# Properties

 Label 567.2.i.c.215.2 Level $567$ Weight $2$ Character 567.215 Analytic conductor $4.528$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$567 = 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 567.i (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.52751779461$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{-5})$$ Defining polynomial: $$x^{4} - 5 x^{2} + 25$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 189) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 215.2 Root $$1.93649 + 1.11803i$$ of defining polynomial Character $$\chi$$ $$=$$ 567.215 Dual form 567.2.i.c.269.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+2.23607i q^{2} -3.00000 q^{4} +(2.50000 + 0.866025i) q^{7} -2.23607i q^{8} +O(q^{10})$$ $$q+2.23607i q^{2} -3.00000 q^{4} +(2.50000 + 0.866025i) q^{7} -2.23607i q^{8} +(3.87298 + 2.23607i) q^{11} +(-1.50000 - 0.866025i) q^{13} +(-1.93649 + 5.59017i) q^{14} -1.00000 q^{16} +(3.87298 + 6.70820i) q^{17} +(-3.00000 - 1.73205i) q^{19} +(-5.00000 + 8.66025i) q^{22} +(-3.87298 + 2.23607i) q^{23} +(2.50000 - 4.33013i) q^{25} +(1.93649 - 3.35410i) q^{26} +(-7.50000 - 2.59808i) q^{28} +(-3.87298 + 2.23607i) q^{29} -1.73205i q^{31} -6.70820i q^{32} +(-15.0000 + 8.66025i) q^{34} +(-2.50000 + 4.33013i) q^{37} +(3.87298 - 6.70820i) q^{38} +(3.87298 - 6.70820i) q^{41} +(3.50000 + 6.06218i) q^{43} +(-11.6190 - 6.70820i) q^{44} +(-5.00000 - 8.66025i) q^{46} -7.74597 q^{47} +(5.50000 + 4.33013i) q^{49} +(9.68246 + 5.59017i) q^{50} +(4.50000 + 2.59808i) q^{52} +(-3.87298 + 2.23607i) q^{53} +(1.93649 - 5.59017i) q^{56} +(-5.00000 - 8.66025i) q^{58} +7.74597 q^{59} -8.66025i q^{61} +3.87298 q^{62} +13.0000 q^{64} -1.00000 q^{67} +(-11.6190 - 20.1246i) q^{68} +8.94427i q^{71} +(6.00000 - 3.46410i) q^{73} +(-9.68246 - 5.59017i) q^{74} +(9.00000 + 5.19615i) q^{76} +(7.74597 + 8.94427i) q^{77} +11.0000 q^{79} +(15.0000 + 8.66025i) q^{82} +(-3.87298 - 6.70820i) q^{83} +(-13.5554 + 7.82624i) q^{86} +(5.00000 - 8.66025i) q^{88} +(7.74597 - 13.4164i) q^{89} +(-3.00000 - 3.46410i) q^{91} +(11.6190 - 6.70820i) q^{92} -17.3205i q^{94} +(-1.50000 + 0.866025i) q^{97} +(-9.68246 + 12.2984i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 12q^{4} + 10q^{7} + O(q^{10})$$ $$4q - 12q^{4} + 10q^{7} - 6q^{13} - 4q^{16} - 12q^{19} - 20q^{22} + 10q^{25} - 30q^{28} - 60q^{34} - 10q^{37} + 14q^{43} - 20q^{46} + 22q^{49} + 18q^{52} - 20q^{58} + 52q^{64} - 4q^{67} + 24q^{73} + 36q^{76} + 44q^{79} + 60q^{82} + 20q^{88} - 12q^{91} - 6q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$$.

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

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.23607i 1.58114i 0.612372 + 0.790569i $$0.290215\pi$$
−0.612372 + 0.790569i $$0.709785\pi$$
$$3$$ 0 0
$$4$$ −3.00000 −1.50000
$$5$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$6$$ 0 0
$$7$$ 2.50000 + 0.866025i 0.944911 + 0.327327i
$$8$$ 2.23607i 0.790569i
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 3.87298 + 2.23607i 1.16775 + 0.674200i 0.953149 0.302502i $$-0.0978220\pi$$
0.214600 + 0.976702i $$0.431155\pi$$
$$12$$ 0 0
$$13$$ −1.50000 0.866025i −0.416025 0.240192i 0.277350 0.960769i $$-0.410544\pi$$
−0.693375 + 0.720577i $$0.743877\pi$$
$$14$$ −1.93649 + 5.59017i −0.517549 + 1.49404i
$$15$$ 0 0
$$16$$ −1.00000 −0.250000
$$17$$ 3.87298 + 6.70820i 0.939336 + 1.62698i 0.766712 + 0.641991i $$0.221891\pi$$
0.172624 + 0.984988i $$0.444775\pi$$
$$18$$ 0 0
$$19$$ −3.00000 1.73205i −0.688247 0.397360i 0.114708 0.993399i $$-0.463407\pi$$
−0.802955 + 0.596040i $$0.796740\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −5.00000 + 8.66025i −1.06600 + 1.84637i
$$23$$ −3.87298 + 2.23607i −0.807573 + 0.466252i −0.846112 0.533005i $$-0.821063\pi$$
0.0385394 + 0.999257i $$0.487729\pi$$
$$24$$ 0 0
$$25$$ 2.50000 4.33013i 0.500000 0.866025i
$$26$$ 1.93649 3.35410i 0.379777 0.657794i
$$27$$ 0 0
$$28$$ −7.50000 2.59808i −1.41737 0.490990i
$$29$$ −3.87298 + 2.23607i −0.719195 + 0.415227i −0.814456 0.580225i $$-0.802965\pi$$
0.0952614 + 0.995452i $$0.469631\pi$$
$$30$$ 0 0
$$31$$ 1.73205i 0.311086i −0.987829 0.155543i $$-0.950287\pi$$
0.987829 0.155543i $$-0.0497126\pi$$
$$32$$ 6.70820i 1.18585i
$$33$$ 0 0
$$34$$ −15.0000 + 8.66025i −2.57248 + 1.48522i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −2.50000 + 4.33013i −0.410997 + 0.711868i −0.994999 0.0998840i $$-0.968153\pi$$
0.584002 + 0.811752i $$0.301486\pi$$
$$38$$ 3.87298 6.70820i 0.628281 1.08821i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 3.87298 6.70820i 0.604858 1.04765i −0.387215 0.921989i $$-0.626563\pi$$
0.992074 0.125656i $$-0.0401036\pi$$
$$42$$ 0 0
$$43$$ 3.50000 + 6.06218i 0.533745 + 0.924473i 0.999223 + 0.0394140i $$0.0125491\pi$$
−0.465478 + 0.885059i $$0.654118\pi$$
$$44$$ −11.6190 6.70820i −1.75162 1.01130i
$$45$$ 0 0
$$46$$ −5.00000 8.66025i −0.737210 1.27688i
$$47$$ −7.74597 −1.12987 −0.564933 0.825137i $$-0.691098\pi$$
−0.564933 + 0.825137i $$0.691098\pi$$
$$48$$ 0 0
$$49$$ 5.50000 + 4.33013i 0.785714 + 0.618590i
$$50$$ 9.68246 + 5.59017i 1.36931 + 0.790569i
$$51$$ 0 0
$$52$$ 4.50000 + 2.59808i 0.624038 + 0.360288i
$$53$$ −3.87298 + 2.23607i −0.531995 + 0.307148i −0.741829 0.670590i $$-0.766041\pi$$
0.209833 + 0.977737i $$0.432708\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 1.93649 5.59017i 0.258775 0.747018i
$$57$$ 0 0
$$58$$ −5.00000 8.66025i −0.656532 1.13715i
$$59$$ 7.74597 1.00844 0.504219 0.863576i $$-0.331780\pi$$
0.504219 + 0.863576i $$0.331780\pi$$
$$60$$ 0 0
$$61$$ 8.66025i 1.10883i −0.832240 0.554416i $$-0.812942\pi$$
0.832240 0.554416i $$-0.187058\pi$$
$$62$$ 3.87298 0.491869
$$63$$ 0 0
$$64$$ 13.0000 1.62500
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −1.00000 −0.122169 −0.0610847 0.998133i $$-0.519456\pi$$
−0.0610847 + 0.998133i $$0.519456\pi$$
$$68$$ −11.6190 20.1246i −1.40900 2.44047i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 8.94427i 1.06149i 0.847532 + 0.530745i $$0.178088\pi$$
−0.847532 + 0.530745i $$0.821912\pi$$
$$72$$ 0 0
$$73$$ 6.00000 3.46410i 0.702247 0.405442i −0.105937 0.994373i $$-0.533784\pi$$
0.808184 + 0.588930i $$0.200451\pi$$
$$74$$ −9.68246 5.59017i −1.12556 0.649844i
$$75$$ 0 0
$$76$$ 9.00000 + 5.19615i 1.03237 + 0.596040i
$$77$$ 7.74597 + 8.94427i 0.882735 + 1.01929i
$$78$$ 0 0
$$79$$ 11.0000 1.23760 0.618798 0.785550i $$-0.287620\pi$$
0.618798 + 0.785550i $$0.287620\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 15.0000 + 8.66025i 1.65647 + 0.956365i
$$83$$ −3.87298 6.70820i −0.425115 0.736321i 0.571316 0.820730i $$-0.306433\pi$$
−0.996431 + 0.0844091i $$0.973100\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −13.5554 + 7.82624i −1.46172 + 0.843925i
$$87$$ 0 0
$$88$$ 5.00000 8.66025i 0.533002 0.923186i
$$89$$ 7.74597 13.4164i 0.821071 1.42214i −0.0838147 0.996481i $$-0.526710\pi$$
0.904886 0.425655i $$-0.139956\pi$$
$$90$$ 0 0
$$91$$ −3.00000 3.46410i −0.314485 0.363137i
$$92$$ 11.6190 6.70820i 1.21136 0.699379i
$$93$$ 0 0
$$94$$ 17.3205i 1.78647i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −1.50000 + 0.866025i −0.152302 + 0.0879316i −0.574214 0.818705i $$-0.694692\pi$$
0.421912 + 0.906637i $$0.361359\pi$$
$$98$$ −9.68246 + 12.2984i −0.978076 + 1.24232i
$$99$$ 0 0
$$100$$ −7.50000 + 12.9904i −0.750000 + 1.29904i
$$101$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$102$$ 0 0
$$103$$ 4.50000 2.59808i 0.443398 0.255996i −0.261640 0.965166i $$-0.584263\pi$$
0.705038 + 0.709170i $$0.250930\pi$$
$$104$$ −1.93649 + 3.35410i −0.189889 + 0.328897i
$$105$$ 0 0
$$106$$ −5.00000 8.66025i −0.485643 0.841158i
$$107$$ 3.87298 + 2.23607i 0.374415 + 0.216169i 0.675386 0.737465i $$-0.263977\pi$$
−0.300970 + 0.953634i $$0.597310\pi$$
$$108$$ 0 0
$$109$$ 0.500000 + 0.866025i 0.0478913 + 0.0829502i 0.888977 0.457951i $$-0.151417\pi$$
−0.841086 + 0.540901i $$0.818083\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −2.50000 0.866025i −0.236228 0.0818317i
$$113$$ −7.74597 4.47214i −0.728679 0.420703i 0.0892596 0.996008i $$-0.471550\pi$$
−0.817939 + 0.575305i $$0.804883\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 11.6190 6.70820i 1.07879 0.622841i
$$117$$ 0 0
$$118$$ 17.3205i 1.59448i
$$119$$ 3.87298 + 20.1246i 0.355036 + 1.84482i
$$120$$ 0 0
$$121$$ 4.50000 + 7.79423i 0.409091 + 0.708566i
$$122$$ 19.3649 1.75322
$$123$$ 0 0
$$124$$ 5.19615i 0.466628i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −1.00000 −0.0887357 −0.0443678 0.999015i $$-0.514127\pi$$
−0.0443678 + 0.999015i $$0.514127\pi$$
$$128$$ 15.6525i 1.38350i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$132$$ 0 0
$$133$$ −6.00000 6.92820i −0.520266 0.600751i
$$134$$ 2.23607i 0.193167i
$$135$$ 0 0
$$136$$ 15.0000 8.66025i 1.28624 0.742611i
$$137$$ 3.87298 + 2.23607i 0.330891 + 0.191040i 0.656237 0.754555i $$-0.272147\pi$$
−0.325345 + 0.945595i $$0.605481\pi$$
$$138$$ 0 0
$$139$$ 7.50000 + 4.33013i 0.636142 + 0.367277i 0.783127 0.621862i $$-0.213624\pi$$
−0.146985 + 0.989139i $$0.546957\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −20.0000 −1.67836
$$143$$ −3.87298 6.70820i −0.323875 0.560968i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 7.74597 + 13.4164i 0.641061 + 1.11035i
$$147$$ 0 0
$$148$$ 7.50000 12.9904i 0.616496 1.06780i
$$149$$ −15.4919 + 8.94427i −1.26915 + 0.732743i −0.974827 0.222963i $$-0.928427\pi$$
−0.294322 + 0.955706i $$0.595094\pi$$
$$150$$ 0 0
$$151$$ 6.50000 11.2583i 0.528962 0.916190i −0.470467 0.882418i $$-0.655915\pi$$
0.999430 0.0337724i $$-0.0107521\pi$$
$$152$$ −3.87298 + 6.70820i −0.314140 + 0.544107i
$$153$$ 0 0
$$154$$ −20.0000 + 17.3205i −1.61165 + 1.39573i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 13.8564i 1.10586i 0.833227 + 0.552931i $$0.186491\pi$$
−0.833227 + 0.552931i $$0.813509\pi$$
$$158$$ 24.5967i 1.95681i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −11.6190 + 2.23607i −0.915702 + 0.176227i
$$162$$ 0 0
$$163$$ 6.50000 11.2583i 0.509119 0.881820i −0.490825 0.871258i $$-0.663305\pi$$
0.999944 0.0105623i $$-0.00336213\pi$$
$$164$$ −11.6190 + 20.1246i −0.907288 + 1.57147i
$$165$$ 0 0
$$166$$ 15.0000 8.66025i 1.16423 0.672166i
$$167$$ 3.87298 6.70820i 0.299700 0.519096i −0.676367 0.736565i $$-0.736447\pi$$
0.976067 + 0.217468i $$0.0697799\pi$$
$$168$$ 0 0
$$169$$ −5.00000 8.66025i −0.384615 0.666173i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −10.5000 18.1865i −0.800617 1.38671i
$$173$$ 15.4919 1.17783 0.588915 0.808195i $$-0.299555\pi$$
0.588915 + 0.808195i $$0.299555\pi$$
$$174$$ 0 0
$$175$$ 10.0000 8.66025i 0.755929 0.654654i
$$176$$ −3.87298 2.23607i −0.291937 0.168550i
$$177$$ 0 0
$$178$$ 30.0000 + 17.3205i 2.24860 + 1.29823i
$$179$$ 7.74597 4.47214i 0.578961 0.334263i −0.181760 0.983343i $$-0.558179\pi$$
0.760720 + 0.649080i $$0.224846\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 7.74597 6.70820i 0.574169 0.497245i
$$183$$ 0 0
$$184$$ 5.00000 + 8.66025i 0.368605 + 0.638442i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 34.6410i 2.53320i
$$188$$ 23.2379 1.69480
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 17.8885i 1.29437i −0.762333 0.647185i $$-0.775946\pi$$
0.762333 0.647185i $$-0.224054\pi$$
$$192$$ 0 0
$$193$$ −7.00000 −0.503871 −0.251936 0.967744i $$-0.581067\pi$$
−0.251936 + 0.967744i $$0.581067\pi$$
$$194$$ −1.93649 3.35410i −0.139032 0.240810i
$$195$$ 0 0
$$196$$ −16.5000 12.9904i −1.17857 0.927884i
$$197$$ 8.94427i 0.637253i 0.947880 + 0.318626i $$0.103222\pi$$
−0.947880 + 0.318626i $$0.896778\pi$$
$$198$$ 0 0
$$199$$ 19.5000 11.2583i 1.38232 0.798082i 0.389885 0.920864i $$-0.372515\pi$$
0.992434 + 0.122782i $$0.0391815\pi$$
$$200$$ −9.68246 5.59017i −0.684653 0.395285i
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −11.6190 + 2.23607i −0.815490 + 0.156941i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 5.80948 + 10.0623i 0.404765 + 0.701074i
$$207$$ 0 0
$$208$$ 1.50000 + 0.866025i 0.104006 + 0.0600481i
$$209$$ −7.74597 13.4164i −0.535800 0.928032i
$$210$$ 0 0
$$211$$ 9.50000 16.4545i 0.654007 1.13277i −0.328135 0.944631i $$-0.606420\pi$$
0.982142 0.188142i $$-0.0602466\pi$$
$$212$$ 11.6190 6.70820i 0.797993 0.460721i
$$213$$ 0 0
$$214$$ −5.00000 + 8.66025i −0.341793 + 0.592003i
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 1.50000 4.33013i 0.101827 0.293948i
$$218$$ −1.93649 + 1.11803i −0.131156 + 0.0757228i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 13.4164i 0.902485i
$$222$$ 0 0
$$223$$ 21.0000 12.1244i 1.40626 0.811907i 0.411239 0.911528i $$-0.365096\pi$$
0.995025 + 0.0996209i $$0.0317630\pi$$
$$224$$ 5.80948 16.7705i 0.388162 1.12053i
$$225$$ 0 0
$$226$$ 10.0000 17.3205i 0.665190 1.15214i
$$227$$ 11.6190 20.1246i 0.771177 1.33572i −0.165742 0.986169i $$-0.553002\pi$$
0.936918 0.349548i $$-0.113665\pi$$
$$228$$ 0 0
$$229$$ −22.5000 + 12.9904i −1.48684 + 0.858429i −0.999888 0.0149989i $$-0.995226\pi$$
−0.486954 + 0.873427i $$0.661892\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 5.00000 + 8.66025i 0.328266 + 0.568574i
$$233$$ −7.74597 4.47214i −0.507455 0.292979i 0.224332 0.974513i $$-0.427980\pi$$
−0.731787 + 0.681533i $$0.761313\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −23.2379 −1.51266
$$237$$ 0 0
$$238$$ −45.0000 + 8.66025i −2.91692 + 0.561361i
$$239$$ −7.74597 4.47214i −0.501045 0.289278i 0.228100 0.973638i $$-0.426749\pi$$
−0.729145 + 0.684359i $$0.760082\pi$$
$$240$$ 0 0
$$241$$ −13.5000 7.79423i −0.869611 0.502070i −0.00239235 0.999997i $$-0.500762\pi$$
−0.867219 + 0.497927i $$0.834095\pi$$
$$242$$ −17.4284 + 10.0623i −1.12034 + 0.646830i
$$243$$ 0 0
$$244$$ 25.9808i 1.66325i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 3.00000 + 5.19615i 0.190885 + 0.330623i
$$248$$ −3.87298 −0.245935
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −23.2379 −1.46676 −0.733382 0.679817i $$-0.762059\pi$$
−0.733382 + 0.679817i $$0.762059\pi$$
$$252$$ 0 0
$$253$$ −20.0000 −1.25739
$$254$$ 2.23607i 0.140303i
$$255$$ 0 0
$$256$$ −9.00000 −0.562500
$$257$$ 11.6190 + 20.1246i 0.724770 + 1.25534i 0.959069 + 0.283174i $$0.0913874\pi$$
−0.234298 + 0.972165i $$0.575279\pi$$
$$258$$ 0 0
$$259$$ −10.0000 + 8.66025i −0.621370 + 0.538122i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 3.87298 + 2.23607i 0.238818 + 0.137882i 0.614634 0.788813i $$-0.289304\pi$$
−0.375815 + 0.926695i $$0.622637\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 15.4919 13.4164i 0.949871 0.822613i
$$267$$ 0 0
$$268$$ 3.00000 0.183254
$$269$$ −7.74597 13.4164i −0.472280 0.818013i 0.527217 0.849731i $$-0.323236\pi$$
−0.999497 + 0.0317179i $$0.989902\pi$$
$$270$$ 0 0
$$271$$ 1.50000 + 0.866025i 0.0911185 + 0.0526073i 0.544867 0.838523i $$-0.316580\pi$$
−0.453748 + 0.891130i $$0.649914\pi$$
$$272$$ −3.87298 6.70820i −0.234834 0.406745i
$$273$$ 0 0
$$274$$ −5.00000 + 8.66025i −0.302061 + 0.523185i
$$275$$ 19.3649 11.1803i 1.16775 0.674200i
$$276$$ 0 0
$$277$$ −2.50000 + 4.33013i −0.150210 + 0.260172i −0.931305 0.364241i $$-0.881328\pi$$
0.781094 + 0.624413i $$0.214662\pi$$
$$278$$ −9.68246 + 16.7705i −0.580715 + 1.00583i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −15.4919 + 8.94427i −0.924171 + 0.533571i −0.884963 0.465661i $$-0.845817\pi$$
−0.0392078 + 0.999231i $$0.512483\pi$$
$$282$$ 0 0
$$283$$ 12.1244i 0.720718i −0.932814 0.360359i $$-0.882654\pi$$
0.932814 0.360359i $$-0.117346\pi$$
$$284$$ 26.8328i 1.59223i
$$285$$ 0 0
$$286$$ 15.0000 8.66025i 0.886969 0.512092i
$$287$$ 15.4919 13.4164i 0.914460 0.791946i
$$288$$ 0 0
$$289$$ −21.5000 + 37.2391i −1.26471 + 2.19053i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ −18.0000 + 10.3923i −1.05337 + 0.608164i
$$293$$ 3.87298 6.70820i 0.226262 0.391897i −0.730435 0.682982i $$-0.760683\pi$$
0.956697 + 0.291084i $$0.0940161\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 9.68246 + 5.59017i 0.562781 + 0.324922i
$$297$$ 0 0
$$298$$ −20.0000 34.6410i −1.15857 2.00670i
$$299$$ 7.74597 0.447961
$$300$$ 0 0
$$301$$ 3.50000 + 18.1865i 0.201737 + 1.04825i
$$302$$ 25.1744 + 14.5344i 1.44862 + 0.836363i
$$303$$ 0 0
$$304$$ 3.00000 + 1.73205i 0.172062 + 0.0993399i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 5.19615i 0.296560i −0.988945 0.148280i $$-0.952626\pi$$
0.988945 0.148280i $$-0.0473737\pi$$
$$308$$ −23.2379 26.8328i −1.32410 1.52894i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −15.4919 −0.878467 −0.439233 0.898373i $$-0.644750\pi$$
−0.439233 + 0.898373i $$0.644750\pi$$
$$312$$ 0 0
$$313$$ 13.8564i 0.783210i −0.920133 0.391605i $$-0.871920\pi$$
0.920133 0.391605i $$-0.128080\pi$$
$$314$$ −30.9839 −1.74852
$$315$$ 0 0
$$316$$ −33.0000 −1.85640
$$317$$ 4.47214i 0.251180i −0.992082 0.125590i $$-0.959918\pi$$
0.992082 0.125590i $$-0.0400824\pi$$
$$318$$ 0 0
$$319$$ −20.0000 −1.11979
$$320$$ 0 0
$$321$$ 0 0
$$322$$ −5.00000 25.9808i −0.278639 1.44785i
$$323$$ 26.8328i 1.49302i
$$324$$ 0 0
$$325$$ −7.50000 + 4.33013i −0.416025 + 0.240192i
$$326$$ 25.1744 + 14.5344i 1.39428 + 0.804988i
$$327$$ 0 0
$$328$$ −15.0000 8.66025i −0.828236 0.478183i
$$329$$ −19.3649 6.70820i −1.06762 0.369835i
$$330$$ 0 0
$$331$$ −4.00000 −0.219860 −0.109930 0.993939i $$-0.535063\pi$$
−0.109930 + 0.993939i $$0.535063\pi$$
$$332$$ 11.6190 + 20.1246i 0.637673 + 1.10448i
$$333$$ 0 0
$$334$$ 15.0000 + 8.66025i 0.820763 + 0.473868i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 5.00000 8.66025i 0.272367 0.471754i −0.697100 0.716974i $$-0.745527\pi$$
0.969468 + 0.245220i $$0.0788601\pi$$
$$338$$ 19.3649 11.1803i 1.05331 0.608130i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 3.87298 6.70820i 0.209734 0.363270i
$$342$$ 0 0
$$343$$ 10.0000 + 15.5885i 0.539949 + 0.841698i
$$344$$ 13.5554 7.82624i 0.730860 0.421962i
$$345$$ 0 0
$$346$$ 34.6410i 1.86231i
$$347$$ 8.94427i 0.480154i 0.970754 + 0.240077i $$0.0771726\pi$$
−0.970754 + 0.240077i $$0.922827\pi$$
$$348$$ 0 0
$$349$$ −19.5000 + 11.2583i −1.04381 + 0.602645i −0.920910 0.389774i $$-0.872553\pi$$
−0.122901 + 0.992419i $$0.539220\pi$$
$$350$$ 19.3649 + 22.3607i 1.03510 + 1.19523i
$$351$$ 0 0
$$352$$ 15.0000 25.9808i 0.799503 1.38478i
$$353$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −23.2379 + 40.2492i −1.23161 + 2.13320i
$$357$$ 0 0
$$358$$ 10.0000 + 17.3205i 0.528516 + 0.915417i
$$359$$ 3.87298 + 2.23607i 0.204408 + 0.118015i 0.598710 0.800966i $$-0.295680\pi$$
−0.394302 + 0.918981i $$0.629014\pi$$
$$360$$ 0 0
$$361$$ −3.50000 6.06218i −0.184211 0.319062i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 9.00000 + 10.3923i 0.471728 + 0.544705i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 9.00000 + 5.19615i 0.469796 + 0.271237i 0.716154 0.697942i $$-0.245901\pi$$
−0.246358 + 0.969179i $$0.579234\pi$$
$$368$$ 3.87298 2.23607i 0.201893 0.116563i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −11.6190 + 2.23607i −0.603226 + 0.116091i
$$372$$ 0 0
$$373$$ −1.00000 1.73205i −0.0517780 0.0896822i 0.838975 0.544170i $$-0.183156\pi$$
−0.890753 + 0.454488i $$0.849822\pi$$
$$374$$ −77.4597 −4.00534
$$375$$ 0 0
$$376$$ 17.3205i 0.893237i
$$377$$ 7.74597 0.398938
$$378$$ 0 0
$$379$$ 17.0000 0.873231 0.436616 0.899648i $$-0.356177\pi$$
0.436616 + 0.899648i $$0.356177\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 40.0000 2.04658
$$383$$ 11.6190 + 20.1246i 0.593701 + 1.02832i 0.993729 + 0.111817i $$0.0356670\pi$$
−0.400028 + 0.916503i $$0.631000\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 15.6525i 0.796690i
$$387$$ 0 0
$$388$$ 4.50000 2.59808i 0.228453 0.131897i
$$389$$ −7.74597 4.47214i −0.392736 0.226746i 0.290609 0.956842i $$-0.406142\pi$$
−0.683345 + 0.730096i $$0.739475\pi$$
$$390$$ 0 0
$$391$$ −30.0000 17.3205i −1.51717 0.875936i
$$392$$ 9.68246 12.2984i 0.489038 0.621162i
$$393$$ 0 0
$$394$$ −20.0000 −1.00759
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −25.5000 14.7224i −1.27981 0.738898i −0.302995 0.952992i $$-0.597987\pi$$
−0.976813 + 0.214094i $$0.931320\pi$$
$$398$$ 25.1744 + 43.6033i 1.26188 + 2.18564i
$$399$$ 0 0
$$400$$ −2.50000 + 4.33013i −0.125000 + 0.216506i
$$401$$ 19.3649 11.1803i 0.967038 0.558320i 0.0687059 0.997637i $$-0.478113\pi$$
0.898332 + 0.439317i $$0.144780\pi$$
$$402$$ 0 0
$$403$$ −1.50000 + 2.59808i −0.0747203 + 0.129419i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ −5.00000 25.9808i −0.248146 1.28940i
$$407$$ −19.3649 + 11.1803i −0.959883 + 0.554189i
$$408$$ 0 0
$$409$$ 22.5167i 1.11338i −0.830721 0.556689i $$-0.812072\pi$$
0.830721 0.556689i $$-0.187928\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −13.5000 + 7.79423i −0.665097 + 0.383994i
$$413$$ 19.3649 + 6.70820i 0.952885 + 0.330089i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ −5.80948 + 10.0623i −0.284833 + 0.493345i
$$417$$ 0 0
$$418$$ 30.0000 17.3205i 1.46735 0.847174i
$$419$$ −7.74597 + 13.4164i −0.378415 + 0.655434i −0.990832 0.135101i $$-0.956864\pi$$
0.612417 + 0.790535i $$0.290198\pi$$
$$420$$ 0 0
$$421$$ 17.0000 + 29.4449i 0.828529 + 1.43505i 0.899192 + 0.437555i $$0.144155\pi$$
−0.0706626 + 0.997500i $$0.522511\pi$$
$$422$$ 36.7933 + 21.2426i 1.79107 + 1.03408i
$$423$$ 0 0
$$424$$ 5.00000 + 8.66025i 0.242821 + 0.420579i
$$425$$ 38.7298 1.87867
$$426$$ 0 0
$$427$$ 7.50000 21.6506i 0.362950 1.04775i
$$428$$ −11.6190 6.70820i −0.561623 0.324253i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −27.1109 + 15.6525i −1.30589 + 0.753953i −0.981407 0.191940i $$-0.938522\pi$$
−0.324479 + 0.945893i $$0.605189\pi$$
$$432$$ 0 0
$$433$$ 15.5885i 0.749133i 0.927200 + 0.374567i $$0.122209\pi$$
−0.927200 + 0.374567i $$0.877791\pi$$
$$434$$ 9.68246 + 3.35410i 0.464773 + 0.161002i
$$435$$ 0 0
$$436$$ −1.50000 2.59808i −0.0718370 0.124425i
$$437$$ 15.4919 0.741080
$$438$$ 0 0
$$439$$ 3.46410i 0.165333i −0.996577 0.0826663i $$-0.973656\pi$$
0.996577 0.0826663i $$-0.0263436\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 30.0000 1.42695
$$443$$ 35.7771i 1.69982i 0.526927 + 0.849910i $$0.323344\pi$$
−0.526927 + 0.849910i $$0.676656\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 27.1109 + 46.9574i 1.28374 + 2.22350i
$$447$$ 0 0
$$448$$ 32.5000 + 11.2583i 1.53548 + 0.531906i
$$449$$ 8.94427i 0.422106i 0.977475 + 0.211053i $$0.0676893\pi$$
−0.977475 + 0.211053i $$0.932311\pi$$
$$450$$ 0 0
$$451$$ 30.0000 17.3205i 1.41264 0.815591i
$$452$$ 23.2379 + 13.4164i 1.09302 + 0.631055i
$$453$$ 0 0
$$454$$ 45.0000 + 25.9808i 2.11195 + 1.21934i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 11.0000 0.514558 0.257279 0.966337i $$-0.417174\pi$$
0.257279 + 0.966337i $$0.417174\pi$$
$$458$$ −29.0474 50.3115i −1.35729 2.35090i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −3.87298 6.70820i −0.180383 0.312432i 0.761628 0.648014i $$-0.224400\pi$$
−0.942011 + 0.335582i $$0.891067\pi$$
$$462$$ 0 0
$$463$$ −4.00000 + 6.92820i −0.185896 + 0.321981i −0.943878 0.330294i $$-0.892852\pi$$
0.757982 + 0.652275i $$0.226185\pi$$
$$464$$ 3.87298 2.23607i 0.179799 0.103807i
$$465$$ 0 0
$$466$$ 10.0000 17.3205i 0.463241 0.802357i
$$467$$ −15.4919 + 26.8328i −0.716881 + 1.24167i 0.245348 + 0.969435i $$0.421098\pi$$
−0.962229 + 0.272240i $$0.912236\pi$$
$$468$$ 0 0
$$469$$ −2.50000 0.866025i −0.115439 0.0399893i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 17.3205i 0.797241i
$$473$$ 31.3050i 1.43940i
$$474$$ 0 0
$$475$$ −15.0000 + 8.66025i −0.688247 + 0.397360i
$$476$$ −11.6190 60.3738i −0.532554 2.76723i
$$477$$ 0 0
$$478$$ 10.0000 17.3205i 0.457389 0.792222i
$$479$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$480$$ 0 0
$$481$$ 7.50000 4.33013i 0.341971 0.197437i
$$482$$ 17.4284 30.1869i 0.793843 1.37498i
$$483$$ 0 0
$$484$$ −13.5000 23.3827i −0.613636 1.06285i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 20.0000 + 34.6410i 0.906287 + 1.56973i 0.819181 + 0.573535i $$0.194428\pi$$
0.0871056 + 0.996199i $$0.472238\pi$$
$$488$$ −19.3649 −0.876609
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −19.3649 11.1803i −0.873926 0.504562i −0.00527540 0.999986i $$-0.501679\pi$$
−0.868651 + 0.495424i $$0.835013\pi$$
$$492$$ 0 0
$$493$$ −30.0000 17.3205i −1.35113 0.780076i
$$494$$ −11.6190 + 6.70820i −0.522761 + 0.301816i
$$495$$ 0 0
$$496$$ 1.73205i 0.0777714i
$$497$$ −7.74597 + 22.3607i −0.347454 + 1.00301i
$$498$$ 0 0
$$499$$ 15.5000 + 26.8468i 0.693875 + 1.20183i 0.970558 + 0.240866i $$0.0774314\pi$$
−0.276683 + 0.960961i $$0.589235\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 51.9615i 2.31916i
$$503$$ 23.2379 1.03613 0.518063 0.855342i $$-0.326653\pi$$
0.518063 + 0.855342i $$0.326653\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 44.7214i 1.98811i
$$507$$ 0 0
$$508$$ 3.00000 0.133103
$$509$$ −11.6190 20.1246i −0.515001 0.892008i −0.999848 0.0174091i $$-0.994458\pi$$
0.484848 0.874599i $$-0.338875\pi$$
$$510$$ 0 0
$$511$$ 18.0000 3.46410i 0.796273 0.153243i
$$512$$ 11.1803i 0.494106i
$$513$$ 0 0
$$514$$ −45.0000 + 25.9808i −1.98486 + 1.14596i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −30.0000 17.3205i −1.31940 0.761755i
$$518$$ −19.3649 22.3607i −0.850846 0.982472i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 3.87298 + 6.70820i 0.169678 + 0.293892i 0.938307 0.345804i $$-0.112394\pi$$
−0.768628 + 0.639696i $$0.779060\pi$$
$$522$$ 0 0
$$523$$ −16.5000 9.52628i −0.721495 0.416555i 0.0938079 0.995590i $$-0.470096\pi$$
−0.815303 + 0.579035i $$0.803429\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ −5.00000 + 8.66025i −0.218010 + 0.377605i
$$527$$ 11.6190 6.70820i 0.506129 0.292214i
$$528$$ 0 0
$$529$$ −1.50000 + 2.59808i −0.0652174 + 0.112960i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 18.0000 + 20.7846i 0.780399 + 0.901127i
$$533$$ −11.6190 + 6.70820i −0.503273 + 0.290565i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 2.23607i 0.0965834i
$$537$$ 0 0
$$538$$ 30.0000 17.3205i 1.29339 0.746740i
$$539$$ 11.6190 + 29.0689i 0.500464 + 1.25209i
$$540$$ 0 0
$$541$$ −7.00000 + 12.1244i −0.300954 + 0.521267i −0.976352 0.216186i $$-0.930638\pi$$
0.675399 + 0.737453i $$0.263972\pi$$
$$542$$ −1.93649 + 3.35410i −0.0831794 + 0.144071i
$$543$$ 0 0
$$544$$ 45.0000 25.9808i 1.92936 1.11392i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −5.50000 9.52628i −0.235163 0.407314i 0.724157 0.689635i $$-0.242229\pi$$
−0.959320 + 0.282321i $$0.908896\pi$$
$$548$$ −11.6190 6.70820i −0.496337 0.286560i
$$549$$ 0 0
$$550$$ 25.0000 + 43.3013i 1.06600 + 1.84637i
$$551$$ 15.4919 0.659979
$$552$$ 0 0
$$553$$ 27.5000 + 9.52628i 1.16942 + 0.405099i
$$554$$ −9.68246 5.59017i −0.411368 0.237504i
$$555$$ 0 0
$$556$$ −22.5000 12.9904i −0.954213 0.550915i
$$557$$ 30.9839 17.8885i 1.31283 0.757962i 0.330265 0.943888i $$-0.392862\pi$$
0.982564 + 0.185926i $$0.0595286\pi$$
$$558$$ 0 0
$$559$$ 12.1244i 0.512806i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −20.0000 34.6410i −0.843649 1.46124i
$$563$$ 7.74597 0.326454 0.163227 0.986589i $$-0.447810\pi$$
0.163227 + 0.986589i $$0.447810\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 27.1109 1.13956
$$567$$ 0 0
$$568$$ 20.0000 0.839181
$$569$$ 17.8885i 0.749927i −0.927040 0.374963i $$-0.877655\pi$$
0.927040 0.374963i $$-0.122345\pi$$
$$570$$ 0 0
$$571$$ −16.0000 −0.669579 −0.334790 0.942293i $$-0.608665\pi$$
−0.334790 + 0.942293i $$0.608665\pi$$
$$572$$ 11.6190 + 20.1246i 0.485813 + 0.841452i
$$573$$ 0 0
$$574$$ 30.0000 + 34.6410i 1.25218 + 1.44589i
$$575$$ 22.3607i 0.932505i
$$576$$ 0 0
$$577$$ −34.5000 + 19.9186i −1.43625 + 0.829222i −0.997587 0.0694283i $$-0.977883\pi$$
−0.438667 + 0.898650i $$0.644549\pi$$
$$578$$ −83.2691 48.0755i −3.46354 1.99968i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −3.87298 20.1246i −0.160678 0.834910i
$$582$$ 0 0
$$583$$ −20.0000 −0.828315
$$584$$ −7.74597 13.4164i −0.320530 0.555175i
$$585$$ 0 0
$$586$$ 15.0000 + 8.66025i 0.619644 + 0.357752i
$$587$$ −15.4919 26.8328i −0.639421 1.10751i −0.985560 0.169326i $$-0.945841\pi$$
0.346140 0.938183i $$-0.387492\pi$$
$$588$$ 0 0
$$589$$ −3.00000 + 5.19615i −0.123613 + 0.214104i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 2.50000 4.33013i 0.102749 0.177967i
$$593$$ −15.4919 + 26.8328i −0.636177 + 1.10189i 0.350087 + 0.936717i $$0.386152\pi$$
−0.986264 + 0.165174i $$0.947181\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 46.4758 26.8328i 1.90372 1.09911i
$$597$$ 0 0
$$598$$ 17.3205i 0.708288i
$$599$$ 8.94427i 0.365453i 0.983164 + 0.182727i $$0.0584923\pi$$
−0.983164 + 0.182727i $$0.941508\pi$$
$$600$$ 0 0
$$601$$ −37.5000 + 21.6506i −1.52966 + 0.883148i −0.530281 + 0.847822i $$0.677914\pi$$
−0.999376 + 0.0353259i $$0.988753\pi$$
$$602$$ −40.6663 + 7.82624i −1.65744 + 0.318974i
$$603$$ 0 0
$$604$$ −19.5000 + 33.7750i −0.793444 + 1.37428i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −27.0000 + 15.5885i −1.09590 + 0.632716i −0.935140 0.354278i $$-0.884727\pi$$
−0.160756 + 0.986994i $$0.551393\pi$$
$$608$$ −11.6190 + 20.1246i −0.471211 + 0.816161i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 11.6190 + 6.70820i 0.470052 + 0.271385i
$$612$$ 0 0
$$613$$ −11.5000 19.9186i −0.464481 0.804504i 0.534697 0.845044i $$-0.320426\pi$$
−0.999178 + 0.0405396i $$0.987092\pi$$
$$614$$ 11.6190 0.468903
$$615$$ 0 0
$$616$$ 20.0000 17.3205i 0.805823 0.697863i
$$617$$ −19.3649 11.1803i −0.779602 0.450104i 0.0566871 0.998392i $$-0.481946\pi$$
−0.836289 + 0.548288i $$0.815280\pi$$
$$618$$ 0 0
$$619$$ −4.50000 2.59808i −0.180870 0.104425i 0.406831 0.913503i $$-0.366634\pi$$
−0.587701 + 0.809078i $$0.699967\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 34.6410i 1.38898i
$$623$$ 30.9839 26.8328i 1.24134 1.07503i
$$624$$ 0 0
$$625$$ −12.5000 21.6506i −0.500000 0.866025i
$$626$$ 30.9839 1.23836
$$627$$ 0 0
$$628$$ 41.5692i 1.65879i
$$629$$ −38.7298 −1.54426
$$630$$ 0 0
$$631$$ 29.0000 1.15447 0.577236 0.816577i $$-0.304131\pi$$
0.577236 + 0.816577i $$0.304131\pi$$
$$632$$ 24.5967i 0.978406i
$$633$$ 0 0
$$634$$ 10.0000 0.397151
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −4.50000 11.2583i −0.178296 0.446071i
$$638$$ 44.7214i 1.77054i
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 3.87298 + 2.23607i 0.152974 + 0.0883194i 0.574533 0.818481i $$-0.305184\pi$$
−0.421559 + 0.906801i $$0.638517\pi$$
$$642$$ 0 0
$$643$$ 16.5000 + 9.52628i 0.650696 + 0.375680i 0.788723 0.614749i $$-0.210743\pi$$
−0.138027 + 0.990429i $$0.544076\pi$$
$$644$$ 34.8569 6.70820i 1.37355 0.264340i
$$645$$ 0 0
$$646$$ 60.0000 2.36067
$$647$$ −7.74597 13.4164i −0.304525 0.527453i 0.672630 0.739979i $$-0.265165\pi$$
−0.977156 + 0.212525i $$0.931831\pi$$
$$648$$ 0 0
$$649$$ 30.0000 + 17.3205i 1.17760 + 0.679889i
$$650$$ −9.68246 16.7705i −0.379777 0.657794i
$$651$$ 0 0
$$652$$ −19.5000 + 33.7750i −0.763679 + 1.32273i
$$653$$ 19.3649 11.1803i 0.757808 0.437521i −0.0707003 0.997498i $$-0.522523\pi$$
0.828508 + 0.559977i $$0.189190\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −3.87298 + 6.70820i −0.151215 + 0.261911i
$$657$$ 0 0
$$658$$ 15.0000 43.3013i 0.584761 1.68806i
$$659$$ −15.4919 + 8.94427i −0.603480 + 0.348419i −0.770409 0.637549i $$-0.779948\pi$$
0.166929 + 0.985969i $$0.446615\pi$$
$$660$$ 0 0
$$661$$ 27.7128i 1.07790i −0.842337 0.538952i $$-0.818821\pi$$
0.842337 0.538952i $$-0.181179\pi$$
$$662$$ 8.94427i 0.347629i
$$663$$ 0 0
$$664$$ −15.0000 + 8.66025i −0.582113 + 0.336083i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 10.0000 17.3205i 0.387202 0.670653i
$$668$$ −11.6190 + 20.1246i −0.449551 + 0.778645i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 19.3649 33.5410i 0.747574 1.29484i
$$672$$ 0 0
$$673$$ −1.00000 1.73205i −0.0385472 0.0667657i 0.846108 0.533011i $$-0.178940\pi$$
−0.884655 + 0.466246i $$0.845606\pi$$
$$674$$ 19.3649 + 11.1803i 0.745909 + 0.430651i
$$675$$ 0 0
$$676$$ 15.0000 + 25.9808i 0.576923 + 0.999260i
$$677$$ −30.9839 −1.19081 −0.595403 0.803427i $$-0.703008\pi$$
−0.595403 + 0.803427i $$0.703008\pi$$
$$678$$ 0 0
$$679$$ −4.50000 + 0.866025i −0.172694 + 0.0332350i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 15.0000 + 8.66025i 0.574380 + 0.331618i
$$683$$ 30.9839 17.8885i 1.18556 0.684486i 0.228269 0.973598i $$-0.426693\pi$$
0.957295 + 0.289112i $$0.0933600\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −34.8569 + 22.3607i −1.33084 + 0.853735i
$$687$$ 0 0
$$688$$ −3.50000 6.06218i −0.133436 0.231118i
$$689$$ 7.74597 0.295098
$$690$$ 0 0
$$691$$ 32.9090i 1.25192i 0.779857 + 0.625958i $$0.215292\pi$$
−0.779857 + 0.625958i $$0.784708\pi$$
$$692$$ −46.4758 −1.76674
$$693$$ 0 0
$$694$$ −20.0000 −0.759190
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 60.0000 2.27266
$$698$$ −25.1744 43.6033i −0.952865 1.65041i
$$699$$ 0 0
$$700$$ −30.0000 + 25.9808i −1.13389 + 0.981981i
$$701$$ 8.94427i 0.337820i 0.985631 + 0.168910i $$0.0540248\pi$$
−0.985631 + 0.168910i $$0.945975\pi$$
$$702$$ 0 0
$$703$$ 15.0000 8.66025i 0.565736 0.326628i
$$704$$ 50.3488 + 29.0689i 1.89759 + 1.09557i
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 11.0000 0.413114 0.206557 0.978435i $$-0.433774\pi$$
0.206557 + 0.978435i $$0.433774\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −30.0000 17.3205i −1.12430 0.649113i
$$713$$ 3.87298 + 6.70820i 0.145044 + 0.251224i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −23.2379 + 13.4164i −0.868441 + 0.501395i
$$717$$ 0 0
$$718$$ −5.00000 + 8.66025i −0.186598 + 0.323198i
$$719$$ 7.74597 13.4164i 0.288876 0.500348i −0.684666 0.728857i $$-0.740052\pi$$
0.973542 + 0.228509i $$0.0733852\pi$$
$$720$$ 0 0
$$721$$ 13.5000 2.59808i 0.502766 0.0967574i
$$722$$ 13.5554 7.82624i 0.504481 0.291262i
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 22.3607i 0.830455i
$$726$$ 0 0
$$727$$ 16.5000 9.52628i 0.611951 0.353310i −0.161778 0.986827i $$-0.551723\pi$$
0.773729 + 0.633517i $$0.218389\pi$$
$$728$$ −7.74597 + 6.70820i −0.287085 + 0.248623i
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −27.1109 + 46.9574i −1.00273 + 1.73678i
$$732$$ 0 0
$$733$$ −31.5000 + 18.1865i −1.16348 + 0.671735i −0.952135 0.305677i $$-0.901117\pi$$
−0.211344 + 0.977412i $$0.567784\pi$$
$$734$$ −11.6190 + 20.1246i −0.428863 + 0.742813i
$$735$$ 0 0
$$736$$ 15.0000 + 25.9808i 0.552907 + 0.957664i
$$737$$ −3.87298 2.23607i −0.142663 0.0823666i
$$738$$ 0 0
$$739$$ −11.5000 19.9186i −0.423034 0.732717i 0.573200 0.819415i $$-0.305702\pi$$
−0.996235 + 0.0866983i $$0.972368\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −5.00000 25.9808i −0.183556 0.953784i
$$743$$ 27.1109 + 15.6525i 0.994602 + 0.574234i 0.906647 0.421891i $$-0.138633\pi$$
0.0879552 + 0.996124i $$0.471967\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 3.87298 2.23607i 0.141800 0.0818683i
$$747$$ 0 0
$$748$$ 103.923i 3.79980i
$$749$$ 7.74597 + 8.94427i 0.283031 + 0.326817i
$$750$$ 0 0
$$751$$ 8.00000 + 13.8564i 0.291924 + 0.505627i 0.974265 0.225407i $$-0.0723712\pi$$
−0.682341 + 0.731034i $$0.739038\pi$$
$$752$$ 7.74597 0.282466
$$753$$ 0 0
$$754$$ 17.3205i 0.630776i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −25.0000 −0.908640 −0.454320 0.890838i $$-0.650118\pi$$
−0.454320 + 0.890838i $$0.650118\pi$$
$$758$$ 38.0132i 1.38070i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$762$$ 0 0
$$763$$ 0.500000 + 2.59808i 0.0181012 + 0.0940567i
$$764$$ 53.6656i 1.94155i
$$765$$ 0 0
$$766$$ −45.0000 + 25.9808i −1.62592 + 0.938723i
$$767$$ −11.6190 6.70820i −0.419536 0.242219i
$$768$$ 0 0
$$769$$ 30.0000 + 17.3205i 1.08183 + 0.624593i 0.931389 0.364026i $$-0.118598\pi$$
0.150439 + 0.988619i $$0.451931\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 21.0000 0.755807
$$773$$ 15.4919 + 26.8328i 0.557206 + 0.965109i 0.997728 + 0.0673675i $$0.0214600\pi$$
−0.440522 + 0.897742i $$0.645207\pi$$
$$774$$ 0 0
$$775$$ −7.50000 4.33013i −0.269408 0.155543i
$$776$$ 1.93649 + 3.35410i 0.0695160 + 0.120405i
$$777$$ 0 0
$$778$$ 10.0000 17.3205i 0.358517 0.620970i
$$779$$ −23.2379 + 13.4164i −0.832584 + 0.480693i
$$780$$ 0 0
$$781$$ −20.0000 + 34.6410i −0.715656 + 1.23955i
$$782$$ 38.7298 67.0820i 1.38498 2.39885i
$$783$$ 0 0
$$784$$ −5.50000 4.33013i −0.196429 0.154647i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 19.0526i 0.679150i 0.940579 + 0.339575i $$0.110283\pi$$
−0.940579 + 0.339575i $$0.889717\pi$$
$$788$$ 26.8328i 0.955879i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −15.4919 17.8885i −0.550830 0.636043i
$$792$$ 0 0