Properties

Label 117.2.x.a.11.4
Level $117$
Weight $2$
Character 117.11
Analytic conductor $0.934$
Analytic rank $0$
Dimension $48$
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] = [117,2,Mod(2,117)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(117, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([2, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("117.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 117.x (of order \(12\), degree \(4\), 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: \(0.934249703649\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 11.4
Character \(\chi\) \(=\) 117.11
Dual form 117.2.x.a.32.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.841634 + 0.841634i) q^{2} +(-0.947612 - 1.44984i) q^{3} +0.583303i q^{4} +(-2.77680 - 0.744040i) q^{5} +(2.01778 + 0.422691i) q^{6} +(-1.42554 - 0.381973i) q^{7} +(-2.17420 - 2.17420i) q^{8} +(-1.20406 + 2.74777i) q^{9} +O(q^{10})\) \(q+(-0.841634 + 0.841634i) q^{2} +(-0.947612 - 1.44984i) q^{3} +0.583303i q^{4} +(-2.77680 - 0.744040i) q^{5} +(2.01778 + 0.422691i) q^{6} +(-1.42554 - 0.381973i) q^{7} +(-2.17420 - 2.17420i) q^{8} +(-1.20406 + 2.74777i) q^{9} +(2.96326 - 1.71084i) q^{10} +(-1.23230 - 1.23230i) q^{11} +(0.845695 - 0.552745i) q^{12} +(-3.60363 + 0.117561i) q^{13} +(1.52127 - 0.878303i) q^{14} +(1.55259 + 4.73097i) q^{15} +2.49315 q^{16} +(0.939625 - 1.62748i) q^{17} +(-1.29924 - 3.32600i) q^{18} +(4.34907 - 1.16533i) q^{19} +(0.434001 - 1.61971i) q^{20} +(0.797061 + 2.42877i) q^{21} +2.07429 q^{22} +(-2.82588 + 4.89457i) q^{23} +(-1.09194 + 5.21253i) q^{24} +(2.82688 + 1.63210i) q^{25} +(2.93400 - 3.13189i) q^{26} +(5.12481 - 0.858121i) q^{27} +(0.222806 - 0.831522i) q^{28} +6.70089i q^{29} +(-5.28846 - 2.67504i) q^{30} +(0.676611 - 2.52515i) q^{31} +(2.25007 - 2.25007i) q^{32} +(-0.618892 + 2.95437i) q^{33} +(0.578921 + 2.16056i) q^{34} +(3.67424 + 2.12132i) q^{35} +(-1.60278 - 0.702333i) q^{36} +(-11.1775 - 2.99499i) q^{37} +(-2.67955 + 4.64111i) q^{38} +(3.58529 + 5.11328i) q^{39} +(4.41961 + 7.65499i) q^{40} +(0.168067 + 0.627234i) q^{41} +(-2.71497 - 1.37330i) q^{42} +(1.78065 - 1.02806i) q^{43} +(0.718802 - 0.718802i) q^{44} +(5.38789 - 6.73412i) q^{45} +(-1.74108 - 6.49779i) q^{46} +(2.31288 - 0.619735i) q^{47} +(-2.36254 - 3.61467i) q^{48} +(-4.17591 - 2.41096i) q^{49} +(-3.75283 + 1.00557i) q^{50} +(-3.24998 + 0.179913i) q^{51} +(-0.0685738 - 2.10201i) q^{52} -11.5633i q^{53} +(-3.59099 + 5.03544i) q^{54} +(2.50496 + 4.33872i) q^{55} +(2.26892 + 3.92989i) q^{56} +(-5.81077 - 5.20117i) q^{57} +(-5.63970 - 5.63970i) q^{58} +(-9.15908 - 9.15908i) q^{59} +(-2.75959 + 0.905629i) q^{60} +(-5.24278 - 9.08077i) q^{61} +(1.55579 + 2.69471i) q^{62} +(2.76601 - 3.45714i) q^{63} +8.77378i q^{64} +(10.0940 + 2.35481i) q^{65} +(-1.96562 - 3.00738i) q^{66} +(3.50643 - 0.939544i) q^{67} +(0.949313 + 0.548086i) q^{68} +(9.77417 - 0.541081i) q^{69} +(-4.87774 + 1.30699i) q^{70} +(2.99663 + 11.1836i) q^{71} +(8.59206 - 3.35632i) q^{72} +(-8.97423 + 8.97423i) q^{73} +(11.9280 - 6.88665i) q^{74} +(-0.312504 - 5.64511i) q^{75} +(0.679740 + 2.53683i) q^{76} +(1.28599 + 2.22739i) q^{77} +(-7.32102 - 1.28601i) q^{78} +(-4.85927 + 8.41651i) q^{79} +(-6.92298 - 1.85501i) q^{80} +(-6.10046 - 6.61697i) q^{81} +(-0.669352 - 0.386451i) q^{82} +(0.712145 + 2.65776i) q^{83} +(-1.41671 + 0.464928i) q^{84} +(-3.82006 + 3.82006i) q^{85} +(-0.633407 + 2.36391i) q^{86} +(9.71522 - 6.34985i) q^{87} +5.35851i q^{88} +(-1.57286 + 5.86998i) q^{89} +(1.13304 + 10.2023i) q^{90} +(5.18203 + 1.20890i) q^{91} +(-2.85501 - 1.64834i) q^{92} +(-4.30222 + 1.41188i) q^{93} +(-1.42501 + 2.46819i) q^{94} -12.9435 q^{95} +(-5.39443 - 1.13004i) q^{96} +(-1.35706 + 5.06463i) q^{97} +(5.54374 - 1.48544i) q^{98} +(4.86983 - 1.90230i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9} - 12 q^{10} - 6 q^{11} + 18 q^{12} - 2 q^{13} - 12 q^{14} - 26 q^{15} - 28 q^{16} - 14 q^{18} - 4 q^{19} - 18 q^{20} - 8 q^{21} - 4 q^{22} - 6 q^{23} + 6 q^{24} - 48 q^{26} - 32 q^{27} + 42 q^{30} - 18 q^{31} + 54 q^{32} + 28 q^{33} + 6 q^{34} + 6 q^{35} + 24 q^{36} - 6 q^{37} + 36 q^{38} + 10 q^{39} - 12 q^{40} + 18 q^{41} - 70 q^{42} - 30 q^{43} + 12 q^{44} + 40 q^{45} - 12 q^{46} - 36 q^{47} - 14 q^{48} - 6 q^{49} - 60 q^{50} + 56 q^{52} + 34 q^{54} - 4 q^{55} - 6 q^{56} - 56 q^{57} + 50 q^{58} - 6 q^{59} + 44 q^{60} + 2 q^{61} + 18 q^{62} + 22 q^{63} + 72 q^{65} + 32 q^{66} + 26 q^{67} + 42 q^{68} + 30 q^{69} - 16 q^{70} - 48 q^{71} + 30 q^{72} - 22 q^{73} + 30 q^{74} - 24 q^{75} + 6 q^{76} + 72 q^{77} - 20 q^{78} + 8 q^{79} - 54 q^{80} + 82 q^{81} - 12 q^{82} + 54 q^{83} - 38 q^{84} - 24 q^{85} - 54 q^{86} + 2 q^{87} - 114 q^{90} - 16 q^{91} + 120 q^{92} + 52 q^{93} + 26 q^{94} - 12 q^{95} + 94 q^{96} - 24 q^{97} + 36 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.841634 + 0.841634i −0.595125 + 0.595125i −0.939011 0.343886i \(-0.888257\pi\)
0.343886 + 0.939011i \(0.388257\pi\)
\(3\) −0.947612 1.44984i −0.547104 0.837065i
\(4\) 0.583303i 0.291651i
\(5\) −2.77680 0.744040i −1.24182 0.332745i −0.422650 0.906293i \(-0.638900\pi\)
−0.819172 + 0.573548i \(0.805567\pi\)
\(6\) 2.01778 + 0.422691i 0.823754 + 0.172563i
\(7\) −1.42554 0.381973i −0.538804 0.144372i −0.0208532 0.999783i \(-0.506638\pi\)
−0.517951 + 0.855410i \(0.673305\pi\)
\(8\) −2.17420 2.17420i −0.768695 0.768695i
\(9\) −1.20406 + 2.74777i −0.401354 + 0.915923i
\(10\) 2.96326 1.71084i 0.937065 0.541014i
\(11\) −1.23230 1.23230i −0.371552 0.371552i 0.496491 0.868042i \(-0.334622\pi\)
−0.868042 + 0.496491i \(0.834622\pi\)
\(12\) 0.845695 0.552745i 0.244131 0.159564i
\(13\) −3.60363 + 0.117561i −0.999468 + 0.0326056i
\(14\) 1.52127 0.878303i 0.406575 0.234736i
\(15\) 1.55259 + 4.73097i 0.400876 + 1.22153i
\(16\) 2.49315 0.623288
\(17\) 0.939625 1.62748i 0.227893 0.394722i −0.729291 0.684204i \(-0.760150\pi\)
0.957183 + 0.289482i \(0.0934831\pi\)
\(18\) −1.29924 3.32600i −0.306233 0.783945i
\(19\) 4.34907 1.16533i 0.997745 0.267345i 0.277245 0.960799i \(-0.410579\pi\)
0.720501 + 0.693454i \(0.243912\pi\)
\(20\) 0.434001 1.61971i 0.0970455 0.362179i
\(21\) 0.797061 + 2.42877i 0.173933 + 0.530000i
\(22\) 2.07429 0.442240
\(23\) −2.82588 + 4.89457i −0.589237 + 1.02059i 0.405096 + 0.914274i \(0.367238\pi\)
−0.994333 + 0.106314i \(0.966095\pi\)
\(24\) −1.09194 + 5.21253i −0.222891 + 1.06400i
\(25\) 2.82688 + 1.63210i 0.565376 + 0.326420i
\(26\) 2.93400 3.13189i 0.575405 0.614213i
\(27\) 5.12481 0.858121i 0.986269 0.165146i
\(28\) 0.222806 0.831522i 0.0421063 0.157143i
\(29\) 6.70089i 1.24432i 0.782888 + 0.622162i \(0.213746\pi\)
−0.782888 + 0.622162i \(0.786254\pi\)
\(30\) −5.28846 2.67504i −0.965536 0.488392i
\(31\) 0.676611 2.52515i 0.121523 0.453530i −0.878169 0.478350i \(-0.841235\pi\)
0.999692 + 0.0248208i \(0.00790153\pi\)
\(32\) 2.25007 2.25007i 0.397760 0.397760i
\(33\) −0.618892 + 2.95437i −0.107735 + 0.514290i
\(34\) 0.578921 + 2.16056i 0.0992842 + 0.370534i
\(35\) 3.67424 + 2.12132i 0.621059 + 0.358569i
\(36\) −1.60278 0.702333i −0.267130 0.117056i
\(37\) −11.1775 2.99499i −1.83756 0.492374i −0.838912 0.544267i \(-0.816808\pi\)
−0.998653 + 0.0518927i \(0.983475\pi\)
\(38\) −2.67955 + 4.64111i −0.434680 + 0.752888i
\(39\) 3.58529 + 5.11328i 0.574106 + 0.818781i
\(40\) 4.41961 + 7.65499i 0.698802 + 1.21036i
\(41\) 0.168067 + 0.627234i 0.0262476 + 0.0979574i 0.977807 0.209507i \(-0.0671860\pi\)
−0.951559 + 0.307465i \(0.900519\pi\)
\(42\) −2.71497 1.37330i −0.418929 0.211905i
\(43\) 1.78065 1.02806i 0.271547 0.156778i −0.358044 0.933705i \(-0.616556\pi\)
0.629590 + 0.776927i \(0.283223\pi\)
\(44\) 0.718802 0.718802i 0.108364 0.108364i
\(45\) 5.38789 6.73412i 0.803179 1.00386i
\(46\) −1.74108 6.49779i −0.256708 0.958048i
\(47\) 2.31288 0.619735i 0.337369 0.0903977i −0.0861575 0.996282i \(-0.527459\pi\)
0.423526 + 0.905884i \(0.360792\pi\)
\(48\) −2.36254 3.61467i −0.341003 0.521732i
\(49\) −4.17591 2.41096i −0.596559 0.344424i
\(50\) −3.75283 + 1.00557i −0.530730 + 0.142209i
\(51\) −3.24998 + 0.179913i −0.455088 + 0.0251929i
\(52\) −0.0685738 2.10201i −0.00950947 0.291496i
\(53\) 11.5633i 1.58834i −0.607698 0.794168i \(-0.707907\pi\)
0.607698 0.794168i \(-0.292093\pi\)
\(54\) −3.59099 + 5.03544i −0.488672 + 0.685236i
\(55\) 2.50496 + 4.33872i 0.337769 + 0.585033i
\(56\) 2.26892 + 3.92989i 0.303198 + 0.525154i
\(57\) −5.81077 5.20117i −0.769656 0.688912i
\(58\) −5.63970 5.63970i −0.740529 0.740529i
\(59\) −9.15908 9.15908i −1.19241 1.19241i −0.976388 0.216023i \(-0.930691\pi\)
−0.216023 0.976388i \(-0.569309\pi\)
\(60\) −2.75959 + 0.905629i −0.356261 + 0.116916i
\(61\) −5.24278 9.08077i −0.671269 1.16267i −0.977544 0.210730i \(-0.932416\pi\)
0.306275 0.951943i \(-0.400917\pi\)
\(62\) 1.55579 + 2.69471i 0.197586 + 0.342228i
\(63\) 2.76601 3.45714i 0.348485 0.435558i
\(64\) 8.77378i 1.09672i
\(65\) 10.0940 + 2.35481i 1.25201 + 0.292078i
\(66\) −1.96562 3.00738i −0.241951 0.370183i
\(67\) 3.50643 0.939544i 0.428378 0.114784i −0.0381866 0.999271i \(-0.512158\pi\)
0.466565 + 0.884487i \(0.345491\pi\)
\(68\) 0.949313 + 0.548086i 0.115121 + 0.0664652i
\(69\) 9.77417 0.541081i 1.17667 0.0651385i
\(70\) −4.87774 + 1.30699i −0.583001 + 0.156215i
\(71\) 2.99663 + 11.1836i 0.355635 + 1.32725i 0.879684 + 0.475559i \(0.157754\pi\)
−0.524049 + 0.851688i \(0.675579\pi\)
\(72\) 8.59206 3.35632i 1.01258 0.395546i
\(73\) −8.97423 + 8.97423i −1.05035 + 1.05035i −0.0516906 + 0.998663i \(0.516461\pi\)
−0.998663 + 0.0516906i \(0.983539\pi\)
\(74\) 11.9280 6.88665i 1.38661 0.800557i
\(75\) −0.312504 5.64511i −0.0360848 0.651841i
\(76\) 0.679740 + 2.53683i 0.0779716 + 0.290994i
\(77\) 1.28599 + 2.22739i 0.146552 + 0.253835i
\(78\) −7.32102 1.28601i −0.828943 0.145612i
\(79\) −4.85927 + 8.41651i −0.546711 + 0.946931i 0.451786 + 0.892126i \(0.350787\pi\)
−0.998497 + 0.0548048i \(0.982546\pi\)
\(80\) −6.92298 1.85501i −0.774012 0.207396i
\(81\) −6.10046 6.61697i −0.677829 0.735219i
\(82\) −0.669352 0.386451i −0.0739176 0.0426763i
\(83\) 0.712145 + 2.65776i 0.0781681 + 0.291727i 0.993933 0.109987i \(-0.0350810\pi\)
−0.915765 + 0.401715i \(0.868414\pi\)
\(84\) −1.41671 + 0.464928i −0.154575 + 0.0507278i
\(85\) −3.82006 + 3.82006i −0.414344 + 0.414344i
\(86\) −0.633407 + 2.36391i −0.0683020 + 0.254907i
\(87\) 9.71522 6.34985i 1.04158 0.680775i
\(88\) 5.35851i 0.571219i
\(89\) −1.57286 + 5.86998i −0.166722 + 0.622217i 0.831092 + 0.556135i \(0.187716\pi\)
−0.997814 + 0.0660814i \(0.978950\pi\)
\(90\) 1.13304 + 10.2023i 0.119433 + 1.07542i
\(91\) 5.18203 + 1.20890i 0.543225 + 0.126727i
\(92\) −2.85501 1.64834i −0.297656 0.171852i
\(93\) −4.30222 + 1.41188i −0.446119 + 0.146405i
\(94\) −1.42501 + 2.46819i −0.146979 + 0.254575i
\(95\) −12.9435 −1.32798
\(96\) −5.39443 1.13004i −0.550567 0.115335i
\(97\) −1.35706 + 5.06463i −0.137789 + 0.514235i 0.862182 + 0.506599i \(0.169097\pi\)
−0.999971 + 0.00763623i \(0.997569\pi\)
\(98\) 5.54374 1.48544i 0.560003 0.150052i
\(99\) 4.86983 1.90230i 0.489436 0.191189i
\(100\) −0.952008 + 1.64893i −0.0952008 + 0.164893i
\(101\) −3.02851 −0.301348 −0.150674 0.988584i \(-0.548144\pi\)
−0.150674 + 0.988584i \(0.548144\pi\)
\(102\) 2.58388 2.88672i 0.255842 0.285828i
\(103\) 15.9431 9.20475i 1.57092 0.906971i 0.574864 0.818249i \(-0.305055\pi\)
0.996056 0.0887220i \(-0.0282783\pi\)
\(104\) 8.09061 + 7.57941i 0.793350 + 0.743222i
\(105\) −0.406177 7.33724i −0.0396388 0.716041i
\(106\) 9.73204 + 9.73204i 0.945259 + 0.945259i
\(107\) 3.97340 2.29404i 0.384123 0.221774i −0.295487 0.955347i \(-0.595482\pi\)
0.679611 + 0.733573i \(0.262149\pi\)
\(108\) 0.500545 + 2.98931i 0.0481649 + 0.287647i
\(109\) 0.138592 + 0.138592i 0.0132747 + 0.0132747i 0.713713 0.700438i \(-0.247012\pi\)
−0.700438 + 0.713713i \(0.747012\pi\)
\(110\) −5.75988 1.54335i −0.549183 0.147153i
\(111\) 6.24965 + 19.0436i 0.593190 + 1.80754i
\(112\) −3.55409 0.952316i −0.335830 0.0899854i
\(113\) 7.46794i 0.702524i −0.936277 0.351262i \(-0.885753\pi\)
0.936277 0.351262i \(-0.114247\pi\)
\(114\) 9.26803 0.513062i 0.868031 0.0480527i
\(115\) 11.4887 11.4887i 1.07132 1.07132i
\(116\) −3.90865 −0.362909
\(117\) 4.01597 10.0435i 0.371277 0.928522i
\(118\) 15.4172 1.41927
\(119\) −1.96113 + 1.96113i −0.179776 + 0.179776i
\(120\) 6.91043 13.6617i 0.630833 1.24714i
\(121\) 7.96289i 0.723899i
\(122\) 12.0552 + 3.23018i 1.09143 + 0.292447i
\(123\) 0.750125 0.838044i 0.0676365 0.0755639i
\(124\) 1.47292 + 0.394669i 0.132273 + 0.0354423i
\(125\) 3.52846 + 3.52846i 0.315595 + 0.315595i
\(126\) 0.581674 + 5.23762i 0.0518196 + 0.466604i
\(127\) −9.37062 + 5.41013i −0.831508 + 0.480071i −0.854369 0.519667i \(-0.826056\pi\)
0.0228608 + 0.999739i \(0.492723\pi\)
\(128\) −2.88417 2.88417i −0.254927 0.254927i
\(129\) −3.17789 1.60745i −0.279797 0.141528i
\(130\) −10.4774 + 6.51360i −0.918926 + 0.571280i
\(131\) 6.84566 3.95234i 0.598108 0.345318i −0.170189 0.985411i \(-0.554438\pi\)
0.768297 + 0.640094i \(0.221104\pi\)
\(132\) −1.72329 0.361002i −0.149993 0.0314212i
\(133\) −6.64490 −0.576186
\(134\) −2.16038 + 3.74188i −0.186628 + 0.323249i
\(135\) −14.8690 1.43023i −1.27972 0.123095i
\(136\) −5.58139 + 1.49553i −0.478600 + 0.128241i
\(137\) −2.19061 + 8.17545i −0.187156 + 0.698476i 0.807003 + 0.590548i \(0.201088\pi\)
−0.994159 + 0.107928i \(0.965578\pi\)
\(138\) −7.77089 + 8.68167i −0.661502 + 0.739033i
\(139\) 0.469919 0.0398580 0.0199290 0.999801i \(-0.493656\pi\)
0.0199290 + 0.999801i \(0.493656\pi\)
\(140\) −1.23737 + 2.14319i −0.104577 + 0.181133i
\(141\) −3.09023 2.76604i −0.260244 0.232942i
\(142\) −11.9346 6.89042i −1.00153 0.578231i
\(143\) 4.58562 + 4.29588i 0.383469 + 0.359239i
\(144\) −3.00191 + 6.85061i −0.250159 + 0.570884i
\(145\) 4.98574 18.6070i 0.414043 1.54523i
\(146\) 15.1060i 1.25018i
\(147\) 0.461636 + 8.33906i 0.0380751 + 0.687794i
\(148\) 1.74699 6.51985i 0.143602 0.535928i
\(149\) −3.83653 + 3.83653i −0.314301 + 0.314301i −0.846573 0.532272i \(-0.821338\pi\)
0.532272 + 0.846573i \(0.321338\pi\)
\(150\) 5.01414 + 4.48811i 0.409402 + 0.366452i
\(151\) −5.12016 19.1087i −0.416673 1.55504i −0.781462 0.623953i \(-0.785525\pi\)
0.364789 0.931090i \(-0.381141\pi\)
\(152\) −11.9894 6.92208i −0.972468 0.561455i
\(153\) 3.34057 + 4.54146i 0.270069 + 0.367155i
\(154\) −2.95698 0.792321i −0.238280 0.0638470i
\(155\) −3.75762 + 6.50839i −0.301819 + 0.522767i
\(156\) −2.98259 + 2.09131i −0.238799 + 0.167439i
\(157\) 11.5326 + 19.9750i 0.920401 + 1.59418i 0.798796 + 0.601602i \(0.205471\pi\)
0.121605 + 0.992579i \(0.461196\pi\)
\(158\) −2.99389 11.1734i −0.238181 0.888904i
\(159\) −16.7649 + 10.9575i −1.32954 + 0.868985i
\(160\) −7.92213 + 4.57384i −0.626300 + 0.361594i
\(161\) 5.89800 5.89800i 0.464827 0.464827i
\(162\) 10.7034 + 0.434712i 0.840941 + 0.0341542i
\(163\) 1.15428 + 4.30782i 0.0904100 + 0.337415i 0.996284 0.0861334i \(-0.0274511\pi\)
−0.905874 + 0.423548i \(0.860784\pi\)
\(164\) −0.365867 + 0.0980338i −0.0285694 + 0.00765515i
\(165\) 3.91671 7.74321i 0.304915 0.602808i
\(166\) −2.83623 1.63750i −0.220134 0.127095i
\(167\) 0.344237 0.0922379i 0.0266378 0.00713759i −0.245476 0.969403i \(-0.578944\pi\)
0.272113 + 0.962265i \(0.412277\pi\)
\(168\) 3.54765 7.01358i 0.273707 0.541110i
\(169\) 12.9724 0.847295i 0.997874 0.0651766i
\(170\) 6.43019i 0.493173i
\(171\) −2.03450 + 13.3534i −0.155582 + 1.02116i
\(172\) 0.599670 + 1.03866i 0.0457244 + 0.0791970i
\(173\) −5.94881 10.3036i −0.452280 0.783371i 0.546248 0.837624i \(-0.316056\pi\)
−0.998527 + 0.0542525i \(0.982722\pi\)
\(174\) −2.83241 + 13.5209i −0.214724 + 1.02502i
\(175\) −3.40641 3.40641i −0.257501 0.257501i
\(176\) −3.07230 3.07230i −0.231584 0.231584i
\(177\) −4.59993 + 21.9585i −0.345752 + 1.65050i
\(178\) −3.61661 6.26415i −0.271076 0.469518i
\(179\) −2.92970 5.07439i −0.218976 0.379278i 0.735519 0.677504i \(-0.236938\pi\)
−0.954495 + 0.298226i \(0.903605\pi\)
\(180\) 3.92803 + 3.14277i 0.292778 + 0.234248i
\(181\) 8.29778i 0.616769i −0.951262 0.308384i \(-0.900212\pi\)
0.951262 0.308384i \(-0.0997883\pi\)
\(182\) −5.37883 + 3.34393i −0.398705 + 0.247868i
\(183\) −8.19752 + 16.2062i −0.605978 + 1.19800i
\(184\) 16.7858 4.49773i 1.23746 0.331577i
\(185\) 28.8092 + 16.6330i 2.11809 + 1.22288i
\(186\) 2.43261 4.80918i 0.178367 0.352627i
\(187\) −3.16344 + 0.847640i −0.231333 + 0.0619856i
\(188\) 0.361493 + 1.34911i 0.0263646 + 0.0983940i
\(189\) −7.63340 0.734248i −0.555248 0.0534087i
\(190\) 10.8937 10.8937i 0.790314 0.790314i
\(191\) −6.20085 + 3.58006i −0.448678 + 0.259044i −0.707272 0.706942i \(-0.750074\pi\)
0.258594 + 0.965986i \(0.416741\pi\)
\(192\) 12.7206 8.31414i 0.918027 0.600021i
\(193\) −0.709019 2.64609i −0.0510363 0.190470i 0.935701 0.352793i \(-0.114768\pi\)
−0.986738 + 0.162323i \(0.948101\pi\)
\(194\) −3.12041 5.40471i −0.224033 0.388036i
\(195\) −6.15114 16.8662i −0.440492 1.20781i
\(196\) 1.40632 2.43582i 0.100452 0.173987i
\(197\) −23.1428 6.20110i −1.64886 0.441810i −0.689564 0.724224i \(-0.742198\pi\)
−0.959292 + 0.282414i \(0.908865\pi\)
\(198\) −2.49757 + 5.69966i −0.177495 + 0.405057i
\(199\) 8.08608 + 4.66850i 0.573207 + 0.330941i 0.758429 0.651755i \(-0.225967\pi\)
−0.185222 + 0.982697i \(0.559300\pi\)
\(200\) −2.59768 9.69469i −0.183684 0.685518i
\(201\) −4.68492 4.19343i −0.330449 0.295782i
\(202\) 2.54890 2.54890i 0.179340 0.179340i
\(203\) 2.55956 9.55240i 0.179646 0.670447i
\(204\) −0.104944 1.89572i −0.00734755 0.132727i
\(205\) 1.86675i 0.130379i
\(206\) −5.67122 + 21.1653i −0.395133 + 1.47466i
\(207\) −10.0466 13.6582i −0.698287 0.949313i
\(208\) −8.98441 + 0.293098i −0.622957 + 0.0203227i
\(209\) −6.79538 3.92332i −0.470046 0.271381i
\(210\) 6.51712 + 5.83342i 0.449724 + 0.402544i
\(211\) −2.60557 + 4.51298i −0.179375 + 0.310687i −0.941667 0.336547i \(-0.890741\pi\)
0.762292 + 0.647234i \(0.224074\pi\)
\(212\) 6.74488 0.463240
\(213\) 13.3747 14.9423i 0.916422 1.02383i
\(214\) −1.41341 + 5.27490i −0.0966184 + 0.360585i
\(215\) −5.70942 + 1.52984i −0.389379 + 0.104334i
\(216\) −13.0081 9.27661i −0.885086 0.631193i
\(217\) −1.92907 + 3.34125i −0.130954 + 0.226819i
\(218\) −0.233287 −0.0158002
\(219\) 21.5153 + 4.50709i 1.45387 + 0.304561i
\(220\) −2.53079 + 1.46115i −0.170626 + 0.0985107i
\(221\) −3.19474 + 5.97530i −0.214901 + 0.401942i
\(222\) −21.2877 10.7678i −1.42874 0.722691i
\(223\) 4.83926 + 4.83926i 0.324061 + 0.324061i 0.850323 0.526262i \(-0.176407\pi\)
−0.526262 + 0.850323i \(0.676407\pi\)
\(224\) −4.06703 + 2.34810i −0.271740 + 0.156889i
\(225\) −7.88837 + 5.80246i −0.525891 + 0.386830i
\(226\) 6.28527 + 6.28527i 0.418090 + 0.418090i
\(227\) −12.3360 3.30542i −0.818769 0.219389i −0.174961 0.984575i \(-0.555980\pi\)
−0.643808 + 0.765187i \(0.722647\pi\)
\(228\) 3.03386 3.38944i 0.200922 0.224471i
\(229\) 17.6101 + 4.71861i 1.16371 + 0.311815i 0.788446 0.615104i \(-0.210886\pi\)
0.375263 + 0.926919i \(0.377553\pi\)
\(230\) 19.3385i 1.27514i
\(231\) 2.01075 3.97518i 0.132297 0.261547i
\(232\) 14.5691 14.5691i 0.956506 0.956506i
\(233\) 4.27048 0.279769 0.139884 0.990168i \(-0.455327\pi\)
0.139884 + 0.990168i \(0.455327\pi\)
\(234\) 5.07298 + 11.8329i 0.331631 + 0.773543i
\(235\) −6.88351 −0.449031
\(236\) 5.34252 5.34252i 0.347768 0.347768i
\(237\) 16.8073 0.930423i 1.09175 0.0604374i
\(238\) 3.30110i 0.213979i
\(239\) −1.08816 0.291572i −0.0703874 0.0188603i 0.223453 0.974715i \(-0.428267\pi\)
−0.293841 + 0.955854i \(0.594934\pi\)
\(240\) 3.87084 + 11.7950i 0.249861 + 0.761366i
\(241\) 8.52710 + 2.28483i 0.549279 + 0.147179i 0.522776 0.852470i \(-0.324896\pi\)
0.0265026 + 0.999649i \(0.491563\pi\)
\(242\) 6.70184 + 6.70184i 0.430811 + 0.430811i
\(243\) −3.81267 + 15.1150i −0.244583 + 0.969628i
\(244\) 5.29684 3.05813i 0.339095 0.195777i
\(245\) 9.80181 + 9.80181i 0.626215 + 0.626215i
\(246\) 0.0739951 + 1.33666i 0.00471776 + 0.0852222i
\(247\) −15.5355 + 4.71071i −0.988498 + 0.299735i
\(248\) −6.96125 + 4.01908i −0.442040 + 0.255212i
\(249\) 3.17849 3.55102i 0.201429 0.225037i
\(250\) −5.93935 −0.375638
\(251\) 8.72352 15.1096i 0.550624 0.953708i −0.447606 0.894231i \(-0.647723\pi\)
0.998230 0.0594773i \(-0.0189434\pi\)
\(252\) 2.01656 + 1.61342i 0.127031 + 0.101636i
\(253\) 9.51388 2.54924i 0.598133 0.160269i
\(254\) 3.33328 12.4400i 0.209149 0.780554i
\(255\) 9.15840 + 1.91853i 0.573521 + 0.120143i
\(256\) −12.6927 −0.793295
\(257\) 1.62517 2.81488i 0.101376 0.175588i −0.810876 0.585218i \(-0.801009\pi\)
0.912252 + 0.409630i \(0.134342\pi\)
\(258\) 4.02751 1.32173i 0.250742 0.0822872i
\(259\) 14.7899 + 8.53897i 0.919002 + 0.530586i
\(260\) −1.37356 + 5.88788i −0.0851849 + 0.365151i
\(261\) −18.4125 8.06830i −1.13971 0.499415i
\(262\) −2.43511 + 9.08797i −0.150442 + 0.561457i
\(263\) 18.0770i 1.11467i −0.830286 0.557337i \(-0.811823\pi\)
0.830286 0.557337i \(-0.188177\pi\)
\(264\) 7.76898 5.07779i 0.478148 0.312516i
\(265\) −8.60353 + 32.1088i −0.528511 + 1.97243i
\(266\) 5.59258 5.59258i 0.342903 0.342903i
\(267\) 10.0010 3.28208i 0.612050 0.200860i
\(268\) 0.548039 + 2.04531i 0.0334768 + 0.124937i
\(269\) −0.992035 0.572752i −0.0604854 0.0349213i 0.469452 0.882958i \(-0.344451\pi\)
−0.529938 + 0.848037i \(0.677785\pi\)
\(270\) 13.7180 11.3105i 0.834852 0.688338i
\(271\) −8.64641 2.31680i −0.525232 0.140736i −0.0135464 0.999908i \(-0.504312\pi\)
−0.511686 + 0.859173i \(0.670979\pi\)
\(272\) 2.34263 4.05755i 0.142043 0.246025i
\(273\) −3.15785 8.65868i −0.191122 0.524047i
\(274\) −5.03705 8.72443i −0.304299 0.527062i
\(275\) −1.47232 5.49478i −0.0887844 0.331348i
\(276\) 0.315614 + 5.70130i 0.0189977 + 0.343178i
\(277\) −22.2593 + 12.8514i −1.33743 + 0.772165i −0.986426 0.164209i \(-0.947493\pi\)
−0.351003 + 0.936374i \(0.614159\pi\)
\(278\) −0.395500 + 0.395500i −0.0237205 + 0.0237205i
\(279\) 6.12384 + 4.89961i 0.366624 + 0.293332i
\(280\) −3.37634 12.6007i −0.201775 0.753035i
\(281\) 0.868838 0.232804i 0.0518305 0.0138879i −0.232811 0.972522i \(-0.574792\pi\)
0.284641 + 0.958634i \(0.408126\pi\)
\(282\) 4.92884 0.272852i 0.293508 0.0162481i
\(283\) −15.7574 9.09752i −0.936678 0.540791i −0.0477608 0.998859i \(-0.515209\pi\)
−0.888917 + 0.458067i \(0.848542\pi\)
\(284\) −6.52341 + 1.74794i −0.387093 + 0.103721i
\(285\) 12.2655 + 18.7660i 0.726543 + 1.11160i
\(286\) −7.47497 + 0.243856i −0.442004 + 0.0144195i
\(287\) 0.958344i 0.0565693i
\(288\) 3.47345 + 8.89190i 0.204675 + 0.523960i
\(289\) 6.73421 + 11.6640i 0.396130 + 0.686117i
\(290\) 11.4641 + 19.8565i 0.673198 + 1.16601i
\(291\) 8.62886 2.83178i 0.505833 0.166002i
\(292\) −5.23469 5.23469i −0.306337 0.306337i
\(293\) −3.24724 3.24724i −0.189706 0.189706i 0.605863 0.795569i \(-0.292828\pi\)
−0.795569 + 0.605863i \(0.792828\pi\)
\(294\) −7.40697 6.62991i −0.431983 0.386664i
\(295\) 18.6182 + 32.2476i 1.08399 + 1.87753i
\(296\) 17.7903 + 30.8137i 1.03404 + 1.79101i
\(297\) −7.37274 5.25782i −0.427810 0.305090i
\(298\) 6.45792i 0.374097i
\(299\) 9.60803 17.9704i 0.555646 1.03926i
\(300\) 3.29281 0.182284i 0.190110 0.0105242i
\(301\) −2.93108 + 0.785381i −0.168945 + 0.0452686i
\(302\) 20.3918 + 11.7732i 1.17342 + 0.677474i
\(303\) 2.86985 + 4.39085i 0.164869 + 0.252248i
\(304\) 10.8429 2.90535i 0.621883 0.166633i
\(305\) 7.80168 + 29.1163i 0.446723 + 1.66719i
\(306\) −6.63379 1.01071i −0.379228 0.0577786i
\(307\) 3.93098 3.93098i 0.224353 0.224353i −0.585976 0.810329i \(-0.699289\pi\)
0.810329 + 0.585976i \(0.199289\pi\)
\(308\) −1.29925 + 0.750119i −0.0740314 + 0.0427420i
\(309\) −28.4533 14.3924i −1.61865 0.818754i
\(310\) −2.31514 8.64023i −0.131491 0.490732i
\(311\) −10.9466 18.9600i −0.620724 1.07513i −0.989351 0.145548i \(-0.953506\pi\)
0.368627 0.929577i \(-0.379828\pi\)
\(312\) 3.32216 18.9124i 0.188080 1.07070i
\(313\) −3.78444 + 6.55485i −0.213909 + 0.370502i −0.952935 0.303176i \(-0.901953\pi\)
0.739025 + 0.673678i \(0.235286\pi\)
\(314\) −26.5179 7.10545i −1.49649 0.400984i
\(315\) −10.2529 + 7.54174i −0.577686 + 0.424929i
\(316\) −4.90937 2.83443i −0.276174 0.159449i
\(317\) 7.64018 + 28.5136i 0.429116 + 1.60148i 0.754768 + 0.655992i \(0.227749\pi\)
−0.325653 + 0.945489i \(0.605584\pi\)
\(318\) 4.88769 23.3321i 0.274088 1.30840i
\(319\) 8.25749 8.25749i 0.462331 0.462331i
\(320\) 6.52805 24.3630i 0.364929 1.36193i
\(321\) −7.09124 3.58693i −0.395794 0.200203i
\(322\) 9.92792i 0.553261i
\(323\) 2.18995 8.17300i 0.121852 0.454758i
\(324\) 3.85970 3.55842i 0.214428 0.197690i
\(325\) −10.3789 5.54916i −0.575718 0.307812i
\(326\) −4.59709 2.65413i −0.254609 0.146999i
\(327\) 0.0696043 0.332266i 0.00384913 0.0183744i
\(328\) 0.998319 1.72914i 0.0551230 0.0954758i
\(329\) −3.53383 −0.194826
\(330\) 3.22051 + 9.81339i 0.177283 + 0.540209i
\(331\) 4.98513 18.6048i 0.274008 1.02261i −0.682496 0.730890i \(-0.739105\pi\)
0.956503 0.291721i \(-0.0942280\pi\)
\(332\) −1.55028 + 0.415396i −0.0850827 + 0.0227978i
\(333\) 21.6879 27.1069i 1.18849 1.48545i
\(334\) −0.212091 + 0.367352i −0.0116051 + 0.0201006i
\(335\) −10.4357 −0.570163
\(336\) 1.98720 + 6.05528i 0.108410 + 0.330343i
\(337\) −15.6291 + 9.02348i −0.851373 + 0.491541i −0.861114 0.508412i \(-0.830233\pi\)
0.00974077 + 0.999953i \(0.496899\pi\)
\(338\) −10.2049 + 11.6311i −0.555072 + 0.632648i
\(339\) −10.8273 + 7.07671i −0.588058 + 0.384354i
\(340\) −2.22825 2.22825i −0.120844 0.120844i
\(341\) −3.94552 + 2.27794i −0.213662 + 0.123358i
\(342\) −9.52636 12.9510i −0.515126 0.700308i
\(343\) 12.3370 + 12.3370i 0.666135 + 0.666135i
\(344\) −6.10669 1.63628i −0.329251 0.0882224i
\(345\) −27.5435 5.76990i −1.48289 0.310641i
\(346\) 13.6786 + 3.66518i 0.735367 + 0.197041i
\(347\) 25.1292i 1.34901i 0.738272 + 0.674503i \(0.235642\pi\)
−0.738272 + 0.674503i \(0.764358\pi\)
\(348\) 3.70388 + 5.66691i 0.198549 + 0.303778i
\(349\) −16.5014 + 16.5014i −0.883300 + 0.883300i −0.993868 0.110569i \(-0.964733\pi\)
0.110569 + 0.993868i \(0.464733\pi\)
\(350\) 5.73391 0.306490
\(351\) −18.3670 + 3.69483i −0.980360 + 0.197216i
\(352\) −5.54551 −0.295577
\(353\) 14.1500 14.1500i 0.753127 0.753127i −0.221935 0.975061i \(-0.571237\pi\)
0.975061 + 0.221935i \(0.0712373\pi\)
\(354\) −14.6095 22.3525i −0.776488 1.18802i
\(355\) 33.2841i 1.76654i
\(356\) −3.42398 0.917452i −0.181470 0.0486248i
\(357\) 4.70170 + 0.984930i 0.248841 + 0.0521280i
\(358\) 6.73652 + 1.80504i 0.356036 + 0.0953996i
\(359\) −1.97346 1.97346i −0.104155 0.104155i 0.653109 0.757264i \(-0.273464\pi\)
−0.757264 + 0.653109i \(0.773464\pi\)
\(360\) −26.3556 + 2.92698i −1.38906 + 0.154265i
\(361\) 1.10195 0.636209i 0.0579972 0.0334847i
\(362\) 6.98370 + 6.98370i 0.367055 + 0.367055i
\(363\) −11.5449 + 7.54573i −0.605950 + 0.396048i
\(364\) −0.705155 + 3.02269i −0.0369602 + 0.158432i
\(365\) 31.5968 18.2424i 1.65385 0.954852i
\(366\) −6.74041 20.5390i −0.352327 1.07359i
\(367\) −32.9892 −1.72202 −0.861011 0.508587i \(-0.830168\pi\)
−0.861011 + 0.508587i \(0.830168\pi\)
\(368\) −7.04535 + 12.2029i −0.367264 + 0.636120i
\(369\) −1.92586 0.293420i −0.100256 0.0152749i
\(370\) −38.2457 + 10.2479i −1.98830 + 0.532763i
\(371\) −4.41685 + 16.4839i −0.229311 + 0.855802i
\(372\) −0.823555 2.50950i −0.0426993 0.130111i
\(373\) −4.70461 −0.243596 −0.121798 0.992555i \(-0.538866\pi\)
−0.121798 + 0.992555i \(0.538866\pi\)
\(374\) 1.94905 3.37586i 0.100783 0.174562i
\(375\) 1.77209 8.45932i 0.0915102 0.436837i
\(376\) −6.37609 3.68124i −0.328822 0.189845i
\(377\) −0.787765 24.1476i −0.0405720 1.24366i
\(378\) 7.04250 5.80656i 0.362227 0.298657i
\(379\) 5.09903 19.0299i 0.261920 0.977498i −0.702189 0.711991i \(-0.747794\pi\)
0.964109 0.265507i \(-0.0855394\pi\)
\(380\) 7.55000i 0.387307i
\(381\) 16.7235 + 8.45918i 0.856772 + 0.433377i
\(382\) 2.20574 8.23195i 0.112856 0.421183i
\(383\) 4.04582 4.04582i 0.206732 0.206732i −0.596145 0.802877i \(-0.703302\pi\)
0.802877 + 0.596145i \(0.203302\pi\)
\(384\) −1.44851 + 6.91466i −0.0739189 + 0.352862i
\(385\) −1.91365 7.14185i −0.0975287 0.363982i
\(386\) 2.82378 + 1.63031i 0.143727 + 0.0829806i
\(387\) 0.680853 + 6.13066i 0.0346097 + 0.311639i
\(388\) −2.95421 0.791578i −0.149977 0.0401863i
\(389\) 8.59884 14.8936i 0.435978 0.755137i −0.561397 0.827547i \(-0.689736\pi\)
0.997375 + 0.0724102i \(0.0230691\pi\)
\(390\) 19.3721 + 9.01813i 0.980947 + 0.456651i
\(391\) 5.31054 + 9.19812i 0.268565 + 0.465169i
\(392\) 3.83735 + 14.3212i 0.193815 + 0.723328i
\(393\) −12.2173 6.17981i −0.616281 0.311730i
\(394\) 24.6968 14.2587i 1.24421 0.718344i
\(395\) 19.7554 19.7554i 0.994004 0.994004i
\(396\) 1.10962 + 2.84059i 0.0557605 + 0.142745i
\(397\) −0.701121 2.61662i −0.0351882 0.131324i 0.946097 0.323882i \(-0.104988\pi\)
−0.981286 + 0.192558i \(0.938322\pi\)
\(398\) −10.7347 + 2.87635i −0.538082 + 0.144179i
\(399\) 6.29679 + 9.63404i 0.315234 + 0.482305i
\(400\) 7.04784 + 4.06907i 0.352392 + 0.203454i
\(401\) 7.48577 2.00581i 0.373822 0.100165i −0.0670163 0.997752i \(-0.521348\pi\)
0.440838 + 0.897587i \(0.354681\pi\)
\(402\) 7.47232 0.413655i 0.372686 0.0206312i
\(403\) −2.14140 + 9.17925i −0.106671 + 0.457251i
\(404\) 1.76654i 0.0878886i
\(405\) 12.0165 + 22.9130i 0.597102 + 1.13856i
\(406\) 5.88542 + 10.1938i 0.292088 + 0.505912i
\(407\) 10.0832 + 17.4647i 0.499808 + 0.865692i
\(408\) 7.45727 + 6.67493i 0.369190 + 0.330458i
\(409\) −5.60298 5.60298i −0.277050 0.277050i 0.554880 0.831930i \(-0.312764\pi\)
−0.831930 + 0.554880i \(0.812764\pi\)
\(410\) 1.57112 + 1.57112i 0.0775921 + 0.0775921i
\(411\) 13.9289 4.57113i 0.687063 0.225477i
\(412\) 5.36916 + 9.29965i 0.264519 + 0.458161i
\(413\) 9.55813 + 16.5552i 0.470325 + 0.814627i
\(414\) 19.9508 + 3.03967i 0.980529 + 0.149392i
\(415\) 7.90993i 0.388283i
\(416\) −7.84391 + 8.37295i −0.384579 + 0.410518i
\(417\) −0.445301 0.681306i −0.0218065 0.0333637i
\(418\) 9.02123 2.41723i 0.441243 0.118231i
\(419\) −26.4028 15.2436i −1.28986 0.744700i −0.311230 0.950335i \(-0.600741\pi\)
−0.978629 + 0.205634i \(0.934074\pi\)
\(420\) 4.27983 0.236924i 0.208834 0.0115607i
\(421\) −7.53981 + 2.02029i −0.367468 + 0.0984628i −0.437828 0.899059i \(-0.644252\pi\)
0.0703596 + 0.997522i \(0.477585\pi\)
\(422\) −1.60534 5.99122i −0.0781469 0.291648i
\(423\) −1.08197 + 7.10147i −0.0526071 + 0.345285i
\(424\) −25.1408 + 25.1408i −1.22095 + 1.22095i
\(425\) 5.31241 3.06712i 0.257690 0.148777i
\(426\) 1.31933 + 23.8326i 0.0639219 + 1.15469i
\(427\) 4.00520 + 14.9476i 0.193825 + 0.723365i
\(428\) 1.33812 + 2.31770i 0.0646806 + 0.112030i
\(429\) 1.88294 10.7192i 0.0909093 0.517529i
\(430\) 3.51769 6.09281i 0.169638 0.293821i
\(431\) 30.9395 + 8.29022i 1.49030 + 0.399326i 0.909840 0.414960i \(-0.136204\pi\)
0.580465 + 0.814285i \(0.302871\pi\)
\(432\) 12.7769 2.13943i 0.614730 0.102933i
\(433\) 19.6303 + 11.3335i 0.943371 + 0.544655i 0.891015 0.453973i \(-0.149994\pi\)
0.0523555 + 0.998629i \(0.483327\pi\)
\(434\) −1.18854 4.43569i −0.0570517 0.212920i
\(435\) −31.7017 + 10.4037i −1.51998 + 0.498820i
\(436\) −0.0808408 + 0.0808408i −0.00387157 + 0.00387157i
\(437\) −6.58617 + 24.5799i −0.315059 + 1.17582i
\(438\) −21.9013 + 14.3147i −1.04649 + 0.683981i
\(439\) 32.3810i 1.54546i −0.634735 0.772730i \(-0.718891\pi\)
0.634735 0.772730i \(-0.281109\pi\)
\(440\) 3.98695 14.8795i 0.190070 0.709352i
\(441\) 11.6528 8.57149i 0.554897 0.408166i
\(442\) −2.34022 7.71782i −0.111313 0.367099i
\(443\) 21.0067 + 12.1282i 0.998059 + 0.576230i 0.907673 0.419677i \(-0.137857\pi\)
0.0903854 + 0.995907i \(0.471190\pi\)
\(444\) −11.1082 + 3.64544i −0.527172 + 0.173005i
\(445\) 8.73501 15.1295i 0.414079 0.717206i
\(446\) −8.14578 −0.385714
\(447\) 9.19790 + 1.92681i 0.435046 + 0.0911350i
\(448\) 3.35134 12.5074i 0.158336 0.590918i
\(449\) −10.4048 + 2.78796i −0.491032 + 0.131572i −0.495835 0.868417i \(-0.665138\pi\)
0.00480262 + 0.999988i \(0.498471\pi\)
\(450\) 1.75558 11.5227i 0.0827586 0.543184i
\(451\) 0.565830 0.980046i 0.0266439 0.0461486i
\(452\) 4.35607 0.204892
\(453\) −22.8526 + 25.5310i −1.07371 + 1.19955i
\(454\) 13.1644 7.60045i 0.617834 0.356707i
\(455\) −13.4900 7.21252i −0.632420 0.338128i
\(456\) 1.32540 + 23.9421i 0.0620673 + 1.12119i
\(457\) −17.0357 17.0357i −0.796895 0.796895i 0.185710 0.982605i \(-0.440541\pi\)
−0.982605 + 0.185710i \(0.940541\pi\)
\(458\) −18.7926 + 10.8499i −0.878122 + 0.506984i
\(459\) 3.41882 9.14683i 0.159577 0.426937i
\(460\) 6.70136 + 6.70136i 0.312453 + 0.312453i
\(461\) 2.85339 + 0.764563i 0.132896 + 0.0356092i 0.324654 0.945833i \(-0.394752\pi\)
−0.191758 + 0.981442i \(0.561419\pi\)
\(462\) 1.65333 + 5.03796i 0.0769201 + 0.234387i
\(463\) 1.79433 + 0.480789i 0.0833896 + 0.0223442i 0.300273 0.953853i \(-0.402922\pi\)
−0.216883 + 0.976198i \(0.569589\pi\)
\(464\) 16.7064i 0.775573i
\(465\) 12.9969 0.719485i 0.602716 0.0333653i
\(466\) −3.59419 + 3.59419i −0.166497 + 0.166497i
\(467\) −16.0374 −0.742122 −0.371061 0.928608i \(-0.621006\pi\)
−0.371061 + 0.928608i \(0.621006\pi\)
\(468\) 5.85840 + 2.34253i 0.270805 + 0.108283i
\(469\) −5.35743 −0.247383
\(470\) 5.79340 5.79340i 0.267230 0.267230i
\(471\) 18.0321 35.6490i 0.830877 1.64262i
\(472\) 39.8273i 1.83320i
\(473\) −3.46117 0.927416i −0.159145 0.0426427i
\(474\) −13.3625 + 14.9287i −0.613761 + 0.685696i
\(475\) 14.1962 + 3.80387i 0.651368 + 0.174533i
\(476\) −1.14393 1.14393i −0.0524320 0.0524320i
\(477\) 31.7732 + 13.9229i 1.45479 + 0.637486i
\(478\) 1.16123 0.670438i 0.0531136 0.0306651i
\(479\) −26.1930 26.1930i −1.19679 1.19679i −0.975123 0.221664i \(-0.928851\pi\)
−0.221664 0.975123i \(-0.571149\pi\)
\(480\) 14.1384 + 7.15158i 0.645329 + 0.326424i
\(481\) 40.6316 + 9.47883i 1.85264 + 0.432197i
\(482\) −9.09969 + 5.25371i −0.414480 + 0.239300i
\(483\) −14.1402 2.96213i −0.643399 0.134782i
\(484\) 4.64477 0.211126
\(485\) 7.53657 13.0537i 0.342218 0.592739i
\(486\) −9.51244 15.9302i −0.431493 0.722608i
\(487\) 19.5635 5.24201i 0.886505 0.237538i 0.213293 0.976988i \(-0.431581\pi\)
0.673212 + 0.739450i \(0.264914\pi\)
\(488\) −8.34453 + 31.1422i −0.377739 + 1.40974i
\(489\) 5.15184 5.75566i 0.232974 0.260280i
\(490\) −16.4991 −0.745352
\(491\) 5.66933 9.81958i 0.255854 0.443151i −0.709273 0.704933i \(-0.750977\pi\)
0.965127 + 0.261782i \(0.0843102\pi\)
\(492\) 0.488833 + 0.437550i 0.0220383 + 0.0197263i
\(493\) 10.9056 + 6.29633i 0.491162 + 0.283572i
\(494\) 9.11049 17.0399i 0.409900 0.766660i
\(495\) −14.9379 + 1.65896i −0.671410 + 0.0745647i
\(496\) 1.68689 6.29557i 0.0757438 0.282680i
\(497\) 17.0873i 0.766469i
\(498\) 0.313538 + 5.66379i 0.0140500 + 0.253800i
\(499\) −1.32264 + 4.93618i −0.0592097 + 0.220974i −0.989191 0.146634i \(-0.953156\pi\)
0.929981 + 0.367607i \(0.119823\pi\)
\(500\) −2.05816 + 2.05816i −0.0920438 + 0.0920438i
\(501\) −0.459933 0.411682i −0.0205483 0.0183926i
\(502\) 5.37473 + 20.0588i 0.239886 + 0.895266i
\(503\) −16.1644 9.33251i −0.720734 0.416116i 0.0942889 0.995545i \(-0.469942\pi\)
−0.815023 + 0.579429i \(0.803276\pi\)
\(504\) −13.5304 + 1.50264i −0.602690 + 0.0669329i
\(505\) 8.40956 + 2.25333i 0.374220 + 0.100272i
\(506\) −5.86169 + 10.1527i −0.260584 + 0.451344i
\(507\) −13.5212 18.0049i −0.600498 0.799626i
\(508\) −3.15574 5.46591i −0.140013 0.242510i
\(509\) 0.836359 + 3.12134i 0.0370710 + 0.138351i 0.981981 0.188979i \(-0.0605178\pi\)
−0.944910 + 0.327330i \(0.893851\pi\)
\(510\) −9.32273 + 6.09332i −0.412818 + 0.269817i
\(511\) 16.2210 9.36522i 0.717576 0.414293i
\(512\) 16.4510 16.4510i 0.727037 0.727037i
\(513\) 21.2881 9.70412i 0.939895 0.428447i
\(514\) 1.00130 + 3.73691i 0.0441655 + 0.164828i
\(515\) −51.1195 + 13.6974i −2.25259 + 0.603580i
\(516\) 0.937633 1.85367i 0.0412770 0.0816032i
\(517\) −3.61386 2.08646i −0.158937 0.0917625i
\(518\) −19.6344 + 5.26103i −0.862687 + 0.231156i
\(519\) −9.30145 + 18.3887i −0.408288 + 0.807173i
\(520\) −16.8266 27.0662i −0.737895 1.18693i
\(521\) 21.9128i 0.960018i −0.877263 0.480009i \(-0.840633\pi\)
0.877263 0.480009i \(-0.159367\pi\)
\(522\) 22.2872 8.70604i 0.975483 0.381053i
\(523\) 9.66002 + 16.7316i 0.422403 + 0.731624i 0.996174 0.0873922i \(-0.0278533\pi\)
−0.573771 + 0.819016i \(0.694520\pi\)
\(524\) 2.30541 + 3.99309i 0.100712 + 0.174439i
\(525\) −1.71079 + 8.16671i −0.0746650 + 0.356424i
\(526\) 15.2142 + 15.2142i 0.663371 + 0.663371i
\(527\) −3.47386 3.47386i −0.151324 0.151324i
\(528\) −1.54299 + 7.36570i −0.0671501 + 0.320551i
\(529\) −4.47119 7.74433i −0.194400 0.336710i
\(530\) −19.7829 34.2649i −0.859313 1.48837i
\(531\) 36.1952 14.1389i 1.57074 0.613577i
\(532\) 3.87599i 0.168046i
\(533\) −0.679389 2.24056i −0.0294276 0.0970495i
\(534\) −5.65486 + 11.1795i −0.244710 + 0.483783i
\(535\) −12.7402 + 3.41372i −0.550807 + 0.147588i
\(536\) −9.66641 5.58091i −0.417525 0.241058i
\(537\) −4.58083 + 9.05615i −0.197677 + 0.390802i
\(538\) 1.31698 0.352883i 0.0567790 0.0152139i
\(539\) 2.17494 + 8.11699i 0.0936814 + 0.349624i
\(540\) 0.834259 8.67314i 0.0359008 0.373233i
\(541\) −1.88126 + 1.88126i −0.0808815 + 0.0808815i −0.746390 0.665509i \(-0.768215\pi\)
0.665509 + 0.746390i \(0.268215\pi\)
\(542\) 9.22702 5.32722i 0.396334 0.228824i
\(543\) −12.0304 + 7.86307i −0.516275 + 0.337437i
\(544\) −1.54772 5.77617i −0.0663579 0.247651i
\(545\) −0.281723 0.487958i −0.0120677 0.0209018i
\(546\) 9.94520 + 4.62969i 0.425615 + 0.198133i
\(547\) 14.0438 24.3246i 0.600469 1.04004i −0.392281 0.919846i \(-0.628314\pi\)
0.992750 0.120198i \(-0.0383529\pi\)
\(548\) −4.76876 1.27779i −0.203711 0.0545843i
\(549\) 31.2645 3.47214i 1.33434 0.148187i
\(550\) 5.86376 + 3.38544i 0.250031 + 0.144356i
\(551\) 7.80876 + 29.1427i 0.332664 + 1.24152i
\(552\) −22.4274 20.0745i −0.954573 0.854430i
\(553\) 10.1420 10.1420i 0.431280 0.431280i
\(554\) 7.91798 29.5503i 0.336403 1.25547i
\(555\) −3.18478 57.5303i −0.135186 2.44202i
\(556\) 0.274105i 0.0116246i
\(557\) −3.91190 + 14.5994i −0.165753 + 0.618597i 0.832190 + 0.554490i \(0.187087\pi\)
−0.997943 + 0.0641073i \(0.979580\pi\)
\(558\) −9.27771 + 1.03035i −0.392757 + 0.0436184i
\(559\) −6.29595 + 3.91408i −0.266290 + 0.165548i
\(560\) 9.16043 + 5.28878i 0.387099 + 0.223492i
\(561\) 4.22665 + 3.78324i 0.178449 + 0.159728i
\(562\) −0.535308 + 0.927180i −0.0225806 + 0.0391107i
\(563\) −25.4105 −1.07093 −0.535463 0.844558i \(-0.679863\pi\)
−0.535463 + 0.844558i \(0.679863\pi\)
\(564\) 1.61344 1.80254i 0.0679380 0.0759006i
\(565\) −5.55645 + 20.7369i −0.233762 + 0.872410i
\(566\) 20.9187 5.60516i 0.879280 0.235602i
\(567\) 6.16896 + 11.7630i 0.259072 + 0.493999i
\(568\) 17.8000 30.8306i 0.746873 1.29362i
\(569\) 25.0364 1.04958 0.524789 0.851232i \(-0.324144\pi\)
0.524789 + 0.851232i \(0.324144\pi\)
\(570\) −26.1172 5.47112i −1.09393 0.229160i
\(571\) −23.2909 + 13.4470i −0.974693 + 0.562739i −0.900664 0.434517i \(-0.856919\pi\)
−0.0740294 + 0.997256i \(0.523586\pi\)
\(572\) −2.50580 + 2.67480i −0.104773 + 0.111839i
\(573\) 11.0665 + 5.59772i 0.462310 + 0.233848i
\(574\) 0.806576 + 0.806576i 0.0336658 + 0.0336658i
\(575\) −15.9768 + 9.22423i −0.666280 + 0.384677i
\(576\) −24.1083 10.5642i −1.00451 0.440174i
\(577\) −12.8490 12.8490i −0.534912 0.534912i 0.387118 0.922030i \(-0.373470\pi\)
−0.922030 + 0.387118i \(0.873470\pi\)
\(578\) −15.4846 4.14907i −0.644073 0.172579i
\(579\) −3.16453 + 3.53543i −0.131514 + 0.146928i
\(580\) 10.8535 + 2.90819i 0.450668 + 0.120756i
\(581\) 4.06077i 0.168469i
\(582\) −4.87902 + 9.64567i −0.202242 + 0.399826i
\(583\) −14.2494 + 14.2494i −0.590149 + 0.590149i
\(584\) 39.0235 1.61480
\(585\) −18.6243 + 24.9007i −0.770021 + 1.02952i
\(586\) 5.46598 0.225797
\(587\) −10.0666 + 10.0666i −0.415495 + 0.415495i −0.883648 0.468153i \(-0.844920\pi\)
0.468153 + 0.883648i \(0.344920\pi\)
\(588\) −4.86420 + 0.269274i −0.200596 + 0.0111047i
\(589\) 11.7705i 0.484996i
\(590\) −42.8104 11.4710i −1.76248 0.472255i
\(591\) 12.9398 + 39.4296i 0.532273 + 1.62192i
\(592\) −27.8671 7.46698i −1.14533 0.306891i
\(593\) −14.8629 14.8629i −0.610345 0.610345i 0.332691 0.943036i \(-0.392043\pi\)
−0.943036 + 0.332691i \(0.892043\pi\)
\(594\) 10.6303 1.77999i 0.436167 0.0730339i
\(595\) 6.90481 3.98649i 0.283070 0.163430i
\(596\) −2.23786 2.23786i −0.0916664 0.0916664i
\(597\) −0.893895 16.1474i −0.0365847 0.660871i
\(598\) 7.03810 + 23.2110i 0.287809 + 0.949168i
\(599\) −29.6012 + 17.0903i −1.20947 + 0.698289i −0.962644 0.270770i \(-0.912722\pi\)
−0.246828 + 0.969059i \(0.579388\pi\)
\(600\) −11.5941 + 12.9530i −0.473329 + 0.528805i
\(601\) 8.94270 0.364780 0.182390 0.983226i \(-0.441617\pi\)
0.182390 + 0.983226i \(0.441617\pi\)
\(602\) 1.80590 3.12790i 0.0736028 0.127484i
\(603\) −1.64031 + 10.7661i −0.0667985 + 0.438430i
\(604\) 11.1462 2.98660i 0.453531 0.121523i
\(605\) −5.92471 + 22.1113i −0.240874 + 0.898953i
\(606\) −6.11086 1.28012i −0.248237 0.0520015i
\(607\) 9.16628 0.372048 0.186024 0.982545i \(-0.440440\pi\)
0.186024 + 0.982545i \(0.440440\pi\)
\(608\) 7.16364 12.4078i 0.290524 0.503202i
\(609\) −16.2749 + 5.34102i −0.659492 + 0.216429i
\(610\) −31.0714 17.9391i −1.25805 0.726333i
\(611\) −8.26193 + 2.50520i −0.334242 + 0.101350i
\(612\) −2.64905 + 1.94856i −0.107081 + 0.0787660i
\(613\) −0.197913 + 0.738622i −0.00799364 + 0.0298327i −0.969807 0.243872i \(-0.921582\pi\)
0.961814 + 0.273705i \(0.0882490\pi\)
\(614\) 6.61690i 0.267037i
\(615\) −2.70648 + 1.76895i −0.109136 + 0.0713311i
\(616\) 2.04680 7.63878i 0.0824681 0.307775i
\(617\) 11.7973 11.7973i 0.474940 0.474940i −0.428569 0.903509i \(-0.640982\pi\)
0.903509 + 0.428569i \(0.140982\pi\)
\(618\) 36.0604 11.8341i 1.45056 0.476039i
\(619\) −0.995076 3.71367i −0.0399955 0.149265i 0.943041 0.332678i \(-0.107952\pi\)
−0.983036 + 0.183413i \(0.941286\pi\)
\(620\) −3.79636 2.19183i −0.152466 0.0880261i
\(621\) −10.2819 + 27.5087i −0.412600 + 1.10388i
\(622\) 25.1704 + 6.74440i 1.00924 + 0.270426i
\(623\) 4.48434 7.76711i 0.179661 0.311183i
\(624\) 8.93868 + 12.7482i 0.357834 + 0.510336i
\(625\) −15.3330 26.5575i −0.613320 1.06230i
\(626\) −2.33167 8.70190i −0.0931922 0.347798i
\(627\) 0.751211 + 13.5700i 0.0300005 + 0.541933i
\(628\) −11.6515 + 6.72699i −0.464945 + 0.268436i
\(629\) −15.3769 + 15.3769i −0.613118 + 0.613118i
\(630\) 2.28181 14.9766i 0.0909095 0.596682i
\(631\) 3.46710 + 12.9394i 0.138023 + 0.515110i 0.999967 + 0.00810607i \(0.00258027\pi\)
−0.861944 + 0.507004i \(0.830753\pi\)
\(632\) 28.8642 7.73413i 1.14815 0.307647i
\(633\) 9.01217 0.498898i 0.358202 0.0198294i
\(634\) −30.4282 17.5678i −1.20846 0.697705i
\(635\) 30.0457 8.05071i 1.19233 0.319483i
\(636\) −6.39153 9.77899i −0.253441 0.387762i
\(637\) 15.3319 + 8.19731i 0.607472 + 0.324789i
\(638\) 13.8996i 0.550290i
\(639\) −34.3380 5.23169i −1.35839 0.206962i
\(640\) 5.86282 + 10.1547i 0.231748 + 0.401400i
\(641\) −12.7444 22.0740i −0.503375 0.871870i −0.999992 0.00390095i \(-0.998758\pi\)
0.496618 0.867969i \(-0.334575\pi\)
\(642\) 8.98711 2.94935i 0.354693 0.116402i
\(643\) −3.94884 3.94884i −0.155727 0.155727i 0.624943 0.780670i \(-0.285122\pi\)
−0.780670 + 0.624943i \(0.785122\pi\)
\(644\) 3.44032 + 3.44032i 0.135568 + 0.135568i
\(645\) 7.62833 + 6.82805i 0.300365 + 0.268854i
\(646\) 5.03554 + 8.72181i 0.198121 + 0.343155i
\(647\) 1.23117 + 2.13245i 0.0484024 + 0.0838354i 0.889212 0.457496i \(-0.151254\pi\)
−0.840809 + 0.541332i \(0.817920\pi\)
\(648\) −1.12299 + 27.6502i −0.0441153 + 1.08620i
\(649\) 22.5734i 0.886085i
\(650\) 13.4056 4.06488i 0.525811 0.159438i
\(651\) 6.67229 0.369367i 0.261508 0.0144766i
\(652\) −2.51276 + 0.673293i −0.0984075 + 0.0263682i
\(653\) 27.7948 + 16.0473i 1.08769 + 0.627981i 0.932962 0.359975i \(-0.117215\pi\)
0.154733 + 0.987956i \(0.450548\pi\)
\(654\) 0.221065 + 0.338228i 0.00864434 + 0.0132258i
\(655\) −21.9497 + 5.88141i −0.857646 + 0.229806i
\(656\) 0.419016 + 1.56379i 0.0163598 + 0.0610557i
\(657\) −13.8536 35.4646i −0.540479 1.38361i
\(658\) 2.97419 2.97419i 0.115946 0.115946i
\(659\) 4.60604 2.65930i 0.179426 0.103591i −0.407597 0.913162i \(-0.633633\pi\)
0.587023 + 0.809570i \(0.300300\pi\)
\(660\) 4.51663 + 2.28463i 0.175810 + 0.0889290i
\(661\) −5.92362 22.1073i −0.230402 0.859872i −0.980168 0.198169i \(-0.936500\pi\)
0.749766 0.661703i \(-0.230166\pi\)
\(662\) 11.4628 + 19.8541i 0.445513 + 0.771651i
\(663\) 11.6906 1.03041i 0.454025 0.0400180i
\(664\) 4.23015 7.32684i 0.164162 0.284337i
\(665\) 18.4516 + 4.94408i 0.715520 + 0.191723i
\(666\) 4.56083 + 41.0674i 0.176728 + 1.59133i
\(667\) −32.7980 18.9359i −1.26994 0.733202i
\(668\) 0.0538026 + 0.200794i 0.00208169 + 0.00776896i
\(669\) 2.43041 11.6019i 0.0939650 0.448555i
\(670\) 8.78304 8.78304i 0.339318 0.339318i
\(671\) −4.72954 + 17.6509i −0.182582 + 0.681404i
\(672\) 7.25834 + 3.67145i 0.279996 + 0.141629i
\(673\) 28.4168i 1.09539i 0.836679 + 0.547693i \(0.184494\pi\)
−0.836679 + 0.547693i \(0.815506\pi\)
\(674\) 5.55954 20.7485i 0.214146 0.799202i
\(675\) 15.8877 + 5.93838i 0.611519 + 0.228568i
\(676\) 0.494230 + 7.56681i 0.0190088 + 0.291031i
\(677\) 19.5004 + 11.2586i 0.749461 + 0.432701i 0.825499 0.564404i \(-0.190894\pi\)
−0.0760383 + 0.997105i \(0.524227\pi\)
\(678\) 3.15663 15.0686i 0.121230 0.578707i
\(679\) 3.86910 6.70147i 0.148482 0.257179i
\(680\) 16.6111 0.637007
\(681\) 6.89741 + 21.0175i 0.264309 + 0.805391i
\(682\) 1.40349 5.23788i 0.0537422 0.200569i
\(683\) 38.9958 10.4489i 1.49213 0.399816i 0.581677 0.813420i \(-0.302397\pi\)
0.910457 + 0.413604i \(0.135730\pi\)
\(684\) −7.78906 1.18673i −0.297822 0.0453757i
\(685\) 12.1657 21.0717i 0.464829 0.805107i
\(686\) −20.7665 −0.792868
\(687\) −9.84632 30.0032i −0.375661 1.14469i
\(688\) 4.43943 2.56311i 0.169252 0.0977176i
\(689\) 1.35939 + 41.6698i 0.0517887 + 1.58749i
\(690\) 28.0377 18.3254i 1.06738 0.697635i
\(691\) 23.7637 + 23.7637i 0.904015 + 0.904015i 0.995781 0.0917661i \(-0.0292512\pi\)
−0.0917661 + 0.995781i \(0.529251\pi\)
\(692\) 6.01014 3.46996i 0.228471 0.131908i
\(693\) −7.66877 + 0.851670i −0.291313 + 0.0323523i
\(694\) −21.1496 21.1496i −0.802828 0.802828i
\(695\) −1.30487 0.349639i −0.0494965 0.0132625i
\(696\) −34.9286 7.31697i −1.32397 0.277349i
\(697\) 1.17873 + 0.315840i 0.0446476 + 0.0119633i
\(698\) 27.7763i 1.05135i
\(699\) −4.04676 6.19151i −0.153063 0.234184i
\(700\) 1.98697 1.98697i 0.0751004 0.0751004i
\(701\) −34.8493 −1.31624 −0.658120 0.752913i \(-0.728648\pi\)
−0.658120 + 0.752913i \(0.728648\pi\)
\(702\) 12.3486 18.5680i 0.466069 0.700805i
\(703\) −52.1018 −1.96506
\(704\) 10.8119 10.8119i 0.407489 0.407489i
\(705\) 6.52290 + 9.97998i 0.245667 + 0.375868i
\(706\) 23.8182i 0.896410i
\(707\) 4.31727 + 1.15681i 0.162367 + 0.0435062i
\(708\) −12.8084 2.68315i −0.481370 0.100839i
\(709\) 8.53384 + 2.28664i 0.320495 + 0.0858764i 0.415480 0.909602i \(-0.363614\pi\)
−0.0949849 + 0.995479i \(0.530280\pi\)
\(710\) 28.0131 + 28.0131i 1.05131 + 1.05131i
\(711\) −17.2757 23.4862i −0.647891 0.880800i
\(712\) 16.1822 9.34279i 0.606453 0.350136i
\(713\) 10.4475 + 10.4475i 0.391261 + 0.391261i
\(714\) −4.78607 + 3.12817i −0.179114 + 0.117069i
\(715\) −9.53702 15.3407i −0.356664 0.573708i
\(716\) 2.95991 1.70890i 0.110617 0.0638647i
\(717\) 0.608424 + 1.85396i 0.0227220 + 0.0692374i
\(718\) 3.32187 0.123971
\(719\) 12.4677 21.5947i 0.464966 0.805345i −0.534234 0.845337i \(-0.679400\pi\)
0.999200 + 0.0399915i \(0.0127331\pi\)
\(720\) 13.4328 16.7892i 0.500612 0.625696i
\(721\) −26.2435 + 7.03193i −0.977359 + 0.261883i
\(722\) −0.391981 + 1.46289i −0.0145880 + 0.0544432i
\(723\) −4.76775 14.5281i −0.177314 0.540304i
\(724\) 4.84012 0.179882
\(725\) −10.9365 + 18.9426i −0.406172 + 0.703511i
\(726\) 3.36584 16.0673i 0.124918 0.596315i
\(727\) 15.7972 + 9.12055i 0.585888 + 0.338262i 0.763470 0.645844i \(-0.223494\pi\)
−0.177582 + 0.984106i \(0.556828\pi\)
\(728\) −8.63837 13.8951i −0.320159 0.514989i
\(729\) 25.5273 8.79541i 0.945454 0.325756i
\(730\) −11.2395 + 41.9464i −0.415993 + 1.55251i
\(731\) 3.86396i 0.142914i
\(732\) −9.45314 4.78164i −0.349398 0.176734i
\(733\) 5.98357 22.3310i 0.221008 0.824814i −0.762956 0.646450i \(-0.776253\pi\)
0.983965 0.178364i \(-0.0570805\pi\)
\(734\) 27.7648 27.7648i 1.02482 1.02482i
\(735\) 4.92273 23.4993i 0.181578 0.866787i
\(736\) 4.65469 + 17.3715i 0.171574 + 0.640324i
\(737\) −5.47876 3.16316i −0.201813 0.116517i
\(738\) 1.86782 1.37391i 0.0687554 0.0505745i
\(739\) 11.4323 + 3.06326i 0.420542 + 0.112684i 0.462883 0.886419i \(-0.346815\pi\)
−0.0423409 + 0.999103i \(0.513482\pi\)
\(740\) −9.70206 + 16.8045i −0.356655 + 0.617745i
\(741\) 21.5514 + 18.0600i 0.791709 + 0.663450i
\(742\) −10.1560 17.5908i −0.372840 0.645778i
\(743\) 11.3842 + 42.4865i 0.417647 + 1.55868i 0.779474 + 0.626434i \(0.215486\pi\)
−0.361827 + 0.932245i \(0.617847\pi\)
\(744\) 12.4236 + 6.28416i 0.455471 + 0.230388i
\(745\) 13.5078 7.79874i 0.494888 0.285724i
\(746\) 3.95957 3.95957i 0.144970 0.144970i
\(747\) −8.16038 1.24330i −0.298573 0.0454901i
\(748\) −0.494431 1.84524i −0.0180782 0.0674687i
\(749\) −6.54051 + 1.75252i −0.238985 + 0.0640358i
\(750\) 5.62820 + 8.61110i 0.205513 + 0.314433i
\(751\) 32.0454 + 18.5014i 1.16935 + 0.675126i 0.953528 0.301306i \(-0.0974225\pi\)
0.215825 + 0.976432i \(0.430756\pi\)
\(752\) 5.76637 1.54509i 0.210278 0.0563438i
\(753\) −30.1730 + 1.67032i −1.09956 + 0.0608700i
\(754\) 20.9864 + 19.6604i 0.764281 + 0.715990i
\(755\) 56.8706i 2.06973i
\(756\) 0.428289 4.45258i 0.0155767 0.161939i
\(757\) −23.2842 40.3294i −0.846278 1.46580i −0.884507 0.466527i \(-0.845505\pi\)
0.0382287 0.999269i \(-0.487828\pi\)
\(758\) 11.7247 + 20.3077i 0.425859 + 0.737609i
\(759\) −12.7115 11.3779i −0.461397 0.412992i
\(760\) 28.1418 + 28.1418i 1.02081 + 1.02081i
\(761\) −21.4108 21.4108i −0.776142 0.776142i 0.203031 0.979172i \(-0.434921\pi\)
−0.979172 + 0.203031i \(0.934921\pi\)
\(762\) −21.1946 + 6.95556i −0.767800 + 0.251973i
\(763\) −0.144630 0.250506i −0.00523595 0.00906893i
\(764\) −2.08826 3.61697i −0.0755506 0.130857i
\(765\) −5.89705 15.0962i −0.213208 0.545805i
\(766\) 6.81020i 0.246062i
\(767\) 34.0827 + 31.9292i 1.23066 + 1.15290i
\(768\) 12.0278 + 18.4024i 0.434015 + 0.664039i
\(769\) −50.7997 + 13.6117i −1.83188 + 0.490852i −0.998121 0.0612700i \(-0.980485\pi\)
−0.833763 + 0.552122i \(0.813818\pi\)
\(770\) 7.62142 + 4.40023i 0.274657 + 0.158573i
\(771\) −5.62116 + 0.311178i −0.202441 + 0.0112068i
\(772\) 1.54347 0.413573i 0.0555508 0.0148848i
\(773\) 5.09988 + 19.0330i 0.183430 + 0.684570i 0.994961 + 0.100261i \(0.0319677\pi\)
−0.811531 + 0.584309i \(0.801366\pi\)
\(774\) −5.73281 4.58675i −0.206062 0.164867i
\(775\) 6.03398 6.03398i 0.216747 0.216747i
\(776\) 13.9620 8.06097i 0.501207 0.289372i
\(777\) −1.63499 29.5347i −0.0586549 1.05955i
\(778\) 5.29791 + 19.7721i 0.189939 + 0.708863i
\(779\) 1.46187 + 2.53203i 0.0523769 + 0.0907194i
\(780\) 9.83808 3.58797i 0.352260 0.128470i
\(781\) 10.0888 17.4742i 0.361004 0.625277i
\(782\) −12.2110 3.27192i −0.436664 0.117004i
\(783\) 5.75018 + 34.3408i 0.205495 + 1.22724i
\(784\) −10.4112 6.01090i −0.371828 0.214675i
\(785\) −17.1614 64.0473i −0.612517 2.28595i
\(786\) 15.4836 5.08135i 0.552283 0.181246i
\(787\) −7.17503 + 7.17503i −0.255762 + 0.255762i −0.823328 0.567566i \(-0.807885\pi\)
0.567566 + 0.823328i \(0.307885\pi\)
\(788\) 3.61712 13.4993i 0.128854 0.480891i
\(789\) −26.2087 + 17.1300i −0.933055 + 0.609843i
\(790\) 33.2537i 1.18311i
\(791\) −2.85255 + 10.6459i −0.101425 + 0.378523i
\(792\) −14.7240 6.45199i −0.523193 0.229261i
\(793\) 19.9606 + 32.1074i 0.708822 + 1.14017i
\(794\) 2.79232 + 1.61215i 0.0990958 + 0.0572130i
\(795\) 54.7054 17.9530i 1.94020 0.636726i
\(796\) −2.72315 + 4.71663i −0.0965195 + 0.167177i
\(797\) −41.2377 −1.46072 −0.730358 0.683065i \(-0.760647\pi\)
−0.730358 + 0.683065i \(0.760647\pi\)
\(798\) −13.4079 2.80874i −0.474636 0.0994284i
\(799\) 1.16464 4.34649i 0.0412019 0.153768i
\(800\) 10.0330 2.68834i 0.354720 0.0950471i
\(801\) −14.2355 11.3897i −0.502988 0.402434i
\(802\) −4.61213 + 7.98844i −0.162860 + 0.282082i
\(803\) 22.1178 0.780521
\(804\) 2.44604 2.73273i 0.0862651 0.0963758i
\(805\) −20.7659 + 11.9892i −0.731902 + 0.422564i
\(806\) −5.92330 9.52785i −0.208639 0.335604i
\(807\) 0.109667 + 1.98104i 0.00386045 + 0.0697358i
\(808\) 6.58458 + 6.58458i 0.231645 + 0.231645i
\(809\) −22.9401 + 13.2445i −0.806532 + 0.465651i −0.845750 0.533579i \(-0.820847\pi\)
0.0392184 + 0.999231i \(0.487513\pi\)
\(810\) −29.3978 9.17090i −1.03293 0.322232i
\(811\) −27.7759 27.7759i −0.975343 0.975343i 0.0243602 0.999703i \(-0.492245\pi\)
−0.999703 + 0.0243602i \(0.992245\pi\)
\(812\) 5.57194 + 1.49300i 0.195537 + 0.0523939i
\(813\) 4.83446 + 14.7313i 0.169552 + 0.516650i
\(814\) −23.1853 6.21248i −0.812644 0.217747i
\(815\) 12.8208i 0.449092i
\(816\) −8.10270 + 0.448552i −0.283651 + 0.0157025i
\(817\) 6.54615 6.54615i 0.229021 0.229021i
\(818\) 9.43133 0.329759
\(819\) −9.56128 + 12.7834i −0.334098 + 0.446689i
\(820\) 1.08888 0.0380253
\(821\) −20.0159 + 20.0159i −0.698561 + 0.698561i −0.964100 0.265539i \(-0.914450\pi\)
0.265539 + 0.964100i \(0.414450\pi\)
\(822\) −7.87584 + 15.5703i −0.274702 + 0.543076i
\(823\) 3.18802i 0.111127i 0.998455 + 0.0555636i \(0.0176956\pi\)
−0.998455 + 0.0555636i \(0.982304\pi\)
\(824\) −54.6764 14.6505i −1.90474 0.510374i
\(825\) −6.57136 + 7.34155i −0.228785 + 0.255600i
\(826\) −21.9779 5.88895i −0.764707 0.204903i
\(827\) 40.4226 + 40.4226i 1.40563 + 1.40563i 0.780603 + 0.625027i \(0.214912\pi\)
0.625027 + 0.780603i \(0.285088\pi\)
\(828\) 7.96688 5.86021i 0.276868 0.203656i
\(829\) 0.372721 0.215190i 0.0129451 0.00747387i −0.493513 0.869738i \(-0.664288\pi\)
0.506459 + 0.862264i \(0.330954\pi\)
\(830\) 6.65727 + 6.65727i 0.231077 + 0.231077i
\(831\) 39.7256 + 20.0942i 1.37806 + 0.697060i
\(832\) −1.03146 31.6175i −0.0357593 1.09614i
\(833\) −7.84759 + 4.53081i −0.271903 + 0.156983i
\(834\) 0.948191 + 0.198630i 0.0328332 + 0.00687801i
\(835\) −1.02450 −0.0354544
\(836\) 2.28848 3.96376i 0.0791488 0.137090i
\(837\) 1.30062 13.5215i 0.0449559 0.467371i
\(838\) 35.0510 9.39190i 1.21082 0.324438i
\(839\) 1.25045 4.66673i 0.0431702 0.161113i −0.940976 0.338474i \(-0.890089\pi\)
0.984146 + 0.177361i \(0.0567559\pi\)
\(840\) −15.0695 + 16.8357i −0.519947 + 0.580887i
\(841\) −15.9020 −0.548345
\(842\) 4.64542 8.04611i 0.160092 0.277287i
\(843\) −1.16085 1.03907i −0.0399818 0.0357873i
\(844\) −2.63244 1.51984i −0.0906122 0.0523150i
\(845\) −36.6520 7.29919i −1.26087 0.251100i
\(846\) −5.06622 6.88746i −0.174180 0.236796i
\(847\) −3.04160 + 11.3514i −0.104511 + 0.390040i
\(848\) 28.8290i 0.989991i
\(849\) 1.74194 + 31.4666i 0.0597831 + 1.07993i
\(850\) −1.88971 + 7.05251i −0.0648166 + 0.241899i
\(851\) 46.2454 46.2454i 1.58527 1.58527i
\(852\) 8.71590 + 7.80152i 0.298602 + 0.267276i
\(853\) −11.5603 43.1437i −0.395818 1.47721i −0.820383 0.571815i \(-0.806240\pi\)
0.424565 0.905397i \(-0.360427\pi\)
\(854\) −15.9513 9.20951i −0.545843 0.315143i
\(855\) 15.5848 35.5659i 0.532990 1.21633i
\(856\) −13.6267 3.65125i −0.465750 0.124797i
\(857\) 25.1388 43.5417i 0.858725 1.48736i −0.0144207 0.999896i \(-0.504590\pi\)
0.873146 0.487459i \(-0.162076\pi\)
\(858\) 7.43693 + 10.6064i 0.253892 + 0.362097i
\(859\) 25.1679 + 43.5920i 0.858717 + 1.48734i 0.873153 + 0.487445i \(0.162071\pi\)
−0.0144366 + 0.999896i \(0.504595\pi\)
\(860\) −0.892357 3.33032i −0.0304291 0.113563i
\(861\) −1.38944 + 0.908138i −0.0473521 + 0.0309493i
\(862\) −33.0171 + 19.0624i −1.12457 + 0.649269i
\(863\) −29.3689 + 29.3689i −0.999728 + 0.999728i −1.00000 0.000272025i \(-0.999913\pi\)
0.000272025 1.00000i \(0.499913\pi\)
\(864\) 9.60034 13.4620i 0.326610 0.457987i
\(865\) 8.85231 + 33.0373i 0.300988 + 1.12330i
\(866\) −26.0602 + 6.98281i −0.885562 + 0.237286i
\(867\) 10.5295 20.8165i 0.357600 0.706964i
\(868\) −1.94896 1.12523i −0.0661521 0.0381929i
\(869\) 16.3597 4.38357i 0.554965 0.148702i
\(870\) 17.9251 35.4374i 0.607719 1.20144i
\(871\) −12.5254 + 3.79799i −0.424408 + 0.128690i
\(872\) 0.602650i 0.0204083i
\(873\) −12.2824 9.82702i −0.415697 0.332594i
\(874\) −15.1442 26.2304i −0.512259 0.887258i
\(875\) −3.68219 6.37775i −0.124481 0.215607i
\(876\) −2.62900 + 12.5499i −0.0888257 + 0.424022i
\(877\) −12.4238 12.4238i −0.419523 0.419523i 0.465516 0.885039i \(-0.345869\pi\)
−0.885039 + 0.465516i \(0.845869\pi\)
\(878\) 27.2529 + 27.2529i 0.919742 + 0.919742i
\(879\) −1.63085 + 7.78510i −0.0550072 + 0.262585i
\(880\) 6.24525 + 10.8171i 0.210527 + 0.364644i
\(881\) −11.7668 20.3807i −0.396434 0.686644i 0.596849 0.802354i \(-0.296419\pi\)
−0.993283 + 0.115710i \(0.963086\pi\)
\(882\) −2.59337 + 17.0215i −0.0873232 + 0.573143i
\(883\) 5.09275i 0.171385i 0.996322 + 0.0856923i \(0.0273102\pi\)
−0.996322 + 0.0856923i \(0.972690\pi\)
\(884\) −3.48541 1.86350i −0.117227 0.0626763i
\(885\) 29.1111 57.5516i 0.978558 1.93458i
\(886\) −27.8875 + 7.47243i −0.936899 + 0.251041i
\(887\) 11.4511 + 6.61127i 0.384489 + 0.221985i 0.679769 0.733426i \(-0.262080\pi\)
−0.295281 + 0.955411i \(0.595413\pi\)
\(888\) 27.8166 54.9925i 0.933464 1.84543i
\(889\) 15.4247 4.13304i 0.517329 0.138618i
\(890\) 5.38181 + 20.0852i 0.180399 + 0.673256i
\(891\) −0.636493 + 15.6717i −0.0213233 + 0.525020i
\(892\) −2.82276 + 2.82276i −0.0945129 + 0.0945129i
\(893\) 9.33670 5.39054i 0.312441 0.180388i
\(894\) −9.36294 + 6.11960i −0.313144 + 0.204670i
\(895\) 4.35963 + 16.2704i 0.145726 + 0.543858i
\(896\) 3.00983 + 5.21318i 0.100551 + 0.174160i
\(897\) −35.1589 + 3.09892i −1.17392 + 0.103470i
\(898\) 6.41059 11.1035i 0.213924 0.370528i
\(899\) 16.9207 + 4.53390i 0.564338 + 0.151214i
\(900\) −3.38459 4.60131i −0.112820 0.153377i
\(901\) −18.8190 10.8651i −0.626951 0.361970i
\(902\) 0.348619 + 1.30106i 0.0116077 + 0.0433207i
\(903\) 3.91620 + 3.50536i 0.130323 + 0.116651i
\(904\) −16.2368 + 16.2368i −0.540027 + 0.540027i
\(905\) −6.17388 + 23.0412i −0.205227 + 0.765917i
\(906\) −2.25426 40.7213i −0.0748929 1.35288i
\(907\) 9.89130i 0.328435i −0.986424 0.164218i \(-0.947490\pi\)
0.986424 0.164218i \(-0.0525099\pi\)
\(908\) 1.92806 7.19562i 0.0639850 0.238795i
\(909\) 3.64652 8.32164i 0.120947 0.276012i
\(910\) 17.4239 5.28333i 0.577598 0.175141i
\(911\) −10.2559 5.92123i −0.339792 0.196179i 0.320388 0.947286i \(-0.396187\pi\)
−0.660180 + 0.751107i \(0.729520\pi\)
\(912\) −14.4871 12.9673i −0.479717 0.429391i
\(913\) 2.39758 4.15273i 0.0793483 0.137435i
\(914\) 28.6756 0.948504
\(915\) 34.8209 38.9021i 1.15114 1.28606i
\(916\) −2.75238 + 10.2720i −0.0909412 + 0.339397i
\(917\) −11.2685 + 3.01937i −0.372117 + 0.0997085i
\(918\) 4.82088 + 10.5757i 0.159113 + 0.349050i
\(919\) −1.00599 + 1.74243i −0.0331846 + 0.0574775i −0.882141 0.470986i \(-0.843898\pi\)
0.848956 + 0.528463i \(0.177232\pi\)
\(920\) −49.9572 −1.64704
\(921\) −9.42434 1.97424i −0.310543 0.0650536i
\(922\) −3.04499 + 1.75803i −0.100281 + 0.0578975i
\(923\) −12.1135 39.9492i −0.398721 1.31495i
\(924\) 2.31873 + 1.17287i 0.0762807 + 0.0385847i
\(925\) −26.7092 26.7092i −0.878194 0.878194i
\(926\) −1.91482 + 1.10552i −0.0629248 + 0.0363297i
\(927\) 6.09603 + 54.8910i 0.200220 + 1.80286i
\(928\) 15.0775 + 15.0775i 0.494943 + 0.494943i
\(929\) −40.2389 10.7820i −1.32019 0.353745i −0.471144 0.882056i \(-0.656159\pi\)
−0.849051 + 0.528311i \(0.822825\pi\)
\(930\) −10.3331 + 11.5442i −0.338835 + 0.378548i
\(931\) −20.9709 5.61914i −0.687294 0.184160i
\(932\) 2.49098i 0.0815949i
\(933\) −17.1159 + 33.8375i −0.560349 + 1.10779i
\(934\) 13.4976 13.4976i 0.441656 0.441656i
\(935\) 9.41490 0.307900
\(936\) −30.5681 + 13.1050i −0.999148 + 0.428352i
\(937\) 47.9819 1.56750 0.783750 0.621077i \(-0.213304\pi\)
0.783750 + 0.621077i \(0.213304\pi\)
\(938\) 4.50900 4.50900i 0.147224 0.147224i
\(939\) 13.0896 0.724621i 0.427165 0.0236471i
\(940\) 4.01517i 0.130960i
\(941\) 23.7536 + 6.36477i 0.774346 + 0.207485i 0.624291 0.781192i \(-0.285388\pi\)
0.150056 + 0.988678i \(0.452055\pi\)
\(942\) 14.8269 + 45.1799i 0.483087 + 1.47204i
\(943\) −3.54497 0.949873i −0.115440 0.0309321i
\(944\) −22.8350 22.8350i −0.743216 0.743216i
\(945\) 20.6501 + 7.71841i 0.671747 + 0.251080i
\(946\) 3.69358 2.13249i 0.120089 0.0693332i
\(947\) −29.5660 29.5660i −0.960767 0.960767i 0.0384921 0.999259i \(-0.487745\pi\)
−0.999259 + 0.0384921i \(0.987745\pi\)
\(948\) 0.542718 + 9.80373i 0.0176267 + 0.318410i
\(949\) 31.2848 33.3949i 1.01555 1.08404i
\(950\) −15.1495 + 8.74657i −0.491515 + 0.283776i
\(951\) 34.1001 38.0968i 1.10577 1.23537i
\(952\) 8.52775 0.276386
\(953\) −3.67150 + 6.35923i −0.118932 + 0.205996i −0.919345 0.393453i \(-0.871280\pi\)
0.800413 + 0.599449i \(0.204614\pi\)
\(954\) −38.4594 + 15.0234i −1.24517 + 0.486401i
\(955\) 19.8822 5.32742i 0.643373 0.172391i
\(956\) 0.170075 0.634729i 0.00550062 0.0205286i
\(957\) −19.7969 4.14713i −0.639944 0.134058i
\(958\) 44.0898 1.42448
\(959\) 6.24560 10.8177i 0.201681 0.349321i
\(960\) −41.5085 + 13.6221i −1.33968 + 0.439650i
\(961\) 20.9282 + 12.0829i 0.675104 + 0.389772i
\(962\) −42.1747 + 26.2193i −1.35977 + 0.845343i
\(963\) 1.51928 + 13.6802i 0.0489580 + 0.440837i
\(964\) −1.33275 + 4.97388i −0.0429249 + 0.160198i
\(965\) 7.87520i 0.253512i
\(966\) 14.3939 9.40781i 0.463115 0.302691i
\(967\) 6.78898 25.3368i 0.218319 0.814778i −0.766653 0.642062i \(-0.778079\pi\)
0.984972 0.172716i \(-0.0552542\pi\)
\(968\) −17.3129 + 17.3129i −0.556457 + 0.556457i
\(969\) −13.9247 + 4.56976i −0.447327 + 0.146802i
\(970\) 4.64343 + 17.3295i 0.149091 + 0.556417i
\(971\) −11.1860 6.45823i −0.358975 0.207255i 0.309656 0.950849i \(-0.399786\pi\)
−0.668631 + 0.743594i \(0.733120\pi\)
\(972\) −8.81663 2.22394i −0.282793 0.0713329i
\(973\) −0.669888 0.179496i −0.0214756 0.00575438i
\(974\) −12.0534 + 20.8771i −0.386217 + 0.668947i
\(975\) 1.78980 + 20.3062i 0.0573193 + 0.650318i
\(976\) −13.0711 22.6397i −0.418394 0.724680i
\(977\) 8.97618 + 33.4996i 0.287174 + 1.07175i 0.947236 + 0.320536i \(0.103863\pi\)
−0.660063 + 0.751210i \(0.729470\pi\)
\(978\) 0.508196 + 9.18013i 0.0162503 + 0.293548i
\(979\) 9.17179 5.29533i 0.293132 0.169240i
\(980\) −5.71742 + 5.71742i −0.182636 + 0.182636i
\(981\) −0.547690 + 0.213944i −0.0174864 + 0.00683072i
\(982\) 3.49299 + 13.0360i 0.111466 + 0.415996i
\(983\) 27.3813 7.33678i 0.873326 0.234007i 0.205801 0.978594i \(-0.434020\pi\)
0.667526 + 0.744587i \(0.267353\pi\)
\(984\) −3.45299 + 0.191152i −0.110077 + 0.00609370i
\(985\) 59.6490 + 34.4384i 1.90058 + 1.09730i
\(986\) −14.4777 + 3.87929i −0.461064 + 0.123542i
\(987\) 3.34870 + 5.12348i 0.106590 + 0.163082i
\(988\) −2.74777 9.06188i −0.0874181 0.288297i
\(989\) 11.6207i 0.369516i
\(990\) 11.1760 13.9685i 0.355198 0.443948i
\(991\) 0.249119 + 0.431486i 0.00791352 + 0.0137066i 0.869955 0.493131i \(-0.164148\pi\)
−0.862042 + 0.506838i \(0.830814\pi\)
\(992\) −4.15933 7.20418i −0.132059 0.228733i
\(993\) −31.6979 + 10.4025i −1.00590 + 0.330112i
\(994\) 14.3812 + 14.3812i 0.456145 + 0.456145i
\(995\) −18.9798 18.9798i −0.601702 0.601702i
\(996\) 2.07132 + 1.85402i 0.0656323 + 0.0587469i
\(997\) −19.9952 34.6328i −0.633255 1.09683i −0.986882 0.161444i \(-0.948385\pi\)
0.353626 0.935387i \(-0.384948\pi\)
\(998\) −3.04127 5.26764i −0.0962698 0.166744i
\(999\) −59.8524 5.75714i −1.89365 0.182148i
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 117.2.x.a.11.4 48
3.2 odd 2 351.2.ba.a.89.9 48
9.4 even 3 351.2.bf.a.206.4 48
9.5 odd 6 117.2.bc.a.50.9 yes 48
13.6 odd 12 117.2.bc.a.110.9 yes 48
39.32 even 12 351.2.bf.a.305.4 48
117.32 even 12 inner 117.2.x.a.32.4 yes 48
117.58 odd 12 351.2.ba.a.71.9 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
117.2.x.a.11.4 48 1.1 even 1 trivial
117.2.x.a.32.4 yes 48 117.32 even 12 inner
117.2.bc.a.50.9 yes 48 9.5 odd 6
117.2.bc.a.110.9 yes 48 13.6 odd 12
351.2.ba.a.71.9 48 117.58 odd 12
351.2.ba.a.89.9 48 3.2 odd 2
351.2.bf.a.206.4 48 9.4 even 3
351.2.bf.a.305.4 48 39.32 even 12