# Properties

 Label 441.4.e.c.361.1 Level $441$ Weight $4$ Character 441.361 Analytic conductor $26.020$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 441.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$26.0198423125$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{4}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 21) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 361.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 441.361 Dual form 441.4.e.c.226.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.50000 - 2.59808i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} -21.0000 q^{8} +O(q^{10})$$ $$q+(-1.50000 - 2.59808i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} -21.0000 q^{8} +(4.50000 - 7.79423i) q^{10} +(-7.50000 + 12.9904i) q^{11} +64.0000 q^{13} +(35.5000 + 61.4878i) q^{16} +(-42.0000 + 72.7461i) q^{17} +(-8.00000 - 13.8564i) q^{19} -3.00000 q^{20} +45.0000 q^{22} +(-42.0000 - 72.7461i) q^{23} +(58.0000 - 100.459i) q^{25} +(-96.0000 - 166.277i) q^{26} +297.000 q^{29} +(-126.500 + 219.104i) q^{31} +(22.5000 - 38.9711i) q^{32} +252.000 q^{34} +(158.000 + 273.664i) q^{37} +(-24.0000 + 41.5692i) q^{38} +(-31.5000 - 54.5596i) q^{40} +360.000 q^{41} +26.0000 q^{43} +(-7.50000 - 12.9904i) q^{44} +(-126.000 + 218.238i) q^{46} +(15.0000 + 25.9808i) q^{47} -348.000 q^{50} +(-32.0000 + 55.4256i) q^{52} +(181.500 - 314.367i) q^{53} -45.0000 q^{55} +(-445.500 - 771.629i) q^{58} +(7.50000 - 12.9904i) q^{59} +(-59.0000 - 102.191i) q^{61} +759.000 q^{62} +433.000 q^{64} +(96.0000 + 166.277i) q^{65} +(185.000 - 320.429i) q^{67} +(-42.0000 - 72.7461i) q^{68} +342.000 q^{71} +(181.000 - 313.501i) q^{73} +(474.000 - 820.992i) q^{74} +16.0000 q^{76} +(-233.500 - 404.434i) q^{79} +(-106.500 + 184.463i) q^{80} +(-540.000 - 935.307i) q^{82} +477.000 q^{83} -252.000 q^{85} +(-39.0000 - 67.5500i) q^{86} +(157.500 - 272.798i) q^{88} +(-453.000 - 784.619i) q^{89} +84.0000 q^{92} +(45.0000 - 77.9423i) q^{94} +(24.0000 - 41.5692i) q^{95} -503.000 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 3q^{2} - q^{4} + 3q^{5} - 42q^{8} + O(q^{10})$$ $$2q - 3q^{2} - q^{4} + 3q^{5} - 42q^{8} + 9q^{10} - 15q^{11} + 128q^{13} + 71q^{16} - 84q^{17} - 16q^{19} - 6q^{20} + 90q^{22} - 84q^{23} + 116q^{25} - 192q^{26} + 594q^{29} - 253q^{31} + 45q^{32} + 504q^{34} + 316q^{37} - 48q^{38} - 63q^{40} + 720q^{41} + 52q^{43} - 15q^{44} - 252q^{46} + 30q^{47} - 696q^{50} - 64q^{52} + 363q^{53} - 90q^{55} - 891q^{58} + 15q^{59} - 118q^{61} + 1518q^{62} + 866q^{64} + 192q^{65} + 370q^{67} - 84q^{68} + 684q^{71} + 362q^{73} + 948q^{74} + 32q^{76} - 467q^{79} - 213q^{80} - 1080q^{82} + 954q^{83} - 504q^{85} - 78q^{86} + 315q^{88} - 906q^{89} + 168q^{92} + 90q^{94} + 48q^{95} - 1006q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$$.

 $$n$$ $$199$$ $$344$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.50000 2.59808i −0.530330 0.918559i −0.999374 0.0353837i $$-0.988735\pi$$
0.469044 0.883175i $$-0.344599\pi$$
$$3$$ 0 0
$$4$$ −0.500000 + 0.866025i −0.0625000 + 0.108253i
$$5$$ 1.50000 + 2.59808i 0.134164 + 0.232379i 0.925278 0.379290i $$-0.123832\pi$$
−0.791114 + 0.611669i $$0.790498\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ −21.0000 −0.928078
$$9$$ 0 0
$$10$$ 4.50000 7.79423i 0.142302 0.246475i
$$11$$ −7.50000 + 12.9904i −0.205576 + 0.356068i −0.950316 0.311287i $$-0.899240\pi$$
0.744740 + 0.667355i $$0.232573\pi$$
$$12$$ 0 0
$$13$$ 64.0000 1.36542 0.682708 0.730691i $$-0.260802\pi$$
0.682708 + 0.730691i $$0.260802\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 35.5000 + 61.4878i 0.554688 + 0.960747i
$$17$$ −42.0000 + 72.7461i −0.599206 + 1.03785i 0.393733 + 0.919225i $$0.371183\pi$$
−0.992939 + 0.118630i $$0.962150\pi$$
$$18$$ 0 0
$$19$$ −8.00000 13.8564i −0.0965961 0.167309i 0.813678 0.581317i $$-0.197462\pi$$
−0.910274 + 0.414007i $$0.864129\pi$$
$$20$$ −3.00000 −0.0335410
$$21$$ 0 0
$$22$$ 45.0000 0.436092
$$23$$ −42.0000 72.7461i −0.380765 0.659505i 0.610406 0.792088i $$-0.291006\pi$$
−0.991172 + 0.132583i $$0.957673\pi$$
$$24$$ 0 0
$$25$$ 58.0000 100.459i 0.464000 0.803672i
$$26$$ −96.0000 166.277i −0.724121 1.25421i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 297.000 1.90178 0.950888 0.309535i $$-0.100173\pi$$
0.950888 + 0.309535i $$0.100173\pi$$
$$30$$ 0 0
$$31$$ −126.500 + 219.104i −0.732906 + 1.26943i 0.222731 + 0.974880i $$0.428503\pi$$
−0.955636 + 0.294550i $$0.904830\pi$$
$$32$$ 22.5000 38.9711i 0.124296 0.215287i
$$33$$ 0 0
$$34$$ 252.000 1.27111
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 158.000 + 273.664i 0.702028 + 1.21595i 0.967753 + 0.251900i $$0.0810553\pi$$
−0.265725 + 0.964049i $$0.585611\pi$$
$$38$$ −24.0000 + 41.5692i −0.102456 + 0.177458i
$$39$$ 0 0
$$40$$ −31.5000 54.5596i −0.124515 0.215666i
$$41$$ 360.000 1.37128 0.685641 0.727940i $$-0.259522\pi$$
0.685641 + 0.727940i $$0.259522\pi$$
$$42$$ 0 0
$$43$$ 26.0000 0.0922084 0.0461042 0.998937i $$-0.485319\pi$$
0.0461042 + 0.998937i $$0.485319\pi$$
$$44$$ −7.50000 12.9904i −0.0256970 0.0445085i
$$45$$ 0 0
$$46$$ −126.000 + 218.238i −0.403863 + 0.699511i
$$47$$ 15.0000 + 25.9808i 0.0465527 + 0.0806316i 0.888363 0.459142i $$-0.151843\pi$$
−0.841810 + 0.539774i $$0.818510\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ −348.000 −0.984293
$$51$$ 0 0
$$52$$ −32.0000 + 55.4256i −0.0853385 + 0.147811i
$$53$$ 181.500 314.367i 0.470395 0.814748i −0.529032 0.848602i $$-0.677445\pi$$
0.999427 + 0.0338538i $$0.0107781\pi$$
$$54$$ 0 0
$$55$$ −45.0000 −0.110324
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −445.500 771.629i −1.00857 1.74689i
$$59$$ 7.50000 12.9904i 0.0165494 0.0286645i −0.857632 0.514264i $$-0.828065\pi$$
0.874182 + 0.485599i $$0.161399\pi$$
$$60$$ 0 0
$$61$$ −59.0000 102.191i −0.123839 0.214495i 0.797440 0.603399i $$-0.206187\pi$$
−0.921279 + 0.388903i $$0.872854\pi$$
$$62$$ 759.000 1.55473
$$63$$ 0 0
$$64$$ 433.000 0.845703
$$65$$ 96.0000 + 166.277i 0.183190 + 0.317294i
$$66$$ 0 0
$$67$$ 185.000 320.429i 0.337334 0.584279i −0.646597 0.762832i $$-0.723808\pi$$
0.983930 + 0.178553i $$0.0571417\pi$$
$$68$$ −42.0000 72.7461i −0.0749007 0.129732i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 342.000 0.571661 0.285831 0.958280i $$-0.407731\pi$$
0.285831 + 0.958280i $$0.407731\pi$$
$$72$$ 0 0
$$73$$ 181.000 313.501i 0.290198 0.502638i −0.683658 0.729802i $$-0.739612\pi$$
0.973856 + 0.227165i $$0.0729455\pi$$
$$74$$ 474.000 820.992i 0.744613 1.28971i
$$75$$ 0 0
$$76$$ 16.0000 0.0241490
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −233.500 404.434i −0.332542 0.575979i 0.650468 0.759534i $$-0.274573\pi$$
−0.983010 + 0.183555i $$0.941240\pi$$
$$80$$ −106.500 + 184.463i −0.148838 + 0.257795i
$$81$$ 0 0
$$82$$ −540.000 935.307i −0.727232 1.25960i
$$83$$ 477.000 0.630814 0.315407 0.948957i $$-0.397859\pi$$
0.315407 + 0.948957i $$0.397859\pi$$
$$84$$ 0 0
$$85$$ −252.000 −0.321568
$$86$$ −39.0000 67.5500i −0.0489009 0.0846989i
$$87$$ 0 0
$$88$$ 157.500 272.798i 0.190790 0.330459i
$$89$$ −453.000 784.619i −0.539527 0.934488i −0.998929 0.0462600i $$-0.985270\pi$$
0.459402 0.888228i $$-0.348064\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 84.0000 0.0951914
$$93$$ 0 0
$$94$$ 45.0000 77.9423i 0.0493765 0.0855227i
$$95$$ 24.0000 41.5692i 0.0259195 0.0448938i
$$96$$ 0 0
$$97$$ −503.000 −0.526515 −0.263257 0.964726i $$-0.584797\pi$$
−0.263257 + 0.964726i $$0.584797\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 58.0000 + 100.459i 0.0580000 + 0.100459i
$$101$$ 543.000 940.504i 0.534956 0.926570i −0.464210 0.885725i $$-0.653662\pi$$
0.999165 0.0408451i $$-0.0130050\pi$$
$$102$$ 0 0
$$103$$ 868.000 + 1503.42i 0.830355 + 1.43822i 0.897757 + 0.440491i $$0.145196\pi$$
−0.0674017 + 0.997726i $$0.521471\pi$$
$$104$$ −1344.00 −1.26721
$$105$$ 0 0
$$106$$ −1089.00 −0.997859
$$107$$ −676.500 1171.73i −0.611212 1.05865i −0.991036 0.133592i $$-0.957349\pi$$
0.379824 0.925059i $$-0.375985\pi$$
$$108$$ 0 0
$$109$$ 185.000 320.429i 0.162567 0.281574i −0.773222 0.634136i $$-0.781356\pi$$
0.935789 + 0.352562i $$0.114689\pi$$
$$110$$ 67.5000 + 116.913i 0.0585079 + 0.101339i
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 648.000 0.539458 0.269729 0.962936i $$-0.413066\pi$$
0.269729 + 0.962936i $$0.413066\pi$$
$$114$$ 0 0
$$115$$ 126.000 218.238i 0.102170 0.176964i
$$116$$ −148.500 + 257.210i −0.118861 + 0.205873i
$$117$$ 0 0
$$118$$ −45.0000 −0.0351067
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 553.000 + 957.824i 0.415477 + 0.719627i
$$122$$ −177.000 + 306.573i −0.131351 + 0.227507i
$$123$$ 0 0
$$124$$ −126.500 219.104i −0.0916132 0.158679i
$$125$$ 723.000 0.517337
$$126$$ 0 0
$$127$$ 377.000 0.263412 0.131706 0.991289i $$-0.457954\pi$$
0.131706 + 0.991289i $$0.457954\pi$$
$$128$$ −829.500 1436.74i −0.572798 0.992115i
$$129$$ 0 0
$$130$$ 288.000 498.831i 0.194302 0.336541i
$$131$$ 325.500 + 563.783i 0.217092 + 0.376015i 0.953918 0.300068i $$-0.0970095\pi$$
−0.736826 + 0.676083i $$0.763676\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −1110.00 −0.715593
$$135$$ 0 0
$$136$$ 882.000 1527.67i 0.556109 0.963210i
$$137$$ −885.000 + 1532.86i −0.551903 + 0.955923i 0.446235 + 0.894916i $$0.352765\pi$$
−0.998137 + 0.0610074i $$0.980569\pi$$
$$138$$ 0 0
$$139$$ 1558.00 0.950704 0.475352 0.879796i $$-0.342321\pi$$
0.475352 + 0.879796i $$0.342321\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −513.000 888.542i −0.303169 0.525104i
$$143$$ −480.000 + 831.384i −0.280697 + 0.486181i
$$144$$ 0 0
$$145$$ 445.500 + 771.629i 0.255150 + 0.441933i
$$146$$ −1086.00 −0.615603
$$147$$ 0 0
$$148$$ −316.000 −0.175507
$$149$$ 1227.00 + 2125.23i 0.674629 + 1.16849i 0.976577 + 0.215168i $$0.0690298\pi$$
−0.301948 + 0.953324i $$0.597637\pi$$
$$150$$ 0 0
$$151$$ −629.500 + 1090.33i −0.339258 + 0.587612i −0.984293 0.176540i $$-0.943509\pi$$
0.645035 + 0.764153i $$0.276843\pi$$
$$152$$ 168.000 + 290.985i 0.0896487 + 0.155276i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −759.000 −0.393318
$$156$$ 0 0
$$157$$ −98.0000 + 169.741i −0.0498169 + 0.0862854i −0.889859 0.456236i $$-0.849197\pi$$
0.840042 + 0.542522i $$0.182530\pi$$
$$158$$ −700.500 + 1213.30i −0.352714 + 0.610918i
$$159$$ 0 0
$$160$$ 135.000 0.0667043
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 626.000 + 1084.26i 0.300810 + 0.521019i 0.976320 0.216332i $$-0.0694095\pi$$
−0.675509 + 0.737351i $$0.736076\pi$$
$$164$$ −180.000 + 311.769i −0.0857051 + 0.148446i
$$165$$ 0 0
$$166$$ −715.500 1239.28i −0.334540 0.579440i
$$167$$ −2646.00 −1.22607 −0.613035 0.790056i $$-0.710051\pi$$
−0.613035 + 0.790056i $$0.710051\pi$$
$$168$$ 0 0
$$169$$ 1899.00 0.864360
$$170$$ 378.000 + 654.715i 0.170537 + 0.295379i
$$171$$ 0 0
$$172$$ −13.0000 + 22.5167i −0.00576303 + 0.00998186i
$$173$$ 393.000 + 680.696i 0.172712 + 0.299147i 0.939367 0.342913i $$-0.111414\pi$$
−0.766655 + 0.642059i $$0.778080\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −1065.00 −0.456122
$$177$$ 0 0
$$178$$ −1359.00 + 2353.86i −0.572255 + 0.991174i
$$179$$ 1446.00 2504.55i 0.603794 1.04580i −0.388447 0.921471i $$-0.626988\pi$$
0.992241 0.124331i $$-0.0396784\pi$$
$$180$$ 0 0
$$181$$ −1352.00 −0.555212 −0.277606 0.960695i $$-0.589541\pi$$
−0.277606 + 0.960695i $$0.589541\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 882.000 + 1527.67i 0.353380 + 0.612072i
$$185$$ −474.000 + 820.992i −0.188374 + 0.326273i
$$186$$ 0 0
$$187$$ −630.000 1091.19i −0.246365 0.426716i
$$188$$ −30.0000 −0.0116382
$$189$$ 0 0
$$190$$ −144.000 −0.0549835
$$191$$ 1956.00 + 3387.89i 0.741001 + 1.28345i 0.952040 + 0.305974i $$0.0989820\pi$$
−0.211039 + 0.977478i $$0.567685\pi$$
$$192$$ 0 0
$$193$$ −746.500 + 1292.98i −0.278416 + 0.482230i −0.970991 0.239115i $$-0.923143\pi$$
0.692575 + 0.721345i $$0.256476\pi$$
$$194$$ 754.500 + 1306.83i 0.279227 + 0.483635i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 4086.00 1.47774 0.738872 0.673846i $$-0.235359\pi$$
0.738872 + 0.673846i $$0.235359\pi$$
$$198$$ 0 0
$$199$$ −1778.00 + 3079.59i −0.633362 + 1.09702i 0.353497 + 0.935436i $$0.384992\pi$$
−0.986860 + 0.161580i $$0.948341\pi$$
$$200$$ −1218.00 + 2109.64i −0.430628 + 0.745870i
$$201$$ 0 0
$$202$$ −3258.00 −1.13481
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 540.000 + 935.307i 0.183977 + 0.318657i
$$206$$ 2604.00 4510.26i 0.880725 1.52546i
$$207$$ 0 0
$$208$$ 2272.00 + 3935.22i 0.757379 + 1.31182i
$$209$$ 240.000 0.0794313
$$210$$ 0 0
$$211$$ 1250.00 0.407837 0.203918 0.978988i $$-0.434632\pi$$
0.203918 + 0.978988i $$0.434632\pi$$
$$212$$ 181.500 + 314.367i 0.0587994 + 0.101844i
$$213$$ 0 0
$$214$$ −2029.50 + 3515.20i −0.648289 + 1.12287i
$$215$$ 39.0000 + 67.5500i 0.0123711 + 0.0214273i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −1110.00 −0.344856
$$219$$ 0 0
$$220$$ 22.5000 38.9711i 0.00689523 0.0119429i
$$221$$ −2688.00 + 4655.75i −0.818165 + 1.41710i
$$222$$ 0 0
$$223$$ −425.000 −0.127624 −0.0638119 0.997962i $$-0.520326\pi$$
−0.0638119 + 0.997962i $$0.520326\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −972.000 1683.55i −0.286091 0.495523i
$$227$$ −1927.50 + 3338.53i −0.563580 + 0.976149i 0.433600 + 0.901105i $$0.357243\pi$$
−0.997180 + 0.0750439i $$0.976090\pi$$
$$228$$ 0 0
$$229$$ −1094.00 1894.86i −0.315692 0.546795i 0.663892 0.747828i $$-0.268903\pi$$
−0.979584 + 0.201033i $$0.935570\pi$$
$$230$$ −756.000 −0.216735
$$231$$ 0 0
$$232$$ −6237.00 −1.76500
$$233$$ 426.000 + 737.854i 0.119778 + 0.207461i 0.919679 0.392670i $$-0.128449\pi$$
−0.799902 + 0.600131i $$0.795115\pi$$
$$234$$ 0 0
$$235$$ −45.0000 + 77.9423i −0.0124914 + 0.0216357i
$$236$$ 7.50000 + 12.9904i 0.00206868 + 0.00358306i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −5508.00 −1.49072 −0.745362 0.666660i $$-0.767723\pi$$
−0.745362 + 0.666660i $$0.767723\pi$$
$$240$$ 0 0
$$241$$ 395.500 685.026i 0.105711 0.183097i −0.808317 0.588747i $$-0.799621\pi$$
0.914029 + 0.405650i $$0.132955\pi$$
$$242$$ 1659.00 2873.47i 0.440680 0.763280i
$$243$$ 0 0
$$244$$ 118.000 0.0309597
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −512.000 886.810i −0.131894 0.228447i
$$248$$ 2656.50 4601.19i 0.680193 1.17813i
$$249$$ 0 0
$$250$$ −1084.50 1878.41i −0.274359 0.475204i
$$251$$ 5265.00 1.32400 0.662000 0.749504i $$-0.269708\pi$$
0.662000 + 0.749504i $$0.269708\pi$$
$$252$$ 0 0
$$253$$ 1260.00 0.313105
$$254$$ −565.500 979.475i −0.139695 0.241959i
$$255$$ 0 0
$$256$$ −756.500 + 1310.30i −0.184692 + 0.319897i
$$257$$ 3435.00 + 5949.59i 0.833733 + 1.44407i 0.895058 + 0.445950i $$0.147134\pi$$
−0.0613246 + 0.998118i $$0.519532\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ −192.000 −0.0457974
$$261$$ 0 0
$$262$$ 976.500 1691.35i 0.230261 0.398824i
$$263$$ −111.000 + 192.258i −0.0260249 + 0.0450765i −0.878745 0.477292i $$-0.841618\pi$$
0.852720 + 0.522369i $$0.174952\pi$$
$$264$$ 0 0
$$265$$ 1089.00 0.252441
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 185.000 + 320.429i 0.0421667 + 0.0730349i
$$269$$ −3925.50 + 6799.17i −0.889747 + 1.54109i −0.0495729 + 0.998771i $$0.515786\pi$$
−0.840174 + 0.542317i $$0.817547\pi$$
$$270$$ 0 0
$$271$$ 2591.50 + 4488.61i 0.580895 + 1.00614i 0.995374 + 0.0960800i $$0.0306305\pi$$
−0.414479 + 0.910059i $$0.636036\pi$$
$$272$$ −5964.00 −1.32949
$$273$$ 0 0
$$274$$ 5310.00 1.17076
$$275$$ 870.000 + 1506.88i 0.190774 + 0.330431i
$$276$$ 0 0
$$277$$ 2480.00 4295.49i 0.537938 0.931736i −0.461077 0.887360i $$-0.652537\pi$$
0.999015 0.0443755i $$-0.0141298\pi$$
$$278$$ −2337.00 4047.80i −0.504187 0.873277i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 774.000 0.164317 0.0821583 0.996619i $$-0.473819\pi$$
0.0821583 + 0.996619i $$0.473819\pi$$
$$282$$ 0 0
$$283$$ 1849.00 3202.56i 0.388380 0.672695i −0.603852 0.797097i $$-0.706368\pi$$
0.992232 + 0.124402i $$0.0397013\pi$$
$$284$$ −171.000 + 296.181i −0.0357288 + 0.0618841i
$$285$$ 0 0
$$286$$ 2880.00 0.595447
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −1071.50 1855.89i −0.218095 0.377751i
$$290$$ 1336.50 2314.89i 0.270628 0.468741i
$$291$$ 0 0
$$292$$ 181.000 + 313.501i 0.0362747 + 0.0628297i
$$293$$ −6273.00 −1.25076 −0.625380 0.780321i $$-0.715056\pi$$
−0.625380 + 0.780321i $$0.715056\pi$$
$$294$$ 0 0
$$295$$ 45.0000 0.00888136
$$296$$ −3318.00 5746.94i −0.651537 1.12849i
$$297$$ 0 0
$$298$$ 3681.00 6375.68i 0.715552 1.23937i
$$299$$ −2688.00 4655.75i −0.519903 0.900499i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 3777.00 0.719675
$$303$$ 0 0
$$304$$ 568.000 983.805i 0.107161 0.185609i
$$305$$ 177.000 306.573i 0.0332295 0.0575551i
$$306$$ 0 0
$$307$$ 1684.00 0.313065 0.156533 0.987673i $$-0.449968\pi$$
0.156533 + 0.987673i $$0.449968\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 1138.50 + 1971.94i 0.208589 + 0.361286i
$$311$$ 660.000 1143.15i 0.120338 0.208432i −0.799563 0.600582i $$-0.794935\pi$$
0.919901 + 0.392151i $$0.128269\pi$$
$$312$$ 0 0
$$313$$ −4251.50 7363.81i −0.767760 1.32980i −0.938775 0.344531i $$-0.888038\pi$$
0.171014 0.985269i $$-0.445296\pi$$
$$314$$ 588.000 0.105678
$$315$$ 0 0
$$316$$ 467.000 0.0831355
$$317$$ −1288.50 2231.75i −0.228295 0.395418i 0.729008 0.684505i $$-0.239982\pi$$
−0.957303 + 0.289087i $$0.906648\pi$$
$$318$$ 0 0
$$319$$ −2227.50 + 3858.14i −0.390959 + 0.677162i
$$320$$ 649.500 + 1124.97i 0.113463 + 0.196524i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 1344.00 0.231524
$$324$$ 0 0
$$325$$ 3712.00 6429.37i 0.633553 1.09735i
$$326$$ 1878.00 3252.79i 0.319058 0.552624i
$$327$$ 0 0
$$328$$ −7560.00 −1.27266
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 242.000 + 419.156i 0.0401859 + 0.0696040i 0.885419 0.464794i $$-0.153872\pi$$
−0.845233 + 0.534398i $$0.820538\pi$$
$$332$$ −238.500 + 413.094i −0.0394259 + 0.0682876i
$$333$$ 0 0
$$334$$ 3969.00 + 6874.51i 0.650222 + 1.12622i
$$335$$ 1110.00 0.181032
$$336$$ 0 0
$$337$$ −8359.00 −1.35117 −0.675584 0.737283i $$-0.736109\pi$$
−0.675584 + 0.737283i $$0.736109\pi$$
$$338$$ −2848.50 4933.75i −0.458396 0.793966i
$$339$$ 0 0
$$340$$ 126.000 218.238i 0.0200980 0.0348107i
$$341$$ −1897.50 3286.57i −0.301335 0.521928i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ −546.000 −0.0855766
$$345$$ 0 0
$$346$$ 1179.00 2042.09i 0.183189 0.317293i
$$347$$ −930.000 + 1610.81i −0.143876 + 0.249201i −0.928953 0.370197i $$-0.879290\pi$$
0.785077 + 0.619398i $$0.212623\pi$$
$$348$$ 0 0
$$349$$ 1918.00 0.294178 0.147089 0.989123i $$-0.453010\pi$$
0.147089 + 0.989123i $$0.453010\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 337.500 + 584.567i 0.0511046 + 0.0885157i
$$353$$ 1524.00 2639.65i 0.229786 0.398000i −0.727959 0.685621i $$-0.759531\pi$$
0.957744 + 0.287620i $$0.0928642\pi$$
$$354$$ 0 0
$$355$$ 513.000 + 888.542i 0.0766964 + 0.132842i
$$356$$ 906.000 0.134882
$$357$$ 0 0
$$358$$ −8676.00 −1.28084
$$359$$ −15.0000 25.9808i −0.00220521 0.00381953i 0.864921 0.501909i $$-0.167369\pi$$
−0.867126 + 0.498089i $$0.834035\pi$$
$$360$$ 0 0
$$361$$ 3301.50 5718.37i 0.481338 0.833703i
$$362$$ 2028.00 + 3512.60i 0.294446 + 0.509995i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 1086.00 0.155737
$$366$$ 0 0
$$367$$ −5655.50 + 9795.61i −0.804400 + 1.39326i 0.112296 + 0.993675i $$0.464180\pi$$
−0.916696 + 0.399586i $$0.869154\pi$$
$$368$$ 2982.00 5164.98i 0.422412 0.731638i
$$369$$ 0 0
$$370$$ 2844.00 0.399601
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −604.000 1046.16i −0.0838443 0.145223i 0.821054 0.570851i $$-0.193387\pi$$
−0.904898 + 0.425628i $$0.860053\pi$$
$$374$$ −1890.00 + 3273.58i −0.261309 + 0.452600i
$$375$$ 0 0
$$376$$ −315.000 545.596i −0.0432045 0.0748324i
$$377$$ 19008.0 2.59672
$$378$$ 0 0
$$379$$ 7640.00 1.03546 0.517731 0.855543i $$-0.326777\pi$$
0.517731 + 0.855543i $$0.326777\pi$$
$$380$$ 24.0000 + 41.5692i 0.00323993 + 0.00561173i
$$381$$ 0 0
$$382$$ 5868.00 10163.7i 0.785950 1.36131i
$$383$$ −6375.00 11041.8i −0.850515 1.47314i −0.880744 0.473592i $$-0.842957\pi$$
0.0302291 0.999543i $$-0.490376\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 4479.00 0.590609
$$387$$ 0 0
$$388$$ 251.500 435.611i 0.0329072 0.0569969i
$$389$$ 1563.00 2707.20i 0.203720 0.352854i −0.746004 0.665942i $$-0.768030\pi$$
0.949724 + 0.313087i $$0.101363\pi$$
$$390$$ 0 0
$$391$$ 7056.00 0.912627
$$392$$ 0 0
$$393$$ 0 0
$$394$$ −6129.00 10615.7i −0.783692 1.35739i
$$395$$ 700.500 1213.30i 0.0892303 0.154551i
$$396$$ 0 0
$$397$$ −2966.00 5137.26i −0.374960 0.649450i 0.615361 0.788246i $$-0.289010\pi$$
−0.990321 + 0.138795i $$0.955677\pi$$
$$398$$ 10668.0 1.34356
$$399$$ 0 0
$$400$$ 8236.00 1.02950
$$401$$ 804.000 + 1392.57i 0.100124 + 0.173420i 0.911736 0.410777i $$-0.134743\pi$$
−0.811611 + 0.584198i $$0.801409\pi$$
$$402$$ 0 0
$$403$$ −8096.00 + 14022.7i −1.00072 + 1.73330i
$$404$$ 543.000 + 940.504i 0.0668695 + 0.115821i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −4740.00 −0.577280
$$408$$ 0 0
$$409$$ −2232.50 + 3866.80i −0.269902 + 0.467484i −0.968836 0.247702i $$-0.920325\pi$$
0.698934 + 0.715186i $$0.253658\pi$$
$$410$$ 1620.00 2805.92i 0.195137 0.337987i
$$411$$ 0 0
$$412$$ −1736.00 −0.207589
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 715.500 + 1239.28i 0.0846326 + 0.146588i
$$416$$ 1440.00 2494.15i 0.169716 0.293957i
$$417$$ 0 0
$$418$$ −360.000 623.538i −0.0421248 0.0729623i
$$419$$ −1584.00 −0.184686 −0.0923430 0.995727i $$-0.529436\pi$$
−0.0923430 + 0.995727i $$0.529436\pi$$
$$420$$ 0 0
$$421$$ −1330.00 −0.153967 −0.0769837 0.997032i $$-0.524529\pi$$
−0.0769837 + 0.997032i $$0.524529\pi$$
$$422$$ −1875.00 3247.60i −0.216288 0.374622i
$$423$$ 0 0
$$424$$ −3811.50 + 6601.71i −0.436563 + 0.756150i
$$425$$ 4872.00 + 8438.55i 0.556063 + 0.963129i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 1353.00 0.152803
$$429$$ 0 0
$$430$$ 117.000 202.650i 0.0131215 0.0227271i
$$431$$ 4794.00 8303.45i 0.535775 0.927989i −0.463351 0.886175i $$-0.653353\pi$$
0.999125 0.0418139i $$-0.0133137\pi$$
$$432$$ 0 0
$$433$$ −494.000 −0.0548271 −0.0274135 0.999624i $$-0.508727\pi$$
−0.0274135 + 0.999624i $$0.508727\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 185.000 + 320.429i 0.0203209 + 0.0351968i
$$437$$ −672.000 + 1163.94i −0.0735609 + 0.127411i
$$438$$ 0 0
$$439$$ −8004.50 13864.2i −0.870237 1.50729i −0.861752 0.507330i $$-0.830632\pi$$
−0.00848508 0.999964i $$-0.502701\pi$$
$$440$$ 945.000 0.102389
$$441$$ 0 0
$$442$$ 16128.0 1.73559
$$443$$ 3886.50 + 6731.62i 0.416824 + 0.721961i 0.995618 0.0935130i $$-0.0298097\pi$$
−0.578794 + 0.815474i $$0.696476\pi$$
$$444$$ 0 0
$$445$$ 1359.00 2353.86i 0.144770 0.250749i
$$446$$ 637.500 + 1104.18i 0.0676827 + 0.117230i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −864.000 −0.0908122 −0.0454061 0.998969i $$-0.514458\pi$$
−0.0454061 + 0.998969i $$0.514458\pi$$
$$450$$ 0 0
$$451$$ −2700.00 + 4676.54i −0.281903 + 0.488269i
$$452$$ −324.000 + 561.184i −0.0337161 + 0.0583980i
$$453$$ 0 0
$$454$$ 11565.0 1.19553
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −1259.50 2181.52i −0.128921 0.223298i 0.794338 0.607476i $$-0.207818\pi$$
−0.923259 + 0.384179i $$0.874485\pi$$
$$458$$ −3282.00 + 5684.59i −0.334842 + 0.579964i
$$459$$ 0 0
$$460$$ 126.000 + 218.238i 0.0127713 + 0.0221205i
$$461$$ −342.000 −0.0345521 −0.0172761 0.999851i $$-0.505499\pi$$
−0.0172761 + 0.999851i $$0.505499\pi$$
$$462$$ 0 0
$$463$$ −4336.00 −0.435229 −0.217614 0.976035i $$-0.569828\pi$$
−0.217614 + 0.976035i $$0.569828\pi$$
$$464$$ 10543.5 + 18261.9i 1.05489 + 1.82713i
$$465$$ 0 0
$$466$$ 1278.00 2213.56i 0.127043 0.220046i
$$467$$ −9318.00 16139.2i −0.923310 1.59922i −0.794257 0.607581i $$-0.792140\pi$$
−0.129052 0.991638i $$-0.541194\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 270.000 0.0264982
$$471$$ 0 0
$$472$$ −157.500 + 272.798i −0.0153592 + 0.0266029i
$$473$$ −195.000 + 337.750i −0.0189558 + 0.0328325i
$$474$$ 0 0
$$475$$ −1856.00 −0.179282
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 8262.00 + 14310.2i 0.790575 + 1.36932i
$$479$$ −7539.00 + 13057.9i −0.719135 + 1.24558i 0.242208 + 0.970224i $$0.422128\pi$$
−0.961343 + 0.275354i $$0.911205\pi$$
$$480$$ 0 0
$$481$$ 10112.0 + 17514.5i 0.958560 + 1.66028i
$$482$$ −2373.00 −0.224247
$$483$$ 0 0
$$484$$ −1106.00 −0.103869
$$485$$ −754.500 1306.83i −0.0706393 0.122351i
$$486$$ 0 0
$$487$$ −3110.50 + 5387.54i −0.289425 + 0.501300i −0.973673 0.227950i $$-0.926798\pi$$
0.684247 + 0.729250i $$0.260131\pi$$
$$488$$ 1239.00 + 2146.01i 0.114932 + 0.199068i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 7371.00 0.677492 0.338746 0.940878i $$-0.389997\pi$$
0.338746 + 0.940878i $$0.389997\pi$$
$$492$$ 0 0
$$493$$ −12474.0 + 21605.6i −1.13956 + 1.97377i
$$494$$ −1536.00 + 2660.43i −0.139895 + 0.242304i
$$495$$ 0 0
$$496$$ −17963.0 −1.62613
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −2137.00 3701.39i −0.191714 0.332058i 0.754104 0.656755i $$-0.228071\pi$$
−0.945818 + 0.324696i $$0.894738\pi$$
$$500$$ −361.500 + 626.136i −0.0323335 + 0.0560033i
$$501$$ 0 0
$$502$$ −7897.50 13678.9i −0.702157 1.21617i
$$503$$ −2520.00 −0.223382 −0.111691 0.993743i $$-0.535627\pi$$
−0.111691 + 0.993743i $$0.535627\pi$$
$$504$$ 0 0
$$505$$ 3258.00 0.287087
$$506$$ −1890.00 3273.58i −0.166049 0.287605i
$$507$$ 0 0
$$508$$ −188.500 + 326.492i −0.0164633 + 0.0285152i
$$509$$ 7138.50 + 12364.2i 0.621628 + 1.07669i 0.989183 + 0.146689i $$0.0468616\pi$$
−0.367555 + 0.930002i $$0.619805\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −8733.00 −0.753804
$$513$$ 0 0
$$514$$ 10305.0 17848.8i 0.884308 1.53167i
$$515$$ −2604.00 + 4510.26i −0.222808 + 0.385914i
$$516$$ 0 0
$$517$$ −450.000 −0.0382804
$$518$$ 0 0
$$519$$ 0 0
$$520$$ −2016.00 3491.81i −0.170014 0.294473i
$$521$$ 3153.00 5461.16i 0.265135 0.459228i −0.702464 0.711719i $$-0.747917\pi$$
0.967599 + 0.252492i $$0.0812501\pi$$
$$522$$ 0 0
$$523$$ 4036.00 + 6990.56i 0.337442 + 0.584466i 0.983951 0.178440i $$-0.0571051\pi$$
−0.646509 + 0.762906i $$0.723772\pi$$
$$524$$ −651.000 −0.0542730
$$525$$ 0 0
$$526$$ 666.000 0.0552072
$$527$$ −10626.0 18404.8i −0.878322 1.52130i
$$528$$ 0 0
$$529$$ 2555.50 4426.26i 0.210035 0.363792i
$$530$$ −1633.50 2829.30i −0.133877 0.231881i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 23040.0 1.87237
$$534$$ 0 0
$$535$$ 2029.50 3515.20i 0.164005 0.284066i
$$536$$ −3885.00 + 6729.02i −0.313072 + 0.542256i
$$537$$ 0 0
$$538$$ 23553.0 1.88744
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 11429.0 + 19795.6i 0.908264 + 1.57316i 0.816474 + 0.577382i $$0.195926\pi$$
0.0917903 + 0.995778i $$0.470741\pi$$
$$542$$ 7774.50 13465.8i 0.616132 1.06717i
$$543$$ 0 0
$$544$$ 1890.00 + 3273.58i 0.148958 + 0.258003i
$$545$$ 1110.00 0.0872425
$$546$$ 0 0
$$547$$ −24724.0 −1.93258 −0.966291 0.257454i $$-0.917116\pi$$
−0.966291 + 0.257454i $$0.917116\pi$$
$$548$$ −885.000 1532.86i −0.0689878 0.119490i
$$549$$ 0 0
$$550$$ 2610.00 4520.65i 0.202347 0.350475i
$$551$$ −2376.00 4115.35i −0.183704 0.318185i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −14880.0 −1.14114
$$555$$ 0 0
$$556$$ −779.000 + 1349.27i −0.0594190 + 0.102917i
$$557$$ −4921.50 + 8524.29i −0.374382 + 0.648448i −0.990234 0.139413i $$-0.955478\pi$$
0.615853 + 0.787861i $$0.288812\pi$$
$$558$$ 0 0
$$559$$ 1664.00 0.125903
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −1161.00 2010.91i −0.0871420 0.150934i
$$563$$ 6685.50 11579.6i 0.500462 0.866826i −0.499538 0.866292i $$-0.666497\pi$$
1.00000 0.000533812i $$-0.000169918\pi$$
$$564$$ 0 0
$$565$$ 972.000 + 1683.55i 0.0723758 + 0.125359i
$$566$$ −11094.0 −0.823879
$$567$$ 0 0
$$568$$ −7182.00 −0.530546
$$569$$ −2616.00 4531.04i −0.192739 0.333834i 0.753418 0.657542i $$-0.228404\pi$$
−0.946157 + 0.323708i $$0.895070\pi$$
$$570$$ 0 0
$$571$$ 7199.00 12469.0i 0.527616 0.913858i −0.471866 0.881670i $$-0.656419\pi$$
0.999482 0.0321874i $$-0.0102474\pi$$
$$572$$ −480.000 831.384i −0.0350871 0.0607726i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −9744.00 −0.706701
$$576$$ 0 0
$$577$$ 9935.50 17208.8i 0.716846 1.24161i −0.245397 0.969423i $$-0.578918\pi$$
0.962243 0.272191i $$-0.0877484\pi$$
$$578$$ −3214.50 + 5567.68i −0.231325 + 0.400666i
$$579$$ 0 0
$$580$$ −891.000 −0.0637875
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 2722.50 + 4715.51i 0.193404 + 0.334985i
$$584$$ −3801.00 + 6583.53i −0.269326 + 0.466487i
$$585$$ 0 0
$$586$$ 9409.50 + 16297.7i 0.663315 + 1.14890i
$$587$$ −16137.0 −1.13466 −0.567330 0.823491i $$-0.692024\pi$$
−0.567330 + 0.823491i $$0.692024\pi$$
$$588$$ 0 0
$$589$$ 4048.00 0.283183
$$590$$ −67.5000 116.913i −0.00471005 0.00815805i
$$591$$ 0 0
$$592$$ −11218.0 + 19430.1i −0.778812 + 1.34894i
$$593$$ 10662.0 + 18467.1i 0.738340 + 1.27884i 0.953242 + 0.302207i $$0.0977235\pi$$
−0.214902 + 0.976636i $$0.568943\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −2454.00 −0.168657
$$597$$ 0 0
$$598$$ −8064.00 + 13967.3i −0.551441 + 0.955123i
$$599$$ −4323.00 + 7487.66i −0.294880 + 0.510747i −0.974957 0.222394i $$-0.928613\pi$$
0.680077 + 0.733141i $$0.261946\pi$$
$$600$$ 0 0
$$601$$ −11195.0 −0.759823 −0.379911 0.925023i $$-0.624046\pi$$
−0.379911 + 0.925023i $$0.624046\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −629.500 1090.33i −0.0424073 0.0734515i
$$605$$ −1659.00 + 2873.47i −0.111484 + 0.193096i
$$606$$ 0 0
$$607$$ −4485.50 7769.11i −0.299935 0.519503i 0.676185 0.736731i $$-0.263632\pi$$
−0.976121 + 0.217228i $$0.930298\pi$$
$$608$$ −720.000 −0.0480261
$$609$$ 0 0
$$610$$ −1062.00 −0.0704904
$$611$$ 960.000 + 1662.77i 0.0635637 + 0.110096i
$$612$$ 0 0
$$613$$ 6386.00 11060.9i 0.420764 0.728784i −0.575251 0.817977i $$-0.695096\pi$$
0.996014 + 0.0891932i $$0.0284288\pi$$
$$614$$ −2526.00 4375.16i −0.166028 0.287569i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −12762.0 −0.832705 −0.416352 0.909203i $$-0.636692\pi$$
−0.416352 + 0.909203i $$0.636692\pi$$
$$618$$ 0 0
$$619$$ 6421.00 11121.5i 0.416933 0.722150i −0.578696 0.815543i $$-0.696438\pi$$
0.995629 + 0.0933936i $$0.0297715\pi$$
$$620$$ 379.500 657.313i 0.0245824 0.0425780i
$$621$$ 0 0
$$622$$ −3960.00 −0.255276
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −6165.50 10679.0i −0.394592 0.683453i
$$626$$ −12754.5 + 22091.4i −0.814333 + 1.41047i
$$627$$ 0 0
$$628$$ −98.0000 169.741i −0.00622711 0.0107857i
$$629$$ −26544.0 −1.68264
$$630$$ 0 0
$$631$$ 21365.0 1.34790 0.673952 0.738775i $$-0.264596\pi$$
0.673952 + 0.738775i $$0.264596\pi$$
$$632$$ 4903.50 + 8493.11i 0.308625 + 0.534554i
$$633$$ 0 0
$$634$$ −3865.50 + 6695.24i −0.242143 + 0.419404i
$$635$$ 565.500 + 979.475i 0.0353404 + 0.0612114i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 13365.0 0.829350
$$639$$ 0 0
$$640$$ 2488.50 4310.21i 0.153698 0.266212i
$$641$$ 4137.00 7165.49i 0.254917 0.441529i −0.709956 0.704246i $$-0.751285\pi$$
0.964873 + 0.262717i $$0.0846186\pi$$
$$642$$ 0 0
$$643$$ −27998.0 −1.71716 −0.858580 0.512680i $$-0.828653\pi$$
−0.858580 + 0.512680i $$0.828653\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −2016.00 3491.81i −0.122784 0.212668i
$$647$$ 8733.00 15126.0i 0.530649 0.919110i −0.468712 0.883351i $$-0.655282\pi$$
0.999360 0.0357592i $$-0.0113849\pi$$
$$648$$ 0 0
$$649$$ 112.500 + 194.856i 0.00680433 + 0.0117854i
$$650$$ −22272.0 −1.34397
$$651$$ 0 0
$$652$$ −1252.00 −0.0752026
$$653$$ 1078.50 + 1868.02i 0.0646324 + 0.111947i 0.896531 0.442981i $$-0.146079\pi$$
−0.831898 + 0.554928i $$0.812746\pi$$
$$654$$ 0 0
$$655$$ −976.500 + 1691.35i −0.0582519 + 0.100895i
$$656$$ 12780.0 + 22135.6i 0.760633 + 1.31745i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −19944.0 −1.17892 −0.589460 0.807798i $$-0.700659\pi$$
−0.589460 + 0.807798i $$0.700659\pi$$
$$660$$ 0 0
$$661$$ 13753.0 23820.9i 0.809273 1.40170i −0.104095 0.994567i $$-0.533194\pi$$
0.913368 0.407135i $$-0.133472\pi$$
$$662$$ 726.000 1257.47i 0.0426236 0.0738262i
$$663$$ 0 0
$$664$$ −10017.0 −0.585444
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −12474.0 21605.6i −0.724131 1.25423i
$$668$$ 1323.00 2291.50i 0.0766294 0.132726i
$$669$$ 0 0
$$670$$ −1665.00 2883.86i −0.0960068 0.166289i
$$671$$ 1770.00 0.101833
$$672$$ 0 0
$$673$$ −19123.0 −1.09530 −0.547650 0.836707i $$-0.684478\pi$$
−0.547650 + 0.836707i $$0.684478\pi$$
$$674$$ 12538.5 + 21717.3i 0.716565 + 1.24113i
$$675$$ 0 0
$$676$$ −949.500 + 1644.58i −0.0540225 + 0.0935698i
$$677$$ −6928.50 12000.5i −0.393329 0.681266i 0.599557 0.800332i $$-0.295343\pi$$
−0.992886 + 0.119066i $$0.962010\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 5292.00 0.298440
$$681$$ 0 0
$$682$$ −5692.50 + 9859.70i −0.319615 + 0.553589i
$$683$$ −11122.5 + 19264.7i −0.623120 + 1.07927i 0.365782 + 0.930701i $$0.380802\pi$$
−0.988901 + 0.148574i $$0.952532\pi$$
$$684$$ 0 0
$$685$$ −5310.00 −0.296182
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 923.000 + 1598.68i 0.0511469 + 0.0885890i
$$689$$ 11616.0 20119.5i 0.642285 1.11247i
$$690$$ 0 0
$$691$$ −320.000 554.256i −0.0176170 0.0305136i 0.857082 0.515179i $$-0.172275\pi$$
−0.874700 + 0.484666i $$0.838941\pi$$
$$692$$ −786.000 −0.0431781
$$693$$ 0 0
$$694$$ 5580.00 0.305207
$$695$$ 2337.00 + 4047.80i 0.127550 + 0.220924i
$$696$$ 0 0
$$697$$ −15120.0 + 26188.6i −0.821680 + 1.42319i
$$698$$ −2877.00 4983.11i −0.156012 0.270220i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 15561.0 0.838418 0.419209 0.907890i $$-0.362307\pi$$
0.419209 + 0.907890i $$0.362307\pi$$
$$702$$ 0 0
$$703$$ 2528.00 4378.62i 0.135626 0.234912i
$$704$$ −3247.50 + 5624.83i −0.173856 + 0.301128i
$$705$$ 0 0
$$706$$ −9144.00 −0.487449
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −2767.00 4792.58i −0.146568 0.253864i 0.783389 0.621532i $$-0.213489\pi$$
−0.929957 + 0.367668i $$0.880156\pi$$
$$710$$ 1539.00 2665.63i 0.0813488 0.140900i
$$711$$ 0 0
$$712$$ 9513.00 + 16477.0i 0.500723 + 0.867278i
$$713$$ 21252.0 1.11626
$$714$$ 0 0
$$715$$ −2880.00 −0.150638
$$716$$ 1446.00 + 2504.55i 0.0754742 + 0.130725i
$$717$$ 0 0
$$718$$ −45.0000 + 77.9423i −0.00233898 + 0.00405123i
$$719$$ 10923.0 + 18919.2i 0.566564 + 0.981317i 0.996902 + 0.0786494i $$0.0250607\pi$$
−0.430339 + 0.902667i $$0.641606\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −19809.0 −1.02107
$$723$$ 0 0
$$724$$ 676.000 1170.87i 0.0347007 0.0601035i
$$725$$ 17226.0 29836.3i 0.882424 1.52840i
$$726$$ 0 0
$$727$$ 11089.0 0.565706 0.282853 0.959163i $$-0.408719\pi$$
0.282853 + 0.959163i $$0.408719\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −1629.00 2821.51i −0.0825918 0.143053i
$$731$$ −1092.00 + 1891.40i −0.0552518 + 0.0956990i
$$732$$ 0 0
$$733$$ 5881.00 + 10186.2i 0.296343 + 0.513282i 0.975296 0.220900i $$-0.0708994\pi$$
−0.678953 + 0.734182i $$0.737566\pi$$
$$734$$ 33933.0 1.70639
$$735$$ 0 0
$$736$$ −3780.00 −0.189311
$$737$$ 2775.00 + 4806.44i 0.138695 + 0.240227i
$$738$$ 0 0
$$739$$ 11363.0 19681.3i 0.565622 0.979686i −0.431369 0.902175i $$-0.641969\pi$$
0.996992 0.0775108i $$-0.0246972\pi$$
$$740$$ −474.000 820.992i −0.0235467 0.0407841i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −6678.00 −0.329734 −0.164867 0.986316i $$-0.552719\pi$$
−0.164867 + 0.986316i $$0.552719\pi$$
$$744$$ 0 0
$$745$$ −3681.00 + 6375.68i −0.181022 + 0.313539i
$$746$$ −1812.00 + 3138.48i −0.0889303 + 0.154032i
$$747$$ 0 0
$$748$$ 1260.00 0.0615911
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 9993.50 + 17309.2i 0.485577 + 0.841043i 0.999863 0.0165754i $$-0.00527637\pi$$
−0.514286 + 0.857619i $$0.671943\pi$$
$$752$$ −1065.00 + 1844.63i −0.0516444 + 0.0894506i
$$753$$ 0 0
$$754$$ −28512.0 49384.2i −1.37712 2.38524i
$$755$$ −3777.00 −0.182065
$$756$$ 0 0
$$757$$ 314.000 0.0150760 0.00753799 0.999972i $$-0.497601\pi$$
0.00753799 + 0.999972i $$0.497601\pi$$
$$758$$ −11460.0 19849.3i −0.549137 0.951133i
$$759$$ 0 0
$$760$$ −504.000 + 872.954i −0.0240553 + 0.0416649i
$$761$$ 5748.00 + 9955.83i 0.273804 + 0.474242i 0.969833 0.243772i $$-0.0783847\pi$$
−0.696029 + 0.718014i $$0.745051\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −3912.00 −0.185250
$$765$$ 0 0
$$766$$ −19125.0 + 33125.5i −0.902107 + 1.56250i
$$767$$ 480.000 831.384i 0.0225969 0.0391389i
$$768$$ 0 0
$$769$$ −2765.00 −0.129660 −0.0648299 0.997896i $$-0.520650\pi$$
−0.0648299 + 0.997896i $$0.520650\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −746.500 1292.98i −0.0348020 0.0602788i
$$773$$ 7023.00 12164.2i 0.326778 0.565997i −0.655092 0.755549i $$-0.727370\pi$$
0.981871 + 0.189552i $$0.0607036\pi$$
$$774$$ 0 0
$$775$$ 14674.0 + 25416.1i 0.680136 + 1.17803i
$$776$$ 10563.0 0.488646
$$777$$ 0 0
$$778$$ −9378.00 −0.432156
$$779$$ −2880.00 4988.31i −0.132460 0.229428i
$$780$$ 0 0
$$781$$ −2565.00 + 4442.71i −0.117520 + 0.203550i
$$782$$ −10584.0 18332.0i −0.483994 0.838302i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −588.000 −0.0267345
$$786$$ 0 0
$$787$$ −9257.00 + 16033.6i −0.419284 + 0.726221i −0.995868 0.0908171i $$-0.971052\pi$$
0.576584 + 0.817038i $$0.304385\pi$$
$$788$$ −2043.00 + 3538.58i −0.0923590 + 0.159970i
$$789$$ 0 0
$$790$$ −4203.00 −0.189286