# Properties

 Label 441.4.e.b.226.1 Level $441$ Weight $4$ Character 441.226 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: $$\Z[a_1, \ldots, a_{4}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 21) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 226.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 441.226 Dual form 441.4.e.b.361.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.50000 + 2.59808i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-9.00000 + 15.5885i) q^{5} -21.0000 q^{8} +O(q^{10})$$ $$q+(-1.50000 + 2.59808i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-9.00000 + 15.5885i) q^{5} -21.0000 q^{8} +(-27.0000 - 46.7654i) q^{10} +(-18.0000 - 31.1769i) q^{11} -34.0000 q^{13} +(35.5000 - 61.4878i) q^{16} +(21.0000 + 36.3731i) q^{17} +(62.0000 - 107.387i) q^{19} +18.0000 q^{20} +108.000 q^{22} +(-99.5000 - 172.339i) q^{25} +(51.0000 - 88.3346i) q^{26} -102.000 q^{29} +(80.0000 + 138.564i) q^{31} +(22.5000 + 38.9711i) q^{32} -126.000 q^{34} +(-199.000 + 344.678i) q^{37} +(186.000 + 322.161i) q^{38} +(189.000 - 327.358i) q^{40} +318.000 q^{41} -268.000 q^{43} +(-18.0000 + 31.1769i) q^{44} +(120.000 - 207.846i) q^{47} +597.000 q^{50} +(17.0000 + 29.4449i) q^{52} +(-249.000 - 431.281i) q^{53} +648.000 q^{55} +(153.000 - 265.004i) q^{58} +(-66.0000 - 114.315i) q^{59} +(-199.000 + 344.678i) q^{61} -480.000 q^{62} +433.000 q^{64} +(306.000 - 530.008i) q^{65} +(-46.0000 - 79.6743i) q^{67} +(21.0000 - 36.3731i) q^{68} +720.000 q^{71} +(251.000 + 434.745i) q^{73} +(-597.000 - 1034.03i) q^{74} -124.000 q^{76} +(512.000 - 886.810i) q^{79} +(639.000 + 1106.78i) q^{80} +(-477.000 + 826.188i) q^{82} +204.000 q^{83} -756.000 q^{85} +(402.000 - 696.284i) q^{86} +(378.000 + 654.715i) q^{88} +(177.000 - 306.573i) q^{89} +(360.000 + 623.538i) q^{94} +(1116.00 + 1932.97i) q^{95} -286.000 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 3q^{2} - q^{4} - 18q^{5} - 42q^{8} + O(q^{10})$$ $$2q - 3q^{2} - q^{4} - 18q^{5} - 42q^{8} - 54q^{10} - 36q^{11} - 68q^{13} + 71q^{16} + 42q^{17} + 124q^{19} + 36q^{20} + 216q^{22} - 199q^{25} + 102q^{26} - 204q^{29} + 160q^{31} + 45q^{32} - 252q^{34} - 398q^{37} + 372q^{38} + 378q^{40} + 636q^{41} - 536q^{43} - 36q^{44} + 240q^{47} + 1194q^{50} + 34q^{52} - 498q^{53} + 1296q^{55} + 306q^{58} - 132q^{59} - 398q^{61} - 960q^{62} + 866q^{64} + 612q^{65} - 92q^{67} + 42q^{68} + 1440q^{71} + 502q^{73} - 1194q^{74} - 248q^{76} + 1024q^{79} + 1278q^{80} - 954q^{82} + 408q^{83} - 1512q^{85} + 804q^{86} + 756q^{88} + 354q^{89} + 720q^{94} + 2232q^{95} - 572q^{97} + O(q^{100})$$

## Character values

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

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

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.50000 + 2.59808i −0.530330 + 0.918559i 0.469044 + 0.883175i $$0.344599\pi$$
−0.999374 + 0.0353837i $$0.988735\pi$$
$$3$$ 0 0
$$4$$ −0.500000 0.866025i −0.0625000 0.108253i
$$5$$ −9.00000 + 15.5885i −0.804984 + 1.39427i 0.111317 + 0.993785i $$0.464493\pi$$
−0.916302 + 0.400489i $$0.868840\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ −21.0000 −0.928078
$$9$$ 0 0
$$10$$ −27.0000 46.7654i −0.853815 1.47885i
$$11$$ −18.0000 31.1769i −0.493382 0.854563i 0.506589 0.862188i $$-0.330906\pi$$
−0.999971 + 0.00762479i $$0.997573\pi$$
$$12$$ 0 0
$$13$$ −34.0000 −0.725377 −0.362689 0.931910i $$-0.618141\pi$$
−0.362689 + 0.931910i $$0.618141\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 35.5000 61.4878i 0.554688 0.960747i
$$17$$ 21.0000 + 36.3731i 0.299603 + 0.518927i 0.976045 0.217568i $$-0.0698125\pi$$
−0.676442 + 0.736496i $$0.736479\pi$$
$$18$$ 0 0
$$19$$ 62.0000 107.387i 0.748620 1.29665i −0.199865 0.979824i $$-0.564050\pi$$
0.948484 0.316824i $$-0.102616\pi$$
$$20$$ 18.0000 0.201246
$$21$$ 0 0
$$22$$ 108.000 1.04662
$$23$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$24$$ 0 0
$$25$$ −99.5000 172.339i −0.796000 1.37871i
$$26$$ 51.0000 88.3346i 0.384689 0.666301i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −102.000 −0.653135 −0.326568 0.945174i $$-0.605892\pi$$
−0.326568 + 0.945174i $$0.605892\pi$$
$$30$$ 0 0
$$31$$ 80.0000 + 138.564i 0.463498 + 0.802801i 0.999132 0.0416484i $$-0.0132609\pi$$
−0.535635 + 0.844450i $$0.679928\pi$$
$$32$$ 22.5000 + 38.9711i 0.124296 + 0.215287i
$$33$$ 0 0
$$34$$ −126.000 −0.635554
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −199.000 + 344.678i −0.884200 + 1.53148i −0.0375721 + 0.999294i $$0.511962\pi$$
−0.846628 + 0.532185i $$0.821371\pi$$
$$38$$ 186.000 + 322.161i 0.794031 + 1.37530i
$$39$$ 0 0
$$40$$ 189.000 327.358i 0.747088 1.29399i
$$41$$ 318.000 1.21130 0.605649 0.795732i $$-0.292913\pi$$
0.605649 + 0.795732i $$0.292913\pi$$
$$42$$ 0 0
$$43$$ −268.000 −0.950456 −0.475228 0.879863i $$-0.657634\pi$$
−0.475228 + 0.879863i $$0.657634\pi$$
$$44$$ −18.0000 + 31.1769i −0.0616728 + 0.106820i
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 120.000 207.846i 0.372421 0.645053i −0.617516 0.786558i $$-0.711861\pi$$
0.989937 + 0.141506i $$0.0451943\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 597.000 1.68857
$$51$$ 0 0
$$52$$ 17.0000 + 29.4449i 0.0453361 + 0.0785244i
$$53$$ −249.000 431.281i −0.645335 1.11775i −0.984224 0.176927i $$-0.943384\pi$$
0.338888 0.940827i $$-0.389949\pi$$
$$54$$ 0 0
$$55$$ 648.000 1.58866
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 153.000 265.004i 0.346377 0.599943i
$$59$$ −66.0000 114.315i −0.145635 0.252247i 0.783975 0.620793i $$-0.213189\pi$$
−0.929610 + 0.368546i $$0.879856\pi$$
$$60$$ 0 0
$$61$$ −199.000 + 344.678i −0.417694 + 0.723467i −0.995707 0.0925602i $$-0.970495\pi$$
0.578013 + 0.816028i $$0.303828\pi$$
$$62$$ −480.000 −0.983227
$$63$$ 0 0
$$64$$ 433.000 0.845703
$$65$$ 306.000 530.008i 0.583917 1.01137i
$$66$$ 0 0
$$67$$ −46.0000 79.6743i −0.0838775 0.145280i 0.821035 0.570878i $$-0.193397\pi$$
−0.904912 + 0.425598i $$0.860064\pi$$
$$68$$ 21.0000 36.3731i 0.0374504 0.0648659i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 720.000 1.20350 0.601748 0.798686i $$-0.294471\pi$$
0.601748 + 0.798686i $$0.294471\pi$$
$$72$$ 0 0
$$73$$ 251.000 + 434.745i 0.402429 + 0.697028i 0.994019 0.109212i $$-0.0348326\pi$$
−0.591589 + 0.806239i $$0.701499\pi$$
$$74$$ −597.000 1034.03i −0.937836 1.62438i
$$75$$ 0 0
$$76$$ −124.000 −0.187155
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 512.000 886.810i 0.729171 1.26296i −0.228063 0.973646i $$-0.573239\pi$$
0.957234 0.289315i $$-0.0934274\pi$$
$$80$$ 639.000 + 1106.78i 0.893030 + 1.54677i
$$81$$ 0 0
$$82$$ −477.000 + 826.188i −0.642388 + 1.11265i
$$83$$ 204.000 0.269782 0.134891 0.990860i $$-0.456932\pi$$
0.134891 + 0.990860i $$0.456932\pi$$
$$84$$ 0 0
$$85$$ −756.000 −0.964703
$$86$$ 402.000 696.284i 0.504056 0.873050i
$$87$$ 0 0
$$88$$ 378.000 + 654.715i 0.457897 + 0.793101i
$$89$$ 177.000 306.573i 0.210809 0.365131i −0.741159 0.671329i $$-0.765724\pi$$
0.951968 + 0.306198i $$0.0990570\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 360.000 + 623.538i 0.395012 + 0.684182i
$$95$$ 1116.00 + 1932.97i 1.20525 + 2.08756i
$$96$$ 0 0
$$97$$ −286.000 −0.299370 −0.149685 0.988734i $$-0.547826\pi$$
−0.149685 + 0.988734i $$0.547826\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −99.5000 + 172.339i −0.0995000 + 0.172339i
$$101$$ 207.000 + 358.535i 0.203933 + 0.353223i 0.949792 0.312881i $$-0.101294\pi$$
−0.745859 + 0.666104i $$0.767961\pi$$
$$102$$ 0 0
$$103$$ −28.0000 + 48.4974i −0.0267857 + 0.0463941i −0.879107 0.476624i $$-0.841860\pi$$
0.852322 + 0.523018i $$0.175194\pi$$
$$104$$ 714.000 0.673206
$$105$$ 0 0
$$106$$ 1494.00 1.36896
$$107$$ 6.00000 10.3923i 0.00542095 0.00938936i −0.863302 0.504687i $$-0.831608\pi$$
0.868723 + 0.495298i $$0.164941\pi$$
$$108$$ 0 0
$$109$$ −739.000 1279.99i −0.649389 1.12477i −0.983269 0.182159i $$-0.941692\pi$$
0.333880 0.942615i $$-0.391642\pi$$
$$110$$ −972.000 + 1683.55i −0.842514 + 1.45928i
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −402.000 −0.334664 −0.167332 0.985901i $$-0.553515\pi$$
−0.167332 + 0.985901i $$0.553515\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 51.0000 + 88.3346i 0.0408210 + 0.0707040i
$$117$$ 0 0
$$118$$ 396.000 0.308939
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 17.5000 30.3109i 0.0131480 0.0227730i
$$122$$ −597.000 1034.03i −0.443031 0.767353i
$$123$$ 0 0
$$124$$ 80.0000 138.564i 0.0579372 0.100350i
$$125$$ 1332.00 0.953102
$$126$$ 0 0
$$127$$ 1280.00 0.894344 0.447172 0.894448i $$-0.352431\pi$$
0.447172 + 0.894448i $$0.352431\pi$$
$$128$$ −829.500 + 1436.74i −0.572798 + 0.992115i
$$129$$ 0 0
$$130$$ 918.000 + 1590.02i 0.619338 + 1.07272i
$$131$$ 882.000 1527.67i 0.588250 1.01888i −0.406212 0.913779i $$-0.633151\pi$$
0.994462 0.105099i $$-0.0335161\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 276.000 0.177931
$$135$$ 0 0
$$136$$ −441.000 763.834i −0.278055 0.481605i
$$137$$ −1179.00 2042.09i −0.735246 1.27348i −0.954615 0.297842i $$-0.903733\pi$$
0.219369 0.975642i $$-0.429600\pi$$
$$138$$ 0 0
$$139$$ −52.0000 −0.0317308 −0.0158654 0.999874i $$-0.505050\pi$$
−0.0158654 + 0.999874i $$0.505050\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −1080.00 + 1870.61i −0.638251 + 1.10548i
$$143$$ 612.000 + 1060.02i 0.357888 + 0.619881i
$$144$$ 0 0
$$145$$ 918.000 1590.02i 0.525764 0.910650i
$$146$$ −1506.00 −0.853681
$$147$$ 0 0
$$148$$ 398.000 0.221050
$$149$$ −873.000 + 1512.08i −0.479993 + 0.831372i −0.999737 0.0229501i $$-0.992694\pi$$
0.519744 + 0.854322i $$0.326027\pi$$
$$150$$ 0 0
$$151$$ 116.000 + 200.918i 0.0625162 + 0.108281i 0.895590 0.444881i $$-0.146754\pi$$
−0.833073 + 0.553163i $$0.813421\pi$$
$$152$$ −1302.00 + 2255.13i −0.694777 + 1.20339i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −2880.00 −1.49243
$$156$$ 0 0
$$157$$ −847.000 1467.05i −0.430560 0.745752i 0.566361 0.824157i $$-0.308351\pi$$
−0.996922 + 0.0784048i $$0.975017\pi$$
$$158$$ 1536.00 + 2660.43i 0.773403 + 1.33957i
$$159$$ 0 0
$$160$$ −810.000 −0.400226
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 1466.00 2539.19i 0.704454 1.22015i −0.262434 0.964950i $$-0.584525\pi$$
0.966888 0.255200i $$-0.0821413\pi$$
$$164$$ −159.000 275.396i −0.0757062 0.131127i
$$165$$ 0 0
$$166$$ −306.000 + 530.008i −0.143074 + 0.247811i
$$167$$ −1176.00 −0.544920 −0.272460 0.962167i $$-0.587837\pi$$
−0.272460 + 0.962167i $$0.587837\pi$$
$$168$$ 0 0
$$169$$ −1041.00 −0.473828
$$170$$ 1134.00 1964.15i 0.511611 0.886136i
$$171$$ 0 0
$$172$$ 134.000 + 232.095i 0.0594035 + 0.102890i
$$173$$ 435.000 753.442i 0.191170 0.331116i −0.754468 0.656337i $$-0.772105\pi$$
0.945638 + 0.325220i $$0.105438\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −2556.00 −1.09469
$$177$$ 0 0
$$178$$ 531.000 + 919.719i 0.223596 + 0.387280i
$$179$$ −1158.00 2005.71i −0.483536 0.837509i 0.516285 0.856417i $$-0.327315\pi$$
−0.999821 + 0.0189075i $$0.993981\pi$$
$$180$$ 0 0
$$181$$ −106.000 −0.0435299 −0.0217650 0.999763i $$-0.506929\pi$$
−0.0217650 + 0.999763i $$0.506929\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −3582.00 6204.21i −1.42353 2.46563i
$$186$$ 0 0
$$187$$ 756.000 1309.43i 0.295637 0.512059i
$$188$$ −240.000 −0.0931053
$$189$$ 0 0
$$190$$ −6696.00 −2.55673
$$191$$ −564.000 + 976.877i −0.213663 + 0.370075i −0.952858 0.303416i $$-0.901873\pi$$
0.739195 + 0.673491i $$0.235206\pi$$
$$192$$ 0 0
$$193$$ −2017.00 3493.55i −0.752263 1.30296i −0.946723 0.322048i $$-0.895629\pi$$
0.194460 0.980910i $$-0.437705\pi$$
$$194$$ 429.000 743.050i 0.158765 0.274989i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 1314.00 0.475221 0.237611 0.971360i $$-0.423636\pi$$
0.237611 + 0.971360i $$0.423636\pi$$
$$198$$ 0 0
$$199$$ −2548.00 4413.27i −0.907653 1.57210i −0.817316 0.576190i $$-0.804539\pi$$
−0.0903369 0.995911i $$-0.528794\pi$$
$$200$$ 2089.50 + 3619.12i 0.738750 + 1.27955i
$$201$$ 0 0
$$202$$ −1242.00 −0.432608
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −2862.00 + 4957.13i −0.975077 + 1.68888i
$$206$$ −84.0000 145.492i −0.0284105 0.0492084i
$$207$$ 0 0
$$208$$ −1207.00 + 2090.59i −0.402358 + 0.696904i
$$209$$ −4464.00 −1.47742
$$210$$ 0 0
$$211$$ −3076.00 −1.00360 −0.501802 0.864982i $$-0.667330\pi$$
−0.501802 + 0.864982i $$0.667330\pi$$
$$212$$ −249.000 + 431.281i −0.0806669 + 0.139719i
$$213$$ 0 0
$$214$$ 18.0000 + 31.1769i 0.00574979 + 0.00995893i
$$215$$ 2412.00 4177.71i 0.765102 1.32520i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 4434.00 1.37756
$$219$$ 0 0
$$220$$ −324.000 561.184i −0.0992913 0.171977i
$$221$$ −714.000 1236.68i −0.217325 0.376418i
$$222$$ 0 0
$$223$$ −1888.00 −0.566950 −0.283475 0.958980i $$-0.591487\pi$$
−0.283475 + 0.958980i $$0.591487\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 603.000 1044.43i 0.177482 0.307408i
$$227$$ −2358.00 4084.18i −0.689454 1.19417i −0.972015 0.234919i $$-0.924517\pi$$
0.282561 0.959249i $$-0.408816\pi$$
$$228$$ 0 0
$$229$$ 845.000 1463.58i 0.243839 0.422342i −0.717965 0.696079i $$-0.754926\pi$$
0.961805 + 0.273737i $$0.0882598\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 2142.00 0.606160
$$233$$ 69.0000 119.512i 0.0194006 0.0336028i −0.856162 0.516707i $$-0.827158\pi$$
0.875563 + 0.483104i $$0.160491\pi$$
$$234$$ 0 0
$$235$$ 2160.00 + 3741.23i 0.599587 + 1.03851i
$$236$$ −66.0000 + 114.315i −0.0182044 + 0.0315309i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −1896.00 −0.513147 −0.256573 0.966525i $$-0.582594\pi$$
−0.256573 + 0.966525i $$0.582594\pi$$
$$240$$ 0 0
$$241$$ 1799.00 + 3115.96i 0.480846 + 0.832849i 0.999758 0.0219782i $$-0.00699644\pi$$
−0.518913 + 0.854827i $$0.673663\pi$$
$$242$$ 52.5000 + 90.9327i 0.0139456 + 0.0241544i
$$243$$ 0 0
$$244$$ 398.000 0.104424
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −2108.00 + 3651.16i −0.543032 + 0.940558i
$$248$$ −1680.00 2909.85i −0.430162 0.745062i
$$249$$ 0 0
$$250$$ −1998.00 + 3460.64i −0.505458 + 0.875480i
$$251$$ 3060.00 0.769504 0.384752 0.923020i $$-0.374287\pi$$
0.384752 + 0.923020i $$0.374287\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ −1920.00 + 3325.54i −0.474297 + 0.821507i
$$255$$ 0 0
$$256$$ −756.500 1310.30i −0.184692 0.319897i
$$257$$ −3411.00 + 5908.03i −0.827908 + 1.43398i 0.0717686 + 0.997421i $$0.477136\pi$$
−0.899676 + 0.436557i $$0.856198\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ −612.000 −0.145979
$$261$$ 0 0
$$262$$ 2646.00 + 4583.01i 0.623933 + 1.08068i
$$263$$ 1296.00 + 2244.74i 0.303858 + 0.526298i 0.977007 0.213209i $$-0.0683917\pi$$
−0.673148 + 0.739508i $$0.735058\pi$$
$$264$$ 0 0
$$265$$ 8964.00 2.07794
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −46.0000 + 79.6743i −0.0104847 + 0.0181600i
$$269$$ 4107.00 + 7113.53i 0.930886 + 1.61234i 0.781811 + 0.623515i $$0.214296\pi$$
0.149074 + 0.988826i $$0.452371\pi$$
$$270$$ 0 0
$$271$$ 2672.00 4628.04i 0.598939 1.03739i −0.394039 0.919094i $$-0.628923\pi$$
0.992978 0.118299i $$-0.0377441\pi$$
$$272$$ 2982.00 0.664744
$$273$$ 0 0
$$274$$ 7074.00 1.55969
$$275$$ −3582.00 + 6204.21i −0.785464 + 1.36046i
$$276$$ 0 0
$$277$$ 3257.00 + 5641.29i 0.706477 + 1.22365i 0.966156 + 0.257959i $$0.0830500\pi$$
−0.259679 + 0.965695i $$0.583617\pi$$
$$278$$ 78.0000 135.100i 0.0168278 0.0291466i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −6618.00 −1.40497 −0.702485 0.711698i $$-0.747926\pi$$
−0.702485 + 0.711698i $$0.747926\pi$$
$$282$$ 0 0
$$283$$ −1630.00 2823.24i −0.342380 0.593019i 0.642494 0.766290i $$-0.277900\pi$$
−0.984874 + 0.173271i $$0.944566\pi$$
$$284$$ −360.000 623.538i −0.0752186 0.130282i
$$285$$ 0 0
$$286$$ −3672.00 −0.759195
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 1574.50 2727.11i 0.320476 0.555081i
$$290$$ 2754.00 + 4770.07i 0.557657 + 0.965890i
$$291$$ 0 0
$$292$$ 251.000 434.745i 0.0503036 0.0871285i
$$293$$ −5118.00 −1.02047 −0.510233 0.860036i $$-0.670441\pi$$
−0.510233 + 0.860036i $$0.670441\pi$$
$$294$$ 0 0
$$295$$ 2376.00 0.468936
$$296$$ 4179.00 7238.24i 0.820606 1.42133i
$$297$$ 0 0
$$298$$ −2619.00 4536.24i −0.509109 0.881803i
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −696.000 −0.132617
$$303$$ 0 0
$$304$$ −4402.00 7624.49i −0.830500 1.43847i
$$305$$ −3582.00 6204.21i −0.672475 1.16476i
$$306$$ 0 0
$$307$$ 452.000 0.0840293 0.0420147 0.999117i $$-0.486622\pi$$
0.0420147 + 0.999117i $$0.486622\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 4320.00 7482.46i 0.791482 1.37089i
$$311$$ 2508.00 + 4343.98i 0.457285 + 0.792041i 0.998816 0.0486397i $$-0.0154886\pi$$
−0.541531 + 0.840681i $$0.682155\pi$$
$$312$$ 0 0
$$313$$ −2701.00 + 4678.27i −0.487762 + 0.844829i −0.999901 0.0140739i $$-0.995520\pi$$
0.512139 + 0.858903i $$0.328853\pi$$
$$314$$ 5082.00 0.913356
$$315$$ 0 0
$$316$$ −1024.00 −0.182293
$$317$$ 5043.00 8734.73i 0.893511 1.54761i 0.0578751 0.998324i $$-0.481567\pi$$
0.835636 0.549283i $$-0.185099\pi$$
$$318$$ 0 0
$$319$$ 1836.00 + 3180.05i 0.322245 + 0.558145i
$$320$$ −3897.00 + 6749.80i −0.680778 + 1.17914i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 5208.00 0.897154
$$324$$ 0 0
$$325$$ 3383.00 + 5859.53i 0.577400 + 1.00009i
$$326$$ 4398.00 + 7617.56i 0.747186 + 1.29416i
$$327$$ 0 0
$$328$$ −6678.00 −1.12418
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 4022.00 6966.31i 0.667883 1.15681i −0.310613 0.950537i $$-0.600534\pi$$
0.978495 0.206270i $$-0.0661325\pi$$
$$332$$ −102.000 176.669i −0.0168614 0.0292048i
$$333$$ 0 0
$$334$$ 1764.00 3055.34i 0.288987 0.500541i
$$335$$ 1656.00 0.270080
$$336$$ 0 0
$$337$$ 4178.00 0.675342 0.337671 0.941264i $$-0.390361\pi$$
0.337671 + 0.941264i $$0.390361\pi$$
$$338$$ 1561.50 2704.60i 0.251285 0.435239i
$$339$$ 0 0
$$340$$ 378.000 + 654.715i 0.0602939 + 0.104432i
$$341$$ 2880.00 4988.31i 0.457363 0.792176i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 5628.00 0.882097
$$345$$ 0 0
$$346$$ 1305.00 + 2260.33i 0.202767 + 0.351202i
$$347$$ 78.0000 + 135.100i 0.0120670 + 0.0209007i 0.871996 0.489513i $$-0.162826\pi$$
−0.859929 + 0.510414i $$0.829492\pi$$
$$348$$ 0 0
$$349$$ −12418.0 −1.90464 −0.952321 0.305097i $$-0.901311\pi$$
−0.952321 + 0.305097i $$0.901311\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 810.000 1402.96i 0.122651 0.212438i
$$353$$ −3915.00 6780.98i −0.590296 1.02242i −0.994192 0.107618i $$-0.965678\pi$$
0.403897 0.914805i $$-0.367656\pi$$
$$354$$ 0 0
$$355$$ −6480.00 + 11223.7i −0.968796 + 1.67800i
$$356$$ −354.000 −0.0527021
$$357$$ 0 0
$$358$$ 6948.00 1.02574
$$359$$ −4656.00 + 8064.43i −0.684497 + 1.18558i 0.289098 + 0.957299i $$0.406645\pi$$
−0.973595 + 0.228283i $$0.926689\pi$$
$$360$$ 0 0
$$361$$ −4258.50 7375.94i −0.620863 1.07537i
$$362$$ 159.000 275.396i 0.0230852 0.0399848i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −9036.00 −1.29580
$$366$$ 0 0
$$367$$ 1880.00 + 3256.26i 0.267398 + 0.463148i 0.968189 0.250219i $$-0.0805027\pi$$
−0.700791 + 0.713367i $$0.747169\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 21492.0 3.01977
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −2935.00 + 5083.57i −0.407422 + 0.705676i −0.994600 0.103782i $$-0.966906\pi$$
0.587178 + 0.809458i $$0.300239\pi$$
$$374$$ 2268.00 + 3928.29i 0.313571 + 0.543121i
$$375$$ 0 0
$$376$$ −2520.00 + 4364.77i −0.345636 + 0.598659i
$$377$$ 3468.00 0.473769
$$378$$ 0 0
$$379$$ −1852.00 −0.251005 −0.125502 0.992093i $$-0.540054\pi$$
−0.125502 + 0.992093i $$0.540054\pi$$
$$380$$ 1116.00 1932.97i 0.150657 0.260945i
$$381$$ 0 0
$$382$$ −1692.00 2930.63i −0.226624 0.392524i
$$383$$ 1080.00 1870.61i 0.144087 0.249566i −0.784945 0.619566i $$-0.787309\pi$$
0.929032 + 0.369999i $$0.120642\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 12102.0 1.59579
$$387$$ 0 0
$$388$$ 143.000 + 247.683i 0.0187106 + 0.0324078i
$$389$$ −3393.00 5876.85i −0.442241 0.765985i 0.555614 0.831440i $$-0.312483\pi$$
−0.997855 + 0.0654557i $$0.979150\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ −1971.00 + 3413.87i −0.252024 + 0.436519i
$$395$$ 9216.00 + 15962.6i 1.17394 + 2.03333i
$$396$$ 0 0
$$397$$ 3257.00 5641.29i 0.411748 0.713169i −0.583333 0.812233i $$-0.698252\pi$$
0.995081 + 0.0990641i $$0.0315849\pi$$
$$398$$ 15288.0 1.92542
$$399$$ 0 0
$$400$$ −14129.0 −1.76612
$$401$$ 1665.00 2883.86i 0.207347 0.359135i −0.743531 0.668701i $$-0.766850\pi$$
0.950878 + 0.309566i $$0.100184\pi$$
$$402$$ 0 0
$$403$$ −2720.00 4711.18i −0.336211 0.582334i
$$404$$ 207.000 358.535i 0.0254917 0.0441529i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 14328.0 1.74499
$$408$$ 0 0
$$409$$ 2699.00 + 4674.81i 0.326301 + 0.565169i 0.981775 0.190048i $$-0.0608645\pi$$
−0.655474 + 0.755218i $$0.727531\pi$$
$$410$$ −8586.00 14871.4i −1.03423 1.79133i
$$411$$ 0 0
$$412$$ 56.0000 0.00669641
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −1836.00 + 3180.05i −0.217170 + 0.376150i
$$416$$ −765.000 1325.02i −0.0901616 0.156164i
$$417$$ 0 0
$$418$$ 6696.00 11597.8i 0.783522 1.35710i
$$419$$ −13092.0 −1.52646 −0.763229 0.646128i $$-0.776387\pi$$
−0.763229 + 0.646128i $$0.776387\pi$$
$$420$$ 0 0
$$421$$ −322.000 −0.0372763 −0.0186381 0.999826i $$-0.505933\pi$$
−0.0186381 + 0.999826i $$0.505933\pi$$
$$422$$ 4614.00 7991.68i 0.532242 0.921870i
$$423$$ 0 0
$$424$$ 5229.00 + 9056.89i 0.598921 + 1.03736i
$$425$$ 4179.00 7238.24i 0.476968 0.826132i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −12.0000 −0.00135524
$$429$$ 0 0
$$430$$ 7236.00 + 12533.1i 0.811514 + 1.40558i
$$431$$ 1308.00 + 2265.52i 0.146181 + 0.253193i 0.929813 0.368032i $$-0.119968\pi$$
−0.783632 + 0.621226i $$0.786635\pi$$
$$432$$ 0 0
$$433$$ 4322.00 0.479681 0.239841 0.970812i $$-0.422905\pi$$
0.239841 + 0.970812i $$0.422905\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −739.000 + 1279.99i −0.0811736 + 0.140597i
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 4508.00 7808.09i 0.490103 0.848883i −0.509832 0.860274i $$-0.670293\pi$$
0.999935 + 0.0113909i $$0.00362592\pi$$
$$440$$ −13608.0 −1.47440
$$441$$ 0 0
$$442$$ 4284.00 0.461016
$$443$$ −2634.00 + 4562.22i −0.282495 + 0.489295i −0.971999 0.234987i $$-0.924495\pi$$
0.689504 + 0.724282i $$0.257829\pi$$
$$444$$ 0 0
$$445$$ 3186.00 + 5518.31i 0.339395 + 0.587850i
$$446$$ 2832.00 4905.17i 0.300671 0.520777i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 5310.00 0.558117 0.279058 0.960274i $$-0.409978\pi$$
0.279058 + 0.960274i $$0.409978\pi$$
$$450$$ 0 0
$$451$$ −5724.00 9914.26i −0.597633 1.03513i
$$452$$ 201.000 + 348.142i 0.0209165 + 0.0362284i
$$453$$ 0 0
$$454$$ 14148.0 1.46255
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −7885.00 + 13657.2i −0.807100 + 1.39794i 0.107764 + 0.994177i $$0.465631\pi$$
−0.914864 + 0.403762i $$0.867702\pi$$
$$458$$ 2535.00 + 4390.75i 0.258631 + 0.447961i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 5370.00 0.542529 0.271264 0.962505i $$-0.412558\pi$$
0.271264 + 0.962505i $$0.412558\pi$$
$$462$$ 0 0
$$463$$ −3328.00 −0.334050 −0.167025 0.985953i $$-0.553416\pi$$
−0.167025 + 0.985953i $$0.553416\pi$$
$$464$$ −3621.00 + 6271.76i −0.362286 + 0.627498i
$$465$$ 0 0
$$466$$ 207.000 + 358.535i 0.0205774 + 0.0356412i
$$467$$ 2274.00 3938.68i 0.225328 0.390280i −0.731090 0.682281i $$-0.760988\pi$$
0.956418 + 0.292002i $$0.0943213\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ −12960.0 −1.27192
$$471$$ 0 0
$$472$$ 1386.00 + 2400.62i 0.135161 + 0.234105i
$$473$$ 4824.00 + 8355.41i 0.468938 + 0.812225i
$$474$$ 0 0
$$475$$ −24676.0 −2.38361
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 2844.00 4925.95i 0.272137 0.471355i
$$479$$ −4032.00 6983.63i −0.384607 0.666159i 0.607108 0.794620i $$-0.292330\pi$$
−0.991715 + 0.128461i $$0.958996\pi$$
$$480$$ 0 0
$$481$$ 6766.00 11719.1i 0.641378 1.11090i
$$482$$ −10794.0 −1.02003
$$483$$ 0 0
$$484$$ −35.0000 −0.00328700
$$485$$ 2574.00 4458.30i 0.240988 0.417404i
$$486$$ 0 0
$$487$$ −8308.00 14389.9i −0.773042 1.33895i −0.935888 0.352296i $$-0.885401\pi$$
0.162847 0.986651i $$-0.447932\pi$$
$$488$$ 4179.00 7238.24i 0.387653 0.671434i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 7140.00 0.656260 0.328130 0.944633i $$-0.393582\pi$$
0.328130 + 0.944633i $$0.393582\pi$$
$$492$$ 0 0
$$493$$ −2142.00 3710.05i −0.195681 0.338930i
$$494$$ −6324.00 10953.5i −0.575972 0.997613i
$$495$$ 0 0
$$496$$ 11360.0 1.02839
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 4562.00 7901.62i 0.409265 0.708868i −0.585543 0.810642i $$-0.699119\pi$$
0.994808 + 0.101774i $$0.0324519\pi$$
$$500$$ −666.000 1153.55i −0.0595689 0.103176i
$$501$$ 0 0
$$502$$ −4590.00 + 7950.11i −0.408091 + 0.706834i
$$503$$ 6552.00 0.580794 0.290397 0.956906i $$-0.406213\pi$$
0.290397 + 0.956906i $$0.406213\pi$$
$$504$$ 0 0
$$505$$ −7452.00 −0.656653
$$506$$ 0 0
$$507$$ 0 0
$$508$$ −640.000 1108.51i −0.0558965 0.0968155i
$$509$$ 1395.00 2416.21i 0.121478 0.210406i −0.798873 0.601500i $$-0.794570\pi$$
0.920351 + 0.391094i $$0.127903\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −8733.00 −0.753804
$$513$$ 0 0
$$514$$ −10233.0 17724.1i −0.878129 1.52096i
$$515$$ −504.000 872.954i −0.0431241 0.0746931i
$$516$$ 0 0
$$517$$ −8640.00 −0.734984
$$518$$ 0 0
$$519$$ 0 0
$$520$$ −6426.00 + 11130.2i −0.541921 + 0.938634i
$$521$$ −7431.00 12870.9i −0.624871 1.08231i −0.988566 0.150791i $$-0.951818\pi$$
0.363694 0.931518i $$-0.381515\pi$$
$$522$$ 0 0
$$523$$ −8830.00 + 15294.0i −0.738258 + 1.27870i 0.215021 + 0.976609i $$0.431018\pi$$
−0.953279 + 0.302091i $$0.902315\pi$$
$$524$$ −1764.00 −0.147062
$$525$$ 0 0
$$526$$ −7776.00 −0.644581
$$527$$ −3360.00 + 5819.69i −0.277730 + 0.481043i
$$528$$ 0 0
$$529$$ 6083.50 + 10536.9i 0.500000 + 0.866025i
$$530$$ −13446.0 + 23289.2i −1.10199 + 1.90871i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −10812.0 −0.878649
$$534$$ 0 0
$$535$$ 108.000 + 187.061i 0.00872756 + 0.0151166i
$$536$$ 966.000 + 1673.16i 0.0778449 + 0.134831i
$$537$$ 0 0
$$538$$ −24642.0 −1.97471
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 9917.00 17176.7i 0.788106 1.36504i −0.139021 0.990290i $$-0.544395\pi$$
0.927126 0.374749i $$-0.122271\pi$$
$$542$$ 8016.00 + 13884.1i 0.635271 + 1.10032i
$$543$$ 0 0
$$544$$ −945.000 + 1636.79i −0.0744789 + 0.129001i
$$545$$ 26604.0 2.09099
$$546$$ 0 0
$$547$$ 20972.0 1.63930 0.819651 0.572863i $$-0.194167\pi$$
0.819651 + 0.572863i $$0.194167\pi$$
$$548$$ −1179.00 + 2042.09i −0.0919058 + 0.159186i
$$549$$ 0 0
$$550$$ −10746.0 18612.6i −0.833111 1.44299i
$$551$$ −6324.00 + 10953.5i −0.488950 + 0.846886i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −19542.0 −1.49866
$$555$$ 0 0
$$556$$ 26.0000 + 45.0333i 0.00198318 + 0.00343496i
$$557$$ 10587.0 + 18337.2i 0.805360 + 1.39492i 0.916048 + 0.401069i $$0.131361\pi$$
−0.110688 + 0.993855i $$0.535305\pi$$
$$558$$ 0 0
$$559$$ 9112.00 0.689439
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 9927.00 17194.1i 0.745098 1.29055i
$$563$$ −8886.00 15391.0i −0.665187 1.15214i −0.979235 0.202730i $$-0.935019\pi$$
0.314048 0.949407i $$-0.398315\pi$$
$$564$$ 0 0
$$565$$ 3618.00 6266.56i 0.269399 0.466613i
$$566$$ 9780.00 0.726297
$$567$$ 0 0
$$568$$ −15120.0 −1.11694
$$569$$ 4125.00 7144.71i 0.303917 0.526400i −0.673102 0.739549i $$-0.735039\pi$$
0.977020 + 0.213149i $$0.0683720\pi$$
$$570$$ 0 0
$$571$$ −10378.0 17975.2i −0.760606 1.31741i −0.942539 0.334097i $$-0.891569\pi$$
0.181933 0.983311i $$-0.441765\pi$$
$$572$$ 612.000 1060.02i 0.0447360 0.0774851i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −1.00000 1.73205i −7.21500e−5 0.000124967i 0.865989 0.500062i $$-0.166690\pi$$
−0.866061 + 0.499938i $$0.833356\pi$$
$$578$$ 4723.50 + 8181.34i 0.339916 + 0.588753i
$$579$$ 0 0
$$580$$ −1836.00 −0.131441
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −8964.00 + 15526.1i −0.636794 + 1.10296i
$$584$$ −5271.00 9129.64i −0.373485 0.646896i
$$585$$ 0 0
$$586$$ 7677.00 13297.0i 0.541184 0.937359i
$$587$$ −26364.0 −1.85376 −0.926881 0.375354i $$-0.877521\pi$$
−0.926881 + 0.375354i $$0.877521\pi$$
$$588$$ 0 0
$$589$$ 19840.0 1.38793
$$590$$ −3564.00 + 6173.03i −0.248691 + 0.430745i
$$591$$ 0 0
$$592$$ 14129.0 + 24472.1i 0.980909 + 1.69898i
$$593$$ 1149.00 1990.13i 0.0795679 0.137816i −0.823496 0.567323i $$-0.807979\pi$$
0.903064 + 0.429507i $$0.141313\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 1746.00 0.119998
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 1536.00 + 2660.43i 0.104773 + 0.181473i 0.913646 0.406512i $$-0.133255\pi$$
−0.808872 + 0.587984i $$0.799922\pi$$
$$600$$ 0 0
$$601$$ 24554.0 1.66652 0.833260 0.552881i $$-0.186472\pi$$
0.833260 + 0.552881i $$0.186472\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 116.000 200.918i 0.00781452 0.0135352i
$$605$$ 315.000 + 545.596i 0.0211679 + 0.0366639i
$$606$$ 0 0
$$607$$ −8416.00 + 14576.9i −0.562759 + 0.974728i 0.434495 + 0.900674i $$0.356927\pi$$
−0.997254 + 0.0740535i $$0.976406\pi$$
$$608$$ 5580.00 0.372202
$$609$$ 0 0
$$610$$ 21492.0 1.42653
$$611$$ −4080.00 + 7066.77i −0.270146 + 0.467906i
$$612$$ 0 0
$$613$$ 1241.00 + 2149.48i 0.0817676 + 0.141626i 0.904009 0.427513i $$-0.140610\pi$$
−0.822242 + 0.569139i $$0.807277\pi$$
$$614$$ −678.000 + 1174.33i −0.0445633 + 0.0771859i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 15798.0 1.03080 0.515400 0.856950i $$-0.327643\pi$$
0.515400 + 0.856950i $$0.327643\pi$$
$$618$$ 0 0
$$619$$ 7730.00 + 13388.8i 0.501930 + 0.869369i 0.999998 + 0.00223050i $$0.000709990\pi$$
−0.498067 + 0.867138i $$0.665957\pi$$
$$620$$ 1440.00 + 2494.15i 0.0932771 + 0.161561i
$$621$$ 0 0
$$622$$ −15048.0 −0.970048
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 449.500 778.557i 0.0287680 0.0498276i
$$626$$ −8103.00 14034.8i −0.517350 0.896076i
$$627$$ 0 0
$$628$$ −847.000 + 1467.05i −0.0538200 + 0.0932190i
$$629$$ −16716.0 −1.05964
$$630$$ 0 0
$$631$$ −7720.00 −0.487050 −0.243525 0.969895i $$-0.578304\pi$$
−0.243525 + 0.969895i $$0.578304\pi$$
$$632$$ −10752.0 + 18623.0i −0.676727 + 1.17213i
$$633$$ 0 0
$$634$$ 15129.0 + 26204.2i 0.947712 + 1.64149i
$$635$$ −11520.0 + 19953.2i −0.719933 + 1.24696i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ −11016.0 −0.683586
$$639$$ 0 0
$$640$$ −14931.0 25861.3i −0.922187 1.59727i
$$641$$ −8631.00 14949.3i −0.531832 0.921159i −0.999310 0.0371545i $$-0.988171\pi$$
0.467478 0.884005i $$-0.345163\pi$$
$$642$$ 0 0
$$643$$ −12220.0 −0.749471 −0.374735 0.927132i $$-0.622266\pi$$
−0.374735 + 0.927132i $$0.622266\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −7812.00 + 13530.8i −0.475788 + 0.824089i
$$647$$ 6780.00 + 11743.3i 0.411977 + 0.713566i 0.995106 0.0988143i $$-0.0315050\pi$$
−0.583129 + 0.812380i $$0.698172\pi$$
$$648$$ 0 0
$$649$$ −2376.00 + 4115.35i −0.143707 + 0.248909i
$$650$$ −20298.0 −1.22485
$$651$$ 0 0
$$652$$ −2932.00 −0.176113
$$653$$ 11547.0 20000.0i 0.691989 1.19856i −0.279196 0.960234i $$-0.590068\pi$$
0.971185 0.238326i $$-0.0765988\pi$$
$$654$$ 0 0
$$655$$ 15876.0 + 27498.0i 0.947064 + 1.64036i
$$656$$ 11289.0 19553.1i 0.671892 1.16375i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −22548.0 −1.33285 −0.666423 0.745574i $$-0.732175\pi$$
−0.666423 + 0.745574i $$0.732175\pi$$
$$660$$ 0 0
$$661$$ −8731.00 15122.5i −0.513762 0.889862i −0.999873 0.0159643i $$-0.994918\pi$$
0.486111 0.873897i $$-0.338415\pi$$
$$662$$ 12066.0 + 20898.9i 0.708396 + 1.22698i
$$663$$ 0 0
$$664$$ −4284.00 −0.250379
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 588.000 + 1018.45i 0.0340575 + 0.0589893i
$$669$$ 0 0
$$670$$ −2484.00 + 4302.41i −0.143232 + 0.248085i
$$671$$ 14328.0 0.824331
$$672$$ 0 0
$$673$$ −22462.0 −1.28655 −0.643274 0.765636i $$-0.722424\pi$$
−0.643274 + 0.765636i $$0.722424\pi$$
$$674$$ −6267.00 + 10854.8i −0.358154 + 0.620341i
$$675$$ 0 0
$$676$$ 520.500 + 901.532i 0.0296142 + 0.0512934i
$$677$$ −12777.0 + 22130.4i −0.725347 + 1.25634i 0.233484 + 0.972361i $$0.424987\pi$$
−0.958831 + 0.283977i $$0.908346\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 15876.0 0.895319
$$681$$ 0 0
$$682$$ 8640.00 + 14964.9i 0.485107 + 0.840229i
$$683$$ 4638.00 + 8033.25i 0.259836 + 0.450050i 0.966198 0.257802i $$-0.0829981\pi$$
−0.706362 + 0.707851i $$0.749665\pi$$
$$684$$ 0 0
$$685$$ 42444.0 2.36745
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −9514.00 + 16478.7i −0.527206 + 0.913148i
$$689$$ 8466.00 + 14663.5i 0.468112 + 0.810793i
$$690$$ 0 0
$$691$$ −13690.0 + 23711.8i −0.753679 + 1.30541i 0.192349 + 0.981326i $$0.438389\pi$$
−0.946028 + 0.324084i $$0.894944\pi$$
$$692$$ −870.000 −0.0477925
$$693$$ 0 0
$$694$$ −468.000 −0.0255980
$$695$$ 468.000 810.600i 0.0255428 0.0442414i
$$696$$ 0 0
$$697$$ 6678.00 + 11566.6i 0.362909 + 0.628576i
$$698$$ 18627.0 32262.9i 1.01009 1.74953i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −25830.0 −1.39171 −0.695853 0.718184i $$-0.744973\pi$$
−0.695853 + 0.718184i $$0.744973\pi$$
$$702$$ 0 0
$$703$$ 24676.0 + 42740.1i 1.32386 + 2.29299i
$$704$$ −7794.00 13499.6i −0.417255 0.722707i
$$705$$ 0 0
$$706$$ 23490.0 1.25221
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 3113.00 5391.87i 0.164896 0.285608i −0.771722 0.635959i $$-0.780605\pi$$
0.936618 + 0.350351i $$0.113938\pi$$
$$710$$ −19440.0 33671.1i −1.02756 1.77979i
$$711$$ 0 0
$$712$$ −3717.00 + 6438.03i −0.195647 + 0.338870i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −22032.0 −1.15238
$$716$$ −1158.00 + 2005.71i −0.0604420 + 0.104689i
$$717$$ 0 0
$$718$$ −13968.0 24193.3i −0.726018 1.25750i
$$719$$ −7536.00 + 13052.7i −0.390884 + 0.677030i −0.992566 0.121705i $$-0.961164\pi$$
0.601683 + 0.798735i $$0.294497\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 25551.0 1.31705
$$723$$ 0 0
$$724$$ 53.0000 + 91.7987i 0.00272062 + 0.00471225i
$$725$$ 10149.0 + 17578.6i 0.519896 + 0.900486i
$$726$$ 0 0
$$727$$ −32920.0 −1.67942 −0.839708 0.543038i $$-0.817274\pi$$
−0.839708 + 0.543038i $$0.817274\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 13554.0 23476.2i 0.687200 1.19027i
$$731$$ −5628.00 9747.98i −0.284759 0.493218i
$$732$$ 0 0
$$733$$ 3473.00 6015.41i 0.175004 0.303116i −0.765158 0.643842i $$-0.777339\pi$$
0.940163 + 0.340726i $$0.110673\pi$$
$$734$$ −11280.0 −0.567238
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −1656.00 + 2868.28i −0.0827674 + 0.143357i
$$738$$ 0 0
$$739$$ 1178.00 + 2040.36i 0.0586379 + 0.101564i 0.893854 0.448358i $$-0.147991\pi$$
−0.835216 + 0.549922i $$0.814658\pi$$
$$740$$ −3582.00 + 6204.21i −0.177942 + 0.308204i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 23520.0 1.16133 0.580663 0.814144i $$-0.302793\pi$$
0.580663 + 0.814144i $$0.302793\pi$$
$$744$$ 0 0
$$745$$ −15714.0 27217.4i −0.772774 1.33848i
$$746$$ −8805.00 15250.7i −0.432137 0.748483i
$$747$$ 0 0
$$748$$ −1512.00 −0.0739094
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −1504.00 + 2605.00i −0.0730782 + 0.126575i −0.900249 0.435376i $$-0.856616\pi$$
0.827171 + 0.561951i $$0.189949\pi$$
$$752$$ −8520.00 14757.1i −0.413155 0.715605i
$$753$$ 0 0
$$754$$ −5202.00 + 9010.13i −0.251254 + 0.435185i
$$755$$ −4176.00 −0.201298
$$756$$ 0 0
$$757$$ −20770.0 −0.997224 −0.498612 0.866825i $$-0.666157\pi$$
−0.498612 + 0.866825i $$0.666157\pi$$
$$758$$ 2778.00 4811.64i 0.133115 0.230563i
$$759$$ 0 0
$$760$$ −23436.0 40592.3i −1.11857 1.93742i
$$761$$ 5769.00 9992.20i 0.274804 0.475975i −0.695281 0.718738i $$-0.744720\pi$$
0.970086 + 0.242763i $$0.0780536\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 1128.00 0.0534157
$$765$$ 0 0
$$766$$ 3240.00 + 5611.84i 0.152828 + 0.264705i
$$767$$ 2244.00 + 3886.72i 0.105640 + 0.182974i
$$768$$ 0 0
$$769$$ 8498.00 0.398499 0.199249 0.979949i $$-0.436150\pi$$
0.199249 + 0.979949i $$0.436150\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −2017.00 + 3493.55i −0.0940329 + 0.162870i
$$773$$ −16161.0 27991.7i −0.751967 1.30245i −0.946868 0.321623i $$-0.895772\pi$$
0.194901 0.980823i $$-0.437562\pi$$
$$774$$ 0 0
$$775$$ 15920.0 27574.2i 0.737888 1.27806i
$$776$$ 6006.00 0.277839
$$777$$ 0 0
$$778$$ 20358.0 0.938136
$$779$$ 19716.0 34149.1i 0.906802 1.57063i
$$780$$ 0 0
$$781$$ −12960.0 22447.4i −0.593784 1.02846i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 30492.0 1.38638
$$786$$ 0 0
$$787$$ −13114.0 22714.1i −0.593982 1.02881i −0.993690 0.112164i $$-0.964222\pi$$
0.399708 0.916643i $$-0.369112\pi$$
$$788$$ −657.000 1137.96i −0.0297013 0.0514442i
$$789$$ 0 0
$$790$$ −55296.0 −2.49031
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 6766.00 11719.1i 0.302986 0.524787i
$$794$$ 9771.00 + 16923.9i 0.436725 + 0.756430i
$$795$$ 0 0
$$796$$ −2548.00 + 4413.27i −0.113457 + 0.196513i
$$797$$ 43338.0 1.92611 0.963056 0.269302i $$-0.0867931\pi$$
0.963056 + 0.269302i $$0.0867931\pi$$
$$798$$ 0 0
$$799$$ 10080.0 0.446314
$$800$$ 4477.50 7755.26i 0.197879 0.342737i
$$801$$ 0 0
$$802$$ 4995.00 + 8651.59i 0.219925 + 0.380921i
$$803$$ 9036.00 15650.8i 0.397103 0.687802i
$$804$$ 0 0
$$805$$ 0 0