Properties

Label 43.2.e.b.16.1
Level $43$
Weight $2$
Character 43.16
Analytic conductor $0.343$
Analytic rank $0$
Dimension $6$
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] = [43,2,Mod(4,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 43.e (of order \(7\), degree \(6\), 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: \(0.343356728692\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{14})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label 16.1
Root \(0.900969 + 0.433884i\) of defining polynomial
Character \(\chi\) \(=\) 43.16
Dual form 43.2.e.b.35.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 2.19064i) q^{2} +(0.346011 - 1.51597i) q^{3} +(-2.74698 + 1.32288i) q^{4} +(-1.24698 - 1.56366i) q^{5} +3.49396 q^{6} -4.24698 q^{7} +(-1.46950 - 1.84270i) q^{8} +(0.524459 + 0.252566i) q^{9} +O(q^{10})\) \(q+(0.500000 + 2.19064i) q^{2} +(0.346011 - 1.51597i) q^{3} +(-2.74698 + 1.32288i) q^{4} +(-1.24698 - 1.56366i) q^{5} +3.49396 q^{6} -4.24698 q^{7} +(-1.46950 - 1.84270i) q^{8} +(0.524459 + 0.252566i) q^{9} +(2.80194 - 3.51352i) q^{10} +(3.96950 + 1.91161i) q^{11} +(1.05496 + 4.62207i) q^{12} +(0.192021 + 0.240787i) q^{13} +(-2.12349 - 9.30362i) q^{14} +(-2.80194 + 1.34934i) q^{15} +(-0.500000 + 0.626980i) q^{16} +(2.80194 - 3.51352i) q^{17} +(-0.291053 + 1.27518i) q^{18} +(-5.12833 + 2.46968i) q^{19} +(5.49396 + 2.64575i) q^{20} +(-1.46950 + 6.43830i) q^{21} +(-2.20291 + 9.65156i) q^{22} +(-1.98039 - 0.953703i) q^{23} +(-3.30194 + 1.59013i) q^{24} +(0.222521 - 0.974928i) q^{25} +(-0.431468 + 0.541044i) q^{26} +(3.47285 - 4.35482i) q^{27} +(11.6664 - 5.61823i) q^{28} +(0.653989 + 2.86531i) q^{29} +(-4.35690 - 5.46337i) q^{30} +(-0.797093 - 3.49229i) q^{31} +(-5.87047 - 2.82707i) q^{32} +(4.27144 - 5.35621i) q^{33} +(9.09783 + 4.38129i) q^{34} +(5.29590 + 6.64084i) q^{35} -1.77479 q^{36} +4.87263 q^{37} +(-7.97434 - 9.99951i) q^{38} +(0.431468 - 0.207784i) q^{39} +(-1.04892 + 4.59561i) q^{40} +(0.896125 + 3.92618i) q^{41} -14.8388 q^{42} +(-6.46950 + 1.07031i) q^{43} -13.4330 q^{44} +(-0.259061 - 1.13502i) q^{45} +(1.09903 - 4.81517i) q^{46} +(0.900969 - 0.433884i) q^{47} +(0.777479 + 0.974928i) q^{48} +11.0368 q^{49} +2.24698 q^{50} +(-4.35690 - 5.46337i) q^{51} +(-0.846011 - 0.407417i) q^{52} +(-0.876510 + 1.09911i) q^{53} +(11.2763 + 5.43037i) q^{54} +(-1.96077 - 8.59070i) q^{55} +(6.24094 + 7.82589i) q^{56} +(1.96950 + 8.62895i) q^{57} +(-5.94989 + 2.86531i) q^{58} +(-2.03199 + 2.54804i) q^{59} +(5.91185 - 7.41323i) q^{60} +(-0.504844 + 2.21187i) q^{61} +(7.25182 - 3.49229i) q^{62} +(-2.22737 - 1.07264i) q^{63} +(2.90097 - 12.7100i) q^{64} +(0.137063 - 0.600514i) q^{65} +(13.8693 + 6.67909i) q^{66} +(-3.77144 + 1.81623i) q^{67} +(-3.04892 + 13.3582i) q^{68} +(-2.13102 + 2.67222i) q^{69} +(-11.8998 + 14.9218i) q^{70} +(7.93900 - 3.82322i) q^{71} +(-0.305290 - 1.33756i) q^{72} +(2.65399 + 3.32800i) q^{73} +(2.43631 + 10.6742i) q^{74} +(-1.40097 - 0.674671i) q^{75} +(10.8204 - 13.5683i) q^{76} +(-16.8584 - 8.11857i) q^{77} +(0.670915 + 0.841301i) q^{78} +3.71379 q^{79} +1.60388 q^{80} +(-4.31133 - 5.40624i) q^{81} +(-8.15279 + 3.92618i) q^{82} +(-2.26175 + 9.90937i) q^{83} +(-4.48039 - 19.6299i) q^{84} -8.98792 q^{85} +(-5.57942 - 13.6372i) q^{86} +4.57002 q^{87} +(-2.31067 - 10.1237i) q^{88} +(-1.11207 + 4.87231i) q^{89} +(2.35690 - 1.13502i) q^{90} +(-0.815511 - 1.02262i) q^{91} +6.70171 q^{92} -5.57002 q^{93} +(1.40097 + 1.75676i) q^{94} +(10.2567 + 4.93935i) q^{95} +(-6.31700 + 7.92127i) q^{96} +(-16.4400 - 7.91707i) q^{97} +(5.51842 + 24.1778i) q^{98} +(1.59903 + 2.00512i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} - 3 q^{3} - 7 q^{4} + 2 q^{5} + 2 q^{6} - 16 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} - 3 q^{3} - 7 q^{4} + 2 q^{5} + 2 q^{6} - 16 q^{7} + q^{8} - 6 q^{9} + 8 q^{10} + 14 q^{11} + 7 q^{12} - 9 q^{13} - 8 q^{14} - 8 q^{15} - 3 q^{16} + 8 q^{17} + 4 q^{18} - 4 q^{19} + 14 q^{20} + q^{21} + q^{23} - 11 q^{24} + q^{25} - 8 q^{26} + 33 q^{27} + 28 q^{28} + 9 q^{29} - 18 q^{30} - 18 q^{31} - 21 q^{32} + 7 q^{33} + 18 q^{34} + 4 q^{35} - 14 q^{36} - 4 q^{37} - 16 q^{38} + 8 q^{39} + 12 q^{40} + 23 q^{41} - 24 q^{42} - 29 q^{43} - 42 q^{44} - 30 q^{45} + 11 q^{46} + q^{47} + 5 q^{48} + 10 q^{49} + 4 q^{50} - 18 q^{51} - 10 q^{53} + 27 q^{54} + 14 q^{55} + 9 q^{56} + 2 q^{57} - 13 q^{58} + 22 q^{59} + 28 q^{60} + 19 q^{61} + 12 q^{62} + 9 q^{63} + 13 q^{64} - 10 q^{65} + 28 q^{66} - 4 q^{67} + 17 q^{69} - 26 q^{70} + 28 q^{71} - 15 q^{72} + 21 q^{73} - 2 q^{74} - 4 q^{75} + 28 q^{76} - 49 q^{77} + 25 q^{78} + 6 q^{79} - 8 q^{80} - 58 q^{81} - 13 q^{82} - 39 q^{83} - 14 q^{84} - 16 q^{85} - 25 q^{86} - 22 q^{87} - 21 q^{88} + 11 q^{89} + 6 q^{90} + 10 q^{91} - 14 q^{92} + 16 q^{93} + 4 q^{94} + 8 q^{95} + 21 q^{96} - 19 q^{97} + 5 q^{98} + 14 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{4}{7}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 2.19064i 0.353553 + 1.54902i 0.768908 + 0.639359i \(0.220800\pi\)
−0.415355 + 0.909659i \(0.636343\pi\)
\(3\) 0.346011 1.51597i 0.199769 0.875247i −0.771304 0.636467i \(-0.780395\pi\)
0.971074 0.238780i \(-0.0767476\pi\)
\(4\) −2.74698 + 1.32288i −1.37349 + 0.661438i
\(5\) −1.24698 1.56366i −0.557666 0.699291i 0.420458 0.907312i \(-0.361869\pi\)
−0.978124 + 0.208021i \(0.933298\pi\)
\(6\) 3.49396 1.42640
\(7\) −4.24698 −1.60521 −0.802604 0.596513i \(-0.796553\pi\)
−0.802604 + 0.596513i \(0.796553\pi\)
\(8\) −1.46950 1.84270i −0.519547 0.651491i
\(9\) 0.524459 + 0.252566i 0.174820 + 0.0841887i
\(10\) 2.80194 3.51352i 0.886051 1.11107i
\(11\) 3.96950 + 1.91161i 1.19685 + 0.576372i 0.922776 0.385336i \(-0.125915\pi\)
0.274073 + 0.961709i \(0.411629\pi\)
\(12\) 1.05496 + 4.62207i 0.304540 + 1.33428i
\(13\) 0.192021 + 0.240787i 0.0532572 + 0.0667824i 0.807747 0.589530i \(-0.200687\pi\)
−0.754490 + 0.656312i \(0.772115\pi\)
\(14\) −2.12349 9.30362i −0.567527 2.48650i
\(15\) −2.80194 + 1.34934i −0.723457 + 0.348399i
\(16\) −0.500000 + 0.626980i −0.125000 + 0.156745i
\(17\) 2.80194 3.51352i 0.679570 0.852153i −0.315745 0.948844i \(-0.602254\pi\)
0.995314 + 0.0966907i \(0.0308258\pi\)
\(18\) −0.291053 + 1.27518i −0.0686018 + 0.300564i
\(19\) −5.12833 + 2.46968i −1.17652 + 0.566582i −0.916896 0.399127i \(-0.869313\pi\)
−0.259625 + 0.965710i \(0.583599\pi\)
\(20\) 5.49396 + 2.64575i 1.22849 + 0.591608i
\(21\) −1.46950 + 6.43830i −0.320671 + 1.40495i
\(22\) −2.20291 + 9.65156i −0.469661 + 2.05772i
\(23\) −1.98039 0.953703i −0.412939 0.198861i 0.215868 0.976423i \(-0.430742\pi\)
−0.628807 + 0.777562i \(0.716456\pi\)
\(24\) −3.30194 + 1.59013i −0.674005 + 0.324584i
\(25\) 0.222521 0.974928i 0.0445042 0.194986i
\(26\) −0.431468 + 0.541044i −0.0846179 + 0.106107i
\(27\) 3.47285 4.35482i 0.668351 0.838085i
\(28\) 11.6664 5.61823i 2.20474 1.06174i
\(29\) 0.653989 + 2.86531i 0.121443 + 0.532075i 0.998649 + 0.0519619i \(0.0165474\pi\)
−0.877206 + 0.480114i \(0.840595\pi\)
\(30\) −4.35690 5.46337i −0.795457 0.997471i
\(31\) −0.797093 3.49229i −0.143162 0.627235i −0.994689 0.102924i \(-0.967180\pi\)
0.851527 0.524311i \(-0.175677\pi\)
\(32\) −5.87047 2.82707i −1.03776 0.499760i
\(33\) 4.27144 5.35621i 0.743562 0.932397i
\(34\) 9.09783 + 4.38129i 1.56027 + 0.751384i
\(35\) 5.29590 + 6.64084i 0.895170 + 1.12251i
\(36\) −1.77479 −0.295798
\(37\) 4.87263 0.801055 0.400527 0.916285i \(-0.368827\pi\)
0.400527 + 0.916285i \(0.368827\pi\)
\(38\) −7.97434 9.99951i −1.29361 1.62214i
\(39\) 0.431468 0.207784i 0.0690902 0.0332721i
\(40\) −1.04892 + 4.59561i −0.165848 + 0.726629i
\(41\) 0.896125 + 3.92618i 0.139951 + 0.613166i 0.995444 + 0.0953509i \(0.0303973\pi\)
−0.855493 + 0.517815i \(0.826746\pi\)
\(42\) −14.8388 −2.28967
\(43\) −6.46950 + 1.07031i −0.986590 + 0.163221i
\(44\) −13.4330 −2.02509
\(45\) −0.259061 1.13502i −0.0386186 0.169199i
\(46\) 1.09903 4.81517i 0.162043 0.709958i
\(47\) 0.900969 0.433884i 0.131420 0.0632884i −0.367018 0.930214i \(-0.619621\pi\)
0.498438 + 0.866925i \(0.333907\pi\)
\(48\) 0.777479 + 0.974928i 0.112219 + 0.140719i
\(49\) 11.0368 1.57669
\(50\) 2.24698 0.317771
\(51\) −4.35690 5.46337i −0.610087 0.765025i
\(52\) −0.846011 0.407417i −0.117321 0.0564986i
\(53\) −0.876510 + 1.09911i −0.120398 + 0.150974i −0.838378 0.545090i \(-0.816496\pi\)
0.717980 + 0.696064i \(0.245067\pi\)
\(54\) 11.2763 + 5.43037i 1.53451 + 0.738980i
\(55\) −1.96077 8.59070i −0.264390 1.15837i
\(56\) 6.24094 + 7.82589i 0.833981 + 1.04578i
\(57\) 1.96950 + 8.62895i 0.260867 + 1.14293i
\(58\) −5.94989 + 2.86531i −0.781258 + 0.376234i
\(59\) −2.03199 + 2.54804i −0.264543 + 0.331726i −0.896307 0.443435i \(-0.853760\pi\)
0.631764 + 0.775161i \(0.282331\pi\)
\(60\) 5.91185 7.41323i 0.763217 0.957044i
\(61\) −0.504844 + 2.21187i −0.0646387 + 0.283201i −0.996909 0.0785611i \(-0.974967\pi\)
0.932271 + 0.361762i \(0.117825\pi\)
\(62\) 7.25182 3.49229i 0.920983 0.443522i
\(63\) −2.22737 1.07264i −0.280622 0.135140i
\(64\) 2.90097 12.7100i 0.362621 1.58875i
\(65\) 0.137063 0.600514i 0.0170006 0.0744846i
\(66\) 13.8693 + 6.67909i 1.70719 + 0.822139i
\(67\) −3.77144 + 1.81623i −0.460755 + 0.221888i −0.649837 0.760074i \(-0.725163\pi\)
0.189083 + 0.981961i \(0.439449\pi\)
\(68\) −3.04892 + 13.3582i −0.369736 + 1.61992i
\(69\) −2.13102 + 2.67222i −0.256545 + 0.321697i
\(70\) −11.8998 + 14.9218i −1.42229 + 1.78350i
\(71\) 7.93900 3.82322i 0.942186 0.453733i 0.101246 0.994861i \(-0.467717\pi\)
0.840940 + 0.541128i \(0.182003\pi\)
\(72\) −0.305290 1.33756i −0.0359788 0.157633i
\(73\) 2.65399 + 3.32800i 0.310626 + 0.389513i 0.912499 0.409079i \(-0.134150\pi\)
−0.601873 + 0.798592i \(0.705579\pi\)
\(74\) 2.43631 + 10.6742i 0.283216 + 1.24085i
\(75\) −1.40097 0.674671i −0.161770 0.0779043i
\(76\) 10.8204 13.5683i 1.24118 1.55639i
\(77\) −16.8584 8.11857i −1.92119 0.925197i
\(78\) 0.670915 + 0.841301i 0.0759662 + 0.0952586i
\(79\) 3.71379 0.417834 0.208917 0.977933i \(-0.433006\pi\)
0.208917 + 0.977933i \(0.433006\pi\)
\(80\) 1.60388 0.179319
\(81\) −4.31133 5.40624i −0.479037 0.600693i
\(82\) −8.15279 + 3.92618i −0.900325 + 0.433574i
\(83\) −2.26175 + 9.90937i −0.248259 + 1.08769i 0.685015 + 0.728529i \(0.259796\pi\)
−0.933274 + 0.359166i \(0.883061\pi\)
\(84\) −4.48039 19.6299i −0.488850 2.14179i
\(85\) −8.98792 −0.974877
\(86\) −5.57942 13.6372i −0.601644 1.47054i
\(87\) 4.57002 0.489958
\(88\) −2.31067 10.1237i −0.246318 1.07919i
\(89\) −1.11207 + 4.87231i −0.117879 + 0.516463i 0.881167 + 0.472805i \(0.156758\pi\)
−0.999047 + 0.0436585i \(0.986099\pi\)
\(90\) 2.35690 1.13502i 0.248439 0.119642i
\(91\) −0.815511 1.02262i −0.0854888 0.107200i
\(92\) 6.70171 0.698702
\(93\) −5.57002 −0.577585
\(94\) 1.40097 + 1.75676i 0.144499 + 0.181196i
\(95\) 10.2567 + 4.93935i 1.05231 + 0.506767i
\(96\) −6.31700 + 7.92127i −0.644726 + 0.808461i
\(97\) −16.4400 7.91707i −1.66923 0.803856i −0.998041 0.0625659i \(-0.980072\pi\)
−0.671184 0.741291i \(-0.734214\pi\)
\(98\) 5.51842 + 24.1778i 0.557444 + 2.44232i
\(99\) 1.59903 + 2.00512i 0.160709 + 0.201522i
\(100\) 0.678448 + 2.97247i 0.0678448 + 0.297247i
\(101\) 8.30678 4.00034i 0.826556 0.398048i 0.0277334 0.999615i \(-0.491171\pi\)
0.798822 + 0.601567i \(0.205457\pi\)
\(102\) 9.78986 12.2761i 0.969340 1.21551i
\(103\) −0.725873 + 0.910216i −0.0715224 + 0.0896863i −0.816306 0.577620i \(-0.803981\pi\)
0.744783 + 0.667307i \(0.232553\pi\)
\(104\) 0.161522 0.707674i 0.0158385 0.0693932i
\(105\) 11.8998 5.73063i 1.16130 0.559252i
\(106\) −2.84601 1.37057i −0.276429 0.133121i
\(107\) 3.48039 15.2486i 0.336462 1.47413i −0.469904 0.882717i \(-0.655712\pi\)
0.806366 0.591417i \(-0.201431\pi\)
\(108\) −3.77897 + 16.5568i −0.363632 + 1.59317i
\(109\) −8.06249 3.88269i −0.772247 0.371894i 0.00589553 0.999983i \(-0.498123\pi\)
−0.778142 + 0.628088i \(0.783838\pi\)
\(110\) 17.8388 8.59070i 1.70086 0.819091i
\(111\) 1.68598 7.38676i 0.160026 0.701121i
\(112\) 2.12349 2.66277i 0.200651 0.251608i
\(113\) 5.82640 7.30607i 0.548101 0.687297i −0.428207 0.903681i \(-0.640855\pi\)
0.976308 + 0.216383i \(0.0694261\pi\)
\(114\) −17.9182 + 8.62895i −1.67819 + 0.808175i
\(115\) 0.978230 + 4.28590i 0.0912204 + 0.399663i
\(116\) −5.58695 7.00581i −0.518735 0.650473i
\(117\) 0.0398926 + 0.174781i 0.00368808 + 0.0161585i
\(118\) −6.59783 3.17735i −0.607380 0.292499i
\(119\) −11.8998 + 14.9218i −1.09085 + 1.36788i
\(120\) 6.60388 + 3.18026i 0.602849 + 0.290317i
\(121\) 5.24429 + 6.57613i 0.476754 + 0.597830i
\(122\) −5.09783 −0.461536
\(123\) 6.26205 0.564630
\(124\) 6.80947 + 8.53881i 0.611509 + 0.766807i
\(125\) −10.8116 + 5.20660i −0.967021 + 0.465693i
\(126\) 1.23609 5.41568i 0.110120 0.482467i
\(127\) 3.25786 + 14.2736i 0.289089 + 1.26658i 0.885778 + 0.464108i \(0.153625\pi\)
−0.596690 + 0.802472i \(0.703518\pi\)
\(128\) 16.2620 1.43738
\(129\) −0.615957 + 10.1779i −0.0542320 + 0.896116i
\(130\) 1.38404 0.121389
\(131\) 2.33513 + 10.2309i 0.204021 + 0.893874i 0.968458 + 0.249176i \(0.0801597\pi\)
−0.764437 + 0.644698i \(0.776983\pi\)
\(132\) −4.64795 + 20.3640i −0.404552 + 1.77246i
\(133\) 21.7799 10.4887i 1.88856 0.909482i
\(134\) −5.86443 7.35376i −0.506609 0.635268i
\(135\) −11.1400 −0.958783
\(136\) −10.5918 −0.908239
\(137\) −5.57942 6.99637i −0.476682 0.597740i 0.484111 0.875006i \(-0.339143\pi\)
−0.960793 + 0.277266i \(0.910572\pi\)
\(138\) −6.91939 3.33220i −0.589017 0.283656i
\(139\) 5.24847 6.58138i 0.445170 0.558225i −0.507728 0.861517i \(-0.669514\pi\)
0.952898 + 0.303292i \(0.0980859\pi\)
\(140\) −23.3327 11.2365i −1.97198 0.949654i
\(141\) −0.346011 1.51597i −0.0291394 0.127668i
\(142\) 12.3448 + 15.4799i 1.03595 + 1.29904i
\(143\) 0.301938 + 1.32288i 0.0252493 + 0.110624i
\(144\) −0.420583 + 0.202542i −0.0350486 + 0.0168785i
\(145\) 3.66487 4.59561i 0.304351 0.381644i
\(146\) −5.96346 + 7.47794i −0.493539 + 0.618879i
\(147\) 3.81886 16.7315i 0.314975 1.37999i
\(148\) −13.3850 + 6.44588i −1.10024 + 0.529848i
\(149\) 5.61745 + 2.70522i 0.460199 + 0.221620i 0.649595 0.760281i \(-0.274939\pi\)
−0.189396 + 0.981901i \(0.560653\pi\)
\(150\) 0.777479 3.40636i 0.0634809 0.278128i
\(151\) 1.24698 5.46337i 0.101478 0.444603i −0.898506 0.438961i \(-0.855347\pi\)
0.999984 0.00564254i \(-0.00179609\pi\)
\(152\) 12.0869 + 5.82077i 0.980381 + 0.472127i
\(153\) 2.35690 1.13502i 0.190544 0.0917610i
\(154\) 9.35570 40.9900i 0.753904 3.30307i
\(155\) −4.46681 + 5.60121i −0.358783 + 0.449900i
\(156\) −0.910362 + 1.14156i −0.0728873 + 0.0913978i
\(157\) −9.54892 + 4.59852i −0.762087 + 0.367002i −0.774213 0.632925i \(-0.781854\pi\)
0.0121266 + 0.999926i \(0.496140\pi\)
\(158\) 1.85690 + 8.13559i 0.147727 + 0.647233i
\(159\) 1.36294 + 1.70907i 0.108088 + 0.135538i
\(160\) 2.89977 + 12.7047i 0.229247 + 1.00440i
\(161\) 8.41066 + 4.05036i 0.662853 + 0.319213i
\(162\) 9.68747 12.1477i 0.761120 0.954414i
\(163\) 21.0966 + 10.1596i 1.65242 + 0.795762i 0.999257 + 0.0385411i \(0.0122711\pi\)
0.653159 + 0.757221i \(0.273443\pi\)
\(164\) −7.65548 9.59967i −0.597793 0.749608i
\(165\) −13.7017 −1.06668
\(166\) −22.8388 −1.77263
\(167\) 6.18180 + 7.75173i 0.478362 + 0.599847i 0.961197 0.275865i \(-0.0889641\pi\)
−0.482834 + 0.875712i \(0.660393\pi\)
\(168\) 14.0233 6.75325i 1.08192 0.521024i
\(169\) 2.87167 12.5816i 0.220897 0.967815i
\(170\) −4.49396 19.6893i −0.344671 1.51010i
\(171\) −3.31336 −0.253379
\(172\) 16.3557 11.4985i 1.24711 0.876750i
\(173\) −1.53319 −0.116566 −0.0582831 0.998300i \(-0.518563\pi\)
−0.0582831 + 0.998300i \(0.518563\pi\)
\(174\) 2.28501 + 10.0113i 0.173226 + 0.758954i
\(175\) −0.945042 + 4.14050i −0.0714385 + 0.312992i
\(176\) −3.18329 + 1.53299i −0.239950 + 0.115554i
\(177\) 3.15966 + 3.96209i 0.237495 + 0.297809i
\(178\) −11.2295 −0.841688
\(179\) −17.2228 −1.28729 −0.643647 0.765323i \(-0.722579\pi\)
−0.643647 + 0.765323i \(0.722579\pi\)
\(180\) 2.21313 + 2.77517i 0.164957 + 0.206849i
\(181\) −10.9330 5.26504i −0.812641 0.391347i −0.0190646 0.999818i \(-0.506069\pi\)
−0.793576 + 0.608471i \(0.791783\pi\)
\(182\) 1.83244 2.29780i 0.135829 0.170325i
\(183\) 3.17845 + 1.53066i 0.234958 + 0.113150i
\(184\) 1.15279 + 5.05072i 0.0849850 + 0.372344i
\(185\) −6.07606 7.61914i −0.446721 0.560171i
\(186\) −2.78501 12.2019i −0.204207 0.894689i
\(187\) 17.8388 8.59070i 1.30450 0.628214i
\(188\) −1.90097 + 2.38374i −0.138642 + 0.173852i
\(189\) −14.7491 + 18.4948i −1.07284 + 1.34530i
\(190\) −5.69202 + 24.9384i −0.412943 + 1.80922i
\(191\) 14.4351 6.95159i 1.04449 0.502999i 0.168686 0.985670i \(-0.446047\pi\)
0.875802 + 0.482671i \(0.160333\pi\)
\(192\) −18.2642 8.79558i −1.31811 0.634766i
\(193\) −5.29321 + 23.1911i −0.381013 + 1.66933i 0.313298 + 0.949655i \(0.398566\pi\)
−0.694312 + 0.719674i \(0.744291\pi\)
\(194\) 9.12349 39.9726i 0.655028 2.86987i
\(195\) −0.862937 0.415568i −0.0617962 0.0297595i
\(196\) −30.3180 + 14.6004i −2.16557 + 1.04288i
\(197\) −3.52811 + 15.4576i −0.251367 + 1.10131i 0.678843 + 0.734284i \(0.262482\pi\)
−0.930210 + 0.367028i \(0.880375\pi\)
\(198\) −3.59299 + 4.50547i −0.255343 + 0.320190i
\(199\) 5.46077 6.84759i 0.387104 0.485413i −0.549653 0.835393i \(-0.685240\pi\)
0.936757 + 0.349980i \(0.113812\pi\)
\(200\) −2.12349 + 1.02262i −0.150153 + 0.0723101i
\(201\) 1.44839 + 6.34583i 0.102162 + 0.447600i
\(202\) 12.9167 + 16.1970i 0.908816 + 1.13962i
\(203\) −2.77748 12.1689i −0.194941 0.854092i
\(204\) 19.1957 + 9.24415i 1.34397 + 0.647220i
\(205\) 5.02177 6.29710i 0.350736 0.439809i
\(206\) −2.35690 1.13502i −0.164213 0.0790807i
\(207\) −0.797757 1.00036i −0.0554480 0.0695296i
\(208\) −0.246980 −0.0171250
\(209\) −25.0780 −1.73468
\(210\) 18.5036 + 23.2028i 1.27687 + 1.60115i
\(211\) −7.73609 + 3.72551i −0.532575 + 0.256474i −0.680787 0.732481i \(-0.738362\pi\)
0.148213 + 0.988956i \(0.452648\pi\)
\(212\) 0.953771 4.17874i 0.0655053 0.286997i
\(213\) −3.04892 13.3582i −0.208908 0.915287i
\(214\) 35.1444 2.40242
\(215\) 9.74094 + 8.78146i 0.664327 + 0.598891i
\(216\) −13.1280 −0.893245
\(217\) 3.38524 + 14.8317i 0.229805 + 1.00684i
\(218\) 4.47434 19.6034i 0.303041 1.32771i
\(219\) 5.96346 2.87185i 0.402973 0.194062i
\(220\) 16.7506 + 21.0046i 1.12933 + 1.41613i
\(221\) 1.38404 0.0931008
\(222\) 17.0248 1.14263
\(223\) −4.74094 5.94495i −0.317477 0.398103i 0.597330 0.801996i \(-0.296228\pi\)
−0.914806 + 0.403893i \(0.867657\pi\)
\(224\) 24.9318 + 12.0065i 1.66582 + 0.802218i
\(225\) 0.362937 0.455108i 0.0241958 0.0303405i
\(226\) 18.9182 + 9.11052i 1.25842 + 0.606023i
\(227\) −3.45204 15.1244i −0.229120 1.00384i −0.950359 0.311155i \(-0.899284\pi\)
0.721239 0.692686i \(-0.243573\pi\)
\(228\) −16.8252 21.0981i −1.11428 1.39726i
\(229\) 5.25936 + 23.0427i 0.347548 + 1.52271i 0.782728 + 0.622364i \(0.213828\pi\)
−0.435180 + 0.900344i \(0.643315\pi\)
\(230\) −8.89977 + 4.28590i −0.586834 + 0.282604i
\(231\) −18.1407 + 22.7477i −1.19357 + 1.49669i
\(232\) 4.31886 5.41568i 0.283547 0.355557i
\(233\) 4.82036 21.1194i 0.315792 1.38358i −0.529064 0.848582i \(-0.677457\pi\)
0.844856 0.534993i \(-0.179686\pi\)
\(234\) −0.362937 + 0.174781i −0.0237259 + 0.0114258i
\(235\) −1.80194 0.867767i −0.117545 0.0566069i
\(236\) 2.21110 9.68748i 0.143931 0.630601i
\(237\) 1.28501 5.63000i 0.0834705 0.365708i
\(238\) −38.6383 18.6072i −2.50455 1.20613i
\(239\) 15.4976 7.46325i 1.00246 0.482758i 0.140685 0.990054i \(-0.455069\pi\)
0.861772 + 0.507297i \(0.169355\pi\)
\(240\) 0.554958 2.43143i 0.0358224 0.156948i
\(241\) 15.7676 19.7719i 1.01568 1.27362i 0.0542596 0.998527i \(-0.482720\pi\)
0.961418 0.275092i \(-0.0887084\pi\)
\(242\) −11.7838 + 14.7764i −0.757492 + 0.949865i
\(243\) 5.36778 2.58499i 0.344343 0.165827i
\(244\) −1.53923 6.74380i −0.0985390 0.431728i
\(245\) −13.7627 17.2579i −0.879267 1.10257i
\(246\) 3.13102 + 13.7179i 0.199627 + 0.874622i
\(247\) −1.57942 0.760607i −0.100496 0.0483963i
\(248\) −5.26391 + 6.60073i −0.334258 + 0.419147i
\(249\) 14.2397 + 6.85750i 0.902407 + 0.434576i
\(250\) −16.8116 21.0811i −1.06326 1.33329i
\(251\) −1.94139 −0.122540 −0.0612699 0.998121i \(-0.519515\pi\)
−0.0612699 + 0.998121i \(0.519515\pi\)
\(252\) 7.53750 0.474818
\(253\) −6.03803 7.57145i −0.379608 0.476013i
\(254\) −29.6395 + 14.2736i −1.85975 + 0.895608i
\(255\) −3.10992 + 13.6254i −0.194751 + 0.853258i
\(256\) 2.32908 + 10.2044i 0.145568 + 0.637774i
\(257\) 15.7168 0.980386 0.490193 0.871614i \(-0.336926\pi\)
0.490193 + 0.871614i \(0.336926\pi\)
\(258\) −22.6042 + 3.73962i −1.40727 + 0.232818i
\(259\) −20.6939 −1.28586
\(260\) 0.417895 + 1.83092i 0.0259167 + 0.113549i
\(261\) −0.380691 + 1.66791i −0.0235642 + 0.103241i
\(262\) −21.2446 + 10.2309i −1.31249 + 0.632064i
\(263\) −9.15093 11.4749i −0.564271 0.707573i 0.415070 0.909789i \(-0.363757\pi\)
−0.979341 + 0.202216i \(0.935186\pi\)
\(264\) −16.1468 −0.993764
\(265\) 2.81163 0.172717
\(266\) 33.8669 + 42.4677i 2.07651 + 2.60386i
\(267\) 7.00149 + 3.37174i 0.428484 + 0.206347i
\(268\) 7.95742 9.97829i 0.486077 0.609521i
\(269\) 13.5831 + 6.54126i 0.828174 + 0.398828i 0.799430 0.600759i \(-0.205135\pi\)
0.0287440 + 0.999587i \(0.490849\pi\)
\(270\) −5.57002 24.4039i −0.338981 1.48517i
\(271\) −14.4242 18.0874i −0.876210 1.09873i −0.994394 0.105740i \(-0.966279\pi\)
0.118184 0.992992i \(-0.462293\pi\)
\(272\) 0.801938 + 3.51352i 0.0486246 + 0.213038i
\(273\) −1.83244 + 0.882455i −0.110904 + 0.0534086i
\(274\) 12.5368 15.7207i 0.757378 0.949722i
\(275\) 2.74698 3.44460i 0.165649 0.207717i
\(276\) 2.31886 10.1596i 0.139579 0.611536i
\(277\) −18.7240 + 9.01701i −1.12502 + 0.541780i −0.901439 0.432906i \(-0.857488\pi\)
−0.223578 + 0.974686i \(0.571774\pi\)
\(278\) 17.0417 + 8.20684i 1.02209 + 0.492214i
\(279\) 0.463992 2.03288i 0.0277785 0.121706i
\(280\) 4.45473 19.5174i 0.266221 1.16639i
\(281\) −16.9710 8.17280i −1.01240 0.487548i −0.147274 0.989096i \(-0.547050\pi\)
−0.865130 + 0.501547i \(0.832764\pi\)
\(282\) 3.14795 1.51597i 0.187458 0.0902748i
\(283\) 2.90246 12.7165i 0.172533 0.755918i −0.812416 0.583078i \(-0.801848\pi\)
0.984950 0.172841i \(-0.0552945\pi\)
\(284\) −16.7506 + 21.0046i −0.993967 + 1.24640i
\(285\) 11.0368 13.8398i 0.653766 0.819796i
\(286\) −2.74698 + 1.32288i −0.162432 + 0.0782233i
\(287\) −3.80582 16.6744i −0.224651 0.984259i
\(288\) −2.36480 2.96536i −0.139347 0.174736i
\(289\) −0.711103 3.11555i −0.0418296 0.183267i
\(290\) 11.8998 + 5.73063i 0.698779 + 0.336514i
\(291\) −17.6905 + 22.1831i −1.03703 + 1.30040i
\(292\) −11.6930 5.63104i −0.684280 0.329532i
\(293\) 16.5410 + 20.7418i 0.966336 + 1.21175i 0.977311 + 0.211808i \(0.0679351\pi\)
−0.0109749 + 0.999940i \(0.503493\pi\)
\(294\) 38.5623 2.24900
\(295\) 6.51812 0.379500
\(296\) −7.16033 8.97876i −0.416185 0.521880i
\(297\) 22.1102 10.6477i 1.28296 0.617843i
\(298\) −3.11745 + 13.6584i −0.180589 + 0.791212i
\(299\) −0.150637 0.659983i −0.00871156 0.0381678i
\(300\) 4.74094 0.273718
\(301\) 27.4758 4.54558i 1.58368 0.262003i
\(302\) 12.5918 0.724576
\(303\) −3.19016 13.9770i −0.183270 0.802958i
\(304\) 1.01573 4.45020i 0.0582561 0.255237i
\(305\) 4.08815 1.96875i 0.234087 0.112730i
\(306\) 3.66487 + 4.59561i 0.209507 + 0.262713i
\(307\) −7.08277 −0.404235 −0.202117 0.979361i \(-0.564782\pi\)
−0.202117 + 0.979361i \(0.564782\pi\)
\(308\) 57.0495 3.25070
\(309\) 1.12870 + 1.41535i 0.0642096 + 0.0805164i
\(310\) −14.5036 6.98459i −0.823752 0.396698i
\(311\) −11.7947 + 14.7901i −0.668816 + 0.838669i −0.994271 0.106889i \(-0.965911\pi\)
0.325455 + 0.945558i \(0.394483\pi\)
\(312\) −1.01693 0.489726i −0.0575721 0.0277253i
\(313\) 4.14071 + 18.1416i 0.234047 + 1.02543i 0.946246 + 0.323449i \(0.104842\pi\)
−0.712199 + 0.701978i \(0.752301\pi\)
\(314\) −14.8482 18.6190i −0.837931 1.05073i
\(315\) 1.10023 + 4.82041i 0.0619908 + 0.271599i
\(316\) −10.2017 + 4.91288i −0.573891 + 0.276371i
\(317\) −8.92274 + 11.1888i −0.501151 + 0.628423i −0.966489 0.256710i \(-0.917362\pi\)
0.465338 + 0.885133i \(0.345933\pi\)
\(318\) −3.06249 + 3.84024i −0.171736 + 0.215350i
\(319\) −2.88135 + 12.6240i −0.161325 + 0.706810i
\(320\) −23.4916 + 11.3129i −1.31322 + 0.632413i
\(321\) −21.9121 10.5523i −1.22302 0.588974i
\(322\) −4.66756 + 20.4499i −0.260113 + 1.13963i
\(323\) −5.69202 + 24.9384i −0.316713 + 1.38761i
\(324\) 18.9949 + 9.14747i 1.05527 + 0.508193i
\(325\) 0.277479 0.133627i 0.0153918 0.00741229i
\(326\) −11.7078 + 51.2950i −0.648432 + 2.84097i
\(327\) −8.67576 + 10.8791i −0.479771 + 0.601613i
\(328\) 5.91789 7.42081i 0.326761 0.409745i
\(329\) −3.82640 + 1.84270i −0.210956 + 0.101591i
\(330\) −6.85086 30.0156i −0.377127 1.65230i
\(331\) 12.1374 + 15.2198i 0.667130 + 0.836554i 0.994099 0.108481i \(-0.0345987\pi\)
−0.326969 + 0.945035i \(0.606027\pi\)
\(332\) −6.89589 30.2129i −0.378461 1.65815i
\(333\) 2.55549 + 1.23066i 0.140040 + 0.0674397i
\(334\) −13.8904 + 17.4180i −0.760048 + 0.953070i
\(335\) 7.54288 + 3.63246i 0.412111 + 0.198462i
\(336\) −3.30194 4.14050i −0.180135 0.225883i
\(337\) −7.66786 −0.417695 −0.208847 0.977948i \(-0.566971\pi\)
−0.208847 + 0.977948i \(0.566971\pi\)
\(338\) 28.9976 1.57726
\(339\) −9.05980 11.3606i −0.492061 0.617025i
\(340\) 24.6896 11.8899i 1.33898 0.644820i
\(341\) 3.51184 15.3864i 0.190177 0.833220i
\(342\) −1.65668 7.25838i −0.0895829 0.392488i
\(343\) −17.1444 −0.925708
\(344\) 11.4792 + 10.3485i 0.618916 + 0.557954i
\(345\) 6.83579 0.368027
\(346\) −0.766594 3.35867i −0.0412123 0.180563i
\(347\) −1.22976 + 5.38792i −0.0660169 + 0.289239i −0.997150 0.0754397i \(-0.975964\pi\)
0.931133 + 0.364679i \(0.118821\pi\)
\(348\) −12.5538 + 6.04557i −0.672952 + 0.324077i
\(349\) −1.60656 2.01457i −0.0859974 0.107837i 0.736971 0.675924i \(-0.236255\pi\)
−0.822969 + 0.568087i \(0.807684\pi\)
\(350\) −9.54288 −0.510088
\(351\) 1.71545 0.0915638
\(352\) −17.8986 22.4441i −0.953997 1.19627i
\(353\) −21.6015 10.4027i −1.14973 0.553681i −0.240778 0.970580i \(-0.577403\pi\)
−0.908953 + 0.416899i \(0.863117\pi\)
\(354\) −7.09970 + 8.90274i −0.377345 + 0.473175i
\(355\) −15.8780 7.64644i −0.842717 0.405831i
\(356\) −3.39062 14.8553i −0.179702 0.787327i
\(357\) 18.5036 + 23.2028i 0.979317 + 1.22802i
\(358\) −8.61141 37.7290i −0.455127 1.99404i
\(359\) 2.45204 1.18084i 0.129414 0.0623224i −0.368056 0.929803i \(-0.619977\pi\)
0.497470 + 0.867481i \(0.334262\pi\)
\(360\) −1.71081 + 2.14529i −0.0901675 + 0.113066i
\(361\) 8.35421 10.4758i 0.439695 0.551360i
\(362\) 6.06734 26.5827i 0.318892 1.39716i
\(363\) 11.7838 5.67479i 0.618490 0.297849i
\(364\) 3.59299 + 1.73029i 0.188324 + 0.0906920i
\(365\) 1.89440 8.29989i 0.0991572 0.434436i
\(366\) −1.76391 + 7.72818i −0.0922008 + 0.403958i
\(367\) 17.5260 + 8.44005i 0.914847 + 0.440567i 0.831229 0.555931i \(-0.187638\pi\)
0.0836185 + 0.996498i \(0.473352\pi\)
\(368\) 1.58815 0.764811i 0.0827878 0.0398685i
\(369\) −0.521639 + 2.28545i −0.0271554 + 0.118976i
\(370\) 13.6528 17.1201i 0.709775 0.890030i
\(371\) 3.72252 4.66789i 0.193264 0.242345i
\(372\) 15.3007 7.36845i 0.793306 0.382036i
\(373\) 3.98158 + 17.4445i 0.206159 + 0.903239i 0.967095 + 0.254414i \(0.0818825\pi\)
−0.760937 + 0.648826i \(0.775260\pi\)
\(374\) 27.7385 + 34.7830i 1.43433 + 1.79859i
\(375\) 4.15213 + 18.1917i 0.214415 + 0.939414i
\(376\) −2.12349 1.02262i −0.109511 0.0527375i
\(377\) −0.564351 + 0.707674i −0.0290656 + 0.0364471i
\(378\) −47.8901 23.0627i −2.46320 1.18622i
\(379\) 3.01693 + 3.78311i 0.154969 + 0.194325i 0.853255 0.521494i \(-0.174625\pi\)
−0.698286 + 0.715819i \(0.746054\pi\)
\(380\) −34.7090 −1.78053
\(381\) 22.7657 1.16632
\(382\) 22.4460 + 28.1464i 1.14844 + 1.44009i
\(383\) 3.89708 1.87674i 0.199132 0.0958968i −0.331660 0.943399i \(-0.607609\pi\)
0.530792 + 0.847502i \(0.321895\pi\)
\(384\) 5.62684 24.6528i 0.287144 1.25806i
\(385\) 8.32736 + 36.4845i 0.424401 + 1.85942i
\(386\) −53.4499 −2.72053
\(387\) −3.66331 1.07264i −0.186216 0.0545255i
\(388\) 55.6335 2.82436
\(389\) −6.60872 28.9547i −0.335075 1.46806i −0.809163 0.587584i \(-0.800079\pi\)
0.474088 0.880477i \(-0.342778\pi\)
\(390\) 0.478894 2.09817i 0.0242497 0.106245i
\(391\) −8.89977 + 4.28590i −0.450081 + 0.216748i
\(392\) −16.2186 20.3375i −0.819165 1.02720i
\(393\) 16.3177 0.823117
\(394\) −35.6262 −1.79482
\(395\) −4.63102 5.80712i −0.233012 0.292188i
\(396\) −7.04503 3.39271i −0.354026 0.170490i
\(397\) 5.17510 6.48936i 0.259731 0.325692i −0.634819 0.772661i \(-0.718925\pi\)
0.894549 + 0.446969i \(0.147497\pi\)
\(398\) 17.7310 + 8.53881i 0.888775 + 0.428012i
\(399\) −8.36443 36.6470i −0.418745 1.83464i
\(400\) 0.500000 + 0.626980i 0.0250000 + 0.0313490i
\(401\) 0.208283 + 0.912549i 0.0104012 + 0.0455705i 0.979862 0.199675i \(-0.0639886\pi\)
−0.969461 + 0.245245i \(0.921131\pi\)
\(402\) −13.1773 + 6.34583i −0.657222 + 0.316501i
\(403\) 0.687841 0.862525i 0.0342638 0.0429655i
\(404\) −17.5266 + 21.9777i −0.871982 + 1.09343i
\(405\) −3.07739 + 13.4829i −0.152917 + 0.669973i
\(406\) 25.2690 12.1689i 1.25408 0.603934i
\(407\) 19.3419 + 9.31456i 0.958742 + 0.461706i
\(408\) −3.66487 + 16.0569i −0.181438 + 0.794933i
\(409\) −0.761750 + 3.33744i −0.0376661 + 0.165026i −0.990263 0.139210i \(-0.955544\pi\)
0.952597 + 0.304236i \(0.0984010\pi\)
\(410\) 16.3056 + 7.85236i 0.805275 + 0.387800i
\(411\) −12.5368 + 6.03742i −0.618397 + 0.297804i
\(412\) 0.789856 3.46059i 0.0389134 0.170491i
\(413\) 8.62983 10.8215i 0.424646 0.532489i
\(414\) 1.79254 2.24778i 0.0880988 0.110472i
\(415\) 18.3153 8.82017i 0.899061 0.432965i
\(416\) −0.446534 1.95639i −0.0218931 0.0959200i
\(417\) −8.16115 10.2338i −0.399653 0.501150i
\(418\) −12.5390 54.9369i −0.613302 2.68705i
\(419\) −2.83997 1.36766i −0.138742 0.0668144i 0.363225 0.931701i \(-0.381676\pi\)
−0.501967 + 0.864887i \(0.667390\pi\)
\(420\) −25.1075 + 31.4838i −1.22512 + 1.53625i
\(421\) −29.2494 14.0858i −1.42553 0.686499i −0.447369 0.894349i \(-0.647639\pi\)
−0.978161 + 0.207850i \(0.933353\pi\)
\(422\) −12.0293 15.0843i −0.585577 0.734291i
\(423\) 0.582105 0.0283029
\(424\) 3.31336 0.160911
\(425\) −2.80194 3.51352i −0.135914 0.170431i
\(426\) 27.7385 13.3582i 1.34394 0.647206i
\(427\) 2.14406 9.39376i 0.103759 0.454596i
\(428\) 10.6114 + 46.4916i 0.512922 + 2.24726i
\(429\) 2.10992 0.101868
\(430\) −14.3666 + 25.7297i −0.692818 + 1.24079i
\(431\) 35.9148 1.72996 0.864978 0.501809i \(-0.167332\pi\)
0.864978 + 0.501809i \(0.167332\pi\)
\(432\) 0.993959 + 4.35482i 0.0478219 + 0.209521i
\(433\) −5.91119 + 25.8986i −0.284074 + 1.24461i 0.608444 + 0.793596i \(0.291794\pi\)
−0.892518 + 0.451012i \(0.851063\pi\)
\(434\) −30.7983 + 14.8317i −1.47837 + 0.711945i
\(435\) −5.69873 7.14598i −0.273233 0.342623i
\(436\) 27.2838 1.30666
\(437\) 12.5114 0.598502
\(438\) 9.27293 + 11.6279i 0.443078 + 0.555602i
\(439\) −36.0393 17.3556i −1.72006 0.828338i −0.989333 0.145669i \(-0.953467\pi\)
−0.730728 0.682669i \(-0.760819\pi\)
\(440\) −12.9487 + 16.2371i −0.617305 + 0.774075i
\(441\) 5.78836 + 2.78753i 0.275636 + 0.132739i
\(442\) 0.692021 + 3.03194i 0.0329161 + 0.144215i
\(443\) 9.85152 + 12.3534i 0.468060 + 0.586928i 0.958695 0.284437i \(-0.0918066\pi\)
−0.490635 + 0.871365i \(0.663235\pi\)
\(444\) 5.14042 + 22.5216i 0.243953 + 1.06883i
\(445\) 9.00538 4.33676i 0.426896 0.205582i
\(446\) 10.6528 13.3582i 0.504424 0.632528i
\(447\) 6.04474 7.57986i 0.285906 0.358515i
\(448\) −12.3204 + 53.9790i −0.582082 + 2.55027i
\(449\) 11.7310 5.64936i 0.553621 0.266610i −0.136088 0.990697i \(-0.543453\pi\)
0.689709 + 0.724087i \(0.257739\pi\)
\(450\) 1.17845 + 0.567511i 0.0555526 + 0.0267527i
\(451\) −3.94816 + 17.2980i −0.185911 + 0.814531i
\(452\) −6.33997 + 27.7772i −0.298207 + 1.30653i
\(453\) −7.85086 3.78077i −0.368865 0.177636i
\(454\) 31.4061 15.1244i 1.47396 0.709823i
\(455\) −0.582105 + 2.55037i −0.0272895 + 0.119563i
\(456\) 13.0063 16.3094i 0.609078 0.763759i
\(457\) −15.3787 + 19.2842i −0.719384 + 0.902079i −0.998303 0.0582360i \(-0.981452\pi\)
0.278919 + 0.960315i \(0.410024\pi\)
\(458\) −47.8488 + 23.0427i −2.23583 + 1.07672i
\(459\) −5.57002 24.4039i −0.259986 1.13908i
\(460\) −8.35690 10.4792i −0.389642 0.488596i
\(461\) −2.26218 9.91124i −0.105360 0.461613i −0.999893 0.0146111i \(-0.995349\pi\)
0.894533 0.447002i \(-0.147508\pi\)
\(462\) −58.9025 28.3660i −2.74039 1.31970i
\(463\) 9.08426 11.3913i 0.422181 0.529399i −0.524569 0.851368i \(-0.675773\pi\)
0.946750 + 0.321969i \(0.104345\pi\)
\(464\) −2.12349 1.02262i −0.0985805 0.0474739i
\(465\) 6.94571 + 8.70964i 0.322099 + 0.403900i
\(466\) 48.6752 2.25483
\(467\) 9.56704 0.442710 0.221355 0.975193i \(-0.428952\pi\)
0.221355 + 0.975193i \(0.428952\pi\)
\(468\) −0.340798 0.427347i −0.0157534 0.0197541i
\(469\) 16.0172 7.71349i 0.739607 0.356176i
\(470\) 1.00000 4.38129i 0.0461266 0.202094i
\(471\) 3.66719 + 16.0670i 0.168975 + 0.740330i
\(472\) 7.68127 0.353559
\(473\) −27.7267 8.11857i −1.27488 0.373292i
\(474\) 12.9758 0.596000
\(475\) 1.26659 + 5.54931i 0.0581153 + 0.254620i
\(476\) 12.9487 56.7319i 0.593502 2.60030i
\(477\) −0.737291 + 0.355061i −0.0337582 + 0.0162571i
\(478\) 24.0981 + 30.2181i 1.10222 + 1.38214i
\(479\) −24.7851 −1.13246 −0.566229 0.824248i \(-0.691598\pi\)
−0.566229 + 0.824248i \(0.691598\pi\)
\(480\) 20.2634 0.924892
\(481\) 0.935649 + 1.17327i 0.0426619 + 0.0534963i
\(482\) 51.1969 + 24.6551i 2.33196 + 1.12301i
\(483\) 9.05041 11.3489i 0.411808 0.516391i
\(484\) −23.1054 11.1270i −1.05024 0.505771i
\(485\) 8.12067 + 35.5790i 0.368741 + 1.61556i
\(486\) 8.34667 + 10.4664i 0.378613 + 0.474766i
\(487\) −5.76487 25.2575i −0.261231 1.14453i −0.919918 0.392111i \(-0.871745\pi\)
0.658687 0.752417i \(-0.271112\pi\)
\(488\) 4.81767 2.32007i 0.218086 0.105024i
\(489\) 22.7013 28.4666i 1.02659 1.28730i
\(490\) 30.9245 38.7781i 1.39703 1.75182i
\(491\) −5.49731 + 24.0853i −0.248090 + 1.08695i 0.685348 + 0.728216i \(0.259650\pi\)
−0.933438 + 0.358738i \(0.883207\pi\)
\(492\) −17.2017 + 8.28391i −0.775513 + 0.373467i
\(493\) 11.8998 + 5.73063i 0.535939 + 0.258095i
\(494\) 0.876510 3.84024i 0.0394361 0.172781i
\(495\) 1.14138 5.00069i 0.0513010 0.224764i
\(496\) 2.58815 + 1.24639i 0.116211 + 0.0559644i
\(497\) −33.7168 + 16.2371i −1.51240 + 0.728335i
\(498\) −7.90246 + 34.6229i −0.354118 + 1.55149i
\(499\) −17.5082 + 21.9546i −0.783775 + 0.982822i 0.216205 + 0.976348i \(0.430632\pi\)
−0.999979 + 0.00647407i \(0.997939\pi\)
\(500\) 22.8116 28.6049i 1.02017 1.27925i
\(501\) 13.8904 6.68925i 0.620576 0.298854i
\(502\) −0.970697 4.25290i −0.0433243 0.189816i
\(503\) −18.0262 22.6042i −0.803751 1.00787i −0.999629 0.0272431i \(-0.991327\pi\)
0.195878 0.980628i \(-0.437244\pi\)
\(504\) 1.29656 + 5.68060i 0.0577534 + 0.253034i
\(505\) −16.6136 8.00067i −0.739294 0.356025i
\(506\) 13.5673 17.0129i 0.603142 0.756316i
\(507\) −18.0797 8.70673i −0.802948 0.386679i
\(508\) −27.8315 34.8996i −1.23482 1.54842i
\(509\) 3.65040 0.161801 0.0809006 0.996722i \(-0.474220\pi\)
0.0809006 + 0.996722i \(0.474220\pi\)
\(510\) −31.4034 −1.39057
\(511\) −11.2714 14.1339i −0.498619 0.625249i
\(512\) 8.11356 3.90729i 0.358572 0.172679i
\(513\) −7.05496 + 30.9098i −0.311484 + 1.36470i
\(514\) 7.85839 + 34.4298i 0.346619 + 1.51864i
\(515\) 2.32842 0.102602
\(516\) −11.7721 28.7734i −0.518238 1.26668i
\(517\) 4.40581 0.193767
\(518\) −10.3470 45.3330i −0.454620 1.99182i
\(519\) −0.530499 + 2.32427i −0.0232863 + 0.102024i
\(520\) −1.30798 + 0.629889i −0.0573587 + 0.0276225i
\(521\) −8.49545 10.6530i −0.372192 0.466715i 0.560097 0.828427i \(-0.310764\pi\)
−0.932290 + 0.361712i \(0.882192\pi\)
\(522\) −3.84415 −0.168254
\(523\) 4.45904 0.194980 0.0974902 0.995236i \(-0.468919\pi\)
0.0974902 + 0.995236i \(0.468919\pi\)
\(524\) −19.9487 25.0149i −0.871463 1.09278i
\(525\) 5.94989 + 2.86531i 0.259674 + 0.125053i
\(526\) 20.5620 25.7839i 0.896544 1.12423i
\(527\) −14.5036 6.98459i −0.631789 0.304253i
\(528\) 1.22252 + 5.35621i 0.0532034 + 0.233099i
\(529\) −11.3279 14.2047i −0.492517 0.617597i
\(530\) 1.40581 + 6.15927i 0.0610646 + 0.267542i
\(531\) −1.70924 + 0.823128i −0.0741748 + 0.0357207i
\(532\) −45.9538 + 57.6243i −1.99235 + 2.49833i
\(533\) −0.773299 + 0.969686i −0.0334953 + 0.0420018i
\(534\) −3.88553 + 17.0236i −0.168144 + 0.736685i
\(535\) −28.1836 + 13.5725i −1.21848 + 0.586790i
\(536\) 8.88889 + 4.28066i 0.383941 + 0.184896i
\(537\) −5.95928 + 26.1093i −0.257162 + 1.12670i
\(538\) −7.53803 + 33.0263i −0.324988 + 1.42386i
\(539\) 43.8107 + 21.0981i 1.88706 + 0.908761i
\(540\) 30.6015 14.7369i 1.31688 0.634175i
\(541\) 3.74482 16.4071i 0.161003 0.705398i −0.828392 0.560148i \(-0.810744\pi\)
0.989395 0.145250i \(-0.0463987\pi\)
\(542\) 32.4110 40.6420i 1.39217 1.74573i
\(543\) −11.7646 + 14.7523i −0.504866 + 0.633082i
\(544\) −26.3817 + 12.7047i −1.13110 + 0.544711i
\(545\) 3.98254 + 17.4487i 0.170593 + 0.747418i
\(546\) −2.84936 3.57299i −0.121941 0.152910i
\(547\) 1.76606 + 7.73762i 0.0755113 + 0.330837i 0.998548 0.0538761i \(-0.0171576\pi\)
−0.923036 + 0.384713i \(0.874300\pi\)
\(548\) 24.5819 + 11.8380i 1.05009 + 0.505694i
\(549\) −0.823413 + 1.03253i −0.0351424 + 0.0440672i
\(550\) 8.91939 + 4.29535i 0.380324 + 0.183154i
\(551\) −10.4303 13.0791i −0.444345 0.557190i
\(552\) 8.05562 0.342870
\(553\) −15.7724 −0.670711
\(554\) −29.1151 36.5091i −1.23698 1.55112i
\(555\) −13.6528 + 6.57484i −0.579529 + 0.279086i
\(556\) −5.71110 + 25.0220i −0.242205 + 1.06117i
\(557\) 3.22318 + 14.1217i 0.136571 + 0.598355i 0.996174 + 0.0873932i \(0.0278537\pi\)
−0.859603 + 0.510962i \(0.829289\pi\)
\(558\) 4.68532 0.198345
\(559\) −1.50000 1.35225i −0.0634432 0.0571941i
\(560\) −6.81163 −0.287844
\(561\) −6.85086 30.0156i −0.289243 1.26726i
\(562\) 9.41819 41.2638i 0.397282 1.74061i
\(563\) 6.05884 2.91779i 0.255350 0.122970i −0.301830 0.953362i \(-0.597598\pi\)
0.557180 + 0.830392i \(0.311883\pi\)
\(564\) 2.95593 + 3.70662i 0.124467 + 0.156077i
\(565\) −18.6896 −0.786279
\(566\) 29.3086 1.23193
\(567\) 18.3101 + 22.9602i 0.768953 + 0.964237i
\(568\) −18.7114 9.01093i −0.785113 0.378090i
\(569\) −26.3357 + 33.0239i −1.10405 + 1.38444i −0.188577 + 0.982058i \(0.560387\pi\)
−0.915474 + 0.402377i \(0.868184\pi\)
\(570\) 35.8364 + 17.2579i 1.50102 + 0.722854i
\(571\) −3.62551 15.8844i −0.151723 0.664742i −0.992384 0.123181i \(-0.960691\pi\)
0.840661 0.541561i \(-0.182167\pi\)
\(572\) −2.57942 3.23449i −0.107851 0.135241i
\(573\) −5.54370 24.2886i −0.231592 1.01467i
\(574\) 34.6247 16.6744i 1.44521 0.695976i
\(575\) −1.37047 + 1.71851i −0.0571525 + 0.0716670i
\(576\) 4.73155 5.93317i 0.197148 0.247215i
\(577\) 9.89858 43.3685i 0.412083 1.80545i −0.162155 0.986765i \(-0.551844\pi\)
0.574238 0.818689i \(-0.305299\pi\)
\(578\) 6.46950 3.11555i 0.269096 0.129590i
\(579\) 33.3255 + 16.0487i 1.38496 + 0.666962i
\(580\) −3.98792 + 17.4722i −0.165589 + 0.725494i
\(581\) 9.60560 42.0849i 0.398508 1.74598i
\(582\) −57.4406 27.6619i −2.38099 1.14662i
\(583\) −5.58038 + 2.68737i −0.231116 + 0.111299i
\(584\) 2.23245 9.78099i 0.0923793 0.404740i
\(585\) 0.223553 0.280327i 0.00924280 0.0115901i
\(586\) −37.1673 + 46.6064i −1.53537 + 1.92529i
\(587\) 27.4034 13.1968i 1.13106 0.544690i 0.227768 0.973715i \(-0.426857\pi\)
0.903292 + 0.429026i \(0.141143\pi\)
\(588\) 11.6434 + 51.0131i 0.480166 + 2.10374i
\(589\) 12.7126 + 15.9411i 0.523813 + 0.656841i
\(590\) 3.25906 + 14.2789i 0.134173 + 0.587852i
\(591\) 22.2126 + 10.6970i 0.913704 + 0.440017i
\(592\) −2.43631 + 3.05504i −0.100132 + 0.125561i
\(593\) 2.05400 + 0.989154i 0.0843476 + 0.0406197i 0.475582 0.879671i \(-0.342238\pi\)
−0.391234 + 0.920291i \(0.627952\pi\)
\(594\) 34.3805 + 43.1117i 1.41065 + 1.76890i
\(595\) 38.1715 1.56488
\(596\) −19.0097 −0.778667
\(597\) −8.49127 10.6477i −0.347525 0.435782i
\(598\) 1.37047 0.659983i 0.0560427 0.0269887i
\(599\) 4.87853 21.3743i 0.199332 0.873328i −0.772004 0.635617i \(-0.780746\pi\)
0.971336 0.237711i \(-0.0763972\pi\)
\(600\) 0.815511 + 3.57299i 0.0332931 + 0.145867i
\(601\) 8.27173 0.337411 0.168706 0.985666i \(-0.446041\pi\)
0.168706 + 0.985666i \(0.446041\pi\)
\(602\) 23.6957 + 57.9170i 0.965763 + 2.36052i
\(603\) −2.43668 −0.0992293
\(604\) 3.80194 + 16.6574i 0.154699 + 0.677779i
\(605\) 3.74333 16.4006i 0.152188 0.666780i
\(606\) 29.0236 13.9770i 1.17900 0.567777i
\(607\) 7.42543 + 9.31119i 0.301389 + 0.377930i 0.909346 0.416040i \(-0.136582\pi\)
−0.607958 + 0.793970i \(0.708011\pi\)
\(608\) 37.0877 1.50410
\(609\) −19.4088 −0.786484
\(610\) 6.35690 + 7.97130i 0.257383 + 0.322748i
\(611\) 0.277479 + 0.133627i 0.0112256 + 0.00540596i
\(612\) −4.97285 + 6.23576i −0.201016 + 0.252066i
\(613\) 1.70948 + 0.823242i 0.0690452 + 0.0332504i 0.468088 0.883682i \(-0.344943\pi\)
−0.399042 + 0.916932i \(0.630657\pi\)
\(614\) −3.54138 15.5158i −0.142919 0.626168i
\(615\) −7.80864 9.79173i −0.314875 0.394841i
\(616\) 9.81336 + 42.9951i 0.395391 + 1.73232i
\(617\) −43.7323 + 21.0604i −1.76059 + 0.847858i −0.787889 + 0.615818i \(0.788826\pi\)
−0.972706 + 0.232040i \(0.925460\pi\)
\(618\) −2.53617 + 3.18026i −0.102020 + 0.127929i
\(619\) 10.0420 12.5923i 0.403624 0.506129i −0.537930 0.842989i \(-0.680794\pi\)
0.941554 + 0.336861i \(0.109365\pi\)
\(620\) 4.86054 21.2954i 0.195204 0.855245i
\(621\) −11.0308 + 5.31215i −0.442651 + 0.213169i
\(622\) −38.2972 18.4429i −1.53558 0.739494i
\(623\) 4.72295 20.6926i 0.189221 0.829031i
\(624\) −0.0854576 + 0.374414i −0.00342104 + 0.0149886i
\(625\) 17.1184 + 8.24379i 0.684736 + 0.329752i
\(626\) −37.6715 + 18.1416i −1.50566 + 0.725086i
\(627\) −8.67725 + 38.0175i −0.346536 + 1.51827i
\(628\) 20.1474 25.2641i 0.803969 1.00815i
\(629\) 13.6528 17.1201i 0.544372 0.682622i
\(630\) −10.0097 + 4.82041i −0.398796 + 0.192050i
\(631\) 6.84362 + 29.9838i 0.272440 + 1.19364i 0.907123 + 0.420866i \(0.138274\pi\)
−0.634683 + 0.772773i \(0.718869\pi\)
\(632\) −5.45742 6.84339i −0.217084 0.272215i
\(633\) 2.97099 + 13.0168i 0.118086 + 0.517370i
\(634\) −28.9720 13.9522i −1.15062 0.554111i
\(635\) 18.2567 22.8931i 0.724494 0.908486i
\(636\) −6.00484 2.89178i −0.238108 0.114667i
\(637\) 2.11931 + 2.65753i 0.0839701 + 0.105295i
\(638\) −29.0954 −1.15190
\(639\) 5.12929 0.202912
\(640\) −20.2784 25.4284i −0.801576 1.00514i
\(641\) 18.8436 9.07461i 0.744278 0.358425i −0.0230038 0.999735i \(-0.507323\pi\)
0.767282 + 0.641310i \(0.221609\pi\)
\(642\) 12.1603 53.2779i 0.479930 2.10271i
\(643\) −7.03146 30.8068i −0.277294 1.21490i −0.901200 0.433404i \(-0.857312\pi\)
0.623906 0.781499i \(-0.285545\pi\)
\(644\) −28.4620 −1.12156
\(645\) 16.6829 11.7285i 0.656889 0.461810i
\(646\) −57.4771 −2.26141
\(647\) 8.21744 + 36.0030i 0.323061 + 1.41542i 0.832075 + 0.554664i \(0.187153\pi\)
−0.509014 + 0.860758i \(0.669990\pi\)
\(648\) −3.62655 + 15.8889i −0.142464 + 0.624176i
\(649\) −12.9368 + 6.23006i −0.507816 + 0.244551i
\(650\) 0.431468 + 0.541044i 0.0169236 + 0.0212215i
\(651\) 23.6558 0.927143
\(652\) −71.3919 −2.79592
\(653\) −3.11679 3.90832i −0.121969 0.152945i 0.717098 0.696972i \(-0.245470\pi\)
−0.839067 + 0.544028i \(0.816899\pi\)
\(654\) −28.1700 13.5660i −1.10153 0.530471i
\(655\) 13.0858 16.4090i 0.511303 0.641153i
\(656\) −2.90970 1.40124i −0.113605 0.0547091i
\(657\) 0.551369 + 2.41570i 0.0215109 + 0.0942456i
\(658\) −5.94989 7.46092i −0.231951 0.290857i
\(659\) 0.945469 + 4.14237i 0.0368302 + 0.161364i 0.989999 0.141076i \(-0.0450561\pi\)
−0.953169 + 0.302440i \(0.902199\pi\)
\(660\) 37.6383 18.1257i 1.46507 0.705540i
\(661\) −27.5221 + 34.5116i −1.07048 + 1.34234i −0.134258 + 0.990946i \(0.542865\pi\)
−0.936226 + 0.351398i \(0.885706\pi\)
\(662\) −27.2724 + 34.1985i −1.05997 + 1.32916i
\(663\) 0.478894 2.09817i 0.0185987 0.0814862i
\(664\) 21.5836 10.3941i 0.837606 0.403370i
\(665\) −43.5599 20.9773i −1.68918 0.813466i
\(666\) −1.41819 + 6.21350i −0.0549538 + 0.240768i
\(667\) 1.43751 6.29814i 0.0556606 0.243865i
\(668\) −27.2359 13.1161i −1.05379 0.507477i
\(669\) −10.6528 + 5.13011i −0.411861 + 0.198342i
\(670\) −4.18598 + 18.3400i −0.161719 + 0.708535i
\(671\) −6.23221 + 7.81494i −0.240592 + 0.301693i
\(672\) 26.8282 33.6415i 1.03492 1.29775i
\(673\) 10.7497 5.17677i 0.414369 0.199550i −0.215071 0.976598i \(-0.568998\pi\)
0.629441 + 0.777049i \(0.283284\pi\)
\(674\) −3.83393 16.7975i −0.147677 0.647017i
\(675\) −3.47285 4.35482i −0.133670 0.167617i
\(676\) 8.75547 + 38.3602i 0.336749 + 1.47539i
\(677\) 32.4180 + 15.6117i 1.24592 + 0.600005i 0.936416 0.350892i \(-0.114122\pi\)
0.309507 + 0.950897i \(0.399836\pi\)
\(678\) 20.3572 25.5271i 0.781813 0.980363i
\(679\) 69.8202 + 33.6236i 2.67945 + 1.29036i
\(680\) 13.2078 + 16.5620i 0.506494 + 0.635124i
\(681\) −24.1226 −0.924380
\(682\) 35.4620 1.35791
\(683\) 17.6645 + 22.1506i 0.675914 + 0.847569i 0.994971 0.100167i \(-0.0319376\pi\)
−0.319057 + 0.947735i \(0.603366\pi\)
\(684\) 9.10172 4.38316i 0.348013 0.167594i
\(685\) −3.98254 + 17.4487i −0.152165 + 0.666679i
\(686\) −8.57218 37.5572i −0.327287 1.43394i
\(687\) 36.7520 1.40217
\(688\) 2.56369 4.59140i 0.0977397 0.175046i
\(689\) −0.432960 −0.0164945
\(690\) 3.41789 + 14.9748i 0.130117 + 0.570080i
\(691\) 1.45928 6.39352i 0.0555136 0.243221i −0.939557 0.342393i \(-0.888762\pi\)
0.995070 + 0.0991725i \(0.0316196\pi\)
\(692\) 4.21164 2.02822i 0.160102 0.0771012i
\(693\) −6.79105 8.51571i −0.257971 0.323485i
\(694\) −12.4179 −0.471377
\(695\) −16.8358 −0.638618
\(696\) −6.71565 8.42116i −0.254556 0.319203i
\(697\) 16.3056 + 7.85236i 0.617618 + 0.297429i
\(698\) 3.60992 4.52669i 0.136637 0.171338i
\(699\) −30.3485 14.6150i −1.14788 0.552792i
\(700\) −2.88135 12.6240i −0.108905 0.477144i
\(701\) 22.3869 + 28.0722i 0.845540 + 1.06027i 0.997414 + 0.0718739i \(0.0228979\pi\)
−0.151874 + 0.988400i \(0.548531\pi\)
\(702\) 0.857724 + 3.75793i 0.0323727 + 0.141834i
\(703\) −24.9885 + 12.0338i −0.942457 + 0.453864i
\(704\) 35.8119 44.9067i 1.34971 1.69249i
\(705\) −1.93900 + 2.43143i −0.0730270 + 0.0915730i
\(706\) 11.9879 52.5225i 0.451171 1.97671i
\(707\) −35.2787 + 16.9893i −1.32679 + 0.638950i
\(708\) −13.9209 6.70394i −0.523179 0.251950i
\(709\) 9.32185 40.8417i 0.350089 1.53384i −0.426883 0.904307i \(-0.640388\pi\)
0.776972 0.629535i \(-0.216754\pi\)
\(710\) 8.81163 38.6063i 0.330694 1.44887i
\(711\) 1.94773 + 0.937977i 0.0730456 + 0.0351769i
\(712\) 10.6124 5.11065i 0.397715 0.191530i
\(713\) −1.75206 + 7.67628i −0.0656152 + 0.287479i
\(714\) −41.5773 + 52.1363i −1.55599 + 1.95115i
\(715\) 1.69202 2.12173i 0.0632780 0.0793481i
\(716\) 47.3107 22.7836i 1.76808 0.851465i
\(717\) −5.95175 26.0763i −0.222272 0.973837i
\(718\) 3.81282 + 4.78113i 0.142293 + 0.178430i
\(719\) −7.37076 32.2934i −0.274883 1.20434i −0.904171 0.427170i \(-0.859511\pi\)
0.629288 0.777172i \(-0.283346\pi\)
\(720\) 0.841166 + 0.405084i 0.0313484 + 0.0150966i
\(721\) 3.08277 3.86567i 0.114808 0.143965i
\(722\) 27.1259 + 13.0632i 1.00952 + 0.486161i
\(723\) −24.5179 30.7445i −0.911830 1.14340i
\(724\) 36.9976 1.37501
\(725\) 2.93900 0.109152
\(726\) 18.3233 + 22.9767i 0.680043 + 0.852747i
\(727\) 6.27048 3.01970i 0.232559 0.111995i −0.313975 0.949431i \(-0.601661\pi\)
0.546535 + 0.837437i \(0.315947\pi\)
\(728\) −0.685981 + 3.00548i −0.0254241 + 0.111390i
\(729\) −6.67755 29.2562i −0.247317 1.08356i
\(730\) 19.1293 0.708007
\(731\) −14.3666 + 25.7297i −0.531367 + 0.951646i
\(732\) −10.7560 −0.397553
\(733\) −8.59126 37.6408i −0.317325 1.39029i −0.842223 0.539129i \(-0.818754\pi\)
0.524898 0.851165i \(-0.324103\pi\)
\(734\) −9.72617 + 42.6131i −0.358999 + 1.57288i
\(735\) −30.9245 + 14.8925i −1.14067 + 0.549317i
\(736\) 8.92961 + 11.1974i 0.329150 + 0.412741i
\(737\) −18.4426 −0.679344
\(738\) −5.26742 −0.193896
\(739\) 21.4103 + 26.8477i 0.787590 + 0.987607i 0.999946 + 0.0104144i \(0.00331507\pi\)
−0.212356 + 0.977192i \(0.568113\pi\)
\(740\) 26.7700 + 12.8918i 0.984085 + 0.473910i
\(741\) −1.69955 + 2.13117i −0.0624347 + 0.0782906i
\(742\) 12.0869 + 5.82077i 0.443726 + 0.213687i
\(743\) 2.75475 + 12.0693i 0.101062 + 0.442781i 0.999989 + 0.00468306i \(0.00149067\pi\)
−0.898927 + 0.438098i \(0.855652\pi\)
\(744\) 8.18515 + 10.2639i 0.300082 + 0.376291i
\(745\) −2.77479 12.1572i −0.101660 0.445404i
\(746\) −36.2238 + 17.4445i −1.32625 + 0.638687i
\(747\) −3.68896 + 4.62582i −0.134972 + 0.169250i
\(748\) −37.6383 + 47.1970i −1.37619 + 1.72569i
\(749\) −14.7811 + 64.7603i −0.540091 + 2.36629i
\(750\) −37.7754 + 18.1917i −1.37936 + 0.664266i
\(751\) 16.5978 + 7.99310i 0.605664 + 0.291672i 0.711472 0.702714i \(-0.248029\pi\)
−0.105809 + 0.994387i \(0.533743\pi\)
\(752\) −0.178448 + 0.781831i −0.00650733 + 0.0285105i
\(753\) −0.671743 + 2.94310i −0.0244797 + 0.107252i
\(754\) −1.83244 0.882455i −0.0667334 0.0321371i
\(755\) −10.0978 + 4.86286i −0.367498 + 0.176978i
\(756\) 16.0492 70.3162i 0.583704 2.55738i
\(757\) 0.945870 1.18608i 0.0343782 0.0431089i −0.764345 0.644807i \(-0.776938\pi\)
0.798723 + 0.601698i \(0.205509\pi\)
\(758\) −6.77897 + 8.50056i −0.246223 + 0.308754i
\(759\) −13.5673 + 6.53368i −0.492463 + 0.237158i
\(760\) −5.97046 26.1583i −0.216571 0.948861i
\(761\) 3.67174 + 4.60422i 0.133101 + 0.166903i 0.843915 0.536476i \(-0.180245\pi\)
−0.710815 + 0.703379i \(0.751674\pi\)
\(762\) 11.3828 + 49.8715i 0.412357 + 1.80665i
\(763\) 34.2412 + 16.4897i 1.23962 + 0.596968i
\(764\) −30.4569 + 38.1917i −1.10189 + 1.38173i
\(765\) −4.71379 2.27004i −0.170427 0.0820736i
\(766\) 6.05980 + 7.59875i 0.218950 + 0.274554i
\(767\) −1.00372 −0.0362423
\(768\) 16.2755 0.587290
\(769\) 6.45175 + 8.09023i 0.232656 + 0.291741i 0.884431 0.466671i \(-0.154547\pi\)
−0.651775 + 0.758412i \(0.725975\pi\)
\(770\) −75.7609 + 36.4845i −2.73023 + 1.31481i
\(771\) 5.43817 23.8262i 0.195851 0.858079i
\(772\) −16.1386 70.7076i −0.580839 2.54482i
\(773\) 21.6601 0.779059 0.389530 0.921014i \(-0.372638\pi\)
0.389530 + 0.921014i \(0.372638\pi\)
\(774\) 0.518122 8.56133i 0.0186235 0.307730i
\(775\) −3.58211 −0.128673
\(776\) 9.56979 + 41.9280i 0.343535 + 1.50513i
\(777\) −7.16033 + 31.3714i −0.256875 + 1.12544i
\(778\) 60.1250 28.9547i 2.15559 1.03808i
\(779\) −14.2920 17.9216i −0.512064 0.642109i
\(780\) 2.92021 0.104560
\(781\) 38.8224 1.38917
\(782\) −13.8388 17.3533i −0.494874 0.620552i
\(783\) 14.7491 + 7.10281i 0.527091 + 0.253834i
\(784\) −5.51842 + 6.91988i −0.197086 + 0.247138i
\(785\) 19.0978 + 9.19703i 0.681631 + 0.328256i
\(786\) 8.15883 + 35.7462i 0.291016 + 1.27502i
\(787\) −20.7024 25.9600i −0.737960 0.925372i 0.261244 0.965273i \(-0.415867\pi\)
−0.999204 + 0.0399004i \(0.987296\pi\)
\(788\) −10.7569 47.1291i −0.383199 1.67890i
\(789\) −20.5620 + 9.90212i −0.732025 + 0.352525i
\(790\) 10.4058 13.0485i 0.370222 0.464244i
\(791\) −24.7446 + 31.0287i −0.879816 + 1.10325i
\(792\) 1.34505 5.89305i 0.0477943 0.209401i
\(793\) −0.629531 + 0.303166i −0.0223553 + 0.0107657i
\(794\) 16.8034 + 8.09211i 0.596331 + 0.287178i
\(795\) 0.972853 4.26235i 0.0345035 0.151170i
\(796\) −5.94212 + 26.0341i −0.210613 + 0.922755i
\(797\) 9.10872 + 4.38653i 0.322647 + 0.155379i 0.588195 0.808719i \(-0.299839\pi\)
−0.265548 + 0.964098i \(0.585553\pi\)
\(798\) 76.0982 36.6470i 2.69385 1.29729i
\(799\) 1.00000 4.38129i 0.0353775 0.154999i
\(800\) −4.06249 + 5.09420i −0.143631 + 0.180107i
\(801\) −1.81381 + 2.27445i −0.0640880 + 0.0803638i
\(802\) −1.89493 + 0.912549i −0.0669122 + 0.0322232i
\(803\) 4.17318 + 18.2839i 0.147268 + 0.645224i
\(804\) −12.3735 15.5158i −0.436378 0.547201i
\(805\) −4.15452 18.2021i −0.146428 0.641541i
\(806\) 2.23341 + 1.07555i 0.0786684 + 0.0378847i
\(807\) 14.6163 18.3282i 0.514516 0.645183i
\(808\) −19.5782 9.42837i −0.688759 0.331689i
\(809\) −23.3210 29.2436i −0.819923 1.02815i −0.999017 0.0443194i \(-0.985888\pi\)
0.179094 0.983832i \(-0.442683\pi\)
\(810\) −31.0750 −1.09186
\(811\) −53.9245 −1.89355 −0.946773 0.321902i \(-0.895678\pi\)
−0.946773 + 0.321902i \(0.895678\pi\)
\(812\) 23.7277 + 29.7535i 0.832678 + 1.04414i
\(813\) −32.4110 + 15.6083i −1.13670 + 0.547407i
\(814\) −10.7339 + 47.0285i −0.376224 + 1.64835i
\(815\) −10.4209 45.6569i −0.365027 1.59929i
\(816\) 5.60388 0.196175
\(817\) 30.5344 21.4665i 1.06826 0.751017i
\(818\) −7.69202 −0.268945
\(819\) −0.169423 0.742292i −0.00592013 0.0259378i
\(820\) −5.46442 + 23.9412i −0.190826 + 0.836062i
\(821\) 41.4146 19.9442i 1.44538 0.696058i 0.463593 0.886048i \(-0.346560\pi\)
0.981786 + 0.189990i \(0.0608455\pi\)
\(822\) −19.4943 24.4450i −0.679940 0.852618i
\(823\) 17.6420 0.614963 0.307481 0.951554i \(-0.400514\pi\)
0.307481 + 0.951554i \(0.400514\pi\)
\(824\) 2.74392 0.0955891
\(825\) −4.27144 5.35621i −0.148712 0.186479i
\(826\) 28.0209 + 13.4941i 0.974971 + 0.469521i
\(827\) 25.2611 31.6765i 0.878416 1.10150i −0.115711 0.993283i \(-0.536915\pi\)
0.994127 0.108216i \(-0.0345138\pi\)
\(828\) 3.51477 + 1.69262i 0.122147 + 0.0588228i
\(829\) 10.3216 + 45.2217i 0.358482 + 1.57061i 0.756976 + 0.653443i \(0.226676\pi\)
−0.398494 + 0.917171i \(0.630467\pi\)
\(830\) 28.4795 + 35.7121i 0.988537 + 1.23959i
\(831\) 7.19083 + 31.5051i 0.249447 + 1.09290i
\(832\) 3.61745 1.74207i 0.125412 0.0603955i
\(833\) 30.9245 38.7781i 1.07147 1.34358i
\(834\) 18.3379 22.9951i 0.634991 0.796254i
\(835\) 4.41252 19.3325i 0.152701 0.669029i
\(836\) 68.8887 33.1751i 2.38257 1.14738i
\(837\) −17.9765 8.65703i −0.621359 0.299231i
\(838\) 1.57606 6.90519i 0.0544442 0.238536i
\(839\) 1.01411 4.44309i 0.0350108 0.153392i −0.954401 0.298528i \(-0.903505\pi\)
0.989412 + 0.145135i \(0.0463617\pi\)
\(840\) −28.0465 13.5065i −0.967697 0.466018i
\(841\) 18.3458 8.83486i 0.632613 0.304650i
\(842\) 16.2322 71.1180i 0.559399 2.45089i
\(843\) −18.2619 + 22.8997i −0.628973 + 0.788707i
\(844\) 16.3225 20.4678i 0.561844 0.704530i
\(845\) −23.2543 + 11.1987i −0.799971 + 0.385246i
\(846\) 0.291053 + 1.27518i 0.0100066 + 0.0438418i
\(847\) −22.2724 27.9287i −0.765289 0.959642i
\(848\) −0.250864 1.09911i −0.00861472 0.0377436i
\(849\) −18.2736 8.80010i −0.627148 0.302019i
\(850\) 6.29590 7.89481i 0.215947 0.270790i
\(851\) −9.64968 4.64704i −0.330787 0.159298i
\(852\) 26.0465 + 32.6613i 0.892339 + 1.11896i
\(853\) −52.9197 −1.81194 −0.905969 0.423345i \(-0.860856\pi\)
−0.905969 + 0.423345i \(0.860856\pi\)
\(854\) 21.6504 0.740861
\(855\) 4.13169 + 5.18097i 0.141301 + 0.177185i
\(856\) −33.2129 + 15.9945i −1.13519 + 0.546680i
\(857\) −3.84535 + 16.8476i −0.131355 + 0.575502i 0.865818 + 0.500359i \(0.166799\pi\)
−0.997173 + 0.0751432i \(0.976059\pi\)
\(858\) 1.05496 + 4.62207i 0.0360157 + 0.157795i
\(859\) −14.8616 −0.507072 −0.253536 0.967326i \(-0.581594\pi\)
−0.253536 + 0.967326i \(0.581594\pi\)
\(860\) −38.3749 11.2365i −1.30857 0.383160i
\(861\) −26.5948 −0.906348
\(862\) 17.9574 + 78.6766i 0.611632 + 2.67974i
\(863\) −7.38178 + 32.3417i −0.251279 + 1.10092i 0.679019 + 0.734120i \(0.262405\pi\)
−0.930298 + 0.366804i \(0.880452\pi\)
\(864\) −32.6987 + 15.7468i −1.11243 + 0.535718i
\(865\) 1.91185 + 2.39739i 0.0650050 + 0.0815137i
\(866\) −59.6902 −2.02836
\(867\) −4.96913 −0.168761
\(868\) −28.9197 36.2641i −0.981598 1.23088i
\(869\) 14.7419 + 7.09932i 0.500085 + 0.240828i
\(870\) 12.8049 16.0569i 0.434128 0.544379i
\(871\) −1.16152 0.559360i −0.0393567 0.0189532i
\(872\) 4.69322 + 20.5623i 0.158932 + 0.696328i
\(873\) −6.62250 8.30435i −0.224138 0.281060i
\(874\) 6.25571 + 27.4081i 0.211603 + 0.927091i
\(875\) 45.9168 22.1123i 1.55227 0.747534i
\(876\) −12.5824 + 15.7778i −0.425120 + 0.533084i
\(877\) 13.7744 17.2726i 0.465129 0.583254i −0.492842 0.870119i \(-0.664042\pi\)
0.957971 + 0.286865i \(0.0926133\pi\)
\(878\) 20.0003 87.6270i 0.674977 2.95727i
\(879\) 37.1673 17.8988i 1.25362 0.603713i
\(880\) 6.36658 + 3.06599i 0.214618 + 0.103354i
\(881\) −8.01291 + 35.1069i −0.269962 + 1.18278i 0.640095 + 0.768296i \(0.278895\pi\)
−0.910057 + 0.414484i \(0.863962\pi\)
\(882\) −3.21230 + 14.0740i −0.108164 + 0.473896i
\(883\) −10.7235 5.16416i −0.360874 0.173788i 0.244657 0.969610i \(-0.421325\pi\)
−0.605531 + 0.795822i \(0.707039\pi\)
\(884\) −3.80194 + 1.83092i −0.127873 + 0.0615804i
\(885\) 2.25534 9.88129i 0.0758124 0.332156i
\(886\) −22.1362 + 27.7579i −0.743679 + 0.932544i
\(887\) −7.53833 + 9.45276i −0.253112 + 0.317393i −0.892112 0.451814i \(-0.850777\pi\)
0.639000 + 0.769207i \(0.279348\pi\)
\(888\) −16.0891 + 7.74810i −0.539915 + 0.260009i
\(889\) −13.8361 60.6198i −0.464047 2.03312i
\(890\) 14.0030 + 17.5592i 0.469381 + 0.588585i
\(891\) −6.77921 29.7017i −0.227112 0.995043i
\(892\) 20.8877 + 10.0590i 0.699372 + 0.336800i
\(893\) −3.54892 + 4.45020i −0.118760 + 0.148920i
\(894\) 19.6271 + 9.45193i 0.656430 + 0.316120i
\(895\) 21.4765 + 26.9307i 0.717880 + 0.900193i
\(896\) −69.0646 −2.30729
\(897\) −1.05264 −0.0351466
\(898\) 18.2412 + 22.8738i 0.608718 + 0.763308i
\(899\) 9.48523 4.56785i 0.316350 0.152346i
\(900\) −0.394928 + 1.73029i −0.0131643 + 0.0576764i
\(901\) 1.40581 + 6.15927i 0.0468344 + 0.205195i
\(902\) −39.8678 −1.32745
\(903\) 2.61596 43.2254i 0.0870536 1.43845i
\(904\) −22.0248 −0.732532
\(905\) 5.40044 + 23.6609i 0.179517 + 0.786514i
\(906\) 4.35690 19.0888i 0.144748 0.634183i
\(907\) −11.4547 + 5.51631i −0.380348 + 0.183166i −0.614282 0.789086i \(-0.710554\pi\)
0.233934 + 0.972252i \(0.424840\pi\)
\(908\) 29.4904 + 36.9798i 0.978672 + 1.22722i
\(909\) 5.36691 0.178009
\(910\) −5.87800 −0.194854
\(911\) 20.4556 + 25.6505i 0.677723 + 0.849838i 0.995142 0.0984477i \(-0.0313877\pi\)
−0.317419 + 0.948285i \(0.602816\pi\)
\(912\) −6.39493 3.07964i −0.211757 0.101977i
\(913\) −27.9209 + 35.0117i −0.924046 + 1.15872i
\(914\) −49.9342 24.0471i −1.65168 0.795406i
\(915\) −1.57002 6.87872i −0.0519034 0.227404i
\(916\) −44.9300 56.3405i −1.48453 1.86154i
\(917\) −9.91723 43.4502i −0.327496 1.43485i
\(918\) 50.6752 24.4039i 1.67253 0.805448i
\(919\) 5.43714 6.81796i 0.179355 0.224904i −0.684025 0.729459i \(-0.739772\pi\)
0.863380 + 0.504555i \(0.168343\pi\)
\(920\) 6.46011 8.10072i 0.212983 0.267073i
\(921\) −2.45071 + 10.7373i −0.0807538 + 0.353805i
\(922\) 20.5809 9.91124i 0.677796 0.326409i
\(923\) 2.44504 + 1.17747i 0.0804795 + 0.0387569i
\(924\) 19.7397 86.4855i 0.649390 2.84516i
\(925\) 1.08426 4.75046i 0.0356503 0.156194i
\(926\) 29.4964 + 14.2047i 0.969312 + 0.466796i
\(927\) −0.610580 + 0.294040i −0.0200541 + 0.00965754i
\(928\) 4.26122 18.6696i 0.139881 0.612860i
\(929\) −2.58844 + 3.24580i −0.0849240 + 0.106491i −0.822478 0.568797i \(-0.807409\pi\)
0.737554 + 0.675288i \(0.235981\pi\)
\(930\) −15.6069 + 19.5704i −0.511769 + 0.641738i
\(931\) −56.6006 + 27.2574i −1.85501 + 0.893325i
\(932\) 14.6969 + 64.3912i 0.481412 + 2.10920i
\(933\) 18.3403 + 22.9980i 0.600433 + 0.752920i
\(934\) 4.78352 + 20.9580i 0.156522 + 0.685766i
\(935\) −35.6775 17.1814i −1.16678 0.561892i
\(936\) 0.263446 0.330351i 0.00861100 0.0107979i
\(937\) −3.40581 1.64015i −0.111263 0.0535815i 0.377424 0.926040i \(-0.376810\pi\)
−0.488687 + 0.872459i \(0.662524\pi\)
\(938\) 24.9061 + 31.2313i 0.813213 + 1.01974i
\(939\) 28.9350 0.944256
\(940\) 6.09783 0.198889
\(941\) 36.2766 + 45.4894i 1.18258 + 1.48291i 0.839291 + 0.543683i \(0.182971\pi\)
0.343292 + 0.939229i \(0.388458\pi\)
\(942\) −33.3635 + 16.0670i −1.08704 + 0.523492i
\(943\) 1.96974 8.62998i 0.0641435 0.281031i
\(944\) −0.581573 2.54804i −0.0189286 0.0829315i
\(945\) 47.3116 1.53904
\(946\) 3.92154 64.7986i 0.127500 2.10678i
\(947\) −16.1105 −0.523521 −0.261761 0.965133i \(-0.584303\pi\)
−0.261761 + 0.965133i \(0.584303\pi\)
\(948\) 3.91789 + 17.1654i 0.127247 + 0.557507i
\(949\) −0.291717 + 1.27809i −0.00946952 + 0.0414887i
\(950\) −11.5233 + 5.54931i −0.373864 + 0.180043i
\(951\) 13.8745 + 17.3981i 0.449911 + 0.564171i
\(952\) 44.9831 1.45791
\(953\) 15.3381 0.496850 0.248425 0.968651i \(-0.420087\pi\)
0.248425 + 0.968651i \(0.420087\pi\)
\(954\) −1.14646 1.43761i −0.0371179 0.0465444i
\(955\) −28.8702 13.9032i −0.934219 0.449896i
\(956\) −32.6987 + 41.0028i −1.05755 + 1.32613i
\(957\) 18.1407 + 8.73611i 0.586406 + 0.282398i
\(958\) −12.3925 54.2952i −0.400385 1.75420i
\(959\) 23.6957 + 29.7134i 0.765173 + 0.959497i
\(960\) 9.02177 + 39.5270i 0.291176 + 1.27573i
\(961\) 16.3693 7.88303i 0.528041 0.254291i
\(962\) −2.10238 + 2.63631i −0.0677836 + 0.0849979i
\(963\) 5.67659 7.11822i 0.182925 0.229381i
\(964\) −17.1574 + 75.1715i −0.552603 + 2.42111i
\(965\) 42.8635 20.6420i 1.37983 0.664489i
\(966\) 29.3865 + 14.1518i 0.945495 + 0.455326i
\(967\) 11.7067 51.2902i 0.376461 1.64938i −0.331740 0.943371i \(-0.607636\pi\)
0.708200 0.706012i \(-0.249507\pi\)
\(968\) 4.41132 19.3273i 0.141785 0.621202i
\(969\) 35.8364 + 17.2579i 1.15123 + 0.554403i
\(970\) −73.8805 + 35.5790i −2.37216 + 1.14237i
\(971\) −2.03093 + 8.89807i −0.0651755 + 0.285553i −0.997004 0.0773455i \(-0.975356\pi\)
0.931829 + 0.362898i \(0.118213\pi\)
\(972\) −11.3256 + 14.2018i −0.363268 + 0.455523i
\(973\) −22.2902 + 27.9510i −0.714589 + 0.896067i
\(974\) 52.4478 25.2575i 1.68054 0.809303i
\(975\) −0.106564 0.466887i −0.00341278 0.0149523i
\(976\) −1.13437 1.42246i −0.0363105 0.0455319i
\(977\) 9.04689 + 39.6370i 0.289436 + 1.26810i 0.885302 + 0.465017i \(0.153952\pi\)
−0.595866 + 0.803084i \(0.703191\pi\)
\(978\) 73.7108 + 35.4972i 2.35701 + 1.13508i
\(979\) −13.7283 + 17.2148i −0.438759 + 0.550187i
\(980\) 60.6359 + 29.2007i 1.93694 + 0.932783i
\(981\) −3.24781 4.07262i −0.103695 0.130029i
\(982\) −55.5109 −1.77143
\(983\) −46.1135 −1.47079 −0.735396 0.677638i \(-0.763004\pi\)
−0.735396 + 0.677638i \(0.763004\pi\)
\(984\) −9.20208 11.5390i −0.293352 0.367851i
\(985\) 28.5700 13.7586i 0.910317 0.438385i
\(986\) −6.60388 + 28.9335i −0.210310 + 0.921429i
\(987\) 1.46950 + 6.43830i 0.0467747 + 0.204933i
\(988\) 5.34481 0.170041
\(989\) 13.8329 + 4.05036i 0.439859 + 0.128794i
\(990\) 11.5254 0.366302
\(991\) −8.03827 35.2180i −0.255344 1.11874i −0.926166 0.377117i \(-0.876916\pi\)
0.670822 0.741619i \(-0.265942\pi\)
\(992\) −5.19364 + 22.7548i −0.164898 + 0.722467i
\(993\) 27.2724 13.1337i 0.865463 0.416785i
\(994\) −52.4282 65.7429i −1.66292 2.08524i
\(995\) −17.5168 −0.555320
\(996\) −48.1879 −1.52689
\(997\) −12.4936 15.6665i −0.395676 0.496162i 0.543591 0.839351i \(-0.317064\pi\)
−0.939267 + 0.343189i \(0.888493\pi\)
\(998\) −56.8488 27.3769i −1.79952 0.866601i
\(999\) 16.9219 21.2194i 0.535386 0.671352i
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 43.2.e.b.16.1 6
3.2 odd 2 387.2.u.a.145.1 6
4.3 odd 2 688.2.u.c.145.1 6
43.11 even 7 1849.2.a.i.1.1 3
43.32 odd 14 1849.2.a.l.1.3 3
43.35 even 7 inner 43.2.e.b.35.1 yes 6
129.35 odd 14 387.2.u.a.379.1 6
172.35 odd 14 688.2.u.c.465.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.2.e.b.16.1 6 1.1 even 1 trivial
43.2.e.b.35.1 yes 6 43.35 even 7 inner
387.2.u.a.145.1 6 3.2 odd 2
387.2.u.a.379.1 6 129.35 odd 14
688.2.u.c.145.1 6 4.3 odd 2
688.2.u.c.465.1 6 172.35 odd 14
1849.2.a.i.1.1 3 43.11 even 7
1849.2.a.l.1.3 3 43.32 odd 14