# Properties

 Label 63.4.e.b.46.1 Level $63$ Weight $4$ Character 63.46 Analytic conductor $3.717$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$63 = 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 63.e (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.71712033036$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 7) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 46.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 63.46 Dual form 63.4.e.b.37.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.00000 + 1.73205i) q^{2} +(2.00000 - 3.46410i) q^{4} +(3.50000 + 6.06218i) q^{5} +(14.0000 + 12.1244i) q^{7} +24.0000 q^{8} +O(q^{10})$$ $$q+(1.00000 + 1.73205i) q^{2} +(2.00000 - 3.46410i) q^{4} +(3.50000 + 6.06218i) q^{5} +(14.0000 + 12.1244i) q^{7} +24.0000 q^{8} +(-7.00000 + 12.1244i) q^{10} +(-2.50000 + 4.33013i) q^{11} -14.0000 q^{13} +(-7.00000 + 36.3731i) q^{14} +(8.00000 + 13.8564i) q^{16} +(-10.5000 + 18.1865i) q^{17} +(-24.5000 - 42.4352i) q^{19} +28.0000 q^{20} -10.0000 q^{22} +(-79.5000 - 137.698i) q^{23} +(38.0000 - 65.8179i) q^{25} +(-14.0000 - 24.2487i) q^{26} +(70.0000 - 24.2487i) q^{28} -58.0000 q^{29} +(-73.5000 + 127.306i) q^{31} +(80.0000 - 138.564i) q^{32} -42.0000 q^{34} +(-24.5000 + 127.306i) q^{35} +(-109.500 - 189.660i) q^{37} +(49.0000 - 84.8705i) q^{38} +(84.0000 + 145.492i) q^{40} -350.000 q^{41} -124.000 q^{43} +(10.0000 + 17.3205i) q^{44} +(159.000 - 275.396i) q^{46} +(262.500 + 454.663i) q^{47} +(49.0000 + 339.482i) q^{49} +152.000 q^{50} +(-28.0000 + 48.4974i) q^{52} +(151.500 - 262.406i) q^{53} -35.0000 q^{55} +(336.000 + 290.985i) q^{56} +(-58.0000 - 100.459i) q^{58} +(-52.5000 + 90.9327i) q^{59} +(206.500 + 357.668i) q^{61} -294.000 q^{62} +448.000 q^{64} +(-49.0000 - 84.8705i) q^{65} +(-207.500 + 359.401i) q^{67} +(42.0000 + 72.7461i) q^{68} +(-245.000 + 84.8705i) q^{70} +432.000 q^{71} +(556.500 - 963.886i) q^{73} +(219.000 - 379.319i) q^{74} -196.000 q^{76} +(-87.5000 + 30.3109i) q^{77} +(51.5000 + 89.2006i) q^{79} +(-56.0000 + 96.9948i) q^{80} +(-350.000 - 606.218i) q^{82} -1092.00 q^{83} -147.000 q^{85} +(-124.000 - 214.774i) q^{86} +(-60.0000 + 103.923i) q^{88} +(-164.500 - 284.922i) q^{89} +(-196.000 - 169.741i) q^{91} -636.000 q^{92} +(-525.000 + 909.327i) q^{94} +(171.500 - 297.047i) q^{95} -882.000 q^{97} +(-539.000 + 424.352i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 2q^{2} + 4q^{4} + 7q^{5} + 28q^{7} + 48q^{8} + O(q^{10})$$ $$2q + 2q^{2} + 4q^{4} + 7q^{5} + 28q^{7} + 48q^{8} - 14q^{10} - 5q^{11} - 28q^{13} - 14q^{14} + 16q^{16} - 21q^{17} - 49q^{19} + 56q^{20} - 20q^{22} - 159q^{23} + 76q^{25} - 28q^{26} + 140q^{28} - 116q^{29} - 147q^{31} + 160q^{32} - 84q^{34} - 49q^{35} - 219q^{37} + 98q^{38} + 168q^{40} - 700q^{41} - 248q^{43} + 20q^{44} + 318q^{46} + 525q^{47} + 98q^{49} + 304q^{50} - 56q^{52} + 303q^{53} - 70q^{55} + 672q^{56} - 116q^{58} - 105q^{59} + 413q^{61} - 588q^{62} + 896q^{64} - 98q^{65} - 415q^{67} + 84q^{68} - 490q^{70} + 864q^{71} + 1113q^{73} + 438q^{74} - 392q^{76} - 175q^{77} + 103q^{79} - 112q^{80} - 700q^{82} - 2184q^{83} - 294q^{85} - 248q^{86} - 120q^{88} - 329q^{89} - 392q^{91} - 1272q^{92} - 1050q^{94} + 343q^{95} - 1764q^{97} - 1078q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$$.

 $$n$$ $$10$$ $$29$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 + 1.73205i 0.353553 + 0.612372i 0.986869 0.161521i $$-0.0516399\pi$$
−0.633316 + 0.773893i $$0.718307\pi$$
$$3$$ 0 0
$$4$$ 2.00000 3.46410i 0.250000 0.433013i
$$5$$ 3.50000 + 6.06218i 0.313050 + 0.542218i 0.979021 0.203760i $$-0.0653161\pi$$
−0.665971 + 0.745977i $$0.731983\pi$$
$$6$$ 0 0
$$7$$ 14.0000 + 12.1244i 0.755929 + 0.654654i
$$8$$ 24.0000 1.06066
$$9$$ 0 0
$$10$$ −7.00000 + 12.1244i −0.221359 + 0.383406i
$$11$$ −2.50000 + 4.33013i −0.0685253 + 0.118689i −0.898252 0.439480i $$-0.855163\pi$$
0.829727 + 0.558169i $$0.188496\pi$$
$$12$$ 0 0
$$13$$ −14.0000 −0.298685 −0.149342 0.988786i $$-0.547716\pi$$
−0.149342 + 0.988786i $$0.547716\pi$$
$$14$$ −7.00000 + 36.3731i −0.133631 + 0.694365i
$$15$$ 0 0
$$16$$ 8.00000 + 13.8564i 0.125000 + 0.216506i
$$17$$ −10.5000 + 18.1865i −0.149801 + 0.259464i −0.931154 0.364626i $$-0.881197\pi$$
0.781353 + 0.624090i $$0.214530\pi$$
$$18$$ 0 0
$$19$$ −24.5000 42.4352i −0.295826 0.512385i 0.679351 0.733813i $$-0.262261\pi$$
−0.975177 + 0.221429i $$0.928928\pi$$
$$20$$ 28.0000 0.313050
$$21$$ 0 0
$$22$$ −10.0000 −0.0969094
$$23$$ −79.5000 137.698i −0.720735 1.24835i −0.960706 0.277569i $$-0.910471\pi$$
0.239971 0.970780i $$-0.422862\pi$$
$$24$$ 0 0
$$25$$ 38.0000 65.8179i 0.304000 0.526543i
$$26$$ −14.0000 24.2487i −0.105601 0.182906i
$$27$$ 0 0
$$28$$ 70.0000 24.2487i 0.472456 0.163663i
$$29$$ −58.0000 −0.371391 −0.185695 0.982607i $$-0.559454\pi$$
−0.185695 + 0.982607i $$0.559454\pi$$
$$30$$ 0 0
$$31$$ −73.5000 + 127.306i −0.425838 + 0.737574i −0.996498 0.0836128i $$-0.973354\pi$$
0.570660 + 0.821186i $$0.306687\pi$$
$$32$$ 80.0000 138.564i 0.441942 0.765466i
$$33$$ 0 0
$$34$$ −42.0000 −0.211851
$$35$$ −24.5000 + 127.306i −0.118322 + 0.614817i
$$36$$ 0 0
$$37$$ −109.500 189.660i −0.486532 0.842698i 0.513348 0.858181i $$-0.328405\pi$$
−0.999880 + 0.0154821i $$0.995072\pi$$
$$38$$ 49.0000 84.8705i 0.209180 0.362311i
$$39$$ 0 0
$$40$$ 84.0000 + 145.492i 0.332039 + 0.575109i
$$41$$ −350.000 −1.33319 −0.666595 0.745420i $$-0.732249\pi$$
−0.666595 + 0.745420i $$0.732249\pi$$
$$42$$ 0 0
$$43$$ −124.000 −0.439763 −0.219882 0.975527i $$-0.570567\pi$$
−0.219882 + 0.975527i $$0.570567\pi$$
$$44$$ 10.0000 + 17.3205i 0.0342627 + 0.0593447i
$$45$$ 0 0
$$46$$ 159.000 275.396i 0.509636 0.882716i
$$47$$ 262.500 + 454.663i 0.814671 + 1.41105i 0.909564 + 0.415565i $$0.136416\pi$$
−0.0948921 + 0.995488i $$0.530251\pi$$
$$48$$ 0 0
$$49$$ 49.0000 + 339.482i 0.142857 + 0.989743i
$$50$$ 152.000 0.429921
$$51$$ 0 0
$$52$$ −28.0000 + 48.4974i −0.0746712 + 0.129334i
$$53$$ 151.500 262.406i 0.392644 0.680079i −0.600153 0.799885i $$-0.704894\pi$$
0.992797 + 0.119806i $$0.0382272\pi$$
$$54$$ 0 0
$$55$$ −35.0000 −0.0858073
$$56$$ 336.000 + 290.985i 0.801784 + 0.694365i
$$57$$ 0 0
$$58$$ −58.0000 100.459i −0.131306 0.227429i
$$59$$ −52.5000 + 90.9327i −0.115846 + 0.200651i −0.918118 0.396308i $$-0.870291\pi$$
0.802272 + 0.596959i $$0.203625\pi$$
$$60$$ 0 0
$$61$$ 206.500 + 357.668i 0.433436 + 0.750734i 0.997167 0.0752252i $$-0.0239676\pi$$
−0.563730 + 0.825959i $$0.690634\pi$$
$$62$$ −294.000 −0.602226
$$63$$ 0 0
$$64$$ 448.000 0.875000
$$65$$ −49.0000 84.8705i −0.0935031 0.161952i
$$66$$ 0 0
$$67$$ −207.500 + 359.401i −0.378361 + 0.655340i −0.990824 0.135159i $$-0.956845\pi$$
0.612463 + 0.790499i $$0.290179\pi$$
$$68$$ 42.0000 + 72.7461i 0.0749007 + 0.129732i
$$69$$ 0 0
$$70$$ −245.000 + 84.8705i −0.418330 + 0.144914i
$$71$$ 432.000 0.722098 0.361049 0.932547i $$-0.382419\pi$$
0.361049 + 0.932547i $$0.382419\pi$$
$$72$$ 0 0
$$73$$ 556.500 963.886i 0.892238 1.54540i 0.0550526 0.998483i $$-0.482467\pi$$
0.837186 0.546919i $$-0.184199\pi$$
$$74$$ 219.000 379.319i 0.344030 0.595878i
$$75$$ 0 0
$$76$$ −196.000 −0.295826
$$77$$ −87.5000 + 30.3109i −0.129501 + 0.0448603i
$$78$$ 0 0
$$79$$ 51.5000 + 89.2006i 0.0733443 + 0.127036i 0.900365 0.435135i $$-0.143299\pi$$
−0.827021 + 0.562171i $$0.809966\pi$$
$$80$$ −56.0000 + 96.9948i −0.0782624 + 0.135554i
$$81$$ 0 0
$$82$$ −350.000 606.218i −0.471354 0.816409i
$$83$$ −1092.00 −1.44413 −0.722064 0.691827i $$-0.756806\pi$$
−0.722064 + 0.691827i $$0.756806\pi$$
$$84$$ 0 0
$$85$$ −147.000 −0.187581
$$86$$ −124.000 214.774i −0.155480 0.269299i
$$87$$ 0 0
$$88$$ −60.0000 + 103.923i −0.0726821 + 0.125889i
$$89$$ −164.500 284.922i −0.195921 0.339345i 0.751281 0.659982i $$-0.229436\pi$$
−0.947202 + 0.320637i $$0.896103\pi$$
$$90$$ 0 0
$$91$$ −196.000 169.741i −0.225784 0.195535i
$$92$$ −636.000 −0.720735
$$93$$ 0 0
$$94$$ −525.000 + 909.327i −0.576060 + 0.997765i
$$95$$ 171.500 297.047i 0.185216 0.320804i
$$96$$ 0 0
$$97$$ −882.000 −0.923232 −0.461616 0.887080i $$-0.652730\pi$$
−0.461616 + 0.887080i $$0.652730\pi$$
$$98$$ −539.000 + 424.352i −0.555584 + 0.437409i
$$99$$ 0 0
$$100$$ −152.000 263.272i −0.152000 0.263272i
$$101$$ 689.500 1194.25i 0.679285 1.17656i −0.295911 0.955215i $$-0.595623\pi$$
0.975196 0.221341i $$-0.0710434\pi$$
$$102$$ 0 0
$$103$$ 339.500 + 588.031i 0.324776 + 0.562529i 0.981467 0.191631i $$-0.0613777\pi$$
−0.656691 + 0.754160i $$0.728044\pi$$
$$104$$ −336.000 −0.316803
$$105$$ 0 0
$$106$$ 606.000 0.555282
$$107$$ 228.500 + 395.774i 0.206448 + 0.357578i 0.950593 0.310440i $$-0.100476\pi$$
−0.744145 + 0.668018i $$0.767143\pi$$
$$108$$ 0 0
$$109$$ 562.500 974.279i 0.494291 0.856137i −0.505687 0.862717i $$-0.668761\pi$$
0.999978 + 0.00657959i $$0.00209436\pi$$
$$110$$ −35.0000 60.6218i −0.0303374 0.0525460i
$$111$$ 0 0
$$112$$ −56.0000 + 290.985i −0.0472456 + 0.245495i
$$113$$ 1538.00 1.28038 0.640190 0.768217i $$-0.278856\pi$$
0.640190 + 0.768217i $$0.278856\pi$$
$$114$$ 0 0
$$115$$ 556.500 963.886i 0.451251 0.781590i
$$116$$ −116.000 + 200.918i −0.0928477 + 0.160817i
$$117$$ 0 0
$$118$$ −210.000 −0.163831
$$119$$ −367.500 + 127.306i −0.283098 + 0.0980680i
$$120$$ 0 0
$$121$$ 653.000 + 1131.03i 0.490609 + 0.849759i
$$122$$ −413.000 + 715.337i −0.306486 + 0.530849i
$$123$$ 0 0
$$124$$ 294.000 + 509.223i 0.212919 + 0.368787i
$$125$$ 1407.00 1.00677
$$126$$ 0 0
$$127$$ 72.0000 0.0503068 0.0251534 0.999684i $$-0.491993\pi$$
0.0251534 + 0.999684i $$0.491993\pi$$
$$128$$ −192.000 332.554i −0.132583 0.229640i
$$129$$ 0 0
$$130$$ 98.0000 169.741i 0.0661167 0.114517i
$$131$$ 1074.50 + 1861.09i 0.716637 + 1.24125i 0.962325 + 0.271903i $$0.0876531\pi$$
−0.245687 + 0.969349i $$0.579014\pi$$
$$132$$ 0 0
$$133$$ 171.500 891.140i 0.111812 0.580990i
$$134$$ −830.000 −0.535083
$$135$$ 0 0
$$136$$ −252.000 + 436.477i −0.158888 + 0.275203i
$$137$$ −562.500 + 974.279i −0.350786 + 0.607578i −0.986387 0.164439i $$-0.947419\pi$$
0.635602 + 0.772017i $$0.280752\pi$$
$$138$$ 0 0
$$139$$ 252.000 0.153772 0.0768862 0.997040i $$-0.475502\pi$$
0.0768862 + 0.997040i $$0.475502\pi$$
$$140$$ 392.000 + 339.482i 0.236643 + 0.204939i
$$141$$ 0 0
$$142$$ 432.000 + 748.246i 0.255300 + 0.442193i
$$143$$ 35.0000 60.6218i 0.0204675 0.0354507i
$$144$$ 0 0
$$145$$ −203.000 351.606i −0.116264 0.201375i
$$146$$ 2226.00 1.26182
$$147$$ 0 0
$$148$$ −876.000 −0.486532
$$149$$ −100.500 174.071i −0.0552569 0.0957078i 0.837074 0.547090i $$-0.184264\pi$$
−0.892331 + 0.451382i $$0.850931\pi$$
$$150$$ 0 0
$$151$$ −809.500 + 1402.10i −0.436266 + 0.755635i −0.997398 0.0720914i $$-0.977033\pi$$
0.561132 + 0.827726i $$0.310366\pi$$
$$152$$ −588.000 1018.45i −0.313770 0.543466i
$$153$$ 0 0
$$154$$ −140.000 121.244i −0.0732566 0.0634421i
$$155$$ −1029.00 −0.533234
$$156$$ 0 0
$$157$$ −339.500 + 588.031i −0.172580 + 0.298917i −0.939321 0.343039i $$-0.888544\pi$$
0.766741 + 0.641956i $$0.221877\pi$$
$$158$$ −103.000 + 178.401i −0.0518623 + 0.0898281i
$$159$$ 0 0
$$160$$ 1120.00 0.553399
$$161$$ 556.500 2891.66i 0.272412 1.41549i
$$162$$ 0 0
$$163$$ 233.500 + 404.434i 0.112203 + 0.194342i 0.916658 0.399672i $$-0.130876\pi$$
−0.804455 + 0.594014i $$0.797543\pi$$
$$164$$ −700.000 + 1212.44i −0.333298 + 0.577288i
$$165$$ 0 0
$$166$$ −1092.00 1891.40i −0.510576 0.884344i
$$167$$ −1204.00 −0.557894 −0.278947 0.960306i $$-0.589985\pi$$
−0.278947 + 0.960306i $$0.589985\pi$$
$$168$$ 0 0
$$169$$ −2001.00 −0.910787
$$170$$ −147.000 254.611i −0.0663199 0.114869i
$$171$$ 0 0
$$172$$ −248.000 + 429.549i −0.109941 + 0.190423i
$$173$$ −1410.50 2443.06i −0.619875 1.07365i −0.989508 0.144477i $$-0.953850\pi$$
0.369633 0.929178i $$-0.379483\pi$$
$$174$$ 0 0
$$175$$ 1330.00 460.726i 0.574506 0.199015i
$$176$$ −80.0000 −0.0342627
$$177$$ 0 0
$$178$$ 329.000 569.845i 0.138537 0.239953i
$$179$$ −1626.50 + 2817.18i −0.679164 + 1.17635i 0.296069 + 0.955166i $$0.404324\pi$$
−0.975233 + 0.221180i $$0.929009\pi$$
$$180$$ 0 0
$$181$$ 1582.00 0.649664 0.324832 0.945772i $$-0.394692\pi$$
0.324832 + 0.945772i $$0.394692\pi$$
$$182$$ 98.0000 509.223i 0.0399134 0.207396i
$$183$$ 0 0
$$184$$ −1908.00 3304.75i −0.764454 1.32407i
$$185$$ 766.500 1327.62i 0.304617 0.527613i
$$186$$ 0 0
$$187$$ −52.5000 90.9327i −0.0205304 0.0355597i
$$188$$ 2100.00 0.814671
$$189$$ 0 0
$$190$$ 686.000 0.261935
$$191$$ 1278.50 + 2214.43i 0.484340 + 0.838902i 0.999838 0.0179887i $$-0.00572630\pi$$
−0.515498 + 0.856891i $$0.672393\pi$$
$$192$$ 0 0
$$193$$ 198.500 343.812i 0.0740329 0.128229i −0.826632 0.562742i $$-0.809746\pi$$
0.900665 + 0.434514i $$0.143080\pi$$
$$194$$ −882.000 1527.67i −0.326412 0.565362i
$$195$$ 0 0
$$196$$ 1274.00 + 509.223i 0.464286 + 0.185577i
$$197$$ −2914.00 −1.05388 −0.526939 0.849903i $$-0.676660\pi$$
−0.526939 + 0.849903i $$0.676660\pi$$
$$198$$ 0 0
$$199$$ −1669.50 + 2891.66i −0.594712 + 1.03007i 0.398875 + 0.917005i $$0.369401\pi$$
−0.993587 + 0.113066i $$0.963933\pi$$
$$200$$ 912.000 1579.63i 0.322441 0.558484i
$$201$$ 0 0
$$202$$ 2758.00 0.960654
$$203$$ −812.000 703.213i −0.280745 0.243132i
$$204$$ 0 0
$$205$$ −1225.00 2121.76i −0.417355 0.722880i
$$206$$ −679.000 + 1176.06i −0.229651 + 0.397768i
$$207$$ 0 0
$$208$$ −112.000 193.990i −0.0373356 0.0646671i
$$209$$ 245.000 0.0810861
$$210$$ 0 0
$$211$$ 1780.00 0.580759 0.290380 0.956911i $$-0.406218\pi$$
0.290380 + 0.956911i $$0.406218\pi$$
$$212$$ −606.000 1049.62i −0.196322 0.340040i
$$213$$ 0 0
$$214$$ −457.000 + 791.547i −0.145981 + 0.252846i
$$215$$ −434.000 751.710i −0.137668 0.238447i
$$216$$ 0 0
$$217$$ −2572.50 + 891.140i −0.804759 + 0.278777i
$$218$$ 2250.00 0.699033
$$219$$ 0 0
$$220$$ −70.0000 + 121.244i −0.0214518 + 0.0371556i
$$221$$ 147.000 254.611i 0.0447434 0.0774978i
$$222$$ 0 0
$$223$$ −1400.00 −0.420408 −0.210204 0.977658i $$-0.567413\pi$$
−0.210204 + 0.977658i $$0.567413\pi$$
$$224$$ 2800.00 969.948i 0.835191 0.289319i
$$225$$ 0 0
$$226$$ 1538.00 + 2663.89i 0.452682 + 0.784069i
$$227$$ −1102.50 + 1909.59i −0.322359 + 0.558342i −0.980974 0.194138i $$-0.937809\pi$$
0.658615 + 0.752480i $$0.271142\pi$$
$$228$$ 0 0
$$229$$ −143.500 248.549i −0.0414094 0.0717231i 0.844578 0.535433i $$-0.179851\pi$$
−0.885987 + 0.463710i $$0.846518\pi$$
$$230$$ 2226.00 0.638166
$$231$$ 0 0
$$232$$ −1392.00 −0.393919
$$233$$ 2293.50 + 3972.46i 0.644859 + 1.11693i 0.984334 + 0.176314i $$0.0564173\pi$$
−0.339475 + 0.940615i $$0.610249\pi$$
$$234$$ 0 0
$$235$$ −1837.50 + 3182.64i −0.510065 + 0.883459i
$$236$$ 210.000 + 363.731i 0.0579230 + 0.100326i
$$237$$ 0 0
$$238$$ −588.000 509.223i −0.160144 0.138689i
$$239$$ −1668.00 −0.451439 −0.225720 0.974192i $$-0.572473\pi$$
−0.225720 + 0.974192i $$0.572473\pi$$
$$240$$ 0 0
$$241$$ 1704.50 2952.28i 0.455587 0.789100i −0.543135 0.839646i $$-0.682763\pi$$
0.998722 + 0.0505456i $$0.0160960\pi$$
$$242$$ −1306.00 + 2262.06i −0.346913 + 0.600870i
$$243$$ 0 0
$$244$$ 1652.00 0.433436
$$245$$ −1886.50 + 1485.23i −0.491935 + 0.387298i
$$246$$ 0 0
$$247$$ 343.000 + 594.093i 0.0883586 + 0.153042i
$$248$$ −1764.00 + 3055.34i −0.451670 + 0.782315i
$$249$$ 0 0
$$250$$ 1407.00 + 2437.00i 0.355946 + 0.616517i
$$251$$ 4760.00 1.19701 0.598503 0.801121i $$-0.295762\pi$$
0.598503 + 0.801121i $$0.295762\pi$$
$$252$$ 0 0
$$253$$ 795.000 0.197554
$$254$$ 72.0000 + 124.708i 0.0177861 + 0.0308065i
$$255$$ 0 0
$$256$$ 2176.00 3768.94i 0.531250 0.920152i
$$257$$ −402.500 697.150i −0.0976936 0.169210i 0.813036 0.582213i $$-0.197813\pi$$
−0.910730 + 0.413003i $$0.864480\pi$$
$$258$$ 0 0
$$259$$ 766.500 3982.85i 0.183892 0.955530i
$$260$$ −392.000 −0.0935031
$$261$$ 0 0
$$262$$ −2149.00 + 3722.18i −0.506739 + 0.877698i
$$263$$ −128.500 + 222.569i −0.0301279 + 0.0521831i −0.880696 0.473681i $$-0.842925\pi$$
0.850568 + 0.525865i $$0.176258\pi$$
$$264$$ 0 0
$$265$$ 2121.00 0.491668
$$266$$ 1715.00 594.093i 0.395314 0.136941i
$$267$$ 0 0
$$268$$ 830.000 + 1437.60i 0.189180 + 0.327670i
$$269$$ 1795.50 3109.90i 0.406965 0.704884i −0.587583 0.809164i $$-0.699920\pi$$
0.994548 + 0.104280i $$0.0332538\pi$$
$$270$$ 0 0
$$271$$ −696.500 1206.37i −0.156123 0.270413i 0.777344 0.629075i $$-0.216566\pi$$
−0.933467 + 0.358662i $$0.883233\pi$$
$$272$$ −336.000 −0.0749007
$$273$$ 0 0
$$274$$ −2250.00 −0.496086
$$275$$ 190.000 + 329.090i 0.0416634 + 0.0721631i
$$276$$ 0 0
$$277$$ −207.500 + 359.401i −0.0450089 + 0.0779577i −0.887652 0.460514i $$-0.847665\pi$$
0.842643 + 0.538472i $$0.180998\pi$$
$$278$$ 252.000 + 436.477i 0.0543667 + 0.0941660i
$$279$$ 0 0
$$280$$ −588.000 + 3055.34i −0.125499 + 0.652112i
$$281$$ 4954.00 1.05171 0.525856 0.850574i $$-0.323745\pi$$
0.525856 + 0.850574i $$0.323745\pi$$
$$282$$ 0 0
$$283$$ 2138.50 3703.99i 0.449190 0.778019i −0.549144 0.835728i $$-0.685046\pi$$
0.998333 + 0.0577087i $$0.0183795\pi$$
$$284$$ 864.000 1496.49i 0.180525 0.312678i
$$285$$ 0 0
$$286$$ 140.000 0.0289454
$$287$$ −4900.00 4243.52i −1.00780 0.872778i
$$288$$ 0 0
$$289$$ 2236.00 + 3872.87i 0.455119 + 0.788289i
$$290$$ 406.000 703.213i 0.0822108 0.142393i
$$291$$ 0 0
$$292$$ −2226.00 3855.55i −0.446119 0.772701i
$$293$$ −7742.00 −1.54366 −0.771830 0.635829i $$-0.780658\pi$$
−0.771830 + 0.635829i $$0.780658\pi$$
$$294$$ 0 0
$$295$$ −735.000 −0.145062
$$296$$ −2628.00 4551.83i −0.516045 0.893817i
$$297$$ 0 0
$$298$$ 201.000 348.142i 0.0390725 0.0676756i
$$299$$ 1113.00 + 1927.77i 0.215272 + 0.372863i
$$300$$ 0 0
$$301$$ −1736.00 1503.42i −0.332430 0.287893i
$$302$$ −3238.00 −0.616973
$$303$$ 0 0
$$304$$ 392.000 678.964i 0.0739564 0.128096i
$$305$$ −1445.50 + 2503.68i −0.271374 + 0.470034i
$$306$$ 0 0
$$307$$ −7364.00 −1.36901 −0.684504 0.729009i $$-0.739981\pi$$
−0.684504 + 0.729009i $$0.739981\pi$$
$$308$$ −70.0000 + 363.731i −0.0129501 + 0.0672905i
$$309$$ 0 0
$$310$$ −1029.00 1782.28i −0.188527 0.326538i
$$311$$ 4987.50 8638.60i 0.909374 1.57508i 0.0944372 0.995531i $$-0.469895\pi$$
0.814936 0.579550i $$-0.196772\pi$$
$$312$$ 0 0
$$313$$ 2376.50 + 4116.22i 0.429162 + 0.743330i 0.996799 0.0799485i $$-0.0254756\pi$$
−0.567637 + 0.823279i $$0.692142\pi$$
$$314$$ −1358.00 −0.244065
$$315$$ 0 0
$$316$$ 412.000 0.0733443
$$317$$ −1738.50 3011.17i −0.308025 0.533515i 0.669905 0.742447i $$-0.266335\pi$$
−0.977930 + 0.208932i $$0.933001\pi$$
$$318$$ 0 0
$$319$$ 145.000 251.147i 0.0254497 0.0440801i
$$320$$ 1568.00 + 2715.86i 0.273918 + 0.474440i
$$321$$ 0 0
$$322$$ 5565.00 1927.77i 0.963122 0.333635i
$$323$$ 1029.00 0.177260
$$324$$ 0 0
$$325$$ −532.000 + 921.451i −0.0908002 + 0.157270i
$$326$$ −467.000 + 808.868i −0.0793397 + 0.137420i
$$327$$ 0 0
$$328$$ −8400.00 −1.41406
$$329$$ −1837.50 + 9547.93i −0.307917 + 1.59998i
$$330$$ 0 0
$$331$$ −1670.50 2893.39i −0.277399 0.480469i 0.693339 0.720612i $$-0.256139\pi$$
−0.970738 + 0.240143i $$0.922806\pi$$
$$332$$ −2184.00 + 3782.80i −0.361032 + 0.625325i
$$333$$ 0 0
$$334$$ −1204.00 2085.39i −0.197245 0.341639i
$$335$$ −2905.00 −0.473782
$$336$$ 0 0
$$337$$ 7366.00 1.19066 0.595329 0.803482i $$-0.297022\pi$$
0.595329 + 0.803482i $$0.297022\pi$$
$$338$$ −2001.00 3465.83i −0.322012 0.557741i
$$339$$ 0 0
$$340$$ −294.000 + 509.223i −0.0468953 + 0.0812250i
$$341$$ −367.500 636.529i −0.0583614 0.101085i
$$342$$ 0 0
$$343$$ −3430.00 + 5346.84i −0.539949 + 0.841698i
$$344$$ −2976.00 −0.466439
$$345$$ 0 0
$$346$$ 2821.00 4886.12i 0.438318 0.759188i
$$347$$ 3707.50 6421.58i 0.573571 0.993454i −0.422625 0.906305i $$-0.638891\pi$$
0.996195 0.0871487i $$-0.0277755\pi$$
$$348$$ 0 0
$$349$$ −3878.00 −0.594798 −0.297399 0.954753i $$-0.596119\pi$$
−0.297399 + 0.954753i $$0.596119\pi$$
$$350$$ 2128.00 + 1842.90i 0.324990 + 0.281449i
$$351$$ 0 0
$$352$$ 400.000 + 692.820i 0.0605684 + 0.104908i
$$353$$ 633.500 1097.25i 0.0955179 0.165442i −0.814307 0.580435i $$-0.802883\pi$$
0.909825 + 0.414993i $$0.136216\pi$$
$$354$$ 0 0
$$355$$ 1512.00 + 2618.86i 0.226052 + 0.391534i
$$356$$ −1316.00 −0.195921
$$357$$ 0 0
$$358$$ −6506.00 −0.960483
$$359$$ 2342.50 + 4057.33i 0.344380 + 0.596484i 0.985241 0.171173i $$-0.0547558\pi$$
−0.640861 + 0.767657i $$0.721422\pi$$
$$360$$ 0 0
$$361$$ 2229.00 3860.74i 0.324974 0.562872i
$$362$$ 1582.00 + 2740.10i 0.229691 + 0.397836i
$$363$$ 0 0
$$364$$ −980.000 + 339.482i −0.141115 + 0.0488838i
$$365$$ 7791.00 1.11726
$$366$$ 0 0
$$367$$ 2320.50 4019.22i 0.330052 0.571667i −0.652470 0.757815i $$-0.726267\pi$$
0.982522 + 0.186148i $$0.0596004\pi$$
$$368$$ 1272.00 2203.17i 0.180184 0.312087i
$$369$$ 0 0
$$370$$ 3066.00 0.430794
$$371$$ 5302.50 1836.84i 0.742027 0.257046i
$$372$$ 0 0
$$373$$ 4398.50 + 7618.43i 0.610578 + 1.05755i 0.991143 + 0.132798i $$0.0423963\pi$$
−0.380565 + 0.924754i $$0.624270\pi$$
$$374$$ 105.000 181.865i 0.0145172 0.0251445i
$$375$$ 0 0
$$376$$ 6300.00 + 10911.9i 0.864090 + 1.49665i
$$377$$ 812.000 0.110929
$$378$$ 0 0
$$379$$ 13680.0 1.85407 0.927037 0.374969i $$-0.122347\pi$$
0.927037 + 0.374969i $$0.122347\pi$$
$$380$$ −686.000 1188.19i −0.0926080 0.160402i
$$381$$ 0 0
$$382$$ −2557.00 + 4428.85i −0.342480 + 0.593193i
$$383$$ 4882.50 + 8456.74i 0.651395 + 1.12825i 0.982785 + 0.184755i $$0.0591490\pi$$
−0.331390 + 0.943494i $$0.607518\pi$$
$$384$$ 0 0
$$385$$ −490.000 424.352i −0.0648642 0.0561740i
$$386$$ 794.000 0.104698
$$387$$ 0 0
$$388$$ −1764.00 + 3055.34i −0.230808 + 0.399771i
$$389$$ 865.500 1499.09i 0.112809 0.195390i −0.804093 0.594504i $$-0.797349\pi$$
0.916902 + 0.399113i $$0.130682\pi$$
$$390$$ 0 0
$$391$$ 3339.00 0.431868
$$392$$ 1176.00 + 8147.57i 0.151523 + 1.04978i
$$393$$ 0 0
$$394$$ −2914.00 5047.20i −0.372602 0.645366i
$$395$$ −360.500 + 624.404i −0.0459208 + 0.0795372i
$$396$$ 0 0
$$397$$ −5491.50 9511.56i −0.694233 1.20245i −0.970439 0.241348i $$-0.922410\pi$$
0.276206 0.961099i $$-0.410923\pi$$
$$398$$ −6678.00 −0.841050
$$399$$ 0 0
$$400$$ 1216.00 0.152000
$$401$$ 3301.50 + 5718.37i 0.411145 + 0.712124i 0.995015 0.0997232i $$-0.0317957\pi$$
−0.583870 + 0.811847i $$0.698462\pi$$
$$402$$ 0 0
$$403$$ 1029.00 1782.28i 0.127191 0.220302i
$$404$$ −2758.00 4777.00i −0.339643 0.588278i
$$405$$ 0 0
$$406$$ 406.000 2109.64i 0.0496292 0.257881i
$$407$$ 1095.00 0.133359
$$408$$ 0 0
$$409$$ −5477.50 + 9487.31i −0.662213 + 1.14699i 0.317820 + 0.948151i $$0.397049\pi$$
−0.980033 + 0.198835i $$0.936284\pi$$
$$410$$ 2450.00 4243.52i 0.295114 0.511153i
$$411$$ 0 0
$$412$$ 2716.00 0.324776
$$413$$ −1837.50 + 636.529i −0.218928 + 0.0758391i
$$414$$ 0 0
$$415$$ −3822.00 6619.90i −0.452083 0.783031i
$$416$$ −1120.00 + 1939.90i −0.132001 + 0.228633i
$$417$$ 0 0
$$418$$ 245.000 + 424.352i 0.0286683 + 0.0496549i
$$419$$ −6636.00 −0.773723 −0.386861 0.922138i $$-0.626441\pi$$
−0.386861 + 0.922138i $$0.626441\pi$$
$$420$$ 0 0
$$421$$ −16630.0 −1.92517 −0.962585 0.270980i $$-0.912652\pi$$
−0.962585 + 0.270980i $$0.912652\pi$$
$$422$$ 1780.00 + 3083.05i 0.205329 + 0.355641i
$$423$$ 0 0
$$424$$ 3636.00 6297.74i 0.416462 0.721333i
$$425$$ 798.000 + 1382.18i 0.0910793 + 0.157754i
$$426$$ 0 0
$$427$$ −1445.50 + 7511.04i −0.163824 + 0.851252i
$$428$$ 1828.00 0.206448
$$429$$ 0 0
$$430$$ 868.000 1503.42i 0.0973458 0.168608i
$$431$$ 2461.50 4263.44i 0.275096 0.476480i −0.695064 0.718948i $$-0.744624\pi$$
0.970159 + 0.242468i $$0.0779571\pi$$
$$432$$ 0 0
$$433$$ 8974.00 0.995988 0.497994 0.867180i $$-0.334070\pi$$
0.497994 + 0.867180i $$0.334070\pi$$
$$434$$ −4116.00 3564.56i −0.455240 0.394250i
$$435$$ 0 0
$$436$$ −2250.00 3897.11i −0.247146 0.428069i
$$437$$ −3895.50 + 6747.20i −0.426423 + 0.738587i
$$438$$ 0 0
$$439$$ 2089.50 + 3619.12i 0.227167 + 0.393465i 0.956967 0.290195i $$-0.0937203\pi$$
−0.729800 + 0.683660i $$0.760387\pi$$
$$440$$ −840.000 −0.0910123
$$441$$ 0 0
$$442$$ 588.000 0.0632767
$$443$$ −6463.50 11195.1i −0.693206 1.20067i −0.970782 0.239964i $$-0.922864\pi$$
0.277576 0.960704i $$-0.410469\pi$$
$$444$$ 0 0
$$445$$ 1151.50 1994.46i 0.122666 0.212464i
$$446$$ −1400.00 2424.87i −0.148637 0.257446i
$$447$$ 0 0
$$448$$ 6272.00 + 5431.71i 0.661438 + 0.572822i
$$449$$ 2826.00 0.297032 0.148516 0.988910i $$-0.452550\pi$$
0.148516 + 0.988910i $$0.452550\pi$$
$$450$$ 0 0
$$451$$ 875.000 1515.54i 0.0913573 0.158235i
$$452$$ 3076.00 5327.79i 0.320095 0.554421i
$$453$$ 0 0
$$454$$ −4410.00 −0.455884
$$455$$ 343.000 1782.28i 0.0353409 0.183636i
$$456$$ 0 0
$$457$$ −4239.50 7343.03i −0.433951 0.751625i 0.563259 0.826281i $$-0.309547\pi$$
−0.997209 + 0.0746560i $$0.976214\pi$$
$$458$$ 287.000 497.099i 0.0292808 0.0507159i
$$459$$ 0 0
$$460$$ −2226.00 3855.55i −0.225626 0.390795i
$$461$$ −9338.00 −0.943414 −0.471707 0.881755i $$-0.656362\pi$$
−0.471707 + 0.881755i $$0.656362\pi$$
$$462$$ 0 0
$$463$$ −4016.00 −0.403109 −0.201554 0.979477i $$-0.564599\pi$$
−0.201554 + 0.979477i $$0.564599\pi$$
$$464$$ −464.000 803.672i −0.0464238 0.0804084i
$$465$$ 0 0
$$466$$ −4587.00 + 7944.92i −0.455984 + 0.789788i
$$467$$ −2929.50 5074.04i −0.290281 0.502781i 0.683595 0.729861i $$-0.260415\pi$$
−0.973876 + 0.227080i $$0.927082\pi$$
$$468$$ 0 0
$$469$$ −7262.50 + 2515.80i −0.715034 + 0.247695i
$$470$$ −7350.00 −0.721341
$$471$$ 0 0
$$472$$ −1260.00 + 2182.38i −0.122873 + 0.212823i
$$473$$ 310.000 536.936i 0.0301349 0.0521952i
$$474$$ 0 0
$$475$$ −3724.00 −0.359724
$$476$$ −294.000 + 1527.67i −0.0283098 + 0.147102i
$$477$$ 0 0
$$478$$ −1668.00 2889.06i −0.159608 0.276449i
$$479$$ 3251.50 5631.76i 0.310156 0.537206i −0.668240 0.743946i $$-0.732952\pi$$
0.978396 + 0.206740i $$0.0662853\pi$$
$$480$$ 0 0
$$481$$ 1533.00 + 2655.23i 0.145320 + 0.251701i
$$482$$ 6818.00 0.644297
$$483$$ 0 0
$$484$$ 5224.00 0.490609
$$485$$ −3087.00 5346.84i −0.289017 0.500593i
$$486$$ 0 0
$$487$$ 8024.50 13898.8i 0.746663 1.29326i −0.202751 0.979230i $$-0.564988\pi$$
0.949414 0.314028i $$-0.101678\pi$$
$$488$$ 4956.00 + 8584.04i 0.459729 + 0.796273i
$$489$$ 0 0
$$490$$ −4459.00 1782.28i −0.411096 0.164317i
$$491$$ −8864.00 −0.814718 −0.407359 0.913268i $$-0.633550\pi$$
−0.407359 + 0.913268i $$0.633550\pi$$
$$492$$ 0 0
$$493$$ 609.000 1054.82i 0.0556348 0.0963624i
$$494$$ −686.000 + 1188.19i −0.0624789 + 0.108217i
$$495$$ 0 0
$$496$$ −2352.00 −0.212919
$$497$$ 6048.00 + 5237.72i 0.545855 + 0.472724i
$$498$$ 0 0
$$499$$ 5105.50 + 8842.99i 0.458023 + 0.793319i 0.998856 0.0478104i $$-0.0152243\pi$$
−0.540833 + 0.841130i $$0.681891\pi$$
$$500$$ 2814.00 4873.99i 0.251692 0.435943i
$$501$$ 0 0
$$502$$ 4760.00 + 8244.56i 0.423206 + 0.733014i
$$503$$ 1680.00 0.148921 0.0744607 0.997224i $$-0.476276\pi$$
0.0744607 + 0.997224i $$0.476276\pi$$
$$504$$ 0 0
$$505$$ 9653.00 0.850600
$$506$$ 795.000 + 1376.98i 0.0698460 + 0.120977i
$$507$$ 0 0
$$508$$ 144.000 249.415i 0.0125767 0.0217835i
$$509$$ −4728.50 8190.00i −0.411762 0.713193i 0.583320 0.812242i $$-0.301753\pi$$
−0.995083 + 0.0990489i $$0.968420\pi$$
$$510$$ 0 0
$$511$$ 19477.5 6747.20i 1.68617 0.584107i
$$512$$ 5632.00 0.486136
$$513$$ 0 0
$$514$$ 805.000 1394.30i 0.0690798 0.119650i
$$515$$ −2376.50 + 4116.22i −0.203342 + 0.352199i
$$516$$ 0 0
$$517$$ −2625.00 −0.223302
$$518$$ 7665.00 2655.23i 0.650156 0.225221i
$$519$$ 0 0
$$520$$ −1176.00 2036.89i −0.0991750 0.171776i
$$521$$ −9040.50 + 15658.6i −0.760214 + 1.31673i 0.182526 + 0.983201i $$0.441573\pi$$
−0.942740 + 0.333528i $$0.891761\pi$$
$$522$$ 0 0
$$523$$ −10188.5 17647.0i −0.851839 1.47543i −0.879546 0.475813i $$-0.842154\pi$$
0.0277071 0.999616i $$-0.491179\pi$$
$$524$$ 8596.00 0.716637
$$525$$ 0 0
$$526$$ −514.000 −0.0426073
$$527$$ −1543.50 2673.42i −0.127582 0.220979i
$$528$$ 0 0
$$529$$ −6557.00 + 11357.1i −0.538917 + 0.933431i
$$530$$ 2121.00 + 3673.68i 0.173831 + 0.301084i
$$531$$ 0 0
$$532$$ −2744.00 2376.37i −0.223623 0.193663i
$$533$$ 4900.00 0.398204
$$534$$ 0 0
$$535$$ −1599.50 + 2770.42i −0.129257 + 0.223879i
$$536$$ −4980.00 + 8625.61i −0.401312 + 0.695093i
$$537$$ 0 0
$$538$$ 7182.00 0.575535
$$539$$ −1592.50 636.529i −0.127261 0.0508668i
$$540$$ 0 0
$$541$$ 3096.50 + 5363.30i 0.246079 + 0.426222i 0.962435 0.271514i $$-0.0875243\pi$$
−0.716355 + 0.697736i $$0.754191\pi$$
$$542$$ 1393.00 2412.75i 0.110396 0.191211i
$$543$$ 0 0
$$544$$ 1680.00 + 2909.85i 0.132407 + 0.229336i
$$545$$ 7875.00 0.618950
$$546$$ 0 0
$$547$$ −18464.0 −1.44326 −0.721630 0.692279i $$-0.756607\pi$$
−0.721630 + 0.692279i $$0.756607\pi$$
$$548$$ 2250.00 + 3897.11i 0.175393 + 0.303789i
$$549$$ 0 0
$$550$$ −380.000 + 658.179i −0.0294605 + 0.0510270i
$$551$$ 1421.00 + 2461.24i 0.109867 + 0.190295i
$$552$$ 0 0
$$553$$ −360.500 + 1873.21i −0.0277216 + 0.144045i
$$554$$ −830.000 −0.0636522
$$555$$ 0 0
$$556$$ 504.000 872.954i 0.0384431 0.0665854i
$$557$$ −4706.50 + 8151.90i −0.358027 + 0.620120i −0.987631 0.156796i $$-0.949884\pi$$
0.629604 + 0.776916i $$0.283217\pi$$
$$558$$ 0 0
$$559$$ 1736.00 0.131351
$$560$$ −1960.00 + 678.964i −0.147902 + 0.0512348i
$$561$$ 0 0
$$562$$ 4954.00 + 8580.58i 0.371836 + 0.644039i
$$563$$ 1599.50 2770.42i 0.119735 0.207387i −0.799928 0.600097i $$-0.795129\pi$$
0.919663 + 0.392709i $$0.128462\pi$$
$$564$$ 0 0
$$565$$ 5383.00 + 9323.63i 0.400822 + 0.694244i
$$566$$ 8554.00 0.635250
$$567$$ 0 0
$$568$$ 10368.0 0.765901
$$569$$ 10791.5 + 18691.4i 0.795085 + 1.37713i 0.922785 + 0.385314i $$0.125907\pi$$
−0.127701 + 0.991813i $$0.540760\pi$$
$$570$$ 0 0
$$571$$ −10133.5 + 17551.7i −0.742686 + 1.28637i 0.208582 + 0.978005i $$0.433115\pi$$
−0.951268 + 0.308365i $$0.900218\pi$$
$$572$$ −140.000 242.487i −0.0102337 0.0177253i
$$573$$ 0 0
$$574$$ 2450.00 12730.6i 0.178155 0.925721i
$$575$$ −12084.0 −0.876413
$$576$$ 0 0
$$577$$ −6975.50 + 12081.9i −0.503282 + 0.871710i 0.496711 + 0.867916i $$0.334541\pi$$
−0.999993 + 0.00379418i $$0.998792\pi$$
$$578$$ −4472.00 + 7745.73i −0.321818 + 0.557405i
$$579$$ 0 0
$$580$$ −1624.00 −0.116264
$$581$$ −15288.0 13239.8i −1.09166 0.945403i
$$582$$ 0 0
$$583$$ 757.500 + 1312.03i 0.0538121 + 0.0932053i
$$584$$ 13356.0 23133.3i 0.946362 1.63915i
$$585$$ 0 0
$$586$$ −7742.00 13409.5i −0.545766 0.945295i
$$587$$ 20972.0 1.47463 0.737314 0.675550i $$-0.236094\pi$$
0.737314 + 0.675550i $$0.236094\pi$$
$$588$$ 0 0
$$589$$ 7203.00 0.503895
$$590$$ −735.000 1273.06i −0.0512872 0.0888321i
$$591$$ 0 0
$$592$$ 1752.00 3034.55i 0.121633 0.210675i
$$593$$ −94.5000 163.679i −0.00654410 0.0113347i 0.862735 0.505657i $$-0.168750\pi$$
−0.869279 + 0.494322i $$0.835416\pi$$
$$594$$ 0 0
$$595$$ −2058.00 1782.28i −0.141798 0.122801i
$$596$$ −804.000 −0.0552569
$$597$$ 0 0
$$598$$ −2226.00 + 3855.55i −0.152221 + 0.263654i
$$599$$ −5140.50 + 8903.61i −0.350643 + 0.607331i −0.986362 0.164589i $$-0.947370\pi$$
0.635719 + 0.771920i $$0.280704\pi$$
$$600$$ 0 0
$$601$$ −6090.00 −0.413338 −0.206669 0.978411i $$-0.566262\pi$$
−0.206669 + 0.978411i $$0.566262\pi$$
$$602$$ 868.000 4510.26i 0.0587658 0.305356i
$$603$$ 0 0
$$604$$ 3238.00 + 5608.38i 0.218133 + 0.377817i
$$605$$ −4571.00 + 7917.20i −0.307170 + 0.532033i
$$606$$ 0 0
$$607$$ −2474.50 4285.96i −0.165464 0.286593i 0.771356 0.636404i $$-0.219579\pi$$
−0.936820 + 0.349812i $$0.886246\pi$$
$$608$$ −7840.00 −0.522951
$$609$$ 0 0
$$610$$ −5782.00 −0.383781
$$611$$ −3675.00 6365.29i −0.243330 0.421460i
$$612$$ 0 0
$$613$$ 7898.50 13680.6i 0.520420 0.901394i −0.479298 0.877652i $$-0.659109\pi$$
0.999718 0.0237416i $$-0.00755791\pi$$
$$614$$ −7364.00 12754.8i −0.484018 0.838343i
$$615$$ 0 0
$$616$$ −2100.00 + 727.461i −0.137356 + 0.0475816i
$$617$$ 9378.00 0.611903 0.305951 0.952047i $$-0.401025\pi$$
0.305951 + 0.952047i $$0.401025\pi$$
$$618$$ 0 0
$$619$$ 12176.5 21090.3i 0.790654 1.36945i −0.134908 0.990858i $$-0.543074\pi$$
0.925562 0.378595i $$-0.123593\pi$$
$$620$$ −2058.00 + 3564.56i −0.133308 + 0.230897i
$$621$$ 0 0
$$622$$ 19950.0 1.28605
$$623$$ 1151.50 5983.37i 0.0740512 0.384781i
$$624$$ 0 0
$$625$$ 174.500 + 302.243i 0.0111680 + 0.0193435i
$$626$$ −4753.00 + 8232.44i −0.303463 + 0.525614i
$$627$$ 0 0
$$628$$ 1358.00 + 2352.12i 0.0862900 + 0.149459i
$$629$$ 4599.00 0.291533
$$630$$ 0 0
$$631$$ −12640.0 −0.797449 −0.398725 0.917071i $$-0.630547\pi$$
−0.398725 + 0.917071i $$0.630547\pi$$
$$632$$ 1236.00 + 2140.81i 0.0777934 + 0.134742i
$$633$$ 0 0
$$634$$ 3477.00 6022.34i 0.217806 0.377252i
$$635$$ 252.000 + 436.477i 0.0157485 + 0.0272772i
$$636$$ 0 0
$$637$$ −686.000 4752.75i −0.0426692 0.295621i
$$638$$ 580.000 0.0359913
$$639$$ 0 0
$$640$$ 1344.00 2327.88i 0.0830098 0.143777i
$$641$$ −520.500 + 901.532i −0.0320726 + 0.0555513i −0.881616 0.471967i $$-0.843544\pi$$
0.849544 + 0.527518i $$0.176877\pi$$
$$642$$ 0 0
$$643$$ 9548.00 0.585593 0.292797 0.956175i $$-0.405414\pi$$
0.292797 + 0.956175i $$0.405414\pi$$
$$644$$ −8904.00 7711.09i −0.544824 0.471832i
$$645$$ 0 0
$$646$$ 1029.00 + 1782.28i 0.0626710 + 0.108549i
$$647$$ −1620.50 + 2806.79i −0.0984674 + 0.170551i −0.911050 0.412295i $$-0.864727\pi$$
0.812583 + 0.582845i $$0.198061\pi$$
$$648$$ 0 0
$$649$$ −262.500 454.663i −0.0158768 0.0274994i
$$650$$ −2128.00 −0.128411
$$651$$ 0 0
$$652$$ 1868.00 0.112203
$$653$$ −4426.50 7666.92i −0.265272 0.459464i 0.702363 0.711819i $$-0.252128\pi$$
−0.967635 + 0.252355i $$0.918795\pi$$
$$654$$ 0 0
$$655$$ −7521.50 + 13027.6i −0.448686 + 0.777147i
$$656$$ −2800.00 4849.74i −0.166649 0.288644i
$$657$$ 0 0
$$658$$ −18375.0 + 6365.29i −1.08865 + 0.377120i
$$659$$ −7044.00 −0.416381 −0.208191 0.978088i $$-0.566757\pi$$
−0.208191 + 0.978088i $$0.566757\pi$$
$$660$$ 0 0
$$661$$ 6044.50 10469.4i 0.355679 0.616054i −0.631555 0.775331i $$-0.717583\pi$$
0.987234 + 0.159277i $$0.0509163\pi$$
$$662$$ 3341.00 5786.78i 0.196151 0.339743i
$$663$$ 0 0
$$664$$ −26208.0 −1.53173
$$665$$ 6002.50 2079.33i 0.350026 0.121252i
$$666$$ 0 0
$$667$$ 4611.00 + 7986.49i 0.267674 + 0.463625i
$$668$$ −2408.00 + 4170.78i −0.139474 + 0.241575i
$$669$$ 0 0
$$670$$ −2905.00 5031.61i −0.167507 0.290131i
$$671$$ −2065.00 −0.118805
$$672$$ 0 0
$$673$$ 982.000 0.0562456 0.0281228 0.999604i $$-0.491047\pi$$
0.0281228 + 0.999604i $$0.491047\pi$$
$$674$$ 7366.00 + 12758.3i 0.420961 + 0.729126i
$$675$$ 0 0
$$676$$ −4002.00 + 6931.67i −0.227697 + 0.394383i
$$677$$ −15256.5 26425.0i −0.866108 1.50014i −0.865943 0.500143i $$-0.833281\pi$$
−0.000164659 1.00000i $$-0.500052\pi$$
$$678$$ 0 0
$$679$$ −12348.0 10693.7i −0.697898 0.604397i
$$680$$ −3528.00 −0.198960
$$681$$ 0 0
$$682$$ 735.000 1273.06i 0.0412677 0.0714778i
$$683$$ 5737.50 9937.64i 0.321434 0.556740i −0.659350 0.751836i $$-0.729169\pi$$
0.980784 + 0.195096i $$0.0625019\pi$$
$$684$$ 0 0
$$685$$ −7875.00 −0.439253
$$686$$ −12691.0 594.093i −0.706333 0.0330650i
$$687$$ 0 0
$$688$$ −992.000 1718.19i −0.0549704 0.0952116i
$$689$$ −2121.00 + 3673.68i −0.117277 + 0.203129i
$$690$$ 0 0
$$691$$ 14157.5 + 24521.5i 0.779416 + 1.34999i 0.932279 + 0.361741i $$0.117818\pi$$
−0.152862 + 0.988248i $$0.548849\pi$$
$$692$$ −11284.0 −0.619875
$$693$$ 0 0
$$694$$ 14830.0 0.811151
$$695$$ 882.000 + 1527.67i 0.0481384 + 0.0833781i
$$696$$ 0 0
$$697$$ 3675.00 6365.29i 0.199714 0.345915i
$$698$$ −3878.00 6716.89i −0.210293 0.364238i
$$699$$ 0 0
$$700$$ 1064.00 5528.71i 0.0574506 0.298522i
$$701$$ −10614.0 −0.571876 −0.285938 0.958248i $$-0.592305\pi$$
−0.285938 + 0.958248i $$0.592305\pi$$
$$702$$ 0 0
$$703$$ −5365.50 + 9293.32i −0.287857 + 0.498583i
$$704$$ −1120.00 + 1939.90i −0.0599596 + 0.103853i
$$705$$ 0 0
$$706$$ 2534.00 0.135083
$$707$$ 24132.5 8359.74i 1.28373 0.444697i
$$708$$ 0 0
$$709$$ −5149.50 8919.20i −0.272769 0.472451i 0.696801 0.717265i $$-0.254606\pi$$
−0.969570 + 0.244814i $$0.921273\pi$$
$$710$$ −3024.00 + 5237.72i −0.159843 + 0.276857i
$$711$$ 0 0
$$712$$ −3948.00 6838.14i −0.207806 0.359930i
$$713$$ 23373.0 1.22767
$$714$$ 0 0
$$715$$ 490.000 0.0256293
$$716$$ 6506.00 + 11268.7i 0.339582 + 0.588173i
$$717$$ 0 0
$$718$$ −4685.00 + 8114.66i −0.243513 + 0.421778i
$$719$$ 16264.5 + 28170.9i 0.843621 + 1.46119i 0.886813 + 0.462128i $$0.152914\pi$$
−0.0431924 + 0.999067i $$0.513753\pi$$
$$720$$ 0 0
$$721$$ −2376.50 + 12348.7i −0.122754 + 0.637847i
$$722$$ 8916.00 0.459583
$$723$$ 0 0
$$724$$ 3164.00 5480.21i 0.162416 0.281313i
$$725$$ −2204.00 + 3817.44i −0.112903 + 0.195553i
$$726$$ 0 0
$$727$$ 29456.0 1.50270 0.751350 0.659904i $$-0.229403\pi$$
0.751350 + 0.659904i $$0.229403\pi$$
$$728$$ −4704.00 4073.78i −0.239481 0.207396i
$$729$$ 0 0
$$730$$ 7791.00 + 13494.4i 0.395011 + 0.684179i
$$731$$ 1302.00 2255.13i 0.0658772 0.114103i
$$732$$ 0 0
$$733$$ −13933.5 24133.5i −0.702109 1.21609i −0.967725 0.252009i $$-0.918909\pi$$
0.265616 0.964079i $$-0.414425\pi$$
$$734$$ 9282.00 0.466764
$$735$$ 0 0
$$736$$ −25440.0 −1.27409
$$737$$ −1037.50 1797.00i −0.0518546 0.0898147i
$$738$$ 0 0
$$739$$ −9769.50 + 16921.3i −0.486302 + 0.842299i −0.999876 0.0157460i $$-0.994988\pi$$
0.513574 + 0.858045i $$0.328321\pi$$
$$740$$ −3066.00 5310.47i −0.152309 0.263806i
$$741$$ 0 0
$$742$$ 8484.00 + 7347.36i 0.419754 + 0.363518i
$$743$$ −1248.00 −0.0616214 −0.0308107 0.999525i $$-0.509809\pi$$
−0.0308107 + 0.999525i $$0.509809\pi$$
$$744$$ 0 0
$$745$$ 703.500 1218.50i 0.0345963 0.0599226i
$$746$$ −8797.00 + 15236.9i −0.431744 + 0.747803i
$$747$$ 0 0
$$748$$ −420.000 −0.0205304
$$749$$ −1599.50 + 8311.25i −0.0780300 + 0.405456i
$$750$$ 0 0
$$751$$ −14046.5 24329.3i −0.682509 1.18214i −0.974213 0.225631i $$-0.927556\pi$$
0.291704 0.956509i $$-0.405778\pi$$
$$752$$ −4200.00 + 7274.61i −0.203668 + 0.352763i
$$753$$ 0 0
$$754$$ 812.000 + 1406.43i 0.0392192 + 0.0679297i
$$755$$ −11333.0 −0.546292
$$756$$ 0 0
$$757$$ 35954.0 1.72625 0.863124 0.504991i $$-0.168504\pi$$
0.863124 + 0.504991i $$0.168504\pi$$
$$758$$ 13680.0 + 23694.5i 0.655514 + 1.13538i
$$759$$ 0 0
$$760$$ 4116.00 7129.12i 0.196451 0.340264i
$$761$$ −430.500 745.648i −0.0205067 0.0355187i 0.855590 0.517654i $$-0.173195\pi$$
−0.876097 + 0.482136i $$0.839861\pi$$
$$762$$ 0 0
$$763$$ 19687.5 6819.95i 0.934122 0.323589i
$$764$$ 10228.0 0.484340
$$765$$ 0 0
$$766$$ −9765.00 + 16913.5i −0.460605 + 0.797792i
$$767$$ 735.000 1273.06i 0.0346014 0.0599315i
$$768$$ 0 0
$$769$$ 24710.0 1.15873 0.579366 0.815067i $$-0.303300\pi$$
0.579366 + 0.815067i $$0.303300\pi$$
$$770$$ 245.000 1273.06i 0.0114665 0.0595816i
$$771$$ 0 0
$$772$$ −794.000 1375.25i −0.0370164 0.0641143i
$$773$$ 8249.50 14288.6i 0.383847 0.664843i −0.607761 0.794120i $$-0.707932\pi$$
0.991609 + 0.129277i $$0.0412656\pi$$
$$774$$ 0 0
$$775$$ 5586.00 + 9675.24i 0.258910 + 0.448445i
$$776$$ −21168.0 −0.979236
$$777$$ 0 0
$$778$$ 3462.00 0.159536
$$779$$ 8575.00 + 14852.3i 0.394392 + 0.683107i
$$780$$ 0 0
$$781$$ −1080.00 + 1870.61i −0.0494820 + 0.0857053i
$$782$$ 3339.00 + 5783.32i 0.152688 + 0.264464i
$$783$$ 0 0
$$784$$ −4312.00 + 3394.82i −0.196429 + 0.154647i
$$785$$ −4753.00 −0.216104
$$786$$ 0 0