# Properties

 Label 33.5.c.a.10.6 Level $33$ Weight $5$ Character 33.10 Analytic conductor $3.411$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$33 = 3 \cdot 11$$ Weight: $$k$$ $$=$$ $$5$$ Character orbit: $$[\chi]$$ $$=$$ 33.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.41120878177$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ Defining polynomial: $$x^{8} + 102 x^{6} + 2913 x^{4} + 23292 x^{2} + 41364$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{2}\cdot 3^{3}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 10.6 Root $$3.00247i$$ of defining polynomial Character $$\chi$$ $$=$$ 33.10 Dual form 33.5.c.a.10.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+3.00247i q^{2} +5.19615 q^{3} +6.98517 q^{4} +8.72578 q^{5} +15.6013i q^{6} +1.45810i q^{7} +69.0123i q^{8} +27.0000 q^{9} +O(q^{10})$$ $$q+3.00247i q^{2} +5.19615 q^{3} +6.98517 q^{4} +8.72578 q^{5} +15.6013i q^{6} +1.45810i q^{7} +69.0123i q^{8} +27.0000 q^{9} +26.1989i q^{10} +(-62.2476 + 103.760i) q^{11} +36.2960 q^{12} -162.221i q^{13} -4.37791 q^{14} +45.3405 q^{15} -95.4447 q^{16} -189.734i q^{17} +81.0667i q^{18} -590.443i q^{19} +60.9511 q^{20} +7.57652i q^{21} +(-311.538 - 186.897i) q^{22} -12.8557 q^{23} +358.598i q^{24} -548.861 q^{25} +487.064 q^{26} +140.296 q^{27} +10.1851i q^{28} +282.359i q^{29} +136.134i q^{30} -304.206 q^{31} +817.627i q^{32} +(-323.448 + 539.155i) q^{33} +569.671 q^{34} +12.7231i q^{35} +188.600 q^{36} +464.276 q^{37} +1772.79 q^{38} -842.925i q^{39} +602.186i q^{40} -1193.81i q^{41} -22.7483 q^{42} +1591.11i q^{43} +(-434.810 + 724.784i) q^{44} +235.596 q^{45} -38.5989i q^{46} -1825.87 q^{47} -495.945 q^{48} +2398.87 q^{49} -1647.94i q^{50} -985.887i q^{51} -1133.14i q^{52} -4023.28 q^{53} +421.235i q^{54} +(-543.159 + 905.391i) q^{55} -100.627 q^{56} -3068.03i q^{57} -847.774 q^{58} -1489.12 q^{59} +316.711 q^{60} +356.601i q^{61} -913.368i q^{62} +39.3688i q^{63} -3982.02 q^{64} -1415.51i q^{65} +(-1618.80 - 971.143i) q^{66} +8259.07 q^{67} -1325.32i q^{68} -66.8002 q^{69} -38.2007 q^{70} +7971.63 q^{71} +1863.33i q^{72} +5780.93i q^{73} +1393.98i q^{74} -2851.96 q^{75} -4124.34i q^{76} +(-151.293 - 90.7633i) q^{77} +2530.86 q^{78} +11304.5i q^{79} -832.830 q^{80} +729.000 q^{81} +3584.37 q^{82} +5449.44i q^{83} +52.9233i q^{84} -1655.58i q^{85} -4777.26 q^{86} +1467.18i q^{87} +(-7160.75 - 4295.85i) q^{88} +7332.12 q^{89} +707.371i q^{90} +236.535 q^{91} -89.7992 q^{92} -1580.70 q^{93} -5482.13i q^{94} -5152.08i q^{95} +4248.51i q^{96} -11228.1 q^{97} +7202.55i q^{98} +(-1680.69 + 2801.53i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 76q^{4} - 36q^{5} + 216q^{9} + O(q^{10})$$ $$8q - 76q^{4} - 36q^{5} + 216q^{9} + 36q^{11} - 360q^{12} - 1140q^{14} + 108q^{15} + 1412q^{16} + 2532q^{20} - 780q^{22} + 516q^{23} - 2280q^{25} - 1524q^{26} + 2752q^{31} + 1008q^{33} - 4920q^{34} - 2052q^{36} + 5296q^{37} + 696q^{38} - 4356q^{42} - 6540q^{44} - 972q^{45} + 420q^{47} + 9936q^{48} - 6832q^{49} + 3540q^{53} + 3784q^{55} + 17964q^{56} + 21624q^{58} - 16632q^{59} - 612q^{60} - 27508q^{64} + 360q^{66} - 3656q^{67} + 9036q^{69} + 3312q^{70} - 13212q^{71} - 9288q^{75} + 23268q^{77} - 13140q^{78} - 4476q^{80} + 5832q^{81} + 17088q^{82} + 19896q^{86} - 12516q^{88} + 15528q^{89} - 19752q^{91} - 81180q^{92} - 21384q^{93} + 7624q^{97} + 972q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$$.

 $$n$$ $$13$$ $$23$$ $$\chi(n)$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 3.00247i 0.750618i 0.926900 + 0.375309i $$0.122463\pi$$
−0.926900 + 0.375309i $$0.877537\pi$$
$$3$$ 5.19615 0.577350
$$4$$ 6.98517 0.436573
$$5$$ 8.72578 0.349031 0.174516 0.984654i $$-0.444164\pi$$
0.174516 + 0.984654i $$0.444164\pi$$
$$6$$ 15.6013i 0.433369i
$$7$$ 1.45810i 0.0297572i 0.999889 + 0.0148786i $$0.00473618\pi$$
−0.999889 + 0.0148786i $$0.995264\pi$$
$$8$$ 69.0123i 1.07832i
$$9$$ 27.0000 0.333333
$$10$$ 26.1989i 0.261989i
$$11$$ −62.2476 + 103.760i −0.514443 + 0.857525i
$$12$$ 36.2960 0.252056
$$13$$ 162.221i 0.959888i −0.877299 0.479944i $$-0.840657\pi$$
0.877299 0.479944i $$-0.159343\pi$$
$$14$$ −4.37791 −0.0223363
$$15$$ 45.3405 0.201513
$$16$$ −95.4447 −0.372831
$$17$$ 189.734i 0.656519i −0.944588 0.328259i $$-0.893538\pi$$
0.944588 0.328259i $$-0.106462\pi$$
$$18$$ 81.0667i 0.250206i
$$19$$ 590.443i 1.63558i −0.575520 0.817788i $$-0.695200\pi$$
0.575520 0.817788i $$-0.304800\pi$$
$$20$$ 60.9511 0.152378
$$21$$ 7.57652i 0.0171803i
$$22$$ −311.538 186.897i −0.643673 0.386150i
$$23$$ −12.8557 −0.0243019 −0.0121509 0.999926i $$-0.503868\pi$$
−0.0121509 + 0.999926i $$0.503868\pi$$
$$24$$ 358.598i 0.622567i
$$25$$ −548.861 −0.878177
$$26$$ 487.064 0.720509
$$27$$ 140.296 0.192450
$$28$$ 10.1851i 0.0129912i
$$29$$ 282.359i 0.335742i 0.985809 + 0.167871i $$0.0536892\pi$$
−0.985809 + 0.167871i $$0.946311\pi$$
$$30$$ 136.134i 0.151259i
$$31$$ −304.206 −0.316551 −0.158275 0.987395i $$-0.550593\pi$$
−0.158275 + 0.987395i $$0.550593\pi$$
$$32$$ 817.627i 0.798464i
$$33$$ −323.448 + 539.155i −0.297014 + 0.495092i
$$34$$ 569.671 0.492795
$$35$$ 12.7231i 0.0103862i
$$36$$ 188.600 0.145524
$$37$$ 464.276 0.339135 0.169568 0.985519i $$-0.445763\pi$$
0.169568 + 0.985519i $$0.445763\pi$$
$$38$$ 1772.79 1.22769
$$39$$ 842.925i 0.554191i
$$40$$ 602.186i 0.376366i
$$41$$ 1193.81i 0.710177i −0.934833 0.355089i $$-0.884451\pi$$
0.934833 0.355089i $$-0.115549\pi$$
$$42$$ −22.7483 −0.0128959
$$43$$ 1591.11i 0.860525i 0.902704 + 0.430263i $$0.141579\pi$$
−0.902704 + 0.430263i $$0.858421\pi$$
$$44$$ −434.810 + 724.784i −0.224592 + 0.374372i
$$45$$ 235.596 0.116344
$$46$$ 38.5989i 0.0182414i
$$47$$ −1825.87 −0.826561 −0.413281 0.910604i $$-0.635617\pi$$
−0.413281 + 0.910604i $$0.635617\pi$$
$$48$$ −495.945 −0.215254
$$49$$ 2398.87 0.999115
$$50$$ 1647.94i 0.659175i
$$51$$ 985.887i 0.379041i
$$52$$ 1133.14i 0.419061i
$$53$$ −4023.28 −1.43228 −0.716141 0.697955i $$-0.754093\pi$$
−0.716141 + 0.697955i $$0.754093\pi$$
$$54$$ 421.235i 0.144456i
$$55$$ −543.159 + 905.391i −0.179557 + 0.299303i
$$56$$ −100.627 −0.0320877
$$57$$ 3068.03i 0.944300i
$$58$$ −847.774 −0.252014
$$59$$ −1489.12 −0.427785 −0.213893 0.976857i $$-0.568614\pi$$
−0.213893 + 0.976857i $$0.568614\pi$$
$$60$$ 316.711 0.0879753
$$61$$ 356.601i 0.0958346i 0.998851 + 0.0479173i $$0.0152584\pi$$
−0.998851 + 0.0479173i $$0.984742\pi$$
$$62$$ 913.368i 0.237609i
$$63$$ 39.3688i 0.00991906i
$$64$$ −3982.02 −0.972172
$$65$$ 1415.51i 0.335031i
$$66$$ −1618.80 971.143i −0.371625 0.222944i
$$67$$ 8259.07 1.83985 0.919923 0.392098i $$-0.128251\pi$$
0.919923 + 0.392098i $$0.128251\pi$$
$$68$$ 1325.32i 0.286618i
$$69$$ −66.8002 −0.0140307
$$70$$ −38.2007 −0.00779606
$$71$$ 7971.63 1.58136 0.790680 0.612230i $$-0.209727\pi$$
0.790680 + 0.612230i $$0.209727\pi$$
$$72$$ 1863.33i 0.359439i
$$73$$ 5780.93i 1.08481i 0.840118 + 0.542403i $$0.182485\pi$$
−0.840118 + 0.542403i $$0.817515\pi$$
$$74$$ 1393.98i 0.254561i
$$75$$ −2851.96 −0.507016
$$76$$ 4124.34i 0.714048i
$$77$$ −151.293 90.7633i −0.0255175 0.0153084i
$$78$$ 2530.86 0.415986
$$79$$ 11304.5i 1.81133i 0.423998 + 0.905663i $$0.360626\pi$$
−0.423998 + 0.905663i $$0.639374\pi$$
$$80$$ −832.830 −0.130130
$$81$$ 729.000 0.111111
$$82$$ 3584.37 0.533071
$$83$$ 5449.44i 0.791036i 0.918458 + 0.395518i $$0.129435\pi$$
−0.918458 + 0.395518i $$0.870565\pi$$
$$84$$ 52.9233i 0.00750046i
$$85$$ 1655.58i 0.229146i
$$86$$ −4777.26 −0.645925
$$87$$ 1467.18i 0.193841i
$$88$$ −7160.75 4295.85i −0.924684 0.554733i
$$89$$ 7332.12 0.925656 0.462828 0.886448i $$-0.346835\pi$$
0.462828 + 0.886448i $$0.346835\pi$$
$$90$$ 707.371i 0.0873297i
$$91$$ 236.535 0.0285636
$$92$$ −89.7992 −0.0106096
$$93$$ −1580.70 −0.182761
$$94$$ 5482.13i 0.620432i
$$95$$ 5152.08i 0.570867i
$$96$$ 4248.51i 0.460993i
$$97$$ −11228.1 −1.19334 −0.596669 0.802487i $$-0.703509\pi$$
−0.596669 + 0.802487i $$0.703509\pi$$
$$98$$ 7202.55i 0.749953i
$$99$$ −1680.69 + 2801.53i −0.171481 + 0.285842i
$$100$$ −3833.88 −0.383388
$$101$$ 12735.1i 1.24842i −0.781258 0.624209i $$-0.785422\pi$$
0.781258 0.624209i $$-0.214578\pi$$
$$102$$ 2960.10 0.284515
$$103$$ 4637.37 0.437117 0.218558 0.975824i $$-0.429865\pi$$
0.218558 + 0.975824i $$0.429865\pi$$
$$104$$ 11195.2 1.03506
$$105$$ 66.1111i 0.00599647i
$$106$$ 12079.8i 1.07510i
$$107$$ 15858.6i 1.38515i 0.721347 + 0.692574i $$0.243524\pi$$
−0.721347 + 0.692574i $$0.756476\pi$$
$$108$$ 979.992 0.0840185
$$109$$ 19516.7i 1.64268i −0.570438 0.821341i $$-0.693226\pi$$
0.570438 0.821341i $$-0.306774\pi$$
$$110$$ −2718.41 1630.82i −0.224662 0.134778i
$$111$$ 2412.45 0.195800
$$112$$ 139.168i 0.0110944i
$$113$$ −15343.5 −1.20162 −0.600811 0.799391i $$-0.705156\pi$$
−0.600811 + 0.799391i $$0.705156\pi$$
$$114$$ 9211.67 0.708808
$$115$$ −112.176 −0.00848212
$$116$$ 1972.32i 0.146576i
$$117$$ 4379.97i 0.319963i
$$118$$ 4471.04i 0.321103i
$$119$$ 276.652 0.0195362
$$120$$ 3129.05i 0.217295i
$$121$$ −6891.47 12917.7i −0.470697 0.882295i
$$122$$ −1070.68 −0.0719351
$$123$$ 6203.21i 0.410021i
$$124$$ −2124.93 −0.138198
$$125$$ −10242.9 −0.655543
$$126$$ −118.204 −0.00744542
$$127$$ 19359.4i 1.20028i 0.799893 + 0.600142i $$0.204889\pi$$
−0.799893 + 0.600142i $$0.795111\pi$$
$$128$$ 1126.14i 0.0687341i
$$129$$ 8267.66i 0.496824i
$$130$$ 4250.01 0.251480
$$131$$ 13966.3i 0.813842i −0.913463 0.406921i $$-0.866602\pi$$
0.913463 0.406921i $$-0.133398\pi$$
$$132$$ −2259.34 + 3766.09i −0.129668 + 0.216144i
$$133$$ 860.926 0.0486701
$$134$$ 24797.6i 1.38102i
$$135$$ 1224.19 0.0671711
$$136$$ 13094.0 0.707936
$$137$$ 10923.8 0.582010 0.291005 0.956721i $$-0.406010\pi$$
0.291005 + 0.956721i $$0.406010\pi$$
$$138$$ 200.566i 0.0105317i
$$139$$ 27425.4i 1.41946i 0.704474 + 0.709730i $$0.251183\pi$$
−0.704474 + 0.709730i $$0.748817\pi$$
$$140$$ 88.8729i 0.00453433i
$$141$$ −9487.52 −0.477215
$$142$$ 23934.6i 1.18700i
$$143$$ 16832.1 + 10097.9i 0.823127 + 0.493807i
$$144$$ −2577.01 −0.124277
$$145$$ 2463.80i 0.117184i
$$146$$ −17357.1 −0.814275
$$147$$ 12464.9 0.576839
$$148$$ 3243.05 0.148057
$$149$$ 17646.6i 0.794856i −0.917633 0.397428i $$-0.869903\pi$$
0.917633 0.397428i $$-0.130097\pi$$
$$150$$ 8562.94i 0.380575i
$$151$$ 19482.1i 0.854441i −0.904147 0.427221i $$-0.859493\pi$$
0.904147 0.427221i $$-0.140507\pi$$
$$152$$ 40747.8 1.76367
$$153$$ 5122.82i 0.218840i
$$154$$ 272.514 454.254i 0.0114907 0.0191539i
$$155$$ −2654.43 −0.110486
$$156$$ 5887.97i 0.241945i
$$157$$ 20642.6 0.837462 0.418731 0.908110i $$-0.362475\pi$$
0.418731 + 0.908110i $$0.362475\pi$$
$$158$$ −33941.4 −1.35961
$$159$$ −20905.6 −0.826929
$$160$$ 7134.43i 0.278689i
$$161$$ 18.7449i 0.000723156i
$$162$$ 2188.80i 0.0834020i
$$163$$ 5888.63 0.221635 0.110818 0.993841i $$-0.464653\pi$$
0.110818 + 0.993841i $$0.464653\pi$$
$$164$$ 8338.95i 0.310044i
$$165$$ −2822.34 + 4704.55i −0.103667 + 0.172803i
$$166$$ −16361.8 −0.593765
$$167$$ 25996.3i 0.932135i −0.884749 0.466067i $$-0.845670\pi$$
0.884749 0.466067i $$-0.154330\pi$$
$$168$$ −522.873 −0.0185258
$$169$$ 2245.35 0.0786159
$$170$$ 4970.82 0.172001
$$171$$ 15942.0i 0.545192i
$$172$$ 11114.2i 0.375682i
$$173$$ 22355.9i 0.746964i −0.927637 0.373482i $$-0.878164\pi$$
0.927637 0.373482i $$-0.121836\pi$$
$$174$$ −4405.16 −0.145500
$$175$$ 800.295i 0.0261321i
$$176$$ 5941.21 9903.39i 0.191800 0.319712i
$$177$$ −7737.70 −0.246982
$$178$$ 22014.5i 0.694814i
$$179$$ 9227.98 0.288005 0.144003 0.989577i $$-0.454003\pi$$
0.144003 + 0.989577i $$0.454003\pi$$
$$180$$ 1645.68 0.0507925
$$181$$ −52256.0 −1.59507 −0.797534 0.603274i $$-0.793862\pi$$
−0.797534 + 0.603274i $$0.793862\pi$$
$$182$$ 710.189i 0.0214403i
$$183$$ 1852.95i 0.0553301i
$$184$$ 887.202i 0.0262052i
$$185$$ 4051.17 0.118369
$$186$$ 4746.00i 0.137184i
$$187$$ 19686.9 + 11810.5i 0.562981 + 0.337742i
$$188$$ −12754.0 −0.360854
$$189$$ 204.566i 0.00572677i
$$190$$ 15469.0 0.428503
$$191$$ −70655.7 −1.93678 −0.968390 0.249442i $$-0.919753\pi$$
−0.968390 + 0.249442i $$0.919753\pi$$
$$192$$ −20691.2 −0.561284
$$193$$ 21752.7i 0.583981i −0.956421 0.291991i $$-0.905682\pi$$
0.956421 0.291991i $$-0.0943176\pi$$
$$194$$ 33712.1i 0.895741i
$$195$$ 7355.18i 0.193430i
$$196$$ 16756.5 0.436186
$$197$$ 67346.7i 1.73534i 0.497144 + 0.867668i $$0.334382\pi$$
−0.497144 + 0.867668i $$0.665618\pi$$
$$198$$ −8411.52 5046.21i −0.214558 0.128717i
$$199$$ 4956.39 0.125158 0.0625791 0.998040i $$-0.480067\pi$$
0.0625791 + 0.998040i $$0.480067\pi$$
$$200$$ 37878.1i 0.946954i
$$201$$ 42915.4 1.06224
$$202$$ 38236.8 0.937084
$$203$$ −411.708 −0.00999073
$$204$$ 6886.58i 0.165479i
$$205$$ 10416.9i 0.247874i
$$206$$ 13923.6i 0.328108i
$$207$$ −347.104 −0.00810063
$$208$$ 15483.1i 0.357876i
$$209$$ 61264.6 + 36753.6i 1.40255 + 0.841410i
$$210$$ −198.497 −0.00450106
$$211$$ 5230.33i 0.117480i −0.998273 0.0587400i $$-0.981292\pi$$
0.998273 0.0587400i $$-0.0187083\pi$$
$$212$$ −28103.3 −0.625296
$$213$$ 41421.8 0.912998
$$214$$ −47614.9 −1.03972
$$215$$ 13883.7i 0.300350i
$$216$$ 9682.16i 0.207522i
$$217$$ 443.563i 0.00941967i
$$218$$ 58598.3 1.23303
$$219$$ 30038.6i 0.626313i
$$220$$ −3794.06 + 6324.31i −0.0783896 + 0.130668i
$$221$$ −30778.8 −0.630184
$$222$$ 7243.31i 0.146971i
$$223$$ 70116.0 1.40996 0.704981 0.709226i $$-0.250956\pi$$
0.704981 + 0.709226i $$0.250956\pi$$
$$224$$ −1192.18 −0.0237600
$$225$$ −14819.2 −0.292726
$$226$$ 46068.5i 0.901960i
$$227$$ 69181.4i 1.34257i 0.741198 + 0.671287i $$0.234258\pi$$
−0.741198 + 0.671287i $$0.765742\pi$$
$$228$$ 21430.7i 0.412256i
$$229$$ −27970.4 −0.533369 −0.266685 0.963784i $$-0.585928\pi$$
−0.266685 + 0.963784i $$0.585928\pi$$
$$230$$ 336.805i 0.00636683i
$$231$$ −786.143 471.620i −0.0147325 0.00883829i
$$232$$ −19486.2 −0.362036
$$233$$ 67591.9i 1.24504i 0.782604 + 0.622519i $$0.213891\pi$$
−0.782604 + 0.622519i $$0.786109\pi$$
$$234$$ 13150.7 0.240170
$$235$$ −15932.2 −0.288496
$$236$$ −10401.8 −0.186759
$$237$$ 58739.8i 1.04577i
$$238$$ 830.638i 0.0146642i
$$239$$ 31589.5i 0.553028i −0.961010 0.276514i $$-0.910821\pi$$
0.961010 0.276514i $$-0.0891792\pi$$
$$240$$ −4327.51 −0.0751304
$$241$$ 64415.3i 1.10906i −0.832164 0.554530i $$-0.812898\pi$$
0.832164 0.554530i $$-0.187102\pi$$
$$242$$ 38785.0 20691.4i 0.662266 0.353313i
$$243$$ 3788.00 0.0641500
$$244$$ 2490.91i 0.0418388i
$$245$$ 20932.1 0.348722
$$246$$ 18624.9 0.307769
$$247$$ −95782.2 −1.56997
$$248$$ 20993.9i 0.341342i
$$249$$ 28316.1i 0.456705i
$$250$$ 30753.9i 0.492062i
$$251$$ 34822.1 0.552722 0.276361 0.961054i $$-0.410871\pi$$
0.276361 + 0.961054i $$0.410871\pi$$
$$252$$ 274.997i 0.00433039i
$$253$$ 800.237 1333.91i 0.0125019 0.0208395i
$$254$$ −58126.0 −0.900955
$$255$$ 8602.63i 0.132297i
$$256$$ −67093.5 −1.02376
$$257$$ −73746.1 −1.11654 −0.558268 0.829661i $$-0.688534\pi$$
−0.558268 + 0.829661i $$0.688534\pi$$
$$258$$ −24823.4 −0.372925
$$259$$ 676.962i 0.0100917i
$$260$$ 9887.54i 0.146265i
$$261$$ 7623.69i 0.111914i
$$262$$ 41933.5 0.610884
$$263$$ 103570.i 1.49734i −0.662942 0.748671i $$-0.730692\pi$$
0.662942 0.748671i $$-0.269308\pi$$
$$264$$ −37208.3 22321.9i −0.533866 0.320275i
$$265$$ −35106.3 −0.499911
$$266$$ 2584.91i 0.0365327i
$$267$$ 38098.8 0.534428
$$268$$ 57691.0 0.803227
$$269$$ 118870. 1.64274 0.821371 0.570395i $$-0.193210\pi$$
0.821371 + 0.570395i $$0.193210\pi$$
$$270$$ 3675.60i 0.0504198i
$$271$$ 102742.i 1.39897i −0.714646 0.699486i $$-0.753412\pi$$
0.714646 0.699486i $$-0.246588\pi$$
$$272$$ 18109.1i 0.244771i
$$273$$ 1229.07 0.0164912
$$274$$ 32798.3i 0.436867i
$$275$$ 34165.3 56950.1i 0.451772 0.753059i
$$276$$ −466.611 −0.00612543
$$277$$ 103336.i 1.34677i −0.739292 0.673385i $$-0.764839\pi$$
0.739292 0.673385i $$-0.235161\pi$$
$$278$$ −82343.9 −1.06547
$$279$$ −8213.55 −0.105517
$$280$$ −878.049 −0.0111996
$$281$$ 37257.8i 0.471850i 0.971771 + 0.235925i $$0.0758120\pi$$
−0.971771 + 0.235925i $$0.924188\pi$$
$$282$$ 28486.0i 0.358206i
$$283$$ 126640.i 1.58124i 0.612310 + 0.790618i $$0.290241\pi$$
−0.612310 + 0.790618i $$0.709759\pi$$
$$284$$ 55683.2 0.690379
$$285$$ 26771.0i 0.329590i
$$286$$ −30318.6 + 50538.0i −0.370661 + 0.617854i
$$287$$ 1740.69 0.0211329
$$288$$ 22075.9i 0.266155i
$$289$$ 47522.0 0.568983
$$290$$ −7397.49 −0.0879607
$$291$$ −58343.0 −0.688974
$$292$$ 40380.8i 0.473597i
$$293$$ 1337.08i 0.0155748i −0.999970 0.00778741i $$-0.997521\pi$$
0.999970 0.00778741i $$-0.00247883\pi$$
$$294$$ 37425.5i 0.432986i
$$295$$ −12993.7 −0.149310
$$296$$ 32040.8i 0.365695i
$$297$$ −8733.10 + 14557.2i −0.0990046 + 0.165031i
$$298$$ 52983.4 0.596633
$$299$$ 2085.46i 0.0233271i
$$300$$ −19921.4 −0.221349
$$301$$ −2320.00 −0.0256068
$$302$$ 58494.5 0.641359
$$303$$ 66173.5i 0.720774i
$$304$$ 56354.7i 0.609793i
$$305$$ 3111.62i 0.0334493i
$$306$$ 15381.1 0.164265
$$307$$ 70825.1i 0.751468i 0.926728 + 0.375734i $$0.122609\pi$$
−0.926728 + 0.375734i $$0.877391\pi$$
$$308$$ −1056.81 633.997i −0.0111403 0.00668322i
$$309$$ 24096.5 0.252369
$$310$$ 7969.85i 0.0829329i
$$311$$ −79979.1 −0.826905 −0.413453 0.910526i $$-0.635677\pi$$
−0.413453 + 0.910526i $$0.635677\pi$$
$$312$$ 58172.2 0.597594
$$313$$ 45118.3 0.460537 0.230268 0.973127i $$-0.426040\pi$$
0.230268 + 0.973127i $$0.426040\pi$$
$$314$$ 61978.8i 0.628614i
$$315$$ 343.523i 0.00346206i
$$316$$ 78963.7i 0.790776i
$$317$$ −53392.1 −0.531322 −0.265661 0.964066i $$-0.585590\pi$$
−0.265661 + 0.964066i $$0.585590\pi$$
$$318$$ 62768.4i 0.620707i
$$319$$ −29297.7 17576.2i −0.287907 0.172720i
$$320$$ −34746.2 −0.339318
$$321$$ 82403.5i 0.799716i
$$322$$ 56.2811 0.000542814
$$323$$ −112027. −1.07379
$$324$$ 5092.19 0.0485081
$$325$$ 89036.7i 0.842951i
$$326$$ 17680.4i 0.166363i
$$327$$ 101412.i 0.948403i
$$328$$ 82387.4 0.765796
$$329$$ 2662.31i 0.0245961i
$$330$$ −14125.3 8473.98i −0.129709 0.0778144i
$$331$$ 97744.9 0.892151 0.446075 0.894995i $$-0.352821\pi$$
0.446075 + 0.894995i $$0.352821\pi$$
$$332$$ 38065.3i 0.345345i
$$333$$ 12535.5 0.113045
$$334$$ 78053.2 0.699677
$$335$$ 72066.9 0.642164
$$336$$ 723.139i 0.00640536i
$$337$$ 75385.5i 0.663786i −0.943317 0.331893i $$-0.892313\pi$$
0.943317 0.331893i $$-0.107687\pi$$
$$338$$ 6741.59i 0.0590105i
$$339$$ −79727.3 −0.693757
$$340$$ 11564.5i 0.100039i
$$341$$ 18936.1 31564.5i 0.162847 0.271450i
$$342$$ 47865.3 0.409231
$$343$$ 6998.71i 0.0594880i
$$344$$ −109806. −0.927919
$$345$$ −582.884 −0.00489716
$$346$$ 67122.9 0.560684
$$347$$ 95151.0i 0.790232i −0.918631 0.395116i $$-0.870704\pi$$
0.918631 0.395116i $$-0.129296\pi$$
$$348$$ 10248.5i 0.0846256i
$$349$$ 106717.i 0.876156i 0.898937 + 0.438078i $$0.144341\pi$$
−0.898937 + 0.438078i $$0.855659\pi$$
$$350$$ 2402.86 0.0196152
$$351$$ 22759.0i 0.184730i
$$352$$ −84837.3 50895.3i −0.684702 0.410764i
$$353$$ 62919.0 0.504932 0.252466 0.967606i $$-0.418758\pi$$
0.252466 + 0.967606i $$0.418758\pi$$
$$354$$ 23232.2i 0.185389i
$$355$$ 69558.7 0.551944
$$356$$ 51216.1 0.404116
$$357$$ 1437.52 0.0112792
$$358$$ 27706.7i 0.216182i
$$359$$ 147077.i 1.14119i −0.821232 0.570594i $$-0.806713\pi$$
0.821232 0.570594i $$-0.193287\pi$$
$$360$$ 16259.0i 0.125455i
$$361$$ −218302. −1.67511
$$362$$ 156897.i 1.19729i
$$363$$ −35809.1 67122.2i −0.271757 0.509393i
$$364$$ 1652.24 0.0124701
$$365$$ 50443.2i 0.378631i
$$366$$ −5563.43 −0.0415318
$$367$$ −50293.7 −0.373406 −0.186703 0.982416i $$-0.559780\pi$$
−0.186703 + 0.982416i $$0.559780\pi$$
$$368$$ 1227.01 0.00906050
$$369$$ 32232.8i 0.236726i
$$370$$ 12163.5i 0.0888497i
$$371$$ 5866.36i 0.0426207i
$$372$$ −11041.4 −0.0797884
$$373$$ 29786.2i 0.214090i 0.994254 + 0.107045i $$0.0341389\pi$$
−0.994254 + 0.107045i $$0.965861\pi$$
$$374$$ −35460.6 + 59109.3i −0.253515 + 0.422584i
$$375$$ −53223.4 −0.378478
$$376$$ 126008.i 0.891295i
$$377$$ 45804.5 0.322274
$$378$$ −614.204 −0.00429862
$$379$$ 80930.7 0.563423 0.281712 0.959499i $$-0.409098\pi$$
0.281712 + 0.959499i $$0.409098\pi$$
$$380$$ 35988.1i 0.249225i
$$381$$ 100594.i 0.692985i
$$382$$ 212142.i 1.45378i
$$383$$ −266517. −1.81688 −0.908441 0.418012i $$-0.862727\pi$$
−0.908441 + 0.418012i $$0.862727\pi$$
$$384$$ 5851.59i 0.0396836i
$$385$$ −1320.15 791.981i −0.00890641 0.00534310i
$$386$$ 65311.9 0.438347
$$387$$ 42960.0i 0.286842i
$$388$$ −78430.3 −0.520979
$$389$$ 4358.49 0.0288029 0.0144015 0.999896i $$-0.495416\pi$$
0.0144015 + 0.999896i $$0.495416\pi$$
$$390$$ 22083.7 0.145192
$$391$$ 2439.16i 0.0159547i
$$392$$ 165552.i 1.07736i
$$393$$ 72571.2i 0.469872i
$$394$$ −202206. −1.30257
$$395$$ 98640.5i 0.632209i
$$396$$ −11739.9 + 19569.2i −0.0748640 + 0.124791i
$$397$$ −11014.6 −0.0698859 −0.0349429 0.999389i $$-0.511125\pi$$
−0.0349429 + 0.999389i $$0.511125\pi$$
$$398$$ 14881.4i 0.0939459i
$$399$$ 4473.50 0.0280997
$$400$$ 52385.9 0.327412
$$401$$ 244214. 1.51873 0.759366 0.650664i $$-0.225509\pi$$
0.759366 + 0.650664i $$0.225509\pi$$
$$402$$ 128852.i 0.797333i
$$403$$ 49348.5i 0.303853i
$$404$$ 88956.8i 0.545025i
$$405$$ 6361.10 0.0387813
$$406$$ 1236.14i 0.00749922i
$$407$$ −28900.1 + 48173.5i −0.174466 + 0.290817i
$$408$$ 68038.3 0.408727
$$409$$ 9069.88i 0.0542194i −0.999632 0.0271097i $$-0.991370\pi$$
0.999632 0.0271097i $$-0.00863035\pi$$
$$410$$ 31276.5 0.186059
$$411$$ 56761.5 0.336024
$$412$$ 32392.8 0.190833
$$413$$ 2171.29i 0.0127297i
$$414$$ 1042.17i 0.00608048i
$$415$$ 47550.7i 0.276096i
$$416$$ 132636. 0.766435
$$417$$ 142506.i 0.819525i
$$418$$ −110352. + 183945.i −0.631578 + 1.05278i
$$419$$ 317776. 1.81006 0.905029 0.425350i $$-0.139849\pi$$
0.905029 + 0.425350i $$0.139849\pi$$
$$420$$ 461.797i 0.00261790i
$$421$$ 89267.7 0.503651 0.251826 0.967773i $$-0.418969\pi$$
0.251826 + 0.967773i $$0.418969\pi$$
$$422$$ 15703.9 0.0881826
$$423$$ −49298.6 −0.275520
$$424$$ 277656.i 1.54445i
$$425$$ 104138.i 0.576540i
$$426$$ 124368.i 0.685313i
$$427$$ −519.960 −0.00285177
$$428$$ 110775.i 0.604718i
$$429$$ 87462.3 + 52470.1i 0.475233 + 0.285100i
$$430$$ −41685.4 −0.225448
$$431$$ 80855.4i 0.435266i −0.976031 0.217633i $$-0.930166\pi$$
0.976031 0.217633i $$-0.0698335\pi$$
$$432$$ −13390.5 −0.0717514
$$433$$ 17118.8 0.0913057 0.0456529 0.998957i $$-0.485463\pi$$
0.0456529 + 0.998957i $$0.485463\pi$$
$$434$$ 1331.78 0.00707057
$$435$$ 12802.3i 0.0676564i
$$436$$ 136327.i 0.717150i
$$437$$ 7590.56i 0.0397476i
$$438$$ −90190.1 −0.470122
$$439$$ 32476.8i 0.168517i 0.996444 + 0.0842585i $$0.0268522\pi$$
−0.996444 + 0.0842585i $$0.973148\pi$$
$$440$$ −62483.1 37484.6i −0.322743 0.193619i
$$441$$ 64769.6 0.333038
$$442$$ 92412.6i 0.473028i
$$443$$ 4735.01 0.0241276 0.0120638 0.999927i $$-0.496160\pi$$
0.0120638 + 0.999927i $$0.496160\pi$$
$$444$$ 16851.4 0.0854809
$$445$$ 63978.5 0.323083
$$446$$ 210521.i 1.05834i
$$447$$ 91694.4i 0.458910i
$$448$$ 5806.19i 0.0289291i
$$449$$ −217096. −1.07686 −0.538430 0.842670i $$-0.680982\pi$$
−0.538430 + 0.842670i $$0.680982\pi$$
$$450$$ 44494.3i 0.219725i
$$451$$ 123870. + 74311.7i 0.608994 + 0.365346i
$$452$$ −107177. −0.524596
$$453$$ 101232.i 0.493312i
$$454$$ −207715. −1.00776
$$455$$ 2063.95 0.00996957
$$456$$ 211732. 1.01826
$$457$$ 226266.i 1.08340i −0.840573 0.541698i $$-0.817782\pi$$
0.840573 0.541698i $$-0.182218\pi$$
$$458$$ 83980.4i 0.400356i
$$459$$ 26618.9i 0.126347i
$$460$$ −783.569 −0.00370307
$$461$$ 280319.i 1.31902i 0.751697 + 0.659509i $$0.229236\pi$$
−0.751697 + 0.659509i $$0.770764\pi$$
$$462$$ 1416.03 2360.37i 0.00663418 0.0110585i
$$463$$ 176739. 0.824463 0.412231 0.911079i $$-0.364750\pi$$
0.412231 + 0.911079i $$0.364750\pi$$
$$464$$ 26949.7i 0.125175i
$$465$$ −13792.8 −0.0637892
$$466$$ −202943. −0.934548
$$467$$ −211683. −0.970625 −0.485312 0.874341i $$-0.661294\pi$$
−0.485312 + 0.874341i $$0.661294\pi$$
$$468$$ 30594.8i 0.139687i
$$469$$ 12042.6i 0.0547487i
$$470$$ 47835.9i 0.216550i
$$471$$ 107262. 0.483509
$$472$$ 102768.i 0.461288i
$$473$$ −165094. 99042.8i −0.737921 0.442691i
$$474$$ −176365. −0.784973
$$475$$ 324071.i 1.43633i
$$476$$ 1932.46 0.00852896
$$477$$ −108629. −0.477428
$$478$$ 94846.5 0.415112
$$479$$ 80152.2i 0.349337i −0.984627 0.174668i $$-0.944115\pi$$
0.984627 0.174668i $$-0.0558854\pi$$
$$480$$ 37071.6i 0.160901i
$$481$$ 75315.3i 0.325532i
$$482$$ 193405. 0.832480
$$483$$ 97.4015i 0.000417514i
$$484$$ −48138.1 90232.2i −0.205494 0.385186i
$$485$$ −97974.1 −0.416512
$$486$$ 11373.3i 0.0481522i
$$487$$ −173605. −0.731988 −0.365994 0.930617i $$-0.619271\pi$$
−0.365994 + 0.930617i $$0.619271\pi$$
$$488$$ −24609.8 −0.103340
$$489$$ 30598.2 0.127961
$$490$$ 62847.9i 0.261757i
$$491$$ 152879.i 0.634138i 0.948402 + 0.317069i $$0.102699\pi$$
−0.948402 + 0.317069i $$0.897301\pi$$
$$492$$ 43330.4i 0.179004i
$$493$$ 53573.1 0.220421
$$494$$ 287583.i 1.17845i
$$495$$ −14665.3 + 24445.6i −0.0598522 + 0.0997676i
$$496$$ 29034.8 0.118020
$$497$$ 11623.5i 0.0470568i
$$498$$ −85018.4 −0.342811
$$499$$ 122586. 0.492312 0.246156 0.969230i $$-0.420832\pi$$
0.246156 + 0.969230i $$0.420832\pi$$
$$500$$ −71548.0 −0.286192
$$501$$ 135081.i 0.538168i
$$502$$ 104552.i 0.414883i
$$503$$ 355305.i 1.40432i −0.712020 0.702159i $$-0.752220\pi$$
0.712020 0.702159i $$-0.247780\pi$$
$$504$$ −2716.93 −0.0106959
$$505$$ 111124.i 0.435737i
$$506$$ 4005.04 + 2402.69i 0.0156425 + 0.00938418i
$$507$$ 11667.2 0.0453889
$$508$$ 135229.i 0.524012i
$$509$$ 34844.7 0.134493 0.0672467 0.997736i $$-0.478579\pi$$
0.0672467 + 0.997736i $$0.478579\pi$$
$$510$$ 25829.2 0.0993047
$$511$$ −8429.19 −0.0322808
$$512$$ 183428.i 0.699722i
$$513$$ 82836.8i 0.314767i
$$514$$ 221421.i 0.838092i
$$515$$ 40464.7 0.152567
$$516$$ 57751.0i 0.216900i
$$517$$ 113656. 189454.i 0.425219 0.708797i
$$518$$ −2032.56 −0.00757501
$$519$$ 116165.i 0.431260i
$$520$$ 97687.3 0.361269
$$521$$ 130516. 0.480825 0.240412 0.970671i $$-0.422717\pi$$
0.240412 + 0.970671i $$0.422717\pi$$
$$522$$ −22889.9 −0.0840046
$$523$$ 436331.i 1.59519i 0.603192 + 0.797596i $$0.293895\pi$$
−0.603192 + 0.797596i $$0.706105\pi$$
$$524$$ 97557.3i 0.355301i
$$525$$ 4158.45i 0.0150874i
$$526$$ 310965. 1.12393
$$527$$ 57718.1i 0.207822i
$$528$$ 30871.4 51459.5i 0.110736 0.184586i
$$529$$ −279676. −0.999409
$$530$$ 105406.i 0.375242i
$$531$$ −40206.2 −0.142595
$$532$$ 6013.71 0.0212481
$$533$$ −193661. −0.681690
$$534$$ 114391.i 0.401151i
$$535$$ 138378.i 0.483460i
$$536$$ 569978.i 1.98394i
$$537$$ 47950.0 0.166280
$$538$$ 356905.i 1.23307i
$$539$$ −149324. + 248908.i −0.513987 + 0.856765i
$$540$$ 8551.20 0.0293251
$$541$$ 80892.7i 0.276385i 0.990405 + 0.138193i $$0.0441293\pi$$
−0.990405 + 0.138193i $$0.955871\pi$$
$$542$$ 308480. 1.05009
$$543$$ −271530. −0.920913
$$544$$ 155132. 0.524206
$$545$$ 170298.i 0.573347i
$$546$$ 3690.25i 0.0123786i
$$547$$ 231848.i 0.774870i 0.921897 + 0.387435i $$0.126639\pi$$
−0.921897 + 0.387435i $$0.873361\pi$$
$$548$$ 76304.2 0.254090
$$549$$ 9628.21i 0.0319449i
$$550$$ 170991. + 102580.i 0.565259 + 0.339108i
$$551$$ 166717. 0.549131
$$552$$ 4610.03i 0.0151296i
$$553$$ −16483.1 −0.0539000
$$554$$ 310264. 1.01091
$$555$$ 21050.5 0.0683402
$$556$$ 191571.i 0.619698i
$$557$$ 461600.i 1.48784i −0.668270 0.743919i $$-0.732965\pi$$
0.668270 0.743919i $$-0.267035\pi$$
$$558$$ 24660.9i 0.0792029i
$$559$$ 258112. 0.826007
$$560$$ 1214.35i 0.00387229i
$$561$$ 102296. + 61369.1i 0.325037 + 0.194995i
$$562$$ −111865. −0.354179
$$563$$ 35282.9i 0.111313i −0.998450 0.0556566i $$-0.982275\pi$$
0.998450 0.0556566i $$-0.0177252\pi$$
$$564$$ −66271.9 −0.208339
$$565$$ −133884. −0.419404
$$566$$ −380232. −1.18690
$$567$$ 1062.96i 0.00330635i
$$568$$ 550141.i 1.70521i
$$569$$ 296349.i 0.915332i 0.889124 + 0.457666i $$0.151314\pi$$
−0.889124 + 0.457666i $$0.848686\pi$$
$$570$$ 80379.1 0.247396
$$571$$ 241258.i 0.739963i −0.929039 0.369982i $$-0.879364\pi$$
0.929039 0.369982i $$-0.120636\pi$$
$$572$$ 117575. + 70535.3i 0.359355 + 0.215583i
$$573$$ −367138. −1.11820
$$574$$ 5226.38i 0.0158627i
$$575$$ 7055.99 0.0213414
$$576$$ −107514. −0.324057
$$577$$ −457944. −1.37550 −0.687750 0.725948i $$-0.741401\pi$$
−0.687750 + 0.725948i $$0.741401\pi$$
$$578$$ 142683.i 0.427089i
$$579$$ 113030.i 0.337162i
$$580$$ 17210.1i 0.0511595i
$$581$$ −7945.85 −0.0235390
$$582$$ 175173.i 0.517156i
$$583$$ 250440. 417458.i 0.736828 1.22822i
$$584$$ −398956. −1.16977
$$585$$ 38218.6i 0.111677i
$$586$$ 4014.55 0.0116907
$$587$$ 481837. 1.39838 0.699188 0.714938i $$-0.253545\pi$$
0.699188 + 0.714938i $$0.253545\pi$$
$$588$$ 87069.5 0.251832
$$589$$ 179616.i 0.517743i
$$590$$ 39013.3i 0.112075i
$$591$$ 349944.i 1.00190i
$$592$$ −44312.7 −0.126440
$$593$$ 495129.i 1.40802i −0.710190 0.704010i $$-0.751391\pi$$
0.710190 0.704010i $$-0.248609\pi$$
$$594$$ −43707.5 26220.9i −0.123875 0.0743146i
$$595$$ 2414.00 0.00681873
$$596$$ 123264.i 0.347013i
$$597$$ 25754.1 0.0722601
$$598$$ −6261.55 −0.0175097
$$599$$ −341737. −0.952442 −0.476221 0.879326i $$-0.657994\pi$$
−0.476221 + 0.879326i $$0.657994\pi$$
$$600$$ 196821.i 0.546724i
$$601$$ 404022.i 1.11855i −0.828982 0.559275i $$-0.811080\pi$$
0.828982 0.559275i $$-0.188920\pi$$
$$602$$ 6965.74i 0.0192209i
$$603$$ 222995. 0.613282
$$604$$ 136086.i 0.373026i
$$605$$ −60133.5 112717.i −0.164288 0.307949i
$$606$$ 198684. 0.541026
$$607$$ 85001.6i 0.230701i −0.993325 0.115351i $$-0.963201\pi$$
0.993325 0.115351i $$-0.0367991\pi$$
$$608$$ 482762. 1.30595
$$609$$ −2139.30 −0.00576815
$$610$$ −9342.54 −0.0251076
$$611$$ 296195.i 0.793406i
$$612$$ 35783.7i 0.0955395i
$$613$$ 296743.i 0.789695i −0.918747 0.394847i $$-0.870797\pi$$
0.918747 0.394847i $$-0.129203\pi$$
$$614$$ −212650. −0.564065
$$615$$ 54127.8i 0.143110i
$$616$$ 6263.79 10441.1i 0.0165073 0.0275160i
$$617$$ −205712. −0.540368 −0.270184 0.962809i $$-0.587085\pi$$
−0.270184 + 0.962809i $$0.587085\pi$$
$$618$$ 72349.0i 0.189433i
$$619$$ −23798.6 −0.0621112 −0.0310556 0.999518i $$-0.509887\pi$$
−0.0310556 + 0.999518i $$0.509887\pi$$
$$620$$ −18541.6 −0.0482353
$$621$$ −1803.61 −0.00467690
$$622$$ 240135.i 0.620690i
$$623$$ 10691.0i 0.0275449i
$$624$$ 80452.8i 0.206620i
$$625$$ 253661. 0.649372
$$626$$ 135466.i 0.345687i
$$627$$ 318340. + 190978.i 0.809761 + 0.485789i
$$628$$ 144192. 0.365613
$$629$$ 88088.9i 0.222649i
$$630$$ −1031.42 −0.00259869
$$631$$ −464381. −1.16631 −0.583157 0.812359i $$-0.698183\pi$$
−0.583157 + 0.812359i $$0.698183\pi$$
$$632$$ −780149. −1.95318
$$633$$ 27177.6i 0.0678271i
$$634$$ 160308.i 0.398820i
$$635$$ 168926.i 0.418937i
$$636$$ −146029. −0.361015
$$637$$ 389148.i 0.959038i
$$638$$ 52771.9 87965.4i 0.129647 0.216108i
$$639$$ 215234. 0.527120
$$640$$ 9826.44i 0.0239903i
$$641$$ 433460. 1.05495 0.527476 0.849570i $$-0.323138\pi$$
0.527476 + 0.849570i $$0.323138\pi$$
$$642$$ −247414. −0.600281
$$643$$ −228934. −0.553718 −0.276859 0.960910i $$-0.589294\pi$$
−0.276859 + 0.960910i $$0.589294\pi$$
$$644$$ 130.936i 0.000315710i
$$645$$ 72141.8i 0.173407i
$$646$$ 336358.i 0.806003i
$$647$$ −83987.4 −0.200634 −0.100317 0.994956i $$-0.531986\pi$$
−0.100317 + 0.994956i $$0.531986\pi$$
$$648$$ 50310.0i 0.119813i
$$649$$ 92694.1 154512.i 0.220071 0.366836i
$$650$$ −267330. −0.632734
$$651$$ 2304.82i 0.00543845i
$$652$$ 41133.1 0.0967600
$$653$$ 337789. 0.792172 0.396086 0.918213i $$-0.370368\pi$$
0.396086 + 0.918213i $$0.370368\pi$$
$$654$$ 304486. 0.711888
$$655$$ 121867.i 0.284056i
$$656$$ 113943.i 0.264776i
$$657$$ 156085.i 0.361602i
$$658$$ 7993.51 0.0184623
$$659$$ 586098.i 1.34958i 0.738008 + 0.674791i $$0.235766\pi$$
−0.738008 + 0.674791i $$0.764234\pi$$
$$660$$ −19714.5 + 32862.1i −0.0452583 + 0.0754410i
$$661$$ −660271. −1.51119 −0.755596 0.655038i $$-0.772652\pi$$
−0.755596 + 0.655038i $$0.772652\pi$$
$$662$$ 293476.i 0.669664i
$$663$$ −159932. −0.363837
$$664$$ −376079. −0.852987
$$665$$ 7512.25 0.0169874
$$666$$ 37637.3i 0.0848536i
$$667$$ 3629.92i 0.00815916i
$$668$$ 181589.i 0.406945i
$$669$$ 364333. 0.814042
$$670$$ 216379.i 0.482020i
$$671$$ −37001.0 22197.5i −0.0821805 0.0493014i
$$672$$ −6194.77 −0.0137179
$$673$$ 362391.i 0.800105i 0.916492 + 0.400052i $$0.131008\pi$$
−0.916492 + 0.400052i $$0.868992\pi$$
$$674$$ 226343. 0.498249
$$675$$ −77003.0 −0.169005
$$676$$ 15684.1 0.0343216
$$677$$ 92662.7i 0.202175i 0.994878 + 0.101088i $$0.0322322\pi$$
−0.994878 + 0.101088i $$0.967768\pi$$
$$678$$ 239379.i 0.520747i
$$679$$ 16371.7i 0.0355104i
$$680$$ 114255. 0.247092
$$681$$ 359477.i 0.775135i
$$682$$ 94771.5 + 56855.0i 0.203755 + 0.122236i
$$683$$ 448358. 0.961132 0.480566 0.876958i $$-0.340431\pi$$
0.480566 + 0.876958i $$0.340431\pi$$
$$684$$ 111357.i 0.238016i
$$685$$ 95318.3 0.203140
$$686$$ −21013.4 −0.0446528
$$687$$ −145339. −0.307941
$$688$$ 151863.i 0.320830i
$$689$$ 652661.i 1.37483i
$$690$$ 1750.09i 0.00367589i
$$691$$ 358700. 0.751234 0.375617 0.926775i $$-0.377431\pi$$
0.375617 + 0.926775i $$0.377431\pi$$
$$692$$ 156160.i 0.326104i
$$693$$ −4084.92 2450.61i −0.00850584 0.00510279i
$$694$$ 285688. 0.593162
$$695$$ 239308.i 0.495436i
$$696$$ −101253. −0.209022
$$697$$ −226506. −0.466245
$$698$$ −320414. −0.657659
$$699$$ 351218.i 0.718823i
$$700$$ 5590.19i 0.0114086i
$$701$$ 159779.i 0.325150i −0.986696 0.162575i $$-0.948020\pi$$
0.986696 0.162575i $$-0.0519799\pi$$
$$702$$ 68333.2 0.138662
$$703$$ 274128.i 0.554681i
$$704$$ 247871. 413176.i 0.500127 0.833661i
$$705$$ −82786.0 −0.166563
$$706$$ 188913.i 0.379011i
$$707$$ 18569.1 0.0371494
$$708$$ −54049.1 −0.107826
$$709$$ 455705. 0.906550 0.453275 0.891371i $$-0.350256\pi$$
0.453275 + 0.891371i $$0.350256\pi$$
$$710$$ 208848.i 0.414299i
$$711$$ 305221.i 0.603775i
$$712$$ 506006.i 0.998151i
$$713$$ 3910.78 0.00769279
$$714$$ 4316.12i 0.00846637i
$$715$$ 146873. + 88111.8i 0.287297 + 0.172354i
$$716$$ 64459.0 0.125735
$$717$$ 164144.i 0.319291i
$$718$$ 441596. 0.856596
$$719$$ 640858. 1.23966 0.619832 0.784735i $$-0.287201\pi$$
0.619832 + 0.784735i $$0.287201\pi$$
$$720$$ −22486.4 −0.0433766
$$721$$ 6761.76i 0.0130074i
$$722$$ 655445.i 1.25737i
$$723$$ 334712.i 0.640316i
$$724$$ −365017. −0.696363
$$725$$ 154976.i 0.294841i
$$726$$ 201533. 107516.i 0.382360 0.203986i
$$727$$ −324283. −0.613558 −0.306779 0.951781i $$-0.599251\pi$$
−0.306779 + 0.951781i $$0.599251\pi$$
$$728$$ 16323.8i 0.0308006i
$$729$$ 19683.0 0.0370370
$$730$$ −151454. −0.284207
$$731$$ 301888. 0.564951
$$732$$ 12943.2i 0.0241556i
$$733$$ 633078.i 1.17828i 0.808030 + 0.589141i $$0.200534\pi$$
−0.808030 + 0.589141i $$0.799466\pi$$
$$734$$ 151005.i 0.280285i
$$735$$ 108766. 0.201335
$$736$$ 10511.2i 0.0194042i
$$737$$ −514107. + 856965.i −0.946496 + 1.57771i
$$738$$ 96778.1 0.177690
$$739$$ 218657.i 0.400382i −0.979757 0.200191i $$-0.935844\pi$$
0.979757 0.200191i $$-0.0641562\pi$$
$$740$$ 28298.1 0.0516766
$$741$$ −497699. −0.906422
$$742$$ 17613.6 0.0319919
$$743$$ 740582.i 1.34152i −0.741677 0.670758i $$-0.765969\pi$$
0.741677 0.670758i $$-0.234031\pi$$
$$744$$ 109088.i 0.197074i
$$745$$ 153980.i 0.277430i
$$746$$ −89432.1 −0.160700
$$747$$ 147135.i 0.263679i
$$748$$ 137516. + 82498.2i 0.245782 + 0.147449i
$$749$$ −23123.4 −0.0412181
$$750$$ 159802.i 0.284092i
$$751$$ −1.08089e6 −1.91647 −0.958235 0.285982i $$-0.907680\pi$$
−0.958235 + 0.285982i $$0.907680\pi$$
$$752$$ 174270. 0.308168
$$753$$ 180941. 0.319114
$$754$$ 137527.i 0.241905i
$$755$$ 169997.i 0.298227i
$$756$$ 1428.93i 0.00250015i
$$757$$ 604976. 1.05571 0.527857 0.849333i $$-0.322996\pi$$
0.527857 + 0.849333i $$0.322996\pi$$
$$758$$ 242992.i 0.422916i
$$759$$ 4158.15 6931.22i 0.00721800 0.0120317i
$$760$$ 355557. 0.615576
$$761$$ 1.06160e6i 1.83312i −0.399901 0.916558i $$-0.630955\pi$$
0.399901 0.916558i $$-0.369045\pi$$
$$762$$ −302032. −0.520167
$$763$$ 28457.3 0.0488816
$$764$$ −493542. −0.845546
$$765$$ 44700.6i 0.0763819i
$$766$$ 800209.i 1.36378i
$$767$$ 241567.i 0.410626i
$$768$$ −348628. −0.591071
$$769$$ 405621.i 0.685912i 0.939352 + 0.342956i $$0.111428\pi$$
−0.939352 + 0.342956i $$0.888572\pi$$
$$770$$ 2377.90 3963.72i 0.00401063 0.00668531i
$$771$$ −383196. −0.644633
$$772$$ 151946.i 0.254950i
$$773$$ −279272. −0.467377 −0.233689 0.972311i $$-0.575080\pi$$
−0.233689 + 0.972311i $$0.575080\pi$$
$$774$$ −128986. −0.215308
$$775$$ 166966. 0.277988
$$776$$ 774878.i 1.28680i
$$777$$ 3517.60i 0.00582645i
$$778$$ 13086.2i 0.0216200i
$$779$$ −704875. −1.16155
$$780$$ 51377.2i 0.0844464i
$$781$$ −496215. + 827141.i −0.813519 + 1.35605i
$$782$$ −7323.52 −0.0119758
$$783$$ 39613.8i 0.0646135i
$$784$$ −228960. −0.372501
$$785$$ 180123. 0.292301