# Properties

 Label 666.2.bj.c.289.2 Level $666$ Weight $2$ Character 666.289 Analytic conductor $5.318$ Analytic rank $0$ Dimension $12$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$666 = 2 \cdot 3^{2} \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 666.bj (of order $$18$$, degree $$6$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.31803677462$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$2$$ over $$\Q(\zeta_{18})$$ Coefficient field: $$\Q(\zeta_{36})$$ Defining polynomial: $$x^{12} - x^{6} + 1$$ x^12 - x^6 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 74) Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

## Embedding invariants

 Embedding label 289.2 Root $$0.342020 + 0.939693i$$ of defining polynomial Character $$\chi$$ $$=$$ 666.289 Dual form 666.2.bj.c.613.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.342020 + 0.939693i) q^{2} +(-0.766044 + 0.642788i) q^{4} +(-2.57176 + 0.453471i) q^{5} +(-0.361075 - 2.04776i) q^{7} +(-0.866025 - 0.500000i) q^{8} +O(q^{10})$$ $$q+(0.342020 + 0.939693i) q^{2} +(-0.766044 + 0.642788i) q^{4} +(-2.57176 + 0.453471i) q^{5} +(-0.361075 - 2.04776i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-1.30572 - 2.26157i) q^{10} +(2.99810 - 5.19285i) q^{11} +(2.64632 + 3.15377i) q^{13} +(1.80077 - 1.03967i) q^{14} +(0.173648 - 0.984808i) q^{16} +(0.618710 - 0.737350i) q^{17} +(0.534946 - 1.46975i) q^{19} +(1.67860 - 2.00048i) q^{20} +(5.90509 + 1.04123i) q^{22} +(5.51705 - 3.18527i) q^{23} +(1.70986 - 0.622339i) q^{25} +(-2.05847 + 3.56538i) q^{26} +(1.59287 + 1.33658i) q^{28} +(3.51193 + 2.02761i) q^{29} -3.39997i q^{31} +(0.984808 - 0.173648i) q^{32} +(0.904494 + 0.329209i) q^{34} +(1.85720 + 5.10261i) q^{35} +(6.07068 - 0.383130i) q^{37} +1.56408 q^{38} +(2.45395 + 0.893164i) q^{40} +(-7.94502 + 6.66666i) q^{41} -3.76932i q^{43} +(1.04123 + 5.90509i) q^{44} +(4.88011 + 4.09490i) q^{46} +(-3.08750 - 5.34771i) q^{47} +(2.51491 - 0.915354i) q^{49} +(1.16962 + 1.39389i) q^{50} +(-4.05440 - 0.714901i) q^{52} +(1.39401 - 7.90585i) q^{53} +(-5.35558 + 14.7143i) q^{55} +(-0.711179 + 1.95395i) q^{56} +(-0.704183 + 3.99362i) q^{58} +(-5.02269 - 0.885636i) q^{59} +(-6.25519 - 7.45465i) q^{61} +(3.19493 - 1.16286i) q^{62} +(0.500000 + 0.866025i) q^{64} +(-8.23586 - 6.91071i) q^{65} +(-1.83263 - 10.3934i) q^{67} +0.962542i q^{68} +(-4.15968 + 3.49039i) q^{70} +(10.1503 + 3.69442i) q^{71} +3.55293 q^{73} +(2.43632 + 5.57354i) q^{74} +(0.534946 + 1.46975i) q^{76} +(-11.7162 - 4.26436i) q^{77} +(2.51098 - 0.442753i) q^{79} +2.61144i q^{80} +(-8.98197 - 5.18574i) q^{82} +(-5.29798 - 4.44553i) q^{83} +(-1.25681 + 2.17686i) q^{85} +(3.54200 - 1.28918i) q^{86} +(-5.19285 + 2.99810i) q^{88} +(16.0165 + 2.82414i) q^{89} +(5.50263 - 6.55778i) q^{91} +(-2.17885 + 5.98635i) q^{92} +(3.96922 - 4.73033i) q^{94} +(-0.709264 + 4.02243i) q^{95} +(-14.1175 + 8.15074i) q^{97} +(1.72030 + 2.05018i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q - 12 q^{7}+O(q^{10})$$ 12 * q - 12 * q^7 $$12 q - 12 q^{7} + 6 q^{10} + 6 q^{11} + 6 q^{13} + 18 q^{14} - 18 q^{19} - 18 q^{25} - 12 q^{26} - 6 q^{28} - 18 q^{29} + 12 q^{34} - 18 q^{35} + 30 q^{37} + 24 q^{38} + 12 q^{40} - 24 q^{41} - 6 q^{44} + 30 q^{46} - 6 q^{47} + 12 q^{49} + 36 q^{50} - 12 q^{52} + 12 q^{53} - 18 q^{55} + 6 q^{58} - 36 q^{61} + 6 q^{64} - 36 q^{65} - 30 q^{67} - 12 q^{70} - 12 q^{71} + 48 q^{74} - 18 q^{76} - 12 q^{77} + 6 q^{79} + 48 q^{83} + 18 q^{85} + 36 q^{86} - 36 q^{88} + 18 q^{89} - 6 q^{91} - 18 q^{92} + 36 q^{97} - 36 q^{98}+O(q^{100})$$ 12 * q - 12 * q^7 + 6 * q^10 + 6 * q^11 + 6 * q^13 + 18 * q^14 - 18 * q^19 - 18 * q^25 - 12 * q^26 - 6 * q^28 - 18 * q^29 + 12 * q^34 - 18 * q^35 + 30 * q^37 + 24 * q^38 + 12 * q^40 - 24 * q^41 - 6 * q^44 + 30 * q^46 - 6 * q^47 + 12 * q^49 + 36 * q^50 - 12 * q^52 + 12 * q^53 - 18 * q^55 + 6 * q^58 - 36 * q^61 + 6 * q^64 - 36 * q^65 - 30 * q^67 - 12 * q^70 - 12 * q^71 + 48 * q^74 - 18 * q^76 - 12 * q^77 + 6 * q^79 + 48 * q^83 + 18 * q^85 + 36 * q^86 - 36 * q^88 + 18 * q^89 - 6 * q^91 - 18 * q^92 + 36 * q^97 - 36 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$$.

 $$n$$ $$371$$ $$631$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{7}{18}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.342020 + 0.939693i 0.241845 + 0.664463i
$$3$$ 0 0
$$4$$ −0.766044 + 0.642788i −0.383022 + 0.321394i
$$5$$ −2.57176 + 0.453471i −1.15013 + 0.202798i −0.716031 0.698068i $$-0.754043\pi$$
−0.434096 + 0.900867i $$0.642932\pi$$
$$6$$ 0 0
$$7$$ −0.361075 2.04776i −0.136473 0.773979i −0.973822 0.227311i $$-0.927007\pi$$
0.837349 0.546669i $$-0.184104\pi$$
$$8$$ −0.866025 0.500000i −0.306186 0.176777i
$$9$$ 0 0
$$10$$ −1.30572 2.26157i −0.412904 0.715171i
$$11$$ 2.99810 5.19285i 0.903960 1.56570i 0.0816522 0.996661i $$-0.473980\pi$$
0.822308 0.569043i $$-0.192686\pi$$
$$12$$ 0 0
$$13$$ 2.64632 + 3.15377i 0.733958 + 0.874697i 0.995907 0.0903843i $$-0.0288095\pi$$
−0.261949 + 0.965082i $$0.584365\pi$$
$$14$$ 1.80077 1.03967i 0.481275 0.277864i
$$15$$ 0 0
$$16$$ 0.173648 0.984808i 0.0434120 0.246202i
$$17$$ 0.618710 0.737350i 0.150059 0.178834i −0.685778 0.727810i $$-0.740538\pi$$
0.835838 + 0.548977i $$0.184982\pi$$
$$18$$ 0 0
$$19$$ 0.534946 1.46975i 0.122725 0.337184i −0.863083 0.505063i $$-0.831469\pi$$
0.985808 + 0.167878i $$0.0536916\pi$$
$$20$$ 1.67860 2.00048i 0.375346 0.447320i
$$21$$ 0 0
$$22$$ 5.90509 + 1.04123i 1.25897 + 0.221990i
$$23$$ 5.51705 3.18527i 1.15038 0.664174i 0.201403 0.979508i $$-0.435450\pi$$
0.948981 + 0.315334i $$0.102117\pi$$
$$24$$ 0 0
$$25$$ 1.70986 0.622339i 0.341973 0.124468i
$$26$$ −2.05847 + 3.56538i −0.403700 + 0.699229i
$$27$$ 0 0
$$28$$ 1.59287 + 1.33658i 0.301025 + 0.252590i
$$29$$ 3.51193 + 2.02761i 0.652149 + 0.376519i 0.789279 0.614035i $$-0.210454\pi$$
−0.137130 + 0.990553i $$0.543788\pi$$
$$30$$ 0 0
$$31$$ 3.39997i 0.610653i −0.952248 0.305326i $$-0.901234\pi$$
0.952248 0.305326i $$-0.0987655\pi$$
$$32$$ 0.984808 0.173648i 0.174091 0.0306970i
$$33$$ 0 0
$$34$$ 0.904494 + 0.329209i 0.155119 + 0.0564588i
$$35$$ 1.85720 + 5.10261i 0.313924 + 0.862498i
$$36$$ 0 0
$$37$$ 6.07068 0.383130i 0.998014 0.0629862i
$$38$$ 1.56408 0.253727
$$39$$ 0 0
$$40$$ 2.45395 + 0.893164i 0.388003 + 0.141222i
$$41$$ −7.94502 + 6.66666i −1.24080 + 1.04116i −0.243343 + 0.969940i $$0.578244\pi$$
−0.997461 + 0.0712179i $$0.977311\pi$$
$$42$$ 0 0
$$43$$ 3.76932i 0.574816i −0.957808 0.287408i $$-0.907206\pi$$
0.957808 0.287408i $$-0.0927936\pi$$
$$44$$ 1.04123 + 5.90509i 0.156971 + 0.890227i
$$45$$ 0 0
$$46$$ 4.88011 + 4.09490i 0.719534 + 0.603760i
$$47$$ −3.08750 5.34771i −0.450359 0.780044i 0.548050 0.836446i $$-0.315371\pi$$
−0.998408 + 0.0564019i $$0.982037\pi$$
$$48$$ 0 0
$$49$$ 2.51491 0.915354i 0.359273 0.130765i
$$50$$ 1.16962 + 1.39389i 0.165409 + 0.197126i
$$51$$ 0 0
$$52$$ −4.05440 0.714901i −0.562245 0.0991389i
$$53$$ 1.39401 7.90585i 0.191483 1.08595i −0.725857 0.687846i $$-0.758556\pi$$
0.917339 0.398106i $$-0.130332\pi$$
$$54$$ 0 0
$$55$$ −5.35558 + 14.7143i −0.722146 + 1.98408i
$$56$$ −0.711179 + 1.95395i −0.0950352 + 0.261107i
$$57$$ 0 0
$$58$$ −0.704183 + 3.99362i −0.0924638 + 0.524388i
$$59$$ −5.02269 0.885636i −0.653899 0.115300i −0.163150 0.986601i $$-0.552166\pi$$
−0.490749 + 0.871301i $$0.663277\pi$$
$$60$$ 0 0
$$61$$ −6.25519 7.45465i −0.800895 0.954470i 0.198778 0.980045i $$-0.436303\pi$$
−0.999673 + 0.0255750i $$0.991858\pi$$
$$62$$ 3.19493 1.16286i 0.405756 0.147683i
$$63$$ 0 0
$$64$$ 0.500000 + 0.866025i 0.0625000 + 0.108253i
$$65$$ −8.23586 6.91071i −1.02153 0.857168i
$$66$$ 0 0
$$67$$ −1.83263 10.3934i −0.223892 1.26975i −0.864792 0.502130i $$-0.832550\pi$$
0.640901 0.767624i $$-0.278561\pi$$
$$68$$ 0.962542i 0.116725i
$$69$$ 0 0
$$70$$ −4.15968 + 3.49039i −0.497177 + 0.417181i
$$71$$ 10.1503 + 3.69442i 1.20462 + 0.438447i 0.864835 0.502056i $$-0.167423\pi$$
0.339787 + 0.940502i $$0.389645\pi$$
$$72$$ 0 0
$$73$$ 3.55293 0.415839 0.207920 0.978146i $$-0.433331\pi$$
0.207920 + 0.978146i $$0.433331\pi$$
$$74$$ 2.43632 + 5.57354i 0.283217 + 0.647911i
$$75$$ 0 0
$$76$$ 0.534946 + 1.46975i 0.0613625 + 0.168592i
$$77$$ −11.7162 4.26436i −1.33519 0.485969i
$$78$$ 0 0
$$79$$ 2.51098 0.442753i 0.282507 0.0498136i −0.0305991 0.999532i $$-0.509742\pi$$
0.313106 + 0.949718i $$0.398630\pi$$
$$80$$ 2.61144i 0.291967i
$$81$$ 0 0
$$82$$ −8.98197 5.18574i −0.991893 0.572670i
$$83$$ −5.29798 4.44553i −0.581529 0.487960i 0.303920 0.952698i $$-0.401704\pi$$
−0.885449 + 0.464737i $$0.846149\pi$$
$$84$$ 0 0
$$85$$ −1.25681 + 2.17686i −0.136320 + 0.236113i
$$86$$ 3.54200 1.28918i 0.381944 0.139016i
$$87$$ 0 0
$$88$$ −5.19285 + 2.99810i −0.553560 + 0.319598i
$$89$$ 16.0165 + 2.82414i 1.69774 + 0.299358i 0.936905 0.349584i $$-0.113677\pi$$
0.760838 + 0.648942i $$0.224788\pi$$
$$90$$ 0 0
$$91$$ 5.50263 6.55778i 0.576832 0.687442i
$$92$$ −2.17885 + 5.98635i −0.227161 + 0.624120i
$$93$$ 0 0
$$94$$ 3.96922 4.73033i 0.409394 0.487896i
$$95$$ −0.709264 + 4.02243i −0.0727689 + 0.412693i
$$96$$ 0 0
$$97$$ −14.1175 + 8.15074i −1.43342 + 0.827583i −0.997380 0.0723469i $$-0.976951\pi$$
−0.436036 + 0.899929i $$0.643618\pi$$
$$98$$ 1.72030 + 2.05018i 0.173777 + 0.207099i
$$99$$ 0 0
$$100$$ −0.909799 + 1.57582i −0.0909799 + 0.157582i
$$101$$ 2.05124 + 3.55285i 0.204106 + 0.353521i 0.949847 0.312714i $$-0.101238\pi$$
−0.745742 + 0.666235i $$0.767905\pi$$
$$102$$ 0 0
$$103$$ 9.35250 + 5.39967i 0.921530 + 0.532045i 0.884123 0.467255i $$-0.154757\pi$$
0.0374069 + 0.999300i $$0.488090\pi$$
$$104$$ −0.714901 4.05440i −0.0701018 0.397567i
$$105$$ 0 0
$$106$$ 7.90585 1.39401i 0.767884 0.135399i
$$107$$ −15.5549 + 13.0521i −1.50375 + 1.26180i −0.628823 + 0.777549i $$0.716463\pi$$
−0.874930 + 0.484249i $$0.839093\pi$$
$$108$$ 0 0
$$109$$ 2.13072 + 5.85411i 0.204086 + 0.560722i 0.998938 0.0460817i $$-0.0146734\pi$$
−0.794851 + 0.606804i $$0.792451\pi$$
$$110$$ −15.6587 −1.49300
$$111$$ 0 0
$$112$$ −2.07935 −0.196480
$$113$$ −2.09726 5.76217i −0.197294 0.542059i 0.801112 0.598515i $$-0.204242\pi$$
−0.998405 + 0.0564555i $$0.982020\pi$$
$$114$$ 0 0
$$115$$ −12.7441 + 10.6936i −1.18839 + 0.997181i
$$116$$ −3.99362 + 0.704183i −0.370798 + 0.0653818i
$$117$$ 0 0
$$118$$ −0.885636 5.02269i −0.0815294 0.462376i
$$119$$ −1.73331 1.00073i −0.158893 0.0917367i
$$120$$ 0 0
$$121$$ −12.4772 21.6111i −1.13429 1.96464i
$$122$$ 4.86567 8.42760i 0.440517 0.762999i
$$123$$ 0 0
$$124$$ 2.18546 + 2.60453i 0.196260 + 0.233893i
$$125$$ 7.19270 4.15271i 0.643335 0.371429i
$$126$$ 0 0
$$127$$ −1.10807 + 6.28420i −0.0983257 + 0.557633i 0.895352 + 0.445360i $$0.146924\pi$$
−0.993677 + 0.112273i $$0.964187\pi$$
$$128$$ −0.642788 + 0.766044i −0.0568149 + 0.0677094i
$$129$$ 0 0
$$130$$ 3.67711 10.1028i 0.322504 0.886072i
$$131$$ −6.71929 + 8.00774i −0.587067 + 0.699640i −0.975039 0.222032i $$-0.928731\pi$$
0.387972 + 0.921671i $$0.373176\pi$$
$$132$$ 0 0
$$133$$ −3.20285 0.564749i −0.277722 0.0489699i
$$134$$ 9.13979 5.27686i 0.789557 0.455851i
$$135$$ 0 0
$$136$$ −0.904494 + 0.329209i −0.0775597 + 0.0282294i
$$137$$ 3.12091 5.40557i 0.266637 0.461829i −0.701354 0.712813i $$-0.747421\pi$$
0.967991 + 0.250984i $$0.0807542\pi$$
$$138$$ 0 0
$$139$$ 5.27989 + 4.43035i 0.447834 + 0.375778i 0.838632 0.544699i $$-0.183356\pi$$
−0.390797 + 0.920477i $$0.627801\pi$$
$$140$$ −4.70259 2.71504i −0.397441 0.229463i
$$141$$ 0 0
$$142$$ 10.8018i 0.906463i
$$143$$ 24.3110 4.28668i 2.03299 0.358470i
$$144$$ 0 0
$$145$$ −9.95132 3.62198i −0.826412 0.300789i
$$146$$ 1.21517 + 3.33866i 0.100569 + 0.276310i
$$147$$ 0 0
$$148$$ −4.40414 + 4.19566i −0.362018 + 0.344881i
$$149$$ −3.49508 −0.286328 −0.143164 0.989699i $$-0.545728\pi$$
−0.143164 + 0.989699i $$0.545728\pi$$
$$150$$ 0 0
$$151$$ 8.84115 + 3.21791i 0.719482 + 0.261870i 0.675706 0.737171i $$-0.263839\pi$$
0.0437763 + 0.999041i $$0.486061\pi$$
$$152$$ −1.19815 + 1.00537i −0.0971830 + 0.0815462i
$$153$$ 0 0
$$154$$ 12.4682i 1.00471i
$$155$$ 1.54179 + 8.74391i 0.123839 + 0.702328i
$$156$$ 0 0
$$157$$ 1.94170 + 1.62928i 0.154964 + 0.130030i 0.716973 0.697101i $$-0.245527\pi$$
−0.562009 + 0.827131i $$0.689971\pi$$
$$158$$ 1.27486 + 2.20812i 0.101422 + 0.175668i
$$159$$ 0 0
$$160$$ −2.45395 + 0.893164i −0.194002 + 0.0706108i
$$161$$ −8.51472 10.1475i −0.671054 0.799731i
$$162$$ 0 0
$$163$$ −9.23549 1.62847i −0.723379 0.127551i −0.200177 0.979760i $$-0.564152\pi$$
−0.523202 + 0.852208i $$0.675263\pi$$
$$164$$ 1.80099 10.2139i 0.140634 0.797573i
$$165$$ 0 0
$$166$$ 2.36542 6.49893i 0.183592 0.504415i
$$167$$ 3.56469 9.79392i 0.275844 0.757876i −0.721978 0.691916i $$-0.756767\pi$$
0.997822 0.0659599i $$-0.0210110\pi$$
$$168$$ 0 0
$$169$$ −0.685785 + 3.88928i −0.0527527 + 0.299175i
$$170$$ −2.47543 0.436485i −0.189857 0.0334769i
$$171$$ 0 0
$$172$$ 2.42287 + 2.88747i 0.184742 + 0.220167i
$$173$$ 2.75312 1.00205i 0.209316 0.0761846i −0.235234 0.971939i $$-0.575586\pi$$
0.444550 + 0.895754i $$0.353364\pi$$
$$174$$ 0 0
$$175$$ −1.89179 3.27667i −0.143006 0.247693i
$$176$$ −4.59335 3.85428i −0.346237 0.290527i
$$177$$ 0 0
$$178$$ 2.82414 + 16.0165i 0.211678 + 1.20049i
$$179$$ 8.76703i 0.655279i 0.944803 + 0.327639i $$0.106253\pi$$
−0.944803 + 0.327639i $$0.893747\pi$$
$$180$$ 0 0
$$181$$ −20.4965 + 17.1986i −1.52349 + 1.27836i −0.693740 + 0.720225i $$0.744038\pi$$
−0.829750 + 0.558135i $$0.811517\pi$$
$$182$$ 8.04430 + 2.92789i 0.596283 + 0.217029i
$$183$$ 0 0
$$184$$ −6.37054 −0.469642
$$185$$ −15.4386 + 3.73820i −1.13507 + 0.274838i
$$186$$ 0 0
$$187$$ −1.97400 5.42352i −0.144353 0.396607i
$$188$$ 5.80261 + 2.11198i 0.423199 + 0.154032i
$$189$$ 0 0
$$190$$ −4.02243 + 0.709264i −0.291818 + 0.0514554i
$$191$$ 1.81758i 0.131515i −0.997836 0.0657577i $$-0.979054\pi$$
0.997836 0.0657577i $$-0.0209464\pi$$
$$192$$ 0 0
$$193$$ 0.922363 + 0.532526i 0.0663931 + 0.0383321i 0.532829 0.846223i $$-0.321129\pi$$
−0.466436 + 0.884555i $$0.654462\pi$$
$$194$$ −12.4877 10.4784i −0.896562 0.752305i
$$195$$ 0 0
$$196$$ −1.33816 + 2.31776i −0.0955827 + 0.165554i
$$197$$ −14.8064 + 5.38909i −1.05491 + 0.383957i −0.810515 0.585718i $$-0.800813\pi$$
−0.244398 + 0.969675i $$0.578590\pi$$
$$198$$ 0 0
$$199$$ 17.8722 10.3185i 1.26693 0.731461i 0.292523 0.956259i $$-0.405505\pi$$
0.974406 + 0.224797i $$0.0721719\pi$$
$$200$$ −1.79195 0.315970i −0.126710 0.0223424i
$$201$$ 0 0
$$202$$ −2.63702 + 3.14268i −0.185540 + 0.221118i
$$203$$ 2.88399 7.92370i 0.202417 0.556135i
$$204$$ 0 0
$$205$$ 17.4096 20.7479i 1.21594 1.44910i
$$206$$ −1.87529 + 10.6353i −0.130657 + 0.740995i
$$207$$ 0 0
$$208$$ 3.56538 2.05847i 0.247215 0.142730i
$$209$$ −6.02839 7.18435i −0.416992 0.496952i
$$210$$ 0 0
$$211$$ −3.10070 + 5.37057i −0.213461 + 0.369725i −0.952795 0.303613i $$-0.901807\pi$$
0.739335 + 0.673338i $$0.235140\pi$$
$$212$$ 4.01391 + 6.95229i 0.275676 + 0.477485i
$$213$$ 0 0
$$214$$ −17.5851 10.1528i −1.20209 0.694029i
$$215$$ 1.70928 + 9.69380i 0.116572 + 0.661112i
$$216$$ 0 0
$$217$$ −6.96231 + 1.22764i −0.472633 + 0.0833379i
$$218$$ −4.77232 + 4.00445i −0.323222 + 0.271216i
$$219$$ 0 0
$$220$$ −5.35558 14.7143i −0.361073 0.992040i
$$221$$ 3.96274 0.266563
$$222$$ 0 0
$$223$$ 0.839150 0.0561936 0.0280968 0.999605i $$-0.491055\pi$$
0.0280968 + 0.999605i $$0.491055\pi$$
$$224$$ −0.711179 1.95395i −0.0475176 0.130554i
$$225$$ 0 0
$$226$$ 4.69737 3.94156i 0.312464 0.262188i
$$227$$ −6.42458 + 1.13283i −0.426415 + 0.0751884i −0.382737 0.923857i $$-0.625019\pi$$
−0.0436775 + 0.999046i $$0.513907\pi$$
$$228$$ 0 0
$$229$$ 1.14680 + 6.50380i 0.0757824 + 0.429784i 0.998968 + 0.0454281i $$0.0144652\pi$$
−0.923185 + 0.384355i $$0.874424\pi$$
$$230$$ −14.4074 8.31813i −0.949997 0.548481i
$$231$$ 0 0
$$232$$ −2.02761 3.51193i −0.133119 0.230570i
$$233$$ −11.3047 + 19.5803i −0.740594 + 1.28275i 0.211632 + 0.977349i $$0.432122\pi$$
−0.952225 + 0.305396i $$0.901211\pi$$
$$234$$ 0 0
$$235$$ 10.3654 + 12.3530i 0.676161 + 0.805818i
$$236$$ 4.41688 2.55009i 0.287515 0.165997i
$$237$$ 0 0
$$238$$ 0.347550 1.97105i 0.0225283 0.127764i
$$239$$ 11.0221 13.1357i 0.712962 0.849675i −0.280965 0.959718i $$-0.590654\pi$$
0.993927 + 0.110043i $$0.0350988\pi$$
$$240$$ 0 0
$$241$$ 1.94526 5.34455i 0.125305 0.344273i −0.861139 0.508369i $$-0.830249\pi$$
0.986444 + 0.164096i $$0.0524708\pi$$
$$242$$ 16.0403 19.1161i 1.03111 1.22883i
$$243$$ 0 0
$$244$$ 9.58351 + 1.68983i 0.613521 + 0.108180i
$$245$$ −6.05267 + 3.49451i −0.386691 + 0.223256i
$$246$$ 0 0
$$247$$ 6.05089 2.20235i 0.385009 0.140132i
$$248$$ −1.69998 + 2.94446i −0.107949 + 0.186973i
$$249$$ 0 0
$$250$$ 6.36232 + 5.33862i 0.402388 + 0.337644i
$$251$$ 21.9528 + 12.6745i 1.38565 + 0.800006i 0.992821 0.119606i $$-0.0381630\pi$$
0.392829 + 0.919611i $$0.371496\pi$$
$$252$$ 0 0
$$253$$ 38.1990i 2.40155i
$$254$$ −6.28420 + 1.10807i −0.394306 + 0.0695268i
$$255$$ 0 0
$$256$$ −0.939693 0.342020i −0.0587308 0.0213763i
$$257$$ −1.76857 4.85911i −0.110320 0.303103i 0.872231 0.489094i $$-0.162673\pi$$
−0.982551 + 0.185991i $$0.940450\pi$$
$$258$$ 0 0
$$259$$ −2.97653 12.2929i −0.184953 0.763847i
$$260$$ 10.7512 0.666758
$$261$$ 0 0
$$262$$ −9.82295 3.57526i −0.606864 0.220880i
$$263$$ −7.40923 + 6.21708i −0.456873 + 0.383362i −0.841979 0.539511i $$-0.818609\pi$$
0.385106 + 0.922872i $$0.374165\pi$$
$$264$$ 0 0
$$265$$ 20.9641i 1.28782i
$$266$$ −0.564749 3.20285i −0.0346270 0.196379i
$$267$$ 0 0
$$268$$ 8.08462 + 6.78380i 0.493847 + 0.414386i
$$269$$ −11.9383 20.6777i −0.727889 1.26074i −0.957774 0.287523i $$-0.907168\pi$$
0.229885 0.973218i $$-0.426165\pi$$
$$270$$ 0 0
$$271$$ −17.2047 + 6.26199i −1.04511 + 0.380389i −0.806815 0.590804i $$-0.798811\pi$$
−0.238295 + 0.971193i $$0.576589\pi$$
$$272$$ −0.618710 0.737350i −0.0375148 0.0447084i
$$273$$ 0 0
$$274$$ 6.14698 + 1.08388i 0.371353 + 0.0654795i
$$275$$ 1.89462 10.7449i 0.114250 0.647942i
$$276$$ 0 0
$$277$$ −6.06459 + 16.6623i −0.364386 + 1.00114i 0.613075 + 0.790025i $$0.289932\pi$$
−0.977461 + 0.211117i $$0.932290\pi$$
$$278$$ −2.35734 + 6.47674i −0.141384 + 0.388449i
$$279$$ 0 0
$$280$$ 0.942924 5.34759i 0.0563505 0.319579i
$$281$$ 15.0167 + 2.64786i 0.895824 + 0.157958i 0.602560 0.798074i $$-0.294147\pi$$
0.293264 + 0.956032i $$0.405259\pi$$
$$282$$ 0 0
$$283$$ 15.7182 + 18.7322i 0.934350 + 1.11351i 0.993336 + 0.115256i $$0.0367689\pi$$
−0.0589858 + 0.998259i $$0.518787\pi$$
$$284$$ −10.1503 + 3.69442i −0.602311 + 0.219223i
$$285$$ 0 0
$$286$$ 12.3430 + 21.3787i 0.729857 + 1.26415i
$$287$$ 16.5205 + 13.8623i 0.975172 + 0.818266i
$$288$$ 0 0
$$289$$ 2.79114 + 15.8293i 0.164184 + 0.931136i
$$290$$ 10.5900i 0.621864i
$$291$$ 0 0
$$292$$ −2.72170 + 2.28378i −0.159276 + 0.133648i
$$293$$ 11.8143 + 4.30005i 0.690199 + 0.251212i 0.663220 0.748424i $$-0.269189\pi$$
0.0269784 + 0.999636i $$0.491411\pi$$
$$294$$ 0 0
$$295$$ 13.3188 0.775450
$$296$$ −5.44893 2.70354i −0.316713 0.157140i
$$297$$ 0 0
$$298$$ −1.19539 3.28430i −0.0692469 0.190254i
$$299$$ 24.6455 + 8.97022i 1.42529 + 0.518761i
$$300$$ 0 0
$$301$$ −7.71866 + 1.36101i −0.444896 + 0.0784472i
$$302$$ 9.40855i 0.541401i
$$303$$ 0 0
$$304$$ −1.35453 0.782038i −0.0776876 0.0448530i
$$305$$ 19.4673 + 16.3350i 1.11470 + 0.935341i
$$306$$ 0 0
$$307$$ −4.70103 + 8.14242i −0.268302 + 0.464713i −0.968423 0.249311i $$-0.919796\pi$$
0.700122 + 0.714024i $$0.253129\pi$$
$$308$$ 11.7162 4.26436i 0.667595 0.242985i
$$309$$ 0 0
$$310$$ −7.68927 + 4.43940i −0.436721 + 0.252141i
$$311$$ 15.8568 + 2.79599i 0.899158 + 0.158546i 0.604077 0.796926i $$-0.293542\pi$$
0.295082 + 0.955472i $$0.404653\pi$$
$$312$$ 0 0
$$313$$ 0.370220 0.441211i 0.0209261 0.0249387i −0.755480 0.655172i $$-0.772596\pi$$
0.776406 + 0.630233i $$0.217041\pi$$
$$314$$ −0.866920 + 2.38184i −0.0489231 + 0.134415i
$$315$$ 0 0
$$316$$ −1.63893 + 1.95319i −0.0921967 + 0.109876i
$$317$$ −2.04083 + 11.5741i −0.114624 + 0.650067i 0.872311 + 0.488951i $$0.162620\pi$$
−0.986935 + 0.161116i $$0.948491\pi$$
$$318$$ 0 0
$$319$$ 21.0582 12.1580i 1.17903 0.680715i
$$320$$ −1.67860 2.00048i −0.0938365 0.111830i
$$321$$ 0 0
$$322$$ 6.62328 11.4719i 0.369101 0.639302i
$$323$$ −0.752745 1.30379i −0.0418838 0.0725449i
$$324$$ 0 0
$$325$$ 6.48757 + 3.74560i 0.359865 + 0.207768i
$$326$$ −1.62847 9.23549i −0.0901924 0.511506i
$$327$$ 0 0
$$328$$ 10.2139 1.80099i 0.563970 0.0994430i
$$329$$ −9.83600 + 8.25338i −0.542276 + 0.455024i
$$330$$ 0 0
$$331$$ 4.83530 + 13.2849i 0.265772 + 0.730202i 0.998752 + 0.0499518i $$0.0159068\pi$$
−0.732980 + 0.680250i $$0.761871\pi$$
$$332$$ 6.91602 0.379566
$$333$$ 0 0
$$334$$ 10.4225 0.570292
$$335$$ 9.42620 + 25.8983i 0.515008 + 1.41497i
$$336$$ 0 0
$$337$$ 8.21240 6.89102i 0.447358 0.375378i −0.391096 0.920350i $$-0.627904\pi$$
0.838454 + 0.544972i $$0.183460\pi$$
$$338$$ −3.88928 + 0.685785i −0.211549 + 0.0373018i
$$339$$ 0 0
$$340$$ −0.436485 2.47543i −0.0236717 0.134249i
$$341$$ −17.6555 10.1934i −0.956101 0.552005i
$$342$$ 0 0
$$343$$ −10.0602 17.4248i −0.543200 0.940850i
$$344$$ −1.88466 + 3.26433i −0.101614 + 0.176001i
$$345$$ 0 0
$$346$$ 1.88324 + 2.24436i 0.101244 + 0.120658i
$$347$$ 6.10989 3.52754i 0.327996 0.189368i −0.326955 0.945040i $$-0.606023\pi$$
0.654951 + 0.755671i $$0.272689\pi$$
$$348$$ 0 0
$$349$$ 4.45331 25.2560i 0.238380 1.35192i −0.596996 0.802244i $$-0.703639\pi$$
0.835376 0.549679i $$-0.185250\pi$$
$$350$$ 2.43204 2.89839i 0.129998 0.154925i
$$351$$ 0 0
$$352$$ 2.05082 5.63458i 0.109309 0.300324i
$$353$$ −4.22017 + 5.02940i −0.224617 + 0.267688i −0.866570 0.499056i $$-0.833680\pi$$
0.641953 + 0.766744i $$0.278125\pi$$
$$354$$ 0 0
$$355$$ −27.7795 4.89828i −1.47438 0.259974i
$$356$$ −14.0847 + 8.13178i −0.746485 + 0.430983i
$$357$$ 0 0
$$358$$ −8.23831 + 2.99850i −0.435408 + 0.158476i
$$359$$ 9.92813 17.1960i 0.523987 0.907572i −0.475623 0.879649i $$-0.657777\pi$$
0.999610 0.0279226i $$-0.00888919\pi$$
$$360$$ 0 0
$$361$$ 12.6808 + 10.6405i 0.667413 + 0.560026i
$$362$$ −23.1716 13.3781i −1.21787 0.703138i
$$363$$ 0 0
$$364$$ 8.56057i 0.448696i
$$365$$ −9.13730 + 1.61115i −0.478268 + 0.0843315i
$$366$$ 0 0
$$367$$ 20.2967 + 7.38739i 1.05948 + 0.385619i 0.812233 0.583334i $$-0.198252\pi$$
0.247246 + 0.968953i $$0.420474\pi$$
$$368$$ −2.17885 5.98635i −0.113581 0.312060i
$$369$$ 0 0
$$370$$ −8.79308 13.2290i −0.457130 0.687744i
$$371$$ −16.6926 −0.866637
$$372$$ 0 0
$$373$$ 29.3944 + 10.6987i 1.52198 + 0.553956i 0.961642 0.274306i $$-0.0884482\pi$$
0.560340 + 0.828263i $$0.310670\pi$$
$$374$$ 4.42129 3.70990i 0.228619 0.191835i
$$375$$ 0 0
$$376$$ 6.17501i 0.318452i
$$377$$ 2.89909 + 16.4415i 0.149311 + 0.846782i
$$378$$ 0 0
$$379$$ −15.3668 12.8943i −0.789339 0.662334i 0.156243 0.987719i $$-0.450062\pi$$
−0.945582 + 0.325384i $$0.894506\pi$$
$$380$$ −2.04224 3.53727i −0.104765 0.181458i
$$381$$ 0 0
$$382$$ 1.70796 0.621648i 0.0873871 0.0318063i
$$383$$ −10.6054 12.6391i −0.541913 0.645826i 0.423703 0.905801i $$-0.360730\pi$$
−0.965615 + 0.259975i $$0.916286\pi$$
$$384$$ 0 0
$$385$$ 32.0652 + 5.65395i 1.63419 + 0.288152i
$$386$$ −0.184945 + 1.04887i −0.00941343 + 0.0533862i
$$387$$ 0 0
$$388$$ 5.57544 15.3184i 0.283050 0.777673i
$$389$$ −0.282656 + 0.776592i −0.0143312 + 0.0393748i −0.946652 0.322258i $$-0.895558\pi$$
0.932321 + 0.361632i $$0.117780\pi$$
$$390$$ 0 0
$$391$$ 1.06479 6.03875i 0.0538490 0.305393i
$$392$$ −2.63566 0.464737i −0.133121 0.0234728i
$$393$$ 0 0
$$394$$ −10.1282 12.0703i −0.510251 0.608093i
$$395$$ −6.25687 + 2.27731i −0.314817 + 0.114584i
$$396$$ 0 0
$$397$$ −4.52451 7.83669i −0.227079 0.393312i 0.729862 0.683594i $$-0.239584\pi$$
−0.956941 + 0.290282i $$0.906251\pi$$
$$398$$ 15.8089 + 13.2653i 0.792429 + 0.664927i
$$399$$ 0 0
$$400$$ −0.315970 1.79195i −0.0157985 0.0895977i
$$401$$ 13.1254i 0.655452i −0.944773 0.327726i $$-0.893718\pi$$
0.944773 0.327726i $$-0.106282\pi$$
$$402$$ 0 0
$$403$$ 10.7227 8.99742i 0.534136 0.448194i
$$404$$ −3.85506 1.40313i −0.191797 0.0698083i
$$405$$ 0 0
$$406$$ 8.43223 0.418484
$$407$$ 16.2110 32.6728i 0.803547 1.61953i
$$408$$ 0 0
$$409$$ 2.70223 + 7.42432i 0.133617 + 0.367109i 0.988399 0.151877i $$-0.0485318\pi$$
−0.854783 + 0.518986i $$0.826310\pi$$
$$410$$ 25.4511 + 9.26344i 1.25694 + 0.457489i
$$411$$ 0 0
$$412$$ −10.6353 + 1.87529i −0.523962 + 0.0923887i
$$413$$ 10.6050i 0.521840i
$$414$$ 0 0
$$415$$ 15.6411 + 9.03037i 0.767789 + 0.443283i
$$416$$ 3.15377 + 2.64632i 0.154626 + 0.129747i
$$417$$ 0 0
$$418$$ 4.68925 8.12202i 0.229359 0.397261i
$$419$$ −30.0521 + 10.9381i −1.46814 + 0.534361i −0.947596 0.319472i $$-0.896494\pi$$
−0.520548 + 0.853832i $$0.674272\pi$$
$$420$$ 0 0
$$421$$ −4.86073 + 2.80634i −0.236897 + 0.136773i −0.613750 0.789501i $$-0.710340\pi$$
0.376853 + 0.926273i $$0.377006\pi$$
$$422$$ −6.10718 1.07686i −0.297293 0.0524208i
$$423$$ 0 0
$$424$$ −5.16018 + 6.14966i −0.250600 + 0.298654i
$$425$$ 0.599028 1.64581i 0.0290571 0.0798337i
$$426$$ 0 0
$$427$$ −13.0067 + 15.5008i −0.629439 + 0.750136i
$$428$$ 3.52602 19.9970i 0.170437 0.966594i
$$429$$ 0 0
$$430$$ −8.52459 + 4.92167i −0.411092 + 0.237344i
$$431$$ 12.8250 + 15.2842i 0.617757 + 0.736214i 0.980683 0.195604i $$-0.0626666\pi$$
−0.362926 + 0.931818i $$0.618222\pi$$
$$432$$ 0 0
$$433$$ 7.91046 13.7013i 0.380152 0.658443i −0.610931 0.791684i $$-0.709205\pi$$
0.991084 + 0.133240i $$0.0425382\pi$$
$$434$$ −3.53486 6.12255i −0.169679 0.293892i
$$435$$ 0 0
$$436$$ −5.39518 3.11491i −0.258382 0.149177i
$$437$$ −1.73023 9.81263i −0.0827682 0.469402i
$$438$$ 0 0
$$439$$ 3.01674 0.531932i 0.143981 0.0253878i −0.101193 0.994867i $$-0.532266\pi$$
0.245174 + 0.969479i $$0.421155\pi$$
$$440$$ 11.9952 10.0652i 0.571850 0.479839i
$$441$$ 0 0
$$442$$ 1.35534 + 3.72375i 0.0644668 + 0.177121i
$$443$$ 2.75923 0.131095 0.0655475 0.997849i $$-0.479121\pi$$
0.0655475 + 0.997849i $$0.479121\pi$$
$$444$$ 0 0
$$445$$ −42.4712 −2.01333
$$446$$ 0.287006 + 0.788543i 0.0135901 + 0.0373386i
$$447$$ 0 0
$$448$$ 1.59287 1.33658i 0.0752561 0.0631474i
$$449$$ 22.3120 3.93421i 1.05297 0.185667i 0.379735 0.925095i $$-0.376015\pi$$
0.673235 + 0.739428i $$0.264904\pi$$
$$450$$ 0 0
$$451$$ 10.7991 + 61.2446i 0.508509 + 2.88390i
$$452$$ 5.31045 + 3.06599i 0.249782 + 0.144212i
$$453$$ 0 0
$$454$$ −3.26185 5.64968i −0.153086 0.265153i
$$455$$ −11.1777 + 19.3603i −0.524018 + 0.907626i
$$456$$ 0 0
$$457$$ −18.9638 22.6002i −0.887089 1.05719i −0.997991 0.0633601i $$-0.979818\pi$$
0.110902 0.993831i $$-0.464626\pi$$
$$458$$ −5.71935 + 3.30207i −0.267248 + 0.154296i
$$459$$ 0 0
$$460$$ 2.88885 16.3835i 0.134694 0.763885i
$$461$$ −2.61917 + 3.12141i −0.121987 + 0.145378i −0.823581 0.567198i $$-0.808027\pi$$
0.701594 + 0.712576i $$0.252472\pi$$
$$462$$ 0 0
$$463$$ −1.00637 + 2.76497i −0.0467699 + 0.128499i −0.960879 0.276970i $$-0.910670\pi$$
0.914109 + 0.405469i $$0.132892\pi$$
$$464$$ 2.60665 3.10649i 0.121011 0.144215i
$$465$$ 0 0
$$466$$ −22.2659 3.92607i −1.03145 0.181872i
$$467$$ −4.59204 + 2.65121i −0.212494 + 0.122684i −0.602470 0.798142i $$-0.705817\pi$$
0.389976 + 0.920825i $$0.372483\pi$$
$$468$$ 0 0
$$469$$ −20.6214 + 7.50558i −0.952208 + 0.346575i
$$470$$ −8.06282 + 13.9652i −0.371910 + 0.644167i
$$471$$ 0 0
$$472$$ 3.90696 + 3.27833i 0.179833 + 0.150897i
$$473$$ −19.5735 11.3008i −0.899992 0.519611i
$$474$$ 0 0
$$475$$ 2.84599i 0.130583i
$$476$$ 1.97105 0.347550i 0.0903430 0.0159299i
$$477$$ 0 0
$$478$$ 16.1133 + 5.86475i 0.737004 + 0.268248i
$$479$$ 6.11079 + 16.7893i 0.279209 + 0.767121i 0.997453 + 0.0713293i $$0.0227241\pi$$
−0.718244 + 0.695792i $$0.755054\pi$$
$$480$$ 0 0
$$481$$ 17.2733 + 18.1316i 0.787595 + 0.826731i
$$482$$ 5.68755 0.259061
$$483$$ 0 0
$$484$$ 23.4494 + 8.53487i 1.06588 + 0.387949i
$$485$$ 32.6107 27.3637i 1.48078 1.24252i
$$486$$ 0 0
$$487$$ 31.2962i 1.41817i 0.705124 + 0.709084i $$0.250891\pi$$
−0.705124 + 0.709084i $$0.749109\pi$$
$$488$$ 1.68983 + 9.58351i 0.0764951 + 0.433825i
$$489$$ 0 0
$$490$$ −5.35390 4.49246i −0.241865 0.202949i
$$491$$ −6.72900 11.6550i −0.303676 0.525982i 0.673290 0.739379i $$-0.264881\pi$$
−0.976966 + 0.213397i $$0.931547\pi$$
$$492$$ 0 0
$$493$$ 3.66793 1.33502i 0.165195 0.0601261i
$$494$$ 4.13905 + 4.93273i 0.186225 + 0.221934i
$$495$$ 0 0
$$496$$ −3.34832 0.590399i −0.150344 0.0265097i
$$497$$ 3.90024 22.1194i 0.174950 0.992189i
$$498$$ 0 0
$$499$$ 12.5759 34.5520i 0.562974 1.54676i −0.252279 0.967654i $$-0.581180\pi$$
0.815253 0.579104i $$-0.196598\pi$$
$$500$$ −2.84062 + 7.80454i −0.127036 + 0.349030i
$$501$$ 0 0
$$502$$ −4.40180 + 24.9638i −0.196462 + 1.11419i
$$503$$ −6.15105 1.08460i −0.274262 0.0483597i 0.0348257 0.999393i $$-0.488912\pi$$
−0.309087 + 0.951034i $$0.600024\pi$$
$$504$$ 0 0
$$505$$ −6.88641 8.20690i −0.306441 0.365202i
$$506$$ 35.8953 13.0648i 1.59574 0.580802i
$$507$$ 0 0
$$508$$ −3.19057 5.52624i −0.141559 0.245187i
$$509$$ 6.29668 + 5.28355i 0.279096 + 0.234189i 0.771580 0.636132i $$-0.219467\pi$$
−0.492484 + 0.870321i $$0.663911\pi$$
$$510$$ 0 0
$$511$$ −1.28287 7.27554i −0.0567510 0.321851i
$$512$$ 1.00000i 0.0441942i
$$513$$ 0 0
$$514$$ 3.96118 3.32383i 0.174720 0.146608i
$$515$$ −26.5010 9.64558i −1.16777 0.425035i
$$516$$ 0 0
$$517$$ −37.0265 −1.62842
$$518$$ 10.5336 7.00146i 0.462818 0.307626i
$$519$$ 0 0
$$520$$ 3.67711 + 10.1028i 0.161252 + 0.443036i
$$521$$ 20.8518 + 7.58945i 0.913536 + 0.332500i 0.755664 0.654960i $$-0.227314\pi$$
0.157872 + 0.987460i $$0.449537\pi$$
$$522$$ 0 0
$$523$$ −13.7427 + 2.42321i −0.600927 + 0.105960i −0.465832 0.884873i $$-0.654245\pi$$
−0.135095 + 0.990833i $$0.543134\pi$$
$$524$$ 10.4534i 0.456657i
$$525$$ 0 0
$$526$$ −8.37625 4.83603i −0.365222 0.210861i
$$527$$ −2.50697 2.10360i −0.109205 0.0916340i
$$528$$ 0 0
$$529$$ 8.79187 15.2280i 0.382255 0.662086i
$$530$$ −19.6998 + 7.17015i −0.855706 + 0.311451i
$$531$$ 0 0
$$532$$ 2.81654 1.62613i 0.122112 0.0705016i
$$533$$ −42.0502 7.41459i −1.82140 0.321161i
$$534$$ 0 0
$$535$$ 34.0848 40.6207i 1.47362 1.75619i
$$536$$ −3.60958 + 9.91725i −0.155910 + 0.428360i
$$537$$ 0 0
$$538$$ 15.3475 18.2905i 0.661679 0.788559i
$$539$$ 2.78665 15.8039i 0.120030 0.680722i
$$540$$ 0 0
$$541$$ 20.9379 12.0885i 0.900192 0.519726i 0.0229292 0.999737i $$-0.492701\pi$$
0.877262 + 0.480011i $$0.159367\pi$$
$$542$$ −11.7687 14.0254i −0.505509 0.602442i
$$543$$ 0 0
$$544$$ 0.481271 0.833586i 0.0206343 0.0357397i
$$545$$ −8.13439 14.0892i −0.348439 0.603514i
$$546$$ 0 0
$$547$$ −32.2382 18.6127i −1.37840 0.795822i −0.386437 0.922316i $$-0.626294\pi$$
−0.991967 + 0.126494i $$0.959628\pi$$
$$548$$ 1.08388 + 6.14698i 0.0463010 + 0.262586i
$$549$$ 0 0
$$550$$ 10.7449 1.89462i 0.458164 0.0807867i
$$551$$ 4.85878 4.07700i 0.206991 0.173686i
$$552$$ 0 0
$$553$$ −1.81330 4.98201i −0.0771095 0.211857i
$$554$$ −17.7317 −0.753347
$$555$$ 0 0
$$556$$ −6.89241 −0.292303
$$557$$ −0.974054 2.67619i −0.0412720 0.113394i 0.917345 0.398094i $$-0.130328\pi$$
−0.958617 + 0.284700i $$0.908106\pi$$
$$558$$ 0 0
$$559$$ 11.8876 9.97485i 0.502790 0.421891i
$$560$$ 5.34759 0.942924i 0.225977 0.0398458i
$$561$$ 0 0
$$562$$ 2.64786 + 15.0167i 0.111693 + 0.633443i
$$563$$ 21.5088 + 12.4181i 0.906489 + 0.523362i 0.879300 0.476268i $$-0.158011\pi$$
0.0271895 + 0.999630i $$0.491344\pi$$
$$564$$ 0 0
$$565$$ 8.00663 + 13.8679i 0.336841 + 0.583427i
$$566$$ −12.2266 + 21.1771i −0.513922 + 0.890139i
$$567$$ 0 0
$$568$$ −6.94323 8.27462i −0.291332 0.347195i
$$569$$ 8.80519 5.08368i 0.369133 0.213119i −0.303947 0.952689i $$-0.598304\pi$$
0.673080 + 0.739570i $$0.264971\pi$$
$$570$$ 0 0
$$571$$ 3.25922 18.4839i 0.136394 0.773528i −0.837485 0.546460i $$-0.815975\pi$$
0.973879 0.227068i $$-0.0729140\pi$$
$$572$$ −15.8679 + 18.9106i −0.663469 + 0.790691i
$$573$$ 0 0
$$574$$ −7.37598 + 20.2653i −0.307868 + 0.845859i
$$575$$ 7.45108 8.87985i 0.310731 0.370315i
$$576$$ 0 0
$$577$$ −18.5265 3.26672i −0.771267 0.135995i −0.225852 0.974162i $$-0.572517\pi$$
−0.545415 + 0.838166i $$0.683628\pi$$
$$578$$ −13.9201 + 8.03676i −0.578999 + 0.334285i
$$579$$ 0 0
$$580$$ 9.95132 3.62198i 0.413206 0.150395i
$$581$$ −7.19040 + 12.4541i −0.298308 + 0.516685i
$$582$$ 0 0
$$583$$ −36.8745 30.9414i −1.52719 1.28146i
$$584$$ −3.07693 1.77647i −0.127324 0.0735107i
$$585$$ 0 0
$$586$$ 12.5725i 0.519366i
$$587$$ −30.2531 + 5.33444i −1.24868 + 0.220176i −0.758632 0.651520i $$-0.774132\pi$$
−0.490048 + 0.871696i $$0.663021\pi$$
$$588$$ 0 0
$$589$$ −4.99711 1.81880i −0.205902 0.0749423i
$$590$$ 4.55529 + 12.5156i 0.187538 + 0.515258i
$$591$$ 0 0
$$592$$ 0.676854 6.04499i 0.0278185 0.248447i
$$593$$ −6.18887 −0.254147 −0.127073 0.991893i $$-0.540558\pi$$
−0.127073 + 0.991893i $$0.540558\pi$$
$$594$$ 0 0
$$595$$ 4.91147 + 1.78763i 0.201351 + 0.0732857i
$$596$$ 2.67738 2.24659i 0.109670 0.0920240i
$$597$$ 0 0
$$598$$ 26.2272i 1.07251i
$$599$$ 0.183355 + 1.03986i 0.00749169 + 0.0424875i 0.988324 0.152364i $$-0.0486886\pi$$
−0.980833 + 0.194852i $$0.937578\pi$$
$$600$$ 0 0
$$601$$ −11.9378 10.0170i −0.486954 0.408603i 0.365979 0.930623i $$-0.380734\pi$$
−0.852933 + 0.522020i $$0.825179\pi$$
$$602$$ −3.91887 6.78767i −0.159721 0.276645i
$$603$$ 0 0
$$604$$ −8.84115 + 3.21791i −0.359741 + 0.130935i
$$605$$ 41.8883 + 49.9205i 1.70300 + 2.02956i
$$606$$ 0 0
$$607$$ −31.7497 5.59834i −1.28868 0.227229i −0.513020 0.858377i $$-0.671473\pi$$
−0.775663 + 0.631147i $$0.782584\pi$$
$$608$$ 0.271599 1.54031i 0.0110148 0.0624680i
$$609$$ 0 0
$$610$$ −8.69169 + 23.8802i −0.351916 + 0.966882i
$$611$$ 8.69490 23.8890i 0.351758 0.966447i
$$612$$ 0 0
$$613$$ −0.968237 + 5.49114i −0.0391067 + 0.221785i −0.998098 0.0616512i $$-0.980363\pi$$
0.958991 + 0.283436i $$0.0914745\pi$$
$$614$$ −9.25922 1.63265i −0.373672 0.0658884i
$$615$$ 0 0
$$616$$ 8.01438 + 9.55117i 0.322909 + 0.384827i
$$617$$ 3.80891 1.38633i 0.153341 0.0558116i −0.264209 0.964465i $$-0.585111\pi$$
0.417550 + 0.908654i $$0.362889\pi$$
$$618$$ 0 0
$$619$$ 3.68705 + 6.38616i 0.148195 + 0.256681i 0.930560 0.366138i $$-0.119320\pi$$
−0.782365 + 0.622820i $$0.785987\pi$$
$$620$$ −6.80156 5.70718i −0.273157 0.229206i
$$621$$ 0 0
$$622$$ 2.79599 + 15.8568i 0.112109 + 0.635801i
$$623$$ 33.8176i 1.35487i
$$624$$ 0 0
$$625$$ −23.5843 + 19.7895i −0.943370 + 0.791581i
$$626$$ 0.541225 + 0.196990i 0.0216317 + 0.00787330i
$$627$$ 0 0
$$628$$ −2.53470 −0.101146
$$629$$ 3.47349 4.71327i 0.138497 0.187930i
$$630$$ 0 0
$$631$$ 2.86348 + 7.86734i 0.113993 + 0.313194i 0.983549 0.180641i $$-0.0578171\pi$$
−0.869556 + 0.493834i $$0.835595\pi$$
$$632$$ −2.39595 0.872054i −0.0953057 0.0346884i
$$633$$ 0 0
$$634$$ −11.5741 + 2.04083i −0.459667 + 0.0810517i
$$635$$ 16.6640i 0.661289i
$$636$$ 0 0
$$637$$ 9.54209 + 5.50913i 0.378071 + 0.218280i
$$638$$ 18.6271 + 15.6300i 0.737453 + 0.618797i
$$639$$ 0 0
$$640$$ 1.30572 2.26157i 0.0516130 0.0893964i
$$641$$ −11.1583 + 4.06129i −0.440726 + 0.160411i −0.552846 0.833283i $$-0.686458\pi$$
0.112120 + 0.993695i $$0.464236\pi$$
$$642$$ 0 0
$$643$$ −33.5232 + 19.3547i −1.32203 + 0.763273i −0.984052 0.177882i $$-0.943076\pi$$
−0.337976 + 0.941155i $$0.609742\pi$$
$$644$$ 13.0453 + 2.30024i 0.514057 + 0.0906422i
$$645$$ 0 0
$$646$$ 0.967710 1.15327i 0.0380740 0.0453749i
$$647$$ −6.03672 + 16.5857i −0.237328 + 0.652053i 0.762658 + 0.646801i $$0.223894\pi$$
−0.999986 + 0.00525130i $$0.998328\pi$$
$$648$$ 0 0
$$649$$ −19.6575 + 23.4269i −0.771624 + 0.919586i
$$650$$ −1.30083 + 7.37739i −0.0510228 + 0.289365i
$$651$$ 0 0
$$652$$ 8.12155 4.68898i 0.318065 0.183635i
$$653$$ −9.49773 11.3189i −0.371675 0.442945i 0.547493 0.836810i $$-0.315582\pi$$
−0.919168 + 0.393865i $$0.871138\pi$$
$$654$$ 0 0
$$655$$ 13.6491 23.6410i 0.533316 0.923731i
$$656$$ 5.18574 + 8.98197i 0.202469 + 0.350687i
$$657$$ 0 0
$$658$$ −11.1198 6.41999i −0.433493 0.250277i
$$659$$ −1.14933 6.51815i −0.0447714 0.253911i 0.954205 0.299155i $$-0.0967047\pi$$
−0.998976 + 0.0452437i $$0.985594\pi$$
$$660$$ 0 0
$$661$$ 6.22992 1.09850i 0.242316 0.0427268i −0.0511712 0.998690i $$-0.516295\pi$$
0.293487 + 0.955963i $$0.405184\pi$$
$$662$$ −10.8299 + 9.08738i −0.420917 + 0.353191i
$$663$$ 0 0
$$664$$ 2.36542 + 6.49893i 0.0917960 + 0.252207i
$$665$$ 8.49307 0.329347
$$666$$ 0 0
$$667$$ 25.8340 1.00030
$$668$$ 3.56469 + 9.79392i 0.137922 + 0.378938i
$$669$$ 0 0
$$670$$ −21.1125 + 17.7155i −0.815645 + 0.684408i
$$671$$ −57.4645 + 10.1325i −2.21839 + 0.391163i
$$672$$ 0 0
$$673$$ 4.26450 + 24.1852i 0.164384 + 0.932269i 0.949697 + 0.313170i $$0.101391\pi$$
−0.785313 + 0.619099i $$0.787498\pi$$
$$674$$ 9.28425 + 5.36027i 0.357616 + 0.206470i
$$675$$ 0 0
$$676$$ −1.97464 3.42017i −0.0759476 0.131545i
$$677$$ −11.2322 + 19.4547i −0.431687 + 0.747704i −0.997019 0.0771600i $$-0.975415\pi$$
0.565332 + 0.824864i $$0.308748\pi$$
$$678$$ 0 0
$$679$$ 21.7882 + 25.9662i 0.836155 + 0.996491i
$$680$$ 2.17686 1.25681i 0.0834786 0.0481964i
$$681$$ 0 0
$$682$$ 3.54014 20.0771i 0.135559 0.768794i
$$683$$ −21.2410 + 25.3140i −0.812764 + 0.968614i −0.999906 0.0137189i $$-0.995633\pi$$
0.187142 + 0.982333i $$0.440077\pi$$
$$684$$ 0 0
$$685$$ −5.57496 + 15.3171i −0.213008 + 0.585235i
$$686$$ 12.9332 15.4131i 0.493790 0.588476i
$$687$$ 0 0
$$688$$ −3.71206 0.654536i −0.141521 0.0249540i
$$689$$ 28.6222 16.5251i 1.09042 0.629554i
$$690$$ 0 0
$$691$$ −32.8077 + 11.9410i −1.24806 + 0.454258i −0.879747 0.475442i $$-0.842288\pi$$
−0.368317 + 0.929700i $$0.620066\pi$$
$$692$$ −1.46490 + 2.53729i −0.0556872 + 0.0964531i
$$693$$ 0 0
$$694$$ 5.40451 + 4.53492i 0.205152 + 0.172143i
$$695$$ −15.5877 8.99954i −0.591274 0.341372i
$$696$$ 0 0
$$697$$ 9.98299i 0.378133i
$$698$$ 25.2560 4.45331i 0.955954 0.168560i
$$699$$ 0 0
$$700$$ 3.55540 + 1.29406i 0.134381 + 0.0489108i
$$701$$ −9.15308 25.1479i −0.345707 0.949823i −0.983706 0.179785i $$-0.942460\pi$$
0.637999 0.770037i $$-0.279763\pi$$
$$702$$ 0 0
$$703$$ 2.68438 9.12735i 0.101243 0.344245i
$$704$$ 5.99619 0.225990
$$705$$ 0 0
$$706$$ −6.16948 2.24551i −0.232191 0.0845107i
$$707$$ 6.53472 5.48328i 0.245763 0.206220i
$$708$$ 0 0
$$709$$ 6.67084i 0.250529i −0.992123 0.125264i $$-0.960022\pi$$
0.992123 0.125264i $$-0.0399779\pi$$
$$710$$ −4.89828 27.7795i −0.183829 1.04255i
$$711$$ 0 0
$$712$$ −12.4586 10.4540i −0.466906 0.391781i
$$713$$ −10.8298 18.7578i −0.405580 0.702485i
$$714$$ 0 0
$$715$$ −60.5782 + 22.0487i −2.26550 + 0.824573i
$$716$$ −5.63534 6.71594i −0.210603 0.250986i
$$717$$ 0 0
$$718$$ 19.5546 + 3.44800i 0.729771 + 0.128678i
$$719$$ −8.26991 + 46.9010i −0.308416 + 1.74911i 0.298559 + 0.954391i $$0.403494\pi$$
−0.606975 + 0.794721i $$0.707617\pi$$
$$720$$ 0 0
$$721$$ 7.68026 21.1013i 0.286028 0.785855i
$$722$$ −5.66169 + 15.5554i −0.210706 + 0.578910i
$$723$$ 0 0
$$724$$ 4.64617 26.3498i 0.172674 0.979281i
$$725$$ 7.26679 + 1.28133i 0.269882 + 0.0475874i
$$726$$ 0 0
$$727$$ −32.2308 38.4112i −1.19537 1.42459i −0.879572 0.475766i $$-0.842171\pi$$
−0.315802 0.948825i $$-0.602274\pi$$
$$728$$ −8.04430 + 2.92789i −0.298142 + 0.108515i
$$729$$ 0 0
$$730$$ −4.63913 8.03520i −0.171702 0.297396i
$$731$$ −2.77931 2.33212i −0.102796 0.0862565i
$$732$$ 0 0
$$733$$ 4.88298 + 27.6927i 0.180357 + 1.02285i 0.931777 + 0.363031i $$0.118258\pi$$
−0.751420 + 0.659824i $$0.770631\pi$$
$$734$$ 21.5993i 0.797244i
$$735$$ 0 0
$$736$$ 4.88011 4.09490i 0.179883 0.150940i
$$737$$ −59.4657 21.6438i −2.19045 0.797258i
$$738$$ 0 0
$$739$$ 32.3511 1.19006 0.595028 0.803705i $$-0.297141\pi$$
0.595028 + 0.803705i $$0.297141\pi$$
$$740$$ 9.42380 12.7874i 0.346426 0.470073i
$$741$$ 0 0
$$742$$ −5.70921 15.6859i −0.209592 0.575848i
$$743$$ 7.05630 + 2.56828i 0.258871 + 0.0942212i 0.468195 0.883625i $$-0.344904\pi$$
−0.209325 + 0.977846i $$0.567127\pi$$
$$744$$ 0 0
$$745$$ 8.98851 1.58492i 0.329313 0.0580668i
$$746$$ 31.2808i 1.14527i
$$747$$ 0 0
$$748$$ 4.99834 + 2.88579i 0.182757 + 0.105515i
$$749$$ 32.3441 + 27.1399i 1.18183 + 0.991672i
$$750$$ 0 0
$$751$$ −7.37086 + 12.7667i −0.268966 + 0.465863i −0.968595 0.248643i $$-0.920015\pi$$
0.699629 + 0.714506i $$0.253349\pi$$
$$752$$ −5.80261 + 2.11198i −0.211599 + 0.0770159i
$$753$$ 0 0
$$754$$ −14.4584 + 8.34759i −0.526546 + 0.304001i
$$755$$ −24.1966 4.26651i −0.880603 0.155274i
$$756$$ 0 0
$$757$$ −14.2111 + 16.9361i −0.516511 + 0.615553i −0.959752 0.280849i $$-0.909384\pi$$
0.443241 + 0.896402i $$0.353828\pi$$
$$758$$ 6.86090 18.8502i 0.249199 0.684669i
$$759$$ 0 0
$$760$$ 2.62546 3.12890i 0.0952353 0.113497i
$$761$$ −5.52983 + 31.3612i −0.200456 + 1.13684i 0.703975 + 0.710225i $$0.251407\pi$$
−0.904431 + 0.426619i $$0.859704\pi$$
$$762$$ 0 0
$$763$$ 11.2185 6.47698i 0.406135 0.234482i
$$764$$ 1.16832 + 1.39235i 0.0422682 + 0.0503733i
$$765$$ 0 0
$$766$$ 8.24957 14.2887i 0.298069 0.516271i
$$767$$ −10.4986 18.1841i −0.379082 0.656589i
$$768$$ 0 0
$$769$$ 19.6375 + 11.3377i 0.708148 + 0.408849i 0.810375 0.585912i $$-0.199263\pi$$
−0.102227 + 0.994761i $$0.532597\pi$$
$$770$$ 5.65395 + 32.0652i 0.203754 + 1.15555i
$$771$$ 0 0
$$772$$ −1.04887 + 0.184945i −0.0377497 + 0.00665630i
$$773$$ −9.05550 + 7.59846i −0.325704 + 0.273298i −0.790947 0.611885i $$-0.790411\pi$$
0.465243 + 0.885183i $$0.345967\pi$$
$$774$$ 0 0
$$775$$ −2.11593 5.81348i −0.0760066 0.208826i
$$776$$ 16.3015 0.585189
$$777$$ 0 0
$$778$$ −0.826432 −0.0296290
$$779$$ 5.54818 + 15.2435i 0.198784 + 0.546155i
$$780$$ 0 0
$$781$$ 49.6162 41.6329i 1.77541 1.48974i
$$782$$ 6.03875 1.06479i 0.215945 0.0380770i
$$783$$ 0 0
$$784$$ −0.464737 2.63566i −0.0165978 0.0941306i
$$785$$