# Properties

 Label 384.3.i.d.353.6 Level $384$ Weight $3$ Character 384.353 Analytic conductor $10.463$ Analytic rank $0$ Dimension $20$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$384 = 2^{7} \cdot 3$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 384.i (of order $$4$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$10.4632421514$$ Analytic rank: $$0$$ Dimension: $$20$$ Relative dimension: $$10$$ over $$\Q(i)$$ Coefficient field: $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ Defining polynomial: $$x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + 24576 x^{4} - 131072 x^{2} + 1048576$$ Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2^{23}$$ Twist minimal: no (minimal twist has level 48) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 353.6 Root $$-0.312316 + 1.97546i$$ of defining polynomial Character $$\chi$$ $$=$$ 384.353 Dual form 384.3.i.d.161.6

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.18505 + 2.75602i) q^{3} +(0.00985921 - 0.00985921i) q^{5} -6.42277i q^{7} +(-6.19134 + 6.53203i) q^{9} +O(q^{10})$$ $$q+(1.18505 + 2.75602i) q^{3} +(0.00985921 - 0.00985921i) q^{5} -6.42277i q^{7} +(-6.19134 + 6.53203i) q^{9} +(-9.07186 + 9.07186i) q^{11} +(-12.6098 + 12.6098i) q^{13} +(0.0388558 + 0.0154886i) q^{15} +19.0155i q^{17} +(2.07165 - 2.07165i) q^{19} +(17.7013 - 7.61127i) q^{21} +19.5712 q^{23} +24.9998i q^{25} +(-25.3394 - 9.32272i) q^{27} +(11.1742 + 11.1742i) q^{29} -59.9385 q^{31} +(-35.7528 - 14.2517i) q^{33} +(-0.0633234 - 0.0633234i) q^{35} +(-9.32707 - 9.32707i) q^{37} +(-49.6962 - 19.8098i) q^{39} +47.2639 q^{41} +(-24.1220 - 24.1220i) q^{43} +(0.00335893 + 0.125442i) q^{45} +6.29702i q^{47} +7.74808 q^{49} +(-52.4073 + 22.5343i) q^{51} +(-20.6409 + 20.6409i) q^{53} +0.178883i q^{55} +(8.16452 + 3.25452i) q^{57} +(60.3533 - 60.3533i) q^{59} +(-48.0230 + 48.0230i) q^{61} +(41.9537 + 39.7655i) q^{63} +0.248646i q^{65} +(23.7768 - 23.7768i) q^{67} +(23.1928 + 53.9388i) q^{69} +13.5743 q^{71} -31.4516i q^{73} +(-68.9001 + 29.6259i) q^{75} +(58.2665 + 58.2665i) q^{77} +47.4718 q^{79} +(-4.33472 - 80.8839i) q^{81} +(70.3318 + 70.3318i) q^{83} +(0.187478 + 0.187478i) q^{85} +(-17.5545 + 44.0385i) q^{87} -95.1729 q^{89} +(80.9900 + 80.9900i) q^{91} +(-71.0298 - 165.192i) q^{93} -0.0408497i q^{95} +61.6218 q^{97} +(-3.09069 - 115.425i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$20q + 6q^{3} + O(q^{10})$$ $$20q + 6q^{3} - 92q^{13} - 116q^{15} + 52q^{19} - 48q^{21} - 18q^{27} - 80q^{31} + 60q^{33} + 116q^{37} - 172q^{43} - 60q^{45} - 364q^{49} - 128q^{51} + 244q^{61} + 296q^{63} - 356q^{67} + 20q^{69} + 146q^{75} + 384q^{79} - 188q^{81} - 48q^{85} - 136q^{91} + 132q^{93} + 472q^{97} + 452q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$133$$ $$257$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{4}\right)$$ $$-1$$

## 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
$$3$$ 1.18505 + 2.75602i 0.395015 + 0.918675i
$$4$$ 0 0
$$5$$ 0.00985921 0.00985921i 0.00197184 0.00197184i −0.706120 0.708092i $$-0.749556\pi$$
0.708092 + 0.706120i $$0.249556\pi$$
$$6$$ 0 0
$$7$$ 6.42277i 0.917538i −0.888556 0.458769i $$-0.848291\pi$$
0.888556 0.458769i $$-0.151709\pi$$
$$8$$ 0 0
$$9$$ −6.19134 + 6.53203i −0.687926 + 0.725781i
$$10$$ 0 0
$$11$$ −9.07186 + 9.07186i −0.824715 + 0.824715i −0.986780 0.162065i $$-0.948185\pi$$
0.162065 + 0.986780i $$0.448185\pi$$
$$12$$ 0 0
$$13$$ −12.6098 + 12.6098i −0.969987 + 0.969987i −0.999563 0.0295753i $$-0.990585\pi$$
0.0295753 + 0.999563i $$0.490585\pi$$
$$14$$ 0 0
$$15$$ 0.0388558 + 0.0154886i 0.00259039 + 0.00103257i
$$16$$ 0 0
$$17$$ 19.0155i 1.11856i 0.828978 + 0.559281i $$0.188923\pi$$
−0.828978 + 0.559281i $$0.811077\pi$$
$$18$$ 0 0
$$19$$ 2.07165 2.07165i 0.109034 0.109034i −0.650485 0.759519i $$-0.725434\pi$$
0.759519 + 0.650485i $$0.225434\pi$$
$$20$$ 0 0
$$21$$ 17.7013 7.61127i 0.842919 0.362441i
$$22$$ 0 0
$$23$$ 19.5712 0.850923 0.425461 0.904977i $$-0.360112\pi$$
0.425461 + 0.904977i $$0.360112\pi$$
$$24$$ 0 0
$$25$$ 24.9998i 0.999992i
$$26$$ 0 0
$$27$$ −25.3394 9.32272i −0.938497 0.345286i
$$28$$ 0 0
$$29$$ 11.1742 + 11.1742i 0.385319 + 0.385319i 0.873014 0.487695i $$-0.162162\pi$$
−0.487695 + 0.873014i $$0.662162\pi$$
$$30$$ 0 0
$$31$$ −59.9385 −1.93350 −0.966750 0.255725i $$-0.917686\pi$$
−0.966750 + 0.255725i $$0.917686\pi$$
$$32$$ 0 0
$$33$$ −35.7528 14.2517i −1.08342 0.431870i
$$34$$ 0 0
$$35$$ −0.0633234 0.0633234i −0.00180924 0.00180924i
$$36$$ 0 0
$$37$$ −9.32707 9.32707i −0.252083 0.252083i 0.569741 0.821824i $$-0.307043\pi$$
−0.821824 + 0.569741i $$0.807043\pi$$
$$38$$ 0 0
$$39$$ −49.6962 19.8098i −1.27426 0.507943i
$$40$$ 0 0
$$41$$ 47.2639 1.15278 0.576389 0.817176i $$-0.304461\pi$$
0.576389 + 0.817176i $$0.304461\pi$$
$$42$$ 0 0
$$43$$ −24.1220 24.1220i −0.560978 0.560978i 0.368607 0.929585i $$-0.379835\pi$$
−0.929585 + 0.368607i $$0.879835\pi$$
$$44$$ 0 0
$$45$$ 0.00335893 + 0.125442i 7.46430e−5 + 0.00278761i
$$46$$ 0 0
$$47$$ 6.29702i 0.133979i 0.997754 + 0.0669896i $$0.0213394\pi$$
−0.997754 + 0.0669896i $$0.978661\pi$$
$$48$$ 0 0
$$49$$ 7.74808 0.158124
$$50$$ 0 0
$$51$$ −52.4073 + 22.5343i −1.02759 + 0.441849i
$$52$$ 0 0
$$53$$ −20.6409 + 20.6409i −0.389450 + 0.389450i −0.874491 0.485041i $$-0.838805\pi$$
0.485041 + 0.874491i $$0.338805\pi$$
$$54$$ 0 0
$$55$$ 0.178883i 0.00325242i
$$56$$ 0 0
$$57$$ 8.16452 + 3.25452i 0.143237 + 0.0570968i
$$58$$ 0 0
$$59$$ 60.3533 60.3533i 1.02294 1.02294i 0.0232062 0.999731i $$-0.492613\pi$$
0.999731 0.0232062i $$-0.00738742\pi$$
$$60$$ 0 0
$$61$$ −48.0230 + 48.0230i −0.787262 + 0.787262i −0.981045 0.193782i $$-0.937924\pi$$
0.193782 + 0.981045i $$0.437924\pi$$
$$62$$ 0 0
$$63$$ 41.9537 + 39.7655i 0.665931 + 0.631198i
$$64$$ 0 0
$$65$$ 0.248646i 0.00382532i
$$66$$ 0 0
$$67$$ 23.7768 23.7768i 0.354878 0.354878i −0.507043 0.861921i $$-0.669262\pi$$
0.861921 + 0.507043i $$0.169262\pi$$
$$68$$ 0 0
$$69$$ 23.1928 + 53.9388i 0.336127 + 0.781721i
$$70$$ 0 0
$$71$$ 13.5743 0.191188 0.0955938 0.995420i $$-0.469525\pi$$
0.0955938 + 0.995420i $$0.469525\pi$$
$$72$$ 0 0
$$73$$ 31.4516i 0.430844i −0.976521 0.215422i $$-0.930887\pi$$
0.976521 0.215422i $$-0.0691127\pi$$
$$74$$ 0 0
$$75$$ −68.9001 + 29.6259i −0.918668 + 0.395012i
$$76$$ 0 0
$$77$$ 58.2665 + 58.2665i 0.756707 + 0.756707i
$$78$$ 0 0
$$79$$ 47.4718 0.600909 0.300455 0.953796i $$-0.402862\pi$$
0.300455 + 0.953796i $$0.402862\pi$$
$$80$$ 0 0
$$81$$ −4.33472 80.8839i −0.0535151 0.998567i
$$82$$ 0 0
$$83$$ 70.3318 + 70.3318i 0.847372 + 0.847372i 0.989804 0.142433i $$-0.0454925\pi$$
−0.142433 + 0.989804i $$0.545493\pi$$
$$84$$ 0 0
$$85$$ 0.187478 + 0.187478i 0.00220563 + 0.00220563i
$$86$$ 0 0
$$87$$ −17.5545 + 44.0385i −0.201776 + 0.506189i
$$88$$ 0 0
$$89$$ −95.1729 −1.06936 −0.534679 0.845055i $$-0.679568\pi$$
−0.534679 + 0.845055i $$0.679568\pi$$
$$90$$ 0 0
$$91$$ 80.9900 + 80.9900i 0.890000 + 0.890000i
$$92$$ 0 0
$$93$$ −71.0298 165.192i −0.763761 1.77626i
$$94$$ 0 0
$$95$$ 0.0408497i 0.000429997i
$$96$$ 0 0
$$97$$ 61.6218 0.635276 0.317638 0.948212i $$-0.397110\pi$$
0.317638 + 0.948212i $$0.397110\pi$$
$$98$$ 0 0
$$99$$ −3.09069 115.425i −0.0312191 1.16591i
$$100$$ 0 0
$$101$$ −48.1867 + 48.1867i −0.477096 + 0.477096i −0.904202 0.427106i $$-0.859533\pi$$
0.427106 + 0.904202i $$0.359533\pi$$
$$102$$ 0 0
$$103$$ 4.73669i 0.0459873i 0.999736 + 0.0229936i $$0.00731975\pi$$
−0.999736 + 0.0229936i $$0.992680\pi$$
$$104$$ 0 0
$$105$$ 0.0994797 0.249562i 0.000947426 0.00237678i
$$106$$ 0 0
$$107$$ 40.9462 40.9462i 0.382674 0.382674i −0.489390 0.872065i $$-0.662781\pi$$
0.872065 + 0.489390i $$0.162781\pi$$
$$108$$ 0 0
$$109$$ 120.437 120.437i 1.10493 1.10493i 0.111123 0.993807i $$-0.464555\pi$$
0.993807 0.111123i $$-0.0354447\pi$$
$$110$$ 0 0
$$111$$ 14.6526 36.7586i 0.132006 0.331159i
$$112$$ 0 0
$$113$$ 205.193i 1.81587i 0.419110 + 0.907936i $$0.362342\pi$$
−0.419110 + 0.907936i $$0.637658\pi$$
$$114$$ 0 0
$$115$$ 0.192957 0.192957i 0.00167789 0.00167789i
$$116$$ 0 0
$$117$$ −4.29604 160.439i −0.0367183 1.37128i
$$118$$ 0 0
$$119$$ 122.132 1.02632
$$120$$ 0 0
$$121$$ 43.5974i 0.360309i
$$122$$ 0 0
$$123$$ 56.0098 + 130.260i 0.455365 + 1.05903i
$$124$$ 0 0
$$125$$ 0.492959 + 0.492959i 0.00394367 + 0.00394367i
$$126$$ 0 0
$$127$$ 54.1458 0.426345 0.213173 0.977015i $$-0.431620\pi$$
0.213173 + 0.977015i $$0.431620\pi$$
$$128$$ 0 0
$$129$$ 37.8952 95.0666i 0.293761 0.736951i
$$130$$ 0 0
$$131$$ −31.2584 31.2584i −0.238614 0.238614i 0.577662 0.816276i $$-0.303965\pi$$
−0.816276 + 0.577662i $$0.803965\pi$$
$$132$$ 0 0
$$133$$ −13.3057 13.3057i −0.100043 0.100043i
$$134$$ 0 0
$$135$$ −0.341742 + 0.157912i −0.00253142 + 0.00116972i
$$136$$ 0 0
$$137$$ 42.9176 0.313267 0.156633 0.987657i $$-0.449936\pi$$
0.156633 + 0.987657i $$0.449936\pi$$
$$138$$ 0 0
$$139$$ 47.0945 + 47.0945i 0.338809 + 0.338809i 0.855919 0.517110i $$-0.172992\pi$$
−0.517110 + 0.855919i $$0.672992\pi$$
$$140$$ 0 0
$$141$$ −17.3547 + 7.46225i −0.123083 + 0.0529238i
$$142$$ 0 0
$$143$$ 228.789i 1.59993i
$$144$$ 0 0
$$145$$ 0.220339 0.00151958
$$146$$ 0 0
$$147$$ 9.18183 + 21.3539i 0.0624614 + 0.145265i
$$148$$ 0 0
$$149$$ 131.532 131.532i 0.882766 0.882766i −0.111049 0.993815i $$-0.535421\pi$$
0.993815 + 0.111049i $$0.0354210\pi$$
$$150$$ 0 0
$$151$$ 145.908i 0.966281i 0.875543 + 0.483140i $$0.160504\pi$$
−0.875543 + 0.483140i $$0.839496\pi$$
$$152$$ 0 0
$$153$$ −124.210 117.732i −0.811830 0.769488i
$$154$$ 0 0
$$155$$ −0.590946 + 0.590946i −0.00381256 + 0.00381256i
$$156$$ 0 0
$$157$$ 55.2586 55.2586i 0.351966 0.351966i −0.508875 0.860840i $$-0.669938\pi$$
0.860840 + 0.508875i $$0.169938\pi$$
$$158$$ 0 0
$$159$$ −81.3470 32.4263i −0.511617 0.203939i
$$160$$ 0 0
$$161$$ 125.701i 0.780754i
$$162$$ 0 0
$$163$$ −70.6156 + 70.6156i −0.433225 + 0.433225i −0.889724 0.456499i $$-0.849103\pi$$
0.456499 + 0.889724i $$0.349103\pi$$
$$164$$ 0 0
$$165$$ −0.493006 + 0.211984i −0.00298791 + 0.00128475i
$$166$$ 0 0
$$167$$ 86.2013 0.516176 0.258088 0.966121i $$-0.416908\pi$$
0.258088 + 0.966121i $$0.416908\pi$$
$$168$$ 0 0
$$169$$ 149.016i 0.881751i
$$170$$ 0 0
$$171$$ 0.705790 + 26.3584i 0.00412743 + 0.154142i
$$172$$ 0 0
$$173$$ 58.2425 + 58.2425i 0.336662 + 0.336662i 0.855109 0.518448i $$-0.173490\pi$$
−0.518448 + 0.855109i $$0.673490\pi$$
$$174$$ 0 0
$$175$$ 160.568 0.917531
$$176$$ 0 0
$$177$$ 237.856 + 94.8137i 1.34382 + 0.535671i
$$178$$ 0 0
$$179$$ −18.9272 18.9272i −0.105738 0.105738i 0.652258 0.757997i $$-0.273822\pi$$
−0.757997 + 0.652258i $$0.773822\pi$$
$$180$$ 0 0
$$181$$ −24.5109 24.5109i −0.135420 0.135420i 0.636148 0.771567i $$-0.280527\pi$$
−0.771567 + 0.636148i $$0.780527\pi$$
$$182$$ 0 0
$$183$$ −189.262 75.4431i −1.03422 0.412257i
$$184$$ 0 0
$$185$$ −0.183915 −0.000994136
$$186$$ 0 0
$$187$$ −172.506 172.506i −0.922494 0.922494i
$$188$$ 0 0
$$189$$ −59.8777 + 162.749i −0.316813 + 0.861107i
$$190$$ 0 0
$$191$$ 156.422i 0.818962i 0.912319 + 0.409481i $$0.134290\pi$$
−0.912319 + 0.409481i $$0.865710\pi$$
$$192$$ 0 0
$$193$$ −217.972 −1.12939 −0.564695 0.825299i $$-0.691006\pi$$
−0.564695 + 0.825299i $$0.691006\pi$$
$$194$$ 0 0
$$195$$ −0.685275 + 0.294657i −0.00351423 + 0.00151106i
$$196$$ 0 0
$$197$$ −245.945 + 245.945i −1.24845 + 1.24845i −0.292050 + 0.956403i $$0.594337\pi$$
−0.956403 + 0.292050i $$0.905663\pi$$
$$198$$ 0 0
$$199$$ 233.190i 1.17181i −0.810379 0.585905i $$-0.800739\pi$$
0.810379 0.585905i $$-0.199261\pi$$
$$200$$ 0 0
$$201$$ 93.7060 + 37.3528i 0.466199 + 0.185835i
$$202$$ 0 0
$$203$$ 71.7695 71.7695i 0.353545 0.353545i
$$204$$ 0 0
$$205$$ 0.465985 0.465985i 0.00227310 0.00227310i
$$206$$ 0 0
$$207$$ −121.172 + 127.840i −0.585372 + 0.617583i
$$208$$ 0 0
$$209$$ 37.5875i 0.179844i
$$210$$ 0 0
$$211$$ 8.49504 8.49504i 0.0402609 0.0402609i −0.686690 0.726951i $$-0.740937\pi$$
0.726951 + 0.686690i $$0.240937\pi$$
$$212$$ 0 0
$$213$$ 16.0862 + 37.4111i 0.0755220 + 0.175639i
$$214$$ 0 0
$$215$$ −0.475649 −0.00221232
$$216$$ 0 0
$$217$$ 384.971i 1.77406i
$$218$$ 0 0
$$219$$ 86.6814 37.2716i 0.395806 0.170190i
$$220$$ 0 0
$$221$$ −239.783 239.783i −1.08499 1.08499i
$$222$$ 0 0
$$223$$ −10.9290 −0.0490090 −0.0245045 0.999700i $$-0.507801\pi$$
−0.0245045 + 0.999700i $$0.507801\pi$$
$$224$$ 0 0
$$225$$ −163.299 154.782i −0.725775 0.687921i
$$226$$ 0 0
$$227$$ 99.9027 + 99.9027i 0.440100 + 0.440100i 0.892045 0.451946i $$-0.149270\pi$$
−0.451946 + 0.892045i $$0.649270\pi$$
$$228$$ 0 0
$$229$$ 231.857 + 231.857i 1.01248 + 1.01248i 0.999921 + 0.0125555i $$0.00399663\pi$$
0.0125555 + 0.999921i $$0.496003\pi$$
$$230$$ 0 0
$$231$$ −91.5354 + 229.632i −0.396257 + 0.994079i
$$232$$ 0 0
$$233$$ 316.641 1.35897 0.679486 0.733688i $$-0.262203\pi$$
0.679486 + 0.733688i $$0.262203\pi$$
$$234$$ 0 0
$$235$$ 0.0620836 + 0.0620836i 0.000264186 + 0.000264186i
$$236$$ 0 0
$$237$$ 56.2562 + 130.833i 0.237368 + 0.552040i
$$238$$ 0 0
$$239$$ 382.691i 1.60122i 0.599187 + 0.800609i $$0.295491\pi$$
−0.599187 + 0.800609i $$0.704509\pi$$
$$240$$ 0 0
$$241$$ −91.3157 −0.378903 −0.189452 0.981890i $$-0.560671\pi$$
−0.189452 + 0.981890i $$0.560671\pi$$
$$242$$ 0 0
$$243$$ 217.781 107.798i 0.896219 0.443612i
$$244$$ 0 0
$$245$$ 0.0763900 0.0763900i 0.000311796 0.000311796i
$$246$$ 0 0
$$247$$ 52.2463i 0.211524i
$$248$$ 0 0
$$249$$ −110.490 + 277.183i −0.443734 + 1.11318i
$$250$$ 0 0
$$251$$ −128.768 + 128.768i −0.513021 + 0.513021i −0.915451 0.402430i $$-0.868166\pi$$
0.402430 + 0.915451i $$0.368166\pi$$
$$252$$ 0 0
$$253$$ −177.547 + 177.547i −0.701769 + 0.701769i
$$254$$ 0 0
$$255$$ −0.294524 + 0.738865i −0.00115500 + 0.00289751i
$$256$$ 0 0
$$257$$ 123.915i 0.482159i −0.970505 0.241079i $$-0.922499\pi$$
0.970505 0.241079i $$-0.0775014\pi$$
$$258$$ 0 0
$$259$$ −59.9056 + 59.9056i −0.231296 + 0.231296i
$$260$$ 0 0
$$261$$ −142.174 + 3.80695i −0.544728 + 0.0145860i
$$262$$ 0 0
$$263$$ −194.379 −0.739085 −0.369542 0.929214i $$-0.620486\pi$$
−0.369542 + 0.929214i $$0.620486\pi$$
$$264$$ 0 0
$$265$$ 0.407005i 0.00153587i
$$266$$ 0 0
$$267$$ −112.784 262.299i −0.422413 0.982393i
$$268$$ 0 0
$$269$$ 296.636 + 296.636i 1.10274 + 1.10274i 0.994079 + 0.108658i $$0.0346555\pi$$
0.108658 + 0.994079i $$0.465345\pi$$
$$270$$ 0 0
$$271$$ −278.227 −1.02667 −0.513334 0.858189i $$-0.671590\pi$$
−0.513334 + 0.858189i $$0.671590\pi$$
$$272$$ 0 0
$$273$$ −127.234 + 319.187i −0.466057 + 1.16918i
$$274$$ 0 0
$$275$$ −226.795 226.795i −0.824709 0.824709i
$$276$$ 0 0
$$277$$ 60.1513 + 60.1513i 0.217153 + 0.217153i 0.807297 0.590145i $$-0.200929\pi$$
−0.590145 + 0.807297i $$0.700929\pi$$
$$278$$ 0 0
$$279$$ 371.099 391.520i 1.33010 1.40330i
$$280$$ 0 0
$$281$$ −313.645 −1.11617 −0.558087 0.829782i $$-0.688465\pi$$
−0.558087 + 0.829782i $$0.688465\pi$$
$$282$$ 0 0
$$283$$ −286.980 286.980i −1.01406 1.01406i −0.999900 0.0141627i $$-0.995492\pi$$
−0.0141627 0.999900i $$-0.504508\pi$$
$$284$$ 0 0
$$285$$ 0.112583 0.0484087i 0.000395027 0.000169855i
$$286$$ 0 0
$$287$$ 303.565i 1.05772i
$$288$$ 0 0
$$289$$ −72.5910 −0.251180
$$290$$ 0 0
$$291$$ 73.0246 + 169.831i 0.250944 + 0.583612i
$$292$$ 0 0
$$293$$ 176.501 176.501i 0.602394 0.602394i −0.338553 0.940947i $$-0.609938\pi$$
0.940947 + 0.338553i $$0.109938\pi$$
$$294$$ 0 0
$$295$$ 1.19007i 0.00403414i
$$296$$ 0 0
$$297$$ 314.450 145.301i 1.05876 0.489230i
$$298$$ 0 0
$$299$$ −246.790 + 246.790i −0.825384 + 0.825384i
$$300$$ 0 0
$$301$$ −154.930 + 154.930i −0.514718 + 0.514718i
$$302$$ 0 0
$$303$$ −189.907 75.7002i −0.626756 0.249836i
$$304$$ 0 0
$$305$$ 0.946938i 0.00310471i
$$306$$ 0 0
$$307$$ −63.9904 + 63.9904i −0.208438 + 0.208438i −0.803603 0.595165i $$-0.797087\pi$$
0.595165 + 0.803603i $$0.297087\pi$$
$$308$$ 0 0
$$309$$ −13.0544 + 5.61319i −0.0422473 + 0.0181657i
$$310$$ 0 0
$$311$$ −532.288 −1.71154 −0.855769 0.517359i $$-0.826915\pi$$
−0.855769 + 0.517359i $$0.826915\pi$$
$$312$$ 0 0
$$313$$ 185.676i 0.593215i −0.954999 0.296607i $$-0.904145\pi$$
0.954999 0.296607i $$-0.0958553\pi$$
$$314$$ 0 0
$$315$$ 0.805687 0.0215736i 0.00255774 6.84878e-5i
$$316$$ 0 0
$$317$$ −168.127 168.127i −0.530370 0.530370i 0.390312 0.920683i $$-0.372367\pi$$
−0.920683 + 0.390312i $$0.872367\pi$$
$$318$$ 0 0
$$319$$ −202.742 −0.635556
$$320$$ 0 0
$$321$$ 161.372 + 64.3256i 0.502715 + 0.200391i
$$322$$ 0 0
$$323$$ 39.3936 + 39.3936i 0.121962 + 0.121962i
$$324$$ 0 0
$$325$$ −315.243 315.243i −0.969980 0.969980i
$$326$$ 0 0
$$327$$ 474.652 + 189.204i 1.45153 + 0.578607i
$$328$$ 0 0
$$329$$ 40.4443 0.122931
$$330$$ 0 0
$$331$$ 241.678 + 241.678i 0.730144 + 0.730144i 0.970648 0.240504i $$-0.0773127\pi$$
−0.240504 + 0.970648i $$0.577313\pi$$
$$332$$ 0 0
$$333$$ 118.672 3.17764i 0.356371 0.00954245i
$$334$$ 0 0
$$335$$ 0.468841i 0.00139953i
$$336$$ 0 0
$$337$$ 396.856 1.17762 0.588808 0.808273i $$-0.299598\pi$$
0.588808 + 0.808273i $$0.299598\pi$$
$$338$$ 0 0
$$339$$ −565.518 + 243.163i −1.66819 + 0.717296i
$$340$$ 0 0
$$341$$ 543.754 543.754i 1.59459 1.59459i
$$342$$ 0 0
$$343$$ 364.480i 1.06262i
$$344$$ 0 0
$$345$$ 0.760456 + 0.303131i 0.00220422 + 0.000878641i
$$346$$ 0 0
$$347$$ −38.5699 + 38.5699i −0.111153 + 0.111153i −0.760496 0.649343i $$-0.775044\pi$$
0.649343 + 0.760496i $$0.275044\pi$$
$$348$$ 0 0
$$349$$ −10.4065 + 10.4065i −0.0298180 + 0.0298180i −0.721859 0.692041i $$-0.756712\pi$$
0.692041 + 0.721859i $$0.256712\pi$$
$$350$$ 0 0
$$351$$ 437.084 201.968i 1.24525 0.575408i
$$352$$ 0 0
$$353$$ 209.294i 0.592900i −0.955048 0.296450i $$-0.904197\pi$$
0.955048 0.296450i $$-0.0958028\pi$$
$$354$$ 0 0
$$355$$ 0.133832 0.133832i 0.000376992 0.000376992i
$$356$$ 0 0
$$357$$ 144.732 + 336.600i 0.405413 + 0.942857i
$$358$$ 0 0
$$359$$ 42.6682 0.118853 0.0594264 0.998233i $$-0.481073\pi$$
0.0594264 + 0.998233i $$0.481073\pi$$
$$360$$ 0 0
$$361$$ 352.417i 0.976223i
$$362$$ 0 0
$$363$$ 120.156 51.6649i 0.331007 0.142328i
$$364$$ 0 0
$$365$$ −0.310088 0.310088i −0.000849557 0.000849557i
$$366$$ 0 0
$$367$$ −16.2444 −0.0442627 −0.0221313 0.999755i $$-0.507045\pi$$
−0.0221313 + 0.999755i $$0.507045\pi$$
$$368$$ 0 0
$$369$$ −292.627 + 308.729i −0.793026 + 0.836664i
$$370$$ 0 0
$$371$$ 132.571 + 132.571i 0.357335 + 0.357335i
$$372$$ 0 0
$$373$$ −351.379 351.379i −0.942035 0.942035i 0.0563743 0.998410i $$-0.482046\pi$$
−0.998410 + 0.0563743i $$0.982046\pi$$
$$374$$ 0 0
$$375$$ −0.774428 + 1.94278i −0.00206514 + 0.00518076i
$$376$$ 0 0
$$377$$ −281.811 −0.747509
$$378$$ 0 0
$$379$$ 170.505 + 170.505i 0.449880 + 0.449880i 0.895315 0.445435i $$-0.146951\pi$$
−0.445435 + 0.895315i $$0.646951\pi$$
$$380$$ 0 0
$$381$$ 64.1653 + 149.227i 0.168413 + 0.391673i
$$382$$ 0 0
$$383$$ 256.234i 0.669017i −0.942393 0.334509i $$-0.891430\pi$$
0.942393 0.334509i $$-0.108570\pi$$
$$384$$ 0 0
$$385$$ 1.14892 0.00298422
$$386$$ 0 0
$$387$$ 306.913 8.21813i 0.793058 0.0212355i
$$388$$ 0 0
$$389$$ −376.214 + 376.214i −0.967130 + 0.967130i −0.999477 0.0323468i $$-0.989702\pi$$
0.0323468 + 0.999477i $$0.489702\pi$$
$$390$$ 0 0
$$391$$ 372.158i 0.951810i
$$392$$ 0 0
$$393$$ 49.1063 123.192i 0.124953 0.313465i
$$394$$ 0 0
$$395$$ 0.468035 0.468035i 0.00118490 0.00118490i
$$396$$ 0 0
$$397$$ 312.905 312.905i 0.788174 0.788174i −0.193021 0.981195i $$-0.561828\pi$$
0.981195 + 0.193021i $$0.0618284\pi$$
$$398$$ 0 0
$$399$$ 20.9030 52.4388i 0.0523885 0.131426i
$$400$$ 0 0
$$401$$ 9.22373i 0.0230018i −0.999934 0.0115009i $$-0.996339\pi$$
0.999934 0.0115009i $$-0.00366093\pi$$
$$402$$ 0 0
$$403$$ 755.814 755.814i 1.87547 1.87547i
$$404$$ 0 0
$$405$$ −0.840189 0.754715i −0.00207454 0.00186349i
$$406$$ 0 0
$$407$$ 169.228 0.415793
$$408$$ 0 0
$$409$$ 322.436i 0.788352i −0.919035 0.394176i $$-0.871030\pi$$
0.919035 0.394176i $$-0.128970\pi$$
$$410$$ 0 0
$$411$$ 50.8592 + 118.282i 0.123745 + 0.287790i
$$412$$ 0 0
$$413$$ −387.635 387.635i −0.938583 0.938583i
$$414$$ 0 0
$$415$$ 1.38683 0.00334177
$$416$$ 0 0
$$417$$ −73.9845 + 185.603i −0.177421 + 0.445090i
$$418$$ 0 0
$$419$$ −226.569 226.569i −0.540738 0.540738i 0.383007 0.923745i $$-0.374888\pi$$
−0.923745 + 0.383007i $$0.874888\pi$$
$$420$$ 0 0
$$421$$ 498.861 + 498.861i 1.18494 + 1.18494i 0.978448 + 0.206495i $$0.0662058\pi$$
0.206495 + 0.978448i $$0.433794\pi$$
$$422$$ 0 0
$$423$$ −41.1323 38.9870i −0.0972394 0.0921677i
$$424$$ 0 0
$$425$$ −475.385 −1.11855
$$426$$ 0 0
$$427$$ 308.440 + 308.440i 0.722343 + 0.722343i
$$428$$ 0 0
$$429$$ 630.549 271.126i 1.46981 0.631995i
$$430$$ 0 0
$$431$$ 452.283i 1.04938i 0.851293 + 0.524690i $$0.175819\pi$$
−0.851293 + 0.524690i $$0.824181\pi$$
$$432$$ 0 0
$$433$$ 379.557 0.876574 0.438287 0.898835i $$-0.355585\pi$$
0.438287 + 0.898835i $$0.355585\pi$$
$$434$$ 0 0
$$435$$ 0.261111 + 0.607258i 0.000600255 + 0.00139600i
$$436$$ 0 0
$$437$$ 40.5447 40.5447i 0.0927797 0.0927797i
$$438$$ 0 0
$$439$$ 689.509i 1.57063i 0.619094 + 0.785317i $$0.287500\pi$$
−0.619094 + 0.785317i $$0.712500\pi$$
$$440$$ 0 0
$$441$$ −47.9710 + 50.6107i −0.108778 + 0.114763i
$$442$$ 0 0
$$443$$ −97.5600 + 97.5600i −0.220226 + 0.220226i −0.808593 0.588368i $$-0.799771\pi$$
0.588368 + 0.808593i $$0.299771\pi$$
$$444$$ 0 0
$$445$$ −0.938330 + 0.938330i −0.00210861 + 0.00210861i
$$446$$ 0 0
$$447$$ 518.377 + 206.634i 1.15968 + 0.462269i
$$448$$ 0 0
$$449$$ 718.711i 1.60069i −0.599538 0.800347i $$-0.704649\pi$$
0.599538 0.800347i $$-0.295351\pi$$
$$450$$ 0 0
$$451$$ −428.772 + 428.772i −0.950713 + 0.950713i
$$452$$ 0 0
$$453$$ −402.127 + 172.908i −0.887698 + 0.381695i
$$454$$ 0 0
$$455$$ 1.59700 0.00350988
$$456$$ 0 0
$$457$$ 489.021i 1.07007i −0.844830 0.535034i $$-0.820299\pi$$
0.844830 0.535034i $$-0.179701\pi$$
$$458$$ 0 0
$$459$$ 177.277 481.843i 0.386224 1.04977i
$$460$$ 0 0
$$461$$ −459.082 459.082i −0.995840 0.995840i 0.00415179 0.999991i $$-0.498678\pi$$
−0.999991 + 0.00415179i $$0.998678\pi$$
$$462$$ 0 0
$$463$$ 587.611 1.26914 0.634569 0.772866i $$-0.281178\pi$$
0.634569 + 0.772866i $$0.281178\pi$$
$$464$$ 0 0
$$465$$ −2.32896 0.928364i −0.00500852 0.00199648i
$$466$$ 0 0
$$467$$ −89.5077 89.5077i −0.191665 0.191665i 0.604750 0.796415i $$-0.293273\pi$$
−0.796415 + 0.604750i $$0.793273\pi$$
$$468$$ 0 0
$$469$$ −152.713 152.713i −0.325614 0.325614i
$$470$$ 0 0
$$471$$ 217.778 + 86.8101i 0.462374 + 0.184310i
$$472$$ 0 0
$$473$$ 437.664 0.925293
$$474$$ 0 0
$$475$$ 51.7909 + 51.7909i 0.109033 + 0.109033i
$$476$$ 0 0
$$477$$ −7.03213 262.621i −0.0147424 0.550568i
$$478$$ 0 0
$$479$$ 439.291i 0.917101i 0.888668 + 0.458550i $$0.151631\pi$$
−0.888668 + 0.458550i $$0.848369\pi$$
$$480$$ 0 0
$$481$$ 235.226 0.489034
$$482$$ 0 0
$$483$$ 346.436 148.962i 0.717259 0.308410i
$$484$$ 0 0
$$485$$ 0.607542 0.607542i 0.00125266 0.00125266i
$$486$$ 0 0
$$487$$ 499.716i 1.02611i −0.858355 0.513056i $$-0.828513\pi$$
0.858355 0.513056i $$-0.171487\pi$$
$$488$$ 0 0
$$489$$ −278.301 110.936i −0.569123 0.226862i
$$490$$ 0 0
$$491$$ 359.246 359.246i 0.731663 0.731663i −0.239286 0.970949i $$-0.576913\pi$$
0.970949 + 0.239286i $$0.0769134\pi$$
$$492$$ 0 0
$$493$$ −212.484 + 212.484i −0.431003 + 0.431003i
$$494$$ 0 0
$$495$$ −1.16847 1.10752i −0.00236054 0.00223742i
$$496$$ 0 0
$$497$$ 87.1846i 0.175422i
$$498$$ 0 0
$$499$$ 64.4682 64.4682i 0.129195 0.129195i −0.639553 0.768747i $$-0.720880\pi$$
0.768747 + 0.639553i $$0.220880\pi$$
$$500$$ 0 0
$$501$$ 102.152 + 237.573i 0.203897 + 0.474197i
$$502$$ 0 0
$$503$$ −597.277 −1.18743 −0.593714 0.804676i $$-0.702339\pi$$
−0.593714 + 0.804676i $$0.702339\pi$$
$$504$$ 0 0
$$505$$ 0.950165i 0.00188151i
$$506$$ 0 0
$$507$$ 410.691 176.591i 0.810042 0.348305i
$$508$$ 0 0
$$509$$ 359.574 + 359.574i 0.706433 + 0.706433i 0.965783 0.259350i $$-0.0835084\pi$$
−0.259350 + 0.965783i $$0.583508\pi$$
$$510$$ 0 0
$$511$$ −202.006 −0.395316
$$512$$ 0 0
$$513$$ −71.8079 + 33.1810i −0.139976 + 0.0646804i
$$514$$ 0 0
$$515$$ 0.0467000 + 0.0467000i 9.06796e−5 + 9.06796e-5i
$$516$$ 0 0
$$517$$ −57.1257 57.1257i −0.110495 0.110495i
$$518$$ 0 0
$$519$$ −91.4977 + 229.538i −0.176296 + 0.442269i
$$520$$ 0 0
$$521$$ 862.399 1.65528 0.827639 0.561261i $$-0.189684\pi$$
0.827639 + 0.561261i $$0.189684\pi$$
$$522$$ 0 0
$$523$$ 256.574 + 256.574i 0.490581 + 0.490581i 0.908489 0.417908i $$-0.137237\pi$$
−0.417908 + 0.908489i $$0.637237\pi$$
$$524$$ 0 0
$$525$$ 190.280 + 442.529i 0.362438 + 0.842912i
$$526$$ 0 0
$$527$$ 1139.76i 2.16274i
$$528$$ 0 0
$$529$$ −145.967 −0.275930
$$530$$ 0 0
$$531$$ 20.5617 + 767.897i 0.0387227 + 1.44613i
$$532$$ 0 0
$$533$$ −595.990 + 595.990i −1.11818 + 1.11818i
$$534$$ 0 0
$$535$$ 0.807394i 0.00150915i
$$536$$ 0 0
$$537$$ 29.7342 74.5933i 0.0553709 0.138907i
$$538$$ 0 0
$$539$$ −70.2895 + 70.2895i −0.130407 + 0.130407i
$$540$$ 0 0
$$541$$ 431.469 431.469i 0.797540 0.797540i −0.185167 0.982707i $$-0.559283\pi$$
0.982707 + 0.185167i $$0.0592826\pi$$
$$542$$ 0 0
$$543$$ 38.5062 96.5993i 0.0709137 0.177899i
$$544$$ 0 0
$$545$$ 2.37483i 0.00435749i
$$546$$ 0 0
$$547$$ −335.381 + 335.381i −0.613127 + 0.613127i −0.943760 0.330632i $$-0.892738\pi$$
0.330632 + 0.943760i $$0.392738\pi$$
$$548$$ 0 0
$$549$$ −16.3609 611.014i −0.0298014 1.11296i
$$550$$ 0 0
$$551$$ 46.2983 0.0840259
$$552$$ 0 0
$$553$$ 304.900i 0.551357i
$$554$$ 0 0
$$555$$ −0.217948 0.506874i −0.000392699 0.000913287i
$$556$$ 0 0
$$557$$ 118.642 + 118.642i 0.213001 + 0.213001i 0.805541 0.592540i $$-0.201875\pi$$
−0.592540 + 0.805541i $$0.701875\pi$$
$$558$$ 0 0
$$559$$ 608.350 1.08828
$$560$$ 0 0
$$561$$ 271.004 679.860i 0.483073 1.21187i
$$562$$ 0 0
$$563$$ −290.766 290.766i −0.516459 0.516459i 0.400039 0.916498i $$-0.368997\pi$$
−0.916498 + 0.400039i $$0.868997\pi$$
$$564$$ 0 0
$$565$$ 2.02305 + 2.02305i 0.00358061 + 0.00358061i
$$566$$ 0 0
$$567$$ −519.499 + 27.8409i −0.916223 + 0.0491021i
$$568$$ 0 0
$$569$$ −669.398 −1.17645 −0.588223 0.808699i $$-0.700172\pi$$
−0.588223 + 0.808699i $$0.700172\pi$$
$$570$$ 0 0
$$571$$ −454.971 454.971i −0.796798 0.796798i 0.185792 0.982589i $$-0.440515\pi$$
−0.982589 + 0.185792i $$0.940515\pi$$
$$572$$ 0 0
$$573$$ −431.102 + 185.367i −0.752359 + 0.323502i
$$574$$ 0 0
$$575$$ 489.277i 0.850916i
$$576$$ 0 0
$$577$$ −288.393 −0.499814 −0.249907 0.968270i $$-0.580400\pi$$
−0.249907 + 0.968270i $$0.580400\pi$$
$$578$$ 0 0
$$579$$ −258.307 600.737i −0.446126 1.03754i
$$580$$ 0 0
$$581$$ 451.725 451.725i 0.777496 0.777496i
$$582$$ 0 0
$$583$$ 374.502i 0.642371i
$$584$$ 0 0
$$585$$ −1.62416 1.53945i −0.00277635 0.00263154i
$$586$$ 0 0
$$587$$ −393.610 + 393.610i −0.670545 + 0.670545i −0.957842 0.287297i $$-0.907243\pi$$
0.287297 + 0.957842i $$0.407243\pi$$
$$588$$ 0 0
$$589$$ −124.172 + 124.172i −0.210818 + 0.210818i
$$590$$ 0 0
$$591$$ −969.287 386.375i −1.64008 0.653764i
$$592$$ 0 0
$$593$$ 707.638i 1.19332i 0.802495 + 0.596659i $$0.203506\pi$$
−0.802495 + 0.596659i $$0.796494\pi$$
$$594$$ 0 0
$$595$$ 1.20413 1.20413i 0.00202375 0.00202375i
$$596$$ 0 0
$$597$$ 642.678 276.341i 1.07651 0.462883i
$$598$$ 0 0
$$599$$ 996.581 1.66374 0.831870 0.554970i $$-0.187270\pi$$
0.831870 + 0.554970i $$0.187270\pi$$
$$600$$ 0 0
$$601$$ 214.386i 0.356716i 0.983966 + 0.178358i $$0.0570785\pi$$
−0.983966 + 0.178358i $$0.942921\pi$$
$$602$$ 0 0
$$603$$ 8.10051 + 302.521i 0.0134337 + 0.501693i
$$604$$ 0 0
$$605$$ −0.429836 0.429836i −0.000710474 0.000710474i
$$606$$ 0 0
$$607$$ −989.981 −1.63094 −0.815470 0.578799i $$-0.803522\pi$$
−0.815470 + 0.578799i $$0.803522\pi$$
$$608$$ 0 0
$$609$$ 282.849 + 112.748i 0.464448 + 0.185137i
$$610$$ 0 0
$$611$$ −79.4044 79.4044i −0.129958 0.129958i
$$612$$ 0 0
$$613$$ −277.427 277.427i −0.452572 0.452572i 0.443636 0.896207i $$-0.353688\pi$$
−0.896207 + 0.443636i $$0.853688\pi$$
$$614$$ 0 0
$$615$$ 1.83648 + 0.732052i 0.00298614 + 0.00119033i
$$616$$ 0 0
$$617$$ 294.951 0.478040 0.239020 0.971015i $$-0.423174\pi$$
0.239020 + 0.971015i $$0.423174\pi$$
$$618$$ 0 0
$$619$$ −717.374 717.374i −1.15892 1.15892i −0.984707 0.174218i $$-0.944260\pi$$
−0.174218 0.984707i $$-0.555740\pi$$
$$620$$ 0 0
$$621$$ −495.924 182.457i −0.798589 0.293812i
$$622$$ 0 0
$$623$$ 611.273i 0.981177i
$$624$$ 0 0
$$625$$ −624.985 −0.999977
$$626$$ 0 0
$$627$$ −103.592 + 44.5428i −0.165218 + 0.0710412i
$$628$$ 0 0
$$629$$ 177.359 177.359i 0.281970 0.281970i
$$630$$ 0 0
$$631$$ 526.114i 0.833779i 0.908957 + 0.416889i $$0.136880\pi$$
−0.908957 + 0.416889i $$0.863120\pi$$
$$632$$ 0 0
$$633$$ 33.4795 + 13.3455i 0.0528903 + 0.0210830i
$$634$$ 0 0
$$635$$ 0.533835 0.533835i 0.000840686 0.000840686i
$$636$$ 0 0
$$637$$ −97.7020 + 97.7020i −0.153378 + 0.153378i
$$638$$ 0 0
$$639$$ −84.0431 + 88.6678i −0.131523 + 0.138760i
$$640$$ 0 0
$$641$$ 1025.84i 1.60037i 0.599754 + 0.800184i $$0.295265\pi$$
−0.599754 + 0.800184i $$0.704735\pi$$
$$642$$ 0 0
$$643$$ 366.197 366.197i 0.569514 0.569514i −0.362479 0.931992i $$-0.618069\pi$$
0.931992 + 0.362479i $$0.118069\pi$$
$$644$$ 0 0
$$645$$ −0.563665 1.31090i −0.000873900 0.00203240i
$$646$$ 0 0
$$647$$ 90.9084 0.140508 0.0702538 0.997529i $$-0.477619\pi$$
0.0702538 + 0.997529i $$0.477619\pi$$
$$648$$ 0 0
$$649$$ 1095.03i 1.68726i
$$650$$ 0 0
$$651$$ −1060.99 + 456.208i −1.62978 + 0.700780i
$$652$$ 0 0
$$653$$ 291.274 + 291.274i 0.446056 + 0.446056i 0.894041 0.447985i $$-0.147858\pi$$
−0.447985 + 0.894041i $$0.647858\pi$$
$$654$$ 0 0
$$655$$ −0.616367 −0.000941019
$$656$$ 0 0
$$657$$ 205.443 + 194.728i 0.312698 + 0.296389i
$$658$$ 0 0
$$659$$ 817.853 + 817.853i 1.24105 + 1.24105i 0.959565 + 0.281486i $$0.0908273\pi$$
0.281486 + 0.959565i $$0.409173\pi$$
$$660$$ 0 0
$$661$$ 673.995 + 673.995i 1.01966 + 1.01966i 0.999803 + 0.0198568i $$0.00632103\pi$$
0.0198568 + 0.999803i $$0.493679\pi$$
$$662$$ 0 0
$$663$$ 376.694 945.001i 0.568166 1.42534i
$$664$$ 0 0
$$665$$ −0.262368 −0.000394538
$$666$$ 0 0
$$667$$ 218.694 + 218.694i 0.327877 + 0.327877i
$$668$$ 0 0
$$669$$ −12.9514 30.1206i −0.0193593 0.0450233i
$$670$$ 0 0
$$671$$ 871.316i 1.29853i
$$672$$ 0 0
$$673$$ −526.059 −0.781662 −0.390831 0.920462i $$-0.627812\pi$$
−0.390831 + 0.920462i $$0.627812\pi$$
$$674$$ 0 0
$$675$$ 233.066 633.481i 0.345283 0.938490i
$$676$$ 0 0
$$677$$ 143.663 143.663i 0.212205 0.212205i −0.592998 0.805204i $$-0.702056\pi$$
0.805204 + 0.592998i $$0.202056\pi$$
$$678$$ 0 0
$$679$$ 395.782i 0.582890i
$$680$$ 0 0
$$681$$ −156.945 + 393.723i −0.230462 + 0.578155i
$$682$$ 0 0
$$683$$ 50.6262 50.6262i 0.0741232 0.0741232i −0.669073 0.743196i $$-0.733309\pi$$
0.743196 + 0.669073i $$0.233309\pi$$
$$684$$ 0 0
$$685$$ 0.423133 0.423133i 0.000617713 0.000617713i
$$686$$ 0 0
$$687$$ −364.243 + 913.765i −0.530193 + 1.33008i
$$688$$ 0 0
$$689$$ 520.556i 0.755523i
$$690$$ 0 0
$$691$$ −396.186 + 396.186i −0.573351 + 0.573351i −0.933063 0.359712i $$-0.882875\pi$$
0.359712 + 0.933063i $$0.382875\pi$$
$$692$$ 0 0
$$693$$ −741.345 + 19.8508i −1.06976 + 0.0286447i
$$694$$ 0 0
$$695$$ 0.928629 0.00133616
$$696$$ 0 0
$$697$$ 898.749i 1.28945i
$$698$$ 0 0
$$699$$ 375.233 + 872.669i 0.536815 + 1.24845i
$$700$$ 0 0
$$701$$ 525.886 + 525.886i 0.750195 + 0.750195i 0.974515 0.224321i $$-0.0720164\pi$$
−0.224321 + 0.974515i $$0.572016\pi$$
$$702$$ 0 0
$$703$$ −38.6449 −0.0549713
$$704$$ 0 0
$$705$$ −0.0975321 + 0.244676i −0.000138343 + 0.000347058i
$$706$$ 0 0
$$707$$ 309.492 + 309.492i 0.437753 + 0.437753i
$$708$$ 0 0
$$709$$ 99.4062 + 99.4062i 0.140206 + 0.140206i 0.773726 0.633520i $$-0.218391\pi$$
−0.633520 + 0.773726i $$0.718391\pi$$
$$710$$ 0 0
$$711$$ −293.914 + 310.087i −0.413381 + 0.436128i
$$712$$ 0 0
$$713$$ −1173.07 −1.64526
$$714$$ 0 0
$$715$$ −2.25568 2.25568i −0.00315480 0.00315480i
$$716$$ 0 0
$$717$$ −1054.71 + 453.506i −1.47100 + 0.632505i
$$718$$ 0 0
$$719$$ 551.765i 0.767406i −0.923456 0.383703i $$-0.874649\pi$$
0.923456 0.383703i $$-0.125351\pi$$
$$720$$ 0 0
$$721$$ 30.4226 0.0421951
$$722$$ 0 0
$$723$$ −108.213 251.668i −0.149673 0.348089i
$$724$$ 0 0
$$725$$ −279.354 + 279.354i −0.385316 + 0.385316i
$$726$$ 0 0
$$727$$ 75.0947i 0.103294i 0.998665 + 0.0516470i $$0.0164471\pi$$
−0.998665 + 0.0516470i $$0.983553\pi$$
$$728$$ 0 0
$$729$$ 555.174 + 472.465i 0.761555 + 0.648100i
$$730$$ 0 0
$$731$$ 458.694 458.694i 0.627488 0.627488i
$$732$$ 0 0
$$733$$ −442.709 + 442.709i −0.603968 + 0.603968i −0.941363 0.337395i $$-0.890454\pi$$
0.337395 + 0.941363i $$0.390454\pi$$
$$734$$ 0 0
$$735$$ 0.301058 + 0.120007i 0.000409603 + 0.000163275i
$$736$$ 0 0
$$737$$ 431.400i 0.585346i
$$738$$ 0 0
$$739$$ −283.395 + 283.395i −0.383485 + 0.383485i −0.872356 0.488871i $$-0.837409\pi$$
0.488871 + 0.872356i $$0.337409\pi$$
$$740$$ 0 0
$$741$$ −143.992 + 61.9143i −0.194321 + 0.0835550i
$$742$$ 0 0
$$743$$ −835.949 −1.12510 −0.562550 0.826763i $$-0.690180\pi$$
−0.562550 + 0.826763i $$0.690180\pi$$
$$744$$ 0 0
$$745$$ 2.59361i 0.00348135i
$$746$$ 0 0
$$747$$ −894.857 + 23.9613i −1.19794 + 0.0320768i
$$748$$ 0 0
$$749$$ −262.988 262.988i −0.351118 0.351118i
$$750$$ 0 0
$$751$$ 753.712 1.00361 0.501806 0.864980i $$-0.332669\pi$$
0.501806 + 0.864980i $$0.332669\pi$$
$$752$$ 0 0
$$753$$ −507.485 202.292i −0.673951 0.268648i
$$754$$ 0 0
$$755$$ 1.43854 + 1.43854i 0.00190535 + 0.00190535i
$$756$$ 0 0
$$757$$ 335.789 + 335.789i 0.443578 + 0.443578i 0.893213 0.449634i $$-0.148446\pi$$
−0.449634 + 0.893213i $$0.648446\pi$$
$$758$$ 0 0
$$759$$ −699.727 278.923i −0.921906 0.367488i
$$760$$ 0 0
$$761$$ 1094.53 1.43828 0.719138 0.694868i $$-0.244537\pi$$
0.719138 + 0.694868i $$0.244537\pi$$
$$762$$ 0 0
$$763$$ −773.541 773.541i −1.01381 1.01381i
$$764$$ 0 0
$$765$$ −2.38535 + 0.0638720i −0.00311811 + 8.34928e-5i
$$766$$ 0 0
$$767$$ 1522.09i 1.98447i
$$768$$ 0 0
$$769$$ 290.367 0.377590 0.188795 0.982016i $$-0.439542\pi$$
0.188795 + 0.982016i $$0.439542\pi$$
$$770$$ 0 0
$$771$$ 341.512 146.845i 0.442947 0.190460i
$$772$$ 0 0
$$773$$ 193.239 193.239i 0.249986 0.249986i −0.570979 0.820965i $$-0.693436\pi$$
0.820965 + 0.570979i $$0.193436\pi$$
$$774$$ 0 0
$$775$$ 1498.45i 1.93348i
$$776$$ 0 0
$$777$$ −236.092 94.1104i −0.303851 0.121120i
$$778$$ 0 0
$$779$$ 97.9143 97.9143i 0.125692 0.125692i
$$780$$ 0 0
$$781$$ −123.144 + 123.144i −0.157675 + 0.157675i
$$782$$ 0 0
$$783$$ −178.975 387.323i −0.228575 0.494666i
$$784$$ 0 0
$$785$$ 1.08961i 0.00138804i
$$786$$ 0 0
$$787$$ −483.899 + 483.899i −0.614865 + 0.614865i −0.944210 0.329345i $$-0.893172\pi$$
0.329345 + 0.944210i $$0.393172\pi$$
$$788$$ 0 0
$$789$$ −230.348 535.714i −0.291950 0.678979i
$$790$$ 0 0
$$791$$ 1317.91 1.66613
$$792$$ 0 0
$$793$$ 1211.12i 1.52727i
$$794$$ 0 0
$$795$$ −1.12172 + 0.482320i −0.00141096 + 0.000606691i
$$796$$