Properties

Label 336.3.bv.a.325.35
Level $336$
Weight $3$
Character 336.325
Analytic conductor $9.155$
Analytic rank $0$
Dimension $256$
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] = [336,3,Mod(61,336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(336, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 9, 0, 10]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("336.61");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 336.bv (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.15533688251\)
Analytic rank: \(0\)
Dimension: \(256\)
Relative dimension: \(64\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 325.35
Character \(\chi\) \(=\) 336.325
Dual form 336.3.bv.a.61.35

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.371304 + 1.96523i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(-3.72427 + 1.45940i) q^{4} +(5.47260 + 1.46638i) q^{5} +(-1.50219 - 3.12144i) q^{6} +(-1.24400 - 6.88857i) q^{7} +(-4.25089 - 6.77716i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\) \(q+(0.371304 + 1.96523i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(-3.72427 + 1.45940i) q^{4} +(5.47260 + 1.46638i) q^{5} +(-1.50219 - 3.12144i) q^{6} +(-1.24400 - 6.88857i) q^{7} +(-4.25089 - 6.77716i) q^{8} +(2.59808 - 1.50000i) q^{9} +(-0.849773 + 11.2994i) q^{10} +(-16.2920 + 4.36543i) q^{11} +(5.57659 - 4.11116i) q^{12} +(-17.7032 - 17.7032i) q^{13} +(13.0757 - 5.00251i) q^{14} -9.81319 q^{15} +(11.7403 - 10.8704i) q^{16} +(4.91334 + 2.83672i) q^{17} +(3.91252 + 4.54886i) q^{18} +(3.96048 - 14.7807i) q^{19} +(-22.5214 + 2.52551i) q^{20} +(5.16932 + 10.9671i) q^{21} +(-14.6284 - 30.3967i) q^{22} +(-29.4512 + 17.0037i) q^{23} +(10.1500 + 9.43279i) q^{24} +(6.14843 + 3.54980i) q^{25} +(28.2175 - 41.3641i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(14.6862 + 23.8394i) q^{28} +(18.7595 - 18.7595i) q^{29} +(-3.64368 - 19.2852i) q^{30} +(-12.9915 - 7.50062i) q^{31} +(25.7220 + 19.0362i) q^{32} +(25.3001 - 14.6070i) q^{33} +(-3.75047 + 10.7091i) q^{34} +(3.29334 - 39.5226i) q^{35} +(-7.48683 + 9.37802i) q^{36} +(10.7520 - 40.1271i) q^{37} +(30.5181 + 2.29512i) q^{38} +(37.5541 + 21.6819i) q^{39} +(-13.3255 - 43.3221i) q^{40} +73.7328 q^{41} +(-19.6336 + 14.2310i) q^{42} +(21.1854 + 21.1854i) q^{43} +(54.3049 - 40.0345i) q^{44} +(16.4178 - 4.39913i) q^{45} +(-44.3515 - 51.5649i) q^{46} +(-23.1350 + 13.3570i) q^{47} +(-14.7689 + 23.4495i) q^{48} +(-45.9049 + 17.1388i) q^{49} +(-4.69323 + 13.4011i) q^{50} +(-9.49185 - 2.54333i) q^{51} +(91.7672 + 40.0953i) q^{52} +(-66.9387 + 17.9362i) q^{53} +(-8.58498 - 5.85646i) q^{54} -95.5610 q^{55} +(-41.3969 + 37.7134i) q^{56} +26.5041i q^{57} +(43.8322 + 29.9012i) q^{58} +(-18.9722 - 70.8053i) q^{59} +(36.5469 - 14.3213i) q^{60} +(-16.4776 + 61.4951i) q^{61} +(9.91667 - 28.3162i) q^{62} +(-13.5649 - 16.0310i) q^{63} +(-27.8599 + 57.6179i) q^{64} +(-70.9227 - 122.842i) q^{65} +(38.1002 + 44.2969i) q^{66} +(-9.66353 - 36.0648i) q^{67} +(-22.4385 - 3.39418i) q^{68} +(41.6503 - 41.6503i) q^{69} +(78.8938 - 8.20273i) q^{70} -4.09974i q^{71} +(-21.2099 - 11.2313i) q^{72} +(-66.4417 + 115.080i) q^{73} +(82.8513 + 6.23085i) q^{74} +(-11.8779 - 3.18266i) q^{75} +(6.82105 + 60.8272i) q^{76} +(50.3389 + 106.798i) q^{77} +(-28.6659 + 81.8530i) q^{78} +(-20.4157 - 35.3611i) q^{79} +(80.1901 - 42.2734i) q^{80} +(4.50000 - 7.79423i) q^{81} +(27.3773 + 144.902i) q^{82} +(-25.0898 - 25.0898i) q^{83} +(-35.2573 - 33.3005i) q^{84} +(22.7291 + 22.7291i) q^{85} +(-33.7681 + 49.5005i) q^{86} +(-22.9756 + 39.7948i) q^{87} +(98.8408 + 91.8566i) q^{88} +(-2.52926 - 4.38081i) q^{89} +(14.7413 + 30.6313i) q^{90} +(-99.9268 + 143.972i) q^{91} +(84.8690 - 106.307i) q^{92} +(25.0976 + 6.72487i) q^{93} +(-34.8398 - 40.5062i) q^{94} +(43.3482 - 75.0814i) q^{95} +(-51.5675 - 20.3174i) q^{96} +29.6822i q^{97} +(-50.7264 - 83.8501i) q^{98} +(-35.7797 + 35.7797i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 256 q - 12 q^{4} - 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 256 q - 12 q^{4} - 24 q^{8} + 108 q^{10} + 32 q^{11} + 32 q^{14} - 4 q^{16} + 12 q^{18} + 48 q^{22} - 64 q^{29} - 96 q^{35} - 96 q^{37} + 60 q^{40} - 60 q^{42} - 192 q^{43} + 228 q^{44} + 180 q^{46} - 32 q^{50} + 720 q^{52} + 160 q^{53} - 56 q^{56} - 312 q^{58} + 384 q^{59} + 72 q^{60} - 96 q^{64} - 216 q^{66} - 320 q^{67} - 780 q^{68} - 828 q^{70} + 60 q^{72} - 88 q^{74} - 72 q^{78} - 612 q^{80} + 1152 q^{81} + 780 q^{82} - 72 q^{84} - 212 q^{86} - 464 q^{88} - 480 q^{91} - 488 q^{92} - 612 q^{94} + 768 q^{95} - 900 q^{96} - 196 q^{98} + 192 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.371304 + 1.96523i 0.185652 + 0.982616i
\(3\) −1.67303 + 0.448288i −0.557678 + 0.149429i
\(4\) −3.72427 + 1.45940i −0.931067 + 0.364849i
\(5\) 5.47260 + 1.46638i 1.09452 + 0.293276i 0.760531 0.649301i \(-0.224939\pi\)
0.333989 + 0.942577i \(0.391605\pi\)
\(6\) −1.50219 3.12144i −0.250366 0.520241i
\(7\) −1.24400 6.88857i −0.177714 0.984082i
\(8\) −4.25089 6.77716i −0.531361 0.847145i
\(9\) 2.59808 1.50000i 0.288675 0.166667i
\(10\) −0.849773 + 11.2994i −0.0849773 + 1.12994i
\(11\) −16.2920 + 4.36543i −1.48109 + 0.396857i −0.906719 0.421736i \(-0.861421\pi\)
−0.574373 + 0.818594i \(0.694754\pi\)
\(12\) 5.57659 4.11116i 0.464716 0.342597i
\(13\) −17.7032 17.7032i −1.36178 1.36178i −0.871647 0.490135i \(-0.836948\pi\)
−0.490135 0.871647i \(-0.663052\pi\)
\(14\) 13.0757 5.00251i 0.933981 0.357322i
\(15\) −9.81319 −0.654213
\(16\) 11.7403 10.8704i 0.733770 0.679398i
\(17\) 4.91334 + 2.83672i 0.289020 + 0.166866i 0.637500 0.770450i \(-0.279969\pi\)
−0.348480 + 0.937316i \(0.613302\pi\)
\(18\) 3.91252 + 4.54886i 0.217362 + 0.252715i
\(19\) 3.96048 14.7807i 0.208446 0.777932i −0.779925 0.625873i \(-0.784743\pi\)
0.988371 0.152059i \(-0.0485905\pi\)
\(20\) −22.5214 + 2.52551i −1.12607 + 0.126276i
\(21\) 5.16932 + 10.9671i 0.246158 + 0.522245i
\(22\) −14.6284 30.3967i −0.664926 1.38167i
\(23\) −29.4512 + 17.0037i −1.28049 + 0.739289i −0.976937 0.213526i \(-0.931505\pi\)
−0.303549 + 0.952816i \(0.598172\pi\)
\(24\) 10.1500 + 9.43279i 0.422916 + 0.393033i
\(25\) 6.14843 + 3.54980i 0.245937 + 0.141992i
\(26\) 28.2175 41.3641i 1.08529 1.59093i
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) 14.6862 + 23.8394i 0.524506 + 0.851407i
\(29\) 18.7595 18.7595i 0.646878 0.646878i −0.305359 0.952237i \(-0.598777\pi\)
0.952237 + 0.305359i \(0.0987765\pi\)
\(30\) −3.64368 19.2852i −0.121456 0.642840i
\(31\) −12.9915 7.50062i −0.419079 0.241956i 0.275604 0.961271i \(-0.411122\pi\)
−0.694683 + 0.719316i \(0.744455\pi\)
\(32\) 25.7220 + 19.0362i 0.803813 + 0.594882i
\(33\) 25.3001 14.6070i 0.766670 0.442637i
\(34\) −3.75047 + 10.7091i −0.110308 + 0.314975i
\(35\) 3.29334 39.5226i 0.0940954 1.12922i
\(36\) −7.48683 + 9.37802i −0.207968 + 0.260501i
\(37\) 10.7520 40.1271i 0.290595 1.08452i −0.654058 0.756445i \(-0.726935\pi\)
0.944653 0.328071i \(-0.106399\pi\)
\(38\) 30.5181 + 2.29512i 0.803107 + 0.0603978i
\(39\) 37.5541 + 21.6819i 0.962925 + 0.555945i
\(40\) −13.3255 43.3221i −0.333138 1.08305i
\(41\) 73.7328 1.79836 0.899181 0.437577i \(-0.144163\pi\)
0.899181 + 0.437577i \(0.144163\pi\)
\(42\) −19.6336 + 14.2310i −0.467466 + 0.338835i
\(43\) 21.1854 + 21.1854i 0.492685 + 0.492685i 0.909151 0.416466i \(-0.136732\pi\)
−0.416466 + 0.909151i \(0.636732\pi\)
\(44\) 54.3049 40.0345i 1.23420 0.909876i
\(45\) 16.4178 4.39913i 0.364840 0.0977586i
\(46\) −44.3515 51.5649i −0.964162 1.12098i
\(47\) −23.1350 + 13.3570i −0.492235 + 0.284192i −0.725501 0.688221i \(-0.758392\pi\)
0.233266 + 0.972413i \(0.425059\pi\)
\(48\) −14.7689 + 23.4495i −0.307685 + 0.488532i
\(49\) −45.9049 + 17.1388i −0.936835 + 0.349771i
\(50\) −4.69323 + 13.4011i −0.0938647 + 0.268023i
\(51\) −9.49185 2.54333i −0.186115 0.0498693i
\(52\) 91.7672 + 40.0953i 1.76475 + 0.771064i
\(53\) −66.9387 + 17.9362i −1.26300 + 0.338419i −0.827343 0.561697i \(-0.810149\pi\)
−0.435652 + 0.900115i \(0.643482\pi\)
\(54\) −8.58498 5.85646i −0.158981 0.108453i
\(55\) −95.5610 −1.73747
\(56\) −41.3969 + 37.7134i −0.739230 + 0.673453i
\(57\) 26.5041i 0.464983i
\(58\) 43.8322 + 29.9012i 0.755727 + 0.515538i
\(59\) −18.9722 70.8053i −0.321563 1.20009i −0.917722 0.397223i \(-0.869974\pi\)
0.596159 0.802866i \(-0.296693\pi\)
\(60\) 36.5469 14.3213i 0.609116 0.238689i
\(61\) −16.4776 + 61.4951i −0.270124 + 1.00812i 0.688915 + 0.724842i \(0.258087\pi\)
−0.959039 + 0.283274i \(0.908579\pi\)
\(62\) 9.91667 28.3162i 0.159946 0.456713i
\(63\) −13.5649 16.0310i −0.215315 0.254461i
\(64\) −27.8599 + 57.6179i −0.435311 + 0.900280i
\(65\) −70.9227 122.842i −1.09112 1.88987i
\(66\) 38.1002 + 44.2969i 0.577276 + 0.671165i
\(67\) −9.66353 36.0648i −0.144232 0.538280i −0.999788 0.0205711i \(-0.993452\pi\)
0.855557 0.517709i \(-0.173215\pi\)
\(68\) −22.4385 3.39418i −0.329978 0.0499144i
\(69\) 41.6503 41.6503i 0.603627 0.603627i
\(70\) 78.8938 8.20273i 1.12705 0.117182i
\(71\) 4.09974i 0.0577428i −0.999583 0.0288714i \(-0.990809\pi\)
0.999583 0.0288714i \(-0.00919133\pi\)
\(72\) −21.2099 11.2313i −0.294582 0.155990i
\(73\) −66.4417 + 115.080i −0.910160 + 1.57644i −0.0963234 + 0.995350i \(0.530708\pi\)
−0.813837 + 0.581094i \(0.802625\pi\)
\(74\) 82.8513 + 6.23085i 1.11961 + 0.0842006i
\(75\) −11.8779 3.18266i −0.158371 0.0424355i
\(76\) 6.82105 + 60.8272i 0.0897507 + 0.800358i
\(77\) 50.3389 + 106.798i 0.653752 + 1.38699i
\(78\) −28.6659 + 81.8530i −0.367511 + 1.04940i
\(79\) −20.4157 35.3611i −0.258427 0.447608i 0.707394 0.706820i \(-0.249871\pi\)
−0.965821 + 0.259211i \(0.916537\pi\)
\(80\) 80.1901 42.2734i 1.00238 0.528418i
\(81\) 4.50000 7.79423i 0.0555556 0.0962250i
\(82\) 27.3773 + 144.902i 0.333870 + 1.76710i
\(83\) −25.0898 25.0898i −0.302287 0.302287i 0.539621 0.841908i \(-0.318567\pi\)
−0.841908 + 0.539621i \(0.818567\pi\)
\(84\) −35.2573 33.3005i −0.419730 0.396434i
\(85\) 22.7291 + 22.7291i 0.267401 + 0.267401i
\(86\) −33.7681 + 49.5005i −0.392652 + 0.575588i
\(87\) −22.9756 + 39.7948i −0.264087 + 0.457412i
\(88\) 98.8408 + 91.8566i 1.12319 + 1.04383i
\(89\) −2.52926 4.38081i −0.0284187 0.0492226i 0.851466 0.524409i \(-0.175714\pi\)
−0.879885 + 0.475187i \(0.842381\pi\)
\(90\) 14.7413 + 30.6313i 0.163792 + 0.340348i
\(91\) −99.9268 + 143.972i −1.09810 + 1.58211i
\(92\) 84.8690 106.307i 0.922489 1.15551i
\(93\) 25.0976 + 6.72487i 0.269866 + 0.0723105i
\(94\) −34.8398 40.5062i −0.370636 0.430917i
\(95\) 43.3482 75.0814i 0.456297 0.790330i
\(96\) −51.5675 20.3174i −0.537161 0.211639i
\(97\) 29.6822i 0.306002i 0.988226 + 0.153001i \(0.0488938\pi\)
−0.988226 + 0.153001i \(0.951106\pi\)
\(98\) −50.7264 83.8501i −0.517616 0.855613i
\(99\) −35.7797 + 35.7797i −0.361411 + 0.361411i
\(100\) −28.0790 4.24739i −0.280790 0.0424739i
\(101\) 6.98560 + 26.0706i 0.0691644 + 0.258125i 0.991847 0.127436i \(-0.0406747\pi\)
−0.922682 + 0.385561i \(0.874008\pi\)
\(102\) 1.47387 19.5980i 0.0144497 0.192138i
\(103\) 5.37211 + 9.30477i 0.0521564 + 0.0903376i 0.890925 0.454151i \(-0.150057\pi\)
−0.838768 + 0.544488i \(0.816724\pi\)
\(104\) −44.7230 + 195.231i −0.430029 + 1.87722i
\(105\) 12.2076 + 67.5989i 0.116263 + 0.643799i
\(106\) −60.1034 124.890i −0.567013 1.17821i
\(107\) 37.6390 140.471i 0.351767 1.31281i −0.532738 0.846280i \(-0.678837\pi\)
0.884505 0.466531i \(-0.154496\pi\)
\(108\) 8.32166 19.0460i 0.0770524 0.176352i
\(109\) −43.1716 161.119i −0.396070 1.47815i −0.819950 0.572435i \(-0.805999\pi\)
0.423880 0.905718i \(-0.360668\pi\)
\(110\) −35.4822 187.799i −0.322565 1.70727i
\(111\) 71.9539i 0.648234i
\(112\) −89.4863 67.3513i −0.798985 0.601351i
\(113\) −2.00439 −0.0177380 −0.00886898 0.999961i \(-0.502823\pi\)
−0.00886898 + 0.999961i \(0.502823\pi\)
\(114\) −52.0866 + 9.84107i −0.456900 + 0.0863252i
\(115\) −186.108 + 49.8676i −1.61833 + 0.433631i
\(116\) −42.4877 + 97.2428i −0.366274 + 0.838300i
\(117\) −72.5489 19.4394i −0.620076 0.166149i
\(118\) 132.104 63.5751i 1.11953 0.538772i
\(119\) 13.4288 37.3748i 0.112847 0.314074i
\(120\) 41.7148 + 66.5056i 0.347623 + 0.554214i
\(121\) 141.584 81.7433i 1.17011 0.675564i
\(122\) −126.970 9.54883i −1.04074 0.0782691i
\(123\) −123.357 + 33.0535i −1.00291 + 0.268728i
\(124\) 59.3300 + 8.97461i 0.478468 + 0.0723759i
\(125\) −71.7130 71.7130i −0.573704 0.573704i
\(126\) 26.4680 32.6105i 0.210064 0.258813i
\(127\) 6.29435 0.0495618 0.0247809 0.999693i \(-0.492111\pi\)
0.0247809 + 0.999693i \(0.492111\pi\)
\(128\) −123.577 33.3573i −0.965446 0.260604i
\(129\) −44.9411 25.9468i −0.348381 0.201138i
\(130\) 215.079 184.991i 1.65445 1.42301i
\(131\) −50.0488 + 186.785i −0.382052 + 1.42584i 0.460710 + 0.887551i \(0.347595\pi\)
−0.842762 + 0.538286i \(0.819072\pi\)
\(132\) −72.9068 + 91.3233i −0.552325 + 0.691843i
\(133\) −106.745 8.89484i −0.802593 0.0668785i
\(134\) 67.2875 32.3821i 0.502146 0.241657i
\(135\) −25.4954 + 14.7198i −0.188855 + 0.109035i
\(136\) −1.66116 45.3571i −0.0122144 0.333508i
\(137\) 135.668 + 78.3279i 0.990276 + 0.571736i 0.905357 0.424652i \(-0.139603\pi\)
0.0849193 + 0.996388i \(0.472937\pi\)
\(138\) 97.3174 + 66.3875i 0.705198 + 0.481069i
\(139\) −89.5730 + 89.5730i −0.644410 + 0.644410i −0.951637 0.307226i \(-0.900599\pi\)
0.307226 + 0.951637i \(0.400599\pi\)
\(140\) 45.4139 + 151.999i 0.324385 + 1.08571i
\(141\) 32.7179 32.7179i 0.232042 0.232042i
\(142\) 8.05693 1.52225i 0.0567390 0.0107201i
\(143\) 365.702 + 211.138i 2.55736 + 1.47649i
\(144\) 14.1967 45.8525i 0.0985881 0.318420i
\(145\) 130.171 75.1545i 0.897734 0.518307i
\(146\) −250.830 87.8434i −1.71801 0.601667i
\(147\) 69.1173 49.2524i 0.470186 0.335050i
\(148\) 18.5180 + 165.135i 0.125121 + 1.11578i
\(149\) 45.1142 168.368i 0.302780 1.12999i −0.632060 0.774919i \(-0.717790\pi\)
0.934840 0.355070i \(-0.115543\pi\)
\(150\) 1.84437 24.5245i 0.0122958 0.163496i
\(151\) −47.8118 27.6042i −0.316635 0.182809i 0.333257 0.942836i \(-0.391852\pi\)
−0.649892 + 0.760027i \(0.725186\pi\)
\(152\) −117.007 + 35.9904i −0.769782 + 0.236779i
\(153\) 17.0203 0.111244
\(154\) −191.192 + 138.582i −1.24151 + 0.899884i
\(155\) −60.0983 60.0983i −0.387731 0.387731i
\(156\) −171.504 25.9427i −1.09938 0.166299i
\(157\) −107.675 + 28.8514i −0.685827 + 0.183767i −0.584874 0.811124i \(-0.698856\pi\)
−0.100953 + 0.994891i \(0.532189\pi\)
\(158\) 61.9122 53.2513i 0.391849 0.337034i
\(159\) 103.950 60.0156i 0.653774 0.377457i
\(160\) 112.852 + 141.896i 0.705325 + 0.886849i
\(161\) 153.768 + 181.724i 0.955082 + 1.12872i
\(162\) 16.9883 + 5.94951i 0.104866 + 0.0367254i
\(163\) 63.3583 + 16.9768i 0.388701 + 0.104152i 0.447876 0.894095i \(-0.352180\pi\)
−0.0591753 + 0.998248i \(0.518847\pi\)
\(164\) −274.601 + 107.605i −1.67439 + 0.656131i
\(165\) 159.877 42.8388i 0.968949 0.259629i
\(166\) 39.9913 58.6232i 0.240911 0.353152i
\(167\) 19.3847 0.116076 0.0580381 0.998314i \(-0.481516\pi\)
0.0580381 + 0.998314i \(0.481516\pi\)
\(168\) 52.3519 81.6534i 0.311618 0.486032i
\(169\) 457.804i 2.70890i
\(170\) −36.2284 + 53.1072i −0.213109 + 0.312396i
\(171\) −11.8814 44.3421i −0.0694821 0.259311i
\(172\) −109.818 47.9823i −0.638478 0.278967i
\(173\) 6.80585 25.3998i 0.0393402 0.146819i −0.943462 0.331480i \(-0.892452\pi\)
0.982802 + 0.184661i \(0.0591186\pi\)
\(174\) −86.7370 30.3763i −0.498488 0.174576i
\(175\) 16.8044 46.7699i 0.0960251 0.267256i
\(176\) −143.820 + 228.352i −0.817157 + 1.29745i
\(177\) 63.4823 + 109.955i 0.358657 + 0.621212i
\(178\) 7.67018 6.59720i 0.0430909 0.0370629i
\(179\) −12.2381 45.6732i −0.0683693 0.255158i 0.923279 0.384130i \(-0.125499\pi\)
−0.991648 + 0.128973i \(0.958832\pi\)
\(180\) −54.7242 + 40.3436i −0.304023 + 0.224131i
\(181\) 73.4458 73.4458i 0.405778 0.405778i −0.474485 0.880263i \(-0.657366\pi\)
0.880263 + 0.474485i \(0.157366\pi\)
\(182\) −320.042 142.922i −1.75847 0.785284i
\(183\) 110.270i 0.602568i
\(184\) 240.430 + 127.315i 1.30669 + 0.691929i
\(185\) 117.683 203.833i 0.636124 1.10180i
\(186\) −3.89710 + 51.8195i −0.0209521 + 0.278599i
\(187\) −92.4318 24.7670i −0.494287 0.132444i
\(188\) 66.6678 83.5083i 0.354616 0.444193i
\(189\) 29.8810 + 20.7395i 0.158100 + 0.109733i
\(190\) 163.648 + 57.3113i 0.861303 + 0.301638i
\(191\) 41.0655 + 71.1276i 0.215003 + 0.372396i 0.953273 0.302109i \(-0.0976906\pi\)
−0.738271 + 0.674505i \(0.764357\pi\)
\(192\) 20.7811 108.886i 0.108235 0.567114i
\(193\) 124.767 216.103i 0.646460 1.11970i −0.337502 0.941325i \(-0.609582\pi\)
0.983962 0.178377i \(-0.0570848\pi\)
\(194\) −58.3324 + 11.0211i −0.300682 + 0.0568099i
\(195\) 173.725 + 173.725i 0.890895 + 0.890895i
\(196\) 145.950 130.823i 0.744642 0.667464i
\(197\) −161.821 161.821i −0.821427 0.821427i 0.164885 0.986313i \(-0.447275\pi\)
−0.986313 + 0.164885i \(0.947275\pi\)
\(198\) −83.6006 57.0303i −0.422225 0.288032i
\(199\) 158.069 273.784i 0.794317 1.37580i −0.128955 0.991650i \(-0.541162\pi\)
0.923272 0.384147i \(-0.125504\pi\)
\(200\) −2.07873 56.7587i −0.0103937 0.283794i
\(201\) 32.3348 + 56.0055i 0.160870 + 0.278634i
\(202\) −48.6410 + 23.4084i −0.240797 + 0.115883i
\(203\) −152.563 105.889i −0.751541 0.521622i
\(204\) 39.0619 4.38033i 0.191480 0.0214722i
\(205\) 403.510 + 108.120i 1.96834 + 0.527416i
\(206\) −16.2913 + 14.0123i −0.0790842 + 0.0680211i
\(207\) −51.0110 + 88.3536i −0.246430 + 0.426829i
\(208\) −400.281 15.4009i −1.92443 0.0740427i
\(209\) 258.097i 1.23491i
\(210\) −128.315 + 49.0906i −0.611023 + 0.233765i
\(211\) 28.1210 28.1210i 0.133275 0.133275i −0.637322 0.770597i \(-0.719958\pi\)
0.770597 + 0.637322i \(0.219958\pi\)
\(212\) 223.122 164.489i 1.05246 0.775893i
\(213\) 1.83786 + 6.85900i 0.00862846 + 0.0322019i
\(214\) 290.033 + 21.8120i 1.35529 + 0.101925i
\(215\) 84.8736 + 147.005i 0.394761 + 0.683746i
\(216\) 40.5197 + 9.28213i 0.187591 + 0.0429728i
\(217\) −35.5072 + 98.8234i −0.163628 + 0.455407i
\(218\) 300.606 144.666i 1.37893 0.663607i
\(219\) 59.5700 222.318i 0.272009 1.01515i
\(220\) 355.895 139.461i 1.61770 0.633916i
\(221\) −36.7628 137.201i −0.166348 0.620817i
\(222\) −141.406 + 26.7168i −0.636964 + 0.120346i
\(223\) 63.8505i 0.286325i 0.989699 + 0.143162i \(0.0457272\pi\)
−0.989699 + 0.143162i \(0.954273\pi\)
\(224\) 99.1342 200.869i 0.442564 0.896737i
\(225\) 21.2988 0.0946613
\(226\) −0.744238 3.93909i −0.00329309 0.0174296i
\(227\) −82.8266 + 22.1933i −0.364875 + 0.0977679i −0.436598 0.899657i \(-0.643817\pi\)
0.0717233 + 0.997425i \(0.477150\pi\)
\(228\) −38.6799 98.7082i −0.169649 0.432931i
\(229\) 194.273 + 52.0553i 0.848353 + 0.227316i 0.656705 0.754148i \(-0.271950\pi\)
0.191649 + 0.981464i \(0.438617\pi\)
\(230\) −167.104 347.230i −0.726540 1.50970i
\(231\) −132.095 156.110i −0.571839 0.675803i
\(232\) −206.880 47.3916i −0.891726 0.204274i
\(233\) −47.5751 + 27.4675i −0.204185 + 0.117886i −0.598606 0.801044i \(-0.704279\pi\)
0.394421 + 0.918930i \(0.370945\pi\)
\(234\) 11.2652 149.793i 0.0481420 0.640142i
\(235\) −146.195 + 39.1729i −0.622107 + 0.166693i
\(236\) 173.991 + 236.010i 0.737248 + 1.00004i
\(237\) 50.0081 + 50.0081i 0.211005 + 0.211005i
\(238\) 78.4363 + 12.5132i 0.329564 + 0.0525764i
\(239\) 431.394 1.80500 0.902498 0.430693i \(-0.141731\pi\)
0.902498 + 0.430693i \(0.141731\pi\)
\(240\) −115.210 + 106.673i −0.480042 + 0.444471i
\(241\) −73.0553 42.1785i −0.303134 0.175014i 0.340716 0.940166i \(-0.389331\pi\)
−0.643850 + 0.765152i \(0.722664\pi\)
\(242\) 213.215 + 247.893i 0.881054 + 1.02435i
\(243\) −4.03459 + 15.0573i −0.0166032 + 0.0619642i
\(244\) −28.3790 253.071i −0.116307 1.03718i
\(245\) −276.351 + 26.4797i −1.12796 + 0.108080i
\(246\) −110.761 230.153i −0.450248 0.935581i
\(247\) −331.778 + 191.552i −1.34323 + 0.775516i
\(248\) 4.39230 + 119.930i 0.0177109 + 0.483587i
\(249\) 53.2235 + 30.7286i 0.213749 + 0.123408i
\(250\) 114.305 167.560i 0.457221 0.670239i
\(251\) −142.401 + 142.401i −0.567334 + 0.567334i −0.931381 0.364046i \(-0.881395\pi\)
0.364046 + 0.931381i \(0.381395\pi\)
\(252\) 73.9149 + 39.9073i 0.293313 + 0.158362i
\(253\) 405.591 405.591i 1.60313 1.60313i
\(254\) 2.33712 + 12.3699i 0.00920126 + 0.0487002i
\(255\) −48.2156 27.8373i −0.189081 0.109166i
\(256\) 19.6702 255.243i 0.0768366 0.997044i
\(257\) −196.254 + 113.307i −0.763633 + 0.440884i −0.830598 0.556872i \(-0.812001\pi\)
0.0669658 + 0.997755i \(0.478668\pi\)
\(258\) 34.3046 97.9538i 0.132963 0.379666i
\(259\) −289.794 24.1480i −1.11890 0.0932354i
\(260\) 443.410 + 353.991i 1.70542 + 1.36150i
\(261\) 20.5993 76.8777i 0.0789246 0.294551i
\(262\) −385.658 29.0035i −1.47198 0.110700i
\(263\) 47.9089 + 27.6602i 0.182163 + 0.105172i 0.588309 0.808637i \(-0.299794\pi\)
−0.406145 + 0.913808i \(0.633127\pi\)
\(264\) −206.542 109.370i −0.782356 0.414281i
\(265\) −392.630 −1.48162
\(266\) −22.1544 213.081i −0.0832873 0.801057i
\(267\) 6.19540 + 6.19540i 0.0232038 + 0.0232038i
\(268\) 88.6224 + 120.212i 0.330681 + 0.448552i
\(269\) 379.120 101.585i 1.40937 0.377639i 0.527670 0.849450i \(-0.323066\pi\)
0.881700 + 0.471810i \(0.156399\pi\)
\(270\) −38.3944 44.6389i −0.142201 0.165329i
\(271\) 302.380 174.579i 1.11579 0.644204i 0.175470 0.984485i \(-0.443855\pi\)
0.940324 + 0.340281i \(0.110522\pi\)
\(272\) 88.5204 20.1059i 0.325443 0.0739186i
\(273\) 102.640 285.666i 0.375970 1.04640i
\(274\) −103.558 + 295.702i −0.377950 + 1.07920i
\(275\) −115.667 30.9928i −0.420606 0.112701i
\(276\) −94.3324 + 215.901i −0.341784 + 0.782250i
\(277\) −421.979 + 113.069i −1.52339 + 0.408191i −0.920856 0.389903i \(-0.872508\pi\)
−0.602533 + 0.798094i \(0.705842\pi\)
\(278\) −209.291 142.773i −0.752844 0.513571i
\(279\) −45.0037 −0.161304
\(280\) −281.851 + 145.687i −1.00661 + 0.520309i
\(281\) 154.441i 0.549611i 0.961500 + 0.274806i \(0.0886135\pi\)
−0.961500 + 0.274806i \(0.911386\pi\)
\(282\) 76.4465 + 52.1499i 0.271087 + 0.184929i
\(283\) −3.19516 11.9245i −0.0112903 0.0421360i 0.960051 0.279825i \(-0.0902766\pi\)
−0.971341 + 0.237689i \(0.923610\pi\)
\(284\) 5.98315 + 15.2685i 0.0210674 + 0.0537624i
\(285\) −38.8650 + 145.046i −0.136368 + 0.508933i
\(286\) −279.148 + 797.085i −0.976044 + 2.78701i
\(287\) −91.7237 507.914i −0.319595 1.76974i
\(288\) 95.3821 + 10.8745i 0.331188 + 0.0377588i
\(289\) −128.406 222.406i −0.444312 0.769570i
\(290\) 196.029 + 227.912i 0.675963 + 0.785903i
\(291\) −13.3062 49.6593i −0.0457256 0.170650i
\(292\) 79.4985 525.555i 0.272255 1.79985i
\(293\) −56.0630 + 56.0630i −0.191341 + 0.191341i −0.796276 0.604934i \(-0.793199\pi\)
0.604934 + 0.796276i \(0.293199\pi\)
\(294\) 122.456 + 117.544i 0.416516 + 0.399809i
\(295\) 415.309i 1.40783i
\(296\) −317.653 + 97.7076i −1.07315 + 0.330093i
\(297\) 43.8210 75.9003i 0.147546 0.255557i
\(298\) 347.634 + 26.1439i 1.16656 + 0.0877311i
\(299\) 822.398 + 220.361i 2.75049 + 0.736993i
\(300\) 48.8811 5.48143i 0.162937 0.0182714i
\(301\) 119.583 172.292i 0.397285 0.572400i
\(302\) 36.4958 104.211i 0.120847 0.345069i
\(303\) −23.3743 40.4854i −0.0771428 0.133615i
\(304\) −114.175 216.582i −0.375574 0.712441i
\(305\) −180.350 + 312.376i −0.591312 + 1.02418i
\(306\) 6.31972 + 33.4489i 0.0206527 + 0.109310i
\(307\) 345.622 + 345.622i 1.12581 + 1.12581i 0.990852 + 0.134954i \(0.0430888\pi\)
0.134954 + 0.990852i \(0.456911\pi\)
\(308\) −343.336 324.280i −1.11473 1.05286i
\(309\) −13.1589 13.1589i −0.0425855 0.0425855i
\(310\) 95.7923 140.422i 0.309007 0.452973i
\(311\) −47.8031 + 82.7974i −0.153708 + 0.266230i −0.932588 0.360943i \(-0.882455\pi\)
0.778880 + 0.627173i \(0.215788\pi\)
\(312\) −12.6967 346.677i −0.0406946 1.11114i
\(313\) 29.1835 + 50.5473i 0.0932380 + 0.161493i 0.908872 0.417075i \(-0.136945\pi\)
−0.815634 + 0.578568i \(0.803612\pi\)
\(314\) −96.6798 200.893i −0.307897 0.639788i
\(315\) −50.7275 107.623i −0.161040 0.341659i
\(316\) 127.639 + 101.899i 0.403922 + 0.322466i
\(317\) −221.503 59.3517i −0.698749 0.187229i −0.108079 0.994142i \(-0.534470\pi\)
−0.590670 + 0.806913i \(0.701137\pi\)
\(318\) 156.542 + 182.002i 0.492270 + 0.572333i
\(319\) −223.736 + 387.523i −0.701368 + 1.21480i
\(320\) −236.956 + 274.467i −0.740486 + 0.857708i
\(321\) 251.885i 0.784689i
\(322\) −300.035 + 369.665i −0.931786 + 1.14803i
\(323\) 61.3880 61.3880i 0.190056 0.190056i
\(324\) −5.38432 + 35.5951i −0.0166183 + 0.109861i
\(325\) −46.0040 171.689i −0.141551 0.528275i
\(326\) −9.83814 + 130.817i −0.0301783 + 0.401280i
\(327\) 144.455 + 250.204i 0.441759 + 0.765149i
\(328\) −313.430 499.699i −0.955579 1.52347i
\(329\) 120.791 + 142.751i 0.367145 + 0.433894i
\(330\) 143.551 + 298.288i 0.435003 + 0.903904i
\(331\) −1.67587 + 6.25442i −0.00506304 + 0.0188955i −0.968411 0.249359i \(-0.919780\pi\)
0.963348 + 0.268254i \(0.0864468\pi\)
\(332\) 130.057 + 56.8251i 0.391738 + 0.171160i
\(333\) −32.2561 120.381i −0.0968650 0.361505i
\(334\) 7.19763 + 38.0955i 0.0215498 + 0.114058i
\(335\) 211.538i 0.631458i
\(336\) 179.906 + 72.5653i 0.535435 + 0.215968i
\(337\) −484.927 −1.43895 −0.719477 0.694516i \(-0.755618\pi\)
−0.719477 + 0.694516i \(0.755618\pi\)
\(338\) −899.690 + 169.984i −2.66180 + 0.502913i
\(339\) 3.35341 0.898543i 0.00989206 0.00265057i
\(340\) −117.820 51.4783i −0.346529 0.151407i
\(341\) 244.400 + 65.4869i 0.716717 + 0.192044i
\(342\) 82.7309 39.8142i 0.241903 0.116416i
\(343\) 175.168 + 294.899i 0.510693 + 0.859763i
\(344\) 53.5203 233.634i 0.155582 0.679169i
\(345\) 289.010 166.860i 0.837711 0.483653i
\(346\) 52.4435 + 3.94402i 0.151571 + 0.0113989i
\(347\) −75.9409 + 20.3483i −0.218850 + 0.0586406i −0.366578 0.930387i \(-0.619471\pi\)
0.147728 + 0.989028i \(0.452804\pi\)
\(348\) 27.4906 181.737i 0.0789960 0.522233i
\(349\) −65.0127 65.0127i −0.186283 0.186283i 0.607804 0.794087i \(-0.292051\pi\)
−0.794087 + 0.607804i \(0.792051\pi\)
\(350\) 98.1532 + 15.6587i 0.280438 + 0.0447390i
\(351\) 130.091 0.370630
\(352\) −502.165 197.851i −1.42660 0.562076i
\(353\) −68.3365 39.4541i −0.193588 0.111768i 0.400073 0.916483i \(-0.368985\pi\)
−0.593661 + 0.804715i \(0.702318\pi\)
\(354\) −192.515 + 165.584i −0.543827 + 0.467751i
\(355\) 6.01177 22.4362i 0.0169346 0.0632006i
\(356\) 15.8130 + 12.6241i 0.0444185 + 0.0354610i
\(357\) −5.71207 + 68.5492i −0.0160002 + 0.192015i
\(358\) 85.2144 41.0094i 0.238029 0.114551i
\(359\) 572.263 330.396i 1.59405 0.920324i 0.601446 0.798913i \(-0.294591\pi\)
0.992602 0.121411i \(-0.0387420\pi\)
\(360\) −99.6039 92.5658i −0.276677 0.257127i
\(361\) 109.851 + 63.4225i 0.304296 + 0.175686i
\(362\) 171.609 + 117.067i 0.474057 + 0.323390i
\(363\) −200.229 + 200.229i −0.551596 + 0.551596i
\(364\) 162.041 682.024i 0.445168 1.87369i
\(365\) −532.360 + 532.360i −1.45852 + 1.45852i
\(366\) 216.706 40.9437i 0.592093 0.111868i
\(367\) −371.309 214.375i −1.01174 0.584129i −0.100040 0.994983i \(-0.531897\pi\)
−0.911701 + 0.410855i \(0.865230\pi\)
\(368\) −160.930 + 519.774i −0.437311 + 1.41243i
\(369\) 191.564 110.599i 0.519142 0.299727i
\(370\) 444.275 + 155.590i 1.20074 + 0.420514i
\(371\) 206.827 + 438.800i 0.557484 + 1.18275i
\(372\) −103.284 + 11.5821i −0.277646 + 0.0311347i
\(373\) 41.7518 155.820i 0.111935 0.417747i −0.887104 0.461569i \(-0.847287\pi\)
0.999039 + 0.0438218i \(0.0139534\pi\)
\(374\) 14.3526 190.846i 0.0383759 0.510283i
\(375\) 152.126 + 87.8301i 0.405670 + 0.234214i
\(376\) 188.867 + 100.011i 0.502306 + 0.265986i
\(377\) −664.204 −1.76181
\(378\) −29.6629 + 66.4237i −0.0784734 + 0.175724i
\(379\) −300.585 300.585i −0.793100 0.793100i 0.188897 0.981997i \(-0.439509\pi\)
−0.981997 + 0.188897i \(0.939509\pi\)
\(380\) −51.8669 + 342.885i −0.136492 + 0.902330i
\(381\) −10.5307 + 2.82168i −0.0276395 + 0.00740598i
\(382\) −124.534 + 107.113i −0.326006 + 0.280401i
\(383\) 515.251 297.481i 1.34530 0.776712i 0.357724 0.933827i \(-0.383553\pi\)
0.987580 + 0.157116i \(0.0502196\pi\)
\(384\) 221.702 + 0.409826i 0.577349 + 0.00106725i
\(385\) 118.878 + 658.279i 0.308774 + 1.70982i
\(386\) 471.018 + 164.956i 1.22025 + 0.427347i
\(387\) 86.8196 + 23.2632i 0.224340 + 0.0601117i
\(388\) −43.3181 110.544i −0.111645 0.284908i
\(389\) −546.994 + 146.567i −1.40615 + 0.376778i −0.880551 0.473952i \(-0.842827\pi\)
−0.525604 + 0.850730i \(0.676160\pi\)
\(390\) −276.904 + 405.914i −0.710011 + 1.04080i
\(391\) −192.938 −0.493449
\(392\) 311.289 + 238.250i 0.794105 + 0.607781i
\(393\) 334.933i 0.852247i
\(394\) 257.931 378.101i 0.654648 0.959647i
\(395\) −59.8743 223.454i −0.151581 0.565706i
\(396\) 81.0364 185.470i 0.204637 0.468359i
\(397\) 170.959 638.027i 0.430627 1.60712i −0.320693 0.947183i \(-0.603916\pi\)
0.751320 0.659939i \(-0.229418\pi\)
\(398\) 596.740 + 208.985i 1.49935 + 0.525088i
\(399\) 182.575 32.9711i 0.457582 0.0826343i
\(400\) 110.772 25.1599i 0.276930 0.0628999i
\(401\) −123.258 213.489i −0.307376 0.532391i 0.670411 0.741990i \(-0.266118\pi\)
−0.977788 + 0.209598i \(0.932784\pi\)
\(402\) −98.0577 + 84.3404i −0.243925 + 0.209802i
\(403\) 97.2051 + 362.775i 0.241204 + 0.900185i
\(404\) −64.0636 86.8991i −0.158573 0.215097i
\(405\) 36.0560 36.0560i 0.0890271 0.0890271i
\(406\) 151.450 339.138i 0.373028 0.835316i
\(407\) 700.688i 1.72159i
\(408\) 23.1122 + 75.1393i 0.0566476 + 0.184165i
\(409\) −48.1017 + 83.3146i −0.117608 + 0.203703i −0.918819 0.394678i \(-0.870856\pi\)
0.801211 + 0.598382i \(0.204189\pi\)
\(410\) −62.6562 + 833.136i −0.152820 + 2.03204i
\(411\) −262.090 70.2268i −0.637689 0.170868i
\(412\) −33.5865 26.8134i −0.0815207 0.0650811i
\(413\) −464.146 + 218.773i −1.12384 + 0.529718i
\(414\) −192.576 67.4423i −0.465159 0.162904i
\(415\) −100.515 174.097i −0.242205 0.419512i
\(416\) −118.360 792.362i −0.284518 1.90472i
\(417\) 109.704 190.013i 0.263079 0.455667i
\(418\) −507.220 + 95.8324i −1.21344 + 0.229264i
\(419\) −14.0201 14.0201i −0.0334609 0.0334609i 0.690178 0.723639i \(-0.257532\pi\)
−0.723639 + 0.690178i \(0.757532\pi\)
\(420\) −144.118 233.941i −0.343138 0.557001i
\(421\) 534.508 + 534.508i 1.26961 + 1.26961i 0.946287 + 0.323328i \(0.104802\pi\)
0.323328 + 0.946287i \(0.395198\pi\)
\(422\) 65.7056 + 44.8228i 0.155701 + 0.106215i
\(423\) −40.0711 + 69.4051i −0.0947306 + 0.164078i
\(424\) 406.106 + 377.410i 0.957796 + 0.890118i
\(425\) 20.1396 + 34.8828i 0.0473872 + 0.0820771i
\(426\) −12.7971 + 6.15860i −0.0300402 + 0.0144568i
\(427\) 444.112 + 37.0070i 1.04007 + 0.0866674i
\(428\) 64.8249 + 578.081i 0.151460 + 1.35066i
\(429\) −706.482 189.301i −1.64681 0.441262i
\(430\) −257.386 + 221.380i −0.598571 + 0.514837i
\(431\) −106.667 + 184.753i −0.247488 + 0.428661i −0.962828 0.270115i \(-0.912938\pi\)
0.715341 + 0.698776i \(0.246272\pi\)
\(432\) −3.19640 + 83.0770i −0.00739908 + 0.192308i
\(433\) 449.685i 1.03853i −0.854612 0.519267i \(-0.826205\pi\)
0.854612 0.519267i \(-0.173795\pi\)
\(434\) −207.395 33.0863i −0.477868 0.0762358i
\(435\) −184.090 + 184.090i −0.423196 + 0.423196i
\(436\) 395.919 + 537.045i 0.908071 + 1.23175i
\(437\) 134.685 + 502.652i 0.308204 + 1.15023i
\(438\) 459.025 + 34.5211i 1.04800 + 0.0788153i
\(439\) 95.0244 + 164.587i 0.216456 + 0.374914i 0.953722 0.300689i \(-0.0972167\pi\)
−0.737266 + 0.675603i \(0.763883\pi\)
\(440\) 406.219 + 647.632i 0.923225 + 1.47189i
\(441\) −93.5563 + 113.385i −0.212146 + 0.257109i
\(442\) 255.981 123.191i 0.579142 0.278712i
\(443\) 114.283 426.509i 0.257975 0.962775i −0.708437 0.705774i \(-0.750599\pi\)
0.966411 0.257000i \(-0.0827341\pi\)
\(444\) −105.009 267.976i −0.236508 0.603549i
\(445\) −7.41771 27.6833i −0.0166690 0.0622096i
\(446\) −125.481 + 23.7080i −0.281347 + 0.0531568i
\(447\) 301.910i 0.675414i
\(448\) 431.563 + 120.238i 0.963311 + 0.268389i
\(449\) 418.691 0.932497 0.466249 0.884654i \(-0.345605\pi\)
0.466249 + 0.884654i \(0.345605\pi\)
\(450\) 7.90833 + 41.8570i 0.0175741 + 0.0930156i
\(451\) −1201.26 + 321.876i −2.66354 + 0.713693i
\(452\) 7.46488 2.92520i 0.0165152 0.00647168i
\(453\) 92.3654 + 24.7492i 0.203897 + 0.0546340i
\(454\) −74.3689 154.533i −0.163808 0.340381i
\(455\) −757.977 + 641.372i −1.66588 + 1.40961i
\(456\) 179.622 112.666i 0.393909 0.247074i
\(457\) 143.065 82.5987i 0.313053 0.180741i −0.335239 0.942133i \(-0.608817\pi\)
0.648292 + 0.761392i \(0.275484\pi\)
\(458\) −30.1663 + 401.120i −0.0658652 + 0.875807i
\(459\) −28.4756 + 7.63000i −0.0620382 + 0.0166231i
\(460\) 620.340 457.326i 1.34857 0.994187i
\(461\) 401.809 + 401.809i 0.871604 + 0.871604i 0.992647 0.121044i \(-0.0386241\pi\)
−0.121044 + 0.992647i \(0.538624\pi\)
\(462\) 257.746 317.561i 0.557891 0.687362i
\(463\) −318.936 −0.688846 −0.344423 0.938815i \(-0.611925\pi\)
−0.344423 + 0.938815i \(0.611925\pi\)
\(464\) 16.3198 424.164i 0.0351720 0.914147i
\(465\) 127.488 + 73.6051i 0.274167 + 0.158290i
\(466\) −71.6449 83.2973i −0.153744 0.178750i
\(467\) 155.524 580.425i 0.333029 1.24288i −0.572962 0.819582i \(-0.694206\pi\)
0.905991 0.423298i \(-0.139128\pi\)
\(468\) 298.561 33.4801i 0.637951 0.0715387i
\(469\) −236.413 + 111.433i −0.504080 + 0.237596i
\(470\) −131.267 272.762i −0.279291 0.580345i
\(471\) 167.210 96.5386i 0.355010 0.204965i
\(472\) −399.210 + 429.563i −0.845784 + 0.910092i
\(473\) −437.637 252.670i −0.925237 0.534186i
\(474\) −79.7092 + 116.846i −0.168163 + 0.246510i
\(475\) 76.8193 76.8193i 0.161725 0.161725i
\(476\) 4.53245 + 158.792i 0.00952195 + 0.333596i
\(477\) −147.008 + 147.008i −0.308192 + 0.308192i
\(478\) 160.179 + 847.789i 0.335102 + 1.77362i
\(479\) −143.845 83.0487i −0.300302 0.173379i 0.342277 0.939599i \(-0.388802\pi\)
−0.642579 + 0.766220i \(0.722135\pi\)
\(480\) −252.415 186.806i −0.525865 0.389180i
\(481\) −900.721 + 520.031i −1.87260 + 1.08115i
\(482\) 55.7647 159.231i 0.115694 0.330356i
\(483\) −338.724 235.098i −0.701292 0.486746i
\(484\) −407.999 + 511.060i −0.842973 + 1.05591i
\(485\) −43.5253 + 162.439i −0.0897429 + 0.334925i
\(486\) −31.0891 2.33806i −0.0639694 0.00481083i
\(487\) −85.2002 49.1904i −0.174949 0.101007i 0.409968 0.912100i \(-0.365540\pi\)
−0.584917 + 0.811093i \(0.698873\pi\)
\(488\) 486.807 149.738i 0.997555 0.306840i
\(489\) −113.611 −0.232333
\(490\) −154.649 533.262i −0.315610 1.08829i
\(491\) 100.134 + 100.134i 0.203939 + 0.203939i 0.801685 0.597746i \(-0.203937\pi\)
−0.597746 + 0.801685i \(0.703937\pi\)
\(492\) 411.178 303.128i 0.835727 0.616113i
\(493\) 145.387 38.9563i 0.294903 0.0790190i
\(494\) −499.635 580.897i −1.01141 1.17590i
\(495\) −248.275 + 143.341i −0.501565 + 0.289579i
\(496\) −234.058 + 53.1622i −0.471892 + 0.107182i
\(497\) −28.2414 + 5.10008i −0.0568236 + 0.0102617i
\(498\) −40.6267 + 116.006i −0.0815797 + 0.232944i
\(499\) 580.638 + 155.582i 1.16360 + 0.311787i 0.788404 0.615157i \(-0.210907\pi\)
0.375200 + 0.926944i \(0.377574\pi\)
\(500\) 371.736 + 162.420i 0.743472 + 0.324841i
\(501\) −32.4313 + 8.68993i −0.0647331 + 0.0173452i
\(502\) −332.725 226.977i −0.662798 0.452145i
\(503\) 267.735 0.532277 0.266139 0.963935i \(-0.414252\pi\)
0.266139 + 0.963935i \(0.414252\pi\)
\(504\) −50.9822 + 160.078i −0.101155 + 0.317614i
\(505\) 152.918i 0.302807i
\(506\) 947.677 + 646.482i 1.87288 + 1.27763i
\(507\) −205.228 765.920i −0.404789 1.51069i
\(508\) −23.4418 + 9.18596i −0.0461454 + 0.0180826i
\(509\) 9.05089 33.7784i 0.0177817 0.0663622i −0.956465 0.291847i \(-0.905730\pi\)
0.974247 + 0.225485i \(0.0723967\pi\)
\(510\) 36.8041 105.091i 0.0721648 0.206061i
\(511\) 875.393 + 314.528i 1.71310 + 0.615516i
\(512\) 508.915 56.1164i 0.993976 0.109602i
\(513\) 39.7561 + 68.8596i 0.0774972 + 0.134229i
\(514\) −295.544 343.612i −0.574989 0.668506i
\(515\) 15.7551 + 58.7988i 0.0305924 + 0.114172i
\(516\) 205.239 + 31.0457i 0.397751 + 0.0601661i
\(517\) 318.607 318.607i 0.616261 0.616261i
\(518\) −60.1454 578.478i −0.116111 1.11675i
\(519\) 45.5456i 0.0877565i
\(520\) −531.034 + 1002.84i −1.02122 + 1.92854i
\(521\) 59.3480 102.794i 0.113912 0.197301i −0.803432 0.595396i \(-0.796995\pi\)
0.917344 + 0.398095i \(0.130329\pi\)
\(522\) 158.731 + 11.9374i 0.304083 + 0.0228686i
\(523\) 202.090 + 54.1498i 0.386405 + 0.103537i 0.446791 0.894638i \(-0.352567\pi\)
−0.0603865 + 0.998175i \(0.519233\pi\)
\(524\) −86.1979 768.677i −0.164500 1.46694i
\(525\) −7.14794 + 85.7807i −0.0136151 + 0.163392i
\(526\) −36.5699 + 104.422i −0.0695246 + 0.198522i
\(527\) −42.5543 73.7063i −0.0807483 0.139860i
\(528\) 138.248 446.512i 0.261832 0.845667i
\(529\) 313.749 543.429i 0.593098 1.02728i
\(530\) −145.785 771.609i −0.275066 1.45587i
\(531\) −155.499 155.499i −0.292842 0.292842i
\(532\) 410.528 122.656i 0.771668 0.230557i
\(533\) −1305.30 1305.30i −2.44898 2.44898i
\(534\) −9.87502 + 14.4758i −0.0184925 + 0.0271082i
\(535\) 411.966 713.547i 0.770031 1.33373i
\(536\) −203.338 + 218.799i −0.379363 + 0.408207i
\(537\) 40.9495 + 70.9266i 0.0762561 + 0.132079i
\(538\) 340.407 + 707.340i 0.632727 + 1.31476i
\(539\) 673.065 479.620i 1.24873 0.889833i
\(540\) 73.4697 92.0284i 0.136055 0.170423i
\(541\) −658.546 176.457i −1.21728 0.326168i −0.407663 0.913133i \(-0.633656\pi\)
−0.809612 + 0.586965i \(0.800323\pi\)
\(542\) 455.364 + 529.425i 0.840155 + 0.976799i
\(543\) −89.9524 + 155.802i −0.165658 + 0.286928i
\(544\) 72.3807 + 166.498i 0.133053 + 0.306062i
\(545\) 945.044i 1.73403i
\(546\) 599.511 + 95.6418i 1.09801 + 0.175168i
\(547\) 697.897 697.897i 1.27586 1.27586i 0.332901 0.942962i \(-0.391973\pi\)
0.942962 0.332901i \(-0.108027\pi\)
\(548\) −619.575 93.7205i −1.13061 0.171023i
\(549\) 49.4327 + 184.485i 0.0900413 + 0.336039i
\(550\) 17.9605 238.820i 0.0326554 0.434217i
\(551\) −202.982 351.575i −0.368388 0.638067i
\(552\) −459.321 105.220i −0.832104 0.190616i
\(553\) −218.190 + 184.624i −0.394557 + 0.333860i
\(554\) −378.889 787.303i −0.683915 1.42112i
\(555\) −105.512 + 393.775i −0.190111 + 0.709504i
\(556\) 202.871 464.316i 0.364876 0.835102i
\(557\) −138.984 518.695i −0.249522 0.931229i −0.971056 0.238851i \(-0.923229\pi\)
0.721534 0.692379i \(-0.243437\pi\)
\(558\) −16.7101 88.4427i −0.0299464 0.158500i
\(559\) 750.099i 1.34186i
\(560\) −390.960 499.807i −0.698143 0.892513i
\(561\) 165.744 0.295444
\(562\) −303.512 + 57.3445i −0.540057 + 0.102036i
\(563\) −456.888 + 122.423i −0.811523 + 0.217447i −0.640637 0.767844i \(-0.721330\pi\)
−0.170886 + 0.985291i \(0.554663\pi\)
\(564\) −74.1017 + 169.598i −0.131386 + 0.300707i
\(565\) −10.9692 2.93919i −0.0194145 0.00520211i
\(566\) 22.2480 10.7068i 0.0393074 0.0189167i
\(567\) −59.2891 21.3026i −0.104566 0.0375706i
\(568\) −27.7846 + 17.4275i −0.0489165 + 0.0306823i
\(569\) −233.933 + 135.061i −0.411130 + 0.237366i −0.691275 0.722592i \(-0.742951\pi\)
0.280145 + 0.959958i \(0.409617\pi\)
\(570\) −299.480 22.5224i −0.525403 0.0395130i
\(571\) 635.575 170.302i 1.11309 0.298252i 0.345007 0.938600i \(-0.387877\pi\)
0.768085 + 0.640348i \(0.221210\pi\)
\(572\) −1670.11 252.630i −2.91977 0.441661i
\(573\) −100.590 100.590i −0.175549 0.175549i
\(574\) 964.111 368.849i 1.67964 0.642594i
\(575\) −241.438 −0.419892
\(576\) 14.0448 + 191.486i 0.0243833 + 0.332440i
\(577\) 231.479 + 133.645i 0.401177 + 0.231620i 0.686992 0.726665i \(-0.258931\pi\)
−0.285815 + 0.958285i \(0.592264\pi\)
\(578\) 389.401 334.928i 0.673704 0.579460i
\(579\) −111.863 + 417.478i −0.193200 + 0.721033i
\(580\) −375.113 + 469.867i −0.646746 + 0.810116i
\(581\) −141.621 + 204.045i −0.243754 + 0.351195i
\(582\) 92.6513 44.5884i 0.159195 0.0766123i
\(583\) 1012.27 584.433i 1.73631 1.00246i
\(584\) 1062.35 38.9077i 1.81910 0.0666228i
\(585\) −368.525 212.768i −0.629958 0.363706i
\(586\) −130.993 89.3604i −0.223538 0.152492i
\(587\) −651.491 + 651.491i −1.10987 + 1.10987i −0.116699 + 0.993167i \(0.537231\pi\)
−0.993167 + 0.116699i \(0.962769\pi\)
\(588\) −185.533 + 284.299i −0.315532 + 0.483501i
\(589\) −162.317 + 162.317i −0.275581 + 0.275581i
\(590\) 816.179 154.206i 1.38335 0.261366i
\(591\) 343.275 + 198.190i 0.580837 + 0.335346i
\(592\) −309.964 587.983i −0.523588 0.993215i
\(593\) −459.684 + 265.399i −0.775184 + 0.447553i −0.834721 0.550673i \(-0.814371\pi\)
0.0595367 + 0.998226i \(0.481038\pi\)
\(594\) 165.433 + 57.9364i 0.278506 + 0.0975360i
\(595\) 128.296 184.846i 0.215623 0.310665i
\(596\) 77.6992 + 692.888i 0.130368 + 1.16256i
\(597\) −141.721 + 528.909i −0.237388 + 0.885945i
\(598\) −127.700 + 1698.02i −0.213545 + 2.83950i
\(599\) 579.307 + 334.463i 0.967123 + 0.558369i 0.898358 0.439264i \(-0.144761\pi\)
0.0687652 + 0.997633i \(0.478094\pi\)
\(600\) 28.9220 + 94.0273i 0.0482034 + 0.156712i
\(601\) −533.881 −0.888321 −0.444161 0.895947i \(-0.646498\pi\)
−0.444161 + 0.895947i \(0.646498\pi\)
\(602\) 382.996 + 171.035i 0.636206 + 0.284111i
\(603\) −79.2038 79.2038i −0.131350 0.131350i
\(604\) 218.349 + 33.0288i 0.361506 + 0.0546835i
\(605\) 894.696 239.733i 1.47884 0.396253i
\(606\) 70.8843 60.9683i 0.116971 0.100608i
\(607\) −611.157 + 352.852i −1.00685 + 0.581304i −0.910267 0.414021i \(-0.864124\pi\)
−0.0965812 + 0.995325i \(0.530791\pi\)
\(608\) 383.241 304.797i 0.630330 0.501311i
\(609\) 302.711 + 108.764i 0.497063 + 0.178594i
\(610\) −680.855 238.443i −1.11616 0.390891i
\(611\) 646.025 + 173.102i 1.05732 + 0.283309i
\(612\) −63.3882 + 24.8394i −0.103576 + 0.0405873i
\(613\) −207.891 + 55.7041i −0.339136 + 0.0908713i −0.424368 0.905490i \(-0.639504\pi\)
0.0852315 + 0.996361i \(0.472837\pi\)
\(614\) −550.897 + 807.559i −0.897226 + 1.31524i
\(615\) −723.555 −1.17651
\(616\) 509.803 795.142i 0.827603 1.29081i
\(617\) 556.548i 0.902022i −0.892518 0.451011i \(-0.851064\pi\)
0.892518 0.451011i \(-0.148936\pi\)
\(618\) 20.9744 30.7463i 0.0339391 0.0497513i
\(619\) 148.469 + 554.094i 0.239853 + 0.895143i 0.975901 + 0.218214i \(0.0700231\pi\)
−0.736048 + 0.676929i \(0.763310\pi\)
\(620\) 311.529 + 136.115i 0.502467 + 0.219540i
\(621\) 45.7352 170.686i 0.0736476 0.274857i
\(622\) −180.466 63.2011i −0.290138 0.101610i
\(623\) −27.0311 + 22.8728i −0.0433887 + 0.0367139i
\(624\) 676.587 153.675i 1.08427 0.246274i
\(625\) −376.043 651.325i −0.601669 1.04212i
\(626\) −88.5012 + 76.1207i −0.141376 + 0.121599i
\(627\) −115.702 431.804i −0.184532 0.688683i
\(628\) 358.904 264.591i 0.571503 0.421323i
\(629\) 166.658 166.658i 0.264957 0.264957i
\(630\) 192.668 139.652i 0.305822 0.221670i
\(631\) 295.557i 0.468395i −0.972189 0.234197i \(-0.924754\pi\)
0.972189 0.234197i \(-0.0752462\pi\)
\(632\) −152.863 + 288.677i −0.241871 + 0.456767i
\(633\) −34.4410 + 59.6536i −0.0544092 + 0.0942395i
\(634\) 34.3946 457.343i 0.0542501 0.721361i
\(635\) 34.4465 + 9.22990i 0.0542464 + 0.0145353i
\(636\) −299.551 + 375.219i −0.470993 + 0.589967i
\(637\) 1116.07 + 509.251i 1.75208 + 0.799453i
\(638\) −844.646 295.805i −1.32390 0.463644i
\(639\) −6.14961 10.6514i −0.00962380 0.0166689i
\(640\) −627.373 363.762i −0.980270 0.568378i
\(641\) −87.1057 + 150.871i −0.135890 + 0.235369i −0.925937 0.377678i \(-0.876723\pi\)
0.790047 + 0.613046i \(0.210056\pi\)
\(642\) −495.013 + 93.5261i −0.771048 + 0.145679i
\(643\) −92.0384 92.0384i −0.143139 0.143139i 0.631906 0.775045i \(-0.282273\pi\)
−0.775045 + 0.631906i \(0.782273\pi\)
\(644\) −837.882 452.380i −1.30106 0.702454i
\(645\) −207.897 207.897i −0.322321 0.322321i
\(646\) 143.435 + 97.8479i 0.222036 + 0.151467i
\(647\) 93.7285 162.343i 0.144866 0.250916i −0.784457 0.620184i \(-0.787058\pi\)
0.929323 + 0.369268i \(0.120391\pi\)
\(648\) −71.9518 + 2.63516i −0.111037 + 0.00406661i
\(649\) 618.191 + 1070.74i 0.952529 + 1.64983i
\(650\) 320.328 154.157i 0.492812 0.237165i
\(651\) 15.1034 181.252i 0.0232003 0.278421i
\(652\) −260.739 + 29.2388i −0.399906 + 0.0448448i
\(653\) −522.499 140.003i −0.800152 0.214400i −0.164501 0.986377i \(-0.552601\pi\)
−0.635651 + 0.771977i \(0.719268\pi\)
\(654\) −438.071 + 376.789i −0.669833 + 0.576130i
\(655\) −547.794 + 948.807i −0.836326 + 1.44856i
\(656\) 865.647 801.503i 1.31958 1.22180i
\(657\) 398.650i 0.606773i
\(658\) −235.689 + 290.386i −0.358190 + 0.441316i
\(659\) −34.4272 + 34.4272i −0.0522416 + 0.0522416i −0.732745 0.680503i \(-0.761761\pi\)
0.680503 + 0.732745i \(0.261761\pi\)
\(660\) −532.904 + 392.867i −0.807431 + 0.595253i
\(661\) −166.073 619.794i −0.251246 0.937661i −0.970141 0.242543i \(-0.922019\pi\)
0.718895 0.695118i \(-0.244648\pi\)
\(662\) −12.9136 0.971173i −0.0195070 0.00146703i
\(663\) 123.011 + 213.061i 0.185537 + 0.321359i
\(664\) −63.3837 + 276.691i −0.0954574 + 0.416704i
\(665\) −571.129 205.206i −0.858840 0.308581i
\(666\) 224.600 108.089i 0.337238 0.162295i
\(667\) −233.509 + 871.468i −0.350089 + 1.30655i
\(668\) −72.1939 + 28.2900i −0.108075 + 0.0423503i
\(669\) −28.6234 106.824i −0.0427853 0.159677i
\(670\) 415.722 78.5451i 0.620480 0.117232i
\(671\) 1073.81i 1.60031i
\(672\) −75.8077 + 380.501i −0.112809 + 0.566222i
\(673\) −74.3641 −0.110496 −0.0552482 0.998473i \(-0.517595\pi\)
−0.0552482 + 0.998473i \(0.517595\pi\)
\(674\) −180.056 952.994i −0.267145 1.41394i
\(675\) −35.6336 + 9.54799i −0.0527905 + 0.0141452i
\(676\) −668.117 1704.98i −0.988339 2.52216i
\(677\) 589.030 + 157.830i 0.870060 + 0.233132i 0.666114 0.745850i \(-0.267957\pi\)
0.203946 + 0.978982i \(0.434623\pi\)
\(678\) 3.01098 + 6.25659i 0.00444097 + 0.00922801i
\(679\) 204.468 36.9247i 0.301131 0.0543810i
\(680\) 57.4198 250.657i 0.0844409 0.368614i
\(681\) 128.623 74.2603i 0.188873 0.109046i
\(682\) −37.9500 + 504.619i −0.0556451 + 0.739910i
\(683\) −451.301 + 120.926i −0.660764 + 0.177051i −0.573591 0.819142i \(-0.694450\pi\)
−0.0871730 + 0.996193i \(0.527783\pi\)
\(684\) 108.962 + 147.802i 0.159302 + 0.216085i
\(685\) 627.597 + 627.597i 0.916200 + 0.916200i
\(686\) −514.504 + 453.742i −0.750006 + 0.661431i
\(687\) −348.361 −0.507075
\(688\) 479.018 + 18.4303i 0.696246 + 0.0267882i
\(689\) 1502.55 + 867.500i 2.18078 + 1.25907i
\(690\) 435.230 + 506.016i 0.630767 + 0.733357i
\(691\) 38.2694 142.823i 0.0553827 0.206691i −0.932690 0.360679i \(-0.882545\pi\)
0.988073 + 0.153988i \(0.0492117\pi\)
\(692\) 11.7216 + 104.528i 0.0169387 + 0.151052i
\(693\) 290.981 + 201.961i 0.419887 + 0.291431i
\(694\) −68.1863 141.686i −0.0982511 0.204158i
\(695\) −621.545 + 358.849i −0.894310 + 0.516330i
\(696\) 367.363 13.4543i 0.527820 0.0193309i
\(697\) 362.275 + 209.159i 0.519763 + 0.300085i
\(698\) 103.625 151.904i 0.148461 0.217628i
\(699\) 67.2814 67.2814i 0.0962538 0.0962538i
\(700\) 5.67179 + 198.708i 0.00810255 + 0.283868i
\(701\) 629.153 629.153i 0.897508 0.897508i −0.0977076 0.995215i \(-0.531151\pi\)
0.995215 + 0.0977076i \(0.0311510\pi\)
\(702\) 48.3034 + 255.659i 0.0688082 + 0.364187i
\(703\) −550.524 317.845i −0.783107 0.452127i
\(704\) 202.366 1060.33i 0.287452 1.50615i
\(705\) 227.029 131.075i 0.322026 0.185922i
\(706\) 52.1628 148.947i 0.0738850 0.210972i
\(707\) 170.899 80.5527i 0.241725 0.113936i
\(708\) −396.892 316.854i −0.560582 0.447534i
\(709\) −33.6859 + 125.717i −0.0475118 + 0.177316i −0.985604 0.169068i \(-0.945924\pi\)
0.938093 + 0.346385i \(0.112591\pi\)
\(710\) 46.3245 + 3.48385i 0.0652458 + 0.00490683i
\(711\) −106.083 61.2471i −0.149203 0.0861422i
\(712\) −18.9379 + 35.7636i −0.0265981 + 0.0502297i
\(713\) 510.152 0.715501
\(714\) −136.836 + 14.2271i −0.191647 + 0.0199259i
\(715\) 1691.73 + 1691.73i 2.36606 + 2.36606i
\(716\) 112.233 + 152.239i 0.156751 + 0.212624i
\(717\) −721.737 + 193.389i −1.00661 + 0.269719i
\(718\) 861.789 + 1001.95i 1.20026 + 1.39548i
\(719\) −115.680 + 66.7877i −0.160890 + 0.0928897i −0.578283 0.815836i \(-0.696277\pi\)
0.417393 + 0.908726i \(0.362944\pi\)
\(720\) 144.930 230.115i 0.201292 0.319604i
\(721\) 57.4137 48.5813i 0.0796307 0.0673805i
\(722\) −83.8517 + 239.432i −0.116138 + 0.331623i
\(723\) 141.132 + 37.8162i 0.195203 + 0.0523045i
\(724\) −166.345 + 380.718i −0.229759 + 0.525854i
\(725\) 181.934 48.7490i 0.250943 0.0672399i
\(726\) −467.843 319.151i −0.644412 0.439602i
\(727\) 1271.83 1.74942 0.874710 0.484646i \(-0.161052\pi\)
0.874710 + 0.484646i \(0.161052\pi\)
\(728\) 1400.50 + 65.2100i 1.92377 + 0.0895742i
\(729\) 27.0000i 0.0370370i
\(730\) −1243.88 848.543i −1.70394 1.16239i
\(731\) 43.9942 + 164.189i 0.0601836 + 0.224608i
\(732\) 160.928 + 410.675i 0.219847 + 0.561031i
\(733\) −140.784 + 525.414i −0.192066 + 0.716800i 0.800941 + 0.598743i \(0.204333\pi\)
−0.993007 + 0.118056i \(0.962334\pi\)
\(734\) 283.428 809.306i 0.386142 1.10260i
\(735\) 450.474 168.186i 0.612890 0.228825i
\(736\) −1081.23 123.271i −1.46906 0.167488i
\(737\) 314.877 + 545.382i 0.427241 + 0.740003i
\(738\) 288.481 + 335.401i 0.390896 + 0.454472i
\(739\) −183.241 683.867i −0.247959 0.925395i −0.971873 0.235505i \(-0.924326\pi\)
0.723914 0.689890i \(-0.242341\pi\)
\(740\) −140.810 + 930.874i −0.190283 + 1.25794i
\(741\) 469.205 469.205i 0.633206 0.633206i
\(742\) −785.548 + 569.390i −1.05869 + 0.767372i
\(743\) 929.675i 1.25124i −0.780126 0.625622i \(-0.784845\pi\)
0.780126 0.625622i \(-0.215155\pi\)
\(744\) −61.1114 198.677i −0.0821390 0.267039i
\(745\) 493.784 855.258i 0.662797 1.14800i
\(746\) 321.724 + 24.1953i 0.431266 + 0.0324334i
\(747\) −102.820 27.5505i −0.137644 0.0368815i
\(748\) 380.385 42.6557i 0.508537 0.0570263i
\(749\) −1014.47 84.5335i −1.35443 0.112862i
\(750\) −116.121 + 331.575i −0.154828 + 0.442100i
\(751\) 214.090 + 370.815i 0.285074 + 0.493762i 0.972627 0.232372i \(-0.0746486\pi\)
−0.687553 + 0.726134i \(0.741315\pi\)
\(752\) −126.417 + 408.302i −0.168108 + 0.542955i
\(753\) 174.405 302.078i 0.231613 0.401166i
\(754\) −246.622 1305.31i −0.327084 1.73119i
\(755\) −221.177 221.177i −0.292949 0.292949i
\(756\) −141.552 33.6311i −0.187238 0.0444856i
\(757\) −218.356 218.356i −0.288449 0.288449i 0.548018 0.836467i \(-0.315383\pi\)
−0.836467 + 0.548018i \(0.815383\pi\)
\(758\) 479.110 702.327i 0.632071 0.926553i
\(759\) −496.745 + 860.388i −0.654473 + 1.13358i
\(760\) −693.107 + 25.3844i −0.911983 + 0.0334005i
\(761\) −412.048 713.688i −0.541456 0.937829i −0.998821 0.0485498i \(-0.984540\pi\)
0.457365 0.889279i \(-0.348793\pi\)
\(762\) −9.45533 19.6475i −0.0124086 0.0257841i
\(763\) −1056.17 + 497.823i −1.38424 + 0.652455i
\(764\) −256.742 204.967i −0.336050 0.268282i
\(765\) 93.1454 + 24.9582i 0.121759 + 0.0326251i
\(766\) 775.933 + 902.132i 1.01297 + 1.17772i
\(767\) −917.609 + 1589.35i −1.19636 + 2.07216i
\(768\) 81.5135 + 435.848i 0.106137 + 0.567511i
\(769\) 387.514i 0.503919i 0.967738 + 0.251960i \(0.0810750\pi\)
−0.967738 + 0.251960i \(0.918925\pi\)
\(770\) −1249.53 + 478.044i −1.62277 + 0.620837i
\(771\) 277.544 277.544i 0.359980 0.359980i
\(772\) −149.286 + 986.908i −0.193375 + 1.27838i
\(773\) −58.5545 218.528i −0.0757497 0.282702i 0.917653 0.397384i \(-0.130082\pi\)
−0.993402 + 0.114682i \(0.963415\pi\)
\(774\) −13.4812 + 179.258i −0.0174175 + 0.231600i
\(775\) −53.2514 92.2341i −0.0687115 0.119012i
\(776\) 201.161 126.176i 0.259228 0.162598i
\(777\) 495.660 89.5107i 0.637915 0.115200i
\(778\) −491.138 1020.55i −0.631283 1.31176i
\(779\) 292.017 1089.82i 0.374862 1.39900i
\(780\) −900.530 393.463i −1.15453 0.504440i
\(781\) 17.8971 + 66.7930i 0.0229156 + 0.0855224i
\(782\) −71.6389 379.169i −0.0916098 0.484870i
\(783\) 137.853i 0.176058i
\(784\) −352.634 + 700.218i −0.449788 + 0.893136i
\(785\) −631.568 −0.804545
\(786\) 658.221 124.362i 0.837431 0.158221i
\(787\) 270.356 72.4416i 0.343527 0.0920478i −0.0829306 0.996555i \(-0.526428\pi\)
0.426458 + 0.904508i \(0.359761\pi\)
\(788\) 838.827 + 366.504i 1.06450 + 0.465106i
\(789\) −92.5529 24.7995i −0.117304 0.0314315i
\(790\) 416.907 200.636i 0.527731 0.253970i
\(791\) 2.49346 + 13.8074i 0.00315229 + 0.0174556i
\(792\) 394.581 + 90.3894i 0.498208 + 0.114128i
\(793\) 1380.36 796.953i 1.74068 1.00498i
\(794\) 1317.35 + 99.0715i 1.65913 + 0.124775i
\(795\) 656.883 176.011i 0.826268 0.221398i
\(796\) −189.132 + 1250.33i −0.237603 + 1.57076i
\(797\) 82.7487 + 82.7487i 0.103825 + 0.103825i 0.757111 0.653286i \(-0.226610\pi\)
−0.653286 + 0.757111i \(0.726610\pi\)
\(798\) 132.587 + 346.560i 0.166149 + 0.434286i
\(799\) −151.561 −0.189688
\(800\) 90.5753 + 208.351i 0.113219 + 0.260439i
\(801\) −13.1424 7.58779i −0.0164075 0.00947290i
\(802\) 373.789 321.499i 0.466071 0.400872i
\(803\) 580.093 2164.94i 0.722407 2.69606i
\(804\) −202.158 161.390i −0.251440 0.200734i
\(805\) 575.036 + 1219.99i 0.714330 + 1.51551i
\(806\) −676.843 + 325.730i −0.839756 + 0.404132i
\(807\) −588.742 + 339.910i −0.729543 + 0.421202i
\(808\) 146.990 158.166i 0.181918 0.195750i
\(809\) 419.670 + 242.297i 0.518752 + 0.299502i 0.736424 0.676520i \(-0.236513\pi\)
−0.217672 + 0.976022i \(0.569846\pi\)
\(810\) 84.2461 + 57.4706i 0.104007 + 0.0709513i
\(811\) 1033.29 1033.29i 1.27409 1.27409i 0.330168 0.943922i \(-0.392895\pi\)
0.943922 0.330168i \(-0.107105\pi\)
\(812\) 722.719 + 171.710i 0.890048 + 0.211465i
\(813\) −427.630 + 427.630i −0.525990 + 0.525990i
\(814\) −1377.01 + 260.168i −1.69166 + 0.319617i
\(815\) 321.840 + 185.814i 0.394896 + 0.227993i
\(816\) −139.084 + 73.3204i −0.170447 + 0.0898534i
\(817\) 397.041 229.232i 0.485974 0.280577i
\(818\) −181.593 63.5959i −0.221996 0.0777456i
\(819\) −43.6590 + 523.941i −0.0533077 + 0.639733i
\(820\) −1660.57 + 186.213i −2.02508 + 0.227089i
\(821\) −117.557 + 438.730i −0.143188 + 0.534385i 0.856641 + 0.515913i \(0.172547\pi\)
−0.999829 + 0.0184729i \(0.994120\pi\)
\(822\) 40.6968 541.143i 0.0495095 0.658325i
\(823\) −915.273 528.433i −1.11212 0.642081i −0.172741 0.984967i \(-0.555262\pi\)
−0.939377 + 0.342886i \(0.888596\pi\)
\(824\) 40.2237 75.9612i 0.0488152 0.0921860i
\(825\) 207.408 0.251403
\(826\) −602.280 830.923i −0.729152 1.00596i
\(827\) −82.6632 82.6632i −0.0999555 0.0999555i 0.655361 0.755316i \(-0.272517\pi\)
−0.755316 + 0.655361i \(0.772517\pi\)
\(828\) 61.0354 403.498i 0.0737143 0.487316i
\(829\) 549.953 147.359i 0.663393 0.177756i 0.0886163 0.996066i \(-0.471756\pi\)
0.574777 + 0.818310i \(0.305089\pi\)
\(830\) 304.820 262.179i 0.367253 0.315878i
\(831\) 655.297 378.336i 0.788564 0.455278i
\(832\) 1513.23 526.811i 1.81878 0.633187i
\(833\) −274.165 46.0107i −0.329129 0.0552349i
\(834\) 414.153 + 145.041i 0.496587 + 0.173910i
\(835\) 106.085 + 28.4253i 0.127048 + 0.0340423i
\(836\) −376.666 961.221i −0.450557 1.14979i
\(837\) 75.2927 20.1746i 0.0899554 0.0241035i
\(838\) 22.3470 32.7585i 0.0266671 0.0390912i
\(839\) −477.107 −0.568662 −0.284331 0.958726i \(-0.591771\pi\)
−0.284331 + 0.958726i \(0.591771\pi\)
\(840\) 406.236 370.089i 0.483614 0.440582i
\(841\) 137.165i 0.163097i
\(842\) −851.966 + 1248.90i −1.01184 + 1.48325i
\(843\) −69.2339 258.384i −0.0821280 0.306506i
\(844\) −63.6903 + 145.770i −0.0754625 + 0.172713i
\(845\) −671.313 + 2505.38i −0.794454 + 2.96494i
\(846\) −151.276 52.9785i −0.178813 0.0626223i
\(847\) −739.225 873.620i −0.872756 1.03143i
\(848\) −590.909 + 938.225i −0.696827 + 1.10640i
\(849\) 10.6912 + 18.5177i 0.0125927 + 0.0218112i
\(850\) −61.0748 + 52.5310i −0.0718527 + 0.0618012i
\(851\) 365.647 + 1364.61i 0.429668 + 1.60354i
\(852\) −16.8547 22.8626i −0.0197825 0.0268340i
\(853\) −39.2721 + 39.2721i −0.0460399 + 0.0460399i −0.729752 0.683712i \(-0.760364\pi\)
0.683712 + 0.729752i \(0.260364\pi\)
\(854\) 92.1734 + 886.523i 0.107931 + 1.03808i
\(855\) 260.089i 0.304198i
\(856\) −1111.99 + 342.040i −1.29906 + 0.399579i
\(857\) 357.357 618.961i 0.416986 0.722241i −0.578649 0.815577i \(-0.696420\pi\)
0.995635 + 0.0933358i \(0.0297530\pi\)
\(858\) 109.701 1458.69i 0.127857 1.70010i
\(859\) −234.311 62.7835i −0.272772 0.0730890i 0.119840 0.992793i \(-0.461762\pi\)
−0.392612 + 0.919704i \(0.628428\pi\)
\(860\) −530.631 423.623i −0.617013 0.492585i
\(861\) 381.148 + 808.638i 0.442681 + 0.939185i
\(862\) −402.688 141.026i −0.467156 0.163603i
\(863\) 824.318 + 1427.76i 0.955177 + 1.65442i 0.733962 + 0.679191i \(0.237669\pi\)
0.221216 + 0.975225i \(0.428997\pi\)
\(864\) −164.452 + 24.5652i −0.190338 + 0.0284319i
\(865\) 74.4913 129.023i 0.0861172 0.149159i
\(866\) 883.735 166.970i 1.02048 0.192806i
\(867\) 314.529 + 314.529i 0.362779 + 0.362779i
\(868\) −11.9843 419.864i −0.0138068 0.483714i
\(869\) 486.979 + 486.979i 0.560390 + 0.560390i
\(870\) −430.133 293.426i −0.494406 0.337272i
\(871\) −467.386 + 809.536i −0.536608 + 0.929432i
\(872\) −908.410 + 977.479i −1.04175 + 1.12096i
\(873\) 44.5233 + 77.1166i 0.0510003 + 0.0883352i
\(874\) −937.819 + 451.325i −1.07302 + 0.516390i
\(875\) −404.789 + 583.211i −0.462616 + 0.666527i
\(876\) 102.596 + 914.909i 0.117119 + 1.04442i
\(877\) 806.688 + 216.151i 0.919827 + 0.246467i 0.687511 0.726174i \(-0.258703\pi\)
0.232315 + 0.972641i \(0.425370\pi\)
\(878\) −288.169 + 247.857i −0.328210 + 0.282297i
\(879\) 68.6629 118.928i 0.0781148 0.135299i
\(880\) −1121.92 + 1038.78i −1.27491 + 1.18044i
\(881\) 330.602i 0.375258i 0.982240 + 0.187629i \(0.0600803\pi\)
−0.982240 + 0.187629i \(0.939920\pi\)
\(882\) −257.566 141.759i −0.292025 0.160725i
\(883\) 162.782 162.782i 0.184351 0.184351i −0.608898 0.793249i \(-0.708388\pi\)
0.793249 + 0.608898i \(0.208388\pi\)
\(884\) 337.145 + 457.320i 0.381385 + 0.517330i
\(885\) 186.178 + 694.826i 0.210371 + 0.785114i
\(886\) 880.623 + 66.2274i 0.993931 + 0.0747488i
\(887\) −64.9925 112.570i −0.0732722 0.126911i 0.827061 0.562112i \(-0.190011\pi\)
−0.900334 + 0.435200i \(0.856678\pi\)
\(888\) 487.643 305.868i 0.549148 0.344446i
\(889\) −7.83018 43.3591i −0.00880785 0.0487729i
\(890\) 51.6498 24.8564i 0.0580335 0.0279286i
\(891\) −39.2889 + 146.628i −0.0440953 + 0.164566i
\(892\) −93.1832 237.796i −0.104465 0.266588i
\(893\) 105.800 + 394.853i 0.118478 + 0.442164i
\(894\) −593.323 + 112.100i −0.663672 + 0.125392i
\(895\) 267.897i 0.299326i
\(896\) −76.0545 + 892.766i −0.0848823 + 0.996391i
\(897\) −1474.68 −1.64402
\(898\) 155.462 + 822.825i 0.173120 + 0.916286i
\(899\) −384.420 + 103.005i −0.427609 + 0.114577i
\(900\) −79.3224 + 31.0834i −0.0881360 + 0.0345371i
\(901\) −379.773 101.760i −0.421502 0.112941i
\(902\) −1078.59 2241.23i −1.19578 2.48474i
\(903\) −122.829 + 341.858i −0.136024 + 0.378580i
\(904\) 8.52043 + 13.5841i 0.00942526 + 0.0150266i
\(905\) 509.639 294.240i 0.563137 0.325127i
\(906\) −14.3423 + 190.709i −0.0158303 + 0.210495i
\(907\) −1521.62 + 407.716i −1.67764 + 0.449521i −0.967153 0.254194i \(-0.918190\pi\)
−0.710482 + 0.703715i \(0.751523\pi\)
\(908\) 276.079 203.531i 0.304052 0.224153i
\(909\) 57.2550 + 57.2550i 0.0629868 + 0.0629868i
\(910\) −1541.88 1251.46i −1.69438 1.37523i
\(911\) −1125.46 −1.23541 −0.617706 0.786409i \(-0.711938\pi\)
−0.617706 + 0.786409i \(0.711938\pi\)
\(912\) 288.109 + 311.166i 0.315909 + 0.341191i
\(913\) 518.291 + 299.235i 0.567679 + 0.327749i
\(914\) 215.446 + 250.487i 0.235718 + 0.274056i
\(915\) 161.698 603.464i 0.176719 0.659523i
\(916\) −799.493 + 89.6537i −0.872809 + 0.0978752i
\(917\) 1348.94 + 112.405i 1.47104 + 0.122579i
\(918\) −25.5678 53.1280i −0.0278516 0.0578736i
\(919\) −843.217 + 486.831i −0.917537 + 0.529740i −0.882849 0.469658i \(-0.844377\pi\)
−0.0346888 + 0.999398i \(0.511044\pi\)
\(920\) 1129.09 + 1049.31i 1.22727 + 1.14055i
\(921\) −733.176 423.299i −0.796065 0.459608i
\(922\) −640.455 + 938.842i −0.694636 + 1.01827i
\(923\) −72.5783 + 72.5783i −0.0786331 + 0.0786331i
\(924\) 719.784 + 388.618i 0.778987 + 0.420582i
\(925\) 208.551 208.551i 0.225461 0.225461i
\(926\) −118.422 626.782i −0.127886 0.676871i
\(927\) 27.9143 + 16.1163i 0.0301125 + 0.0173855i
\(928\) 839.641 125.422i 0.904785 0.135153i
\(929\) 339.800 196.183i 0.365769 0.211177i −0.305839 0.952083i \(-0.598937\pi\)
0.671609 + 0.740906i \(0.265604\pi\)
\(930\) −97.3142 + 277.873i −0.104639 + 0.298788i
\(931\) 71.5180 + 746.385i 0.0768184 + 0.801703i
\(932\) 137.096 171.727i 0.147099 0.184257i
\(933\) 42.8591 159.952i 0.0459369 0.171439i
\(934\) 1198.42 + 90.1271i 1.28310 + 0.0964958i
\(935\) −469.524 271.080i −0.502165 0.289925i
\(936\) 176.653 + 574.311i 0.188732 + 0.613580i
\(937\) −1345.02 −1.43545 −0.717726 0.696326i \(-0.754817\pi\)
−0.717726 + 0.696326i \(0.754817\pi\)
\(938\) −306.772 423.232i −0.327049 0.451207i
\(939\) −71.4847 71.4847i −0.0761285 0.0761285i
\(940\) 487.301 359.247i 0.518405 0.382178i
\(941\) −447.057 + 119.789i −0.475087 + 0.127299i −0.488414 0.872612i \(-0.662424\pi\)
0.0133269 + 0.999911i \(0.495758\pi\)
\(942\) 251.806 + 292.761i 0.267310 + 0.310786i
\(943\) −2171.52 + 1253.73i −2.30278 + 1.32951i
\(944\) −992.419 625.042i −1.05129 0.662120i
\(945\) 133.115 + 157.316i 0.140862 + 0.166472i
\(946\) 334.058 953.875i 0.353127 1.00833i
\(947\) −1152.67 308.858i −1.21719 0.326144i −0.407608 0.913157i \(-0.633637\pi\)
−0.809578 + 0.587013i \(0.800304\pi\)
\(948\) −259.225 113.262i −0.273444 0.119474i
\(949\) 3213.51 861.059i 3.38621 0.907332i
\(950\) 179.491 + 122.444i 0.188938 + 0.128889i
\(951\) 397.189 0.417654
\(952\) −310.379 + 67.8673i −0.326029 + 0.0712892i
\(953\) 1440.54i 1.51158i 0.654813 + 0.755791i \(0.272747\pi\)
−0.654813 + 0.755791i \(0.727253\pi\)
\(954\) −343.489 234.320i −0.360051 0.245618i
\(955\) 120.435 + 449.470i 0.126110 + 0.470650i
\(956\) −1606.63 + 629.576i −1.68057 + 0.658552i
\(957\) 200.596 748.636i 0.209610 0.782274i
\(958\) 109.800 313.524i 0.114614 0.327270i
\(959\) 370.796 1032.00i 0.386649 1.07612i
\(960\) 273.394 565.416i 0.284786 0.588975i
\(961\) −367.981 637.362i −0.382915 0.663228i
\(962\) −1356.42 1577.03i −1.41000 1.63933i
\(963\) −112.917 421.412i −0.117256 0.437604i
\(964\) 333.632 + 50.4672i 0.346092 + 0.0523519i
\(965\) 999.687 999.687i 1.03595 1.03595i
\(966\) 336.252 752.964i 0.348087 0.779466i
\(967\) 1828.35i 1.89075i −0.325986 0.945375i \(-0.605696\pi\)
0.325986 0.945375i \(-0.394304\pi\)
\(968\) −1155.84 612.053i −1.19405 0.632286i
\(969\) −75.1846 + 130.224i −0.0775899 + 0.134390i
\(970\) −335.391 25.2231i −0.345764 0.0260032i
\(971\) 301.047 + 80.6654i 0.310038 + 0.0830745i 0.410483 0.911868i \(-0.365360\pi\)
−0.100445 + 0.994943i \(0.532027\pi\)
\(972\) −6.94869 61.9654i −0.00714886 0.0637505i
\(973\) 728.459 + 505.602i 0.748674 + 0.519632i
\(974\) 65.0353 185.703i 0.0667713 0.190660i
\(975\) 153.932 + 266.619i 0.157879 + 0.273455i
\(976\) 475.023 + 901.089i 0.486704 + 0.923247i
\(977\) 713.538 1235.88i 0.730336 1.26498i −0.226404 0.974033i \(-0.572697\pi\)
0.956740 0.290945i \(-0.0939697\pi\)
\(978\) −42.1842 223.272i −0.0431332 0.228294i
\(979\) 60.3309 + 60.3309i 0.0616250 + 0.0616250i
\(980\) 990.561 501.924i 1.01078 0.512167i
\(981\) −353.841 353.841i −0.360695 0.360695i
\(982\) −159.606 + 233.967i −0.162532 + 0.238255i
\(983\) −707.090 + 1224.72i −0.719318 + 1.24590i 0.241952 + 0.970288i \(0.422212\pi\)
−0.961270 + 0.275608i \(0.911121\pi\)
\(984\) 748.388 + 695.507i 0.760557 + 0.706816i
\(985\) −648.291 1122.87i −0.658164 1.13997i
\(986\) 130.541 + 271.255i 0.132395 + 0.275106i
\(987\) −266.081 184.678i −0.269585 0.187111i
\(988\) 956.080 1197.59i 0.967692 1.21213i
\(989\) −984.167 263.707i −0.995113 0.266640i
\(990\) −373.885 434.694i −0.377661 0.439085i
\(991\) 17.9331 31.0611i 0.0180960 0.0313432i −0.856836 0.515590i \(-0.827573\pi\)
0.874932 + 0.484247i \(0.160906\pi\)
\(992\) −191.383 440.239i −0.192926 0.443790i
\(993\) 11.2151i 0.0112942i
\(994\) −20.5090 53.6071i −0.0206328 0.0539307i
\(995\) 1266.52 1266.52i 1.27288 1.27288i
\(996\) −243.064 36.7672i −0.244040 0.0369149i
\(997\) 343.406 + 1281.61i 0.344439 + 1.28546i 0.893266 + 0.449528i \(0.148408\pi\)
−0.548827 + 0.835936i \(0.684925\pi\)
\(998\) −90.1603 + 1198.86i −0.0903410 + 1.20126i
\(999\) 107.931 + 186.942i 0.108039 + 0.187129i
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 336.3.bv.a.325.35 yes 256
7.5 odd 6 inner 336.3.bv.a.229.52 yes 256
16.13 even 4 inner 336.3.bv.a.157.52 yes 256
112.61 odd 12 inner 336.3.bv.a.61.35 256
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
336.3.bv.a.61.35 256 112.61 odd 12 inner
336.3.bv.a.157.52 yes 256 16.13 even 4 inner
336.3.bv.a.229.52 yes 256 7.5 odd 6 inner
336.3.bv.a.325.35 yes 256 1.1 even 1 trivial