# Properties

 Label 245.4.e.p.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.p.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 0.881597 0.472003i $$-0.156469\pi$$
−0.849565 + 0.527484i $$0.823135\pi$$
$$4$$ 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 $$-0.239524\pi$$
0.729991 + 0.683456i $$0.239524\pi$$
$$14$$ 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 $$-0.899479\pi$$
0.206309 0.978487i $$-0.433855\pi$$
$$18$$ 22.2651 + 38.5643i 0.291552 + 0.504982i
$$19$$ −35.9465 + 62.2611i −0.434036 + 0.751772i −0.997216 0.0745616i $$-0.976244\pi$$
0.563180 + 0.826334i $$0.309578\pi$$
$$20$$ 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 0.952762 0.303716i $$-0.0982275\pi$$
−0.739407 + 0.673258i $$0.764894\pi$$
$$32$$ −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 $$-0.207583\pi$$
0.794786 + 0.606889i $$0.207583\pi$$
$$42$$ 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 $$-0.907956\pi$$
0.726189 + 0.687495i $$0.241290\pi$$
$$48$$ −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 $$0.0269864\pi$$
−0.424870 + 0.905254i $$0.639680\pi$$
$$60$$ 4.37536 + 7.57834i 0.00941427 + 0.0163060i
$$61$$ 109.963 190.461i 0.230808 0.399771i −0.727238 0.686385i $$-0.759196\pi$$
0.958046 + 0.286614i $$0.0925297\pi$$
$$62$$ −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 $$-0.916588\pi$$
0.258579 0.965990i $$-0.416746\pi$$
$$74$$ 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 $$-0.485076\pi$$
0.0468694 + 0.998901i $$0.485076\pi$$
$$84$$ 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 $$-0.991952\pi$$
0.521733 + 0.853109i $$0.325286\pi$$
$$90$$ 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 $$-0.475712\pi$$
0.0762283 + 0.997090i $$0.475712\pi$$
$$98$$ 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 $$-0.0679670\pi$$
−0.672161 + 0.740405i $$0.734634\pi$$
$$102$$ 28.7581 + 49.8105i 0.0279165 + 0.0483527i
$$103$$ 911.040 1577.97i 0.871528 1.50953i 0.0111125 0.999938i $$-0.496463\pi$$
0.860416 0.509593i $$-0.170204\pi$$
$$104$$ −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 $$0.372810\pi$$
−0.992319 + 0.123702i $$0.960523\pi$$
$$132$$ 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 $$-0.561133\pi$$
−0.190875 + 0.981614i $$0.561133\pi$$
$$140$$ 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 $$0.00886484\pi$$
−0.475691 + 0.879613i $$0.657802\pi$$
$$158$$ −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 $$-0.269934\pi$$
0.661467 + 0.749974i $$0.269934\pi$$
$$168$$ 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 $$-0.722468\pi$$
0.984673 + 0.174408i $$0.0558011\pi$$
$$174$$ 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 $$-0.348635\pi$$
0.457806 + 0.889052i $$0.348635\pi$$
$$182$$ 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 $$-0.838317\pi$$
0.0156567 0.999877i $$-0.495016\pi$$
$$200$$ 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 $$-0.273842\pi$$
0.652211 + 0.758037i $$0.273842\pi$$
$$224$$ 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 $$-0.0401560\pi$$
−0.604989 + 0.796234i $$0.706823\pi$$
$$228$$ −62.9114 108.966i −0.0182737 0.0316510i
$$229$$ 722.545 1251.49i 0.208503 0.361137i −0.742740 0.669580i $$-0.766474\pi$$
0.951243 + 0.308442i $$0.0998076\pi$$
$$230$$ 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 0.548044 0.836449i $$-0.315373\pi$$
−0.998409 + 0.0563953i $$0.982039\pi$$
$$242$$ −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 $$-0.649191\pi$$
−0.451724 + 0.892158i $$0.649191\pi$$
$$252$$ 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 $$-0.833223\pi$$
0.866198 + 0.499701i $$0.166557\pi$$
$$258$$ −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 0.936313 0.351168i $$-0.114215\pi$$
−0.772276 + 0.635287i $$0.780882\pi$$
$$270$$ 74.2704 + 128.640i 0.0167406 + 0.0289955i
$$271$$ −4027.25 + 6975.40i −0.902724 + 1.56356i −0.0787797 + 0.996892i $$0.525102\pi$$
−0.823944 + 0.566671i $$0.808231\pi$$
$$272$$ 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 0.637244 0.770662i $$-0.280074\pi$$
−0.986035 + 0.166538i $$0.946741\pi$$
$$284$$ −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 $$-0.667921\pi$$
−0.503408 + 0.864049i $$0.667921\pi$$
$$294$$ 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 $$-0.545595\pi$$
−0.142750 + 0.989759i $$0.545595\pi$$
$$308$$ 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 $$0.154503\pi$$
−0.0382037 + 0.999270i $$0.512164\pi$$
$$312$$ −250.073 433.140i −0.0453770 0.0785952i
$$313$$ −3012.72 + 5218.18i −0.544054 + 0.942329i 0.454612 + 0.890690i $$0.349778\pi$$
−0.998666 + 0.0516393i $$0.983555\pi$$
$$314$$ −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 $$-0.549433\pi$$
−0.154674 + 0.987966i $$0.549433\pi$$
$$350$$ 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 $$0.0272270\pi$$
−0.424186 + 0.905575i $$0.639440\pi$$
$$354$$ −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 0.925387 0.379024i $$-0.123740\pi$$
−0.790938 + 0.611896i $$0.790407\pi$$
$$368$$ 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 $$-0.620479\pi$$
0.989491 0.144594i $$-0.0461876\pi$$
$$384$$ 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 −0.728371 0.685183i $$-0.759722\pi$$
0.957571 + 0.288196i $$0.0930556\pi$$
$$398$$ 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 $$0.176718\pi$$
0.0315714 + 0.999502i $$0.489949\pi$$
$$410$$ 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 $$-0.547261\pi$$
−0.147931 + 0.988998i $$0.547261\pi$$
$$420$$ 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 $$-0.283231\pi$$
0.629570 + 0.776944i $$0.283231\pi$$
$$434$$ 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 $$0.386212\pi$$
−0.986233 + 0.165360i $$0.947121\pi$$
$$440$$ 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 $$-0.492722\pi$$
0.0228614 + 0.999739i $$0.492722\pi$$
$$462$$ 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 $$-0.848697\pi$$
0.840894 + 0.541200i $$0.182030\pi$$
$$468$$ 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 $$-0.320002\pi$$
−0.999123 + 0.0418680i $$0.986669\pi$$
$$480$$ −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 $$-0.525037\pi$$
−0.0785757 + 0.996908i $$0.525037\pi$$
$$504$$ 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 $$-0.877153\pi$$
0.789218 + 0.614113i $$0.210486\pi$$
$$510$$ 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 $$-0.0131778\pi$$
−0.535414 + 0.844590i $$0.679844\pi$$
$$522$$ −2552.93 4421.80i −0.214059 0.370760i
$$523$$ −7224.21 + 12512.7i −0.604002 + 1.04616i 0.388207 + 0.921572i $$0.373095\pi$$
−0.992208 + 0.124589i $$0.960239\pi$$
$$524$$ −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 0.957917 0.287046i $$-0.0926732\pi$$
−0.727547 + 0.686057i $$0.759340\pi$$
$$564$$ −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 0.783401 0.621517i $$-0.213483\pi$$
−0.929950 + 0.367686i $$0.880150\pi$$
$$578$$ −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 $$-0.595280\pi$$
−0.294880 + 0.955534i $$0.595280\pi$$
$$588$$ 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 $$-0.655061\pi$$
0.999335 0.0364520i $$-0.0116056\pi$$
$$594$$ 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 $$-0.723087\pi$$
−0.644866 + 0.764295i $$0.723087\pi$$
$$602$$ 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 $$0.610973\pi$$
−0.643121 + 0.765765i $$0.722361\pi$$
$$608$$ 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 0.871088 0.491126i $$-0.163415\pi$$
−0.860872 + 0.508821i $$0.830081\pi$$
$$620$$ 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 $$-0.274391\pi$$
0.650902 + 0.759162i $$0.274391\pi$$
$$644$$ 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 $$-0.140134\pi$$
−0.821390 + 0.570367i $$0.806801\pi$$
$$648$$ 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 0.538889 0.842377i $$-0.318844\pi$$
−0.998964 + 0.0455035i $$0.985511\pi$$
$$662$$ −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 $$-0.907732\pi$$
0.726673 + 0.686983i $$0.241065\pi$$
$$678$$ 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 −0.853124 0.521708i $$-0.825295\pi$$
0.878374 + 0.477973i $$0.158628\pi$$
$$692$$ 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 −0.810612 0.585583i $$-0.800866\pi$$
0.912436 + 0.409219i $$0.134199\pi$$
$$720$$ 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 $$-0.680621\pi$$
−0.537474 + 0.843281i $$0.680621\pi$$
$$728$$ 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 $$-0.638152\pi$$
0.995990 0.0894605i $$-0.0285143\pi$$
$$734$$ −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 −0.901449 0.432886i $$-0.857495\pi$$
0.825615 + 0.564234i $$0.190828\pi$$
$$762$$ 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 $$-0.211267\pi$$
0.787708 + 0.616048i $$0.211267\pi$$
$$770$$ 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 $$-0.871507\pi$$
0.119638 0.992818i $$-0.461826\pi$$
$$774$$ 6928.33 + 12000.2i 0.321749 + 0.557285i
$$775$$ 920.631 1594.58i 0.0426710 0.0739084i
$$776$$ −3197.72 −0.147927