Properties

Label 418.2.f.f.229.3
Level $418$
Weight $2$
Character 418.229
Analytic conductor $3.338$
Analytic rank $0$
Dimension $16$
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] = [418,2,Mod(115,418)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(418, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("418.115");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 418 = 2 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 418.f (of order \(5\), 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: \(3.33774680449\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 6 x^{15} + 24 x^{14} - 62 x^{13} + 148 x^{12} - 232 x^{11} + 432 x^{10} - 356 x^{9} + 424 x^{8} - 320 x^{7} + 712 x^{6} - 936 x^{5} + 968 x^{4} - 336 x^{3} + 208 x^{2} + \cdots + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 229.3
Root \(-0.151066 + 0.464934i\) of defining polynomial
Character \(\chi\) \(=\) 418.229
Dual form 418.2.f.f.115.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.309017 - 0.951057i) q^{2} +(-0.128416 + 0.0932996i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.950820 + 2.92632i) q^{5} +(0.0490505 + 0.150962i) q^{6} +(-1.09378 - 0.794679i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.919265 + 2.82921i) q^{9} +O(q^{10})\) \(q+(0.309017 - 0.951057i) q^{2} +(-0.128416 + 0.0932996i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.950820 + 2.92632i) q^{5} +(0.0490505 + 0.150962i) q^{6} +(-1.09378 - 0.794679i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.919265 + 2.82921i) q^{9} +3.07692 q^{10} +(3.30564 - 0.269725i) q^{11} +0.158731 q^{12} +(-0.162774 + 0.500965i) q^{13} +(-1.09378 + 0.794679i) q^{14} +(-0.395125 - 0.287075i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.23602 + 6.88177i) q^{17} +(2.40667 + 1.74855i) q^{18} +(0.809017 - 0.587785i) q^{19} +(0.950820 - 2.92632i) q^{20} +0.214602 q^{21} +(0.764975 - 3.22720i) q^{22} +2.09183 q^{23} +(0.0490505 - 0.150962i) q^{24} +(-3.61422 + 2.62588i) q^{25} +(0.426147 + 0.309614i) q^{26} +(-0.293067 - 0.901968i) q^{27} +(0.417787 + 1.28582i) q^{28} +(0.224804 + 0.163330i) q^{29} +(-0.395125 + 0.287075i) q^{30} +(-0.532890 + 1.64007i) q^{31} +1.00000 q^{32} +(-0.399331 + 0.343052i) q^{33} +7.23593 q^{34} +(1.28550 - 3.95635i) q^{35} +(2.40667 - 1.74855i) q^{36} +(-7.21017 - 5.23850i) q^{37} +(-0.309017 - 0.951057i) q^{38} +(-0.0258372 - 0.0795186i) q^{39} +(-2.48928 - 1.80857i) q^{40} +(6.77434 - 4.92185i) q^{41} +(0.0663157 - 0.204099i) q^{42} +6.30119 q^{43} +(-2.83286 - 1.72479i) q^{44} -9.15323 q^{45} +(0.646410 - 1.98944i) q^{46} +(-1.59143 + 1.15624i) q^{47} +(-0.128416 - 0.0932996i) q^{48} +(-1.59828 - 4.91899i) q^{49} +(1.38051 + 4.24877i) q^{50} +(-0.929207 - 0.675109i) q^{51} +(0.426147 - 0.309614i) q^{52} +(-0.682009 + 2.09901i) q^{53} -0.948385 q^{54} +(3.93237 + 9.41690i) q^{55} +1.35199 q^{56} +(-0.0490505 + 0.150962i) q^{57} +(0.224804 - 0.163330i) q^{58} +(-7.05701 - 5.12722i) q^{59} +(0.150924 + 0.464497i) q^{60} +(1.97372 + 6.07450i) q^{61} +(1.39512 + 1.01362i) q^{62} +(3.25379 - 2.36401i) q^{63} +(0.309017 - 0.951057i) q^{64} -1.62075 q^{65} +(0.202861 + 0.485795i) q^{66} -1.02001 q^{67} +(2.23602 - 6.88177i) q^{68} +(-0.268624 + 0.195166i) q^{69} +(-3.36547 - 2.44516i) q^{70} +(-1.14764 - 3.53208i) q^{71} +(-0.919265 - 2.82921i) q^{72} +(-1.39281 - 1.01194i) q^{73} +(-7.21017 + 5.23850i) q^{74} +(0.219129 - 0.674410i) q^{75} -1.00000 q^{76} +(-3.82999 - 2.33190i) q^{77} -0.0836108 q^{78} +(2.32820 - 7.16548i) q^{79} +(-2.48928 + 1.80857i) q^{80} +(-7.09821 - 5.15715i) q^{81} +(-2.58757 - 7.96371i) q^{82} +(2.00766 + 6.17895i) q^{83} +(-0.173617 - 0.126140i) q^{84} +(-18.0122 + 13.0867i) q^{85} +(1.94718 - 5.99279i) q^{86} -0.0441070 q^{87} +(-2.51578 + 2.16122i) q^{88} -10.3518 q^{89} +(-2.82850 + 8.70524i) q^{90} +(0.576145 - 0.418594i) q^{91} +(-1.69232 - 1.22954i) q^{92} +(-0.0845860 - 0.260329i) q^{93} +(0.607871 + 1.87083i) q^{94} +(2.48928 + 1.80857i) q^{95} +(-0.128416 + 0.0932996i) q^{96} +(-3.22678 + 9.93100i) q^{97} -5.17213 q^{98} +(-2.27565 + 9.60029i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{7} - 4 q^{8} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{7} - 4 q^{8} - 20 q^{9} + 4 q^{10} + 2 q^{11} - 14 q^{13} + 6 q^{14} - 10 q^{15} - 4 q^{16} + 8 q^{17} + 4 q^{19} + 4 q^{20} + 28 q^{21} + 2 q^{22} + 24 q^{23} - 4 q^{26} - 18 q^{27} - 14 q^{28} - 22 q^{29} - 10 q^{30} - 24 q^{31} + 16 q^{32} + 2 q^{33} + 8 q^{34} - 20 q^{35} + 6 q^{37} + 4 q^{38} + 72 q^{39} - 6 q^{40} - 14 q^{41} - 22 q^{42} + 56 q^{43} + 12 q^{44} - 56 q^{45} + 4 q^{46} - 38 q^{47} - 36 q^{49} + 56 q^{51} - 4 q^{52} + 22 q^{53} - 48 q^{54} - 6 q^{55} + 16 q^{56} - 22 q^{58} - 28 q^{59} + 12 q^{61} + 26 q^{62} - 20 q^{63} - 4 q^{64} - 32 q^{65} + 12 q^{66} - 44 q^{67} + 8 q^{68} + 64 q^{69} - 20 q^{70} + 16 q^{71} - 20 q^{72} + 12 q^{73} + 6 q^{74} + 32 q^{75} - 16 q^{76} - 12 q^{77} - 8 q^{78} + 48 q^{79} - 6 q^{80} - 64 q^{81} + 6 q^{82} + 14 q^{83} + 8 q^{84} + 6 q^{85} - 14 q^{86} + 84 q^{87} - 8 q^{88} - 56 q^{89} + 34 q^{90} + 26 q^{91} - 16 q^{92} - 46 q^{93} + 32 q^{94} + 6 q^{95} - 24 q^{97} + 64 q^{98} - 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(343\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.309017 0.951057i 0.218508 0.672499i
\(3\) −0.128416 + 0.0932996i −0.0741409 + 0.0538665i −0.624238 0.781234i \(-0.714591\pi\)
0.550097 + 0.835100i \(0.314591\pi\)
\(4\) −0.809017 0.587785i −0.404508 0.293893i
\(5\) 0.950820 + 2.92632i 0.425219 + 1.30869i 0.902784 + 0.430094i \(0.141520\pi\)
−0.477565 + 0.878597i \(0.658480\pi\)
\(6\) 0.0490505 + 0.150962i 0.0200248 + 0.0616299i
\(7\) −1.09378 0.794679i −0.413410 0.300360i 0.361571 0.932345i \(-0.382241\pi\)
−0.774981 + 0.631984i \(0.782241\pi\)
\(8\) −0.809017 + 0.587785i −0.286031 + 0.207813i
\(9\) −0.919265 + 2.82921i −0.306422 + 0.943069i
\(10\) 3.07692 0.973007
\(11\) 3.30564 0.269725i 0.996688 0.0813250i
\(12\) 0.158731 0.0458216
\(13\) −0.162774 + 0.500965i −0.0451453 + 0.138943i −0.971088 0.238720i \(-0.923272\pi\)
0.925943 + 0.377663i \(0.123272\pi\)
\(14\) −1.09378 + 0.794679i −0.292325 + 0.212387i
\(15\) −0.395125 0.287075i −0.102021 0.0741224i
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) 2.23602 + 6.88177i 0.542315 + 1.66908i 0.727289 + 0.686332i \(0.240780\pi\)
−0.184973 + 0.982744i \(0.559220\pi\)
\(18\) 2.40667 + 1.74855i 0.567257 + 0.412136i
\(19\) 0.809017 0.587785i 0.185601 0.134847i
\(20\) 0.950820 2.92632i 0.212610 0.654345i
\(21\) 0.214602 0.0468300
\(22\) 0.764975 3.22720i 0.163093 0.688041i
\(23\) 2.09183 0.436176 0.218088 0.975929i \(-0.430018\pi\)
0.218088 + 0.975929i \(0.430018\pi\)
\(24\) 0.0490505 0.150962i 0.0100124 0.0308150i
\(25\) −3.61422 + 2.62588i −0.722843 + 0.525176i
\(26\) 0.426147 + 0.309614i 0.0835742 + 0.0607202i
\(27\) −0.293067 0.901968i −0.0564008 0.173584i
\(28\) 0.417787 + 1.28582i 0.0789544 + 0.242997i
\(29\) 0.224804 + 0.163330i 0.0417451 + 0.0303296i 0.608462 0.793583i \(-0.291787\pi\)
−0.566717 + 0.823912i \(0.691787\pi\)
\(30\) −0.395125 + 0.287075i −0.0721396 + 0.0524125i
\(31\) −0.532890 + 1.64007i −0.0957099 + 0.294565i −0.987438 0.158007i \(-0.949493\pi\)
0.891728 + 0.452571i \(0.149493\pi\)
\(32\) 1.00000 0.176777
\(33\) −0.399331 + 0.343052i −0.0695146 + 0.0597176i
\(34\) 7.23593 1.24095
\(35\) 1.28550 3.95635i 0.217289 0.668746i
\(36\) 2.40667 1.74855i 0.401111 0.291424i
\(37\) −7.21017 5.23850i −1.18535 0.861204i −0.192581 0.981281i \(-0.561686\pi\)
−0.992765 + 0.120077i \(0.961686\pi\)
\(38\) −0.309017 0.951057i −0.0501292 0.154282i
\(39\) −0.0258372 0.0795186i −0.00413726 0.0127332i
\(40\) −2.48928 1.80857i −0.393589 0.285959i
\(41\) 6.77434 4.92185i 1.05797 0.768663i 0.0842616 0.996444i \(-0.473147\pi\)
0.973713 + 0.227780i \(0.0731469\pi\)
\(42\) 0.0663157 0.204099i 0.0102327 0.0314931i
\(43\) 6.30119 0.960923 0.480461 0.877016i \(-0.340469\pi\)
0.480461 + 0.877016i \(0.340469\pi\)
\(44\) −2.83286 1.72479i −0.427069 0.260022i
\(45\) −9.15323 −1.36448
\(46\) 0.646410 1.98944i 0.0953079 0.293328i
\(47\) −1.59143 + 1.15624i −0.232133 + 0.168655i −0.697771 0.716320i \(-0.745825\pi\)
0.465638 + 0.884975i \(0.345825\pi\)
\(48\) −0.128416 0.0932996i −0.0185352 0.0134666i
\(49\) −1.59828 4.91899i −0.228325 0.702712i
\(50\) 1.38051 + 4.24877i 0.195233 + 0.600866i
\(51\) −0.929207 0.675109i −0.130115 0.0945341i
\(52\) 0.426147 0.309614i 0.0590959 0.0429357i
\(53\) −0.682009 + 2.09901i −0.0936811 + 0.288321i −0.986908 0.161286i \(-0.948436\pi\)
0.893227 + 0.449607i \(0.148436\pi\)
\(54\) −0.948385 −0.129059
\(55\) 3.93237 + 9.41690i 0.530240 + 1.26978i
\(56\) 1.35199 0.180667
\(57\) −0.0490505 + 0.150962i −0.00649690 + 0.0199954i
\(58\) 0.224804 0.163330i 0.0295182 0.0214463i
\(59\) −7.05701 5.12722i −0.918745 0.667507i 0.0244664 0.999701i \(-0.492211\pi\)
−0.943211 + 0.332193i \(0.892211\pi\)
\(60\) 0.150924 + 0.464497i 0.0194842 + 0.0599663i
\(61\) 1.97372 + 6.07450i 0.252709 + 0.777759i 0.994272 + 0.106876i \(0.0340848\pi\)
−0.741563 + 0.670883i \(0.765915\pi\)
\(62\) 1.39512 + 1.01362i 0.177181 + 0.128730i
\(63\) 3.25379 2.36401i 0.409938 0.297838i
\(64\) 0.309017 0.951057i 0.0386271 0.118882i
\(65\) −1.62075 −0.201030
\(66\) 0.202861 + 0.485795i 0.0249705 + 0.0597973i
\(67\) −1.02001 −0.124614 −0.0623071 0.998057i \(-0.519846\pi\)
−0.0623071 + 0.998057i \(0.519846\pi\)
\(68\) 2.23602 6.88177i 0.271158 0.834538i
\(69\) −0.268624 + 0.195166i −0.0323385 + 0.0234953i
\(70\) −3.36547 2.44516i −0.402251 0.292253i
\(71\) −1.14764 3.53208i −0.136200 0.419181i 0.859575 0.511010i \(-0.170729\pi\)
−0.995775 + 0.0918293i \(0.970729\pi\)
\(72\) −0.919265 2.82921i −0.108336 0.333425i
\(73\) −1.39281 1.01194i −0.163016 0.118438i 0.503286 0.864120i \(-0.332124\pi\)
−0.666303 + 0.745681i \(0.732124\pi\)
\(74\) −7.21017 + 5.23850i −0.838166 + 0.608963i
\(75\) 0.219129 0.674410i 0.0253028 0.0778741i
\(76\) −1.00000 −0.114708
\(77\) −3.82999 2.33190i −0.436468 0.265745i
\(78\) −0.0836108 −0.00946706
\(79\) 2.32820 7.16548i 0.261943 0.806179i −0.730438 0.682979i \(-0.760684\pi\)
0.992382 0.123200i \(-0.0393158\pi\)
\(80\) −2.48928 + 1.80857i −0.278310 + 0.202204i
\(81\) −7.09821 5.15715i −0.788691 0.573017i
\(82\) −2.58757 7.96371i −0.285749 0.879445i
\(83\) 2.00766 + 6.17895i 0.220369 + 0.678228i 0.998729 + 0.0504083i \(0.0160523\pi\)
−0.778359 + 0.627819i \(0.783948\pi\)
\(84\) −0.173617 0.126140i −0.0189431 0.0137630i
\(85\) −18.0122 + 13.0867i −1.95370 + 1.41945i
\(86\) 1.94718 5.99279i 0.209969 0.646219i
\(87\) −0.0441070 −0.00472877
\(88\) −2.51578 + 2.16122i −0.268183 + 0.230387i
\(89\) −10.3518 −1.09728 −0.548642 0.836057i \(-0.684855\pi\)
−0.548642 + 0.836057i \(0.684855\pi\)
\(90\) −2.82850 + 8.70524i −0.298150 + 0.917612i
\(91\) 0.576145 0.418594i 0.0603964 0.0438806i
\(92\) −1.69232 1.22954i −0.176437 0.128189i
\(93\) −0.0845860 0.260329i −0.00877116 0.0269949i
\(94\) 0.607871 + 1.87083i 0.0626971 + 0.192962i
\(95\) 2.48928 + 1.80857i 0.255395 + 0.185555i
\(96\) −0.128416 + 0.0932996i −0.0131064 + 0.00952235i
\(97\) −3.22678 + 9.93100i −0.327630 + 1.00834i 0.642610 + 0.766194i \(0.277852\pi\)
−0.970240 + 0.242147i \(0.922148\pi\)
\(98\) −5.17213 −0.522464
\(99\) −2.27565 + 9.60029i −0.228712 + 0.964865i
\(100\) 4.46742 0.446742
\(101\) 5.13200 15.7947i 0.510653 1.57163i −0.280401 0.959883i \(-0.590468\pi\)
0.791054 0.611746i \(-0.209532\pi\)
\(102\) −0.929207 + 0.675109i −0.0920052 + 0.0668457i
\(103\) 5.10366 + 3.70802i 0.502878 + 0.365362i 0.810115 0.586271i \(-0.199404\pi\)
−0.307237 + 0.951633i \(0.599404\pi\)
\(104\) −0.162774 0.500965i −0.0159613 0.0491237i
\(105\) 0.204048 + 0.627995i 0.0199130 + 0.0612860i
\(106\) 1.78552 + 1.29726i 0.173425 + 0.126001i
\(107\) −10.6789 + 7.75871i −1.03237 + 0.750063i −0.968782 0.247914i \(-0.920255\pi\)
−0.0635904 + 0.997976i \(0.520255\pi\)
\(108\) −0.293067 + 0.901968i −0.0282004 + 0.0867919i
\(109\) 4.47355 0.428488 0.214244 0.976780i \(-0.431271\pi\)
0.214244 + 0.976780i \(0.431271\pi\)
\(110\) 10.1712 0.829920i 0.969784 0.0791298i
\(111\) 1.41465 0.134273
\(112\) 0.417787 1.28582i 0.0394772 0.121498i
\(113\) 10.1613 7.38265i 0.955899 0.694501i 0.00370440 0.999993i \(-0.498821\pi\)
0.952195 + 0.305492i \(0.0988208\pi\)
\(114\) 0.128416 + 0.0932996i 0.0120272 + 0.00873830i
\(115\) 1.98895 + 6.12135i 0.185470 + 0.570819i
\(116\) −0.0858676 0.264273i −0.00797261 0.0245372i
\(117\) −1.26770 0.921040i −0.117199 0.0851502i
\(118\) −7.05701 + 5.12722i −0.649651 + 0.471999i
\(119\) 3.02308 9.30408i 0.277125 0.852903i
\(120\) 0.488401 0.0445847
\(121\) 10.8545 1.78322i 0.986772 0.162111i
\(122\) 6.38710 0.578261
\(123\) −0.410726 + 1.26409i −0.0370340 + 0.113979i
\(124\) 1.39512 1.01362i 0.125286 0.0910255i
\(125\) 1.32575 + 0.963213i 0.118579 + 0.0861523i
\(126\) −1.24284 3.82505i −0.110721 0.340763i
\(127\) −5.08585 15.6526i −0.451296 1.38895i −0.875429 0.483347i \(-0.839421\pi\)
0.424133 0.905600i \(-0.360579\pi\)
\(128\) −0.809017 0.587785i −0.0715077 0.0519534i
\(129\) −0.809173 + 0.587899i −0.0712437 + 0.0517616i
\(130\) −0.500841 + 1.54143i −0.0439266 + 0.135192i
\(131\) 15.1571 1.32428 0.662140 0.749380i \(-0.269648\pi\)
0.662140 + 0.749380i \(0.269648\pi\)
\(132\) 0.524706 0.0428136i 0.0456698 0.00372644i
\(133\) −1.35199 −0.117232
\(134\) −0.315201 + 0.970088i −0.0272292 + 0.0838029i
\(135\) 2.36079 1.71522i 0.203185 0.147622i
\(136\) −5.85399 4.25317i −0.501975 0.364706i
\(137\) −1.68735 5.19313i −0.144160 0.443679i 0.852742 0.522333i \(-0.174938\pi\)
−0.996902 + 0.0786532i \(0.974938\pi\)
\(138\) 0.102605 + 0.315786i 0.00873432 + 0.0268815i
\(139\) 7.46676 + 5.42492i 0.633323 + 0.460136i 0.857550 0.514401i \(-0.171986\pi\)
−0.224227 + 0.974537i \(0.571986\pi\)
\(140\) −3.36547 + 2.44516i −0.284434 + 0.206654i
\(141\) 0.0964878 0.296959i 0.00812574 0.0250084i
\(142\) −3.71385 −0.311659
\(143\) −0.402948 + 1.69991i −0.0336962 + 0.142154i
\(144\) −2.97480 −0.247900
\(145\) −0.264207 + 0.813147i −0.0219412 + 0.0675282i
\(146\) −1.39281 + 1.01194i −0.115270 + 0.0837485i
\(147\) 0.664183 + 0.482557i 0.0547809 + 0.0398007i
\(148\) 2.75404 + 8.47607i 0.226381 + 0.696728i
\(149\) −3.81024 11.7267i −0.312147 0.960690i −0.976913 0.213638i \(-0.931469\pi\)
0.664766 0.747052i \(-0.268531\pi\)
\(150\) −0.573687 0.416808i −0.0468413 0.0340322i
\(151\) −2.94044 + 2.13636i −0.239290 + 0.173854i −0.700967 0.713194i \(-0.747248\pi\)
0.461677 + 0.887048i \(0.347248\pi\)
\(152\) −0.309017 + 0.951057i −0.0250646 + 0.0771409i
\(153\) −21.5255 −1.74023
\(154\) −3.40130 + 2.92194i −0.274085 + 0.235457i
\(155\) −5.30605 −0.426192
\(156\) −0.0258372 + 0.0795186i −0.00206863 + 0.00636658i
\(157\) 0.705098 0.512284i 0.0562729 0.0408847i −0.559293 0.828970i \(-0.688927\pi\)
0.615566 + 0.788085i \(0.288927\pi\)
\(158\) −6.09532 4.42851i −0.484917 0.352313i
\(159\) −0.108256 0.333177i −0.00858524 0.0264226i
\(160\) 0.950820 + 2.92632i 0.0751689 + 0.231346i
\(161\) −2.28800 1.66233i −0.180320 0.131010i
\(162\) −7.09821 + 5.15715i −0.557688 + 0.405184i
\(163\) −2.39047 + 7.35710i −0.187236 + 0.576253i −0.999980 0.00636854i \(-0.997973\pi\)
0.812744 + 0.582621i \(0.197973\pi\)
\(164\) −8.37354 −0.653864
\(165\) −1.38357 0.842391i −0.107711 0.0655801i
\(166\) 6.49693 0.504259
\(167\) 6.74535 20.7600i 0.521971 1.60646i −0.248259 0.968694i \(-0.579858\pi\)
0.770229 0.637767i \(-0.220142\pi\)
\(168\) −0.173617 + 0.126140i −0.0133948 + 0.00973190i
\(169\) 10.2927 + 7.47812i 0.791750 + 0.575240i
\(170\) 6.88006 + 21.1746i 0.527676 + 1.62402i
\(171\) 0.919265 + 2.82921i 0.0702980 + 0.216355i
\(172\) −5.09777 3.70375i −0.388701 0.282408i
\(173\) 8.90740 6.47160i 0.677217 0.492027i −0.195216 0.980760i \(-0.562541\pi\)
0.872433 + 0.488733i \(0.162541\pi\)
\(174\) −0.0136298 + 0.0419483i −0.00103327 + 0.00318009i
\(175\) 6.03989 0.456573
\(176\) 1.27802 + 3.06050i 0.0963345 + 0.230694i
\(177\) 1.38460 0.104073
\(178\) −3.19887 + 9.84510i −0.239765 + 0.737922i
\(179\) 10.1553 7.37829i 0.759046 0.551479i −0.139571 0.990212i \(-0.544572\pi\)
0.898618 + 0.438733i \(0.144572\pi\)
\(180\) 7.40512 + 5.38013i 0.551945 + 0.401011i
\(181\) −1.06703 3.28398i −0.0793117 0.244096i 0.903537 0.428510i \(-0.140961\pi\)
−0.982849 + 0.184414i \(0.940961\pi\)
\(182\) −0.220068 0.677299i −0.0163125 0.0502048i
\(183\) −0.820205 0.595914i −0.0606313 0.0440512i
\(184\) −1.69232 + 1.22954i −0.124760 + 0.0906432i
\(185\) 8.47396 26.0802i 0.623018 1.91745i
\(186\) −0.273726 −0.0200706
\(187\) 9.24767 + 22.1455i 0.676257 + 1.61944i
\(188\) 1.96711 0.143466
\(189\) −0.396223 + 1.21945i −0.0288210 + 0.0887019i
\(190\) 2.48928 1.80857i 0.180591 0.131207i
\(191\) −17.2497 12.5327i −1.24815 0.906832i −0.250034 0.968237i \(-0.580442\pi\)
−0.998113 + 0.0614054i \(0.980442\pi\)
\(192\) 0.0490505 + 0.150962i 0.00353991 + 0.0108947i
\(193\) 7.24713 + 22.3044i 0.521660 + 1.60550i 0.770828 + 0.637044i \(0.219843\pi\)
−0.249168 + 0.968460i \(0.580157\pi\)
\(194\) 8.44782 + 6.13770i 0.606518 + 0.440661i
\(195\) 0.208131 0.151216i 0.0149045 0.0108288i
\(196\) −1.59828 + 4.91899i −0.114163 + 0.351356i
\(197\) −7.79605 −0.555445 −0.277723 0.960661i \(-0.589580\pi\)
−0.277723 + 0.960661i \(0.589580\pi\)
\(198\) 8.42720 + 5.13093i 0.598895 + 0.364639i
\(199\) −9.48281 −0.672219 −0.336109 0.941823i \(-0.609111\pi\)
−0.336109 + 0.941823i \(0.609111\pi\)
\(200\) 1.38051 4.24877i 0.0976166 0.300433i
\(201\) 0.130986 0.0951666i 0.00923901 0.00671254i
\(202\) −13.4358 9.76165i −0.945336 0.686827i
\(203\) −0.116092 0.357294i −0.00814806 0.0250771i
\(204\) 0.354926 + 1.09235i 0.0248498 + 0.0764797i
\(205\) 20.8441 + 15.1441i 1.45581 + 1.05771i
\(206\) 5.10366 3.70802i 0.355589 0.258350i
\(207\) −1.92294 + 5.91821i −0.133654 + 0.411344i
\(208\) −0.526746 −0.0365233
\(209\) 2.51578 2.16122i 0.174020 0.149495i
\(210\) 0.660313 0.0455659
\(211\) 4.81914 14.8318i 0.331763 1.02106i −0.636531 0.771251i \(-0.719631\pi\)
0.968294 0.249812i \(-0.0803687\pi\)
\(212\) 1.78552 1.29726i 0.122630 0.0890960i
\(213\) 0.476917 + 0.346501i 0.0326778 + 0.0237418i
\(214\) 4.07899 + 12.5539i 0.278834 + 0.858164i
\(215\) 5.99130 + 18.4393i 0.408603 + 1.25755i
\(216\) 0.767260 + 0.557447i 0.0522054 + 0.0379294i
\(217\) 1.88619 1.37040i 0.128043 0.0930287i
\(218\) 1.38240 4.25460i 0.0936281 0.288158i
\(219\) 0.273272 0.0184660
\(220\) 2.35377 9.92982i 0.158691 0.669468i
\(221\) −3.81150 −0.256389
\(222\) 0.437151 1.34541i 0.0293396 0.0902981i
\(223\) 19.7704 14.3640i 1.32392 0.961887i 0.324049 0.946040i \(-0.394956\pi\)
0.999874 0.0158463i \(-0.00504425\pi\)
\(224\) −1.09378 0.794679i −0.0730813 0.0530967i
\(225\) −4.10674 12.6392i −0.273783 0.842616i
\(226\) −3.88129 11.9454i −0.258180 0.794595i
\(227\) 18.8116 + 13.6674i 1.24857 + 0.907139i 0.998138 0.0609952i \(-0.0194274\pi\)
0.250432 + 0.968134i \(0.419427\pi\)
\(228\) 0.128416 0.0932996i 0.00850455 0.00617891i
\(229\) −0.600618 + 1.84851i −0.0396900 + 0.122153i −0.968938 0.247303i \(-0.920456\pi\)
0.929248 + 0.369456i \(0.120456\pi\)
\(230\) 6.43637 0.424402
\(231\) 0.709397 0.0578834i 0.0466749 0.00380845i
\(232\) −0.277873 −0.0182433
\(233\) 1.68804 5.19524i 0.110587 0.340352i −0.880414 0.474206i \(-0.842735\pi\)
0.991001 + 0.133854i \(0.0427353\pi\)
\(234\) −1.26770 + 0.921040i −0.0828723 + 0.0602103i
\(235\) −4.89669 3.55765i −0.319425 0.232076i
\(236\) 2.69554 + 8.29602i 0.175465 + 0.540025i
\(237\) 0.369557 + 1.13738i 0.0240053 + 0.0738808i
\(238\) −7.91452 5.75024i −0.513022 0.372732i
\(239\) 13.0723 9.49758i 0.845577 0.614347i −0.0783463 0.996926i \(-0.524964\pi\)
0.923923 + 0.382579i \(0.124964\pi\)
\(240\) 0.150924 0.464497i 0.00974212 0.0299832i
\(241\) −17.9215 −1.15442 −0.577212 0.816594i \(-0.695859\pi\)
−0.577212 + 0.816594i \(0.695859\pi\)
\(242\) 1.65828 10.8743i 0.106598 0.699026i
\(243\) 4.23784 0.271857
\(244\) 1.97372 6.07450i 0.126355 0.388880i
\(245\) 12.8749 9.35414i 0.822545 0.597614i
\(246\) 1.07530 + 0.781248i 0.0685583 + 0.0498106i
\(247\) 0.162774 + 0.500965i 0.0103570 + 0.0318757i
\(248\) −0.532890 1.64007i −0.0338386 0.104144i
\(249\) −0.834309 0.606161i −0.0528722 0.0384139i
\(250\) 1.32575 0.963213i 0.0838477 0.0609189i
\(251\) 8.32956 25.6357i 0.525757 1.61811i −0.237057 0.971496i \(-0.576183\pi\)
0.762814 0.646618i \(-0.223817\pi\)
\(252\) −4.02190 −0.253356
\(253\) 6.91482 0.564217i 0.434731 0.0354720i
\(254\) −16.4582 −1.03268
\(255\) 1.09208 3.36107i 0.0683885 0.210478i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) 17.9850 + 13.0669i 1.12188 + 0.815090i 0.984492 0.175428i \(-0.0561309\pi\)
0.137383 + 0.990518i \(0.456131\pi\)
\(258\) 0.309077 + 0.951240i 0.0192423 + 0.0592216i
\(259\) 3.72343 + 11.4595i 0.231363 + 0.712061i
\(260\) 1.31122 + 0.952655i 0.0813183 + 0.0590812i
\(261\) −0.668749 + 0.485874i −0.0413945 + 0.0300749i
\(262\) 4.68379 14.4152i 0.289366 0.890576i
\(263\) −0.840832 −0.0518479 −0.0259240 0.999664i \(-0.508253\pi\)
−0.0259240 + 0.999664i \(0.508253\pi\)
\(264\) 0.121425 0.512256i 0.00747320 0.0315271i
\(265\) −6.79084 −0.417158
\(266\) −0.417787 + 1.28582i −0.0256162 + 0.0788385i
\(267\) 1.32933 0.965814i 0.0813536 0.0591069i
\(268\) 0.825206 + 0.599548i 0.0504075 + 0.0366232i
\(269\) 8.22851 + 25.3248i 0.501701 + 1.54408i 0.806246 + 0.591580i \(0.201496\pi\)
−0.304545 + 0.952498i \(0.598504\pi\)
\(270\) −0.901743 2.77528i −0.0548783 0.168898i
\(271\) 20.5335 + 14.9185i 1.24732 + 0.906234i 0.998064 0.0622026i \(-0.0198125\pi\)
0.249260 + 0.968436i \(0.419812\pi\)
\(272\) −5.85399 + 4.25317i −0.354950 + 0.257886i
\(273\) −0.0349315 + 0.107508i −0.00211415 + 0.00650669i
\(274\) −5.46038 −0.329874
\(275\) −11.2390 + 9.65506i −0.677739 + 0.582222i
\(276\) 0.332037 0.0199863
\(277\) −9.32650 + 28.7040i −0.560375 + 1.72466i 0.120933 + 0.992661i \(0.461411\pi\)
−0.681308 + 0.731997i \(0.738589\pi\)
\(278\) 7.46676 5.42492i 0.447827 0.325365i
\(279\) −4.15022 3.01531i −0.248467 0.180522i
\(280\) 1.28550 + 3.95635i 0.0768231 + 0.236437i
\(281\) 5.19980 + 16.0033i 0.310194 + 0.954679i 0.977688 + 0.210063i \(0.0673670\pi\)
−0.667494 + 0.744615i \(0.732633\pi\)
\(282\) −0.252608 0.183531i −0.0150426 0.0109291i
\(283\) 8.44637 6.13665i 0.502085 0.364786i −0.307728 0.951474i \(-0.599569\pi\)
0.809813 + 0.586688i \(0.199569\pi\)
\(284\) −1.14764 + 3.53208i −0.0681001 + 0.209590i
\(285\) −0.488401 −0.0289304
\(286\) 1.49220 + 0.908529i 0.0882355 + 0.0537224i
\(287\) −11.3209 −0.668253
\(288\) −0.919265 + 2.82921i −0.0541682 + 0.166713i
\(289\) −28.6057 + 20.7833i −1.68269 + 1.22255i
\(290\) 0.691704 + 0.502552i 0.0406183 + 0.0295109i
\(291\) −0.512189 1.57635i −0.0300250 0.0924076i
\(292\) 0.532006 + 1.63735i 0.0311333 + 0.0958185i
\(293\) −10.8426 7.87761i −0.633432 0.460215i 0.224156 0.974553i \(-0.428038\pi\)
−0.857587 + 0.514338i \(0.828038\pi\)
\(294\) 0.664183 0.482557i 0.0387359 0.0281433i
\(295\) 8.29395 25.5262i 0.482892 1.48619i
\(296\) 8.91226 0.518015
\(297\) −1.21206 2.90253i −0.0703307 0.168422i
\(298\) −12.3302 −0.714270
\(299\) −0.340494 + 1.04793i −0.0196913 + 0.0606035i
\(300\) −0.573687 + 0.416808i −0.0331218 + 0.0240644i
\(301\) −6.89213 5.00742i −0.397256 0.288623i
\(302\) 1.12315 + 3.45670i 0.0646300 + 0.198911i
\(303\) 0.814606 + 2.50710i 0.0467979 + 0.144029i
\(304\) 0.809017 + 0.587785i 0.0464003 + 0.0337118i
\(305\) −15.8993 + 11.5515i −0.910390 + 0.661437i
\(306\) −6.65173 + 20.4719i −0.380254 + 1.17030i
\(307\) −18.9800 −1.08325 −0.541623 0.840622i \(-0.682190\pi\)
−0.541623 + 0.840622i \(0.682190\pi\)
\(308\) 1.72787 + 4.13776i 0.0984545 + 0.235771i
\(309\) −1.00135 −0.0569646
\(310\) −1.63966 + 5.04635i −0.0931264 + 0.286614i
\(311\) −10.0930 + 7.33301i −0.572323 + 0.415817i −0.835948 0.548808i \(-0.815082\pi\)
0.263626 + 0.964625i \(0.415082\pi\)
\(312\) 0.0676426 + 0.0491452i 0.00382951 + 0.00278230i
\(313\) −5.64703 17.3798i −0.319189 0.982364i −0.973996 0.226567i \(-0.927250\pi\)
0.654806 0.755797i \(-0.272750\pi\)
\(314\) −0.269323 0.828892i −0.0151988 0.0467771i
\(315\) 10.0116 + 7.27387i 0.564091 + 0.409836i
\(316\) −6.09532 + 4.42851i −0.342888 + 0.249123i
\(317\) −4.07378 + 12.5378i −0.228806 + 0.704193i 0.769077 + 0.639156i \(0.220716\pi\)
−0.997883 + 0.0650364i \(0.979284\pi\)
\(318\) −0.350323 −0.0196451
\(319\) 0.787176 + 0.479274i 0.0440734 + 0.0268342i
\(320\) 3.07692 0.172005
\(321\) 0.647462 1.99268i 0.0361378 0.111221i
\(322\) −2.28800 + 1.66233i −0.127505 + 0.0926380i
\(323\) 5.85399 + 4.25317i 0.325725 + 0.236653i
\(324\) 2.71128 + 8.34445i 0.150626 + 0.463581i
\(325\) −0.727177 2.23802i −0.0403365 0.124143i
\(326\) 6.25832 + 4.54694i 0.346616 + 0.251832i
\(327\) −0.574475 + 0.417380i −0.0317685 + 0.0230812i
\(328\) −2.58757 + 7.96371i −0.142875 + 0.439723i
\(329\) 2.65951 0.146624
\(330\) −1.22871 + 1.05554i −0.0676382 + 0.0581056i
\(331\) 3.69222 0.202943 0.101471 0.994838i \(-0.467645\pi\)
0.101471 + 0.994838i \(0.467645\pi\)
\(332\) 2.00766 6.17895i 0.110185 0.339114i
\(333\) 21.4489 15.5835i 1.17539 0.853971i
\(334\) −17.6596 12.8304i −0.966288 0.702049i
\(335\) −0.969847 2.98488i −0.0529884 0.163081i
\(336\) 0.0663157 + 0.204099i 0.00361782 + 0.0111345i
\(337\) −21.2757 15.4577i −1.15896 0.842036i −0.169317 0.985562i \(-0.554156\pi\)
−0.989647 + 0.143525i \(0.954156\pi\)
\(338\) 10.2927 7.47812i 0.559852 0.406756i
\(339\) −0.616080 + 1.89610i −0.0334609 + 0.102982i
\(340\) 22.2643 1.20745
\(341\) −1.31918 + 5.56520i −0.0714374 + 0.301373i
\(342\) 2.97480 0.160859
\(343\) −5.08536 + 15.6511i −0.274584 + 0.845082i
\(344\) −5.09777 + 3.70375i −0.274853 + 0.199693i
\(345\) −0.826532 0.600511i −0.0444990 0.0323304i
\(346\) −3.40232 10.4713i −0.182910 0.562939i
\(347\) −1.64812 5.07239i −0.0884757 0.272300i 0.897023 0.441984i \(-0.145725\pi\)
−0.985499 + 0.169684i \(0.945725\pi\)
\(348\) 0.0356833 + 0.0259255i 0.00191283 + 0.00138975i
\(349\) −15.7313 + 11.4295i −0.842078 + 0.611806i −0.922950 0.384919i \(-0.874229\pi\)
0.0808722 + 0.996724i \(0.474229\pi\)
\(350\) 1.86643 5.74428i 0.0997649 0.307045i
\(351\) 0.499558 0.0266644
\(352\) 3.30564 0.269725i 0.176191 0.0143764i
\(353\) −27.8728 −1.48352 −0.741761 0.670665i \(-0.766009\pi\)
−0.741761 + 0.670665i \(0.766009\pi\)
\(354\) 0.427865 1.31683i 0.0227408 0.0699889i
\(355\) 9.24480 6.71674i 0.490663 0.356488i
\(356\) 8.37475 + 6.08461i 0.443861 + 0.322484i
\(357\) 0.479855 + 1.47684i 0.0253966 + 0.0781628i
\(358\) −3.87900 11.9383i −0.205011 0.630960i
\(359\) −28.9092 21.0038i −1.52577 1.10854i −0.958533 0.284982i \(-0.908012\pi\)
−0.567237 0.823555i \(-0.691988\pi\)
\(360\) 7.40512 5.38013i 0.390284 0.283558i
\(361\) 0.309017 0.951057i 0.0162641 0.0500556i
\(362\) −3.45298 −0.181485
\(363\) −1.22752 + 1.24171i −0.0644278 + 0.0651731i
\(364\) −0.712155 −0.0373270
\(365\) 1.63694 5.03798i 0.0856813 0.263700i
\(366\) −0.820205 + 0.595914i −0.0428728 + 0.0311489i
\(367\) −30.5927 22.2269i −1.59693 1.16024i −0.893092 0.449873i \(-0.851469\pi\)
−0.703836 0.710363i \(-0.748531\pi\)
\(368\) 0.646410 + 1.98944i 0.0336964 + 0.103707i
\(369\) 7.69751 + 23.6905i 0.400716 + 1.23328i
\(370\) −22.1851 16.1184i −1.15335 0.837957i
\(371\) 2.41400 1.75388i 0.125329 0.0910567i
\(372\) −0.0845860 + 0.260329i −0.00438558 + 0.0134974i
\(373\) −20.1806 −1.04491 −0.522456 0.852667i \(-0.674984\pi\)
−0.522456 + 0.852667i \(0.674984\pi\)
\(374\) 23.9194 1.95171i 1.23684 0.100920i
\(375\) −0.260114 −0.0134322
\(376\) 0.607871 1.87083i 0.0313486 0.0964809i
\(377\) −0.118415 + 0.0860334i −0.00609867 + 0.00443095i
\(378\) 1.03733 + 0.753661i 0.0533543 + 0.0387642i
\(379\) −10.1095 31.1140i −0.519293 1.59822i −0.775333 0.631552i \(-0.782418\pi\)
0.256041 0.966666i \(-0.417582\pi\)
\(380\) −0.950820 2.92632i −0.0487760 0.150117i
\(381\) 2.11349 + 1.53554i 0.108277 + 0.0786680i
\(382\) −17.2497 + 12.5327i −0.882573 + 0.641227i
\(383\) −7.93607 + 24.4247i −0.405514 + 1.24805i 0.514950 + 0.857220i \(0.327810\pi\)
−0.920465 + 0.390825i \(0.872190\pi\)
\(384\) 0.158731 0.00810019
\(385\) 3.18226 13.4250i 0.162183 0.684201i
\(386\) 23.4522 1.19369
\(387\) −5.79247 + 17.8274i −0.294448 + 0.906217i
\(388\) 8.44782 6.13770i 0.428873 0.311594i
\(389\) 3.61505 + 2.62649i 0.183290 + 0.133168i 0.675647 0.737225i \(-0.263864\pi\)
−0.492357 + 0.870394i \(0.663864\pi\)
\(390\) −0.0794988 0.244672i −0.00402558 0.0123895i
\(391\) 4.67737 + 14.3955i 0.236545 + 0.728010i
\(392\) 4.18434 + 3.04010i 0.211341 + 0.153548i
\(393\) −1.94641 + 1.41415i −0.0981833 + 0.0713344i
\(394\) −2.40911 + 7.41448i −0.121369 + 0.373536i
\(395\) 23.1822 1.16642
\(396\) 7.48395 6.42920i 0.376083 0.323079i
\(397\) 28.8810 1.44950 0.724748 0.689014i \(-0.241956\pi\)
0.724748 + 0.689014i \(0.241956\pi\)
\(398\) −2.93035 + 9.01869i −0.146885 + 0.452066i
\(399\) 0.173617 0.126140i 0.00869171 0.00631489i
\(400\) −3.61422 2.62588i −0.180711 0.131294i
\(401\) 0.246422 + 0.758410i 0.0123057 + 0.0378732i 0.957021 0.290019i \(-0.0936617\pi\)
−0.944715 + 0.327892i \(0.893662\pi\)
\(402\) −0.0500320 0.153983i −0.00249537 0.00767996i
\(403\) −0.734877 0.533919i −0.0366068 0.0265964i
\(404\) −13.4358 + 9.76165i −0.668454 + 0.485660i
\(405\) 8.34237 25.6752i 0.414536 1.27581i
\(406\) −0.375681 −0.0186448
\(407\) −25.2472 15.3718i −1.25146 0.761953i
\(408\) 1.14856 0.0568624
\(409\) 7.02210 21.6118i 0.347220 1.06863i −0.613164 0.789956i \(-0.710103\pi\)
0.960384 0.278679i \(-0.0898965\pi\)
\(410\) 20.8441 15.1441i 1.02942 0.747914i
\(411\) 0.701200 + 0.509451i 0.0345876 + 0.0251294i
\(412\) −1.94942 5.99971i −0.0960412 0.295584i
\(413\) 3.64434 + 11.2161i 0.179326 + 0.551909i
\(414\) 5.03433 + 3.65765i 0.247424 + 0.179764i
\(415\) −16.1727 + 11.7501i −0.793885 + 0.576791i
\(416\) −0.162774 + 0.500965i −0.00798063 + 0.0245619i
\(417\) −1.46499 −0.0717410
\(418\) −1.27802 3.06050i −0.0625101 0.149694i
\(419\) −0.427754 −0.0208971 −0.0104486 0.999945i \(-0.503326\pi\)
−0.0104486 + 0.999945i \(0.503326\pi\)
\(420\) 0.204048 0.627995i 0.00995651 0.0306430i
\(421\) 7.84525 5.69990i 0.382354 0.277796i −0.379961 0.925002i \(-0.624063\pi\)
0.762315 + 0.647206i \(0.224063\pi\)
\(422\) −12.6167 9.16655i −0.614170 0.446221i
\(423\) −1.80830 5.56537i −0.0879224 0.270597i
\(424\) −0.682009 2.09901i −0.0331213 0.101937i
\(425\) −26.1522 19.0007i −1.26857 0.921669i
\(426\) 0.476917 0.346501i 0.0231067 0.0167880i
\(427\) 2.66845 8.21265i 0.129135 0.397438i
\(428\) 13.1999 0.638041
\(429\) −0.106856 0.255891i −0.00515908 0.0123545i
\(430\) 19.3882 0.934984
\(431\) −2.07150 + 6.37543i −0.0997808 + 0.307094i −0.988470 0.151416i \(-0.951617\pi\)
0.888689 + 0.458510i \(0.151617\pi\)
\(432\) 0.767260 0.557447i 0.0369148 0.0268202i
\(433\) 12.4405 + 9.03858i 0.597854 + 0.434366i 0.845117 0.534582i \(-0.179531\pi\)
−0.247262 + 0.968949i \(0.579531\pi\)
\(434\) −0.720461 2.21735i −0.0345832 0.106436i
\(435\) −0.0419378 0.129071i −0.00201077 0.00618850i
\(436\) −3.61918 2.62949i −0.173327 0.125930i
\(437\) 1.69232 1.22954i 0.0809548 0.0588171i
\(438\) 0.0844458 0.259897i 0.00403497 0.0124184i
\(439\) −2.15073 −0.102649 −0.0513244 0.998682i \(-0.516344\pi\)
−0.0513244 + 0.998682i \(0.516344\pi\)
\(440\) −8.71647 5.30705i −0.415541 0.253004i
\(441\) 15.3861 0.732670
\(442\) −1.17782 + 3.62495i −0.0560231 + 0.172421i
\(443\) −24.5813 + 17.8593i −1.16789 + 0.848523i −0.990755 0.135663i \(-0.956683\pi\)
−0.177137 + 0.984186i \(0.556683\pi\)
\(444\) −1.14448 0.831510i −0.0543144 0.0394617i
\(445\) −9.84265 30.2926i −0.466586 1.43601i
\(446\) −7.55162 23.2415i −0.357579 1.10052i
\(447\) 1.58339 + 1.15040i 0.0748919 + 0.0544122i
\(448\) −1.09378 + 0.794679i −0.0516763 + 0.0375450i
\(449\) 1.03260 3.17801i 0.0487313 0.149979i −0.923730 0.383045i \(-0.874876\pi\)
0.972461 + 0.233065i \(0.0748756\pi\)
\(450\) −13.2897 −0.626482
\(451\) 21.0660 18.0971i 0.991958 0.852157i
\(452\) −12.5601 −0.590778
\(453\) 0.178278 0.548684i 0.00837625 0.0257794i
\(454\) 18.8116 13.6674i 0.882872 0.641444i
\(455\) 1.77275 + 1.28798i 0.0831078 + 0.0603814i
\(456\) −0.0490505 0.150962i −0.00229700 0.00706944i
\(457\) 9.08138 + 27.9496i 0.424809 + 1.30743i 0.903177 + 0.429269i \(0.141229\pi\)
−0.478368 + 0.878160i \(0.658771\pi\)
\(458\) 1.57244 + 1.14244i 0.0734752 + 0.0533829i
\(459\) 5.55183 4.03364i 0.259137 0.188274i
\(460\) 1.98895 6.12135i 0.0927352 0.285410i
\(461\) −1.74308 −0.0811833 −0.0405917 0.999176i \(-0.512924\pi\)
−0.0405917 + 0.999176i \(0.512924\pi\)
\(462\) 0.164165 0.692563i 0.00763766 0.0322210i
\(463\) −31.2015 −1.45006 −0.725029 0.688718i \(-0.758174\pi\)
−0.725029 + 0.688718i \(0.758174\pi\)
\(464\) −0.0858676 + 0.264273i −0.00398630 + 0.0122686i
\(465\) 0.681381 0.495052i 0.0315983 0.0229575i
\(466\) −4.41934 3.21084i −0.204722 0.148739i
\(467\) 8.05709 + 24.7972i 0.372838 + 1.14748i 0.944926 + 0.327284i \(0.106133\pi\)
−0.572088 + 0.820192i \(0.693867\pi\)
\(468\) 0.484219 + 1.49027i 0.0223831 + 0.0688880i
\(469\) 1.11567 + 0.810581i 0.0515168 + 0.0374292i
\(470\) −4.89669 + 3.55765i −0.225867 + 0.164102i
\(471\) −0.0427499 + 0.131571i −0.00196981 + 0.00606246i
\(472\) 8.72295 0.401506
\(473\) 20.8295 1.69959i 0.957740 0.0781470i
\(474\) 1.19591 0.0549301
\(475\) −1.38051 + 4.24877i −0.0633420 + 0.194947i
\(476\) −7.91452 + 5.75024i −0.362761 + 0.263562i
\(477\) −5.31158 3.85909i −0.243200 0.176695i
\(478\) −4.99317 15.3674i −0.228382 0.702889i
\(479\) −9.08342 27.9559i −0.415032 1.27734i −0.912222 0.409696i \(-0.865635\pi\)
0.497190 0.867642i \(-0.334365\pi\)
\(480\) −0.395125 0.287075i −0.0180349 0.0131031i
\(481\) 3.79793 2.75936i 0.173171 0.125816i
\(482\) −5.53804 + 17.0443i −0.252251 + 0.776349i
\(483\) 0.448910 0.0204261
\(484\) −9.82963 4.93746i −0.446801 0.224430i
\(485\) −32.1294 −1.45892
\(486\) 1.30956 4.03042i 0.0594030 0.182824i
\(487\) −34.8621 + 25.3288i −1.57975 + 1.14776i −0.662771 + 0.748822i \(0.730620\pi\)
−0.916980 + 0.398934i \(0.869380\pi\)
\(488\) −5.16727 3.75424i −0.233912 0.169947i
\(489\) −0.379440 1.16780i −0.0171589 0.0528096i
\(490\) −4.91776 15.1353i −0.222162 0.683744i
\(491\) 23.8984 + 17.3632i 1.07852 + 0.783591i 0.977424 0.211285i \(-0.0677649\pi\)
0.101097 + 0.994877i \(0.467765\pi\)
\(492\) 1.07530 0.781248i 0.0484781 0.0352214i
\(493\) −0.621332 + 1.91226i −0.0279834 + 0.0861239i
\(494\) 0.526746 0.0236994
\(495\) −30.2573 + 2.46885i −1.35996 + 0.110967i
\(496\) −1.72447 −0.0774309
\(497\) −1.55160 + 4.77533i −0.0695987 + 0.214203i
\(498\) −0.834309 + 0.606161i −0.0373863 + 0.0271627i
\(499\) 22.5647 + 16.3942i 1.01013 + 0.733905i 0.964237 0.265041i \(-0.0853855\pi\)
0.0458967 + 0.998946i \(0.485385\pi\)
\(500\) −0.506391 1.55851i −0.0226465 0.0696987i
\(501\) 1.07069 + 3.29526i 0.0478351 + 0.147221i
\(502\) −21.8071 15.8438i −0.973297 0.707142i
\(503\) −0.0392283 + 0.0285010i −0.00174910 + 0.00127080i −0.588659 0.808381i \(-0.700344\pi\)
0.586910 + 0.809652i \(0.300344\pi\)
\(504\) −1.24284 + 3.82505i −0.0553603 + 0.170381i
\(505\) 51.0999 2.27392
\(506\) 1.60020 6.75074i 0.0711373 0.300107i
\(507\) −2.01946 −0.0896873
\(508\) −5.08585 + 15.6526i −0.225648 + 0.694473i
\(509\) −7.89027 + 5.73262i −0.349730 + 0.254094i −0.748756 0.662846i \(-0.769348\pi\)
0.399026 + 0.916940i \(0.369348\pi\)
\(510\) −2.85909 2.07725i −0.126603 0.0919823i
\(511\) 0.719266 + 2.21367i 0.0318185 + 0.0979272i
\(512\) 0.309017 + 0.951057i 0.0136568 + 0.0420312i
\(513\) −0.767260 0.557447i −0.0338753 0.0246119i
\(514\) 17.9850 13.0669i 0.793286 0.576356i
\(515\) −5.99821 + 18.4606i −0.264313 + 0.813471i
\(516\) 1.00019 0.0440310
\(517\) −4.94882 + 4.25136i −0.217649 + 0.186974i
\(518\) 12.0493 0.529415
\(519\) −0.540053 + 1.66211i −0.0237057 + 0.0729587i
\(520\) 1.31122 0.952655i 0.0575007 0.0417767i
\(521\) 32.6905 + 23.7511i 1.43220 + 1.04055i 0.989602 + 0.143831i \(0.0459423\pi\)
0.442596 + 0.896721i \(0.354058\pi\)
\(522\) 0.255439 + 0.786161i 0.0111803 + 0.0344093i
\(523\) 7.03688 + 21.6573i 0.307701 + 0.947007i 0.978655 + 0.205508i \(0.0658846\pi\)
−0.670954 + 0.741499i \(0.734115\pi\)
\(524\) −12.2623 8.90910i −0.535682 0.389196i
\(525\) −0.775618 + 0.563519i −0.0338507 + 0.0245940i
\(526\) −0.259831 + 0.799678i −0.0113292 + 0.0348676i
\(527\) −12.4781 −0.543556
\(528\) −0.449662 0.273778i −0.0195690 0.0119146i
\(529\) −18.6243 −0.809751
\(530\) −2.09848 + 6.45847i −0.0911523 + 0.280538i
\(531\) 20.9932 15.2525i 0.911029 0.661901i
\(532\) 1.09378 + 0.794679i 0.0474214 + 0.0344537i
\(533\) 1.36299 + 4.19486i 0.0590377 + 0.181699i
\(534\) −0.507759 1.56272i −0.0219729 0.0676255i
\(535\) −32.8582 23.8729i −1.42058 1.03212i
\(536\) 0.825206 0.599548i 0.0356435 0.0258965i
\(537\) −0.615716 + 1.89498i −0.0265701 + 0.0817744i
\(538\) 26.6280 1.14802
\(539\) −6.61009 15.8293i −0.284717 0.681816i
\(540\) −2.91810 −0.125575
\(541\) −2.29152 + 7.05258i −0.0985202 + 0.303214i −0.988155 0.153459i \(-0.950959\pi\)
0.889635 + 0.456672i \(0.150959\pi\)
\(542\) 20.5335 14.9185i 0.881991 0.640804i
\(543\) 0.443417 + 0.322162i 0.0190289 + 0.0138253i
\(544\) 2.23602 + 6.88177i 0.0958687 + 0.295054i
\(545\) 4.25354 + 13.0910i 0.182202 + 0.560759i
\(546\) 0.0914519 + 0.0664437i 0.00391378 + 0.00284353i
\(547\) −1.95709 + 1.42191i −0.0836793 + 0.0607966i −0.628838 0.777536i \(-0.716469\pi\)
0.545159 + 0.838333i \(0.316469\pi\)
\(548\) −1.68735 + 5.19313i −0.0720801 + 0.221840i
\(549\) −19.0004 −0.810917
\(550\) 5.70946 + 13.6725i 0.243452 + 0.582999i
\(551\) 0.277873 0.0118378
\(552\) 0.102605 0.315786i 0.00436716 0.0134407i
\(553\) −8.24080 + 5.98729i −0.350434 + 0.254605i
\(554\) 24.4171 + 17.7401i 1.03738 + 0.753703i
\(555\) 1.34508 + 4.13972i 0.0570953 + 0.175721i
\(556\) −2.85205 8.77771i −0.120954 0.372258i
\(557\) −0.333458 0.242271i −0.0141291 0.0102654i 0.580698 0.814119i \(-0.302780\pi\)
−0.594827 + 0.803853i \(0.702780\pi\)
\(558\) −4.15022 + 3.01531i −0.175693 + 0.127648i
\(559\) −1.02567 + 3.15668i −0.0433811 + 0.133513i
\(560\) 4.15995 0.175790
\(561\) −3.25372 1.98104i −0.137372 0.0836394i
\(562\) 16.8269 0.709800
\(563\) 1.38762 4.27067i 0.0584814 0.179987i −0.917548 0.397624i \(-0.869835\pi\)
0.976030 + 0.217637i \(0.0698348\pi\)
\(564\) −0.252608 + 0.183531i −0.0106367 + 0.00772804i
\(565\) 31.2656 + 22.7158i 1.31535 + 0.955661i
\(566\) −3.22623 9.92931i −0.135608 0.417360i
\(567\) 3.66561 + 11.2816i 0.153941 + 0.473783i
\(568\) 3.00457 + 2.18295i 0.126069 + 0.0915944i
\(569\) 26.3998 19.1806i 1.10674 0.804091i 0.124589 0.992208i \(-0.460239\pi\)
0.982146 + 0.188118i \(0.0602387\pi\)
\(570\) −0.150924 + 0.464497i −0.00632152 + 0.0194556i
\(571\) 18.1484 0.759486 0.379743 0.925092i \(-0.376012\pi\)
0.379743 + 0.925092i \(0.376012\pi\)
\(572\) 1.32518 1.13841i 0.0554084 0.0475994i
\(573\) 3.38443 0.141387
\(574\) −3.49836 + 10.7668i −0.146019 + 0.449399i
\(575\) −7.56031 + 5.49289i −0.315287 + 0.229069i
\(576\) 2.40667 + 1.74855i 0.100278 + 0.0728561i
\(577\) −6.77358 20.8469i −0.281988 0.867870i −0.987285 0.158958i \(-0.949186\pi\)
0.705297 0.708912i \(-0.250814\pi\)
\(578\) 10.9264 + 33.6280i 0.454479 + 1.39874i
\(579\) −3.01164 2.18808i −0.125159 0.0909335i
\(580\) 0.691704 0.502552i 0.0287214 0.0208674i
\(581\) 2.71433 8.35386i 0.112610 0.346577i
\(582\) −1.65748 −0.0687047
\(583\) −1.68832 + 7.12251i −0.0699231 + 0.294984i
\(584\) 1.72161 0.0712407
\(585\) 1.48990 4.58545i 0.0615999 0.189585i
\(586\) −10.8426 + 7.87761i −0.447904 + 0.325421i
\(587\) −13.6928 9.94843i −0.565164 0.410616i 0.268181 0.963368i \(-0.413577\pi\)
−0.833345 + 0.552753i \(0.813577\pi\)
\(588\) −0.253695 0.780794i −0.0104622 0.0321994i
\(589\) 0.532890 + 1.64007i 0.0219574 + 0.0675778i
\(590\) −21.7138 15.7760i −0.893945 0.649489i
\(591\) 1.00114 0.727368i 0.0411812 0.0299199i
\(592\) 2.75404 8.47607i 0.113190 0.348364i
\(593\) 9.83301 0.403793 0.201897 0.979407i \(-0.435290\pi\)
0.201897 + 0.979407i \(0.435290\pi\)
\(594\) −3.13502 + 0.255803i −0.128631 + 0.0104957i
\(595\) 30.1011 1.23403
\(596\) −3.81024 + 11.7267i −0.156074 + 0.480345i
\(597\) 1.21774 0.884742i 0.0498389 0.0362101i
\(598\) 0.891425 + 0.647658i 0.0364531 + 0.0264847i
\(599\) 13.3537 + 41.0985i 0.545618 + 1.67924i 0.719515 + 0.694477i \(0.244364\pi\)
−0.173896 + 0.984764i \(0.555636\pi\)
\(600\) 0.219129 + 0.674410i 0.00894590 + 0.0275327i
\(601\) 5.34288 + 3.88183i 0.217941 + 0.158343i 0.691399 0.722473i \(-0.256995\pi\)
−0.473459 + 0.880816i \(0.656995\pi\)
\(602\) −6.89213 + 5.00742i −0.280902 + 0.204087i
\(603\) 0.937661 2.88582i 0.0381845 0.117520i
\(604\) 3.63459 0.147889
\(605\) 15.5390 + 30.0682i 0.631748 + 1.22245i
\(606\) 2.63612 0.107085
\(607\) 6.07820 18.7068i 0.246707 0.759285i −0.748645 0.662972i \(-0.769295\pi\)
0.995351 0.0963130i \(-0.0307050\pi\)
\(608\) 0.809017 0.587785i 0.0328100 0.0238378i
\(609\) 0.0482435 + 0.0350509i 0.00195492 + 0.00142033i
\(610\) 6.07298 + 18.6907i 0.245888 + 0.756765i
\(611\) −0.320194 0.985455i −0.0129537 0.0398672i
\(612\) 17.4145 + 12.6524i 0.703938 + 0.511441i
\(613\) 1.25872 0.914512i 0.0508392 0.0369368i −0.562075 0.827086i \(-0.689997\pi\)
0.612915 + 0.790149i \(0.289997\pi\)
\(614\) −5.86514 + 18.0510i −0.236698 + 0.728481i
\(615\) −4.08965 −0.164911
\(616\) 4.46918 0.364664i 0.180069 0.0146927i
\(617\) −43.2521 −1.74126 −0.870632 0.491935i \(-0.836290\pi\)
−0.870632 + 0.491935i \(0.836290\pi\)
\(618\) −0.309433 + 0.952338i −0.0124472 + 0.0383086i
\(619\) −2.64523 + 1.92188i −0.106321 + 0.0772467i −0.639675 0.768645i \(-0.720931\pi\)
0.533354 + 0.845892i \(0.320931\pi\)
\(620\) 4.29268 + 3.11882i 0.172398 + 0.125255i
\(621\) −0.613045 1.88676i −0.0246007 0.0757130i
\(622\) 3.85519 + 11.8651i 0.154579 + 0.475745i
\(623\) 11.3226 + 8.22632i 0.453629 + 0.329581i
\(624\) 0.0676426 0.0491452i 0.00270787 0.00196738i
\(625\) −8.46066 + 26.0392i −0.338426 + 1.04157i
\(626\) −18.2742 −0.730383
\(627\) −0.121425 + 0.512256i −0.00484925 + 0.0204575i
\(628\) −0.871549 −0.0347786
\(629\) 19.9280 61.3322i 0.794583 2.44547i
\(630\) 10.0116 7.27387i 0.398873 0.289798i
\(631\) −22.3797 16.2598i −0.890922 0.647293i 0.0451964 0.998978i \(-0.485609\pi\)
−0.936118 + 0.351686i \(0.885609\pi\)
\(632\) 2.32820 + 7.16548i 0.0926110 + 0.285027i
\(633\) 0.764946 + 2.35426i 0.0304039 + 0.0935735i
\(634\) 10.6653 + 7.74878i 0.423573 + 0.307744i
\(635\) 40.9689 29.7657i 1.62580 1.18121i
\(636\) −0.108256 + 0.333177i −0.00429262 + 0.0132113i
\(637\) 2.72440 0.107945
\(638\) 0.699068 0.600545i 0.0276764 0.0237758i
\(639\) 11.0480 0.437051
\(640\) 0.950820 2.92632i 0.0375844 0.115673i
\(641\) 32.4824 23.5998i 1.28298 0.932138i 0.283339 0.959020i \(-0.408558\pi\)
0.999639 + 0.0268823i \(0.00855792\pi\)
\(642\) −1.69508 1.23155i −0.0668993 0.0486052i
\(643\) −9.08177 27.9508i −0.358150 1.10227i −0.954160 0.299296i \(-0.903248\pi\)
0.596010 0.802977i \(-0.296752\pi\)
\(644\) 0.873938 + 2.68971i 0.0344380 + 0.105989i
\(645\) −2.48976 1.80891i −0.0980341 0.0712259i
\(646\) 5.85399 4.25317i 0.230322 0.167339i
\(647\) 1.12215 3.45362i 0.0441162 0.135776i −0.926572 0.376117i \(-0.877259\pi\)
0.970689 + 0.240341i \(0.0772592\pi\)
\(648\) 8.77388 0.344670
\(649\) −24.7109 15.0453i −0.969987 0.590579i
\(650\) −2.35319 −0.0922999
\(651\) −0.114359 + 0.351962i −0.00448210 + 0.0137945i
\(652\) 6.25832 4.54694i 0.245095 0.178072i
\(653\) 20.9597 + 15.2281i 0.820216 + 0.595922i 0.916774 0.399405i \(-0.130783\pi\)
−0.0965583 + 0.995327i \(0.530783\pi\)
\(654\) 0.219430 + 0.675335i 0.00858038 + 0.0264077i
\(655\) 14.4116 + 44.3545i 0.563109 + 1.73307i
\(656\) 6.77434 + 4.92185i 0.264494 + 0.192166i
\(657\) 4.14334 3.01031i 0.161647 0.117444i
\(658\) 0.821834 2.52935i 0.0320384 0.0986042i
\(659\) −22.9664 −0.894644 −0.447322 0.894373i \(-0.647622\pi\)
−0.447322 + 0.894373i \(0.647622\pi\)
\(660\) 0.624187 + 1.49475i 0.0242965 + 0.0581831i
\(661\) 43.4685 1.69073 0.845365 0.534189i \(-0.179383\pi\)
0.845365 + 0.534189i \(0.179383\pi\)
\(662\) 1.14096 3.51151i 0.0443446 0.136479i
\(663\) 0.489456 0.355611i 0.0190089 0.0138108i
\(664\) −5.25613 3.81880i −0.203977 0.148198i
\(665\) −1.28550 3.95635i −0.0498494 0.153421i
\(666\) −8.19273 25.2146i −0.317462 0.977048i
\(667\) 0.470251 + 0.341658i 0.0182082 + 0.0132290i
\(668\) −17.6596 + 12.8304i −0.683269 + 0.496424i
\(669\) −1.19867 + 3.68914i −0.0463434 + 0.142630i
\(670\) −3.13849 −0.121250
\(671\) 8.16286 + 19.5477i 0.315124 + 0.754632i
\(672\) 0.214602 0.00827845
\(673\) −9.05222 + 27.8599i −0.348937 + 1.07392i 0.610505 + 0.792013i \(0.290967\pi\)
−0.959442 + 0.281906i \(0.909033\pi\)
\(674\) −21.2757 + 15.4577i −0.819511 + 0.595410i
\(675\) 3.42767 + 2.49035i 0.131931 + 0.0958535i
\(676\) −3.93148 12.0999i −0.151211 0.465379i
\(677\) −12.0513 37.0900i −0.463168 1.42549i −0.861272 0.508145i \(-0.830331\pi\)
0.398103 0.917341i \(-0.369669\pi\)
\(678\) 1.61292 + 1.17185i 0.0619437 + 0.0450048i
\(679\) 11.4213 8.29809i 0.438311 0.318452i
\(680\) 6.88006 21.1746i 0.263838 0.812011i
\(681\) −3.69087 −0.141435
\(682\) 4.88518 + 2.97435i 0.187063 + 0.113894i
\(683\) −13.6716 −0.523130 −0.261565 0.965186i \(-0.584239\pi\)
−0.261565 + 0.965186i \(0.584239\pi\)
\(684\) 0.919265 2.82921i 0.0351490 0.108177i
\(685\) 13.5924 9.87546i 0.519339 0.377322i
\(686\) 13.3136 + 9.67293i 0.508317 + 0.369314i
\(687\) −0.0953365 0.293416i −0.00363732 0.0111945i
\(688\) 1.94718 + 5.99279i 0.0742354 + 0.228473i
\(689\) −0.940517 0.683326i −0.0358308 0.0260326i
\(690\) −0.826532 + 0.600511i −0.0314655 + 0.0228611i
\(691\) 2.49096 7.66639i 0.0947607 0.291643i −0.892431 0.451185i \(-0.851002\pi\)
0.987191 + 0.159541i \(0.0510016\pi\)
\(692\) −11.0102 −0.418543
\(693\) 10.1182 8.69220i 0.384359 0.330189i
\(694\) −5.33343 −0.202454
\(695\) −8.77552 + 27.0083i −0.332874 + 1.02448i
\(696\) 0.0356833 0.0259255i 0.00135257 0.000982702i
\(697\) 49.0186 + 35.6141i 1.85671 + 1.34898i
\(698\) 6.00883 + 18.4933i 0.227438 + 0.699981i
\(699\) 0.267943 + 0.824644i 0.0101345 + 0.0311909i
\(700\) −4.88638 3.55016i −0.184688 0.134183i
\(701\) 8.90452 6.46951i 0.336319 0.244350i −0.406788 0.913523i \(-0.633351\pi\)
0.743107 + 0.669172i \(0.233351\pi\)
\(702\) 0.154372 0.475108i 0.00582639 0.0179318i
\(703\) −8.91226 −0.336132
\(704\) 0.764975 3.22720i 0.0288311 0.121630i
\(705\) 0.960740 0.0361836
\(706\) −8.61318 + 26.5086i −0.324161 + 0.997666i
\(707\) −18.1650 + 13.1976i −0.683164 + 0.496348i
\(708\) −1.12016 0.813847i −0.0420984 0.0305863i
\(709\) 1.18035 + 3.63276i 0.0443291 + 0.136431i 0.970772 0.240006i \(-0.0771493\pi\)
−0.926442 + 0.376437i \(0.877149\pi\)
\(710\) −3.53120 10.8679i −0.132524 0.407866i
\(711\) 18.1324 + 13.1739i 0.680017 + 0.494061i
\(712\) 8.37475 6.08461i 0.313857 0.228030i
\(713\) −1.11471 + 3.43074i −0.0417464 + 0.128482i
\(714\) 1.55284 0.0581137
\(715\) −5.35763 + 0.437157i −0.200364 + 0.0163488i
\(716\) −12.5527 −0.469116
\(717\) −0.792570 + 2.43928i −0.0295991 + 0.0910965i
\(718\) −28.9092 + 21.0038i −1.07888 + 0.783854i
\(719\) −10.1081 7.34396i −0.376968 0.273883i 0.383126 0.923696i \(-0.374847\pi\)
−0.760095 + 0.649813i \(0.774847\pi\)
\(720\) −2.82850 8.70524i −0.105412 0.324425i
\(721\) −2.63560 8.11153i −0.0981547 0.302089i
\(722\) −0.809017 0.587785i −0.0301085 0.0218751i
\(723\) 2.30140 1.67207i 0.0855901 0.0621848i
\(724\) −1.06703 + 3.28398i −0.0396558 + 0.122048i
\(725\) −1.24138 −0.0461036
\(726\) 0.801617 + 1.55115i 0.0297508 + 0.0575685i
\(727\) 21.9023 0.812311 0.406155 0.913804i \(-0.366869\pi\)
0.406155 + 0.913804i \(0.366869\pi\)
\(728\) −0.220068 + 0.677299i −0.00815626 + 0.0251024i
\(729\) 20.7504 15.0761i 0.768535 0.558373i
\(730\) −4.28556 3.11364i −0.158616 0.115241i
\(731\) 14.0896 + 43.3634i 0.521123 + 1.60385i
\(732\) 0.313290 + 0.964209i 0.0115795 + 0.0356382i
\(733\) −22.1120 16.0653i −0.816726 0.593386i 0.0990470 0.995083i \(-0.468421\pi\)
−0.915773 + 0.401697i \(0.868421\pi\)
\(734\) −30.5927 + 22.2269i −1.12920 + 0.820411i
\(735\) −0.780600 + 2.40244i −0.0287928 + 0.0886153i
\(736\) 2.09183 0.0771057
\(737\) −3.37179 + 0.275122i −0.124201 + 0.0101343i
\(738\) 24.9097 0.916937
\(739\) −2.12308 + 6.53417i −0.0780988 + 0.240363i −0.982482 0.186358i \(-0.940332\pi\)
0.904383 + 0.426722i \(0.140332\pi\)
\(740\) −22.1851 + 16.1184i −0.815541 + 0.592525i
\(741\) −0.0676426 0.0491452i −0.00248491 0.00180539i
\(742\) −0.922068 2.83783i −0.0338502 0.104180i
\(743\) −11.9074 36.6473i −0.436841 1.34446i −0.891188 0.453634i \(-0.850127\pi\)
0.454347 0.890825i \(-0.349873\pi\)
\(744\) 0.221449 + 0.160892i 0.00811872 + 0.00589859i
\(745\) 30.6933 22.3000i 1.12452 0.817008i
\(746\) −6.23614 + 19.1929i −0.228321 + 0.702701i
\(747\) −19.3271 −0.707141
\(748\) 5.53530 23.3518i 0.202391 0.853825i
\(749\) 17.8461 0.652083
\(750\) −0.0803798 + 0.247383i −0.00293505 + 0.00903317i
\(751\) −15.3957 + 11.1856i −0.561796 + 0.408168i −0.832116 0.554602i \(-0.812870\pi\)
0.270320 + 0.962771i \(0.412870\pi\)
\(752\) −1.59143 1.15624i −0.0580334 0.0421637i
\(753\) 1.32216 + 4.06918i 0.0481821 + 0.148289i
\(754\) 0.0452304 + 0.139205i 0.00164720 + 0.00506955i
\(755\) −9.04750 6.57340i −0.329272 0.239230i
\(756\) 1.03733 0.753661i 0.0377272 0.0274104i
\(757\) −12.9789 + 39.9448i −0.471724 + 1.45182i 0.378600 + 0.925560i \(0.376405\pi\)
−0.850325 + 0.526258i \(0.823595\pi\)
\(758\) −32.7152 −1.18827
\(759\) −0.835331 + 0.717604i −0.0303206 + 0.0260474i
\(760\) −3.07692 −0.111612
\(761\) −6.77668 + 20.8565i −0.245654 + 0.756047i 0.749874 + 0.661581i \(0.230114\pi\)
−0.995528 + 0.0944657i \(0.969886\pi\)
\(762\) 2.11349 1.53554i 0.0765636 0.0556267i
\(763\) −4.89309 3.55503i −0.177142 0.128701i
\(764\) 6.58881 + 20.2783i 0.238375 + 0.733642i
\(765\) −20.4668 62.9904i −0.739980 2.27742i
\(766\) 20.7769 + 15.0953i 0.750700 + 0.545416i
\(767\) 3.71726 2.70074i 0.134222 0.0975182i
\(768\) 0.0490505 0.150962i 0.00176996 0.00544737i
\(769\) −20.9969 −0.757167 −0.378584 0.925567i \(-0.623589\pi\)
−0.378584 + 0.925567i \(0.623589\pi\)
\(770\) −11.7846 7.17507i −0.424686 0.258571i
\(771\) −3.52870 −0.127083
\(772\) 7.24713 22.3044i 0.260830 0.802752i
\(773\) −31.0161 + 22.5345i −1.11557 + 0.810509i −0.983532 0.180735i \(-0.942152\pi\)
−0.132039 + 0.991245i \(0.542152\pi\)
\(774\) 15.1649 + 11.0179i 0.545090 + 0.396031i
\(775\) −2.38064 7.32687i −0.0855152 0.263189i
\(776\) −3.22678 9.93100i −0.115835 0.356502i
\(777\) −1.54732 1.12419i −0.0555097 0.0403302i
\(778\) 3.61505 2.62649i 0.129606 0.0941642i
\(779\) 2.58757 7.96371i 0.0927092 0.285330i
\(780\) −0.257263 −0.00921151
\(781\) −4.74638 11.3662i −0.169839 0.406716i
\(782\) 15.1363 0.541273
\(783\) 0.0814355 0.250633i 0.00291027 0.00895689i
\(784\) 4.18434 3.04010i 0.149441 0.108575i
\(785\) 2.16953 + 1.57625i 0.0774338 + 0.0562589i
\(786\) 0.743462 + 2.28814i 0.0265184 + 0.0816153i
\(787\) 1.19143 + 3.66684i 0.0424699 + 0.130709i 0.970043 0.242932i \(-0.0781092\pi\)
−0.927573 + 0.373641i \(0.878109\pi\)
\(788\) 6.30714 + 4.58240i 0.224682 + 0.163241i
\(789\) 0.107976 0.0784492i 0.00384405 0.00279287i
\(790\) 7.16369 22.0476i 0.254873 0.784417i
\(791\) −16.9811 −0.603779
\(792\) −3.80187 9.10439i −0.135093 0.323510i
\(793\) −3.36438 −0.119473
\(794\) 8.92472 27.4675i 0.316726 0.974784i
\(795\) 0.872051 0.633582i 0.0309285 0.0224708i
\(796\) 7.67176 + 5.57386i 0.271918 + 0.197560i
\(797\) 2.38773 + 7.34867i 0.0845777 + 0.260303i 0.984398 0.175958i \(-0.0563023\pi\)
−0.899820 + 0.436261i \(0.856302\pi\)
\(798\) −0.0663157 0.204099i −0.00234755 0.00722501i
\(799\) −11.5154 8.36646i −0.407387 0.295984i
\(800\) −3.61422 + 2.62588i −0.127782 + 0.0928389i
\(801\) 9.51601 29.2873i 0.336232 1.03481i
\(802\) 0.797439 0.0281586
\(803\) −4.87707 2.96942i −0.172108 0.104789i
\(804\) −0.161907 −0.00571002
\(805\) 2.68904 8.27600i 0.0947760 0.291691i
\(806\) −0.734877 + 0.533919i −0.0258849 + 0.0188065i
\(807\) −3.41946 2.48438i −0.120371 0.0874544i
\(808\) 5.13200 + 15.7947i 0.180543 + 0.555655i
\(809\) −14.1679 43.6043i −0.498117 1.53305i −0.812043 0.583598i \(-0.801644\pi\)
0.313926 0.949447i \(-0.398356\pi\)
\(810\) −21.8406 15.8681i −0.767401 0.557549i
\(811\) 9.63305 6.99882i 0.338262 0.245762i −0.405666 0.914021i \(-0.632960\pi\)
0.743928 + 0.668260i \(0.232960\pi\)
\(812\) −0.116092 + 0.357294i −0.00407403 + 0.0125386i
\(813\) −4.02872 −0.141293
\(814\) −22.4213 + 19.2613i −0.785865 + 0.675110i
\(815\) −23.8021 −0.833753
\(816\) 0.354926 1.09235i 0.0124249 0.0382399i
\(817\) 5.09777 3.70375i 0.178348 0.129578i
\(818\) −18.3841 13.3568i −0.642785 0.467010i
\(819\) 0.654659 + 2.01483i 0.0228756 + 0.0704040i
\(820\) −7.96173 24.5037i −0.278036 0.855706i
\(821\) 20.2569 + 14.7175i 0.706971 + 0.513645i 0.882195 0.470884i \(-0.156065\pi\)
−0.175224 + 0.984529i \(0.556065\pi\)
\(822\) 0.701200 0.509451i 0.0244571 0.0177692i
\(823\) −1.28125 + 3.94328i −0.0446615 + 0.137454i −0.970901 0.239482i \(-0.923022\pi\)
0.926239 + 0.376936i \(0.123022\pi\)
\(824\) −6.30847 −0.219766
\(825\) 0.542456 2.28846i 0.0188859 0.0796739i
\(826\) 11.7933 0.410342
\(827\) −14.7114 + 45.2770i −0.511565 + 1.57443i 0.277881 + 0.960615i \(0.410368\pi\)
−0.789446 + 0.613820i \(0.789632\pi\)
\(828\) 5.03433 3.65765i 0.174955 0.127112i
\(829\) −4.20085 3.05210i −0.145902 0.106004i 0.512440 0.858723i \(-0.328742\pi\)
−0.658342 + 0.752719i \(0.728742\pi\)
\(830\) 6.17741 + 19.0121i 0.214421 + 0.659920i
\(831\) −1.48040 4.55621i −0.0513546 0.158053i
\(832\) 0.426147 + 0.309614i 0.0147740 + 0.0107339i
\(833\) 30.2776 21.9979i 1.04906 0.762184i
\(834\) −0.452708 + 1.39329i −0.0156760 + 0.0482457i
\(835\) 67.1642 2.32431
\(836\) −3.30564 + 0.269725i −0.114328 + 0.00932862i
\(837\) 1.63546 0.0565298
\(838\) −0.132183 + 0.406818i −0.00456619 + 0.0140533i
\(839\) 35.1566 25.5428i 1.21374 0.881835i 0.218176 0.975909i \(-0.429989\pi\)
0.995565 + 0.0940749i \(0.0299893\pi\)
\(840\) −0.534204 0.388122i −0.0184318 0.0133915i
\(841\) −8.93763 27.5072i −0.308194 0.948524i
\(842\) −2.99662 9.22264i −0.103270 0.317833i
\(843\) −2.16084 1.56994i −0.0744233 0.0540717i
\(844\) −12.6167 + 9.16655i −0.434284 + 0.315526i
\(845\) −12.0968 + 37.2302i −0.416144 + 1.28076i
\(846\) −5.85177 −0.201188
\(847\) −13.2895 6.67538i −0.456634 0.229369i
\(848\) −2.20703 −0.0757896
\(849\) −0.512101 + 1.57609i −0.0175753 + 0.0540911i
\(850\) −26.1522 + 19.0007i −0.897013 + 0.651718i
\(851\) −15.0824 10.9580i −0.517019 0.375636i
\(852\) −0.182166 0.560650i −0.00624091 0.0192075i
\(853\) −9.05969 27.8829i −0.310198 0.954691i −0.977686 0.210071i \(-0.932631\pi\)
0.667488 0.744620i \(-0.267369\pi\)
\(854\) −6.98609 5.07569i −0.239059 0.173687i
\(855\) −7.40512 + 5.38013i −0.253250 + 0.183997i
\(856\) 4.07899 12.5539i 0.139417 0.429082i
\(857\) 3.67262 0.125454 0.0627272 0.998031i \(-0.480020\pi\)
0.0627272 + 0.998031i \(0.480020\pi\)
\(858\) −0.276387 + 0.0225519i −0.00943570 + 0.000769909i
\(859\) −19.7758 −0.674742 −0.337371 0.941372i \(-0.609538\pi\)
−0.337371 + 0.941372i \(0.609538\pi\)
\(860\) 5.99130 18.4393i 0.204302 0.628775i
\(861\) 1.45379 1.05624i 0.0495449 0.0359965i
\(862\) 5.42326 + 3.94023i 0.184717 + 0.134205i
\(863\) −10.2765 31.6278i −0.349816 1.07662i −0.958954 0.283560i \(-0.908484\pi\)
0.609138 0.793064i \(-0.291516\pi\)
\(864\) −0.293067 0.901968i −0.00997034 0.0306856i
\(865\) 27.4073 + 19.9126i 0.931877 + 0.677048i
\(866\) 12.4405 9.03858i 0.422747 0.307143i
\(867\) 1.73436 5.33780i 0.0589019 0.181281i
\(868\) −2.33146 −0.0791350
\(869\) 5.76350 24.3144i 0.195513 0.824811i
\(870\) −0.135714 −0.00460112
\(871\) 0.166031 0.510990i 0.00562574 0.0173142i
\(872\) −3.61918 + 2.62949i −0.122561 + 0.0890457i
\(873\) −25.1306 18.2584i −0.850542 0.617955i
\(874\) −0.646410 1.98944i −0.0218651 0.0672940i
\(875\) −0.684634 2.10709i −0.0231449 0.0712326i
\(876\) −0.221082 0.160625i −0.00746966 0.00542703i
\(877\) 11.9088 8.65222i 0.402130 0.292165i −0.368278 0.929716i \(-0.620052\pi\)
0.770408 + 0.637551i \(0.220052\pi\)
\(878\) −0.664613 + 2.04547i −0.0224296 + 0.0690312i
\(879\) 2.12734 0.0717534
\(880\) −7.74084 + 6.64989i −0.260944 + 0.224168i
\(881\) −2.16151 −0.0728230 −0.0364115 0.999337i \(-0.511593\pi\)
−0.0364115 + 0.999337i \(0.511593\pi\)
\(882\) 4.75456 14.6330i 0.160094 0.492720i
\(883\) 9.39844 6.82836i 0.316283 0.229793i −0.418305 0.908307i \(-0.637376\pi\)
0.734588 + 0.678514i \(0.237376\pi\)
\(884\) 3.08357 + 2.24034i 0.103712 + 0.0753508i
\(885\) 1.31650 + 4.05178i 0.0442538 + 0.136199i
\(886\) 9.38921 + 28.8970i 0.315437 + 0.970815i
\(887\) −18.2423 13.2538i −0.612515 0.445019i 0.237784 0.971318i \(-0.423579\pi\)
−0.850299 + 0.526300i \(0.823579\pi\)
\(888\) −1.14448 + 0.831510i −0.0384061 + 0.0279037i
\(889\) −6.87601 + 21.1622i −0.230614 + 0.709757i
\(890\) −31.8515 −1.06766
\(891\) −24.8551 15.1331i −0.832679 0.506979i
\(892\) −24.4375 −0.818230
\(893\) −0.607871 + 1.87083i −0.0203416 + 0.0626051i
\(894\) 1.58339 1.15040i 0.0529566 0.0384752i
\(895\) 31.2472 + 22.7024i 1.04448 + 0.758857i
\(896\) 0.417787 + 1.28582i 0.0139573 + 0.0429561i
\(897\) −0.0540468 0.166339i −0.00180457 0.00555390i
\(898\) −2.70337 1.96412i −0.0902128 0.0655434i
\(899\) −0.387668 + 0.281657i −0.0129295 + 0.00939380i
\(900\) −4.10674 + 12.6392i −0.136891 + 0.421308i
\(901\) −15.9699 −0.532034
\(902\) −10.7016 25.6272i −0.356323 0.853294i
\(903\) 1.35225 0.0450000
\(904\) −3.88129 + 11.9454i −0.129090 + 0.397297i
\(905\) 8.59543 6.24494i 0.285722 0.207589i
\(906\) −0.466739 0.339106i −0.0155064 0.0112660i
\(907\) 5.68321 + 17.4911i 0.188708 + 0.580783i 0.999993 0.00386810i \(-0.00123126\pi\)
−0.811285 + 0.584651i \(0.801231\pi\)
\(908\) −7.18539 22.1144i −0.238456 0.733891i
\(909\) 39.9687 + 29.0390i 1.32568 + 0.963162i
\(910\) 1.77275 1.28798i 0.0587661 0.0426961i
\(911\) 14.5996 44.9330i 0.483706 1.48870i −0.350139 0.936698i \(-0.613866\pi\)
0.833846 0.551998i \(-0.186134\pi\)
\(912\) −0.158731 −0.00525610
\(913\) 8.30322 + 19.8839i 0.274796 + 0.658059i
\(914\) 29.3880 0.972068
\(915\) 0.963969 2.96679i 0.0318678 0.0980791i
\(916\) 1.57244 1.14244i 0.0519548 0.0377474i
\(917\) −16.5785 12.0450i −0.547471 0.397761i
\(918\) −2.12061 6.52657i −0.0699906 0.215409i
\(919\) −3.02680 9.31552i −0.0998448 0.307291i 0.888641 0.458603i \(-0.151650\pi\)
−0.988486 + 0.151312i \(0.951650\pi\)
\(920\) −5.20714 3.78321i −0.171674 0.124729i
\(921\) 2.43733 1.77083i 0.0803128 0.0583507i
\(922\) −0.538641 + 1.65777i −0.0177392 + 0.0545957i
\(923\) 1.95626 0.0643910
\(924\) −0.607937 0.370144i −0.0199997 0.0121769i
\(925\) 39.8148 1.30910
\(926\) −9.64180 + 29.6744i −0.316849 + 0.975162i
\(927\) −15.1824 + 11.0306i −0.498655 + 0.362294i
\(928\) 0.224804 + 0.163330i 0.00737956 + 0.00536157i
\(929\) 7.10495 + 21.8668i 0.233106 + 0.717426i 0.997367 + 0.0725191i \(0.0231038\pi\)
−0.764261 + 0.644907i \(0.776896\pi\)
\(930\) −0.260264 0.801011i −0.00853440 0.0262662i
\(931\) −4.18434 3.04010i −0.137136 0.0996353i
\(932\) −4.41934 + 3.21084i −0.144760 + 0.105174i
\(933\) 0.611937 1.88335i 0.0200339 0.0616581i
\(934\) 26.0733 0.853144
\(935\) −56.0121 + 48.1181i −1.83179 + 1.57363i
\(936\) 1.56697 0.0512179
\(937\) 11.3241 34.8519i 0.369941 1.13856i −0.576887 0.816824i \(-0.695733\pi\)
0.946828 0.321739i \(-0.104267\pi\)
\(938\) 1.11567 0.810581i 0.0364279 0.0264664i
\(939\) 2.34669 + 1.70497i 0.0765815 + 0.0556397i
\(940\) 1.87037 + 5.75640i 0.0610047 + 0.187753i
\(941\) −4.41611 13.5914i −0.143961 0.443067i 0.852915 0.522050i \(-0.174833\pi\)
−0.996876 + 0.0789832i \(0.974833\pi\)
\(942\) 0.111921 + 0.0813151i 0.00364657 + 0.00264939i
\(943\) 14.1707 10.2956i 0.461463 0.335272i
\(944\) 2.69554 8.29602i 0.0877323 0.270012i
\(945\) −3.94524 −0.128339
\(946\) 4.82026 20.3352i 0.156720 0.661154i
\(947\) 49.0452 1.59375 0.796877 0.604142i \(-0.206484\pi\)
0.796877 + 0.604142i \(0.206484\pi\)
\(948\) 0.369557 1.13738i 0.0120027 0.0369404i
\(949\) 0.733658 0.533034i 0.0238155 0.0173030i
\(950\) 3.61422 + 2.62588i 0.117261 + 0.0851948i
\(951\) −0.646633 1.99013i −0.0209685 0.0645345i
\(952\) 3.02308 + 9.30408i 0.0979785 + 0.301547i
\(953\) 8.05441 + 5.85187i 0.260908 + 0.189561i 0.710547 0.703650i \(-0.248447\pi\)
−0.449639 + 0.893210i \(0.648447\pi\)
\(954\) −5.31158 + 3.85909i −0.171969 + 0.124943i
\(955\) 20.2732 62.3946i 0.656026 2.01904i
\(956\) −16.1582 −0.522595
\(957\) −0.145802 + 0.0118967i −0.00471311 + 0.000384567i
\(958\) −29.3946 −0.949695
\(959\) −2.28128 + 7.02105i −0.0736663 + 0.226722i
\(960\) −0.395125 + 0.287075i −0.0127526 + 0.00926531i
\(961\) 22.6737 + 16.4734i 0.731409 + 0.531400i
\(962\) −1.45068 4.46474i −0.0467718 0.143949i
\(963\) −12.1342 37.3453i −0.391019 1.20343i
\(964\) 14.4988 + 10.5340i 0.466975 + 0.339277i
\(965\) −58.3791 + 42.4149i −1.87929 + 1.36538i
\(966\) 0.138721 0.426939i 0.00446327 0.0137365i
\(967\) −12.0203 −0.386546 −0.193273 0.981145i \(-0.561910\pi\)
−0.193273 + 0.981145i \(0.561910\pi\)
\(968\) −7.73332 + 7.82277i −0.248558 + 0.251433i
\(969\) −1.14856 −0.0368972
\(970\) −9.92853 + 30.5569i −0.318786 + 0.981122i
\(971\) −41.9890 + 30.5068i −1.34749 + 0.979010i −0.348359 + 0.937361i \(0.613261\pi\)
−0.999132 + 0.0416490i \(0.986739\pi\)
\(972\) −3.42848 2.49094i −0.109969 0.0798969i
\(973\) −3.85594 11.8674i −0.123616 0.380450i
\(974\) 13.3161 + 40.9828i 0.426676 + 1.31317i
\(975\) 0.302187 + 0.219552i 0.00967774 + 0.00703129i
\(976\) −5.16727 + 3.75424i −0.165400 + 0.120170i
\(977\) −8.88050 + 27.3314i −0.284112 + 0.874408i 0.702551 + 0.711633i \(0.252044\pi\)
−0.986663 + 0.162774i \(0.947956\pi\)
\(978\) −1.22790 −0.0392638
\(979\) −34.2192 + 2.79212i −1.09365 + 0.0892366i
\(980\) −15.9142 −0.508361
\(981\) −4.11238 + 12.6566i −0.131298 + 0.404094i
\(982\) 23.8984 17.3632i 0.762629 0.554083i
\(983\) −29.7601 21.6220i −0.949201 0.689635i 0.00141657 0.999999i \(-0.499549\pi\)
−0.950618 + 0.310364i \(0.899549\pi\)
\(984\) −0.410726 1.26409i −0.0130935 0.0402976i
\(985\) −7.41264 22.8137i −0.236186 0.726906i
\(986\) 1.62667 + 1.18184i 0.0518036 + 0.0376375i
\(987\) −0.341523 + 0.248131i −0.0108708 + 0.00789811i
\(988\) 0.162774 0.500965i 0.00517852 0.0159378i
\(989\) 13.1810 0.419131
\(990\) −7.00199 + 29.5393i −0.222538 + 0.938820i
\(991\) −59.5095 −1.89038 −0.945191 0.326517i \(-0.894125\pi\)
−0.945191 + 0.326517i \(0.894125\pi\)
\(992\) −0.532890 + 1.64007i −0.0169193 + 0.0520722i
\(993\) −0.474140 + 0.344483i −0.0150464 + 0.0109318i
\(994\) 4.06214 + 2.95132i 0.128843 + 0.0936101i
\(995\) −9.01644 27.7498i −0.285840 0.879727i
\(996\) 0.318678 + 0.980789i 0.0100977 + 0.0310775i
\(997\) 22.2675 + 16.1783i 0.705217 + 0.512370i 0.881627 0.471946i \(-0.156448\pi\)
−0.176410 + 0.984317i \(0.556448\pi\)
\(998\) 22.5647 16.3942i 0.714273 0.518949i
\(999\) −2.61189 + 8.03857i −0.0826366 + 0.254329i
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 418.2.f.f.229.3 yes 16
11.4 even 5 4598.2.a.ca.1.4 8
11.5 even 5 inner 418.2.f.f.115.3 16
11.7 odd 10 4598.2.a.bx.1.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.f.f.115.3 16 11.5 even 5 inner
418.2.f.f.229.3 yes 16 1.1 even 1 trivial
4598.2.a.bx.1.4 8 11.7 odd 10
4598.2.a.ca.1.4 8 11.4 even 5