Properties

Label 756.2.ci.a.95.7
Level $756$
Weight $2$
Character 756.95
Analytic conductor $6.037$
Analytic rank $0$
Dimension $840$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [756,2,Mod(95,756)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(756, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 17, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("756.95");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.ci (of order \(18\), degree \(6\), 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: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(840\)
Relative dimension: \(140\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 95.7
Character \(\chi\) \(=\) 756.95
Dual form 756.2.ci.a.191.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.39717 + 0.218922i) q^{2} +(-0.617768 - 1.61814i) q^{3} +(1.90415 - 0.611740i) q^{4} +(3.83680 + 0.676532i) q^{5} +(1.21737 + 2.12556i) q^{6} +(1.64737 - 2.07031i) q^{7} +(-2.52649 + 1.27156i) q^{8} +(-2.23673 + 1.99926i) q^{9} +O(q^{10})\) \(q+(-1.39717 + 0.218922i) q^{2} +(-0.617768 - 1.61814i) q^{3} +(1.90415 - 0.611740i) q^{4} +(3.83680 + 0.676532i) q^{5} +(1.21737 + 2.12556i) q^{6} +(1.64737 - 2.07031i) q^{7} +(-2.52649 + 1.27156i) q^{8} +(-2.23673 + 1.99926i) q^{9} +(-5.50876 - 0.105268i) q^{10} +(-0.722722 - 4.09876i) q^{11} +(-2.16620 - 2.70325i) q^{12} +(0.710264 - 4.02811i) q^{13} +(-1.84841 + 3.25321i) q^{14} +(-1.27553 - 6.62641i) q^{15} +(3.25155 - 2.32969i) q^{16} +(-2.41074 + 1.39184i) q^{17} +(2.68740 - 3.28297i) q^{18} +(-4.22205 - 2.43760i) q^{19} +(7.71970 - 1.05891i) q^{20} +(-4.36773 - 1.38669i) q^{21} +(1.90707 + 5.56843i) q^{22} +(1.82410 + 1.53060i) q^{23} +(3.61834 + 3.30267i) q^{24} +(9.56490 + 3.48134i) q^{25} +(-0.110517 + 5.78343i) q^{26} +(4.61686 + 2.38425i) q^{27} +(1.87033 - 4.94993i) q^{28} +(-0.655746 + 0.115626i) q^{29} +(3.23280 + 8.97895i) q^{30} +(-1.04705 - 0.184623i) q^{31} +(-4.03293 + 3.96679i) q^{32} +(-6.18587 + 3.70154i) q^{33} +(3.06350 - 2.47240i) q^{34} +(7.72125 - 6.82888i) q^{35} +(-3.03602 + 5.17519i) q^{36} -6.60816 q^{37} +(6.43256 + 2.48144i) q^{38} +(-6.95681 + 1.33913i) q^{39} +(-10.5539 + 3.16948i) q^{40} +(7.70796 + 1.35912i) q^{41} +(6.40602 + 0.981246i) q^{42} +(1.21910 + 1.45287i) q^{43} +(-3.88354 - 7.36252i) q^{44} +(-9.93444 + 6.15757i) q^{45} +(-2.88365 - 1.73917i) q^{46} +(0.690809 + 3.91778i) q^{47} +(-5.77845 - 3.82224i) q^{48} +(-1.57237 - 6.82112i) q^{49} +(-14.1259 - 2.77004i) q^{50} +(3.74146 + 3.04107i) q^{51} +(-1.11171 - 8.10461i) q^{52} +(7.76861 + 4.48521i) q^{53} +(-6.97248 - 2.32046i) q^{54} -16.2151i q^{55} +(-1.52952 + 7.32534i) q^{56} +(-1.33613 + 8.33773i) q^{57} +(0.890872 - 0.305105i) q^{58} +(-4.03175 + 1.46744i) q^{59} +(-6.48244 - 11.8374i) q^{60} +(-2.47129 - 14.0154i) q^{61} +(1.50332 + 0.0287271i) q^{62} +(0.454390 + 7.92424i) q^{63} +(4.76626 - 6.42517i) q^{64} +(5.45029 - 14.9745i) q^{65} +(7.83234 - 6.52589i) q^{66} +(-0.0840601 + 0.100179i) q^{67} +(-3.73895 + 4.12501i) q^{68} +(1.34985 - 3.89719i) q^{69} +(-9.29288 + 11.2314i) q^{70} +(-6.37555 + 11.0428i) q^{71} +(3.10887 - 7.89525i) q^{72} +13.3719 q^{73} +(9.23270 - 1.44667i) q^{74} +(-0.275608 - 17.6280i) q^{75} +(-9.53059 - 2.05876i) q^{76} +(-9.67629 - 5.25590i) q^{77} +(9.42665 - 3.39399i) q^{78} +(-3.46913 - 4.13435i) q^{79} +(14.0517 - 6.73877i) q^{80} +(1.00589 - 8.94361i) q^{81} +(-11.0668 - 0.211478i) q^{82} +(-1.83841 - 10.4261i) q^{83} +(-9.16510 + 0.0314543i) q^{84} +(-10.1912 + 3.70928i) q^{85} +(-2.02135 - 1.76301i) q^{86} +(0.592196 + 0.989655i) q^{87} +(7.03777 + 9.43647i) q^{88} +(3.69290 + 2.13210i) q^{89} +(12.5320 - 10.7780i) q^{90} +(-7.16937 - 8.10624i) q^{91} +(4.40968 + 1.79861i) q^{92} +(0.348087 + 1.80832i) q^{93} +(-1.82286 - 5.32255i) q^{94} +(-14.5501 - 12.2090i) q^{95} +(8.91023 + 4.07528i) q^{96} +(-3.87711 + 3.25328i) q^{97} +(3.69015 + 9.18601i) q^{98} +(9.81103 + 7.72289i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 3 q^{10} - 3 q^{12} - 24 q^{13} + 24 q^{14} - 3 q^{16} - 18 q^{17} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} + 48 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} - 21 q^{30} - 63 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} - 12 q^{37} + 45 q^{38} - 33 q^{40} - 24 q^{41} - 21 q^{42} + 6 q^{45} - 6 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} - 63 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} - 54 q^{65} - 3 q^{66} - 12 q^{68} - 48 q^{69} - 21 q^{70} - 9 q^{72} - 12 q^{73} + 15 q^{74} + 12 q^{77} + 6 q^{78} - 54 q^{81} - 6 q^{82} - 39 q^{84} + 6 q^{85} - 9 q^{86} - 27 q^{88} - 18 q^{89} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} + 213 q^{96} - 24 q^{97} + 162 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39717 + 0.218922i −0.987946 + 0.154801i
\(3\) −0.617768 1.61814i −0.356668 0.934231i
\(4\) 1.90415 0.611740i 0.952073 0.305870i
\(5\) 3.83680 + 0.676532i 1.71587 + 0.302554i 0.943193 0.332245i \(-0.107806\pi\)
0.772677 + 0.634799i \(0.218917\pi\)
\(6\) 1.21737 + 2.12556i 0.496989 + 0.867757i
\(7\) 1.64737 2.07031i 0.622646 0.782504i
\(8\) −2.52649 + 1.27156i −0.893248 + 0.449565i
\(9\) −2.23673 + 1.99926i −0.745575 + 0.666421i
\(10\) −5.50876 0.105268i −1.74202 0.0332886i
\(11\) −0.722722 4.09876i −0.217909 1.23582i −0.875787 0.482698i \(-0.839657\pi\)
0.657878 0.753124i \(-0.271454\pi\)
\(12\) −2.16620 2.70325i −0.625328 0.780362i
\(13\) 0.710264 4.02811i 0.196992 1.11720i −0.712562 0.701610i \(-0.752465\pi\)
0.909553 0.415587i \(-0.136424\pi\)
\(14\) −1.84841 + 3.25321i −0.494008 + 0.869457i
\(15\) −1.27553 6.62641i −0.329341 1.71093i
\(16\) 3.25155 2.32969i 0.812887 0.582421i
\(17\) −2.41074 + 1.39184i −0.584690 + 0.337571i −0.762995 0.646404i \(-0.776272\pi\)
0.178305 + 0.983975i \(0.442939\pi\)
\(18\) 2.68740 3.28297i 0.633425 0.773804i
\(19\) −4.22205 2.43760i −0.968606 0.559225i −0.0697947 0.997561i \(-0.522234\pi\)
−0.898811 + 0.438337i \(0.855568\pi\)
\(20\) 7.71970 1.05891i 1.72618 0.236780i
\(21\) −4.36773 1.38669i −0.953117 0.302601i
\(22\) 1.90707 + 5.56843i 0.406589 + 1.18719i
\(23\) 1.82410 + 1.53060i 0.380350 + 0.319152i 0.812840 0.582487i \(-0.197920\pi\)
−0.432490 + 0.901639i \(0.642365\pi\)
\(24\) 3.61834 + 3.30267i 0.738591 + 0.674154i
\(25\) 9.56490 + 3.48134i 1.91298 + 0.696268i
\(26\) −0.110517 + 5.78343i −0.0216741 + 1.13422i
\(27\) 4.61686 + 2.38425i 0.888515 + 0.458848i
\(28\) 1.87033 4.94993i 0.353460 0.935450i
\(29\) −0.655746 + 0.115626i −0.121769 + 0.0214711i −0.234200 0.972188i \(-0.575247\pi\)
0.112432 + 0.993659i \(0.464136\pi\)
\(30\) 3.23280 + 8.97895i 0.590225 + 1.63932i
\(31\) −1.04705 0.184623i −0.188055 0.0331592i 0.0788273 0.996888i \(-0.474882\pi\)
−0.266882 + 0.963729i \(0.585994\pi\)
\(32\) −4.03293 + 3.96679i −0.712929 + 0.701236i
\(33\) −6.18587 + 3.70154i −1.07682 + 0.644356i
\(34\) 3.06350 2.47240i 0.525386 0.424012i
\(35\) 7.72125 6.82888i 1.30513 1.15429i
\(36\) −3.03602 + 5.17519i −0.506004 + 0.862531i
\(37\) −6.60816 −1.08638 −0.543188 0.839611i \(-0.682783\pi\)
−0.543188 + 0.839611i \(0.682783\pi\)
\(38\) 6.43256 + 2.48144i 1.04350 + 0.402542i
\(39\) −6.95681 + 1.33913i −1.11398 + 0.214433i
\(40\) −10.5539 + 3.16948i −1.66871 + 0.501139i
\(41\) 7.70796 + 1.35912i 1.20378 + 0.212259i 0.739332 0.673341i \(-0.235141\pi\)
0.464449 + 0.885600i \(0.346252\pi\)
\(42\) 6.40602 + 0.981246i 0.988471 + 0.151410i
\(43\) 1.21910 + 1.45287i 0.185911 + 0.221560i 0.850947 0.525251i \(-0.176028\pi\)
−0.665037 + 0.746811i \(0.731584\pi\)
\(44\) −3.88354 7.36252i −0.585466 1.10994i
\(45\) −9.93444 + 6.15757i −1.48094 + 0.917916i
\(46\) −2.88365 1.73917i −0.425171 0.256426i
\(47\) 0.690809 + 3.91778i 0.100765 + 0.571466i 0.992828 + 0.119555i \(0.0381467\pi\)
−0.892063 + 0.451912i \(0.850742\pi\)
\(48\) −5.77845 3.82224i −0.834047 0.551693i
\(49\) −1.57237 6.82112i −0.224624 0.974445i
\(50\) −14.1259 2.77004i −1.99770 0.391743i
\(51\) 3.74146 + 3.04107i 0.523910 + 0.425835i
\(52\) −1.11171 8.10461i −0.154166 1.12391i
\(53\) 7.76861 + 4.48521i 1.06710 + 0.616091i 0.927388 0.374102i \(-0.122049\pi\)
0.139712 + 0.990192i \(0.455382\pi\)
\(54\) −6.97248 2.32046i −0.948834 0.315774i
\(55\) 16.2151i 2.18644i
\(56\) −1.52952 + 7.32534i −0.204391 + 0.978889i
\(57\) −1.33613 + 8.33773i −0.176974 + 1.10436i
\(58\) 0.890872 0.305105i 0.116977 0.0400623i
\(59\) −4.03175 + 1.46744i −0.524889 + 0.191044i −0.590855 0.806778i \(-0.701209\pi\)
0.0659659 + 0.997822i \(0.478987\pi\)
\(60\) −6.48244 11.8374i −0.836879 1.52820i
\(61\) −2.47129 14.0154i −0.316417 1.79449i −0.564164 0.825663i \(-0.690801\pi\)
0.247747 0.968825i \(-0.420310\pi\)
\(62\) 1.50332 + 0.0287271i 0.190921 + 0.00364835i
\(63\) 0.454390 + 7.92424i 0.0572478 + 0.998360i
\(64\) 4.76626 6.42517i 0.595783 0.803146i
\(65\) 5.45029 14.9745i 0.676025 1.85736i
\(66\) 7.83234 6.52589i 0.964095 0.803282i
\(67\) −0.0840601 + 0.100179i −0.0102696 + 0.0122388i −0.771155 0.636648i \(-0.780321\pi\)
0.760885 + 0.648887i \(0.224765\pi\)
\(68\) −3.73895 + 4.12501i −0.453415 + 0.500231i
\(69\) 1.34985 3.89719i 0.162503 0.469167i
\(70\) −9.29288 + 11.2314i −1.11071 + 1.34241i
\(71\) −6.37555 + 11.0428i −0.756639 + 1.31054i 0.187917 + 0.982185i \(0.439827\pi\)
−0.944555 + 0.328352i \(0.893507\pi\)
\(72\) 3.10887 7.89525i 0.366384 0.930464i
\(73\) 13.3719 1.56507 0.782534 0.622608i \(-0.213927\pi\)
0.782534 + 0.622608i \(0.213927\pi\)
\(74\) 9.23270 1.44667i 1.07328 0.168172i
\(75\) −0.275608 17.6280i −0.0318245 2.03550i
\(76\) −9.53059 2.05876i −1.09323 0.236155i
\(77\) −9.67629 5.25590i −1.10272 0.598965i
\(78\) 9.42665 3.39399i 1.06736 0.384293i
\(79\) −3.46913 4.13435i −0.390308 0.465151i 0.534731 0.845022i \(-0.320413\pi\)
−0.925039 + 0.379871i \(0.875968\pi\)
\(80\) 14.0517 6.73877i 1.57102 0.753417i
\(81\) 1.00589 8.94361i 0.111765 0.993735i
\(82\) −11.0668 0.211478i −1.22213 0.0233539i
\(83\) −1.83841 10.4261i −0.201791 1.14441i −0.902410 0.430879i \(-0.858204\pi\)
0.700619 0.713536i \(-0.252907\pi\)
\(84\) −9.16510 + 0.0314543i −0.999994 + 0.00343194i
\(85\) −10.1912 + 3.70928i −1.10539 + 0.402328i
\(86\) −2.02135 1.76301i −0.217968 0.190110i
\(87\) 0.592196 + 0.989655i 0.0634901 + 0.106102i
\(88\) 7.03777 + 9.43647i 0.750229 + 1.00593i
\(89\) 3.69290 + 2.13210i 0.391447 + 0.226002i 0.682787 0.730618i \(-0.260768\pi\)
−0.291340 + 0.956620i \(0.594101\pi\)
\(90\) 12.5320 10.7780i 1.32099 1.13610i
\(91\) −7.16937 8.10624i −0.751554 0.849765i
\(92\) 4.40968 + 1.79861i 0.459740 + 0.187518i
\(93\) 0.348087 + 1.80832i 0.0360950 + 0.187514i
\(94\) −1.82286 5.32255i −0.188014 0.548979i
\(95\) −14.5501 12.2090i −1.49281 1.25261i
\(96\) 8.91023 + 4.07528i 0.909396 + 0.415931i
\(97\) −3.87711 + 3.25328i −0.393661 + 0.330321i −0.818037 0.575165i \(-0.804938\pi\)
0.424376 + 0.905486i \(0.360493\pi\)
\(98\) 3.69015 + 9.18601i 0.372762 + 0.927927i
\(99\) 9.81103 + 7.72289i 0.986046 + 0.776179i
\(100\) 20.3426 + 0.777746i 2.03426 + 0.0777746i
\(101\) −6.16138 7.34284i −0.613080 0.730640i 0.366784 0.930306i \(-0.380459\pi\)
−0.979864 + 0.199666i \(0.936014\pi\)
\(102\) −5.89320 3.42979i −0.583514 0.339600i
\(103\) 6.72004 + 1.18492i 0.662146 + 0.116754i 0.494614 0.869113i \(-0.335309\pi\)
0.167531 + 0.985867i \(0.446420\pi\)
\(104\) 3.32752 + 11.0801i 0.326290 + 1.08649i
\(105\) −15.8200 8.27537i −1.54387 0.807593i
\(106\) −11.8359 4.56586i −1.14961 0.443476i
\(107\) 8.97074 + 15.5378i 0.867234 + 1.50209i 0.864812 + 0.502096i \(0.167438\pi\)
0.00242209 + 0.999997i \(0.499229\pi\)
\(108\) 10.2497 + 1.71564i 0.986279 + 0.165087i
\(109\) −3.34863 + 5.80000i −0.320741 + 0.555540i −0.980641 0.195814i \(-0.937265\pi\)
0.659900 + 0.751353i \(0.270599\pi\)
\(110\) 3.54983 + 22.6551i 0.338463 + 2.16008i
\(111\) 4.08231 + 10.6929i 0.387476 + 1.01493i
\(112\) 0.533318 10.5696i 0.0503938 0.998729i
\(113\) −0.394125 + 0.469700i −0.0370761 + 0.0441856i −0.784264 0.620427i \(-0.786959\pi\)
0.747188 + 0.664613i \(0.231404\pi\)
\(114\) 0.0414785 11.9417i 0.00388481 1.11844i
\(115\) 5.96320 + 7.10666i 0.556071 + 0.662700i
\(116\) −1.17790 + 0.621314i −0.109366 + 0.0576876i
\(117\) 6.46459 + 10.4298i 0.597651 + 0.964234i
\(118\) 5.31177 2.93289i 0.488988 0.269994i
\(119\) −1.08983 + 7.28385i −0.0999043 + 0.667709i
\(120\) 11.6485 + 15.1196i 1.06336 + 1.38022i
\(121\) −5.94087 + 2.16230i −0.540079 + 0.196573i
\(122\) 6.52108 + 19.0408i 0.590391 + 1.72387i
\(123\) −2.56249 13.3122i −0.231052 1.20032i
\(124\) −2.10667 + 0.288972i −0.189185 + 0.0259505i
\(125\) 17.4732 + 10.0882i 1.56285 + 0.902315i
\(126\) −2.36965 10.9720i −0.211105 0.977463i
\(127\) 1.66530 0.961459i 0.147771 0.0853157i −0.424291 0.905526i \(-0.639477\pi\)
0.572063 + 0.820210i \(0.306143\pi\)
\(128\) −5.25265 + 10.0205i −0.464273 + 0.885692i
\(129\) 1.59781 2.87020i 0.140680 0.252707i
\(130\) −4.33671 + 22.1151i −0.380354 + 1.93962i
\(131\) 0.613263 + 0.514589i 0.0535810 + 0.0449598i 0.669185 0.743096i \(-0.266643\pi\)
−0.615604 + 0.788056i \(0.711088\pi\)
\(132\) −9.51443 + 10.8324i −0.828124 + 0.942842i
\(133\) −12.0019 + 4.72533i −1.04069 + 0.409739i
\(134\) 0.0955146 0.158369i 0.00825120 0.0136810i
\(135\) 16.1010 + 12.2713i 1.38575 + 1.05615i
\(136\) 4.32089 6.58187i 0.370513 0.564391i
\(137\) 3.82045 10.4966i 0.326403 0.896785i −0.662611 0.748964i \(-0.730552\pi\)
0.989014 0.147821i \(-0.0472260\pi\)
\(138\) −1.03278 + 5.74053i −0.0879163 + 0.488667i
\(139\) 3.17828 + 8.73224i 0.269578 + 0.740659i 0.998431 + 0.0559895i \(0.0178313\pi\)
−0.728853 + 0.684670i \(0.759946\pi\)
\(140\) 10.5249 17.7266i 0.889516 1.49817i
\(141\) 5.91273 3.53810i 0.497942 0.297962i
\(142\) 6.49020 16.8243i 0.544646 1.41187i
\(143\) −17.0236 −1.42358
\(144\) −2.61517 + 11.7116i −0.217930 + 0.975964i
\(145\) −2.59419 −0.215436
\(146\) −18.6828 + 2.92741i −1.54620 + 0.242274i
\(147\) −10.0661 + 6.75817i −0.830241 + 0.557405i
\(148\) −12.5829 + 4.04248i −1.03431 + 0.332290i
\(149\) −5.94768 16.3411i −0.487253 1.33872i −0.903158 0.429308i \(-0.858757\pi\)
0.415905 0.909408i \(-0.363465\pi\)
\(150\) 4.24421 + 24.5689i 0.346539 + 2.00604i
\(151\) 14.8082 2.61109i 1.20508 0.212488i 0.465185 0.885213i \(-0.345988\pi\)
0.739892 + 0.672726i \(0.234877\pi\)
\(152\) 13.7665 + 0.789970i 1.11661 + 0.0640750i
\(153\) 2.60950 7.93287i 0.210966 0.641334i
\(154\) 14.6700 + 5.22501i 1.18214 + 0.421043i
\(155\) −3.89241 1.41672i −0.312646 0.113794i
\(156\) −12.4276 + 6.80566i −0.995003 + 0.544889i
\(157\) −17.3721 + 6.32292i −1.38644 + 0.504624i −0.924125 0.382090i \(-0.875204\pi\)
−0.462318 + 0.886714i \(0.652982\pi\)
\(158\) 5.75205 + 5.01691i 0.457609 + 0.399124i
\(159\) 2.45848 15.3415i 0.194970 1.21666i
\(160\) −18.1572 + 12.4914i −1.43546 + 0.987531i
\(161\) 6.17377 1.25499i 0.486561 0.0989070i
\(162\) 0.552561 + 12.7159i 0.0434133 + 0.999057i
\(163\) 2.30587 1.33129i 0.180609 0.104275i −0.406970 0.913442i \(-0.633414\pi\)
0.587579 + 0.809167i \(0.300081\pi\)
\(164\) 15.5085 2.12730i 1.21101 0.166114i
\(165\) −26.2382 + 10.0171i −2.04264 + 0.779834i
\(166\) 4.85106 + 14.1645i 0.376515 + 1.09938i
\(167\) 13.9345 + 11.6924i 1.07828 + 0.904787i 0.995777 0.0918034i \(-0.0292631\pi\)
0.0825062 + 0.996591i \(0.473708\pi\)
\(168\) 12.7983 2.05039i 0.987409 0.158191i
\(169\) −3.50519 1.27578i −0.269630 0.0981372i
\(170\) 13.4267 7.41354i 1.02978 0.568593i
\(171\) 14.3170 2.98875i 1.09485 0.228555i
\(172\) 3.21012 + 2.02070i 0.244769 + 0.154077i
\(173\) −0.843726 + 2.31812i −0.0641473 + 0.176243i −0.967625 0.252391i \(-0.918783\pi\)
0.903478 + 0.428635i \(0.141005\pi\)
\(174\) −1.04405 1.25307i −0.0791495 0.0949949i
\(175\) 22.9643 14.0673i 1.73594 1.06339i
\(176\) −11.8988 11.6436i −0.896904 0.877669i
\(177\) 4.86519 + 5.61738i 0.365690 + 0.422228i
\(178\) −5.62636 2.17044i −0.421714 0.162681i
\(179\) −12.3184 21.3361i −0.920721 1.59474i −0.798302 0.602257i \(-0.794268\pi\)
−0.122419 0.992479i \(-0.539065\pi\)
\(180\) −15.1498 + 17.8022i −1.12920 + 1.32690i
\(181\) 10.5131 + 18.2093i 0.781434 + 1.35348i 0.931106 + 0.364748i \(0.118845\pi\)
−0.149672 + 0.988736i \(0.547822\pi\)
\(182\) 11.7914 + 9.75623i 0.874039 + 0.723180i
\(183\) −21.1521 + 12.6571i −1.56361 + 0.935643i
\(184\) −6.55480 1.54758i −0.483227 0.114089i
\(185\) −25.3542 4.47063i −1.86408 0.328687i
\(186\) −0.882216 2.45032i −0.0646872 0.179666i
\(187\) 7.44711 + 8.87512i 0.544587 + 0.649013i
\(188\) 3.71206 + 7.03742i 0.270730 + 0.513257i
\(189\) 12.5418 5.63060i 0.912280 0.409566i
\(190\) 23.0017 + 13.8726i 1.66872 + 1.00643i
\(191\) 2.40806 2.02060i 0.174241 0.146205i −0.551497 0.834177i \(-0.685943\pi\)
0.725738 + 0.687972i \(0.241499\pi\)
\(192\) −13.3412 3.74320i −0.962820 0.270142i
\(193\) −1.77209 + 10.0500i −0.127558 + 0.723415i 0.852198 + 0.523219i \(0.175269\pi\)
−0.979756 + 0.200196i \(0.935842\pi\)
\(194\) 4.70476 5.39416i 0.337782 0.387278i
\(195\) −27.5979 + 0.431485i −1.97632 + 0.0308993i
\(196\) −7.16677 12.0265i −0.511912 0.859038i
\(197\) 7.58334 4.37824i 0.540291 0.311937i −0.204906 0.978782i \(-0.565689\pi\)
0.745197 + 0.666845i \(0.232356\pi\)
\(198\) −15.3983 8.64231i −1.09431 0.614182i
\(199\) 17.3529 10.0187i 1.23011 0.710205i 0.263059 0.964780i \(-0.415269\pi\)
0.967053 + 0.254574i \(0.0819354\pi\)
\(200\) −28.5923 + 3.36681i −2.02178 + 0.238069i
\(201\) 0.214033 + 0.0741333i 0.0150967 + 0.00522896i
\(202\) 10.2160 + 8.91031i 0.718794 + 0.626928i
\(203\) −0.840872 + 1.54807i −0.0590177 + 0.108654i
\(204\) 8.98464 + 3.50184i 0.629050 + 0.245178i
\(205\) 28.6544 + 10.4294i 2.00131 + 0.728418i
\(206\) −9.64842 0.184373i −0.672237 0.0128459i
\(207\) −7.14007 + 0.223321i −0.496270 + 0.0155219i
\(208\) −7.07477 14.7523i −0.490547 1.02289i
\(209\) −6.93978 + 19.0669i −0.480035 + 1.31888i
\(210\) 23.9148 + 8.09873i 1.65028 + 0.558865i
\(211\) 12.9947 15.4865i 0.894593 1.06613i −0.102852 0.994697i \(-0.532797\pi\)
0.997445 0.0714379i \(-0.0227588\pi\)
\(212\) 17.5363 + 3.78812i 1.20440 + 0.260169i
\(213\) 21.8073 + 3.49463i 1.49421 + 0.239448i
\(214\) −15.9352 19.7450i −1.08931 1.34974i
\(215\) 3.69453 + 6.39912i 0.251965 + 0.436416i
\(216\) −14.6961 0.153142i −0.999946 0.0104200i
\(217\) −2.10710 + 1.86357i −0.143039 + 0.126507i
\(218\) 3.40885 8.83666i 0.230876 0.598494i
\(219\) −8.26076 21.6376i −0.558210 1.46214i
\(220\) −9.91941 30.8759i −0.668766 2.08165i
\(221\) 3.89422 + 10.6993i 0.261954 + 0.719712i
\(222\) −8.04457 14.0461i −0.539916 0.942709i
\(223\) −7.75985 + 21.3200i −0.519638 + 1.42769i 0.351283 + 0.936269i \(0.385746\pi\)
−0.870921 + 0.491424i \(0.836477\pi\)
\(224\) 1.56877 + 14.8842i 0.104818 + 0.994491i
\(225\) −28.3542 + 11.3360i −1.89028 + 0.755730i
\(226\) 0.447830 0.742531i 0.0297892 0.0493924i
\(227\) 2.52386 + 14.3135i 0.167515 + 0.950023i 0.946434 + 0.322898i \(0.104657\pi\)
−0.778919 + 0.627124i \(0.784232\pi\)
\(228\) 2.55635 + 16.6936i 0.169298 + 1.10556i
\(229\) 20.2624 7.37491i 1.33898 0.487348i 0.429487 0.903073i \(-0.358694\pi\)
0.909490 + 0.415725i \(0.136472\pi\)
\(230\) −9.88738 8.62372i −0.651955 0.568631i
\(231\) −2.52706 + 18.9045i −0.166268 + 1.24382i
\(232\) 1.50971 1.12595i 0.0991171 0.0739221i
\(233\) 1.52840i 0.100129i 0.998746 + 0.0500643i \(0.0159426\pi\)
−0.998746 + 0.0500643i \(0.984057\pi\)
\(234\) −11.3154 13.1569i −0.739711 0.860094i
\(235\) 15.4991i 1.01105i
\(236\) −6.77935 + 5.26060i −0.441298 + 0.342436i
\(237\) −4.54682 + 8.16760i −0.295348 + 0.530542i
\(238\) −0.0719226 10.4153i −0.00466205 0.675126i
\(239\) −23.2418 + 8.45931i −1.50338 + 0.547187i −0.956934 0.290305i \(-0.906243\pi\)
−0.546450 + 0.837492i \(0.684021\pi\)
\(240\) −19.5849 18.5745i −1.26420 1.19898i
\(241\) 4.85001 + 1.76526i 0.312417 + 0.113710i 0.493470 0.869763i \(-0.335728\pi\)
−0.181053 + 0.983473i \(0.557951\pi\)
\(242\) 7.82701 4.32168i 0.503139 0.277808i
\(243\) −15.0934 + 3.89741i −0.968241 + 0.250019i
\(244\) −13.2795 25.1756i −0.850132 1.61170i
\(245\) −1.41817 27.2350i −0.0906033 1.73998i
\(246\) 6.49454 + 18.0383i 0.414077 + 1.15008i
\(247\) −12.8177 + 15.2756i −0.815571 + 0.971960i
\(248\) 2.88011 0.864938i 0.182887 0.0549236i
\(249\) −15.7352 + 9.41571i −0.997175 + 0.596696i
\(250\) −26.6216 10.2696i −1.68369 0.649506i
\(251\) 6.23110 + 10.7926i 0.393304 + 0.681222i 0.992883 0.119093i \(-0.0379988\pi\)
−0.599579 + 0.800315i \(0.704665\pi\)
\(252\) 5.71280 + 14.8109i 0.359873 + 0.933001i
\(253\) 4.95524 8.58273i 0.311533 0.539591i
\(254\) −2.11621 + 1.70789i −0.132783 + 0.107162i
\(255\) 12.2979 + 14.1992i 0.770123 + 0.889188i
\(256\) 5.14513 15.1502i 0.321571 0.946886i
\(257\) 1.23755 + 3.40015i 0.0771965 + 0.212096i 0.972288 0.233787i \(-0.0751120\pi\)
−0.895091 + 0.445883i \(0.852890\pi\)
\(258\) −1.60406 + 4.35995i −0.0998646 + 0.271438i
\(259\) −10.8861 + 13.6809i −0.676427 + 0.850093i
\(260\) 1.21762 31.8479i 0.0755135 1.97512i
\(261\) 1.23556 1.56963i 0.0764791 0.0971577i
\(262\) −0.969485 0.584709i −0.0598950 0.0361235i
\(263\) −2.07446 + 1.74068i −0.127917 + 0.107335i −0.704502 0.709702i \(-0.748829\pi\)
0.576585 + 0.817037i \(0.304385\pi\)
\(264\) 10.9218 17.2176i 0.672189 1.05967i
\(265\) 26.7722 + 22.4646i 1.64460 + 1.37999i
\(266\) 15.7341 9.22955i 0.964721 0.565900i
\(267\) 1.16867 7.29276i 0.0715214 0.446310i
\(268\) −0.0987793 + 0.242178i −0.00603390 + 0.0147934i
\(269\) 23.7867 + 13.7333i 1.45030 + 0.837332i 0.998498 0.0547854i \(-0.0174475\pi\)
0.451804 + 0.892117i \(0.350781\pi\)
\(270\) −25.1822 13.6202i −1.53254 0.828901i
\(271\) 12.1508 7.01526i 0.738108 0.426147i −0.0832732 0.996527i \(-0.526537\pi\)
0.821381 + 0.570380i \(0.193204\pi\)
\(272\) −4.59608 + 10.1419i −0.278678 + 0.614943i
\(273\) −8.68799 + 16.6088i −0.525821 + 1.00521i
\(274\) −3.03987 + 15.5019i −0.183645 + 0.936502i
\(275\) 7.35640 41.7202i 0.443608 2.51582i
\(276\) 0.186241 8.24658i 0.0112104 0.496386i
\(277\) 4.80166 4.02907i 0.288504 0.242084i −0.487036 0.873382i \(-0.661922\pi\)
0.775540 + 0.631298i \(0.217478\pi\)
\(278\) −6.35226 11.5046i −0.380983 0.690000i
\(279\) 2.71107 1.68037i 0.162307 0.100601i
\(280\) −10.8243 + 27.0711i −0.646875 + 1.61781i
\(281\) −12.9329 15.4128i −0.771512 0.919452i 0.227005 0.973894i \(-0.427107\pi\)
−0.998517 + 0.0544412i \(0.982662\pi\)
\(282\) −7.48650 + 6.23774i −0.445815 + 0.371452i
\(283\) −1.41460 + 1.68585i −0.0840891 + 0.100214i −0.806449 0.591304i \(-0.798613\pi\)
0.722359 + 0.691518i \(0.243058\pi\)
\(284\) −5.38467 + 24.9273i −0.319522 + 1.47916i
\(285\) −10.7672 + 31.0863i −0.637793 + 1.84139i
\(286\) 23.7848 3.72683i 1.40642 0.220372i
\(287\) 15.5116 13.7189i 0.915623 0.809801i
\(288\) 1.08990 16.9355i 0.0642231 0.997936i
\(289\) −4.62556 + 8.01170i −0.272092 + 0.471277i
\(290\) 3.62452 0.567925i 0.212839 0.0333497i
\(291\) 7.65941 + 4.26392i 0.449003 + 0.249956i
\(292\) 25.4621 8.18016i 1.49006 0.478707i
\(293\) −4.32159 11.8735i −0.252470 0.693655i −0.999581 0.0289558i \(-0.990782\pi\)
0.747111 0.664699i \(-0.231440\pi\)
\(294\) 12.5846 11.6460i 0.733946 0.679208i
\(295\) −16.4618 + 2.90266i −0.958442 + 0.168999i
\(296\) 16.6954 8.40268i 0.970402 0.488396i
\(297\) 6.43574 20.6465i 0.373440 1.19803i
\(298\) 11.8873 + 21.5292i 0.688614 + 1.24715i
\(299\) 7.46101 6.26053i 0.431481 0.362056i
\(300\) −11.3085 33.3976i −0.652898 1.92821i
\(301\) 5.01619 0.130511i 0.289128 0.00752256i
\(302\) −20.1179 + 6.88997i −1.15766 + 0.396473i
\(303\) −8.07542 + 14.5061i −0.463921 + 0.833355i
\(304\) −19.4071 + 1.91007i −1.11307 + 0.109550i
\(305\) 55.4462i 3.17484i
\(306\) −1.90923 + 11.6548i −0.109144 + 0.666261i
\(307\) 17.1538 + 9.90376i 0.979020 + 0.565237i 0.901974 0.431790i \(-0.142118\pi\)
0.0770457 + 0.997028i \(0.475451\pi\)
\(308\) −21.6403 4.08863i −1.23307 0.232971i
\(309\) −2.23406 11.6059i −0.127091 0.660239i
\(310\) 5.74849 + 1.12726i 0.326492 + 0.0640242i
\(311\) −16.3182 13.6926i −0.925323 0.776438i 0.0496489 0.998767i \(-0.484190\pi\)
−0.974972 + 0.222329i \(0.928634\pi\)
\(312\) 15.8735 12.2293i 0.898659 0.692348i
\(313\) 22.2201 + 8.08747i 1.25596 + 0.457131i 0.882410 0.470481i \(-0.155920\pi\)
0.373546 + 0.927612i \(0.378142\pi\)
\(314\) 22.8875 12.6373i 1.29161 0.713164i
\(315\) −3.61759 + 30.7111i −0.203828 + 1.73038i
\(316\) −9.13489 5.75020i −0.513877 0.323474i
\(317\) 0.0412626 0.00727572i 0.00231754 0.000408645i −0.172489 0.985011i \(-0.555181\pi\)
0.174807 + 0.984603i \(0.444070\pi\)
\(318\) −0.0763207 + 21.9728i −0.00427985 + 1.23217i
\(319\) 0.947843 + 2.60418i 0.0530690 + 0.145806i
\(320\) 22.6340 21.4276i 1.26528 1.19784i
\(321\) 19.6004 24.1146i 1.09399 1.34595i
\(322\) −8.35104 + 3.10500i −0.465385 + 0.173035i
\(323\) 13.5710 0.755112
\(324\) −3.55581 17.6453i −0.197545 0.980294i
\(325\) 20.8168 36.0558i 1.15471 2.00001i
\(326\) −2.93023 + 2.36484i −0.162290 + 0.130976i
\(327\) 11.4539 + 1.83549i 0.633400 + 0.101503i
\(328\) −21.2023 + 6.36735i −1.17070 + 0.351578i
\(329\) 9.24903 + 5.02382i 0.509915 + 0.276972i
\(330\) 34.4661 19.7397i 1.89730 1.08664i
\(331\) 12.9530 2.28396i 0.711962 0.125538i 0.194074 0.980987i \(-0.437830\pi\)
0.517887 + 0.855449i \(0.326719\pi\)
\(332\) −9.87867 18.7282i −0.542162 1.02784i
\(333\) 14.7806 13.2115i 0.809974 0.723984i
\(334\) −22.0285 13.2857i −1.20535 0.726961i
\(335\) −0.390296 + 0.327497i −0.0213242 + 0.0178931i
\(336\) −17.4324 + 5.66655i −0.951018 + 0.309136i
\(337\) −3.90993 + 22.1743i −0.212988 + 1.20791i 0.671377 + 0.741116i \(0.265703\pi\)
−0.884365 + 0.466797i \(0.845408\pi\)
\(338\) 5.17663 + 1.01512i 0.281571 + 0.0552153i
\(339\) 1.00352 + 0.347582i 0.0545035 + 0.0188781i
\(340\) −17.1363 + 13.2973i −0.929348 + 0.721150i
\(341\) 4.42502i 0.239628i
\(342\) −19.3489 + 7.31008i −1.04627 + 0.395284i
\(343\) −16.7121 7.98159i −0.902369 0.430965i
\(344\) −4.92745 2.12049i −0.265670 0.114329i
\(345\) 7.81567 14.0395i 0.420782 0.755863i
\(346\) 0.671339 3.42351i 0.0360914 0.184049i
\(347\) −2.68325 + 15.2175i −0.144044 + 0.816916i 0.824085 + 0.566466i \(0.191690\pi\)
−0.968130 + 0.250450i \(0.919421\pi\)
\(348\) 1.73304 + 1.52218i 0.0929007 + 0.0815973i
\(349\) 2.21904 + 12.5848i 0.118783 + 0.673649i 0.984808 + 0.173649i \(0.0555557\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(350\) −29.0054 + 24.6817i −1.55040 + 1.31929i
\(351\) 12.8832 16.9038i 0.687654 0.902256i
\(352\) 19.1736 + 13.6631i 1.02196 + 0.728247i
\(353\) −8.66363 + 23.8031i −0.461118 + 1.26691i 0.463527 + 0.886083i \(0.346584\pi\)
−0.924645 + 0.380829i \(0.875639\pi\)
\(354\) −8.02725 6.78332i −0.426644 0.360529i
\(355\) −31.9325 + 38.0557i −1.69480 + 2.01979i
\(356\) 8.33612 + 1.80073i 0.441814 + 0.0954386i
\(357\) 12.4595 2.73624i 0.659427 0.144817i
\(358\) 21.8818 + 27.1133i 1.15649 + 1.43298i
\(359\) −16.4990 + 28.5771i −0.870783 + 1.50824i −0.00959585 + 0.999954i \(0.503054\pi\)
−0.861188 + 0.508287i \(0.830279\pi\)
\(360\) 17.2695 28.1893i 0.910183 1.48570i
\(361\) 2.38383 + 4.12891i 0.125465 + 0.217311i
\(362\) −18.6750 23.1398i −0.981535 1.21620i
\(363\) 7.16897 + 8.27733i 0.376273 + 0.434447i
\(364\) −18.6104 11.0497i −0.975452 0.579160i
\(365\) 51.3055 + 9.04655i 2.68545 + 0.473518i
\(366\) 26.7821 22.3148i 1.39992 1.16641i
\(367\) −14.5034 + 2.55735i −0.757073 + 0.133492i −0.538844 0.842405i \(-0.681139\pi\)
−0.218228 + 0.975898i \(0.570028\pi\)
\(368\) 9.49695 + 0.727244i 0.495063 + 0.0379102i
\(369\) −19.9578 + 12.3703i −1.03896 + 0.643971i
\(370\) 36.4028 + 0.695627i 1.89249 + 0.0361639i
\(371\) 22.0835 8.69465i 1.14652 0.451404i
\(372\) 1.76903 + 3.23036i 0.0917199 + 0.167487i
\(373\) 5.41895 30.7324i 0.280582 1.59126i −0.440068 0.897964i \(-0.645046\pi\)
0.720651 0.693298i \(-0.243843\pi\)
\(374\) −12.3478 10.7697i −0.638490 0.556887i
\(375\) 5.52964 34.5062i 0.285549 1.78189i
\(376\) −6.72701 9.01980i −0.346919 0.465161i
\(377\) 2.72354i 0.140269i
\(378\) −16.2903 + 10.6126i −0.837882 + 0.545851i
\(379\) 5.82132i 0.299021i −0.988760 0.149511i \(-0.952230\pi\)
0.988760 0.149511i \(-0.0477698\pi\)
\(380\) −35.1742 14.3468i −1.80440 0.735975i
\(381\) −2.58454 2.10072i −0.132410 0.107623i
\(382\) −2.92210 + 3.35029i −0.149508 + 0.171416i
\(383\) 4.16512 23.6216i 0.212828 1.20701i −0.671809 0.740725i \(-0.734482\pi\)
0.884636 0.466281i \(-0.154407\pi\)
\(384\) 19.4594 + 2.30918i 0.993033 + 0.117840i
\(385\) −33.5702 26.7122i −1.71090 1.36138i
\(386\) 0.275735 14.4295i 0.0140346 0.734441i
\(387\) −5.63146 0.812362i −0.286263 0.0412947i
\(388\) −5.39243 + 8.56652i −0.273759 + 0.434899i
\(389\) 4.19854 0.740316i 0.212874 0.0375355i −0.0661938 0.997807i \(-0.521086\pi\)
0.279068 + 0.960271i \(0.409974\pi\)
\(390\) 38.4643 6.64463i 1.94772 0.336464i
\(391\) −6.52777 1.15102i −0.330123 0.0582097i
\(392\) 12.6460 + 15.2341i 0.638722 + 0.769438i
\(393\) 0.453820 1.31024i 0.0228922 0.0660928i
\(394\) −9.63669 + 7.77729i −0.485490 + 0.391814i
\(395\) −10.5134 18.2097i −0.528984 0.916228i
\(396\) 23.4060 + 8.70371i 1.17620 + 0.437378i
\(397\) −12.6626 + 21.9323i −0.635518 + 1.10075i 0.350888 + 0.936418i \(0.385880\pi\)
−0.986405 + 0.164331i \(0.947453\pi\)
\(398\) −22.0515 + 17.7967i −1.10534 + 0.892067i
\(399\) 15.0606 + 16.5015i 0.753973 + 0.826108i
\(400\) 39.2111 10.9635i 1.96056 0.548173i
\(401\) −8.37448 + 9.98032i −0.418202 + 0.498393i −0.933480 0.358630i \(-0.883244\pi\)
0.515278 + 0.857023i \(0.327689\pi\)
\(402\) −0.315269 0.0567202i −0.0157242 0.00282894i
\(403\) −1.48736 + 4.08649i −0.0740907 + 0.203562i
\(404\) −16.2241 10.2127i −0.807178 0.508100i
\(405\) 9.91003 33.6344i 0.492433 1.67130i
\(406\) 0.835931 2.34700i 0.0414866 0.116480i
\(407\) 4.77586 + 27.0853i 0.236731 + 1.34257i
\(408\) −13.3197 2.92571i −0.659421 0.144844i
\(409\) −1.54905 + 8.78511i −0.0765957 + 0.434396i 0.922260 + 0.386570i \(0.126340\pi\)
−0.998856 + 0.0478257i \(0.984771\pi\)
\(410\) −42.3182 8.29847i −2.08995 0.409832i
\(411\) −19.3451 + 0.302455i −0.954222 + 0.0149190i
\(412\) 13.5208 1.85465i 0.666123 0.0913720i
\(413\) −3.60372 + 10.7644i −0.177327 + 0.529680i
\(414\) 9.92698 1.87513i 0.487885 0.0921578i
\(415\) 41.2467i 2.02472i
\(416\) 13.1142 + 19.0626i 0.642978 + 0.934619i
\(417\) 12.1665 10.5374i 0.595797 0.516018i
\(418\) 5.52187 28.1589i 0.270083 1.37730i
\(419\) −1.06481 + 6.03885i −0.0520195 + 0.295017i −0.999708 0.0241806i \(-0.992302\pi\)
0.947688 + 0.319198i \(0.103413\pi\)
\(420\) −35.1860 6.07980i −1.71690 0.296664i
\(421\) 5.46986 4.58976i 0.266585 0.223691i −0.499690 0.866204i \(-0.666553\pi\)
0.766275 + 0.642513i \(0.222108\pi\)
\(422\) −14.7654 + 24.4820i −0.718771 + 1.19177i
\(423\) −9.37782 7.38188i −0.455965 0.358919i
\(424\) −25.3305 1.45355i −1.23016 0.0705906i
\(425\) −27.9039 + 4.92022i −1.35354 + 0.238666i
\(426\) −31.2335 0.108487i −1.51327 0.00525621i
\(427\) −33.0873 17.9721i −1.60121 0.869733i
\(428\) 26.5867 + 24.0984i 1.28512 + 1.16484i
\(429\) 10.5166 + 27.5464i 0.507747 + 1.32995i
\(430\) −6.56279 8.13182i −0.316486 0.392151i
\(431\) −16.6690 + 28.8715i −0.802917 + 1.39069i 0.114772 + 0.993392i \(0.463386\pi\)
−0.917688 + 0.397301i \(0.869947\pi\)
\(432\) 20.5665 3.00334i 0.989505 0.144498i
\(433\) −34.9783 −1.68095 −0.840475 0.541850i \(-0.817724\pi\)
−0.840475 + 0.541850i \(0.817724\pi\)
\(434\) 2.53599 3.06501i 0.121731 0.147125i
\(435\) 1.60261 + 4.19775i 0.0768391 + 0.201267i
\(436\) −2.82819 + 13.0926i −0.135446 + 0.627019i
\(437\) −3.97044 10.9087i −0.189932 0.521834i
\(438\) 16.2786 + 28.4229i 0.777821 + 1.35810i
\(439\) 10.4721 1.84652i 0.499807 0.0881295i 0.0819394 0.996637i \(-0.473889\pi\)
0.417868 + 0.908508i \(0.362778\pi\)
\(440\) 20.6185 + 40.9671i 0.982947 + 1.95303i
\(441\) 17.1542 + 12.1134i 0.816866 + 0.576828i
\(442\) −7.78319 14.0962i −0.370208 0.670486i
\(443\) −7.19710 2.61953i −0.341945 0.124458i 0.165339 0.986237i \(-0.447128\pi\)
−0.507284 + 0.861779i \(0.669350\pi\)
\(444\) 14.3146 + 17.8635i 0.679340 + 0.847766i
\(445\) 12.7265 + 10.6788i 0.603295 + 0.506224i
\(446\) 6.17438 31.4864i 0.292366 1.49092i
\(447\) −22.7679 + 19.7192i −1.07688 + 0.932684i
\(448\) −5.45031 20.4522i −0.257503 0.966278i
\(449\) −24.9801 14.4222i −1.17888 0.680628i −0.223126 0.974790i \(-0.571626\pi\)
−0.955756 + 0.294162i \(0.904959\pi\)
\(450\) 37.1338 22.0456i 1.75050 1.03924i
\(451\) 32.5753i 1.53391i
\(452\) −0.463137 + 1.13548i −0.0217841 + 0.0534084i
\(453\) −13.3732 22.3487i −0.628325 1.05003i
\(454\) −6.65980 19.4459i −0.312560 0.912639i
\(455\) −22.0233 35.9523i −1.03247 1.68547i
\(456\) −7.22624 22.7641i −0.338399 1.06603i
\(457\) 6.02556 5.05604i 0.281864 0.236512i −0.490884 0.871225i \(-0.663326\pi\)
0.772748 + 0.634713i \(0.218882\pi\)
\(458\) −26.6954 + 14.7399i −1.24739 + 0.688748i
\(459\) −14.4485 + 0.678138i −0.674399 + 0.0316528i
\(460\) 15.7022 + 9.88420i 0.732121 + 0.460853i
\(461\) 28.0788 4.95105i 1.30776 0.230594i 0.524033 0.851698i \(-0.324427\pi\)
0.783728 + 0.621104i \(0.213316\pi\)
\(462\) −0.607882 26.9659i −0.0282812 1.25457i
\(463\) 11.5525 + 31.7401i 0.536888 + 1.47509i 0.850725 + 0.525612i \(0.176163\pi\)
−0.313836 + 0.949477i \(0.601614\pi\)
\(464\) −1.86282 + 1.90364i −0.0864791 + 0.0883744i
\(465\) 0.112158 + 7.17365i 0.00520120 + 0.332670i
\(466\) −0.334599 2.13543i −0.0155000 0.0989217i
\(467\) 6.47959 11.2230i 0.299839 0.519337i −0.676260 0.736663i \(-0.736400\pi\)
0.976099 + 0.217326i \(0.0697335\pi\)
\(468\) 18.6898 + 15.9052i 0.863938 + 0.735218i
\(469\) 0.0689237 + 0.339062i 0.00318260 + 0.0156564i
\(470\) −3.39309 21.6548i −0.156511 0.998861i
\(471\) 20.9633 + 24.2043i 0.965936 + 1.11527i
\(472\) 8.32022 8.83407i 0.382969 0.406621i
\(473\) 5.07388 6.04681i 0.233297 0.278033i
\(474\) 4.56460 12.4069i 0.209659 0.569867i
\(475\) −31.8974 38.0138i −1.46355 1.74419i
\(476\) 2.38063 + 14.5362i 0.109116 + 0.666266i
\(477\) −26.3434 + 5.49932i −1.20618 + 0.251796i
\(478\) 30.6207 16.9072i 1.40056 0.773316i
\(479\) 1.54094 1.29300i 0.0704072 0.0590786i −0.606905 0.794774i \(-0.707589\pi\)
0.677312 + 0.735696i \(0.263145\pi\)
\(480\) 31.4297 + 21.6641i 1.43456 + 0.988826i
\(481\) −4.69354 + 26.6184i −0.214007 + 1.21369i
\(482\) −7.16272 1.40459i −0.326253 0.0639772i
\(483\) −5.84470 9.21470i −0.265943 0.419284i
\(484\) −9.98952 + 7.75160i −0.454069 + 0.352346i
\(485\) −17.0767 + 9.85922i −0.775412 + 0.447684i
\(486\) 20.2347 8.74961i 0.917866 0.396890i
\(487\) −21.8004 12.5864i −0.987869 0.570346i −0.0832323 0.996530i \(-0.526524\pi\)
−0.904637 + 0.426184i \(0.859858\pi\)
\(488\) 24.0651 + 32.2673i 1.08938 + 1.46067i
\(489\) −3.57870 2.90878i −0.161835 0.131539i
\(490\) 7.94376 + 37.7414i 0.358862 + 1.70498i
\(491\) −2.37673 1.99431i −0.107260 0.0900022i 0.587580 0.809166i \(-0.300081\pi\)
−0.694841 + 0.719164i \(0.744525\pi\)
\(492\) −13.0229 23.7807i −0.587119 1.07212i
\(493\) 1.41990 1.19144i 0.0639490 0.0536596i
\(494\) 14.5643 24.1486i 0.655280 1.08650i
\(495\) 32.4182 + 36.2687i 1.45709 + 1.63016i
\(496\) −3.83464 + 1.83898i −0.172180 + 0.0825727i
\(497\) 12.3591 + 31.3909i 0.554382 + 1.40807i
\(498\) 19.9233 16.6001i 0.892786 0.743867i
\(499\) 2.33168 + 6.40624i 0.104380 + 0.286783i 0.980878 0.194623i \(-0.0623485\pi\)
−0.876498 + 0.481406i \(0.840126\pi\)
\(500\) 39.4430 + 8.52029i 1.76394 + 0.381039i
\(501\) 10.3117 29.7711i 0.460691 1.33007i
\(502\) −11.0686 13.7149i −0.494016 0.612126i
\(503\) 9.14395 15.8378i 0.407709 0.706172i −0.586924 0.809642i \(-0.699661\pi\)
0.994633 + 0.103470i \(0.0329945\pi\)
\(504\) −11.2242 19.4427i −0.499964 0.866046i
\(505\) −18.6723 32.3414i −0.830908 1.43917i
\(506\) −5.04435 + 13.0763i −0.224249 + 0.581313i
\(507\) 0.101000 + 6.46001i 0.00448558 + 0.286899i
\(508\) 2.58280 2.84949i 0.114593 0.126426i
\(509\) −3.21230 + 3.82827i −0.142383 + 0.169685i −0.832523 0.553991i \(-0.813104\pi\)
0.690140 + 0.723676i \(0.257549\pi\)
\(510\) −20.2907 17.1464i −0.898487 0.759254i
\(511\) 22.0285 27.6841i 0.974483 1.22467i
\(512\) −3.87190 + 22.2937i −0.171115 + 0.985251i
\(513\) −13.6808 21.3205i −0.604021 0.941322i
\(514\) −2.47344 4.47965i −0.109099 0.197589i
\(515\) 24.9818 + 9.09265i 1.10083 + 0.400670i
\(516\) 1.28665 6.44273i 0.0566418 0.283626i
\(517\) 15.5587 5.66292i 0.684273 0.249055i
\(518\) 12.2146 21.4977i 0.536678 0.944557i
\(519\) 4.27226 0.0667956i 0.187531 0.00293200i
\(520\) 5.27098 + 44.7634i 0.231148 + 1.96300i
\(521\) 39.3780i 1.72518i 0.505901 + 0.862592i \(0.331160\pi\)
−0.505901 + 0.862592i \(0.668840\pi\)
\(522\) −1.38265 + 2.46353i −0.0605170 + 0.107826i
\(523\) 13.1015i 0.572891i 0.958097 + 0.286445i \(0.0924737\pi\)
−0.958097 + 0.286445i \(0.907526\pi\)
\(524\) 1.48254 + 0.604695i 0.0647649 + 0.0264162i
\(525\) −36.9494 28.4691i −1.61260 1.24249i
\(526\) 2.51729 2.88616i 0.109759 0.125843i
\(527\) 2.78112 1.01225i 0.121148 0.0440941i
\(528\) −11.4902 + 26.4469i −0.500048 + 1.15095i
\(529\) −3.00931 17.0667i −0.130840 0.742029i
\(530\) −42.3232 25.5257i −1.83840 1.10877i
\(531\) 6.08412 11.3428i 0.264028 0.492235i
\(532\) −19.9626 + 16.3398i −0.865490 + 0.708418i
\(533\) 10.9494 30.0832i 0.474270 1.30305i
\(534\) −0.0362800 + 10.4450i −0.00156999 + 0.452001i
\(535\) 23.9072 + 65.6844i 1.03360 + 2.83978i
\(536\) 0.0849929 0.359988i 0.00367114 0.0155491i
\(537\) −26.9148 + 33.1136i −1.16146 + 1.42896i
\(538\) −36.2405 13.9802i −1.56244 0.602730i
\(539\) −26.8217 + 11.3745i −1.15529 + 0.489936i
\(540\) 38.1654 + 13.5168i 1.64238 + 0.581671i
\(541\) 14.3269 + 24.8149i 0.615961 + 1.06688i 0.990215 + 0.139549i \(0.0445654\pi\)
−0.374254 + 0.927326i \(0.622101\pi\)
\(542\) −15.4409 + 12.4616i −0.663242 + 0.535270i
\(543\) 22.9704 28.2608i 0.985754 1.21278i
\(544\) 4.20121 15.1761i 0.180125 0.650670i
\(545\) −16.7719 + 19.9880i −0.718431 + 0.856192i
\(546\) 8.50254 25.1072i 0.363875 1.07449i
\(547\) 3.58656 9.85400i 0.153350 0.421327i −0.839099 0.543978i \(-0.816917\pi\)
0.992450 + 0.122651i \(0.0391397\pi\)
\(548\) 0.853505 22.3242i 0.0364599 0.953642i
\(549\) 33.5481 + 26.4078i 1.43180 + 1.12706i
\(550\) −1.14465 + 59.9006i −0.0488081 + 2.55417i
\(551\) 3.05044 + 1.11027i 0.129953 + 0.0472991i
\(552\) 1.54514 + 11.5626i 0.0657657 + 0.492137i
\(553\) −14.2743 + 0.371390i −0.607006 + 0.0157931i
\(554\) −5.82667 + 6.68047i −0.247551 + 0.283826i
\(555\) 8.42893 + 43.7884i 0.357788 + 1.85871i
\(556\) 11.3938 + 14.6832i 0.483203 + 0.622706i
\(557\) −7.76924 + 4.48557i −0.329193 + 0.190060i −0.655483 0.755210i \(-0.727535\pi\)
0.326290 + 0.945270i \(0.394202\pi\)
\(558\) −3.41994 + 2.94127i −0.144778 + 0.124514i
\(559\) 6.71819 3.87875i 0.284149 0.164054i
\(560\) 9.19688 40.1925i 0.388639 1.69844i
\(561\) 9.76056 17.5332i 0.412091 0.740252i
\(562\) 21.4436 + 18.7030i 0.904544 + 0.788938i
\(563\) 1.80166 10.2177i 0.0759307 0.430625i −0.923017 0.384759i \(-0.874284\pi\)
0.998948 0.0458652i \(-0.0146045\pi\)
\(564\) 9.09431 10.3541i 0.382940 0.435987i
\(565\) −1.82995 + 1.53551i −0.0769864 + 0.0645992i
\(566\) 1.60736 2.66510i 0.0675623 0.112023i
\(567\) −16.8590 16.8159i −0.708011 0.706201i
\(568\) 2.06617 36.0063i 0.0866944 1.51079i
\(569\) −20.3836 24.2923i −0.854527 1.01839i −0.999581 0.0289614i \(-0.990780\pi\)
0.145054 0.989424i \(-0.453664\pi\)
\(570\) 8.23808 45.7899i 0.345055 1.91793i
\(571\) −23.9566 4.22419i −1.00255 0.176777i −0.351806 0.936073i \(-0.614432\pi\)
−0.650745 + 0.759296i \(0.725543\pi\)
\(572\) −32.4154 + 10.4140i −1.35535 + 0.435431i
\(573\) −4.75722 2.64830i −0.198736 0.110634i
\(574\) −18.6690 + 22.5634i −0.779228 + 0.941779i
\(575\) 12.1188 + 20.9903i 0.505387 + 0.875357i
\(576\) 2.18478 + 23.9004i 0.0910325 + 0.995848i
\(577\) 12.0911 + 20.9424i 0.503359 + 0.871843i 0.999992 + 0.00388258i \(0.00123587\pi\)
−0.496634 + 0.867960i \(0.665431\pi\)
\(578\) 4.70874 12.2063i 0.195858 0.507716i
\(579\) 17.3570 3.34109i 0.721332 0.138851i
\(580\) −4.93972 + 1.58697i −0.205111 + 0.0658954i
\(581\) −24.6138 13.3696i −1.02115 0.554663i
\(582\) −11.6349 4.28059i −0.482284 0.177436i
\(583\) 12.7692 35.0832i 0.528848 1.45300i
\(584\) −33.7840 + 17.0033i −1.39799 + 0.703600i
\(585\) 17.7473 + 44.3905i 0.733759 + 1.83532i
\(586\) 8.63734 + 15.6431i 0.356805 + 0.646211i
\(587\) 4.36298 + 1.58800i 0.180080 + 0.0655436i 0.430486 0.902597i \(-0.358342\pi\)
−0.250407 + 0.968141i \(0.580564\pi\)
\(588\) −15.0332 + 19.0264i −0.619957 + 0.784636i
\(589\) 3.97065 + 3.33177i 0.163608 + 0.137283i
\(590\) 22.3644 7.65934i 0.920728 0.315330i
\(591\) −11.7693 9.56613i −0.484126 0.393498i
\(592\) −21.4868 + 15.3949i −0.883100 + 0.632728i
\(593\) 18.7268 10.8119i 0.769017 0.443992i −0.0635067 0.997981i \(-0.520228\pi\)
0.832524 + 0.553989i \(0.186895\pi\)
\(594\) −4.47183 + 30.2556i −0.183481 + 1.24140i
\(595\) −9.10921 + 27.2094i −0.373441 + 1.11548i
\(596\) −21.3218 27.4774i −0.873374 1.12552i
\(597\) −26.9316 21.8901i −1.10224 0.895901i
\(598\) −9.05370 + 10.3804i −0.370233 + 0.424485i
\(599\) −28.0768 + 10.2191i −1.14719 + 0.417542i −0.844504 0.535549i \(-0.820105\pi\)
−0.302684 + 0.953091i \(0.597883\pi\)
\(600\) 23.1114 + 44.1863i 0.943517 + 1.80390i
\(601\) −2.49170 0.906904i −0.101638 0.0369934i 0.290700 0.956814i \(-0.406112\pi\)
−0.392339 + 0.919821i \(0.628334\pi\)
\(602\) −6.97988 + 1.28050i −0.284478 + 0.0521892i
\(603\) −0.0122647 0.392131i −0.000499458 0.0159688i
\(604\) 26.5997 14.0307i 1.08233 0.570901i
\(605\) −24.2568 + 4.27713i −0.986180 + 0.173890i
\(606\) 8.10700 22.0353i 0.329324 0.895125i
\(607\) 6.50329 + 17.8676i 0.263960 + 0.725225i 0.998891 + 0.0470830i \(0.0149925\pi\)
−0.734931 + 0.678142i \(0.762785\pi\)
\(608\) 26.6967 6.91732i 1.08270 0.280534i
\(609\) 3.02446 + 0.404295i 0.122557 + 0.0163828i
\(610\) 12.1384 + 77.4676i 0.491469 + 3.13657i
\(611\) 16.2719 0.658290
\(612\) 0.116025 16.7017i 0.00469004 0.675126i
\(613\) −13.8130 −0.557903 −0.278952 0.960305i \(-0.589987\pi\)
−0.278952 + 0.960305i \(0.589987\pi\)
\(614\) −26.1349 10.0819i −1.05472 0.406870i
\(615\) −0.825665 52.8097i −0.0332940 2.12949i
\(616\) 31.1302 + 0.974954i 1.25427 + 0.0392820i
\(617\) 9.29920 + 25.5493i 0.374372 + 1.02858i 0.973652 + 0.228039i \(0.0732312\pi\)
−0.599280 + 0.800539i \(0.704547\pi\)
\(618\) 5.66214 + 15.7264i 0.227765 + 0.632607i
\(619\) −9.49220 + 26.0796i −0.381524 + 1.04823i 0.589191 + 0.807994i \(0.299447\pi\)
−0.970715 + 0.240234i \(0.922776\pi\)
\(620\) −8.27838 0.316502i −0.332468 0.0127110i
\(621\) 4.77227 + 11.4156i 0.191505 + 0.458094i
\(622\) 25.7969 + 15.5585i 1.03436 + 0.623838i
\(623\) 10.4977 4.13311i 0.420580 0.165590i
\(624\) −19.5006 + 20.5614i −0.780650 + 0.823116i
\(625\) 21.2296 + 17.8137i 0.849182 + 0.712548i
\(626\) −32.8157 6.43506i −1.31158 0.257197i
\(627\) 35.1400 0.549404i 1.40336 0.0219411i
\(628\) −29.2110 + 22.6670i −1.16565 + 0.904510i
\(629\) 15.9305 9.19751i 0.635193 0.366729i
\(630\) −1.66896 43.7005i −0.0664929 1.74107i
\(631\) −5.88940 3.40025i −0.234453 0.135362i 0.378171 0.925736i \(-0.376553\pi\)
−0.612625 + 0.790374i \(0.709886\pi\)
\(632\) 14.0218 + 6.03416i 0.557757 + 0.240026i
\(633\) −33.0870 11.4602i −1.31509 0.455500i
\(634\) −0.0560579 + 0.0191987i −0.00222635 + 0.000762477i
\(635\) 7.03987 2.56230i 0.279369 0.101682i
\(636\) −4.70369 30.7164i −0.186514 1.21798i
\(637\) −28.5930 + 1.48888i −1.13290 + 0.0589915i
\(638\) −1.89441 3.43096i −0.0750002 0.135833i
\(639\) −7.81707 37.4461i −0.309239 1.48134i
\(640\) −26.9325 + 34.8930i −1.06460 + 1.37926i
\(641\) 16.2604 + 19.3784i 0.642248 + 0.765401i 0.984723 0.174125i \(-0.0557098\pi\)
−0.342476 + 0.939527i \(0.611265\pi\)
\(642\) −22.1058 + 37.9831i −0.872446 + 1.49907i
\(643\) 3.89097 4.63708i 0.153445 0.182868i −0.683846 0.729627i \(-0.739694\pi\)
0.837291 + 0.546758i \(0.184138\pi\)
\(644\) 10.9880 6.16643i 0.432989 0.242991i
\(645\) 8.07228 9.93143i 0.317846 0.391050i
\(646\) −18.9610 + 2.97099i −0.746010 + 0.116892i
\(647\) 7.42869 12.8669i 0.292052 0.505849i −0.682243 0.731126i \(-0.738995\pi\)
0.974295 + 0.225277i \(0.0723287\pi\)
\(648\) 8.83100 + 23.8750i 0.346914 + 0.937897i
\(649\) 8.92850 + 15.4646i 0.350474 + 0.607039i
\(650\) −21.1912 + 54.9332i −0.831185 + 2.15466i
\(651\) 4.31721 + 2.25831i 0.169205 + 0.0885102i
\(652\) 3.57630 3.94557i 0.140059 0.154520i
\(653\) −0.751903 0.132581i −0.0294242 0.00518828i 0.158917 0.987292i \(-0.449200\pi\)
−0.188341 + 0.982104i \(0.560311\pi\)
\(654\) −16.4048 0.0569806i −0.641478 0.00222812i
\(655\) 2.00483 + 2.38927i 0.0783353 + 0.0933564i
\(656\) 28.2291 13.5379i 1.10216 0.528565i
\(657\) −29.9094 + 26.7341i −1.16688 + 1.04299i
\(658\) −14.0223 4.99430i −0.546644 0.194698i
\(659\) 4.48244 3.76122i 0.174611 0.146516i −0.551294 0.834311i \(-0.685866\pi\)
0.725905 + 0.687795i \(0.241421\pi\)
\(660\) −43.8335 + 35.1251i −1.70621 + 1.36724i
\(661\) −20.9188 17.5529i −0.813646 0.682730i 0.137829 0.990456i \(-0.455987\pi\)
−0.951475 + 0.307726i \(0.900432\pi\)
\(662\) −17.5975 + 6.02677i −0.683946 + 0.234237i
\(663\) 14.9072 12.9111i 0.578947 0.501424i
\(664\) 17.9022 + 24.0038i 0.694738 + 0.931528i
\(665\) −49.2456 + 10.0105i −1.90966 + 0.388192i
\(666\) −17.7587 + 21.6944i −0.688137 + 0.840641i
\(667\) −1.37312 0.792771i −0.0531674 0.0306962i
\(668\) 33.6860 + 13.7398i 1.30335 + 0.531609i
\(669\) 39.2925 0.614326i 1.51913 0.0237512i
\(670\) 0.473612 0.543013i 0.0182972 0.0209784i
\(671\) −55.6597 + 20.2585i −2.14872 + 0.782069i
\(672\) 23.1155 11.7335i 0.891700 0.452628i
\(673\) −4.59125 26.0383i −0.176980 1.00370i −0.935834 0.352442i \(-0.885352\pi\)
0.758854 0.651261i \(-0.225760\pi\)
\(674\) 0.608382 31.8372i 0.0234340 1.22632i
\(675\) 35.8594 + 38.8779i 1.38023 + 1.49641i
\(676\) −7.45484 0.285016i −0.286725 0.0109621i
\(677\) 13.4529 + 16.0325i 0.517035 + 0.616179i 0.959877 0.280421i \(-0.0904741\pi\)
−0.442842 + 0.896600i \(0.646030\pi\)
\(678\) −1.47817 0.265939i −0.0567688 0.0102133i
\(679\) 0.348282 + 13.3862i 0.0133659 + 0.513714i
\(680\) 21.0312 22.3301i 0.806511 0.856321i
\(681\) 21.6021 12.9264i 0.827793 0.495340i
\(682\) −0.968734 6.18249i −0.0370947 0.236740i
\(683\) 21.4966 0.822546 0.411273 0.911512i \(-0.365084\pi\)
0.411273 + 0.911512i \(0.365084\pi\)
\(684\) 25.4333 14.4493i 0.972467 0.552483i
\(685\) 21.7596 37.6887i 0.831391 1.44001i
\(686\) 25.0969 + 7.49296i 0.958205 + 0.286083i
\(687\) −24.4511 28.2313i −0.932866 1.07709i
\(688\) 7.34868 + 1.88395i 0.280166 + 0.0718248i
\(689\) 23.5847 28.1071i 0.898504 1.07080i
\(690\) −7.84624 + 21.3266i −0.298701 + 0.811889i
\(691\) 3.43222 9.42996i 0.130568 0.358733i −0.857131 0.515098i \(-0.827756\pi\)
0.987699 + 0.156365i \(0.0499778\pi\)
\(692\) −0.188492 + 4.93018i −0.00716540 + 0.187417i
\(693\) 32.1511 7.58945i 1.22132 0.288299i
\(694\) 0.417511 21.8487i 0.0158485 0.829367i
\(695\) 6.28678 + 35.6541i 0.238471 + 1.35244i
\(696\) −2.75458 1.74734i −0.104412 0.0662326i
\(697\) −20.4736 + 7.45177i −0.775492 + 0.282256i
\(698\) −5.85546 17.0973i −0.221632 0.647141i
\(699\) 2.47315 0.944195i 0.0935433 0.0357127i
\(700\) 35.1220 40.8343i 1.32749 1.54339i
\(701\) 1.83466i 0.0692943i 0.999400 + 0.0346472i \(0.0110307\pi\)
−0.999400 + 0.0346472i \(0.988969\pi\)
\(702\) −14.2994 + 26.4378i −0.539694 + 0.997830i
\(703\) 27.9000 + 16.1081i 1.05227 + 0.607528i
\(704\) −29.7799 14.8921i −1.12237 0.561269i
\(705\) 25.0796 9.57484i 0.944553 0.360609i
\(706\) 6.89350 35.1536i 0.259440 1.32302i
\(707\) −25.3520 + 0.659610i −0.953461 + 0.0248072i
\(708\) 12.7004 + 7.72008i 0.477311 + 0.290138i
\(709\) 5.02741 + 28.5119i 0.188808 + 1.07079i 0.920964 + 0.389648i \(0.127403\pi\)
−0.732156 + 0.681137i \(0.761486\pi\)
\(710\) 36.2838 60.1609i 1.36171 2.25780i
\(711\) 16.0252 + 2.31170i 0.600990 + 0.0866955i
\(712\) −12.0412 0.690963i −0.451262 0.0258949i
\(713\) −1.62733 1.93938i −0.0609440 0.0726303i
\(714\) −16.8090 + 6.55064i −0.629061 + 0.245151i
\(715\) −65.3161 11.5170i −2.44268 0.430711i
\(716\) −36.5082 33.0914i −1.36438 1.23668i
\(717\) 28.0463 + 32.3824i 1.04741 + 1.20934i
\(718\) 16.7957 43.5389i 0.626809 1.62486i
\(719\) 31.4616 1.17332 0.586659 0.809834i \(-0.300443\pi\)
0.586659 + 0.809834i \(0.300443\pi\)
\(720\) −17.9571 + 43.1657i −0.669222 + 1.60869i
\(721\) 13.5235 11.9606i 0.503643 0.445435i
\(722\) −4.23451 5.24690i −0.157592 0.195269i
\(723\) −0.139751 8.93849i −0.00519739 0.332426i
\(724\) 31.1579 + 28.2418i 1.15797 + 1.04960i
\(725\) −6.67467 1.17692i −0.247891 0.0437099i
\(726\) −11.8283 9.99537i −0.438991 0.370963i
\(727\) 43.0438 7.58979i 1.59641 0.281490i 0.696495 0.717561i \(-0.254742\pi\)
0.899912 + 0.436072i \(0.143631\pi\)
\(728\) 28.4209 + 11.3640i 1.05335 + 0.421178i
\(729\) 15.6307 + 22.0154i 0.578917 + 0.815387i
\(730\) −73.6628 1.40764i −2.72638 0.0520989i
\(731\) −4.96109 1.80569i −0.183493 0.0667858i
\(732\) −32.5339 + 37.0407i −1.20249 + 1.36906i
\(733\) 22.9204 + 19.2325i 0.846585 + 0.710369i 0.959035 0.283288i \(-0.0914252\pi\)
−0.112450 + 0.993657i \(0.535870\pi\)
\(734\) 19.7038 6.74815i 0.727282 0.249079i
\(735\) −43.1939 + 19.1197i −1.59323 + 0.705241i
\(736\) −13.4280 + 1.06301i −0.494964 + 0.0391830i
\(737\) 0.471361 + 0.272140i 0.0173628 + 0.0100244i
\(738\) 25.1763 21.6525i 0.926753 0.797041i
\(739\) −13.5104 + 7.80022i −0.496987 + 0.286936i −0.727468 0.686141i \(-0.759303\pi\)
0.230481 + 0.973077i \(0.425970\pi\)
\(740\) −51.0130 + 6.99745i −1.87528 + 0.257231i
\(741\) 32.6363 + 11.3041i 1.19892 + 0.415265i
\(742\) −28.9509 + 16.9824i −1.06282 + 0.623445i
\(743\) −4.67648 + 26.5216i −0.171563 + 0.972984i 0.770473 + 0.637473i \(0.220020\pi\)
−0.942036 + 0.335511i \(0.891091\pi\)
\(744\) −3.17883 4.12607i −0.116541 0.151269i
\(745\) −11.7648 66.7214i −0.431028 2.44448i
\(746\) −0.843184 + 44.1246i −0.0308712 + 1.61552i
\(747\) 24.9566 + 19.6449i 0.913113 + 0.718769i
\(748\) 19.6097 + 12.3438i 0.717000 + 0.451335i
\(749\) 46.9461 + 7.02419i 1.71537 + 0.256658i
\(750\) −0.171661 + 49.4215i −0.00626819 + 1.80462i
\(751\) −34.4848 6.08060i −1.25837 0.221884i −0.495597 0.868553i \(-0.665051\pi\)
−0.762771 + 0.646669i \(0.776162\pi\)
\(752\) 11.3734 + 11.1295i 0.414745 + 0.405850i
\(753\) 13.6145 16.7501i 0.496140 0.610407i
\(754\) −0.596242 3.80524i −0.0217139 0.138579i
\(755\) 58.5828 2.13205
\(756\) 20.4369 18.3938i 0.743284 0.668976i
\(757\) 5.58419 0.202961 0.101480 0.994838i \(-0.467642\pi\)
0.101480 + 0.994838i \(0.467642\pi\)
\(758\) 1.27441 + 8.13335i 0.0462888 + 0.295417i
\(759\) −16.9492 2.71612i −0.615217 0.0985888i
\(760\) 52.2850 + 12.3444i 1.89658 + 0.447780i
\(761\) −0.608474 0.107290i −0.0220572 0.00388927i 0.162609 0.986691i \(-0.448009\pi\)
−0.184666 + 0.982801i \(0.559120\pi\)
\(762\) 4.07092 + 2.36924i 0.147474 + 0.0858285i
\(763\) 6.49138 + 16.4874i 0.235004 + 0.596885i
\(764\) 3.34921 5.32062i 0.121170 0.192493i
\(765\) 15.3790 28.6714i 0.556029 1.03662i
\(766\) −0.648089 + 33.9151i −0.0234164 + 1.22540i
\(767\) 3.04739 + 17.2826i 0.110035 + 0.624038i
\(768\) −27.6935 + 1.03377i −0.999304 + 0.0373029i
\(769\) −4.85604 + 27.5399i −0.175113 + 0.993116i 0.762900 + 0.646516i \(0.223775\pi\)
−0.938013 + 0.346599i \(0.887336\pi\)
\(770\) 52.7511 + 29.9721i 1.90102 + 1.08012i
\(771\) 4.73739 4.10303i 0.170613 0.147767i
\(772\) 2.77368 + 20.2207i 0.0998268 + 0.727760i
\(773\) −18.3914 + 10.6183i −0.661492 + 0.381913i −0.792845 0.609423i \(-0.791401\pi\)
0.131353 + 0.991336i \(0.458068\pi\)
\(774\) 8.04592 0.0978436i 0.289205 0.00351692i
\(775\) −9.37216 5.41102i −0.336658 0.194370i
\(776\) 5.65872 13.1494i 0.203136 0.472035i
\(777\) 28.8627 + 9.16348i 1.03544 + 0.328738i
\(778\) −5.70399 + 1.95350i −0.204498 + 0.0700362i
\(779\) −29.2304 24.5272i −1.04729 0.878780i
\(780\) −52.2864 + 17.7043i −1.87215 + 0.633917i
\(781\) 49.8694 + 18.1510i 1.78447 + 0.649493i
\(782\) 9.37236 + 0.179098i 0.335155 + 0.00640453i
\(783\) −3.30316 1.02963i −0.118045 0.0367960i
\(784\) −21.0037 18.5161i −0.750132 0.661288i
\(785\) −70.9309 + 12.5070i −2.53163 + 0.446395i
\(786\) −0.347223 + 1.92997i −0.0123850 + 0.0688398i
\(787\) −2.73316 0.481931i −0.0974268 0.0171790i 0.124722 0.992192i \(-0.460196\pi\)
−0.222149 + 0.975013i \(0.571307\pi\)
\(788\) 11.7614 12.9758i 0.418984 0.462246i
\(789\) 4.09818 + 2.28142i 0.145899 + 0.0812207i
\(790\) 18.6754 + 23.1403i 0.664441 + 0.823296i
\(791\) 0.323156 + 1.58973i 0.0114901 + 0.0565242i
\(792\) −34.6076 7.03644i −1.22973 0.250029i
\(793\) −58.2108 −2.06713
\(794\) 12.8903 33.4151i 0.457460 1.18586i
\(795\) 19.8117 57.1990i 0.702648 2.02864i
\(796\) 26.9136 29.6925i 0.953926 1.05242i
\(797\) −51.3870 9.06092i −1.82022 0.320954i −0.843773 0.536700i \(-0.819671\pi\)
−0.976450 + 0.215746i \(0.930782\pi\)
\(798\) −24.6547 19.7582i −0.872767 0.699434i
\(799\) −7.11828 8.48324i −0.251827 0.300115i
\(800\) −52.3843 + 23.9020i −1.85207 + 0.845062i
\(801\) −12.5226 + 2.61417i −0.442466 + 0.0923671i
\(802\) 9.51563 15.7775i 0.336009 0.557124i
\(803\) −9.66419 54.8084i −0.341042 1.93415i
\(804\) 0.452900 + 0.0102283i 0.0159725 + 0.000360725i
\(805\) 24.5366 0.638394i 0.864801 0.0225004i
\(806\) 1.18347 6.03512i 0.0416859 0.212578i
\(807\) 7.52762 46.9741i 0.264985 1.65357i
\(808\) 24.9035 + 10.7170i 0.876103 + 0.377023i
\(809\) −14.5294 8.38857i −0.510827 0.294926i 0.222346 0.974968i \(-0.428628\pi\)
−0.733174 + 0.680041i \(0.761962\pi\)
\(810\) −6.48266 + 49.1623i −0.227777 + 1.72739i
\(811\) 33.2486i 1.16752i −0.811928 0.583758i \(-0.801582\pi\)
0.811928 0.583758i \(-0.198418\pi\)
\(812\) −0.654124 + 3.46216i −0.0229553 + 0.121498i
\(813\) −18.8580 15.3278i −0.661379 0.537570i
\(814\) −12.6022 36.7971i −0.441708 1.28974i
\(815\) 9.74782 3.54792i 0.341451 0.124278i
\(816\) 19.2503 + 1.17174i 0.673895 + 0.0410193i
\(817\) −1.60559 9.10576i −0.0561725 0.318570i
\(818\) 0.241031 12.6134i 0.00842746 0.441017i
\(819\) 32.2424 + 3.79797i 1.12664 + 0.132712i
\(820\) 60.9423 + 2.32997i 2.12820 + 0.0813659i
\(821\) 8.53887 23.4604i 0.298009 0.818772i −0.696824 0.717242i \(-0.745404\pi\)
0.994833 0.101530i \(-0.0323737\pi\)
\(822\) 26.9621 4.65763i 0.940410 0.162454i
\(823\) 27.3750 32.6243i 0.954234 1.13721i −0.0362166 0.999344i \(-0.511531\pi\)
0.990451 0.137868i \(-0.0440249\pi\)
\(824\) −18.4848 + 5.55125i −0.643948 + 0.193387i
\(825\) −72.0535 + 13.8698i −2.50858 + 0.482883i
\(826\) 2.67844 15.8286i 0.0931947 0.550746i
\(827\) −2.59253 + 4.49040i −0.0901512 + 0.156146i −0.907575 0.419891i \(-0.862068\pi\)
0.817423 + 0.576037i \(0.195402\pi\)
\(828\) −13.4591 + 4.79311i −0.467737 + 0.166572i
\(829\) −15.3864 −0.534393 −0.267196 0.963642i \(-0.586097\pi\)
−0.267196 + 0.963642i \(0.586097\pi\)
\(830\) 9.02980 + 57.6285i 0.313429 + 2.00031i
\(831\) −9.48590 5.28071i −0.329062 0.183186i
\(832\) −22.4960 23.7626i −0.779907 0.823820i
\(833\) 13.2845 + 14.2554i 0.460280 + 0.493922i
\(834\) −14.6918 + 17.3860i −0.508735 + 0.602027i
\(835\) 45.5536 + 54.2887i 1.57645 + 1.87874i
\(836\) −1.55038 + 40.5515i −0.0536209 + 1.40250i
\(837\) −4.39388 3.34879i −0.151875 0.115751i
\(838\) 0.165684 8.67039i 0.00572346 0.299514i
\(839\) −0.636862 3.61182i −0.0219869 0.124694i 0.971839 0.235647i \(-0.0757208\pi\)
−0.993826 + 0.110953i \(0.964610\pi\)
\(840\) 50.4916 + 0.791516i 1.74213 + 0.0273099i
\(841\) −26.8345 + 9.76694i −0.925326 + 0.336791i
\(842\) −6.63750 + 7.61012i −0.228743 + 0.262262i
\(843\) −16.9505 + 30.4487i −0.583807 + 1.04871i
\(844\) 15.2701 37.4380i 0.525620 1.28867i
\(845\) −12.5856 7.26630i −0.432958 0.249968i
\(846\) 14.7184 + 8.26070i 0.506030 + 0.284009i
\(847\) −5.31016 + 15.8615i −0.182459 + 0.545009i
\(848\) 35.7091 3.51455i 1.22626 0.120690i
\(849\) 3.60183 + 1.24755i 0.123615 + 0.0428157i
\(850\) 37.9093 12.9831i 1.30028 0.445318i
\(851\) −12.0539 10.1144i −0.413203 0.346719i
\(852\) 43.6622 6.68612i 1.49584 0.229063i
\(853\) 10.2789 8.62506i 0.351944 0.295316i −0.449626 0.893217i \(-0.648443\pi\)
0.801570 + 0.597901i \(0.203998\pi\)
\(854\) 50.1630 + 17.8665i 1.71654 + 0.611380i
\(855\) 56.9535 1.78134i 1.94777 0.0609205i
\(856\) −42.4217 27.8491i −1.44994 0.951863i
\(857\) −18.5795 22.1421i −0.634662 0.756361i 0.348855 0.937177i \(-0.386571\pi\)
−0.983517 + 0.180816i \(0.942126\pi\)
\(858\) −20.7240 36.1846i −0.707505 1.23532i
\(859\) 4.66705 + 0.822927i 0.159238 + 0.0280779i 0.252699 0.967545i \(-0.418682\pi\)
−0.0934608 + 0.995623i \(0.529793\pi\)
\(860\) 10.9495 + 9.92477i 0.373376 + 0.338432i
\(861\) −31.7816 16.6248i −1.08312 0.566573i
\(862\) 16.9687 43.9875i 0.577957 1.49822i
\(863\) −8.74192 15.1414i −0.297578 0.515421i 0.678003 0.735059i \(-0.262846\pi\)
−0.975581 + 0.219638i \(0.929512\pi\)
\(864\) −28.0773 + 8.69861i −0.955209 + 0.295933i
\(865\) −4.80549 + 8.32336i −0.163392 + 0.283003i
\(866\) 48.8705 7.65751i 1.66069 0.260213i
\(867\) 15.8215 + 2.53541i 0.537328 + 0.0861070i
\(868\) −2.87220 + 4.83751i −0.0974887 + 0.164196i
\(869\) −14.4385 + 17.2071i −0.489792 + 0.583712i
\(870\) −3.15809 5.51411i −0.107069 0.186946i
\(871\) 0.343827 + 0.409757i 0.0116501 + 0.0138841i
\(872\) 1.08521 18.9116i 0.0367500 0.640428i
\(873\) 2.16787 15.0281i 0.0733711 0.508623i
\(874\) 7.93551 + 14.3720i 0.268423 + 0.486142i
\(875\) 49.6705 19.5561i 1.67917 0.661117i
\(876\) −28.9663 36.1478i −0.978680 1.22132i
\(877\) 7.94195 2.89063i 0.268181 0.0976098i −0.204430 0.978881i \(-0.565534\pi\)
0.472610 + 0.881271i \(0.343312\pi\)
\(878\) −14.2271 + 4.87247i −0.480140 + 0.164438i
\(879\) −16.5431 + 14.3280i −0.557986 + 0.483270i
\(880\) −37.7760 52.7241i −1.27343 1.77733i
\(881\) −14.9372 8.62402i −0.503248 0.290551i 0.226806 0.973940i \(-0.427172\pi\)
−0.730054 + 0.683390i \(0.760505\pi\)
\(882\) −26.6191 13.1690i −0.896312 0.443423i
\(883\) 20.2218 11.6751i 0.680518 0.392897i −0.119532 0.992830i \(-0.538140\pi\)
0.800050 + 0.599933i \(0.204806\pi\)
\(884\) 13.9604 + 17.9908i 0.469538 + 0.605095i
\(885\) 14.8665 + 24.8442i 0.499730 + 0.835130i
\(886\) 10.6290 + 2.08432i 0.357089 + 0.0700240i
\(887\) 21.7117 + 18.2183i 0.729007 + 0.611709i 0.929861 0.367912i \(-0.119927\pi\)
−0.200854 + 0.979621i \(0.564372\pi\)
\(888\) −23.9106 21.8246i −0.802387 0.732384i
\(889\) 0.752834 5.03156i 0.0252492 0.168753i
\(890\) −20.1189 12.1340i −0.674386 0.406731i
\(891\) −37.3847 + 2.34086i −1.25243 + 0.0784217i
\(892\) −1.73358 + 45.3434i −0.0580447 + 1.51821i
\(893\) 6.63335 18.2250i 0.221977 0.609876i
\(894\) 27.4935 32.5353i 0.919521 1.08814i
\(895\) −32.8287 90.1962i −1.09734 3.01493i
\(896\) 12.0924 + 27.3820i 0.403980 + 0.914768i
\(897\) −14.7396 8.20537i −0.492140 0.273969i
\(898\) 38.0586 + 14.6816i 1.27003 + 0.489931i
\(899\) 0.707943 0.0236112
\(900\) −47.0558 + 38.9307i −1.56853 + 1.29769i
\(901\) −24.9708 −0.831897
\(902\) 7.13145 + 45.5132i 0.237451 + 1.51542i
\(903\) −3.31002 8.03625i −0.110151 0.267430i
\(904\) 0.398499 1.68784i 0.0132539 0.0561368i
\(905\) 28.0176 + 76.9778i 0.931338 + 2.55883i
\(906\) 23.5771 + 28.2972i 0.783298 + 0.940110i
\(907\) 2.02850 0.357680i 0.0673554 0.0118766i −0.139869 0.990170i \(-0.544668\pi\)
0.207224 + 0.978293i \(0.433557\pi\)
\(908\) 13.5620 + 25.7111i 0.450070 + 0.853253i
\(909\) 28.4616 + 4.10571i 0.944012 + 0.136178i
\(910\) 38.6410 + 45.4100i 1.28094 + 1.50533i
\(911\) −10.7908 3.92754i −0.357516 0.130125i 0.157016 0.987596i \(-0.449812\pi\)
−0.514533 + 0.857471i \(0.672035\pi\)
\(912\) 15.0798 + 30.2233i 0.499343 + 1.00079i
\(913\) −41.4055 + 15.0704i −1.37032 + 0.498756i
\(914\) −7.31183 + 8.38326i −0.241854 + 0.277293i
\(915\) −89.7195 + 34.2529i −2.96604 + 1.13237i
\(916\) 34.0710 26.4382i 1.12574 0.873544i
\(917\) 2.07563 0.421929i 0.0685432 0.0139333i
\(918\) 20.0385 4.11057i 0.661370 0.135669i
\(919\) 26.4017 15.2430i 0.870911 0.502821i 0.00326006 0.999995i \(-0.498962\pi\)
0.867651 + 0.497174i \(0.165629\pi\)
\(920\) −24.1025 10.3723i −0.794636 0.341965i
\(921\) 5.42855 33.8754i 0.178877 1.11623i
\(922\) −38.1469 + 13.0645i −1.25630 + 0.430257i
\(923\) 39.9532 + 33.5247i 1.31508 + 1.10348i
\(924\) 6.75274 + 37.5428i 0.222149 + 1.23507i
\(925\) −63.2064 23.0052i −2.07821 0.756408i
\(926\) −23.0893 41.8171i −0.758762 1.37420i
\(927\) −17.3999 + 10.7848i −0.571487 + 0.354219i
\(928\) 2.18592 3.06752i 0.0717562 0.100696i
\(929\) 13.3102 36.5694i 0.436693 1.19980i −0.504938 0.863156i \(-0.668485\pi\)
0.941631 0.336648i \(-0.109293\pi\)
\(930\) −1.72717 9.99823i −0.0566362 0.327855i
\(931\) −9.98856 + 32.6319i −0.327362 + 1.06947i
\(932\) 0.934982 + 2.91029i 0.0306264 + 0.0953298i
\(933\) −12.0757 + 34.8640i −0.395339 + 1.14140i
\(934\) −6.59611 + 17.0989i −0.215831 + 0.559492i
\(935\) 22.5688 + 39.0903i 0.738078 + 1.27839i
\(936\) −29.5948 18.1306i −0.967336 0.592616i
\(937\) −9.42164 16.3188i −0.307791 0.533110i 0.670087 0.742282i \(-0.266257\pi\)
−0.977879 + 0.209172i \(0.932923\pi\)
\(938\) −0.170526 0.458637i −0.00556787 0.0149750i
\(939\) −0.640263 40.9514i −0.0208942 1.33640i
\(940\) 9.48141 + 29.5125i 0.309250 + 0.962593i
\(941\) −36.2973 6.40019i −1.18326 0.208640i −0.452809 0.891608i \(-0.649578\pi\)
−0.730449 + 0.682967i \(0.760689\pi\)
\(942\) −34.5880 29.2281i −1.12694 0.952303i
\(943\) 11.9798 + 14.2770i 0.390116 + 0.464922i
\(944\) −9.69076 + 14.1641i −0.315407 + 0.461004i
\(945\) 51.9296 13.1186i 1.68927 0.426748i
\(946\) −5.76527 + 9.55918i −0.187445 + 0.310796i
\(947\) −21.6574 + 18.1727i −0.703770 + 0.590533i −0.922843 0.385176i \(-0.874141\pi\)
0.219074 + 0.975708i \(0.429696\pi\)
\(948\) −3.66137 + 18.3338i −0.118916 + 0.595453i
\(949\) 9.49762 53.8637i 0.308306 1.74849i
\(950\) 52.8880 + 46.1286i 1.71591 + 1.49661i
\(951\) −0.0372638 0.0622738i −0.00120836 0.00201937i
\(952\) −6.50843 19.7883i −0.210939 0.641343i
\(953\) 16.0353 9.25799i 0.519435 0.299896i −0.217269 0.976112i \(-0.569715\pi\)
0.736703 + 0.676216i \(0.236381\pi\)
\(954\) 35.6021 13.4506i 1.15266 0.435479i
\(955\) 10.6062 6.12351i 0.343210 0.198152i
\(956\) −39.0808 + 30.3257i −1.26396 + 0.980802i
\(957\) 3.62836 3.14251i 0.117288 0.101583i
\(958\) −1.86988 + 2.14388i −0.0604130 + 0.0692656i
\(959\) −15.4375 25.2013i −0.498504 0.813791i
\(960\) −48.6553 23.3877i −1.57034 0.754834i
\(961\) −28.0682 10.2160i −0.905427 0.329549i
\(962\) 0.730311 38.2178i 0.0235462 1.23219i
\(963\) −51.1292 16.8189i −1.64762 0.541980i
\(964\) 10.3150 + 0.394367i 0.332224 + 0.0127017i
\(965\) −13.5983 + 37.3610i −0.437744 + 1.20269i
\(966\) 10.1833 + 11.5949i 0.327643 + 0.373061i
\(967\) −0.0926803 + 0.110452i −0.00298040 + 0.00355190i −0.767533 0.641010i \(-0.778516\pi\)
0.764552 + 0.644562i \(0.222960\pi\)
\(968\) 12.2600 13.0172i 0.394052 0.418389i
\(969\) −8.38374 21.9598i −0.269325 0.705449i
\(970\) 21.7005 17.5134i 0.696763 0.562322i
\(971\) 4.86559 + 8.42744i 0.156144 + 0.270450i 0.933475 0.358642i \(-0.116760\pi\)
−0.777331 + 0.629092i \(0.783427\pi\)
\(972\) −26.3558 + 16.6545i −0.845363 + 0.534193i
\(973\) 23.3142 + 7.80518i 0.747420 + 0.250223i
\(974\) 33.2142 + 12.8128i 1.06425 + 0.410548i
\(975\) −71.2031 11.4103i −2.28032 0.365423i
\(976\) −40.6870 39.8144i −1.30236 1.27443i
\(977\) −4.17452 11.4694i −0.133555 0.366939i 0.854831 0.518907i \(-0.173661\pi\)
−0.988385 + 0.151969i \(0.951439\pi\)
\(978\) 5.63684 + 3.28059i 0.180246 + 0.104902i
\(979\) 6.07002 16.6772i 0.193999 0.533007i
\(980\) −19.3612 50.9920i −0.618470 1.62888i
\(981\) −4.10576 19.6678i −0.131087 0.627945i
\(982\) 3.75729 + 2.26607i 0.119900 + 0.0723132i
\(983\) 3.62590 + 20.5635i 0.115648 + 0.655874i 0.986427 + 0.164199i \(0.0525039\pi\)
−0.870779 + 0.491675i \(0.836385\pi\)
\(984\) 23.4013 + 30.3746i 0.746006 + 0.968307i
\(985\) 32.0578 11.6681i 1.02145 0.371776i
\(986\) −1.72300 + 1.97548i −0.0548716 + 0.0629121i
\(987\) 2.41547 18.0697i 0.0768854 0.575166i
\(988\) −15.0621 + 36.9280i −0.479190 + 1.17484i
\(989\) 4.51612i 0.143604i
\(990\) −53.2336 43.5763i −1.69188 1.38495i
\(991\) 15.2588i 0.484713i 0.970187 + 0.242356i \(0.0779203\pi\)
−0.970187 + 0.242356i \(0.922080\pi\)
\(992\) 4.95503 3.40885i 0.157322 0.108231i
\(993\) −11.6977 19.5488i −0.371216 0.620361i
\(994\) −24.1399 41.1526i −0.765670 1.30528i
\(995\) 73.3575 26.6999i 2.32559 0.846445i
\(996\) −24.2021 + 27.5547i −0.766872 + 0.873105i
\(997\) −27.8044 10.1200i −0.880574 0.320503i −0.138133 0.990414i \(-0.544110\pi\)
−0.742441 + 0.669911i \(0.766332\pi\)
\(998\) −4.66021 8.44012i −0.147516 0.267167i
\(999\) −30.5089 15.7555i −0.965260 0.498481i
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 756.2.ci.a.95.7 yes 840
4.3 odd 2 inner 756.2.ci.a.95.87 yes 840
7.2 even 3 756.2.bs.a.527.101 yes 840
27.2 odd 18 756.2.bs.a.515.10 840
28.23 odd 6 756.2.bs.a.527.10 yes 840
108.83 even 18 756.2.bs.a.515.101 yes 840
189.2 odd 18 inner 756.2.ci.a.191.87 yes 840
756.191 even 18 inner 756.2.ci.a.191.7 yes 840
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
756.2.bs.a.515.10 840 27.2 odd 18
756.2.bs.a.515.101 yes 840 108.83 even 18
756.2.bs.a.527.10 yes 840 28.23 odd 6
756.2.bs.a.527.101 yes 840 7.2 even 3
756.2.ci.a.95.7 yes 840 1.1 even 1 trivial
756.2.ci.a.95.87 yes 840 4.3 odd 2 inner
756.2.ci.a.191.7 yes 840 756.191 even 18 inner
756.2.ci.a.191.87 yes 840 189.2 odd 18 inner