# Properties

 Label 637.2.h.l.165.3 Level $637$ Weight $2$ Character 637.165 Analytic conductor $5.086$ Analytic rank $0$ Dimension $12$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$637 = 7^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 637.h (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.08647060876$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$6$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ Defining polynomial: $$x^{12} - x^{11} + 7 x^{10} - 2 x^{9} + 33 x^{8} - 11 x^{7} + 55 x^{6} + 17 x^{5} + 47 x^{4} + x^{3} + 8 x^{2} + x + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 91) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 165.3 Root $$0.756174 - 1.30973i$$ of defining polynomial Character $$\chi$$ $$=$$ 637.165 Dual form 637.2.h.l.471.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-0.851125 q^{2} +(0.330612 + 0.572636i) q^{3} -1.27559 q^{4} +(1.72074 + 2.98041i) q^{5} +(-0.281392 - 0.487385i) q^{6} +2.78793 q^{8} +(1.28139 - 2.21944i) q^{9} +O(q^{10})$$ $$q-0.851125 q^{2} +(0.330612 + 0.572636i) q^{3} -1.27559 q^{4} +(1.72074 + 2.98041i) q^{5} +(-0.281392 - 0.487385i) q^{6} +2.78793 q^{8} +(1.28139 - 2.21944i) q^{9} +(-1.46456 - 2.53670i) q^{10} +(0.448993 + 0.777679i) q^{11} +(-0.421723 - 0.730446i) q^{12} +(3.07517 + 1.88237i) q^{13} +(-1.13779 + 1.97071i) q^{15} +0.178289 q^{16} -1.93681 q^{17} +(-1.09063 + 1.88902i) q^{18} +(0.519020 - 0.898968i) q^{19} +(-2.19495 - 3.80177i) q^{20} +(-0.382150 - 0.661902i) q^{22} +5.65013 q^{23} +(0.921723 + 1.59647i) q^{24} +(-3.42189 + 5.92688i) q^{25} +(-2.61736 - 1.60213i) q^{26} +3.67824 q^{27} +(0.917969 - 1.58997i) q^{29} +(0.968404 - 1.67733i) q^{30} +(-4.56692 + 7.91014i) q^{31} -5.72761 q^{32} +(-0.296885 + 0.514219i) q^{33} +1.64847 q^{34} +(-1.63452 + 2.83108i) q^{36} -10.6000 q^{37} +(-0.441751 + 0.765135i) q^{38} +(-0.0612242 + 2.38329i) q^{39} +(4.79731 + 8.30918i) q^{40} +(-2.66571 + 4.61715i) q^{41} +(1.95732 + 3.39018i) q^{43} +(-0.572729 - 0.991996i) q^{44} +8.81977 q^{45} -4.80897 q^{46} +(3.59565 + 6.22784i) q^{47} +(0.0589445 + 0.102095i) q^{48} +(2.91246 - 5.04452i) q^{50} +(-0.640331 - 1.10909i) q^{51} +(-3.92265 - 2.40112i) q^{52} +(4.69324 - 8.12893i) q^{53} -3.13065 q^{54} +(-1.54520 + 2.67637i) q^{55} +0.686375 q^{57} +(-0.781307 + 1.35326i) q^{58} +0.510517 q^{59} +(1.45135 - 2.51382i) q^{60} +(0.718095 - 1.24378i) q^{61} +(3.88702 - 6.73252i) q^{62} +4.51834 q^{64} +(-0.318655 + 12.4043i) q^{65} +(0.252686 - 0.437665i) q^{66} +(4.22466 + 7.31732i) q^{67} +2.47057 q^{68} +(1.86800 + 3.23547i) q^{69} +(1.72419 + 2.98638i) q^{71} +(3.57244 - 6.18764i) q^{72} +(5.45026 - 9.44013i) q^{73} +9.02195 q^{74} -4.52526 q^{75} +(-0.662054 + 1.14671i) q^{76} +(0.0521095 - 2.02848i) q^{78} +(6.04589 + 10.4718i) q^{79} +(0.306789 + 0.531375i) q^{80} +(-2.62811 - 4.55201i) q^{81} +(2.26886 - 3.92977i) q^{82} -1.51669 q^{83} +(-3.33274 - 5.77248i) q^{85} +(-1.66593 - 2.88547i) q^{86} +1.21396 q^{87} +(1.25176 + 2.16812i) q^{88} -13.6078 q^{89} -7.50673 q^{90} -7.20722 q^{92} -6.03951 q^{93} +(-3.06035 - 5.30067i) q^{94} +3.57239 q^{95} +(-1.89362 - 3.27984i) q^{96} +(0.253120 + 0.438417i) q^{97} +2.30134 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12q - 4q^{2} - q^{3} + 8q^{4} - q^{5} + 9q^{6} - 6q^{8} + 3q^{9} + O(q^{10})$$ $$12q - 4q^{2} - q^{3} + 8q^{4} - q^{5} + 9q^{6} - 6q^{8} + 3q^{9} - 4q^{10} + 4q^{11} - 5q^{12} + 2q^{13} - 2q^{15} - 16q^{16} + 10q^{17} + 3q^{18} + q^{19} + q^{20} - 5q^{22} + 2q^{23} + 11q^{24} + 7q^{25} + 16q^{26} + 8q^{27} + 3q^{29} - 5q^{30} - 16q^{31} - 16q^{32} - 16q^{33} - 32q^{34} - 21q^{36} + 26q^{37} + 17q^{38} - 20q^{39} + 5q^{40} + 8q^{41} - 11q^{43} + 21q^{44} - 14q^{45} - 32q^{46} + q^{47} - 21q^{48} + 6q^{50} - 20q^{51} - 41q^{52} - 2q^{53} - 36q^{54} - 9q^{55} + 42q^{57} - 8q^{58} + 26q^{59} + 20q^{60} + 5q^{61} - 5q^{62} - 30q^{64} - 5q^{65} - 18q^{66} - 11q^{67} + 58q^{68} - 23q^{69} + 6q^{71} + 25q^{72} + 30q^{73} + 6q^{74} - 6q^{75} + 9q^{76} + 16q^{78} + 7q^{79} + 7q^{80} - 6q^{81} - q^{82} + 54q^{83} - q^{85} - 7q^{86} + 32q^{87} + 8q^{89} + 16q^{90} + 54q^{92} + 14q^{93} - 45q^{94} + 12q^{95} - 19q^{96} + 35q^{97} - 20q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$$.

 $$n$$ $$197$$ $$248$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.851125 −0.601837 −0.300918 0.953650i $$-0.597293\pi$$
−0.300918 + 0.953650i $$0.597293\pi$$
$$3$$ 0.330612 + 0.572636i 0.190879 + 0.330612i 0.945542 0.325501i $$-0.105533\pi$$
−0.754663 + 0.656113i $$0.772200\pi$$
$$4$$ −1.27559 −0.637793
$$5$$ 1.72074 + 2.98041i 0.769538 + 1.33288i 0.937814 + 0.347139i $$0.112847\pi$$
−0.168276 + 0.985740i $$0.553820\pi$$
$$6$$ −0.281392 0.487385i −0.114878 0.198974i
$$7$$ 0 0
$$8$$ 2.78793 0.985684
$$9$$ 1.28139 2.21944i 0.427131 0.739812i
$$10$$ −1.46456 2.53670i −0.463136 0.802175i
$$11$$ 0.448993 + 0.777679i 0.135377 + 0.234479i 0.925741 0.378158i $$-0.123442\pi$$
−0.790365 + 0.612637i $$0.790109\pi$$
$$12$$ −0.421723 0.730446i −0.121741 0.210862i
$$13$$ 3.07517 + 1.88237i 0.852900 + 0.522075i
$$14$$ 0 0
$$15$$ −1.13779 + 1.97071i −0.293777 + 0.508836i
$$16$$ 0.178289 0.0445723
$$17$$ −1.93681 −0.469745 −0.234873 0.972026i $$-0.575467\pi$$
−0.234873 + 0.972026i $$0.575467\pi$$
$$18$$ −1.09063 + 1.88902i −0.257063 + 0.445246i
$$19$$ 0.519020 0.898968i 0.119071 0.206237i −0.800329 0.599562i $$-0.795342\pi$$
0.919400 + 0.393324i $$0.128675\pi$$
$$20$$ −2.19495 3.80177i −0.490806 0.850101i
$$21$$ 0 0
$$22$$ −0.382150 0.661902i −0.0814745 0.141118i
$$23$$ 5.65013 1.17813 0.589067 0.808084i $$-0.299496\pi$$
0.589067 + 0.808084i $$0.299496\pi$$
$$24$$ 0.921723 + 1.59647i 0.188146 + 0.325878i
$$25$$ −3.42189 + 5.92688i −0.684378 + 1.18538i
$$26$$ −2.61736 1.60213i −0.513306 0.314204i
$$27$$ 3.67824 0.707878
$$28$$ 0 0
$$29$$ 0.917969 1.58997i 0.170463 0.295250i −0.768119 0.640307i $$-0.778807\pi$$
0.938582 + 0.345057i $$0.112140\pi$$
$$30$$ 0.968404 1.67733i 0.176806 0.306236i
$$31$$ −4.56692 + 7.91014i −0.820244 + 1.42070i 0.0852573 + 0.996359i $$0.472829\pi$$
−0.905501 + 0.424345i $$0.860505\pi$$
$$32$$ −5.72761 −1.01251
$$33$$ −0.296885 + 0.514219i −0.0516810 + 0.0895141i
$$34$$ 1.64847 0.282710
$$35$$ 0 0
$$36$$ −1.63452 + 2.83108i −0.272421 + 0.471847i
$$37$$ −10.6000 −1.74263 −0.871316 0.490722i $$-0.836733\pi$$
−0.871316 + 0.490722i $$0.836733\pi$$
$$38$$ −0.441751 + 0.765135i −0.0716614 + 0.124121i
$$39$$ −0.0612242 + 2.38329i −0.00980372 + 0.381631i
$$40$$ 4.79731 + 8.30918i 0.758521 + 1.31380i
$$41$$ −2.66571 + 4.61715i −0.416314 + 0.721078i −0.995565 0.0940715i $$-0.970012\pi$$
0.579251 + 0.815149i $$0.303345\pi$$
$$42$$ 0 0
$$43$$ 1.95732 + 3.39018i 0.298489 + 0.516998i 0.975790 0.218708i $$-0.0701841\pi$$
−0.677302 + 0.735706i $$0.736851\pi$$
$$44$$ −0.572729 0.991996i −0.0863422 0.149549i
$$45$$ 8.81977 1.31477
$$46$$ −4.80897 −0.709044
$$47$$ 3.59565 + 6.22784i 0.524479 + 0.908424i 0.999594 + 0.0285004i $$0.00907317\pi$$
−0.475115 + 0.879924i $$0.657593\pi$$
$$48$$ 0.0589445 + 0.102095i 0.00850791 + 0.0147361i
$$49$$ 0 0
$$50$$ 2.91246 5.04452i 0.411883 0.713403i
$$51$$ −0.640331 1.10909i −0.0896643 0.155303i
$$52$$ −3.92265 2.40112i −0.543973 0.332976i
$$53$$ 4.69324 8.12893i 0.644666 1.11659i −0.339712 0.940529i $$-0.610330\pi$$
0.984378 0.176065i $$-0.0563370\pi$$
$$54$$ −3.13065 −0.426027
$$55$$ −1.54520 + 2.67637i −0.208355 + 0.360881i
$$56$$ 0 0
$$57$$ 0.686375 0.0909127
$$58$$ −0.781307 + 1.35326i −0.102591 + 0.177692i
$$59$$ 0.510517 0.0664637 0.0332318 0.999448i $$-0.489420\pi$$
0.0332318 + 0.999448i $$0.489420\pi$$
$$60$$ 1.45135 2.51382i 0.187369 0.324532i
$$61$$ 0.718095 1.24378i 0.0919426 0.159249i −0.816386 0.577507i $$-0.804026\pi$$
0.908328 + 0.418258i $$0.137359\pi$$
$$62$$ 3.88702 6.73252i 0.493653 0.855031i
$$63$$ 0 0
$$64$$ 4.51834 0.564792
$$65$$ −0.318655 + 12.4043i −0.0395242 + 1.53857i
$$66$$ 0.252686 0.437665i 0.0311035 0.0538729i
$$67$$ 4.22466 + 7.31732i 0.516124 + 0.893953i 0.999825 + 0.0187197i $$0.00595900\pi$$
−0.483701 + 0.875233i $$0.660708\pi$$
$$68$$ 2.47057 0.299600
$$69$$ 1.86800 + 3.23547i 0.224881 + 0.389504i
$$70$$ 0 0
$$71$$ 1.72419 + 2.98638i 0.204623 + 0.354418i 0.950013 0.312211i $$-0.101070\pi$$
−0.745389 + 0.666629i $$0.767736\pi$$
$$72$$ 3.57244 6.18764i 0.421016 0.729221i
$$73$$ 5.45026 9.44013i 0.637905 1.10488i −0.347987 0.937499i $$-0.613135\pi$$
0.985892 0.167384i $$-0.0535320\pi$$
$$74$$ 9.02195 1.04878
$$75$$ −4.52526 −0.522532
$$76$$ −0.662054 + 1.14671i −0.0759428 + 0.131537i
$$77$$ 0 0
$$78$$ 0.0521095 2.02848i 0.00590024 0.229680i
$$79$$ 6.04589 + 10.4718i 0.680216 + 1.17817i 0.974915 + 0.222578i $$0.0714472\pi$$
−0.294699 + 0.955590i $$0.595219\pi$$
$$80$$ 0.306789 + 0.531375i 0.0343001 + 0.0594095i
$$81$$ −2.62811 4.55201i −0.292012 0.505779i
$$82$$ 2.26886 3.92977i 0.250553 0.433971i
$$83$$ −1.51669 −0.166479 −0.0832393 0.996530i $$-0.526527\pi$$
−0.0832393 + 0.996530i $$0.526527\pi$$
$$84$$ 0 0
$$85$$ −3.33274 5.77248i −0.361487 0.626113i
$$86$$ −1.66593 2.88547i −0.179642 0.311148i
$$87$$ 1.21396 0.130151
$$88$$ 1.25176 + 2.16812i 0.133438 + 0.231122i
$$89$$ −13.6078 −1.44243 −0.721213 0.692714i $$-0.756415\pi$$
−0.721213 + 0.692714i $$0.756415\pi$$
$$90$$ −7.50673 −0.791279
$$91$$ 0 0
$$92$$ −7.20722 −0.751405
$$93$$ −6.03951 −0.626268
$$94$$ −3.06035 5.30067i −0.315651 0.546723i
$$95$$ 3.57239 0.366519
$$96$$ −1.89362 3.27984i −0.193266 0.334747i
$$97$$ 0.253120 + 0.438417i 0.0257005 + 0.0445145i 0.878590 0.477578i $$-0.158485\pi$$
−0.852889 + 0.522092i $$0.825152\pi$$
$$98$$ 0 0
$$99$$ 2.30134 0.231294
$$100$$ 4.36491 7.56025i 0.436491 0.756025i
$$101$$ −2.99327 5.18450i −0.297842 0.515877i 0.677800 0.735246i $$-0.262933\pi$$
−0.975642 + 0.219369i $$0.929600\pi$$
$$102$$ 0.545002 + 0.943972i 0.0539633 + 0.0934671i
$$103$$ −2.06651 3.57930i −0.203619 0.352679i 0.746073 0.665865i $$-0.231937\pi$$
−0.949692 + 0.313186i $$0.898604\pi$$
$$104$$ 8.57338 + 5.24792i 0.840689 + 0.514601i
$$105$$ 0 0
$$106$$ −3.99454 + 6.91874i −0.387984 + 0.672008i
$$107$$ −14.1234 −1.36536 −0.682679 0.730718i $$-0.739185\pi$$
−0.682679 + 0.730718i $$0.739185\pi$$
$$108$$ −4.69191 −0.451479
$$109$$ 2.10119 3.63936i 0.201257 0.348588i −0.747677 0.664063i $$-0.768831\pi$$
0.948934 + 0.315475i $$0.102164\pi$$
$$110$$ 1.31516 2.27792i 0.125396 0.217191i
$$111$$ −3.50449 6.06995i −0.332631 0.576135i
$$112$$ 0 0
$$113$$ −6.88472 11.9247i −0.647660 1.12178i −0.983680 0.179926i $$-0.942414\pi$$
0.336020 0.941855i $$-0.390919\pi$$
$$114$$ −0.584192 −0.0547146
$$115$$ 9.72240 + 16.8397i 0.906618 + 1.57031i
$$116$$ −1.17095 + 2.02814i −0.108720 + 0.188308i
$$117$$ 8.11830 4.41310i 0.750537 0.407991i
$$118$$ −0.434514 −0.0400003
$$119$$ 0 0
$$120$$ −3.17209 + 5.49422i −0.289571 + 0.501552i
$$121$$ 5.09681 8.82793i 0.463346 0.802539i
$$122$$ −0.611189 + 1.05861i −0.0553344 + 0.0958420i
$$123$$ −3.52526 −0.317862
$$124$$ 5.82550 10.0901i 0.523145 0.906114i
$$125$$ −6.34531 −0.567542
$$126$$ 0 0
$$127$$ −0.972482 + 1.68439i −0.0862938 + 0.149465i −0.905942 0.423402i $$-0.860836\pi$$
0.819648 + 0.572868i $$0.194169\pi$$
$$128$$ 7.60956 0.672596
$$129$$ −1.29423 + 2.24167i −0.113950 + 0.197368i
$$130$$ 0.271215 10.5576i 0.0237871 0.925967i
$$131$$ −6.01770 10.4230i −0.525769 0.910659i −0.999549 0.0300158i $$-0.990444\pi$$
0.473780 0.880643i $$-0.342889\pi$$
$$132$$ 0.378702 0.655931i 0.0329618 0.0570914i
$$133$$ 0 0
$$134$$ −3.59571 6.22796i −0.310622 0.538014i
$$135$$ 6.32930 + 10.9627i 0.544739 + 0.943516i
$$136$$ −5.39970 −0.463020
$$137$$ 8.71715 0.744756 0.372378 0.928081i $$-0.378543\pi$$
0.372378 + 0.928081i $$0.378543\pi$$
$$138$$ −1.58990 2.75379i −0.135341 0.234418i
$$139$$ 2.10625 + 3.64813i 0.178650 + 0.309430i 0.941418 0.337241i $$-0.109494\pi$$
−0.762769 + 0.646672i $$0.776160\pi$$
$$140$$ 0 0
$$141$$ −2.37752 + 4.11799i −0.200224 + 0.346798i
$$142$$ −1.46750 2.54178i −0.123150 0.213302i
$$143$$ −0.0831467 + 3.23667i −0.00695307 + 0.270664i
$$144$$ 0.228459 0.395702i 0.0190382 0.0329751i
$$145$$ 6.31834 0.524710
$$146$$ −4.63885 + 8.03473i −0.383914 + 0.664959i
$$147$$ 0 0
$$148$$ 13.5212 1.11144
$$149$$ −2.93242 + 5.07910i −0.240233 + 0.416096i −0.960781 0.277310i $$-0.910557\pi$$
0.720548 + 0.693406i $$0.243891\pi$$
$$150$$ 3.85157 0.314479
$$151$$ 8.42840 14.5984i 0.685893 1.18800i −0.287262 0.957852i $$-0.592745\pi$$
0.973155 0.230150i $$-0.0739216\pi$$
$$152$$ 1.44699 2.50626i 0.117367 0.203285i
$$153$$ −2.48181 + 4.29862i −0.200643 + 0.347523i
$$154$$ 0 0
$$155$$ −31.4339 −2.52483
$$156$$ 0.0780967 3.04009i 0.00625274 0.243402i
$$157$$ −0.969500 + 1.67922i −0.0773746 + 0.134017i −0.902116 0.431493i $$-0.857987\pi$$
0.824742 + 0.565509i $$0.191320\pi$$
$$158$$ −5.14581 8.91280i −0.409379 0.709065i
$$159$$ 6.20656 0.492212
$$160$$ −9.85573 17.0706i −0.779164 1.34955i
$$161$$ 0 0
$$162$$ 2.23685 + 3.87433i 0.175743 + 0.304396i
$$163$$ 5.94797 10.3022i 0.465881 0.806929i −0.533360 0.845888i $$-0.679071\pi$$
0.999241 + 0.0389590i $$0.0124042\pi$$
$$164$$ 3.40035 5.88957i 0.265522 0.459898i
$$165$$ −2.04344 −0.159082
$$166$$ 1.29090 0.100193
$$167$$ 8.28801 14.3553i 0.641346 1.11084i −0.343787 0.939048i $$-0.611710\pi$$
0.985133 0.171796i $$-0.0549569\pi$$
$$168$$ 0 0
$$169$$ 5.91338 + 11.5772i 0.454875 + 0.890555i
$$170$$ 2.83658 + 4.91310i 0.217556 + 0.376818i
$$171$$ −1.33013 2.30386i −0.101718 0.176181i
$$172$$ −2.49673 4.32447i −0.190374 0.329738i
$$173$$ −4.99328 + 8.64862i −0.379632 + 0.657542i −0.991009 0.133798i $$-0.957283\pi$$
0.611377 + 0.791340i $$0.290616\pi$$
$$174$$ −1.03324 −0.0783295
$$175$$ 0 0
$$176$$ 0.0800507 + 0.138652i 0.00603405 + 0.0104513i
$$177$$ 0.168783 + 0.292341i 0.0126865 + 0.0219737i
$$178$$ 11.5820 0.868105
$$179$$ −4.58829 7.94715i −0.342945 0.593998i 0.642033 0.766677i $$-0.278091\pi$$
−0.984978 + 0.172679i $$0.944758\pi$$
$$180$$ −11.2504 −0.838553
$$181$$ −6.00489 −0.446340 −0.223170 0.974780i $$-0.571640\pi$$
−0.223170 + 0.974780i $$0.571640\pi$$
$$182$$ 0 0
$$183$$ 0.949642 0.0701995
$$184$$ 15.7522 1.16127
$$185$$ −18.2399 31.5924i −1.34102 2.32272i
$$186$$ 5.14038 0.376911
$$187$$ −0.869614 1.50622i −0.0635925 0.110145i
$$188$$ −4.58655 7.94415i −0.334509 0.579386i
$$189$$ 0 0
$$190$$ −3.04055 −0.220585
$$191$$ −0.658061 + 1.13980i −0.0476156 + 0.0824727i −0.888851 0.458197i $$-0.848496\pi$$
0.841235 + 0.540669i $$0.181829\pi$$
$$192$$ 1.49382 + 2.58736i 0.107807 + 0.186727i
$$193$$ 8.21270 + 14.2248i 0.591163 + 1.02392i 0.994076 + 0.108686i $$0.0346643\pi$$
−0.402913 + 0.915238i $$0.632002\pi$$
$$194$$ −0.215437 0.373148i −0.0154675 0.0267905i
$$195$$ −7.20852 + 3.91854i −0.516213 + 0.280613i
$$196$$ 0 0
$$197$$ 12.7938 22.1594i 0.911517 1.57879i 0.0995951 0.995028i $$-0.468245\pi$$
0.811922 0.583766i $$-0.198421\pi$$
$$198$$ −1.95873 −0.139201
$$199$$ 25.3788 1.79906 0.899528 0.436864i $$-0.143911\pi$$
0.899528 + 0.436864i $$0.143911\pi$$
$$200$$ −9.54000 + 16.5238i −0.674580 + 1.16841i
$$201$$ −2.79344 + 4.83838i −0.197034 + 0.341273i
$$202$$ 2.54765 + 4.41266i 0.179252 + 0.310473i
$$203$$ 0 0
$$204$$ 0.816797 + 1.41473i 0.0571873 + 0.0990512i
$$205$$ −18.3480 −1.28148
$$206$$ 1.75886 + 3.04643i 0.122546 + 0.212255i
$$207$$ 7.24003 12.5401i 0.503217 0.871597i
$$208$$ 0.548271 + 0.335606i 0.0380157 + 0.0232701i
$$209$$ 0.932145 0.0644778
$$210$$ 0 0
$$211$$ 2.84824 4.93330i 0.196081 0.339622i −0.751173 0.660105i $$-0.770512\pi$$
0.947254 + 0.320483i $$0.103845\pi$$
$$212$$ −5.98663 + 10.3691i −0.411164 + 0.712156i
$$213$$ −1.14007 + 1.97466i −0.0781165 + 0.135302i
$$214$$ 12.0208 0.821723
$$215$$ −6.73608 + 11.6672i −0.459397 + 0.795699i
$$216$$ 10.2547 0.697744
$$217$$ 0 0
$$218$$ −1.78837 + 3.09755i −0.121124 + 0.209793i
$$219$$ 7.20768 0.487050
$$220$$ 1.97104 3.41393i 0.132887 0.230167i
$$221$$ −5.95602 3.64579i −0.400645 0.245242i
$$222$$ 2.98276 + 5.16629i 0.200190 + 0.346739i
$$223$$ 1.17906 2.04219i 0.0789558 0.136755i −0.823844 0.566817i $$-0.808175\pi$$
0.902800 + 0.430061i $$0.141508\pi$$
$$224$$ 0 0
$$225$$ 8.76956 + 15.1893i 0.584637 + 1.01262i
$$226$$ 5.85976 + 10.1494i 0.389786 + 0.675129i
$$227$$ −26.2926 −1.74510 −0.872551 0.488523i $$-0.837536\pi$$
−0.872551 + 0.488523i $$0.837536\pi$$
$$228$$ −0.875531 −0.0579834
$$229$$ 0.0342777 + 0.0593708i 0.00226514 + 0.00392333i 0.867156 0.498037i $$-0.165946\pi$$
−0.864891 + 0.501960i $$0.832612\pi$$
$$230$$ −8.27498 14.3327i −0.545636 0.945069i
$$231$$ 0 0
$$232$$ 2.55924 4.43273i 0.168022 0.291023i
$$233$$ −7.33514 12.7048i −0.480541 0.832322i 0.519210 0.854647i $$-0.326226\pi$$
−0.999751 + 0.0223253i $$0.992893\pi$$
$$234$$ −6.90969 + 3.75610i −0.451701 + 0.245544i
$$235$$ −12.3743 + 21.4330i −0.807213 + 1.39813i
$$236$$ −0.651208 −0.0423901
$$237$$ −3.99768 + 6.92419i −0.259677 + 0.449774i
$$238$$ 0 0
$$239$$ 3.35434 0.216974 0.108487 0.994098i $$-0.465399\pi$$
0.108487 + 0.994098i $$0.465399\pi$$
$$240$$ −0.202856 + 0.351357i −0.0130943 + 0.0226800i
$$241$$ 8.57978 0.552672 0.276336 0.961061i $$-0.410880\pi$$
0.276336 + 0.961061i $$0.410880\pi$$
$$242$$ −4.33802 + 7.51368i −0.278859 + 0.482998i
$$243$$ 7.25513 12.5662i 0.465417 0.806125i
$$244$$ −0.915991 + 1.58654i −0.0586403 + 0.101568i
$$245$$ 0 0
$$246$$ 3.00044 0.191301
$$247$$ 3.28826 1.78750i 0.209227 0.113736i
$$248$$ −12.7323 + 22.0530i −0.808501 + 1.40036i
$$249$$ −0.501436 0.868513i −0.0317772 0.0550398i
$$250$$ 5.40066 0.341568
$$251$$ 10.7575 + 18.6326i 0.679010 + 1.17608i 0.975280 + 0.220975i $$0.0709238\pi$$
−0.296270 + 0.955104i $$0.595743\pi$$
$$252$$ 0 0
$$253$$ 2.53687 + 4.39399i 0.159492 + 0.276248i
$$254$$ 0.827704 1.43363i 0.0519348 0.0899537i
$$255$$ 2.20369 3.81690i 0.138000 0.239023i
$$256$$ −15.5134 −0.969585
$$257$$ −4.93792 −0.308019 −0.154010 0.988069i $$-0.549219\pi$$
−0.154010 + 0.988069i $$0.549219\pi$$
$$258$$ 1.10155 1.90794i 0.0685795 0.118783i
$$259$$ 0 0
$$260$$ 0.406471 15.8228i 0.0252083 0.981288i
$$261$$ −2.35256 4.07475i −0.145620 0.252221i
$$262$$ 5.12182 + 8.87125i 0.316427 + 0.548068i
$$263$$ 4.47719 + 7.75473i 0.276076 + 0.478177i 0.970406 0.241480i $$-0.0776327\pi$$
−0.694330 + 0.719656i $$0.744299\pi$$
$$264$$ −0.827695 + 1.43361i −0.0509411 + 0.0882326i
$$265$$ 32.3034 1.98438
$$266$$ 0 0
$$267$$ −4.49890 7.79233i −0.275328 0.476883i
$$268$$ −5.38891 9.33387i −0.329180 0.570157i
$$269$$ 4.82345 0.294091 0.147045 0.989130i $$-0.453024\pi$$
0.147045 + 0.989130i $$0.453024\pi$$
$$270$$ −5.38702 9.33060i −0.327844 0.567842i
$$271$$ 7.42144 0.450820 0.225410 0.974264i $$-0.427628\pi$$
0.225410 + 0.974264i $$0.427628\pi$$
$$272$$ −0.345312 −0.0209376
$$273$$ 0 0
$$274$$ −7.41938 −0.448221
$$275$$ −6.14562 −0.370595
$$276$$ −2.38279 4.12712i −0.143427 0.248423i
$$277$$ 3.81631 0.229300 0.114650 0.993406i $$-0.463425\pi$$
0.114650 + 0.993406i $$0.463425\pi$$
$$278$$ −1.79268 3.10502i −0.107518 0.186226i
$$279$$ 11.7040 + 20.2720i 0.700702 + 1.21365i
$$280$$ 0 0
$$281$$ 8.54978 0.510037 0.255019 0.966936i $$-0.417918\pi$$
0.255019 + 0.966936i $$0.417918\pi$$
$$282$$ 2.02357 3.50493i 0.120502 0.208715i
$$283$$ 7.63217 + 13.2193i 0.453686 + 0.785807i 0.998612 0.0526775i $$-0.0167755\pi$$
−0.544926 + 0.838484i $$0.683442\pi$$
$$284$$ −2.19935 3.80938i −0.130507 0.226045i
$$285$$ 1.18107 + 2.04568i 0.0699607 + 0.121176i
$$286$$ 0.0707683 2.75481i 0.00418461 0.162895i
$$287$$ 0 0
$$288$$ −7.33932 + 12.7121i −0.432474 + 0.749066i
$$289$$ −13.2488 −0.779340
$$290$$ −5.37770 −0.315790
$$291$$ −0.167369 + 0.289892i −0.00981135 + 0.0169938i
$$292$$ −6.95227 + 12.0417i −0.406851 + 0.704687i
$$293$$ −2.96982 5.14388i −0.173499 0.300509i 0.766142 0.642671i $$-0.222174\pi$$
−0.939641 + 0.342163i $$0.888841\pi$$
$$294$$ 0 0
$$295$$ 0.878467 + 1.52155i 0.0511463 + 0.0885881i
$$296$$ −29.5522 −1.71768
$$297$$ 1.65151 + 2.86049i 0.0958301 + 0.165983i
$$298$$ 2.49586 4.32295i 0.144581 0.250422i
$$299$$ 17.3751 + 10.6356i 1.00483 + 0.615074i
$$300$$ 5.77236 0.333267
$$301$$ 0 0
$$302$$ −7.17362 + 12.4251i −0.412796 + 0.714983i
$$303$$ 1.97922 3.42811i 0.113703 0.196940i
$$304$$ 0.0925356 0.160276i 0.00530728 0.00919248i
$$305$$ 4.94262 0.283013
$$306$$ 2.11233 3.65867i 0.120754 0.209152i
$$307$$ −22.2133 −1.26778 −0.633891 0.773422i $$-0.718543\pi$$
−0.633891 + 0.773422i $$0.718543\pi$$
$$308$$ 0 0
$$309$$ 1.36642 2.36672i 0.0777332 0.134638i
$$310$$ 26.7542 1.51954
$$311$$ 4.92130 8.52394i 0.279061 0.483348i −0.692091 0.721811i $$-0.743310\pi$$
0.971152 + 0.238463i $$0.0766435\pi$$
$$312$$ −0.170689 + 6.64445i −0.00966337 + 0.376168i
$$313$$ −10.4563 18.1108i −0.591023 1.02368i −0.994095 0.108513i $$-0.965391\pi$$
0.403072 0.915168i $$-0.367942\pi$$
$$314$$ 0.825166 1.42923i 0.0465668 0.0806561i
$$315$$ 0 0
$$316$$ −7.71205 13.3577i −0.433837 0.751427i
$$317$$ 12.6801 + 21.9626i 0.712188 + 1.23355i 0.964034 + 0.265778i $$0.0856288\pi$$
−0.251847 + 0.967767i $$0.581038\pi$$
$$318$$ −5.28256 −0.296231
$$319$$ 1.64865 0.0923065
$$320$$ 7.77489 + 13.4665i 0.434629 + 0.752800i
$$321$$ −4.66935 8.08755i −0.260618 0.451403i
$$322$$ 0 0
$$323$$ −1.00524 + 1.74113i −0.0559331 + 0.0968790i
$$324$$ 3.35237 + 5.80648i 0.186243 + 0.322582i
$$325$$ −21.6795 + 11.7849i −1.20256 + 0.653711i
$$326$$ −5.06247 + 8.76845i −0.280384 + 0.485640i
$$327$$ 2.77871 0.153663
$$328$$ −7.43183 + 12.8723i −0.410354 + 0.710755i
$$329$$ 0 0
$$330$$ 1.73923 0.0957413
$$331$$ −0.891417 + 1.54398i −0.0489967 + 0.0848648i −0.889484 0.456967i $$-0.848936\pi$$
0.840487 + 0.541832i $$0.182269\pi$$
$$332$$ 1.93467 0.106179
$$333$$ −13.5828 + 23.5261i −0.744332 + 1.28922i
$$334$$ −7.05414 + 12.2181i −0.385985 + 0.668546i
$$335$$ −14.5391 + 25.1824i −0.794354 + 1.37586i
$$336$$ 0 0
$$337$$ 9.56149 0.520848 0.260424 0.965494i $$-0.416138\pi$$
0.260424 + 0.965494i $$0.416138\pi$$
$$338$$ −5.03303 9.85366i −0.273761 0.535969i
$$339$$ 4.55234 7.88488i 0.247249 0.428248i
$$340$$ 4.25120 + 7.36329i 0.230554 + 0.399331i
$$341$$ −8.20207 −0.444167
$$342$$ 1.13211 + 1.96087i 0.0612176 + 0.106032i
$$343$$ 0 0
$$344$$ 5.45689 + 9.45160i 0.294216 + 0.509596i
$$345$$ −6.42867 + 11.1348i −0.346108 + 0.599477i
$$346$$ 4.24991 7.36106i 0.228477 0.395733i
$$347$$ 0.633389 0.0340021 0.0170010 0.999855i $$-0.494588\pi$$
0.0170010 + 0.999855i $$0.494588\pi$$
$$348$$ −1.54852 −0.0830092
$$349$$ 15.2994 26.4994i 0.818960 1.41848i −0.0874885 0.996166i $$-0.527884\pi$$
0.906449 0.422315i $$-0.138783\pi$$
$$350$$ 0 0
$$351$$ 11.3112 + 6.92381i 0.603749 + 0.369565i
$$352$$ −2.57166 4.45425i −0.137070 0.237412i
$$353$$ −0.550173 0.952928i −0.0292828 0.0507192i 0.851013 0.525145i $$-0.175989\pi$$
−0.880295 + 0.474426i $$0.842656\pi$$
$$354$$ −0.143655 0.248819i −0.00763520 0.0132246i
$$355$$ −5.93375 + 10.2776i −0.314931 + 0.545476i
$$356$$ 17.3579 0.919969
$$357$$ 0 0
$$358$$ 3.90521 + 6.76402i 0.206397 + 0.357489i
$$359$$ 4.88693 + 8.46441i 0.257922 + 0.446734i 0.965685 0.259716i $$-0.0836288\pi$$
−0.707763 + 0.706450i $$0.750295\pi$$
$$360$$ 24.5889 1.29595
$$361$$ 8.96124 + 15.5213i 0.471644 + 0.816912i
$$362$$ 5.11091 0.268624
$$363$$ 6.74026 0.353772
$$364$$ 0 0
$$365$$ 37.5139 1.96357
$$366$$ −0.808264 −0.0422487
$$367$$ −5.57363 9.65381i −0.290941 0.503925i 0.683092 0.730333i $$-0.260635\pi$$
−0.974033 + 0.226408i $$0.927302\pi$$
$$368$$ 1.00736 0.0525121
$$369$$ 6.83165 + 11.8328i 0.355641 + 0.615989i
$$370$$ 15.5244 + 26.8891i 0.807076 + 1.39790i
$$371$$ 0 0
$$372$$ 7.70391 0.399429
$$373$$ 15.3651 26.6131i 0.795573 1.37797i −0.126902 0.991915i $$-0.540504\pi$$
0.922475 0.386057i $$-0.126163\pi$$
$$374$$ 0.740150 + 1.28198i 0.0382723 + 0.0662895i
$$375$$ −2.09783 3.63355i −0.108332 0.187636i
$$376$$ 10.0244 + 17.3628i 0.516970 + 0.895419i
$$377$$ 5.81582 3.16147i 0.299530 0.162824i
$$378$$ 0 0
$$379$$ −11.3286 + 19.6217i −0.581912 + 1.00790i 0.413341 + 0.910576i $$0.364362\pi$$
−0.995253 + 0.0973246i $$0.968972\pi$$
$$380$$ −4.55689 −0.233763
$$381$$ −1.28606 −0.0658866
$$382$$ 0.560093 0.970109i 0.0286568 0.0496351i
$$383$$ −0.294631 + 0.510317i −0.0150550 + 0.0260760i −0.873455 0.486905i $$-0.838126\pi$$
0.858400 + 0.512981i $$0.171459\pi$$
$$384$$ 2.51581 + 4.35751i 0.128384 + 0.222368i
$$385$$ 0 0
$$386$$ −6.99004 12.1071i −0.355783 0.616235i
$$387$$ 10.0324 0.509975
$$388$$ −0.322877 0.559239i −0.0163916 0.0283910i
$$389$$ −2.84973 + 4.93587i −0.144487 + 0.250259i −0.929181 0.369624i $$-0.879486\pi$$
0.784695 + 0.619883i $$0.212820\pi$$
$$390$$ 6.13536 3.33517i 0.310676 0.168883i
$$391$$ −10.9432 −0.553422
$$392$$ 0 0
$$393$$ 3.97904 6.89191i 0.200716 0.347651i
$$394$$ −10.8891 + 18.8605i −0.548584 + 0.950176i
$$395$$ −20.8068 + 36.0384i −1.04690 + 1.81329i
$$396$$ −2.93556 −0.147518
$$397$$ −12.7641 + 22.1082i −0.640614 + 1.10958i 0.344682 + 0.938720i $$0.387987\pi$$
−0.985296 + 0.170857i $$0.945346\pi$$
$$398$$ −21.6005 −1.08274
$$399$$ 0 0
$$400$$ −0.610086 + 1.05670i −0.0305043 + 0.0528350i
$$401$$ 25.5011 1.27347 0.636733 0.771085i $$-0.280286\pi$$
0.636733 + 0.771085i $$0.280286\pi$$
$$402$$ 2.37757 4.11807i 0.118582 0.205391i
$$403$$ −28.9339 + 15.7284i −1.44130 + 0.783489i
$$404$$ 3.81817 + 6.61327i 0.189961 + 0.329022i
$$405$$ 9.04457 15.6657i 0.449428 0.778433i
$$406$$ 0 0
$$407$$ −4.75934 8.24341i −0.235912 0.408611i
$$408$$ −1.78520 3.09206i −0.0883807 0.153080i
$$409$$ −0.146988 −0.00726807 −0.00363403 0.999993i $$-0.501157\pi$$
−0.00363403 + 0.999993i $$0.501157\pi$$
$$410$$ 15.6164 0.771241
$$411$$ 2.88199 + 4.99175i 0.142158 + 0.246225i
$$412$$ 2.63601 + 4.56570i 0.129867 + 0.224936i
$$413$$ 0 0
$$414$$ −6.16217 + 10.6732i −0.302854 + 0.524559i
$$415$$ −2.60983 4.52036i −0.128112 0.221896i
$$416$$ −17.6134 10.7815i −0.863568 0.528606i
$$417$$ −1.39270 + 2.41223i −0.0682008 + 0.118127i
$$418$$ −0.793372 −0.0388051
$$419$$ 6.84795 11.8610i 0.334544 0.579447i −0.648853 0.760914i $$-0.724751\pi$$
0.983397 + 0.181466i $$0.0580844\pi$$
$$420$$ 0 0
$$421$$ 3.44169 0.167738 0.0838688 0.996477i $$-0.473272\pi$$
0.0838688 + 0.996477i $$0.473272\pi$$
$$422$$ −2.42421 + 4.19885i −0.118009 + 0.204397i
$$423$$ 18.4297 0.896084
$$424$$ 13.0844 22.6629i 0.635437 1.10061i
$$425$$ 6.62754 11.4792i 0.321483 0.556825i
$$426$$ 0.970345 1.68069i 0.0470134 0.0814295i
$$427$$ 0 0
$$428$$ 18.0156 0.870816
$$429$$ −1.88092 + 1.02247i −0.0908118 + 0.0493652i
$$430$$ 5.73325 9.93028i 0.276482 0.478881i
$$431$$ −11.1455 19.3046i −0.536861 0.929870i −0.999071 0.0430997i $$-0.986277\pi$$
0.462210 0.886771i $$-0.347057\pi$$
$$432$$ 0.655791 0.0315518
$$433$$ −12.9481 22.4268i −0.622247 1.07776i −0.989066 0.147472i $$-0.952886\pi$$
0.366819 0.930292i $$-0.380447\pi$$
$$434$$ 0 0
$$435$$ 2.08892 + 3.61811i 0.100156 + 0.173475i
$$436$$ −2.68024 + 4.64232i −0.128360 + 0.222327i
$$437$$ 2.93253 5.07929i 0.140282 0.242975i
$$438$$ −6.13464 −0.293124
$$439$$ 27.9838 1.33560 0.667798 0.744343i $$-0.267237\pi$$
0.667798 + 0.744343i $$0.267237\pi$$
$$440$$ −4.30792 + 7.46153i −0.205372 + 0.355715i
$$441$$ 0 0
$$442$$ 5.06932 + 3.10302i 0.241123 + 0.147596i
$$443$$ −16.6044 28.7597i −0.788900 1.36642i −0.926641 0.375947i $$-0.877317\pi$$
0.137741 0.990468i $$-0.456016\pi$$
$$444$$ 4.47028 + 7.74275i 0.212150 + 0.367454i
$$445$$ −23.4155 40.5568i −1.11000 1.92258i
$$446$$ −1.00353 + 1.73816i −0.0475185 + 0.0823044i
$$447$$ −3.87796 −0.183421
$$448$$ 0 0
$$449$$ −9.84320 17.0489i −0.464529 0.804589i 0.534651 0.845073i $$-0.320443\pi$$
−0.999180 + 0.0404845i $$0.987110\pi$$
$$450$$ −7.46399 12.9280i −0.351856 0.609433i
$$451$$ −4.78755 −0.225437
$$452$$ 8.78205 + 15.2110i 0.413073 + 0.715464i
$$453$$ 11.1461 0.523690
$$454$$ 22.3783 1.05027
$$455$$ 0 0
$$456$$ 1.91357 0.0896111
$$457$$ −0.746942 −0.0349405 −0.0174702 0.999847i $$-0.505561\pi$$
−0.0174702 + 0.999847i $$0.505561\pi$$
$$458$$ −0.0291746 0.0505320i −0.00136324 0.00236120i
$$459$$ −7.12405 −0.332522
$$460$$ −12.4017 21.4805i −0.578235 1.00153i
$$461$$ −16.5855 28.7269i −0.772464 1.33795i −0.936209 0.351445i $$-0.885691\pi$$
0.163744 0.986503i $$-0.447643\pi$$
$$462$$ 0 0
$$463$$ −30.7521 −1.42917 −0.714586 0.699548i $$-0.753385\pi$$
−0.714586 + 0.699548i $$0.753385\pi$$
$$464$$ 0.163664 0.283475i 0.00759792 0.0131600i
$$465$$ −10.3924 18.0002i −0.481937 0.834740i
$$466$$ 6.24313 + 10.8134i 0.289207 + 0.500922i
$$467$$ −14.8033 25.6400i −0.685013 1.18648i −0.973433 0.228973i $$-0.926463\pi$$
0.288420 0.957504i $$-0.406870\pi$$
$$468$$ −10.3556 + 5.62928i −0.478687 + 0.260214i
$$469$$ 0 0
$$470$$ 10.5321 18.2422i 0.485810 0.841448i
$$471$$ −1.28211 −0.0590766
$$472$$ 1.42329 0.0655122
$$473$$ −1.75765 + 3.04434i −0.0808168 + 0.139979i
$$474$$ 3.40253 5.89335i 0.156283 0.270691i
$$475$$ 3.55205 + 6.15234i 0.162979 + 0.282289i
$$476$$ 0 0
$$477$$ −12.0278 20.8327i −0.550714 0.953864i
$$478$$ −2.85496 −0.130583
$$479$$ 7.04527 + 12.2028i 0.321907 + 0.557559i 0.980881 0.194606i $$-0.0623429\pi$$
−0.658975 + 0.752165i $$0.729010\pi$$
$$480$$ 6.51684 11.2875i 0.297452 0.515201i
$$481$$ −32.5969 19.9531i −1.48629 0.909785i
$$482$$ −7.30247 −0.332618
$$483$$ 0 0
$$484$$ −6.50142 + 11.2608i −0.295519 + 0.511854i
$$485$$ −0.871108 + 1.50880i −0.0395550 + 0.0685112i
$$486$$ −6.17502 + 10.6955i −0.280105 + 0.485156i
$$487$$ −16.7955 −0.761075 −0.380537 0.924766i $$-0.624261\pi$$
−0.380537 + 0.924766i $$0.624261\pi$$
$$488$$ 2.00200 3.46757i 0.0906263 0.156969i
$$489$$ 7.86587 0.355707
$$490$$ 0 0
$$491$$ −10.8345 + 18.7659i −0.488954 + 0.846893i −0.999919 0.0127081i $$-0.995955\pi$$
0.510965 + 0.859601i $$0.329288\pi$$
$$492$$ 4.49677 0.202730
$$493$$ −1.77793 + 3.07947i −0.0800740 + 0.138692i
$$494$$ −2.79873 + 1.52138i −0.125921 + 0.0684503i
$$495$$ 3.96001 + 6.85895i 0.177989 + 0.308287i
$$496$$ −0.814234 + 1.41029i −0.0365602 + 0.0633241i
$$497$$ 0 0
$$498$$ 0.426785 + 0.739213i 0.0191247 + 0.0331249i
$$499$$ 11.6524 + 20.1825i 0.521633 + 0.903495i 0.999683 + 0.0251622i $$0.00801023\pi$$
−0.478051 + 0.878332i $$0.658656\pi$$
$$500$$ 8.09399 0.361974
$$501$$ 10.9605 0.489677
$$502$$ −9.15601 15.8587i −0.408653 0.707807i
$$503$$ −21.9415 38.0037i −0.978322 1.69450i −0.668506 0.743707i $$-0.733066\pi$$
−0.309816 0.950796i $$-0.600268\pi$$
$$504$$ 0 0
$$505$$ 10.3013 17.8423i 0.458401 0.793974i
$$506$$ −2.15919 3.73983i −0.0959879 0.166256i
$$507$$ −4.67450 + 7.21378i −0.207602 + 0.320375i
$$508$$ 1.24048 2.14858i 0.0550376 0.0953279i
$$509$$ −19.9242 −0.883125 −0.441563 0.897230i $$-0.645576\pi$$
−0.441563 + 0.897230i $$0.645576\pi$$
$$510$$ −1.87561 + 3.24866i −0.0830536 + 0.143853i
$$511$$ 0 0
$$512$$ −2.01529 −0.0890641
$$513$$ 1.90908 3.30662i 0.0842879 0.145991i
$$514$$ 4.20279 0.185377
$$515$$ 7.11185 12.3181i 0.313386 0.542800i
$$516$$ 1.65090 2.85944i 0.0726767 0.125880i
$$517$$ −3.22884 + 5.59252i −0.142004 + 0.245959i
$$518$$ 0 0
$$519$$ −6.60335 −0.289855
$$520$$ −0.888388 + 34.5825i −0.0389584 + 1.51654i
$$521$$ −8.26204 + 14.3103i −0.361967 + 0.626944i −0.988284 0.152623i $$-0.951228\pi$$
0.626318 + 0.779568i $$0.284561\pi$$
$$522$$ 2.00232 + 3.46812i 0.0876392 + 0.151796i
$$523$$ 11.9962 0.524556 0.262278 0.964992i $$-0.415526\pi$$
0.262278 + 0.964992i $$0.415526\pi$$
$$524$$ 7.67609 + 13.2954i 0.335332 + 0.580812i
$$525$$ 0 0
$$526$$ −3.81065 6.60024i −0.166152 0.287784i
$$527$$ 8.84526 15.3204i 0.385305 0.667369i
$$528$$ −0.0529314 + 0.0916798i −0.00230354 + 0.00398985i
$$529$$ 8.92395 0.387998
$$530$$ −27.4942 −1.19427
$$531$$ 0.654173 1.13306i 0.0283887 0.0491706i
$$532$$ 0 0
$$533$$ −16.8887 + 9.18068i −0.731531 + 0.397660i
$$534$$ 3.82913 + 6.63225i 0.165703 + 0.287005i
$$535$$ −24.3026 42.0934i −1.05070 1.81986i
$$536$$ 11.7781 + 20.4002i 0.508735 + 0.881155i
$$537$$ 3.03388 5.25484i 0.130922 0.226763i
$$538$$ −4.10536 −0.176995
$$539$$ 0 0
$$540$$ −8.07356 13.9838i −0.347431 0.601767i
$$541$$ −18.1158 31.3775i −0.778860 1.34903i −0.932599 0.360914i $$-0.882465\pi$$
0.153739 0.988112i $$-0.450869\pi$$
$$542$$ −6.31658 −0.271320
$$543$$ −1.98529 3.43862i −0.0851968 0.147565i
$$544$$ 11.0933 0.475621
$$545$$ 14.4624 0.619500
$$546$$ 0 0
$$547$$ −7.34857 −0.314202 −0.157101 0.987583i $$-0.550215\pi$$
−0.157101 + 0.987583i $$0.550215\pi$$
$$548$$ −11.1195 −0.475000
$$549$$ −1.84032 3.18753i −0.0785430 0.136040i
$$550$$ 5.23069 0.223037
$$551$$ −0.952888 1.65045i −0.0405944 0.0703115i
$$552$$ 5.20786 + 9.02027i 0.221661 + 0.383928i
$$553$$ 0 0
$$554$$ −3.24816 −0.138001
$$555$$ 12.0606 20.8896i 0.511945 0.886715i
$$556$$ −2.68670 4.65350i −0.113941 0.197352i
$$557$$ −5.41399 9.37731i −0.229398 0.397329i 0.728232 0.685331i $$-0.240342\pi$$
−0.957630 + 0.288002i $$0.907009\pi$$
$$558$$ −9.96160 17.2540i −0.421708 0.730420i
$$559$$ −0.362466 + 14.1098i −0.0153307 + 0.596781i
$$560$$ 0 0
$$561$$ 0.575009 0.995945i 0.0242769 0.0420488i
$$562$$ −7.27694 −0.306959
$$563$$ 13.8599 0.584127 0.292064 0.956399i $$-0.405658\pi$$
0.292064 + 0.956399i $$0.405658\pi$$
$$564$$ 3.03274 5.25285i 0.127701 0.221185i
$$565$$ 23.6936 41.0386i 0.996798 1.72651i
$$566$$ −6.49594 11.2513i −0.273045 0.472927i
$$567$$ 0 0
$$568$$ 4.80692 + 8.32583i 0.201694 + 0.349344i
$$569$$ 27.4120 1.14917 0.574586 0.818444i $$-0.305163\pi$$
0.574586 + 0.818444i $$0.305163\pi$$
$$570$$ −1.00524 1.74113i −0.0421049 0.0729279i
$$571$$ 0.103879 0.179923i 0.00434719 0.00752956i −0.863844 0.503760i $$-0.831950\pi$$
0.868191 + 0.496230i $$0.165283\pi$$
$$572$$ 0.106061 4.12865i 0.00443462 0.172627i
$$573$$ −0.870251 −0.0363552
$$574$$ 0 0
$$575$$ −19.3341 + 33.4876i −0.806288 + 1.39653i
$$576$$ 5.78976 10.0282i 0.241240 0.417840i
$$577$$ −1.66328 + 2.88089i −0.0692434 + 0.119933i −0.898568 0.438833i $$-0.855392\pi$$
0.829325 + 0.558766i $$0.188725\pi$$
$$578$$ 11.2764 0.469035
$$579$$ −5.43043 + 9.40577i −0.225681 + 0.390891i
$$580$$ −8.05959 −0.334656
$$581$$ 0 0
$$582$$ 0.142452 0.246734i 0.00590483 0.0102275i
$$583$$ 8.42893 0.349091
$$584$$ 15.1950 26.3185i 0.628772 1.08907i
$$585$$ 27.1223 + 16.6020i 1.12137 + 0.686410i
$$586$$ 2.52769 + 4.37809i 0.104418 + 0.180857i
$$587$$ −7.54051 + 13.0606i −0.311230 + 0.539067i −0.978629 0.205634i $$-0.934074\pi$$
0.667399 + 0.744701i $$0.267408\pi$$
$$588$$ 0 0
$$589$$ 4.74064 + 8.21104i 0.195335 + 0.338330i
$$590$$ −0.747686 1.29503i −0.0307817 0.0533155i
$$591$$ 16.9191 0.695957
$$592$$ −1.88987 −0.0776732
$$593$$ 12.9245 + 22.3859i 0.530747 + 0.919281i 0.999356 + 0.0358751i $$0.0114218\pi$$
−0.468609 + 0.883405i $$0.655245\pi$$
$$594$$ −1.40564 2.43464i −0.0576740 0.0998944i
$$595$$ 0 0
$$596$$ 3.74055 6.47882i 0.153219 0.265383i
$$597$$ 8.39052 + 14.5328i 0.343401 + 0.594788i
$$598$$ −14.7884 9.05225i −0.604743 0.370174i
$$599$$ 17.7734 30.7845i 0.726203 1.25782i −0.232274 0.972650i $$-0.574617\pi$$
0.958477 0.285170i $$-0.0920501\pi$$
$$600$$ −12.6161 −0.515052
$$601$$ −13.6474 + 23.6379i −0.556688 + 0.964212i 0.441082 + 0.897467i $$0.354595\pi$$
−0.997770 + 0.0667449i $$0.978739\pi$$
$$602$$ 0 0
$$603$$ 21.6538 0.881810
$$604$$ −10.7511 + 18.6215i −0.437458 + 0.757699i
$$605$$ 35.0811 1.42625
$$606$$ −1.68456 + 2.91775i −0.0684308 + 0.118526i
$$607$$ −19.4629 + 33.7108i −0.789976 + 1.36828i 0.136006 + 0.990708i $$0.456574\pi$$
−0.925981 + 0.377570i $$0.876760\pi$$
$$608$$ −2.97274 + 5.14894i −0.120561 + 0.208817i
$$609$$ 0 0
$$610$$ −4.20679 −0.170328
$$611$$ −0.665859 + 25.9200i −0.0269378 + 1.04861i
$$612$$ 3.16576 5.48326i 0.127968 0.221648i
$$613$$ −0.443322 0.767857i −0.0179056 0.0310135i 0.856934 0.515427i $$-0.172367\pi$$
−0.874839 + 0.484413i $$0.839033\pi$$
$$614$$ 18.9063 0.762997
$$615$$ −6.06606 10.5067i −0.244607 0.423672i
$$616$$ 0 0
$$617$$ −17.3944 30.1280i −0.700272 1.21291i −0.968371 0.249515i $$-0.919729\pi$$
0.268099 0.963391i $$-0.413605\pi$$
$$618$$ −1.16300 + 2.01437i −0.0467827 + 0.0810300i
$$619$$ 1.02781 1.78021i 0.0413111 0.0715529i −0.844631 0.535350i $$-0.820180\pi$$
0.885942 + 0.463797i $$0.153513\pi$$
$$620$$ 40.0967 1.61032
$$621$$ 20.7825 0.833975
$$622$$ −4.18864 + 7.25494i −0.167949 + 0.290897i
$$623$$ 0 0
$$624$$ −0.0109156 + 0.424915i −0.000436975 + 0.0170102i
$$625$$ 6.19081 + 10.7228i 0.247632 + 0.428912i
$$626$$ 8.89959 + 15.4145i 0.355699 + 0.616089i
$$627$$ 0.308178 + 0.533780i 0.0123074 + 0.0213171i
$$628$$ 1.23668 2.14199i 0.0493489 0.0854749i
$$629$$ 20.5302 0.818593
$$630$$ 0 0
$$631$$ 22.6169 + 39.1736i 0.900363 + 1.55947i 0.827023 + 0.562168i $$0.190033\pi$$
0.0733401 + 0.997307i $$0.476634\pi$$
$$632$$ 16.8555 + 29.1946i 0.670477 + 1.16130i
$$633$$ 3.76665 0.149711
$$634$$ −10.7924 18.6930i −0.428621 0.742393i
$$635$$ −6.69355 −0.265625
$$636$$ −7.91700 −0.313929
$$637$$ 0 0
$$638$$ −1.40321 −0.0555534
$$639$$ 8.83744 0.349604
$$640$$ 13.0941 + 22.6796i 0.517588 + 0.896489i
$$641$$ −19.0619 −0.752902 −0.376451 0.926437i $$-0.622856\pi$$
−0.376451 + 0.926437i $$0.622856\pi$$
$$642$$ 3.97420 + 6.88352i 0.156849 + 0.271671i
$$643$$ −5.26755 9.12367i −0.207732 0.359802i 0.743268 0.668994i $$-0.233275\pi$$
−0.951000 + 0.309192i $$0.899942\pi$$
$$644$$ 0 0
$$645$$ −8.90811 −0.350756
$$646$$ 0.855587 1.48192i 0.0336626 0.0583053i
$$647$$ −12.0804 20.9239i −0.474930 0.822603i 0.524658 0.851313i $$-0.324193\pi$$
−0.999588 + 0.0287105i $$0.990860\pi$$
$$648$$ −7.32699 12.6907i −0.287831 0.498538i
$$649$$ 0.229219 + 0.397019i 0.00899762 + 0.0155843i
$$650$$ 18.4520 10.0305i 0.723745 0.393427i
$$651$$ 0 0
$$652$$ −7.58714 + 13.1413i −0.297135 + 0.514654i
$$653$$ −33.6890 −1.31835 −0.659176 0.751988i $$-0.729095\pi$$
−0.659176 + 0.751988i $$0.729095\pi$$
$$654$$ −2.36503 −0.0924799
$$655$$ 20.7098 35.8704i 0.809199 1.40157i
$$656$$ −0.475268 + 0.823189i −0.0185561 + 0.0321401i
$$657$$ −13.9678 24.1930i −0.544937 0.943859i
$$658$$ 0 0
$$659$$ 2.10030 + 3.63782i 0.0818159 + 0.141709i 0.904030 0.427469i $$-0.140595\pi$$
−0.822214 + 0.569178i $$0.807261\pi$$
$$660$$ 2.60659 0.101461
$$661$$ 8.83631 + 15.3049i 0.343693 + 0.595293i 0.985115 0.171894i $$-0.0549888\pi$$
−0.641423 + 0.767188i $$0.721655\pi$$
$$662$$ 0.758708 1.31412i 0.0294880 0.0510748i
$$663$$ 0.118580 4.61597i 0.00460525 0.179270i
$$664$$ −4.22844 −0.164095
$$665$$ 0 0
$$666$$ 11.5607 20.0236i 0.447966 0.775900i
$$667$$ 5.18664 8.98353i 0.200828 0.347844i
$$668$$ −10.5721 + 18.3114i −0.409046 + 0.708488i
$$669$$ 1.55925 0.0602839
$$670$$ 12.3746 21.4334i 0.478071 0.828044i
$$671$$ 1.28968 0.0497875
$$672$$ 0 0
$$673$$ 10.3052 17.8491i 0.397235 0.688031i −0.596149 0.802874i $$-0.703303\pi$$
0.993384 + 0.114843i $$0.0366366\pi$$
$$674$$ −8.13803 −0.313465
$$675$$ −12.5865 + 21.8005i −0.484456 + 0.839102i
$$676$$ −7.54302 14.7677i −0.290116 0.567990i
$$677$$ −10.6537 18.4527i −0.409455 0.709196i 0.585374 0.810763i $$-0.300948\pi$$
−0.994829 + 0.101567i $$0.967614\pi$$
$$678$$ −3.87461 + 6.71102i −0.148804 + 0.257735i
$$679$$ 0 0
$$680$$ −9.29147 16.0933i −0.356312 0.617150i
$$681$$ −8.69264 15.0561i −0.333103 0.576951i
$$682$$ 6.98099 0.267316
$$683$$ −6.69757 −0.256275 −0.128138 0.991756i $$-0.540900\pi$$
−0.128138 + 0.991756i $$0.540900\pi$$
$$684$$ 1.69670 + 2.93877i 0.0648750 + 0.112367i
$$685$$ 14.9999 + 25.9806i 0.573118 + 0.992670i
$$686$$ 0 0
$$687$$ −0.0226652 + 0.0392573i −0.000864732 + 0.00149776i
$$688$$ 0.348970 + 0.604433i 0.0133043 + 0.0230438i
$$689$$ 29.7342 16.1635i 1.13278 0.615779i
$$690$$ 5.47161 9.47710i 0.208301 0.360787i
$$691$$ 24.9263 0.948242 0.474121 0.880460i $$-0.342766\pi$$
0.474121 + 0.880460i $$0.342766\pi$$
$$692$$ 6.36936 11.0321i 0.242127 0.419376i
$$693$$ 0 0
$$694$$ −0.539093 −0.0204637
$$695$$ −7.24861 + 12.5550i −0.274955 + 0.476237i
$$696$$ 3.38445 0.128287
$$697$$ 5.16298 8.94254i 0.195562 0.338723i
$$698$$ −13.0217 + 22.5543i −0.492880 + 0.853694i
$$699$$ 4.85017 8.40073i 0.183450 0.317745i
$$700$$ 0 0
$$701$$ −4.94583 −0.186801 −0.0934007 0.995629i $$-0.529774\pi$$
−0.0934007 + 0.995629i $$0.529774\pi$$
$$702$$ −9.62728 5.89303i −0.363358 0.222418i
$$703$$ −5.50162 + 9.52908i −0.207497 + 0.359396i
$$704$$ 2.02870 + 3.51382i 0.0764597 + 0.132432i
$$705$$ −16.3644 −0.616319
$$706$$ 0.468266 + 0.811061i 0.0176234 + 0.0305247i
$$707$$ 0 0
$$708$$ −0.215297 0.372905i −0.00809136 0.0140146i
$$709$$ 2.32249 4.02267i 0.0872228 0.151074i −0.819113 0.573632i $$-0.805534\pi$$
0.906336 + 0.422557i $$0.138867\pi$$
$$710$$ 5.05037 8.74749i 0.189537 0.328288i
$$711$$ 30.9886 1.16216
$$712$$ −37.9377 −1.42178
$$713$$ −25.8037 + 44.6933i −0.966356 + 1.67378i
$$714$$ 0 0
$$715$$ −9.78966 + 5.32165i −0.366113 + 0.199018i
$$716$$ 5.85275 + 10.1373i 0.218728 + 0.378847i
$$717$$ 1.10898 + 1.92082i 0.0414157 + 0.0717342i
$$718$$ −4.15939 7.20427i −0.155227 0.268861i
$$719$$ 15.8706 27.4887i 0.591875 1.02516i −0.402105 0.915594i $$-0.631721\pi$$
0.993980 0.109564i $$-0.0349453\pi$$
$$720$$ 1.57247 0.0586025
$$721$$ 0 0
$$722$$ −7.62714 13.2106i −0.283853 0.491647i
$$723$$ 2.83658 + 4.91309i 0.105493 + 0.182720i
$$724$$ 7.65975 0.284672
$$725$$ 6.28237 + 10.8814i 0.233322 + 0.404125i
$$726$$ −5.73681 −0.212913
$$727$$ −47.8755 −1.77560 −0.887801 0.460227i $$-0.847768\pi$$
−0.887801 + 0.460227i $$0.847768\pi$$
$$728$$ 0 0
$$729$$ −6.17412 −0.228671
$$730$$ −31.9290 −1.18175
$$731$$ −3.79096 6.56613i −0.140214 0.242857i
$$732$$ −1.21135 −0.0447728
$$733$$ −3.80104 6.58359i −0.140395 0.243171i 0.787251 0.616633i $$-0.211504\pi$$
−0.927645 + 0.373463i $$0.878170\pi$$
$$734$$ 4.74386 + 8.21660i 0.175099 + 0.303280i
$$735$$ 0 0
$$736$$ −32.3618 −1.19287
$$737$$ −3.79368 + 6.57086i −0.139742 + 0.242041i
$$738$$ −5.81459 10.0712i −0.214038 0.370725i
$$739$$ 16.7118 + 28.9457i 0.614754 + 1.06479i 0.990428 + 0.138033i $$0.0440781\pi$$
−0.375673 + 0.926752i $$0.622589\pi$$
$$740$$ 23.2665 + 40.2988i 0.855294 + 1.48141i
$$741$$ 2.11072 + 1.29201i 0.0775394 + 0.0474632i
$$742$$ 0 0
$$743$$ 1.46912 2.54458i 0.0538966 0.0933517i −0.837818 0.545949i $$-0.816169\pi$$
0.891715 + 0.452597i $$0.149503\pi$$
$$744$$ −16.8378 −0.617302
$$745$$ −20.1837 −0.739474
$$746$$ −13.0776 + 22.6511i −0.478805 + 0.829314i
$$747$$ −1.94348 + 3.36620i −0.0711081 + 0.123163i
$$748$$ 1.10927 + 1.92131i 0.0405588 + 0.0702499i
$$749$$ 0 0
$$750$$ 1.78552 + 3.09261i 0.0651980 + 0.112926i
$$751$$ 1.19678 0.0436711 0.0218355 0.999762i $$-0.493049\pi$$
0.0218355 + 0.999762i $$0.493049\pi$$
$$752$$ 0.641065 + 1.11036i 0.0233773 + 0.0404906i
$$753$$ −7.11313 + 12.3203i −0.259217 + 0.448977i
$$754$$ −4.94999 + 2.69081i −0.180268 + 0.0979936i
$$755$$ 58.0123 2.11128
$$756$$ 0 0
$$757$$ −5.77321 + 9.99950i −0.209831 + 0.363438i −0.951661 0.307150i $$-0.900625\pi$$
0.741830 + 0.670588i $$0.233958\pi$$
$$758$$ 9.64207 16.7006i 0.350216 0.606592i
$$759$$ −1.67744 + 2.90541i −0.0608871 + 0.105460i
$$760$$ 9.95959 0.361272
$$761$$ 17.3249 30.0075i 0.628026 1.08777i −0.359921 0.932983i $$-0.617197\pi$$
0.987947 0.154790i $$-0.0494702\pi$$
$$762$$ 1.09459 0.0396530
$$763$$ 0 0
$$764$$ 0.839413 1.45391i 0.0303689 0.0526005i
$$765$$ −17.0822 −0.617608
$$766$$ 0.250768 0.434344i 0.00906063 0.0156935i
$$767$$ 1.56993 + 0.960982i 0.0566869 + 0.0346990i
$$768$$ −5.12890 8.88351i −0.185073 0.320556i
$$769$$ −3.27437 + 5.67138i −0.118077 + 0.204515i −0.919006 0.394245i $$-0.871006\pi$$
0.800929 + 0.598760i $$0.204340\pi$$
$$770$$ 0 0
$$771$$ −1.63253 2.82763i −0.0587943 0.101835i
$$772$$ −10.4760 18.1450i −0.377039 0.653051i
$$773$$ −33.9275 −1.22029 −0.610143 0.792291i $$-0.708888\pi$$
−0.610143 + 0.792291i $$0.708888\pi$$
$$774$$ −8.53882 −0.306922
$$775$$ −31.2550 54.1352i −1.12271 1.94459i
$$776$$ 0.705683 + 1.22228i 0.0253325 + 0.0438772i
$$777$$ 0 0
$$778$$ 2.42547 4.20104i 0.0869575 0.150615i
$$779$$ 2.76711 + 4.79278i 0.0991422 + 0.171719i
$$780$$ 9.19508 4.99844i 0.329237 0.178973i
$$781$$ −1.54830 + 2.68173i −0.0554024 + 0.0959598i
$$782$$ 9.31405 0.333070
$$783$$ 3.37651 5.84829