Properties

 Label 490.2.e.j.361.2 Level $490$ Weight $2$ Character 490.361 Analytic conductor $3.913$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$490 = 2 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 490.e (of order $$3$$, degree $$2$$, not minimal)

Newform invariants

 Self dual: no Analytic conductor: $$3.91266969904$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ 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: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

 Embedding label 361.2 Root $$0.707107 - 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 490.361 Dual form 490.2.e.j.471.2

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{2} +(1.70711 - 2.95680i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.41421 q^{6} -1.00000 q^{8} +(-4.32843 - 7.49706i) q^{9} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{2} +(1.70711 - 2.95680i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.41421 q^{6} -1.00000 q^{8} +(-4.32843 - 7.49706i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(0.414214 - 0.717439i) q^{11} +(1.70711 + 2.95680i) q^{12} +4.82843 q^{13} +3.41421 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.29289 - 2.23936i) q^{17} +(4.32843 - 7.49706i) q^{18} +(0.292893 + 0.507306i) q^{19} -1.00000 q^{20} +0.828427 q^{22} +(0.585786 + 1.01461i) q^{23} +(-1.70711 + 2.95680i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.41421 + 4.18154i) q^{26} -19.3137 q^{27} -4.82843 q^{29} +(1.70711 + 2.95680i) q^{30} +(-1.41421 + 2.44949i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.41421 - 2.44949i) q^{33} +2.58579 q^{34} +8.65685 q^{36} +(3.82843 + 6.63103i) q^{37} +(-0.292893 + 0.507306i) q^{38} +(8.24264 - 14.2767i) q^{39} +(-0.500000 - 0.866025i) q^{40} +3.07107 q^{41} -8.82843 q^{43} +(0.414214 + 0.717439i) q^{44} +(4.32843 - 7.49706i) q^{45} +(-0.585786 + 1.01461i) q^{46} +(2.58579 + 4.47871i) q^{47} -3.41421 q^{48} -1.00000 q^{50} +(-4.41421 - 7.64564i) q^{51} +(-2.41421 + 4.18154i) q^{52} +(-3.24264 + 5.61642i) q^{53} +(-9.65685 - 16.7262i) q^{54} +0.828427 q^{55} +2.00000 q^{57} +(-2.41421 - 4.18154i) q^{58} +(4.29289 - 7.43551i) q^{59} +(-1.70711 + 2.95680i) q^{60} +(4.65685 + 8.06591i) q^{61} -2.82843 q^{62} +1.00000 q^{64} +(2.41421 + 4.18154i) q^{65} +(1.41421 - 2.44949i) q^{66} +(-0.828427 + 1.43488i) q^{67} +(1.29289 + 2.23936i) q^{68} +4.00000 q^{69} -4.48528 q^{71} +(4.32843 + 7.49706i) q^{72} +(-4.70711 + 8.15295i) q^{73} +(-3.82843 + 6.63103i) q^{74} +(1.70711 + 2.95680i) q^{75} -0.585786 q^{76} +16.4853 q^{78} +(3.41421 + 5.91359i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-19.9853 + 34.6155i) q^{81} +(1.53553 + 2.65962i) q^{82} +2.24264 q^{83} +2.58579 q^{85} +(-4.41421 - 7.64564i) q^{86} +(-8.24264 + 14.2767i) q^{87} +(-0.414214 + 0.717439i) q^{88} +(6.36396 + 11.0227i) q^{89} +8.65685 q^{90} -1.17157 q^{92} +(4.82843 + 8.36308i) q^{93} +(-2.58579 + 4.47871i) q^{94} +(-0.292893 + 0.507306i) q^{95} +(-1.70711 - 2.95680i) q^{96} +7.75736 q^{97} -7.17157 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 2q^{2} + 4q^{3} - 2q^{4} + 2q^{5} + 8q^{6} - 4q^{8} - 6q^{9} + O(q^{10})$$ $$4q + 2q^{2} + 4q^{3} - 2q^{4} + 2q^{5} + 8q^{6} - 4q^{8} - 6q^{9} - 2q^{10} - 4q^{11} + 4q^{12} + 8q^{13} + 8q^{15} - 2q^{16} + 8q^{17} + 6q^{18} + 4q^{19} - 4q^{20} - 8q^{22} + 8q^{23} - 4q^{24} - 2q^{25} + 4q^{26} - 32q^{27} - 8q^{29} + 4q^{30} + 2q^{32} + 16q^{34} + 12q^{36} + 4q^{37} - 4q^{38} + 16q^{39} - 2q^{40} - 16q^{41} - 24q^{43} - 4q^{44} + 6q^{45} - 8q^{46} + 16q^{47} - 8q^{48} - 4q^{50} - 12q^{51} - 4q^{52} + 4q^{53} - 16q^{54} - 8q^{55} + 8q^{57} - 4q^{58} + 20q^{59} - 4q^{60} - 4q^{61} + 4q^{64} + 4q^{65} + 8q^{67} + 8q^{68} + 16q^{69} + 16q^{71} + 6q^{72} - 16q^{73} - 4q^{74} + 4q^{75} - 8q^{76} + 32q^{78} + 8q^{79} + 2q^{80} - 46q^{81} - 8q^{82} - 8q^{83} + 16q^{85} - 12q^{86} - 16q^{87} + 4q^{88} + 12q^{90} - 16q^{92} + 8q^{93} - 16q^{94} - 4q^{95} - 4q^{96} + 48q^{97} - 40q^{99} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$197$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 + 0.866025i 0.353553 + 0.612372i
$$3$$ 1.70711 2.95680i 0.985599 1.70711i 0.346353 0.938104i $$-0.387420\pi$$
0.639246 0.769002i $$-0.279247\pi$$
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ 0.500000 + 0.866025i 0.223607 + 0.387298i
$$6$$ 3.41421 1.39385
$$7$$ 0 0
$$8$$ −1.00000 −0.353553
$$9$$ −4.32843 7.49706i −1.44281 2.49902i
$$10$$ −0.500000 + 0.866025i −0.158114 + 0.273861i
$$11$$ 0.414214 0.717439i 0.124890 0.216316i −0.796800 0.604243i $$-0.793476\pi$$
0.921690 + 0.387927i $$0.126809\pi$$
$$12$$ 1.70711 + 2.95680i 0.492799 + 0.853553i
$$13$$ 4.82843 1.33916 0.669582 0.742738i $$-0.266473\pi$$
0.669582 + 0.742738i $$0.266473\pi$$
$$14$$ 0 0
$$15$$ 3.41421 0.881546
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 1.29289 2.23936i 0.313573 0.543124i −0.665560 0.746344i $$-0.731807\pi$$
0.979133 + 0.203220i $$0.0651407\pi$$
$$18$$ 4.32843 7.49706i 1.02022 1.76707i
$$19$$ 0.292893 + 0.507306i 0.0671943 + 0.116384i 0.897665 0.440678i $$-0.145262\pi$$
−0.830471 + 0.557062i $$0.811929\pi$$
$$20$$ −1.00000 −0.223607
$$21$$ 0 0
$$22$$ 0.828427 0.176621
$$23$$ 0.585786 + 1.01461i 0.122145 + 0.211561i 0.920613 0.390476i $$-0.127689\pi$$
−0.798468 + 0.602037i $$0.794356\pi$$
$$24$$ −1.70711 + 2.95680i −0.348462 + 0.603553i
$$25$$ −0.500000 + 0.866025i −0.100000 + 0.173205i
$$26$$ 2.41421 + 4.18154i 0.473466 + 0.820068i
$$27$$ −19.3137 −3.71692
$$28$$ 0 0
$$29$$ −4.82843 −0.896616 −0.448308 0.893879i $$-0.647973\pi$$
−0.448308 + 0.893879i $$0.647973\pi$$
$$30$$ 1.70711 + 2.95680i 0.311674 + 0.539835i
$$31$$ −1.41421 + 2.44949i −0.254000 + 0.439941i −0.964623 0.263631i $$-0.915080\pi$$
0.710623 + 0.703573i $$0.248413\pi$$
$$32$$ 0.500000 0.866025i 0.0883883 0.153093i
$$33$$ −1.41421 2.44949i −0.246183 0.426401i
$$34$$ 2.58579 0.443459
$$35$$ 0 0
$$36$$ 8.65685 1.44281
$$37$$ 3.82843 + 6.63103i 0.629390 + 1.09013i 0.987674 + 0.156522i $$0.0500283\pi$$
−0.358285 + 0.933612i $$0.616638\pi$$
$$38$$ −0.292893 + 0.507306i −0.0475136 + 0.0822959i
$$39$$ 8.24264 14.2767i 1.31988 2.28610i
$$40$$ −0.500000 0.866025i −0.0790569 0.136931i
$$41$$ 3.07107 0.479620 0.239810 0.970820i $$-0.422915\pi$$
0.239810 + 0.970820i $$0.422915\pi$$
$$42$$ 0 0
$$43$$ −8.82843 −1.34632 −0.673161 0.739496i $$-0.735064\pi$$
−0.673161 + 0.739496i $$0.735064\pi$$
$$44$$ 0.414214 + 0.717439i 0.0624450 + 0.108158i
$$45$$ 4.32843 7.49706i 0.645244 1.11760i
$$46$$ −0.585786 + 1.01461i −0.0863695 + 0.149596i
$$47$$ 2.58579 + 4.47871i 0.377176 + 0.653288i 0.990650 0.136427i $$-0.0435619\pi$$
−0.613474 + 0.789715i $$0.710229\pi$$
$$48$$ −3.41421 −0.492799
$$49$$ 0 0
$$50$$ −1.00000 −0.141421
$$51$$ −4.41421 7.64564i −0.618114 1.07060i
$$52$$ −2.41421 + 4.18154i −0.334791 + 0.579875i
$$53$$ −3.24264 + 5.61642i −0.445411 + 0.771474i −0.998081 0.0619259i $$-0.980276\pi$$
0.552670 + 0.833400i $$0.313609\pi$$
$$54$$ −9.65685 16.7262i −1.31413 2.27614i
$$55$$ 0.828427 0.111705
$$56$$ 0 0
$$57$$ 2.00000 0.264906
$$58$$ −2.41421 4.18154i −0.317002 0.549063i
$$59$$ 4.29289 7.43551i 0.558887 0.968021i −0.438703 0.898632i $$-0.644562\pi$$
0.997590 0.0693885i $$-0.0221048\pi$$
$$60$$ −1.70711 + 2.95680i −0.220387 + 0.381721i
$$61$$ 4.65685 + 8.06591i 0.596249 + 1.03273i 0.993369 + 0.114967i $$0.0366763\pi$$
−0.397120 + 0.917767i $$0.629990\pi$$
$$62$$ −2.82843 −0.359211
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 2.41421 + 4.18154i 0.299446 + 0.518656i
$$66$$ 1.41421 2.44949i 0.174078 0.301511i
$$67$$ −0.828427 + 1.43488i −0.101208 + 0.175298i −0.912183 0.409784i $$-0.865604\pi$$
0.810974 + 0.585082i $$0.198938\pi$$
$$68$$ 1.29289 + 2.23936i 0.156786 + 0.271562i
$$69$$ 4.00000 0.481543
$$70$$ 0 0
$$71$$ −4.48528 −0.532305 −0.266152 0.963931i $$-0.585752\pi$$
−0.266152 + 0.963931i $$0.585752\pi$$
$$72$$ 4.32843 + 7.49706i 0.510110 + 0.883536i
$$73$$ −4.70711 + 8.15295i −0.550925 + 0.954230i 0.447283 + 0.894393i $$0.352392\pi$$
−0.998208 + 0.0598379i $$0.980942\pi$$
$$74$$ −3.82843 + 6.63103i −0.445046 + 0.770842i
$$75$$ 1.70711 + 2.95680i 0.197120 + 0.341421i
$$76$$ −0.585786 −0.0671943
$$77$$ 0 0
$$78$$ 16.4853 1.86659
$$79$$ 3.41421 + 5.91359i 0.384129 + 0.665331i 0.991648 0.128974i $$-0.0411684\pi$$
−0.607519 + 0.794305i $$0.707835\pi$$
$$80$$ 0.500000 0.866025i 0.0559017 0.0968246i
$$81$$ −19.9853 + 34.6155i −2.22059 + 3.84617i
$$82$$ 1.53553 + 2.65962i 0.169571 + 0.293706i
$$83$$ 2.24264 0.246162 0.123081 0.992397i $$-0.460723\pi$$
0.123081 + 0.992397i $$0.460723\pi$$
$$84$$ 0 0
$$85$$ 2.58579 0.280468
$$86$$ −4.41421 7.64564i −0.475997 0.824451i
$$87$$ −8.24264 + 14.2767i −0.883704 + 1.53062i
$$88$$ −0.414214 + 0.717439i −0.0441553 + 0.0764792i
$$89$$ 6.36396 + 11.0227i 0.674579 + 1.16840i 0.976592 + 0.215101i $$0.0690079\pi$$
−0.302013 + 0.953304i $$0.597659\pi$$
$$90$$ 8.65685 0.912513
$$91$$ 0 0
$$92$$ −1.17157 −0.122145
$$93$$ 4.82843 + 8.36308i 0.500685 + 0.867211i
$$94$$ −2.58579 + 4.47871i −0.266704 + 0.461944i
$$95$$ −0.292893 + 0.507306i −0.0300502 + 0.0520485i
$$96$$ −1.70711 2.95680i −0.174231 0.301777i
$$97$$ 7.75736 0.787641 0.393820 0.919187i $$-0.371153\pi$$
0.393820 + 0.919187i $$0.371153\pi$$
$$98$$ 0 0
$$99$$ −7.17157 −0.720770
$$100$$ −0.500000 0.866025i −0.0500000 0.0866025i
$$101$$ 6.65685 11.5300i 0.662382 1.14728i −0.317606 0.948223i $$-0.602879\pi$$
0.979988 0.199056i $$-0.0637876\pi$$
$$102$$ 4.41421 7.64564i 0.437072 0.757031i
$$103$$ −7.41421 12.8418i −0.730544 1.26534i −0.956651 0.291237i $$-0.905933\pi$$
0.226107 0.974103i $$-0.427400\pi$$
$$104$$ −4.82843 −0.473466
$$105$$ 0 0
$$106$$ −6.48528 −0.629906
$$107$$ −4.82843 8.36308i −0.466782 0.808490i 0.532498 0.846431i $$-0.321253\pi$$
−0.999280 + 0.0379415i $$0.987920\pi$$
$$108$$ 9.65685 16.7262i 0.929231 1.60948i
$$109$$ −1.24264 + 2.15232i −0.119023 + 0.206155i −0.919381 0.393368i $$-0.871310\pi$$
0.800358 + 0.599523i $$0.204643\pi$$
$$110$$ 0.414214 + 0.717439i 0.0394937 + 0.0684051i
$$111$$ 26.1421 2.48130
$$112$$ 0 0
$$113$$ −15.3137 −1.44059 −0.720296 0.693667i $$-0.755994\pi$$
−0.720296 + 0.693667i $$0.755994\pi$$
$$114$$ 1.00000 + 1.73205i 0.0936586 + 0.162221i
$$115$$ −0.585786 + 1.01461i −0.0546249 + 0.0946130i
$$116$$ 2.41421 4.18154i 0.224154 0.388246i
$$117$$ −20.8995 36.1990i −1.93216 3.34660i
$$118$$ 8.58579 0.790386
$$119$$ 0 0
$$120$$ −3.41421 −0.311674
$$121$$ 5.15685 + 8.93193i 0.468805 + 0.811994i
$$122$$ −4.65685 + 8.06591i −0.421612 + 0.730253i
$$123$$ 5.24264 9.08052i 0.472713 0.818763i
$$124$$ −1.41421 2.44949i −0.127000 0.219971i
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ 2.82843 0.250982 0.125491 0.992095i $$-0.459949\pi$$
0.125491 + 0.992095i $$0.459949\pi$$
$$128$$ 0.500000 + 0.866025i 0.0441942 + 0.0765466i
$$129$$ −15.0711 + 26.1039i −1.32693 + 2.29832i
$$130$$ −2.41421 + 4.18154i −0.211741 + 0.366745i
$$131$$ −3.12132 5.40629i −0.272711 0.472349i 0.696844 0.717223i $$-0.254587\pi$$
−0.969555 + 0.244873i $$0.921254\pi$$
$$132$$ 2.82843 0.246183
$$133$$ 0 0
$$134$$ −1.65685 −0.143130
$$135$$ −9.65685 16.7262i −0.831130 1.43956i
$$136$$ −1.29289 + 2.23936i −0.110865 + 0.192023i
$$137$$ 8.00000 13.8564i 0.683486 1.18383i −0.290424 0.956898i $$-0.593796\pi$$
0.973910 0.226935i $$-0.0728704\pi$$
$$138$$ 2.00000 + 3.46410i 0.170251 + 0.294884i
$$139$$ −19.8995 −1.68785 −0.843927 0.536459i $$-0.819762\pi$$
−0.843927 + 0.536459i $$0.819762\pi$$
$$140$$ 0 0
$$141$$ 17.6569 1.48698
$$142$$ −2.24264 3.88437i −0.188198 0.325969i
$$143$$ 2.00000 3.46410i 0.167248 0.289683i
$$144$$ −4.32843 + 7.49706i −0.360702 + 0.624755i
$$145$$ −2.41421 4.18154i −0.200490 0.347258i
$$146$$ −9.41421 −0.779126
$$147$$ 0 0
$$148$$ −7.65685 −0.629390
$$149$$ 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i $$-0.0876260\pi$$
−0.716578 + 0.697507i $$0.754293\pi$$
$$150$$ −1.70711 + 2.95680i −0.139385 + 0.241421i
$$151$$ 5.65685 9.79796i 0.460348 0.797347i −0.538630 0.842542i $$-0.681058\pi$$
0.998978 + 0.0451959i $$0.0143912\pi$$
$$152$$ −0.292893 0.507306i −0.0237568 0.0411479i
$$153$$ −22.3848 −1.80970
$$154$$ 0 0
$$155$$ −2.82843 −0.227185
$$156$$ 8.24264 + 14.2767i 0.659939 + 1.14305i
$$157$$ 3.24264 5.61642i 0.258791 0.448239i −0.707127 0.707086i $$-0.750009\pi$$
0.965918 + 0.258847i $$0.0833426\pi$$
$$158$$ −3.41421 + 5.91359i −0.271620 + 0.470460i
$$159$$ 11.0711 + 19.1757i 0.877993 + 1.52073i
$$160$$ 1.00000 0.0790569
$$161$$ 0 0
$$162$$ −39.9706 −3.14038
$$163$$ 10.0711 + 17.4436i 0.788827 + 1.36629i 0.926686 + 0.375836i $$0.122645\pi$$
−0.137859 + 0.990452i $$0.544022\pi$$
$$164$$ −1.53553 + 2.65962i −0.119905 + 0.207682i
$$165$$ 1.41421 2.44949i 0.110096 0.190693i
$$166$$ 1.12132 + 1.94218i 0.0870313 + 0.150743i
$$167$$ −15.7990 −1.22256 −0.611281 0.791413i $$-0.709346\pi$$
−0.611281 + 0.791413i $$0.709346\pi$$
$$168$$ 0 0
$$169$$ 10.3137 0.793362
$$170$$ 1.29289 + 2.23936i 0.0991604 + 0.171751i
$$171$$ 2.53553 4.39167i 0.193897 0.335840i
$$172$$ 4.41421 7.64564i 0.336581 0.582975i
$$173$$ −4.41421 7.64564i −0.335606 0.581287i 0.647995 0.761645i $$-0.275608\pi$$
−0.983601 + 0.180357i $$0.942275\pi$$
$$174$$ −16.4853 −1.24975
$$175$$ 0 0
$$176$$ −0.828427 −0.0624450
$$177$$ −14.6569 25.3864i −1.10168 1.90816i
$$178$$ −6.36396 + 11.0227i −0.476999 + 0.826187i
$$179$$ −2.00000 + 3.46410i −0.149487 + 0.258919i −0.931038 0.364922i $$-0.881096\pi$$
0.781551 + 0.623841i $$0.214429\pi$$
$$180$$ 4.32843 + 7.49706i 0.322622 + 0.558798i
$$181$$ 2.48528 0.184730 0.0923648 0.995725i $$-0.470557\pi$$
0.0923648 + 0.995725i $$0.470557\pi$$
$$182$$ 0 0
$$183$$ 31.7990 2.35065
$$184$$ −0.585786 1.01461i −0.0431847 0.0747982i
$$185$$ −3.82843 + 6.63103i −0.281472 + 0.487523i
$$186$$ −4.82843 + 8.36308i −0.354037 + 0.613211i
$$187$$ −1.07107 1.85514i −0.0783242 0.135662i
$$188$$ −5.17157 −0.377176
$$189$$ 0 0
$$190$$ −0.585786 −0.0424974
$$191$$ −5.07107 8.78335i −0.366930 0.635541i 0.622154 0.782895i $$-0.286258\pi$$
−0.989084 + 0.147354i $$0.952924\pi$$
$$192$$ 1.70711 2.95680i 0.123200 0.213388i
$$193$$ −2.82843 + 4.89898i −0.203595 + 0.352636i −0.949684 0.313210i $$-0.898596\pi$$
0.746089 + 0.665846i $$0.231929\pi$$
$$194$$ 3.87868 + 6.71807i 0.278473 + 0.482329i
$$195$$ 16.4853 1.18054
$$196$$ 0 0
$$197$$ −25.7990 −1.83810 −0.919051 0.394139i $$-0.871043\pi$$
−0.919051 + 0.394139i $$0.871043\pi$$
$$198$$ −3.58579 6.21076i −0.254831 0.441380i
$$199$$ 8.24264 14.2767i 0.584305 1.01205i −0.410656 0.911790i $$-0.634700\pi$$
0.994962 0.100256i $$-0.0319663\pi$$
$$200$$ 0.500000 0.866025i 0.0353553 0.0612372i
$$201$$ 2.82843 + 4.89898i 0.199502 + 0.345547i
$$202$$ 13.3137 0.936749
$$203$$ 0 0
$$204$$ 8.82843 0.618114
$$205$$ 1.53553 + 2.65962i 0.107246 + 0.185756i
$$206$$ 7.41421 12.8418i 0.516573 0.894730i
$$207$$ 5.07107 8.78335i 0.352464 0.610485i
$$208$$ −2.41421 4.18154i −0.167396 0.289938i
$$209$$ 0.485281 0.0335676
$$210$$ 0 0
$$211$$ 18.6274 1.28236 0.641182 0.767389i $$-0.278444\pi$$
0.641182 + 0.767389i $$0.278444\pi$$
$$212$$ −3.24264 5.61642i −0.222705 0.385737i
$$213$$ −7.65685 + 13.2621i −0.524639 + 0.908701i
$$214$$ 4.82843 8.36308i 0.330064 0.571688i
$$215$$ −4.41421 7.64564i −0.301047 0.521428i
$$216$$ 19.3137 1.31413
$$217$$ 0 0
$$218$$ −2.48528 −0.168324
$$219$$ 16.0711 + 27.8359i 1.08598 + 1.88098i
$$220$$ −0.414214 + 0.717439i −0.0279263 + 0.0483697i
$$221$$ 6.24264 10.8126i 0.419925 0.727332i
$$222$$ 13.0711 + 22.6398i 0.877273 + 1.51948i
$$223$$ 7.31371 0.489762 0.244881 0.969553i $$-0.421251\pi$$
0.244881 + 0.969553i $$0.421251\pi$$
$$224$$ 0 0
$$225$$ 8.65685 0.577124
$$226$$ −7.65685 13.2621i −0.509326 0.882179i
$$227$$ 9.12132 15.7986i 0.605403 1.04859i −0.386584 0.922254i $$-0.626345\pi$$
0.991988 0.126335i $$-0.0403215\pi$$
$$228$$ −1.00000 + 1.73205i −0.0662266 + 0.114708i
$$229$$ −8.07107 13.9795i −0.533351 0.923791i −0.999241 0.0389487i $$-0.987599\pi$$
0.465890 0.884843i $$-0.345734\pi$$
$$230$$ −1.17157 −0.0772512
$$231$$ 0 0
$$232$$ 4.82843 0.317002
$$233$$ −11.6569 20.1903i −0.763666 1.32271i −0.940949 0.338548i $$-0.890064\pi$$
0.177283 0.984160i $$-0.443269\pi$$
$$234$$ 20.8995 36.1990i 1.36624 2.36640i
$$235$$ −2.58579 + 4.47871i −0.168678 + 0.292159i
$$236$$ 4.29289 + 7.43551i 0.279444 + 0.484010i
$$237$$ 23.3137 1.51439
$$238$$ 0 0
$$239$$ 1.65685 0.107173 0.0535865 0.998563i $$-0.482935\pi$$
0.0535865 + 0.998563i $$0.482935\pi$$
$$240$$ −1.70711 2.95680i −0.110193 0.190860i
$$241$$ −6.70711 + 11.6170i −0.432043 + 0.748320i −0.997049 0.0767666i $$-0.975540\pi$$
0.565006 + 0.825087i $$0.308874\pi$$
$$242$$ −5.15685 + 8.93193i −0.331495 + 0.574166i
$$243$$ 39.2635 + 68.0063i 2.51875 + 4.36261i
$$244$$ −9.31371 −0.596249
$$245$$ 0 0
$$246$$ 10.4853 0.668517
$$247$$ 1.41421 + 2.44949i 0.0899843 + 0.155857i
$$248$$ 1.41421 2.44949i 0.0898027 0.155543i
$$249$$ 3.82843 6.63103i 0.242617 0.420224i
$$250$$ −0.500000 0.866025i −0.0316228 0.0547723i
$$251$$ −0.585786 −0.0369745 −0.0184873 0.999829i $$-0.505885\pi$$
−0.0184873 + 0.999829i $$0.505885\pi$$
$$252$$ 0 0
$$253$$ 0.970563 0.0610188
$$254$$ 1.41421 + 2.44949i 0.0887357 + 0.153695i
$$255$$ 4.41421 7.64564i 0.276429 0.478789i
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −4.94975 8.57321i −0.308757 0.534782i 0.669334 0.742962i $$-0.266580\pi$$
−0.978091 + 0.208179i $$0.933246\pi$$
$$258$$ −30.1421 −1.87657
$$259$$ 0 0
$$260$$ −4.82843 −0.299446
$$261$$ 20.8995 + 36.1990i 1.29365 + 2.24066i
$$262$$ 3.12132 5.40629i 0.192836 0.334001i
$$263$$ −14.0000 + 24.2487i −0.863277 + 1.49524i 0.00547092 + 0.999985i $$0.498259\pi$$
−0.868748 + 0.495255i $$0.835075\pi$$
$$264$$ 1.41421 + 2.44949i 0.0870388 + 0.150756i
$$265$$ −6.48528 −0.398388
$$266$$ 0 0
$$267$$ 43.4558 2.65945
$$268$$ −0.828427 1.43488i −0.0506042 0.0876491i
$$269$$ 9.24264 16.0087i 0.563534 0.976069i −0.433651 0.901081i $$-0.642775\pi$$
0.997184 0.0749880i $$-0.0238919\pi$$
$$270$$ 9.65685 16.7262i 0.587697 1.01792i
$$271$$ 6.00000 + 10.3923i 0.364474 + 0.631288i 0.988692 0.149963i $$-0.0479155\pi$$
−0.624218 + 0.781251i $$0.714582\pi$$
$$272$$ −2.58579 −0.156786
$$273$$ 0 0
$$274$$ 16.0000 0.966595
$$275$$ 0.414214 + 0.717439i 0.0249780 + 0.0432632i
$$276$$ −2.00000 + 3.46410i −0.120386 + 0.208514i
$$277$$ 4.07107 7.05130i 0.244607 0.423671i −0.717414 0.696647i $$-0.754674\pi$$
0.962021 + 0.272976i $$0.0880078\pi$$
$$278$$ −9.94975 17.2335i −0.596746 1.03359i
$$279$$ 24.4853 1.46590
$$280$$ 0 0
$$281$$ 8.00000 0.477240 0.238620 0.971113i $$-0.423305\pi$$
0.238620 + 0.971113i $$0.423305\pi$$
$$282$$ 8.82843 + 15.2913i 0.525725 + 0.910583i
$$283$$ −1.12132 + 1.94218i −0.0666556 + 0.115451i −0.897427 0.441163i $$-0.854566\pi$$
0.830772 + 0.556613i $$0.187900\pi$$
$$284$$ 2.24264 3.88437i 0.133076 0.230495i
$$285$$ 1.00000 + 1.73205i 0.0592349 + 0.102598i
$$286$$ 4.00000 0.236525
$$287$$ 0 0
$$288$$ −8.65685 −0.510110
$$289$$ 5.15685 + 8.93193i 0.303344 + 0.525408i
$$290$$ 2.41421 4.18154i 0.141768 0.245549i
$$291$$ 13.2426 22.9369i 0.776297 1.34459i
$$292$$ −4.70711 8.15295i −0.275463 0.477115i
$$293$$ 8.34315 0.487412 0.243706 0.969849i $$-0.421637\pi$$
0.243706 + 0.969849i $$0.421637\pi$$
$$294$$ 0 0
$$295$$ 8.58579 0.499884
$$296$$ −3.82843 6.63103i −0.222523 0.385421i
$$297$$ −8.00000 + 13.8564i −0.464207 + 0.804030i
$$298$$ −3.00000 + 5.19615i −0.173785 + 0.301005i
$$299$$ 2.82843 + 4.89898i 0.163572 + 0.283315i
$$300$$ −3.41421 −0.197120
$$301$$ 0 0
$$302$$ 11.3137 0.651031
$$303$$ −22.7279 39.3659i −1.30569 2.26151i
$$304$$ 0.292893 0.507306i 0.0167986 0.0290960i
$$305$$ −4.65685 + 8.06591i −0.266651 + 0.461853i
$$306$$ −11.1924 19.3858i −0.639826 1.10821i
$$307$$ −14.9289 −0.852039 −0.426020 0.904714i $$-0.640085\pi$$
−0.426020 + 0.904714i $$0.640085\pi$$
$$308$$ 0 0
$$309$$ −50.6274 −2.88009
$$310$$ −1.41421 2.44949i −0.0803219 0.139122i
$$311$$ 2.00000 3.46410i 0.113410 0.196431i −0.803733 0.594990i $$-0.797156\pi$$
0.917143 + 0.398559i $$0.130489\pi$$
$$312$$ −8.24264 + 14.2767i −0.466648 + 0.808257i
$$313$$ 7.19239 + 12.4576i 0.406538 + 0.704144i 0.994499 0.104745i $$-0.0334026\pi$$
−0.587961 + 0.808889i $$0.700069\pi$$
$$314$$ 6.48528 0.365986
$$315$$ 0 0
$$316$$ −6.82843 −0.384129
$$317$$ −5.24264 9.08052i −0.294456 0.510013i 0.680402 0.732839i $$-0.261805\pi$$
−0.974858 + 0.222826i $$0.928472\pi$$
$$318$$ −11.0711 + 19.1757i −0.620835 + 1.07532i
$$319$$ −2.00000 + 3.46410i −0.111979 + 0.193952i
$$320$$ 0.500000 + 0.866025i 0.0279508 + 0.0484123i
$$321$$ −32.9706 −1.84024
$$322$$ 0 0
$$323$$ 1.51472 0.0842812
$$324$$ −19.9853 34.6155i −1.11029 1.92308i
$$325$$ −2.41421 + 4.18154i −0.133916 + 0.231950i
$$326$$ −10.0711 + 17.4436i −0.557785 + 0.966112i
$$327$$ 4.24264 + 7.34847i 0.234619 + 0.406371i
$$328$$ −3.07107 −0.169571
$$329$$ 0 0
$$330$$ 2.82843 0.155700
$$331$$ −16.8995 29.2708i −0.928880 1.60887i −0.785199 0.619244i $$-0.787439\pi$$
−0.143681 0.989624i $$-0.545894\pi$$
$$332$$ −1.12132 + 1.94218i −0.0615404 + 0.106591i
$$333$$ 33.1421 57.4039i 1.81618 3.14571i
$$334$$ −7.89949 13.6823i −0.432241 0.748664i
$$335$$ −1.65685 −0.0905236
$$336$$ 0 0
$$337$$ 6.00000 0.326841 0.163420 0.986557i $$-0.447747\pi$$
0.163420 + 0.986557i $$0.447747\pi$$
$$338$$ 5.15685 + 8.93193i 0.280496 + 0.485833i
$$339$$ −26.1421 + 45.2795i −1.41985 + 2.45925i
$$340$$ −1.29289 + 2.23936i −0.0701170 + 0.121446i
$$341$$ 1.17157 + 2.02922i 0.0634442 + 0.109889i
$$342$$ 5.07107 0.274212
$$343$$ 0 0
$$344$$ 8.82843 0.475997
$$345$$ 2.00000 + 3.46410i 0.107676 + 0.186501i
$$346$$ 4.41421 7.64564i 0.237310 0.411032i
$$347$$ 1.58579 2.74666i 0.0851295 0.147449i −0.820317 0.571909i $$-0.806203\pi$$
0.905446 + 0.424461i $$0.139536\pi$$
$$348$$ −8.24264 14.2767i −0.441852 0.765310i
$$349$$ −2.48528 −0.133034 −0.0665170 0.997785i $$-0.521189\pi$$
−0.0665170 + 0.997785i $$0.521189\pi$$
$$350$$ 0 0
$$351$$ −93.2548 −4.97757
$$352$$ −0.414214 0.717439i −0.0220777 0.0382396i
$$353$$ −1.19239 + 2.06528i −0.0634644 + 0.109924i −0.896012 0.444030i $$-0.853548\pi$$
0.832547 + 0.553954i $$0.186882\pi$$
$$354$$ 14.6569 25.3864i 0.779003 1.34927i
$$355$$ −2.24264 3.88437i −0.119027 0.206161i
$$356$$ −12.7279 −0.674579
$$357$$ 0 0
$$358$$ −4.00000 −0.211407
$$359$$ −14.1421 24.4949i −0.746393 1.29279i −0.949541 0.313643i $$-0.898450\pi$$
0.203148 0.979148i $$-0.434883\pi$$
$$360$$ −4.32843 + 7.49706i −0.228128 + 0.395130i
$$361$$ 9.32843 16.1573i 0.490970 0.850385i
$$362$$ 1.24264 + 2.15232i 0.0653117 + 0.113123i
$$363$$ 35.2132 1.84821
$$364$$ 0 0
$$365$$ −9.41421 −0.492762
$$366$$ 15.8995 + 27.5387i 0.831080 + 1.43947i
$$367$$ 12.4853 21.6251i 0.651726 1.12882i −0.330977 0.943639i $$-0.607378\pi$$
0.982704 0.185185i $$-0.0592883\pi$$
$$368$$ 0.585786 1.01461i 0.0305362 0.0528903i
$$369$$ −13.2929 23.0240i −0.692000 1.19858i
$$370$$ −7.65685 −0.398061
$$371$$ 0 0
$$372$$ −9.65685 −0.500685
$$373$$ 15.2426 + 26.4010i 0.789234 + 1.36699i 0.926437 + 0.376450i $$0.122855\pi$$
−0.137203 + 0.990543i $$0.543811\pi$$
$$374$$ 1.07107 1.85514i 0.0553836 0.0959272i
$$375$$ −1.70711 + 2.95680i −0.0881546 + 0.152688i
$$376$$ −2.58579 4.47871i −0.133352 0.230972i
$$377$$ −23.3137 −1.20072
$$378$$ 0 0
$$379$$ 34.4853 1.77139 0.885695 0.464268i $$-0.153682\pi$$
0.885695 + 0.464268i $$0.153682\pi$$
$$380$$ −0.292893 0.507306i −0.0150251 0.0260242i
$$381$$ 4.82843 8.36308i 0.247368 0.428454i
$$382$$ 5.07107 8.78335i 0.259458 0.449395i
$$383$$ −16.2426 28.1331i −0.829960 1.43753i −0.898069 0.439855i $$-0.855030\pi$$
0.0681085 0.997678i $$-0.478304\pi$$
$$384$$ 3.41421 0.174231
$$385$$ 0 0
$$386$$ −5.65685 −0.287926
$$387$$ 38.2132 + 66.1872i 1.94249 + 3.36448i
$$388$$ −3.87868 + 6.71807i −0.196910 + 0.341058i
$$389$$ −14.0711 + 24.3718i −0.713431 + 1.23570i 0.250130 + 0.968212i $$0.419527\pi$$
−0.963561 + 0.267487i $$0.913807\pi$$
$$390$$ 8.24264 + 14.2767i 0.417382 + 0.722927i
$$391$$ 3.02944 0.153205
$$392$$ 0 0
$$393$$ −21.3137 −1.07513
$$394$$ −12.8995 22.3426i −0.649867 1.12560i
$$395$$ −3.41421 + 5.91359i −0.171788 + 0.297545i
$$396$$ 3.58579 6.21076i 0.180193 0.312103i
$$397$$ 16.8995 + 29.2708i 0.848161 + 1.46906i 0.882847 + 0.469660i $$0.155624\pi$$
−0.0346859 + 0.999398i $$0.511043\pi$$
$$398$$ 16.4853 0.826332
$$399$$ 0 0
$$400$$ 1.00000 0.0500000
$$401$$ 3.00000 + 5.19615i 0.149813 + 0.259483i 0.931158 0.364615i $$-0.118800\pi$$
−0.781345 + 0.624099i $$0.785466\pi$$
$$402$$ −2.82843 + 4.89898i −0.141069 + 0.244339i
$$403$$ −6.82843 + 11.8272i −0.340148 + 0.589154i
$$404$$ 6.65685 + 11.5300i 0.331191 + 0.573639i
$$405$$ −39.9706 −1.98615
$$406$$ 0 0
$$407$$ 6.34315 0.314418
$$408$$ 4.41421 + 7.64564i 0.218536 + 0.378516i
$$409$$ −5.29289 + 9.16756i −0.261717 + 0.453307i −0.966698 0.255919i $$-0.917622\pi$$
0.704981 + 0.709226i $$0.250955\pi$$
$$410$$ −1.53553 + 2.65962i −0.0758346 + 0.131349i
$$411$$ −27.3137 47.3087i −1.34729 2.33357i
$$412$$ 14.8284 0.730544
$$413$$ 0 0
$$414$$ 10.1421 0.498459
$$415$$ 1.12132 + 1.94218i 0.0550435 + 0.0953381i
$$416$$ 2.41421 4.18154i 0.118367 0.205017i
$$417$$ −33.9706 + 58.8387i −1.66355 + 2.88135i
$$418$$ 0.242641 + 0.420266i 0.0118679 + 0.0205559i
$$419$$ 20.8701 1.01957 0.509785 0.860302i $$-0.329725\pi$$
0.509785 + 0.860302i $$0.329725\pi$$
$$420$$ 0 0
$$421$$ 17.3137 0.843819 0.421909 0.906638i $$-0.361360\pi$$
0.421909 + 0.906638i $$0.361360\pi$$
$$422$$ 9.31371 + 16.1318i 0.453384 + 0.785285i
$$423$$ 22.3848 38.7716i 1.08839 1.88514i
$$424$$ 3.24264 5.61642i 0.157477 0.272757i
$$425$$ 1.29289 + 2.23936i 0.0627145 + 0.108625i
$$426$$ −15.3137 −0.741952
$$427$$ 0 0
$$428$$ 9.65685 0.466782
$$429$$ −6.82843 11.8272i −0.329680 0.571022i
$$430$$ 4.41421 7.64564i 0.212872 0.368706i
$$431$$ 11.1716 19.3497i 0.538116 0.932044i −0.460890 0.887457i $$-0.652470\pi$$
0.999006 0.0445864i $$-0.0141970\pi$$
$$432$$ 9.65685 + 16.7262i 0.464616 + 0.804738i
$$433$$ −10.5858 −0.508720 −0.254360 0.967110i $$-0.581865\pi$$
−0.254360 + 0.967110i $$0.581865\pi$$
$$434$$ 0 0
$$435$$ −16.4853 −0.790409
$$436$$ −1.24264 2.15232i −0.0595117 0.103077i
$$437$$ −0.343146 + 0.594346i −0.0164149 + 0.0284314i
$$438$$ −16.0711 + 27.8359i −0.767905 + 1.33005i
$$439$$ −12.4853 21.6251i −0.595890 1.03211i −0.993421 0.114523i $$-0.963466\pi$$
0.397531 0.917589i $$-0.369867\pi$$
$$440$$ −0.828427 −0.0394937
$$441$$ 0 0
$$442$$ 12.4853 0.593864
$$443$$ −1.51472 2.62357i −0.0719665 0.124650i 0.827797 0.561028i $$-0.189594\pi$$
−0.899763 + 0.436379i $$0.856261\pi$$
$$444$$ −13.0711 + 22.6398i −0.620325 + 1.07444i
$$445$$ −6.36396 + 11.0227i −0.301681 + 0.522526i
$$446$$ 3.65685 + 6.33386i 0.173157 + 0.299917i
$$447$$ 20.4853 0.968921
$$448$$ 0 0
$$449$$ −16.6274 −0.784696 −0.392348 0.919817i $$-0.628337\pi$$
−0.392348 + 0.919817i $$0.628337\pi$$
$$450$$ 4.32843 + 7.49706i 0.204044 + 0.353415i
$$451$$ 1.27208 2.20330i 0.0598998 0.103750i
$$452$$ 7.65685 13.2621i 0.360148 0.623795i
$$453$$ −19.3137 33.4523i −0.907437 1.57173i
$$454$$ 18.2426 0.856170
$$455$$ 0 0
$$456$$ −2.00000 −0.0936586
$$457$$ −10.8284 18.7554i −0.506532 0.877340i −0.999971 0.00755953i $$-0.997594\pi$$
0.493439 0.869780i $$-0.335740\pi$$
$$458$$ 8.07107 13.9795i 0.377136 0.653219i
$$459$$ −24.9706 + 43.2503i −1.16553 + 2.01875i
$$460$$ −0.585786 1.01461i −0.0273124 0.0473065i
$$461$$ 12.8284 0.597479 0.298740 0.954335i $$-0.403434\pi$$
0.298740 + 0.954335i $$0.403434\pi$$
$$462$$ 0 0
$$463$$ −16.9706 −0.788689 −0.394344 0.918963i $$-0.629028\pi$$
−0.394344 + 0.918963i $$0.629028\pi$$
$$464$$ 2.41421 + 4.18154i 0.112077 + 0.194123i
$$465$$ −4.82843 + 8.36308i −0.223913 + 0.387829i
$$466$$ 11.6569 20.1903i 0.539993 0.935296i
$$467$$ −7.94975 13.7694i −0.367870 0.637170i 0.621362 0.783524i $$-0.286580\pi$$
−0.989232 + 0.146353i $$0.953246\pi$$
$$468$$ 41.7990 1.93216
$$469$$ 0 0
$$470$$ −5.17157 −0.238547
$$471$$ −11.0711 19.1757i −0.510128 0.883567i
$$472$$ −4.29289 + 7.43551i −0.197596 + 0.342247i
$$473$$ −3.65685 + 6.33386i −0.168142 + 0.291231i
$$474$$ 11.6569 + 20.1903i 0.535417 + 0.927370i
$$475$$ −0.585786 −0.0268777
$$476$$ 0 0
$$477$$ 56.1421 2.57057
$$478$$ 0.828427 + 1.43488i 0.0378914 + 0.0656298i
$$479$$ −8.58579 + 14.8710i −0.392295 + 0.679474i −0.992752 0.120183i $$-0.961652\pi$$
0.600457 + 0.799657i $$0.294985\pi$$
$$480$$ 1.70711 2.95680i 0.0779184 0.134959i
$$481$$ 18.4853 + 32.0174i 0.842856 + 1.45987i
$$482$$ −13.4142 −0.611001
$$483$$ 0 0
$$484$$ −10.3137 −0.468805
$$485$$ 3.87868 + 6.71807i 0.176122 + 0.305052i
$$486$$ −39.2635 + 68.0063i −1.78103 + 3.08483i
$$487$$ −15.8995 + 27.5387i −0.720475 + 1.24790i 0.240335 + 0.970690i $$0.422743\pi$$
−0.960810 + 0.277209i $$0.910591\pi$$
$$488$$ −4.65685 8.06591i −0.210806 0.365127i
$$489$$ 68.7696 3.10987
$$490$$ 0 0
$$491$$ 32.2843 1.45697 0.728484 0.685062i $$-0.240225\pi$$
0.728484 + 0.685062i $$0.240225\pi$$
$$492$$ 5.24264 + 9.08052i 0.236356 + 0.409381i
$$493$$ −6.24264 + 10.8126i −0.281154 + 0.486974i
$$494$$ −1.41421 + 2.44949i −0.0636285 + 0.110208i
$$495$$ −3.58579 6.21076i −0.161169 0.279153i
$$496$$ 2.82843 0.127000
$$497$$ 0 0
$$498$$ 7.65685 0.343112
$$499$$ −15.1716 26.2779i −0.679173 1.17636i −0.975230 0.221192i $$-0.929005\pi$$
0.296057 0.955170i $$-0.404328\pi$$
$$500$$ 0.500000 0.866025i 0.0223607 0.0387298i
$$501$$ −26.9706 + 46.7144i −1.20496 + 2.08704i
$$502$$ −0.292893 0.507306i −0.0130725 0.0226422i
$$503$$ −17.6569 −0.787280 −0.393640 0.919265i $$-0.628784\pi$$
−0.393640 + 0.919265i $$0.628784\pi$$
$$504$$ 0 0
$$505$$ 13.3137 0.592452
$$506$$ 0.485281 + 0.840532i 0.0215734 + 0.0373662i
$$507$$ 17.6066 30.4955i 0.781937 1.35435i
$$508$$ −1.41421 + 2.44949i −0.0627456 + 0.108679i
$$509$$ 2.89949 + 5.02207i 0.128518 + 0.222599i 0.923103 0.384554i $$-0.125645\pi$$
−0.794585 + 0.607153i $$0.792311\pi$$
$$510$$ 8.82843 0.390929
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ −5.65685 9.79796i −0.249756 0.432590i
$$514$$ 4.94975 8.57321i 0.218324 0.378148i
$$515$$ 7.41421 12.8418i 0.326709 0.565877i
$$516$$ −15.0711 26.1039i −0.663467 1.14916i
$$517$$ 4.28427 0.188422
$$518$$ 0 0
$$519$$ −30.1421 −1.32309
$$520$$ −2.41421 4.18154i −0.105870 0.183373i
$$521$$ 9.53553 16.5160i 0.417759 0.723580i −0.577954 0.816069i $$-0.696149\pi$$
0.995714 + 0.0924887i $$0.0294822\pi$$
$$522$$ −20.8995 + 36.1990i −0.914746 + 1.58439i
$$523$$ 11.9497 + 20.6976i 0.522526 + 0.905042i 0.999656 + 0.0262091i $$0.00834357\pi$$
−0.477131 + 0.878832i $$0.658323\pi$$
$$524$$ 6.24264 0.272711
$$525$$ 0 0
$$526$$ −28.0000 −1.22086
$$527$$ 3.65685 + 6.33386i 0.159295 + 0.275907i
$$528$$ −1.41421 + 2.44949i −0.0615457 + 0.106600i
$$529$$ 10.8137 18.7299i 0.470161 0.814343i
$$530$$ −3.24264 5.61642i −0.140851 0.243962i
$$531$$ −74.3259 −3.22547
$$532$$ 0 0
$$533$$ 14.8284 0.642290
$$534$$ 21.7279 + 37.6339i 0.940259 + 1.62858i
$$535$$ 4.82843 8.36308i 0.208751 0.361568i
$$536$$ 0.828427 1.43488i 0.0357826 0.0619773i
$$537$$ 6.82843 + 11.8272i 0.294668 + 0.510381i
$$538$$ 18.4853 0.796957
$$539$$ 0 0
$$540$$ 19.3137 0.831130
$$541$$ 7.48528 + 12.9649i 0.321817 + 0.557404i 0.980863 0.194699i $$-0.0623730\pi$$
−0.659046 + 0.752103i $$0.729040\pi$$
$$542$$ −6.00000 + 10.3923i −0.257722 + 0.446388i
$$543$$ 4.24264 7.34847i 0.182069 0.315353i
$$544$$ −1.29289 2.23936i −0.0554323 0.0960116i
$$545$$ −2.48528 −0.106458
$$546$$ 0 0
$$547$$ −10.4853 −0.448318 −0.224159 0.974553i $$-0.571964\pi$$
−0.224159 + 0.974553i $$0.571964\pi$$
$$548$$ 8.00000 + 13.8564i 0.341743 + 0.591916i
$$549$$ 40.3137 69.8254i 1.72055 2.98008i
$$550$$ −0.414214 + 0.717439i −0.0176621 + 0.0305917i
$$551$$ −1.41421 2.44949i −0.0602475 0.104352i
$$552$$ −4.00000 −0.170251
$$553$$ 0 0
$$554$$ 8.14214 0.345926
$$555$$ 13.0711 + 22.6398i 0.554836 + 0.961004i
$$556$$ 9.94975 17.2335i 0.421963 0.730862i
$$557$$ −7.58579 + 13.1390i −0.321420 + 0.556716i −0.980781 0.195110i $$-0.937493\pi$$
0.659361 + 0.751826i $$0.270827\pi$$
$$558$$ 12.2426 + 21.2049i 0.518272 + 0.897674i
$$559$$ −42.6274 −1.80295
$$560$$ 0 0
$$561$$ −7.31371 −0.308785
$$562$$ 4.00000 + 6.92820i 0.168730 + 0.292249i
$$563$$ −18.2929 + 31.6842i −0.770954 + 1.33533i 0.166087 + 0.986111i $$0.446887\pi$$
−0.937041 + 0.349220i $$0.886447\pi$$
$$564$$ −8.82843 + 15.2913i −0.371744 + 0.643879i
$$565$$ −7.65685 13.2621i −0.322126 0.557939i
$$566$$ −2.24264 −0.0942652
$$567$$ 0 0
$$568$$ 4.48528 0.188198
$$569$$ 14.6569 + 25.3864i 0.614447 + 1.06425i 0.990481 + 0.137648i $$0.0439543\pi$$
−0.376034 + 0.926606i $$0.622712\pi$$
$$570$$ −1.00000 + 1.73205i −0.0418854 + 0.0725476i
$$571$$ 1.10051 1.90613i 0.0460547 0.0797691i −0.842079 0.539354i $$-0.818668\pi$$
0.888134 + 0.459585i $$0.152002\pi$$
$$572$$ 2.00000 + 3.46410i 0.0836242 + 0.144841i
$$573$$ −34.6274 −1.44658
$$574$$ 0 0
$$575$$ −1.17157 −0.0488580
$$576$$ −4.32843 7.49706i −0.180351 0.312377i
$$577$$ 3.05025 5.28319i 0.126984 0.219942i −0.795523 0.605923i $$-0.792804\pi$$
0.922507 + 0.385981i $$0.126137\pi$$
$$578$$ −5.15685 + 8.93193i −0.214497 + 0.371519i
$$579$$ 9.65685 + 16.7262i 0.401325 + 0.695116i
$$580$$ 4.82843 0.200490
$$581$$ 0 0
$$582$$ 26.4853 1.09785
$$583$$ 2.68629 + 4.65279i 0.111255 + 0.192699i
$$584$$ 4.70711 8.15295i 0.194781 0.337371i
$$585$$ 20.8995 36.1990i 0.864088 1.49664i
$$586$$ 4.17157 + 7.22538i 0.172326 + 0.298478i
$$587$$ −17.0711 −0.704598 −0.352299 0.935887i $$-0.614600\pi$$
−0.352299 + 0.935887i $$0.614600\pi$$
$$588$$ 0 0
$$589$$ −1.65685 −0.0682695
$$590$$ 4.29289 + 7.43551i 0.176736 + 0.306115i
$$591$$ −44.0416 + 76.2823i −1.81163 + 3.13784i
$$592$$ 3.82843 6.63103i 0.157347 0.272534i
$$593$$ 1.63604 + 2.83370i 0.0671841 + 0.116366i 0.897661 0.440687i $$-0.145265\pi$$
−0.830477 + 0.557053i $$0.811932\pi$$
$$594$$ −16.0000 −0.656488
$$595$$ 0 0
$$596$$ −6.00000 −0.245770
$$597$$ −28.1421 48.7436i −1.15178 1.99494i
$$598$$ −2.82843 + 4.89898i −0.115663 + 0.200334i
$$599$$ 5.41421 9.37769i 0.221219 0.383162i −0.733960 0.679193i $$-0.762330\pi$$
0.955178 + 0.296031i $$0.0956632\pi$$
$$600$$ −1.70711 2.95680i −0.0696923 0.120711i
$$601$$ −6.58579 −0.268640 −0.134320 0.990938i $$-0.542885\pi$$
−0.134320 + 0.990938i $$0.542885\pi$$
$$602$$ 0 0
$$603$$ 14.3431 0.584098
$$604$$ 5.65685 + 9.79796i 0.230174 + 0.398673i
$$605$$ −5.15685 + 8.93193i −0.209656 + 0.363135i
$$606$$ 22.7279 39.3659i 0.923259 1.59913i
$$607$$ 8.14214 + 14.1026i 0.330479 + 0.572407i 0.982606 0.185703i $$-0.0594564\pi$$
−0.652127 + 0.758110i $$0.726123\pi$$
$$608$$ 0.585786 0.0237568
$$609$$ 0 0
$$610$$ −9.31371 −0.377101
$$611$$ 12.4853 + 21.6251i 0.505100 + 0.874860i
$$612$$ 11.1924 19.3858i 0.452425 0.783624i
$$613$$ 6.17157 10.6895i 0.249267 0.431744i −0.714055 0.700089i $$-0.753144\pi$$
0.963323 + 0.268345i $$0.0864768\pi$$
$$614$$ −7.46447 12.9288i −0.301241 0.521765i
$$615$$ 10.4853 0.422807
$$616$$ 0 0
$$617$$ −33.3137 −1.34116 −0.670580 0.741837i $$-0.733955\pi$$
−0.670580 + 0.741837i $$0.733955\pi$$
$$618$$ −25.3137 43.8446i −1.01827 1.76369i
$$619$$ 14.5355 25.1763i 0.584232 1.01192i −0.410738 0.911753i $$-0.634729\pi$$
0.994971 0.100167i $$-0.0319377\pi$$
$$620$$ 1.41421 2.44949i 0.0567962 0.0983739i
$$621$$ −11.3137 19.5959i −0.454003 0.786357i
$$622$$ 4.00000 0.160385
$$623$$ 0 0
$$624$$ −16.4853 −0.659939
$$625$$ −0.500000 0.866025i −0.0200000 0.0346410i
$$626$$ −7.19239 + 12.4576i −0.287466 + 0.497905i
$$627$$ 0.828427 1.43488i 0.0330842 0.0573035i
$$628$$ 3.24264 + 5.61642i 0.129395 + 0.224119i
$$629$$ 19.7990 0.789437
$$630$$ 0 0
$$631$$ −12.4853 −0.497031 −0.248516 0.968628i $$-0.579943\pi$$
−0.248516 + 0.968628i $$0.579943\pi$$
$$632$$ −3.41421 5.91359i −0.135810 0.235230i
$$633$$ 31.7990 55.0775i 1.26390 2.18913i
$$634$$ 5.24264 9.08052i 0.208212 0.360634i
$$635$$ 1.41421 + 2.44949i 0.0561214 + 0.0972050i
$$636$$ −22.1421 −0.877993
$$637$$ 0 0
$$638$$ −4.00000 −0.158362
$$639$$ 19.4142 + 33.6264i 0.768014 + 1.33024i
$$640$$ −0.500000 + 0.866025i −0.0197642 + 0.0342327i
$$641$$ 12.3137 21.3280i 0.486362 0.842404i −0.513515 0.858081i $$-0.671657\pi$$
0.999877 + 0.0156766i $$0.00499021\pi$$
$$642$$ −16.4853 28.5533i −0.650622 1.12691i
$$643$$ −4.78680 −0.188773 −0.0943864 0.995536i $$-0.530089\pi$$
−0.0943864 + 0.995536i $$0.530089\pi$$
$$644$$ 0 0
$$645$$ −30.1421 −1.18685
$$646$$ 0.757359 + 1.31178i 0.0297979 + 0.0516115i
$$647$$ −11.5563 + 20.0162i −0.454327 + 0.786917i −0.998649 0.0519588i $$-0.983454\pi$$
0.544322 + 0.838876i $$0.316787\pi$$
$$648$$ 19.9853 34.6155i 0.785096 1.35983i
$$649$$ −3.55635 6.15978i −0.139599 0.241792i
$$650$$ −4.82843 −0.189386
$$651$$ 0 0
$$652$$ −20.1421 −0.788827
$$653$$ −2.17157 3.76127i −0.0849802 0.147190i 0.820403 0.571786i $$-0.193749\pi$$
−0.905383 + 0.424596i $$0.860416\pi$$
$$654$$ −4.24264 + 7.34847i −0.165900 + 0.287348i
$$655$$ 3.12132 5.40629i 0.121960 0.211241i
$$656$$ −1.53553 2.65962i −0.0599525 0.103841i
$$657$$ 81.4975 3.17952
$$658$$ 0 0
$$659$$ −27.1716 −1.05845 −0.529227 0.848480i $$-0.677518\pi$$
−0.529227 + 0.848480i $$0.677518\pi$$
$$660$$ 1.41421 + 2.44949i 0.0550482 + 0.0953463i
$$661$$ −19.1421 + 33.1552i −0.744543 + 1.28959i 0.205865 + 0.978580i $$0.433999\pi$$
−0.950408 + 0.311006i $$0.899334\pi$$
$$662$$ 16.8995 29.2708i 0.656818 1.13764i
$$663$$ −21.3137 36.9164i −0.827756 1.43372i
$$664$$ −2.24264 −0.0870313
$$665$$ 0 0
$$666$$ 66.2843 2.56846
$$667$$ −2.82843 4.89898i −0.109517 0.189689i
$$668$$ 7.89949 13.6823i 0.305641 0.529385i
$$669$$ 12.4853 21.6251i 0.482709 0.836076i
$$670$$ −0.828427 1.43488i −0.0320049 0.0554342i
$$671$$ 7.71573 0.297862
$$672$$ 0 0
$$673$$ −48.0000 −1.85026 −0.925132 0.379646i $$-0.876046\pi$$
−0.925132 + 0.379646i $$0.876046\pi$$
$$674$$ 3.00000 + 5.19615i 0.115556 + 0.200148i
$$675$$ 9.65685 16.7262i 0.371692 0.643790i
$$676$$ −5.15685 + 8.93193i −0.198341 + 0.343536i
$$677$$ 19.7279 + 34.1698i 0.758206 + 1.31325i 0.943765 + 0.330618i $$0.107257\pi$$
−0.185559 + 0.982633i $$0.559410\pi$$
$$678$$ −52.2843 −2.00797
$$679$$ 0 0
$$680$$ −2.58579 −0.0991604
$$681$$ −31.1421 53.9398i −1.19337 2.06698i
$$682$$ −1.17157 + 2.02922i −0.0448618 + 0.0777030i
$$683$$ −16.8284 + 29.1477i −0.643922 + 1.11531i 0.340628 + 0.940198i $$0.389360\pi$$
−0.984549 + 0.175107i $$0.943973\pi$$
$$684$$ 2.53553 + 4.39167i 0.0969486 + 0.167920i
$$685$$ 16.0000 0.611329
$$686$$ 0 0
$$687$$ −55.1127 −2.10268
$$688$$ 4.41421 + 7.64564i 0.168290 + 0.291487i
$$689$$ −15.6569 + 27.1185i −0.596479 + 1.03313i
$$690$$ −2.00000 + 3.46410i −0.0761387 + 0.131876i
$$691$$ 0.878680 + 1.52192i 0.0334265 + 0.0578965i 0.882255 0.470772i $$-0.156025\pi$$
−0.848828 + 0.528669i $$0.822691\pi$$
$$692$$ 8.82843 0.335606
$$693$$ 0 0
$$694$$ 3.17157 0.120391
$$695$$ −9.94975 17.2335i −0.377415 0.653703i
$$696$$ 8.24264 14.2767i 0.312436 0.541156i
$$697$$ 3.97056 6.87722i 0.150396 0.260493i
$$698$$ −1.24264 2.15232i −0.0470346 0.0814664i
$$699$$ −79.5980 −3.01067
$$700$$ 0 0
$$701$$ 2.48528 0.0938678 0.0469339 0.998898i $$-0.485055\pi$$
0.0469339 + 0.998898i $$0.485055\pi$$
$$702$$ −46.6274 80.7611i −1.75984 3.04813i
$$703$$ −2.24264 + 3.88437i −0.0845828 + 0.146502i
$$704$$ 0.414214 0.717439i 0.0156113 0.0270395i
$$705$$ 8.82843 + 15.2913i 0.332498 + 0.575903i
$$706$$ −2.38478 −0.0897522
$$707$$ 0 0
$$708$$ 29.3137 1.10168
$$709$$ −22.5563 39.0687i −0.847121 1.46726i −0.883766 0.467929i $$-0.845000\pi$$
0.0366445 0.999328i $$-0.488333\pi$$
$$710$$ 2.24264 3.88437i 0.0841648 0.145778i
$$711$$ 29.5563 51.1931i 1.10845 1.91989i
$$712$$ −6.36396 11.0227i −0.238500 0.413093i
$$713$$ −3.31371 −0.124099
$$714$$ 0 0
$$715$$ 4.00000 0.149592
$$716$$ −2.00000 3.46410i −0.0747435 0.129460i
$$717$$ 2.82843 4.89898i 0.105630 0.182956i
$$718$$ 14.1421 24.4949i 0.527780 0.914141i
$$719$$ 20.7279 + 35.9018i 0.773021 + 1.33891i 0.935900 + 0.352266i $$0.114589\pi$$
−0.162879 + 0.986646i $$0.552078\pi$$
$$720$$ −8.65685 −0.322622
$$721$$ 0 0
$$722$$ 18.6569 0.694336
$$723$$ 22.8995 + 39.6631i 0.851641 + 1.47509i
$$724$$ −1.24264 + 2.15232i −0.0461824 + 0.0799902i
$$725$$ 2.41421 4.18154i 0.0896616 0.155299i
$$726$$ 17.6066 + 30.4955i 0.653442 + 1.13180i
$$727$$ 3.51472 0.130354 0.0651768 0.997874i $$-0.479239\pi$$
0.0651768 + 0.997874i $$0.479239\pi$$
$$728$$ 0 0
$$729$$ 148.196 5.48874
$$730$$ −4.70711 8.15295i −0.174218 0.301754i
$$731$$ −11.4142 + 19.7700i −0.422170 + 0.731220i
$$732$$ −15.8995 + 27.5387i −0.587662 + 1.01786i
$$733$$ 17.0000 + 29.4449i 0.627909 + 1.08757i 0.987971 + 0.154642i $$0.0494225\pi$$
−0.360061 + 0.932929i $$0.617244\pi$$
$$734$$ 24.9706 0.921680
$$735$$ 0 0
$$736$$ 1.17157 0.0431847
$$737$$ 0.686292 + 1.18869i 0.0252799 + 0.0437860i
$$738$$ 13.2929 23.0240i 0.489318 0.847524i
$$739$$ −1.58579 + 2.74666i −0.0583341 + 0.101038i −0.893718 0.448630i $$-0.851912\pi$$
0.835384 + 0.549667i $$0.185246\pi$$
$$740$$ −3.82843 6.63103i −0.140736 0.243762i
$$741$$ 9.65685 0.354753
$$742$$ 0 0
$$743$$ 51.7990 1.90032 0.950160 0.311762i $$-0.100919\pi$$
0.950160 + 0.311762i $$0.100919\pi$$
$$744$$ −4.82843 8.36308i −0.177019 0.306605i
$$745$$ −3.00000 + 5.19615i −0.109911 + 0.190372i
$$746$$ −15.2426 + 26.4010i −0.558073 + 0.966610i
$$747$$ −9.70711 16.8132i −0.355164 0.615163i
$$748$$ 2.14214 0.0783242
$$749$$ 0 0
$$750$$ −3.41421 −0.124669
$$751$$ 19.6569 + 34.0467i 0.717289 + 1.24238i 0.962070 + 0.272802i $$0.0879505\pi$$
−0.244781 + 0.969578i $$0.578716\pi$$
$$752$$ 2.58579 4.47871i 0.0942939 0.163322i
$$753$$ −1.00000 + 1.73205i −0.0364420 + 0.0631194i
$$754$$ −11.6569 20.1903i −0.424518 0.735286i
$$755$$ 11.3137 0.411748
$$756$$ 0 0
$$757$$ 3.65685 0.132911 0.0664553 0.997789i $$-0.478831\pi$$
0.0664553 + 0.997789i $$0.478831\pi$$
$$758$$ 17.2426 + 29.8651i 0.626281 + 1.08475i
$$759$$ 1.65685 2.86976i 0.0601400 0.104166i
$$760$$ 0.292893 0.507306i 0.0106244 0.0184019i
$$761$$ 11.1924 + 19.3858i 0.405724 + 0.702734i 0.994405 0.105631i $$-0.0336862\pi$$
−0.588682 + 0.808365i $$0.700353\pi$$
$$762$$ 9.65685 0.349831
$$763$$ 0 0
$$764$$ 10.1421 0.366930
$$765$$ −11.1924 19.3858i −0.404662 0.700895i
$$766$$ 16.2426 28.1331i 0.586870 1.01649i
$$767$$ 20.7279 35.9018i 0.748442 1.29634i
$$768$$ 1.70711 + 2.95680i 0.0615999 + 0.106694i
$$769$$ −19.5563 −0.705220 −0.352610 0.935770i $$-0.614706\pi$$
−0.352610 + 0.935770i $$0.614706\pi$$
$$770$$ 0 0
$$771$$ −33.7990 −1.21724
$$772$$ −2.82843 4.89898i −0.101797 0.176318i
$$773$$ −1.00000 + 1.73205i −0.0359675 + 0.0622975i −0.883449 0.468528i $$-0.844785\pi$$
0.847481 + 0.530825i $$0.178118\pi$$
$$774$$ −38.2132 + 66.1872i −1.37355 + 2.37905i
$$775$$ −1.41421 2.44949i −0.0508001 0.0879883i
$$776$$ −7.75736 −0.278473
$$777$$ 0 0
$$778$$ −28.1421 −1.00894
$$779$$ 0.899495 + 1.55797i 0.0322278 + 0.0558201i
$$780$$ −8.24264 + 14.2767i −0.295134 + 0.511187i
$$781$$ −1.85786 + 3.21792i −0.0664796 + 0.115146i
$$782$$ 1.51472 + 2.62357i 0.0541662 + 0.0938187i
$$783$$ 93.2548 3.33266
$$784$$