# Properties

 Label 105.4.d.b.64.7 Level $105$ Weight $4$ Character 105.64 Analytic conductor $6.195$ Analytic rank $0$ Dimension $10$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$105 = 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 105.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.19520055060$$ Analytic rank: $$0$$ Dimension: $$10$$ Coefficient field: $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ Defining polynomial: $$x^{10} + 37 x^{8} + 398 x^{6} + 1149 x^{4} + 1040 x^{2} + 100$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{9}\cdot 5$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 64.7 Root $$-1.35311i$$ of defining polynomial Character $$\chi$$ $$=$$ 105.64 Dual form 105.4.d.b.64.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+2.20666i q^{2} -3.00000i q^{3} +3.13065 q^{4} +(-1.50045 + 11.0792i) q^{5} +6.61998 q^{6} -7.00000i q^{7} +24.5616i q^{8} -9.00000 q^{9} +O(q^{10})$$ $$q+2.20666i q^{2} -3.00000i q^{3} +3.13065 q^{4} +(-1.50045 + 11.0792i) q^{5} +6.61998 q^{6} -7.00000i q^{7} +24.5616i q^{8} -9.00000 q^{9} +(-24.4480 - 3.31098i) q^{10} +56.2010 q^{11} -9.39196i q^{12} +38.9026i q^{13} +15.4466 q^{14} +(33.2376 + 4.50134i) q^{15} -29.1538 q^{16} +119.322i q^{17} -19.8599i q^{18} +13.0045 q^{19} +(-4.69738 + 34.6851i) q^{20} -21.0000 q^{21} +124.016i q^{22} -130.565i q^{23} +73.6847 q^{24} +(-120.497 - 33.2475i) q^{25} -85.8448 q^{26} +27.0000i q^{27} -21.9146i q^{28} -77.9925 q^{29} +(-9.93293 + 73.3441i) q^{30} +61.0660 q^{31} +132.160i q^{32} -168.603i q^{33} -263.303 q^{34} +(77.5544 + 10.5031i) q^{35} -28.1759 q^{36} -167.391i q^{37} +28.6964i q^{38} +116.708 q^{39} +(-272.122 - 36.8533i) q^{40} +436.142 q^{41} -46.3398i q^{42} -393.030i q^{43} +175.946 q^{44} +(13.5040 - 99.7128i) q^{45} +288.112 q^{46} -365.271i q^{47} +87.4613i q^{48} -49.0000 q^{49} +(73.3659 - 265.897i) q^{50} +357.966 q^{51} +121.791i q^{52} -282.048i q^{53} -59.5798 q^{54} +(-84.3266 + 622.662i) q^{55} +171.931 q^{56} -39.0134i q^{57} -172.103i q^{58} -414.842 q^{59} +(104.055 + 14.0921i) q^{60} -563.802 q^{61} +134.752i q^{62} +63.0000i q^{63} -524.862 q^{64} +(-431.009 - 58.3713i) q^{65} +372.049 q^{66} -395.230i q^{67} +373.556i q^{68} -391.694 q^{69} +(-23.1768 + 171.136i) q^{70} +103.990 q^{71} -221.054i q^{72} -128.026i q^{73} +369.376 q^{74} +(-99.7426 + 361.492i) q^{75} +40.7125 q^{76} -393.407i q^{77} +257.534i q^{78} +641.999 q^{79} +(43.7437 - 323.000i) q^{80} +81.0000 q^{81} +962.417i q^{82} +512.010i q^{83} -65.7437 q^{84} +(-1321.99 - 179.037i) q^{85} +867.283 q^{86} +233.977i q^{87} +1380.38i q^{88} -1225.10 q^{89} +(220.032 + 29.7988i) q^{90} +272.318 q^{91} -408.753i q^{92} -183.198i q^{93} +806.028 q^{94} +(-19.5125 + 144.079i) q^{95} +396.480 q^{96} -186.760i q^{97} -108.126i q^{98} -505.809 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$10q - 54q^{4} - 14q^{5} - 6q^{6} - 90q^{9} + O(q^{10})$$ $$10q - 54q^{4} - 14q^{5} - 6q^{6} - 90q^{9} + 92q^{10} + 132q^{11} - 14q^{14} + 310q^{16} - 348q^{19} + 366q^{20} - 210q^{21} + 198q^{24} - 374q^{25} + 892q^{26} - 740q^{29} - 378q^{30} + 684q^{31} - 224q^{34} + 486q^{36} - 12q^{39} - 2156q^{40} + 1604q^{41} - 580q^{44} + 126q^{45} + 1280q^{46} - 490q^{49} - 2504q^{50} - 648q^{51} + 54q^{54} - 452q^{55} + 462q^{56} - 1408q^{59} - 852q^{60} + 1300q^{61} - 150q^{64} - 3296q^{65} + 3036q^{66} - 696q^{69} - 882q^{70} + 2940q^{71} + 2624q^{74} - 408q^{75} + 8740q^{76} + 1640q^{79} - 4126q^{80} + 810q^{81} + 1134q^{84} - 1704q^{85} + 1664q^{86} - 572q^{89} - 828q^{90} - 28q^{91} - 5080q^{94} + 1268q^{95} + 330q^{96} - 1188q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$$.

 $$n$$ $$22$$ $$31$$ $$71$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.20666i 0.780172i 0.920778 + 0.390086i $$0.127555\pi$$
−0.920778 + 0.390086i $$0.872445\pi$$
$$3$$ 3.00000i 0.577350i
$$4$$ 3.13065 0.391332
$$5$$ −1.50045 + 11.0792i −0.134204 + 0.990954i
$$6$$ 6.61998 0.450432
$$7$$ 7.00000i 0.377964i
$$8$$ 24.5616i 1.08548i
$$9$$ −9.00000 −0.333333
$$10$$ −24.4480 3.31098i −0.773114 0.104702i
$$11$$ 56.2010 1.54048 0.770238 0.637757i $$-0.220138\pi$$
0.770238 + 0.637757i $$0.220138\pi$$
$$12$$ 9.39196i 0.225936i
$$13$$ 38.9026i 0.829972i 0.909828 + 0.414986i $$0.136214\pi$$
−0.909828 + 0.414986i $$0.863786\pi$$
$$14$$ 15.4466 0.294877
$$15$$ 33.2376 + 4.50134i 0.572127 + 0.0774828i
$$16$$ −29.1538 −0.455528
$$17$$ 119.322i 1.70235i 0.524886 + 0.851173i $$0.324108\pi$$
−0.524886 + 0.851173i $$0.675892\pi$$
$$18$$ 19.8599i 0.260057i
$$19$$ 13.0045 0.157023 0.0785113 0.996913i $$-0.474983\pi$$
0.0785113 + 0.996913i $$0.474983\pi$$
$$20$$ −4.69738 + 34.6851i −0.0525183 + 0.387792i
$$21$$ −21.0000 −0.218218
$$22$$ 124.016i 1.20184i
$$23$$ 130.565i 1.18368i −0.806055 0.591840i $$-0.798402\pi$$
0.806055 0.591840i $$-0.201598\pi$$
$$24$$ 73.6847 0.626701
$$25$$ −120.497 33.2475i −0.963979 0.265980i
$$26$$ −85.8448 −0.647521
$$27$$ 27.0000i 0.192450i
$$28$$ 21.9146i 0.147910i
$$29$$ −77.9925 −0.499408 −0.249704 0.968322i $$-0.580333\pi$$
−0.249704 + 0.968322i $$0.580333\pi$$
$$30$$ −9.93293 + 73.3441i −0.0604499 + 0.446358i
$$31$$ 61.0660 0.353799 0.176900 0.984229i $$-0.443393\pi$$
0.176900 + 0.984229i $$0.443393\pi$$
$$32$$ 132.160i 0.730088i
$$33$$ 168.603i 0.889394i
$$34$$ −263.303 −1.32812
$$35$$ 77.5544 + 10.5031i 0.374545 + 0.0507244i
$$36$$ −28.1759 −0.130444
$$37$$ 167.391i 0.743757i −0.928282 0.371878i $$-0.878714\pi$$
0.928282 0.371878i $$-0.121286\pi$$
$$38$$ 28.6964i 0.122505i
$$39$$ 116.708 0.479185
$$40$$ −272.122 36.8533i −1.07566 0.145676i
$$41$$ 436.142 1.66132 0.830658 0.556783i $$-0.187964\pi$$
0.830658 + 0.556783i $$0.187964\pi$$
$$42$$ 46.3398i 0.170247i
$$43$$ 393.030i 1.39387i −0.717134 0.696936i $$-0.754546\pi$$
0.717134 0.696936i $$-0.245454\pi$$
$$44$$ 175.946 0.602837
$$45$$ 13.5040 99.7128i 0.0447347 0.330318i
$$46$$ 288.112 0.923474
$$47$$ 365.271i 1.13362i −0.823848 0.566811i $$-0.808177\pi$$
0.823848 0.566811i $$-0.191823\pi$$
$$48$$ 87.4613i 0.262999i
$$49$$ −49.0000 −0.142857
$$50$$ 73.3659 265.897i 0.207510 0.752069i
$$51$$ 357.966 0.982849
$$52$$ 121.791i 0.324794i
$$53$$ 282.048i 0.730987i −0.930814 0.365494i $$-0.880900\pi$$
0.930814 0.365494i $$-0.119100\pi$$
$$54$$ −59.5798 −0.150144
$$55$$ −84.3266 + 622.662i −0.206738 + 1.52654i
$$56$$ 171.931 0.410272
$$57$$ 39.0134i 0.0906570i
$$58$$ 172.103i 0.389624i
$$59$$ −414.842 −0.915388 −0.457694 0.889110i $$-0.651324\pi$$
−0.457694 + 0.889110i $$0.651324\pi$$
$$60$$ 104.055 + 14.0921i 0.223892 + 0.0303215i
$$61$$ −563.802 −1.18340 −0.591701 0.806158i $$-0.701543\pi$$
−0.591701 + 0.806158i $$0.701543\pi$$
$$62$$ 134.752i 0.276024i
$$63$$ 63.0000i 0.125988i
$$64$$ −524.862 −1.02512
$$65$$ −431.009 58.3713i −0.822464 0.111386i
$$66$$ 372.049 0.693880
$$67$$ 395.230i 0.720673i −0.932822 0.360336i $$-0.882662\pi$$
0.932822 0.360336i $$-0.117338\pi$$
$$68$$ 373.556i 0.666182i
$$69$$ −391.694 −0.683398
$$70$$ −23.1768 + 171.136i −0.0395737 + 0.292210i
$$71$$ 103.990 0.173821 0.0869107 0.996216i $$-0.472301\pi$$
0.0869107 + 0.996216i $$0.472301\pi$$
$$72$$ 221.054i 0.361826i
$$73$$ 128.026i 0.205264i −0.994719 0.102632i $$-0.967274\pi$$
0.994719 0.102632i $$-0.0327264\pi$$
$$74$$ 369.376 0.580258
$$75$$ −99.7426 + 361.492i −0.153564 + 0.556553i
$$76$$ 40.7125 0.0614479
$$77$$ 393.407i 0.582245i
$$78$$ 257.534i 0.373846i
$$79$$ 641.999 0.914310 0.457155 0.889387i $$-0.348868\pi$$
0.457155 + 0.889387i $$0.348868\pi$$
$$80$$ 43.7437 323.000i 0.0611337 0.451407i
$$81$$ 81.0000 0.111111
$$82$$ 962.417i 1.29611i
$$83$$ 512.010i 0.677113i 0.940946 + 0.338557i $$0.109939\pi$$
−0.940946 + 0.338557i $$0.890061\pi$$
$$84$$ −65.7437 −0.0853956
$$85$$ −1321.99 179.037i −1.68695 0.228462i
$$86$$ 867.283 1.08746
$$87$$ 233.977i 0.288333i
$$88$$ 1380.38i 1.67215i
$$89$$ −1225.10 −1.45911 −0.729554 0.683923i $$-0.760272\pi$$
−0.729554 + 0.683923i $$0.760272\pi$$
$$90$$ 220.032 + 29.7988i 0.257705 + 0.0349008i
$$91$$ 272.318 0.313700
$$92$$ 408.753i 0.463212i
$$93$$ 183.198i 0.204266i
$$94$$ 806.028 0.884420
$$95$$ −19.5125 + 144.079i −0.0210731 + 0.155602i
$$96$$ 396.480 0.421517
$$97$$ 186.760i 0.195491i −0.995211 0.0977454i $$-0.968837\pi$$
0.995211 0.0977454i $$-0.0311631\pi$$
$$98$$ 108.126i 0.111453i
$$99$$ −505.809 −0.513492
$$100$$ −377.235 104.086i −0.377235 0.104086i
$$101$$ 1650.68 1.62623 0.813114 0.582104i $$-0.197770\pi$$
0.813114 + 0.582104i $$0.197770\pi$$
$$102$$ 789.910i 0.766792i
$$103$$ 72.1876i 0.0690568i −0.999404 0.0345284i $$-0.989007\pi$$
0.999404 0.0345284i $$-0.0109929\pi$$
$$104$$ −955.508 −0.900916
$$105$$ 31.5094 232.663i 0.0292857 0.216244i
$$106$$ 622.385 0.570296
$$107$$ 1202.55i 1.08649i 0.839574 + 0.543246i $$0.182805\pi$$
−0.839574 + 0.543246i $$0.817195\pi$$
$$108$$ 84.5277i 0.0753118i
$$109$$ 1551.36 1.36324 0.681622 0.731704i $$-0.261275\pi$$
0.681622 + 0.731704i $$0.261275\pi$$
$$110$$ −1374.00 186.080i −1.19096 0.161291i
$$111$$ −502.174 −0.429408
$$112$$ 204.076i 0.172173i
$$113$$ 2080.90i 1.73234i 0.499749 + 0.866170i $$0.333426\pi$$
−0.499749 + 0.866170i $$0.666574\pi$$
$$114$$ 86.0893 0.0707281
$$115$$ 1446.55 + 195.906i 1.17297 + 0.158855i
$$116$$ −244.167 −0.195434
$$117$$ 350.123i 0.276657i
$$118$$ 915.416i 0.714160i
$$119$$ 835.255 0.643426
$$120$$ −110.560 + 816.367i −0.0841059 + 0.621032i
$$121$$ 1827.55 1.37306
$$122$$ 1244.12i 0.923257i
$$123$$ 1308.43i 0.959161i
$$124$$ 191.177 0.138453
$$125$$ 549.156 1285.13i 0.392944 0.919562i
$$126$$ −139.020 −0.0982924
$$127$$ 1414.70i 0.988461i −0.869331 0.494231i $$-0.835450\pi$$
0.869331 0.494231i $$-0.164550\pi$$
$$128$$ 100.912i 0.0696832i
$$129$$ −1179.09 −0.804752
$$130$$ 128.806 951.091i 0.0869000 0.641663i
$$131$$ −2472.51 −1.64904 −0.824520 0.565833i $$-0.808555\pi$$
−0.824520 + 0.565833i $$0.808555\pi$$
$$132$$ 527.837i 0.348048i
$$133$$ 91.0313i 0.0593490i
$$134$$ 872.139 0.562249
$$135$$ −299.138 40.5121i −0.190709 0.0258276i
$$136$$ −2930.74 −1.84786
$$137$$ 214.391i 0.133698i 0.997763 + 0.0668491i $$0.0212946\pi$$
−0.997763 + 0.0668491i $$0.978705\pi$$
$$138$$ 864.336i 0.533168i
$$139$$ −942.774 −0.575288 −0.287644 0.957737i $$-0.592872\pi$$
−0.287644 + 0.957737i $$0.592872\pi$$
$$140$$ 242.796 + 32.8817i 0.146571 + 0.0198501i
$$141$$ −1095.81 −0.654497
$$142$$ 229.470i 0.135611i
$$143$$ 2186.36i 1.27855i
$$144$$ 262.384 0.151843
$$145$$ 117.024 864.094i 0.0670226 0.494890i
$$146$$ 282.509 0.160141
$$147$$ 147.000i 0.0824786i
$$148$$ 524.045i 0.291056i
$$149$$ −1693.07 −0.930882 −0.465441 0.885079i $$-0.654104\pi$$
−0.465441 + 0.885079i $$0.654104\pi$$
$$150$$ −797.690 220.098i −0.434207 0.119806i
$$151$$ 2519.69 1.35795 0.678973 0.734163i $$-0.262425\pi$$
0.678973 + 0.734163i $$0.262425\pi$$
$$152$$ 319.410i 0.170445i
$$153$$ 1073.90i 0.567448i
$$154$$ 868.115 0.454251
$$155$$ −91.6263 + 676.562i −0.0474813 + 0.350599i
$$156$$ 365.372 0.187520
$$157$$ 1621.48i 0.824258i −0.911125 0.412129i $$-0.864785\pi$$
0.911125 0.412129i $$-0.135215\pi$$
$$158$$ 1416.67i 0.713319i
$$159$$ −846.145 −0.422036
$$160$$ −1464.23 198.299i −0.723484 0.0979808i
$$161$$ −913.954 −0.447389
$$162$$ 178.739i 0.0866858i
$$163$$ 925.194i 0.444582i 0.974980 + 0.222291i $$0.0713534\pi$$
−0.974980 + 0.222291i $$0.928647\pi$$
$$164$$ 1365.41 0.650126
$$165$$ 1867.98 + 252.980i 0.881348 + 0.119360i
$$166$$ −1129.83 −0.528265
$$167$$ 2681.55i 1.24254i −0.783596 0.621271i $$-0.786617\pi$$
0.783596 0.621271i $$-0.213383\pi$$
$$168$$ 515.793i 0.236871i
$$169$$ 683.589 0.311147
$$170$$ 395.073 2917.19i 0.178239 1.31611i
$$171$$ −117.040 −0.0523409
$$172$$ 1230.44i 0.545466i
$$173$$ 287.591i 0.126388i 0.998001 + 0.0631940i $$0.0201287\pi$$
−0.998001 + 0.0631940i $$0.979871\pi$$
$$174$$ −516.308 −0.224950
$$175$$ −232.733 + 843.481i −0.100531 + 0.364350i
$$176$$ −1638.47 −0.701729
$$177$$ 1244.53i 0.528499i
$$178$$ 2703.38i 1.13835i
$$179$$ −3683.47 −1.53808 −0.769038 0.639203i $$-0.779265\pi$$
−0.769038 + 0.639203i $$0.779265\pi$$
$$180$$ 42.2764 312.166i 0.0175061 0.129264i
$$181$$ 3132.65 1.28645 0.643227 0.765676i $$-0.277595\pi$$
0.643227 + 0.765676i $$0.277595\pi$$
$$182$$ 600.913i 0.244740i
$$183$$ 1691.41i 0.683237i
$$184$$ 3206.88 1.28486
$$185$$ 1854.56 + 251.162i 0.737028 + 0.0998152i
$$186$$ 404.256 0.159363
$$187$$ 6706.02i 2.62242i
$$188$$ 1143.54i 0.443622i
$$189$$ 189.000 0.0727393
$$190$$ −317.933 43.0575i −0.121396 0.0164406i
$$191$$ 1586.93 0.601184 0.300592 0.953753i $$-0.402816\pi$$
0.300592 + 0.953753i $$0.402816\pi$$
$$192$$ 1574.59i 0.591854i
$$193$$ 5179.00i 1.93157i −0.259352 0.965783i $$-0.583509\pi$$
0.259352 0.965783i $$-0.416491\pi$$
$$194$$ 412.116 0.152516
$$195$$ −175.114 + 1293.03i −0.0643085 + 0.474850i
$$196$$ −153.402 −0.0559045
$$197$$ 903.798i 0.326868i −0.986554 0.163434i $$-0.947743\pi$$
0.986554 0.163434i $$-0.0522570\pi$$
$$198$$ 1116.15i 0.400612i
$$199$$ 1171.51 0.417317 0.208659 0.977989i $$-0.433090\pi$$
0.208659 + 0.977989i $$0.433090\pi$$
$$200$$ 816.611 2959.60i 0.288716 1.04638i
$$201$$ −1185.69 −0.416081
$$202$$ 3642.50i 1.26874i
$$203$$ 545.947i 0.188759i
$$204$$ 1120.67 0.384620
$$205$$ −654.409 + 4832.11i −0.222955 + 1.64629i
$$206$$ 159.293 0.0538762
$$207$$ 1175.08i 0.394560i
$$208$$ 1134.16i 0.378075i
$$209$$ 730.864 0.241889
$$210$$ 513.408 + 69.5305i 0.168707 + 0.0228479i
$$211$$ −1103.16 −0.359928 −0.179964 0.983673i $$-0.557598\pi$$
−0.179964 + 0.983673i $$0.557598\pi$$
$$212$$ 882.996i 0.286059i
$$213$$ 311.969i 0.100356i
$$214$$ −2653.61 −0.847651
$$215$$ 4354.45 + 589.721i 1.38126 + 0.187063i
$$216$$ −663.162 −0.208900
$$217$$ 427.462i 0.133724i
$$218$$ 3423.33i 1.06357i
$$219$$ −384.077 −0.118509
$$220$$ −263.997 + 1949.34i −0.0809032 + 0.597383i
$$221$$ −4641.94 −1.41290
$$222$$ 1108.13i 0.335012i
$$223$$ 4079.95i 1.22517i 0.790404 + 0.612586i $$0.209871\pi$$
−0.790404 + 0.612586i $$0.790129\pi$$
$$224$$ 925.120 0.275947
$$225$$ 1084.48 + 299.228i 0.321326 + 0.0886600i
$$226$$ −4591.83 −1.35152
$$227$$ 931.964i 0.272496i −0.990675 0.136248i $$-0.956496\pi$$
0.990675 0.136248i $$-0.0435044\pi$$
$$228$$ 122.137i 0.0354770i
$$229$$ 1471.55 0.424641 0.212321 0.977200i $$-0.431898\pi$$
0.212321 + 0.977200i $$0.431898\pi$$
$$230$$ −432.297 + 3192.05i −0.123934 + 0.915120i
$$231$$ −1180.22 −0.336159
$$232$$ 1915.62i 0.542097i
$$233$$ 2479.06i 0.697034i 0.937303 + 0.348517i $$0.113315\pi$$
−0.937303 + 0.348517i $$0.886685\pi$$
$$234$$ 772.603 0.215840
$$235$$ 4046.91 + 548.070i 1.12337 + 0.152137i
$$236$$ −1298.73 −0.358220
$$237$$ 1926.00i 0.527877i
$$238$$ 1843.12i 0.501983i
$$239$$ 954.068 0.258216 0.129108 0.991631i $$-0.458789\pi$$
0.129108 + 0.991631i $$0.458789\pi$$
$$240$$ −969.001 131.231i −0.260620 0.0352956i
$$241$$ −5297.02 −1.41581 −0.707906 0.706306i $$-0.750360\pi$$
−0.707906 + 0.706306i $$0.750360\pi$$
$$242$$ 4032.77i 1.07123i
$$243$$ 243.000i 0.0641500i
$$244$$ −1765.07 −0.463103
$$245$$ 73.5219 542.881i 0.0191720 0.141565i
$$246$$ 2887.25 0.748311
$$247$$ 505.907i 0.130324i
$$248$$ 1499.88i 0.384041i
$$249$$ 1536.03 0.390931
$$250$$ 2835.84 + 1211.80i 0.717417 + 0.306564i
$$251$$ 1855.17 0.466524 0.233262 0.972414i $$-0.425060\pi$$
0.233262 + 0.972414i $$0.425060\pi$$
$$252$$ 197.231i 0.0493032i
$$253$$ 7337.87i 1.82343i
$$254$$ 3121.77 0.771170
$$255$$ −537.110 + 3965.98i −0.131902 + 0.973958i
$$256$$ −3976.22 −0.970757
$$257$$ 6233.09i 1.51288i −0.654065 0.756438i $$-0.726938\pi$$
0.654065 0.756438i $$-0.273062\pi$$
$$258$$ 2601.85i 0.627845i
$$259$$ −1171.74 −0.281114
$$260$$ −1349.34 182.740i −0.321856 0.0435887i
$$261$$ 701.932 0.166469
$$262$$ 5455.99i 1.28653i
$$263$$ 1184.50i 0.277716i 0.990312 + 0.138858i $$0.0443432\pi$$
−0.990312 + 0.138858i $$0.955657\pi$$
$$264$$ 4141.15 0.965417
$$265$$ 3124.87 + 423.199i 0.724375 + 0.0981015i
$$266$$ 200.875 0.0463024
$$267$$ 3675.31i 0.842416i
$$268$$ 1237.33i 0.282022i
$$269$$ 1916.03 0.434283 0.217141 0.976140i $$-0.430327\pi$$
0.217141 + 0.976140i $$0.430327\pi$$
$$270$$ 89.3964 660.097i 0.0201500 0.148786i
$$271$$ −1168.95 −0.262025 −0.131013 0.991381i $$-0.541823\pi$$
−0.131013 + 0.991381i $$0.541823\pi$$
$$272$$ 3478.69i 0.775465i
$$273$$ 816.954i 0.181115i
$$274$$ −473.088 −0.104308
$$275$$ −6772.06 1868.54i −1.48498 0.409736i
$$276$$ −1226.26 −0.267435
$$277$$ 7269.54i 1.57684i 0.615138 + 0.788419i $$0.289100\pi$$
−0.615138 + 0.788419i $$0.710900\pi$$
$$278$$ 2080.38i 0.448824i
$$279$$ −549.594 −0.117933
$$280$$ −257.973 + 1904.86i −0.0550602 + 0.406561i
$$281$$ 298.126 0.0632908 0.0316454 0.999499i $$-0.489925\pi$$
0.0316454 + 0.999499i $$0.489925\pi$$
$$282$$ 2418.09i 0.510620i
$$283$$ 4496.30i 0.944444i 0.881480 + 0.472222i $$0.156548\pi$$
−0.881480 + 0.472222i $$0.843452\pi$$
$$284$$ 325.556 0.0680218
$$285$$ 432.237 + 58.5376i 0.0898369 + 0.0121665i
$$286$$ −4824.56 −0.997490
$$287$$ 3053.00i 0.627919i
$$288$$ 1189.44i 0.243363i
$$289$$ −9324.77 −1.89798
$$290$$ 1906.76 + 258.231i 0.386100 + 0.0522892i
$$291$$ −560.280 −0.112867
$$292$$ 400.804i 0.0803264i
$$293$$ 1644.33i 0.327859i 0.986472 + 0.163929i $$0.0524169\pi$$
−0.986472 + 0.163929i $$0.947583\pi$$
$$294$$ −324.379 −0.0643475
$$295$$ 622.449 4596.12i 0.122849 0.907107i
$$296$$ 4111.40 0.807331
$$297$$ 1517.43i 0.296465i
$$298$$ 3736.02i 0.726248i
$$299$$ 5079.31 0.982421
$$300$$ −312.259 + 1131.71i −0.0600944 + 0.217797i
$$301$$ −2751.21 −0.526834
$$302$$ 5560.11i 1.05943i
$$303$$ 4952.05i 0.938904i
$$304$$ −379.129 −0.0715281
$$305$$ 845.956 6246.48i 0.158817 1.17270i
$$306$$ 2369.73 0.442707
$$307$$ 4726.18i 0.878623i −0.898335 0.439312i $$-0.855222\pi$$
0.898335 0.439312i $$-0.144778\pi$$
$$308$$ 1231.62i 0.227851i
$$309$$ −216.563 −0.0398700
$$310$$ −1492.94 202.188i −0.273527 0.0370436i
$$311$$ −4853.99 −0.885031 −0.442515 0.896761i $$-0.645914\pi$$
−0.442515 + 0.896761i $$0.645914\pi$$
$$312$$ 2866.52i 0.520144i
$$313$$ 1690.87i 0.305348i −0.988277 0.152674i $$-0.951212\pi$$
0.988277 0.152674i $$-0.0487884\pi$$
$$314$$ 3578.06 0.643063
$$315$$ −697.990 94.5282i −0.124848 0.0169081i
$$316$$ 2009.88 0.357799
$$317$$ 3878.38i 0.687166i −0.939122 0.343583i $$-0.888359\pi$$
0.939122 0.343583i $$-0.111641\pi$$
$$318$$ 1867.15i 0.329260i
$$319$$ −4383.25 −0.769326
$$320$$ 787.529 5815.06i 0.137576 1.01585i
$$321$$ 3607.64 0.627286
$$322$$ 2016.78i 0.349040i
$$323$$ 1551.72i 0.267307i
$$324$$ 253.583 0.0434813
$$325$$ 1293.41 4687.66i 0.220756 0.800075i
$$326$$ −2041.59 −0.346850
$$327$$ 4654.09i 0.787070i
$$328$$ 10712.3i 1.80332i
$$329$$ −2556.90 −0.428469
$$330$$ −558.240 + 4122.01i −0.0931215 + 0.687603i
$$331$$ 9927.71 1.64857 0.824284 0.566176i $$-0.191578\pi$$
0.824284 + 0.566176i $$0.191578\pi$$
$$332$$ 1602.93i 0.264976i
$$333$$ 1506.52i 0.247919i
$$334$$ 5917.26 0.969396
$$335$$ 4378.84 + 593.023i 0.714153 + 0.0967173i
$$336$$ 612.229 0.0994043
$$337$$ 5283.88i 0.854099i −0.904228 0.427050i $$-0.859553\pi$$
0.904228 0.427050i $$-0.140447\pi$$
$$338$$ 1508.45i 0.242748i
$$339$$ 6242.70 1.00017
$$340$$ −4138.71 560.502i −0.660155 0.0894043i
$$341$$ 3431.97 0.545019
$$342$$ 258.268i 0.0408349i
$$343$$ 343.000i 0.0539949i
$$344$$ 9653.42 1.51302
$$345$$ 587.717 4339.66i 0.0917148 0.677216i
$$346$$ −634.615 −0.0986044
$$347$$ 10548.3i 1.63188i 0.578137 + 0.815940i $$0.303780\pi$$
−0.578137 + 0.815940i $$0.696220\pi$$
$$348$$ 732.502i 0.112834i
$$349$$ −628.411 −0.0963841 −0.0481921 0.998838i $$-0.515346\pi$$
−0.0481921 + 0.998838i $$0.515346\pi$$
$$350$$ −1861.28 513.562i −0.284255 0.0784315i
$$351$$ −1050.37 −0.159728
$$352$$ 7427.52i 1.12468i
$$353$$ 2548.17i 0.384209i 0.981375 + 0.192104i $$0.0615312\pi$$
−0.981375 + 0.192104i $$0.938469\pi$$
$$354$$ −2746.25 −0.412320
$$355$$ −156.031 + 1152.12i −0.0233275 + 0.172249i
$$356$$ −3835.37 −0.570995
$$357$$ 2505.76i 0.371482i
$$358$$ 8128.17i 1.19996i
$$359$$ −13046.3 −1.91799 −0.958996 0.283420i $$-0.908531\pi$$
−0.958996 + 0.283420i $$0.908531\pi$$
$$360$$ 2449.10 + 331.680i 0.358553 + 0.0485585i
$$361$$ −6689.88 −0.975344
$$362$$ 6912.69i 1.00366i
$$363$$ 5482.64i 0.792738i
$$364$$ 852.534 0.122761
$$365$$ 1418.42 + 192.096i 0.203407 + 0.0275473i
$$366$$ −3732.36 −0.533043
$$367$$ 8068.23i 1.14757i −0.819006 0.573785i $$-0.805475\pi$$
0.819006 0.573785i $$-0.194525\pi$$
$$368$$ 3806.46i 0.539199i
$$369$$ −3925.28 −0.553772
$$370$$ −554.229 + 4092.39i −0.0778730 + 0.575009i
$$371$$ −1974.34 −0.276287
$$372$$ 573.530i 0.0799358i
$$373$$ 3623.32i 0.502972i −0.967861 0.251486i $$-0.919081\pi$$
0.967861 0.251486i $$-0.0809193\pi$$
$$374$$ −14797.9 −2.04594
$$375$$ −3855.38 1647.47i −0.530910 0.226866i
$$376$$ 8971.62 1.23052
$$377$$ 3034.11i 0.414495i
$$378$$ 417.059i 0.0567492i
$$379$$ −7486.58 −1.01467 −0.507335 0.861749i $$-0.669369\pi$$
−0.507335 + 0.861749i $$0.669369\pi$$
$$380$$ −61.0870 + 451.062i −0.00824657 + 0.0608921i
$$381$$ −4244.11 −0.570688
$$382$$ 3501.81i 0.469027i
$$383$$ 8926.58i 1.19093i 0.803381 + 0.595466i $$0.203033\pi$$
−0.803381 + 0.595466i $$0.796967\pi$$
$$384$$ −302.736 −0.0402316
$$385$$ 4358.63 + 590.286i 0.576978 + 0.0781397i
$$386$$ 11428.3 1.50695
$$387$$ 3537.27i 0.464624i
$$388$$ 584.681i 0.0765018i
$$389$$ 12600.1 1.64228 0.821141 0.570725i $$-0.193338\pi$$
0.821141 + 0.570725i $$0.193338\pi$$
$$390$$ −2853.27 386.417i −0.370464 0.0501717i
$$391$$ 15579.3 2.01503
$$392$$ 1203.52i 0.155068i
$$393$$ 7417.53i 0.952074i
$$394$$ 1994.37 0.255013
$$395$$ −963.286 + 7112.83i −0.122704 + 0.906039i
$$396$$ −1583.51 −0.200946
$$397$$ 12713.4i 1.60722i 0.595154 + 0.803612i $$0.297091\pi$$
−0.595154 + 0.803612i $$0.702909\pi$$
$$398$$ 2585.12i 0.325579i
$$399$$ −273.094 −0.0342651
$$400$$ 3512.95 + 969.290i 0.439119 + 0.121161i
$$401$$ −6133.51 −0.763822 −0.381911 0.924199i $$-0.624734\pi$$
−0.381911 + 0.924199i $$0.624734\pi$$
$$402$$ 2616.42i 0.324614i
$$403$$ 2375.62i 0.293643i
$$404$$ 5167.72 0.636395
$$405$$ −121.536 + 897.415i −0.0149116 + 0.110106i
$$406$$ −1204.72 −0.147264
$$407$$ 9407.56i 1.14574i
$$408$$ 8792.21i 1.06686i
$$409$$ −10600.3 −1.28154 −0.640769 0.767733i $$-0.721385\pi$$
−0.640769 + 0.767733i $$0.721385\pi$$
$$410$$ −10662.8 1444.06i −1.28439 0.173944i
$$411$$ 643.173 0.0771907
$$412$$ 225.994i 0.0270241i
$$413$$ 2903.90i 0.345984i
$$414$$ −2593.01 −0.307825
$$415$$ −5672.66 768.244i −0.670988 0.0908714i
$$416$$ −5141.37 −0.605953
$$417$$ 2828.32i 0.332143i
$$418$$ 1612.77i 0.188715i
$$419$$ −4296.43 −0.500941 −0.250470 0.968124i $$-0.580585\pi$$
−0.250470 + 0.968124i $$0.580585\pi$$
$$420$$ 98.6450 728.388i 0.0114604 0.0846231i
$$421$$ 3916.78 0.453425 0.226713 0.973962i $$-0.427202\pi$$
0.226713 + 0.973962i $$0.427202\pi$$
$$422$$ 2434.30i 0.280806i
$$423$$ 3287.44i 0.377874i
$$424$$ 6927.55 0.793471
$$425$$ 3967.16 14378.0i 0.452790 1.64102i
$$426$$ 688.410 0.0782948
$$427$$ 3946.62i 0.447284i
$$428$$ 3764.76i 0.425179i
$$429$$ 6559.09 0.738172
$$430$$ −1301.31 + 9608.80i −0.145942 + 1.07762i
$$431$$ 13408.9 1.49857 0.749287 0.662246i $$-0.230396\pi$$
0.749287 + 0.662246i $$0.230396\pi$$
$$432$$ 787.152i 0.0876663i
$$433$$ 7792.31i 0.864837i 0.901673 + 0.432419i $$0.142340\pi$$
−0.901673 + 0.432419i $$0.857660\pi$$
$$434$$ 943.263 0.104327
$$435$$ −2592.28 351.071i −0.285725 0.0386955i
$$436$$ 4856.78 0.533481
$$437$$ 1697.93i 0.185865i
$$438$$ 847.528i 0.0924576i
$$439$$ −1039.29 −0.112990 −0.0564948 0.998403i $$-0.517992\pi$$
−0.0564948 + 0.998403i $$0.517992\pi$$
$$440$$ −15293.5 2071.19i −1.65702 0.224410i
$$441$$ 441.000 0.0476190
$$442$$ 10243.2i 1.10230i
$$443$$ 2846.33i 0.305267i −0.988283 0.152633i $$-0.951225\pi$$
0.988283 0.152633i $$-0.0487754\pi$$
$$444$$ −1572.13 −0.168041
$$445$$ 1838.20 13573.2i 0.195818 1.44591i
$$446$$ −9003.05 −0.955845
$$447$$ 5079.20i 0.537445i
$$448$$ 3674.04i 0.387460i
$$449$$ −7472.64 −0.785425 −0.392713 0.919661i $$-0.628463\pi$$
−0.392713 + 0.919661i $$0.628463\pi$$
$$450$$ −660.294 + 2393.07i −0.0691701 + 0.250690i
$$451$$ 24511.6 2.55922
$$452$$ 6514.57i 0.677920i
$$453$$ 7559.08i 0.784010i
$$454$$ 2056.53 0.212594
$$455$$ −408.599 + 3017.07i −0.0420998 + 0.310862i
$$456$$ 958.230 0.0984062
$$457$$ 11014.3i 1.12742i 0.825974 + 0.563708i $$0.190626\pi$$
−0.825974 + 0.563708i $$0.809374\pi$$
$$458$$ 3247.21i 0.331293i
$$459$$ −3221.70 −0.327616
$$460$$ 4528.66 + 613.313i 0.459021 + 0.0621649i
$$461$$ 7944.67 0.802647 0.401323 0.915936i $$-0.368550\pi$$
0.401323 + 0.915936i $$0.368550\pi$$
$$462$$ 2604.34i 0.262262i
$$463$$ 7627.25i 0.765591i −0.923833 0.382795i $$-0.874961\pi$$
0.923833 0.382795i $$-0.125039\pi$$
$$464$$ 2273.77 0.227494
$$465$$ 2029.69 + 274.879i 0.202418 + 0.0274133i
$$466$$ −5470.45 −0.543806
$$467$$ 3284.28i 0.325436i 0.986673 + 0.162718i $$0.0520260\pi$$
−0.986673 + 0.162718i $$0.947974\pi$$
$$468$$ 1096.11i 0.108265i
$$469$$ −2766.61 −0.272389
$$470$$ −1209.40 + 8930.15i −0.118693 + 0.876419i
$$471$$ −4864.45 −0.475886
$$472$$ 10189.2i 0.993633i
$$473$$ 22088.6i 2.14722i
$$474$$ 4250.02 0.411835
$$475$$ −1567.00 432.366i −0.151366 0.0417649i
$$476$$ 2614.89 0.251793
$$477$$ 2538.44i 0.243662i
$$478$$ 2105.30i 0.201453i
$$479$$ 2909.45 0.277528 0.138764 0.990325i $$-0.455687\pi$$
0.138764 + 0.990325i $$0.455687\pi$$
$$480$$ −594.898 + 4392.68i −0.0565693 + 0.417703i
$$481$$ 6511.96 0.617297
$$482$$ 11688.7i 1.10458i
$$483$$ 2741.86i 0.258300i
$$484$$ 5721.42 0.537323
$$485$$ 2069.15 + 280.224i 0.193722 + 0.0262357i
$$486$$ 536.218 0.0500481
$$487$$ 2201.84i 0.204876i 0.994739 + 0.102438i $$0.0326644\pi$$
−0.994739 + 0.102438i $$0.967336\pi$$
$$488$$ 13847.9i 1.28456i
$$489$$ 2775.58 0.256679
$$490$$ 1197.95 + 162.238i 0.110445 + 0.0149575i
$$491$$ −11827.6 −1.08711 −0.543556 0.839373i $$-0.682922\pi$$
−0.543556 + 0.839373i $$0.682922\pi$$
$$492$$ 4096.23i 0.375350i
$$493$$ 9306.23i 0.850165i
$$494$$ −1116.37 −0.101675
$$495$$ 758.939 5603.95i 0.0689127 0.508846i
$$496$$ −1780.30 −0.161165
$$497$$ 727.928i 0.0656983i
$$498$$ 3389.49i 0.304994i
$$499$$ −1408.66 −0.126374 −0.0631868 0.998002i $$-0.520126\pi$$
−0.0631868 + 0.998002i $$0.520126\pi$$
$$500$$ 1719.22 4023.29i 0.153771 0.359854i
$$501$$ −8044.65 −0.717382
$$502$$ 4093.74i 0.363969i
$$503$$ 11018.9i 0.976758i −0.872632 0.488379i $$-0.837588\pi$$
0.872632 0.488379i $$-0.162412\pi$$
$$504$$ −1547.38 −0.136757
$$505$$ −2476.76 + 18288.2i −0.218247 + 1.61152i
$$506$$ 16192.2 1.42259
$$507$$ 2050.77i 0.179641i
$$508$$ 4428.95i 0.386816i
$$509$$ −7032.93 −0.612434 −0.306217 0.951962i $$-0.599063\pi$$
−0.306217 + 0.951962i $$0.599063\pi$$
$$510$$ −8751.57 1185.22i −0.759855 0.102907i
$$511$$ −896.180 −0.0775825
$$512$$ 9581.46i 0.827041i
$$513$$ 351.121i 0.0302190i
$$514$$ 13754.3 1.18030
$$515$$ 799.781 + 108.314i 0.0684321 + 0.00926771i
$$516$$ −3691.32 −0.314925
$$517$$ 20528.6i 1.74632i
$$518$$ 2585.63i 0.219317i
$$519$$ 862.773 0.0729702
$$520$$ 1433.69 10586.3i 0.120907 0.892766i
$$521$$ 3049.04 0.256394 0.128197 0.991749i $$-0.459081\pi$$
0.128197 + 0.991749i $$0.459081\pi$$
$$522$$ 1548.93i 0.129875i
$$523$$ 8714.06i 0.728564i 0.931289 + 0.364282i $$0.118686\pi$$
−0.931289 + 0.364282i $$0.881314\pi$$
$$524$$ −7740.58 −0.645322
$$525$$ 2530.44 + 698.198i 0.210357 + 0.0580416i
$$526$$ −2613.79 −0.216666
$$527$$ 7286.52i 0.602288i
$$528$$ 4915.41i 0.405143i
$$529$$ −4880.17 −0.401099
$$530$$ −933.856 + 6895.53i −0.0765361 + 0.565137i
$$531$$ 3733.58 0.305129
$$532$$ 284.987i 0.0232251i
$$533$$ 16967.1i 1.37885i
$$534$$ −8110.15 −0.657230
$$535$$ −13323.3 1804.36i −1.07666 0.145812i
$$536$$ 9707.48 0.782275
$$537$$ 11050.4i 0.888009i
$$538$$ 4228.02i 0.338815i
$$539$$ −2753.85 −0.220068
$$540$$ −936.499 126.829i −0.0746305 0.0101072i
$$541$$ −5999.45 −0.476778 −0.238389 0.971170i $$-0.576619\pi$$
−0.238389 + 0.971170i $$0.576619\pi$$
$$542$$ 2579.48i 0.204425i
$$543$$ 9397.95i 0.742734i
$$544$$ −15769.6 −1.24286
$$545$$ −2327.74 + 17187.9i −0.182953 + 1.35091i
$$546$$ 1802.74 0.141301
$$547$$ 7759.95i 0.606566i −0.952901 0.303283i $$-0.901917\pi$$
0.952901 0.303283i $$-0.0980828\pi$$
$$548$$ 671.184i 0.0523203i
$$549$$ 5074.22 0.394467
$$550$$ 4123.24 14943.6i 0.319664 1.15854i
$$551$$ −1014.25 −0.0784184
$$552$$ 9620.63i 0.741814i
$$553$$ 4493.99i 0.345577i
$$554$$ −16041.4 −1.23021
$$555$$ 753.487 5563.69i 0.0576283 0.425523i
$$556$$ −2951.50 −0.225128
$$557$$ 6392.82i 0.486306i 0.969988 + 0.243153i $$0.0781817\pi$$
−0.969988 + 0.243153i $$0.921818\pi$$
$$558$$ 1212.77i 0.0920081i
$$559$$ 15289.9 1.15687
$$560$$ −2261.00 306.206i −0.170616 0.0231064i
$$561$$ 20118.1 1.51406
$$562$$ 657.863i 0.0493777i
$$563$$ 7682.70i 0.575111i −0.957764 0.287555i $$-0.907157\pi$$
0.957764 0.287555i $$-0.0928425\pi$$
$$564$$ −3430.61 −0.256125
$$565$$ −23054.7 3122.28i −1.71667 0.232487i
$$566$$ −9921.81 −0.736828
$$567$$ 567.000i 0.0419961i
$$568$$ 2554.15i 0.188679i
$$569$$ −143.175 −0.0105487 −0.00527434 0.999986i $$-0.501679\pi$$
−0.00527434 + 0.999986i $$0.501679\pi$$
$$570$$ −129.172 + 953.800i −0.00949200 + 0.0700883i
$$571$$ 1077.72 0.0789863 0.0394932 0.999220i $$-0.487426\pi$$
0.0394932 + 0.999220i $$0.487426\pi$$
$$572$$ 6844.74i 0.500338i
$$573$$ 4760.78i 0.347094i
$$574$$ 6736.92 0.489884
$$575$$ −4340.96 + 15732.7i −0.314835 + 1.14104i
$$576$$ 4723.76 0.341707
$$577$$ 12651.7i 0.912818i 0.889770 + 0.456409i $$0.150865\pi$$
−0.889770 + 0.456409i $$0.849135\pi$$
$$578$$ 20576.6i 1.48075i
$$579$$ −15537.0 −1.11519
$$580$$ 366.361 2705.18i 0.0262281 0.193666i
$$581$$ 3584.07 0.255925
$$582$$ 1236.35i 0.0880554i
$$583$$ 15851.4i 1.12607i
$$584$$ 3144.51 0.222810
$$585$$ 3879.09 + 525.342i 0.274155 + 0.0371286i
$$586$$ −3628.47 −0.255786
$$587$$ 2920.89i 0.205380i 0.994713 + 0.102690i $$0.0327450\pi$$
−0.994713 + 0.102690i $$0.967255\pi$$
$$588$$ 460.206i 0.0322765i
$$589$$ 794.131 0.0555545
$$590$$ 10142.1 + 1373.53i 0.707699 + 0.0958432i
$$591$$ −2711.39 −0.188717
$$592$$ 4880.09i 0.338802i
$$593$$ 9801.70i 0.678765i −0.940648 0.339382i $$-0.889782\pi$$
0.940648 0.339382i $$-0.110218\pi$$
$$594$$ −3348.44 −0.231293
$$595$$ −1253.26 + 9253.96i −0.0863504 + 0.637605i
$$596$$ −5300.41 −0.364284
$$597$$ 3514.53i 0.240938i
$$598$$ 11208.3i 0.766458i
$$599$$ 6992.54 0.476974 0.238487 0.971146i $$-0.423349\pi$$
0.238487 + 0.971146i $$0.423349\pi$$
$$600$$ −8878.81 2449.83i −0.604126 0.166690i
$$601$$ −26159.1 −1.77546 −0.887730 0.460364i $$-0.847719\pi$$
−0.887730 + 0.460364i $$0.847719\pi$$
$$602$$ 6070.98i 0.411021i
$$603$$ 3557.07i 0.240224i
$$604$$ 7888.29 0.531407
$$605$$ −2742.14 + 20247.8i −0.184271 + 1.36064i
$$606$$ 10927.5 0.732506
$$607$$ 264.526i 0.0176883i −0.999961 0.00884415i $$-0.997185\pi$$
0.999961 0.00884415i $$-0.00281522\pi$$
$$608$$ 1718.67i 0.114640i
$$609$$ 1637.84 0.108980
$$610$$ 13783.9 + 1866.74i 0.914905 + 0.123905i
$$611$$ 14210.0 0.940875
$$612$$ 3362.01i 0.222061i
$$613$$ 29371.1i 1.93521i 0.252461 + 0.967607i $$0.418760\pi$$
−0.252461 + 0.967607i $$0.581240\pi$$
$$614$$ 10429.1 0.685477
$$615$$ 14496.3 + 1963.23i 0.950485 + 0.128723i
$$616$$ 9662.68 0.632014
$$617$$ 26226.1i 1.71122i 0.517622 + 0.855609i $$0.326817\pi$$
−0.517622 + 0.855609i $$0.673183\pi$$
$$618$$ 477.880i 0.0311054i
$$619$$ 8903.12 0.578105 0.289052 0.957313i $$-0.406660\pi$$
0.289052 + 0.957313i $$0.406660\pi$$
$$620$$ −286.850 + 2118.08i −0.0185809 + 0.137200i
$$621$$ 3525.25 0.227799
$$622$$ 10711.1i 0.690476i
$$623$$ 8575.72i 0.551491i
$$624$$ −3402.47 −0.218282
$$625$$ 13414.2 + 8012.47i 0.858509 + 0.512798i
$$626$$ 3731.18 0.238224
$$627$$ 2192.59i 0.139655i
$$628$$ 5076.31i 0.322558i
$$629$$ 19973.5 1.26613
$$630$$ 208.592 1540.23i 0.0131912 0.0974032i
$$631$$ −14136.0 −0.891832 −0.445916 0.895075i $$-0.647122\pi$$
−0.445916 + 0.895075i $$0.647122\pi$$
$$632$$ 15768.5i 0.992464i
$$633$$ 3309.49i 0.207805i
$$634$$ 8558.27 0.536108
$$635$$ 15673.8 + 2122.69i 0.979519 + 0.132656i
$$636$$ −2648.99 −0.165156
$$637$$ 1906.23i 0.118567i
$$638$$ 9672.34i 0.600206i
$$639$$ −935.908 −0.0579404
$$640$$ 1118.02 + 151.413i 0.0690528 + 0.00935177i
$$641$$ 17665.7 1.08854 0.544270 0.838910i $$-0.316807\pi$$
0.544270 + 0.838910i $$0.316807\pi$$
$$642$$ 7960.84i 0.489391i
$$643$$ 10890.0i 0.667901i 0.942591 + 0.333951i $$0.108382\pi$$
−0.942591 + 0.333951i $$0.891618\pi$$
$$644$$ −2861.27 −0.175078
$$645$$ 1769.16 13063.4i 0.108001 0.797472i
$$646$$ −3424.12 −0.208545
$$647$$ 24281.0i 1.47540i −0.675128 0.737701i $$-0.735911\pi$$
0.675128 0.737701i $$-0.264089\pi$$
$$648$$ 1989.49i 0.120609i
$$649$$ −23314.5 −1.41013
$$650$$ 10344.1 + 2854.12i 0.624196 + 0.172228i
$$651$$ −1282.39 −0.0772053
$$652$$ 2896.46i 0.173979i
$$653$$ 1865.16i 0.111776i 0.998437 + 0.0558878i $$0.0177989\pi$$
−0.998437 + 0.0558878i $$0.982201\pi$$
$$654$$ 10270.0 0.614050
$$655$$ 3709.87 27393.4i 0.221308 1.63412i
$$656$$ −12715.2 −0.756775
$$657$$ 1152.23i 0.0684214i
$$658$$ 5642.20i 0.334279i
$$659$$ 8327.14 0.492230 0.246115 0.969241i $$-0.420846\pi$$
0.246115 + 0.969241i $$0.420846\pi$$
$$660$$ 5848.01 + 791.992i 0.344899 + 0.0467095i
$$661$$ −20665.7 −1.21604 −0.608021 0.793921i $$-0.708036\pi$$
−0.608021 + 0.793921i $$0.708036\pi$$
$$662$$ 21907.1i 1.28617i
$$663$$ 13925.8i 0.815737i
$$664$$ −12575.8 −0.734991
$$665$$ 1008.55 + 136.588i 0.0588121 + 0.00796488i
$$666$$ −3324.38 −0.193419
$$667$$ 10183.1i 0.591140i
$$668$$ 8395.00i 0.486246i
$$669$$ 12239.8 0.707353
$$670$$ −1308.60 + 9662.60i −0.0754561 + 0.557163i
$$671$$ −31686.2 −1.82300
$$672$$ 2775.36i 0.159318i
$$673$$ 1283.48i 0.0735136i −0.999324 0.0367568i $$-0.988297\pi$$
0.999324 0.0367568i $$-0.0117027\pi$$
$$674$$ 11659.7 0.666344
$$675$$ 897.683 3253.43i 0.0511879 0.185518i
$$676$$ 2140.08 0.121762
$$677$$ 13783.2i 0.782467i 0.920291 + 0.391234i $$0.127952\pi$$
−0.920291 + 0.391234i $$0.872048\pi$$
$$678$$ 13775.5i 0.780302i
$$679$$ −1307.32 −0.0738886
$$680$$ 4397.42 32470.2i 0.247990 1.83114i
$$681$$ −2795.89 −0.157326
$$682$$ 7573.18i 0.425208i
$$683$$ 10796.5i 0.604856i 0.953172 + 0.302428i $$0.0977972\pi$$
−0.953172 + 0.302428i $$0.902203\pi$$
$$684$$ −366.412 −0.0204826
$$685$$ −2375.28 321.682i −0.132489 0.0179428i
$$686$$ −756.884 −0.0421253
$$687$$ 4414.66i 0.245167i
$$688$$ 11458.3i 0.634947i
$$689$$ 10972.4 0.606699
$$690$$ 9576.15 + 1296.89i 0.528345 + 0.0715533i
$$691$$ −12082.4 −0.665173 −0.332587 0.943073i $$-0.607921\pi$$
−0.332587 + 0.943073i $$0.607921\pi$$
$$692$$ 900.348i 0.0494597i
$$693$$ 3540.66i 0.194082i
$$694$$ −23276.5 −1.27315
$$695$$ 1414.58 10445.2i 0.0772060 0.570084i
$$696$$ −5746.85 −0.312980
$$697$$ 52041.4i 2.82813i
$$698$$ 1386.69i 0.0751962i
$$699$$ 7437.19 0.402433
$$700$$ −728.605 + 2640.65i −0.0393410 + 0.142582i
$$701$$ −28753.5 −1.54922 −0.774610 0.632439i $$-0.782054\pi$$
−0.774610 + 0.632439i $$0.782054\pi$$
$$702$$ 2317.81i 0.124615i
$$703$$ 2176.84i 0.116787i
$$704$$ −29497.8 −1.57917
$$705$$ 1644.21 12140.7i 0.0878362 0.648576i
$$706$$ −5622.95 −0.299749
$$707$$ 11554.8i 0.614657i
$$708$$ 3896.18i 0.206819i
$$709$$ −4577.21 −0.242455 −0.121228 0.992625i $$-0.538683\pi$$
−0.121228 + 0.992625i $$0.538683\pi$$
$$710$$ −2542.34 344.308i −0.134384 0.0181995i
$$711$$ −5777.99 −0.304770
$$712$$ 30090.4i 1.58383i
$$713$$ 7973.07i 0.418785i
$$714$$ 5529.37 0.289820
$$715$$ −24223.1 3280.52i −1.26698 0.171587i
$$716$$ −11531.7 −0.601898
$$717$$ 2862.20i 0.149081i
$$718$$ 28788.8i 1.49636i
$$719$$ −30875.9 −1.60150 −0.800749 0.599000i $$-0.795565\pi$$
−0.800749 + 0.599000i $$0.795565\pi$$
$$720$$ −393.693 + 2907.00i −0.0203779 + 0.150469i
$$721$$ −505.313 −0.0261010
$$722$$ 14762.3i 0.760936i
$$723$$ 15891.1i 0.817420i
$$724$$ 9807.25 0.503430
$$725$$ 9397.88 + 2593.06i 0.481419 + 0.132833i
$$726$$ 12098.3 0.618472
$$727$$ 520.090i 0.0265324i 0.999912 + 0.0132662i $$0.00422289\pi$$
−0.999912 + 0.0132662i $$0.995777\pi$$
$$728$$ 6688.56i 0.340514i
$$729$$ −729.000 −0.0370370
$$730$$ −423.890 + 3129.98i −0.0214916 + 0.158693i
$$731$$ 46897.1 2.37285
$$732$$ 5295.21i 0.267372i
$$733$$ 393.396i 0.0198232i 0.999951 + 0.00991160i $$0.00315501\pi$$
−0.999951 + 0.00991160i $$0.996845\pi$$
$$734$$ 17803.8 0.895301
$$735$$ −1628.64 220.566i −0.0817325 0.0110690i
$$736$$ 17255.5 0.864191
$$737$$ 22212.3i 1.11018i
$$738$$ 8661.76i 0.432037i
$$739$$ 9348.92 0.465366 0.232683 0.972553i $$-0.425250\pi$$
0.232683 + 0.972553i $$0.425250\pi$$
$$740$$ 5806.00 + 786.302i 0.288423 + 0.0390609i
$$741$$ 1517.72 0.0752428
$$742$$ 4356.69i 0.215552i
$$743$$ 33710.8i 1.66451i −0.554394 0.832254i $$-0.687050\pi$$
0.554394 0.832254i $$-0.312950\pi$$
$$744$$ 4499.63 0.221726
$$745$$ 2540.36 18757.8i 0.124928 0.922461i
$$746$$ 7995.44 0.392405
$$747$$ 4608.09i 0.225704i
$$748$$ 20994.2i 1.02624i
$$749$$ 8417.83 0.410655
$$750$$ 3635.40 8507.52i 0.176995 0.414201i
$$751$$ −21116.6 −1.02604 −0.513019 0.858377i $$-0.671473\pi$$
−0.513019 + 0.858377i $$0.671473\pi$$
$$752$$ 10649.0i 0.516396i
$$753$$ 5565.52i 0.269348i
$$754$$ 6695.24 0.323377
$$755$$ −3780.67 + 27916.2i −0.182242 + 1.34566i
$$756$$ 591.694 0.0284652
$$757$$ 7385.25i 0.354586i −0.984158 0.177293i $$-0.943266\pi$$
0.984158 0.177293i $$-0.0567340\pi$$
$$758$$ 16520.3i 0.791616i
$$759$$ −22013.6 −1.05276
$$760$$ −3538.81 479.258i −0.168903 0.0228744i
$$761$$ −27682.0 −1.31862 −0.659311 0.751871i $$-0.729152\pi$$
−0.659311 + 0.751871i $$0.729152\pi$$
$$762$$ 9365.30i 0.445235i
$$763$$ 10859.5i 0.515258i
$$764$$ 4968.12 0.235262
$$765$$ 11897.9 + 1611.33i 0.562315 + 0.0761539i
$$766$$ −19697.9 −0.929132
$$767$$ 16138.4i 0.759746i
$$768$$ 11928.7i 0.560467i
$$769$$ 22248.6 1.04331 0.521654 0.853157i $$-0.325315\pi$$
0.521654 + 0.853157i $$0.325315\pi$$
$$770$$ −1302.56 + 9618.01i −0.0609624 + 0.450142i
$$771$$ −18699.3 −0.873460
$$772$$ 16213.6i 0.755883i
$$773$$ 11372.3i 0.529152i 0.964365 + 0.264576i $$0.0852321\pi$$
−0.964365 + 0.264576i $$0.914768\pi$$
$$774$$ −7805.54 −0.362486
$$775$$ −7358.29 2030.29i −0.341055 0.0941036i
$$776$$ 4587.12 0.212201
$$777$$ 3515.22i 0.162301i
$$778$$ 27804.0i 1.28126i
$$779$$ 5671.80 0.260864
$$780$$ −548.221 + 4048.02i −0.0251660 + 0.185824i
$$781$$ 5844.32 0.267767
$$782$$ 34378.1i 1.57207i
$$783$$ 2105.80i 0.0961112i
$$784$$ 1428.53