Properties

Label 55.2.g.b.16.1
Level $55$
Weight $2$
Character 55.16
Analytic conductor $0.439$
Analytic rank $0$
Dimension $8$
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] = [55,2,Mod(16,55)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(55, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("55.16");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 55 = 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 55.g (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.439177211117\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.13140625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 16.1
Root \(1.69513 + 1.23158i\) of defining polynomial
Character \(\chi\) \(=\) 55.16
Dual form 55.2.g.b.31.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.647481 - 1.99274i) q^{2} +(-1.54765 - 1.12443i) q^{3} +(-1.93376 + 1.40496i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-1.23863 + 3.81211i) q^{6} +(2.48141 - 1.80285i) q^{7} +(0.661536 + 0.480634i) q^{8} +(0.203814 + 0.627276i) q^{9} +O(q^{10})\) \(q+(-0.647481 - 1.99274i) q^{2} +(-1.54765 - 1.12443i) q^{3} +(-1.93376 + 1.40496i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-1.23863 + 3.81211i) q^{6} +(2.48141 - 1.80285i) q^{7} +(0.661536 + 0.480634i) q^{8} +(0.203814 + 0.627276i) q^{9} +2.09529 q^{10} +(1.86337 - 2.74369i) q^{11} +4.57255 q^{12} +(0.942444 + 2.90055i) q^{13} +(-5.19927 - 3.77749i) q^{14} +(1.54765 - 1.12443i) q^{15} +(-0.947813 + 2.91707i) q^{16} +(-0.143336 + 0.441143i) q^{17} +(1.11803 - 0.812299i) q^{18} +(6.38769 + 4.64093i) q^{19} +(-0.738630 - 2.27327i) q^{20} -5.86752 q^{21} +(-6.67397 - 1.93673i) q^{22} -1.39026 q^{23} +(-0.483384 - 1.48770i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(5.16983 - 3.75610i) q^{26} +(-1.38355 + 4.25813i) q^{27} +(-2.26552 + 6.97254i) q^{28} +(-3.01085 + 2.18751i) q^{29} +(-3.24278 - 2.35601i) q^{30} +(-3.23741 - 9.96371i) q^{31} +8.06206 q^{32} +(-5.96893 + 2.15103i) q^{33} +0.971892 q^{34} +(0.947813 + 2.91707i) q^{35} +(-1.27542 - 0.926650i) q^{36} +(-1.49226 + 1.08419i) q^{37} +(5.11227 - 15.7340i) q^{38} +(1.80289 - 5.54873i) q^{39} +(-0.661536 + 0.480634i) q^{40} +(3.56585 + 2.59074i) q^{41} +(3.79911 + 11.6925i) q^{42} -1.31478 q^{43} +(0.251461 + 7.92360i) q^{44} -0.659557 q^{45} +(0.900166 + 2.77042i) q^{46} +(2.41102 + 1.75171i) q^{47} +(4.74692 - 3.44884i) q^{48} +(0.743998 - 2.28979i) q^{49} +(-0.647481 + 1.99274i) q^{50} +(0.717868 - 0.521562i) q^{51} +(-5.89760 - 4.28486i) q^{52} +(1.29421 + 3.98316i) q^{53} +9.38118 q^{54} +(2.03359 + 2.62002i) q^{55} +2.50805 q^{56} +(-4.66749 - 14.3650i) q^{57} +(6.30862 + 4.58348i) q^{58} +(-2.27740 + 1.65463i) q^{59} +(-1.41300 + 4.34876i) q^{60} +(-0.623402 + 1.91863i) q^{61} +(-17.7590 + 12.9026i) q^{62} +(1.63663 + 1.18908i) q^{63} +(-3.32441 - 10.2315i) q^{64} -3.04981 q^{65} +(8.15123 + 10.5018i) q^{66} -6.75753 q^{67} +(-0.342610 - 1.05444i) q^{68} +(2.15163 + 1.56325i) q^{69} +(5.19927 - 3.77749i) q^{70} +(-2.01539 + 6.20274i) q^{71} +(-0.166660 + 0.512925i) q^{72} +(7.98970 - 5.80485i) q^{73} +(3.12672 + 2.27169i) q^{74} +(0.591149 + 1.81937i) q^{75} -18.8726 q^{76} +(-0.322676 - 10.1676i) q^{77} -12.2245 q^{78} +(-3.57158 - 10.9922i) q^{79} +(-2.48141 - 1.80285i) q^{80} +(8.53000 - 6.19741i) q^{81} +(2.85386 - 8.78327i) q^{82} +(2.75600 - 8.48210i) q^{83} +(11.3464 - 8.24361i) q^{84} +(-0.375259 - 0.272641i) q^{85} +(0.851296 + 2.62002i) q^{86} +7.11945 q^{87} +(2.55140 - 0.919451i) q^{88} -6.76978 q^{89} +(0.427051 + 1.31433i) q^{90} +(7.56782 + 5.49835i) q^{91} +(2.68842 - 1.95325i) q^{92} +(-6.19315 + 19.0606i) q^{93} +(1.92961 - 5.93874i) q^{94} +(-6.38769 + 4.64093i) q^{95} +(-12.4772 - 9.06524i) q^{96} +(4.74475 + 14.6029i) q^{97} -5.04469 q^{98} +(2.10083 + 0.609644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + 2 q^{5} - 7 q^{6} - q^{7} + 4 q^{8} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + 2 q^{5} - 7 q^{6} - q^{7} + 4 q^{8} - 5 q^{9} + 2 q^{10} + 3 q^{11} + 16 q^{12} - 2 q^{13} - 16 q^{14} + 5 q^{15} + 4 q^{16} - 13 q^{17} + 15 q^{19} - 3 q^{20} - 20 q^{21} - 7 q^{22} + 10 q^{23} + 13 q^{24} - 2 q^{25} + 10 q^{26} + 10 q^{27} - 6 q^{28} - 9 q^{29} - 8 q^{30} - 10 q^{31} + 16 q^{32} + 5 q^{33} + 4 q^{34} - 4 q^{35} - 15 q^{36} + 24 q^{37} + 21 q^{39} - 4 q^{40} + 8 q^{41} + 9 q^{42} - 38 q^{43} - 12 q^{44} + 3 q^{46} + 5 q^{48} + q^{49} - 2 q^{50} + q^{51} - 28 q^{52} + 13 q^{53} + 16 q^{54} + 7 q^{55} + 22 q^{56} - 45 q^{57} + 12 q^{58} - 27 q^{59} + 4 q^{60} + 6 q^{61} - 30 q^{62} + 25 q^{63} - 26 q^{64} + 2 q^{65} + 13 q^{66} - 38 q^{67} + 11 q^{68} - q^{69} + 16 q^{70} - 20 q^{71} - 30 q^{72} + 13 q^{73} + 20 q^{74} + 5 q^{75} + 34 q^{77} - 16 q^{78} + 37 q^{79} + q^{80} + 8 q^{81} + 28 q^{82} + 27 q^{83} + 28 q^{84} - 12 q^{85} - 3 q^{86} + 38 q^{87} - 36 q^{88} - 16 q^{89} - 10 q^{90} + 44 q^{91} + 11 q^{92} - 35 q^{93} + 17 q^{94} - 15 q^{95} - 17 q^{96} + 24 q^{97} + 16 q^{98} - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/55\mathbb{Z}\right)^\times\).

\(n\) \(12\) \(46\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.647481 1.99274i −0.457839 1.40908i −0.867770 0.496966i \(-0.834447\pi\)
0.409932 0.912116i \(-0.365553\pi\)
\(3\) −1.54765 1.12443i −0.893534 0.649191i 0.0432627 0.999064i \(-0.486225\pi\)
−0.936797 + 0.349873i \(0.886225\pi\)
\(4\) −1.93376 + 1.40496i −0.966879 + 0.702479i
\(5\) −0.309017 + 0.951057i −0.138197 + 0.425325i
\(6\) −1.23863 + 3.81211i −0.505669 + 1.55629i
\(7\) 2.48141 1.80285i 0.937883 0.681412i −0.0100271 0.999950i \(-0.503192\pi\)
0.947910 + 0.318538i \(0.103192\pi\)
\(8\) 0.661536 + 0.480634i 0.233888 + 0.169930i
\(9\) 0.203814 + 0.627276i 0.0679381 + 0.209092i
\(10\) 2.09529 0.662590
\(11\) 1.86337 2.74369i 0.561828 0.827254i
\(12\) 4.57255 1.31998
\(13\) 0.942444 + 2.90055i 0.261387 + 0.804467i 0.992504 + 0.122214i \(0.0389995\pi\)
−0.731117 + 0.682252i \(0.761001\pi\)
\(14\) −5.19927 3.77749i −1.38956 1.00958i
\(15\) 1.54765 1.12443i 0.399601 0.290327i
\(16\) −0.947813 + 2.91707i −0.236953 + 0.729267i
\(17\) −0.143336 + 0.441143i −0.0347641 + 0.106993i −0.966933 0.255031i \(-0.917914\pi\)
0.932169 + 0.362024i \(0.117914\pi\)
\(18\) 1.11803 0.812299i 0.263523 0.191461i
\(19\) 6.38769 + 4.64093i 1.46544 + 1.06470i 0.981904 + 0.189377i \(0.0606468\pi\)
0.483533 + 0.875326i \(0.339353\pi\)
\(20\) −0.738630 2.27327i −0.165163 0.508318i
\(21\) −5.86752 −1.28040
\(22\) −6.67397 1.93673i −1.42290 0.412912i
\(23\) −1.39026 −0.289889 −0.144944 0.989440i \(-0.546300\pi\)
−0.144944 + 0.989440i \(0.546300\pi\)
\(24\) −0.483384 1.48770i −0.0986703 0.303676i
\(25\) −0.809017 0.587785i −0.161803 0.117557i
\(26\) 5.16983 3.75610i 1.01389 0.736632i
\(27\) −1.38355 + 4.25813i −0.266264 + 0.819477i
\(28\) −2.26552 + 6.97254i −0.428142 + 1.31769i
\(29\) −3.01085 + 2.18751i −0.559101 + 0.406211i −0.831130 0.556078i \(-0.812305\pi\)
0.272029 + 0.962289i \(0.412305\pi\)
\(30\) −3.24278 2.35601i −0.592047 0.430147i
\(31\) −3.23741 9.96371i −0.581456 1.78954i −0.613061 0.790036i \(-0.710062\pi\)
0.0316054 0.999500i \(-0.489938\pi\)
\(32\) 8.06206 1.42518
\(33\) −5.96893 + 2.15103i −1.03906 + 0.374447i
\(34\) 0.971892 0.166678
\(35\) 0.947813 + 2.91707i 0.160210 + 0.493074i
\(36\) −1.27542 0.926650i −0.212571 0.154442i
\(37\) −1.49226 + 1.08419i −0.245326 + 0.178240i −0.703653 0.710544i \(-0.748449\pi\)
0.458327 + 0.888784i \(0.348449\pi\)
\(38\) 5.11227 15.7340i 0.829320 2.55238i
\(39\) 1.80289 5.54873i 0.288694 0.888509i
\(40\) −0.661536 + 0.480634i −0.104598 + 0.0759949i
\(41\) 3.56585 + 2.59074i 0.556892 + 0.404605i 0.830320 0.557287i \(-0.188158\pi\)
−0.273428 + 0.961892i \(0.588158\pi\)
\(42\) 3.79911 + 11.6925i 0.586215 + 1.80418i
\(43\) −1.31478 −0.200502 −0.100251 0.994962i \(-0.531965\pi\)
−0.100251 + 0.994962i \(0.531965\pi\)
\(44\) 0.251461 + 7.92360i 0.0379092 + 1.19453i
\(45\) −0.659557 −0.0983210
\(46\) 0.900166 + 2.77042i 0.132722 + 0.408477i
\(47\) 2.41102 + 1.75171i 0.351683 + 0.255513i 0.749575 0.661920i \(-0.230258\pi\)
−0.397892 + 0.917432i \(0.630258\pi\)
\(48\) 4.74692 3.44884i 0.685159 0.497797i
\(49\) 0.743998 2.28979i 0.106285 0.327113i
\(50\) −0.647481 + 1.99274i −0.0915677 + 0.281816i
\(51\) 0.717868 0.521562i 0.100522 0.0730333i
\(52\) −5.89760 4.28486i −0.817850 0.594203i
\(53\) 1.29421 + 3.98316i 0.177773 + 0.547129i 0.999749 0.0223927i \(-0.00712841\pi\)
−0.821976 + 0.569522i \(0.807128\pi\)
\(54\) 9.38118 1.27662
\(55\) 2.03359 + 2.62002i 0.274210 + 0.353283i
\(56\) 2.50805 0.335152
\(57\) −4.66749 14.3650i −0.618224 1.90270i
\(58\) 6.30862 + 4.58348i 0.828363 + 0.601841i
\(59\) −2.27740 + 1.65463i −0.296493 + 0.215414i −0.726079 0.687611i \(-0.758659\pi\)
0.429586 + 0.903026i \(0.358659\pi\)
\(60\) −1.41300 + 4.34876i −0.182417 + 0.561422i
\(61\) −0.623402 + 1.91863i −0.0798185 + 0.245656i −0.983001 0.183601i \(-0.941225\pi\)
0.903182 + 0.429257i \(0.141225\pi\)
\(62\) −17.7590 + 12.9026i −2.25539 + 1.63864i
\(63\) 1.63663 + 1.18908i 0.206196 + 0.149810i
\(64\) −3.32441 10.2315i −0.415551 1.27894i
\(65\) −3.04981 −0.378283
\(66\) 8.15123 + 10.5018i 1.00335 + 1.29268i
\(67\) −6.75753 −0.825564 −0.412782 0.910830i \(-0.635443\pi\)
−0.412782 + 0.910830i \(0.635443\pi\)
\(68\) −0.342610 1.05444i −0.0415476 0.127870i
\(69\) 2.15163 + 1.56325i 0.259025 + 0.188193i
\(70\) 5.19927 3.77749i 0.621432 0.451497i
\(71\) −2.01539 + 6.20274i −0.239183 + 0.736130i 0.757356 + 0.653003i \(0.226491\pi\)
−0.996539 + 0.0831276i \(0.973509\pi\)
\(72\) −0.166660 + 0.512925i −0.0196410 + 0.0604488i
\(73\) 7.98970 5.80485i 0.935123 0.679407i −0.0121186 0.999927i \(-0.503858\pi\)
0.947242 + 0.320520i \(0.103858\pi\)
\(74\) 3.12672 + 2.27169i 0.363474 + 0.264079i
\(75\) 0.591149 + 1.81937i 0.0682600 + 0.210083i
\(76\) −18.8726 −2.16483
\(77\) −0.322676 10.1676i −0.0367723 1.15870i
\(78\) −12.2245 −1.38416
\(79\) −3.57158 10.9922i −0.401834 1.23672i −0.923510 0.383573i \(-0.874693\pi\)
0.521677 0.853143i \(-0.325307\pi\)
\(80\) −2.48141 1.80285i −0.277430 0.201564i
\(81\) 8.53000 6.19741i 0.947777 0.688601i
\(82\) 2.85386 8.78327i 0.315156 0.969950i
\(83\) 2.75600 8.48210i 0.302510 0.931032i −0.678084 0.734984i \(-0.737189\pi\)
0.980594 0.196047i \(-0.0628106\pi\)
\(84\) 11.3464 8.24361i 1.23799 0.899452i
\(85\) −0.375259 0.272641i −0.0407025 0.0295721i
\(86\) 0.851296 + 2.62002i 0.0917976 + 0.282524i
\(87\) 7.11945 0.763285
\(88\) 2.55140 0.919451i 0.271980 0.0980138i
\(89\) −6.76978 −0.717595 −0.358797 0.933415i \(-0.616813\pi\)
−0.358797 + 0.933415i \(0.616813\pi\)
\(90\) 0.427051 + 1.31433i 0.0450151 + 0.138542i
\(91\) 7.56782 + 5.49835i 0.793324 + 0.576383i
\(92\) 2.68842 1.95325i 0.280287 0.203641i
\(93\) −6.19315 + 19.0606i −0.642200 + 1.97649i
\(94\) 1.92961 5.93874i 0.199024 0.612534i
\(95\) −6.38769 + 4.64093i −0.655364 + 0.476150i
\(96\) −12.4772 9.06524i −1.27345 0.925217i
\(97\) 4.74475 + 14.6029i 0.481757 + 1.48269i 0.836624 + 0.547778i \(0.184526\pi\)
−0.354867 + 0.934917i \(0.615474\pi\)
\(98\) −5.04469 −0.509591
\(99\) 2.10083 + 0.609644i 0.211142 + 0.0612716i
\(100\) 2.39026 0.239026
\(101\) 3.62557 + 11.1584i 0.360758 + 1.11030i 0.952595 + 0.304241i \(0.0984027\pi\)
−0.591838 + 0.806057i \(0.701597\pi\)
\(102\) −1.50415 1.09283i −0.148933 0.108206i
\(103\) −11.2357 + 8.16319i −1.10708 + 0.804343i −0.982202 0.187828i \(-0.939855\pi\)
−0.124882 + 0.992172i \(0.539855\pi\)
\(104\) −0.770639 + 2.37178i −0.0755674 + 0.232573i
\(105\) 1.81316 5.58034i 0.176947 0.544585i
\(106\) 7.09944 5.15804i 0.689559 0.500994i
\(107\) 5.92282 + 4.30318i 0.572580 + 0.416004i 0.836042 0.548666i \(-0.184864\pi\)
−0.263461 + 0.964670i \(0.584864\pi\)
\(108\) −3.30704 10.1780i −0.318220 0.979380i
\(109\) −7.43306 −0.711958 −0.355979 0.934494i \(-0.615853\pi\)
−0.355979 + 0.934494i \(0.615853\pi\)
\(110\) 3.90431 5.74884i 0.372261 0.548131i
\(111\) 3.52859 0.334919
\(112\) 2.90712 + 8.94719i 0.274697 + 0.845430i
\(113\) 2.45650 + 1.78475i 0.231088 + 0.167895i 0.697304 0.716776i \(-0.254383\pi\)
−0.466216 + 0.884671i \(0.654383\pi\)
\(114\) −25.6037 + 18.6022i −2.39801 + 1.74226i
\(115\) 0.429613 1.32221i 0.0400616 0.123297i
\(116\) 2.74890 8.46024i 0.255229 0.785514i
\(117\) −1.62736 + 1.18235i −0.150449 + 0.109308i
\(118\) 4.77183 + 3.46694i 0.439282 + 0.319157i
\(119\) 0.439638 + 1.35307i 0.0403016 + 0.124035i
\(120\) 1.56426 0.142797
\(121\) −4.05569 10.2250i −0.368699 0.929549i
\(122\) 4.22699 0.382693
\(123\) −2.60556 8.01910i −0.234936 0.723058i
\(124\) 20.2590 + 14.7190i 1.81931 + 1.32181i
\(125\) 0.809017 0.587785i 0.0723607 0.0525731i
\(126\) 1.30984 4.03129i 0.116690 0.359136i
\(127\) −0.139551 + 0.429495i −0.0123832 + 0.0381115i −0.957057 0.289899i \(-0.906378\pi\)
0.944674 + 0.328011i \(0.106378\pi\)
\(128\) −5.19153 + 3.77187i −0.458871 + 0.333389i
\(129\) 2.03482 + 1.47838i 0.179156 + 0.130164i
\(130\) 1.97470 + 6.07750i 0.173192 + 0.533032i
\(131\) 0.629003 0.0549563 0.0274781 0.999622i \(-0.491252\pi\)
0.0274781 + 0.999622i \(0.491252\pi\)
\(132\) 8.52037 12.5457i 0.741603 1.09196i
\(133\) 24.2173 2.09991
\(134\) 4.37538 + 13.4660i 0.377975 + 1.16329i
\(135\) −3.62218 2.63167i −0.311748 0.226498i
\(136\) −0.306850 + 0.222940i −0.0263122 + 0.0191169i
\(137\) 3.45586 10.6360i 0.295254 0.908698i −0.687882 0.725823i \(-0.741459\pi\)
0.983136 0.182876i \(-0.0585406\pi\)
\(138\) 1.72201 5.29981i 0.146588 0.451150i
\(139\) 1.92138 1.39596i 0.162969 0.118404i −0.503312 0.864105i \(-0.667885\pi\)
0.666281 + 0.745701i \(0.267885\pi\)
\(140\) −5.93120 4.30927i −0.501278 0.364199i
\(141\) −1.76173 5.42205i −0.148364 0.456619i
\(142\) 13.6654 1.14678
\(143\) 9.71433 + 2.81902i 0.812353 + 0.235738i
\(144\) −2.02298 −0.168582
\(145\) −1.15004 3.53947i −0.0955059 0.293937i
\(146\) −16.7408 12.1629i −1.38548 1.00661i
\(147\) −3.72616 + 2.70721i −0.307328 + 0.223287i
\(148\) 1.36243 4.19312i 0.111991 0.344672i
\(149\) −2.69473 + 8.29354i −0.220761 + 0.679433i 0.777933 + 0.628347i \(0.216268\pi\)
−0.998694 + 0.0510859i \(0.983732\pi\)
\(150\) 3.24278 2.35601i 0.264772 0.192368i
\(151\) −9.65596 7.01547i −0.785791 0.570911i 0.120920 0.992662i \(-0.461415\pi\)
−0.906711 + 0.421752i \(0.861415\pi\)
\(152\) 1.99510 + 6.14028i 0.161824 + 0.498043i
\(153\) −0.305932 −0.0247332
\(154\) −20.0525 + 7.22633i −1.61587 + 0.582315i
\(155\) 10.4765 0.841490
\(156\) 4.30938 + 13.2629i 0.345026 + 1.06188i
\(157\) −3.13520 2.27786i −0.250216 0.181793i 0.455606 0.890181i \(-0.349422\pi\)
−0.705823 + 0.708389i \(0.749422\pi\)
\(158\) −19.5921 + 14.2345i −1.55866 + 1.13243i
\(159\) 2.47581 7.61977i 0.196345 0.604287i
\(160\) −2.49131 + 7.66748i −0.196956 + 0.606167i
\(161\) −3.44979 + 2.50642i −0.271882 + 0.197534i
\(162\) −17.8729 12.9854i −1.40422 1.02023i
\(163\) −3.07046 9.44990i −0.240497 0.740173i −0.996345 0.0854258i \(-0.972775\pi\)
0.755848 0.654748i \(-0.227225\pi\)
\(164\) −10.5354 −0.822674
\(165\) −0.201252 6.34150i −0.0156675 0.493685i
\(166\) −18.6871 −1.45040
\(167\) 4.30152 + 13.2387i 0.332862 + 1.02444i 0.967766 + 0.251852i \(0.0810395\pi\)
−0.634904 + 0.772591i \(0.718960\pi\)
\(168\) −3.88157 2.82013i −0.299470 0.217577i
\(169\) 2.99226 2.17400i 0.230174 0.167231i
\(170\) −0.300331 + 0.924324i −0.0230343 + 0.0708924i
\(171\) −1.60924 + 4.95274i −0.123062 + 0.378745i
\(172\) 2.54247 1.84721i 0.193861 0.140848i
\(173\) −8.76256 6.36637i −0.666205 0.484026i 0.202548 0.979272i \(-0.435078\pi\)
−0.868753 + 0.495246i \(0.835078\pi\)
\(174\) −4.60971 14.1872i −0.349461 1.07553i
\(175\) −3.06719 −0.231857
\(176\) 6.23741 + 8.03609i 0.470162 + 0.605743i
\(177\) 5.38513 0.404771
\(178\) 4.38331 + 13.4904i 0.328543 + 1.01115i
\(179\) −18.3918 13.3624i −1.37466 0.998752i −0.997356 0.0726638i \(-0.976850\pi\)
−0.377307 0.926088i \(-0.623150\pi\)
\(180\) 1.27542 0.926650i 0.0950645 0.0690684i
\(181\) 0.741120 2.28093i 0.0550870 0.169540i −0.919728 0.392557i \(-0.871590\pi\)
0.974815 + 0.223017i \(0.0715905\pi\)
\(182\) 6.05677 18.6408i 0.448957 1.38175i
\(183\) 3.12218 2.26840i 0.230798 0.167685i
\(184\) −0.919704 0.668204i −0.0678015 0.0492607i
\(185\) −0.569992 1.75425i −0.0419066 0.128975i
\(186\) 41.9927 3.07906
\(187\) 0.943272 + 1.21528i 0.0689789 + 0.0888703i
\(188\) −7.12340 −0.519527
\(189\) 4.24360 + 13.0605i 0.308677 + 0.950009i
\(190\) 13.3841 + 9.72412i 0.970985 + 0.705462i
\(191\) −13.9525 + 10.1371i −1.00957 + 0.733494i −0.964118 0.265473i \(-0.914472\pi\)
−0.0454496 + 0.998967i \(0.514472\pi\)
\(192\) −6.35959 + 19.5728i −0.458964 + 1.41254i
\(193\) −0.799036 + 2.45918i −0.0575159 + 0.177016i −0.975687 0.219168i \(-0.929666\pi\)
0.918171 + 0.396184i \(0.129666\pi\)
\(194\) 26.0276 18.9102i 1.86867 1.35767i
\(195\) 4.72004 + 3.42931i 0.338009 + 0.245578i
\(196\) 1.77835 + 5.47319i 0.127025 + 0.390942i
\(197\) 0.144731 0.0103116 0.00515582 0.999987i \(-0.498359\pi\)
0.00515582 + 0.999987i \(0.498359\pi\)
\(198\) −0.145386 4.58116i −0.0103322 0.325569i
\(199\) −7.54177 −0.534622 −0.267311 0.963610i \(-0.586135\pi\)
−0.267311 + 0.963610i \(0.586135\pi\)
\(200\) −0.252684 0.777682i −0.0178675 0.0549904i
\(201\) 10.4583 + 7.59838i 0.737670 + 0.535948i
\(202\) 19.8882 14.4497i 1.39933 1.01667i
\(203\) −3.52740 + 10.8562i −0.247575 + 0.761957i
\(204\) −0.655412 + 2.01715i −0.0458880 + 0.141229i
\(205\) −3.56585 + 2.59074i −0.249050 + 0.180945i
\(206\) 23.5420 + 17.1043i 1.64025 + 1.19171i
\(207\) −0.283354 0.872075i −0.0196945 0.0606134i
\(208\) −9.35435 −0.648607
\(209\) 24.6359 8.87809i 1.70410 0.614110i
\(210\) −12.2942 −0.848379
\(211\) −0.701101 2.15777i −0.0482658 0.148547i 0.924019 0.382347i \(-0.124884\pi\)
−0.972285 + 0.233800i \(0.924884\pi\)
\(212\) −8.09886 5.88416i −0.556232 0.404126i
\(213\) 10.0937 7.33349i 0.691607 0.502482i
\(214\) 4.74021 14.5889i 0.324034 0.997275i
\(215\) 0.406289 1.25043i 0.0277087 0.0852786i
\(216\) −2.96187 + 2.15192i −0.201529 + 0.146420i
\(217\) −25.9964 18.8875i −1.76475 1.28216i
\(218\) 4.81277 + 14.8122i 0.325962 + 1.00321i
\(219\) −18.8924 −1.27663
\(220\) −7.61349 2.20937i −0.513302 0.148956i
\(221\) −1.41464 −0.0951591
\(222\) −2.28469 7.03156i −0.153339 0.471928i
\(223\) −6.94111 5.04301i −0.464811 0.337705i 0.330605 0.943769i \(-0.392747\pi\)
−0.795415 + 0.606065i \(0.792747\pi\)
\(224\) 20.0052 14.5347i 1.33666 0.971138i
\(225\) 0.203814 0.627276i 0.0135876 0.0418184i
\(226\) 1.96601 6.05076i 0.130777 0.402491i
\(227\) −5.01622 + 3.64450i −0.332938 + 0.241894i −0.741676 0.670758i \(-0.765969\pi\)
0.408738 + 0.912652i \(0.365969\pi\)
\(228\) 29.2081 + 21.2209i 1.93435 + 1.40539i
\(229\) 7.15865 + 22.0321i 0.473057 + 1.45592i 0.848560 + 0.529099i \(0.177470\pi\)
−0.375503 + 0.926821i \(0.622530\pi\)
\(230\) −2.91300 −0.192077
\(231\) −10.9334 + 16.0987i −0.719362 + 1.05921i
\(232\) −3.04318 −0.199794
\(233\) −8.61005 26.4990i −0.564063 1.73601i −0.670719 0.741711i \(-0.734014\pi\)
0.106656 0.994296i \(-0.465986\pi\)
\(234\) 3.40980 + 2.47736i 0.222905 + 0.161950i
\(235\) −2.41102 + 1.75171i −0.157278 + 0.114269i
\(236\) 2.07926 6.39931i 0.135348 0.416560i
\(237\) −6.83241 + 21.0280i −0.443813 + 1.36592i
\(238\) 2.41166 1.75217i 0.156325 0.113576i
\(239\) 13.1758 + 9.57280i 0.852274 + 0.619213i 0.925772 0.378082i \(-0.123416\pi\)
−0.0734982 + 0.997295i \(0.523416\pi\)
\(240\) 1.81316 + 5.58034i 0.117039 + 0.360209i
\(241\) 4.39063 0.282826 0.141413 0.989951i \(-0.454836\pi\)
0.141413 + 0.989951i \(0.454836\pi\)
\(242\) −17.7499 + 14.7025i −1.14101 + 0.945111i
\(243\) −6.73820 −0.432256
\(244\) −1.49009 4.58603i −0.0953933 0.293590i
\(245\) 1.94781 + 1.41517i 0.124441 + 0.0904118i
\(246\) −14.2930 + 10.3844i −0.911285 + 0.662087i
\(247\) −7.44119 + 22.9016i −0.473471 + 1.45720i
\(248\) 2.64724 8.14736i 0.168100 0.517358i
\(249\) −13.8029 + 10.0284i −0.874721 + 0.635522i
\(250\) −1.69513 1.23158i −0.107209 0.0778921i
\(251\) −0.824050 2.53616i −0.0520136 0.160081i 0.921676 0.387961i \(-0.126821\pi\)
−0.973689 + 0.227880i \(0.926821\pi\)
\(252\) −4.83545 −0.304605
\(253\) −2.59056 + 3.81444i −0.162867 + 0.239812i
\(254\) 0.946229 0.0593717
\(255\) 0.274201 + 0.843905i 0.0171712 + 0.0528474i
\(256\) −6.52905 4.74363i −0.408066 0.296477i
\(257\) 17.5012 12.7154i 1.09169 0.793162i 0.112010 0.993707i \(-0.464271\pi\)
0.979685 + 0.200545i \(0.0642713\pi\)
\(258\) 1.62853 5.01209i 0.101388 0.312039i
\(259\) −1.74827 + 5.38063i −0.108632 + 0.334336i
\(260\) 5.89760 4.28486i 0.365754 0.265736i
\(261\) −1.98583 1.44279i −0.122920 0.0893064i
\(262\) −0.407268 1.25344i −0.0251611 0.0774379i
\(263\) 22.1392 1.36516 0.682581 0.730810i \(-0.260858\pi\)
0.682581 + 0.730810i \(0.260858\pi\)
\(264\) −4.98252 1.44589i −0.306653 0.0889881i
\(265\) −4.18814 −0.257276
\(266\) −15.6803 48.2590i −0.961420 2.95895i
\(267\) 10.4772 + 7.61215i 0.641196 + 0.465856i
\(268\) 13.0674 9.49404i 0.798220 0.579941i
\(269\) 6.40233 19.7044i 0.390357 1.20140i −0.542162 0.840274i \(-0.682394\pi\)
0.932519 0.361121i \(-0.117606\pi\)
\(270\) −2.89894 + 8.92203i −0.176424 + 0.542977i
\(271\) 0.342305 0.248699i 0.0207935 0.0151074i −0.577340 0.816504i \(-0.695909\pi\)
0.598133 + 0.801396i \(0.295909\pi\)
\(272\) −1.15099 0.836242i −0.0697889 0.0507046i
\(273\) −5.52981 17.0190i −0.334679 1.03004i
\(274\) −23.4325 −1.41561
\(275\) −3.12020 + 1.12443i −0.188155 + 0.0678058i
\(276\) −6.35702 −0.382648
\(277\) −2.64906 8.15298i −0.159167 0.489865i 0.839392 0.543526i \(-0.182911\pi\)
−0.998559 + 0.0536607i \(0.982911\pi\)
\(278\) −4.02585 2.92495i −0.241455 0.175427i
\(279\) 5.59017 4.06150i 0.334675 0.243155i
\(280\) −0.775029 + 2.38529i −0.0463168 + 0.142549i
\(281\) −2.16654 + 6.66793i −0.129245 + 0.397776i −0.994651 0.103297i \(-0.967061\pi\)
0.865405 + 0.501072i \(0.167061\pi\)
\(282\) −9.66406 + 7.02135i −0.575487 + 0.418115i
\(283\) −8.05229 5.85033i −0.478659 0.347766i 0.322147 0.946690i \(-0.395595\pi\)
−0.800806 + 0.598924i \(0.795595\pi\)
\(284\) −4.81731 14.8261i −0.285855 0.879770i
\(285\) 15.1043 0.894702
\(286\) −0.672272 21.1834i −0.0397523 1.25260i
\(287\) 13.5190 0.798002
\(288\) 1.64316 + 5.05714i 0.0968244 + 0.297995i
\(289\) 13.5792 + 9.86589i 0.798778 + 0.580346i
\(290\) −6.30862 + 4.58348i −0.370455 + 0.269151i
\(291\) 9.07670 27.9352i 0.532086 1.63759i
\(292\) −7.29457 + 22.4504i −0.426882 + 1.31381i
\(293\) −17.6535 + 12.8260i −1.03133 + 0.749302i −0.968574 0.248727i \(-0.919988\pi\)
−0.0627522 + 0.998029i \(0.519988\pi\)
\(294\) 7.80740 + 5.67241i 0.455337 + 0.330822i
\(295\) −0.869890 2.67725i −0.0506470 0.155875i
\(296\) −1.50828 −0.0876670
\(297\) 9.10492 + 11.7305i 0.528321 + 0.680673i
\(298\) 18.2717 1.05845
\(299\) −1.31024 4.03250i −0.0757731 0.233206i
\(300\) −3.69927 2.68768i −0.213578 0.155173i
\(301\) −3.26250 + 2.37035i −0.188048 + 0.136625i
\(302\) −7.72797 + 23.7842i −0.444694 + 1.36863i
\(303\) 6.93570 21.3459i 0.398446 1.22629i
\(304\) −19.5922 + 14.2346i −1.12369 + 0.816410i
\(305\) −1.63209 1.18578i −0.0934531 0.0678976i
\(306\) 0.198085 + 0.609644i 0.0113238 + 0.0348511i
\(307\) −30.8674 −1.76170 −0.880849 0.473397i \(-0.843028\pi\)
−0.880849 + 0.473397i \(0.843028\pi\)
\(308\) 14.9090 + 19.2083i 0.849519 + 1.09449i
\(309\) 26.5678 1.51139
\(310\) −6.78332 20.8769i −0.385267 1.18573i
\(311\) 15.7071 + 11.4119i 0.890667 + 0.647107i 0.936052 0.351862i \(-0.114451\pi\)
−0.0453850 + 0.998970i \(0.514451\pi\)
\(312\) 3.85959 2.80415i 0.218506 0.158754i
\(313\) 0.324922 1.00001i 0.0183657 0.0565237i −0.941454 0.337142i \(-0.890540\pi\)
0.959819 + 0.280619i \(0.0905396\pi\)
\(314\) −2.50920 + 7.72252i −0.141602 + 0.435807i
\(315\) −1.63663 + 1.18908i −0.0922136 + 0.0669971i
\(316\) 22.3501 + 16.2383i 1.25729 + 0.913476i
\(317\) −7.36432 22.6650i −0.413621 1.27300i −0.913478 0.406887i \(-0.866614\pi\)
0.499857 0.866108i \(-0.333386\pi\)
\(318\) −16.7873 −0.941385
\(319\) 0.391524 + 12.3370i 0.0219211 + 0.690740i
\(320\) 10.7580 0.601391
\(321\) −4.32780 13.3196i −0.241554 0.743428i
\(322\) 7.22833 + 5.25169i 0.402819 + 0.292665i
\(323\) −2.96290 + 2.15267i −0.164860 + 0.119778i
\(324\) −7.78786 + 23.9686i −0.432659 + 1.33159i
\(325\) 0.942444 2.90055i 0.0522774 0.160893i
\(326\) −16.8432 + 12.2373i −0.932856 + 0.677760i
\(327\) 11.5038 + 8.35796i 0.636159 + 0.462196i
\(328\) 1.11374 + 3.42773i 0.0614959 + 0.189265i
\(329\) 9.14077 0.503947
\(330\) −12.5067 + 4.50705i −0.688470 + 0.248105i
\(331\) 25.6693 1.41091 0.705457 0.708753i \(-0.250742\pi\)
0.705457 + 0.708753i \(0.250742\pi\)
\(332\) 6.58755 + 20.2744i 0.361539 + 1.11270i
\(333\) −0.984230 0.715085i −0.0539354 0.0391864i
\(334\) 23.5962 17.1436i 1.29113 0.938059i
\(335\) 2.08819 6.42679i 0.114090 0.351133i
\(336\) 5.56131 17.1159i 0.303394 0.933751i
\(337\) 19.3292 14.0435i 1.05293 0.764996i 0.0801597 0.996782i \(-0.474457\pi\)
0.972767 + 0.231786i \(0.0744570\pi\)
\(338\) −6.26966 4.55518i −0.341025 0.247769i
\(339\) −1.79496 5.52433i −0.0974890 0.300040i
\(340\) 1.10871 0.0601282
\(341\) −33.3699 9.68365i −1.80708 0.524399i
\(342\) 10.9115 0.590026
\(343\) 4.35271 + 13.3963i 0.235024 + 0.723330i
\(344\) −0.869774 0.631928i −0.0468951 0.0340713i
\(345\) −2.15163 + 1.56325i −0.115840 + 0.0841625i
\(346\) −7.01295 + 21.5836i −0.377018 + 1.16034i
\(347\) −0.102641 + 0.315895i −0.00551004 + 0.0169582i −0.953774 0.300526i \(-0.902838\pi\)
0.948264 + 0.317484i \(0.102838\pi\)
\(348\) −13.7673 + 10.0025i −0.738004 + 0.536191i
\(349\) −0.988203 0.717971i −0.0528973 0.0384321i 0.561022 0.827801i \(-0.310408\pi\)
−0.613920 + 0.789368i \(0.710408\pi\)
\(350\) 1.98595 + 6.11211i 0.106153 + 0.326706i
\(351\) −13.6548 −0.728840
\(352\) 15.0226 22.1198i 0.800708 1.17899i
\(353\) −25.7038 −1.36808 −0.684039 0.729446i \(-0.739778\pi\)
−0.684039 + 0.729446i \(0.739778\pi\)
\(354\) −3.48677 10.7312i −0.185320 0.570356i
\(355\) −5.27637 3.83351i −0.280041 0.203461i
\(356\) 13.0911 9.51125i 0.693828 0.504095i
\(357\) 0.841026 2.58841i 0.0445118 0.136993i
\(358\) −14.7195 + 45.3019i −0.777949 + 2.39428i
\(359\) 14.5069 10.5399i 0.765643 0.556272i −0.134993 0.990847i \(-0.543101\pi\)
0.900636 + 0.434574i \(0.143101\pi\)
\(360\) −0.436320 0.317005i −0.0229961 0.0167077i
\(361\) 13.3931 + 41.2196i 0.704899 + 2.16945i
\(362\) −5.02517 −0.264117
\(363\) −5.22057 + 20.3851i −0.274009 + 1.06994i
\(364\) −22.3593 −1.17195
\(365\) 3.05179 + 9.39245i 0.159738 + 0.491623i
\(366\) −6.54188 4.75296i −0.341950 0.248441i
\(367\) 6.86929 4.99083i 0.358574 0.260519i −0.393883 0.919161i \(-0.628869\pi\)
0.752457 + 0.658641i \(0.228869\pi\)
\(368\) 1.31770 4.05547i 0.0686900 0.211406i
\(369\) −0.898338 + 2.76480i −0.0467656 + 0.143930i
\(370\) −3.12672 + 2.27169i −0.162550 + 0.118100i
\(371\) 10.3925 + 7.55058i 0.539551 + 0.392006i
\(372\) −14.8032 45.5596i −0.767511 2.36216i
\(373\) 35.8450 1.85598 0.927991 0.372604i \(-0.121535\pi\)
0.927991 + 0.372604i \(0.121535\pi\)
\(374\) 1.81100 2.66657i 0.0936443 0.137885i
\(375\) −1.91300 −0.0987867
\(376\) 0.753045 + 2.31763i 0.0388353 + 0.119523i
\(377\) −9.18254 6.67151i −0.472925 0.343600i
\(378\) 23.2785 16.9128i 1.19732 0.869902i
\(379\) 5.42373 16.6925i 0.278598 0.857438i −0.709646 0.704558i \(-0.751145\pi\)
0.988245 0.152880i \(-0.0488547\pi\)
\(380\) 5.83195 17.9489i 0.299172 0.920758i
\(381\) 0.698913 0.507790i 0.0358064 0.0260149i
\(382\) 29.2346 + 21.2402i 1.49577 + 1.08674i
\(383\) −6.68251 20.5666i −0.341460 1.05091i −0.963452 0.267882i \(-0.913676\pi\)
0.621991 0.783024i \(-0.286324\pi\)
\(384\) 12.2759 0.626450
\(385\) 9.76966 + 2.83507i 0.497908 + 0.144489i
\(386\) 5.41788 0.275763
\(387\) −0.267971 0.824730i −0.0136217 0.0419234i
\(388\) −29.6916 21.5722i −1.50736 1.09516i
\(389\) −28.9156 + 21.0084i −1.46608 + 1.06517i −0.484352 + 0.874873i \(0.660944\pi\)
−0.981727 + 0.190295i \(0.939056\pi\)
\(390\) 3.77759 11.6262i 0.191286 0.588717i
\(391\) 0.199274 0.613302i 0.0100777 0.0310160i
\(392\) 1.59273 1.15719i 0.0804451 0.0584468i
\(393\) −0.973475 0.707271i −0.0491053 0.0356771i
\(394\) −0.0937106 0.288411i −0.00472107 0.0145300i
\(395\) 11.5579 0.581539
\(396\) −4.91903 + 1.77268i −0.247191 + 0.0890804i
\(397\) −20.0447 −1.00601 −0.503007 0.864282i \(-0.667773\pi\)
−0.503007 + 0.864282i \(0.667773\pi\)
\(398\) 4.88315 + 15.0288i 0.244770 + 0.753326i
\(399\) −37.4799 27.2307i −1.87634 1.36324i
\(400\) 2.48141 1.80285i 0.124070 0.0901423i
\(401\) −6.45805 + 19.8758i −0.322500 + 0.992551i 0.650057 + 0.759885i \(0.274745\pi\)
−0.972557 + 0.232666i \(0.925255\pi\)
\(402\) 8.37008 25.7605i 0.417462 1.28481i
\(403\) 25.8491 18.7805i 1.28764 0.935523i
\(404\) −22.6880 16.4838i −1.12877 0.820099i
\(405\) 3.25817 + 10.0276i 0.161900 + 0.498276i
\(406\) 23.9176 1.18701
\(407\) 0.194050 + 6.11454i 0.00961869 + 0.303087i
\(408\) 0.725576 0.0359214
\(409\) 7.26134 + 22.3481i 0.359050 + 1.10504i 0.953624 + 0.301001i \(0.0973208\pi\)
−0.594574 + 0.804041i \(0.702679\pi\)
\(410\) 7.47150 + 5.42836i 0.368991 + 0.268088i
\(411\) −17.3079 + 12.5750i −0.853738 + 0.620277i
\(412\) 10.2581 31.5713i 0.505382 1.55541i
\(413\) −2.66812 + 8.21161i −0.131289 + 0.404067i
\(414\) −1.55435 + 1.12930i −0.0763924 + 0.0555023i
\(415\) 7.21531 + 5.24223i 0.354185 + 0.257331i
\(416\) 7.59804 + 23.3844i 0.372525 + 1.14651i
\(417\) −4.54328 −0.222485
\(418\) −33.6431 43.3447i −1.64554 2.12006i
\(419\) −10.1128 −0.494043 −0.247022 0.969010i \(-0.579452\pi\)
−0.247022 + 0.969010i \(0.579452\pi\)
\(420\) 4.33392 + 13.3384i 0.211474 + 0.650850i
\(421\) −7.21872 5.24471i −0.351819 0.255611i 0.397813 0.917467i \(-0.369769\pi\)
−0.749632 + 0.661855i \(0.769769\pi\)
\(422\) −3.84593 + 2.79423i −0.187217 + 0.136021i
\(423\) −0.607404 + 1.86940i −0.0295330 + 0.0908932i
\(424\) −1.05828 + 3.25704i −0.0513945 + 0.158176i
\(425\) 0.375259 0.272641i 0.0182027 0.0132250i
\(426\) −21.1492 15.3658i −1.02468 0.744476i
\(427\) 1.91209 + 5.88481i 0.0925325 + 0.284786i
\(428\) −17.4991 −0.845850
\(429\) −11.8646 15.2859i −0.572826 0.738012i
\(430\) −2.75485 −0.132851
\(431\) −5.44248 16.7502i −0.262155 0.806831i −0.992335 0.123576i \(-0.960564\pi\)
0.730180 0.683255i \(-0.239436\pi\)
\(432\) −11.1099 8.07181i −0.534525 0.388355i
\(433\) −7.39763 + 5.37469i −0.355507 + 0.258291i −0.751176 0.660102i \(-0.770513\pi\)
0.395668 + 0.918393i \(0.370513\pi\)
\(434\) −20.8057 + 64.0334i −0.998706 + 3.07370i
\(435\) −2.20003 + 6.77099i −0.105483 + 0.324644i
\(436\) 14.3737 10.4431i 0.688377 0.500135i
\(437\) −8.88054 6.45209i −0.424814 0.308645i
\(438\) 12.2325 + 37.6477i 0.584490 + 1.79888i
\(439\) 6.46946 0.308770 0.154385 0.988011i \(-0.450660\pi\)
0.154385 + 0.988011i \(0.450660\pi\)
\(440\) 0.0860245 + 2.71065i 0.00410106 + 0.129225i
\(441\) 1.58797 0.0756176
\(442\) 0.915954 + 2.81902i 0.0435675 + 0.134087i
\(443\) 33.0760 + 24.0311i 1.57149 + 1.14175i 0.925714 + 0.378224i \(0.123465\pi\)
0.645774 + 0.763529i \(0.276535\pi\)
\(444\) −6.82343 + 4.95751i −0.323826 + 0.235273i
\(445\) 2.09198 6.43844i 0.0991692 0.305211i
\(446\) −5.55518 + 17.0971i −0.263045 + 0.809571i
\(447\) 13.4960 9.80542i 0.638339 0.463781i
\(448\) −26.6950 19.3951i −1.26122 0.916330i
\(449\) −3.75788 11.5656i −0.177345 0.545813i 0.822387 0.568928i \(-0.192642\pi\)
−0.999733 + 0.0231150i \(0.992642\pi\)
\(450\) −1.38197 −0.0651465
\(451\) 13.7527 4.95608i 0.647589 0.233373i
\(452\) −7.25777 −0.341377
\(453\) 7.05561 + 21.7149i 0.331501 + 1.02026i
\(454\) 10.5105 + 7.63629i 0.493280 + 0.358389i
\(455\) −7.56782 + 5.49835i −0.354785 + 0.257766i
\(456\) 3.81662 11.7463i 0.178730 0.550073i
\(457\) −3.06001 + 9.41775i −0.143141 + 0.440544i −0.996767 0.0803428i \(-0.974398\pi\)
0.853626 + 0.520886i \(0.174398\pi\)
\(458\) 39.2691 28.5307i 1.83493 1.33315i
\(459\) −1.68013 1.22069i −0.0784218 0.0569767i
\(460\) 1.02689 + 3.16043i 0.0478788 + 0.147356i
\(461\) −3.12529 −0.145559 −0.0727796 0.997348i \(-0.523187\pi\)
−0.0727796 + 0.997348i \(0.523187\pi\)
\(462\) 39.1596 + 11.3638i 1.82187 + 0.528692i
\(463\) −24.3518 −1.13173 −0.565863 0.824499i \(-0.691457\pi\)
−0.565863 + 0.824499i \(0.691457\pi\)
\(464\) −3.52740 10.8562i −0.163755 0.503987i
\(465\) −16.2139 11.7801i −0.751901 0.546288i
\(466\) −47.2309 + 34.3152i −2.18793 + 1.58962i
\(467\) 10.2512 31.5501i 0.474371 1.45996i −0.372434 0.928059i \(-0.621477\pi\)
0.846805 0.531904i \(-0.178523\pi\)
\(468\) 1.48577 4.57274i 0.0686799 0.211375i
\(469\) −16.7682 + 12.1828i −0.774282 + 0.562549i
\(470\) 5.05179 + 3.67034i 0.233022 + 0.169300i
\(471\) 2.29089 + 7.05063i 0.105559 + 0.324876i
\(472\) −2.30185 −0.105951
\(473\) −2.44992 + 3.60735i −0.112648 + 0.165866i
\(474\) 46.3273 2.12788
\(475\) −2.43988 7.50919i −0.111949 0.344545i
\(476\) −2.75116 1.99883i −0.126099 0.0916163i
\(477\) −2.23476 + 1.62365i −0.102323 + 0.0743418i
\(478\) 10.5450 32.4543i 0.482318 1.48442i
\(479\) −5.34529 + 16.4511i −0.244232 + 0.751670i 0.751529 + 0.659700i \(0.229317\pi\)
−0.995762 + 0.0919705i \(0.970683\pi\)
\(480\) 12.4772 9.06524i 0.569505 0.413769i
\(481\) −4.55111 3.30658i −0.207513 0.150767i
\(482\) −2.84285 8.74941i −0.129488 0.398524i
\(483\) 8.15736 0.371173
\(484\) 22.2085 + 14.0747i 1.00948 + 0.639758i
\(485\) −15.3543 −0.697205
\(486\) 4.36286 + 13.4275i 0.197903 + 0.609084i
\(487\) −6.18138 4.49104i −0.280105 0.203508i 0.438858 0.898556i \(-0.355383\pi\)
−0.718963 + 0.695048i \(0.755383\pi\)
\(488\) −1.33456 + 0.969617i −0.0604128 + 0.0438925i
\(489\) −5.87378 + 18.0776i −0.265621 + 0.817499i
\(490\) 1.55889 4.79779i 0.0704237 0.216742i
\(491\) 24.8015 18.0193i 1.11928 0.813201i 0.135176 0.990822i \(-0.456840\pi\)
0.984099 + 0.177620i \(0.0568399\pi\)
\(492\) 16.3050 + 11.8463i 0.735087 + 0.534072i
\(493\) −0.533442 1.64177i −0.0240250 0.0739414i
\(494\) 50.4551 2.27008
\(495\) −1.22900 + 1.80962i −0.0552394 + 0.0813364i
\(496\) 32.1333 1.44283
\(497\) 6.18159 + 19.0250i 0.277282 + 0.853386i
\(498\) 28.9210 + 21.0124i 1.29598 + 0.941587i
\(499\) 30.3206 22.0292i 1.35734 0.986162i 0.358726 0.933443i \(-0.383211\pi\)
0.998609 0.0527188i \(-0.0167887\pi\)
\(500\) −0.738630 + 2.27327i −0.0330325 + 0.101664i
\(501\) 8.22879 25.3256i 0.367635 1.13147i
\(502\) −4.52037 + 3.28424i −0.201754 + 0.146583i
\(503\) −6.85800 4.98263i −0.305783 0.222164i 0.424302 0.905521i \(-0.360520\pi\)
−0.730085 + 0.683356i \(0.760520\pi\)
\(504\) 0.511176 + 1.57324i 0.0227696 + 0.0700776i
\(505\) −11.7326 −0.522093
\(506\) 9.27854 + 2.69255i 0.412481 + 0.119699i
\(507\) −7.07548 −0.314233
\(508\) −0.333563 1.02660i −0.0147995 0.0455481i
\(509\) 1.37309 + 0.997609i 0.0608612 + 0.0442183i 0.617800 0.786335i \(-0.288024\pi\)
−0.556939 + 0.830554i \(0.688024\pi\)
\(510\) 1.50415 1.09283i 0.0666047 0.0483911i
\(511\) 9.36041 28.8084i 0.414080 1.27441i
\(512\) −9.19138 + 28.2882i −0.406206 + 1.25017i
\(513\) −28.5994 + 20.7787i −1.26269 + 0.917400i
\(514\) −36.6701 26.6424i −1.61745 1.17515i
\(515\) −4.29165 13.2083i −0.189112 0.582028i
\(516\) −6.01190 −0.264659
\(517\) 9.29877 3.35101i 0.408959 0.147377i
\(518\) 11.8542 0.520843
\(519\) 6.40280 + 19.7058i 0.281052 + 0.864988i
\(520\) −2.01756 1.46584i −0.0884759 0.0642815i
\(521\) 30.0088 21.8027i 1.31471 0.955192i 0.314728 0.949182i \(-0.398087\pi\)
0.999982 0.00601047i \(-0.00191320\pi\)
\(522\) −1.58932 + 4.89143i −0.0695627 + 0.214092i
\(523\) −5.58759 + 17.1968i −0.244328 + 0.751965i 0.751418 + 0.659826i \(0.229370\pi\)
−0.995746 + 0.0921382i \(0.970630\pi\)
\(524\) −1.21634 + 0.883723i −0.0531361 + 0.0386056i
\(525\) 4.74692 + 3.44884i 0.207173 + 0.150520i
\(526\) −14.3347 44.1177i −0.625023 1.92362i
\(527\) 4.85946 0.211681
\(528\) −0.617278 19.4506i −0.0268636 0.846477i
\(529\) −21.0672 −0.915965
\(530\) 2.71174 + 8.34589i 0.117791 + 0.362522i
\(531\) −1.50208 1.09132i −0.0651846 0.0473594i
\(532\) −46.8305 + 34.0244i −2.03036 + 1.47514i
\(533\) −4.15394 + 12.7845i −0.179927 + 0.553759i
\(534\) 8.38525 25.8071i 0.362865 1.11678i
\(535\) −5.92282 + 4.30318i −0.256066 + 0.186043i
\(536\) −4.47035 3.24790i −0.193090 0.140288i
\(537\) 13.4388 + 41.3605i 0.579929 + 1.78484i
\(538\) −43.4111 −1.87159
\(539\) −4.89614 6.30803i −0.210892 0.271706i
\(540\) 10.7018 0.460532
\(541\) 3.63169 + 11.1772i 0.156139 + 0.480545i 0.998274 0.0587201i \(-0.0187019\pi\)
−0.842136 + 0.539265i \(0.818702\pi\)
\(542\) −0.717229 0.521098i −0.0308076 0.0223831i
\(543\) −3.71174 + 2.69674i −0.159286 + 0.115728i
\(544\) −1.15558 + 3.55652i −0.0495452 + 0.152485i
\(545\) 2.29694 7.06926i 0.0983902 0.302814i
\(546\) −30.3340 + 22.0390i −1.29818 + 0.943181i
\(547\) 17.6017 + 12.7884i 0.752593 + 0.546791i 0.896629 0.442782i \(-0.146008\pi\)
−0.144037 + 0.989572i \(0.546008\pi\)
\(548\) 8.26039 + 25.4229i 0.352866 + 1.08601i
\(549\) −1.33057 −0.0567874
\(550\) 4.26097 + 5.48971i 0.181689 + 0.234082i
\(551\) −29.3845 −1.25182
\(552\) 0.672028 + 2.06829i 0.0286034 + 0.0880322i
\(553\) −28.6797 20.8370i −1.21959 0.886081i
\(554\) −14.5316 + 10.5578i −0.617388 + 0.448558i
\(555\) −1.09039 + 3.35588i −0.0462846 + 0.142449i
\(556\) −1.75421 + 5.39891i −0.0743952 + 0.228965i
\(557\) −3.91104 + 2.84154i −0.165716 + 0.120400i −0.667552 0.744563i \(-0.732658\pi\)
0.501836 + 0.864963i \(0.332658\pi\)
\(558\) −11.7130 8.51003i −0.495853 0.360258i
\(559\) −1.23911 3.81358i −0.0524086 0.161297i
\(560\) −9.40763 −0.397545
\(561\) −0.0933499 2.94147i −0.00394124 0.124189i
\(562\) 14.6903 0.619672
\(563\) 1.47463 + 4.53843i 0.0621481 + 0.191272i 0.977310 0.211815i \(-0.0679373\pi\)
−0.915162 + 0.403087i \(0.867937\pi\)
\(564\) 11.0245 + 8.00978i 0.464216 + 0.337272i
\(565\) −2.45650 + 1.78475i −0.103346 + 0.0750850i
\(566\) −6.44449 + 19.8341i −0.270882 + 0.833690i
\(567\) 9.99341 30.7566i 0.419684 1.29165i
\(568\) −4.31450 + 3.13467i −0.181032 + 0.131528i
\(569\) −28.8971 20.9949i −1.21143 0.880154i −0.216068 0.976378i \(-0.569323\pi\)
−0.995360 + 0.0962246i \(0.969323\pi\)
\(570\) −9.77976 30.0990i −0.409629 1.26071i
\(571\) −33.9838 −1.42218 −0.711090 0.703101i \(-0.751798\pi\)
−0.711090 + 0.703101i \(0.751798\pi\)
\(572\) −22.7458 + 8.19692i −0.951048 + 0.342731i
\(573\) 32.9920 1.37826
\(574\) −8.75331 26.9399i −0.365356 1.12445i
\(575\) 1.12474 + 0.817172i 0.0469050 + 0.0340784i
\(576\) 5.74040 4.17065i 0.239183 0.173777i
\(577\) −6.38364 + 19.6468i −0.265755 + 0.817909i 0.725764 + 0.687944i \(0.241486\pi\)
−0.991519 + 0.129965i \(0.958514\pi\)
\(578\) 10.8679 33.4479i 0.452044 1.39125i
\(579\) 4.00181 2.90748i 0.166309 0.120831i
\(580\) 7.19671 + 5.22872i 0.298827 + 0.217111i
\(581\) −8.45317 26.0162i −0.350697 1.07933i
\(582\) −61.5447 −2.55111
\(583\) 13.3402 + 3.87120i 0.552493 + 0.160329i
\(584\) 8.07548 0.334166
\(585\) −0.621596 1.91308i −0.0256998 0.0790959i
\(586\) 36.9892 + 26.8742i 1.52801 + 1.11016i
\(587\) −10.8085 + 7.85284i −0.446115 + 0.324121i −0.788060 0.615599i \(-0.788914\pi\)
0.341945 + 0.939720i \(0.388914\pi\)
\(588\) 3.40197 10.4702i 0.140295 0.431783i
\(589\) 25.5614 78.6698i 1.05324 3.24153i
\(590\) −4.77183 + 3.46694i −0.196453 + 0.142731i
\(591\) −0.223992 0.162740i −0.00921381 0.00669423i
\(592\) −1.74827 5.38063i −0.0718535 0.221142i
\(593\) 20.8062 0.854410 0.427205 0.904155i \(-0.359498\pi\)
0.427205 + 0.904155i \(0.359498\pi\)
\(594\) 17.4806 25.7391i 0.717238 1.05609i
\(595\) −1.42270 −0.0583250
\(596\) −6.44111 19.8237i −0.263838 0.812010i
\(597\) 11.6720 + 8.48020i 0.477703 + 0.347071i
\(598\) −7.18739 + 5.22194i −0.293914 + 0.213541i
\(599\) −4.40214 + 13.5484i −0.179867 + 0.553573i −0.999822 0.0188544i \(-0.993998\pi\)
0.819956 + 0.572427i \(0.193998\pi\)
\(600\) −0.483384 + 1.48770i −0.0197341 + 0.0607352i
\(601\) 16.7840 12.1943i 0.684634 0.497416i −0.190257 0.981734i \(-0.560932\pi\)
0.874892 + 0.484318i \(0.160932\pi\)
\(602\) 6.83590 + 4.96657i 0.278611 + 0.202422i
\(603\) −1.37728 4.23884i −0.0560872 0.172619i
\(604\) 28.5287 1.16082
\(605\) 10.9779 0.697484i 0.446314 0.0283568i
\(606\) −47.0276 −1.91037
\(607\) 5.53818 + 17.0448i 0.224788 + 0.691825i 0.998313 + 0.0580601i \(0.0184915\pi\)
−0.773525 + 0.633765i \(0.781508\pi\)
\(608\) 51.4980 + 37.4155i 2.08852 + 1.51740i
\(609\) 17.6662 12.8353i 0.715872 0.520111i
\(610\) −1.30621 + 4.02010i −0.0528869 + 0.162769i
\(611\) −2.80866 + 8.64416i −0.113626 + 0.349705i
\(612\) 0.591599 0.429822i 0.0239140 0.0173745i
\(613\) 22.8158 + 16.5766i 0.921521 + 0.669524i 0.943902 0.330225i \(-0.107125\pi\)
−0.0223811 + 0.999750i \(0.507125\pi\)
\(614\) 19.9861 + 61.5109i 0.806573 + 2.48238i
\(615\) 8.43178 0.340002
\(616\) 4.67342 6.88131i 0.188298 0.277256i
\(617\) −4.72930 −0.190394 −0.0951972 0.995458i \(-0.530348\pi\)
−0.0951972 + 0.995458i \(0.530348\pi\)
\(618\) −17.2022 52.9428i −0.691972 2.12967i
\(619\) 24.3170 + 17.6673i 0.977383 + 0.710110i 0.957122 0.289684i \(-0.0935503\pi\)
0.0202609 + 0.999795i \(0.493550\pi\)
\(620\) −20.2590 + 14.7190i −0.813619 + 0.591129i
\(621\) 1.92349 5.91989i 0.0771870 0.237557i
\(622\) 12.5709 38.6891i 0.504046 1.55129i
\(623\) −16.7986 + 12.2049i −0.673020 + 0.488978i
\(624\) 14.4772 + 10.5183i 0.579553 + 0.421070i
\(625\) 0.309017 + 0.951057i 0.0123607 + 0.0380423i
\(626\) −2.20314 −0.0880551
\(627\) −48.1105 13.9613i −1.92135 0.557560i
\(628\) 9.26301 0.369634
\(629\) −0.264388 0.813702i −0.0105418 0.0324444i
\(630\) 3.42922 + 2.49147i 0.136623 + 0.0992626i
\(631\) 25.6487 18.6349i 1.02106 0.741843i 0.0545601 0.998510i \(-0.482624\pi\)
0.966500 + 0.256667i \(0.0826244\pi\)
\(632\) 2.92049 8.98834i 0.116171 0.357537i
\(633\) −1.34120 + 4.12780i −0.0533081 + 0.164065i
\(634\) −40.3973 + 29.3504i −1.60438 + 1.16565i
\(635\) −0.365350 0.265442i −0.0144985 0.0105338i
\(636\) 5.91783 + 18.2132i 0.234657 + 0.722201i
\(637\) 7.34282 0.290933
\(638\) 24.3310 8.76819i 0.963272 0.347136i
\(639\) −4.30160 −0.170169
\(640\) −1.98299 6.10301i −0.0783845 0.241243i
\(641\) 15.3368 + 11.1428i 0.605768 + 0.440116i 0.847921 0.530122i \(-0.177854\pi\)
−0.242154 + 0.970238i \(0.577854\pi\)
\(642\) −23.7404 + 17.2484i −0.936958 + 0.680740i
\(643\) −11.2015 + 34.4747i −0.441745 + 1.35955i 0.444270 + 0.895893i \(0.353463\pi\)
−0.886015 + 0.463657i \(0.846537\pi\)
\(644\) 3.14965 9.69362i 0.124114 0.381982i
\(645\) −2.03482 + 1.47838i −0.0801208 + 0.0582112i
\(646\) 6.20815 + 4.51048i 0.244256 + 0.177463i
\(647\) −10.8007 33.2412i −0.424620 1.30685i −0.903357 0.428889i \(-0.858905\pi\)
0.478737 0.877958i \(-0.341095\pi\)
\(648\) 8.62158 0.338688
\(649\) 0.296148 + 9.33168i 0.0116248 + 0.366301i
\(650\) −6.39026 −0.250646
\(651\) 18.9955 + 58.4623i 0.744494 + 2.29132i
\(652\) 19.2142 + 13.9600i 0.752488 + 0.546714i
\(653\) 24.1000 17.5097i 0.943106 0.685207i −0.00605995 0.999982i \(-0.501929\pi\)
0.949166 + 0.314775i \(0.101929\pi\)
\(654\) 9.20681 28.3356i 0.360015 1.10801i
\(655\) −0.194373 + 0.598218i −0.00759477 + 0.0233743i
\(656\) −10.9371 + 7.94628i −0.427023 + 0.310250i
\(657\) 5.26966 + 3.82863i 0.205589 + 0.149369i
\(658\) −5.91848 18.2152i −0.230726 0.710103i
\(659\) −7.30532 −0.284575 −0.142287 0.989825i \(-0.545446\pi\)
−0.142287 + 0.989825i \(0.545446\pi\)
\(660\) 9.29871 + 11.9802i 0.361952 + 0.466328i
\(661\) −22.7352 −0.884296 −0.442148 0.896942i \(-0.645783\pi\)
−0.442148 + 0.896942i \(0.645783\pi\)
\(662\) −16.6204 51.1524i −0.645971 1.98809i
\(663\) 2.18937 + 1.59067i 0.0850279 + 0.0617764i
\(664\) 5.89998 4.28658i 0.228964 0.166352i
\(665\) −7.48357 + 23.0321i −0.290200 + 0.893145i
\(666\) −0.787710 + 2.42432i −0.0305231 + 0.0939405i
\(667\) 4.18586 3.04120i 0.162077 0.117756i
\(668\) −26.9179 19.5570i −1.04149 0.756684i
\(669\) 5.07186 + 15.6096i 0.196090 + 0.603502i
\(670\) −14.1590 −0.547010
\(671\) 4.10251 + 5.28555i 0.158376 + 0.204046i
\(672\) −47.3043 −1.82480
\(673\) −5.48354 16.8766i −0.211375 0.650546i −0.999391 0.0348910i \(-0.988892\pi\)
0.788016 0.615655i \(-0.211108\pi\)
\(674\) −40.5003 29.4252i −1.56001 1.13342i
\(675\) 3.62218 2.63167i 0.139418 0.101293i
\(676\) −2.73192 + 8.40799i −0.105074 + 0.323384i
\(677\) 2.52224 7.76267i 0.0969377 0.298344i −0.890816 0.454364i \(-0.849867\pi\)
0.987754 + 0.156020i \(0.0498665\pi\)
\(678\) −9.84636 + 7.15380i −0.378147 + 0.274740i
\(679\) 38.1004 + 27.6815i 1.46216 + 1.06232i
\(680\) −0.117206 0.360724i −0.00449466 0.0138331i
\(681\) 11.8613 0.454527
\(682\) 2.30933 + 72.7675i 0.0884289 + 2.78641i
\(683\) −6.19100 −0.236892 −0.118446 0.992960i \(-0.537791\pi\)
−0.118446 + 0.992960i \(0.537791\pi\)
\(684\) −3.84650 11.8383i −0.147075 0.452649i
\(685\) 9.04756 + 6.57343i 0.345689 + 0.251158i
\(686\) 23.8770 17.3477i 0.911628 0.662336i
\(687\) 13.6945 42.1473i 0.522477 1.60802i
\(688\) 1.24617 3.83530i 0.0475096 0.146220i
\(689\) −10.3336 + 7.50781i −0.393680 + 0.286025i
\(690\) 4.50829 + 3.27547i 0.171628 + 0.124695i
\(691\) 7.29438 + 22.4498i 0.277491 + 0.854030i 0.988549 + 0.150897i \(0.0482162\pi\)
−0.711058 + 0.703133i \(0.751784\pi\)
\(692\) 25.8892 0.984158
\(693\) 6.31212 2.27471i 0.239778 0.0864090i
\(694\) 0.695956 0.0264181
\(695\) 0.733901 + 2.25872i 0.0278385 + 0.0856779i
\(696\) 4.70977 + 3.42185i 0.178523 + 0.129705i
\(697\) −1.65400 + 1.20170i −0.0626497 + 0.0455177i
\(698\) −0.790889 + 2.43411i −0.0299356 + 0.0921323i
\(699\) −16.4710 + 50.6925i −0.622990 + 1.91737i
\(700\) 5.93120 4.30927i 0.224178 0.162875i
\(701\) −30.1184 21.8823i −1.13756 0.826483i −0.150779 0.988567i \(-0.548178\pi\)
−0.986777 + 0.162084i \(0.948178\pi\)
\(702\) 8.84124 + 27.2105i 0.333691 + 1.02700i
\(703\) −14.5637 −0.549282
\(704\) −34.2667 9.94389i −1.29147 0.374775i
\(705\) 5.70108 0.214715
\(706\) 16.6428 + 51.2211i 0.626358 + 1.92773i
\(707\) 29.1133 + 21.1521i 1.09492 + 0.795505i
\(708\) −10.4135 + 7.56588i −0.391365 + 0.284343i
\(709\) 5.64072 17.3603i 0.211842 0.651981i −0.787521 0.616288i \(-0.788636\pi\)
0.999363 0.0356939i \(-0.0113641\pi\)
\(710\) −4.22284 + 12.9966i −0.158480 + 0.487753i
\(711\) 6.16719 4.48073i 0.231288 0.168040i
\(712\) −4.47845 3.25378i −0.167837 0.121941i
\(713\) 4.50083 + 13.8521i 0.168557 + 0.518766i
\(714\) −5.70259 −0.213414
\(715\) −5.68294 + 8.36775i −0.212530 + 0.312936i
\(716\) 54.3388 2.03074
\(717\) −9.62758 29.6306i −0.359549 1.10658i
\(718\) −30.3961 22.0841i −1.13437 0.824171i
\(719\) −7.74544 + 5.62739i −0.288856 + 0.209866i −0.722771 0.691088i \(-0.757132\pi\)
0.433915 + 0.900954i \(0.357132\pi\)
\(720\) 0.625136 1.92397i 0.0232975 0.0717022i
\(721\) −13.1633 + 40.5124i −0.490226 + 1.50876i
\(722\) 73.4684 53.3779i 2.73421 1.98652i
\(723\) −6.79515 4.93697i −0.252714 0.183608i
\(724\) 1.77147 + 5.45202i 0.0658361 + 0.202623i
\(725\) 3.72162 0.138217
\(726\) 44.0025 2.79572i 1.63309 0.103759i
\(727\) −14.0175 −0.519882 −0.259941 0.965625i \(-0.583703\pi\)
−0.259941 + 0.965625i \(0.583703\pi\)
\(728\) 2.36369 + 7.27470i 0.0876043 + 0.269618i
\(729\) −15.1616 11.0156i −0.561542 0.407984i
\(730\) 16.7408 12.1629i 0.619603 0.450168i
\(731\) 0.188455 0.580006i 0.00697027 0.0214523i
\(732\) −2.85054 + 8.77306i −0.105359 + 0.324262i
\(733\) −7.51392 + 5.45918i −0.277533 + 0.201640i −0.717841 0.696207i \(-0.754869\pi\)
0.440308 + 0.897847i \(0.354869\pi\)
\(734\) −14.3932 10.4573i −0.531262 0.385984i
\(735\) −1.42327 4.38036i −0.0524980 0.161572i
\(736\) −11.2083 −0.413145
\(737\) −12.5918 + 18.5406i −0.463824 + 0.682951i
\(738\) 6.09119 0.224220
\(739\) −12.0389 37.0519i −0.442857 1.36298i −0.884816 0.465940i \(-0.845716\pi\)
0.441959 0.897035i \(-0.354284\pi\)
\(740\) 3.56688 + 2.59149i 0.131121 + 0.0952651i
\(741\) 37.2676 27.0765i 1.36906 0.994681i
\(742\) 8.31742 25.5984i 0.305342 0.939747i
\(743\) 14.1930 43.6817i 0.520692 1.60252i −0.251989 0.967730i \(-0.581085\pi\)
0.772681 0.634795i \(-0.218915\pi\)
\(744\) −13.2581 + 9.63260i −0.486067 + 0.353148i
\(745\) −7.05490 5.12569i −0.258472 0.187791i
\(746\) −23.2089 71.4298i −0.849740 2.61523i
\(747\) 5.88233 0.215223
\(748\) −3.53148 1.02481i −0.129124 0.0374706i
\(749\) 22.4549 0.820483
\(750\) 1.23863 + 3.81211i 0.0452284 + 0.139199i
\(751\) −18.7634 13.6324i −0.684686 0.497453i 0.190223 0.981741i \(-0.439079\pi\)
−0.874909 + 0.484288i \(0.839079\pi\)
\(752\) −7.39504 + 5.37281i −0.269669 + 0.195926i
\(753\) −1.57640 + 4.85167i −0.0574474 + 0.176805i
\(754\) −7.34907 + 22.6181i −0.267637 + 0.823703i
\(755\) 9.65596 7.01547i 0.351416 0.255319i
\(756\) −26.5555 19.2937i −0.965815 0.701705i
\(757\) −2.01541 6.20281i −0.0732515 0.225445i 0.907727 0.419561i \(-0.137816\pi\)
−0.980979 + 0.194116i \(0.937816\pi\)
\(758\) −36.7757 −1.33575
\(759\) 8.29835 2.99049i 0.301211 0.108548i
\(760\) −6.45628 −0.234194
\(761\) −2.02926 6.24542i −0.0735606 0.226396i 0.907516 0.420018i \(-0.137976\pi\)
−0.981076 + 0.193622i \(0.937976\pi\)
\(762\) −1.46443 1.06397i −0.0530507 0.0385436i
\(763\) −18.4444 + 13.4007i −0.667733 + 0.485137i
\(764\) 12.7386 39.2054i 0.460866 1.41840i
\(765\) 0.0945383 0.290959i 0.00341804 0.0105196i
\(766\) −36.6572 + 26.6330i −1.32448 + 0.962291i
\(767\) −6.94565 5.04631i −0.250793 0.182212i
\(768\) 4.77078 + 14.6829i 0.172151 + 0.529825i
\(769\) 12.5950 0.454188 0.227094 0.973873i \(-0.427078\pi\)
0.227094 + 0.973873i \(0.427078\pi\)
\(770\) −0.676101 21.3041i −0.0243650 0.767746i
\(771\) −41.3832 −1.49038
\(772\) −1.90990 5.87807i −0.0687389 0.211557i
\(773\) −17.7537 12.8988i −0.638557 0.463939i 0.220797 0.975320i \(-0.429134\pi\)
−0.859354 + 0.511381i \(0.829134\pi\)
\(774\) −1.46997 + 1.06799i −0.0528369 + 0.0383883i
\(775\) −3.23741 + 9.96371i −0.116291 + 0.357907i
\(776\) −3.87980 + 11.9408i −0.139277 + 0.428650i
\(777\) 8.75585 6.36150i 0.314114 0.228217i
\(778\) 60.5867 + 44.0188i 2.17214 + 1.57815i
\(779\) 10.7541 + 33.0977i 0.385305 + 1.18585i
\(780\) −13.9454 −0.499327
\(781\) 13.2630 + 17.0876i 0.474587 + 0.611444i
\(782\) −1.35118 −0.0483181
\(783\) −5.14904 15.8471i −0.184012 0.566330i
\(784\) 5.97430 + 4.34059i 0.213368 + 0.155021i
\(785\) 3.13520 2.27786i 0.111900 0.0813002i
\(786\) −0.779102 + 2.39783i −0.0277897 + 0.0855278i
\(787\) 5.16981 15.9110i 0.184284 0.567167i −0.815652 0.578543i \(-0.803621\pi\)
0.999935 + 0.0113766i \(0.00362136\pi\)
\(788\) −0.279875 + 0.203341i −0.00997012 + 0.00724372i
\(789\) −34.2637 24.8940i −1.21982 0.886250i
\(790\) −7.48350 23.0318i −0.266251 0.819436i
\(791\) 9.31320 0.331139
\(792\) 1.09676 + 1.41303i 0.0389717 + 0.0502100i
\(793\) −6.15261 −0.218486
\(794\) 12.9786 + 39.9439i 0.460592 + 1.41756i
\(795\) 6.48177 + 4.70928i 0.229885 + 0.167021i
\(796\) 14.5840 10.5959i 0.516915 0.375560i
\(797\) −3.63735 + 11.1946i −0.128842 + 0.396533i −0.994581 0.103961i \(-0.966848\pi\)
0.865740 + 0.500494i \(0.166848\pi\)
\(798\) −29.9963 + 92.3192i −1.06186 + 3.26807i
\(799\) −1.11834 + 0.812521i −0.0395640 + 0.0287449i
\(800\) −6.52234 4.73876i −0.230600 0.167541i
\(801\) −1.37978 4.24652i −0.0487521 0.150043i
\(802\) 43.7889 1.54624
\(803\) −1.03896 32.7379i −0.0366641 1.15529i
\(804\) −30.8992 −1.08973
\(805\) −1.31770 4.05547i −0.0464429 0.142937i
\(806\) −54.1615 39.3507i −1.90776 1.38607i
\(807\) −32.0647 + 23.2964i −1.12873 + 0.820072i
\(808\) −2.96464 + 9.12422i −0.104296 + 0.320989i
\(809\) 0.369567 1.13741i 0.0129933 0.0399893i −0.944350 0.328943i \(-0.893307\pi\)
0.957343 + 0.288954i \(0.0933075\pi\)
\(810\) 17.8729 12.9854i 0.627988 0.456260i
\(811\) −28.9833 21.0576i −1.01774 0.739431i −0.0519216 0.998651i \(-0.516535\pi\)
−0.965818 + 0.259220i \(0.916535\pi\)
\(812\) −8.43138 25.9491i −0.295884 0.910636i
\(813\) −0.809412 −0.0283873
\(814\) 12.0591 4.34575i 0.422670 0.152318i
\(815\) 9.93621 0.348050
\(816\) 0.841026 + 2.58841i 0.0294418 + 0.0906126i
\(817\) −8.39841 6.10181i −0.293823 0.213475i
\(818\) 39.8324 28.9400i 1.39271 1.01186i
\(819\) −1.90655 + 5.86776i −0.0666202 + 0.205036i
\(820\) 3.25561 10.0197i 0.113691 0.349904i
\(821\) −4.44312 + 3.22811i −0.155066 + 0.112662i −0.662613 0.748962i \(-0.730552\pi\)
0.507547 + 0.861624i \(0.330552\pi\)
\(822\) 36.2652 + 26.3482i 1.26490 + 0.919000i
\(823\) 13.2028 + 40.6341i 0.460222 + 1.41642i 0.864894 + 0.501955i \(0.167386\pi\)
−0.404672 + 0.914462i \(0.632614\pi\)
\(824\) −11.3563 −0.395616
\(825\) 6.09332 + 1.76823i 0.212142 + 0.0615618i
\(826\) 18.0912 0.629473
\(827\) 10.0186 + 30.8340i 0.348380 + 1.07220i 0.959749 + 0.280858i \(0.0906190\pi\)
−0.611369 + 0.791345i \(0.709381\pi\)
\(828\) 1.77317 + 1.28828i 0.0616218 + 0.0447709i
\(829\) 2.35544 1.71133i 0.0818079 0.0594369i −0.546130 0.837701i \(-0.683899\pi\)
0.627937 + 0.778264i \(0.283899\pi\)
\(830\) 5.77463 17.7725i 0.200440 0.616892i
\(831\) −5.06765 + 15.5966i −0.175795 + 0.541041i
\(832\) 26.5438 19.2852i 0.920241 0.668594i
\(833\) 0.903483 + 0.656419i 0.0313038 + 0.0227436i
\(834\) 2.94169 + 9.05359i 0.101862 + 0.313500i
\(835\) −13.9200 −0.481722
\(836\) −35.1666 + 51.7805i −1.21626 + 1.79087i
\(837\) 46.9059 1.62130
\(838\) 6.54786 + 20.1522i 0.226192 + 0.696147i
\(839\) 16.8652 + 12.2533i 0.582250 + 0.423030i 0.839535 0.543306i \(-0.182828\pi\)
−0.257284 + 0.966336i \(0.582828\pi\)
\(840\) 3.88157 2.82013i 0.133927 0.0973036i
\(841\) −4.68147 + 14.4081i −0.161430 + 0.496830i
\(842\) −5.77737 + 17.7809i −0.199101 + 0.612771i
\(843\) 10.8507 7.88348i 0.373717 0.271521i
\(844\) 4.38733 + 3.18758i 0.151018 + 0.109721i
\(845\) 1.14294 + 3.51761i 0.0393184 + 0.121009i
\(846\) 4.11851 0.141597
\(847\) −28.4980 18.0607i −0.979203 0.620572i
\(848\) −12.8458 −0.441127
\(849\) 5.88380 + 18.1085i 0.201932 + 0.621482i
\(850\) −0.786277 0.571264i −0.0269691 0.0195942i
\(851\) 2.07462 1.50730i 0.0711171 0.0516696i
\(852\) −9.21549 + 28.3624i −0.315718 + 0.971679i
\(853\) 10.6768 32.8599i 0.365567 1.12510i −0.584058 0.811712i \(-0.698536\pi\)
0.949625 0.313388i \(-0.101464\pi\)
\(854\) 10.4889 7.62061i 0.358922 0.260772i
\(855\) −4.21305 3.06096i −0.144083 0.104683i
\(856\) 1.84990 + 5.69341i 0.0632283 + 0.194597i
\(857\) 33.2969 1.13740 0.568699 0.822545i \(-0.307447\pi\)
0.568699 + 0.822545i \(0.307447\pi\)
\(858\) −22.7789 + 33.5404i −0.777658 + 1.14505i
\(859\) −16.7665 −0.572067 −0.286034 0.958220i \(-0.592337\pi\)
−0.286034 + 0.958220i \(0.592337\pi\)
\(860\) 0.971136 + 2.98885i 0.0331155 + 0.101919i
\(861\) −20.9227 15.2012i −0.713043 0.518056i
\(862\) −29.8550 + 21.6909i −1.01687 + 0.738796i
\(863\) −0.458628 + 1.41151i −0.0156119 + 0.0480484i −0.958559 0.284894i \(-0.908042\pi\)
0.942947 + 0.332943i \(0.108042\pi\)
\(864\) −11.1543 + 34.3293i −0.379476 + 1.16791i
\(865\) 8.76256 6.36637i 0.297936 0.216463i
\(866\) 15.5002 + 11.2616i 0.526719 + 0.382683i
\(867\) −9.92234 30.5378i −0.336980 1.03712i
\(868\) 76.8068 2.60699
\(869\) −36.8143 10.6832i −1.24884 0.362403i
\(870\) 14.9173 0.505745
\(871\) −6.36860 19.6005i −0.215792 0.664138i
\(872\) −4.91723 3.57258i −0.166518 0.120983i
\(873\) −8.19297 + 5.95254i −0.277290 + 0.201463i
\(874\) −7.10737 + 21.8742i −0.240410 + 0.739907i
\(875\) 0.947813 2.91707i 0.0320419 0.0986149i
\(876\) 36.5333 26.5430i 1.23435 0.896805i
\(877\) 20.1134 + 14.6132i 0.679180 + 0.493453i 0.873086 0.487567i \(-0.162115\pi\)
−0.193905 + 0.981020i \(0.562115\pi\)
\(878\) −4.18885 12.8920i −0.141367 0.435083i
\(879\) 41.7433 1.40797
\(880\) −9.57024 + 3.44884i −0.322613 + 0.116260i
\(881\) 32.6968 1.10158 0.550792 0.834643i \(-0.314326\pi\)
0.550792 + 0.834643i \(0.314326\pi\)
\(882\) −1.02818 3.16441i −0.0346206 0.106551i
\(883\) −38.5268 27.9914i −1.29653 0.941985i −0.296615 0.954997i \(-0.595858\pi\)
−0.999915 + 0.0130124i \(0.995858\pi\)
\(884\) 2.73557 1.98751i 0.0920073 0.0668472i
\(885\) −1.66410 + 5.12157i −0.0559380 + 0.172160i
\(886\) 26.4717 81.4717i 0.889336 2.73709i
\(887\) −47.8097 + 34.7358i −1.60529 + 1.16631i −0.729025 + 0.684487i \(0.760026\pi\)
−0.876267 + 0.481826i \(0.839974\pi\)
\(888\) 2.33428 + 1.69596i 0.0783335 + 0.0569126i
\(889\) 0.428030 + 1.31734i 0.0143557 + 0.0441822i
\(890\) −14.1847 −0.475471
\(891\) −1.10922 34.9518i −0.0371603 1.17093i
\(892\) 20.5076 0.686646
\(893\) 7.27130 + 22.3787i 0.243325 + 0.748876i
\(894\) −28.2781 20.5452i −0.945761 0.687136i
\(895\) 18.3918 13.3624i 0.614768 0.446655i
\(896\) −6.08220 + 18.7191i −0.203192 + 0.625360i
\(897\) −2.50648 + 7.71417i −0.0836891 + 0.257569i
\(898\) −20.6140 + 14.9770i −0.687900 + 0.499788i
\(899\) 31.5431 + 22.9174i 1.05202 + 0.764338i
\(900\) 0.487169 + 1.49935i 0.0162390 + 0.0499784i
\(901\) −1.94265 −0.0647190
\(902\) −18.7808 24.1966i −0.625332 0.805659i
\(903\) 7.71450 0.256722
\(904\) 0.767250 + 2.36135i 0.0255183 + 0.0785374i
\(905\) 1.94028 + 1.40969i 0.0644970 + 0.0468598i
\(906\) 38.7039 28.1200i 1.28585 0.934225i
\(907\) 10.7098 32.9613i 0.355612 1.09446i −0.600041 0.799969i \(-0.704849\pi\)
0.955654 0.294493i \(-0.0951508\pi\)
\(908\) 4.57979 14.0952i 0.151986 0.467764i
\(909\) −6.26043 + 4.54847i −0.207645 + 0.150863i
\(910\) 15.8568 + 11.5207i 0.525648 + 0.381906i
\(911\) −3.14834 9.68961i −0.104309 0.321031i 0.885258 0.465099i \(-0.153981\pi\)
−0.989568 + 0.144069i \(0.953981\pi\)
\(912\) 46.3277 1.53406
\(913\) −18.1368 23.3669i −0.600241 0.773332i
\(914\) 20.7484 0.686298
\(915\) 1.19257 + 3.67034i 0.0394250 + 0.121338i
\(916\) −44.7972 32.5471i −1.48014 1.07539i
\(917\) 1.56081 1.13400i 0.0515426 0.0374479i
\(918\) −1.34466 + 4.13844i −0.0443804 + 0.136589i
\(919\) −11.1644 + 34.3606i −0.368281 + 1.13345i 0.579620 + 0.814887i \(0.303201\pi\)
−0.947901 + 0.318565i \(0.896799\pi\)
\(920\) 0.919704 0.668204i 0.0303218 0.0220300i
\(921\) 47.7719 + 34.7083i 1.57414 + 1.14368i
\(922\) 2.02357 + 6.22790i 0.0666427 + 0.205105i
\(923\) −19.8907 −0.654711
\(924\) −1.47545 46.4918i −0.0485389 1.52947i
\(925\) 1.84453 0.0606479
\(926\) 15.7674 + 48.5269i 0.518148 + 1.59469i
\(927\) −7.41057 5.38409i −0.243395 0.176837i
\(928\) −24.2737 + 17.6359i −0.796823 + 0.578926i
\(929\) 8.69078 26.7475i 0.285135 0.877556i −0.701223 0.712942i \(-0.747362\pi\)
0.986358 0.164614i \(-0.0526379\pi\)
\(930\) −12.9765 + 39.9375i −0.425515 + 1.30960i
\(931\) 15.3792 11.1736i 0.504033 0.366201i
\(932\) 53.8797 + 39.1459i 1.76489 + 1.28227i
\(933\) −11.4772 35.3231i −0.375745 1.15643i
\(934\) −69.5087 −2.27439
\(935\) −1.44729 + 0.521562i −0.0473314 + 0.0170569i
\(936\) −1.64483 −0.0537630
\(937\) 0.0263183 + 0.0809993i 0.000859781 + 0.00264613i 0.951485 0.307694i \(-0.0995572\pi\)
−0.950626 + 0.310340i \(0.899557\pi\)
\(938\) 35.1342 + 25.5265i 1.14717 + 0.833471i
\(939\) −1.62730 + 1.18231i −0.0531050 + 0.0385831i
\(940\) 2.20125 6.77476i 0.0717969 0.220968i
\(941\) −12.9217 + 39.7688i −0.421234 + 1.29643i 0.485320 + 0.874337i \(0.338703\pi\)
−0.906554 + 0.422089i \(0.861297\pi\)
\(942\) 12.5668 9.13031i 0.409448 0.297482i
\(943\) −4.95744 3.60179i −0.161437 0.117291i
\(944\) −2.66812 8.21161i −0.0868398 0.267265i
\(945\) −13.7326 −0.446721
\(946\) 8.77481 + 2.54638i 0.285294 + 0.0827898i
\(947\) 8.92463 0.290012 0.145006 0.989431i \(-0.453680\pi\)
0.145006 + 0.989431i \(0.453680\pi\)
\(948\) −16.3312 50.2623i −0.530413 1.63244i
\(949\) 24.3671 + 17.7037i 0.790989 + 0.574687i
\(950\) −13.3841 + 9.72412i −0.434237 + 0.315492i
\(951\) −14.0879 + 43.3581i −0.456832 + 1.40598i
\(952\) −0.359493 + 1.10641i −0.0116512 + 0.0358589i
\(953\) −4.25853 + 3.09400i −0.137947 + 0.100225i −0.654619 0.755959i \(-0.727171\pi\)
0.516672 + 0.856184i \(0.327171\pi\)
\(954\) 4.68249 + 3.40202i 0.151601 + 0.110145i
\(955\) −5.32938 16.4022i −0.172455 0.530761i
\(956\) −38.9283 −1.25903
\(957\) 13.2662 19.5336i 0.428834 0.631431i
\(958\) 36.2438 1.17098
\(959\) −10.5998 32.6227i −0.342284 1.05344i
\(960\) −16.6496 12.0967i −0.537364 0.390418i
\(961\) −63.7153 + 46.2919i −2.05533 + 1.49329i
\(962\) −3.64240 + 11.2101i −0.117436 + 0.361429i
\(963\) −1.49213 + 4.59229i −0.0480831 + 0.147984i
\(964\) −8.49043 + 6.16866i −0.273458 + 0.198679i
\(965\) −2.09190 1.51986i −0.0673408 0.0489259i
\(966\) −5.28174 16.2555i −0.169937 0.523013i
\(967\) −18.5421 −0.596275 −0.298138 0.954523i \(-0.596365\pi\)
−0.298138 + 0.954523i \(0.596365\pi\)
\(968\) 2.23151 8.71353i 0.0717235 0.280063i
\(969\) 7.00606 0.225067
\(970\) 9.94165 + 30.5973i 0.319207 + 0.982419i
\(971\) 19.5968 + 14.2379i 0.628893 + 0.456917i 0.856016 0.516949i \(-0.172932\pi\)
−0.227124 + 0.973866i \(0.572932\pi\)
\(972\) 13.0301 9.46689i 0.417939 0.303651i
\(973\) 2.25101 6.92790i 0.0721641 0.222098i
\(974\) −4.94715 + 15.2258i −0.158517 + 0.487865i
\(975\) −4.72004 + 3.42931i −0.151162 + 0.109826i
\(976\) −5.00592 3.63701i −0.160236 0.116418i
\(977\) 15.1609 + 46.6606i 0.485041 + 1.49280i 0.831921 + 0.554894i \(0.187241\pi\)
−0.346880 + 0.937910i \(0.612759\pi\)
\(978\) 39.8272 1.27353
\(979\) −12.6146 + 18.5742i −0.403165 + 0.593634i
\(980\) −5.75485 −0.183832
\(981\) −1.51496 4.66258i −0.0483691 0.148865i
\(982\) −51.9664 37.7558i −1.65831 1.20484i
\(983\) −39.7546 + 28.8834i −1.26798 + 0.921239i −0.999120 0.0419415i \(-0.986646\pi\)
−0.268856 + 0.963180i \(0.586646\pi\)
\(984\) 2.13058 6.55724i 0.0679203 0.209037i
\(985\) −0.0447243 + 0.137647i −0.00142503 + 0.00438581i
\(986\) −2.92622 + 2.12603i −0.0931899 + 0.0677064i
\(987\) −14.1467 10.2782i −0.450294 0.327158i
\(988\) −17.7863 54.7408i −0.565859 1.74154i
\(989\) 1.82788 0.0581233
\(990\) 4.40187 + 1.27738i 0.139900 + 0.0405979i
\(991\) 30.9620 0.983541 0.491771 0.870725i \(-0.336350\pi\)
0.491771 + 0.870725i \(0.336350\pi\)
\(992\) −26.1002 80.3281i −0.828681 2.55042i
\(993\) −39.7271 28.8634i −1.26070 0.915952i
\(994\) 33.9094 24.6366i 1.07554 0.781426i
\(995\) 2.33053 7.17265i 0.0738829 0.227388i
\(996\) 12.6020 38.7849i 0.399309 1.22895i
\(997\) −18.5216 + 13.4567i −0.586584 + 0.426178i −0.841092 0.540892i \(-0.818087\pi\)
0.254507 + 0.967071i \(0.418087\pi\)
\(998\) −63.5305 46.1576i −2.01102 1.46109i
\(999\) −2.55200 7.85426i −0.0807418 0.248498i
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 55.2.g.b.16.1 8
3.2 odd 2 495.2.n.e.181.2 8
4.3 odd 2 880.2.bo.h.401.2 8
5.2 odd 4 275.2.z.a.49.4 16
5.3 odd 4 275.2.z.a.49.1 16
5.4 even 2 275.2.h.a.126.2 8
11.2 odd 10 605.2.g.k.251.2 8
11.3 even 5 605.2.a.j.1.1 4
11.4 even 5 605.2.g.m.366.2 8
11.5 even 5 605.2.g.m.81.2 8
11.6 odd 10 605.2.g.e.81.1 8
11.7 odd 10 605.2.g.e.366.1 8
11.8 odd 10 605.2.a.k.1.4 4
11.9 even 5 inner 55.2.g.b.31.1 yes 8
11.10 odd 2 605.2.g.k.511.2 8
33.8 even 10 5445.2.a.bi.1.1 4
33.14 odd 10 5445.2.a.bp.1.4 4
33.20 odd 10 495.2.n.e.361.2 8
44.3 odd 10 9680.2.a.cn.1.1 4
44.19 even 10 9680.2.a.cm.1.1 4
44.31 odd 10 880.2.bo.h.801.2 8
55.9 even 10 275.2.h.a.251.2 8
55.14 even 10 3025.2.a.bd.1.4 4
55.19 odd 10 3025.2.a.w.1.1 4
55.42 odd 20 275.2.z.a.174.1 16
55.53 odd 20 275.2.z.a.174.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.g.b.16.1 8 1.1 even 1 trivial
55.2.g.b.31.1 yes 8 11.9 even 5 inner
275.2.h.a.126.2 8 5.4 even 2
275.2.h.a.251.2 8 55.9 even 10
275.2.z.a.49.1 16 5.3 odd 4
275.2.z.a.49.4 16 5.2 odd 4
275.2.z.a.174.1 16 55.42 odd 20
275.2.z.a.174.4 16 55.53 odd 20
495.2.n.e.181.2 8 3.2 odd 2
495.2.n.e.361.2 8 33.20 odd 10
605.2.a.j.1.1 4 11.3 even 5
605.2.a.k.1.4 4 11.8 odd 10
605.2.g.e.81.1 8 11.6 odd 10
605.2.g.e.366.1 8 11.7 odd 10
605.2.g.k.251.2 8 11.2 odd 10
605.2.g.k.511.2 8 11.10 odd 2
605.2.g.m.81.2 8 11.5 even 5
605.2.g.m.366.2 8 11.4 even 5
880.2.bo.h.401.2 8 4.3 odd 2
880.2.bo.h.801.2 8 44.31 odd 10
3025.2.a.w.1.1 4 55.19 odd 10
3025.2.a.bd.1.4 4 55.14 even 10
5445.2.a.bi.1.1 4 33.8 even 10
5445.2.a.bp.1.4 4 33.14 odd 10
9680.2.a.cm.1.1 4 44.19 even 10
9680.2.a.cn.1.1 4 44.3 odd 10