Properties

Label 380.2.k.c.343.25
Level $380$
Weight $2$
Character 380.343
Analytic conductor $3.034$
Analytic rank $0$
Dimension $52$
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] = [380,2,Mod(267,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("380.267");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.k (of order \(4\), 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: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(52\)
Relative dimension: \(26\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 343.25
Character \(\chi\) \(=\) 380.343
Dual form 380.2.k.c.267.25

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.38545 + 0.283752i) q^{2} +(-1.20015 + 1.20015i) q^{3} +(1.83897 + 0.786251i) q^{4} +(-2.06624 - 0.854787i) q^{5} +(-2.00330 + 1.32221i) q^{6} +(1.52124 + 1.52124i) q^{7} +(2.32471 + 1.61113i) q^{8} +0.119262i q^{9} +O(q^{10})\) \(q+(1.38545 + 0.283752i) q^{2} +(-1.20015 + 1.20015i) q^{3} +(1.83897 + 0.786251i) q^{4} +(-2.06624 - 0.854787i) q^{5} +(-2.00330 + 1.32221i) q^{6} +(1.52124 + 1.52124i) q^{7} +(2.32471 + 1.61113i) q^{8} +0.119262i q^{9} +(-2.62013 - 1.77057i) q^{10} +4.01379i q^{11} +(-3.15067 + 1.26342i) q^{12} +(-1.50202 - 1.50202i) q^{13} +(1.67595 + 2.53926i) q^{14} +(3.50568 - 1.45393i) q^{15} +(2.76362 + 2.89178i) q^{16} +(-3.94831 + 3.94831i) q^{17} +(-0.0338407 + 0.165232i) q^{18} +1.00000 q^{19} +(-3.12767 - 3.19651i) q^{20} -3.65143 q^{21} +(-1.13892 + 5.56092i) q^{22} +(4.78362 - 4.78362i) q^{23} +(-4.72361 + 0.856407i) q^{24} +(3.53868 + 3.53239i) q^{25} +(-1.65478 - 2.50718i) q^{26} +(-3.74359 - 3.74359i) q^{27} +(1.60143 + 3.99358i) q^{28} -7.97836i q^{29} +(5.26951 - 1.01961i) q^{30} +10.3376i q^{31} +(3.00832 + 4.79062i) q^{32} +(-4.81717 - 4.81717i) q^{33} +(-6.59054 + 4.34986i) q^{34} +(-1.84290 - 4.44357i) q^{35} +(-0.0937696 + 0.219318i) q^{36} +(6.01436 - 6.01436i) q^{37} +(1.38545 + 0.283752i) q^{38} +3.60530 q^{39} +(-3.42623 - 5.31610i) q^{40} +4.47478 q^{41} +(-5.05889 - 1.03610i) q^{42} +(1.96095 - 1.96095i) q^{43} +(-3.15585 + 7.38124i) q^{44} +(0.101943 - 0.246423i) q^{45} +(7.98484 - 5.27012i) q^{46} +(-2.21501 - 2.21501i) q^{47} +(-6.78735 - 0.153821i) q^{48} -2.37169i q^{49} +(3.90036 + 5.89807i) q^{50} -9.47715i q^{51} +(-1.58120 - 3.94313i) q^{52} +(-5.27852 - 5.27852i) q^{53} +(-4.12433 - 6.24883i) q^{54} +(3.43093 - 8.29345i) q^{55} +(1.08552 + 5.98733i) q^{56} +(-1.20015 + 1.20015i) q^{57} +(2.26388 - 11.0537i) q^{58} +5.37196 q^{59} +(7.58999 + 0.0826166i) q^{60} +12.0386 q^{61} +(-2.93332 + 14.3223i) q^{62} +(-0.181425 + 0.181425i) q^{63} +(2.80854 + 7.49080i) q^{64} +(1.81962 + 4.38743i) q^{65} +(-5.30708 - 8.04085i) q^{66} +(0.631476 + 0.631476i) q^{67} +(-10.3652 + 4.15645i) q^{68} +11.4821i q^{69} +(-1.29239 - 6.67929i) q^{70} +6.42369i q^{71} +(-0.192146 + 0.277248i) q^{72} +(-2.26914 - 2.26914i) q^{73} +(10.0392 - 6.62604i) q^{74} +(-8.48637 + 0.00755284i) q^{75} +(1.83897 + 0.786251i) q^{76} +(-6.10592 + 6.10592i) q^{77} +(4.99499 + 1.02301i) q^{78} +4.54855 q^{79} +(-3.23843 - 8.33742i) q^{80} +8.62799 q^{81} +(6.19961 + 1.26973i) q^{82} +(-4.42714 + 4.42714i) q^{83} +(-6.71487 - 2.87094i) q^{84} +(11.5331 - 4.78318i) q^{85} +(3.27323 - 2.16038i) q^{86} +(9.57526 + 9.57526i) q^{87} +(-6.46673 + 9.33089i) q^{88} -8.81939i q^{89} +(0.211161 - 0.312481i) q^{90} -4.56984i q^{91} +(12.5580 - 5.03580i) q^{92} +(-12.4067 - 12.4067i) q^{93} +(-2.44029 - 3.69731i) q^{94} +(-2.06624 - 0.854787i) q^{95} +(-9.35992 - 2.13904i) q^{96} +(8.06581 - 8.06581i) q^{97} +(0.672971 - 3.28586i) q^{98} -0.478691 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.38545 + 0.283752i 0.979664 + 0.200643i
\(3\) −1.20015 + 1.20015i −0.692909 + 0.692909i −0.962871 0.269962i \(-0.912989\pi\)
0.269962 + 0.962871i \(0.412989\pi\)
\(4\) 1.83897 + 0.786251i 0.919485 + 0.393126i
\(5\) −2.06624 0.854787i −0.924050 0.382272i
\(6\) −2.00330 + 1.32221i −0.817846 + 0.539791i
\(7\) 1.52124 + 1.52124i 0.574973 + 0.574973i 0.933514 0.358541i \(-0.116726\pi\)
−0.358541 + 0.933514i \(0.616726\pi\)
\(8\) 2.32471 + 1.61113i 0.821908 + 0.569620i
\(9\) 0.119262i 0.0397539i
\(10\) −2.62013 1.77057i −0.828558 0.559903i
\(11\) 4.01379i 1.21020i 0.796148 + 0.605102i \(0.206868\pi\)
−0.796148 + 0.605102i \(0.793132\pi\)
\(12\) −3.15067 + 1.26342i −0.909520 + 0.364719i
\(13\) −1.50202 1.50202i −0.416585 0.416585i 0.467440 0.884025i \(-0.345176\pi\)
−0.884025 + 0.467440i \(0.845176\pi\)
\(14\) 1.67595 + 2.53926i 0.447916 + 0.678645i
\(15\) 3.50568 1.45393i 0.905162 0.375403i
\(16\) 2.76362 + 2.89178i 0.690904 + 0.722946i
\(17\) −3.94831 + 3.94831i −0.957605 + 0.957605i −0.999137 0.0415323i \(-0.986776\pi\)
0.0415323 + 0.999137i \(0.486776\pi\)
\(18\) −0.0338407 + 0.165232i −0.00797634 + 0.0389455i
\(19\) 1.00000 0.229416
\(20\) −3.12767 3.19651i −0.699369 0.714761i
\(21\) −3.65143 −0.796808
\(22\) −1.13892 + 5.56092i −0.242819 + 1.18559i
\(23\) 4.78362 4.78362i 0.997453 0.997453i −0.00254405 0.999997i \(-0.500810\pi\)
0.999997 + 0.00254405i \(0.000809798\pi\)
\(24\) −4.72361 + 0.856407i −0.964202 + 0.174813i
\(25\) 3.53868 + 3.53239i 0.707736 + 0.706477i
\(26\) −1.65478 2.50718i −0.324528 0.491698i
\(27\) −3.74359 3.74359i −0.720455 0.720455i
\(28\) 1.60143 + 3.99358i 0.302642 + 0.754715i
\(29\) 7.97836i 1.48154i −0.671757 0.740772i \(-0.734460\pi\)
0.671757 0.740772i \(-0.265540\pi\)
\(30\) 5.26951 1.01961i 0.962077 0.186154i
\(31\) 10.3376i 1.85669i 0.371719 + 0.928345i \(0.378768\pi\)
−0.371719 + 0.928345i \(0.621232\pi\)
\(32\) 3.00832 + 4.79062i 0.531800 + 0.846870i
\(33\) −4.81717 4.81717i −0.838561 0.838561i
\(34\) −6.59054 + 4.34986i −1.13027 + 0.745995i
\(35\) −1.84290 4.44357i −0.311507 0.751100i
\(36\) −0.0937696 + 0.219318i −0.0156283 + 0.0365531i
\(37\) 6.01436 6.01436i 0.988755 0.988755i −0.0111828 0.999937i \(-0.503560\pi\)
0.999937 + 0.0111828i \(0.00355967\pi\)
\(38\) 1.38545 + 0.283752i 0.224750 + 0.0460307i
\(39\) 3.60530 0.577311
\(40\) −3.42623 5.31610i −0.541735 0.840550i
\(41\) 4.47478 0.698844 0.349422 0.936965i \(-0.386378\pi\)
0.349422 + 0.936965i \(0.386378\pi\)
\(42\) −5.05889 1.03610i −0.780604 0.159874i
\(43\) 1.96095 1.96095i 0.299042 0.299042i −0.541597 0.840639i \(-0.682180\pi\)
0.840639 + 0.541597i \(0.182180\pi\)
\(44\) −3.15585 + 7.38124i −0.475762 + 1.11276i
\(45\) 0.101943 0.246423i 0.0151968 0.0367346i
\(46\) 7.98484 5.27012i 1.17730 0.777037i
\(47\) −2.21501 2.21501i −0.323093 0.323093i 0.526860 0.849952i \(-0.323369\pi\)
−0.849952 + 0.526860i \(0.823369\pi\)
\(48\) −6.78735 0.153821i −0.979670 0.0222022i
\(49\) 2.37169i 0.338812i
\(50\) 3.90036 + 5.89807i 0.551594 + 0.834113i
\(51\) 9.47715i 1.32707i
\(52\) −1.58120 3.94313i −0.219273 0.546813i
\(53\) −5.27852 5.27852i −0.725060 0.725060i 0.244571 0.969631i \(-0.421353\pi\)
−0.969631 + 0.244571i \(0.921353\pi\)
\(54\) −4.12433 6.24883i −0.561250 0.850358i
\(55\) 3.43093 8.29345i 0.462627 1.11829i
\(56\) 1.08552 + 5.98733i 0.145059 + 0.800091i
\(57\) −1.20015 + 1.20015i −0.158964 + 0.158964i
\(58\) 2.26388 11.0537i 0.297262 1.45142i
\(59\) 5.37196 0.699370 0.349685 0.936867i \(-0.386289\pi\)
0.349685 + 0.936867i \(0.386289\pi\)
\(60\) 7.58999 + 0.0826166i 0.979863 + 0.0106658i
\(61\) 12.0386 1.54138 0.770692 0.637208i \(-0.219911\pi\)
0.770692 + 0.637208i \(0.219911\pi\)
\(62\) −2.93332 + 14.3223i −0.372532 + 1.81893i
\(63\) −0.181425 + 0.181425i −0.0228574 + 0.0228574i
\(64\) 2.80854 + 7.49080i 0.351067 + 0.936350i
\(65\) 1.81962 + 4.38743i 0.225696 + 0.544194i
\(66\) −5.30708 8.04085i −0.653257 0.989760i
\(67\) 0.631476 + 0.631476i 0.0771471 + 0.0771471i 0.744627 0.667480i \(-0.232627\pi\)
−0.667480 + 0.744627i \(0.732627\pi\)
\(68\) −10.3652 + 4.15645i −1.25696 + 0.504044i
\(69\) 11.4821i 1.38229i
\(70\) −1.29239 6.67929i −0.154470 0.798327i
\(71\) 6.42369i 0.762352i 0.924502 + 0.381176i \(0.124481\pi\)
−0.924502 + 0.381176i \(0.875519\pi\)
\(72\) −0.192146 + 0.277248i −0.0226446 + 0.0326740i
\(73\) −2.26914 2.26914i −0.265583 0.265583i 0.561735 0.827317i \(-0.310134\pi\)
−0.827317 + 0.561735i \(0.810134\pi\)
\(74\) 10.0392 6.62604i 1.16703 0.770261i
\(75\) −8.48637 + 0.00755284i −0.979921 + 0.000872127i
\(76\) 1.83897 + 0.786251i 0.210944 + 0.0901892i
\(77\) −6.10592 + 6.10592i −0.695834 + 0.695834i
\(78\) 4.99499 + 1.02301i 0.565571 + 0.115833i
\(79\) 4.54855 0.511751 0.255876 0.966710i \(-0.417636\pi\)
0.255876 + 0.966710i \(0.417636\pi\)
\(80\) −3.23843 8.33742i −0.362068 0.932152i
\(81\) 8.62799 0.958666
\(82\) 6.19961 + 1.26973i 0.684632 + 0.140218i
\(83\) −4.42714 + 4.42714i −0.485942 + 0.485942i −0.907023 0.421081i \(-0.861651\pi\)
0.421081 + 0.907023i \(0.361651\pi\)
\(84\) −6.71487 2.87094i −0.732653 0.313246i
\(85\) 11.5331 4.78318i 1.25094 0.518809i
\(86\) 3.27323 2.16038i 0.352961 0.232960i
\(87\) 9.57526 + 9.57526i 1.02658 + 1.02658i
\(88\) −6.46673 + 9.33089i −0.689355 + 0.994676i
\(89\) 8.81939i 0.934854i −0.884032 0.467427i \(-0.845181\pi\)
0.884032 0.467427i \(-0.154819\pi\)
\(90\) 0.211161 0.312481i 0.0222583 0.0329384i
\(91\) 4.56984i 0.479050i
\(92\) 12.5580 5.03580i 1.30927 0.525018i
\(93\) −12.4067 12.4067i −1.28652 1.28652i
\(94\) −2.44029 3.69731i −0.251696 0.381349i
\(95\) −2.06624 0.854787i −0.211992 0.0876993i
\(96\) −9.35992 2.13904i −0.955293 0.218315i
\(97\) 8.06581 8.06581i 0.818959 0.818959i −0.166998 0.985957i \(-0.553407\pi\)
0.985957 + 0.166998i \(0.0534074\pi\)
\(98\) 0.672971 3.28586i 0.0679804 0.331922i
\(99\) −0.478691 −0.0481103
\(100\) 3.73018 + 9.27824i 0.373018 + 0.927824i
\(101\) −12.2526 −1.21918 −0.609589 0.792718i \(-0.708666\pi\)
−0.609589 + 0.792718i \(0.708666\pi\)
\(102\) 2.68916 13.1302i 0.266267 1.30008i
\(103\) −1.67647 + 1.67647i −0.165187 + 0.165187i −0.784860 0.619673i \(-0.787265\pi\)
0.619673 + 0.784860i \(0.287265\pi\)
\(104\) −1.07181 5.91169i −0.105100 0.579689i
\(105\) 7.54473 + 3.12120i 0.736290 + 0.304598i
\(106\) −5.81536 8.81094i −0.564837 0.855794i
\(107\) −5.31906 5.31906i −0.514212 0.514212i 0.401602 0.915814i \(-0.368454\pi\)
−0.915814 + 0.401602i \(0.868454\pi\)
\(108\) −3.94095 9.82776i −0.379218 0.945677i
\(109\) 14.3543i 1.37489i 0.726237 + 0.687444i \(0.241267\pi\)
−0.726237 + 0.687444i \(0.758733\pi\)
\(110\) 7.10669 10.5167i 0.677596 1.00272i
\(111\) 14.4363i 1.37023i
\(112\) −0.194973 + 8.60320i −0.0184233 + 0.812926i
\(113\) 1.96246 + 1.96246i 0.184613 + 0.184613i 0.793362 0.608750i \(-0.208329\pi\)
−0.608750 + 0.793362i \(0.708329\pi\)
\(114\) −2.00330 + 1.32221i −0.187627 + 0.123837i
\(115\) −13.9731 + 5.79512i −1.30299 + 0.540397i
\(116\) 6.27300 14.6720i 0.582433 1.36226i
\(117\) 0.179133 0.179133i 0.0165609 0.0165609i
\(118\) 7.44261 + 1.52431i 0.685148 + 0.140324i
\(119\) −12.0126 −1.10119
\(120\) 10.4921 + 2.26814i 0.957797 + 0.207052i
\(121\) −5.11051 −0.464592
\(122\) 16.6789 + 3.41598i 1.51004 + 0.309268i
\(123\) −5.37043 + 5.37043i −0.484235 + 0.484235i
\(124\) −8.12796 + 19.0106i −0.729913 + 1.70720i
\(125\) −4.29232 10.3236i −0.383916 0.923368i
\(126\) −0.302836 + 0.199876i −0.0269788 + 0.0178064i
\(127\) −7.79354 7.79354i −0.691565 0.691565i 0.271012 0.962576i \(-0.412642\pi\)
−0.962576 + 0.271012i \(0.912642\pi\)
\(128\) 1.76557 + 11.1751i 0.156056 + 0.987748i
\(129\) 4.70688i 0.414418i
\(130\) 1.27606 + 6.59491i 0.111918 + 0.578412i
\(131\) 3.57377i 0.312242i 0.987738 + 0.156121i \(0.0498989\pi\)
−0.987738 + 0.156121i \(0.950101\pi\)
\(132\) −5.07112 12.6461i −0.441384 1.10070i
\(133\) 1.52124 + 1.52124i 0.131908 + 0.131908i
\(134\) 0.695699 + 1.05406i 0.0600992 + 0.0910573i
\(135\) 4.53518 + 10.9351i 0.390326 + 0.941146i
\(136\) −15.5399 + 2.81744i −1.33253 + 0.241593i
\(137\) −15.5792 + 15.5792i −1.33102 + 1.33102i −0.426565 + 0.904457i \(0.640276\pi\)
−0.904457 + 0.426565i \(0.859724\pi\)
\(138\) −3.25808 + 15.9080i −0.277347 + 1.35418i
\(139\) −6.05603 −0.513666 −0.256833 0.966456i \(-0.582679\pi\)
−0.256833 + 0.966456i \(0.582679\pi\)
\(140\) 0.104719 9.62057i 0.00885040 0.813086i
\(141\) 5.31671 0.447748
\(142\) −1.82274 + 8.89973i −0.152961 + 0.746849i
\(143\) 6.02878 6.02878i 0.504152 0.504152i
\(144\) −0.344879 + 0.329593i −0.0287399 + 0.0274661i
\(145\) −6.81979 + 16.4852i −0.566353 + 1.36902i
\(146\) −2.49992 3.78766i −0.206895 0.313469i
\(147\) 2.84639 + 2.84639i 0.234766 + 0.234766i
\(148\) 15.7890 6.33142i 1.29785 0.520440i
\(149\) 4.53121i 0.371211i 0.982624 + 0.185606i \(0.0594247\pi\)
−0.982624 + 0.185606i \(0.940575\pi\)
\(150\) −11.7596 2.39756i −0.960169 0.195760i
\(151\) 14.4169i 1.17323i −0.809864 0.586617i \(-0.800459\pi\)
0.809864 0.586617i \(-0.199541\pi\)
\(152\) 2.32471 + 1.61113i 0.188559 + 0.130680i
\(153\) −0.470881 0.470881i −0.0380685 0.0380685i
\(154\) −10.1920 + 6.72691i −0.821298 + 0.542070i
\(155\) 8.83646 21.3600i 0.709761 1.71567i
\(156\) 6.63004 + 2.83468i 0.530828 + 0.226956i
\(157\) 1.75431 1.75431i 0.140009 0.140009i −0.633629 0.773637i \(-0.718435\pi\)
0.773637 + 0.633629i \(0.218435\pi\)
\(158\) 6.30181 + 1.29066i 0.501345 + 0.102679i
\(159\) 12.6701 1.00480
\(160\) −2.12094 12.4700i −0.167675 0.985842i
\(161\) 14.5540 1.14702
\(162\) 11.9537 + 2.44821i 0.939171 + 0.192350i
\(163\) −9.41490 + 9.41490i −0.737432 + 0.737432i −0.972080 0.234648i \(-0.924606\pi\)
0.234648 + 0.972080i \(0.424606\pi\)
\(164\) 8.22899 + 3.51831i 0.642576 + 0.274733i
\(165\) 5.83576 + 14.0711i 0.454313 + 1.09543i
\(166\) −7.38981 + 4.87739i −0.573561 + 0.378559i
\(167\) 8.94130 + 8.94130i 0.691899 + 0.691899i 0.962649 0.270751i \(-0.0872719\pi\)
−0.270751 + 0.962649i \(0.587272\pi\)
\(168\) −8.48852 5.88292i −0.654903 0.453877i
\(169\) 8.48789i 0.652914i
\(170\) 17.3358 3.35434i 1.32960 0.257266i
\(171\) 0.119262i 0.00912016i
\(172\) 5.14793 2.06433i 0.392526 0.157403i
\(173\) −2.06373 2.06373i −0.156902 0.156902i 0.624290 0.781193i \(-0.285388\pi\)
−0.781193 + 0.624290i \(0.785388\pi\)
\(174\) 10.5491 + 15.9831i 0.799724 + 1.21167i
\(175\) 0.00957348 + 10.7568i 0.000723687 + 0.813134i
\(176\) −11.6070 + 11.0926i −0.874912 + 0.836135i
\(177\) −6.44718 + 6.44718i −0.484600 + 0.484600i
\(178\) 2.50252 12.2189i 0.187572 0.915843i
\(179\) −1.70622 −0.127529 −0.0637645 0.997965i \(-0.520311\pi\)
−0.0637645 + 0.997965i \(0.520311\pi\)
\(180\) 0.381221 0.373011i 0.0284145 0.0278026i
\(181\) 20.1290 1.49618 0.748089 0.663599i \(-0.230972\pi\)
0.748089 + 0.663599i \(0.230972\pi\)
\(182\) 1.29670 6.33131i 0.0961180 0.469308i
\(183\) −14.4482 + 14.4482i −1.06804 + 1.06804i
\(184\) 18.8275 3.41350i 1.38798 0.251646i
\(185\) −17.5681 + 7.28610i −1.29163 + 0.535685i
\(186\) −13.6685 20.7094i −1.00222 1.51849i
\(187\) −15.8477 15.8477i −1.15890 1.15890i
\(188\) −2.33178 5.81490i −0.170063 0.424095i
\(189\) 11.3898i 0.828484i
\(190\) −2.62013 1.77057i −0.190084 0.128450i
\(191\) 16.2481i 1.17567i −0.808980 0.587836i \(-0.799980\pi\)
0.808980 0.587836i \(-0.200020\pi\)
\(192\) −12.3608 5.61944i −0.892063 0.405548i
\(193\) 6.47432 + 6.47432i 0.466031 + 0.466031i 0.900626 0.434595i \(-0.143108\pi\)
−0.434595 + 0.900626i \(0.643108\pi\)
\(194\) 13.4635 8.88612i 0.966623 0.637987i
\(195\) −7.44942 3.08177i −0.533464 0.220690i
\(196\) 1.86474 4.36146i 0.133196 0.311533i
\(197\) −4.14788 + 4.14788i −0.295524 + 0.295524i −0.839258 0.543734i \(-0.817010\pi\)
0.543734 + 0.839258i \(0.317010\pi\)
\(198\) −0.663205 0.135830i −0.0471319 0.00965299i
\(199\) 10.4993 0.744272 0.372136 0.928178i \(-0.378625\pi\)
0.372136 + 0.928178i \(0.378625\pi\)
\(200\) 2.53527 + 13.9130i 0.179271 + 0.983800i
\(201\) −1.51574 −0.106912
\(202\) −16.9754 3.47670i −1.19439 0.244620i
\(203\) 12.1370 12.1370i 0.851847 0.851847i
\(204\) 7.45142 17.4282i 0.521704 1.22022i
\(205\) −9.24597 3.82499i −0.645766 0.267149i
\(206\) −2.79837 + 1.84697i −0.194972 + 0.128685i
\(207\) 0.570502 + 0.570502i 0.0396526 + 0.0396526i
\(208\) 0.192510 8.49451i 0.0133482 0.588989i
\(209\) 4.01379i 0.277640i
\(210\) 9.56723 + 6.46511i 0.660202 + 0.446135i
\(211\) 16.0916i 1.10779i 0.832585 + 0.553897i \(0.186860\pi\)
−0.832585 + 0.553897i \(0.813140\pi\)
\(212\) −5.55679 13.8573i −0.381642 0.951721i
\(213\) −7.70942 7.70942i −0.528241 0.528241i
\(214\) −5.86002 8.87860i −0.400583 0.606929i
\(215\) −5.72798 + 2.37559i −0.390645 + 0.162014i
\(216\) −2.67136 14.7342i −0.181763 1.00253i
\(217\) −15.7259 + 15.7259i −1.06755 + 1.06755i
\(218\) −4.07305 + 19.8872i −0.275862 + 1.34693i
\(219\) 5.44663 0.368049
\(220\) 12.8301 12.5538i 0.865006 0.846378i
\(221\) 11.8609 0.797847
\(222\) −4.09634 + 20.0009i −0.274928 + 1.34237i
\(223\) 11.4105 11.4105i 0.764105 0.764105i −0.212957 0.977062i \(-0.568309\pi\)
0.977062 + 0.212957i \(0.0683094\pi\)
\(224\) −2.71130 + 11.8640i −0.181157 + 0.792698i
\(225\) −0.421278 + 0.422029i −0.0280852 + 0.0281352i
\(226\) 2.16205 + 3.27575i 0.143817 + 0.217900i
\(227\) 2.06920 + 2.06920i 0.137338 + 0.137338i 0.772433 0.635096i \(-0.219039\pi\)
−0.635096 + 0.772433i \(0.719039\pi\)
\(228\) −3.15067 + 1.26342i −0.208658 + 0.0836723i
\(229\) 21.9098i 1.44784i 0.689885 + 0.723919i \(0.257661\pi\)
−0.689885 + 0.723919i \(0.742339\pi\)
\(230\) −21.0034 + 4.06399i −1.38492 + 0.267971i
\(231\) 14.6561i 0.964299i
\(232\) 12.8542 18.5474i 0.843916 1.21769i
\(233\) 9.03376 + 9.03376i 0.591821 + 0.591821i 0.938123 0.346302i \(-0.112563\pi\)
−0.346302 + 0.938123i \(0.612563\pi\)
\(234\) 0.299010 0.197351i 0.0195469 0.0129013i
\(235\) 2.68338 + 6.47011i 0.175044 + 0.422063i
\(236\) 9.87887 + 4.22371i 0.643060 + 0.274940i
\(237\) −5.45896 + 5.45896i −0.354597 + 0.354597i
\(238\) −16.6429 3.40860i −1.07880 0.220947i
\(239\) −8.80262 −0.569394 −0.284697 0.958618i \(-0.591893\pi\)
−0.284697 + 0.958618i \(0.591893\pi\)
\(240\) 13.8928 + 6.11957i 0.896776 + 0.395017i
\(241\) −2.16116 −0.139212 −0.0696062 0.997575i \(-0.522174\pi\)
−0.0696062 + 0.997575i \(0.522174\pi\)
\(242\) −7.08038 1.45012i −0.455144 0.0932171i
\(243\) 0.875864 0.875864i 0.0561867 0.0561867i
\(244\) 22.1386 + 9.46536i 1.41728 + 0.605958i
\(245\) −2.02729 + 4.90047i −0.129519 + 0.313080i
\(246\) −8.96436 + 5.91661i −0.571546 + 0.377230i
\(247\) −1.50202 1.50202i −0.0955711 0.0955711i
\(248\) −16.6552 + 24.0319i −1.05761 + 1.52603i
\(249\) 10.6265i 0.673427i
\(250\) −3.01748 15.5208i −0.190842 0.981621i
\(251\) 19.5275i 1.23256i −0.787526 0.616282i \(-0.788638\pi\)
0.787526 0.616282i \(-0.211362\pi\)
\(252\) −0.476281 + 0.190989i −0.0300029 + 0.0120312i
\(253\) 19.2004 + 19.2004i 1.20712 + 1.20712i
\(254\) −8.58616 13.0090i −0.538744 0.816259i
\(255\) −8.10094 + 19.5820i −0.507301 + 1.22628i
\(256\) −0.724840 + 15.9836i −0.0453025 + 0.998973i
\(257\) 9.86907 9.86907i 0.615616 0.615616i −0.328788 0.944404i \(-0.606640\pi\)
0.944404 + 0.328788i \(0.106640\pi\)
\(258\) −1.33559 + 6.52117i −0.0831501 + 0.405990i
\(259\) 18.2985 1.13701
\(260\) −0.103396 + 9.49903i −0.00641237 + 0.589105i
\(261\) 0.951512 0.0588971
\(262\) −1.01406 + 4.95129i −0.0626491 + 0.305892i
\(263\) −4.12699 + 4.12699i −0.254481 + 0.254481i −0.822805 0.568324i \(-0.807592\pi\)
0.568324 + 0.822805i \(0.307592\pi\)
\(264\) −3.43744 18.9596i −0.211560 1.16688i
\(265\) 6.39467 + 15.4187i 0.392821 + 0.947162i
\(266\) 1.67595 + 2.53926i 0.102759 + 0.155692i
\(267\) 10.5846 + 10.5846i 0.647769 + 0.647769i
\(268\) 0.664766 + 1.65776i 0.0406070 + 0.101264i
\(269\) 17.1547i 1.04594i −0.852351 0.522970i \(-0.824824\pi\)
0.852351 0.522970i \(-0.175176\pi\)
\(270\) 3.18042 + 16.4370i 0.193554 + 1.00032i
\(271\) 24.3506i 1.47919i 0.673050 + 0.739597i \(0.264984\pi\)
−0.673050 + 0.739597i \(0.735016\pi\)
\(272\) −22.3293 0.506046i −1.35391 0.0306835i
\(273\) 5.48452 + 5.48452i 0.331938 + 0.331938i
\(274\) −26.0049 + 17.1637i −1.57101 + 1.03689i
\(275\) −14.1783 + 14.2035i −0.854981 + 0.856504i
\(276\) −9.02786 + 21.1153i −0.543413 + 1.27099i
\(277\) −10.5003 + 10.5003i −0.630902 + 0.630902i −0.948294 0.317393i \(-0.897193\pi\)
0.317393 + 0.948294i \(0.397193\pi\)
\(278\) −8.39035 1.71841i −0.503220 0.103063i
\(279\) −1.23288 −0.0738106
\(280\) 2.87494 13.2991i 0.171811 0.794776i
\(281\) −1.50845 −0.0899866 −0.0449933 0.998987i \(-0.514327\pi\)
−0.0449933 + 0.998987i \(0.514327\pi\)
\(282\) 7.36606 + 1.50863i 0.438643 + 0.0898375i
\(283\) 12.4817 12.4817i 0.741959 0.741959i −0.230996 0.972955i \(-0.574198\pi\)
0.972955 + 0.230996i \(0.0741985\pi\)
\(284\) −5.05064 + 11.8130i −0.299700 + 0.700971i
\(285\) 3.50568 1.45393i 0.207659 0.0861233i
\(286\) 10.0633 6.64193i 0.595055 0.392745i
\(287\) 6.80720 + 6.80720i 0.401816 + 0.401816i
\(288\) −0.571337 + 0.358777i −0.0336664 + 0.0211411i
\(289\) 14.1782i 0.834014i
\(290\) −14.1262 + 20.9043i −0.829520 + 1.22755i
\(291\) 19.3604i 1.13493i
\(292\) −2.38876 5.95699i −0.139792 0.348607i
\(293\) −0.143152 0.143152i −0.00836306 0.00836306i 0.702913 0.711276i \(-0.251882\pi\)
−0.711276 + 0.702913i \(0.751882\pi\)
\(294\) 3.13587 + 4.75121i 0.182888 + 0.277096i
\(295\) −11.0997 4.59188i −0.646252 0.267350i
\(296\) 23.6715 4.29173i 1.37588 0.249452i
\(297\) 15.0260 15.0260i 0.871897 0.871897i
\(298\) −1.28574 + 6.27779i −0.0744809 + 0.363662i
\(299\) −14.3701 −0.831047
\(300\) −15.6121 6.65853i −0.901365 0.384430i
\(301\) 5.96613 0.343882
\(302\) 4.09084 19.9740i 0.235401 1.14938i
\(303\) 14.7050 14.7050i 0.844780 0.844780i
\(304\) 2.76362 + 2.89178i 0.158504 + 0.165855i
\(305\) −24.8746 10.2904i −1.42432 0.589228i
\(306\) −0.518771 0.785999i −0.0296562 0.0449325i
\(307\) −22.5165 22.5165i −1.28508 1.28508i −0.937736 0.347348i \(-0.887082\pi\)
−0.347348 0.937736i \(-0.612918\pi\)
\(308\) −16.0294 + 6.42781i −0.913359 + 0.366258i
\(309\) 4.02404i 0.228920i
\(310\) 18.3034 27.0859i 1.03957 1.53838i
\(311\) 10.0019i 0.567158i 0.958949 + 0.283579i \(0.0915219\pi\)
−0.958949 + 0.283579i \(0.908478\pi\)
\(312\) 8.38128 + 5.80860i 0.474497 + 0.328847i
\(313\) −19.1644 19.1644i −1.08324 1.08324i −0.996206 0.0870306i \(-0.972262\pi\)
−0.0870306 0.996206i \(-0.527738\pi\)
\(314\) 2.92830 1.93272i 0.165253 0.109070i
\(315\) 0.529947 0.219788i 0.0298591 0.0123836i
\(316\) 8.36464 + 3.57630i 0.470548 + 0.201183i
\(317\) 9.07885 9.07885i 0.509919 0.509919i −0.404583 0.914501i \(-0.632583\pi\)
0.914501 + 0.404583i \(0.132583\pi\)
\(318\) 17.5538 + 3.59516i 0.984368 + 0.201606i
\(319\) 32.0235 1.79297
\(320\) 0.599932 17.8785i 0.0335372 0.999437i
\(321\) 12.7674 0.712605
\(322\) 20.1639 + 4.12973i 1.12369 + 0.230141i
\(323\) −3.94831 + 3.94831i −0.219690 + 0.219690i
\(324\) 15.8666 + 6.78377i 0.881479 + 0.376876i
\(325\) −0.00945254 10.6209i −0.000524332 0.589140i
\(326\) −15.7154 + 10.3724i −0.870396 + 0.574475i
\(327\) −17.2273 17.2273i −0.952673 0.952673i
\(328\) 10.4026 + 7.20945i 0.574386 + 0.398075i
\(329\) 6.73911i 0.371539i
\(330\) 4.09249 + 21.1507i 0.225284 + 1.16431i
\(331\) 7.53646i 0.414242i 0.978315 + 0.207121i \(0.0664093\pi\)
−0.978315 + 0.207121i \(0.933591\pi\)
\(332\) −11.6222 + 4.66053i −0.637852 + 0.255780i
\(333\) 0.717282 + 0.717282i 0.0393068 + 0.0393068i
\(334\) 9.85066 + 14.9249i 0.539004 + 0.816653i
\(335\) −0.765002 1.84456i −0.0417965 0.100779i
\(336\) −10.0912 10.5592i −0.550518 0.576049i
\(337\) 7.14595 7.14595i 0.389264 0.389264i −0.485161 0.874425i \(-0.661239\pi\)
0.874425 + 0.485161i \(0.161239\pi\)
\(338\) 2.40846 11.7596i 0.131003 0.639637i
\(339\) −4.71051 −0.255840
\(340\) 24.9698 + 0.271795i 1.35418 + 0.0147401i
\(341\) −41.4930 −2.24697
\(342\) −0.0338407 + 0.165232i −0.00182990 + 0.00893470i
\(343\) 14.2565 14.2565i 0.769781 0.769781i
\(344\) 7.71797 1.39930i 0.416125 0.0754450i
\(345\) 9.81479 23.7249i 0.528410 1.27730i
\(346\) −2.27362 3.44479i −0.122230 0.185193i
\(347\) −2.43847 2.43847i −0.130904 0.130904i 0.638619 0.769523i \(-0.279506\pi\)
−0.769523 + 0.638619i \(0.779506\pi\)
\(348\) 10.0800 + 25.1372i 0.540347 + 1.34749i
\(349\) 25.9387i 1.38847i −0.719750 0.694233i \(-0.755744\pi\)
0.719750 0.694233i \(-0.244256\pi\)
\(350\) −3.03899 + 14.9057i −0.162441 + 0.796744i
\(351\) 11.2459i 0.600261i
\(352\) −19.2285 + 12.0747i −1.02488 + 0.643586i
\(353\) −15.6893 15.6893i −0.835056 0.835056i 0.153148 0.988203i \(-0.451059\pi\)
−0.988203 + 0.153148i \(0.951059\pi\)
\(354\) −10.7617 + 7.10287i −0.571977 + 0.377513i
\(355\) 5.49089 13.2729i 0.291426 0.704451i
\(356\) 6.93426 16.2186i 0.367515 0.859584i
\(357\) 14.4170 14.4170i 0.763027 0.763027i
\(358\) −2.36389 0.484144i −0.124936 0.0255878i
\(359\) −15.8725 −0.837718 −0.418859 0.908051i \(-0.637570\pi\)
−0.418859 + 0.908051i \(0.637570\pi\)
\(360\) 0.634007 0.408618i 0.0334151 0.0215360i
\(361\) 1.00000 0.0526316
\(362\) 27.8878 + 5.71165i 1.46575 + 0.300198i
\(363\) 6.13340 6.13340i 0.321920 0.321920i
\(364\) 3.59305 8.40380i 0.188327 0.440479i
\(365\) 2.74895 + 6.62821i 0.143887 + 0.346937i
\(366\) −24.1170 + 15.9176i −1.26061 + 0.832025i
\(367\) 9.08519 + 9.08519i 0.474243 + 0.474243i 0.903285 0.429042i \(-0.141149\pi\)
−0.429042 + 0.903285i \(0.641149\pi\)
\(368\) 27.0533 + 0.613105i 1.41025 + 0.0319603i
\(369\) 0.533670i 0.0277817i
\(370\) −26.4072 + 5.10958i −1.37285 + 0.265635i
\(371\) 16.0597i 0.833780i
\(372\) −13.0608 32.5704i −0.677170 1.68870i
\(373\) −3.81246 3.81246i −0.197402 0.197402i 0.601483 0.798885i \(-0.294577\pi\)
−0.798885 + 0.601483i \(0.794577\pi\)
\(374\) −17.4594 26.4530i −0.902805 1.36785i
\(375\) 17.5413 + 7.23843i 0.905829 + 0.373791i
\(376\) −1.58059 8.71793i −0.0815128 0.449593i
\(377\) −11.9836 + 11.9836i −0.617189 + 0.617189i
\(378\) 3.23187 15.7800i 0.166230 0.811636i
\(379\) −10.9007 −0.559930 −0.279965 0.960010i \(-0.590323\pi\)
−0.279965 + 0.960010i \(0.590323\pi\)
\(380\) −3.12767 3.19651i −0.160446 0.163977i
\(381\) 18.7069 0.958383
\(382\) 4.61044 22.5110i 0.235891 1.15176i
\(383\) 14.5162 14.5162i 0.741744 0.741744i −0.231170 0.972913i \(-0.574255\pi\)
0.972913 + 0.231170i \(0.0742553\pi\)
\(384\) −15.5308 11.2929i −0.792552 0.576287i
\(385\) 17.8355 7.39702i 0.908983 0.376987i
\(386\) 7.13277 + 10.8070i 0.363048 + 0.550060i
\(387\) 0.233866 + 0.233866i 0.0118881 + 0.0118881i
\(388\) 21.1745 8.49102i 1.07497 0.431066i
\(389\) 15.6390i 0.792929i −0.918050 0.396465i \(-0.870237\pi\)
0.918050 0.396465i \(-0.129763\pi\)
\(390\) −9.44637 6.38344i −0.478336 0.323238i
\(391\) 37.7744i 1.91033i
\(392\) 3.82109 5.51348i 0.192994 0.278473i
\(393\) −4.28907 4.28907i −0.216355 0.216355i
\(394\) −6.92367 + 4.56973i −0.348810 + 0.230220i
\(395\) −9.39838 3.88804i −0.472884 0.195628i
\(396\) −0.880298 0.376372i −0.0442367 0.0189134i
\(397\) 4.42602 4.42602i 0.222136 0.222136i −0.587262 0.809397i \(-0.699794\pi\)
0.809397 + 0.587262i \(0.199794\pi\)
\(398\) 14.5462 + 2.97919i 0.729137 + 0.149333i
\(399\) −3.65143 −0.182800
\(400\) −0.435346 + 19.9953i −0.0217673 + 0.999763i
\(401\) 11.7922 0.588875 0.294438 0.955671i \(-0.404868\pi\)
0.294438 + 0.955671i \(0.404868\pi\)
\(402\) −2.09998 0.430093i −0.104738 0.0214511i
\(403\) 15.5273 15.5273i 0.773469 0.773469i
\(404\) −22.5321 9.63362i −1.12102 0.479290i
\(405\) −17.8275 7.37509i −0.885855 0.366471i
\(406\) 20.2591 13.3713i 1.00544 0.663607i
\(407\) 24.1404 + 24.1404i 1.19659 + 1.19659i
\(408\) 15.2689 22.0316i 0.755923 1.09073i
\(409\) 23.9203i 1.18278i −0.806385 0.591391i \(-0.798579\pi\)
0.806385 0.591391i \(-0.201421\pi\)
\(410\) −11.7245 7.92291i −0.579033 0.391285i
\(411\) 37.3949i 1.84455i
\(412\) −4.40110 + 1.76485i −0.216827 + 0.0869479i
\(413\) 8.17202 + 8.17202i 0.402119 + 0.402119i
\(414\) 0.628523 + 0.952285i 0.0308902 + 0.0468023i
\(415\) 12.9318 5.36326i 0.634796 0.263272i
\(416\) 2.67705 11.7141i 0.131253 0.574333i
\(417\) 7.26816 7.26816i 0.355924 0.355924i
\(418\) −1.13892 + 5.56092i −0.0557065 + 0.271994i
\(419\) −23.7000 −1.15782 −0.578910 0.815391i \(-0.696522\pi\)
−0.578910 + 0.815391i \(0.696522\pi\)
\(420\) 11.4205 + 11.6718i 0.557262 + 0.569527i
\(421\) −27.6593 −1.34803 −0.674015 0.738718i \(-0.735432\pi\)
−0.674015 + 0.738718i \(0.735432\pi\)
\(422\) −4.56604 + 22.2942i −0.222271 + 1.08527i
\(423\) 0.264166 0.264166i 0.0128442 0.0128442i
\(424\) −3.76665 20.7754i −0.182925 1.00894i
\(425\) −27.9187 + 0.0248476i −1.35426 + 0.00120528i
\(426\) −8.49349 12.8686i −0.411511 0.623486i
\(427\) 18.3135 + 18.3135i 0.886254 + 0.886254i
\(428\) −5.59946 13.9637i −0.270660 0.674961i
\(429\) 14.4709i 0.698663i
\(430\) −8.60994 + 1.66595i −0.415208 + 0.0803393i
\(431\) 11.7110i 0.564099i −0.959400 0.282049i \(-0.908986\pi\)
0.959400 0.282049i \(-0.0910142\pi\)
\(432\) 0.479808 21.1715i 0.0230848 1.01862i
\(433\) −4.06976 4.06976i −0.195580 0.195580i 0.602522 0.798102i \(-0.294163\pi\)
−0.798102 + 0.602522i \(0.794163\pi\)
\(434\) −26.2498 + 17.3253i −1.26003 + 0.831641i
\(435\) −11.6000 27.9696i −0.556175 1.34104i
\(436\) −11.2861 + 26.3970i −0.540504 + 1.26419i
\(437\) 4.78362 4.78362i 0.228831 0.228831i
\(438\) 7.54607 + 1.54549i 0.360565 + 0.0738466i
\(439\) −25.7007 −1.22663 −0.613313 0.789840i \(-0.710164\pi\)
−0.613313 + 0.789840i \(0.710164\pi\)
\(440\) 21.3377 13.7522i 1.01724 0.655609i
\(441\) 0.282851 0.0134691
\(442\) 16.4327 + 3.36554i 0.781622 + 0.160082i
\(443\) −17.7355 + 17.7355i −0.842640 + 0.842640i −0.989202 0.146561i \(-0.953179\pi\)
0.146561 + 0.989202i \(0.453179\pi\)
\(444\) −11.3506 + 26.5479i −0.538674 + 1.25991i
\(445\) −7.53870 + 18.2230i −0.357369 + 0.863851i
\(446\) 19.0465 12.5710i 0.901878 0.595254i
\(447\) −5.43815 5.43815i −0.257216 0.257216i
\(448\) −7.12283 + 15.6677i −0.336522 + 0.740230i
\(449\) 5.66338i 0.267272i 0.991031 + 0.133636i \(0.0426652\pi\)
−0.991031 + 0.133636i \(0.957335\pi\)
\(450\) −0.703413 + 0.465163i −0.0331592 + 0.0219280i
\(451\) 17.9608i 0.845743i
\(452\) 2.06592 + 5.15189i 0.0971726 + 0.242325i
\(453\) 17.3025 + 17.3025i 0.812945 + 0.812945i
\(454\) 2.27964 + 3.45392i 0.106989 + 0.162101i
\(455\) −3.90624 + 9.44239i −0.183127 + 0.442666i
\(456\) −4.72361 + 0.856407i −0.221203 + 0.0401049i
\(457\) 19.7589 19.7589i 0.924284 0.924284i −0.0730444 0.997329i \(-0.523271\pi\)
0.997329 + 0.0730444i \(0.0232715\pi\)
\(458\) −6.21694 + 30.3550i −0.290499 + 1.41840i
\(459\) 29.5617 1.37982
\(460\) −30.2524 0.329296i −1.41053 0.0153535i
\(461\) 31.3335 1.45935 0.729674 0.683795i \(-0.239672\pi\)
0.729674 + 0.683795i \(0.239672\pi\)
\(462\) 4.15870 20.3053i 0.193480 0.944690i
\(463\) −9.54706 + 9.54706i −0.443689 + 0.443689i −0.893250 0.449560i \(-0.851581\pi\)
0.449560 + 0.893250i \(0.351581\pi\)
\(464\) 23.0717 22.0491i 1.07108 1.02360i
\(465\) 15.0301 + 36.2404i 0.697006 + 1.68061i
\(466\) 9.95251 + 15.0792i 0.461041 + 0.698531i
\(467\) 17.6594 + 17.6594i 0.817178 + 0.817178i 0.985698 0.168520i \(-0.0538989\pi\)
−0.168520 + 0.985698i \(0.553899\pi\)
\(468\) 0.470264 0.188577i 0.0217380 0.00871696i
\(469\) 1.92125i 0.0887149i
\(470\) 1.88179 + 9.72546i 0.0868007 + 0.448602i
\(471\) 4.21087i 0.194027i
\(472\) 12.4882 + 8.65491i 0.574818 + 0.398375i
\(473\) 7.87084 + 7.87084i 0.361902 + 0.361902i
\(474\) −9.11213 + 6.01415i −0.418534 + 0.276239i
\(475\) 3.53868 + 3.53239i 0.162366 + 0.162077i
\(476\) −22.0908 9.44493i −1.01253 0.432908i
\(477\) 0.629525 0.629525i 0.0288239 0.0288239i
\(478\) −12.1956 2.49776i −0.557815 0.114245i
\(479\) 21.7112 0.992010 0.496005 0.868320i \(-0.334800\pi\)
0.496005 + 0.868320i \(0.334800\pi\)
\(480\) 17.5114 + 12.4205i 0.799283 + 0.566916i
\(481\) −18.0673 −0.823800
\(482\) −2.99418 0.613233i −0.136381 0.0279320i
\(483\) −17.4670 + 17.4670i −0.794778 + 0.794778i
\(484\) −9.39807 4.01815i −0.427185 0.182643i
\(485\) −23.5604 + 9.77134i −1.06982 + 0.443694i
\(486\) 1.46200 0.964942i 0.0663176 0.0437706i
\(487\) −11.2980 11.2980i −0.511962 0.511962i 0.403165 0.915127i \(-0.367910\pi\)
−0.915127 + 0.403165i \(0.867910\pi\)
\(488\) 27.9862 + 19.3957i 1.26688 + 0.878002i
\(489\) 22.5987i 1.02195i
\(490\) −4.19923 + 6.21413i −0.189702 + 0.280726i
\(491\) 21.1601i 0.954942i −0.878647 0.477471i \(-0.841554\pi\)
0.878647 0.477471i \(-0.158446\pi\)
\(492\) −14.0986 + 5.65355i −0.635612 + 0.254882i
\(493\) 31.5010 + 31.5010i 1.41873 + 1.41873i
\(494\) −1.65478 2.50718i −0.0744519 0.112803i
\(495\) 0.989090 + 0.409179i 0.0444563 + 0.0183912i
\(496\) −29.8942 + 28.5692i −1.34229 + 1.28280i
\(497\) −9.77195 + 9.77195i −0.438332 + 0.438332i
\(498\) 3.01529 14.7225i 0.135118 0.659732i
\(499\) −24.0759 −1.07778 −0.538892 0.842375i \(-0.681157\pi\)
−0.538892 + 0.842375i \(0.681157\pi\)
\(500\) 0.223480 22.3596i 0.00999435 0.999950i
\(501\) −21.4619 −0.958846
\(502\) 5.54097 27.0544i 0.247305 1.20750i
\(503\) 20.3664 20.3664i 0.908093 0.908093i −0.0880249 0.996118i \(-0.528056\pi\)
0.996118 + 0.0880249i \(0.0280555\pi\)
\(504\) −0.714059 + 0.129461i −0.0318067 + 0.00576667i
\(505\) 25.3168 + 10.4734i 1.12658 + 0.466058i
\(506\) 21.1532 + 32.0495i 0.940373 + 1.42477i
\(507\) 10.1868 + 10.1868i 0.452410 + 0.452410i
\(508\) −8.20440 20.4598i −0.364011 0.907755i
\(509\) 28.6068i 1.26798i 0.773343 + 0.633988i \(0.218583\pi\)
−0.773343 + 0.633988i \(0.781417\pi\)
\(510\) −16.7799 + 24.8314i −0.743028 + 1.09955i
\(511\) 6.90379i 0.305406i
\(512\) −5.53961 + 21.9388i −0.244818 + 0.969569i
\(513\) −3.74359 3.74359i −0.165284 0.165284i
\(514\) 16.4735 10.8728i 0.726616 0.479578i
\(515\) 4.89701 2.03096i 0.215788 0.0894948i
\(516\) −3.70079 + 8.65581i −0.162918 + 0.381051i
\(517\) 8.89060 8.89060i 0.391008 0.391008i
\(518\) 25.3518 + 5.19224i 1.11389 + 0.228134i
\(519\) 4.95359 0.217438
\(520\) −2.83862 + 13.1311i −0.124482 + 0.575838i
\(521\) −33.7509 −1.47866 −0.739328 0.673346i \(-0.764857\pi\)
−0.739328 + 0.673346i \(0.764857\pi\)
\(522\) 1.31828 + 0.269994i 0.0576994 + 0.0118173i
\(523\) −10.9977 + 10.9977i −0.480897 + 0.480897i −0.905418 0.424521i \(-0.860442\pi\)
0.424521 + 0.905418i \(0.360442\pi\)
\(524\) −2.80988 + 6.57205i −0.122750 + 0.287101i
\(525\) −12.9212 12.8983i −0.563929 0.562927i
\(526\) −6.88880 + 4.54671i −0.300366 + 0.198246i
\(527\) −40.8161 40.8161i −1.77798 1.77798i
\(528\) 0.617405 27.2430i 0.0268691 1.18560i
\(529\) 22.7659i 0.989824i
\(530\) 4.48444 + 23.1764i 0.194791 + 1.00672i
\(531\) 0.640669i 0.0278027i
\(532\) 1.60143 + 3.99358i 0.0694309 + 0.173144i
\(533\) −6.72120 6.72120i −0.291128 0.291128i
\(534\) 11.6611 + 17.6679i 0.504626 + 0.764566i
\(535\) 6.44378 + 15.5371i 0.278589 + 0.671727i
\(536\) 0.450609 + 2.48539i 0.0194634 + 0.107352i
\(537\) 2.04773 2.04773i 0.0883660 0.0883660i
\(538\) 4.86768 23.7671i 0.209861 1.02467i
\(539\) 9.51945 0.410032
\(540\) −0.257703 + 23.6752i −0.0110898 + 1.01882i
\(541\) −44.1197 −1.89685 −0.948427 0.316995i \(-0.897326\pi\)
−0.948427 + 0.316995i \(0.897326\pi\)
\(542\) −6.90954 + 33.7367i −0.296790 + 1.44911i
\(543\) −24.1579 + 24.1579i −1.03671 + 1.03671i
\(544\) −30.7926 7.03708i −1.32022 0.301712i
\(545\) 12.2698 29.6593i 0.525582 1.27047i
\(546\) 6.04230 + 9.15479i 0.258587 + 0.391789i
\(547\) 15.0359 + 15.0359i 0.642887 + 0.642887i 0.951264 0.308377i \(-0.0997858\pi\)
−0.308377 + 0.951264i \(0.599786\pi\)
\(548\) −40.8989 + 16.4005i −1.74711 + 0.700595i
\(549\) 1.43574i 0.0612760i
\(550\) −23.6736 + 15.6552i −1.00945 + 0.667541i
\(551\) 7.97836i 0.339889i
\(552\) −18.4992 + 26.6926i −0.787378 + 1.13611i
\(553\) 6.91941 + 6.91941i 0.294243 + 0.294243i
\(554\) −17.5272 + 11.5682i −0.744658 + 0.491486i
\(555\) 12.3400 29.8289i 0.523803 1.26616i
\(556\) −11.1368 4.76156i −0.472308 0.201935i
\(557\) −5.74079 + 5.74079i −0.243245 + 0.243245i −0.818191 0.574946i \(-0.805023\pi\)
0.574946 + 0.818191i \(0.305023\pi\)
\(558\) −1.70810 0.349833i −0.0723096 0.0148096i
\(559\) −5.89076 −0.249153
\(560\) 7.75676 17.6096i 0.327783 0.744141i
\(561\) 38.0393 1.60602
\(562\) −2.08989 0.428026i −0.0881567 0.0180552i
\(563\) −21.8581 + 21.8581i −0.921210 + 0.921210i −0.997115 0.0759053i \(-0.975815\pi\)
0.0759053 + 0.997115i \(0.475815\pi\)
\(564\) 9.77727 + 4.18027i 0.411697 + 0.176021i
\(565\) −2.37742 5.73239i −0.100019 0.241164i
\(566\) 20.8345 13.7511i 0.875739 0.578002i
\(567\) 13.1252 + 13.1252i 0.551207 + 0.551207i
\(568\) −10.3494 + 14.9332i −0.434251 + 0.626584i
\(569\) 3.55621i 0.149084i 0.997218 + 0.0745421i \(0.0237495\pi\)
−0.997218 + 0.0745421i \(0.976250\pi\)
\(570\) 5.26951 1.01961i 0.220716 0.0427066i
\(571\) 33.7698i 1.41322i −0.707602 0.706611i \(-0.750223\pi\)
0.707602 0.706611i \(-0.249777\pi\)
\(572\) 15.8269 6.34661i 0.661755 0.265365i
\(573\) 19.5002 + 19.5002i 0.814634 + 0.814634i
\(574\) 7.49951 + 11.3626i 0.313023 + 0.474267i
\(575\) 33.8253 0.0301044i 1.41061 0.00125544i
\(576\) −0.893365 + 0.334951i −0.0372236 + 0.0139563i
\(577\) 2.38287 2.38287i 0.0992004 0.0992004i −0.655765 0.754965i \(-0.727654\pi\)
0.754965 + 0.655765i \(0.227654\pi\)
\(578\) 4.02311 19.6433i 0.167339 0.817054i
\(579\) −15.5403 −0.645835
\(580\) −25.5029 + 24.9537i −1.05895 + 1.03615i
\(581\) −13.4694 −0.558806
\(582\) −5.49356 + 26.8230i −0.227716 + 1.11185i
\(583\) 21.1869 21.1869i 0.877470 0.877470i
\(584\) −1.61922 8.93096i −0.0670036 0.369566i
\(585\) −0.523252 + 0.217011i −0.0216338 + 0.00897230i
\(586\) −0.157711 0.238951i −0.00651500 0.00987098i
\(587\) 18.4563 + 18.4563i 0.761773 + 0.761773i 0.976643 0.214870i \(-0.0689327\pi\)
−0.214870 + 0.976643i \(0.568933\pi\)
\(588\) 2.99644 + 7.47240i 0.123571 + 0.308157i
\(589\) 10.3376i 0.425954i
\(590\) −14.0752 9.51142i −0.579469 0.391579i
\(591\) 9.95619i 0.409543i
\(592\) 34.0136 + 0.770847i 1.39795 + 0.0316816i
\(593\) −21.7190 21.7190i −0.891894 0.891894i 0.102807 0.994701i \(-0.467218\pi\)
−0.994701 + 0.102807i \(0.967218\pi\)
\(594\) 25.0815 16.5542i 1.02911 0.679226i
\(595\) 24.8209 + 10.2682i 1.01756 + 0.420956i
\(596\) −3.56267 + 8.33276i −0.145933 + 0.341323i
\(597\) −12.6007 + 12.6007i −0.515713 + 0.515713i
\(598\) −19.9092 4.07756i −0.814147 0.166744i
\(599\) −8.38180 −0.342471 −0.171236 0.985230i \(-0.554776\pi\)
−0.171236 + 0.985230i \(0.554776\pi\)
\(600\) −19.7405 13.6551i −0.805902 0.557465i
\(601\) 12.0065 0.489754 0.244877 0.969554i \(-0.421252\pi\)
0.244877 + 0.969554i \(0.421252\pi\)
\(602\) 8.26580 + 1.69290i 0.336889 + 0.0689976i
\(603\) −0.0753108 + 0.0753108i −0.00306689 + 0.00306689i
\(604\) 11.3353 26.5123i 0.461229 1.07877i
\(605\) 10.5595 + 4.36840i 0.429306 + 0.177601i
\(606\) 24.5457 16.2005i 0.997100 0.658101i
\(607\) 29.9324 + 29.9324i 1.21492 + 1.21492i 0.969389 + 0.245532i \(0.0789626\pi\)
0.245532 + 0.969389i \(0.421037\pi\)
\(608\) 3.00832 + 4.79062i 0.122003 + 0.194285i
\(609\) 29.1324i 1.18051i
\(610\) −31.5427 21.3151i −1.27713 0.863025i
\(611\) 6.65398i 0.269191i
\(612\) −0.495705 1.23617i −0.0200377 0.0499691i
\(613\) 6.30403 + 6.30403i 0.254617 + 0.254617i 0.822861 0.568243i \(-0.192377\pi\)
−0.568243 + 0.822861i \(0.692377\pi\)
\(614\) −24.8065 37.5847i −1.00111 1.51679i
\(615\) 15.6872 6.50601i 0.632567 0.262348i
\(616\) −24.0319 + 4.35707i −0.968273 + 0.175551i
\(617\) −9.96310 + 9.96310i −0.401099 + 0.401099i −0.878620 0.477521i \(-0.841535\pi\)
0.477521 + 0.878620i \(0.341535\pi\)
\(618\) 1.14183 5.57513i 0.0459312 0.224264i
\(619\) 8.56649 0.344316 0.172158 0.985069i \(-0.444926\pi\)
0.172158 + 0.985069i \(0.444926\pi\)
\(620\) 33.0443 32.3327i 1.32709 1.29851i
\(621\) −35.8158 −1.43724
\(622\) −2.83807 + 13.8572i −0.113796 + 0.555625i
\(623\) 13.4164 13.4164i 0.537516 0.537516i
\(624\) 9.96368 + 10.4258i 0.398866 + 0.417365i
\(625\) 0.0444998 + 25.0000i 0.00177999 + 0.999998i
\(626\) −21.1135 31.9894i −0.843864 1.27855i
\(627\) −4.81717 4.81717i −0.192379 0.192379i
\(628\) 4.60544 1.84679i 0.183777 0.0736949i
\(629\) 47.4931i 1.89367i
\(630\) 0.796583 0.154132i 0.0317366 0.00614077i
\(631\) 25.1719i 1.00208i 0.865425 + 0.501039i \(0.167049\pi\)
−0.865425 + 0.501039i \(0.832951\pi\)
\(632\) 10.5740 + 7.32829i 0.420613 + 0.291504i
\(633\) −19.3124 19.3124i −0.767601 0.767601i
\(634\) 15.1545 10.0022i 0.601861 0.397238i
\(635\) 9.44149 + 22.7651i 0.374674 + 0.903406i
\(636\) 23.2999 + 9.96186i 0.923900 + 0.395013i
\(637\) −3.56232 + 3.56232i −0.141144 + 0.141144i
\(638\) 44.3670 + 9.08672i 1.75651 + 0.359747i
\(639\) −0.766100 −0.0303064
\(640\) 5.90424 24.5996i 0.233385 0.972384i
\(641\) 21.8637 0.863565 0.431783 0.901978i \(-0.357885\pi\)
0.431783 + 0.901978i \(0.357885\pi\)
\(642\) 17.6886 + 3.62277i 0.698114 + 0.142979i
\(643\) −22.8913 + 22.8913i −0.902746 + 0.902746i −0.995673 0.0929271i \(-0.970378\pi\)
0.0929271 + 0.995673i \(0.470378\pi\)
\(644\) 26.7644 + 11.4431i 1.05466 + 0.450922i
\(645\) 4.02338 9.72554i 0.158420 0.382943i
\(646\) −6.59054 + 4.34986i −0.259301 + 0.171143i
\(647\) −6.94398 6.94398i −0.272996 0.272996i 0.557309 0.830305i \(-0.311834\pi\)
−0.830305 + 0.557309i \(0.811834\pi\)
\(648\) 20.0576 + 13.9008i 0.787936 + 0.546075i
\(649\) 21.5619i 0.846379i
\(650\) 3.00060 14.7174i 0.117693 0.577264i
\(651\) 37.7471i 1.47943i
\(652\) −24.7162 + 9.91123i −0.967961 + 0.388154i
\(653\) 3.48781 + 3.48781i 0.136489 + 0.136489i 0.772050 0.635562i \(-0.219231\pi\)
−0.635562 + 0.772050i \(0.719231\pi\)
\(654\) −18.9794 28.7560i −0.742153 1.12445i
\(655\) 3.05481 7.38425i 0.119361 0.288527i
\(656\) 12.3666 + 12.9401i 0.482834 + 0.505226i
\(657\) 0.270621 0.270621i 0.0105579 0.0105579i
\(658\) 1.91224 9.33673i 0.0745468 0.363984i
\(659\) −20.3040 −0.790932 −0.395466 0.918481i \(-0.629417\pi\)
−0.395466 + 0.918481i \(0.629417\pi\)
\(660\) −0.331606 + 30.4646i −0.0129077 + 1.18583i
\(661\) −29.3931 −1.14326 −0.571629 0.820512i \(-0.693688\pi\)
−0.571629 + 0.820512i \(0.693688\pi\)
\(662\) −2.13849 + 10.4414i −0.0831147 + 0.405818i
\(663\) −14.2348 + 14.2348i −0.552836 + 0.552836i
\(664\) −17.4245 + 3.15912i −0.676201 + 0.122598i
\(665\) −1.84290 4.44357i −0.0714647 0.172314i
\(666\) 0.790232 + 1.19729i 0.0306209 + 0.0463941i
\(667\) −38.1654 38.1654i −1.47777 1.47777i
\(668\) 9.41267 + 23.4729i 0.364187 + 0.908194i
\(669\) 27.3887i 1.05891i
\(670\) −0.536479 2.77262i −0.0207260 0.107116i
\(671\) 48.3204i 1.86539i
\(672\) −10.9847 17.4926i −0.423743 0.674793i
\(673\) −22.6855 22.6855i −0.874464 0.874464i 0.118492 0.992955i \(-0.462194\pi\)
−0.992955 + 0.118492i \(0.962194\pi\)
\(674\) 11.9281 7.87271i 0.459452 0.303245i
\(675\) −0.0235593 26.4712i −0.000906797 1.01888i
\(676\) 6.67361 15.6090i 0.256677 0.600345i
\(677\) 19.9465 19.9465i 0.766605 0.766605i −0.210902 0.977507i \(-0.567640\pi\)
0.977507 + 0.210902i \(0.0676401\pi\)
\(678\) −6.52620 1.33662i −0.250637 0.0513325i
\(679\) 24.5400 0.941758
\(680\) 34.5174 + 7.46179i 1.32368 + 0.286147i
\(681\) −4.96672 −0.190325
\(682\) −57.4867 11.7737i −2.20128 0.450839i
\(683\) −6.48834 + 6.48834i −0.248270 + 0.248270i −0.820260 0.571991i \(-0.806171\pi\)
0.571991 + 0.820260i \(0.306171\pi\)
\(684\) −0.0937696 + 0.219318i −0.00358537 + 0.00838585i
\(685\) 45.5073 18.8735i 1.73874 0.721118i
\(686\) 23.7971 15.7065i 0.908578 0.599676i
\(687\) −26.2951 26.2951i −1.00322 1.00322i
\(688\) 11.0900 + 0.251331i 0.422801 + 0.00958189i
\(689\) 15.8569i 0.604098i
\(690\) 20.3299 30.0847i 0.773947 1.14531i
\(691\) 37.0957i 1.41119i 0.708617 + 0.705593i \(0.249319\pi\)
−0.708617 + 0.705593i \(0.750681\pi\)
\(692\) −2.17252 5.41775i −0.0825870 0.205952i
\(693\) −0.728202 0.728202i −0.0276621 0.0276621i
\(694\) −2.68647 4.07032i −0.101977 0.154507i
\(695\) 12.5132 + 5.17661i 0.474652 + 0.196360i
\(696\) 6.83272 + 37.6866i 0.258994 + 1.42851i
\(697\) −17.6678 + 17.6678i −0.669216 + 0.669216i
\(698\) 7.36016 35.9369i 0.278586 1.36023i
\(699\) −21.6838 −0.820157
\(700\) −8.43991 + 19.7889i −0.318999 + 0.747949i
\(701\) 11.2588 0.425239 0.212619 0.977135i \(-0.431801\pi\)
0.212619 + 0.977135i \(0.431801\pi\)
\(702\) −3.19104 + 15.5807i −0.120438 + 0.588054i
\(703\) 6.01436 6.01436i 0.226836 0.226836i
\(704\) −30.0665 + 11.2729i −1.13317 + 0.424863i
\(705\) −10.9856 4.54466i −0.413741 0.171162i
\(706\) −17.2849 26.1886i −0.650526 0.985622i
\(707\) −18.6391 18.6391i −0.700994 0.700994i
\(708\) −16.9253 + 6.78706i −0.636091 + 0.255073i
\(709\) 14.2210i 0.534080i −0.963685 0.267040i \(-0.913954\pi\)
0.963685 0.267040i \(-0.0860455\pi\)
\(710\) 11.3736 16.8309i 0.426843 0.631653i
\(711\) 0.542467i 0.0203441i
\(712\) 14.2092 20.5025i 0.532511 0.768364i
\(713\) 49.4512 + 49.4512i 1.85196 + 1.85196i
\(714\) 24.0649 15.8832i 0.900607 0.594414i
\(715\) −17.6102 + 7.30358i −0.658585 + 0.273138i
\(716\) −3.13769 1.34152i −0.117261 0.0501349i
\(717\) 10.5645 10.5645i 0.394538 0.394538i
\(718\) −21.9906 4.50385i −0.820682 0.168082i
\(719\) −14.7950 −0.551761 −0.275880 0.961192i \(-0.588969\pi\)
−0.275880 + 0.961192i \(0.588969\pi\)
\(720\) 0.994334 0.386221i 0.0370566 0.0143936i
\(721\) −5.10061 −0.189957
\(722\) 1.38545 + 0.283752i 0.0515613 + 0.0105602i
\(723\) 2.59372 2.59372i 0.0964615 0.0964615i
\(724\) 37.0166 + 15.8265i 1.37571 + 0.588186i
\(725\) 28.1826 28.2328i 1.04668 1.04854i
\(726\) 10.2379 6.75718i 0.379964 0.250782i
\(727\) −18.6479 18.6479i −0.691613 0.691613i 0.270973 0.962587i \(-0.412654\pi\)
−0.962587 + 0.270973i \(0.912654\pi\)
\(728\) 7.36260 10.6236i 0.272876 0.393735i
\(729\) 27.9863i 1.03653i
\(730\) 1.92778 + 9.96311i 0.0713503 + 0.368751i
\(731\) 15.4849i 0.572728i
\(732\) −37.9296 + 15.2098i −1.40192 + 0.562172i
\(733\) 4.09933 + 4.09933i 0.151412 + 0.151412i 0.778748 0.627336i \(-0.215855\pi\)
−0.627336 + 0.778748i \(0.715855\pi\)
\(734\) 10.0092 + 15.1651i 0.369446 + 0.559753i
\(735\) −3.44826 8.31437i −0.127191 0.306680i
\(736\) 37.3071 + 8.52585i 1.37516 + 0.314267i
\(737\) −2.53461 + 2.53461i −0.0933636 + 0.0933636i
\(738\) −0.151430 + 0.739376i −0.00557422 + 0.0272168i
\(739\) 14.1367 0.520025 0.260013 0.965605i \(-0.416273\pi\)
0.260013 + 0.965605i \(0.416273\pi\)
\(740\) −38.0359 0.414018i −1.39823 0.0152196i
\(741\) 3.60530 0.132444
\(742\) 4.55698 22.2500i 0.167292 0.816824i
\(743\) 10.3395 10.3395i 0.379321 0.379321i −0.491536 0.870857i \(-0.663565\pi\)
0.870857 + 0.491536i \(0.163565\pi\)
\(744\) −8.85320 48.8308i −0.324574 1.79023i
\(745\) 3.87322 9.36256i 0.141904 0.343018i
\(746\) −4.20020 6.36379i −0.153780 0.232995i
\(747\) −0.527988 0.527988i −0.0193181 0.0193181i
\(748\) −16.6831 41.6036i −0.609996 1.52118i
\(749\) 16.1831i 0.591316i
\(750\) 22.2488 + 15.0059i 0.812410 + 0.547938i
\(751\) 31.7895i 1.16002i −0.814611 0.580008i \(-0.803049\pi\)
0.814611 0.580008i \(-0.196951\pi\)
\(752\) 0.283893 12.5268i 0.0103525 0.456805i
\(753\) 23.4360 + 23.4360i 0.854055 + 0.854055i
\(754\) −20.0032 + 13.2024i −0.728472 + 0.480803i
\(755\) −12.3234 + 29.7888i −0.448495 + 1.08413i
\(756\) 8.95523 20.9454i 0.325698 0.761778i
\(757\) −3.32343 + 3.32343i −0.120792 + 0.120792i −0.764919 0.644127i \(-0.777221\pi\)
0.644127 + 0.764919i \(0.277221\pi\)
\(758\) −15.1024 3.09309i −0.548543 0.112346i
\(759\) −46.0869 −1.67285
\(760\) −3.42623 5.31610i −0.124282 0.192835i
\(761\) −7.45399 −0.270207 −0.135103 0.990831i \(-0.543137\pi\)
−0.135103 + 0.990831i \(0.543137\pi\)
\(762\) 25.9175 + 5.30812i 0.938894 + 0.192293i
\(763\) −21.8362 + 21.8362i −0.790524 + 0.790524i
\(764\) 12.7751 29.8798i 0.462187 1.08101i
\(765\) 0.570450 + 1.37546i 0.0206247 + 0.0497297i
\(766\) 24.2306 15.9925i 0.875486 0.577834i
\(767\) −8.06878 8.06878i −0.291347 0.291347i
\(768\) −18.3128 20.0527i −0.660807 0.723588i
\(769\) 2.73507i 0.0986291i −0.998783 0.0493145i \(-0.984296\pi\)
0.998783 0.0493145i \(-0.0157037\pi\)
\(770\) 26.8093 5.18737i 0.966138 0.186940i
\(771\) 23.6888i 0.853132i
\(772\) 6.81563 + 16.9965i 0.245300 + 0.611718i
\(773\) 22.8002 + 22.8002i 0.820068 + 0.820068i 0.986117 0.166050i \(-0.0531012\pi\)
−0.166050 + 0.986117i \(0.553101\pi\)
\(774\) 0.257651 + 0.390371i 0.00926107 + 0.0140316i
\(775\) −36.5164 + 36.5815i −1.31171 + 1.31405i
\(776\) 31.7457 5.75561i 1.13960 0.206614i
\(777\) −21.9610 + 21.9610i −0.787848 + 0.787848i
\(778\) 4.43760 21.6671i 0.159096 0.776805i
\(779\) 4.47478 0.160326
\(780\) −11.2762 11.5244i −0.403753 0.412639i
\(781\) −25.7834 −0.922601
\(782\) −10.7186 + 52.3347i −0.383295 + 1.87148i
\(783\) −29.8677 + 29.8677i −1.06739 + 1.06739i
\(784\) 6.85841 6.55443i 0.244943 0.234087i
\(785\) −5.12437 + 2.12526i −0.182897 + 0.0758536i
\(786\) −4.72528 7.15935i −0.168545 0.255365i
\(787\) −7.21929 7.21929i −0.257340 0.257340i 0.566632 0.823971i \(-0.308246\pi\)
−0.823971 + 0.566632i \(0.808246\pi\)
\(788\) −10.8891 + 4.36655i −0.387908 + 0.155552i
\(789\) 9.90604i 0.352664i
\(790\) −11.9178 8.05351i −0.424016 0.286531i
\(791\) 5.97073i 0.212295i
\(792\) −1.11282 0.771232i −0.0395422 0.0274045i
\(793\) −18.0822 18.0822i −0.642117 0.642117i
\(794\) 7.38795 4.87616i 0.262189 0.173048i
\(795\) −26.1794 10.8302i −0.928487 0.384108i
\(796\) 19.3078 + 8.25505i 0.684347 + 0.292593i
\(797\) 24.0462 24.0462i 0.851760 0.851760i −0.138590 0.990350i \(-0.544257\pi\)
0.990350 + 0.138590i \(0.0442569\pi\)
\(798\) −5.05889 1.03610i −0.179083 0.0366776i
\(799\) 17.4911 0.618791
\(800\) −6.27685 + 27.5790i −0.221920 + 0.975065i
\(801\) 1.05182 0.0371641
\(802\) 16.3376 + 3.34607i 0.576900 + 0.118154i
\(803\) 9.10785 9.10785i 0.321409 0.321409i
\(804\) −2.78739 1.19175i −0.0983038 0.0420298i
\(805\) −30.0720 12.4406i −1.05990 0.438473i
\(806\) 25.9182 17.1064i 0.912931 0.602549i
\(807\) 20.5883 + 20.5883i 0.724742 + 0.724742i
\(808\) −28.4837 19.7405i −1.00205 0.694468i
\(809\) 49.8101i 1.75123i 0.483009 + 0.875615i \(0.339544\pi\)
−0.483009 + 0.875615i \(0.660456\pi\)
\(810\) −22.6065 15.2764i −0.794311 0.536760i
\(811\) 21.6879i 0.761564i −0.924665 0.380782i \(-0.875655\pi\)
0.924665 0.380782i \(-0.124345\pi\)
\(812\) 31.8622 12.7768i 1.11814 0.448378i
\(813\) −29.2245 29.2245i −1.02495 1.02495i
\(814\) 26.5955 + 40.2953i 0.932172 + 1.41235i
\(815\) 27.5012 11.4057i 0.963324 0.399524i
\(816\) 27.4059 26.1912i 0.959398 0.916876i
\(817\) 1.96095 1.96095i 0.0686049 0.0686049i
\(818\) 6.78743 33.1405i 0.237317 1.15873i
\(819\) 0.545007 0.0190441
\(820\) −13.9957 14.3037i −0.488749 0.499506i
\(821\) 33.5950 1.17247 0.586236 0.810140i \(-0.300609\pi\)
0.586236 + 0.810140i \(0.300609\pi\)
\(822\) 10.6109 51.8089i 0.370097 1.80704i
\(823\) −33.8797 + 33.8797i −1.18097 + 1.18097i −0.201479 + 0.979493i \(0.564575\pi\)
−0.979493 + 0.201479i \(0.935425\pi\)
\(824\) −6.59831 + 1.19630i −0.229863 + 0.0416750i
\(825\) −0.0303155 34.0625i −0.00105545 1.18590i
\(826\) 9.00313 + 13.6408i 0.313259 + 0.474624i
\(827\) −25.8243 25.8243i −0.897997 0.897997i 0.0972616 0.995259i \(-0.468992\pi\)
−0.995259 + 0.0972616i \(0.968992\pi\)
\(828\) 0.600577 + 1.49769i 0.0208715 + 0.0520484i
\(829\) 38.9493i 1.35276i −0.736551 0.676382i \(-0.763547\pi\)
0.736551 0.676382i \(-0.236453\pi\)
\(830\) 19.4382 3.76114i 0.674711 0.130551i
\(831\) 25.2039i 0.874315i
\(832\) 7.03284 15.4698i 0.243820 0.536318i
\(833\) 9.36415 + 9.36415i 0.324448 + 0.324448i
\(834\) 12.1321 8.00735i 0.420099 0.277272i
\(835\) −10.8320 26.1178i −0.374855 0.903843i
\(836\) −3.15585 + 7.38124i −0.109147 + 0.255285i
\(837\) 38.6998 38.6998i 1.33766 1.33766i
\(838\) −32.8353 6.72493i −1.13428 0.232309i
\(839\) −16.6669 −0.575406 −0.287703 0.957720i \(-0.592892\pi\)
−0.287703 + 0.957720i \(0.592892\pi\)
\(840\) 12.5106 + 19.4114i 0.431658 + 0.669757i
\(841\) −34.6542 −1.19497
\(842\) −38.3207 7.84838i −1.32062 0.270473i
\(843\) 1.81037 1.81037i 0.0623526 0.0623526i
\(844\) −12.6521 + 29.5920i −0.435502 + 1.01860i
\(845\) −7.25533 + 17.5380i −0.249591 + 0.603325i
\(846\) 0.440948 0.291032i 0.0151601 0.0100059i
\(847\) −7.77429 7.77429i −0.267128 0.267128i
\(848\) 0.676536 29.8521i 0.0232323 1.02513i
\(849\) 29.9599i 1.02822i
\(850\) −38.6872 7.88757i −1.32696 0.270542i
\(851\) 57.5408i 1.97247i
\(852\) −8.11584 20.2389i −0.278044 0.693374i
\(853\) 23.5705 + 23.5705i 0.807039 + 0.807039i 0.984185 0.177145i \(-0.0566863\pi\)
−0.177145 + 0.984185i \(0.556686\pi\)
\(854\) 20.1761 + 30.5691i 0.690411 + 1.04605i
\(855\) 0.101943 0.246423i 0.00348639 0.00842749i
\(856\) −3.79558 20.9349i −0.129730 0.715541i
\(857\) −5.00669 + 5.00669i −0.171025 + 0.171025i −0.787430 0.616404i \(-0.788589\pi\)
0.616404 + 0.787430i \(0.288589\pi\)
\(858\) −4.10616 + 20.0488i −0.140182 + 0.684456i
\(859\) 10.6947 0.364898 0.182449 0.983215i \(-0.441598\pi\)
0.182449 + 0.983215i \(0.441598\pi\)
\(860\) −12.4014 0.134988i −0.422884 0.00460307i
\(861\) −16.3394 −0.556844
\(862\) 3.32302 16.2251i 0.113182 0.552627i
\(863\) 30.2137 30.2137i 1.02849 1.02849i 0.0289054 0.999582i \(-0.490798\pi\)
0.999582 0.0289054i \(-0.00920215\pi\)
\(864\) 6.67222 29.1960i 0.226994 0.993270i
\(865\) 2.50011 + 6.02820i 0.0850062 + 0.204965i
\(866\) −4.48366 6.79327i −0.152361 0.230845i
\(867\) 17.0161 + 17.0161i 0.577896 + 0.577896i
\(868\) −41.2841 + 16.5550i −1.40127 + 0.561913i
\(869\) 18.2569i 0.619323i
\(870\) −8.13479 42.0421i −0.275795 1.42536i
\(871\) 1.89698i 0.0642766i
\(872\) −23.1265 + 33.3695i −0.783163 + 1.13003i
\(873\) 0.961942 + 0.961942i 0.0325568 + 0.0325568i
\(874\) 7.98484 5.27012i 0.270091 0.178265i
\(875\) 9.17495 22.2342i 0.310170 0.751653i
\(876\) 10.0162 + 4.28242i 0.338416 + 0.144690i
\(877\) 6.44438 6.44438i 0.217611 0.217611i −0.589880 0.807491i \(-0.700825\pi\)
0.807491 + 0.589880i \(0.200825\pi\)
\(878\) −35.6071 7.29262i −1.20168 0.246114i
\(879\) 0.343610 0.0115897
\(880\) 33.4647 12.9984i 1.12809 0.438175i
\(881\) 27.9286 0.940938 0.470469 0.882417i \(-0.344085\pi\)
0.470469 + 0.882417i \(0.344085\pi\)
\(882\) 0.391878 + 0.0802596i 0.0131952 + 0.00270248i
\(883\) −24.6095 + 24.6095i −0.828175 + 0.828175i −0.987264 0.159089i \(-0.949144\pi\)
0.159089 + 0.987264i \(0.449144\pi\)
\(884\) 21.8117 + 9.32561i 0.733608 + 0.313654i
\(885\) 18.8324 7.81044i 0.633043 0.262545i
\(886\) −29.6043 + 19.5393i −0.994575 + 0.656435i
\(887\) 12.1805 + 12.1805i 0.408980 + 0.408980i 0.881383 0.472403i \(-0.156613\pi\)
−0.472403 + 0.881383i \(0.656613\pi\)
\(888\) −23.2587 + 33.5602i −0.780512 + 1.12621i
\(889\) 23.7116i 0.795262i
\(890\) −15.6153 + 23.1080i −0.523427 + 0.774581i
\(891\) 34.6309i 1.16018i
\(892\) 29.9551 12.0121i 1.00297 0.402193i
\(893\) −2.21501 2.21501i −0.0741226 0.0741226i
\(894\) −5.99122 9.07739i −0.200376 0.303593i
\(895\) 3.52546 + 1.45846i 0.117843 + 0.0487508i
\(896\) −14.3141 + 19.6858i −0.478201 + 0.657656i
\(897\) 17.2464 17.2464i 0.575840 0.575840i
\(898\) −1.60700 + 7.84636i −0.0536262 + 0.261836i
\(899\) 82.4772 2.75077
\(900\) −1.10654 + 0.444867i −0.0368846 + 0.0148289i
\(901\) 41.6824 1.38864
\(902\) −5.09643 + 24.8839i −0.169692 + 0.828544i
\(903\) −7.16027 + 7.16027i −0.238279 + 0.238279i
\(904\) 1.40037 + 7.72392i 0.0465757 + 0.256894i
\(905\) −41.5913 17.2060i −1.38254 0.571947i
\(906\) 19.0623 + 28.8815i 0.633301 + 0.959525i
\(907\) 37.7176 + 37.7176i 1.25239 + 1.25239i 0.954644 + 0.297749i \(0.0962360\pi\)
0.297749 + 0.954644i \(0.403764\pi\)
\(908\) 2.17828 + 5.43211i 0.0722889 + 0.180271i
\(909\) 1.46126i 0.0484671i
\(910\) −8.09122 + 11.9736i −0.268221 + 0.396921i
\(911\) 47.4298i 1.57142i −0.618596 0.785709i \(-0.712298\pi\)
0.618596 0.785709i \(-0.287702\pi\)
\(912\) −6.78735 0.153821i −0.224752 0.00509352i
\(913\) −17.7696 17.7696i −0.588088 0.588088i
\(914\) 32.9818 21.7685i 1.09094 0.720037i
\(915\) 42.2034 17.5032i 1.39520 0.578639i
\(916\) −17.2266 + 40.2914i −0.569183 + 1.33127i
\(917\) −5.43654 + 5.43654i −0.179530 + 0.179530i
\(918\) 40.9564 + 8.38820i 1.35176 + 0.276852i
\(919\) −24.1651 −0.797132 −0.398566 0.917140i \(-0.630492\pi\)
−0.398566 + 0.917140i \(0.630492\pi\)
\(920\) −41.8200 9.04042i −1.37876 0.298054i
\(921\) 54.0465 1.78089
\(922\) 43.4112 + 8.89096i 1.42967 + 0.292808i
\(923\) 9.64850 9.64850i 0.317584 0.317584i
\(924\) 11.5234 26.9521i 0.379091 0.886659i
\(925\) 42.5279 0.0378497i 1.39831 0.00124449i
\(926\) −15.9360 + 10.5180i −0.523690 + 0.345644i
\(927\) −0.199938 0.199938i −0.00656684 0.00656684i
\(928\) 38.2213 24.0014i 1.25467 0.787885i
\(929\) 52.8659i 1.73447i −0.497896 0.867237i \(-0.665894\pi\)
0.497896 0.867237i \(-0.334106\pi\)
\(930\) 10.5403 + 54.4742i 0.345630 + 1.78628i
\(931\) 2.37169i 0.0777289i
\(932\) 9.51000 + 23.7156i 0.311510 + 0.776831i
\(933\) −12.0039 12.0039i −0.392989 0.392989i
\(934\) 19.4554 + 29.4771i 0.636599 + 0.964521i
\(935\) 19.1987 + 46.2914i 0.627864 + 1.51389i
\(936\) 0.705038 0.127826i 0.0230449 0.00417812i
\(937\) −19.2914 + 19.2914i −0.630222 + 0.630222i −0.948124 0.317902i \(-0.897022\pi\)
0.317902 + 0.948124i \(0.397022\pi\)
\(938\) −0.545158 + 2.66180i −0.0178000 + 0.0869109i
\(939\) 46.0005 1.50117
\(940\) −0.152478 + 14.0081i −0.00497328 + 0.456895i
\(941\) −57.1900 −1.86434 −0.932170 0.362020i \(-0.882087\pi\)
−0.932170 + 0.362020i \(0.882087\pi\)
\(942\) −1.19484 + 5.83397i −0.0389301 + 0.190081i
\(943\) 21.4056 21.4056i 0.697064 0.697064i
\(944\) 14.8460 + 15.5346i 0.483197 + 0.505607i
\(945\) −9.73583 + 23.5340i −0.316706 + 0.765561i
\(946\) 8.67132 + 13.1381i 0.281929 + 0.427155i
\(947\) 26.9305 + 26.9305i 0.875124 + 0.875124i 0.993025 0.117901i \(-0.0376166\pi\)
−0.117901 + 0.993025i \(0.537617\pi\)
\(948\) −14.3310 + 5.74674i −0.465448 + 0.186645i
\(949\) 6.81658i 0.221275i
\(950\) 3.90036 + 5.89807i 0.126544 + 0.191359i
\(951\) 21.7920i 0.706655i
\(952\) −27.9258 19.3538i −0.905080 0.627261i
\(953\) −10.7214 10.7214i −0.347301 0.347301i 0.511802 0.859103i \(-0.328978\pi\)
−0.859103 + 0.511802i \(0.828978\pi\)
\(954\) 1.05081 0.693549i 0.0340211 0.0224545i
\(955\) −13.8887 + 33.5725i −0.449427 + 1.08638i
\(956\) −16.1877 6.92107i −0.523549 0.223843i
\(957\) −38.4331 + 38.4331i −1.24236 + 1.24236i
\(958\) 30.0799 + 6.16060i 0.971837 + 0.199040i
\(959\) −47.3993 −1.53060
\(960\) 20.7369 + 22.1769i 0.669281 + 0.715758i
\(961\) −75.8663 −2.44730
\(962\) −25.0315 5.12665i −0.807048 0.165290i
\(963\) 0.634359 0.634359i 0.0204419 0.0204419i
\(964\) −3.97430 1.69921i −0.128004 0.0547280i
\(965\) −7.84332 18.9116i −0.252485 0.608787i
\(966\) −29.1561 + 19.2435i −0.938083 + 0.619149i
\(967\) −28.2118 28.2118i −0.907231 0.907231i 0.0888168 0.996048i \(-0.471691\pi\)
−0.996048 + 0.0888168i \(0.971691\pi\)
\(968\) −11.8804 8.23368i −0.381852 0.264641i
\(969\) 9.47715i 0.304450i
\(970\) −35.4146 + 6.85242i −1.13709 + 0.220018i
\(971\) 15.3403i 0.492294i 0.969232 + 0.246147i \(0.0791646\pi\)
−0.969232 + 0.246147i \(0.920835\pi\)
\(972\) 2.29934 0.922038i 0.0737513 0.0295744i
\(973\) −9.21264 9.21264i −0.295344 0.295344i
\(974\) −12.4470 18.8587i −0.398829 0.604272i
\(975\) 12.7580 + 12.7353i 0.408583 + 0.407857i
\(976\) 33.2701 + 34.8130i 1.06495 + 1.11434i
\(977\) 43.0518 43.0518i 1.37735 1.37735i 0.528276 0.849073i \(-0.322839\pi\)
0.849073 0.528276i \(-0.177161\pi\)
\(978\) 6.41242 31.3094i 0.205047 1.00116i
\(979\) 35.3992 1.13136
\(980\) −7.58112 + 7.41786i −0.242170 + 0.236955i
\(981\) −1.71191 −0.0546572
\(982\) 6.00423 29.3164i 0.191603 0.935523i
\(983\) −19.7481 + 19.7481i −0.629867 + 0.629867i −0.948034 0.318168i \(-0.896932\pi\)
0.318168 + 0.948034i \(0.396932\pi\)
\(984\) −21.1371 + 3.83224i −0.673827 + 0.122167i
\(985\) 12.1161 5.02496i 0.386050 0.160108i
\(986\) 34.7047 + 52.5817i 1.10522 + 1.67454i
\(987\) 8.08797 + 8.08797i 0.257443 + 0.257443i
\(988\) −1.58120 3.94313i −0.0503047 0.125448i
\(989\) 18.7609i 0.596560i
\(990\) 1.25423 + 0.847555i 0.0398622 + 0.0269371i
\(991\) 34.3112i 1.08993i −0.838458 0.544966i \(-0.816543\pi\)
0.838458 0.544966i \(-0.183457\pi\)
\(992\) −49.5236 + 31.0988i −1.57237 + 0.987388i
\(993\) −9.04492 9.04492i −0.287032 0.287032i
\(994\) −16.3114 + 10.7658i −0.517366 + 0.341470i
\(995\) −21.6940 8.97462i −0.687745 0.284515i
\(996\) 8.35510 19.5418i 0.264741 0.619206i
\(997\) −5.61418 + 5.61418i −0.177803 + 0.177803i −0.790397 0.612594i \(-0.790126\pi\)
0.612594 + 0.790397i \(0.290126\pi\)
\(998\) −33.3561 6.83159i −1.05587 0.216250i
\(999\) −45.0306 −1.42471
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 380.2.k.c.343.25 yes 52
4.3 odd 2 380.2.k.d.343.11 yes 52
5.2 odd 4 380.2.k.d.267.11 yes 52
20.7 even 4 inner 380.2.k.c.267.25 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
380.2.k.c.267.25 52 20.7 even 4 inner
380.2.k.c.343.25 yes 52 1.1 even 1 trivial
380.2.k.d.267.11 yes 52 5.2 odd 4
380.2.k.d.343.11 yes 52 4.3 odd 2