# Properties

 Label 1260.2.c.e.811.9 Level $1260$ Weight $2$ Character 1260.811 Analytic conductor $10.061$ Analytic rank $0$ Dimension $16$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1260.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$10.0611506547$$ Analytic rank: $$0$$ Dimension: $$16$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ Defining polynomial: $$x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 3 x^{12} + 2 x^{11} - 7 x^{10} + 12 x^{9} - 28 x^{8} + 24 x^{7} - 28 x^{6} + 16 x^{5} + 48 x^{4} - 128 x^{3} + 192 x^{2} - 256 x + 256$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{8}$$ Twist minimal: no (minimal twist has level 420) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 811.9 Root $$-0.102186 - 1.41052i$$ of defining polynomial Character $$\chi$$ $$=$$ 1260.811 Dual form 1260.2.c.e.811.10

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.102186 - 1.41052i) q^{2} +(-1.97912 - 0.288270i) q^{4} +1.00000i q^{5} +(0.178143 - 2.63975i) q^{7} +(-0.608847 + 2.76212i) q^{8} +O(q^{10})$$ $$q+(0.102186 - 1.41052i) q^{2} +(-1.97912 - 0.288270i) q^{4} +1.00000i q^{5} +(0.178143 - 2.63975i) q^{7} +(-0.608847 + 2.76212i) q^{8} +(1.41052 + 0.102186i) q^{10} +5.22855i q^{11} -4.52534i q^{13} +(-3.70520 - 0.521019i) q^{14} +(3.83380 + 1.14104i) q^{16} -6.70156i q^{17} -2.81981 q^{19} +(0.288270 - 1.97912i) q^{20} +(7.37496 + 0.534284i) q^{22} -0.858617i q^{23} -1.00000 q^{25} +(-6.38308 - 0.462426i) q^{26} +(-1.11353 + 5.17301i) q^{28} -6.47333 q^{29} -2.60723 q^{31} +(2.00121 - 5.29104i) q^{32} +(-9.45266 - 0.684805i) q^{34} +(2.63975 + 0.178143i) q^{35} +2.13976 q^{37} +(-0.288144 + 3.97738i) q^{38} +(-2.76212 - 0.608847i) q^{40} -8.71476i q^{41} -7.42042i q^{43} +(1.50723 - 10.3479i) q^{44} +(-1.21109 - 0.0877385i) q^{46} -9.82671 q^{47} +(-6.93653 - 0.940508i) q^{49} +(-0.102186 + 1.41052i) q^{50} +(-1.30452 + 8.95618i) q^{52} -3.69301 q^{53} -5.22855 q^{55} +(7.18284 + 2.09926i) q^{56} +(-0.661483 + 9.13075i) q^{58} +4.27962 q^{59} +10.7054i q^{61} +(-0.266423 + 3.67755i) q^{62} +(-7.25861 - 3.36342i) q^{64} +4.52534 q^{65} +4.52269i q^{67} +(-1.93186 + 13.2632i) q^{68} +(0.521019 - 3.70520i) q^{70} +7.23513i q^{71} -9.24697i q^{73} +(0.218653 - 3.01816i) q^{74} +(5.58072 + 0.812865i) q^{76} +(13.8020 + 0.931432i) q^{77} +2.68314i q^{79} +(-1.14104 + 3.83380i) q^{80} +(-12.2923 - 0.890525i) q^{82} -16.2812 q^{83} +6.70156 q^{85} +(-10.4666 - 0.758262i) q^{86} +(-14.4419 - 3.18339i) q^{88} -8.53516i q^{89} +(-11.9458 - 0.806161i) q^{91} +(-0.247513 + 1.69930i) q^{92} +(-1.00415 + 13.8607i) q^{94} -2.81981i q^{95} -10.5209i q^{97} +(-2.03542 + 9.68799i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} + O(q^{10})$$ $$16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} - 10 q^{14} + 6 q^{16} + 24 q^{19} - 12 q^{22} - 16 q^{25} - 12 q^{26} - 22 q^{28} - 16 q^{29} - 8 q^{31} + 18 q^{32} - 24 q^{34} + 24 q^{37} + 28 q^{38} - 12 q^{40} + 8 q^{44} - 20 q^{46} + 16 q^{47} - 16 q^{49} + 2 q^{50} + 20 q^{52} + 32 q^{53} + 2 q^{56} - 32 q^{58} + 8 q^{59} + 16 q^{62} - 2 q^{64} + 8 q^{65} + 4 q^{68} - 20 q^{70} + 4 q^{74} - 16 q^{76} + 8 q^{77} - 16 q^{80} + 4 q^{82} + 8 q^{83} - 64 q^{86} - 52 q^{88} - 16 q^{91} - 64 q^{92} - 16 q^{94} - 2 q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$$.

 $$n$$ $$281$$ $$631$$ $$757$$ $$1081$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.102186 1.41052i 0.0722563 0.997386i
$$3$$ 0 0
$$4$$ −1.97912 0.288270i −0.989558 0.144135i
$$5$$ 1.00000i 0.447214i
$$6$$ 0 0
$$7$$ 0.178143 2.63975i 0.0673319 0.997731i
$$8$$ −0.608847 + 2.76212i −0.215260 + 0.976557i
$$9$$ 0 0
$$10$$ 1.41052 + 0.102186i 0.446045 + 0.0323140i
$$11$$ 5.22855i 1.57647i 0.615376 + 0.788234i $$0.289004\pi$$
−0.615376 + 0.788234i $$0.710996\pi$$
$$12$$ 0 0
$$13$$ 4.52534i 1.25510i −0.778574 0.627552i $$-0.784057\pi$$
0.778574 0.627552i $$-0.215943\pi$$
$$14$$ −3.70520 0.521019i −0.990258 0.139248i
$$15$$ 0 0
$$16$$ 3.83380 + 1.14104i 0.958450 + 0.285260i
$$17$$ 6.70156i 1.62537i −0.582705 0.812684i $$-0.698006\pi$$
0.582705 0.812684i $$-0.301994\pi$$
$$18$$ 0 0
$$19$$ −2.81981 −0.646908 −0.323454 0.946244i $$-0.604844\pi$$
−0.323454 + 0.946244i $$0.604844\pi$$
$$20$$ 0.288270 1.97912i 0.0644591 0.442544i
$$21$$ 0 0
$$22$$ 7.37496 + 0.534284i 1.57235 + 0.113910i
$$23$$ 0.858617i 0.179034i −0.995985 0.0895170i $$-0.971468\pi$$
0.995985 0.0895170i $$-0.0285323\pi$$
$$24$$ 0 0
$$25$$ −1.00000 −0.200000
$$26$$ −6.38308 0.462426i −1.25182 0.0906893i
$$27$$ 0 0
$$28$$ −1.11353 + 5.17301i −0.210437 + 0.977607i
$$29$$ −6.47333 −1.20207 −0.601034 0.799224i $$-0.705244\pi$$
−0.601034 + 0.799224i $$0.705244\pi$$
$$30$$ 0 0
$$31$$ −2.60723 −0.468273 −0.234137 0.972204i $$-0.575226\pi$$
−0.234137 + 0.972204i $$0.575226\pi$$
$$32$$ 2.00121 5.29104i 0.353768 0.935333i
$$33$$ 0 0
$$34$$ −9.45266 0.684805i −1.62112 0.117443i
$$35$$ 2.63975 + 0.178143i 0.446199 + 0.0301117i
$$36$$ 0 0
$$37$$ 2.13976 0.351774 0.175887 0.984410i $$-0.443721\pi$$
0.175887 + 0.984410i $$0.443721\pi$$
$$38$$ −0.288144 + 3.97738i −0.0467432 + 0.645217i
$$39$$ 0 0
$$40$$ −2.76212 0.608847i −0.436729 0.0962672i
$$41$$ 8.71476i 1.36102i −0.732740 0.680508i $$-0.761759\pi$$
0.732740 0.680508i $$-0.238241\pi$$
$$42$$ 0 0
$$43$$ 7.42042i 1.13160i −0.824541 0.565802i $$-0.808567\pi$$
0.824541 0.565802i $$-0.191433\pi$$
$$44$$ 1.50723 10.3479i 0.227224 1.56001i
$$45$$ 0 0
$$46$$ −1.21109 0.0877385i −0.178566 0.0129363i
$$47$$ −9.82671 −1.43337 −0.716686 0.697396i $$-0.754342\pi$$
−0.716686 + 0.697396i $$0.754342\pi$$
$$48$$ 0 0
$$49$$ −6.93653 0.940508i −0.990933 0.134358i
$$50$$ −0.102186 + 1.41052i −0.0144513 + 0.199477i
$$51$$ 0 0
$$52$$ −1.30452 + 8.95618i −0.180904 + 1.24200i
$$53$$ −3.69301 −0.507274 −0.253637 0.967299i $$-0.581627\pi$$
−0.253637 + 0.967299i $$0.581627\pi$$
$$54$$ 0 0
$$55$$ −5.22855 −0.705018
$$56$$ 7.18284 + 2.09926i 0.959847 + 0.280525i
$$57$$ 0 0
$$58$$ −0.661483 + 9.13075i −0.0868570 + 1.19893i
$$59$$ 4.27962 0.557159 0.278579 0.960413i $$-0.410136\pi$$
0.278579 + 0.960413i $$0.410136\pi$$
$$60$$ 0 0
$$61$$ 10.7054i 1.37069i 0.728221 + 0.685343i $$0.240347\pi$$
−0.728221 + 0.685343i $$0.759653\pi$$
$$62$$ −0.266423 + 3.67755i −0.0338357 + 0.467049i
$$63$$ 0 0
$$64$$ −7.25861 3.36342i −0.907326 0.420427i
$$65$$ 4.52534 0.561300
$$66$$ 0 0
$$67$$ 4.52269i 0.552534i 0.961081 + 0.276267i $$0.0890975\pi$$
−0.961081 + 0.276267i $$0.910903\pi$$
$$68$$ −1.93186 + 13.2632i −0.234272 + 1.60840i
$$69$$ 0 0
$$70$$ 0.521019 3.70520i 0.0622737 0.442857i
$$71$$ 7.23513i 0.858652i 0.903150 + 0.429326i $$0.141249\pi$$
−0.903150 + 0.429326i $$0.858751\pi$$
$$72$$ 0 0
$$73$$ 9.24697i 1.08228i −0.840934 0.541138i $$-0.817994\pi$$
0.840934 0.541138i $$-0.182006\pi$$
$$74$$ 0.218653 3.01816i 0.0254179 0.350854i
$$75$$ 0 0
$$76$$ 5.58072 + 0.812865i 0.640153 + 0.0932420i
$$77$$ 13.8020 + 0.931432i 1.57289 + 0.106147i
$$78$$ 0 0
$$79$$ 2.68314i 0.301877i 0.988543 + 0.150938i $$0.0482295\pi$$
−0.988543 + 0.150938i $$0.951770\pi$$
$$80$$ −1.14104 + 3.83380i −0.127572 + 0.428632i
$$81$$ 0 0
$$82$$ −12.2923 0.890525i −1.35746 0.0983421i
$$83$$ −16.2812 −1.78710 −0.893548 0.448967i $$-0.851792\pi$$
−0.893548 + 0.448967i $$0.851792\pi$$
$$84$$ 0 0
$$85$$ 6.70156 0.726886
$$86$$ −10.4666 0.758262i −1.12865 0.0817655i
$$87$$ 0 0
$$88$$ −14.4419 3.18339i −1.53951 0.339350i
$$89$$ 8.53516i 0.904725i −0.891834 0.452362i $$-0.850581\pi$$
0.891834 0.452362i $$-0.149419\pi$$
$$90$$ 0 0
$$91$$ −11.9458 0.806161i −1.25226 0.0845086i
$$92$$ −0.247513 + 1.69930i −0.0258051 + 0.177165i
$$93$$ 0 0
$$94$$ −1.00415 + 13.8607i −0.103570 + 1.42963i
$$95$$ 2.81981i 0.289306i
$$96$$ 0 0
$$97$$ 10.5209i 1.06824i −0.845410 0.534118i $$-0.820644\pi$$
0.845410 0.534118i $$-0.179356\pi$$
$$98$$ −2.03542 + 9.68799i −0.205608 + 0.978634i
$$99$$ 0 0
$$100$$ 1.97912 + 0.288270i 0.197912 + 0.0288270i
$$101$$ 3.97836i 0.395861i −0.980216 0.197931i $$-0.936578\pi$$
0.980216 0.197931i $$-0.0634221\pi$$
$$102$$ 0 0
$$103$$ −3.78934 −0.373375 −0.186688 0.982419i $$-0.559775\pi$$
−0.186688 + 0.982419i $$0.559775\pi$$
$$104$$ 12.4995 + 2.75524i 1.22568 + 0.270174i
$$105$$ 0 0
$$106$$ −0.377374 + 5.20906i −0.0366538 + 0.505948i
$$107$$ 2.38868i 0.230922i −0.993312 0.115461i $$-0.963165\pi$$
0.993312 0.115461i $$-0.0368346\pi$$
$$108$$ 0 0
$$109$$ 5.79748 0.555298 0.277649 0.960683i $$-0.410445\pi$$
0.277649 + 0.960683i $$0.410445\pi$$
$$110$$ −0.534284 + 7.37496i −0.0509420 + 0.703175i
$$111$$ 0 0
$$112$$ 3.69502 9.91700i 0.349147 0.937068i
$$113$$ 6.86598 0.645897 0.322948 0.946417i $$-0.395326\pi$$
0.322948 + 0.946417i $$0.395326\pi$$
$$114$$ 0 0
$$115$$ 0.858617 0.0800665
$$116$$ 12.8115 + 1.86607i 1.18952 + 0.173260i
$$117$$ 0 0
$$118$$ 0.437316 6.03647i 0.0402582 0.555702i
$$119$$ −17.6904 1.19384i −1.62168 0.109439i
$$120$$ 0 0
$$121$$ −16.3377 −1.48525
$$122$$ 15.1001 + 1.09394i 1.36710 + 0.0990407i
$$123$$ 0 0
$$124$$ 5.16002 + 0.751587i 0.463384 + 0.0674945i
$$125$$ 1.00000i 0.0894427i
$$126$$ 0 0
$$127$$ 10.4834i 0.930250i −0.885245 0.465125i $$-0.846009\pi$$
0.885245 0.465125i $$-0.153991\pi$$
$$128$$ −5.48588 + 9.89470i −0.484888 + 0.874576i
$$129$$ 0 0
$$130$$ 0.462426 6.38308i 0.0405575 0.559833i
$$131$$ 19.0936 1.66821 0.834106 0.551604i $$-0.185984\pi$$
0.834106 + 0.551604i $$0.185984\pi$$
$$132$$ 0 0
$$133$$ −0.502330 + 7.44358i −0.0435576 + 0.645440i
$$134$$ 6.37933 + 0.462155i 0.551090 + 0.0399241i
$$135$$ 0 0
$$136$$ 18.5105 + 4.08023i 1.58726 + 0.349876i
$$137$$ −5.47214 −0.467516 −0.233758 0.972295i $$-0.575102\pi$$
−0.233758 + 0.972295i $$0.575102\pi$$
$$138$$ 0 0
$$139$$ 2.83943 0.240838 0.120419 0.992723i $$-0.461576\pi$$
0.120419 + 0.992723i $$0.461576\pi$$
$$140$$ −5.17301 1.11353i −0.437199 0.0941101i
$$141$$ 0 0
$$142$$ 10.2053 + 0.739328i 0.856407 + 0.0620430i
$$143$$ 23.6610 1.97863
$$144$$ 0 0
$$145$$ 6.47333i 0.537581i
$$146$$ −13.0430 0.944910i −1.07945 0.0782013i
$$147$$ 0 0
$$148$$ −4.23483 0.616827i −0.348101 0.0507029i
$$149$$ −1.72856 −0.141609 −0.0708045 0.997490i $$-0.522557\pi$$
−0.0708045 + 0.997490i $$0.522557\pi$$
$$150$$ 0 0
$$151$$ 14.9532i 1.21687i 0.793603 + 0.608436i $$0.208203\pi$$
−0.793603 + 0.608436i $$0.791797\pi$$
$$152$$ 1.71683 7.78864i 0.139253 0.631742i
$$153$$ 0 0
$$154$$ 2.72418 19.3728i 0.219520 1.56111i
$$155$$ 2.60723i 0.209418i
$$156$$ 0 0
$$157$$ 11.0383i 0.880953i 0.897764 + 0.440476i $$0.145190\pi$$
−0.897764 + 0.440476i $$0.854810\pi$$
$$158$$ 3.78461 + 0.274179i 0.301088 + 0.0218125i
$$159$$ 0 0
$$160$$ 5.29104 + 2.00121i 0.418294 + 0.158210i
$$161$$ −2.26653 0.152957i −0.178628 0.0120547i
$$162$$ 0 0
$$163$$ 18.7969i 1.47229i 0.676826 + 0.736143i $$0.263355\pi$$
−0.676826 + 0.736143i $$0.736645\pi$$
$$164$$ −2.51220 + 17.2475i −0.196170 + 1.34681i
$$165$$ 0 0
$$166$$ −1.66371 + 22.9649i −0.129129 + 1.78243i
$$167$$ −1.89315 −0.146496 −0.0732481 0.997314i $$-0.523337\pi$$
−0.0732481 + 0.997314i $$0.523337\pi$$
$$168$$ 0 0
$$169$$ −7.47874 −0.575288
$$170$$ 0.684805 9.45266i 0.0525221 0.724986i
$$171$$ 0 0
$$172$$ −2.13908 + 14.6859i −0.163104 + 1.11979i
$$173$$ 9.43306i 0.717182i 0.933495 + 0.358591i $$0.116743\pi$$
−0.933495 + 0.358591i $$0.883257\pi$$
$$174$$ 0 0
$$175$$ −0.178143 + 2.63975i −0.0134664 + 0.199546i
$$176$$ −5.96598 + 20.0452i −0.449703 + 1.51097i
$$177$$ 0 0
$$178$$ −12.0390 0.872173i −0.902360 0.0653721i
$$179$$ 21.4618i 1.60413i −0.597239 0.802063i $$-0.703736\pi$$
0.597239 0.802063i $$-0.296264\pi$$
$$180$$ 0 0
$$181$$ 24.1736i 1.79681i −0.439171 0.898403i $$-0.644728\pi$$
0.439171 0.898403i $$-0.355272\pi$$
$$182$$ −2.35779 + 16.7673i −0.174771 + 1.24288i
$$183$$ 0 0
$$184$$ 2.37160 + 0.522767i 0.174837 + 0.0385389i
$$185$$ 2.13976i 0.157318i
$$186$$ 0 0
$$187$$ 35.0394 2.56234
$$188$$ 19.4482 + 2.83274i 1.41841 + 0.206599i
$$189$$ 0 0
$$190$$ −3.97738 0.288144i −0.288550 0.0209042i
$$191$$ 18.9822i 1.37350i −0.726892 0.686751i $$-0.759036\pi$$
0.726892 0.686751i $$-0.240964\pi$$
$$192$$ 0 0
$$193$$ 26.5854 1.91366 0.956828 0.290654i $$-0.0938728\pi$$
0.956828 + 0.290654i $$0.0938728\pi$$
$$194$$ −14.8399 1.07509i −1.06544 0.0771868i
$$195$$ 0 0
$$196$$ 13.4571 + 3.86097i 0.961220 + 0.275783i
$$197$$ −23.2008 −1.65299 −0.826494 0.562945i $$-0.809668\pi$$
−0.826494 + 0.562945i $$0.809668\pi$$
$$198$$ 0 0
$$199$$ 19.8867 1.40973 0.704866 0.709341i $$-0.251007\pi$$
0.704866 + 0.709341i $$0.251007\pi$$
$$200$$ 0.608847 2.76212i 0.0430520 0.195311i
$$201$$ 0 0
$$202$$ −5.61154 0.406532i −0.394827 0.0286035i
$$203$$ −1.15318 + 17.0880i −0.0809375 + 1.19934i
$$204$$ 0 0
$$205$$ 8.71476 0.608665
$$206$$ −0.387217 + 5.34493i −0.0269787 + 0.372399i
$$207$$ 0 0
$$208$$ 5.16359 17.3493i 0.358031 1.20296i
$$209$$ 14.7435i 1.01983i
$$210$$ 0 0
$$211$$ 2.51318i 0.173014i 0.996251 + 0.0865072i $$0.0275706\pi$$
−0.996251 + 0.0865072i $$0.972429\pi$$
$$212$$ 7.30890 + 1.06458i 0.501977 + 0.0731159i
$$213$$ 0 0
$$214$$ −3.36927 0.244089i −0.230319 0.0166856i
$$215$$ 7.42042 0.506068
$$216$$ 0 0
$$217$$ −0.464462 + 6.88244i −0.0315297 + 0.467211i
$$218$$ 0.592420 8.17744i 0.0401238 0.553846i
$$219$$ 0 0
$$220$$ 10.3479 + 1.50723i 0.697656 + 0.101618i
$$221$$ −30.3269 −2.04001
$$222$$ 0 0
$$223$$ 1.23567 0.0827463 0.0413732 0.999144i $$-0.486827\pi$$
0.0413732 + 0.999144i $$0.486827\pi$$
$$224$$ −13.6105 6.22527i −0.909391 0.415943i
$$225$$ 0 0
$$226$$ 0.701606 9.68458i 0.0466701 0.644208i
$$227$$ 1.76552 0.117182 0.0585909 0.998282i $$-0.481339\pi$$
0.0585909 + 0.998282i $$0.481339\pi$$
$$228$$ 0 0
$$229$$ 8.94803i 0.591302i −0.955296 0.295651i $$-0.904463\pi$$
0.955296 0.295651i $$-0.0955366\pi$$
$$230$$ 0.0877385 1.21109i 0.00578531 0.0798572i
$$231$$ 0 0
$$232$$ 3.94127 17.8801i 0.258757 1.17389i
$$233$$ 21.8087 1.42874 0.714368 0.699770i $$-0.246714\pi$$
0.714368 + 0.699770i $$0.246714\pi$$
$$234$$ 0 0
$$235$$ 9.82671i 0.641024i
$$236$$ −8.46986 1.23368i −0.551341 0.0803060i
$$237$$ 0 0
$$238$$ −3.49164 + 24.8306i −0.226330 + 1.60953i
$$239$$ 14.7558i 0.954471i −0.878776 0.477235i $$-0.841639\pi$$
0.878776 0.477235i $$-0.158361\pi$$
$$240$$ 0 0
$$241$$ 15.3302i 0.987503i 0.869603 + 0.493751i $$0.164375\pi$$
−0.869603 + 0.493751i $$0.835625\pi$$
$$242$$ −1.66949 + 23.0447i −0.107319 + 1.48137i
$$243$$ 0 0
$$244$$ 3.08604 21.1872i 0.197564 1.35637i
$$245$$ 0.940508 6.93653i 0.0600868 0.443159i
$$246$$ 0 0
$$247$$ 12.7606i 0.811937i
$$248$$ 1.58741 7.20149i 0.100800 0.457295i
$$249$$ 0 0
$$250$$ −1.41052 0.102186i −0.0892089 0.00646280i
$$251$$ 15.4063 0.972435 0.486218 0.873838i $$-0.338376\pi$$
0.486218 + 0.873838i $$0.338376\pi$$
$$252$$ 0 0
$$253$$ 4.48932 0.282241
$$254$$ −14.7870 1.07125i −0.927818 0.0672164i
$$255$$ 0 0
$$256$$ 13.3961 + 8.74903i 0.837254 + 0.546814i
$$257$$ 11.6114i 0.724298i −0.932120 0.362149i $$-0.882043\pi$$
0.932120 0.362149i $$-0.117957\pi$$
$$258$$ 0 0
$$259$$ 0.381184 5.64842i 0.0236856 0.350976i
$$260$$ −8.95618 1.30452i −0.555439 0.0809029i
$$261$$ 0 0
$$262$$ 1.95109 26.9318i 0.120539 1.66385i
$$263$$ 14.4160i 0.888927i 0.895797 + 0.444463i $$0.146606\pi$$
−0.895797 + 0.444463i $$0.853394\pi$$
$$264$$ 0 0
$$265$$ 3.69301i 0.226860i
$$266$$ 10.4480 + 1.46917i 0.640605 + 0.0900808i
$$267$$ 0 0
$$268$$ 1.30375 8.95093i 0.0796395 0.546765i
$$269$$ 10.8482i 0.661425i 0.943732 + 0.330712i $$0.107289\pi$$
−0.943732 + 0.330712i $$0.892711\pi$$
$$270$$ 0 0
$$271$$ −18.9758 −1.15270 −0.576349 0.817204i $$-0.695523\pi$$
−0.576349 + 0.817204i $$0.695523\pi$$
$$272$$ 7.64674 25.6924i 0.463652 1.55783i
$$273$$ 0 0
$$274$$ −0.559175 + 7.71854i −0.0337810 + 0.466294i
$$275$$ 5.22855i 0.315293i
$$276$$ 0 0
$$277$$ 11.0960 0.666692 0.333346 0.942804i $$-0.391822\pi$$
0.333346 + 0.942804i $$0.391822\pi$$
$$278$$ 0.290150 4.00507i 0.0174020 0.240208i
$$279$$ 0 0
$$280$$ −2.09926 + 7.18284i −0.125455 + 0.429257i
$$281$$ 26.1397 1.55937 0.779683 0.626175i $$-0.215380\pi$$
0.779683 + 0.626175i $$0.215380\pi$$
$$282$$ 0 0
$$283$$ 15.0023 0.891793 0.445897 0.895084i $$-0.352885\pi$$
0.445897 + 0.895084i $$0.352885\pi$$
$$284$$ 2.08567 14.3192i 0.123762 0.849686i
$$285$$ 0 0
$$286$$ 2.41782 33.3742i 0.142969 1.97346i
$$287$$ −23.0048 1.55248i −1.35793 0.0916399i
$$288$$ 0 0
$$289$$ −27.9109 −1.64182
$$290$$ −9.13075 0.661483i −0.536176 0.0388436i
$$291$$ 0 0
$$292$$ −2.66562 + 18.3008i −0.155994 + 1.07097i
$$293$$ 30.1766i 1.76293i −0.472245 0.881467i $$-0.656556\pi$$
0.472245 0.881467i $$-0.343444\pi$$
$$294$$ 0 0
$$295$$ 4.27962i 0.249169i
$$296$$ −1.30278 + 5.91026i −0.0757228 + 0.343527i
$$297$$ 0 0
$$298$$ −0.176634 + 2.43816i −0.0102321 + 0.141239i
$$299$$ −3.88554 −0.224706
$$300$$ 0 0
$$301$$ −19.5880 1.32190i −1.12904 0.0761930i
$$302$$ 21.0917 + 1.52800i 1.21369 + 0.0879267i
$$303$$ 0 0
$$304$$ −10.8106 3.21751i −0.620029 0.184537i
$$305$$ −10.7054 −0.612989
$$306$$ 0 0
$$307$$ −6.17458 −0.352402 −0.176201 0.984354i $$-0.556381\pi$$
−0.176201 + 0.984354i $$0.556381\pi$$
$$308$$ −27.0474 5.82213i −1.54117 0.331746i
$$309$$ 0 0
$$310$$ −3.67755 0.266423i −0.208871 0.0151318i
$$311$$ −3.80564 −0.215798 −0.107899 0.994162i $$-0.534412\pi$$
−0.107899 + 0.994162i $$0.534412\pi$$
$$312$$ 0 0
$$313$$ 16.5774i 0.937011i −0.883461 0.468506i $$-0.844793\pi$$
0.883461 0.468506i $$-0.155207\pi$$
$$314$$ 15.5697 + 1.12796i 0.878650 + 0.0636544i
$$315$$ 0 0
$$316$$ 0.773468 5.31025i 0.0435110 0.298725i
$$317$$ 11.1118 0.624098 0.312049 0.950066i $$-0.398985\pi$$
0.312049 + 0.950066i $$0.398985\pi$$
$$318$$ 0 0
$$319$$ 33.8461i 1.89502i
$$320$$ 3.36342 7.25861i 0.188021 0.405769i
$$321$$ 0 0
$$322$$ −0.447356 + 3.18135i −0.0249302 + 0.177290i
$$323$$ 18.8971i 1.05146i
$$324$$ 0 0
$$325$$ 4.52534i 0.251021i
$$326$$ 26.5133 + 1.92078i 1.46844 + 0.106382i
$$327$$ 0 0
$$328$$ 24.0712 + 5.30596i 1.32911 + 0.292972i
$$329$$ −1.75056 + 25.9400i −0.0965117 + 1.43012i
$$330$$ 0 0
$$331$$ 22.4709i 1.23511i −0.786526 0.617557i $$-0.788123\pi$$
0.786526 0.617557i $$-0.211877\pi$$
$$332$$ 32.2224 + 4.69339i 1.76844 + 0.257583i
$$333$$ 0 0
$$334$$ −0.193453 + 2.67032i −0.0105853 + 0.146113i
$$335$$ −4.52269 −0.247101
$$336$$ 0 0
$$337$$ −6.02729 −0.328328 −0.164164 0.986433i $$-0.552493\pi$$
−0.164164 + 0.986433i $$0.552493\pi$$
$$338$$ −0.764222 + 10.5489i −0.0415682 + 0.573784i
$$339$$ 0 0
$$340$$ −13.2632 1.93186i −0.719296 0.104770i
$$341$$ 13.6321i 0.738217i
$$342$$ 0 0
$$343$$ −3.71840 + 18.1431i −0.200775 + 0.979637i
$$344$$ 20.4961 + 4.51790i 1.10508 + 0.243589i
$$345$$ 0 0
$$346$$ 13.3055 + 0.963925i 0.715307 + 0.0518209i
$$347$$ 9.57093i 0.513794i 0.966439 + 0.256897i $$0.0827001\pi$$
−0.966439 + 0.256897i $$0.917300\pi$$
$$348$$ 0 0
$$349$$ 12.9442i 0.692884i 0.938071 + 0.346442i $$0.112610\pi$$
−0.938071 + 0.346442i $$0.887390\pi$$
$$350$$ 3.70520 + 0.521019i 0.198052 + 0.0278497i
$$351$$ 0 0
$$352$$ 27.6645 + 10.4635i 1.47452 + 0.557704i
$$353$$ 11.6209i 0.618520i 0.950978 + 0.309260i $$0.100081\pi$$
−0.950978 + 0.309260i $$0.899919\pi$$
$$354$$ 0 0
$$355$$ −7.23513 −0.384001
$$356$$ −2.46043 + 16.8921i −0.130402 + 0.895278i
$$357$$ 0 0
$$358$$ −30.2722 2.19309i −1.59993 0.115908i
$$359$$ 5.42483i 0.286312i 0.989700 + 0.143156i $$0.0457250\pi$$
−0.989700 + 0.143156i $$0.954275\pi$$
$$360$$ 0 0
$$361$$ −11.0487 −0.581510
$$362$$ −34.0972 2.47020i −1.79211 0.129831i
$$363$$ 0 0
$$364$$ 23.4097 + 5.03909i 1.22700 + 0.264120i
$$365$$ 9.24697 0.484009
$$366$$ 0 0
$$367$$ −28.4203 −1.48353 −0.741763 0.670662i $$-0.766010\pi$$
−0.741763 + 0.670662i $$0.766010\pi$$
$$368$$ 0.979715 3.29177i 0.0510712 0.171595i
$$369$$ 0 0
$$370$$ 3.01816 + 0.218653i 0.156907 + 0.0113672i
$$371$$ −0.657886 + 9.74862i −0.0341557 + 0.506123i
$$372$$ 0 0
$$373$$ 23.0923 1.19568 0.597838 0.801617i $$-0.296027\pi$$
0.597838 + 0.801617i $$0.296027\pi$$
$$374$$ 3.58054 49.4237i 0.185145 2.55564i
$$375$$ 0 0
$$376$$ 5.98296 27.1425i 0.308548 1.39977i
$$377$$ 29.2941i 1.50872i
$$378$$ 0 0
$$379$$ 12.0804i 0.620527i 0.950651 + 0.310263i $$0.100417\pi$$
−0.950651 + 0.310263i $$0.899583\pi$$
$$380$$ −0.812865 + 5.58072i −0.0416991 + 0.286285i
$$381$$ 0 0
$$382$$ −26.7747 1.93971i −1.36991 0.0992443i
$$383$$ 4.05602 0.207253 0.103626 0.994616i $$-0.466955\pi$$
0.103626 + 0.994616i $$0.466955\pi$$
$$384$$ 0 0
$$385$$ −0.931432 + 13.8020i −0.0474702 + 0.703418i
$$386$$ 2.71665 37.4991i 0.138274 1.90865i
$$387$$ 0 0
$$388$$ −3.03286 + 20.8221i −0.153970 + 1.05708i
$$389$$ −5.28804 −0.268114 −0.134057 0.990974i $$-0.542801\pi$$
−0.134057 + 0.990974i $$0.542801\pi$$
$$390$$ 0 0
$$391$$ −5.75407 −0.290996
$$392$$ 6.82108 18.5869i 0.344517 0.938780i
$$393$$ 0 0
$$394$$ −2.37079 + 32.7251i −0.119439 + 1.64867i
$$395$$ −2.68314 −0.135003
$$396$$ 0 0
$$397$$ 15.0058i 0.753121i −0.926392 0.376561i $$-0.877107\pi$$
0.926392 0.376561i $$-0.122893\pi$$
$$398$$ 2.03214 28.0505i 0.101862 1.40605i
$$399$$ 0 0
$$400$$ −3.83380 1.14104i −0.191690 0.0570519i
$$401$$ −19.3630 −0.966942 −0.483471 0.875360i $$-0.660624\pi$$
−0.483471 + 0.875360i $$0.660624\pi$$
$$402$$ 0 0
$$403$$ 11.7986i 0.587732i
$$404$$ −1.14684 + 7.87363i −0.0570574 + 0.391728i
$$405$$ 0 0
$$406$$ 23.9850 + 3.37273i 1.19036 + 0.167386i
$$407$$ 11.1878i 0.554560i
$$408$$ 0 0
$$409$$ 0.432474i 0.0213845i −0.999943 0.0106922i $$-0.996596\pi$$
0.999943 0.0106922i $$-0.00340351\pi$$
$$410$$ 0.890525 12.2923i 0.0439799 0.607074i
$$411$$ 0 0
$$412$$ 7.49955 + 1.09235i 0.369476 + 0.0538164i
$$413$$ 0.762386 11.2971i 0.0375146 0.555894i
$$414$$ 0 0
$$415$$ 16.2812i 0.799214i
$$416$$ −23.9438 9.05619i −1.17394 0.444016i
$$417$$ 0 0
$$418$$ −20.7960 1.50658i −1.01716 0.0736891i
$$419$$ −5.56216 −0.271729 −0.135865 0.990727i $$-0.543381\pi$$
−0.135865 + 0.990727i $$0.543381\pi$$
$$420$$ 0 0
$$421$$ −1.97874 −0.0964379 −0.0482190 0.998837i $$-0.515355\pi$$
−0.0482190 + 0.998837i $$0.515355\pi$$
$$422$$ 3.54488 + 0.256811i 0.172562 + 0.0125014i
$$423$$ 0 0
$$424$$ 2.24848 10.2005i 0.109196 0.495382i
$$425$$ 6.70156i 0.325073i
$$426$$ 0 0
$$427$$ 28.2595 + 1.90710i 1.36757 + 0.0922908i
$$428$$ −0.688584 + 4.72747i −0.0332840 + 0.228511i
$$429$$ 0 0
$$430$$ 0.758262 10.4666i 0.0365666 0.504746i
$$431$$ 14.0974i 0.679048i 0.940597 + 0.339524i $$0.110266\pi$$
−0.940597 + 0.339524i $$0.889734\pi$$
$$432$$ 0 0
$$433$$ 18.3496i 0.881826i 0.897550 + 0.440913i $$0.145345\pi$$
−0.897550 + 0.440913i $$0.854655\pi$$
$$434$$ 9.66034 + 1.35842i 0.463711 + 0.0652062i
$$435$$ 0 0
$$436$$ −11.4739 1.67124i −0.549499 0.0800378i
$$437$$ 2.42113i 0.115819i
$$438$$ 0 0
$$439$$ 8.36492 0.399236 0.199618 0.979874i $$-0.436030\pi$$
0.199618 + 0.979874i $$0.436030\pi$$
$$440$$ 3.18339 14.4419i 0.151762 0.688490i
$$441$$ 0 0
$$442$$ −3.09898 + 42.7766i −0.147403 + 2.03467i
$$443$$ 1.47488i 0.0700737i 0.999386 + 0.0350368i $$0.0111549\pi$$
−0.999386 + 0.0350368i $$0.988845\pi$$
$$444$$ 0 0
$$445$$ 8.53516 0.404605
$$446$$ 0.126268 1.74293i 0.00597895 0.0825300i
$$447$$ 0 0
$$448$$ −10.1716 + 18.5617i −0.480565 + 0.876959i
$$449$$ 16.1871 0.763918 0.381959 0.924179i $$-0.375250\pi$$
0.381959 + 0.924179i $$0.375250\pi$$
$$450$$ 0 0
$$451$$ 45.5656 2.14560
$$452$$ −13.5886 1.97925i −0.639152 0.0930963i
$$453$$ 0 0
$$454$$ 0.180411 2.49030i 0.00846713 0.116876i
$$455$$ 0.806161 11.9458i 0.0377934 0.560026i
$$456$$ 0 0
$$457$$ −26.6551 −1.24687 −0.623435 0.781875i $$-0.714264\pi$$
−0.623435 + 0.781875i $$0.714264\pi$$
$$458$$ −12.6213 0.914362i −0.589757 0.0427253i
$$459$$ 0 0
$$460$$ −1.69930 0.247513i −0.0792304 0.0115404i
$$461$$ 34.3308i 1.59895i 0.600703 + 0.799473i $$0.294888\pi$$
−0.600703 + 0.799473i $$0.705112\pi$$
$$462$$ 0 0
$$463$$ 16.8787i 0.784421i −0.919875 0.392210i $$-0.871710\pi$$
0.919875 0.392210i $$-0.128290\pi$$
$$464$$ −24.8175 7.38632i −1.15212 0.342902i
$$465$$ 0 0
$$466$$ 2.22854 30.7615i 0.103235 1.42500i
$$467$$ 33.4884 1.54966 0.774829 0.632171i $$-0.217836\pi$$
0.774829 + 0.632171i $$0.217836\pi$$
$$468$$ 0 0
$$469$$ 11.9388 + 0.805688i 0.551280 + 0.0372032i
$$470$$ −13.8607 1.00415i −0.639348 0.0463180i
$$471$$ 0 0
$$472$$ −2.60563 + 11.8208i −0.119934 + 0.544097i
$$473$$ 38.7980 1.78394
$$474$$ 0 0
$$475$$ 2.81981 0.129382
$$476$$ 34.6673 + 7.46236i 1.58897 + 0.342037i
$$477$$ 0 0
$$478$$ −20.8132 1.50783i −0.951976 0.0689665i
$$479$$ 21.1342 0.965644 0.482822 0.875718i $$-0.339612\pi$$
0.482822 + 0.875718i $$0.339612\pi$$
$$480$$ 0 0
$$481$$ 9.68314i 0.441513i
$$482$$ 21.6235 + 1.56653i 0.984921 + 0.0713533i
$$483$$ 0 0
$$484$$ 32.3343 + 4.70968i 1.46974 + 0.214076i
$$485$$ 10.5209 0.477730
$$486$$ 0 0
$$487$$ 13.3600i 0.605399i −0.953086 0.302699i $$-0.902112\pi$$
0.953086 0.302699i $$-0.0978878\pi$$
$$488$$ −29.5696 6.51795i −1.33855 0.295054i
$$489$$ 0 0
$$490$$ −9.68799 2.03542i −0.437659 0.0919508i
$$491$$ 10.6077i 0.478717i −0.970931 0.239359i $$-0.923063\pi$$
0.970931 0.239359i $$-0.0769372\pi$$
$$492$$ 0 0
$$493$$ 43.3814i 1.95380i
$$494$$ 17.9990 + 1.30395i 0.809815 + 0.0586676i
$$495$$ 0 0
$$496$$ −9.99562 2.97496i −0.448817 0.133579i
$$497$$ 19.0989 + 1.28889i 0.856703 + 0.0578147i
$$498$$ 0 0
$$499$$ 22.9131i 1.02573i −0.858470 0.512865i $$-0.828584\pi$$
0.858470 0.512865i $$-0.171416\pi$$
$$500$$ −0.288270 + 1.97912i −0.0128918 + 0.0885088i
$$501$$ 0 0
$$502$$ 1.57430 21.7308i 0.0702646 0.969893i
$$503$$ −15.2517 −0.680040 −0.340020 0.940418i $$-0.610434\pi$$
−0.340020 + 0.940418i $$0.610434\pi$$
$$504$$ 0 0
$$505$$ 3.97836 0.177035
$$506$$ 0.458745 6.33227i 0.0203937 0.281504i
$$507$$ 0 0
$$508$$ −3.02204 + 20.7478i −0.134081 + 0.920536i
$$509$$ 6.06153i 0.268673i 0.990936 + 0.134336i $$0.0428902\pi$$
−0.990936 + 0.134336i $$0.957110\pi$$
$$510$$ 0 0
$$511$$ −24.4097 1.64729i −1.07982 0.0728717i
$$512$$ 13.7095 18.0013i 0.605882 0.795555i
$$513$$ 0 0
$$514$$ −16.3781 1.18652i −0.722405 0.0523351i
$$515$$ 3.78934i 0.166978i
$$516$$ 0 0
$$517$$ 51.3794i 2.25967i
$$518$$ −7.92824 1.11485i −0.348347 0.0489839i
$$519$$ 0 0
$$520$$ −2.75524 + 12.4995i −0.120825 + 0.548141i
$$521$$ 33.7238i 1.47747i 0.673998 + 0.738733i $$0.264576\pi$$
−0.673998 + 0.738733i $$0.735424\pi$$
$$522$$ 0 0
$$523$$ 17.5830 0.768852 0.384426 0.923156i $$-0.374399\pi$$
0.384426 + 0.923156i $$0.374399\pi$$
$$524$$ −37.7884 5.50410i −1.65079 0.240448i
$$525$$ 0 0
$$526$$ 20.3340 + 1.47311i 0.886603 + 0.0642306i
$$527$$ 17.4725i 0.761116i
$$528$$ 0 0
$$529$$ 22.2628 0.967947
$$530$$ −5.20906 0.377374i −0.226267 0.0163921i
$$531$$ 0 0
$$532$$ 3.13993 14.5869i 0.136133 0.632422i
$$533$$ −39.4373 −1.70822
$$534$$ 0 0
$$535$$ 2.38868 0.103272
$$536$$ −12.4922 2.75363i −0.539581 0.118939i
$$537$$ 0 0
$$538$$ 15.3015 + 1.10853i 0.659696 + 0.0477921i
$$539$$ 4.91749 36.2680i 0.211811 1.56217i
$$540$$ 0 0
$$541$$ −22.7960 −0.980079 −0.490039 0.871700i $$-0.663018\pi$$
−0.490039 + 0.871700i $$0.663018\pi$$
$$542$$ −1.93906 + 26.7657i −0.0832897 + 1.14968i
$$543$$ 0 0
$$544$$ −35.4582 13.4113i −1.52026 0.575003i
$$545$$ 5.79748i 0.248337i
$$546$$ 0 0
$$547$$ 14.4784i 0.619053i 0.950891 + 0.309527i $$0.100171\pi$$
−0.950891 + 0.309527i $$0.899829\pi$$
$$548$$ 10.8300 + 1.57745i 0.462635 + 0.0673854i
$$549$$ 0 0
$$550$$ −7.37496 0.534284i −0.314469 0.0227819i
$$551$$ 18.2535 0.777627
$$552$$ 0 0
$$553$$ 7.08281 + 0.477984i 0.301192 + 0.0203259i
$$554$$ 1.13385 15.6511i 0.0481727 0.664950i
$$555$$ 0 0
$$556$$ −5.61957 0.818523i −0.238323 0.0347131i
$$557$$ −14.9697 −0.634288 −0.317144 0.948377i $$-0.602724\pi$$
−0.317144 + 0.948377i $$0.602724\pi$$
$$558$$ 0 0
$$559$$ −33.5800 −1.42028
$$560$$ 9.91700 + 3.69502i 0.419070 + 0.156143i
$$561$$ 0 0
$$562$$ 2.67111 36.8705i 0.112674 1.55529i
$$563$$ −6.81282 −0.287126 −0.143563 0.989641i $$-0.545856\pi$$
−0.143563 + 0.989641i $$0.545856\pi$$
$$564$$ 0 0
$$565$$ 6.86598i 0.288854i
$$566$$ 1.53302 21.1610i 0.0644377 0.889462i
$$567$$ 0 0
$$568$$ −19.9843 4.40509i −0.838522 0.184833i
$$569$$ −15.3819 −0.644841 −0.322421 0.946597i $$-0.604497\pi$$
−0.322421 + 0.946597i $$0.604497\pi$$
$$570$$ 0 0
$$571$$ 33.9875i 1.42233i 0.703024 + 0.711167i $$0.251833\pi$$
−0.703024 + 0.711167i $$0.748167\pi$$
$$572$$ −46.8278 6.82075i −1.95797 0.285190i
$$573$$ 0 0
$$574$$ −4.54056 + 32.2900i −0.189519 + 1.34776i
$$575$$ 0.858617i 0.0358068i
$$576$$ 0 0
$$577$$ 41.9819i 1.74773i 0.486170 + 0.873864i $$0.338394\pi$$
−0.486170 + 0.873864i $$0.661606\pi$$
$$578$$ −2.85210 + 39.3688i −0.118632 + 1.63753i
$$579$$ 0 0
$$580$$ −1.86607 + 12.8115i −0.0774842 + 0.531968i
$$581$$ −2.90039 + 42.9783i −0.120329 + 1.78304i
$$582$$ 0 0
$$583$$ 19.3091i 0.799701i
$$584$$ 25.5412 + 5.62999i 1.05690 + 0.232971i
$$585$$ 0 0
$$586$$ −42.5646 3.08362i −1.75833 0.127383i
$$587$$ −12.5442 −0.517756 −0.258878 0.965910i $$-0.583353\pi$$
−0.258878 + 0.965910i $$0.583353\pi$$
$$588$$ 0 0
$$589$$ 7.35190 0.302930
$$590$$ 6.03647 + 0.437316i 0.248518 + 0.0180040i
$$591$$ 0 0
$$592$$ 8.20340 + 2.44155i 0.337158 + 0.100347i
$$593$$ 9.26081i 0.380296i 0.981755 + 0.190148i $$0.0608968\pi$$
−0.981755 + 0.190148i $$0.939103\pi$$
$$594$$ 0 0
$$595$$ 1.19384 17.6904i 0.0489426 0.725237i
$$596$$ 3.42102 + 0.498291i 0.140130 + 0.0204108i
$$597$$ 0 0
$$598$$ −0.397047 + 5.48062i −0.0162365 + 0.224119i
$$599$$ 15.8991i 0.649618i 0.945780 + 0.324809i $$0.105300\pi$$
−0.945780 + 0.324809i $$0.894700\pi$$
$$600$$ 0 0
$$601$$ 31.4061i 1.28108i 0.767925 + 0.640540i $$0.221289\pi$$
−0.767925 + 0.640540i $$0.778711\pi$$
$$602$$ −3.86618 + 27.4942i −0.157574 + 1.12058i
$$603$$ 0 0
$$604$$ 4.31055 29.5941i 0.175394 1.20417i
$$605$$ 16.3377i 0.664223i
$$606$$ 0 0
$$607$$ −14.6628 −0.595147 −0.297573 0.954699i $$-0.596177\pi$$
−0.297573 + 0.954699i $$0.596177\pi$$
$$608$$ −5.64304 + 14.9197i −0.228855 + 0.605074i
$$609$$ 0 0
$$610$$ −1.09394 + 15.1001i −0.0442923 + 0.611387i
$$611$$ 44.4692i 1.79903i
$$612$$ 0 0
$$613$$ 35.6120 1.43836 0.719178 0.694826i $$-0.244519\pi$$
0.719178 + 0.694826i $$0.244519\pi$$
$$614$$ −0.630955 + 8.70935i −0.0254633 + 0.351481i
$$615$$ 0 0
$$616$$ −10.9761 + 37.5558i −0.442238 + 1.51317i
$$617$$ −22.0702 −0.888513 −0.444256 0.895900i $$-0.646532\pi$$
−0.444256 + 0.895900i $$0.646532\pi$$
$$618$$ 0 0
$$619$$ −29.1671 −1.17232 −0.586162 0.810194i $$-0.699362\pi$$
−0.586162 + 0.810194i $$0.699362\pi$$
$$620$$ −0.751587 + 5.16002i −0.0301845 + 0.207231i
$$621$$ 0 0
$$622$$ −0.388882 + 5.36792i −0.0155928 + 0.215234i
$$623$$ −22.5307 1.52048i −0.902672 0.0609169i
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ −23.3827 1.69398i −0.934562 0.0677050i
$$627$$ 0 0
$$628$$ 3.18201 21.8461i 0.126976 0.871754i
$$629$$ 14.3397i 0.571762i
$$630$$ 0 0
$$631$$ 0.162149i 0.00645504i −0.999995 0.00322752i $$-0.998973\pi$$
0.999995 0.00322752i $$-0.00102735\pi$$
$$632$$ −7.41115 1.63362i −0.294800 0.0649820i
$$633$$ 0 0
$$634$$ 1.13546 15.6733i 0.0450950 0.622467i
$$635$$ 10.4834 0.416020
$$636$$ 0 0
$$637$$ −4.25612 + 31.3902i −0.168634 + 1.24372i
$$638$$ −47.7406 3.45860i −1.89007 0.136927i
$$639$$ 0 0
$$640$$ −9.89470 5.48588i −0.391122 0.216849i
$$641$$ −12.4758 −0.492766 −0.246383 0.969173i $$-0.579242\pi$$
−0.246383 + 0.969173i $$0.579242\pi$$
$$642$$ 0 0
$$643$$ −28.4881 −1.12346 −0.561731 0.827320i $$-0.689864\pi$$
−0.561731 + 0.827320i $$0.689864\pi$$
$$644$$ 4.44164 + 0.956093i 0.175025 + 0.0376753i
$$645$$ 0 0
$$646$$ 26.6547 + 1.93102i 1.04871 + 0.0759748i
$$647$$ 24.4328 0.960554 0.480277 0.877117i $$-0.340536\pi$$
0.480277 + 0.877117i $$0.340536\pi$$
$$648$$ 0 0
$$649$$ 22.3762i 0.878342i
$$650$$ 6.38308 + 0.462426i 0.250365 + 0.0181379i
$$651$$ 0 0
$$652$$ 5.41858 37.2012i 0.212208 1.45691i
$$653$$ 39.9022 1.56149 0.780746 0.624848i $$-0.214839\pi$$
0.780746 + 0.624848i $$0.214839\pi$$
$$654$$ 0 0
$$655$$ 19.0936i 0.746047i
$$656$$ 9.94388 33.4107i 0.388243 1.30447i
$$657$$ 0 0
$$658$$ 36.4100 + 5.11990i 1.41941 + 0.199595i
$$659$$ 2.24981i 0.0876403i −0.999039 0.0438202i $$-0.986047\pi$$
0.999039 0.0438202i $$-0.0139529\pi$$
$$660$$ 0 0
$$661$$ 26.0267i 1.01232i −0.862439 0.506162i $$-0.831064\pi$$
0.862439 0.506162i $$-0.168936\pi$$
$$662$$ −31.6956 2.29621i −1.23188 0.0892447i
$$663$$ 0 0
$$664$$ 9.91278 44.9707i 0.384690 1.74520i
$$665$$ −7.44358 0.502330i −0.288650 0.0194795i
$$666$$ 0 0
$$667$$ 5.55812i 0.215211i
$$668$$ 3.74676 + 0.545738i 0.144967 + 0.0211152i
$$669$$ 0 0
$$670$$ −0.462155 + 6.37933i −0.0178546 + 0.246455i
$$671$$ −55.9737 −2.16084
$$672$$ 0 0
$$673$$ 34.4184 1.32673 0.663365 0.748296i $$-0.269127\pi$$
0.663365 + 0.748296i $$0.269127\pi$$
$$674$$ −0.615904 + 8.50160i −0.0237237 + 0.327469i
$$675$$ 0 0
$$676$$ 14.8013 + 2.15590i 0.569281 + 0.0829191i
$$677$$ 37.6392i 1.44659i 0.690538 + 0.723296i $$0.257374\pi$$
−0.690538 + 0.723296i $$0.742626\pi$$
$$678$$ 0 0
$$679$$ −27.7725 1.87423i −1.06581 0.0719264i
$$680$$ −4.08023 + 18.5105i −0.156470 + 0.709846i
$$681$$ 0 0
$$682$$ −19.2282 1.39300i −0.736288 0.0533409i
$$683$$ 25.5973i 0.979454i −0.871876 0.489727i $$-0.837096\pi$$
0.871876 0.489727i $$-0.162904\pi$$
$$684$$ 0 0
$$685$$ 5.47214i 0.209080i
$$686$$ 25.2112 + 7.09884i 0.962570 + 0.271035i
$$687$$ 0 0
$$688$$ 8.46699 28.4484i 0.322801 1.08459i
$$689$$ 16.7122i 0.636682i
$$690$$ 0 0
$$691$$ 20.4140 0.776585 0.388293 0.921536i $$-0.373065\pi$$
0.388293 + 0.921536i $$0.373065\pi$$
$$692$$ 2.71927 18.6691i 0.103371 0.709693i
$$693$$ 0 0
$$694$$ 13.5000 + 0.978013i 0.512451 + 0.0371249i
$$695$$ 2.83943i 0.107706i
$$696$$ 0 0
$$697$$ −58.4025 −2.21215
$$698$$ 18.2579 + 1.32271i 0.691073 + 0.0500653i
$$699$$ 0 0
$$700$$ 1.11353 5.17301i 0.0420873 0.195521i
$$701$$ 7.73141 0.292011 0.146006 0.989284i $$-0.453358\pi$$
0.146006 + 0.989284i $$0.453358\pi$$
$$702$$ 0 0
$$703$$ −6.03370 −0.227565
$$704$$ 17.5858 37.9520i 0.662790 1.43037i
$$705$$ 0 0
$$706$$ 16.3915 + 1.18750i 0.616903 + 0.0446920i
$$707$$ −10.5019 0.708718i −0.394963 0.0266541i
$$708$$ 0 0
$$709$$ 29.7793 1.11839 0.559193 0.829038i $$-0.311111\pi$$
0.559193 + 0.829038i $$0.311111\pi$$
$$710$$ −0.739328 + 10.2053i −0.0277465 + 0.382997i
$$711$$ 0 0
$$712$$ 23.5751 + 5.19661i 0.883515 + 0.194751i
$$713$$ 2.23862i 0.0838369i
$$714$$ 0 0
$$715$$ 23.6610i 0.884871i
$$716$$ −6.18677 + 42.4753i −0.231211 + 1.58738i
$$717$$ 0 0
$$718$$ 7.65182 + 0.554341i 0.285563 + 0.0206878i
$$719$$ 18.4203 0.686963 0.343481 0.939160i $$-0.388394\pi$$
0.343481 + 0.939160i $$0.388394\pi$$
$$720$$ 0 0
$$721$$ −0.675047 + 10.0029i −0.0251401 + 0.372528i
$$722$$ −1.12902 + 15.5844i −0.0420178 + 0.579990i
$$723$$ 0 0
$$724$$ −6.96851 + 47.8423i −0.258983 + 1.77804i
$$725$$ 6.47333 0.240414
$$726$$ 0 0
$$727$$ −30.7292 −1.13968 −0.569842 0.821754i $$-0.692996\pi$$
−0.569842 + 0.821754i $$0.692996\pi$$
$$728$$ 9.49986 32.5048i 0.352088 1.20471i
$$729$$ 0 0
$$730$$ 0.944910 13.0430i 0.0349727 0.482743i
$$731$$ −49.7284 −1.83927
$$732$$ 0 0
$$733$$ 5.09061i 0.188026i −0.995571 0.0940130i $$-0.970030\pi$$
0.995571 0.0940130i $$-0.0299695\pi$$
$$734$$ −2.90415 + 40.0873i −0.107194 + 1.47965i
$$735$$ 0 0
$$736$$ −4.54298 1.71828i −0.167456 0.0633365i
$$737$$ −23.6471 −0.871052
$$738$$ 0 0
$$739$$ 15.1154i 0.556030i −0.960577 0.278015i $$-0.910323\pi$$
0.960577 0.278015i $$-0.0896765\pi$$
$$740$$ 0.616827 4.23483i 0.0226750 0.155675i
$$741$$ 0 0
$$742$$ 13.6834 + 1.92413i 0.502332 + 0.0706370i
$$743$$ 42.0496i 1.54265i −0.636440 0.771326i $$-0.719594\pi$$
0.636440 0.771326i $$-0.280406\pi$$
$$744$$ 0 0
$$745$$ 1.72856i 0.0633295i
$$746$$ 2.35971 32.5721i 0.0863951 1.19255i
$$747$$ 0 0
$$748$$ −69.3471 10.1008i −2.53558 0.369322i
$$749$$ −6.30551 0.425527i −0.230398 0.0155484i
$$750$$ 0 0
$$751$$ 24.8965i 0.908487i 0.890877 + 0.454244i $$0.150090\pi$$
−0.890877 + 0.454244i $$0.849910\pi$$
$$752$$ −37.6736 11.2127i −1.37382 0.408884i
$$753$$ 0 0
$$754$$ 41.3198 + 2.99344i 1.50478 + 0.109015i
$$755$$ −14.9532 −0.544202
$$756$$ 0 0
$$757$$ −39.7946 −1.44636 −0.723179 0.690661i $$-0.757320\pi$$
−0.723179 + 0.690661i $$0.757320\pi$$
$$758$$ 17.0396 + 1.23444i 0.618905 + 0.0448370i
$$759$$ 0 0
$$760$$ 7.78864 + 1.71683i 0.282524 + 0.0622760i
$$761$$ 27.5663i 0.999279i −0.866234 0.499639i $$-0.833466\pi$$
0.866234 0.499639i $$-0.166534\pi$$
$$762$$ 0 0
$$763$$ 1.03278 15.3039i 0.0373893 0.554038i
$$764$$ −5.47199 + 37.5680i −0.197970 + 1.35916i
$$765$$ 0 0
$$766$$ 0.414468 5.72108i 0.0149753 0.206711i
$$767$$ 19.3667i 0.699292i
$$768$$ 0 0
$$769$$ 5.38100i 0.194044i −0.995282 0.0970219i $$-0.969068\pi$$
0.995282 0.0970219i $$-0.0309317\pi$$
$$770$$ 19.3728 + 2.72418i 0.698149 + 0.0981725i
$$771$$ 0 0
$$772$$ −52.6155 7.66376i −1.89367 0.275825i
$$773$$ 18.8696i 0.678693i 0.940661 + 0.339347i $$0.110206\pi$$
−0.940661 + 0.339347i $$0.889794\pi$$
$$774$$ 0 0
$$775$$ 2.60723 0.0936546
$$776$$ 29.0600 + 6.40563i 1.04319 + 0.229949i
$$777$$ 0 0
$$778$$ −0.540363 + 7.45887i −0.0193730 + 0.267413i
$$779$$ 24.5739i 0.880453i
$$780$$ 0 0
$$781$$ −37.8292 −1.35364
$$782$$ −0.587985 + 8.11622i −0.0210263 + 0.290235i
$$783$$ 0 0
$$784$$ −25.5201 11.5206i −0.911433 0.411449i
$$785$$ −11.0383 −0.393974
$$786$$ 0 0
$$787$$ −36.8177 −1.31241 −0.656204 0.754583i $$-0.727839\pi$$
−0.656204 + 0.754583i $$0.727839\pi$$
$$788$$ 45.9171 + 6.68809i 1.63573 + 0.238253i
$$789$$ 0 0
$$790$$ −0.274179 + 3.78461i −0.00975485 + 0.134651i
$$791$$ 1.22313 18.1244i 0.0434895 0.644431i
$$792$$