Properties

 Label 560.2.q.h.401.1 Level $560$ Weight $2$ Character 560.401 Analytic conductor $4.472$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$560 = 2^{4} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 560.q (of order $$3$$, degree $$2$$, not minimal)

Newform invariants

 Self dual: no Analytic conductor: $$4.47162251319$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 280) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

 Embedding label 401.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 560.401 Dual form 560.2.q.h.81.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.50000 + 0.866025i) q^{7} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.50000 + 0.866025i) q^{7} +(1.00000 - 1.73205i) q^{9} +(1.00000 + 1.73205i) q^{11} +1.00000 q^{15} +(-2.00000 - 3.46410i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(0.500000 + 2.59808i) q^{21} +(0.500000 - 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{25} +5.00000 q^{27} +9.00000 q^{29} +(2.00000 + 3.46410i) q^{31} +(-1.00000 + 1.73205i) q^{33} +(2.00000 - 1.73205i) q^{35} +(-2.00000 + 3.46410i) q^{37} +1.00000 q^{41} -9.00000 q^{43} +(-1.00000 - 1.73205i) q^{45} +(5.50000 + 4.33013i) q^{49} +(2.00000 - 3.46410i) q^{51} +(5.00000 + 8.66025i) q^{53} +2.00000 q^{55} -2.00000 q^{57} +(-5.00000 - 8.66025i) q^{59} +(-4.50000 + 7.79423i) q^{61} +(4.00000 - 3.46410i) q^{63} +(2.50000 + 4.33013i) q^{67} +1.00000 q^{69} -14.0000 q^{71} +(-6.00000 - 10.3923i) q^{73} +(0.500000 - 0.866025i) q^{75} +(1.00000 + 5.19615i) q^{77} +(7.00000 - 12.1244i) q^{79} +(-0.500000 - 0.866025i) q^{81} -11.0000 q^{83} -4.00000 q^{85} +(4.50000 + 7.79423i) q^{87} +(7.50000 - 12.9904i) q^{89} +(-2.00000 + 3.46410i) q^{93} +(1.00000 + 1.73205i) q^{95} -18.0000 q^{97} +4.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{3} + q^{5} + 5 q^{7} + 2 q^{9}+O(q^{10})$$ 2 * q + q^3 + q^5 + 5 * q^7 + 2 * q^9 $$2 q + q^{3} + q^{5} + 5 q^{7} + 2 q^{9} + 2 q^{11} + 2 q^{15} - 4 q^{17} - 2 q^{19} + q^{21} + q^{23} - q^{25} + 10 q^{27} + 18 q^{29} + 4 q^{31} - 2 q^{33} + 4 q^{35} - 4 q^{37} + 2 q^{41} - 18 q^{43} - 2 q^{45} + 11 q^{49} + 4 q^{51} + 10 q^{53} + 4 q^{55} - 4 q^{57} - 10 q^{59} - 9 q^{61} + 8 q^{63} + 5 q^{67} + 2 q^{69} - 28 q^{71} - 12 q^{73} + q^{75} + 2 q^{77} + 14 q^{79} - q^{81} - 22 q^{83} - 8 q^{85} + 9 q^{87} + 15 q^{89} - 4 q^{93} + 2 q^{95} - 36 q^{97} + 8 q^{99}+O(q^{100})$$ 2 * q + q^3 + q^5 + 5 * q^7 + 2 * q^9 + 2 * q^11 + 2 * q^15 - 4 * q^17 - 2 * q^19 + q^21 + q^23 - q^25 + 10 * q^27 + 18 * q^29 + 4 * q^31 - 2 * q^33 + 4 * q^35 - 4 * q^37 + 2 * q^41 - 18 * q^43 - 2 * q^45 + 11 * q^49 + 4 * q^51 + 10 * q^53 + 4 * q^55 - 4 * q^57 - 10 * q^59 - 9 * q^61 + 8 * q^63 + 5 * q^67 + 2 * q^69 - 28 * q^71 - 12 * q^73 + q^75 + 2 * q^77 + 14 * q^79 - q^81 - 22 * q^83 - 8 * q^85 + 9 * q^87 + 15 * q^89 - 4 * q^93 + 2 * q^95 - 36 * q^97 + 8 * q^99

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$$.

 $$n$$ $$241$$ $$337$$ $$351$$ $$421$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$ $$1$$

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
$$3$$ 0.500000 + 0.866025i 0.288675 + 0.500000i 0.973494 0.228714i $$-0.0734519\pi$$
−0.684819 + 0.728714i $$0.740119\pi$$
$$4$$ 0 0
$$5$$ 0.500000 0.866025i 0.223607 0.387298i
$$6$$ 0 0
$$7$$ 2.50000 + 0.866025i 0.944911 + 0.327327i
$$8$$ 0 0
$$9$$ 1.00000 1.73205i 0.333333 0.577350i
$$10$$ 0 0
$$11$$ 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i $$-0.0691756\pi$$
−0.674967 + 0.737848i $$0.735842\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ 1.00000 0.258199
$$16$$ 0 0
$$17$$ −2.00000 3.46410i −0.485071 0.840168i 0.514782 0.857321i $$-0.327873\pi$$
−0.999853 + 0.0171533i $$0.994540\pi$$
$$18$$ 0 0
$$19$$ −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i $$-0.907015\pi$$
0.728219 + 0.685344i $$0.240348\pi$$
$$20$$ 0 0
$$21$$ 0.500000 + 2.59808i 0.109109 + 0.566947i
$$22$$ 0 0
$$23$$ 0.500000 0.866025i 0.104257 0.180579i −0.809177 0.587565i $$-0.800087\pi$$
0.913434 + 0.406986i $$0.133420\pi$$
$$24$$ 0 0
$$25$$ −0.500000 0.866025i −0.100000 0.173205i
$$26$$ 0 0
$$27$$ 5.00000 0.962250
$$28$$ 0 0
$$29$$ 9.00000 1.67126 0.835629 0.549294i $$-0.185103\pi$$
0.835629 + 0.549294i $$0.185103\pi$$
$$30$$ 0 0
$$31$$ 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i $$-0.0497126\pi$$
−0.628619 + 0.777714i $$0.716379\pi$$
$$32$$ 0 0
$$33$$ −1.00000 + 1.73205i −0.174078 + 0.301511i
$$34$$ 0 0
$$35$$ 2.00000 1.73205i 0.338062 0.292770i
$$36$$ 0 0
$$37$$ −2.00000 + 3.46410i −0.328798 + 0.569495i −0.982274 0.187453i $$-0.939977\pi$$
0.653476 + 0.756948i $$0.273310\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 1.00000 0.156174 0.0780869 0.996947i $$-0.475119\pi$$
0.0780869 + 0.996947i $$0.475119\pi$$
$$42$$ 0 0
$$43$$ −9.00000 −1.37249 −0.686244 0.727372i $$-0.740742\pi$$
−0.686244 + 0.727372i $$0.740742\pi$$
$$44$$ 0 0
$$45$$ −1.00000 1.73205i −0.149071 0.258199i
$$46$$ 0 0
$$47$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$48$$ 0 0
$$49$$ 5.50000 + 4.33013i 0.785714 + 0.618590i
$$50$$ 0 0
$$51$$ 2.00000 3.46410i 0.280056 0.485071i
$$52$$ 0 0
$$53$$ 5.00000 + 8.66025i 0.686803 + 1.18958i 0.972867 + 0.231367i $$0.0743197\pi$$
−0.286064 + 0.958211i $$0.592347\pi$$
$$54$$ 0 0
$$55$$ 2.00000 0.269680
$$56$$ 0 0
$$57$$ −2.00000 −0.264906
$$58$$ 0 0
$$59$$ −5.00000 8.66025i −0.650945 1.12747i −0.982894 0.184172i $$-0.941040\pi$$
0.331949 0.943297i $$-0.392294\pi$$
$$60$$ 0 0
$$61$$ −4.50000 + 7.79423i −0.576166 + 0.997949i 0.419748 + 0.907641i $$0.362118\pi$$
−0.995914 + 0.0903080i $$0.971215\pi$$
$$62$$ 0 0
$$63$$ 4.00000 3.46410i 0.503953 0.436436i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 2.50000 + 4.33013i 0.305424 + 0.529009i 0.977356 0.211604i $$-0.0678686\pi$$
−0.671932 + 0.740613i $$0.734535\pi$$
$$68$$ 0 0
$$69$$ 1.00000 0.120386
$$70$$ 0 0
$$71$$ −14.0000 −1.66149 −0.830747 0.556650i $$-0.812086\pi$$
−0.830747 + 0.556650i $$0.812086\pi$$
$$72$$ 0 0
$$73$$ −6.00000 10.3923i −0.702247 1.21633i −0.967676 0.252197i $$-0.918847\pi$$
0.265429 0.964130i $$-0.414486\pi$$
$$74$$ 0 0
$$75$$ 0.500000 0.866025i 0.0577350 0.100000i
$$76$$ 0 0
$$77$$ 1.00000 + 5.19615i 0.113961 + 0.592157i
$$78$$ 0 0
$$79$$ 7.00000 12.1244i 0.787562 1.36410i −0.139895 0.990166i $$-0.544677\pi$$
0.927457 0.373930i $$-0.121990\pi$$
$$80$$ 0 0
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ 0 0
$$83$$ −11.0000 −1.20741 −0.603703 0.797209i $$-0.706309\pi$$
−0.603703 + 0.797209i $$0.706309\pi$$
$$84$$ 0 0
$$85$$ −4.00000 −0.433861
$$86$$ 0 0
$$87$$ 4.50000 + 7.79423i 0.482451 + 0.835629i
$$88$$ 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
$$91$$ 0 0
$$92$$ 0 0
$$93$$ −2.00000 + 3.46410i −0.207390 + 0.359211i
$$94$$ 0 0
$$95$$ 1.00000 + 1.73205i 0.102598 + 0.177705i
$$96$$ 0 0
$$97$$ −18.0000 −1.82762 −0.913812 0.406138i $$-0.866875\pi$$
−0.913812 + 0.406138i $$0.866875\pi$$
$$98$$ 0 0
$$99$$ 4.00000 0.402015
$$100$$ 0 0
$$101$$ −1.50000 2.59808i −0.149256 0.258518i 0.781697 0.623658i $$-0.214354\pi$$
−0.930953 + 0.365140i $$0.881021\pi$$
$$102$$ 0 0
$$103$$ −6.50000 + 11.2583i −0.640464 + 1.10932i 0.344865 + 0.938652i $$0.387925\pi$$
−0.985329 + 0.170664i $$0.945409\pi$$
$$104$$ 0 0
$$105$$ 2.50000 + 0.866025i 0.243975 + 0.0845154i
$$106$$ 0 0
$$107$$ 4.50000 7.79423i 0.435031 0.753497i −0.562267 0.826956i $$-0.690071\pi$$
0.997298 + 0.0734594i $$0.0234039\pi$$
$$108$$ 0 0
$$109$$ 0.500000 + 0.866025i 0.0478913 + 0.0829502i 0.888977 0.457951i $$-0.151417\pi$$
−0.841086 + 0.540901i $$0.818083\pi$$
$$110$$ 0 0
$$111$$ −4.00000 −0.379663
$$112$$ 0 0
$$113$$ 2.00000 0.188144 0.0940721 0.995565i $$-0.470012\pi$$
0.0940721 + 0.995565i $$0.470012\pi$$
$$114$$ 0 0
$$115$$ −0.500000 0.866025i −0.0466252 0.0807573i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −2.00000 10.3923i −0.183340 0.952661i
$$120$$ 0 0
$$121$$ 3.50000 6.06218i 0.318182 0.551107i
$$122$$ 0 0
$$123$$ 0.500000 + 0.866025i 0.0450835 + 0.0780869i
$$124$$ 0 0
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ −8.00000 −0.709885 −0.354943 0.934888i $$-0.615500\pi$$
−0.354943 + 0.934888i $$0.615500\pi$$
$$128$$ 0 0
$$129$$ −4.50000 7.79423i −0.396203 0.686244i
$$130$$ 0 0
$$131$$ −4.00000 + 6.92820i −0.349482 + 0.605320i −0.986157 0.165812i $$-0.946976\pi$$
0.636676 + 0.771132i $$0.280309\pi$$
$$132$$ 0 0
$$133$$ −4.00000 + 3.46410i −0.346844 + 0.300376i
$$134$$ 0 0
$$135$$ 2.50000 4.33013i 0.215166 0.372678i
$$136$$ 0 0
$$137$$ −6.00000 10.3923i −0.512615 0.887875i −0.999893 0.0146279i $$-0.995344\pi$$
0.487278 0.873247i $$-0.337990\pi$$
$$138$$ 0 0
$$139$$ 2.00000 0.169638 0.0848189 0.996396i $$-0.472969\pi$$
0.0848189 + 0.996396i $$0.472969\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 4.50000 7.79423i 0.373705 0.647275i
$$146$$ 0 0
$$147$$ −1.00000 + 6.92820i −0.0824786 + 0.571429i
$$148$$ 0 0
$$149$$ 2.50000 4.33013i 0.204808 0.354738i −0.745264 0.666770i $$-0.767676\pi$$
0.950072 + 0.312032i $$0.101010\pi$$
$$150$$ 0 0
$$151$$ 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i $$-0.0611289\pi$$
−0.656101 + 0.754673i $$0.727796\pi$$
$$152$$ 0 0
$$153$$ −8.00000 −0.646762
$$154$$ 0 0
$$155$$ 4.00000 0.321288
$$156$$ 0 0
$$157$$ −1.00000 1.73205i −0.0798087 0.138233i 0.823359 0.567521i $$-0.192098\pi$$
−0.903167 + 0.429289i $$0.858764\pi$$
$$158$$ 0 0
$$159$$ −5.00000 + 8.66025i −0.396526 + 0.686803i
$$160$$ 0 0
$$161$$ 2.00000 1.73205i 0.157622 0.136505i
$$162$$ 0 0
$$163$$ −10.0000 + 17.3205i −0.783260 + 1.35665i 0.146772 + 0.989170i $$0.453112\pi$$
−0.930033 + 0.367477i $$0.880222\pi$$
$$164$$ 0 0
$$165$$ 1.00000 + 1.73205i 0.0778499 + 0.134840i
$$166$$ 0 0
$$167$$ −17.0000 −1.31550 −0.657750 0.753237i $$-0.728492\pi$$
−0.657750 + 0.753237i $$0.728492\pi$$
$$168$$ 0 0
$$169$$ −13.0000 −1.00000
$$170$$ 0 0
$$171$$ 2.00000 + 3.46410i 0.152944 + 0.264906i
$$172$$ 0 0
$$173$$ −8.00000 + 13.8564i −0.608229 + 1.05348i 0.383304 + 0.923622i $$0.374786\pi$$
−0.991532 + 0.129861i $$0.958547\pi$$
$$174$$ 0 0
$$175$$ −0.500000 2.59808i −0.0377964 0.196396i
$$176$$ 0 0
$$177$$ 5.00000 8.66025i 0.375823 0.650945i
$$178$$ 0 0
$$179$$ 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i $$-0.0186389\pi$$
−0.549825 + 0.835280i $$0.685306\pi$$
$$180$$ 0 0
$$181$$ −25.0000 −1.85824 −0.929118 0.369784i $$-0.879432\pi$$
−0.929118 + 0.369784i $$0.879432\pi$$
$$182$$ 0 0
$$183$$ −9.00000 −0.665299
$$184$$ 0 0
$$185$$ 2.00000 + 3.46410i 0.147043 + 0.254686i
$$186$$ 0 0
$$187$$ 4.00000 6.92820i 0.292509 0.506640i
$$188$$ 0 0
$$189$$ 12.5000 + 4.33013i 0.909241 + 0.314970i
$$190$$ 0 0
$$191$$ 9.00000 15.5885i 0.651217 1.12794i −0.331611 0.943416i $$-0.607592\pi$$
0.982828 0.184525i $$-0.0590746\pi$$
$$192$$ 0 0
$$193$$ 7.00000 + 12.1244i 0.503871 + 0.872730i 0.999990 + 0.00447566i $$0.00142465\pi$$
−0.496119 + 0.868255i $$0.665242\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 18.0000 1.28245 0.641223 0.767354i $$-0.278427\pi$$
0.641223 + 0.767354i $$0.278427\pi$$
$$198$$ 0 0
$$199$$ −2.00000 3.46410i −0.141776 0.245564i 0.786389 0.617731i $$-0.211948\pi$$
−0.928166 + 0.372168i $$0.878615\pi$$
$$200$$ 0 0
$$201$$ −2.50000 + 4.33013i −0.176336 + 0.305424i
$$202$$ 0 0
$$203$$ 22.5000 + 7.79423i 1.57919 + 0.547048i
$$204$$ 0 0
$$205$$ 0.500000 0.866025i 0.0349215 0.0604858i
$$206$$ 0 0
$$207$$ −1.00000 1.73205i −0.0695048 0.120386i
$$208$$ 0 0
$$209$$ −4.00000 −0.276686
$$210$$ 0 0
$$211$$ −2.00000 −0.137686 −0.0688428 0.997628i $$-0.521931\pi$$
−0.0688428 + 0.997628i $$0.521931\pi$$
$$212$$ 0 0
$$213$$ −7.00000 12.1244i −0.479632 0.830747i
$$214$$ 0 0
$$215$$ −4.50000 + 7.79423i −0.306897 + 0.531562i
$$216$$ 0 0
$$217$$ 2.00000 + 10.3923i 0.135769 + 0.705476i
$$218$$ 0 0
$$219$$ 6.00000 10.3923i 0.405442 0.702247i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 4.00000 0.267860 0.133930 0.990991i $$-0.457240\pi$$
0.133930 + 0.990991i $$0.457240\pi$$
$$224$$ 0 0
$$225$$ −2.00000 −0.133333
$$226$$ 0 0
$$227$$ −10.0000 17.3205i −0.663723 1.14960i −0.979630 0.200812i $$-0.935642\pi$$
0.315906 0.948790i $$-0.397691\pi$$
$$228$$ 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
$$231$$ −4.00000 + 3.46410i −0.263181 + 0.227921i
$$232$$ 0 0
$$233$$ −4.00000 + 6.92820i −0.262049 + 0.453882i −0.966786 0.255586i $$-0.917731\pi$$
0.704737 + 0.709468i $$0.251065\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 14.0000 0.909398
$$238$$ 0 0
$$239$$ 24.0000 1.55243 0.776215 0.630468i $$-0.217137\pi$$
0.776215 + 0.630468i $$0.217137\pi$$
$$240$$ 0 0
$$241$$ 11.0000 + 19.0526i 0.708572 + 1.22728i 0.965387 + 0.260822i $$0.0839937\pi$$
−0.256814 + 0.966461i $$0.582673\pi$$
$$242$$ 0 0
$$243$$ 8.00000 13.8564i 0.513200 0.888889i
$$244$$ 0 0
$$245$$ 6.50000 2.59808i 0.415270 0.165985i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −5.50000 9.52628i −0.348548 0.603703i
$$250$$ 0 0
$$251$$ −8.00000 −0.504956 −0.252478 0.967603i $$-0.581245\pi$$
−0.252478 + 0.967603i $$0.581245\pi$$
$$252$$ 0 0
$$253$$ 2.00000 0.125739
$$254$$ 0 0
$$255$$ −2.00000 3.46410i −0.125245 0.216930i
$$256$$ 0 0
$$257$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$258$$ 0 0
$$259$$ −8.00000 + 6.92820i −0.497096 + 0.430498i
$$260$$ 0 0
$$261$$ 9.00000 15.5885i 0.557086 0.964901i
$$262$$ 0 0
$$263$$ −0.500000 0.866025i −0.0308313 0.0534014i 0.850198 0.526463i $$-0.176482\pi$$
−0.881029 + 0.473062i $$0.843149\pi$$
$$264$$ 0 0
$$265$$ 10.0000 0.614295
$$266$$ 0 0
$$267$$ 15.0000 0.917985
$$268$$ 0 0
$$269$$ 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
$$271$$ 11.0000 19.0526i 0.668202 1.15736i −0.310204 0.950670i $$-0.600397\pi$$
0.978406 0.206691i $$-0.0662693\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 1.00000 1.73205i 0.0603023 0.104447i
$$276$$ 0 0
$$277$$ 14.0000 + 24.2487i 0.841178 + 1.45696i 0.888899 + 0.458103i $$0.151471\pi$$
−0.0477206 + 0.998861i $$0.515196\pi$$
$$278$$ 0 0
$$279$$ 8.00000 0.478947
$$280$$ 0 0
$$281$$ 18.0000 1.07379 0.536895 0.843649i $$-0.319597\pi$$
0.536895 + 0.843649i $$0.319597\pi$$
$$282$$ 0 0
$$283$$ −2.00000 3.46410i −0.118888 0.205919i 0.800439 0.599414i $$-0.204600\pi$$
−0.919327 + 0.393494i $$0.871266\pi$$
$$284$$ 0 0
$$285$$ −1.00000 + 1.73205i −0.0592349 + 0.102598i
$$286$$ 0 0
$$287$$ 2.50000 + 0.866025i 0.147570 + 0.0511199i
$$288$$ 0 0
$$289$$ 0.500000 0.866025i 0.0294118 0.0509427i
$$290$$ 0 0
$$291$$ −9.00000 15.5885i −0.527589 0.913812i
$$292$$ 0 0
$$293$$ 12.0000 0.701047 0.350524 0.936554i $$-0.386004\pi$$
0.350524 + 0.936554i $$0.386004\pi$$
$$294$$ 0 0
$$295$$ −10.0000 −0.582223
$$296$$ 0 0
$$297$$ 5.00000 + 8.66025i 0.290129 + 0.502519i
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −22.5000 7.79423i −1.29688 0.449252i
$$302$$ 0 0
$$303$$ 1.50000 2.59808i 0.0861727 0.149256i
$$304$$ 0 0
$$305$$ 4.50000 + 7.79423i 0.257669 + 0.446296i
$$306$$ 0 0
$$307$$ −21.0000 −1.19853 −0.599267 0.800549i $$-0.704541\pi$$
−0.599267 + 0.800549i $$0.704541\pi$$
$$308$$ 0 0
$$309$$ −13.0000 −0.739544
$$310$$ 0 0
$$311$$ 13.0000 + 22.5167i 0.737162 + 1.27680i 0.953768 + 0.300544i $$0.0971681\pi$$
−0.216606 + 0.976259i $$0.569499\pi$$
$$312$$ 0 0
$$313$$ −8.00000 + 13.8564i −0.452187 + 0.783210i −0.998522 0.0543564i $$-0.982689\pi$$
0.546335 + 0.837567i $$0.316023\pi$$
$$314$$ 0 0
$$315$$ −1.00000 5.19615i −0.0563436 0.292770i
$$316$$ 0 0
$$317$$ 8.00000 13.8564i 0.449325 0.778253i −0.549017 0.835811i $$-0.684998\pi$$
0.998342 + 0.0575576i $$0.0183313\pi$$
$$318$$ 0 0
$$319$$ 9.00000 + 15.5885i 0.503903 + 0.872786i
$$320$$ 0 0
$$321$$ 9.00000 0.502331
$$322$$ 0 0
$$323$$ 8.00000 0.445132
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −0.500000 + 0.866025i −0.0276501 + 0.0478913i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$332$$ 0 0
$$333$$ 4.00000 + 6.92820i 0.219199 + 0.379663i
$$334$$ 0 0
$$335$$ 5.00000 0.273179
$$336$$ 0 0
$$337$$ −2.00000 −0.108947 −0.0544735 0.998515i $$-0.517348\pi$$
−0.0544735 + 0.998515i $$0.517348\pi$$
$$338$$ 0 0
$$339$$ 1.00000 + 1.73205i 0.0543125 + 0.0940721i
$$340$$ 0 0
$$341$$ −4.00000 + 6.92820i −0.216612 + 0.375183i
$$342$$ 0 0
$$343$$ 10.0000 + 15.5885i 0.539949 + 0.841698i
$$344$$ 0 0
$$345$$ 0.500000 0.866025i 0.0269191 0.0466252i
$$346$$ 0 0
$$347$$ −3.50000 6.06218i −0.187890 0.325435i 0.756657 0.653812i $$-0.226831\pi$$
−0.944547 + 0.328378i $$0.893498\pi$$
$$348$$ 0 0
$$349$$ −19.0000 −1.01705 −0.508523 0.861048i $$-0.669808\pi$$
−0.508523 + 0.861048i $$0.669808\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −7.00000 12.1244i −0.372572 0.645314i 0.617388 0.786659i $$-0.288191\pi$$
−0.989960 + 0.141344i $$0.954858\pi$$
$$354$$ 0 0
$$355$$ −7.00000 + 12.1244i −0.371521 + 0.643494i
$$356$$ 0 0
$$357$$ 8.00000 6.92820i 0.423405 0.366679i
$$358$$ 0 0
$$359$$ 6.00000 10.3923i 0.316668 0.548485i −0.663123 0.748511i $$-0.730769\pi$$
0.979791 + 0.200026i $$0.0641026\pi$$
$$360$$ 0 0
$$361$$ 7.50000 + 12.9904i 0.394737 + 0.683704i
$$362$$ 0 0
$$363$$ 7.00000 0.367405
$$364$$ 0 0
$$365$$ −12.0000 −0.628109
$$366$$ 0 0
$$367$$ 3.50000 + 6.06218i 0.182699 + 0.316443i 0.942799 0.333363i $$-0.108183\pi$$
−0.760100 + 0.649806i $$0.774850\pi$$
$$368$$ 0 0
$$369$$ 1.00000 1.73205i 0.0520579 0.0901670i
$$370$$ 0 0
$$371$$ 5.00000 + 25.9808i 0.259587 + 1.34885i
$$372$$ 0 0
$$373$$ 14.0000 24.2487i 0.724893 1.25555i −0.234126 0.972206i $$-0.575223\pi$$
0.959018 0.283344i $$-0.0914439\pi$$
$$374$$ 0 0
$$375$$ −0.500000 0.866025i −0.0258199 0.0447214i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 30.0000 1.54100 0.770498 0.637442i $$-0.220007\pi$$
0.770498 + 0.637442i $$0.220007\pi$$
$$380$$ 0 0
$$381$$ −4.00000 6.92820i −0.204926 0.354943i
$$382$$ 0 0
$$383$$ 10.5000 18.1865i 0.536525 0.929288i −0.462563 0.886586i $$-0.653070\pi$$
0.999088 0.0427020i $$-0.0135966\pi$$
$$384$$ 0 0
$$385$$ 5.00000 + 1.73205i 0.254824 + 0.0882735i
$$386$$ 0 0
$$387$$ −9.00000 + 15.5885i −0.457496 + 0.792406i
$$388$$ 0 0
$$389$$ −13.0000 22.5167i −0.659126 1.14164i −0.980842 0.194804i $$-0.937593\pi$$
0.321716 0.946836i $$-0.395740\pi$$
$$390$$ 0 0
$$391$$ −4.00000 −0.202289
$$392$$ 0 0
$$393$$ −8.00000 −0.403547
$$394$$ 0 0
$$395$$ −7.00000 12.1244i −0.352208 0.610043i
$$396$$ 0 0
$$397$$ −3.00000 + 5.19615i −0.150566 + 0.260787i −0.931436 0.363906i $$-0.881443\pi$$
0.780870 + 0.624694i $$0.214776\pi$$
$$398$$ 0 0
$$399$$ −5.00000 1.73205i −0.250313 0.0867110i
$$400$$ 0 0
$$401$$ 8.50000 14.7224i 0.424470 0.735203i −0.571901 0.820323i $$-0.693794\pi$$
0.996371 + 0.0851195i $$0.0271272\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ −1.00000 −0.0496904
$$406$$ 0 0
$$407$$ −8.00000 −0.396545
$$408$$ 0 0
$$409$$ 10.5000 + 18.1865i 0.519192 + 0.899266i 0.999751 + 0.0223042i $$0.00710022\pi$$
−0.480560 + 0.876962i $$0.659566\pi$$
$$410$$ 0 0
$$411$$ 6.00000 10.3923i 0.295958 0.512615i
$$412$$ 0 0
$$413$$ −5.00000 25.9808i −0.246034 1.27843i
$$414$$ 0 0
$$415$$ −5.50000 + 9.52628i −0.269984 + 0.467627i
$$416$$ 0 0
$$417$$ 1.00000 + 1.73205i 0.0489702 + 0.0848189i
$$418$$ 0 0
$$419$$ −16.0000 −0.781651 −0.390826 0.920465i $$-0.627810\pi$$
−0.390826 + 0.920465i $$0.627810\pi$$
$$420$$ 0 0
$$421$$ −27.0000 −1.31590 −0.657950 0.753062i $$-0.728576\pi$$
−0.657950 + 0.753062i $$0.728576\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −2.00000 + 3.46410i −0.0970143 + 0.168034i
$$426$$ 0 0
$$427$$ −18.0000 + 15.5885i −0.871081 + 0.754378i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 7.00000 + 12.1244i 0.337178 + 0.584010i 0.983901 0.178716i $$-0.0571942\pi$$
−0.646723 + 0.762725i $$0.723861\pi$$
$$432$$ 0 0
$$433$$ 30.0000 1.44171 0.720854 0.693087i $$-0.243750\pi$$
0.720854 + 0.693087i $$0.243750\pi$$
$$434$$ 0 0
$$435$$ 9.00000 0.431517
$$436$$ 0 0
$$437$$ 1.00000 + 1.73205i 0.0478365 + 0.0828552i
$$438$$ 0 0
$$439$$ −14.0000 + 24.2487i −0.668184 + 1.15733i 0.310228 + 0.950662i $$0.399595\pi$$
−0.978412 + 0.206666i $$0.933739\pi$$
$$440$$ 0 0
$$441$$ 13.0000 5.19615i 0.619048 0.247436i
$$442$$ 0 0
$$443$$ −5.50000 + 9.52628i −0.261313 + 0.452607i −0.966591 0.256323i $$-0.917489\pi$$
0.705278 + 0.708931i $$0.250822\pi$$
$$444$$ 0 0
$$445$$ −7.50000 12.9904i −0.355534 0.615803i
$$446$$ 0 0
$$447$$ 5.00000 0.236492
$$448$$ 0 0
$$449$$ −41.0000 −1.93491 −0.967455 0.253044i $$-0.918568\pi$$
−0.967455 + 0.253044i $$0.918568\pi$$
$$450$$ 0 0
$$451$$ 1.00000 + 1.73205i 0.0470882 + 0.0815591i
$$452$$ 0 0
$$453$$ −4.00000 + 6.92820i −0.187936 + 0.325515i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −4.00000 + 6.92820i −0.187112 + 0.324088i −0.944286 0.329125i $$-0.893246\pi$$
0.757174 + 0.653213i $$0.226579\pi$$
$$458$$ 0 0
$$459$$ −10.0000 17.3205i −0.466760 0.808452i
$$460$$ 0 0
$$461$$ 2.00000 0.0931493 0.0465746 0.998915i $$-0.485169\pi$$
0.0465746 + 0.998915i $$0.485169\pi$$
$$462$$ 0 0
$$463$$ −39.0000 −1.81248 −0.906242 0.422760i $$-0.861061\pi$$
−0.906242 + 0.422760i $$0.861061\pi$$
$$464$$ 0 0
$$465$$ 2.00000 + 3.46410i 0.0927478 + 0.160644i
$$466$$ 0 0
$$467$$ −3.50000 + 6.06218i −0.161961 + 0.280524i −0.935572 0.353137i $$-0.885115\pi$$
0.773611 + 0.633661i $$0.218448\pi$$
$$468$$ 0 0
$$469$$ 2.50000 + 12.9904i 0.115439 + 0.599840i
$$470$$ 0 0
$$471$$ 1.00000 1.73205i 0.0460776 0.0798087i
$$472$$ 0 0
$$473$$ −9.00000 15.5885i −0.413820 0.716758i
$$474$$ 0 0
$$475$$ 2.00000 0.0917663
$$476$$ 0 0
$$477$$ 20.0000 0.915737
$$478$$ 0 0
$$479$$ −8.00000 13.8564i −0.365529 0.633115i 0.623332 0.781958i $$-0.285779\pi$$
−0.988861 + 0.148842i $$0.952445\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 2.50000 + 0.866025i 0.113754 + 0.0394055i
$$484$$ 0 0
$$485$$ −9.00000 + 15.5885i −0.408669 + 0.707835i
$$486$$ 0 0
$$487$$ −4.00000 6.92820i −0.181257 0.313947i 0.761052 0.648691i $$-0.224683\pi$$
−0.942309 + 0.334744i $$0.891350\pi$$
$$488$$ 0 0
$$489$$ −20.0000 −0.904431
$$490$$ 0 0
$$491$$ 20.0000 0.902587 0.451294 0.892375i $$-0.350963\pi$$
0.451294 + 0.892375i $$0.350963\pi$$
$$492$$ 0 0
$$493$$ −18.0000 31.1769i −0.810679 1.40414i
$$494$$ 0 0
$$495$$ 2.00000 3.46410i 0.0898933 0.155700i
$$496$$ 0 0
$$497$$ −35.0000 12.1244i −1.56996 0.543852i
$$498$$ 0 0
$$499$$ −19.0000 + 32.9090i −0.850557 + 1.47321i 0.0301498 + 0.999545i $$0.490402\pi$$
−0.880707 + 0.473662i $$0.842932\pi$$
$$500$$ 0 0
$$501$$ −8.50000 14.7224i −0.379752 0.657750i
$$502$$ 0 0
$$503$$ 23.0000 1.02552 0.512760 0.858532i $$-0.328623\pi$$
0.512760 + 0.858532i $$0.328623\pi$$
$$504$$ 0 0
$$505$$ −3.00000 −0.133498
$$506$$ 0 0
$$507$$ −6.50000 11.2583i −0.288675 0.500000i
$$508$$ 0 0
$$509$$ 7.50000 12.9904i 0.332432 0.575789i −0.650556 0.759458i $$-0.725464\pi$$
0.982988 + 0.183669i $$0.0587976\pi$$
$$510$$ 0 0
$$511$$ −6.00000 31.1769i −0.265424 1.37919i
$$512$$ 0 0
$$513$$ −5.00000 + 8.66025i −0.220755 + 0.382360i
$$514$$ 0 0
$$515$$ 6.50000 + 11.2583i 0.286424 + 0.496101i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ −16.0000 −0.702322
$$520$$ 0 0
$$521$$ 21.0000 + 36.3731i 0.920027 + 1.59353i 0.799370 + 0.600839i $$0.205167\pi$$
0.120656 + 0.992694i $$0.461500\pi$$
$$522$$ 0 0
$$523$$ 14.0000 24.2487i 0.612177 1.06032i −0.378695 0.925521i $$-0.623627\pi$$
0.990873 0.134801i $$-0.0430394\pi$$
$$524$$ 0 0
$$525$$ 2.00000 1.73205i 0.0872872 0.0755929i
$$526$$ 0 0
$$527$$ 8.00000 13.8564i 0.348485 0.603595i
$$528$$ 0 0
$$529$$ 11.0000 + 19.0526i 0.478261 + 0.828372i
$$530$$ 0 0
$$531$$ −20.0000 −0.867926
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ −4.50000 7.79423i −0.194552 0.336974i
$$536$$ 0 0
$$537$$ −6.00000 + 10.3923i −0.258919 + 0.448461i
$$538$$ 0 0
$$539$$ −2.00000 + 13.8564i −0.0861461 + 0.596838i
$$540$$ 0 0
$$541$$ 6.50000 11.2583i 0.279457 0.484033i −0.691793 0.722096i $$-0.743179\pi$$
0.971250 + 0.238062i $$0.0765123\pi$$
$$542$$ 0 0
$$543$$ −12.5000 21.6506i −0.536426 0.929118i
$$544$$ 0 0
$$545$$ 1.00000 0.0428353
$$546$$ 0 0
$$547$$ 35.0000 1.49649 0.748246 0.663421i $$-0.230896\pi$$
0.748246 + 0.663421i $$0.230896\pi$$
$$548$$ 0 0
$$549$$ 9.00000 + 15.5885i 0.384111 + 0.665299i
$$550$$ 0 0
$$551$$ −9.00000 + 15.5885i −0.383413 + 0.664091i
$$552$$ 0 0
$$553$$ 28.0000 24.2487i 1.19068 1.03116i
$$554$$ 0 0
$$555$$ −2.00000 + 3.46410i −0.0848953 + 0.147043i
$$556$$ 0 0
$$557$$ −15.0000 25.9808i −0.635570 1.10084i −0.986394 0.164399i $$-0.947432\pi$$
0.350824 0.936442i $$-0.385902\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 8.00000 0.337760
$$562$$ 0 0
$$563$$ −22.5000 38.9711i −0.948262 1.64244i −0.749085 0.662474i $$-0.769506\pi$$
−0.199177 0.979963i $$-0.563827\pi$$
$$564$$ 0 0
$$565$$ 1.00000 1.73205i 0.0420703 0.0728679i
$$566$$ 0 0
$$567$$ −0.500000 2.59808i −0.0209980 0.109109i
$$568$$ 0 0
$$569$$ −23.0000 + 39.8372i −0.964210 + 1.67006i −0.252488 + 0.967600i $$0.581249\pi$$
−0.711722 + 0.702461i $$0.752085\pi$$
$$570$$ 0 0
$$571$$ −13.0000 22.5167i −0.544033 0.942293i −0.998667 0.0516146i $$-0.983563\pi$$
0.454634 0.890678i $$-0.349770\pi$$
$$572$$ 0 0
$$573$$ 18.0000 0.751961
$$574$$ 0 0
$$575$$ −1.00000 −0.0417029
$$576$$ 0 0
$$577$$ −1.00000 1.73205i −0.0416305 0.0721062i 0.844459 0.535620i $$-0.179922\pi$$
−0.886090 + 0.463513i $$0.846589\pi$$
$$578$$ 0 0
$$579$$ −7.00000 + 12.1244i −0.290910 + 0.503871i
$$580$$ 0 0
$$581$$ −27.5000 9.52628i −1.14089 0.395217i
$$582$$ 0 0
$$583$$ −10.0000 + 17.3205i −0.414158 + 0.717342i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 12.0000 0.495293 0.247647 0.968850i $$-0.420343\pi$$
0.247647 + 0.968850i $$0.420343\pi$$
$$588$$ 0 0
$$589$$ −8.00000 −0.329634
$$590$$ 0 0
$$591$$ 9.00000 + 15.5885i 0.370211 + 0.641223i
$$592$$ 0 0
$$593$$ −9.00000 + 15.5885i −0.369586 + 0.640141i −0.989501 0.144528i $$-0.953834\pi$$
0.619915 + 0.784669i $$0.287167\pi$$
$$594$$ 0 0
$$595$$ −10.0000 3.46410i −0.409960 0.142014i
$$596$$ 0 0
$$597$$ 2.00000 3.46410i 0.0818546 0.141776i
$$598$$ 0 0
$$599$$ 2.00000 + 3.46410i 0.0817178 + 0.141539i 0.903988 0.427558i $$-0.140626\pi$$
−0.822270 + 0.569097i $$0.807293\pi$$
$$600$$ 0 0
$$601$$ 10.0000 0.407909 0.203954 0.978980i $$-0.434621\pi$$
0.203954 + 0.978980i $$0.434621\pi$$
$$602$$ 0 0
$$603$$ 10.0000 0.407231
$$604$$ 0 0
$$605$$ −3.50000 6.06218i −0.142295 0.246463i
$$606$$ 0 0
$$607$$ 13.5000 23.3827i 0.547948 0.949074i −0.450467 0.892793i $$-0.648742\pi$$
0.998415 0.0562808i $$-0.0179242\pi$$
$$608$$ 0 0
$$609$$ 4.50000 + 23.3827i 0.182349 + 0.947514i
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 10.0000 + 17.3205i 0.403896 + 0.699569i 0.994192 0.107618i $$-0.0343224\pi$$
−0.590296 + 0.807187i $$0.700989\pi$$
$$614$$ 0 0
$$615$$ 1.00000 0.0403239
$$616$$ 0 0
$$617$$ −12.0000 −0.483102 −0.241551 0.970388i $$-0.577656\pi$$
−0.241551 + 0.970388i $$0.577656\pi$$
$$618$$ 0 0
$$619$$ −17.0000 29.4449i −0.683288 1.18349i −0.973972 0.226670i $$-0.927216\pi$$
0.290684 0.956819i $$-0.406117\pi$$
$$620$$ 0 0
$$621$$ 2.50000 4.33013i 0.100322 0.173762i
$$622$$ 0 0
$$623$$ 30.0000 25.9808i 1.20192 1.04090i
$$624$$ 0 0
$$625$$ −0.500000 + 0.866025i −0.0200000 + 0.0346410i
$$626$$ 0 0
$$627$$ −2.00000 3.46410i −0.0798723 0.138343i
$$628$$ 0 0
$$629$$ 16.0000 0.637962
$$630$$ 0 0
$$631$$ 2.00000 0.0796187 0.0398094 0.999207i $$-0.487325\pi$$
0.0398094 + 0.999207i $$0.487325\pi$$
$$632$$ 0 0
$$633$$ −1.00000 1.73205i −0.0397464 0.0688428i
$$634$$ 0 0
$$635$$ −4.00000 + 6.92820i −0.158735 + 0.274937i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ −14.0000 + 24.2487i −0.553831 + 0.959264i
$$640$$ 0 0
$$641$$ 9.50000 + 16.4545i 0.375227 + 0.649913i 0.990361 0.138510i $$-0.0442313\pi$$
−0.615134 + 0.788423i $$0.710898\pi$$
$$642$$ 0 0
$$643$$ 4.00000 0.157745 0.0788723 0.996885i $$-0.474868\pi$$
0.0788723 + 0.996885i $$0.474868\pi$$
$$644$$ 0 0
$$645$$ −9.00000 −0.354375
$$646$$ 0 0
$$647$$ 11.5000 + 19.9186i 0.452112 + 0.783080i 0.998517 0.0544405i $$-0.0173375\pi$$
−0.546405 + 0.837521i $$0.684004\pi$$
$$648$$ 0 0
$$649$$ 10.0000 17.3205i 0.392534 0.679889i
$$650$$ 0 0
$$651$$ −8.00000 + 6.92820i −0.313545 + 0.271538i
$$652$$ 0 0
$$653$$ −18.0000 + 31.1769i −0.704394 + 1.22005i 0.262515 + 0.964928i $$0.415448\pi$$
−0.966910 + 0.255119i $$0.917885\pi$$
$$654$$ 0 0
$$655$$ 4.00000 + 6.92820i 0.156293 + 0.270707i
$$656$$ 0 0
$$657$$ −24.0000 −0.936329
$$658$$ 0 0
$$659$$ −2.00000 −0.0779089 −0.0389545 0.999241i $$-0.512403\pi$$
−0.0389545 + 0.999241i $$0.512403\pi$$
$$660$$ 0 0
$$661$$ 1.50000 + 2.59808i 0.0583432 + 0.101053i 0.893722 0.448622i $$-0.148085\pi$$
−0.835379 + 0.549675i $$0.814752\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 1.00000 + 5.19615i 0.0387783 + 0.201498i
$$666$$ 0 0
$$667$$ 4.50000 7.79423i 0.174241 0.301794i
$$668$$ 0 0
$$669$$ 2.00000 + 3.46410i 0.0773245 + 0.133930i
$$670$$ 0 0
$$671$$ −18.0000 −0.694882
$$672$$ 0 0
$$673$$ 24.0000 0.925132 0.462566 0.886585i $$-0.346929\pi$$
0.462566 + 0.886585i $$0.346929\pi$$
$$674$$ 0 0
$$675$$ −2.50000 4.33013i −0.0962250 0.166667i
$$676$$ 0 0
$$677$$ 12.0000 20.7846i 0.461197 0.798817i −0.537823 0.843057i $$-0.680753\pi$$
0.999021 + 0.0442400i $$0.0140866\pi$$
$$678$$ 0 0
$$679$$ −45.0000 15.5885i −1.72694 0.598230i
$$680$$ 0 0
$$681$$ 10.0000 17.3205i 0.383201 0.663723i
$$682$$ 0 0
$$683$$ 4.50000 + 7.79423i 0.172188 + 0.298238i 0.939184 0.343413i $$-0.111583\pi$$
−0.766997 + 0.641651i $$0.778250\pi$$
$$684$$ 0 0
$$685$$ −12.0000 −0.458496
$$686$$ 0 0
$$687$$ 10.0000 0.381524
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 25.0000 43.3013i 0.951045 1.64726i 0.207875 0.978155i $$-0.433345\pi$$
0.743170 0.669102i $$-0.233321\pi$$
$$692$$ 0 0
$$693$$ 10.0000 + 3.46410i 0.379869 + 0.131590i
$$694$$ 0 0
$$695$$ 1.00000 1.73205i 0.0379322 0.0657004i
$$696$$ 0 0
$$697$$ −2.00000 3.46410i −0.0757554 0.131212i
$$698$$ 0 0
$$699$$ −8.00000 −0.302588
$$700$$ 0 0
$$701$$ 9.00000 0.339925 0.169963 0.985451i $$-0.445635\pi$$
0.169963 + 0.985451i $$0.445635\pi$$
$$702$$ 0 0
$$703$$ −4.00000 6.92820i −0.150863 0.261302i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −1.50000 7.79423i −0.0564133 0.293132i
$$708$$ 0 0
$$709$$ −10.5000 + 18.1865i −0.394336 + 0.683010i −0.993016 0.117978i $$-0.962359\pi$$
0.598680 + 0.800988i $$0.295692\pi$$
$$710$$ 0 0
$$711$$ −14.0000 24.2487i −0.525041 0.909398i
$$712$$ 0 0
$$713$$ 4.00000 0.149801
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 12.0000 + 20.7846i 0.448148 + 0.776215i
$$718$$ 0 0
$$719$$ −21.0000 + 36.3731i −0.783168 + 1.35649i 0.146920 + 0.989148i $$0.453064\pi$$
−0.930087 + 0.367338i $$0.880269\pi$$
$$720$$ 0 0
$$721$$ −26.0000 + 22.5167i −0.968291 + 0.838564i
$$722$$ 0 0
$$723$$ −11.0000 + 19.0526i −0.409094 + 0.708572i
$$724$$ 0 0
$$725$$ −4.50000 7.79423i −0.167126 0.289470i
$$726$$ 0 0
$$727$$ 31.0000 1.14973 0.574863 0.818250i $$-0.305055\pi$$
0.574863 + 0.818250i $$0.305055\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ 18.0000 + 31.1769i 0.665754 + 1.15312i
$$732$$ 0 0
$$733$$ 13.0000 22.5167i 0.480166 0.831672i −0.519575 0.854425i $$-0.673910\pi$$
0.999741 + 0.0227529i $$0.00724310\pi$$
$$734$$ 0 0
$$735$$ 5.50000 + 4.33013i 0.202871 + 0.159719i
$$736$$ 0 0
$$737$$ −5.00000 + 8.66025i −0.184177 + 0.319005i
$$738$$ 0 0
$$739$$ 5.00000 + 8.66025i 0.183928 + 0.318573i 0.943215 0.332184i $$-0.107785\pi$$
−0.759287 + 0.650756i $$0.774452\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −27.0000 −0.990534 −0.495267 0.868741i $$-0.664930\pi$$
−0.495267 + 0.868741i $$0.664930\pi$$
$$744$$ 0 0
$$745$$ −2.50000 4.33013i −0.0915929 0.158644i
$$746$$ 0 0
$$747$$ −11.0000 + 19.0526i −0.402469 + 0.697097i
$$748$$ 0 0
$$749$$ 18.0000 15.5885i 0.657706 0.569590i
$$750$$ 0 0
$$751$$ 6.00000 10.3923i 0.218943 0.379221i −0.735542 0.677479i $$-0.763072\pi$$
0.954485 + 0.298259i $$0.0964058\pi$$
$$752$$ 0 0
$$753$$ −4.00000 6.92820i −0.145768 0.252478i
$$754$$ 0 0
$$755$$ 8.00000 0.291150
$$756$$ 0 0
$$757$$ −24.0000 −0.872295 −0.436147 0.899875i $$-0.643657\pi$$
−0.436147 + 0.899875i $$0.643657\pi$$
$$758$$ 0 0
$$759$$ 1.00000 + 1.73205i 0.0362977 + 0.0628695i
$$760$$ 0 0
$$761$$ 3.00000 5.19615i 0.108750 0.188360i −0.806514 0.591215i $$-0.798649\pi$$
0.915264 + 0.402854i $$0.131982\pi$$
$$762$$ 0 0
$$763$$ 0.500000 + 2.59808i 0.0181012 + 0.0940567i
$$764$$ 0 0
$$765$$ −4.00000 + 6.92820i −0.144620 + 0.250490i
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 34.0000 1.22607 0.613036 0.790055i $$-0.289948\pi$$
0.613036 + 0.790055i $$0.289948\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$774$$ 0 0
$$775$$ 2.00000 3.46410i 0.0718421 0.124434i
$$776$$ 0 0
$$777$$ −10.0000 3.46410i −0.358748 0.124274i
$$778$$ 0 0
$$779$$ −1.00000 + 1.73205i −0.0358287 + 0.0620572i
$$780$$ 0 0
$$781$$ −14.0000 24.2487i −0.500959 0.867687i
$$782$$ 0 0
$$783$$ 45.0000 1.60817
$$784$$ 0 0
$$785$$ −2.00000 −0.0713831
$$786$$ 0 0
$$787$$ 22.5000 + 38.9711i 0.802038 + 1.38917i 0.918272 + 0.395949i $$0.129584\pi$$
−0.116234 + 0.993222i $$0.537082\pi$$
$$788$$ 0 0
$$789$$ 0.500000 0.866025i 0.0178005 0.0308313i
$$790$$ 0 0
$$791$$ 5.00000 + 1.73205i 0.177780 + 0.0615846i
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 5.00000 + 8.66025i 0.177332 + 0.307148i
$$796$$ 0 0
$$797$$