# Properties

 Label 637.2.e.h.508.2 Level $637$ Weight $2$ Character 637.508 Analytic conductor $5.086$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$637 = 7^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 637.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.08647060876$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{5})$$ Defining polynomial: $$x^{4} - x^{3} + 2 x^{2} + x + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 91) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 508.2 Root $$0.809017 + 1.40126i$$ of defining polynomial Character $$\chi$$ $$=$$ 637.508 Dual form 637.2.e.h.79.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.30902 + 2.26728i) q^{2} +(-1.11803 + 1.93649i) q^{3} +(-2.42705 + 4.20378i) q^{4} +(1.11803 + 1.93649i) q^{5} -5.85410 q^{6} -7.47214 q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})$$ $$q+(1.30902 + 2.26728i) q^{2} +(-1.11803 + 1.93649i) q^{3} +(-2.42705 + 4.20378i) q^{4} +(1.11803 + 1.93649i) q^{5} -5.85410 q^{6} -7.47214 q^{8} +(-1.00000 - 1.73205i) q^{9} +(-2.92705 + 5.06980i) q^{10} +(1.50000 - 2.59808i) q^{11} +(-5.42705 - 9.39993i) q^{12} +1.00000 q^{13} -5.00000 q^{15} +(-4.92705 - 8.53390i) q^{16} +(0.736068 - 1.27491i) q^{17} +(2.61803 - 4.53457i) q^{18} +(1.50000 + 2.59808i) q^{19} -10.8541 q^{20} +7.85410 q^{22} +(4.11803 + 7.13264i) q^{23} +(8.35410 - 14.4697i) q^{24} +(1.30902 + 2.26728i) q^{26} -2.23607 q^{27} +4.47214 q^{29} +(-6.54508 - 11.3364i) q^{30} +(2.50000 - 4.33013i) q^{31} +(5.42705 - 9.39993i) q^{32} +(3.35410 + 5.80948i) q^{33} +3.85410 q^{34} +9.70820 q^{36} +(-2.35410 - 4.07742i) q^{37} +(-3.92705 + 6.80185i) q^{38} +(-1.11803 + 1.93649i) q^{39} +(-8.35410 - 14.4697i) q^{40} +4.47214 q^{41} -8.00000 q^{43} +(7.28115 + 12.6113i) q^{44} +(2.23607 - 3.87298i) q^{45} +(-10.7812 + 18.6735i) q^{46} +(-3.73607 - 6.47106i) q^{47} +22.0344 q^{48} +(1.64590 + 2.85078i) q^{51} +(-2.42705 + 4.20378i) q^{52} +(3.73607 - 6.47106i) q^{53} +(-2.92705 - 5.06980i) q^{54} +6.70820 q^{55} -6.70820 q^{57} +(5.85410 + 10.1396i) q^{58} +(-0.736068 + 1.27491i) q^{59} +(12.1353 - 21.0189i) q^{60} +(1.50000 + 2.59808i) q^{61} +13.0902 q^{62} +8.70820 q^{64} +(1.11803 + 1.93649i) q^{65} +(-8.78115 + 15.2094i) q^{66} +(1.50000 - 2.59808i) q^{67} +(3.57295 + 6.18853i) q^{68} -18.4164 q^{69} -8.94427 q^{71} +(7.47214 + 12.9421i) q^{72} +(-1.35410 + 2.34537i) q^{73} +(6.16312 - 10.6748i) q^{74} -14.5623 q^{76} -5.85410 q^{78} +(1.35410 + 2.34537i) q^{79} +(11.0172 - 19.0824i) q^{80} +(5.50000 - 9.52628i) q^{81} +(5.85410 + 10.1396i) q^{82} +3.29180 q^{85} +(-10.4721 - 18.1383i) q^{86} +(-5.00000 + 8.66025i) q^{87} +(-11.2082 + 19.4132i) q^{88} +(1.11803 + 1.93649i) q^{89} +11.7082 q^{90} -39.9787 q^{92} +(5.59017 + 9.68246i) q^{93} +(9.78115 - 16.9415i) q^{94} +(-3.35410 + 5.80948i) q^{95} +(12.1353 + 21.0189i) q^{96} -9.41641 q^{97} -6.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 3 q^{2} - 3 q^{4} - 10 q^{6} - 12 q^{8} - 4 q^{9} + O(q^{10})$$ $$4 q + 3 q^{2} - 3 q^{4} - 10 q^{6} - 12 q^{8} - 4 q^{9} - 5 q^{10} + 6 q^{11} - 15 q^{12} + 4 q^{13} - 20 q^{15} - 13 q^{16} - 6 q^{17} + 6 q^{18} + 6 q^{19} - 30 q^{20} + 18 q^{22} + 12 q^{23} + 20 q^{24} + 3 q^{26} - 15 q^{30} + 10 q^{31} + 15 q^{32} + 2 q^{34} + 12 q^{36} + 4 q^{37} - 9 q^{38} - 20 q^{40} - 32 q^{43} + 9 q^{44} - 23 q^{46} - 6 q^{47} + 30 q^{48} + 20 q^{51} - 3 q^{52} + 6 q^{53} - 5 q^{54} + 10 q^{58} + 6 q^{59} + 15 q^{60} + 6 q^{61} + 30 q^{62} + 8 q^{64} - 15 q^{66} + 6 q^{67} + 21 q^{68} - 20 q^{69} + 12 q^{72} + 8 q^{73} + 9 q^{74} - 18 q^{76} - 10 q^{78} - 8 q^{79} + 15 q^{80} + 22 q^{81} + 10 q^{82} + 40 q^{85} - 24 q^{86} - 20 q^{87} - 18 q^{88} + 20 q^{90} - 66 q^{92} + 19 q^{94} + 15 q^{96} + 16 q^{97} - 24 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$$.

 $$n$$ $$197$$ $$248$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.30902 + 2.26728i 0.925615 + 1.60321i 0.790569 + 0.612372i $$0.209785\pi$$
0.135045 + 0.990839i $$0.456882\pi$$
$$3$$ −1.11803 + 1.93649i −0.645497 + 1.11803i 0.338689 + 0.940898i $$0.390016\pi$$
−0.984186 + 0.177136i $$0.943317\pi$$
$$4$$ −2.42705 + 4.20378i −1.21353 + 2.10189i
$$5$$ 1.11803 + 1.93649i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$6$$ −5.85410 −2.38993
$$7$$ 0 0
$$8$$ −7.47214 −2.64180
$$9$$ −1.00000 1.73205i −0.333333 0.577350i
$$10$$ −2.92705 + 5.06980i −0.925615 + 1.60321i
$$11$$ 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i $$-0.683949\pi$$
0.998526 + 0.0542666i $$0.0172821\pi$$
$$12$$ −5.42705 9.39993i −1.56665 2.71353i
$$13$$ 1.00000 0.277350
$$14$$ 0 0
$$15$$ −5.00000 −1.29099
$$16$$ −4.92705 8.53390i −1.23176 2.13348i
$$17$$ 0.736068 1.27491i 0.178523 0.309210i −0.762852 0.646573i $$-0.776202\pi$$
0.941375 + 0.337363i $$0.109535\pi$$
$$18$$ 2.61803 4.53457i 0.617077 1.06881i
$$19$$ 1.50000 + 2.59808i 0.344124 + 0.596040i 0.985194 0.171442i $$-0.0548427\pi$$
−0.641071 + 0.767482i $$0.721509\pi$$
$$20$$ −10.8541 −2.42705
$$21$$ 0 0
$$22$$ 7.85410 1.67450
$$23$$ 4.11803 + 7.13264i 0.858669 + 1.48726i 0.873199 + 0.487365i $$0.162042\pi$$
−0.0145291 + 0.999894i $$0.504625\pi$$
$$24$$ 8.35410 14.4697i 1.70527 2.95362i
$$25$$ 0 0
$$26$$ 1.30902 + 2.26728i 0.256719 + 0.444651i
$$27$$ −2.23607 −0.430331
$$28$$ 0 0
$$29$$ 4.47214 0.830455 0.415227 0.909718i $$-0.363702\pi$$
0.415227 + 0.909718i $$0.363702\pi$$
$$30$$ −6.54508 11.3364i −1.19496 2.06974i
$$31$$ 2.50000 4.33013i 0.449013 0.777714i −0.549309 0.835619i $$-0.685109\pi$$
0.998322 + 0.0579057i $$0.0184423\pi$$
$$32$$ 5.42705 9.39993i 0.959376 1.66169i
$$33$$ 3.35410 + 5.80948i 0.583874 + 1.01130i
$$34$$ 3.85410 0.660973
$$35$$ 0 0
$$36$$ 9.70820 1.61803
$$37$$ −2.35410 4.07742i −0.387012 0.670324i 0.605034 0.796200i $$-0.293159\pi$$
−0.992046 + 0.125875i $$0.959826\pi$$
$$38$$ −3.92705 + 6.80185i −0.637052 + 1.10341i
$$39$$ −1.11803 + 1.93649i −0.179029 + 0.310087i
$$40$$ −8.35410 14.4697i −1.32090 2.28787i
$$41$$ 4.47214 0.698430 0.349215 0.937043i $$-0.386448\pi$$
0.349215 + 0.937043i $$0.386448\pi$$
$$42$$ 0 0
$$43$$ −8.00000 −1.21999 −0.609994 0.792406i $$-0.708828\pi$$
−0.609994 + 0.792406i $$0.708828\pi$$
$$44$$ 7.28115 + 12.6113i 1.09768 + 1.90123i
$$45$$ 2.23607 3.87298i 0.333333 0.577350i
$$46$$ −10.7812 + 18.6735i −1.58959 + 2.75326i
$$47$$ −3.73607 6.47106i −0.544962 0.943901i −0.998609 0.0527200i $$-0.983211\pi$$
0.453648 0.891181i $$-0.350122\pi$$
$$48$$ 22.0344 3.18040
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 1.64590 + 2.85078i 0.230472 + 0.399189i
$$52$$ −2.42705 + 4.20378i −0.336571 + 0.582959i
$$53$$ 3.73607 6.47106i 0.513188 0.888868i −0.486695 0.873572i $$-0.661798\pi$$
0.999883 0.0152962i $$-0.00486912\pi$$
$$54$$ −2.92705 5.06980i −0.398321 0.689913i
$$55$$ 6.70820 0.904534
$$56$$ 0 0
$$57$$ −6.70820 −0.888523
$$58$$ 5.85410 + 10.1396i 0.768681 + 1.33139i
$$59$$ −0.736068 + 1.27491i −0.0958279 + 0.165979i −0.909954 0.414710i $$-0.863883\pi$$
0.814126 + 0.580688i $$0.197217\pi$$
$$60$$ 12.1353 21.0189i 1.56665 2.71353i
$$61$$ 1.50000 + 2.59808i 0.192055 + 0.332650i 0.945931 0.324367i $$-0.105151\pi$$
−0.753876 + 0.657017i $$0.771818\pi$$
$$62$$ 13.0902 1.66245
$$63$$ 0 0
$$64$$ 8.70820 1.08853
$$65$$ 1.11803 + 1.93649i 0.138675 + 0.240192i
$$66$$ −8.78115 + 15.2094i −1.08089 + 1.87215i
$$67$$ 1.50000 2.59808i 0.183254 0.317406i −0.759733 0.650236i $$-0.774670\pi$$
0.942987 + 0.332830i $$0.108004\pi$$
$$68$$ 3.57295 + 6.18853i 0.433284 + 0.750469i
$$69$$ −18.4164 −2.21707
$$70$$ 0 0
$$71$$ −8.94427 −1.06149 −0.530745 0.847532i $$-0.678088\pi$$
−0.530745 + 0.847532i $$0.678088\pi$$
$$72$$ 7.47214 + 12.9421i 0.880600 + 1.52524i
$$73$$ −1.35410 + 2.34537i −0.158486 + 0.274505i −0.934323 0.356428i $$-0.883994\pi$$
0.775837 + 0.630933i $$0.217328\pi$$
$$74$$ 6.16312 10.6748i 0.716448 1.24092i
$$75$$ 0 0
$$76$$ −14.5623 −1.67041
$$77$$ 0 0
$$78$$ −5.85410 −0.662847
$$79$$ 1.35410 + 2.34537i 0.152348 + 0.263875i 0.932090 0.362226i $$-0.117983\pi$$
−0.779742 + 0.626101i $$0.784650\pi$$
$$80$$ 11.0172 19.0824i 1.23176 2.13348i
$$81$$ 5.50000 9.52628i 0.611111 1.05848i
$$82$$ 5.85410 + 10.1396i 0.646477 + 1.11973i
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 3.29180 0.357045
$$86$$ −10.4721 18.1383i −1.12924 1.95590i
$$87$$ −5.00000 + 8.66025i −0.536056 + 0.928477i
$$88$$ −11.2082 + 19.4132i −1.19480 + 2.06945i
$$89$$ 1.11803 + 1.93649i 0.118511 + 0.205268i 0.919178 0.393842i $$-0.128854\pi$$
−0.800667 + 0.599110i $$0.795521\pi$$
$$90$$ 11.7082 1.23415
$$91$$ 0 0
$$92$$ −39.9787 −4.16807
$$93$$ 5.59017 + 9.68246i 0.579674 + 1.00402i
$$94$$ 9.78115 16.9415i 1.00885 1.74738i
$$95$$ −3.35410 + 5.80948i −0.344124 + 0.596040i
$$96$$ 12.1353 + 21.0189i 1.23855 + 2.14523i
$$97$$ −9.41641 −0.956091 −0.478046 0.878335i $$-0.658655\pi$$
−0.478046 + 0.878335i $$0.658655\pi$$
$$98$$ 0 0
$$99$$ −6.00000 −0.603023
$$100$$ 0 0
$$101$$ −4.50000 + 7.79423i −0.447767 + 0.775555i −0.998240 0.0592978i $$-0.981114\pi$$
0.550474 + 0.834853i $$0.314447\pi$$
$$102$$ −4.30902 + 7.46344i −0.426656 + 0.738990i
$$103$$ −1.35410 2.34537i −0.133424 0.231097i 0.791571 0.611078i $$-0.209264\pi$$
−0.924994 + 0.379981i $$0.875930\pi$$
$$104$$ −7.47214 −0.732703
$$105$$ 0 0
$$106$$ 19.5623 1.90006
$$107$$ 4.88197 + 8.45581i 0.471957 + 0.817454i 0.999485 0.0320835i $$-0.0102142\pi$$
−0.527528 + 0.849538i $$0.676881\pi$$
$$108$$ 5.42705 9.39993i 0.522218 0.904508i
$$109$$ 1.35410 2.34537i 0.129699 0.224646i −0.793861 0.608100i $$-0.791932\pi$$
0.923560 + 0.383454i $$0.125265\pi$$
$$110$$ 8.78115 + 15.2094i 0.837250 + 1.45016i
$$111$$ 10.5279 0.999261
$$112$$ 0 0
$$113$$ 2.94427 0.276974 0.138487 0.990364i $$-0.455776\pi$$
0.138487 + 0.990364i $$0.455776\pi$$
$$114$$ −8.78115 15.2094i −0.822430 1.42449i
$$115$$ −9.20820 + 15.9491i −0.858669 + 1.48726i
$$116$$ −10.8541 + 18.7999i −1.00778 + 1.74552i
$$117$$ −1.00000 1.73205i −0.0924500 0.160128i
$$118$$ −3.85410 −0.354799
$$119$$ 0 0
$$120$$ 37.3607 3.41055
$$121$$ 1.00000 + 1.73205i 0.0909091 + 0.157459i
$$122$$ −3.92705 + 6.80185i −0.355538 + 0.615811i
$$123$$ −5.00000 + 8.66025i −0.450835 + 0.780869i
$$124$$ 12.1353 + 21.0189i 1.08978 + 1.88755i
$$125$$ 11.1803 1.00000
$$126$$ 0 0
$$127$$ −11.4164 −1.01304 −0.506521 0.862228i $$-0.669069\pi$$
−0.506521 + 0.862228i $$0.669069\pi$$
$$128$$ 0.545085 + 0.944115i 0.0481792 + 0.0834488i
$$129$$ 8.94427 15.4919i 0.787499 1.36399i
$$130$$ −2.92705 + 5.06980i −0.256719 + 0.444651i
$$131$$ −4.11803 7.13264i −0.359794 0.623182i 0.628132 0.778107i $$-0.283820\pi$$
−0.987926 + 0.154925i $$0.950486\pi$$
$$132$$ −32.5623 −2.83418
$$133$$ 0 0
$$134$$ 7.85410 0.678491
$$135$$ −2.50000 4.33013i −0.215166 0.372678i
$$136$$ −5.50000 + 9.52628i −0.471621 + 0.816872i
$$137$$ 4.11803 7.13264i 0.351827 0.609383i −0.634742 0.772724i $$-0.718894\pi$$
0.986570 + 0.163341i $$0.0522271\pi$$
$$138$$ −24.1074 41.7552i −2.05216 3.55444i
$$139$$ 23.4164 1.98615 0.993077 0.117466i $$-0.0374771\pi$$
0.993077 + 0.117466i $$0.0374771\pi$$
$$140$$ 0 0
$$141$$ 16.7082 1.40708
$$142$$ −11.7082 20.2792i −0.982531 1.70179i
$$143$$ 1.50000 2.59808i 0.125436 0.217262i
$$144$$ −9.85410 + 17.0678i −0.821175 + 1.42232i
$$145$$ 5.00000 + 8.66025i 0.415227 + 0.719195i
$$146$$ −7.09017 −0.586787
$$147$$ 0 0
$$148$$ 22.8541 1.87860
$$149$$ −0.354102 0.613323i −0.0290092 0.0502453i 0.851156 0.524912i $$-0.175902\pi$$
−0.880166 + 0.474667i $$0.842569\pi$$
$$150$$ 0 0
$$151$$ −10.2082 + 17.6811i −0.830732 + 1.43887i 0.0667268 + 0.997771i $$0.478744\pi$$
−0.897459 + 0.441098i $$0.854589\pi$$
$$152$$ −11.2082 19.4132i −0.909105 1.57462i
$$153$$ −2.94427 −0.238030
$$154$$ 0 0
$$155$$ 11.1803 0.898027
$$156$$ −5.42705 9.39993i −0.434512 0.752597i
$$157$$ 3.50000 6.06218i 0.279330 0.483814i −0.691888 0.722005i $$-0.743221\pi$$
0.971219 + 0.238190i $$0.0765542\pi$$
$$158$$ −3.54508 + 6.14027i −0.282032 + 0.488493i
$$159$$ 8.35410 + 14.4697i 0.662523 + 1.14752i
$$160$$ 24.2705 1.91875
$$161$$ 0 0
$$162$$ 28.7984 2.26261
$$163$$ 8.20820 + 14.2170i 0.642916 + 1.11356i 0.984779 + 0.173813i $$0.0556090\pi$$
−0.341862 + 0.939750i $$0.611058\pi$$
$$164$$ −10.8541 + 18.7999i −0.847563 + 1.46802i
$$165$$ −7.50000 + 12.9904i −0.583874 + 1.01130i
$$166$$ 0 0
$$167$$ −22.4721 −1.73895 −0.869473 0.493980i $$-0.835541\pi$$
−0.869473 + 0.493980i $$0.835541\pi$$
$$168$$ 0 0
$$169$$ 1.00000 0.0769231
$$170$$ 4.30902 + 7.46344i 0.330487 + 0.572419i
$$171$$ 3.00000 5.19615i 0.229416 0.397360i
$$172$$ 19.4164 33.6302i 1.48049 2.56428i
$$173$$ −8.20820 14.2170i −0.624058 1.08090i −0.988722 0.149761i $$-0.952149\pi$$
0.364664 0.931139i $$-0.381184\pi$$
$$174$$ −26.1803 −1.98473
$$175$$ 0 0
$$176$$ −29.5623 −2.22834
$$177$$ −1.64590 2.85078i −0.123713 0.214278i
$$178$$ −2.92705 + 5.06980i −0.219392 + 0.379998i
$$179$$ 10.0623 17.4284i 0.752092 1.30266i −0.194715 0.980860i $$-0.562378\pi$$
0.946807 0.321802i $$-0.104288\pi$$
$$180$$ 10.8541 + 18.7999i 0.809017 + 1.40126i
$$181$$ 25.4164 1.88919 0.944593 0.328243i $$-0.106456\pi$$
0.944593 + 0.328243i $$0.106456\pi$$
$$182$$ 0 0
$$183$$ −6.70820 −0.495885
$$184$$ −30.7705 53.2961i −2.26843 3.92904i
$$185$$ 5.26393 9.11740i 0.387012 0.670324i
$$186$$ −14.6353 + 25.3490i −1.07311 + 1.85868i
$$187$$ −2.20820 3.82472i −0.161480 0.279691i
$$188$$ 36.2705 2.64530
$$189$$ 0 0
$$190$$ −17.5623 −1.27410
$$191$$ −5.59017 9.68246i −0.404491 0.700598i 0.589772 0.807570i $$-0.299218\pi$$
−0.994262 + 0.106972i $$0.965884\pi$$
$$192$$ −9.73607 + 16.8634i −0.702640 + 1.21701i
$$193$$ −0.354102 + 0.613323i −0.0254888 + 0.0441479i −0.878488 0.477764i $$-0.841448\pi$$
0.853000 + 0.521912i $$0.174781\pi$$
$$194$$ −12.3262 21.3497i −0.884972 1.53282i
$$195$$ −5.00000 −0.358057
$$196$$ 0 0
$$197$$ −9.05573 −0.645194 −0.322597 0.946536i $$-0.604556\pi$$
−0.322597 + 0.946536i $$0.604556\pi$$
$$198$$ −7.85410 13.6037i −0.558167 0.966773i
$$199$$ −10.3541 + 17.9338i −0.733983 + 1.27130i 0.221185 + 0.975232i $$0.429007\pi$$
−0.955168 + 0.296064i $$0.904326\pi$$
$$200$$ 0 0
$$201$$ 3.35410 + 5.80948i 0.236580 + 0.409769i
$$202$$ −23.5623 −1.65784
$$203$$ 0 0
$$204$$ −15.9787 −1.11873
$$205$$ 5.00000 + 8.66025i 0.349215 + 0.604858i
$$206$$ 3.54508 6.14027i 0.246998 0.427813i
$$207$$ 8.23607 14.2653i 0.572446 0.991506i
$$208$$ −4.92705 8.53390i −0.341630 0.591720i
$$209$$ 9.00000 0.622543
$$210$$ 0 0
$$211$$ 4.00000 0.275371 0.137686 0.990476i $$-0.456034\pi$$
0.137686 + 0.990476i $$0.456034\pi$$
$$212$$ 18.1353 + 31.4112i 1.24553 + 2.15733i
$$213$$ 10.0000 17.3205i 0.685189 1.18678i
$$214$$ −12.7812 + 22.1376i −0.873702 + 1.51330i
$$215$$ −8.94427 15.4919i −0.609994 1.05654i
$$216$$ 16.7082 1.13685
$$217$$ 0 0
$$218$$ 7.09017 0.480207
$$219$$ −3.02786 5.24441i −0.204604 0.354385i
$$220$$ −16.2812 + 28.1998i −1.09768 + 1.90123i
$$221$$ 0.736068 1.27491i 0.0495133 0.0857595i
$$222$$ 13.7812 + 23.8697i 0.924930 + 1.60203i
$$223$$ 4.00000 0.267860 0.133930 0.990991i $$-0.457240\pi$$
0.133930 + 0.990991i $$0.457240\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 3.85410 + 6.67550i 0.256371 + 0.444048i
$$227$$ 2.97214 5.14789i 0.197268 0.341677i −0.750374 0.661014i $$-0.770127\pi$$
0.947642 + 0.319336i $$0.103460\pi$$
$$228$$ 16.2812 28.1998i 1.07825 1.86758i
$$229$$ 12.0623 + 20.8925i 0.797100 + 1.38062i 0.921497 + 0.388385i $$0.126967\pi$$
−0.124398 + 0.992232i $$0.539700\pi$$
$$230$$ −48.2148 −3.17919
$$231$$ 0 0
$$232$$ −33.4164 −2.19389
$$233$$ −5.97214 10.3440i −0.391248 0.677661i 0.601367 0.798973i $$-0.294623\pi$$
−0.992614 + 0.121312i $$0.961290\pi$$
$$234$$ 2.61803 4.53457i 0.171146 0.296434i
$$235$$ 8.35410 14.4697i 0.544962 0.943901i
$$236$$ −3.57295 6.18853i −0.232579 0.402839i
$$237$$ −6.05573 −0.393362
$$238$$ 0 0
$$239$$ 19.4164 1.25594 0.627972 0.778236i $$-0.283885\pi$$
0.627972 + 0.778236i $$0.283885\pi$$
$$240$$ 24.6353 + 42.6695i 1.59020 + 2.75431i
$$241$$ 2.35410 4.07742i 0.151641 0.262650i −0.780190 0.625543i $$-0.784878\pi$$
0.931831 + 0.362893i $$0.118211\pi$$
$$242$$ −2.61803 + 4.53457i −0.168294 + 0.291493i
$$243$$ 8.94427 + 15.4919i 0.573775 + 0.993808i
$$244$$ −14.5623 −0.932256
$$245$$ 0 0
$$246$$ −26.1803 −1.66920
$$247$$ 1.50000 + 2.59808i 0.0954427 + 0.165312i
$$248$$ −18.6803 + 32.3553i −1.18620 + 2.05456i
$$249$$ 0 0
$$250$$ 14.6353 + 25.3490i 0.925615 + 1.60321i
$$251$$ −1.52786 −0.0964379 −0.0482190 0.998837i $$-0.515355\pi$$
−0.0482190 + 0.998837i $$0.515355\pi$$
$$252$$ 0 0
$$253$$ 24.7082 1.55339
$$254$$ −14.9443 25.8842i −0.937687 1.62412i
$$255$$ −3.68034 + 6.37454i −0.230472 + 0.399189i
$$256$$ 7.28115 12.6113i 0.455072 0.788208i
$$257$$ −0.0278640 0.0482619i −0.00173811 0.00301050i 0.865155 0.501504i $$-0.167220\pi$$
−0.866893 + 0.498494i $$0.833887\pi$$
$$258$$ 46.8328 2.91568
$$259$$ 0 0
$$260$$ −10.8541 −0.673143
$$261$$ −4.47214 7.74597i −0.276818 0.479463i
$$262$$ 10.7812 18.6735i 0.666062 1.15365i
$$263$$ −13.0623 + 22.6246i −0.805456 + 1.39509i 0.110526 + 0.993873i $$0.464746\pi$$
−0.915983 + 0.401218i $$0.868587\pi$$
$$264$$ −25.0623 43.4092i −1.54248 2.67165i
$$265$$ 16.7082 1.02638
$$266$$ 0 0
$$267$$ −5.00000 −0.305995
$$268$$ 7.28115 + 12.6113i 0.444767 + 0.770359i
$$269$$ 6.73607 11.6672i 0.410705 0.711362i −0.584262 0.811565i $$-0.698616\pi$$
0.994967 + 0.100203i $$0.0319492\pi$$
$$270$$ 6.54508 11.3364i 0.398321 0.689913i
$$271$$ −10.2082 17.6811i −0.620104 1.07405i −0.989466 0.144766i $$-0.953757\pi$$
0.369362 0.929286i $$-0.379576\pi$$
$$272$$ −14.5066 −0.879590
$$273$$ 0 0
$$274$$ 21.5623 1.30263
$$275$$ 0 0
$$276$$ 44.6976 77.4184i 2.69048 4.66004i
$$277$$ 0.208204 0.360620i 0.0125098 0.0216675i −0.859703 0.510795i $$-0.829351\pi$$
0.872213 + 0.489127i $$0.162685\pi$$
$$278$$ 30.6525 + 53.0916i 1.83841 + 3.18423i
$$279$$ −10.0000 −0.598684
$$280$$ 0 0
$$281$$ 26.9443 1.60736 0.803680 0.595061i $$-0.202872\pi$$
0.803680 + 0.595061i $$0.202872\pi$$
$$282$$ 21.8713 + 37.8822i 1.30242 + 2.25585i
$$283$$ 13.0623 22.6246i 0.776473 1.34489i −0.157489 0.987521i $$-0.550340\pi$$
0.933963 0.357371i $$-0.116327\pi$$
$$284$$ 21.7082 37.5997i 1.28814 2.23113i
$$285$$ −7.50000 12.9904i −0.444262 0.769484i
$$286$$ 7.85410 0.464423
$$287$$ 0 0
$$288$$ −21.7082 −1.27917
$$289$$ 7.41641 + 12.8456i 0.436259 + 0.755623i
$$290$$ −13.0902 + 22.6728i −0.768681 + 1.33139i
$$291$$ 10.5279 18.2348i 0.617154 1.06894i
$$292$$ −6.57295 11.3847i −0.384653 0.666238i
$$293$$ 14.9443 0.873054 0.436527 0.899691i $$-0.356208\pi$$
0.436527 + 0.899691i $$0.356208\pi$$
$$294$$ 0 0
$$295$$ −3.29180 −0.191656
$$296$$ 17.5902 + 30.4671i 1.02241 + 1.77086i
$$297$$ −3.35410 + 5.80948i −0.194625 + 0.337100i
$$298$$ 0.927051 1.60570i 0.0537026 0.0930157i
$$299$$ 4.11803 + 7.13264i 0.238152 + 0.412491i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −53.4508 −3.07575
$$303$$ −10.0623 17.4284i −0.578064 1.00124i
$$304$$ 14.7812 25.6017i 0.847757 1.46836i
$$305$$ −3.35410 + 5.80948i −0.192055 + 0.332650i
$$306$$ −3.85410 6.67550i −0.220324 0.381613i
$$307$$ −19.4164 −1.10815 −0.554076 0.832466i $$-0.686928\pi$$
−0.554076 + 0.832466i $$0.686928\pi$$
$$308$$ 0 0
$$309$$ 6.05573 0.344498
$$310$$ 14.6353 + 25.3490i 0.831227 + 1.43973i
$$311$$ −13.8820 + 24.0443i −0.787174 + 1.36343i 0.140518 + 0.990078i $$0.455123\pi$$
−0.927692 + 0.373347i $$0.878210\pi$$
$$312$$ 8.35410 14.4697i 0.472958 0.819187i
$$313$$ −2.79180 4.83553i −0.157802 0.273320i 0.776274 0.630396i $$-0.217107\pi$$
−0.934076 + 0.357075i $$0.883774\pi$$
$$314$$ 18.3262 1.03421
$$315$$ 0 0
$$316$$ −13.1459 −0.739515
$$317$$ 4.11803 + 7.13264i 0.231292 + 0.400609i 0.958189 0.286138i $$-0.0923714\pi$$
−0.726897 + 0.686747i $$0.759038\pi$$
$$318$$ −21.8713 + 37.8822i −1.22648 + 2.12433i
$$319$$ 6.70820 11.6190i 0.375587 0.650536i
$$320$$ 9.73607 + 16.8634i 0.544263 + 0.942691i
$$321$$ −21.8328 −1.21859
$$322$$ 0 0
$$323$$ 4.41641 0.245736
$$324$$ 26.6976 + 46.2415i 1.48320 + 2.56897i
$$325$$ 0 0
$$326$$ −21.4894 + 37.2207i −1.19019 + 2.06146i
$$327$$ 3.02786 + 5.24441i 0.167441 + 0.290017i
$$328$$ −33.4164 −1.84511
$$329$$ 0 0
$$330$$ −39.2705 −2.16177
$$331$$ 0.791796 + 1.37143i 0.0435210 + 0.0753807i 0.886965 0.461836i $$-0.152809\pi$$
−0.843444 + 0.537217i $$0.819476\pi$$
$$332$$ 0 0
$$333$$ −4.70820 + 8.15485i −0.258008 + 0.446883i
$$334$$ −29.4164 50.9507i −1.60959 2.78790i
$$335$$ 6.70820 0.366508
$$336$$ 0 0
$$337$$ 18.0000 0.980522 0.490261 0.871576i $$-0.336901\pi$$
0.490261 + 0.871576i $$0.336901\pi$$
$$338$$ 1.30902 + 2.26728i 0.0712011 + 0.123324i
$$339$$ −3.29180 + 5.70156i −0.178786 + 0.309666i
$$340$$ −7.98936 + 13.8380i −0.433284 + 0.750469i
$$341$$ −7.50000 12.9904i −0.406148 0.703469i
$$342$$ 15.7082 0.849402
$$343$$ 0 0
$$344$$ 59.7771 3.22296
$$345$$ −20.5902 35.6632i −1.10854 1.92004i
$$346$$ 21.4894 37.2207i 1.15527 2.00099i
$$347$$ −11.5344 + 19.9782i −0.619201 + 1.07249i 0.370430 + 0.928860i $$0.379210\pi$$
−0.989632 + 0.143628i $$0.954123\pi$$
$$348$$ −24.2705 42.0378i −1.30104 2.25346i
$$349$$ 29.4164 1.57462 0.787312 0.616555i $$-0.211472\pi$$
0.787312 + 0.616555i $$0.211472\pi$$
$$350$$ 0 0
$$351$$ −2.23607 −0.119352
$$352$$ −16.2812 28.1998i −0.867788 1.50305i
$$353$$ 8.64590 14.9751i 0.460175 0.797046i −0.538795 0.842437i $$-0.681120\pi$$
0.998969 + 0.0453912i $$0.0144534\pi$$
$$354$$ 4.30902 7.46344i 0.229022 0.396677i
$$355$$ −10.0000 17.3205i −0.530745 0.919277i
$$356$$ −10.8541 −0.575266
$$357$$ 0 0
$$358$$ 52.6869 2.78459
$$359$$ −5.97214 10.3440i −0.315197 0.545938i 0.664282 0.747482i $$-0.268737\pi$$
−0.979479 + 0.201544i $$0.935404\pi$$
$$360$$ −16.7082 + 28.9395i −0.880600 + 1.52524i
$$361$$ 5.00000 8.66025i 0.263158 0.455803i
$$362$$ 33.2705 + 57.6262i 1.74866 + 3.02877i
$$363$$ −4.47214 −0.234726
$$364$$ 0 0
$$365$$ −6.05573 −0.316971
$$366$$ −8.78115 15.2094i −0.458998 0.795008i
$$367$$ −6.35410 + 11.0056i −0.331681 + 0.574489i −0.982842 0.184451i $$-0.940949\pi$$
0.651160 + 0.758940i $$0.274283\pi$$
$$368$$ 40.5795 70.2858i 2.11535 3.66390i
$$369$$ −4.47214 7.74597i −0.232810 0.403239i
$$370$$ 27.5623 1.43290
$$371$$ 0 0
$$372$$ −54.2705 −2.81379
$$373$$ 0.791796 + 1.37143i 0.0409976 + 0.0710100i 0.885796 0.464075i $$-0.153613\pi$$
−0.844798 + 0.535085i $$0.820280\pi$$
$$374$$ 5.78115 10.0133i 0.298936 0.517773i
$$375$$ −12.5000 + 21.6506i −0.645497 + 1.11803i
$$376$$ 27.9164 + 48.3526i 1.43968 + 2.49360i
$$377$$ 4.47214 0.230327
$$378$$ 0 0
$$379$$ −15.4164 −0.791888 −0.395944 0.918275i $$-0.629583\pi$$
−0.395944 + 0.918275i $$0.629583\pi$$
$$380$$ −16.2812 28.1998i −0.835206 1.44662i
$$381$$ 12.7639 22.1078i 0.653916 1.13262i
$$382$$ 14.6353 25.3490i 0.748805 1.29697i
$$383$$ 7.50000 + 12.9904i 0.383232 + 0.663777i 0.991522 0.129937i $$-0.0414776\pi$$
−0.608290 + 0.793715i $$0.708144\pi$$
$$384$$ −2.43769 −0.124398
$$385$$ 0 0
$$386$$ −1.85410 −0.0943713
$$387$$ 8.00000 + 13.8564i 0.406663 + 0.704361i
$$388$$ 22.8541 39.5845i 1.16024 2.00960i
$$389$$ −0.736068 + 1.27491i −0.0373201 + 0.0646404i −0.884082 0.467332i $$-0.845215\pi$$
0.846762 + 0.531972i $$0.178549\pi$$
$$390$$ −6.54508 11.3364i −0.331423 0.574042i
$$391$$ 12.1246 0.613168
$$392$$ 0 0
$$393$$ 18.4164 0.928985
$$394$$ −11.8541 20.5319i −0.597201 1.03438i
$$395$$ −3.02786 + 5.24441i −0.152348 + 0.263875i
$$396$$ 14.5623 25.2227i 0.731783 1.26749i
$$397$$ −13.0623 22.6246i −0.655578 1.13549i −0.981748 0.190184i $$-0.939092\pi$$
0.326170 0.945311i $$-0.394242\pi$$
$$398$$ −54.2148 −2.71754
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −7.11803 12.3288i −0.355458 0.615671i 0.631739 0.775182i $$-0.282342\pi$$
−0.987196 + 0.159511i $$0.949008\pi$$
$$402$$ −8.78115 + 15.2094i −0.437964 + 0.758576i
$$403$$ 2.50000 4.33013i 0.124534 0.215699i
$$404$$ −21.8435 37.8340i −1.08675 1.88231i
$$405$$ 24.5967 1.22222
$$406$$ 0 0
$$407$$ −14.1246 −0.700131
$$408$$ −12.2984 21.3014i −0.608860 1.05458i
$$409$$ 4.35410 7.54153i 0.215296 0.372904i −0.738068 0.674727i $$-0.764262\pi$$
0.953364 + 0.301822i $$0.0975949\pi$$
$$410$$ −13.0902 + 22.6728i −0.646477 + 1.11973i
$$411$$ 9.20820 + 15.9491i 0.454207 + 0.786710i
$$412$$ 13.1459 0.647652
$$413$$ 0 0
$$414$$ 43.1246 2.11946
$$415$$ 0 0
$$416$$ 5.42705 9.39993i 0.266083 0.460869i
$$417$$ −26.1803 + 45.3457i −1.28206 + 2.22059i
$$418$$ 11.7812 + 20.4056i 0.576235 + 0.998068i
$$419$$ −32.9443 −1.60943 −0.804717 0.593659i $$-0.797683\pi$$
−0.804717 + 0.593659i $$0.797683\pi$$
$$420$$ 0 0
$$421$$ 13.4164 0.653876 0.326938 0.945046i $$-0.393983\pi$$
0.326938 + 0.945046i $$0.393983\pi$$
$$422$$ 5.23607 + 9.06914i 0.254888 + 0.441479i
$$423$$ −7.47214 + 12.9421i −0.363308 + 0.629267i
$$424$$ −27.9164 + 48.3526i −1.35574 + 2.34821i
$$425$$ 0 0
$$426$$ 52.3607 2.53688
$$427$$ 0 0
$$428$$ −47.3951 −2.29093
$$429$$ 3.35410 + 5.80948i 0.161938 + 0.280484i
$$430$$ 23.4164 40.5584i 1.12924 1.95590i
$$431$$ 15.6803 27.1591i 0.755295 1.30821i −0.189932 0.981797i $$-0.560827\pi$$
0.945227 0.326413i $$-0.105840\pi$$
$$432$$ 11.0172 + 19.0824i 0.530066 + 0.918102i
$$433$$ −29.4164 −1.41366 −0.706831 0.707382i $$-0.749876\pi$$
−0.706831 + 0.707382i $$0.749876\pi$$
$$434$$ 0 0
$$435$$ −22.3607 −1.07211
$$436$$ 6.57295 + 11.3847i 0.314787 + 0.545227i
$$437$$ −12.3541 + 21.3979i −0.590977 + 1.02360i
$$438$$ 7.92705 13.7301i 0.378769 0.656047i
$$439$$ 12.0623 + 20.8925i 0.575702 + 0.997146i 0.995965 + 0.0897433i $$0.0286047\pi$$
−0.420262 + 0.907403i $$0.638062\pi$$
$$440$$ −50.1246 −2.38960
$$441$$ 0 0
$$442$$ 3.85410 0.183321
$$443$$ −1.11803 1.93649i −0.0531194 0.0920055i 0.838243 0.545297i $$-0.183583\pi$$
−0.891362 + 0.453291i $$0.850250\pi$$
$$444$$ −25.5517 + 44.2568i −1.21263 + 2.10033i
$$445$$ −2.50000 + 4.33013i −0.118511 + 0.205268i
$$446$$ 5.23607 + 9.06914i 0.247935 + 0.429436i
$$447$$ 1.58359 0.0749013
$$448$$ 0 0
$$449$$ −34.3607 −1.62158 −0.810790 0.585337i $$-0.800962\pi$$
−0.810790 + 0.585337i $$0.800962\pi$$
$$450$$ 0 0
$$451$$ 6.70820 11.6190i 0.315877 0.547115i
$$452$$ −7.14590 + 12.3771i −0.336115 + 0.582168i
$$453$$ −22.8262 39.5362i −1.07247 1.85757i
$$454$$ 15.5623 0.730375
$$455$$ 0 0
$$456$$ 50.1246 2.34730
$$457$$ 3.06231 + 5.30407i 0.143249 + 0.248114i 0.928718 0.370786i $$-0.120912\pi$$
−0.785470 + 0.618900i $$0.787578\pi$$
$$458$$ −31.5795 + 54.6973i −1.47561 + 2.55584i
$$459$$ −1.64590 + 2.85078i −0.0768239 + 0.133063i
$$460$$ −44.6976 77.4184i −2.08403 3.60965i
$$461$$ −34.3607 −1.60034 −0.800168 0.599776i $$-0.795256\pi$$
−0.800168 + 0.599776i $$0.795256\pi$$
$$462$$ 0 0
$$463$$ −24.0000 −1.11537 −0.557687 0.830051i $$-0.688311\pi$$
−0.557687 + 0.830051i $$0.688311\pi$$
$$464$$ −22.0344 38.1648i −1.02292 1.77176i
$$465$$ −12.5000 + 21.6506i −0.579674 + 1.00402i
$$466$$ 15.6353 27.0811i 0.724289 1.25451i
$$467$$ 4.82624 + 8.35929i 0.223332 + 0.386822i 0.955818 0.293960i $$-0.0949734\pi$$
−0.732486 + 0.680782i $$0.761640\pi$$
$$468$$ 9.70820 0.448762
$$469$$ 0 0
$$470$$ 43.7426 2.01770
$$471$$ 7.82624 + 13.5554i 0.360614 + 0.624602i
$$472$$ 5.50000 9.52628i 0.253158 0.438483i
$$473$$ −12.0000 + 20.7846i −0.551761 + 0.955677i
$$474$$ −7.92705 13.7301i −0.364102 0.630642i
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −14.9443 −0.684251
$$478$$ 25.4164 + 44.0225i 1.16252 + 2.01354i
$$479$$ 11.9164 20.6398i 0.544475 0.943058i −0.454165 0.890917i $$-0.650062\pi$$
0.998640 0.0521401i $$-0.0166043\pi$$
$$480$$ −27.1353 + 46.9996i −1.23855 + 2.14523i
$$481$$ −2.35410 4.07742i −0.107338 0.185915i
$$482$$ 12.3262 0.561445
$$483$$ 0 0
$$484$$ −9.70820 −0.441282
$$485$$ −10.5279 18.2348i −0.478046 0.827999i
$$486$$ −23.4164 + 40.5584i −1.06219 + 1.83977i
$$487$$ 10.9164 18.9078i 0.494670 0.856793i −0.505311 0.862937i $$-0.668622\pi$$
0.999981 + 0.00614405i $$0.00195572\pi$$
$$488$$ −11.2082 19.4132i −0.507372 0.878793i
$$489$$ −36.7082 −1.66000
$$490$$ 0 0
$$491$$ −25.5279 −1.15206 −0.576028 0.817430i $$-0.695398\pi$$
−0.576028 + 0.817430i $$0.695398\pi$$
$$492$$ −24.2705 42.0378i −1.09420 1.89521i
$$493$$ 3.29180 5.70156i 0.148255 0.256785i
$$494$$ −3.92705 + 6.80185i −0.176686 + 0.306030i
$$495$$ −6.70820 11.6190i −0.301511 0.522233i
$$496$$ −49.2705 −2.21231
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −13.2082 22.8773i −0.591280 1.02413i −0.994060 0.108831i $$-0.965289\pi$$
0.402780 0.915297i $$-0.368044\pi$$
$$500$$ −27.1353 + 46.9996i −1.21353 + 2.10189i
$$501$$ 25.1246 43.5171i 1.12248 1.94420i
$$502$$ −2.00000 3.46410i −0.0892644 0.154610i
$$503$$ −20.9443 −0.933859 −0.466929 0.884295i $$-0.654640\pi$$
−0.466929 + 0.884295i $$0.654640\pi$$
$$504$$ 0 0
$$505$$ −20.1246 −0.895533
$$506$$ 32.3435 + 56.0205i 1.43784 + 2.49042i
$$507$$ −1.11803 + 1.93649i −0.0496536 + 0.0860026i
$$508$$ 27.7082 47.9920i 1.22935 2.12930i
$$509$$ −10.1180 17.5249i −0.448474 0.776780i 0.549813 0.835288i $$-0.314699\pi$$
−0.998287 + 0.0585081i $$0.981366\pi$$
$$510$$ −19.2705 −0.853313
$$511$$ 0 0
$$512$$ 40.3050 1.78124
$$513$$ −3.35410 5.80948i −0.148087 0.256495i
$$514$$ 0.0729490 0.126351i 0.00321764 0.00557312i
$$515$$ 3.02786 5.24441i 0.133424 0.231097i
$$516$$ 43.4164 + 75.1994i 1.91130 + 3.31047i
$$517$$ −22.4164 −0.985872
$$518$$ 0 0
$$519$$ 36.7082 1.61131
$$520$$ −8.35410 14.4697i −0.366352 0.634540i
$$521$$ −8.97214 + 15.5402i −0.393076 + 0.680828i −0.992854 0.119339i $$-0.961923\pi$$
0.599777 + 0.800167i $$0.295256\pi$$
$$522$$ 11.7082 20.2792i 0.512454 0.887597i
$$523$$ 16.3541 + 28.3261i 0.715115 + 1.23862i 0.962915 + 0.269804i $$0.0869590\pi$$
−0.247800 + 0.968811i $$0.579708\pi$$
$$524$$ 39.9787 1.74648
$$525$$ 0 0
$$526$$ −68.3951 −2.98217
$$527$$ −3.68034 6.37454i −0.160318 0.277679i
$$528$$ 33.0517 57.2472i 1.43839 2.49136i
$$529$$ −22.4164 + 38.8264i −0.974626 + 1.68810i
$$530$$ 21.8713 + 37.8822i 0.950030 + 1.64550i
$$531$$ 2.94427 0.127771
$$532$$ 0 0
$$533$$ 4.47214 0.193710
$$534$$ −6.54508 11.3364i −0.283234 0.490575i
$$535$$ −10.9164 + 18.9078i −0.471957 + 0.817454i
$$536$$ −11.2082 + 19.4132i −0.484121 + 0.838522i
$$537$$ 22.5000 + 38.9711i 0.970947 + 1.68173i
$$538$$ 35.2705 1.52062
$$539$$ 0 0
$$540$$ 24.2705 1.04444
$$541$$ −0.645898 1.11873i −0.0277693 0.0480979i 0.851807 0.523856i $$-0.175507\pi$$
−0.879576 + 0.475758i $$0.842174\pi$$
$$542$$ 26.7254 46.2898i 1.14796 1.98832i
$$543$$ −28.4164 + 49.2187i −1.21946 + 2.11217i
$$544$$ −7.98936 13.8380i −0.342541 0.593298i
$$545$$ 6.05573 0.259399
$$546$$ 0 0
$$547$$ −4.58359 −0.195980 −0.0979901 0.995187i $$-0.531241\pi$$
−0.0979901 + 0.995187i $$0.531241\pi$$
$$548$$ 19.9894 + 34.6226i 0.853903 + 1.47900i
$$549$$ 3.00000 5.19615i 0.128037 0.221766i
$$550$$ 0 0
$$551$$ 6.70820 + 11.6190i 0.285779 + 0.494984i
$$552$$ 137.610 5.85707
$$553$$ 0 0
$$554$$ 1.09017 0.0463169
$$555$$ 11.7705 + 20.3871i 0.499630 + 0.865385i
$$556$$ −56.8328 + 98.4373i −2.41025 + 4.17467i
$$557$$ 9.35410 16.2018i 0.396346 0.686491i −0.596926 0.802296i $$-0.703611\pi$$
0.993272 + 0.115805i $$0.0369447\pi$$
$$558$$ −13.0902 22.6728i −0.554151 0.959818i
$$559$$ −8.00000 −0.338364
$$560$$ 0 0
$$561$$ 9.87539 0.416939
$$562$$ 35.2705 + 61.0903i 1.48780 + 2.57694i
$$563$$ 6.29837 10.9091i 0.265445 0.459764i −0.702235 0.711945i $$-0.747815\pi$$
0.967680 + 0.252181i $$0.0811479\pi$$
$$564$$ −40.5517 + 70.2375i −1.70753 + 2.95753i
$$565$$ 3.29180 + 5.70156i 0.138487 + 0.239866i
$$566$$ 68.3951 2.87486
$$567$$ 0 0
$$568$$ 66.8328 2.80424
$$569$$ −12.7361 22.0595i −0.533924 0.924783i −0.999215 0.0396252i $$-0.987384\pi$$
0.465291 0.885158i $$-0.345950\pi$$
$$570$$ 19.6353 34.0093i 0.822430 1.42449i
$$571$$ 18.0623 31.2848i 0.755884 1.30923i −0.189050 0.981968i $$-0.560541\pi$$
0.944934 0.327262i $$-0.106126\pi$$
$$572$$ 7.28115 + 12.6113i 0.304440 + 0.527306i
$$573$$ 25.0000 1.04439
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −8.70820 15.0831i −0.362842 0.628460i
$$577$$ −9.64590 + 16.7072i −0.401564 + 0.695529i −0.993915 0.110151i $$-0.964867\pi$$
0.592351 + 0.805680i $$0.298200\pi$$
$$578$$ −19.4164 + 33.6302i −0.807616 + 1.39883i
$$579$$ −0.791796 1.37143i −0.0329059 0.0569947i
$$580$$ −48.5410 −2.01556
$$581$$ 0 0
$$582$$ 55.1246 2.28499
$$583$$ −11.2082 19.4132i −0.464196 0.804012i
$$584$$ 10.1180 17.5249i 0.418687 0.725188i
$$585$$ 2.23607 3.87298i 0.0924500 0.160128i
$$586$$ 19.5623 + 33.8829i 0.808111 + 1.39969i
$$587$$ 6.11146 0.252247 0.126123 0.992015i $$-0.459746\pi$$
0.126123 + 0.992015i $$0.459746\pi$$
$$588$$ 0 0
$$589$$ 15.0000 0.618064
$$590$$ −4.30902 7.46344i −0.177399 0.307265i
$$591$$ 10.1246 17.5363i 0.416471 0.721349i
$$592$$ −23.1976 + 40.1794i −0.953414 + 1.65136i
$$593$$ 13.8820 + 24.0443i 0.570064 + 0.987380i 0.996559 + 0.0828898i $$0.0264149\pi$$
−0.426495 + 0.904490i $$0.640252\pi$$
$$594$$ −17.5623 −0.720590
$$595$$ 0 0
$$596$$ 3.43769 0.140813
$$597$$ −23.1525 40.1013i −0.947568 1.64124i
$$598$$ −10.7812 + 18.6735i −0.440874 + 0.763616i
$$599$$ 8.53444 14.7821i 0.348708 0.603980i −0.637312 0.770606i $$-0.719954\pi$$
0.986020 + 0.166626i $$0.0532872\pi$$
$$600$$ 0 0
$$601$$ 22.0000 0.897399 0.448699 0.893683i $$-0.351887\pi$$
0.448699 + 0.893683i $$0.351887\pi$$
$$602$$ 0 0
$$603$$ −6.00000 −0.244339
$$604$$ −49.5517 85.8260i −2.01623 3.49221i
$$605$$ −2.23607 + 3.87298i −0.0909091 + 0.157459i
$$606$$ 26.3435 45.6282i 1.07013 1.85352i
$$607$$ 12.0623 + 20.8925i 0.489594 + 0.848001i 0.999928 0.0119745i $$-0.00381171\pi$$
−0.510334 + 0.859976i $$0.670478\pi$$
$$608$$ 32.5623 1.32058
$$609$$ 0 0
$$610$$ −17.5623 −0.711077
$$611$$ −3.73607 6.47106i −0.151145 0.261791i
$$612$$ 7.14590 12.3771i 0.288856 0.500313i
$$613$$ 9.06231 15.6964i 0.366023 0.633971i −0.622917 0.782288i $$-0.714052\pi$$
0.988940 + 0.148318i $$0.0473858\pi$$
$$614$$ −25.4164 44.0225i −1.02572 1.77660i
$$615$$ −22.3607 −0.901670
$$616$$ 0 0
$$617$$ −4.47214 −0.180041 −0.0900207 0.995940i $$-0.528693\pi$$
−0.0900207 + 0.995940i $$0.528693\pi$$
$$618$$ 7.92705 + 13.7301i 0.318873 + 0.552304i
$$619$$ 8.50000 14.7224i 0.341644 0.591744i −0.643094 0.765787i $$-0.722350\pi$$
0.984738 + 0.174042i $$0.0556830\pi$$
$$620$$ −27.1353 + 46.9996i −1.08978 + 1.88755i
$$621$$ −9.20820 15.9491i −0.369512 0.640014i
$$622$$ −72.6869 −2.91448
$$623$$ 0 0
$$624$$ 22.0344 0.882084
$$625$$ 12.5000 + 21.6506i 0.500000 + 0.866025i
$$626$$ 7.30902 12.6596i 0.292127 0.505979i
$$627$$ −10.0623 + 17.4284i −0.401850 + 0.696024i
$$628$$ 16.9894 + 29.4264i 0.677949 + 1.17424i
$$629$$ −6.93112 −0.276362
$$630$$ 0 0
$$631$$ 22.8328 0.908960 0.454480 0.890757i $$-0.349825\pi$$
0.454480 + 0.890757i $$0.349825\pi$$
$$632$$ −10.1180 17.5249i −0.402474 0.697105i
$$633$$ −4.47214 + 7.74597i −0.177751 + 0.307875i
$$634$$ −10.7812 + 18.6735i −0.428174 + 0.741620i
$$635$$ −12.7639 22.1078i −0.506521 0.877320i
$$636$$ −81.1033 −3.21596
$$637$$ 0 0
$$638$$ 35.1246 1.39060
$$639$$ 8.94427 + 15.4919i 0.353830 + 0.612851i
$$640$$ −1.21885 + 2.11111i −0.0481792 + 0.0834488i
$$641$$ −5.97214 + 10.3440i −0.235885 + 0.408565i −0.959530 0.281608i $$-0.909132\pi$$
0.723644 + 0.690173i $$0.242466\pi$$
$$642$$ −28.5795 49.5012i −1.12794 1.95366i
$$643$$ −34.8328 −1.37367 −0.686836 0.726812i $$-0.741001\pi$$
−0.686836 + 0.726812i $$0.741001\pi$$
$$644$$ 0 0
$$645$$ 40.0000 1.57500
$$646$$ 5.78115 + 10.0133i 0.227456 + 0.393966i
$$647$$ 10.1180 17.5249i 0.397781 0.688977i −0.595671 0.803229i $$-0.703114\pi$$
0.993452 + 0.114252i $$0.0364471\pi$$
$$648$$ −41.0967 + 71.1817i −1.61443 + 2.79628i
$$649$$ 2.20820 + 3.82472i 0.0866796 + 0.150133i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −79.6869 −3.12078
$$653$$ −2.26393 3.92125i −0.0885945 0.153450i 0.818323 0.574759i $$-0.194904\pi$$
−0.906917 + 0.421309i $$0.861571\pi$$
$$654$$ −7.92705 + 13.7301i −0.309972 + 0.536888i
$$655$$ 9.20820 15.9491i 0.359794 0.623182i
$$656$$ −22.0344 38.1648i −0.860300 1.49008i
$$657$$ 5.41641 0.211314
$$658$$ 0 0
$$659$$ −8.94427 −0.348419 −0.174210 0.984709i $$-0.555737\pi$$
−0.174210 + 0.984709i $$0.555737\pi$$
$$660$$ −36.4058 63.0566i −1.41709 2.45448i
$$661$$ −3.35410 + 5.80948i −0.130459 + 0.225962i −0.923854 0.382746i $$-0.874979\pi$$
0.793394 + 0.608708i $$0.208312\pi$$
$$662$$ −2.07295 + 3.59045i −0.0805675 + 0.139547i
$$663$$ 1.64590 + 2.85078i 0.0639214 + 0.110715i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ −24.6525 −0.955264
$$667$$ 18.4164 + 31.8982i 0.713086 + 1.23510i
$$668$$ 54.5410 94.4678i 2.11026 3.65507i
$$669$$ −4.47214 + 7.74597i −0.172903 + 0.299476i
$$670$$ 8.78115 + 15.2094i 0.339246 + 0.587591i
$$671$$ 9.00000 0.347441
$$672$$ 0 0
$$673$$ −9.41641 −0.362976 −0.181488 0.983393i $$-0.558091\pi$$
−0.181488 + 0.983393i $$0.558091\pi$$
$$674$$ 23.5623 + 40.8111i 0.907586 + 1.57199i
$$675$$ 0 0
$$676$$ −2.42705 + 4.20378i −0.0933481 + 0.161684i
$$677$$ −1.44427 2.50155i −0.0555079 0.0961425i 0.836936 0.547300i $$-0.184344\pi$$
−0.892444 + 0.451158i $$0.851011\pi$$
$$678$$ −17.2361 −0.661947
$$679$$ 0 0
$$680$$ −24.5967 −0.943242
$$681$$ 6.64590 + 11.5110i 0.254671 + 0.441104i
$$682$$ 19.6353 34.0093i 0.751873 1.30228i
$$683$$ 6.73607 11.6672i 0.257748 0.446433i −0.707890 0.706323i $$-0.750353\pi$$
0.965638 + 0.259889i $$0.0836861\pi$$
$$684$$ 14.5623 + 25.2227i 0.556804 + 0.964412i
$$685$$ 18.4164 0.703655
$$686$$ 0 0
$$687$$ −53.9443 −2.05810
$$688$$ 39.4164 + 68.2712i 1.50274 + 2.60282i
$$689$$ 3.73607 6.47106i 0.142333 0.246528i
$$690$$ 53.9058 93.3675i 2.05216 3.55444i
$$691$$ −25.9164 44.8885i −0.985907 1.70764i −0.637836 0.770172i $$-0.720170\pi$$
−0.348070 0.937468i $$-0.613163\pi$$
$$692$$ 79.6869 3.02924
$$693$$ 0 0
$$694$$ −60.3951 −2.29257
$$695$$ 26.1803 + 45.3457i 0.993077 + 1.72006i
$$696$$ 37.3607 64.7106i 1.41615 2.45285i
$$697$$ 3.29180 5.70156i 0.124686 0.215962i
$$698$$ 38.5066 + 66.6953i 1.45750 + 2.52446i
$$699$$ 26.7082 1.01020
$$700$$ 0 0
$$701$$ −22.3607 −0.844551 −0.422276 0.906467i $$-0.638769\pi$$
−0.422276 + 0.906467i $$0.638769\pi$$
$$702$$ −2.92705 5.06980i −0.110474 0.191347i
$$703$$ 7.06231 12.2323i 0.266360 0.461349i
$$704$$ 13.0623 22.6246i 0.492304 0.852696i
$$705$$ 18.6803 + 32.3553i 0.703542 + 1.21857i
$$706$$ 45.2705 1.70378
$$707$$ 0 0
$$708$$ 15.9787 0.600517
$$709$$ 25.0623 + 43.4092i 0.941235 + 1.63027i 0.763120 + 0.646256i $$0.223666\pi$$
0.178114 + 0.984010i $$0.443000\pi$$
$$710$$ 26.1803 45.3457i 0.982531 1.70179i
$$711$$ 2.70820 4.69075i 0.101566 0.175917i
$$712$$ −8.35410 14.4697i −0.313083 0.542276i
$$713$$ 41.1803 1.54222
$$714$$ 0 0
$$715$$ 6.70820 0.250873
$$716$$ 48.8435 + 84.5994i 1.82537 + 3.16163i
$$717$$ −21.7082 + 37.5997i −0.810708 + 1.40419i
$$718$$ 15.6353 27.0811i 0.583503 1.01066i
$$719$$ 12.3541 + 21.3979i 0.460730 + 0.798008i 0.998998 0.0447660i $$-0.0142542\pi$$
−0.538267 + 0.842774i $$0.680921\pi$$
$$720$$ −44.0689 −1.64235
$$721$$ 0 0
$$722$$ 26.1803 0.974331
$$723$$ 5.26393 + 9.11740i 0.195768 + 0.339080i
$$724$$ −61.6869 + 106.845i −2.29258 + 3.97086i
$$725$$ 0 0
$$726$$ −5.85410 10.1396i −0.217266 0.376316i
$$727$$ 38.8328 1.44023 0.720115 0.693855i $$-0.244089\pi$$
0.720115 + 0.693855i $$0.244089\pi$$
$$728$$ 0 0
$$729$$ −7.00000 −0.259259
$$730$$ −7.92705 13.7301i −0.293393 0.508172i
$$731$$ −5.88854 + 10.1993i −0.217796 + 0.377233i
$$732$$ 16.2812 28.1998i 0.601769 1.04229i
$$733$$ 14.3541 + 24.8620i 0.530181 + 0.918300i 0.999380 + 0.0352078i $$0.0112093\pi$$
−0.469199 + 0.883092i $$0.655457\pi$$
$$734$$ −33.2705 −1.22804
$$735$$ 0 0
$$736$$ 89.3951 3.29515
$$737$$ −4.50000 7.79423i −0.165760 0.287104i
$$738$$ 11.7082 20.2792i 0.430985 0.746488i
$$739$$ 8.91641 15.4437i 0.327995 0.568105i −0.654119 0.756392i $$-0.726960\pi$$
0.982114 + 0.188287i $$0.0602936\pi$$
$$740$$ 25.5517 + 44.2568i 0.939298 + 1.62691i
$$741$$ −6.70820 −0.246432
$$742$$ 0 0
$$743$$ 32.9443 1.20861 0.604304 0.796754i $$-0.293451\pi$$
0.604304 + 0.796754i $$0.293451\pi$$
$$744$$ −41.7705 72.3486i −1.53138 2.65243i
$$745$$ 0.791796 1.37143i 0.0290092 0.0502453i
$$746$$ −2.07295 + 3.59045i −0.0758961 + 0.131456i
$$747$$ 0 0
$$748$$ 21.4377 0.783840
$$749$$ 0 0
$$750$$ −65.4508 −2.38993
$$751$$ 5.06231 + 8.76817i 0.184726 + 0.319955i 0.943484 0.331417i $$-0.107527\pi$$
−0.758758 + 0.651373i $$0.774194\pi$$
$$752$$ −36.8156 + 63.7665i −1.34253 + 2.32532i
$$753$$ 1.70820 2.95870i 0.0622504 0.107821i
$$754$$ 5.85410 + 10.1396i 0.213194 + 0.369263i
$$755$$ −45.6525 −1.66146
$$756$$ 0 0
$$757$$ −52.8328 −1.92024 −0.960121 0.279586i $$-0.909803\pi$$
−0.960121 + 0.279586i $$0.909803\pi$$
$$758$$ −20.1803 34.9534i −0.732983 1.26956i
$$759$$ −27.6246 + 47.8472i −1.00271 + 1.73674i
$$760$$ 25.0623 43.4092i 0.909105 1.57462i
$$761$$ −16.7705 29.0474i −0.607931 1.05297i −0.991581 0.129488i $$-0.958667\pi$$
0.383650 0.923478i $$-0.374667\pi$$
$$762$$ 66.8328 2.42110
$$763$$ 0 0
$$764$$ 54.2705 1.96344
$$765$$ −3.29180 5.70156i −0.119015 0.206140i
$$766$$ −19.6353 + 34.0093i −0.709451 + 1.22880i
$$767$$ −0.736068 + 1.27491i −0.0265779 + 0.0460342i
$$768$$ 16.2812 + 28.1998i 0.587496 + 1.01757i
$$769$$ −46.0000 −1.65880 −0.829401 0.558653i $$-0.811318\pi$$
−0.829401 + 0.558653i $$0.811318\pi$$
$$770$$ 0 0
$$771$$ 0.124612 0.00448778
$$772$$ −1.71885 2.97713i −0.0618627 0.107149i
$$773$$ −23.5344 + 40.7628i −0.846475 + 1.46614i 0.0378590 + 0.999283i $$0.487946\pi$$
−0.884334 + 0.466855i $$0.845387\pi$$
$$774$$ −20.9443 + 36.2765i −0.752826 + 1.30393i
$$775$$ 0 0
$$776$$ 70.3607 2.52580
$$777$$ 0 0
$$778$$ −3.85410 −0.138176
$$779$$ 6.70820 + 11.6190i 0.240346 + 0.416292i
$$780$$ 12.1353 21.0189i 0.434512 0.752597i
$$781$$ −13.4164 + 23.2379i −0.480077 + 0.831517i
$$782$$ 15.8713 + 27.4899i 0.567557 + 0.983038i
$$783$$ −10.0000 −0.357371
$$784$$ 0