Properties

Label 50.3.f.b.17.2
Level $50$
Weight $3$
Character 50.17
Analytic conductor $1.362$
Analytic rank $0$
Dimension $24$
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] = [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 17.2
Character \(\chi\) \(=\) 50.17
Dual form 50.3.f.b.3.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.642040 - 1.26007i) q^{2} +(0.304004 - 1.91941i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(-3.29532 - 3.76044i) q^{5} +(-2.22341 - 1.61540i) q^{6} +(6.96775 + 6.96775i) q^{7} +(-2.79360 + 0.442463i) q^{8} +(4.96781 + 1.61414i) q^{9} +O(q^{10})\) \(q+(0.642040 - 1.26007i) q^{2} +(0.304004 - 1.91941i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(-3.29532 - 3.76044i) q^{5} +(-2.22341 - 1.61540i) q^{6} +(6.96775 + 6.96775i) q^{7} +(-2.79360 + 0.442463i) q^{8} +(4.96781 + 1.61414i) q^{9} +(-6.85415 + 1.73799i) q^{10} +(-2.27872 - 7.01318i) q^{11} +(-3.46304 + 1.76451i) q^{12} +(2.19652 + 4.31091i) q^{13} +(13.2534 - 4.30631i) q^{14} +(-8.21960 + 5.18186i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(4.91496 + 31.0318i) q^{17} +(5.22346 - 5.22346i) q^{18} +(2.91847 - 4.01693i) q^{19} +(-2.21064 + 9.75259i) q^{20} +(15.4922 - 11.2557i) q^{21} +(-10.3002 - 1.63138i) q^{22} +(-30.5816 - 15.5821i) q^{23} +5.49657i q^{24} +(-3.28179 + 24.7837i) q^{25} +6.84231 q^{26} +(12.5487 - 24.6282i) q^{27} +(3.08298 - 19.4651i) q^{28} +(-7.51040 - 10.3372i) q^{29} +(1.25222 + 13.6843i) q^{30} +(-8.48508 - 6.16477i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-14.1539 + 2.24176i) q^{33} +(42.2580 + 13.7305i) q^{34} +(3.24086 - 49.1627i) q^{35} +(-3.22828 - 9.93561i) q^{36} +(-36.3060 + 18.4988i) q^{37} +(-3.18785 - 6.25651i) q^{38} +(8.94214 - 2.90548i) q^{39} +(10.8697 + 9.04712i) q^{40} +(15.0755 - 46.3975i) q^{41} +(-4.23645 - 26.7479i) q^{42} +(-8.60508 + 8.60508i) q^{43} +(-8.66877 + 11.9315i) q^{44} +(-10.3006 - 24.0002i) q^{45} +(-39.2692 + 28.5307i) q^{46} +(48.5171 + 7.68435i) q^{47} +(6.92609 + 3.52902i) q^{48} +48.0991i q^{49} +(29.1222 + 20.0474i) q^{50} +61.0569 q^{51} +(4.39304 - 8.62182i) q^{52} +(-7.71392 + 48.7038i) q^{53} +(-22.9766 - 31.6246i) q^{54} +(-18.8635 + 31.6796i) q^{55} +(-22.5481 - 16.3822i) q^{56} +(-6.82289 - 6.82289i) q^{57} +(-17.8476 + 2.82678i) q^{58} +(-66.1155 - 21.4822i) q^{59} +(18.0471 + 7.20795i) q^{60} +(23.3342 + 71.8153i) q^{61} +(-13.2158 + 6.73380i) q^{62} +(23.3675 + 45.8613i) q^{63} +(7.60845 - 2.47214i) q^{64} +(8.97269 - 22.4657i) q^{65} +(-6.26258 + 19.2742i) q^{66} +(-0.769216 - 4.85664i) q^{67} +(44.4327 - 44.4327i) q^{68} +(-39.2053 + 53.9615i) q^{69} +(-59.8679 - 35.6481i) q^{70} +(-46.2320 + 33.5895i) q^{71} +(-14.5923 - 2.31119i) q^{72} +(50.0339 + 25.4935i) q^{73} +57.6252i q^{74} +(46.5722 + 13.8334i) q^{75} -9.93039 q^{76} +(32.9886 - 64.7437i) q^{77} +(2.08009 - 13.1332i) q^{78} +(-89.5179 - 123.211i) q^{79} +(18.3788 - 7.88797i) q^{80} +(-5.42390 - 3.94069i) q^{81} +(-48.7852 - 48.7852i) q^{82} +(107.353 - 17.0030i) q^{83} +(-36.4243 - 11.8350i) q^{84} +(100.497 - 120.742i) q^{85} +(5.31823 + 16.3678i) q^{86} +(-22.1244 + 11.2730i) q^{87} +(9.46892 + 18.5838i) q^{88} +(125.692 - 40.8397i) q^{89} +(-36.8555 - 2.42955i) q^{90} +(-14.7325 + 45.3421i) q^{91} +(10.7384 + 67.7999i) q^{92} +(-14.4122 + 14.4122i) q^{93} +(40.8327 - 56.2014i) q^{94} +(-24.7227 + 2.26232i) q^{95} +(8.89364 - 6.46161i) q^{96} +(-54.9088 - 8.69669i) q^{97} +(60.6084 + 30.8815i) q^{98} -38.5183i 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
\(3\) 0.304004 1.91941i 0.101335 0.639802i −0.883780 0.467903i \(-0.845010\pi\)
0.985115 0.171899i \(-0.0549903\pi\)
\(4\) −1.17557 1.61803i −0.293893 0.404508i
\(5\) −3.29532 3.76044i −0.659063 0.752088i
\(6\) −2.22341 1.61540i −0.370568 0.269234i
\(7\) 6.96775 + 6.96775i 0.995393 + 0.995393i 0.999989 0.00459653i \(-0.00146312\pi\)
−0.00459653 + 0.999989i \(0.501463\pi\)
\(8\) −2.79360 + 0.442463i −0.349201 + 0.0553079i
\(9\) 4.96781 + 1.61414i 0.551979 + 0.179349i
\(10\) −6.85415 + 1.73799i −0.685415 + 0.173799i
\(11\) −2.27872 7.01318i −0.207157 0.637562i −0.999618 0.0276401i \(-0.991201\pi\)
0.792461 0.609922i \(-0.208799\pi\)
\(12\) −3.46304 + 1.76451i −0.288587 + 0.147042i
\(13\) 2.19652 + 4.31091i 0.168963 + 0.331608i 0.959925 0.280257i \(-0.0904196\pi\)
−0.790962 + 0.611865i \(0.790420\pi\)
\(14\) 13.2534 4.30631i 0.946675 0.307593i
\(15\) −8.21960 + 5.18186i −0.547973 + 0.345457i
\(16\) −1.23607 + 3.80423i −0.0772542 + 0.237764i
\(17\) 4.91496 + 31.0318i 0.289115 + 1.82540i 0.522056 + 0.852911i \(0.325165\pi\)
−0.232940 + 0.972491i \(0.574835\pi\)
\(18\) 5.22346 5.22346i 0.290192 0.290192i
\(19\) 2.91847 4.01693i 0.153604 0.211417i −0.725279 0.688455i \(-0.758289\pi\)
0.878883 + 0.477038i \(0.158289\pi\)
\(20\) −2.21064 + 9.75259i −0.110532 + 0.487630i
\(21\) 15.4922 11.2557i 0.737722 0.535987i
\(22\) −10.3002 1.63138i −0.468189 0.0741538i
\(23\) −30.5816 15.5821i −1.32963 0.677482i −0.362556 0.931962i \(-0.618096\pi\)
−0.967078 + 0.254480i \(0.918096\pi\)
\(24\) 5.49657i 0.229024i
\(25\) −3.28179 + 24.7837i −0.131272 + 0.991346i
\(26\) 6.84231 0.263166
\(27\) 12.5487 24.6282i 0.464767 0.912157i
\(28\) 3.08298 19.4651i 0.110106 0.695184i
\(29\) −7.51040 10.3372i −0.258979 0.356455i 0.659651 0.751572i \(-0.270704\pi\)
−0.918631 + 0.395117i \(0.870704\pi\)
\(30\) 1.25222 + 13.6843i 0.0417406 + 0.456142i
\(31\) −8.48508 6.16477i −0.273712 0.198864i 0.442458 0.896789i \(-0.354107\pi\)
−0.716170 + 0.697926i \(0.754107\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) −14.1539 + 2.24176i −0.428906 + 0.0679320i
\(34\) 42.2580 + 13.7305i 1.24288 + 0.403837i
\(35\) 3.24086 49.1627i 0.0925959 1.40465i
\(36\) −3.22828 9.93561i −0.0896743 0.275989i
\(37\) −36.3060 + 18.4988i −0.981243 + 0.499968i −0.869587 0.493779i \(-0.835615\pi\)
−0.111655 + 0.993747i \(0.535615\pi\)
\(38\) −3.18785 6.25651i −0.0838908 0.164645i
\(39\) 8.94214 2.90548i 0.229286 0.0744994i
\(40\) 10.8697 + 9.04712i 0.271742 + 0.226178i
\(41\) 15.0755 46.3975i 0.367694 1.13165i −0.580583 0.814201i \(-0.697175\pi\)
0.948277 0.317445i \(-0.102825\pi\)
\(42\) −4.23645 26.7479i −0.100868 0.636854i
\(43\) −8.60508 + 8.60508i −0.200118 + 0.200118i −0.800051 0.599932i \(-0.795194\pi\)
0.599932 + 0.800051i \(0.295194\pi\)
\(44\) −8.66877 + 11.9315i −0.197018 + 0.271171i
\(45\) −10.3006 24.0002i −0.228903 0.533338i
\(46\) −39.2692 + 28.5307i −0.853678 + 0.620233i
\(47\) 48.5171 + 7.68435i 1.03228 + 0.163497i 0.649514 0.760349i \(-0.274972\pi\)
0.382764 + 0.923846i \(0.374972\pi\)
\(48\) 6.92609 + 3.52902i 0.144293 + 0.0735212i
\(49\) 48.0991i 0.981614i
\(50\) 29.1222 + 20.0474i 0.582444 + 0.400948i
\(51\) 61.0569 1.19719
\(52\) 4.39304 8.62182i 0.0844814 0.165804i
\(53\) −7.71392 + 48.7038i −0.145546 + 0.918939i 0.801536 + 0.597946i \(0.204016\pi\)
−0.947082 + 0.320993i \(0.895984\pi\)
\(54\) −22.9766 31.6246i −0.425493 0.585641i
\(55\) −18.8635 + 31.6796i −0.342973 + 0.575994i
\(56\) −22.5481 16.3822i −0.402645 0.292539i
\(57\) −6.82289 6.82289i −0.119700 0.119700i
\(58\) −17.8476 + 2.82678i −0.307717 + 0.0487376i
\(59\) −66.1155 21.4822i −1.12060 0.364106i −0.310604 0.950539i \(-0.600531\pi\)
−0.809997 + 0.586434i \(0.800531\pi\)
\(60\) 18.0471 + 7.20795i 0.300786 + 0.120132i
\(61\) 23.3342 + 71.8153i 0.382528 + 1.17730i 0.938258 + 0.345937i \(0.112439\pi\)
−0.555730 + 0.831363i \(0.687561\pi\)
\(62\) −13.2158 + 6.73380i −0.213158 + 0.108610i
\(63\) 23.3675 + 45.8613i 0.370913 + 0.727958i
\(64\) 7.60845 2.47214i 0.118882 0.0386271i
\(65\) 8.97269 22.4657i 0.138041 0.345626i
\(66\) −6.26258 + 19.2742i −0.0948876 + 0.292034i
\(67\) −0.769216 4.85664i −0.0114808 0.0724872i 0.981283 0.192573i \(-0.0616831\pi\)
−0.992764 + 0.120086i \(0.961683\pi\)
\(68\) 44.4327 44.4327i 0.653422 0.653422i
\(69\) −39.2053 + 53.9615i −0.568193 + 0.782050i
\(70\) −59.8679 35.6481i −0.855256 0.509259i
\(71\) −46.2320 + 33.5895i −0.651155 + 0.473092i −0.863665 0.504067i \(-0.831836\pi\)
0.212509 + 0.977159i \(0.431836\pi\)
\(72\) −14.5923 2.31119i −0.202671 0.0320999i
\(73\) 50.0339 + 25.4935i 0.685395 + 0.349226i 0.761765 0.647853i \(-0.224333\pi\)
−0.0763699 + 0.997080i \(0.524333\pi\)
\(74\) 57.6252i 0.778719i
\(75\) 46.5722 + 13.8334i 0.620963 + 0.184446i
\(76\) −9.93039 −0.130663
\(77\) 32.9886 64.7437i 0.428423 0.840827i
\(78\) 2.08009 13.1332i 0.0266678 0.168374i
\(79\) −89.5179 123.211i −1.13314 1.55963i −0.781968 0.623319i \(-0.785784\pi\)
−0.351170 0.936312i \(-0.614216\pi\)
\(80\) 18.3788 7.88797i 0.229735 0.0985996i
\(81\) −5.42390 3.94069i −0.0669617 0.0486505i
\(82\) −48.7852 48.7852i −0.594941 0.594941i
\(83\) 107.353 17.0030i 1.29341 0.204856i 0.528466 0.848955i \(-0.322767\pi\)
0.764942 + 0.644099i \(0.222767\pi\)
\(84\) −36.4243 11.8350i −0.433622 0.140892i
\(85\) 100.497 120.742i 1.18232 1.42050i
\(86\) 5.31823 + 16.3678i 0.0618399 + 0.190324i
\(87\) −22.1244 + 11.2730i −0.254304 + 0.129574i
\(88\) 9.46892 + 18.5838i 0.107601 + 0.211180i
\(89\) 125.692 40.8397i 1.41227 0.458873i 0.499130 0.866527i \(-0.333653\pi\)
0.913136 + 0.407654i \(0.133653\pi\)
\(90\) −36.8555 2.42955i −0.409505 0.0269950i
\(91\) −14.7325 + 45.3421i −0.161896 + 0.498265i
\(92\) 10.7384 + 67.7999i 0.116722 + 0.736955i
\(93\) −14.4122 + 14.4122i −0.154970 + 0.154970i
\(94\) 40.8327 56.2014i 0.434391 0.597888i
\(95\) −24.7227 + 2.26232i −0.260239 + 0.0238139i
\(96\) 8.89364 6.46161i 0.0926421 0.0673084i
\(97\) −54.9088 8.69669i −0.566070 0.0896566i −0.133161 0.991094i \(-0.542513\pi\)
−0.432909 + 0.901438i \(0.642513\pi\)
\(98\) 60.6084 + 30.8815i 0.618453 + 0.315118i
\(99\) 38.5183i 0.389074i
\(100\) 43.9588 23.8249i 0.439588 0.238249i
\(101\) −182.579 −1.80771 −0.903855 0.427839i \(-0.859275\pi\)
−0.903855 + 0.427839i \(0.859275\pi\)
\(102\) 39.2009 76.9362i 0.384323 0.754276i
\(103\) 3.02075 19.0722i 0.0293276 0.185167i −0.968676 0.248329i \(-0.920118\pi\)
0.998003 + 0.0631620i \(0.0201185\pi\)
\(104\) −8.04362 11.0711i −0.0773425 0.106453i
\(105\) −93.3780 21.1662i −0.889314 0.201583i
\(106\) 56.4177 + 40.9899i 0.532242 + 0.386697i
\(107\) −2.49555 2.49555i −0.0233229 0.0233229i 0.695349 0.718672i \(-0.255250\pi\)
−0.718672 + 0.695349i \(0.755250\pi\)
\(108\) −54.6012 + 8.64798i −0.505567 + 0.0800739i
\(109\) 19.1934 + 6.23632i 0.176086 + 0.0572139i 0.395733 0.918366i \(-0.370491\pi\)
−0.219647 + 0.975579i \(0.570491\pi\)
\(110\) 27.8075 + 44.1090i 0.252796 + 0.400991i
\(111\) 24.4696 + 75.3096i 0.220447 + 0.678465i
\(112\) −35.1195 + 17.8943i −0.313567 + 0.159770i
\(113\) −54.5747 107.109i −0.482962 0.947866i −0.995988 0.0894924i \(-0.971476\pi\)
0.513026 0.858373i \(-0.328524\pi\)
\(114\) −12.9779 + 4.21678i −0.113841 + 0.0369893i
\(115\) 42.1805 + 166.348i 0.366787 + 1.44650i
\(116\) −7.89691 + 24.3042i −0.0680768 + 0.209519i
\(117\) 3.95347 + 24.9612i 0.0337904 + 0.213344i
\(118\) −69.5179 + 69.5179i −0.589135 + 0.589135i
\(119\) −181.976 + 250.468i −1.52921 + 2.10478i
\(120\) 20.6695 18.1129i 0.172246 0.150941i
\(121\) 53.8989 39.1598i 0.445445 0.323635i
\(122\) 105.474 + 16.7054i 0.864541 + 0.136930i
\(123\) −84.4726 43.0409i −0.686769 0.349926i
\(124\) 20.9763i 0.169163i
\(125\) 104.012 69.3290i 0.832096 0.554632i
\(126\) 72.7915 0.577711
\(127\) 43.6037 85.5772i 0.343337 0.673836i −0.653183 0.757201i \(-0.726567\pi\)
0.996519 + 0.0833645i \(0.0265666\pi\)
\(128\) 1.76985 11.1744i 0.0138270 0.0873001i
\(129\) 13.9007 + 19.1326i 0.107757 + 0.148315i
\(130\) −22.5476 25.7301i −0.173443 0.197924i
\(131\) 18.7606 + 13.6303i 0.143210 + 0.104048i 0.657084 0.753818i \(-0.271790\pi\)
−0.513873 + 0.857866i \(0.671790\pi\)
\(132\) 20.2661 + 20.2661i 0.153531 + 0.153531i
\(133\) 48.3241 7.65378i 0.363339 0.0575472i
\(134\) −6.61359 2.14889i −0.0493552 0.0160365i
\(135\) −133.965 + 33.9691i −0.992332 + 0.251623i
\(136\) −27.4609 84.5160i −0.201918 0.621441i
\(137\) −121.194 + 61.7516i −0.884630 + 0.450741i −0.836416 0.548096i \(-0.815353\pi\)
−0.0482140 + 0.998837i \(0.515353\pi\)
\(138\) 42.8241 + 84.0469i 0.310319 + 0.609036i
\(139\) 248.403 80.7112i 1.78707 0.580656i 0.787702 0.616057i \(-0.211271\pi\)
0.999373 + 0.0354010i \(0.0112708\pi\)
\(140\) −83.3568 + 52.5504i −0.595406 + 0.375360i
\(141\) 29.4988 90.7879i 0.209211 0.643886i
\(142\) 12.6425 + 79.8216i 0.0890316 + 0.562124i
\(143\) 25.2279 25.2279i 0.176419 0.176419i
\(144\) −12.2811 + 16.9035i −0.0852854 + 0.117385i
\(145\) −14.1232 + 62.3067i −0.0974013 + 0.429701i
\(146\) 64.2474 46.6785i 0.440051 0.319716i
\(147\) 92.3217 + 14.6223i 0.628039 + 0.0994716i
\(148\) 72.6120 + 36.9976i 0.490621 + 0.249984i
\(149\) 63.1967i 0.424139i 0.977255 + 0.212069i \(0.0680203\pi\)
−0.977255 + 0.212069i \(0.931980\pi\)
\(150\) 47.3323 49.8028i 0.315549 0.332019i
\(151\) 71.0637 0.470621 0.235310 0.971920i \(-0.424389\pi\)
0.235310 + 0.971920i \(0.424389\pi\)
\(152\) −6.37570 + 12.5130i −0.0419454 + 0.0823225i
\(153\) −25.6731 + 162.094i −0.167798 + 1.05944i
\(154\) −60.4018 83.1360i −0.392220 0.539844i
\(155\) 4.77877 + 52.2225i 0.0308308 + 0.336919i
\(156\) −15.2133 11.0531i −0.0975210 0.0708531i
\(157\) −150.002 150.002i −0.955427 0.955427i 0.0436208 0.999048i \(-0.486111\pi\)
−0.999048 + 0.0436208i \(0.986111\pi\)
\(158\) −212.729 + 33.6929i −1.34638 + 0.213246i
\(159\) 91.1373 + 29.6123i 0.573190 + 0.186241i
\(160\) 1.86049 28.2230i 0.0116281 0.176394i
\(161\) −104.513 321.657i −0.649147 1.99787i
\(162\) −8.44792 + 4.30443i −0.0521477 + 0.0265706i
\(163\) −125.792 246.881i −0.771730 1.51461i −0.855317 0.518105i \(-0.826638\pi\)
0.0835873 0.996500i \(-0.473362\pi\)
\(164\) −92.7949 + 30.1509i −0.565823 + 0.183847i
\(165\) 55.0715 + 45.8375i 0.333767 + 0.277803i
\(166\) 47.4997 146.189i 0.286143 0.880657i
\(167\) 28.4957 + 179.915i 0.170633 + 1.07734i 0.913184 + 0.407546i \(0.133616\pi\)
−0.742551 + 0.669789i \(0.766384\pi\)
\(168\) −38.2987 + 38.2987i −0.227969 + 0.227969i
\(169\) 85.5765 117.786i 0.506370 0.696958i
\(170\) −87.6209 204.155i −0.515417 1.20091i
\(171\) 20.9823 15.2445i 0.122703 0.0891491i
\(172\) 24.0392 + 3.80744i 0.139763 + 0.0221363i
\(173\) −70.6137 35.9795i −0.408171 0.207974i 0.237835 0.971306i \(-0.423562\pi\)
−0.646007 + 0.763332i \(0.723562\pi\)
\(174\) 35.1161i 0.201817i
\(175\) −195.553 + 149.820i −1.11745 + 0.856112i
\(176\) 29.4964 0.167593
\(177\) −61.3325 + 120.372i −0.346511 + 0.680067i
\(178\) 29.2380 184.601i 0.164258 1.03709i
\(179\) 0.398502 + 0.548491i 0.00222627 + 0.00306420i 0.810129 0.586252i \(-0.199397\pi\)
−0.807902 + 0.589316i \(0.799397\pi\)
\(180\) −26.7241 + 44.8807i −0.148467 + 0.249337i
\(181\) 37.0773 + 26.9382i 0.204847 + 0.148830i 0.685479 0.728092i \(-0.259593\pi\)
−0.480632 + 0.876922i \(0.659593\pi\)
\(182\) 47.6755 + 47.6755i 0.261953 + 0.261953i
\(183\) 144.936 22.9557i 0.792002 0.125441i
\(184\) 92.3274 + 29.9990i 0.501779 + 0.163038i
\(185\) 189.203 + 75.5669i 1.02272 + 0.408470i
\(186\) 8.90723 + 27.4136i 0.0478883 + 0.147385i
\(187\) 206.432 105.182i 1.10392 0.562473i
\(188\) −44.6017 87.5358i −0.237243 0.465616i
\(189\) 259.040 84.1671i 1.37058 0.445328i
\(190\) −13.0222 + 32.6049i −0.0685381 + 0.171605i
\(191\) −60.9194 + 187.491i −0.318950 + 0.981627i 0.655148 + 0.755501i \(0.272606\pi\)
−0.974098 + 0.226126i \(0.927394\pi\)
\(192\) −2.43203 15.3553i −0.0126668 0.0799753i
\(193\) −74.7620 + 74.7620i −0.387368 + 0.387368i −0.873748 0.486380i \(-0.838317\pi\)
0.486380 + 0.873748i \(0.338317\pi\)
\(194\) −46.2121 + 63.6054i −0.238206 + 0.327863i
\(195\) −40.3930 24.0519i −0.207144 0.123343i
\(196\) 77.8260 56.5439i 0.397071 0.288489i
\(197\) 175.706 + 27.8291i 0.891908 + 0.141264i 0.585535 0.810647i \(-0.300885\pi\)
0.306373 + 0.951912i \(0.400885\pi\)
\(198\) −48.5359 24.7303i −0.245131 0.124900i
\(199\) 14.6408i 0.0735720i 0.999323 + 0.0367860i \(0.0117120\pi\)
−0.999323 + 0.0367860i \(0.988288\pi\)
\(200\) −1.79784 70.6878i −0.00898921 0.353439i
\(201\) −9.55571 −0.0475409
\(202\) −117.223 + 230.063i −0.580311 + 1.13892i
\(203\) 19.6963 124.358i 0.0970261 0.612599i
\(204\) −71.7767 98.7921i −0.351846 0.484275i
\(205\) −224.153 + 96.2040i −1.09343 + 0.469288i
\(206\) −22.0930 16.0515i −0.107247 0.0779198i
\(207\) −126.772 126.772i −0.612424 0.612424i
\(208\) −19.1147 + 3.02747i −0.0918977 + 0.0145552i
\(209\) −34.8218 11.3143i −0.166612 0.0541354i
\(210\) −86.6233 + 104.074i −0.412492 + 0.495589i
\(211\) 50.9278 + 156.740i 0.241364 + 0.742842i 0.996213 + 0.0869438i \(0.0277100\pi\)
−0.754849 + 0.655898i \(0.772290\pi\)
\(212\) 87.8726 44.7733i 0.414493 0.211195i
\(213\) 50.4172 + 98.9494i 0.236701 + 0.464551i
\(214\) −4.74682 + 1.54234i −0.0221814 + 0.00720718i
\(215\) 60.7154 + 4.00242i 0.282397 + 0.0186159i
\(216\) −24.1590 + 74.3539i −0.111847 + 0.344231i
\(217\) −16.1673 102.077i −0.0745038 0.470399i
\(218\) 20.1812 20.1812i 0.0925741 0.0925741i
\(219\) 64.1429 88.2852i 0.292890 0.403129i
\(220\) 73.4342 6.71981i 0.333792 0.0305446i
\(221\) −122.980 + 89.3499i −0.556469 + 0.404298i
\(222\) 110.606 + 17.5183i 0.498226 + 0.0789112i
\(223\) −107.607 54.8286i −0.482543 0.245868i 0.195758 0.980652i \(-0.437283\pi\)
−0.678301 + 0.734784i \(0.737283\pi\)
\(224\) 55.7420i 0.248848i
\(225\) −56.3076 + 117.823i −0.250256 + 0.523659i
\(226\) −170.004 −0.752230
\(227\) −145.398 + 285.359i −0.640519 + 1.25709i 0.311266 + 0.950323i \(0.399247\pi\)
−0.951785 + 0.306766i \(0.900753\pi\)
\(228\) −3.01888 + 19.0604i −0.0132407 + 0.0835984i
\(229\) 155.195 + 213.607i 0.677706 + 0.932782i 0.999904 0.0138901i \(-0.00442151\pi\)
−0.322197 + 0.946672i \(0.604422\pi\)
\(230\) 236.692 + 53.6515i 1.02910 + 0.233268i
\(231\) −114.241 83.0008i −0.494549 0.359311i
\(232\) 25.5549 + 25.5549i 0.110151 + 0.110151i
\(233\) 144.484 22.8840i 0.620102 0.0982145i 0.161524 0.986869i \(-0.448359\pi\)
0.458578 + 0.888654i \(0.348359\pi\)
\(234\) 33.9913 + 11.0444i 0.145262 + 0.0471985i
\(235\) −130.983 207.768i −0.557373 0.884119i
\(236\) 42.9644 + 132.231i 0.182053 + 0.560301i
\(237\) −263.705 + 134.365i −1.11268 + 0.566939i
\(238\) 198.773 + 390.114i 0.835180 + 1.63913i
\(239\) −161.553 + 52.4917i −0.675953 + 0.219630i −0.626823 0.779162i \(-0.715645\pi\)
−0.0491301 + 0.998792i \(0.515645\pi\)
\(240\) −9.55299 37.6743i −0.0398041 0.156976i
\(241\) −29.0163 + 89.3031i −0.120400 + 0.370552i −0.993035 0.117820i \(-0.962409\pi\)
0.872635 + 0.488373i \(0.162409\pi\)
\(242\) −14.7391 93.0587i −0.0609052 0.384540i
\(243\) 166.693 166.693i 0.685979 0.685979i
\(244\) 88.7686 122.179i 0.363806 0.500735i
\(245\) 180.874 158.502i 0.738260 0.646946i
\(246\) −108.470 + 78.8077i −0.440933 + 0.320357i
\(247\) 23.7271 + 3.75800i 0.0960610 + 0.0152146i
\(248\) 26.4316 + 13.4676i 0.106579 + 0.0543048i
\(249\) 211.223i 0.848284i
\(250\) −20.5799 175.575i −0.0823195 0.702299i
\(251\) 123.629 0.492545 0.246272 0.969201i \(-0.420794\pi\)
0.246272 + 0.969201i \(0.420794\pi\)
\(252\) 46.7350 91.7227i 0.185457 0.363979i
\(253\) −39.5932 + 249.982i −0.156495 + 0.988069i
\(254\) −79.8382 109.888i −0.314324 0.432629i
\(255\) −201.202 229.601i −0.789026 0.900395i
\(256\) −12.9443 9.40456i −0.0505636 0.0367366i
\(257\) 45.6784 + 45.6784i 0.177737 + 0.177737i 0.790369 0.612632i \(-0.209889\pi\)
−0.612632 + 0.790369i \(0.709889\pi\)
\(258\) 33.0333 5.23196i 0.128036 0.0202789i
\(259\) −381.866 124.076i −1.47439 0.479057i
\(260\) −46.8982 + 11.8919i −0.180378 + 0.0457380i
\(261\) −20.6246 63.4760i −0.0790214 0.243203i
\(262\) 29.2202 14.8885i 0.111528 0.0568262i
\(263\) −17.2068 33.7702i −0.0654249 0.128404i 0.855978 0.517012i \(-0.172956\pi\)
−0.921403 + 0.388609i \(0.872956\pi\)
\(264\) 38.5485 12.5252i 0.146017 0.0474438i
\(265\) 208.567 131.487i 0.787046 0.496176i
\(266\) 21.3816 65.8059i 0.0803821 0.247391i
\(267\) −40.1772 253.669i −0.150476 0.950071i
\(268\) −6.95394 + 6.95394i −0.0259475 + 0.0259475i
\(269\) −64.8044 + 89.1956i −0.240908 + 0.331582i −0.912301 0.409520i \(-0.865696\pi\)
0.671393 + 0.741102i \(0.265696\pi\)
\(270\) −43.2071 + 190.615i −0.160026 + 0.705982i
\(271\) 146.860 106.700i 0.541918 0.393727i −0.282879 0.959156i \(-0.591289\pi\)
0.824797 + 0.565429i \(0.191289\pi\)
\(272\) −124.127 19.6598i −0.456351 0.0722788i
\(273\) 82.5512 + 42.0619i 0.302385 + 0.154073i
\(274\) 192.361i 0.702046i
\(275\) 181.291 33.4593i 0.659239 0.121670i
\(276\) 133.400 0.483334
\(277\) 145.052 284.680i 0.523652 1.02772i −0.466074 0.884746i \(-0.654332\pi\)
0.989726 0.142979i \(-0.0456681\pi\)
\(278\) 57.7828 364.826i 0.207852 1.31232i
\(279\) −32.2014 44.3215i −0.115417 0.158858i
\(280\) 12.6990 + 138.775i 0.0453537 + 0.495626i
\(281\) 21.3424 + 15.5062i 0.0759516 + 0.0551821i 0.625113 0.780534i \(-0.285053\pi\)
−0.549162 + 0.835716i \(0.685053\pi\)
\(282\) −95.4601 95.4601i −0.338511 0.338511i
\(283\) −66.9720 + 10.6073i −0.236650 + 0.0374817i −0.273633 0.961834i \(-0.588225\pi\)
0.0369828 + 0.999316i \(0.488225\pi\)
\(284\) 108.698 + 35.3181i 0.382739 + 0.124360i
\(285\) −3.17348 + 48.1406i −0.0111350 + 0.168914i
\(286\) −15.5917 47.9864i −0.0545165 0.167785i
\(287\) 428.328 218.244i 1.49243 0.760432i
\(288\) 13.4147 + 26.3278i 0.0465787 + 0.0914159i
\(289\) −663.963 + 215.735i −2.29745 + 0.746487i
\(290\) 69.4434 + 57.7996i 0.239460 + 0.199309i
\(291\) −33.3850 + 102.748i −0.114725 + 0.353087i
\(292\) −17.5689 110.926i −0.0601676 0.379883i
\(293\) 0.372340 0.372340i 0.00127079 0.00127079i −0.706471 0.707742i \(-0.749714\pi\)
0.707742 + 0.706471i \(0.249714\pi\)
\(294\) 77.6994 106.944i 0.264284 0.363755i
\(295\) 137.089 + 319.414i 0.464708 + 1.08276i
\(296\) 93.2395 67.7425i 0.314998 0.228860i
\(297\) −201.317 31.8855i −0.677836 0.107359i
\(298\) 79.6325 + 40.5748i 0.267223 + 0.136157i
\(299\) 166.061i 0.555387i
\(300\) −32.3660 91.6176i −0.107887 0.305392i
\(301\) −119.916 −0.398393
\(302\) 45.6257 89.5455i 0.151079 0.296508i
\(303\) −55.5047 + 350.443i −0.183184 + 1.15658i
\(304\) 11.6739 + 16.0677i 0.0384009 + 0.0528543i
\(305\) 193.163 324.401i 0.633322 1.06361i
\(306\) 187.767 + 136.421i 0.613617 + 0.445819i
\(307\) 72.1739 + 72.1739i 0.235094 + 0.235094i 0.814815 0.579721i \(-0.196838\pi\)
−0.579721 + 0.814815i \(0.696838\pi\)
\(308\) −143.538 + 22.7342i −0.466032 + 0.0738122i
\(309\) −35.6890 11.5961i −0.115499 0.0375277i
\(310\) 68.8723 + 27.5073i 0.222169 + 0.0887332i
\(311\) −76.9184 236.730i −0.247326 0.761191i −0.995245 0.0974014i \(-0.968947\pi\)
0.747919 0.663790i \(-0.231053\pi\)
\(312\) −23.6952 + 12.0733i −0.0759462 + 0.0386965i
\(313\) 155.789 + 305.754i 0.497729 + 0.976849i 0.994072 + 0.108722i \(0.0346759\pi\)
−0.496343 + 0.868127i \(0.665324\pi\)
\(314\) −285.321 + 92.7064i −0.908665 + 0.295243i
\(315\) 95.4554 239.000i 0.303033 0.758729i
\(316\) −94.1247 + 289.686i −0.297863 + 0.916728i
\(317\) 24.4560 + 154.409i 0.0771483 + 0.487095i 0.995764 + 0.0919436i \(0.0293079\pi\)
−0.918616 + 0.395152i \(0.870692\pi\)
\(318\) 95.8274 95.8274i 0.301344 0.301344i
\(319\) −55.3825 + 76.2274i −0.173613 + 0.238957i
\(320\) −34.3686 20.4646i −0.107402 0.0639520i
\(321\) −5.54863 + 4.03132i −0.0172855 + 0.0125586i
\(322\) −472.413 74.8228i −1.46712 0.232369i
\(323\) 138.997 + 70.8224i 0.430330 + 0.219264i
\(324\) 13.4086i 0.0413846i
\(325\) −114.049 + 40.2902i −0.350919 + 0.123970i
\(326\) −391.851 −1.20200
\(327\) 17.8049 34.9441i 0.0544493 0.106863i
\(328\) −21.5857 + 136.287i −0.0658100 + 0.415508i
\(329\) 284.512 + 391.598i 0.864779 + 1.19027i
\(330\) 93.1168 39.9647i 0.282172 0.121105i
\(331\) 402.818 + 292.664i 1.21697 + 0.884182i 0.995845 0.0910633i \(-0.0290266\pi\)
0.221127 + 0.975245i \(0.429027\pi\)
\(332\) −153.712 153.712i −0.462989 0.462989i
\(333\) −210.221 + 33.2957i −0.631293 + 0.0999871i
\(334\) 245.002 + 79.6058i 0.733538 + 0.238341i
\(335\) −15.7283 + 18.8968i −0.0469501 + 0.0564082i
\(336\) 23.6699 + 72.8485i 0.0704462 + 0.216811i
\(337\) −22.6810 + 11.5565i −0.0673026 + 0.0342924i −0.487318 0.873225i \(-0.662025\pi\)
0.420015 + 0.907517i \(0.362025\pi\)
\(338\) −93.4754 183.456i −0.276554 0.542769i
\(339\) −222.176 + 72.1894i −0.655387 + 0.212948i
\(340\) −313.506 20.6666i −0.922077 0.0607843i
\(341\) −23.8995 + 73.5552i −0.0700866 + 0.215704i
\(342\) −5.73775 36.2268i −0.0167771 0.105926i
\(343\) 6.27731 6.27731i 0.0183012 0.0183012i
\(344\) 20.2318 27.8466i 0.0588133 0.0809495i
\(345\) 332.113 30.3910i 0.962645 0.0880897i
\(346\) −90.6735 + 65.8782i −0.262062 + 0.190399i
\(347\) −427.376 67.6897i −1.23163 0.195071i −0.493510 0.869740i \(-0.664286\pi\)
−0.738121 + 0.674669i \(0.764286\pi\)
\(348\) 44.2489 + 22.5459i 0.127152 + 0.0647872i
\(349\) 16.9445i 0.0485515i 0.999705 + 0.0242757i \(0.00772796\pi\)
−0.999705 + 0.0242757i \(0.992272\pi\)
\(350\) 63.2310 + 342.601i 0.180660 + 0.978861i
\(351\) 133.733 0.381007
\(352\) 18.9378 37.1676i 0.0538007 0.105590i
\(353\) −25.5006 + 161.004i −0.0722396 + 0.456103i 0.924880 + 0.380259i \(0.124165\pi\)
−0.997120 + 0.0758440i \(0.975835\pi\)
\(354\) 112.299 + 154.567i 0.317230 + 0.436630i
\(355\) 278.660 + 63.1646i 0.784959 + 0.177928i
\(356\) −213.839 155.363i −0.600673 0.436414i
\(357\) 425.429 + 425.429i 1.19168 + 1.19168i
\(358\) 0.946994 0.149989i 0.00264523 0.000418964i
\(359\) 35.6372 + 11.5792i 0.0992679 + 0.0322541i 0.358230 0.933633i \(-0.383380\pi\)
−0.258962 + 0.965888i \(0.583380\pi\)
\(360\) 39.3951 + 62.4895i 0.109431 + 0.173582i
\(361\) 103.937 + 319.885i 0.287914 + 0.886108i
\(362\) 57.7492 29.4247i 0.159528 0.0812837i
\(363\) −58.7781 115.359i −0.161923 0.317792i
\(364\) 90.6842 29.4651i 0.249133 0.0809481i
\(365\) −69.0105 272.158i −0.189070 0.745640i
\(366\) 64.1291 197.369i 0.175216 0.539259i
\(367\) 1.52982 + 9.65893i 0.00416846 + 0.0263186i 0.989685 0.143261i \(-0.0457589\pi\)
−0.985516 + 0.169580i \(0.945759\pi\)
\(368\) 97.0787 97.0787i 0.263801 0.263801i
\(369\) 149.784 206.160i 0.405918 0.558699i
\(370\) 216.696 189.893i 0.585665 0.513225i
\(371\) −393.104 + 285.607i −1.05958 + 0.769830i
\(372\) 40.2620 + 6.37687i 0.108231 + 0.0171421i
\(373\) −407.559 207.662i −1.09265 0.556734i −0.187691 0.982228i \(-0.560100\pi\)
−0.904961 + 0.425494i \(0.860100\pi\)
\(374\) 327.651i 0.876072i
\(375\) −101.450 220.718i −0.270535 0.588580i
\(376\) −138.938 −0.369515
\(377\) 28.0659 55.0825i 0.0744454 0.146107i
\(378\) 60.2570 380.448i 0.159410 1.00647i
\(379\) −97.0905 133.634i −0.256176 0.352595i 0.661487 0.749957i \(-0.269926\pi\)
−0.917662 + 0.397362i \(0.869926\pi\)
\(380\) 32.7238 + 37.3426i 0.0861151 + 0.0982700i
\(381\) −151.002 109.709i −0.396330 0.287950i
\(382\) 197.139 + 197.139i 0.516072 + 0.516072i
\(383\) 250.949 39.7465i 0.655220 0.103777i 0.180032 0.983661i \(-0.442380\pi\)
0.475188 + 0.879884i \(0.342380\pi\)
\(384\) −20.9102 6.79414i −0.0544537 0.0176931i
\(385\) −352.172 + 89.2994i −0.914733 + 0.231947i
\(386\) 46.2055 + 142.206i 0.119703 + 0.368409i
\(387\) −56.6382 + 28.8586i −0.146352 + 0.0745700i
\(388\) 50.4776 + 99.0678i 0.130097 + 0.255329i
\(389\) 323.557 105.130i 0.831766 0.270257i 0.137977 0.990435i \(-0.455940\pi\)
0.693789 + 0.720178i \(0.255940\pi\)
\(390\) −56.2411 + 35.4559i −0.144208 + 0.0909126i
\(391\) 333.234 1025.59i 0.852260 2.62299i
\(392\) −21.2821 134.370i −0.0542910 0.342780i
\(393\) 31.8654 31.8654i 0.0810826 0.0810826i
\(394\) 147.877 203.535i 0.375322 0.516586i
\(395\) −168.337 + 742.645i −0.426169 + 1.88011i
\(396\) −62.3239 + 45.2810i −0.157384 + 0.114346i
\(397\) 131.048 + 20.7559i 0.330095 + 0.0522819i 0.319282 0.947660i \(-0.396558\pi\)
0.0108126 + 0.999942i \(0.496558\pi\)
\(398\) 18.4485 + 9.39999i 0.0463531 + 0.0236181i
\(399\) 95.0803i 0.238297i
\(400\) −90.2261 43.1190i −0.225565 0.107797i
\(401\) 391.076 0.975253 0.487626 0.873052i \(-0.337863\pi\)
0.487626 + 0.873052i \(0.337863\pi\)
\(402\) −6.13514 + 12.0409i −0.0152616 + 0.0299525i
\(403\) 7.93814 50.1194i 0.0196976 0.124366i
\(404\) 214.634 + 295.419i 0.531273 + 0.731234i
\(405\) 3.05473 + 33.3821i 0.00754253 + 0.0824248i
\(406\) −144.054 104.661i −0.354812 0.257786i
\(407\) 212.467 + 212.467i 0.522032 + 0.522032i
\(408\) −170.569 + 27.0154i −0.418061 + 0.0662143i
\(409\) −176.459 57.3352i −0.431441 0.140184i 0.0852422 0.996360i \(-0.472834\pi\)
−0.516683 + 0.856176i \(0.672834\pi\)
\(410\) −22.6911 + 344.216i −0.0553441 + 0.839552i
\(411\) 81.6828 + 251.394i 0.198742 + 0.611664i
\(412\) −34.4106 + 17.5331i −0.0835209 + 0.0425560i
\(413\) −310.993 610.359i −0.753011 1.47787i
\(414\) −241.134 + 78.3492i −0.582450 + 0.189249i
\(415\) −417.700 347.664i −1.00651 0.837743i
\(416\) −8.45756 + 26.0297i −0.0203307 + 0.0625714i
\(417\) −79.4019 501.324i −0.190412 1.20221i
\(418\) −36.6138 + 36.6138i −0.0875929 + 0.0875929i
\(419\) 125.580 172.846i 0.299714 0.412521i −0.632425 0.774622i \(-0.717940\pi\)
0.932139 + 0.362101i \(0.117940\pi\)
\(420\) 75.5248 + 175.971i 0.179821 + 0.418979i
\(421\) 582.175 422.975i 1.38284 1.00469i 0.386229 0.922403i \(-0.373777\pi\)
0.996609 0.0822874i \(-0.0262226\pi\)
\(422\) 230.201 + 36.4603i 0.545501 + 0.0863988i
\(423\) 228.620 + 116.488i 0.540473 + 0.275385i
\(424\) 139.472i 0.328944i
\(425\) −785.212 + 19.9707i −1.84756 + 0.0469900i
\(426\) 157.053 0.368670
\(427\) −337.804 + 662.978i −0.791110 + 1.55264i
\(428\) −1.10419 + 6.97158i −0.00257988 + 0.0162887i
\(429\) −40.7533 56.0921i −0.0949960 0.130751i
\(430\) 44.0250 73.9361i 0.102384 0.171944i
\(431\) −364.855 265.083i −0.846531 0.615041i 0.0776561 0.996980i \(-0.475256\pi\)
−0.924187 + 0.381939i \(0.875256\pi\)
\(432\) 78.1803 + 78.1803i 0.180973 + 0.180973i
\(433\) 283.110 44.8402i 0.653834 0.103557i 0.179300 0.983794i \(-0.442617\pi\)
0.474534 + 0.880237i \(0.342617\pi\)
\(434\) −139.004 45.1651i −0.320286 0.104067i
\(435\) 115.298 + 46.0496i 0.265054 + 0.105861i
\(436\) −12.4726 38.3868i −0.0286070 0.0880432i
\(437\) −151.843 + 77.3681i −0.347468 + 0.177044i
\(438\) −70.0635 137.507i −0.159962 0.313944i
\(439\) −109.894 + 35.7066i −0.250327 + 0.0813362i −0.431493 0.902116i \(-0.642013\pi\)
0.181166 + 0.983453i \(0.442013\pi\)
\(440\) 38.6802 96.8468i 0.0879095 0.220106i
\(441\) −77.6386 + 238.947i −0.176051 + 0.541830i
\(442\) 33.6297 + 212.330i 0.0760853 + 0.480384i
\(443\) −516.584 + 516.584i −1.16610 + 1.16610i −0.182988 + 0.983115i \(0.558577\pi\)
−0.983115 + 0.182988i \(0.941423\pi\)
\(444\) 93.0878 128.124i 0.209657 0.288568i
\(445\) −567.769 338.076i −1.27589 0.759722i
\(446\) −138.176 + 100.391i −0.309812 + 0.225091i
\(447\) 121.300 + 19.2121i 0.271365 + 0.0429800i
\(448\) 70.2390 + 35.7886i 0.156784 + 0.0798852i
\(449\) 611.042i 1.36090i −0.732796 0.680448i \(-0.761785\pi\)
0.732796 0.680448i \(-0.238215\pi\)
\(450\) 112.314 + 146.599i 0.249587 + 0.325775i
\(451\) −359.747 −0.797665
\(452\) −109.149 + 214.218i −0.241481 + 0.473933i
\(453\) 21.6037 136.400i 0.0476902 0.301104i
\(454\) 266.222 + 366.424i 0.586393 + 0.807101i
\(455\) 219.055 94.0158i 0.481439 0.206628i
\(456\) 22.0793 + 16.0416i 0.0484196 + 0.0351789i
\(457\) 445.089 + 445.089i 0.973936 + 0.973936i 0.999669 0.0257328i \(-0.00819192\pi\)
−0.0257328 + 0.999669i \(0.508192\pi\)
\(458\) 368.802 58.4125i 0.805244 0.127538i
\(459\) 825.936 + 268.363i 1.79942 + 0.584668i
\(460\) 219.571 263.803i 0.477328 0.573485i
\(461\) −129.655 399.038i −0.281248 0.865592i −0.987498 0.157630i \(-0.949615\pi\)
0.706251 0.707962i \(-0.250385\pi\)
\(462\) −177.934 + 90.6620i −0.385139 + 0.196238i
\(463\) 132.982 + 260.991i 0.287218 + 0.563696i 0.988863 0.148830i \(-0.0475508\pi\)
−0.701645 + 0.712526i \(0.747551\pi\)
\(464\) 48.6084 15.7938i 0.104759 0.0340384i
\(465\) 101.689 + 6.70344i 0.218686 + 0.0144160i
\(466\) 63.9288 196.752i 0.137186 0.422216i
\(467\) 45.6149 + 288.001i 0.0976765 + 0.616705i 0.987160 + 0.159737i \(0.0510647\pi\)
−0.889483 + 0.456968i \(0.848935\pi\)
\(468\) 35.7406 35.7406i 0.0763687 0.0763687i
\(469\) 28.4802 39.1996i 0.0607253 0.0835812i
\(470\) −345.899 + 31.6525i −0.735955 + 0.0673457i
\(471\) −333.516 + 242.314i −0.708102 + 0.514466i
\(472\) 194.206 + 30.7591i 0.411453 + 0.0651677i
\(473\) 79.9576 + 40.7404i 0.169044 + 0.0861320i
\(474\) 418.556i 0.883029i
\(475\) 89.9763 + 85.5130i 0.189424 + 0.180027i
\(476\) 619.192 1.30082
\(477\) −116.936 + 229.500i −0.245149 + 0.481131i
\(478\) −37.5799 + 237.270i −0.0786190 + 0.496381i
\(479\) 492.895 + 678.412i 1.02901 + 1.41631i 0.905690 + 0.423941i \(0.139354\pi\)
0.123319 + 0.992367i \(0.460646\pi\)
\(480\) −53.6058 12.1509i −0.111679 0.0253145i
\(481\) −159.493 115.879i −0.331587 0.240912i
\(482\) 93.8989 + 93.8989i 0.194811 + 0.194811i
\(483\) −649.163 + 102.817i −1.34402 + 0.212872i
\(484\) −126.724 41.1751i −0.261826 0.0850725i
\(485\) 148.238 + 235.139i 0.305646 + 0.484823i
\(486\) −103.022 317.069i −0.211979 0.652405i
\(487\) 756.556 385.485i 1.55350 0.791549i 0.554334 0.832294i \(-0.312973\pi\)
0.999170 + 0.0407450i \(0.0129731\pi\)
\(488\) −96.9621 190.299i −0.198693 0.389957i
\(489\) −512.106 + 166.393i −1.04725 + 0.340272i
\(490\) −83.5957 329.678i −0.170604 0.672813i
\(491\) 1.50701 4.63810i 0.00306926 0.00944622i −0.949510 0.313736i \(-0.898419\pi\)
0.952579 + 0.304290i \(0.0984192\pi\)
\(492\) 29.6618 + 187.277i 0.0602882 + 0.380645i
\(493\) 283.868 283.868i 0.575798 0.575798i
\(494\) 19.9691 27.4851i 0.0404232 0.0556378i
\(495\) −144.846 + 126.930i −0.292618 + 0.256424i
\(496\) 33.9403 24.6591i 0.0684281 0.0497159i
\(497\) −556.177 88.0897i −1.11907 0.177243i
\(498\) −266.156 135.613i −0.534450 0.272316i
\(499\) 363.411i 0.728279i −0.931344 0.364139i \(-0.881363\pi\)
0.931344 0.364139i \(-0.118637\pi\)
\(500\) −234.450 86.7937i −0.468900 0.173587i
\(501\) 353.993 0.706573
\(502\) 79.3745 155.781i 0.158117 0.310321i
\(503\) −33.2643 + 210.023i −0.0661318 + 0.417540i 0.932306 + 0.361670i \(0.117793\pi\)
−0.998438 + 0.0558701i \(0.982207\pi\)
\(504\) −85.5716 117.779i −0.169785 0.233689i
\(505\) 601.654 + 686.576i 1.19139 + 1.35956i
\(506\) 289.575 + 210.388i 0.572282 + 0.415787i
\(507\) −200.063 200.063i −0.394602 0.394602i
\(508\) −189.726 + 30.0497i −0.373477 + 0.0591529i
\(509\) −340.104 110.506i −0.668180 0.217105i −0.0447671 0.998997i \(-0.514255\pi\)
−0.623413 + 0.781892i \(0.714255\pi\)
\(510\) −418.493 + 106.116i −0.820575 + 0.208071i
\(511\) 170.991 + 526.256i 0.334620 + 1.02986i
\(512\) −20.1612 + 10.2726i −0.0393773 + 0.0200637i
\(513\) −62.3068 122.284i −0.121456 0.238370i
\(514\) 86.8854 28.2308i 0.169038 0.0549237i
\(515\) −81.6743 + 51.4897i −0.158591 + 0.0999800i
\(516\) 14.6160 44.9835i 0.0283256 0.0871774i
\(517\) −56.6652 357.770i −0.109604 0.692011i
\(518\) −401.518 + 401.518i −0.775131 + 0.775131i
\(519\) −90.5260 + 124.598i −0.174424 + 0.240074i
\(520\) −15.1259 + 66.7303i −0.0290883 + 0.128327i
\(521\) 261.371 189.897i 0.501671 0.364485i −0.307984 0.951392i \(-0.599654\pi\)
0.809655 + 0.586906i \(0.199654\pi\)
\(522\) −93.2262 14.7656i −0.178594 0.0282865i
\(523\) −545.090 277.737i −1.04224 0.531046i −0.152872 0.988246i \(-0.548852\pi\)
−0.889364 + 0.457200i \(0.848852\pi\)
\(524\) 46.3786i 0.0885089i
\(525\) 228.116 + 420.892i 0.434506 + 0.801698i
\(526\) −53.6003 −0.101902
\(527\) 149.600 293.607i 0.283872 0.557129i
\(528\) 8.96702 56.6156i 0.0169830 0.107226i
\(529\) 381.493 + 525.080i 0.721159 + 0.992590i
\(530\) −31.7743 347.230i −0.0599515 0.655150i
\(531\) −293.774 213.439i −0.553246 0.401957i
\(532\) −69.1925 69.1925i −0.130061 0.130061i
\(533\) 233.129 36.9240i 0.437390 0.0692757i
\(534\) −345.437 112.239i −0.646885 0.210186i
\(535\) −1.16074 + 17.6080i −0.00216960 + 0.0329121i
\(536\) 4.29777 + 13.2272i 0.00801823 + 0.0246776i
\(537\) 1.17392 0.598144i 0.00218608 0.00111386i
\(538\) 70.7860 + 138.925i 0.131573 + 0.258226i
\(539\) 337.328 109.604i 0.625840 0.203348i
\(540\) 212.448 + 176.827i 0.393423 + 0.327457i
\(541\) −140.029 + 430.965i −0.258834 + 0.796609i 0.734216 + 0.678916i \(0.237550\pi\)
−0.993050 + 0.117693i \(0.962450\pi\)
\(542\) −40.1599 253.560i −0.0740958 0.467823i
\(543\) 62.9770 62.9770i 0.115980 0.115980i
\(544\) −104.468 + 143.787i −0.192036 + 0.264315i
\(545\) −39.7971 92.7263i −0.0730221 0.170140i
\(546\) 106.002 77.0152i 0.194143 0.141053i
\(547\) −445.065 70.4914i −0.813648 0.128869i −0.264276 0.964447i \(-0.585133\pi\)
−0.549372 + 0.835578i \(0.685133\pi\)
\(548\) 242.389 + 123.503i 0.442315 + 0.225371i
\(549\) 394.429i 0.718450i
\(550\) 74.2346 249.922i 0.134972 0.454403i
\(551\) −63.4426 −0.115141
\(552\) 85.6481 168.094i 0.155160 0.304518i
\(553\) 234.764 1482.24i 0.424528 2.68036i
\(554\) −265.589 365.551i −0.479402 0.659840i
\(555\) 202.562 340.185i 0.364977 0.612947i
\(556\) −422.609 307.044i −0.760088 0.552237i
\(557\) −37.6917 37.6917i −0.0676692 0.0676692i 0.672462 0.740131i \(-0.265237\pi\)
−0.740131 + 0.672462i \(0.765237\pi\)
\(558\) −76.5229 + 12.1200i −0.137138 + 0.0217205i
\(559\) −55.9970 18.1945i −0.100173 0.0325483i
\(560\) 183.020 + 73.0974i 0.326822 + 0.130531i
\(561\) −139.132 428.203i −0.248006 0.763285i
\(562\) 33.2416 16.9374i 0.0591487 0.0301378i
\(563\) −11.5693 22.7061i −0.0205494 0.0403305i 0.880504 0.474039i \(-0.157205\pi\)
−0.901053 + 0.433709i \(0.857205\pi\)
\(564\) −181.576 + 58.9976i −0.321943 + 0.104606i
\(565\) −222.935 + 558.182i −0.394576 + 0.987933i
\(566\) −29.6327 + 91.1999i −0.0523545 + 0.161131i
\(567\) −10.3346 65.2501i −0.0182268 0.115080i
\(568\) 114.292 114.292i 0.201218 0.201218i
\(569\) 328.912 452.709i 0.578053 0.795622i −0.415427 0.909627i \(-0.636368\pi\)
0.993480 + 0.114004i \(0.0363678\pi\)
\(570\) 58.6232 + 34.9070i 0.102848 + 0.0612403i
\(571\) −98.3806 + 71.4777i −0.172295 + 0.125180i −0.670591 0.741827i \(-0.733959\pi\)
0.498296 + 0.867007i \(0.333959\pi\)
\(572\) −70.4769 11.1624i −0.123211 0.0195148i
\(573\) 341.351 + 173.927i 0.595726 + 0.303538i
\(574\) 679.846i 1.18440i
\(575\) 486.544 706.786i 0.846163 1.22919i
\(576\) 41.7877 0.0725481
\(577\) 277.724 545.065i 0.481325 0.944653i −0.514851 0.857280i \(-0.672153\pi\)
0.996176 0.0873732i \(-0.0278472\pi\)
\(578\) −154.449 + 975.152i −0.267213 + 1.68711i
\(579\) 120.771 + 166.227i 0.208585 + 0.287093i
\(580\) 117.417 50.3941i 0.202443 0.0868864i
\(581\) 866.481 + 629.535i 1.49136 + 1.08354i
\(582\) 108.036 + 108.036i 0.185629 + 0.185629i
\(583\) 359.146 56.8832i 0.616032 0.0975698i
\(584\) −151.055 49.0807i −0.258655 0.0840422i
\(585\) 80.8373 97.1220i 0.138183 0.166020i
\(586\) −0.230119 0.708233i −0.000392695 0.00120859i
\(587\) −678.013 + 345.465i −1.15505 + 0.588526i −0.923235 0.384235i \(-0.874465\pi\)
−0.231812 + 0.972761i \(0.574465\pi\)
\(588\) −84.8713 166.569i −0.144339 0.283281i
\(589\) −49.5269 + 16.0923i −0.0840863 + 0.0273213i
\(590\) 490.501 + 32.3344i 0.831358 + 0.0548040i
\(591\) 106.831 328.791i 0.180762 0.556329i
\(592\) −25.4970 160.982i −0.0430693 0.271929i
\(593\) −362.694 + 362.694i −0.611625 + 0.611625i −0.943369 0.331744i \(-0.892363\pi\)
0.331744 + 0.943369i \(0.392363\pi\)
\(594\) −169.432 + 233.203i −0.285239 + 0.392597i
\(595\) 1541.54 141.063i 2.59082 0.237081i
\(596\) 102.254 74.2922i 0.171568 0.124651i
\(597\) 28.1017 + 4.45087i 0.0470715 + 0.00745540i
\(598\) −209.249 106.618i −0.349914 0.178290i
\(599\) 654.617i 1.09285i 0.837508 + 0.546425i \(0.184012\pi\)
−0.837508 + 0.546425i \(0.815988\pi\)
\(600\) −136.225 18.0386i −0.227042 0.0300643i
\(601\) −911.373 −1.51643 −0.758213 0.652006i \(-0.773928\pi\)
−0.758213 + 0.652006i \(0.773928\pi\)
\(602\) −76.9909 + 151.103i −0.127892 + 0.251002i
\(603\) 4.01797 25.3685i 0.00666330 0.0420704i
\(604\) −83.5404 114.984i −0.138312 0.190370i
\(605\) −324.872 73.6394i −0.536978 0.121718i
\(606\) 405.947 + 294.938i 0.669880 + 0.486696i
\(607\) −656.124 656.124i −1.08093 1.08093i −0.996423 0.0845069i \(-0.973068\pi\)
−0.0845069 0.996423i \(-0.526932\pi\)
\(608\) 27.7416 4.39383i 0.0456276 0.00722670i
\(609\) −232.705 75.6104i −0.382110 0.124155i
\(610\) −284.750 451.678i −0.466804 0.740456i
\(611\) 73.4421 + 226.032i 0.120200 + 0.369937i
\(612\) 292.454 149.013i 0.477865 0.243484i
\(613\) 344.538 + 676.194i 0.562052 + 1.10309i 0.980805 + 0.194989i \(0.0624672\pi\)
−0.418753 + 0.908100i \(0.637533\pi\)
\(614\) 137.283 44.6059i 0.223588 0.0726481i
\(615\) 116.511 + 459.487i 0.189449 + 0.747134i
\(616\) −63.5103 + 195.464i −0.103101 + 0.317312i
\(617\) −27.9487 176.461i −0.0452977 0.285998i 0.954633 0.297785i \(-0.0962480\pi\)
−0.999931 + 0.0117871i \(0.996248\pi\)
\(618\) −37.5257 + 37.5257i −0.0607212 + 0.0607212i
\(619\) −28.4751 + 39.1926i −0.0460017 + 0.0633159i −0.831398 0.555677i \(-0.812459\pi\)
0.785396 + 0.618993i \(0.212459\pi\)
\(620\) 78.8800 69.1234i 0.127226 0.111489i
\(621\) −767.519 + 557.635i −1.23594 + 0.897963i
\(622\) −347.682 55.0675i −0.558975 0.0885329i
\(623\) 1160.35 + 591.227i 1.86252 + 0.949001i
\(624\) 37.6093i 0.0602713i
\(625\) −603.460 162.670i −0.965536 0.260271i
\(626\) 485.295 0.775232
\(627\) −32.3027 + 63.3976i −0.0515195 + 0.101113i
\(628\) −66.3704 + 419.047i −0.105685 + 0.667272i
\(629\) −752.495 1035.72i −1.19634 1.64661i
\(630\) −239.871 273.728i −0.380748 0.434489i
\(631\) −456.354 331.561i −0.723224 0.525453i 0.164189 0.986429i \(-0.447499\pi\)
−0.887412 + 0.460976i \(0.847499\pi\)
\(632\) 304.594 + 304.594i 0.481952 + 0.481952i
\(633\) 316.329 50.1017i 0.499731 0.0791495i
\(634\) 210.269 + 68.3204i 0.331654 + 0.107761i
\(635\) −465.496 + 118.035i −0.733064 + 0.185881i
\(636\) −59.2246 182.275i −0.0931204 0.286595i
\(637\) −207.351 + 105.650i −0.325511 + 0.165856i
\(638\) 60.4944 + 118.727i 0.0948188 + 0.186092i
\(639\) −283.890 + 92.2414i −0.444272 + 0.144353i
\(640\) −47.8529 + 30.1678i −0.0747702 + 0.0471372i
\(641\) −360.242 + 1108.71i −0.562000 + 1.72966i 0.114701 + 0.993400i \(0.463409\pi\)
−0.676701 + 0.736258i \(0.736591\pi\)
\(642\) 1.51732 + 9.57995i 0.00236342 + 0.0149220i
\(643\) 286.144 286.144i 0.445014 0.445014i −0.448679 0.893693i \(-0.648105\pi\)
0.893693 + 0.448679i \(0.148105\pi\)
\(644\) −397.590 + 547.236i −0.617376 + 0.849745i
\(645\) 26.1400 115.321i 0.0405271 0.178792i
\(646\) 178.483 129.675i 0.276289 0.200736i
\(647\) −254.625 40.3286i −0.393547 0.0623317i −0.0434750 0.999055i \(-0.513843\pi\)
−0.350072 + 0.936723i \(0.613843\pi\)
\(648\) 16.8958 + 8.60886i 0.0260738 + 0.0132853i
\(649\) 512.632i 0.789880i
\(650\) −22.4550 + 169.578i −0.0345462 + 0.260889i
\(651\) −200.841 −0.308512
\(652\) −251.584 + 493.761i −0.385865 + 0.757303i
\(653\) −12.6590 + 79.9258i −0.0193859 + 0.122398i −0.995483 0.0949350i \(-0.969736\pi\)
0.976098 + 0.217333i \(0.0697357\pi\)
\(654\) −32.6007 44.8710i −0.0498481 0.0686101i
\(655\) −10.5659 115.464i −0.0161311 0.176281i
\(656\) 157.872 + 114.701i 0.240659 + 0.174849i
\(657\) 207.408 + 207.408i 0.315690 + 0.315690i
\(658\) 676.110 107.085i 1.02752 0.162744i
\(659\) −155.596 50.5561i −0.236109 0.0767164i 0.188573 0.982059i \(-0.439614\pi\)
−0.424681 + 0.905343i \(0.639614\pi\)
\(660\) 9.42624 142.993i 0.0142822 0.216656i
\(661\) 167.623 + 515.891i 0.253590 + 0.780470i 0.994104 + 0.108429i \(0.0345821\pi\)
−0.740514 + 0.672041i \(0.765418\pi\)
\(662\) 627.403 319.678i 0.947739 0.482897i
\(663\) 134.113 + 263.211i 0.202281 + 0.396999i
\(664\) −292.378 + 94.9995i −0.440329 + 0.143071i
\(665\) −188.025 156.498i −0.282744 0.235335i
\(666\) −93.0150 + 286.271i −0.139662 + 0.429836i
\(667\) 68.6051 + 433.155i 0.102856 + 0.649408i
\(668\) 257.610 257.610i 0.385644 0.385644i
\(669\) −137.951 + 189.874i −0.206205 + 0.283817i
\(670\) 13.7131 + 31.9513i 0.0204673 + 0.0476884i
\(671\) 450.482 327.294i 0.671358 0.487770i
\(672\) 106.992 + 16.9458i 0.159214 + 0.0252170i
\(673\) −847.508 431.827i −1.25930 0.641645i −0.308432 0.951246i \(-0.599804\pi\)
−0.950866 + 0.309602i \(0.899804\pi\)
\(674\) 35.9995i 0.0534116i
\(675\) 569.195 + 391.828i 0.843252 + 0.580485i
\(676\) −291.183 −0.430744
\(677\) 498.680 978.716i 0.736603 1.44567i −0.152664 0.988278i \(-0.548785\pi\)
0.889268 0.457387i \(-0.151215\pi\)
\(678\) −51.6819 + 326.307i −0.0762270 + 0.481279i
\(679\) −321.994 443.187i −0.474218 0.652705i
\(680\) −227.325 + 381.772i −0.334301 + 0.561429i
\(681\) 503.519 + 365.828i 0.739381 + 0.537192i
\(682\) 77.3405 + 77.3405i 0.113403 + 0.113403i
\(683\) −707.782 + 112.102i −1.03628 + 0.164131i −0.651322 0.758801i \(-0.725785\pi\)
−0.384962 + 0.922933i \(0.625785\pi\)
\(684\) −49.3322 16.0290i −0.0721232 0.0234342i
\(685\) 631.586 + 252.253i 0.922024 + 0.368252i
\(686\) −3.87959 11.9402i −0.00565538 0.0174055i
\(687\) 457.179 232.944i 0.665471 0.339075i
\(688\) −22.0992 43.3722i −0.0321210 0.0630409i
\(689\) −226.901 + 73.7247i −0.329320 + 0.107002i
\(690\) 174.935 437.998i 0.253528 0.634780i
\(691\) −24.3198 + 74.8487i −0.0351951 + 0.108319i −0.967111 0.254356i \(-0.918137\pi\)
0.931916 + 0.362675i \(0.118137\pi\)
\(692\) 24.7954 + 156.552i 0.0358314 + 0.226231i
\(693\) 268.386 268.386i 0.387281 0.387281i
\(694\) −359.686 + 495.066i −0.518280 + 0.713351i
\(695\) −1122.08 668.137i −1.61450 0.961348i
\(696\) 56.8191 41.2815i 0.0816366 0.0593125i
\(697\) 1513.89 + 239.777i 2.17201 + 0.344013i
\(698\) 21.3513 + 10.8790i 0.0305892 + 0.0155860i
\(699\) 284.280i 0.406695i
\(700\) 472.300 + 140.288i 0.674714 + 0.200411i
\(701\) −484.373 −0.690974 −0.345487 0.938424i \(-0.612286\pi\)
−0.345487 + 0.938424i \(0.612286\pi\)
\(702\) 85.8622 168.514i 0.122311 0.240048i
\(703\) −31.6494 + 199.827i −0.0450205 + 0.284248i
\(704\) −34.6751 47.7262i −0.0492544 0.0677928i
\(705\) −438.610 + 188.247i −0.622142 + 0.267016i
\(706\) 186.505 + 135.504i 0.264171 + 0.191932i
\(707\) −1272.16 1272.16i −1.79938 1.79938i
\(708\) 266.866 42.2675i 0.376930 0.0596998i
\(709\) 448.636 + 145.771i 0.632773 + 0.205600i 0.607803 0.794088i \(-0.292051\pi\)
0.0249697 + 0.999688i \(0.492051\pi\)
\(710\) 258.503 310.579i 0.364089 0.437435i
\(711\) −245.828 756.582i −0.345750 1.06411i
\(712\) −333.063 + 169.704i −0.467785 + 0.238348i
\(713\) 163.427 + 320.744i 0.229211 + 0.449851i
\(714\) 809.214 262.930i 1.13335 0.368249i
\(715\) −178.002 11.7341i −0.248954 0.0164113i
\(716\) 0.419010 1.28958i 0.000585210 0.00180109i
\(717\) 51.6401 + 326.043i 0.0720225 + 0.454732i
\(718\) 37.4711 37.4711i 0.0521882 0.0521882i
\(719\) 552.973 761.102i 0.769086 1.05856i −0.227317 0.973821i \(-0.572995\pi\)
0.996403 0.0847357i \(-0.0270046\pi\)
\(720\) 104.035 9.51999i 0.144492 0.0132222i
\(721\) 153.938 111.843i 0.213507 0.155122i
\(722\) 469.810 + 74.4106i 0.650706 + 0.103062i
\(723\) 162.588 + 82.8427i 0.224880 + 0.114582i
\(724\) 91.6601i 0.126602i
\(725\) 280.841 152.211i 0.387367 0.209946i
\(726\) −183.098 −0.252201
\(727\) −460.348 + 903.484i −0.633216 + 1.24276i 0.321969 + 0.946750i \(0.395655\pi\)
−0.955186 + 0.296007i \(0.904345\pi\)
\(728\) 21.0947 133.187i 0.0289762 0.182949i
\(729\) −304.742 419.442i −0.418028 0.575366i
\(730\) −387.247 87.7781i −0.530476 0.120244i
\(731\) −309.325 224.738i −0.423154 0.307439i
\(732\) −207.526 207.526i −0.283505 0.283505i
\(733\) −459.050 + 72.7064i −0.626262 + 0.0991902i −0.461496 0.887142i \(-0.652687\pi\)
−0.164766 + 0.986333i \(0.552687\pi\)
\(734\) 13.1532 + 4.27373i 0.0179199 + 0.00582251i
\(735\) −249.243 395.355i −0.339106 0.537898i
\(736\) −59.9980 184.655i −0.0815190 0.250890i
\(737\) −32.3077 + 16.4616i −0.0438368 + 0.0223359i
\(738\) −163.609 321.101i −0.221693 0.435097i
\(739\) 548.414 178.190i 0.742103 0.241124i 0.0865231 0.996250i \(-0.472424\pi\)
0.655580 + 0.755126i \(0.272424\pi\)
\(740\) −100.152 394.972i −0.135340 0.533745i
\(741\) 14.4262 44.3994i 0.0194686 0.0599183i
\(742\) 107.497 + 678.711i 0.144875 + 0.914705i
\(743\) 406.087 406.087i 0.546550 0.546550i −0.378891 0.925441i \(-0.623695\pi\)
0.925441 + 0.378891i \(0.123695\pi\)
\(744\) 33.8851 46.6389i 0.0455445 0.0626866i
\(745\) 237.647 208.253i 0.318990 0.279534i
\(746\) −523.338 + 380.227i −0.701526 + 0.509688i
\(747\) 560.754 + 88.8146i 0.750674 + 0.118895i
\(748\) −412.864 210.365i −0.551958 0.281236i
\(749\) 34.7768i 0.0464309i
\(750\) −343.256 13.8743i −0.457674 0.0184991i
\(751\) 183.361 0.244156 0.122078 0.992520i \(-0.461044\pi\)
0.122078 + 0.992520i \(0.461044\pi\)
\(752\) −89.2034 + 175.072i −0.118622 + 0.232808i
\(753\) 37.5836 237.294i 0.0499119 0.315131i
\(754\) −51.3885 70.7302i −0.0681545 0.0938067i
\(755\) −234.177 267.231i −0.310169 0.353948i
\(756\) −440.705 320.191i −0.582942 0.423532i
\(757\) −145.626 145.626i −0.192373 0.192373i 0.604348 0.796721i \(-0.293434\pi\)
−0.796721 + 0.604348i \(0.793434\pi\)
\(758\) −230.724 + 36.5431i −0.304385 + 0.0482099i
\(759\) 467.780 + 151.991i 0.616310 + 0.200251i
\(760\) 68.0644 17.2589i 0.0895584 0.0227091i
\(761\) 41.7820 + 128.592i 0.0549041 + 0.168978i 0.974748 0.223306i \(-0.0716851\pi\)
−0.919844 + 0.392284i \(0.871685\pi\)
\(762\) −235.191 + 119.836i −0.308649 + 0.157265i
\(763\) 90.2818 + 177.188i 0.118325 + 0.232225i
\(764\) 374.981 121.839i 0.490813 0.159475i
\(765\) 694.144 437.607i 0.907378 0.572036i
\(766\) 111.036 341.733i 0.144956 0.446127i
\(767\) −52.6159 332.204i −0.0685996 0.433121i
\(768\) −21.9863 + 21.9863i −0.0286280 + 0.0286280i
\(769\) −257.147 + 353.933i −0.334392 + 0.460251i −0.942793 0.333379i \(-0.891811\pi\)
0.608401 + 0.793630i \(0.291811\pi\)
\(770\) −113.585 + 501.097i −0.147513 + 0.650775i
\(771\) 101.562 73.7889i 0.131727 0.0957055i
\(772\) 208.856 + 33.0795i 0.270538 + 0.0428491i
\(773\) 692.294 + 352.742i 0.895594 + 0.456328i 0.840287 0.542141i \(-0.182386\pi\)
0.0553069 + 0.998469i \(0.482386\pi\)
\(774\) 89.8966i 0.116146i
\(775\) 180.632 190.060i 0.233073 0.245239i
\(776\) 157.241 0.202631
\(777\) −354.241 + 695.237i −0.455908 + 0.894771i
\(778\) 75.2648 475.203i 0.0967413 0.610801i
\(779\) −142.378 195.966i −0.182770 0.251562i
\(780\) 8.56807 + 93.6320i 0.0109847 + 0.120041i
\(781\) 340.919 + 247.693i 0.436517 + 0.317148i
\(782\) −1078.37 1078.37i −1.37899 1.37899i
\(783\) −348.832 + 55.2496i −0.445508 + 0.0705615i
\(784\) −182.980 59.4537i −0.233393 0.0758339i
\(785\) −69.7694 + 1058.38i −0.0888782 + 1.34825i
\(786\) −19.6939 60.6117i −0.0250559 0.0771141i
\(787\) −863.979 + 440.219i −1.09781 + 0.559364i −0.906517 0.422169i \(-0.861269\pi\)
−0.191296 + 0.981532i \(0.561269\pi\)
\(788\) −161.526 317.013i −0.204983 0.402301i
\(789\) −70.0496 + 22.7605i −0.0887828 + 0.0288473i
\(790\) 827.708 + 688.924i 1.04773 + 0.872056i
\(791\) 366.045 1126.57i 0.462762 1.42424i
\(792\) 17.0429 + 107.605i 0.0215189 + 0.135865i
\(793\) −258.335 + 258.335i −0.325769 + 0.325769i
\(794\) 110.292 151.804i 0.138907 0.191188i
\(795\) −188.971 440.298i −0.237699 0.553834i
\(796\) 23.6894 17.2113i 0.0297605 0.0216223i
\(797\) 416.756 + 66.0077i 0.522906 + 0.0828202i 0.412307 0.911045i \(-0.364723\pi\)
0.110599 + 0.993865i \(0.464723\pi\)
\(798\) −119.808 61.0453i −0.150136 0.0764979i
\(799\) 1543.34i 1.93159i
\(800\) −112.262 + 86.0075i −0.140327 + 0.107509i
\(801\) 690.333 0.861839
\(802\) 251.086 492.785i 0.313075 0.614445i
\(803\) 64.7775 408.989i 0.0806694 0.509327i
\(804\) 11.2334 + 15.4615i 0.0139719 + 0.0192307i
\(805\) −865.169 + 1452.97i −1.07474 + 1.80494i
\(806\) −58.0576 42.1813i −0.0720317 0.0523341i
\(807\) 151.502 + 151.502i 0.187735 + 0.187735i
\(808\) 510.053 80.7844i 0.631253 0.0999807i
\(809\) 1217.64 + 395.634i 1.50511 + 0.489041i 0.941505 0.337000i \(-0.109412\pi\)
0.563610 + 0.826041i \(0.309412\pi\)
\(810\) 44.0251 + 17.5834i 0.0543520 + 0.0217079i
\(811\) 343.527 + 1057.27i 0.423585 + 1.30366i 0.904343 + 0.426807i \(0.140362\pi\)
−0.480758 + 0.876853i \(0.659638\pi\)
\(812\) −224.369 + 114.322i −0.276317 + 0.140790i
\(813\) −160.155 314.321i −0.196992 0.386619i
\(814\) 404.136 131.312i 0.496481 0.161317i
\(815\) −513.855 + 1286.58i −0.630497 + 1.57863i
\(816\) −75.4705 + 232.274i −0.0924883 + 0.284650i
\(817\) 9.45233 + 59.6796i 0.0115696 + 0.0730473i
\(818\) −185.540 + 185.540i −0.226822 + 0.226822i
\(819\) −146.377 + 201.471i −0.178726 + 0.245996i
\(820\) 419.169 + 249.593i 0.511182 + 0.304382i
\(821\) 736.621 535.186i 0.897224 0.651871i −0.0405274 0.999178i \(-0.512904\pi\)
0.937751 + 0.347307i \(0.112904\pi\)
\(822\) 369.218 + 58.4784i 0.449171 + 0.0711416i
\(823\) −977.955 498.293i −1.18828 0.605459i −0.255818 0.966725i \(-0.582345\pi\)
−0.932463 + 0.361266i \(0.882345\pi\)
\(824\) 54.6168i 0.0662826i
\(825\) −9.10882 358.142i −0.0110410 0.434112i
\(826\) −968.767 −1.17284
\(827\) −324.913 + 637.677i −0.392881 + 0.771073i −0.999718 0.0237538i \(-0.992438\pi\)
0.606837 + 0.794827i \(0.292438\pi\)
\(828\) −56.0919 + 354.150i −0.0677438 + 0.427717i
\(829\) −836.025 1150.69i −1.00847 1.38805i −0.919978 0.391969i \(-0.871794\pi\)
−0.0884961 0.996077i \(-0.528206\pi\)
\(830\) −706.262 + 303.120i −0.850918 + 0.365204i
\(831\) −502.320 364.957i −0.604476 0.439178i
\(832\) 27.3693 + 27.3693i 0.0328957 + 0.0328957i
\(833\) −1492.60 + 236.405i −1.79184 + 0.283800i
\(834\) −682.684 221.817i −0.818566 0.265968i
\(835\) 582.657 700.033i 0.697793 0.838363i
\(836\) 22.6286 + 69.6436i 0.0270677 + 0.0833058i
\(837\) −258.304 + 131.613i −0.308607 + 0.157243i
\(838\) −137.172 269.214i −0.163689 0.321258i
\(839\) 549.819 178.647i 0.655327 0.212928i 0.0375652 0.999294i \(-0.488040\pi\)
0.617761 + 0.786366i \(0.288040\pi\)
\(840\) 270.227 + 17.8136i 0.321698 + 0.0212067i
\(841\) 209.432 644.566i 0.249027 0.766428i
\(842\) −159.200 1005.15i −0.189074 1.19376i
\(843\) 36.2508 36.2508i 0.0430021 0.0430021i
\(844\) 193.741 266.662i 0.229551 0.315950i
\(845\) −724.928 + 66.3367i −0.857903 + 0.0785050i
\(846\) 293.566 213.288i 0.347005 0.252114i
\(847\) 648.410 + 102.698i 0.765537 + 0.121249i
\(848\) −175.745 89.5467i −0.207247 0.105597i
\(849\) 131.771i 0.155207i
\(850\) −478.973 + 1002.25i −0.563497 + 1.17911i
\(851\) 1398.54 1.64341
\(852\) 100.834 197.899i 0.118350 0.232276i
\(853\) 54.9523 346.955i 0.0644224 0.406747i −0.934312 0.356456i \(-0.883985\pi\)
0.998735 0.0502913i \(-0.0160150\pi\)
\(854\) 618.517 + 851.316i 0.724259 + 0.996857i
\(855\) −126.469 28.6670i −0.147917 0.0335287i
\(856\) 8.07577 + 5.86739i 0.00943431 + 0.00685443i
\(857\) 942.292 + 942.292i 1.09952 + 1.09952i 0.994466 + 0.105058i \(0.0335029\pi\)
0.105058 + 0.994466i \(0.466497\pi\)
\(858\) −96.8453 + 15.3388i −0.112873 + 0.0178774i
\(859\) 540.757 + 175.703i 0.629519 + 0.204543i 0.606362 0.795189i \(-0.292628\pi\)
0.0231569 + 0.999732i \(0.492628\pi\)
\(860\) −64.8991 102.945i −0.0754641 0.119703i
\(861\) −288.685 888.483i −0.335291 1.03192i
\(862\) −568.275 + 289.551i −0.659252 + 0.335906i
\(863\) 415.861 + 816.174i 0.481879 + 0.945740i 0.996113 + 0.0880901i \(0.0280764\pi\)
−0.514234 + 0.857650i \(0.671924\pi\)
\(864\) 148.708 48.3181i 0.172115 0.0559237i
\(865\) 97.3958 + 384.102i 0.112596 + 0.444048i
\(866\) 125.266 385.529i 0.144649 0.445183i
\(867\) 212.235 + 1340.00i 0.244792 + 1.54556i
\(868\) −146.157 + 146.157i −0.168384 + 0.168384i
\(869\) −660.114 + 908.569i −0.759625 + 1.04553i
\(870\) 132.052 115.719i 0.151784 0.133010i
\(871\) 19.2469 13.9837i 0.0220975 0.0160548i
\(872\) −56.3782 8.92942i −0.0646538 0.0102402i
\(873\) −258.738 131.834i −0.296378 0.151012i
\(874\) 241.007i 0.275752i
\(875\) 1207.80 + 241.662i 1.38034 + 0.276185i
\(876\) −218.253 −0.249147
\(877\) 361.033 708.567i 0.411668 0.807944i −0.588332 0.808620i \(-0.700215\pi\)
1.00000 0.000675700i \(0.000215082\pi\)
\(878\) −25.5631 + 161.399i −0.0291152 + 0.183826i
\(879\) −0.601479 0.827865i −0.000684277 0.000941826i
\(880\) −97.1999 110.919i −0.110454 0.126045i
\(881\) 422.550 + 307.001i 0.479626 + 0.348468i 0.801181 0.598423i \(-0.204206\pi\)
−0.321555 + 0.946891i \(0.604206\pi\)
\(882\) 251.244 + 251.244i 0.284857 + 0.284857i
\(883\) −401.805 + 63.6396i −0.455045 + 0.0720721i −0.379750 0.925089i \(-0.623990\pi\)
−0.0752953 + 0.997161i \(0.523990\pi\)
\(884\) 289.142 + 93.9481i 0.327084 + 0.106276i
\(885\) 654.761 166.026i 0.739843 0.187600i
\(886\) 319.266 + 982.601i 0.360346 + 1.10903i
\(887\) 1105.57 563.317i 1.24642 0.635081i 0.298746 0.954333i \(-0.403432\pi\)
0.947670 + 0.319252i \(0.103432\pi\)
\(888\) −101.680 199.558i −0.114505 0.224728i
\(889\) 900.100 292.460i 1.01249 0.328977i
\(890\) −790.531 + 498.372i −0.888237 + 0.559969i
\(891\) −15.2772 + 47.0185i −0.0171462 + 0.0527705i
\(892\) 37.7853 + 238.567i 0.0423602 + 0.267452i
\(893\) 172.463 172.463i 0.193128 0.193128i
\(894\) 102.088 140.512i 0.114192 0.157172i
\(895\) 0.749377 3.30600i 0.000837293 0.00369385i
\(896\) 90.1925 65.5287i 0.100661 0.0731347i
\(897\) −318.738 50.4831i −0.355338 0.0562800i
\(898\) −769.958 392.313i −0.857415 0.436875i
\(899\) 134.012i 0.149068i
\(900\) 256.835 47.4019i 0.285373 0.0526688i
\(901\) −1549.28 −1.71951
\(902\) −230.972 + 453.307i −0.256066 + 0.502558i
\(903\) −36.4550 + 230.168i −0.0403710 + 0.254892i
\(904\) 199.852 + 275.072i 0.221075 + 0.304284i
\(905\) −20.8818 228.197i −0.0230738 0.252151i
\(906\) −158.004 114.796i −0.174397 0.126707i
\(907\) −334.245 334.245i −0.368517 0.368517i 0.498419 0.866936i \(-0.333914\pi\)
−0.866936 + 0.498419i \(0.833914\pi\)
\(908\) 632.646 100.201i 0.696747 0.110354i
\(909\) −907.016 294.707i −0.997817 0.324210i
\(910\) 22.1750 336.387i 0.0243681 0.369656i
\(911\) −483.718 1488.73i −0.530975 1.63417i −0.752189 0.658948i \(-0.771002\pi\)
0.221213 0.975225i \(-0.428998\pi\)
\(912\) 34.3894 17.5223i 0.0377076 0.0192130i
\(913\) −363.873 714.140i −0.398546 0.782191i
\(914\) 846.609 275.080i 0.926268 0.300963i
\(915\) −563.934 469.378i −0.616322 0.512982i
\(916\) 163.181 502.221i 0.178146 0.548276i
\(917\) 35.7461 + 225.692i 0.0389815 + 0.246120i
\(918\) 868.440 868.440i 0.946013 0.946013i
\(919\) −418.432 + 575.923i −0.455313 + 0.626684i −0.973528 0.228566i \(-0.926596\pi\)
0.518216 + 0.855250i \(0.326596\pi\)
\(920\) −191.438 446.047i −0.208085 0.484834i
\(921\) 160.472 116.590i 0.174237 0.126591i
\(922\) −586.061 92.8229i −0.635641 0.100676i
\(923\) −246.351 125.522i −0.266902 0.135994i
\(924\) 282.419i 0.305648i
\(925\) −339.320 960.504i −0.366832 1.03838i
\(926\) 414.248 0.447352
\(927\) 45.7917 89.8713i 0.0493977 0.0969485i
\(928\) 11.3071 71.3903i 0.0121844 0.0769293i
\(929\) −720.018 991.019i −0.775046 1.06676i −0.995811 0.0914321i \(-0.970856\pi\)
0.220765 0.975327i \(-0.429144\pi\)
\(930\) 73.7351 123.832i 0.0792851 0.133152i
\(931\) 193.210 + 140.376i 0.207530 + 0.150779i
\(932\) −206.878 206.878i −0.221972 0.221972i
\(933\) −477.765 + 75.6706i −0.512074 + 0.0811046i
\(934\) 392.190 + 127.430i 0.419903 + 0.136435i
\(935\) −1075.79 429.666i −1.15058 0.459536i
\(936\) −22.0889 67.9826i −0.0235992 0.0726310i
\(937\) −104.962 + 53.4806i −0.112019 + 0.0570764i −0.509102 0.860706i \(-0.670022\pi\)
0.397083 + 0.917783i \(0.370022\pi\)
\(938\) −31.1090 61.0548i −0.0331652 0.0650904i
\(939\) 634.226 206.073i 0.675427 0.219460i
\(940\) −182.196 + 456.180i −0.193826 + 0.485298i
\(941\) 20.7873 63.9766i 0.0220906 0.0679879i −0.939403 0.342813i \(-0.888620\pi\)
0.961494 + 0.274826i \(0.0886201\pi\)
\(942\) 91.2025 + 575.830i 0.0968179 + 0.611284i
\(943\) −1184.00 + 1184.00i −1.25557 + 1.25557i
\(944\) 163.446 224.965i 0.173142 0.238310i
\(945\) −1170.12 696.745i −1.23822 0.737297i
\(946\) 102.672 74.5955i 0.108533 0.0788536i
\(947\) −42.5385 6.73744i −0.0449193 0.00711451i 0.133934 0.990990i \(-0.457239\pi\)
−0.178854 + 0.983876i \(0.557239\pi\)
\(948\) 527.411 + 268.729i 0.556341 + 0.283470i
\(949\) 271.688i 0.286289i
\(950\) 165.521 58.4741i 0.174233 0.0615516i
\(951\) 303.809 0.319462
\(952\) 397.546 780.227i 0.417590 0.819566i
\(953\) −175.898 + 1110.58i −0.184573 + 1.16535i 0.705221 + 0.708988i \(0.250848\pi\)
−0.889794 + 0.456363i \(0.849152\pi\)
\(954\) 214.109 + 294.696i 0.224433 + 0.308905i
\(955\) 905.796 388.757i 0.948478 0.407076i
\(956\) 274.850 + 199.690i 0.287500 + 0.208881i
\(957\) 129.475 + 129.475i 0.135292 + 0.135292i
\(958\) 1171.31 185.517i 1.22266 0.193650i
\(959\) −1274.72 414.182i −1.32922 0.431889i
\(960\) −49.7282 + 59.7459i −0.0518002 + 0.0622353i
\(961\) −262.973 809.348i −0.273645 0.842194i
\(962\) −248.417 + 126.575i −0.258230 + 0.131575i
\(963\) −8.36925 16.4256i −0.00869081 0.0170567i
\(964\) 178.606 58.0327i 0.185276 0.0601999i
\(965\) 527.502 + 34.7735i 0.546635 + 0.0360347i
\(966\) −287.231 + 884.005i −0.297340 + 0.915120i
\(967\) 210.501 + 1329.05i 0.217685 + 1.37441i 0.818264 + 0.574842i \(0.194937\pi\)
−0.600580 + 0.799565i \(0.705063\pi\)
\(968\) −133.245 + 133.245i −0.137650 + 0.137650i
\(969\) 178.193 245.261i 0.183893 0.253107i
\(970\) 391.468 35.8224i 0.403575 0.0369303i
\(971\) −642.430 + 466.753i −0.661617 + 0.480693i −0.867209 0.497945i \(-0.834088\pi\)
0.205592 + 0.978638i \(0.434088\pi\)
\(972\) −465.674 73.7556i −0.479089 0.0758802i
\(973\) 2293.19 + 1168.44i 2.35682 + 1.20086i
\(974\) 1200.81i 1.23287i
\(975\) 42.6621 + 231.154i 0.0437560 + 0.237081i
\(976\) −302.044 −0.309471
\(977\) 517.073 1014.81i 0.529245 1.03870i −0.459371 0.888244i \(-0.651925\pi\)
0.988616 0.150458i \(-0.0480748\pi\)
\(978\) −119.124 + 752.122i −0.121804 + 0.769040i
\(979\) −572.833 788.437i −0.585120 0.805349i
\(980\) −469.091 106.330i −0.478664 0.108500i
\(981\) 85.2829 + 61.9616i 0.0869346 + 0.0631617i
\(982\) −4.87678 4.87678i −0.00496617 0.00496617i
\(983\) 325.742 51.5924i 0.331375 0.0524847i 0.0114699 0.999934i \(-0.496349\pi\)
0.319905 + 0.947450i \(0.396349\pi\)
\(984\) 255.027 + 82.8633i 0.259174 + 0.0842107i
\(985\) −474.357 752.436i −0.481580 0.763895i
\(986\) −175.440 539.950i −0.177931 0.547617i
\(987\) 838.128 427.047i 0.849167 0.432672i
\(988\) −21.8123 42.8090i −0.0220772 0.0433289i
\(989\) 397.242 129.072i 0.401661 0.130507i
\(990\) 66.9444 + 264.010i 0.0676206 + 0.266677i
\(991\) −377.775 + 1162.67i −0.381206 + 1.17323i 0.557989 + 0.829848i \(0.311573\pi\)
−0.939195 + 0.343383i \(0.888427\pi\)
\(992\) −9.28123 58.5994i −0.00935608 0.0590720i
\(993\) 684.200 684.200i 0.689023 0.689023i
\(994\) −468.087 + 644.266i −0.470912 + 0.648155i
\(995\) 55.0559 48.2461i 0.0553326 0.0484886i
\(996\) −341.766 + 248.307i −0.343138 + 0.249304i
\(997\) −651.668 103.214i −0.653629 0.103525i −0.179192 0.983814i \(-0.557348\pi\)
−0.474437 + 0.880289i \(0.657348\pi\)
\(998\) −457.925 233.324i −0.458843 0.233792i
\(999\) 1126.29i 1.12742i
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.17.2 yes 24
4.3 odd 2 400.3.bg.b.17.2 24
5.2 odd 4 250.3.f.d.143.2 24
5.3 odd 4 250.3.f.f.143.2 24
5.4 even 2 250.3.f.e.107.2 24
25.3 odd 20 inner 50.3.f.b.3.2 24
25.4 even 10 250.3.f.d.7.2 24
25.21 even 5 250.3.f.f.7.2 24
25.22 odd 20 250.3.f.e.243.2 24
100.3 even 20 400.3.bg.b.353.2 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
50.3.f.b.3.2 24 25.3 odd 20 inner
50.3.f.b.17.2 yes 24 1.1 even 1 trivial
250.3.f.d.7.2 24 25.4 even 10
250.3.f.d.143.2 24 5.2 odd 4
250.3.f.e.107.2 24 5.4 even 2
250.3.f.e.243.2 24 25.22 odd 20
250.3.f.f.7.2 24 25.21 even 5
250.3.f.f.143.2 24 5.3 odd 4
400.3.bg.b.17.2 24 4.3 odd 2
400.3.bg.b.353.2 24 100.3 even 20