# Properties

 Label 624.4.q.b.529.1 Level $624$ Weight $4$ Character 624.529 Analytic conductor $36.817$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$624 = 2^{4} \cdot 3 \cdot 13$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 624.q (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$36.8171918436$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 39) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 529.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 624.529 Dual form 624.4.q.b.289.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.50000 - 2.59808i) q^{3} -9.00000 q^{5} +(1.00000 + 1.73205i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$$ $$q+(1.50000 - 2.59808i) q^{3} -9.00000 q^{5} +(1.00000 + 1.73205i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(15.0000 - 25.9808i) q^{11} +(32.5000 + 33.7750i) q^{13} +(-13.5000 + 23.3827i) q^{15} +(55.5000 + 96.1288i) q^{17} +(-23.0000 - 39.8372i) q^{19} +6.00000 q^{21} +(-3.00000 + 5.19615i) q^{23} -44.0000 q^{25} -27.0000 q^{27} +(52.5000 - 90.9327i) q^{29} +100.000 q^{31} +(-45.0000 - 77.9423i) q^{33} +(-9.00000 - 15.5885i) q^{35} +(-8.50000 + 14.7224i) q^{37} +(136.500 - 33.7750i) q^{39} +(115.500 - 200.052i) q^{41} +(-257.000 - 445.137i) q^{43} +(40.5000 + 70.1481i) q^{45} +162.000 q^{47} +(169.500 - 293.583i) q^{49} +333.000 q^{51} +639.000 q^{53} +(-135.000 + 233.827i) q^{55} -138.000 q^{57} +(300.000 + 519.615i) q^{59} +(-116.500 - 201.784i) q^{61} +(9.00000 - 15.5885i) q^{63} +(-292.500 - 303.975i) q^{65} +(463.000 - 801.940i) q^{67} +(9.00000 + 15.5885i) q^{69} +(-465.000 - 805.404i) q^{71} -253.000 q^{73} +(-66.0000 + 114.315i) q^{75} +60.0000 q^{77} +1324.00 q^{79} +(-40.5000 + 70.1481i) q^{81} -810.000 q^{83} +(-499.500 - 865.159i) q^{85} +(-157.500 - 272.798i) q^{87} +(-249.000 + 431.281i) q^{89} +(-26.0000 + 90.0666i) q^{91} +(150.000 - 259.808i) q^{93} +(207.000 + 358.535i) q^{95} +(-679.000 - 1176.06i) q^{97} -270.000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 3 q^{3} - 18 q^{5} + 2 q^{7} - 9 q^{9}+O(q^{10})$$ 2 * q + 3 * q^3 - 18 * q^5 + 2 * q^7 - 9 * q^9 $$2 q + 3 q^{3} - 18 q^{5} + 2 q^{7} - 9 q^{9} + 30 q^{11} + 65 q^{13} - 27 q^{15} + 111 q^{17} - 46 q^{19} + 12 q^{21} - 6 q^{23} - 88 q^{25} - 54 q^{27} + 105 q^{29} + 200 q^{31} - 90 q^{33} - 18 q^{35} - 17 q^{37} + 273 q^{39} + 231 q^{41} - 514 q^{43} + 81 q^{45} + 324 q^{47} + 339 q^{49} + 666 q^{51} + 1278 q^{53} - 270 q^{55} - 276 q^{57} + 600 q^{59} - 233 q^{61} + 18 q^{63} - 585 q^{65} + 926 q^{67} + 18 q^{69} - 930 q^{71} - 506 q^{73} - 132 q^{75} + 120 q^{77} + 2648 q^{79} - 81 q^{81} - 1620 q^{83} - 999 q^{85} - 315 q^{87} - 498 q^{89} - 52 q^{91} + 300 q^{93} + 414 q^{95} - 1358 q^{97} - 540 q^{99}+O(q^{100})$$ 2 * q + 3 * q^3 - 18 * q^5 + 2 * q^7 - 9 * q^9 + 30 * q^11 + 65 * q^13 - 27 * q^15 + 111 * q^17 - 46 * q^19 + 12 * q^21 - 6 * q^23 - 88 * q^25 - 54 * q^27 + 105 * q^29 + 200 * q^31 - 90 * q^33 - 18 * q^35 - 17 * q^37 + 273 * q^39 + 231 * q^41 - 514 * q^43 + 81 * q^45 + 324 * q^47 + 339 * q^49 + 666 * q^51 + 1278 * q^53 - 270 * q^55 - 276 * q^57 + 600 * q^59 - 233 * q^61 + 18 * q^63 - 585 * q^65 + 926 * q^67 + 18 * q^69 - 930 * q^71 - 506 * q^73 - 132 * q^75 + 120 * q^77 + 2648 * q^79 - 81 * q^81 - 1620 * q^83 - 999 * q^85 - 315 * q^87 - 498 * q^89 - 52 * q^91 + 300 * q^93 + 414 * q^95 - 1358 * q^97 - 540 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$$.

 $$n$$ $$79$$ $$145$$ $$209$$ $$469$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 1.50000 2.59808i 0.288675 0.500000i
$$4$$ 0 0
$$5$$ −9.00000 −0.804984 −0.402492 0.915423i $$-0.631856\pi$$
−0.402492 + 0.915423i $$0.631856\pi$$
$$6$$ 0 0
$$7$$ 1.00000 + 1.73205i 0.0539949 + 0.0935220i 0.891760 0.452510i $$-0.149471\pi$$
−0.837765 + 0.546032i $$0.816138\pi$$
$$8$$ 0 0
$$9$$ −4.50000 7.79423i −0.166667 0.288675i
$$10$$ 0 0
$$11$$ 15.0000 25.9808i 0.411152 0.712136i −0.583864 0.811851i $$-0.698460\pi$$
0.995016 + 0.0997155i $$0.0317933\pi$$
$$12$$ 0 0
$$13$$ 32.5000 + 33.7750i 0.693375 + 0.720577i
$$14$$ 0 0
$$15$$ −13.5000 + 23.3827i −0.232379 + 0.402492i
$$16$$ 0 0
$$17$$ 55.5000 + 96.1288i 0.791807 + 1.37145i 0.924847 + 0.380340i $$0.124193\pi$$
−0.133039 + 0.991111i $$0.542474\pi$$
$$18$$ 0 0
$$19$$ −23.0000 39.8372i −0.277714 0.481014i 0.693102 0.720839i $$-0.256243\pi$$
−0.970816 + 0.239825i $$0.922910\pi$$
$$20$$ 0 0
$$21$$ 6.00000 0.0623480
$$22$$ 0 0
$$23$$ −3.00000 + 5.19615i −0.0271975 + 0.0471075i −0.879304 0.476261i $$-0.841992\pi$$
0.852106 + 0.523369i $$0.175325\pi$$
$$24$$ 0 0
$$25$$ −44.0000 −0.352000
$$26$$ 0 0
$$27$$ −27.0000 −0.192450
$$28$$ 0 0
$$29$$ 52.5000 90.9327i 0.336173 0.582268i −0.647537 0.762034i $$-0.724201\pi$$
0.983709 + 0.179766i $$0.0575341\pi$$
$$30$$ 0 0
$$31$$ 100.000 0.579372 0.289686 0.957122i $$-0.406449\pi$$
0.289686 + 0.957122i $$0.406449\pi$$
$$32$$ 0 0
$$33$$ −45.0000 77.9423i −0.237379 0.411152i
$$34$$ 0 0
$$35$$ −9.00000 15.5885i −0.0434651 0.0752837i
$$36$$ 0 0
$$37$$ −8.50000 + 14.7224i −0.0377673 + 0.0654149i −0.884291 0.466936i $$-0.845358\pi$$
0.846524 + 0.532351i $$0.178691\pi$$
$$38$$ 0 0
$$39$$ 136.500 33.7750i 0.560449 0.138675i
$$40$$ 0 0
$$41$$ 115.500 200.052i 0.439953 0.762021i −0.557732 0.830021i $$-0.688328\pi$$
0.997685 + 0.0680000i $$0.0216618\pi$$
$$42$$ 0 0
$$43$$ −257.000 445.137i −0.911445 1.57867i −0.812024 0.583623i $$-0.801634\pi$$
−0.0994205 0.995046i $$-0.531699\pi$$
$$44$$ 0 0
$$45$$ 40.5000 + 70.1481i 0.134164 + 0.232379i
$$46$$ 0 0
$$47$$ 162.000 0.502769 0.251384 0.967887i $$-0.419114\pi$$
0.251384 + 0.967887i $$0.419114\pi$$
$$48$$ 0 0
$$49$$ 169.500 293.583i 0.494169 0.855926i
$$50$$ 0 0
$$51$$ 333.000 0.914301
$$52$$ 0 0
$$53$$ 639.000 1.65610 0.828051 0.560653i $$-0.189450\pi$$
0.828051 + 0.560653i $$0.189450\pi$$
$$54$$ 0 0
$$55$$ −135.000 + 233.827i −0.330971 + 0.573258i
$$56$$ 0 0
$$57$$ −138.000 −0.320676
$$58$$ 0 0
$$59$$ 300.000 + 519.615i 0.661978 + 1.14658i 0.980095 + 0.198527i $$0.0636159\pi$$
−0.318118 + 0.948051i $$0.603051\pi$$
$$60$$ 0 0
$$61$$ −116.500 201.784i −0.244529 0.423537i 0.717470 0.696590i $$-0.245300\pi$$
−0.961999 + 0.273052i $$0.911967\pi$$
$$62$$ 0 0
$$63$$ 9.00000 15.5885i 0.0179983 0.0311740i
$$64$$ 0 0
$$65$$ −292.500 303.975i −0.558156 0.580053i
$$66$$ 0 0
$$67$$ 463.000 801.940i 0.844246 1.46228i −0.0420292 0.999116i $$-0.513382\pi$$
0.886275 0.463160i $$-0.153284\pi$$
$$68$$ 0 0
$$69$$ 9.00000 + 15.5885i 0.0157025 + 0.0271975i
$$70$$ 0 0
$$71$$ −465.000 805.404i −0.777258 1.34625i −0.933516 0.358535i $$-0.883276\pi$$
0.156258 0.987716i $$-0.450057\pi$$
$$72$$ 0 0
$$73$$ −253.000 −0.405636 −0.202818 0.979216i $$-0.565010\pi$$
−0.202818 + 0.979216i $$0.565010\pi$$
$$74$$ 0 0
$$75$$ −66.0000 + 114.315i −0.101614 + 0.176000i
$$76$$ 0 0
$$77$$ 60.0000 0.0888004
$$78$$ 0 0
$$79$$ 1324.00 1.88559 0.942795 0.333373i $$-0.108187\pi$$
0.942795 + 0.333373i $$0.108187\pi$$
$$80$$ 0 0
$$81$$ −40.5000 + 70.1481i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ −810.000 −1.07119 −0.535597 0.844474i $$-0.679913\pi$$
−0.535597 + 0.844474i $$0.679913\pi$$
$$84$$ 0 0
$$85$$ −499.500 865.159i −0.637393 1.10400i
$$86$$ 0 0
$$87$$ −157.500 272.798i −0.194089 0.336173i
$$88$$ 0 0
$$89$$ −249.000 + 431.281i −0.296561 + 0.513659i −0.975347 0.220677i $$-0.929173\pi$$
0.678786 + 0.734336i $$0.262507\pi$$
$$90$$ 0 0
$$91$$ −26.0000 + 90.0666i −0.0299510 + 0.103753i
$$92$$ 0 0
$$93$$ 150.000 259.808i 0.167250 0.289686i
$$94$$ 0 0
$$95$$ 207.000 + 358.535i 0.223555 + 0.387209i
$$96$$ 0 0
$$97$$ −679.000 1176.06i −0.710742 1.23104i −0.964579 0.263795i $$-0.915026\pi$$
0.253837 0.967247i $$-0.418307\pi$$
$$98$$ 0 0
$$99$$ −270.000 −0.274101
$$100$$ 0 0
$$101$$ 178.500 309.171i 0.175856 0.304591i −0.764601 0.644503i $$-0.777064\pi$$
0.940457 + 0.339913i $$0.110397\pi$$
$$102$$ 0 0
$$103$$ −1118.00 −1.06951 −0.534756 0.845006i $$-0.679597\pi$$
−0.534756 + 0.845006i $$0.679597\pi$$
$$104$$ 0 0
$$105$$ −54.0000 −0.0501891
$$106$$ 0 0
$$107$$ 357.000 618.342i 0.322547 0.558667i −0.658466 0.752610i $$-0.728794\pi$$
0.981013 + 0.193943i $$0.0621277\pi$$
$$108$$ 0 0
$$109$$ 2006.00 1.76275 0.881376 0.472416i $$-0.156618\pi$$
0.881376 + 0.472416i $$0.156618\pi$$
$$110$$ 0 0
$$111$$ 25.5000 + 44.1673i 0.0218050 + 0.0377673i
$$112$$ 0 0
$$113$$ 559.500 + 969.082i 0.465782 + 0.806758i 0.999236 0.0390710i $$-0.0124399\pi$$
−0.533455 + 0.845829i $$0.679107\pi$$
$$114$$ 0 0
$$115$$ 27.0000 46.7654i 0.0218936 0.0379208i
$$116$$ 0 0
$$117$$ 117.000 405.300i 0.0924500 0.320256i
$$118$$ 0 0
$$119$$ −111.000 + 192.258i −0.0855072 + 0.148103i
$$120$$ 0 0
$$121$$ 215.500 + 373.257i 0.161908 + 0.280433i
$$122$$ 0 0
$$123$$ −346.500 600.156i −0.254007 0.439953i
$$124$$ 0 0
$$125$$ 1521.00 1.08834
$$126$$ 0 0
$$127$$ −302.000 + 523.079i −0.211009 + 0.365479i −0.952031 0.306003i $$-0.901008\pi$$
0.741021 + 0.671481i $$0.234342\pi$$
$$128$$ 0 0
$$129$$ −1542.00 −1.05245
$$130$$ 0 0
$$131$$ 1584.00 1.05645 0.528224 0.849105i $$-0.322858\pi$$
0.528224 + 0.849105i $$0.322858\pi$$
$$132$$ 0 0
$$133$$ 46.0000 79.6743i 0.0299903 0.0519447i
$$134$$ 0 0
$$135$$ 243.000 0.154919
$$136$$ 0 0
$$137$$ −358.500 620.940i −0.223567 0.387230i 0.732321 0.680959i $$-0.238437\pi$$
−0.955889 + 0.293729i $$0.905104\pi$$
$$138$$ 0 0
$$139$$ −410.000 710.141i −0.250185 0.433334i 0.713391 0.700766i $$-0.247158\pi$$
−0.963577 + 0.267432i $$0.913825\pi$$
$$140$$ 0 0
$$141$$ 243.000 420.888i 0.145137 0.251384i
$$142$$ 0 0
$$143$$ 1365.00 337.750i 0.798231 0.197511i
$$144$$ 0 0
$$145$$ −472.500 + 818.394i −0.270614 + 0.468717i
$$146$$ 0 0
$$147$$ −508.500 880.748i −0.285309 0.494169i
$$148$$ 0 0
$$149$$ 874.500 + 1514.68i 0.480818 + 0.832801i 0.999758 0.0220100i $$-0.00700656\pi$$
−0.518940 + 0.854811i $$0.673673\pi$$
$$150$$ 0 0
$$151$$ 370.000 0.199405 0.0997026 0.995017i $$-0.468211\pi$$
0.0997026 + 0.995017i $$0.468211\pi$$
$$152$$ 0 0
$$153$$ 499.500 865.159i 0.263936 0.457150i
$$154$$ 0 0
$$155$$ −900.000 −0.466385
$$156$$ 0 0
$$157$$ −2611.00 −1.32726 −0.663632 0.748059i $$-0.730986\pi$$
−0.663632 + 0.748059i $$0.730986\pi$$
$$158$$ 0 0
$$159$$ 958.500 1660.17i 0.478075 0.828051i
$$160$$ 0 0
$$161$$ −12.0000 −0.00587411
$$162$$ 0 0
$$163$$ −818.000 1416.82i −0.393072 0.680820i 0.599781 0.800164i $$-0.295254\pi$$
−0.992853 + 0.119344i $$0.961921\pi$$
$$164$$ 0 0
$$165$$ 405.000 + 701.481i 0.191086 + 0.330971i
$$166$$ 0 0
$$167$$ 132.000 228.631i 0.0611645 0.105940i −0.833822 0.552034i $$-0.813852\pi$$
0.894986 + 0.446094i $$0.147185\pi$$
$$168$$ 0 0
$$169$$ −84.5000 + 2195.37i −0.0384615 + 0.999260i
$$170$$ 0 0
$$171$$ −207.000 + 358.535i −0.0925713 + 0.160338i
$$172$$ 0 0
$$173$$ −705.000 1221.10i −0.309827 0.536637i 0.668497 0.743715i $$-0.266938\pi$$
−0.978324 + 0.207078i $$0.933605\pi$$
$$174$$ 0 0
$$175$$ −44.0000 76.2102i −0.0190062 0.0329197i
$$176$$ 0 0
$$177$$ 1800.00 0.764386
$$178$$ 0 0
$$179$$ −237.000 + 410.496i −0.0989621 + 0.171407i −0.911255 0.411842i $$-0.864886\pi$$
0.812293 + 0.583249i $$0.198219\pi$$
$$180$$ 0 0
$$181$$ 2249.00 0.923574 0.461787 0.886991i $$-0.347208\pi$$
0.461787 + 0.886991i $$0.347208\pi$$
$$182$$ 0 0
$$183$$ −699.000 −0.282358
$$184$$ 0 0
$$185$$ 76.5000 132.502i 0.0304021 0.0526580i
$$186$$ 0 0
$$187$$ 3330.00 1.30221
$$188$$ 0 0
$$189$$ −27.0000 46.7654i −0.0103913 0.0179983i
$$190$$ 0 0
$$191$$ 1722.00 + 2982.59i 0.652354 + 1.12991i 0.982550 + 0.185997i $$0.0595516\pi$$
−0.330197 + 0.943912i $$0.607115\pi$$
$$192$$ 0 0
$$193$$ 2136.50 3700.53i 0.796832 1.38015i −0.124837 0.992177i $$-0.539841\pi$$
0.921669 0.387977i $$-0.126826\pi$$
$$194$$ 0 0
$$195$$ −1228.50 + 303.975i −0.451152 + 0.111631i
$$196$$ 0 0
$$197$$ 993.000 1719.93i 0.359129 0.622029i −0.628687 0.777658i $$-0.716407\pi$$
0.987815 + 0.155630i $$0.0497406\pi$$
$$198$$ 0 0
$$199$$ −1193.00 2066.34i −0.424973 0.736074i 0.571445 0.820640i $$-0.306383\pi$$
−0.996418 + 0.0845661i $$0.973050\pi$$
$$200$$ 0 0
$$201$$ −1389.00 2405.82i −0.487425 0.844246i
$$202$$ 0 0
$$203$$ 210.000 0.0726065
$$204$$ 0 0
$$205$$ −1039.50 + 1800.47i −0.354155 + 0.613415i
$$206$$ 0 0
$$207$$ 54.0000 0.0181317
$$208$$ 0 0
$$209$$ −1380.00 −0.456730
$$210$$ 0 0
$$211$$ −800.000 + 1385.64i −0.261016 + 0.452092i −0.966512 0.256621i $$-0.917391\pi$$
0.705497 + 0.708713i $$0.250724\pi$$
$$212$$ 0 0
$$213$$ −2790.00 −0.897501
$$214$$ 0 0
$$215$$ 2313.00 + 4006.23i 0.733699 + 1.27080i
$$216$$ 0 0
$$217$$ 100.000 + 173.205i 0.0312831 + 0.0541840i
$$218$$ 0 0
$$219$$ −379.500 + 657.313i −0.117097 + 0.202818i
$$220$$ 0 0
$$221$$ −1443.00 + 4998.70i −0.439216 + 1.52149i
$$222$$ 0 0
$$223$$ −1916.00 + 3318.61i −0.575358 + 0.996549i 0.420645 + 0.907226i $$0.361804\pi$$
−0.996003 + 0.0893239i $$0.971529\pi$$
$$224$$ 0 0
$$225$$ 198.000 + 342.946i 0.0586667 + 0.101614i
$$226$$ 0 0
$$227$$ −699.000 1210.70i −0.204380 0.353997i 0.745555 0.666444i $$-0.232184\pi$$
−0.949935 + 0.312448i $$0.898851\pi$$
$$228$$ 0 0
$$229$$ 4466.00 1.28874 0.644370 0.764714i $$-0.277120\pi$$
0.644370 + 0.764714i $$0.277120\pi$$
$$230$$ 0 0
$$231$$ 90.0000 155.885i 0.0256345 0.0444002i
$$232$$ 0 0
$$233$$ −1638.00 −0.460553 −0.230277 0.973125i $$-0.573963\pi$$
−0.230277 + 0.973125i $$0.573963\pi$$
$$234$$ 0 0
$$235$$ −1458.00 −0.404721
$$236$$ 0 0
$$237$$ 1986.00 3439.85i 0.544323 0.942795i
$$238$$ 0 0
$$239$$ 594.000 0.160764 0.0803821 0.996764i $$-0.474386\pi$$
0.0803821 + 0.996764i $$0.474386\pi$$
$$240$$ 0 0
$$241$$ −1151.50 1994.46i −0.307779 0.533088i 0.670098 0.742273i $$-0.266252\pi$$
−0.977876 + 0.209185i $$0.932919\pi$$
$$242$$ 0 0
$$243$$ 121.500 + 210.444i 0.0320750 + 0.0555556i
$$244$$ 0 0
$$245$$ −1525.50 + 2642.24i −0.397798 + 0.689007i
$$246$$ 0 0
$$247$$ 598.000 2071.53i 0.154048 0.533638i
$$248$$ 0 0
$$249$$ −1215.00 + 2104.44i −0.309227 + 0.535597i
$$250$$ 0 0
$$251$$ 3162.00 + 5476.74i 0.795154 + 1.37725i 0.922741 + 0.385420i $$0.125943\pi$$
−0.127587 + 0.991827i $$0.540723\pi$$
$$252$$ 0 0
$$253$$ 90.0000 + 155.885i 0.0223646 + 0.0387367i
$$254$$ 0 0
$$255$$ −2997.00 −0.735998
$$256$$ 0 0
$$257$$ −3916.50 + 6783.58i −0.950601 + 1.64649i −0.206474 + 0.978452i $$0.566199\pi$$
−0.744127 + 0.668038i $$0.767134\pi$$
$$258$$ 0 0
$$259$$ −34.0000 −0.00815698
$$260$$ 0 0
$$261$$ −945.000 −0.224115
$$262$$ 0 0
$$263$$ −1515.00 + 2624.06i −0.355205 + 0.615233i −0.987153 0.159778i $$-0.948922\pi$$
0.631948 + 0.775011i $$0.282256\pi$$
$$264$$ 0 0
$$265$$ −5751.00 −1.33314
$$266$$ 0 0
$$267$$ 747.000 + 1293.84i 0.171220 + 0.296561i
$$268$$ 0 0
$$269$$ 267.000 + 462.458i 0.0605178 + 0.104820i 0.894697 0.446674i $$-0.147391\pi$$
−0.834179 + 0.551493i $$0.814058\pi$$
$$270$$ 0 0
$$271$$ −1844.00 + 3193.90i −0.413340 + 0.715925i −0.995253 0.0973259i $$-0.968971\pi$$
0.581913 + 0.813251i $$0.302304\pi$$
$$272$$ 0 0
$$273$$ 195.000 + 202.650i 0.0432305 + 0.0449265i
$$274$$ 0 0
$$275$$ −660.000 + 1143.15i −0.144725 + 0.250672i
$$276$$ 0 0
$$277$$ −932.500 1615.14i −0.202269 0.350340i 0.746990 0.664835i $$-0.231498\pi$$
−0.949259 + 0.314495i $$0.898165\pi$$
$$278$$ 0 0
$$279$$ −450.000 779.423i −0.0965620 0.167250i
$$280$$ 0 0
$$281$$ 2997.00 0.636249 0.318125 0.948049i $$-0.396947\pi$$
0.318125 + 0.948049i $$0.396947\pi$$
$$282$$ 0 0
$$283$$ −2057.00 + 3562.83i −0.432071 + 0.748368i −0.997051 0.0767359i $$-0.975550\pi$$
0.564981 + 0.825104i $$0.308884\pi$$
$$284$$ 0 0
$$285$$ 1242.00 0.258139
$$286$$ 0 0
$$287$$ 462.000 0.0950209
$$288$$ 0 0
$$289$$ −3704.00 + 6415.52i −0.753918 + 1.30582i
$$290$$ 0 0
$$291$$ −4074.00 −0.820695
$$292$$ 0 0
$$293$$ 2332.50 + 4040.01i 0.465072 + 0.805528i 0.999205 0.0398722i $$-0.0126951\pi$$
−0.534133 + 0.845401i $$0.679362\pi$$
$$294$$ 0 0
$$295$$ −2700.00 4676.54i −0.532882 0.922978i
$$296$$ 0 0
$$297$$ −405.000 + 701.481i −0.0791262 + 0.137051i
$$298$$ 0 0
$$299$$ −273.000 + 67.5500i −0.0528027 + 0.0130653i
$$300$$ 0 0
$$301$$ 514.000 890.274i 0.0984268 0.170480i
$$302$$ 0 0
$$303$$ −535.500 927.513i −0.101530 0.175856i
$$304$$ 0 0
$$305$$ 1048.50 + 1816.06i 0.196842 + 0.340941i
$$306$$ 0 0
$$307$$ −1502.00 −0.279230 −0.139615 0.990206i $$-0.544587\pi$$
−0.139615 + 0.990206i $$0.544587\pi$$
$$308$$ 0 0
$$309$$ −1677.00 + 2904.65i −0.308742 + 0.534756i
$$310$$ 0 0
$$311$$ −2106.00 −0.383988 −0.191994 0.981396i $$-0.561495\pi$$
−0.191994 + 0.981396i $$0.561495\pi$$
$$312$$ 0 0
$$313$$ −3898.00 −0.703923 −0.351962 0.936014i $$-0.614485\pi$$
−0.351962 + 0.936014i $$0.614485\pi$$
$$314$$ 0 0
$$315$$ −81.0000 + 140.296i −0.0144884 + 0.0250946i
$$316$$ 0 0
$$317$$ 9351.00 1.65680 0.828398 0.560140i $$-0.189253\pi$$
0.828398 + 0.560140i $$0.189253\pi$$
$$318$$ 0 0
$$319$$ −1575.00 2727.98i −0.276436 0.478801i
$$320$$ 0 0
$$321$$ −1071.00 1855.03i −0.186222 0.322547i
$$322$$ 0 0
$$323$$ 2553.00 4421.93i 0.439792 0.761742i
$$324$$ 0 0
$$325$$ −1430.00 1486.10i −0.244068 0.253643i
$$326$$ 0 0
$$327$$ 3009.00 5211.74i 0.508863 0.881376i
$$328$$ 0 0
$$329$$ 162.000 + 280.592i 0.0271470 + 0.0470199i
$$330$$ 0 0
$$331$$ −4586.00 7943.19i −0.761539 1.31902i −0.942057 0.335452i $$-0.891111\pi$$
0.180518 0.983572i $$-0.442222\pi$$
$$332$$ 0 0
$$333$$ 153.000 0.0251782
$$334$$ 0 0
$$335$$ −4167.00 + 7217.46i −0.679605 + 1.17711i
$$336$$ 0 0
$$337$$ −11089.0 −1.79245 −0.896226 0.443598i $$-0.853702\pi$$
−0.896226 + 0.443598i $$0.853702\pi$$
$$338$$ 0 0
$$339$$ 3357.00 0.537838
$$340$$ 0 0
$$341$$ 1500.00 2598.08i 0.238210 0.412592i
$$342$$ 0 0
$$343$$ 1364.00 0.214720
$$344$$ 0 0
$$345$$ −81.0000 140.296i −0.0126403 0.0218936i
$$346$$ 0 0
$$347$$ 4881.00 + 8454.14i 0.755118 + 1.30790i 0.945316 + 0.326156i $$0.105754\pi$$
−0.190198 + 0.981746i $$0.560913\pi$$
$$348$$ 0 0
$$349$$ 4145.00 7179.35i 0.635750 1.10115i −0.350606 0.936523i $$-0.614024\pi$$
0.986356 0.164628i $$-0.0526424\pi$$
$$350$$ 0 0
$$351$$ −877.500 911.925i −0.133440 0.138675i
$$352$$ 0 0
$$353$$ −6202.50 + 10743.0i −0.935200 + 1.61981i −0.160924 + 0.986967i $$0.551448\pi$$
−0.774276 + 0.632848i $$0.781886\pi$$
$$354$$ 0 0
$$355$$ 4185.00 + 7248.63i 0.625681 + 1.08371i
$$356$$ 0 0
$$357$$ 333.000 + 576.773i 0.0493676 + 0.0855072i
$$358$$ 0 0
$$359$$ 1098.00 0.161421 0.0807106 0.996738i $$-0.474281\pi$$
0.0807106 + 0.996738i $$0.474281\pi$$
$$360$$ 0 0
$$361$$ 2371.50 4107.56i 0.345750 0.598857i
$$362$$ 0 0
$$363$$ 1293.00 0.186956
$$364$$ 0 0
$$365$$ 2277.00 0.326530
$$366$$ 0 0
$$367$$ −2867.00 + 4965.79i −0.407783 + 0.706300i −0.994641 0.103390i $$-0.967031\pi$$
0.586858 + 0.809690i $$0.300365\pi$$
$$368$$ 0 0
$$369$$ −2079.00 −0.293302
$$370$$ 0 0
$$371$$ 639.000 + 1106.78i 0.0894211 + 0.154882i
$$372$$ 0 0
$$373$$ 4485.50 + 7769.11i 0.622655 + 1.07847i 0.988989 + 0.147987i $$0.0472794\pi$$
−0.366334 + 0.930483i $$0.619387\pi$$
$$374$$ 0 0
$$375$$ 2281.50 3951.67i 0.314176 0.544170i
$$376$$ 0 0
$$377$$ 4777.50 1182.12i 0.652663 0.161492i
$$378$$ 0 0
$$379$$ 3622.00 6273.49i 0.490896 0.850257i −0.509049 0.860738i $$-0.670003\pi$$
0.999945 + 0.0104805i $$0.00333611\pi$$
$$380$$ 0 0
$$381$$ 906.000 + 1569.24i 0.121826 + 0.211009i
$$382$$ 0 0
$$383$$ −3156.00 5466.35i −0.421055 0.729289i 0.574988 0.818162i $$-0.305007\pi$$
−0.996043 + 0.0888732i $$0.971673\pi$$
$$384$$ 0 0
$$385$$ −540.000 −0.0714830
$$386$$ 0 0
$$387$$ −2313.00 + 4006.23i −0.303815 + 0.526223i
$$388$$ 0 0
$$389$$ 3627.00 0.472741 0.236370 0.971663i $$-0.424042\pi$$
0.236370 + 0.971663i $$0.424042\pi$$
$$390$$ 0 0
$$391$$ −666.000 −0.0861408
$$392$$ 0 0
$$393$$ 2376.00 4115.35i 0.304970 0.528224i
$$394$$ 0 0
$$395$$ −11916.0 −1.51787
$$396$$ 0 0
$$397$$ 1949.00 + 3375.77i 0.246392 + 0.426763i 0.962522 0.271204i $$-0.0874217\pi$$
−0.716130 + 0.697967i $$0.754088\pi$$
$$398$$ 0 0
$$399$$ −138.000 239.023i −0.0173149 0.0299903i
$$400$$ 0 0
$$401$$ 2851.50 4938.94i 0.355105 0.615060i −0.632031 0.774943i $$-0.717778\pi$$
0.987136 + 0.159883i $$0.0511118\pi$$
$$402$$ 0 0
$$403$$ 3250.00 + 3377.50i 0.401722 + 0.417482i
$$404$$ 0 0
$$405$$ 364.500 631.333i 0.0447214 0.0774597i
$$406$$ 0 0
$$407$$ 255.000 + 441.673i 0.0310562 + 0.0537909i
$$408$$ 0 0
$$409$$ −3155.50 5465.49i −0.381490 0.660760i 0.609785 0.792567i $$-0.291256\pi$$
−0.991275 + 0.131806i $$0.957922\pi$$
$$410$$ 0 0
$$411$$ −2151.00 −0.258153
$$412$$ 0 0
$$413$$ −600.000 + 1039.23i −0.0714869 + 0.123819i
$$414$$ 0 0
$$415$$ 7290.00 0.862294
$$416$$ 0 0
$$417$$ −2460.00 −0.288889
$$418$$ 0 0
$$419$$ −1164.00 + 2016.11i −0.135716 + 0.235067i −0.925871 0.377840i $$-0.876667\pi$$
0.790155 + 0.612908i $$0.210000\pi$$
$$420$$ 0 0
$$421$$ 2045.00 0.236739 0.118370 0.992970i $$-0.462233\pi$$
0.118370 + 0.992970i $$0.462233\pi$$
$$422$$ 0 0
$$423$$ −729.000 1262.67i −0.0837948 0.145137i
$$424$$ 0 0
$$425$$ −2442.00 4229.67i −0.278716 0.482751i
$$426$$ 0 0
$$427$$ 233.000 403.568i 0.0264067 0.0457377i
$$428$$ 0 0
$$429$$ 1170.00 4053.00i 0.131674 0.456132i
$$430$$ 0 0
$$431$$ 2517.00 4359.57i 0.281298 0.487223i −0.690406 0.723422i $$-0.742568\pi$$
0.971705 + 0.236199i $$0.0759016\pi$$
$$432$$ 0 0
$$433$$ −2141.50 3709.19i −0.237676 0.411668i 0.722371 0.691506i $$-0.243052\pi$$
−0.960047 + 0.279838i $$0.909719\pi$$
$$434$$ 0 0
$$435$$ 1417.50 + 2455.18i 0.156239 + 0.270614i
$$436$$ 0 0
$$437$$ 276.000 0.0302125
$$438$$ 0 0
$$439$$ −653.000 + 1131.03i −0.0709931 + 0.122964i −0.899337 0.437257i $$-0.855950\pi$$
0.828344 + 0.560220i $$0.189284\pi$$
$$440$$ 0 0
$$441$$ −3051.00 −0.329446
$$442$$ 0 0
$$443$$ 5796.00 0.621617 0.310808 0.950473i $$-0.399400\pi$$
0.310808 + 0.950473i $$0.399400\pi$$
$$444$$ 0 0
$$445$$ 2241.00 3881.53i 0.238727 0.413488i
$$446$$ 0 0
$$447$$ 5247.00 0.555200
$$448$$ 0 0
$$449$$ −1353.00 2343.46i −0.142209 0.246314i 0.786119 0.618075i $$-0.212087\pi$$
−0.928328 + 0.371761i $$0.878754\pi$$
$$450$$ 0 0
$$451$$ −3465.00 6001.56i −0.361775 0.626612i
$$452$$ 0 0
$$453$$ 555.000 961.288i 0.0575633 0.0997026i
$$454$$ 0 0
$$455$$ 234.000 810.600i 0.0241101 0.0835198i
$$456$$ 0 0
$$457$$ 414.500 717.935i 0.0424278 0.0734871i −0.844032 0.536293i $$-0.819824\pi$$
0.886459 + 0.462806i $$0.153157\pi$$
$$458$$ 0 0
$$459$$ −1498.50 2595.48i −0.152383 0.263936i
$$460$$ 0 0
$$461$$ 2746.50 + 4757.08i 0.277478 + 0.480606i 0.970757 0.240063i $$-0.0771682\pi$$
−0.693279 + 0.720669i $$0.743835\pi$$
$$462$$ 0 0
$$463$$ 15346.0 1.54037 0.770183 0.637823i $$-0.220165\pi$$
0.770183 + 0.637823i $$0.220165\pi$$
$$464$$ 0 0
$$465$$ −1350.00 + 2338.27i −0.134634 + 0.233193i
$$466$$ 0 0
$$467$$ 9594.00 0.950658 0.475329 0.879808i $$-0.342329\pi$$
0.475329 + 0.879808i $$0.342329\pi$$
$$468$$ 0 0
$$469$$ 1852.00 0.182340
$$470$$ 0 0
$$471$$ −3916.50 + 6783.58i −0.383148 + 0.663632i
$$472$$ 0 0
$$473$$ −15420.0 −1.49897
$$474$$ 0 0
$$475$$ 1012.00 + 1752.84i 0.0977553 + 0.169317i
$$476$$ 0 0
$$477$$ −2875.50 4980.51i −0.276017 0.478075i
$$478$$ 0 0
$$479$$ −6420.00 + 11119.8i −0.612395 + 1.06070i 0.378440 + 0.925626i $$0.376461\pi$$
−0.990836 + 0.135074i $$0.956873\pi$$
$$480$$ 0 0
$$481$$ −773.500 + 191.392i −0.0733234 + 0.0181428i
$$482$$ 0 0
$$483$$ −18.0000 + 31.1769i −0.00169571 + 0.00293706i
$$484$$ 0 0
$$485$$ 6111.00 + 10584.6i 0.572137 + 0.990970i
$$486$$ 0 0
$$487$$ −7043.00 12198.8i −0.655336 1.13508i −0.981809 0.189869i $$-0.939194\pi$$
0.326473 0.945207i $$-0.394140\pi$$
$$488$$ 0 0
$$489$$ −4908.00 −0.453880
$$490$$ 0 0
$$491$$ 5847.00 10127.3i 0.537416 0.930832i −0.461626 0.887075i $$-0.652734\pi$$
0.999042 0.0437577i $$-0.0139329\pi$$
$$492$$ 0 0
$$493$$ 11655.0 1.06474
$$494$$ 0 0
$$495$$ 2430.00 0.220647
$$496$$ 0 0
$$497$$ 930.000 1610.81i 0.0839360 0.145381i
$$498$$ 0 0
$$499$$ 3688.00 0.330857 0.165428 0.986222i $$-0.447099\pi$$
0.165428 + 0.986222i $$0.447099\pi$$
$$500$$ 0 0
$$501$$ −396.000 685.892i −0.0353133 0.0611645i
$$502$$ 0 0
$$503$$ −2373.00 4110.16i −0.210352 0.364340i 0.741473 0.670983i $$-0.234128\pi$$
−0.951825 + 0.306643i $$0.900794\pi$$
$$504$$ 0 0
$$505$$ −1606.50 + 2782.54i −0.141561 + 0.245191i
$$506$$ 0 0
$$507$$ 5577.00 + 3512.60i 0.488527 + 0.307692i
$$508$$ 0 0
$$509$$ 7252.50 12561.7i 0.631555 1.09389i −0.355679 0.934608i $$-0.615750\pi$$
0.987234 0.159277i $$-0.0509163\pi$$
$$510$$ 0 0
$$511$$ −253.000 438.209i −0.0219023 0.0379358i
$$512$$ 0 0
$$513$$ 621.000 + 1075.60i 0.0534460 + 0.0925713i
$$514$$ 0 0
$$515$$ 10062.0 0.860941
$$516$$ 0 0
$$517$$ 2430.00 4208.88i 0.206714 0.358040i
$$518$$ 0 0
$$519$$ −4230.00 −0.357758
$$520$$ 0 0
$$521$$ 5085.00 0.427597 0.213798 0.976878i $$-0.431416\pi$$
0.213798 + 0.976878i $$0.431416\pi$$
$$522$$ 0 0
$$523$$ −5441.00 + 9424.09i −0.454911 + 0.787929i −0.998683 0.0513043i $$-0.983662\pi$$
0.543772 + 0.839233i $$0.316996\pi$$
$$524$$ 0 0
$$525$$ −264.000 −0.0219465
$$526$$ 0 0
$$527$$ 5550.00 + 9612.88i 0.458751 + 0.794580i
$$528$$ 0 0
$$529$$ 6065.50 + 10505.8i 0.498521 + 0.863463i
$$530$$ 0 0
$$531$$ 2700.00 4676.54i 0.220659 0.382193i
$$532$$ 0 0
$$533$$ 10510.5 2600.67i 0.854147 0.211347i
$$534$$ 0 0
$$535$$ −3213.00 + 5565.08i −0.259645 + 0.449718i
$$536$$ 0 0
$$537$$ 711.000 + 1231.49i 0.0571358 + 0.0989621i
$$538$$ 0 0
$$539$$ −5085.00 8807.48i −0.406357 0.703831i
$$540$$ 0 0
$$541$$ −4699.00 −0.373430 −0.186715 0.982414i $$-0.559784\pi$$
−0.186715 + 0.982414i $$0.559784\pi$$
$$542$$ 0 0
$$543$$ 3373.50 5843.07i 0.266613 0.461787i
$$544$$ 0 0
$$545$$ −18054.0 −1.41899
$$546$$ 0 0
$$547$$ −8270.00 −0.646434 −0.323217 0.946325i $$-0.604764\pi$$
−0.323217 + 0.946325i $$0.604764\pi$$
$$548$$ 0 0
$$549$$ −1048.50 + 1816.06i −0.0815098 + 0.141179i
$$550$$ 0 0
$$551$$ −4830.00 −0.373439
$$552$$ 0 0
$$553$$ 1324.00 + 2293.24i 0.101812 + 0.176344i
$$554$$ 0 0
$$555$$ −229.500 397.506i −0.0175527 0.0304021i
$$556$$ 0 0
$$557$$ 11392.5 19732.4i 0.866635 1.50106i 0.00122056 0.999999i $$-0.499611\pi$$
0.865414 0.501057i $$-0.167055\pi$$
$$558$$ 0 0
$$559$$ 6682.00 23147.1i 0.505579 1.75138i
$$560$$ 0 0
$$561$$ 4995.00 8651.59i 0.375916 0.651106i
$$562$$ 0 0
$$563$$ −5964.00 10330.0i −0.446452 0.773278i 0.551700 0.834043i $$-0.313979\pi$$
−0.998152 + 0.0607647i $$0.980646\pi$$
$$564$$ 0 0
$$565$$ −5035.50 8721.74i −0.374947 0.649427i
$$566$$ 0 0
$$567$$ −162.000 −0.0119989
$$568$$ 0 0
$$569$$ 3981.00 6895.29i 0.293308 0.508024i −0.681282 0.732021i $$-0.738577\pi$$
0.974590 + 0.223997i $$0.0719106\pi$$
$$570$$ 0 0
$$571$$ −20618.0 −1.51110 −0.755549 0.655093i $$-0.772630\pi$$
−0.755549 + 0.655093i $$0.772630\pi$$
$$572$$ 0 0
$$573$$ 10332.0 0.753273
$$574$$ 0 0
$$575$$ 132.000 228.631i 0.00957353 0.0165818i
$$576$$ 0 0
$$577$$ −3493.00 −0.252020 −0.126010 0.992029i $$-0.540217\pi$$
−0.126010 + 0.992029i $$0.540217\pi$$
$$578$$ 0 0
$$579$$ −6409.50 11101.6i −0.460051 0.796832i
$$580$$ 0 0
$$581$$ −810.000 1402.96i −0.0578390 0.100180i
$$582$$ 0 0
$$583$$ 9585.00 16601.7i 0.680909 1.17937i
$$584$$ 0 0
$$585$$ −1053.00 + 3647.70i −0.0744208 + 0.257801i
$$586$$ 0 0
$$587$$ 5208.00 9020.52i 0.366196 0.634270i −0.622771 0.782404i $$-0.713993\pi$$
0.988967 + 0.148134i $$0.0473266\pi$$
$$588$$ 0 0
$$589$$ −2300.00 3983.72i −0.160900 0.278686i
$$590$$ 0 0
$$591$$ −2979.00 5159.78i −0.207343 0.359129i
$$592$$ 0 0
$$593$$ 2061.00 0.142724 0.0713618 0.997450i $$-0.477266\pi$$
0.0713618 + 0.997450i $$0.477266\pi$$
$$594$$ 0 0
$$595$$ 999.000 1730.32i 0.0688319 0.119220i
$$596$$ 0 0
$$597$$ −7158.00 −0.490716
$$598$$ 0 0
$$599$$ −12456.0 −0.849647 −0.424823 0.905276i $$-0.639664\pi$$
−0.424823 + 0.905276i $$0.639664\pi$$
$$600$$ 0 0
$$601$$ 390.500 676.366i 0.0265039 0.0459061i −0.852469 0.522777i $$-0.824896\pi$$
0.878973 + 0.476871i $$0.158229\pi$$
$$602$$ 0 0
$$603$$ −8334.00 −0.562830
$$604$$ 0 0
$$605$$ −1939.50 3359.31i −0.130334 0.225745i
$$606$$ 0 0
$$607$$ 9652.00 + 16717.8i 0.645408 + 1.11788i 0.984207 + 0.177021i $$0.0566459\pi$$
−0.338799 + 0.940859i $$0.610021\pi$$
$$608$$ 0 0
$$609$$ 315.000 545.596i 0.0209597 0.0363032i
$$610$$ 0 0
$$611$$ 5265.00 + 5471.55i 0.348607 + 0.362283i
$$612$$ 0 0
$$613$$ −6020.50 + 10427.8i −0.396681 + 0.687072i −0.993314 0.115442i $$-0.963172\pi$$
0.596633 + 0.802514i $$0.296505\pi$$
$$614$$ 0 0
$$615$$ 3118.50 + 5401.40i 0.204472 + 0.354155i
$$616$$ 0 0
$$617$$ −4858.50 8415.17i −0.317011 0.549079i 0.662852 0.748751i $$-0.269346\pi$$
−0.979863 + 0.199671i $$0.936013\pi$$
$$618$$ 0 0
$$619$$ 21040.0 1.36619 0.683093 0.730332i $$-0.260634\pi$$
0.683093 + 0.730332i $$0.260634\pi$$
$$620$$ 0 0
$$621$$ 81.0000 140.296i 0.00523417 0.00906584i
$$622$$ 0 0
$$623$$ −996.000 −0.0640512
$$624$$ 0 0
$$625$$ −8189.00 −0.524096
$$626$$ 0 0
$$627$$ −2070.00 + 3585.35i −0.131847 + 0.228365i
$$628$$ 0 0
$$629$$ −1887.00 −0.119618
$$630$$ 0 0
$$631$$ −2534.00 4389.02i −0.159868 0.276900i 0.774953 0.632019i $$-0.217774\pi$$
−0.934821 + 0.355119i $$0.884440\pi$$
$$632$$ 0 0
$$633$$ 2400.00 + 4156.92i 0.150697 + 0.261016i
$$634$$ 0 0
$$635$$ 2718.00 4707.71i 0.169859 0.294205i
$$636$$ 0 0
$$637$$ 15424.5 3816.57i 0.959405 0.237391i
$$638$$ 0 0
$$639$$ −4185.00 + 7248.63i −0.259086 + 0.448750i
$$640$$ 0 0
$$641$$ −5092.50 8820.47i −0.313794 0.543506i 0.665387 0.746499i $$-0.268267\pi$$
−0.979180 + 0.202992i $$0.934933\pi$$
$$642$$ 0 0
$$643$$ 12964.0 + 22454.3i 0.795101 + 1.37716i 0.922775 + 0.385340i $$0.125916\pi$$
−0.127673 + 0.991816i $$0.540751\pi$$
$$644$$ 0 0
$$645$$ 13878.0 0.847203
$$646$$ 0 0
$$647$$ 11580.0 20057.1i 0.703643 1.21874i −0.263537 0.964649i $$-0.584889\pi$$
0.967179 0.254095i $$-0.0817777\pi$$
$$648$$ 0 0
$$649$$ 18000.0 1.08869
$$650$$ 0 0
$$651$$ 600.000 0.0361227
$$652$$ 0 0
$$653$$ −8313.00 + 14398.5i −0.498182 + 0.862876i −0.999998 0.00209801i $$-0.999332\pi$$
0.501816 + 0.864974i $$0.332666\pi$$
$$654$$ 0 0
$$655$$ −14256.0 −0.850424
$$656$$ 0 0
$$657$$ 1138.50 + 1971.94i 0.0676060 + 0.117097i
$$658$$ 0 0
$$659$$ −7404.00 12824.1i −0.437661 0.758052i 0.559847 0.828596i $$-0.310860\pi$$
−0.997509 + 0.0705440i $$0.977526\pi$$
$$660$$ 0 0
$$661$$ −2426.50 + 4202.82i −0.142784 + 0.247308i −0.928544 0.371223i $$-0.878939\pi$$
0.785760 + 0.618531i $$0.212272\pi$$
$$662$$ 0 0
$$663$$ 10822.5 + 11247.1i 0.633953 + 0.658824i
$$664$$ 0 0
$$665$$ −414.000 + 717.069i −0.0241417 + 0.0418147i
$$666$$ 0 0
$$667$$ 315.000 + 545.596i 0.0182861 + 0.0316725i
$$668$$ 0 0
$$669$$ 5748.00 + 9955.83i 0.332183 + 0.575358i
$$670$$ 0 0
$$671$$ −6990.00 −0.402155
$$672$$ 0 0
$$673$$ 8082.50 13999.3i 0.462938 0.801833i −0.536168 0.844112i $$-0.680128\pi$$
0.999106 + 0.0422789i $$0.0134618\pi$$
$$674$$ 0 0
$$675$$ 1188.00 0.0677424
$$676$$ 0 0
$$677$$ −25686.0 −1.45819 −0.729094 0.684414i $$-0.760058\pi$$
−0.729094 + 0.684414i $$0.760058\pi$$
$$678$$ 0 0
$$679$$ 1358.00 2352.12i 0.0767530 0.132940i
$$680$$ 0 0
$$681$$ −4194.00 −0.235998
$$682$$ 0 0
$$683$$ −9528.00 16503.0i −0.533790 0.924552i −0.999221 0.0394675i $$-0.987434\pi$$
0.465431 0.885084i $$-0.345900\pi$$
$$684$$ 0 0
$$685$$ 3226.50 + 5588.46i 0.179968 + 0.311714i
$$686$$ 0 0
$$687$$ 6699.00 11603.0i 0.372027 0.644370i
$$688$$ 0 0
$$689$$ 20767.5 + 21582.2i 1.14830 + 1.19335i
$$690$$ 0 0
$$691$$ −8195.00 + 14194.2i −0.451161 + 0.781434i −0.998458 0.0555040i $$-0.982323\pi$$
0.547297 + 0.836938i $$0.315657\pi$$
$$692$$ 0 0
$$693$$ −270.000 467.654i −0.0148001 0.0256345i
$$694$$ 0 0
$$695$$ 3690.00 + 6391.27i 0.201395 + 0.348827i
$$696$$ 0 0
$$697$$ 25641.0 1.39343
$$698$$ 0 0
$$699$$ −2457.00 + 4255.65i −0.132950 + 0.230277i
$$700$$ 0 0
$$701$$ −27846.0 −1.50033 −0.750163 0.661253i $$-0.770025\pi$$
−0.750163 + 0.661253i $$0.770025\pi$$
$$702$$ 0 0
$$703$$ 782.000 0.0419540
$$704$$ 0 0
$$705$$ −2187.00 + 3788.00i −0.116833 + 0.202360i
$$706$$ 0 0
$$707$$ 714.000 0.0379812
$$708$$ 0 0
$$709$$ 6141.50 + 10637.4i 0.325316 + 0.563463i 0.981576 0.191071i $$-0.0611961\pi$$
−0.656260 + 0.754534i $$0.727863\pi$$
$$710$$ 0 0
$$711$$ −5958.00 10319.6i −0.314265 0.544323i
$$712$$ 0 0
$$713$$ −300.000 + 519.615i −0.0157575 + 0.0272928i
$$714$$ 0 0
$$715$$ −12285.0 + 3039.75i −0.642564 + 0.158993i
$$716$$ 0 0
$$717$$ 891.000 1543.26i 0.0464087 0.0803821i
$$718$$ 0 0
$$719$$ 12756.0 + 22094.0i 0.661639 + 1.14599i 0.980185 + 0.198085i $$0.0634722\pi$$
−0.318546 + 0.947908i $$0.603194\pi$$
$$720$$ 0 0
$$721$$ −1118.00 1936.43i −0.0577483 0.100023i
$$722$$ 0 0
$$723$$ −6909.00 −0.355392
$$724$$ 0 0
$$725$$ −2310.00 + 4001.04i −0.118333 + 0.204958i
$$726$$ 0 0
$$727$$ −6110.00 −0.311702 −0.155851 0.987781i $$-0.549812\pi$$
−0.155851 + 0.987781i $$0.549812\pi$$
$$728$$ 0 0
$$729$$ 729.000 0.0370370
$$730$$ 0 0
$$731$$ 28527.0 49410.2i 1.44338 2.50000i
$$732$$ 0 0
$$733$$ −27127.0 −1.36693 −0.683464 0.729984i $$-0.739527\pi$$
−0.683464 + 0.729984i $$0.739527\pi$$
$$734$$ 0 0
$$735$$ 4576.50 + 7926.73i 0.229669 + 0.397798i
$$736$$ 0 0
$$737$$ −13890.0 24058.2i −0.694226 1.20244i
$$738$$ 0 0
$$739$$ −440.000 + 762.102i −0.0219021 + 0.0379356i −0.876769 0.480912i $$-0.840306\pi$$
0.854867 + 0.518848i $$0.173639\pi$$
$$740$$ 0 0
$$741$$ −4485.00 4660.95i −0.222349 0.231072i
$$742$$ 0 0
$$743$$ −10938.0 + 18945.2i −0.540076 + 0.935439i 0.458823 + 0.888528i $$0.348271\pi$$
−0.998899 + 0.0469111i $$0.985062\pi$$
$$744$$ 0 0
$$745$$ −7870.50 13632.1i −0.387051 0.670392i
$$746$$ 0 0
$$747$$ 3645.00 + 6313.33i 0.178532 + 0.309227i
$$748$$ 0 0
$$749$$ 1428.00 0.0696635
$$750$$ 0 0
$$751$$ 5899.00 10217.4i 0.286628 0.496454i −0.686375 0.727248i $$-0.740799\pi$$
0.973003 + 0.230794i $$0.0741323\pi$$
$$752$$ 0 0
$$753$$ 18972.0 0.918165
$$754$$ 0 0
$$755$$ −3330.00 −0.160518
$$756$$ 0 0
$$757$$ 4037.00 6992.29i 0.193827 0.335719i −0.752688 0.658377i $$-0.771243\pi$$
0.946515 + 0.322658i $$0.104577\pi$$
$$758$$ 0 0
$$759$$ 540.000 0.0258245
$$760$$ 0 0
$$761$$ −9777.00 16934.3i −0.465724 0.806658i 0.533510 0.845794i $$-0.320873\pi$$
−0.999234 + 0.0391362i $$0.987539\pi$$
$$762$$ 0 0
$$763$$ 2006.00 + 3474.49i 0.0951797 + 0.164856i
$$764$$ 0 0
$$765$$ −4495.50 + 7786.43i −0.212464 + 0.367999i
$$766$$ 0 0
$$767$$ −7800.00 + 27020.0i −0.367199 + 1.27201i
$$768$$ 0 0
$$769$$ −7015.00 + 12150.3i −0.328956 + 0.569769i −0.982305 0.187288i $$-0.940030\pi$$
0.653349 + 0.757057i $$0.273364\pi$$
$$770$$ 0 0
$$771$$ 11749.5 + 20350.7i 0.548830 + 0.950601i
$$772$$ 0 0
$$773$$ −18021.0 31213.3i −0.838513 1.45235i −0.891138 0.453732i $$-0.850092\pi$$
0.0526253 0.998614i $$-0.483241\pi$$
$$774$$ 0 0
$$775$$ −4400.00 −0.203939
$$776$$ 0 0
$$777$$ −51.0000 + 88.3346i −0.00235472 + 0.00407849i
$$778$$ 0 0
$$779$$ −10626.0 −0.488724
$$780$$ 0 0
$$781$$ −27900.0 −1.27828
$$782$$ 0 0
$$783$$ −1417.50 + 2455.18i −0.0646964 + 0.112058i
$$784$$ 0 0
$$785$$ 23499.0 1.06843
$$786$$ 0 0
$$787$$ 14314.0 + 24792.6i 0.648334 + 1.12295i 0.983521 + 0.180796i $$0.0578674\pi$$
−0.335186 + 0.942152i $$0.608799\pi$$
$$788$$ 0 0
$$789$$ 4545.00 + 7872.17i 0.205078 + 0.355205i
$$790$$ 0 0