# Properties

 Label 735.2.d.b.589.3 Level $735$ Weight $2$ Character 735.589 Analytic conductor $5.869$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$735 = 3 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 735.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.86900454856$$ Analytic rank: $$0$$ Dimension: $$6$$ Coefficient field: 6.0.350464.1 Defining polynomial: $$x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2$$ x^6 - 2*x^5 + 2*x^4 + 2*x^3 + 4*x^2 - 4*x + 2 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 105) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 589.3 Root $$0.403032 - 0.403032i$$ of defining polynomial Character $$\chi$$ $$=$$ 735.589 Dual form 735.2.d.b.589.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-0.193937i q^{2} +1.00000i q^{3} +1.96239 q^{4} +(1.48119 + 1.67513i) q^{5} +0.193937 q^{6} -0.768452i q^{8} -1.00000 q^{9} +O(q^{10})$$ $$q-0.193937i q^{2} +1.00000i q^{3} +1.96239 q^{4} +(1.48119 + 1.67513i) q^{5} +0.193937 q^{6} -0.768452i q^{8} -1.00000 q^{9} +(0.324869 - 0.287258i) q^{10} +2.00000 q^{11} +1.96239i q^{12} -1.35026i q^{13} +(-1.67513 + 1.48119i) q^{15} +3.77575 q^{16} -3.35026i q^{17} +0.193937i q^{18} +5.35026 q^{19} +(2.90668 + 3.28726i) q^{20} -0.387873i q^{22} +4.96239i q^{23} +0.768452 q^{24} +(-0.612127 + 4.96239i) q^{25} -0.261865 q^{26} -1.00000i q^{27} -7.92478 q^{29} +(0.287258 + 0.324869i) q^{30} -4.57452 q^{31} -2.26916i q^{32} +2.00000i q^{33} -0.649738 q^{34} -1.96239 q^{36} +0.775746i q^{37} -1.03761i q^{38} +1.35026 q^{39} +(1.28726 - 1.13823i) q^{40} -3.73813 q^{41} -12.6253i q^{43} +3.92478 q^{44} +(-1.48119 - 1.67513i) q^{45} +0.962389 q^{46} +9.92478i q^{47} +3.77575i q^{48} +(0.962389 + 0.118714i) q^{50} +3.35026 q^{51} -2.64974i q^{52} +8.57452i q^{53} -0.193937 q^{54} +(2.96239 + 3.35026i) q^{55} +5.35026i q^{57} +1.53690i q^{58} -8.62530 q^{59} +(-3.28726 + 2.90668i) q^{60} +8.70052 q^{61} +0.887166i q^{62} +7.11142 q^{64} +(2.26187 - 2.00000i) q^{65} +0.387873 q^{66} -9.92478i q^{67} -6.57452i q^{68} -4.96239 q^{69} +2.00000 q^{71} +0.768452i q^{72} +9.35026i q^{73} +0.150446 q^{74} +(-4.96239 - 0.612127i) q^{75} +10.4993 q^{76} -0.261865i q^{78} -10.7005 q^{79} +(5.59261 + 6.32487i) q^{80} +1.00000 q^{81} +0.724961i q^{82} -3.22425i q^{83} +(5.61213 - 4.96239i) q^{85} -2.44851 q^{86} -7.92478i q^{87} -1.53690i q^{88} +1.03761 q^{89} +(-0.324869 + 0.287258i) q^{90} +9.73813i q^{92} -4.57452i q^{93} +1.92478 q^{94} +(7.92478 + 8.96239i) q^{95} +2.26916 q^{96} -18.4993i q^{97} -2.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q - 10 q^{4} - 2 q^{5} + 2 q^{6} - 6 q^{9}+O(q^{10})$$ 6 * q - 10 * q^4 - 2 * q^5 + 2 * q^6 - 6 * q^9 $$6 q - 10 q^{4} - 2 q^{5} + 2 q^{6} - 6 q^{9} + 12 q^{10} + 12 q^{11} + 26 q^{16} + 12 q^{19} + 30 q^{20} - 18 q^{24} - 2 q^{25} - 20 q^{26} - 4 q^{29} - 10 q^{30} - 4 q^{31} - 24 q^{34} + 10 q^{36} - 12 q^{39} - 4 q^{40} - 4 q^{41} - 20 q^{44} + 2 q^{45} - 16 q^{46} - 16 q^{50} - 2 q^{54} - 4 q^{55} + 32 q^{59} - 8 q^{60} + 12 q^{61} - 26 q^{64} + 32 q^{65} + 4 q^{66} - 8 q^{69} + 12 q^{71} + 88 q^{74} - 8 q^{75} - 4 q^{76} - 24 q^{79} - 46 q^{80} + 6 q^{81} + 32 q^{85} - 8 q^{86} + 28 q^{89} - 12 q^{90} - 32 q^{94} + 4 q^{95} + 58 q^{96} - 12 q^{99}+O(q^{100})$$ 6 * q - 10 * q^4 - 2 * q^5 + 2 * q^6 - 6 * q^9 + 12 * q^10 + 12 * q^11 + 26 * q^16 + 12 * q^19 + 30 * q^20 - 18 * q^24 - 2 * q^25 - 20 * q^26 - 4 * q^29 - 10 * q^30 - 4 * q^31 - 24 * q^34 + 10 * q^36 - 12 * q^39 - 4 * q^40 - 4 * q^41 - 20 * q^44 + 2 * q^45 - 16 * q^46 - 16 * q^50 - 2 * q^54 - 4 * q^55 + 32 * q^59 - 8 * q^60 + 12 * q^61 - 26 * q^64 + 32 * q^65 + 4 * q^66 - 8 * q^69 + 12 * q^71 + 88 * q^74 - 8 * q^75 - 4 * q^76 - 24 * q^79 - 46 * q^80 + 6 * q^81 + 32 * q^85 - 8 * q^86 + 28 * q^89 - 12 * q^90 - 32 * q^94 + 4 * q^95 + 58 * q^96 - 12 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$$.

 $$n$$ $$346$$ $$442$$ $$491$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.193937i 0.137134i −0.997647 0.0685669i $$-0.978157\pi$$
0.997647 0.0685669i $$-0.0218427\pi$$
$$3$$ 1.00000i 0.577350i
$$4$$ 1.96239 0.981194
$$5$$ 1.48119 + 1.67513i 0.662410 + 0.749141i
$$6$$ 0.193937 0.0791743
$$7$$ 0 0
$$8$$ 0.768452i 0.271689i
$$9$$ −1.00000 −0.333333
$$10$$ 0.324869 0.287258i 0.102733 0.0908389i
$$11$$ 2.00000 0.603023 0.301511 0.953463i $$-0.402509\pi$$
0.301511 + 0.953463i $$0.402509\pi$$
$$12$$ 1.96239i 0.566493i
$$13$$ 1.35026i 0.374495i −0.982313 0.187248i $$-0.940043\pi$$
0.982313 0.187248i $$-0.0599567\pi$$
$$14$$ 0 0
$$15$$ −1.67513 + 1.48119i −0.432517 + 0.382443i
$$16$$ 3.77575 0.943937
$$17$$ 3.35026i 0.812558i −0.913749 0.406279i $$-0.866826\pi$$
0.913749 0.406279i $$-0.133174\pi$$
$$18$$ 0.193937i 0.0457113i
$$19$$ 5.35026 1.22743 0.613717 0.789526i $$-0.289674\pi$$
0.613717 + 0.789526i $$0.289674\pi$$
$$20$$ 2.90668 + 3.28726i 0.649953 + 0.735053i
$$21$$ 0 0
$$22$$ 0.387873i 0.0826948i
$$23$$ 4.96239i 1.03473i 0.855765 + 0.517365i $$0.173087\pi$$
−0.855765 + 0.517365i $$0.826913\pi$$
$$24$$ 0.768452 0.156860
$$25$$ −0.612127 + 4.96239i −0.122425 + 0.992478i
$$26$$ −0.261865 −0.0513560
$$27$$ 1.00000i 0.192450i
$$28$$ 0 0
$$29$$ −7.92478 −1.47159 −0.735797 0.677202i $$-0.763192\pi$$
−0.735797 + 0.677202i $$0.763192\pi$$
$$30$$ 0.287258 + 0.324869i 0.0524458 + 0.0593127i
$$31$$ −4.57452 −0.821607 −0.410804 0.911724i $$-0.634752\pi$$
−0.410804 + 0.911724i $$0.634752\pi$$
$$32$$ 2.26916i 0.401134i
$$33$$ 2.00000i 0.348155i
$$34$$ −0.649738 −0.111429
$$35$$ 0 0
$$36$$ −1.96239 −0.327065
$$37$$ 0.775746i 0.127532i 0.997965 + 0.0637660i $$0.0203111\pi$$
−0.997965 + 0.0637660i $$0.979689\pi$$
$$38$$ 1.03761i 0.168323i
$$39$$ 1.35026 0.216215
$$40$$ 1.28726 1.13823i 0.203533 0.179969i
$$41$$ −3.73813 −0.583799 −0.291899 0.956449i $$-0.594287\pi$$
−0.291899 + 0.956449i $$0.594287\pi$$
$$42$$ 0 0
$$43$$ 12.6253i 1.92534i −0.270677 0.962670i $$-0.587248\pi$$
0.270677 0.962670i $$-0.412752\pi$$
$$44$$ 3.92478 0.591682
$$45$$ −1.48119 1.67513i −0.220803 0.249714i
$$46$$ 0.962389 0.141896
$$47$$ 9.92478i 1.44768i 0.689969 + 0.723839i $$0.257624\pi$$
−0.689969 + 0.723839i $$0.742376\pi$$
$$48$$ 3.77575i 0.544982i
$$49$$ 0 0
$$50$$ 0.962389 + 0.118714i 0.136102 + 0.0167887i
$$51$$ 3.35026 0.469130
$$52$$ 2.64974i 0.367453i
$$53$$ 8.57452i 1.17780i 0.808206 + 0.588900i $$0.200439\pi$$
−0.808206 + 0.588900i $$0.799561\pi$$
$$54$$ −0.193937 −0.0263914
$$55$$ 2.96239 + 3.35026i 0.399448 + 0.451749i
$$56$$ 0 0
$$57$$ 5.35026i 0.708659i
$$58$$ 1.53690i 0.201805i
$$59$$ −8.62530 −1.12292 −0.561459 0.827504i $$-0.689760\pi$$
−0.561459 + 0.827504i $$0.689760\pi$$
$$60$$ −3.28726 + 2.90668i −0.424383 + 0.375251i
$$61$$ 8.70052 1.11399 0.556994 0.830517i $$-0.311955\pi$$
0.556994 + 0.830517i $$0.311955\pi$$
$$62$$ 0.887166i 0.112670i
$$63$$ 0 0
$$64$$ 7.11142 0.888927
$$65$$ 2.26187 2.00000i 0.280550 0.248069i
$$66$$ 0.387873 0.0477439
$$67$$ 9.92478i 1.21250i −0.795272 0.606252i $$-0.792672\pi$$
0.795272 0.606252i $$-0.207328\pi$$
$$68$$ 6.57452i 0.797277i
$$69$$ −4.96239 −0.597401
$$70$$ 0 0
$$71$$ 2.00000 0.237356 0.118678 0.992933i $$-0.462134\pi$$
0.118678 + 0.992933i $$0.462134\pi$$
$$72$$ 0.768452i 0.0905629i
$$73$$ 9.35026i 1.09437i 0.837013 + 0.547183i $$0.184300\pi$$
−0.837013 + 0.547183i $$0.815700\pi$$
$$74$$ 0.150446 0.0174889
$$75$$ −4.96239 0.612127i −0.573007 0.0706823i
$$76$$ 10.4993 1.20435
$$77$$ 0 0
$$78$$ 0.261865i 0.0296504i
$$79$$ −10.7005 −1.20390 −0.601951 0.798533i $$-0.705610\pi$$
−0.601951 + 0.798533i $$0.705610\pi$$
$$80$$ 5.59261 + 6.32487i 0.625273 + 0.707142i
$$81$$ 1.00000 0.111111
$$82$$ 0.724961i 0.0800586i
$$83$$ 3.22425i 0.353908i −0.984219 0.176954i $$-0.943376\pi$$
0.984219 0.176954i $$-0.0566244\pi$$
$$84$$ 0 0
$$85$$ 5.61213 4.96239i 0.608721 0.538247i
$$86$$ −2.44851 −0.264029
$$87$$ 7.92478i 0.849625i
$$88$$ 1.53690i 0.163835i
$$89$$ 1.03761 0.109987 0.0549933 0.998487i $$-0.482486\pi$$
0.0549933 + 0.998487i $$0.482486\pi$$
$$90$$ −0.324869 + 0.287258i −0.0342442 + 0.0302796i
$$91$$ 0 0
$$92$$ 9.73813i 1.01527i
$$93$$ 4.57452i 0.474355i
$$94$$ 1.92478 0.198526
$$95$$ 7.92478 + 8.96239i 0.813065 + 0.919522i
$$96$$ 2.26916 0.231595
$$97$$ 18.4993i 1.87832i −0.343482 0.939159i $$-0.611606\pi$$
0.343482 0.939159i $$-0.388394\pi$$
$$98$$ 0 0
$$99$$ −2.00000 −0.201008
$$100$$ −1.20123 + 9.73813i −0.120123 + 0.973813i
$$101$$ 17.6629 1.75753 0.878763 0.477259i $$-0.158370\pi$$
0.878763 + 0.477259i $$0.158370\pi$$
$$102$$ 0.649738i 0.0643337i
$$103$$ 6.70052i 0.660222i −0.943942 0.330111i $$-0.892914\pi$$
0.943942 0.330111i $$-0.107086\pi$$
$$104$$ −1.03761 −0.101746
$$105$$ 0 0
$$106$$ 1.66291 0.161516
$$107$$ 13.7381i 1.32812i −0.747681 0.664058i $$-0.768833\pi$$
0.747681 0.664058i $$-0.231167\pi$$
$$108$$ 1.96239i 0.188831i
$$109$$ 2.77575 0.265868 0.132934 0.991125i $$-0.457560\pi$$
0.132934 + 0.991125i $$0.457560\pi$$
$$110$$ 0.649738 0.574515i 0.0619501 0.0547779i
$$111$$ −0.775746 −0.0736306
$$112$$ 0 0
$$113$$ 12.0508i 1.13364i 0.823841 + 0.566821i $$0.191827\pi$$
−0.823841 + 0.566821i $$0.808173\pi$$
$$114$$ 1.03761 0.0971812
$$115$$ −8.31265 + 7.35026i −0.775159 + 0.685415i
$$116$$ −15.5515 −1.44392
$$117$$ 1.35026i 0.124832i
$$118$$ 1.67276i 0.153990i
$$119$$ 0 0
$$120$$ 1.13823 + 1.28726i 0.103905 + 0.117510i
$$121$$ −7.00000 −0.636364
$$122$$ 1.68735i 0.152765i
$$123$$ 3.73813i 0.337056i
$$124$$ −8.97698 −0.806156
$$125$$ −9.21933 + 6.32487i −0.824602 + 0.565713i
$$126$$ 0 0
$$127$$ 2.70052i 0.239633i −0.992796 0.119816i $$-0.961769\pi$$
0.992796 0.119816i $$-0.0382306\pi$$
$$128$$ 5.91748i 0.523037i
$$129$$ 12.6253 1.11160
$$130$$ −0.387873 0.438658i −0.0340187 0.0384729i
$$131$$ −20.6253 −1.80204 −0.901020 0.433777i $$-0.857181\pi$$
−0.901020 + 0.433777i $$0.857181\pi$$
$$132$$ 3.92478i 0.341608i
$$133$$ 0 0
$$134$$ −1.92478 −0.166275
$$135$$ 1.67513 1.48119i 0.144172 0.127481i
$$136$$ −2.57452 −0.220763
$$137$$ 22.4993i 1.92224i −0.276124 0.961122i $$-0.589050\pi$$
0.276124 0.961122i $$-0.410950\pi$$
$$138$$ 0.962389i 0.0819240i
$$139$$ −3.27504 −0.277785 −0.138893 0.990307i $$-0.544354\pi$$
−0.138893 + 0.990307i $$0.544354\pi$$
$$140$$ 0 0
$$141$$ −9.92478 −0.835817
$$142$$ 0.387873i 0.0325496i
$$143$$ 2.70052i 0.225829i
$$144$$ −3.77575 −0.314646
$$145$$ −11.7381 13.2750i −0.974799 1.10243i
$$146$$ 1.81336 0.150075
$$147$$ 0 0
$$148$$ 1.52232i 0.125134i
$$149$$ 4.44851 0.364436 0.182218 0.983258i $$-0.441672\pi$$
0.182218 + 0.983258i $$0.441672\pi$$
$$150$$ −0.118714 + 0.962389i −0.00969294 + 0.0785787i
$$151$$ 1.29948 0.105750 0.0528749 0.998601i $$-0.483162\pi$$
0.0528749 + 0.998601i $$0.483162\pi$$
$$152$$ 4.11142i 0.333480i
$$153$$ 3.35026i 0.270853i
$$154$$ 0 0
$$155$$ −6.77575 7.66291i −0.544241 0.615500i
$$156$$ 2.64974 0.212149
$$157$$ 2.64974i 0.211472i −0.994394 0.105736i $$-0.966280\pi$$
0.994394 0.105736i $$-0.0337199\pi$$
$$158$$ 2.07522i 0.165096i
$$159$$ −8.57452 −0.680003
$$160$$ 3.80114 3.36107i 0.300506 0.265716i
$$161$$ 0 0
$$162$$ 0.193937i 0.0152371i
$$163$$ 5.29948i 0.415087i 0.978226 + 0.207544i $$0.0665469\pi$$
−0.978226 + 0.207544i $$0.933453\pi$$
$$164$$ −7.33567 −0.572820
$$165$$ −3.35026 + 2.96239i −0.260818 + 0.230622i
$$166$$ −0.625301 −0.0485327
$$167$$ 14.5501i 1.12592i −0.826485 0.562959i $$-0.809663\pi$$
0.826485 0.562959i $$-0.190337\pi$$
$$168$$ 0 0
$$169$$ 11.1768 0.859753
$$170$$ −0.962389 1.08840i −0.0738118 0.0834762i
$$171$$ −5.35026 −0.409145
$$172$$ 24.7757i 1.88913i
$$173$$ 4.49929i 0.342075i 0.985265 + 0.171037i $$0.0547119\pi$$
−0.985265 + 0.171037i $$0.945288\pi$$
$$174$$ −1.53690 −0.116512
$$175$$ 0 0
$$176$$ 7.55149 0.569215
$$177$$ 8.62530i 0.648317i
$$178$$ 0.201231i 0.0150829i
$$179$$ −10.0000 −0.747435 −0.373718 0.927543i $$-0.621917\pi$$
−0.373718 + 0.927543i $$0.621917\pi$$
$$180$$ −2.90668 3.28726i −0.216651 0.245018i
$$181$$ −10.6253 −0.789772 −0.394886 0.918730i $$-0.629216\pi$$
−0.394886 + 0.918730i $$0.629216\pi$$
$$182$$ 0 0
$$183$$ 8.70052i 0.643161i
$$184$$ 3.81336 0.281124
$$185$$ −1.29948 + 1.14903i −0.0955394 + 0.0844784i
$$186$$ −0.887166 −0.0650502
$$187$$ 6.70052i 0.489991i
$$188$$ 19.4763i 1.42045i
$$189$$ 0 0
$$190$$ 1.73813 1.53690i 0.126098 0.111499i
$$191$$ −13.8496 −1.00212 −0.501059 0.865413i $$-0.667056\pi$$
−0.501059 + 0.865413i $$0.667056\pi$$
$$192$$ 7.11142i 0.513222i
$$193$$ 15.3258i 1.10318i 0.834116 + 0.551588i $$0.185978\pi$$
−0.834116 + 0.551588i $$0.814022\pi$$
$$194$$ −3.58769 −0.257581
$$195$$ 2.00000 + 2.26187i 0.143223 + 0.161976i
$$196$$ 0 0
$$197$$ 0.574515i 0.0409325i 0.999791 + 0.0204663i $$0.00651507\pi$$
−0.999791 + 0.0204663i $$0.993485\pi$$
$$198$$ 0.387873i 0.0275649i
$$199$$ −0.201231 −0.0142649 −0.00713244 0.999975i $$-0.502270\pi$$
−0.00713244 + 0.999975i $$0.502270\pi$$
$$200$$ 3.81336 + 0.470390i 0.269645 + 0.0332616i
$$201$$ 9.92478 0.700040
$$202$$ 3.42548i 0.241016i
$$203$$ 0 0
$$204$$ 6.57452 0.460308
$$205$$ −5.53690 6.26187i −0.386714 0.437348i
$$206$$ −1.29948 −0.0905388
$$207$$ 4.96239i 0.344910i
$$208$$ 5.09825i 0.353500i
$$209$$ 10.7005 0.740171
$$210$$ 0 0
$$211$$ 6.44851 0.443934 0.221967 0.975054i $$-0.428752\pi$$
0.221967 + 0.975054i $$0.428752\pi$$
$$212$$ 16.8265i 1.15565i
$$213$$ 2.00000i 0.137038i
$$214$$ −2.66433 −0.182130
$$215$$ 21.1490 18.7005i 1.44235 1.27537i
$$216$$ −0.768452 −0.0522865
$$217$$ 0 0
$$218$$ 0.538319i 0.0364595i
$$219$$ −9.35026 −0.631832
$$220$$ 5.81336 + 6.57452i 0.391936 + 0.443254i
$$221$$ −4.52373 −0.304299
$$222$$ 0.150446i 0.0100972i
$$223$$ 1.55149i 0.103896i −0.998650 0.0519478i $$-0.983457\pi$$
0.998650 0.0519478i $$-0.0165429\pi$$
$$224$$ 0 0
$$225$$ 0.612127 4.96239i 0.0408085 0.330826i
$$226$$ 2.33709 0.155461
$$227$$ 13.1490i 0.872732i −0.899769 0.436366i $$-0.856265\pi$$
0.899769 0.436366i $$-0.143735\pi$$
$$228$$ 10.4993i 0.695333i
$$229$$ 2.77575 0.183426 0.0917132 0.995785i $$-0.470766\pi$$
0.0917132 + 0.995785i $$0.470766\pi$$
$$230$$ 1.42548 + 1.61213i 0.0939937 + 0.106300i
$$231$$ 0 0
$$232$$ 6.08981i 0.399816i
$$233$$ 0.0507852i 0.00332705i −0.999999 0.00166353i $$-0.999470\pi$$
0.999999 0.00166353i $$-0.000529517\pi$$
$$234$$ 0.261865 0.0171187
$$235$$ −16.6253 + 14.7005i −1.08452 + 0.958956i
$$236$$ −16.9262 −1.10180
$$237$$ 10.7005i 0.695074i
$$238$$ 0 0
$$239$$ −5.84955 −0.378376 −0.189188 0.981941i $$-0.560586\pi$$
−0.189188 + 0.981941i $$0.560586\pi$$
$$240$$ −6.32487 + 5.59261i −0.408269 + 0.361002i
$$241$$ 0.0752228 0.00484553 0.00242276 0.999997i $$-0.499229\pi$$
0.00242276 + 0.999997i $$0.499229\pi$$
$$242$$ 1.35756i 0.0872670i
$$243$$ 1.00000i 0.0641500i
$$244$$ 17.0738 1.09304
$$245$$ 0 0
$$246$$ −0.724961 −0.0462218
$$247$$ 7.22425i 0.459668i
$$248$$ 3.51530i 0.223222i
$$249$$ 3.22425 0.204329
$$250$$ 1.22662 + 1.78797i 0.0775785 + 0.113081i
$$251$$ −19.2243 −1.21342 −0.606712 0.794922i $$-0.707512\pi$$
−0.606712 + 0.794922i $$0.707512\pi$$
$$252$$ 0 0
$$253$$ 9.92478i 0.623965i
$$254$$ −0.523730 −0.0328618
$$255$$ 4.96239 + 5.61213i 0.310757 + 0.351445i
$$256$$ 13.0752 0.817201
$$257$$ 7.35026i 0.458497i 0.973368 + 0.229248i $$0.0736268\pi$$
−0.973368 + 0.229248i $$0.926373\pi$$
$$258$$ 2.44851i 0.152437i
$$259$$ 0 0
$$260$$ 4.43866 3.92478i 0.275274 0.243404i
$$261$$ 7.92478 0.490531
$$262$$ 4.00000i 0.247121i
$$263$$ 12.9624i 0.799295i −0.916669 0.399648i $$-0.869133\pi$$
0.916669 0.399648i $$-0.130867\pi$$
$$264$$ 1.53690 0.0945899
$$265$$ −14.3634 + 12.7005i −0.882339 + 0.780187i
$$266$$ 0 0
$$267$$ 1.03761i 0.0635008i
$$268$$ 19.4763i 1.18970i
$$269$$ 4.11142 0.250678 0.125339 0.992114i $$-0.459998\pi$$
0.125339 + 0.992114i $$0.459998\pi$$
$$270$$ −0.287258 0.324869i −0.0174819 0.0197709i
$$271$$ 16.4241 0.997691 0.498846 0.866691i $$-0.333757\pi$$
0.498846 + 0.866691i $$0.333757\pi$$
$$272$$ 12.6497i 0.767003i
$$273$$ 0 0
$$274$$ −4.36344 −0.263605
$$275$$ −1.22425 + 9.92478i −0.0738253 + 0.598487i
$$276$$ −9.73813 −0.586167
$$277$$ 11.0738i 0.665361i 0.943040 + 0.332680i $$0.107953\pi$$
−0.943040 + 0.332680i $$0.892047\pi$$
$$278$$ 0.635150i 0.0380938i
$$279$$ 4.57452 0.273869
$$280$$ 0 0
$$281$$ 14.3733 0.857438 0.428719 0.903438i $$-0.358965\pi$$
0.428719 + 0.903438i $$0.358965\pi$$
$$282$$ 1.92478i 0.114619i
$$283$$ 1.14903i 0.0683028i −0.999417 0.0341514i $$-0.989127\pi$$
0.999417 0.0341514i $$-0.0108728\pi$$
$$284$$ 3.92478 0.232893
$$285$$ −8.96239 + 7.92478i −0.530886 + 0.469423i
$$286$$ −0.523730 −0.0309688
$$287$$ 0 0
$$288$$ 2.26916i 0.133711i
$$289$$ 5.77575 0.339750
$$290$$ −2.57452 + 2.27645i −0.151181 + 0.133678i
$$291$$ 18.4993 1.08445
$$292$$ 18.3488i 1.07379i
$$293$$ 0.649738i 0.0379581i −0.999820 0.0189791i $$-0.993958\pi$$
0.999820 0.0189791i $$-0.00604158\pi$$
$$294$$ 0 0
$$295$$ −12.7757 14.4485i −0.743833 0.841225i
$$296$$ 0.596124 0.0346490
$$297$$ 2.00000i 0.116052i
$$298$$ 0.862728i 0.0499765i
$$299$$ 6.70052 0.387501
$$300$$ −9.73813 1.20123i −0.562231 0.0693531i
$$301$$ 0 0
$$302$$ 0.252016i 0.0145019i
$$303$$ 17.6629i 1.01471i
$$304$$ 20.2012 1.15862
$$305$$ 12.8872 + 14.5745i 0.737917 + 0.834534i
$$306$$ 0.649738 0.0371431
$$307$$ 24.1016i 1.37555i 0.725924 + 0.687775i $$0.241412\pi$$
−0.725924 + 0.687775i $$0.758588\pi$$
$$308$$ 0 0
$$309$$ 6.70052 0.381179
$$310$$ −1.48612 + 1.31406i −0.0844059 + 0.0746339i
$$311$$ −8.25202 −0.467929 −0.233964 0.972245i $$-0.575170\pi$$
−0.233964 + 0.972245i $$0.575170\pi$$
$$312$$ 1.03761i 0.0587432i
$$313$$ 14.9018i 0.842297i 0.906992 + 0.421148i $$0.138373\pi$$
−0.906992 + 0.421148i $$0.861627\pi$$
$$314$$ −0.513881 −0.0290000
$$315$$ 0 0
$$316$$ −20.9986 −1.18126
$$317$$ 10.1260i 0.568733i −0.958716 0.284367i $$-0.908217\pi$$
0.958716 0.284367i $$-0.0917833\pi$$
$$318$$ 1.66291i 0.0932515i
$$319$$ −15.8496 −0.887405
$$320$$ 10.5334 + 11.9126i 0.588835 + 0.665932i
$$321$$ 13.7381 0.766788
$$322$$ 0 0
$$323$$ 17.9248i 0.997361i
$$324$$ 1.96239 0.109022
$$325$$ 6.70052 + 0.826531i 0.371678 + 0.0458477i
$$326$$ 1.02776 0.0569225
$$327$$ 2.77575i 0.153499i
$$328$$ 2.87258i 0.158612i
$$329$$ 0 0
$$330$$ 0.574515 + 0.649738i 0.0316260 + 0.0357669i
$$331$$ 27.8496 1.53075 0.765375 0.643585i $$-0.222554\pi$$
0.765375 + 0.643585i $$0.222554\pi$$
$$332$$ 6.32724i 0.347252i
$$333$$ 0.775746i 0.0425106i
$$334$$ −2.82179 −0.154402
$$335$$ 16.6253 14.7005i 0.908337 0.803175i
$$336$$ 0 0
$$337$$ 3.84955i 0.209699i 0.994488 + 0.104849i $$0.0334360\pi$$
−0.994488 + 0.104849i $$0.966564\pi$$
$$338$$ 2.16759i 0.117901i
$$339$$ −12.0508 −0.654509
$$340$$ 11.0132 9.73813i 0.597273 0.528125i
$$341$$ −9.14903 −0.495448
$$342$$ 1.03761i 0.0561076i
$$343$$ 0 0
$$344$$ −9.70194 −0.523093
$$345$$ −7.35026 8.31265i −0.395725 0.447538i
$$346$$ 0.872577 0.0469101
$$347$$ 9.58769i 0.514694i −0.966319 0.257347i $$-0.917152\pi$$
0.966319 0.257347i $$-0.0828484\pi$$
$$348$$ 15.5515i 0.833648i
$$349$$ −15.1490 −0.810909 −0.405455 0.914115i $$-0.632887\pi$$
−0.405455 + 0.914115i $$0.632887\pi$$
$$350$$ 0 0
$$351$$ −1.35026 −0.0720716
$$352$$ 4.53832i 0.241893i
$$353$$ 20.3488i 1.08306i 0.840681 + 0.541530i $$0.182155\pi$$
−0.840681 + 0.541530i $$0.817845\pi$$
$$354$$ −1.67276 −0.0889063
$$355$$ 2.96239 + 3.35026i 0.157227 + 0.177813i
$$356$$ 2.03620 0.107918
$$357$$ 0 0
$$358$$ 1.93937i 0.102499i
$$359$$ 31.4010 1.65728 0.828642 0.559779i $$-0.189114\pi$$
0.828642 + 0.559779i $$0.189114\pi$$
$$360$$ −1.28726 + 1.13823i −0.0678444 + 0.0599898i
$$361$$ 9.62530 0.506595
$$362$$ 2.06063i 0.108305i
$$363$$ 7.00000i 0.367405i
$$364$$ 0 0
$$365$$ −15.6629 + 13.8496i −0.819834 + 0.724919i
$$366$$ 1.68735 0.0881992
$$367$$ 29.4010i 1.53472i −0.641215 0.767361i $$-0.721569\pi$$
0.641215 0.767361i $$-0.278431\pi$$
$$368$$ 18.7367i 0.976719i
$$369$$ 3.73813 0.194600
$$370$$ 0.222839 + 0.252016i 0.0115849 + 0.0131017i
$$371$$ 0 0
$$372$$ 8.97698i 0.465435i
$$373$$ 16.0000i 0.828449i 0.910175 + 0.414224i $$0.135947\pi$$
−0.910175 + 0.414224i $$0.864053\pi$$
$$374$$ −1.29948 −0.0671943
$$375$$ −6.32487 9.21933i −0.326615 0.476084i
$$376$$ 7.62672 0.393318
$$377$$ 10.7005i 0.551105i
$$378$$ 0 0
$$379$$ −10.7005 −0.549649 −0.274824 0.961494i $$-0.588620\pi$$
−0.274824 + 0.961494i $$0.588620\pi$$
$$380$$ 15.5515 + 17.5877i 0.797775 + 0.902229i
$$381$$ 2.70052 0.138352
$$382$$ 2.68594i 0.137424i
$$383$$ 16.7757i 0.857201i 0.903494 + 0.428600i $$0.140993\pi$$
−0.903494 + 0.428600i $$0.859007\pi$$
$$384$$ 5.91748 0.301975
$$385$$ 0 0
$$386$$ 2.97224 0.151283
$$387$$ 12.6253i 0.641780i
$$388$$ 36.3028i 1.84300i
$$389$$ 29.3258 1.48688 0.743439 0.668804i $$-0.233193\pi$$
0.743439 + 0.668804i $$0.233193\pi$$
$$390$$ 0.438658 0.387873i 0.0222123 0.0196407i
$$391$$ 16.6253 0.840778
$$392$$ 0 0
$$393$$ 20.6253i 1.04041i
$$394$$ 0.111420 0.00561324
$$395$$ −15.8496 17.9248i −0.797478 0.901893i
$$396$$ −3.92478 −0.197227
$$397$$ 18.3488i 0.920902i 0.887685 + 0.460451i $$0.152312\pi$$
−0.887685 + 0.460451i $$0.847688\pi$$
$$398$$ 0.0390260i 0.00195620i
$$399$$ 0 0
$$400$$ −2.31124 + 18.7367i −0.115562 + 0.936836i
$$401$$ −37.3258 −1.86396 −0.931981 0.362506i $$-0.881921\pi$$
−0.931981 + 0.362506i $$0.881921\pi$$
$$402$$ 1.92478i 0.0959992i
$$403$$ 6.17679i 0.307688i
$$404$$ 34.6615 1.72447
$$405$$ 1.48119 + 1.67513i 0.0736011 + 0.0832379i
$$406$$ 0 0
$$407$$ 1.55149i 0.0769046i
$$408$$ 2.57452i 0.127458i
$$409$$ −22.3733 −1.10629 −0.553144 0.833086i $$-0.686572\pi$$
−0.553144 + 0.833086i $$0.686572\pi$$
$$410$$ −1.21440 + 1.07381i −0.0599752 + 0.0530316i
$$411$$ 22.4993 1.10981
$$412$$ 13.1490i 0.647806i
$$413$$ 0 0
$$414$$ −0.962389 −0.0472988
$$415$$ 5.40105 4.77575i 0.265127 0.234432i
$$416$$ −3.06396 −0.150223
$$417$$ 3.27504i 0.160379i
$$418$$ 2.07522i 0.101502i
$$419$$ 23.4763 1.14689 0.573445 0.819244i $$-0.305606\pi$$
0.573445 + 0.819244i $$0.305606\pi$$
$$420$$ 0 0
$$421$$ −25.2243 −1.22935 −0.614677 0.788779i $$-0.710714\pi$$
−0.614677 + 0.788779i $$0.710714\pi$$
$$422$$ 1.25060i 0.0608783i
$$423$$ 9.92478i 0.482559i
$$424$$ 6.58910 0.319995
$$425$$ 16.6253 + 2.05079i 0.806446 + 0.0994777i
$$426$$ 0.387873 0.0187925
$$427$$ 0 0
$$428$$ 26.9596i 1.30314i
$$429$$ 2.70052 0.130383
$$430$$ −3.62672 4.10157i −0.174896 0.197795i
$$431$$ −19.4010 −0.934516 −0.467258 0.884121i $$-0.654758\pi$$
−0.467258 + 0.884121i $$0.654758\pi$$
$$432$$ 3.77575i 0.181661i
$$433$$ 6.49929i 0.312336i −0.987731 0.156168i $$-0.950086\pi$$
0.987731 0.156168i $$-0.0499141\pi$$
$$434$$ 0 0
$$435$$ 13.2750 11.7381i 0.636489 0.562800i
$$436$$ 5.44709 0.260868
$$437$$ 26.5501i 1.27006i
$$438$$ 1.81336i 0.0866456i
$$439$$ −14.6497 −0.699194 −0.349597 0.936900i $$-0.613681\pi$$
−0.349597 + 0.936900i $$0.613681\pi$$
$$440$$ 2.57452 2.27645i 0.122735 0.108526i
$$441$$ 0 0
$$442$$ 0.877317i 0.0417297i
$$443$$ 19.1392i 0.909330i 0.890663 + 0.454665i $$0.150241\pi$$
−0.890663 + 0.454665i $$0.849759\pi$$
$$444$$ −1.52232 −0.0722459
$$445$$ 1.53690 + 1.73813i 0.0728562 + 0.0823955i
$$446$$ −0.300891 −0.0142476
$$447$$ 4.44851i 0.210407i
$$448$$ 0 0
$$449$$ 32.8021 1.54803 0.774013 0.633169i $$-0.218246\pi$$
0.774013 + 0.633169i $$0.218246\pi$$
$$450$$ −0.962389 0.118714i −0.0453674 0.00559622i
$$451$$ −7.47627 −0.352044
$$452$$ 23.6483i 1.11232i
$$453$$ 1.29948i 0.0610547i
$$454$$ −2.55008 −0.119681
$$455$$ 0 0
$$456$$ 4.11142 0.192535
$$457$$ 18.7005i 0.874774i 0.899273 + 0.437387i $$0.144096\pi$$
−0.899273 + 0.437387i $$0.855904\pi$$
$$458$$ 0.538319i 0.0251540i
$$459$$ −3.35026 −0.156377
$$460$$ −16.3127 + 14.4241i −0.760581 + 0.672526i
$$461$$ 6.96239 0.324271 0.162135 0.986769i $$-0.448162\pi$$
0.162135 + 0.986769i $$0.448162\pi$$
$$462$$ 0 0
$$463$$ 5.29948i 0.246288i 0.992389 + 0.123144i $$0.0392976\pi$$
−0.992389 + 0.123144i $$0.960702\pi$$
$$464$$ −29.9219 −1.38909
$$465$$ 7.66291 6.77575i 0.355359 0.314218i
$$466$$ −0.00984911 −0.000456251
$$467$$ 13.1490i 0.608465i −0.952598 0.304232i $$-0.901600\pi$$
0.952598 0.304232i $$-0.0983999\pi$$
$$468$$ 2.64974i 0.122484i
$$469$$ 0 0
$$470$$ 2.85097 + 3.22425i 0.131505 + 0.148724i
$$471$$ 2.64974 0.122093
$$472$$ 6.62813i 0.305084i
$$473$$ 25.2506i 1.16102i
$$474$$ −2.07522 −0.0953181
$$475$$ −3.27504 + 26.5501i −0.150269 + 1.21820i
$$476$$ 0 0
$$477$$ 8.57452i 0.392600i
$$478$$ 1.13444i 0.0518882i
$$479$$ 5.14903 0.235265 0.117633 0.993057i $$-0.462469\pi$$
0.117633 + 0.993057i $$0.462469\pi$$
$$480$$ 3.36107 + 3.80114i 0.153411 + 0.173497i
$$481$$ 1.04746 0.0477601
$$482$$ 0.0145884i 0.000664486i
$$483$$ 0 0
$$484$$ −13.7367 −0.624396
$$485$$ 30.9887 27.4010i 1.40713 1.24422i
$$486$$ 0.193937 0.00879714
$$487$$ 22.1768i 1.00493i 0.864599 + 0.502463i $$0.167573\pi$$
−0.864599 + 0.502463i $$0.832427\pi$$
$$488$$ 6.68594i 0.302658i
$$489$$ −5.29948 −0.239651
$$490$$ 0 0
$$491$$ 2.00000 0.0902587 0.0451294 0.998981i $$-0.485630\pi$$
0.0451294 + 0.998981i $$0.485630\pi$$
$$492$$ 7.33567i 0.330718i
$$493$$ 26.5501i 1.19576i
$$494$$ −1.40105 −0.0630361
$$495$$ −2.96239 3.35026i −0.133149 0.150583i
$$496$$ −17.2722 −0.775545
$$497$$ 0 0
$$498$$ 0.625301i 0.0280204i
$$499$$ 6.55008 0.293222 0.146611 0.989194i $$-0.453163\pi$$
0.146611 + 0.989194i $$0.453163\pi$$
$$500$$ −18.0919 + 12.4119i −0.809095 + 0.555075i
$$501$$ 14.5501 0.650050
$$502$$ 3.72829i 0.166402i
$$503$$ 8.77575i 0.391291i −0.980675 0.195646i $$-0.937320\pi$$
0.980675 0.195646i $$-0.0626802\pi$$
$$504$$ 0 0
$$505$$ 26.1622 + 29.5877i 1.16420 + 1.31663i
$$506$$ 1.92478 0.0855668
$$507$$ 11.1768i 0.496379i
$$508$$ 5.29948i 0.235126i
$$509$$ 13.1392 0.582384 0.291192 0.956665i $$-0.405948\pi$$
0.291192 + 0.956665i $$0.405948\pi$$
$$510$$ 1.08840 0.962389i 0.0481950 0.0426153i
$$511$$ 0 0
$$512$$ 14.3707i 0.635103i
$$513$$ 5.35026i 0.236220i
$$514$$ 1.42548 0.0628754
$$515$$ 11.2243 9.92478i 0.494600 0.437338i
$$516$$ 24.7757 1.09069
$$517$$ 19.8496i 0.872982i
$$518$$ 0 0
$$519$$ −4.49929 −0.197497
$$520$$ −1.53690 1.73813i −0.0673977 0.0762223i
$$521$$ 37.6629 1.65004 0.825021 0.565102i $$-0.191163\pi$$
0.825021 + 0.565102i $$0.191163\pi$$
$$522$$ 1.53690i 0.0672685i
$$523$$ 4.00000i 0.174908i 0.996169 + 0.0874539i $$0.0278730\pi$$
−0.996169 + 0.0874539i $$0.972127\pi$$
$$524$$ −40.4749 −1.76815
$$525$$ 0 0
$$526$$ −2.51388 −0.109610
$$527$$ 15.3258i 0.667603i
$$528$$ 7.55149i 0.328637i
$$529$$ −1.62530 −0.0706652
$$530$$ 2.46310 + 2.78560i 0.106990 + 0.120999i
$$531$$ 8.62530 0.374306
$$532$$ 0 0
$$533$$ 5.04746i 0.218630i
$$534$$ 0.201231 0.00870811
$$535$$ 23.0132 20.3488i 0.994946 0.879757i
$$536$$ −7.62672 −0.329424
$$537$$ 10.0000i 0.431532i
$$538$$ 0.797355i 0.0343764i
$$539$$ 0 0
$$540$$ 3.28726 2.90668i 0.141461 0.125084i
$$541$$ −22.4749 −0.966269 −0.483135 0.875546i $$-0.660502\pi$$
−0.483135 + 0.875546i $$0.660502\pi$$
$$542$$ 3.18523i 0.136817i
$$543$$ 10.6253i 0.455975i
$$544$$ −7.60228 −0.325945
$$545$$ 4.11142 + 4.64974i 0.176114 + 0.199173i
$$546$$ 0 0
$$547$$ 25.9248i 1.10846i 0.832362 + 0.554232i $$0.186988\pi$$
−0.832362 + 0.554232i $$0.813012\pi$$
$$548$$ 44.1524i 1.88610i
$$549$$ −8.70052 −0.371329
$$550$$ 1.92478 + 0.237428i 0.0820728 + 0.0101239i
$$551$$ −42.3996 −1.80629
$$552$$ 3.81336i 0.162307i
$$553$$ 0 0
$$554$$ 2.14762 0.0912435
$$555$$ −1.14903 1.29948i −0.0487736 0.0551597i
$$556$$ −6.42690 −0.272561
$$557$$ 28.5256i 1.20867i 0.796730 + 0.604335i $$0.206561\pi$$
−0.796730 + 0.604335i $$0.793439\pi$$
$$558$$ 0.887166i 0.0375567i
$$559$$ −17.0475 −0.721031
$$560$$ 0 0
$$561$$ 6.70052 0.282896
$$562$$ 2.78751i 0.117584i
$$563$$ 11.6267i 0.490008i 0.969522 + 0.245004i $$0.0787892\pi$$
−0.969522 + 0.245004i $$0.921211\pi$$
$$564$$ −19.4763 −0.820099
$$565$$ −20.1866 + 17.8496i −0.849258 + 0.750936i
$$566$$ −0.222839 −0.00936663
$$567$$ 0 0
$$568$$ 1.53690i 0.0644871i
$$569$$ −9.32582 −0.390959 −0.195479 0.980708i $$-0.562626\pi$$
−0.195479 + 0.980708i $$0.562626\pi$$
$$570$$ 1.53690 + 1.73813i 0.0643738 + 0.0728025i
$$571$$ −19.6991 −0.824382 −0.412191 0.911097i $$-0.635236\pi$$
−0.412191 + 0.911097i $$0.635236\pi$$
$$572$$ 5.29948i 0.221582i
$$573$$ 13.8496i 0.578573i
$$574$$ 0 0
$$575$$ −24.6253 3.03761i −1.02695 0.126677i
$$576$$ −7.11142 −0.296309
$$577$$ 32.7974i 1.36537i 0.730712 + 0.682686i $$0.239188\pi$$
−0.730712 + 0.682686i $$0.760812\pi$$
$$578$$ 1.12013i 0.0465912i
$$579$$ −15.3258 −0.636920
$$580$$ −23.0348 26.0508i −0.956467 1.08170i
$$581$$ 0 0
$$582$$ 3.58769i 0.148715i
$$583$$ 17.1490i 0.710240i
$$584$$ 7.18523 0.297327
$$585$$ −2.26187 + 2.00000i −0.0935166 + 0.0826898i
$$586$$ −0.126008 −0.00520534
$$587$$ 18.8218i 0.776859i 0.921479 + 0.388429i $$0.126982\pi$$
−0.921479 + 0.388429i $$0.873018\pi$$
$$588$$ 0 0
$$589$$ −24.4749 −1.00847
$$590$$ −2.80209 + 2.47768i −0.115360 + 0.102005i
$$591$$ −0.574515 −0.0236324
$$592$$ 2.92902i 0.120382i
$$593$$ 33.7499i 1.38594i −0.720965 0.692971i $$-0.756301\pi$$
0.720965 0.692971i $$-0.243699\pi$$
$$594$$ −0.387873 −0.0159146
$$595$$ 0 0
$$596$$ 8.72970 0.357582
$$597$$ 0.201231i 0.00823583i
$$598$$ 1.29948i 0.0531395i
$$599$$ 20.2981 0.829356 0.414678 0.909968i $$-0.363894\pi$$
0.414678 + 0.909968i $$0.363894\pi$$
$$600$$ −0.470390 + 3.81336i −0.0192036 + 0.155680i
$$601$$ 13.8496 0.564935 0.282468 0.959277i $$-0.408847\pi$$
0.282468 + 0.959277i $$0.408847\pi$$
$$602$$ 0 0
$$603$$ 9.92478i 0.404168i
$$604$$ 2.55008 0.103761
$$605$$ −10.3684 11.7259i −0.421534 0.476726i
$$606$$ 3.42548 0.139151
$$607$$ 25.2506i 1.02489i −0.858720 0.512445i $$-0.828740\pi$$
0.858720 0.512445i $$-0.171260\pi$$
$$608$$ 12.1406i 0.492366i
$$609$$ 0 0
$$610$$ 2.82653 2.49929i 0.114443 0.101193i
$$611$$ 13.4010 0.542148
$$612$$ 6.57452i 0.265759i
$$613$$ 9.14903i 0.369526i −0.982783 0.184763i $$-0.940848\pi$$
0.982783 0.184763i $$-0.0591517\pi$$
$$614$$ 4.67418 0.188634
$$615$$ 6.26187 5.53690i 0.252503 0.223270i
$$616$$ 0 0
$$617$$ 15.9492i 0.642091i −0.947064 0.321046i $$-0.895966\pi$$
0.947064 0.321046i $$-0.104034\pi$$
$$618$$ 1.29948i 0.0522726i
$$619$$ 11.1735 0.449100 0.224550 0.974463i $$-0.427909\pi$$
0.224550 + 0.974463i $$0.427909\pi$$
$$620$$ −13.2966 15.0376i −0.534006 0.603925i
$$621$$ 4.96239 0.199134
$$622$$ 1.60037i 0.0641689i
$$623$$ 0 0
$$624$$ 5.09825 0.204093
$$625$$ −24.2506 6.07522i −0.970024 0.243009i
$$626$$ 2.89000 0.115507
$$627$$ 10.7005i 0.427338i
$$628$$ 5.19982i 0.207495i
$$629$$ 2.59895 0.103627
$$630$$ 0 0
$$631$$ −14.5501 −0.579229 −0.289615 0.957143i $$-0.593527\pi$$
−0.289615 + 0.957143i $$0.593527\pi$$
$$632$$ 8.22284i 0.327087i
$$633$$ 6.44851i 0.256305i
$$634$$ −1.96380 −0.0779926
$$635$$ 4.52373 4.00000i 0.179519 0.158735i
$$636$$ −16.8265 −0.667215
$$637$$ 0 0
$$638$$ 3.07381i 0.121693i
$$639$$ −2.00000 −0.0791188
$$640$$ 9.91256 8.76494i 0.391828 0.346465i
$$641$$ −38.7269 −1.52962 −0.764810 0.644256i $$-0.777167\pi$$
−0.764810 + 0.644256i $$0.777167\pi$$
$$642$$ 2.66433i 0.105153i
$$643$$ 11.9511i 0.471306i 0.971837 + 0.235653i $$0.0757229\pi$$
−0.971837 + 0.235653i $$0.924277\pi$$
$$644$$ 0 0
$$645$$ 18.7005 + 21.1490i 0.736332 + 0.832742i
$$646$$ −3.47627 −0.136772
$$647$$ 14.5501i 0.572023i −0.958226 0.286011i $$-0.907671\pi$$
0.958226 0.286011i $$-0.0923295\pi$$
$$648$$ 0.768452i 0.0301876i
$$649$$ −17.2506 −0.677145
$$650$$ 0.160295 1.29948i 0.00628727 0.0509697i
$$651$$ 0 0
$$652$$ 10.3996i 0.407281i
$$653$$ 49.9756i 1.95569i 0.209319 + 0.977847i $$0.432875\pi$$
−0.209319 + 0.977847i $$0.567125\pi$$
$$654$$ 0.538319 0.0210499
$$655$$ −30.5501 34.5501i −1.19369 1.34998i
$$656$$ −14.1142 −0.551069
$$657$$ 9.35026i 0.364788i
$$658$$ 0 0
$$659$$ 16.9525 0.660377 0.330189 0.943915i $$-0.392888\pi$$
0.330189 + 0.943915i $$0.392888\pi$$
$$660$$ −6.57452 + 5.81336i −0.255913 + 0.226285i
$$661$$ 15.6531 0.608834 0.304417 0.952539i $$-0.401538\pi$$
0.304417 + 0.952539i $$0.401538\pi$$
$$662$$ 5.40105i 0.209918i
$$663$$ 4.52373i 0.175687i
$$664$$ −2.47768 −0.0961528
$$665$$ 0 0
$$666$$ −0.150446 −0.00582965
$$667$$ 39.3258i 1.52270i
$$668$$ 28.5529i 1.10475i
$$669$$ 1.55149 0.0599842
$$670$$ −2.85097 3.22425i −0.110143 0.124564i
$$671$$ 17.4010 0.671760
$$672$$ 0 0
$$673$$ 26.0263i 1.00324i 0.865088 + 0.501621i $$0.167263\pi$$
−0.865088 + 0.501621i $$0.832737\pi$$
$$674$$ 0.746569 0.0287568
$$675$$ 4.96239 + 0.612127i 0.191002 + 0.0235608i
$$676$$ 21.9332 0.843585
$$677$$ 35.4518i 1.36252i −0.732039 0.681262i $$-0.761431\pi$$
0.732039 0.681262i $$-0.238569\pi$$
$$678$$ 2.33709i 0.0897553i
$$679$$ 0 0
$$680$$ −3.81336 4.31265i −0.146236 0.165383i
$$681$$ 13.1490 0.503872
$$682$$ 1.77433i 0.0679427i
$$683$$ 23.6629i 0.905436i −0.891654 0.452718i $$-0.850454\pi$$
0.891654 0.452718i $$-0.149546\pi$$
$$684$$ −10.4993 −0.401450
$$685$$ 37.6893 33.3258i 1.44003 1.27331i
$$686$$ 0 0
$$687$$ 2.77575i 0.105901i
$$688$$ 47.6699i 1.81740i
$$689$$ 11.5778 0.441081
$$690$$ −1.61213 + 1.42548i −0.0613726 + 0.0542673i
$$691$$ 0.574515 0.0218556 0.0109278 0.999940i $$-0.496522\pi$$
0.0109278 + 0.999940i $$0.496522\pi$$
$$692$$ 8.82936i 0.335642i
$$693$$ 0 0
$$694$$ −1.85940 −0.0705820
$$695$$ −4.85097 5.48612i −0.184008 0.208100i
$$696$$ −6.08981 −0.230834
$$697$$ 12.5237i 0.474370i
$$698$$ 2.93795i 0.111203i
$$699$$ 0.0507852 0.00192087
$$700$$ 0 0
$$701$$ 42.7269 1.61377 0.806886 0.590707i $$-0.201151\pi$$
0.806886 + 0.590707i $$0.201151\pi$$
$$702$$ 0.261865i 0.00988346i
$$703$$ 4.15045i 0.156537i
$$704$$ 14.2228 0.536043
$$705$$ −14.7005 16.6253i −0.553654 0.626145i
$$706$$ 3.94639 0.148524
$$707$$ 0 0
$$708$$ 16.9262i 0.636125i
$$709$$ −27.2506 −1.02342 −0.511709 0.859159i $$-0.670987\pi$$
−0.511709 + 0.859159i $$0.670987\pi$$
$$710$$ 0.649738 0.574515i 0.0243842 0.0215612i
$$711$$ 10.7005 0.401301
$$712$$ 0.797355i 0.0298821i
$$713$$ 22.7005i 0.850141i
$$714$$ 0 0
$$715$$ 4.52373 4.00000i 0.169178 0.149592i
$$716$$ −19.6239 −0.733379
$$717$$ 5.84955i 0.218456i
$$718$$ 6.08981i 0.227270i
$$719$$ −10.7005 −0.399062 −0.199531 0.979891i $$-0.563942\pi$$
−0.199531 + 0.979891i $$0.563942\pi$$
$$720$$ −5.59261 6.32487i −0.208424 0.235714i
$$721$$ 0 0
$$722$$ 1.86670i 0.0694713i
$$723$$ 0.0752228i 0.00279757i
$$724$$ −20.8510 −0.774920
$$725$$ 4.85097 39.3258i 0.180160 1.46052i
$$726$$ −1.35756 −0.0503836
$$727$$ 39.9511i 1.48171i 0.671668 + 0.740853i $$0.265578\pi$$
−0.671668 + 0.740853i $$0.734422\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −0.0370370
$$730$$ 2.68594 + 3.03761i 0.0994109 + 0.112427i
$$731$$ −42.2981 −1.56445
$$732$$ 17.0738i 0.631066i
$$733$$ 30.3488i 1.12096i 0.828168 + 0.560480i $$0.189383\pi$$
−0.828168 + 0.560480i $$0.810617\pi$$
$$734$$ −5.70194 −0.210462
$$735$$ 0 0
$$736$$ 11.2605 0.415066
$$737$$ 19.8496i 0.731168i
$$738$$ 0.724961i 0.0266862i
$$739$$ −37.2506 −1.37029 −0.685143 0.728409i $$-0.740260\pi$$
−0.685143 + 0.728409i $$0.740260\pi$$
$$740$$ −2.55008 + 2.25485i −0.0937427 + 0.0828898i
$$741$$ 7.22425 0.265390
$$742$$ 0 0
$$743$$ 26.3634i 0.967181i 0.875294 + 0.483590i $$0.160668\pi$$
−0.875294 + 0.483590i $$0.839332\pi$$
$$744$$ −3.51530 −0.128877
$$745$$ 6.58910 + 7.45183i 0.241406 + 0.273014i
$$746$$ 3.10299 0.113608
$$747$$ 3.22425i 0.117969i
$$748$$ 13.1490i 0.480776i
$$749$$ 0 0
$$750$$ −1.78797 + 1.22662i −0.0652873 + 0.0447900i
$$751$$ 50.6516 1.84830 0.924152 0.382024i $$-0.124773\pi$$
0.924152 + 0.382024i $$0.124773\pi$$
$$752$$ 37.4734i 1.36652i
$$753$$ 19.2243i 0.700571i
$$754$$ 2.07522 0.0755752
$$755$$ 1.92478 + 2.17679i 0.0700498 + 0.0792216i
$$756$$ 0 0
$$757$$ 38.9525i 1.41575i −0.706336 0.707877i $$-0.749653\pi$$
0.706336 0.707877i $$-0.250347\pi$$
$$758$$ 2.07522i 0.0753755i
$$759$$ −9.92478 −0.360247
$$760$$ 6.88717 6.08981i 0.249824 0.220901i
$$761$$ −48.2130 −1.74772 −0.873860 0.486178i $$-0.838391\pi$$
−0.873860 + 0.486178i $$0.838391\pi$$
$$762$$ 0.523730i 0.0189727i
$$763$$ 0 0
$$764$$ −27.1782 −0.983273
$$765$$ −5.61213 + 4.96239i −0.202907 + 0.179416i
$$766$$ 3.25343 0.117551
$$767$$ 11.6464i 0.420528i
$$768$$ 13.0752i 0.471811i
$$769$$ 4.44851 0.160417 0.0802086 0.996778i $$-0.474441\pi$$
0.0802086 + 0.996778i $$0.474441\pi$$
$$770$$ 0 0
$$771$$ −7.35026 −0.264713
$$772$$ 30.0752i 1.08243i
$$773$$ 39.3014i 1.41357i −0.707427 0.706786i $$-0.750144\pi$$
0.707427 0.706786i $$-0.249856\pi$$
$$774$$ 2.44851 0.0880098
$$775$$ 2.80018 22.7005i 0.100586 0.815427i
$$776$$ −14.2158 −0.510318
$$777$$ 0 0
$$778$$ 5.68735i 0.203901i
$$779$$ −20.0000 −0.716574
$$780$$ 3.92478 + 4.43866i 0.140530 + 0.158929i
$$781$$ 4.00000 0.143131
$$782$$ 3.22425i 0.115299i
$$783$$ 7.92478i 0.283208i
$$784$$ 0 0
$$785$$ 4.43866 3.92478i 0.158423 0.140081i
$$786$$ −4.00000 −0.142675
$$787$$ 0.897015i 0.0319751i 0.999872 + 0.0159876i $$0.00508922\pi$$
−0.999872 + 0.0159876i $$0.994911\pi$$
$$788$$ 1.12742i 0.0401628i
$$789$$ 12.9624