# Properties

 Label 245.4.e.q.116.2 Level $245$ Weight $4$ Character 245.116 Analytic conductor $14.455$ Analytic rank $0$ Dimension $12$ CM no Inner twists $2$

# Learn more

## 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 116.2 Root $$-0.120924 + 0.209447i$$ of defining polynomial Character $$\chi$$ $$=$$ 245.116 Dual form 245.4.e.q.226.2

## $q$-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 $$\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$$.

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

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.828031 1.43419i −0.292753 0.507063i 0.681707 0.731626i $$-0.261238\pi$$
−0.974460 + 0.224562i $$0.927905\pi$$
$$3$$ −0.166444 + 0.288289i −0.0320321 + 0.0554813i −0.881597 0.472003i $$-0.843531\pi$$
0.849565 + 0.527484i $$0.176865\pi$$
$$4$$ 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 −0.215727 + 0.976454i $$0.569212\pi$$
−0.737770 + 0.675052i $$0.764121\pi$$
$$12$$ 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 −0.206309 0.978487i $$-0.566145\pi$$
0.950549 0.310574i $$-0.100521\pi$$
$$18$$ 22.2651 38.5643i 0.291552 0.504982i
$$19$$ 35.9465 + 62.2611i 0.434036 + 0.751772i 0.997216 0.0745616i $$-0.0237557\pi$$
−0.563180 + 0.826334i $$0.690422\pi$$
$$20$$ −26.2873 −0.293901
$$21$$ 0 0
$$22$$ 115.217 1.11656
$$23$$ 50.5154 + 87.4952i 0.457964 + 0.793218i 0.998853 0.0478764i $$-0.0152453\pi$$
−0.540889 + 0.841094i $$0.681912\pi$$
$$24$$ 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 −0.952762 0.303716i $$-0.901772\pi$$
0.739407 + 0.673258i $$0.235106\pi$$
$$32$$ −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 0.998148 0.0608289i $$-0.0193744\pi$$
−0.551753 + 0.834007i $$0.686041\pi$$
$$38$$ 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 0.958483 0.285151i $$-0.0920438\pi$$
−0.726189 + 0.687495i $$0.758710\pi$$
$$48$$ 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 −0.986563 0.163379i $$-0.947761\pi$$
0.634772 + 0.772699i $$0.281094\pi$$
$$54$$ 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 0.424870 + 0.905254i $$0.360320\pi$$
−0.996408 + 0.0846788i $$0.973014\pi$$
$$60$$ 4.37536 7.57834i 0.00941427 0.0163060i
$$61$$ −109.963 190.461i −0.230808 0.399771i 0.727238 0.686385i $$-0.240804\pi$$
−0.958046 + 0.286614i $$0.907470\pi$$
$$62$$ 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 −0.900464 0.434931i $$-0.856773\pi$$
0.826893 + 0.562359i $$0.190106\pi$$
$$68$$ −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 −0.258579 0.965990i $$-0.583254\pi$$
0.965861 0.259059i $$-0.0834125\pi$$
$$74$$ 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 0.569458 0.822020i $$-0.307153\pi$$
−0.996620 + 0.0821553i $$0.973820\pi$$
$$80$$ −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 0.999680 0.0252802i $$-0.00804778\pi$$
−0.521733 + 0.853109i $$0.674714\pi$$
$$90$$ −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 −0.977290 0.211906i $$-0.932033\pi$$
0.672161 + 0.740405i $$0.265366\pi$$
$$102$$ 28.7581 49.8105i 0.0279165 0.0483527i
$$103$$ −911.040 1577.97i −0.871528 1.50953i −0.860416 0.509593i $$-0.829796\pi$$
−0.0111125 0.999938i $$-0.503537\pi$$
$$104$$ 1502.45 1.41661
$$105$$ 0 0
$$106$$ 449.578 0.411952
$$107$$ −544.851 943.709i −0.492268 0.852634i 0.507692 0.861539i $$-0.330499\pi$$
−0.999960 + 0.00890504i $$0.997165\pi$$
$$108$$ −47.1569 + 81.6781i −0.0420155 + 0.0727730i
$$109$$ −294.833 + 510.666i −0.259082 + 0.448743i −0.965996 0.258556i $$-0.916753\pi$$
0.706914 + 0.707299i $$0.250087\pi$$
$$110$$ −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 0.992319 + 0.123702i $$0.0394766\pi$$
−0.389031 + 0.921225i $$0.627190\pi$$
$$132$$ −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 −0.863125 0.504991i $$-0.831496\pi$$
0.868897 + 0.494992i $$0.164829\pi$$
$$138$$ 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 0.972069 0.234696i $$-0.0754095\pi$$
−0.689287 + 0.724488i $$0.742076\pi$$
$$150$$ −6.89103 + 11.9356i −0.00375100 + 0.00649693i
$$151$$ −35.5037 + 61.4942i −0.0191341 + 0.0331412i −0.875434 0.483338i $$-0.839424\pi$$
0.856300 + 0.516479i $$0.172758\pi$$
$$152$$ −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 0.475691 + 0.879613i $$0.342198\pi$$
−0.999612 + 0.0278461i $$0.991135\pi$$
$$158$$ −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 0.999481 0.0322280i $$-0.0102603\pi$$
−0.527651 + 0.849462i $$0.676927\pi$$
$$164$$ −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 0.643378 0.765548i $$-0.277532\pi$$
−0.984673 + 0.174408i $$0.944199\pi$$
$$174$$ −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 −0.892819 0.450416i $$-0.851276\pi$$
0.836481 + 0.547996i $$0.184609\pi$$
$$180$$ −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 0.906773 0.421619i $$-0.138538\pi$$
−0.818520 + 0.574479i $$0.805205\pi$$
$$192$$ −43.4257 + 75.2154i −0.0163228 + 0.0282719i
$$193$$ 2207.23 3823.04i 0.823212 1.42585i −0.0800657 0.996790i $$-0.525513\pi$$
0.903278 0.429056i $$-0.141154\pi$$
$$194$$ 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 −0.0156567 0.999877i $$-0.504984\pi$$
0.873748 0.486380i $$-0.161683\pi$$
$$200$$ 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 −0.992053 0.125819i $$-0.959844\pi$$
0.604989 + 0.796234i $$0.293177\pi$$
$$228$$ −62.9114 + 108.966i −0.0182737 + 0.0316510i
$$229$$ −722.545 1251.49i −0.208503 0.361137i 0.742740 0.669580i $$-0.233526\pi$$
−0.951243 + 0.308442i $$0.900192\pi$$
$$230$$ −836.566 −0.239833
$$231$$ 0 0
$$232$$ 2517.39 0.712392
$$233$$ 3122.96 + 5409.12i 0.878076 + 1.52087i 0.853450 + 0.521175i $$0.174506\pi$$
0.0246255 + 0.999697i $$0.492161\pi$$
$$234$$ −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 −0.548044 0.836449i $$-0.684627\pi$$
0.998409 + 0.0563953i $$0.0179607\pi$$
$$242$$ −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 0.865853 0.500299i $$-0.166777\pi$$
−0.866198 + 0.499701i $$0.833443\pi$$
$$258$$ 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 −0.652316 0.757947i $$-0.726202\pi$$
0.982560 + 0.185948i $$0.0595357\pi$$
$$264$$ 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 −0.936313 0.351168i $$-0.885785\pi$$
0.772276 + 0.635287i $$0.219118\pi$$
$$270$$ 74.2704 128.640i 0.0167406 0.0289955i
$$271$$ 4027.25 + 6975.40i 0.902724 + 1.56356i 0.823944 + 0.566671i $$0.191769\pi$$
0.0787797 + 0.996892i $$0.474898\pi$$
$$272$$ −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 −0.833381 0.552699i $$-0.813598\pi$$
0.895342 + 0.445380i $$0.146931\pi$$
$$278$$ −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 −0.637244 0.770662i $$-0.719926\pi$$
0.986035 + 0.166538i $$0.0532590\pi$$
$$284$$ −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 0.0382037 + 0.999270i $$0.487836\pi$$
−0.884495 + 0.466550i $$0.845497\pi$$
$$312$$ −250.073 + 433.140i −0.0453770 + 0.0785952i
$$313$$ 3012.72 + 5218.18i 0.544054 + 0.942329i 0.998666 + 0.0516393i $$0.0164446\pi$$
−0.454612 + 0.890690i $$0.650222\pi$$
$$314$$ 3413.68 0.613519
$$315$$ 0 0
$$316$$ −3153.83 −0.561445
$$317$$ 3488.79 + 6042.76i 0.618139 + 1.07065i 0.989825 + 0.142289i $$0.0454464\pi$$
−0.371686 + 0.928358i $$0.621220\pi$$
$$318$$ −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 0.822239 0.569143i $$-0.192725\pi$$
−0.904012 + 0.427508i $$0.859392\pi$$
$$332$$ −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 0.0164299 0.999865i $$-0.494770\pi$$
0.857694 0.514161i $$-0.171897\pi$$
$$348$$ −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 0.424186 + 0.905575i $$0.360560\pi$$
−0.996344 + 0.0854319i $$0.972773\pi$$
$$354$$ −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 −0.984980 0.172671i $$-0.944760\pi$$
0.342952 0.939353i $$-0.388573\pi$$
$$360$$ −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 −0.925387 0.379024i $$-0.876260\pi$$
0.790938 + 0.611896i $$0.209593\pi$$
$$368$$ 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 0.756341 0.654178i $$-0.226985\pi$$
−0.944705 + 0.327922i $$0.893652\pi$$
$$374$$ 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 −0.989491 0.144594i $$-0.953812\pi$$
0.369524 0.929221i $$-0.379521\pi$$
$$384$$ −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 0.293242 + 0.956038i $$0.405266\pi$$
−0.974574 + 0.224065i $$0.928067\pi$$
$$390$$ 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 0.728371 0.685183i $$-0.240278\pi$$
−0.957571 + 0.288196i $$0.906944\pi$$
$$398$$ −7978.47 −1.00484
$$399$$ 0 0
$$400$$ 142.513 0.0178141
$$401$$ 4211.26 + 7294.12i 0.524440 + 0.908356i 0.999595 + 0.0284542i $$0.00905846\pi$$
−0.475156 + 0.879902i $$0.657608\pi$$
$$402$$ −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 −0.0315714 + 0.999502i $$0.510051\pi$$
−0.849808 + 0.527092i $$0.823282\pi$$
$$410$$ 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 −0.588588 0.808433i $$-0.700316\pi$$
0.994418 + 0.105515i $$0.0336492\pi$$
$$432$$ 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 0.986233 + 0.165360i $$0.0528786\pi$$
−0.349911 + 0.936783i $$0.613788\pi$$
$$440$$ −7637.40 −0.827497
$$441$$ 0 0
$$442$$ 11823.8 1.27240
$$443$$ −7538.99 13057.9i −0.808551 1.40045i −0.913867 0.406013i $$-0.866919\pi$$
0.105316 0.994439i $$-0.466415\pi$$
$$444$$ −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 0.998308 + 0.0581472i $$0.0185193\pi$$
−0.448797 + 0.893634i $$0.648147\pi$$
$$458$$ −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 0.889140 0.457635i $$-0.151303\pi$$
−0.840894 + 0.541200i $$0.817970\pi$$
$$468$$ −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 −0.535820 0.844332i $$-0.679998\pi$$
0.999123 + 0.0418680i $$0.0133309\pi$$
$$480$$ −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 −0.886706 0.462334i $$-0.847012\pi$$
0.843746 + 0.536743i $$0.180345\pi$$
$$488$$ 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 0.864608 + 0.502447i $$0.167567\pi$$
0.00282829 + 0.999996i $$0.499100\pi$$
$$500$$ 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 0.926447 0.376426i $$-0.122847\pi$$
−0.789218 + 0.614113i $$0.789514\pi$$
$$510$$ −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 −0.999143 0.0413875i $$-0.986822\pi$$
0.535414 + 0.844590i $$0.320156\pi$$
$$522$$ −2552.93 + 4421.80i −0.214059 + 0.370760i
$$523$$ 7224.21 + 12512.7i 0.604002 + 1.04616i 0.992208 + 0.124589i $$0.0397613\pi$$
−0.388207 + 0.921572i $$0.626905\pi$$
$$524$$ 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 0.845609 + 0.533802i $$0.179237\pi$$
0.0394817 + 0.999220i $$0.487429\pi$$
$$542$$ 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 −0.0940446 0.995568i $$-0.529980\pi$$
0.909209 0.416339i $$-0.136687\pi$$
$$558$$ 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 −0.957917 0.287046i $$-0.907327\pi$$
0.727547 + 0.686057i $$0.240660\pi$$
$$564$$ −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 0.978160 0.207853i $$-0.0666475\pi$$
−0.669086 + 0.743185i $$0.733314\pi$$
$$570$$ 99.0833 171.617i 0.00728095 0.0126110i
$$571$$ 300.251 520.050i 0.0220055 0.0381146i −0.854813 0.518936i $$-0.826328\pi$$
0.876818 + 0.480822i $$0.159662\pi$$
$$572$$ −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 −0.783401 0.621517i $$-0.786517\pi$$
0.929950 + 0.367686i $$0.119850\pi$$
$$578$$ −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 −0.999335 0.0364520i $$-0.988394\pi$$
0.468099 0.883676i $$-0.344939\pi$$
$$594$$ −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 −0.305111 0.952317i $$-0.598694\pi$$
0.977286 0.211925i $$-0.0679731\pi$$
$$600$$ 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 0.643121 + 0.765765i $$0.277639\pi$$
0.341612 + 0.939841i $$0.389027\pi$$
$$608$$ −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 −0.982318 0.187219i $$-0.940053\pi$$
0.653295 + 0.757103i $$0.273386\pi$$
$$614$$ −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 −0.871088 0.491126i $$-0.836585\pi$$
0.860872 + 0.508821i $$0.169919\pi$$
$$620$$ 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 −0.908598 0.417671i $$-0.862847\pi$$
0.816013 + 0.578034i $$0.196180\pi$$
$$642$$ −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 −0.904647 0.426162i $$-0.859866\pi$$
0.821390 + 0.570367i $$0.193199\pi$$
$$648$$ 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 −0.974092 0.226153i $$-0.927385\pi$$
0.291191 0.956665i $$-0.405948\pi$$
$$654$$ −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 −0.538889 0.842377i $$-0.681156\pi$$
0.998964 + 0.0455035i $$0.0144892\pi$$
$$662$$ −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 0.958282 0.285826i $$-0.0922680\pi$$
−0.726673 + 0.686983i $$0.758935\pi$$
$$678$$ −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 −0.420976 0.907072i $$-0.638312\pi$$
0.996035 0.0889598i $$-0.0283543\pi$$
$$684$$ 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 0.853124 0.521708i $$-0.174705\pi$$
−0.878374 + 0.477973i $$0.841372\pi$$
$$692$$ −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 −0.987278 0.159002i $$-0.949172\pi$$
0.355939 0.934509i $$-0.384161\pi$$
$$710$$ 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 0.810612 0.585583i $$-0.199134\pi$$
−0.912436 + 0.409219i $$0.865801\pi$$
$$720$$ −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 −0.995990 0.0894605i $$-0.971486\pi$$
0.420520 0.907283i $$-0.361848\pi$$
$$734$$ 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 −0.968792 0.247877i $$-0.920267\pi$$
0.699063 + 0.715060i $$0.253600\pi$$
$$740$$ −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 0.992852 0.119349i $$-0.0380808\pi$$
−0.599786 + 0.800161i $$0.704747\pi$$
$$752$$ 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 0.901449 0.432886i $$-0.142505\pi$$
−0.825615 + 0.564234i $$0.809172\pi$$
$$762$$ −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 −0.119638 0.992818i $$-0.538174\pi$$
0.919624 0.392799i $$-0.128493\pi$$
$$774$$ 6928.33 12000.2i 0.321749 0.557285i
$$775$$ −920.631 1594.58i −0.0426710 0.0739084i
$$776$$ 3197.72 0.147927