# Properties

 Label 169.4.e.f.23.3 Level $169$ Weight $4$ Character 169.23 Analytic conductor $9.971$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$169 = 13^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 169.e (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.97132279097$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{6})$$ Coefficient field: 8.0.1731891456.1 Defining polynomial: $$x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256$$ x^8 - 9*x^6 + 65*x^4 - 144*x^2 + 256 Coefficient ring: $$\Z[a_1, \ldots, a_{9}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 13) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 23.3 Root $$1.35234 - 0.780776i$$ of defining polynomial Character $$\chi$$ $$=$$ 169.23 Dual form 169.4.e.f.147.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.35234 - 0.780776i) q^{2} +(-4.34233 - 7.52113i) q^{3} +(-2.78078 + 4.81645i) q^{4} +3.56155i q^{5} +(-11.7446 - 6.78078i) q^{6} +(23.5360 + 13.5885i) q^{7} +21.1771i q^{8} +(-24.2116 + 41.9358i) q^{9} +O(q^{10})$$ $$q+(1.35234 - 0.780776i) q^{2} +(-4.34233 - 7.52113i) q^{3} +(-2.78078 + 4.81645i) q^{4} +3.56155i q^{5} +(-11.7446 - 6.78078i) q^{6} +(23.5360 + 13.5885i) q^{7} +21.1771i q^{8} +(-24.2116 + 41.9358i) q^{9} +(2.78078 + 4.81645i) q^{10} +(13.2167 - 7.63068i) q^{11} +48.3002 q^{12} +42.4384 q^{14} +(26.7869 - 15.4654i) q^{15} +(-5.71165 - 9.89286i) q^{16} +(22.2732 - 38.5783i) q^{17} +75.6155i q^{18} +(20.7584 + 11.9848i) q^{19} +(-17.1540 - 9.90388i) q^{20} -236.024i q^{21} +(11.9157 - 20.6386i) q^{22} +(61.3693 + 106.295i) q^{23} +(159.276 - 91.9579i) q^{24} +112.315 q^{25} +186.054 q^{27} +(-130.897 + 75.5734i) q^{28} +(109.955 + 190.447i) q^{29} +(24.1501 - 41.8292i) q^{30} -27.0928i q^{31} +(-162.167 - 93.6274i) q^{32} +(-114.783 - 66.2699i) q^{33} -69.5616i q^{34} +(-48.3963 + 83.8249i) q^{35} +(-134.654 - 233.228i) q^{36} +(81.5729 - 47.0961i) q^{37} +37.4299 q^{38} -75.4233 q^{40} +(138.871 - 80.1771i) q^{41} +(-184.282 - 319.185i) q^{42} +(-75.6510 + 131.031i) q^{43} +84.8769i q^{44} +(-149.357 - 86.2311i) q^{45} +(165.985 + 95.8314i) q^{46} +466.948i q^{47} +(-49.6037 + 85.9161i) q^{48} +(197.797 + 342.594i) q^{49} +(151.889 - 87.6932i) q^{50} -386.870 q^{51} -120.847 q^{53} +(251.609 - 145.267i) q^{54} +(27.1771 + 47.0721i) q^{55} +(-287.766 + 498.425i) q^{56} -208.169i q^{57} +(297.393 + 171.700i) q^{58} +(380.733 + 219.816i) q^{59} +172.024i q^{60} +(68.6525 - 118.910i) q^{61} +(-21.1534 - 36.6388i) q^{62} +(-1139.69 + 658.002i) q^{63} -201.022 q^{64} -206.968 q^{66} +(-443.648 + 256.140i) q^{67} +(123.874 + 214.555i) q^{68} +(532.972 - 923.134i) q^{69} +151.147i q^{70} +(355.693 + 205.359i) q^{71} +(-888.078 - 512.732i) q^{72} -308.004i q^{73} +(73.5431 - 127.380i) q^{74} +(-487.710 - 844.739i) q^{75} +(-115.449 + 66.6543i) q^{76} +414.759 q^{77} -586.462 q^{79} +(35.2339 - 20.3423i) q^{80} +(-154.193 - 267.070i) q^{81} +(125.201 - 216.854i) q^{82} -1354.20i q^{83} +(1136.80 + 656.329i) q^{84} +(137.399 + 79.3272i) q^{85} +236.266i q^{86} +(954.918 - 1653.97i) q^{87} +(161.596 + 279.892i) q^{88} +(380.949 - 219.941i) q^{89} -269.309 q^{90} -682.617 q^{92} +(-203.769 + 117.646i) q^{93} +(364.582 + 631.474i) q^{94} +(-42.6847 + 73.9320i) q^{95} +1626.24i q^{96} +(-1308.80 - 755.634i) q^{97} +(534.979 + 308.870i) q^{98} +739.006i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q - 10 q^{3} - 14 q^{4} - 70 q^{9}+O(q^{10})$$ 8 * q - 10 * q^3 - 14 * q^4 - 70 * q^9 $$8 q - 10 q^{3} - 14 q^{4} - 70 q^{9} + 14 q^{10} + 172 q^{12} + 356 q^{14} + 78 q^{16} + 38 q^{17} - 284 q^{22} + 392 q^{23} + 948 q^{25} + 1340 q^{27} + 88 q^{29} + 86 q^{30} - 214 q^{35} - 500 q^{36} + 1256 q^{38} - 356 q^{40} - 394 q^{42} + 574 q^{43} - 570 q^{48} + 766 q^{49} - 1924 q^{51} - 472 q^{53} + 36 q^{55} - 2030 q^{56} + 2116 q^{61} - 664 q^{62} - 3076 q^{64} - 3272 q^{66} + 422 q^{68} + 1592 q^{69} - 294 q^{74} - 1032 q^{75} - 3048 q^{77} - 4032 q^{79} - 244 q^{81} + 144 q^{82} + 5116 q^{87} - 2484 q^{88} - 1000 q^{90} - 3152 q^{92} + 1622 q^{94} - 292 q^{95}+O(q^{100})$$ 8 * q - 10 * q^3 - 14 * q^4 - 70 * q^9 + 14 * q^10 + 172 * q^12 + 356 * q^14 + 78 * q^16 + 38 * q^17 - 284 * q^22 + 392 * q^23 + 948 * q^25 + 1340 * q^27 + 88 * q^29 + 86 * q^30 - 214 * q^35 - 500 * q^36 + 1256 * q^38 - 356 * q^40 - 394 * q^42 + 574 * q^43 - 570 * q^48 + 766 * q^49 - 1924 * q^51 - 472 * q^53 + 36 * q^55 - 2030 * q^56 + 2116 * q^61 - 664 * q^62 - 3076 * q^64 - 3272 * q^66 + 422 * q^68 + 1592 * q^69 - 294 * q^74 - 1032 * q^75 - 3048 * q^77 - 4032 * q^79 - 244 * q^81 + 144 * q^82 + 5116 * q^87 - 2484 * q^88 - 1000 * q^90 - 3152 * q^92 + 1622 * q^94 - 292 * q^95

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$$.

 $$n$$ $$2$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.35234 0.780776i 0.478126 0.276046i −0.241509 0.970399i $$-0.577642\pi$$
0.719635 + 0.694352i $$0.244309\pi$$
$$3$$ −4.34233 7.52113i −0.835682 1.44744i −0.893474 0.449114i $$-0.851740\pi$$
0.0577926 0.998329i $$-0.481594\pi$$
$$4$$ −2.78078 + 4.81645i −0.347597 + 0.602056i
$$5$$ 3.56155i 0.318555i 0.987234 + 0.159277i $$0.0509165\pi$$
−0.987234 + 0.159277i $$0.949084\pi$$
$$6$$ −11.7446 6.78078i −0.799122 0.461373i
$$7$$ 23.5360 + 13.5885i 1.27083 + 0.733712i 0.975144 0.221574i $$-0.0711194\pi$$
0.295683 + 0.955286i $$0.404453\pi$$
$$8$$ 21.1771i 0.935904i
$$9$$ −24.2116 + 41.9358i −0.896728 + 1.55318i
$$10$$ 2.78078 + 4.81645i 0.0879359 + 0.152309i
$$11$$ 13.2167 7.63068i 0.362272 0.209158i −0.307805 0.951450i $$-0.599594\pi$$
0.670077 + 0.742292i $$0.266261\pi$$
$$12$$ 48.3002 1.16192
$$13$$ 0 0
$$14$$ 42.4384 0.810154
$$15$$ 26.7869 15.4654i 0.461090 0.266211i
$$16$$ −5.71165 9.89286i −0.0892445 0.154576i
$$17$$ 22.2732 38.5783i 0.317767 0.550389i −0.662255 0.749279i $$-0.730400\pi$$
0.980022 + 0.198890i $$0.0637336\pi$$
$$18$$ 75.6155i 0.990153i
$$19$$ 20.7584 + 11.9848i 0.250647 + 0.144711i 0.620061 0.784554i $$-0.287108\pi$$
−0.369413 + 0.929265i $$0.620441\pi$$
$$20$$ −17.1540 9.90388i −0.191788 0.110729i
$$21$$ 236.024i 2.45260i
$$22$$ 11.9157 20.6386i 0.115474 0.200008i
$$23$$ 61.3693 + 106.295i 0.556365 + 0.963652i 0.997796 + 0.0663568i $$0.0211376\pi$$
−0.441431 + 0.897295i $$0.645529\pi$$
$$24$$ 159.276 91.9579i 1.35467 0.782117i
$$25$$ 112.315 0.898523
$$26$$ 0 0
$$27$$ 186.054 1.32615
$$28$$ −130.897 + 75.5734i −0.883471 + 0.510072i
$$29$$ 109.955 + 190.447i 0.704071 + 1.21949i 0.967026 + 0.254678i $$0.0819694\pi$$
−0.262955 + 0.964808i $$0.584697\pi$$
$$30$$ 24.1501 41.8292i 0.146973 0.254564i
$$31$$ 27.0928i 0.156968i −0.996915 0.0784840i $$-0.974992\pi$$
0.996915 0.0784840i $$-0.0250080\pi$$
$$32$$ −162.167 93.6274i −0.895856 0.517223i
$$33$$ −114.783 66.2699i −0.605488 0.349579i
$$34$$ 69.5616i 0.350874i
$$35$$ −48.3963 + 83.8249i −0.233728 + 0.404828i
$$36$$ −134.654 233.228i −0.623400 1.07976i
$$37$$ 81.5729 47.0961i 0.362446 0.209258i −0.307707 0.951481i $$-0.599562\pi$$
0.670153 + 0.742223i $$0.266228\pi$$
$$38$$ 37.4299 0.159788
$$39$$ 0 0
$$40$$ −75.4233 −0.298137
$$41$$ 138.871 80.1771i 0.528975 0.305404i −0.211624 0.977351i $$-0.567875\pi$$
0.740599 + 0.671947i $$0.234542\pi$$
$$42$$ −184.282 319.185i −0.677031 1.17265i
$$43$$ −75.6510 + 131.031i −0.268295 + 0.464700i −0.968422 0.249318i $$-0.919793\pi$$
0.700127 + 0.714018i $$0.253127\pi$$
$$44$$ 84.8769i 0.290811i
$$45$$ −149.357 86.2311i −0.494773 0.285657i
$$46$$ 165.985 + 95.8314i 0.532025 + 0.307165i
$$47$$ 466.948i 1.44918i 0.689181 + 0.724589i $$0.257970\pi$$
−0.689181 + 0.724589i $$0.742030\pi$$
$$48$$ −49.6037 + 85.9161i −0.149160 + 0.258353i
$$49$$ 197.797 + 342.594i 0.576667 + 0.998817i
$$50$$ 151.889 87.6932i 0.429607 0.248034i
$$51$$ −386.870 −1.06221
$$52$$ 0 0
$$53$$ −120.847 −0.313199 −0.156600 0.987662i $$-0.550053\pi$$
−0.156600 + 0.987662i $$0.550053\pi$$
$$54$$ 251.609 145.267i 0.634068 0.366079i
$$55$$ 27.1771 + 47.0721i 0.0666283 + 0.115404i
$$56$$ −287.766 + 498.425i −0.686684 + 1.18937i
$$57$$ 208.169i 0.483730i
$$58$$ 297.393 + 171.700i 0.673269 + 0.388712i
$$59$$ 380.733 + 219.816i 0.840122 + 0.485045i 0.857306 0.514808i $$-0.172137\pi$$
−0.0171836 + 0.999852i $$0.505470\pi$$
$$60$$ 172.024i 0.370136i
$$61$$ 68.6525 118.910i 0.144099 0.249587i −0.784937 0.619575i $$-0.787305\pi$$
0.929037 + 0.369988i $$0.120638\pi$$
$$62$$ −21.1534 36.6388i −0.0433304 0.0750505i
$$63$$ −1139.69 + 658.002i −2.27917 + 1.31588i
$$64$$ −201.022 −0.392621
$$65$$ 0 0
$$66$$ −206.968 −0.386000
$$67$$ −443.648 + 256.140i −0.808958 + 0.467052i −0.846594 0.532239i $$-0.821351\pi$$
0.0376358 + 0.999292i $$0.488017\pi$$
$$68$$ 123.874 + 214.555i 0.220910 + 0.382627i
$$69$$ 532.972 923.134i 0.929887 1.61061i
$$70$$ 151.147i 0.258078i
$$71$$ 355.693 + 205.359i 0.594549 + 0.343263i 0.766894 0.641774i $$-0.221801\pi$$
−0.172345 + 0.985037i $$0.555134\pi$$
$$72$$ −888.078 512.732i −1.45362 0.839251i
$$73$$ 308.004i 0.493823i −0.969038 0.246912i $$-0.920584\pi$$
0.969038 0.246912i $$-0.0794158\pi$$
$$74$$ 73.5431 127.380i 0.115530 0.200104i
$$75$$ −487.710 844.739i −0.750879 1.30056i
$$76$$ −115.449 + 66.6543i −0.174248 + 0.100602i
$$77$$ 414.759 0.613847
$$78$$ 0 0
$$79$$ −586.462 −0.835217 −0.417608 0.908627i $$-0.637132\pi$$
−0.417608 + 0.908627i $$0.637132\pi$$
$$80$$ 35.2339 20.3423i 0.0492409 0.0284293i
$$81$$ −154.193 267.070i −0.211513 0.366352i
$$82$$ 125.201 216.854i 0.168611 0.292043i
$$83$$ 1354.20i 1.79088i −0.445182 0.895440i $$-0.646861\pi$$
0.445182 0.895440i $$-0.353139\pi$$
$$84$$ 1136.80 + 656.329i 1.47660 + 0.852516i
$$85$$ 137.399 + 79.3272i 0.175329 + 0.101226i
$$86$$ 236.266i 0.296247i
$$87$$ 954.918 1653.97i 1.17676 2.03820i
$$88$$ 161.596 + 279.892i 0.195752 + 0.339052i
$$89$$ 380.949 219.941i 0.453714 0.261952i −0.255683 0.966761i $$-0.582300\pi$$
0.709398 + 0.704809i $$0.248967\pi$$
$$90$$ −269.309 −0.315418
$$91$$ 0 0
$$92$$ −682.617 −0.773563
$$93$$ −203.769 + 117.646i −0.227202 + 0.131175i
$$94$$ 364.582 + 631.474i 0.400040 + 0.692889i
$$95$$ −42.6847 + 73.9320i −0.0460985 + 0.0798449i
$$96$$ 1626.24i 1.72894i
$$97$$ −1308.80 755.634i −1.36998 0.790959i −0.379056 0.925374i $$-0.623751\pi$$
−0.990925 + 0.134414i $$0.957085\pi$$
$$98$$ 534.979 + 308.870i 0.551439 + 0.318374i
$$99$$ 739.006i 0.750231i
$$100$$ −312.324 + 540.961i −0.312324 + 0.540961i
$$101$$ 168.130 + 291.209i 0.165639 + 0.286895i 0.936882 0.349646i $$-0.113698\pi$$
−0.771243 + 0.636541i $$0.780365\pi$$
$$102$$ −523.182 + 302.059i −0.507870 + 0.293219i
$$103$$ −322.712 −0.308716 −0.154358 0.988015i $$-0.549331\pi$$
−0.154358 + 0.988015i $$0.549331\pi$$
$$104$$ 0 0
$$105$$ 840.611 0.781288
$$106$$ −163.426 + 94.3542i −0.149749 + 0.0864574i
$$107$$ −717.309 1242.42i −0.648083 1.12251i −0.983580 0.180471i $$-0.942238\pi$$
0.335498 0.942041i $$-0.391096\pi$$
$$108$$ −517.375 + 896.119i −0.460967 + 0.798417i
$$109$$ 849.147i 0.746179i −0.927795 0.373089i $$-0.878298\pi$$
0.927795 0.373089i $$-0.121702\pi$$
$$110$$ 73.5055 + 42.4384i 0.0637134 + 0.0367850i
$$111$$ −708.433 409.014i −0.605779 0.349747i
$$112$$ 310.452i 0.261919i
$$113$$ −807.263 + 1398.22i −0.672044 + 1.16401i 0.305280 + 0.952263i $$0.401250\pi$$
−0.977324 + 0.211751i $$0.932083\pi$$
$$114$$ −162.533 281.516i −0.133532 0.231284i
$$115$$ −378.574 + 218.570i −0.306976 + 0.177233i
$$116$$ −1223.04 −0.978931
$$117$$ 0 0
$$118$$ 686.509 0.535579
$$119$$ 1048.45 605.321i 0.807654 0.466300i
$$120$$ 327.513 + 567.269i 0.249147 + 0.431536i
$$121$$ −549.045 + 950.974i −0.412506 + 0.714481i
$$122$$ 214.409i 0.159112i
$$123$$ −1206.05 696.311i −0.884109 0.510441i
$$124$$ 130.491 + 75.3390i 0.0945035 + 0.0545616i
$$125$$ 845.211i 0.604784i
$$126$$ −1027.50 + 1779.69i −0.726487 + 1.25831i
$$127$$ 432.587 + 749.263i 0.302251 + 0.523514i 0.976646 0.214857i $$-0.0689285\pi$$
−0.674394 + 0.738371i $$0.735595\pi$$
$$128$$ 1025.49 592.066i 0.708134 0.408842i
$$129$$ 1314.01 0.896836
$$130$$ 0 0
$$131$$ −281.400 −0.187680 −0.0938400 0.995587i $$-0.529914\pi$$
−0.0938400 + 0.995587i $$0.529914\pi$$
$$132$$ 638.371 368.563i 0.420932 0.243025i
$$133$$ 325.713 + 564.152i 0.212353 + 0.367806i
$$134$$ −399.976 + 692.779i −0.257856 + 0.446620i
$$135$$ 662.641i 0.422452i
$$136$$ 816.976 + 471.681i 0.515111 + 0.297400i
$$137$$ 2287.55 + 1320.72i 1.42656 + 0.823624i 0.996847 0.0793428i $$-0.0252822\pi$$
0.429711 + 0.902967i $$0.358616\pi$$
$$138$$ 1664.53i 1.02677i
$$139$$ 999.318 1730.87i 0.609791 1.05619i −0.381483 0.924376i $$-0.624587\pi$$
0.991274 0.131814i $$-0.0420801\pi$$
$$140$$ −269.159 466.196i −0.162486 0.281434i
$$141$$ 3511.98 2027.64i 2.09760 1.21105i
$$142$$ 641.359 0.379026
$$143$$ 0 0
$$144$$ 553.153 0.320112
$$145$$ −678.286 + 391.609i −0.388473 + 0.224285i
$$146$$ −240.482 416.527i −0.136318 0.236110i
$$147$$ 1717.80 2975.31i 0.963820 1.66939i
$$148$$ 523.855i 0.290950i
$$149$$ −1518.13 876.491i −0.834696 0.481912i 0.0207617 0.999784i $$-0.493391\pi$$
−0.855458 + 0.517872i $$0.826724\pi$$
$$150$$ −1319.10 761.585i −0.718029 0.414554i
$$151$$ 2794.64i 1.50613i −0.657949 0.753063i $$-0.728576\pi$$
0.657949 0.753063i $$-0.271424\pi$$
$$152$$ −253.804 + 439.601i −0.135436 + 0.234582i
$$153$$ 1078.54 + 1868.09i 0.569901 + 0.987098i
$$154$$ 560.898 323.834i 0.293496 0.169450i
$$155$$ 96.4924 0.0500030
$$156$$ 0 0
$$157$$ 3244.87 1.64949 0.824743 0.565508i $$-0.191320\pi$$
0.824743 + 0.565508i $$0.191320\pi$$
$$158$$ −793.099 + 457.896i −0.399339 + 0.230558i
$$159$$ 524.756 + 908.903i 0.261735 + 0.453338i
$$160$$ 333.459 577.568i 0.164764 0.285380i
$$161$$ 3335.68i 1.63285i
$$162$$ −417.045 240.781i −0.202260 0.116775i
$$163$$ −2841.83 1640.73i −1.36558 0.788418i −0.375221 0.926936i $$-0.622433\pi$$
−0.990360 + 0.138517i $$0.955766\pi$$
$$164$$ 891.818i 0.424630i
$$165$$ 236.024 408.805i 0.111360 0.192881i
$$166$$ −1057.33 1831.35i −0.494366 0.856266i
$$167$$ −2707.65 + 1563.26i −1.25463 + 0.724364i −0.972026 0.234872i $$-0.924533\pi$$
−0.282608 + 0.959235i $$0.591200\pi$$
$$168$$ 4998.29 2.29540
$$169$$ 0 0
$$170$$ 247.747 0.111773
$$171$$ −1005.19 + 580.346i −0.449524 + 0.259533i
$$172$$ −420.737 728.738i −0.186517 0.323057i
$$173$$ 48.7849 84.4980i 0.0214396 0.0371345i −0.855107 0.518452i $$-0.826508\pi$$
0.876546 + 0.481318i $$0.159842\pi$$
$$174$$ 2982.31i 1.29936i
$$175$$ 2643.46 + 1526.20i 1.14187 + 0.659257i
$$176$$ −150.979 87.1675i −0.0646616 0.0373324i
$$177$$ 3818.06i 1.62137i
$$178$$ 343.450 594.873i 0.144622 0.250492i
$$179$$ −17.3575 30.0640i −0.00724782 0.0125536i 0.862379 0.506264i $$-0.168974\pi$$
−0.869627 + 0.493710i $$0.835640\pi$$
$$180$$ 830.654 479.579i 0.343963 0.198587i
$$181$$ 1229.35 0.504843 0.252422 0.967617i $$-0.418773\pi$$
0.252422 + 0.967617i $$0.418773\pi$$
$$182$$ 0 0
$$183$$ −1192.45 −0.481684
$$184$$ −2251.01 + 1299.62i −0.901885 + 0.520704i
$$185$$ 167.735 + 290.526i 0.0666602 + 0.115459i
$$186$$ −183.710 + 318.195i −0.0724209 + 0.125437i
$$187$$ 679.839i 0.265854i
$$188$$ −2249.03 1298.48i −0.872486 0.503730i
$$189$$ 4378.97 + 2528.20i 1.68531 + 0.973014i
$$190$$ 133.309i 0.0509012i
$$191$$ −2140.40 + 3707.28i −0.810858 + 1.40445i 0.101407 + 0.994845i $$0.467666\pi$$
−0.912265 + 0.409602i $$0.865668\pi$$
$$192$$ 872.903 + 1511.91i 0.328106 + 0.568296i
$$193$$ 409.041 236.160i 0.152557 0.0880786i −0.421778 0.906699i $$-0.638594\pi$$
0.574335 + 0.818620i $$0.305261\pi$$
$$194$$ −2359.93 −0.873365
$$195$$ 0 0
$$196$$ −2200.12 −0.801791
$$197$$ 3883.58 2242.18i 1.40453 0.810908i 0.409681 0.912229i $$-0.365640\pi$$
0.994854 + 0.101321i $$0.0323068\pi$$
$$198$$ 576.998 + 999.390i 0.207098 + 0.358705i
$$199$$ −183.120 + 317.173i −0.0652314 + 0.112984i −0.896797 0.442443i $$-0.854112\pi$$
0.831565 + 0.555427i $$0.187445\pi$$
$$200$$ 2378.51i 0.840931i
$$201$$ 3852.93 + 2224.49i 1.35206 + 0.780614i
$$202$$ 454.739 + 262.543i 0.158393 + 0.0914480i
$$203$$ 5976.49i 2.06634i
$$204$$ 1075.80 1863.34i 0.369221 0.639509i
$$205$$ 285.555 + 494.596i 0.0972879 + 0.168508i
$$206$$ −436.418 + 251.966i −0.147605 + 0.0852199i
$$207$$ −5943.41 −1.99563
$$208$$ 0 0
$$209$$ 365.810 0.121070
$$210$$ 1136.80 656.329i 0.373554 0.215671i
$$211$$ −1061.28 1838.19i −0.346262 0.599744i 0.639320 0.768941i $$-0.279216\pi$$
−0.985582 + 0.169197i $$0.945883\pi$$
$$212$$ 336.047 582.051i 0.108867 0.188563i
$$213$$ 3566.95i 1.14743i
$$214$$ −1940.10 1120.12i −0.619730 0.357801i
$$215$$ −466.675 269.435i −0.148033 0.0854666i
$$216$$ 3940.08i 1.24115i
$$217$$ 368.152 637.657i 0.115169 0.199479i
$$218$$ −662.994 1148.34i −0.205980 0.356768i
$$219$$ −2316.54 + 1337.45i −0.714781 + 0.412679i
$$220$$ −302.294 −0.0926392
$$221$$ 0 0
$$222$$ −1277.39 −0.386185
$$223$$ 5132.43 2963.21i 1.54122 0.889826i 0.542461 0.840081i $$-0.317493\pi$$
0.998762 0.0497449i $$-0.0158408\pi$$
$$224$$ −2544.52 4407.24i −0.758986 1.31460i
$$225$$ −2719.34 + 4710.03i −0.805730 + 1.39557i
$$226$$ 2521.17i 0.742060i
$$227$$ −775.665 447.830i −0.226796 0.130941i 0.382297 0.924039i $$-0.375133\pi$$
−0.609093 + 0.793099i $$0.708466\pi$$
$$228$$ 1002.63 + 578.870i 0.291232 + 0.168143i
$$229$$ 627.717i 0.181138i 0.995890 + 0.0905692i $$0.0288686\pi$$
−0.995890 + 0.0905692i $$0.971131\pi$$
$$230$$ −341.309 + 591.164i −0.0978488 + 0.169479i
$$231$$ −1801.02 3119.46i −0.512981 0.888509i
$$232$$ −4033.11 + 2328.52i −1.14132 + 0.658942i
$$233$$ −2303.72 −0.647734 −0.323867 0.946103i $$-0.604983\pi$$
−0.323867 + 0.946103i $$0.604983\pi$$
$$234$$ 0 0
$$235$$ −1663.06 −0.461643
$$236$$ −2117.47 + 1222.52i −0.584048 + 0.337200i
$$237$$ 2546.61 + 4410.86i 0.697976 + 1.20893i
$$238$$ 945.240 1637.20i 0.257440 0.445900i
$$239$$ 544.622i 0.147400i −0.997280 0.0737001i $$-0.976519\pi$$
0.997280 0.0737001i $$-0.0234808\pi$$
$$240$$ −305.995 176.666i −0.0822995 0.0475156i
$$241$$ −4699.14 2713.05i −1.25601 0.725157i −0.283713 0.958909i $$-0.591566\pi$$
−0.972296 + 0.233752i $$0.924900\pi$$
$$242$$ 1714.73i 0.455483i
$$243$$ 1172.61 2031.03i 0.309561 0.536175i
$$244$$ 381.814 + 661.322i 0.100177 + 0.173511i
$$245$$ −1220.17 + 704.464i −0.318178 + 0.183700i
$$246$$ −2174.65 −0.563621
$$247$$ 0 0
$$248$$ 573.746 0.146907
$$249$$ −10185.1 + 5880.39i −2.59220 + 1.49661i
$$250$$ 659.921 + 1143.02i 0.166948 + 0.289163i
$$251$$ −2610.61 + 4521.71i −0.656494 + 1.13708i 0.325022 + 0.945706i $$0.394628\pi$$
−0.981517 + 0.191375i $$0.938705\pi$$
$$252$$ 7319.02i 1.82958i
$$253$$ 1622.20 + 936.580i 0.403111 + 0.232736i
$$254$$ 1170.01 + 675.508i 0.289028 + 0.166871i
$$255$$ 1377.86i 0.338372i
$$256$$ 1728.63 2994.07i 0.422029 0.730975i
$$257$$ 329.103 + 570.023i 0.0798789 + 0.138354i 0.903198 0.429225i $$-0.141213\pi$$
−0.823319 + 0.567579i $$0.807880\pi$$
$$258$$ 1776.99 1025.95i 0.428801 0.247568i
$$259$$ 2559.87 0.614141
$$260$$ 0 0
$$261$$ −10648.7 −2.52544
$$262$$ −380.550 + 219.711i −0.0897346 + 0.0518083i
$$263$$ −1623.23 2811.51i −0.380580 0.659184i 0.610565 0.791966i $$-0.290942\pi$$
−0.991145 + 0.132782i $$0.957609\pi$$
$$264$$ 1403.40 2430.76i 0.327172 0.566679i
$$265$$ 430.401i 0.0997711i
$$266$$ 880.953 + 508.618i 0.203063 + 0.117238i
$$267$$ −3308.42 1910.11i −0.758321 0.437817i
$$268$$ 2849.07i 0.649384i
$$269$$ 1292.90 2239.37i 0.293047 0.507572i −0.681482 0.731835i $$-0.738664\pi$$
0.974529 + 0.224263i $$0.0719976\pi$$
$$270$$ 517.375 + 896.119i 0.116616 + 0.201985i
$$271$$ 856.441 494.466i 0.191974 0.110836i −0.400932 0.916108i $$-0.631314\pi$$
0.592907 + 0.805271i $$0.297980\pi$$
$$272$$ −508.867 −0.113436
$$273$$ 0 0
$$274$$ 4124.74 0.909433
$$275$$ 1484.44 857.043i 0.325510 0.187933i
$$276$$ 2964.15 + 5134.06i 0.646452 + 1.11969i
$$277$$ 4071.20 7051.53i 0.883086 1.52955i 0.0351939 0.999381i $$-0.488795\pi$$
0.847892 0.530169i $$-0.177872\pi$$
$$278$$ 3120.97i 0.673322i
$$279$$ 1136.16 + 655.961i 0.243799 + 0.140758i
$$280$$ −1775.17 1024.89i −0.378880 0.218747i
$$281$$ 1534.21i 0.325705i 0.986650 + 0.162853i $$0.0520695\pi$$
−0.986650 + 0.162853i $$0.947930\pi$$
$$282$$ 3166.27 5484.14i 0.668612 1.15807i
$$283$$ −3482.50 6031.87i −0.731495 1.26699i −0.956244 0.292570i $$-0.905490\pi$$
0.224749 0.974417i $$-0.427844\pi$$
$$284$$ −1978.20 + 1142.12i −0.413327 + 0.238634i
$$285$$ 741.403 0.154095
$$286$$ 0 0
$$287$$ 4357.96 0.896314
$$288$$ 7852.68 4533.75i 1.60668 0.927616i
$$289$$ 1464.31 + 2536.26i 0.298048 + 0.516234i
$$290$$ −611.518 + 1059.18i −0.123826 + 0.214473i
$$291$$ 13124.9i 2.64396i
$$292$$ 1483.48 + 856.490i 0.297309 + 0.171652i
$$293$$ −554.281 320.015i −0.110517 0.0638070i 0.443723 0.896164i $$-0.353658\pi$$
−0.554240 + 0.832357i $$0.686991\pi$$
$$294$$ 5364.87i 1.06424i
$$295$$ −782.887 + 1356.00i −0.154513 + 0.267625i
$$296$$ 997.358 + 1727.48i 0.195846 + 0.339214i
$$297$$ 2459.03 1419.72i 0.480428 0.277375i
$$298$$ −2737.37 −0.532120
$$299$$ 0 0
$$300$$ 5424.85 1.04401
$$301$$ −3561.05 + 2055.97i −0.681912 + 0.393702i
$$302$$ −2181.99 3779.32i −0.415760 0.720118i
$$303$$ 1460.15 2529.05i 0.276843 0.479506i
$$304$$ 273.813i 0.0516587i
$$305$$ 423.503 + 244.509i 0.0795072 + 0.0459035i
$$306$$ 2917.12 + 1684.20i 0.544969 + 0.314638i
$$307$$ 100.406i 0.0186660i −0.999956 0.00933299i $$-0.997029\pi$$
0.999956 0.00933299i $$-0.00297083\pi$$
$$308$$ −1153.35 + 1997.67i −0.213371 + 0.369570i
$$309$$ 1401.32 + 2427.16i 0.257988 + 0.446849i
$$310$$ 130.491 75.3390i 0.0239077 0.0138031i
$$311$$ 3878.92 0.707245 0.353623 0.935388i $$-0.384950\pi$$
0.353623 + 0.935388i $$0.384950\pi$$
$$312$$ 0 0
$$313$$ −3789.39 −0.684311 −0.342155 0.939643i $$-0.611157\pi$$
−0.342155 + 0.939643i $$0.611157\pi$$
$$314$$ 4388.19 2533.52i 0.788662 0.455334i
$$315$$ −2343.51 4059.08i −0.419180 0.726041i
$$316$$ 1630.82 2824.66i 0.290319 0.502847i
$$317$$ 4406.81i 0.780791i −0.920647 0.390396i $$-0.872338\pi$$
0.920647 0.390396i $$-0.127662\pi$$
$$318$$ 1419.30 + 819.434i 0.250284 + 0.144502i
$$319$$ 2906.48 + 1678.06i 0.510130 + 0.294524i
$$320$$ 715.950i 0.125071i
$$321$$ −6229.58 + 10790.0i −1.08318 + 1.87613i
$$322$$ 2604.42 + 4510.99i 0.450741 + 0.780706i
$$323$$ 924.710 533.882i 0.159295 0.0919690i
$$324$$ 1715.11 0.294086
$$325$$ 0 0
$$326$$ −5124.19 −0.870559
$$327$$ −6386.55 + 3687.27i −1.08005 + 0.623568i
$$328$$ 1697.92 + 2940.88i 0.285829 + 0.495070i
$$329$$ −6345.14 + 10990.1i −1.06328 + 1.84165i
$$330$$ 737.127i 0.122962i
$$331$$ −3577.98 2065.75i −0.594149 0.343032i 0.172587 0.984994i $$-0.444787\pi$$
−0.766736 + 0.641962i $$0.778121\pi$$
$$332$$ 6522.44 + 3765.73i 1.07821 + 0.622505i
$$333$$ 4561.10i 0.750591i
$$334$$ −2441.11 + 4228.13i −0.399916 + 0.692674i
$$335$$ −912.257 1580.07i −0.148782 0.257698i
$$336$$ −2334.95 + 1348.08i −0.379113 + 0.218881i
$$337$$ 4560.82 0.737221 0.368611 0.929584i $$-0.379834\pi$$
0.368611 + 0.929584i $$0.379834\pi$$
$$338$$ 0 0
$$339$$ 14021.6 2.24646
$$340$$ −764.150 + 441.182i −0.121888 + 0.0703720i
$$341$$ −206.737 358.078i −0.0328311 0.0568652i
$$342$$ −906.240 + 1569.65i −0.143286 + 0.248179i
$$343$$ 1429.34i 0.225007i
$$344$$ −2774.86 1602.07i −0.434914 0.251098i
$$345$$ 3287.79 + 1898.21i 0.513069 + 0.296220i
$$346$$ 152.360i 0.0236733i
$$347$$ −5034.70 + 8720.36i −0.778896 + 1.34909i 0.153683 + 0.988120i $$0.450887\pi$$
−0.932579 + 0.360967i $$0.882447\pi$$
$$348$$ 5310.82 + 9198.62i 0.818075 + 1.41695i
$$349$$ 5091.64 2939.66i 0.780944 0.450878i −0.0558207 0.998441i $$-0.517778\pi$$
0.836765 + 0.547563i $$0.184444\pi$$
$$350$$ 4766.49 0.727942
$$351$$ 0 0
$$352$$ −2857.76 −0.432725
$$353$$ 7917.69 4571.28i 1.19381 0.689249i 0.234644 0.972081i $$-0.424607\pi$$
0.959169 + 0.282833i $$0.0912741\pi$$
$$354$$ −2981.05 5163.33i −0.447574 0.775220i
$$355$$ −731.398 + 1266.82i −0.109348 + 0.189397i
$$356$$ 2446.43i 0.364215i
$$357$$ −9105.39 5257.00i −1.34988 0.779356i
$$358$$ −46.9466 27.1046i −0.00693074 0.00400146i
$$359$$ 2754.32i 0.404924i −0.979290 0.202462i $$-0.935106\pi$$
0.979290 0.202462i $$-0.0648942\pi$$
$$360$$ 1826.12 3162.94i 0.267347 0.463059i
$$361$$ −3142.23 5442.50i −0.458117 0.793483i
$$362$$ 1662.50 959.845i 0.241379 0.139360i
$$363$$ 9536.54 1.37889
$$364$$ 0 0
$$365$$ 1096.97 0.157310
$$366$$ −1612.60 + 931.034i −0.230306 + 0.132967i
$$367$$ −1520.09 2632.88i −0.216208 0.374483i 0.737438 0.675415i $$-0.236036\pi$$
−0.953646 + 0.300932i $$0.902702\pi$$
$$368$$ 701.040 1214.24i 0.0993049 0.172001i
$$369$$ 7764.88i 1.09546i
$$370$$ 453.672 + 261.928i 0.0637440 + 0.0368026i
$$371$$ −2844.25 1642.13i −0.398022 0.229798i
$$372$$ 1308.59i 0.182385i
$$373$$ 2692.36 4663.31i 0.373740 0.647337i −0.616397 0.787435i $$-0.711408\pi$$
0.990138 + 0.140098i $$0.0447418\pi$$
$$374$$ −530.802 919.376i −0.0733880 0.127112i
$$375$$ 6356.95 3670.18i 0.875390 0.505407i
$$376$$ −9888.59 −1.35629
$$377$$ 0 0
$$378$$ 7895.84 1.07439
$$379$$ 2965.50 1712.13i 0.401920 0.232049i −0.285392 0.958411i $$-0.592124\pi$$
0.687312 + 0.726362i $$0.258791\pi$$
$$380$$ −237.393 411.177i −0.0320474 0.0555077i
$$381$$ 3756.87 6507.09i 0.505171 0.874983i
$$382$$ 6684.69i 0.895336i
$$383$$ −331.675 191.493i −0.0442501 0.0255478i 0.477712 0.878517i $$-0.341466\pi$$
−0.521962 + 0.852969i $$0.674800\pi$$
$$384$$ −8906.01 5141.89i −1.18355 0.683323i
$$385$$ 1477.19i 0.195544i
$$386$$ 368.776 638.739i 0.0486275 0.0842253i
$$387$$ −3663.27 6344.97i −0.481175 0.833419i
$$388$$ 7278.94 4202.50i 0.952403 0.549870i
$$389$$ −8588.34 −1.11940 −0.559699 0.828696i $$-0.689083\pi$$
−0.559699 + 0.828696i $$0.689083\pi$$
$$390$$ 0 0
$$391$$ 5467.56 0.707178
$$392$$ −7255.15 + 4188.76i −0.934796 + 0.539705i
$$393$$ 1221.93 + 2116.45i 0.156841 + 0.271656i
$$394$$ 3501.29 6064.41i 0.447696 0.775433i
$$395$$ 2088.72i 0.266063i
$$396$$ −3559.38 2055.01i −0.451681 0.260778i
$$397$$ 6269.30 + 3619.58i 0.792562 + 0.457586i 0.840864 0.541247i $$-0.182048\pi$$
−0.0483020 + 0.998833i $$0.515381\pi$$
$$398$$ 571.904i 0.0720275i
$$399$$ 2828.71 4899.46i 0.354918 0.614737i
$$400$$ −641.505 1111.12i −0.0801882 0.138890i
$$401$$ 3697.60 2134.81i 0.460472 0.265854i −0.251770 0.967787i $$-0.581013\pi$$
0.712243 + 0.701933i $$0.247679\pi$$
$$402$$ 6947.32 0.861942
$$403$$ 0 0
$$404$$ −1870.12 −0.230302
$$405$$ 951.185 549.167i 0.116703 0.0673786i
$$406$$ 4666.30 + 8082.27i 0.570405 + 0.987971i
$$407$$ 718.751 1244.91i 0.0875360 0.151617i
$$408$$ 8192.78i 0.994125i
$$409$$ 11745.5 + 6781.26i 1.41999 + 0.819834i 0.996298 0.0859711i $$-0.0273993\pi$$
0.423696 + 0.905805i $$0.360733\pi$$
$$410$$ 772.337 + 445.909i 0.0930317 + 0.0537119i
$$411$$ 22939.9i 2.75315i
$$412$$ 897.390 1554.33i 0.107309 0.185864i
$$413$$ 5973.96 + 10347.2i 0.711767 + 1.23282i
$$414$$ −8037.54 + 4640.47i −0.954163 + 0.550886i
$$415$$ 4823.06 0.570494
$$416$$ 0 0
$$417$$ −17357.5 −2.03837
$$418$$ 494.701 285.616i 0.0578867 0.0334209i
$$419$$ 7288.44 + 12624.0i 0.849794 + 1.47189i 0.881392 + 0.472386i $$0.156607\pi$$
−0.0315973 + 0.999501i $$0.510059\pi$$
$$420$$ −2337.55 + 4048.76i −0.271573 + 0.470379i
$$421$$ 15848.4i 1.83469i −0.398099 0.917343i $$-0.630330\pi$$
0.398099 0.917343i $$-0.369670\pi$$
$$422$$ −2870.42 1657.24i −0.331114 0.191169i
$$423$$ −19581.8 11305.6i −2.25083 1.29952i
$$424$$ 2559.18i 0.293124i
$$425$$ 2501.62 4332.94i 0.285521 0.494537i
$$426$$ −2784.99 4823.75i −0.316745 0.548618i
$$427$$ 3231.62 1865.77i 0.366250 0.211455i
$$428$$ 7978.70 0.901087
$$429$$ 0 0
$$430$$ −841.474 −0.0943709
$$431$$ −9261.90 + 5347.36i −1.03510 + 0.597618i −0.918443 0.395554i $$-0.870553\pi$$
−0.116662 + 0.993172i $$0.537219\pi$$
$$432$$ −1062.67 1840.61i −0.118352 0.204991i
$$433$$ −8039.50 + 13924.8i −0.892272 + 1.54546i −0.0551273 + 0.998479i $$0.517556\pi$$
−0.837145 + 0.546981i $$0.815777\pi$$
$$434$$ 1149.78i 0.127168i
$$435$$ 5890.69 + 3400.99i 0.649280 + 0.374862i
$$436$$ 4089.87 + 2361.29i 0.449241 + 0.259370i
$$437$$ 2942.01i 0.322049i
$$438$$ −2088.50 + 3617.40i −0.227837 + 0.394625i
$$439$$ 3017.90 + 5227.16i 0.328101 + 0.568288i 0.982135 0.188177i $$-0.0602579\pi$$
−0.654034 + 0.756465i $$0.726925\pi$$
$$440$$ −996.849 + 575.531i −0.108007 + 0.0623577i
$$441$$ −19156.0 −2.06845
$$442$$ 0 0
$$443$$ 10201.3 1.09409 0.547043 0.837105i $$-0.315753\pi$$
0.547043 + 0.837105i $$0.315753\pi$$
$$444$$ 3939.98 2274.75i 0.421134 0.243142i
$$445$$ 783.332 + 1356.77i 0.0834461 + 0.144533i
$$446$$ 4627.21 8014.56i 0.491266 0.850897i
$$447$$ 15224.0i 1.61090i
$$448$$ −4731.26 2731.59i −0.498953 0.288071i
$$449$$ 5042.47 + 2911.27i 0.529997 + 0.305994i 0.741015 0.671488i $$-0.234345\pi$$
−0.211018 + 0.977482i $$0.567678\pi$$
$$450$$ 8492.78i 0.889675i
$$451$$ 1223.61 2119.36i 0.127755 0.221279i
$$452$$ −4489.64 7776.28i −0.467201 0.809216i
$$453$$ −21018.9 + 12135.3i −2.18003 + 1.25864i
$$454$$ −1398.62 −0.144583
$$455$$ 0 0
$$456$$ 4408.40 0.452724
$$457$$ −4002.42 + 2310.80i −0.409684 + 0.236531i −0.690654 0.723186i $$-0.742677\pi$$
0.280970 + 0.959717i $$0.409344\pi$$
$$458$$ 490.106 + 848.889i 0.0500026 + 0.0866070i
$$459$$ 4144.02 7177.65i 0.421408 0.729900i
$$460$$ 2431.18i 0.246422i
$$461$$ 4440.78 + 2563.88i 0.448650 + 0.259028i 0.707260 0.706954i $$-0.249931\pi$$
−0.258610 + 0.965982i $$0.583264\pi$$
$$462$$ −4871.20 2812.39i −0.490539 0.283213i
$$463$$ 6486.27i 0.651064i 0.945531 + 0.325532i $$0.105543\pi$$
−0.945531 + 0.325532i $$0.894457\pi$$
$$464$$ 1256.04 2175.53i 0.125669 0.217665i
$$465$$ −419.002 725.733i −0.0417866 0.0723764i
$$466$$ −3115.43 + 1798.69i −0.309698 + 0.178804i
$$467$$ −12978.0 −1.28598 −0.642990 0.765875i $$-0.722306\pi$$
−0.642990 + 0.765875i $$0.722306\pi$$
$$468$$ 0 0
$$469$$ −13922.3 −1.37073
$$470$$ −2249.03 + 1298.48i −0.220723 + 0.127435i
$$471$$ −14090.3 24405.1i −1.37844 2.38754i
$$472$$ −4655.07 + 8062.81i −0.453955 + 0.786273i
$$473$$ 2309.08i 0.224464i
$$474$$ 6887.79 + 3976.67i 0.667440 + 0.385347i
$$475$$ 2331.48 + 1346.08i 0.225212 + 0.130026i
$$476$$ 6733.04i 0.648337i
$$477$$ 2925.89 5067.80i 0.280854 0.486454i
$$478$$ −425.228 736.516i −0.0406893 0.0704759i
$$479$$ −5030.71 + 2904.48i −0.479873 + 0.277055i −0.720363 0.693597i $$-0.756025\pi$$
0.240491 + 0.970651i $$0.422692\pi$$
$$480$$ −5791.95 −0.550761
$$481$$ 0 0
$$482$$ −8473.14 −0.800707
$$483$$ 25088.1 14484.6i 2.36345 1.36454i
$$484$$ −3053.54 5288.89i −0.286772 0.496703i
$$485$$ 2691.23 4661.35i 0.251964 0.436414i
$$486$$ 3662.20i 0.341812i
$$487$$ −4665.40 2693.57i −0.434106 0.250631i 0.266989 0.963700i $$-0.413971\pi$$
−0.701094 + 0.713069i $$0.747305\pi$$
$$488$$ 2518.16 + 1453.86i 0.233589 + 0.134863i
$$489$$ 28498.4i 2.63547i
$$490$$ −1100.06 + 1905.36i −0.101419 + 0.175664i
$$491$$ 7629.53 + 13214.7i 0.701255 + 1.21461i 0.968026 + 0.250849i $$0.0807097\pi$$
−0.266772 + 0.963760i $$0.585957\pi$$
$$492$$ 6707.48 3872.57i 0.614628 0.354855i
$$493$$ 9796.16 0.894922
$$494$$ 0 0
$$495$$ −2632.01 −0.238990
$$496$$ −268.025 + 154.744i −0.0242635 + 0.0140085i
$$497$$ 5581.07 + 9666.69i 0.503712 + 0.872456i
$$498$$ −9182.55 + 15904.6i −0.826264 + 1.43113i
$$499$$ 1856.04i 0.166509i −0.996528 0.0832544i $$-0.973469\pi$$
0.996528 0.0832544i $$-0.0265314\pi$$
$$500$$ −4070.91 2350.34i −0.364114 0.210221i
$$501$$ 23515.0 + 13576.4i 2.09695 + 1.21067i
$$502$$ 8153.20i 0.724891i
$$503$$ −524.732 + 908.862i −0.0465142 + 0.0805649i −0.888345 0.459176i $$-0.848145\pi$$
0.841831 + 0.539741i $$0.181478\pi$$
$$504$$ −13934.6 24135.4i −1.23154 2.13308i
$$505$$ −1037.16 + 598.803i −0.0913919 + 0.0527651i
$$506$$ 2925.04 0.256984
$$507$$ 0 0
$$508$$ −4811.71 −0.420246
$$509$$ 477.272 275.553i 0.0415613 0.0239954i −0.479075 0.877774i $$-0.659028\pi$$
0.520637 + 0.853778i $$0.325695\pi$$
$$510$$ −1075.80 1863.34i −0.0934063 0.161784i
$$511$$ 4185.32 7249.19i 0.362324 0.627564i
$$512$$ 4074.36i 0.351686i
$$513$$ 3862.18 + 2229.83i 0.332396 + 0.191909i
$$514$$ 890.121 + 513.911i 0.0763843 + 0.0441005i
$$515$$ 1149.36i 0.0983431i
$$516$$ −3653.96 + 6328.84i −0.311738 + 0.539945i
$$517$$ 3563.13 + 6171.52i 0.303107 + 0.524997i
$$518$$ 3461.83 1998.69i 0.293637 0.169531i
$$519$$ −847.361 −0.0716667
$$520$$ 0 0
$$521$$ −8995.30 −0.756413 −0.378206 0.925721i $$-0.623459\pi$$
−0.378206 + 0.925721i $$0.623459\pi$$
$$522$$ −14400.7 + 8314.27i −1.20748 + 0.697137i
$$523$$ −1331.96 2307.02i −0.111362 0.192885i 0.804958 0.593332i $$-0.202188\pi$$
−0.916320 + 0.400448i $$0.868855\pi$$
$$524$$ 782.512 1355.35i 0.0652370 0.112994i
$$525$$ 26509.1i 2.20372i
$$526$$ −4390.32 2534.76i −0.363930 0.210115i
$$527$$ −1045.19 603.443i −0.0863935 0.0498793i
$$528$$ 1514.04i 0.124792i
$$529$$ −1448.89 + 2509.54i −0.119083 + 0.206258i
$$530$$ −336.047 582.051i −0.0275414 0.0477032i
$$531$$ −18436.3 + 10644.2i −1.50672 + 0.869906i
$$532$$ −3622.94 −0.295253
$$533$$ 0 0
$$534$$ −5965.49 −0.483431
$$535$$ 4424.93 2554.73i 0.357582 0.206450i
$$536$$ −5424.30 9395.16i −0.437116 0.757107i
$$537$$ −150.744 + 261.096i −0.0121137 + 0.0209816i
$$538$$ 4037.86i 0.323577i
$$539$$ 5228.46 + 3018.65i 0.417821 + 0.241229i
$$540$$ −3191.57 1842.66i −0.254340 0.146843i
$$541$$ 6169.23i 0.490270i −0.969489 0.245135i $$-0.921168\pi$$
0.969489 0.245135i $$-0.0788322\pi$$
$$542$$ 772.135 1337.38i 0.0611920 0.105988i
$$543$$ −5338.23 9246.08i −0.421888 0.730732i
$$544$$ −7223.97 + 4170.76i −0.569348 + 0.328713i
$$545$$ 3024.28 0.237699
$$546$$ 0 0
$$547$$ 5140.42 0.401807 0.200904 0.979611i $$-0.435612\pi$$
0.200904 + 0.979611i $$0.435612\pi$$
$$548$$ −12722.3 + 7345.24i −0.991735 + 0.572578i
$$549$$ 3324.38 + 5757.99i 0.258435 + 0.447623i
$$550$$ 1338.32 2318.03i 0.103756 0.179711i
$$551$$ 5271.15i 0.407547i
$$552$$ 19549.3 + 11286.8i 1.50738 + 0.870285i
$$553$$ −13803.0 7969.16i −1.06142 0.612809i
$$554$$ 12714.8i 0.975090i
$$555$$ 1456.72 2523.12i 0.111413 0.192974i
$$556$$ 5557.76 + 9626.32i 0.423923 + 0.734257i
$$557$$ 2406.30 1389.28i 0.183049 0.105683i −0.405675 0.914017i $$-0.632964\pi$$
0.588724 + 0.808334i $$0.299630\pi$$
$$558$$ 2048.64 0.155422
$$559$$ 0 0
$$560$$ 1105.69 0.0834356
$$561$$ −5113.16 + 2952.08i −0.384809 + 0.222170i
$$562$$ 1197.87 + 2074.78i 0.0899097 + 0.155728i
$$563$$ 2453.07 4248.85i 0.183632 0.318059i −0.759483 0.650527i $$-0.774548\pi$$
0.943115 + 0.332468i $$0.107881\pi$$
$$564$$ 22553.7i 1.68383i
$$565$$ −4979.84 2875.11i −0.370802 0.214083i
$$566$$ −9419.08 5438.11i −0.699494 0.403853i
$$567$$ 8381.04i 0.620759i
$$568$$ −4348.91 + 7532.54i −0.321261 + 0.556440i
$$569$$ −4681.58 8108.73i −0.344924 0.597426i 0.640416 0.768028i $$-0.278762\pi$$
−0.985340 + 0.170602i $$0.945429\pi$$
$$570$$ 1002.63 578.870i 0.0736766 0.0425372i
$$571$$ −7199.32 −0.527640 −0.263820 0.964572i $$-0.584982\pi$$
−0.263820 + 0.964572i $$0.584982\pi$$
$$572$$ 0 0
$$573$$ 37177.3 2.71048
$$574$$ 5893.46 3402.59i 0.428551 0.247424i
$$575$$ 6892.72 + 11938.5i 0.499906 + 0.865863i
$$576$$ 4867.07 8430.01i 0.352074 0.609810i
$$577$$ 11449.6i 0.826086i 0.910711 + 0.413043i $$0.135534\pi$$
−0.910711 + 0.413043i $$0.864466\pi$$
$$578$$ 3960.50 + 2286.60i 0.285009 + 0.164550i
$$579$$ −3552.38 2050.97i −0.254978 0.147211i
$$580$$ 4355.91i 0.311843i
$$581$$ 18401.6 31872.6i 1.31399 2.27590i
$$582$$ 10247.6 + 17749.3i 0.729855 + 1.26415i
$$583$$ −1597.20 + 922.142i −0.113463 + 0.0655081i
$$584$$ 6522.62 0.462171
$$585$$ 0 0
$$586$$ −999.439 −0.0704547
$$587$$ 4710.65 2719.70i 0.331226 0.191233i −0.325160 0.945659i $$-0.605418\pi$$
0.656385 + 0.754426i $$0.272085\pi$$
$$588$$ 9553.63 + 16547.4i 0.670042 + 1.16055i
$$589$$ 324.703 562.402i 0.0227150 0.0393436i
$$590$$ 2445.04i 0.170611i
$$591$$ −33727.5 19472.6i −2.34749 1.35532i
$$592$$ −931.831 537.993i −0.0646926 0.0373503i
$$593$$ 28405.8i 1.96709i −0.180651 0.983547i $$-0.557820\pi$$
0.180651 0.983547i $$-0.442180\pi$$
$$594$$ 2216.97 3839.90i 0.153137 0.265241i
$$595$$ 2155.88 + 3734.10i 0.148542 + 0.257282i
$$596$$ 8443.14 4874.65i 0.580276 0.335022i
$$597$$ 3180.67 0.218051
$$598$$ 0 0
$$599$$ −10482.3 −0.715020 −0.357510 0.933909i $$-0.616374\pi$$
−0.357510 + 0.933909i $$0.616374\pi$$
$$600$$ 17889.1 10328.3i 1.21720 0.702750i
$$601$$ −1599.77 2770.88i −0.108579 0.188064i 0.806616 0.591076i $$-0.201297\pi$$
−0.915195 + 0.403012i $$0.867963\pi$$
$$602$$ −3210.51 + 5560.77i −0.217360 + 0.376479i
$$603$$ 24806.3i 1.67527i
$$604$$ 13460.3 + 7771.28i 0.906772 + 0.523525i
$$605$$ −3386.95 1955.45i −0.227602 0.131406i
$$606$$ 4560.20i 0.305686i
$$607$$ −5671.40 + 9823.15i −0.379234 + 0.656853i −0.990951 0.134224i $$-0.957146\pi$$
0.611717 + 0.791077i $$0.290479\pi$$
$$608$$ −2244.22 3887.10i −0.149696 0.259281i
$$609$$ 44950.0 25951.9i 2.99091 1.72680i
$$610$$ 763.629 0.0506859
$$611$$ 0 0
$$612$$ −11996.7 −0.792384
$$613$$ −12458.1 + 7192.70i −0.820846 + 0.473916i −0.850708 0.525638i $$-0.823826\pi$$
0.0298622 + 0.999554i $$0.490493\pi$$
$$614$$ −78.3944 135.783i −0.00515267 0.00892469i
$$615$$ 2479.95 4295.39i 0.162603 0.281637i
$$616$$ 8783.39i 0.574502i
$$617$$ 19101.7 + 11028.4i 1.24636 + 0.719588i 0.970382 0.241575i $$-0.0776640\pi$$
0.275981 + 0.961163i $$0.410997\pi$$
$$618$$ 3790.14 + 2188.24i 0.246702 + 0.142433i
$$619$$ 13621.4i 0.884477i 0.896898 + 0.442238i $$0.145815\pi$$
−0.896898 + 0.442238i $$0.854185\pi$$
$$620$$ −268.324 + 464.751i −0.0173809 + 0.0301046i
$$621$$ 11418.0 + 19776.6i 0.737824 + 1.27795i
$$622$$ 5245.63 3028.57i 0.338152 0.195232i
$$623$$ 11954.7 0.768789
$$624$$ 0 0
$$625$$ 11029.2 0.705866
$$626$$ −5124.57 + 2958.67i −0.327187 + 0.188901i
$$627$$ −1588.47 2751.31i −0.101176 0.175242i
$$628$$ −9023.27 + 15628.8i −0.573356 + 0.993082i
$$629$$ 4195.92i 0.265982i
$$630$$ −6338.46 3659.51i −0.400842 0.231426i
$$631$$ 16227.1 + 9368.74i 1.02376 + 0.591068i 0.915191 0.403021i $$-0.132040\pi$$
0.108569 + 0.994089i $$0.465373\pi$$
$$632$$ 12419.6i 0.781683i
$$633$$ −9216.83 + 15964.0i −0.578730 + 1.00239i
$$634$$ −3440.73 5959.52i −0.215534 0.373317i
$$635$$ −2668.54 + 1540.68i −0.166768 + 0.0962836i
$$636$$ −5836.91 −0.363913
$$637$$ 0 0
$$638$$ 5240.75 0.325209
$$639$$ −17223.8 + 9944.18i −1.06630 + 0.615627i
$$640$$ 2108.67 + 3652.33i 0.130239 + 0.225580i
$$641$$ 14899.4 25806.5i 0.918081 1.59016i 0.115753 0.993278i $$-0.463072\pi$$
0.802327 0.596884i $$-0.203595\pi$$
$$642$$ 19455.6i 1.19603i
$$643$$ −19904.3 11491.8i −1.22076 0.704807i −0.255681 0.966761i $$-0.582300\pi$$
−0.965080 + 0.261955i $$0.915633\pi$$
$$644$$ −16066.1 9275.77i −0.983064 0.567573i
$$645$$ 4679.90i 0.285692i
$$646$$ 833.684 1443.98i 0.0507753 0.0879455i
$$647$$ −12452.7 21568.7i −0.756672 1.31059i −0.944539 0.328400i $$-0.893491\pi$$
0.187866 0.982195i $$-0.439843\pi$$
$$648$$ 5655.77 3265.36i 0.342870 0.197956i
$$649$$ 6709.39 0.405804
$$650$$ 0 0
$$651$$ −6394.54 −0.384980
$$652$$ 15805.0 9125.03i 0.949344 0.548104i
$$653$$ −5038.92 8727.67i −0.301973 0.523033i 0.674610 0.738175i $$-0.264312\pi$$
−0.976583 + 0.215142i $$0.930979\pi$$
$$654$$ −5757.87 + 9972.93i −0.344267 + 0.596288i
$$655$$ 1002.22i 0.0597864i
$$656$$ −1586.36 915.886i −0.0944162 0.0545112i
$$657$$ 12916.4 + 7457.28i 0.766996 + 0.442825i
$$658$$ 19816.5i 1.17406i
$$659$$ −6167.30 + 10682.1i −0.364558 + 0.631433i −0.988705 0.149874i $$-0.952113\pi$$
0.624147 + 0.781307i $$0.285447\pi$$
$$660$$ 1312.66 + 2273.59i 0.0774169 + 0.134090i
$$661$$ −11041.1 + 6374.56i −0.649694 + 0.375101i −0.788339 0.615241i $$-0.789059\pi$$
0.138645 + 0.990342i $$0.455725\pi$$
$$662$$ −6451.54 −0.378771
$$663$$ 0 0
$$664$$ 28678.1 1.67609
$$665$$ −2009.26 + 1160.04i −0.117166 + 0.0676460i
$$666$$ 3561.20 + 6168.18i 0.207198 + 0.358877i
$$667$$ −13495.7 + 23375.2i −0.783440 + 1.35696i
$$668$$ 17388.3i 1.00715i
$$669$$ −44573.4 25734.5i −2.57594 1.48722i
$$670$$ −2467.37 1424.54i −0.142273 0.0821413i
$$671$$ 2095.46i 0.120558i
$$672$$ −22098.3 + 38275.3i −1.26854 + 2.19718i
$$673$$ −6809.12 11793.7i −0.390004 0.675506i 0.602446 0.798160i $$-0.294193\pi$$
−0.992450 + 0.122654i $$0.960860\pi$$
$$674$$ 6167.80 3560.98i 0.352485 0.203507i
$$675$$ 20896.7 1.19158
$$676$$ 0 0
$$677$$ 9655.67 0.548150 0.274075 0.961708i $$-0.411628\pi$$
0.274075 + 0.961708i $$0.411628\pi$$
$$678$$ 18962.0 10947.7i 1.07409 0.620126i
$$679$$ −20535.9 35569.3i −1.16067 2.01034i
$$680$$ −1679.92 + 2909.70i −0.0947381 + 0.164091i
$$681$$ 7778.51i 0.437699i
$$682$$ −559.158 322.830i −0.0313948 0.0181258i
$$683$$ −14130.7 8158.38i −0.791650 0.457060i 0.0488929 0.998804i $$-0.484431\pi$$
−0.840543 + 0.541744i $$0.817764\pi$$
$$684$$ 6455.25i 0.360852i
$$685$$ −4703.80 + 8147.23i −0.262369 + 0.454437i
$$686$$ 1116.00 + 1932.97i 0.0621123 + 0.107582i
$$687$$ 4721.14 2725.75i 0.262188 0.151374i
$$688$$ 1728.37 0.0957753
$$689$$ 0 0
$$690$$ 5928.30 0.327082
$$691$$ −2035.89 + 1175.42i −0.112082 + 0.0647106i −0.554993 0.831855i $$-0.687279\pi$$
0.442911 + 0.896566i $$0.353946\pi$$
$$692$$ 271.320 + 469.940i 0.0149047 + 0.0258157i
$$693$$ −10042.0 + 17393.3i −0.550454 + 0.953414i
$$694$$ 15723.9i 0.860045i
$$695$$ 6164.58 + 3559.12i 0.336455 + 0.194252i
$$696$$ 35026.2 + 20222.4i 1.90756 + 1.10133i
$$697$$ 7143.20i 0.388189i
$$698$$ 4590.44 7950.87i 0.248926 0.431153i
$$699$$ 10003.5 + 17326.6i 0.541299 + 0.937558i
$$700$$ −14701.7 + 8488.05i −0.793819 + 0.458312i
$$701$$ 8076.90 0.435179 0.217589 0.976040i $$-0.430181\pi$$
0.217589 + 0.976040i $$0.430181\pi$$
$$702$$ 0 0
$$703$$ 2257.76 0.121128
$$704$$ −2656.85 + 1533.93i −0.142236 + 0.0821197i
$$705$$ 7221.55 + 12508.1i 0.385786 + 0.668202i
$$706$$ 7138.30 12363.9i 0.380529 0.659095i
$$707$$ 9138.55i 0.486125i
$$708$$ 18389.5 + 10617.2i 0.976156 + 0.563584i
$$709$$ 11799.5 + 6812.44i 0.625021 + 0.360856i 0.778821 0.627246i $$-0.215818\pi$$
−0.153801 + 0.988102i $$0.549151\pi$$
$$710$$ 2284.23i 0.120741i
$$711$$ 14199.2 24593.8i 0.748962 1.29724i
$$712$$ 4657.71 + 8067.40i 0.245162 + 0.424633i
$$713$$ 2879.82 1662.67i 0.151263 0.0873315i
$$714$$ −16418.2 −0.860553
$$715$$ 0 0
$$716$$ 193.069 0.0100773
$$717$$ −4096.18 + 2364.93i −0.213354 + 0.123180i
$$718$$ −2150.51 3724.79i −0.111778 0.193605i
$$719$$ 8117.89 14060.6i 0.421066 0.729307i −0.574978 0.818169i $$-0.694990\pi$$
0.996044 + 0.0888616i $$0.0283229\pi$$
$$720$$ 1970.09i 0.101973i
$$721$$ −7595.36 4385.19i −0.392325 0.226509i
$$722$$ −8498.75 4906.75i −0.438076 0.252923i
$$723$$ 47123.8i 2.42400i
$$724$$ −3418.54 + 5921.08i −0.175482 + 0.303944i
$$725$$ 12349.6 + 21390.1i 0.632623 + 1.09574i
$$726$$ 12896.7 7445.91i 0.659285 0.380638i
$$727$$ −24181.2 −1.23361 −0.616803 0.787118i $$-0.711572\pi$$
−0.616803 + 0.787118i $$0.711572\pi$$
$$728$$ 0 0
$$729$$ −28693.9 −1.45780
$$730$$ 1483.48 856.490i 0.0752139 0.0434248i
$$731$$ 3369.98 + 5836.98i 0.170511 + 0.295333i
$$732$$ 3315.93 5743.36i 0.167432 0.290001i
$$733$$ 3053.70i 0.153876i −0.997036 0.0769379i $$-0.975486\pi$$
0.997036 0.0769379i $$-0.0245143\pi$$
$$734$$ −4111.38 2373.71i −0.206749 0.119367i
$$735$$ 10596.7 + 6118.03i 0.531791 + 0.307030i
$$736$$ 22983.4i 1.15106i
$$737$$ −3909.05 + 6770.67i −0.195375 + 0.338400i
$$738$$ 6062.63 + 10500.8i 0.302396 + 0.523766i
$$739$$ −6957.32 + 4016.81i −0.346318 + 0.199947i −0.663062 0.748564i $$-0.730744\pi$$
0.316744 + 0.948511i $$0.397410\pi$$
$$740$$ −1865.74 −0.0926836
$$741$$ 0 0
$$742$$ −5128.54 −0.253739
$$743$$ 13977.3 8069.81i 0.690146 0.398456i −0.113521 0.993536i $$-0.536213\pi$$
0.803667 + 0.595080i $$0.202880\pi$$
$$744$$ −2491.40 4315.22i −0.122767 0.212639i
$$745$$ 3121.67 5406.89i 0.153515 0.265897i
$$746$$ 8408.53i 0.412678i
$$747$$ 56789.6 + 32787.5i 2.78156 + 1.60593i
$$748$$ 3274.41 + 1890.48i 0.160059 + 0.0924102i
$$749$$ 38988.7i 1.90202i
$$750$$ 5731.19 9926.71i 0.279031 0.483296i
$$751$$ −9245.56 16013.8i −0.449235 0.778097i 0.549102 0.835755i $$-0.314970\pi$$
−0.998336 + 0.0576584i $$0.981637\pi$$
$$752$$ 4619.45 2667.04i 0.224008 0.129331i
$$753$$ 45344.5 2.19448
$$754$$ 0 0
$$755$$ 9953.28 0.479784
$$756$$ −24353.9 + 14060.7i −1.17162 + 0.676434i
$$757$$ −80.3149 139.109i −0.00385613 0.00667902i 0.864091 0.503336i $$-0.167894\pi$$
−0.867947 + 0.496657i $$0.834561\pi$$
$$758$$ 2673.59 4630.79i 0.128112 0.221897i
$$759$$ 16267.7i 0.777973i
$$760$$ −1565.66 903.936i −0.0747271 0.0431437i
$$761$$ −23208.7 13399.5i −1.10554 0.638282i −0.167867 0.985810i $$-0.553688\pi$$
−0.937670 + 0.347528i $$0.887021\pi$$
$$762$$ 11733.1i 0.557803i
$$763$$ 11538.7 19985.6i 0.547481 0.948264i
$$764$$ −11903.9 20618.2i −0.563703 0.976363i
$$765$$ −6653.30 + 3841.28i −0.314445 + 0.181545i
$$766$$ −598.052 −0.0282095
$$767$$ 0 0
$$768$$ −30025.1 −1.41073
$$769$$ 4456.41 2572.91i 0.208976 0.120652i −0.391860 0.920025i $$-0.628168\pi$$
0.600835 + 0.799373i $$0.294835\pi$$
$$770$$ 1153.35 + 1997.67i 0.0539792 + 0.0934947i
$$771$$ 2858.15 4950.45i 0.133507 0.231240i
$$772$$ 2626.83i 0.122463i
$$773$$ 11094.3 + 6405.28i 0.516214 + 0.298036i 0.735384 0.677650i $$-0.237002\pi$$
−0.219170 + 0.975687i $$0.570335\pi$$
$$774$$ −9908.01