# Properties

 Label 42.3.g.a.19.1 Level $42$ Weight $3$ Character 42.19 Analytic conductor $1.144$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$42 = 2 \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 42.g (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.14441711031$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\sqrt{2}, \sqrt{-3})$$ Defining polynomial: $$x^{4} + 2 x^{2} + 4$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 19.1 Root $$-0.707107 + 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 42.19 Dual form 42.3.g.a.31.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(7.24264 + 4.18154i) q^{5} +2.44949i q^{6} +(-6.74264 + 1.88064i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$$ $$q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(7.24264 + 4.18154i) q^{5} +2.44949i q^{6} +(-6.74264 + 1.88064i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(-10.2426 + 5.91359i) q^{10} +(-3.00000 - 5.19615i) q^{11} +(-3.00000 - 1.73205i) q^{12} -17.8639i q^{13} +(2.46447 - 9.58783i) q^{14} +14.4853 q^{15} +(-2.00000 + 3.46410i) q^{16} +(-16.2426 + 9.37769i) q^{17} +(2.12132 + 3.67423i) q^{18} +(-14.7426 - 8.51167i) q^{19} -16.7262i q^{20} +(-8.48528 + 8.66025i) q^{21} +8.48528 q^{22} +(-6.72792 + 11.6531i) q^{23} +(4.24264 - 2.44949i) q^{24} +(22.4706 + 38.9202i) q^{25} +(21.8787 + 12.6317i) q^{26} -5.19615i q^{27} +(10.0000 + 9.79796i) q^{28} +33.9411 q^{29} +(-10.2426 + 17.7408i) q^{30} +(12.7721 - 7.37396i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(-9.00000 - 5.19615i) q^{33} -26.5241i q^{34} +(-56.6985 - 14.5738i) q^{35} -6.00000 q^{36} +(-2.98528 + 5.17066i) q^{37} +(20.8492 - 12.0373i) q^{38} +(-15.4706 - 26.7958i) q^{39} +(20.4853 + 11.8272i) q^{40} +35.2354i q^{41} +(-4.60660 - 16.5160i) q^{42} +15.4853 q^{43} +(-6.00000 + 10.3923i) q^{44} +(21.7279 - 12.5446i) q^{45} +(-9.51472 - 16.4800i) q^{46} +(-28.7574 - 16.6031i) q^{47} +6.92820i q^{48} +(41.9264 - 25.3609i) q^{49} -63.5563 q^{50} +(-16.2426 + 28.1331i) q^{51} +(-30.9411 + 17.8639i) q^{52} +(17.2721 + 29.9161i) q^{53} +(6.36396 + 3.67423i) q^{54} -50.1785i q^{55} +(-19.0711 + 5.31925i) q^{56} -29.4853 q^{57} +(-24.0000 + 41.5692i) q^{58} +(23.6985 - 13.6823i) q^{59} +(-14.4853 - 25.0892i) q^{60} +(-34.9706 - 20.1903i) q^{61} +20.8567i q^{62} +(-5.22792 + 20.3389i) q^{63} +8.00000 q^{64} +(74.6985 - 129.382i) q^{65} +(12.7279 - 7.34847i) q^{66} +(57.1985 + 99.0707i) q^{67} +(32.4853 + 18.7554i) q^{68} +23.3062i q^{69} +(57.9411 - 59.1359i) q^{70} +18.6030 q^{71} +(4.24264 - 7.34847i) q^{72} +(-101.353 + 58.5161i) q^{73} +(-4.22183 - 7.31242i) q^{74} +(67.4117 + 38.9202i) q^{75} +34.0467i q^{76} +(30.0000 + 29.3939i) q^{77} +43.7574 q^{78} +(44.1690 - 76.5030i) q^{79} +(-28.9706 + 16.7262i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-43.1543 - 24.9152i) q^{82} +75.7601i q^{83} +(23.4853 + 6.03668i) q^{84} -156.853 q^{85} +(-10.9497 + 18.9655i) q^{86} +(50.9117 - 29.3939i) q^{87} +(-8.48528 - 14.6969i) q^{88} +(-18.0000 - 10.3923i) q^{89} +35.4815i q^{90} +(33.5955 + 120.450i) q^{91} +26.9117 q^{92} +(12.7721 - 22.1219i) q^{93} +(40.6690 - 23.4803i) q^{94} +(-71.1838 - 123.294i) q^{95} +(-8.48528 - 4.89898i) q^{96} +30.5826i q^{97} +(1.41421 + 69.2820i) q^{98} -18.0000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 6q^{3} - 4q^{4} + 12q^{5} - 10q^{7} + 6q^{9} + O(q^{10})$$ $$4q + 6q^{3} - 4q^{4} + 12q^{5} - 10q^{7} + 6q^{9} - 24q^{10} - 12q^{11} - 12q^{12} + 24q^{14} + 24q^{15} - 8q^{16} - 48q^{17} - 42q^{19} + 24q^{23} + 22q^{25} + 96q^{26} + 40q^{28} - 24q^{30} + 102q^{31} - 36q^{33} - 108q^{35} - 24q^{36} + 22q^{37} + 24q^{38} + 6q^{39} + 48q^{40} + 24q^{42} + 28q^{43} - 24q^{44} + 36q^{45} - 72q^{46} - 132q^{47} - 2q^{49} - 192q^{50} - 48q^{51} + 12q^{52} + 120q^{53} - 48q^{56} - 84q^{57} - 96q^{58} - 24q^{59} - 24q^{60} - 72q^{61} + 30q^{63} + 32q^{64} + 180q^{65} + 110q^{67} + 96q^{68} + 96q^{70} + 312q^{71} - 66q^{73} - 48q^{74} + 66q^{75} + 120q^{77} + 192q^{78} - 10q^{79} - 48q^{80} - 18q^{81} + 48q^{82} + 60q^{84} - 288q^{85} - 24q^{86} - 72q^{89} - 222q^{91} - 96q^{92} + 102q^{93} - 24q^{94} - 132q^{95} - 72q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$31$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.707107 + 1.22474i −0.353553 + 0.612372i
$$3$$ 1.50000 0.866025i 0.500000 0.288675i
$$4$$ −1.00000 1.73205i −0.250000 0.433013i
$$5$$ 7.24264 + 4.18154i 1.44853 + 0.836308i 0.998394 0.0566528i $$-0.0180428\pi$$
0.450134 + 0.892961i $$0.351376\pi$$
$$6$$ 2.44949i 0.408248i
$$7$$ −6.74264 + 1.88064i −0.963234 + 0.268662i
$$8$$ 2.82843 0.353553
$$9$$ 1.50000 2.59808i 0.166667 0.288675i
$$10$$ −10.2426 + 5.91359i −1.02426 + 0.591359i
$$11$$ −3.00000 5.19615i −0.272727 0.472377i 0.696832 0.717234i $$-0.254592\pi$$
−0.969559 + 0.244857i $$0.921259\pi$$
$$12$$ −3.00000 1.73205i −0.250000 0.144338i
$$13$$ 17.8639i 1.37414i −0.726590 0.687072i $$-0.758896\pi$$
0.726590 0.687072i $$-0.241104\pi$$
$$14$$ 2.46447 9.58783i 0.176033 0.684845i
$$15$$ 14.4853 0.965685
$$16$$ −2.00000 + 3.46410i −0.125000 + 0.216506i
$$17$$ −16.2426 + 9.37769i −0.955449 + 0.551629i −0.894770 0.446528i $$-0.852660\pi$$
−0.0606799 + 0.998157i $$0.519327\pi$$
$$18$$ 2.12132 + 3.67423i 0.117851 + 0.204124i
$$19$$ −14.7426 8.51167i −0.775928 0.447983i 0.0590569 0.998255i $$-0.481191\pi$$
−0.834985 + 0.550272i $$0.814524\pi$$
$$20$$ 16.7262i 0.836308i
$$21$$ −8.48528 + 8.66025i −0.404061 + 0.412393i
$$22$$ 8.48528 0.385695
$$23$$ −6.72792 + 11.6531i −0.292518 + 0.506657i −0.974405 0.224802i $$-0.927827\pi$$
0.681886 + 0.731458i $$0.261160\pi$$
$$24$$ 4.24264 2.44949i 0.176777 0.102062i
$$25$$ 22.4706 + 38.9202i 0.898823 + 1.55681i
$$26$$ 21.8787 + 12.6317i 0.841488 + 0.485833i
$$27$$ 5.19615i 0.192450i
$$28$$ 10.0000 + 9.79796i 0.357143 + 0.349927i
$$29$$ 33.9411 1.17038 0.585192 0.810895i $$-0.301019\pi$$
0.585192 + 0.810895i $$0.301019\pi$$
$$30$$ −10.2426 + 17.7408i −0.341421 + 0.591359i
$$31$$ 12.7721 7.37396i 0.412003 0.237870i −0.279647 0.960103i $$-0.590218\pi$$
0.691650 + 0.722233i $$0.256884\pi$$
$$32$$ −2.82843 4.89898i −0.0883883 0.153093i
$$33$$ −9.00000 5.19615i −0.272727 0.157459i
$$34$$ 26.5241i 0.780121i
$$35$$ −56.6985 14.5738i −1.61996 0.416396i
$$36$$ −6.00000 −0.166667
$$37$$ −2.98528 + 5.17066i −0.0806833 + 0.139748i −0.903544 0.428496i $$-0.859044\pi$$
0.822860 + 0.568244i $$0.192377\pi$$
$$38$$ 20.8492 12.0373i 0.548664 0.316771i
$$39$$ −15.4706 26.7958i −0.396681 0.687072i
$$40$$ 20.4853 + 11.8272i 0.512132 + 0.295680i
$$41$$ 35.2354i 0.859399i 0.902972 + 0.429700i $$0.141381\pi$$
−0.902972 + 0.429700i $$0.858619\pi$$
$$42$$ −4.60660 16.5160i −0.109681 0.393239i
$$43$$ 15.4853 0.360123 0.180061 0.983655i $$-0.442370\pi$$
0.180061 + 0.983655i $$0.442370\pi$$
$$44$$ −6.00000 + 10.3923i −0.136364 + 0.236189i
$$45$$ 21.7279 12.5446i 0.482843 0.278769i
$$46$$ −9.51472 16.4800i −0.206842 0.358260i
$$47$$ −28.7574 16.6031i −0.611859 0.353257i 0.161834 0.986818i $$-0.448259\pi$$
−0.773693 + 0.633561i $$0.781592\pi$$
$$48$$ 6.92820i 0.144338i
$$49$$ 41.9264 25.3609i 0.855641 0.517570i
$$50$$ −63.5563 −1.27113
$$51$$ −16.2426 + 28.1331i −0.318483 + 0.551629i
$$52$$ −30.9411 + 17.8639i −0.595022 + 0.343536i
$$53$$ 17.2721 + 29.9161i 0.325888 + 0.564455i 0.981692 0.190477i $$-0.0610033\pi$$
−0.655803 + 0.754932i $$0.727670\pi$$
$$54$$ 6.36396 + 3.67423i 0.117851 + 0.0680414i
$$55$$ 50.1785i 0.912336i
$$56$$ −19.0711 + 5.31925i −0.340555 + 0.0949865i
$$57$$ −29.4853 −0.517286
$$58$$ −24.0000 + 41.5692i −0.413793 + 0.716711i
$$59$$ 23.6985 13.6823i 0.401669 0.231904i −0.285535 0.958368i $$-0.592171\pi$$
0.687204 + 0.726465i $$0.258838\pi$$
$$60$$ −14.4853 25.0892i −0.241421 0.418154i
$$61$$ −34.9706 20.1903i −0.573288 0.330988i 0.185174 0.982706i $$-0.440715\pi$$
−0.758461 + 0.651718i $$0.774049\pi$$
$$62$$ 20.8567i 0.336399i
$$63$$ −5.22792 + 20.3389i −0.0829829 + 0.322839i
$$64$$ 8.00000 0.125000
$$65$$ 74.6985 129.382i 1.14921 1.99049i
$$66$$ 12.7279 7.34847i 0.192847 0.111340i
$$67$$ 57.1985 + 99.0707i 0.853709 + 1.47867i 0.877838 + 0.478958i $$0.158985\pi$$
−0.0241291 + 0.999709i $$0.507681\pi$$
$$68$$ 32.4853 + 18.7554i 0.477725 + 0.275814i
$$69$$ 23.3062i 0.337771i
$$70$$ 57.9411 59.1359i 0.827730 0.844799i
$$71$$ 18.6030 0.262015 0.131007 0.991381i $$-0.458179\pi$$
0.131007 + 0.991381i $$0.458179\pi$$
$$72$$ 4.24264 7.34847i 0.0589256 0.102062i
$$73$$ −101.353 + 58.5161i −1.38839 + 0.801590i −0.993134 0.116979i $$-0.962679\pi$$
−0.395260 + 0.918569i $$0.629346\pi$$
$$74$$ −4.22183 7.31242i −0.0570517 0.0988164i
$$75$$ 67.4117 + 38.9202i 0.898823 + 0.518935i
$$76$$ 34.0467i 0.447983i
$$77$$ 30.0000 + 29.3939i 0.389610 + 0.381739i
$$78$$ 43.7574 0.560992
$$79$$ 44.1690 76.5030i 0.559102 0.968393i −0.438470 0.898746i $$-0.644479\pi$$
0.997572 0.0696469i $$-0.0221873\pi$$
$$80$$ −28.9706 + 16.7262i −0.362132 + 0.209077i
$$81$$ −4.50000 7.79423i −0.0555556 0.0962250i
$$82$$ −43.1543 24.9152i −0.526272 0.303843i
$$83$$ 75.7601i 0.912772i 0.889782 + 0.456386i $$0.150856\pi$$
−0.889782 + 0.456386i $$0.849144\pi$$
$$84$$ 23.4853 + 6.03668i 0.279587 + 0.0718653i
$$85$$ −156.853 −1.84533
$$86$$ −10.9497 + 18.9655i −0.127323 + 0.220529i
$$87$$ 50.9117 29.3939i 0.585192 0.337861i
$$88$$ −8.48528 14.6969i −0.0964237 0.167011i
$$89$$ −18.0000 10.3923i −0.202247 0.116767i 0.395456 0.918485i $$-0.370587\pi$$
−0.597703 + 0.801717i $$0.703920\pi$$
$$90$$ 35.4815i 0.394239i
$$91$$ 33.5955 + 120.450i 0.369181 + 1.32362i
$$92$$ 26.9117 0.292518
$$93$$ 12.7721 22.1219i 0.137334 0.237870i
$$94$$ 40.6690 23.4803i 0.432649 0.249790i
$$95$$ −71.1838 123.294i −0.749303 1.29783i
$$96$$ −8.48528 4.89898i −0.0883883 0.0510310i
$$97$$ 30.5826i 0.315284i 0.987496 + 0.157642i $$0.0503892\pi$$
−0.987496 + 0.157642i $$0.949611\pi$$
$$98$$ 1.41421 + 69.2820i 0.0144308 + 0.706960i
$$99$$ −18.0000 −0.181818
$$100$$ 44.9411 77.8403i 0.449411 0.778403i
$$101$$ 110.823 63.9839i 1.09726 0.633504i 0.161761 0.986830i $$-0.448283\pi$$
0.935500 + 0.353326i $$0.114949\pi$$
$$102$$ −22.9706 39.7862i −0.225202 0.390061i
$$103$$ −70.1102 40.4781i −0.680681 0.392992i 0.119430 0.992843i $$-0.461893\pi$$
−0.800112 + 0.599851i $$0.795226\pi$$
$$104$$ 50.5266i 0.485833i
$$105$$ −97.6690 + 27.2416i −0.930181 + 0.259443i
$$106$$ −48.8528 −0.460876
$$107$$ −84.7279 + 146.753i −0.791850 + 1.37152i 0.132971 + 0.991120i $$0.457548\pi$$
−0.924820 + 0.380404i $$0.875785\pi$$
$$108$$ −9.00000 + 5.19615i −0.0833333 + 0.0481125i
$$109$$ −89.4706 154.968i −0.820831 1.42172i −0.905064 0.425275i $$-0.860177\pi$$
0.0842335 0.996446i $$-0.473156\pi$$
$$110$$ 61.4558 + 35.4815i 0.558689 + 0.322560i
$$111$$ 10.3413i 0.0931650i
$$112$$ 6.97056 27.1185i 0.0622372 0.242129i
$$113$$ −17.3970 −0.153955 −0.0769777 0.997033i $$-0.524527\pi$$
−0.0769777 + 0.997033i $$0.524527\pi$$
$$114$$ 20.8492 36.1119i 0.182888 0.316771i
$$115$$ −97.4558 + 56.2662i −0.847442 + 0.489271i
$$116$$ −33.9411 58.7878i −0.292596 0.506791i
$$117$$ −46.4117 26.7958i −0.396681 0.229024i
$$118$$ 38.6995i 0.327962i
$$119$$ 91.8823 93.7769i 0.772120 0.788041i
$$120$$ 40.9706 0.341421
$$121$$ 42.5000 73.6122i 0.351240 0.608365i
$$122$$ 49.4558 28.5533i 0.405376 0.234044i
$$123$$ 30.5147 + 52.8530i 0.248087 + 0.429700i
$$124$$ −25.5442 14.7479i −0.206001 0.118935i
$$125$$ 166.769i 1.33415i
$$126$$ −21.2132 20.7846i −0.168359 0.164957i
$$127$$ 167.426 1.31832 0.659159 0.752004i $$-0.270912\pi$$
0.659159 + 0.752004i $$0.270912\pi$$
$$128$$ −5.65685 + 9.79796i −0.0441942 + 0.0765466i
$$129$$ 23.2279 13.4106i 0.180061 0.103959i
$$130$$ 105.640 + 182.973i 0.812612 + 1.40749i
$$131$$ −1.54416 0.891519i −0.0117874 0.00680549i 0.494095 0.869408i $$-0.335500\pi$$
−0.505882 + 0.862603i $$0.668833\pi$$
$$132$$ 20.7846i 0.157459i
$$133$$ 115.412 + 29.6656i 0.867757 + 0.223049i
$$134$$ −161.782 −1.20733
$$135$$ 21.7279 37.6339i 0.160948 0.278769i
$$136$$ −45.9411 + 26.5241i −0.337802 + 0.195030i
$$137$$ −50.4853 87.4431i −0.368506 0.638271i 0.620826 0.783948i $$-0.286797\pi$$
−0.989332 + 0.145677i $$0.953464\pi$$
$$138$$ −28.5442 16.4800i −0.206842 0.119420i
$$139$$ 140.542i 1.01110i −0.862799 0.505548i $$-0.831290\pi$$
0.862799 0.505548i $$-0.168710\pi$$
$$140$$ 31.4558 + 112.779i 0.224685 + 0.805561i
$$141$$ −57.5147 −0.407906
$$142$$ −13.1543 + 22.7840i −0.0926361 + 0.160450i
$$143$$ −92.8234 + 53.5916i −0.649115 + 0.374766i
$$144$$ 6.00000 + 10.3923i 0.0416667 + 0.0721688i
$$145$$ 245.823 + 141.926i 1.69533 + 0.978801i
$$146$$ 165.508i 1.13362i
$$147$$ 40.9264 74.3507i 0.278411 0.505787i
$$148$$ 11.9411 0.0806833
$$149$$ −91.4558 + 158.406i −0.613798 + 1.06313i 0.376797 + 0.926296i $$0.377026\pi$$
−0.990594 + 0.136833i $$0.956308\pi$$
$$150$$ −95.3345 + 55.0414i −0.635563 + 0.366943i
$$151$$ 144.397 + 250.103i 0.956271 + 1.65631i 0.731432 + 0.681915i $$0.238852\pi$$
0.224840 + 0.974396i $$0.427814\pi$$
$$152$$ −41.6985 24.0746i −0.274332 0.158386i
$$153$$ 56.2662i 0.367753i
$$154$$ −57.2132 + 15.9577i −0.371514 + 0.103622i
$$155$$ 123.338 0.795730
$$156$$ −30.9411 + 53.5916i −0.198341 + 0.343536i
$$157$$ 162.000 93.5307i 1.03185 0.595737i 0.114334 0.993442i $$-0.463527\pi$$
0.917513 + 0.397705i $$0.130193\pi$$
$$158$$ 62.4645 + 108.192i 0.395345 + 0.684757i
$$159$$ 51.8162 + 29.9161i 0.325888 + 0.188152i
$$160$$ 47.3087i 0.295680i
$$161$$ 23.4487 91.2255i 0.145644 0.566618i
$$162$$ 12.7279 0.0785674
$$163$$ −8.02944 + 13.9074i −0.0492604 + 0.0853214i −0.889604 0.456732i $$-0.849020\pi$$
0.840344 + 0.542054i $$0.182353\pi$$
$$164$$ 61.0294 35.2354i 0.372131 0.214850i
$$165$$ −43.4558 75.2677i −0.263369 0.456168i
$$166$$ −92.7868 53.5705i −0.558957 0.322714i
$$167$$ 176.117i 1.05459i −0.849681 0.527297i $$-0.823206\pi$$
0.849681 0.527297i $$-0.176794\pi$$
$$168$$ −24.0000 + 24.4949i −0.142857 + 0.145803i
$$169$$ −150.118 −0.888271
$$170$$ 110.912 192.105i 0.652422 1.13003i
$$171$$ −44.2279 + 25.5350i −0.258643 + 0.149328i
$$172$$ −15.4853 26.8213i −0.0900307 0.155938i
$$173$$ −200.184 115.576i −1.15713 0.668070i −0.206517 0.978443i $$-0.566213\pi$$
−0.950615 + 0.310373i $$0.899546\pi$$
$$174$$ 83.1384i 0.477807i
$$175$$ −224.706 220.166i −1.28403 1.25809i
$$176$$ 24.0000 0.136364
$$177$$ 23.6985 41.0470i 0.133890 0.231904i
$$178$$ 25.4558 14.6969i 0.143010 0.0825671i
$$179$$ 42.6396 + 73.8540i 0.238210 + 0.412592i 0.960201 0.279311i $$-0.0901060\pi$$
−0.721991 + 0.691903i $$0.756773\pi$$
$$180$$ −43.4558 25.0892i −0.241421 0.139385i
$$181$$ 5.58655i 0.0308649i −0.999881 0.0154325i $$-0.995087\pi$$
0.999881 0.0154325i $$-0.00491250\pi$$
$$182$$ −171.276 44.0249i −0.941075 0.241895i
$$183$$ −69.9411 −0.382192
$$184$$ −19.0294 + 32.9600i −0.103421 + 0.179130i
$$185$$ −43.2426 + 24.9662i −0.233744 + 0.134952i
$$186$$ 18.0624 + 31.2851i 0.0971099 + 0.168199i
$$187$$ 97.4558 + 56.2662i 0.521154 + 0.300889i
$$188$$ 66.4123i 0.353257i
$$189$$ 9.77208 + 35.0358i 0.0517041 + 0.185375i
$$190$$ 201.338 1.05967
$$191$$ −92.6985 + 160.558i −0.485332 + 0.840620i −0.999858 0.0168547i $$-0.994635\pi$$
0.514526 + 0.857475i $$0.327968\pi$$
$$192$$ 12.0000 6.92820i 0.0625000 0.0360844i
$$193$$ −113.897 197.275i −0.590140 1.02215i −0.994213 0.107425i $$-0.965739\pi$$
0.404073 0.914727i $$-0.367594\pi$$
$$194$$ −37.4558 21.6251i −0.193071 0.111470i
$$195$$ 258.763i 1.32699i
$$196$$ −85.8528 47.2577i −0.438025 0.241111i
$$197$$ 123.161 0.625185 0.312593 0.949887i $$-0.398803\pi$$
0.312593 + 0.949887i $$0.398803\pi$$
$$198$$ 12.7279 22.0454i 0.0642824 0.111340i
$$199$$ 5.39697 3.11594i 0.0271205 0.0156580i −0.486378 0.873748i $$-0.661682\pi$$
0.513499 + 0.858090i $$0.328349\pi$$
$$200$$ 63.5563 + 110.083i 0.317782 + 0.550414i
$$201$$ 171.595 + 99.0707i 0.853709 + 0.492889i
$$202$$ 180.974i 0.895910i
$$203$$ −228.853 + 63.8309i −1.12735 + 0.314438i
$$204$$ 64.9706 0.318483
$$205$$ −147.338 + 255.197i −0.718722 + 1.24486i
$$206$$ 99.1508 57.2447i 0.481314 0.277887i
$$207$$ 20.1838 + 34.9593i 0.0975061 + 0.168886i
$$208$$ 61.8823 + 35.7277i 0.297511 + 0.171768i
$$209$$ 102.140i 0.488708i
$$210$$ 35.6985 138.882i 0.169993 0.661345i
$$211$$ −124.912 −0.591999 −0.295999 0.955188i $$-0.595653\pi$$
−0.295999 + 0.955188i $$0.595653\pi$$
$$212$$ 34.5442 59.8322i 0.162944 0.282228i
$$213$$ 27.9045 16.1107i 0.131007 0.0756371i
$$214$$ −119.823 207.540i −0.559922 0.969814i
$$215$$ 112.154 + 64.7523i 0.521648 + 0.301174i
$$216$$ 14.6969i 0.0680414i
$$217$$ −72.2498 + 73.7396i −0.332948 + 0.339814i
$$218$$ 253.061 1.16083
$$219$$ −101.353 + 175.548i −0.462798 + 0.801590i
$$220$$ −86.9117 + 50.1785i −0.395053 + 0.228084i
$$221$$ 167.522 + 290.156i 0.758017 + 1.31292i
$$222$$ −12.6655 7.31242i −0.0570517 0.0329388i
$$223$$ 228.631i 1.02525i −0.858613 0.512625i $$-0.828673\pi$$
0.858613 0.512625i $$-0.171327\pi$$
$$224$$ 28.2843 + 27.7128i 0.126269 + 0.123718i
$$225$$ 134.823 0.599215
$$226$$ 12.3015 21.3068i 0.0544315 0.0942781i
$$227$$ −146.823 + 84.7685i −0.646799 + 0.373430i −0.787229 0.616661i $$-0.788485\pi$$
0.140430 + 0.990091i $$0.455152\pi$$
$$228$$ 29.4853 + 51.0700i 0.129321 + 0.223991i
$$229$$ 30.0442 + 17.3460i 0.131197 + 0.0757467i 0.564162 0.825664i $$-0.309199\pi$$
−0.432965 + 0.901411i $$0.642533\pi$$
$$230$$ 159.145i 0.691934i
$$231$$ 70.4558 + 18.1101i 0.305004 + 0.0783985i
$$232$$ 96.0000 0.413793
$$233$$ 127.243 220.391i 0.546106 0.945883i −0.452431 0.891800i $$-0.649443\pi$$
0.998536 0.0540833i $$-0.0172237\pi$$
$$234$$ 65.6360 37.8950i 0.280496 0.161944i
$$235$$ −138.853 240.500i −0.590863 1.02340i
$$236$$ −47.3970 27.3647i −0.200835 0.115952i
$$237$$ 153.006i 0.645595i
$$238$$ 49.8823 + 178.843i 0.209589 + 0.751440i
$$239$$ 197.147 0.824884 0.412442 0.910984i $$-0.364676\pi$$
0.412442 + 0.910984i $$0.364676\pi$$
$$240$$ −28.9706 + 50.1785i −0.120711 + 0.209077i
$$241$$ 76.6173 44.2350i 0.317914 0.183548i −0.332548 0.943086i $$-0.607908\pi$$
0.650462 + 0.759538i $$0.274575\pi$$
$$242$$ 60.1041 + 104.103i 0.248364 + 0.430179i
$$243$$ −13.5000 7.79423i −0.0555556 0.0320750i
$$244$$ 80.7611i 0.330988i
$$245$$ 409.706 8.36308i 1.67227 0.0341350i
$$246$$ −86.3087 −0.350848
$$247$$ −152.051 + 263.361i −0.615592 + 1.06624i
$$248$$ 36.1249 20.8567i 0.145665 0.0840997i
$$249$$ 65.6102 + 113.640i 0.263495 + 0.456386i
$$250$$ −204.250 117.924i −0.816999 0.471695i
$$251$$ 215.903i 0.860172i −0.902788 0.430086i $$-0.858483\pi$$
0.902788 0.430086i $$-0.141517\pi$$
$$252$$ 40.4558 11.2838i 0.160539 0.0447771i
$$253$$ 80.7351 0.319111
$$254$$ −118.388 + 205.055i −0.466096 + 0.807302i
$$255$$ −235.279 + 135.839i −0.922664 + 0.532700i
$$256$$ −8.00000 13.8564i −0.0312500 0.0541266i
$$257$$ −3.72792 2.15232i −0.0145055 0.00837477i 0.492730 0.870182i $$-0.335999\pi$$
−0.507235 + 0.861808i $$0.669332\pi$$
$$258$$ 37.9310i 0.147020i
$$259$$ 10.4045 40.4781i 0.0401720 0.156286i
$$260$$ −298.794 −1.14921
$$261$$ 50.9117 88.1816i 0.195064 0.337861i
$$262$$ 2.18377 1.26080i 0.00833499 0.00481221i
$$263$$ −141.338 244.805i −0.537407 0.930817i −0.999043 0.0437468i $$-0.986071\pi$$
0.461635 0.887070i $$-0.347263\pi$$
$$264$$ −25.4558 14.6969i −0.0964237 0.0556702i
$$265$$ 288.896i 1.09017i
$$266$$ −117.941 + 120.373i −0.443388 + 0.452531i
$$267$$ −36.0000 −0.134831
$$268$$ 114.397 198.141i 0.426854 0.739333i
$$269$$ −330.765 + 190.967i −1.22961 + 0.709914i −0.966948 0.254974i $$-0.917933\pi$$
−0.262660 + 0.964888i $$0.584600\pi$$
$$270$$ 30.7279 + 53.2223i 0.113807 + 0.197120i
$$271$$ −73.0294 42.1636i −0.269481 0.155585i 0.359171 0.933272i $$-0.383060\pi$$
−0.628652 + 0.777687i $$0.716393\pi$$
$$272$$ 75.0215i 0.275814i
$$273$$ 154.706 + 151.580i 0.566687 + 0.555238i
$$274$$ 142.794 0.521146
$$275$$ 134.823 233.521i 0.490267 0.849167i
$$276$$ 40.3675 23.3062i 0.146259 0.0844428i
$$277$$ 68.5589 + 118.747i 0.247505 + 0.428691i 0.962833 0.270098i $$-0.0870560\pi$$
−0.715328 + 0.698789i $$0.753723\pi$$
$$278$$ 172.128 + 99.3784i 0.619167 + 0.357476i
$$279$$ 44.2438i 0.158580i
$$280$$ −160.368 41.2211i −0.572741 0.147218i
$$281$$ −325.103 −1.15695 −0.578474 0.815701i $$-0.696352\pi$$
−0.578474 + 0.815701i $$0.696352\pi$$
$$282$$ 40.6690 70.4409i 0.144216 0.249790i
$$283$$ 168.507 97.2876i 0.595432 0.343773i −0.171811 0.985130i $$-0.554962\pi$$
0.767242 + 0.641357i $$0.221628\pi$$
$$284$$ −18.6030 32.2214i −0.0655036 0.113456i
$$285$$ −213.551 123.294i −0.749303 0.432610i
$$286$$ 151.580i 0.530000i
$$287$$ −66.2649 237.579i −0.230888 0.827803i
$$288$$ −16.9706 −0.0589256
$$289$$ 31.3823 54.3557i 0.108589 0.188082i
$$290$$ −347.647 + 200.714i −1.19878 + 0.692117i
$$291$$ 26.4853 + 45.8739i 0.0910147 + 0.157642i
$$292$$ 202.706 + 117.032i 0.694197 + 0.400795i
$$293$$ 239.702i 0.818095i −0.912513 0.409048i $$-0.865861\pi$$
0.912513 0.409048i $$-0.134139\pi$$
$$294$$ 62.1213 + 102.698i 0.211297 + 0.349314i
$$295$$ 228.853 0.775772
$$296$$ −8.44365 + 14.6248i −0.0285258 + 0.0494082i
$$297$$ −27.0000 + 15.5885i −0.0909091 + 0.0524864i
$$298$$ −129.338 224.020i −0.434020 0.751745i
$$299$$ 208.169 + 120.187i 0.696219 + 0.401962i
$$300$$ 155.681i 0.518935i
$$301$$ −104.412 + 29.1222i −0.346883 + 0.0967515i
$$302$$ −408.416 −1.35237
$$303$$ 110.823 191.952i 0.365754 0.633504i
$$304$$ 58.9706 34.0467i 0.193982 0.111996i
$$305$$ −168.853 292.462i −0.553616 0.958891i
$$306$$ −68.9117 39.7862i −0.225202 0.130020i
$$307$$ 540.272i 1.75984i 0.475120 + 0.879921i $$0.342405\pi$$
−0.475120 + 0.879921i $$0.657595\pi$$
$$308$$ 20.9117 81.3554i 0.0678951 0.264141i
$$309$$ −140.220 −0.453788
$$310$$ −87.2132 + 151.058i −0.281333 + 0.487283i
$$311$$ 350.044 202.098i 1.12554 0.649832i 0.182732 0.983163i $$-0.441506\pi$$
0.942810 + 0.333330i $$0.108172\pi$$
$$312$$ −43.7574 75.7900i −0.140248 0.242917i
$$313$$ −113.706 65.6482i −0.363278 0.209739i 0.307240 0.951632i $$-0.400595\pi$$
−0.670518 + 0.741893i $$0.733928\pi$$
$$314$$ 264.545i 0.842500i
$$315$$ −122.912 + 125.446i −0.390196 + 0.398242i
$$316$$ −176.676 −0.559102
$$317$$ 46.9706 81.3554i 0.148172 0.256642i −0.782380 0.622802i $$-0.785994\pi$$
0.930552 + 0.366160i $$0.119328\pi$$
$$318$$ −73.2792 + 42.3078i −0.230438 + 0.133043i
$$319$$ −101.823 176.363i −0.319196 0.552863i
$$320$$ 57.9411 + 33.4523i 0.181066 + 0.104539i
$$321$$ 293.506i 0.914349i
$$322$$ 95.1472 + 93.2248i 0.295488 + 0.289518i
$$323$$ 319.279 0.988481
$$324$$ −9.00000 + 15.5885i −0.0277778 + 0.0481125i
$$325$$ 695.265 401.411i 2.13928 1.23511i
$$326$$ −11.3553 19.6680i −0.0348323 0.0603314i
$$327$$ −268.412 154.968i −0.820831 0.473907i
$$328$$ 99.6607i 0.303843i
$$329$$ 225.125 + 57.8664i 0.684270 + 0.175886i
$$330$$ 122.912 0.372460
$$331$$ 130.684 226.351i 0.394815 0.683840i −0.598263 0.801300i $$-0.704142\pi$$
0.993078 + 0.117460i $$0.0374754\pi$$
$$332$$ 131.220 75.7601i 0.395242 0.228193i
$$333$$ 8.95584 + 15.5120i 0.0268944 + 0.0465825i
$$334$$ 215.698 + 124.534i 0.645804 + 0.372855i
$$335$$ 956.711i 2.85585i
$$336$$ −13.0294 46.7144i −0.0387781 0.139031i
$$337$$ 136.265 0.404347 0.202173 0.979350i $$-0.435200\pi$$
0.202173 + 0.979350i $$0.435200\pi$$
$$338$$ 106.149 183.856i 0.314051 0.543952i
$$339$$ −26.0955 + 15.0662i −0.0769777 + 0.0444431i
$$340$$ 156.853 + 271.677i 0.461332 + 0.799050i
$$341$$ −76.6325 44.2438i −0.224729 0.129747i
$$342$$ 72.2239i 0.211181i
$$343$$ −235.000 + 249.848i −0.685131 + 0.728420i
$$344$$ 43.7990 0.127323
$$345$$ −97.4558 + 168.798i −0.282481 + 0.489271i
$$346$$ 283.103 163.449i 0.818216 0.472397i
$$347$$ 161.095 + 279.026i 0.464252 + 0.804108i 0.999167 0.0407975i $$-0.0129899\pi$$
−0.534915 + 0.844906i $$0.679657\pi$$
$$348$$ −101.823 58.7878i −0.292596 0.168930i
$$349$$ 346.495i 0.992821i 0.868088 + 0.496411i $$0.165349\pi$$
−0.868088 + 0.496411i $$0.834651\pi$$
$$350$$ 428.538 119.526i 1.22439 0.341504i
$$351$$ −92.8234 −0.264454
$$352$$ −16.9706 + 29.3939i −0.0482118 + 0.0835053i
$$353$$ −537.448 + 310.296i −1.52252 + 0.879025i −0.522869 + 0.852413i $$0.675138\pi$$
−0.999646 + 0.0266116i $$0.991528\pi$$
$$354$$ 33.5147 + 58.0492i 0.0946743 + 0.163981i
$$355$$ 134.735 + 77.7893i 0.379535 + 0.219125i
$$356$$ 41.5692i 0.116767i
$$357$$ 56.6102 220.238i 0.158572 0.616912i
$$358$$ −120.603 −0.336880
$$359$$ −10.1177 + 17.5245i −0.0281831 + 0.0488146i −0.879773 0.475394i $$-0.842305\pi$$
0.851590 + 0.524209i $$0.175639\pi$$
$$360$$ 61.4558 35.4815i 0.170711 0.0985599i
$$361$$ −35.6030 61.6663i −0.0986234 0.170821i
$$362$$ 6.84210 + 3.95029i 0.0189008 + 0.0109124i
$$363$$ 147.224i 0.405577i
$$364$$ 175.029 178.639i 0.480850 0.490766i
$$365$$ −978.749 −2.68151
$$366$$ 49.4558 85.6600i 0.135125 0.234044i
$$367$$ −269.831 + 155.787i −0.735234 + 0.424488i −0.820334 0.571885i $$-0.806212\pi$$
0.0850998 + 0.996372i $$0.472879\pi$$
$$368$$ −26.9117 46.6124i −0.0731296 0.126664i
$$369$$ 91.5442 + 52.8530i 0.248087 + 0.143233i
$$370$$ 70.6149i 0.190851i
$$371$$ −172.721 169.231i −0.465555 0.456149i
$$372$$ −51.0883 −0.137334
$$373$$ 340.691 590.094i 0.913380 1.58202i 0.104125 0.994564i $$-0.466796\pi$$
0.809255 0.587457i $$-0.199871\pi$$
$$374$$ −137.823 + 79.5724i −0.368512 + 0.212760i
$$375$$ 144.426 + 250.154i 0.385137 + 0.667077i
$$376$$ −81.3381 46.9606i −0.216325 0.124895i
$$377$$ 606.320i 1.60828i
$$378$$ −49.8198 12.8057i −0.131798 0.0338776i
$$379$$ −624.779 −1.64849 −0.824246 0.566231i $$-0.808401\pi$$
−0.824246 + 0.566231i $$0.808401\pi$$
$$380$$ −142.368 + 246.588i −0.374651 + 0.648915i
$$381$$ 251.140 144.996i 0.659159 0.380566i
$$382$$ −131.095 227.064i −0.343182 0.594408i
$$383$$ 119.772 + 69.1502i 0.312720 + 0.180549i 0.648143 0.761519i $$-0.275546\pi$$
−0.335423 + 0.942068i $$0.608879\pi$$
$$384$$ 19.5959i 0.0510310i
$$385$$ 94.3675 + 338.336i 0.245110 + 0.878794i
$$386$$ 322.149 0.834584
$$387$$ 23.2279 40.2319i 0.0600205 0.103959i
$$388$$ 52.9706 30.5826i 0.136522 0.0788211i
$$389$$ 281.787 + 488.069i 0.724388 + 1.25468i 0.959226 + 0.282642i $$0.0912107\pi$$
−0.234838 + 0.972035i $$0.575456\pi$$
$$390$$ 316.919 + 182.973i 0.812612 + 0.469162i
$$391$$ 252.370i 0.645446i
$$392$$ 118.586 71.7315i 0.302515 0.182989i
$$393$$ −3.08831 −0.00785830
$$394$$ −87.0883 + 150.841i −0.221036 + 0.382846i
$$395$$ 639.801 369.389i 1.61975 0.935163i
$$396$$ 18.0000 + 31.1769i 0.0454545 + 0.0787296i
$$397$$ −392.603 226.669i −0.988923 0.570955i −0.0839711 0.996468i $$-0.526760\pi$$
−0.904952 + 0.425513i $$0.860094\pi$$
$$398$$ 8.81321i 0.0221438i
$$399$$ 198.809 55.4511i 0.498267 0.138975i
$$400$$ −179.765 −0.449411
$$401$$ 137.875 238.807i 0.343828 0.595528i −0.641312 0.767280i $$-0.721610\pi$$
0.985140 + 0.171752i $$0.0549429\pi$$
$$402$$ −242.673 + 140.107i −0.603663 + 0.348525i
$$403$$ −131.727 228.159i −0.326867 0.566151i
$$404$$ −221.647 127.968i −0.548631 0.316752i
$$405$$ 75.2677i 0.185846i
$$406$$ 83.6468 325.422i 0.206026 0.801531i
$$407$$ 35.8234 0.0880181
$$408$$ −45.9411 + 79.5724i −0.112601 + 0.195030i
$$409$$ −377.441 + 217.916i −0.922839 + 0.532801i −0.884540 0.466465i $$-0.845527\pi$$
−0.0382993 + 0.999266i $$0.512194\pi$$
$$410$$ −208.368 360.903i −0.508213 0.880252i
$$411$$ −151.456 87.4431i −0.368506 0.212757i
$$412$$ 161.913i 0.392992i
$$413$$ −134.059 + 136.823i −0.324598 + 0.331291i
$$414$$ −57.0883 −0.137894
$$415$$ −316.794 + 548.703i −0.763359 + 1.32218i
$$416$$ −87.5147 + 50.5266i −0.210372 + 0.121458i
$$417$$ −121.713 210.813i −0.291878 0.505548i
$$418$$ −125.095 72.2239i −0.299271 0.172784i
$$419$$ 301.257i 0.718991i −0.933147 0.359496i $$-0.882949\pi$$
0.933147 0.359496i $$-0.117051\pi$$
$$420$$ 144.853 + 141.926i 0.344888 + 0.337920i
$$421$$ −203.794 −0.484071 −0.242036 0.970267i $$-0.577815\pi$$
−0.242036 + 0.970267i $$0.577815\pi$$
$$422$$ 88.3259 152.985i 0.209303 0.362524i
$$423$$ −86.2721 + 49.8092i −0.203953 + 0.117752i
$$424$$ 48.8528 + 84.6156i 0.115219 + 0.199565i
$$425$$ −729.963 421.444i −1.71756 0.991633i
$$426$$ 45.5679i 0.106967i
$$427$$ 273.765 + 70.3688i 0.641135 + 0.164798i
$$428$$ 338.912 0.791850
$$429$$ −92.8234 + 160.775i −0.216372 + 0.374766i
$$430$$ −158.610 + 91.5736i −0.368861 + 0.212962i
$$431$$ 197.860 + 342.703i 0.459072 + 0.795136i 0.998912 0.0466317i $$-0.0148487\pi$$
−0.539840 + 0.841767i $$0.681515\pi$$
$$432$$ 18.0000 + 10.3923i 0.0416667 + 0.0240563i
$$433$$ 44.2685i 0.102237i −0.998693 0.0511184i $$-0.983721\pi$$
0.998693 0.0511184i $$-0.0162786\pi$$
$$434$$ −39.2239 140.629i −0.0903777 0.324031i
$$435$$ 491.647 1.13022
$$436$$ −178.941 + 309.935i −0.410415 + 0.710860i
$$437$$ 198.375 114.532i 0.453947 0.262086i
$$438$$ −143.335 248.263i −0.327248 0.566810i
$$439$$ 344.558 + 198.931i 0.784871 + 0.453146i 0.838154 0.545434i $$-0.183635\pi$$
−0.0532827 + 0.998579i $$0.516968\pi$$
$$440$$ 141.926i 0.322560i
$$441$$ −3.00000 146.969i −0.00680272 0.333264i
$$442$$ −473.823 −1.07200
$$443$$ 59.2721 102.662i 0.133797 0.231743i −0.791340 0.611376i $$-0.790616\pi$$
0.925137 + 0.379633i $$0.123950\pi$$
$$444$$ 17.9117 10.3413i 0.0403416 0.0232913i
$$445$$ −86.9117 150.535i −0.195307 0.338282i
$$446$$ 280.014 + 161.666i 0.627835 + 0.362481i
$$447$$ 316.812i 0.708752i
$$448$$ −53.9411 + 15.0451i −0.120404 + 0.0335828i
$$449$$ 713.897 1.58997 0.794985 0.606629i $$-0.207479\pi$$
0.794985 + 0.606629i $$0.207479\pi$$
$$450$$ −95.3345 + 165.124i −0.211854 + 0.366943i
$$451$$ 183.088 105.706i 0.405961 0.234382i
$$452$$ 17.3970 + 30.1324i 0.0384889 + 0.0666647i
$$453$$ 433.191 + 250.103i 0.956271 + 0.552104i
$$454$$ 239.762i 0.528109i
$$455$$ −260.345 + 1012.85i −0.572187 + 2.22605i
$$456$$ −83.3970 −0.182888
$$457$$ 62.5883 108.406i 0.136955 0.237213i −0.789388 0.613895i $$-0.789602\pi$$
0.926342 + 0.376682i $$0.122935\pi$$
$$458$$ −42.4889 + 24.5310i −0.0927704 + 0.0535610i
$$459$$ 48.7279 + 84.3992i 0.106161 + 0.183876i
$$460$$ 194.912 + 112.532i 0.423721 + 0.244635i
$$461$$ 655.767i 1.42249i 0.702945 + 0.711244i $$0.251868\pi$$
−0.702945 + 0.711244i $$0.748132\pi$$
$$462$$ −72.0000 + 73.4847i −0.155844 + 0.159058i
$$463$$ 869.396 1.87775 0.938873 0.344265i $$-0.111872\pi$$
0.938873 + 0.344265i $$0.111872\pi$$
$$464$$ −67.8823 + 117.576i −0.146298 + 0.253395i
$$465$$ 185.007 106.814i 0.397865 0.229707i
$$466$$ 179.948 + 311.680i 0.386155 + 0.668840i
$$467$$ −231.551 133.686i −0.495827 0.286266i 0.231162 0.972915i $$-0.425747\pi$$
−0.726989 + 0.686649i $$0.759081\pi$$
$$468$$ 107.183i 0.229024i
$$469$$ −571.985 560.428i −1.21958 1.19494i
$$470$$ 392.735 0.835607
$$471$$ 162.000 280.592i 0.343949 0.595737i
$$472$$ 67.0294 38.6995i 0.142012 0.0819904i
$$473$$ −46.4558 80.4639i −0.0982153 0.170114i
$$474$$ 187.393 + 108.192i 0.395345 + 0.228252i
$$475$$ 765.048i 1.61063i
$$476$$ −254.309 65.3678i −0.534262 0.137327i
$$477$$ 103.632 0.217259
$$478$$ −139.404 + 241.455i −0.291640 + 0.505136i
$$479$$ 235.331 135.868i 0.491296 0.283650i −0.233816 0.972281i $$-0.575121\pi$$
0.725112 + 0.688631i $$0.241788\pi$$
$$480$$ −40.9706 70.9631i −0.0853553 0.147840i
$$481$$ 92.3680 + 53.3287i 0.192033 + 0.110870i
$$482$$ 125.116i 0.259576i
$$483$$ −43.8305 157.145i −0.0907464 0.325353i
$$484$$ −170.000 −0.351240
$$485$$ −127.882 + 221.499i −0.263675 + 0.456698i
$$486$$ 19.0919 11.0227i 0.0392837 0.0226805i
$$487$$ 280.757 + 486.285i 0.576503 + 0.998532i 0.995877 + 0.0907186i $$0.0289164\pi$$
−0.419374 + 0.907814i $$0.637750\pi$$
$$488$$ −98.9117 57.1067i −0.202688 0.117022i
$$489$$ 27.8148i 0.0568810i
$$490$$ −279.463 + 507.698i −0.570333 + 1.03612i
$$491$$ −406.441 −0.827781 −0.413891 0.910327i $$-0.635830\pi$$
−0.413891 + 0.910327i $$0.635830\pi$$
$$492$$ 61.0294 105.706i 0.124044 0.214850i
$$493$$ −551.294 + 318.289i −1.11824 + 0.645618i
$$494$$ −215.033 372.448i −0.435289 0.753944i
$$495$$ −130.368 75.2677i −0.263369 0.152056i
$$496$$ 58.9917i 0.118935i
$$497$$ −125.434 + 34.9856i −0.252381 + 0.0703935i
$$498$$ −185.574 −0.372638
$$499$$ 185.713 321.665i 0.372171 0.644619i −0.617728 0.786391i $$-0.711947\pi$$
0.989899 + 0.141773i $$0.0452802\pi$$
$$500$$ 288.853 166.769i 0.577706 0.333538i
$$501$$ −152.522 264.176i −0.304435 0.527297i
$$502$$ 264.426 + 152.667i 0.526746 + 0.304117i
$$503$$ 64.6292i 0.128488i 0.997934 + 0.0642438i $$0.0204635\pi$$
−0.997934 + 0.0642438i $$0.979536\pi$$
$$504$$ −14.7868 + 57.5270i −0.0293389 + 0.114141i
$$505$$ 1070.21 2.11922
$$506$$ −57.0883 + 98.8799i −0.112823 + 0.195415i
$$507$$ −225.177 + 130.006i −0.444135 + 0.256422i
$$508$$ −167.426 289.991i −0.329580 0.570849i
$$509$$ 871.889 + 503.385i 1.71294 + 0.988969i 0.930534 + 0.366205i $$0.119343\pi$$
0.782410 + 0.622764i $$0.213990\pi$$
$$510$$ 384.209i 0.753352i
$$511$$ 573.338 585.161i 1.12199 1.14513i
$$512$$ 22.6274 0.0441942
$$513$$ −44.2279 + 76.6050i −0.0862143 + 0.149328i
$$514$$ 5.27208 3.04384i 0.0102570 0.00592186i
$$515$$ −338.522 586.337i −0.657324 1.13852i
$$516$$ −46.4558 26.8213i −0.0900307 0.0519793i
$$517$$ 199.237i 0.385371i
$$518$$ 42.2183 + 41.3653i 0.0815024 + 0.0798557i
$$519$$ −400.368 −0.771421
$$520$$ 211.279 365.946i 0.406306 0.703743i
$$521$$ −322.294 + 186.077i −0.618607 + 0.357153i −0.776327 0.630331i $$-0.782919\pi$$
0.157719 + 0.987484i $$0.449586\pi$$
$$522$$ 72.0000 + 124.708i 0.137931 + 0.238904i
$$523$$ −551.904 318.642i −1.05527 0.609258i −0.131147 0.991363i $$-0.541866\pi$$
−0.924119 + 0.382105i $$0.875199\pi$$
$$524$$ 3.56608i 0.00680549i
$$525$$ −527.727 135.648i −1.00520 0.258377i
$$526$$ 399.765 0.760009
$$527$$ −138.302 + 239.545i −0.262432 + 0.454545i
$$528$$ 36.0000 20.7846i 0.0681818 0.0393648i
$$529$$ 173.970 + 301.325i 0.328866 + 0.569613i
$$530$$ −353.823 204.280i −0.667591 0.385434i
$$531$$ 82.0940i 0.154603i
$$532$$ −64.0294 229.564i −0.120356 0.431512i
$$533$$ 629.440 1.18094
$$534$$ 25.4558 44.0908i 0.0476701 0.0825671i
$$535$$ −1227.31 + 708.586i −2.29403 + 1.32446i
$$536$$ 161.782 + 280.214i 0.301832 + 0.522788i
$$537$$ 127.919 + 73.8540i 0.238210 + 0.137531i
$$538$$ 540.136i 1.00397i
$$539$$ −257.558 141.773i −0.477845 0.263030i
$$540$$ −86.9117 −0.160948
$$541$$ −110.412 + 191.239i −0.204088 + 0.353491i −0.949842 0.312731i $$-0.898756\pi$$
0.745754 + 0.666222i $$0.232090\pi$$
$$542$$ 103.279 59.6283i 0.190552 0.110015i
$$543$$ −4.83810 8.37983i −0.00890994 0.0154325i
$$544$$ 91.8823 + 53.0482i 0.168901 + 0.0975152i
$$545$$ 1496.50i 2.74587i
$$546$$ −295.040 + 82.2917i −0.540367 + 0.150717i
$$547$$ −160.676 −0.293741 −0.146870 0.989156i $$-0.546920\pi$$
−0.146870 + 0.989156i $$0.546920\pi$$
$$548$$ −100.971 + 174.886i −0.184253 + 0.319135i
$$549$$ −104.912 + 60.5708i −0.191096 + 0.110329i
$$550$$ 190.669 + 330.248i 0.346671 + 0.600452i
$$551$$ −500.382 288.896i −0.908134 0.524311i
$$552$$ 65.9199i 0.119420i
$$553$$ −153.942 + 598.898i −0.278375 + 1.08300i
$$554$$ −193.914 −0.350025
$$555$$ −43.2426 + 74.8985i −0.0779147 + 0.134952i
$$556$$ −243.426 + 140.542i −0.437817 + 0.252774i
$$557$$ 237.177 + 410.802i 0.425811 + 0.737526i 0.996496 0.0836431i $$-0.0266556\pi$$
−0.570685 + 0.821169i $$0.693322\pi$$
$$558$$ 54.1873 + 31.2851i 0.0971099 + 0.0560664i
$$559$$ 276.627i 0.494860i
$$560$$ 163.882 167.262i 0.292647 0.298681i
$$561$$ 194.912 0.347436
$$562$$ 229.882 398.168i 0.409043 0.708484i
$$563$$ −430.301 + 248.434i −0.764300 + 0.441269i −0.830837 0.556515i $$-0.812138\pi$$
0.0665378 + 0.997784i $$0.478805\pi$$
$$564$$ 57.5147 + 99.6184i 0.101976 + 0.176628i
$$565$$ −126.000 72.7461i −0.223009 0.128754i
$$566$$ 275.171i 0.486168i
$$567$$ 45.0000 + 44.0908i 0.0793651 + 0.0777616i
$$568$$ 52.6173 0.0926361
$$569$$ −392.647 + 680.084i −0.690065 + 1.19523i 0.281752 + 0.959487i $$0.409085\pi$$
−0.971816 + 0.235740i $$0.924249\pi$$
$$570$$ 302.007 174.364i 0.529837 0.305902i
$$571$$ 357.521 + 619.245i 0.626132 + 1.08449i 0.988321 + 0.152388i $$0.0486963\pi$$
−0.362189 + 0.932105i $$0.617970\pi$$
$$572$$ 185.647 + 107.183i 0.324557 + 0.187383i
$$573$$ 321.117i 0.560414i
$$574$$ 337.831 + 86.8364i 0.588555 + 0.151283i
$$575$$ −604.721 −1.05169
$$576$$ 12.0000 20.7846i 0.0208333 0.0360844i
$$577$$ 669.117 386.315i 1.15965 0.669524i 0.208429 0.978038i $$-0.433165\pi$$
0.951220 + 0.308514i $$0.0998317\pi$$
$$578$$ 44.3812 + 76.8705i 0.0767841 + 0.132994i
$$579$$ −341.691 197.275i −0.590140 0.340717i
$$580$$ 567.705i 0.978801i
$$581$$ −142.477 510.823i −0.245228 0.879214i
$$582$$ −74.9117 −0.128714
$$583$$ 103.632 179.497i 0.177757 0.307885i
$$584$$ −286.669 + 165.508i −0.490872 + 0.283405i
$$585$$ −224.095 388.145i −0.383069 0.663495i
$$586$$ 293.574 + 169.495i 0.500979 + 0.289240i
$$587$$ 436.477i 0.743572i −0.928318 0.371786i $$-0.878746\pi$$
0.928318 0.371786i $$-0.121254\pi$$
$$588$$ −169.706 + 3.46410i −0.288615 + 0.00589133i
$$589$$ −251.059 −0.426246
$$590$$ −161.823 + 280.286i −0.274277 + 0.475062i
$$591$$ 184.742 106.661i 0.312593 0.180475i
$$592$$ −11.9411 20.6826i −0.0201708 0.0349369i
$$593$$ 722.397 + 417.076i 1.21821 + 0.703332i 0.964534 0.263958i $$-0.0850279\pi$$
0.253673 + 0.967290i $$0.418361\pi$$
$$594$$ 44.0908i 0.0742270i
$$595$$ 1057.60 294.983i 1.77748 0.495770i
$$596$$ 365.823 0.613798
$$597$$ 5.39697 9.34783i 0.00904015 0.0156580i
$$598$$ −294.396 + 169.970i −0.492301 + 0.284230i
$$599$$ −436.794 756.549i −0.729205 1.26302i −0.957220 0.289363i $$-0.906557\pi$$
0.228014 0.973658i $$-0.426777\pi$$
$$600$$ 190.669 + 110.083i 0.317782 + 0.183471i
$$601$$ 198.982i 0.331085i 0.986203 + 0.165542i $$0.0529375\pi$$
−0.986203 + 0.165542i $$0.947063\pi$$
$$602$$ 38.1630 148.470i 0.0633936 0.246628i
$$603$$ 343.191 0.569139
$$604$$ 288.794 500.206i 0.478136 0.828155i
$$605$$ 615.624 355.431i 1.01756 0.587489i
$$606$$ 156.728 + 271.461i 0.258627 + 0.447955i
$$607$$ 137.654 + 79.4748i 0.226778 + 0.130930i 0.609085 0.793105i $$-0.291537\pi$$
−0.382307 + 0.924035i $$0.624870\pi$$
$$608$$ 96.2985i 0.158386i
$$609$$ −288.000 + 293.939i −0.472906 + 0.482658i
$$610$$ 477.588 0.782931
$$611$$ −296.595 + 513.718i −0.485426 + 0.840782i
$$612$$ 97.4558 56.2662i 0.159242 0.0919382i
$$613$$ 357.368 + 618.979i 0.582981 + 1.00975i 0.995124 + 0.0986338i $$0.0314473\pi$$
−0.412143 + 0.911119i $$0.635219\pi$$
$$614$$ −661.695 382.030i −1.07768 0.622198i
$$615$$ 510.394i 0.829909i
$$616$$ 84.8528 + 83.1384i 0.137748 + 0.134965i
$$617$$ −639.381 −1.03627 −0.518137 0.855298i $$-0.673374\pi$$
−0.518137 + 0.855298i $$0.673374\pi$$
$$618$$ 99.1508 171.734i 0.160438 0.277887i
$$619$$ 148.978 86.0126i 0.240676 0.138954i −0.374812 0.927101i $$-0.622293\pi$$
0.615487 + 0.788147i $$0.288959\pi$$
$$620$$ −123.338 213.628i −0.198932 0.344561i
$$621$$ 60.5513 + 34.9593i 0.0975061 + 0.0562952i
$$622$$ 571.619i 0.919002i
$$623$$ 140.912 + 36.2201i 0.226182 + 0.0581382i
$$624$$ 123.765 0.198341
$$625$$ −135.588 + 234.846i −0.216941 + 0.375753i
$$626$$ 160.805 92.8406i 0.256876 0.148308i
$$627$$ 88.4558 + 153.210i 0.141078 + 0.244354i
$$628$$ −324.000 187.061i −0.515924 0.297869i
$$629$$ 111.980i 0.178029i
$$630$$ −66.7279 239.239i −0.105917 0.379745i
$$631$$ −1141.06 −1.80833 −0.904166 0.427180i $$-0.859507\pi$$
−0.904166 + 0.427180i $$0.859507\pi$$
$$632$$ 124.929 216.383i 0.197672 0.342379i
$$633$$ −187.368 + 108.177i −0.295999 + 0.170895i
$$634$$ 66.4264 + 115.054i 0.104774 + 0.181473i
$$635$$ 1212.61 + 700.100i 1.90962 + 1.10252i
$$636$$ 119.664i 0.188152i
$$637$$ −453.044 748.968i −0.711215 1.17577i
$$638$$ 288.000 0.451411
$$639$$ 27.9045 48.3321i 0.0436691 0.0756371i
$$640$$ −81.9411 + 47.3087i −0.128033 + 0.0739199i
$$641$$ −114.551 198.409i −0.178707 0.309530i 0.762731 0.646716i $$-0.223858\pi$$
−0.941438 + 0.337186i $$0.890525\pi$$
$$642$$ −359.470 207.540i −0.559922 0.323271i
$$643$$ 707.670i 1.10058i 0.834975 + 0.550288i $$0.185482\pi$$
−0.834975 + 0.550288i $$0.814518\pi$$
$$644$$ −181.456 + 50.6111i −0.281764 + 0.0785887i
$$645$$ 224.309 0.347765
$$646$$ −225.765 + 391.036i −0.349481 + 0.605318i
$$647$$ 1021.37 589.687i 1.57862 0.911417i 0.583568 0.812064i $$-0.301656\pi$$
0.995052 0.0993530i $$-0.0316773\pi$$
$$648$$ −12.7279 22.0454i −0.0196419 0.0340207i
$$649$$ −142.191 82.0940i −0.219092 0.126493i
$$650$$ 1135.36i 1.74671i
$$651$$ −44.5143 + 173.180i −0.0683783 + 0.266021i
$$652$$ 32.1177 0.0492604
$$653$$ 77.3818 134.029i 0.118502 0.205252i −0.800672 0.599103i $$-0.795524\pi$$
0.919174 + 0.393851i $$0.128857\pi$$
$$654$$ 379.591 219.157i 0.580415 0.335103i
$$655$$ −7.45584 12.9139i −0.0113830 0.0197159i
$$656$$ −122.059 70.4707i −0.186065 0.107425i
$$657$$ 351.096i 0.534393i
$$658$$ −230.059 + 234.803i −0.349634 + 0.356843i
$$659$$ 591.308 0.897280 0.448640 0.893712i $$-0.351908\pi$$
0.448640 + 0.893712i $$0.351908\pi$$
$$660$$ −86.9117 + 150.535i −0.131684 + 0.228084i
$$661$$ 140.441 81.0837i 0.212468 0.122668i −0.389990 0.920819i $$-0.627522\pi$$
0.602458 + 0.798151i $$0.294188\pi$$
$$662$$ 184.815 + 320.109i 0.279176 + 0.483548i
$$663$$ 502.566 + 290.156i 0.758017 + 0.437642i
$$664$$ 214.282i 0.322714i
$$665$$ 711.838 + 697.456i 1.07043 + 1.04881i
$$666$$ −25.3310 −0.0380345
$$667$$ −228.353 + 395.519i −0.342359 + 0.592983i
$$668$$ −305.044 + 176.117i −0.456652 + 0.263648i
$$669$$ −198.000 342.946i −0.295964 0.512625i
$$670$$ −1171.73 676.497i −1.74885 1.00970i
$$671$$ 242.283i 0.361078i
$$672$$ 66.4264 + 17.0743i 0.0988488 + 0.0254082i
$$673$$ 42.3238 0.0628883 0.0314441 0.999506i $$-0.489989\pi$$
0.0314441 + 0.999506i $$0.489989\pi$$
$$674$$ −96.3539 + 166.890i −0.142958 + 0.247611i
$$675$$ 202.235 116.760i 0.299608 0.172978i
$$676$$ 150.118 + 260.012i 0.222068 + 0.384632i
$$677$$ 430.721 + 248.677i 0.636220 + 0.367322i 0.783157 0.621824i $$-0.213608\pi$$
−0.146937 + 0.989146i $$0.546941\pi$$
$$678$$ 42.6137i 0.0628521i
$$679$$ −57.5147 206.207i −0.0847050 0.303693i
$$680$$ −443.647 −0.652422
$$681$$ −146.823 + 254.306i −0.215600 + 0.373430i
$$682$$ 108.375 62.5701i 0.158907 0.0917451i
$$683$$ −608.080 1053.23i −0.890308 1.54206i −0.839506 0.543350i $$-0.817156\pi$$
−0.0508015 0.998709i $$-0.516178\pi$$
$$684$$ 88.4558 + 51.0700i 0.129321 + 0.0746638i
$$685$$ 844.425i 1.23274i
$$686$$ −139.830 464.484i −0.203834 0.677091i
$$687$$ 60.0883 0.0874648
$$688$$ −30.9706 + 53.6426i −0.0450154 + 0.0779689i
$$689$$ 534.418 308.546i 0.775642 0.447817i
$$690$$ −137.823 238.717i −0.199744 0.345967i
$$691$$ −932.182 538.196i −1.34903 0.778865i −0.360921 0.932596i $$-0.617538\pi$$
−0.988113 + 0.153731i $$0.950871\pi$$
$$692$$ 462.305i 0.668070i
$$693$$ 121.368 33.8515i 0.175134 0.0488477i
$$694$$ −455.647 −0.656552
$$695$$ 587.683 1017.90i 0.845588 1.46460i
$$696$$ 144.000 83.1384i 0.206897 0.119452i
$$697$$ −330.426 572.315i −0.474069 0.821112i
$$698$$ −424.368 245.009i −0.607976 0.351015i
$$699$$ 440.781i 0.630589i
$$700$$ −156.632 + 609.367i −0.223761 + 0.870525i
$$701$$ −695.897 −0.992720 −0.496360 0.868117i $$-0.665330\pi$$
−0.496360 + 0.868117i $$0.665330\pi$$
$$702$$ 65.6360 113.685i 0.0934986 0.161944i
$$703$$ 88.0219 50.8194i 0.125209 0.0722894i
$$704$$ −24.0000 41.5692i −0.0340909 0.0590472i
$$705$$ −416.558 240.500i −0.590863 0.341135i
$$706$$ 877.649i 1.24313i
$$707$$ −626.912 + 639.839i −0.886721 + 0.905006i
$$708$$ −94.7939 −0.133890
$$709$$ −127.412 + 220.684i −0.179707 + 0.311261i −0.941780 0.336229i $$-0.890848\pi$$
0.762073 + 0.647491i $$0.224182\pi$$
$$710$$ −190.544 + 110.011i −0.268372 + 0.154945i
$$711$$ −132.507 229.509i −0.186367 0.322798i
$$712$$ −50.9117 29.3939i −0.0715052 0.0412835i
$$713$$ 198.446i 0.278325i
$$714$$ 229.706 + 225.065i 0.321717 + 0.315217i
$$715$$ −896.382 −1.25368
$$716$$ 85.2792 147.708i 0.119105 0.206296i
$$717$$ 295.721 170.734i 0.412442 0.238123i
$$718$$ −14.3087 24.7833i −0.0199285 0.0345172i
$$719$$ −964.925 557.100i −1.34204 0.774826i −0.354931 0.934892i $$-0.615496\pi$$
−0.987106 + 0.160066i $$0.948829\pi$$
$$720$$ 100.357i 0.139385i
$$721$$ 548.852 + 141.078i 0.761238 + 0.195669i
$$722$$ 100.701 0.139474
$$723$$ 76.6173 132.705i 0.105971 0.183548i
$$724$$ −9.67619 + 5.58655i −0.0133649 + 0.00771623i
$$725$$ 762.676 + 1320.99i 1.05197 + 1.82206i
$$726$$ 180.312 + 104.103i 0.248364 + 0.143393i
$$727$$ 398.345i 0.547930i −0.961740 0.273965i $$-0.911665\pi$$
0.961740 0.273965i $$-0.0883353\pi$$
$$728$$ 95.0223 + 340.683i 0.130525 + 0.467971i
$$729$$ −27.0000 −0.0370370
$$730$$ 692.080 1198.72i 0.948055 1.64208i
$$731$$ −251.522 + 145.216i −0.344079 + 0.198654i
$$732$$ 69.9411 + 121.142i 0.0955480 + 0.165494i
$$733$$ 818.514 + 472.569i 1.11666 + 0.644706i 0.940547 0.339663i $$-0.110313\pi$$
0.176116 + 0.984369i $$0.443646\pi$$
$$734$$ 440.632i 0.600316i
$$735$$ 607.316 367.360i 0.826280 0.499810i
$$736$$ 76.1177 0.103421
$$737$$ 343.191 594.424i 0.465659 0.806546i
$$738$$ −129.463 + 74.7455i −0.175424 + 0.101281i
$$739$$ −96.3162 166.825i −0.130333 0.225744i 0.793472 0.608607i $$-0.208271\pi$$
−0.923805 + 0.382863i $$0.874938\pi$$
$$740$$ 86.4853 + 49.9323i 0.116872 + 0.0674761i
$$741$$ 526.721i 0.710825i
$$742$$ 329.397 91.8744i 0.443931 0.123820i
$$743$$ −911.616 −1.22694 −0.613470 0.789718i $$-0.710227\pi$$
−0.613470 + 0.789718i $$0.710227\pi$$
$$744$$ 36.1249 62.5701i 0.0485550 0.0840997i
$$745$$ −1324.76 + 764.853i −1.77821 + 1.02665i
$$746$$ 481.810 + 834.519i 0.645858 + 1.11866i
$$747$$ 196.831 + 113.640i 0.263495 + 0.152129i
$$748$$ 225.065i 0.300889i
$$749$$ 295.301 1148.85i 0.394260 1.53384i
$$750$$ −408.500 −0.544666
$$751$$ 195.831 339.189i 0.260760 0.451650i −0.705684 0.708527i $$-0.749360\pi$$
0.966444 + 0.256877i $$0.0826935\pi$$
$$752$$ 115.029 66.4123i 0.152965 0.0883142i
$$753$$ −186.978 323.855i −0.248310 0.430086i
$$754$$ 742.587 + 428.733i 0.984863 + 0.568611i
$$755$$ 2415.21i 3.19895i
$$756$$ 50.9117 51.9615i 0.0673435 0.0687322i
$$757$$ −152.823 −0.201879 −0.100940 0.994893i $$-0.532185\pi$$
−0.100940 + 0.994893i $$0.532185\pi$$
$$758$$ 441.785 765.195i 0.582830 1.00949i
$$759$$ 121.103 69.9186i 0.159555 0.0921194i
$$760$$ −201.338 348.728i −0.264919 0.458852i
$$761$$ −109.331 63.1223i −0.143667 0.0829465i 0.426443 0.904514i $$-0.359766\pi$$
−0.570111 + 0.821568i $$0.693100\pi$$
$$762$$ 410.109i 0.538201i
$$763$$ 894.706 + 876.629i 1.17262 + 1.14892i
$$764$$ 370.794 0.485332
$$765$$ −235.279 + 407.516i −0.307555 + 0.532700i
$$766$$ −169.383 + 97.7931i −0.221126 + 0.127667i
$$767$$ −244.419 423.347i −0.318669 0.551951i
$$768$$ −24.0000 13.8564i −0.0312500 0.0180422i
$$769$$ 369.148i 0.480037i −0.970768 0.240018i $$-0.922847\pi$$
0.970768 0.240018i $$-0.0771535\pi$$
$$770$$ −481.103 123.663i −0.624809 0.160602i
$$771$$ −7.45584 −0.00967036
$$772$$ −227.794 + 394.551i −0.295070 + 0.511076i
$$773$$ −1215.65 + 701.853i −1.57263 + 0.907961i −0.576789 + 0.816893i $$0.695695\pi$$