# Properties

 Label 147.4.c.a.146.11 Level $147$ Weight $4$ Character 147.146 Analytic conductor $8.673$ Analytic rank $0$ Dimension $12$ CM no Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$147 = 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 147.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.67328077084$$ Analytic rank: $$0$$ Dimension: $$12$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ Defining polynomial: $$x^{12} - x^{11} - 29 x^{9} + 6 x^{8} - 49 x^{7} + 1564 x^{6} - 441 x^{5} + 486 x^{4} - 21141 x^{3} - 59049 x + 531441$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{6}\cdot 3^{3}$$ Twist minimal: no (minimal twist has level 21) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 146.11 Root $$-0.232749 + 2.99096i$$ of defining polynomial Character $$\chi$$ $$=$$ 147.146 Dual form 147.4.c.a.146.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+4.54551i q^{2} +(-2.93937 - 4.28487i) q^{3} -12.6617 q^{4} +11.6039 q^{5} +(19.4769 - 13.3609i) q^{6} -21.1897i q^{8} +(-9.72022 + 25.1896i) q^{9} +O(q^{10})$$ $$q+4.54551i q^{2} +(-2.93937 - 4.28487i) q^{3} -12.6617 q^{4} +11.6039 q^{5} +(19.4769 - 13.3609i) q^{6} -21.1897i q^{8} +(-9.72022 + 25.1896i) q^{9} +52.7455i q^{10} +17.9160i q^{11} +(37.2174 + 54.2537i) q^{12} +62.4185i q^{13} +(-34.1081 - 49.7211i) q^{15} -4.97524 q^{16} -21.4164 q^{17} +(-114.500 - 44.1834i) q^{18} -10.9783i q^{19} -146.925 q^{20} -81.4374 q^{22} +69.0934i q^{23} +(-90.7953 + 62.2845i) q^{24} +9.64979 q^{25} -283.724 q^{26} +(136.506 - 32.3918i) q^{27} +265.583i q^{29} +(226.008 - 155.039i) q^{30} +10.2283i q^{31} -192.133i q^{32} +(76.7677 - 52.6617i) q^{33} -97.3486i q^{34} +(123.074 - 318.943i) q^{36} +41.6514 q^{37} +49.9019 q^{38} +(267.455 - 183.471i) q^{39} -245.883i q^{40} -31.0035 q^{41} -224.550 q^{43} -226.847i q^{44} +(-112.792 + 292.297i) q^{45} -314.065 q^{46} +163.719 q^{47} +(14.6241 + 21.3182i) q^{48} +43.8633i q^{50} +(62.9508 + 91.7665i) q^{51} -790.323i q^{52} +527.220i q^{53} +(147.237 + 620.488i) q^{54} +207.895i q^{55} +(-47.0405 + 32.2692i) q^{57} -1207.21 q^{58} +411.956 q^{59} +(431.865 + 629.552i) q^{60} -258.431i q^{61} -46.4928 q^{62} +833.541 q^{64} +724.296i q^{65} +(239.375 + 348.949i) q^{66} +323.474 q^{67} +271.168 q^{68} +(296.056 - 203.091i) q^{69} -45.4199i q^{71} +(533.762 + 205.969i) q^{72} -562.199i q^{73} +189.327i q^{74} +(-28.3643 - 41.3481i) q^{75} +139.004i q^{76} +(833.969 + 1215.72i) q^{78} +289.221 q^{79} -57.7320 q^{80} +(-540.035 - 489.697i) q^{81} -140.927i q^{82} +448.767 q^{83} -248.513 q^{85} -1020.70i q^{86} +(1137.99 - 780.647i) q^{87} +379.635 q^{88} +561.628 q^{89} +(-1328.64 - 512.698i) q^{90} -874.839i q^{92} +(43.8268 - 30.0647i) q^{93} +744.187i q^{94} -127.391i q^{95} +(-823.265 + 564.750i) q^{96} -214.364i q^{97} +(-451.297 - 174.147i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q - 28 q^{4} + 6 q^{9} + O(q^{10})$$ $$12 q - 28 q^{4} + 6 q^{9} + 6 q^{15} - 268 q^{16} - 132 q^{18} - 268 q^{22} + 84 q^{25} + 1644 q^{30} + 852 q^{36} - 1528 q^{37} + 852 q^{39} - 1012 q^{43} - 1216 q^{46} + 2682 q^{51} + 270 q^{57} - 5740 q^{58} + 1836 q^{60} - 548 q^{64} - 1584 q^{67} + 5424 q^{72} + 4296 q^{78} - 3348 q^{79} - 1674 q^{81} + 348 q^{85} + 1108 q^{88} + 2958 q^{93} - 3354 q^{99} + O(q^{100})$$

## Character values

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

 $$n$$ $$50$$ $$52$$ $$\chi(n)$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 4.54551i 1.60708i 0.595250 + 0.803541i $$0.297053\pi$$
−0.595250 + 0.803541i $$0.702947\pi$$
$$3$$ −2.93937 4.28487i −0.565682 0.824624i
$$4$$ −12.6617 −1.58271
$$5$$ 11.6039 1.03788 0.518941 0.854810i $$-0.326326\pi$$
0.518941 + 0.854810i $$0.326326\pi$$
$$6$$ 19.4769 13.3609i 1.32524 0.909097i
$$7$$ 0 0
$$8$$ 21.1897i 0.936463i
$$9$$ −9.72022 + 25.1896i −0.360008 + 0.932949i
$$10$$ 52.7455i 1.66796i
$$11$$ 17.9160i 0.491080i 0.969387 + 0.245540i $$0.0789652\pi$$
−0.969387 + 0.245540i $$0.921035\pi$$
$$12$$ 37.2174 + 54.2537i 0.895311 + 1.30514i
$$13$$ 62.4185i 1.33167i 0.746097 + 0.665837i $$0.231925\pi$$
−0.746097 + 0.665837i $$0.768075\pi$$
$$14$$ 0 0
$$15$$ −34.1081 49.7211i −0.587111 0.855862i
$$16$$ −4.97524 −0.0777381
$$17$$ −21.4164 −0.305544 −0.152772 0.988261i $$-0.548820\pi$$
−0.152772 + 0.988261i $$0.548820\pi$$
$$18$$ −114.500 44.1834i −1.49933 0.578562i
$$19$$ 10.9783i 0.132557i −0.997801 0.0662787i $$-0.978887\pi$$
0.997801 0.0662787i $$-0.0211126\pi$$
$$20$$ −146.925 −1.64267
$$21$$ 0 0
$$22$$ −81.4374 −0.789205
$$23$$ 69.0934i 0.626390i 0.949689 + 0.313195i $$0.101399\pi$$
−0.949689 + 0.313195i $$0.898601\pi$$
$$24$$ −90.7953 + 62.2845i −0.772230 + 0.529740i
$$25$$ 9.64979 0.0771983
$$26$$ −283.724 −2.14011
$$27$$ 136.506 32.3918i 0.972982 0.230881i
$$28$$ 0 0
$$29$$ 265.583i 1.70061i 0.526294 + 0.850303i $$0.323581\pi$$
−0.526294 + 0.850303i $$0.676419\pi$$
$$30$$ 226.008 155.039i 1.37544 0.943535i
$$31$$ 10.2283i 0.0592598i 0.999561 + 0.0296299i $$0.00943286\pi$$
−0.999561 + 0.0296299i $$0.990567\pi$$
$$32$$ 192.133i 1.06139i
$$33$$ 76.7677 52.6617i 0.404956 0.277795i
$$34$$ 97.3486i 0.491034i
$$35$$ 0 0
$$36$$ 123.074 318.943i 0.569788 1.47659i
$$37$$ 41.6514 0.185066 0.0925331 0.995710i $$-0.470504\pi$$
0.0925331 + 0.995710i $$0.470504\pi$$
$$38$$ 49.9019 0.213031
$$39$$ 267.455 183.471i 1.09813 0.753304i
$$40$$ 245.883i 0.971938i
$$41$$ −31.0035 −0.118096 −0.0590480 0.998255i $$-0.518807\pi$$
−0.0590480 + 0.998255i $$0.518807\pi$$
$$42$$ 0 0
$$43$$ −224.550 −0.796363 −0.398181 0.917307i $$-0.630359\pi$$
−0.398181 + 0.917307i $$0.630359\pi$$
$$44$$ 226.847i 0.777237i
$$45$$ −112.792 + 292.297i −0.373646 + 0.968291i
$$46$$ −314.065 −1.00666
$$47$$ 163.719 0.508103 0.254052 0.967191i $$-0.418237\pi$$
0.254052 + 0.967191i $$0.418237\pi$$
$$48$$ 14.6241 + 21.3182i 0.0439750 + 0.0641046i
$$49$$ 0 0
$$50$$ 43.8633i 0.124064i
$$51$$ 62.9508 + 91.7665i 0.172841 + 0.251959i
$$52$$ 790.323i 2.10765i
$$53$$ 527.220i 1.36640i 0.730231 + 0.683200i $$0.239412\pi$$
−0.730231 + 0.683200i $$0.760588\pi$$
$$54$$ 147.237 + 620.488i 0.371045 + 1.56366i
$$55$$ 207.895i 0.509682i
$$56$$ 0 0
$$57$$ −47.0405 + 32.2692i −0.109310 + 0.0749853i
$$58$$ −1207.21 −2.73301
$$59$$ 411.956 0.909020 0.454510 0.890742i $$-0.349814\pi$$
0.454510 + 0.890742i $$0.349814\pi$$
$$60$$ 431.865 + 629.552i 0.929227 + 1.35458i
$$61$$ 258.431i 0.542437i −0.962518 0.271218i $$-0.912573\pi$$
0.962518 0.271218i $$-0.0874266\pi$$
$$62$$ −46.4928 −0.0952352
$$63$$ 0 0
$$64$$ 833.541 1.62801
$$65$$ 724.296i 1.38212i
$$66$$ 239.375 + 348.949i 0.446439 + 0.650797i
$$67$$ 323.474 0.589831 0.294915 0.955523i $$-0.404709\pi$$
0.294915 + 0.955523i $$0.404709\pi$$
$$68$$ 271.168 0.483587
$$69$$ 296.056 203.091i 0.516536 0.354338i
$$70$$ 0 0
$$71$$ 45.4199i 0.0759205i −0.999279 0.0379603i $$-0.987914\pi$$
0.999279 0.0379603i $$-0.0120860\pi$$
$$72$$ 533.762 + 205.969i 0.873673 + 0.337134i
$$73$$ 562.199i 0.901376i −0.892682 0.450688i $$-0.851179\pi$$
0.892682 0.450688i $$-0.148821\pi$$
$$74$$ 189.327i 0.297416i
$$75$$ −28.3643 41.3481i −0.0436697 0.0636596i
$$76$$ 139.004i 0.209800i
$$77$$ 0 0
$$78$$ 833.969 + 1215.72i 1.21062 + 1.76478i
$$79$$ 289.221 0.411898 0.205949 0.978563i $$-0.433972\pi$$
0.205949 + 0.978563i $$0.433972\pi$$
$$80$$ −57.7320 −0.0806829
$$81$$ −540.035 489.697i −0.740789 0.671738i
$$82$$ 140.927i 0.189790i
$$83$$ 448.767 0.593477 0.296738 0.954959i $$-0.404101\pi$$
0.296738 + 0.954959i $$0.404101\pi$$
$$84$$ 0 0
$$85$$ −248.513 −0.317118
$$86$$ 1020.70i 1.27982i
$$87$$ 1137.99 780.647i 1.40236 0.962002i
$$88$$ 379.635 0.459878
$$89$$ 561.628 0.668904 0.334452 0.942413i $$-0.391449\pi$$
0.334452 + 0.942413i $$0.391449\pi$$
$$90$$ −1328.64 512.698i −1.55612 0.600479i
$$91$$ 0 0
$$92$$ 874.839i 0.991394i
$$93$$ 43.8268 30.0647i 0.0488670 0.0335222i
$$94$$ 744.187i 0.816564i
$$95$$ 127.391i 0.137579i
$$96$$ −823.265 + 564.750i −0.875251 + 0.600412i
$$97$$ 214.364i 0.224385i −0.993686 0.112192i $$-0.964213\pi$$
0.993686 0.112192i $$-0.0357873\pi$$
$$98$$ 0 0
$$99$$ −451.297 174.147i −0.458152 0.176793i
$$100$$ −122.183 −0.122183
$$101$$ −1717.69 −1.69224 −0.846122 0.532990i $$-0.821068\pi$$
−0.846122 + 0.532990i $$0.821068\pi$$
$$102$$ −417.126 + 286.143i −0.404918 + 0.277769i
$$103$$ 1157.71i 1.10750i −0.832683 0.553750i $$-0.813196\pi$$
0.832683 0.553750i $$-0.186804\pi$$
$$104$$ 1322.63 1.24706
$$105$$ 0 0
$$106$$ −2396.48 −2.19592
$$107$$ 1217.79i 1.10027i −0.835077 0.550134i $$-0.814577\pi$$
0.835077 0.550134i $$-0.185423\pi$$
$$108$$ −1728.39 + 410.134i −1.53995 + 0.365418i
$$109$$ 1298.26 1.14084 0.570418 0.821355i $$-0.306781\pi$$
0.570418 + 0.821355i $$0.306781\pi$$
$$110$$ −944.989 −0.819101
$$111$$ −122.429 178.471i −0.104689 0.152610i
$$112$$ 0 0
$$113$$ 1437.86i 1.19701i −0.801118 0.598506i $$-0.795761\pi$$
0.801118 0.598506i $$-0.204239\pi$$
$$114$$ −146.680 213.823i −0.120508 0.175670i
$$115$$ 801.751i 0.650119i
$$116$$ 3362.73i 2.69157i
$$117$$ −1572.30 606.721i −1.24238 0.479413i
$$118$$ 1872.55i 1.46087i
$$119$$ 0 0
$$120$$ −1053.58 + 722.741i −0.801483 + 0.549808i
$$121$$ 1010.02 0.758841
$$122$$ 1174.70 0.871740
$$123$$ 91.1308 + 132.846i 0.0668048 + 0.0973848i
$$124$$ 129.507i 0.0937910i
$$125$$ −1338.51 −0.957759
$$126$$ 0 0
$$127$$ 2686.32 1.87695 0.938475 0.345347i $$-0.112239\pi$$
0.938475 + 0.345347i $$0.112239\pi$$
$$128$$ 2251.81i 1.55495i
$$129$$ 660.036 + 962.169i 0.450488 + 0.656699i
$$130$$ −3292.29 −2.22118
$$131$$ 1603.27 1.06930 0.534651 0.845073i $$-0.320443\pi$$
0.534651 + 0.845073i $$0.320443\pi$$
$$132$$ −972.008 + 666.786i −0.640928 + 0.439669i
$$133$$ 0 0
$$134$$ 1470.36i 0.947906i
$$135$$ 1583.99 375.870i 1.00984 0.239628i
$$136$$ 453.808i 0.286130i
$$137$$ 2318.52i 1.44588i 0.690913 + 0.722938i $$0.257209\pi$$
−0.690913 + 0.722938i $$0.742791\pi$$
$$138$$ 923.153 + 1345.73i 0.569449 + 0.830116i
$$139$$ 1841.57i 1.12374i −0.827225 0.561871i $$-0.810082\pi$$
0.827225 0.561871i $$-0.189918\pi$$
$$140$$ 0 0
$$141$$ −481.230 701.514i −0.287425 0.418994i
$$142$$ 206.457 0.122010
$$143$$ −1118.29 −0.653958
$$144$$ 48.3604 125.324i 0.0279863 0.0725257i
$$145$$ 3081.79i 1.76503i
$$146$$ 2555.48 1.44858
$$147$$ 0 0
$$148$$ −527.377 −0.292906
$$149$$ 1300.98i 0.715302i 0.933855 + 0.357651i $$0.116422\pi$$
−0.933855 + 0.357651i $$0.883578\pi$$
$$150$$ 187.948 128.930i 0.102306 0.0701808i
$$151$$ −2616.49 −1.41011 −0.705055 0.709152i $$-0.749078\pi$$
−0.705055 + 0.709152i $$0.749078\pi$$
$$152$$ −232.627 −0.124135
$$153$$ 208.172 539.472i 0.109998 0.285057i
$$154$$ 0 0
$$155$$ 118.688i 0.0615046i
$$156$$ −3386.43 + 2323.05i −1.73802 + 1.19226i
$$157$$ 935.164i 0.475377i −0.971341 0.237689i $$-0.923610\pi$$
0.971341 0.237689i $$-0.0763898\pi$$
$$158$$ 1314.66i 0.661953i
$$159$$ 2259.07 1549.69i 1.12677 0.772948i
$$160$$ 2229.49i 1.10160i
$$161$$ 0 0
$$162$$ 2225.92 2454.74i 1.07954 1.19051i
$$163$$ −518.158 −0.248989 −0.124495 0.992220i $$-0.539731\pi$$
−0.124495 + 0.992220i $$0.539731\pi$$
$$164$$ 392.557 0.186912
$$165$$ 890.802 611.080i 0.420296 0.288318i
$$166$$ 2039.88i 0.953765i
$$167$$ −3767.97 −1.74595 −0.872977 0.487761i $$-0.837814\pi$$
−0.872977 + 0.487761i $$0.837814\pi$$
$$168$$ 0 0
$$169$$ −1699.06 −0.773356
$$170$$ 1129.62i 0.509635i
$$171$$ 276.539 + 106.711i 0.123669 + 0.0477217i
$$172$$ 2843.18 1.26041
$$173$$ −2393.06 −1.05168 −0.525841 0.850583i $$-0.676249\pi$$
−0.525841 + 0.850583i $$0.676249\pi$$
$$174$$ 3548.44 + 5172.74i 1.54602 + 2.25371i
$$175$$ 0 0
$$176$$ 89.1363i 0.0381756i
$$177$$ −1210.89 1765.18i −0.514216 0.749599i
$$178$$ 2552.89i 1.07498i
$$179$$ 640.144i 0.267299i 0.991029 + 0.133650i $$0.0426697\pi$$
−0.991029 + 0.133650i $$0.957330\pi$$
$$180$$ 1428.14 3700.97i 0.591373 1.53252i
$$181$$ 4204.05i 1.72643i 0.504833 + 0.863217i $$0.331554\pi$$
−0.504833 + 0.863217i $$0.668446\pi$$
$$182$$ 0 0
$$183$$ −1107.34 + 759.623i −0.447306 + 0.306847i
$$184$$ 1464.07 0.586591
$$185$$ 483.318 0.192077
$$186$$ 136.659 + 199.215i 0.0538729 + 0.0785332i
$$187$$ 383.696i 0.150046i
$$188$$ −2072.96 −0.804181
$$189$$ 0 0
$$190$$ 579.056 0.221101
$$191$$ 1457.06i 0.551985i 0.961160 + 0.275993i $$0.0890066\pi$$
−0.961160 + 0.275993i $$0.910993\pi$$
$$192$$ −2450.08 3571.61i −0.920935 1.34249i
$$193$$ 1829.27 0.682246 0.341123 0.940019i $$-0.389193\pi$$
0.341123 + 0.940019i $$0.389193\pi$$
$$194$$ 974.393 0.360605
$$195$$ 3103.51 2128.97i 1.13973 0.781840i
$$196$$ 0 0
$$197$$ 661.168i 0.239118i 0.992827 + 0.119559i $$0.0381481\pi$$
−0.992827 + 0.119559i $$0.961852\pi$$
$$198$$ 791.589 2051.38i 0.284120 0.736288i
$$199$$ 1949.13i 0.694322i −0.937806 0.347161i $$-0.887146\pi$$
0.937806 0.347161i $$-0.112854\pi$$
$$200$$ 204.477i 0.0722934i
$$201$$ −950.810 1386.04i −0.333657 0.486388i
$$202$$ 7807.78i 2.71957i
$$203$$ 0 0
$$204$$ −797.063 1161.92i −0.273557 0.398777i
$$205$$ −359.761 −0.122570
$$206$$ 5262.38 1.77984
$$207$$ −1740.44 671.603i −0.584390 0.225505i
$$208$$ 310.547i 0.103522i
$$209$$ 196.687 0.0650963
$$210$$ 0 0
$$211$$ 3341.96 1.09038 0.545189 0.838313i $$-0.316458\pi$$
0.545189 + 0.838313i $$0.316458\pi$$
$$212$$ 6675.49i 2.16262i
$$213$$ −194.619 + 133.506i −0.0626058 + 0.0429469i
$$214$$ 5535.50 1.76822
$$215$$ −2605.65 −0.826530
$$216$$ −686.373 2892.52i −0.216212 0.911162i
$$217$$ 0 0
$$218$$ 5901.27i 1.83342i
$$219$$ −2408.95 + 1652.51i −0.743296 + 0.509892i
$$220$$ 2632.30i 0.806680i
$$221$$ 1336.78i 0.406885i
$$222$$ 811.242 556.502i 0.245257 0.168243i
$$223$$ 2143.28i 0.643608i 0.946806 + 0.321804i $$0.104289\pi$$
−0.946806 + 0.321804i $$0.895711\pi$$
$$224$$ 0 0
$$225$$ −93.7981 + 243.075i −0.0277920 + 0.0720221i
$$226$$ 6535.80 1.92370
$$227$$ −2569.11 −0.751178 −0.375589 0.926786i $$-0.622560\pi$$
−0.375589 + 0.926786i $$0.622560\pi$$
$$228$$ 595.612 408.583i 0.173006 0.118680i
$$229$$ 105.173i 0.0303495i −0.999885 0.0151748i $$-0.995170\pi$$
0.999885 0.0151748i $$-0.00483046\pi$$
$$230$$ −3644.37 −1.04479
$$231$$ 0 0
$$232$$ 5627.64 1.59255
$$233$$ 2625.72i 0.738270i −0.929376 0.369135i $$-0.879654\pi$$
0.929376 0.369135i $$-0.120346\pi$$
$$234$$ 2757.86 7146.90i 0.770456 1.99661i
$$235$$ 1899.77 0.527351
$$236$$ −5216.06 −1.43872
$$237$$ −850.127 1239.27i −0.233003 0.339660i
$$238$$ 0 0
$$239$$ 6080.85i 1.64576i 0.568212 + 0.822882i $$0.307635\pi$$
−0.568212 + 0.822882i $$0.692365\pi$$
$$240$$ 169.696 + 247.374i 0.0456409 + 0.0665330i
$$241$$ 4628.89i 1.23723i 0.785693 + 0.618616i $$0.212306\pi$$
−0.785693 + 0.618616i $$0.787694\pi$$
$$242$$ 4591.05i 1.21952i
$$243$$ −510.927 + 3753.38i −0.134881 + 0.990862i
$$244$$ 3272.17i 0.858521i
$$245$$ 0 0
$$246$$ −603.853 + 414.236i −0.156505 + 0.107361i
$$247$$ 685.248 0.176523
$$248$$ 216.735 0.0554946
$$249$$ −1319.09 1922.91i −0.335719 0.489395i
$$250$$ 6084.21i 1.53920i
$$251$$ 5967.85 1.50075 0.750373 0.661015i $$-0.229874\pi$$
0.750373 + 0.661015i $$0.229874\pi$$
$$252$$ 0 0
$$253$$ −1237.88 −0.307607
$$254$$ 12210.7i 3.01641i
$$255$$ 730.472 + 1064.85i 0.179388 + 0.261503i
$$256$$ −3567.29 −0.870920
$$257$$ 5639.40 1.36878 0.684389 0.729117i $$-0.260069\pi$$
0.684389 + 0.729117i $$0.260069\pi$$
$$258$$ −4373.55 + 3000.20i −1.05537 + 0.723971i
$$259$$ 0 0
$$260$$ 9170.80i 2.18750i
$$261$$ −6689.94 2581.53i −1.58658 0.612232i
$$262$$ 7287.70i 1.71846i
$$263$$ 3485.62i 0.817234i −0.912706 0.408617i $$-0.866011\pi$$
0.912706 0.408617i $$-0.133989\pi$$
$$264$$ −1115.89 1626.69i −0.260145 0.379226i
$$265$$ 6117.79i 1.41816i
$$266$$ 0 0
$$267$$ −1650.83 2406.50i −0.378387 0.551594i
$$268$$ −4095.73 −0.933531
$$269$$ 3794.55 0.860066 0.430033 0.902813i $$-0.358502\pi$$
0.430033 + 0.902813i $$0.358502\pi$$
$$270$$ 1708.52 + 7200.06i 0.385101 + 1.62290i
$$271$$ 7457.62i 1.67165i 0.548993 + 0.835827i $$0.315011\pi$$
−0.548993 + 0.835827i $$0.684989\pi$$
$$272$$ 106.552 0.0237524
$$273$$ 0 0
$$274$$ −10538.9 −2.32364
$$275$$ 172.886i 0.0379105i
$$276$$ −3748.57 + 2571.48i −0.817527 + 0.560814i
$$277$$ −3415.49 −0.740856 −0.370428 0.928861i $$-0.620789\pi$$
−0.370428 + 0.928861i $$0.620789\pi$$
$$278$$ 8370.89 1.80595
$$279$$ −257.646 99.4210i −0.0552863 0.0213340i
$$280$$ 0 0
$$281$$ 2762.14i 0.586390i −0.956053 0.293195i $$-0.905281\pi$$
0.956053 0.293195i $$-0.0947185\pi$$
$$282$$ 3188.74 2187.44i 0.673358 0.461915i
$$283$$ 5505.20i 1.15636i −0.815909 0.578181i $$-0.803763\pi$$
0.815909 0.578181i $$-0.196237\pi$$
$$284$$ 575.093i 0.120160i
$$285$$ −545.852 + 374.448i −0.113451 + 0.0778259i
$$286$$ 5083.19i 1.05096i
$$287$$ 0 0
$$288$$ 4839.76 + 1867.57i 0.990227 + 0.382110i
$$289$$ −4454.34 −0.906643
$$290$$ −14008.3 −2.83654
$$291$$ −918.520 + 630.094i −0.185033 + 0.126930i
$$292$$ 7118.39i 1.42662i
$$293$$ 4101.08 0.817705 0.408853 0.912600i $$-0.365929\pi$$
0.408853 + 0.912600i $$0.365929\pi$$
$$294$$ 0 0
$$295$$ 4780.29 0.943455
$$296$$ 882.583i 0.173308i
$$297$$ 580.331 + 2445.63i 0.113381 + 0.477812i
$$298$$ −5913.60 −1.14955
$$299$$ −4312.70 −0.834148
$$300$$ 359.140 + 523.537i 0.0691165 + 0.100755i
$$301$$ 0 0
$$302$$ 11893.3i 2.26616i
$$303$$ 5048.93 + 7360.08i 0.957271 + 1.39546i
$$304$$ 54.6196i 0.0103048i
$$305$$ 2998.80i 0.562985i
$$306$$ 2452.17 + 946.249i 0.458109 + 0.176776i
$$307$$ 8281.42i 1.53956i −0.638308 0.769781i $$-0.720365\pi$$
0.638308 0.769781i $$-0.279635\pi$$
$$308$$ 0 0
$$309$$ −4960.63 + 3402.94i −0.913270 + 0.626493i
$$310$$ −539.496 −0.0988429
$$311$$ 6871.05 1.25280 0.626401 0.779501i $$-0.284527\pi$$
0.626401 + 0.779501i $$0.284527\pi$$
$$312$$ −3887.70 5667.30i −0.705441 1.02836i
$$313$$ 3374.49i 0.609386i 0.952451 + 0.304693i $$0.0985538\pi$$
−0.952451 + 0.304693i $$0.901446\pi$$
$$314$$ 4250.80 0.763970
$$315$$ 0 0
$$316$$ −3662.02 −0.651914
$$317$$ 2369.77i 0.419872i −0.977715 0.209936i $$-0.932674\pi$$
0.977715 0.209936i $$-0.0673255\pi$$
$$318$$ 7044.15 + 10268.6i 1.24219 + 1.81080i
$$319$$ −4758.19 −0.835133
$$320$$ 9672.30 1.68968
$$321$$ −5218.09 + 3579.55i −0.907306 + 0.622401i
$$322$$ 0 0
$$323$$ 235.116i 0.0405021i
$$324$$ 6837.75 + 6200.39i 1.17245 + 1.06317i
$$325$$ 602.325i 0.102803i
$$326$$ 2355.29i 0.400146i
$$327$$ −3816.08 5562.89i −0.645350 0.940760i
$$328$$ 656.957i 0.110593i
$$329$$ 0 0
$$330$$ 2777.67 + 4049.15i 0.463351 + 0.675450i
$$331$$ 3803.61 0.631617 0.315808 0.948823i $$-0.397724\pi$$
0.315808 + 0.948823i $$0.397724\pi$$
$$332$$ −5682.14 −0.939302
$$333$$ −404.861 + 1049.18i −0.0666253 + 0.172657i
$$334$$ 17127.4i 2.80589i
$$335$$ 3753.55 0.612175
$$336$$ 0 0
$$337$$ −592.955 −0.0958466 −0.0479233 0.998851i $$-0.515260\pi$$
−0.0479233 + 0.998851i $$0.515260\pi$$
$$338$$ 7723.11i 1.24285i
$$339$$ −6161.04 + 4226.40i −0.987084 + 0.677128i
$$340$$ 3146.60 0.501906
$$341$$ −183.250 −0.0291013
$$342$$ −485.058 + 1257.01i −0.0766927 + 0.198747i
$$343$$ 0 0
$$344$$ 4758.16i 0.745764i
$$345$$ 3435.40 2356.64i 0.536103 0.367760i
$$346$$ 10877.7i 1.69014i
$$347$$ 4777.16i 0.739054i −0.929220 0.369527i $$-0.879520\pi$$
0.929220 0.369527i $$-0.120480\pi$$
$$348$$ −14408.9 + 9884.31i −2.21953 + 1.52257i
$$349$$ 7358.26i 1.12859i 0.825573 + 0.564296i $$0.190852\pi$$
−0.825573 + 0.564296i $$0.809148\pi$$
$$350$$ 0 0
$$351$$ 2021.84 + 8520.47i 0.307459 + 1.29569i
$$352$$ 3442.25 0.521229
$$353$$ −3305.55 −0.498405 −0.249202 0.968451i $$-0.580168\pi$$
−0.249202 + 0.968451i $$0.580168\pi$$
$$354$$ 8023.65 5504.13i 1.20467 0.826387i
$$355$$ 527.047i 0.0787965i
$$356$$ −7111.16 −1.05868
$$357$$ 0 0
$$358$$ −2909.78 −0.429572
$$359$$ 414.716i 0.0609689i 0.999535 + 0.0304845i $$0.00970501\pi$$
−0.999535 + 0.0304845i $$0.990295\pi$$
$$360$$ 6193.70 + 2390.04i 0.906769 + 0.349905i
$$361$$ 6738.48 0.982429
$$362$$ −19109.6 −2.77452
$$363$$ −2968.81 4327.79i −0.429263 0.625758i
$$364$$ 0 0
$$365$$ 6523.69i 0.935522i
$$366$$ −3452.88 5033.43i −0.493128 0.718858i
$$367$$ 76.1227i 0.0108272i −0.999985 0.00541359i $$-0.998277\pi$$
0.999985 0.00541359i $$-0.00172321\pi$$
$$368$$ 343.756i 0.0486944i
$$369$$ 301.361 780.967i 0.0425155 0.110178i
$$370$$ 2196.93i 0.308683i
$$371$$ 0 0
$$372$$ −554.921 + 380.669i −0.0773423 + 0.0530559i
$$373$$ −12301.0 −1.70756 −0.853781 0.520632i $$-0.825696\pi$$
−0.853781 + 0.520632i $$0.825696\pi$$
$$374$$ 1744.10 0.241137
$$375$$ 3934.37 + 5735.34i 0.541787 + 0.789791i
$$376$$ 3469.16i 0.475820i
$$377$$ −16577.3 −2.26465
$$378$$ 0 0
$$379$$ −1429.02 −0.193678 −0.0968389 0.995300i $$-0.530873\pi$$
−0.0968389 + 0.995300i $$0.530873\pi$$
$$380$$ 1612.98i 0.217748i
$$381$$ −7896.10 11510.5i −1.06176 1.54778i
$$382$$ −6623.09 −0.887086
$$383$$ −5110.90 −0.681866 −0.340933 0.940088i $$-0.610743\pi$$
−0.340933 + 0.940088i $$0.610743\pi$$
$$384$$ 9648.70 6618.89i 1.28225 0.879606i
$$385$$ 0 0
$$386$$ 8314.95i 1.09642i
$$387$$ 2182.68 5656.34i 0.286697 0.742966i
$$388$$ 2714.20i 0.355136i
$$389$$ 7320.62i 0.954165i 0.878858 + 0.477083i $$0.158306\pi$$
−0.878858 + 0.477083i $$0.841694\pi$$
$$390$$ 9677.27 + 14107.1i 1.25648 + 1.83164i
$$391$$ 1479.73i 0.191390i
$$392$$ 0 0
$$393$$ −4712.61 6869.82i −0.604885 0.881772i
$$394$$ −3005.35 −0.384283
$$395$$ 3356.08 0.427501
$$396$$ 5714.18 + 2205.00i 0.725122 + 0.279811i
$$397$$ 8679.44i 1.09725i −0.836068 0.548625i $$-0.815151\pi$$
0.836068 0.548625i $$-0.184849\pi$$
$$398$$ 8859.79 1.11583
$$399$$ 0 0
$$400$$ −48.0100 −0.00600125
$$401$$ 9754.54i 1.21476i −0.794412 0.607379i $$-0.792221\pi$$
0.794412 0.607379i $$-0.207779\pi$$
$$402$$ 6300.28 4321.92i 0.781666 0.536213i
$$403$$ −638.433 −0.0789147
$$404$$ 21748.9 2.67833
$$405$$ −6266.49 5682.38i −0.768851 0.697185i
$$406$$ 0 0
$$407$$ 746.226i 0.0908822i
$$408$$ 1944.51 1333.91i 0.235950 0.161859i
$$409$$ 3389.41i 0.409769i 0.978786 + 0.204885i $$0.0656819\pi$$
−0.978786 + 0.204885i $$0.934318\pi$$
$$410$$ 1635.30i 0.196979i
$$411$$ 9934.58 6815.00i 1.19230 0.817906i
$$412$$ 14658.5i 1.75285i
$$413$$ 0 0
$$414$$ 3052.78 7911.18i 0.362406 0.939163i
$$415$$ 5207.43 0.615959
$$416$$ 11992.6 1.41343
$$417$$ −7890.90 + 5413.06i −0.926664 + 0.635681i
$$418$$ 894.043i 0.104615i
$$419$$ 12777.4 1.48977 0.744887 0.667191i $$-0.232504\pi$$
0.744887 + 0.667191i $$0.232504\pi$$
$$420$$ 0 0
$$421$$ 11005.4 1.27404 0.637020 0.770848i $$-0.280167\pi$$
0.637020 + 0.770848i $$0.280167\pi$$
$$422$$ 15190.9i 1.75233i
$$423$$ −1591.38 + 4124.02i −0.182921 + 0.474035i
$$424$$ 11171.6 1.27958
$$425$$ −206.664 −0.0235875
$$426$$ −606.853 884.641i −0.0690191 0.100613i
$$427$$ 0 0
$$428$$ 15419.3i 1.74140i
$$429$$ 3287.06 + 4791.72i 0.369932 + 0.539269i
$$430$$ 11844.0i 1.32830i
$$431$$ 3786.41i 0.423167i 0.977360 + 0.211584i $$0.0678621\pi$$
−0.977360 + 0.211584i $$0.932138\pi$$
$$432$$ −679.147 + 161.157i −0.0756377 + 0.0179483i
$$433$$ 3191.67i 0.354230i −0.984190 0.177115i $$-0.943323\pi$$
0.984190 0.177115i $$-0.0566765\pi$$
$$434$$ 0 0
$$435$$ 13205.1 9058.53i 1.45548 0.998444i
$$436$$ −16438.2 −1.80561
$$437$$ 758.527 0.0830327
$$438$$ −7511.51 10949.9i −0.819438 1.19454i
$$439$$ 3317.34i 0.360656i 0.983607 + 0.180328i $$0.0577159\pi$$
−0.983607 + 0.180328i $$0.942284\pi$$
$$440$$ 4405.24 0.477299
$$441$$ 0 0
$$442$$ 6076.35 0.653897
$$443$$ 10700.5i 1.14763i 0.818986 + 0.573813i $$0.194536\pi$$
−0.818986 + 0.573813i $$0.805464\pi$$
$$444$$ 1550.16 + 2259.74i 0.165692 + 0.241537i
$$445$$ 6517.06 0.694243
$$446$$ −9742.29 −1.03433
$$447$$ 5574.51 3824.05i 0.589855 0.404634i
$$448$$ 0 0
$$449$$ 4017.92i 0.422310i −0.977453 0.211155i $$-0.932278\pi$$
0.977453 0.211155i $$-0.0677225\pi$$
$$450$$ −1104.90 426.360i −0.115745 0.0446640i
$$451$$ 555.459i 0.0579945i
$$452$$ 18205.7i 1.89452i
$$453$$ 7690.82 + 11211.3i 0.797674 + 1.16281i
$$454$$ 11677.9i 1.20720i
$$455$$ 0 0
$$456$$ 683.777 + 996.777i 0.0702210 + 0.102365i
$$457$$ 9169.65 0.938596 0.469298 0.883040i $$-0.344507\pi$$
0.469298 + 0.883040i $$0.344507\pi$$
$$458$$ 478.066 0.0487742
$$459$$ −2923.46 + 693.716i −0.297289 + 0.0705444i
$$460$$ 10151.5i 1.02895i
$$461$$ −1289.80 −0.130308 −0.0651542 0.997875i $$-0.520754\pi$$
−0.0651542 + 0.997875i $$0.520754\pi$$
$$462$$ 0 0
$$463$$ 6976.52 0.700273 0.350137 0.936699i $$-0.386135\pi$$
0.350137 + 0.936699i $$0.386135\pi$$
$$464$$ 1321.34i 0.132202i
$$465$$ 508.561 348.867i 0.0507182 0.0347920i
$$466$$ 11935.3 1.18646
$$467$$ 7863.66 0.779201 0.389600 0.920984i $$-0.372613\pi$$
0.389600 + 0.920984i $$0.372613\pi$$
$$468$$ 19907.9 + 7682.11i 1.96633 + 0.758772i
$$469$$ 0 0
$$470$$ 8635.44i 0.847496i
$$471$$ −4007.06 + 2748.79i −0.392007 + 0.268912i
$$472$$ 8729.25i 0.851263i
$$473$$ 4023.04i 0.391077i
$$474$$ 5633.14 3864.26i 0.545862 0.374455i
$$475$$ 105.938i 0.0102332i
$$476$$ 0 0
$$477$$ −13280.5 5124.69i −1.27478 0.491915i
$$478$$ −27640.6 −2.64488
$$479$$ −3694.27 −0.352391 −0.176196 0.984355i $$-0.556379\pi$$
−0.176196 + 0.984355i $$0.556379\pi$$
$$480$$ −9553.05 + 6553.28i −0.908407 + 0.623156i
$$481$$ 2599.82i 0.246448i
$$482$$ −21040.7 −1.98833
$$483$$ 0 0
$$484$$ −12788.5 −1.20103
$$485$$ 2487.45i 0.232885i
$$486$$ −17061.0 2322.42i −1.59240 0.216764i
$$487$$ −1052.72 −0.0979533 −0.0489766 0.998800i $$-0.515596\pi$$
−0.0489766 + 0.998800i $$0.515596\pi$$
$$488$$ −5476.08 −0.507972
$$489$$ 1523.06 + 2220.24i 0.140849 + 0.205322i
$$490$$ 0 0
$$491$$ 2378.40i 0.218607i 0.994008 + 0.109303i $$0.0348620\pi$$
−0.994008 + 0.109303i $$0.965138\pi$$
$$492$$ −1153.87 1682.05i −0.105733 0.154132i
$$493$$ 5687.84i 0.519609i
$$494$$ 3114.80i 0.283687i
$$495$$ −5236.79 2020.78i −0.475508 0.183490i
$$496$$ 50.8881i 0.00460674i
$$497$$ 0 0
$$498$$ 8740.60 5995.95i 0.786497 0.539528i
$$499$$ 18771.5 1.68402 0.842011 0.539461i $$-0.181372\pi$$
0.842011 + 0.539461i $$0.181372\pi$$
$$500$$ 16947.8 1.51586
$$501$$ 11075.5 + 16145.3i 0.987655 + 1.43975i
$$502$$ 27126.9i 2.41182i
$$503$$ −16095.2 −1.42674 −0.713370 0.700788i $$-0.752832\pi$$
−0.713370 + 0.700788i $$0.752832\pi$$
$$504$$ 0 0
$$505$$ −19931.9 −1.75635
$$506$$ 5626.79i 0.494350i
$$507$$ 4994.17 + 7280.26i 0.437473 + 0.637728i
$$508$$ −34013.4 −2.97067
$$509$$ −3150.63 −0.274360 −0.137180 0.990546i $$-0.543804\pi$$
−0.137180 + 0.990546i $$0.543804\pi$$
$$510$$ −4840.28 + 3320.37i −0.420257 + 0.288291i
$$511$$ 0 0
$$512$$ 1799.30i 0.155310i
$$513$$ −355.606 1498.60i −0.0306051 0.128976i
$$514$$ 25633.9i 2.19974i
$$515$$ 13433.9i 1.14945i
$$516$$ −8357.17 12182.7i −0.712992 1.03937i
$$517$$ 2933.19i 0.249519i
$$518$$ 0 0
$$519$$ 7034.08 + 10253.9i 0.594917 + 0.867241i
$$520$$ 15347.6 1.29430
$$521$$ 4979.20 0.418700 0.209350 0.977841i $$-0.432865\pi$$
0.209350 + 0.977841i $$0.432865\pi$$
$$522$$ 11734.4 30409.2i 0.983906 2.54976i
$$523$$ 13829.8i 1.15628i −0.815936 0.578142i $$-0.803778\pi$$
0.815936 0.578142i $$-0.196222\pi$$
$$524$$ −20300.1 −1.69240
$$525$$ 0 0
$$526$$ 15843.9 1.31336
$$527$$ 219.053i 0.0181064i
$$528$$ −381.937 + 262.005i −0.0314805 + 0.0215952i
$$529$$ 7393.10 0.607635
$$530$$ −27808.5 −2.27910
$$531$$ −4004.31 + 10377.0i −0.327254 + 0.848069i
$$532$$ 0 0
$$533$$ 1935.19i 0.157265i
$$534$$ 10938.8 7503.88i 0.886456 0.608098i
$$535$$ 14131.1i 1.14195i
$$536$$ 6854.33i 0.552355i
$$537$$ 2742.93 1881.62i 0.220421 0.151206i
$$538$$ 17248.2i 1.38220i
$$539$$ 0 0
$$540$$ −20056.0 + 4759.15i −1.59828 + 0.379261i
$$541$$ 5317.95 0.422618 0.211309 0.977419i $$-0.432227\pi$$
0.211309 + 0.977419i $$0.432227\pi$$
$$542$$ −33898.7 −2.68648
$$543$$ 18013.8 12357.3i 1.42366 0.976613i
$$544$$ 4114.80i 0.324302i
$$545$$ 15064.9 1.18405
$$546$$ 0 0
$$547$$ −9266.96 −0.724363 −0.362181 0.932108i $$-0.617968\pi$$
−0.362181 + 0.932108i $$0.617968\pi$$
$$548$$ 29356.4i 2.28840i
$$549$$ 6509.77 + 2512.00i 0.506066 + 0.195282i
$$550$$ −785.854 −0.0609253
$$551$$ 2915.65 0.225428
$$552$$ −4303.45 6273.36i −0.331824 0.483717i
$$553$$ 0 0
$$554$$ 15525.2i 1.19062i
$$555$$ −1420.65 2070.95i −0.108654 0.158391i
$$556$$ 23317.4i 1.77856i
$$557$$ 145.400i 0.0110607i −0.999985 0.00553033i $$-0.998240\pi$$
0.999985 0.00553033i $$-0.00176037\pi$$
$$558$$ 451.920 1171.14i 0.0342854 0.0888497i
$$559$$ 14016.1i 1.06050i
$$560$$ 0 0
$$561$$ −1644.09 + 1127.83i −0.123732 + 0.0848785i
$$562$$ 12555.4 0.942376
$$563$$ −3916.24 −0.293161 −0.146581 0.989199i $$-0.546827\pi$$
−0.146581 + 0.989199i $$0.546827\pi$$
$$564$$ 6093.19 + 8882.35i 0.454910 + 0.663146i
$$565$$ 16684.7i 1.24236i
$$566$$ 25024.0 1.85837
$$567$$ 0 0
$$568$$ −962.437 −0.0710968
$$569$$ 8550.53i 0.629977i 0.949096 + 0.314988i $$0.102001\pi$$
−0.949096 + 0.314988i $$0.897999\pi$$
$$570$$ −1702.06 2481.18i −0.125073 0.182325i
$$571$$ −23913.7 −1.75264 −0.876318 0.481733i $$-0.840007\pi$$
−0.876318 + 0.481733i $$0.840007\pi$$
$$572$$ 14159.4 1.03503
$$573$$ 6243.32 4282.84i 0.455180 0.312248i
$$574$$ 0 0
$$575$$ 666.737i 0.0483563i
$$576$$ −8102.20 + 20996.6i −0.586096 + 1.51885i
$$577$$ 13103.3i 0.945405i 0.881222 + 0.472703i $$0.156721\pi$$
−0.881222 + 0.472703i $$0.843279\pi$$
$$578$$ 20247.2i 1.45705i
$$579$$ −5376.89 7838.16i −0.385934 0.562596i
$$580$$ 39020.7i 2.79353i
$$581$$ 0 0
$$582$$ −2864.10 4175.15i −0.203988 0.297363i
$$583$$ −9445.66 −0.671011
$$584$$ −11912.9 −0.844106
$$585$$ −18244.7 7040.31i −1.28945 0.497574i
$$586$$ 18641.5i 1.31412i
$$587$$ 18034.7 1.26809 0.634047 0.773294i $$-0.281392\pi$$
0.634047 + 0.773294i $$0.281392\pi$$
$$588$$ 0 0
$$589$$ 112.289 0.00785532
$$590$$ 21728.9i 1.51621i
$$591$$ 2833.02 1943.42i 0.197183 0.135265i
$$592$$ −207.226 −0.0143867
$$593$$ −22716.2 −1.57309 −0.786547 0.617531i $$-0.788133\pi$$
−0.786547 + 0.617531i $$0.788133\pi$$
$$594$$ −11116.7 + 2637.90i −0.767882 + 0.182213i
$$595$$ 0 0
$$596$$ 16472.5i 1.13212i
$$597$$ −8351.76 + 5729.21i −0.572554 + 0.392765i
$$598$$ 19603.5i 1.34054i
$$599$$ 13533.6i 0.923149i 0.887101 + 0.461575i $$0.152715\pi$$
−0.887101 + 0.461575i $$0.847285\pi$$
$$600$$ −876.156 + 601.032i −0.0596148 + 0.0408951i
$$601$$ 3667.98i 0.248952i 0.992223 + 0.124476i $$0.0397250\pi$$
−0.992223 + 0.124476i $$0.960275\pi$$
$$602$$ 0 0
$$603$$ −3144.24 + 8148.20i −0.212344 + 0.550282i
$$604$$ 33129.1 2.23180
$$605$$ 11720.1 0.787587
$$606$$ −33455.3 + 22950.0i −2.24262 + 1.53841i
$$607$$ 8017.00i 0.536079i 0.963408 + 0.268039i $$0.0863758\pi$$
−0.963408 + 0.268039i $$0.913624\pi$$
$$608$$ −2109.29 −0.140696
$$609$$ 0 0
$$610$$ 13631.1 0.904763
$$611$$ 10219.1i 0.676628i
$$612$$ −2635.81 + 6830.62i −0.174095 + 0.451162i
$$613$$ 9396.52 0.619122 0.309561 0.950880i $$-0.399818\pi$$
0.309561 + 0.950880i $$0.399818\pi$$
$$614$$ 37643.3 2.47420
$$615$$ 1057.47 + 1541.53i 0.0693355 + 0.101074i
$$616$$ 0 0
$$617$$ 8906.76i 0.581155i 0.956851 + 0.290578i $$0.0938474\pi$$
−0.956851 + 0.290578i $$0.906153\pi$$
$$618$$ −15468.1 22548.6i −1.00682 1.46770i
$$619$$ 7034.12i 0.456745i −0.973574 0.228373i $$-0.926660\pi$$
0.973574 0.228373i $$-0.0733404\pi$$
$$620$$ 1502.78i 0.0973440i
$$621$$ 2238.06 + 9431.64i 0.144622 + 0.609466i
$$622$$ 31232.4i 2.01335i
$$623$$ 0 0
$$624$$ −1330.65 + 912.811i −0.0853665 + 0.0585604i
$$625$$ −16738.1 −1.07124
$$626$$ −15338.8 −0.979332
$$627$$ −578.135 842.778i −0.0368238 0.0536799i
$$628$$ 11840.8i 0.752385i
$$629$$ −892.024 −0.0565458
$$630$$ 0 0
$$631$$ −12628.6 −0.796728 −0.398364 0.917227i $$-0.630422\pi$$
−0.398364 + 0.917227i $$0.630422\pi$$
$$632$$ 6128.52i 0.385727i
$$633$$ −9823.25 14319.9i −0.616808 0.899152i
$$634$$ 10771.8 0.674768
$$635$$ 31171.8 1.94805
$$636$$ −28603.6 + 19621.7i −1.78334 + 1.22335i
$$637$$ 0 0
$$638$$ 21628.4i 1.34213i
$$639$$ 1144.11 + 441.492i 0.0708300 + 0.0273320i
$$640$$ 26129.7i 1.61385i
$$641$$ 9923.02i 0.611444i −0.952121 0.305722i $$-0.901102\pi$$
0.952121 0.305722i $$-0.0988978\pi$$
$$642$$ −16270.9 23718.9i −1.00025 1.45811i
$$643$$ 294.191i 0.0180432i −0.999959 0.00902160i $$-0.997128\pi$$
0.999959 0.00902160i $$-0.00287170\pi$$
$$644$$ 0 0
$$645$$ 7658.97 + 11164.9i 0.467553 + 0.681576i
$$646$$ −1068.72 −0.0650902
$$647$$ 7718.79 0.469021 0.234511 0.972114i $$-0.424651\pi$$
0.234511 + 0.972114i $$0.424651\pi$$
$$648$$ −10376.6 + 11443.2i −0.629058 + 0.693721i
$$649$$ 7380.61i 0.446401i
$$650$$ −2737.88 −0.165213
$$651$$ 0 0
$$652$$ 6560.75 0.394078
$$653$$ 11370.2i 0.681395i 0.940173 + 0.340697i $$0.110663\pi$$
−0.940173 + 0.340697i $$0.889337\pi$$
$$654$$ 25286.2 17346.0i 1.51188 1.03713i
$$655$$ 18604.2 1.10981
$$656$$ 154.250 0.00918056
$$657$$ 14161.6 + 5464.70i 0.840938 + 0.324503i
$$658$$ 0 0
$$659$$ 19795.1i 1.17012i −0.810990 0.585060i $$-0.801071\pi$$
0.810990 0.585060i $$-0.198929\pi$$
$$660$$ −11279.1 + 7737.30i −0.665207 + 0.456324i
$$661$$ 31057.5i 1.82753i 0.406247 + 0.913763i $$0.366837\pi$$
−0.406247 + 0.913763i $$0.633163\pi$$
$$662$$ 17289.3i 1.01506i
$$663$$ −5727.93 + 3929.29i −0.335527 + 0.230167i
$$664$$ 9509.25i 0.555769i
$$665$$ 0 0
$$666$$ −4769.08 1840.30i −0.277474 0.107072i
$$667$$ −18350.1 −1.06524
$$668$$ 47708.9 2.76334
$$669$$ 9183.66 6299.88i 0.530734 0.364077i
$$670$$ 17061.8i 0.983814i
$$671$$ 4630.04 0.266380
$$672$$ 0 0
$$673$$ 5340.26 0.305872 0.152936 0.988236i $$-0.451127\pi$$
0.152936 + 0.988236i $$0.451127\pi$$
$$674$$ 2695.28i 0.154033i
$$675$$ 1317.25 312.574i 0.0751126 0.0178237i
$$676$$ 21513.0 1.22400
$$677$$ 24956.6 1.41678 0.708389 0.705822i $$-0.249422\pi$$
0.708389 + 0.705822i $$0.249422\pi$$
$$678$$ −19211.1 28005.1i −1.08820 1.58632i
$$679$$ 0 0
$$680$$ 5265.93i 0.296970i
$$681$$ 7551.55 + 11008.3i 0.424928 + 0.619439i
$$682$$ 832.964i 0.0467681i
$$683$$ 11208.5i 0.627937i 0.949433 + 0.313968i $$0.101659\pi$$
−0.949433 + 0.313968i $$0.898341\pi$$
$$684$$ −3501.45 1351.14i −0.195733 0.0755297i
$$685$$ 26903.9i 1.50065i
$$686$$ 0 0
$$687$$ −450.654 + 309.143i −0.0250269 + 0.0171682i
$$688$$ 1117.19 0.0619077
$$689$$ −32908.2 −1.81960
$$690$$ 10712.1 + 15615.6i 0.591021 + 0.861562i
$$691$$ 10937.8i 0.602159i 0.953599 + 0.301079i $$0.0973469\pi$$
−0.953599 + 0.301079i $$0.902653\pi$$
$$692$$ 30300.2 1.66451
$$693$$ 0 0
$$694$$ 21714.7 1.18772
$$695$$ 21369.4i 1.16631i
$$696$$ −16541.7 24113.7i −0.900879 1.31326i
$$697$$ 663.984 0.0360835
$$698$$ −33447.1 −1.81374
$$699$$ −11250.9 + 7717.97i −0.608795 + 0.417626i
$$700$$ 0 0
$$701$$ 27949.3i 1.50589i 0.658082 + 0.752947i $$0.271368\pi$$
−0.658082 + 0.752947i $$0.728632\pi$$
$$702$$ −38729.9 + 9190.32i −2.08229 + 0.494111i
$$703$$ 457.261i 0.0245319i
$$704$$ 14933.7i 0.799482i
$$705$$ −5584.14 8140.28i −0.298313 0.434866i
$$706$$ 15025.4i 0.800977i
$$707$$ 0 0
$$708$$ 15331.9 + 22350.1i 0.813855 + 1.18640i
$$709$$ 20945.4 1.10948 0.554741 0.832023i $$-0.312817\pi$$
0.554741 + 0.832023i $$0.312817\pi$$
$$710$$ 2395.70 0.126632
$$711$$ −2811.29 + 7285.37i −0.148286 + 0.384279i
$$712$$ 11900.8i 0.626404i
$$713$$ −706.707 −0.0371197
$$714$$ 0 0
$$715$$ −12976.5 −0.678731
$$716$$ 8105.30i 0.423058i
$$717$$ 26055.7 17873.9i 1.35714 0.930979i
$$718$$ −1885.09 −0.0979820
$$719$$ −8300.21 −0.430522 −0.215261 0.976557i $$-0.569060\pi$$
−0.215261 + 0.976557i $$0.569060\pi$$
$$720$$ 561.167 1454.25i 0.0290465 0.0752731i
$$721$$ 0 0
$$722$$ 30629.8i 1.57884i
$$723$$ 19834.2 13606.0i 1.02025 0.699880i
$$724$$ 53230.4i 2.73245i
$$725$$ 2562.82i 0.131284i
$$726$$ 19672.0 13494.8i 1.00564 0.689860i
$$727$$ 20951.5i 1.06884i −0.845218 0.534421i $$-0.820530\pi$$
0.845218 0.534421i $$-0.179470\pi$$
$$728$$ 0 0
$$729$$ 17584.5 8843.31i 0.893388 0.449287i
$$730$$ 29653.5 1.50346
$$731$$ 4809.06 0.243324
$$732$$ 14020.8 9618.11i 0.707956 0.485650i
$$733$$ 5641.56i 0.284278i −0.989847 0.142139i $$-0.954602\pi$$
0.989847 0.142139i $$-0.0453980\pi$$
$$734$$ 346.017 0.0174001
$$735$$ 0 0
$$736$$ 13275.1 0.664847
$$737$$ 5795.36i 0.289654i
$$738$$ 3549.90 + 1369.84i 0.177064 + 0.0683259i
$$739$$ −11382.2 −0.566576 −0.283288 0.959035i $$-0.591425\pi$$
−0.283288 + 0.959035i $$0.591425\pi$$
$$740$$ −6119.61 −0.304002
$$741$$ −2014.20 2936.20i −0.0998560 0.145565i
$$742$$ 0 0
$$743$$ 4665.46i 0.230362i −0.993345 0.115181i $$-0.963255\pi$$
0.993345 0.115181i $$-0.0367449\pi$$
$$744$$ −637.063 928.679i −0.0313923 0.0457621i
$$745$$ 15096.3i 0.742399i
$$746$$ 55914.3i 2.74419i
$$747$$ −4362.11 + 11304.3i −0.213656 + 0.553684i
$$748$$ 4858.24i 0.237480i
$$749$$ 0 0
$$750$$ −26070.0 + 17883.7i −1.26926 + 0.870696i
$$751$$ −9560.86 −0.464555 −0.232277 0.972650i $$-0.574618\pi$$
−0.232277 + 0.972650i $$0.574618\pi$$
$$752$$ −814.540 −0.0394990
$$753$$ −17541.7 25571.5i −0.848945 1.23755i
$$754$$ 75352.3i 3.63948i
$$755$$ −30361.4 −1.46353
$$756$$ 0 0
$$757$$ 31574.1 1.51596 0.757979 0.652279i $$-0.226187\pi$$
0.757979 + 0.652279i $$0.226187\pi$$
$$758$$ 6495.63i 0.311256i
$$759$$ 3638.58 + 5304.14i 0.174008 + 0.253660i
$$760$$ −2699.37 −0.128838
$$761$$ −22429.9 −1.06844 −0.534221 0.845345i $$-0.679395\pi$$
−0.534221 + 0.845345i $$0.679395\pi$$
$$762$$ 52321.3 35891.8i 2.48740 1.70633i
$$763$$ 0 0
$$764$$ 18448.8i 0.873633i
$$765$$ 2415.60 6259.96i 0.114165 0.295855i
$$766$$ 23231.6i 1.09581i
$$767$$ 25713.7i 1.21052i
$$768$$ 10485.6 + 15285.4i 0.492664 + 0.718181i
$$769$$ 26887.4i 1.26084i −0.776254 0.630420i $$-0.782883\pi$$
0.776254 0.630420i $$-0.217117\pi$$
$$770$$ 0 0
$$771$$ −16576.3 24164.1i −0.774293 1.12873i
$$772$$ −23161.6 −1.07980
$$773$$ −22209.1 −1.03339 −0.516693 0.856171i $$-0.672837\pi$$
−0.516693 + 0.856171i $$0.672837\pi$$
$$774$$ 25711.0 + 9921.39i 1.19401 + 0.460745i
$$775$$ 98.7007i 0.00457476i
$$776$$ −4542.31 −0.210128
$$777$$ 0 0
$$778$$ −33276.0 −1.53342
$$779$$ 340.366i 0.0156545i
$$780$$ −39295.7 + 26956.4i −1.80386 + 1.23743i
$$781$$ 813.743 0.0372830
$$782$$ 6726.15 0.307579
$$783$$ 8602.71 + 36253.6i 0.392638 + 1.65466i
$$784$$ 0 0
$$785$$ 10851.5i 0.493385i
$$786$$ 31226.8 21421.2i 1.41708 0.972100i
$$787$$ 20095.5i