Properties

Label 304.2.k.b.77.18
Level $304$
Weight $2$
Character 304.77
Analytic conductor $2.427$
Analytic rank $0$
Dimension $68$
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] = [304,2,Mod(77,304)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(304, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("304.77");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 304.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: \(2.42745222145\)
Analytic rank: \(0\)
Dimension: \(68\)
Relative dimension: \(34\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 77.18
Character \(\chi\) \(=\) 304.77
Dual form 304.2.k.b.229.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0411449 - 1.41361i) q^{2} +(1.66448 + 1.66448i) q^{3} +(-1.99661 - 0.116326i) q^{4} +(-2.15868 + 2.15868i) q^{5} +(2.42142 - 2.28445i) q^{6} +1.65346i q^{7} +(-0.246591 + 2.81766i) q^{8} +2.54100i q^{9} +O(q^{10})\) \(q+(0.0411449 - 1.41361i) q^{2} +(1.66448 + 1.66448i) q^{3} +(-1.99661 - 0.116326i) q^{4} +(-2.15868 + 2.15868i) q^{5} +(2.42142 - 2.28445i) q^{6} +1.65346i q^{7} +(-0.246591 + 2.81766i) q^{8} +2.54100i q^{9} +(2.96272 + 3.14036i) q^{10} +(-2.90962 + 2.90962i) q^{11} +(-3.12970 - 3.51695i) q^{12} +(-1.83379 - 1.83379i) q^{13} +(2.33735 + 0.0680314i) q^{14} -7.18615 q^{15} +(3.97294 + 0.464517i) q^{16} +6.74010 q^{17} +(3.59199 + 0.104549i) q^{18} +(0.707107 + 0.707107i) q^{19} +(4.56115 - 4.05893i) q^{20} +(-2.75215 + 2.75215i) q^{21} +(3.99336 + 4.23279i) q^{22} +2.23617i q^{23} +(-5.10038 + 4.27949i) q^{24} -4.31977i q^{25} +(-2.66772 + 2.51682i) q^{26} +(0.764004 - 0.764004i) q^{27} +(0.192340 - 3.30132i) q^{28} +(-3.73185 - 3.73185i) q^{29} +(-0.295674 + 10.1585i) q^{30} +6.94654 q^{31} +(0.820115 - 5.59709i) q^{32} -9.68600 q^{33} +(0.277321 - 9.52791i) q^{34} +(-3.56928 - 3.56928i) q^{35} +(0.295584 - 5.07339i) q^{36} +(-1.89479 + 1.89479i) q^{37} +(1.02867 - 0.970483i) q^{38} -6.10461i q^{39} +(-5.55010 - 6.61472i) q^{40} +6.17447i q^{41} +(3.77724 + 4.00372i) q^{42} +(4.55725 - 4.55725i) q^{43} +(6.14784 - 5.47092i) q^{44} +(-5.48519 - 5.48519i) q^{45} +(3.16108 + 0.0920071i) q^{46} +8.44701 q^{47} +(5.83970 + 7.38606i) q^{48} +4.26608 q^{49} +(-6.10649 - 0.177737i) q^{50} +(11.2188 + 11.2188i) q^{51} +(3.44805 + 3.87469i) q^{52} +(-4.47968 + 4.47968i) q^{53} +(-1.04857 - 1.11144i) q^{54} -12.5618i q^{55} +(-4.65888 - 0.407728i) q^{56} +2.35393i q^{57} +(-5.42895 + 5.12186i) q^{58} +(1.79258 - 1.79258i) q^{59} +(14.3480 + 0.835938i) q^{60} +(-7.56656 - 7.56656i) q^{61} +(0.285815 - 9.81974i) q^{62} -4.20143 q^{63} +(-7.87839 - 1.38962i) q^{64} +7.91711 q^{65} +(-0.398530 + 13.6923i) q^{66} +(-4.88385 - 4.88385i) q^{67} +(-13.4574 - 0.784051i) q^{68} +(-3.72206 + 3.72206i) q^{69} +(-5.19244 + 4.89873i) q^{70} +12.6271i q^{71} +(-7.15966 - 0.626587i) q^{72} -4.06266i q^{73} +(2.60054 + 2.75647i) q^{74} +(7.19017 - 7.19017i) q^{75} +(-1.32956 - 1.49407i) q^{76} +(-4.81093 - 4.81093i) q^{77} +(-8.62957 - 0.251174i) q^{78} -7.88110 q^{79} +(-9.57903 + 7.57354i) q^{80} +10.1663 q^{81} +(8.72832 + 0.254048i) q^{82} +(7.61886 + 7.61886i) q^{83} +(5.81513 - 5.17483i) q^{84} +(-14.5497 + 14.5497i) q^{85} +(-6.25469 - 6.62970i) q^{86} -12.4232i q^{87} +(-7.48082 - 8.91579i) q^{88} +9.46463i q^{89} +(-7.97963 + 7.52826i) q^{90} +(3.03209 - 3.03209i) q^{91} +(0.260125 - 4.46477i) q^{92} +(11.5624 + 11.5624i) q^{93} +(0.347552 - 11.9408i) q^{94} -3.05283 q^{95} +(10.6813 - 7.95119i) q^{96} -14.3016 q^{97} +(0.175528 - 6.03059i) q^{98} +(-7.39332 - 7.39332i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(191\) \(229\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0411449 1.41361i 0.0290939 0.999577i
\(3\) 1.66448 + 1.66448i 0.960989 + 0.960989i 0.999267 0.0382784i \(-0.0121874\pi\)
−0.0382784 + 0.999267i \(0.512187\pi\)
\(4\) −1.99661 0.116326i −0.998307 0.0581631i
\(5\) −2.15868 + 2.15868i −0.965389 + 0.965389i −0.999421 0.0340313i \(-0.989165\pi\)
0.0340313 + 0.999421i \(0.489165\pi\)
\(6\) 2.42142 2.28445i 0.988541 0.932623i
\(7\) 1.65346i 0.624948i 0.949926 + 0.312474i \(0.101158\pi\)
−0.949926 + 0.312474i \(0.898842\pi\)
\(8\) −0.246591 + 2.81766i −0.0871831 + 0.996192i
\(9\) 2.54100i 0.846999i
\(10\) 2.96272 + 3.14036i 0.936894 + 0.993068i
\(11\) −2.90962 + 2.90962i −0.877282 + 0.877282i −0.993253 0.115970i \(-0.963002\pi\)
0.115970 + 0.993253i \(0.463002\pi\)
\(12\) −3.12970 3.51695i −0.903468 1.01526i
\(13\) −1.83379 1.83379i −0.508601 0.508601i 0.405496 0.914097i \(-0.367099\pi\)
−0.914097 + 0.405496i \(0.867099\pi\)
\(14\) 2.33735 + 0.0680314i 0.624684 + 0.0181822i
\(15\) −7.18615 −1.85546
\(16\) 3.97294 + 0.464517i 0.993234 + 0.116129i
\(17\) 6.74010 1.63471 0.817357 0.576131i \(-0.195438\pi\)
0.817357 + 0.576131i \(0.195438\pi\)
\(18\) 3.59199 + 0.104549i 0.846640 + 0.0246425i
\(19\) 0.707107 + 0.707107i 0.162221 + 0.162221i
\(20\) 4.56115 4.05893i 1.01991 0.907605i
\(21\) −2.75215 + 2.75215i −0.600568 + 0.600568i
\(22\) 3.99336 + 4.23279i 0.851387 + 0.902434i
\(23\) 2.23617i 0.466274i 0.972444 + 0.233137i \(0.0748990\pi\)
−0.972444 + 0.233137i \(0.925101\pi\)
\(24\) −5.10038 + 4.27949i −1.04111 + 0.873548i
\(25\) 4.31977i 0.863954i
\(26\) −2.66772 + 2.51682i −0.523183 + 0.493589i
\(27\) 0.764004 0.764004i 0.147033 0.147033i
\(28\) 0.192340 3.30132i 0.0363489 0.623890i
\(29\) −3.73185 3.73185i −0.692988 0.692988i 0.269900 0.962888i \(-0.413009\pi\)
−0.962888 + 0.269900i \(0.913009\pi\)
\(30\) −0.295674 + 10.1585i −0.0539824 + 1.85467i
\(31\) 6.94654 1.24764 0.623818 0.781570i \(-0.285581\pi\)
0.623818 + 0.781570i \(0.285581\pi\)
\(32\) 0.820115 5.59709i 0.144977 0.989435i
\(33\) −9.68600 −1.68612
\(34\) 0.277321 9.52791i 0.0475602 1.63402i
\(35\) −3.56928 3.56928i −0.603318 0.603318i
\(36\) 0.295584 5.07339i 0.0492641 0.845565i
\(37\) −1.89479 + 1.89479i −0.311502 + 0.311502i −0.845491 0.533989i \(-0.820692\pi\)
0.533989 + 0.845491i \(0.320692\pi\)
\(38\) 1.02867 0.970483i 0.166872 0.157433i
\(39\) 6.10461i 0.977520i
\(40\) −5.55010 6.61472i −0.877548 1.04588i
\(41\) 6.17447i 0.964290i 0.876092 + 0.482145i \(0.160142\pi\)
−0.876092 + 0.482145i \(0.839858\pi\)
\(42\) 3.77724 + 4.00372i 0.582841 + 0.617787i
\(43\) 4.55725 4.55725i 0.694974 0.694974i −0.268348 0.963322i \(-0.586478\pi\)
0.963322 + 0.268348i \(0.0864777\pi\)
\(44\) 6.14784 5.47092i 0.926822 0.824772i
\(45\) −5.48519 5.48519i −0.817684 0.817684i
\(46\) 3.16108 + 0.0920071i 0.466076 + 0.0135657i
\(47\) 8.44701 1.23212 0.616062 0.787698i \(-0.288727\pi\)
0.616062 + 0.787698i \(0.288727\pi\)
\(48\) 5.83970 + 7.38606i 0.842888 + 1.06609i
\(49\) 4.26608 0.609440
\(50\) −6.10649 0.177737i −0.863588 0.0251358i
\(51\) 11.2188 + 11.2188i 1.57094 + 1.57094i
\(52\) 3.44805 + 3.87469i 0.478159 + 0.537322i
\(53\) −4.47968 + 4.47968i −0.615332 + 0.615332i −0.944330 0.328999i \(-0.893289\pi\)
0.328999 + 0.944330i \(0.393289\pi\)
\(54\) −1.04857 1.11144i −0.142693 0.151248i
\(55\) 12.5618i 1.69384i
\(56\) −4.65888 0.407728i −0.622569 0.0544849i
\(57\) 2.35393i 0.311786i
\(58\) −5.42895 + 5.12186i −0.712856 + 0.672533i
\(59\) 1.79258 1.79258i 0.233375 0.233375i −0.580725 0.814100i \(-0.697231\pi\)
0.814100 + 0.580725i \(0.197231\pi\)
\(60\) 14.3480 + 0.835938i 1.85232 + 0.107919i
\(61\) −7.56656 7.56656i −0.968798 0.968798i 0.0307295 0.999528i \(-0.490217\pi\)
−0.999528 + 0.0307295i \(0.990217\pi\)
\(62\) 0.285815 9.81974i 0.0362986 1.24711i
\(63\) −4.20143 −0.529330
\(64\) −7.87839 1.38962i −0.984798 0.173702i
\(65\) 7.91711 0.981997
\(66\) −0.398530 + 13.6923i −0.0490557 + 1.68540i
\(67\) −4.88385 4.88385i −0.596657 0.596657i 0.342764 0.939421i \(-0.388637\pi\)
−0.939421 + 0.342764i \(0.888637\pi\)
\(68\) −13.4574 0.784051i −1.63195 0.0950801i
\(69\) −3.72206 + 3.72206i −0.448084 + 0.448084i
\(70\) −5.19244 + 4.89873i −0.620616 + 0.585510i
\(71\) 12.6271i 1.49856i 0.662254 + 0.749280i \(0.269600\pi\)
−0.662254 + 0.749280i \(0.730400\pi\)
\(72\) −7.15966 0.626587i −0.843774 0.0738440i
\(73\) 4.06266i 0.475498i −0.971327 0.237749i \(-0.923590\pi\)
0.971327 0.237749i \(-0.0764096\pi\)
\(74\) 2.60054 + 2.75647i 0.302307 + 0.320433i
\(75\) 7.19017 7.19017i 0.830250 0.830250i
\(76\) −1.32956 1.49407i −0.152511 0.171382i
\(77\) −4.81093 4.81093i −0.548256 0.548256i
\(78\) −8.62957 0.251174i −0.977107 0.0284399i
\(79\) −7.88110 −0.886693 −0.443346 0.896350i \(-0.646209\pi\)
−0.443346 + 0.896350i \(0.646209\pi\)
\(80\) −9.57903 + 7.57354i −1.07097 + 0.846748i
\(81\) 10.1663 1.12959
\(82\) 8.72832 + 0.254048i 0.963881 + 0.0280549i
\(83\) 7.61886 + 7.61886i 0.836279 + 0.836279i 0.988367 0.152088i \(-0.0485997\pi\)
−0.152088 + 0.988367i \(0.548600\pi\)
\(84\) 5.81513 5.17483i 0.634482 0.564621i
\(85\) −14.5497 + 14.5497i −1.57814 + 1.57814i
\(86\) −6.25469 6.62970i −0.674460 0.714899i
\(87\) 12.4232i 1.33191i
\(88\) −7.48082 8.91579i −0.797458 0.950426i
\(89\) 9.46463i 1.00325i 0.865086 + 0.501624i \(0.167264\pi\)
−0.865086 + 0.501624i \(0.832736\pi\)
\(90\) −7.97963 + 7.52826i −0.841127 + 0.793548i
\(91\) 3.03209 3.03209i 0.317849 0.317849i
\(92\) 0.260125 4.46477i 0.0271199 0.465484i
\(93\) 11.5624 + 11.5624i 1.19896 + 1.19896i
\(94\) 0.347552 11.9408i 0.0358472 1.23160i
\(95\) −3.05283 −0.313214
\(96\) 10.6813 7.95119i 1.09016 0.811514i
\(97\) −14.3016 −1.45211 −0.726056 0.687635i \(-0.758649\pi\)
−0.726056 + 0.687635i \(0.758649\pi\)
\(98\) 0.175528 6.03059i 0.0177310 0.609182i
\(99\) −7.39332 7.39332i −0.743057 0.743057i
\(100\) −0.502502 + 8.62491i −0.0502502 + 0.862491i
\(101\) 0.159188 0.159188i 0.0158398 0.0158398i −0.699143 0.714982i \(-0.746435\pi\)
0.714982 + 0.699143i \(0.246435\pi\)
\(102\) 16.3206 15.3974i 1.61598 1.52457i
\(103\) 10.2611i 1.01106i −0.862810 0.505528i \(-0.831298\pi\)
0.862810 0.505528i \(-0.168702\pi\)
\(104\) 5.61918 4.71479i 0.551006 0.462323i
\(105\) 11.8820i 1.15956i
\(106\) 6.14823 + 6.51686i 0.597169 + 0.632974i
\(107\) 3.76195 3.76195i 0.363682 0.363682i −0.501485 0.865166i \(-0.667213\pi\)
0.865166 + 0.501485i \(0.167213\pi\)
\(108\) −1.61429 + 1.43655i −0.155336 + 0.138232i
\(109\) 12.0574 + 12.0574i 1.15489 + 1.15489i 0.985560 + 0.169327i \(0.0541594\pi\)
0.169327 + 0.985560i \(0.445841\pi\)
\(110\) −17.7576 0.516856i −1.69312 0.0492803i
\(111\) −6.30769 −0.598699
\(112\) −0.768059 + 6.56908i −0.0725748 + 0.620720i
\(113\) −18.0518 −1.69817 −0.849084 0.528258i \(-0.822846\pi\)
−0.849084 + 0.528258i \(0.822846\pi\)
\(114\) 3.32755 + 0.0968524i 0.311654 + 0.00907106i
\(115\) −4.82717 4.82717i −0.450136 0.450136i
\(116\) 7.01696 + 7.88519i 0.651508 + 0.732121i
\(117\) 4.65965 4.65965i 0.430785 0.430785i
\(118\) −2.46027 2.60778i −0.226486 0.240066i
\(119\) 11.1445i 1.02161i
\(120\) 1.77204 20.2481i 0.161764 1.84839i
\(121\) 5.93173i 0.539248i
\(122\) −11.0075 + 10.3849i −0.996574 + 0.940202i
\(123\) −10.2773 + 10.2773i −0.926671 + 0.926671i
\(124\) −13.8696 0.808065i −1.24552 0.0725664i
\(125\) −1.46840 1.46840i −0.131338 0.131338i
\(126\) −0.172868 + 5.93920i −0.0154003 + 0.529106i
\(127\) 18.9412 1.68076 0.840380 0.541997i \(-0.182332\pi\)
0.840380 + 0.541997i \(0.182332\pi\)
\(128\) −2.28854 + 11.0798i −0.202280 + 0.979328i
\(129\) 15.1709 1.33572
\(130\) 0.325749 11.1917i 0.0285701 0.981581i
\(131\) 6.28136 + 6.28136i 0.548805 + 0.548805i 0.926095 0.377290i \(-0.123144\pi\)
−0.377290 + 0.926095i \(0.623144\pi\)
\(132\) 19.3392 + 1.12674i 1.68326 + 0.0980698i
\(133\) −1.16917 + 1.16917i −0.101380 + 0.101380i
\(134\) −7.10483 + 6.70294i −0.613764 + 0.579046i
\(135\) 3.29847i 0.283887i
\(136\) −1.66205 + 18.9913i −0.142520 + 1.62849i
\(137\) 19.5253i 1.66816i −0.551645 0.834079i \(-0.686000\pi\)
0.551645 0.834079i \(-0.314000\pi\)
\(138\) 5.10842 + 5.41471i 0.434858 + 0.460931i
\(139\) 8.73082 8.73082i 0.740539 0.740539i −0.232143 0.972682i \(-0.574574\pi\)
0.972682 + 0.232143i \(0.0745737\pi\)
\(140\) 6.71127 + 7.54168i 0.567206 + 0.637388i
\(141\) 14.0599 + 14.0599i 1.18406 + 1.18406i
\(142\) 17.8498 + 0.519541i 1.49793 + 0.0435989i
\(143\) 10.6712 0.892374
\(144\) −1.18034 + 10.0952i −0.0983614 + 0.841268i
\(145\) 16.1117 1.33801
\(146\) −5.74303 0.167158i −0.475297 0.0138341i
\(147\) 7.10081 + 7.10081i 0.585665 + 0.585665i
\(148\) 4.00358 3.56275i 0.329092 0.292856i
\(149\) 0.282217 0.282217i 0.0231201 0.0231201i −0.695452 0.718572i \(-0.744796\pi\)
0.718572 + 0.695452i \(0.244796\pi\)
\(150\) −9.86830 10.4600i −0.805743 0.854054i
\(151\) 20.6379i 1.67949i −0.542980 0.839746i \(-0.682704\pi\)
0.542980 0.839746i \(-0.317296\pi\)
\(152\) −2.16675 + 1.81802i −0.175747 + 0.147461i
\(153\) 17.1266i 1.38460i
\(154\) −6.99874 + 6.60285i −0.563975 + 0.532073i
\(155\) −14.9953 + 14.9953i −1.20445 + 1.20445i
\(156\) −0.710127 + 12.1886i −0.0568556 + 0.975866i
\(157\) 7.90285 + 7.90285i 0.630716 + 0.630716i 0.948248 0.317532i \(-0.102854\pi\)
−0.317532 + 0.948248i \(0.602854\pi\)
\(158\) −0.324267 + 11.1408i −0.0257973 + 0.886317i
\(159\) −14.9127 −1.18265
\(160\) 10.3119 + 13.8527i 0.815231 + 1.09515i
\(161\) −3.69741 −0.291397
\(162\) 0.418293 14.3713i 0.0328642 1.12911i
\(163\) 16.8892 + 16.8892i 1.32287 + 1.32287i 0.911445 + 0.411422i \(0.134968\pi\)
0.411422 + 0.911445i \(0.365032\pi\)
\(164\) 0.718252 12.3280i 0.0560861 0.962657i
\(165\) 20.9089 20.9089i 1.62776 1.62776i
\(166\) 11.0836 10.4567i 0.860256 0.811594i
\(167\) 6.82763i 0.528338i 0.964476 + 0.264169i \(0.0850976\pi\)
−0.964476 + 0.264169i \(0.914902\pi\)
\(168\) −7.07596 8.43327i −0.545922 0.650641i
\(169\) 6.27444i 0.482649i
\(170\) 19.9690 + 21.1663i 1.53155 + 1.62338i
\(171\) −1.79676 + 1.79676i −0.137401 + 0.137401i
\(172\) −9.62919 + 8.56894i −0.734219 + 0.653376i
\(173\) 1.70937 + 1.70937i 0.129961 + 0.129961i 0.769095 0.639134i \(-0.220707\pi\)
−0.639134 + 0.769095i \(0.720707\pi\)
\(174\) −17.5616 0.511152i −1.33134 0.0387503i
\(175\) 7.14255 0.539926
\(176\) −12.9113 + 10.2082i −0.973225 + 0.769468i
\(177\) 5.96745 0.448541
\(178\) 13.3793 + 0.389422i 1.00282 + 0.0291884i
\(179\) −3.93881 3.93881i −0.294401 0.294401i 0.544415 0.838816i \(-0.316752\pi\)
−0.838816 + 0.544415i \(0.816752\pi\)
\(180\) 10.3137 + 11.5899i 0.768740 + 0.863858i
\(181\) 5.72963 5.72963i 0.425880 0.425880i −0.461342 0.887222i \(-0.652632\pi\)
0.887222 + 0.461342i \(0.152632\pi\)
\(182\) −4.16145 4.41096i −0.308467 0.326962i
\(183\) 25.1888i 1.86201i
\(184\) −6.30076 0.551420i −0.464498 0.0406512i
\(185\) 8.18048i 0.601441i
\(186\) 16.8205 15.8690i 1.23334 1.16357i
\(187\) −19.6111 + 19.6111i −1.43411 + 1.43411i
\(188\) −16.8654 0.982609i −1.23004 0.0716641i
\(189\) 1.26325 + 1.26325i 0.0918877 + 0.0918877i
\(190\) −0.125609 + 4.31553i −0.00911260 + 0.313081i
\(191\) −2.86264 −0.207134 −0.103567 0.994622i \(-0.533026\pi\)
−0.103567 + 0.994622i \(0.533026\pi\)
\(192\) −10.8004 15.4264i −0.779454 1.11331i
\(193\) 8.17302 0.588307 0.294154 0.955758i \(-0.404962\pi\)
0.294154 + 0.955758i \(0.404962\pi\)
\(194\) −0.588441 + 20.2170i −0.0422476 + 1.45150i
\(195\) 13.1779 + 13.1779i 0.943688 + 0.943688i
\(196\) −8.51771 0.496257i −0.608408 0.0354469i
\(197\) 17.4841 17.4841i 1.24569 1.24569i 0.288083 0.957606i \(-0.406982\pi\)
0.957606 0.288083i \(-0.0930178\pi\)
\(198\) −10.7555 + 10.1471i −0.764361 + 0.721124i
\(199\) 11.4643i 0.812679i −0.913722 0.406340i \(-0.866805\pi\)
0.913722 0.406340i \(-0.133195\pi\)
\(200\) 12.1716 + 1.06522i 0.860664 + 0.0753222i
\(201\) 16.2582i 1.14676i
\(202\) −0.218481 0.231581i −0.0153723 0.0162940i
\(203\) 6.17046 6.17046i 0.433082 0.433082i
\(204\) −21.0945 23.7046i −1.47691 1.65965i
\(205\) −13.3287 13.3287i −0.930915 0.930915i
\(206\) −14.5052 0.422192i −1.01063 0.0294155i
\(207\) −5.68210 −0.394933
\(208\) −6.43370 8.13735i −0.446097 0.564224i
\(209\) −4.11482 −0.284628
\(210\) −16.7966 0.488884i −1.15907 0.0337362i
\(211\) −7.40651 7.40651i −0.509885 0.509885i 0.404606 0.914491i \(-0.367409\pi\)
−0.914491 + 0.404606i \(0.867409\pi\)
\(212\) 9.46530 8.42309i 0.650080 0.578500i
\(213\) −21.0176 + 21.0176i −1.44010 + 1.44010i
\(214\) −5.16316 5.47273i −0.352947 0.374108i
\(215\) 19.6753i 1.34184i
\(216\) 1.96430 + 2.34110i 0.133654 + 0.159291i
\(217\) 11.4858i 0.779708i
\(218\) 17.5406 16.5484i 1.18800 1.12080i
\(219\) 6.76222 6.76222i 0.456948 0.456948i
\(220\) −1.46127 + 25.0811i −0.0985189 + 1.69097i
\(221\) −12.3599 12.3599i −0.831418 0.831418i
\(222\) −0.259530 + 8.91664i −0.0174185 + 0.598446i
\(223\) −10.4533 −0.700005 −0.350002 0.936749i \(-0.613819\pi\)
−0.350002 + 0.936749i \(0.613819\pi\)
\(224\) 9.25455 + 1.35602i 0.618346 + 0.0906032i
\(225\) 10.9765 0.731768
\(226\) −0.742739 + 25.5183i −0.0494063 + 1.69745i
\(227\) −5.88958 5.88958i −0.390905 0.390905i 0.484105 0.875010i \(-0.339145\pi\)
−0.875010 + 0.484105i \(0.839145\pi\)
\(228\) 0.273824 4.69989i 0.0181344 0.311258i
\(229\) 1.11702 1.11702i 0.0738150 0.0738150i −0.669235 0.743050i \(-0.733378\pi\)
0.743050 + 0.669235i \(0.233378\pi\)
\(230\) −7.02237 + 6.62514i −0.463041 + 0.436849i
\(231\) 16.0154i 1.05374i
\(232\) 11.4353 9.59484i 0.750766 0.629932i
\(233\) 0.804275i 0.0526898i 0.999653 + 0.0263449i \(0.00838681\pi\)
−0.999653 + 0.0263449i \(0.991613\pi\)
\(234\) −6.39523 6.77867i −0.418069 0.443136i
\(235\) −18.2344 + 18.2344i −1.18948 + 1.18948i
\(236\) −3.78763 + 3.37058i −0.246553 + 0.219406i
\(237\) −13.1179 13.1179i −0.852102 0.852102i
\(238\) 15.7540 + 0.458539i 1.02118 + 0.0297227i
\(239\) 15.3510 0.992973 0.496487 0.868044i \(-0.334623\pi\)
0.496487 + 0.868044i \(0.334623\pi\)
\(240\) −28.5501 3.33809i −1.84290 0.215473i
\(241\) −15.6408 −1.00751 −0.503755 0.863847i \(-0.668049\pi\)
−0.503755 + 0.863847i \(0.668049\pi\)
\(242\) −8.38518 0.244061i −0.539020 0.0156888i
\(243\) 14.6297 + 14.6297i 0.938493 + 0.938493i
\(244\) 14.2273 + 15.9877i 0.910810 + 1.02351i
\(245\) −9.20908 + 9.20908i −0.588347 + 0.588347i
\(246\) 14.1053 + 14.9510i 0.899319 + 0.953240i
\(247\) 2.59337i 0.165012i
\(248\) −1.71296 + 19.5730i −0.108773 + 1.24289i
\(249\) 25.3629i 1.60731i
\(250\) −2.13617 + 2.01533i −0.135103 + 0.127461i
\(251\) −14.6363 + 14.6363i −0.923835 + 0.923835i −0.997298 0.0734625i \(-0.976595\pi\)
0.0734625 + 0.997298i \(0.476595\pi\)
\(252\) 8.38863 + 0.488736i 0.528434 + 0.0307875i
\(253\) −6.50640 6.50640i −0.409054 0.409054i
\(254\) 0.779335 26.7756i 0.0488998 1.68005i
\(255\) −48.4354 −3.03314
\(256\) 15.5684 + 3.69099i 0.973028 + 0.230687i
\(257\) −25.4029 −1.58459 −0.792293 0.610140i \(-0.791113\pi\)
−0.792293 + 0.610140i \(0.791113\pi\)
\(258\) 0.624206 21.4458i 0.0388614 1.33516i
\(259\) −3.13296 3.13296i −0.194672 0.194672i
\(260\) −15.8074 0.920968i −0.980334 0.0571160i
\(261\) 9.48263 9.48263i 0.586960 0.586960i
\(262\) 9.13788 8.62098i 0.564540 0.532606i
\(263\) 16.4692i 1.01553i 0.861494 + 0.507767i \(0.169529\pi\)
−0.861494 + 0.507767i \(0.830471\pi\)
\(264\) 2.38848 27.2918i 0.147001 1.67970i
\(265\) 19.3404i 1.18807i
\(266\) 1.60465 + 1.70086i 0.0983875 + 0.104287i
\(267\) −15.7537 + 15.7537i −0.964110 + 0.964110i
\(268\) 9.18305 + 10.3193i 0.560944 + 0.630351i
\(269\) 2.53313 + 2.53313i 0.154448 + 0.154448i 0.780101 0.625653i \(-0.215168\pi\)
−0.625653 + 0.780101i \(0.715168\pi\)
\(270\) 4.66277 + 0.135716i 0.283767 + 0.00825938i
\(271\) 6.26221 0.380402 0.190201 0.981745i \(-0.439086\pi\)
0.190201 + 0.981745i \(0.439086\pi\)
\(272\) 26.7780 + 3.13089i 1.62365 + 0.189838i
\(273\) 10.0937 0.610900
\(274\) −27.6012 0.803367i −1.66745 0.0485332i
\(275\) 12.5689 + 12.5689i 0.757931 + 0.757931i
\(276\) 7.86450 6.99855i 0.473387 0.421263i
\(277\) −3.69833 + 3.69833i −0.222211 + 0.222211i −0.809429 0.587218i \(-0.800223\pi\)
0.587218 + 0.809429i \(0.300223\pi\)
\(278\) −11.9828 12.7012i −0.718680 0.761770i
\(279\) 17.6511i 1.05675i
\(280\) 10.9372 9.17685i 0.653620 0.548422i
\(281\) 29.3927i 1.75342i −0.481019 0.876710i \(-0.659733\pi\)
0.481019 0.876710i \(-0.340267\pi\)
\(282\) 20.4538 19.2968i 1.21800 1.14911i
\(283\) −4.02760 + 4.02760i −0.239416 + 0.239416i −0.816608 0.577192i \(-0.804148\pi\)
0.577192 + 0.816608i \(0.304148\pi\)
\(284\) 1.46886 25.2114i 0.0871609 1.49602i
\(285\) −5.08138 5.08138i −0.300995 0.300995i
\(286\) 0.439068 15.0850i 0.0259626 0.891996i
\(287\) −10.2092 −0.602631
\(288\) 14.2222 + 2.08391i 0.838050 + 0.122795i
\(289\) 28.4290 1.67229
\(290\) 0.662916 22.7758i 0.0389278 1.33744i
\(291\) −23.8048 23.8048i −1.39546 1.39546i
\(292\) −0.472594 + 8.11156i −0.0276564 + 0.474693i
\(293\) 6.39444 6.39444i 0.373567 0.373567i −0.495208 0.868775i \(-0.664908\pi\)
0.868775 + 0.495208i \(0.164908\pi\)
\(294\) 10.3300 9.74565i 0.602456 0.568378i
\(295\) 7.73922i 0.450595i
\(296\) −4.87163 5.80611i −0.283158 0.337473i
\(297\) 4.44591i 0.257978i
\(298\) −0.387334 0.410558i −0.0224377 0.0237830i
\(299\) 4.10066 4.10066i 0.237147 0.237147i
\(300\) −15.1924 + 13.5196i −0.877134 + 0.780554i
\(301\) 7.53522 + 7.53522i 0.434323 + 0.434323i
\(302\) −29.1741 0.849147i −1.67878 0.0488629i
\(303\) 0.529932 0.0304438
\(304\) 2.48083 + 3.13775i 0.142285 + 0.179963i
\(305\) 32.6675 1.87054
\(306\) 24.2104 + 0.704672i 1.38402 + 0.0402834i
\(307\) −6.56296 6.56296i −0.374568 0.374568i 0.494570 0.869138i \(-0.335326\pi\)
−0.869138 + 0.494570i \(0.835326\pi\)
\(308\) 9.04593 + 10.1652i 0.515439 + 0.579216i
\(309\) 17.0794 17.0794i 0.971613 0.971613i
\(310\) 20.5807 + 21.8146i 1.16890 + 1.23899i
\(311\) 22.5153i 1.27673i −0.769735 0.638364i \(-0.779612\pi\)
0.769735 0.638364i \(-0.220388\pi\)
\(312\) 17.2007 + 1.50534i 0.973798 + 0.0852233i
\(313\) 27.5578i 1.55766i 0.627235 + 0.778830i \(0.284187\pi\)
−0.627235 + 0.778830i \(0.715813\pi\)
\(314\) 11.4967 10.8464i 0.648799 0.612099i
\(315\) 9.06953 9.06953i 0.511010 0.511010i
\(316\) 15.7355 + 0.916778i 0.885192 + 0.0515728i
\(317\) 4.12845 + 4.12845i 0.231877 + 0.231877i 0.813476 0.581599i \(-0.197573\pi\)
−0.581599 + 0.813476i \(0.697573\pi\)
\(318\) −0.613582 + 21.0808i −0.0344080 + 1.18215i
\(319\) 21.7165 1.21589
\(320\) 20.0066 14.0071i 1.11840 0.783023i
\(321\) 12.5234 0.698988
\(322\) −0.152130 + 5.22672i −0.00847786 + 0.291274i
\(323\) 4.76597 + 4.76597i 0.265186 + 0.265186i
\(324\) −20.2982 1.18261i −1.12768 0.0657006i
\(325\) −7.92154 + 7.92154i −0.439408 + 0.439408i
\(326\) 24.5698 23.1800i 1.36079 1.28382i
\(327\) 40.1385i 2.21967i
\(328\) −17.3975 1.52257i −0.960618 0.0840698i
\(329\) 13.9668i 0.770013i
\(330\) −28.6969 30.4175i −1.57971 1.67443i
\(331\) 3.94813 3.94813i 0.217009 0.217009i −0.590228 0.807237i \(-0.700962\pi\)
0.807237 + 0.590228i \(0.200962\pi\)
\(332\) −14.3257 16.0982i −0.786223 0.883504i
\(333\) −4.81466 4.81466i −0.263842 0.263842i
\(334\) 9.65164 + 0.280922i 0.528114 + 0.0153714i
\(335\) 21.0853 1.15201
\(336\) −12.2125 + 9.65569i −0.666248 + 0.526761i
\(337\) −32.5626 −1.77380 −0.886900 0.461962i \(-0.847146\pi\)
−0.886900 + 0.461962i \(0.847146\pi\)
\(338\) −8.86964 0.258162i −0.482445 0.0140421i
\(339\) −30.0468 30.0468i −1.63192 1.63192i
\(340\) 30.7427 27.3576i 1.66725 1.48368i
\(341\) −20.2118 + 20.2118i −1.09453 + 1.09453i
\(342\) 2.46599 + 2.61385i 0.133346 + 0.141341i
\(343\) 18.6280i 1.00582i
\(344\) 11.7170 + 13.9645i 0.631738 + 0.752918i
\(345\) 16.0695i 0.865151i
\(346\) 2.48673 2.34606i 0.133687 0.126125i
\(347\) −9.28304 + 9.28304i −0.498340 + 0.498340i −0.910921 0.412581i \(-0.864627\pi\)
0.412581 + 0.910921i \(0.364627\pi\)
\(348\) −1.44514 + 24.8043i −0.0774679 + 1.32965i
\(349\) −1.00511 1.00511i −0.0538024 0.0538024i 0.679694 0.733496i \(-0.262113\pi\)
−0.733496 + 0.679694i \(0.762113\pi\)
\(350\) 0.293880 10.0968i 0.0157085 0.539698i
\(351\) −2.80204 −0.149562
\(352\) 13.8992 + 18.6716i 0.740828 + 0.995200i
\(353\) −31.7333 −1.68899 −0.844496 0.535562i \(-0.820100\pi\)
−0.844496 + 0.535562i \(0.820100\pi\)
\(354\) 0.245530 8.43567i 0.0130498 0.448351i
\(355\) −27.2578 27.2578i −1.44669 1.44669i
\(356\) 1.10098 18.8972i 0.0583521 1.00155i
\(357\) −18.5498 + 18.5498i −0.981758 + 0.981758i
\(358\) −5.73002 + 5.40590i −0.302841 + 0.285711i
\(359\) 17.1036i 0.902693i −0.892349 0.451346i \(-0.850944\pi\)
0.892349 0.451346i \(-0.149056\pi\)
\(360\) 16.8080 14.1028i 0.885858 0.743282i
\(361\) 1.00000i 0.0526316i
\(362\) −7.86375 8.33524i −0.413309 0.438090i
\(363\) 9.87325 9.87325i 0.518211 0.518211i
\(364\) −6.40663 + 5.70120i −0.335799 + 0.298824i
\(365\) 8.76996 + 8.76996i 0.459041 + 0.459041i
\(366\) −35.6072 1.03639i −1.86122 0.0541730i
\(367\) 4.19527 0.218991 0.109496 0.993987i \(-0.465076\pi\)
0.109496 + 0.993987i \(0.465076\pi\)
\(368\) −1.03874 + 8.88416i −0.0541480 + 0.463119i
\(369\) −15.6893 −0.816752
\(370\) −11.5641 0.336586i −0.601186 0.0174982i
\(371\) −7.40696 7.40696i −0.384550 0.384550i
\(372\) −21.7406 24.4306i −1.12720 1.26667i
\(373\) 15.1359 15.1359i 0.783710 0.783710i −0.196745 0.980455i \(-0.563037\pi\)
0.980455 + 0.196745i \(0.0630372\pi\)
\(374\) 26.9157 + 28.5295i 1.39178 + 1.47522i
\(375\) 4.88825i 0.252428i
\(376\) −2.08296 + 23.8008i −0.107420 + 1.22743i
\(377\) 13.6869i 0.704909i
\(378\) 1.83772 1.73377i 0.0945222 0.0891755i
\(379\) −6.14466 + 6.14466i −0.315630 + 0.315630i −0.847086 0.531456i \(-0.821645\pi\)
0.531456 + 0.847086i \(0.321645\pi\)
\(380\) 6.09532 + 0.355124i 0.312683 + 0.0182175i
\(381\) 31.5273 + 31.5273i 1.61519 + 1.61519i
\(382\) −0.117783 + 4.04668i −0.00602632 + 0.207046i
\(383\) −8.35520 −0.426931 −0.213465 0.976951i \(-0.568475\pi\)
−0.213465 + 0.976951i \(0.568475\pi\)
\(384\) −22.2514 + 14.6329i −1.13551 + 0.746734i
\(385\) 20.7705 1.05856
\(386\) 0.336279 11.5535i 0.0171161 0.588058i
\(387\) 11.5799 + 11.5799i 0.588642 + 0.588642i
\(388\) 28.5549 + 1.66366i 1.44965 + 0.0844594i
\(389\) 1.50516 1.50516i 0.0763145 0.0763145i −0.667919 0.744234i \(-0.732815\pi\)
0.744234 + 0.667919i \(0.232815\pi\)
\(390\) 19.1707 18.0863i 0.970744 0.915833i
\(391\) 15.0720i 0.762225i
\(392\) −1.05198 + 12.0203i −0.0531329 + 0.607119i
\(393\) 20.9104i 1.05479i
\(394\) −23.9964 25.4351i −1.20892 1.28140i
\(395\) 17.0127 17.0127i 0.856004 0.856004i
\(396\) 13.9016 + 15.6216i 0.698580 + 0.785017i
\(397\) 0.0297571 + 0.0297571i 0.00149347 + 0.00149347i 0.707853 0.706360i \(-0.249664\pi\)
−0.706360 + 0.707853i \(0.749664\pi\)
\(398\) −16.2060 0.471696i −0.812335 0.0236440i
\(399\) −3.89213 −0.194850
\(400\) 2.00661 17.1622i 0.100330 0.858108i
\(401\) 3.99217 0.199359 0.0996797 0.995020i \(-0.468218\pi\)
0.0996797 + 0.995020i \(0.468218\pi\)
\(402\) −22.9828 0.668941i −1.14628 0.0333637i
\(403\) −12.7385 12.7385i −0.634549 0.634549i
\(404\) −0.336355 + 0.299320i −0.0167343 + 0.0148917i
\(405\) −21.9458 + 21.9458i −1.09050 + 1.09050i
\(406\) −8.46877 8.97654i −0.420298 0.445498i
\(407\) 11.0262i 0.546550i
\(408\) −34.3771 + 28.8442i −1.70192 + 1.42800i
\(409\) 6.24741i 0.308915i 0.987999 + 0.154457i \(0.0493629\pi\)
−0.987999 + 0.154457i \(0.950637\pi\)
\(410\) −19.3900 + 18.2932i −0.957605 + 0.903437i
\(411\) 32.4995 32.4995i 1.60308 1.60308i
\(412\) −1.19363 + 20.4874i −0.0588061 + 1.00934i
\(413\) 2.96396 + 2.96396i 0.145847 + 0.145847i
\(414\) −0.233790 + 8.03230i −0.0114901 + 0.394766i
\(415\) −32.8933 −1.61467
\(416\) −11.7678 + 8.75996i −0.576964 + 0.429492i
\(417\) 29.0646 1.42330
\(418\) −0.169304 + 5.81677i −0.00828093 + 0.284507i
\(419\) −12.3865 12.3865i −0.605121 0.605121i 0.336546 0.941667i \(-0.390741\pi\)
−0.941667 + 0.336546i \(0.890741\pi\)
\(420\) −1.38219 + 23.7238i −0.0674439 + 1.15760i
\(421\) 7.38277 7.38277i 0.359814 0.359814i −0.503930 0.863744i \(-0.668113\pi\)
0.863744 + 0.503930i \(0.168113\pi\)
\(422\) −10.7747 + 10.1652i −0.524504 + 0.494835i
\(423\) 21.4638i 1.04361i
\(424\) −11.5176 13.7269i −0.559342 0.666635i
\(425\) 29.1157i 1.41232i
\(426\) 28.8460 + 30.5755i 1.39759 + 1.48139i
\(427\) 12.5110 12.5110i 0.605449 0.605449i
\(428\) −7.94878 + 7.07355i −0.384219 + 0.341913i
\(429\) 17.7621 + 17.7621i 0.857561 + 0.857561i
\(430\) 27.8132 + 0.809537i 1.34127 + 0.0390393i
\(431\) −14.7657 −0.711237 −0.355619 0.934631i \(-0.615730\pi\)
−0.355619 + 0.934631i \(0.615730\pi\)
\(432\) 3.39023 2.68045i 0.163113 0.128963i
\(433\) −22.3572 −1.07442 −0.537209 0.843449i \(-0.680522\pi\)
−0.537209 + 0.843449i \(0.680522\pi\)
\(434\) 16.2365 + 0.472583i 0.779378 + 0.0226847i
\(435\) 26.8177 + 26.8177i 1.28581 + 1.28581i
\(436\) −22.6713 25.4765i −1.08576 1.22010i
\(437\) −1.58121 + 1.58121i −0.0756396 + 0.0756396i
\(438\) −9.28094 9.83740i −0.443460 0.470049i
\(439\) 3.02626i 0.144436i −0.997389 0.0722179i \(-0.976992\pi\)
0.997389 0.0722179i \(-0.0230077\pi\)
\(440\) 35.3950 + 3.09764i 1.68739 + 0.147674i
\(441\) 10.8401i 0.516195i
\(442\) −17.9807 + 16.9636i −0.855255 + 0.806877i
\(443\) 19.1035 19.1035i 0.907634 0.907634i −0.0884471 0.996081i \(-0.528190\pi\)
0.996081 + 0.0884471i \(0.0281904\pi\)
\(444\) 12.5940 + 0.733750i 0.597686 + 0.0348222i
\(445\) −20.4311 20.4311i −0.968526 0.968526i
\(446\) −0.430101 + 14.7769i −0.0203659 + 0.699708i
\(447\) 0.939489 0.0444363
\(448\) 2.29767 13.0266i 0.108555 0.615448i
\(449\) 20.0661 0.946979 0.473489 0.880800i \(-0.342994\pi\)
0.473489 + 0.880800i \(0.342994\pi\)
\(450\) 0.451628 15.5166i 0.0212900 0.731458i
\(451\) −17.9653 17.9653i −0.845954 0.845954i
\(452\) 36.0424 + 2.09990i 1.69529 + 0.0987708i
\(453\) 34.3515 34.3515i 1.61397 1.61397i
\(454\) −8.56792 + 8.08327i −0.402113 + 0.379367i
\(455\) 13.0906i 0.613697i
\(456\) −6.63257 0.580459i −0.310599 0.0271825i
\(457\) 4.19511i 0.196239i −0.995175 0.0981195i \(-0.968717\pi\)
0.995175 0.0981195i \(-0.0312827\pi\)
\(458\) −1.53308 1.62500i −0.0716362 0.0759313i
\(459\) 5.14946 5.14946i 0.240356 0.240356i
\(460\) 9.07647 + 10.1995i 0.423192 + 0.475555i
\(461\) −5.08285 5.08285i −0.236732 0.236732i 0.578764 0.815495i \(-0.303535\pi\)
−0.815495 + 0.578764i \(0.803535\pi\)
\(462\) −22.6396 0.658952i −1.05329 0.0306572i
\(463\) −18.4414 −0.857045 −0.428522 0.903531i \(-0.640966\pi\)
−0.428522 + 0.903531i \(0.640966\pi\)
\(464\) −13.0929 16.5599i −0.607823 0.768775i
\(465\) −49.9189 −2.31494
\(466\) 1.13694 + 0.0330919i 0.0526675 + 0.00153295i
\(467\) −2.27417 2.27417i −0.105236 0.105236i 0.652528 0.757764i \(-0.273708\pi\)
−0.757764 + 0.652528i \(0.773708\pi\)
\(468\) −9.84556 + 8.76148i −0.455111 + 0.405000i
\(469\) 8.07524 8.07524i 0.372880 0.372880i
\(470\) 25.0261 + 26.5266i 1.15437 + 1.22358i
\(471\) 26.3083i 1.21222i
\(472\) 4.60885 + 5.49293i 0.212140 + 0.252832i
\(473\) 26.5197i 1.21938i
\(474\) −19.0834 + 18.0040i −0.876532 + 0.826950i
\(475\) 3.05454 3.05454i 0.140152 0.140152i
\(476\) 1.29639 22.2512i 0.0594201 1.01988i
\(477\) −11.3829 11.3829i −0.521185 0.521185i
\(478\) 0.631616 21.7004i 0.0288894 0.992553i
\(479\) 3.83766 0.175347 0.0876735 0.996149i \(-0.472057\pi\)
0.0876735 + 0.996149i \(0.472057\pi\)
\(480\) −5.89347 + 40.2215i −0.268999 + 1.83585i
\(481\) 6.94929 0.316860
\(482\) −0.643538 + 22.1100i −0.0293124 + 1.00708i
\(483\) −6.15427 6.15427i −0.280029 0.280029i
\(484\) −0.690016 + 11.8434i −0.0313643 + 0.538335i
\(485\) 30.8726 30.8726i 1.40185 1.40185i
\(486\) 21.2826 20.0788i 0.965400 0.910791i
\(487\) 36.6808i 1.66217i 0.556148 + 0.831083i \(0.312279\pi\)
−0.556148 + 0.831083i \(0.687721\pi\)
\(488\) 23.1858 19.4541i 1.04957 0.880647i
\(489\) 56.2236i 2.54252i
\(490\) 12.6392 + 13.3970i 0.570980 + 0.605215i
\(491\) 8.27309 8.27309i 0.373359 0.373359i −0.495340 0.868699i \(-0.664956\pi\)
0.868699 + 0.495340i \(0.164956\pi\)
\(492\) 21.7153 19.3243i 0.979001 0.871205i
\(493\) −25.1531 25.1531i −1.13284 1.13284i
\(494\) −3.66602 0.106704i −0.164942 0.00480084i
\(495\) 31.9196 1.43468
\(496\) 27.5982 + 3.22679i 1.23919 + 0.144887i
\(497\) −20.8784 −0.936522
\(498\) 35.8534 + 1.04356i 1.60663 + 0.0467628i
\(499\) 13.3714 + 13.3714i 0.598588 + 0.598588i 0.939937 0.341349i \(-0.110884\pi\)
−0.341349 + 0.939937i \(0.610884\pi\)
\(500\) 2.76101 + 3.10264i 0.123476 + 0.138754i
\(501\) −11.3645 + 11.3645i −0.507727 + 0.507727i
\(502\) 20.0879 + 21.2923i 0.896566 + 0.950322i
\(503\) 2.50564i 0.111721i −0.998439 0.0558604i \(-0.982210\pi\)
0.998439 0.0558604i \(-0.0177902\pi\)
\(504\) 1.03603 11.8382i 0.0461487 0.527315i
\(505\) 0.687272i 0.0305832i
\(506\) −9.46524 + 8.92983i −0.420781 + 0.396980i
\(507\) 10.4437 10.4437i 0.463821 0.463821i
\(508\) −37.8183 2.20336i −1.67792 0.0977583i
\(509\) −5.50329 5.50329i −0.243929 0.243929i 0.574544 0.818473i \(-0.305179\pi\)
−0.818473 + 0.574544i \(0.805179\pi\)
\(510\) −1.99287 + 68.4690i −0.0882459 + 3.03186i
\(511\) 6.71743 0.297162
\(512\) 5.85821 21.8559i 0.258899 0.965904i
\(513\) 1.08046 0.0477037
\(514\) −1.04520 + 35.9099i −0.0461018 + 1.58392i
\(515\) 22.1504 + 22.1504i 0.976062 + 0.976062i
\(516\) −30.2905 1.76477i −1.33346 0.0776899i
\(517\) −24.5776 + 24.5776i −1.08092 + 1.08092i
\(518\) −4.55770 + 4.29989i −0.200254 + 0.188926i
\(519\) 5.69044i 0.249782i
\(520\) −1.95229 + 22.3077i −0.0856135 + 0.978258i
\(521\) 33.0861i 1.44953i −0.688998 0.724763i \(-0.741949\pi\)
0.688998 0.724763i \(-0.258051\pi\)
\(522\) −13.0146 13.7949i −0.569634 0.603788i
\(523\) −8.01638 + 8.01638i −0.350532 + 0.350532i −0.860307 0.509776i \(-0.829728\pi\)
0.509776 + 0.860307i \(0.329728\pi\)
\(524\) −11.8108 13.2721i −0.515956 0.579797i
\(525\) 11.8886 + 11.8886i 0.518863 + 0.518863i
\(526\) 23.2811 + 0.677624i 1.01510 + 0.0295458i
\(527\) 46.8204 2.03953
\(528\) −38.4819 4.49931i −1.67471 0.195808i
\(529\) 17.9995 0.782589
\(530\) −27.3398 0.795758i −1.18757 0.0345655i
\(531\) 4.55495 + 4.55495i 0.197668 + 0.197668i
\(532\) 2.47039 2.19838i 0.107105 0.0953118i
\(533\) 11.3227 11.3227i 0.490439 0.490439i
\(534\) 21.6215 + 22.9178i 0.935653 + 0.991752i
\(535\) 16.2417i 0.702189i
\(536\) 14.9653 12.5567i 0.646404 0.542367i
\(537\) 13.1122i 0.565831i
\(538\) 3.68510 3.47665i 0.158876 0.149889i
\(539\) −12.4126 + 12.4126i −0.534651 + 0.534651i
\(540\) 0.383699 6.58578i 0.0165118 0.283407i
\(541\) −15.9481 15.9481i −0.685661 0.685661i 0.275609 0.961270i \(-0.411120\pi\)
−0.961270 + 0.275609i \(0.911120\pi\)
\(542\) 0.257658 8.85235i 0.0110674 0.380241i
\(543\) 19.0737 0.818532
\(544\) 5.52766 37.7250i 0.236996 1.61744i
\(545\) −52.0559 −2.22983
\(546\) 0.415305 14.2686i 0.0177734 0.610641i
\(547\) 7.85985 + 7.85985i 0.336063 + 0.336063i 0.854883 0.518820i \(-0.173629\pi\)
−0.518820 + 0.854883i \(0.673629\pi\)
\(548\) −2.27130 + 38.9845i −0.0970253 + 1.66533i
\(549\) 19.2266 19.2266i 0.820571 0.820571i
\(550\) 18.2847 17.2504i 0.779662 0.735559i
\(551\) 5.27764i 0.224835i
\(552\) −9.56967 11.4053i −0.407312 0.485443i
\(553\) 13.0311i 0.554137i
\(554\) 5.07584 + 5.38018i 0.215652 + 0.228582i
\(555\) 13.6163 13.6163i 0.577978 0.577978i
\(556\) −18.4477 + 16.4165i −0.782357 + 0.696213i
\(557\) 32.3716 + 32.3716i 1.37163 + 1.37163i 0.858032 + 0.513596i \(0.171687\pi\)
0.513596 + 0.858032i \(0.328313\pi\)
\(558\) 24.9519 + 0.726255i 1.05630 + 0.0307448i
\(559\) −16.7141 −0.706929
\(560\) −12.5225 15.8385i −0.529173 0.669299i
\(561\) −65.2846 −2.75632
\(562\) −41.5499 1.20936i −1.75268 0.0510138i
\(563\) 7.43471 + 7.43471i 0.313335 + 0.313335i 0.846200 0.532865i \(-0.178885\pi\)
−0.532865 + 0.846200i \(0.678885\pi\)
\(564\) −26.4367 29.7077i −1.11318 1.25092i
\(565\) 38.9679 38.9679i 1.63939 1.63939i
\(566\) 5.52776 + 5.85919i 0.232349 + 0.246280i
\(567\) 16.8096i 0.705936i
\(568\) −35.5788 3.11373i −1.49285 0.130649i
\(569\) 1.59708i 0.0669530i 0.999440 + 0.0334765i \(0.0106579\pi\)
−0.999440 + 0.0334765i \(0.989342\pi\)
\(570\) −7.39218 + 6.97404i −0.309625 + 0.292110i
\(571\) 15.3223 15.3223i 0.641219 0.641219i −0.309636 0.950855i \(-0.600207\pi\)
0.950855 + 0.309636i \(0.100207\pi\)
\(572\) −21.3063 1.24134i −0.890863 0.0519032i
\(573\) −4.76482 4.76482i −0.199053 0.199053i
\(574\) −0.420058 + 14.4319i −0.0175329 + 0.602376i
\(575\) 9.65974 0.402839
\(576\) 3.53101 20.0189i 0.147126 0.834123i
\(577\) −7.28279 −0.303187 −0.151593 0.988443i \(-0.548440\pi\)
−0.151593 + 0.988443i \(0.548440\pi\)
\(578\) 1.16971 40.1876i 0.0486535 1.67158i
\(579\) 13.6038 + 13.6038i 0.565356 + 0.565356i
\(580\) −32.1689 1.87422i −1.33574 0.0778226i
\(581\) −12.5975 + 12.5975i −0.522631 + 0.522631i
\(582\) −34.6303 + 32.6714i −1.43547 + 1.35427i
\(583\) 26.0683i 1.07964i
\(584\) 11.4472 + 1.00182i 0.473688 + 0.0414554i
\(585\) 20.1173i 0.831750i
\(586\) −8.77617 9.30237i −0.362540 0.384277i
\(587\) 20.7800 20.7800i 0.857682 0.857682i −0.133383 0.991065i \(-0.542584\pi\)
0.991065 + 0.133383i \(0.0425839\pi\)
\(588\) −13.3516 15.0036i −0.550609 0.618737i
\(589\) 4.91195 + 4.91195i 0.202393 + 0.202393i
\(590\) 10.9403 + 0.318430i 0.450404 + 0.0131096i
\(591\) 58.2038 2.39418
\(592\) −8.40805 + 6.64772i −0.345569 + 0.273220i
\(593\) −3.64515 −0.149688 −0.0748442 0.997195i \(-0.523846\pi\)
−0.0748442 + 0.997195i \(0.523846\pi\)
\(594\) 6.28481 + 0.182927i 0.257869 + 0.00750558i
\(595\) −24.0573 24.0573i −0.986254 0.986254i
\(596\) −0.596307 + 0.530649i −0.0244257 + 0.0217362i
\(597\) 19.0820 19.0820i 0.780975 0.780975i
\(598\) −5.62804 5.96548i −0.230148 0.243947i
\(599\) 12.4653i 0.509317i 0.967031 + 0.254659i \(0.0819631\pi\)
−0.967031 + 0.254659i \(0.918037\pi\)
\(600\) 18.4864 + 22.0325i 0.754705 + 0.899472i
\(601\) 2.70490i 0.110335i 0.998477 + 0.0551676i \(0.0175693\pi\)
−0.998477 + 0.0551676i \(0.982431\pi\)
\(602\) 10.9619 10.3419i 0.446775 0.421503i
\(603\) 12.4098 12.4098i 0.505368 0.505368i
\(604\) −2.40073 + 41.2060i −0.0976844 + 1.67665i
\(605\) 12.8047 + 12.8047i 0.520584 + 0.520584i
\(606\) 0.0218040 0.749120i 0.000885728 0.0304309i
\(607\) 45.5362 1.84826 0.924129 0.382080i \(-0.124792\pi\)
0.924129 + 0.382080i \(0.124792\pi\)
\(608\) 4.53765 3.37783i 0.184026 0.136989i
\(609\) 20.5412 0.832373
\(610\) 1.34410 46.1793i 0.0544211 1.86974i
\(611\) −15.4900 15.4900i −0.626660 0.626660i
\(612\) 1.99227 34.1952i 0.0805327 1.38226i
\(613\) −31.0423 + 31.0423i −1.25379 + 1.25379i −0.299776 + 0.954010i \(0.596912\pi\)
−0.954010 + 0.299776i \(0.903088\pi\)
\(614\) −9.54753 + 9.00747i −0.385307 + 0.363512i
\(615\) 44.3707i 1.78920i
\(616\) 14.7419 12.3692i 0.593967 0.498370i
\(617\) 40.2158i 1.61903i −0.587103 0.809513i \(-0.699731\pi\)
0.587103 0.809513i \(-0.300269\pi\)
\(618\) −23.4409 24.8464i −0.942933 0.999469i
\(619\) −18.8734 + 18.8734i −0.758587 + 0.758587i −0.976065 0.217478i \(-0.930217\pi\)
0.217478 + 0.976065i \(0.430217\pi\)
\(620\) 31.6843 28.1956i 1.27247 1.13236i
\(621\) 1.70844 + 1.70844i 0.0685574 + 0.0685574i
\(622\) −31.8280 0.926392i −1.27619 0.0371449i
\(623\) −15.6494 −0.626978
\(624\) 2.83570 24.2532i 0.113519 0.970907i
\(625\) 27.9384 1.11754
\(626\) 38.9561 + 1.13386i 1.55700 + 0.0453184i
\(627\) −6.84904 6.84904i −0.273524 0.273524i
\(628\) −14.8596 16.6982i −0.592964 0.666332i
\(629\) −12.7711 + 12.7711i −0.509217 + 0.509217i
\(630\) −12.4477 13.1940i −0.495926 0.525661i
\(631\) 9.83337i 0.391460i −0.980658 0.195730i \(-0.937292\pi\)
0.980658 0.195730i \(-0.0627077\pi\)
\(632\) 1.94341 22.2062i 0.0773046 0.883316i
\(633\) 24.6560i 0.979988i
\(634\) 6.00591 5.66618i 0.238525 0.225033i
\(635\) −40.8879 + 40.8879i −1.62259 + 1.62259i
\(636\) 29.7749 + 1.73474i 1.18065 + 0.0687868i
\(637\) −7.82309 7.82309i −0.309962 0.309962i
\(638\) 0.893525 30.6988i 0.0353750 1.21538i
\(639\) −32.0854 −1.26928
\(640\) −18.9775 28.8580i −0.750153 1.14071i
\(641\) 32.2957 1.27560 0.637801 0.770201i \(-0.279844\pi\)
0.637801 + 0.770201i \(0.279844\pi\)
\(642\) 0.515274 17.7033i 0.0203363 0.698692i
\(643\) −21.1614 21.1614i −0.834525 0.834525i 0.153607 0.988132i \(-0.450911\pi\)
−0.988132 + 0.153607i \(0.950911\pi\)
\(644\) 7.38231 + 0.430106i 0.290904 + 0.0169486i
\(645\) −32.7491 + 32.7491i −1.28949 + 1.28949i
\(646\) 6.93334 6.54115i 0.272789 0.257358i
\(647\) 35.5368i 1.39710i 0.715564 + 0.698548i \(0.246170\pi\)
−0.715564 + 0.698548i \(0.753830\pi\)
\(648\) −2.50693 + 28.6452i −0.0984813 + 1.12529i
\(649\) 10.4315i 0.409471i
\(650\) 10.8721 + 11.5239i 0.426438 + 0.452006i
\(651\) −19.1179 + 19.1179i −0.749291 + 0.749291i
\(652\) −31.7566 35.6859i −1.24369 1.39757i
\(653\) −17.2398 17.2398i −0.674645 0.674645i 0.284138 0.958783i \(-0.408293\pi\)
−0.958783 + 0.284138i \(0.908293\pi\)
\(654\) 56.7404 + 1.65150i 2.21873 + 0.0645787i
\(655\) −27.1189 −1.05962
\(656\) −2.86815 + 24.5308i −0.111982 + 0.957765i
\(657\) 10.3232 0.402746
\(658\) 19.7436 + 0.574662i 0.769687 + 0.0224027i
\(659\) −3.11267 3.11267i −0.121253 0.121253i 0.643877 0.765129i \(-0.277325\pi\)
−0.765129 + 0.643877i \(0.777325\pi\)
\(660\) −44.1794 + 39.3148i −1.71968 + 1.53033i
\(661\) 30.0154 30.0154i 1.16746 1.16746i 0.184660 0.982802i \(-0.440882\pi\)
0.982802 0.184660i \(-0.0591185\pi\)
\(662\) −5.41869 5.74358i −0.210603 0.223231i
\(663\) 41.1457i 1.59797i
\(664\) −23.3461 + 19.5886i −0.906004 + 0.760185i
\(665\) 5.04772i 0.195742i
\(666\) −7.00417 + 6.60797i −0.271406 + 0.256054i
\(667\) 8.34506 8.34506i 0.323122 0.323122i
\(668\) 0.794232 13.6321i 0.0307298 0.527443i
\(669\) −17.3993 17.3993i −0.672697 0.672697i
\(670\) 0.867554 29.8065i 0.0335165 1.15153i
\(671\) 44.0315 1.69982
\(672\) 13.1469 + 17.6611i 0.507154 + 0.681292i
\(673\) 8.01937 0.309124 0.154562 0.987983i \(-0.450603\pi\)
0.154562 + 0.987983i \(0.450603\pi\)
\(674\) −1.33979 + 46.0310i −0.0516067 + 1.77305i
\(675\) −3.30032 3.30032i −0.127029 0.127029i
\(676\) −0.729882 + 12.5276i −0.0280724 + 0.481832i
\(677\) −17.7844 + 17.7844i −0.683511 + 0.683511i −0.960790 0.277278i \(-0.910568\pi\)
0.277278 + 0.960790i \(0.410568\pi\)
\(678\) −43.7109 + 41.2384i −1.67871 + 1.58375i
\(679\) 23.6472i 0.907495i
\(680\) −37.4082 44.5839i −1.43454 1.70971i
\(681\) 19.6062i 0.751311i
\(682\) 27.7401 + 29.4033i 1.06222 + 1.12591i
\(683\) −19.5322 + 19.5322i −0.747378 + 0.747378i −0.973986 0.226608i \(-0.927236\pi\)
0.226608 + 0.973986i \(0.427236\pi\)
\(684\) 3.79644 3.37842i 0.145160 0.129177i
\(685\) 42.1488 + 42.1488i 1.61042 + 1.61042i
\(686\) 26.3328 + 0.766447i 1.00539 + 0.0292631i
\(687\) 3.71853 0.141871
\(688\) 20.2226 15.9887i 0.770979 0.609565i
\(689\) 16.4296 0.625917
\(690\) −22.7160 0.661177i −0.864785 0.0251706i
\(691\) 15.7926 + 15.7926i 0.600777 + 0.600777i 0.940519 0.339742i \(-0.110340\pi\)
−0.339742 + 0.940519i \(0.610340\pi\)
\(692\) −3.21411 3.61180i −0.122182 0.137300i
\(693\) 12.2245 12.2245i 0.464372 0.464372i
\(694\) 12.7407 + 13.5046i 0.483630 + 0.512627i
\(695\) 37.6940i 1.42982i
\(696\) 35.0043 + 3.06345i 1.32684 + 0.116120i
\(697\) 41.6165i 1.57634i
\(698\) −1.46220 + 1.37949i −0.0553450 + 0.0522144i
\(699\) −1.33870 + 1.33870i −0.0506343 + 0.0506343i
\(700\) −14.2609 0.830866i −0.539012 0.0314038i
\(701\) −17.6581 17.6581i −0.666935 0.666935i 0.290070 0.957005i \(-0.406321\pi\)
−0.957005 + 0.290070i \(0.906321\pi\)
\(702\) −0.115290 + 3.96101i −0.00435134 + 0.149499i
\(703\) −2.67964 −0.101065
\(704\) 26.9663 18.8798i 1.01633 0.711560i
\(705\) −60.7015 −2.28615
\(706\) −1.30566 + 44.8586i −0.0491393 + 1.68828i
\(707\) 0.263211 + 0.263211i 0.00989907 + 0.00989907i
\(708\) −11.9147 0.694171i −0.447782 0.0260885i
\(709\) 17.4746 17.4746i 0.656272 0.656272i −0.298224 0.954496i \(-0.596394\pi\)
0.954496 + 0.298224i \(0.0963942\pi\)
\(710\) −39.6536 + 37.4105i −1.48817 + 1.40399i
\(711\) 20.0258i 0.751027i
\(712\) −26.6681 2.33389i −0.999428 0.0874663i
\(713\) 15.5337i 0.581740i
\(714\) 25.4590 + 26.9855i 0.952779 + 1.00991i
\(715\) −23.0358 + 23.0358i −0.861488 + 0.861488i
\(716\) 7.40610 + 8.32247i 0.276779 + 0.311025i
\(717\) 25.5514 + 25.5514i 0.954236 + 0.954236i
\(718\) −24.1779 0.703726i −0.902310 0.0262628i
\(719\) −8.66057 −0.322985 −0.161492 0.986874i \(-0.551631\pi\)
−0.161492 + 0.986874i \(0.551631\pi\)
\(720\) −19.2443 24.3403i −0.717194 0.907108i
\(721\) 16.9663 0.631857
\(722\) 1.41361 + 0.0411449i 0.0526093 + 0.00153126i
\(723\) −26.0337 26.0337i −0.968206 0.968206i
\(724\) −12.1064 + 10.7734i −0.449930 + 0.400389i
\(725\) −16.1207 + 16.1207i −0.598710 + 0.598710i
\(726\) −13.5507 14.3632i −0.502915 0.533069i
\(727\) 52.1123i 1.93274i −0.257160 0.966369i \(-0.582787\pi\)
0.257160 0.966369i \(-0.417213\pi\)
\(728\) 7.79571 + 9.29108i 0.288928 + 0.344350i
\(729\) 18.2026i 0.674170i
\(730\) 12.7582 12.0365i 0.472202 0.445491i
\(731\) 30.7163 30.7163i 1.13608 1.13608i
\(732\) −2.93012 + 50.2923i −0.108300 + 1.85886i
\(733\) 23.7514 + 23.7514i 0.877279 + 0.877279i 0.993252 0.115973i \(-0.0369986\pi\)
−0.115973 + 0.993252i \(0.536999\pi\)
\(734\) 0.172614 5.93049i 0.00637130 0.218899i
\(735\) −30.6567 −1.13079
\(736\) 12.5160 + 1.83392i 0.461348 + 0.0675990i
\(737\) 28.4203 1.04687
\(738\) −0.645535 + 22.1786i −0.0237625 + 0.816406i
\(739\) 6.82503 + 6.82503i 0.251063 + 0.251063i 0.821406 0.570344i \(-0.193190\pi\)
−0.570344 + 0.821406i \(0.693190\pi\)
\(740\) −0.951605 + 16.3333i −0.0349817 + 0.600423i
\(741\) 4.31661 4.31661i 0.158575 0.158575i
\(742\) −10.7754 + 10.1658i −0.395576 + 0.373200i
\(743\) 31.3539i 1.15026i 0.818062 + 0.575131i \(0.195049\pi\)
−0.818062 + 0.575131i \(0.804951\pi\)
\(744\) −35.4300 + 29.7277i −1.29893 + 1.08987i
\(745\) 1.21843i 0.0446398i
\(746\) −20.7736 22.0192i −0.760577 0.806179i
\(747\) −19.3595 + 19.3595i −0.708327 + 0.708327i
\(748\) 41.4371 36.8745i 1.51509 1.34827i
\(749\) 6.22023 + 6.22023i 0.227282 + 0.227282i
\(750\) −6.91010 0.201127i −0.252321 0.00734411i
\(751\) 42.7968 1.56168 0.780839 0.624733i \(-0.214792\pi\)
0.780839 + 0.624733i \(0.214792\pi\)
\(752\) 33.5595 + 3.92378i 1.22379 + 0.143086i
\(753\) −48.7237 −1.77559
\(754\) 19.3480 + 0.563145i 0.704611 + 0.0205085i
\(755\) 44.5506 + 44.5506i 1.62136 + 1.62136i
\(756\) −2.37527 2.66917i −0.0863877 0.0970767i
\(757\) 7.73140 7.73140i 0.281002 0.281002i −0.552506 0.833509i \(-0.686328\pi\)
0.833509 + 0.552506i \(0.186328\pi\)
\(758\) 8.43337 + 8.93901i 0.306314 + 0.324679i
\(759\) 21.6596i 0.786192i
\(760\) 0.752801 8.60183i 0.0273069 0.312021i
\(761\) 38.9433i 1.41169i −0.708365 0.705846i \(-0.750567\pi\)
0.708365 0.705846i \(-0.249433\pi\)
\(762\) 45.8646 43.2703i 1.66150 1.56752i
\(763\) −19.9364 + 19.9364i −0.721744 + 0.721744i
\(764\) 5.71560 + 0.333001i 0.206783 + 0.0120475i
\(765\) −36.9707 36.9707i −1.33668 1.33668i
\(766\) −0.343774 + 11.8110i −0.0124211 + 0.426750i
\(767\) −6.57444 −0.237389
\(768\) 19.7698 + 32.0570i 0.713381 + 1.15676i
\(769\) −16.2839 −0.587212 −0.293606 0.955926i \(-0.594855\pi\)
−0.293606 + 0.955926i \(0.594855\pi\)
\(770\) 0.854600 29.3614i 0.0307976 1.05811i
\(771\) −42.2826 42.2826i −1.52277 1.52277i
\(772\) −16.3184 0.950737i −0.587311 0.0342178i
\(773\) 18.1233 18.1233i 0.651851 0.651851i −0.301588 0.953438i \(-0.597517\pi\)
0.953438 + 0.301588i \(0.0975166\pi\)
\(774\) 16.8460 15.8931i 0.605519 0.571267i
\(775\) 30.0075i 1.07790i
\(776\) 3.52666 40.2971i 0.126600 1.44658i
\(777\) 10.4295i 0.374156i
\(778\) −2.06578 2.18964i −0.0740619 0.0785025i
\(779\) −4.36601 + 4.36601i −0.156428 + 0.156428i
\(780\) −24.7782 27.8441i −0.887202 0.996978i
\(781\) −36.7400 36.7400i −1.31466 1.31466i
\(782\) 21.3060 + 0.620137i 0.761902 + 0.0221761i
\(783\) −5.70230 −0.203784
\(784\) 16.9489 + 1.98167i 0.605316 + 0.0707738i
\(785\) −34.1194 −1.21777
\(786\) 29.5593 + 0.860358i 1.05435 + 0.0306880i
\(787\) −8.02876 8.02876i −0.286195 0.286195i 0.549379 0.835573i \(-0.314864\pi\)
−0.835573 + 0.549379i \(0.814864\pi\)
\(788\) −36.9428 + 32.8751i −1.31603 + 1.17113i
\(789\) −27.4127 + 27.4127i −0.975917 + 0.975917i
\(790\) −23.3495 24.7494i −0.830737 0.880546i
\(791\) 29.8478i 1.06127i
\(792\) 22.6550 19.0087i 0.805009 0.675445i
\(793\) 27.7509i 0.985464i
\(794\) 0.0432895 0.0408408i 0.00153629 0.00144938i
\(795\) 32.1917 32.1917i 1.14172 1.14172i
\(796\) −1.33359 + 22.8897i −0.0472679 + 0.811303i
\(797\) 11.0459 + 11.0459i 0.391266 + 0.391266i 0.875138 0.483873i \(-0.160770\pi\)
−0.483873 + 0.875138i \(0.660770\pi\)
\(798\) −0.160141 + 5.50197i −0.00566894 + 0.194768i
\(799\) 56.9337 2.01417
\(800\) −24.1781 3.54271i −0.854826 0.125254i
\(801\) −24.0496 −0.849750
\(802\) 0.164258 5.64339i 0.00580014 0.199275i
\(803\) 11.8208 + 11.8208i 0.417146 + 0.417146i
\(804\) −1.89125 + 32.4613i −0.0666992 + 1.14482i
\(805\) 7.98152 7.98152i 0.281312 0.281312i
\(806\) −18.5314 + 17.4832i −0.652742 + 0.615819i
\(807\) 8.43270i 0.296845i
\(808\) 0.409284 + 0.487793i 0.0143986 + 0.0171605i
\(809\) 5.34576i 0.187947i 0.995575 + 0.0939735i \(0.0299569\pi\)
−0.995575 + 0.0939735i \(0.970043\pi\)
\(810\) 30.1200 + 31.9259i 1.05831 + 1.12176i
\(811\) 8.36280 8.36280i 0.293657 0.293657i −0.544866 0.838523i \(-0.683419\pi\)
0.838523 + 0.544866i \(0.183419\pi\)
\(812\) −13.0378 + 11.6022i −0.457538 + 0.407159i
\(813\) 10.4233 + 10.4233i 0.365562 + 0.365562i
\(814\) −15.5868 0.453674i −0.546318 0.0159013i
\(815\) −72.9168 −2.55416
\(816\) 39.3602 + 49.7828i 1.37788 + 1.74275i
\(817\) 6.44492 0.225479
\(818\) 8.83144 + 0.257050i 0.308784 + 0.00898753i
\(819\) 7.70453 + 7.70453i 0.269218 + 0.269218i
\(820\) 25.0617 + 28.1627i 0.875194 + 0.983484i
\(821\) −21.9983 + 21.9983i −0.767745 + 0.767745i −0.977709 0.209964i \(-0.932665\pi\)
0.209964 + 0.977709i \(0.432665\pi\)
\(822\) −44.6046 47.2789i −1.55576 1.64904i
\(823\) 14.3205i 0.499180i 0.968352 + 0.249590i \(0.0802958\pi\)
−0.968352 + 0.249590i \(0.919704\pi\)
\(824\) 28.9122 + 2.53029i 1.00721 + 0.0881469i
\(825\) 41.8413i 1.45673i
\(826\) 4.31185 4.06795i 0.150029 0.141542i
\(827\) 12.6413 12.6413i 0.439582 0.439582i −0.452289 0.891871i \(-0.649392\pi\)
0.891871 + 0.452289i \(0.149392\pi\)
\(828\) 11.3450 + 0.660977i 0.394265 + 0.0229705i
\(829\) −8.76539 8.76539i −0.304435 0.304435i 0.538311 0.842746i \(-0.319062\pi\)
−0.842746 + 0.538311i \(0.819062\pi\)
\(830\) −1.35339 + 46.4985i −0.0469770 + 1.61399i
\(831\) −12.3116 −0.427084
\(832\) 11.8990 + 16.9956i 0.412525 + 0.589215i
\(833\) 28.7538 0.996260
\(834\) 1.19586 41.0861i 0.0414093 1.42270i
\(835\) −14.7386 14.7386i −0.510052 0.510052i
\(836\) 8.21570 + 0.478661i 0.284146 + 0.0165548i
\(837\) 5.30719 5.30719i 0.183443 0.183443i
\(838\) −18.0194 + 17.0001i −0.622470 + 0.587260i
\(839\) 20.1832i 0.696802i −0.937346 0.348401i \(-0.886725\pi\)
0.937346 0.348401i \(-0.113275\pi\)
\(840\) 33.4794 + 2.92999i 1.15515 + 0.101094i
\(841\) 1.14653i 0.0395354i
\(842\) −10.1326 10.7402i −0.349194 0.370130i
\(843\) 48.9236 48.9236i 1.68502 1.68502i
\(844\) 13.9264 + 15.6495i 0.479365 + 0.538678i
\(845\) 13.5445 + 13.5445i 0.465945 + 0.465945i
\(846\) 30.3416 + 0.883128i 1.04317 + 0.0303626i
\(847\) 9.80786 0.337002
\(848\) −19.8784 + 15.7166i −0.682626 + 0.539710i
\(849\) −13.4077 −0.460152
\(850\) −41.1584 1.19796i −1.41172 0.0410898i
\(851\) −4.23708 4.23708i −0.145245 0.145245i
\(852\) 44.4088 39.5190i 1.52142 1.35390i
\(853\) −21.8924 + 21.8924i −0.749583 + 0.749583i −0.974401 0.224818i \(-0.927821\pi\)
0.224818 + 0.974401i \(0.427821\pi\)
\(854\) −17.1709 18.2005i −0.587578 0.622807i
\(855\) 7.75723i 0.265292i
\(856\) 9.67222 + 11.5276i 0.330590 + 0.394004i
\(857\) 26.5057i 0.905417i −0.891658 0.452709i \(-0.850458\pi\)
0.891658 0.452709i \(-0.149542\pi\)
\(858\) 25.8396 24.3779i 0.882148 0.832248i
\(859\) −20.1778 + 20.1778i −0.688457 + 0.688457i −0.961891 0.273434i \(-0.911841\pi\)
0.273434 + 0.961891i \(0.411841\pi\)
\(860\) 2.28875 39.2839i 0.0780456 1.33957i
\(861\) −16.9931 16.9931i −0.579122 0.579122i
\(862\) −0.607533 + 20.8730i −0.0206926 + 0.710936i
\(863\) −28.4763 −0.969343 −0.484672 0.874696i \(-0.661061\pi\)
−0.484672 + 0.874696i \(0.661061\pi\)
\(864\) −3.64963 4.90277i −0.124163 0.166796i
\(865\) −7.37996 −0.250926
\(866\) −0.919886 + 31.6045i −0.0312590 + 1.07396i
\(867\) 47.3195 + 47.3195i 1.60705 + 1.60705i
\(868\) 1.33610 22.9327i 0.0453502 0.778388i
\(869\) 22.9310 22.9310i 0.777880 0.777880i
\(870\) 39.0133 36.8065i 1.32267 1.24786i
\(871\) 17.9119i 0.606921i
\(872\) −36.9468 + 31.0003i −1.25118 + 1.04980i
\(873\) 36.3404i 1.22994i
\(874\) 2.17016 + 2.30028i 0.0734069 + 0.0778082i
\(875\) 2.42794 2.42794i 0.0820792 0.0820792i
\(876\) −14.2882 + 12.7149i −0.482752 + 0.429597i
\(877\) 2.44906 + 2.44906i 0.0826987 + 0.0826987i 0.747246 0.664547i \(-0.231376\pi\)
−0.664547 + 0.747246i \(0.731376\pi\)
\(878\) −4.27797 0.124515i −0.144375 0.00420219i
\(879\) 21.2868 0.717987
\(880\) 5.83519 49.9074i 0.196704 1.68238i
\(881\) 4.91215 0.165494 0.0827472 0.996571i \(-0.473631\pi\)
0.0827472 + 0.996571i \(0.473631\pi\)
\(882\) 15.3237 + 0.446015i 0.515976 + 0.0150181i
\(883\) 34.4699 + 34.4699i 1.16000 + 1.16000i 0.984474 + 0.175531i \(0.0561641\pi\)
0.175531 + 0.984474i \(0.443836\pi\)
\(884\) 23.2402 + 26.1158i 0.781653 + 0.878369i
\(885\) −12.8818 + 12.8818i −0.433017 + 0.433017i
\(886\) −26.2190 27.7910i −0.880843 0.933656i
\(887\) 34.4251i 1.15588i 0.816079 + 0.577941i \(0.196144\pi\)
−0.816079 + 0.577941i \(0.803856\pi\)
\(888\) 1.55542 17.7729i 0.0521965 0.596420i
\(889\) 31.3185i 1.05039i
\(890\) −29.7223 + 28.0410i −0.996294 + 0.939937i
\(891\) −29.5801 + 29.5801i −0.990971 + 0.990971i
\(892\) 20.8712 + 1.21599i 0.698820 + 0.0407145i
\(893\) 5.97294 + 5.97294i 0.199877 + 0.199877i
\(894\) 0.0386552 1.32808i 0.00129282 0.0444175i
\(895\) 17.0052 0.568422
\(896\) −18.3200 3.78400i −0.612029 0.126415i
\(897\) 13.6510 0.455792
\(898\) 0.825619 28.3658i 0.0275513 0.946578i
\(899\) −25.9235 25.9235i −0.864597 0.864597i
\(900\) −21.9159 1.27686i −0.730529 0.0425619i
\(901\) −30.1935 + 30.1935i −1.00589 + 1.00589i
\(902\) −26.1352 + 24.6569i −0.870208 + 0.820984i
\(903\) 25.0845i 0.834758i
\(904\) 4.45141 50.8637i 0.148052 1.69170i
\(905\) 24.7368i 0.822281i
\(906\) −47.1463 49.9731i −1.56633 1.66025i
\(907\) −13.6078 + 13.6078i −0.451839 + 0.451839i −0.895965 0.444126i \(-0.853514\pi\)
0.444126 + 0.895965i \(0.353514\pi\)
\(908\) 11.0741 + 12.4443i 0.367507 + 0.412980i
\(909\) 0.404497 + 0.404497i 0.0134163 + 0.0134163i
\(910\) 18.5051 + 0.538612i 0.613437 + 0.0178548i
\(911\) −34.7876 −1.15257 −0.576283 0.817250i \(-0.695497\pi\)
−0.576283 + 0.817250i \(0.695497\pi\)
\(912\) −1.09344 + 9.35202i −0.0362075 + 0.309676i
\(913\) −44.3359 −1.46731
\(914\) −5.93027 0.172608i −0.196156 0.00570935i
\(915\) 54.3744 + 54.3744i 1.79756 + 1.79756i
\(916\) −2.36021 + 2.10033i −0.0779834 + 0.0693967i
\(917\) −10.3860 + 10.3860i −0.342975 + 0.342975i
\(918\) −7.06748 7.49123i −0.233262 0.247247i
\(919\) 25.0906i 0.827663i 0.910354 + 0.413831i \(0.135810\pi\)
−0.910354 + 0.413831i \(0.864190\pi\)
\(920\) 14.7916 12.4110i 0.487666 0.409178i
\(921\) 21.8479i 0.719911i
\(922\) −7.39432 + 6.97605i −0.243519 + 0.229744i
\(923\) 23.1554 23.1554i 0.762169 0.762169i
\(924\) −1.86301 + 31.9766i −0.0612885 + 1.05195i
\(925\) 8.18506 + 8.18506i 0.269123 + 0.269123i
\(926\) −0.758771 + 26.0690i −0.0249347 + 0.856682i
\(927\) 26.0734 0.856362
\(928\) −23.9481 + 17.8270i −0.786134 + 0.585199i
\(929\) 25.0250 0.821044 0.410522 0.911851i \(-0.365347\pi\)
0.410522 + 0.911851i \(0.365347\pi\)
\(930\) −2.05391 + 70.5661i −0.0673504 + 2.31396i
\(931\) 3.01657 + 3.01657i 0.0988642 + 0.0988642i
\(932\) 0.0935583 1.60583i 0.00306460 0.0526006i
\(933\) 37.4763 37.4763i 1.22692 1.22692i
\(934\) −3.30838 + 3.12123i −0.108253 + 0.102130i
\(935\) 84.6681i 2.76894i
\(936\) 11.9803 + 14.2783i 0.391587 + 0.466702i
\(937\) 9.64668i 0.315143i 0.987508 + 0.157572i \(0.0503665\pi\)
−0.987508 + 0.157572i \(0.949633\pi\)
\(938\) −11.0830 11.7475i −0.361874 0.383571i
\(939\) −45.8695 + 45.8695i −1.49689 + 1.49689i
\(940\) 38.5281 34.2859i 1.25665 1.11828i
\(941\) 16.4584 + 16.4584i 0.536528 + 0.536528i 0.922507 0.385979i \(-0.126136\pi\)
−0.385979 + 0.922507i \(0.626136\pi\)
\(942\) 37.1898 + 1.08245i 1.21171 + 0.0352682i
\(943\) −13.8072 −0.449623
\(944\) 7.95451 6.28914i 0.258897 0.204694i
\(945\) −5.45389 −0.177415
\(946\) 37.4886 + 1.09115i 1.21886 + 0.0354764i
\(947\) −7.86883 7.86883i −0.255703 0.255703i 0.567601 0.823304i \(-0.307872\pi\)
−0.823304 + 0.567601i \(0.807872\pi\)
\(948\) 24.6655 + 27.7174i 0.801098 + 0.900220i
\(949\) −7.45005 + 7.45005i −0.241839 + 0.241839i
\(950\) −4.19226 4.44362i −0.136015 0.144170i
\(951\) 13.7435i 0.445662i
\(952\) −31.4013 2.74813i −1.01772 0.0890673i
\(953\) 25.8987i 0.838940i −0.907769 0.419470i \(-0.862216\pi\)
0.907769 0.419470i \(-0.137784\pi\)
\(954\) −16.5593 + 15.6226i −0.536128 + 0.505801i
\(955\) 6.17952 6.17952i 0.199965 0.199965i
\(956\) −30.6500 1.78572i −0.991292 0.0577544i
\(957\) 36.1467 + 36.1467i 1.16846 + 1.16846i
\(958\) 0.157900 5.42497i 0.00510152 0.175273i
\(959\) 32.2842 1.04251
\(960\) 56.6153 + 9.98601i 1.82725 + 0.322297i
\(961\) 17.2545 0.556596
\(962\) 0.285928 9.82362i 0.00921870 0.316726i
\(963\) 9.55910 + 9.55910i 0.308038 + 0.308038i
\(964\) 31.2286 + 1.81943i 1.00580 + 0.0585999i
\(965\) −17.6429 + 17.6429i −0.567945 + 0.567945i
\(966\) −8.95299 + 8.44656i −0.288058 + 0.271763i
\(967\) 1.14283i 0.0367508i −0.999831 0.0183754i \(-0.994151\pi\)
0.999831 0.0183754i \(-0.00584940\pi\)
\(968\) 16.7136 + 1.46271i 0.537195 + 0.0470133i
\(969\) 15.8657i 0.509681i
\(970\) −42.3718 44.9123i −1.36048 1.44205i
\(971\) −5.53244 + 5.53244i −0.177544 + 0.177544i −0.790284 0.612740i \(-0.790067\pi\)
0.612740 + 0.790284i \(0.290067\pi\)
\(972\) −27.5080 30.9116i −0.882318 0.991489i
\(973\) 14.4360 + 14.4360i 0.462798 + 0.462798i
\(974\) 51.8525 + 1.50923i 1.66146 + 0.0483589i
\(975\) −26.3705 −0.844532
\(976\) −26.5467 33.5762i −0.849738 1.07475i
\(977\) −40.4617 −1.29449 −0.647243 0.762284i \(-0.724078\pi\)
−0.647243 + 0.762284i \(0.724078\pi\)
\(978\) 79.4786 + 2.31332i 2.54144 + 0.0739718i
\(979\) −27.5384 27.5384i −0.880132 0.880132i
\(980\) 19.4582 17.3157i 0.621571 0.553131i
\(981\) −30.6377 + 30.6377i −0.978188 + 0.978188i
\(982\) −11.3546 12.0354i −0.362339 0.384064i
\(983\) 30.6417i 0.977318i 0.872475 + 0.488659i \(0.162514\pi\)
−0.872475 + 0.488659i \(0.837486\pi\)
\(984\) −26.4236 31.4922i −0.842353 1.00393i
\(985\) 75.4849i 2.40515i
\(986\) −36.5917 + 34.5218i −1.16532 + 1.09940i
\(987\) −23.2474 + 23.2474i −0.739974 + 0.739974i
\(988\) −0.301677 + 5.17796i −0.00959762 + 0.164733i
\(989\) 10.1908 + 10.1908i 0.324048 + 0.324048i
\(990\) 1.31333 45.1220i 0.0417404 1.43407i
\(991\) 21.4041 0.679924 0.339962 0.940439i \(-0.389586\pi\)
0.339962 + 0.940439i \(0.389586\pi\)
\(992\) 5.69696 38.8804i 0.180879 1.23445i
\(993\) 13.1432 0.417086
\(994\) −0.859039 + 29.5139i −0.0272471 + 0.936126i
\(995\) 24.7476 + 24.7476i 0.784552 + 0.784552i
\(996\) 2.95037 50.6399i 0.0934861 1.60459i
\(997\) 3.29934 3.29934i 0.104491 0.104491i −0.652928 0.757420i \(-0.726460\pi\)
0.757420 + 0.652928i \(0.226460\pi\)
\(998\) 19.4522 18.3519i 0.615750 0.580919i
\(999\) 2.89525i 0.0916018i
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 304.2.k.b.77.18 68
4.3 odd 2 1216.2.k.b.913.5 68
16.5 even 4 inner 304.2.k.b.229.18 yes 68
16.11 odd 4 1216.2.k.b.305.5 68
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
304.2.k.b.77.18 68 1.1 even 1 trivial
304.2.k.b.229.18 yes 68 16.5 even 4 inner
1216.2.k.b.305.5 68 16.11 odd 4
1216.2.k.b.913.5 68 4.3 odd 2