# Properties

 Label 147.4.e.n.79.2 Level $147$ Weight $4$ Character 147.79 Analytic conductor $8.673$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$147 = 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 147.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.67328077084$$ Analytic rank: $$0$$ Dimension: $$6$$ Relative dimension: $$3$$ over $$\Q(\zeta_{3})$$ Coefficient field: 6.0.9924270768.1 Defining polynomial: $$x^{6} - x^{5} + 25 x^{4} + 12 x^{3} + 582 x^{2} - 144 x + 36$$ Coefficient ring: $$\Z[a_1, \ldots, a_{4}]$$ Coefficient ring index: $$3$$ Twist minimal: no (minimal twist has level 21) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 79.2 Root $$0.124036 - 0.214837i$$ of defining polynomial Character $$\chi$$ $$=$$ 147.79 Dual form 147.4.e.n.67.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.124036 + 0.214837i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(3.96923 + 6.87491i) q^{4} +(-6.21730 + 10.7687i) q^{5} +0.744216 q^{6} -3.95388 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$$ $$q+(-0.124036 + 0.214837i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(3.96923 + 6.87491i) q^{4} +(-6.21730 + 10.7687i) q^{5} +0.744216 q^{6} -3.95388 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-1.54234 - 2.67141i) q^{10} +(-30.1558 - 52.2313i) q^{11} +(11.9077 - 20.6247i) q^{12} -36.4269 q^{13} +37.3038 q^{15} +(-31.2634 + 54.1498i) q^{16} +(-24.3731 - 42.2154i) q^{17} +(-1.11632 - 1.93353i) q^{18} +(-25.2750 + 43.7776i) q^{19} -98.7116 q^{20} +14.9616 q^{22} +(-69.3962 + 120.198i) q^{23} +(5.93083 + 10.2725i) q^{24} +(-14.8097 - 25.6511i) q^{25} +(4.51824 - 7.82583i) q^{26} +27.0000 q^{27} -61.1345 q^{29} +(-4.62701 + 8.01422i) q^{30} +(-0.584676 - 1.01269i) q^{31} +(-23.5711 - 40.8264i) q^{32} +(-90.4673 + 156.694i) q^{33} +12.0925 q^{34} -71.4461 q^{36} +(-34.7634 + 60.2120i) q^{37} +(-6.27001 - 10.8600i) q^{38} +(54.6403 + 94.6398i) q^{39} +(24.5825 - 42.5781i) q^{40} -308.115 q^{41} +174.443 q^{43} +(239.390 - 414.636i) q^{44} +(-55.9557 - 96.9181i) q^{45} +(-17.2153 - 29.8177i) q^{46} +(194.681 - 337.197i) q^{47} +187.581 q^{48} +7.34774 q^{50} +(-73.1192 + 126.646i) q^{51} +(-144.587 - 250.432i) q^{52} +(-157.467 - 272.742i) q^{53} +(-3.34897 + 5.80059i) q^{54} +749.950 q^{55} +151.650 q^{57} +(7.58287 - 13.1339i) q^{58} +(422.263 + 731.381i) q^{59} +(148.067 + 256.460i) q^{60} +(-169.269 + 293.182i) q^{61} +0.290084 q^{62} -488.520 q^{64} +(226.477 - 392.270i) q^{65} +(-22.4424 - 38.8714i) q^{66} +(485.775 + 841.387i) q^{67} +(193.485 - 335.125i) q^{68} +416.377 q^{69} -98.4698 q^{71} +(17.7925 - 30.8175i) q^{72} +(355.117 + 615.082i) q^{73} +(-8.62383 - 14.9369i) q^{74} +(-44.4291 + 76.9534i) q^{75} -401.289 q^{76} -27.1095 q^{78} +(243.442 - 421.654i) q^{79} +(-388.748 - 673.332i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(38.2174 - 66.1944i) q^{82} -605.688 q^{83} +606.139 q^{85} +(-21.6372 + 37.4767i) q^{86} +(91.7017 + 158.832i) q^{87} +(119.232 + 206.517i) q^{88} +(109.034 - 188.853i) q^{89} +27.7621 q^{90} -1101.80 q^{92} +(-1.75403 + 3.03807i) q^{93} +(48.2949 + 83.6491i) q^{94} +(-314.284 - 544.357i) q^{95} +(-70.7133 + 122.479i) q^{96} +782.288 q^{97} +542.804 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6q - q^{2} - 9q^{3} - 25q^{4} + 11q^{5} + 6q^{6} + 78q^{8} - 27q^{9} + O(q^{10})$$ $$6q - q^{2} - 9q^{3} - 25q^{4} + 11q^{5} + 6q^{6} + 78q^{8} - 27q^{9} - 55q^{10} - 35q^{11} - 75q^{12} - 124q^{13} - 66q^{15} - 241q^{16} + 48q^{17} - 9q^{18} - 202q^{19} - 878q^{20} - 14q^{22} - 216q^{23} - 117q^{24} - 130q^{25} + 274q^{26} + 162q^{27} + 106q^{29} - 165q^{30} - 95q^{31} - 683q^{32} - 105q^{33} + 48q^{34} + 450q^{36} - 262q^{37} - 398q^{38} + 186q^{39} + 21q^{40} - 488q^{41} + 720q^{43} + 905q^{44} + 99q^{45} + 1056q^{46} - 210q^{47} + 1446q^{48} - 2756q^{50} + 144q^{51} + 324q^{52} - 393q^{53} - 27q^{54} + 2062q^{55} + 1212q^{57} + 1249q^{58} + 1143q^{59} + 1317q^{60} - 70q^{61} - 2118q^{62} - 798q^{64} + 472q^{65} + 21q^{66} + 628q^{67} + 1944q^{68} + 1296q^{69} + 636q^{71} - 351q^{72} + 988q^{73} - 1002q^{74} - 390q^{75} + 4680q^{76} - 1644q^{78} - 861q^{79} + 175q^{80} - 243q^{81} + 124q^{82} - 1038q^{83} + 3600q^{85} + 3208q^{86} - 159q^{87} + 891q^{88} + 1766q^{89} + 990q^{90} - 1344q^{92} - 285q^{93} - 3294q^{94} + 736q^{95} - 2049q^{96} - 38q^{97} + 630q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$$.

 $$n$$ $$50$$ $$52$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.124036 + 0.214837i −0.0438533 + 0.0759562i −0.887119 0.461541i $$-0.847297\pi$$
0.843266 + 0.537497i $$0.180630\pi$$
$$3$$ −1.50000 2.59808i −0.288675 0.500000i
$$4$$ 3.96923 + 6.87491i 0.496154 + 0.859364i
$$5$$ −6.21730 + 10.7687i −0.556092 + 0.963180i 0.441725 + 0.897150i $$0.354367\pi$$
−0.997818 + 0.0660299i $$0.978967\pi$$
$$6$$ 0.744216 0.0506375
$$7$$ 0 0
$$8$$ −3.95388 −0.174739
$$9$$ −4.50000 + 7.79423i −0.166667 + 0.288675i
$$10$$ −1.54234 2.67141i −0.0487730 0.0844773i
$$11$$ −30.1558 52.2313i −0.826573 1.43167i −0.900711 0.434419i $$-0.856954\pi$$
0.0741379 0.997248i $$-0.476379\pi$$
$$12$$ 11.9077 20.6247i 0.286455 0.496154i
$$13$$ −36.4269 −0.777154 −0.388577 0.921416i $$-0.627033\pi$$
−0.388577 + 0.921416i $$0.627033\pi$$
$$14$$ 0 0
$$15$$ 37.3038 0.642120
$$16$$ −31.2634 + 54.1498i −0.488491 + 0.846091i
$$17$$ −24.3731 42.2154i −0.347726 0.602279i 0.638119 0.769937i $$-0.279713\pi$$
−0.985845 + 0.167659i $$0.946379\pi$$
$$18$$ −1.11632 1.93353i −0.0146178 0.0253187i
$$19$$ −25.2750 + 43.7776i −0.305183 + 0.528593i −0.977302 0.211851i $$-0.932051\pi$$
0.672119 + 0.740443i $$0.265384\pi$$
$$20$$ −98.7116 −1.10363
$$21$$ 0 0
$$22$$ 14.9616 0.144992
$$23$$ −69.3962 + 120.198i −0.629135 + 1.08969i 0.358590 + 0.933495i $$0.383257\pi$$
−0.987726 + 0.156199i $$0.950076\pi$$
$$24$$ 5.93083 + 10.2725i 0.0504427 + 0.0873693i
$$25$$ −14.8097 25.6511i −0.118478 0.205209i
$$26$$ 4.51824 7.82583i 0.0340808 0.0590297i
$$27$$ 27.0000 0.192450
$$28$$ 0 0
$$29$$ −61.1345 −0.391462 −0.195731 0.980658i $$-0.562708\pi$$
−0.195731 + 0.980658i $$0.562708\pi$$
$$30$$ −4.62701 + 8.01422i −0.0281591 + 0.0487730i
$$31$$ −0.584676 1.01269i −0.00338745 0.00586724i 0.864327 0.502931i $$-0.167745\pi$$
−0.867714 + 0.497064i $$0.834412\pi$$
$$32$$ −23.5711 40.8264i −0.130213 0.225536i
$$33$$ −90.4673 + 156.694i −0.477222 + 0.826573i
$$34$$ 12.0925 0.0609957
$$35$$ 0 0
$$36$$ −71.4461 −0.330769
$$37$$ −34.7634 + 60.2120i −0.154461 + 0.267535i −0.932863 0.360232i $$-0.882698\pi$$
0.778401 + 0.627767i $$0.216031\pi$$
$$38$$ −6.27001 10.8600i −0.0267666 0.0463611i
$$39$$ 54.6403 + 94.6398i 0.224345 + 0.388577i
$$40$$ 24.5825 42.5781i 0.0971708 0.168305i
$$41$$ −308.115 −1.17365 −0.586823 0.809715i $$-0.699622\pi$$
−0.586823 + 0.809715i $$0.699622\pi$$
$$42$$ 0 0
$$43$$ 174.443 0.618657 0.309329 0.950955i $$-0.399896\pi$$
0.309329 + 0.950955i $$0.399896\pi$$
$$44$$ 239.390 414.636i 0.820215 1.42065i
$$45$$ −55.9557 96.9181i −0.185364 0.321060i
$$46$$ −17.2153 29.8177i −0.0551794 0.0955734i
$$47$$ 194.681 337.197i 0.604194 1.04649i −0.387984 0.921666i $$-0.626828\pi$$
0.992178 0.124829i $$-0.0398382\pi$$
$$48$$ 187.581 0.564061
$$49$$ 0 0
$$50$$ 7.34774 0.0207825
$$51$$ −73.1192 + 126.646i −0.200760 + 0.347726i
$$52$$ −144.587 250.432i −0.385588 0.667858i
$$53$$ −157.467 272.742i −0.408110 0.706867i 0.586568 0.809900i $$-0.300479\pi$$
−0.994678 + 0.103033i $$0.967145\pi$$
$$54$$ −3.34897 + 5.80059i −0.00843958 + 0.0146178i
$$55$$ 749.950 1.83860
$$56$$ 0 0
$$57$$ 151.650 0.352395
$$58$$ 7.58287 13.1339i 0.0171669 0.0297339i
$$59$$ 422.263 + 731.381i 0.931762 + 1.61386i 0.780308 + 0.625396i $$0.215062\pi$$
0.151455 + 0.988464i $$0.451604\pi$$
$$60$$ 148.067 + 256.460i 0.318590 + 0.551815i
$$61$$ −169.269 + 293.182i −0.355290 + 0.615380i −0.987167 0.159688i $$-0.948951\pi$$
0.631878 + 0.775068i $$0.282284\pi$$
$$62$$ 0.290084 0.000594204
$$63$$ 0 0
$$64$$ −488.520 −0.954141
$$65$$ 226.477 392.270i 0.432169 0.748539i
$$66$$ −22.4424 38.8714i −0.0418556 0.0724960i
$$67$$ 485.775 + 841.387i 0.885774 + 1.53421i 0.844824 + 0.535044i $$0.179705\pi$$
0.0409498 + 0.999161i $$0.486962\pi$$
$$68$$ 193.485 335.125i 0.345051 0.597646i
$$69$$ 416.377 0.726463
$$70$$ 0 0
$$71$$ −98.4698 −0.164595 −0.0822973 0.996608i $$-0.526226\pi$$
−0.0822973 + 0.996608i $$0.526226\pi$$
$$72$$ 17.7925 30.8175i 0.0291231 0.0504427i
$$73$$ 355.117 + 615.082i 0.569361 + 0.986162i 0.996629 + 0.0820374i $$0.0261427\pi$$
−0.427268 + 0.904125i $$0.640524\pi$$
$$74$$ −8.62383 14.9369i −0.0135473 0.0234646i
$$75$$ −44.4291 + 76.9534i −0.0684030 + 0.118478i
$$76$$ −401.289 −0.605671
$$77$$ 0 0
$$78$$ −27.1095 −0.0393531
$$79$$ 243.442 421.654i 0.346701 0.600504i −0.638960 0.769240i $$-0.720635\pi$$
0.985661 + 0.168736i $$0.0539686\pi$$
$$80$$ −388.748 673.332i −0.543292 0.941010i
$$81$$ −40.5000 70.1481i −0.0555556 0.0962250i
$$82$$ 38.2174 66.1944i 0.0514683 0.0891458i
$$83$$ −605.688 −0.800999 −0.400499 0.916297i $$-0.631163\pi$$
−0.400499 + 0.916297i $$0.631163\pi$$
$$84$$ 0 0
$$85$$ 606.139 0.773470
$$86$$ −21.6372 + 37.4767i −0.0271302 + 0.0469908i
$$87$$ 91.7017 + 158.832i 0.113005 + 0.195731i
$$88$$ 119.232 + 206.517i 0.144434 + 0.250168i
$$89$$ 109.034 188.853i 0.129861 0.224925i −0.793762 0.608229i $$-0.791880\pi$$
0.923622 + 0.383303i $$0.125214\pi$$
$$90$$ 27.7621 0.0325153
$$91$$ 0 0
$$92$$ −1101.80 −1.24859
$$93$$ −1.75403 + 3.03807i −0.00195575 + 0.00338745i
$$94$$ 48.2949 + 83.6491i 0.0529919 + 0.0917846i
$$95$$ −314.284 544.357i −0.339420 0.587893i
$$96$$ −70.7133 + 122.479i −0.0751787 + 0.130213i
$$97$$ 782.288 0.818859 0.409429 0.912342i $$-0.365728\pi$$
0.409429 + 0.912342i $$0.365728\pi$$
$$98$$ 0 0
$$99$$ 542.804 0.551049
$$100$$ 117.566 203.631i 0.117566 0.203631i
$$101$$ −155.823 269.893i −0.153514 0.265895i 0.779003 0.627021i $$-0.215726\pi$$
−0.932517 + 0.361126i $$0.882392\pi$$
$$102$$ −18.1388 31.4174i −0.0176079 0.0304979i
$$103$$ −74.6289 + 129.261i −0.0713922 + 0.123655i −0.899512 0.436897i $$-0.856078\pi$$
0.828119 + 0.560552i $$0.189411\pi$$
$$104$$ 144.028 0.135799
$$105$$ 0 0
$$106$$ 78.1265 0.0715879
$$107$$ −425.760 + 737.437i −0.384670 + 0.666269i −0.991723 0.128393i $$-0.959018\pi$$
0.607053 + 0.794661i $$0.292352\pi$$
$$108$$ 107.169 + 185.623i 0.0954848 + 0.165385i
$$109$$ −680.939 1179.42i −0.598369 1.03640i −0.993062 0.117592i $$-0.962483\pi$$
0.394694 0.918813i $$-0.370851\pi$$
$$110$$ −93.0208 + 161.117i −0.0806289 + 0.139653i
$$111$$ 208.581 0.178357
$$112$$ 0 0
$$113$$ 1048.55 0.872917 0.436459 0.899724i $$-0.356233\pi$$
0.436459 + 0.899724i $$0.356233\pi$$
$$114$$ −18.8100 + 32.5800i −0.0154537 + 0.0267666i
$$115$$ −862.914 1494.61i −0.699715 1.21194i
$$116$$ −242.657 420.294i −0.194225 0.336408i
$$117$$ 163.921 283.920i 0.129526 0.224345i
$$118$$ −209.503 −0.163444
$$119$$ 0 0
$$120$$ −147.495 −0.112203
$$121$$ −1153.24 + 1997.47i −0.866446 + 1.50073i
$$122$$ −41.9909 72.7303i −0.0311613 0.0539729i
$$123$$ 462.173 + 800.507i 0.338803 + 0.586823i
$$124$$ 4.64143 8.03919i 0.00336139 0.00582210i
$$125$$ −1186.02 −0.848647
$$126$$ 0 0
$$127$$ 488.408 0.341254 0.170627 0.985336i $$-0.445421\pi$$
0.170627 + 0.985336i $$0.445421\pi$$
$$128$$ 249.163 431.563i 0.172056 0.298009i
$$129$$ −261.664 453.215i −0.178591 0.309329i
$$130$$ 56.1826 + 97.3111i 0.0379041 + 0.0656519i
$$131$$ −927.114 + 1605.81i −0.618338 + 1.07099i 0.371451 + 0.928453i $$0.378861\pi$$
−0.989789 + 0.142541i $$0.954473\pi$$
$$132$$ −1436.34 −0.947102
$$133$$ 0 0
$$134$$ −241.014 −0.155377
$$135$$ −167.867 + 290.754i −0.107020 + 0.185364i
$$136$$ 96.3683 + 166.915i 0.0607611 + 0.105241i
$$137$$ 255.558 + 442.639i 0.159370 + 0.276038i 0.934642 0.355591i $$-0.115720\pi$$
−0.775271 + 0.631628i $$0.782387\pi$$
$$138$$ −51.6458 + 89.4531i −0.0318578 + 0.0551794i
$$139$$ −2266.10 −1.38279 −0.691397 0.722475i $$-0.743005\pi$$
−0.691397 + 0.722475i $$0.743005\pi$$
$$140$$ 0 0
$$141$$ −1168.09 −0.697663
$$142$$ 12.2138 21.1549i 0.00721802 0.0125020i
$$143$$ 1098.48 + 1902.62i 0.642375 + 1.11263i
$$144$$ −281.371 487.348i −0.162830 0.282030i
$$145$$ 380.091 658.338i 0.217689 0.377048i
$$146$$ −176.189 −0.0998735
$$147$$ 0 0
$$148$$ −551.936 −0.306546
$$149$$ −753.950 + 1305.88i −0.414537 + 0.717999i −0.995380 0.0960168i $$-0.969390\pi$$
0.580843 + 0.814016i $$0.302723\pi$$
$$150$$ −11.0216 19.0900i −0.00599940 0.0103913i
$$151$$ −795.913 1378.56i −0.428943 0.742952i 0.567836 0.823142i $$-0.307781\pi$$
−0.996780 + 0.0801897i $$0.974447\pi$$
$$152$$ 99.9344 173.091i 0.0533273 0.0923656i
$$153$$ 438.715 0.231817
$$154$$ 0 0
$$155$$ 14.5404 0.00753494
$$156$$ −433.760 + 751.295i −0.222619 + 0.385588i
$$157$$ 582.080 + 1008.19i 0.295892 + 0.512500i 0.975192 0.221361i $$-0.0710498\pi$$
−0.679300 + 0.733861i $$0.737717\pi$$
$$158$$ 60.3911 + 104.601i 0.0304080 + 0.0526682i
$$159$$ −472.402 + 818.225i −0.235622 + 0.408110i
$$160$$ 586.195 0.289642
$$161$$ 0 0
$$162$$ 20.0938 0.00974519
$$163$$ 577.940 1001.02i 0.277716 0.481019i −0.693101 0.720841i $$-0.743756\pi$$
0.970817 + 0.239822i $$0.0770892\pi$$
$$164$$ −1222.98 2118.26i −0.582309 1.00859i
$$165$$ −1124.92 1948.43i −0.530759 0.919302i
$$166$$ 75.1271 130.124i 0.0351265 0.0608408i
$$167$$ 2890.61 1.33941 0.669707 0.742626i $$-0.266420\pi$$
0.669707 + 0.742626i $$0.266420\pi$$
$$168$$ 0 0
$$169$$ −870.082 −0.396032
$$170$$ −75.1830 + 130.221i −0.0339193 + 0.0587499i
$$171$$ −227.475 393.998i −0.101728 0.176198i
$$172$$ 692.403 + 1199.28i 0.306949 + 0.531651i
$$173$$ 947.468 1641.06i 0.416385 0.721200i −0.579188 0.815194i $$-0.696630\pi$$
0.995573 + 0.0939940i $$0.0299635\pi$$
$$174$$ −45.4972 −0.0198226
$$175$$ 0 0
$$176$$ 3771.09 1.61509
$$177$$ 1266.79 2194.14i 0.537953 0.931762i
$$178$$ 27.0483 + 46.8491i 0.0113897 + 0.0197275i
$$179$$ 2144.25 + 3713.94i 0.895355 + 1.55080i 0.833365 + 0.552723i $$0.186411\pi$$
0.0619893 + 0.998077i $$0.480256\pi$$
$$180$$ 444.202 769.381i 0.183938 0.318590i
$$181$$ −383.732 −0.157583 −0.0787917 0.996891i $$-0.525106\pi$$
−0.0787917 + 0.996891i $$0.525106\pi$$
$$182$$ 0 0
$$183$$ 1015.61 0.410253
$$184$$ 274.385 475.248i 0.109934 0.190412i
$$185$$ −432.269 748.712i −0.171790 0.297548i
$$186$$ −0.435125 0.753659i −0.000171532 0.000297102i
$$187$$ −1469.98 + 2546.07i −0.574841 + 0.995655i
$$188$$ 3090.93 1.19909
$$189$$ 0 0
$$190$$ 155.930 0.0595388
$$191$$ −192.655 + 333.689i −0.0729845 + 0.126413i −0.900208 0.435460i $$-0.856586\pi$$
0.827224 + 0.561873i $$0.189919\pi$$
$$192$$ 732.780 + 1269.21i 0.275437 + 0.477070i
$$193$$ −315.112 545.790i −0.117525 0.203559i 0.801262 0.598314i $$-0.204163\pi$$
−0.918786 + 0.394756i $$0.870829\pi$$
$$194$$ −97.0318 + 168.064i −0.0359097 + 0.0621974i
$$195$$ −1358.86 −0.499026
$$196$$ 0 0
$$197$$ −1250.23 −0.452158 −0.226079 0.974109i $$-0.572591\pi$$
−0.226079 + 0.974109i $$0.572591\pi$$
$$198$$ −67.3272 + 116.614i −0.0241653 + 0.0418556i
$$199$$ −546.122 945.912i −0.194541 0.336954i 0.752209 0.658924i $$-0.228988\pi$$
−0.946750 + 0.321970i $$0.895655\pi$$
$$200$$ 58.5558 + 101.422i 0.0207026 + 0.0358580i
$$201$$ 1457.32 2524.16i 0.511402 0.885774i
$$202$$ 77.3105 0.0269285
$$203$$ 0 0
$$204$$ −1160.91 −0.398430
$$205$$ 1915.65 3318.00i 0.652656 1.13043i
$$206$$ −18.5133 32.0660i −0.00626158 0.0108454i
$$207$$ −624.566 1081.78i −0.209712 0.363231i
$$208$$ 1138.83 1972.51i 0.379633 0.657543i
$$209$$ 3048.75 1.00902
$$210$$ 0 0
$$211$$ −3620.05 −1.18111 −0.590556 0.806997i $$-0.701091\pi$$
−0.590556 + 0.806997i $$0.701091\pi$$
$$212$$ 1250.05 2165.15i 0.404970 0.701429i
$$213$$ 147.705 + 255.832i 0.0475143 + 0.0822973i
$$214$$ −105.619 182.937i −0.0337382 0.0584362i
$$215$$ −1084.56 + 1878.52i −0.344030 + 0.595878i
$$216$$ −106.755 −0.0336285
$$217$$ 0 0
$$218$$ 337.844 0.104962
$$219$$ 1065.35 1845.24i 0.328721 0.569361i
$$220$$ 2976.72 + 5155.84i 0.912230 + 1.58003i
$$221$$ 887.835 + 1537.78i 0.270236 + 0.468063i
$$222$$ −25.8715 + 44.8107i −0.00782153 + 0.0135473i
$$223$$ 183.844 0.0552069 0.0276034 0.999619i $$-0.491212\pi$$
0.0276034 + 0.999619i $$0.491212\pi$$
$$224$$ 0 0
$$225$$ 266.574 0.0789850
$$226$$ −130.058 + 225.268i −0.0382803 + 0.0663035i
$$227$$ 1139.76 + 1974.12i 0.333253 + 0.577211i 0.983148 0.182813i $$-0.0585203\pi$$
−0.649895 + 0.760024i $$0.725187\pi$$
$$228$$ 601.933 + 1042.58i 0.174842 + 0.302836i
$$229$$ 2706.34 4687.51i 0.780960 1.35266i −0.150424 0.988622i $$-0.548064\pi$$
0.931383 0.364040i $$-0.118603\pi$$
$$230$$ 428.130 0.122739
$$231$$ 0 0
$$232$$ 241.719 0.0684035
$$233$$ −569.184 + 985.856i −0.160036 + 0.277191i −0.934882 0.354960i $$-0.884494\pi$$
0.774845 + 0.632151i $$0.217828\pi$$
$$234$$ 40.6642 + 70.4325i 0.0113603 + 0.0196766i
$$235$$ 2420.78 + 4192.91i 0.671975 + 1.16390i
$$236$$ −3352.12 + 5806.04i −0.924595 + 1.60145i
$$237$$ −1460.65 −0.400336
$$238$$ 0 0
$$239$$ −6226.36 −1.68515 −0.842573 0.538583i $$-0.818960\pi$$
−0.842573 + 0.538583i $$0.818960\pi$$
$$240$$ −1166.24 + 2020.00i −0.313670 + 0.543292i
$$241$$ −1598.10 2767.99i −0.427147 0.739841i 0.569471 0.822012i $$-0.307148\pi$$
−0.996618 + 0.0821704i $$0.973815\pi$$
$$242$$ −286.086 495.516i −0.0759931 0.131624i
$$243$$ −121.500 + 210.444i −0.0320750 + 0.0555556i
$$244$$ −2687.47 −0.705113
$$245$$ 0 0
$$246$$ −229.304 −0.0594305
$$247$$ 920.689 1594.68i 0.237174 0.410798i
$$248$$ 2.31174 + 4.00406i 0.000591919 + 0.00102523i
$$249$$ 908.532 + 1573.62i 0.231228 + 0.400499i
$$250$$ 147.109 254.801i 0.0372160 0.0644600i
$$251$$ −239.608 −0.0602546 −0.0301273 0.999546i $$-0.509591\pi$$
−0.0301273 + 0.999546i $$0.509591\pi$$
$$252$$ 0 0
$$253$$ 8370.78 2.08010
$$254$$ −60.5802 + 104.928i −0.0149651 + 0.0259203i
$$255$$ −909.208 1574.79i −0.223282 0.386735i
$$256$$ −1892.27 3277.51i −0.461980 0.800173i
$$257$$ 349.559 605.453i 0.0848439 0.146954i −0.820481 0.571674i $$-0.806294\pi$$
0.905325 + 0.424720i $$0.139628\pi$$
$$258$$ 129.823 0.0313272
$$259$$ 0 0
$$260$$ 3595.76 0.857690
$$261$$ 275.105 476.496i 0.0652436 0.113005i
$$262$$ −229.991 398.356i −0.0542324 0.0939333i
$$263$$ 459.520 + 795.912i 0.107738 + 0.186609i 0.914854 0.403785i $$-0.132306\pi$$
−0.807115 + 0.590394i $$0.798972\pi$$
$$264$$ 357.697 619.550i 0.0833892 0.144434i
$$265$$ 3916.09 0.907787
$$266$$ 0 0
$$267$$ −654.206 −0.149950
$$268$$ −3856.30 + 6679.32i −0.878960 + 1.52240i
$$269$$ −1389.59 2406.84i −0.314961 0.545529i 0.664468 0.747317i $$-0.268658\pi$$
−0.979429 + 0.201788i $$0.935325\pi$$
$$270$$ −41.6431 72.1280i −0.00938637 0.0162577i
$$271$$ 1113.49 1928.62i 0.249593 0.432308i −0.713820 0.700329i $$-0.753036\pi$$
0.963413 + 0.268021i $$0.0863698\pi$$
$$272$$ 3047.94 0.679443
$$273$$ 0 0
$$274$$ −126.793 −0.0279557
$$275$$ −893.195 + 1547.06i −0.195861 + 0.339241i
$$276$$ 1652.70 + 2862.56i 0.360437 + 0.624296i
$$277$$ −3653.85 6328.65i −0.792557 1.37275i −0.924379 0.381476i $$-0.875416\pi$$
0.131821 0.991273i $$-0.457917\pi$$
$$278$$ 281.078 486.842i 0.0606402 0.105032i
$$279$$ 10.5242 0.00225830
$$280$$ 0 0
$$281$$ 2730.61 0.579696 0.289848 0.957073i $$-0.406395\pi$$
0.289848 + 0.957073i $$0.406395\pi$$
$$282$$ 144.885 250.947i 0.0305949 0.0529919i
$$283$$ −884.926 1532.74i −0.185878 0.321950i 0.757994 0.652261i $$-0.226179\pi$$
−0.943872 + 0.330312i $$0.892846\pi$$
$$284$$ −390.849 676.971i −0.0816642 0.141447i
$$285$$ −942.853 + 1633.07i −0.195964 + 0.339420i
$$286$$ −545.004 −0.112681
$$287$$ 0 0
$$288$$ 424.280 0.0868088
$$289$$ 1268.41 2196.95i 0.258174 0.447170i
$$290$$ 94.2900 + 163.315i 0.0190928 + 0.0330696i
$$291$$ −1173.43 2032.44i −0.236384 0.409429i
$$292$$ −2819.09 + 4882.80i −0.564981 + 0.978576i
$$293$$ −8228.81 −1.64072 −0.820362 0.571844i $$-0.806228\pi$$
−0.820362 + 0.571844i $$0.806228\pi$$
$$294$$ 0 0
$$295$$ −10501.4 −2.07258
$$296$$ 137.451 238.071i 0.0269904 0.0467487i
$$297$$ −814.206 1410.25i −0.159074 0.275524i
$$298$$ −187.034 323.952i −0.0363577 0.0629733i
$$299$$ 2527.89 4378.43i 0.488935 0.846860i
$$300$$ −705.397 −0.135754
$$301$$ 0 0
$$302$$ 394.887 0.0752424
$$303$$ −467.468 + 809.679i −0.0886316 + 0.153514i
$$304$$ −1580.36 2737.27i −0.298158 0.516425i
$$305$$ −2104.79 3645.61i −0.395148 0.684416i
$$306$$ −54.4165 + 94.2521i −0.0101660 + 0.0176079i
$$307$$ −6019.62 −1.11908 −0.559541 0.828803i $$-0.689023\pi$$
−0.559541 + 0.828803i $$0.689023\pi$$
$$308$$ 0 0
$$309$$ 447.773 0.0824366
$$310$$ −1.80354 + 3.12382i −0.000330432 + 0.000572326i
$$311$$ 596.857 + 1033.79i 0.108825 + 0.188491i 0.915295 0.402785i $$-0.131958\pi$$
−0.806469 + 0.591276i $$0.798624\pi$$
$$312$$ −216.042 374.195i −0.0392018 0.0678994i
$$313$$ −4423.02 + 7660.89i −0.798734 + 1.38345i 0.121707 + 0.992566i $$0.461163\pi$$
−0.920441 + 0.390882i $$0.872170\pi$$
$$314$$ −288.795 −0.0519034
$$315$$ 0 0
$$316$$ 3865.11 0.688068
$$317$$ −3040.72 + 5266.68i −0.538750 + 0.933142i 0.460222 + 0.887804i $$0.347770\pi$$
−0.998972 + 0.0453380i $$0.985564\pi$$
$$318$$ −117.190 202.979i −0.0206656 0.0357940i
$$319$$ 1843.56 + 3193.13i 0.323572 + 0.560442i
$$320$$ 3037.28 5260.72i 0.530590 0.919009i
$$321$$ 2554.56 0.444179
$$322$$ 0 0
$$323$$ 2464.12 0.424480
$$324$$ 321.508 556.868i 0.0551282 0.0954848i
$$325$$ 539.471 + 934.391i 0.0920753 + 0.159479i
$$326$$ 143.371 + 248.325i 0.0243576 + 0.0421885i
$$327$$ −2042.82 + 3538.26i −0.345468 + 0.598369i
$$328$$ 1218.25 0.205082
$$329$$ 0 0
$$330$$ 558.125 0.0931023
$$331$$ −1526.65 + 2644.23i −0.253511 + 0.439094i −0.964490 0.264119i $$-0.914919\pi$$
0.710979 + 0.703213i $$0.248252\pi$$
$$332$$ −2404.12 4164.05i −0.397419 0.688349i
$$333$$ −312.871 541.908i −0.0514871 0.0891783i
$$334$$ −358.539 + 621.009i −0.0587377 + 0.101737i
$$335$$ −12080.8 −1.97029
$$336$$ 0 0
$$337$$ 3865.80 0.624877 0.312438 0.949938i $$-0.398854\pi$$
0.312438 + 0.949938i $$0.398854\pi$$
$$338$$ 107.921 186.925i 0.0173673 0.0300811i
$$339$$ −1572.83 2724.22i −0.251989 0.436459i
$$340$$ 2405.90 + 4167.15i 0.383760 + 0.664692i
$$341$$ −35.2627 + 61.0768i −0.00559995 + 0.00969940i
$$342$$ 112.860 0.0178444
$$343$$ 0 0
$$344$$ −689.726 −0.108103
$$345$$ −2588.74 + 4483.83i −0.403980 + 0.699715i
$$346$$ 235.040 + 407.101i 0.0365198 + 0.0632541i
$$347$$ 49.7965 + 86.2501i 0.00770380 + 0.0133434i 0.869852 0.493313i $$-0.164214\pi$$
−0.862148 + 0.506657i $$0.830881\pi$$
$$348$$ −727.970 + 1260.88i −0.112136 + 0.194225i
$$349$$ 3607.34 0.553285 0.276643 0.960973i $$-0.410778\pi$$
0.276643 + 0.960973i $$0.410778\pi$$
$$350$$ 0 0
$$351$$ −983.526 −0.149563
$$352$$ −1421.61 + 2462.30i −0.215262 + 0.372844i
$$353$$ 3565.37 + 6175.40i 0.537579 + 0.931114i 0.999034 + 0.0439501i $$0.0139942\pi$$
−0.461455 + 0.887164i $$0.652672\pi$$
$$354$$ 314.255 + 544.306i 0.0471821 + 0.0817218i
$$355$$ 612.216 1060.39i 0.0915298 0.158534i
$$356$$ 1731.13 0.257724
$$357$$ 0 0
$$358$$ −1063.85 −0.157057
$$359$$ 3250.14 5629.41i 0.477816 0.827602i −0.521860 0.853031i $$-0.674762\pi$$
0.999677 + 0.0254289i $$0.00809514\pi$$
$$360$$ 221.242 + 383.203i 0.0323903 + 0.0561016i
$$361$$ 2151.85 + 3727.11i 0.313727 + 0.543390i
$$362$$ 47.5966 82.4398i 0.00691056 0.0119694i
$$363$$ 6919.44 1.00049
$$364$$ 0 0
$$365$$ −8831.49 −1.26647
$$366$$ −125.973 + 218.191i −0.0179910 + 0.0311613i
$$367$$ 412.443 + 714.372i 0.0586631 + 0.101607i 0.893866 0.448335i $$-0.147983\pi$$
−0.835202 + 0.549943i $$0.814650\pi$$
$$368$$ −4339.12 7515.58i −0.614654 1.06461i
$$369$$ 1386.52 2401.52i 0.195608 0.338803i
$$370$$ 214.468 0.0301342
$$371$$ 0 0
$$372$$ −27.8486 −0.00388140
$$373$$ −666.925 + 1155.15i −0.0925793 + 0.160352i −0.908596 0.417677i $$-0.862845\pi$$
0.816016 + 0.578029i $$0.196178\pi$$
$$374$$ −364.660 631.610i −0.0504174 0.0873255i
$$375$$ 1779.03 + 3081.37i 0.244983 + 0.424324i
$$376$$ −769.746 + 1333.24i −0.105576 + 0.182863i
$$377$$ 2226.94 0.304226
$$378$$ 0 0
$$379$$ −1338.29 −0.181380 −0.0906902 0.995879i $$-0.528907\pi$$
−0.0906902 + 0.995879i $$0.528907\pi$$
$$380$$ 2494.93 4321.35i 0.336809 0.583370i
$$381$$ −732.612 1268.92i −0.0985114 0.170627i
$$382$$ −47.7924 82.7788i −0.00640123 0.0110873i
$$383$$ 176.688 306.032i 0.0235727 0.0408290i −0.853998 0.520276i $$-0.825829\pi$$
0.877571 + 0.479447i $$0.159163\pi$$
$$384$$ −1494.98 −0.198673
$$385$$ 0 0
$$386$$ 156.341 0.0206154
$$387$$ −784.992 + 1359.65i −0.103110 + 0.178591i
$$388$$ 3105.08 + 5378.16i 0.406280 + 0.703697i
$$389$$ −5868.59 10164.7i −0.764908 1.32486i −0.940295 0.340360i $$-0.889451\pi$$
0.175387 0.984500i $$-0.443882\pi$$
$$390$$ 168.548 291.933i 0.0218840 0.0379041i
$$391$$ 6765.59 0.875066
$$392$$ 0 0
$$393$$ 5562.68 0.713996
$$394$$ 155.073 268.595i 0.0198286 0.0343442i
$$395$$ 3027.11 + 5243.10i 0.385595 + 0.667871i
$$396$$ 2154.51 + 3731.73i 0.273405 + 0.473551i
$$397$$ 6640.71 11502.1i 0.839516 1.45408i −0.0507841 0.998710i $$-0.516172\pi$$
0.890300 0.455374i $$-0.150495\pi$$
$$398$$ 270.955 0.0341250
$$399$$ 0 0
$$400$$ 1852.01 0.231501
$$401$$ 3741.18 6479.91i 0.465899 0.806961i −0.533343 0.845899i $$-0.679064\pi$$
0.999242 + 0.0389385i $$0.0123976\pi$$
$$402$$ 361.521 + 626.173i 0.0448534 + 0.0776883i
$$403$$ 21.2979 + 36.8891i 0.00263257 + 0.00455975i
$$404$$ 1236.99 2142.54i 0.152333 0.263849i
$$405$$ 1007.20 0.123576
$$406$$ 0 0
$$407$$ 4193.27 0.510694
$$408$$ 289.105 500.744i 0.0350805 0.0607611i
$$409$$ −6898.30 11948.2i −0.833983 1.44450i −0.894856 0.446355i $$-0.852722\pi$$
0.0608735 0.998145i $$-0.480611\pi$$
$$410$$ 475.218 + 823.102i 0.0572423 + 0.0991466i
$$411$$ 766.673 1327.92i 0.0920126 0.159370i
$$412$$ −1184.88 −0.141686
$$413$$ 0 0
$$414$$ 309.875 0.0367862
$$415$$ 3765.75 6522.46i 0.445429 0.771506i
$$416$$ 858.622 + 1487.18i 0.101196 + 0.175276i
$$417$$ 3399.16 + 5887.51i 0.399179 + 0.691397i
$$418$$ −378.154 + 654.982i −0.0442491 + 0.0766417i
$$419$$ −9497.56 −1.10737 −0.553683 0.832728i $$-0.686778\pi$$
−0.553683 + 0.832728i $$0.686778\pi$$
$$420$$ 0 0
$$421$$ 624.367 0.0722797 0.0361399 0.999347i $$-0.488494\pi$$
0.0361399 + 0.999347i $$0.488494\pi$$
$$422$$ 449.016 777.719i 0.0517957 0.0897127i
$$423$$ 1752.13 + 3034.77i 0.201398 + 0.348832i
$$424$$ 622.608 + 1078.39i 0.0713126 + 0.123517i
$$425$$ −721.915 + 1250.39i −0.0823954 + 0.142713i
$$426$$ −73.2827 −0.00833465
$$427$$ 0 0
$$428$$ −6759.75 −0.763423
$$429$$ 3295.44 5707.87i 0.370875 0.642375i
$$430$$ −269.050 466.007i −0.0301738 0.0522625i
$$431$$ 6698.64 + 11602.4i 0.748636 + 1.29668i 0.948476 + 0.316848i $$0.102624\pi$$
−0.199840 + 0.979829i $$0.564042\pi$$
$$432$$ −844.112 + 1462.05i −0.0940101 + 0.162830i
$$433$$ 14057.3 1.56016 0.780079 0.625681i $$-0.215179\pi$$
0.780079 + 0.625681i $$0.215179\pi$$
$$434$$ 0 0
$$435$$ −2280.55 −0.251365
$$436$$ 5405.61 9362.79i 0.593766 1.02843i
$$437$$ −3507.98 6075.99i −0.384003 0.665112i
$$438$$ 264.284 + 457.753i 0.0288310 + 0.0499368i
$$439$$ −8184.42 + 14175.8i −0.889798 + 1.54117i −0.0496832 + 0.998765i $$0.515821\pi$$
−0.840114 + 0.542409i $$0.817512\pi$$
$$440$$ −2965.22 −0.321275
$$441$$ 0 0
$$442$$ −440.494 −0.0474031
$$443$$ 589.354 1020.79i 0.0632078 0.109479i −0.832690 0.553740i $$-0.813200\pi$$
0.895898 + 0.444261i $$0.146534\pi$$
$$444$$ 827.904 + 1433.97i 0.0884923 + 0.153273i
$$445$$ 1355.80 + 2348.31i 0.144429 + 0.250159i
$$446$$ −22.8033 + 39.4965i −0.00242101 + 0.00419331i
$$447$$ 4523.70 0.478666
$$448$$ 0 0
$$449$$ −12400.9 −1.30342 −0.651709 0.758469i $$-0.725948\pi$$
−0.651709 + 0.758469i $$0.725948\pi$$
$$450$$ −33.0648 + 57.2699i −0.00346376 + 0.00599940i
$$451$$ 9291.45 + 16093.3i 0.970105 + 1.68027i
$$452$$ 4161.95 + 7208.71i 0.433101 + 0.750153i
$$453$$ −2387.74 + 4135.68i −0.247651 + 0.428943i
$$454$$ −565.484 −0.0584570
$$455$$ 0 0
$$456$$ −599.606 −0.0615771
$$457$$ −4962.79 + 8595.81i −0.507986 + 0.879858i 0.491971 + 0.870611i $$0.336277\pi$$
−0.999957 + 0.00924618i $$0.997057\pi$$
$$458$$ 671.366 + 1162.84i 0.0684954 + 0.118637i
$$459$$ −658.073 1139.82i −0.0669198 0.115909i
$$460$$ 6850.21 11864.9i 0.694332 1.20262i
$$461$$ 16010.3 1.61751 0.808755 0.588146i $$-0.200142\pi$$
0.808755 + 0.588146i $$0.200142\pi$$
$$462$$ 0 0
$$463$$ 17372.4 1.74377 0.871883 0.489714i $$-0.162899\pi$$
0.871883 + 0.489714i $$0.162899\pi$$
$$464$$ 1911.27 3310.42i 0.191225 0.331212i
$$465$$ −21.8107 37.7772i −0.00217515 0.00376747i
$$466$$ −141.199 244.563i −0.0140363 0.0243115i
$$467$$ 1054.03 1825.64i 0.104443 0.180900i −0.809068 0.587716i $$-0.800027\pi$$
0.913510 + 0.406815i $$0.133361\pi$$
$$468$$ 2602.56 0.257059
$$469$$ 0 0
$$470$$ −1201.05 −0.117873
$$471$$ 1746.24 3024.58i 0.170833 0.295892i
$$472$$ −1669.58 2891.80i −0.162815 0.282004i
$$473$$ −5260.45 9111.37i −0.511365 0.885711i
$$474$$ 181.173 313.802i 0.0175561 0.0304080i
$$475$$ 1497.26 0.144629
$$476$$ 0 0
$$477$$ 2834.41 0.272073
$$478$$ 772.293 1337.65i 0.0738992 0.127997i
$$479$$ −1225.02 2121.80i −0.116853 0.202395i 0.801666 0.597772i $$-0.203947\pi$$
−0.918519 + 0.395377i $$0.870614\pi$$
$$480$$ −879.292 1522.98i −0.0836126 0.144821i
$$481$$ 1266.32 2193.34i 0.120040 0.207916i
$$482$$ 792.887 0.0749274
$$483$$ 0 0
$$484$$ −18309.9 −1.71956
$$485$$ −4863.72 + 8424.21i −0.455361 + 0.788709i
$$486$$ −30.1407 52.2053i −0.00281319 0.00487259i
$$487$$ −322.618 558.791i −0.0300189 0.0519943i 0.850626 0.525772i $$-0.176223\pi$$
−0.880645 + 0.473778i $$0.842890\pi$$
$$488$$ 669.270 1159.21i 0.0620828 0.107531i
$$489$$ −3467.64 −0.320679
$$490$$ 0 0
$$491$$ 11766.1 1.08146 0.540731 0.841196i $$-0.318148\pi$$
0.540731 + 0.841196i $$0.318148\pi$$
$$492$$ −3668.94 + 6354.79i −0.336196 + 0.582309i
$$493$$ 1490.03 + 2580.81i 0.136121 + 0.235769i
$$494$$ 228.397 + 395.595i 0.0208018 + 0.0360297i
$$495$$ −3374.77 + 5845.28i −0.306434 + 0.530759i
$$496$$ 73.1159 0.00661896
$$497$$ 0 0
$$498$$ −450.763 −0.0405606
$$499$$ 22.0104 38.1232i 0.00197459 0.00342010i −0.865036 0.501709i $$-0.832705\pi$$
0.867011 + 0.498289i $$0.166038\pi$$
$$500$$ −4707.59 8153.78i −0.421059 0.729296i
$$501$$ −4335.91 7510.02i −0.386655 0.669707i
$$502$$ 29.7200 51.4765i 0.00264236 0.00457671i
$$503$$ −8290.27 −0.734880 −0.367440 0.930047i $$-0.619766\pi$$
−0.367440 + 0.930047i $$0.619766\pi$$
$$504$$ 0 0
$$505$$ 3875.19 0.341473
$$506$$ −1038.28 + 1798.35i −0.0912195 + 0.157997i
$$507$$ 1305.12 + 2260.54i 0.114324 + 0.198016i
$$508$$ 1938.60 + 3357.76i 0.169314 + 0.293261i
$$509$$ 3457.52 5988.60i 0.301084 0.521493i −0.675298 0.737545i $$-0.735985\pi$$
0.976382 + 0.216052i $$0.0693181\pi$$
$$510$$ 451.098 0.0391666
$$511$$ 0 0
$$512$$ 4925.45 0.425148
$$513$$ −682.425 + 1181.99i −0.0587325 + 0.101728i
$$514$$ 86.7157 + 150.196i 0.00744137 + 0.0128888i
$$515$$ −927.980 1607.31i −0.0794014 0.137527i
$$516$$ 2077.21 3597.83i 0.177217 0.306949i
$$517$$ −23483.0 −1.99764
$$518$$ 0 0
$$519$$ −5684.81 −0.480800
$$520$$ −895.464 + 1550.99i −0.0755167 + 0.130799i
$$521$$ 6699.64 + 11604.1i 0.563371 + 0.975788i 0.997199 + 0.0747919i $$0.0238293\pi$$
−0.433828 + 0.900996i $$0.642837\pi$$
$$522$$ 68.2458 + 118.205i 0.00572230 + 0.00991131i
$$523$$ −4968.50 + 8605.69i −0.415406 + 0.719504i −0.995471 0.0950662i $$-0.969694\pi$$
0.580065 + 0.814570i $$0.303027\pi$$
$$524$$ −14719.7 −1.22716
$$525$$ 0 0
$$526$$ −227.988 −0.0188988
$$527$$ −28.5007 + 49.3647i −0.00235581 + 0.00408038i
$$528$$ −5656.63 9797.58i −0.466237 0.807547i
$$529$$ −3548.17 6145.60i −0.291622 0.505104i
$$530$$ −485.736 + 841.320i −0.0398095 + 0.0689521i
$$531$$ −7600.74 −0.621175
$$532$$ 0 0
$$533$$ 11223.7 0.912104
$$534$$ 81.1450 140.547i 0.00657582 0.0113897i
$$535$$ −5294.15 9169.74i −0.427825 0.741014i
$$536$$ −1920.70 3326.75i −0.154779 0.268085i
$$537$$ 6432.74 11141.8i 0.516933 0.895355i
$$538$$ 689.435 0.0552484
$$539$$ 0 0
$$540$$ −2665.21 −0.212394
$$541$$ −4643.08 + 8042.06i −0.368987 + 0.639103i −0.989407 0.145166i $$-0.953628\pi$$
0.620421 + 0.784269i $$0.286962\pi$$
$$542$$ 276.226 + 478.437i 0.0218910 + 0.0379163i
$$543$$ 575.599 + 996.966i 0.0454904 + 0.0787917i
$$544$$ −1149.00 + 1990.13i −0.0905570 + 0.156849i
$$545$$ 16934.4 1.33099
$$546$$ 0 0
$$547$$ −16821.6 −1.31488 −0.657438 0.753508i $$-0.728360\pi$$
−0.657438 + 0.753508i $$0.728360\pi$$
$$548$$ −2028.73 + 3513.87i −0.158144 + 0.273914i
$$549$$ −1523.42 2638.64i −0.118430 0.205127i
$$550$$ −221.577 383.782i −0.0171783 0.0297537i
$$551$$ 1545.17 2676.32i 0.119467 0.206924i
$$552$$ −1646.31 −0.126941
$$553$$ 0 0
$$554$$ 1812.83 0.139025
$$555$$ −1296.81 + 2246.14i −0.0991828 + 0.171790i
$$556$$ −8994.69 15579.3i −0.686079 1.18832i
$$557$$ −902.972 1563.99i −0.0686897 0.118974i 0.829635 0.558306i $$-0.188549\pi$$
−0.898325 + 0.439332i $$0.855215\pi$$
$$558$$ −1.30538 + 2.26098i −9.90340e−5 + 0.000171532i
$$559$$ −6354.40 −0.480792
$$560$$ 0 0
$$561$$ 8819.86 0.663770
$$562$$ −338.694 + 586.635i −0.0254216 + 0.0440315i
$$563$$ 6107.45 + 10578.4i 0.457190 + 0.791877i 0.998811 0.0487460i $$-0.0155225\pi$$
−0.541621 + 0.840623i $$0.682189\pi$$
$$564$$ −4636.40 8030.48i −0.346148 0.599546i
$$565$$ −6519.17 + 11291.5i −0.485423 + 0.840776i
$$566$$ 439.050 0.0326054
$$567$$ 0 0
$$568$$ 389.338 0.0287610
$$569$$ −2141.89 + 3709.86i −0.157808 + 0.273331i −0.934078 0.357070i $$-0.883776\pi$$
0.776270 + 0.630400i $$0.217109\pi$$
$$570$$ −233.895 405.119i −0.0171874 0.0297694i
$$571$$ −3179.97 5507.87i −0.233060 0.403673i 0.725647 0.688067i $$-0.241541\pi$$
−0.958707 + 0.284395i $$0.908207\pi$$
$$572$$ −8720.25 + 15103.9i −0.637433 + 1.10407i
$$573$$ 1155.93 0.0842753
$$574$$ 0 0
$$575$$ 4110.95 0.298153
$$576$$ 2198.34 3807.64i 0.159023 0.275437i
$$577$$ 7234.36 + 12530.3i 0.521959 + 0.904059i 0.999674 + 0.0255444i $$0.00813192\pi$$
−0.477715 + 0.878515i $$0.658535\pi$$
$$578$$ 314.656 + 545.001i 0.0226436 + 0.0392198i
$$579$$ −945.335 + 1637.37i −0.0678528 + 0.117525i
$$580$$ 6034.68 0.432028
$$581$$ 0 0
$$582$$ 582.191 0.0414649
$$583$$ −9497.10 + 16449.5i −0.674665 + 1.16855i
$$584$$ −1404.09 2431.96i −0.0994894 0.172321i
$$585$$ 2038.29 + 3530.43i 0.144056 + 0.249513i
$$586$$ 1020.67 1767.85i 0.0719513 0.124623i
$$587$$ 11132.6 0.782777 0.391388 0.920226i $$-0.371995\pi$$
0.391388 + 0.920226i $$0.371995\pi$$
$$588$$ 0 0
$$589$$ 59.1108 0.00413517
$$590$$ 1302.55 2256.07i 0.0908897 0.157426i
$$591$$ 1875.34 + 3248.19i 0.130527 + 0.226079i
$$592$$ −2173.65 3764.87i −0.150906 0.261377i
$$593$$ −9887.81 + 17126.2i −0.684728 + 1.18598i 0.288794 + 0.957391i $$0.406746\pi$$
−0.973522 + 0.228592i $$0.926588\pi$$
$$594$$ 403.963 0.0279037
$$595$$ 0 0
$$596$$ −11970.4 −0.822696
$$597$$ −1638.37 + 2837.73i −0.112318 + 0.194541i
$$598$$ 627.098 + 1086.17i 0.0428829 + 0.0742753i
$$599$$ 11945.5 + 20690.2i 0.814825 + 1.41132i 0.909453 + 0.415806i $$0.136500\pi$$
−0.0946282 + 0.995513i $$0.530166\pi$$
$$600$$ 175.667 304.265i 0.0119527 0.0207026i
$$601$$ −19395.5 −1.31641 −0.658204 0.752840i $$-0.728683\pi$$
−0.658204 + 0.752840i $$0.728683\pi$$
$$602$$ 0 0
$$603$$ −8743.95 −0.590516
$$604$$ 6318.32 10943.7i 0.425644 0.737237i
$$605$$ −14340.1 24837.8i −0.963648 1.66909i
$$606$$ −115.966 200.859i −0.00777358 0.0134642i
$$607$$ 7298.36 12641.1i 0.488025 0.845285i −0.511880 0.859057i $$-0.671051\pi$$
0.999905 + 0.0137724i $$0.00438402\pi$$
$$608$$ 2383.04 0.158956
$$609$$ 0 0
$$610$$ 1044.28 0.0693142
$$611$$ −7091.62 + 12283.0i −0.469552 + 0.813288i
$$612$$ 1741.36 + 3016.13i 0.115017 + 0.199215i
$$613$$ −989.898 1714.55i −0.0652229 0.112969i 0.831570 0.555420i $$-0.187442\pi$$
−0.896793 + 0.442451i $$0.854109\pi$$
$$614$$ 746.650 1293.24i 0.0490755 0.0850012i
$$615$$ −11493.9 −0.753622
$$616$$ 0 0
$$617$$ 16262.4 1.06110 0.530551 0.847653i $$-0.321985\pi$$
0.530551 + 0.847653i $$0.321985\pi$$
$$618$$ −55.5400 + 96.1981i −0.00361512 + 0.00626158i
$$619$$ −6010.49 10410.5i −0.390278 0.675981i 0.602208 0.798339i $$-0.294288\pi$$
−0.992486 + 0.122358i $$0.960954\pi$$
$$620$$ 57.7143 + 99.9642i 0.00373849 + 0.00647526i
$$621$$ −1873.70 + 3245.34i −0.121077 + 0.209712i
$$622$$ −296.127 −0.0190894
$$623$$ 0 0
$$624$$ −6832.97 −0.438362
$$625$$ 9225.06 15978.3i 0.590404 1.02261i
$$626$$ −1097.23 1900.45i −0.0700543 0.121338i
$$627$$ −4573.12 7920.87i −0.291280 0.504512i
$$628$$ −4620.82 + 8003.49i −0.293616 + 0.508557i
$$629$$ 3389.16 0.214841
$$630$$ 0 0
$$631$$ 25347.6 1.59916 0.799582 0.600557i $$-0.205055\pi$$
0.799582 + 0.600557i $$0.205055\pi$$
$$632$$ −962.542 + 1667.17i −0.0605821 + 0.104931i
$$633$$ 5430.07 + 9405.16i 0.340957 + 0.590556i
$$634$$ −754.317 1306.51i −0.0472519 0.0818428i
$$635$$ −3036.58 + 5259.51i −0.189769 + 0.328689i
$$636$$ −7500.29 −0.467620
$$637$$ 0 0
$$638$$ −914.669 −0.0567588
$$639$$ 443.114 767.496i 0.0274324 0.0475143i
$$640$$ 3098.24 + 5366.31i 0.191358 + 0.331441i
$$641$$ 2555.80 + 4426.78i 0.157485 + 0.272772i 0.933961 0.357374i $$-0.116328\pi$$
−0.776476 + 0.630147i $$0.782995\pi$$
$$642$$ −316.857 + 548.812i −0.0194787 + 0.0337382i
$$643$$ 10931.3 0.670435 0.335217 0.942141i $$-0.391190\pi$$
0.335217 + 0.942141i $$0.391190\pi$$
$$644$$ 0 0
$$645$$ 6507.38 0.397252
$$646$$ −305.639 + 529.382i −0.0186149 + 0.0322419i
$$647$$ −9203.06 15940.2i −0.559211 0.968582i −0.997563 0.0697783i $$-0.977771\pi$$
0.438352 0.898804i $$-0.355563\pi$$
$$648$$ 160.132 + 277.357i 0.00970770 + 0.0168142i
$$649$$ 25467.3 44110.7i 1.54034 2.66795i
$$650$$ −267.655 −0.0161512
$$651$$ 0 0
$$652$$ 9175.91 0.551160
$$653$$ −9960.71 + 17252.5i −0.596926 + 1.03391i 0.396346 + 0.918101i $$0.370278\pi$$
−0.993272 + 0.115805i $$0.963055\pi$$
$$654$$ −506.766 877.744i −0.0302999 0.0524809i
$$655$$ −11528.3 19967.6i −0.687707 1.19114i
$$656$$ 9632.74 16684.4i 0.573316 0.993012i
$$657$$ −6392.11 −0.379574
$$658$$ 0 0
$$659$$ −18858.8 −1.11477 −0.557385 0.830254i $$-0.688195\pi$$
−0.557385 + 0.830254i $$0.688195\pi$$
$$660$$ 8930.17 15467.5i 0.526676 0.912230i
$$661$$ 12916.0 + 22371.2i 0.760023 + 1.31640i 0.942838 + 0.333251i $$0.108146\pi$$
−0.182815 + 0.983147i $$0.558521\pi$$
$$662$$ −378.718 655.960i −0.0222346 0.0385115i
$$663$$ 2663.50 4613.33i 0.156021 0.270236i
$$664$$ 2394.82 0.139965
$$665$$ 0 0
$$666$$ 155.229 0.00903153
$$667$$ 4242.50 7348.22i 0.246282 0.426573i
$$668$$ 11473.5 + 19872.7i 0.664555 + 1.15104i
$$669$$ −275.767 477.642i −0.0159369 0.0276034i
$$670$$ 1498.46 2595.41i 0.0864037 0.149656i
$$671$$ 20417.7 1.17469
$$672$$ 0 0
$$673$$ −16275.0 −0.932178 −0.466089 0.884738i $$-0.654337\pi$$
−0.466089 + 0.884738i $$0.654337\pi$$
$$674$$ −479.498 + 830.515i −0.0274029 + 0.0474633i
$$675$$ −399.862 692.581i −0.0228010 0.0394925i
$$676$$ −3453.55 5981.73i −0.196493 0.340335i
$$677$$ −13135.9 + 22752.0i −0.745720 + 1.29163i 0.204137 + 0.978942i $$0.434561\pi$$
−0.949857 + 0.312683i $$0.898772\pi$$
$$678$$ 780.350 0.0442023
$$679$$ 0 0
$$680$$ −2396.60 −0.135155
$$681$$ 3419.28 5922.36i 0.192404 0.333253i
$$682$$ −8.74769 15.1514i −0.000491153 0.000850702i
$$683$$ 4036.14 + 6990.81i 0.226118 + 0.391648i 0.956654 0.291226i $$-0.0940631\pi$$
−0.730536 + 0.682874i $$0.760730\pi$$
$$684$$ 1805.80 3127.74i 0.100945 0.174842i
$$685$$ −6355.51 −0.354499
$$686$$ 0 0
$$687$$ −16238.0 −0.901774
$$688$$ −5453.67 + 9446.04i −0.302208 + 0.523440i
$$689$$ 5736.05 + 9935.13i 0.317164 + 0.549344i
$$690$$ −642.194 1112.31i −0.0354318 0.0613696i
$$691$$ −12242.6 + 21204.9i −0.673997 + 1.16740i 0.302763 + 0.953066i $$0.402091\pi$$
−0.976761 + 0.214332i $$0.931243\pi$$
$$692$$ 15042.9 0.826364
$$693$$ 0 0
$$694$$ −24.7062 −0.00135135
$$695$$ 14089.1 24403.0i 0.768962 1.33188i
$$696$$ −362.578 628.003i −0.0197464 0.0342017i
$$697$$ 7509.71 + 13007.2i 0.408107 + 0.706862i
$$698$$ −447.440 + 774.989i −0.0242634 + 0.0420254i
$$699$$ 3415.10 0.184794
$$700$$ 0 0
$$701$$ 778.448 0.0419423 0.0209712 0.999780i $$-0.493324\pi$$
0.0209712 + 0.999780i $$0.493324\pi$$
$$702$$ 121.993 211.297i 0.00655885 0.0113603i
$$703$$ −1757.29 3043.72i −0.0942780 0.163294i
$$704$$ 14731.7 + 25516.0i 0.788667 + 1.36601i
$$705$$ 7262.34 12578.7i 0.387965 0.671975i
$$706$$ −1768.93 −0.0942985
$$707$$ 0 0
$$708$$ 20112.7 1.06763
$$709$$ 12086.0 20933.6i 0.640197 1.10885i −0.345192 0.938532i $$-0.612186\pi$$
0.985389 0.170322i $$-0.0544806\pi$$
$$710$$ 151.874 + 263.053i 0.00802777 + 0.0139045i
$$711$$ 2190.98 + 3794.89i 0.115567 + 0.200168i
$$712$$ −431.109 + 746.703i −0.0226917 + 0.0393032i
$$713$$ 162.297 0.00852466
$$714$$ 0 0
$$715$$ −27318.3 −1.42888
$$716$$ −17022.0 + 29483.0i −0.888467 + 1.53887i
$$717$$ 9339.54 + 16176.6i 0.486460 + 0.842573i
$$718$$ 806.269 + 1396.50i 0.0419077 + 0.0725862i
$$719$$ −40.9418 + 70.9132i −0.00212360 + 0.00367819i −0.867085 0.498160i $$-0.834009\pi$$
0.864962 + 0.501838i $$0.167343\pi$$
$$720$$ 6997.47 0.362195
$$721$$ 0 0
$$722$$ −1067.63 −0.0550318
$$723$$ −4794.29 + 8303.96i −0.246614 + 0.427147i
$$724$$ −1523.12 2638.13i −0.0781856 0.135421i
$$725$$ 905.382 + 1568.17i 0.0463794 + 0.0803315i
$$726$$ −858.259 + 1486.55i −0.0438747 + 0.0759931i
$$727$$ 32542.9 1.66018 0.830088 0.557632i $$-0.188290\pi$$
0.830088 + 0.557632i $$0.188290\pi$$
$$728$$ 0 0
$$729$$ 729.000 0.0370370
$$730$$ 1095.42 1897.33i 0.0555389 0.0961962i
$$731$$ −4251.70 7364.16i −0.215123 0.372604i
$$732$$ 4031.20 + 6982.25i 0.203549 + 0.352557i
$$733$$ −2534.47 + 4389.83i −0.127712 + 0.221203i −0.922790 0.385304i $$-0.874097\pi$$
0.795078 + 0.606507i $$0.207430\pi$$
$$734$$ −204.631 −0.0102903
$$735$$ 0 0
$$736$$ 6542.98 0.327687
$$737$$ 29297.8 50745.3i 1.46431 2.53627i
$$738$$ 343.956 + 595.750i 0.0171561 + 0.0297153i
$$739$$ 19214.2 + 33280.0i 0.956437 + 1.65660i 0.731045 + 0.682329i $$0.239033\pi$$
0.225392 + 0.974268i $$0.427634\pi$$
$$740$$ 3431.55 5943.62i 0.170468 0.295259i
$$741$$ −5524.14 −0.273865
$$742$$ 0 0
$$743$$ 21592.9 1.06617 0.533086 0.846061i $$-0.321032\pi$$
0.533086 + 0.846061i $$0.321032\pi$$
$$744$$ 6.93523 12.0122i 0.000341744 0.000591919i
$$745$$ −9375.07 16238.1i −0.461042 0.798548i
$$746$$ −165.445 286.560i −0.00811982 0.0140639i
$$747$$ 2725.60 4720.87i 0.133500 0.231228i
$$748$$ −23338.7 −1.14084
$$749$$ 0 0
$$750$$ −882.655 −0.0429733
$$751$$ −4056.30 + 7025.72i −0.197093 + 0.341374i −0.947585 0.319505i $$-0.896483\pi$$
0.750492 + 0.660880i $$0.229817\pi$$
$$752$$ 12172.8 + 21083.9i 0.590287 + 1.02241i
$$753$$ 359.411 + 622.519i 0.0173940 + 0.0301273i
$$754$$ −276.220 + 478.428i −0.0133413 + 0.0231078i
$$755$$ 19793.7 0.954129
$$756$$ 0 0
$$757$$ 3108.01 0.149224 0.0746120 0.997213i $$-0.476228\pi$$
0.0746120 + 0.997213i $$0.476228\pi$$
$$758$$ 165.996 287.513i 0.00795414 0.0137770i
$$759$$ −12556.2 21747.9i −0.600475 1.04005i
$$760$$ 1242.64 + 2152.32i 0.0593098 + 0.102728i
$$761$$ −3605.96 + 6245.71i −0.171769 + 0.297512i −0.939038 0.343812i $$-0.888282\pi$$
0.767269 + 0.641325i $$0.221615\pi$$
$$762$$ 363.481 0.0172802
$$763$$ 0 0
$$764$$ −3058.77 −0.144846
$$765$$ −2727.62 + 4724.38i −0.128912 + 0.223282i
$$766$$ 43.8313 + 75.9181i 0.00206748 + 0.00358098i
$$767$$ −15381.7 26641.9i −0.724123 1.25422i
$$768$$ −5676.81 + 9832.52i −0.266724 + 0.461980i
$$769$$ 7533.07 0.353250 0.176625 0.984278i $$-0.443482\pi$$
0.176625 + 0.984278i $$0.443482\pi$$
$$770$$ 0 0
$$771$$ −2097.35 −0.0979693
$$772$$ 2501.50 4332.73i 0.116621 0.201993i
$$773$$ −12416.3 21505.7i −0.577728 1.00065i −0.995739 0.0922122i $$-0.970606\pi$$
0.418012 0.908442i $$-0.362727\pi$$
$$774$$ −194.734 337.290i −0.00904339 0.0156636i
$$775$$ −17.3178 + 29.9952i −0.000802674 + 0.00139027i
$$776$$ −3093.08 −0.143086
$$777$$ 0 0
$$778$$ 2911.66 0.134175
$$779$$ 7787.61 13488.5i 0.358177 0.620381i