Properties

Label 930.2.z.b.349.4
Level $930$
Weight $2$
Character 930.349
Analytic conductor $7.426$
Analytic rank $0$
Dimension $16$
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(109,930)]
 
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([0, 5, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.z (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: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 6 x^{15} + 18 x^{14} - 44 x^{13} + 63 x^{12} - 46 x^{11} + 110 x^{10} - 120 x^{9} - 79 x^{8} + 120 x^{7} + 110 x^{6} + 46 x^{5} + 63 x^{4} + 44 x^{3} + 18 x^{2} + 6 x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 349.4
Root \(-0.582991 + 0.297049i\) of defining polynomial
Character \(\chi\) \(=\) 930.349
Dual form 930.2.z.b.469.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.951057 + 0.309017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(2.21127 - 0.332092i) q^{5} -1.00000 q^{6} +(0.907165 - 1.24861i) q^{7} +(0.587785 + 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(0.951057 + 0.309017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(2.21127 - 0.332092i) q^{5} -1.00000 q^{6} +(0.907165 - 1.24861i) q^{7} +(0.587785 + 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +(2.20566 + 0.367482i) q^{10} +(1.74861 + 1.27044i) q^{11} +(-0.951057 - 0.309017i) q^{12} +(-0.363271 + 0.118034i) q^{13} +(1.24861 - 0.907165i) q^{14} +(-2.00042 + 0.999158i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.638760 + 0.879178i) q^{17} +(0.951057 - 0.309017i) q^{18} +(1.32328 - 4.07263i) q^{19} +(1.98415 + 1.03108i) q^{20} +(-0.476925 + 1.46782i) q^{21} +(1.27044 + 1.74861i) q^{22} +(-2.62866 - 3.61803i) q^{23} +(-0.809017 - 0.587785i) q^{24} +(4.77943 - 1.46869i) q^{25} -0.381966 q^{26} +(-0.587785 + 0.809017i) q^{27} +(1.46782 - 0.476925i) q^{28} +(-1.31677 + 4.05259i) q^{29} +(-2.21127 + 0.332092i) q^{30} +(5.47414 + 1.01677i) q^{31} +1.00000i q^{32} +(-2.05561 - 0.667908i) q^{33} +(0.335816 + 1.03354i) q^{34} +(1.59134 - 3.06227i) q^{35} +1.00000 q^{36} +3.70476i q^{37} +(2.51702 - 3.46439i) q^{38} +(0.309017 - 0.224514i) q^{39} +(1.56842 + 1.59376i) q^{40} +(0.587210 - 1.80725i) q^{41} +(-0.907165 + 1.24861i) q^{42} +(-7.37483 - 2.39623i) q^{43} +(0.667908 + 2.05561i) q^{44} +(1.59376 - 1.56842i) q^{45} +(-1.38197 - 4.25325i) q^{46} +(9.01470 - 2.92905i) q^{47} +(-0.587785 - 0.809017i) q^{48} +(1.42705 + 4.39201i) q^{49} +(4.99936 + 0.0801180i) q^{50} +(-0.879178 - 0.638760i) q^{51} +(-0.363271 - 0.118034i) q^{52} +(3.47954 + 4.78918i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(4.28854 + 2.22858i) q^{55} +1.54336 q^{56} +4.28222i q^{57} +(-2.50464 + 3.44734i) q^{58} +(1.08442 + 3.33751i) q^{59} +(-2.20566 - 0.367482i) q^{60} -4.97335 q^{61} +(4.89201 + 2.65861i) q^{62} -1.54336i q^{63} +(-0.309017 + 0.951057i) q^{64} +(-0.764093 + 0.381644i) q^{65} +(-1.74861 - 1.27044i) q^{66} -2.20197i q^{67} +1.08672i q^{68} +(3.61803 + 2.62866i) q^{69} +(2.45974 - 2.42064i) q^{70} +(-4.31677 + 3.13631i) q^{71} +(0.951057 + 0.309017i) q^{72} +(-3.86791 + 5.32373i) q^{73} +(-1.14483 + 3.52343i) q^{74} +(-4.09166 + 2.87373i) q^{75} +(3.46439 - 2.51702i) q^{76} +(3.17255 - 1.03082i) q^{77} +(0.363271 - 0.118034i) q^{78} +(4.01750 - 2.91888i) q^{79} +(0.999158 + 2.00042i) q^{80} +(0.309017 - 0.951057i) q^{81} +(1.11694 - 1.53734i) q^{82} +(-1.57743 - 0.512538i) q^{83} +(-1.24861 + 0.907165i) q^{84} +(1.70444 + 1.73197i) q^{85} +(-6.27340 - 4.55789i) q^{86} -4.26114i q^{87} +2.16140i q^{88} +(-0.341842 - 0.248363i) q^{89} +(2.00042 - 0.999158i) q^{90} +(-0.182169 + 0.560659i) q^{91} -4.47214i q^{92} +(-5.52041 + 0.724595i) q^{93} +9.47861 q^{94} +(1.57364 - 9.44514i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(-8.18713 + 11.2686i) q^{97} +4.61803i q^{98} +2.16140 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{4} + 12 q^{5} - 16 q^{6} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{4} + 12 q^{5} - 16 q^{6} + 4 q^{9} + 4 q^{10} + 8 q^{11} + 4 q^{15} - 4 q^{16} + 8 q^{19} - 2 q^{20} - 4 q^{24} + 16 q^{25} - 24 q^{26} + 36 q^{29} - 12 q^{30} + 40 q^{31} + 8 q^{34} + 14 q^{35} + 16 q^{36} - 4 q^{39} + 6 q^{40} + 32 q^{41} + 12 q^{44} - 2 q^{45} - 40 q^{46} - 4 q^{49} - 8 q^{50} + 8 q^{51} - 4 q^{54} + 24 q^{55} - 4 q^{60} - 16 q^{61} + 4 q^{64} + 6 q^{65} - 8 q^{66} + 40 q^{69} + 18 q^{70} - 12 q^{71} - 12 q^{74} - 8 q^{75} + 32 q^{76} - 8 q^{79} - 8 q^{80} - 4 q^{81} - 40 q^{85} - 68 q^{86} + 20 q^{89} - 4 q^{90} - 56 q^{94} - 18 q^{95} + 4 q^{96} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.951057 + 0.309017i 0.672499 + 0.218508i
\(3\) −0.951057 + 0.309017i −0.549093 + 0.178411i
\(4\) 0.809017 + 0.587785i 0.404508 + 0.293893i
\(5\) 2.21127 0.332092i 0.988910 0.148516i
\(6\) −1.00000 −0.408248
\(7\) 0.907165 1.24861i 0.342876 0.471929i −0.602402 0.798192i \(-0.705790\pi\)
0.945279 + 0.326264i \(0.105790\pi\)
\(8\) 0.587785 + 0.809017i 0.207813 + 0.286031i
\(9\) 0.809017 0.587785i 0.269672 0.195928i
\(10\) 2.20566 + 0.367482i 0.697492 + 0.116208i
\(11\) 1.74861 + 1.27044i 0.527225 + 0.383051i 0.819319 0.573339i \(-0.194352\pi\)
−0.292094 + 0.956390i \(0.594352\pi\)
\(12\) −0.951057 0.309017i −0.274546 0.0892055i
\(13\) −0.363271 + 0.118034i −0.100753 + 0.0327367i −0.358960 0.933353i \(-0.616869\pi\)
0.258207 + 0.966090i \(0.416869\pi\)
\(14\) 1.24861 0.907165i 0.333704 0.242450i
\(15\) −2.00042 + 0.999158i −0.516506 + 0.257982i
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) 0.638760 + 0.879178i 0.154922 + 0.213232i 0.879422 0.476043i \(-0.157929\pi\)
−0.724500 + 0.689275i \(0.757929\pi\)
\(18\) 0.951057 0.309017i 0.224166 0.0728360i
\(19\) 1.32328 4.07263i 0.303581 0.934326i −0.676622 0.736330i \(-0.736557\pi\)
0.980203 0.197995i \(-0.0634431\pi\)
\(20\) 1.98415 + 1.03108i 0.443670 + 0.230557i
\(21\) −0.476925 + 1.46782i −0.104074 + 0.320306i
\(22\) 1.27044 + 1.74861i 0.270858 + 0.372804i
\(23\) −2.62866 3.61803i −0.548113 0.754412i 0.441642 0.897191i \(-0.354396\pi\)
−0.989755 + 0.142779i \(0.954396\pi\)
\(24\) −0.809017 0.587785i −0.165140 0.119981i
\(25\) 4.77943 1.46869i 0.955886 0.293738i
\(26\) −0.381966 −0.0749097
\(27\) −0.587785 + 0.809017i −0.113119 + 0.155695i
\(28\) 1.46782 0.476925i 0.277393 0.0901304i
\(29\) −1.31677 + 4.05259i −0.244517 + 0.752547i 0.751198 + 0.660077i \(0.229476\pi\)
−0.995715 + 0.0924701i \(0.970524\pi\)
\(30\) −2.21127 + 0.332092i −0.403721 + 0.0606314i
\(31\) 5.47414 + 1.01677i 0.983184 + 0.182617i
\(32\) 1.00000i 0.176777i
\(33\) −2.05561 0.667908i −0.357836 0.116268i
\(34\) 0.335816 + 1.03354i 0.0575920 + 0.177250i
\(35\) 1.59134 3.06227i 0.268985 0.517618i
\(36\) 1.00000 0.166667
\(37\) 3.70476i 0.609058i 0.952503 + 0.304529i \(0.0984991\pi\)
−0.952503 + 0.304529i \(0.901501\pi\)
\(38\) 2.51702 3.46439i 0.408315 0.561998i
\(39\) 0.309017 0.224514i 0.0494823 0.0359510i
\(40\) 1.56842 + 1.59376i 0.247989 + 0.251995i
\(41\) 0.587210 1.80725i 0.0917068 0.282245i −0.894675 0.446718i \(-0.852593\pi\)
0.986381 + 0.164474i \(0.0525926\pi\)
\(42\) −0.907165 + 1.24861i −0.139979 + 0.192664i
\(43\) −7.37483 2.39623i −1.12465 0.365421i −0.313110 0.949717i \(-0.601371\pi\)
−0.811541 + 0.584296i \(0.801371\pi\)
\(44\) 0.667908 + 2.05561i 0.100691 + 0.309895i
\(45\) 1.59376 1.56842i 0.237583 0.233806i
\(46\) −1.38197 4.25325i −0.203760 0.627108i
\(47\) 9.01470 2.92905i 1.31493 0.427246i 0.434178 0.900827i \(-0.357039\pi\)
0.880750 + 0.473581i \(0.157039\pi\)
\(48\) −0.587785 0.809017i −0.0848395 0.116772i
\(49\) 1.42705 + 4.39201i 0.203864 + 0.627430i
\(50\) 4.99936 + 0.0801180i 0.707016 + 0.0113304i
\(51\) −0.879178 0.638760i −0.123110 0.0894443i
\(52\) −0.363271 0.118034i −0.0503767 0.0163684i
\(53\) 3.47954 + 4.78918i 0.477952 + 0.657844i 0.978110 0.208090i \(-0.0667246\pi\)
−0.500158 + 0.865934i \(0.666725\pi\)
\(54\) −0.809017 + 0.587785i −0.110093 + 0.0799874i
\(55\) 4.28854 + 2.22858i 0.578267 + 0.300502i
\(56\) 1.54336 0.206240
\(57\) 4.28222i 0.567194i
\(58\) −2.50464 + 3.44734i −0.328875 + 0.452658i
\(59\) 1.08442 + 3.33751i 0.141180 + 0.434507i 0.996500 0.0835931i \(-0.0266396\pi\)
−0.855320 + 0.518100i \(0.826640\pi\)
\(60\) −2.20566 0.367482i −0.284750 0.0474417i
\(61\) −4.97335 −0.636772 −0.318386 0.947961i \(-0.603141\pi\)
−0.318386 + 0.947961i \(0.603141\pi\)
\(62\) 4.89201 + 2.65861i 0.621286 + 0.337644i
\(63\) 1.54336i 0.194445i
\(64\) −0.309017 + 0.951057i −0.0386271 + 0.118882i
\(65\) −0.764093 + 0.381644i −0.0947740 + 0.0473372i
\(66\) −1.74861 1.27044i −0.215239 0.156380i
\(67\) 2.20197i 0.269013i −0.990913 0.134507i \(-0.957055\pi\)
0.990913 0.134507i \(-0.0429450\pi\)
\(68\) 1.08672i 0.131785i
\(69\) 3.61803 + 2.62866i 0.435560 + 0.316453i
\(70\) 2.45974 2.42064i 0.293995 0.289322i
\(71\) −4.31677 + 3.13631i −0.512306 + 0.372212i −0.813698 0.581288i \(-0.802549\pi\)
0.301392 + 0.953500i \(0.402549\pi\)
\(72\) 0.951057 + 0.309017i 0.112083 + 0.0364180i
\(73\) −3.86791 + 5.32373i −0.452705 + 0.623095i −0.972976 0.230906i \(-0.925831\pi\)
0.520271 + 0.854001i \(0.325831\pi\)
\(74\) −1.14483 + 3.52343i −0.133084 + 0.409591i
\(75\) −4.09166 + 2.87373i −0.472464 + 0.331830i
\(76\) 3.46439 2.51702i 0.397392 0.288723i
\(77\) 3.17255 1.03082i 0.361546 0.117473i
\(78\) 0.363271 0.118034i 0.0411324 0.0133647i
\(79\) 4.01750 2.91888i 0.452004 0.328400i −0.338383 0.941009i \(-0.609880\pi\)
0.790386 + 0.612609i \(0.209880\pi\)
\(80\) 0.999158 + 2.00042i 0.111709 + 0.223654i
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 1.11694 1.53734i 0.123345 0.169770i
\(83\) −1.57743 0.512538i −0.173145 0.0562584i 0.221161 0.975237i \(-0.429015\pi\)
−0.394307 + 0.918979i \(0.629015\pi\)
\(84\) −1.24861 + 0.907165i −0.136234 + 0.0989799i
\(85\) 1.70444 + 1.73197i 0.184872 + 0.187859i
\(86\) −6.27340 4.55789i −0.676479 0.491490i
\(87\) 4.26114i 0.456843i
\(88\) 2.16140i 0.230406i
\(89\) −0.341842 0.248363i −0.0362352 0.0263264i 0.569520 0.821977i \(-0.307129\pi\)
−0.605755 + 0.795651i \(0.707129\pi\)
\(90\) 2.00042 0.999158i 0.210863 0.105321i
\(91\) −0.182169 + 0.560659i −0.0190965 + 0.0587730i
\(92\) 4.47214i 0.466252i
\(93\) −5.52041 + 0.724595i −0.572440 + 0.0751370i
\(94\) 9.47861 0.977644
\(95\) 1.57364 9.44514i 0.161452 0.969051i
\(96\) −0.309017 0.951057i −0.0315389 0.0970668i
\(97\) −8.18713 + 11.2686i −0.831277 + 1.14415i 0.156407 + 0.987693i \(0.450009\pi\)
−0.987684 + 0.156462i \(0.949991\pi\)
\(98\) 4.61803i 0.466492i
\(99\) 2.16140 0.217228
\(100\) 4.72991 + 1.62108i 0.472991 + 0.162108i
\(101\) −0.627784 + 0.456112i −0.0624668 + 0.0453848i −0.618580 0.785721i \(-0.712292\pi\)
0.556114 + 0.831106i \(0.312292\pi\)
\(102\) −0.638760 0.879178i −0.0632467 0.0870516i
\(103\) −16.0896 5.22783i −1.58536 0.515114i −0.621927 0.783075i \(-0.713650\pi\)
−0.963430 + 0.267961i \(0.913650\pi\)
\(104\) −0.309017 0.224514i −0.0303016 0.0220154i
\(105\) −0.567157 + 3.40414i −0.0553489 + 0.332210i
\(106\) 1.82930 + 5.63002i 0.177678 + 0.546836i
\(107\) −0.530255 0.729834i −0.0512617 0.0705557i 0.782617 0.622504i \(-0.213885\pi\)
−0.833878 + 0.551948i \(0.813885\pi\)
\(108\) −0.951057 + 0.309017i −0.0915155 + 0.0297352i
\(109\) −4.32528 13.3118i −0.414287 1.27504i −0.912887 0.408211i \(-0.866153\pi\)
0.498601 0.866832i \(-0.333847\pi\)
\(110\) 3.38998 + 3.44474i 0.323222 + 0.328443i
\(111\) −1.14483 3.52343i −0.108663 0.334430i
\(112\) 1.46782 + 0.476925i 0.138696 + 0.0450652i
\(113\) −2.39446 + 3.29569i −0.225252 + 0.310033i −0.906653 0.421878i \(-0.861371\pi\)
0.681401 + 0.731911i \(0.261371\pi\)
\(114\) −1.32328 + 4.07263i −0.123936 + 0.381437i
\(115\) −7.01419 7.12749i −0.654076 0.664642i
\(116\) −3.44734 + 2.50464i −0.320077 + 0.232550i
\(117\) −0.224514 + 0.309017i −0.0207563 + 0.0285686i
\(118\) 3.50926i 0.323054i
\(119\) 1.67721 0.153749
\(120\) −1.98415 1.03108i −0.181128 0.0941246i
\(121\) −1.95557 6.01864i −0.177779 0.547149i
\(122\) −4.72994 1.53685i −0.428228 0.139140i
\(123\) 1.90025i 0.171340i
\(124\) 3.83103 + 4.04020i 0.344036 + 0.362821i
\(125\) 10.0809 4.83488i 0.901660 0.432445i
\(126\) 0.476925 1.46782i 0.0424879 0.130764i
\(127\) 0.316103 0.102708i 0.0280496 0.00911386i −0.294959 0.955510i \(-0.595306\pi\)
0.323008 + 0.946396i \(0.395306\pi\)
\(128\) −0.587785 + 0.809017i −0.0519534 + 0.0715077i
\(129\) 7.75435 0.682733
\(130\) −0.844630 + 0.126848i −0.0740789 + 0.0111253i
\(131\) 0.571884 + 0.415498i 0.0499657 + 0.0363022i 0.612488 0.790480i \(-0.290169\pi\)
−0.562522 + 0.826782i \(0.690169\pi\)
\(132\) −1.27044 1.74861i −0.110577 0.152197i
\(133\) −3.88468 5.34680i −0.336844 0.463627i
\(134\) 0.680446 2.09420i 0.0587816 0.180911i
\(135\) −1.03108 + 1.98415i −0.0887416 + 0.170769i
\(136\) −0.335816 + 1.03354i −0.0287960 + 0.0886250i
\(137\) 18.0471 5.86385i 1.54187 0.500983i 0.589976 0.807421i \(-0.299137\pi\)
0.951891 + 0.306438i \(0.0991373\pi\)
\(138\) 2.62866 + 3.61803i 0.223766 + 0.307988i
\(139\) −3.32758 10.2412i −0.282242 0.868651i −0.987212 0.159414i \(-0.949040\pi\)
0.704970 0.709237i \(-0.250960\pi\)
\(140\) 3.08737 1.54206i 0.260931 0.130328i
\(141\) −7.66836 + 5.57139i −0.645792 + 0.469196i
\(142\) −5.07466 + 1.64886i −0.425856 + 0.138369i
\(143\) −0.785173 0.255118i −0.0656595 0.0213341i
\(144\) 0.809017 + 0.587785i 0.0674181 + 0.0489821i
\(145\) −1.56589 + 9.39866i −0.130040 + 0.780516i
\(146\) −5.32373 + 3.86791i −0.440595 + 0.320111i
\(147\) −2.71441 3.73607i −0.223881 0.308146i
\(148\) −2.17760 + 2.99721i −0.178998 + 0.246369i
\(149\) −8.77543 −0.718911 −0.359456 0.933162i \(-0.617038\pi\)
−0.359456 + 0.933162i \(0.617038\pi\)
\(150\) −4.77943 + 1.46869i −0.390239 + 0.119918i
\(151\) −14.6157 10.6189i −1.18941 0.864156i −0.196207 0.980563i \(-0.562862\pi\)
−0.993202 + 0.116407i \(0.962862\pi\)
\(152\) 4.07263 1.32328i 0.330334 0.107332i
\(153\) 1.03354 + 0.335816i 0.0835564 + 0.0271491i
\(154\) 3.33582 0.268808
\(155\) 12.4425 + 0.430438i 0.999402 + 0.0345736i
\(156\) 0.381966 0.0305818
\(157\) 6.68360 + 2.17163i 0.533409 + 0.173315i 0.563322 0.826237i \(-0.309523\pi\)
−0.0299130 + 0.999553i \(0.509523\pi\)
\(158\) 4.72285 1.53455i 0.375730 0.122082i
\(159\) −4.78918 3.47954i −0.379807 0.275946i
\(160\) 0.332092 + 2.21127i 0.0262542 + 0.174816i
\(161\) −6.90212 −0.543964
\(162\) 0.587785 0.809017i 0.0461808 0.0635624i
\(163\) −11.4835 15.8056i −0.899453 1.23799i −0.970642 0.240528i \(-0.922679\pi\)
0.0711888 0.997463i \(-0.477321\pi\)
\(164\) 1.53734 1.11694i 0.120046 0.0872184i
\(165\) −4.76731 0.794274i −0.371135 0.0618341i
\(166\) −1.34184 0.974905i −0.104147 0.0756673i
\(167\) −4.67718 1.51971i −0.361931 0.117599i 0.122406 0.992480i \(-0.460939\pi\)
−0.484337 + 0.874882i \(0.660939\pi\)
\(168\) −1.46782 + 0.476925i −0.113245 + 0.0367956i
\(169\) −10.3992 + 7.55545i −0.799937 + 0.581189i
\(170\) 1.08581 + 2.17390i 0.0832778 + 0.166731i
\(171\) −1.32328 4.07263i −0.101194 0.311442i
\(172\) −4.55789 6.27340i −0.347536 0.478343i
\(173\) 4.02967 1.30932i 0.306370 0.0995456i −0.151797 0.988412i \(-0.548506\pi\)
0.458167 + 0.888866i \(0.348506\pi\)
\(174\) 1.31677 4.05259i 0.0998238 0.307226i
\(175\) 2.50192 7.29997i 0.189127 0.551826i
\(176\) −0.667908 + 2.05561i −0.0503455 + 0.154947i
\(177\) −2.06269 2.83905i −0.155042 0.213396i
\(178\) −0.248363 0.341842i −0.0186156 0.0256221i
\(179\) −2.55841 1.85879i −0.191225 0.138933i 0.488054 0.872814i \(-0.337707\pi\)
−0.679278 + 0.733881i \(0.737707\pi\)
\(180\) 2.21127 0.332092i 0.164818 0.0247527i
\(181\) −20.7015 −1.53873 −0.769364 0.638811i \(-0.779427\pi\)
−0.769364 + 0.638811i \(0.779427\pi\)
\(182\) −0.346506 + 0.476925i −0.0256848 + 0.0353520i
\(183\) 4.72994 1.53685i 0.349647 0.113607i
\(184\) 1.38197 4.25325i 0.101880 0.313554i
\(185\) 1.23032 + 8.19222i 0.0904549 + 0.602304i
\(186\) −5.47414 1.01677i −0.401383 0.0745533i
\(187\) 2.34884i 0.171764i
\(188\) 9.01470 + 2.92905i 0.657464 + 0.213623i
\(189\) 0.476925 + 1.46782i 0.0346912 + 0.106769i
\(190\) 4.41533 8.49658i 0.320321 0.616407i
\(191\) −20.7597 −1.50212 −0.751059 0.660236i \(-0.770456\pi\)
−0.751059 + 0.660236i \(0.770456\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) −6.48891 + 8.93123i −0.467082 + 0.642884i −0.975959 0.217956i \(-0.930061\pi\)
0.508876 + 0.860840i \(0.330061\pi\)
\(194\) −11.2686 + 8.18713i −0.809039 + 0.587802i
\(195\) 0.608761 0.599083i 0.0435943 0.0429012i
\(196\) −1.42705 + 4.39201i −0.101932 + 0.313715i
\(197\) −2.27044 + 3.12500i −0.161762 + 0.222647i −0.882202 0.470871i \(-0.843940\pi\)
0.720440 + 0.693517i \(0.243940\pi\)
\(198\) 2.05561 + 0.667908i 0.146086 + 0.0474662i
\(199\) 1.22394 + 3.76689i 0.0867626 + 0.267028i 0.985020 0.172443i \(-0.0551660\pi\)
−0.898257 + 0.439471i \(0.855166\pi\)
\(200\) 3.99747 + 3.00337i 0.282664 + 0.212370i
\(201\) 0.680446 + 2.09420i 0.0479950 + 0.147713i
\(202\) −0.738004 + 0.239792i −0.0519258 + 0.0168717i
\(203\) 3.86556 + 5.32049i 0.271309 + 0.373425i
\(204\) −0.335816 1.03354i −0.0235118 0.0723620i
\(205\) 0.698308 4.19132i 0.0487719 0.292734i
\(206\) −13.6866 9.94393i −0.953594 0.692826i
\(207\) −4.25325 1.38197i −0.295622 0.0960533i
\(208\) −0.224514 0.309017i −0.0155672 0.0214265i
\(209\) 7.48791 5.44029i 0.517950 0.376312i
\(210\) −1.59134 + 3.06227i −0.109813 + 0.211317i
\(211\) −21.2293 −1.46148 −0.730741 0.682654i \(-0.760825\pi\)
−0.730741 + 0.682654i \(0.760825\pi\)
\(212\) 5.91975i 0.406570i
\(213\) 3.13631 4.31677i 0.214897 0.295780i
\(214\) −0.278772 0.857971i −0.0190564 0.0586497i
\(215\) −17.1035 2.84958i −1.16645 0.194340i
\(216\) −1.00000 −0.0680414
\(217\) 6.23549 5.91266i 0.423293 0.401378i
\(218\) 13.9969i 0.947990i
\(219\) 2.03348 6.25842i 0.137410 0.422905i
\(220\) 2.15958 + 4.32370i 0.145599 + 0.291504i
\(221\) −0.335816 0.243985i −0.0225894 0.0164122i
\(222\) 3.70476i 0.248647i
\(223\) 15.4742i 1.03623i 0.855311 + 0.518114i \(0.173366\pi\)
−0.855311 + 0.518114i \(0.826634\pi\)
\(224\) 1.24861 + 0.907165i 0.0834260 + 0.0606125i
\(225\) 3.00337 3.99747i 0.200224 0.266498i
\(226\) −3.29569 + 2.39446i −0.219226 + 0.159277i
\(227\) −1.40592 0.456810i −0.0933140 0.0303195i 0.261988 0.965071i \(-0.415622\pi\)
−0.355302 + 0.934752i \(0.615622\pi\)
\(228\) −2.51702 + 3.46439i −0.166694 + 0.229435i
\(229\) −4.18554 + 12.8818i −0.276588 + 0.851250i 0.712207 + 0.701970i \(0.247696\pi\)
−0.988795 + 0.149281i \(0.952304\pi\)
\(230\) −4.46837 8.94615i −0.294636 0.589892i
\(231\) −2.69873 + 1.96074i −0.177564 + 0.129007i
\(232\) −4.05259 + 1.31677i −0.266065 + 0.0864499i
\(233\) 14.9173 4.84693i 0.977266 0.317533i 0.223521 0.974699i \(-0.428245\pi\)
0.753746 + 0.657166i \(0.228245\pi\)
\(234\) −0.309017 + 0.224514i −0.0202011 + 0.0146769i
\(235\) 18.9612 9.47063i 1.23689 0.617796i
\(236\) −1.08442 + 3.33751i −0.0705899 + 0.217253i
\(237\) −2.91888 + 4.01750i −0.189602 + 0.260965i
\(238\) 1.59512 + 0.518286i 0.103396 + 0.0335955i
\(239\) 6.30172 4.57847i 0.407624 0.296156i −0.365015 0.931002i \(-0.618936\pi\)
0.772639 + 0.634845i \(0.218936\pi\)
\(240\) −1.56842 1.59376i −0.101241 0.102877i
\(241\) −10.6586 7.74393i −0.686581 0.498831i 0.188953 0.981986i \(-0.439491\pi\)
−0.875535 + 0.483156i \(0.839491\pi\)
\(242\) 6.32837i 0.406803i
\(243\) 1.00000i 0.0641500i
\(244\) −4.02352 2.92326i −0.257580 0.187143i
\(245\) 4.61415 + 9.23801i 0.294787 + 0.590195i
\(246\) −0.587210 + 1.80725i −0.0374391 + 0.115226i
\(247\) 1.63566i 0.104075i
\(248\) 2.39503 + 5.02631i 0.152085 + 0.319171i
\(249\) 1.65861 0.105110
\(250\) 11.0815 1.48308i 0.700858 0.0937985i
\(251\) 0.590934 + 1.81871i 0.0372994 + 0.114796i 0.967973 0.251056i \(-0.0807778\pi\)
−0.930673 + 0.365852i \(0.880778\pi\)
\(252\) 0.907165 1.24861i 0.0571460 0.0786548i
\(253\) 9.66606i 0.607700i
\(254\) 0.332370 0.0208548
\(255\) −2.15623 1.12050i −0.135028 0.0701686i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) 11.1510 + 15.3480i 0.695580 + 0.957384i 0.999988 + 0.00484260i \(0.00154146\pi\)
−0.304408 + 0.952542i \(0.598459\pi\)
\(258\) 7.37483 + 2.39623i 0.459137 + 0.149183i
\(259\) 4.62578 + 3.36083i 0.287432 + 0.208832i
\(260\) −0.842489 0.140366i −0.0522489 0.00870510i
\(261\) 1.31677 + 4.05259i 0.0815058 + 0.250849i
\(262\) 0.415498 + 0.571884i 0.0256696 + 0.0353311i
\(263\) 17.5103 5.68943i 1.07973 0.350825i 0.285460 0.958391i \(-0.407854\pi\)
0.794270 + 0.607565i \(0.207854\pi\)
\(264\) −0.667908 2.05561i −0.0411069 0.126514i
\(265\) 9.28466 + 9.43464i 0.570352 + 0.579565i
\(266\) −2.04230 6.28554i −0.125221 0.385391i
\(267\) 0.401859 + 0.130572i 0.0245934 + 0.00799088i
\(268\) 1.29429 1.78143i 0.0790611 0.108818i
\(269\) −9.02322 + 27.7706i −0.550156 + 1.69321i 0.158249 + 0.987399i \(0.449415\pi\)
−0.708405 + 0.705806i \(0.750585\pi\)
\(270\) −1.59376 + 1.56842i −0.0969929 + 0.0954510i
\(271\) −8.12751 + 5.90498i −0.493711 + 0.358702i −0.806610 0.591085i \(-0.798700\pi\)
0.312899 + 0.949786i \(0.398700\pi\)
\(272\) −0.638760 + 0.879178i −0.0387305 + 0.0533080i
\(273\) 0.589512i 0.0356789i
\(274\) 18.9758 1.14637
\(275\) 10.2232 + 3.50380i 0.616483 + 0.211287i
\(276\) 1.38197 + 4.25325i 0.0831846 + 0.256016i
\(277\) 7.30801 + 2.37452i 0.439096 + 0.142671i 0.520219 0.854033i \(-0.325851\pi\)
−0.0811225 + 0.996704i \(0.525851\pi\)
\(278\) 10.7683i 0.645838i
\(279\) 5.02631 2.39503i 0.300917 0.143387i
\(280\) 3.41279 0.512538i 0.203953 0.0306300i
\(281\) 4.63726 14.2720i 0.276636 0.851397i −0.712147 0.702031i \(-0.752277\pi\)
0.988782 0.149366i \(-0.0477232\pi\)
\(282\) −9.01470 + 2.92905i −0.536817 + 0.174423i
\(283\) −2.11242 + 2.90749i −0.125570 + 0.172832i −0.867173 0.498006i \(-0.834066\pi\)
0.741603 + 0.670839i \(0.234066\pi\)
\(284\) −5.33582 −0.316622
\(285\) 1.42209 + 9.46914i 0.0842373 + 0.560903i
\(286\) −0.667908 0.485264i −0.0394942 0.0286942i
\(287\) −1.72384 2.37267i −0.101755 0.140054i
\(288\) 0.587785 + 0.809017i 0.0346356 + 0.0476718i
\(289\) 4.88835 15.0448i 0.287550 0.884988i
\(290\) −4.39360 + 8.45476i −0.258001 + 0.496481i
\(291\) 4.30423 13.2471i 0.252318 0.776556i
\(292\) −6.25842 + 2.03348i −0.366246 + 0.119001i
\(293\) −2.60793 3.58951i −0.152357 0.209702i 0.726015 0.687679i \(-0.241370\pi\)
−0.878372 + 0.477977i \(0.841370\pi\)
\(294\) −1.42705 4.39201i −0.0832273 0.256147i
\(295\) 3.50631 + 7.02000i 0.204145 + 0.408720i
\(296\) −2.99721 + 2.17760i −0.174209 + 0.126571i
\(297\) −2.05561 + 0.667908i −0.119279 + 0.0387560i
\(298\) −8.34593 2.71176i −0.483467 0.157088i
\(299\) 1.38197 + 1.00406i 0.0799212 + 0.0580661i
\(300\) −4.99936 0.0801180i −0.288638 0.00462562i
\(301\) −9.68213 + 7.03448i −0.558069 + 0.405461i
\(302\) −10.6189 14.6157i −0.611050 0.841039i
\(303\) 0.456112 0.627784i 0.0262029 0.0360653i
\(304\) 4.28222 0.245602
\(305\) −10.9974 + 1.65161i −0.629710 + 0.0945709i
\(306\) 0.879178 + 0.638760i 0.0502593 + 0.0365155i
\(307\) 22.9191 7.44685i 1.30806 0.425014i 0.429681 0.902981i \(-0.358626\pi\)
0.878378 + 0.477966i \(0.158626\pi\)
\(308\) 3.17255 + 1.03082i 0.180773 + 0.0587366i
\(309\) 16.9176 0.962410
\(310\) 11.7005 + 4.25430i 0.664542 + 0.241628i
\(311\) 32.7345 1.85620 0.928102 0.372325i \(-0.121439\pi\)
0.928102 + 0.372325i \(0.121439\pi\)
\(312\) 0.363271 + 0.118034i 0.0205662 + 0.00668236i
\(313\) −11.8328 + 3.84472i −0.668832 + 0.217317i −0.623699 0.781664i \(-0.714371\pi\)
−0.0451324 + 0.998981i \(0.514371\pi\)
\(314\) 5.68541 + 4.13069i 0.320846 + 0.233108i
\(315\) −0.512538 3.41279i −0.0288782 0.192289i
\(316\) 4.96590 0.279354
\(317\) −0.284396 + 0.391438i −0.0159733 + 0.0219853i −0.816929 0.576738i \(-0.804325\pi\)
0.800956 + 0.598724i \(0.204325\pi\)
\(318\) −3.47954 4.78918i −0.195123 0.268564i
\(319\) −7.45106 + 5.41351i −0.417179 + 0.303099i
\(320\) −0.367482 + 2.20566i −0.0205429 + 0.123300i
\(321\) 0.729834 + 0.530255i 0.0407354 + 0.0295960i
\(322\) −6.56431 2.13287i −0.365815 0.118860i
\(323\) 4.42583 1.43804i 0.246260 0.0800146i
\(324\) 0.809017 0.587785i 0.0449454 0.0326547i
\(325\) −1.56287 + 1.09767i −0.0866927 + 0.0608877i
\(326\) −6.03721 18.5806i −0.334370 1.02909i
\(327\) 8.22717 + 11.3237i 0.454964 + 0.626204i
\(328\) 1.80725 0.587210i 0.0997885 0.0324233i
\(329\) 4.52059 13.9129i 0.249228 0.767045i
\(330\) −4.28854 2.22858i −0.236076 0.122679i
\(331\) −9.00648 + 27.7191i −0.495041 + 1.52358i 0.321853 + 0.946790i \(0.395694\pi\)
−0.816893 + 0.576789i \(0.804306\pi\)
\(332\) −0.974905 1.34184i −0.0535049 0.0736431i
\(333\) 2.17760 + 2.99721i 0.119332 + 0.164246i
\(334\) −3.97865 2.89066i −0.217702 0.158170i
\(335\) −0.731256 4.86915i −0.0399528 0.266030i
\(336\) −1.54336 −0.0841973
\(337\) 9.72394 13.3839i 0.529697 0.729065i −0.457387 0.889268i \(-0.651215\pi\)
0.987084 + 0.160202i \(0.0512147\pi\)
\(338\) −12.2250 + 3.97214i −0.664951 + 0.216056i
\(339\) 1.25884 3.87432i 0.0683709 0.210424i
\(340\) 0.360892 + 2.40304i 0.0195721 + 0.130323i
\(341\) 8.28037 + 8.73248i 0.448407 + 0.472890i
\(342\) 4.28222i 0.231556i
\(343\) 17.0532 + 5.54093i 0.920788 + 0.299182i
\(344\) −2.39623 7.37483i −0.129196 0.397624i
\(345\) 8.87341 + 4.61115i 0.477728 + 0.248256i
\(346\) 4.23704 0.227785
\(347\) 16.8460i 0.904340i 0.891932 + 0.452170i \(0.149350\pi\)
−0.891932 + 0.452170i \(0.850650\pi\)
\(348\) 2.50464 3.44734i 0.134263 0.184797i
\(349\) −1.27971 + 0.929762i −0.0685012 + 0.0497690i −0.621509 0.783407i \(-0.713480\pi\)
0.553008 + 0.833176i \(0.313480\pi\)
\(350\) 4.63528 6.16955i 0.247766 0.329776i
\(351\) 0.118034 0.363271i 0.00630019 0.0193900i
\(352\) −1.27044 + 1.74861i −0.0677145 + 0.0932010i
\(353\) 3.82933 + 1.24422i 0.203814 + 0.0662233i 0.409145 0.912469i \(-0.365827\pi\)
−0.205331 + 0.978693i \(0.565827\pi\)
\(354\) −1.08442 3.33751i −0.0576364 0.177387i
\(355\) −8.50399 + 8.36880i −0.451345 + 0.444170i
\(356\) −0.130572 0.401859i −0.00692030 0.0212985i
\(357\) −1.59512 + 0.518286i −0.0844227 + 0.0274306i
\(358\) −1.85879 2.55841i −0.0982403 0.135216i
\(359\) −3.33697 10.2701i −0.176119 0.542038i 0.823564 0.567223i \(-0.191982\pi\)
−0.999683 + 0.0251856i \(0.991982\pi\)
\(360\) 2.20566 + 0.367482i 0.116249 + 0.0193680i
\(361\) 0.536063 + 0.389473i 0.0282138 + 0.0204986i
\(362\) −19.6883 6.39711i −1.03479 0.336224i
\(363\) 3.71972 + 5.11976i 0.195235 + 0.268718i
\(364\) −0.476925 + 0.346506i −0.0249977 + 0.0181619i
\(365\) −6.78504 + 13.0567i −0.355145 + 0.683419i
\(366\) 4.97335 0.259961
\(367\) 5.82229i 0.303921i −0.988387 0.151961i \(-0.951441\pi\)
0.988387 0.151961i \(-0.0485587\pi\)
\(368\) 2.62866 3.61803i 0.137028 0.188603i
\(369\) −0.587210 1.80725i −0.0305689 0.0940815i
\(370\) −1.36143 + 8.17145i −0.0707774 + 0.424814i
\(371\) 9.13632 0.474334
\(372\) −4.89201 2.65861i −0.253639 0.137842i
\(373\) 13.3684i 0.692189i 0.938200 + 0.346094i \(0.112492\pi\)
−0.938200 + 0.346094i \(0.887508\pi\)
\(374\) −0.725832 + 2.23388i −0.0375319 + 0.115511i
\(375\) −8.09342 + 7.71340i −0.417942 + 0.398318i
\(376\) 7.66836 + 5.57139i 0.395465 + 0.287322i
\(377\) 1.62761i 0.0838263i
\(378\) 1.54336i 0.0793820i
\(379\) 16.0037 + 11.6274i 0.822057 + 0.597260i 0.917301 0.398194i \(-0.130363\pi\)
−0.0952438 + 0.995454i \(0.530363\pi\)
\(380\) 6.82481 6.71632i 0.350105 0.344540i
\(381\) −0.268893 + 0.195362i −0.0137758 + 0.0100087i
\(382\) −19.7436 6.41509i −1.01017 0.328225i
\(383\) −0.198993 + 0.273890i −0.0101681 + 0.0139951i −0.814071 0.580766i \(-0.802753\pi\)
0.803903 + 0.594761i \(0.202753\pi\)
\(384\) 0.309017 0.951057i 0.0157695 0.0485334i
\(385\) 6.67304 3.33301i 0.340089 0.169866i
\(386\) −8.93123 + 6.48891i −0.454587 + 0.330277i
\(387\) −7.37483 + 2.39623i −0.374884 + 0.121807i
\(388\) −13.2471 + 4.30423i −0.672517 + 0.218514i
\(389\) −4.37570 + 3.17913i −0.221857 + 0.161188i −0.693162 0.720782i \(-0.743783\pi\)
0.471305 + 0.881970i \(0.343783\pi\)
\(390\) 0.764093 0.381644i 0.0386913 0.0193253i
\(391\) 1.50182 4.62211i 0.0759501 0.233750i
\(392\) −2.71441 + 3.73607i −0.137099 + 0.188700i
\(393\) −0.672290 0.218440i −0.0339125 0.0110189i
\(394\) −3.12500 + 2.27044i −0.157435 + 0.114383i
\(395\) 7.91444 7.78862i 0.398219 0.391888i
\(396\) 1.74861 + 1.27044i 0.0878708 + 0.0638418i
\(397\) 13.5456i 0.679833i 0.940456 + 0.339917i \(0.110399\pi\)
−0.940456 + 0.339917i \(0.889601\pi\)
\(398\) 3.96074i 0.198534i
\(399\) 5.34680 + 3.88468i 0.267675 + 0.194477i
\(400\) 2.87373 + 4.09166i 0.143687 + 0.204583i
\(401\) 9.56816 29.4478i 0.477811 1.47055i −0.364318 0.931275i \(-0.618698\pi\)
0.842129 0.539277i \(-0.181302\pi\)
\(402\) 2.20197i 0.109824i
\(403\) −2.10861 + 0.276771i −0.105037 + 0.0137869i
\(404\) −0.775984 −0.0386066
\(405\) 0.367482 2.20566i 0.0182603 0.109600i
\(406\) 2.03225 + 6.25461i 0.100859 + 0.310411i
\(407\) −4.70666 + 6.47816i −0.233300 + 0.321111i
\(408\) 1.08672i 0.0538008i
\(409\) −5.96474 −0.294938 −0.147469 0.989067i \(-0.547113\pi\)
−0.147469 + 0.989067i \(0.547113\pi\)
\(410\) 1.95932 3.77039i 0.0967639 0.186206i
\(411\) −15.3518 + 11.1537i −0.757247 + 0.550172i
\(412\) −9.94393 13.6866i −0.489902 0.674293i
\(413\) 5.15098 + 1.67366i 0.253463 + 0.0823552i
\(414\) −3.61803 2.62866i −0.177817 0.129191i
\(415\) −3.65833 0.609508i −0.179581 0.0299196i
\(416\) −0.118034 0.363271i −0.00578709 0.0178108i
\(417\) 6.32944 + 8.71172i 0.309954 + 0.426615i
\(418\) 8.80257 2.86013i 0.430548 0.139893i
\(419\) −7.19594 22.1468i −0.351545 1.08194i −0.957986 0.286815i \(-0.907403\pi\)
0.606441 0.795128i \(-0.292597\pi\)
\(420\) −2.45974 + 2.42064i −0.120023 + 0.118115i
\(421\) −9.05571 27.8706i −0.441349 1.35833i −0.886439 0.462845i \(-0.846828\pi\)
0.445090 0.895486i \(-0.353172\pi\)
\(422\) −20.1902 6.56020i −0.982845 0.319346i
\(423\) 5.57139 7.66836i 0.270890 0.372848i
\(424\) −1.82930 + 5.63002i −0.0888389 + 0.273418i
\(425\) 4.34415 + 3.26383i 0.210722 + 0.158319i
\(426\) 4.31677 3.13631i 0.209148 0.151955i
\(427\) −4.51165 + 6.20976i −0.218334 + 0.300511i
\(428\) 0.902124i 0.0436058i
\(429\) 0.825580 0.0398594
\(430\) −15.3858 7.99539i −0.741971 0.385572i
\(431\) 4.88405 + 15.0316i 0.235256 + 0.724044i 0.997087 + 0.0762685i \(0.0243006\pi\)
−0.761831 + 0.647776i \(0.775699\pi\)
\(432\) −0.951057 0.309017i −0.0457577 0.0148676i
\(433\) 21.4746i 1.03200i −0.856587 0.516002i \(-0.827420\pi\)
0.856587 0.516002i \(-0.172580\pi\)
\(434\) 7.75742 3.69640i 0.372368 0.177433i
\(435\) −1.41509 9.42254i −0.0678484 0.451776i
\(436\) 4.32528 13.3118i 0.207143 0.637522i
\(437\) −18.2134 + 5.91788i −0.871263 + 0.283091i
\(438\) 3.86791 5.32373i 0.184816 0.254378i
\(439\) 32.1050 1.53229 0.766144 0.642669i \(-0.222173\pi\)
0.766144 + 0.642669i \(0.222173\pi\)
\(440\) 0.717782 + 4.77943i 0.0342189 + 0.227850i
\(441\) 3.73607 + 2.71441i 0.177908 + 0.129258i
\(442\) −0.243985 0.335816i −0.0116052 0.0159731i
\(443\) 4.30918 + 5.93108i 0.204735 + 0.281794i 0.899021 0.437906i \(-0.144280\pi\)
−0.694286 + 0.719699i \(0.744280\pi\)
\(444\) 1.14483 3.52343i 0.0543314 0.167215i
\(445\) −0.838384 0.435674i −0.0397432 0.0206529i
\(446\) −4.78179 + 14.7168i −0.226424 + 0.696862i
\(447\) 8.34593 2.71176i 0.394749 0.128262i
\(448\) 0.907165 + 1.24861i 0.0428595 + 0.0589911i
\(449\) 4.42971 + 13.6332i 0.209051 + 0.643393i 0.999523 + 0.0308941i \(0.00983547\pi\)
−0.790472 + 0.612499i \(0.790165\pi\)
\(450\) 4.09166 2.87373i 0.192883 0.135469i
\(451\) 3.32279 2.41415i 0.156464 0.113678i
\(452\) −3.87432 + 1.25884i −0.182233 + 0.0592110i
\(453\) 17.1818 + 5.58270i 0.807270 + 0.262298i
\(454\) −1.19594 0.868904i −0.0561284 0.0407797i
\(455\) −0.216635 + 1.30027i −0.0101560 + 0.0609574i
\(456\) −3.46439 + 2.51702i −0.162235 + 0.117870i
\(457\) 16.6365 + 22.8981i 0.778221 + 1.07113i 0.995476 + 0.0950141i \(0.0302896\pi\)
−0.217255 + 0.976115i \(0.569710\pi\)
\(458\) −7.96136 + 10.9579i −0.372010 + 0.512028i
\(459\) −1.08672 −0.0507239
\(460\) −1.48516 9.88910i −0.0692460 0.461082i
\(461\) −4.14049 3.00824i −0.192842 0.140108i 0.487175 0.873305i \(-0.338027\pi\)
−0.680017 + 0.733197i \(0.738027\pi\)
\(462\) −3.17255 + 1.03082i −0.147600 + 0.0479583i
\(463\) −28.8048 9.35925i −1.33867 0.434961i −0.449806 0.893126i \(-0.648507\pi\)
−0.888867 + 0.458165i \(0.848507\pi\)
\(464\) −4.26114 −0.197819
\(465\) −11.9665 + 3.43556i −0.554933 + 0.159320i
\(466\) 15.6850 0.726594
\(467\) −1.96730 0.639214i −0.0910357 0.0295793i 0.263145 0.964756i \(-0.415240\pi\)
−0.354181 + 0.935177i \(0.615240\pi\)
\(468\) −0.363271 + 0.118034i −0.0167922 + 0.00545612i
\(469\) −2.74939 1.99755i −0.126955 0.0922383i
\(470\) 20.9598 3.14777i 0.966802 0.145196i
\(471\) −7.02755 −0.323812
\(472\) −2.06269 + 2.83905i −0.0949432 + 0.130678i
\(473\) −9.85142 13.5593i −0.452969 0.623458i
\(474\) −4.01750 + 2.91888i −0.184530 + 0.134069i
\(475\) 0.343083 21.4083i 0.0157417 0.982282i
\(476\) 1.35689 + 0.985838i 0.0621929 + 0.0451858i
\(477\) 5.63002 + 1.82930i 0.257781 + 0.0837581i
\(478\) 7.40811 2.40704i 0.338839 0.110096i
\(479\) −24.3612 + 17.6995i −1.11309 + 0.808710i −0.983148 0.182812i \(-0.941480\pi\)
−0.129945 + 0.991521i \(0.541480\pi\)
\(480\) −0.999158 2.00042i −0.0456051 0.0913063i
\(481\) −0.437287 1.34583i −0.0199386 0.0613647i
\(482\) −7.74393 10.6586i −0.352726 0.485486i
\(483\) 6.56431 2.13287i 0.298686 0.0970491i
\(484\) 1.95557 6.01864i 0.0888897 0.273574i
\(485\) −14.3617 + 27.6368i −0.652133 + 1.25492i
\(486\) −0.309017 + 0.951057i −0.0140173 + 0.0431408i
\(487\) −25.0188 34.4354i −1.13371 1.56042i −0.780823 0.624752i \(-0.785200\pi\)
−0.352887 0.935666i \(-0.614800\pi\)
\(488\) −2.92326 4.02352i −0.132330 0.182136i
\(489\) 15.8056 + 11.4835i 0.714755 + 0.519300i
\(490\) 1.53361 + 10.2117i 0.0692815 + 0.461318i
\(491\) 9.09452 0.410430 0.205215 0.978717i \(-0.434211\pi\)
0.205215 + 0.978717i \(0.434211\pi\)
\(492\) −1.11694 + 1.53734i −0.0503555 + 0.0693085i
\(493\) −4.40404 + 1.43096i −0.198348 + 0.0644472i
\(494\) −0.505447 + 1.55561i −0.0227411 + 0.0699901i
\(495\) 4.77943 0.717782i 0.214819 0.0322619i
\(496\) 0.724595 + 5.52041i 0.0325353 + 0.247874i
\(497\) 8.23510i 0.369395i
\(498\) 1.57743 + 0.512538i 0.0706863 + 0.0229674i
\(499\) 3.73432 + 11.4931i 0.167171 + 0.514500i 0.999190 0.0402477i \(-0.0128147\pi\)
−0.832018 + 0.554748i \(0.812815\pi\)
\(500\) 10.9975 + 2.01389i 0.491822 + 0.0900637i
\(501\) 4.91788 0.219715
\(502\) 1.91230i 0.0853503i
\(503\) 9.18621 12.6437i 0.409593 0.563756i −0.553526 0.832832i \(-0.686718\pi\)
0.963119 + 0.269076i \(0.0867181\pi\)
\(504\) 1.24861 0.907165i 0.0556173 0.0404084i
\(505\) −1.23673 + 1.21707i −0.0550337 + 0.0541588i
\(506\) 2.98698 9.19297i 0.132787 0.408677i
\(507\) 7.55545 10.3992i 0.335549 0.461844i
\(508\) 0.316103 + 0.102708i 0.0140248 + 0.00455693i
\(509\) 6.59412 + 20.2946i 0.292279 + 0.899542i 0.984122 + 0.177494i \(0.0567991\pi\)
−0.691843 + 0.722048i \(0.743201\pi\)
\(510\) −1.70444 1.73197i −0.0754738 0.0766930i
\(511\) 3.13840 + 9.65900i 0.138835 + 0.427289i
\(512\) −0.951057 + 0.309017i −0.0420312 + 0.0136568i
\(513\) 2.51702 + 3.46439i 0.111129 + 0.152956i
\(514\) 5.86243 + 18.0427i 0.258581 + 0.795830i
\(515\) −37.3146 6.21692i −1.64428 0.273950i
\(516\) 6.27340 + 4.55789i 0.276171 + 0.200650i
\(517\) 19.4843 + 6.33084i 0.856920 + 0.278430i
\(518\) 3.36083 + 4.62578i 0.147666 + 0.203245i
\(519\) −3.42784 + 2.49047i −0.150465 + 0.109319i
\(520\) −0.757879 0.393839i −0.0332352 0.0172710i
\(521\) 21.3473 0.935243 0.467621 0.883929i \(-0.345111\pi\)
0.467621 + 0.883929i \(0.345111\pi\)
\(522\) 4.26114i 0.186505i
\(523\) −9.91781 + 13.6507i −0.433676 + 0.596903i −0.968792 0.247875i \(-0.920268\pi\)
0.535116 + 0.844778i \(0.320268\pi\)
\(524\) 0.218440 + 0.672290i 0.00954261 + 0.0293691i
\(525\) −0.123651 + 7.71582i −0.00539658 + 0.336746i
\(526\) 18.4114 0.802775
\(527\) 2.60274 + 5.46221i 0.113377 + 0.237938i
\(528\) 2.16140i 0.0940627i
\(529\) 0.927051 2.85317i 0.0403066 0.124051i
\(530\) 5.91477 + 11.8420i 0.256921 + 0.514383i
\(531\) 2.83905 + 2.06269i 0.123204 + 0.0895133i
\(532\) 6.60901i 0.286537i
\(533\) 0.725832i 0.0314393i
\(534\) 0.341842 + 0.248363i 0.0147930 + 0.0107477i
\(535\) −1.41491 1.43777i −0.0611719 0.0621601i
\(536\) 1.78143 1.29429i 0.0769461 0.0559046i
\(537\) 3.00759 + 0.977226i 0.129787 + 0.0421704i
\(538\) −17.1632 + 23.6231i −0.739958 + 1.01846i
\(539\) −3.08442 + 9.49288i −0.132855 + 0.408887i
\(540\) −2.00042 + 0.999158i −0.0860844 + 0.0429969i
\(541\) 13.4650 9.78290i 0.578906 0.420600i −0.259424 0.965764i \(-0.583533\pi\)
0.838330 + 0.545164i \(0.183533\pi\)
\(542\) −9.55446 + 3.10443i −0.410399 + 0.133347i
\(543\) 19.6883 6.39711i 0.844904 0.274526i
\(544\) −0.879178 + 0.638760i −0.0376944 + 0.0273866i
\(545\) −13.9851 27.9997i −0.599057 1.19937i
\(546\) 0.182169 0.560659i 0.00779612 0.0239940i
\(547\) −16.5742 + 22.8124i −0.708662 + 0.975389i 0.291163 + 0.956673i \(0.405958\pi\)
−0.999825 + 0.0187156i \(0.994042\pi\)
\(548\) 18.0471 + 5.86385i 0.770933 + 0.250491i
\(549\) −4.02352 + 2.92326i −0.171720 + 0.124762i
\(550\) 8.64012 + 6.49146i 0.368416 + 0.276797i
\(551\) 14.7623 + 10.7254i 0.628893 + 0.456918i
\(552\) 4.47214i 0.190347i
\(553\) 7.66418i 0.325914i
\(554\) 6.21657 + 4.51660i 0.264117 + 0.191892i
\(555\) −3.70164 7.41107i −0.157126 0.314583i
\(556\) 3.32758 10.2412i 0.141121 0.434325i
\(557\) 26.1159i 1.10657i −0.832993 0.553283i \(-0.813375\pi\)
0.832993 0.553283i \(-0.186625\pi\)
\(558\) 5.52041 0.724595i 0.233698 0.0306745i
\(559\) 2.96190 0.125275
\(560\) 3.40414 + 0.567157i 0.143851 + 0.0239668i
\(561\) −0.725832 2.23388i −0.0306446 0.0943145i
\(562\) 8.82059 12.1405i 0.372074 0.512116i
\(563\) 0.639524i 0.0269527i 0.999909 + 0.0134764i \(0.00428979\pi\)
−0.999909 + 0.0134764i \(0.995710\pi\)
\(564\) −9.47861 −0.399122
\(565\) −4.20033 + 8.08285i −0.176709 + 0.340048i
\(566\) −2.90749 + 2.11242i −0.122211 + 0.0887915i
\(567\) −0.907165 1.24861i −0.0380974 0.0524365i
\(568\) −5.07466 1.64886i −0.212928 0.0691845i
\(569\) 8.67741 + 6.30451i 0.363776 + 0.264299i 0.754625 0.656156i \(-0.227819\pi\)
−0.390849 + 0.920455i \(0.627819\pi\)
\(570\) −1.57364 + 9.44514i −0.0659124 + 0.395613i
\(571\) 3.86828 + 11.9054i 0.161883 + 0.498223i 0.998793 0.0491164i \(-0.0156405\pi\)
−0.836910 + 0.547340i \(0.815641\pi\)
\(572\) −0.485264 0.667908i −0.0202899 0.0279266i
\(573\) 19.7436 6.41509i 0.824802 0.267994i
\(574\) −0.906278 2.78924i −0.0378273 0.116420i
\(575\) −17.8772 13.4315i −0.745533 0.560131i
\(576\) 0.309017 + 0.951057i 0.0128757 + 0.0396274i
\(577\) 32.0347 + 10.4087i 1.33362 + 0.433321i 0.887152 0.461477i \(-0.152680\pi\)
0.446471 + 0.894798i \(0.352680\pi\)
\(578\) 9.29819 12.7979i 0.386754 0.532321i
\(579\) 3.41142 10.4993i 0.141774 0.436335i
\(580\) −6.79123 + 6.68326i −0.281990 + 0.277507i
\(581\) −2.07095 + 1.50463i −0.0859174 + 0.0624226i
\(582\) 8.18713 11.2686i 0.339367 0.467099i
\(583\) 12.7949i 0.529912i
\(584\) −6.58049 −0.272303
\(585\) −0.393839 + 0.757879i −0.0162832 + 0.0313345i
\(586\) −1.37107 4.21972i −0.0566384 0.174315i
\(587\) −25.8363 8.39473i −1.06638 0.346488i −0.277303 0.960783i \(-0.589441\pi\)
−0.789077 + 0.614295i \(0.789441\pi\)
\(588\) 4.61803i 0.190445i
\(589\) 11.3847 20.9487i 0.469100 0.863175i
\(590\) 1.16540 + 7.75993i 0.0479787 + 0.319471i
\(591\) 1.19364 3.67365i 0.0490999 0.151114i
\(592\) −3.52343 + 1.14483i −0.144812 + 0.0470524i
\(593\) −23.2183 + 31.9572i −0.953461 + 1.31233i −0.00348754 + 0.999994i \(0.501110\pi\)
−0.949973 + 0.312332i \(0.898890\pi\)
\(594\) −2.16140 −0.0886831
\(595\) 3.70876 0.556987i 0.152044 0.0228343i
\(596\) −7.09947 5.15807i −0.290806 0.211283i
\(597\) −2.32807 3.20431i −0.0952814 0.131144i
\(598\) 1.00406 + 1.38197i 0.0410589 + 0.0565128i
\(599\) 10.7618 33.1214i 0.439715 1.35330i −0.448461 0.893802i \(-0.648028\pi\)
0.888177 0.459502i \(-0.151972\pi\)
\(600\) −4.72991 1.62108i −0.193098 0.0661805i
\(601\) 0.651067 2.00378i 0.0265576 0.0817358i −0.936899 0.349599i \(-0.886318\pi\)
0.963457 + 0.267864i \(0.0863177\pi\)
\(602\) −11.3820 + 3.69825i −0.463897 + 0.150729i
\(603\) −1.29429 1.78143i −0.0527074 0.0725455i
\(604\) −5.58270 17.1818i −0.227157 0.699117i
\(605\) −6.32304 12.6594i −0.257068 0.514678i
\(606\) 0.627784 0.456112i 0.0255020 0.0185283i
\(607\) 35.3225 11.4770i 1.43370 0.465836i 0.513769 0.857928i \(-0.328249\pi\)
0.919926 + 0.392093i \(0.128249\pi\)
\(608\) 4.07263 + 1.32328i 0.165167 + 0.0536660i
\(609\) −5.32049 3.86556i −0.215597 0.156640i
\(610\) −10.9695 1.82762i −0.444144 0.0739980i
\(611\) −2.92905 + 2.12808i −0.118497 + 0.0860929i
\(612\) 0.638760 + 0.879178i 0.0258204 + 0.0355387i
\(613\) −1.97399 + 2.71696i −0.0797286 + 0.109737i −0.847019 0.531563i \(-0.821605\pi\)
0.767290 + 0.641300i \(0.221605\pi\)
\(614\) 24.0985 0.972537
\(615\) 0.631058 + 4.20197i 0.0254467 + 0.169440i
\(616\) 2.69873 + 1.96074i 0.108735 + 0.0790006i
\(617\) −0.838896 + 0.272574i −0.0337727 + 0.0109734i −0.325855 0.945420i \(-0.605652\pi\)
0.292082 + 0.956393i \(0.405652\pi\)
\(618\) 16.0896 + 5.22783i 0.647219 + 0.210294i
\(619\) 7.56844 0.304201 0.152101 0.988365i \(-0.451396\pi\)
0.152101 + 0.988365i \(0.451396\pi\)
\(620\) 9.81315 + 7.66172i 0.394106 + 0.307702i
\(621\) 4.47214 0.179461
\(622\) 31.1324 + 10.1155i 1.24829 + 0.405596i
\(623\) −0.620214 + 0.201520i −0.0248484 + 0.00807372i
\(624\) 0.309017 + 0.224514i 0.0123706 + 0.00898775i
\(625\) 20.6859 14.0390i 0.827436 0.561560i
\(626\) −12.4418 −0.497274
\(627\) −5.44029 + 7.48791i −0.217264 + 0.299038i
\(628\) 4.13069 + 5.68541i 0.164832 + 0.226872i
\(629\) −3.25714 + 2.36645i −0.129871 + 0.0943566i
\(630\) 0.567157 3.40414i 0.0225961 0.135624i
\(631\) 25.6058 + 18.6037i 1.01935 + 0.740601i 0.966150 0.257983i \(-0.0830578\pi\)
0.0532005 + 0.998584i \(0.483058\pi\)
\(632\) 4.72285 + 1.53455i 0.187865 + 0.0610410i
\(633\) 20.1902 6.56020i 0.802490 0.260745i
\(634\) −0.391438 + 0.284396i −0.0155460 + 0.0112948i
\(635\) 0.664880 0.332090i 0.0263850 0.0131786i
\(636\) −1.82930 5.63002i −0.0725366 0.223245i
\(637\) −1.03681 1.42705i −0.0410800 0.0565418i
\(638\) −8.75925 + 2.84605i −0.346782 + 0.112676i
\(639\) −1.64886 + 5.07466i −0.0652278 + 0.200751i
\(640\) −1.03108 + 1.98415i −0.0407572 + 0.0784306i
\(641\) −2.80980 + 8.64769i −0.110981 + 0.341563i −0.991088 0.133212i \(-0.957471\pi\)
0.880107 + 0.474776i \(0.157471\pi\)
\(642\) 0.530255 + 0.729834i 0.0209275 + 0.0288042i
\(643\) 18.5094 + 25.4759i 0.729938 + 1.00467i 0.999135 + 0.0415878i \(0.0132416\pi\)
−0.269197 + 0.963085i \(0.586758\pi\)
\(644\) −5.58394 4.05697i −0.220038 0.159867i
\(645\) 17.1470 2.57516i 0.675161 0.101397i
\(646\) 4.65359 0.183093
\(647\) 14.0749 19.3724i 0.553340 0.761607i −0.437121 0.899403i \(-0.644002\pi\)
0.990461 + 0.137796i \(0.0440017\pi\)
\(648\) 0.951057 0.309017i 0.0373610 0.0121393i
\(649\) −2.34387 + 7.21368i −0.0920048 + 0.283162i
\(650\) −1.82558 + 0.560990i −0.0716051 + 0.0220038i
\(651\) −4.10319 + 7.55015i −0.160817 + 0.295914i
\(652\) 19.5368i 0.765121i
\(653\) 31.9211 + 10.3718i 1.24917 + 0.405879i 0.857623 0.514279i \(-0.171941\pi\)
0.391546 + 0.920159i \(0.371941\pi\)
\(654\) 4.32528 + 13.3118i 0.169132 + 0.520534i
\(655\) 1.40257 + 0.728860i 0.0548031 + 0.0284789i
\(656\) 1.90025 0.0741924
\(657\) 6.58049i 0.256729i
\(658\) 8.59867 11.8351i 0.335211 0.461378i
\(659\) −32.1516 + 23.3595i −1.25245 + 0.909957i −0.998361 0.0572244i \(-0.981775\pi\)
−0.254087 + 0.967181i \(0.581775\pi\)
\(660\) −3.38998 3.44474i −0.131955 0.134086i
\(661\) 2.04838 6.30427i 0.0796727 0.245208i −0.903284 0.429042i \(-0.858851\pi\)
0.982957 + 0.183835i \(0.0588511\pi\)
\(662\) −17.1313 + 23.5793i −0.665828 + 0.916434i
\(663\) 0.394776 + 0.128270i 0.0153318 + 0.00498161i
\(664\) −0.512538 1.57743i −0.0198903 0.0612162i
\(665\) −10.3657 10.5332i −0.401965 0.408458i
\(666\) 1.14483 + 3.52343i 0.0443614 + 0.136530i
\(667\) 18.1237 5.88876i 0.701754 0.228014i
\(668\) −2.89066 3.97865i −0.111843 0.153939i
\(669\) −4.78179 14.7168i −0.184875 0.568986i
\(670\) 0.809184 4.85681i 0.0312615 0.187635i
\(671\) −8.69643 6.31833i −0.335722 0.243916i
\(672\) −1.46782 0.476925i −0.0566226 0.0183978i
\(673\) −10.3303 14.2184i −0.398203 0.548079i 0.562089 0.827077i \(-0.309998\pi\)
−0.960292 + 0.278998i \(0.909998\pi\)
\(674\) 13.3839 9.72394i 0.515527 0.374552i
\(675\) −1.62108 + 4.72991i −0.0623955 + 0.182054i
\(676\) −12.8541 −0.494389
\(677\) 48.5416i 1.86560i 0.360389 + 0.932802i \(0.382644\pi\)
−0.360389 + 0.932802i \(0.617356\pi\)
\(678\) 2.39446 3.29569i 0.0919587 0.126570i
\(679\) 6.64298 + 20.4450i 0.254934 + 0.784607i
\(680\) −0.399351 + 2.39695i −0.0153144 + 0.0919188i
\(681\) 1.47827 0.0566474
\(682\) 5.17661 + 10.8639i 0.198223 + 0.415998i
\(683\) 36.3529i 1.39101i 0.718523 + 0.695503i \(0.244818\pi\)
−0.718523 + 0.695503i \(0.755182\pi\)
\(684\) 1.32328 4.07263i 0.0505968 0.155721i
\(685\) 37.9596 18.9599i 1.45036 0.724419i
\(686\) 14.5063 + 10.5395i 0.553855 + 0.402399i
\(687\) 13.5447i 0.516762i
\(688\) 7.75435i 0.295632i
\(689\) −1.82930 1.32907i −0.0696909 0.0506334i
\(690\) 7.01419 + 7.12749i 0.267026 + 0.271339i
\(691\) 10.4505 7.59271i 0.397554 0.288840i −0.370990 0.928637i \(-0.620982\pi\)
0.768544 + 0.639797i \(0.220982\pi\)
\(692\) 4.02967 + 1.30932i 0.153185 + 0.0497728i
\(693\) 1.96074 2.69873i 0.0744825 0.102516i
\(694\) −5.20569 + 16.0215i −0.197605 + 0.608167i
\(695\) −10.7592 21.5411i −0.408120 0.817100i
\(696\) 3.44734 2.50464i 0.130671 0.0949380i
\(697\) 1.96398 0.638135i 0.0743910 0.0241711i
\(698\) −1.50439 + 0.488805i −0.0569419 + 0.0185015i
\(699\) −12.6894 + 9.21941i −0.479958 + 0.348710i
\(700\) 6.31491 4.43521i 0.238681 0.167635i
\(701\) −5.56088 + 17.1146i −0.210032 + 0.646411i 0.789437 + 0.613831i \(0.210372\pi\)
−0.999469 + 0.0325800i \(0.989628\pi\)
\(702\) 0.224514 0.309017i 0.00847373 0.0116631i
\(703\) 15.0881 + 4.90242i 0.569059 + 0.184898i
\(704\) −1.74861 + 1.27044i −0.0659031 + 0.0478814i
\(705\) −15.1066 + 14.8664i −0.568947 + 0.559903i
\(706\) 3.25742 + 2.36665i 0.122595 + 0.0890702i
\(707\) 1.19762i 0.0450413i
\(708\) 3.50926i 0.131886i
\(709\) −40.0514 29.0990i −1.50416 1.09284i −0.968687 0.248286i \(-0.920133\pi\)
−0.535475 0.844551i \(-0.679867\pi\)
\(710\) −10.6739 + 5.33132i −0.400583 + 0.200081i
\(711\) 1.53455 4.72285i 0.0575500 0.177121i
\(712\) 0.422540i 0.0158354i
\(713\) −10.7109 22.4784i −0.401127 0.841821i
\(714\) −1.67721 −0.0627679
\(715\) −1.82095 0.303386i −0.0680998 0.0113460i
\(716\) −0.977226 3.00759i −0.0365206 0.112399i
\(717\) −4.57847 + 6.30172i −0.170986 + 0.235342i
\(718\) 10.7987i 0.403003i
\(719\) −42.9610 −1.60217 −0.801087 0.598548i \(-0.795745\pi\)
−0.801087 + 0.598548i \(0.795745\pi\)
\(720\) 1.98415 + 1.03108i 0.0739450 + 0.0384262i
\(721\) −21.1234 + 15.3471i −0.786678 + 0.571555i
\(722\) 0.389473 + 0.536063i 0.0144947 + 0.0199502i
\(723\) 12.5299 + 4.07123i 0.465994 + 0.151411i
\(724\) −16.7478 12.1680i −0.622429 0.452221i
\(725\) −0.341394 + 21.3030i −0.0126791 + 0.791173i
\(726\) 1.95557 + 6.01864i 0.0725781 + 0.223373i
\(727\) −2.54743 3.50623i −0.0944789 0.130039i 0.759161 0.650903i \(-0.225610\pi\)
−0.853639 + 0.520864i \(0.825610\pi\)
\(728\) −0.560659 + 0.182169i −0.0207794 + 0.00675164i
\(729\) −0.309017 0.951057i −0.0114451 0.0352243i
\(730\) −10.4877 + 10.3210i −0.388167 + 0.381996i
\(731\) −2.60404 8.01440i −0.0963138 0.296423i
\(732\) 4.72994 + 1.53685i 0.174824 + 0.0568036i
\(733\) 7.20897 9.92230i 0.266269 0.366488i −0.654856 0.755753i \(-0.727271\pi\)
0.921126 + 0.389265i \(0.127271\pi\)
\(734\) 1.79919 5.53733i 0.0664092 0.204387i
\(735\) −7.24302 7.36002i −0.267163 0.271478i
\(736\) 3.61803 2.62866i 0.133363 0.0968935i
\(737\) 2.79746 3.85038i 0.103046 0.141830i
\(738\) 1.90025i 0.0699492i
\(739\) 41.9260 1.54227 0.771136 0.636671i \(-0.219689\pi\)
0.771136 + 0.636671i \(0.219689\pi\)
\(740\) −3.81992 + 7.35081i −0.140423 + 0.270221i
\(741\) −0.505447 1.55561i −0.0185681 0.0571466i
\(742\) 8.68916 + 2.82328i 0.318989 + 0.103646i
\(743\) 33.8788i 1.24289i −0.783456 0.621447i \(-0.786545\pi\)
0.783456 0.621447i \(-0.213455\pi\)
\(744\) −3.83103 4.04020i −0.140452 0.148121i
\(745\) −19.4048 + 2.91425i −0.710938 + 0.106770i
\(746\) −4.13106 + 12.7141i −0.151249 + 0.465496i
\(747\) −1.57743 + 0.512538i −0.0577151 + 0.0187528i
\(748\) −1.38061 + 1.90025i −0.0504802 + 0.0694801i
\(749\) −1.39230 −0.0508737
\(750\) −10.0809 + 4.83488i −0.368101 + 0.176545i
\(751\) −28.7838 20.9126i −1.05033 0.763113i −0.0780588 0.996949i \(-0.524872\pi\)
−0.972276 + 0.233836i \(0.924872\pi\)
\(752\) 5.57139 + 7.66836i 0.203168 + 0.279636i
\(753\) −1.12402 1.54709i −0.0409617 0.0563790i
\(754\) 0.502960 1.54795i 0.0183167 0.0563731i
\(755\) −35.8457 18.6276i −1.30456 0.677926i
\(756\) −0.476925 + 1.46782i −0.0173456 + 0.0533843i
\(757\) 38.4509 12.4935i 1.39752 0.454082i 0.489133 0.872209i \(-0.337313\pi\)
0.908389 + 0.418127i \(0.137313\pi\)
\(758\) 11.6274 + 16.0037i 0.422326 + 0.581282i
\(759\) 2.98698 + 9.19297i 0.108420 + 0.333684i
\(760\) 8.56624 4.27861i 0.310730 0.155202i
\(761\) 13.1439 9.54963i 0.476467 0.346174i −0.323489 0.946232i \(-0.604856\pi\)
0.799956 + 0.600058i \(0.204856\pi\)
\(762\) −0.316103 + 0.102708i −0.0114512 + 0.00372072i
\(763\) −20.5450 6.67547i −0.743779 0.241668i
\(764\) −16.7949 12.2022i −0.607619 0.441461i
\(765\) 2.39695 + 0.399351i 0.0866619 + 0.0144386i
\(766\) −0.273890 + 0.198993i −0.00989606 + 0.00718991i
\(767\) −0.787879 1.08442i −0.0284487 0.0391562i
\(768\) 0.587785 0.809017i 0.0212099 0.0291929i
\(769\) −11.0518 −0.398537 −0.199268 0.979945i \(-0.563857\pi\)
−0.199268 + 0.979945i \(0.563857\pi\)
\(770\) 7.37639 1.10780i 0.265827 0.0399223i
\(771\) −15.3480 11.1510i −0.552746 0.401594i
\(772\) −10.4993 + 3.41142i −0.377878 + 0.122780i
\(773\) −24.6045 7.99449i −0.884963 0.287542i −0.168946 0.985625i \(-0.554036\pi\)
−0.716016 + 0.698083i \(0.754036\pi\)
\(774\) −7.75435 −0.278724
\(775\) 27.6566 3.18022i 0.993454 0.114237i
\(776\) −13.9288 −0.500014
\(777\) −5.43793 1.76689i −0.195085 0.0633869i
\(778\) −5.14394 + 1.67137i −0.184419 + 0.0599214i
\(779\) −6.58321 4.78298i −0.235868 0.171368i
\(780\) 0.844630 0.126848i 0.0302426 0.00454188i
\(781\) −11.5328 −0.412676
\(782\) 2.85662 3.93180i 0.102153 0.140601i
\(783\) −2.50464 3.44734i −0.0895084 0.123198i
\(784\) −3.73607 + 2.71441i −0.133431 + 0.0969433i
\(785\) 15.5004 + 2.58250i 0.553234 + 0.0921733i
\(786\) −0.571884 0.415498i −0.0203984 0.0148203i
\(787\) 27.1539 + 8.82285i 0.967933 + 0.314501i 0.749981 0.661459i \(-0.230062\pi\)
0.217952 + 0.975960i \(0.430062\pi\)
\(788\) −3.67365 + 1.19364i −0.130868 + 0.0425217i
\(789\) −14.8951 + 10.8219i −0.530281 + 0.385271i
\(790\) 9.93389 4.96172i 0.353432 0.176530i
\(791\) 1.94285 + 5.97948i 0.0690798 + 0.212606i
\(792\) 1.27044 + 1.74861i 0.0451430 + 0.0621340i
\(793\) 1.80668 0.587024i 0.0641569 0.0208458i
\(794\) −4.18581 + 12.8826i −0.148549 + 0.457187i
\(795\) −11.7457 6.10376i −0.416577 0.216478i
\(796\) −1.22394 + 3.76689i −0.0433813 + 0.133514i
\(797\) −3.38685 4.66160i −0.119969 0.165122i 0.744809 0.667278i \(-0.232541\pi\)
−0.864777 + 0.502155i \(0.832541\pi\)
\(798\) 3.88468 + 5.34680i 0.137516 + 0.189275i
\(799\) 8.33339 + 6.05456i 0.294814 + 0.214195i
\(800\) 1.46869 + 4.77943i 0.0519260 + 0.168978i
\(801\) −0.422540 −0.0149297
\(802\) 18.1997 25.0498i 0.642655 0.884538i
\(803\) −13.5269 + 4.39516i −0.477355 + 0.155102i
\(804\) −0.680446 + 2.09420i −0.0239975 + 0.0738567i
\(805\) −15.2625 + 2.29214i −0.537931 + 0.0807873i
\(806\) −2.09093 0.388372i −0.0736500 0.0136798i
\(807\) 29.1998i 1.02788i
\(808\) −0.738004 0.239792i −0.0259629 0.00843586i
\(809\) −4.93207 15.1793i −0.173402 0.533677i 0.826155 0.563444i \(-0.190524\pi\)
−0.999557 + 0.0297661i \(0.990524\pi\)
\(810\) 1.03108 1.98415i 0.0362286 0.0697161i
\(811\) 45.9838 1.61471 0.807354 0.590067i \(-0.200899\pi\)
0.807354 + 0.590067i \(0.200899\pi\)
\(812\) 6.57649i 0.230789i
\(813\) 5.90498 8.12751i 0.207097 0.285044i
\(814\) −6.47816 + 4.70666i −0.227059 + 0.164968i
\(815\) −30.6419 31.1369i −1.07334 1.09068i
\(816\) 0.335816 1.03354i 0.0117559 0.0361810i
\(817\) −19.5179 + 26.8641i −0.682845 + 0.939855i
\(818\) −5.67281 1.84321i −0.198345 0.0644462i
\(819\) 0.182169 + 0.560659i 0.00636551 + 0.0195910i
\(820\) 3.02854 2.98039i 0.105761 0.104080i
\(821\) −4.51697 13.9018i −0.157643 0.485176i 0.840776 0.541383i \(-0.182099\pi\)
−0.998419 + 0.0562072i \(0.982099\pi\)
\(822\) −18.0471 + 5.86385i −0.629464 + 0.204525i
\(823\) −7.74274 10.6570i −0.269895 0.371478i 0.652459 0.757824i \(-0.273737\pi\)
−0.922354 + 0.386345i \(0.873737\pi\)
\(824\) −5.22783 16.0896i −0.182120 0.560508i
\(825\) −10.8056 0.173167i −0.376202 0.00602889i
\(826\) 4.38169 + 3.18348i 0.152458 + 0.110768i
\(827\) −19.7216 6.40792i −0.685786 0.222825i −0.0546590 0.998505i \(-0.517407\pi\)
−0.631127 + 0.775680i \(0.717407\pi\)
\(828\) −2.62866 3.61803i −0.0913521 0.125735i
\(829\) 13.8841 10.0874i 0.482215 0.350350i −0.319968 0.947428i \(-0.603672\pi\)
0.802183 + 0.597079i \(0.203672\pi\)
\(830\) −3.29093 1.71016i −0.114230 0.0593607i
\(831\) −7.68410 −0.266558
\(832\) 0.381966i 0.0132423i
\(833\) −2.94982 + 4.06007i −0.102205 + 0.140673i
\(834\) 3.32758 + 10.2412i 0.115225 + 0.354625i
\(835\) −10.8472 1.80723i −0.375383 0.0625418i
\(836\) 9.25557 0.320111
\(837\) −4.04020 + 3.83103i −0.139650 + 0.132420i
\(838\) 23.2866i 0.804421i
\(839\) 8.25219 25.3976i 0.284897 0.876823i −0.701532 0.712638i \(-0.747500\pi\)
0.986429 0.164186i \(-0.0524996\pi\)
\(840\) −3.08737 + 1.54206i −0.106524 + 0.0532062i
\(841\) 8.77189 + 6.37315i 0.302479 + 0.219764i
\(842\) 29.3049i 1.00991i
\(843\) 15.0065i 0.516850i
\(844\) −17.1748 12.4782i −0.591182 0.429519i
\(845\) −20.4863 + 20.1606i −0.704750 + 0.693547i
\(846\) 7.66836 5.57139i 0.263644 0.191548i
\(847\) −9.28893 3.01816i −0.319172 0.103705i
\(848\) −3.47954 + 4.78918i −0.119488 + 0.164461i
\(849\) 1.11056 3.41796i 0.0381144 0.117304i
\(850\) 3.12295 + 4.44650i 0.107116 + 0.152514i
\(851\) 13.4039 9.73853i 0.459481 0.333833i
\(852\) 5.07466 1.64886i 0.173855 0.0564889i
\(853\) −42.8187 + 13.9126i −1.46609 + 0.476360i −0.929923 0.367755i \(-0.880127\pi\)
−0.536162 + 0.844115i \(0.680127\pi\)
\(854\) −6.20976 + 4.51165i −0.212493 + 0.154386i
\(855\) −4.27861 8.56624i −0.146325 0.292959i
\(856\) 0.278772 0.857971i 0.00952822 0.0293249i
\(857\) −26.3941 + 36.3283i −0.901604 + 1.24095i 0.0683494 + 0.997661i \(0.478227\pi\)
−0.969954 + 0.243290i \(0.921773\pi\)
\(858\) 0.785173 + 0.255118i 0.0268054 + 0.00870959i
\(859\) −32.0553 + 23.2896i −1.09371 + 0.794630i −0.980023 0.198887i \(-0.936267\pi\)
−0.113691 + 0.993516i \(0.536267\pi\)
\(860\) −12.1621 12.3585i −0.414724 0.421423i
\(861\) 2.37267 + 1.72384i 0.0808602 + 0.0587484i
\(862\) 15.8051i 0.538324i
\(863\) 12.1695i 0.414256i 0.978314 + 0.207128i \(0.0664116\pi\)
−0.978314 + 0.207128i \(0.933588\pi\)
\(864\) −0.809017 0.587785i −0.0275233 0.0199969i
\(865\) 8.47586 4.23347i 0.288188 0.143942i
\(866\) 6.63602 20.4236i 0.225501 0.694021i
\(867\) 15.8190i 0.537242i
\(868\) 8.52000 1.11831i 0.289187 0.0379580i
\(869\) 10.7333 0.364102
\(870\) 1.56589 9.39866i 0.0530887 0.318644i
\(871\) 0.259907 + 0.799912i 0.00880662 + 0.0271040i
\(872\) 8.22717 11.3237i 0.278607 0.383470i
\(873\) 13.9288i 0.471418i
\(874\) −19.1507 −0.647781
\(875\) 3.10816 16.9731i 0.105075 0.573795i
\(876\) 5.32373 3.86791i 0.179872 0.130685i
\(877\) −10.1133 13.9198i −0.341502 0.470037i 0.603378 0.797456i \(-0.293821\pi\)
−0.944879 + 0.327419i \(0.893821\pi\)
\(878\) 30.5337 + 9.92099i 1.03046 + 0.334817i
\(879\) 3.58951 + 2.60793i 0.121071 + 0.0879634i
\(880\) −0.794274 + 4.76731i −0.0267750 + 0.160706i
\(881\) 2.53060 + 7.78839i 0.0852582 + 0.262398i 0.984593 0.174864i \(-0.0559485\pi\)
−0.899334 + 0.437261i \(0.855948\pi\)
\(882\) 2.71441 + 3.73607i 0.0913990 + 0.125800i
\(883\) 9.26933 3.01179i 0.311938 0.101355i −0.148864 0.988858i \(-0.547562\pi\)
0.460802 + 0.887503i \(0.347562\pi\)
\(884\) −0.128270 0.394776i −0.00431420 0.0132777i
\(885\) −5.50400 5.59291i −0.185015 0.188004i
\(886\) 2.26547 + 6.97240i 0.0761099 + 0.234242i
\(887\) −16.5248 5.36922i −0.554847 0.180281i 0.0181542 0.999835i \(-0.494221\pi\)
−0.573001 + 0.819554i \(0.694221\pi\)
\(888\) 2.17760 2.99721i 0.0730755 0.100580i
\(889\) 0.158516 0.487861i 0.00531644 0.0163623i
\(890\) −0.662720 0.673426i −0.0222144 0.0225733i
\(891\) 1.74861 1.27044i 0.0585805 0.0425612i
\(892\) −9.09550 + 12.5189i −0.304540 + 0.419163i
\(893\) 40.5895i 1.35828i
\(894\) 8.77543 0.293494
\(895\) −6.27463 3.26067i −0.209738 0.108992i
\(896\) 0.476925 + 1.46782i 0.0159329 + 0.0490366i
\(897\) −1.62460 0.527864i −0.0542438 0.0176249i
\(898\) 14.3348i 0.478360i
\(899\) −11.3287 + 20.8456i −0.377834 + 0.695239i
\(900\) 4.77943 1.46869i 0.159314 0.0489563i
\(901\) −1.98795 + 6.11828i −0.0662282 + 0.203829i
\(902\) 3.90618 1.26919i 0.130061 0.0422595i
\(903\) 7.03448 9.68213i 0.234093 0.322201i
\(904\) −4.07370 −0.135489
\(905\) −45.7765 + 6.87479i −1.52166 + 0.228526i
\(906\) 14.6157 + 10.6189i 0.485574 + 0.352790i
\(907\) 15.7307 + 21.6514i 0.522329 + 0.718925i 0.985937 0.167116i \(-0.0534454\pi\)
−0.463608 + 0.886040i \(0.653445\pi\)
\(908\) −0.868904 1.19594i −0.0288356 0.0396888i
\(909\) −0.239792 + 0.738004i −0.00795340 + 0.0244781i
\(910\) −0.607836 + 1.16968i −0.0201496 + 0.0387746i
\(911\) −5.50126 + 16.9311i −0.182265 + 0.560954i −0.999891 0.0147966i \(-0.995290\pi\)
0.817626 + 0.575750i \(0.195290\pi\)
\(912\) −4.07263 + 1.32328i −0.134858 + 0.0438181i
\(913\) −2.10716 2.90025i −0.0697367 0.0959843i
\(914\) 8.74630 + 26.9184i 0.289302 + 0.890380i
\(915\) 9.94879 4.96916i 0.328897 0.164275i
\(916\) −10.9579 + 7.96136i −0.362058 + 0.263051i
\(917\) 1.03759 0.337132i 0.0342641 0.0111331i
\(918\) −1.03354 0.335816i −0.0341118 0.0110836i
\(919\) −23.7431 17.2504i −0.783212 0.569037i 0.122729 0.992440i \(-0.460835\pi\)
−0.905941 + 0.423404i \(0.860835\pi\)
\(920\) 1.64343 9.86403i 0.0541822 0.325208i
\(921\) −19.4961 + 14.1648i −0.642419 + 0.466745i
\(922\) −3.00824 4.14049i −0.0990713 0.136360i
\(923\) 1.19797 1.64886i 0.0394315 0.0542728i
\(924\) −3.33582 −0.109740
\(925\) 5.44114 + 17.7066i 0.178904 + 0.582190i
\(926\) −24.5028 17.8023i −0.805213 0.585021i
\(927\) −16.0896 + 5.22783i −0.528452 + 0.171705i
\(928\) −4.05259 1.31677i −0.133033 0.0432250i
\(929\) 8.79320 0.288495 0.144248 0.989542i \(-0.453924\pi\)
0.144248 + 0.989542i \(0.453924\pi\)
\(930\) −12.4425 0.430438i −0.408004 0.0141146i
\(931\) 19.7754 0.648113
\(932\) 14.9173 + 4.84693i 0.488633 + 0.158767i
\(933\) −31.1324 + 10.1155i −1.01923 + 0.331167i
\(934\) −1.67348 1.21586i −0.0547581 0.0397841i
\(935\) 0.780031 + 5.19392i 0.0255097 + 0.169859i
\(936\) −0.381966 −0.0124849
\(937\) 3.17240 4.36643i 0.103638 0.142645i −0.754048 0.656819i \(-0.771901\pi\)
0.857686 + 0.514174i \(0.171901\pi\)
\(938\) −1.99755 2.74939i −0.0652223 0.0897709i
\(939\) 10.0656 7.31310i 0.328479 0.238654i
\(940\) 20.9066 + 3.48322i 0.681899 + 0.113610i
\(941\) 47.5574 + 34.5524i 1.55033 + 1.12638i 0.943419 + 0.331604i \(0.107590\pi\)
0.606907 + 0.794773i \(0.292410\pi\)
\(942\) −6.68360 2.17163i −0.217763 0.0707556i
\(943\) −8.08225 + 2.62608i −0.263194 + 0.0855170i
\(944\) −2.83905 + 2.06269i −0.0924033 + 0.0671350i
\(945\) 1.54206 + 3.08737i 0.0501633 + 0.100432i
\(946\) −5.17920 15.9399i −0.168390 0.518252i
\(947\) 4.66622 + 6.42251i 0.151632 + 0.208703i 0.878075 0.478523i \(-0.158828\pi\)
−0.726443 + 0.687227i \(0.758828\pi\)
\(948\) −4.72285 + 1.53455i −0.153391 + 0.0498398i
\(949\) 0.776721 2.39050i 0.0252134 0.0775990i
\(950\) 6.94183 20.2545i 0.225223 0.657144i
\(951\) 0.149516 0.460163i 0.00484839 0.0149218i
\(952\) 0.985838 + 1.35689i 0.0319512 + 0.0439771i
\(953\) −29.4647 40.5546i −0.954454 1.31369i −0.949520 0.313706i \(-0.898429\pi\)
−0.00493387 0.999988i \(-0.501571\pi\)
\(954\) 4.78918 + 3.47954i 0.155055 + 0.112654i
\(955\) −45.9052 + 6.89412i −1.48546 + 0.223088i
\(956\) 7.78935 0.251926
\(957\) 5.41351 7.45106i 0.174994 0.240859i
\(958\) −28.6384 + 9.30516i −0.925263 + 0.300636i
\(959\) 9.05005 27.8532i 0.292241 0.899426i
\(960\) −0.332092 2.21127i −0.0107182 0.0713684i
\(961\) 28.9324 + 11.1319i 0.933302 + 0.359093i
\(962\) 1.41509i 0.0456244i
\(963\) −0.857971 0.278772i −0.0276477 0.00898329i
\(964\) −4.07123 12.5299i −0.131125 0.403562i
\(965\) −11.3828 + 21.9043i −0.366424 + 0.705123i
\(966\) 6.90212 0.222072
\(967\) 43.3024i 1.39251i −0.717794 0.696256i \(-0.754848\pi\)
0.717794 0.696256i \(-0.245152\pi\)
\(968\) 3.71972 5.11976i 0.119556 0.164555i
\(969\) −3.76483 + 2.73531i −0.120944 + 0.0878708i
\(970\) −22.1991 + 21.8462i −0.712769 + 0.701438i
\(971\) 6.81223 20.9659i 0.218615 0.672828i −0.780262 0.625453i \(-0.784914\pi\)
0.998877 0.0473751i \(-0.0150856\pi\)
\(972\) −0.587785 + 0.809017i −0.0188532 + 0.0259492i
\(973\) −15.8059 5.13566i −0.506715 0.164642i
\(974\) −13.1532 40.4813i −0.421454 1.29710i
\(975\) 1.14718 1.52690i 0.0367393 0.0488999i
\(976\) −1.53685 4.72994i −0.0491934 0.151402i
\(977\) 9.52121 3.09363i 0.304611 0.0989740i −0.152723 0.988269i \(-0.548804\pi\)
0.457334 + 0.889295i \(0.348804\pi\)
\(978\) 11.4835 + 15.8056i 0.367200 + 0.505408i
\(979\) −0.282218 0.868577i −0.00901972 0.0277598i
\(980\) −1.69704 + 10.1858i −0.0542101 + 0.325375i
\(981\) −11.3237 8.22717i −0.361539 0.262673i
\(982\) 8.64940 + 2.81036i 0.276013 + 0.0896822i
\(983\) −0.266884 0.367334i −0.00851228 0.0117161i 0.804740 0.593628i \(-0.202305\pi\)
−0.813252 + 0.581912i \(0.802305\pi\)
\(984\) −1.53734 + 1.11694i −0.0490085 + 0.0356067i
\(985\) −3.98278 + 7.66421i −0.126902 + 0.244202i
\(986\) −4.63069 −0.147471
\(987\) 14.6289i 0.465644i
\(988\) −0.961418 + 1.32328i −0.0305868 + 0.0420991i
\(989\) 10.7163 + 32.9812i 0.340757 + 1.04874i
\(990\) 4.76731 + 0.794274i 0.151515 + 0.0252437i
\(991\) 41.3457 1.31339 0.656695 0.754156i \(-0.271954\pi\)
0.656695 + 0.754156i \(0.271954\pi\)
\(992\) −1.01677 + 5.47414i −0.0322825 + 0.173804i
\(993\) 29.1456i 0.924907i
\(994\) −2.54478 + 7.83204i −0.0807157 + 0.248417i
\(995\) 3.95741 + 7.92315i 0.125458 + 0.251181i
\(996\) 1.34184 + 0.974905i 0.0425179 + 0.0308911i
\(997\) 4.24883i 0.134562i −0.997734 0.0672810i \(-0.978568\pi\)
0.997734 0.0672810i \(-0.0214324\pi\)
\(998\) 12.0845i 0.382529i
\(999\) −2.99721 2.17760i −0.0948276 0.0688963i
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.z.b.349.4 yes 16
5.4 even 2 inner 930.2.z.b.349.2 16
31.4 even 5 inner 930.2.z.b.469.2 yes 16
155.4 even 10 inner 930.2.z.b.469.4 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.z.b.349.2 16 5.4 even 2 inner
930.2.z.b.349.4 yes 16 1.1 even 1 trivial
930.2.z.b.469.2 yes 16 31.4 even 5 inner
930.2.z.b.469.4 yes 16 155.4 even 10 inner