# Properties

 Label 245.4.e.q.226.2 Level $245$ Weight $4$ Character 245.226 Analytic conductor $14.455$ Analytic rank $0$ Dimension $12$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$245 = 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 245.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$14.4554679514$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$6$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ Defining polynomial: $$x^{12} - 2 x^{11} + 27 x^{10} + 22 x^{9} + 399 x^{8} + 492 x^{7} + 4046 x^{6} + 8784 x^{5} + 22536 x^{4} + 22736 x^{3} + 18792 x^{2} + 4256 x + 784$$ x^12 - 2*x^11 + 27*x^10 + 22*x^9 + 399*x^8 + 492*x^7 + 4046*x^6 + 8784*x^5 + 22536*x^4 + 22736*x^3 + 18792*x^2 + 4256*x + 784 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2^{2}\cdot 7^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 226.2 Root $$-0.120924 - 0.209447i$$ of defining polynomial Character $$\chi$$ $$=$$ 245.226 Dual form 245.4.e.q.116.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.828031 + 1.43419i) q^{2} +(-0.166444 - 0.288289i) q^{3} +(2.62873 + 4.55309i) q^{4} +(-2.50000 + 4.33013i) q^{5} +0.551283 q^{6} -21.9552 q^{8} +(13.4446 - 23.2867i) q^{9} +O(q^{10})$$ $$q+(-0.828031 + 1.43419i) q^{2} +(-0.166444 - 0.288289i) q^{3} +(2.62873 + 4.55309i) q^{4} +(-2.50000 + 4.33013i) q^{5} +0.551283 q^{6} -21.9552 q^{8} +(13.4446 - 23.2867i) q^{9} +(-4.14016 - 7.17096i) q^{10} +(-34.7863 - 60.2517i) q^{11} +(0.875071 - 1.51567i) q^{12} -68.4326 q^{13} +1.66444 q^{15} +(-2.85026 + 4.93680i) q^{16} +(52.1659 + 90.3539i) q^{17} +(22.2651 + 38.5643i) q^{18} +(35.9465 - 62.2611i) q^{19} -26.2873 q^{20} +115.217 q^{22} +(50.5154 - 87.4952i) q^{23} +(3.65430 + 6.32944i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(56.6643 - 98.1454i) q^{26} -17.9390 q^{27} -114.661 q^{29} +(-1.37821 + 2.38712i) q^{30} +(-36.8252 - 63.7832i) q^{31} +(-92.5409 - 160.286i) q^{32} +(-11.5799 + 20.0570i) q^{33} -172.780 q^{34} +141.369 q^{36} +(100.467 - 174.013i) q^{37} +(59.5296 + 103.108i) q^{38} +(11.3902 + 19.7284i) q^{39} +(54.8879 - 95.0687i) q^{40} -417.308 q^{41} +311.175 q^{43} +(182.888 - 316.771i) q^{44} +(67.2230 + 116.434i) q^{45} +(83.6566 + 144.897i) q^{46} +(74.8485 - 129.641i) q^{47} +1.89763 q^{48} +41.4016 q^{50} +(17.3654 - 30.0777i) q^{51} +(-179.891 - 311.580i) q^{52} +(-135.737 - 235.104i) q^{53} +(14.8541 - 25.7280i) q^{54} +347.863 q^{55} -23.9323 q^{57} +(94.9425 - 164.445i) q^{58} +(-259.014 - 448.625i) q^{59} +(4.37536 + 7.57834i) q^{60} +(-109.963 + 190.461i) q^{61} +121.970 q^{62} +260.903 q^{64} +(171.081 - 296.322i) q^{65} +(-19.1771 - 33.2157i) q^{66} +(-40.3475 - 69.8839i) q^{67} +(-274.260 + 475.032i) q^{68} -33.6319 q^{69} -91.0463 q^{71} +(-295.178 + 511.264i) q^{72} +(441.141 + 764.078i) q^{73} +(166.379 + 288.177i) q^{74} +(-4.16110 + 7.20723i) q^{75} +377.974 q^{76} -37.7257 q^{78} +(-299.939 + 519.509i) q^{79} +(-14.2513 - 24.6840i) q^{80} +(-360.018 - 623.570i) q^{81} +(345.544 - 598.499i) q^{82} -70.8820 q^{83} -521.659 q^{85} +(-257.662 + 446.284i) q^{86} +(19.0845 + 33.0554i) q^{87} +(763.740 + 1322.84i) q^{88} +(401.296 - 695.065i) q^{89} -222.651 q^{90} +531.165 q^{92} +(-12.2587 + 21.2326i) q^{93} +(123.954 + 214.694i) q^{94} +(179.732 + 311.305i) q^{95} +(-30.8057 + 53.3571i) q^{96} -145.648 q^{97} -1870.75 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q + 2 q^{2} + 16 q^{3} - 14 q^{4} - 30 q^{5} - 48 q^{6} - 132 q^{8} - 70 q^{9}+O(q^{10})$$ 12 * q + 2 * q^2 + 16 * q^3 - 14 * q^4 - 30 * q^5 - 48 * q^6 - 132 * q^8 - 70 * q^9 $$12 q + 2 q^{2} + 16 q^{3} - 14 q^{4} - 30 q^{5} - 48 q^{6} - 132 q^{8} - 70 q^{9} + 10 q^{10} + 16 q^{11} + 160 q^{12} - 336 q^{13} - 160 q^{15} - 298 q^{16} - 4 q^{17} - 354 q^{18} + 308 q^{19} + 140 q^{20} - 472 q^{22} + 336 q^{23} - 92 q^{24} - 150 q^{25} + 56 q^{26} - 1928 q^{27} + 352 q^{29} + 120 q^{30} + 392 q^{31} + 770 q^{32} + 188 q^{33} - 1624 q^{34} + 460 q^{36} + 140 q^{37} + 20 q^{38} - 140 q^{39} + 330 q^{40} - 1312 q^{41} - 776 q^{43} + 160 q^{44} - 350 q^{45} + 388 q^{46} + 628 q^{47} - 2792 q^{48} - 100 q^{50} - 744 q^{51} + 1520 q^{52} + 676 q^{53} + 2284 q^{54} - 160 q^{55} + 2936 q^{57} + 2012 q^{58} + 996 q^{59} + 800 q^{60} + 740 q^{61} + 728 q^{62} + 2852 q^{64} + 840 q^{65} - 3620 q^{66} - 1768 q^{67} - 2940 q^{68} + 2096 q^{69} - 448 q^{71} - 2858 q^{72} + 2640 q^{73} - 928 q^{74} + 400 q^{75} + 2680 q^{76} + 16 q^{78} - 1636 q^{79} - 1490 q^{80} - 4442 q^{81} - 1756 q^{82} - 280 q^{83} + 40 q^{85} - 1180 q^{86} + 1940 q^{87} + 5652 q^{88} - 1904 q^{89} + 3540 q^{90} - 3904 q^{92} + 1592 q^{93} - 3332 q^{94} + 1540 q^{95} - 6460 q^{96} - 1032 q^{97} - 5608 q^{99}+O(q^{100})$$ 12 * q + 2 * q^2 + 16 * q^3 - 14 * q^4 - 30 * q^5 - 48 * q^6 - 132 * q^8 - 70 * q^9 + 10 * q^10 + 16 * q^11 + 160 * q^12 - 336 * q^13 - 160 * q^15 - 298 * q^16 - 4 * q^17 - 354 * q^18 + 308 * q^19 + 140 * q^20 - 472 * q^22 + 336 * q^23 - 92 * q^24 - 150 * q^25 + 56 * q^26 - 1928 * q^27 + 352 * q^29 + 120 * q^30 + 392 * q^31 + 770 * q^32 + 188 * q^33 - 1624 * q^34 + 460 * q^36 + 140 * q^37 + 20 * q^38 - 140 * q^39 + 330 * q^40 - 1312 * q^41 - 776 * q^43 + 160 * q^44 - 350 * q^45 + 388 * q^46 + 628 * q^47 - 2792 * q^48 - 100 * q^50 - 744 * q^51 + 1520 * q^52 + 676 * q^53 + 2284 * q^54 - 160 * q^55 + 2936 * q^57 + 2012 * q^58 + 996 * q^59 + 800 * q^60 + 740 * q^61 + 728 * q^62 + 2852 * q^64 + 840 * q^65 - 3620 * q^66 - 1768 * q^67 - 2940 * q^68 + 2096 * q^69 - 448 * q^71 - 2858 * q^72 + 2640 * q^73 - 928 * q^74 + 400 * q^75 + 2680 * q^76 + 16 * q^78 - 1636 * q^79 - 1490 * q^80 - 4442 * q^81 - 1756 * q^82 - 280 * q^83 + 40 * q^85 - 1180 * q^86 + 1940 * q^87 + 5652 * q^88 - 1904 * q^89 + 3540 * q^90 - 3904 * q^92 + 1592 * q^93 - 3332 * q^94 + 1540 * q^95 - 6460 * q^96 - 1032 * q^97 - 5608 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$$.

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

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.828031 + 1.43419i −0.292753 + 0.507063i −0.974460 0.224562i $$-0.927905\pi$$
0.681707 + 0.731626i $$0.261238\pi$$
$$3$$ −0.166444 0.288289i −0.0320321 0.0554813i 0.849565 0.527484i $$-0.176865\pi$$
−0.881597 + 0.472003i $$0.843531\pi$$
$$4$$ 2.62873 + 4.55309i 0.328591 + 0.569137i
$$5$$ −2.50000 + 4.33013i −0.223607 + 0.387298i
$$6$$ 0.551283 0.0375100
$$7$$ 0 0
$$8$$ −21.9552 −0.970291
$$9$$ 13.4446 23.2867i 0.497948 0.862471i
$$10$$ −4.14016 7.17096i −0.130923 0.226766i
$$11$$ −34.7863 60.2517i −0.953497 1.65151i −0.737770 0.675052i $$-0.764121\pi$$
−0.215727 0.976454i $$-0.569212\pi$$
$$12$$ 0.875071 1.51567i 0.0210509 0.0364613i
$$13$$ −68.4326 −1.45998 −0.729991 0.683456i $$-0.760476\pi$$
−0.729991 + 0.683456i $$0.760476\pi$$
$$14$$ 0 0
$$15$$ 1.66444 0.0286504
$$16$$ −2.85026 + 4.93680i −0.0445354 + 0.0771375i
$$17$$ 52.1659 + 90.3539i 0.744240 + 1.28906i 0.950549 + 0.310574i $$0.100521\pi$$
−0.206309 + 0.978487i $$0.566145\pi$$
$$18$$ 22.2651 + 38.5643i 0.291552 + 0.504982i
$$19$$ 35.9465 62.2611i 0.434036 0.751772i −0.563180 0.826334i $$-0.690422\pi$$
0.997216 + 0.0745616i $$0.0237557\pi$$
$$20$$ −26.2873 −0.293901
$$21$$ 0 0
$$22$$ 115.217 1.11656
$$23$$ 50.5154 87.4952i 0.457964 0.793218i −0.540889 0.841094i $$-0.681912\pi$$
0.998853 + 0.0478764i $$0.0152453\pi$$
$$24$$ 3.65430 + 6.32944i 0.0310805 + 0.0538330i
$$25$$ −12.5000 21.6506i −0.100000 0.173205i
$$26$$ 56.6643 98.1454i 0.427415 0.740304i
$$27$$ −17.9390 −0.127866
$$28$$ 0 0
$$29$$ −114.661 −0.734205 −0.367102 0.930181i $$-0.619650\pi$$
−0.367102 + 0.930181i $$0.619650\pi$$
$$30$$ −1.37821 + 2.38712i −0.00838750 + 0.0145276i
$$31$$ −36.8252 63.7832i −0.213355 0.369542i 0.739407 0.673258i $$-0.235106\pi$$
−0.952762 + 0.303716i $$0.901772\pi$$
$$32$$ −92.5409 160.286i −0.511221 0.885461i
$$33$$ −11.5799 + 20.0570i −0.0610851 + 0.105802i
$$34$$ −172.780 −0.871514
$$35$$ 0 0
$$36$$ 141.369 0.654485
$$37$$ 100.467 174.013i 0.446395 0.773178i −0.551753 0.834007i $$-0.686041\pi$$
0.998148 + 0.0608289i $$0.0193744\pi$$
$$38$$ 59.5296 + 103.108i 0.254131 + 0.440168i
$$39$$ 11.3902 + 19.7284i 0.0467663 + 0.0810017i
$$40$$ 54.8879 95.0687i 0.216964 0.375792i
$$41$$ −417.308 −1.58957 −0.794786 0.606889i $$-0.792417\pi$$
−0.794786 + 0.606889i $$0.792417\pi$$
$$42$$ 0 0
$$43$$ 311.175 1.10357 0.551787 0.833985i $$-0.313946\pi$$
0.551787 + 0.833985i $$0.313946\pi$$
$$44$$ 182.888 316.771i 0.626621 1.08534i
$$45$$ 67.2230 + 116.434i 0.222689 + 0.385709i
$$46$$ 83.6566 + 144.897i 0.268141 + 0.464434i
$$47$$ 74.8485 129.641i 0.232293 0.402344i −0.726189 0.687495i $$-0.758710\pi$$
0.958483 + 0.285151i $$0.0920438\pi$$
$$48$$ 1.89763 0.00570625
$$49$$ 0 0
$$50$$ 41.4016 0.117101
$$51$$ 17.3654 30.0777i 0.0476792 0.0825827i
$$52$$ −179.891 311.580i −0.479737 0.830929i
$$53$$ −135.737 235.104i −0.351791 0.609320i 0.634772 0.772699i $$-0.281094\pi$$
−0.986563 + 0.163379i $$0.947761\pi$$
$$54$$ 14.8541 25.7280i 0.0374331 0.0648360i
$$55$$ 347.863 0.852834
$$56$$ 0 0
$$57$$ −23.9323 −0.0556124
$$58$$ 94.9425 164.445i 0.214941 0.372288i
$$59$$ −259.014 448.625i −0.571538 0.989933i −0.996408 0.0846788i $$-0.973014\pi$$
0.424870 0.905254i $$-0.360320\pi$$
$$60$$ 4.37536 + 7.57834i 0.00941427 + 0.0163060i
$$61$$ −109.963 + 190.461i −0.230808 + 0.399771i −0.958046 0.286614i $$-0.907470\pi$$
0.727238 + 0.686385i $$0.240804\pi$$
$$62$$ 121.970 0.249842
$$63$$ 0 0
$$64$$ 260.903 0.509576
$$65$$ 171.081 296.322i 0.326462 0.565449i
$$66$$ −19.1771 33.2157i −0.0357657 0.0619480i
$$67$$ −40.3475 69.8839i −0.0735706 0.127428i 0.826893 0.562359i $$-0.190106\pi$$
−0.900464 + 0.434931i $$0.856773\pi$$
$$68$$ −274.260 + 475.032i −0.489101 + 0.847148i
$$69$$ −33.6319 −0.0586783
$$70$$ 0 0
$$71$$ −91.0463 −0.152186 −0.0760930 0.997101i $$-0.524245\pi$$
−0.0760930 + 0.997101i $$0.524245\pi$$
$$72$$ −295.178 + 511.264i −0.483154 + 0.836848i
$$73$$ 441.141 + 764.078i 0.707283 + 1.22505i 0.965861 + 0.259059i $$0.0834125\pi$$
−0.258579 + 0.965990i $$0.583254\pi$$
$$74$$ 166.379 + 288.177i 0.261367 + 0.452701i
$$75$$ −4.16110 + 7.20723i −0.00640643 + 0.0110963i
$$76$$ 377.974 0.570481
$$77$$ 0 0
$$78$$ −37.7257 −0.0547640
$$79$$ −299.939 + 519.509i −0.427161 + 0.739865i −0.996620 0.0821553i $$-0.973820\pi$$
0.569458 + 0.822020i $$0.307153\pi$$
$$80$$ −14.2513 24.6840i −0.0199168 0.0344969i
$$81$$ −360.018 623.570i −0.493852 0.855377i
$$82$$ 345.544 598.499i 0.465353 0.806014i
$$83$$ −70.8820 −0.0937387 −0.0468694 0.998901i $$-0.514924\pi$$
−0.0468694 + 0.998901i $$0.514924\pi$$
$$84$$ 0 0
$$85$$ −521.659 −0.665668
$$86$$ −257.662 + 446.284i −0.323075 + 0.559582i
$$87$$ 19.0845 + 33.0554i 0.0235181 + 0.0407346i
$$88$$ 763.740 + 1322.84i 0.925170 + 1.60244i
$$89$$ 401.296 695.065i 0.477947 0.827828i −0.521733 0.853109i $$-0.674714\pi$$
0.999680 + 0.0252802i $$0.00804778\pi$$
$$90$$ −222.651 −0.260772
$$91$$ 0 0
$$92$$ 531.165 0.601932
$$93$$ −12.2587 + 21.2326i −0.0136684 + 0.0236744i
$$94$$ 123.954 + 214.694i 0.136009 + 0.235575i
$$95$$ 179.732 + 311.305i 0.194107 + 0.336203i
$$96$$ −30.8057 + 53.3571i −0.0327510 + 0.0567264i
$$97$$ −145.648 −0.152457 −0.0762283 0.997090i $$-0.524288\pi$$
−0.0762283 + 0.997090i $$0.524288\pi$$
$$98$$ 0 0
$$99$$ −1870.75 −1.89917
$$100$$ 65.7182 113.827i 0.0657182 0.113827i
$$101$$ −309.718 536.447i −0.305129 0.528499i 0.672161 0.740405i $$-0.265366\pi$$
−0.977290 + 0.211906i $$0.932033\pi$$
$$102$$ 28.7581 + 49.8105i 0.0279165 + 0.0483527i
$$103$$ −911.040 + 1577.97i −0.871528 + 1.50953i −0.0111125 + 0.999938i $$0.503537\pi$$
−0.860416 + 0.509593i $$0.829796\pi$$
$$104$$ 1502.45 1.41661
$$105$$ 0 0
$$106$$ 449.578 0.411952
$$107$$ −544.851 + 943.709i −0.492268 + 0.852634i −0.999960 0.00890504i $$-0.997165\pi$$
0.507692 + 0.861539i $$0.330499\pi$$
$$108$$ −47.1569 81.6781i −0.0420155 0.0727730i
$$109$$ −294.833 510.666i −0.259082 0.448743i 0.706914 0.707299i $$-0.250087\pi$$
−0.965996 + 0.258556i $$0.916753\pi$$
$$110$$ −288.042 + 498.903i −0.249670 + 0.432441i
$$111$$ −66.8882 −0.0571959
$$112$$ 0 0
$$113$$ −900.358 −0.749544 −0.374772 0.927117i $$-0.622279\pi$$
−0.374772 + 0.927117i $$0.622279\pi$$
$$114$$ 19.8167 34.3235i 0.0162807 0.0281990i
$$115$$ 252.577 + 437.476i 0.204808 + 0.354738i
$$116$$ −301.412 522.060i −0.241253 0.417863i
$$117$$ −920.048 + 1593.57i −0.726995 + 1.25919i
$$118$$ 857.887 0.669279
$$119$$ 0 0
$$120$$ −36.5430 −0.0277992
$$121$$ −1754.68 + 3039.19i −1.31831 + 2.28339i
$$122$$ −182.105 315.415i −0.135140 0.234069i
$$123$$ 69.4583 + 120.305i 0.0509174 + 0.0881915i
$$124$$ 193.607 335.337i 0.140213 0.242856i
$$125$$ 125.000 0.0894427
$$126$$ 0 0
$$127$$ −1755.75 −1.22676 −0.613378 0.789790i $$-0.710190\pi$$
−0.613378 + 0.789790i $$0.710190\pi$$
$$128$$ 524.292 908.100i 0.362041 0.627074i
$$129$$ −51.7931 89.7083i −0.0353498 0.0612277i
$$130$$ 283.321 + 490.727i 0.191146 + 0.331074i
$$131$$ 904.549 1566.72i 0.603289 1.04493i −0.389031 0.921225i $$-0.627190\pi$$
0.992319 0.123702i $$-0.0394766\pi$$
$$132$$ −121.762 −0.0802881
$$133$$ 0 0
$$134$$ 133.636 0.0861521
$$135$$ 44.8476 77.6783i 0.0285916 0.0495221i
$$136$$ −1145.31 1983.74i −0.722129 1.25076i
$$137$$ 9.25670 + 16.0331i 0.00577265 + 0.00999852i 0.868897 0.494992i $$-0.164829\pi$$
−0.863125 + 0.504991i $$0.831496\pi$$
$$138$$ 27.8482 48.2346i 0.0171783 0.0297536i
$$139$$ 625.608 0.381751 0.190875 0.981614i $$-0.438867\pi$$
0.190875 + 0.981614i $$0.438867\pi$$
$$140$$ 0 0
$$141$$ −49.8323 −0.0297634
$$142$$ 75.3892 130.578i 0.0445530 0.0771680i
$$143$$ 2380.52 + 4123.18i 1.39209 + 2.41117i
$$144$$ 76.6413 + 132.747i 0.0443526 + 0.0768209i
$$145$$ 286.651 496.495i 0.164173 0.284356i
$$146$$ −1461.11 −0.828237
$$147$$ 0 0
$$148$$ 1056.40 0.586725
$$149$$ 514.317 890.823i 0.282782 0.489792i −0.689287 0.724488i $$-0.742076\pi$$
0.972069 + 0.234696i $$0.0754095\pi$$
$$150$$ −6.89103 11.9356i −0.00375100 0.00649693i
$$151$$ −35.5037 61.4942i −0.0191341 0.0331412i 0.856300 0.516479i $$-0.172758\pi$$
−0.875434 + 0.483338i $$0.839424\pi$$
$$152$$ −789.211 + 1366.95i −0.421141 + 0.729438i
$$153$$ 2805.39 1.48237
$$154$$ 0 0
$$155$$ 368.252 0.190831
$$156$$ −59.8834 + 103.721i −0.0307340 + 0.0532329i
$$157$$ −1030.66 1785.16i −0.523922 0.907459i −0.999612 0.0278461i $$-0.991135\pi$$
0.475691 0.879613i $$-0.342198\pi$$
$$158$$ −496.717 860.339i −0.250106 0.433196i
$$159$$ −45.1852 + 78.2631i −0.0225372 + 0.0390356i
$$160$$ 925.409 0.457250
$$161$$ 0 0
$$162$$ 1192.42 0.578307
$$163$$ 981.899 1700.70i 0.471830 0.817234i −0.527651 0.849462i $$-0.676927\pi$$
0.999481 + 0.0322280i $$0.0102603\pi$$
$$164$$ −1096.99 1900.04i −0.522320 0.904684i
$$165$$ −57.8997 100.285i −0.0273181 0.0473163i
$$166$$ 58.6925 101.658i 0.0274423 0.0475315i
$$167$$ −2855.04 −1.32293 −0.661467 0.749974i $$-0.730066\pi$$
−0.661467 + 0.749974i $$0.730066\pi$$
$$168$$ 0 0
$$169$$ 2486.01 1.13155
$$170$$ 431.950 748.158i 0.194877 0.337536i
$$171$$ −966.571 1674.15i −0.432255 0.748687i
$$172$$ 817.994 + 1416.81i 0.362625 + 0.628084i
$$173$$ −776.603 + 1345.12i −0.341295 + 0.591140i −0.984673 0.174408i $$-0.944199\pi$$
0.643378 + 0.765548i $$0.277532\pi$$
$$174$$ −63.2104 −0.0275400
$$175$$ 0 0
$$176$$ 396.601 0.169857
$$177$$ −86.2226 + 149.342i −0.0366152 + 0.0634193i
$$178$$ 664.571 + 1151.07i 0.279841 + 0.484699i
$$179$$ −134.920 233.689i −0.0563376 0.0975795i 0.836481 0.547996i $$-0.184609\pi$$
−0.892819 + 0.450416i $$0.851276\pi$$
$$180$$ −353.422 + 612.145i −0.146347 + 0.253481i
$$181$$ −2229.61 −0.915613 −0.457806 0.889052i $$-0.651365\pi$$
−0.457806 + 0.889052i $$0.651365\pi$$
$$182$$ 0 0
$$183$$ 73.2105 0.0295731
$$184$$ −1109.07 + 1920.97i −0.444359 + 0.769652i
$$185$$ 502.333 + 870.066i 0.199634 + 0.345776i
$$186$$ −20.3011 35.1626i −0.00800296 0.0138615i
$$187$$ 3629.32 6286.16i 1.41926 2.45823i
$$188$$ 787.026 0.305318
$$189$$ 0 0
$$190$$ −595.296 −0.227302
$$191$$ 232.960 403.498i 0.0882533 0.152859i −0.818520 0.574479i $$-0.805205\pi$$
0.906773 + 0.421619i $$0.138538\pi$$
$$192$$ −43.4257 75.2154i −0.0163228 0.0282719i
$$193$$ 2207.23 + 3823.04i 0.823212 + 1.42585i 0.903278 + 0.429056i $$0.141154\pi$$
−0.0800657 + 0.996790i $$0.525513\pi$$
$$194$$ 120.601 208.887i 0.0446321 0.0773051i
$$195$$ −113.902 −0.0418291
$$196$$ 0 0
$$197$$ −289.812 −0.104814 −0.0524068 0.998626i $$-0.516689\pi$$
−0.0524068 + 0.998626i $$0.516689\pi$$
$$198$$ 1549.04 2683.02i 0.555987 0.962998i
$$199$$ 2408.87 + 4172.28i 0.858091 + 1.48626i 0.873748 + 0.486380i $$0.161683\pi$$
−0.0156567 + 0.999877i $$0.504984\pi$$
$$200$$ 274.440 + 475.343i 0.0970291 + 0.168059i
$$201$$ −13.4312 + 23.2635i −0.00471324 + 0.00816358i
$$202$$ 1025.82 0.357310
$$203$$ 0 0
$$204$$ 182.595 0.0626678
$$205$$ 1043.27 1806.99i 0.355439 0.615639i
$$206$$ −1508.74 2613.21i −0.510285 0.883840i
$$207$$ −1358.32 2352.67i −0.456085 0.789962i
$$208$$ 195.051 337.838i 0.0650209 0.112619i
$$209$$ −5001.78 −1.65541
$$210$$ 0 0
$$211$$ 2022.01 0.659719 0.329859 0.944030i $$-0.392999\pi$$
0.329859 + 0.944030i $$0.392999\pi$$
$$212$$ 713.632 1236.05i 0.231191 0.400434i
$$213$$ 15.1541 + 26.2477i 0.00487484 + 0.00844347i
$$214$$ −902.306 1562.84i −0.288226 0.499222i
$$215$$ −777.937 + 1347.43i −0.246767 + 0.427412i
$$216$$ 393.855 0.124067
$$217$$ 0 0
$$218$$ 976.525 0.303388
$$219$$ 146.850 254.352i 0.0453115 0.0784819i
$$220$$ 914.438 + 1583.85i 0.280234 + 0.485379i
$$221$$ −3569.84 6183.15i −1.08658 1.88201i
$$222$$ 55.3855 95.9305i 0.0167443 0.0290019i
$$223$$ −4343.86 −1.30442 −0.652211 0.758037i $$-0.726158\pi$$
−0.652211 + 0.758037i $$0.726158\pi$$
$$224$$ 0 0
$$225$$ −672.230 −0.199179
$$226$$ 745.524 1291.29i 0.219432 0.380067i
$$227$$ −1323.80 2292.88i −0.387064 0.670414i 0.604989 0.796234i $$-0.293177\pi$$
−0.992053 + 0.125819i $$0.959844\pi$$
$$228$$ −62.9114 108.966i −0.0182737 0.0316510i
$$229$$ −722.545 + 1251.49i −0.208503 + 0.361137i −0.951243 0.308442i $$-0.900192\pi$$
0.742740 + 0.669580i $$0.233526\pi$$
$$230$$ −836.566 −0.239833
$$231$$ 0 0
$$232$$ 2517.39 0.712392
$$233$$ 3122.96 5409.12i 0.878076 1.52087i 0.0246255 0.999697i $$-0.492161\pi$$
0.853450 0.521175i $$-0.174506\pi$$
$$234$$ −1523.66 2639.05i −0.425660 0.737265i
$$235$$ 374.243 + 648.207i 0.103885 + 0.179934i
$$236$$ 1361.76 2358.63i 0.375605 0.650566i
$$237$$ 199.692 0.0547315
$$238$$ 0 0
$$239$$ 1340.24 0.362731 0.181366 0.983416i $$-0.441948\pi$$
0.181366 + 0.983416i $$0.441948\pi$$
$$240$$ −4.74409 + 8.21700i −0.00127596 + 0.00221002i
$$241$$ 1684.96 + 2918.44i 0.450364 + 0.780054i 0.998409 0.0563953i $$-0.0179607\pi$$
−0.548044 + 0.836449i $$0.684627\pi$$
$$242$$ −2905.85 5033.08i −0.771881 1.33694i
$$243$$ −362.023 + 627.042i −0.0955710 + 0.165534i
$$244$$ −1156.25 −0.303366
$$245$$ 0 0
$$246$$ −230.054 −0.0596249
$$247$$ −2459.91 + 4260.69i −0.633685 + 1.09757i
$$248$$ 808.504 + 1400.37i 0.207016 + 0.358563i
$$249$$ 11.7979 + 20.4345i 0.00300265 + 0.00520074i
$$250$$ −103.504 + 179.274i −0.0261846 + 0.0453531i
$$251$$ 3592.64 0.903449 0.451724 0.892158i $$-0.350809\pi$$
0.451724 + 0.892158i $$0.350809\pi$$
$$252$$ 0 0
$$253$$ −7028.97 −1.74667
$$254$$ 1453.82 2518.09i 0.359137 0.622043i
$$255$$ 86.8268 + 150.388i 0.0213228 + 0.0369321i
$$256$$ 1911.87 + 3311.46i 0.466765 + 0.808461i
$$257$$ −1.42381 + 2.46612i −0.000345584 + 0.000598569i −0.866198 0.499701i $$-0.833443\pi$$
0.865853 + 0.500299i $$0.166777\pi$$
$$258$$ 171.545 0.0413951
$$259$$ 0 0
$$260$$ 1798.91 0.429090
$$261$$ −1541.56 + 2670.07i −0.365596 + 0.633230i
$$262$$ 1497.99 + 2594.59i 0.353229 + 0.611811i
$$263$$ 1408.54 + 2439.66i 0.330244 + 0.571999i 0.982560 0.185948i $$-0.0595357\pi$$
−0.652316 + 0.757947i $$0.726202\pi$$
$$264$$ 254.239 440.356i 0.0592703 0.102659i
$$265$$ 1357.37 0.314652
$$266$$ 0 0
$$267$$ −267.173 −0.0612386
$$268$$ 212.125 367.412i 0.0483493 0.0837434i
$$269$$ −723.716 1253.51i −0.164036 0.284119i 0.772276 0.635287i $$-0.219118\pi$$
−0.936313 + 0.351168i $$0.885785\pi$$
$$270$$ 74.2704 + 128.640i 0.0167406 + 0.0289955i
$$271$$ 4027.25 6975.40i 0.902724 1.56356i 0.0787797 0.996892i $$-0.474898\pi$$
0.823944 0.566671i $$-0.191769\pi$$
$$272$$ −594.746 −0.132580
$$273$$ 0 0
$$274$$ −30.6593 −0.00675985
$$275$$ −869.658 + 1506.29i −0.190699 + 0.330301i
$$276$$ −88.4091 153.129i −0.0192812 0.0333960i
$$277$$ 285.650 + 494.760i 0.0619604 + 0.107319i 0.895342 0.445380i $$-0.146931\pi$$
−0.833381 + 0.552699i $$0.813598\pi$$
$$278$$ −518.023 + 897.242i −0.111759 + 0.193572i
$$279$$ −1980.40 −0.424959
$$280$$ 0 0
$$281$$ −1784.48 −0.378837 −0.189418 0.981896i $$-0.560660\pi$$
−0.189418 + 0.981896i $$0.560660\pi$$
$$282$$ 41.2627 71.4691i 0.00871333 0.0150919i
$$283$$ 1660.52 + 2876.11i 0.348791 + 0.604124i 0.986035 0.166538i $$-0.0532590\pi$$
−0.637244 + 0.770662i $$0.719926\pi$$
$$284$$ −239.336 414.542i −0.0500070 0.0866146i
$$285$$ 59.8307 103.630i 0.0124353 0.0215386i
$$286$$ −7884.57 −1.63015
$$287$$ 0 0
$$288$$ −4976.70 −1.01825
$$289$$ −2986.05 + 5172.00i −0.607786 + 1.05272i
$$290$$ 474.713 + 822.226i 0.0961244 + 0.166492i
$$291$$ 24.2422 + 41.9887i 0.00488351 + 0.00845848i
$$292$$ −2319.28 + 4017.11i −0.464814 + 0.805081i
$$293$$ 5049.54 1.00682 0.503408 0.864049i $$-0.332079\pi$$
0.503408 + 0.864049i $$0.332079\pi$$
$$294$$ 0 0
$$295$$ 2590.14 0.511199
$$296$$ −2205.76 + 3820.49i −0.433133 + 0.750208i
$$297$$ 624.033 + 1080.86i 0.121919 + 0.211171i
$$298$$ 851.740 + 1475.26i 0.165570 + 0.286776i
$$299$$ −3456.90 + 5987.52i −0.668620 + 1.15808i
$$300$$ −43.7536 −0.00842038
$$301$$ 0 0
$$302$$ 117.593 0.0224063
$$303$$ −103.101 + 178.576i −0.0195479 + 0.0338579i
$$304$$ 204.914 + 354.921i 0.0386599 + 0.0669609i
$$305$$ −549.814 952.305i −0.103220 0.178783i
$$306$$ −2322.95 + 4023.47i −0.433969 + 0.751656i
$$307$$ 1535.73 0.285500 0.142750 0.989759i $$-0.454405\pi$$
0.142750 + 0.989759i $$0.454405\pi$$
$$308$$ 0 0
$$309$$ 606.548 0.111668
$$310$$ −304.924 + 528.145i −0.0558663 + 0.0967632i
$$311$$ −4641.52 8039.35i −0.846291 1.46582i −0.884495 0.466550i $$-0.845497\pi$$
0.0382037 0.999270i $$-0.487836\pi$$
$$312$$ −250.073 433.140i −0.0453770 0.0785952i
$$313$$ 3012.72 5218.18i 0.544054 0.942329i −0.454612 0.890690i $$-0.650222\pi$$
0.998666 0.0516393i $$-0.0164446\pi$$
$$314$$ 3413.68 0.613519
$$315$$ 0 0
$$316$$ −3153.83 −0.561445
$$317$$ 3488.79 6042.76i 0.618139 1.07065i −0.371686 0.928358i $$-0.621220\pi$$
0.989825 0.142289i $$-0.0454464\pi$$
$$318$$ −74.8295 129.609i −0.0131957 0.0228556i
$$319$$ 3988.62 + 6908.49i 0.700062 + 1.21254i
$$320$$ −652.257 + 1129.74i −0.113945 + 0.197358i
$$321$$ 362.748 0.0630736
$$322$$ 0 0
$$323$$ 7500.71 1.29211
$$324$$ 1892.78 3278.39i 0.324551 0.562139i
$$325$$ 855.407 + 1481.61i 0.145998 + 0.252876i
$$326$$ 1626.09 + 2816.46i 0.276259 + 0.478495i
$$327$$ −98.1464 + 169.995i −0.0165979 + 0.0287484i
$$328$$ 9162.06 1.54235
$$329$$ 0 0
$$330$$ 191.771 0.0319898
$$331$$ −492.439 + 852.930i −0.0817731 + 0.141635i −0.904012 0.427508i $$-0.859392\pi$$
0.822239 + 0.569143i $$0.192725\pi$$
$$332$$ −186.330 322.732i −0.0308017 0.0533501i
$$333$$ −2701.46 4679.07i −0.444563 0.770005i
$$334$$ 2364.07 4094.68i 0.387293 0.670812i
$$335$$ 403.475 0.0658035
$$336$$ 0 0
$$337$$ 51.9653 0.00839979 0.00419990 0.999991i $$-0.498663\pi$$
0.00419990 + 0.999991i $$0.498663\pi$$
$$338$$ −2058.50 + 3565.42i −0.331265 + 0.573767i
$$339$$ 149.859 + 259.563i 0.0240095 + 0.0415857i
$$340$$ −1371.30 2375.16i −0.218733 0.378856i
$$341$$ −2562.03 + 4437.56i −0.406867 + 0.704714i
$$342$$ 3201.40 0.506176
$$343$$ 0 0
$$344$$ −6831.89 −1.07079
$$345$$ 84.0797 145.630i 0.0131209 0.0227260i
$$346$$ −1286.10 2227.60i −0.199830 0.346116i
$$347$$ 5650.24 + 9786.50i 0.874123 + 1.51403i 0.857694 + 0.514161i $$0.171897\pi$$
0.0164299 + 0.999865i $$0.494770\pi$$
$$348$$ −100.336 + 173.787i −0.0154557 + 0.0267701i
$$349$$ 2016.91 0.309349 0.154674 0.987966i $$-0.450567\pi$$
0.154674 + 0.987966i $$0.450567\pi$$
$$350$$ 0 0
$$351$$ 1227.61 0.186682
$$352$$ −6438.31 + 11151.5i −0.974896 + 1.68857i
$$353$$ −3794.71 6572.62i −0.572158 0.991007i −0.996344 0.0854319i $$-0.972773\pi$$
0.424186 0.905575i $$-0.360560\pi$$
$$354$$ −142.790 247.319i −0.0214384 0.0371324i
$$355$$ 227.616 394.242i 0.0340298 0.0589414i
$$356$$ 4219.59 0.628196
$$357$$ 0 0
$$358$$ 446.873 0.0659720
$$359$$ −4367.12 + 7564.08i −0.642027 + 1.11202i 0.342952 + 0.939353i $$0.388573\pi$$
−0.984980 + 0.172671i $$0.944760\pi$$
$$360$$ −1475.89 2556.32i −0.216073 0.374250i
$$361$$ 845.204 + 1463.94i 0.123226 + 0.213433i
$$362$$ 1846.19 3197.69i 0.268049 0.464274i
$$363$$ 1168.22 0.168914
$$364$$ 0 0
$$365$$ −4411.41 −0.632613
$$366$$ −60.6206 + 104.998i −0.00865762 + 0.0149954i
$$367$$ −945.271 1637.26i −0.134449 0.232872i 0.790938 0.611896i $$-0.209593\pi$$
−0.925387 + 0.379024i $$0.876260\pi$$
$$368$$ 287.964 + 498.769i 0.0407912 + 0.0706525i
$$369$$ −5610.53 + 9717.72i −0.791524 + 1.37096i
$$370$$ −1663.79 −0.233774
$$371$$ 0 0
$$372$$ −128.899 −0.0179653
$$373$$ −1356.94 + 2350.29i −0.188364 + 0.326256i −0.944705 0.327922i $$-0.893652\pi$$
0.756341 + 0.654178i $$0.226985\pi$$
$$374$$ 6010.37 + 10410.3i 0.830987 + 1.43931i
$$375$$ −20.8055 36.0361i −0.00286504 0.00496240i
$$376$$ −1643.31 + 2846.30i −0.225392 + 0.390390i
$$377$$ 7846.52 1.07193
$$378$$ 0 0
$$379$$ 8941.19 1.21182 0.605908 0.795535i $$-0.292810\pi$$
0.605908 + 0.795535i $$0.292810\pi$$
$$380$$ −944.935 + 1636.68i −0.127564 + 0.220947i
$$381$$ 292.234 + 506.165i 0.0392956 + 0.0680620i
$$382$$ 385.796 + 668.218i 0.0516729 + 0.0895001i
$$383$$ −4646.94 + 8048.74i −0.619968 + 1.07382i 0.369524 + 0.929221i $$0.379521\pi$$
−0.989491 + 0.144594i $$0.953812\pi$$
$$384$$ −349.060 −0.0463878
$$385$$ 0 0
$$386$$ −7310.62 −0.963992
$$387$$ 4183.62 7246.24i 0.549522 0.951801i
$$388$$ −382.868 663.147i −0.0500959 0.0867686i
$$389$$ −5227.38 9054.08i −0.681333 1.18010i −0.974574 0.224065i $$-0.928067\pi$$
0.293242 0.956038i $$-0.405266\pi$$
$$390$$ 94.3142 163.357i 0.0122456 0.0212100i
$$391$$ 10540.7 1.36334
$$392$$ 0 0
$$393$$ −602.226 −0.0772985
$$394$$ 239.974 415.646i 0.0306845 0.0531471i
$$395$$ −1499.69 2597.54i −0.191032 0.330878i
$$396$$ −4917.70 8517.70i −0.624050 1.08089i
$$397$$ −1813.01 + 3140.23i −0.229200 + 0.396987i −0.957571 0.288196i $$-0.906944\pi$$
0.728371 + 0.685183i $$0.240278\pi$$
$$398$$ −7978.47 −1.00484
$$399$$ 0 0
$$400$$ 142.513 0.0178141
$$401$$ 4211.26 7294.12i 0.524440 0.908356i −0.475156 0.879902i $$-0.657608\pi$$
0.999595 0.0284542i $$-0.00905846\pi$$
$$402$$ −22.2429 38.5258i −0.00275963 0.00477983i
$$403$$ 2520.04 + 4364.85i 0.311495 + 0.539525i
$$404$$ 1628.33 2820.35i 0.200526 0.347320i
$$405$$ 3600.18 0.441715
$$406$$ 0 0
$$407$$ −13979.5 −1.70254
$$408$$ −381.260 + 660.361i −0.0462627 + 0.0801293i
$$409$$ −7290.34 12627.2i −0.881379 1.52659i −0.849808 0.527092i $$-0.823282\pi$$
−0.0315714 0.999502i $$-0.510051\pi$$
$$410$$ 1727.72 + 2992.50i 0.208112 + 0.360461i
$$411$$ 3.08144 5.33721i 0.000369820 0.000640548i
$$412$$ −9579.51 −1.14551
$$413$$ 0 0
$$414$$ 4498.92 0.534081
$$415$$ 177.205 306.928i 0.0209606 0.0363049i
$$416$$ 6332.81 + 10968.8i 0.746374 + 1.29276i
$$417$$ −104.129 180.356i −0.0122283 0.0211800i
$$418$$ 4141.63 7173.51i 0.484626 0.839397i
$$419$$ 2537.53 0.295863 0.147931 0.988998i $$-0.452739\pi$$
0.147931 + 0.988998i $$0.452739\pi$$
$$420$$ 0 0
$$421$$ 9649.52 1.11708 0.558538 0.829479i $$-0.311363\pi$$
0.558538 + 0.829479i $$0.311363\pi$$
$$422$$ −1674.28 + 2899.94i −0.193135 + 0.334519i
$$423$$ −2012.62 3485.95i −0.231340 0.400692i
$$424$$ 2980.13 + 5161.74i 0.341340 + 0.591218i
$$425$$ 1304.15 2258.85i 0.148848 0.257812i
$$426$$ −50.1922 −0.00570850
$$427$$ 0 0
$$428$$ −5729.06 −0.647020
$$429$$ 792.444 1372.55i 0.0891832 0.154470i
$$430$$ −1288.31 2231.42i −0.144483 0.250253i
$$431$$ 3631.28 + 6289.57i 0.405830 + 0.702918i 0.994418 0.105515i $$-0.0336492\pi$$
−0.588588 + 0.808433i $$0.700316\pi$$
$$432$$ 51.1310 88.5615i 0.00569454 0.00986323i
$$433$$ −11345.0 −1.25914 −0.629570 0.776944i $$-0.716769\pi$$
−0.629570 + 0.776944i $$0.716769\pi$$
$$434$$ 0 0
$$435$$ −190.845 −0.0210353
$$436$$ 1550.07 2684.81i 0.170264 0.294906i
$$437$$ −3631.70 6290.28i −0.397546 0.688570i
$$438$$ 243.193 + 421.223i 0.0265302 + 0.0459516i
$$439$$ 5852.94 10137.6i 0.636323 1.10214i −0.349911 0.936783i $$-0.613788\pi$$
0.986233 0.165360i $$-0.0528786\pi$$
$$440$$ −7637.40 −0.827497
$$441$$ 0 0
$$442$$ 11823.8 1.27240
$$443$$ −7538.99 + 13057.9i −0.808551 + 1.40045i 0.105316 + 0.994439i $$0.466415\pi$$
−0.913867 + 0.406013i $$0.866919\pi$$
$$444$$ −175.831 304.548i −0.0187941 0.0325523i
$$445$$ 2006.48 + 3475.32i 0.213744 + 0.370216i
$$446$$ 3596.85 6229.92i 0.381874 0.661425i
$$447$$ −342.419 −0.0362324
$$448$$ 0 0
$$449$$ 1075.45 0.113037 0.0565185 0.998402i $$-0.482000\pi$$
0.0565185 + 0.998402i $$0.482000\pi$$
$$450$$ 556.627 964.106i 0.0583103 0.100996i
$$451$$ 14516.6 + 25143.5i 1.51565 + 2.62519i
$$452$$ −2366.80 4099.41i −0.246294 0.426593i
$$453$$ −11.8187 + 20.4706i −0.00122581 + 0.00212317i
$$454$$ 4384.58 0.453257
$$455$$ 0 0
$$456$$ 525.437 0.0539602
$$457$$ 5368.47 9298.47i 0.549511 0.951781i −0.448797 0.893634i $$-0.648147\pi$$
0.998308 0.0581472i $$-0.0185193\pi$$
$$458$$ −1196.58 2072.54i −0.122080 0.211448i
$$459$$ −935.805 1620.86i −0.0951627 0.164827i
$$460$$ −1327.91 + 2300.01i −0.134596 + 0.233127i
$$461$$ −452.568 −0.0457228 −0.0228614 0.999739i $$-0.507278\pi$$
−0.0228614 + 0.999739i $$0.507278\pi$$
$$462$$ 0 0
$$463$$ 7118.15 0.714489 0.357244 0.934011i $$-0.383716\pi$$
0.357244 + 0.934011i $$0.383716\pi$$
$$464$$ 326.813 566.057i 0.0326981 0.0566347i
$$465$$ −61.2933 106.163i −0.00611271 0.0105875i
$$466$$ 5171.81 + 8957.83i 0.514119 + 0.890480i
$$467$$ 486.900 843.335i 0.0482463 0.0835651i −0.840894 0.541200i $$-0.817970\pi$$
0.889140 + 0.457635i $$0.151303\pi$$
$$468$$ −9674.23 −0.955537
$$469$$ 0 0
$$470$$ −1239.54 −0.121650
$$471$$ −343.094 + 594.257i −0.0335646 + 0.0581357i
$$472$$ 5686.70 + 9849.65i 0.554558 + 0.960523i
$$473$$ −10824.6 18748.8i −1.05225 1.82256i
$$474$$ −165.351 + 286.396i −0.0160228 + 0.0277524i
$$475$$ −1797.32 −0.173614
$$476$$ 0 0
$$477$$ −7299.72 −0.700695
$$478$$ −1109.76 + 1922.16i −0.106191 + 0.183928i
$$479$$ 4857.00 + 8412.57i 0.463303 + 0.802464i 0.999123 0.0418680i $$-0.0133309\pi$$
−0.535820 + 0.844332i $$0.679998\pi$$
$$480$$ −154.029 266.785i −0.0146467 0.0253688i
$$481$$ −6875.19 + 11908.2i −0.651729 + 1.12883i
$$482$$ −5580.80 −0.527383
$$483$$ 0 0
$$484$$ −18450.3 −1.73274
$$485$$ 364.119 630.673i 0.0340903 0.0590462i
$$486$$ −599.532 1038.42i −0.0559575 0.0969212i
$$487$$ −461.694 799.678i −0.0429597 0.0744084i 0.843746 0.536743i $$-0.180345\pi$$
−0.886706 + 0.462334i $$0.847012\pi$$
$$488$$ 2414.25 4181.61i 0.223951 0.387894i
$$489$$ −653.724 −0.0604549
$$490$$ 0 0
$$491$$ 1289.11 0.118486 0.0592430 0.998244i $$-0.481131\pi$$
0.0592430 + 0.998244i $$0.481131\pi$$
$$492$$ −365.174 + 632.500i −0.0334620 + 0.0579579i
$$493$$ −5981.37 10360.0i −0.546424 0.946435i
$$494$$ −4073.76 7055.96i −0.371027 0.642637i
$$495$$ 4676.88 8100.59i 0.424667 0.735544i
$$496$$ 419.846 0.0380074
$$497$$ 0 0
$$498$$ −39.0760 −0.00351614
$$499$$ 9669.15 16747.5i 0.867436 1.50244i 0.00282829 0.999996i $$-0.499100\pi$$
0.864608 0.502447i $$-0.167567\pi$$
$$500$$ 328.591 + 569.137i 0.0293901 + 0.0509051i
$$501$$ 475.205 + 823.078i 0.0423764 + 0.0733981i
$$502$$ −2974.82 + 5152.54i −0.264488 + 0.458106i
$$503$$ 1772.84 0.157151 0.0785757 0.996908i $$-0.474963\pi$$
0.0785757 + 0.996908i $$0.474963\pi$$
$$504$$ 0 0
$$505$$ 3097.18 0.272916
$$506$$ 5820.21 10080.9i 0.511344 0.885673i
$$507$$ −413.782 716.691i −0.0362459 0.0627798i
$$508$$ −4615.40 7994.11i −0.403101 0.698192i
$$509$$ 1575.88 2729.50i 0.137229 0.237687i −0.789218 0.614113i $$-0.789514\pi$$
0.926447 + 0.376426i $$0.122847\pi$$
$$510$$ −287.581 −0.0249692
$$511$$ 0 0
$$512$$ 2056.31 0.177494
$$513$$ −644.845 + 1116.90i −0.0554983 + 0.0961258i
$$514$$ −2.35792 4.08404i −0.000202341 0.000350466i
$$515$$ −4555.20 7889.83i −0.389759 0.675083i
$$516$$ 272.300 471.637i 0.0232313 0.0402377i
$$517$$ −10414.8 −0.885964
$$518$$ 0 0
$$519$$ 517.043 0.0437296
$$520$$ −3756.12 + 6505.79i −0.316763 + 0.548650i
$$521$$ −5514.69 9551.72i −0.463729 0.803202i 0.535414 0.844590i $$-0.320156\pi$$
−0.999143 + 0.0413875i $$0.986822\pi$$
$$522$$ −2552.93 4421.80i −0.214059 0.370760i
$$523$$ 7224.21 12512.7i 0.604002 1.04616i −0.388207 0.921572i $$-0.626905\pi$$
0.992208 0.124589i $$-0.0397613\pi$$
$$524$$ 9511.26 0.792941
$$525$$ 0 0
$$526$$ −4665.25 −0.386720
$$527$$ 3842.04 6654.61i 0.317575 0.550056i
$$528$$ −66.0117 114.336i −0.00544089 0.00942390i
$$529$$ 979.894 + 1697.23i 0.0805371 + 0.139494i
$$530$$ −1123.95 + 1946.73i −0.0921153 + 0.159548i
$$531$$ −13929.4 −1.13838
$$532$$ 0 0
$$533$$ 28557.4 2.32075
$$534$$ 221.227 383.177i 0.0179278 0.0310519i
$$535$$ −2724.25 4718.54i −0.220149 0.381309i
$$536$$ 885.836 + 1534.31i 0.0713849 + 0.123642i
$$537$$ −44.9133 + 77.7922i −0.00360922 + 0.00625136i
$$538$$ 2397.04 0.192089
$$539$$ 0 0
$$540$$ 471.569 0.0375798
$$541$$ 11137.4 19290.5i 0.885091 1.53302i 0.0394817 0.999220i $$-0.487429\pi$$
0.845609 0.533802i $$-0.179237\pi$$
$$542$$ 6669.38 + 11551.7i 0.528551 + 0.915476i
$$543$$ 371.105 + 642.773i 0.0293290 + 0.0507994i
$$544$$ 9654.95 16722.9i 0.760942 1.31799i
$$545$$ 2948.33 0.231730
$$546$$ 0 0
$$547$$ 18642.6 1.45722 0.728609 0.684930i $$-0.240167\pi$$
0.728609 + 0.684930i $$0.240167\pi$$
$$548$$ −48.6667 + 84.2932i −0.00379368 + 0.00657085i
$$549$$ 2956.81 + 5121.34i 0.229861 + 0.398130i
$$550$$ −1440.21 2494.51i −0.111656 0.193393i
$$551$$ −4121.64 + 7138.89i −0.318671 + 0.551955i
$$552$$ 738.394 0.0569350
$$553$$ 0 0
$$554$$ −946.108 −0.0725565
$$555$$ 167.220 289.634i 0.0127894 0.0221519i
$$556$$ 1644.55 + 2848.45i 0.125440 + 0.217268i
$$557$$ 10715.9 + 18560.5i 0.815165 + 1.41191i 0.909209 + 0.416339i $$0.136687\pi$$
−0.0940446 + 0.995568i $$0.529980\pi$$
$$558$$ 1639.83 2840.28i 0.124408 0.215481i
$$559$$ −21294.5 −1.61120
$$560$$ 0 0
$$561$$ −2416.31 −0.181848
$$562$$ 1477.60 2559.29i 0.110906 0.192094i
$$563$$ −3077.43 5330.26i −0.230370 0.399012i 0.727547 0.686057i $$-0.240660\pi$$
−0.957917 + 0.287046i $$0.907327\pi$$
$$564$$ −130.996 226.891i −0.00977998 0.0169394i
$$565$$ 2250.89 3898.66i 0.167603 0.290297i
$$566$$ −5499.86 −0.408439
$$567$$ 0 0
$$568$$ 1998.94 0.147665
$$569$$ 4194.99 7265.94i 0.309074 0.535333i −0.669086 0.743185i $$-0.733314\pi$$
0.978160 + 0.207853i $$0.0666475\pi$$
$$570$$ 99.0833 + 171.617i 0.00728095 + 0.0126110i
$$571$$ 300.251 + 520.050i 0.0220055 + 0.0381146i 0.876818 0.480822i $$-0.159662\pi$$
−0.854813 + 0.518936i $$0.826328\pi$$
$$572$$ −12515.5 + 21677.4i −0.914856 + 1.58458i
$$573$$ −155.099 −0.0113078
$$574$$ 0 0
$$575$$ −2525.77 −0.183186
$$576$$ 3507.73 6075.57i 0.253742 0.439494i
$$577$$ 2031.17 + 3518.10i 0.146549 + 0.253831i 0.929950 0.367686i $$-0.119850\pi$$
−0.783401 + 0.621517i $$0.786517\pi$$
$$578$$ −4945.09 8565.15i −0.355863 0.616372i
$$579$$ 734.760 1272.64i 0.0527385 0.0913457i
$$580$$ 3014.12 0.215783
$$581$$ 0 0
$$582$$ −80.2931 −0.00571865
$$583$$ −9443.59 + 16356.8i −0.670864 + 1.16197i
$$584$$ −9685.32 16775.5i −0.686270 1.18865i
$$585$$ −4600.24 7967.85i −0.325122 0.563128i
$$586$$ −4181.18 + 7242.01i −0.294749 + 0.510520i
$$587$$ 8387.50 0.589760 0.294880 0.955534i $$-0.404720\pi$$
0.294880 + 0.955534i $$0.404720\pi$$
$$588$$ 0 0
$$589$$ −5294.95 −0.370415
$$590$$ −2144.72 + 3714.76i −0.149655 + 0.259210i
$$591$$ 48.2375 + 83.5497i 0.00335740 + 0.00581519i
$$592$$ 572.713 + 991.967i 0.0397607 + 0.0688676i
$$593$$ −7671.31 + 13287.1i −0.531236 + 0.920128i 0.468099 + 0.883676i $$0.344939\pi$$
−0.999335 + 0.0364520i $$0.988394\pi$$
$$594$$ −2066.88 −0.142769
$$595$$ 0 0
$$596$$ 5408.00 0.371678
$$597$$ 801.882 1388.90i 0.0549730 0.0952159i
$$598$$ −5724.83 9915.70i −0.391481 0.678066i
$$599$$ 9854.23 + 17068.0i 0.672175 + 1.16424i 0.977286 + 0.211925i $$0.0679731\pi$$
−0.305111 + 0.952317i $$0.598694\pi$$
$$600$$ 91.3576 158.236i 0.00621610 0.0107666i
$$601$$ 19002.5 1.28973 0.644866 0.764295i $$-0.276913\pi$$
0.644866 + 0.764295i $$0.276913\pi$$
$$602$$ 0 0
$$603$$ −2169.82 −0.146537
$$604$$ 186.659 323.303i 0.0125746 0.0217798i
$$605$$ −8773.38 15195.9i −0.589568 1.02116i
$$606$$ −170.742 295.734i −0.0114454 0.0198240i
$$607$$ 14726.6 25507.1i 0.984732 1.70561i 0.341612 0.939841i $$-0.389027\pi$$
0.643121 0.765765i $$-0.277639\pi$$
$$608$$ −13306.1 −0.887553
$$609$$ 0 0
$$610$$ 1821.05 0.120873
$$611$$ −5122.08 + 8871.70i −0.339144 + 0.587415i
$$612$$ 7374.62 + 12773.2i 0.487094 + 0.843671i
$$613$$ −4993.63 8649.23i −0.329023 0.569884i 0.653295 0.757103i $$-0.273386\pi$$
−0.982318 + 0.187219i $$0.940053\pi$$
$$614$$ −1271.63 + 2202.53i −0.0835811 + 0.144767i
$$615$$ −694.583 −0.0455419
$$616$$ 0 0
$$617$$ −21076.1 −1.37519 −0.687593 0.726096i $$-0.741333\pi$$
−0.687593 + 0.726096i $$0.741333\pi$$
$$618$$ −502.240 + 869.906i −0.0326910 + 0.0566226i
$$619$$ −157.334 272.511i −0.0102161 0.0176949i 0.860872 0.508821i $$-0.169919\pi$$
−0.871088 + 0.491126i $$0.836585\pi$$
$$620$$ 968.036 + 1676.69i 0.0627052 + 0.108609i
$$621$$ −906.197 + 1569.58i −0.0585579 + 0.101425i
$$622$$ 15373.3 0.991018
$$623$$ 0 0
$$624$$ −129.860 −0.00833103
$$625$$ −312.500 + 541.266i −0.0200000 + 0.0346410i
$$626$$ 4989.25 + 8641.63i 0.318547 + 0.551740i
$$627$$ 832.515 + 1441.96i 0.0530262 + 0.0918442i
$$628$$ 5418.66 9385.39i 0.344312 0.596366i
$$629$$ 20963.7 1.32890
$$630$$ 0 0
$$631$$ 3314.96 0.209138 0.104569 0.994518i $$-0.466654\pi$$
0.104569 + 0.994518i $$0.466654\pi$$
$$632$$ 6585.21 11405.9i 0.414471 0.717884i
$$633$$ −336.550 582.922i −0.0211322 0.0366020i
$$634$$ 5777.65 + 10007.2i 0.361924 + 0.626871i
$$635$$ 4389.39 7602.64i 0.274311 0.475121i
$$636$$ −475.119 −0.0296221
$$637$$ 0 0
$$638$$ −13210.8 −0.819782
$$639$$ −1224.08 + 2120.17i −0.0757807 + 0.131256i
$$640$$ 2621.46 + 4540.50i 0.161910 + 0.280436i
$$641$$ −1502.56 2602.51i −0.0925858 0.160363i 0.816013 0.578034i $$-0.196180\pi$$
−0.908598 + 0.417671i $$0.862847\pi$$
$$642$$ −300.367 + 520.250i −0.0184650 + 0.0319823i
$$643$$ −21225.7 −1.30180 −0.650902 0.759162i $$-0.725609\pi$$
−0.650902 + 0.759162i $$0.725609\pi$$
$$644$$ 0 0
$$645$$ 517.931 0.0316178
$$646$$ −6210.82 + 10757.5i −0.378269 + 0.655180i
$$647$$ −1370.18 2373.21i −0.0832568 0.144205i 0.821390 0.570367i $$-0.193199\pi$$
−0.904647 + 0.426162i $$0.859866\pi$$
$$648$$ 7904.26 + 13690.6i 0.479180 + 0.829964i
$$649$$ −18020.3 + 31212.1i −1.08992 + 1.88780i
$$650$$ −2833.21 −0.170966
$$651$$ 0 0
$$652$$ 10324.6 0.620157
$$653$$ −11395.3 + 19737.3i −0.682900 + 1.18282i 0.291191 + 0.956665i $$0.405948\pi$$
−0.974092 + 0.226153i $$0.927385\pi$$
$$654$$ −162.536 281.521i −0.00971817 0.0168324i
$$655$$ 4522.74 + 7833.62i 0.269799 + 0.467305i
$$656$$ 1189.44 2060.16i 0.0707922 0.122616i
$$657$$ 23723.8 1.40876
$$658$$ 0 0
$$659$$ 19405.1 1.14706 0.573532 0.819183i $$-0.305573\pi$$
0.573532 + 0.819183i $$0.305573\pi$$
$$660$$ 304.405 527.245i 0.0179530 0.0310954i
$$661$$ 7818.63 + 13542.3i 0.460075 + 0.796873i 0.998964 0.0455035i $$-0.0144892\pi$$
−0.538889 + 0.842377i $$0.681156\pi$$
$$662$$ −815.510 1412.50i −0.0478787 0.0829283i
$$663$$ −1188.36 + 2058.29i −0.0696108 + 0.120569i
$$664$$ 1556.23 0.0909538
$$665$$ 0 0
$$666$$ 8947.59 0.520589
$$667$$ −5792.12 + 10032.3i −0.336240 + 0.582384i
$$668$$ −7505.14 12999.3i −0.434704 0.752930i
$$669$$ 723.008 + 1252.29i 0.0417834 + 0.0723710i
$$670$$ −334.090 + 578.660i −0.0192642 + 0.0333666i
$$671$$ 15300.8 0.880299
$$672$$ 0 0
$$673$$ −2579.54 −0.147747 −0.0738735 0.997268i $$-0.523536\pi$$
−0.0738735 + 0.997268i $$0.523536\pi$$
$$674$$ −43.0289 + 74.5282i −0.00245907 + 0.00425923i
$$675$$ 224.238 + 388.392i 0.0127866 + 0.0221470i
$$676$$ 6535.06 + 11319.1i 0.371817 + 0.644006i
$$677$$ 4079.78 7066.39i 0.231608 0.401157i −0.726673 0.686983i $$-0.758935\pi$$
0.958282 + 0.285826i $$0.0922680\pi$$
$$678$$ −496.351 −0.0281154
$$679$$ 0 0
$$680$$ 11453.1 0.645892
$$681$$ −440.676 + 763.272i −0.0247969 + 0.0429496i
$$682$$ −4242.88 7348.88i −0.238223 0.412615i
$$683$$ 10264.6 + 17778.9i 0.575059 + 0.996032i 0.996035 + 0.0889598i $$0.0283543\pi$$
−0.420976 + 0.907072i $$0.638312\pi$$
$$684$$ 5081.71 8801.77i 0.284070 0.492024i
$$685$$ −92.5670 −0.00516321
$$686$$ 0 0
$$687$$ 481.053 0.0267151
$$688$$ −886.930 + 1536.21i −0.0491481 + 0.0851270i
$$689$$ 9288.84 + 16088.7i 0.513609 + 0.889597i
$$690$$ 139.241 + 241.173i 0.00768235 + 0.0133062i
$$691$$ −458.647 + 794.401i −0.0252500 + 0.0437343i −0.878374 0.477973i $$-0.841372\pi$$
0.853124 + 0.521708i $$0.174705\pi$$
$$692$$ −8165.92 −0.448586
$$693$$ 0 0
$$694$$ −18714.3 −1.02361
$$695$$ −1564.02 + 2708.96i −0.0853621 + 0.147851i
$$696$$ −419.005 725.737i −0.0228194 0.0395244i
$$697$$ −21769.2 37705.4i −1.18302 2.04906i
$$698$$ −1670.06 + 2892.63i −0.0905628 + 0.156859i
$$699$$ −2079.19 −0.112507
$$700$$ 0 0
$$701$$ −10491.3 −0.565266 −0.282633 0.959228i $$-0.591208\pi$$
−0.282633 + 0.959228i $$0.591208\pi$$
$$702$$ −1016.50 + 1760.63i −0.0546516 + 0.0946594i
$$703$$ −7222.84 12510.3i −0.387503 0.671175i
$$704$$ −9075.85 15719.8i −0.485879 0.841567i
$$705$$ 124.581 215.780i 0.00665530 0.0115273i
$$706$$ 12568.5 0.670005
$$707$$ 0 0
$$708$$ −906.623 −0.0481257
$$709$$ −11918.8 + 20643.9i −0.631339 + 1.09351i 0.355939 + 0.934509i $$0.384161\pi$$
−0.987278 + 0.159002i $$0.949172\pi$$
$$710$$ 376.946 + 652.889i 0.0199247 + 0.0345106i
$$711$$ 8065.11 + 13969.2i 0.425408 + 0.736828i
$$712$$ −8810.52 + 15260.3i −0.463748 + 0.803234i
$$713$$ −7440.96 −0.390836
$$714$$ 0 0
$$715$$ −23805.2 −1.24512
$$716$$ 709.338 1228.61i 0.0370240 0.0641275i
$$717$$ −223.074 386.376i −0.0116190 0.0201248i
$$718$$ −7232.22 12526.6i −0.375911 0.651097i
$$719$$ −1963.10 + 3400.18i −0.101824 + 0.176364i −0.912436 0.409219i $$-0.865801\pi$$
0.810612 + 0.585583i $$0.199134\pi$$
$$720$$ −766.413 −0.0396702
$$721$$ 0 0
$$722$$ −2799.42 −0.144299
$$723$$ 560.902 971.512i 0.0288523 0.0499736i
$$724$$ −5861.05 10151.6i −0.300862 0.521109i
$$725$$ 1433.26 + 2482.47i 0.0734205 + 0.127168i
$$726$$ −967.322 + 1675.45i −0.0494500 + 0.0856499i
$$727$$ 21071.2 1.07495 0.537474 0.843281i $$-0.319379\pi$$
0.537474 + 0.843281i $$0.319379\pi$$
$$728$$ 0 0
$$729$$ −19200.0 −0.975459
$$730$$ 3652.78 6326.81i 0.185199 0.320775i
$$731$$ 16232.7 + 28115.8i 0.821324 + 1.42257i
$$732$$ 192.451 + 333.334i 0.00971745 + 0.0168311i
$$733$$ −11420.3 + 19780.6i −0.575470 + 0.996744i 0.420520 + 0.907283i $$0.361848\pi$$
−0.995990 + 0.0894605i $$0.971486\pi$$
$$734$$ 3130.86 0.157441
$$735$$ 0 0
$$736$$ −18699.0 −0.936485
$$737$$ −2807.08 + 4862.01i −0.140299 + 0.243004i
$$738$$ −9291.39 16093.2i −0.463443 0.802706i
$$739$$ −5418.67 9385.42i −0.269728 0.467183i 0.699063 0.715060i $$-0.253600\pi$$
−0.968792 + 0.247877i $$0.920267\pi$$
$$740$$ −2640.99 + 4574.34i −0.131196 + 0.227238i
$$741$$ 1637.75 0.0811931
$$742$$ 0 0
$$743$$ −21631.9 −1.06810 −0.534050 0.845453i $$-0.679331\pi$$
−0.534050 + 0.845453i $$0.679331\pi$$
$$744$$ 269.141 466.166i 0.0132624 0.0229711i
$$745$$ 2571.58 + 4454.11i 0.126464 + 0.219042i
$$746$$ −2247.18 3892.23i −0.110288 0.191025i
$$747$$ −952.980 + 1650.61i −0.0466770 + 0.0808469i
$$748$$ 38161.9 1.86543
$$749$$ 0 0
$$750$$ 68.9103 0.00335500
$$751$$ 8089.58 14011.6i 0.393067 0.680812i −0.599786 0.800161i $$-0.704747\pi$$
0.992852 + 0.119349i $$0.0380808\pi$$
$$752$$ 426.676 + 739.025i 0.0206905 + 0.0358370i
$$753$$ −597.973 1035.72i −0.0289394 0.0501245i
$$754$$ −6497.16 + 11253.4i −0.313810 + 0.543535i
$$755$$ 355.037 0.0171140
$$756$$ 0 0
$$757$$ −40930.9 −1.96520 −0.982601 0.185727i $$-0.940536\pi$$
−0.982601 + 0.185727i $$0.940536\pi$$
$$758$$ −7403.59 + 12823.4i −0.354763 + 0.614467i
$$759$$ 1169.93 + 2026.38i 0.0559496 + 0.0969075i
$$760$$ −3946.05 6834.77i −0.188340 0.326215i
$$761$$ 1591.99 2757.40i 0.0758337 0.131348i −0.825615 0.564234i $$-0.809172\pi$$
0.901449 + 0.432886i $$0.142505\pi$$
$$762$$ −967.917 −0.0460157
$$763$$ 0 0
$$764$$ 2449.55 0.115997
$$765$$ −7013.49 + 12147.7i −0.331468 + 0.574120i
$$766$$ −7695.62 13329.2i −0.362995 0.628726i
$$767$$ 17725.0 + 30700.6i 0.834436 + 1.44529i
$$768$$ 636.438 1102.34i 0.0299030 0.0517935i
$$769$$ −33595.8 −1.57542 −0.787708 0.616048i $$-0.788733\pi$$
−0.787708 + 0.616048i $$0.788733\pi$$
$$770$$ 0 0
$$771$$ 0.947940 4.42791e−5
$$772$$ −11604.4 + 20099.5i −0.541000 + 0.937040i
$$773$$ 17193.0 + 29779.1i 0.799986 + 1.38562i 0.919624 + 0.392799i $$0.128493\pi$$
−0.119638 + 0.992818i $$0.538174\pi$$
$$774$$ 6928.33 + 12000.2i 0.321749 + 0.557285i
$$775$$ −920.631 + 1594.58i −0.0426710 + 0.0739084i
$$776$$ 3197.72 0.147927