# Properties

 Label 441.4.e.f.361.1 Level $441$ Weight $4$ Character 441.361 Analytic conductor $26.020$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 441.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$26.0198423125$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 147) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 361.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 441.361 Dual form 441.4.e.f.226.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(3.50000 - 6.06218i) q^{4} +(-6.00000 - 10.3923i) q^{5} -15.0000 q^{8} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(3.50000 - 6.06218i) q^{4} +(-6.00000 - 10.3923i) q^{5} -15.0000 q^{8} +(-6.00000 + 10.3923i) q^{10} +(10.0000 - 17.3205i) q^{11} +84.0000 q^{13} +(-20.5000 - 35.5070i) q^{16} +(48.0000 - 83.1384i) q^{17} +(6.00000 + 10.3923i) q^{19} -84.0000 q^{20} -20.0000 q^{22} +(-88.0000 - 152.420i) q^{23} +(-9.50000 + 16.4545i) q^{25} +(-42.0000 - 72.7461i) q^{26} -58.0000 q^{29} +(-132.000 + 228.631i) q^{31} +(-80.5000 + 139.430i) q^{32} -96.0000 q^{34} +(-129.000 - 223.435i) q^{37} +(6.00000 - 10.3923i) q^{38} +(90.0000 + 155.885i) q^{40} +156.000 q^{43} +(-70.0000 - 121.244i) q^{44} +(-88.0000 + 152.420i) q^{46} +(204.000 + 353.338i) q^{47} +19.0000 q^{50} +(294.000 - 509.223i) q^{52} +(-361.000 + 625.270i) q^{53} -240.000 q^{55} +(29.0000 + 50.2295i) q^{58} +(-246.000 + 426.084i) q^{59} +(-246.000 - 426.084i) q^{61} +264.000 q^{62} -167.000 q^{64} +(-504.000 - 872.954i) q^{65} +(-206.000 + 356.802i) q^{67} +(-336.000 - 581.969i) q^{68} -296.000 q^{71} +(120.000 - 207.846i) q^{73} +(-129.000 + 223.435i) q^{74} +84.0000 q^{76} +(-388.000 - 672.036i) q^{79} +(-246.000 + 426.084i) q^{80} +924.000 q^{83} -1152.00 q^{85} +(-78.0000 - 135.100i) q^{86} +(-150.000 + 259.808i) q^{88} +(372.000 + 644.323i) q^{89} -1232.00 q^{92} +(204.000 - 353.338i) q^{94} +(72.0000 - 124.708i) q^{95} +168.000 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{2} + 7 q^{4} - 12 q^{5} - 30 q^{8} + O(q^{10})$$ $$2 q - q^{2} + 7 q^{4} - 12 q^{5} - 30 q^{8} - 12 q^{10} + 20 q^{11} + 168 q^{13} - 41 q^{16} + 96 q^{17} + 12 q^{19} - 168 q^{20} - 40 q^{22} - 176 q^{23} - 19 q^{25} - 84 q^{26} - 116 q^{29} - 264 q^{31} - 161 q^{32} - 192 q^{34} - 258 q^{37} + 12 q^{38} + 180 q^{40} + 312 q^{43} - 140 q^{44} - 176 q^{46} + 408 q^{47} + 38 q^{50} + 588 q^{52} - 722 q^{53} - 480 q^{55} + 58 q^{58} - 492 q^{59} - 492 q^{61} + 528 q^{62} - 334 q^{64} - 1008 q^{65} - 412 q^{67} - 672 q^{68} - 592 q^{71} + 240 q^{73} - 258 q^{74} + 168 q^{76} - 776 q^{79} - 492 q^{80} + 1848 q^{83} - 2304 q^{85} - 156 q^{86} - 300 q^{88} + 744 q^{89} - 2464 q^{92} + 408 q^{94} + 144 q^{95} + 336 q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$$.

 $$n$$ $$199$$ $$344$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 0.866025i −0.176777 0.306186i 0.763998 0.645219i $$-0.223234\pi$$
−0.940775 + 0.339032i $$0.889900\pi$$
$$3$$ 0 0
$$4$$ 3.50000 6.06218i 0.437500 0.757772i
$$5$$ −6.00000 10.3923i −0.536656 0.929516i −0.999081 0.0428575i $$-0.986354\pi$$
0.462425 0.886658i $$-0.346979\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ −15.0000 −0.662913
$$9$$ 0 0
$$10$$ −6.00000 + 10.3923i −0.189737 + 0.328634i
$$11$$ 10.0000 17.3205i 0.274101 0.474757i −0.695807 0.718229i $$-0.744953\pi$$
0.969908 + 0.243472i $$0.0782863\pi$$
$$12$$ 0 0
$$13$$ 84.0000 1.79211 0.896054 0.443945i $$-0.146421\pi$$
0.896054 + 0.443945i $$0.146421\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −20.5000 35.5070i −0.320312 0.554798i
$$17$$ 48.0000 83.1384i 0.684806 1.18612i −0.288691 0.957422i $$-0.593220\pi$$
0.973498 0.228697i $$-0.0734466\pi$$
$$18$$ 0 0
$$19$$ 6.00000 + 10.3923i 0.0724471 + 0.125482i 0.899973 0.435945i $$-0.143586\pi$$
−0.827526 + 0.561427i $$0.810252\pi$$
$$20$$ −84.0000 −0.939149
$$21$$ 0 0
$$22$$ −20.0000 −0.193819
$$23$$ −88.0000 152.420i −0.797794 1.38182i −0.921050 0.389445i $$-0.872667\pi$$
0.123255 0.992375i $$-0.460667\pi$$
$$24$$ 0 0
$$25$$ −9.50000 + 16.4545i −0.0760000 + 0.131636i
$$26$$ −42.0000 72.7461i −0.316803 0.548719i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −58.0000 −0.371391 −0.185695 0.982607i $$-0.559454\pi$$
−0.185695 + 0.982607i $$0.559454\pi$$
$$30$$ 0 0
$$31$$ −132.000 + 228.631i −0.764771 + 1.32462i 0.175597 + 0.984462i $$0.443815\pi$$
−0.940368 + 0.340160i $$0.889519\pi$$
$$32$$ −80.5000 + 139.430i −0.444704 + 0.770250i
$$33$$ 0 0
$$34$$ −96.0000 −0.484231
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −129.000 223.435i −0.573175 0.992768i −0.996237 0.0866674i $$-0.972378\pi$$
0.423062 0.906101i $$-0.360955\pi$$
$$38$$ 6.00000 10.3923i 0.0256139 0.0443646i
$$39$$ 0 0
$$40$$ 90.0000 + 155.885i 0.355756 + 0.616188i
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ 156.000 0.553251 0.276625 0.960978i $$-0.410784\pi$$
0.276625 + 0.960978i $$0.410784\pi$$
$$44$$ −70.0000 121.244i −0.239839 0.415413i
$$45$$ 0 0
$$46$$ −88.0000 + 152.420i −0.282063 + 0.488547i
$$47$$ 204.000 + 353.338i 0.633116 + 1.09659i 0.986911 + 0.161266i $$0.0515578\pi$$
−0.353795 + 0.935323i $$0.615109\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 19.0000 0.0537401
$$51$$ 0 0
$$52$$ 294.000 509.223i 0.784047 1.35801i
$$53$$ −361.000 + 625.270i −0.935607 + 1.62052i −0.162059 + 0.986781i $$0.551813\pi$$
−0.773548 + 0.633737i $$0.781520\pi$$
$$54$$ 0 0
$$55$$ −240.000 −0.588393
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 29.0000 + 50.2295i 0.0656532 + 0.113715i
$$59$$ −246.000 + 426.084i −0.542822 + 0.940195i 0.455919 + 0.890021i $$0.349311\pi$$
−0.998741 + 0.0501732i $$0.984023\pi$$
$$60$$ 0 0
$$61$$ −246.000 426.084i −0.516345 0.894337i −0.999820 0.0189781i $$-0.993959\pi$$
0.483474 0.875358i $$-0.339375\pi$$
$$62$$ 264.000 0.540775
$$63$$ 0 0
$$64$$ −167.000 −0.326172
$$65$$ −504.000 872.954i −0.961746 1.66579i
$$66$$ 0 0
$$67$$ −206.000 + 356.802i −0.375625 + 0.650602i −0.990420 0.138085i $$-0.955905\pi$$
0.614795 + 0.788687i $$0.289239\pi$$
$$68$$ −336.000 581.969i −0.599206 1.03785i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −296.000 −0.494771 −0.247385 0.968917i $$-0.579571\pi$$
−0.247385 + 0.968917i $$0.579571\pi$$
$$72$$ 0 0
$$73$$ 120.000 207.846i 0.192396 0.333240i −0.753647 0.657279i $$-0.771707\pi$$
0.946044 + 0.324038i $$0.105041\pi$$
$$74$$ −129.000 + 223.435i −0.202648 + 0.350996i
$$75$$ 0 0
$$76$$ 84.0000 0.126782
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −388.000 672.036i −0.552575 0.957088i −0.998088 0.0618122i $$-0.980312\pi$$
0.445513 0.895275i $$-0.353021\pi$$
$$80$$ −246.000 + 426.084i −0.343795 + 0.595471i
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 924.000 1.22195 0.610977 0.791648i $$-0.290777\pi$$
0.610977 + 0.791648i $$0.290777\pi$$
$$84$$ 0 0
$$85$$ −1152.00 −1.47002
$$86$$ −78.0000 135.100i −0.0978018 0.169398i
$$87$$ 0 0
$$88$$ −150.000 + 259.808i −0.181705 + 0.314723i
$$89$$ 372.000 + 644.323i 0.443055 + 0.767394i 0.997914 0.0645500i $$-0.0205612\pi$$
−0.554859 + 0.831944i $$0.687228\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −1232.00 −1.39614
$$93$$ 0 0
$$94$$ 204.000 353.338i 0.223840 0.387703i
$$95$$ 72.0000 124.708i 0.0777584 0.134681i
$$96$$ 0 0
$$97$$ 168.000 0.175854 0.0879269 0.996127i $$-0.471976\pi$$
0.0879269 + 0.996127i $$0.471976\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 66.5000 + 115.181i 0.0665000 + 0.115181i
$$101$$ 762.000 1319.82i 0.750711 1.30027i −0.196767 0.980450i $$-0.563044\pi$$
0.947478 0.319820i $$-0.103622\pi$$
$$102$$ 0 0
$$103$$ −204.000 353.338i −0.195153 0.338014i 0.751798 0.659394i $$-0.229187\pi$$
−0.946951 + 0.321379i $$0.895854\pi$$
$$104$$ −1260.00 −1.18801
$$105$$ 0 0
$$106$$ 722.000 0.661574
$$107$$ −410.000 710.141i −0.370432 0.641607i 0.619200 0.785233i $$-0.287457\pi$$
−0.989632 + 0.143627i $$0.954124\pi$$
$$108$$ 0 0
$$109$$ 459.000 795.011i 0.403342 0.698608i −0.590785 0.806829i $$-0.701182\pi$$
0.994127 + 0.108221i $$0.0345153\pi$$
$$110$$ 120.000 + 207.846i 0.104014 + 0.180158i
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 110.000 0.0915746 0.0457873 0.998951i $$-0.485420\pi$$
0.0457873 + 0.998951i $$0.485420\pi$$
$$114$$ 0 0
$$115$$ −1056.00 + 1829.05i −0.856283 + 1.48313i
$$116$$ −203.000 + 351.606i −0.162483 + 0.281430i
$$117$$ 0 0
$$118$$ 492.000 0.383833
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 465.500 + 806.270i 0.349737 + 0.605762i
$$122$$ −246.000 + 426.084i −0.182556 + 0.316196i
$$123$$ 0 0
$$124$$ 924.000 + 1600.41i 0.669175 + 1.15904i
$$125$$ −1272.00 −0.910169
$$126$$ 0 0
$$127$$ 16.0000 0.0111793 0.00558965 0.999984i $$-0.498221\pi$$
0.00558965 + 0.999984i $$0.498221\pi$$
$$128$$ 727.500 + 1260.07i 0.502363 + 0.870119i
$$129$$ 0 0
$$130$$ −504.000 + 872.954i −0.340029 + 0.588947i
$$131$$ −846.000 1465.31i −0.564239 0.977291i −0.997120 0.0758401i $$-0.975836\pi$$
0.432881 0.901451i $$-0.357497\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 412.000 0.265607
$$135$$ 0 0
$$136$$ −720.000 + 1247.08i −0.453967 + 0.786294i
$$137$$ 563.000 975.145i 0.351097 0.608118i −0.635345 0.772229i $$-0.719142\pi$$
0.986442 + 0.164110i $$0.0524753\pi$$
$$138$$ 0 0
$$139$$ −1092.00 −0.666347 −0.333173 0.942866i $$-0.608119\pi$$
−0.333173 + 0.942866i $$0.608119\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 148.000 + 256.344i 0.0874640 + 0.151492i
$$143$$ 840.000 1454.92i 0.491219 0.850816i
$$144$$ 0 0
$$145$$ 348.000 + 602.754i 0.199309 + 0.345214i
$$146$$ −240.000 −0.136045
$$147$$ 0 0
$$148$$ −1806.00 −1.00306
$$149$$ 535.000 + 926.647i 0.294154 + 0.509489i 0.974788 0.223134i $$-0.0716289\pi$$
−0.680634 + 0.732624i $$0.738296\pi$$
$$150$$ 0 0
$$151$$ 60.0000 103.923i 0.0323360 0.0560075i −0.849405 0.527742i $$-0.823039\pi$$
0.881741 + 0.471735i $$0.156372\pi$$
$$152$$ −90.0000 155.885i −0.0480261 0.0831836i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 3168.00 1.64168
$$156$$ 0 0
$$157$$ 918.000 1590.02i 0.466652 0.808265i −0.532622 0.846353i $$-0.678793\pi$$
0.999274 + 0.0380879i $$0.0121267\pi$$
$$158$$ −388.000 + 672.036i −0.195365 + 0.338382i
$$159$$ 0 0
$$160$$ 1932.00 0.954613
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −458.000 793.279i −0.220082 0.381193i 0.734751 0.678337i $$-0.237299\pi$$
−0.954833 + 0.297144i $$0.903966\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ −462.000 800.207i −0.216013 0.374145i
$$167$$ 504.000 0.233537 0.116769 0.993159i $$-0.462746\pi$$
0.116769 + 0.993159i $$0.462746\pi$$
$$168$$ 0 0
$$169$$ 4859.00 2.21165
$$170$$ 576.000 + 997.661i 0.259866 + 0.450101i
$$171$$ 0 0
$$172$$ 546.000 945.700i 0.242047 0.419238i
$$173$$ 918.000 + 1590.02i 0.403435 + 0.698770i 0.994138 0.108119i $$-0.0344828\pi$$
−0.590703 + 0.806889i $$0.701149\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −820.000 −0.351192
$$177$$ 0 0
$$178$$ 372.000 644.323i 0.156644 0.271315i
$$179$$ 1186.00 2054.21i 0.495228 0.857760i −0.504757 0.863262i $$-0.668418\pi$$
0.999985 + 0.00550156i $$0.00175121\pi$$
$$180$$ 0 0
$$181$$ 1092.00 0.448440 0.224220 0.974539i $$-0.428017\pi$$
0.224220 + 0.974539i $$0.428017\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 1320.00 + 2286.31i 0.528868 + 0.916026i
$$185$$ −1548.00 + 2681.21i −0.615196 + 1.06555i
$$186$$ 0 0
$$187$$ −960.000 1662.77i −0.375413 0.650234i
$$188$$ 2856.00 1.10795
$$189$$ 0 0
$$190$$ −144.000 −0.0549835
$$191$$ 1256.00 + 2175.46i 0.475817 + 0.824139i 0.999616 0.0277030i $$-0.00881927\pi$$
−0.523800 + 0.851842i $$0.675486\pi$$
$$192$$ 0 0
$$193$$ 1215.00 2104.44i 0.453148 0.784876i −0.545431 0.838155i $$-0.683634\pi$$
0.998580 + 0.0532797i $$0.0169675\pi$$
$$194$$ −84.0000 145.492i −0.0310868 0.0538440i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 1762.00 0.637245 0.318623 0.947882i $$-0.396780\pi$$
0.318623 + 0.947882i $$0.396780\pi$$
$$198$$ 0 0
$$199$$ 1548.00 2681.21i 0.551431 0.955107i −0.446740 0.894664i $$-0.647415\pi$$
0.998172 0.0604433i $$-0.0192514\pi$$
$$200$$ 142.500 246.817i 0.0503814 0.0872631i
$$201$$ 0 0
$$202$$ −1524.00 −0.530833
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −204.000 + 353.338i −0.0689969 + 0.119506i
$$207$$ 0 0
$$208$$ −1722.00 2982.59i −0.574035 0.994257i
$$209$$ 240.000 0.0794313
$$210$$ 0 0
$$211$$ 156.000 0.0508980 0.0254490 0.999676i $$-0.491898\pi$$
0.0254490 + 0.999676i $$0.491898\pi$$
$$212$$ 2527.00 + 4376.89i 0.818656 + 1.41795i
$$213$$ 0 0
$$214$$ −410.000 + 710.141i −0.130967 + 0.226842i
$$215$$ −936.000 1621.20i −0.296905 0.514255i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −918.000 −0.285206
$$219$$ 0 0
$$220$$ −840.000 + 1454.92i −0.257422 + 0.445868i
$$221$$ 4032.00 6983.63i 1.22725 2.12565i
$$222$$ 0 0
$$223$$ −5040.00 −1.51347 −0.756734 0.653723i $$-0.773206\pi$$
−0.756734 + 0.653723i $$0.773206\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −55.0000 95.2628i −0.0161883 0.0280389i
$$227$$ −1086.00 + 1881.01i −0.317535 + 0.549986i −0.979973 0.199130i $$-0.936188\pi$$
0.662438 + 0.749116i $$0.269522\pi$$
$$228$$ 0 0
$$229$$ 1350.00 + 2338.27i 0.389566 + 0.674747i 0.992391 0.123126i $$-0.0392918\pi$$
−0.602826 + 0.797873i $$0.705959\pi$$
$$230$$ 2112.00 0.605483
$$231$$ 0 0
$$232$$ 870.000 0.246200
$$233$$ −1901.00 3292.63i −0.534501 0.925782i −0.999187 0.0403071i $$-0.987166\pi$$
0.464687 0.885475i $$-0.346167\pi$$
$$234$$ 0 0
$$235$$ 2448.00 4240.06i 0.679532 1.17698i
$$236$$ 1722.00 + 2982.59i 0.474969 + 0.822670i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 4408.00 1.19301 0.596506 0.802609i $$-0.296555\pi$$
0.596506 + 0.802609i $$0.296555\pi$$
$$240$$ 0 0
$$241$$ 1548.00 2681.21i 0.413757 0.716648i −0.581540 0.813518i $$-0.697550\pi$$
0.995297 + 0.0968696i $$0.0308830\pi$$
$$242$$ 465.500 806.270i 0.123651 0.214169i
$$243$$ 0 0
$$244$$ −3444.00 −0.903605
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 504.000 + 872.954i 0.129833 + 0.224877i
$$248$$ 1980.00 3429.46i 0.506976 0.878109i
$$249$$ 0 0
$$250$$ 636.000 + 1101.58i 0.160897 + 0.278681i
$$251$$ −924.000 −0.232360 −0.116180 0.993228i $$-0.537065\pi$$
−0.116180 + 0.993228i $$0.537065\pi$$
$$252$$ 0 0
$$253$$ −3520.00 −0.874706
$$254$$ −8.00000 13.8564i −0.00197624 0.00342295i
$$255$$ 0 0
$$256$$ 59.5000 103.057i 0.0145264 0.0251604i
$$257$$ 1380.00 + 2390.23i 0.334950 + 0.580150i 0.983475 0.181043i $$-0.0579474\pi$$
−0.648526 + 0.761193i $$0.724614\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ −7056.00 −1.68306
$$261$$ 0 0
$$262$$ −846.000 + 1465.31i −0.199489 + 0.345525i
$$263$$ −1180.00 + 2043.82i −0.276661 + 0.479191i −0.970553 0.240888i $$-0.922561\pi$$
0.693892 + 0.720079i $$0.255895\pi$$
$$264$$ 0 0
$$265$$ 8664.00 2.00840
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 1442.00 + 2497.62i 0.328672 + 0.569277i
$$269$$ −2010.00 + 3481.42i −0.455583 + 0.789093i −0.998722 0.0505501i $$-0.983903\pi$$
0.543138 + 0.839643i $$0.317236\pi$$
$$270$$ 0 0
$$271$$ 2400.00 + 4156.92i 0.537969 + 0.931790i 0.999013 + 0.0444126i $$0.0141416\pi$$
−0.461044 + 0.887377i $$0.652525\pi$$
$$272$$ −3936.00 −0.877408
$$273$$ 0 0
$$274$$ −1126.00 −0.248263
$$275$$ 190.000 + 329.090i 0.0416634 + 0.0721631i
$$276$$ 0 0
$$277$$ −3223.00 + 5582.40i −0.699102 + 1.21088i 0.269676 + 0.962951i $$0.413083\pi$$
−0.968778 + 0.247929i $$0.920250\pi$$
$$278$$ 546.000 + 945.700i 0.117795 + 0.204026i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 2602.00 0.552393 0.276196 0.961101i $$-0.410926\pi$$
0.276196 + 0.961101i $$0.410926\pi$$
$$282$$ 0 0
$$283$$ −3450.00 + 5975.58i −0.724669 + 1.25516i 0.234442 + 0.972130i $$0.424674\pi$$
−0.959110 + 0.283033i $$0.908660\pi$$
$$284$$ −1036.00 + 1794.40i −0.216462 + 0.374924i
$$285$$ 0 0
$$286$$ −1680.00 −0.347344
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −2151.50 3726.51i −0.437920 0.758499i
$$290$$ 348.000 602.754i 0.0704664 0.122051i
$$291$$ 0 0
$$292$$ −840.000 1454.92i −0.168347 0.291585i
$$293$$ −4452.00 −0.887674 −0.443837 0.896107i $$-0.646383\pi$$
−0.443837 + 0.896107i $$0.646383\pi$$
$$294$$ 0 0
$$295$$ 5904.00 1.16523
$$296$$ 1935.00 + 3351.52i 0.379965 + 0.658118i
$$297$$ 0 0
$$298$$ 535.000 926.647i 0.103999 0.180132i
$$299$$ −7392.00 12803.3i −1.42973 2.47637i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −120.000 −0.0228650
$$303$$ 0 0
$$304$$ 246.000 426.084i 0.0464114 0.0803869i
$$305$$ −2952.00 + 5113.01i −0.554200 + 0.959903i
$$306$$ 0 0
$$307$$ 2436.00 0.452866 0.226433 0.974027i $$-0.427294\pi$$
0.226433 + 0.974027i $$0.427294\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ −1584.00 2743.57i −0.290210 0.502659i
$$311$$ 3744.00 6484.80i 0.682646 1.18238i −0.291525 0.956563i $$-0.594163\pi$$
0.974171 0.225814i $$-0.0725040\pi$$
$$312$$ 0 0
$$313$$ −876.000 1517.28i −0.158193 0.273999i 0.776024 0.630703i $$-0.217234\pi$$
−0.934217 + 0.356705i $$0.883900\pi$$
$$314$$ −1836.00 −0.329973
$$315$$ 0 0
$$316$$ −5432.00 −0.967006
$$317$$ −781.000 1352.73i −0.138376 0.239675i 0.788506 0.615027i $$-0.210855\pi$$
−0.926882 + 0.375352i $$0.877522\pi$$
$$318$$ 0 0
$$319$$ −580.000 + 1004.59i −0.101799 + 0.176320i
$$320$$ 1002.00 + 1735.51i 0.175042 + 0.303182i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 1152.00 0.198449
$$324$$ 0 0
$$325$$ −798.000 + 1382.18i −0.136200 + 0.235906i
$$326$$ −458.000 + 793.279i −0.0778107 + 0.134772i
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 3546.00 + 6141.85i 0.588839 + 1.01990i 0.994385 + 0.105825i $$0.0337482\pi$$
−0.405546 + 0.914075i $$0.632918\pi$$
$$332$$ 3234.00 5601.45i 0.534605 0.925963i
$$333$$ 0 0
$$334$$ −252.000 436.477i −0.0412839 0.0715058i
$$335$$ 4944.00 0.806327
$$336$$ 0 0
$$337$$ 366.000 0.0591611 0.0295805 0.999562i $$-0.490583\pi$$
0.0295805 + 0.999562i $$0.490583\pi$$
$$338$$ −2429.50 4208.02i −0.390969 0.677177i
$$339$$ 0 0
$$340$$ −4032.00 + 6983.63i −0.643135 + 1.11394i
$$341$$ 2640.00 + 4572.61i 0.419249 + 0.726161i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ −2340.00 −0.366757
$$345$$ 0 0
$$346$$ 918.000 1590.02i 0.142636 0.247052i
$$347$$ −3182.00 + 5511.39i −0.492273 + 0.852642i −0.999960 0.00889958i $$-0.997167\pi$$
0.507687 + 0.861541i $$0.330500\pi$$
$$348$$ 0 0
$$349$$ 10500.0 1.61046 0.805232 0.592960i $$-0.202041\pi$$
0.805232 + 0.592960i $$0.202041\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 1610.00 + 2788.60i 0.243788 + 0.422253i
$$353$$ −204.000 + 353.338i −0.0307587 + 0.0532756i −0.880995 0.473126i $$-0.843126\pi$$
0.850236 + 0.526401i $$0.176459\pi$$
$$354$$ 0 0
$$355$$ 1776.00 + 3076.12i 0.265522 + 0.459898i
$$356$$ 5208.00 0.775347
$$357$$ 0 0
$$358$$ −2372.00 −0.350179
$$359$$ −5968.00 10336.9i −0.877379 1.51966i −0.854207 0.519933i $$-0.825957\pi$$
−0.0231719 0.999731i $$-0.507376\pi$$
$$360$$ 0 0
$$361$$ 3357.50 5815.36i 0.489503 0.847844i
$$362$$ −546.000 945.700i −0.0792738 0.137306i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −2880.00 −0.413003
$$366$$ 0 0
$$367$$ −1224.00 + 2120.03i −0.174093 + 0.301539i −0.939847 0.341595i $$-0.889033\pi$$
0.765754 + 0.643134i $$0.222366\pi$$
$$368$$ −3608.00 + 6249.24i −0.511087 + 0.885229i
$$369$$ 0 0
$$370$$ 3096.00 0.435009
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −5687.00 9850.17i −0.789442 1.36735i −0.926309 0.376764i $$-0.877037\pi$$
0.136868 0.990589i $$-0.456296\pi$$
$$374$$ −960.000 + 1662.77i −0.132728 + 0.229892i
$$375$$ 0 0
$$376$$ −3060.00 5300.08i −0.419701 0.726943i
$$377$$ −4872.00 −0.665572
$$378$$ 0 0
$$379$$ −5892.00 −0.798553 −0.399277 0.916830i $$-0.630739\pi$$
−0.399277 + 0.916830i $$0.630739\pi$$
$$380$$ −504.000 872.954i −0.0680386 0.117846i
$$381$$ 0 0
$$382$$ 1256.00 2175.46i 0.168227 0.291377i
$$383$$ 5244.00 + 9082.87i 0.699624 + 1.21178i 0.968597 + 0.248636i $$0.0799823\pi$$
−0.268973 + 0.963148i $$0.586684\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −2430.00 −0.320424
$$387$$ 0 0
$$388$$ 588.000 1018.45i 0.0769360 0.133257i
$$389$$ 2257.00 3909.24i 0.294176 0.509528i −0.680617 0.732639i $$-0.738288\pi$$
0.974793 + 0.223112i $$0.0716215\pi$$
$$390$$ 0 0
$$391$$ −16896.0 −2.18534
$$392$$ 0 0
$$393$$ 0 0
$$394$$ −881.000 1525.94i −0.112650 0.195116i
$$395$$ −4656.00 + 8064.43i −0.593086 + 1.02725i
$$396$$ 0 0
$$397$$ −3018.00 5227.33i −0.381534 0.660837i 0.609748 0.792596i $$-0.291271\pi$$
−0.991282 + 0.131759i $$0.957937\pi$$
$$398$$ −3096.00 −0.389921
$$399$$ 0 0
$$400$$ 779.000 0.0973750
$$401$$ −3385.00 5862.99i −0.421543 0.730134i 0.574547 0.818471i $$-0.305178\pi$$
−0.996091 + 0.0883370i $$0.971845\pi$$
$$402$$ 0 0
$$403$$ −11088.0 + 19205.0i −1.37055 + 2.37387i
$$404$$ −5334.00 9238.76i −0.656872 1.13774i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −5160.00 −0.628432
$$408$$ 0 0
$$409$$ 6252.00 10828.8i 0.755847 1.30917i −0.189105 0.981957i $$-0.560559\pi$$
0.944952 0.327209i $$-0.106108\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −2856.00 −0.341517
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −5544.00 9602.49i −0.655769 1.13583i
$$416$$ −6762.00 + 11712.1i −0.796958 + 1.38037i
$$417$$ 0 0
$$418$$ −120.000 207.846i −0.0140416 0.0243208i
$$419$$ 9492.00 1.10672 0.553359 0.832943i $$-0.313346\pi$$
0.553359 + 0.832943i $$0.313346\pi$$
$$420$$ 0 0
$$421$$ 5182.00 0.599894 0.299947 0.953956i $$-0.403031\pi$$
0.299947 + 0.953956i $$0.403031\pi$$
$$422$$ −78.0000 135.100i −0.00899758 0.0155843i
$$423$$ 0 0
$$424$$ 5415.00 9379.06i 0.620226 1.07426i
$$425$$ 912.000 + 1579.63i 0.104091 + 0.180290i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −5740.00 −0.648256
$$429$$ 0 0
$$430$$ −936.000 + 1621.20i −0.104972 + 0.181817i
$$431$$ −2860.00 + 4953.67i −0.319632 + 0.553619i −0.980411 0.196962i $$-0.936893\pi$$
0.660779 + 0.750580i $$0.270226\pi$$
$$432$$ 0 0
$$433$$ −13608.0 −1.51030 −0.755149 0.655554i $$-0.772435\pi$$
−0.755149 + 0.655554i $$0.772435\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −3213.00 5565.08i −0.352924 0.611282i
$$437$$ 1056.00 1829.05i 0.115596 0.200218i
$$438$$ 0 0
$$439$$ 6432.00 + 11140.6i 0.699277 + 1.21118i 0.968717 + 0.248166i $$0.0798279\pi$$
−0.269440 + 0.963017i $$0.586839\pi$$
$$440$$ 3600.00 0.390053
$$441$$ 0 0
$$442$$ −8064.00 −0.867795
$$443$$ −6626.00 11476.6i −0.710634 1.23085i −0.964620 0.263646i $$-0.915075\pi$$
0.253986 0.967208i $$-0.418258\pi$$
$$444$$ 0 0
$$445$$ 4464.00 7731.87i 0.475537 0.823654i
$$446$$ 2520.00 + 4364.77i 0.267546 + 0.463403i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −226.000 −0.0237541 −0.0118771 0.999929i $$-0.503781\pi$$
−0.0118771 + 0.999929i $$0.503781\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 385.000 666.840i 0.0400639 0.0693927i
$$453$$ 0 0
$$454$$ 2172.00 0.224531
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 5667.00 + 9815.53i 0.580068 + 1.00471i 0.995471 + 0.0950696i $$0.0303074\pi$$
−0.415403 + 0.909638i $$0.636359\pi$$
$$458$$ 1350.00 2338.27i 0.137732 0.238559i
$$459$$ 0 0
$$460$$ 7392.00 + 12803.3i 0.749247 + 1.29773i
$$461$$ −1596.00 −0.161243 −0.0806216 0.996745i $$-0.525691\pi$$
−0.0806216 + 0.996745i $$0.525691\pi$$
$$462$$ 0 0
$$463$$ 12728.0 1.27758 0.638791 0.769380i $$-0.279435\pi$$
0.638791 + 0.769380i $$0.279435\pi$$
$$464$$ 1189.00 + 2059.41i 0.118961 + 0.206047i
$$465$$ 0 0
$$466$$ −1901.00 + 3292.63i −0.188975 + 0.327313i
$$467$$ 1506.00 + 2608.47i 0.149228 + 0.258470i 0.930942 0.365166i $$-0.118988\pi$$
−0.781715 + 0.623636i $$0.785655\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ −4896.00 −0.480501
$$471$$ 0 0
$$472$$ 3690.00 6391.27i 0.359843 0.623267i
$$473$$ 1560.00 2702.00i 0.151647 0.262660i
$$474$$ 0 0
$$475$$ −228.000 −0.0220239
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −2204.00 3817.44i −0.210897 0.365284i
$$479$$ 2148.00 3720.45i 0.204895 0.354888i −0.745204 0.666836i $$-0.767648\pi$$
0.950099 + 0.311948i $$0.100981\pi$$
$$480$$ 0 0
$$481$$ −10836.0 18768.5i −1.02719 1.77915i
$$482$$ −3096.00 −0.292570
$$483$$ 0 0
$$484$$ 6517.00 0.612040
$$485$$ −1008.00 1745.91i −0.0943730 0.163459i
$$486$$ 0 0
$$487$$ 4092.00 7087.55i 0.380752 0.659482i −0.610418 0.792079i $$-0.708998\pi$$
0.991170 + 0.132598i $$0.0423318\pi$$
$$488$$ 3690.00 + 6391.27i 0.342292 + 0.592867i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 12164.0 1.11803 0.559016 0.829157i $$-0.311179\pi$$
0.559016 + 0.829157i $$0.311179\pi$$
$$492$$ 0 0
$$493$$ −2784.00 + 4822.03i −0.254331 + 0.440514i
$$494$$ 504.000 872.954i 0.0459029 0.0795062i
$$495$$ 0 0
$$496$$ 10824.0 0.979863
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −486.000 841.777i −0.0435999 0.0755172i 0.843402 0.537283i $$-0.180549\pi$$
−0.887002 + 0.461766i $$0.847216\pi$$
$$500$$ −4452.00 + 7711.09i −0.398199 + 0.689701i
$$501$$ 0 0
$$502$$ 462.000 + 800.207i 0.0410758 + 0.0711454i
$$503$$ 7728.00 0.685039 0.342519 0.939511i $$-0.388720\pi$$
0.342519 + 0.939511i $$0.388720\pi$$
$$504$$ 0 0
$$505$$ −18288.0 −1.61150
$$506$$ 1760.00 + 3048.41i 0.154628 + 0.267823i
$$507$$ 0 0
$$508$$ 56.0000 96.9948i 0.00489094 0.00847136i
$$509$$ −5802.00 10049.4i −0.505244 0.875108i −0.999982 0.00606572i $$-0.998069\pi$$
0.494738 0.869042i $$-0.335264\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 11521.0 0.994455
$$513$$ 0 0
$$514$$ 1380.00 2390.23i 0.118423 0.205114i
$$515$$ −2448.00 + 4240.06i −0.209460 + 0.362795i
$$516$$ 0 0
$$517$$ 8160.00 0.694152
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 7560.00 + 13094.3i 0.637554 + 1.10428i
$$521$$ 5424.00 9394.64i 0.456103 0.789994i −0.542648 0.839960i $$-0.682578\pi$$
0.998751 + 0.0499665i $$0.0159115\pi$$
$$522$$ 0 0
$$523$$ −9066.00 15702.8i −0.757989 1.31288i −0.943874 0.330305i $$-0.892848\pi$$
0.185885 0.982572i $$-0.440485\pi$$
$$524$$ −11844.0 −0.987419
$$525$$ 0 0
$$526$$ 2360.00 0.195629
$$527$$ 12672.0 + 21948.5i 1.04744 + 1.81422i
$$528$$ 0 0
$$529$$ −9404.50 + 16289.1i −0.772951 + 1.33879i
$$530$$ −4332.00 7503.24i −0.355038 0.614944i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ −4920.00 + 8521.69i −0.397589 + 0.688644i
$$536$$ 3090.00 5352.04i 0.249007 0.431293i
$$537$$ 0 0
$$538$$ 4020.00 0.322146
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −3475.00 6018.88i −0.276159 0.478321i 0.694268 0.719717i $$-0.255728\pi$$
−0.970427 + 0.241395i $$0.922395\pi$$
$$542$$ 2400.00 4156.92i 0.190201 0.329437i
$$543$$ 0 0
$$544$$ 7728.00 + 13385.3i 0.609072 + 1.05494i
$$545$$ −11016.0 −0.865823
$$546$$ 0 0
$$547$$ 17012.0 1.32976 0.664882 0.746949i $$-0.268482\pi$$
0.664882 + 0.746949i $$0.268482\pi$$
$$548$$ −3941.00 6826.01i −0.307210 0.532104i
$$549$$ 0 0
$$550$$ 190.000 329.090i 0.0147302 0.0255135i
$$551$$ −348.000 602.754i −0.0269062 0.0466028i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 6446.00 0.494340
$$555$$ 0 0
$$556$$ −3822.00 + 6619.90i −0.291527 + 0.504939i
$$557$$ 1963.00 3400.02i 0.149327 0.258641i −0.781652 0.623715i $$-0.785623\pi$$
0.930979 + 0.365073i $$0.118956\pi$$
$$558$$ 0 0
$$559$$ 13104.0 0.991485
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −1301.00 2253.40i −0.0976501 0.169135i
$$563$$ 9414.00 16305.5i 0.704712 1.22060i −0.262084 0.965045i $$-0.584410\pi$$
0.966795 0.255552i $$-0.0822571\pi$$
$$564$$ 0 0
$$565$$ −660.000 1143.15i −0.0491441 0.0851201i
$$566$$ 6900.00 0.512418
$$567$$ 0 0
$$568$$ 4440.00 0.327990
$$569$$ 5995.00 + 10383.6i 0.441693 + 0.765035i 0.997815 0.0660655i $$-0.0210446\pi$$
−0.556122 + 0.831101i $$0.687711\pi$$
$$570$$ 0 0
$$571$$ 7858.00 13610.5i 0.575914 0.997513i −0.420027 0.907511i $$-0.637980\pi$$
0.995942 0.0900014i $$-0.0286871\pi$$
$$572$$ −5880.00 10184.5i −0.429817 0.744464i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 3344.00 0.242529
$$576$$ 0 0
$$577$$ −6936.00 + 12013.5i −0.500432 + 0.866774i 0.499568 + 0.866275i $$0.333492\pi$$
−1.00000 0.000499291i $$0.999841\pi$$
$$578$$ −2151.50 + 3726.51i −0.154828 + 0.268170i
$$579$$ 0 0
$$580$$ 4872.00 0.348791
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 7220.00 + 12505.4i 0.512902 + 0.888372i
$$584$$ −1800.00 + 3117.69i −0.127542 + 0.220909i
$$585$$ 0 0
$$586$$ 2226.00 + 3855.55i 0.156920 + 0.271794i
$$587$$ 8820.00 0.620171 0.310085 0.950709i $$-0.399642\pi$$
0.310085 + 0.950709i $$0.399642\pi$$
$$588$$ 0 0
$$589$$ −3168.00 −0.221622
$$590$$ −2952.00 5113.01i −0.205986 0.356779i
$$591$$ 0 0
$$592$$ −5289.00 + 9160.82i −0.367190 + 0.635992i
$$593$$ 8436.00 + 14611.6i 0.584191 + 1.01185i 0.994976 + 0.100116i $$0.0319213\pi$$
−0.410785 + 0.911732i $$0.634745\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 7490.00 0.514769
$$597$$ 0 0
$$598$$ −7392.00 + 12803.3i −0.505487 + 0.875530i
$$599$$ −3028.00 + 5244.65i −0.206545 + 0.357747i −0.950624 0.310345i $$-0.899555\pi$$
0.744079 + 0.668092i $$0.232889\pi$$
$$600$$ 0 0
$$601$$ −10752.0 −0.729756 −0.364878 0.931055i $$-0.618889\pi$$
−0.364878 + 0.931055i $$0.618889\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −420.000 727.461i −0.0282940 0.0490066i
$$605$$ 5586.00 9675.24i 0.375377 0.650172i
$$606$$ 0 0
$$607$$ 10128.0 + 17542.2i 0.677237 + 1.17301i 0.975810 + 0.218622i $$0.0701561\pi$$
−0.298573 + 0.954387i $$0.596511\pi$$
$$608$$ −1932.00 −0.128870
$$609$$ 0 0
$$610$$ 5904.00 0.391879
$$611$$ 17136.0 + 29680.4i 1.13461 + 1.96521i
$$612$$ 0 0
$$613$$ 14095.0 24413.3i 0.928698 1.60855i 0.143194 0.989695i $$-0.454263\pi$$
0.785504 0.618857i $$-0.212404\pi$$
$$614$$ −1218.00 2109.64i −0.0800562 0.138661i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −29318.0 −1.91296 −0.956482 0.291793i $$-0.905748\pi$$
−0.956482 + 0.291793i $$0.905748\pi$$
$$618$$ 0 0
$$619$$ 12174.0 21086.0i 0.790492 1.36917i −0.135171 0.990822i $$-0.543158\pi$$
0.925663 0.378350i $$-0.123508\pi$$
$$620$$ 11088.0 19205.0i 0.718234 1.24402i
$$621$$ 0 0
$$622$$ −7488.00 −0.482703
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 8819.50 + 15275.8i 0.564448 + 0.977653i
$$626$$ −876.000 + 1517.28i −0.0559297 + 0.0968731i
$$627$$ 0 0
$$628$$ −6426.00 11130.2i −0.408321 0.707232i
$$629$$ −24768.0 −1.57006
$$630$$ 0 0
$$631$$ −25184.0 −1.58884 −0.794421 0.607368i $$-0.792226\pi$$
−0.794421 + 0.607368i $$0.792226\pi$$
$$632$$ 5820.00 + 10080.5i 0.366309 + 0.634465i
$$633$$ 0 0
$$634$$ −781.000 + 1352.73i −0.0489235 + 0.0847379i
$$635$$ −96.0000 166.277i −0.00599944 0.0103913i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 1160.00 0.0719825
$$639$$ 0 0
$$640$$ 8730.00 15120.8i 0.539193 0.933910i
$$641$$ 16159.0 27988.2i 0.995698 1.72460i 0.417600 0.908631i $$-0.362871\pi$$
0.578097 0.815968i $$-0.303795\pi$$
$$642$$ 0 0
$$643$$ 3948.00 0.242137 0.121068 0.992644i $$-0.461368\pi$$
0.121068 + 0.992644i $$0.461368\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −576.000 997.661i −0.0350811 0.0607623i
$$647$$ −6924.00 + 11992.7i −0.420727 + 0.728721i −0.996011 0.0892331i $$-0.971558\pi$$
0.575284 + 0.817954i $$0.304892\pi$$
$$648$$ 0 0
$$649$$ 4920.00 + 8521.69i 0.297576 + 0.515417i
$$650$$ 1596.00 0.0963081
$$651$$ 0 0
$$652$$ −6412.00 −0.385143
$$653$$ −1579.00 2734.91i −0.0946264 0.163898i 0.814826 0.579705i $$-0.196832\pi$$
−0.909453 + 0.415808i $$0.863499\pi$$
$$654$$ 0 0
$$655$$ −10152.0 + 17583.8i −0.605605 + 1.04894i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 24596.0 1.45391 0.726953 0.686687i $$-0.240936\pi$$
0.726953 + 0.686687i $$0.240936\pi$$
$$660$$ 0 0
$$661$$ −7734.00 + 13395.7i −0.455095 + 0.788248i −0.998694 0.0510977i $$-0.983728\pi$$
0.543599 + 0.839345i $$0.317061\pi$$
$$662$$ 3546.00 6141.85i 0.208186 0.360589i
$$663$$ 0 0
$$664$$ −13860.0 −0.810049
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 5104.00 + 8840.39i 0.296293 + 0.513195i
$$668$$ 1764.00 3055.34i 0.102172 0.176968i
$$669$$ 0 0
$$670$$ −2472.00 4281.63i −0.142540 0.246886i
$$671$$ −9840.00 −0.566124
$$672$$ 0 0
$$673$$ 13470.0 0.771516 0.385758 0.922600i $$-0.373940\pi$$
0.385758 + 0.922600i $$0.373940\pi$$
$$674$$ −183.000 316.965i −0.0104583 0.0181143i
$$675$$ 0 0
$$676$$ 17006.5 29456.1i 0.967598 1.67593i
$$677$$ 4782.00 + 8282.67i 0.271473 + 0.470205i 0.969239 0.246121i $$-0.0791559\pi$$
−0.697766 + 0.716326i $$0.745823\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 17280.0 0.974497
$$681$$ 0 0
$$682$$ 2640.00 4572.61i 0.148227 0.256737i
$$683$$ 6926.00 11996.2i 0.388018 0.672066i −0.604165 0.796859i $$-0.706493\pi$$
0.992183 + 0.124793i $$0.0398266\pi$$
$$684$$ 0 0
$$685$$ −13512.0 −0.753674
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −3198.00 5539.10i −0.177213 0.306942i
$$689$$ −30324.0 + 52522.7i −1.67671 + 2.90414i
$$690$$ 0 0
$$691$$ −162.000 280.592i −0.00891863 0.0154475i 0.861532 0.507704i $$-0.169506\pi$$
−0.870450 + 0.492256i $$0.836172\pi$$
$$692$$ 12852.0 0.706011
$$693$$ 0 0
$$694$$ 6364.00 0.348090
$$695$$ 6552.00 + 11348.4i 0.357599 + 0.619380i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ −5250.00 9093.27i −0.284693 0.493102i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −24922.0 −1.34278 −0.671392 0.741103i $$-0.734303\pi$$
−0.671392 + 0.741103i $$0.734303\pi$$
$$702$$ 0 0
$$703$$ 1548.00 2681.21i 0.0830497 0.143846i
$$704$$ −1670.00 + 2892.52i −0.0894041 + 0.154852i
$$705$$ 0 0
$$706$$ 408.000 0.0217497
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 8943.00 + 15489.7i 0.473711 + 0.820492i 0.999547 0.0300939i $$-0.00958064\pi$$
−0.525836 + 0.850586i $$0.676247\pi$$
$$710$$ 1776.00 3076.12i 0.0938762 0.162598i
$$711$$ 0 0
$$712$$ −5580.00 9664.84i −0.293707 0.508715i
$$713$$ 46464.0 2.44052
$$714$$ 0 0
$$715$$ −20160.0 −1.05446
$$716$$ −8302.00 14379.5i −0.433324 0.750540i
$$717$$ 0 0
$$718$$ −5968.00 + 10336.9i −0.310200 + 0.537283i
$$719$$ 3396.00 + 5882.04i 0.176147 + 0.305095i 0.940557 0.339635i $$-0.110303\pi$$
−0.764411 + 0.644729i $$0.776970\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −6715.00 −0.346131
$$723$$ 0 0
$$724$$ 3822.00 6619.90i 0.196193 0.339816i
$$725$$ 551.000 954.360i 0.0282257 0.0488883i
$$726$$ 0 0
$$727$$ −1512.00 −0.0771348 −0.0385674 0.999256i $$-0.512279\pi$$
−0.0385674 + 0.999256i $$0.512279\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 1440.00 + 2494.15i 0.0730093 + 0.126456i
$$731$$ 7488.00 12969.6i 0.378870 0.656221i
$$732$$ 0 0
$$733$$ −5622.00 9737.59i −0.283292 0.490677i 0.688901 0.724855i $$-0.258093\pi$$
−0.972194 + 0.234178i $$0.924760\pi$$
$$734$$ 2448.00 0.123103
$$735$$ 0 0
$$736$$ 28336.0 1.41913
$$737$$ 4120.00 + 7136.05i 0.205919 + 0.356662i
$$738$$ 0 0
$$739$$ 998.000 1728.59i 0.0496780 0.0860448i −0.840117 0.542405i $$-0.817514\pi$$
0.889795 + 0.456360i $$0.150847\pi$$
$$740$$ 10836.0 + 18768.5i 0.538296 + 0.932357i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 656.000 0.0323907 0.0161954 0.999869i $$-0.494845\pi$$
0.0161954 + 0.999869i $$0.494845\pi$$
$$744$$ 0 0
$$745$$ 6420.00 11119.8i 0.315719 0.546841i
$$746$$ −5687.00 + 9850.17i −0.279110 + 0.483432i
$$747$$ 0 0
$$748$$ −13440.0 −0.656972
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −528.000 914.523i −0.0256551 0.0444360i 0.852913 0.522053i $$-0.174834\pi$$
−0.878568 + 0.477617i $$0.841501\pi$$
$$752$$ 8364.00 14486.9i 0.405590 0.702503i
$$753$$ 0 0
$$754$$ 2436.00 + 4219.28i 0.117658 + 0.203789i
$$755$$ −1440.00 −0.0694132
$$756$$ 0 0
$$757$$ −18702.0 −0.897934 −0.448967 0.893548i $$-0.648208\pi$$
−0.448967 + 0.893548i $$0.648208\pi$$
$$758$$ 2946.00 + 5102.62i 0.141166 + 0.244506i
$$759$$ 0 0
$$760$$ −1080.00 + 1870.61i −0.0515470 + 0.0892820i
$$761$$ −8952.00 15505.3i −0.426425 0.738590i 0.570127 0.821557i $$-0.306894\pi$$
−0.996552 + 0.0829661i $$0.973561\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 17584.0 0.832679
$$765$$ 0 0
$$766$$ 5244.00 9082.87i 0.247354 0.428430i
$$767$$ −20664.0 + 35791.1i −0.972795 + 1.68493i
$$768$$ 0 0
$$769$$ 7560.00 0.354513 0.177257 0.984165i $$-0.443278\pi$$
0.177257 + 0.984165i $$0.443278\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −8505.00 14731.1i −0.396505 0.686766i
$$773$$ 7146.00 12377.2i 0.332502 0.575910i −0.650500 0.759506i $$-0.725441\pi$$
0.983002 + 0.183596i $$0.0587740\pi$$
$$774$$ 0 0
$$775$$ −2508.00 4343.98i −0.116245 0.201343i
$$776$$ −2520.00 −0.116576
$$777$$ 0 0
$$778$$ −4514.00 −0.208014
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −2960.00 + 5126.87i −0.135617 + 0.234896i
$$782$$ 8448.00 + 14632.4i 0.386317 + 0.669121i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −22032.0 −1.00173
$$786$$ 0 0
$$787$$ 13182.0 22831.9i 0.597062 1.03414i −0.396191 0.918168i $$-0.629668\pi$$
0.993252 0.115973i $$-0.0369986\pi$$
$$788$$ 6167.00 10681.6i 0.278795 0.482887i
$$789$$ 0 0
$$790$$