# Properties

 Label 1134.2.l.d.215.2 Level $1134$ Weight $2$ Character 1134.215 Analytic conductor $9.055$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1134 = 2 \cdot 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1134.l (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.05503558921$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 378) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 215.2 Root $$0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1134.215 Dual form 1134.2.l.d.269.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000i q^{2} -1.00000 q^{4} +(2.00000 - 1.73205i) q^{7} -1.00000i q^{8} +O(q^{10})$$ $$q+1.00000i q^{2} -1.00000 q^{4} +(2.00000 - 1.73205i) q^{7} -1.00000i q^{8} +(2.59808 + 1.50000i) q^{11} +(-3.00000 - 1.73205i) q^{13} +(1.73205 + 2.00000i) q^{14} +1.00000 q^{16} +(-1.50000 + 2.59808i) q^{22} +(2.50000 - 4.33013i) q^{25} +(1.73205 - 3.00000i) q^{26} +(-2.00000 + 1.73205i) q^{28} +(7.79423 - 4.50000i) q^{29} -1.73205i q^{31} +1.00000i q^{32} +(4.00000 - 6.92820i) q^{37} +(-5.19615 + 9.00000i) q^{41} +(-2.00000 - 3.46410i) q^{43} +(-2.59808 - 1.50000i) q^{44} +10.3923 q^{47} +(1.00000 - 6.92820i) q^{49} +(4.33013 + 2.50000i) q^{50} +(3.00000 + 1.73205i) q^{52} +(5.19615 - 3.00000i) q^{53} +(-1.73205 - 2.00000i) q^{56} +(4.50000 + 7.79423i) q^{58} +5.19615 q^{59} +13.8564i q^{61} +1.73205 q^{62} -1.00000 q^{64} +2.00000 q^{67} +12.0000i q^{71} +(4.50000 - 2.59808i) q^{73} +(6.92820 + 4.00000i) q^{74} +(7.79423 - 1.50000i) q^{77} -13.0000 q^{79} +(-9.00000 - 5.19615i) q^{82} +(2.59808 + 4.50000i) q^{83} +(3.46410 - 2.00000i) q^{86} +(1.50000 - 2.59808i) q^{88} +(5.19615 - 9.00000i) q^{89} +(-9.00000 + 1.73205i) q^{91} +10.3923i q^{94} +(-7.50000 + 4.33013i) q^{97} +(6.92820 + 1.00000i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 4 q^{4} + 8 q^{7} + O(q^{10})$$ $$4 q - 4 q^{4} + 8 q^{7} - 12 q^{13} + 4 q^{16} - 6 q^{22} + 10 q^{25} - 8 q^{28} + 16 q^{37} - 8 q^{43} + 4 q^{49} + 12 q^{52} + 18 q^{58} - 4 q^{64} + 8 q^{67} + 18 q^{73} - 52 q^{79} - 36 q^{82} + 6 q^{88} - 36 q^{91} - 30 q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$407$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ 0 0
$$4$$ −1.00000 −0.500000
$$5$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$6$$ 0 0
$$7$$ 2.00000 1.73205i 0.755929 0.654654i
$$8$$ 1.00000i 0.353553i
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 2.59808 + 1.50000i 0.783349 + 0.452267i 0.837616 0.546259i $$-0.183949\pi$$
−0.0542666 + 0.998526i $$0.517282\pi$$
$$12$$ 0 0
$$13$$ −3.00000 1.73205i −0.832050 0.480384i 0.0225039 0.999747i $$-0.492836\pi$$
−0.854554 + 0.519362i $$0.826170\pi$$
$$14$$ 1.73205 + 2.00000i 0.462910 + 0.534522i
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$18$$ 0 0
$$19$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −1.50000 + 2.59808i −0.319801 + 0.553912i
$$23$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$24$$ 0 0
$$25$$ 2.50000 4.33013i 0.500000 0.866025i
$$26$$ 1.73205 3.00000i 0.339683 0.588348i
$$27$$ 0 0
$$28$$ −2.00000 + 1.73205i −0.377964 + 0.327327i
$$29$$ 7.79423 4.50000i 1.44735 0.835629i 0.449029 0.893517i $$-0.351770\pi$$
0.998323 + 0.0578882i $$0.0184367\pi$$
$$30$$ 0 0
$$31$$ 1.73205i 0.311086i −0.987829 0.155543i $$-0.950287\pi$$
0.987829 0.155543i $$-0.0497126\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 4.00000 6.92820i 0.657596 1.13899i −0.323640 0.946180i $$-0.604907\pi$$
0.981236 0.192809i $$-0.0617599\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −5.19615 + 9.00000i −0.811503 + 1.40556i 0.100309 + 0.994956i $$0.468017\pi$$
−0.911812 + 0.410608i $$0.865317\pi$$
$$42$$ 0 0
$$43$$ −2.00000 3.46410i −0.304997 0.528271i 0.672264 0.740312i $$-0.265322\pi$$
−0.977261 + 0.212041i $$0.931989\pi$$
$$44$$ −2.59808 1.50000i −0.391675 0.226134i
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 10.3923 1.51587 0.757937 0.652328i $$-0.226208\pi$$
0.757937 + 0.652328i $$0.226208\pi$$
$$48$$ 0 0
$$49$$ 1.00000 6.92820i 0.142857 0.989743i
$$50$$ 4.33013 + 2.50000i 0.612372 + 0.353553i
$$51$$ 0 0
$$52$$ 3.00000 + 1.73205i 0.416025 + 0.240192i
$$53$$ 5.19615 3.00000i 0.713746 0.412082i −0.0987002 0.995117i $$-0.531468\pi$$
0.812447 + 0.583036i $$0.198135\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ −1.73205 2.00000i −0.231455 0.267261i
$$57$$ 0 0
$$58$$ 4.50000 + 7.79423i 0.590879 + 1.02343i
$$59$$ 5.19615 0.676481 0.338241 0.941060i $$-0.390168\pi$$
0.338241 + 0.941060i $$0.390168\pi$$
$$60$$ 0 0
$$61$$ 13.8564i 1.77413i 0.461644 + 0.887066i $$0.347260\pi$$
−0.461644 + 0.887066i $$0.652740\pi$$
$$62$$ 1.73205 0.219971
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 2.00000 0.244339 0.122169 0.992509i $$-0.461015\pi$$
0.122169 + 0.992509i $$0.461015\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 12.0000i 1.42414i 0.702109 + 0.712069i $$0.252242\pi$$
−0.702109 + 0.712069i $$0.747758\pi$$
$$72$$ 0 0
$$73$$ 4.50000 2.59808i 0.526685 0.304082i −0.212980 0.977056i $$-0.568317\pi$$
0.739666 + 0.672975i $$0.234984\pi$$
$$74$$ 6.92820 + 4.00000i 0.805387 + 0.464991i
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 7.79423 1.50000i 0.888235 0.170941i
$$78$$ 0 0
$$79$$ −13.0000 −1.46261 −0.731307 0.682048i $$-0.761089\pi$$
−0.731307 + 0.682048i $$0.761089\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ −9.00000 5.19615i −0.993884 0.573819i
$$83$$ 2.59808 + 4.50000i 0.285176 + 0.493939i 0.972652 0.232268i $$-0.0746146\pi$$
−0.687476 + 0.726207i $$0.741281\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 3.46410 2.00000i 0.373544 0.215666i
$$87$$ 0 0
$$88$$ 1.50000 2.59808i 0.159901 0.276956i
$$89$$ 5.19615 9.00000i 0.550791 0.953998i −0.447427 0.894321i $$-0.647659\pi$$
0.998218 0.0596775i $$-0.0190072\pi$$
$$90$$ 0 0
$$91$$ −9.00000 + 1.73205i −0.943456 + 0.181568i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 10.3923i 1.07188i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −7.50000 + 4.33013i −0.761510 + 0.439658i −0.829837 0.558005i $$-0.811567\pi$$
0.0683279 + 0.997663i $$0.478234\pi$$
$$98$$ 6.92820 + 1.00000i 0.699854 + 0.101015i
$$99$$ 0 0
$$100$$ −2.50000 + 4.33013i −0.250000 + 0.433013i
$$101$$ −2.59808 + 4.50000i −0.258518 + 0.447767i −0.965845 0.259120i $$-0.916568\pi$$
0.707327 + 0.706887i $$0.249901\pi$$
$$102$$ 0 0
$$103$$ 15.0000 8.66025i 1.47799 0.853320i 0.478303 0.878195i $$-0.341252\pi$$
0.999691 + 0.0248745i $$0.00791862\pi$$
$$104$$ −1.73205 + 3.00000i −0.169842 + 0.294174i
$$105$$ 0 0
$$106$$ 3.00000 + 5.19615i 0.291386 + 0.504695i
$$107$$ −10.3923 6.00000i −1.00466 0.580042i −0.0950377 0.995474i $$-0.530297\pi$$
−0.909624 + 0.415432i $$0.863630\pi$$
$$108$$ 0 0
$$109$$ 4.00000 + 6.92820i 0.383131 + 0.663602i 0.991508 0.130046i $$-0.0415126\pi$$
−0.608377 + 0.793648i $$0.708179\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 2.00000 1.73205i 0.188982 0.163663i
$$113$$ 10.3923 + 6.00000i 0.977626 + 0.564433i 0.901553 0.432670i $$-0.142428\pi$$
0.0760733 + 0.997102i $$0.475762\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −7.79423 + 4.50000i −0.723676 + 0.417815i
$$117$$ 0 0
$$118$$ 5.19615i 0.478345i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −1.00000 1.73205i −0.0909091 0.157459i
$$122$$ −13.8564 −1.25450
$$123$$ 0 0
$$124$$ 1.73205i 0.155543i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 8.00000 0.709885 0.354943 0.934888i $$-0.384500\pi$$
0.354943 + 0.934888i $$0.384500\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −7.79423 13.5000i −0.680985 1.17950i −0.974681 0.223602i $$-0.928219\pi$$
0.293696 0.955899i $$-0.405115\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 2.00000i 0.172774i
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −10.3923 6.00000i −0.887875 0.512615i −0.0146279 0.999893i $$-0.504656\pi$$
−0.873247 + 0.487278i $$0.837990\pi$$
$$138$$ 0 0
$$139$$ −6.00000 3.46410i −0.508913 0.293821i 0.223474 0.974710i $$-0.428260\pi$$
−0.732387 + 0.680889i $$0.761594\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −12.0000 −1.00702
$$143$$ −5.19615 9.00000i −0.434524 0.752618i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 2.59808 + 4.50000i 0.215018 + 0.372423i
$$147$$ 0 0
$$148$$ −4.00000 + 6.92820i −0.328798 + 0.569495i
$$149$$ −12.9904 + 7.50000i −1.06421 + 0.614424i −0.926595 0.376061i $$-0.877278\pi$$
−0.137619 + 0.990485i $$0.543945\pi$$
$$150$$ 0 0
$$151$$ 11.5000 19.9186i 0.935857 1.62095i 0.162758 0.986666i $$-0.447961\pi$$
0.773099 0.634285i $$-0.218706\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 1.50000 + 7.79423i 0.120873 + 0.628077i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 10.3923i 0.829396i 0.909959 + 0.414698i $$0.136113\pi$$
−0.909959 + 0.414698i $$0.863887\pi$$
$$158$$ 13.0000i 1.03422i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 5.00000 8.66025i 0.391630 0.678323i −0.601035 0.799223i $$-0.705245\pi$$
0.992665 + 0.120900i $$0.0385779\pi$$
$$164$$ 5.19615 9.00000i 0.405751 0.702782i
$$165$$ 0 0
$$166$$ −4.50000 + 2.59808i −0.349268 + 0.201650i
$$167$$ −5.19615 + 9.00000i −0.402090 + 0.696441i −0.993978 0.109580i $$-0.965050\pi$$
0.591888 + 0.806020i $$0.298383\pi$$
$$168$$ 0 0
$$169$$ −0.500000 0.866025i −0.0384615 0.0666173i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 2.00000 + 3.46410i 0.152499 + 0.264135i
$$173$$ −25.9808 −1.97528 −0.987640 0.156737i $$-0.949903\pi$$
−0.987640 + 0.156737i $$0.949903\pi$$
$$174$$ 0 0
$$175$$ −2.50000 12.9904i −0.188982 0.981981i
$$176$$ 2.59808 + 1.50000i 0.195837 + 0.113067i
$$177$$ 0 0
$$178$$ 9.00000 + 5.19615i 0.674579 + 0.389468i
$$179$$ 7.79423 4.50000i 0.582568 0.336346i −0.179585 0.983742i $$-0.557476\pi$$
0.762153 + 0.647397i $$0.224142\pi$$
$$180$$ 0 0
$$181$$ 20.7846i 1.54491i 0.635071 + 0.772454i $$0.280971\pi$$
−0.635071 + 0.772454i $$0.719029\pi$$
$$182$$ −1.73205 9.00000i −0.128388 0.667124i
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ −10.3923 −0.757937
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 6.00000i 0.434145i −0.976156 0.217072i $$-0.930349\pi$$
0.976156 0.217072i $$-0.0696508\pi$$
$$192$$ 0 0
$$193$$ −11.0000 −0.791797 −0.395899 0.918294i $$-0.629567\pi$$
−0.395899 + 0.918294i $$0.629567\pi$$
$$194$$ −4.33013 7.50000i −0.310885 0.538469i
$$195$$ 0 0
$$196$$ −1.00000 + 6.92820i −0.0714286 + 0.494872i
$$197$$ 15.0000i 1.06871i 0.845262 + 0.534353i $$0.179445\pi$$
−0.845262 + 0.534353i $$0.820555\pi$$
$$198$$ 0 0
$$199$$ 1.50000 0.866025i 0.106332 0.0613909i −0.445891 0.895087i $$-0.647113\pi$$
0.552223 + 0.833696i $$0.313780\pi$$
$$200$$ −4.33013 2.50000i −0.306186 0.176777i
$$201$$ 0 0
$$202$$ −4.50000 2.59808i −0.316619 0.182800i
$$203$$ 7.79423 22.5000i 0.547048 1.57919i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 8.66025 + 15.0000i 0.603388 + 1.04510i
$$207$$ 0 0
$$208$$ −3.00000 1.73205i −0.208013 0.120096i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 1.00000 1.73205i 0.0688428 0.119239i −0.829549 0.558433i $$-0.811403\pi$$
0.898392 + 0.439194i $$0.144736\pi$$
$$212$$ −5.19615 + 3.00000i −0.356873 + 0.206041i
$$213$$ 0 0
$$214$$ 6.00000 10.3923i 0.410152 0.710403i
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −3.00000 3.46410i −0.203653 0.235159i
$$218$$ −6.92820 + 4.00000i −0.469237 + 0.270914i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 4.50000 2.59808i 0.301342 0.173980i −0.341703 0.939808i $$-0.611004\pi$$
0.643046 + 0.765828i $$0.277671\pi$$
$$224$$ 1.73205 + 2.00000i 0.115728 + 0.133631i
$$225$$ 0 0
$$226$$ −6.00000 + 10.3923i −0.399114 + 0.691286i
$$227$$ −12.9904 + 22.5000i −0.862202 + 1.49338i 0.00759708 + 0.999971i $$0.497582\pi$$
−0.869799 + 0.493406i $$0.835752\pi$$
$$228$$ 0 0
$$229$$ −6.00000 + 3.46410i −0.396491 + 0.228914i −0.684969 0.728572i $$-0.740184\pi$$
0.288478 + 0.957487i $$0.406851\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −4.50000 7.79423i −0.295439 0.511716i
$$233$$ 15.5885 + 9.00000i 1.02123 + 0.589610i 0.914461 0.404674i $$-0.132615\pi$$
0.106773 + 0.994283i $$0.465948\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −5.19615 −0.338241
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 10.3923 + 6.00000i 0.672222 + 0.388108i 0.796918 0.604087i $$-0.206462\pi$$
−0.124696 + 0.992195i $$0.539796\pi$$
$$240$$ 0 0
$$241$$ 10.5000 + 6.06218i 0.676364 + 0.390499i 0.798484 0.602016i $$-0.205636\pi$$
−0.122119 + 0.992515i $$0.538969\pi$$
$$242$$ 1.73205 1.00000i 0.111340 0.0642824i
$$243$$ 0 0
$$244$$ 13.8564i 0.887066i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ −1.73205 −0.109985
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −25.9808 −1.63989 −0.819946 0.572441i $$-0.805996\pi$$
−0.819946 + 0.572441i $$0.805996\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 8.00000i 0.501965i
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −10.3923 18.0000i −0.648254 1.12281i −0.983540 0.180693i $$-0.942166\pi$$
0.335285 0.942117i $$-0.391167\pi$$
$$258$$ 0 0
$$259$$ −4.00000 20.7846i −0.248548 1.29149i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 13.5000 7.79423i 0.834033 0.481529i
$$263$$ −20.7846 12.0000i −1.28163 0.739952i −0.304487 0.952517i $$-0.598485\pi$$
−0.977147 + 0.212565i $$0.931818\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −2.00000 −0.122169
$$269$$ −7.79423 13.5000i −0.475223 0.823110i 0.524375 0.851488i $$-0.324299\pi$$
−0.999597 + 0.0283781i $$0.990966\pi$$
$$270$$ 0 0
$$271$$ 3.00000 + 1.73205i 0.182237 + 0.105215i 0.588343 0.808611i $$-0.299780\pi$$
−0.406106 + 0.913826i $$0.633114\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 6.00000 10.3923i 0.362473 0.627822i
$$275$$ 12.9904 7.50000i 0.783349 0.452267i
$$276$$ 0 0
$$277$$ −7.00000 + 12.1244i −0.420589 + 0.728482i −0.995997 0.0893846i $$-0.971510\pi$$
0.575408 + 0.817867i $$0.304843\pi$$
$$278$$ 3.46410 6.00000i 0.207763 0.359856i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −5.19615 + 3.00000i −0.309976 + 0.178965i −0.646916 0.762561i $$-0.723942\pi$$
0.336939 + 0.941526i $$0.390608\pi$$
$$282$$ 0 0
$$283$$ 6.92820i 0.411839i 0.978569 + 0.205919i $$0.0660185\pi$$
−0.978569 + 0.205919i $$0.933982\pi$$
$$284$$ 12.0000i 0.712069i
$$285$$ 0 0
$$286$$ 9.00000 5.19615i 0.532181 0.307255i
$$287$$ 5.19615 + 27.0000i 0.306719 + 1.59376i
$$288$$ 0 0
$$289$$ 8.50000 14.7224i 0.500000 0.866025i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ −4.50000 + 2.59808i −0.263343 + 0.152041i
$$293$$ −2.59808 + 4.50000i −0.151781 + 0.262893i −0.931882 0.362761i $$-0.881834\pi$$
0.780101 + 0.625653i $$0.215168\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −6.92820 4.00000i −0.402694 0.232495i
$$297$$ 0 0
$$298$$ −7.50000 12.9904i −0.434463 0.752513i
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −10.0000 3.46410i −0.576390 0.199667i
$$302$$ 19.9186 + 11.5000i 1.14619 + 0.661751i
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 17.3205i 0.988534i −0.869310 0.494267i $$-0.835437\pi$$
0.869310 0.494267i $$-0.164563\pi$$
$$308$$ −7.79423 + 1.50000i −0.444117 + 0.0854704i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −31.1769 −1.76788 −0.883940 0.467600i $$-0.845119\pi$$
−0.883940 + 0.467600i $$0.845119\pi$$
$$312$$ 0 0
$$313$$ 20.7846i 1.17482i 0.809291 + 0.587408i $$0.199852\pi$$
−0.809291 + 0.587408i $$0.800148\pi$$
$$314$$ −10.3923 −0.586472
$$315$$ 0 0
$$316$$ 13.0000 0.731307
$$317$$ 9.00000i 0.505490i −0.967533 0.252745i $$-0.918667\pi$$
0.967533 0.252745i $$-0.0813334\pi$$
$$318$$ 0 0
$$319$$ 27.0000 1.51171
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ −15.0000 + 8.66025i −0.832050 + 0.480384i
$$326$$ 8.66025 + 5.00000i 0.479647 + 0.276924i
$$327$$ 0 0
$$328$$ 9.00000 + 5.19615i 0.496942 + 0.286910i
$$329$$ 20.7846 18.0000i 1.14589 0.992372i
$$330$$ 0 0
$$331$$ 28.0000 1.53902 0.769510 0.638635i $$-0.220501\pi$$
0.769510 + 0.638635i $$0.220501\pi$$
$$332$$ −2.59808 4.50000i −0.142588 0.246970i
$$333$$ 0 0
$$334$$ −9.00000 5.19615i −0.492458 0.284321i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −6.50000 + 11.2583i −0.354078 + 0.613280i −0.986960 0.160968i $$-0.948538\pi$$
0.632882 + 0.774248i $$0.281872\pi$$
$$338$$ 0.866025 0.500000i 0.0471056 0.0271964i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 2.59808 4.50000i 0.140694 0.243689i
$$342$$ 0 0
$$343$$ −10.0000 15.5885i −0.539949 0.841698i
$$344$$ −3.46410 + 2.00000i −0.186772 + 0.107833i
$$345$$ 0 0
$$346$$ 25.9808i 1.39673i
$$347$$ 3.00000i 0.161048i 0.996753 + 0.0805242i $$0.0256594\pi$$
−0.996753 + 0.0805242i $$0.974341\pi$$
$$348$$ 0 0
$$349$$ −24.0000 + 13.8564i −1.28469 + 0.741716i −0.977702 0.209997i $$-0.932655\pi$$
−0.306988 + 0.951713i $$0.599321\pi$$
$$350$$ 12.9904 2.50000i 0.694365 0.133631i
$$351$$ 0 0
$$352$$ −1.50000 + 2.59808i −0.0799503 + 0.138478i
$$353$$ 5.19615 9.00000i 0.276563 0.479022i −0.693965 0.720009i $$-0.744138\pi$$
0.970528 + 0.240987i $$0.0774711\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −5.19615 + 9.00000i −0.275396 + 0.476999i
$$357$$ 0 0
$$358$$ 4.50000 + 7.79423i 0.237832 + 0.411938i
$$359$$ 10.3923 + 6.00000i 0.548485 + 0.316668i 0.748511 0.663123i $$-0.230769\pi$$
−0.200026 + 0.979791i $$0.564103\pi$$
$$360$$ 0 0
$$361$$ −9.50000 16.4545i −0.500000 0.866025i
$$362$$ −20.7846 −1.09241
$$363$$ 0 0
$$364$$ 9.00000 1.73205i 0.471728 0.0907841i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −9.00000 5.19615i −0.469796 0.271237i 0.246358 0.969179i $$-0.420766\pi$$
−0.716154 + 0.697942i $$0.754099\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 5.19615 15.0000i 0.269771 0.778761i
$$372$$ 0 0
$$373$$ 2.00000 + 3.46410i 0.103556 + 0.179364i 0.913147 0.407630i $$-0.133645\pi$$
−0.809591 + 0.586994i $$0.800311\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 10.3923i 0.535942i
$$377$$ −31.1769 −1.60569
$$378$$ 0 0
$$379$$ −26.0000 −1.33553 −0.667765 0.744372i $$-0.732749\pi$$
−0.667765 + 0.744372i $$0.732749\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 6.00000 0.306987
$$383$$ −10.3923 18.0000i −0.531022 0.919757i −0.999345 0.0361995i $$-0.988475\pi$$
0.468323 0.883558i $$-0.344859\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 11.0000i 0.559885i
$$387$$ 0 0
$$388$$ 7.50000 4.33013i 0.380755 0.219829i
$$389$$ 7.79423 + 4.50000i 0.395183 + 0.228159i 0.684403 0.729103i $$-0.260063\pi$$
−0.289220 + 0.957263i $$0.593396\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ −6.92820 1.00000i −0.349927 0.0505076i
$$393$$ 0 0
$$394$$ −15.0000 −0.755689
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 21.0000 + 12.1244i 1.05396 + 0.608504i 0.923755 0.382983i $$-0.125103\pi$$
0.130204 + 0.991487i $$0.458437\pi$$
$$398$$ 0.866025 + 1.50000i 0.0434099 + 0.0751882i
$$399$$ 0 0
$$400$$ 2.50000 4.33013i 0.125000 0.216506i
$$401$$ −25.9808 + 15.0000i −1.29742 + 0.749064i −0.979957 0.199207i $$-0.936163\pi$$
−0.317460 + 0.948272i $$0.602830\pi$$
$$402$$ 0 0
$$403$$ −3.00000 + 5.19615i −0.149441 + 0.258839i
$$404$$ 2.59808 4.50000i 0.129259 0.223883i
$$405$$ 0 0
$$406$$ 22.5000 + 7.79423i 1.11666 + 0.386821i
$$407$$ 20.7846 12.0000i 1.03025 0.594818i
$$408$$ 0 0
$$409$$ 6.92820i 0.342578i 0.985221 + 0.171289i $$0.0547931\pi$$
−0.985221 + 0.171289i $$0.945207\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −15.0000 + 8.66025i −0.738997 + 0.426660i
$$413$$ 10.3923 9.00000i 0.511372 0.442861i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 1.73205 3.00000i 0.0849208 0.147087i
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −15.5885 + 27.0000i −0.761546 + 1.31904i 0.180508 + 0.983574i $$0.442226\pi$$
−0.942053 + 0.335463i $$0.891107\pi$$
$$420$$ 0 0
$$421$$ 5.00000 + 8.66025i 0.243685 + 0.422075i 0.961761 0.273890i $$-0.0883103\pi$$
−0.718076 + 0.695965i $$0.754977\pi$$
$$422$$ 1.73205 + 1.00000i 0.0843149 + 0.0486792i
$$423$$ 0 0
$$424$$ −3.00000 5.19615i −0.145693 0.252347i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 24.0000 + 27.7128i 1.16144 + 1.34112i
$$428$$ 10.3923 + 6.00000i 0.502331 + 0.290021i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 15.5885 9.00000i 0.750870 0.433515i −0.0751385 0.997173i $$-0.523940\pi$$
0.826008 + 0.563658i $$0.190607\pi$$
$$432$$ 0 0
$$433$$ 12.1244i 0.582659i 0.956623 + 0.291330i $$0.0940977\pi$$
−0.956623 + 0.291330i $$0.905902\pi$$
$$434$$ 3.46410 3.00000i 0.166282 0.144005i
$$435$$ 0 0
$$436$$ −4.00000 6.92820i −0.191565 0.331801i
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 15.5885i 0.743996i −0.928233 0.371998i $$-0.878673\pi$$
0.928233 0.371998i $$-0.121327\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 27.0000i 1.28281i 0.767203 + 0.641404i $$0.221648\pi$$
−0.767203 + 0.641404i $$0.778352\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 2.59808 + 4.50000i 0.123022 + 0.213081i
$$447$$ 0 0
$$448$$ −2.00000 + 1.73205i −0.0944911 + 0.0818317i
$$449$$ 30.0000i 1.41579i 0.706319 + 0.707894i $$0.250354\pi$$
−0.706319 + 0.707894i $$0.749646\pi$$
$$450$$ 0 0
$$451$$ −27.0000 + 15.5885i −1.27138 + 0.734032i
$$452$$ −10.3923 6.00000i −0.488813 0.282216i
$$453$$ 0 0
$$454$$ −22.5000 12.9904i −1.05598 0.609669i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 22.0000 1.02912 0.514558 0.857455i $$-0.327956\pi$$
0.514558 + 0.857455i $$0.327956\pi$$
$$458$$ −3.46410 6.00000i −0.161867 0.280362i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 7.79423 + 13.5000i 0.363013 + 0.628758i 0.988455 0.151513i $$-0.0484146\pi$$
−0.625442 + 0.780271i $$0.715081\pi$$
$$462$$ 0 0
$$463$$ −2.50000 + 4.33013i −0.116185 + 0.201238i −0.918253 0.395995i $$-0.870400\pi$$
0.802068 + 0.597233i $$0.203733\pi$$
$$464$$ 7.79423 4.50000i 0.361838 0.208907i
$$465$$ 0 0
$$466$$ −9.00000 + 15.5885i −0.416917 + 0.722121i
$$467$$ −2.59808 + 4.50000i −0.120225 + 0.208235i −0.919856 0.392256i $$-0.871695\pi$$
0.799632 + 0.600491i $$0.205028\pi$$
$$468$$ 0 0
$$469$$ 4.00000 3.46410i 0.184703 0.159957i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 5.19615i 0.239172i
$$473$$ 12.0000i 0.551761i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −6.00000 + 10.3923i −0.274434 + 0.475333i
$$479$$ 5.19615 9.00000i 0.237418 0.411220i −0.722554 0.691314i $$-0.757032\pi$$
0.959973 + 0.280094i $$0.0903655\pi$$
$$480$$ 0 0
$$481$$ −24.0000 + 13.8564i −1.09431 + 0.631798i
$$482$$ −6.06218 + 10.5000i −0.276125 + 0.478262i
$$483$$ 0 0
$$484$$ 1.00000 + 1.73205i 0.0454545 + 0.0787296i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 5.50000 + 9.52628i 0.249229 + 0.431677i 0.963312 0.268384i $$-0.0864896\pi$$
−0.714083 + 0.700061i $$0.753156\pi$$
$$488$$ 13.8564 0.627250
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 31.1769 + 18.0000i 1.40699 + 0.812329i 0.995097 0.0989017i $$-0.0315329\pi$$
0.411897 + 0.911230i $$0.364866\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 1.73205i 0.0777714i
$$497$$ 20.7846 + 24.0000i 0.932317 + 1.07655i
$$498$$ 0 0
$$499$$ −8.00000 13.8564i −0.358129 0.620298i 0.629519 0.776985i $$-0.283252\pi$$
−0.987648 + 0.156687i $$0.949919\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 25.9808i 1.15958i
$$503$$ 31.1769 1.39011 0.695055 0.718957i $$-0.255380\pi$$
0.695055 + 0.718957i $$0.255380\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ −8.00000 −0.354943
$$509$$ 2.59808 + 4.50000i 0.115158 + 0.199459i 0.917843 0.396944i $$-0.129929\pi$$
−0.802685 + 0.596403i $$0.796596\pi$$
$$510$$ 0 0
$$511$$ 4.50000 12.9904i 0.199068 0.574661i
$$512$$ 1.00000i 0.0441942i
$$513$$ 0 0
$$514$$ 18.0000 10.3923i 0.793946 0.458385i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 27.0000 + 15.5885i 1.18746 + 0.685580i
$$518$$ 20.7846 4.00000i 0.913223 0.175750i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −10.3923 18.0000i −0.455295 0.788594i 0.543410 0.839467i $$-0.317133\pi$$
−0.998705 + 0.0508731i $$0.983800\pi$$
$$522$$ 0 0
$$523$$ 33.0000 + 19.0526i 1.44299 + 0.833110i 0.998048 0.0624496i $$-0.0198913\pi$$
0.444941 + 0.895560i $$0.353225\pi$$
$$524$$ 7.79423 + 13.5000i 0.340492 + 0.589750i
$$525$$ 0 0
$$526$$ 12.0000 20.7846i 0.523225 0.906252i
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −11.5000 + 19.9186i −0.500000 + 0.866025i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 31.1769 18.0000i 1.35042 0.779667i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 2.00000i 0.0863868i
$$537$$ 0 0
$$538$$ 13.5000 7.79423i 0.582026 0.336033i
$$539$$ 12.9904 16.5000i 0.559535 0.710705i
$$540$$ 0 0
$$541$$ −19.0000 + 32.9090i −0.816874 + 1.41487i 0.0911008 + 0.995842i $$0.470961\pi$$
−0.907975 + 0.419025i $$0.862372\pi$$
$$542$$ −1.73205 + 3.00000i −0.0743980 + 0.128861i
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −7.00000 12.1244i −0.299298 0.518400i 0.676677 0.736280i $$-0.263419\pi$$
−0.975976 + 0.217880i $$0.930086\pi$$
$$548$$ 10.3923 + 6.00000i 0.443937 + 0.256307i
$$549$$ 0 0
$$550$$ 7.50000 + 12.9904i 0.319801 + 0.553912i
$$551$$ 0 0
$$552$$ 0 0
$$553$$ −26.0000 + 22.5167i −1.10563 + 0.957506i
$$554$$ −12.1244 7.00000i −0.515115 0.297402i
$$555$$ 0 0
$$556$$ 6.00000 + 3.46410i 0.254457 + 0.146911i
$$557$$ −18.1865 + 10.5000i −0.770588 + 0.444899i −0.833084 0.553146i $$-0.813427\pi$$
0.0624962 + 0.998045i $$0.480094\pi$$
$$558$$ 0 0
$$559$$ 13.8564i 0.586064i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −3.00000 5.19615i −0.126547 0.219186i
$$563$$ 31.1769 1.31395 0.656975 0.753912i $$-0.271836\pi$$
0.656975 + 0.753912i $$0.271836\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ −6.92820 −0.291214
$$567$$ 0 0
$$568$$ 12.0000 0.503509
$$569$$ 12.0000i 0.503066i −0.967849 0.251533i $$-0.919065\pi$$
0.967849 0.251533i $$-0.0809347\pi$$
$$570$$ 0 0
$$571$$ −4.00000 −0.167395 −0.0836974 0.996491i $$-0.526673\pi$$
−0.0836974 + 0.996491i $$0.526673\pi$$
$$572$$ 5.19615 + 9.00000i 0.217262 + 0.376309i
$$573$$ 0 0
$$574$$ −27.0000 + 5.19615i −1.12696 + 0.216883i
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −7.50000 + 4.33013i −0.312229 + 0.180266i −0.647924 0.761705i $$-0.724362\pi$$
0.335694 + 0.941971i $$0.391029\pi$$
$$578$$ 14.7224 + 8.50000i 0.612372 + 0.353553i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 12.9904 + 4.50000i 0.538932 + 0.186691i
$$582$$ 0 0
$$583$$ 18.0000 0.745484
$$584$$ −2.59808 4.50000i −0.107509 0.186211i
$$585$$ 0 0
$$586$$ −4.50000 2.59808i −0.185893 0.107326i
$$587$$ 5.19615 + 9.00000i 0.214468 + 0.371470i 0.953108 0.302631i $$-0.0978648\pi$$
−0.738640 + 0.674100i $$0.764532\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 4.00000 6.92820i 0.164399 0.284747i
$$593$$ 10.3923 18.0000i 0.426761 0.739171i −0.569822 0.821768i $$-0.692988\pi$$
0.996583 + 0.0825966i $$0.0263213\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 12.9904 7.50000i 0.532107 0.307212i
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 30.0000i 1.22577i 0.790173 + 0.612883i $$0.209990\pi$$
−0.790173 + 0.612883i $$0.790010\pi$$
$$600$$ 0 0
$$601$$ 30.0000 17.3205i 1.22373 0.706518i 0.258015 0.966141i $$-0.416931\pi$$
0.965710 + 0.259623i $$0.0835982\pi$$
$$602$$ 3.46410 10.0000i 0.141186 0.407570i
$$603$$ 0 0
$$604$$ −11.5000 + 19.9186i −0.467928 + 0.810476i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 4.50000 2.59808i 0.182649 0.105453i −0.405887 0.913923i $$-0.633038\pi$$
0.588537 + 0.808470i $$0.299704\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −31.1769 18.0000i −1.26128 0.728202i
$$612$$ 0 0
$$613$$ 5.00000 + 8.66025i 0.201948 + 0.349784i 0.949156 0.314806i $$-0.101939\pi$$
−0.747208 + 0.664590i $$0.768606\pi$$
$$614$$ 17.3205 0.698999
$$615$$ 0 0
$$616$$ −1.50000 7.79423i −0.0604367 0.314038i
$$617$$ 15.5885 + 9.00000i 0.627568 + 0.362326i 0.779809 0.626017i $$-0.215316\pi$$
−0.152242 + 0.988343i $$0.548649\pi$$
$$618$$ 0 0
$$619$$ −30.0000 17.3205i −1.20580 0.696170i −0.243962 0.969785i $$-0.578447\pi$$
−0.961839 + 0.273615i $$0.911781\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 31.1769i 1.25008i
$$623$$ −5.19615 27.0000i −0.208179 1.08173i
$$624$$ 0 0
$$625$$ −12.5000 21.6506i −0.500000 0.866025i
$$626$$ −20.7846 −0.830720
$$627$$ 0 0
$$628$$ 10.3923i 0.414698i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −37.0000 −1.47295 −0.736473 0.676467i $$-0.763510\pi$$
−0.736473 + 0.676467i $$0.763510\pi$$
$$632$$ 13.0000i 0.517112i
$$633$$ 0 0
$$634$$ 9.00000 0.357436
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −15.0000 + 19.0526i −0.594322 + 0.754890i
$$638$$ 27.0000i 1.06894i
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 36.3731 + 21.0000i 1.43665 + 0.829450i 0.997615 0.0690201i $$-0.0219873\pi$$
0.439034 + 0.898470i $$0.355321\pi$$
$$642$$ 0 0
$$643$$ 3.00000 + 1.73205i 0.118308 + 0.0683054i 0.557986 0.829850i $$-0.311574\pi$$
−0.439678 + 0.898155i $$0.644907\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −5.19615 9.00000i −0.204282 0.353827i 0.745622 0.666369i $$-0.232153\pi$$
−0.949904 + 0.312543i $$0.898819\pi$$
$$648$$ 0 0
$$649$$ 13.5000 + 7.79423i 0.529921 + 0.305950i
$$650$$ −8.66025 15.0000i −0.339683 0.588348i
$$651$$ 0 0
$$652$$ −5.00000 + 8.66025i −0.195815 + 0.339162i
$$653$$ 25.9808 15.0000i 1.01671 0.586995i 0.103558 0.994623i $$-0.466977\pi$$
0.913148 + 0.407628i $$0.133644\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −5.19615 + 9.00000i −0.202876 + 0.351391i
$$657$$ 0 0
$$658$$ 18.0000 + 20.7846i 0.701713 + 0.810268i
$$659$$ −12.9904 + 7.50000i −0.506033 + 0.292159i −0.731202 0.682161i $$-0.761040\pi$$
0.225168 + 0.974320i $$0.427707\pi$$
$$660$$ 0 0
$$661$$ 10.3923i 0.404214i 0.979363 + 0.202107i $$0.0647788\pi$$
−0.979363 + 0.202107i $$0.935221\pi$$
$$662$$ 28.0000i 1.08825i
$$663$$ 0 0
$$664$$ 4.50000 2.59808i 0.174634 0.100825i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 5.19615 9.00000i 0.201045 0.348220i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −20.7846 + 36.0000i −0.802381 + 1.38976i
$$672$$ 0 0
$$673$$ 13.0000 + 22.5167i 0.501113 + 0.867953i 0.999999 + 0.00128586i $$0.000409302\pi$$
−0.498886 + 0.866668i $$0.666257\pi$$
$$674$$ −11.2583 6.50000i −0.433655 0.250371i
$$675$$ 0 0
$$676$$ 0.500000 + 0.866025i 0.0192308 + 0.0333087i
$$677$$ 15.5885 0.599113 0.299557 0.954079i $$-0.403161\pi$$
0.299557 + 0.954079i $$0.403161\pi$$
$$678$$ 0 0
$$679$$ −7.50000 + 21.6506i −0.287824 + 0.830875i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 4.50000 + 2.59808i 0.172314 + 0.0994855i
$$683$$ 18.1865 10.5000i 0.695888 0.401771i −0.109926 0.993940i $$-0.535061\pi$$
0.805814 + 0.592168i $$0.201728\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 15.5885 10.0000i 0.595170 0.381802i
$$687$$ 0 0
$$688$$ −2.00000 3.46410i −0.0762493 0.132068i
$$689$$ −20.7846 −0.791831
$$690$$ 0 0
$$691$$ 13.8564i 0.527123i −0.964643 0.263561i $$-0.915103\pi$$
0.964643 0.263561i $$-0.0848971\pi$$
$$692$$ 25.9808 0.987640
$$693$$ 0 0
$$694$$ −3.00000 −0.113878
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ −13.8564 24.0000i −0.524473 0.908413i
$$699$$ 0 0
$$700$$ 2.50000 + 12.9904i 0.0944911 + 0.490990i
$$701$$ 6.00000i 0.226617i −0.993560 0.113308i $$-0.963855\pi$$
0.993560 0.113308i $$-0.0361448\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ −2.59808 1.50000i −0.0979187 0.0565334i
$$705$$ 0 0
$$706$$ 9.00000 + 5.19615i 0.338719 + 0.195560i
$$707$$ 2.59808 + 13.5000i 0.0977107 + 0.507720i
$$708$$ 0 0
$$709$$ 4.00000 0.150223 0.0751116 0.997175i $$-0.476069\pi$$
0.0751116 + 0.997175i $$0.476069\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −9.00000 5.19615i −0.337289 0.194734i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −7.79423 + 4.50000i −0.291284 + 0.168173i
$$717$$ 0 0
$$718$$ −6.00000 + 10.3923i −0.223918 + 0.387837i
$$719$$ 5.19615 9.00000i 0.193784 0.335643i −0.752717 0.658344i $$-0.771257\pi$$
0.946501 + 0.322700i $$0.104591\pi$$
$$720$$ 0 0
$$721$$ 15.0000 43.3013i 0.558629 1.61262i
$$722$$ 16.4545 9.50000i 0.612372 0.353553i
$$723$$ 0 0
$$724$$ 20.7846i 0.772454i
$$725$$ 45.0000i 1.67126i
$$726$$ 0 0
$$727$$ −21.0000 + 12.1244i −0.778847 + 0.449667i −0.836021 0.548697i $$-0.815124\pi$$
0.0571746 + 0.998364i $$0.481791\pi$$
$$728$$ 1.73205 + 9.00000i 0.0641941 + 0.333562i
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −12.0000 + 6.92820i −0.443230 + 0.255899i −0.704967 0.709240i $$-0.749038\pi$$
0.261737 + 0.965139i $$0.415705\pi$$
$$734$$ 5.19615 9.00000i 0.191793 0.332196i
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 5.19615 + 3.00000i 0.191403 + 0.110506i
$$738$$ 0 0
$$739$$ −13.0000 22.5167i −0.478213 0.828289i 0.521475 0.853266i $$-0.325382\pi$$
−0.999688 + 0.0249776i $$0.992049\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 15.0000 + 5.19615i 0.550667 + 0.190757i
$$743$$ 5.19615 + 3.00000i 0.190628 + 0.110059i 0.592277 0.805735i $$-0.298229\pi$$
−0.401648 + 0.915794i $$0.631563\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −3.46410 + 2.00000i −0.126830 + 0.0732252i
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −31.1769 + 6.00000i −1.13918 + 0.219235i
$$750$$ 0 0
$$751$$ −2.00000 3.46410i −0.0729810 0.126407i 0.827225 0.561870i $$-0.189918\pi$$
−0.900207 + 0.435463i $$0.856585\pi$$
$$752$$ 10.3923 0.378968
$$753$$ 0 0
$$754$$ 31.1769i 1.13540i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 10.0000 0.363456 0.181728 0.983349i $$-0.441831\pi$$
0.181728 + 0.983349i $$0.441831\pi$$
$$758$$ 26.0000i 0.944363i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 20.7846 + 36.0000i 0.753442 + 1.30500i 0.946145 + 0.323742i $$0.104941\pi$$
−0.192704 + 0.981257i $$0.561726\pi$$
$$762$$ 0 0
$$763$$ 20.0000 + 6.92820i 0.724049 + 0.250818i
$$764$$ 6.00000i 0.217072i
$$765$$ 0 0
$$766$$ 18.0000 10.3923i 0.650366 0.375489i
$$767$$ −15.5885 9.00000i −0.562867 0.324971i
$$768$$ 0 0
$$769$$ 13.5000 + 7.79423i 0.486822 + 0.281067i 0.723255 0.690581i $$-0.242645\pi$$
−0.236433 + 0.971648i $$0.575978\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 11.0000 0.395899
$$773$$ 20.7846 + 36.0000i 0.747570 + 1.29483i 0.948984 + 0.315324i $$0.102113\pi$$
−0.201414 + 0.979506i $$0.564554\pi$$
$$774$$ 0 0
$$775$$ −7.50000 4.33013i −0.269408 0.155543i
$$776$$ 4.33013 + 7.50000i 0.155443 + 0.269234i
$$777$$ 0 0
$$778$$ −4.50000 + 7.79423i −0.161333 + 0.279437i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −18.0000 + 31.1769i −0.644091 + 1.11560i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 1.00000 6.92820i 0.0357143 0.247436i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 24.2487i 0.864373i −0.901784 0.432187i $$-0.857742\pi$$
0.901784 0.432187i $$-0.142258\pi$$
$$788$$ 15.0000i 0.534353i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 31.1769 6.00000i 1.10852 0.213335i
$$792$$ 0 0
$$793$$ 24.0000 41.5692i 0.852265 1.47617i
$$794$$ −12.1244 + 21.0000i −0.430277 + 0.745262i
$$795$$ 0 0
$$796$$ −1.50000 + 0.866025i −0.0531661 + 0.0306955i