Properties

Label 69.3.f.a.10.7
Level $69$
Weight $3$
Character 69.10
Analytic conductor $1.880$
Analytic rank $0$
Dimension $80$
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] = [69,3,Mod(7,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 19]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 69.f (of order \(22\), degree \(10\), 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: \(1.88011382409\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(8\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 10.7
Character \(\chi\) \(=\) 69.10
Dual form 69.3.f.a.7.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.89640 + 2.18856i) q^{2} +(1.45709 + 0.936417i) q^{3} +(-0.624207 + 4.34145i) q^{4} +(-2.49041 - 1.13733i) q^{5} +(0.713823 + 4.96475i) q^{6} +(0.240886 - 0.820382i) q^{7} +(-0.940602 + 0.604488i) q^{8} +(1.24625 + 2.72890i) q^{9} +O(q^{10})\) \(q+(1.89640 + 2.18856i) q^{2} +(1.45709 + 0.936417i) q^{3} +(-0.624207 + 4.34145i) q^{4} +(-2.49041 - 1.13733i) q^{5} +(0.713823 + 4.96475i) q^{6} +(0.240886 - 0.820382i) q^{7} +(-0.940602 + 0.604488i) q^{8} +(1.24625 + 2.72890i) q^{9} +(-2.23369 - 7.60725i) q^{10} +(-10.8512 - 9.40266i) q^{11} +(-4.97494 + 5.74139i) q^{12} +(7.40140 - 2.17325i) q^{13} +(2.25227 - 1.02858i) q^{14} +(-2.56375 - 3.98927i) q^{15} +(13.7270 + 4.03062i) q^{16} +(-12.5308 + 1.80166i) q^{17} +(-3.60897 + 7.90255i) q^{18} +(7.61098 + 1.09429i) q^{19} +(6.49222 - 10.1021i) q^{20} +(1.11921 - 0.969804i) q^{21} -41.5797i q^{22} +(-1.01882 + 22.9774i) q^{23} -1.93660 q^{24} +(-11.4629 - 13.2289i) q^{25} +(18.7923 + 12.0770i) q^{26} +(-0.739490 + 5.14326i) q^{27} +(3.41129 + 1.55788i) q^{28} +(-2.50758 - 17.4406i) q^{29} +(3.86886 - 13.1761i) q^{30} +(20.4018 - 13.1114i) q^{31} +(19.0685 + 41.7542i) q^{32} +(-7.00647 - 23.8618i) q^{33} +(-27.7064 - 24.0077i) q^{34} +(-1.53295 + 1.76912i) q^{35} +(-12.6253 + 3.70712i) q^{36} +(-40.2970 + 18.4030i) q^{37} +(12.0385 + 18.7323i) q^{38} +(12.8196 + 3.76417i) q^{39} +(3.02999 - 0.435647i) q^{40} +(-23.1881 + 50.7749i) q^{41} +(4.24494 + 0.610331i) q^{42} +(-0.430823 + 0.670374i) q^{43} +(47.5946 - 41.2410i) q^{44} -8.21348i q^{45} +(-52.2195 + 41.3445i) q^{46} -77.4206 q^{47} +(16.2272 + 18.7272i) q^{48} +(40.6064 + 26.0962i) q^{49} +(7.21398 - 50.1744i) q^{50} +(-19.9457 - 9.10888i) q^{51} +(4.81505 + 33.4894i) q^{52} +(-3.33004 + 11.3411i) q^{53} +(-12.6587 + 8.13525i) q^{54} +(16.3301 + 35.7580i) q^{55} +(0.269333 + 0.917265i) q^{56} +(10.0652 + 8.72155i) q^{57} +(33.4144 - 38.5623i) q^{58} +(56.4505 - 16.5754i) q^{59} +(18.9195 - 8.64027i) q^{60} +(45.9499 + 71.4994i) q^{61} +(67.3850 + 19.7860i) q^{62} +(2.53894 - 0.365044i) q^{63} +(-31.4475 + 68.8603i) q^{64} +(-20.9043 - 3.00558i) q^{65} +(38.9360 - 60.5856i) q^{66} +(48.6048 - 42.1163i) q^{67} -55.5265i q^{68} +(-23.0010 + 32.5262i) q^{69} -6.77891 q^{70} +(-63.4447 - 73.2190i) q^{71} +(-2.82181 - 1.81346i) q^{72} +(-9.77406 + 67.9801i) q^{73} +(-116.695 - 53.2929i) q^{74} +(-4.31475 - 30.0098i) q^{75} +(-9.50166 + 32.3597i) q^{76} +(-10.3277 + 6.63720i) q^{77} +(16.0729 + 35.1948i) q^{78} +(-36.1212 - 123.018i) q^{79} +(-29.6018 - 25.6501i) q^{80} +(-5.89375 + 6.80175i) q^{81} +(-155.098 + 45.5408i) q^{82} +(112.277 - 51.2752i) q^{83} +(3.51174 + 5.46437i) q^{84} +(33.2560 + 9.76483i) q^{85} +(-2.28416 + 0.328413i) q^{86} +(12.6779 - 27.7608i) q^{87} +(15.8905 + 2.28471i) q^{88} +(75.4594 - 117.417i) q^{89} +(17.9757 - 15.5760i) q^{90} -6.59548i q^{91} +(-99.1195 - 18.7658i) q^{92} +42.0051 q^{93} +(-146.820 - 169.439i) q^{94} +(-17.7099 - 11.3815i) q^{95} +(-11.3148 + 78.6959i) q^{96} +(69.0088 + 31.5153i) q^{97} +(19.8929 + 138.358i) q^{98} +(12.1356 - 41.3299i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + 4 q^{2} - 12 q^{6} - 4 q^{8} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q + 4 q^{2} - 12 q^{6} - 4 q^{8} - 24 q^{9} + 8 q^{13} - 208 q^{16} - 110 q^{17} + 12 q^{18} - 66 q^{19} - 176 q^{20} - 8 q^{23} - 12 q^{24} + 244 q^{25} + 328 q^{26} + 528 q^{28} + 50 q^{29} + 182 q^{31} + 428 q^{32} - 242 q^{34} - 536 q^{35} - 198 q^{36} - 352 q^{37} - 770 q^{38} - 216 q^{39} - 110 q^{40} - 208 q^{41} - 330 q^{42} - 88 q^{43} - 154 q^{44} - 72 q^{46} + 24 q^{47} + 360 q^{48} + 256 q^{49} + 726 q^{50} + 264 q^{51} + 506 q^{52} + 352 q^{53} + 162 q^{54} - 38 q^{55} + 1210 q^{56} + 528 q^{57} - 306 q^{58} + 776 q^{59} + 330 q^{60} - 308 q^{61} + 392 q^{62} - 288 q^{64} - 22 q^{67} - 108 q^{69} + 344 q^{70} - 80 q^{71} - 12 q^{72} + 46 q^{73} - 374 q^{74} + 72 q^{75} - 946 q^{76} - 728 q^{77} - 144 q^{78} - 572 q^{79} - 2178 q^{80} - 72 q^{81} - 820 q^{82} - 704 q^{83} - 922 q^{85} - 1100 q^{86} + 192 q^{87} - 528 q^{88} - 264 q^{89} + 330 q^{92} + 24 q^{93} + 874 q^{94} + 622 q^{95} - 468 q^{96} + 792 q^{97} - 724 q^{98} - 330 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{3}{22}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.89640 + 2.18856i 0.948198 + 1.09428i 0.995439 + 0.0953951i \(0.0304115\pi\)
−0.0472417 + 0.998883i \(0.515043\pi\)
\(3\) 1.45709 + 0.936417i 0.485698 + 0.312139i
\(4\) −0.624207 + 4.34145i −0.156052 + 1.08536i
\(5\) −2.49041 1.13733i −0.498083 0.227467i 0.150501 0.988610i \(-0.451911\pi\)
−0.648584 + 0.761143i \(0.724639\pi\)
\(6\) 0.713823 + 4.96475i 0.118971 + 0.827459i
\(7\) 0.240886 0.820382i 0.0344123 0.117197i −0.940496 0.339805i \(-0.889639\pi\)
0.974908 + 0.222608i \(0.0714570\pi\)
\(8\) −0.940602 + 0.604488i −0.117575 + 0.0755610i
\(9\) 1.24625 + 2.72890i 0.138472 + 0.303211i
\(10\) −2.23369 7.60725i −0.223369 0.760725i
\(11\) −10.8512 9.40266i −0.986477 0.854787i 0.00292443 0.999996i \(-0.499069\pi\)
−0.989401 + 0.145209i \(0.953615\pi\)
\(12\) −4.97494 + 5.74139i −0.414579 + 0.478449i
\(13\) 7.40140 2.17325i 0.569338 0.167173i 0.0156216 0.999878i \(-0.495027\pi\)
0.553717 + 0.832705i \(0.313209\pi\)
\(14\) 2.25227 1.02858i 0.160876 0.0734697i
\(15\) −2.56375 3.98927i −0.170917 0.265951i
\(16\) 13.7270 + 4.03062i 0.857938 + 0.251913i
\(17\) −12.5308 + 1.80166i −0.737106 + 0.105980i −0.500635 0.865659i \(-0.666900\pi\)
−0.236471 + 0.971638i \(0.575991\pi\)
\(18\) −3.60897 + 7.90255i −0.200498 + 0.439030i
\(19\) 7.61098 + 1.09429i 0.400578 + 0.0575944i 0.339660 0.940548i \(-0.389688\pi\)
0.0609182 + 0.998143i \(0.480597\pi\)
\(20\) 6.49222 10.1021i 0.324611 0.505104i
\(21\) 1.11921 0.969804i 0.0532959 0.0461811i
\(22\) 41.5797i 1.88999i
\(23\) −1.01882 + 22.9774i −0.0442966 + 0.999018i
\(24\) −1.93660 −0.0806916
\(25\) −11.4629 13.2289i −0.458515 0.529155i
\(26\) 18.7923 + 12.0770i 0.722779 + 0.464502i
\(27\) −0.739490 + 5.14326i −0.0273885 + 0.190491i
\(28\) 3.41129 + 1.55788i 0.121832 + 0.0556387i
\(29\) −2.50758 17.4406i −0.0864683 0.601400i −0.986275 0.165111i \(-0.947202\pi\)
0.899807 0.436289i \(-0.143707\pi\)
\(30\) 3.86886 13.1761i 0.128962 0.439205i
\(31\) 20.4018 13.1114i 0.658123 0.422950i −0.168504 0.985701i \(-0.553893\pi\)
0.826626 + 0.562751i \(0.190257\pi\)
\(32\) 19.0685 + 41.7542i 0.595891 + 1.30482i
\(33\) −7.00647 23.8618i −0.212317 0.723086i
\(34\) −27.7064 24.0077i −0.814894 0.706109i
\(35\) −1.53295 + 1.76912i −0.0437987 + 0.0505464i
\(36\) −12.6253 + 3.70712i −0.350703 + 0.102976i
\(37\) −40.2970 + 18.4030i −1.08911 + 0.497379i −0.877305 0.479933i \(-0.840661\pi\)
−0.211803 + 0.977312i \(0.567934\pi\)
\(38\) 12.0385 + 18.7323i 0.316803 + 0.492955i
\(39\) 12.8196 + 3.76417i 0.328708 + 0.0965173i
\(40\) 3.02999 0.435647i 0.0757498 0.0108912i
\(41\) −23.1881 + 50.7749i −0.565564 + 1.23841i 0.383562 + 0.923515i \(0.374697\pi\)
−0.949126 + 0.314897i \(0.898030\pi\)
\(42\) 4.24494 + 0.610331i 0.101070 + 0.0145317i
\(43\) −0.430823 + 0.670374i −0.0100191 + 0.0155901i −0.846227 0.532823i \(-0.821131\pi\)
0.836208 + 0.548413i \(0.184768\pi\)
\(44\) 47.5946 41.2410i 1.08170 0.937295i
\(45\) 8.21348i 0.182522i
\(46\) −52.2195 + 41.3445i −1.13521 + 0.898794i
\(47\) −77.4206 −1.64725 −0.823623 0.567137i \(-0.808051\pi\)
−0.823623 + 0.567137i \(0.808051\pi\)
\(48\) 16.2272 + 18.7272i 0.338067 + 0.390150i
\(49\) 40.6064 + 26.0962i 0.828703 + 0.532575i
\(50\) 7.21398 50.1744i 0.144280 1.00349i
\(51\) −19.9457 9.10888i −0.391091 0.178605i
\(52\) 4.81505 + 33.4894i 0.0925971 + 0.644027i
\(53\) −3.33004 + 11.3411i −0.0628309 + 0.213982i −0.984925 0.172984i \(-0.944659\pi\)
0.922094 + 0.386967i \(0.126477\pi\)
\(54\) −12.6587 + 8.13525i −0.234420 + 0.150653i
\(55\) 16.3301 + 35.7580i 0.296911 + 0.650145i
\(56\) 0.269333 + 0.917265i 0.00480952 + 0.0163797i
\(57\) 10.0652 + 8.72155i 0.176582 + 0.153010i
\(58\) 33.4144 38.5623i 0.576111 0.664867i
\(59\) 56.4505 16.5754i 0.956788 0.280938i 0.234178 0.972194i \(-0.424760\pi\)
0.722610 + 0.691256i \(0.242942\pi\)
\(60\) 18.9195 8.64027i 0.315326 0.144004i
\(61\) 45.9499 + 71.4994i 0.753276 + 1.17212i 0.980162 + 0.198200i \(0.0635094\pi\)
−0.226885 + 0.973922i \(0.572854\pi\)
\(62\) 67.3850 + 19.7860i 1.08686 + 0.319130i
\(63\) 2.53894 0.365044i 0.0403006 0.00579436i
\(64\) −31.4475 + 68.8603i −0.491367 + 1.07594i
\(65\) −20.9043 3.00558i −0.321604 0.0462397i
\(66\) 38.9360 60.5856i 0.589939 0.917963i
\(67\) 48.6048 42.1163i 0.725444 0.628601i −0.211784 0.977316i \(-0.567927\pi\)
0.937229 + 0.348715i \(0.113382\pi\)
\(68\) 55.5265i 0.816566i
\(69\) −23.0010 + 32.5262i −0.333348 + 0.471394i
\(70\) −6.77891 −0.0968416
\(71\) −63.4447 73.2190i −0.893587 1.03125i −0.999320 0.0368595i \(-0.988265\pi\)
0.105734 0.994394i \(-0.466281\pi\)
\(72\) −2.82181 1.81346i −0.0391917 0.0251870i
\(73\) −9.77406 + 67.9801i −0.133891 + 0.931234i 0.806523 + 0.591203i \(0.201347\pi\)
−0.940414 + 0.340031i \(0.889562\pi\)
\(74\) −116.695 53.2929i −1.57696 0.720174i
\(75\) −4.31475 30.0098i −0.0575300 0.400130i
\(76\) −9.50166 + 32.3597i −0.125022 + 0.425785i
\(77\) −10.3277 + 6.63720i −0.134126 + 0.0861974i
\(78\) 16.0729 + 35.1948i 0.206063 + 0.451215i
\(79\) −36.1212 123.018i −0.457231 1.55719i −0.789347 0.613947i \(-0.789581\pi\)
0.332116 0.943238i \(-0.392237\pi\)
\(80\) −29.6018 25.6501i −0.370022 0.320626i
\(81\) −5.89375 + 6.80175i −0.0727623 + 0.0839722i
\(82\) −155.098 + 45.5408i −1.89143 + 0.555375i
\(83\) 112.277 51.2752i 1.35274 0.617774i 0.398594 0.917128i \(-0.369498\pi\)
0.954142 + 0.299354i \(0.0967711\pi\)
\(84\) 3.51174 + 5.46437i 0.0418064 + 0.0650520i
\(85\) 33.2560 + 9.76483i 0.391247 + 0.114880i
\(86\) −2.28416 + 0.328413i −0.0265600 + 0.00381876i
\(87\) 12.6779 27.7608i 0.145723 0.319089i
\(88\) 15.8905 + 2.28471i 0.180574 + 0.0259626i
\(89\) 75.4594 117.417i 0.847858 1.31929i −0.0981567 0.995171i \(-0.531295\pi\)
0.946015 0.324123i \(-0.105069\pi\)
\(90\) 17.9757 15.5760i 0.199730 0.173067i
\(91\) 6.59548i 0.0724778i
\(92\) −99.1195 18.7658i −1.07739 0.203977i
\(93\) 42.0051 0.451668
\(94\) −146.820 169.439i −1.56192 1.80255i
\(95\) −17.7099 11.3815i −0.186420 0.119805i
\(96\) −11.3148 + 78.6959i −0.117862 + 0.819749i
\(97\) 69.0088 + 31.5153i 0.711431 + 0.324900i 0.738050 0.674746i \(-0.235747\pi\)
−0.0266189 + 0.999646i \(0.508474\pi\)
\(98\) 19.8929 + 138.358i 0.202989 + 1.41182i
\(99\) 12.1356 41.3299i 0.122581 0.417474i
\(100\) 64.5878 41.5080i 0.645878 0.415080i
\(101\) 14.7084 + 32.2069i 0.145628 + 0.318880i 0.968364 0.249544i \(-0.0802806\pi\)
−0.822736 + 0.568424i \(0.807553\pi\)
\(102\) −17.8896 60.9262i −0.175388 0.597316i
\(103\) 54.5575 + 47.2744i 0.529685 + 0.458974i 0.878176 0.478338i \(-0.158760\pi\)
−0.348491 + 0.937312i \(0.613306\pi\)
\(104\) −5.64807 + 6.51821i −0.0543083 + 0.0626751i
\(105\) −3.89030 + 1.14229i −0.0370504 + 0.0108790i
\(106\) −31.1357 + 14.2192i −0.293733 + 0.134143i
\(107\) 74.3782 + 115.735i 0.695123 + 1.08163i 0.991941 + 0.126699i \(0.0404381\pi\)
−0.296818 + 0.954934i \(0.595926\pi\)
\(108\) −21.8677 6.42092i −0.202478 0.0594530i
\(109\) −111.760 + 16.0687i −1.02532 + 0.147419i −0.634400 0.773005i \(-0.718753\pi\)
−0.390922 + 0.920424i \(0.627844\pi\)
\(110\) −47.2900 + 103.551i −0.429909 + 0.941370i
\(111\) −75.9494 10.9199i −0.684229 0.0983773i
\(112\) 6.61329 10.2905i 0.0590472 0.0918793i
\(113\) 84.1728 72.9361i 0.744892 0.645452i −0.197370 0.980329i \(-0.563240\pi\)
0.942262 + 0.334877i \(0.108695\pi\)
\(114\) 38.5678i 0.338314i
\(115\) 28.6703 56.0646i 0.249307 0.487518i
\(116\) 77.2829 0.666232
\(117\) 15.1545 + 17.4892i 0.129526 + 0.149481i
\(118\) 143.329 + 92.1117i 1.21465 + 0.780607i
\(119\) −1.54045 + 10.7140i −0.0129449 + 0.0900339i
\(120\) 4.82293 + 2.20256i 0.0401911 + 0.0183547i
\(121\) 12.1194 + 84.2926i 0.100161 + 0.696633i
\(122\) −69.3414 + 236.155i −0.568372 + 1.93570i
\(123\) −81.3338 + 52.2700i −0.661250 + 0.424960i
\(124\) 44.1878 + 96.7578i 0.356353 + 0.780305i
\(125\) 32.7850 + 111.656i 0.262280 + 0.893245i
\(126\) 5.61375 + 4.86435i 0.0445536 + 0.0386059i
\(127\) 131.118 151.318i 1.03242 1.19148i 0.0511833 0.998689i \(-0.483701\pi\)
0.981240 0.192791i \(-0.0617538\pi\)
\(128\) −34.1698 + 10.0332i −0.266952 + 0.0783841i
\(129\) −1.25550 + 0.573367i −0.00973255 + 0.00444471i
\(130\) −33.0649 51.4499i −0.254345 0.395769i
\(131\) −24.1650 7.09549i −0.184466 0.0541641i 0.188195 0.982132i \(-0.439736\pi\)
−0.372661 + 0.927968i \(0.621554\pi\)
\(132\) 107.969 15.5235i 0.817944 0.117603i
\(133\) 2.73112 5.98031i 0.0205347 0.0449648i
\(134\) 184.348 + 26.5052i 1.37573 + 0.197800i
\(135\) 7.69124 11.9678i 0.0569722 0.0886504i
\(136\) 10.6974 9.26936i 0.0786574 0.0681571i
\(137\) 152.155i 1.11062i 0.831642 + 0.555312i \(0.187401\pi\)
−0.831642 + 0.555312i \(0.812599\pi\)
\(138\) −114.804 + 11.3436i −0.831916 + 0.0822002i
\(139\) 125.829 0.905248 0.452624 0.891702i \(-0.350488\pi\)
0.452624 + 0.891702i \(0.350488\pi\)
\(140\) −6.72369 7.75955i −0.0480263 0.0554254i
\(141\) −112.809 72.4980i −0.800064 0.514170i
\(142\) 39.9279 277.705i 0.281182 1.95567i
\(143\) −100.749 46.0104i −0.704536 0.321751i
\(144\) 6.10809 + 42.4827i 0.0424173 + 0.295019i
\(145\) −13.5909 + 46.2863i −0.0937302 + 0.319216i
\(146\) −167.314 + 107.526i −1.14599 + 0.736480i
\(147\) 34.7305 + 76.0491i 0.236262 + 0.517341i
\(148\) −54.7422 186.435i −0.369880 1.25970i
\(149\) −89.4941 77.5471i −0.600632 0.520450i 0.300621 0.953744i \(-0.402806\pi\)
−0.901253 + 0.433293i \(0.857351\pi\)
\(150\) 57.4956 66.3534i 0.383304 0.442356i
\(151\) −203.060 + 59.6239i −1.34477 + 0.394860i −0.873369 0.487059i \(-0.838070\pi\)
−0.471401 + 0.881919i \(0.656252\pi\)
\(152\) −7.82039 + 3.57145i −0.0514499 + 0.0234964i
\(153\) −20.5330 31.9499i −0.134202 0.208823i
\(154\) −34.1113 10.0160i −0.221502 0.0650387i
\(155\) −65.7210 + 9.44926i −0.424007 + 0.0609630i
\(156\) −24.3441 + 53.3061i −0.156052 + 0.341706i
\(157\) −173.765 24.9836i −1.10678 0.159131i −0.435395 0.900239i \(-0.643391\pi\)
−0.671385 + 0.741108i \(0.734300\pi\)
\(158\) 200.731 312.344i 1.27045 1.97686i
\(159\) −15.4722 + 13.4067i −0.0973092 + 0.0843189i
\(160\) 125.673i 0.785454i
\(161\) 18.6048 + 6.37076i 0.115558 + 0.0395699i
\(162\) −26.0629 −0.160882
\(163\) −145.264 167.644i −0.891191 1.02849i −0.999409 0.0343623i \(-0.989060\pi\)
0.108218 0.994127i \(-0.465485\pi\)
\(164\) −205.963 132.364i −1.25587 0.807099i
\(165\) −9.68988 + 67.3946i −0.0587265 + 0.408452i
\(166\) 325.141 + 148.487i 1.95868 + 0.894498i
\(167\) −4.95824 34.4853i −0.0296901 0.206499i 0.969577 0.244788i \(-0.0787184\pi\)
−0.999267 + 0.0382889i \(0.987809\pi\)
\(168\) −0.466499 + 1.58875i −0.00277678 + 0.00945685i
\(169\) −92.1142 + 59.1982i −0.545054 + 0.350285i
\(170\) 41.6956 + 91.3006i 0.245268 + 0.537062i
\(171\) 6.49893 + 22.1333i 0.0380055 + 0.129435i
\(172\) −2.64147 2.28885i −0.0153574 0.0133073i
\(173\) −48.0161 + 55.4136i −0.277550 + 0.320310i −0.877360 0.479833i \(-0.840697\pi\)
0.599810 + 0.800142i \(0.295243\pi\)
\(174\) 84.7983 24.8990i 0.487347 0.143098i
\(175\) −13.6140 + 6.21729i −0.0777942 + 0.0355274i
\(176\) −111.057 172.808i −0.631004 0.981861i
\(177\) 97.7751 + 28.7094i 0.552402 + 0.162200i
\(178\) 400.075 57.5221i 2.24761 0.323158i
\(179\) 56.9706 124.748i 0.318271 0.696917i −0.681107 0.732184i \(-0.738501\pi\)
0.999378 + 0.0352673i \(0.0112282\pi\)
\(180\) 35.6584 + 5.12691i 0.198102 + 0.0284828i
\(181\) −162.535 + 252.909i −0.897982 + 1.39729i 0.0196295 + 0.999807i \(0.493751\pi\)
−0.917611 + 0.397479i \(0.869885\pi\)
\(182\) 14.4346 12.5076i 0.0793109 0.0687233i
\(183\) 147.210i 0.804424i
\(184\) −12.9313 22.2285i −0.0702786 0.120807i
\(185\) 121.287 0.655603
\(186\) 79.6583 + 91.9306i 0.428271 + 0.494251i
\(187\) 152.915 + 98.2726i 0.817728 + 0.525522i
\(188\) 48.3265 336.118i 0.257056 1.78786i
\(189\) 4.04131 + 1.84560i 0.0213826 + 0.00976510i
\(190\) −8.67601 60.3430i −0.0456632 0.317595i
\(191\) 7.79755 26.5560i 0.0408249 0.139037i −0.936559 0.350511i \(-0.886008\pi\)
0.977384 + 0.211474i \(0.0678263\pi\)
\(192\) −110.304 + 70.8880i −0.574500 + 0.369209i
\(193\) −55.4373 121.391i −0.287240 0.628967i 0.709920 0.704282i \(-0.248731\pi\)
−0.997160 + 0.0753150i \(0.976004\pi\)
\(194\) 61.8951 + 210.795i 0.319047 + 1.08657i
\(195\) −27.6450 23.9545i −0.141769 0.122844i
\(196\) −138.642 + 160.002i −0.707358 + 0.816334i
\(197\) 149.905 44.0160i 0.760938 0.223432i 0.121833 0.992551i \(-0.461123\pi\)
0.639106 + 0.769119i \(0.279305\pi\)
\(198\) 113.467 51.8185i 0.573064 0.261710i
\(199\) −32.8050 51.0456i −0.164849 0.256511i 0.748995 0.662576i \(-0.230537\pi\)
−0.913844 + 0.406065i \(0.866901\pi\)
\(200\) 18.7787 + 5.51393i 0.0938935 + 0.0275696i
\(201\) 110.260 15.8530i 0.548558 0.0788707i
\(202\) −42.5937 + 93.2673i −0.210860 + 0.461719i
\(203\) −14.9120 2.14402i −0.0734582 0.0105617i
\(204\) 51.9960 80.9073i 0.254882 0.396605i
\(205\) 115.496 100.078i 0.563395 0.488185i
\(206\) 209.053i 1.01482i
\(207\) −63.9727 + 25.8552i −0.309047 + 0.124905i
\(208\) 110.359 0.530570
\(209\) −72.2994 83.4379i −0.345930 0.399224i
\(210\) −9.87751 6.34789i −0.0470358 0.0302281i
\(211\) −1.27382 + 8.85960i −0.00603705 + 0.0419886i −0.992617 0.121289i \(-0.961297\pi\)
0.986580 + 0.163277i \(0.0522065\pi\)
\(212\) −47.1581 21.5364i −0.222444 0.101587i
\(213\) −23.8812 166.098i −0.112119 0.779801i
\(214\) −112.242 + 382.260i −0.524493 + 1.78626i
\(215\) 1.83537 1.17952i 0.00853659 0.00548613i
\(216\) −2.41348 5.28477i −0.0111735 0.0244665i
\(217\) −5.84189 19.8956i −0.0269211 0.0916849i
\(218\) −247.109 214.121i −1.13353 0.982206i
\(219\) −77.8995 + 89.9008i −0.355705 + 0.410506i
\(220\) −165.435 + 48.5761i −0.751978 + 0.220801i
\(221\) −88.8300 + 40.5673i −0.401946 + 0.183562i
\(222\) −120.131 186.928i −0.541132 0.842018i
\(223\) −146.921 43.1400i −0.658840 0.193453i −0.0648124 0.997897i \(-0.520645\pi\)
−0.594028 + 0.804445i \(0.702463\pi\)
\(224\) 38.8477 5.58546i 0.173427 0.0249351i
\(225\) 21.8147 47.7674i 0.0969540 0.212300i
\(226\) 319.250 + 45.9012i 1.41261 + 0.203103i
\(227\) −155.468 + 241.913i −0.684882 + 1.06570i 0.308543 + 0.951210i \(0.400159\pi\)
−0.993425 + 0.114487i \(0.963478\pi\)
\(228\) −44.1470 + 38.2536i −0.193627 + 0.167779i
\(229\) 260.408i 1.13715i 0.822630 + 0.568577i \(0.192506\pi\)
−0.822630 + 0.568577i \(0.807494\pi\)
\(230\) 177.071 43.5740i 0.769873 0.189452i
\(231\) −21.2636 −0.0920501
\(232\) 12.9013 + 14.8889i 0.0556090 + 0.0641762i
\(233\) −84.4992 54.3044i −0.362658 0.233066i 0.346604 0.938012i \(-0.387335\pi\)
−0.709261 + 0.704946i \(0.750971\pi\)
\(234\) −9.53725 + 66.3331i −0.0407575 + 0.283475i
\(235\) 192.809 + 88.0531i 0.820465 + 0.374694i
\(236\) 36.7244 + 255.424i 0.155612 + 1.08230i
\(237\) 62.5638 213.073i 0.263982 0.899041i
\(238\) −26.3696 + 16.9467i −0.110797 + 0.0712046i
\(239\) 18.0220 + 39.4626i 0.0754058 + 0.165116i 0.943581 0.331143i \(-0.107434\pi\)
−0.868175 + 0.496258i \(0.834707\pi\)
\(240\) −19.1134 65.0942i −0.0796391 0.271226i
\(241\) −337.253 292.232i −1.39939 1.21258i −0.947194 0.320662i \(-0.896095\pi\)
−0.452198 0.891918i \(-0.649360\pi\)
\(242\) −161.496 + 186.376i −0.667338 + 0.770150i
\(243\) −14.9570 + 4.39178i −0.0615515 + 0.0180732i
\(244\) −339.094 + 154.859i −1.38973 + 0.634667i
\(245\) −71.4468 111.173i −0.291619 0.453769i
\(246\) −268.637 78.8789i −1.09202 0.320646i
\(247\) 58.7101 8.44123i 0.237693 0.0341750i
\(248\) −11.2643 + 24.6653i −0.0454204 + 0.0994568i
\(249\) 211.613 + 30.4254i 0.849852 + 0.122190i
\(250\) −182.191 + 283.495i −0.728765 + 1.13398i
\(251\) 225.612 195.494i 0.898853 0.778861i −0.0770584 0.997027i \(-0.524553\pi\)
0.975912 + 0.218166i \(0.0700073\pi\)
\(252\) 11.2506i 0.0446451i
\(253\) 227.104 239.754i 0.897645 0.947644i
\(254\) 579.819 2.28275
\(255\) 39.3131 + 45.3697i 0.154169 + 0.177921i
\(256\) 167.978 + 107.953i 0.656166 + 0.421692i
\(257\) −38.1648 + 265.442i −0.148501 + 1.03285i 0.770173 + 0.637835i \(0.220170\pi\)
−0.918675 + 0.395015i \(0.870739\pi\)
\(258\) −3.63577 1.66040i −0.0140921 0.00643566i
\(259\) 5.39053 + 37.4920i 0.0208129 + 0.144757i
\(260\) 26.0972 88.8788i 0.100374 0.341841i
\(261\) 44.4686 28.5782i 0.170378 0.109495i
\(262\) −30.2976 66.3424i −0.115640 0.253215i
\(263\) −5.72193 19.4871i −0.0217564 0.0740955i 0.947899 0.318570i \(-0.103203\pi\)
−0.969656 + 0.244475i \(0.921384\pi\)
\(264\) 21.0145 + 18.2092i 0.0796004 + 0.0689741i
\(265\) 21.1918 24.4566i 0.0799689 0.0922890i
\(266\) 18.2675 5.36383i 0.0686749 0.0201648i
\(267\) 219.903 100.426i 0.823606 0.376128i
\(268\) 152.506 + 237.305i 0.569054 + 0.885465i
\(269\) 331.096 + 97.2184i 1.23084 + 0.361407i 0.831566 0.555425i \(-0.187445\pi\)
0.399272 + 0.916832i \(0.369263\pi\)
\(270\) 40.7779 5.86297i 0.151029 0.0217147i
\(271\) 161.598 353.851i 0.596303 1.30572i −0.335254 0.942128i \(-0.608822\pi\)
0.931557 0.363594i \(-0.118451\pi\)
\(272\) −179.272 25.7755i −0.659089 0.0947627i
\(273\) 6.17612 9.61023i 0.0226231 0.0352023i
\(274\) −333.001 + 288.547i −1.21533 + 1.05309i
\(275\) 251.331i 0.913932i
\(276\) −126.854 120.161i −0.459615 0.435365i
\(277\) −87.8143 −0.317019 −0.158510 0.987357i \(-0.550669\pi\)
−0.158510 + 0.987357i \(0.550669\pi\)
\(278\) 238.622 + 275.385i 0.858354 + 0.990593i
\(279\) 61.2054 + 39.3343i 0.219374 + 0.140983i
\(280\) 0.372485 2.59069i 0.00133030 0.00925247i
\(281\) −229.204 104.674i −0.815671 0.372505i −0.0365141 0.999333i \(-0.511625\pi\)
−0.779157 + 0.626829i \(0.784353\pi\)
\(282\) −55.2646 384.374i −0.195974 1.36303i
\(283\) −41.1308 + 140.079i −0.145338 + 0.494977i −0.999695 0.0247106i \(-0.992134\pi\)
0.854356 + 0.519688i \(0.173952\pi\)
\(284\) 357.480 229.738i 1.25873 0.808938i
\(285\) −15.1472 33.1678i −0.0531481 0.116378i
\(286\) −90.3630 307.748i −0.315954 1.07604i
\(287\) 36.0691 + 31.2541i 0.125676 + 0.108899i
\(288\) −90.1789 + 104.072i −0.313121 + 0.361361i
\(289\) −123.518 + 36.2683i −0.427400 + 0.125496i
\(290\) −127.074 + 58.0327i −0.438186 + 0.200113i
\(291\) 71.0409 + 110.542i 0.244127 + 0.379869i
\(292\) −289.032 84.8673i −0.989834 0.290641i
\(293\) 180.430 25.9419i 0.615801 0.0885388i 0.172646 0.984984i \(-0.444768\pi\)
0.443155 + 0.896445i \(0.353859\pi\)
\(294\) −100.575 + 220.229i −0.342092 + 0.749078i
\(295\) −159.437 22.9236i −0.540464 0.0777070i
\(296\) 26.7790 41.6690i 0.0904696 0.140774i
\(297\) 56.3847 48.8576i 0.189848 0.164504i
\(298\) 342.923i 1.15075i
\(299\) 42.3949 + 172.279i 0.141789 + 0.576185i
\(300\) 132.979 0.443264
\(301\) 0.446183 + 0.514923i 0.00148234 + 0.00171071i
\(302\) −515.573 331.339i −1.70720 1.09715i
\(303\) −8.72759 + 60.7017i −0.0288039 + 0.200336i
\(304\) 100.065 + 45.6983i 0.329163 + 0.150323i
\(305\) −33.1155 230.323i −0.108575 0.755159i
\(306\) 30.9856 105.527i 0.101260 0.344861i
\(307\) 301.838 193.979i 0.983185 0.631855i 0.0528644 0.998602i \(-0.483165\pi\)
0.930321 + 0.366747i \(0.119529\pi\)
\(308\) −22.3685 48.9801i −0.0726249 0.159026i
\(309\) 35.2269 + 119.972i 0.114003 + 0.388258i
\(310\) −145.313 125.915i −0.468753 0.406176i
\(311\) −373.961 + 431.574i −1.20245 + 1.38770i −0.301672 + 0.953412i \(0.597545\pi\)
−0.900775 + 0.434286i \(0.857001\pi\)
\(312\) −14.3335 + 4.20870i −0.0459408 + 0.0134894i
\(313\) 141.745 64.7326i 0.452858 0.206814i −0.175910 0.984406i \(-0.556287\pi\)
0.628768 + 0.777593i \(0.283559\pi\)
\(314\) −274.848 427.672i −0.875313 1.36201i
\(315\) −6.73819 1.97851i −0.0213911 0.00628099i
\(316\) 556.623 80.0303i 1.76146 0.253260i
\(317\) 182.895 400.484i 0.576955 1.26336i −0.366055 0.930593i \(-0.619292\pi\)
0.943011 0.332763i \(-0.107981\pi\)
\(318\) −58.6827 8.43729i −0.184537 0.0265324i
\(319\) −136.778 + 212.830i −0.428770 + 0.667179i
\(320\) 156.634 135.725i 0.489483 0.424139i
\(321\) 238.285i 0.742322i
\(322\) 21.3394 + 52.7992i 0.0662713 + 0.163973i
\(323\) −97.3432 −0.301372
\(324\) −25.8506 29.8331i −0.0797857 0.0920776i
\(325\) −113.591 73.0005i −0.349511 0.224617i
\(326\) 91.4197 635.838i 0.280428 1.95042i
\(327\) −177.892 81.2406i −0.544012 0.248442i
\(328\) −8.88203 61.7759i −0.0270794 0.188341i
\(329\) −18.6495 + 63.5145i −0.0566855 + 0.193053i
\(330\) −165.873 + 106.600i −0.502645 + 0.323030i
\(331\) −109.190 239.093i −0.329880 0.722336i 0.669918 0.742435i \(-0.266329\pi\)
−0.999798 + 0.0200987i \(0.993602\pi\)
\(332\) 152.525 + 519.452i 0.459412 + 1.56462i
\(333\) −100.440 87.0316i −0.301621 0.261356i
\(334\) 66.0704 76.2493i 0.197815 0.228291i
\(335\) −168.946 + 49.6071i −0.504317 + 0.148081i
\(336\) 19.2724 8.80139i 0.0573582 0.0261946i
\(337\) 231.670 + 360.485i 0.687447 + 1.06969i 0.993069 + 0.117535i \(0.0374993\pi\)
−0.305622 + 0.952153i \(0.598864\pi\)
\(338\) −304.244 89.3340i −0.900129 0.264302i
\(339\) 190.946 27.4539i 0.563263 0.0809850i
\(340\) −63.1522 + 138.284i −0.185742 + 0.406718i
\(341\) −344.667 49.5557i −1.01075 0.145325i
\(342\) −36.1155 + 56.1969i −0.105601 + 0.164318i
\(343\) 62.8531 54.4625i 0.183245 0.158783i
\(344\) 0.890982i 0.00259006i
\(345\) 94.2751 54.8440i 0.273261 0.158968i
\(346\) −212.333 −0.613680
\(347\) 154.365 + 178.146i 0.444855 + 0.513390i 0.933248 0.359234i \(-0.116962\pi\)
−0.488392 + 0.872624i \(0.662416\pi\)
\(348\) 112.608 + 72.3690i 0.323587 + 0.207957i
\(349\) −16.3941 + 114.024i −0.0469745 + 0.326715i 0.952761 + 0.303721i \(0.0982290\pi\)
−0.999736 + 0.0229943i \(0.992680\pi\)
\(350\) −39.4244 18.0045i −0.112641 0.0514415i
\(351\) 5.70432 + 39.6744i 0.0162516 + 0.113033i
\(352\) 185.683 632.380i 0.527510 1.79653i
\(353\) 149.047 95.7870i 0.422231 0.271351i −0.312225 0.950008i \(-0.601074\pi\)
0.734455 + 0.678657i \(0.237438\pi\)
\(354\) 122.588 + 268.431i 0.346294 + 0.758279i
\(355\) 74.7290 + 254.503i 0.210504 + 0.716911i
\(356\) 462.659 + 400.896i 1.29960 + 1.12611i
\(357\) −12.2774 + 14.1689i −0.0343904 + 0.0396887i
\(358\) 381.057 111.888i 1.06441 0.312538i
\(359\) −120.224 + 54.9043i −0.334885 + 0.152937i −0.575759 0.817620i \(-0.695293\pi\)
0.240874 + 0.970556i \(0.422566\pi\)
\(360\) 4.96495 + 7.72561i 0.0137915 + 0.0214600i
\(361\) −289.647 85.0481i −0.802347 0.235590i
\(362\) −861.736 + 123.899i −2.38049 + 0.342262i
\(363\) −61.2739 + 134.171i −0.168799 + 0.369617i
\(364\) 28.6340 + 4.11694i 0.0786647 + 0.0113103i
\(365\) 101.658 158.182i 0.278514 0.433376i
\(366\) −322.177 + 279.168i −0.880264 + 0.762753i
\(367\) 136.353i 0.371533i 0.982594 + 0.185767i \(0.0594769\pi\)
−0.982594 + 0.185767i \(0.940523\pi\)
\(368\) −106.599 + 311.305i −0.289670 + 0.845937i
\(369\) −167.458 −0.453814
\(370\) 230.007 + 265.443i 0.621641 + 0.717412i
\(371\) 8.50185 + 5.46381i 0.0229160 + 0.0147272i
\(372\) −26.2199 + 182.363i −0.0704836 + 0.490224i
\(373\) 192.825 + 88.0602i 0.516957 + 0.236086i 0.656769 0.754092i \(-0.271923\pi\)
−0.139812 + 0.990178i \(0.544650\pi\)
\(374\) 74.9124 + 521.027i 0.200301 + 1.39312i
\(375\) −56.7854 + 193.393i −0.151428 + 0.515715i
\(376\) 72.8219 46.7998i 0.193675 0.124468i
\(377\) −56.4624 123.635i −0.149768 0.327945i
\(378\) 3.62471 + 12.3446i 0.00958918 + 0.0326577i
\(379\) 322.445 + 279.400i 0.850779 + 0.737204i 0.966661 0.256059i \(-0.0824242\pi\)
−0.115883 + 0.993263i \(0.536970\pi\)
\(380\) 60.4668 69.7824i 0.159123 0.183638i
\(381\) 332.748 97.7035i 0.873353 0.256440i
\(382\) 72.9066 33.2953i 0.190855 0.0871606i
\(383\) −47.8290 74.4234i −0.124880 0.194317i 0.773184 0.634182i \(-0.218663\pi\)
−0.898064 + 0.439865i \(0.855026\pi\)
\(384\) −59.1839 17.3780i −0.154125 0.0452551i
\(385\) 33.2689 4.78335i 0.0864127 0.0124243i
\(386\) 160.539 351.532i 0.415905 0.910706i
\(387\) −2.36629 0.340221i −0.00611445 0.000879125i
\(388\) −179.898 + 279.927i −0.463654 + 0.721460i
\(389\) 251.801 218.187i 0.647304 0.560892i −0.268119 0.963386i \(-0.586402\pi\)
0.915423 + 0.402494i \(0.131857\pi\)
\(390\) 105.930i 0.271615i
\(391\) −28.6308 289.761i −0.0732245 0.741077i
\(392\) −53.9693 −0.137677
\(393\) −28.5664 32.9673i −0.0726880 0.0838864i
\(394\) 380.610 + 244.603i 0.966016 + 0.620821i
\(395\) −49.9553 + 347.447i −0.126469 + 0.879612i
\(396\) 171.857 + 78.4844i 0.433982 + 0.198193i
\(397\) −7.83946 54.5247i −0.0197468 0.137342i 0.977563 0.210643i \(-0.0675557\pi\)
−0.997310 + 0.0733011i \(0.976647\pi\)
\(398\) 49.5050 168.598i 0.124384 0.423614i
\(399\) 9.57956 6.15641i 0.0240089 0.0154296i
\(400\) −104.031 227.795i −0.260077 0.569489i
\(401\) −3.28237 11.1787i −0.00818547 0.0278772i 0.955299 0.295641i \(-0.0955333\pi\)
−0.963484 + 0.267764i \(0.913715\pi\)
\(402\) 243.792 + 211.247i 0.606448 + 0.525490i
\(403\) 122.507 141.381i 0.303989 0.350822i
\(404\) −149.006 + 43.7521i −0.368827 + 0.108297i
\(405\) 22.4137 10.2360i 0.0553425 0.0252741i
\(406\) −23.5867 36.7017i −0.0580954 0.0903983i
\(407\) 610.310 + 179.203i 1.49953 + 0.440302i
\(408\) 24.2671 3.48909i 0.0594782 0.00855168i
\(409\) 12.1546 26.6148i 0.0297178 0.0650730i −0.894191 0.447686i \(-0.852248\pi\)
0.923909 + 0.382613i \(0.124976\pi\)
\(410\) 438.052 + 62.9824i 1.06842 + 0.153616i
\(411\) −142.481 + 221.705i −0.346669 + 0.539427i
\(412\) −239.295 + 207.350i −0.580812 + 0.503277i
\(413\) 50.3037i 0.121801i
\(414\) −177.903 90.9762i −0.429718 0.219749i
\(415\) −337.933 −0.814298
\(416\) 231.876 + 267.599i 0.557394 + 0.643267i
\(417\) 183.345 + 117.829i 0.439677 + 0.282563i
\(418\) 45.5004 316.463i 0.108853 0.757087i
\(419\) −63.1631 28.8456i −0.150747 0.0688440i 0.338613 0.940926i \(-0.390042\pi\)
−0.489360 + 0.872082i \(0.662770\pi\)
\(420\) −2.53087 17.6026i −0.00602587 0.0419109i
\(421\) −36.5955 + 124.633i −0.0869253 + 0.296040i −0.991469 0.130340i \(-0.958393\pi\)
0.904544 + 0.426380i \(0.140211\pi\)
\(422\) −21.8054 + 14.0135i −0.0516716 + 0.0332073i
\(423\) −96.4850 211.273i −0.228097 0.499463i
\(424\) −3.72330 12.6804i −0.00878137 0.0299066i
\(425\) 167.473 + 145.116i 0.394054 + 0.341450i
\(426\) 318.226 367.252i 0.747009 0.862095i
\(427\) 69.7255 20.4732i 0.163292 0.0479467i
\(428\) −548.884 + 250.667i −1.28244 + 0.585671i
\(429\) −103.715 161.384i −0.241761 0.376187i
\(430\) 6.06203 + 1.77997i 0.0140977 + 0.00413947i
\(431\) −466.243 + 67.0356i −1.08177 + 0.155535i −0.660073 0.751202i \(-0.729475\pi\)
−0.421697 + 0.906737i \(0.638565\pi\)
\(432\) −30.8815 + 67.6211i −0.0714850 + 0.156530i
\(433\) −696.818 100.187i −1.60928 0.231379i −0.721758 0.692145i \(-0.756666\pi\)
−0.887522 + 0.460766i \(0.847575\pi\)
\(434\) 32.4642 50.5153i 0.0748023 0.116395i
\(435\) −63.1465 + 54.7168i −0.145164 + 0.125786i
\(436\) 495.232i 1.13585i
\(437\) −32.8983 + 173.766i −0.0752822 + 0.397634i
\(438\) −344.481 −0.786487
\(439\) −537.557 620.374i −1.22450 1.41315i −0.880408 0.474217i \(-0.842731\pi\)
−0.344095 0.938935i \(-0.611814\pi\)
\(440\) −36.9754 23.7627i −0.0840351 0.0540060i
\(441\) −20.6082 + 143.333i −0.0467305 + 0.325018i
\(442\) −257.241 117.478i −0.581992 0.265787i
\(443\) 53.7758 + 374.019i 0.121390 + 0.844286i 0.955984 + 0.293420i \(0.0947935\pi\)
−0.834594 + 0.550866i \(0.814297\pi\)
\(444\) 94.8163 322.915i 0.213550 0.727285i
\(445\) −321.468 + 206.595i −0.722399 + 0.464258i
\(446\) −184.207 403.356i −0.413019 0.904386i
\(447\) −57.7849 196.797i −0.129273 0.440262i
\(448\) 48.9165 + 42.3864i 0.109189 + 0.0946125i
\(449\) 524.556 605.370i 1.16828 1.34826i 0.242519 0.970147i \(-0.422026\pi\)
0.925758 0.378117i \(-0.123428\pi\)
\(450\) 145.911 42.8433i 0.324247 0.0952074i
\(451\) 729.039 332.941i 1.61649 0.738228i
\(452\) 264.108 + 410.959i 0.584309 + 0.909202i
\(453\) −351.711 103.272i −0.776404 0.227973i
\(454\) −824.270 + 118.512i −1.81557 + 0.261040i
\(455\) −7.50126 + 16.4255i −0.0164863 + 0.0360999i
\(456\) −14.7394 2.11921i −0.0323233 0.00464739i
\(457\) 386.985 602.160i 0.846793 1.31764i −0.0997346 0.995014i \(-0.531799\pi\)
0.946528 0.322622i \(-0.104564\pi\)
\(458\) −569.918 + 493.837i −1.24436 + 1.07825i
\(459\) 65.7815i 0.143315i
\(460\) 225.506 + 159.467i 0.490229 + 0.346667i
\(461\) 117.233 0.254302 0.127151 0.991883i \(-0.459417\pi\)
0.127151 + 0.991883i \(0.459417\pi\)
\(462\) −40.3242 46.5366i −0.0872818 0.100729i
\(463\) 293.087 + 188.356i 0.633018 + 0.406816i 0.817426 0.576034i \(-0.195400\pi\)
−0.184408 + 0.982850i \(0.559037\pi\)
\(464\) 35.8748 249.515i 0.0773164 0.537747i
\(465\) −104.610 47.7739i −0.224968 0.102739i
\(466\) −41.3958 287.914i −0.0888321 0.617841i
\(467\) 62.2036 211.846i 0.133198 0.453631i −0.865700 0.500563i \(-0.833126\pi\)
0.998898 + 0.0469320i \(0.0149444\pi\)
\(468\) −85.3883 + 54.8757i −0.182454 + 0.117256i
\(469\) −22.8432 50.0197i −0.0487062 0.106652i
\(470\) 172.934 + 588.958i 0.367944 + 1.25310i
\(471\) −229.796 199.120i −0.487890 0.422759i
\(472\) −43.0778 + 49.7144i −0.0912666 + 0.105327i
\(473\) 10.9783 3.22351i 0.0232098 0.00681503i
\(474\) 584.968 267.146i 1.23411 0.563599i
\(475\) −72.7675 113.229i −0.153195 0.238376i
\(476\) −45.5529 13.3756i −0.0956995 0.0280999i
\(477\) −35.0986 + 5.04642i −0.0735821 + 0.0105795i
\(478\) −52.1894 + 114.279i −0.109183 + 0.239077i
\(479\) −267.088 38.4015i −0.557595 0.0801701i −0.142245 0.989832i \(-0.545432\pi\)
−0.415350 + 0.909661i \(0.636341\pi\)
\(480\) 117.682 183.117i 0.245171 0.381493i
\(481\) −258.260 + 223.783i −0.536923 + 0.465246i
\(482\) 1292.29i 2.68109i
\(483\) 21.1433 + 26.7047i 0.0437750 + 0.0552892i
\(484\) −373.518 −0.771730
\(485\) −136.017 156.972i −0.280448 0.323654i
\(486\) −37.9761 24.4057i −0.0781401 0.0502176i
\(487\) −122.674 + 853.214i −0.251897 + 1.75198i 0.334909 + 0.942251i \(0.391295\pi\)
−0.586805 + 0.809728i \(0.699615\pi\)
\(488\) −86.4410 39.4763i −0.177133 0.0808941i
\(489\) −54.6790 380.301i −0.111818 0.777711i
\(490\) 107.818 367.194i 0.220036 0.749375i
\(491\) 373.657 240.135i 0.761013 0.489073i −0.101670 0.994818i \(-0.532419\pi\)
0.862683 + 0.505745i \(0.168782\pi\)
\(492\) −176.159 385.734i −0.358047 0.784013i
\(493\) 62.8440 + 214.027i 0.127473 + 0.434132i
\(494\) 129.812 + 112.482i 0.262777 + 0.227697i
\(495\) −77.2285 + 89.1264i −0.156017 + 0.180053i
\(496\) 332.903 97.7492i 0.671176 0.197075i
\(497\) −75.3505 + 34.4114i −0.151611 + 0.0692383i
\(498\) 334.715 + 520.826i 0.672118 + 1.04584i
\(499\) 312.089 + 91.6375i 0.625428 + 0.183642i 0.579064 0.815282i \(-0.303418\pi\)
0.0463644 + 0.998925i \(0.485236\pi\)
\(500\) −505.213 + 72.6386i −1.01043 + 0.145277i
\(501\) 25.0680 54.8914i 0.0500360 0.109564i
\(502\) 855.700 + 123.031i 1.70458 + 0.245082i
\(503\) 230.636 358.876i 0.458521 0.713472i −0.532610 0.846361i \(-0.678789\pi\)
0.991131 + 0.132888i \(0.0424252\pi\)
\(504\) −2.16747 + 1.87812i −0.00430053 + 0.00372643i
\(505\) 96.9369i 0.191954i
\(506\) 955.395 + 42.3624i 1.88813 + 0.0837201i
\(507\) −189.653 −0.374069
\(508\) 575.095 + 663.696i 1.13208 + 1.30649i
\(509\) −225.058 144.636i −0.442158 0.284158i 0.300559 0.953763i \(-0.402827\pi\)
−0.742717 + 0.669606i \(0.766463\pi\)
\(510\) −24.7411 + 172.078i −0.0485119 + 0.337408i
\(511\) 53.4152 + 24.3939i 0.104531 + 0.0477376i
\(512\) 102.564 + 713.352i 0.200321 + 1.39327i
\(513\) −11.2565 + 38.3361i −0.0219425 + 0.0747292i
\(514\) −653.311 + 419.858i −1.27103 + 0.816844i
\(515\) −82.1041 179.783i −0.159425 0.349093i
\(516\) −1.70556 5.80859i −0.00330534 0.0112570i
\(517\) 840.110 + 727.959i 1.62497 + 1.40804i
\(518\) −71.8307 + 82.8971i −0.138669 + 0.160033i
\(519\) −121.854 + 35.7796i −0.234787 + 0.0689395i
\(520\) 21.4794 9.80932i 0.0413066 0.0188641i
\(521\) 190.231 + 296.006i 0.365127 + 0.568149i 0.974403 0.224810i \(-0.0721760\pi\)
−0.609275 + 0.792959i \(0.708540\pi\)
\(522\) 146.875 + 43.1264i 0.281370 + 0.0826176i
\(523\) −595.088 + 85.5608i −1.13784 + 0.163596i −0.685377 0.728189i \(-0.740362\pi\)
−0.452459 + 0.891785i \(0.649453\pi\)
\(524\) 45.8887 100.482i 0.0875739 0.191760i
\(525\) −25.6588 3.68918i −0.0488740 0.00702701i
\(526\) 31.7976 49.4780i 0.0604517 0.0940647i
\(527\) −232.029 + 201.054i −0.440282 + 0.381507i
\(528\) 355.792i 0.673849i
\(529\) −526.924 46.8199i −0.996076 0.0885063i
\(530\) 93.7126 0.176816
\(531\) 115.584 + 133.391i 0.217671 + 0.251206i
\(532\) 24.2585 + 15.5900i 0.0455986 + 0.0293045i
\(533\) −61.2781 + 426.199i −0.114968 + 0.799622i
\(534\) 636.811 + 290.822i 1.19253 + 0.544611i
\(535\) −53.6034 372.820i −0.100193 0.696860i
\(536\) −20.2589 + 68.9956i −0.0377965 + 0.128723i
\(537\) 199.828 128.422i 0.372119 0.239146i
\(538\) 415.120 + 908.986i 0.771599 + 1.68957i
\(539\) −195.257 664.984i −0.362258 1.23374i
\(540\) 47.1568 + 40.8616i 0.0873274 + 0.0756696i
\(541\) 74.0082 85.4100i 0.136799 0.157874i −0.683216 0.730216i \(-0.739419\pi\)
0.820015 + 0.572342i \(0.193965\pi\)
\(542\) 1080.88 317.374i 1.99424 0.585561i
\(543\) −473.657 + 216.312i −0.872296 + 0.398364i
\(544\) −314.171 488.859i −0.577519 0.898638i
\(545\) 296.605 + 87.0910i 0.544229 + 0.159800i
\(546\) 32.7449 4.70801i 0.0599723 0.00862272i
\(547\) −339.801 + 744.061i −0.621209 + 1.36026i 0.293428 + 0.955981i \(0.405204\pi\)
−0.914637 + 0.404276i \(0.867523\pi\)
\(548\) −660.576 94.9765i −1.20543 0.173315i
\(549\) −137.850 + 214.498i −0.251092 + 0.390707i
\(550\) −550.053 + 476.624i −1.00010 + 0.866588i
\(551\) 135.484i 0.245888i
\(552\) 1.97305 44.4980i 0.00357437 0.0806124i
\(553\) −109.623 −0.198232
\(554\) −166.531 192.187i −0.300597 0.346907i
\(555\) 176.726 + 113.575i 0.318425 + 0.204639i
\(556\) −78.5436 + 546.283i −0.141266 + 0.982523i
\(557\) −776.631 354.675i −1.39431 0.636760i −0.430315 0.902679i \(-0.641597\pi\)
−0.963995 + 0.265919i \(0.914325\pi\)
\(558\) 29.9842 + 208.545i 0.0537352 + 0.373737i
\(559\) −1.73181 + 5.89799i −0.00309804 + 0.0105510i
\(560\) −28.1735 + 18.1060i −0.0503099 + 0.0323322i
\(561\) 130.788 + 286.385i 0.233133 + 0.510490i
\(562\) −205.576 700.128i −0.365794 1.24578i
\(563\) 283.181 + 245.378i 0.502986 + 0.435840i 0.869031 0.494757i \(-0.164743\pi\)
−0.366045 + 0.930597i \(0.619288\pi\)
\(564\) 385.163 444.502i 0.682913 0.788124i
\(565\) −292.578 + 85.9086i −0.517837 + 0.152051i
\(566\) −384.570 + 175.627i −0.679453 + 0.310296i
\(567\) 4.16031 + 6.47357i 0.00733741 + 0.0114172i
\(568\) 103.936 + 30.5184i 0.182986 + 0.0537296i
\(569\) −478.219 + 68.7575i −0.840456 + 0.120839i −0.549080 0.835770i \(-0.685022\pi\)
−0.291375 + 0.956609i \(0.594113\pi\)
\(570\) 43.8644 96.0497i 0.0769551 0.168508i
\(571\) −26.3161 3.78369i −0.0460878 0.00662643i 0.119232 0.992866i \(-0.461957\pi\)
−0.165320 + 0.986240i \(0.552866\pi\)
\(572\) 262.640 408.676i 0.459161 0.714468i
\(573\) 36.2293 31.3929i 0.0632274 0.0547868i
\(574\) 138.209i 0.240783i
\(575\) 315.644 249.910i 0.548946 0.434626i
\(576\) −227.104 −0.394278
\(577\) 647.681 + 747.464i 1.12250 + 1.29543i 0.950635 + 0.310311i \(0.100433\pi\)
0.171863 + 0.985121i \(0.445021\pi\)
\(578\) −313.615 201.548i −0.542587 0.348699i
\(579\) 32.8950 228.790i 0.0568135 0.395147i
\(580\) −192.466 87.8965i −0.331839 0.151546i
\(581\) −15.0193 104.462i −0.0258508 0.179796i
\(582\) −107.205 + 365.108i −0.184202 + 0.627333i
\(583\) 142.771 91.7535i 0.244891 0.157382i
\(584\) −31.8997 69.8505i −0.0546227 0.119607i
\(585\) −17.8499 60.7912i −0.0305127 0.103917i
\(586\) 398.941 + 345.684i 0.680787 + 0.589905i
\(587\) 334.354 385.865i 0.569598 0.657351i −0.395738 0.918364i \(-0.629511\pi\)
0.965335 + 0.261013i \(0.0840565\pi\)
\(588\) −351.843 + 103.310i −0.598372 + 0.175698i
\(589\) 169.626 77.4654i 0.287989 0.131520i
\(590\) −252.186 392.409i −0.427433 0.665099i
\(591\) 259.643 + 76.2380i 0.439328 + 0.128998i
\(592\) −627.333 + 90.1969i −1.05968 + 0.152360i
\(593\) −203.227 + 445.005i −0.342710 + 0.750430i −0.999995 0.00321219i \(-0.998978\pi\)
0.657285 + 0.753642i \(0.271705\pi\)
\(594\) 213.855 + 30.7478i 0.360026 + 0.0517639i
\(595\) 16.0218 24.9304i 0.0269274 0.0418998i
\(596\) 392.530 340.129i 0.658608 0.570687i
\(597\) 105.097i 0.176043i
\(598\) −296.645 + 419.493i −0.496063 + 0.701494i
\(599\) −1110.24 −1.85350 −0.926748 0.375684i \(-0.877408\pi\)
−0.926748 + 0.375684i \(0.877408\pi\)
\(600\) 22.1990 + 25.6190i 0.0369983 + 0.0426984i
\(601\) −548.157 352.279i −0.912075 0.586155i −0.00172727 0.999999i \(-0.500550\pi\)
−0.910348 + 0.413843i \(0.864186\pi\)
\(602\) −0.280798 + 1.95300i −0.000466442 + 0.00324418i
\(603\) 175.504 + 80.1502i 0.291052 + 0.132919i
\(604\) −132.103 918.795i −0.218713 1.52118i
\(605\) 65.6864 223.707i 0.108573 0.369764i
\(606\) −149.400 + 96.0136i −0.246535 + 0.158438i
\(607\) −155.937 341.454i −0.256898 0.562527i 0.736607 0.676321i \(-0.236427\pi\)
−0.993504 + 0.113794i \(0.963700\pi\)
\(608\) 99.4387 + 338.657i 0.163551 + 0.557002i
\(609\) −19.7205 17.0879i −0.0323818 0.0280590i
\(610\) 441.276 509.260i 0.723403 0.834852i
\(611\) −573.021 + 168.254i −0.937841 + 0.275375i
\(612\) 151.526 69.1996i 0.247592 0.113071i
\(613\) 388.086 + 603.873i 0.633093 + 0.985111i 0.998526 + 0.0542738i \(0.0172844\pi\)
−0.365434 + 0.930837i \(0.619079\pi\)
\(614\) 996.939 + 292.728i 1.62368 + 0.476755i
\(615\) 262.003 37.6704i 0.426022 0.0612527i
\(616\) 5.70213 12.4859i 0.00925670 0.0202693i
\(617\) 604.408 + 86.9008i 0.979592 + 0.140844i 0.613466 0.789721i \(-0.289775\pi\)
0.366126 + 0.930565i \(0.380684\pi\)
\(618\) −195.761 + 304.610i −0.316765 + 0.492897i
\(619\) 613.035 531.198i 0.990364 0.858155i 0.000474794 1.00000i \(-0.499849\pi\)
0.989889 + 0.141845i \(0.0453034\pi\)
\(620\) 291.223i 0.469715i
\(621\) −117.426 22.2316i −0.189091 0.0357997i
\(622\) −1653.70 −2.65869
\(623\) −78.1498 90.1897i −0.125441 0.144767i
\(624\) 160.803 + 103.342i 0.257697 + 0.165612i
\(625\) −16.9367 + 117.797i −0.0270987 + 0.188476i
\(626\) 410.475 + 187.458i 0.655711 + 0.299453i
\(627\) −27.2142 189.279i −0.0434039 0.301881i
\(628\) 216.930 738.796i 0.345430 1.17643i
\(629\) 471.798 303.206i 0.750076 0.482044i
\(630\) −8.44819 18.4990i −0.0134098 0.0293634i
\(631\) 229.796 + 782.613i 0.364177 + 1.24027i 0.914248 + 0.405155i \(0.132783\pi\)
−0.550071 + 0.835118i \(0.685399\pi\)
\(632\) 108.338 + 93.8758i 0.171422 + 0.148538i
\(633\) −10.1524 + 11.7164i −0.0160385 + 0.0185094i
\(634\) 1223.32 359.200i 1.92953 0.566561i
\(635\) −498.637 + 227.720i −0.785254 + 0.358614i
\(636\) −48.5468 75.5402i −0.0763314 0.118774i
\(637\) 357.258 + 104.900i 0.560844 + 0.164679i
\(638\) −725.176 + 104.265i −1.13664 + 0.163424i
\(639\) 120.740 264.383i 0.188951 0.413744i
\(640\) 96.5081 + 13.8758i 0.150794 + 0.0216809i
\(641\) −459.259 + 714.621i −0.716473 + 1.11485i 0.271829 + 0.962346i \(0.412371\pi\)
−0.988302 + 0.152508i \(0.951265\pi\)
\(642\) −521.501 + 451.883i −0.812307 + 0.703868i
\(643\) 42.6111i 0.0662693i −0.999451 0.0331346i \(-0.989451\pi\)
0.999451 0.0331346i \(-0.0105490\pi\)
\(644\) −39.2716 + 76.7954i −0.0609808 + 0.119248i
\(645\) 3.77882 0.00585864
\(646\) −184.601 213.041i −0.285761 0.329785i
\(647\) 388.242 + 249.508i 0.600066 + 0.385639i 0.805120 0.593112i \(-0.202101\pi\)
−0.205054 + 0.978751i \(0.565737\pi\)
\(648\) 1.43209 9.96043i 0.00221002 0.0153710i
\(649\) −768.410 350.921i −1.18399 0.540711i
\(650\) −55.6477 387.038i −0.0856118 0.595443i
\(651\) 10.1184 34.4602i 0.0155429 0.0529343i
\(652\) 818.493 526.013i 1.25536 0.806769i
\(653\) 210.580 + 461.106i 0.322481 + 0.706136i 0.999557 0.0297783i \(-0.00948012\pi\)
−0.677075 + 0.735914i \(0.736753\pi\)
\(654\) −159.554 543.391i −0.243966 0.830873i
\(655\) 52.1110 + 45.1544i 0.0795587 + 0.0689380i
\(656\) −522.958 + 603.525i −0.797192 + 0.920008i
\(657\) −197.692 + 58.0475i −0.300900 + 0.0883523i
\(658\) −174.372 + 79.6330i −0.265003 + 0.121023i
\(659\) 607.900 + 945.912i 0.922459 + 1.43537i 0.900129 + 0.435624i \(0.143472\pi\)
0.0223300 + 0.999751i \(0.492892\pi\)
\(660\) −286.542 84.1363i −0.434155 0.127479i
\(661\) 1037.33 149.146i 1.56934 0.225637i 0.697921 0.716175i \(-0.254109\pi\)
0.871420 + 0.490538i \(0.163200\pi\)
\(662\) 316.202 692.385i 0.477646 1.04590i
\(663\) −167.422 24.0716i −0.252521 0.0363071i
\(664\) −74.6128 + 116.100i −0.112369 + 0.174849i
\(665\) −13.6032 + 11.7873i −0.0204560 + 0.0177252i
\(666\) 384.865i 0.577875i
\(667\) 403.295 39.8489i 0.604640 0.0597434i
\(668\) 152.812 0.228760
\(669\) −173.681 200.439i −0.259613 0.299610i
\(670\) −428.957 275.674i −0.640234 0.411454i
\(671\) 173.671 1207.91i 0.258824 1.80016i
\(672\) 61.8351 + 28.2392i 0.0920166 + 0.0420226i
\(673\) −32.5414 226.330i −0.0483528 0.336301i −0.999611 0.0279042i \(-0.991117\pi\)
0.951258 0.308397i \(-0.0997924\pi\)
\(674\) −349.605 + 1190.64i −0.518701 + 1.76653i
\(675\) 76.5163 49.1740i 0.113357 0.0728504i
\(676\) −199.508 436.861i −0.295130 0.646245i
\(677\) −63.6998 216.942i −0.0940913 0.320446i 0.898975 0.438000i \(-0.144313\pi\)
−0.993066 + 0.117554i \(0.962495\pi\)
\(678\) 422.194 + 365.833i 0.622705 + 0.539577i
\(679\) 42.4778 49.0220i 0.0625594 0.0721974i
\(680\) −37.1833 + 10.9180i −0.0546814 + 0.0160559i
\(681\) −453.063 + 206.907i −0.665291 + 0.303828i
\(682\) −545.170 848.301i −0.799370 1.24384i
\(683\) 625.039 + 183.528i 0.915137 + 0.268709i 0.705202 0.709007i \(-0.250856\pi\)
0.209936 + 0.977715i \(0.432675\pi\)
\(684\) −100.148 + 14.3990i −0.146415 + 0.0210512i
\(685\) 173.052 378.930i 0.252630 0.553182i
\(686\) 238.389 + 34.2751i 0.347505 + 0.0499637i
\(687\) −243.851 + 379.439i −0.354950 + 0.552313i
\(688\) −8.61593 + 7.46575i −0.0125232 + 0.0108514i
\(689\) 91.1768i 0.132332i
\(690\) 298.812 + 102.321i 0.433061 + 0.148291i
\(691\) 1334.12 1.93071 0.965354 0.260943i \(-0.0840336\pi\)
0.965354 + 0.260943i \(0.0840336\pi\)
\(692\) −210.603 243.049i −0.304340 0.351227i
\(693\) −30.9830 19.9116i −0.0447086 0.0287325i
\(694\) −97.1470 + 675.672i −0.139981 + 0.973591i
\(695\) −313.367 143.110i −0.450888 0.205914i
\(696\) 4.85618 + 33.7755i 0.00697727 + 0.0485280i
\(697\) 199.087 678.027i 0.285634 0.972779i
\(698\) −280.637 + 180.354i −0.402059 + 0.258387i
\(699\) −72.2718 158.253i −0.103393 0.226399i
\(700\) −18.4942 62.9853i −0.0264202 0.0899791i
\(701\) −627.300 543.559i −0.894865 0.775405i 0.0803266 0.996769i \(-0.474404\pi\)
−0.975191 + 0.221364i \(0.928949\pi\)
\(702\) −76.0121 + 87.7226i −0.108279 + 0.124961i
\(703\) −326.838 + 95.9683i −0.464919 + 0.136513i
\(704\) 988.714 451.531i 1.40442 0.641379i
\(705\) 198.487 + 308.852i 0.281542 + 0.438087i
\(706\) 492.288 + 144.549i 0.697292 + 0.204743i
\(707\) 29.9650 4.30832i 0.0423833 0.00609381i
\(708\) −185.672 + 406.566i −0.262249 + 0.574245i
\(709\) −285.731 41.0819i −0.403006 0.0579435i −0.0621683 0.998066i \(-0.519802\pi\)
−0.340838 + 0.940122i \(0.610711\pi\)
\(710\) −415.280 + 646.188i −0.584901 + 0.910124i
\(711\) 290.686 251.881i 0.408842 0.354263i
\(712\) 156.057i 0.219181i
\(713\) 280.481 + 482.139i 0.393382 + 0.676212i
\(714\) −54.2921 −0.0760394
\(715\) 198.577 + 229.170i 0.277730 + 0.320517i
\(716\) 506.027 + 325.204i 0.706742 + 0.454195i
\(717\) −10.6938 + 74.3768i −0.0149146 + 0.103733i
\(718\) −348.153 158.996i −0.484892 0.221443i
\(719\) −46.2131 321.419i −0.0642741 0.447036i −0.996391 0.0848792i \(-0.972950\pi\)
0.932117 0.362157i \(-0.117960\pi\)
\(720\) 33.1054 112.747i 0.0459797 0.156592i
\(721\) 51.9252 33.3703i 0.0720183 0.0462833i
\(722\) −363.153 795.195i −0.502982 1.10138i
\(723\) −217.759 741.619i −0.301188 1.02575i
\(724\) −996.537 863.504i −1.37643 1.19269i
\(725\) −201.976 + 233.092i −0.278587 + 0.321507i
\(726\) −409.841 + 120.340i −0.564519 + 0.165758i
\(727\) 79.0155 36.0852i 0.108687 0.0496357i −0.360329 0.932825i \(-0.617336\pi\)
0.469017 + 0.883189i \(0.344608\pi\)
\(728\) 3.98689 + 6.20372i 0.00547649 + 0.00852159i
\(729\) −25.9063 7.60678i −0.0355368 0.0104345i
\(730\) 538.974 77.4927i 0.738320 0.106154i
\(731\) 4.19077 9.17651i 0.00573293 0.0125534i
\(732\) −639.104 91.8892i −0.873093 0.125532i
\(733\) 643.772 1001.73i 0.878271 1.36662i −0.0515763 0.998669i \(-0.516425\pi\)
0.929847 0.367947i \(-0.119939\pi\)
\(734\) −298.416 + 258.579i −0.406561 + 0.352287i
\(735\) 228.894i 0.311420i
\(736\) −978.832 + 395.605i −1.32993 + 0.537507i
\(737\) −923.427 −1.25295
\(738\) −317.566 366.490i −0.430306 0.496599i
\(739\) −949.406 610.146i −1.28472 0.825638i −0.293255 0.956034i \(-0.594739\pi\)
−0.991462 + 0.130397i \(0.958375\pi\)
\(740\) −75.7079 + 526.560i −0.102308 + 0.711568i
\(741\) 93.4506 + 42.6775i 0.126114 + 0.0575944i
\(742\) 4.16502 + 28.9683i 0.00561323 + 0.0390409i
\(743\) −205.752 + 700.726i −0.276920 + 0.943103i 0.697163 + 0.716913i \(0.254445\pi\)
−0.974083 + 0.226191i \(0.927373\pi\)
\(744\) −39.5101 + 25.3916i −0.0531050 + 0.0341285i
\(745\) 134.680 + 294.909i 0.180779 + 0.395851i
\(746\) 172.948 + 589.005i 0.231833 + 0.789551i
\(747\) 279.850 + 242.491i 0.374631 + 0.324620i
\(748\) −522.097 + 602.532i −0.697990 + 0.805524i
\(749\) 112.863 33.1397i 0.150685 0.0442452i
\(750\) −530.940 + 242.472i −0.707920 + 0.323296i
\(751\) −462.909 720.300i −0.616390 0.959121i −0.999374 0.0353663i \(-0.988740\pi\)
0.382985 0.923755i \(-0.374896\pi\)
\(752\) −1062.75 312.053i −1.41324 0.414964i
\(753\) 511.802 73.5860i 0.679684 0.0977238i
\(754\) 163.508 358.033i 0.216854 0.474844i
\(755\) 573.517 + 82.4593i 0.759625 + 0.109218i
\(756\) −10.5352 + 16.3931i −0.0139355 + 0.0216840i
\(757\) −826.671 + 716.314i −1.09204 + 0.946254i −0.998780 0.0493880i \(-0.984273\pi\)
−0.0932559 + 0.995642i \(0.529727\pi\)
\(758\) 1235.54i 1.63000i
\(759\) 555.422 136.680i 0.731781 0.180079i
\(760\) 23.5379 0.0309710
\(761\) 410.943 + 474.253i 0.540003 + 0.623197i 0.958525 0.285010i \(-0.0919969\pi\)
−0.418521 + 0.908207i \(0.637451\pi\)
\(762\) 844.851 + 542.953i 1.10873 + 0.712536i
\(763\) −13.7390 + 95.5567i −0.0180065 + 0.125238i
\(764\) 110.425 + 50.4292i 0.144535 + 0.0660068i
\(765\) 14.7979 + 102.921i 0.0193436 + 0.134538i
\(766\) 72.1771 245.813i 0.0942260 0.320904i
\(767\) 381.790 245.362i 0.497771 0.319898i
\(768\) 143.671 + 314.596i 0.187072 + 0.409630i
\(769\) −76.5691 260.770i −0.0995696 0.339103i 0.894609 0.446850i \(-0.147454\pi\)
−0.994178 + 0.107747i \(0.965636\pi\)
\(770\) 73.5596 + 63.7398i 0.0955320 + 0.0827789i
\(771\) −304.175 + 351.036i −0.394519 + 0.455300i
\(772\) 561.617 164.905i 0.727483 0.213608i
\(773\) −29.3699 + 13.4128i −0.0379947 + 0.0173516i −0.434322 0.900758i \(-0.643012\pi\)
0.396327 + 0.918109i \(0.370285\pi\)
\(774\) −3.74283 5.82396i −0.00483570 0.00752449i
\(775\) −407.313 119.598i −0.525565 0.154320i
\(776\) −83.9604 + 12.0717i −0.108196 + 0.0155563i
\(777\) −27.2536 + 59.6771i −0.0350754 + 0.0768045i
\(778\) 955.029 + 137.312i 1.22754 + 0.176494i
\(779\) −232.047 + 361.072i −0.297878 + 0.463507i
\(780\) 121.254 105.067i 0.155453 0.134701i
\(781\) 1391.07i 1.78113i
\(782\) 579.863 612.162i 0.741513 0.782815i
\(783\) 91.5560 0.116930
\(784\) 452.221 + 521.891i 0.576813 + 0.665678i
\(785\) 404.331 + 259.848i 0.515071 + 0.331016i
\(786\) 17.9778 125.038i 0.0228725 0.159082i
\(787\) −388.115 177.246i −0.493158 0.225218i 0.153282 0.988182i \(-0.451016\pi\)
−0.646440 + 0.762965i \(0.723743\pi\)
\(788\) 97.5220 + 678.280i 0.123759 + 0.860762i
\(789\) 9.91068 33.7527i 0.0125611 0.0427790i
\(790\) −855.142 + 549.567i −1.08246 + 0.695654i
\(791\) −39.5594 86.6231i −0.0500119 0.109511i
\(792\) 13.5687 + 46.2108i 0.0171322 + 0.0583470i
\(793\) 495.479 + 429.335i 0.624816 + 0.541406i
\(794\) 104.464 120.557i 0.131566 0.151836i
\(795\) 53.7800 15.7912i 0.0676478 0.0198632i
\(796\) 242.089 110.559i 0.304132 0.138893i
\(797\) 455.304 + 708.467i 0.571272 + 0.888917i 0.999894 0.0145671i \(-0.00463700\pi\)
−0.428622 + 0.903484i \(0.641001\pi\)
\(798\) 31.6403 + 9.29043i 0.0396495 + 0.0116421i
\(799\) 970.142 139.485i 1.21420 0.174575i
\(800\) 333.781 730.879i 0.417226 0.913599i
\(801\) 414.460 + 59.5904i 0.517428 + 0.0743949i
\(802\) 18.2406 28.3830i 0.0227439 0.0353902i
\(803\) 745.254 645.766i 0.928087 0.804192i
\(804\) 488.585i 0.607693i
\(805\) −39.0881 37.0258i −0.0485566 0.0459947i
\(806\) 541.743 0.672138
\(807\) 391.400 + 451.700i 0.485007 + 0.559728i
\(808\) −33.3035 21.4028i −0.0412171 0.0264886i
\(809\) 84.8513 590.154i 0.104884 0.729485i −0.867726 0.497043i \(-0.834419\pi\)
0.972610 0.232442i \(-0.0746717\pi\)
\(810\) 64.9074 + 29.6422i 0.0801326 + 0.0365953i
\(811\) −0.941029 6.54500i −0.00116033 0.00807028i 0.989233 0.146349i \(-0.0467522\pi\)
−0.990393 + 0.138279i \(0.955843\pi\)
\(812\) 18.6164 63.4015i 0.0229265 0.0780806i
\(813\) 566.816 364.270i 0.697190 0.448057i
\(814\) 765.192 + 1675.54i 0.940040 + 2.05840i
\(815\) 171.101 + 582.716i 0.209940 + 0.714989i
\(816\) −237.080 205.431i −0.290539 0.251754i
\(817\) −4.01257 + 4.63076i −0.00491135 + 0.00566800i
\(818\) 81.2980 23.8713i 0.0993864 0.0291825i
\(819\) 17.9984 8.21958i 0.0219760 0.0100361i
\(820\) 362.390 + 563.890i 0.441939 + 0.687671i
\(821\) −1091.63 320.533i −1.32964 0.390417i −0.461678 0.887048i \(-0.652752\pi\)
−0.867962 + 0.496630i \(0.834570\pi\)
\(822\) −755.414 + 108.612i −0.918995 + 0.132131i
\(823\) −112.820 + 247.040i −0.137083 + 0.300170i −0.965706 0.259636i \(-0.916397\pi\)
0.828623 + 0.559807i \(0.189125\pi\)
\(824\) −79.8937 11.4870i −0.0969584 0.0139405i
\(825\) −235.351 + 366.213i −0.285274 + 0.443895i
\(826\) 110.093 95.3958i 0.133284 0.115491i
\(827\) 1399.96i 1.69282i −0.532529 0.846412i \(-0.678758\pi\)
0.532529 0.846412i \(-0.321242\pi\)
\(828\) −72.3171 293.874i −0.0873395 0.354920i
\(829\) 1082.27 1.30551 0.652754 0.757570i \(-0.273614\pi\)
0.652754 + 0.757570i \(0.273614\pi\)
\(830\) −640.856 739.587i −0.772115 0.891068i
\(831\) −127.954 82.2308i −0.153975 0.0989540i
\(832\) −83.1047 + 578.006i −0.0998855 + 0.694719i
\(833\) −555.847 253.847i −0.667284 0.304738i
\(834\) 89.8200 + 624.712i 0.107698 + 0.749055i
\(835\) −26.8733 + 91.5220i −0.0321836 + 0.109607i
\(836\) 407.372 261.802i 0.487287 0.313160i
\(837\) 52.3487 + 114.628i 0.0625432 + 0.136951i
\(838\) −56.6520 192.939i −0.0676038 0.230237i
\(839\) −550.390 476.916i −0.656008 0.568434i 0.261965 0.965077i \(-0.415629\pi\)
−0.917973 + 0.396644i \(0.870175\pi\)
\(840\) 2.96872 3.42608i 0.00353418 0.00407867i
\(841\) 509.047 149.470i 0.605287 0.177728i
\(842\) −342.166 + 156.262i −0.406373 + 0.185584i
\(843\) −235.953 367.150i −0.279897 0.435528i
\(844\) −37.6684 11.0605i −0.0446309 0.0131048i
\(845\) 296.731 42.6634i 0.351160 0.0504892i
\(846\) 279.409 611.820i 0.330270 0.723191i
\(847\) 72.0715 + 10.3623i 0.0850903 + 0.0122341i
\(848\) −91.4230 + 142.257i −0.107810 + 0.167756i
\(849\) −191.103 + 165.592i −0.225092 + 0.195044i
\(850\) 641.722i 0.754967i
\(851\) −381.798 944.670i −0.448647 1.11007i
\(852\) 736.012 0.863864
\(853\) −41.5302 47.9284i −0.0486872 0.0561880i 0.730884 0.682502i \(-0.239108\pi\)
−0.779571 + 0.626314i \(0.784563\pi\)
\(854\) 177.034 + 113.773i 0.207300 + 0.133223i
\(855\) 8.98796 62.5126i 0.0105122 0.0731142i
\(856\) −139.920 63.8995i −0.163458 0.0746490i
\(857\) −97.9562 681.300i −0.114301 0.794983i −0.963653 0.267156i \(-0.913916\pi\)
0.849352 0.527827i \(-0.176993\pi\)
\(858\) 156.513 533.035i 0.182416 0.621253i
\(859\) −1102.39 + 708.466i −1.28335 + 0.824757i −0.991297 0.131646i \(-0.957974\pi\)
−0.292050 + 0.956403i \(0.594337\pi\)
\(860\) 3.97518 + 8.70443i 0.00462230 + 0.0101214i
\(861\) 23.2892 + 79.3159i 0.0270491 + 0.0921206i
\(862\) −1030.89 893.273i −1.19593 1.03628i
\(863\) −374.610 + 432.323i −0.434078 + 0.500953i −0.930074 0.367372i \(-0.880258\pi\)
0.495996 + 0.868325i \(0.334803\pi\)
\(864\) −228.854 + 67.1976i −0.264877 + 0.0777750i
\(865\) 182.604 83.3923i 0.211103 0.0964073i
\(866\) −1102.18 1715.02i −1.27272 1.98039i
\(867\) −213.940 62.8185i −0.246759 0.0724551i
\(868\) 90.0225 12.9433i 0.103713 0.0149116i
\(869\) −764.732 + 1674.53i −0.880014 + 1.92696i
\(870\) −239.501 34.4351i −0.275289 0.0395806i
\(871\) 268.214 417.349i 0.307938 0.479161i
\(872\) 95.4085 82.6719i 0.109413 0.0948072i
\(873\) 227.594i 0.260703i
\(874\) −442.685 + 257.529i −0.506504 + 0.294656i
\(875\) 99.4977 0.113712
\(876\) −341.675 394.314i −0.390040 0.450130i
\(877\) −832.011 534.701i −0.948701 0.609693i −0.0278519 0.999612i \(-0.508867\pi\)
−0.920849 + 0.389919i \(0.872503\pi\)
\(878\) 338.303 2352.95i 0.385311 2.67989i
\(879\) 287.195 + 131.158i 0.326729 + 0.149212i
\(880\) 80.0372 + 556.671i 0.0909514 + 0.632581i
\(881\) −126.141 + 429.595i −0.143179 + 0.487622i −0.999589 0.0286741i \(-0.990871\pi\)
0.856410 + 0.516296i \(0.172690\pi\)
\(882\) −352.774 + 226.714i −0.399970 + 0.257045i
\(883\) −537.361 1176.66i −0.608562 1.33257i −0.923553 0.383471i \(-0.874729\pi\)
0.314990 0.949095i \(-0.397999\pi\)
\(884\) −120.673 410.974i −0.136508 0.464902i
\(885\) −210.848 182.701i −0.238247 0.206442i
\(886\) −716.581 + 826.979i −0.808783 + 0.933385i
\(887\) −495.183 + 145.399i −0.558268 + 0.163922i −0.548681 0.836032i \(-0.684870\pi\)
−0.00958679 + 0.999954i \(0.503052\pi\)
\(888\) 78.0391 35.6393i 0.0878818 0.0401343i
\(889\) −92.5541 144.017i −0.104110 0.161999i
\(890\) −1061.77 311.765i −1.19300 0.350298i
\(891\) 127.909 18.3905i 0.143557 0.0206403i
\(892\) 279.000 610.924i 0.312780 0.684893i
\(893\) −589.247 84.7209i −0.659851 0.0948722i
\(894\) 321.119 499.671i 0.359194 0.558916i
\(895\) −283.761 + 245.880i −0.317051 + 0.274726i
\(896\) 30.4492i 0.0339834i
\(897\) −99.5519 + 290.726i −0.110983 + 0.324110i
\(898\) 2319.65 2.58313
\(899\) −279.831 322.942i −0.311269 0.359224i
\(900\) 193.763 + 124.524i 0.215293 + 0.138360i
\(901\) 21.2953 148.112i 0.0236352 0.164387i
\(902\) 2111.21 + 964.156i 2.34058 + 1.06891i
\(903\) 0.167948 + 1.16810i 0.000185989 + 0.00129358i
\(904\) −35.0840 + 119.485i −0.0388098 + 0.132174i
\(905\) 692.421 444.992i 0.765106 0.491703i
\(906\) −440.967 965.583i −0.486719 1.06577i
\(907\) 268.938 + 915.917i 0.296513 + 1.00983i 0.964153 + 0.265347i \(0.0854865\pi\)
−0.667640 + 0.744485i \(0.732695\pi\)
\(908\) −953.211 825.962i −1.04979 0.909650i
\(909\) −69.5591 + 80.2754i −0.0765226 + 0.0883118i
\(910\) −50.1734 + 14.7322i −0.0551356 + 0.0161893i
\(911\) 607.800 277.573i 0.667179 0.304691i −0.0528823 0.998601i \(-0.516841\pi\)
0.720062 + 0.693910i \(0.244114\pi\)
\(912\) 103.012 + 160.290i 0.112952 + 0.175756i
\(913\) −1700.47 499.303i −1.86251 0.546881i
\(914\) 2051.74 294.995i 2.24479 0.322752i
\(915\) 167.426 366.613i 0.182980 0.400670i
\(916\) −1130.55 162.549i −1.23423 0.177455i
\(917\) −11.6420 + 18.1153i −0.0126958 + 0.0197550i
\(918\) 143.967 124.748i 0.156826 0.135891i
\(919\) 424.555i 0.461974i 0.972957 + 0.230987i \(0.0741956\pi\)
−0.972957 + 0.230987i \(0.925804\pi\)
\(920\) 6.92302 + 70.0653i 0.00752503 + 0.0761579i
\(921\) 621.452 0.674758
\(922\) 222.320 + 256.571i 0.241128 + 0.278277i
\(923\) −628.702 404.042i −0.681151 0.437749i
\(924\) 13.2729 92.3149i 0.0143646 0.0999079i
\(925\) 705.371 + 322.132i 0.762563 + 0.348251i
\(926\) 143.582 + 998.636i 0.155056 + 1.07844i
\(927\) −61.0148 + 207.797i −0.0658196 + 0.224161i
\(928\) 680.403 437.269i 0.733193 0.471195i
\(929\) 293.584 + 642.860i 0.316022 + 0.691991i 0.999270 0.0381947i \(-0.0121607\pi\)
−0.683249 + 0.730186i \(0.739433\pi\)
\(930\) −93.8264 319.543i −0.100889 0.343595i
\(931\) 280.498 + 243.053i 0.301287 + 0.261066i
\(932\) 288.505 332.952i 0.309555 0.357245i
\(933\) −949.030 + 278.660i −1.01718 + 0.298671i
\(934\) 581.599 265.608i 0.622697 0.284376i
\(935\) −269.053 418.655i −0.287757 0.447759i
\(936\) −24.8264 7.28969i −0.0265239 0.00778813i
\(937\) −824.620 + 118.562i −0.880064 + 0.126534i −0.567511 0.823366i \(-0.692093\pi\)
−0.312553 + 0.949900i \(0.601184\pi\)
\(938\) 66.1512 144.851i 0.0705236 0.154425i
\(939\) 267.152 + 38.4107i 0.284507 + 0.0409059i
\(940\) −502.631 + 782.110i −0.534714 + 0.832032i
\(941\) −415.039 + 359.633i −0.441062 + 0.382182i −0.846891 0.531767i \(-0.821528\pi\)
0.405829 + 0.913949i \(0.366983\pi\)
\(942\) 880.532i 0.934747i
\(943\) −1143.05 584.534i −1.21214 0.619866i
\(944\) 841.706 0.891637
\(945\) −7.96546 9.19263i −0.00842906 0.00972765i
\(946\) 27.8740 + 17.9135i 0.0294651 + 0.0189360i
\(947\) −24.0411 + 167.210i −0.0253866 + 0.176568i −0.998570 0.0534638i \(-0.982974\pi\)
0.973183 + 0.230031i \(0.0738829\pi\)
\(948\) 885.993 + 404.620i 0.934592 + 0.426814i
\(949\) 75.3958 + 524.389i 0.0794476 + 0.552570i
\(950\) 109.811 373.982i 0.115591 0.393665i
\(951\) 641.515 412.277i 0.674569 0.433519i
\(952\) −5.02756 11.0088i −0.00528105 0.0115639i
\(953\) 227.401 + 774.457i 0.238616 + 0.812651i 0.988518 + 0.151102i \(0.0482823\pi\)
−0.749902 + 0.661549i \(0.769899\pi\)
\(954\) −77.6053 67.2454i −0.0813473 0.0704878i
\(955\) −49.6222 + 57.2671i −0.0519604 + 0.0599655i
\(956\) −182.575 + 53.6087i −0.190978 + 0.0560761i
\(957\) −398.596 + 182.033i −0.416506 + 0.190212i
\(958\) −422.461 657.362i −0.440982 0.686181i
\(959\) 124.826 + 36.6521i 0.130162 + 0.0382191i
\(960\) 355.326 51.0881i 0.370131 0.0532168i
\(961\) −154.890 + 339.162i −0.161176 + 0.352926i
\(962\) −979.525 140.834i −1.01822 0.146398i
\(963\) −223.134 + 347.204i −0.231708 + 0.360544i
\(964\) 1479.23 1281.76i 1.53447 1.32962i
\(965\) 365.364i 0.378615i
\(966\) −18.3487 + 96.9160i −0.0189945 + 0.100327i
\(967\) −622.547 −0.643792 −0.321896 0.946775i \(-0.604320\pi\)
−0.321896 + 0.946775i \(0.604320\pi\)
\(968\) −62.3534 71.9597i −0.0644147 0.0743385i
\(969\) −141.838 91.1539i −0.146376 0.0940701i
\(970\) 85.6002 595.363i 0.0882477 0.613776i
\(971\) 1172.88 + 535.638i 1.20791 + 0.551635i 0.914592 0.404379i \(-0.132512\pi\)
0.293321 + 0.956014i \(0.405239\pi\)
\(972\) −9.73042 67.6766i −0.0100107 0.0696261i
\(973\) 30.3105 103.228i 0.0311516 0.106093i
\(974\) −2099.94 + 1349.55i −2.15600 + 1.38558i
\(975\) −97.1538 212.737i −0.0996449 0.218192i
\(976\) 342.568 + 1166.68i 0.350992 + 1.19537i
\(977\) 1138.04 + 986.115i 1.16483 + 1.00933i 0.999734 + 0.0230521i \(0.00733837\pi\)
0.165095 + 0.986278i \(0.447207\pi\)
\(978\) 728.617 840.869i 0.745007 0.859784i
\(979\) −1922.86 + 564.603i −1.96411 + 0.576714i
\(980\) 527.252 240.788i 0.538012 0.245702i
\(981\) −183.130 284.956i −0.186677 0.290475i
\(982\) 1234.15 + 362.379i 1.25677 + 0.369022i
\(983\) 1007.88 144.912i 1.02531 0.147418i 0.390917 0.920426i \(-0.372158\pi\)
0.634396 + 0.773008i \(0.281249\pi\)
\(984\) 44.9061 98.3306i 0.0456362 0.0999294i
\(985\) −423.386 60.8737i −0.429833 0.0618007i
\(986\) −349.233 + 543.418i −0.354192 + 0.551134i
\(987\) −86.6502 + 75.0828i −0.0877914 + 0.0760717i
\(988\) 260.156i 0.263316i
\(989\) −14.9645 10.5822i −0.0151310 0.0106999i
\(990\) −341.514 −0.344964
\(991\) 619.800 + 715.288i 0.625429 + 0.721784i 0.976729 0.214479i \(-0.0688055\pi\)
−0.351299 + 0.936263i \(0.614260\pi\)
\(992\) 936.490 + 601.846i 0.944043 + 0.606699i
\(993\) 64.7907 450.629i 0.0652474 0.453806i
\(994\) −218.206 99.6512i −0.219523 0.100253i
\(995\) 23.6422 + 164.435i 0.0237610 + 0.165261i
\(996\) −264.181 + 899.718i −0.265242 + 0.903331i
\(997\) −946.834 + 608.493i −0.949683 + 0.610324i −0.921125 0.389268i \(-0.872728\pi\)
−0.0285585 + 0.999592i \(0.509092\pi\)
\(998\) 391.290 + 856.805i 0.392074 + 0.858522i
\(999\) −64.8524 220.867i −0.0649173 0.221088i
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 69.3.f.a.10.7 yes 80
3.2 odd 2 207.3.j.b.10.2 80
23.7 odd 22 inner 69.3.f.a.7.7 80
69.53 even 22 207.3.j.b.145.2 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.3.f.a.7.7 80 23.7 odd 22 inner
69.3.f.a.10.7 yes 80 1.1 even 1 trivial
207.3.j.b.10.2 80 3.2 odd 2
207.3.j.b.145.2 80 69.53 even 22