Properties

 Label 475.2.e.b.26.1 Level $475$ Weight $2$ Character 475.26 Analytic conductor $3.793$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$475 = 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 475.e (of order $$3$$, degree $$2$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$3.79289409601$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{9}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 95) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

 Embedding label 26.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 475.26 Dual form 475.2.e.b.201.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.00000 - 1.73205i) q^{3} +(1.00000 - 1.73205i) q^{4} +4.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(-1.00000 - 1.73205i) q^{3} +(1.00000 - 1.73205i) q^{4} +4.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +3.00000 q^{11} -4.00000 q^{12} +(1.00000 - 1.73205i) q^{13} +(-2.00000 - 3.46410i) q^{16} +(3.00000 + 5.19615i) q^{17} +(-3.50000 + 2.59808i) q^{19} +(-4.00000 - 6.92820i) q^{21} -4.00000 q^{27} +(4.00000 - 6.92820i) q^{28} +(1.50000 - 2.59808i) q^{29} -7.00000 q^{31} +(-3.00000 - 5.19615i) q^{33} +(1.00000 + 1.73205i) q^{36} -8.00000 q^{37} -4.00000 q^{39} +(3.00000 + 5.19615i) q^{41} +(-2.00000 - 3.46410i) q^{43} +(3.00000 - 5.19615i) q^{44} +(3.00000 - 5.19615i) q^{47} +(-4.00000 + 6.92820i) q^{48} +9.00000 q^{49} +(6.00000 - 10.3923i) q^{51} +(-2.00000 - 3.46410i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(8.00000 + 3.46410i) q^{57} +(7.50000 + 12.9904i) q^{59} +(-2.50000 + 4.33013i) q^{61} +(-2.00000 + 3.46410i) q^{63} -8.00000 q^{64} +(1.00000 - 1.73205i) q^{67} +12.0000 q^{68} +(1.50000 + 2.59808i) q^{71} +(4.00000 + 6.92820i) q^{73} +(1.00000 + 8.66025i) q^{76} +12.0000 q^{77} +(-2.50000 - 4.33013i) q^{79} +(5.50000 + 9.52628i) q^{81} -12.0000 q^{83} -16.0000 q^{84} -6.00000 q^{87} +(7.50000 - 12.9904i) q^{89} +(4.00000 - 6.92820i) q^{91} +(7.00000 + 12.1244i) q^{93} +(4.00000 + 6.92820i) q^{97} +(-1.50000 + 2.59808i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{3} + 2 q^{4} + 8 q^{7} - q^{9}+O(q^{10})$$ 2 * q - 2 * q^3 + 2 * q^4 + 8 * q^7 - q^9 $$2 q - 2 q^{3} + 2 q^{4} + 8 q^{7} - q^{9} + 6 q^{11} - 8 q^{12} + 2 q^{13} - 4 q^{16} + 6 q^{17} - 7 q^{19} - 8 q^{21} - 8 q^{27} + 8 q^{28} + 3 q^{29} - 14 q^{31} - 6 q^{33} + 2 q^{36} - 16 q^{37} - 8 q^{39} + 6 q^{41} - 4 q^{43} + 6 q^{44} + 6 q^{47} - 8 q^{48} + 18 q^{49} + 12 q^{51} - 4 q^{52} - 6 q^{53} + 16 q^{57} + 15 q^{59} - 5 q^{61} - 4 q^{63} - 16 q^{64} + 2 q^{67} + 24 q^{68} + 3 q^{71} + 8 q^{73} + 2 q^{76} + 24 q^{77} - 5 q^{79} + 11 q^{81} - 24 q^{83} - 32 q^{84} - 12 q^{87} + 15 q^{89} + 8 q^{91} + 14 q^{93} + 8 q^{97} - 3 q^{99}+O(q^{100})$$ 2 * q - 2 * q^3 + 2 * q^4 + 8 * q^7 - q^9 + 6 * q^11 - 8 * q^12 + 2 * q^13 - 4 * q^16 + 6 * q^17 - 7 * q^19 - 8 * q^21 - 8 * q^27 + 8 * q^28 + 3 * q^29 - 14 * q^31 - 6 * q^33 + 2 * q^36 - 16 * q^37 - 8 * q^39 + 6 * q^41 - 4 * q^43 + 6 * q^44 + 6 * q^47 - 8 * q^48 + 18 * q^49 + 12 * q^51 - 4 * q^52 - 6 * q^53 + 16 * q^57 + 15 * q^59 - 5 * q^61 - 4 * q^63 - 16 * q^64 + 2 * q^67 + 24 * q^68 + 3 * q^71 + 8 * q^73 + 2 * q^76 + 24 * q^77 - 5 * q^79 + 11 * q^81 - 24 * q^83 - 32 * q^84 - 12 * q^87 + 15 * q^89 + 8 * q^91 + 14 * q^93 + 8 * q^97 - 3 * q^99

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$$.

 $$n$$ $$77$$ $$401$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$3$$ −1.00000 1.73205i −0.577350 1.00000i −0.995782 0.0917517i $$-0.970753\pi$$
0.418432 0.908248i $$-0.362580\pi$$
$$4$$ 1.00000 1.73205i 0.500000 0.866025i
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 4.00000 1.51186 0.755929 0.654654i $$-0.227186\pi$$
0.755929 + 0.654654i $$0.227186\pi$$
$$8$$ 0 0
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ 0 0
$$11$$ 3.00000 0.904534 0.452267 0.891883i $$-0.350615\pi$$
0.452267 + 0.891883i $$0.350615\pi$$
$$12$$ −4.00000 −1.15470
$$13$$ 1.00000 1.73205i 0.277350 0.480384i −0.693375 0.720577i $$-0.743877\pi$$
0.970725 + 0.240192i $$0.0772105\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −2.00000 3.46410i −0.500000 0.866025i
$$17$$ 3.00000 + 5.19615i 0.727607 + 1.26025i 0.957892 + 0.287129i $$0.0927008\pi$$
−0.230285 + 0.973123i $$0.573966\pi$$
$$18$$ 0 0
$$19$$ −3.50000 + 2.59808i −0.802955 + 0.596040i
$$20$$ 0 0
$$21$$ −4.00000 6.92820i −0.872872 1.51186i
$$22$$ 0 0
$$23$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −4.00000 −0.769800
$$28$$ 4.00000 6.92820i 0.755929 1.30931i
$$29$$ 1.50000 2.59808i 0.278543 0.482451i −0.692480 0.721437i $$-0.743482\pi$$
0.971023 + 0.238987i $$0.0768152\pi$$
$$30$$ 0 0
$$31$$ −7.00000 −1.25724 −0.628619 0.777714i $$-0.716379\pi$$
−0.628619 + 0.777714i $$0.716379\pi$$
$$32$$ 0 0
$$33$$ −3.00000 5.19615i −0.522233 0.904534i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 1.00000 + 1.73205i 0.166667 + 0.288675i
$$37$$ −8.00000 −1.31519 −0.657596 0.753371i $$-0.728427\pi$$
−0.657596 + 0.753371i $$0.728427\pi$$
$$38$$ 0 0
$$39$$ −4.00000 −0.640513
$$40$$ 0 0
$$41$$ 3.00000 + 5.19615i 0.468521 + 0.811503i 0.999353 0.0359748i $$-0.0114536\pi$$
−0.530831 + 0.847477i $$0.678120\pi$$
$$42$$ 0 0
$$43$$ −2.00000 3.46410i −0.304997 0.528271i 0.672264 0.740312i $$-0.265322\pi$$
−0.977261 + 0.212041i $$0.931989\pi$$
$$44$$ 3.00000 5.19615i 0.452267 0.783349i
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i $$-0.689164\pi$$
0.997503 + 0.0706177i $$0.0224970\pi$$
$$48$$ −4.00000 + 6.92820i −0.577350 + 1.00000i
$$49$$ 9.00000 1.28571
$$50$$ 0 0
$$51$$ 6.00000 10.3923i 0.840168 1.45521i
$$52$$ −2.00000 3.46410i −0.277350 0.480384i
$$53$$ −3.00000 + 5.19615i −0.412082 + 0.713746i −0.995117 0.0987002i $$-0.968532\pi$$
0.583036 + 0.812447i $$0.301865\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 8.00000 + 3.46410i 1.05963 + 0.458831i
$$58$$ 0 0
$$59$$ 7.50000 + 12.9904i 0.976417 + 1.69120i 0.675178 + 0.737655i $$0.264067\pi$$
0.301239 + 0.953549i $$0.402600\pi$$
$$60$$ 0 0
$$61$$ −2.50000 + 4.33013i −0.320092 + 0.554416i −0.980507 0.196485i $$-0.937047\pi$$
0.660415 + 0.750901i $$0.270381\pi$$
$$62$$ 0 0
$$63$$ −2.00000 + 3.46410i −0.251976 + 0.436436i
$$64$$ −8.00000 −1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 1.00000 1.73205i 0.122169 0.211604i −0.798454 0.602056i $$-0.794348\pi$$
0.920623 + 0.390453i $$0.127682\pi$$
$$68$$ 12.0000 1.45521
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 1.50000 + 2.59808i 0.178017 + 0.308335i 0.941201 0.337846i $$-0.109698\pi$$
−0.763184 + 0.646181i $$0.776365\pi$$
$$72$$ 0 0
$$73$$ 4.00000 + 6.92820i 0.468165 + 0.810885i 0.999338 0.0363782i $$-0.0115821\pi$$
−0.531174 + 0.847263i $$0.678249\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 1.00000 + 8.66025i 0.114708 + 0.993399i
$$77$$ 12.0000 1.36753
$$78$$ 0 0
$$79$$ −2.50000 4.33013i −0.281272 0.487177i 0.690426 0.723403i $$-0.257423\pi$$
−0.971698 + 0.236225i $$0.924090\pi$$
$$80$$ 0 0
$$81$$ 5.50000 + 9.52628i 0.611111 + 1.05848i
$$82$$ 0 0
$$83$$ −12.0000 −1.31717 −0.658586 0.752506i $$-0.728845\pi$$
−0.658586 + 0.752506i $$0.728845\pi$$
$$84$$ −16.0000 −1.74574
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −6.00000 −0.643268
$$88$$ 0 0
$$89$$ 7.50000 12.9904i 0.794998 1.37698i −0.127842 0.991795i $$-0.540805\pi$$
0.922840 0.385183i $$-0.125862\pi$$
$$90$$ 0 0
$$91$$ 4.00000 6.92820i 0.419314 0.726273i
$$92$$ 0 0
$$93$$ 7.00000 + 12.1244i 0.725866 + 1.25724i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 4.00000 + 6.92820i 0.406138 + 0.703452i 0.994453 0.105180i $$-0.0335417\pi$$
−0.588315 + 0.808632i $$0.700208\pi$$
$$98$$ 0 0
$$99$$ −1.50000 + 2.59808i −0.150756 + 0.261116i
$$100$$ 0 0
$$101$$ −7.50000 + 12.9904i −0.746278 + 1.29259i 0.203317 + 0.979113i $$0.434828\pi$$
−0.949595 + 0.313478i $$0.898506\pi$$
$$102$$ 0 0
$$103$$ 16.0000 1.57653 0.788263 0.615338i $$-0.210980\pi$$
0.788263 + 0.615338i $$0.210980\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ −4.00000 + 6.92820i −0.384900 + 0.666667i
$$109$$ −5.50000 9.52628i −0.526804 0.912452i −0.999512 0.0312328i $$-0.990057\pi$$
0.472708 0.881219i $$-0.343277\pi$$
$$110$$ 0 0
$$111$$ 8.00000 + 13.8564i 0.759326 + 1.31519i
$$112$$ −8.00000 13.8564i −0.755929 1.30931i
$$113$$ −6.00000 −0.564433 −0.282216 0.959351i $$-0.591070\pi$$
−0.282216 + 0.959351i $$0.591070\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −3.00000 5.19615i −0.278543 0.482451i
$$117$$ 1.00000 + 1.73205i 0.0924500 + 0.160128i
$$118$$ 0 0
$$119$$ 12.0000 + 20.7846i 1.10004 + 1.90532i
$$120$$ 0 0
$$121$$ −2.00000 −0.181818
$$122$$ 0 0
$$123$$ 6.00000 10.3923i 0.541002 0.937043i
$$124$$ −7.00000 + 12.1244i −0.628619 + 1.08880i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 1.00000 1.73205i 0.0887357 0.153695i −0.818241 0.574875i $$-0.805051\pi$$
0.906977 + 0.421180i $$0.138384\pi$$
$$128$$ 0 0
$$129$$ −4.00000 + 6.92820i −0.352180 + 0.609994i
$$130$$ 0 0
$$131$$ −6.00000 10.3923i −0.524222 0.907980i −0.999602 0.0281993i $$-0.991023\pi$$
0.475380 0.879781i $$-0.342311\pi$$
$$132$$ −12.0000 −1.04447
$$133$$ −14.0000 + 10.3923i −1.21395 + 0.901127i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i $$0.337990\pi$$
−0.999893 + 0.0146279i $$0.995344\pi$$
$$138$$ 0 0
$$139$$ 8.00000 13.8564i 0.678551 1.17529i −0.296866 0.954919i $$-0.595942\pi$$
0.975417 0.220366i $$-0.0707252\pi$$
$$140$$ 0 0
$$141$$ −12.0000 −1.01058
$$142$$ 0 0
$$143$$ 3.00000 5.19615i 0.250873 0.434524i
$$144$$ 4.00000 0.333333
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −9.00000 15.5885i −0.742307 1.28571i
$$148$$ −8.00000 + 13.8564i −0.657596 + 1.13899i
$$149$$ −1.50000 2.59808i −0.122885 0.212843i 0.798019 0.602632i $$-0.205881\pi$$
−0.920904 + 0.389789i $$0.872548\pi$$
$$150$$ 0 0
$$151$$ 17.0000 1.38344 0.691720 0.722166i $$-0.256853\pi$$
0.691720 + 0.722166i $$0.256853\pi$$
$$152$$ 0 0
$$153$$ −6.00000 −0.485071
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −4.00000 + 6.92820i −0.320256 + 0.554700i
$$157$$ 1.00000 + 1.73205i 0.0798087 + 0.138233i 0.903167 0.429289i $$-0.141236\pi$$
−0.823359 + 0.567521i $$0.807902\pi$$
$$158$$ 0 0
$$159$$ 12.0000 0.951662
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 10.0000 0.783260 0.391630 0.920123i $$-0.371911\pi$$
0.391630 + 0.920123i $$0.371911\pi$$
$$164$$ 12.0000 0.937043
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$168$$ 0 0
$$169$$ 4.50000 + 7.79423i 0.346154 + 0.599556i
$$170$$ 0 0
$$171$$ −0.500000 4.33013i −0.0382360 0.331133i
$$172$$ −8.00000 −0.609994
$$173$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −6.00000 10.3923i −0.452267 0.783349i
$$177$$ 15.0000 25.9808i 1.12747 1.95283i
$$178$$ 0 0
$$179$$ −9.00000 −0.672692 −0.336346 0.941739i $$-0.609191\pi$$
−0.336346 + 0.941739i $$0.609191\pi$$
$$180$$ 0 0
$$181$$ −1.00000 + 1.73205i −0.0743294 + 0.128742i −0.900794 0.434246i $$-0.857015\pi$$
0.826465 + 0.562988i $$0.190348\pi$$
$$182$$ 0 0
$$183$$ 10.0000 0.739221
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 9.00000 + 15.5885i 0.658145 + 1.13994i
$$188$$ −6.00000 10.3923i −0.437595 0.757937i
$$189$$ −16.0000 −1.16383
$$190$$ 0 0
$$191$$ −15.0000 −1.08536 −0.542681 0.839939i $$-0.682591\pi$$
−0.542681 + 0.839939i $$0.682591\pi$$
$$192$$ 8.00000 + 13.8564i 0.577350 + 1.00000i
$$193$$ −8.00000 13.8564i −0.575853 0.997406i −0.995948 0.0899262i $$-0.971337\pi$$
0.420096 0.907480i $$-0.361996\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 9.00000 15.5885i 0.642857 1.11346i
$$197$$ 18.0000 1.28245 0.641223 0.767354i $$-0.278427\pi$$
0.641223 + 0.767354i $$0.278427\pi$$
$$198$$ 0 0
$$199$$ 9.50000 16.4545i 0.673437 1.16643i −0.303486 0.952836i $$-0.598151\pi$$
0.976923 0.213591i $$-0.0685161\pi$$
$$200$$ 0 0
$$201$$ −4.00000 −0.282138
$$202$$ 0 0
$$203$$ 6.00000 10.3923i 0.421117 0.729397i
$$204$$ −12.0000 20.7846i −0.840168 1.45521i
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ −8.00000 −0.554700
$$209$$ −10.5000 + 7.79423i −0.726300 + 0.539138i
$$210$$ 0 0
$$211$$ 3.50000 + 6.06218i 0.240950 + 0.417338i 0.960985 0.276600i $$-0.0892077\pi$$
−0.720035 + 0.693938i $$0.755874\pi$$
$$212$$ 6.00000 + 10.3923i 0.412082 + 0.713746i
$$213$$ 3.00000 5.19615i 0.205557 0.356034i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −28.0000 −1.90076
$$218$$ 0 0
$$219$$ 8.00000 13.8564i 0.540590 0.936329i
$$220$$ 0 0
$$221$$ 12.0000 0.807207
$$222$$ 0 0
$$223$$ −2.00000 3.46410i −0.133930 0.231973i 0.791258 0.611482i $$-0.209426\pi$$
−0.925188 + 0.379509i $$0.876093\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 24.0000 1.59294 0.796468 0.604681i $$-0.206699\pi$$
0.796468 + 0.604681i $$0.206699\pi$$
$$228$$ 14.0000 10.3923i 0.927173 0.688247i
$$229$$ −7.00000 −0.462573 −0.231287 0.972886i $$-0.574293\pi$$
−0.231287 + 0.972886i $$0.574293\pi$$
$$230$$ 0 0
$$231$$ −12.0000 20.7846i −0.789542 1.36753i
$$232$$ 0 0
$$233$$ 3.00000 + 5.19615i 0.196537 + 0.340411i 0.947403 0.320043i $$-0.103697\pi$$
−0.750867 + 0.660454i $$0.770364\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 30.0000 1.95283
$$237$$ −5.00000 + 8.66025i −0.324785 + 0.562544i
$$238$$ 0 0
$$239$$ −3.00000 −0.194054 −0.0970269 0.995282i $$-0.530933\pi$$
−0.0970269 + 0.995282i $$0.530933\pi$$
$$240$$ 0 0
$$241$$ −2.50000 + 4.33013i −0.161039 + 0.278928i −0.935242 0.354010i $$-0.884818\pi$$
0.774202 + 0.632938i $$0.218151\pi$$
$$242$$ 0 0
$$243$$ 5.00000 8.66025i 0.320750 0.555556i
$$244$$ 5.00000 + 8.66025i 0.320092 + 0.554416i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 1.00000 + 8.66025i 0.0636285 + 0.551039i
$$248$$ 0 0
$$249$$ 12.0000 + 20.7846i 0.760469 + 1.31717i
$$250$$ 0 0
$$251$$ 7.50000 12.9904i 0.473396 0.819946i −0.526140 0.850398i $$-0.676361\pi$$
0.999536 + 0.0304521i $$0.00969471\pi$$
$$252$$ 4.00000 + 6.92820i 0.251976 + 0.436436i
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −8.00000 + 13.8564i −0.500000 + 0.866025i
$$257$$ −9.00000 + 15.5885i −0.561405 + 0.972381i 0.435970 + 0.899961i $$0.356405\pi$$
−0.997374 + 0.0724199i $$0.976928\pi$$
$$258$$ 0 0
$$259$$ −32.0000 −1.98838
$$260$$ 0 0
$$261$$ 1.50000 + 2.59808i 0.0928477 + 0.160817i
$$262$$ 0 0
$$263$$ −9.00000 15.5885i −0.554964 0.961225i −0.997906 0.0646755i $$-0.979399\pi$$
0.442943 0.896550i $$-0.353935\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −30.0000 −1.83597
$$268$$ −2.00000 3.46410i −0.122169 0.211604i
$$269$$ 10.5000 + 18.1865i 0.640196 + 1.10885i 0.985389 + 0.170321i $$0.0544803\pi$$
−0.345192 + 0.938532i $$0.612186\pi$$
$$270$$ 0 0
$$271$$ −5.50000 9.52628i −0.334101 0.578680i 0.649211 0.760609i $$-0.275099\pi$$
−0.983312 + 0.181928i $$0.941766\pi$$
$$272$$ 12.0000 20.7846i 0.727607 1.26025i
$$273$$ −16.0000 −0.968364
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −8.00000 −0.480673 −0.240337 0.970690i $$-0.577258\pi$$
−0.240337 + 0.970690i $$0.577258\pi$$
$$278$$ 0 0
$$279$$ 3.50000 6.06218i 0.209540 0.362933i
$$280$$ 0 0
$$281$$ −3.00000 + 5.19615i −0.178965 + 0.309976i −0.941526 0.336939i $$-0.890608\pi$$
0.762561 + 0.646916i $$0.223942\pi$$
$$282$$ 0 0
$$283$$ 7.00000 + 12.1244i 0.416107 + 0.720718i 0.995544 0.0942988i $$-0.0300609\pi$$
−0.579437 + 0.815017i $$0.696728\pi$$
$$284$$ 6.00000 0.356034
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 12.0000 + 20.7846i 0.708338 + 1.22688i
$$288$$ 0 0
$$289$$ −9.50000 + 16.4545i −0.558824 + 0.967911i
$$290$$ 0 0
$$291$$ 8.00000 13.8564i 0.468968 0.812277i
$$292$$ 16.0000 0.936329
$$293$$ −24.0000 −1.40209 −0.701047 0.713115i $$-0.747284\pi$$
−0.701047 + 0.713115i $$0.747284\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −12.0000 −0.696311
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −8.00000 13.8564i −0.461112 0.798670i
$$302$$ 0 0
$$303$$ 30.0000 1.72345
$$304$$ 16.0000 + 6.92820i 0.917663 + 0.397360i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −17.0000 29.4449i −0.970241 1.68051i −0.694820 0.719183i $$-0.744516\pi$$
−0.275421 0.961324i $$-0.588817\pi$$
$$308$$ 12.0000 20.7846i 0.683763 1.18431i
$$309$$ −16.0000 27.7128i −0.910208 1.57653i
$$310$$ 0 0
$$311$$ 24.0000 1.36092 0.680458 0.732787i $$-0.261781\pi$$
0.680458 + 0.732787i $$0.261781\pi$$
$$312$$ 0 0
$$313$$ −5.00000 + 8.66025i −0.282617 + 0.489506i −0.972028 0.234863i $$-0.924536\pi$$
0.689412 + 0.724370i $$0.257869\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ −10.0000 −0.562544
$$317$$ 12.0000 20.7846i 0.673987 1.16738i −0.302777 0.953062i $$-0.597914\pi$$
0.976764 0.214318i $$-0.0687530\pi$$
$$318$$ 0 0
$$319$$ 4.50000 7.79423i 0.251952 0.436393i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −24.0000 10.3923i −1.33540 0.578243i
$$324$$ 22.0000 1.22222
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −11.0000 + 19.0526i −0.608301 + 1.05361i
$$328$$ 0 0
$$329$$ 12.0000 20.7846i 0.661581 1.14589i
$$330$$ 0 0
$$331$$ −4.00000 −0.219860 −0.109930 0.993939i $$-0.535063\pi$$
−0.109930 + 0.993939i $$0.535063\pi$$
$$332$$ −12.0000 + 20.7846i −0.658586 + 1.14070i
$$333$$ 4.00000 6.92820i 0.219199 0.379663i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ −16.0000 + 27.7128i −0.872872 + 1.51186i
$$337$$ −8.00000 13.8564i −0.435788 0.754807i 0.561572 0.827428i $$-0.310197\pi$$
−0.997360 + 0.0726214i $$0.976864\pi$$
$$338$$ 0 0
$$339$$ 6.00000 + 10.3923i 0.325875 + 0.564433i
$$340$$ 0 0
$$341$$ −21.0000 −1.13721
$$342$$ 0 0
$$343$$ 8.00000 0.431959
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 6.00000 + 10.3923i 0.322097 + 0.557888i 0.980921 0.194409i $$-0.0622790\pi$$
−0.658824 + 0.752297i $$0.728946\pi$$
$$348$$ −6.00000 + 10.3923i −0.321634 + 0.557086i
$$349$$ 14.0000 0.749403 0.374701 0.927146i $$-0.377745\pi$$
0.374701 + 0.927146i $$0.377745\pi$$
$$350$$ 0 0
$$351$$ −4.00000 + 6.92820i −0.213504 + 0.369800i
$$352$$ 0 0
$$353$$ −12.0000 −0.638696 −0.319348 0.947638i $$-0.603464\pi$$
−0.319348 + 0.947638i $$0.603464\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −15.0000 25.9808i −0.794998 1.37698i
$$357$$ 24.0000 41.5692i 1.27021 2.20008i
$$358$$ 0 0
$$359$$ −12.0000 20.7846i −0.633336 1.09697i −0.986865 0.161546i $$-0.948352\pi$$
0.353529 0.935423i $$-0.384981\pi$$
$$360$$ 0 0
$$361$$ 5.50000 18.1865i 0.289474 0.957186i
$$362$$ 0 0
$$363$$ 2.00000 + 3.46410i 0.104973 + 0.181818i
$$364$$ −8.00000 13.8564i −0.419314 0.726273i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −2.00000 + 3.46410i −0.104399 + 0.180825i −0.913493 0.406855i $$-0.866625\pi$$
0.809093 + 0.587680i $$0.199959\pi$$
$$368$$ 0 0
$$369$$ −6.00000 −0.312348
$$370$$ 0 0
$$371$$ −12.0000 + 20.7846i −0.623009 + 1.07908i
$$372$$ 28.0000 1.45173
$$373$$ 4.00000 0.207112 0.103556 0.994624i $$-0.466978\pi$$
0.103556 + 0.994624i $$0.466978\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −3.00000 5.19615i −0.154508 0.267615i
$$378$$ 0 0
$$379$$ −37.0000 −1.90056 −0.950281 0.311393i $$-0.899204\pi$$
−0.950281 + 0.311393i $$0.899204\pi$$
$$380$$ 0 0
$$381$$ −4.00000 −0.204926
$$382$$ 0 0
$$383$$ 15.0000 + 25.9808i 0.766464 + 1.32755i 0.939469 + 0.342634i $$0.111319\pi$$
−0.173005 + 0.984921i $$0.555348\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 4.00000 0.203331
$$388$$ 16.0000 0.812277
$$389$$ −7.50000 + 12.9904i −0.380265 + 0.658638i −0.991100 0.133120i $$-0.957501\pi$$
0.610835 + 0.791758i $$0.290834\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ −12.0000 + 20.7846i −0.605320 + 1.04844i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 3.00000 + 5.19615i 0.150756 + 0.261116i
$$397$$ 4.00000 + 6.92820i 0.200754 + 0.347717i 0.948772 0.315963i $$-0.102327\pi$$
−0.748017 + 0.663679i $$0.768994\pi$$
$$398$$ 0 0
$$399$$ 32.0000 + 13.8564i 1.60200 + 0.693688i
$$400$$ 0 0
$$401$$ 16.5000 + 28.5788i 0.823971 + 1.42716i 0.902703 + 0.430263i $$0.141579\pi$$
−0.0787327 + 0.996896i $$0.525087\pi$$
$$402$$ 0 0
$$403$$ −7.00000 + 12.1244i −0.348695 + 0.603957i
$$404$$ 15.0000 + 25.9808i 0.746278 + 1.29259i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −24.0000 −1.18964
$$408$$ 0 0
$$409$$ −11.5000 + 19.9186i −0.568638 + 0.984911i 0.428063 + 0.903749i $$0.359196\pi$$
−0.996701 + 0.0811615i $$0.974137\pi$$
$$410$$ 0 0
$$411$$ 24.0000 1.18383
$$412$$ 16.0000 27.7128i 0.788263 1.36531i
$$413$$ 30.0000 + 51.9615i 1.47620 + 2.55686i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −32.0000 −1.56705
$$418$$ 0 0
$$419$$ −3.00000 −0.146560 −0.0732798 0.997311i $$-0.523347\pi$$
−0.0732798 + 0.997311i $$0.523347\pi$$
$$420$$ 0 0
$$421$$ 9.50000 + 16.4545i 0.463002 + 0.801942i 0.999109 0.0422075i $$-0.0134391\pi$$
−0.536107 + 0.844150i $$0.680106\pi$$
$$422$$ 0 0
$$423$$ 3.00000 + 5.19615i 0.145865 + 0.252646i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −10.0000 + 17.3205i −0.483934 + 0.838198i
$$428$$ 0 0
$$429$$ −12.0000 −0.579365
$$430$$ 0 0
$$431$$ 7.50000 12.9904i 0.361262 0.625725i −0.626907 0.779094i $$-0.715679\pi$$
0.988169 + 0.153370i $$0.0490126\pi$$
$$432$$ 8.00000 + 13.8564i 0.384900 + 0.666667i
$$433$$ 4.00000 6.92820i 0.192228 0.332948i −0.753760 0.657149i $$-0.771762\pi$$
0.945988 + 0.324201i $$0.105095\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −22.0000 −1.05361
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 6.50000 + 11.2583i 0.310228 + 0.537331i 0.978412 0.206666i $$-0.0662612\pi$$
−0.668184 + 0.743996i $$0.732928\pi$$
$$440$$ 0 0
$$441$$ −4.50000 + 7.79423i −0.214286 + 0.371154i
$$442$$ 0 0
$$443$$ −6.00000 + 10.3923i −0.285069 + 0.493753i −0.972626 0.232377i $$-0.925350\pi$$
0.687557 + 0.726130i $$0.258683\pi$$
$$444$$ 32.0000 1.51865
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −3.00000 + 5.19615i −0.141895 + 0.245770i
$$448$$ −32.0000 −1.51186
$$449$$ −9.00000 −0.424736 −0.212368 0.977190i $$-0.568118\pi$$
−0.212368 + 0.977190i $$0.568118\pi$$
$$450$$ 0 0
$$451$$ 9.00000 + 15.5885i 0.423793 + 0.734032i
$$452$$ −6.00000 + 10.3923i −0.282216 + 0.488813i
$$453$$ −17.0000 29.4449i −0.798730 1.38344i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 22.0000 1.02912 0.514558 0.857455i $$-0.327956\pi$$
0.514558 + 0.857455i $$0.327956\pi$$
$$458$$ 0 0
$$459$$ −12.0000 20.7846i −0.560112 0.970143i
$$460$$ 0 0
$$461$$ 4.50000 + 7.79423i 0.209586 + 0.363013i 0.951584 0.307388i $$-0.0994551\pi$$
−0.741998 + 0.670402i $$0.766122\pi$$
$$462$$ 0 0
$$463$$ 16.0000 0.743583 0.371792 0.928316i $$-0.378744\pi$$
0.371792 + 0.928316i $$0.378744\pi$$
$$464$$ −12.0000 −0.557086
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$468$$ 4.00000 0.184900
$$469$$ 4.00000 6.92820i 0.184703 0.319915i
$$470$$ 0 0
$$471$$ 2.00000 3.46410i 0.0921551 0.159617i
$$472$$ 0 0
$$473$$ −6.00000 10.3923i −0.275880 0.477839i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 48.0000 2.20008
$$477$$ −3.00000 5.19615i −0.137361 0.237915i
$$478$$ 0 0
$$479$$ −7.50000 + 12.9904i −0.342684 + 0.593546i −0.984930 0.172953i $$-0.944669\pi$$
0.642246 + 0.766498i $$0.278003\pi$$
$$480$$ 0 0
$$481$$ −8.00000 + 13.8564i −0.364769 + 0.631798i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ −2.00000 + 3.46410i −0.0909091 + 0.157459i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −2.00000 −0.0906287 −0.0453143 0.998973i $$-0.514429\pi$$
−0.0453143 + 0.998973i $$0.514429\pi$$
$$488$$ 0 0
$$489$$ −10.0000 17.3205i −0.452216 0.783260i
$$490$$ 0 0
$$491$$ 7.50000 + 12.9904i 0.338470 + 0.586248i 0.984145 0.177365i $$-0.0567572\pi$$
−0.645675 + 0.763612i $$0.723424\pi$$
$$492$$ −12.0000 20.7846i −0.541002 0.937043i
$$493$$ 18.0000 0.810679
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 14.0000 + 24.2487i 0.628619 + 1.08880i
$$497$$ 6.00000 + 10.3923i 0.269137 + 0.466159i
$$498$$ 0 0
$$499$$ −10.0000 17.3205i −0.447661 0.775372i 0.550572 0.834788i $$-0.314410\pi$$
−0.998233 + 0.0594153i $$0.981076\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −21.0000 + 36.3731i −0.936344 + 1.62179i −0.164124 + 0.986440i $$0.552480\pi$$
−0.772220 + 0.635355i $$0.780854\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 9.00000 15.5885i 0.399704 0.692308i
$$508$$ −2.00000 3.46410i −0.0887357 0.153695i
$$509$$ 9.00000 15.5885i 0.398918 0.690946i −0.594675 0.803966i $$-0.702719\pi$$
0.993593 + 0.113020i $$0.0360525\pi$$
$$510$$ 0 0
$$511$$ 16.0000 + 27.7128i 0.707798 + 1.22594i
$$512$$ 0 0
$$513$$ 14.0000 10.3923i 0.618115 0.458831i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 8.00000 + 13.8564i 0.352180 + 0.609994i
$$517$$ 9.00000 15.5885i 0.395820 0.685580i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −45.0000 −1.97149 −0.985743 0.168259i $$-0.946186\pi$$
−0.985743 + 0.168259i $$0.946186\pi$$
$$522$$ 0 0
$$523$$ 13.0000 22.5167i 0.568450 0.984585i −0.428269 0.903651i $$-0.640876\pi$$
0.996719 0.0809336i $$-0.0257902\pi$$
$$524$$ −24.0000 −1.04844
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −21.0000 36.3731i −0.914774 1.58444i
$$528$$ −12.0000 + 20.7846i −0.522233 + 0.904534i
$$529$$ 11.5000 + 19.9186i 0.500000 + 0.866025i
$$530$$ 0 0
$$531$$ −15.0000 −0.650945
$$532$$ 4.00000 + 34.6410i 0.173422 + 1.50188i
$$533$$ 12.0000 0.519778
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 9.00000 + 15.5885i 0.388379 + 0.672692i
$$538$$ 0 0
$$539$$ 27.0000 1.16297
$$540$$ 0 0
$$541$$ 18.5000 32.0429i 0.795377 1.37763i −0.127222 0.991874i $$-0.540606\pi$$
0.922599 0.385759i $$-0.126061\pi$$
$$542$$ 0 0
$$543$$ 4.00000 0.171656
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −2.00000 + 3.46410i −0.0855138 + 0.148114i −0.905610 0.424111i $$-0.860587\pi$$
0.820096 + 0.572226i $$0.193920\pi$$
$$548$$ 12.0000 + 20.7846i 0.512615 + 0.887875i
$$549$$ −2.50000 4.33013i −0.106697 0.184805i
$$550$$ 0 0
$$551$$ 1.50000 + 12.9904i 0.0639021 + 0.553409i
$$552$$ 0 0
$$553$$ −10.0000 17.3205i −0.425243 0.736543i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −16.0000 27.7128i −0.678551 1.17529i
$$557$$ 6.00000 10.3923i 0.254228 0.440336i −0.710457 0.703740i $$-0.751512\pi$$
0.964686 + 0.263404i $$0.0848453\pi$$
$$558$$ 0 0
$$559$$ −8.00000 −0.338364
$$560$$ 0 0
$$561$$ 18.0000 31.1769i 0.759961 1.31629i
$$562$$ 0 0
$$563$$ −6.00000 −0.252870 −0.126435 0.991975i $$-0.540353\pi$$
−0.126435 + 0.991975i $$0.540353\pi$$
$$564$$ −12.0000 + 20.7846i −0.505291 + 0.875190i
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 22.0000 + 38.1051i 0.923913 + 1.60026i
$$568$$ 0 0
$$569$$ 39.0000 1.63497 0.817483 0.575953i $$-0.195369\pi$$
0.817483 + 0.575953i $$0.195369\pi$$
$$570$$ 0 0
$$571$$ −7.00000 −0.292941 −0.146470 0.989215i $$-0.546791\pi$$
−0.146470 + 0.989215i $$0.546791\pi$$
$$572$$ −6.00000 10.3923i −0.250873 0.434524i
$$573$$ 15.0000 + 25.9808i 0.626634 + 1.08536i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 4.00000 6.92820i 0.166667 0.288675i
$$577$$ 16.0000 0.666089 0.333044 0.942911i $$-0.391924\pi$$
0.333044 + 0.942911i $$0.391924\pi$$
$$578$$ 0 0
$$579$$ −16.0000 + 27.7128i −0.664937 + 1.15171i
$$580$$ 0 0
$$581$$ −48.0000 −1.99138
$$582$$ 0 0
$$583$$ −9.00000 + 15.5885i −0.372742 + 0.645608i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −18.0000 31.1769i −0.742940 1.28681i −0.951151 0.308725i $$-0.900098\pi$$
0.208212 0.978084i $$-0.433236\pi$$
$$588$$ −36.0000 −1.48461
$$589$$ 24.5000 18.1865i 1.00950 0.749363i
$$590$$ 0 0
$$591$$ −18.0000 31.1769i −0.740421 1.28245i
$$592$$ 16.0000 + 27.7128i 0.657596 + 1.13899i
$$593$$ 6.00000 10.3923i 0.246390 0.426761i −0.716131 0.697966i $$-0.754089\pi$$
0.962522 + 0.271205i $$0.0874221\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −6.00000 −0.245770
$$597$$ −38.0000 −1.55524
$$598$$ 0 0
$$599$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$600$$ 0 0
$$601$$ −31.0000 −1.26452 −0.632258 0.774758i $$-0.717872\pi$$
−0.632258 + 0.774758i $$0.717872\pi$$
$$602$$ 0 0
$$603$$ 1.00000 + 1.73205i 0.0407231 + 0.0705346i
$$604$$ 17.0000 29.4449i 0.691720 1.19809i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −2.00000 −0.0811775 −0.0405887 0.999176i $$-0.512923\pi$$
−0.0405887 + 0.999176i $$0.512923\pi$$
$$608$$ 0 0
$$609$$ −24.0000 −0.972529
$$610$$ 0 0
$$611$$ −6.00000 10.3923i −0.242734 0.420428i
$$612$$ −6.00000 + 10.3923i −0.242536 + 0.420084i
$$613$$ 1.00000 + 1.73205i 0.0403896 + 0.0699569i 0.885514 0.464614i $$-0.153807\pi$$
−0.845124 + 0.534570i $$0.820473\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 18.0000 31.1769i 0.724653 1.25514i −0.234464 0.972125i $$-0.575334\pi$$
0.959117 0.283011i $$-0.0913331\pi$$
$$618$$ 0 0
$$619$$ −4.00000 −0.160774 −0.0803868 0.996764i $$-0.525616\pi$$
−0.0803868 + 0.996764i $$0.525616\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 30.0000 51.9615i 1.20192 2.08179i
$$624$$ 8.00000 + 13.8564i 0.320256 + 0.554700i
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 24.0000 + 10.3923i 0.958468 + 0.415029i
$$628$$ 4.00000 0.159617
$$629$$ −24.0000 41.5692i −0.956943 1.65747i
$$630$$ 0 0
$$631$$ 9.50000 16.4545i 0.378189 0.655043i −0.612610 0.790386i $$-0.709880\pi$$
0.990799 + 0.135343i $$0.0432136\pi$$
$$632$$ 0 0
$$633$$ 7.00000 12.1244i 0.278225 0.481900i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 12.0000 20.7846i 0.475831 0.824163i
$$637$$ 9.00000 15.5885i 0.356593 0.617637i
$$638$$ 0 0
$$639$$ −3.00000 −0.118678
$$640$$ 0 0
$$641$$ −4.50000 7.79423i −0.177739 0.307854i 0.763367 0.645966i $$-0.223545\pi$$
−0.941106 + 0.338112i $$0.890212\pi$$
$$642$$ 0 0
$$643$$ −17.0000 29.4449i −0.670415 1.16119i −0.977787 0.209603i $$-0.932783\pi$$
0.307372 0.951589i $$-0.400550\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −18.0000 −0.707653 −0.353827 0.935311i $$-0.615120\pi$$
−0.353827 + 0.935311i $$0.615120\pi$$
$$648$$ 0 0
$$649$$ 22.5000 + 38.9711i 0.883202 + 1.52975i
$$650$$ 0 0
$$651$$ 28.0000 + 48.4974i 1.09741 + 1.90076i
$$652$$ 10.0000 17.3205i 0.391630 0.678323i
$$653$$ −24.0000 −0.939193 −0.469596 0.882881i $$-0.655601\pi$$
−0.469596 + 0.882881i $$0.655601\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 12.0000 20.7846i 0.468521 0.811503i
$$657$$ −8.00000 −0.312110
$$658$$ 0 0
$$659$$ 6.00000 10.3923i 0.233727 0.404827i −0.725175 0.688565i $$-0.758241\pi$$
0.958902 + 0.283738i $$0.0915745\pi$$
$$660$$ 0 0
$$661$$ −2.50000 + 4.33013i −0.0972387 + 0.168422i −0.910541 0.413419i $$-0.864334\pi$$
0.813302 + 0.581842i $$0.197668\pi$$
$$662$$ 0 0
$$663$$ −12.0000 20.7846i −0.466041 0.807207i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ −4.00000 + 6.92820i −0.154649 + 0.267860i
$$670$$ 0 0
$$671$$ −7.50000 + 12.9904i −0.289534 + 0.501488i
$$672$$ 0 0
$$673$$ 4.00000 0.154189 0.0770943 0.997024i $$-0.475436\pi$$
0.0770943 + 0.997024i $$0.475436\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 18.0000 0.692308
$$677$$ −48.0000 −1.84479 −0.922395 0.386248i $$-0.873771\pi$$
−0.922395 + 0.386248i $$0.873771\pi$$
$$678$$ 0 0
$$679$$ 16.0000 + 27.7128i 0.614024 + 1.06352i
$$680$$ 0 0
$$681$$ −24.0000 41.5692i −0.919682 1.59294i
$$682$$ 0 0
$$683$$ 18.0000 0.688751 0.344375 0.938832i $$-0.388091\pi$$
0.344375 + 0.938832i $$0.388091\pi$$
$$684$$ −8.00000 3.46410i −0.305888 0.132453i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 7.00000 + 12.1244i 0.267067 + 0.462573i
$$688$$ −8.00000 + 13.8564i −0.304997 + 0.528271i
$$689$$ 6.00000 + 10.3923i 0.228582 + 0.395915i
$$690$$ 0 0
$$691$$ −37.0000 −1.40755 −0.703773 0.710425i $$-0.748503\pi$$
−0.703773 + 0.710425i $$0.748503\pi$$
$$692$$ 0 0
$$693$$ −6.00000 + 10.3923i −0.227921 + 0.394771i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −18.0000 + 31.1769i −0.681799 + 1.18091i
$$698$$ 0 0
$$699$$ 6.00000 10.3923i 0.226941 0.393073i
$$700$$ 0 0
$$701$$ −3.00000 5.19615i −0.113308 0.196256i 0.803794 0.594908i $$-0.202811\pi$$
−0.917102 + 0.398652i $$0.869478\pi$$
$$702$$ 0 0
$$703$$ 28.0000 20.7846i 1.05604 0.783906i
$$704$$ −24.0000 −0.904534
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −30.0000 + 51.9615i −1.12827 + 1.95421i
$$708$$ −30.0000 51.9615i −1.12747 1.95283i
$$709$$ 15.5000 26.8468i 0.582115 1.00825i −0.413114 0.910679i $$-0.635559\pi$$
0.995228 0.0975728i $$-0.0311079\pi$$
$$710$$ 0 0
$$711$$ 5.00000 0.187515
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −9.00000 + 15.5885i −0.336346 + 0.582568i
$$717$$ 3.00000 + 5.19615i 0.112037 + 0.194054i
$$718$$ 0 0
$$719$$ −7.50000 12.9904i −0.279703 0.484459i 0.691608 0.722273i $$-0.256903\pi$$
−0.971311 + 0.237814i $$0.923569\pi$$
$$720$$ 0 0
$$721$$ 64.0000 2.38348
$$722$$ 0 0
$$723$$ 10.0000 0.371904
$$724$$ 2.00000 + 3.46410i 0.0743294 + 0.128742i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 7.00000 + 12.1244i 0.259616 + 0.449667i 0.966139 0.258022i $$-0.0830708\pi$$
−0.706523 + 0.707690i $$0.749737\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ 12.0000 20.7846i 0.443836 0.768747i
$$732$$ 10.0000 17.3205i 0.369611 0.640184i
$$733$$ −32.0000 −1.18195 −0.590973 0.806691i $$-0.701256\pi$$
−0.590973 + 0.806691i $$0.701256\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 3.00000 5.19615i 0.110506 0.191403i
$$738$$ 0 0
$$739$$ −17.5000 30.3109i −0.643748 1.11500i −0.984589 0.174883i $$-0.944045\pi$$
0.340841 0.940121i $$-0.389288\pi$$
$$740$$ 0 0
$$741$$ 14.0000 10.3923i 0.514303 0.381771i
$$742$$ 0 0
$$743$$ −12.0000 20.7846i −0.440237 0.762513i 0.557470 0.830197i $$-0.311772\pi$$
−0.997707 + 0.0676840i $$0.978439\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 6.00000 10.3923i 0.219529 0.380235i
$$748$$ 36.0000 1.31629
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 3.50000 6.06218i 0.127717 0.221212i −0.795075 0.606511i $$-0.792568\pi$$
0.922792 + 0.385299i $$0.125902\pi$$
$$752$$ −24.0000 −0.875190
$$753$$ −30.0000 −1.09326
$$754$$ 0 0
$$755$$ 0 0
$$756$$ −16.0000 + 27.7128i −0.581914 + 1.00791i
$$757$$ −5.00000 8.66025i −0.181728 0.314762i 0.760741 0.649056i $$-0.224836\pi$$
−0.942469 + 0.334293i $$0.891502\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 6.00000 0.217500 0.108750 0.994069i $$-0.465315\pi$$
0.108750 + 0.994069i $$0.465315\pi$$
$$762$$ 0 0
$$763$$ −22.0000 38.1051i −0.796453 1.37950i
$$764$$ −15.0000 + 25.9808i −0.542681 + 0.939951i
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 30.0000 1.08324
$$768$$ 32.0000 1.15470
$$769$$ −14.5000 + 25.1147i −0.522883 + 0.905661i 0.476762 + 0.879032i $$0.341810\pi$$
−0.999645 + 0.0266282i $$0.991523\pi$$
$$770$$ 0 0
$$771$$ 36.0000 1.29651
$$772$$ −32.0000 −1.15171
$$773$$ 15.0000 25.9808i 0.539513 0.934463i −0.459418 0.888220i $$-0.651942\pi$$
0.998930 0.0462427i $$-0.0147248\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 32.0000 + 55.4256i 1.14799 + 1.98838i
$$778$$ 0 0
$$779$$ −24.0000 10.3923i −0.859889 0.372343i
$$780$$ 0 0
$$781$$ 4.50000 + 7.79423i 0.161023 + 0.278899i
$$782$$ 0 0
$$783$$ −6.00000 + 10.3923i −0.214423 + 0.371391i
$$784$$ −18.0000 31.1769i −0.642857 1.11346i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 34.0000 1.21197 0.605985 0.795476i $$-0.292779\pi$$
0.605985 + 0.795476i $$0.292779\pi$$
$$788$$ 18.0000 31.1769i 0.641223 1.11063i
$$789$$ −18.0000 + 31.1769i −0.640817 + 1.10993i
$$790$$ 0 0
$$791$$ −24.0000 −0.853342
$$792$$ 0 0
$$793$$ 5.00000 + 8.66025i 0.177555 + 0.307535i