Properties

Label 370.2.e.e.121.1
Level $370$
Weight $2$
Character 370.121
Analytic conductor $2.954$
Analytic rank $0$
Dimension $4$
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] = [370,2,Mod(121,370)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(370, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("370.121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.e (of order \(3\), 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: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 10x^{2} + 100 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 121.1
Root \(-1.58114 - 2.73861i\) of defining polynomial
Character \(\chi\) \(=\) 370.121
Dual form 370.2.e.e.211.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-2.58114 - 4.47066i) q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-2.58114 - 4.47066i) q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} -1.00000 q^{10} -1.16228 q^{11} +(0.500000 - 0.866025i) q^{12} +(2.08114 + 3.60464i) q^{13} -5.16228 q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.581139 + 1.00656i) q^{17} +(-1.00000 - 1.73205i) q^{18} +(-4.16228 - 7.20928i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(2.58114 - 4.47066i) q^{21} +(-0.581139 + 1.00656i) q^{22} +3.16228 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +4.16228 q^{26} +5.00000 q^{27} +(-2.58114 + 4.47066i) q^{28} +8.32456 q^{29} +(-0.500000 - 0.866025i) q^{30} +4.16228 q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.581139 - 1.00656i) q^{33} +(0.581139 + 1.00656i) q^{34} +(-2.58114 + 4.47066i) q^{35} -2.00000 q^{36} +(-6.08114 - 0.140537i) q^{37} -8.32456 q^{38} +(-2.08114 + 3.60464i) q^{39} +(0.500000 + 0.866025i) q^{40} +(-2.66228 - 4.61120i) q^{41} +(-2.58114 - 4.47066i) q^{42} +7.32456 q^{43} +(0.581139 + 1.00656i) q^{44} -2.00000 q^{45} +(1.58114 - 2.73861i) q^{46} +5.16228 q^{47} -1.00000 q^{48} +(-9.82456 + 17.0166i) q^{49} +(0.500000 + 0.866025i) q^{50} -1.16228 q^{51} +(2.08114 - 3.60464i) q^{52} +(-7.08114 + 12.2649i) q^{53} +(2.50000 - 4.33013i) q^{54} +(0.581139 + 1.00656i) q^{55} +(2.58114 + 4.47066i) q^{56} +(4.16228 - 7.20928i) q^{57} +(4.16228 - 7.20928i) q^{58} +(0.581139 - 1.00656i) q^{59} -1.00000 q^{60} +(4.16228 + 7.20928i) q^{61} +(2.08114 - 3.60464i) q^{62} -10.3246 q^{63} +1.00000 q^{64} +(2.08114 - 3.60464i) q^{65} -1.16228 q^{66} +(4.16228 + 7.20928i) q^{67} +1.16228 q^{68} +(1.58114 + 2.73861i) q^{69} +(2.58114 + 4.47066i) q^{70} +(-3.16228 - 5.47723i) q^{71} +(-1.00000 + 1.73205i) q^{72} +3.48683 q^{73} +(-3.16228 + 5.19615i) q^{74} -1.00000 q^{75} +(-4.16228 + 7.20928i) q^{76} +(3.00000 + 5.19615i) q^{77} +(2.08114 + 3.60464i) q^{78} +(1.00000 + 1.73205i) q^{79} +1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} -5.32456 q^{82} +(2.00000 - 3.46410i) q^{83} -5.16228 q^{84} +1.16228 q^{85} +(3.66228 - 6.34325i) q^{86} +(4.16228 + 7.20928i) q^{87} +1.16228 q^{88} +(8.32456 - 14.4186i) q^{89} +(-1.00000 + 1.73205i) q^{90} +(10.7434 - 18.6081i) q^{91} +(-1.58114 - 2.73861i) q^{92} +(2.08114 + 3.60464i) q^{93} +(2.58114 - 4.47066i) q^{94} +(-4.16228 + 7.20928i) q^{95} +(-0.500000 + 0.866025i) q^{96} -12.3246 q^{97} +(9.82456 + 17.0166i) q^{98} +(-1.16228 + 2.01312i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{9} - 4 q^{10} + 8 q^{11} + 2 q^{12} + 2 q^{13} - 8 q^{14} + 2 q^{15} - 2 q^{16} + 4 q^{17} - 4 q^{18} - 4 q^{19} - 2 q^{20} + 4 q^{21} + 4 q^{22} - 2 q^{24} - 2 q^{25} + 4 q^{26} + 20 q^{27} - 4 q^{28} + 8 q^{29} - 2 q^{30} + 4 q^{31} + 2 q^{32} + 4 q^{33} - 4 q^{34} - 4 q^{35} - 8 q^{36} - 18 q^{37} - 8 q^{38} - 2 q^{39} + 2 q^{40} + 2 q^{41} - 4 q^{42} + 4 q^{43} - 4 q^{44} - 8 q^{45} + 8 q^{47} - 4 q^{48} - 14 q^{49} + 2 q^{50} + 8 q^{51} + 2 q^{52} - 22 q^{53} + 10 q^{54} - 4 q^{55} + 4 q^{56} + 4 q^{57} + 4 q^{58} - 4 q^{59} - 4 q^{60} + 4 q^{61} + 2 q^{62} - 16 q^{63} + 4 q^{64} + 2 q^{65} + 8 q^{66} + 4 q^{67} - 8 q^{68} + 4 q^{70} - 4 q^{72} - 24 q^{73} - 4 q^{75} - 4 q^{76} + 12 q^{77} + 2 q^{78} + 4 q^{79} + 4 q^{80} - 2 q^{81} + 4 q^{82} + 8 q^{83} - 8 q^{84} - 8 q^{85} + 2 q^{86} + 4 q^{87} - 8 q^{88} + 8 q^{89} - 4 q^{90} + 24 q^{91} + 2 q^{93} + 4 q^{94} - 4 q^{95} - 2 q^{96} - 24 q^{97} + 14 q^{98} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i 0.973494 0.228714i \(-0.0734519\pi\)
−0.684819 + 0.728714i \(0.740119\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 1.00000 0.408248
\(7\) −2.58114 4.47066i −0.975579 1.68975i −0.678012 0.735051i \(-0.737158\pi\)
−0.297567 0.954701i \(-0.596175\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 1.73205i 0.333333 0.577350i
\(10\) −1.00000 −0.316228
\(11\) −1.16228 −0.350440 −0.175220 0.984529i \(-0.556064\pi\)
−0.175220 + 0.984529i \(0.556064\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) 2.08114 + 3.60464i 0.577204 + 0.999747i 0.995798 + 0.0915734i \(0.0291896\pi\)
−0.418594 + 0.908173i \(0.637477\pi\)
\(14\) −5.16228 −1.37968
\(15\) 0.500000 0.866025i 0.129099 0.223607i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.581139 + 1.00656i −0.140947 + 0.244127i −0.927853 0.372945i \(-0.878348\pi\)
0.786907 + 0.617072i \(0.211681\pi\)
\(18\) −1.00000 1.73205i −0.235702 0.408248i
\(19\) −4.16228 7.20928i −0.954892 1.65392i −0.734615 0.678484i \(-0.762637\pi\)
−0.220277 0.975437i \(-0.570696\pi\)
\(20\) −0.500000 + 0.866025i −0.111803 + 0.193649i
\(21\) 2.58114 4.47066i 0.563251 0.975579i
\(22\) −0.581139 + 1.00656i −0.123899 + 0.214600i
\(23\) 3.16228 0.659380 0.329690 0.944089i \(-0.393056\pi\)
0.329690 + 0.944089i \(0.393056\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 4.16228 0.816290
\(27\) 5.00000 0.962250
\(28\) −2.58114 + 4.47066i −0.487789 + 0.844876i
\(29\) 8.32456 1.54583 0.772916 0.634509i \(-0.218798\pi\)
0.772916 + 0.634509i \(0.218798\pi\)
\(30\) −0.500000 0.866025i −0.0912871 0.158114i
\(31\) 4.16228 0.747567 0.373784 0.927516i \(-0.378060\pi\)
0.373784 + 0.927516i \(0.378060\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −0.581139 1.00656i −0.101163 0.175220i
\(34\) 0.581139 + 1.00656i 0.0996645 + 0.172624i
\(35\) −2.58114 + 4.47066i −0.436292 + 0.755680i
\(36\) −2.00000 −0.333333
\(37\) −6.08114 0.140537i −0.999733 0.0231041i
\(38\) −8.32456 −1.35042
\(39\) −2.08114 + 3.60464i −0.333249 + 0.577204i
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) −2.66228 4.61120i −0.415778 0.720148i 0.579732 0.814807i \(-0.303157\pi\)
−0.995510 + 0.0946588i \(0.969824\pi\)
\(42\) −2.58114 4.47066i −0.398278 0.689838i
\(43\) 7.32456 1.11698 0.558492 0.829510i \(-0.311380\pi\)
0.558492 + 0.829510i \(0.311380\pi\)
\(44\) 0.581139 + 1.00656i 0.0876100 + 0.151745i
\(45\) −2.00000 −0.298142
\(46\) 1.58114 2.73861i 0.233126 0.403786i
\(47\) 5.16228 0.752996 0.376498 0.926418i \(-0.377128\pi\)
0.376498 + 0.926418i \(0.377128\pi\)
\(48\) −1.00000 −0.144338
\(49\) −9.82456 + 17.0166i −1.40351 + 2.43095i
\(50\) 0.500000 + 0.866025i 0.0707107 + 0.122474i
\(51\) −1.16228 −0.162751
\(52\) 2.08114 3.60464i 0.288602 0.499873i
\(53\) −7.08114 + 12.2649i −0.972669 + 1.68471i −0.285248 + 0.958454i \(0.592076\pi\)
−0.687422 + 0.726259i \(0.741257\pi\)
\(54\) 2.50000 4.33013i 0.340207 0.589256i
\(55\) 0.581139 + 1.00656i 0.0783607 + 0.135725i
\(56\) 2.58114 + 4.47066i 0.344919 + 0.597418i
\(57\) 4.16228 7.20928i 0.551307 0.954892i
\(58\) 4.16228 7.20928i 0.546534 0.946624i
\(59\) 0.581139 1.00656i 0.0756578 0.131043i −0.825714 0.564089i \(-0.809228\pi\)
0.901372 + 0.433045i \(0.142561\pi\)
\(60\) −1.00000 −0.129099
\(61\) 4.16228 + 7.20928i 0.532925 + 0.923053i 0.999261 + 0.0384454i \(0.0122406\pi\)
−0.466336 + 0.884608i \(0.654426\pi\)
\(62\) 2.08114 3.60464i 0.264305 0.457790i
\(63\) −10.3246 −1.30077
\(64\) 1.00000 0.125000
\(65\) 2.08114 3.60464i 0.258134 0.447100i
\(66\) −1.16228 −0.143066
\(67\) 4.16228 + 7.20928i 0.508503 + 0.880753i 0.999952 + 0.00984658i \(0.00313431\pi\)
−0.491448 + 0.870907i \(0.663532\pi\)
\(68\) 1.16228 0.140947
\(69\) 1.58114 + 2.73861i 0.190347 + 0.329690i
\(70\) 2.58114 + 4.47066i 0.308505 + 0.534347i
\(71\) −3.16228 5.47723i −0.375293 0.650027i 0.615078 0.788467i \(-0.289125\pi\)
−0.990371 + 0.138440i \(0.955791\pi\)
\(72\) −1.00000 + 1.73205i −0.117851 + 0.204124i
\(73\) 3.48683 0.408103 0.204051 0.978960i \(-0.434589\pi\)
0.204051 + 0.978960i \(0.434589\pi\)
\(74\) −3.16228 + 5.19615i −0.367607 + 0.604040i
\(75\) −1.00000 −0.115470
\(76\) −4.16228 + 7.20928i −0.477446 + 0.826961i
\(77\) 3.00000 + 5.19615i 0.341882 + 0.592157i
\(78\) 2.08114 + 3.60464i 0.235643 + 0.408145i
\(79\) 1.00000 + 1.73205i 0.112509 + 0.194871i 0.916781 0.399390i \(-0.130778\pi\)
−0.804272 + 0.594261i \(0.797445\pi\)
\(80\) 1.00000 0.111803
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −5.32456 −0.587999
\(83\) 2.00000 3.46410i 0.219529 0.380235i −0.735135 0.677920i \(-0.762881\pi\)
0.954664 + 0.297686i \(0.0962148\pi\)
\(84\) −5.16228 −0.563251
\(85\) 1.16228 0.126067
\(86\) 3.66228 6.34325i 0.394914 0.684010i
\(87\) 4.16228 + 7.20928i 0.446243 + 0.772916i
\(88\) 1.16228 0.123899
\(89\) 8.32456 14.4186i 0.882401 1.52836i 0.0337374 0.999431i \(-0.489259\pi\)
0.848664 0.528933i \(-0.177408\pi\)
\(90\) −1.00000 + 1.73205i −0.105409 + 0.182574i
\(91\) 10.7434 18.6081i 1.12622 1.95066i
\(92\) −1.58114 2.73861i −0.164845 0.285520i
\(93\) 2.08114 + 3.60464i 0.215804 + 0.373784i
\(94\) 2.58114 4.47066i 0.266224 0.461114i
\(95\) −4.16228 + 7.20928i −0.427041 + 0.739656i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) −12.3246 −1.25137 −0.625684 0.780076i \(-0.715180\pi\)
−0.625684 + 0.780076i \(0.715180\pi\)
\(98\) 9.82456 + 17.0166i 0.992430 + 1.71894i
\(99\) −1.16228 + 2.01312i −0.116813 + 0.202327i
\(100\) 1.00000 0.100000
\(101\) 12.8377 1.27740 0.638701 0.769455i \(-0.279472\pi\)
0.638701 + 0.769455i \(0.279472\pi\)
\(102\) −0.581139 + 1.00656i −0.0575413 + 0.0996645i
\(103\) −13.4868 −1.32890 −0.664449 0.747334i \(-0.731334\pi\)
−0.664449 + 0.747334i \(0.731334\pi\)
\(104\) −2.08114 3.60464i −0.204072 0.353464i
\(105\) −5.16228 −0.503787
\(106\) 7.08114 + 12.2649i 0.687781 + 1.19127i
\(107\) 3.50000 + 6.06218i 0.338358 + 0.586053i 0.984124 0.177482i \(-0.0567953\pi\)
−0.645766 + 0.763535i \(0.723462\pi\)
\(108\) −2.50000 4.33013i −0.240563 0.416667i
\(109\) −1.83772 + 3.18303i −0.176022 + 0.304879i −0.940514 0.339754i \(-0.889656\pi\)
0.764493 + 0.644633i \(0.222990\pi\)
\(110\) 1.16228 0.110819
\(111\) −2.91886 5.33669i −0.277046 0.506536i
\(112\) 5.16228 0.487789
\(113\) 3.16228 5.47723i 0.297482 0.515254i −0.678077 0.734991i \(-0.737186\pi\)
0.975559 + 0.219737i \(0.0705198\pi\)
\(114\) −4.16228 7.20928i −0.389833 0.675211i
\(115\) −1.58114 2.73861i −0.147442 0.255377i
\(116\) −4.16228 7.20928i −0.386458 0.669365i
\(117\) 8.32456 0.769605
\(118\) −0.581139 1.00656i −0.0534982 0.0926615i
\(119\) 6.00000 0.550019
\(120\) −0.500000 + 0.866025i −0.0456435 + 0.0790569i
\(121\) −9.64911 −0.877192
\(122\) 8.32456 0.753670
\(123\) 2.66228 4.61120i 0.240049 0.415778i
\(124\) −2.08114 3.60464i −0.186892 0.323706i
\(125\) 1.00000 0.0894427
\(126\) −5.16228 + 8.94133i −0.459892 + 0.796557i
\(127\) −2.83772 + 4.91508i −0.251807 + 0.436143i −0.964023 0.265817i \(-0.914358\pi\)
0.712216 + 0.701960i \(0.247692\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 3.66228 + 6.34325i 0.322446 + 0.558492i
\(130\) −2.08114 3.60464i −0.182528 0.316148i
\(131\) 9.00000 15.5885i 0.786334 1.36197i −0.141865 0.989886i \(-0.545310\pi\)
0.928199 0.372084i \(-0.121357\pi\)
\(132\) −0.581139 + 1.00656i −0.0505816 + 0.0876100i
\(133\) −21.4868 + 37.2163i −1.86314 + 3.22706i
\(134\) 8.32456 0.719132
\(135\) −2.50000 4.33013i −0.215166 0.372678i
\(136\) 0.581139 1.00656i 0.0498322 0.0863120i
\(137\) 11.4868 0.981386 0.490693 0.871332i \(-0.336744\pi\)
0.490693 + 0.871332i \(0.336744\pi\)
\(138\) 3.16228 0.269191
\(139\) 7.74342 13.4120i 0.656788 1.13759i −0.324654 0.945833i \(-0.605248\pi\)
0.981442 0.191757i \(-0.0614187\pi\)
\(140\) 5.16228 0.436292
\(141\) 2.58114 + 4.47066i 0.217371 + 0.376498i
\(142\) −6.32456 −0.530745
\(143\) −2.41886 4.18959i −0.202275 0.350351i
\(144\) 1.00000 + 1.73205i 0.0833333 + 0.144338i
\(145\) −4.16228 7.20928i −0.345658 0.598698i
\(146\) 1.74342 3.01969i 0.144286 0.249911i
\(147\) −19.6491 −1.62063
\(148\) 2.91886 + 5.33669i 0.239929 + 0.438673i
\(149\) 12.0000 0.983078 0.491539 0.870855i \(-0.336434\pi\)
0.491539 + 0.870855i \(0.336434\pi\)
\(150\) −0.500000 + 0.866025i −0.0408248 + 0.0707107i
\(151\) −1.75658 3.04249i −0.142949 0.247594i 0.785657 0.618662i \(-0.212325\pi\)
−0.928606 + 0.371068i \(0.878992\pi\)
\(152\) 4.16228 + 7.20928i 0.337605 + 0.584750i
\(153\) 1.16228 + 2.01312i 0.0939646 + 0.162751i
\(154\) 6.00000 0.483494
\(155\) −2.08114 3.60464i −0.167161 0.289532i
\(156\) 4.16228 0.333249
\(157\) 5.08114 8.80079i 0.405519 0.702380i −0.588863 0.808233i \(-0.700424\pi\)
0.994382 + 0.105854i \(0.0337575\pi\)
\(158\) 2.00000 0.159111
\(159\) −14.1623 −1.12314
\(160\) 0.500000 0.866025i 0.0395285 0.0684653i
\(161\) −8.16228 14.1375i −0.643278 1.11419i
\(162\) −1.00000 −0.0785674
\(163\) −2.82456 + 4.89227i −0.221236 + 0.383192i −0.955184 0.296014i \(-0.904343\pi\)
0.733947 + 0.679206i \(0.237676\pi\)
\(164\) −2.66228 + 4.61120i −0.207889 + 0.360074i
\(165\) −0.581139 + 1.00656i −0.0452416 + 0.0783607i
\(166\) −2.00000 3.46410i −0.155230 0.268866i
\(167\) 4.16228 + 7.20928i 0.322087 + 0.557871i 0.980918 0.194420i \(-0.0622824\pi\)
−0.658832 + 0.752290i \(0.728949\pi\)
\(168\) −2.58114 + 4.47066i −0.199139 + 0.344919i
\(169\) −2.16228 + 3.74517i −0.166329 + 0.288090i
\(170\) 0.581139 1.00656i 0.0445713 0.0771998i
\(171\) −16.6491 −1.27319
\(172\) −3.66228 6.34325i −0.279246 0.483668i
\(173\) −1.16228 + 2.01312i −0.0883663 + 0.153055i −0.906821 0.421517i \(-0.861498\pi\)
0.818454 + 0.574572i \(0.194831\pi\)
\(174\) 8.32456 0.631083
\(175\) 5.16228 0.390232
\(176\) 0.581139 1.00656i 0.0438050 0.0758725i
\(177\) 1.16228 0.0873621
\(178\) −8.32456 14.4186i −0.623952 1.08072i
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 1.00000 + 1.73205i 0.0745356 + 0.129099i
\(181\) −2.25658 3.90852i −0.167731 0.290518i 0.769891 0.638175i \(-0.220311\pi\)
−0.937622 + 0.347658i \(0.886977\pi\)
\(182\) −10.7434 18.6081i −0.796355 1.37933i
\(183\) −4.16228 + 7.20928i −0.307684 + 0.532925i
\(184\) −3.16228 −0.233126
\(185\) 2.91886 + 5.33669i 0.214599 + 0.392361i
\(186\) 4.16228 0.305193
\(187\) 0.675445 1.16990i 0.0493934 0.0855519i
\(188\) −2.58114 4.47066i −0.188249 0.326057i
\(189\) −12.9057 22.3533i −0.938751 1.62596i
\(190\) 4.16228 + 7.20928i 0.301963 + 0.523016i
\(191\) −8.81139 −0.637570 −0.318785 0.947827i \(-0.603275\pi\)
−0.318785 + 0.947827i \(0.603275\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −0.513167 −0.0369386 −0.0184693 0.999829i \(-0.505879\pi\)
−0.0184693 + 0.999829i \(0.505879\pi\)
\(194\) −6.16228 + 10.6734i −0.442426 + 0.766304i
\(195\) 4.16228 0.298067
\(196\) 19.6491 1.40351
\(197\) −6.91886 + 11.9838i −0.492948 + 0.853812i −0.999967 0.00812338i \(-0.997414\pi\)
0.507019 + 0.861935i \(0.330748\pi\)
\(198\) 1.16228 + 2.01312i 0.0825995 + 0.143066i
\(199\) −5.83772 −0.413825 −0.206913 0.978359i \(-0.566342\pi\)
−0.206913 + 0.978359i \(0.566342\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) −4.16228 + 7.20928i −0.293584 + 0.508503i
\(202\) 6.41886 11.1178i 0.451629 0.782245i
\(203\) −21.4868 37.2163i −1.50808 2.61207i
\(204\) 0.581139 + 1.00656i 0.0406879 + 0.0704734i
\(205\) −2.66228 + 4.61120i −0.185942 + 0.322060i
\(206\) −6.74342 + 11.6799i −0.469836 + 0.813780i
\(207\) 3.16228 5.47723i 0.219793 0.380693i
\(208\) −4.16228 −0.288602
\(209\) 4.83772 + 8.37918i 0.334632 + 0.579600i
\(210\) −2.58114 + 4.47066i −0.178116 + 0.308505i
\(211\) −8.32456 −0.573086 −0.286543 0.958067i \(-0.592506\pi\)
−0.286543 + 0.958067i \(0.592506\pi\)
\(212\) 14.1623 0.972669
\(213\) 3.16228 5.47723i 0.216676 0.375293i
\(214\) 7.00000 0.478510
\(215\) −3.66228 6.34325i −0.249765 0.432606i
\(216\) −5.00000 −0.340207
\(217\) −10.7434 18.6081i −0.729311 1.26320i
\(218\) 1.83772 + 3.18303i 0.124466 + 0.215582i
\(219\) 1.74342 + 3.01969i 0.117809 + 0.204051i
\(220\) 0.581139 1.00656i 0.0391804 0.0678624i
\(221\) −4.83772 −0.325420
\(222\) −6.08114 0.140537i −0.408139 0.00943220i
\(223\) 0.837722 0.0560980 0.0280490 0.999607i \(-0.491071\pi\)
0.0280490 + 0.999607i \(0.491071\pi\)
\(224\) 2.58114 4.47066i 0.172460 0.298709i
\(225\) 1.00000 + 1.73205i 0.0666667 + 0.115470i
\(226\) −3.16228 5.47723i −0.210352 0.364340i
\(227\) 1.33772 + 2.31700i 0.0887878 + 0.153785i 0.906999 0.421133i \(-0.138367\pi\)
−0.818211 + 0.574918i \(0.805034\pi\)
\(228\) −8.32456 −0.551307
\(229\) 5.41886 + 9.38574i 0.358088 + 0.620227i 0.987641 0.156730i \(-0.0500953\pi\)
−0.629553 + 0.776958i \(0.716762\pi\)
\(230\) −3.16228 −0.208514
\(231\) −3.00000 + 5.19615i −0.197386 + 0.341882i
\(232\) −8.32456 −0.546534
\(233\) 13.4868 0.883552 0.441776 0.897125i \(-0.354349\pi\)
0.441776 + 0.897125i \(0.354349\pi\)
\(234\) 4.16228 7.20928i 0.272097 0.471285i
\(235\) −2.58114 4.47066i −0.168375 0.291634i
\(236\) −1.16228 −0.0756578
\(237\) −1.00000 + 1.73205i −0.0649570 + 0.112509i
\(238\) 3.00000 5.19615i 0.194461 0.336817i
\(239\) −5.32456 + 9.22240i −0.344417 + 0.596547i −0.985248 0.171135i \(-0.945257\pi\)
0.640831 + 0.767682i \(0.278590\pi\)
\(240\) 0.500000 + 0.866025i 0.0322749 + 0.0559017i
\(241\) 5.32456 + 9.22240i 0.342985 + 0.594067i 0.984986 0.172637i \(-0.0552287\pi\)
−0.642001 + 0.766704i \(0.721895\pi\)
\(242\) −4.82456 + 8.35637i −0.310134 + 0.537168i
\(243\) 8.00000 13.8564i 0.513200 0.888889i
\(244\) 4.16228 7.20928i 0.266463 0.461527i
\(245\) 19.6491 1.25534
\(246\) −2.66228 4.61120i −0.169741 0.293999i
\(247\) 17.3246 30.0070i 1.10234 1.90930i
\(248\) −4.16228 −0.264305
\(249\) 4.00000 0.253490
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) 6.00000 0.378717 0.189358 0.981908i \(-0.439359\pi\)
0.189358 + 0.981908i \(0.439359\pi\)
\(252\) 5.16228 + 8.94133i 0.325193 + 0.563251i
\(253\) −3.67544 −0.231073
\(254\) 2.83772 + 4.91508i 0.178055 + 0.308400i
\(255\) 0.581139 + 1.00656i 0.0363923 + 0.0630334i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −8.74342 + 15.1440i −0.545399 + 0.944659i 0.453182 + 0.891418i \(0.350289\pi\)
−0.998582 + 0.0532415i \(0.983045\pi\)
\(258\) 7.32456 0.456007
\(259\) 15.0680 + 27.5495i 0.936278 + 1.71184i
\(260\) −4.16228 −0.258134
\(261\) 8.32456 14.4186i 0.515277 0.892486i
\(262\) −9.00000 15.5885i −0.556022 0.963058i
\(263\) 3.74342 + 6.48379i 0.230829 + 0.399807i 0.958052 0.286593i \(-0.0925229\pi\)
−0.727223 + 0.686401i \(0.759190\pi\)
\(264\) 0.581139 + 1.00656i 0.0357666 + 0.0619496i
\(265\) 14.1623 0.869982
\(266\) 21.4868 + 37.2163i 1.31744 + 2.28188i
\(267\) 16.6491 1.01891
\(268\) 4.16228 7.20928i 0.254252 0.440377i
\(269\) 27.1623 1.65611 0.828057 0.560644i \(-0.189447\pi\)
0.828057 + 0.560644i \(0.189447\pi\)
\(270\) −5.00000 −0.304290
\(271\) −13.2434 + 22.9383i −0.804480 + 1.39340i 0.112161 + 0.993690i \(0.464223\pi\)
−0.916641 + 0.399711i \(0.869111\pi\)
\(272\) −0.581139 1.00656i −0.0352367 0.0610318i
\(273\) 21.4868 1.30044
\(274\) 5.74342 9.94789i 0.346972 0.600974i
\(275\) 0.581139 1.00656i 0.0350440 0.0606980i
\(276\) 1.58114 2.73861i 0.0951734 0.164845i
\(277\) 4.24342 + 7.34981i 0.254962 + 0.441607i 0.964885 0.262672i \(-0.0846036\pi\)
−0.709923 + 0.704279i \(0.751270\pi\)
\(278\) −7.74342 13.4120i −0.464419 0.804398i
\(279\) 4.16228 7.20928i 0.249189 0.431608i
\(280\) 2.58114 4.47066i 0.154253 0.267173i
\(281\) 0.824555 1.42817i 0.0491888 0.0851976i −0.840383 0.541994i \(-0.817670\pi\)
0.889571 + 0.456796i \(0.151003\pi\)
\(282\) 5.16228 0.307409
\(283\) −15.3114 26.5201i −0.910168 1.57646i −0.813826 0.581108i \(-0.802619\pi\)
−0.0963412 0.995348i \(-0.530714\pi\)
\(284\) −3.16228 + 5.47723i −0.187647 + 0.325014i
\(285\) −8.32456 −0.493104
\(286\) −4.83772 −0.286061
\(287\) −13.7434 + 23.8043i −0.811248 + 1.40512i
\(288\) 2.00000 0.117851
\(289\) 7.82456 + 13.5525i 0.460268 + 0.797207i
\(290\) −8.32456 −0.488835
\(291\) −6.16228 10.6734i −0.361239 0.625684i
\(292\) −1.74342 3.01969i −0.102026 0.176714i
\(293\) −0.243416 0.421610i −0.0142205 0.0246307i 0.858828 0.512265i \(-0.171193\pi\)
−0.873048 + 0.487634i \(0.837860\pi\)
\(294\) −9.82456 + 17.0166i −0.572980 + 0.992430i
\(295\) −1.16228 −0.0676704
\(296\) 6.08114 + 0.140537i 0.353459 + 0.00816852i
\(297\) −5.81139 −0.337211
\(298\) 6.00000 10.3923i 0.347571 0.602010i
\(299\) 6.58114 + 11.3989i 0.380597 + 0.659213i
\(300\) 0.500000 + 0.866025i 0.0288675 + 0.0500000i
\(301\) −18.9057 32.7456i −1.08971 1.88743i
\(302\) −3.51317 −0.202160
\(303\) 6.41886 + 11.1178i 0.368754 + 0.638701i
\(304\) 8.32456 0.477446
\(305\) 4.16228 7.20928i 0.238331 0.412802i
\(306\) 2.32456 0.132886
\(307\) −26.2982 −1.50092 −0.750459 0.660917i \(-0.770168\pi\)
−0.750459 + 0.660917i \(0.770168\pi\)
\(308\) 3.00000 5.19615i 0.170941 0.296078i
\(309\) −6.74342 11.6799i −0.383620 0.664449i
\(310\) −4.16228 −0.236401
\(311\) −4.08114 + 7.06874i −0.231420 + 0.400831i −0.958226 0.286011i \(-0.907671\pi\)
0.726806 + 0.686843i \(0.241004\pi\)
\(312\) 2.08114 3.60464i 0.117821 0.204072i
\(313\) 5.00000 8.66025i 0.282617 0.489506i −0.689412 0.724370i \(-0.742131\pi\)
0.972028 + 0.234863i \(0.0754642\pi\)
\(314\) −5.08114 8.80079i −0.286745 0.496657i
\(315\) 5.16228 + 8.94133i 0.290861 + 0.503787i
\(316\) 1.00000 1.73205i 0.0562544 0.0974355i
\(317\) 3.24342 5.61776i 0.182168 0.315525i −0.760450 0.649396i \(-0.775022\pi\)
0.942619 + 0.333871i \(0.108355\pi\)
\(318\) −7.08114 + 12.2649i −0.397091 + 0.687781i
\(319\) −9.67544 −0.541721
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) −3.50000 + 6.06218i −0.195351 + 0.338358i
\(322\) −16.3246 −0.909732
\(323\) 9.67544 0.538356
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −4.16228 −0.230882
\(326\) 2.82456 + 4.89227i 0.156438 + 0.270958i
\(327\) −3.67544 −0.203253
\(328\) 2.66228 + 4.61120i 0.147000 + 0.254611i
\(329\) −13.3246 23.0788i −0.734607 1.27238i
\(330\) 0.581139 + 1.00656i 0.0319906 + 0.0554094i
\(331\) −7.25658 + 12.5688i −0.398858 + 0.690842i −0.993585 0.113085i \(-0.963927\pi\)
0.594727 + 0.803927i \(0.297260\pi\)
\(332\) −4.00000 −0.219529
\(333\) −6.32456 + 10.3923i −0.346583 + 0.569495i
\(334\) 8.32456 0.455499
\(335\) 4.16228 7.20928i 0.227410 0.393885i
\(336\) 2.58114 + 4.47066i 0.140813 + 0.243895i
\(337\) 13.6491 + 23.6410i 0.743514 + 1.28780i 0.950886 + 0.309542i \(0.100176\pi\)
−0.207371 + 0.978262i \(0.566491\pi\)
\(338\) 2.16228 + 3.74517i 0.117612 + 0.203711i
\(339\) 6.32456 0.343503
\(340\) −0.581139 1.00656i −0.0315167 0.0545885i
\(341\) −4.83772 −0.261977
\(342\) −8.32456 + 14.4186i −0.450140 + 0.779666i
\(343\) 65.2982 3.52577
\(344\) −7.32456 −0.394914
\(345\) 1.58114 2.73861i 0.0851257 0.147442i
\(346\) 1.16228 + 2.01312i 0.0624844 + 0.108226i
\(347\) −7.67544 −0.412039 −0.206020 0.978548i \(-0.566051\pi\)
−0.206020 + 0.978548i \(0.566051\pi\)
\(348\) 4.16228 7.20928i 0.223122 0.386458i
\(349\) −1.00000 + 1.73205i −0.0535288 + 0.0927146i −0.891548 0.452926i \(-0.850380\pi\)
0.838019 + 0.545640i \(0.183714\pi\)
\(350\) 2.58114 4.47066i 0.137968 0.238967i
\(351\) 10.4057 + 18.0232i 0.555415 + 0.962007i
\(352\) −0.581139 1.00656i −0.0309748 0.0536499i
\(353\) −7.90569 + 13.6931i −0.420778 + 0.728808i −0.996016 0.0891778i \(-0.971576\pi\)
0.575238 + 0.817986i \(0.304909\pi\)
\(354\) 0.581139 1.00656i 0.0308872 0.0534982i
\(355\) −3.16228 + 5.47723i −0.167836 + 0.290701i
\(356\) −16.6491 −0.882401
\(357\) 3.00000 + 5.19615i 0.158777 + 0.275010i
\(358\) −6.00000 + 10.3923i −0.317110 + 0.549250i
\(359\) 4.48683 0.236806 0.118403 0.992966i \(-0.462223\pi\)
0.118403 + 0.992966i \(0.462223\pi\)
\(360\) 2.00000 0.105409
\(361\) −25.1491 + 43.5595i −1.32364 + 2.29261i
\(362\) −4.51317 −0.237207
\(363\) −4.82456 8.35637i −0.253223 0.438596i
\(364\) −21.4868 −1.12622
\(365\) −1.74342 3.01969i −0.0912546 0.158058i
\(366\) 4.16228 + 7.20928i 0.217566 + 0.376835i
\(367\) 3.32456 + 5.75830i 0.173540 + 0.300581i 0.939655 0.342123i \(-0.111146\pi\)
−0.766115 + 0.642704i \(0.777813\pi\)
\(368\) −1.58114 + 2.73861i −0.0824226 + 0.142760i
\(369\) −10.6491 −0.554371
\(370\) 6.08114 + 0.140537i 0.316143 + 0.00730615i
\(371\) 73.1096 3.79566
\(372\) 2.08114 3.60464i 0.107902 0.186892i
\(373\) −5.24342 9.08186i −0.271494 0.470241i 0.697751 0.716341i \(-0.254184\pi\)
−0.969245 + 0.246100i \(0.920851\pi\)
\(374\) −0.675445 1.16990i −0.0349264 0.0604943i
\(375\) 0.500000 + 0.866025i 0.0258199 + 0.0447214i
\(376\) −5.16228 −0.266224
\(377\) 17.3246 + 30.0070i 0.892260 + 1.54544i
\(378\) −25.8114 −1.32759
\(379\) −15.7434 + 27.2684i −0.808685 + 1.40068i 0.105090 + 0.994463i \(0.466487\pi\)
−0.913775 + 0.406221i \(0.866846\pi\)
\(380\) 8.32456 0.427041
\(381\) −5.67544 −0.290762
\(382\) −4.40569 + 7.63089i −0.225415 + 0.390430i
\(383\) 0.581139 + 1.00656i 0.0296948 + 0.0514329i 0.880491 0.474063i \(-0.157213\pi\)
−0.850796 + 0.525496i \(0.823880\pi\)
\(384\) 1.00000 0.0510310
\(385\) 3.00000 5.19615i 0.152894 0.264820i
\(386\) −0.256584 + 0.444416i −0.0130598 + 0.0226202i
\(387\) 7.32456 12.6865i 0.372328 0.644891i
\(388\) 6.16228 + 10.6734i 0.312842 + 0.541859i
\(389\) −14.3246 24.8109i −0.726284 1.25796i −0.958443 0.285283i \(-0.907913\pi\)
0.232160 0.972678i \(-0.425421\pi\)
\(390\) 2.08114 3.60464i 0.105383 0.182528i
\(391\) −1.83772 + 3.18303i −0.0929376 + 0.160973i
\(392\) 9.82456 17.0166i 0.496215 0.859470i
\(393\) 18.0000 0.907980
\(394\) 6.91886 + 11.9838i 0.348567 + 0.603736i
\(395\) 1.00000 1.73205i 0.0503155 0.0871489i
\(396\) 2.32456 0.116813
\(397\) 4.16228 0.208899 0.104449 0.994530i \(-0.466692\pi\)
0.104449 + 0.994530i \(0.466692\pi\)
\(398\) −2.91886 + 5.05562i −0.146309 + 0.253415i
\(399\) −42.9737 −2.15137
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) −8.00000 −0.399501 −0.199750 0.979847i \(-0.564013\pi\)
−0.199750 + 0.979847i \(0.564013\pi\)
\(402\) 4.16228 + 7.20928i 0.207596 + 0.359566i
\(403\) 8.66228 + 15.0035i 0.431499 + 0.747378i
\(404\) −6.41886 11.1178i −0.319350 0.553131i
\(405\) −0.500000 + 0.866025i −0.0248452 + 0.0430331i
\(406\) −42.9737 −2.13275
\(407\) 7.06797 + 0.163343i 0.350346 + 0.00809659i
\(408\) 1.16228 0.0575413
\(409\) 9.82456 17.0166i 0.485793 0.841418i −0.514074 0.857746i \(-0.671864\pi\)
0.999867 + 0.0163279i \(0.00519755\pi\)
\(410\) 2.66228 + 4.61120i 0.131481 + 0.227731i
\(411\) 5.74342 + 9.94789i 0.283302 + 0.490693i
\(412\) 6.74342 + 11.6799i 0.332224 + 0.575429i
\(413\) −6.00000 −0.295241
\(414\) −3.16228 5.47723i −0.155417 0.269191i
\(415\) −4.00000 −0.196352
\(416\) −2.08114 + 3.60464i −0.102036 + 0.176732i
\(417\) 15.4868 0.758393
\(418\) 9.67544 0.473241
\(419\) 8.90569 15.4251i 0.435072 0.753566i −0.562230 0.826981i \(-0.690056\pi\)
0.997301 + 0.0734148i \(0.0233897\pi\)
\(420\) 2.58114 + 4.47066i 0.125947 + 0.218146i
\(421\) −11.4868 −0.559834 −0.279917 0.960024i \(-0.590307\pi\)
−0.279917 + 0.960024i \(0.590307\pi\)
\(422\) −4.16228 + 7.20928i −0.202617 + 0.350942i
\(423\) 5.16228 8.94133i 0.250999 0.434742i
\(424\) 7.08114 12.2649i 0.343891 0.595636i
\(425\) −0.581139 1.00656i −0.0281894 0.0488254i
\(426\) −3.16228 5.47723i −0.153213 0.265372i
\(427\) 21.4868 37.2163i 1.03982 1.80102i
\(428\) 3.50000 6.06218i 0.169179 0.293026i
\(429\) 2.41886 4.18959i 0.116784 0.202275i
\(430\) −7.32456 −0.353221
\(431\) 13.5680 + 23.5004i 0.653546 + 1.13198i 0.982256 + 0.187544i \(0.0600528\pi\)
−0.328710 + 0.944431i \(0.606614\pi\)
\(432\) −2.50000 + 4.33013i −0.120281 + 0.208333i
\(433\) −16.0000 −0.768911 −0.384455 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) −21.4868 −1.03140
\(435\) 4.16228 7.20928i 0.199566 0.345658i
\(436\) 3.67544 0.176022
\(437\) −13.1623 22.7977i −0.629637 1.09056i
\(438\) 3.48683 0.166607
\(439\) 2.40569 + 4.16678i 0.114818 + 0.198870i 0.917707 0.397258i \(-0.130038\pi\)
−0.802889 + 0.596128i \(0.796705\pi\)
\(440\) −0.581139 1.00656i −0.0277047 0.0479860i
\(441\) 19.6491 + 34.0333i 0.935672 + 1.62063i
\(442\) −2.41886 + 4.18959i −0.115053 + 0.199278i
\(443\) 37.3246 1.77334 0.886672 0.462400i \(-0.153011\pi\)
0.886672 + 0.462400i \(0.153011\pi\)
\(444\) −3.16228 + 5.19615i −0.150075 + 0.246598i
\(445\) −16.6491 −0.789244
\(446\) 0.418861 0.725489i 0.0198337 0.0343529i
\(447\) 6.00000 + 10.3923i 0.283790 + 0.491539i
\(448\) −2.58114 4.47066i −0.121947 0.211219i
\(449\) −3.17544 5.50003i −0.149858 0.259563i 0.781317 0.624135i \(-0.214548\pi\)
−0.931175 + 0.364572i \(0.881215\pi\)
\(450\) 2.00000 0.0942809
\(451\) 3.09431 + 5.35949i 0.145705 + 0.252369i
\(452\) −6.32456 −0.297482
\(453\) 1.75658 3.04249i 0.0825315 0.142949i
\(454\) 2.67544 0.125565
\(455\) −21.4868 −1.00732
\(456\) −4.16228 + 7.20928i −0.194917 + 0.337605i
\(457\) −3.48683 6.03937i −0.163107 0.282510i 0.772874 0.634559i \(-0.218818\pi\)
−0.935981 + 0.352049i \(0.885485\pi\)
\(458\) 10.8377 0.506414
\(459\) −2.90569 + 5.03281i −0.135626 + 0.234911i
\(460\) −1.58114 + 2.73861i −0.0737210 + 0.127688i
\(461\) 3.83772 6.64713i 0.178741 0.309588i −0.762709 0.646742i \(-0.776131\pi\)
0.941449 + 0.337154i \(0.109464\pi\)
\(462\) 3.00000 + 5.19615i 0.139573 + 0.241747i
\(463\) −9.48683 16.4317i −0.440891 0.763645i 0.556865 0.830603i \(-0.312004\pi\)
−0.997756 + 0.0669581i \(0.978671\pi\)
\(464\) −4.16228 + 7.20928i −0.193229 + 0.334682i
\(465\) 2.08114 3.60464i 0.0965105 0.167161i
\(466\) 6.74342 11.6799i 0.312383 0.541063i
\(467\) −41.6491 −1.92729 −0.963645 0.267184i \(-0.913907\pi\)
−0.963645 + 0.267184i \(0.913907\pi\)
\(468\) −4.16228 7.20928i −0.192401 0.333249i
\(469\) 21.4868 37.2163i 0.992170 1.71849i
\(470\) −5.16228 −0.238118
\(471\) 10.1623 0.468253
\(472\) −0.581139 + 1.00656i −0.0267491 + 0.0463308i
\(473\) −8.51317 −0.391436
\(474\) 1.00000 + 1.73205i 0.0459315 + 0.0795557i
\(475\) 8.32456 0.381957
\(476\) −3.00000 5.19615i −0.137505 0.238165i
\(477\) 14.1623 + 24.5298i 0.648446 + 1.12314i
\(478\) 5.32456 + 9.22240i 0.243539 + 0.421823i
\(479\) −16.0811 + 27.8533i −0.734766 + 1.27265i 0.220060 + 0.975486i \(0.429375\pi\)
−0.954826 + 0.297166i \(0.903959\pi\)
\(480\) 1.00000 0.0456435
\(481\) −12.1491 22.2128i −0.553952 1.01282i
\(482\) 10.6491 0.485054
\(483\) 8.16228 14.1375i 0.371396 0.643278i
\(484\) 4.82456 + 8.35637i 0.219298 + 0.379835i
\(485\) 6.16228 + 10.6734i 0.279815 + 0.484653i
\(486\) −8.00000 13.8564i −0.362887 0.628539i
\(487\) −23.2982 −1.05574 −0.527872 0.849324i \(-0.677010\pi\)
−0.527872 + 0.849324i \(0.677010\pi\)
\(488\) −4.16228 7.20928i −0.188417 0.326349i
\(489\) −5.64911 −0.255462
\(490\) 9.82456 17.0166i 0.443828 0.768733i
\(491\) 12.5132 0.564711 0.282356 0.959310i \(-0.408884\pi\)
0.282356 + 0.959310i \(0.408884\pi\)
\(492\) −5.32456 −0.240049
\(493\) −4.83772 + 8.37918i −0.217880 + 0.377379i
\(494\) −17.3246 30.0070i −0.779469 1.35008i
\(495\) 2.32456 0.104481
\(496\) −2.08114 + 3.60464i −0.0934459 + 0.161853i
\(497\) −16.3246 + 28.2750i −0.732256 + 1.26831i
\(498\) 2.00000 3.46410i 0.0896221 0.155230i
\(499\) 5.67544 + 9.83016i 0.254068 + 0.440058i 0.964642 0.263564i \(-0.0848980\pi\)
−0.710574 + 0.703622i \(0.751565\pi\)
\(500\) −0.500000 0.866025i −0.0223607 0.0387298i
\(501\) −4.16228 + 7.20928i −0.185957 + 0.322087i
\(502\) 3.00000 5.19615i 0.133897 0.231916i
\(503\) 1.74342 3.01969i 0.0777351 0.134641i −0.824537 0.565808i \(-0.808564\pi\)
0.902272 + 0.431166i \(0.141898\pi\)
\(504\) 10.3246 0.459892
\(505\) −6.41886 11.1178i −0.285636 0.494735i
\(506\) −1.83772 + 3.18303i −0.0816967 + 0.141503i
\(507\) −4.32456 −0.192060
\(508\) 5.67544 0.251807
\(509\) −18.3925 + 31.8568i −0.815234 + 1.41203i 0.0939250 + 0.995579i \(0.470059\pi\)
−0.909159 + 0.416448i \(0.863275\pi\)
\(510\) 1.16228 0.0514665
\(511\) −9.00000 15.5885i −0.398137 0.689593i
\(512\) −1.00000 −0.0441942
\(513\) −20.8114 36.0464i −0.918845 1.59149i
\(514\) 8.74342 + 15.1440i 0.385656 + 0.667975i
\(515\) 6.74342 + 11.6799i 0.297150 + 0.514680i
\(516\) 3.66228 6.34325i 0.161223 0.279246i
\(517\) −6.00000 −0.263880
\(518\) 31.3925 + 0.725489i 1.37931 + 0.0318761i
\(519\) −2.32456 −0.102037
\(520\) −2.08114 + 3.60464i −0.0912640 + 0.158074i
\(521\) −11.8246 20.4807i −0.518043 0.897277i −0.999780 0.0209613i \(-0.993327\pi\)
0.481737 0.876316i \(-0.340006\pi\)
\(522\) −8.32456 14.4186i −0.364356 0.631083i
\(523\) 11.9868 + 20.7618i 0.524148 + 0.907850i 0.999605 + 0.0281114i \(0.00894932\pi\)
−0.475457 + 0.879739i \(0.657717\pi\)
\(524\) −18.0000 −0.786334
\(525\) 2.58114 + 4.47066i 0.112650 + 0.195116i
\(526\) 7.48683 0.326441
\(527\) −2.41886 + 4.18959i −0.105367 + 0.182501i
\(528\) 1.16228 0.0505816
\(529\) −13.0000 −0.565217
\(530\) 7.08114 12.2649i 0.307585 0.532753i
\(531\) −1.16228 2.01312i −0.0504386 0.0873621i
\(532\) 42.9737 1.86314
\(533\) 11.0811 19.1931i 0.479977 0.831345i
\(534\) 8.32456 14.4186i 0.360239 0.623952i
\(535\) 3.50000 6.06218i 0.151318 0.262091i
\(536\) −4.16228 7.20928i −0.179783 0.311393i
\(537\) −6.00000 10.3923i −0.258919 0.448461i
\(538\) 13.5811 23.5232i 0.585524 1.01416i
\(539\) 11.4189 19.7780i 0.491845 0.851901i
\(540\) −2.50000 + 4.33013i −0.107583 + 0.186339i
\(541\) 33.6228 1.44556 0.722778 0.691080i \(-0.242865\pi\)
0.722778 + 0.691080i \(0.242865\pi\)
\(542\) 13.2434 + 22.9383i 0.568853 + 0.985283i
\(543\) 2.25658 3.90852i 0.0968393 0.167731i
\(544\) −1.16228 −0.0498322
\(545\) 3.67544 0.157439
\(546\) 10.7434 18.6081i 0.459776 0.796355i
\(547\) 23.9737 1.02504 0.512520 0.858675i \(-0.328712\pi\)
0.512520 + 0.858675i \(0.328712\pi\)
\(548\) −5.74342 9.94789i −0.245347 0.424953i
\(549\) 16.6491 0.710567
\(550\) −0.581139 1.00656i −0.0247798 0.0429199i
\(551\) −34.6491 60.0140i −1.47610 2.55668i
\(552\) −1.58114 2.73861i −0.0672977 0.116563i
\(553\) 5.16228 8.94133i 0.219522 0.380224i
\(554\) 8.48683 0.360571
\(555\) −3.16228 + 5.19615i −0.134231 + 0.220564i
\(556\) −15.4868 −0.656788
\(557\) 3.59431 6.22552i 0.152296 0.263784i −0.779775 0.626059i \(-0.784667\pi\)
0.932071 + 0.362276i \(0.118000\pi\)
\(558\) −4.16228 7.20928i −0.176203 0.305193i
\(559\) 15.2434 + 26.4024i 0.644728 + 1.11670i
\(560\) −2.58114 4.47066i −0.109073 0.188920i
\(561\) 1.35089 0.0570346
\(562\) −0.824555 1.42817i −0.0347818 0.0602438i
\(563\) −11.2982 −0.476163 −0.238082 0.971245i \(-0.576519\pi\)
−0.238082 + 0.971245i \(0.576519\pi\)
\(564\) 2.58114 4.47066i 0.108686 0.188249i
\(565\) −6.32456 −0.266076
\(566\) −30.6228 −1.28717
\(567\) −2.58114 + 4.47066i −0.108398 + 0.187750i
\(568\) 3.16228 + 5.47723i 0.132686 + 0.229819i
\(569\) 27.3246 1.14550 0.572752 0.819728i \(-0.305876\pi\)
0.572752 + 0.819728i \(0.305876\pi\)
\(570\) −4.16228 + 7.20928i −0.174339 + 0.301963i
\(571\) −11.1623 + 19.3336i −0.467127 + 0.809087i −0.999295 0.0375515i \(-0.988044\pi\)
0.532168 + 0.846639i \(0.321378\pi\)
\(572\) −2.41886 + 4.18959i −0.101138 + 0.175176i
\(573\) −4.40569 7.63089i −0.184051 0.318785i
\(574\) 13.7434 + 23.8043i 0.573639 + 0.993572i
\(575\) −1.58114 + 2.73861i −0.0659380 + 0.114208i
\(576\) 1.00000 1.73205i 0.0416667 0.0721688i
\(577\) 21.5811 37.3796i 0.898435 1.55613i 0.0689391 0.997621i \(-0.478039\pi\)
0.829495 0.558513i \(-0.188628\pi\)
\(578\) 15.6491 0.650917
\(579\) −0.256584 0.444416i −0.0106632 0.0184693i
\(580\) −4.16228 + 7.20928i −0.172829 + 0.299349i
\(581\) −20.6491 −0.856669
\(582\) −12.3246 −0.510869
\(583\) 8.23025 14.2552i 0.340862 0.590390i
\(584\) −3.48683 −0.144286
\(585\) −4.16228 7.20928i −0.172089 0.298067i
\(586\) −0.486833 −0.0201109
\(587\) 9.31139 + 16.1278i 0.384322 + 0.665665i 0.991675 0.128767i \(-0.0411019\pi\)
−0.607353 + 0.794432i \(0.707769\pi\)
\(588\) 9.82456 + 17.0166i 0.405158 + 0.701754i
\(589\) −17.3246 30.0070i −0.713846 1.23642i
\(590\) −0.581139 + 1.00656i −0.0239251 + 0.0414395i
\(591\) −13.8377 −0.569208
\(592\) 3.16228 5.19615i 0.129969 0.213561i
\(593\) −44.1359 −1.81245 −0.906223 0.422800i \(-0.861047\pi\)
−0.906223 + 0.422800i \(0.861047\pi\)
\(594\) −2.90569 + 5.03281i −0.119222 + 0.206499i
\(595\) −3.00000 5.19615i −0.122988 0.213021i
\(596\) −6.00000 10.3923i −0.245770 0.425685i
\(597\) −2.91886 5.05562i −0.119461 0.206913i
\(598\) 13.1623 0.538246
\(599\) 21.7302 + 37.6379i 0.887874 + 1.53784i 0.842384 + 0.538878i \(0.181152\pi\)
0.0454901 + 0.998965i \(0.485515\pi\)
\(600\) 1.00000 0.0408248
\(601\) −3.82456 + 6.62432i −0.156007 + 0.270212i −0.933425 0.358772i \(-0.883196\pi\)
0.777418 + 0.628984i \(0.216529\pi\)
\(602\) −37.8114 −1.54108
\(603\) 16.6491 0.678004
\(604\) −1.75658 + 3.04249i −0.0714744 + 0.123797i
\(605\) 4.82456 + 8.35637i 0.196146 + 0.339735i
\(606\) 12.8377 0.521497
\(607\) 8.25658 14.3008i 0.335124 0.580452i −0.648384 0.761313i \(-0.724555\pi\)
0.983509 + 0.180861i \(0.0578883\pi\)
\(608\) 4.16228 7.20928i 0.168803 0.292375i
\(609\) 21.4868 37.2163i 0.870690 1.50808i
\(610\) −4.16228 7.20928i −0.168526 0.291895i
\(611\) 10.7434 + 18.6081i 0.434632 + 0.752805i
\(612\) 1.16228 2.01312i 0.0469823 0.0813757i
\(613\) 12.1623 21.0657i 0.491230 0.850835i −0.508719 0.860932i \(-0.669881\pi\)
0.999949 + 0.0100976i \(0.00321421\pi\)
\(614\) −13.1491 + 22.7749i −0.530655 + 0.919121i
\(615\) −5.32456 −0.214707
\(616\) −3.00000 5.19615i −0.120873 0.209359i
\(617\) −0.486833 + 0.843219i −0.0195992 + 0.0339467i −0.875659 0.482931i \(-0.839572\pi\)
0.856059 + 0.516877i \(0.172906\pi\)
\(618\) −13.4868 −0.542520
\(619\) −34.0000 −1.36658 −0.683288 0.730149i \(-0.739451\pi\)
−0.683288 + 0.730149i \(0.739451\pi\)
\(620\) −2.08114 + 3.60464i −0.0835805 + 0.144766i
\(621\) 15.8114 0.634489
\(622\) 4.08114 + 7.06874i 0.163639 + 0.283431i
\(623\) −85.9473 −3.44341
\(624\) −2.08114 3.60464i −0.0833122 0.144301i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −5.00000 8.66025i −0.199840 0.346133i
\(627\) −4.83772 + 8.37918i −0.193200 + 0.334632i
\(628\) −10.1623 −0.405519
\(629\) 3.67544 6.03937i 0.146550 0.240806i
\(630\) 10.3246 0.411340
\(631\) −5.91886 + 10.2518i −0.235626 + 0.408116i −0.959454 0.281864i \(-0.909047\pi\)
0.723828 + 0.689980i \(0.242381\pi\)
\(632\) −1.00000 1.73205i −0.0397779 0.0688973i
\(633\) −4.16228 7.20928i −0.165436 0.286543i
\(634\) −3.24342 5.61776i −0.128813 0.223110i
\(635\) 5.67544 0.225223
\(636\) 7.08114 + 12.2649i 0.280785 + 0.486335i
\(637\) −81.7851 −3.24044
\(638\) −4.83772 + 8.37918i −0.191527 + 0.331735i
\(639\) −12.6491 −0.500391
\(640\) −1.00000 −0.0395285
\(641\) −9.33772 + 16.1734i −0.368818 + 0.638811i −0.989381 0.145345i \(-0.953571\pi\)
0.620563 + 0.784156i \(0.286904\pi\)
\(642\) 3.50000 + 6.06218i 0.138134 + 0.239255i
\(643\) 10.0263 0.395400 0.197700 0.980263i \(-0.436653\pi\)
0.197700 + 0.980263i \(0.436653\pi\)
\(644\) −8.16228 + 14.1375i −0.321639 + 0.557095i
\(645\) 3.66228 6.34325i 0.144202 0.249765i
\(646\) 4.83772 8.37918i 0.190338 0.329674i
\(647\) −13.1623 22.7977i −0.517463 0.896271i −0.999794 0.0202828i \(-0.993543\pi\)
0.482332 0.875989i \(-0.339790\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −0.675445 + 1.16990i −0.0265135 + 0.0459228i
\(650\) −2.08114 + 3.60464i −0.0816290 + 0.141386i
\(651\) 10.7434 18.6081i 0.421068 0.729311i
\(652\) 5.64911 0.221236
\(653\) 9.73025 + 16.8533i 0.380774 + 0.659520i 0.991173 0.132574i \(-0.0423242\pi\)
−0.610399 + 0.792094i \(0.708991\pi\)
\(654\) −1.83772 + 3.18303i −0.0718606 + 0.124466i
\(655\) −18.0000 −0.703318
\(656\) 5.32456 0.207889
\(657\) 3.48683 6.03937i 0.136034 0.235618i
\(658\) −26.6491 −1.03889
\(659\) −21.4868 37.2163i −0.837008 1.44974i −0.892385 0.451275i \(-0.850969\pi\)
0.0553767 0.998466i \(-0.482364\pi\)
\(660\) 1.16228 0.0452416
\(661\) −1.09431 1.89539i −0.0425636 0.0737223i 0.843959 0.536408i \(-0.180219\pi\)
−0.886522 + 0.462686i \(0.846886\pi\)
\(662\) 7.25658 + 12.5688i 0.282035 + 0.488499i
\(663\) −2.41886 4.18959i −0.0939408 0.162710i
\(664\) −2.00000 + 3.46410i −0.0776151 + 0.134433i
\(665\) 42.9737 1.66645
\(666\) 5.83772 + 10.6734i 0.226207 + 0.413585i
\(667\) 26.3246 1.01929
\(668\) 4.16228 7.20928i 0.161043 0.278935i
\(669\) 0.418861 + 0.725489i 0.0161941 + 0.0280490i
\(670\) −4.16228 7.20928i −0.160803 0.278519i
\(671\) −4.83772 8.37918i −0.186758 0.323475i
\(672\) 5.16228 0.199139
\(673\) 7.90569 + 13.6931i 0.304742 + 0.527829i 0.977204 0.212303i \(-0.0680964\pi\)
−0.672462 + 0.740132i \(0.734763\pi\)
\(674\) 27.2982 1.05149
\(675\) −2.50000 + 4.33013i −0.0962250 + 0.166667i
\(676\) 4.32456 0.166329
\(677\) 21.6228 0.831031 0.415515 0.909586i \(-0.363601\pi\)
0.415515 + 0.909586i \(0.363601\pi\)
\(678\) 3.16228 5.47723i 0.121447 0.210352i
\(679\) 31.8114 + 55.0989i 1.22081 + 2.11450i
\(680\) −1.16228 −0.0445713
\(681\) −1.33772 + 2.31700i −0.0512616 + 0.0887878i
\(682\) −2.41886 + 4.18959i −0.0926230 + 0.160428i
\(683\) −13.8246 + 23.9448i −0.528982 + 0.916224i 0.470447 + 0.882428i \(0.344093\pi\)
−0.999429 + 0.0337952i \(0.989241\pi\)
\(684\) 8.32456 + 14.4186i 0.318297 + 0.551307i
\(685\) −5.74342 9.94789i −0.219445 0.380089i
\(686\) 32.6491 56.5499i 1.24655 2.15909i
\(687\) −5.41886 + 9.38574i −0.206742 + 0.358088i
\(688\) −3.66228 + 6.34325i −0.139623 + 0.241834i
\(689\) −58.9473 −2.24571
\(690\) −1.58114 2.73861i −0.0601929 0.104257i
\(691\) 1.90569 3.30076i 0.0724960 0.125567i −0.827499 0.561468i \(-0.810237\pi\)
0.899995 + 0.435901i \(0.143570\pi\)
\(692\) 2.32456 0.0883663
\(693\) 12.0000 0.455842
\(694\) −3.83772 + 6.64713i −0.145678 + 0.252322i
\(695\) −15.4868 −0.587449
\(696\) −4.16228 7.20928i −0.157771 0.273267i
\(697\) 6.18861 0.234410
\(698\) 1.00000 + 1.73205i 0.0378506 + 0.0655591i
\(699\) 6.74342 + 11.6799i 0.255059 + 0.441776i
\(700\) −2.58114 4.47066i −0.0975579 0.168975i
\(701\) −4.48683 + 7.77142i −0.169465 + 0.293523i −0.938232 0.346007i \(-0.887537\pi\)
0.768767 + 0.639529i \(0.220871\pi\)
\(702\) 20.8114 0.785475
\(703\) 24.2982 + 44.4256i 0.916425 + 1.67554i
\(704\) −1.16228 −0.0438050
\(705\) 2.58114 4.47066i 0.0972113 0.168375i
\(706\) 7.90569 + 13.6931i 0.297535 + 0.515345i
\(707\) −33.1359 57.3931i −1.24621 2.15849i
\(708\) −0.581139 1.00656i −0.0218405 0.0378289i
\(709\) 3.35089 0.125845 0.0629226 0.998018i \(-0.479958\pi\)
0.0629226 + 0.998018i \(0.479958\pi\)
\(710\) 3.16228 + 5.47723i 0.118678 + 0.205557i
\(711\) 4.00000 0.150012
\(712\) −8.32456 + 14.4186i −0.311976 + 0.540358i
\(713\) 13.1623 0.492931
\(714\) 6.00000 0.224544
\(715\) −2.41886 + 4.18959i −0.0904603 + 0.156682i
\(716\) 6.00000 + 10.3923i 0.224231 + 0.388379i
\(717\) −10.6491 −0.397698
\(718\) 2.24342 3.88571i 0.0837236 0.145013i
\(719\) 2.56797 4.44786i 0.0957692 0.165877i −0.814160 0.580640i \(-0.802802\pi\)
0.909929 + 0.414763i \(0.136136\pi\)
\(720\) 1.00000 1.73205i 0.0372678 0.0645497i
\(721\) 34.8114 + 60.2951i 1.29644 + 2.24551i
\(722\) 25.1491 + 43.5595i 0.935953 + 1.62112i
\(723\) −5.32456 + 9.22240i −0.198022 + 0.342985i
\(724\) −2.25658 + 3.90852i −0.0838653 + 0.145259i
\(725\) −4.16228 + 7.20928i −0.154583 + 0.267746i
\(726\) −9.64911 −0.358112
\(727\) −0.837722 1.45098i −0.0310694 0.0538138i 0.850073 0.526666i \(-0.176558\pi\)
−0.881142 + 0.472852i \(0.843225\pi\)
\(728\) −10.7434 + 18.6081i −0.398178 + 0.689664i
\(729\) 13.0000 0.481481
\(730\) −3.48683 −0.129053
\(731\) −4.25658 + 7.37262i −0.157435 + 0.272686i
\(732\) 8.32456 0.307684
\(733\) 3.32456 + 5.75830i 0.122795 + 0.212688i 0.920869 0.389872i \(-0.127481\pi\)
−0.798074 + 0.602560i \(0.794147\pi\)
\(734\) 6.64911 0.245423
\(735\) 9.82456 + 17.0166i 0.362384 + 0.627668i
\(736\) 1.58114 + 2.73861i 0.0582816 + 0.100947i
\(737\) −4.83772 8.37918i −0.178200 0.308651i
\(738\) −5.32456 + 9.22240i −0.196000 + 0.339481i
\(739\) 15.4868 0.569692 0.284846 0.958573i \(-0.408057\pi\)
0.284846 + 0.958573i \(0.408057\pi\)
\(740\) 3.16228 5.19615i 0.116248 0.191014i
\(741\) 34.6491 1.27287
\(742\) 36.5548 63.3148i 1.34197 2.32436i
\(743\) 2.41886 + 4.18959i 0.0887394 + 0.153701i 0.906979 0.421177i \(-0.138383\pi\)
−0.818239 + 0.574878i \(0.805049\pi\)
\(744\) −2.08114 3.60464i −0.0762983 0.132152i
\(745\) −6.00000 10.3923i −0.219823 0.380745i
\(746\) −10.4868 −0.383950
\(747\) −4.00000 6.92820i −0.146352 0.253490i
\(748\) −1.35089 −0.0493934
\(749\) 18.0680 31.2946i 0.660189 1.14348i
\(750\) 1.00000 0.0365148
\(751\) 14.4868 0.528632 0.264316 0.964436i \(-0.414854\pi\)
0.264316 + 0.964436i \(0.414854\pi\)
\(752\) −2.58114 + 4.47066i −0.0941244 + 0.163028i
\(753\) 3.00000 + 5.19615i 0.109326 + 0.189358i
\(754\) 34.6491 1.26185
\(755\) −1.75658 + 3.04249i −0.0639286 + 0.110728i
\(756\) −12.9057 + 22.3533i −0.469376 + 0.812982i
\(757\) −11.2434 + 19.4742i −0.408649 + 0.707801i −0.994739 0.102445i \(-0.967333\pi\)
0.586090 + 0.810246i \(0.300667\pi\)
\(758\) 15.7434 + 27.2684i 0.571827 + 0.990433i
\(759\) −1.83772 3.18303i −0.0667051 0.115537i
\(760\) 4.16228 7.20928i 0.150982 0.261508i
\(761\) −7.16228 + 12.4054i −0.259632 + 0.449696i −0.966143 0.258006i \(-0.916935\pi\)
0.706511 + 0.707702i \(0.250268\pi\)
\(762\) −2.83772 + 4.91508i −0.102800 + 0.178055i
\(763\) 18.9737 0.686893
\(764\) 4.40569 + 7.63089i 0.159392 + 0.276076i
\(765\) 1.16228 2.01312i 0.0420222 0.0727847i
\(766\) 1.16228 0.0419948
\(767\) 4.83772 0.174680
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) 14.9737 0.539964 0.269982 0.962865i \(-0.412982\pi\)
0.269982 + 0.962865i \(0.412982\pi\)
\(770\) −3.00000 5.19615i −0.108112 0.187256i
\(771\) −17.4868 −0.629773
\(772\) 0.256584 + 0.444416i 0.00923464 + 0.0159949i
\(773\) 14.8925 + 25.7946i 0.535647 + 0.927768i 0.999132 + 0.0416629i \(0.0132655\pi\)
−0.463485 + 0.886105i \(0.653401\pi\)
\(774\) −7.32456 12.6865i −0.263276 0.456007i
\(775\) −2.08114 + 3.60464i −0.0747567 + 0.129482i
\(776\) 12.3246 0.442426
\(777\) −16.3246 + 26.8240i −0.585640 + 0.962305i
\(778\) −28.6491 −1.02712
\(779\) −22.1623 + 38.3862i −0.794046 + 1.37533i
\(780\) −2.08114 3.60464i −0.0745167 0.129067i
\(781\) 3.67544 + 6.36606i 0.131518 + 0.227795i
\(782\) 1.83772 + 3.18303i 0.0657168 + 0.113825i
\(783\) 41.6228 1.48748
\(784\) −9.82456 17.0166i −0.350877 0.607737i
\(785\) −10.1623 −0.362707
\(786\) 9.00000 15.5885i 0.321019 0.556022i
\(787\) −7.97367 −0.284230 −0.142115 0.989850i \(-0.545390\pi\)
−0.142115 + 0.989850i \(0.545390\pi\)
\(788\) 13.8377 0.492948
\(789\) −3.74342 + 6.48379i −0.133269 + 0.230829i
\(790\) −1.00000 1.73205i −0.0355784 0.0616236i
\(791\) −32.6491 −1.16087
\(792\) 1.16228 2.01312i 0.0412997 0.0715332i
\(793\) −17.3246 + 30.0070i −0.615213 + 1.06558i
\(794\) 2.08114 3.60464i 0.0738569 0.127924i
\(795\) 7.08114 + 12.2649i 0.251142 + 0.434991i
\(796\) 2.91886 + 5.05562i 0.103456 + 0.179192i
\(797\) 18.0811 31.3175i 0.640467 1.10932i −0.344862 0.938653i \(-0.612074\pi\)
0.985329 0.170668i \(-0.0545924\pi\)
\(798\) −21.4868 + 37.2163i −0.760626 + 1.31744i
\(799\) −3.00000 + 5.19615i −0.106132 + 0.183827i
\(800\) −1.00000 −0.0353553
\(801\) −16.6491 28.8371i −0.588267 1.01891i
\(802\) −4.00000 + 6.92820i −0.141245 + 0.244643i
\(803\) −4.05267 −0.143016
\(804\) 8.32456 0.293584
\(805\) −8.16228 + 14.1375i −0.287682 + 0.498281i
\(806\) 17.3246 0.610231
\(807\) 13.5811 + 23.5232i 0.478079 + 0.828057i
\(808\) −12.8377 −0.451629
\(809\) −20.1491 34.8993i −0.708405 1.22699i −0.965449 0.260594i \(-0.916082\pi\)
0.257044 0.966400i \(-0.417252\pi\)
\(810\) 0.500000 + 0.866025i 0.0175682 + 0.0304290i
\(811\) −16.9737 29.3993i −0.596026 1.03235i −0.993401 0.114691i \(-0.963412\pi\)
0.397375 0.917656i \(-0.369921\pi\)
\(812\) −21.4868 + 37.2163i −0.754040 + 1.30604i
\(813\) −26.4868 −0.928934
\(814\) 3.67544 6.03937i 0.128824 0.211680i
\(815\) 5.64911 0.197880
\(816\) 0.581139 1.00656i 0.0203439 0.0352367i
\(817\) −30.4868 52.8047i −1.06660 1.84740i
\(818\) −9.82456 17.0166i −0.343508 0.594972i
\(819\) −21.4868 37.2163i −0.750811 1.30044i
\(820\) 5.32456 0.185942
\(821\) 15.8377 + 27.4317i 0.552740 + 0.957374i 0.998076 + 0.0620104i \(0.0197512\pi\)
−0.445335 + 0.895364i \(0.646915\pi\)
\(822\) 11.4868 0.400649
\(823\) −1.93203 + 3.34637i −0.0673463 + 0.116647i −0.897732 0.440541i \(-0.854787\pi\)
0.830386 + 0.557188i \(0.188120\pi\)
\(824\) 13.4868 0.469836
\(825\) 1.16228 0.0404653
\(826\) −3.00000 + 5.19615i −0.104383 + 0.180797i
\(827\) 14.1623 + 24.5298i 0.492471 + 0.852984i 0.999962 0.00867244i \(-0.00276056\pi\)
−0.507492 + 0.861657i \(0.669427\pi\)
\(828\) −6.32456 −0.219793
\(829\) −19.5548 + 33.8699i −0.679166 + 1.17635i 0.296066 + 0.955168i \(0.404325\pi\)
−0.975232 + 0.221183i \(0.929008\pi\)
\(830\) −2.00000 + 3.46410i −0.0694210 + 0.120241i
\(831\) −4.24342 + 7.34981i −0.147202 + 0.254962i
\(832\) 2.08114 + 3.60464i 0.0721505 + 0.124968i
\(833\) −11.4189 19.7780i −0.395640 0.685269i
\(834\) 7.74342 13.4120i 0.268133 0.464419i
\(835\) 4.16228 7.20928i 0.144042 0.249487i
\(836\) 4.83772 8.37918i 0.167316 0.289800i
\(837\) 20.8114 0.719347
\(838\) −8.90569 15.4251i −0.307642 0.532852i
\(839\) 8.75658 15.1668i 0.302311 0.523618i −0.674348 0.738414i \(-0.735575\pi\)
0.976659 + 0.214796i \(0.0689086\pi\)
\(840\) 5.16228 0.178116
\(841\) 40.2982 1.38959
\(842\) −5.74342 + 9.94789i −0.197931 + 0.342827i
\(843\) 1.64911 0.0567984
\(844\) 4.16228 + 7.20928i 0.143272 + 0.248154i
\(845\) 4.32456 0.148769
\(846\) −5.16228 8.94133i −0.177483 0.307409i
\(847\) 24.9057 + 43.1379i 0.855770 + 1.48224i
\(848\) −7.08114 12.2649i −0.243167 0.421178i
\(849\) 15.3114 26.5201i 0.525485 0.910168i
\(850\) −1.16228 −0.0398658
\(851\) −19.2302 0.444416i −0.659204 0.0152344i
\(852\) −6.32456 −0.216676
\(853\) −22.5680 + 39.0889i −0.772713 + 1.33838i 0.163359 + 0.986567i \(0.447767\pi\)
−0.936071 + 0.351811i \(0.885566\pi\)
\(854\) −21.4868 37.2163i −0.735264 1.27352i
\(855\) 8.32456 + 14.4186i 0.284694 + 0.493104i
\(856\) −3.50000 6.06218i −0.119628 0.207201i
\(857\) 8.51317 0.290804 0.145402 0.989373i \(-0.453552\pi\)
0.145402 + 0.989373i \(0.453552\pi\)
\(858\) −2.41886 4.18959i −0.0825786 0.143030i
\(859\) 12.0000 0.409435 0.204717 0.978821i \(-0.434372\pi\)
0.204717 + 0.978821i \(0.434372\pi\)
\(860\) −3.66228 + 6.34325i −0.124883 + 0.216303i
\(861\) −27.4868 −0.936749
\(862\) 27.1359 0.924254
\(863\) −18.9737 + 32.8634i −0.645871 + 1.11868i 0.338228 + 0.941064i \(0.390172\pi\)
−0.984100 + 0.177618i \(0.943161\pi\)
\(864\) 2.50000 + 4.33013i 0.0850517 + 0.147314i
\(865\) 2.32456 0.0790373
\(866\) −8.00000 + 13.8564i −0.271851 + 0.470860i
\(867\) −7.82456 + 13.5525i −0.265736 + 0.460268i
\(868\) −10.7434 + 18.6081i −0.364655 + 0.631602i
\(869\) −1.16228 2.01312i −0.0394276 0.0682906i
\(870\) −4.16228 7.20928i −0.141114 0.244417i
\(871\) −17.3246 + 30.0070i −0.587020 + 1.01675i
\(872\) 1.83772 3.18303i 0.0622331 0.107791i
\(873\) −12.3246 + 21.3468i −0.417123 + 0.722478i
\(874\) −26.3246 −0.890441
\(875\) −2.58114 4.47066i −0.0872584 0.151136i
\(876\) 1.74342 3.01969i 0.0589046 0.102026i
\(877\) 33.8377 1.14262 0.571309 0.820735i \(-0.306436\pi\)
0.571309 + 0.820735i \(0.306436\pi\)
\(878\) 4.81139 0.162376
\(879\) 0.243416 0.421610i 0.00821023 0.0142205i
\(880\) −1.16228 −0.0391804
\(881\) −8.51317 14.7452i −0.286816 0.496780i 0.686232 0.727383i \(-0.259263\pi\)
−0.973048 + 0.230603i \(0.925930\pi\)
\(882\) 39.2982 1.32324
\(883\) 3.50000 + 6.06218i 0.117784 + 0.204009i 0.918889 0.394515i \(-0.129088\pi\)
−0.801105 + 0.598524i \(0.795754\pi\)
\(884\) 2.41886 + 4.18959i 0.0813551 + 0.140911i
\(885\) −0.581139 1.00656i −0.0195348 0.0338352i
\(886\) 18.6623 32.3240i 0.626971 1.08595i
\(887\) −12.9737 −0.435613 −0.217807 0.975992i \(-0.569890\pi\)
−0.217807 + 0.975992i \(0.569890\pi\)
\(888\) 2.91886 + 5.33669i 0.0979506 + 0.179088i
\(889\) 29.2982 0.982631
\(890\) −8.32456 + 14.4186i −0.279040 + 0.483311i
\(891\) 0.581139 + 1.00656i 0.0194689 + 0.0337211i
\(892\) −0.418861 0.725489i −0.0140245 0.0242912i
\(893\) −21.4868 37.2163i −0.719029 1.24540i
\(894\) 12.0000 0.401340
\(895\) 6.00000 + 10.3923i 0.200558 + 0.347376i
\(896\) −5.16228 −0.172460
\(897\) −6.58114 + 11.3989i −0.219738 + 0.380597i
\(898\) −6.35089 −0.211932
\(899\) 34.6491 1.15561
\(900\) 1.00000 1.73205i 0.0333333 0.0577350i
\(901\) −8.23025 14.2552i −0.274189 0.474910i
\(902\) 6.18861 0.206058
\(903\) 18.9057 32.7456i 0.629142 1.08971i
\(904\) −3.16228 + 5.47723i −0.105176 + 0.182170i
\(905\) −2.25658 + 3.90852i −0.0750114 + 0.129924i
\(906\) −1.75658 3.04249i −0.0583586 0.101080i
\(907\) −24.4868 42.4124i −0.813072 1.40828i −0.910704 0.413059i \(-0.864460\pi\)
0.0976322 0.995223i \(-0.468873\pi\)
\(908\) 1.33772 2.31700i 0.0443939 0.0768924i
\(909\) 12.8377 22.2356i 0.425800 0.737508i
\(910\) −10.7434 + 18.6081i −0.356141 + 0.616854i
\(911\) 28.1623 0.933058 0.466529 0.884506i \(-0.345504\pi\)
0.466529 + 0.884506i \(0.345504\pi\)
\(912\) 4.16228 + 7.20928i 0.137827 + 0.238723i
\(913\) −2.32456 + 4.02625i −0.0769316 + 0.133249i
\(914\) −6.97367 −0.230668
\(915\) 8.32456 0.275201
\(916\) 5.41886 9.38574i 0.179044 0.310114i
\(917\) −92.9210 −3.06852
\(918\) 2.90569 + 5.03281i 0.0959022 + 0.166107i
\(919\) 22.3246 0.736419 0.368210 0.929743i \(-0.379971\pi\)
0.368210 + 0.929743i \(0.379971\pi\)
\(920\) 1.58114 + 2.73861i 0.0521286 + 0.0902894i
\(921\) −13.1491 22.7749i −0.433278 0.750459i
\(922\) −3.83772 6.64713i −0.126389 0.218912i
\(923\) 13.1623 22.7977i 0.433242 0.750397i
\(924\) 6.00000 0.197386
\(925\) 3.16228 5.19615i 0.103975 0.170848i
\(926\) −18.9737 −0.623513
\(927\) −13.4868 + 23.3599i −0.442966 + 0.767239i
\(928\) 4.16228 + 7.20928i 0.136633 + 0.236656i
\(929\) 9.82456 + 17.0166i 0.322333 + 0.558297i 0.980969 0.194164i \(-0.0621995\pi\)
−0.658636 + 0.752462i \(0.728866\pi\)
\(930\) −2.08114 3.60464i −0.0682432 0.118201i
\(931\) 163.570 5.36079
\(932\) −6.74342 11.6799i −0.220888 0.382589i
\(933\) −8.16228 −0.267221
\(934\) −20.8246 + 36.0692i −0.681400 + 1.18022i
\(935\) −1.35089 −0.0441788
\(936\) −8.32456 −0.272097
\(937\) 22.2982 38.6217i 0.728451 1.26171i −0.229086 0.973406i \(-0.573574\pi\)
0.957538 0.288308i \(-0.0930928\pi\)
\(938\) −21.4868 37.2163i −0.701570 1.21515i
\(939\) 10.0000 0.326338
\(940\) −2.58114 + 4.47066i −0.0841875 + 0.145817i
\(941\) 14.2302 24.6475i 0.463893 0.803486i −0.535258 0.844689i \(-0.679786\pi\)
0.999151 + 0.0412026i \(0.0131189\pi\)
\(942\) 5.08114 8.80079i 0.165552 0.286745i
\(943\) −8.41886 14.5819i −0.274156 0.474852i
\(944\) 0.581139 + 1.00656i 0.0189145 + 0.0327608i
\(945\) −12.9057 + 22.3533i −0.419822 + 0.727153i
\(946\) −4.25658 + 7.37262i −0.138393 + 0.239705i
\(947\) 18.3377 31.7619i 0.595896 1.03212i −0.397524 0.917592i \(-0.630130\pi\)
0.993420 0.114530i \(-0.0365363\pi\)
\(948\) 2.00000 0.0649570
\(949\) 7.25658 + 12.5688i 0.235559 + 0.408000i
\(950\) 4.16228 7.20928i 0.135042 0.233900i
\(951\) 6.48683 0.210350
\(952\) −6.00000 −0.194461
\(953\) −18.5811 + 32.1835i −0.601902 + 1.04253i 0.390631 + 0.920547i \(0.372257\pi\)
−0.992533 + 0.121978i \(0.961076\pi\)
\(954\) 28.3246 0.917041
\(955\) 4.40569 + 7.63089i 0.142565 + 0.246930i
\(956\) 10.6491 0.344417
\(957\) −4.83772 8.37918i −0.156381 0.270860i
\(958\) 16.0811 + 27.8533i 0.519558 + 0.899901i
\(959\) −29.6491 51.3538i −0.957420 1.65830i
\(960\) 0.500000 0.866025i 0.0161374 0.0279508i
\(961\) −13.6754 −0.441143
\(962\) −25.3114 0.584952i −0.816072 0.0188596i
\(963\) 14.0000 0.451144
\(964\) 5.32456 9.22240i 0.171492 0.297034i
\(965\) 0.256584 + 0.444416i 0.00825972 + 0.0143062i
\(966\) −8.16228 14.1375i −0.262617 0.454866i
\(967\) −2.32456 4.02625i −0.0747527 0.129475i 0.826226 0.563339i \(-0.190483\pi\)
−0.900979 + 0.433863i \(0.857150\pi\)
\(968\) 9.64911 0.310134
\(969\) 4.83772 + 8.37918i 0.155410 + 0.269178i
\(970\) 12.3246 0.395718
\(971\) 1.93203 3.34637i 0.0620017 0.107390i −0.833358 0.552733i \(-0.813585\pi\)
0.895360 + 0.445343i \(0.146918\pi\)
\(972\) −16.0000 −0.513200
\(973\) −79.9473 −2.56299
\(974\) −11.6491 + 20.1769i −0.373262 + 0.646508i
\(975\) −2.08114 3.60464i −0.0666498 0.115441i
\(976\) −8.32456 −0.266463
\(977\) 23.9737 41.5236i 0.766986 1.32846i −0.172205 0.985061i \(-0.555089\pi\)
0.939190 0.343397i \(-0.111578\pi\)
\(978\) −2.82456 + 4.89227i −0.0903193 + 0.156438i
\(979\) −9.67544 + 16.7584i −0.309229 + 0.535600i
\(980\) −9.82456 17.0166i −0.313834 0.543576i
\(981\) 3.67544 + 6.36606i 0.117348 + 0.203253i
\(982\) 6.25658 10.8367i 0.199656 0.345814i
\(983\) −6.48683 + 11.2355i −0.206898 + 0.358358i −0.950736 0.310002i \(-0.899670\pi\)
0.743838 + 0.668360i \(0.233003\pi\)
\(984\) −2.66228 + 4.61120i −0.0848703 + 0.147000i
\(985\) 13.8377 0.440906
\(986\) 4.83772 + 8.37918i 0.154064 + 0.266847i
\(987\) 13.3246 23.0788i 0.424125 0.734607i
\(988\) −34.6491 −1.10234
\(989\) 23.1623 0.736518
\(990\) 1.16228 2.01312i 0.0369396 0.0639813i
\(991\) −10.1623 −0.322815 −0.161408 0.986888i \(-0.551603\pi\)
−0.161408 + 0.986888i \(0.551603\pi\)
\(992\) 2.08114 + 3.60464i 0.0660762 + 0.114447i
\(993\) −14.5132 −0.460561
\(994\) 16.3246 + 28.2750i 0.517783 + 0.896827i
\(995\) 2.91886 + 5.05562i 0.0925341 + 0.160274i
\(996\) −2.00000 3.46410i −0.0633724 0.109764i
\(997\) 21.7302 37.6379i 0.688204 1.19200i −0.284214 0.958761i \(-0.591733\pi\)
0.972418 0.233243i \(-0.0749339\pi\)
\(998\) 11.3509 0.359306
\(999\) −30.4057 0.702683i −0.961994 0.0222319i
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 370.2.e.e.121.1 4
37.26 even 3 inner 370.2.e.e.211.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
370.2.e.e.121.1 4 1.1 even 1 trivial
370.2.e.e.211.1 yes 4 37.26 even 3 inner