# Properties

 Label 810.2.e.b.271.1 Level $810$ Weight $2$ Character 810.271 Analytic conductor $6.468$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$810 = 2 \cdot 3^{4} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 810.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.46788256372$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 30) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 271.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 810.271 Dual form 810.2.e.b.541.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +1.00000 q^{10} +(-1.00000 + 1.73205i) q^{13} +(2.00000 - 3.46410i) q^{14} +(-0.500000 - 0.866025i) q^{16} -6.00000 q^{17} -4.00000 q^{19} +(-0.500000 - 0.866025i) q^{20} +(-0.500000 - 0.866025i) q^{25} +2.00000 q^{26} -4.00000 q^{28} +(-3.00000 - 5.19615i) q^{29} +(-4.00000 + 6.92820i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{34} -4.00000 q^{35} +2.00000 q^{37} +(2.00000 + 3.46410i) q^{38} +(-0.500000 + 0.866025i) q^{40} +(-3.00000 + 5.19615i) q^{41} +(2.00000 + 3.46410i) q^{43} +(-4.50000 + 7.79423i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-1.00000 - 1.73205i) q^{52} +6.00000 q^{53} +(2.00000 + 3.46410i) q^{56} +(-3.00000 + 5.19615i) q^{58} +(5.00000 + 8.66025i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(-1.00000 - 1.73205i) q^{65} +(2.00000 - 3.46410i) q^{67} +(3.00000 - 5.19615i) q^{68} +(2.00000 + 3.46410i) q^{70} +2.00000 q^{73} +(-1.00000 - 1.73205i) q^{74} +(2.00000 - 3.46410i) q^{76} +(-4.00000 - 6.92820i) q^{79} +1.00000 q^{80} +6.00000 q^{82} +(6.00000 + 10.3923i) q^{83} +(3.00000 - 5.19615i) q^{85} +(2.00000 - 3.46410i) q^{86} -18.0000 q^{89} -8.00000 q^{91} +(2.00000 - 3.46410i) q^{95} +(-1.00000 - 1.73205i) q^{97} +9.00000 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{2} - q^{4} - q^{5} + 4q^{7} + 2q^{8} + O(q^{10})$$ $$2q - q^{2} - q^{4} - q^{5} + 4q^{7} + 2q^{8} + 2q^{10} - 2q^{13} + 4q^{14} - q^{16} - 12q^{17} - 8q^{19} - q^{20} - q^{25} + 4q^{26} - 8q^{28} - 6q^{29} - 8q^{31} - q^{32} + 6q^{34} - 8q^{35} + 4q^{37} + 4q^{38} - q^{40} - 6q^{41} + 4q^{43} - 9q^{49} - q^{50} - 2q^{52} + 12q^{53} + 4q^{56} - 6q^{58} + 10q^{61} + 16q^{62} + 2q^{64} - 2q^{65} + 4q^{67} + 6q^{68} + 4q^{70} + 4q^{73} - 2q^{74} + 4q^{76} - 8q^{79} + 2q^{80} + 12q^{82} + 12q^{83} + 6q^{85} + 4q^{86} - 36q^{89} - 16q^{91} + 4q^{95} - 2q^{97} + 18q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$$.

 $$n$$ $$487$$ $$731$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 0.866025i −0.353553 0.612372i
$$3$$ 0 0
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ −0.500000 + 0.866025i −0.223607 + 0.387298i
$$6$$ 0 0
$$7$$ 2.00000 + 3.46410i 0.755929 + 1.30931i 0.944911 + 0.327327i $$0.106148\pi$$
−0.188982 + 0.981981i $$0.560519\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ 1.00000 0.316228
$$11$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$12$$ 0 0
$$13$$ −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i $$-0.922790\pi$$
0.693375 + 0.720577i $$0.256123\pi$$
$$14$$ 2.00000 3.46410i 0.534522 0.925820i
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −6.00000 −1.45521 −0.727607 0.685994i $$-0.759367\pi$$
−0.727607 + 0.685994i $$0.759367\pi$$
$$18$$ 0 0
$$19$$ −4.00000 −0.917663 −0.458831 0.888523i $$-0.651732\pi$$
−0.458831 + 0.888523i $$0.651732\pi$$
$$20$$ −0.500000 0.866025i −0.111803 0.193649i
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$24$$ 0 0
$$25$$ −0.500000 0.866025i −0.100000 0.173205i
$$26$$ 2.00000 0.392232
$$27$$ 0 0
$$28$$ −4.00000 −0.755929
$$29$$ −3.00000 5.19615i −0.557086 0.964901i −0.997738 0.0672232i $$-0.978586\pi$$
0.440652 0.897678i $$-0.354747\pi$$
$$30$$ 0 0
$$31$$ −4.00000 + 6.92820i −0.718421 + 1.24434i 0.243204 + 0.969975i $$0.421802\pi$$
−0.961625 + 0.274367i $$0.911532\pi$$
$$32$$ −0.500000 + 0.866025i −0.0883883 + 0.153093i
$$33$$ 0 0
$$34$$ 3.00000 + 5.19615i 0.514496 + 0.891133i
$$35$$ −4.00000 −0.676123
$$36$$ 0 0
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ 2.00000 + 3.46410i 0.324443 + 0.561951i
$$39$$ 0 0
$$40$$ −0.500000 + 0.866025i −0.0790569 + 0.136931i
$$41$$ −3.00000 + 5.19615i −0.468521 + 0.811503i −0.999353 0.0359748i $$-0.988546\pi$$
0.530831 + 0.847477i $$0.321880\pi$$
$$42$$ 0 0
$$43$$ 2.00000 + 3.46410i 0.304997 + 0.528271i 0.977261 0.212041i $$-0.0680112\pi$$
−0.672264 + 0.740312i $$0.734678\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$48$$ 0 0
$$49$$ −4.50000 + 7.79423i −0.642857 + 1.11346i
$$50$$ −0.500000 + 0.866025i −0.0707107 + 0.122474i
$$51$$ 0 0
$$52$$ −1.00000 1.73205i −0.138675 0.240192i
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 2.00000 + 3.46410i 0.267261 + 0.462910i
$$57$$ 0 0
$$58$$ −3.00000 + 5.19615i −0.393919 + 0.682288i
$$59$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$60$$ 0 0
$$61$$ 5.00000 + 8.66025i 0.640184 + 1.10883i 0.985391 + 0.170305i $$0.0544754\pi$$
−0.345207 + 0.938527i $$0.612191\pi$$
$$62$$ 8.00000 1.01600
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −1.00000 1.73205i −0.124035 0.214834i
$$66$$ 0 0
$$67$$ 2.00000 3.46410i 0.244339 0.423207i −0.717607 0.696449i $$-0.754762\pi$$
0.961946 + 0.273241i $$0.0880957\pi$$
$$68$$ 3.00000 5.19615i 0.363803 0.630126i
$$69$$ 0 0
$$70$$ 2.00000 + 3.46410i 0.239046 + 0.414039i
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ 2.00000 0.234082 0.117041 0.993127i $$-0.462659\pi$$
0.117041 + 0.993127i $$0.462659\pi$$
$$74$$ −1.00000 1.73205i −0.116248 0.201347i
$$75$$ 0 0
$$76$$ 2.00000 3.46410i 0.229416 0.397360i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −4.00000 6.92820i −0.450035 0.779484i 0.548352 0.836247i $$-0.315255\pi$$
−0.998388 + 0.0567635i $$0.981922\pi$$
$$80$$ 1.00000 0.111803
$$81$$ 0 0
$$82$$ 6.00000 0.662589
$$83$$ 6.00000 + 10.3923i 0.658586 + 1.14070i 0.980982 + 0.194099i $$0.0621783\pi$$
−0.322396 + 0.946605i $$0.604488\pi$$
$$84$$ 0 0
$$85$$ 3.00000 5.19615i 0.325396 0.563602i
$$86$$ 2.00000 3.46410i 0.215666 0.373544i
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −18.0000 −1.90800 −0.953998 0.299813i $$-0.903076\pi$$
−0.953998 + 0.299813i $$0.903076\pi$$
$$90$$ 0 0
$$91$$ −8.00000 −0.838628
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 2.00000 3.46410i 0.205196 0.355409i
$$96$$ 0 0
$$97$$ −1.00000 1.73205i −0.101535 0.175863i 0.810782 0.585348i $$-0.199042\pi$$
−0.912317 + 0.409484i $$0.865709\pi$$
$$98$$ 9.00000 0.909137
$$99$$ 0 0
$$100$$ 1.00000 0.100000
$$101$$ 9.00000 + 15.5885i 0.895533 + 1.55111i 0.833143 + 0.553058i $$0.186539\pi$$
0.0623905 + 0.998052i $$0.480128\pi$$
$$102$$ 0 0
$$103$$ 2.00000 3.46410i 0.197066 0.341328i −0.750510 0.660859i $$-0.770192\pi$$
0.947576 + 0.319531i $$0.103525\pi$$
$$104$$ −1.00000 + 1.73205i −0.0980581 + 0.169842i
$$105$$ 0 0
$$106$$ −3.00000 5.19615i −0.291386 0.504695i
$$107$$ 12.0000 1.16008 0.580042 0.814587i $$-0.303036\pi$$
0.580042 + 0.814587i $$0.303036\pi$$
$$108$$ 0 0
$$109$$ −10.0000 −0.957826 −0.478913 0.877862i $$-0.658969\pi$$
−0.478913 + 0.877862i $$0.658969\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 2.00000 3.46410i 0.188982 0.327327i
$$113$$ −9.00000 + 15.5885i −0.846649 + 1.46644i 0.0375328 + 0.999295i $$0.488050\pi$$
−0.884182 + 0.467143i $$0.845283\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 6.00000 0.557086
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −12.0000 20.7846i −1.10004 1.90532i
$$120$$ 0 0
$$121$$ 5.50000 9.52628i 0.500000 0.866025i
$$122$$ 5.00000 8.66025i 0.452679 0.784063i
$$123$$ 0 0
$$124$$ −4.00000 6.92820i −0.359211 0.622171i
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ 20.0000 1.77471 0.887357 0.461084i $$-0.152539\pi$$
0.887357 + 0.461084i $$0.152539\pi$$
$$128$$ −0.500000 0.866025i −0.0441942 0.0765466i
$$129$$ 0 0
$$130$$ −1.00000 + 1.73205i −0.0877058 + 0.151911i
$$131$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$132$$ 0 0
$$133$$ −8.00000 13.8564i −0.693688 1.20150i
$$134$$ −4.00000 −0.345547
$$135$$ 0 0
$$136$$ −6.00000 −0.514496
$$137$$ 3.00000 + 5.19615i 0.256307 + 0.443937i 0.965250 0.261329i $$-0.0841608\pi$$
−0.708942 + 0.705266i $$0.750827\pi$$
$$138$$ 0 0
$$139$$ 2.00000 3.46410i 0.169638 0.293821i −0.768655 0.639664i $$-0.779074\pi$$
0.938293 + 0.345843i $$0.112407\pi$$
$$140$$ 2.00000 3.46410i 0.169031 0.292770i
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 6.00000 0.498273
$$146$$ −1.00000 1.73205i −0.0827606 0.143346i
$$147$$ 0 0
$$148$$ −1.00000 + 1.73205i −0.0821995 + 0.142374i
$$149$$ −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i $$-0.912374\pi$$
0.716578 + 0.697507i $$0.245707\pi$$
$$150$$ 0 0
$$151$$ −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i $$-0.272204\pi$$
−0.981617 + 0.190864i $$0.938871\pi$$
$$152$$ −4.00000 −0.324443
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −4.00000 6.92820i −0.321288 0.556487i
$$156$$ 0 0
$$157$$ −1.00000 + 1.73205i −0.0798087 + 0.138233i −0.903167 0.429289i $$-0.858764\pi$$
0.823359 + 0.567521i $$0.192098\pi$$
$$158$$ −4.00000 + 6.92820i −0.318223 + 0.551178i
$$159$$ 0 0
$$160$$ −0.500000 0.866025i −0.0395285 0.0684653i
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −4.00000 −0.313304 −0.156652 0.987654i $$-0.550070\pi$$
−0.156652 + 0.987654i $$0.550070\pi$$
$$164$$ −3.00000 5.19615i −0.234261 0.405751i
$$165$$ 0 0
$$166$$ 6.00000 10.3923i 0.465690 0.806599i
$$167$$ 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
$$170$$ −6.00000 −0.460179
$$171$$ 0 0
$$172$$ −4.00000 −0.304997
$$173$$ 9.00000 + 15.5885i 0.684257 + 1.18517i 0.973670 + 0.227964i $$0.0732068\pi$$
−0.289412 + 0.957205i $$0.593460\pi$$
$$174$$ 0 0
$$175$$ 2.00000 3.46410i 0.151186 0.261861i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 9.00000 + 15.5885i 0.674579 + 1.16840i
$$179$$ −24.0000 −1.79384 −0.896922 0.442189i $$-0.854202\pi$$
−0.896922 + 0.442189i $$0.854202\pi$$
$$180$$ 0 0
$$181$$ 14.0000 1.04061 0.520306 0.853980i $$-0.325818\pi$$
0.520306 + 0.853980i $$0.325818\pi$$
$$182$$ 4.00000 + 6.92820i 0.296500 + 0.513553i
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −1.00000 + 1.73205i −0.0735215 + 0.127343i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ −4.00000 −0.290191
$$191$$ −12.0000 20.7846i −0.868290 1.50392i −0.863743 0.503932i $$-0.831886\pi$$
−0.00454614 0.999990i $$-0.501447\pi$$
$$192$$ 0 0
$$193$$ 11.0000 19.0526i 0.791797 1.37143i −0.133056 0.991109i $$-0.542479\pi$$
0.924853 0.380325i $$-0.124188\pi$$
$$194$$ −1.00000 + 1.73205i −0.0717958 + 0.124354i
$$195$$ 0 0
$$196$$ −4.50000 7.79423i −0.321429 0.556731i
$$197$$ 6.00000 0.427482 0.213741 0.976890i $$-0.431435\pi$$
0.213741 + 0.976890i $$0.431435\pi$$
$$198$$ 0 0
$$199$$ 8.00000 0.567105 0.283552 0.958957i $$-0.408487\pi$$
0.283552 + 0.958957i $$0.408487\pi$$
$$200$$ −0.500000 0.866025i −0.0353553 0.0612372i
$$201$$ 0 0
$$202$$ 9.00000 15.5885i 0.633238 1.09680i
$$203$$ 12.0000 20.7846i 0.842235 1.45879i
$$204$$ 0 0
$$205$$ −3.00000 5.19615i −0.209529 0.362915i
$$206$$ −4.00000 −0.278693
$$207$$ 0 0
$$208$$ 2.00000 0.138675
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −10.0000 + 17.3205i −0.688428 + 1.19239i 0.283918 + 0.958849i $$0.408366\pi$$
−0.972346 + 0.233544i $$0.924968\pi$$
$$212$$ −3.00000 + 5.19615i −0.206041 + 0.356873i
$$213$$ 0 0
$$214$$ −6.00000 10.3923i −0.410152 0.710403i
$$215$$ −4.00000 −0.272798
$$216$$ 0 0
$$217$$ −32.0000 −2.17230
$$218$$ 5.00000 + 8.66025i 0.338643 + 0.586546i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 6.00000 10.3923i 0.403604 0.699062i
$$222$$ 0 0
$$223$$ −10.0000 17.3205i −0.669650 1.15987i −0.978002 0.208595i $$-0.933111\pi$$
0.308353 0.951272i $$-0.400222\pi$$
$$224$$ −4.00000 −0.267261
$$225$$ 0 0
$$226$$ 18.0000 1.19734
$$227$$ −6.00000 10.3923i −0.398234 0.689761i 0.595274 0.803523i $$-0.297043\pi$$
−0.993508 + 0.113761i $$0.963710\pi$$
$$228$$ 0 0
$$229$$ 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i $$-0.726147\pi$$
0.982592 + 0.185776i $$0.0594799\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −3.00000 5.19615i −0.196960 0.341144i
$$233$$ 18.0000 1.17922 0.589610 0.807688i $$-0.299282\pi$$
0.589610 + 0.807688i $$0.299282\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ −12.0000 + 20.7846i −0.777844 + 1.34727i
$$239$$ 12.0000 20.7846i 0.776215 1.34444i −0.157893 0.987456i $$-0.550470\pi$$
0.934109 0.356988i $$-0.116196\pi$$
$$240$$ 0 0
$$241$$ −1.00000 1.73205i −0.0644157 0.111571i 0.832019 0.554747i $$-0.187185\pi$$
−0.896435 + 0.443176i $$0.853852\pi$$
$$242$$ −11.0000 −0.707107
$$243$$ 0 0
$$244$$ −10.0000 −0.640184
$$245$$ −4.50000 7.79423i −0.287494 0.497955i
$$246$$ 0 0
$$247$$ 4.00000 6.92820i 0.254514 0.440831i
$$248$$ −4.00000 + 6.92820i −0.254000 + 0.439941i
$$249$$ 0 0
$$250$$ −0.500000 0.866025i −0.0316228 0.0547723i
$$251$$ 24.0000 1.51487 0.757433 0.652913i $$-0.226453\pi$$
0.757433 + 0.652913i $$0.226453\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ −10.0000 17.3205i −0.627456 1.08679i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −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
$$259$$ 4.00000 + 6.92820i 0.248548 + 0.430498i
$$260$$ 2.00000 0.124035
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$264$$ 0 0
$$265$$ −3.00000 + 5.19615i −0.184289 + 0.319197i
$$266$$ −8.00000 + 13.8564i −0.490511 + 0.849591i
$$267$$ 0 0
$$268$$ 2.00000 + 3.46410i 0.122169 + 0.211604i
$$269$$ 6.00000 0.365826 0.182913 0.983129i $$-0.441447\pi$$
0.182913 + 0.983129i $$0.441447\pi$$
$$270$$ 0 0
$$271$$ −16.0000 −0.971931 −0.485965 0.873978i $$-0.661532\pi$$
−0.485965 + 0.873978i $$0.661532\pi$$
$$272$$ 3.00000 + 5.19615i 0.181902 + 0.315063i
$$273$$ 0 0
$$274$$ 3.00000 5.19615i 0.181237 0.313911i
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −1.00000 1.73205i −0.0600842 0.104069i 0.834419 0.551131i $$-0.185804\pi$$
−0.894503 + 0.447062i $$0.852470\pi$$
$$278$$ −4.00000 −0.239904
$$279$$ 0 0
$$280$$ −4.00000 −0.239046
$$281$$ 9.00000 + 15.5885i 0.536895 + 0.929929i 0.999069 + 0.0431402i $$0.0137362\pi$$
−0.462174 + 0.886789i $$0.652930\pi$$
$$282$$ 0 0
$$283$$ 14.0000 24.2487i 0.832214 1.44144i −0.0640654 0.997946i $$-0.520407\pi$$
0.896279 0.443491i $$-0.146260\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −24.0000 −1.41668
$$288$$ 0 0
$$289$$ 19.0000 1.11765
$$290$$ −3.00000 5.19615i −0.176166 0.305129i
$$291$$ 0 0
$$292$$ −1.00000 + 1.73205i −0.0585206 + 0.101361i
$$293$$ −3.00000 + 5.19615i −0.175262 + 0.303562i −0.940252 0.340480i $$-0.889411\pi$$
0.764990 + 0.644042i $$0.222744\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 2.00000 0.116248
$$297$$ 0 0
$$298$$ 6.00000 0.347571
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −8.00000 + 13.8564i −0.461112 + 0.798670i
$$302$$ −4.00000 + 6.92820i −0.230174 + 0.398673i
$$303$$ 0 0
$$304$$ 2.00000 + 3.46410i 0.114708 + 0.198680i
$$305$$ −10.0000 −0.572598
$$306$$ 0 0
$$307$$ 20.0000 1.14146 0.570730 0.821138i $$-0.306660\pi$$
0.570730 + 0.821138i $$0.306660\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ −4.00000 + 6.92820i −0.227185 + 0.393496i
$$311$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$312$$ 0 0
$$313$$ −1.00000 1.73205i −0.0565233 0.0979013i 0.836379 0.548151i $$-0.184668\pi$$
−0.892903 + 0.450250i $$0.851335\pi$$
$$314$$ 2.00000 0.112867
$$315$$ 0 0
$$316$$ 8.00000 0.450035
$$317$$ 9.00000 + 15.5885i 0.505490 + 0.875535i 0.999980 + 0.00635137i $$0.00202172\pi$$
−0.494489 + 0.869184i $$0.664645\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ −0.500000 + 0.866025i −0.0279508 + 0.0484123i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 24.0000 1.33540
$$324$$ 0 0
$$325$$ 2.00000 0.110940
$$326$$ 2.00000 + 3.46410i 0.110770 + 0.191859i
$$327$$ 0 0
$$328$$ −3.00000 + 5.19615i −0.165647 + 0.286910i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 14.0000 + 24.2487i 0.769510 + 1.33283i 0.937829 + 0.347097i $$0.112833\pi$$
−0.168320 + 0.985732i $$0.553834\pi$$
$$332$$ −12.0000 −0.658586
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 2.00000 + 3.46410i 0.109272 + 0.189264i
$$336$$ 0 0
$$337$$ −13.0000 + 22.5167i −0.708155 + 1.22656i 0.257386 + 0.966309i $$0.417139\pi$$
−0.965541 + 0.260252i $$0.916194\pi$$
$$338$$ 4.50000 7.79423i 0.244768 0.423950i
$$339$$ 0 0
$$340$$ 3.00000 + 5.19615i 0.162698 + 0.281801i
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −8.00000 −0.431959
$$344$$ 2.00000 + 3.46410i 0.107833 + 0.186772i
$$345$$ 0 0
$$346$$ 9.00000 15.5885i 0.483843 0.838041i
$$347$$ 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i $$-0.728946\pi$$
0.980921 + 0.194409i $$0.0622790\pi$$
$$348$$ 0 0
$$349$$ 5.00000 + 8.66025i 0.267644 + 0.463573i 0.968253 0.249973i $$-0.0804216\pi$$
−0.700609 + 0.713545i $$0.747088\pi$$
$$350$$ −4.00000 −0.213809
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 3.00000 + 5.19615i 0.159674 + 0.276563i 0.934751 0.355303i $$-0.115622\pi$$
−0.775077 + 0.631867i $$0.782289\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 9.00000 15.5885i 0.476999 0.826187i
$$357$$ 0 0
$$358$$ 12.0000 + 20.7846i 0.634220 + 1.09850i
$$359$$ 24.0000 1.26667 0.633336 0.773877i $$-0.281685\pi$$
0.633336 + 0.773877i $$0.281685\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ −7.00000 12.1244i −0.367912 0.637242i
$$363$$ 0 0
$$364$$ 4.00000 6.92820i 0.209657 0.363137i
$$365$$ −1.00000 + 1.73205i −0.0523424 + 0.0906597i
$$366$$ 0 0
$$367$$ 14.0000 + 24.2487i 0.730794 + 1.26577i 0.956544 + 0.291587i $$0.0941834\pi$$
−0.225750 + 0.974185i $$0.572483\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 2.00000 0.103975
$$371$$ 12.0000 + 20.7846i 0.623009 + 1.07908i
$$372$$ 0 0
$$373$$ −13.0000 + 22.5167i −0.673114 + 1.16587i 0.303902 + 0.952703i $$0.401711\pi$$
−0.977016 + 0.213165i $$0.931623\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 12.0000 0.618031
$$378$$ 0 0
$$379$$ −4.00000 −0.205466 −0.102733 0.994709i $$-0.532759\pi$$
−0.102733 + 0.994709i $$0.532759\pi$$
$$380$$ 2.00000 + 3.46410i 0.102598 + 0.177705i
$$381$$ 0 0
$$382$$ −12.0000 + 20.7846i −0.613973 + 1.06343i
$$383$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −22.0000 −1.11977
$$387$$ 0 0
$$388$$ 2.00000 0.101535
$$389$$ −3.00000 5.19615i −0.152106 0.263455i 0.779895 0.625910i $$-0.215272\pi$$
−0.932002 + 0.362454i $$0.881939\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ −4.50000 + 7.79423i −0.227284 + 0.393668i
$$393$$ 0 0
$$394$$ −3.00000 5.19615i −0.151138 0.261778i
$$395$$ 8.00000 0.402524
$$396$$ 0 0
$$397$$ −22.0000 −1.10415 −0.552074 0.833795i $$-0.686163\pi$$
−0.552074 + 0.833795i $$0.686163\pi$$
$$398$$ −4.00000 6.92820i −0.200502 0.347279i
$$399$$ 0 0
$$400$$ −0.500000 + 0.866025i −0.0250000 + 0.0433013i
$$401$$ −3.00000 + 5.19615i −0.149813 + 0.259483i −0.931158 0.364615i $$-0.881200\pi$$
0.781345 + 0.624099i $$0.214534\pi$$
$$402$$ 0 0
$$403$$ −8.00000 13.8564i −0.398508 0.690237i
$$404$$ −18.0000 −0.895533
$$405$$ 0 0
$$406$$ −24.0000 −1.19110
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −13.0000 + 22.5167i −0.642809 + 1.11338i 0.341994 + 0.939702i $$0.388898\pi$$
−0.984803 + 0.173675i $$0.944436\pi$$
$$410$$ −3.00000 + 5.19615i −0.148159 + 0.256620i
$$411$$ 0 0
$$412$$ 2.00000 + 3.46410i 0.0985329 + 0.170664i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −12.0000 −0.589057
$$416$$ −1.00000 1.73205i −0.0490290 0.0849208i
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$420$$ 0 0
$$421$$ 5.00000 + 8.66025i 0.243685 + 0.422075i 0.961761 0.273890i $$-0.0883103\pi$$
−0.718076 + 0.695965i $$0.754977\pi$$
$$422$$ 20.0000 0.973585
$$423$$ 0 0
$$424$$ 6.00000 0.291386
$$425$$ 3.00000 + 5.19615i 0.145521 + 0.252050i
$$426$$ 0 0
$$427$$ −20.0000 + 34.6410i −0.967868 + 1.67640i
$$428$$ −6.00000 + 10.3923i −0.290021 + 0.502331i
$$429$$ 0 0
$$430$$ 2.00000 + 3.46410i 0.0964486 + 0.167054i
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 0 0
$$433$$ 26.0000 1.24948 0.624740 0.780833i $$-0.285205\pi$$
0.624740 + 0.780833i $$0.285205\pi$$
$$434$$ 16.0000 + 27.7128i 0.768025 + 1.33026i
$$435$$ 0 0
$$436$$ 5.00000 8.66025i 0.239457 0.414751i
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −4.00000 6.92820i −0.190910 0.330665i 0.754642 0.656136i $$-0.227810\pi$$
−0.945552 + 0.325471i $$0.894477\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −12.0000 −0.570782
$$443$$ 6.00000 + 10.3923i 0.285069 + 0.493753i 0.972626 0.232377i $$-0.0746503\pi$$
−0.687557 + 0.726130i $$0.741317\pi$$
$$444$$ 0 0
$$445$$ 9.00000 15.5885i 0.426641 0.738964i
$$446$$ −10.0000 + 17.3205i −0.473514 + 0.820150i
$$447$$ 0 0
$$448$$ 2.00000 + 3.46410i 0.0944911 + 0.163663i
$$449$$ 6.00000 0.283158 0.141579 0.989927i $$-0.454782\pi$$
0.141579 + 0.989927i $$0.454782\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ −9.00000 15.5885i −0.423324 0.733219i
$$453$$ 0 0
$$454$$ −6.00000 + 10.3923i −0.281594 + 0.487735i
$$455$$ 4.00000 6.92820i 0.187523 0.324799i
$$456$$ 0 0
$$457$$ −13.0000 22.5167i −0.608114 1.05328i −0.991551 0.129718i $$-0.958593\pi$$
0.383437 0.923567i $$-0.374740\pi$$
$$458$$ −10.0000 −0.467269
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −15.0000 25.9808i −0.698620 1.21004i −0.968945 0.247276i $$-0.920465\pi$$
0.270326 0.962769i $$-0.412869\pi$$
$$462$$ 0 0
$$463$$ 2.00000 3.46410i 0.0929479 0.160990i −0.815802 0.578331i $$-0.803704\pi$$
0.908750 + 0.417340i $$0.137038\pi$$
$$464$$ −3.00000 + 5.19615i −0.139272 + 0.241225i
$$465$$ 0 0
$$466$$ −9.00000 15.5885i −0.416917 0.722121i
$$467$$ 36.0000 1.66588 0.832941 0.553362i $$-0.186655\pi$$
0.832941 + 0.553362i $$0.186655\pi$$
$$468$$ 0 0
$$469$$ 16.0000 0.738811
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 2.00000 + 3.46410i 0.0917663 + 0.158944i
$$476$$ 24.0000 1.10004
$$477$$ 0 0
$$478$$ −24.0000 −1.09773
$$479$$ −12.0000 20.7846i −0.548294 0.949673i −0.998392 0.0566937i $$-0.981944\pi$$
0.450098 0.892979i $$-0.351389\pi$$
$$480$$ 0 0
$$481$$ −2.00000 + 3.46410i −0.0911922 + 0.157949i
$$482$$ −1.00000 + 1.73205i −0.0455488 + 0.0788928i
$$483$$ 0 0
$$484$$ 5.50000 + 9.52628i 0.250000 + 0.433013i
$$485$$ 2.00000 0.0908153
$$486$$ 0 0
$$487$$ −28.0000 −1.26880 −0.634401 0.773004i $$-0.718753\pi$$
−0.634401 + 0.773004i $$0.718753\pi$$
$$488$$ 5.00000 + 8.66025i 0.226339 + 0.392031i
$$489$$ 0 0
$$490$$ −4.50000 + 7.79423i −0.203289 + 0.352107i
$$491$$ 12.0000 20.7846i 0.541552 0.937996i −0.457263 0.889332i $$-0.651170\pi$$
0.998815 0.0486647i $$-0.0154966\pi$$
$$492$$ 0 0
$$493$$ 18.0000 + 31.1769i 0.810679 + 1.40414i
$$494$$ −8.00000 −0.359937
$$495$$ 0 0
$$496$$ 8.00000 0.359211
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 2.00000 3.46410i 0.0895323 0.155074i −0.817781 0.575529i $$-0.804796\pi$$
0.907314 + 0.420455i $$0.138129\pi$$
$$500$$ −0.500000 + 0.866025i −0.0223607 + 0.0387298i
$$501$$ 0 0
$$502$$ −12.0000 20.7846i −0.535586 0.927663i
$$503$$ −24.0000 −1.07011 −0.535054 0.844818i $$-0.679709\pi$$
−0.535054 + 0.844818i $$0.679709\pi$$
$$504$$ 0 0
$$505$$ −18.0000 −0.800989
$$506$$ 0 0
$$507$$ 0 0
$$508$$ −10.0000 + 17.3205i −0.443678 + 0.768473i
$$509$$ −3.00000 + 5.19615i −0.132973 + 0.230315i −0.924821 0.380402i $$-0.875786\pi$$
0.791849 + 0.610718i $$0.209119\pi$$
$$510$$ 0 0
$$511$$ 4.00000 + 6.92820i 0.176950 + 0.306486i
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ 18.0000 0.793946
$$515$$ 2.00000 + 3.46410i 0.0881305 + 0.152647i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 4.00000 6.92820i 0.175750 0.304408i
$$519$$ 0 0
$$520$$ −1.00000 1.73205i −0.0438529 0.0759555i
$$521$$ −18.0000 −0.788594 −0.394297 0.918983i $$-0.629012\pi$$
−0.394297 + 0.918983i $$0.629012\pi$$
$$522$$ 0 0
$$523$$ 20.0000 0.874539 0.437269 0.899331i $$-0.355946\pi$$
0.437269 + 0.899331i $$0.355946\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 24.0000 41.5692i 1.04546 1.81078i
$$528$$ 0 0
$$529$$ 11.5000 + 19.9186i 0.500000 + 0.866025i
$$530$$ 6.00000 0.260623
$$531$$ 0 0
$$532$$ 16.0000 0.693688
$$533$$ −6.00000 10.3923i −0.259889 0.450141i
$$534$$ 0 0
$$535$$ −6.00000 + 10.3923i −0.259403 + 0.449299i
$$536$$ 2.00000 3.46410i 0.0863868 0.149626i
$$537$$ 0 0
$$538$$ −3.00000 5.19615i −0.129339 0.224022i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −10.0000 −0.429934 −0.214967 0.976621i $$-0.568964\pi$$
−0.214967 + 0.976621i $$0.568964\pi$$
$$542$$ 8.00000 + 13.8564i 0.343629 + 0.595184i
$$543$$ 0 0
$$544$$ 3.00000 5.19615i 0.128624 0.222783i
$$545$$ 5.00000 8.66025i 0.214176 0.370965i
$$546$$ 0 0
$$547$$ 14.0000 + 24.2487i 0.598597 + 1.03680i 0.993028 + 0.117875i $$0.0376081\pi$$
−0.394432 + 0.918925i $$0.629059\pi$$
$$548$$ −6.00000 −0.256307
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 12.0000 + 20.7846i 0.511217 + 0.885454i
$$552$$ 0 0
$$553$$ 16.0000 27.7128i 0.680389 1.17847i
$$554$$ −1.00000 + 1.73205i −0.0424859 + 0.0735878i
$$555$$ 0 0
$$556$$ 2.00000 + 3.46410i 0.0848189 + 0.146911i
$$557$$ −18.0000 −0.762684 −0.381342 0.924434i $$-0.624538\pi$$
−0.381342 + 0.924434i $$0.624538\pi$$
$$558$$ 0 0
$$559$$ −8.00000 −0.338364
$$560$$ 2.00000 + 3.46410i 0.0845154 + 0.146385i
$$561$$ 0 0
$$562$$ 9.00000 15.5885i 0.379642 0.657559i
$$563$$ −6.00000 + 10.3923i −0.252870 + 0.437983i −0.964315 0.264758i $$-0.914708\pi$$
0.711445 + 0.702742i $$0.248041\pi$$
$$564$$ 0 0
$$565$$ −9.00000 15.5885i −0.378633 0.655811i
$$566$$ −28.0000 −1.17693
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 9.00000 + 15.5885i 0.377300 + 0.653502i 0.990668 0.136295i $$-0.0435194\pi$$
−0.613369 + 0.789797i $$0.710186\pi$$
$$570$$ 0 0
$$571$$ −10.0000 + 17.3205i −0.418487 + 0.724841i −0.995788 0.0916910i $$-0.970773\pi$$
0.577301 + 0.816532i $$0.304106\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 12.0000 + 20.7846i 0.500870 + 0.867533i
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 2.00000 0.0832611 0.0416305 0.999133i $$-0.486745\pi$$
0.0416305 + 0.999133i $$0.486745\pi$$
$$578$$ −9.50000 16.4545i −0.395148 0.684416i
$$579$$ 0 0
$$580$$ −3.00000 + 5.19615i −0.124568 + 0.215758i
$$581$$ −24.0000 + 41.5692i −0.995688 + 1.72458i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 2.00000 0.0827606
$$585$$ 0 0
$$586$$ 6.00000 0.247858
$$587$$ −6.00000 10.3923i −0.247647 0.428936i 0.715226 0.698893i $$-0.246324\pi$$
−0.962872 + 0.269957i $$0.912990\pi$$
$$588$$ 0 0
$$589$$ 16.0000 27.7128i 0.659269 1.14189i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −1.00000 1.73205i −0.0410997 0.0711868i
$$593$$ −30.0000 −1.23195 −0.615976 0.787765i $$-0.711238\pi$$
−0.615976 + 0.787765i $$0.711238\pi$$
$$594$$ 0 0
$$595$$ 24.0000 0.983904
$$596$$ −3.00000 5.19615i −0.122885 0.212843i
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −12.0000 + 20.7846i −0.490307 + 0.849236i −0.999938 0.0111569i $$-0.996449\pi$$
0.509631 + 0.860393i $$0.329782\pi$$
$$600$$ 0 0
$$601$$ 11.0000 + 19.0526i 0.448699 + 0.777170i 0.998302 0.0582563i $$-0.0185541\pi$$
−0.549602 + 0.835426i $$0.685221\pi$$
$$602$$ 16.0000 0.652111
$$603$$ 0 0
$$604$$ 8.00000 0.325515
$$605$$ 5.50000 + 9.52628i 0.223607 + 0.387298i
$$606$$ 0 0
$$607$$ 2.00000 3.46410i 0.0811775 0.140604i −0.822578 0.568652i $$-0.807465\pi$$
0.903756 + 0.428048i $$0.140799\pi$$
$$608$$ 2.00000 3.46410i 0.0811107 0.140488i
$$609$$ 0 0
$$610$$ 5.00000 + 8.66025i 0.202444 + 0.350643i
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 2.00000 0.0807792 0.0403896 0.999184i $$-0.487140\pi$$
0.0403896 + 0.999184i $$0.487140\pi$$
$$614$$ −10.0000 17.3205i −0.403567 0.698999i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 15.0000 25.9808i 0.603877 1.04595i −0.388351 0.921512i $$-0.626955\pi$$
0.992228 0.124434i $$-0.0397116\pi$$
$$618$$ 0 0
$$619$$ −22.0000 38.1051i −0.884255 1.53157i −0.846566 0.532284i $$-0.821334\pi$$
−0.0376891 0.999290i $$-0.512000\pi$$
$$620$$ 8.00000 0.321288
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −36.0000 62.3538i −1.44231 2.49815i
$$624$$ 0 0
$$625$$ −0.500000 + 0.866025i −0.0200000 + 0.0346410i
$$626$$ −1.00000 + 1.73205i −0.0399680 + 0.0692267i
$$627$$ 0 0
$$628$$ −1.00000 1.73205i −0.0399043 0.0691164i
$$629$$ −12.0000 −0.478471
$$630$$ 0 0
$$631$$ 32.0000 1.27390 0.636950 0.770905i $$-0.280196\pi$$
0.636950 + 0.770905i $$0.280196\pi$$
$$632$$ −4.00000 6.92820i −0.159111 0.275589i
$$633$$ 0 0
$$634$$ 9.00000 15.5885i 0.357436 0.619097i
$$635$$ −10.0000 + 17.3205i −0.396838 + 0.687343i
$$636$$ 0 0
$$637$$ −9.00000 15.5885i −0.356593 0.617637i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 1.00000 0.0395285
$$641$$ −15.0000 25.9808i −0.592464 1.02618i −0.993899 0.110291i $$-0.964822\pi$$
0.401435 0.915888i $$-0.368512\pi$$
$$642$$ 0 0
$$643$$ 2.00000 3.46410i 0.0788723 0.136611i −0.823891 0.566748i $$-0.808201\pi$$
0.902764 + 0.430137i $$0.141535\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −12.0000 20.7846i −0.472134 0.817760i
$$647$$ −24.0000 −0.943537 −0.471769 0.881722i $$-0.656384\pi$$
−0.471769 + 0.881722i $$0.656384\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ −1.00000 1.73205i −0.0392232 0.0679366i
$$651$$ 0 0
$$652$$ 2.00000 3.46410i 0.0783260 0.135665i
$$653$$ 9.00000 15.5885i 0.352197 0.610023i −0.634437 0.772975i $$-0.718768\pi$$
0.986634 + 0.162951i $$0.0521013\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 6.00000 0.234261
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 24.0000 + 41.5692i 0.934907 + 1.61931i 0.774799 + 0.632207i $$0.217851\pi$$
0.160108 + 0.987099i $$0.448816\pi$$
$$660$$ 0 0
$$661$$ −7.00000 + 12.1244i −0.272268 + 0.471583i −0.969442 0.245319i $$-0.921107\pi$$
0.697174 + 0.716902i $$0.254441\pi$$
$$662$$ 14.0000 24.2487i 0.544125 0.942453i
$$663$$ 0 0
$$664$$ 6.00000 + 10.3923i 0.232845 + 0.403300i
$$665$$ 16.0000 0.620453
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 2.00000 3.46410i 0.0772667 0.133830i
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −13.0000 22.5167i −0.501113 0.867953i −0.999999 0.00128586i $$-0.999591\pi$$
0.498886 0.866668i $$-0.333743\pi$$
$$674$$ 26.0000 1.00148
$$675$$ 0 0
$$676$$ −9.00000 −0.346154
$$677$$ −3.00000 5.19615i −0.115299 0.199704i 0.802600 0.596518i $$-0.203449\pi$$
−0.917899 + 0.396813i $$0.870116\pi$$
$$678$$ 0 0
$$679$$ 4.00000 6.92820i 0.153506 0.265880i
$$680$$ 3.00000 5.19615i 0.115045 0.199263i
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 12.0000 0.459167 0.229584 0.973289i $$-0.426264\pi$$
0.229584 + 0.973289i $$0.426264\pi$$
$$684$$ 0 0
$$685$$ −6.00000 −0.229248
$$686$$ 4.00000 + 6.92820i 0.152721 + 0.264520i
$$687$$ 0 0
$$688$$ 2.00000 3.46410i 0.0762493 0.132068i
$$689$$ −6.00000 + 10.3923i −0.228582 + 0.395915i
$$690$$ 0 0
$$691$$ −22.0000 38.1051i −0.836919 1.44959i −0.892458 0.451130i $$-0.851021\pi$$
0.0555386 0.998457i $$-0.482312\pi$$
$$692$$ −18.0000 −0.684257
$$693$$ 0 0
$$694$$ −12.0000 −0.455514
$$695$$ 2.00000 + 3.46410i 0.0758643 + 0.131401i
$$696$$ 0 0
$$697$$ 18.0000 31.1769i 0.681799 1.18091i
$$698$$ 5.00000 8.66025i 0.189253 0.327795i
$$699$$ 0 0
$$700$$ 2.00000 + 3.46410i 0.0755929 + 0.130931i
$$701$$ 6.00000 0.226617 0.113308 0.993560i $$-0.463855\pi$$
0.113308 + 0.993560i $$0.463855\pi$$
$$702$$ 0 0
$$703$$ −8.00000 −0.301726
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 3.00000 5.19615i 0.112906 0.195560i
$$707$$ −36.0000 + 62.3538i −1.35392 + 2.34506i
$$708$$ 0 0
$$709$$ −19.0000 32.9090i −0.713560 1.23592i −0.963512 0.267664i $$-0.913748\pi$$
0.249952 0.968258i $$-0.419585\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −18.0000 −0.674579
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 12.0000 20.7846i 0.448461 0.776757i
$$717$$ 0 0
$$718$$ −12.0000 20.7846i −0.447836 0.775675i
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ 16.0000 0.595871
$$722$$ 1.50000 + 2.59808i 0.0558242 + 0.0966904i
$$723$$ 0 0
$$724$$ −7.00000 + 12.1244i −0.260153 + 0.450598i
$$725$$ −3.00000 + 5.19615i −0.111417 + 0.192980i
$$726$$ 0 0
$$727$$ 14.0000 + 24.2487i 0.519231 + 0.899335i 0.999750 + 0.0223506i $$0.00711500\pi$$
−0.480519 + 0.876984i $$0.659552\pi$$
$$728$$ −8.00000 −0.296500
$$729$$ 0 0
$$730$$ 2.00000 0.0740233
$$731$$ −12.0000 20.7846i −0.443836 0.768747i
$$732$$ 0 0
$$733$$ 11.0000 19.0526i 0.406294 0.703722i −0.588177 0.808732i $$-0.700154\pi$$
0.994471 + 0.105010i $$0.0334875\pi$$
$$734$$ 14.0000 24.2487i 0.516749 0.895036i
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −52.0000 −1.91285 −0.956425 0.291977i $$-0.905687\pi$$
−0.956425 + 0.291977i $$0.905687\pi$$
$$740$$ −1.00000 1.73205i −0.0367607 0.0636715i
$$741$$ 0 0
$$742$$ 12.0000 20.7846i 0.440534 0.763027i
$$743$$ −12.0000 + 20.7846i −0.440237 + 0.762513i −0.997707 0.0676840i $$-0.978439\pi$$
0.557470 + 0.830197i $$0.311772\pi$$
$$744$$ 0 0
$$745$$ −3.00000 5.19615i −0.109911 0.190372i
$$746$$ 26.0000 0.951928
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 24.0000 + 41.5692i 0.876941 + 1.51891i
$$750$$ 0 0
$$751$$ 20.0000 34.6410i 0.729810 1.26407i −0.227153 0.973859i $$-0.572942\pi$$
0.956963 0.290209i $$-0.0937250\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ −6.00000 10.3923i −0.218507 0.378465i
$$755$$ 8.00000 0.291150
$$756$$ 0 0
$$757$$ 2.00000 0.0726912 0.0363456 0.999339i $$-0.488428\pi$$
0.0363456 + 0.999339i $$0.488428\pi$$
$$758$$ 2.00000 + 3.46410i 0.0726433 + 0.125822i
$$759$$ 0 0
$$760$$ 2.00000 3.46410i 0.0725476 0.125656i
$$761$$ 9.00000 15.5885i 0.326250 0.565081i −0.655515 0.755182i $$-0.727548\pi$$
0.981764 + 0.190101i $$0.0608816\pi$$
$$762$$ 0 0
$$763$$ −20.0000 34.6410i −0.724049 1.25409i
$$764$$ 24.0000 0.868290
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −1.00000 + 1.73205i −0.0360609 + 0.0624593i −0.883493 0.468445i $$-0.844814\pi$$
0.847432 + 0.530904i $$0.178148\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 11.0000 + 19.0526i 0.395899 + 0.685717i
$$773$$ −42.0000 −1.51064 −0.755318 0.655359i $$-0.772517\pi$$
−0.755318 + 0.655359i $$0.772517\pi$$
$$774$$ 0 0
$$775$$ 8.00000 0.287368
$$776$$ −1.00000 1.73205i −0.0358979 0.0621770i
$$777$$ 0 0
$$778$$ −3.00000 + 5.19615i −0.107555 + 0.186291i
$$779$$ 12.0000 20.7846i 0.429945 0.744686i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 9.00000 0.321429
$$785$$ −1.00000 1.73205i −0.0356915 0.0618195i
$$786$$ 0 0
$$787$$ 2.00000 3.46410i 0.0712923 0.123482i −0.828176 0.560469i $$-0.810621\pi$$
0.899468 + 0.436987i $$0.143954\pi$$
$$788$$ −3.00000 + 5.19615i −0.106871 + 0.185105i
$$789$$ 0 0
$$790$$ −4.00000 6.92820i −0.142314 0.246494i
$$791$$ −72.0000 −2.56003
$$792$$ 0 0
$$793$$ −20.0000 −0.710221
$$794$$ 11.0000 + 19.0526i 0.390375 + 0.676150i
$$795$$ 0 0
$$796$$ −4.00000 + 6.92820i −0.141776