# Properties

 Label 2205.2.d.l.1324.3 Level $2205$ Weight $2$ Character 2205.1324 Analytic conductor $17.607$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2205 = 3^{2} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2205.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$17.6070136457$$ Analytic rank: $$0$$ Dimension: $$6$$ Coefficient field: 6.0.350464.1 Defining polynomial: $$x^{6} - 2 x^{5} + 2 x^{4} + 2 x^{3} + 4 x^{2} - 4 x + 2$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{3}$$ Twist minimal: no (minimal twist has level 105) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 1324.3 Root $$0.403032 - 0.403032i$$ of defining polynomial Character $$\chi$$ $$=$$ 2205.1324 Dual form 2205.2.d.l.1324.4

## $q$-expansion

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

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2205\mathbb{Z}\right)^\times$$.

 $$n$$ $$442$$ $$1081$$ $$1226$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$

## 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 $$-0.0218427\pi$$
$$3$$ 0 0
$$4$$ 1.96239 0.981194
$$5$$ −1.48119 + 1.67513i −0.662410 + 0.749141i
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0.768452i 0.271689i
$$9$$ 0 0
$$10$$ 0.324869 + 0.287258i 0.102733 + 0.0908389i
$$11$$ −2.00000 −0.603023 −0.301511 0.953463i $$-0.597491\pi$$
−0.301511 + 0.953463i $$0.597491\pi$$
$$12$$ 0 0
$$13$$ 1.35026i 0.374495i 0.982313 + 0.187248i $$0.0599567\pi$$
−0.982313 + 0.187248i $$0.940043\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 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 0
$$19$$ 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 0
$$25$$ −0.612127 4.96239i −0.122425 0.992478i
$$26$$ 0.261865 0.0513560
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 7.92478 1.47159 0.735797 0.677202i $$-0.236808\pi$$
0.735797 + 0.677202i $$0.236808\pi$$
$$30$$ 0 0
$$31$$ −4.57452 −0.821607 −0.410804 0.911724i $$-0.634752\pi$$
−0.410804 + 0.911724i $$0.634752\pi$$
$$32$$ 2.26916i 0.401134i
$$33$$ 0 0
$$34$$ −0.649738 −0.111429
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 0.775746i 0.127532i −0.997965 0.0637660i $$-0.979689\pi$$
0.997965 0.0637660i $$-0.0203111\pi$$
$$38$$ 1.03761i 0.168323i
$$39$$ 0 0
$$40$$ 1.28726 + 1.13823i 0.203533 + 0.179969i
$$41$$ 3.73813 0.583799 0.291899 0.956449i $$-0.405713\pi$$
0.291899 + 0.956449i $$0.405713\pi$$
$$42$$ 0 0
$$43$$ 12.6253i 1.92534i 0.270677 + 0.962670i $$0.412752\pi$$
−0.270677 + 0.962670i $$0.587248\pi$$
$$44$$ −3.92478 −0.591682
$$45$$ 0 0
$$46$$ 0.962389 0.141896
$$47$$ 9.92478i 1.44768i 0.689969 + 0.723839i $$0.257624\pi$$
−0.689969 + 0.723839i $$0.742376\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ −0.962389 + 0.118714i −0.136102 + 0.0167887i
$$51$$ 0 0
$$52$$ 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 0
$$55$$ 2.96239 3.35026i 0.399448 0.451749i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 1.53690i 0.201805i
$$59$$ 8.62530 1.12292 0.561459 0.827504i $$-0.310240\pi$$
0.561459 + 0.827504i $$0.310240\pi$$
$$60$$ 0 0
$$61$$ 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 0
$$67$$ 9.92478i 1.21250i 0.795272 + 0.606252i $$0.207328\pi$$
−0.795272 + 0.606252i $$0.792672\pi$$
$$68$$ 6.57452i 0.797277i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −2.00000 −0.237356 −0.118678 0.992933i $$-0.537866\pi$$
−0.118678 + 0.992933i $$0.537866\pi$$
$$72$$ 0 0
$$73$$ 9.35026i 1.09437i −0.837013 0.547183i $$-0.815700\pi$$
0.837013 0.547183i $$-0.184300\pi$$
$$74$$ −0.150446 −0.0174889
$$75$$ 0 0
$$76$$ 10.4993 1.20435
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −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
$$81$$ 0 0
$$82$$ 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
$$87$$ 0 0
$$88$$ 1.53690i 0.163835i
$$89$$ −1.03761 −0.109987 −0.0549933 0.998487i $$-0.517514\pi$$
−0.0549933 + 0.998487i $$0.517514\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 9.73813i 1.01527i
$$93$$ 0 0
$$94$$ 1.92478 0.198526
$$95$$ −7.92478 + 8.96239i −0.813065 + 0.919522i
$$96$$ 0 0
$$97$$ 18.4993i 1.87832i 0.343482 + 0.939159i $$0.388394\pi$$
−0.343482 + 0.939159i $$0.611606\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −1.20123 9.73813i −0.120123 0.973813i
$$101$$ −17.6629 −1.75753 −0.878763 0.477259i $$-0.841630\pi$$
−0.878763 + 0.477259i $$0.841630\pi$$
$$102$$ 0 0
$$103$$ 6.70052i 0.660222i 0.943942 + 0.330111i $$0.107086\pi$$
−0.943942 + 0.330111i $$0.892914\pi$$
$$104$$ 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 $$-0.231167\pi$$
$$108$$ 0 0
$$109$$ 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 0
$$112$$ 0 0
$$113$$ 12.0508i 1.13364i 0.823841 + 0.566821i $$0.191827\pi$$
−0.823841 + 0.566821i $$0.808173\pi$$
$$114$$ 0 0
$$115$$ −8.31265 7.35026i −0.775159 0.685415i
$$116$$ 15.5515 1.44392
$$117$$ 0 0
$$118$$ 1.67276i 0.153990i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 1.68735i 0.152765i
$$123$$ 0 0
$$124$$ −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 $$0.0382306\pi$$
−0.992796 + 0.119816i $$0.961769\pi$$
$$128$$ 5.91748i 0.523037i
$$129$$ 0 0
$$130$$ −0.387873 + 0.438658i −0.0340187 + 0.0384729i
$$131$$ 20.6253 1.80204 0.901020 0.433777i $$-0.142819\pi$$
0.901020 + 0.433777i $$0.142819\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 1.92478 0.166275
$$135$$ 0 0
$$136$$ −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 0
$$139$$ −3.27504 −0.277785 −0.138893 0.990307i $$-0.544354\pi$$
−0.138893 + 0.990307i $$0.544354\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0.387873i 0.0325496i
$$143$$ 2.70052i 0.225829i
$$144$$ 0 0
$$145$$ −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 $$-0.558328\pi$$
−0.182218 + 0.983258i $$0.558328\pi$$
$$150$$ 0 0
$$151$$ 1.29948 0.105750 0.0528749 0.998601i $$-0.483162\pi$$
0.0528749 + 0.998601i $$0.483162\pi$$
$$152$$ 4.11142i 0.333480i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 6.77575 7.66291i 0.544241 0.615500i
$$156$$ 0 0
$$157$$ 2.64974i 0.211472i 0.994394 + 0.105736i $$0.0337199\pi$$
−0.994394 + 0.105736i $$0.966280\pi$$
$$158$$ 2.07522i 0.165096i
$$159$$ 0 0
$$160$$ 3.80114 + 3.36107i 0.300506 + 0.265716i
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 5.29948i 0.415087i −0.978226 0.207544i $$-0.933453\pi$$
0.978226 0.207544i $$-0.0665469\pi$$
$$164$$ 7.33567 0.572820
$$165$$ 0 0
$$166$$ −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
$$171$$ 0 0
$$172$$ 24.7757i 1.88913i
$$173$$ 4.49929i 0.342075i 0.985265 + 0.171037i $$0.0547119\pi$$
−0.985265 + 0.171037i $$0.945288\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −7.55149 −0.569215
$$177$$ 0 0
$$178$$ 0.201231i 0.0150829i
$$179$$ 10.0000 0.747435 0.373718 0.927543i $$-0.378083\pi$$
0.373718 + 0.927543i $$0.378083\pi$$
$$180$$ 0 0
$$181$$ −10.6253 −0.789772 −0.394886 0.918730i $$-0.629216\pi$$
−0.394886 + 0.918730i $$0.629216\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 3.81336 0.281124
$$185$$ 1.29948 + 1.14903i 0.0955394 + 0.0844784i
$$186$$ 0 0
$$187$$ 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 $$-0.332944\pi$$
0.501059 + 0.865413i $$0.332944\pi$$
$$192$$ 0 0
$$193$$ 15.3258i 1.10318i −0.834116 0.551588i $$-0.814022\pi$$
0.834116 0.551588i $$-0.185978\pi$$
$$194$$ 3.58769 0.257581
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0.574515i 0.0409325i 0.999791 + 0.0204663i $$0.00651507\pi$$
−0.999791 + 0.0204663i $$0.993485\pi$$
$$198$$ 0 0
$$199$$ −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
$$201$$ 0 0
$$202$$ 3.42548i 0.241016i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −5.53690 + 6.26187i −0.386714 + 0.437348i
$$206$$ 1.29948 0.0905388
$$207$$ 0 0
$$208$$ 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
$$213$$ 0 0
$$214$$ −2.66433 −0.182130
$$215$$ −21.1490 18.7005i −1.44235 1.27537i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0.538319i 0.0364595i
$$219$$ 0 0
$$220$$ 5.81336 6.57452i 0.391936 0.443254i
$$221$$ 4.52373 0.304299
$$222$$ 0 0
$$223$$ 1.55149i 0.103896i 0.998650 + 0.0519478i $$0.0165429\pi$$
−0.998650 + 0.0519478i $$0.983457\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 2.33709 0.155461
$$227$$ 13.1490i 0.872732i −0.899769 0.436366i $$-0.856265\pi$$
0.899769 0.436366i $$-0.143735\pi$$
$$228$$ 0 0
$$229$$ 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 0
$$235$$ −16.6253 14.7005i −1.08452 0.958956i
$$236$$ 16.9262 1.10180
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 5.84955 0.378376 0.189188 0.981941i $$-0.439414\pi$$
0.189188 + 0.981941i $$0.439414\pi$$
$$240$$ 0 0
$$241$$ 0.0752228 0.00484553 0.00242276 0.999997i $$-0.499229\pi$$
0.00242276 + 0.999997i $$0.499229\pi$$
$$242$$ 1.35756i 0.0872670i
$$243$$ 0 0
$$244$$ 17.0738 1.09304
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 7.22425i 0.459668i
$$248$$ 3.51530i 0.223222i
$$249$$ 0 0
$$250$$ 1.22662 1.78797i 0.0775785 0.113081i
$$251$$ 19.2243 1.21342 0.606712 0.794922i $$-0.292488\pi$$
0.606712 + 0.794922i $$0.292488\pi$$
$$252$$ 0 0
$$253$$ 9.92478i 0.623965i
$$254$$ 0.523730 0.0328618
$$255$$ 0 0
$$256$$ 13.0752 0.817201
$$257$$ 7.35026i 0.458497i 0.973368 + 0.229248i $$0.0736268\pi$$
−0.973368 + 0.229248i $$0.926373\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ −4.43866 3.92478i −0.275274 0.243404i
$$261$$ 0 0
$$262$$ 4.00000i 0.247121i
$$263$$ 12.9624i 0.799295i −0.916669 0.399648i $$-0.869133\pi$$
0.916669 0.399648i $$-0.130867\pi$$
$$264$$ 0 0
$$265$$ −14.3634 12.7005i −0.882339 0.780187i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 19.4763i 1.18970i
$$269$$ −4.11142 −0.250678 −0.125339 0.992114i $$-0.540002\pi$$
−0.125339 + 0.992114i $$0.540002\pi$$
$$270$$ 0 0
$$271$$ 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
$$276$$ 0 0
$$277$$ 11.0738i 0.665361i −0.943040 0.332680i $$-0.892047\pi$$
0.943040 0.332680i $$-0.107953\pi$$
$$278$$ 0.635150i 0.0380938i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −14.3733 −0.857438 −0.428719 0.903438i $$-0.641035\pi$$
−0.428719 + 0.903438i $$0.641035\pi$$
$$282$$ 0 0
$$283$$ 1.14903i 0.0683028i 0.999417 + 0.0341514i $$0.0108728\pi$$
−0.999417 + 0.0341514i $$0.989127\pi$$
$$284$$ −3.92478 −0.232893
$$285$$ 0 0
$$286$$ −0.523730 −0.0309688
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 5.77575 0.339750
$$290$$ 2.57452 + 2.27645i 0.151181 + 0.133678i
$$291$$ 0 0
$$292$$ 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
$$297$$ 0 0
$$298$$ 0.862728i 0.0499765i
$$299$$ −6.70052 −0.387501
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0.252016i 0.0145019i
$$303$$ 0 0
$$304$$ 20.2012 1.15862
$$305$$ −12.8872 + 14.5745i −0.737917 + 0.834534i
$$306$$ 0 0
$$307$$ 24.1016i 1.37555i −0.725924 0.687775i $$-0.758588\pi$$
0.725924 0.687775i $$-0.241412\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ −1.48612 1.31406i −0.0844059 0.0746339i
$$311$$ 8.25202 0.467929 0.233964 0.972245i $$-0.424830\pi$$
0.233964 + 0.972245i $$0.424830\pi$$
$$312$$ 0 0
$$313$$ 14.9018i 0.842297i −0.906992 0.421148i $$-0.861627\pi$$
0.906992 0.421148i $$-0.138373\pi$$
$$314$$ 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 $$-0.0917833\pi$$
$$318$$ 0 0
$$319$$ −15.8496 −0.887405
$$320$$ −10.5334 + 11.9126i −0.588835 + 0.665932i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 17.9248i 0.997361i
$$324$$ 0 0
$$325$$ 6.70052 0.826531i 0.371678 0.0458477i
$$326$$ −1.02776 −0.0569225
$$327$$ 0 0
$$328$$ 2.87258i 0.158612i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 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 0
$$334$$ −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 $$-0.966564\pi$$
0.994488 0.104849i $$-0.0334360\pi$$
$$338$$ 2.16759i 0.117901i
$$339$$ 0 0
$$340$$ 11.0132 + 9.73813i 0.597273 + 0.528125i
$$341$$ 9.14903 0.495448
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 9.70194 0.523093
$$345$$ 0 0
$$346$$ 0.872577 0.0469101
$$347$$ 9.58769i 0.514694i −0.966319 0.257347i $$-0.917152\pi$$
0.966319 0.257347i $$-0.0828484\pi$$
$$348$$ 0 0
$$349$$ −15.1490 −0.810909 −0.405455 0.914115i $$-0.632887\pi$$
−0.405455 + 0.914115i $$0.632887\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 4.53832i 0.241893i
$$353$$ 20.3488i 1.08306i 0.840681 + 0.541530i $$0.182155\pi$$
−0.840681 + 0.541530i $$0.817845\pi$$
$$354$$ 0 0
$$355$$ 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 $$-0.810886\pi$$
−0.828642 + 0.559779i $$0.810886\pi$$
$$360$$ 0 0
$$361$$ 9.62530 0.506595
$$362$$ 2.06063i 0.108305i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 15.6629 + 13.8496i 0.819834 + 0.724919i
$$366$$ 0 0
$$367$$ 29.4010i 1.53472i 0.641215 + 0.767361i $$0.278431\pi$$
−0.641215 + 0.767361i $$0.721569\pi$$
$$368$$ 18.7367i 0.976719i
$$369$$ 0 0
$$370$$ 0.222839 0.252016i 0.0115849 0.0131017i
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 16.0000i 0.828449i −0.910175 0.414224i $$-0.864053\pi$$
0.910175 0.414224i $$-0.135947\pi$$
$$374$$ 1.29948 0.0671943
$$375$$ 0 0
$$376$$ 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
$$381$$ 0 0
$$382$$ 2.68594i 0.137424i
$$383$$ 16.7757i 0.857201i 0.903494 + 0.428600i $$0.140993\pi$$
−0.903494 + 0.428600i $$0.859007\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −2.97224 −0.151283
$$387$$ 0 0
$$388$$ 36.3028i 1.84300i
$$389$$ −29.3258 −1.48688 −0.743439 0.668804i $$-0.766807\pi$$
−0.743439 + 0.668804i $$0.766807\pi$$
$$390$$ 0 0
$$391$$ 16.6253 0.840778
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0.111420 0.00561324
$$395$$ 15.8496 17.9248i 0.797478 0.901893i
$$396$$ 0 0
$$397$$ 18.3488i 0.920902i −0.887685 0.460451i $$-0.847688\pi$$
0.887685 0.460451i $$-0.152312\pi$$
$$398$$ 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 $$-0.118079\pi$$
0.931981 + 0.362506i $$0.118079\pi$$
$$402$$ 0 0
$$403$$ 6.17679i 0.307688i
$$404$$ −34.6615 −1.72447
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 1.55149i 0.0769046i
$$408$$ 0 0
$$409$$ −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
$$411$$ 0 0
$$412$$ 13.1490i 0.647806i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 5.40105 + 4.77575i 0.265127 + 0.234432i
$$416$$ 3.06396 0.150223
$$417$$ 0 0
$$418$$ 2.07522i 0.101502i
$$419$$ −23.4763 −1.14689 −0.573445 0.819244i $$-0.694394\pi$$
−0.573445 + 0.819244i $$0.694394\pi$$
$$420$$ 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
$$423$$ 0 0
$$424$$ 6.58910 0.319995
$$425$$ −16.6253 + 2.05079i −0.806446 + 0.0994777i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 26.9596i 1.30314i
$$429$$ 0 0
$$430$$ −3.62672 + 4.10157i −0.174896 + 0.197795i
$$431$$ 19.4010 0.934516 0.467258 0.884121i $$-0.345242\pi$$
0.467258 + 0.884121i $$0.345242\pi$$
$$432$$ 0 0
$$433$$ 6.49929i 0.312336i 0.987731 + 0.156168i $$0.0499141\pi$$
−0.987731 + 0.156168i $$0.950086\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 5.44709 0.260868
$$437$$ 26.5501i 1.27006i
$$438$$ 0 0
$$439$$ −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 $$0.849759\pi$$
$$444$$ 0 0
$$445$$ 1.53690 1.73813i 0.0728562 0.0823955i
$$446$$ 0.300891 0.0142476
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −32.8021 −1.54803 −0.774013 0.633169i $$-0.781754\pi$$
−0.774013 + 0.633169i $$0.781754\pi$$
$$450$$ 0 0
$$451$$ −7.47627 −0.352044
$$452$$ 23.6483i 1.11232i
$$453$$ 0 0
$$454$$ −2.55008 −0.119681
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 18.7005i 0.874774i −0.899273 0.437387i $$-0.855904\pi$$
0.899273 0.437387i $$-0.144096\pi$$
$$458$$ 0.538319i 0.0251540i
$$459$$ 0 0
$$460$$ −16.3127 14.4241i −0.760581 0.672526i
$$461$$ −6.96239 −0.324271 −0.162135 0.986769i $$-0.551838\pi$$
−0.162135 + 0.986769i $$0.551838\pi$$
$$462$$ 0 0
$$463$$ 5.29948i 0.246288i −0.992389 0.123144i $$-0.960702\pi$$
0.992389 0.123144i $$-0.0392976\pi$$
$$464$$ 29.9219 1.38909
$$465$$ 0 0
$$466$$ −0.00984911 −0.000456251
$$467$$ 13.1490i 0.608465i −0.952598 0.304232i $$-0.901600\pi$$
0.952598 0.304232i $$-0.0983999\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ −2.85097 + 3.22425i −0.131505 + 0.148724i
$$471$$ 0 0
$$472$$ 6.62813i 0.305084i
$$473$$ 25.2506i 1.16102i
$$474$$ 0 0
$$475$$ −3.27504 26.5501i −0.150269 1.21820i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 1.13444i 0.0518882i
$$479$$ −5.14903 −0.235265 −0.117633 0.993057i $$-0.537531\pi$$
−0.117633 + 0.993057i $$0.537531\pi$$
$$480$$ 0 0
$$481$$ 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 0
$$487$$ 22.1768i 1.00493i −0.864599 0.502463i $$-0.832427\pi$$
0.864599 0.502463i $$-0.167573\pi$$
$$488$$ 6.68594i 0.302658i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −2.00000 −0.0902587 −0.0451294 0.998981i $$-0.514370\pi$$
−0.0451294 + 0.998981i $$0.514370\pi$$
$$492$$ 0 0
$$493$$ 26.5501i 1.19576i
$$494$$ 1.40105 0.0630361
$$495$$ 0 0
$$496$$ −17.2722 −0.775545
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 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
$$501$$ 0 0
$$502$$ 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
$$507$$ 0 0
$$508$$ 5.29948i 0.235126i
$$509$$ −13.1392 −0.582384 −0.291192 0.956665i $$-0.594052\pi$$
−0.291192 + 0.956665i $$0.594052\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 14.3707i 0.635103i
$$513$$ 0 0
$$514$$ 1.42548 0.0628754
$$515$$ −11.2243 9.92478i −0.494600 0.437338i
$$516$$ 0 0
$$517$$ 19.8496i 0.872982i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ −1.53690 + 1.73813i −0.0673977 + 0.0762223i
$$521$$ −37.6629 −1.65004 −0.825021 0.565102i $$-0.808837\pi$$
−0.825021 + 0.565102i $$0.808837\pi$$
$$522$$ 0 0
$$523$$ 4.00000i 0.174908i −0.996169 0.0874539i $$-0.972127\pi$$
0.996169 0.0874539i $$-0.0278730\pi$$
$$524$$ 40.4749 1.76815
$$525$$ 0 0
$$526$$ −2.51388 −0.109610
$$527$$ 15.3258i 0.667603i
$$528$$ 0 0
$$529$$ −1.62530 −0.0706652
$$530$$ −2.46310 + 2.78560i −0.106990 + 0.120999i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 5.04746i 0.218630i
$$534$$ 0 0
$$535$$ 23.0132 + 20.3488i 0.994946 + 0.879757i
$$536$$ 7.62672 0.329424
$$537$$ 0 0
$$538$$ 0.797355i 0.0343764i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −22.4749 −0.966269 −0.483135 0.875546i $$-0.660502\pi$$
−0.483135 + 0.875546i $$0.660502\pi$$
$$542$$ 3.18523i 0.136817i
$$543$$ 0 0
$$544$$ −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 $$-0.813012\pi$$
0.832362 0.554232i $$-0.186988\pi$$
$$548$$ 44.1524i 1.88610i
$$549$$ 0 0
$$550$$ 1.92478 0.237428i 0.0820728 0.0101239i
$$551$$ 42.3996 1.80629
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −2.14762 −0.0912435
$$555$$ 0 0
$$556$$ −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 0
$$559$$ −17.0475 −0.721031
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 2.78751i 0.117584i
$$563$$ 11.6267i 0.490008i 0.969522 + 0.245004i $$0.0787892\pi$$
−0.969522 + 0.245004i $$0.921211\pi$$
$$564$$ 0 0
$$565$$ −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 $$-0.437374\pi$$
0.195479 + 0.980708i $$0.437374\pi$$
$$570$$ 0 0
$$571$$ −19.6991 −0.824382 −0.412191 0.911097i $$-0.635236\pi$$
−0.412191 + 0.911097i $$0.635236\pi$$
$$572$$ 5.29948i 0.221582i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 24.6253 3.03761i 1.02695 0.126677i
$$576$$ 0 0
$$577$$ 32.7974i 1.36537i −0.730712 0.682686i $$-0.760812\pi$$
0.730712 0.682686i $$-0.239188\pi$$
$$578$$ 1.12013i 0.0465912i
$$579$$ 0 0
$$580$$ −23.0348 + 26.0508i −0.956467 + 1.08170i
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 17.1490i 0.710240i
$$584$$ −7.18523 −0.297327
$$585$$ 0 0
$$586$$ −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 0
$$592$$ 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 0
$$595$$ 0 0
$$596$$ −8.72970 −0.357582
$$597$$ 0 0
$$598$$ 1.29948i 0.0531395i
$$599$$ −20.2981 −0.829356 −0.414678 0.909968i $$-0.636106\pi$$
−0.414678 + 0.909968i $$0.636106\pi$$
$$600$$ 0 0
$$601$$ 13.8496 0.564935 0.282468 0.959277i $$-0.408847\pi$$
0.282468 + 0.959277i $$0.408847\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 2.55008 0.103761
$$605$$ 10.3684 11.7259i 0.421534 0.476726i
$$606$$ 0 0
$$607$$ 25.2506i 1.02489i 0.858720 + 0.512445i $$0.171260\pi$$
−0.858720 + 0.512445i $$0.828740\pi$$
$$608$$ 12.1406i 0.492366i
$$609$$ 0 0
$$610$$ 2.82653 + 2.49929i 0.114443 + 0.101193i
$$611$$ −13.4010 −0.542148
$$612$$ 0 0
$$613$$ 9.14903i 0.369526i 0.982783 + 0.184763i $$0.0591517\pi$$
−0.982783 + 0.184763i $$0.940848\pi$$
$$614$$ −4.67418 −0.188634
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 15.9492i 0.642091i −0.947064 0.321046i $$-0.895966\pi$$
0.947064 0.321046i $$-0.104034\pi$$
$$618$$ 0 0
$$619$$ 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
$$621$$ 0 0
$$622$$ 1.60037i 0.0641689i
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −24.2506 + 6.07522i −0.970024 + 0.243009i
$$626$$ −2.89000 −0.115507
$$627$$ 0 0
$$628$$ 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
$$633$$ 0 0
$$634$$ −1.96380 −0.0779926
$$635$$ −4.52373 4.00000i −0.179519 0.158735i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 3.07381i 0.121693i
$$639$$ 0 0
$$640$$ 9.91256 + 8.76494i 0.391828 + 0.346465i
$$641$$ 38.7269 1.52962 0.764810 0.644256i $$-0.222833\pi$$
0.764810 + 0.644256i $$0.222833\pi$$
$$642$$ 0 0
$$643$$ 11.9511i 0.471306i −0.971837 0.235653i $$-0.924277\pi$$
0.971837 0.235653i $$-0.0757229\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −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 0
$$649$$ −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 0
$$655$$ −30.5501 + 34.5501i −1.19369 + 1.34998i
$$656$$ 14.1142 0.551069
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −16.9525 −0.660377 −0.330189 0.943915i $$-0.607112\pi$$
−0.330189 + 0.943915i $$0.607112\pi$$
$$660$$ 0 0
$$661$$ 15.6531 0.608834 0.304417 0.952539i $$-0.401538\pi$$
0.304417 + 0.952539i $$0.401538\pi$$
$$662$$ 5.40105i 0.209918i
$$663$$ 0 0
$$664$$ −2.47768 −0.0961528
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 39.3258i 1.52270i
$$668$$ 28.5529i 1.10475i
$$669$$ 0 0
$$670$$ −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 $$-0.832737\pi$$
0.865088 0.501621i $$-0.167263\pi$$
$$674$$ −0.746569 −0.0287568
$$675$$ 0 0
$$676$$ 21.9332 0.843585
$$677$$ 35.4518i 1.36252i −0.732039 0.681262i $$-0.761431\pi$$
0.732039 0.681262i $$-0.238569\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 3.81336 4.31265i 0.146236 0.165383i
$$681$$ 0 0
$$682$$ 1.77433i 0.0679427i
$$683$$ 23.6629i 0.905436i −0.891654 0.452718i $$-0.850454\pi$$
0.891654 0.452718i $$-0.149546\pi$$
$$684$$ 0 0
$$685$$ 37.6893 + 33.3258i 1.44003 + 1.27331i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 47.6699i 1.81740i
$$689$$ −11.5778 −0.441081
$$690$$ 0 0
$$691$$ 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
$$696$$ 0 0
$$697$$ 12.5237i 0.474370i
$$698$$ 2.93795i 0.111203i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −42.7269 −1.61377 −0.806886 0.590707i $$-0.798849\pi$$
−0.806886 + 0.590707i $$0.798849\pi$$
$$702$$ 0 0
$$703$$ 4.15045i 0.156537i
$$704$$ −14.2228 −0.536043
$$705$$ 0 0
$$706$$ 3.94639 0.148524
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −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
$$711$$ 0 0
$$712$$ 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
$$717$$ 0 0
$$718$$ 6.08981i 0.227270i
$$719$$ 10.7005 0.399062 0.199531 0.979891i $$-0.436058\pi$$
0.199531 + 0.979891i $$0.436058\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 1.86670i 0.0694713i
$$723$$ 0 0
$$724$$ −20.8510 −0.774920
$$725$$ −4.85097 39.3258i −0.180160 1.46052i
$$726$$ 0 0
$$727$$ 39.9511i 1.48171i −0.671668 0.740853i $$-0.734422\pi$$
0.671668 0.740853i $$-0.265578\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 2.68594 3.03761i 0.0994109 0.112427i
$$731$$ 42.2981 1.56445
$$732$$ 0 0
$$733$$ 30.3488i 1.12096i −0.828168 0.560480i $$-0.810617\pi$$
0.828168 0.560480i $$-0.189383\pi$$
$$734$$ 5.70194 0.210462
$$735$$ 0 0
$$736$$ 11.2605 0.415066
$$737$$ 19.8496i 0.731168i
$$738$$ 0 0
$$739$$ −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
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 26.3634i 0.967181i 0.875294 + 0.483590i $$0.160668\pi$$
−0.875294 + 0.483590i $$0.839332\pi$$
$$744$$ 0 0
$$745$$ 6.58910 7.45183i 0.241406 0.273014i
$$746$$ −3.10299 −0.113608
$$747$$ 0 0
$$748$$ 13.1490i 0.480776i
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 50.6516 1.84830 0.924152 0.382024i $$-0.124773\pi$$
0.924152 + 0.382024i $$0.124773\pi$$
$$752$$ 37.4734i 1.36652i
$$753$$ 0 0
$$754$$ 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 $$0.250347\pi$$
−0.706336 + 0.707877i $$0.749653\pi$$
$$758$$ 2.07522i 0.0753755i
$$759$$ 0 0
$$760$$ 6.88717 + 6.08981i 0.249824 + 0.220901i
$$761$$ 48.2130 1.74772 0.873860 0.486178i $$-0.161609\pi$$
0.873860 + 0.486178i $$0.161609\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 27.1782 0.983273
$$765$$ 0 0
$$766$$ 3.25343 0.117551
$$767$$ 11.6464i 0.420528i
$$768$$ 0 0
$$769$$ 4.44851 0.160417 0.0802086 0.996778i $$-0.474441\pi$$
0.0802086 + 0.996778i $$0.474441\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 30.0752i 1.08243i
$$773$$ 39.3014i 1.41357i −0.707427 0.706786i $$-0.750144\pi$$
0.707427 0.706786i $$-0.249856\pi$$
$$774$$ 0 0
$$775$$ 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
$$780$$ 0 0
$$781$$ 4.00000 0.143131
$$782$$ 3.22425i 0.115299i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −4.43866 3.92478i −0.158423 0.140081i
$$786$$ 0 0
$$787$$ 0.897015i 0.0319751i −0.999872 0.0159876i $$-0.994911\pi$$
0.999872 0.0159876i $$-0.00508922\pi$$
$$788$$ 1.12742i 0.0401628i
$$789$$ 0 0
$$790$$ −3.47627 3.07381i −0.123680 0.109361i
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 11.7480i 0.417183i
$$794$$ −3.55851 −0.126287
$$795$$ 0 0
$$796$$ −0.394893 −0.0139966
$$797$$ 3.19982i 0.113343i 0.998393 + 0.0566717i $$0.0180488\pi$$
−0.998393 + 0.0566717i $$0.981951\pi$$
$$798$$ 0 0