Properties

Label 50.3.f.b.17.3
Level $50$
Weight $3$
Character 50.17
Analytic conductor $1.362$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [50,3,Mod(3,50)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(50, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([7]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("50.3");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 50.f (of order \(20\), degree \(8\), 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: \(1.36240132180\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(3\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 17.3
Character \(\chi\) \(=\) 50.17
Dual form 50.3.f.b.3.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.642040 - 1.26007i) q^{2} +(0.382399 - 2.41437i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(3.59048 + 3.47972i) q^{5} +(-2.79677 - 2.03197i) q^{6} +(-7.03135 - 7.03135i) q^{7} +(-2.79360 + 0.442463i) q^{8} +(2.87654 + 0.934645i) q^{9} +O(q^{10})\) \(q+(0.642040 - 1.26007i) q^{2} +(0.382399 - 2.41437i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(3.59048 + 3.47972i) q^{5} +(-2.79677 - 2.03197i) q^{6} +(-7.03135 - 7.03135i) q^{7} +(-2.79360 + 0.442463i) q^{8} +(2.87654 + 0.934645i) q^{9} +(6.68993 - 2.29016i) q^{10} +(3.40151 + 10.4688i) q^{11} +(-4.35607 + 2.21953i) q^{12} +(8.34703 + 16.3820i) q^{13} +(-13.3744 + 4.34562i) q^{14} +(9.77433 - 7.33812i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(-2.50049 - 15.7875i) q^{17} +(3.02457 - 3.02457i) q^{18} +(-11.0678 + 15.2336i) q^{19} +(1.40944 - 9.90018i) q^{20} +(-19.6651 + 14.2875i) q^{21} +(15.3753 + 2.43521i) q^{22} +(-2.76788 - 1.41030i) q^{23} +6.91400i q^{24} +(0.783135 + 24.9877i) q^{25} +26.0016 q^{26} +(13.3445 - 26.1900i) q^{27} +(-3.11112 + 19.6428i) q^{28} +(-26.7440 - 36.8099i) q^{29} +(-2.97107 - 17.0277i) q^{30} +(-14.6622 - 10.6527i) q^{31} +(4.00000 + 4.00000i) q^{32} +(26.5762 - 4.20926i) q^{33} +(-21.4988 - 6.98539i) q^{34} +(-0.778832 - 49.7131i) q^{35} +(-1.86929 - 5.75308i) q^{36} +(-20.1713 + 10.2778i) q^{37} +(12.0894 + 23.7268i) q^{38} +(42.7441 - 13.8884i) q^{39} +(-11.5700 - 8.13230i) q^{40} +(-6.91797 + 21.2913i) q^{41} +(5.37757 + 33.9526i) q^{42} +(28.9795 - 28.9795i) q^{43} +(12.9401 - 17.8105i) q^{44} +(7.07587 + 13.3654i) q^{45} +(-3.55417 + 2.58226i) q^{46} +(-49.6696 - 7.86689i) q^{47} +(8.71215 + 4.43906i) q^{48} +49.8799i q^{49} +(31.9892 + 15.0563i) q^{50} -39.0731 q^{51} +(16.6941 - 32.7639i) q^{52} +(3.99767 - 25.2403i) q^{53} +(-24.4336 - 33.6300i) q^{54} +(-24.2153 + 49.4242i) q^{55} +(22.7539 + 16.5317i) q^{56} +(32.5472 + 32.5472i) q^{57} +(-63.5539 + 10.0660i) q^{58} +(61.5688 + 20.0049i) q^{59} +(-23.3638 - 7.18872i) q^{60} +(6.86075 + 21.1152i) q^{61} +(-22.8369 + 11.6360i) q^{62} +(-13.6542 - 26.7978i) q^{63} +(7.60845 - 2.47214i) q^{64} +(-27.0347 + 87.8644i) q^{65} +(11.7590 - 36.1905i) q^{66} +(13.1233 + 82.8575i) q^{67} +(-22.6052 + 22.6052i) q^{68} +(-4.46344 + 6.14339i) q^{69} +(-63.1422 - 30.9364i) q^{70} +(37.0173 - 26.8946i) q^{71} +(-8.44946 - 1.33826i) q^{72} +(-90.4473 - 46.0852i) q^{73} +32.0160i q^{74} +(60.6292 + 7.66451i) q^{75} +37.6594 q^{76} +(49.6924 - 97.5268i) q^{77} +(9.94299 - 62.7775i) q^{78} +(8.49391 + 11.6909i) q^{79} +(-17.6757 + 9.35784i) q^{80} +(-36.1071 - 26.2333i) q^{81} +(22.3870 + 22.3870i) q^{82} +(-1.47391 + 0.233445i) q^{83} +(46.2354 + 15.0228i) q^{84} +(45.9580 - 65.3857i) q^{85} +(-17.9103 - 55.1223i) q^{86} +(-99.0998 + 50.4939i) q^{87} +(-14.1345 - 27.7405i) q^{88} +(148.704 - 48.3169i) q^{89} +(21.3843 - 0.335019i) q^{90} +(56.4965 - 173.878i) q^{91} +(0.971916 + 6.13643i) q^{92} +(-31.3264 + 31.3264i) q^{93} +(-41.8027 + 57.5365i) q^{94} +(-92.7474 + 16.1829i) q^{95} +(11.1871 - 8.12790i) q^{96} +(163.897 + 25.9588i) q^{97} +(62.8523 + 32.0249i) q^{98} +33.2930i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 6 q^{2} + 2 q^{3} - 4 q^{6} - 2 q^{7} - 12 q^{8} + 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 6 q^{2} + 2 q^{3} - 4 q^{6} - 2 q^{7} - 12 q^{8} + 40 q^{9} - 32 q^{11} + 4 q^{12} + 2 q^{13} + 30 q^{14} - 20 q^{15} + 24 q^{16} - 92 q^{17} - 136 q^{18} - 230 q^{19} - 20 q^{20} + 68 q^{21} - 48 q^{22} - 18 q^{23} + 40 q^{25} + 36 q^{26} + 260 q^{27} + 44 q^{28} + 100 q^{29} + 120 q^{30} - 132 q^{31} + 96 q^{32} + 364 q^{33} + 150 q^{34} + 50 q^{35} - 108 q^{36} - 192 q^{37} + 20 q^{38} - 80 q^{39} + 20 q^{40} + 168 q^{41} - 8 q^{42} - 78 q^{43} - 40 q^{44} - 310 q^{45} + 26 q^{46} - 22 q^{47} - 8 q^{48} - 30 q^{50} + 168 q^{51} + 4 q^{52} - 108 q^{53} - 80 q^{54} - 40 q^{55} - 48 q^{56} + 280 q^{57} + 40 q^{58} + 450 q^{59} - 100 q^{60} - 492 q^{61} - 458 q^{62} - 558 q^{63} + 120 q^{65} + 202 q^{66} - 572 q^{67} - 136 q^{68} - 670 q^{69} - 260 q^{70} - 2 q^{71} + 128 q^{72} + 262 q^{73} + 140 q^{75} - 40 q^{76} + 496 q^{77} - 62 q^{78} - 360 q^{79} - 80 q^{80} - 46 q^{81} + 272 q^{82} + 772 q^{83} + 620 q^{84} + 490 q^{85} - 264 q^{86} + 210 q^{87} - 84 q^{88} + 900 q^{89} + 1110 q^{90} + 798 q^{91} - 16 q^{92} + 294 q^{93} - 190 q^{94} + 16 q^{96} + 378 q^{97} + 106 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/50\mathbb{Z}\right)^\times\).

\(n\) \(27\)
\(\chi(n)\) \(e\left(\frac{13}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.642040 1.26007i 0.321020 0.630037i
\(3\) 0.382399 2.41437i 0.127466 0.804791i −0.838268 0.545258i \(-0.816432\pi\)
0.965734 0.259533i \(-0.0835685\pi\)
\(4\) −1.17557 1.61803i −0.293893 0.404508i
\(5\) 3.59048 + 3.47972i 0.718097 + 0.695943i
\(6\) −2.79677 2.03197i −0.466129 0.338662i
\(7\) −7.03135 7.03135i −1.00448 1.00448i −0.999990 0.00448935i \(-0.998571\pi\)
−0.00448935 0.999990i \(-0.501429\pi\)
\(8\) −2.79360 + 0.442463i −0.349201 + 0.0553079i
\(9\) 2.87654 + 0.934645i 0.319616 + 0.103849i
\(10\) 6.68993 2.29016i 0.668993 0.229016i
\(11\) 3.40151 + 10.4688i 0.309228 + 0.951706i 0.978066 + 0.208297i \(0.0667921\pi\)
−0.668838 + 0.743408i \(0.733208\pi\)
\(12\) −4.35607 + 2.21953i −0.363006 + 0.184961i
\(13\) 8.34703 + 16.3820i 0.642079 + 1.26015i 0.951038 + 0.309075i \(0.100020\pi\)
−0.308959 + 0.951075i \(0.599980\pi\)
\(14\) −13.3744 + 4.34562i −0.955317 + 0.310401i
\(15\) 9.77433 7.33812i 0.651622 0.489208i
\(16\) −1.23607 + 3.80423i −0.0772542 + 0.237764i
\(17\) −2.50049 15.7875i −0.147088 0.928676i −0.945277 0.326269i \(-0.894208\pi\)
0.798189 0.602407i \(-0.205792\pi\)
\(18\) 3.02457 3.02457i 0.168032 0.168032i
\(19\) −11.0678 + 15.2336i −0.582518 + 0.801767i −0.993969 0.109665i \(-0.965022\pi\)
0.411451 + 0.911432i \(0.365022\pi\)
\(20\) 1.40944 9.90018i 0.0704718 0.495009i
\(21\) −19.6651 + 14.2875i −0.936433 + 0.680359i
\(22\) 15.3753 + 2.43521i 0.698878 + 0.110691i
\(23\) −2.76788 1.41030i −0.120343 0.0613176i 0.392783 0.919631i \(-0.371512\pi\)
−0.513125 + 0.858314i \(0.671512\pi\)
\(24\) 6.91400i 0.288083i
\(25\) 0.783135 + 24.9877i 0.0313254 + 0.999509i
\(26\) 26.0016 1.00006
\(27\) 13.3445 26.1900i 0.494239 0.969999i
\(28\) −3.11112 + 19.6428i −0.111111 + 0.701529i
\(29\) −26.7440 36.8099i −0.922207 1.26931i −0.962823 0.270134i \(-0.912932\pi\)
0.0406163 0.999175i \(-0.487068\pi\)
\(30\) −2.97107 17.0277i −0.0990356 0.567591i
\(31\) −14.6622 10.6527i −0.472973 0.343635i 0.325626 0.945499i \(-0.394425\pi\)
−0.798599 + 0.601864i \(0.794425\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) 26.5762 4.20926i 0.805340 0.127553i
\(34\) −21.4988 6.98539i −0.632318 0.205453i
\(35\) −0.778832 49.7131i −0.0222523 1.42037i
\(36\) −1.86929 5.75308i −0.0519247 0.159808i
\(37\) −20.1713 + 10.2778i −0.545169 + 0.277777i −0.704808 0.709398i \(-0.748967\pi\)
0.159639 + 0.987175i \(0.448967\pi\)
\(38\) 12.0894 + 23.7268i 0.318143 + 0.624390i
\(39\) 42.7441 13.8884i 1.09600 0.356112i
\(40\) −11.5700 8.13230i −0.289251 0.203307i
\(41\) −6.91797 + 21.2913i −0.168731 + 0.519301i −0.999292 0.0376273i \(-0.988020\pi\)
0.830561 + 0.556928i \(0.188020\pi\)
\(42\) 5.37757 + 33.9526i 0.128037 + 0.808396i
\(43\) 28.9795 28.9795i 0.673942 0.673942i −0.284680 0.958622i \(-0.591887\pi\)
0.958622 + 0.284680i \(0.0918875\pi\)
\(44\) 12.9401 17.8105i 0.294093 0.404785i
\(45\) 7.07587 + 13.3654i 0.157242 + 0.297008i
\(46\) −3.55417 + 2.58226i −0.0772647 + 0.0561361i
\(47\) −49.6696 7.86689i −1.05680 0.167381i −0.396235 0.918149i \(-0.629683\pi\)
−0.660565 + 0.750769i \(0.729683\pi\)
\(48\) 8.71215 + 4.43906i 0.181503 + 0.0924805i
\(49\) 49.8799i 1.01796i
\(50\) 31.9892 + 15.0563i 0.639784 + 0.301126i
\(51\) −39.0731 −0.766139
\(52\) 16.6941 32.7639i 0.321039 0.630075i
\(53\) 3.99767 25.2403i 0.0754277 0.476232i −0.920842 0.389936i \(-0.872497\pi\)
0.996270 0.0862956i \(-0.0275029\pi\)
\(54\) −24.4336 33.6300i −0.452474 0.622778i
\(55\) −24.2153 + 49.4242i −0.440278 + 0.898622i
\(56\) 22.7539 + 16.5317i 0.406320 + 0.295209i
\(57\) 32.5472 + 32.5472i 0.571003 + 0.571003i
\(58\) −63.5539 + 10.0660i −1.09576 + 0.173551i
\(59\) 61.5688 + 20.0049i 1.04354 + 0.339067i 0.780130 0.625618i \(-0.215153\pi\)
0.263410 + 0.964684i \(0.415153\pi\)
\(60\) −23.3638 7.18872i −0.389396 0.119812i
\(61\) 6.86075 + 21.1152i 0.112471 + 0.346151i 0.991411 0.130781i \(-0.0417486\pi\)
−0.878940 + 0.476933i \(0.841749\pi\)
\(62\) −22.8369 + 11.6360i −0.368337 + 0.187677i
\(63\) −13.6542 26.7978i −0.216733 0.425362i
\(64\) 7.60845 2.47214i 0.118882 0.0386271i
\(65\) −27.0347 + 87.8644i −0.415919 + 1.35176i
\(66\) 11.7590 36.1905i 0.178167 0.548341i
\(67\) 13.1233 + 82.8575i 0.195871 + 1.23668i 0.868120 + 0.496354i \(0.165328\pi\)
−0.672249 + 0.740325i \(0.734672\pi\)
\(68\) −22.6052 + 22.6052i −0.332429 + 0.332429i
\(69\) −4.46344 + 6.14339i −0.0646875 + 0.0890347i
\(70\) −63.1422 30.9364i −0.902031 0.441948i
\(71\) 37.0173 26.8946i 0.521370 0.378797i −0.295750 0.955265i \(-0.595569\pi\)
0.817120 + 0.576468i \(0.195569\pi\)
\(72\) −8.44946 1.33826i −0.117354 0.0185870i
\(73\) −90.4473 46.0852i −1.23900 0.631304i −0.293203 0.956050i \(-0.594721\pi\)
−0.945801 + 0.324746i \(0.894721\pi\)
\(74\) 32.0160i 0.432649i
\(75\) 60.6292 + 7.66451i 0.808389 + 0.102193i
\(76\) 37.6594 0.495519
\(77\) 49.6924 97.5268i 0.645356 1.26658i
\(78\) 9.94299 62.7775i 0.127474 0.804840i
\(79\) 8.49391 + 11.6909i 0.107518 + 0.147986i 0.859385 0.511329i \(-0.170847\pi\)
−0.751867 + 0.659315i \(0.770847\pi\)
\(80\) −17.6757 + 9.35784i −0.220946 + 0.116973i
\(81\) −36.1071 26.2333i −0.445766 0.323868i
\(82\) 22.3870 + 22.3870i 0.273012 + 0.273012i
\(83\) −1.47391 + 0.233445i −0.0177580 + 0.00281259i −0.165307 0.986242i \(-0.552862\pi\)
0.147549 + 0.989055i \(0.452862\pi\)
\(84\) 46.2354 + 15.0228i 0.550422 + 0.178843i
\(85\) 45.9580 65.3857i 0.540683 0.769244i
\(86\) −17.9103 55.1223i −0.208260 0.640957i
\(87\) −99.0998 + 50.4939i −1.13908 + 0.580389i
\(88\) −14.1345 27.7405i −0.160619 0.315233i
\(89\) 148.704 48.3169i 1.67083 0.542887i 0.687735 0.725962i \(-0.258605\pi\)
0.983099 + 0.183076i \(0.0586053\pi\)
\(90\) 21.3843 0.335019i 0.237604 0.00372243i
\(91\) 56.4965 173.878i 0.620840 1.91075i
\(92\) 0.971916 + 6.13643i 0.0105643 + 0.0667004i
\(93\) −31.3264 + 31.3264i −0.336843 + 0.336843i
\(94\) −41.8027 + 57.5365i −0.444710 + 0.612090i
\(95\) −92.7474 + 16.1829i −0.976288 + 0.170347i
\(96\) 11.1871 8.12790i 0.116532 0.0846656i
\(97\) 163.897 + 25.9588i 1.68966 + 0.267616i 0.925868 0.377846i \(-0.123335\pi\)
0.763792 + 0.645462i \(0.223335\pi\)
\(98\) 62.8523 + 32.0249i 0.641350 + 0.326784i
\(99\) 33.2930i 0.336293i
\(100\) 39.5104 30.6420i 0.395104 0.306420i
\(101\) 72.3213 0.716052 0.358026 0.933712i \(-0.383450\pi\)
0.358026 + 0.933712i \(0.383450\pi\)
\(102\) −25.0865 + 49.2350i −0.245946 + 0.482696i
\(103\) −20.8613 + 131.713i −0.202537 + 1.27877i 0.651538 + 0.758616i \(0.274124\pi\)
−0.854075 + 0.520150i \(0.825876\pi\)
\(104\) −30.5667 42.0715i −0.293911 0.404533i
\(105\) −120.324 17.1298i −1.14594 0.163141i
\(106\) −29.2380 21.2426i −0.275830 0.200402i
\(107\) −103.823 103.823i −0.970307 0.970307i 0.0292646 0.999572i \(-0.490683\pi\)
−0.999572 + 0.0292646i \(0.990683\pi\)
\(108\) −58.0636 + 9.19637i −0.537626 + 0.0851516i
\(109\) −172.641 56.0943i −1.58386 0.514627i −0.620811 0.783960i \(-0.713197\pi\)
−0.963047 + 0.269334i \(0.913197\pi\)
\(110\) 46.7310 + 62.2453i 0.424827 + 0.565867i
\(111\) 17.1009 + 52.6311i 0.154062 + 0.474154i
\(112\) 35.4401 18.0576i 0.316429 0.161229i
\(113\) −52.7411 103.510i −0.466735 0.916019i −0.997645 0.0685908i \(-0.978150\pi\)
0.530910 0.847428i \(-0.321850\pi\)
\(114\) 61.9084 20.1153i 0.543056 0.176450i
\(115\) −5.03056 14.6951i −0.0437440 0.127784i
\(116\) −28.1203 + 86.5454i −0.242416 + 0.746081i
\(117\) 8.69925 + 54.9249i 0.0743525 + 0.469444i
\(118\) 64.7373 64.7373i 0.548621 0.548621i
\(119\) −93.4256 + 128.589i −0.785089 + 1.08058i
\(120\) −24.0588 + 24.8246i −0.200490 + 0.206872i
\(121\) −0.133680 + 0.0971243i −0.00110479 + 0.000802680i
\(122\) 31.0116 + 4.91176i 0.254194 + 0.0402603i
\(123\) 48.7598 + 24.8443i 0.396421 + 0.201987i
\(124\) 36.2469i 0.292314i
\(125\) −84.1384 + 92.4431i −0.673107 + 0.739545i
\(126\) −42.5337 −0.337569
\(127\) −40.3403 + 79.1723i −0.317640 + 0.623404i −0.993526 0.113602i \(-0.963761\pi\)
0.675886 + 0.737006i \(0.263761\pi\)
\(128\) 1.76985 11.1744i 0.0138270 0.0873001i
\(129\) −58.8856 81.0491i −0.456478 0.628287i
\(130\) 93.3583 + 90.4782i 0.718141 + 0.695986i
\(131\) 78.5965 + 57.1037i 0.599974 + 0.435906i 0.845870 0.533390i \(-0.179082\pi\)
−0.245896 + 0.969296i \(0.579082\pi\)
\(132\) −38.0530 38.0530i −0.288280 0.288280i
\(133\) 184.934 29.2907i 1.39048 0.220231i
\(134\) 112.832 + 36.6614i 0.842032 + 0.273593i
\(135\) 139.047 47.5997i 1.02998 0.352590i
\(136\) 13.9708 + 42.9976i 0.102726 + 0.316159i
\(137\) −45.9845 + 23.4303i −0.335653 + 0.171024i −0.613691 0.789546i \(-0.710316\pi\)
0.278038 + 0.960570i \(0.410316\pi\)
\(138\) 4.87542 + 9.56856i 0.0353292 + 0.0693374i
\(139\) 180.531 58.6581i 1.29878 0.422000i 0.423626 0.905837i \(-0.360757\pi\)
0.875158 + 0.483837i \(0.160757\pi\)
\(140\) −79.5219 + 59.7014i −0.568014 + 0.426439i
\(141\) −37.9872 + 116.913i −0.269413 + 0.829168i
\(142\) −10.1226 63.9119i −0.0712862 0.450084i
\(143\) −143.106 + 143.106i −1.00074 + 1.00074i
\(144\) −7.11120 + 9.78773i −0.0493833 + 0.0679703i
\(145\) 32.0644 225.227i 0.221134 1.55329i
\(146\) −116.141 + 84.3817i −0.795490 + 0.577957i
\(147\) 120.429 + 19.0740i 0.819243 + 0.129755i
\(148\) 40.3425 + 20.5555i 0.272584 + 0.138889i
\(149\) 150.434i 1.00962i −0.863229 0.504812i \(-0.831562\pi\)
0.863229 0.504812i \(-0.168438\pi\)
\(150\) 48.5842 71.4763i 0.323894 0.476509i
\(151\) −183.884 −1.21777 −0.608887 0.793257i \(-0.708384\pi\)
−0.608887 + 0.793257i \(0.708384\pi\)
\(152\) 24.1789 47.4537i 0.159071 0.312195i
\(153\) 7.56293 47.7504i 0.0494309 0.312094i
\(154\) −90.9864 125.232i −0.590821 0.813195i
\(155\) −15.5759 89.2685i −0.100490 0.575926i
\(156\) −72.7205 52.8346i −0.466157 0.338683i
\(157\) −54.7105 54.7105i −0.348475 0.348475i 0.511067 0.859541i \(-0.329251\pi\)
−0.859541 + 0.511067i \(0.829251\pi\)
\(158\) 20.1848 3.19696i 0.127752 0.0202339i
\(159\) −59.4108 19.3037i −0.373653 0.121407i
\(160\) 0.443062 + 28.2808i 0.00276914 + 0.176755i
\(161\) 9.54558 + 29.3783i 0.0592893 + 0.182474i
\(162\) −56.2381 + 28.6547i −0.347149 + 0.176881i
\(163\) 39.7594 + 78.0323i 0.243923 + 0.478726i 0.980214 0.197939i \(-0.0634248\pi\)
−0.736291 + 0.676665i \(0.763425\pi\)
\(164\) 42.5826 13.8359i 0.259650 0.0843655i
\(165\) 110.069 + 77.3645i 0.667082 + 0.468876i
\(166\) −0.652152 + 2.00712i −0.00392863 + 0.0120911i
\(167\) 2.47545 + 15.6294i 0.0148231 + 0.0935891i 0.993991 0.109464i \(-0.0349135\pi\)
−0.979168 + 0.203053i \(0.934914\pi\)
\(168\) 48.6148 48.6148i 0.289374 0.289374i
\(169\) −99.3601 + 136.757i −0.587930 + 0.809216i
\(170\) −52.8840 99.8907i −0.311082 0.587592i
\(171\) −46.0751 + 33.4755i −0.269445 + 0.195763i
\(172\) −80.9573 12.8224i −0.470682 0.0745487i
\(173\) 127.937 + 65.1871i 0.739519 + 0.376804i 0.782812 0.622259i \(-0.213785\pi\)
−0.0432926 + 0.999062i \(0.513785\pi\)
\(174\) 157.292i 0.903978i
\(175\) 170.191 181.204i 0.972521 1.03545i
\(176\) −44.0300 −0.250171
\(177\) 71.8432 141.000i 0.405894 0.796612i
\(178\) 34.5911 218.400i 0.194332 1.22696i
\(179\) −84.1124 115.771i −0.469902 0.646764i 0.506623 0.862168i \(-0.330893\pi\)
−0.976525 + 0.215403i \(0.930893\pi\)
\(180\) 13.3074 27.1609i 0.0739303 0.150894i
\(181\) 126.013 + 91.5538i 0.696205 + 0.505822i 0.878694 0.477386i \(-0.158415\pi\)
−0.182489 + 0.983208i \(0.558415\pi\)
\(182\) −182.826 182.826i −1.00454 1.00454i
\(183\) 53.6036 8.48997i 0.292916 0.0463933i
\(184\) 8.35637 + 2.71515i 0.0454150 + 0.0147562i
\(185\) −108.188 33.2881i −0.584801 0.179936i
\(186\) 19.3608 + 59.5863i 0.104090 + 0.320356i
\(187\) 156.770 79.8783i 0.838343 0.427157i
\(188\) 45.6612 + 89.6152i 0.242879 + 0.476677i
\(189\) −277.981 + 90.3214i −1.47080 + 0.477891i
\(190\) −39.1558 + 127.259i −0.206083 + 0.669782i
\(191\) −37.4768 + 115.342i −0.196214 + 0.603884i 0.803746 + 0.594972i \(0.202837\pi\)
−0.999960 + 0.00891211i \(0.997163\pi\)
\(192\) −3.05919 19.3150i −0.0159333 0.100599i
\(193\) 44.3170 44.3170i 0.229622 0.229622i −0.582913 0.812535i \(-0.698087\pi\)
0.812535 + 0.582913i \(0.198087\pi\)
\(194\) 137.938 189.856i 0.711022 0.978638i
\(195\) 201.799 + 98.8712i 1.03487 + 0.507032i
\(196\) 80.7074 58.6373i 0.411772 0.299170i
\(197\) 27.6934 + 4.38621i 0.140576 + 0.0222650i 0.226326 0.974052i \(-0.427329\pi\)
−0.0857499 + 0.996317i \(0.527329\pi\)
\(198\) 41.9517 + 21.3754i 0.211877 + 0.107957i
\(199\) 62.7744i 0.315449i 0.987483 + 0.157725i \(0.0504158\pi\)
−0.987483 + 0.157725i \(0.949584\pi\)
\(200\) −13.2439 69.4593i −0.0662196 0.347297i
\(201\) 205.067 1.02024
\(202\) 46.4331 91.1301i 0.229867 0.451139i
\(203\) −70.7773 + 446.870i −0.348657 + 2.20133i
\(204\) 45.9332 + 63.2216i 0.225163 + 0.309910i
\(205\) −98.9266 + 52.3736i −0.482569 + 0.255481i
\(206\) 152.574 + 110.852i 0.740651 + 0.538114i
\(207\) −6.64378 6.64378i −0.0320956 0.0320956i
\(208\) −72.6382 + 11.5048i −0.349222 + 0.0553113i
\(209\) −197.124 64.0494i −0.943177 0.306457i
\(210\) −98.8375 + 140.619i −0.470655 + 0.669613i
\(211\) −106.745 328.527i −0.505900 1.55700i −0.799252 0.600996i \(-0.794771\pi\)
0.293352 0.956005i \(-0.405229\pi\)
\(212\) −45.5392 + 23.2034i −0.214807 + 0.109450i
\(213\) −50.7783 99.6580i −0.238396 0.467878i
\(214\) −197.483 + 64.1661i −0.922817 + 0.299841i
\(215\) 204.891 3.20993i 0.952981 0.0149299i
\(216\) −25.6910 + 79.0689i −0.118940 + 0.366060i
\(217\) 28.1921 + 177.998i 0.129917 + 0.820266i
\(218\) −181.525 + 181.525i −0.832683 + 0.832683i
\(219\) −145.854 + 200.751i −0.665999 + 0.916669i
\(220\) 108.437 18.9205i 0.492895 0.0860022i
\(221\) 237.758 172.742i 1.07583 0.781636i
\(222\) 77.2985 + 12.2429i 0.348192 + 0.0551481i
\(223\) −226.547 115.431i −1.01590 0.517629i −0.134961 0.990851i \(-0.543091\pi\)
−0.880943 + 0.473222i \(0.843091\pi\)
\(224\) 56.2508i 0.251120i
\(225\) −21.1019 + 72.6102i −0.0937864 + 0.322712i
\(226\) −164.292 −0.726957
\(227\) −75.3953 + 147.972i −0.332138 + 0.651857i −0.995324 0.0965977i \(-0.969204\pi\)
0.663186 + 0.748455i \(0.269204\pi\)
\(228\) 14.4009 90.9239i 0.0631620 0.398789i
\(229\) 121.840 + 167.699i 0.532053 + 0.732308i 0.987442 0.157984i \(-0.0504996\pi\)
−0.455388 + 0.890293i \(0.650500\pi\)
\(230\) −21.7467 3.09597i −0.0945510 0.0134607i
\(231\) −216.464 157.270i −0.937072 0.680823i
\(232\) 90.9992 + 90.9992i 0.392238 + 0.392238i
\(233\) 32.3059 5.11675i 0.138652 0.0219603i −0.0867228 0.996232i \(-0.527639\pi\)
0.225375 + 0.974272i \(0.427639\pi\)
\(234\) 74.7947 + 24.3023i 0.319635 + 0.103856i
\(235\) −150.963 201.082i −0.642397 0.855669i
\(236\) −40.0099 123.138i −0.169533 0.521770i
\(237\) 31.4742 16.0369i 0.132802 0.0676662i
\(238\) 102.049 + 200.283i 0.428778 + 0.841523i
\(239\) 355.191 115.408i 1.48615 0.482880i 0.550208 0.835027i \(-0.314548\pi\)
0.935945 + 0.352147i \(0.114548\pi\)
\(240\) 15.8341 + 46.2542i 0.0659756 + 0.192726i
\(241\) −101.900 + 313.615i −0.422820 + 1.30131i 0.482247 + 0.876035i \(0.339821\pi\)
−0.905067 + 0.425270i \(0.860179\pi\)
\(242\) 0.0365558 + 0.230804i 0.000151057 + 0.000953737i
\(243\) 109.916 109.916i 0.452329 0.452329i
\(244\) 26.0999 35.9234i 0.106967 0.147227i
\(245\) −173.568 + 179.093i −0.708441 + 0.730992i
\(246\) 62.6114 45.4898i 0.254518 0.184918i
\(247\) −341.939 54.1578i −1.38437 0.219263i
\(248\) 45.6737 + 23.2719i 0.184168 + 0.0938384i
\(249\) 3.64784i 0.0146500i
\(250\) 62.4649 + 165.373i 0.249860 + 0.661491i
\(251\) 185.207 0.737877 0.368939 0.929454i \(-0.379721\pi\)
0.368939 + 0.929454i \(0.379721\pi\)
\(252\) −27.3083 + 53.5956i −0.108366 + 0.212681i
\(253\) 5.34918 33.7734i 0.0211430 0.133492i
\(254\) 73.8629 + 101.664i 0.290799 + 0.400250i
\(255\) −140.291 135.963i −0.550162 0.533189i
\(256\) −12.9443 9.40456i −0.0505636 0.0367366i
\(257\) 14.4526 + 14.4526i 0.0562359 + 0.0562359i 0.734665 0.678430i \(-0.237339\pi\)
−0.678430 + 0.734665i \(0.737339\pi\)
\(258\) −139.935 + 22.1635i −0.542382 + 0.0859049i
\(259\) 214.098 + 69.5646i 0.826633 + 0.268589i
\(260\) 173.949 59.5477i 0.669034 0.229030i
\(261\) −42.5260 130.881i −0.162935 0.501461i
\(262\) 122.417 62.3746i 0.467240 0.238071i
\(263\) −92.5157 181.572i −0.351771 0.690389i 0.645536 0.763730i \(-0.276634\pi\)
−0.997307 + 0.0733408i \(0.976634\pi\)
\(264\) −72.3810 + 23.5180i −0.274171 + 0.0890834i
\(265\) 102.183 76.7141i 0.385595 0.289487i
\(266\) 81.8268 251.837i 0.307619 0.946755i
\(267\) −59.7907 377.504i −0.223935 1.41387i
\(268\) 118.639 118.639i 0.442682 0.442682i
\(269\) 211.695 291.373i 0.786970 1.08317i −0.207508 0.978233i \(-0.566535\pi\)
0.994479 0.104938i \(-0.0334646\pi\)
\(270\) 29.2944 205.770i 0.108498 0.762111i
\(271\) −71.8286 + 52.1865i −0.265050 + 0.192570i −0.712370 0.701804i \(-0.752378\pi\)
0.447320 + 0.894374i \(0.352378\pi\)
\(272\) 63.1500 + 10.0020i 0.232169 + 0.0367720i
\(273\) −398.203 202.894i −1.45862 0.743203i
\(274\) 72.9870i 0.266376i
\(275\) −258.927 + 93.1944i −0.941552 + 0.338889i
\(276\) 15.1873 0.0550264
\(277\) −145.086 + 284.747i −0.523776 + 1.02797i 0.465926 + 0.884824i \(0.345721\pi\)
−0.989702 + 0.143145i \(0.954279\pi\)
\(278\) 41.9945 265.143i 0.151059 0.953752i
\(279\) −32.2199 44.3468i −0.115483 0.158949i
\(280\) 24.1720 + 138.534i 0.0863285 + 0.494765i
\(281\) 206.619 + 150.117i 0.735298 + 0.534225i 0.891235 0.453542i \(-0.149840\pi\)
−0.155937 + 0.987767i \(0.549840\pi\)
\(282\) 122.929 + 122.929i 0.435919 + 0.435919i
\(283\) −1.82209 + 0.288591i −0.00643848 + 0.00101975i −0.159653 0.987173i \(-0.551037\pi\)
0.153214 + 0.988193i \(0.451037\pi\)
\(284\) −87.0328 28.2787i −0.306454 0.0995728i
\(285\) 3.60511 + 230.115i 0.0126495 + 0.807421i
\(286\) 88.4446 + 272.205i 0.309247 + 0.951764i
\(287\) 198.350 101.064i 0.691113 0.352140i
\(288\) 7.76759 + 15.2447i 0.0269708 + 0.0529331i
\(289\) 31.8629 10.3529i 0.110252 0.0358231i
\(290\) −263.216 185.008i −0.907641 0.637959i
\(291\) 125.348 385.782i 0.430750 1.32571i
\(292\) 31.7598 + 200.523i 0.108766 + 0.686723i
\(293\) 195.770 195.770i 0.668157 0.668157i −0.289132 0.957289i \(-0.593367\pi\)
0.957289 + 0.289132i \(0.0933666\pi\)
\(294\) 101.355 139.503i 0.344744 0.474499i
\(295\) 151.450 + 286.069i 0.513391 + 0.969727i
\(296\) 51.8030 37.6371i 0.175010 0.127152i
\(297\) 319.568 + 50.6146i 1.07599 + 0.170419i
\(298\) −189.558 96.5845i −0.636100 0.324109i
\(299\) 57.1151i 0.191020i
\(300\) −58.8724 107.110i −0.196241 0.357034i
\(301\) −407.530 −1.35392
\(302\) −118.061 + 231.707i −0.390929 + 0.767242i
\(303\) 27.6556 174.611i 0.0912726 0.576272i
\(304\) −44.2713 60.9343i −0.145629 0.200442i
\(305\) −48.8416 + 99.6874i −0.160136 + 0.326844i
\(306\) −55.3134 40.1875i −0.180763 0.131332i
\(307\) 85.4904 + 85.4904i 0.278470 + 0.278470i 0.832498 0.554028i \(-0.186910\pi\)
−0.554028 + 0.832498i \(0.686910\pi\)
\(308\) −216.219 + 34.2457i −0.702008 + 0.111187i
\(309\) 310.027 + 100.734i 1.00332 + 0.325999i
\(310\) −122.485 37.6871i −0.395114 0.121571i
\(311\) 81.8905 + 252.033i 0.263314 + 0.810396i 0.992077 + 0.125631i \(0.0400954\pi\)
−0.728763 + 0.684766i \(0.759905\pi\)
\(312\) −113.265 + 57.7113i −0.363028 + 0.184972i
\(313\) 59.0953 + 115.981i 0.188803 + 0.370547i 0.965933 0.258794i \(-0.0833250\pi\)
−0.777130 + 0.629341i \(0.783325\pi\)
\(314\) −104.066 + 33.8130i −0.331419 + 0.107685i
\(315\) 44.2237 143.730i 0.140393 0.456285i
\(316\) 8.93103 27.4869i 0.0282628 0.0869838i
\(317\) −16.9063 106.742i −0.0533321 0.336726i −0.999899 0.0142179i \(-0.995474\pi\)
0.946567 0.322508i \(-0.104526\pi\)
\(318\) −62.4682 + 62.4682i −0.196441 + 0.196441i
\(319\) 294.385 405.186i 0.922836 1.27017i
\(320\) 35.9204 + 17.5991i 0.112251 + 0.0549972i
\(321\) −290.369 + 210.965i −0.904576 + 0.657213i
\(322\) 43.1474 + 6.83388i 0.133998 + 0.0212232i
\(323\) 268.175 + 136.642i 0.830263 + 0.423040i
\(324\) 89.2616i 0.275499i
\(325\) −402.811 + 221.403i −1.23942 + 0.681239i
\(326\) 123.854 0.379919
\(327\) −201.450 + 395.368i −0.616055 + 1.20908i
\(328\) 9.90544 62.5405i 0.0301995 0.190672i
\(329\) 293.930 + 404.559i 0.893403 + 1.22966i
\(330\) 168.153 89.0234i 0.509555 0.269768i
\(331\) −286.033 207.815i −0.864147 0.627839i 0.0648632 0.997894i \(-0.479339\pi\)
−0.929010 + 0.370055i \(0.879339\pi\)
\(332\) 2.11041 + 2.11041i 0.00635665 + 0.00635665i
\(333\) −67.6295 + 10.7115i −0.203092 + 0.0321665i
\(334\) 21.2835 + 6.91543i 0.0637231 + 0.0207049i
\(335\) −241.202 + 343.164i −0.720005 + 1.02437i
\(336\) −30.0456 92.4708i −0.0894214 0.275211i
\(337\) −294.583 + 150.098i −0.874134 + 0.445393i −0.832685 0.553747i \(-0.813197\pi\)
−0.0414489 + 0.999141i \(0.513197\pi\)
\(338\) 108.531 + 213.005i 0.321099 + 0.630191i
\(339\) −270.080 + 87.7544i −0.796697 + 0.258863i
\(340\) −159.823 + 2.50388i −0.470068 + 0.00736434i
\(341\) 61.6470 189.730i 0.180783 0.556393i
\(342\) 12.5996 + 79.5505i 0.0368408 + 0.232604i
\(343\) 6.18691 6.18691i 0.0180376 0.0180376i
\(344\) −68.1349 + 93.7797i −0.198067 + 0.272615i
\(345\) −37.4032 + 6.52625i −0.108415 + 0.0189167i
\(346\) 164.281 119.357i 0.474801 0.344963i
\(347\) −153.702 24.3441i −0.442947 0.0701559i −0.0690224 0.997615i \(-0.521988\pi\)
−0.373924 + 0.927459i \(0.621988\pi\)
\(348\) 198.200 + 100.988i 0.569539 + 0.290195i
\(349\) 260.036i 0.745088i −0.928015 0.372544i \(-0.878486\pi\)
0.928015 0.372544i \(-0.121514\pi\)
\(350\) −119.061 330.793i −0.340174 0.945124i
\(351\) 540.430 1.53969
\(352\) −28.2690 + 55.4811i −0.0803097 + 0.157617i
\(353\) −52.4758 + 331.319i −0.148657 + 0.938581i 0.794749 + 0.606939i \(0.207603\pi\)
−0.943405 + 0.331642i \(0.892397\pi\)
\(354\) −131.545 181.055i −0.371595 0.511456i
\(355\) 226.496 + 32.2450i 0.638016 + 0.0908309i
\(356\) −252.991 183.808i −0.710648 0.516316i
\(357\) 274.737 + 274.737i 0.769571 + 0.769571i
\(358\) −199.883 + 31.6584i −0.558333 + 0.0884313i
\(359\) 61.8646 + 20.1010i 0.172325 + 0.0559917i 0.393909 0.919150i \(-0.371123\pi\)
−0.221584 + 0.975141i \(0.571123\pi\)
\(360\) −25.6809 34.2068i −0.0713358 0.0950188i
\(361\) 1.99054 + 6.12624i 0.00551395 + 0.0169702i
\(362\) 196.270 100.005i 0.542182 0.276256i
\(363\) 0.183375 + 0.359894i 0.000505165 + 0.000991443i
\(364\) −347.757 + 112.993i −0.955375 + 0.310420i
\(365\) −164.386 480.199i −0.450373 1.31561i
\(366\) 23.7176 72.9954i 0.0648023 0.199441i
\(367\) 5.39410 + 34.0570i 0.0146978 + 0.0927984i 0.993947 0.109863i \(-0.0350411\pi\)
−0.979249 + 0.202661i \(0.935041\pi\)
\(368\) 8.78640 8.78640i 0.0238761 0.0238761i
\(369\) −39.7997 + 54.7795i −0.107858 + 0.148454i
\(370\) −111.407 + 114.953i −0.301099 + 0.310683i
\(371\) −205.582 + 149.364i −0.554131 + 0.402599i
\(372\) 87.5135 + 13.8608i 0.235251 + 0.0372601i
\(373\) 91.2870 + 46.5130i 0.244737 + 0.124700i 0.572057 0.820214i \(-0.306146\pi\)
−0.327320 + 0.944914i \(0.606146\pi\)
\(374\) 248.827i 0.665312i
\(375\) 191.018 + 238.492i 0.509380 + 0.635978i
\(376\) 142.238 0.378293
\(377\) 379.786 745.373i 1.00739 1.97712i
\(378\) −64.6630 + 408.266i −0.171066 + 1.08007i
\(379\) 310.779 + 427.751i 0.819998 + 1.12863i 0.989703 + 0.143135i \(0.0457184\pi\)
−0.169705 + 0.985495i \(0.554282\pi\)
\(380\) 135.216 + 131.044i 0.355831 + 0.344853i
\(381\) 175.725 + 127.672i 0.461222 + 0.335097i
\(382\) 121.278 + 121.278i 0.317481 + 0.317481i
\(383\) 185.725 29.4160i 0.484922 0.0768041i 0.0908134 0.995868i \(-0.471053\pi\)
0.394109 + 0.919064i \(0.371053\pi\)
\(384\) −26.3024 8.54617i −0.0684959 0.0222557i
\(385\) 517.785 177.253i 1.34490 0.460397i
\(386\) −27.3894 84.2960i −0.0709571 0.218383i
\(387\) 110.446 56.2752i 0.285391 0.145414i
\(388\) −150.670 295.707i −0.388326 0.762133i
\(389\) −506.513 + 164.576i −1.30209 + 0.423074i −0.876308 0.481752i \(-0.840001\pi\)
−0.425781 + 0.904826i \(0.640001\pi\)
\(390\) 254.148 190.803i 0.651662 0.489238i
\(391\) −15.3441 + 47.2243i −0.0392433 + 0.120778i
\(392\) −22.0700 139.345i −0.0563011 0.355471i
\(393\) 167.925 167.925i 0.427290 0.427290i
\(394\) 23.3072 32.0796i 0.0591554 0.0814204i
\(395\) −10.1837 + 71.5323i −0.0257814 + 0.181094i
\(396\) 53.8692 39.1383i 0.136033 0.0988341i
\(397\) −565.368 89.5455i −1.42410 0.225555i −0.603639 0.797257i \(-0.706283\pi\)
−0.820461 + 0.571702i \(0.806283\pi\)
\(398\) 79.1004 + 40.3036i 0.198745 + 0.101265i
\(399\) 457.702i 1.14712i
\(400\) −96.0270 27.9073i −0.240067 0.0697683i
\(401\) −455.895 −1.13689 −0.568447 0.822720i \(-0.692456\pi\)
−0.568447 + 0.822720i \(0.692456\pi\)
\(402\) 131.661 258.400i 0.327516 0.642786i
\(403\) 52.1264 329.113i 0.129346 0.816658i
\(404\) −85.0188 117.018i −0.210443 0.289649i
\(405\) −38.3573 219.833i −0.0947093 0.542797i
\(406\) 517.648 + 376.093i 1.27499 + 0.926337i
\(407\) −176.208 176.208i −0.432944 0.432944i
\(408\) 109.155 17.2884i 0.267536 0.0423736i
\(409\) −355.067 115.368i −0.868134 0.282074i −0.159112 0.987261i \(-0.550863\pi\)
−0.709022 + 0.705187i \(0.750863\pi\)
\(410\) 2.47971 + 158.281i 0.00604808 + 0.386051i
\(411\) 38.9850 + 119.983i 0.0948540 + 0.291931i
\(412\) 237.640 121.083i 0.576795 0.293892i
\(413\) −292.251 573.574i −0.707629 1.38880i
\(414\) −12.6372 + 4.10608i −0.0305247 + 0.00991808i
\(415\) −6.10438 4.29062i −0.0147093 0.0103388i
\(416\) −32.1397 + 98.9159i −0.0772590 + 0.237779i
\(417\) −72.5876 458.300i −0.174071 1.09904i
\(418\) −207.268 + 207.268i −0.495857 + 0.495857i
\(419\) −353.750 + 486.895i −0.844272 + 1.16204i 0.140824 + 0.990035i \(0.455025\pi\)
−0.985096 + 0.172006i \(0.944975\pi\)
\(420\) 113.732 + 214.825i 0.270791 + 0.511489i
\(421\) 103.378 75.1084i 0.245553 0.178405i −0.458201 0.888849i \(-0.651506\pi\)
0.703754 + 0.710444i \(0.251506\pi\)
\(422\) −482.503 76.4209i −1.14337 0.181092i
\(423\) −135.524 69.0529i −0.320387 0.163246i
\(424\) 72.2802i 0.170472i
\(425\) 392.535 74.8454i 0.923613 0.176107i
\(426\) −158.178 −0.371310
\(427\) 100.228 196.709i 0.234727 0.460677i
\(428\) −45.9378 + 290.040i −0.107331 + 0.677664i
\(429\) 290.788 + 400.236i 0.677829 + 0.932951i
\(430\) 127.503 260.239i 0.296519 0.605206i
\(431\) −24.2496 17.6184i −0.0562636 0.0408779i 0.559298 0.828967i \(-0.311071\pi\)
−0.615562 + 0.788089i \(0.711071\pi\)
\(432\) 83.1379 + 83.1379i 0.192449 + 0.192449i
\(433\) 320.096 50.6983i 0.739253 0.117086i 0.224559 0.974460i \(-0.427906\pi\)
0.514693 + 0.857374i \(0.327906\pi\)
\(434\) 242.391 + 78.7575i 0.558504 + 0.181469i
\(435\) −531.521 163.542i −1.22189 0.375958i
\(436\) 112.189 + 345.281i 0.257313 + 0.791929i
\(437\) 52.1184 26.5556i 0.119264 0.0607681i
\(438\) 159.317 + 312.676i 0.363736 + 0.713873i
\(439\) −419.087 + 136.170i −0.954640 + 0.310181i −0.744600 0.667511i \(-0.767360\pi\)
−0.210041 + 0.977693i \(0.567360\pi\)
\(440\) 45.7795 148.786i 0.104044 0.338150i
\(441\) −46.6200 + 143.482i −0.105714 + 0.325355i
\(442\) −65.0168 410.500i −0.147097 0.928733i
\(443\) −284.421 + 284.421i −0.642035 + 0.642035i −0.951055 0.309020i \(-0.899999\pi\)
0.309020 + 0.951055i \(0.399999\pi\)
\(444\) 65.0557 89.5414i 0.146522 0.201670i
\(445\) 702.049 + 343.967i 1.57764 + 0.772961i
\(446\) −290.904 + 211.354i −0.652251 + 0.473888i
\(447\) −363.204 57.5258i −0.812536 0.128693i
\(448\) −70.8802 36.1153i −0.158215 0.0806144i
\(449\) 191.921i 0.427441i −0.976895 0.213720i \(-0.931442\pi\)
0.976895 0.213720i \(-0.0685581\pi\)
\(450\) 77.9459 + 73.2086i 0.173213 + 0.162686i
\(451\) −246.425 −0.546398
\(452\) −105.482 + 207.020i −0.233368 + 0.458010i
\(453\) −70.3170 + 443.964i −0.155225 + 0.980053i
\(454\) 138.048 + 190.007i 0.304071 + 0.418518i
\(455\) 807.897 427.715i 1.77560 0.940033i
\(456\) −105.325 76.5230i −0.230976 0.167814i
\(457\) 66.8253 + 66.8253i 0.146226 + 0.146226i 0.776430 0.630204i \(-0.217029\pi\)
−0.630204 + 0.776430i \(0.717029\pi\)
\(458\) 289.539 45.8584i 0.632181 0.100128i
\(459\) −446.842 145.188i −0.973511 0.316313i
\(460\) −17.8634 + 25.4148i −0.0388335 + 0.0552495i
\(461\) −39.1750 120.568i −0.0849782 0.261536i 0.899534 0.436850i \(-0.143906\pi\)
−0.984513 + 0.175314i \(0.943906\pi\)
\(462\) −337.150 + 171.787i −0.729762 + 0.371832i
\(463\) 135.437 + 265.811i 0.292521 + 0.574105i 0.989761 0.142732i \(-0.0455888\pi\)
−0.697240 + 0.716838i \(0.745589\pi\)
\(464\) 173.091 56.2406i 0.373040 0.121208i
\(465\) −221.484 + 3.46988i −0.476309 + 0.00746211i
\(466\) 14.2942 43.9929i 0.0306742 0.0944054i
\(467\) 47.0084 + 296.799i 0.100660 + 0.635544i 0.985503 + 0.169655i \(0.0542654\pi\)
−0.884843 + 0.465889i \(0.845735\pi\)
\(468\) 78.6438 78.6438i 0.168042 0.168042i
\(469\) 490.326 674.875i 1.04547 1.43897i
\(470\) −350.303 + 61.1222i −0.745325 + 0.130047i
\(471\) −153.013 + 111.170i −0.324868 + 0.236030i
\(472\) −180.850 28.6439i −0.383158 0.0606862i
\(473\) 401.954 + 204.806i 0.849796 + 0.432993i
\(474\) 49.9561i 0.105393i
\(475\) −389.320 264.630i −0.819621 0.557116i
\(476\) 317.890 0.667837
\(477\) 35.0902 68.8683i 0.0735643 0.144378i
\(478\) 82.6233 521.663i 0.172852 1.09135i
\(479\) 114.943 + 158.205i 0.239964 + 0.330282i 0.911965 0.410268i \(-0.134565\pi\)
−0.672001 + 0.740550i \(0.734565\pi\)
\(480\) 68.4498 + 9.74484i 0.142604 + 0.0203017i
\(481\) −336.740 244.656i −0.700083 0.508640i
\(482\) 329.754 + 329.754i 0.684137 + 0.684137i
\(483\) 74.5804 11.8124i 0.154411 0.0244563i
\(484\) 0.314301 + 0.102122i 0.000649382 + 0.000210997i
\(485\) 498.141 + 663.520i 1.02709 + 1.36808i
\(486\) −67.9318 209.073i −0.139777 0.430191i
\(487\) 303.438 154.610i 0.623077 0.317473i −0.113797 0.993504i \(-0.536301\pi\)
0.736874 + 0.676031i \(0.236301\pi\)
\(488\) −28.5090 55.9520i −0.0584200 0.114656i
\(489\) 203.603 66.1546i 0.416366 0.135286i
\(490\) 114.233 + 333.693i 0.233128 + 0.681006i
\(491\) −226.895 + 698.310i −0.462107 + 1.42222i 0.400477 + 0.916307i \(0.368844\pi\)
−0.862585 + 0.505913i \(0.831156\pi\)
\(492\) −17.1216 108.101i −0.0347999 0.219718i
\(493\) −514.264 + 514.264i −1.04313 + 1.04313i
\(494\) −287.781 + 396.097i −0.582553 + 0.801816i
\(495\) −115.850 + 119.538i −0.234041 + 0.241491i
\(496\) 58.6487 42.6108i 0.118243 0.0859088i
\(497\) −449.387 71.1759i −0.904199 0.143211i
\(498\) 4.59655 + 2.34206i 0.00923002 + 0.00470293i
\(499\) 325.615i 0.652535i 0.945278 + 0.326267i \(0.105791\pi\)
−0.945278 + 0.326267i \(0.894209\pi\)
\(500\) 248.487 + 27.4654i 0.496973 + 0.0549308i
\(501\) 38.6818 0.0772091
\(502\) 118.910 233.375i 0.236873 0.464890i
\(503\) 76.8730 485.357i 0.152829 0.964925i −0.785420 0.618963i \(-0.787553\pi\)
0.938249 0.345961i \(-0.112447\pi\)
\(504\) 50.0014 + 68.8210i 0.0992091 + 0.136550i
\(505\) 259.668 + 251.658i 0.514195 + 0.498332i
\(506\) −39.1226 28.4242i −0.0773174 0.0561744i
\(507\) 292.188 + 292.188i 0.576308 + 0.576308i
\(508\) 175.526 27.8007i 0.345524 0.0547257i
\(509\) −740.771 240.691i −1.45535 0.472870i −0.528701 0.848808i \(-0.677321\pi\)
−0.926645 + 0.375938i \(0.877321\pi\)
\(510\) −261.396 + 89.4835i −0.512542 + 0.175458i
\(511\) 311.926 + 960.009i 0.610422 + 1.87869i
\(512\) −20.1612 + 10.2726i −0.0393773 + 0.0200637i
\(513\) 251.272 + 493.150i 0.489810 + 0.961306i
\(514\) 27.4905 8.93221i 0.0534835 0.0173778i
\(515\) −533.225 + 400.321i −1.03539 + 0.777323i
\(516\) −61.9160 + 190.558i −0.119992 + 0.369298i
\(517\) −86.5949 546.739i −0.167495 1.05752i
\(518\) 225.116 225.116i 0.434587 0.434587i
\(519\) 206.309 283.960i 0.397512 0.547129i
\(520\) 36.6476 257.420i 0.0704761 0.495039i
\(521\) 400.288 290.826i 0.768308 0.558208i −0.133140 0.991097i \(-0.542506\pi\)
0.901447 + 0.432889i \(0.142506\pi\)
\(522\) −192.224 30.4452i −0.368244 0.0583242i
\(523\) 229.600 + 116.987i 0.439005 + 0.223684i 0.659501 0.751704i \(-0.270768\pi\)
−0.220496 + 0.975388i \(0.570768\pi\)
\(524\) 194.301i 0.370804i
\(525\) −372.413 480.197i −0.709359 0.914661i
\(526\) −288.193 −0.547896
\(527\) −131.517 + 258.116i −0.249557 + 0.489783i
\(528\) −16.8370 + 106.305i −0.0318883 + 0.201335i
\(529\) −305.266 420.163i −0.577063 0.794259i
\(530\) −31.0601 178.011i −0.0586039 0.335870i
\(531\) 158.408 + 115.090i 0.298320 + 0.216742i
\(532\) −264.797 264.797i −0.497739 0.497739i
\(533\) −406.538 + 64.3893i −0.762736 + 0.120805i
\(534\) −514.070 167.032i −0.962679 0.312793i
\(535\) −11.5000 734.048i −0.0214953 1.37205i
\(536\) −73.3228 225.664i −0.136796 0.421016i
\(537\) −311.679 + 158.808i −0.580407 + 0.295732i
\(538\) −231.235 453.824i −0.429805 0.843540i
\(539\) −522.181 + 169.667i −0.968796 + 0.314781i
\(540\) −240.477 169.026i −0.445328 0.313010i
\(541\) 290.448 893.906i 0.536872 1.65232i −0.202698 0.979241i \(-0.564971\pi\)
0.739570 0.673080i \(-0.235029\pi\)
\(542\) 19.6421 + 124.015i 0.0362400 + 0.228810i
\(543\) 269.232 269.232i 0.495824 0.495824i
\(544\) 53.1480 73.1519i 0.0976985 0.134470i
\(545\) −424.670 802.146i −0.779212 1.47183i
\(546\) −511.324 + 371.499i −0.936491 + 0.680400i
\(547\) 726.852 + 115.122i 1.32880 + 0.210461i 0.780149 0.625593i \(-0.215143\pi\)
0.548647 + 0.836054i \(0.315143\pi\)
\(548\) 91.9690 + 46.8606i 0.167827 + 0.0855120i
\(549\) 67.1512i 0.122315i
\(550\) −48.8094 + 386.101i −0.0887444 + 0.702002i
\(551\) 856.745 1.55489
\(552\) 9.75085 19.1371i 0.0176646 0.0346687i
\(553\) 22.4789 141.926i 0.0406491 0.256648i
\(554\) 265.652 + 365.638i 0.479515 + 0.659996i
\(555\) −121.741 + 248.477i −0.219353 + 0.447707i
\(556\) −307.138 223.149i −0.552406 0.401346i
\(557\) 763.833 + 763.833i 1.37133 + 1.37133i 0.858469 + 0.512865i \(0.171416\pi\)
0.512865 + 0.858469i \(0.328584\pi\)
\(558\) −76.5667 + 12.1270i −0.137216 + 0.0217329i
\(559\) 716.634 + 232.848i 1.28199 + 0.416545i
\(560\) 190.083 + 58.4859i 0.339433 + 0.104439i
\(561\) −132.907 409.047i −0.236912 0.729139i
\(562\) 321.816 163.974i 0.572627 0.291768i
\(563\) −88.5286 173.747i −0.157244 0.308609i 0.798921 0.601436i \(-0.205404\pi\)
−0.956166 + 0.292826i \(0.905404\pi\)
\(564\) 233.825 75.9744i 0.414584 0.134706i
\(565\) 170.820 555.175i 0.302337 0.982611i
\(566\) −0.806208 + 2.48125i −0.00142440 + 0.00438384i
\(567\) 69.4258 + 438.337i 0.122444 + 0.773082i
\(568\) −91.5117 + 91.5117i −0.161112 + 0.161112i
\(569\) −81.5460 + 112.238i −0.143315 + 0.197256i −0.874640 0.484773i \(-0.838902\pi\)
0.731325 + 0.682029i \(0.238902\pi\)
\(570\) 292.277 + 143.200i 0.512766 + 0.251229i
\(571\) 318.668 231.526i 0.558087 0.405474i −0.272671 0.962107i \(-0.587907\pi\)
0.830758 + 0.556633i \(0.187907\pi\)
\(572\) 399.783 + 63.3194i 0.698921 + 0.110698i
\(573\) 264.147 + 134.590i 0.460990 + 0.234886i
\(574\) 314.822i 0.548471i
\(575\) 33.0727 70.2675i 0.0575177 0.122204i
\(576\) 24.1966 0.0420080
\(577\) −289.629 + 568.429i −0.501957 + 0.985145i 0.491494 + 0.870881i \(0.336451\pi\)
−0.993450 + 0.114264i \(0.963549\pi\)
\(578\) 7.41184 46.7965i 0.0128233 0.0809629i
\(579\) −90.0511 123.945i −0.155529 0.214067i
\(580\) −402.119 + 212.889i −0.693308 + 0.367050i
\(581\) 12.0050 + 8.72216i 0.0206627 + 0.0150123i
\(582\) −405.635 405.635i −0.696968 0.696968i
\(583\) 277.833 44.0044i 0.476557 0.0754792i
\(584\) 273.065 + 88.7242i 0.467577 + 0.151925i
\(585\) −159.889 + 227.478i −0.273314 + 0.388851i
\(586\) −120.993 372.377i −0.206472 0.635455i
\(587\) 795.587 405.372i 1.35534 0.690582i 0.382915 0.923783i \(-0.374920\pi\)
0.972429 + 0.233201i \(0.0749201\pi\)
\(588\) −110.710 217.281i −0.188282 0.369525i
\(589\) 324.557 105.455i 0.551030 0.179041i
\(590\) 457.706 7.17066i 0.775772 0.0121537i
\(591\) 21.1799 65.1850i 0.0358374 0.110296i
\(592\) −14.1659 89.4400i −0.0239289 0.151081i
\(593\) −253.685 + 253.685i −0.427800 + 0.427800i −0.887878 0.460078i \(-0.847821\pi\)
0.460078 + 0.887878i \(0.347821\pi\)
\(594\) 268.953 370.182i 0.452783 0.623203i
\(595\) −782.898 + 136.603i −1.31579 + 0.229585i
\(596\) −243.407 + 176.846i −0.408401 + 0.296721i
\(597\) 151.561 + 24.0049i 0.253871 + 0.0402092i
\(598\) −71.9693 36.6702i −0.120350 0.0613214i
\(599\) 581.488i 0.970764i −0.874302 0.485382i \(-0.838681\pi\)
0.874302 0.485382i \(-0.161319\pi\)
\(600\) −172.765 + 5.41459i −0.287942 + 0.00902432i
\(601\) −171.633 −0.285580 −0.142790 0.989753i \(-0.545607\pi\)
−0.142790 + 0.989753i \(0.545607\pi\)
\(602\) −261.651 + 513.518i −0.434636 + 0.853020i
\(603\) −39.6925 + 250.609i −0.0658251 + 0.415603i
\(604\) 216.168 + 297.530i 0.357895 + 0.492600i
\(605\) −0.817941 0.116446i −0.00135197 0.000192473i
\(606\) −202.266 146.955i −0.333773 0.242500i
\(607\) −523.612 523.612i −0.862622 0.862622i 0.129020 0.991642i \(-0.458817\pi\)
−0.991642 + 0.129020i \(0.958817\pi\)
\(608\) −105.206 + 16.6629i −0.173036 + 0.0274061i
\(609\) 1051.85 + 341.766i 1.72717 + 0.561191i
\(610\) 94.2551 + 125.547i 0.154517 + 0.205815i
\(611\) −285.718 879.351i −0.467624 1.43920i
\(612\) −86.1526 + 43.8969i −0.140772 + 0.0717270i
\(613\) 317.280 + 622.698i 0.517586 + 1.01582i 0.990859 + 0.134904i \(0.0430726\pi\)
−0.473272 + 0.880916i \(0.656927\pi\)
\(614\) 162.612 52.8359i 0.264841 0.0860520i
\(615\) 88.6198 + 258.873i 0.144097 + 0.420932i
\(616\) −95.6688 + 294.438i −0.155307 + 0.477984i
\(617\) 72.1333 + 455.432i 0.116910 + 0.738139i 0.974597 + 0.223967i \(0.0719007\pi\)
−0.857687 + 0.514172i \(0.828099\pi\)
\(618\) 325.981 325.981i 0.527478 0.527478i
\(619\) −158.282 + 217.856i −0.255706 + 0.351949i −0.917499 0.397737i \(-0.869796\pi\)
0.661794 + 0.749686i \(0.269796\pi\)
\(620\) −126.129 + 130.144i −0.203434 + 0.209909i
\(621\) −73.8717 + 53.6709i −0.118956 + 0.0864266i
\(622\) 370.157 + 58.6272i 0.595108 + 0.0942559i
\(623\) −1385.33 705.858i −2.22364 1.13300i
\(624\) 179.775i 0.288101i
\(625\) −623.773 + 39.1375i −0.998037 + 0.0626200i
\(626\) 184.086 0.294068
\(627\) −230.019 + 451.438i −0.366857 + 0.719997i
\(628\) −24.2074 + 152.840i −0.0385468 + 0.243375i
\(629\) 212.698 + 292.754i 0.338153 + 0.465428i
\(630\) −152.717 148.005i −0.242407 0.234929i
\(631\) 194.426 + 141.259i 0.308124 + 0.223865i 0.731091 0.682280i \(-0.239011\pi\)
−0.422967 + 0.906145i \(0.639011\pi\)
\(632\) −28.9014 28.9014i −0.0457301 0.0457301i
\(633\) −834.006 + 132.094i −1.31755 + 0.208679i
\(634\) −145.357 47.2295i −0.229270 0.0744944i
\(635\) −420.339 + 143.894i −0.661951 + 0.226605i
\(636\) 38.6074 + 118.822i 0.0607035 + 0.186826i
\(637\) −817.131 + 416.349i −1.28278 + 0.653609i
\(638\) −321.557 631.092i −0.504008 0.989172i
\(639\) 131.619 42.7655i 0.205976 0.0669256i
\(640\) 45.2384 33.9630i 0.0706851 0.0530671i
\(641\) 83.6971 257.593i 0.130573 0.401861i −0.864302 0.502972i \(-0.832240\pi\)
0.994875 + 0.101111i \(0.0322397\pi\)
\(642\) 79.4035 + 501.334i 0.123682 + 0.780894i
\(643\) −348.420 + 348.420i −0.541866 + 0.541866i −0.924076 0.382210i \(-0.875163\pi\)
0.382210 + 0.924076i \(0.375163\pi\)
\(644\) 36.3136 49.9813i 0.0563875 0.0776108i
\(645\) 70.6001 495.911i 0.109458 0.768854i
\(646\) 344.358 250.191i 0.533061 0.387292i
\(647\) 639.220 + 101.242i 0.987975 + 0.156480i 0.629450 0.777041i \(-0.283280\pi\)
0.358524 + 0.933520i \(0.383280\pi\)
\(648\) 112.476 + 57.3095i 0.173574 + 0.0884405i
\(649\) 712.596i 1.09799i
\(650\) 20.3628 + 649.721i 0.0313273 + 0.999571i
\(651\) 440.534 0.676703
\(652\) 79.5189 156.065i 0.121961 0.239363i
\(653\) 63.2779 399.521i 0.0969034 0.611824i −0.890668 0.454654i \(-0.849763\pi\)
0.987572 0.157170i \(-0.0502370\pi\)
\(654\) 368.854 + 507.684i 0.563997 + 0.776275i
\(655\) 83.4947 + 478.524i 0.127473 + 0.730571i
\(656\) −72.4459 52.6350i −0.110436 0.0802364i
\(657\) −217.102 217.102i −0.330445 0.330445i
\(658\) 698.489 110.630i 1.06153 0.168130i
\(659\) −610.836 198.473i −0.926913 0.301172i −0.193613 0.981078i \(-0.562021\pi\)
−0.733300 + 0.679906i \(0.762021\pi\)
\(660\) −4.21496 269.042i −0.00638630 0.407639i
\(661\) 245.242 + 754.777i 0.371016 + 1.14187i 0.946127 + 0.323795i \(0.104959\pi\)
−0.575111 + 0.818075i \(0.695041\pi\)
\(662\) −445.506 + 226.997i −0.672970 + 0.342895i
\(663\) −326.144 640.094i −0.491922 0.965450i
\(664\) 4.01424 1.30430i 0.00604554 0.00196431i
\(665\) 765.928 + 538.352i 1.15177 + 0.809552i
\(666\) −29.9236 + 92.0953i −0.0449303 + 0.138281i
\(667\) 22.1109 + 139.603i 0.0331497 + 0.209299i
\(668\) 22.3788 22.3788i 0.0335012 0.0335012i
\(669\) −365.325 + 502.827i −0.546077 + 0.751610i
\(670\) 277.551 + 524.257i 0.414255 + 0.782472i
\(671\) −197.713 + 143.647i −0.294655 + 0.214079i
\(672\) −135.811 21.5103i −0.202099 0.0320093i
\(673\) −504.603 257.108i −0.749781 0.382032i 0.0369593 0.999317i \(-0.488233\pi\)
−0.786740 + 0.617284i \(0.788233\pi\)
\(674\) 467.565i 0.693716i
\(675\) 664.878 + 312.937i 0.985005 + 0.463611i
\(676\) 338.083 0.500123
\(677\) −73.6337 + 144.514i −0.108765 + 0.213463i −0.938973 0.343990i \(-0.888221\pi\)
0.830209 + 0.557453i \(0.188221\pi\)
\(678\) −62.8252 + 396.663i −0.0926626 + 0.585048i
\(679\) −969.894 1334.94i −1.42841 1.96604i
\(680\) −99.4578 + 202.997i −0.146261 + 0.298524i
\(681\) 328.428 + 238.617i 0.482272 + 0.350391i
\(682\) −199.494 199.494i −0.292513 0.292513i
\(683\) 155.855 24.6851i 0.228193 0.0361421i −0.0412909 0.999147i \(-0.513147\pi\)
0.269483 + 0.963005i \(0.413147\pi\)
\(684\) 108.329 + 35.1982i 0.158376 + 0.0514594i
\(685\) −246.637 75.8871i −0.360055 0.110784i
\(686\) −3.82372 11.7682i −0.00557394 0.0171548i
\(687\) 451.479 230.040i 0.657174 0.334847i
\(688\) 74.4240 + 146.065i 0.108174 + 0.212304i
\(689\) 446.854 145.192i 0.648554 0.210728i
\(690\) −15.7907 + 51.3208i −0.0228851 + 0.0743780i
\(691\) 347.572 1069.72i 0.502999 1.54807i −0.301111 0.953589i \(-0.597357\pi\)
0.804109 0.594482i \(-0.202643\pi\)
\(692\) −44.9239 283.638i −0.0649189 0.409882i
\(693\) 234.095 234.095i 0.337800 0.337800i
\(694\) −129.358 + 178.047i −0.186395 + 0.256551i
\(695\) 852.307 + 417.586i 1.22634 + 0.600843i
\(696\) 254.504 184.908i 0.365667 0.265672i
\(697\) 353.435 + 55.9786i 0.507080 + 0.0803136i
\(698\) −327.664 166.953i −0.469433 0.239188i
\(699\) 79.9550i 0.114385i
\(700\) −493.266 62.3568i −0.704666 0.0890811i
\(701\) −1207.60 −1.72269 −0.861343 0.508024i \(-0.830376\pi\)
−0.861343 + 0.508024i \(0.830376\pi\)
\(702\) 346.977 680.981i 0.494269 0.970058i
\(703\) 66.6850 421.033i 0.0948578 0.598909i
\(704\) 51.7604 + 71.2421i 0.0735233 + 0.101196i
\(705\) −543.215 + 287.588i −0.770518 + 0.407926i
\(706\) 383.795 + 278.843i 0.543619 + 0.394962i
\(707\) −508.517 508.517i −0.719260 0.719260i
\(708\) −312.600 + 49.5110i −0.441525 + 0.0699308i
\(709\) 1174.03 + 381.465i 1.65590 + 0.538033i 0.980006 0.198970i \(-0.0637596\pi\)
0.675890 + 0.737003i \(0.263760\pi\)
\(710\) 186.050 264.698i 0.262042 0.372815i
\(711\) 13.5063 + 41.5681i 0.0189962 + 0.0584642i
\(712\) −394.042 + 200.775i −0.553430 + 0.281987i
\(713\) 25.5596 + 50.1635i 0.0358479 + 0.0703555i
\(714\) 522.580 169.797i 0.731905 0.237810i
\(715\) −1011.79 + 15.8513i −1.41509 + 0.0221696i
\(716\) −88.4411 + 272.194i −0.123521 + 0.380159i
\(717\) −142.814 901.695i −0.199183 1.25759i
\(718\) 65.0482 65.0482i 0.0905964 0.0905964i
\(719\) 218.357 300.542i 0.303695 0.418001i −0.629707 0.776833i \(-0.716825\pi\)
0.933402 + 0.358832i \(0.116825\pi\)
\(720\) −59.5912 + 10.3977i −0.0827655 + 0.0144413i
\(721\) 1072.80 779.437i 1.48794 1.08105i
\(722\) 8.99751 + 1.42507i 0.0124619 + 0.00197378i
\(723\) 718.216 + 365.949i 0.993383 + 0.506154i
\(724\) 311.521i 0.430278i
\(725\) 898.853 697.099i 1.23980 0.961516i
\(726\) 0.571227 0.000786814
\(727\) 40.7718 80.0192i 0.0560823 0.110068i −0.861264 0.508157i \(-0.830327\pi\)
0.917346 + 0.398090i \(0.130327\pi\)
\(728\) −80.8940 + 510.745i −0.111118 + 0.701572i
\(729\) −459.446 632.374i −0.630242 0.867453i
\(730\) −710.629 101.168i −0.973464 0.138587i
\(731\) −529.977 385.051i −0.725003 0.526745i
\(732\) −76.7519 76.7519i −0.104852 0.104852i
\(733\) −783.969 + 124.168i −1.06953 + 0.169398i −0.666289 0.745694i \(-0.732118\pi\)
−0.403246 + 0.915092i \(0.632118\pi\)
\(734\) 46.3776 + 15.0690i 0.0631847 + 0.0205300i
\(735\) 366.025 + 487.543i 0.497993 + 0.663323i
\(736\) −5.43030 16.7127i −0.00737812 0.0227075i
\(737\) −822.776 + 419.226i −1.11639 + 0.568827i
\(738\) 43.4733 + 85.3211i 0.0589069 + 0.115611i
\(739\) −86.8071 + 28.2053i −0.117466 + 0.0381669i −0.367160 0.930158i \(-0.619670\pi\)
0.249694 + 0.968325i \(0.419670\pi\)
\(740\) 73.3216 + 214.185i 0.0990833 + 0.289439i
\(741\) −261.514 + 804.859i −0.352921 + 1.08618i
\(742\) 56.2180 + 354.947i 0.0757656 + 0.478365i
\(743\) 835.778 835.778i 1.12487 1.12487i 0.133871 0.990999i \(-0.457259\pi\)
0.990999 0.133871i \(-0.0427407\pi\)
\(744\) 73.6527 101.374i 0.0989956 0.136256i
\(745\) 523.467 540.130i 0.702641 0.725007i
\(746\) 117.220 85.1651i 0.157131 0.114162i
\(747\) −4.45796 0.706071i −0.00596781 0.000945208i
\(748\) −313.540 159.757i −0.419171 0.213578i
\(749\) 1460.03i 1.94931i
\(750\) 423.158 87.5753i 0.564211 0.116767i
\(751\) −844.470 −1.12446 −0.562231 0.826981i \(-0.690057\pi\)
−0.562231 + 0.826981i \(0.690057\pi\)
\(752\) 91.3224 179.230i 0.121439 0.238338i
\(753\) 70.8231 447.159i 0.0940545 0.593837i
\(754\) −695.386 957.117i −0.922263 1.26939i
\(755\) −660.232 639.864i −0.874479 0.847502i
\(756\) 472.929 + 343.603i 0.625567 + 0.454501i
\(757\) 191.531 + 191.531i 0.253013 + 0.253013i 0.822205 0.569192i \(-0.192744\pi\)
−0.569192 + 0.822205i \(0.692744\pi\)
\(758\) 738.530 116.972i 0.974314 0.154316i
\(759\) −79.4961 25.8299i −0.104738 0.0340314i
\(760\) 251.939 86.2460i 0.331499 0.113482i
\(761\) −422.046 1298.92i −0.554593 1.70686i −0.697015 0.717057i \(-0.745489\pi\)
0.142421 0.989806i \(-0.454511\pi\)
\(762\) 273.699 139.457i 0.359185 0.183014i
\(763\) 819.478 + 1608.32i 1.07402 + 2.10788i
\(764\) 230.684 74.9537i 0.301942 0.0981069i
\(765\) 193.313 145.130i 0.252696 0.189713i
\(766\) 82.1766 252.914i 0.107280 0.330174i
\(767\) 186.197 + 1175.60i 0.242760 + 1.53272i
\(768\) −27.6560 + 27.6560i −0.0360104 + 0.0360104i
\(769\) −268.751 + 369.904i −0.349481 + 0.481019i −0.947181 0.320701i \(-0.896082\pi\)
0.597700 + 0.801720i \(0.296082\pi\)
\(770\) 109.087 766.251i 0.141671 0.995131i
\(771\) 40.4207 29.3673i 0.0524263 0.0380899i
\(772\) −123.804 19.6087i −0.160368 0.0253998i
\(773\) 838.256 + 427.113i 1.08442 + 0.552539i 0.902463 0.430767i \(-0.141757\pi\)
0.181956 + 0.983307i \(0.441757\pi\)
\(774\) 175.301i 0.226488i
\(775\) 254.704 374.717i 0.328650 0.483506i
\(776\) −469.350 −0.604832
\(777\) 249.826 490.311i 0.321526 0.631030i
\(778\) −117.823 + 743.908i −0.151444 + 0.956179i
\(779\) −247.776 341.034i −0.318069 0.437785i
\(780\) −77.2525 442.748i −0.0990417 0.567626i
\(781\) 407.468 + 296.043i 0.521726 + 0.379056i
\(782\) 49.6546 + 49.6546i 0.0634969 + 0.0634969i
\(783\) −1320.94 + 209.216i −1.68702 + 0.267197i
\(784\) −189.754 61.6550i −0.242034 0.0786415i
\(785\) −6.06004 386.814i −0.00771980 0.492757i
\(786\) −103.783 319.412i −0.132040 0.406377i
\(787\) 1111.97 566.578i 1.41293 0.719921i 0.429812 0.902919i \(-0.358580\pi\)
0.983113 + 0.182997i \(0.0585799\pi\)
\(788\) −25.4586 49.9652i −0.0323078 0.0634076i
\(789\) −473.761 + 153.934i −0.600458 + 0.195100i
\(790\) 83.5976 + 58.7587i 0.105820 + 0.0743781i
\(791\) −356.976 + 1098.66i −0.451297 + 1.38895i
\(792\) −14.7309 93.0076i −0.0185997 0.117434i
\(793\) −288.642 + 288.642i −0.363987 + 0.363987i
\(794\) −475.822 + 654.913i −0.599273 + 0.824828i
\(795\) −146.142 276.042i −0.183826 0.347223i
\(796\) 101.571 73.7957i 0.127602 0.0927082i
\(797\) −157.517 24.9483i −0.197638 0.0313027i 0.0568307 0.998384i \(-0.481900\pi\)
−0.254468 + 0.967081i \(0.581900\pi\)
\(798\) −576.738 293.862i −0.722729 0.368249i
\(799\) 803.830i 1.00604i
\(800\) −96.8184 + 103.083i −0.121023 + 0.128854i
\(801\) 472.913 0.590403
\(802\) −292.702 + 574.461i −0.364966 + 0.716285i
\(803\) 174.798 1103.63i 0.217681 1.37438i
\(804\) −241.071 331.806i −0.299840 0.412694i
\(805\) −67.9549 + 138.698i −0.0844160 + 0.172296i
\(806\) −381.240 276.987i −0.473002 0.343656i
\(807\) −622.532 622.532i −0.771415 0.771415i
\(808\) −202.037 + 31.9995i −0.250046 + 0.0396034i
\(809\) 55.3058 + 17.9699i 0.0683631 + 0.0222125i 0.342999 0.939336i \(-0.388557\pi\)
−0.274636 + 0.961548i \(0.588557\pi\)
\(810\) −301.632 92.8083i −0.372385 0.114578i
\(811\) 465.514 + 1432.71i 0.574000 + 1.76659i 0.639559 + 0.768742i \(0.279117\pi\)
−0.0655584 + 0.997849i \(0.520883\pi\)
\(812\) 806.255 410.807i 0.992925 0.505920i
\(813\) 98.5306 + 193.377i 0.121194 + 0.237856i
\(814\) −335.168 + 108.903i −0.411754 + 0.133787i
\(815\) −128.775 + 418.525i −0.158006 + 0.513528i
\(816\) 48.2970 148.643i 0.0591875 0.182160i
\(817\) 120.721 + 762.202i 0.147761 + 0.932927i
\(818\) −373.339 + 373.339i −0.456405 + 0.456405i
\(819\) 325.029 447.364i 0.396861 0.546232i
\(820\) 201.037 + 98.4979i 0.245168 + 0.120119i
\(821\) −634.135 + 460.726i −0.772393 + 0.561177i −0.902686 0.430299i \(-0.858408\pi\)
0.130293 + 0.991476i \(0.458408\pi\)
\(822\) 176.218 + 27.9102i 0.214377 + 0.0339540i
\(823\) 852.532 + 434.387i 1.03588 + 0.527809i 0.887349 0.461098i \(-0.152544\pi\)
0.148534 + 0.988907i \(0.452544\pi\)
\(824\) 377.184i 0.457747i
\(825\) 125.993 + 660.783i 0.152718 + 0.800949i
\(826\) −910.382 −1.10216
\(827\) 420.983 826.226i 0.509048 0.999064i −0.483284 0.875464i \(-0.660556\pi\)
0.992332 0.123600i \(-0.0394439\pi\)
\(828\) −2.93963 + 18.5601i −0.00355028 + 0.0224156i
\(829\) −89.7223 123.492i −0.108230 0.148965i 0.751466 0.659771i \(-0.229347\pi\)
−0.859696 + 0.510806i \(0.829347\pi\)
\(830\) −9.32574 + 4.93722i −0.0112358 + 0.00594845i
\(831\) 632.005 + 459.179i 0.760536 + 0.552562i
\(832\) 104.006 + 104.006i 0.125008 + 0.125008i
\(833\) 787.479 124.724i 0.945352 0.149729i
\(834\) −624.096 202.781i −0.748316 0.243143i
\(835\) −45.4978 + 64.7309i −0.0544883 + 0.0775220i
\(836\) 128.099 + 394.248i 0.153228 + 0.471588i
\(837\) −474.652 + 241.847i −0.567088 + 0.288946i
\(838\) 386.402 + 758.357i 0.461100 + 0.904961i
\(839\) 685.697 222.797i 0.817279 0.265550i 0.129601 0.991566i \(-0.458630\pi\)
0.687678 + 0.726016i \(0.258630\pi\)
\(840\) 343.716 5.38484i 0.409186 0.00641053i
\(841\) −379.848 + 1169.05i −0.451662 + 1.39007i
\(842\) −28.2695 178.486i −0.0335742 0.211979i
\(843\) 441.450 441.450i 0.523665 0.523665i
\(844\) −406.082 + 558.924i −0.481140 + 0.662232i
\(845\) −832.628 + 145.280i −0.985358 + 0.171929i
\(846\) −174.023 + 126.435i −0.205701 + 0.149451i
\(847\) 1.62287 + 0.257037i 0.00191602 + 0.000303467i
\(848\) 91.0784 + 46.4067i 0.107404 + 0.0547249i
\(849\) 4.50956i 0.00531161i
\(850\) 157.713 542.677i 0.185544 0.638444i
\(851\) 70.3264 0.0826397
\(852\) −101.557 + 199.316i −0.119198 + 0.233939i
\(853\) −104.473 + 659.613i −0.122477 + 0.773287i 0.847627 + 0.530593i \(0.178031\pi\)
−0.970103 + 0.242693i \(0.921969\pi\)
\(854\) −183.517 252.590i −0.214892 0.295773i
\(855\) −281.917 40.1350i −0.329727 0.0469415i
\(856\) 335.978 + 244.102i 0.392497 + 0.285166i
\(857\) −244.838 244.838i −0.285692 0.285692i 0.549682 0.835374i \(-0.314749\pi\)
−0.835374 + 0.549682i \(0.814749\pi\)
\(858\) 691.024 109.448i 0.805390 0.127561i
\(859\) −993.529 322.817i −1.15661 0.375806i −0.332981 0.942934i \(-0.608054\pi\)
−0.823630 + 0.567128i \(0.808054\pi\)
\(860\) −246.058 327.747i −0.286113 0.381101i
\(861\) −168.158 517.537i −0.195305 0.601088i
\(862\) −37.7696 + 19.2446i −0.0438163 + 0.0223255i
\(863\) −221.512 434.742i −0.256677 0.503757i 0.726325 0.687351i \(-0.241227\pi\)
−0.983002 + 0.183595i \(0.941227\pi\)
\(864\) 158.138 51.3821i 0.183030 0.0594700i
\(865\) 232.522 + 679.237i 0.268812 + 0.785245i
\(866\) 141.631 435.895i 0.163546 0.503343i
\(867\) −12.8114 80.8878i −0.0147767 0.0932962i
\(868\) 254.865 254.865i 0.293623 0.293623i
\(869\) −93.4968 + 128.687i −0.107591 + 0.148087i
\(870\) −547.332 + 564.755i −0.629117 + 0.649143i
\(871\) −1247.83 + 906.600i −1.43264 + 1.04087i
\(872\) 507.109 + 80.3182i 0.581547 + 0.0921080i
\(873\) 447.195 + 227.857i 0.512250 + 0.261005i
\(874\) 82.7228i 0.0946485i
\(875\) 1241.61 58.3933i 1.41898 0.0667352i
\(876\) 496.283 0.566533
\(877\) 656.489 1288.43i 0.748563 1.46914i −0.130002 0.991514i \(-0.541498\pi\)
0.878565 0.477623i \(-0.158502\pi\)
\(878\) −97.4867 + 615.507i −0.111033 + 0.701033i
\(879\) −397.800 547.524i −0.452559 0.622895i
\(880\) −158.089 153.212i −0.179647 0.174105i
\(881\) −228.685 166.150i −0.259575 0.188592i 0.450385 0.892835i \(-0.351287\pi\)
−0.709960 + 0.704242i \(0.751287\pi\)
\(882\) 150.865 + 150.865i 0.171049 + 0.171049i
\(883\) −100.742 + 15.9559i −0.114090 + 0.0180701i −0.213219 0.977005i \(-0.568395\pi\)
0.0991282 + 0.995075i \(0.468395\pi\)
\(884\) −559.004 181.631i −0.632357 0.205465i
\(885\) 748.593 256.265i 0.845868 0.289565i
\(886\) 175.782 + 541.002i 0.198400 + 0.610611i
\(887\) −1001.01 + 510.038i −1.12853 + 0.575015i −0.915615 0.402056i \(-0.868296\pi\)
−0.212915 + 0.977071i \(0.568296\pi\)
\(888\) −71.0605 139.464i −0.0800231 0.157054i
\(889\) 840.336 273.042i 0.945260 0.307134i
\(890\) 884.167 663.793i 0.993447 0.745834i
\(891\) 151.812 467.229i 0.170384 0.524387i
\(892\) 79.5498 + 502.258i 0.0891814 + 0.563069i
\(893\) 669.576 669.576i 0.749805 0.749805i
\(894\) −305.678 + 420.729i −0.341921 + 0.470614i
\(895\) 100.846 708.361i 0.112677 0.791465i
\(896\) −91.0158 + 66.1268i −0.101580 + 0.0738023i
\(897\) −137.897 21.8408i −0.153732 0.0243487i
\(898\) −241.834 123.221i −0.269303 0.137217i
\(899\) 824.609i 0.917251i
\(900\) 142.293 51.2147i 0.158103 0.0569053i
\(901\) −408.477 −0.453360
\(902\) −158.215 + 310.514i −0.175404 + 0.344251i
\(903\) −155.839 + 983.930i −0.172579 + 1.08962i
\(904\) 193.137 + 265.830i 0.213647 + 0.294060i
\(905\) 133.866 + 767.212i 0.147918 + 0.847748i
\(906\) 514.281 + 373.647i 0.567639 + 0.412414i
\(907\) −1033.81 1033.81i −1.13981 1.13981i −0.988484 0.151328i \(-0.951645\pi\)
−0.151328 0.988484i \(-0.548355\pi\)
\(908\) 328.056 51.9589i 0.361295 0.0572235i
\(909\) 208.035 + 67.5947i 0.228862 + 0.0743616i
\(910\) −20.2509 1292.62i −0.0222537 1.42046i
\(911\) 38.6335 + 118.902i 0.0424078 + 0.130518i 0.970019 0.243030i \(-0.0781413\pi\)
−0.927611 + 0.373547i \(0.878141\pi\)
\(912\) −164.047 + 83.5863i −0.179876 + 0.0916516i
\(913\) −7.45740 14.6360i −0.00816801 0.0160306i
\(914\) 127.109 41.3003i 0.139069 0.0451864i
\(915\) 222.005 + 156.042i 0.242629 + 0.170538i
\(916\) 128.110 394.283i 0.139858 0.430440i
\(917\) −151.124 954.157i −0.164802 1.04052i
\(918\) −469.837 + 469.837i −0.511805 + 0.511805i
\(919\) 165.018 227.127i 0.179562 0.247146i −0.709743 0.704461i \(-0.751189\pi\)
0.889305 + 0.457315i \(0.151189\pi\)
\(920\) 20.5554 + 38.8265i 0.0223429 + 0.0422027i
\(921\) 239.097 173.714i 0.259606 0.188615i
\(922\) −177.077 28.0462i −0.192057 0.0304188i
\(923\) 749.571 + 381.925i 0.812102 + 0.413787i
\(924\) 535.128i 0.579143i
\(925\) −272.615 495.985i −0.294719 0.536200i
\(926\) 421.897 0.455613
\(927\) −183.113 + 359.380i −0.197533 + 0.387680i
\(928\) 40.2638 254.216i 0.0433877 0.273939i
\(929\) −487.922 671.567i −0.525212 0.722892i 0.461180 0.887307i \(-0.347426\pi\)
−0.986391 + 0.164415i \(0.947426\pi\)
\(930\) −137.829 + 281.314i −0.148203 + 0.302488i
\(931\) −759.849 552.062i −0.816164 0.592978i
\(932\) −46.2569 46.2569i −0.0496319 0.0496319i
\(933\) 639.817 101.337i 0.685763 0.108614i
\(934\) 404.170 + 131.323i 0.432730 + 0.140603i
\(935\) 840.834 + 258.714i 0.899288 + 0.276699i
\(936\) −48.6045 149.589i −0.0519279 0.159818i
\(937\) −1268.27 + 646.215i −1.35354 + 0.689663i −0.972064 0.234715i \(-0.924584\pi\)
−0.381476 + 0.924379i \(0.624584\pi\)
\(938\) −535.584 1051.14i −0.570985 1.12062i
\(939\) 302.620 98.3271i 0.322279 0.104715i
\(940\) −147.890 + 480.650i −0.157329 + 0.511330i
\(941\) −273.663 + 842.248i −0.290821 + 0.895056i 0.693772 + 0.720195i \(0.255948\pi\)
−0.984593 + 0.174861i \(0.944052\pi\)
\(942\) 41.8425 + 264.183i 0.0444188 + 0.280449i
\(943\) 49.1754 49.1754i 0.0521478 0.0521478i
\(944\) −152.207 + 209.494i −0.161236 + 0.221922i
\(945\) −1312.38 642.997i −1.38876 0.680420i
\(946\) 516.140 374.998i 0.545603 0.396404i
\(947\) 1151.78 + 182.424i 1.21624 + 0.192633i 0.731386 0.681964i \(-0.238874\pi\)
0.484851 + 0.874597i \(0.338874\pi\)
\(948\) −62.9484 32.0738i −0.0664012 0.0338331i
\(949\) 1866.38i 1.96668i
\(950\) −583.412 + 320.669i −0.614118 + 0.337546i
\(951\) −264.180 −0.277792
\(952\) 204.098 400.565i 0.214389 0.420762i
\(953\) 67.9658 429.119i 0.0713177 0.450282i −0.926027 0.377457i \(-0.876799\pi\)
0.997345 0.0728250i \(-0.0232015\pi\)
\(954\) −64.2499 88.4324i −0.0673479 0.0926964i
\(955\) −535.917 + 283.724i −0.561170 + 0.297093i
\(956\) −604.286 439.040i −0.632099 0.459247i
\(957\) −865.697 865.697i −0.904595 0.904595i
\(958\) 273.148 43.2624i 0.285123 0.0451591i
\(959\) 488.080 + 158.587i 0.508947 + 0.165367i
\(960\) 56.2267 79.9952i 0.0585695 0.0833284i
\(961\) −195.466 601.582i −0.203398 0.625996i
\(962\) −524.485 + 267.238i −0.545202 + 0.277795i
\(963\) −201.613 395.688i −0.209360 0.410891i
\(964\) 627.229 203.799i 0.650653 0.211410i
\(965\) 313.330 4.90880i 0.324695 0.00508684i
\(966\) 32.9991 101.561i 0.0341605 0.105135i
\(967\) −119.482 754.378i −0.123559 0.780122i −0.969183 0.246343i \(-0.920771\pi\)
0.845624 0.533780i \(-0.179229\pi\)
\(968\) 0.330475 0.330475i 0.000341400 0.000341400i
\(969\) 432.454 595.222i 0.446289 0.614265i
\(970\) 1155.91 201.688i 1.19166 0.207925i
\(971\) −633.295 + 460.115i −0.652209 + 0.473857i −0.864023 0.503453i \(-0.832063\pi\)
0.211814 + 0.977310i \(0.432063\pi\)
\(972\) −307.062 48.6338i −0.315907 0.0500348i
\(973\) −1681.82 856.931i −1.72849 0.880711i
\(974\) 481.620i 0.494476i
\(975\) 380.514 + 1057.20i 0.390270 + 1.08431i
\(976\) −88.8075 −0.0909913
\(977\) −243.958 + 478.795i −0.249701 + 0.490067i −0.981502 0.191452i \(-0.938680\pi\)
0.731801 + 0.681519i \(0.238680\pi\)
\(978\) 47.3615 299.029i 0.0484269 0.305755i
\(979\) 1011.64 + 1392.40i 1.03334 + 1.42227i
\(980\) 493.820 + 70.3025i 0.503898 + 0.0717372i
\(981\) −444.179 322.715i −0.452782 0.328965i
\(982\) 734.246 + 734.246i 0.747705 + 0.747705i
\(983\) −1205.54 + 190.939i −1.22639 + 0.194241i −0.735829 0.677168i \(-0.763207\pi\)
−0.490559 + 0.871408i \(0.663207\pi\)
\(984\) −147.208 47.8309i −0.149602 0.0486086i
\(985\) 84.1700 + 112.114i 0.0854518 + 0.113821i
\(986\) 317.832 + 978.187i 0.322345 + 0.992076i
\(987\) 1089.16 554.953i 1.10350 0.562262i
\(988\) 314.344 + 616.936i 0.318162 + 0.624429i
\(989\) −121.082 + 39.3418i −0.122428 + 0.0397794i
\(990\) 76.2462 + 222.728i 0.0770164 + 0.224978i
\(991\) 562.687 1731.77i 0.567798 1.74750i −0.0916915 0.995787i \(-0.529227\pi\)
0.659489 0.751714i \(-0.270773\pi\)
\(992\) −16.0379 101.259i −0.0161673 0.102076i
\(993\) −611.121 + 611.121i −0.615429 + 0.615429i
\(994\) −378.211 + 520.563i −0.380494 + 0.523705i
\(995\) −218.437 + 225.390i −0.219535 + 0.226523i
\(996\) 5.90233 4.28829i 0.00592604 0.00430552i
\(997\) 430.422 + 68.1721i 0.431717 + 0.0683772i 0.368511 0.929623i \(-0.379868\pi\)
0.0632055 + 0.998001i \(0.479868\pi\)
\(998\) 410.299 + 209.058i 0.411121 + 0.209477i
\(999\) 665.436i 0.666102i
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 50.3.f.b.17.3 yes 24
4.3 odd 2 400.3.bg.b.17.1 24
5.2 odd 4 250.3.f.d.143.1 24
5.3 odd 4 250.3.f.f.143.3 24
5.4 even 2 250.3.f.e.107.1 24
25.3 odd 20 inner 50.3.f.b.3.3 24
25.4 even 10 250.3.f.d.7.1 24
25.21 even 5 250.3.f.f.7.3 24
25.22 odd 20 250.3.f.e.243.1 24
100.3 even 20 400.3.bg.b.353.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
50.3.f.b.3.3 24 25.3 odd 20 inner
50.3.f.b.17.3 yes 24 1.1 even 1 trivial
250.3.f.d.7.1 24 25.4 even 10
250.3.f.d.143.1 24 5.2 odd 4
250.3.f.e.107.1 24 5.4 even 2
250.3.f.e.243.1 24 25.22 odd 20
250.3.f.f.7.3 24 25.21 even 5
250.3.f.f.143.3 24 5.3 odd 4
400.3.bg.b.17.1 24 4.3 odd 2
400.3.bg.b.353.1 24 100.3 even 20