495 −0.00261589
\(627\) −22.1294 11.8425i −0.883763 0.472944i
\(628\) −0.717362 + 2.20781i −0.0286259 + 0.0881013i
\(629\) −14.1803 4.60746i −0.565405 0.183711i
\(630\) −0.595444 + 0.753781i −0.0237231 + 0.0300314i
\(631\) 0.446512 0.145081i 0.0177754 0.00577557i −0.300116 0.953903i \(-0.597025\pi\)
0.317891 + 0.948127i \(0.397025\pi\)
\(632\) −2.88650 2.09716i −0.114819 0.0834207i
\(633\) 7.87344 43.9640i 0.312941 1.74741i
\(634\) 7.38147 22.7178i 0.293155 0.902240i
\(635\) 12.7595 9.27031i 0.506345 0.367881i
\(636\) −0.281397 + 1.57127i −0.0111581 + 0.0623051i
\(637\) 12.1028 + 3.93242i 0.479529 + 0.155808i
\(638\) −20.0955 27.6590i −0.795587 1.09503i
\(639\) −17.8863 14.1292i −0.707571 0.558941i
\(640\) −0.309017 0.951057i −0.0122150 0.0375938i
\(641\) 8.29761 + 6.02857i 0.327736 + 0.238114i 0.739469 0.673190i \(-0.235076\pi\)
−0.411733 + 0.911304i \(0.635076\pi\)
\(642\) −14.5267 29.9876i −0.573323 1.18352i
\(643\) 39.1464 + 12.7194i 1.54378 + 0.501606i 0.952417 0.304797i \(-0.0985886\pi\)
0.591367 + 0.806403i \(0.298589\pi\)
\(644\) −0.109176 0.336008i −0.00430212 0.0132406i
\(645\) −7.26406 + 6.97734i −0.286022 + 0.274732i
\(646\) 16.5199i 0.649966i
\(647\) 10.6853 + 32.8859i 0.420081 + 1.29288i 0.907626 + 0.419779i \(0.137893\pi\)
−0.487545 + 0.873098i \(0.662107\pi\)
\(648\) 4.68728 + 7.68306i 0.184134 + 0.301819i
\(649\) −26.8727 + 36.9871i −1.05485 + 1.45187i
\(650\) 1.84496 0.0723654
\(651\) −1.51137 + 2.69272i −0.0592351 + 0.105536i
\(652\) −17.7322 −0.694448
\(653\) 18.6748 25.7036i 0.730800 1.00586i −0.268295 0.963337i \(-0.586460\pi\)
0.999095 0.0425234i \(-0.0135397\pi\)
\(654\) 2.84424 + 0.509370i 0.111219 + 0.0199180i
\(655\) −4.26796 13.1354i −0.166763 0.513244i
\(656\) 5.41009i 0.211229i
\(657\) −7.32369 0.295010i −0.285724 0.0115094i
\(658\) −0.185200 0.569986i −0.00721984 0.0222204i
\(659\) −42.9622 13.9593i −1.67357 0.543776i −0.689924 0.723882i \(-0.742356\pi\)
−0.983647 + 0.180105i \(0.942356\pi\)
\(660\) 6.16687 2.98738i 0.240045 0.116284i
\(661\) −22.1115 16.0650i −0.860039 0.624855i 0.0678564 0.997695i \(-0.478384\pi\)
−0.927896 + 0.372840i \(0.878384\pi\)
\(662\) 1.35298 + 4.16405i 0.0525851 + 0.161840i
\(663\) 1.96763 + 14.2776i 0.0764163 + 0.554495i
\(664\) 4.29553 + 5.91229i 0.166699 + 0.229441i
\(665\) 1.11542 + 0.362423i 0.0432543 + 0.0140542i
\(666\) 5.50178 + 8.25167i 0.213190 + 0.319746i
\(667\) 7.71406 5.60459i 0.298690 0.217011i
\(668\) −1.82934 + 5.63011i −0.0707791 + 0.217836i
\(669\) −25.0771 4.49100i −0.969535 0.173632i
\(670\) 0.418316 + 0.303925i 0.0161610 + 0.0117416i
\(671\) 3.19429 1.03789i 0.123314 0.0400672i
\(672\) −0.0757150 0.549406i −0.00292077 0.0211938i
\(673\) 43.0944 + 14.0022i 1.66117 + 0.539746i 0.981117 0.193417i \(-0.0619572\pi\)
0.680052 + 0.733164i \(0.261957\pi\)
\(674\) 3.18595 9.80535i 0.122718 0.377688i
\(675\) 2.63413 4.47899i 0.101388 0.172397i
\(676\) −9.59611 −0.369081
\(677\) 32.1320 1.23493 0.617467 0.786597i \(-0.288159\pi\)
0.617467 + 0.786597i \(0.288159\pi\)
\(678\) −22.7877 12.1948i −0.875157 0.468338i
\(679\) −2.22097 + 1.61363i −0.0852329 + 0.0619254i
\(680\) −3.64879 2.65100i −0.139925 0.101661i
\(681\) −23.6176 24.5881i −0.905027 0.942217i
\(682\) 18.0769 12.5866i 0.692201 0.481967i
\(683\) 8.90535i 0.340754i 0.985379 + 0.170377i \(0.0544985\pi\)
−0.985379 + 0.170377i \(0.945501\pi\)
\(684\) 6.81143 8.62268i 0.260441 0.329696i
\(685\) −9.61513 13.2341i −0.367375 0.505649i
\(686\) −4.23215 + 1.37511i −0.161584 + 0.0525019i
\(687\) 3.62392 + 3.77284i 0.138261 + 0.143943i
\(688\) 5.81520i 0.221703i
\(689\) 1.61711 0.525432i 0.0616072 0.0200174i
\(690\) 0.833175 + 1.71993i 0.0317184 + 0.0654766i
\(691\) 0.500396 1.54006i 0.0190360 0.0585867i −0.941087 0.338164i \(-0.890194\pi\)
0.960123 + 0.279577i \(0.0901942\pi\)
\(692\) −9.02889 + 12.4272i −0.343227 + 0.472412i
\(693\) 3.65865 1.02794i 0.138980 0.0390480i
\(694\) 5.62237 7.73852i 0.213422 0.293750i
\(695\) 9.73366 7.07192i 0.369219 0.268253i
\(696\) 13.4706 6.52547i 0.510601 0.247347i
\(697\) 14.3422 + 19.7403i 0.543248 + 0.747717i
\(698\) 9.57109 + 13.1735i 0.362271 + 0.498624i
\(699\) −8.41303 + 4.07547i −0.318210 + 0.154149i
\(700\) −0.259046 + 0.188208i −0.00979100 + 0.00711358i
\(701\) −21.1800 + 29.1518i −0.799957 + 1.10105i 0.192839 + 0.981230i \(0.438230\pi\)
−0.992796 + 0.119816i \(0.961770\pi\)
\(702\) 4.85987 8.26358i 0.183424 0.311889i
\(703\) 7.11740 9.79626i 0.268438 0.369473i
\(704\) −1.22254 + 3.76258i −0.0460760 + 0.141807i
\(705\) 1.41335 + 2.91760i 0.0532300 + 0.109883i
\(706\) −22.2037 + 7.21441i −0.835646 + 0.271518i
\(707\) 4.55266i 0.171220i
\(708\) −13.8656 14.4354i −0.521101 0.542515i
\(709\) −1.54319 + 0.501412i −0.0579557 + 0.0188309i −0.337851 0.941199i \(-0.609700\pi\)
0.279896 + 0.960030i \(0.409700\pi\)
\(710\) −4.46593 6.14683i −0.167603 0.230686i
\(711\) 8.39925 + 6.63493i 0.314996 + 0.248829i
\(712\) 3.44632i 0.129156i
\(713\) 3.51039 + 5.04162i 0.131465 + 0.188810i
\(714\) −1.73275 1.80395i −0.0648464 0.0675111i
\(715\) −5.90506 4.29028i −0.220837 0.160447i
\(716\) 2.56098 1.86066i 0.0957082 0.0695361i
\(717\) 40.0667 + 21.4416i 1.49632 + 0.800751i
\(718\) −1.68287 −0.0628041
\(719\) 12.1477 0.453033 0.226516 0.974007i \(-0.427266\pi\)
0.226516 + 0.974007i \(0.427266\pi\)
\(720\) 0.811463 + 2.88817i 0.0302414 + 0.107636i
\(721\) 0.0606811 0.186757i 0.00225988 0.00695520i
\(722\) 5.31047 + 1.72548i 0.197635 + 0.0642156i
\(723\) −5.20059 37.7367i −0.193412 1.40344i
\(724\) −3.65052 + 1.18613i −0.135671 + 0.0440821i
\(725\) −6.99130 5.07948i −0.259650 0.188647i
\(726\) −7.93059 1.42027i −0.294332 0.0527113i
\(727\) 9.79813 30.1555i 0.363392 1.11841i −0.587589 0.809160i \(-0.699923\pi\)
0.950982 0.309248i \(-0.100077\pi\)
\(728\) −0.477930 + 0.347236i −0.0177133 + 0.0128694i
\(729\) −13.1228 23.5965i −0.486028 0.873943i
\(730\) −2.32363 0.754993i −0.0860014 0.0279435i
\(731\) −15.4161 21.2185i −0.570186 0.784794i
\(732\) 0.200749 + 1.45668i 0.00741988 + 0.0538405i
\(733\) 5.99054 + 18.4370i 0.221266 + 0.680985i 0.998649 + 0.0519587i \(0.0165464\pi\)
−0.777384 + 0.629027i \(0.783454\pi\)
\(734\) 1.17772 + 0.855665i 0.0434705 + 0.0315832i
\(735\) 10.7517 5.20836i 0.396581 0.192113i
\(736\) −1.04938 0.340963i −0.0386805 0.0125681i
\(737\) −0.632133 1.94551i −0.0232849 0.0716636i
\(738\) 0.653252 16.2171i 0.0240465 0.596960i
\(739\) 48.0845i 1.76882i −0.466713 0.884409i \(-0.654562\pi\)
0.466713 0.884409i \(-0.345438\pi\)
\(740\) 1.02157 + 3.14408i 0.0375538 + 0.115579i
\(741\) −11.5215 2.06336i −0.423253 0.0757995i
\(742\) −0.173454 + 0.238739i −0.00636769 + 0.00876437i
\(743\) −12.7128 −0.466386 −0.233193 0.972431i \(-0.574917\pi\)
−0.233193 + 0.972431i \(0.574917\pi\)
\(744\) 4.02907 + 8.76166i 0.147713 + 0.321218i
\(745\) −4.25628 −0.155938
\(746\) 12.9450 17.8173i 0.473951 0.652337i
\(747\) −12.1623 18.2412i −0.444994 0.667409i
\(748\) 5.51382 + 16.9698i 0.201605 + 0.620477i
\(749\) 6.15991i 0.225078i
\(750\) 1.24915 1.19984i 0.0456125 0.0438121i
\(751\) 7.52405 + 23.1567i 0.274557 + 0.844998i 0.989336 + 0.145649i \(0.0465269\pi\)
−0.714780 + 0.699350i \(0.753473\pi\)
\(752\) −1.78011 0.578392i −0.0649138 0.0210918i
\(753\) −3.23958 6.68749i −0.118057 0.243706i
\(754\) −12.8987 9.37145i −0.469743 0.341288i
\(755\) 1.79080 + 5.51151i 0.0651738 + 0.200584i
\(756\) 0.160622 + 1.65603i 0.00584176 + 0.0602291i
\(757\) −14.3270 19.7195i −0.520725 0.716717i 0.464956 0.885334i \(-0.346070\pi\)
−0.985682 + 0.168617i \(0.946070\pi\)
\(758\) 10.4127 + 3.38329i 0.378206 + 0.122886i
\(759\) 1.33283 7.44234i 0.0483788 0.270140i
\(760\) 2.96328 2.15295i 0.107490 0.0780957i
\(761\) 5.83388 17.9548i 0.211478 0.650862i −0.787907 0.615794i \(-0.788835\pi\)
0.999385 0.0350680i \(-0.0111648\pi\)
\(762\) 4.81557 26.8894i 0.174450 0.974100i
\(763\) 0.432153 + 0.313978i 0.0156450 + 0.0113667i
\(764\) −23.6820 + 7.69474i −0.856784 + 0.278386i
\(765\) 10.6174 + 8.38715i 0.383873 + 0.303238i
\(766\) −0.776540 0.252313i −0.0280575 0.00911644i
\(767\) −6.58846 + 20.2772i −0.237895 + 0.732167i
\(768\) −1.52713 0.817239i −0.0551055 0.0294896i
\(769\) −39.7505 −1.43344 −0.716719 0.697362i \(-0.754357\pi\)
−0.716719 + 0.697362i \(0.754357\pi\)
\(770\) 1.26677 0.0456512
\(771\) 9.82480 18.3590i 0.353832 0.661185i
\(772\) 17.5802 12.7728i 0.632725 0.459702i
\(773\) 23.6036 + 17.1490i 0.848963 + 0.616808i 0.924860 0.380308i \(-0.124182\pi\)
−0.0758966 + 0.997116i \(0.524182\pi\)
\(774\) −0.702168 + 17.4315i −0.0252389 + 0.626561i
\(775\) 3.36249 4.43776i 0.120784 0.159409i
\(776\) 8.57366i 0.307776i
\(777\) 0.250305 + 1.81627i 0.00897964 + 0.0651584i
\(778\) −9.10343 12.5298i −0.326374 0.449215i
\(779\) −18.8463 + 6.12354i −0.675239 + 0.219398i
\(780\) 2.30463 2.21367i 0.0825192 0.0792621i
\(781\) 30.0589i 1.07559i
\(782\) −4.73285 + 1.53780i −0.169246 + 0.0549915i
\(783\) −41.1669 + 17.9340i −1.47119 + 0.640909i
\(784\) −2.13144 + 6.55989i −0.0761227 + 0.234282i
\(785\) 1.36450 1.87808i 0.0487012 0.0670315i
\(786\) −21.0918 11.2872i −0.752320 0.402602i
\(787\) 26.3255 36.2339i 0.938401 1.29160i −0.0180899 0.999836i \(-0.505759\pi\)
0.956491 0.291762i \(-0.0942415\pi\)
\(788\) 8.38315 6.09071i 0.298637 0.216973i
\(789\) −5.95628 12.2956i −0.212049 0.437735i
\(790\) 2.09716 + 2.88650i 0.0746137 + 0.102697i
\(791\) −2.80842 3.86546i −0.0998561 0.137440i
\(792\) 4.11895 11.1310i 0.146361 0.395522i
\(793\) 1.26717 0.920652i 0.0449985 0.0326933i
\(794\) −11.1726 + 15.3777i −0.396499 + 0.545734i
\(795\) 0.753175 1.40741i 0.0267124 0.0499159i
\(796\) 1.63733 2.25359i 0.0580335 0.0798762i
\(797\) 8.07205 24.8432i 0.285927 0.879992i −0.700193 0.713954i \(-0.746903\pi\)
0.986119 0.166038i \(-0.0530974\pi\)
\(798\) 1.82818 0.885615i 0.0647170 0.0313504i
\(799\) −8.02856 + 2.60864i −0.284030 + 0.0922869i
\(800\) 1.00000i 0.0353553i
\(801\) 0.416133 10.3306i 0.0147033 0.365013i
\(802\) 6.78880 2.20581i 0.239721 0.0778900i
\(803\) 5.68144 + 7.81983i 0.200494 + 0.275956i
\(804\) 0.887202 0.122267i 0.0312892 0.00431204i
\(805\) 0.353300i 0.0124522i
\(806\) 6.20366 8.18750i 0.218515 0.288392i
\(807\) 32.5182 31.2347i 1.14469 1.09951i
\(808\) 11.5028 + 8.35729i 0.404668 + 0.294008i
\(809\) 4.81718 3.49989i 0.169363 0.123050i −0.499875 0.866098i \(-0.666621\pi\)
0.669238 + 0.743048i \(0.266621\pi\)
\(810\) −2.08368 8.75547i −0.0732130 0.307636i
\(811\) 27.5673 0.968018 0.484009 0.875063i \(-0.339180\pi\)
0.484009 + 0.875063i \(0.339180\pi\)
\(812\) 2.76706 0.0971049
\(813\) −26.5890 + 49.6854i −0.932517 + 1.74254i
\(814\) 4.04156 12.4386i 0.141657 0.435974i
\(815\) 16.8644 + 5.47956i 0.590732 + 0.191941i
\(816\) −7.73868 + 1.06649i −0.270908 + 0.0373344i
\(817\) 20.2575 6.58207i 0.708722 0.230278i
\(818\) −29.9991 21.7956i −1.04889 0.762066i
\(819\) 1.47455 0.983156i 0.0515251 0.0343542i
\(820\) 1.67181 5.14530i 0.0583821 0.179682i
\(821\) 13.7668 10.0021i 0.480464 0.349077i −0.321041 0.947065i \(-0.604033\pi\)
0.801505 + 0.597988i \(0.204033\pi\)
\(822\) −27.8896 4.99469i −0.972761 0.174210i
\(823\) 1.55932 + 0.506654i 0.0543545 + 0.0176609i 0.336068 0.941838i \(-0.390903\pi\)
−0.281714 + 0.959499i \(0.590903\pi\)
\(824\) −0.360472 0.496147i −0.0125576 0.0172841i
\(825\) −6.78819 + 0.935497i −0.236335 + 0.0325698i
\(826\) −1.14344 3.51916i −0.0397855 0.122447i
\(827\) −6.46319 4.69578i −0.224747 0.163288i 0.469714 0.882819i \(-0.344357\pi\)
−0.694461 + 0.719530i \(0.744357\pi\)
\(828\) 3.10441 + 1.14877i 0.107886 + 0.0399225i
\(829\) −6.37547 2.07151i −0.221429 0.0719467i 0.196201 0.980564i \(-0.437139\pi\)
−0.417631 + 0.908617i \(0.637139\pi\)
\(830\) −2.25829 6.95031i −0.0783865 0.241249i
\(831\) 12.9572 + 13.4896i 0.449480 + 0.467950i
\(832\) 1.84496i 0.0639626i
\(833\) 9.61311 + 29.5861i 0.333075 + 1.02510i
\(834\) 3.67359 20.5128i 0.127206 0.710299i
\(835\) 3.47960 4.78926i 0.120417 0.165739i
\(836\) −14.4909 −0.501177
\(837\) −11.0195 26.7502i −0.380889 0.924621i
\(838\) −23.2685 −0.803798
\(839\) 14.3590 19.7635i 0.495728 0.682311i −0.485703 0.874124i \(-0.661436\pi\)
0.981432 + 0.191812i \(0.0614365\pi\)
\(840\) −0.0977667 + 0.545914i −0.00337327 + 0.0188358i
\(841\) 14.1157 + 43.4437i 0.486749 + 1.49806i
\(842\) 12.8970i 0.444461i
\(843\) 6.38151 + 6.64375i 0.219791 + 0.228823i
\(844\) −7.96846 24.5244i −0.274286 0.844165i
\(845\) 9.12644 + 2.96536i 0.313959 + 0.102012i
\(846\) 5.26615 + 1.94871i 0.181054 + 0.0669981i
\(847\) −1.20497 0.875461i −0.0414032 0.0300812i
\(848\) 0.284793 + 0.876502i 0.00977982 + 0.0300992i
\(849\) −1.87237 + 0.258036i −0.0642597 + 0.00885578i
\(850\) 2.65100 + 3.64879i 0.0909287 + 0.125153i
\(851\) 3.46912 + 1.12718i 0.118920 + 0.0386394i
\(852\) −12.9539 2.31988i −0.443792 0.0794778i
\(853\) 35.0470 25.4631i 1.19999 0.871841i 0.205702 0.978615i \(-0.434052\pi\)
0.994283 + 0.106774i \(0.0340521\pi\)
\(854\) −0.0840021 + 0.258532i −0.00287449 + 0.00884678i
\(855\) −9.14261 + 6.09581i −0.312671 + 0.208472i
\(856\) −15.5637 11.3077i −0.531957 0.386489i
\(857\) 20.1331 6.54164i 0.687733 0.223458i 0.0557552 0.998444i \(-0.482243\pi\)
0.631978 + 0.774986i \(0.282243\pi\)
\(858\) −12.5240 + 1.72596i −0.427561 + 0.0589232i
\(859\) 48.4861 + 15.7541i 1.65432 + 0.537522i 0.979671 0.200612i \(-0.0642931\pi\)
0.674653 + 0.738135i \(0.264293\pi\)
\(860\) −1.79700 + 5.53059i −0.0612771 + 0.188591i
\(861\) 1.41570 2.64544i 0.0482470 0.0901565i
\(862\) 4.74053 0.161463
\(863\) −41.6703 −1.41847 −0.709237 0.704970i \(-0.750961\pi\)
−0.709237 + 0.704970i \(0.750961\pi\)
\(864\) 4.47899 + 2.63413i 0.152378 + 0.0896148i
\(865\) 12.4272 9.02889i 0.422538 0.306992i
\(866\) 19.0342 + 13.8292i 0.646809 + 0.469934i
\(867\) −4.17404 + 4.00928i −0.141758 + 0.136162i
\(868\) −0.0358174 + 1.78243i −0.00121572 + 0.0604995i
\(869\) 14.1154i 0.478831i
\(870\) −14.8278 + 2.04345i −0.502708 + 0.0692794i
\(871\) −0.560730 0.771778i −0.0189996 0.0261507i
\(872\) 1.58660 0.515518i 0.0537291 0.0174576i
\(873\) 1.03524 25.7001i 0.0350377 0.869818i
\(874\) 4.04148i 0.136705i
\(875\) 0.304526 0.0989466i 0.0102949 0.00334501i
\(876\) −3.80843 + 1.84490i −0.128675 + 0.0623332i
\(877\) 14.6514 45.0924i 0.494743 1.52266i −0.322615 0.946530i \(-0.604562\pi\)
0.817358 0.576131i \(-0.195438\pi\)
\(878\) −13.8335 + 19.0402i −0.466859 + 0.642577i
\(879\) −23.3445 + 43.6225i −0.787389 + 1.47135i
\(880\) 2.32540 3.20064i 0.0783892 0.107894i
\(881\) −38.4910 + 27.9653i −1.29679 + 0.942175i −0.999919 0.0127412i \(-0.995944\pi\)
−0.296874 + 0.954917i \(0.595944\pi\)
\(882\) 7.18121 19.4063i 0.241804 0.653446i
\(883\) 28.6624 + 39.4504i 0.964567 + 1.32761i 0.944744 + 0.327809i \(0.106310\pi\)
0.0198232 + 0.999804i \(0.493690\pi\)
\(884\) 4.89100 + 6.73189i 0.164502 + 0.226418i
\(885\) 8.72619 + 18.0136i 0.293328 + 0.605519i
\(886\) −18.3426 + 13.3266i −0.616230 + 0.447717i
\(887\) −21.9424 + 30.2011i −0.736753 + 1.01405i 0.262046 + 0.965055i \(0.415603\pi\)
−0.998799 + 0.0489983i \(0.984397\pi\)
\(888\) 5.04851 + 2.70170i 0.169417 + 0.0906630i
\(889\) 2.96833 4.08556i 0.0995547 0.137025i
\(890\) 1.06497 3.27764i 0.0356979 0.109867i
\(891\) −13.6909 + 32.8685i −0.458662 + 1.10114i
\(892\) −13.9887 + 4.54520i −0.468376 + 0.152185i
\(893\) 6.85575i 0.229419i
\(894\) −5.31673 + 5.10688i −0.177818 + 0.170800i
\(895\) −3.01061 + 0.978206i −0.100634 + 0.0326978i
\(896\) −0.188208 0.259046i −0.00628757 0.00865410i
\(897\) −0.481367 3.49291i −0.0160724 0.116625i
\(898\) 8.12222i 0.271042i
\(899\) −46.0497 + 13.9460i −1.53584 + 0.465126i
\(900\) 0.120747 2.99757i 0.00402490 0.0999190i
\(901\) 3.36276 + 2.44319i 0.112030 + 0.0813944i
\(902\) −17.3157 + 12.5806i −0.576551 + 0.418889i
\(903\) −1.52171 + 2.84354i −0.0506394 + 0.0946270i
\(904\) −14.9219 −0.496297
\(905\) 3.83839 0.127592
\(906\) 8.84992 + 4.73601i 0.294019 + 0.157344i
\(907\) 15.3704 47.3052i 0.510365 1.57074i −0.281194 0.959651i \(-0.590730\pi\)
0.791559 0.611092i \(-0.209270\pi\)
\(908\) −18.7205 6.08264i −0.621260 0.201860i
\(909\) −33.4714 26.4405i −1.11018 0.876975i
\(910\) 0.561840 0.182553i 0.0186248 0.00605157i
\(911\) −8.22256 5.97404i −0.272426 0.197929i 0.443181 0.896432i \(-0.353850\pi\)
−0.715607 + 0.698503i \(0.753850\pi\)
\(912\) 1.11838 6.24483i 0.0370331 0.206787i
\(913\) −8.93428 + 27.4969i −0.295681 + 0.910014i
\(914\) −11.5494 + 8.39115i −0.382021 + 0.277555i
\(915\) 0.259216 1.44742i 0.00856941 0.0478502i
\(916\) 2.87250 + 0.933332i 0.0949101 + 0.0308382i
\(917\) −2.59942 3.57779i −0.0858402 0.118149i
\(918\) 23.3260 2.26244i 0.769872 0.0746717i
\(919\) 12.2687 + 37.7591i 0.404706 + 1.24556i 0.921140 + 0.389231i \(0.127259\pi\)
−0.516434 + 0.856327i \(0.672741\pi\)
\(920\) 0.892653 + 0.648550i 0.0294299 + 0.0213821i
\(921\) 9.09248 + 18.7697i 0.299608 + 0.618483i
\(922\) 23.7089 + 7.70348i 0.780811 + 0.253701i
\(923\) 4.33175 + 13.3318i 0.142581 + 0.438820i
\(924\) 1.58238 1.51993i 0.0520566 0.0500019i
\(925\) 3.30588i 0.108697i
\(926\) −4.97673 15.3168i −0.163545 0.503341i
\(927\) 1.02063 + 1.53076i 0.0335219 + 0.0502767i
\(928\) 5.07948 6.99130i 0.166742 0.229501i
\(929\) −20.1623 −0.661504 −0.330752 0.943718i \(-0.607302\pi\)
−0.330752 + 0.943718i \(0.607302\pi\)
\(930\) −1.12437 9.57788i −0.0368696 0.314071i
\(931\) −25.2642 −0.828000
\(932\) −3.17238 + 4.36641i −0.103915 + 0.143027i
\(933\) −57.8269 10.3561i −1.89317 0.339044i
\(934\) 2.05174 + 6.31461i 0.0671350 + 0.206620i
\(935\) 17.8431i 0.583532i
\(936\) 0.222774 5.53041i 0.00728159 0.180767i
\(937\) −2.08096 6.40454i −0.0679820 0.209227i 0.911294 0.411755i \(-0.135084\pi\)
−0.979276 + 0.202528i \(0.935084\pi\)
\(938\) 0.157461 + 0.0511621i 0.00514127 + 0.00167050i
\(939\) 0.102022 0.0494217i 0.00332935 0.00161282i
\(940\) 1.51425 + 1.10017i 0.0493894 + 0.0358835i
\(941\) 4.46996 + 13.7571i 0.145716 + 0.448469i 0.997102 0.0760707i \(-0.0242375\pi\)
−0.851386 + 0.524540i \(0.824237\pi\)
\(942\) −0.548933 3.98319i −0.0178852 0.129779i
\(943\) −3.50872 4.82933i −0.114260 0.157265i
\(944\) −10.9906 3.57105i −0.357712 0.116228i
\(945\) 0.358980 1.62461i 0.0116776 0.0528485i
\(946\) 18.6124 13.5227i 0.605140 0.439660i
\(947\) 3.32806 10.2427i 0.108147 0.332843i −0.882309 0.470671i \(-0.844012\pi\)
0.990456 + 0.137827i \(0.0440119\pi\)
\(948\) 6.08302 + 1.08940i 0.197567 + 0.0353819i
\(949\) 3.64675 + 2.64952i 0.118379 + 0.0860070i
\(950\) −3.48355 + 1.13187i −0.113021 + 0.0367228i
\(951\) 5.64838 + 40.9860i 0.183161 + 1.32906i
\(952\) −1.37346 0.446265i −0.0445141 0.0144635i
\(953\) 9.30400 28.6348i 0.301386 0.927571i −0.679615 0.733569i \(-0.737853\pi\)
0.981001 0.194002i \(-0.0621468\pi\)
\(954\) −0.747851 2.66176i −0.0242126 0.0861778i
\(955\) 24.9007 0.805768
\(956\) 26.2366 0.848553
\(957\) 52.2101 + 27.9401i 1.68771 + 0.903177i
\(958\) 13.9199 10.1134i 0.449731 0.326749i
\(959\) −4.23753 3.07874i −0.136837 0.0994178i
\(960\) 1.19984 + 1.24915i 0.0387248 + 0.0403161i
\(961\) −8.38738 29.8438i −0.270561 0.962703i
\(962\) 6.09923i 0.196647i
\(963\) 45.2879 + 35.7749i 1.45938 + 1.15283i
\(964\) −12.9273 17.7929i −0.416360 0.573071i
\(965\) −20.6668 + 6.71504i −0.665287 + 0.216165i
\(966\) 0.423905 + 0.441324i 0.0136389 + 0.0141994i
\(967\) 21.2015i 0.681793i 0.940101 + 0.340897i \(0.110731\pi\)
−0.940101 + 0.340897i \(0.889269\pi\)
\(968\) −4.42391 + 1.43741i −0.142190 + 0.0462003i
\(969\) −12.4744 25.7509i −0.400734 0.827239i
\(970\) 2.64941 8.15403i 0.0850673 0.261810i
\(971\) 32.6111 44.8854i 1.04654 1.44044i 0.154772 0.987950i \(-0.450536\pi\)
0.891770 0.452490i \(-0.149464\pi\)
\(972\) −13.1080 8.43680i −0.420440 0.270611i
\(973\) 2.26441 3.11670i 0.0725938 0.0999168i
\(974\) −12.1734 + 8.84448i −0.390060 + 0.283395i
\(975\) −2.87590 + 1.39315i −0.0921025 + 0.0446166i
\(976\) 0.499008 + 0.686826i 0.0159729 + 0.0219848i
\(977\) 8.53784 + 11.7513i 0.273150 + 0.375958i 0.923450 0.383719i \(-0.125357\pi\)
−0.650300 + 0.759677i \(0.725357\pi\)
\(978\) 27.6407 13.3898i 0.883852 0.428159i
\(979\) −11.0304 + 8.01407i −0.352534 + 0.256131i
\(980\) 4.05423 5.58017i 0.129508 0.178252i
\(981\) −4.81819 + 1.35372i −0.153833 + 0.0432211i
\(982\) −7.66787 + 10.5539i −0.244692 + 0.336789i
\(983\) 11.0705 34.0716i 0.353095 1.08671i −0.604011 0.796976i \(-0.706432\pi\)
0.957106 0.289739i \(-0.0935684\pi\)
\(984\) −4.08522 8.43316i −0.130232 0.268839i
\(985\) −9.85498 + 3.20208i −0.314006 + 0.102027i
\(986\) 38.9755i 1.24123i
\(987\) 0.719090 + 0.748639i 0.0228889 + 0.0238294i
\(988\) −6.42702 + 2.08826i −0.204471 + 0.0664365i
\(989\) 3.77145 + 5.19096i 0.119925 + 0.165063i
\(990\) −7.35701 + 9.31335i −0.233821 + 0.295998i
\(991\) 5.37964i 0.170890i 0.996343 + 0.0854449i \(0.0272312\pi\)
−0.996343 + 0.0854449i \(0.972769\pi\)
\(992\) 4.43776 + 3.36249i 0.140899 + 0.106759i
\(993\) −5.25332 5.46919i −0.166709 0.173560i
\(994\) −1.96820 1.42998i −0.0624276 0.0453563i
\(995\) −2.25359 + 1.63733i −0.0714435 + 0.0519067i
\(996\) −11.1602 5.97238i −0.353626 0.189242i
\(997\) −35.1088 −1.11191 −0.555953 0.831214i \(-0.687647\pi\)
−0.555953 + 0.831214i \(0.687647\pi\)
\(998\) −28.5720 −0.904431
\(999\) −14.8070 8.70811i −0.468474 0.275513i
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 930.2.v.b.401.7 80
3.2 odd 2 inner 930.2.v.b.401.11 yes 80
31.15 odd 10 inner 930.2.v.b.821.11 yes 80
93.77 even 10 inner 930.2.v.b.821.7 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.v.b.401.7 80 1.1 even 1 trivial
930.2.v.b.401.11 yes 80 3.2 odd 2 inner
930.2.v.b.821.7 yes 80 93.77 even 10 inner
930.2.v.b.821.11 yes 80 31.15 odd 10 inner