# Properties

 Label 567.2.s.e.458.2 Level $567$ Weight $2$ Character 567.458 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.s (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: $$\Z[a_1, \ldots, a_{4}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 189) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 458.2 Root $$1.93649 + 1.11803i$$ of defining polynomial Character $$\chi$$ $$=$$ 567.458 Dual form 567.2.s.e.26.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.93649 + 1.11803i) q^{2} +(1.50000 + 2.59808i) q^{4} +(-0.500000 + 2.59808i) q^{7} +2.23607i q^{8} +O(q^{10})$$ $$q+(1.93649 + 1.11803i) q^{2} +(1.50000 + 2.59808i) q^{4} +(-0.500000 + 2.59808i) q^{7} +2.23607i q^{8} +4.47214i q^{11} +(1.50000 + 0.866025i) q^{13} +(-3.87298 + 4.47214i) q^{14} +(0.500000 - 0.866025i) q^{16} +(3.87298 - 6.70820i) q^{17} +(-3.00000 + 1.73205i) q^{19} +(-5.00000 + 8.66025i) q^{22} +4.47214i q^{23} -5.00000 q^{25} +(1.93649 + 3.35410i) q^{26} +(-7.50000 + 2.59808i) q^{28} +(3.87298 - 2.23607i) q^{29} +(1.50000 - 0.866025i) q^{31} +(5.80948 - 3.35410i) q^{32} +(15.0000 - 8.66025i) q^{34} +(-2.50000 - 4.33013i) q^{37} -7.74597 q^{38} +(3.87298 - 6.70820i) q^{41} +(3.50000 + 6.06218i) q^{43} +(-11.6190 + 6.70820i) q^{44} +(-5.00000 + 8.66025i) q^{46} +(3.87298 - 6.70820i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(-9.68246 - 5.59017i) q^{50} +5.19615i q^{52} +(-3.87298 - 2.23607i) q^{53} +(-5.80948 - 1.11803i) q^{56} +10.0000 q^{58} +(-3.87298 - 6.70820i) q^{59} +(-7.50000 - 4.33013i) q^{61} +3.87298 q^{62} +13.0000 q^{64} +(0.500000 + 0.866025i) q^{67} +23.2379 q^{68} -8.94427i q^{71} +(6.00000 + 3.46410i) q^{73} -11.1803i q^{74} +(-9.00000 - 5.19615i) q^{76} +(-11.6190 - 2.23607i) q^{77} +(-5.50000 + 9.52628i) q^{79} +(15.0000 - 8.66025i) q^{82} +(-3.87298 - 6.70820i) q^{83} +15.6525i q^{86} -10.0000 q^{88} +(7.74597 + 13.4164i) q^{89} +(-3.00000 + 3.46410i) q^{91} +(-11.6190 + 6.70820i) q^{92} +(15.0000 - 8.66025i) q^{94} +(1.50000 - 0.866025i) q^{97} +(-9.68246 - 12.2984i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 6q^{4} - 2q^{7} + O(q^{10})$$ $$4q + 6q^{4} - 2q^{7} + 6q^{13} + 2q^{16} - 12q^{19} - 20q^{22} - 20q^{25} - 30q^{28} + 6q^{31} + 60q^{34} - 10q^{37} + 14q^{43} - 20q^{46} - 26q^{49} + 40q^{58} - 30q^{61} + 52q^{64} + 2q^{67} + 24q^{73} - 36q^{76} - 22q^{79} + 60q^{82} - 40q^{88} - 12q^{91} + 60q^{94} + 6q^{97} + O(q^{100})$$

## Character values

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

 $$n$$ $$325$$ $$407$$ $$\chi(n)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.93649 + 1.11803i 1.36931 + 0.790569i 0.990839 0.135045i $$-0.0431180\pi$$
0.378467 + 0.925615i $$0.376451\pi$$
$$3$$ 0 0
$$4$$ 1.50000 + 2.59808i 0.750000 + 1.29904i
$$5$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$6$$ 0 0
$$7$$ −0.500000 + 2.59808i −0.188982 + 0.981981i
$$8$$ 2.23607i 0.790569i
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 4.47214i 1.34840i 0.738549 + 0.674200i $$0.235511\pi$$
−0.738549 + 0.674200i $$0.764489\pi$$
$$12$$ 0 0
$$13$$ 1.50000 + 0.866025i 0.416025 + 0.240192i 0.693375 0.720577i $$-0.256123\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ −3.87298 + 4.47214i −1.03510 + 1.19523i
$$15$$ 0 0
$$16$$ 0.500000 0.866025i 0.125000 0.216506i
$$17$$ 3.87298 6.70820i 0.939336 1.62698i 0.172624 0.984988i $$-0.444775\pi$$
0.766712 0.641991i $$-0.221891\pi$$
$$18$$ 0 0
$$19$$ −3.00000 + 1.73205i −0.688247 + 0.397360i −0.802955 0.596040i $$-0.796740\pi$$
0.114708 + 0.993399i $$0.463407\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −5.00000 + 8.66025i −1.06600 + 1.84637i
$$23$$ 4.47214i 0.932505i 0.884652 + 0.466252i $$0.154396\pi$$
−0.884652 + 0.466252i $$0.845604\pi$$
$$24$$ 0 0
$$25$$ −5.00000 −1.00000
$$26$$ 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 −0.0952614 0.995452i $$-0.530369\pi$$
0.814456 + 0.580225i $$0.197035\pi$$
$$30$$ 0 0
$$31$$ 1.50000 0.866025i 0.269408 0.155543i −0.359211 0.933257i $$-0.616954\pi$$
0.628619 + 0.777714i $$0.283621\pi$$
$$32$$ 5.80948 3.35410i 1.02698 0.592927i
$$33$$ 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 0.584002 0.811752i $$-0.301486\pi$$
−0.994999 + 0.0998840i $$0.968153\pi$$
$$38$$ −7.74597 −1.25656
$$39$$ 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
$$47$$ 3.87298 6.70820i 0.564933 0.978492i −0.432123 0.901815i $$-0.642235\pi$$
0.997056 0.0766776i $$-0.0244312\pi$$
$$48$$ 0 0
$$49$$ −6.50000 2.59808i −0.928571 0.371154i
$$50$$ −9.68246 5.59017i −1.36931 0.790569i
$$51$$ 0 0
$$52$$ 5.19615i 0.720577i
$$53$$ −3.87298 2.23607i −0.531995 0.307148i 0.209833 0.977737i $$-0.432708\pi$$
−0.741829 + 0.670590i $$0.766041\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ −5.80948 1.11803i −0.776324 0.149404i
$$57$$ 0 0
$$58$$ 10.0000 1.31306
$$59$$ −3.87298 6.70820i −0.504219 0.873334i −0.999988 0.00487911i $$-0.998447\pi$$
0.495769 0.868455i $$-0.334886\pi$$
$$60$$ 0 0
$$61$$ −7.50000 4.33013i −0.960277 0.554416i −0.0640184 0.997949i $$-0.520392\pi$$
−0.896258 + 0.443533i $$0.853725\pi$$
$$62$$ 3.87298 0.491869
$$63$$ 0 0
$$64$$ 13.0000 1.62500
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0.500000 + 0.866025i 0.0610847 + 0.105802i 0.894951 0.446165i $$-0.147211\pi$$
−0.833866 + 0.551967i $$0.813877\pi$$
$$68$$ 23.2379 2.81801
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 8.94427i 1.06149i −0.847532 0.530745i $$-0.821912\pi$$
0.847532 0.530745i $$-0.178088\pi$$
$$72$$ 0 0
$$73$$ 6.00000 + 3.46410i 0.702247 + 0.405442i 0.808184 0.588930i $$-0.200451\pi$$
−0.105937 + 0.994373i $$0.533784\pi$$
$$74$$ 11.1803i 1.29969i
$$75$$ 0 0
$$76$$ −9.00000 5.19615i −1.03237 0.596040i
$$77$$ −11.6190 2.23607i −1.32410 0.254824i
$$78$$ 0 0
$$79$$ −5.50000 + 9.52628i −0.618798 + 1.07179i 0.370907 + 0.928670i $$0.379047\pi$$
−0.989705 + 0.143120i $$0.954286\pi$$
$$80$$ 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
$$86$$ 15.6525i 1.68785i
$$87$$ 0 0
$$88$$ −10.0000 −1.06600
$$89$$ 7.74597 + 13.4164i 0.821071 + 1.42214i 0.904886 + 0.425655i $$0.139956\pi$$
−0.0838147 + 0.996481i $$0.526710\pi$$
$$90$$ 0 0
$$91$$ −3.00000 + 3.46410i −0.314485 + 0.363137i
$$92$$ −11.6190 + 6.70820i −1.21136 + 0.699379i
$$93$$ 0 0
$$94$$ 15.0000 8.66025i 1.54713 0.893237i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 1.50000 0.866025i 0.152302 0.0879316i −0.421912 0.906637i $$-0.638641\pi$$
0.574214 + 0.818705i $$0.305308\pi$$
$$98$$ −9.68246 12.2984i −0.978076 1.24232i
$$99$$ 0 0
$$100$$ −7.50000 12.9904i −0.750000 1.29904i
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ 5.19615i 0.511992i −0.966678 0.255996i $$-0.917597\pi$$
0.966678 0.255996i $$-0.0824034\pi$$
$$104$$ −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 −0.300970 0.953634i $$-0.597310\pi$$
0.675386 + 0.737465i $$0.263977\pi$$
$$108$$ 0 0
$$109$$ 0.500000 0.866025i 0.0478913 0.0829502i −0.841086 0.540901i $$-0.818083\pi$$
0.888977 + 0.457951i $$0.151417\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 2.00000 + 1.73205i 0.188982 + 0.163663i
$$113$$ 7.74597 + 4.47214i 0.728679 + 0.420703i 0.817939 0.575305i $$-0.195117\pi$$
−0.0892596 + 0.996008i $$0.528450\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 11.6190 + 6.70820i 1.07879 + 0.622841i
$$117$$ 0 0
$$118$$ 17.3205i 1.59448i
$$119$$ 15.4919 + 13.4164i 1.42014 + 1.22988i
$$120$$ 0 0
$$121$$ −9.00000 −0.818182
$$122$$ −9.68246 16.7705i −0.876609 1.51833i
$$123$$ 0 0
$$124$$ 4.50000 + 2.59808i 0.404112 + 0.233314i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −1.00000 −0.0887357 −0.0443678 0.999015i $$-0.514127\pi$$
−0.0443678 + 0.999015i $$0.514127\pi$$
$$128$$ 13.5554 + 7.82624i 1.19814 + 0.691748i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ −3.00000 8.66025i −0.260133 0.750939i
$$134$$ 2.23607i 0.193167i
$$135$$ 0 0
$$136$$ 15.0000 + 8.66025i 1.28624 + 0.742611i
$$137$$ 4.47214i 0.382080i 0.981582 + 0.191040i $$0.0611861\pi$$
−0.981582 + 0.191040i $$0.938814\pi$$
$$138$$ 0 0
$$139$$ −7.50000 4.33013i −0.636142 0.367277i 0.146985 0.989139i $$-0.453043\pi$$
−0.783127 + 0.621862i $$0.786376\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 10.0000 17.3205i 0.839181 1.45350i
$$143$$ −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
$$149$$ 17.8885i 1.46549i 0.680505 + 0.732743i $$0.261760\pi$$
−0.680505 + 0.732743i $$0.738240\pi$$
$$150$$ 0 0
$$151$$ −13.0000 −1.05792 −0.528962 0.848645i $$-0.677419\pi$$
−0.528962 + 0.848645i $$0.677419\pi$$
$$152$$ −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
$$157$$ −12.0000 + 6.92820i −0.957704 + 0.552931i −0.895466 0.445130i $$-0.853157\pi$$
−0.0622385 + 0.998061i $$0.519824\pi$$
$$158$$ −21.3014 + 12.2984i −1.69465 + 0.978406i
$$159$$ 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 0.999944 + 0.0105623i $$0.00336213\pi$$
−0.490825 + 0.871258i $$0.663305\pi$$
$$164$$ 23.2379 1.81458
$$165$$ 0 0
$$166$$ 17.3205i 1.34433i
$$167$$ 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
$$173$$ −7.74597 + 13.4164i −0.588915 + 1.02003i 0.405460 + 0.914113i $$0.367111\pi$$
−0.994375 + 0.105918i $$0.966222\pi$$
$$174$$ 0 0
$$175$$ 2.50000 12.9904i 0.188982 0.981981i
$$176$$ 3.87298 + 2.23607i 0.291937 + 0.168550i
$$177$$ 0 0
$$178$$ 34.6410i 2.59645i
$$179$$ 7.74597 + 4.47214i 0.578961 + 0.334263i 0.760720 0.649080i $$-0.224846\pi$$
−0.181760 + 0.983343i $$0.558179\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ −9.68246 + 3.35410i −0.717712 + 0.248623i
$$183$$ 0 0
$$184$$ −10.0000 −0.737210
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 30.0000 + 17.3205i 2.19382 + 1.26660i
$$188$$ 23.2379 1.69480
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −15.4919 8.94427i −1.12096 0.647185i −0.179312 0.983792i $$-0.557387\pi$$
−0.941645 + 0.336607i $$0.890720\pi$$
$$192$$ 0 0
$$193$$ 3.50000 + 6.06218i 0.251936 + 0.436365i 0.964059 0.265689i $$-0.0855996\pi$$
−0.712123 + 0.702055i $$0.752266\pi$$
$$194$$ 3.87298 0.278064
$$195$$ 0 0
$$196$$ −3.00000 20.7846i −0.214286 1.48461i
$$197$$ 8.94427i 0.637253i −0.947880 0.318626i $$-0.896778\pi$$
0.947880 0.318626i $$-0.103222\pi$$
$$198$$ 0 0
$$199$$ 19.5000 + 11.2583i 1.38232 + 0.798082i 0.992434 0.122782i $$-0.0391815\pi$$
0.389885 + 0.920864i $$0.372515\pi$$
$$200$$ 11.1803i 0.790569i
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 3.87298 + 11.1803i 0.271830 + 0.784706i
$$204$$ 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 $$-0.0602466\pi$$
$$212$$ 13.4164i 0.921443i
$$213$$ 0 0
$$214$$ 10.0000 0.683586
$$215$$ 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
$$221$$ 11.6190 6.70820i 0.781575 0.451243i
$$222$$ 0 0
$$223$$ −21.0000 + 12.1244i −1.40626 + 0.811907i −0.995025 0.0996209i $$-0.968237\pi$$
−0.411239 + 0.911528i $$0.634904\pi$$
$$224$$ 5.80948 + 16.7705i 0.388162 + 1.12053i
$$225$$ 0 0
$$226$$ 10.0000 + 17.3205i 0.665190 + 1.15214i
$$227$$ −23.2379 −1.54235 −0.771177 0.636621i $$-0.780332\pi$$
−0.771177 + 0.636621i $$0.780332\pi$$
$$228$$ 0 0
$$229$$ 25.9808i 1.71686i 0.512933 + 0.858429i $$0.328559\pi$$
−0.512933 + 0.858429i $$0.671441\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 5.00000 + 8.66025i 0.328266 + 0.568574i
$$233$$ −7.74597 + 4.47214i −0.507455 + 0.292979i −0.731787 0.681533i $$-0.761313\pi$$
0.224332 + 0.974513i $$0.427980\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 11.6190 20.1246i 0.756329 1.31000i
$$237$$ 0 0
$$238$$ 15.0000 + 43.3013i 0.972306 + 2.80680i
$$239$$ 7.74597 + 4.47214i 0.501045 + 0.289278i 0.729145 0.684359i $$-0.239918\pi$$
−0.228100 + 0.973638i $$0.573251\pi$$
$$240$$ 0 0
$$241$$ 15.5885i 1.00414i −0.864827 0.502070i $$-0.832572\pi$$
0.864827 0.502070i $$-0.167428\pi$$
$$242$$ −17.4284 10.0623i −1.12034 0.646830i
$$243$$ 0 0
$$244$$ 25.9808i 1.66325i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −6.00000 −0.381771
$$248$$ 1.93649 + 3.35410i 0.122967 + 0.212986i
$$249$$ 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
$$254$$ −1.93649 1.11803i −0.121506 0.0701517i
$$255$$ 0 0
$$256$$ 4.50000 + 7.79423i 0.281250 + 0.487139i
$$257$$ −23.2379 −1.44954 −0.724770 0.688991i $$-0.758054\pi$$
−0.724770 + 0.688991i $$0.758054\pi$$
$$258$$ 0 0
$$259$$ 12.5000 4.33013i 0.776712 0.269061i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 4.47214i 0.275764i 0.990449 + 0.137882i $$0.0440294\pi$$
−0.990449 + 0.137882i $$0.955971\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 3.87298 20.1246i 0.237468 1.23392i
$$267$$ 0 0
$$268$$ −1.50000 + 2.59808i −0.0916271 + 0.158703i
$$269$$ −7.74597 + 13.4164i −0.472280 + 0.818013i −0.999497 0.0317179i $$-0.989902\pi$$
0.527217 + 0.849731i $$0.323236\pi$$
$$270$$ 0 0
$$271$$ 1.50000 0.866025i 0.0911185 0.0526073i −0.453748 0.891130i $$-0.649914\pi$$
0.544867 + 0.838523i $$0.316580\pi$$
$$272$$ −3.87298 6.70820i −0.234834 0.406745i
$$273$$ 0 0
$$274$$ −5.00000 + 8.66025i −0.302061 + 0.523185i
$$275$$ 22.3607i 1.34840i
$$276$$ 0 0
$$277$$ 5.00000 0.300421 0.150210 0.988654i $$-0.452005\pi$$
0.150210 + 0.988654i $$0.452005\pi$$
$$278$$ −9.68246 16.7705i −0.580715 1.00583i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 15.4919 8.94427i 0.924171 0.533571i 0.0392078 0.999231i $$-0.487517\pi$$
0.884963 + 0.465661i $$0.154183\pi$$
$$282$$ 0 0
$$283$$ 10.5000 6.06218i 0.624160 0.360359i −0.154327 0.988020i $$-0.549321\pi$$
0.778487 + 0.627661i $$0.215988\pi$$
$$284$$ 23.2379 13.4164i 1.37892 0.796117i
$$285$$ 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
$$292$$ 20.7846i 1.21633i
$$293$$ 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
$$299$$ −3.87298 + 6.70820i −0.223980 + 0.387945i
$$300$$ 0 0
$$301$$ −17.5000 + 6.06218i −1.00868 + 0.349418i
$$302$$ −25.1744 14.5344i −1.44862 0.836363i
$$303$$ 0 0
$$304$$ 3.46410i 0.198680i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 5.19615i 0.296560i 0.988945 + 0.148280i $$0.0473737\pi$$
−0.988945 + 0.148280i $$0.952626\pi$$
$$308$$ −11.6190 33.5410i −0.662051 1.91118i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 7.74597 + 13.4164i 0.439233 + 0.760775i 0.997631 0.0687991i $$-0.0219168\pi$$
−0.558397 + 0.829574i $$0.688583\pi$$
$$312$$ 0 0
$$313$$ −12.0000 6.92820i −0.678280 0.391605i 0.120927 0.992661i $$-0.461413\pi$$
−0.799207 + 0.601056i $$0.794747\pi$$
$$314$$ −30.9839 −1.74852
$$315$$ 0 0
$$316$$ −33.0000 −1.85640
$$317$$ −3.87298 2.23607i −0.217528 0.125590i 0.387277 0.921963i $$-0.373416\pi$$
−0.604805 + 0.796373i $$0.706749\pi$$
$$318$$ 0 0
$$319$$ 10.0000 + 17.3205i 0.559893 + 0.969762i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ −20.0000 17.3205i −1.11456 0.965234i
$$323$$ 26.8328i 1.49302i
$$324$$ 0 0
$$325$$ −7.50000 4.33013i −0.416025 0.240192i
$$326$$ 29.0689i 1.60998i
$$327$$ 0 0
$$328$$ 15.0000 + 8.66025i 0.828236 + 0.478183i
$$329$$ 15.4919 + 13.4164i 0.854098 + 0.739671i
$$330$$ 0 0
$$331$$ 2.00000 3.46410i 0.109930 0.190404i −0.805812 0.592172i $$-0.798271\pi$$
0.915742 + 0.401768i $$0.131604\pi$$
$$332$$ 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 $$0.0788601\pi$$
$$338$$ 22.3607i 1.21626i
$$339$$ 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
$$346$$ −30.0000 + 17.3205i −1.61281 + 0.931156i
$$347$$ −7.74597 + 4.47214i −0.415825 + 0.240077i −0.693290 0.720659i $$-0.743839\pi$$
0.277464 + 0.960736i $$0.410506\pi$$
$$348$$ 0 0
$$349$$ 19.5000 11.2583i 1.04381 0.602645i 0.122901 0.992419i $$-0.460780\pi$$
0.920910 + 0.389774i $$0.127447\pi$$
$$350$$ 19.3649 22.3607i 1.03510 1.19523i
$$351$$ 0 0
$$352$$ 15.0000 + 25.9808i 0.799503 + 1.38478i
$$353$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$354$$ 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 −0.394302 0.918981i $$-0.629014\pi$$
0.598710 + 0.800966i $$0.295680\pi$$
$$360$$ 0 0
$$361$$ −3.50000 + 6.06218i −0.184211 + 0.319062i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ −13.5000 2.59808i −0.707592 0.136176i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 10.3923i 0.542474i 0.962513 + 0.271237i $$0.0874327\pi$$
−0.962513 + 0.271237i $$0.912567\pi$$
$$368$$ 3.87298 + 2.23607i 0.201893 + 0.116563i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 7.74597 8.94427i 0.402151 0.464363i
$$372$$ 0 0
$$373$$ 2.00000 0.103556 0.0517780 0.998659i $$-0.483511\pi$$
0.0517780 + 0.998659i $$0.483511\pi$$
$$374$$ 38.7298 + 67.0820i 2.00267 + 3.46873i
$$375$$ 0 0
$$376$$ 15.0000 + 8.66025i 0.773566 + 0.446619i
$$377$$ 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
$$382$$ −20.0000 34.6410i −1.02329 1.77239i
$$383$$ −23.2379 −1.18740 −0.593701 0.804686i $$-0.702334\pi$$
−0.593701 + 0.804686i $$0.702334\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 15.6525i 0.796690i
$$387$$ 0 0
$$388$$ 4.50000 + 2.59808i 0.228453 + 0.131897i
$$389$$ 8.94427i 0.453493i −0.973954 0.226746i $$-0.927191\pi$$
0.973954 0.226746i $$-0.0728088\pi$$
$$390$$ 0 0
$$391$$ 30.0000 + 17.3205i 1.51717 + 0.875936i
$$392$$ 5.80948 14.5344i 0.293423 0.734100i
$$393$$ 0 0
$$394$$ 10.0000 17.3205i 0.503793 0.872595i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −25.5000 + 14.7224i −1.27981 + 0.738898i −0.976813 0.214094i $$-0.931320\pi$$
−0.302995 + 0.952992i $$0.597987\pi$$
$$398$$ 25.1744 + 43.6033i 1.26188 + 2.18564i
$$399$$ 0 0
$$400$$ −2.50000 + 4.33013i −0.125000 + 0.216506i
$$401$$ 22.3607i 1.11664i −0.829626 0.558320i $$-0.811446\pi$$
0.829626 0.558320i $$-0.188554\pi$$
$$402$$ 0 0
$$403$$ 3.00000 0.149441
$$404$$ 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
$$409$$ 19.5000 11.2583i 0.964213 0.556689i 0.0667458 0.997770i $$-0.478738\pi$$
0.897467 + 0.441081i $$0.145405\pi$$
$$410$$ 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
$$416$$ 11.6190 0.569666
$$417$$ 0 0
$$418$$ 34.6410i 1.69435i
$$419$$ −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
$$425$$ −19.3649 + 33.5410i −0.939336 + 1.62698i
$$426$$ 0 0
$$427$$ 15.0000 17.3205i 0.725901 0.838198i
$$428$$ 11.6190 + 6.70820i 0.561623 + 0.324253i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −27.1109 15.6525i −1.30589 0.753953i −0.324479 0.945893i $$-0.605189\pi$$
−0.981407 + 0.191940i $$0.938522\pi$$
$$432$$ 0 0
$$433$$ 15.5885i 0.749133i −0.927200 0.374567i $$-0.877791\pi$$
0.927200 0.374567i $$-0.122209\pi$$
$$434$$ −1.93649 + 10.0623i −0.0929546 + 0.483006i
$$435$$ 0 0
$$436$$ 3.00000 0.143674
$$437$$ −7.74597 13.4164i −0.370540 0.641794i
$$438$$ 0 0
$$439$$ −3.00000 1.73205i −0.143182 0.0826663i 0.426698 0.904394i $$-0.359677\pi$$
−0.569880 + 0.821728i $$0.693010\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 30.0000 1.42695
$$443$$ 30.9839 + 17.8885i 1.47209 + 0.849910i 0.999508 0.0313772i $$-0.00998932\pi$$
0.472580 + 0.881288i $$0.343323\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −54.2218 −2.56748
$$447$$ 0 0
$$448$$ −6.50000 + 33.7750i −0.307096 + 1.59572i
$$449$$ 8.94427i 0.422106i −0.977475 0.211053i $$-0.932311\pi$$
0.977475 0.211053i $$-0.0676893\pi$$
$$450$$ 0 0
$$451$$ 30.0000 + 17.3205i 1.41264 + 0.815591i
$$452$$ 26.8328i 1.26211i
$$453$$ 0 0
$$454$$ −45.0000 25.9808i −2.11195 1.21934i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −5.50000 + 9.52628i −0.257279 + 0.445621i −0.965512 0.260358i $$-0.916159\pi$$
0.708233 + 0.705979i $$0.249493\pi$$
$$458$$ −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 $$0.226185\pi$$
$$464$$ 4.47214i 0.207614i
$$465$$ 0 0
$$466$$ −20.0000 −0.926482
$$467$$ −15.4919 26.8328i −0.716881 1.24167i −0.962229 0.272240i $$-0.912236\pi$$
0.245348 0.969435i $$-0.421098\pi$$
$$468$$ 0 0
$$469$$ −2.50000 + 0.866025i −0.115439 + 0.0399893i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 15.0000 8.66025i 0.690431 0.398621i
$$473$$ −27.1109 + 15.6525i −1.24656 + 0.719702i
$$474$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ 8.66025i 0.394874i
$$482$$ 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 0.0871056 0.996199i $$-0.472238\pi$$
0.819181 0.573535i $$-0.194428\pi$$
$$488$$ 9.68246 16.7705i 0.438304 0.759165i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 19.3649 + 11.1803i 0.873926 + 0.504562i 0.868651 0.495424i $$-0.164987\pi$$
0.00527540 + 0.999986i $$0.498321\pi$$
$$492$$ 0 0
$$493$$ 34.6410i 1.56015i
$$494$$ −11.6190 6.70820i −0.522761 0.301816i
$$495$$ 0 0
$$496$$ 1.73205i 0.0777714i
$$497$$ 23.2379 + 4.47214i 1.04236 + 0.200603i
$$498$$ 0 0
$$499$$ −31.0000 −1.38775 −0.693875 0.720095i $$-0.744098\pi$$
−0.693875 + 0.720095i $$0.744098\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −45.0000 25.9808i −2.00845 1.15958i
$$503$$ 23.2379 1.03613 0.518063 0.855342i $$-0.326653\pi$$
0.518063 + 0.855342i $$0.326653\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −38.7298 22.3607i −1.72175 0.994053i
$$507$$ 0 0
$$508$$ −1.50000 2.59808i −0.0665517 0.115271i
$$509$$ 23.2379 1.03000 0.515001 0.857190i $$-0.327792\pi$$
0.515001 + 0.857190i $$0.327792\pi$$
$$510$$ 0 0
$$511$$ −12.0000 + 13.8564i −0.530849 + 0.612971i
$$512$$ 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
$$518$$ 29.0474 + 5.59017i 1.27627 + 0.245618i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 3.87298 6.70820i 0.169678 0.293892i −0.768628 0.639696i $$-0.779060\pi$$
0.938307 + 0.345804i $$0.112394\pi$$
$$522$$ 0 0
$$523$$ −16.5000 + 9.52628i −0.721495 + 0.416555i −0.815303 0.579035i $$-0.803429\pi$$
0.0938079 + 0.995590i $$0.470096\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ −5.00000 + 8.66025i −0.218010 + 0.377605i
$$527$$ 13.4164i 0.584428i
$$528$$ 0 0
$$529$$ 3.00000 0.130435
$$530$$ 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
$$536$$ −1.93649 + 1.11803i −0.0836437 + 0.0482917i
$$537$$ 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 0.675399 0.737453i $$-0.263972\pi$$
−0.976352 + 0.216186i $$0.930638\pi$$
$$542$$ 3.87298 0.166359
$$543$$ 0 0
$$544$$ 51.9615i 2.22783i
$$545$$ 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
$$551$$ −7.74597 + 13.4164i −0.329989 + 0.571558i
$$552$$ 0 0
$$553$$ −22.0000 19.0526i −0.935535 0.810197i
$$554$$ 9.68246 + 5.59017i 0.411368 + 0.237504i
$$555$$ 0 0
$$556$$ 25.9808i 1.10183i
$$557$$ 30.9839 + 17.8885i 1.31283 + 0.757962i 0.982564 0.185926i $$-0.0595286\pi$$
0.330265 + 0.943888i $$0.392862\pi$$
$$558$$ 0 0
$$559$$ 12.1244i 0.512806i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 40.0000 1.68730
$$563$$ −3.87298 6.70820i −0.163227 0.282717i 0.772797 0.634653i $$-0.218857\pi$$
−0.936024 + 0.351936i $$0.885524\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 27.1109 1.13956
$$567$$ 0 0
$$568$$ 20.0000 0.839181
$$569$$ −15.4919 8.94427i −0.649456 0.374963i 0.138792 0.990322i $$-0.455678\pi$$
−0.788248 + 0.615358i $$0.789011\pi$$
$$570$$ 0 0
$$571$$ 8.00000 + 13.8564i 0.334790 + 0.579873i 0.983444 0.181210i $$-0.0580014\pi$$
−0.648655 + 0.761083i $$0.724668\pi$$
$$572$$ −23.2379 −0.971625
$$573$$ 0 0
$$574$$ 15.0000 + 43.3013i 0.626088 + 1.80736i
$$575$$ 22.3607i 0.932505i
$$576$$ 0 0
$$577$$ −34.5000 19.9186i −1.43625 0.829222i −0.438667 0.898650i $$-0.644549\pi$$
−0.997587 + 0.0694283i $$0.977883\pi$$
$$578$$ 96.1509i 3.99935i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 19.3649 6.70820i 0.803392 0.278303i
$$582$$ 0 0
$$583$$ 10.0000 17.3205i 0.414158 0.717342i
$$584$$ −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
$$592$$ −5.00000 −0.205499
$$593$$ −15.4919 26.8328i −0.636177 1.10189i −0.986264 0.165174i $$-0.947181\pi$$
0.350087 0.936717i $$-0.386152\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −46.4758 + 26.8328i −1.90372 + 1.09911i
$$597$$ 0 0
$$598$$ −15.0000 + 8.66025i −0.613396 + 0.354144i
$$599$$ −7.74597 + 4.47214i −0.316492 + 0.182727i −0.649828 0.760082i $$-0.725159\pi$$
0.333336 + 0.942808i $$0.391826\pi$$
$$600$$ 0 0
$$601$$ 37.5000 21.6506i 1.52966 0.883148i 0.530281 0.847822i $$-0.322086\pi$$
0.999376 0.0353259i $$-0.0112469\pi$$
$$602$$ −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
$$607$$ 31.1769i 1.26543i 0.774384 + 0.632716i $$0.218060\pi$$
−0.774384 + 0.632716i $$0.781940\pi$$
$$608$$ −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 −0.999178 0.0405396i $$-0.987092\pi$$
0.534697 + 0.845044i $$0.320426\pi$$
$$614$$ −5.80948 + 10.0623i −0.234451 + 0.406082i
$$615$$ 0 0
$$616$$ 5.00000 25.9808i 0.201456 1.04679i
$$617$$ 19.3649 + 11.1803i 0.779602 + 0.450104i 0.836289 0.548288i $$-0.184720\pi$$
−0.0566871 + 0.998392i $$0.518054\pi$$
$$618$$ 0 0
$$619$$ 5.19615i 0.208851i −0.994533 0.104425i $$-0.966700\pi$$
0.994533 0.104425i $$-0.0333004\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 34.6410i 1.38898i
$$623$$ −38.7298 + 13.4164i −1.55168 + 0.537517i
$$624$$ 0 0
$$625$$ 25.0000 1.00000
$$626$$ −15.4919 26.8328i −0.619182 1.07246i
$$627$$ 0 0
$$628$$ −36.0000 20.7846i −1.43656 0.829396i
$$629$$ −38.7298 −1.54426
$$630$$ 0 0
$$631$$ 29.0000 1.15447 0.577236 0.816577i $$-0.304131\pi$$
0.577236 + 0.816577i $$0.304131\pi$$
$$632$$ −21.3014 12.2984i −0.847325 0.489203i
$$633$$ 0 0
$$634$$ −5.00000 8.66025i −0.198575 0.343943i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −7.50000 9.52628i −0.297161 0.377445i
$$638$$ 44.7214i 1.77054i
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 4.47214i 0.176639i 0.996092 + 0.0883194i $$0.0281496\pi$$
−0.996092 + 0.0883194i $$0.971850\pi$$
$$642$$ 0 0
$$643$$ −16.5000 9.52628i −0.650696 0.375680i 0.138027 0.990429i $$-0.455924\pi$$
−0.788723 + 0.614749i $$0.789257\pi$$
$$644$$ −11.6190 33.5410i −0.457851 1.32170i
$$645$$ 0 0
$$646$$ −30.0000 + 51.9615i −1.18033 + 2.04440i
$$647$$ −7.74597 + 13.4164i −0.304525 + 0.527453i −0.977156 0.212525i $$-0.931831\pi$$
0.672630 + 0.739979i $$0.265165\pi$$
$$648$$ 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
$$653$$ 22.3607i 0.875041i −0.899208 0.437521i $$-0.855857\pi$$
0.899208 0.437521i $$-0.144143\pi$$
$$654$$ 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 −0.166929 0.985969i $$-0.553385\pi$$
0.770409 + 0.637549i $$0.220052\pi$$
$$660$$ 0 0
$$661$$ 24.0000 13.8564i 0.933492 0.538952i 0.0455776 0.998961i $$-0.485487\pi$$
0.887914 + 0.460009i $$0.152154\pi$$
$$662$$ 7.74597 4.47214i 0.301056 0.173814i
$$663$$ 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
$$668$$ 23.2379 0.899101
$$669$$ 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
$$677$$ 15.4919 26.8328i 0.595403 1.03127i −0.398086 0.917348i $$-0.630326\pi$$
0.993490 0.113921i $$-0.0363411\pi$$
$$678$$ 0 0
$$679$$ 1.50000 + 4.33013i 0.0575647 + 0.166175i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 17.3205i 0.663237i
$$683$$ 30.9839 + 17.8885i 1.18556 + 0.684486i 0.957295 0.289112i $$-0.0933600\pi$$
0.228269 + 0.973598i $$0.426693\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 36.7933 19.0066i 1.40478 0.725675i
$$687$$ 0 0
$$688$$ 7.00000 0.266872
$$689$$ −3.87298 6.70820i −0.147549 0.255562i
$$690$$ 0 0
$$691$$ 28.5000 + 16.4545i 1.08419 + 0.625958i 0.932024 0.362397i $$-0.118041\pi$$
0.152167 + 0.988355i $$0.451375\pi$$
$$692$$ −46.4758 −1.76674
$$693$$ 0 0
$$694$$ −20.0000 −0.759190
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −30.0000 51.9615i −1.13633 1.96818i
$$698$$ 50.3488 1.90573
$$699$$ 0 0
$$700$$ 37.5000 12.9904i 1.41737 0.490990i
$$701$$ 8.94427i 0.337820i −0.985631 0.168910i $$-0.945975\pi$$
0.985631 0.168910i $$-0.0540248\pi$$
$$702$$ 0 0
$$703$$ 15.0000 + 8.66025i 0.565736 + 0.326628i
$$704$$ 58.1378i 2.19115i
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −5.50000 + 9.52628i −0.206557 + 0.357767i −0.950628 0.310334i $$-0.899559\pi$$
0.744071 + 0.668101i $$0.232892\pi$$
$$710$$ 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
$$716$$ 26.8328i 1.00279i
$$717$$ 0 0
$$718$$ 10.0000 0.373197
$$719$$ 7.74597 + 13.4164i 0.288876 + 0.500348i 0.973542 0.228509i $$-0.0733852\pi$$
−0.684666 + 0.728857i $$0.740052\pi$$
$$720$$ 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
$$725$$ −19.3649 + 11.1803i −0.719195 + 0.415227i
$$726$$ 0 0
$$727$$ −16.5000 + 9.52628i −0.611951 + 0.353310i −0.773729 0.633517i $$-0.781611\pi$$
0.161778 + 0.986827i $$0.448277\pi$$
$$728$$ −7.74597 6.70820i −0.287085 0.248623i
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 54.2218 2.00546
$$732$$ 0 0
$$733$$ 36.3731i 1.34347i 0.740792 + 0.671735i $$0.234451\pi$$
−0.740792 + 0.671735i $$0.765549\pi$$
$$734$$ −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 −0.996235 0.0866983i $$-0.972368\pi$$
0.573200 + 0.819415i $$0.305702\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 25.0000 8.66025i 0.917779 0.317928i
$$743$$ −27.1109 15.6525i −0.994602 0.574234i −0.0879552 0.996124i $$-0.528033\pi$$
−0.906647 + 0.421891i $$0.861367\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 3.87298 + 2.23607i 0.141800 + 0.0818683i
$$747$$ 0 0
$$748$$ 103.923i 3.79980i
$$749$$ 3.87298 + 11.1803i 0.141516 + 0.408521i
$$750$$ 0 0
$$751$$ −16.0000 −0.583848 −0.291924 0.956441i $$-0.594295\pi$$
−0.291924 + 0.956441i $$0.594295\pi$$
$$752$$ −3.87298 6.70820i −0.141233 0.244623i
$$753$$ 0 0
$$754$$ 15.0000 + 8.66025i 0.546268 + 0.315388i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −25.0000 −0.908640 −0.454320 0.890838i $$-0.650118\pi$$
−0.454320 + 0.890838i $$0.650118\pi$$
$$758$$ 32.9204 + 19.0066i 1.19572 + 0.690350i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$762$$ 0 0
$$763$$ 2.00000 + 1.73205i 0.0724049 + 0.0627044i
$$764$$ 53.6656i 1.94155i
$$765$$ 0 0
$$766$$ −45.0000 25.9808i −1.62592 0.938723i
$$767$$ 13.4164i 0.484438i
$$768$$ 0 0
$$769$$ −30.0000 17.3205i −1.08183 0.624593i −0.150439 0.988619i $$-0.548069\pi$$
−0.931389 + 0.364026i $$0.881402\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −10.5000 + 18.1865i −0.377903 + 0.654548i
$$773$$ 15.4919 26.8328i 0.557206 0.965109i −0.440522 0.897742i $$-0.645207\pi$$
0.997728 0.0673675i $$-0.0214600\pi$$
$$774$$ 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
$$779$$ 26.8328i 0.961385i
$$780$$ 0 0
$$781$$ 40.0000 1.43131
$$782$$ 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
$$787$$ −16.5000 + 9.52628i −0.588161 + 0.339575i −0.764370 0.644778i $$-0.776950\pi$$
0.176209 + 0.984353i $$0.443617\pi$$
$$788$$ 23.2379 13.4164i 0.827816 0.477940i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −15.4919 + 17.8885i −0.550830 + 0.636043i
$$792$$ 0 0
$$793$$ −7.50000 12.9904i −0.266333 0.461302i