Properties

Label 210.2.r.b.131.6
Level $210$
Weight $2$
Character 210.131
Analytic conductor $1.677$
Analytic rank $0$
Dimension $12$
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] = [210,2,Mod(101,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.r (of order \(6\), degree \(2\), 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: \(1.67685844245\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 4 x^{11} + 11 x^{10} - 32 x^{9} + 64 x^{8} - 120 x^{7} + 237 x^{6} - 360 x^{5} + 576 x^{4} - 864 x^{3} + 891 x^{2} - 972 x + 729 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 131.6
Root \(1.66557 - 0.475255i\) of defining polynomial
Character \(\chi\) \(=\) 210.131
Dual form 210.2.r.b.101.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(1.20480 + 1.24437i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.421203 + 1.68006i) q^{6} +(0.0551777 - 2.64518i) q^{7} +1.00000i q^{8} +(-0.0969112 + 2.99843i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(1.20480 + 1.24437i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.421203 + 1.68006i) q^{6} +(0.0551777 - 2.64518i) q^{7} +1.00000i q^{8} +(-0.0969112 + 2.99843i) q^{9} +(-0.866025 + 0.500000i) q^{10} +(0.167855 - 0.0969112i) q^{11} +(-0.475255 + 1.66557i) q^{12} -1.54892i q^{13} +(1.37037 - 2.26320i) q^{14} +(-1.68006 + 0.421203i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.264766 - 0.458589i) q^{17} +(-1.58314 + 2.54826i) q^{18} +(-5.53332 - 3.19467i) q^{19} -1.00000 q^{20} +(3.35805 - 3.11825i) q^{21} +0.193822 q^{22} +(3.68040 + 2.12488i) q^{23} +(-1.24437 + 1.20480i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.774462 - 1.34141i) q^{26} +(-3.84792 + 3.49192i) q^{27} +(2.31838 - 1.27480i) q^{28} -4.87349i q^{29} +(-1.66557 - 0.475255i) q^{30} +(8.02559 - 4.63357i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.322825 + 0.0921151i) q^{33} -0.529533i q^{34} +(2.26320 + 1.37037i) q^{35} +(-2.64518 + 1.41529i) q^{36} +(-0.881634 + 1.52704i) q^{37} +(-3.19467 - 5.53332i) q^{38} +(1.92743 - 1.86614i) q^{39} +(-0.866025 - 0.500000i) q^{40} -9.91573 q^{41} +(4.46728 - 1.02145i) q^{42} +11.4865 q^{43} +(0.167855 + 0.0969112i) q^{44} +(-2.54826 - 1.58314i) q^{45} +(2.12488 + 3.68040i) q^{46} +(-4.90186 + 8.49028i) q^{47} +(-1.68006 + 0.421203i) q^{48} +(-6.99391 - 0.291909i) q^{49} -1.00000i q^{50} +(0.251663 - 0.881975i) q^{51} +(1.34141 - 0.774462i) q^{52} +(-0.0562751 + 0.0324905i) q^{53} +(-5.07836 + 1.10013i) q^{54} +0.193822i q^{55} +(2.64518 + 0.0551777i) q^{56} +(-2.69121 - 10.7344i) q^{57} +(2.43674 - 4.22056i) q^{58} +(-6.01371 - 10.4160i) q^{59} +(-1.20480 - 1.24437i) q^{60} +(3.71180 + 2.14301i) q^{61} +9.26715 q^{62} +(7.92604 + 0.421794i) q^{63} -1.00000 q^{64} +(1.34141 + 0.774462i) q^{65} +(0.233517 + 0.241187i) q^{66} +(-2.41529 - 4.18340i) q^{67} +(0.264766 - 0.458589i) q^{68} +(1.79001 + 7.13983i) q^{69} +(1.27480 + 2.31838i) q^{70} +6.29103i q^{71} +(-2.99843 - 0.0969112i) q^{72} +(-7.00763 + 4.04586i) q^{73} +(-1.52704 + 0.881634i) q^{74} +(0.475255 - 1.66557i) q^{75} -6.38933i q^{76} +(-0.247085 - 0.449354i) q^{77} +(2.60228 - 0.652411i) q^{78} +(-3.38883 + 5.86962i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-8.98122 - 0.581164i) q^{81} +(-8.58728 - 4.95787i) q^{82} +2.11036 q^{83} +(4.37951 + 1.34904i) q^{84} +0.529533 q^{85} +(9.94760 + 5.74325i) q^{86} +(6.06442 - 5.87158i) q^{87} +(0.0969112 + 0.167855i) q^{88} +(-8.18773 + 14.1816i) q^{89} +(-1.41529 - 2.64518i) q^{90} +(-4.09717 - 0.0854660i) q^{91} +4.24976i q^{92} +(15.4351 + 4.40426i) q^{93} +(-8.49028 + 4.90186i) q^{94} +(5.53332 - 3.19467i) q^{95} +(-1.66557 - 0.475255i) q^{96} +8.24463i q^{97} +(-5.91095 - 3.74976i) q^{98} +(0.274315 + 0.512694i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{11} - 2 q^{12} - 12 q^{14} - 4 q^{15} - 6 q^{16} - 12 q^{17} - 4 q^{18} - 12 q^{20} + 4 q^{21} + 24 q^{23} - 2 q^{24} - 6 q^{25} + 4 q^{26} + 8 q^{27} + 4 q^{28} - 4 q^{30} + 12 q^{31} - 2 q^{33} - 4 q^{35} + 6 q^{36} - 8 q^{37} - 8 q^{38} - 42 q^{39} + 4 q^{41} + 24 q^{42} + 12 q^{44} + 6 q^{45} + 2 q^{46} - 16 q^{47} - 4 q^{48} - 14 q^{49} - 8 q^{51} - 12 q^{52} + 48 q^{53} - 32 q^{54} - 6 q^{56} - 36 q^{57} + 8 q^{58} - 12 q^{59} - 2 q^{60} - 30 q^{61} - 8 q^{62} + 20 q^{63} - 12 q^{64} - 12 q^{65} - 14 q^{66} - 4 q^{67} + 12 q^{68} - 50 q^{69} + 6 q^{70} + 4 q^{72} + 2 q^{75} - 20 q^{77} + 32 q^{78} - 4 q^{79} - 6 q^{80} - 40 q^{81} + 40 q^{83} + 20 q^{84} + 24 q^{85} + 54 q^{86} + 64 q^{87} - 26 q^{89} + 8 q^{90} + 28 q^{91} + 4 q^{93} + 24 q^{94} - 4 q^{96} - 16 q^{98} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 1.20480 + 1.24437i 0.695592 + 0.718437i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0.421203 + 1.68006i 0.171955 + 0.685880i
\(7\) 0.0551777 2.64518i 0.0208552 0.999783i
\(8\) 1.00000i 0.353553i
\(9\) −0.0969112 + 2.99843i −0.0323037 + 0.999478i
\(10\) −0.866025 + 0.500000i −0.273861 + 0.158114i
\(11\) 0.167855 0.0969112i 0.0506102 0.0292198i −0.474481 0.880266i \(-0.657364\pi\)
0.525092 + 0.851046i \(0.324031\pi\)
\(12\) −0.475255 + 1.66557i −0.137194 + 0.480809i
\(13\) 1.54892i 0.429594i −0.976659 0.214797i \(-0.931091\pi\)
0.976659 0.214797i \(-0.0689090\pi\)
\(14\) 1.37037 2.26320i 0.366248 0.604866i
\(15\) −1.68006 + 0.421203i −0.433789 + 0.108754i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.264766 0.458589i −0.0642153 0.111224i 0.832130 0.554580i \(-0.187121\pi\)
−0.896346 + 0.443356i \(0.853788\pi\)
\(18\) −1.58314 + 2.54826i −0.373151 + 0.600632i
\(19\) −5.53332 3.19467i −1.26943 0.732906i −0.294551 0.955636i \(-0.595170\pi\)
−0.974880 + 0.222729i \(0.928503\pi\)
\(20\) −1.00000 −0.223607
\(21\) 3.35805 3.11825i 0.732788 0.680457i
\(22\) 0.193822 0.0413231
\(23\) 3.68040 + 2.12488i 0.767416 + 0.443068i 0.831952 0.554848i \(-0.187223\pi\)
−0.0645362 + 0.997915i \(0.520557\pi\)
\(24\) −1.24437 + 1.20480i −0.254006 + 0.245929i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0.774462 1.34141i 0.151884 0.263072i
\(27\) −3.84792 + 3.49192i −0.740532 + 0.672021i
\(28\) 2.31838 1.27480i 0.438132 0.240915i
\(29\) 4.87349i 0.904984i −0.891768 0.452492i \(-0.850535\pi\)
0.891768 0.452492i \(-0.149465\pi\)
\(30\) −1.66557 0.475255i −0.304091 0.0867694i
\(31\) 8.02559 4.63357i 1.44144 0.832214i 0.443492 0.896278i \(-0.353739\pi\)
0.997946 + 0.0640639i \(0.0204062\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 0.322825 + 0.0921151i 0.0561967 + 0.0160352i
\(34\) 0.529533i 0.0908141i
\(35\) 2.26320 + 1.37037i 0.382551 + 0.231635i
\(36\) −2.64518 + 1.41529i −0.440863 + 0.235882i
\(37\) −0.881634 + 1.52704i −0.144940 + 0.251043i −0.929350 0.369199i \(-0.879632\pi\)
0.784411 + 0.620242i \(0.212966\pi\)
\(38\) −3.19467 5.53332i −0.518243 0.897623i
\(39\) 1.92743 1.86614i 0.308636 0.298822i
\(40\) −0.866025 0.500000i −0.136931 0.0790569i
\(41\) −9.91573 −1.54858 −0.774289 0.632833i \(-0.781892\pi\)
−0.774289 + 0.632833i \(0.781892\pi\)
\(42\) 4.46728 1.02145i 0.689317 0.157614i
\(43\) 11.4865 1.75168 0.875838 0.482606i \(-0.160310\pi\)
0.875838 + 0.482606i \(0.160310\pi\)
\(44\) 0.167855 + 0.0969112i 0.0253051 + 0.0146099i
\(45\) −2.54826 1.58314i −0.379873 0.236001i
\(46\) 2.12488 + 3.68040i 0.313296 + 0.542645i
\(47\) −4.90186 + 8.49028i −0.715010 + 1.23843i 0.247945 + 0.968774i \(0.420245\pi\)
−0.962956 + 0.269660i \(0.913089\pi\)
\(48\) −1.68006 + 0.421203i −0.242495 + 0.0607954i
\(49\) −6.99391 0.291909i −0.999130 0.0417014i
\(50\) 1.00000i 0.141421i
\(51\) 0.251663 0.881975i 0.0352399 0.123501i
\(52\) 1.34141 0.774462i 0.186020 0.107398i
\(53\) −0.0562751 + 0.0324905i −0.00772998 + 0.00446291i −0.503860 0.863785i \(-0.668087\pi\)
0.496130 + 0.868248i \(0.334754\pi\)
\(54\) −5.07836 + 1.10013i −0.691077 + 0.149709i
\(55\) 0.193822i 0.0261350i
\(56\) 2.64518 + 0.0551777i 0.353476 + 0.00737343i
\(57\) −2.69121 10.7344i −0.356459 1.42181i
\(58\) 2.43674 4.22056i 0.319960 0.554187i
\(59\) −6.01371 10.4160i −0.782918 1.35605i −0.930235 0.366964i \(-0.880397\pi\)
0.147317 0.989089i \(-0.452936\pi\)
\(60\) −1.20480 1.24437i −0.155539 0.160647i
\(61\) 3.71180 + 2.14301i 0.475248 + 0.274384i 0.718434 0.695595i \(-0.244859\pi\)
−0.243186 + 0.969980i \(0.578193\pi\)
\(62\) 9.26715 1.17693
\(63\) 7.92604 + 0.421794i 0.998587 + 0.0531410i
\(64\) −1.00000 −0.125000
\(65\) 1.34141 + 0.774462i 0.166381 + 0.0960601i
\(66\) 0.233517 + 0.241187i 0.0287440 + 0.0296880i
\(67\) −2.41529 4.18340i −0.295075 0.511084i 0.679928 0.733279i \(-0.262011\pi\)
−0.975002 + 0.222195i \(0.928678\pi\)
\(68\) 0.264766 0.458589i 0.0321076 0.0556121i
\(69\) 1.79001 + 7.13983i 0.215492 + 0.859534i
\(70\) 1.27480 + 2.31838i 0.152368 + 0.277099i
\(71\) 6.29103i 0.746608i 0.927709 + 0.373304i \(0.121775\pi\)
−0.927709 + 0.373304i \(0.878225\pi\)
\(72\) −2.99843 0.0969112i −0.353369 0.0114211i
\(73\) −7.00763 + 4.04586i −0.820181 + 0.473532i −0.850479 0.526009i \(-0.823688\pi\)
0.0302980 + 0.999541i \(0.490354\pi\)
\(74\) −1.52704 + 0.881634i −0.177514 + 0.102488i
\(75\) 0.475255 1.66557i 0.0548778 0.192324i
\(76\) 6.38933i 0.732906i
\(77\) −0.247085 0.449354i −0.0281580 0.0512086i
\(78\) 2.60228 0.652411i 0.294650 0.0738710i
\(79\) −3.38883 + 5.86962i −0.381273 + 0.660384i −0.991245 0.132039i \(-0.957848\pi\)
0.609971 + 0.792423i \(0.291181\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −8.98122 0.581164i −0.997913 0.0645738i
\(82\) −8.58728 4.95787i −0.948306 0.547505i
\(83\) 2.11036 0.231642 0.115821 0.993270i \(-0.463050\pi\)
0.115821 + 0.993270i \(0.463050\pi\)
\(84\) 4.37951 + 1.34904i 0.477844 + 0.147192i
\(85\) 0.529533 0.0574359
\(86\) 9.94760 + 5.74325i 1.07268 + 0.619311i
\(87\) 6.06442 5.87158i 0.650174 0.629500i
\(88\) 0.0969112 + 0.167855i 0.0103308 + 0.0178934i
\(89\) −8.18773 + 14.1816i −0.867898 + 1.50324i −0.00375740 + 0.999993i \(0.501196\pi\)
−0.864141 + 0.503250i \(0.832137\pi\)
\(90\) −1.41529 2.64518i −0.149185 0.278826i
\(91\) −4.09717 0.0854660i −0.429501 0.00895927i
\(92\) 4.24976i 0.443068i
\(93\) 15.4351 + 4.40426i 1.60055 + 0.456701i
\(94\) −8.49028 + 4.90186i −0.875705 + 0.505589i
\(95\) 5.53332 3.19467i 0.567707 0.327766i
\(96\) −1.66557 0.475255i −0.169992 0.0485055i
\(97\) 8.24463i 0.837115i 0.908190 + 0.418557i \(0.137464\pi\)
−0.908190 + 0.418557i \(0.862536\pi\)
\(98\) −5.91095 3.74976i −0.597096 0.378783i
\(99\) 0.274315 + 0.512694i 0.0275697 + 0.0515277i
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) −2.22831 3.85955i −0.221725 0.384040i 0.733607 0.679574i \(-0.237836\pi\)
−0.955332 + 0.295535i \(0.904502\pi\)
\(102\) 0.658934 0.637981i 0.0652442 0.0631696i
\(103\) 7.29356 + 4.21094i 0.718656 + 0.414916i 0.814258 0.580504i \(-0.197144\pi\)
−0.0956021 + 0.995420i \(0.530478\pi\)
\(104\) 1.54892 0.151884
\(105\) 1.02145 + 4.46728i 0.0996838 + 0.435962i
\(106\) −0.0649809 −0.00631151
\(107\) 15.4270 + 8.90681i 1.49139 + 0.861054i 0.999951 0.00985883i \(-0.00313821\pi\)
0.491438 + 0.870913i \(0.336472\pi\)
\(108\) −4.94805 1.58643i −0.476127 0.152655i
\(109\) −0.0739017 0.128001i −0.00707850 0.0122603i 0.862464 0.506118i \(-0.168920\pi\)
−0.869543 + 0.493857i \(0.835587\pi\)
\(110\) −0.0969112 + 0.167855i −0.00924012 + 0.0160044i
\(111\) −2.96239 + 0.742694i −0.281178 + 0.0704934i
\(112\) 2.26320 + 1.37037i 0.213852 + 0.129488i
\(113\) 3.44771i 0.324334i 0.986763 + 0.162167i \(0.0518483\pi\)
−0.986763 + 0.162167i \(0.948152\pi\)
\(114\) 3.03656 10.6419i 0.284400 0.996705i
\(115\) −3.68040 + 2.12488i −0.343199 + 0.198146i
\(116\) 4.22056 2.43674i 0.391870 0.226246i
\(117\) 4.64434 + 0.150108i 0.429370 + 0.0138775i
\(118\) 12.0274i 1.10721i
\(119\) −1.22766 + 0.675050i −0.112539 + 0.0618817i
\(120\) −0.421203 1.68006i −0.0384504 0.153367i
\(121\) −5.48122 + 9.49375i −0.498292 + 0.863068i
\(122\) 2.14301 + 3.71180i 0.194019 + 0.336051i
\(123\) −11.9465 12.3388i −1.07718 1.11256i
\(124\) 8.02559 + 4.63357i 0.720719 + 0.416107i
\(125\) 1.00000 0.0894427
\(126\) 6.65325 + 4.32830i 0.592719 + 0.385596i
\(127\) 5.49965 0.488015 0.244007 0.969773i \(-0.421538\pi\)
0.244007 + 0.969773i \(0.421538\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 13.8389 + 14.2935i 1.21845 + 1.25847i
\(130\) 0.774462 + 1.34141i 0.0679248 + 0.117649i
\(131\) 2.99843 5.19344i 0.261974 0.453753i −0.704792 0.709414i \(-0.748960\pi\)
0.966767 + 0.255661i \(0.0822931\pi\)
\(132\) 0.0816386 + 0.325633i 0.00710573 + 0.0283427i
\(133\) −8.75577 + 14.4603i −0.759221 + 1.25387i
\(134\) 4.83058i 0.417298i
\(135\) −1.10013 5.07836i −0.0946844 0.437075i
\(136\) 0.458589 0.264766i 0.0393237 0.0227035i
\(137\) −0.746611 + 0.431056i −0.0637872 + 0.0368276i −0.531554 0.847024i \(-0.678392\pi\)
0.467767 + 0.883852i \(0.345059\pi\)
\(138\) −2.01972 + 7.07828i −0.171930 + 0.602543i
\(139\) 16.1843i 1.37274i −0.727254 0.686368i \(-0.759204\pi\)
0.727254 0.686368i \(-0.240796\pi\)
\(140\) −0.0551777 + 2.64518i −0.00466337 + 0.223558i
\(141\) −16.4708 + 4.12936i −1.38709 + 0.347755i
\(142\) −3.14552 + 5.44820i −0.263966 + 0.457202i
\(143\) −0.150108 0.259995i −0.0125527 0.0217418i
\(144\) −2.54826 1.58314i −0.212355 0.131929i
\(145\) 4.22056 + 2.43674i 0.350499 + 0.202361i
\(146\) −8.09171 −0.669675
\(147\) −8.06302 9.05470i −0.665027 0.746819i
\(148\) −1.76327 −0.144940
\(149\) −11.0505 6.38001i −0.905292 0.522671i −0.0263788 0.999652i \(-0.508398\pi\)
−0.878913 + 0.476981i \(0.841731\pi\)
\(150\) 1.24437 1.20480i 0.101602 0.0983716i
\(151\) 8.75012 + 15.1557i 0.712075 + 1.23335i 0.964077 + 0.265623i \(0.0855778\pi\)
−0.252002 + 0.967727i \(0.581089\pi\)
\(152\) 3.19467 5.53332i 0.259122 0.448812i
\(153\) 1.40071 0.749442i 0.113240 0.0605888i
\(154\) 0.0106947 0.512694i 0.000861802 0.0413141i
\(155\) 9.26715i 0.744355i
\(156\) 2.57984 + 0.736134i 0.206553 + 0.0589379i
\(157\) −2.46479 + 1.42305i −0.196711 + 0.113571i −0.595121 0.803636i \(-0.702896\pi\)
0.398409 + 0.917208i \(0.369562\pi\)
\(158\) −5.86962 + 3.38883i −0.466962 + 0.269601i
\(159\) −0.108230 0.0308825i −0.00858323 0.00244914i
\(160\) 1.00000i 0.0790569i
\(161\) 5.82375 9.61805i 0.458976 0.758009i
\(162\) −7.48738 4.99391i −0.588264 0.392359i
\(163\) −6.17931 + 10.7029i −0.484001 + 0.838315i −0.999831 0.0183763i \(-0.994150\pi\)
0.515830 + 0.856691i \(0.327484\pi\)
\(164\) −4.95787 8.58728i −0.387144 0.670554i
\(165\) −0.241187 + 0.233517i −0.0187764 + 0.0181793i
\(166\) 1.82762 + 1.05518i 0.141851 + 0.0818977i
\(167\) 4.99920 0.386850 0.193425 0.981115i \(-0.438040\pi\)
0.193425 + 0.981115i \(0.438040\pi\)
\(168\) 3.11825 + 3.35805i 0.240578 + 0.259080i
\(169\) 10.6008 0.815449
\(170\) 0.458589 + 0.264766i 0.0351722 + 0.0203067i
\(171\) 10.1152 16.2817i 0.773531 1.24509i
\(172\) 5.74325 + 9.94760i 0.437919 + 0.758498i
\(173\) 3.80403 6.58878i 0.289215 0.500935i −0.684407 0.729100i \(-0.739939\pi\)
0.973623 + 0.228164i \(0.0732724\pi\)
\(174\) 8.18773 2.05273i 0.620710 0.155617i
\(175\) −2.31838 + 1.27480i −0.175253 + 0.0963660i
\(176\) 0.193822i 0.0146099i
\(177\) 5.71609 20.0325i 0.429648 1.50574i
\(178\) −14.1816 + 8.18773i −1.06295 + 0.613697i
\(179\) 14.0520 8.11295i 1.05030 0.606390i 0.127566 0.991830i \(-0.459284\pi\)
0.922733 + 0.385440i \(0.125950\pi\)
\(180\) 0.0969112 2.99843i 0.00722334 0.223490i
\(181\) 4.03153i 0.299661i −0.988712 0.149831i \(-0.952127\pi\)
0.988712 0.149831i \(-0.0478729\pi\)
\(182\) −3.50552 2.12260i −0.259847 0.157338i
\(183\) 1.80529 + 7.20076i 0.133451 + 0.532295i
\(184\) −2.12488 + 3.68040i −0.156648 + 0.271322i
\(185\) −0.881634 1.52704i −0.0648190 0.112270i
\(186\) 11.1651 + 11.5318i 0.818662 + 0.845549i
\(187\) −0.0888848 0.0513177i −0.00649990 0.00375272i
\(188\) −9.80373 −0.715010
\(189\) 9.02443 + 10.3711i 0.656431 + 0.754386i
\(190\) 6.38933 0.463531
\(191\) −21.8544 12.6176i −1.58133 0.912980i −0.994666 0.103147i \(-0.967109\pi\)
−0.586661 0.809832i \(-0.699558\pi\)
\(192\) −1.20480 1.24437i −0.0869490 0.0898046i
\(193\) −12.6183 21.8556i −0.908286 1.57320i −0.816444 0.577424i \(-0.804058\pi\)
−0.0918418 0.995774i \(-0.529275\pi\)
\(194\) −4.12231 + 7.14006i −0.295965 + 0.512626i
\(195\) 0.652411 + 2.60228i 0.0467201 + 0.186353i
\(196\) −3.24415 6.20286i −0.231725 0.443061i
\(197\) 14.7364i 1.04993i −0.851125 0.524964i \(-0.824079\pi\)
0.851125 0.524964i \(-0.175921\pi\)
\(198\) −0.0187836 + 0.581164i −0.00133489 + 0.0413015i
\(199\) 22.3991 12.9321i 1.58783 0.916734i 0.594165 0.804343i \(-0.297483\pi\)
0.993664 0.112391i \(-0.0358508\pi\)
\(200\) 0.866025 0.500000i 0.0612372 0.0353553i
\(201\) 2.29576 8.04568i 0.161930 0.567499i
\(202\) 4.45663i 0.313567i
\(203\) −12.8912 0.268908i −0.904787 0.0188736i
\(204\) 0.889645 0.223041i 0.0622876 0.0156160i
\(205\) 4.95787 8.58728i 0.346272 0.599761i
\(206\) 4.21094 + 7.29356i 0.293390 + 0.508166i
\(207\) −6.72798 + 10.8295i −0.467627 + 0.752703i
\(208\) 1.34141 + 0.774462i 0.0930098 + 0.0536992i
\(209\) −1.23840 −0.0856616
\(210\) −1.34904 + 4.37951i −0.0930924 + 0.302215i
\(211\) −22.8721 −1.57458 −0.787289 0.616585i \(-0.788516\pi\)
−0.787289 + 0.616585i \(0.788516\pi\)
\(212\) −0.0562751 0.0324905i −0.00386499 0.00223145i
\(213\) −7.82837 + 7.57944i −0.536391 + 0.519335i
\(214\) 8.90681 + 15.4270i 0.608857 + 1.05457i
\(215\) −5.74325 + 9.94760i −0.391687 + 0.678421i
\(216\) −3.49192 3.84792i −0.237595 0.261818i
\(217\) −11.8138 21.4848i −0.801972 1.45848i
\(218\) 0.147803i 0.0100105i
\(219\) −13.4773 3.84563i −0.910714 0.259864i
\(220\) −0.167855 + 0.0969112i −0.0113168 + 0.00653375i
\(221\) −0.710319 + 0.410103i −0.0477812 + 0.0275865i
\(222\) −2.93685 0.838003i −0.197109 0.0562431i
\(223\) 0.00626282i 0.000419390i −1.00000 0.000209695i \(-0.999933\pi\)
1.00000 0.000209695i \(-6.67479e-5\pi\)
\(224\) 1.27480 + 2.31838i 0.0851763 + 0.154903i
\(225\) 2.64518 1.41529i 0.176345 0.0943526i
\(226\) −1.72386 + 2.98581i −0.114669 + 0.198613i
\(227\) 9.41373 + 16.3051i 0.624811 + 1.08220i 0.988577 + 0.150715i \(0.0481574\pi\)
−0.363766 + 0.931490i \(0.618509\pi\)
\(228\) 7.95069 7.69787i 0.526547 0.509804i
\(229\) 6.75203 + 3.89829i 0.446187 + 0.257606i 0.706218 0.707994i \(-0.250400\pi\)
−0.260032 + 0.965600i \(0.583733\pi\)
\(230\) −4.24976 −0.280221
\(231\) 0.261474 0.848847i 0.0172037 0.0558500i
\(232\) 4.87349 0.319960
\(233\) −11.2535 6.49718i −0.737238 0.425645i 0.0838262 0.996480i \(-0.473286\pi\)
−0.821064 + 0.570836i \(0.806619\pi\)
\(234\) 3.94707 + 2.45217i 0.258028 + 0.160303i
\(235\) −4.90186 8.49028i −0.319762 0.553845i
\(236\) 6.01371 10.4160i 0.391459 0.678027i
\(237\) −11.3868 + 2.85477i −0.739655 + 0.185437i
\(238\) −1.40071 0.0292184i −0.0907944 0.00189395i
\(239\) 17.1710i 1.11070i −0.831618 0.555349i \(-0.812585\pi\)
0.831618 0.555349i \(-0.187415\pi\)
\(240\) 0.475255 1.66557i 0.0306776 0.107512i
\(241\) 7.10695 4.10320i 0.457799 0.264310i −0.253319 0.967383i \(-0.581522\pi\)
0.711118 + 0.703072i \(0.248189\pi\)
\(242\) −9.49375 + 5.48122i −0.610281 + 0.352346i
\(243\) −10.0974 11.8761i −0.647748 0.761855i
\(244\) 4.28602i 0.274384i
\(245\) 3.74976 5.91095i 0.239563 0.377637i
\(246\) −4.17654 16.6590i −0.266286 1.06214i
\(247\) −4.94829 + 8.57069i −0.314852 + 0.545340i
\(248\) 4.63357 + 8.02559i 0.294232 + 0.509625i
\(249\) 2.54256 + 2.62606i 0.161128 + 0.166420i
\(250\) 0.866025 + 0.500000i 0.0547723 + 0.0316228i
\(251\) 22.9102 1.44608 0.723038 0.690808i \(-0.242745\pi\)
0.723038 + 0.690808i \(0.242745\pi\)
\(252\) 3.59774 + 7.07505i 0.226636 + 0.445686i
\(253\) 0.823698 0.0517855
\(254\) 4.76283 + 2.74982i 0.298847 + 0.172539i
\(255\) 0.637981 + 0.658934i 0.0399519 + 0.0412641i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 3.54324 6.13707i 0.221021 0.382820i −0.734097 0.679044i \(-0.762394\pi\)
0.955118 + 0.296225i \(0.0957277\pi\)
\(258\) 4.83815 + 19.2980i 0.301210 + 1.20144i
\(259\) 3.99063 + 2.41634i 0.247966 + 0.150144i
\(260\) 1.54892i 0.0960601i
\(261\) 14.6128 + 0.472296i 0.904512 + 0.0292344i
\(262\) 5.19344 2.99843i 0.320852 0.185244i
\(263\) 15.4744 8.93416i 0.954194 0.550904i 0.0598127 0.998210i \(-0.480950\pi\)
0.894381 + 0.447306i \(0.147616\pi\)
\(264\) −0.0921151 + 0.322825i −0.00566930 + 0.0198685i
\(265\) 0.0649809i 0.00399175i
\(266\) −14.8129 + 8.14514i −0.908236 + 0.499410i
\(267\) −27.5117 + 6.89740i −1.68369 + 0.422114i
\(268\) 2.41529 4.18340i 0.147537 0.255542i
\(269\) 3.46273 + 5.99762i 0.211126 + 0.365682i 0.952067 0.305889i \(-0.0989535\pi\)
−0.740941 + 0.671570i \(0.765620\pi\)
\(270\) 1.58643 4.94805i 0.0965473 0.301129i
\(271\) −14.6520 8.45932i −0.890044 0.513867i −0.0160872 0.999871i \(-0.505121\pi\)
−0.873957 + 0.486003i \(0.838454\pi\)
\(272\) 0.529533 0.0321076
\(273\) −4.82993 5.20137i −0.292320 0.314801i
\(274\) −0.862112 −0.0520821
\(275\) −0.167855 0.0969112i −0.0101220 0.00584397i
\(276\) −5.28827 + 5.12011i −0.318316 + 0.308194i
\(277\) 10.6505 + 18.4471i 0.639924 + 1.10838i 0.985449 + 0.169972i \(0.0543677\pi\)
−0.345525 + 0.938410i \(0.612299\pi\)
\(278\) 8.09216 14.0160i 0.485336 0.840626i
\(279\) 13.1157 + 24.5132i 0.785216 + 1.46757i
\(280\) −1.37037 + 2.26320i −0.0818955 + 0.135252i
\(281\) 19.5927i 1.16880i 0.811464 + 0.584402i \(0.198671\pi\)
−0.811464 + 0.584402i \(0.801329\pi\)
\(282\) −16.3288 4.65927i −0.972367 0.277456i
\(283\) −13.0751 + 7.54892i −0.777235 + 0.448737i −0.835450 0.549567i \(-0.814793\pi\)
0.0582144 + 0.998304i \(0.481459\pi\)
\(284\) −5.44820 + 3.14552i −0.323291 + 0.186652i
\(285\) 10.6419 + 3.03656i 0.630371 + 0.179870i
\(286\) 0.300216i 0.0177521i
\(287\) −0.547127 + 26.2289i −0.0322959 + 1.54824i
\(288\) −1.41529 2.64518i −0.0833967 0.155868i
\(289\) 8.35980 14.4796i 0.491753 0.851741i
\(290\) 2.43674 + 4.22056i 0.143091 + 0.247840i
\(291\) −10.2594 + 9.93313i −0.601414 + 0.582290i
\(292\) −7.00763 4.04586i −0.410090 0.236766i
\(293\) 8.00534 0.467677 0.233839 0.972275i \(-0.424871\pi\)
0.233839 + 0.972275i \(0.424871\pi\)
\(294\) −2.45543 11.8731i −0.143204 0.692454i
\(295\) 12.0274 0.700263
\(296\) −1.52704 0.881634i −0.0887571 0.0512439i
\(297\) −0.307487 + 0.959044i −0.0178422 + 0.0556494i
\(298\) −6.38001 11.0505i −0.369584 0.640138i
\(299\) 3.29127 5.70065i 0.190339 0.329677i
\(300\) 1.68006 0.421203i 0.0969981 0.0243182i
\(301\) 0.633799 30.3838i 0.0365316 1.75129i
\(302\) 17.5002i 1.00703i
\(303\) 2.11804 7.42283i 0.121678 0.426431i
\(304\) 5.53332 3.19467i 0.317358 0.183227i
\(305\) −3.71180 + 2.14301i −0.212537 + 0.122708i
\(306\) 1.58777 + 0.0513177i 0.0907667 + 0.00293364i
\(307\) 4.33663i 0.247505i −0.992313 0.123752i \(-0.960507\pi\)
0.992313 0.123752i \(-0.0394928\pi\)
\(308\) 0.265609 0.438659i 0.0151345 0.0249949i
\(309\) 3.54732 + 14.1492i 0.201800 + 0.804921i
\(310\) −4.63357 + 8.02559i −0.263169 + 0.455823i
\(311\) 11.4192 + 19.7786i 0.647523 + 1.12154i 0.983713 + 0.179748i \(0.0575284\pi\)
−0.336190 + 0.941794i \(0.609138\pi\)
\(312\) 1.86614 + 1.92743i 0.105650 + 0.109119i
\(313\) 21.9141 + 12.6521i 1.23866 + 0.715140i 0.968820 0.247766i \(-0.0796964\pi\)
0.269838 + 0.962906i \(0.413030\pi\)
\(314\) −2.84609 −0.160614
\(315\) −4.32830 + 6.65325i −0.243872 + 0.374868i
\(316\) −6.77766 −0.381273
\(317\) −13.0681 7.54489i −0.733979 0.423763i 0.0858969 0.996304i \(-0.472624\pi\)
−0.819876 + 0.572541i \(0.805958\pi\)
\(318\) −0.0782891 0.0808603i −0.00439023 0.00453442i
\(319\) −0.472296 0.818040i −0.0264435 0.0458015i
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) 7.50315 + 29.9279i 0.418785 + 1.67041i
\(322\) 9.85254 5.41760i 0.549061 0.301911i
\(323\) 3.38336i 0.188255i
\(324\) −3.98731 8.06854i −0.221517 0.448252i
\(325\) −1.34141 + 0.774462i −0.0744079 + 0.0429594i
\(326\) −10.7029 + 6.17931i −0.592778 + 0.342241i
\(327\) 0.0702443 0.246177i 0.00388452 0.0136136i
\(328\) 9.91573i 0.547505i
\(329\) 22.1878 + 13.4348i 1.22325 + 0.740683i
\(330\) −0.325633 + 0.0816386i −0.0179255 + 0.00449406i
\(331\) −7.53086 + 13.0438i −0.413933 + 0.716954i −0.995316 0.0966768i \(-0.969179\pi\)
0.581382 + 0.813630i \(0.302512\pi\)
\(332\) 1.05518 + 1.82762i 0.0579104 + 0.100304i
\(333\) −4.49327 2.79151i −0.246230 0.152974i
\(334\) 4.32943 + 2.49960i 0.236896 + 0.136772i
\(335\) 4.83058 0.263923
\(336\) 1.02145 + 4.46728i 0.0557249 + 0.243710i
\(337\) 14.9611 0.814983 0.407491 0.913209i \(-0.366404\pi\)
0.407491 + 0.913209i \(0.366404\pi\)
\(338\) 9.18059 + 5.30042i 0.499359 + 0.288305i
\(339\) −4.29023 + 4.15381i −0.233013 + 0.225604i
\(340\) 0.264766 + 0.458589i 0.0143590 + 0.0248705i
\(341\) 0.898091 1.55554i 0.0486343 0.0842371i
\(342\) 16.9009 9.04275i 0.913896 0.488976i
\(343\) −1.15806 + 18.4840i −0.0625294 + 0.998043i
\(344\) 11.4865i 0.619311i
\(345\) −7.07828 2.01972i −0.381082 0.108738i
\(346\) 6.58878 3.80403i 0.354215 0.204506i
\(347\) 3.50448 2.02331i 0.188130 0.108617i −0.402977 0.915210i \(-0.632024\pi\)
0.591107 + 0.806593i \(0.298691\pi\)
\(348\) 8.11715 + 2.31615i 0.435125 + 0.124159i
\(349\) 12.3695i 0.662124i −0.943609 0.331062i \(-0.892593\pi\)
0.943609 0.331062i \(-0.107407\pi\)
\(350\) −2.64518 0.0551777i −0.141391 0.00294937i
\(351\) 5.40872 + 5.96013i 0.288696 + 0.318128i
\(352\) −0.0969112 + 0.167855i −0.00516539 + 0.00894671i
\(353\) 1.83358 + 3.17585i 0.0975914 + 0.169033i 0.910687 0.413097i \(-0.135553\pi\)
−0.813096 + 0.582130i \(0.802220\pi\)
\(354\) 14.9665 14.4906i 0.795463 0.770169i
\(355\) −5.44820 3.14552i −0.289160 0.166947i
\(356\) −16.3755 −0.867898
\(357\) −2.31909 0.714359i −0.122739 0.0378079i
\(358\) 16.2259 0.857565
\(359\) 6.34163 + 3.66134i 0.334699 + 0.193238i 0.657925 0.753083i \(-0.271434\pi\)
−0.323227 + 0.946322i \(0.604768\pi\)
\(360\) 1.58314 2.54826i 0.0834391 0.134305i
\(361\) 10.9118 + 18.8997i 0.574304 + 0.994723i
\(362\) 2.01577 3.49141i 0.105946 0.183504i
\(363\) −18.4175 + 4.61741i −0.966668 + 0.242351i
\(364\) −1.97457 3.59099i −0.103496 0.188219i
\(365\) 8.09171i 0.423540i
\(366\) −2.03696 + 7.13868i −0.106473 + 0.373145i
\(367\) −4.12769 + 2.38312i −0.215464 + 0.124398i −0.603848 0.797100i \(-0.706367\pi\)
0.388384 + 0.921497i \(0.373033\pi\)
\(368\) −3.68040 + 2.12488i −0.191854 + 0.110767i
\(369\) 0.960946 29.7317i 0.0500248 1.54777i
\(370\) 1.76327i 0.0916679i
\(371\) 0.0828379 + 0.150650i 0.00430073 + 0.00782138i
\(372\) 3.90335 + 15.5693i 0.202379 + 0.807232i
\(373\) 8.64813 14.9790i 0.447783 0.775584i −0.550458 0.834863i \(-0.685547\pi\)
0.998241 + 0.0592792i \(0.0188802\pi\)
\(374\) −0.0513177 0.0888848i −0.00265357 0.00459612i
\(375\) 1.20480 + 1.24437i 0.0622156 + 0.0642590i
\(376\) −8.49028 4.90186i −0.437853 0.252794i
\(377\) −7.54866 −0.388776
\(378\) 2.62983 + 13.4938i 0.135264 + 0.694049i
\(379\) −8.76645 −0.450302 −0.225151 0.974324i \(-0.572288\pi\)
−0.225151 + 0.974324i \(0.572288\pi\)
\(380\) 5.53332 + 3.19467i 0.283853 + 0.163883i
\(381\) 6.62598 + 6.84359i 0.339459 + 0.350608i
\(382\) −12.6176 21.8544i −0.645574 1.11817i
\(383\) 14.2377 24.6604i 0.727511 1.26009i −0.230422 0.973091i \(-0.574011\pi\)
0.957932 0.286995i \(-0.0926562\pi\)
\(384\) −0.421203 1.68006i −0.0214944 0.0857350i
\(385\) 0.512694 + 0.0106947i 0.0261293 + 0.000545051i
\(386\) 25.2366i 1.28451i
\(387\) −1.11317 + 34.4415i −0.0565857 + 1.75076i
\(388\) −7.14006 + 4.12231i −0.362481 + 0.209279i
\(389\) −18.2468 + 10.5348i −0.925151 + 0.534136i −0.885275 0.465069i \(-0.846030\pi\)
−0.0398761 + 0.999205i \(0.512696\pi\)
\(390\) −0.736134 + 2.57984i −0.0372756 + 0.130635i
\(391\) 2.25039i 0.113807i
\(392\) 0.291909 6.99391i 0.0147437 0.353246i
\(393\) 10.0751 2.52590i 0.508220 0.127415i
\(394\) 7.36822 12.7621i 0.371205 0.642947i
\(395\) −3.38883 5.86962i −0.170510 0.295333i
\(396\) −0.306849 + 0.493911i −0.0154197 + 0.0248200i
\(397\) 5.71412 + 3.29905i 0.286783 + 0.165574i 0.636490 0.771285i \(-0.280386\pi\)
−0.349707 + 0.936859i \(0.613719\pi\)
\(398\) 25.8642 1.29646
\(399\) −28.5430 + 6.52641i −1.42894 + 0.326729i
\(400\) 1.00000 0.0500000
\(401\) −13.9699 8.06552i −0.697623 0.402773i 0.108839 0.994059i \(-0.465287\pi\)
−0.806461 + 0.591287i \(0.798620\pi\)
\(402\) 6.01103 5.81988i 0.299803 0.290269i
\(403\) −7.17705 12.4310i −0.357514 0.619233i
\(404\) 2.22831 3.85955i 0.110863 0.192020i
\(405\) 4.99391 7.48738i 0.248149 0.372051i
\(406\) −11.0297 6.67850i −0.547394 0.331448i
\(407\) 0.341761i 0.0169405i
\(408\) 0.881975 + 0.251663i 0.0436643 + 0.0124592i
\(409\) −22.8659 + 13.2016i −1.13065 + 0.652779i −0.944097 0.329666i \(-0.893064\pi\)
−0.186549 + 0.982446i \(0.559730\pi\)
\(410\) 8.58728 4.95787i 0.424095 0.244852i
\(411\) −1.43591 0.409723i −0.0708282 0.0202102i
\(412\) 8.42187i 0.414916i
\(413\) −27.8841 + 15.3326i −1.37209 + 0.754467i
\(414\) −11.2414 + 6.01464i −0.552482 + 0.295603i
\(415\) −1.05518 + 1.82762i −0.0517966 + 0.0897144i
\(416\) 0.774462 + 1.34141i 0.0379711 + 0.0657679i
\(417\) 20.1393 19.4989i 0.986225 0.954864i
\(418\) −1.07248 0.619198i −0.0524568 0.0302860i
\(419\) −19.8312 −0.968819 −0.484409 0.874841i \(-0.660965\pi\)
−0.484409 + 0.874841i \(0.660965\pi\)
\(420\) −3.35805 + 3.11825i −0.163856 + 0.152155i
\(421\) 6.28009 0.306073 0.153036 0.988221i \(-0.451095\pi\)
0.153036 + 0.988221i \(0.451095\pi\)
\(422\) −19.8078 11.4360i −0.964228 0.556697i
\(423\) −24.9825 15.5207i −1.21469 0.754643i
\(424\) −0.0324905 0.0562751i −0.00157788 0.00273296i
\(425\) −0.264766 + 0.458589i −0.0128431 + 0.0222448i
\(426\) −10.5693 + 2.64980i −0.512084 + 0.128383i
\(427\) 5.87345 9.70013i 0.284236 0.469422i
\(428\) 17.8136i 0.861054i
\(429\) 0.142679 0.500032i 0.00688862 0.0241418i
\(430\) −9.94760 + 5.74325i −0.479716 + 0.276964i
\(431\) 3.94326 2.27664i 0.189940 0.109662i −0.402014 0.915633i \(-0.631690\pi\)
0.591955 + 0.805971i \(0.298356\pi\)
\(432\) −1.10013 5.07836i −0.0529302 0.244333i
\(433\) 2.62801i 0.126294i 0.998004 + 0.0631471i \(0.0201137\pi\)
−0.998004 + 0.0631471i \(0.979886\pi\)
\(434\) 0.511340 24.5132i 0.0245451 1.17667i
\(435\) 2.05273 + 8.18773i 0.0984208 + 0.392572i
\(436\) 0.0739017 0.128001i 0.00353925 0.00613016i
\(437\) −13.5765 23.5153i −0.649454 1.12489i
\(438\) −9.74890 10.0691i −0.465820 0.481119i
\(439\) −5.05475 2.91836i −0.241250 0.139286i 0.374501 0.927226i \(-0.377814\pi\)
−0.615751 + 0.787941i \(0.711147\pi\)
\(440\) −0.193822 −0.00924012
\(441\) 1.55306 20.9425i 0.0739552 0.997262i
\(442\) −0.820205 −0.0390132
\(443\) −22.8164 13.1730i −1.08404 0.625870i −0.152056 0.988372i \(-0.548589\pi\)
−0.931983 + 0.362502i \(0.881923\pi\)
\(444\) −2.12439 2.19416i −0.100819 0.104130i
\(445\) −8.18773 14.1816i −0.388136 0.672271i
\(446\) 0.00313141 0.00542376i 0.000148277 0.000256823i
\(447\) −5.37456 21.4375i −0.254208 1.01396i
\(448\) −0.0551777 + 2.64518i −0.00260690 + 0.124973i
\(449\) 5.76638i 0.272132i −0.990700 0.136066i \(-0.956554\pi\)
0.990700 0.136066i \(-0.0434460\pi\)
\(450\) 2.99843 + 0.0969112i 0.141348 + 0.00456844i
\(451\) −1.66441 + 0.960946i −0.0783738 + 0.0452492i
\(452\) −2.98581 + 1.72386i −0.140441 + 0.0810834i
\(453\) −8.31709 + 29.1479i −0.390771 + 1.36949i
\(454\) 18.8275i 0.883617i
\(455\) 2.12260 3.50552i 0.0995091 0.164341i
\(456\) 10.7344 2.69121i 0.502686 0.126027i
\(457\) 0.360756 0.624848i 0.0168755 0.0292292i −0.857464 0.514543i \(-0.827961\pi\)
0.874340 + 0.485314i \(0.161295\pi\)
\(458\) 3.89829 + 6.75203i 0.182155 + 0.315502i
\(459\) 2.62016 + 0.840069i 0.122298 + 0.0392111i
\(460\) −3.68040 2.12488i −0.171599 0.0990730i
\(461\) 34.3692 1.60073 0.800365 0.599512i \(-0.204639\pi\)
0.800365 + 0.599512i \(0.204639\pi\)
\(462\) 0.650866 0.604386i 0.0302810 0.0281186i
\(463\) 41.3815 1.92316 0.961581 0.274522i \(-0.0885197\pi\)
0.961581 + 0.274522i \(0.0885197\pi\)
\(464\) 4.22056 + 2.43674i 0.195935 + 0.113123i
\(465\) −11.5318 + 11.1651i −0.534772 + 0.517767i
\(466\) −6.49718 11.2535i −0.300976 0.521306i
\(467\) 8.98343 15.5598i 0.415704 0.720020i −0.579798 0.814760i \(-0.696869\pi\)
0.995502 + 0.0947401i \(0.0302020\pi\)
\(468\) 2.19217 + 4.09717i 0.101333 + 0.189392i
\(469\) −11.1991 + 6.15804i −0.517127 + 0.284352i
\(470\) 9.80373i 0.452212i
\(471\) −4.74037 1.35262i −0.218425 0.0623254i
\(472\) 10.4160 6.01371i 0.479437 0.276803i
\(473\) 1.92807 1.11317i 0.0886527 0.0511837i
\(474\) −11.2887 3.22112i −0.518506 0.147951i
\(475\) 6.38933i 0.293163i
\(476\) −1.19844 0.725657i −0.0549304 0.0332605i
\(477\) −0.0919668 0.171886i −0.00421087 0.00787012i
\(478\) 8.58548 14.8705i 0.392691 0.680160i
\(479\) −4.50559 7.80391i −0.205866 0.356570i 0.744542 0.667575i \(-0.232668\pi\)
−0.950408 + 0.311005i \(0.899334\pi\)
\(480\) 1.24437 1.20480i 0.0567974 0.0549914i
\(481\) 2.36526 + 1.36558i 0.107847 + 0.0622652i
\(482\) 8.20640 0.373791
\(483\) 18.9849 4.34093i 0.863842 0.197519i
\(484\) −10.9624 −0.498292
\(485\) −7.14006 4.12231i −0.324213 0.187185i
\(486\) −2.80653 15.3337i −0.127307 0.695552i
\(487\) 11.3648 + 19.6844i 0.514987 + 0.891984i 0.999849 + 0.0173928i \(0.00553658\pi\)
−0.484862 + 0.874591i \(0.661130\pi\)
\(488\) −2.14301 + 3.71180i −0.0970096 + 0.168025i
\(489\) −20.7632 + 5.20549i −0.938944 + 0.235401i
\(490\) 6.20286 3.24415i 0.280217 0.146556i
\(491\) 32.1654i 1.45160i −0.687904 0.725801i \(-0.741469\pi\)
0.687904 0.725801i \(-0.258531\pi\)
\(492\) 4.71250 16.5154i 0.212456 0.744570i
\(493\) −2.23493 + 1.29034i −0.100656 + 0.0581138i
\(494\) −8.57069 + 4.94829i −0.385614 + 0.222634i
\(495\) −0.581164 0.0187836i −0.0261214 0.000844259i
\(496\) 9.26715i 0.416107i
\(497\) 16.6409 + 0.347125i 0.746446 + 0.0155707i
\(498\) 0.888888 + 3.54552i 0.0398320 + 0.158878i
\(499\) −10.6254 + 18.4037i −0.475658 + 0.823864i −0.999611 0.0278832i \(-0.991123\pi\)
0.523953 + 0.851747i \(0.324457\pi\)
\(500\) 0.500000 + 0.866025i 0.0223607 + 0.0387298i
\(501\) 6.02304 + 6.22085i 0.269089 + 0.277927i
\(502\) 19.8408 + 11.4551i 0.885537 + 0.511265i
\(503\) −20.9913 −0.935957 −0.467978 0.883740i \(-0.655018\pi\)
−0.467978 + 0.883740i \(0.655018\pi\)
\(504\) −0.421794 + 7.92604i −0.0187882 + 0.353054i
\(505\) 4.45663 0.198317
\(506\) 0.713343 + 0.411849i 0.0317120 + 0.0183089i
\(507\) 12.7719 + 13.1914i 0.567220 + 0.585849i
\(508\) 2.74982 + 4.76283i 0.122004 + 0.211317i
\(509\) −6.98403 + 12.0967i −0.309562 + 0.536177i −0.978267 0.207351i \(-0.933516\pi\)
0.668705 + 0.743528i \(0.266849\pi\)
\(510\) 0.223041 + 0.889645i 0.00987641 + 0.0393941i
\(511\) 10.3153 + 18.7597i 0.456324 + 0.829878i
\(512\) 1.00000i 0.0441942i
\(513\) 32.4473 7.02912i 1.43258 0.310343i
\(514\) 6.13707 3.54324i 0.270695 0.156286i
\(515\) −7.29356 + 4.21094i −0.321393 + 0.185556i
\(516\) −5.45902 + 19.1316i −0.240320 + 0.842222i
\(517\) 1.90018i 0.0835699i
\(518\) 2.24782 + 4.08792i 0.0987635 + 0.179613i
\(519\) 12.7820 3.20454i 0.561066 0.140664i
\(520\) −0.774462 + 1.34141i −0.0339624 + 0.0588246i
\(521\) 7.21208 + 12.4917i 0.315967 + 0.547271i 0.979643 0.200750i \(-0.0643378\pi\)
−0.663676 + 0.748020i \(0.731004\pi\)
\(522\) 12.4189 + 7.71544i 0.543562 + 0.337696i
\(523\) −25.2604 14.5841i −1.10456 0.637717i −0.167144 0.985932i \(-0.553455\pi\)
−0.937415 + 0.348215i \(0.886788\pi\)
\(524\) 5.99687 0.261974
\(525\) −4.37951 1.34904i −0.191137 0.0588768i
\(526\) 17.8683 0.779096
\(527\) −4.24981 2.45363i −0.185125 0.106882i
\(528\) −0.241187 + 0.233517i −0.0104963 + 0.0101625i
\(529\) −2.46979 4.27779i −0.107382 0.185991i
\(530\) 0.0324905 0.0562751i 0.00141130 0.00244444i
\(531\) 31.8146 17.0223i 1.38064 0.738704i
\(532\) −16.9009 0.352549i −0.732747 0.0152849i
\(533\) 15.3587i 0.665259i
\(534\) −27.2745 7.78253i −1.18028 0.336783i
\(535\) −15.4270 + 8.90681i −0.666969 + 0.385075i
\(536\) 4.18340 2.41529i 0.180696 0.104325i
\(537\) 27.0254 + 7.71144i 1.16623 + 0.332773i
\(538\) 6.92546i 0.298578i
\(539\) −1.20225 + 0.628790i −0.0517847 + 0.0270839i
\(540\) 3.84792 3.49192i 0.165588 0.150268i
\(541\) 12.4518 21.5672i 0.535345 0.927246i −0.463801 0.885939i \(-0.653515\pi\)
0.999147 0.0413062i \(-0.0131519\pi\)
\(542\) −8.45932 14.6520i −0.363359 0.629356i
\(543\) 5.01672 4.85719i 0.215288 0.208442i
\(544\) 0.458589 + 0.264766i 0.0196618 + 0.0113518i
\(545\) 0.147803 0.00633120
\(546\) −1.58215 6.91948i −0.0677100 0.296126i
\(547\) −0.655376 −0.0280219 −0.0140109 0.999902i \(-0.504460\pi\)
−0.0140109 + 0.999902i \(0.504460\pi\)
\(548\) −0.746611 0.431056i −0.0318936 0.0184138i
\(549\) −6.78539 + 10.9219i −0.289594 + 0.466136i
\(550\) −0.0969112 0.167855i −0.00413231 0.00715737i
\(551\) −15.5692 + 26.9666i −0.663269 + 1.14882i
\(552\) −7.13983 + 1.79001i −0.303891 + 0.0761879i
\(553\) 15.3392 + 9.28792i 0.652289 + 0.394963i
\(554\) 21.3009i 0.904990i
\(555\) 0.838003 2.93685i 0.0355712 0.124662i
\(556\) 14.0160 8.09216i 0.594412 0.343184i
\(557\) 15.4016 8.89212i 0.652587 0.376771i −0.136860 0.990590i \(-0.543701\pi\)
0.789446 + 0.613819i \(0.210368\pi\)
\(558\) −0.898091 + 27.7869i −0.0380192 + 1.17631i
\(559\) 17.7917i 0.752509i
\(560\) −2.31838 + 1.27480i −0.0979694 + 0.0538702i
\(561\) −0.0432303 0.172433i −0.00182519 0.00728013i
\(562\) −9.79636 + 16.9678i −0.413235 + 0.715743i
\(563\) 10.1362 + 17.5563i 0.427188 + 0.739912i 0.996622 0.0821256i \(-0.0261709\pi\)
−0.569434 + 0.822037i \(0.692838\pi\)
\(564\) −11.8115 12.1995i −0.497355 0.513690i
\(565\) −2.98581 1.72386i −0.125614 0.0725232i
\(566\) −15.0978 −0.634610
\(567\) −2.03284 + 23.7248i −0.0853714 + 0.996349i
\(568\) −6.29103 −0.263966
\(569\) 38.9233 + 22.4724i 1.63175 + 0.942092i 0.983553 + 0.180619i \(0.0578101\pi\)
0.648197 + 0.761473i \(0.275523\pi\)
\(570\) 7.69787 + 7.95069i 0.322428 + 0.333018i
\(571\) 5.59451 + 9.68998i 0.234123 + 0.405513i 0.959017 0.283347i \(-0.0914448\pi\)
−0.724894 + 0.688860i \(0.758111\pi\)
\(572\) 0.150108 0.259995i 0.00627633 0.0108709i
\(573\) −10.6292 42.3967i −0.444040 1.77115i
\(574\) −13.5883 + 22.4413i −0.567163 + 0.936681i
\(575\) 4.24976i 0.177227i
\(576\) 0.0969112 2.99843i 0.00403797 0.124935i
\(577\) −8.42967 + 4.86687i −0.350932 + 0.202611i −0.665096 0.746758i \(-0.731609\pi\)
0.314164 + 0.949369i \(0.398276\pi\)
\(578\) 14.4796 8.35980i 0.602272 0.347722i
\(579\) 11.9938 42.0334i 0.498447 1.74685i
\(580\) 4.87349i 0.202361i
\(581\) 0.116445 5.58226i 0.00483094 0.231591i
\(582\) −13.8514 + 3.47266i −0.574160 + 0.143946i
\(583\) −0.00629738 + 0.0109074i −0.000260811 + 0.000451738i
\(584\) −4.04586 7.00763i −0.167419 0.289978i
\(585\) −2.45217 + 3.94707i −0.101385 + 0.163191i
\(586\) 6.93283 + 4.00267i 0.286393 + 0.165349i
\(587\) −32.0185 −1.32155 −0.660773 0.750585i \(-0.729772\pi\)
−0.660773 + 0.750585i \(0.729772\pi\)
\(588\) 3.81009 11.5101i 0.157125 0.474670i
\(589\) −59.2109 −2.43974
\(590\) 10.4160 + 6.01371i 0.428822 + 0.247580i
\(591\) 18.3376 17.7545i 0.754307 0.730321i
\(592\) −0.881634 1.52704i −0.0362349 0.0627608i
\(593\) −16.2006 + 28.0603i −0.665280 + 1.15230i 0.313930 + 0.949446i \(0.398354\pi\)
−0.979209 + 0.202852i \(0.934979\pi\)
\(594\) −0.745813 + 0.676813i −0.0306011 + 0.0277700i
\(595\) 0.0292184 1.40071i 0.00119784 0.0574234i
\(596\) 12.7600i 0.522671i
\(597\) 43.0788 + 12.2921i 1.76310 + 0.503083i
\(598\) 5.70065 3.29127i 0.233117 0.134590i
\(599\) 9.13107 5.27183i 0.373086 0.215401i −0.301720 0.953397i \(-0.597561\pi\)
0.674806 + 0.737996i \(0.264227\pi\)
\(600\) 1.66557 + 0.475255i 0.0679967 + 0.0194022i
\(601\) 24.6793i 1.00669i 0.864086 + 0.503344i \(0.167897\pi\)
−0.864086 + 0.503344i \(0.832103\pi\)
\(602\) 15.7408 25.9963i 0.641547 1.05953i
\(603\) 12.7777 6.83667i 0.520349 0.278411i
\(604\) −8.75012 + 15.1557i −0.356038 + 0.616675i
\(605\) −5.48122 9.49375i −0.222843 0.385976i
\(606\) 5.54569 5.36934i 0.225278 0.218115i
\(607\) −11.2456 6.49268i −0.456447 0.263530i 0.254102 0.967177i \(-0.418220\pi\)
−0.710549 + 0.703648i \(0.751553\pi\)
\(608\) 6.38933 0.259122
\(609\) −15.1967 16.3654i −0.615803 0.663161i
\(610\) −4.28602 −0.173536
\(611\) 13.1508 + 7.59261i 0.532024 + 0.307164i
\(612\) 1.34939 + 0.838327i 0.0545458 + 0.0338874i
\(613\) 13.3643 + 23.1477i 0.539780 + 0.934926i 0.998915 + 0.0465601i \(0.0148259\pi\)
−0.459136 + 0.888366i \(0.651841\pi\)
\(614\) 2.16832 3.75563i 0.0875061 0.151565i
\(615\) 16.6590 4.17654i 0.671755 0.168414i
\(616\) 0.449354 0.247085i 0.0181050 0.00995535i
\(617\) 13.2804i 0.534650i −0.963606 0.267325i \(-0.913860\pi\)
0.963606 0.267325i \(-0.0861397\pi\)
\(618\) −4.00254 + 14.0272i −0.161006 + 0.564259i
\(619\) 8.56249 4.94355i 0.344155 0.198698i −0.317953 0.948107i \(-0.602995\pi\)
0.662108 + 0.749408i \(0.269662\pi\)
\(620\) −8.02559 + 4.63357i −0.322315 + 0.186089i
\(621\) −21.5818 + 4.67530i −0.866047 + 0.187613i
\(622\) 22.8384i 0.915736i
\(623\) 37.0610 + 22.4405i 1.48482 + 0.899060i
\(624\) 0.652411 + 2.60228i 0.0261174 + 0.104174i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 12.6521 + 21.9141i 0.505680 + 0.875864i
\(627\) −1.49202 1.54102i −0.0595855 0.0615425i
\(628\) −2.46479 1.42305i −0.0983557 0.0567857i
\(629\) 0.933708 0.0372294
\(630\) −7.07505 + 3.59774i −0.281877 + 0.143337i
\(631\) −26.4695 −1.05373 −0.526867 0.849948i \(-0.676633\pi\)
−0.526867 + 0.849948i \(0.676633\pi\)
\(632\) −5.86962 3.38883i −0.233481 0.134800i
\(633\) −27.5563 28.4613i −1.09526 1.13123i
\(634\) −7.54489 13.0681i −0.299646 0.519002i
\(635\) −2.74982 + 4.76283i −0.109123 + 0.189007i
\(636\) −0.0273702 0.109172i −0.00108530 0.00432894i
\(637\) −0.452145 + 10.8330i −0.0179147 + 0.429220i
\(638\) 0.944591i 0.0373967i
\(639\) −18.8633 0.609672i −0.746219 0.0241182i
\(640\) 0.866025 0.500000i 0.0342327 0.0197642i
\(641\) −20.3632 + 11.7567i −0.804298 + 0.464362i −0.844972 0.534811i \(-0.820383\pi\)
0.0406739 + 0.999172i \(0.487050\pi\)
\(642\) −8.46602 + 29.6699i −0.334127 + 1.17098i
\(643\) 20.1307i 0.793876i −0.917846 0.396938i \(-0.870073\pi\)
0.917846 0.396938i \(-0.129927\pi\)
\(644\) 11.2414 + 0.234492i 0.442971 + 0.00924027i
\(645\) −19.2980 + 4.83815i −0.759857 + 0.190502i
\(646\) −1.69168 + 2.93008i −0.0665582 + 0.115282i
\(647\) 5.16088 + 8.93890i 0.202895 + 0.351424i 0.949460 0.313888i \(-0.101632\pi\)
−0.746565 + 0.665312i \(0.768298\pi\)
\(648\) 0.581164 8.98122i 0.0228303 0.352816i
\(649\) −2.01886 1.16559i −0.0792473 0.0457535i
\(650\) −1.54892 −0.0607538
\(651\) 12.5017 40.5856i 0.489981 1.59067i
\(652\) −12.3586 −0.484001
\(653\) −2.88758 1.66715i −0.113000 0.0652404i 0.442435 0.896801i \(-0.354115\pi\)
−0.555435 + 0.831560i \(0.687448\pi\)
\(654\) 0.183922 0.178074i 0.00719192 0.00696323i
\(655\) 2.99843 + 5.19344i 0.117159 + 0.202925i
\(656\) 4.95787 8.58728i 0.193572 0.335277i
\(657\) −11.4521 21.4040i −0.446790 0.835050i
\(658\) 12.4978 + 22.7288i 0.487216 + 0.886059i
\(659\) 13.1387i 0.511809i 0.966702 + 0.255905i \(0.0823733\pi\)
−0.966702 + 0.255905i \(0.917627\pi\)
\(660\) −0.322825 0.0921151i −0.0125660 0.00358558i
\(661\) −0.244148 + 0.140959i −0.00949625 + 0.00548266i −0.504741 0.863271i \(-0.668412\pi\)
0.495244 + 0.868754i \(0.335079\pi\)
\(662\) −13.0438 + 7.53086i −0.506963 + 0.292695i
\(663\) −1.36611 0.389807i −0.0530554 0.0151389i
\(664\) 2.11036i 0.0818977i
\(665\) −8.14514 14.8129i −0.315855 0.574419i
\(666\) −2.49554 4.66415i −0.0967000 0.180732i
\(667\) 10.3556 17.9364i 0.400969 0.694499i
\(668\) 2.49960 + 4.32943i 0.0967124 + 0.167511i
\(669\) 0.00779327 0.00754545i 0.000301305 0.000291724i
\(670\) 4.18340 + 2.41529i 0.161619 + 0.0933108i
\(671\) 0.830727 0.0320699
\(672\) −1.34904 + 4.37951i −0.0520402 + 0.168943i
\(673\) −36.0090 −1.38805 −0.694023 0.719953i \(-0.744163\pi\)
−0.694023 + 0.719953i \(0.744163\pi\)
\(674\) 12.9567 + 7.48055i 0.499073 + 0.288140i
\(675\) 4.94805 + 1.58643i 0.190451 + 0.0610619i
\(676\) 5.30042 + 9.18059i 0.203862 + 0.353100i
\(677\) −2.00745 + 3.47701i −0.0771526 + 0.133632i −0.902020 0.431694i \(-0.857916\pi\)
0.824868 + 0.565326i \(0.191250\pi\)
\(678\) −5.79235 + 1.45219i −0.222454 + 0.0557709i
\(679\) 21.8085 + 0.454920i 0.836933 + 0.0174582i
\(680\) 0.529533i 0.0203067i
\(681\) −8.94785 + 31.3585i −0.342882 + 1.20166i
\(682\) 1.55554 0.898091i 0.0595646 0.0343897i
\(683\) −31.6027 + 18.2458i −1.20924 + 0.698156i −0.962594 0.270949i \(-0.912663\pi\)
−0.246649 + 0.969105i \(0.579329\pi\)
\(684\) 19.1580 + 0.619198i 0.732524 + 0.0236756i
\(685\) 0.862112i 0.0329396i
\(686\) −10.2449 + 15.4286i −0.391153 + 0.589067i
\(687\) 3.28394 + 13.0987i 0.125290 + 0.499746i
\(688\) −5.74325 + 9.94760i −0.218959 + 0.379249i
\(689\) 0.0503252 + 0.0871659i 0.00191724 + 0.00332075i
\(690\) −5.12011 5.28827i −0.194919 0.201321i
\(691\) −7.57320 4.37239i −0.288098 0.166334i 0.348986 0.937128i \(-0.386526\pi\)
−0.637084 + 0.770795i \(0.719860\pi\)
\(692\) 7.60806 0.289215
\(693\) 1.37130 0.697322i 0.0520915 0.0264891i
\(694\) 4.04662 0.153608
\(695\) 14.0160 + 8.09216i 0.531659 + 0.306953i
\(696\) 5.87158 + 6.06442i 0.222562 + 0.229871i
\(697\) 2.62535 + 4.54724i 0.0994423 + 0.172239i
\(698\) 6.18475 10.7123i 0.234096 0.405467i
\(699\) −5.47327 21.8313i −0.207018 0.825734i
\(700\) −2.26320 1.37037i −0.0855409 0.0517952i
\(701\) 21.5875i 0.815349i 0.913127 + 0.407674i \(0.133660\pi\)
−0.913127 + 0.407674i \(0.866340\pi\)
\(702\) 1.70402 + 7.86598i 0.0643142 + 0.296882i
\(703\) 9.75673 5.63305i 0.367982 0.212455i
\(704\) −0.167855 + 0.0969112i −0.00632628 + 0.00365248i
\(705\) 4.65927 16.3288i 0.175478 0.614979i
\(706\) 3.66715i 0.138015i
\(707\) −10.3321 + 5.68132i −0.388580 + 0.213668i
\(708\) 20.2067 5.06598i 0.759415 0.190391i
\(709\) 2.50743 4.34300i 0.0941685 0.163105i −0.815093 0.579330i \(-0.803314\pi\)
0.909261 + 0.416226i \(0.136647\pi\)
\(710\) −3.14552 5.44820i −0.118049 0.204467i
\(711\) −17.2713 10.7300i −0.647723 0.402407i
\(712\) −14.1816 8.18773i −0.531477 0.306848i
\(713\) 39.3831 1.47491
\(714\) −1.65121 1.77820i −0.0617951 0.0665475i
\(715\) 0.300216 0.0112274
\(716\) 14.0520 + 8.11295i 0.525149 + 0.303195i
\(717\) 21.3670 20.6876i 0.797966 0.772592i
\(718\) 3.66134 + 6.34163i 0.136640 + 0.236668i
\(719\) −17.1509 + 29.7062i −0.639619 + 1.10785i 0.345897 + 0.938272i \(0.387575\pi\)
−0.985516 + 0.169580i \(0.945759\pi\)
\(720\) 2.64518 1.41529i 0.0985799 0.0527447i
\(721\) 11.5411 19.0604i 0.429813 0.709846i
\(722\) 21.8235i 0.812188i
\(723\) 13.6684 + 3.90013i 0.508331 + 0.145048i
\(724\) 3.49141 2.01577i 0.129757 0.0749154i
\(725\) −4.22056 + 2.43674i −0.156748 + 0.0904984i
\(726\) −18.2587 5.20996i −0.677645 0.193360i
\(727\) 17.4763i 0.648159i −0.946030 0.324080i \(-0.894945\pi\)
0.946030 0.324080i \(-0.105055\pi\)
\(728\) 0.0854660 4.09717i 0.00316758 0.151851i
\(729\) 2.61296 26.8733i 0.0967764 0.995306i
\(730\) 4.04586 7.00763i 0.149744 0.259364i
\(731\) −3.04124 5.26758i −0.112484 0.194829i
\(732\) −5.33340 + 5.16380i −0.197128 + 0.190860i
\(733\) 45.0320 + 25.9992i 1.66330 + 0.960304i 0.971125 + 0.238570i \(0.0766786\pi\)
0.692170 + 0.721734i \(0.256655\pi\)
\(734\) −4.76624 −0.175925
\(735\) 11.8731 2.45543i 0.437946 0.0905700i
\(736\) −4.24976 −0.156648
\(737\) −0.810838 0.468137i −0.0298676 0.0172441i
\(738\) 15.6980 25.2679i 0.577853 0.930125i
\(739\) 12.1033 + 20.9635i 0.445226 + 0.771155i 0.998068 0.0621318i \(-0.0197899\pi\)
−0.552842 + 0.833286i \(0.686457\pi\)
\(740\) 0.881634 1.52704i 0.0324095 0.0561349i
\(741\) −16.6268 + 4.16847i −0.610801 + 0.153133i
\(742\) −0.00358550 + 0.171886i −0.000131628 + 0.00631013i
\(743\) 48.1794i 1.76753i −0.467932 0.883765i \(-0.655001\pi\)
0.467932 0.883765i \(-0.344999\pi\)
\(744\) −4.40426 + 15.4351i −0.161468 + 0.565879i
\(745\) 11.0505 6.38001i 0.404859 0.233745i
\(746\) 14.9790 8.64813i 0.548420 0.316631i
\(747\) −0.204517 + 6.32776i −0.00748289 + 0.231521i
\(748\) 0.102635i 0.00375272i
\(749\) 24.4113 40.3158i 0.891970 1.47311i
\(750\) 0.421203 + 1.68006i 0.0153802 + 0.0613470i
\(751\) −2.58147 + 4.47123i −0.0941991 + 0.163158i −0.909274 0.416198i \(-0.863362\pi\)
0.815075 + 0.579355i \(0.196696\pi\)
\(752\) −4.90186 8.49028i −0.178753 0.309609i
\(753\) 27.6022 + 28.5087i 1.00588 + 1.03891i
\(754\) −6.53733 3.77433i −0.238076 0.137453i
\(755\) −17.5002 −0.636899
\(756\) −4.46942 + 13.0009i −0.162551 + 0.472839i
\(757\) −16.0842 −0.584591 −0.292295 0.956328i \(-0.594419\pi\)
−0.292295 + 0.956328i \(0.594419\pi\)
\(758\) −7.59197 4.38323i −0.275753 0.159206i
\(759\) 0.992392 + 1.02498i 0.0360215 + 0.0372046i
\(760\) 3.19467 + 5.53332i 0.115883 + 0.200715i
\(761\) −5.07895 + 8.79701i −0.184112 + 0.318891i −0.943277 0.332007i \(-0.892274\pi\)
0.759165 + 0.650898i \(0.225608\pi\)
\(762\) 2.31647 + 9.23972i 0.0839168 + 0.334720i
\(763\) −0.342664 + 0.188420i −0.0124053 + 0.00682127i
\(764\) 25.2353i 0.912980i
\(765\) −0.0513177 + 1.58777i −0.00185539 + 0.0574059i
\(766\) 24.6604 14.2377i 0.891015 0.514428i
\(767\) −16.1337 + 9.31477i −0.582552 + 0.336337i
\(768\) 0.475255 1.66557i 0.0171493 0.0601012i
\(769\) 6.68859i 0.241197i 0.992701 + 0.120598i \(0.0384813\pi\)
−0.992701 + 0.120598i \(0.961519\pi\)
\(770\) 0.438659 + 0.265609i 0.0158082 + 0.00957189i
\(771\) 11.9057 2.98485i 0.428773 0.107497i
\(772\) 12.6183 21.8556i 0.454143 0.786599i
\(773\) −13.2852 23.0107i −0.477836 0.827636i 0.521841 0.853043i \(-0.325245\pi\)
−0.999677 + 0.0254064i \(0.991912\pi\)
\(774\) −18.1848 + 29.2707i −0.653639 + 1.05211i
\(775\) −8.02559 4.63357i −0.288288 0.166443i
\(776\) −8.24463 −0.295965
\(777\) 1.80110 + 7.87702i 0.0646141 + 0.282587i
\(778\) −21.0696 −0.755382
\(779\) 54.8669 + 31.6774i 1.96581 + 1.13496i
\(780\) −1.92743 + 1.86614i −0.0690132 + 0.0668187i
\(781\) 0.609672 + 1.05598i 0.0218158 + 0.0377860i
\(782\) 1.12519 1.94889i 0.0402368 0.0696922i
\(783\) 17.0178 + 18.7528i 0.608168 + 0.670170i
\(784\) 3.74976 5.91095i 0.133920 0.211105i
\(785\) 2.84609i 0.101581i
\(786\) 9.98822 + 2.85004i 0.356268 + 0.101658i
\(787\) 25.6272 14.7959i 0.913510 0.527416i 0.0319515 0.999489i \(-0.489828\pi\)
0.881559 + 0.472074i \(0.156494\pi\)
\(788\) 12.7621 7.36822i 0.454632 0.262482i
\(789\) 29.7610 + 8.49202i 1.05952 + 0.302324i
\(790\) 6.77766i 0.241138i
\(791\) 9.11981 + 0.190237i 0.324263 + 0.00676405i
\(792\) −0.512694 + 0.274315i −0.0182178 + 0.00974735i
\(793\) 3.31936 5.74930i 0.117874 0.204164i
\(794\) 3.29905 + 5.71412i 0.117079 + 0.202786i
\(795\) 0.0808603 0.0782891i 0.00286782 0.00277663i
\(796\) 22.3991 + 12.9321i 0.793915 + 0.458367i
\(797\) −34.6019 −1.22566 −0.612830 0.790215i \(-0.709969\pi\)
−0.612830 + 0.790215i \(0.709969\pi\)
\(798\) −27.9821 8.61944i −0.990557 0.305125i
\(799\) 5.19139 0.183658
\(800\) 0.866025 + 0.500000i 0.0306186 + 0.0176777i
\(801\) −41.7290 25.9247i −1.47442 0.916005i
\(802\) −8.06552 13.9699i −0.284803 0.493294i
\(803\) −0.784178 + 1.35824i −0.0276730 + 0.0479311i
\(804\) 8.11564 2.03465i 0.286217 0.0717567i
\(805\) 5.41760 + 9.85254i 0.190945 + 0.347257i
\(806\) 14.3541i 0.505602i
\(807\) −3.29136 + 11.5349i −0.115861 + 0.406046i
\(808\) 3.85955 2.22831i 0.135779 0.0783918i
\(809\) −14.6105 + 8.43536i −0.513677 + 0.296571i −0.734344 0.678778i \(-0.762510\pi\)
0.220667 + 0.975349i \(0.429177\pi\)
\(810\) 8.06854 3.98731i 0.283500 0.140100i
\(811\) 11.1600i 0.391880i 0.980616 + 0.195940i \(0.0627758\pi\)
−0.980616 + 0.195940i \(0.937224\pi\)
\(812\) −6.21274 11.2986i −0.218024 0.396503i
\(813\) −7.12619 28.4243i −0.249926 0.996883i
\(814\) −0.170880 + 0.295974i −0.00598936 + 0.0103739i
\(815\) −6.17931 10.7029i −0.216452 0.374906i
\(816\) 0.637981 + 0.658934i 0.0223338 + 0.0230673i
\(817\) −63.5585 36.6955i −2.22363 1.28381i
\(818\) −26.4033 −0.923169
\(819\) 0.653326 12.2768i 0.0228291 0.428987i
\(820\) 9.91573 0.346272
\(821\) −34.0899 19.6818i −1.18975 0.686901i −0.231498 0.972835i \(-0.574363\pi\)
−0.958249 + 0.285934i \(0.907696\pi\)
\(822\) −1.03867 1.07279i −0.0362279 0.0374177i
\(823\) −20.3585 35.2620i −0.709654 1.22916i −0.964986 0.262303i \(-0.915518\pi\)
0.255332 0.966854i \(-0.417815\pi\)
\(824\) −4.21094 + 7.29356i −0.146695 + 0.254083i
\(825\) −0.0816386 0.325633i −0.00284229 0.0113371i
\(826\) −31.8146 0.663645i −1.10697 0.0230912i
\(827\) 24.7892i 0.862006i −0.902350 0.431003i \(-0.858160\pi\)
0.902350 0.431003i \(-0.141840\pi\)
\(828\) −12.7426 0.411849i −0.442837 0.0143127i
\(829\) −0.897813 + 0.518352i −0.0311823 + 0.0180031i −0.515510 0.856883i \(-0.672398\pi\)
0.484328 + 0.874887i \(0.339064\pi\)
\(830\) −1.82762 + 1.05518i −0.0634377 + 0.0366258i
\(831\) −10.1234 + 35.4782i −0.351176 + 1.23073i
\(832\) 1.54892i 0.0536992i
\(833\) 1.71789 + 3.28462i 0.0595212 + 0.113805i
\(834\) 27.1906 6.81689i 0.941533 0.236050i
\(835\) −2.49960 + 4.32943i −0.0865022 + 0.149826i
\(836\) −0.619198 1.07248i −0.0214154 0.0370926i
\(837\) −14.7017 + 45.8543i −0.508166 + 1.58496i
\(838\) −17.1743 9.91561i −0.593278 0.342529i
\(839\) −19.4880 −0.672801 −0.336401 0.941719i \(-0.609210\pi\)
−0.336401 + 0.941719i \(0.609210\pi\)
\(840\) −4.46728 + 1.02145i −0.154136 + 0.0352435i
\(841\) 5.24911 0.181004
\(842\) 5.43872 + 3.14004i 0.187431 + 0.108213i
\(843\) −24.3806 + 23.6053i −0.839712 + 0.813011i
\(844\) −11.4360 19.8078i −0.393644 0.681812i
\(845\) −5.30042 + 9.18059i −0.182340 + 0.315822i
\(846\) −13.8751 25.9326i −0.477036 0.891581i
\(847\) 24.8102 + 15.0226i 0.852488 + 0.516183i
\(848\) 0.0649809i 0.00223145i
\(849\) −25.1466 7.17533i −0.863028 0.246257i
\(850\) −0.458589 + 0.264766i −0.0157295 + 0.00908141i
\(851\) −6.48953 + 3.74673i −0.222458 + 0.128436i
\(852\) −10.4782 2.98985i −0.358976 0.102430i
\(853\) 3.93413i 0.134702i 0.997729 + 0.0673510i \(0.0214547\pi\)
−0.997729 + 0.0673510i \(0.978545\pi\)
\(854\) 9.93662 5.46383i 0.340024 0.186969i
\(855\) 9.04275 + 16.9009i 0.309256 + 0.577999i
\(856\) −8.90681 + 15.4270i −0.304429 + 0.527286i
\(857\) −4.49804 7.79083i −0.153650 0.266130i 0.778917 0.627128i \(-0.215770\pi\)
−0.932567 + 0.360998i \(0.882436\pi\)
\(858\) 0.373580 0.361700i 0.0127538 0.0123482i
\(859\) 35.2001 + 20.3228i 1.20101 + 0.693404i 0.960780 0.277312i \(-0.0894435\pi\)
0.240231 + 0.970716i \(0.422777\pi\)
\(860\) −11.4865 −0.391687
\(861\) −33.2976 + 30.9197i −1.13478 + 1.05374i
\(862\) 4.55329 0.155086
\(863\) −28.7932 16.6238i −0.980133 0.565880i −0.0778229 0.996967i \(-0.524797\pi\)
−0.902310 + 0.431087i \(0.858130\pi\)
\(864\) 1.58643 4.94805i 0.0539716 0.168336i
\(865\) 3.80403 + 6.58878i 0.129341 + 0.224025i
\(866\) −1.31401 + 2.27592i −0.0446517 + 0.0773391i
\(867\) 28.0899 7.04235i 0.953981 0.239171i
\(868\) 12.6995 20.9734i 0.431047 0.711884i
\(869\) 1.31366i 0.0445629i
\(870\) −2.31615 + 8.11715i −0.0785249 + 0.275197i
\(871\) −6.47977 + 3.74110i −0.219559 + 0.126762i
\(872\) 0.128001 0.0739017i 0.00433468 0.00250263i
\(873\) −24.7210 0.798997i −0.836678 0.0270419i
\(874\) 27.1531i 0.918467i
\(875\) 0.0551777 2.64518i 0.00186535 0.0894233i
\(876\) −3.40825 13.5945i −0.115154 0.459317i
\(877\) −14.1314 + 24.4763i −0.477184 + 0.826506i −0.999658 0.0261486i \(-0.991676\pi\)
0.522474 + 0.852655i \(0.325009\pi\)
\(878\) −2.91836 5.05475i −0.0984899 0.170590i
\(879\) 9.64484 + 9.96160i 0.325312 + 0.335997i
\(880\) −0.167855 0.0969112i −0.00565840 0.00326688i
\(881\) 34.2140 1.15270 0.576350 0.817203i \(-0.304477\pi\)
0.576350 + 0.817203i \(0.304477\pi\)
\(882\) 11.8162 17.3602i 0.397873 0.584548i
\(883\) 4.09672 0.137866 0.0689328 0.997621i \(-0.478041\pi\)
0.0689328 + 0.997621i \(0.478041\pi\)
\(884\) −0.710319 0.410103i −0.0238906 0.0137932i
\(885\) 14.4906 + 14.9665i 0.487097 + 0.503095i
\(886\) −13.1730 22.8164i −0.442557 0.766531i
\(887\) −0.926997 + 1.60561i −0.0311255 + 0.0539110i −0.881169 0.472802i \(-0.843242\pi\)
0.850043 + 0.526713i \(0.176576\pi\)
\(888\) −0.742694 2.96239i −0.0249232 0.0994113i
\(889\) 0.303458 14.5475i 0.0101777 0.487909i
\(890\) 16.3755i 0.548907i
\(891\) −1.56386 + 0.772829i −0.0523914 + 0.0258908i
\(892\) 0.00542376 0.00313141i 0.000181601 0.000104847i
\(893\) 54.2472 31.3196i 1.81531 1.04807i
\(894\) 6.06427 21.2527i 0.202819 0.710798i
\(895\) 16.2259i 0.542372i
\(896\) −1.37037 + 2.26320i −0.0457810 + 0.0756082i
\(897\) 11.0590 2.77259i 0.369251 0.0925740i
\(898\) 2.88319 4.99383i 0.0962134 0.166646i
\(899\) −22.5817 39.1126i −0.753141 1.30448i
\(900\) 2.54826 + 1.58314i 0.0849422 + 0.0527715i
\(901\) 0.0297995 + 0.0172048i 0.000992766 + 0.000573174i
\(902\) −1.92189 −0.0639920
\(903\) 38.5723 35.8178i 1.28361 1.19194i
\(904\) −3.44771 −0.114669
\(905\) 3.49141 + 2.01577i 0.116058 + 0.0670063i
\(906\) −21.7768 + 21.0843i −0.723485 + 0.700479i
\(907\) −16.8711 29.2217i −0.560197 0.970289i −0.997479 0.0709647i \(-0.977392\pi\)
0.437282 0.899324i \(-0.355941\pi\)
\(908\) −9.41373 + 16.3051i −0.312406 + 0.541102i
\(909\) 11.7886 6.30742i 0.391002 0.209204i
\(910\) 3.59099 1.97457i 0.119040 0.0654564i
\(911\) 6.90180i 0.228667i 0.993442 + 0.114333i \(0.0364732\pi\)
−0.993442 + 0.114333i \(0.963527\pi\)
\(912\) 10.6419 + 3.03656i 0.352388 + 0.100551i
\(913\) 0.354234 0.204517i 0.0117234 0.00676853i
\(914\) 0.624848 0.360756i 0.0206682 0.0119328i
\(915\) −7.13868 2.03696i −0.235998 0.0673397i
\(916\) 7.79658i 0.257606i
\(917\) −13.5721 8.21795i −0.448191 0.271381i
\(918\) 1.84909 + 2.03760i 0.0610290 + 0.0672508i
\(919\) 17.5128 30.3330i 0.577693 1.00059i −0.418050 0.908424i \(-0.637286\pi\)
0.995743 0.0921698i \(-0.0293803\pi\)
\(920\) −2.12488 3.68040i −0.0700552 0.121339i
\(921\) 5.39637 5.22477i 0.177816 0.172162i
\(922\) 29.7646 + 17.1846i 0.980243 + 0.565944i
\(923\) 9.74433 0.320738
\(924\) 0.865860 0.197981i 0.0284847 0.00651309i
\(925\) 1.76327 0.0579759
\(926\) 35.8374 + 20.6908i 1.17769 + 0.679940i
\(927\) −13.3330 + 21.4612i −0.437915 + 0.704877i
\(928\) 2.43674 + 4.22056i 0.0799900 + 0.138547i
\(929\) −10.5447 + 18.2639i −0.345960 + 0.599220i −0.985528 0.169515i \(-0.945780\pi\)
0.639568 + 0.768734i \(0.279113\pi\)
\(930\) −15.5693 + 3.90335i −0.510538 + 0.127996i
\(931\) 37.7670 + 23.9584i 1.23776 + 0.785206i
\(932\) 12.9944i 0.425645i
\(933\) −10.8541 + 38.0390i −0.355346 + 1.24534i
\(934\) 15.5598 8.98343i 0.509131 0.293947i
\(935\) 0.0888848 0.0513177i 0.00290684 0.00167827i
\(936\) −0.150108 + 4.64434i −0.00490643 + 0.151805i
\(937\) 44.5007i 1.45378i 0.686756 + 0.726888i \(0.259034\pi\)
−0.686756 + 0.726888i \(0.740966\pi\)
\(938\) −12.7777 0.266540i −0.417208 0.00870285i
\(939\) 10.6582 + 42.5125i 0.347818 + 1.38734i
\(940\) 4.90186 8.49028i 0.159881 0.276922i
\(941\) −21.8197 37.7929i −0.711303 1.23201i −0.964368 0.264564i \(-0.914772\pi\)
0.253065 0.967449i \(-0.418561\pi\)
\(942\) −3.42897 3.54159i −0.111722 0.115391i
\(943\) −36.4938 21.0697i −1.18840 0.686125i
\(944\) 12.0274 0.391459
\(945\) −13.4938 + 2.62983i −0.438955 + 0.0855485i
\(946\) 2.22634 0.0723846
\(947\) −11.1646 6.44589i −0.362801 0.209463i 0.307508 0.951546i \(-0.400505\pi\)
−0.670309 + 0.742082i \(0.733838\pi\)
\(948\) −8.16573 8.43391i −0.265210 0.273921i
\(949\) 6.26672 + 10.8543i 0.203426 + 0.352345i
\(950\) −3.19467 + 5.53332i −0.103649 + 0.179525i
\(951\) −6.35586 25.3517i −0.206103 0.822084i
\(952\) −0.675050 1.22766i −0.0218785 0.0397886i
\(953\) 47.2228i 1.52970i 0.644211 + 0.764848i \(0.277186\pi\)
−0.644211 + 0.764848i \(0.722814\pi\)
\(954\) 0.00629738 0.194841i 0.000203885 0.00630821i
\(955\) 21.8544 12.6176i 0.707191 0.408297i
\(956\) 14.8705 8.58548i 0.480946 0.277674i
\(957\) 0.448922 1.57329i 0.0145116 0.0508571i
\(958\) 9.01118i 0.291138i
\(959\) 1.09902 + 1.99870i 0.0354893 + 0.0645414i
\(960\) 1.68006 0.421203i 0.0542236 0.0135943i
\(961\) 27.4400 47.5275i 0.885162 1.53315i
\(962\) 1.36558 + 2.36526i 0.0440282 + 0.0762590i
\(963\) −28.2015 + 45.3938i −0.908782 + 1.46280i
\(964\) 7.10695 + 4.10320i 0.228899 + 0.132155i
\(965\) 25.2366 0.812396
\(966\) 18.6118 + 5.73308i 0.598826 + 0.184459i
\(967\) −7.93428 −0.255149 −0.127575 0.991829i \(-0.540719\pi\)
−0.127575 + 0.991829i \(0.540719\pi\)
\(968\) −9.49375 5.48122i −0.305141 0.176173i
\(969\) −4.21015 + 4.07627i −0.135249 + 0.130949i
\(970\) −4.12231 7.14006i −0.132359 0.229253i
\(971\) 16.7632 29.0348i 0.537958 0.931770i −0.461056 0.887371i \(-0.652529\pi\)
0.999014 0.0443991i \(-0.0141373\pi\)
\(972\) 5.23634 14.6827i 0.167956 0.470947i
\(973\) −42.8104 0.893014i −1.37244 0.0286287i
\(974\) 22.7295i 0.728302i
\(975\) −2.57984 0.736134i −0.0826211 0.0235752i
\(976\) −3.71180 + 2.14301i −0.118812 + 0.0685961i
\(977\) 11.4767 6.62608i 0.367172 0.211987i −0.305050 0.952336i \(-0.598673\pi\)
0.672222 + 0.740349i \(0.265340\pi\)
\(978\) −20.5842 5.87350i −0.658210 0.187814i
\(979\) 3.17393i 0.101439i
\(980\) 6.99391 + 0.291909i 0.223412 + 0.00932471i
\(981\) 0.390966 0.209185i 0.0124826 0.00667875i
\(982\) 16.0827 27.8560i 0.513219 0.888921i
\(983\) 21.9739 + 38.0599i 0.700858 + 1.21392i 0.968165 + 0.250311i \(0.0805329\pi\)
−0.267307 + 0.963611i \(0.586134\pi\)
\(984\) 12.3388 11.9465i 0.393348 0.380840i
\(985\) 12.7621 + 7.36822i 0.406635 + 0.234771i
\(986\) −2.58067 −0.0821853
\(987\) 10.0141 + 43.7960i 0.318751 + 1.39404i
\(988\) −9.89658 −0.314852
\(989\) 42.2749 + 24.4074i 1.34426 + 0.776111i
\(990\) −0.493911 0.306849i −0.0156975 0.00975230i
\(991\) −5.43257 9.40948i −0.172571 0.298902i 0.766747 0.641950i \(-0.221874\pi\)
−0.939318 + 0.343047i \(0.888541\pi\)
\(992\) −4.63357 + 8.02559i −0.147116 + 0.254813i
\(993\) −25.3045 + 6.34404i −0.803015 + 0.201322i
\(994\) 14.2379 + 8.62106i 0.451598 + 0.273444i
\(995\) 25.8642i 0.819952i
\(996\) −1.00296 + 3.51495i −0.0317799 + 0.111375i
\(997\) −34.8191 + 20.1028i −1.10273 + 0.636662i −0.936937 0.349499i \(-0.886352\pi\)
−0.165794 + 0.986160i \(0.553019\pi\)
\(998\) −18.4037 + 10.6254i −0.582560 + 0.336341i
\(999\) −1.93983 8.95450i −0.0613735 0.283308i
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 210.2.r.b.131.6 yes 12
3.2 odd 2 210.2.r.a.131.2 yes 12
5.2 odd 4 1050.2.u.e.299.5 12
5.3 odd 4 1050.2.u.h.299.2 12
5.4 even 2 1050.2.s.f.551.1 12
7.2 even 3 1470.2.b.a.881.1 12
7.3 odd 6 210.2.r.a.101.2 12
7.5 odd 6 1470.2.b.b.881.6 12
15.2 even 4 1050.2.u.g.299.2 12
15.8 even 4 1050.2.u.f.299.5 12
15.14 odd 2 1050.2.s.g.551.5 12
21.2 odd 6 1470.2.b.b.881.12 12
21.5 even 6 1470.2.b.a.881.7 12
21.17 even 6 inner 210.2.r.b.101.6 yes 12
35.3 even 12 1050.2.u.g.899.2 12
35.17 even 12 1050.2.u.f.899.5 12
35.24 odd 6 1050.2.s.g.101.5 12
105.17 odd 12 1050.2.u.h.899.2 12
105.38 odd 12 1050.2.u.e.899.5 12
105.59 even 6 1050.2.s.f.101.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.r.a.101.2 12 7.3 odd 6
210.2.r.a.131.2 yes 12 3.2 odd 2
210.2.r.b.101.6 yes 12 21.17 even 6 inner
210.2.r.b.131.6 yes 12 1.1 even 1 trivial
1050.2.s.f.101.1 12 105.59 even 6
1050.2.s.f.551.1 12 5.4 even 2
1050.2.s.g.101.5 12 35.24 odd 6
1050.2.s.g.551.5 12 15.14 odd 2
1050.2.u.e.299.5 12 5.2 odd 4
1050.2.u.e.899.5 12 105.38 odd 12
1050.2.u.f.299.5 12 15.8 even 4
1050.2.u.f.899.5 12 35.17 even 12
1050.2.u.g.299.2 12 15.2 even 4
1050.2.u.g.899.2 12 35.3 even 12
1050.2.u.h.299.2 12 5.3 odd 4
1050.2.u.h.899.2 12 105.17 odd 12
1470.2.b.a.881.1 12 7.2 even 3
1470.2.b.a.881.7 12 21.5 even 6
1470.2.b.b.881.6 12 7.5 odd 6
1470.2.b.b.881.12 12 21.2 odd 6