# Properties

 Label 108.4.h.b.71.7 Level 108 Weight 4 Character 108.71 Analytic conductor 6.372 Analytic rank 0 Dimension 24 CM no Inner twists 4

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$108 = 2^{2} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 108.h (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.37220628062$$ Analytic rank: $$0$$ Dimension: $$24$$ Relative dimension: $$12$$ over $$\Q(\zeta_{6})$$ Twist minimal: no (minimal twist has level 36) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 71.7 Character $$\chi$$ $$=$$ 108.71 Dual form 108.4.h.b.35.7

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.157323 - 2.82405i) q^{2} +(-7.95050 - 0.888573i) q^{4} +(1.23846 + 0.715028i) q^{5} +(-23.8818 + 13.7882i) q^{7} +(-3.76017 + 22.3128i) q^{8} +O(q^{10})$$ $$q+(0.157323 - 2.82405i) q^{2} +(-7.95050 - 0.888573i) q^{4} +(1.23846 + 0.715028i) q^{5} +(-23.8818 + 13.7882i) q^{7} +(-3.76017 + 22.3128i) q^{8} +(2.21411 - 3.38499i) q^{10} +(-11.1087 - 19.2409i) q^{11} +(-34.5965 + 59.9229i) q^{13} +(35.1813 + 69.6126i) q^{14} +(62.4209 + 14.1292i) q^{16} -31.4507i q^{17} +11.4986i q^{19} +(-9.21106 - 6.78529i) q^{20} +(-56.0849 + 28.3446i) q^{22} +(-72.6810 + 125.887i) q^{23} +(-61.4775 - 106.482i) q^{25} +(163.782 + 107.129i) q^{26} +(202.124 - 88.4021i) q^{28} +(93.6986 - 54.0969i) q^{29} +(102.800 + 59.3514i) q^{31} +(49.7218 - 174.057i) q^{32} +(-88.8183 - 4.94791i) q^{34} -39.4357 q^{35} -300.439 q^{37} +(32.4725 + 1.80899i) q^{38} +(-20.6111 + 24.9450i) q^{40} +(-344.853 - 199.101i) q^{41} +(-173.261 + 100.032i) q^{43} +(71.2231 + 162.846i) q^{44} +(344.077 + 225.060i) q^{46} +(-151.770 - 262.873i) q^{47} +(208.727 - 361.526i) q^{49} +(-310.382 + 156.863i) q^{50} +(328.305 - 445.675i) q^{52} -243.342i q^{53} -31.7722i q^{55} +(-217.853 - 584.716i) q^{56} +(-138.031 - 273.120i) q^{58} +(-41.9197 + 72.6070i) q^{59} +(199.218 + 345.055i) q^{61} +(183.784 - 280.974i) q^{62} +(-483.722 - 167.800i) q^{64} +(-85.6931 + 49.4749i) q^{65} +(307.763 + 177.687i) q^{67} +(-27.9463 + 250.049i) q^{68} +(-6.20413 + 111.368i) q^{70} +866.235 q^{71} +64.6645 q^{73} +(-47.2658 + 848.453i) q^{74} +(10.2173 - 91.4195i) q^{76} +(530.594 + 306.338i) q^{77} +(-354.896 + 204.899i) q^{79} +(67.2033 + 62.1312i) q^{80} +(-616.524 + 942.559i) q^{82} +(79.8990 + 138.389i) q^{83} +(22.4881 - 38.9506i) q^{85} +(255.238 + 505.035i) q^{86} +(471.089 - 175.518i) q^{88} +1493.47i q^{89} -1908.09i q^{91} +(689.710 - 936.283i) q^{92} +(-766.242 + 387.249i) q^{94} +(-8.22181 + 14.2406i) q^{95} +(700.115 + 1212.63i) q^{97} +(-988.129 - 646.332i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$24q - 12q^{4} + 72q^{5} + O(q^{10})$$ $$24q - 12q^{4} + 72q^{5} + 96q^{10} - 216q^{13} + 36q^{14} - 72q^{16} + 540q^{20} - 192q^{22} + 252q^{25} - 672q^{28} - 576q^{29} - 360q^{32} - 660q^{34} + 1248q^{37} + 144q^{38} + 636q^{40} - 1116q^{41} + 960q^{46} + 348q^{49} + 648q^{50} + 132q^{52} + 1692q^{56} + 516q^{58} - 264q^{61} + 960q^{64} + 2592q^{65} - 5688q^{68} + 564q^{70} - 4776q^{73} - 5652q^{74} - 600q^{76} - 648q^{77} - 4104q^{82} + 720q^{85} + 9540q^{86} + 1956q^{88} + 7416q^{92} - 1188q^{94} + 588q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$55$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.157323 2.82405i 0.0556219 0.998452i
$$3$$ 0 0
$$4$$ −7.95050 0.888573i −0.993812 0.111072i
$$5$$ 1.23846 + 0.715028i 0.110772 + 0.0639540i 0.554362 0.832275i $$-0.312962\pi$$
−0.443591 + 0.896230i $$0.646296\pi$$
$$6$$ 0 0
$$7$$ −23.8818 + 13.7882i −1.28950 + 0.744491i −0.978564 0.205941i $$-0.933974\pi$$
−0.310932 + 0.950432i $$0.600641\pi$$
$$8$$ −3.76017 + 22.3128i −0.166177 + 0.986096i
$$9$$ 0 0
$$10$$ 2.21411 3.38499i 0.0700164 0.107043i
$$11$$ −11.1087 19.2409i −0.304492 0.527396i 0.672656 0.739955i $$-0.265153\pi$$
−0.977148 + 0.212560i $$0.931820\pi$$
$$12$$ 0 0
$$13$$ −34.5965 + 59.9229i −0.738103 + 1.27843i 0.215245 + 0.976560i $$0.430945\pi$$
−0.953348 + 0.301872i $$0.902388\pi$$
$$14$$ 35.1813 + 69.6126i 0.671614 + 1.32891i
$$15$$ 0 0
$$16$$ 62.4209 + 14.1292i 0.975326 + 0.220769i
$$17$$ 31.4507i 0.448701i −0.974509 0.224351i $$-0.927974\pi$$
0.974509 0.224351i $$-0.0720261\pi$$
$$18$$ 0 0
$$19$$ 11.4986i 0.138840i 0.997588 + 0.0694199i $$0.0221148\pi$$
−0.997588 + 0.0694199i $$0.977885\pi$$
$$20$$ −9.21106 6.78529i −0.102983 0.0758619i
$$21$$ 0 0
$$22$$ −56.0849 + 28.3446i −0.543516 + 0.274686i
$$23$$ −72.6810 + 125.887i −0.658914 + 1.14127i 0.321983 + 0.946746i $$0.395651\pi$$
−0.980897 + 0.194528i $$0.937683\pi$$
$$24$$ 0 0
$$25$$ −61.4775 106.482i −0.491820 0.851857i
$$26$$ 163.782 + 107.129i 1.23540 + 0.808070i
$$27$$ 0 0
$$28$$ 202.124 88.4021i 1.36421 0.596658i
$$29$$ 93.6986 54.0969i 0.599979 0.346398i −0.169054 0.985607i $$-0.554071\pi$$
0.769033 + 0.639209i $$0.220738\pi$$
$$30$$ 0 0
$$31$$ 102.800 + 59.3514i 0.595592 + 0.343865i 0.767306 0.641282i $$-0.221597\pi$$
−0.171713 + 0.985147i $$0.554930\pi$$
$$32$$ 49.7218 174.057i 0.274677 0.961537i
$$33$$ 0 0
$$34$$ −88.8183 4.94791i −0.448006 0.0249576i
$$35$$ −39.4357 −0.190453
$$36$$ 0 0
$$37$$ −300.439 −1.33491 −0.667457 0.744649i $$-0.732617\pi$$
−0.667457 + 0.744649i $$0.732617\pi$$
$$38$$ 32.4725 + 1.80899i 0.138625 + 0.00772254i
$$39$$ 0 0
$$40$$ −20.6111 + 24.9450i −0.0814726 + 0.0986037i
$$41$$ −344.853 199.101i −1.31359 0.758399i −0.330897 0.943667i $$-0.607351\pi$$
−0.982688 + 0.185268i $$0.940685\pi$$
$$42$$ 0 0
$$43$$ −173.261 + 100.032i −0.614467 + 0.354763i −0.774712 0.632315i $$-0.782105\pi$$
0.160245 + 0.987077i $$0.448772\pi$$
$$44$$ 71.2231 + 162.846i 0.244029 + 0.557953i
$$45$$ 0 0
$$46$$ 344.077 + 225.060i 1.10286 + 0.721374i
$$47$$ −151.770 262.873i −0.471018 0.815828i 0.528432 0.848976i $$-0.322780\pi$$
−0.999450 + 0.0331478i $$0.989447\pi$$
$$48$$ 0 0
$$49$$ 208.727 361.526i 0.608534 1.05401i
$$50$$ −310.382 + 156.863i −0.877894 + 0.443676i
$$51$$ 0 0
$$52$$ 328.305 445.675i 0.875534 1.18854i
$$53$$ 243.342i 0.630673i −0.948980 0.315336i $$-0.897883\pi$$
0.948980 0.315336i $$-0.102117\pi$$
$$54$$ 0 0
$$55$$ 31.7722i 0.0778940i
$$56$$ −217.853 584.716i −0.519854 1.39528i
$$57$$ 0 0
$$58$$ −138.031 273.120i −0.312490 0.618318i
$$59$$ −41.9197 + 72.6070i −0.0924996 + 0.160214i −0.908562 0.417749i $$-0.862819\pi$$
0.816063 + 0.577963i $$0.196152\pi$$
$$60$$ 0 0
$$61$$ 199.218 + 345.055i 0.418151 + 0.724259i 0.995754 0.0920592i $$-0.0293449\pi$$
−0.577602 + 0.816318i $$0.696012\pi$$
$$62$$ 183.784 280.974i 0.376461 0.575544i
$$63$$ 0 0
$$64$$ −483.722 167.800i −0.944770 0.327734i
$$65$$ −85.6931 + 49.4749i −0.163522 + 0.0944094i
$$66$$ 0 0
$$67$$ 307.763 + 177.687i 0.561183 + 0.323999i 0.753620 0.657310i $$-0.228306\pi$$
−0.192437 + 0.981309i $$0.561639\pi$$
$$68$$ −27.9463 + 250.049i −0.0498380 + 0.445925i
$$69$$ 0 0
$$70$$ −6.20413 + 111.368i −0.0105934 + 0.190158i
$$71$$ 866.235 1.44793 0.723966 0.689836i $$-0.242317\pi$$
0.723966 + 0.689836i $$0.242317\pi$$
$$72$$ 0 0
$$73$$ 64.6645 0.103677 0.0518384 0.998655i $$-0.483492\pi$$
0.0518384 + 0.998655i $$0.483492\pi$$
$$74$$ −47.2658 + 848.453i −0.0742505 + 1.33285i
$$75$$ 0 0
$$76$$ 10.2173 91.4195i 0.0154212 0.137981i
$$77$$ 530.594 + 306.338i 0.785283 + 0.453383i
$$78$$ 0 0
$$79$$ −354.896 + 204.899i −0.505429 + 0.291809i −0.730953 0.682428i $$-0.760924\pi$$
0.225524 + 0.974238i $$0.427591\pi$$
$$80$$ 67.2033 + 62.1312i 0.0939194 + 0.0868310i
$$81$$ 0 0
$$82$$ −616.524 + 942.559i −0.830289 + 1.26937i
$$83$$ 79.8990 + 138.389i 0.105663 + 0.183014i 0.914009 0.405694i $$-0.132970\pi$$
−0.808346 + 0.588708i $$0.799637\pi$$
$$84$$ 0 0
$$85$$ 22.4881 38.9506i 0.0286962 0.0497034i
$$86$$ 255.238 + 505.035i 0.320036 + 0.633248i
$$87$$ 0 0
$$88$$ 471.089 175.518i 0.570662 0.212617i
$$89$$ 1493.47i 1.77873i 0.457195 + 0.889366i $$0.348854\pi$$
−0.457195 + 0.889366i $$0.651146\pi$$
$$90$$ 0 0
$$91$$ 1908.09i 2.19805i
$$92$$ 689.710 936.283i 0.781600 1.06102i
$$93$$ 0 0
$$94$$ −766.242 + 387.249i −0.840764 + 0.424911i
$$95$$ −8.22181 + 14.2406i −0.00887936 + 0.0153795i
$$96$$ 0 0
$$97$$ 700.115 + 1212.63i 0.732844 + 1.26932i 0.955663 + 0.294463i $$0.0951408\pi$$
−0.222819 + 0.974860i $$0.571526\pi$$
$$98$$ −988.129 646.332i −1.01853 0.666218i
$$99$$ 0 0
$$100$$ 394.159 + 901.213i 0.394159 + 0.901213i
$$101$$ 207.342 119.709i 0.204270 0.117936i −0.394375 0.918949i $$-0.629039\pi$$
0.598646 + 0.801014i $$0.295706\pi$$
$$102$$ 0 0
$$103$$ 504.070 + 291.025i 0.482208 + 0.278403i 0.721336 0.692585i $$-0.243528\pi$$
−0.239128 + 0.970988i $$0.576862\pi$$
$$104$$ −1206.96 997.265i −1.13800 0.940287i
$$105$$ 0 0
$$106$$ −687.211 38.2833i −0.629696 0.0350792i
$$107$$ −1470.35 −1.32845 −0.664224 0.747533i $$-0.731238\pi$$
−0.664224 + 0.747533i $$0.731238\pi$$
$$108$$ 0 0
$$109$$ −1.40399 −0.00123374 −0.000616870 1.00000i $$-0.500196\pi$$
−0.000616870 1.00000i $$0.500196\pi$$
$$110$$ −89.7264 4.99849i −0.0777734 0.00433261i
$$111$$ 0 0
$$112$$ −1685.54 + 523.239i −1.42204 + 0.441441i
$$113$$ 1174.77 + 678.256i 0.977996 + 0.564646i 0.901664 0.432436i $$-0.142346\pi$$
0.0763312 + 0.997083i $$0.475679\pi$$
$$114$$ 0 0
$$115$$ −180.026 + 103.938i −0.145978 + 0.0842805i
$$116$$ −793.020 + 346.840i −0.634742 + 0.277614i
$$117$$ 0 0
$$118$$ 198.451 + 129.806i 0.154821 + 0.101268i
$$119$$ 433.648 + 751.100i 0.334054 + 0.578598i
$$120$$ 0 0
$$121$$ 418.692 725.195i 0.314569 0.544850i
$$122$$ 1005.79 508.316i 0.746396 0.377219i
$$123$$ 0 0
$$124$$ −764.570 563.218i −0.553713 0.407891i
$$125$$ 354.589i 0.253724i
$$126$$ 0 0
$$127$$ 547.847i 0.382784i 0.981514 + 0.191392i $$0.0613002\pi$$
−0.981514 + 0.191392i $$0.938700\pi$$
$$128$$ −549.975 + 1339.66i −0.379776 + 0.925078i
$$129$$ 0 0
$$130$$ 126.238 + 249.785i 0.0851678 + 0.168520i
$$131$$ 931.609 1613.59i 0.621336 1.07619i −0.367901 0.929865i $$-0.619923\pi$$
0.989237 0.146321i $$-0.0467433\pi$$
$$132$$ 0 0
$$133$$ −158.544 274.607i −0.103365 0.179033i
$$134$$ 550.216 841.185i 0.354712 0.542293i
$$135$$ 0 0
$$136$$ 701.754 + 118.260i 0.442462 + 0.0745640i
$$137$$ −1253.96 + 723.973i −0.781992 + 0.451483i −0.837136 0.546995i $$-0.815772\pi$$
0.0551439 + 0.998478i $$0.482438\pi$$
$$138$$ 0 0
$$139$$ −324.131 187.137i −0.197787 0.114193i 0.397836 0.917457i $$-0.369761\pi$$
−0.595623 + 0.803264i $$0.703095\pi$$
$$140$$ 313.533 + 35.0415i 0.189274 + 0.0211539i
$$141$$ 0 0
$$142$$ 136.278 2446.29i 0.0805368 1.44569i
$$143$$ 1537.29 0.898986
$$144$$ 0 0
$$145$$ 154.723 0.0886143
$$146$$ 10.1732 182.616i 0.00576670 0.103516i
$$147$$ 0 0
$$148$$ 2388.64 + 266.962i 1.32665 + 0.148271i
$$149$$ −2138.30 1234.55i −1.17568 0.678779i −0.220669 0.975349i $$-0.570824\pi$$
−0.955011 + 0.296570i $$0.904157\pi$$
$$150$$ 0 0
$$151$$ −525.453 + 303.370i −0.283184 + 0.163496i −0.634864 0.772624i $$-0.718944\pi$$
0.351680 + 0.936120i $$0.385610\pi$$
$$152$$ −256.566 43.2366i −0.136909 0.0230720i
$$153$$ 0 0
$$154$$ 948.589 1450.23i 0.496360 0.758849i
$$155$$ 84.8758 + 147.009i 0.0439832 + 0.0761811i
$$156$$ 0 0
$$157$$ 37.1699 64.3801i 0.0188948 0.0327267i −0.856423 0.516274i $$-0.827319\pi$$
0.875318 + 0.483547i $$0.160652\pi$$
$$158$$ 522.812 + 1034.48i 0.263245 + 0.520877i
$$159$$ 0 0
$$160$$ 186.034 180.011i 0.0919205 0.0889443i
$$161$$ 4008.55i 1.96222i
$$162$$ 0 0
$$163$$ 40.4850i 0.0194542i 0.999953 + 0.00972709i $$0.00309628\pi$$
−0.999953 + 0.00972709i $$0.996904\pi$$
$$164$$ 2564.84 + 1889.38i 1.22122 + 0.899608i
$$165$$ 0 0
$$166$$ 403.388 203.867i 0.188608 0.0953201i
$$167$$ −20.5614 + 35.6135i −0.00952750 + 0.0165021i −0.870750 0.491726i $$-0.836366\pi$$
0.861222 + 0.508228i $$0.169699\pi$$
$$168$$ 0 0
$$169$$ −1295.34 2243.59i −0.589593 1.02121i
$$170$$ −106.460 69.6354i −0.0480303 0.0314164i
$$171$$ 0 0
$$172$$ 1466.40 641.352i 0.650069 0.284318i
$$173$$ 952.460 549.903i 0.418579 0.241667i −0.275890 0.961189i $$-0.588973\pi$$
0.694469 + 0.719522i $$0.255639\pi$$
$$174$$ 0 0
$$175$$ 2936.39 + 1695.32i 1.26840 + 0.732311i
$$176$$ −421.559 1357.99i −0.180547 0.581605i
$$177$$ 0 0
$$178$$ 4217.62 + 234.956i 1.77598 + 0.0989366i
$$179$$ −3849.91 −1.60757 −0.803787 0.594917i $$-0.797185\pi$$
−0.803787 + 0.594917i $$0.797185\pi$$
$$180$$ 0 0
$$181$$ −1091.65 −0.448296 −0.224148 0.974555i $$-0.571960\pi$$
−0.224148 + 0.974555i $$0.571960\pi$$
$$182$$ −5388.54 300.186i −2.19464 0.122260i
$$183$$ 0 0
$$184$$ −2535.60 2095.07i −1.01591 0.839407i
$$185$$ −372.083 214.822i −0.147871 0.0853731i
$$186$$ 0 0
$$187$$ −605.140 + 349.378i −0.236643 + 0.136626i
$$188$$ 973.062 + 2224.83i 0.377489 + 0.863097i
$$189$$ 0 0
$$190$$ 38.9226 + 25.4591i 0.0148618 + 0.00972105i
$$191$$ 319.673 + 553.690i 0.121103 + 0.209757i 0.920203 0.391441i $$-0.128023\pi$$
−0.799100 + 0.601199i $$0.794690\pi$$
$$192$$ 0 0
$$193$$ −874.103 + 1513.99i −0.326007 + 0.564660i −0.981716 0.190353i $$-0.939037\pi$$
0.655709 + 0.755014i $$0.272370\pi$$
$$194$$ 3534.68 1786.38i 1.30812 0.661107i
$$195$$ 0 0
$$196$$ −1980.73 + 2688.84i −0.721839 + 0.979899i
$$197$$ 2079.55i 0.752089i 0.926602 + 0.376044i $$0.122716\pi$$
−0.926602 + 0.376044i $$0.877284\pi$$
$$198$$ 0 0
$$199$$ 1834.81i 0.653598i 0.945094 + 0.326799i $$0.105970\pi$$
−0.945094 + 0.326799i $$0.894030\pi$$
$$200$$ 2607.08 971.344i 0.921742 0.343422i
$$201$$ 0 0
$$202$$ −305.444 604.377i −0.106391 0.210514i
$$203$$ −1491.80 + 2583.86i −0.515781 + 0.893358i
$$204$$ 0 0
$$205$$ −284.726 493.159i −0.0970053 0.168018i
$$206$$ 901.169 1377.73i 0.304793 0.465976i
$$207$$ 0 0
$$208$$ −3006.21 + 3251.62i −1.00213 + 1.08394i
$$209$$ 221.243 127.735i 0.0732235 0.0422756i
$$210$$ 0 0
$$211$$ −4307.35 2486.85i −1.40536 0.811383i −0.410421 0.911896i $$-0.634618\pi$$
−0.994936 + 0.100513i $$0.967952\pi$$
$$212$$ −216.228 + 1934.69i −0.0700498 + 0.626770i
$$213$$ 0 0
$$214$$ −231.319 + 4152.34i −0.0738909 + 1.32639i
$$215$$ −286.104 −0.0907540
$$216$$ 0 0
$$217$$ −3273.39 −1.02402
$$218$$ −0.220879 + 3.96493i −6.86230e−5 + 0.00123183i
$$219$$ 0 0
$$220$$ −28.2320 + 252.605i −0.00865181 + 0.0774120i
$$221$$ 1884.62 + 1088.08i 0.573634 + 0.331188i
$$222$$ 0 0
$$223$$ −611.995 + 353.335i −0.183777 + 0.106103i −0.589066 0.808085i $$-0.700504\pi$$
0.405289 + 0.914189i $$0.367171\pi$$
$$224$$ 1212.48 + 4842.36i 0.361661 + 1.44439i
$$225$$ 0 0
$$226$$ 2100.25 3210.92i 0.618170 0.945075i
$$227$$ −1604.80 2779.60i −0.469227 0.812725i 0.530154 0.847901i $$-0.322134\pi$$
−0.999381 + 0.0351765i $$0.988801\pi$$
$$228$$ 0 0
$$229$$ −731.826 + 1267.56i −0.211181 + 0.365776i −0.952084 0.305836i $$-0.901064\pi$$
0.740904 + 0.671611i $$0.234398\pi$$
$$230$$ 265.203 + 524.753i 0.0760304 + 0.150440i
$$231$$ 0 0
$$232$$ 854.732 + 2294.09i 0.241879 + 0.649201i
$$233$$ 1324.13i 0.372303i −0.982521 0.186152i $$-0.940398\pi$$
0.982521 0.186152i $$-0.0596015\pi$$
$$234$$ 0 0
$$235$$ 434.078i 0.120494i
$$236$$ 397.799 540.013i 0.109722 0.148949i
$$237$$ 0 0
$$238$$ 2189.37 1106.48i 0.596283 0.301354i
$$239$$ 394.528 683.342i 0.106778 0.184944i −0.807685 0.589614i $$-0.799280\pi$$
0.914463 + 0.404669i $$0.132613\pi$$
$$240$$ 0 0
$$241$$ 1170.39 + 2027.17i 0.312827 + 0.541832i 0.978973 0.203989i $$-0.0653907\pi$$
−0.666146 + 0.745821i $$0.732057\pi$$
$$242$$ −1982.12 1296.50i −0.526509 0.344388i
$$243$$ 0 0
$$244$$ −1277.27 2920.38i −0.335119 0.766222i
$$245$$ 517.002 298.491i 0.134817 0.0778364i
$$246$$ 0 0
$$247$$ −689.028 397.811i −0.177497 0.102478i
$$248$$ −1710.84 + 2070.58i −0.438058 + 0.530168i
$$249$$ 0 0
$$250$$ −1001.38 55.7849i −0.253331 0.0141126i
$$251$$ 938.044 0.235892 0.117946 0.993020i $$-0.462369\pi$$
0.117946 + 0.993020i $$0.462369\pi$$
$$252$$ 0 0
$$253$$ 3229.58 0.802537
$$254$$ 1547.15 + 86.1887i 0.382191 + 0.0212912i
$$255$$ 0 0
$$256$$ 3696.73 + 1763.91i 0.902522 + 0.430643i
$$257$$ −143.756 82.9975i −0.0348920 0.0201449i 0.482453 0.875922i $$-0.339746\pi$$
−0.517345 + 0.855777i $$0.673079\pi$$
$$258$$ 0 0
$$259$$ 7175.02 4142.50i 1.72137 0.993831i
$$260$$ 725.265 317.206i 0.172996 0.0756626i
$$261$$ 0 0
$$262$$ −4410.31 2884.76i −1.03996 0.680234i
$$263$$ 2415.87 + 4184.41i 0.566422 + 0.981072i 0.996916 + 0.0784782i $$0.0250061\pi$$
−0.430494 + 0.902594i $$0.641661\pi$$
$$264$$ 0 0
$$265$$ 173.997 301.371i 0.0403341 0.0698606i
$$266$$ −800.446 + 404.535i −0.184506 + 0.0932468i
$$267$$ 0 0
$$268$$ −2288.98 1686.17i −0.521724 0.384326i
$$269$$ 5581.42i 1.26508i 0.774529 + 0.632538i $$0.217987\pi$$
−0.774529 + 0.632538i $$0.782013\pi$$
$$270$$ 0 0
$$271$$ 8094.32i 1.81437i 0.420729 + 0.907186i $$0.361774\pi$$
−0.420729 + 0.907186i $$0.638226\pi$$
$$272$$ 444.374 1963.18i 0.0990592 0.437630i
$$273$$ 0 0
$$274$$ 1847.26 + 3655.14i 0.407288 + 0.805894i
$$275$$ −1365.87 + 2365.76i −0.299510 + 0.518767i
$$276$$ 0 0
$$277$$ 922.842 + 1598.41i 0.200174 + 0.346712i 0.948584 0.316524i $$-0.102516\pi$$
−0.748410 + 0.663236i $$0.769183\pi$$
$$278$$ −579.477 + 885.921i −0.125017 + 0.191130i
$$279$$ 0 0
$$280$$ 148.285 879.921i 0.0316490 0.187805i
$$281$$ 2195.00 1267.28i 0.465987 0.269038i −0.248571 0.968614i $$-0.579961\pi$$
0.714558 + 0.699576i $$0.246628\pi$$
$$282$$ 0 0
$$283$$ −2691.52 1553.95i −0.565351 0.326405i 0.189940 0.981796i $$-0.439171\pi$$
−0.755290 + 0.655390i $$0.772504\pi$$
$$284$$ −6887.00 769.713i −1.43897 0.160824i
$$285$$ 0 0
$$286$$ 241.851 4341.39i 0.0500034 0.897595i
$$287$$ 10981.0 2.25848
$$288$$ 0 0
$$289$$ 3923.85 0.798667
$$290$$ 24.3415 436.946i 0.00492890 0.0884771i
$$291$$ 0 0
$$292$$ −514.115 57.4591i −0.103035 0.0115156i
$$293$$ −4824.35 2785.34i −0.961916 0.555363i −0.0651539 0.997875i $$-0.520754\pi$$
−0.896762 + 0.442513i $$0.854087\pi$$
$$294$$ 0 0
$$295$$ −103.832 + 59.9475i −0.0204927 + 0.0118314i
$$296$$ 1129.70 6703.63i 0.221833 1.31635i
$$297$$ 0 0
$$298$$ −3822.83 + 5844.44i −0.743122 + 1.13610i
$$299$$ −5029.02 8710.51i −0.972694 1.68476i
$$300$$ 0 0
$$301$$ 2758.53 4777.91i 0.528235 0.914930i
$$302$$ 774.067 + 1531.63i 0.147492 + 0.291839i
$$303$$ 0 0
$$304$$ −162.466 + 717.751i −0.0306515 + 0.135414i
$$305$$ 569.785i 0.106970i
$$306$$ 0 0
$$307$$ 7746.70i 1.44016i −0.693893 0.720078i $$-0.744106\pi$$
0.693893 0.720078i $$-0.255894\pi$$
$$308$$ −3946.28 2907.01i −0.730066 0.537800i
$$309$$ 0 0
$$310$$ 428.514 216.566i 0.0785096 0.0396777i
$$311$$ 2906.54 5034.28i 0.529951 0.917902i −0.469438 0.882965i $$-0.655544\pi$$
0.999390 0.0349372i $$-0.0111231\pi$$
$$312$$ 0 0
$$313$$ −1367.73 2368.98i −0.246993 0.427805i 0.715697 0.698411i $$-0.246109\pi$$
−0.962690 + 0.270606i $$0.912776\pi$$
$$314$$ −175.965 115.098i −0.0316251 0.0206858i
$$315$$ 0 0
$$316$$ 3003.67 1313.70i 0.534713 0.233865i
$$317$$ −5434.46 + 3137.59i −0.962869 + 0.555913i −0.897055 0.441919i $$-0.854298\pi$$
−0.0658143 + 0.997832i $$0.520965\pi$$
$$318$$ 0 0
$$319$$ −2081.75 1201.90i −0.365378 0.210951i
$$320$$ −479.091 553.689i −0.0836938 0.0967255i
$$321$$ 0 0
$$322$$ −11320.3 630.636i −1.95919 0.109143i
$$323$$ 361.639 0.0622976
$$324$$ 0 0
$$325$$ 8507.62 1.45206
$$326$$ 114.332 + 6.36921i 0.0194241 + 0.00108208i
$$327$$ 0 0
$$328$$ 5739.21 6945.99i 0.966142 1.16929i
$$329$$ 7249.06 + 4185.25i 1.21475 + 0.701338i
$$330$$ 0 0
$$331$$ −302.371 + 174.574i −0.0502110 + 0.0289893i −0.524895 0.851167i $$-0.675896\pi$$
0.474684 + 0.880156i $$0.342562\pi$$
$$332$$ −512.268 1171.26i −0.0846818 0.193618i
$$333$$ 0 0
$$334$$ 97.3394 + 63.6693i 0.0159466 + 0.0104306i
$$335$$ 254.103 + 440.119i 0.0414421 + 0.0717799i
$$336$$ 0 0
$$337$$ −4663.04 + 8076.62i −0.753744 + 1.30552i 0.192252 + 0.981346i $$0.438421\pi$$
−0.945996 + 0.324178i $$0.894912\pi$$
$$338$$ −6539.79 + 3305.13i −1.05242 + 0.531879i
$$339$$ 0 0
$$340$$ −213.402 + 289.694i −0.0340393 + 0.0462085i
$$341$$ 2637.28i 0.418817i
$$342$$ 0 0
$$343$$ 2053.18i 0.323210i
$$344$$ −1580.51 4242.08i −0.247719 0.664877i
$$345$$ 0 0
$$346$$ −1403.11 2776.31i −0.218011 0.431373i
$$347$$ −2780.66 + 4816.24i −0.430183 + 0.745098i −0.996889 0.0788217i $$-0.974884\pi$$
0.566706 + 0.823920i $$0.308218\pi$$
$$348$$ 0 0
$$349$$ −5336.11 9242.41i −0.818439 1.41758i −0.906832 0.421492i $$-0.861506\pi$$
0.0883931 0.996086i $$-0.471827\pi$$
$$350$$ 5249.64 8025.78i 0.801728 1.22570i
$$351$$ 0 0
$$352$$ −3901.36 + 976.860i −0.590747 + 0.147917i
$$353$$ −349.651 + 201.871i −0.0527196 + 0.0304377i −0.526128 0.850405i $$-0.676357\pi$$
0.473409 + 0.880843i $$0.343023\pi$$
$$354$$ 0 0
$$355$$ 1072.80 + 619.382i 0.160390 + 0.0926011i
$$356$$ 1327.06 11873.8i 0.197567 1.76773i
$$357$$ 0 0
$$358$$ −605.678 + 10872.3i −0.0894164 + 1.60509i
$$359$$ −6398.10 −0.940609 −0.470305 0.882504i $$-0.655856\pi$$
−0.470305 + 0.882504i $$0.655856\pi$$
$$360$$ 0 0
$$361$$ 6726.78 0.980724
$$362$$ −171.741 + 3082.87i −0.0249351 + 0.447602i
$$363$$ 0 0
$$364$$ −1695.48 + 15170.3i −0.244141 + 2.18444i
$$365$$ 80.0847 + 46.2369i 0.0114844 + 0.00663055i
$$366$$ 0 0
$$367$$ 9573.58 5527.31i 1.36168 0.786166i 0.371833 0.928300i $$-0.378730\pi$$
0.989848 + 0.142133i $$0.0453962\pi$$
$$368$$ −6315.50 + 6831.06i −0.894614 + 0.967646i
$$369$$ 0 0
$$370$$ −665.205 + 1016.98i −0.0934658 + 0.142893i
$$371$$ 3355.25 + 5811.46i 0.469530 + 0.813250i
$$372$$ 0 0
$$373$$ −1756.18 + 3041.80i −0.243785 + 0.422248i −0.961789 0.273791i $$-0.911722\pi$$
0.718004 + 0.696039i $$0.245056\pi$$
$$374$$ 891.458 + 1763.91i 0.123252 + 0.243876i
$$375$$ 0 0
$$376$$ 6436.10 2397.96i 0.882757 0.328897i
$$377$$ 7486.26i 1.02271i
$$378$$ 0 0
$$379$$ 1238.70i 0.167883i 0.996471 + 0.0839413i $$0.0267508\pi$$
−0.996471 + 0.0839413i $$0.973249\pi$$
$$380$$ 78.0213 105.914i 0.0105326 0.0142981i
$$381$$ 0 0
$$382$$ 1613.94 815.665i 0.216169 0.109249i
$$383$$ −853.999 + 1479.17i −0.113936 + 0.197342i −0.917354 0.398073i $$-0.869679\pi$$
0.803418 + 0.595415i $$0.203012\pi$$
$$384$$ 0 0
$$385$$ 438.081 + 758.779i 0.0579914 + 0.100444i
$$386$$ 4138.07 + 2706.69i 0.545653 + 0.356910i
$$387$$ 0 0
$$388$$ −4488.75 10263.1i −0.587324 1.34287i
$$389$$ 7751.80 4475.50i 1.01036 0.583334i 0.0990663 0.995081i $$-0.468414\pi$$
0.911298 + 0.411746i $$0.135081\pi$$
$$390$$ 0 0
$$391$$ 3959.24 + 2285.87i 0.512091 + 0.295656i
$$392$$ 7281.81 + 6016.69i 0.938232 + 0.775226i
$$393$$ 0 0
$$394$$ 5872.74 + 327.159i 0.750924 + 0.0418326i
$$395$$ −586.034 −0.0746496
$$396$$ 0 0
$$397$$ −9391.26 −1.18724 −0.593619 0.804746i $$-0.702302\pi$$
−0.593619 + 0.804746i $$0.702302\pi$$
$$398$$ 5181.59 + 288.657i 0.652586 + 0.0363544i
$$399$$ 0 0
$$400$$ −2332.97 7515.33i −0.291621 0.939417i
$$401$$ −3528.74 2037.32i −0.439444 0.253713i 0.263918 0.964545i $$-0.414985\pi$$
−0.703362 + 0.710832i $$0.748319\pi$$
$$402$$ 0 0
$$403$$ −7113.02 + 4106.70i −0.879217 + 0.507616i
$$404$$ −1754.84 + 767.508i −0.216106 + 0.0945172i
$$405$$ 0 0
$$406$$ 7062.27 + 4619.40i 0.863287 + 0.564673i
$$407$$ 3337.50 + 5780.71i 0.406471 + 0.704028i
$$408$$ 0 0
$$409$$ 335.715 581.476i 0.0405869 0.0702986i −0.845018 0.534737i $$-0.820411\pi$$
0.885605 + 0.464439i $$0.153744\pi$$
$$410$$ −1437.50 + 726.494i −0.173154 + 0.0875097i
$$411$$ 0 0
$$412$$ −3749.01 2761.69i −0.448302 0.330240i
$$413$$ 2311.98i 0.275460i
$$414$$ 0 0
$$415$$ 228.520i 0.0270304i
$$416$$ 8709.79 + 9001.23i 1.02652 + 1.06087i
$$417$$ 0 0
$$418$$ −325.923 644.897i −0.0381373 0.0754616i
$$419$$ 4703.57 8146.83i 0.548412 0.949877i −0.449972 0.893043i $$-0.648566\pi$$
0.998384 0.0568346i $$-0.0181008\pi$$
$$420$$ 0 0
$$421$$ 6156.19 + 10662.8i 0.712671 + 1.23438i 0.963851 + 0.266441i $$0.0858479\pi$$
−0.251181 + 0.967940i $$0.580819\pi$$
$$422$$ −7700.63 + 11772.9i −0.888296 + 1.35805i
$$423$$ 0 0
$$424$$ 5429.65 + 915.008i 0.621904 + 0.104804i
$$425$$ −3348.94 + 1933.51i −0.382229 + 0.220680i
$$426$$ 0 0
$$427$$ −9515.36 5493.70i −1.07841 0.622620i
$$428$$ 11690.0 + 1306.51i 1.32023 + 0.147553i
$$429$$ 0 0
$$430$$ −45.0106 + 807.971i −0.00504791 + 0.0906135i
$$431$$ −7647.49 −0.854679 −0.427340 0.904091i $$-0.640549\pi$$
−0.427340 + 0.904091i $$0.640549\pi$$
$$432$$ 0 0
$$433$$ −13985.2 −1.55216 −0.776082 0.630632i $$-0.782796\pi$$
−0.776082 + 0.630632i $$0.782796\pi$$
$$434$$ −514.978 + 9244.21i −0.0569579 + 1.02243i
$$435$$ 0 0
$$436$$ 11.1624 + 1.24755i 0.00122611 + 0.000137034i
$$437$$ −1447.52 835.728i −0.158454 0.0914835i
$$438$$ 0 0
$$439$$ −11706.7 + 6758.84i −1.27273 + 0.734811i −0.975501 0.219996i $$-0.929396\pi$$
−0.297228 + 0.954806i $$0.596062\pi$$
$$440$$ 708.928 + 119.469i 0.0768109 + 0.0129442i
$$441$$ 0 0
$$442$$ 3369.30 5151.07i 0.362582 0.554325i
$$443$$ −3270.50 5664.67i −0.350759 0.607532i 0.635624 0.771999i $$-0.280743\pi$$
−0.986383 + 0.164467i $$0.947410\pi$$
$$444$$ 0 0
$$445$$ −1067.87 + 1849.61i −0.113757 + 0.197033i
$$446$$ 901.555 + 1783.89i 0.0957172 + 0.189394i
$$447$$ 0 0
$$448$$ 13865.8 2662.28i 1.46227 0.280761i
$$449$$ 17599.7i 1.84984i −0.380158 0.924921i $$-0.624130\pi$$
0.380158 0.924921i $$-0.375870\pi$$
$$450$$ 0 0
$$451$$ 8847.05i 0.923706i
$$452$$ −8737.36 6436.35i −0.909228 0.669780i
$$453$$ 0 0
$$454$$ −8102.19 + 4094.75i −0.837566 + 0.423295i
$$455$$ 1364.34 2363.10i 0.140574 0.243481i
$$456$$ 0 0
$$457$$ 1199.50 + 2077.59i 0.122779 + 0.212660i 0.920863 0.389887i $$-0.127486\pi$$
−0.798083 + 0.602547i $$0.794153\pi$$
$$458$$ 3464.52 + 2266.13i 0.353463 + 0.231199i
$$459$$ 0 0
$$460$$ 1523.65 666.392i 0.154436 0.0675450i
$$461$$ 3237.72 1869.30i 0.327106 0.188855i −0.327450 0.944869i $$-0.606189\pi$$
0.654555 + 0.756014i $$0.272856\pi$$
$$462$$ 0 0
$$463$$ 2167.70 + 1251.52i 0.217585 + 0.125623i 0.604831 0.796354i $$-0.293240\pi$$
−0.387247 + 0.921976i $$0.626574\pi$$
$$464$$ 6613.10 2052.89i 0.661649 0.205395i
$$465$$ 0 0
$$466$$ −3739.41 208.316i −0.371727 0.0207082i
$$467$$ −5361.30 −0.531245 −0.265622 0.964077i $$-0.585577\pi$$
−0.265622 + 0.964077i $$0.585577\pi$$
$$468$$ 0 0
$$469$$ −9799.93 −0.964859
$$470$$ −1225.86 68.2902i −0.120308 0.00670212i
$$471$$ 0 0
$$472$$ −1462.44 1208.36i −0.142615 0.117837i
$$473$$ 3849.43 + 2222.47i 0.374201 + 0.216045i
$$474$$ 0 0
$$475$$ 1224.39 706.904i 0.118272 0.0682841i
$$476$$ −2780.31 6356.95i −0.267721 0.612122i
$$477$$ 0 0
$$478$$ −1867.72 1221.67i −0.178719 0.116899i
$$479$$ 609.925 + 1056.42i 0.0581799 + 0.100771i 0.893648 0.448768i $$-0.148137\pi$$
−0.835468 + 0.549538i $$0.814804\pi$$
$$480$$ 0 0
$$481$$ 10394.1 18003.2i 0.985304 1.70660i
$$482$$ 5908.96 2986.31i 0.558393 0.282205i
$$483$$ 0 0
$$484$$ −3973.20 + 5393.63i −0.373140 + 0.506539i
$$485$$ 2002.41i 0.187473i
$$486$$ 0 0
$$487$$ 1483.03i 0.137993i 0.997617 + 0.0689964i $$0.0219797\pi$$
−0.997617 + 0.0689964i $$0.978020\pi$$
$$488$$ −8448.24 + 3147.64i −0.783676 + 0.291982i
$$489$$ 0 0
$$490$$ −761.618 1507.00i −0.0702171 0.138937i
$$491$$ −6942.36 + 12024.5i −0.638094 + 1.10521i 0.347756 + 0.937585i $$0.386944\pi$$
−0.985851 + 0.167627i $$0.946390\pi$$
$$492$$ 0 0
$$493$$ −1701.39 2946.89i −0.155429 0.269211i
$$494$$ −1231.84 + 1883.26i −0.112192 + 0.171522i
$$495$$ 0 0
$$496$$ 5578.26 + 5157.24i 0.504982 + 0.466869i
$$497$$ −20687.2 + 11943.8i −1.86710 + 1.07797i
$$498$$ 0 0
$$499$$ 17493.2 + 10099.7i 1.56935 + 0.906063i 0.996245 + 0.0865784i $$0.0275933\pi$$
0.573102 + 0.819484i $$0.305740\pi$$
$$500$$ −315.079 + 2819.16i −0.0281815 + 0.252154i
$$501$$ 0 0
$$502$$ 147.575 2649.08i 0.0131207 0.235526i
$$503$$ −388.562 −0.0344436 −0.0172218 0.999852i $$-0.505482\pi$$
−0.0172218 + 0.999852i $$0.505482\pi$$
$$504$$ 0 0
$$505$$ 342.381 0.0301698
$$506$$ 508.086 9120.48i 0.0446387 0.801294i
$$507$$ 0 0
$$508$$ 486.802 4355.66i 0.0425165 0.380416i
$$509$$ −5854.78 3380.26i −0.509840 0.294356i 0.222928 0.974835i $$-0.428439\pi$$
−0.732768 + 0.680479i $$0.761772\pi$$
$$510$$ 0 0
$$511$$ −1544.30 + 891.605i −0.133691 + 0.0771864i
$$512$$ 5562.96 10162.2i 0.480177 0.877172i
$$513$$ 0 0
$$514$$ −257.005 + 392.916i −0.0220545 + 0.0337175i
$$515$$ 416.182 + 720.848i 0.0356100 + 0.0616783i
$$516$$ 0 0
$$517$$ −3371.94 + 5840.37i −0.286843 + 0.496826i
$$518$$ −10569.8 20914.3i −0.896547 1.77398i
$$519$$ 0 0
$$520$$ −781.704 2098.09i −0.0659230 0.176937i
$$521$$ 17324.6i 1.45683i −0.685139 0.728413i $$-0.740258\pi$$
0.685139 0.728413i $$-0.259742\pi$$
$$522$$ 0 0
$$523$$ 16119.4i 1.34771i −0.738864 0.673855i $$-0.764637\pi$$
0.738864 0.673855i $$-0.235363\pi$$
$$524$$ −8840.55 + 12001.1i −0.737026 + 1.00051i
$$525$$ 0 0
$$526$$ 12197.1 6164.23i 1.01106 0.510976i
$$527$$ 1866.64 3233.12i 0.154293 0.267243i
$$528$$ 0 0
$$529$$ −4481.55 7762.27i −0.368337 0.637978i
$$530$$ −823.712 538.787i −0.0675090 0.0441574i
$$531$$ 0 0
$$532$$ 1016.50 + 2324.14i 0.0828398 + 0.189406i
$$533$$ 23861.4 13776.4i 1.93912 1.11955i
$$534$$ 0 0
$$535$$ −1820.98 1051.34i −0.147154 0.0849597i
$$536$$ −5121.94 + 6198.93i −0.412750 + 0.499539i
$$537$$ 0 0
$$538$$ 15762.2 + 878.084i 1.26312 + 0.0703660i
$$539$$ −9274.78 −0.741175
$$540$$ 0 0
$$541$$ −4412.42 −0.350655 −0.175328 0.984510i $$-0.556099\pi$$
−0.175328 + 0.984510i $$0.556099\pi$$
$$542$$ 22858.8 + 1273.42i 1.81156 + 0.100919i
$$543$$ 0 0
$$544$$ −5474.21 1563.79i −0.431443 0.123248i
$$545$$ −1.73879 1.00389i −0.000136663 7.89026e-5i
$$546$$ 0 0
$$547$$ 5985.94 3455.99i 0.467898 0.270141i −0.247461 0.968898i $$-0.579596\pi$$
0.715360 + 0.698757i $$0.246263\pi$$
$$548$$ 10612.9 4641.71i 0.827300 0.361832i
$$549$$ 0 0
$$550$$ 6466.15 + 4229.49i 0.501305 + 0.327902i
$$551$$ 622.038 + 1077.40i 0.0480938 + 0.0833010i
$$552$$ 0 0
$$553$$ 5650.37 9786.72i 0.434499 0.752574i
$$554$$ 4659.17 2354.69i 0.357309 0.180579i
$$555$$ 0 0
$$556$$ 2410.72 + 1775.85i 0.183880 + 0.135455i
$$557$$ 17257.6i 1.31280i 0.754415 + 0.656398i $$0.227921\pi$$
−0.754415 + 0.656398i $$0.772079\pi$$
$$558$$ 0 0
$$559$$ 13843.1i 1.04741i
$$560$$ −2461.61 557.195i −0.185754 0.0420460i
$$561$$ 0 0
$$562$$ −3233.54 6398.15i −0.242702 0.480230i
$$563$$ 12554.5 21745.1i 0.939805 1.62779i 0.173972 0.984751i $$-0.444340\pi$$
0.765833 0.643039i $$-0.222327\pi$$
$$564$$ 0 0
$$565$$ 969.945 + 1679.99i 0.0722228 + 0.125094i
$$566$$ −4811.86 + 7356.51i −0.357346 + 0.546320i
$$567$$ 0 0
$$568$$ −3257.19 + 19328.1i −0.240614 + 1.42780i
$$569$$ −14813.5 + 8552.60i −1.09142 + 0.630129i −0.933953 0.357396i $$-0.883665\pi$$
−0.157463 + 0.987525i $$0.550331\pi$$
$$570$$ 0 0
$$571$$ 4814.10 + 2779.42i 0.352827 + 0.203705i 0.665929 0.746015i $$-0.268035\pi$$
−0.313103 + 0.949719i $$0.601368\pi$$
$$572$$ −12222.3 1366.00i −0.893424 0.0998519i
$$573$$ 0 0
$$574$$ 1727.55 31010.7i 0.125621 2.25499i
$$575$$ 17873.0 1.29627
$$576$$ 0 0
$$577$$ 19014.3 1.37188 0.685939 0.727659i $$-0.259392\pi$$
0.685939 + 0.727659i $$0.259392\pi$$
$$578$$ 617.311 11081.1i 0.0444234 0.797431i
$$579$$ 0 0
$$580$$ −1230.13 137.483i −0.0880659 0.00984253i
$$581$$ −3816.27 2203.32i −0.272505 0.157331i
$$582$$ 0 0
$$583$$ −4682.13 + 2703.23i −0.332614 + 0.192035i
$$584$$ −243.149 + 1442.85i −0.0172287 + 0.102235i
$$585$$ 0 0
$$586$$ −8624.91 + 13186.0i −0.608006 + 0.929537i
$$587$$ 12597.2 + 21818.9i 0.885759 + 1.53418i 0.844842 + 0.535017i $$0.179695\pi$$
0.0409172 + 0.999163i $$0.486972\pi$$
$$588$$ 0 0
$$589$$ −682.457 + 1182.05i −0.0477422 + 0.0826919i
$$590$$ 152.959 + 302.658i 0.0106733 + 0.0211190i
$$591$$ 0 0
$$592$$ −18753.6 4244.96i −1.30198 0.294707i
$$593$$ 17307.5i 1.19854i 0.800548 + 0.599269i $$0.204542\pi$$
−0.800548 + 0.599269i $$0.795458\pi$$
$$594$$ 0 0
$$595$$ 1240.28i 0.0854564i
$$596$$ 15903.6 + 11715.3i 1.09301 + 0.805164i
$$597$$ 0 0
$$598$$ −25390.1 + 12831.8i −1.73625 + 0.877479i
$$599$$ −10740.8 + 18603.5i −0.732647 + 1.26898i 0.223101 + 0.974795i $$0.428382\pi$$
−0.955748 + 0.294186i $$0.904951\pi$$
$$600$$ 0 0
$$601$$ 2716.74 + 4705.53i 0.184390 + 0.319372i 0.943371 0.331741i $$-0.107636\pi$$
−0.758981 + 0.651113i $$0.774303\pi$$
$$602$$ −13059.1 8541.89i −0.884133 0.578308i
$$603$$ 0 0
$$604$$ 4447.18 1945.04i 0.299591 0.131031i
$$605$$ 1037.07 598.752i 0.0696907 0.0402359i
$$606$$ 0 0
$$607$$ 11684.8 + 6746.19i 0.781333 + 0.451103i 0.836903 0.547352i $$-0.184364\pi$$
−0.0555692 + 0.998455i $$0.517697\pi$$
$$608$$ 2001.41 + 571.730i 0.133500 + 0.0381360i
$$609$$ 0 0
$$610$$ 1609.10 + 89.6401i 0.106804 + 0.00594987i
$$611$$ 21002.8 1.39064
$$612$$ 0 0
$$613$$ 8330.79 0.548903 0.274451 0.961601i $$-0.411504\pi$$
0.274451 + 0.961601i $$0.411504\pi$$
$$614$$ −21877.1 1218.73i −1.43793 0.0801042i
$$615$$ 0 0
$$616$$ −8830.39 + 10687.1i −0.577576 + 0.699022i
$$617$$ 17147.1 + 9899.88i 1.11883 + 0.645955i 0.941101 0.338125i $$-0.109793\pi$$
0.177726 + 0.984080i $$0.443126\pi$$
$$618$$ 0 0
$$619$$ −22673.3 + 13090.4i −1.47224 + 0.849997i −0.999513 0.0312129i $$-0.990063\pi$$
−0.472725 + 0.881210i $$0.656730\pi$$
$$620$$ −544.177 1244.22i −0.0352494 0.0805950i
$$621$$ 0 0
$$622$$ −13759.8 9000.22i −0.887005 0.580186i
$$623$$ −20592.2 35666.7i −1.32425 2.29367i
$$624$$ 0 0
$$625$$ −7431.14 + 12871.1i −0.475593 + 0.823751i
$$626$$ −6905.30 + 3489.85i −0.440880 + 0.222815i
$$627$$ 0 0
$$628$$ −352.726 + 478.826i −0.0224129 + 0.0304255i
$$629$$ 9449.01i 0.598977i
$$630$$ 0 0
$$631$$ 24489.4i 1.54502i −0.635004 0.772509i $$-0.719001\pi$$
0.635004 0.772509i $$-0.280999\pi$$
$$632$$ −3237.41 8689.17i −0.203761 0.546893i
$$633$$ 0 0
$$634$$ 8005.73 + 15840.8i 0.501496 + 0.992300i
$$635$$ −391.726 + 678.489i −0.0244806 + 0.0424016i
$$636$$ 0 0
$$637$$ 14442.5 + 25015.1i 0.898322 + 1.55594i
$$638$$ −3721.72 + 5689.87i −0.230947 + 0.353079i
$$639$$ 0 0
$$640$$ −1639.02 + 1265.87i −0.101231 + 0.0781842i
$$641$$ 20279.7 11708.5i 1.24961 0.721463i 0.278578 0.960414i $$-0.410137\pi$$
0.971032 + 0.238951i $$0.0768035\pi$$
$$642$$ 0 0
$$643$$ 1385.76 + 800.068i 0.0849907 + 0.0490694i 0.541893 0.840447i $$-0.317708\pi$$
−0.456902 + 0.889517i $$0.651041\pi$$
$$644$$ −3561.89 + 31870.0i −0.217947 + 1.95008i
$$645$$ 0 0
$$646$$ 56.8939 1021.28i 0.00346511 0.0622011i
$$647$$ −19887.1 −1.20841 −0.604206 0.796828i $$-0.706509\pi$$
−0.604206 + 0.796828i $$0.706509\pi$$
$$648$$ 0 0
$$649$$ 1862.70 0.112662
$$650$$ 1338.44 24025.9i 0.0807661 1.44981i
$$651$$ 0 0
$$652$$ 35.9739 321.876i 0.00216081 0.0193338i
$$653$$ −3929.91 2268.93i −0.235512 0.135973i 0.377600 0.925969i $$-0.376749\pi$$
−0.613112 + 0.789996i $$0.710083\pi$$
$$654$$ 0 0
$$655$$ 2307.53 1332.25i 0.137653 0.0794739i
$$656$$ −18712.9 17300.6i −1.11374 1.02968i
$$657$$ 0 0
$$658$$ 12959.8 19813.3i 0.767819 1.17386i
$$659$$ 880.483 + 1525.04i 0.0520467 + 0.0901475i 0.890875 0.454249i $$-0.150092\pi$$
−0.838828 + 0.544396i $$0.816759\pi$$
$$660$$ 0 0
$$661$$ 3948.96 6839.80i 0.232370 0.402477i −0.726135 0.687552i $$-0.758685\pi$$
0.958505 + 0.285075i $$0.0920185\pi$$
$$662$$ 445.436 + 881.376i 0.0261516 + 0.0517457i
$$663$$ 0 0
$$664$$ −3388.28 + 1262.40i −0.198028 + 0.0737813i
$$665$$ 453.455i 0.0264424i
$$666$$ 0 0
$$667$$ 15727.3i 0.912987i
$$668$$ 195.119 264.874i 0.0113015 0.0153418i
$$669$$ 0 0
$$670$$ 1282.89 648.358i 0.0739739 0.0373854i
$$671$$ 4426.12 7666.26i 0.254647 0.441062i
$$672$$ 0 0
$$673$$ 8028.88 + 13906.4i 0.459867 + 0.796513i 0.998953 0.0457375i $$-0.0145638\pi$$
−0.539087 + 0.842250i $$0.681230\pi$$
$$674$$ 22075.2 + 14439.3i 1.26158 + 0.825193i
$$675$$ 0 0
$$676$$ 8304.98 + 18988.6i 0.472518 + 1.08037i
$$677$$ −16512.7 + 9533.61i −0.937422 + 0.541221i −0.889151 0.457613i $$-0.848704\pi$$
−0.0482708 + 0.998834i $$0.515371\pi$$
$$678$$ 0 0
$$679$$ −33440.0 19306.6i −1.89000 1.09119i
$$680$$ 784.538 + 648.234i 0.0442436 + 0.0365568i
$$681$$ 0 0
$$682$$ −7447.80 414.903i −0.418169 0.0232954i
$$683$$ 15166.6 0.849682 0.424841 0.905268i $$-0.360330\pi$$
0.424841 + 0.905268i $$0.360330\pi$$
$$684$$ 0 0
$$685$$ −2070.64 −0.115497
$$686$$ 5798.27 + 323.011i 0.322710 + 0.0179776i
$$687$$ 0 0
$$688$$ −12228.5 + 3796.07i −0.677626 + 0.210354i
$$689$$ 14581.8 + 8418.80i 0.806272 + 0.465502i
$$690$$ 0 0
$$691$$ 8692.79 5018.79i 0.478567 0.276301i −0.241252 0.970462i $$-0.577558\pi$$
0.719819 + 0.694162i $$0.244225\pi$$
$$692$$ −8061.16 + 3525.67i −0.442832 + 0.193679i
$$693$$ 0 0
$$694$$ 13163.8 + 8610.41i 0.720017 + 0.470961i
$$695$$ −267.617 463.525i −0.0146061 0.0252986i
$$696$$ 0 0
$$697$$ −6261.87 + 10845.9i −0.340294 + 0.589407i
$$698$$ −26940.5 + 13615.4i −1.46091 + 0.738324i
$$699$$ 0 0
$$700$$ −21839.3 16087.9i −1.17921 0.868663i
$$701$$ 13222.0i 0.712394i 0.934411 + 0.356197i $$0.115927\pi$$
−0.934411 + 0.356197i $$0.884073\pi$$
$$702$$ 0 0
$$703$$ 3454.62i 0.185339i
$$704$$ 2144.93 + 11171.3i 0.114830 + 0.598060i
$$705$$ 0 0
$$706$$ 515.085 + 1019.19i 0.0274582 + 0.0543310i
$$707$$ −3301.14 + 5717.74i −0.175604 + 0.304155i
$$708$$ 0 0
$$709$$ −11792.3 20424.8i −0.624636 1.08190i −0.988611 0.150493i $$-0.951914\pi$$
0.363975 0.931409i $$-0.381419\pi$$
$$710$$ 1917.94 2932.20i 0.101379 0.154991i
$$711$$ 0 0
$$712$$ −33323.4 5615.69i −1.75400 0.295585i
$$713$$ −14943.2 + 8627.44i −0.784889 + 0.453156i
$$714$$ 0 0
$$715$$ 1903.89 + 1099.21i 0.0995822 + 0.0574938i
$$716$$ 30608.7 + 3420.93i 1.59763 + 0.178556i
$$717$$ 0 0
$$718$$ −1006.57 + 18068.5i −0.0523185 + 0.939153i
$$719$$ 19376.4 1.00503 0.502517 0.864567i $$-0.332407\pi$$
0.502517 + 0.864567i $$0.332407\pi$$
$$720$$ 0 0
$$721$$ −16050.8 −0.829074
$$722$$ 1058.27 18996.8i 0.0545497 0.979205i
$$723$$ 0 0
$$724$$ 8679.15 + 970.010i 0.445522 + 0.0497930i
$$725$$ −11520.7 6651.48i −0.590163 0.340731i
$$726$$ 0 0
$$727$$ 19193.8 11081.5i 0.979172 0.565325i 0.0771518 0.997019i $$-0.475417\pi$$
0.902020 + 0.431694i $$0.142084\pi$$
$$728$$ 42574.8 + 7174.74i 2.16748 + 0.365266i
$$729$$ 0 0
$$730$$ 143.174 218.889i 0.00725907 0.0110979i
$$731$$ 3146.09 + 5449.19i 0.159182 + 0.275712i
$$732$$ 0 0
$$733$$ 14834.2 25693.7i 0.747497 1.29470i −0.201522 0.979484i $$-0.564589\pi$$
0.949019 0.315219i $$-0.102078\pi$$
$$734$$ −14103.2 27905.8i −0.709210 1.40330i
$$735$$ 0 0
$$736$$ 18297.7 + 18909.9i 0.916388 + 0.947051i
$$737$$ 7895.53i 0.394621i
$$738$$ 0 0
$$739$$ 14616.0i 0.727549i 0.931487 + 0.363774i $$0.118512\pi$$
−0.931487 + 0.363774i $$0.881488\pi$$
$$740$$ 2767.36 + 2038.56i 0.137473 + 0.101269i
$$741$$ 0 0
$$742$$ 16939.7 8561.10i 0.838107 0.423569i
$$743$$ −17948.9 + 31088.4i −0.886246 + 1.53502i −0.0419682 + 0.999119i $$0.513363\pi$$
−0.844278 + 0.535905i $$0.819971\pi$$
$$744$$ 0 0
$$745$$ −1765.47 3057.89i −0.0868213 0.150379i
$$746$$ 8313.90 + 5438.09i 0.408034 + 0.266894i
$$747$$ 0 0
$$748$$ 5121.62 2240.02i 0.250354 0.109496i
$$749$$ 35114.6 20273.4i 1.71303 0.989018i
$$750$$ 0 0
$$751$$ 23192.8 + 13390.4i 1.12692 + 0.650627i 0.943158 0.332344i $$-0.107839\pi$$
0.183761 + 0.982971i $$0.441173\pi$$
$$752$$ −5759.41 18553.1i −0.279287 0.899684i
$$753$$ 0 0
$$754$$ 21141.6 + 1177.76i 1.02113 + 0.0568852i
$$755$$ −867.673 −0.0418250
$$756$$ 0 0
$$757$$ 1805.80 0.0867016 0.0433508 0.999060i $$-0.486197\pi$$
0.0433508 + 0.999060i $$0.486197\pi$$
$$758$$ 3498.14 + 194.875i 0.167623 + 0.00933795i
$$759$$ 0 0
$$760$$ −286.832 236.998i −0.0136901 0.0113116i
$$761$$ 3770.72 + 2177.03i 0.179617 + 0.103702i 0.587113 0.809505i $$-0.300265\pi$$
−0.407496 + 0.913207i $$0.633598\pi$$
$$762$$ 0 0
$$763$$ 33.5298 19.3584i 0.00159090 0.000918508i
$$764$$ −2049.57 4686.17i −0.0970560 0.221910i
$$765$$ 0 0
$$766$$ 4042.89 + 2644.44i 0.190699 + 0.124736i
$$767$$ −2900.55 5023.90i −0.136549 0.236509i
$$768$$ 0 0
$$769$$ −1390.69 + 2408.74i −0.0652138 + 0.112954i −0.896789 0.442459i $$-0.854106\pi$$
0.831575 + 0.555412i $$0.187440\pi$$
$$770$$ 2211.75 1117.79i 0.103514 0.0523147i
$$771$$ 0 0
$$772$$ 8294.85 11260.3i 0.386707 0.524956i
$$773$$ 7776.95i 0.361860i −0.983496 0.180930i $$-0.942089\pi$$
0.983496 0.180930i $$-0.0579107\pi$$
$$774$$ 0 0
$$775$$ 14595.1i 0.676479i
$$776$$ −29689.8 + 11061.8i −1.37346 + 0.511721i
$$777$$ 0 0
$$778$$ −11419.5 22595.6i −0.526233 1.04125i
$$779$$ 2289.38 3965.32i 0.105296 0.182378i
$$780$$ 0 0