# Properties

 Label 637.2.k.i.569.2 Level $637$ Weight $2$ Character 637.569 Analytic conductor $5.086$ Analytic rank $0$ Dimension $12$ CM no Inner twists $2$

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## Newspace parameters

 Level: $$N$$ $$=$$ $$637 = 7^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 637.k (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.08647060876$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$6$$ over $$\Q(\zeta_{6})$$ Coefficient field: 12.0.2346760387617129.1 Defining polynomial: $$x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 91) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 569.2 Root $$0.874681 + 1.11128i$$ of defining polynomial Character $$\chi$$ $$=$$ 637.569 Dual form 637.2.k.i.459.5

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.34523i q^{2} +(1.02505 - 1.77544i) q^{3} +0.190366 q^{4} +(-3.08979 - 1.78389i) q^{5} +(-2.38837 - 1.37893i) q^{6} -2.94654i q^{8} +(-0.601462 - 1.04176i) q^{9} +O(q^{10})$$ $$q-1.34523i q^{2} +(1.02505 - 1.77544i) q^{3} +0.190366 q^{4} +(-3.08979 - 1.78389i) q^{5} +(-2.38837 - 1.37893i) q^{6} -2.94654i q^{8} +(-0.601462 - 1.04176i) q^{9} +(-2.39973 + 4.15646i) q^{10} +(-1.10736 - 0.639336i) q^{11} +(0.195135 - 0.337984i) q^{12} +(-3.57420 + 0.474474i) q^{13} +(-6.33438 + 3.65716i) q^{15} -3.58303 q^{16} +7.73920 q^{17} +(-1.40141 + 0.809103i) q^{18} +(-0.817422 + 0.471939i) q^{19} +(-0.588191 - 0.339592i) q^{20} +(-0.860052 + 1.48965i) q^{22} -1.64727 q^{23} +(-5.23141 - 3.02035i) q^{24} +(3.86451 + 6.69354i) q^{25} +(0.638275 + 4.80810i) q^{26} +3.68419 q^{27} +(-2.02242 - 3.50293i) q^{29} +(4.91970 + 8.52117i) q^{30} +(-4.46193 + 2.57610i) q^{31} -1.07309i q^{32} +(-2.27021 + 1.31071i) q^{33} -10.4110i q^{34} +(-0.114498 - 0.198317i) q^{36} -1.05608i q^{37} +(0.634865 + 1.09962i) q^{38} +(-2.82133 + 6.83214i) q^{39} +(-5.25629 + 9.10417i) q^{40} +(3.63629 - 2.09941i) q^{41} +(1.91532 - 3.31744i) q^{43} +(-0.210805 - 0.121708i) q^{44} +4.29176i q^{45} +2.21596i q^{46} +(-0.774415 - 0.447109i) q^{47} +(-3.67279 + 6.36146i) q^{48} +(9.00432 - 5.19865i) q^{50} +(7.93308 - 13.7405i) q^{51} +(-0.680407 + 0.0903239i) q^{52} +(0.0399961 + 0.0692754i) q^{53} -4.95607i q^{54} +(2.28101 + 3.95082i) q^{55} +1.93505i q^{57} +(-4.71224 + 2.72061i) q^{58} -11.1847i q^{59} +(-1.20585 + 0.696200i) q^{60} +(-3.81196 - 6.60251i) q^{61} +(3.46543 + 6.00231i) q^{62} -8.60961 q^{64} +(11.8899 + 4.90994i) q^{65} +(1.76319 + 3.05394i) q^{66} +(5.47418 + 3.16052i) q^{67} +1.47328 q^{68} +(-1.68854 + 2.92464i) q^{69} +(9.89346 + 5.71199i) q^{71} +(-3.06959 + 1.77223i) q^{72} +(-0.658617 + 0.380253i) q^{73} -1.42067 q^{74} +15.8453 q^{75} +(-0.155610 + 0.0898413i) q^{76} +(9.19077 + 3.79533i) q^{78} +(1.42765 - 2.47277i) q^{79} +(11.0708 + 6.39172i) q^{80} +(5.58087 - 9.66636i) q^{81} +(-2.82418 - 4.89163i) q^{82} -2.32483i q^{83} +(-23.9125 - 13.8059i) q^{85} +(-4.46270 - 2.57654i) q^{86} -8.29233 q^{87} +(-1.88383 + 3.26289i) q^{88} +7.57626i q^{89} +5.77339 q^{90} -0.313586 q^{92} +10.5625i q^{93} +(-0.601462 + 1.04176i) q^{94} +3.36755 q^{95} +(-1.90522 - 1.09998i) q^{96} +(0.414443 + 0.239279i) q^{97} +1.53815i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12q + 3q^{3} - 8q^{4} + 3q^{5} + 9q^{6} - q^{9} + O(q^{10})$$ $$12q + 3q^{3} - 8q^{4} + 3q^{5} + 9q^{6} - q^{9} - 12q^{10} + 12q^{11} + q^{12} + 2q^{13} - 12q^{15} + 16q^{16} + 34q^{17} + 3q^{18} - 9q^{19} + 3q^{20} - 15q^{22} - 6q^{23} - 15q^{24} - 5q^{25} + 6q^{26} - 12q^{27} - q^{29} + 11q^{30} - 18q^{31} + 6q^{33} - 13q^{36} - 19q^{38} - 4q^{39} + q^{40} + 6q^{41} + 11q^{43} - 33q^{44} + 15q^{47} - 19q^{48} + 18q^{50} + 4q^{51} + 7q^{52} - 8q^{53} + 15q^{55} - 24q^{58} - 30q^{60} - 5q^{61} - 41q^{62} + 2q^{64} + 21q^{65} + 34q^{66} + 15q^{67} - 22q^{68} - 7q^{69} + 30q^{71} + 57q^{72} - 42q^{73} + 66q^{74} + 2q^{75} + 45q^{76} + 44q^{78} - 35q^{79} + 63q^{80} + 14q^{81} - 5q^{82} - 21q^{85} - 57q^{86} + 20q^{87} - 14q^{88} - 66q^{92} - q^{94} - 4q^{95} - 21q^{96} + 3q^{97} + O(q^{100})$$

## Character values

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

 $$n$$ $$197$$ $$248$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.34523i 0.951219i −0.879657 0.475609i $$-0.842228\pi$$
0.879657 0.475609i $$-0.157772\pi$$
$$3$$ 1.02505 1.77544i 0.591814 1.02505i −0.402174 0.915563i $$-0.631745\pi$$
0.993988 0.109489i $$-0.0349213\pi$$
$$4$$ 0.190366 0.0951832
$$5$$ −3.08979 1.78389i −1.38179 0.797779i −0.389422 0.921059i $$-0.627325\pi$$
−0.992372 + 0.123280i $$0.960659\pi$$
$$6$$ −2.38837 1.37893i −0.975048 0.562944i
$$7$$ 0 0
$$8$$ 2.94654i 1.04176i
$$9$$ −0.601462 1.04176i −0.200487 0.347254i
$$10$$ −2.39973 + 4.15646i −0.758862 + 1.31439i
$$11$$ −1.10736 0.639336i −0.333882 0.192767i 0.323681 0.946166i $$-0.395080\pi$$
−0.657563 + 0.753399i $$0.728413\pi$$
$$12$$ 0.195135 0.337984i 0.0563307 0.0975677i
$$13$$ −3.57420 + 0.474474i −0.991304 + 0.131595i
$$14$$ 0 0
$$15$$ −6.33438 + 3.65716i −1.63553 + 0.944273i
$$16$$ −3.58303 −0.895757
$$17$$ 7.73920 1.87703 0.938515 0.345238i $$-0.112202\pi$$
0.938515 + 0.345238i $$0.112202\pi$$
$$18$$ −1.40141 + 0.809103i −0.330315 + 0.190707i
$$19$$ −0.817422 + 0.471939i −0.187530 + 0.108270i −0.590826 0.806799i $$-0.701198\pi$$
0.403296 + 0.915070i $$0.367865\pi$$
$$20$$ −0.588191 0.339592i −0.131524 0.0759352i
$$21$$ 0 0
$$22$$ −0.860052 + 1.48965i −0.183364 + 0.317595i
$$23$$ −1.64727 −0.343481 −0.171740 0.985142i $$-0.554939\pi$$
−0.171740 + 0.985142i $$0.554939\pi$$
$$24$$ −5.23141 3.02035i −1.06786 0.616527i
$$25$$ 3.86451 + 6.69354i 0.772903 + 1.33871i
$$26$$ 0.638275 + 4.80810i 0.125176 + 0.942946i
$$27$$ 3.68419 0.709023
$$28$$ 0 0
$$29$$ −2.02242 3.50293i −0.375554 0.650478i 0.614856 0.788639i $$-0.289214\pi$$
−0.990410 + 0.138161i $$0.955881\pi$$
$$30$$ 4.91970 + 8.52117i 0.898210 + 1.55575i
$$31$$ −4.46193 + 2.57610i −0.801387 + 0.462681i −0.843956 0.536413i $$-0.819779\pi$$
0.0425691 + 0.999094i $$0.486446\pi$$
$$32$$ 1.07309i 0.189698i
$$33$$ −2.27021 + 1.31071i −0.395192 + 0.228164i
$$34$$ 10.4110i 1.78547i
$$35$$ 0 0
$$36$$ −0.114498 0.198317i −0.0190830 0.0330528i
$$37$$ 1.05608i 0.173619i −0.996225 0.0868094i $$-0.972333\pi$$
0.996225 0.0868094i $$-0.0276671\pi$$
$$38$$ 0.634865 + 1.09962i 0.102989 + 0.178382i
$$39$$ −2.82133 + 6.83214i −0.451775 + 1.09402i
$$40$$ −5.25629 + 9.10417i −0.831093 + 1.43950i
$$41$$ 3.63629 2.09941i 0.567893 0.327873i −0.188415 0.982090i $$-0.560335\pi$$
0.756307 + 0.654217i $$0.227002\pi$$
$$42$$ 0 0
$$43$$ 1.91532 3.31744i 0.292084 0.505904i −0.682218 0.731148i $$-0.738985\pi$$
0.974302 + 0.225244i $$0.0723180\pi$$
$$44$$ −0.210805 0.121708i −0.0317800 0.0183482i
$$45$$ 4.29176i 0.639778i
$$46$$ 2.21596i 0.326725i
$$47$$ −0.774415 0.447109i −0.112960 0.0652175i 0.442456 0.896790i $$-0.354107\pi$$
−0.555416 + 0.831573i $$0.687441\pi$$
$$48$$ −3.67279 + 6.36146i −0.530121 + 0.918197i
$$49$$ 0 0
$$50$$ 9.00432 5.19865i 1.27340 0.735200i
$$51$$ 7.93308 13.7405i 1.11085 1.92405i
$$52$$ −0.680407 + 0.0903239i −0.0943554 + 0.0125257i
$$53$$ 0.0399961 + 0.0692754i 0.00549389 + 0.00951570i 0.868759 0.495235i $$-0.164918\pi$$
−0.863265 + 0.504750i $$0.831585\pi$$
$$54$$ 4.95607i 0.674436i
$$55$$ 2.28101 + 3.95082i 0.307571 + 0.532729i
$$56$$ 0 0
$$57$$ 1.93505i 0.256303i
$$58$$ −4.71224 + 2.72061i −0.618747 + 0.357234i
$$59$$ 11.1847i 1.45613i −0.685509 0.728064i $$-0.740420\pi$$
0.685509 0.728064i $$-0.259580\pi$$
$$60$$ −1.20585 + 0.696200i −0.155675 + 0.0898790i
$$61$$ −3.81196 6.60251i −0.488072 0.845365i 0.511834 0.859084i $$-0.328966\pi$$
−0.999906 + 0.0137195i $$0.995633\pi$$
$$62$$ 3.46543 + 6.00231i 0.440111 + 0.762294i
$$63$$ 0 0
$$64$$ −8.60961 −1.07620
$$65$$ 11.8899 + 4.90994i 1.47476 + 0.609003i
$$66$$ 1.76319 + 3.05394i 0.217034 + 0.375914i
$$67$$ 5.47418 + 3.16052i 0.668777 + 0.386119i 0.795613 0.605805i $$-0.207149\pi$$
−0.126836 + 0.991924i $$0.540482\pi$$
$$68$$ 1.47328 0.178662
$$69$$ −1.68854 + 2.92464i −0.203277 + 0.352085i
$$70$$ 0 0
$$71$$ 9.89346 + 5.71199i 1.17414 + 0.677889i 0.954651 0.297727i $$-0.0962285\pi$$
0.219487 + 0.975616i $$0.429562\pi$$
$$72$$ −3.06959 + 1.77223i −0.361755 + 0.208859i
$$73$$ −0.658617 + 0.380253i −0.0770853 + 0.0445052i −0.538047 0.842915i $$-0.680838\pi$$
0.460962 + 0.887420i $$0.347504\pi$$
$$74$$ −1.42067 −0.165149
$$75$$ 15.8453 1.82966
$$76$$ −0.155610 + 0.0898413i −0.0178497 + 0.0103055i
$$77$$ 0 0
$$78$$ 9.19077 + 3.79533i 1.04065 + 0.429737i
$$79$$ 1.42765 2.47277i 0.160624 0.278208i −0.774469 0.632612i $$-0.781983\pi$$
0.935093 + 0.354404i $$0.115316\pi$$
$$80$$ 11.0708 + 6.39172i 1.23775 + 0.714616i
$$81$$ 5.58087 9.66636i 0.620097 1.07404i
$$82$$ −2.82418 4.89163i −0.311879 0.540190i
$$83$$ 2.32483i 0.255183i −0.991827 0.127591i $$-0.959275\pi$$
0.991827 0.127591i $$-0.0407246\pi$$
$$84$$ 0 0
$$85$$ −23.9125 13.8059i −2.59367 1.49746i
$$86$$ −4.46270 2.57654i −0.481226 0.277836i
$$87$$ −8.29233 −0.889032
$$88$$ −1.88383 + 3.26289i −0.200817 + 0.347825i
$$89$$ 7.57626i 0.803082i 0.915841 + 0.401541i $$0.131525\pi$$
−0.915841 + 0.401541i $$0.868475\pi$$
$$90$$ 5.77339 0.608569
$$91$$ 0 0
$$92$$ −0.313586 −0.0326936
$$93$$ 10.5625i 1.09528i
$$94$$ −0.601462 + 1.04176i −0.0620361 + 0.107450i
$$95$$ 3.36755 0.345503
$$96$$ −1.90522 1.09998i −0.194450 0.112266i
$$97$$ 0.414443 + 0.239279i 0.0420803 + 0.0242951i 0.520893 0.853622i $$-0.325599\pi$$
−0.478812 + 0.877917i $$0.658933\pi$$
$$98$$ 0 0
$$99$$ 1.53815i 0.154589i
$$100$$ 0.735674 + 1.27422i 0.0735674 + 0.127422i
$$101$$ −1.43918 + 2.49273i −0.143204 + 0.248036i −0.928701 0.370829i $$-0.879074\pi$$
0.785498 + 0.618865i $$0.212407\pi$$
$$102$$ −18.4841 10.6718i −1.83020 1.05666i
$$103$$ 5.66755 9.81649i 0.558441 0.967248i −0.439186 0.898396i $$-0.644733\pi$$
0.997627 0.0688516i $$-0.0219335\pi$$
$$104$$ 1.39806 + 10.5315i 0.137091 + 1.03270i
$$105$$ 0 0
$$106$$ 0.0931910 0.0538039i 0.00905151 0.00522589i
$$107$$ −6.57206 −0.635345 −0.317673 0.948200i $$-0.602901\pi$$
−0.317673 + 0.948200i $$0.602901\pi$$
$$108$$ 0.701346 0.0674871
$$109$$ −5.05684 + 2.91957i −0.484358 + 0.279644i −0.722231 0.691652i $$-0.756883\pi$$
0.237873 + 0.971296i $$0.423550\pi$$
$$110$$ 5.31475 3.06847i 0.506741 0.292567i
$$111$$ −1.87501 1.08254i −0.177968 0.102750i
$$112$$ 0 0
$$113$$ −3.26617 + 5.65717i −0.307255 + 0.532181i −0.977761 0.209723i $$-0.932744\pi$$
0.670506 + 0.741904i $$0.266077\pi$$
$$114$$ 2.60308 0.243800
$$115$$ 5.08973 + 2.93855i 0.474619 + 0.274022i
$$116$$ −0.385001 0.666841i −0.0357464 0.0619146i
$$117$$ 2.64403 + 3.43809i 0.244441 + 0.317851i
$$118$$ −15.0460 −1.38510
$$119$$ 0 0
$$120$$ 10.7759 + 18.6645i 0.983705 + 1.70383i
$$121$$ −4.68250 8.11033i −0.425682 0.737302i
$$122$$ −8.88187 + 5.12795i −0.804127 + 0.464263i
$$123$$ 8.60802i 0.776159i
$$124$$ −0.849402 + 0.490402i −0.0762786 + 0.0440394i
$$125$$ 9.73656i 0.870865i
$$126$$ 0 0
$$127$$ 7.35818 + 12.7447i 0.652932 + 1.13091i 0.982408 + 0.186748i $$0.0597948\pi$$
−0.329475 + 0.944164i $$0.606872\pi$$
$$128$$ 9.43568i 0.834005i
$$129$$ −3.92661 6.80109i −0.345719 0.598802i
$$130$$ 6.60498 15.9946i 0.579295 1.40282i
$$131$$ 5.59335 9.68796i 0.488693 0.846441i −0.511222 0.859448i $$-0.670807\pi$$
0.999915 + 0.0130074i $$0.00414049\pi$$
$$132$$ −0.432171 + 0.249514i −0.0376157 + 0.0217174i
$$133$$ 0 0
$$134$$ 4.25161 7.36400i 0.367283 0.636153i
$$135$$ −11.3834 6.57219i −0.979724 0.565644i
$$136$$ 22.8038i 1.95541i
$$137$$ 17.6308i 1.50630i −0.657848 0.753151i $$-0.728533\pi$$
0.657848 0.753151i $$-0.271467\pi$$
$$138$$ 3.93430 + 2.27147i 0.334910 + 0.193360i
$$139$$ −2.92855 + 5.07240i −0.248396 + 0.430235i −0.963081 0.269212i $$-0.913237\pi$$
0.714685 + 0.699447i $$0.246570\pi$$
$$140$$ 0 0
$$141$$ −1.58763 + 0.916619i −0.133703 + 0.0771932i
$$142$$ 7.68392 13.3089i 0.644820 1.11686i
$$143$$ 4.26128 + 1.75970i 0.356346 + 0.147153i
$$144$$ 2.15506 + 3.73267i 0.179588 + 0.311055i
$$145$$ 14.4311i 1.19844i
$$146$$ 0.511526 + 0.885989i 0.0423342 + 0.0733250i
$$147$$ 0 0
$$148$$ 0.201043i 0.0165256i
$$149$$ 9.07505 5.23948i 0.743457 0.429235i −0.0798677 0.996805i $$-0.525450\pi$$
0.823325 + 0.567570i $$0.192116\pi$$
$$150$$ 21.3155i 1.74041i
$$151$$ −4.08249 + 2.35703i −0.332229 + 0.191812i −0.656830 0.754039i $$-0.728103\pi$$
0.324602 + 0.945851i $$0.394770\pi$$
$$152$$ 1.39059 + 2.40857i 0.112791 + 0.195361i
$$153$$ −4.65483 8.06241i −0.376321 0.651807i
$$154$$ 0 0
$$155$$ 18.3819 1.47647
$$156$$ −0.537087 + 1.30061i −0.0430014 + 0.104132i
$$157$$ 4.50105 + 7.79604i 0.359223 + 0.622192i 0.987831 0.155530i $$-0.0497085\pi$$
−0.628608 + 0.777722i $$0.716375\pi$$
$$158$$ −3.32643 1.92052i −0.264637 0.152788i
$$159$$ 0.163992 0.0130054
$$160$$ −1.91428 + 3.31563i −0.151337 + 0.262123i
$$161$$ 0 0
$$162$$ −13.0034 7.50754i −1.02165 0.589848i
$$163$$ 10.4203 6.01619i 0.816185 0.471224i −0.0329144 0.999458i $$-0.510479\pi$$
0.849099 + 0.528234i $$0.177146\pi$$
$$164$$ 0.692227 0.399657i 0.0540538 0.0312080i
$$165$$ 9.35261 0.728099
$$166$$ −3.12742 −0.242735
$$167$$ 16.8199 9.71099i 1.30157 0.751459i 0.320893 0.947116i $$-0.396017\pi$$
0.980672 + 0.195657i $$0.0626838\pi$$
$$168$$ 0 0
$$169$$ 12.5497 3.39173i 0.965365 0.260902i
$$170$$ −18.5720 + 32.1677i −1.42441 + 2.46715i
$$171$$ 0.983297 + 0.567707i 0.0751946 + 0.0434136i
$$172$$ 0.364613 0.631528i 0.0278015 0.0481536i
$$173$$ −7.18976 12.4530i −0.546627 0.946786i −0.998503 0.0547049i $$-0.982578\pi$$
0.451875 0.892081i $$-0.350755\pi$$
$$174$$ 11.1551i 0.845663i
$$175$$ 0 0
$$176$$ 3.96771 + 2.29076i 0.299077 + 0.172672i
$$177$$ −19.8578 11.4649i −1.49261 0.861757i
$$178$$ 10.1918 0.763907
$$179$$ 2.71303 4.69911i 0.202781 0.351228i −0.746642 0.665226i $$-0.768335\pi$$
0.949424 + 0.313998i $$0.101669\pi$$
$$180$$ 0.817008i 0.0608962i
$$181$$ 15.4902 1.15138 0.575688 0.817669i $$-0.304734\pi$$
0.575688 + 0.817669i $$0.304734\pi$$
$$182$$ 0 0
$$183$$ −15.6298 −1.15539
$$184$$ 4.85376i 0.357824i
$$185$$ −1.88393 + 3.26307i −0.138509 + 0.239905i
$$186$$ 14.2090 1.04185
$$187$$ −8.57010 4.94795i −0.626707 0.361830i
$$188$$ −0.147423 0.0851144i −0.0107519 0.00620761i
$$189$$ 0 0
$$190$$ 4.53011i 0.328649i
$$191$$ −2.37311 4.11035i −0.171712 0.297414i 0.767306 0.641281i $$-0.221597\pi$$
−0.939019 + 0.343866i $$0.888263\pi$$
$$192$$ −8.82529 + 15.2859i −0.636911 + 1.10316i
$$193$$ 18.2204 + 10.5196i 1.31154 + 0.757215i 0.982350 0.187050i $$-0.0598928\pi$$
0.329185 + 0.944266i $$0.393226\pi$$
$$194$$ 0.321884 0.557519i 0.0231099 0.0400276i
$$195$$ 20.9051 16.0769i 1.49704 1.15129i
$$196$$ 0 0
$$197$$ 5.03342 2.90604i 0.358616 0.207047i −0.309857 0.950783i $$-0.600281\pi$$
0.668474 + 0.743736i $$0.266948\pi$$
$$198$$ 2.06915 0.147048
$$199$$ 10.6182 0.752703 0.376352 0.926477i $$-0.377179\pi$$
0.376352 + 0.926477i $$0.377179\pi$$
$$200$$ 19.7228 11.3869i 1.39461 0.805178i
$$201$$ 11.2226 6.47939i 0.791583 0.457021i
$$202$$ 3.35329 + 1.93602i 0.235936 + 0.136218i
$$203$$ 0 0
$$204$$ 1.51019 2.61573i 0.105735 0.183138i
$$205$$ −14.9805 −1.04628
$$206$$ −13.2054 7.62414i −0.920064 0.531199i
$$207$$ 0.990773 + 1.71607i 0.0688635 + 0.119275i
$$208$$ 12.8064 1.70005i 0.887967 0.117877i
$$209$$ 1.20691 0.0834837
$$210$$ 0 0
$$211$$ 2.33275 + 4.04043i 0.160593 + 0.278155i 0.935081 0.354433i $$-0.115326\pi$$
−0.774489 + 0.632588i $$0.781993\pi$$
$$212$$ 0.00761392 + 0.0131877i 0.000522926 + 0.000905735i
$$213$$ 20.2826 11.7102i 1.38974 0.802368i
$$214$$ 8.84091i 0.604352i
$$215$$ −11.8359 + 6.83344i −0.807200 + 0.466037i
$$216$$ 10.8556i 0.738631i
$$217$$ 0 0
$$218$$ 3.92748 + 6.80260i 0.266003 + 0.460730i
$$219$$ 1.55912i 0.105355i
$$220$$ 0.434227 + 0.752104i 0.0292756 + 0.0507068i
$$221$$ −27.6614 + 3.67205i −1.86071 + 0.247009i
$$222$$ −1.45626 + 2.52232i −0.0977377 + 0.169287i
$$223$$ −20.9798 + 12.1127i −1.40491 + 0.811126i −0.994891 0.100950i $$-0.967812\pi$$
−0.410020 + 0.912076i $$0.634478\pi$$
$$224$$ 0 0
$$225$$ 4.64872 8.05182i 0.309915 0.536788i
$$226$$ 7.61017 + 4.39373i 0.506221 + 0.292267i
$$227$$ 15.3753i 1.02049i 0.860028 + 0.510247i $$0.170446\pi$$
−0.860028 + 0.510247i $$0.829554\pi$$
$$228$$ 0.368368i 0.0243958i
$$229$$ 14.1608 + 8.17573i 0.935771 + 0.540268i 0.888632 0.458621i $$-0.151656\pi$$
0.0471389 + 0.998888i $$0.484990\pi$$
$$230$$ 3.95302 6.84683i 0.260654 0.451467i
$$231$$ 0 0
$$232$$ −10.3215 + 5.95913i −0.677641 + 0.391236i
$$233$$ −14.5554 + 25.2106i −0.953554 + 1.65160i −0.215911 + 0.976413i $$0.569272\pi$$
−0.737643 + 0.675191i $$0.764061\pi$$
$$234$$ 4.62500 3.55682i 0.302346 0.232517i
$$235$$ 1.59518 + 2.76294i 0.104058 + 0.180234i
$$236$$ 2.12920i 0.138599i
$$237$$ −2.92684 5.06943i −0.190119 0.329295i
$$238$$ 0 0
$$239$$ 8.65409i 0.559787i −0.960031 0.279893i $$-0.909701\pi$$
0.960031 0.279893i $$-0.0902991\pi$$
$$240$$ 22.6963 13.1037i 1.46504 0.845840i
$$241$$ 18.1982i 1.17225i −0.810222 0.586124i $$-0.800653\pi$$
0.810222 0.586124i $$-0.199347\pi$$
$$242$$ −10.9102 + 6.29902i −0.701336 + 0.404916i
$$243$$ −5.91508 10.2452i −0.379453 0.657231i
$$244$$ −0.725669 1.25690i −0.0464562 0.0804645i
$$245$$ 0 0
$$246$$ −11.5797 −0.738297
$$247$$ 2.69770 2.07465i 0.171651 0.132007i
$$248$$ 7.59057 + 13.1473i 0.482002 + 0.834851i
$$249$$ −4.12759 2.38307i −0.261576 0.151021i
$$250$$ −13.0979 −0.828383
$$251$$ −7.93598 + 13.7455i −0.500915 + 0.867610i 0.499085 + 0.866553i $$0.333670\pi$$
−0.999999 + 0.00105678i $$0.999664\pi$$
$$252$$ 0 0
$$253$$ 1.82413 + 1.05316i 0.114682 + 0.0662117i
$$254$$ 17.1446 9.89841i 1.07574 0.621082i
$$255$$ −49.0230 + 28.3034i −3.06994 + 1.77243i
$$256$$ −4.52609 −0.282880
$$257$$ −24.3267 −1.51746 −0.758730 0.651406i $$-0.774180\pi$$
−0.758730 + 0.651406i $$0.774180\pi$$
$$258$$ −9.14900 + 5.28218i −0.569592 + 0.328854i
$$259$$ 0 0
$$260$$ 2.26344 + 0.934688i 0.140372 + 0.0579669i
$$261$$ −2.43282 + 4.21376i −0.150588 + 0.260825i
$$262$$ −13.0325 7.52432i −0.805150 0.464854i
$$263$$ −7.71727 + 13.3667i −0.475867 + 0.824226i −0.999618 0.0276456i $$-0.991199\pi$$
0.523751 + 0.851872i $$0.324532\pi$$
$$264$$ 3.86204 + 6.68925i 0.237692 + 0.411695i
$$265$$ 0.285395i 0.0175317i
$$266$$ 0 0
$$267$$ 13.4512 + 7.76606i 0.823201 + 0.475275i
$$268$$ 1.04210 + 0.601656i 0.0636563 + 0.0367520i
$$269$$ 13.0407 0.795106 0.397553 0.917579i $$-0.369859\pi$$
0.397553 + 0.917579i $$0.369859\pi$$
$$270$$ −8.84108 + 15.3132i −0.538051 + 0.931931i
$$271$$ 26.9706i 1.63835i 0.573544 + 0.819174i $$0.305568\pi$$
−0.573544 + 0.819174i $$0.694432\pi$$
$$272$$ −27.7298 −1.68136
$$273$$ 0 0
$$274$$ −23.7174 −1.43282
$$275$$ 9.88289i 0.595961i
$$276$$ −0.321442 + 0.556753i −0.0193485 + 0.0335126i
$$277$$ −12.7015 −0.763156 −0.381578 0.924337i $$-0.624619\pi$$
−0.381578 + 0.924337i $$0.624619\pi$$
$$278$$ 6.82352 + 3.93956i 0.409248 + 0.236279i
$$279$$ 5.36737 + 3.09885i 0.321336 + 0.185523i
$$280$$ 0 0
$$281$$ 26.7216i 1.59408i −0.603930 0.797038i $$-0.706399\pi$$
0.603930 0.797038i $$-0.293601\pi$$
$$282$$ 1.23306 + 2.13572i 0.0734276 + 0.127180i
$$283$$ −7.37113 + 12.7672i −0.438168 + 0.758929i −0.997548 0.0699819i $$-0.977706\pi$$
0.559380 + 0.828911i $$0.311039\pi$$
$$284$$ 1.88338 + 1.08737i 0.111758 + 0.0645236i
$$285$$ 3.45191 5.97888i 0.204473 0.354158i
$$286$$ 2.36719 5.73238i 0.139975 0.338963i
$$287$$ 0 0
$$288$$ −1.11791 + 0.645425i −0.0658734 + 0.0380320i
$$289$$ 42.8952 2.52324
$$290$$ 19.4131 1.13997
$$291$$ 0.849651 0.490546i 0.0498074 0.0287563i
$$292$$ −0.125379 + 0.0723874i −0.00733723 + 0.00423615i
$$293$$ 10.0312 + 5.79153i 0.586030 + 0.338345i 0.763526 0.645777i $$-0.223466\pi$$
−0.177496 + 0.984121i $$0.556800\pi$$
$$294$$ 0 0
$$295$$ −19.9523 + 34.5584i −1.16167 + 2.01207i
$$296$$ −3.11179 −0.180869
$$297$$ −4.07974 2.35544i −0.236730 0.136676i
$$298$$ −7.04829 12.2080i −0.408297 0.707190i
$$299$$ 5.88768 0.781589i 0.340493 0.0452005i
$$300$$ 3.01641 0.174153
$$301$$ 0 0
$$302$$ 3.17074 + 5.49188i 0.182455 + 0.316022i
$$303$$ 2.95047 + 5.11036i 0.169500 + 0.293582i
$$304$$ 2.92885 1.69097i 0.167981 0.0969838i
$$305$$ 27.2004i 1.55749i
$$306$$ −10.8458 + 6.26180i −0.620011 + 0.357963i
$$307$$ 29.3335i 1.67415i 0.547086 + 0.837076i $$0.315737\pi$$
−0.547086 + 0.837076i $$0.684263\pi$$
$$308$$ 0 0
$$309$$ −11.6191 20.1248i −0.660986 1.14486i
$$310$$ 24.7278i 1.40444i
$$311$$ 0.0753271 + 0.130470i 0.00427141 + 0.00739830i 0.868153 0.496296i $$-0.165307\pi$$
−0.863882 + 0.503695i $$0.831974\pi$$
$$312$$ 20.1312 + 8.31317i 1.13970 + 0.470641i
$$313$$ −5.26057 + 9.11157i −0.297345 + 0.515016i −0.975528 0.219877i $$-0.929434\pi$$
0.678183 + 0.734893i $$0.262768\pi$$
$$314$$ 10.4874 6.05493i 0.591841 0.341699i
$$315$$ 0 0
$$316$$ 0.271777 0.470732i 0.0152887 0.0264808i
$$317$$ 1.30489 + 0.753380i 0.0732901 + 0.0423140i 0.536197 0.844093i $$-0.319860\pi$$
−0.462907 + 0.886407i $$0.653194\pi$$
$$318$$ 0.220607i 0.0123710i
$$319$$ 5.17202i 0.289578i
$$320$$ 26.6018 + 15.3586i 1.48709 + 0.858571i
$$321$$ −6.73671 + 11.6683i −0.376006 + 0.651262i
$$322$$ 0 0
$$323$$ −6.32619 + 3.65243i −0.351999 + 0.203227i
$$324$$ 1.06241 1.84015i 0.0590228 0.102231i
$$325$$ −16.9884 22.0904i −0.942349 1.22535i
$$326$$ −8.09314 14.0177i −0.448237 0.776370i
$$327$$ 11.9708i 0.661989i
$$328$$ −6.18600 10.7145i −0.341565 0.591607i
$$329$$ 0 0
$$330$$ 12.5814i 0.692582i
$$331$$ −21.8679 + 12.6254i −1.20197 + 0.693957i −0.960993 0.276574i $$-0.910801\pi$$
−0.240976 + 0.970531i $$0.577467\pi$$
$$332$$ 0.442569i 0.0242891i
$$333$$ −1.10019 + 0.635193i −0.0602899 + 0.0348084i
$$334$$ −13.0635 22.6266i −0.714802 1.23807i
$$335$$ −11.2760 19.5306i −0.616075 1.06707i
$$336$$ 0 0
$$337$$ 32.1811 1.75302 0.876509 0.481386i $$-0.159866\pi$$
0.876509 + 0.481386i $$0.159866\pi$$
$$338$$ −4.56264 16.8823i −0.248175 0.918273i
$$339$$ 6.69598 + 11.5978i 0.363676 + 0.629905i
$$340$$ −4.55213 2.62817i −0.246874 0.142533i
$$341$$ 6.58797 0.356759
$$342$$ 0.763694 1.32276i 0.0412959 0.0715265i
$$343$$ 0 0
$$344$$ −9.77495 5.64357i −0.527030 0.304281i
$$345$$ 10.4345 6.02434i 0.561773 0.324340i
$$346$$ −16.7521 + 9.67185i −0.900600 + 0.519962i
$$347$$ 24.7638 1.32939 0.664695 0.747115i $$-0.268562\pi$$
0.664695 + 0.747115i $$0.268562\pi$$
$$348$$ −1.57858 −0.0846209
$$349$$ 10.0075 5.77782i 0.535688 0.309280i −0.207642 0.978205i $$-0.566579\pi$$
0.743330 + 0.668925i $$0.233245\pi$$
$$350$$ 0 0
$$351$$ −13.1680 + 1.74805i −0.702857 + 0.0933042i
$$352$$ −0.686067 + 1.18830i −0.0365675 + 0.0633368i
$$353$$ 17.3971 + 10.0442i 0.925953 + 0.534599i 0.885529 0.464583i $$-0.153796\pi$$
0.0404237 + 0.999183i $$0.487129\pi$$
$$354$$ −15.4229 + 26.7133i −0.819719 + 1.41980i
$$355$$ −20.3791 35.2977i −1.08161 1.87340i
$$356$$ 1.44227i 0.0764399i
$$357$$ 0 0
$$358$$ −6.32136 3.64964i −0.334094 0.192890i
$$359$$ 13.0346 + 7.52551i 0.687938 + 0.397181i 0.802839 0.596196i $$-0.203322\pi$$
−0.114901 + 0.993377i $$0.536655\pi$$
$$360$$ 12.6458 0.666495
$$361$$ −9.05455 + 15.6829i −0.476555 + 0.825418i
$$362$$ 20.8378i 1.09521i
$$363$$ −19.1992 −1.00770
$$364$$ 0 0
$$365$$ 2.71331 0.142021
$$366$$ 21.0257i 1.09903i
$$367$$ 4.50178 7.79731i 0.234991 0.407016i −0.724279 0.689507i $$-0.757827\pi$$
0.959270 + 0.282491i $$0.0911607\pi$$
$$368$$ 5.90223 0.307675
$$369$$ −4.37418 2.52543i −0.227711 0.131469i
$$370$$ 4.38956 + 2.53431i 0.228202 + 0.131753i
$$371$$ 0 0
$$372$$ 2.01075i 0.104253i
$$373$$ 8.06953 + 13.9768i 0.417824 + 0.723693i 0.995720 0.0924174i $$-0.0294594\pi$$
−0.577896 + 0.816110i $$0.696126\pi$$
$$374$$ −6.65611 + 11.5287i −0.344179 + 0.596136i
$$375$$ −17.2867 9.98048i −0.892681 0.515390i
$$376$$ −1.31742 + 2.28184i −0.0679409 + 0.117677i
$$377$$ 8.89057 + 11.5606i 0.457888 + 0.595400i
$$378$$ 0 0
$$379$$ −13.5668 + 7.83277i −0.696878 + 0.402342i −0.806183 0.591666i $$-0.798471\pi$$
0.109306 + 0.994008i $$0.465137\pi$$
$$380$$ 0.641068 0.0328861
$$381$$ 30.1700 1.54566
$$382$$ −5.52935 + 3.19237i −0.282906 + 0.163336i
$$383$$ −21.3327 + 12.3164i −1.09005 + 0.629339i −0.933589 0.358345i $$-0.883341\pi$$
−0.156459 + 0.987685i $$0.550008\pi$$
$$384$$ 16.7525 + 9.67207i 0.854898 + 0.493576i
$$385$$ 0 0
$$386$$ 14.1512 24.5106i 0.720277 1.24756i
$$387$$ −4.60798 −0.234237
$$388$$ 0.0788960 + 0.0455506i 0.00400534 + 0.00231248i
$$389$$ −9.42834 16.3304i −0.478036 0.827982i 0.521647 0.853161i $$-0.325318\pi$$
−0.999683 + 0.0251791i $$0.991984\pi$$
$$390$$ −21.6270 28.1221i −1.09513 1.42402i
$$391$$ −12.7486 −0.644724
$$392$$ 0 0
$$393$$ −11.4669 19.8613i −0.578431 1.00187i
$$394$$ −3.90929 6.77108i −0.196947 0.341122i
$$395$$ −8.82229 + 5.09355i −0.443897 + 0.256284i
$$396$$ 0.292811i 0.0147143i
$$397$$ 12.5600 7.25149i 0.630366 0.363942i −0.150528 0.988606i $$-0.548097\pi$$
0.780894 + 0.624664i $$0.214764\pi$$
$$398$$ 14.2839i 0.715985i
$$399$$ 0 0
$$400$$ −13.8467 23.9831i −0.692333 1.19916i
$$401$$ 20.9889i 1.04814i −0.851676 0.524069i $$-0.824413\pi$$
0.851676 0.524069i $$-0.175587\pi$$
$$402$$ −8.71624 15.0970i −0.434727 0.752968i
$$403$$ 14.7255 11.3245i 0.733531 0.564116i
$$404$$ −0.273971 + 0.474532i −0.0136306 + 0.0236089i
$$405$$ −34.4874 + 19.9113i −1.71369 + 0.989401i
$$406$$ 0 0
$$407$$ −0.675191 + 1.16947i −0.0334680 + 0.0579683i
$$408$$ −40.4869 23.3751i −2.00440 1.15724i
$$409$$ 21.4276i 1.05953i 0.848146 + 0.529763i $$0.177719\pi$$
−0.848146 + 0.529763i $$0.822281\pi$$
$$410$$ 20.1521i 0.995242i
$$411$$ −31.3025 18.0725i −1.54404 0.891451i
$$412$$ 1.07891 1.86873i 0.0531542 0.0920657i
$$413$$ 0 0
$$414$$ 2.30850 1.33281i 0.113457 0.0655043i
$$415$$ −4.14723 + 7.18321i −0.203580 + 0.352610i
$$416$$ 0.509155 + 3.83545i 0.0249634 + 0.188048i
$$417$$ 6.00383 + 10.3989i 0.294009 + 0.509238i
$$418$$ 1.62357i 0.0794113i
$$419$$ 3.98203 + 6.89708i 0.194535 + 0.336944i 0.946748 0.321976i $$-0.104347\pi$$
−0.752213 + 0.658920i $$0.771014\pi$$
$$420$$ 0 0
$$421$$ 2.81786i 0.137334i 0.997640 + 0.0686670i $$0.0218746\pi$$
−0.997640 + 0.0686670i $$0.978125\pi$$
$$422$$ 5.43530 3.13807i 0.264586 0.152759i
$$423$$ 1.07568i 0.0523011i
$$424$$ 0.204122 0.117850i 0.00991306 0.00572331i
$$425$$ 29.9082 + 51.8026i 1.45076 + 2.51279i
$$426$$ −15.7528 27.2847i −0.763227 1.32195i
$$427$$ 0 0
$$428$$ −1.25110 −0.0604742
$$429$$ 7.49227 5.76187i 0.361730 0.278186i
$$430$$ 9.19253 + 15.9219i 0.443303 + 0.767823i
$$431$$ 4.96775 + 2.86813i 0.239288 + 0.138153i 0.614849 0.788645i $$-0.289217\pi$$
−0.375561 + 0.926797i $$0.622550\pi$$
$$432$$ −13.2006 −0.635112
$$433$$ 12.2628 21.2398i 0.589314 1.02072i −0.405009 0.914313i $$-0.632732\pi$$
0.994322 0.106409i $$-0.0339351\pi$$
$$434$$ 0 0
$$435$$ 25.6215 + 14.7926i 1.22846 + 0.709251i
$$436$$ −0.962653 + 0.555788i −0.0461027 + 0.0266174i
$$437$$ 1.34652 0.777413i 0.0644128 0.0371887i
$$438$$ 2.09736 0.100216
$$439$$ 36.6423 1.74884 0.874420 0.485169i $$-0.161242\pi$$
0.874420 + 0.485169i $$0.161242\pi$$
$$440$$ 11.6412 6.72108i 0.554975 0.320415i
$$441$$ 0 0
$$442$$ 4.93973 + 37.2108i 0.234959 + 1.76994i
$$443$$ −13.5467 + 23.4635i −0.643622 + 1.11479i 0.340996 + 0.940065i $$0.389236\pi$$
−0.984618 + 0.174721i $$0.944098\pi$$
$$444$$ −0.356939 0.206079i −0.0169396 0.00978008i
$$445$$ 13.5152 23.4090i 0.640682 1.10969i
$$446$$ 16.2943 + 28.2226i 0.771558 + 1.33638i
$$447$$ 21.4830i 1.01611i
$$448$$ 0 0
$$449$$ 23.7571 + 13.7162i 1.12117 + 0.647307i 0.941699 0.336456i $$-0.109228\pi$$
0.179470 + 0.983764i $$0.442562\pi$$
$$450$$ −10.8315 6.25358i −0.510602 0.294796i
$$451$$ −5.36892 −0.252812
$$452$$ −0.621768 + 1.07693i −0.0292455 + 0.0506547i
$$453$$ 9.66431i 0.454069i
$$454$$ 20.6832 0.970712
$$455$$ 0 0
$$456$$ 5.70169 0.267006
$$457$$ 39.6639i 1.85540i 0.373327 + 0.927700i $$0.378217\pi$$
−0.373327 + 0.927700i $$0.621783\pi$$
$$458$$ 10.9982 19.0495i 0.513913 0.890123i
$$459$$ 28.5127 1.33086
$$460$$ 0.968913 + 0.559402i 0.0451758 + 0.0260823i
$$461$$ 4.23988 + 2.44790i 0.197471 + 0.114010i 0.595475 0.803374i $$-0.296964\pi$$
−0.398004 + 0.917384i $$0.630297\pi$$
$$462$$ 0 0
$$463$$ 4.71193i 0.218982i −0.993988 0.109491i $$-0.965078\pi$$
0.993988 0.109491i $$-0.0349221\pi$$
$$464$$ 7.24638 + 12.5511i 0.336405 + 0.582670i
$$465$$ 18.8424 32.6360i 0.873794 1.51346i
$$466$$ 33.9140 + 19.5803i 1.57104 + 0.907038i
$$467$$ −16.0081 + 27.7268i −0.740765 + 1.28304i 0.211383 + 0.977403i $$0.432203\pi$$
−0.952147 + 0.305639i $$0.901130\pi$$
$$468$$ 0.503335 + 0.654496i 0.0232667 + 0.0302541i
$$469$$ 0 0
$$470$$ 3.71678 2.14588i 0.171442 0.0989822i
$$471$$ 18.4552 0.850372
$$472$$ −32.9563 −1.51693
$$473$$ −4.24191 + 2.44907i −0.195043 + 0.112608i
$$474$$ −6.81953 + 3.93726i −0.313232 + 0.180844i
$$475$$ −6.31788 3.64763i −0.289884 0.167365i
$$476$$ 0 0
$$477$$ 0.0481123 0.0833330i 0.00220291 0.00381556i
$$478$$ −11.6417 −0.532480
$$479$$ −15.6097 9.01224i −0.713224 0.411780i 0.0990298 0.995084i $$-0.468426\pi$$
−0.812254 + 0.583305i $$0.801759\pi$$
$$480$$ 3.92447 + 6.79738i 0.179127 + 0.310257i
$$481$$ 0.501083 + 3.77464i 0.0228474 + 0.172109i
$$482$$ −24.4807 −1.11506
$$483$$ 0 0
$$484$$ −0.891390 1.54393i −0.0405177 0.0701788i
$$485$$ −0.853693 1.47864i −0.0387642 0.0671416i
$$486$$ −13.7821 + 7.95712i −0.625170 + 0.360942i
$$487$$ 17.6004i 0.797550i −0.917049 0.398775i $$-0.869435\pi$$
0.917049 0.398775i $$-0.130565\pi$$
$$488$$ −19.4545 + 11.2321i −0.880666 + 0.508453i
$$489$$ 24.6676i 1.11551i
$$490$$ 0 0
$$491$$ 1.93180 + 3.34598i 0.0871810 + 0.151002i 0.906318 0.422595i $$-0.138881\pi$$
−0.819138 + 0.573597i $$0.805547\pi$$
$$492$$ 1.63868i 0.0738773i
$$493$$ −15.6519 27.1099i −0.704926 1.22097i
$$494$$ −2.79087 3.62902i −0.125567 0.163277i
$$495$$ 2.74388 4.75254i 0.123328 0.213611i
$$496$$ 15.9872 9.23023i 0.717848 0.414450i
$$497$$ 0 0
$$498$$ −3.20576 + 5.55255i −0.143654 + 0.248816i
$$499$$ −10.9528 6.32363i −0.490317 0.283084i 0.234389 0.972143i $$-0.424691\pi$$
−0.724706 + 0.689058i $$0.758024\pi$$
$$500$$ 1.85351i 0.0828917i
$$501$$ 39.8171i 1.77890i
$$502$$ 18.4908 + 10.6757i 0.825287 + 0.476480i
$$503$$ 11.0180 19.0837i 0.491268 0.850902i −0.508681 0.860955i $$-0.669867\pi$$
0.999949 + 0.0100533i $$0.00320011\pi$$
$$504$$ 0 0
$$505$$ 8.89351 5.13467i 0.395756 0.228490i
$$506$$ 1.41674 2.45387i 0.0629818 0.109088i
$$507$$ 6.84233 25.7580i 0.303879 1.14395i
$$508$$ 1.40075 + 2.42617i 0.0621482 + 0.107644i
$$509$$ 15.6702i 0.694568i −0.937760 0.347284i $$-0.887104\pi$$
0.937760 0.347284i $$-0.112896\pi$$
$$510$$ 38.0745 + 65.9470i 1.68597 + 2.92018i
$$511$$ 0 0
$$512$$ 24.9600i 1.10309i
$$513$$ −3.01154 + 1.73871i −0.132963 + 0.0767661i
$$514$$ 32.7249i 1.44344i
$$515$$ −35.0230 + 20.2206i −1.54330 + 0.891025i
$$516$$ −0.747495 1.29470i −0.0329066 0.0569959i
$$517$$ 0.571705 + 0.990222i 0.0251436 + 0.0435499i
$$518$$ 0 0
$$519$$ −29.4795 −1.29401
$$520$$ 14.4673 35.0341i 0.634435 1.53635i
$$521$$ −12.6207 21.8598i −0.552925 0.957694i −0.998062 0.0622317i $$-0.980178\pi$$
0.445137 0.895463i $$-0.353155\pi$$
$$522$$ 5.66846 + 3.27269i 0.248102 + 0.143242i
$$523$$ 13.2477 0.579279 0.289640 0.957136i $$-0.406465\pi$$
0.289640 + 0.957136i $$0.406465\pi$$
$$524$$ 1.06479 1.84426i 0.0465154 0.0805670i
$$525$$ 0 0
$$526$$ 17.9812 + 10.3815i 0.784019 + 0.452654i
$$527$$ −34.5318 + 19.9369i −1.50423 + 0.868466i
$$528$$ 8.13422 4.69629i 0.353996 0.204380i
$$529$$ −20.2865 −0.882021
$$530$$ −0.383920 −0.0166764
$$531$$ −11.6518 + 6.72720i −0.505647 + 0.291935i
$$532$$ 0 0
$$533$$ −12.0007 + 9.22903i −0.519807 + 0.399754i
$$534$$ 10.4471 18.0949i 0.452091 0.783044i
$$535$$ 20.3063 + 11.7238i 0.877916 + 0.506865i
$$536$$ 9.31258 16.1299i 0.402242 0.696704i
$$537$$ −5.56200 9.63366i −0.240018 0.415723i
$$538$$ 17.5427i 0.756320i
$$539$$ 0 0
$$540$$ −2.16701 1.25112i −0.0932532 0.0538398i
$$541$$ −12.4737 7.20170i −0.536287 0.309625i 0.207286 0.978280i $$-0.433537\pi$$
−0.743573 + 0.668655i $$0.766870\pi$$
$$542$$ 36.2816 1.55843
$$543$$ 15.8782 27.5019i 0.681401 1.18022i
$$544$$ 8.30488i 0.356069i
$$545$$ 20.8328 0.892377
$$546$$ 0 0
$$547$$ 2.00679 0.0858042 0.0429021 0.999079i $$-0.486340\pi$$
0.0429021 + 0.999079i $$0.486340\pi$$
$$548$$ 3.35631i 0.143375i
$$549$$ −4.58550 + 7.94232i −0.195704 + 0.338970i
$$550$$ −13.2947 −0.566889
$$551$$ 3.30634 + 1.90892i 0.140855 + 0.0813226i
$$552$$ 8.61757 + 4.97535i 0.366788 + 0.211765i
$$553$$ 0 0
$$554$$ 17.0863i 0.725928i
$$555$$ 3.86226 + 6.68962i 0.163944 + 0.283959i
$$556$$ −0.557497 + 0.965614i −0.0236432 + 0.0409512i
$$557$$ −7.42977 4.28958i −0.314810 0.181755i 0.334267 0.942478i $$-0.391511\pi$$
−0.649077 + 0.760723i $$0.724845\pi$$
$$558$$ 4.16865 7.22032i 0.176473 0.305661i
$$559$$ −5.27170 + 12.7659i −0.222969 + 0.539942i
$$560$$ 0 0
$$561$$ −17.5696 + 10.1438i −0.741788 + 0.428272i
$$562$$ −35.9466 −1.51631
$$563$$ −12.7744 −0.538375 −0.269188 0.963088i $$-0.586755\pi$$
−0.269188 + 0.963088i $$0.586755\pi$$
$$564$$ −0.302231 + 0.174493i −0.0127262 + 0.00734750i
$$565$$ 20.1835 11.6530i 0.849126 0.490243i
$$566$$ 17.1747 + 9.91583i 0.721908 + 0.416794i
$$567$$ 0 0
$$568$$ 16.8306 29.1515i 0.706196 1.22317i
$$569$$ 5.79116 0.242778 0.121389 0.992605i $$-0.461265\pi$$
0.121389 + 0.992605i $$0.461265\pi$$
$$570$$ −8.04295 4.64360i −0.336882 0.194499i
$$571$$ −22.0666 38.2204i −0.923458 1.59948i −0.794023 0.607888i $$-0.792017\pi$$
−0.129435 0.991588i $$-0.541316\pi$$
$$572$$ 0.811204 + 0.334987i 0.0339182 + 0.0140065i
$$573$$ −9.73025 −0.406487
$$574$$ 0 0
$$575$$ −6.36592 11.0261i −0.265477 0.459820i
$$576$$ 5.17835 + 8.96917i 0.215765 + 0.373715i
$$577$$ −10.3343 + 5.96649i −0.430221 + 0.248388i −0.699441 0.714691i $$-0.746568\pi$$
0.269220 + 0.963079i $$0.413234\pi$$
$$578$$ 57.7037i 2.40016i
$$579$$ 37.3538 21.5662i 1.55237 0.896261i
$$580$$ 2.74719i 0.114071i
$$581$$ 0 0
$$582$$ −0.659895 1.14297i −0.0273535 0.0473777i
$$583$$ 0.102284i 0.00423617i
$$584$$ 1.12043 + 1.94064i 0.0463637 + 0.0803043i
$$585$$ −2.03633 15.3396i −0.0841919 0.634215i
$$586$$ 7.79091 13.4943i 0.321840 0.557443i
$$587$$ −17.6250 + 10.1758i −0.727462 + 0.420000i −0.817493 0.575939i $$-0.804637\pi$$
0.0900312 + 0.995939i $$0.471303\pi$$
$$588$$ 0 0
$$589$$ 2.43152 4.21152i 0.100189 0.173533i
$$590$$ 46.4889 + 26.8404i 1.91392 + 1.10500i
$$591$$ 11.9154i 0.490133i
$$592$$ 3.78397i 0.155520i
$$593$$ −15.7443 9.09000i −0.646543 0.373282i 0.140588 0.990068i $$-0.455101\pi$$
−0.787130 + 0.616787i $$0.788434\pi$$
$$594$$ −3.16859 + 5.48817i −0.130009 + 0.225182i
$$595$$ 0 0
$$596$$ 1.72759 0.997422i 0.0707646 0.0408560i
$$597$$ 10.8842 18.8520i 0.445460 0.771560i
$$598$$ −1.05141 7.92026i −0.0429955 0.323884i
$$599$$ 19.1341 + 33.1412i 0.781797 + 1.35411i 0.930894 + 0.365290i $$0.119030\pi$$
−0.149096 + 0.988823i $$0.547636\pi$$
$$600$$ 46.6888i 1.90606i
$$601$$ −13.4360 23.2718i −0.548064 0.949275i −0.998407 0.0564195i $$-0.982032\pi$$
0.450343 0.892856i $$-0.351302\pi$$
$$602$$ 0 0
$$603$$ 7.60372i 0.309648i
$$604$$ −0.777170 + 0.448699i −0.0316226 + 0.0182573i
$$605$$ 33.4122i 1.35840i
$$606$$ 6.87459 3.96904i 0.279261 0.161231i
$$607$$ −4.70105 8.14245i −0.190810 0.330492i 0.754709 0.656059i $$-0.227778\pi$$
−0.945519 + 0.325568i $$0.894445\pi$$
$$608$$ 0.506435 + 0.877171i 0.0205386 + 0.0355740i
$$609$$ 0 0
$$610$$ 36.5908 1.48152
$$611$$ 2.98005 + 1.23061i 0.120560 + 0.0497853i
$$612$$ −0.886124 1.53481i −0.0358194 0.0620411i
$$613$$ 11.5089 + 6.64469i 0.464842 + 0.268376i 0.714078 0.700066i $$-0.246846\pi$$
−0.249236 + 0.968443i $$0.580180\pi$$
$$614$$ 39.4602 1.59248
$$615$$ −15.3557 + 26.5969i −0.619204 + 1.07249i
$$616$$ 0 0
$$617$$ −9.72211 5.61306i −0.391397 0.225973i 0.291368 0.956611i $$-0.405890\pi$$
−0.682765 + 0.730638i $$0.739223\pi$$
$$618$$ −27.0724 + 15.6303i −1.08901 + 0.628742i
$$619$$ 8.04109 4.64253i 0.323199 0.186599i −0.329619 0.944114i $$-0.606920\pi$$
0.652817 + 0.757515i $$0.273587\pi$$
$$620$$ 3.49929 0.140535
$$621$$ −6.06888 −0.243536
$$622$$ 0.175512 0.101332i 0.00703740 0.00406304i
$$623$$ 0 0
$$624$$ 10.1089 24.4797i 0.404681 0.979974i
$$625$$ 1.95363 3.38379i 0.0781452 0.135351i
$$626$$ 12.2571 + 7.07665i 0.489893 + 0.282840i
$$627$$ 1.23715 2.14280i 0.0494068 0.0855752i
$$628$$ 0.856848 + 1.48410i 0.0341920 + 0.0592222i
$$629$$ 8.17322i 0.325888i
$$630$$ 0 0
$$631$$ 9.00894 + 5.20132i 0.358640 + 0.207061i 0.668484 0.743726i $$-0.266943\pi$$
−0.309844 + 0.950787i $$0.600277\pi$$
$$632$$ −7.28611 4.20664i −0.289826 0.167331i
$$633$$ 9.56474 0.380164
$$634$$ 1.01347 1.75538i 0.0402499 0.0697149i
$$635$$ 52.5046i 2.08358i
$$636$$ 0.0312187 0.00123790
$$637$$ 0 0
$$638$$ 6.95754 0.275452
$$639$$ 13.7422i 0.543632i
$$640$$ 16.8322 29.1542i 0.665351 1.15242i
$$641$$ −14.8591 −0.586899 −0.293449 0.955975i $$-0.594803\pi$$
−0.293449 + 0.955975i $$0.594803\pi$$
$$642$$ 15.6965 + 9.06239i 0.619492 + 0.357664i
$$643$$ −1.98945 1.14861i −0.0784563 0.0452968i 0.460259 0.887785i $$-0.347757\pi$$
−0.538715 + 0.842488i $$0.681090\pi$$
$$644$$ 0 0
$$645$$ 28.0185i 1.10323i
$$646$$ 4.91334 + 8.51016i 0.193313 + 0.334828i
$$647$$ −3.99932 + 6.92703i −0.157230 + 0.272330i −0.933869 0.357616i $$-0.883590\pi$$
0.776639 + 0.629946i $$0.216923\pi$$
$$648$$ −28.4823 16.4443i −1.11889 0.645991i
$$649$$ −7.15081 + 12.3856i −0.280694 + 0.486176i
$$650$$ −29.7166 + 22.8533i −1.16558 + 0.896380i
$$651$$ 0 0
$$652$$ 1.98368 1.14528i 0.0776871 0.0448526i
$$653$$ 3.98444 0.155923 0.0779615 0.996956i $$-0.475159\pi$$
0.0779615 + 0.996956i $$0.475159\pi$$
$$654$$ 16.1035 0.629696
$$655$$ −34.5645 + 19.9558i −1.35055 + 0.779738i
$$656$$ −13.0289 + 7.52225i −0.508694 + 0.293695i
$$657$$ 0.792267 + 0.457415i 0.0309093 + 0.0178455i
$$658$$ 0 0
$$659$$ 13.7501 23.8159i 0.535629 0.927737i −0.463504 0.886095i $$-0.653408\pi$$
0.999133 0.0416417i $$-0.0132588\pi$$
$$660$$ 1.78042 0.0693028
$$661$$ −6.05023 3.49310i −0.235327 0.135866i 0.377700 0.925928i $$-0.376715\pi$$
−0.613027 + 0.790062i $$0.710048\pi$$
$$662$$ 16.9841 + 29.4173i 0.660105 + 1.14333i
$$663$$ −21.8349 + 52.8752i −0.847996 + 2.05350i
$$664$$ −6.85019 −0.265839
$$665$$ 0 0
$$666$$ 0.854479 + 1.48000i 0.0331104 + 0.0573488i
$$667$$ 3.33148 + 5.77029i 0.128995 + 0.223427i
$$668$$ 3.20195 1.84865i 0.123887 0.0715263i
$$669$$ 49.6646i 1.92014i
$$670$$ −26.2731 + 15.1688i −1.01502 + 0.586022i
$$671$$ 9.74849i 0.376336i
$$672$$ 0 0
$$673$$ 2.72783 + 4.72474i 0.105150 + 0.182125i 0.913800 0.406166i $$-0.133134\pi$$
−0.808649 + 0.588291i $$0.799801\pi$$
$$674$$ 43.2909i 1.66750i
$$675$$ 14.2376 + 24.6603i 0.548006 + 0.949174i
$$676$$ 2.38905 0.645671i 0.0918866 0.0248335i
$$677$$ 16.8961 29.2649i 0.649371 1.12474i −0.333903 0.942607i $$-0.608366\pi$$
0.983273 0.182135i $$-0.0583009\pi$$
$$678$$ 15.6016 9.00761i 0.599177 0.345935i
$$679$$ 0 0
$$680$$ −40.6795 + 70.4590i −1.55999 + 2.70198i
$$681$$ 27.2979 + 15.7605i 1.04606 + 0.603942i
$$682$$ 8.86231i 0.339355i
$$683$$ 12.2988i 0.470602i −0.971923 0.235301i $$-0.924392\pi$$
0.971923 0.235301i $$-0.0756076\pi$$
$$684$$ 0.187187 + 0.108072i 0.00715726 + 0.00413225i
$$685$$ −31.4514 + 54.4754i −1.20170 + 2.08140i
$$686$$ 0 0
$$687$$ 29.0311 16.7611i 1.10760 0.639476i
$$688$$ −6.86265 + 11.8865i −0.261636 + 0.453167i
$$689$$ −0.175823 0.228627i −0.00669834 0.00870998i
$$690$$ −8.10410 14.0367i −0.308518 0.534369i
$$691$$ 11.0897i 0.421871i 0.977500 + 0.210935i $$0.0676509\pi$$
−0.977500 + 0.210935i $$0.932349\pi$$
$$692$$ −1.36869 2.37064i −0.0520297 0.0901181i
$$693$$ 0 0
$$694$$ 33.3129i 1.26454i
$$695$$ 18.0972 10.4484i 0.686465 0.396331i
$$696$$ 24.4337i 0.926156i
$$697$$ 28.1419 16.2478i 1.06595 0.615428i
$$698$$ −7.77247 13.4623i −0.294193 0.509556i
$$699$$ 29.8400 + 51.6844i 1.12865 + 1.95488i
$$700$$ 0 0
$$701$$ 10.6470 0.402133 0.201066 0.979578i $$-0.435559\pi$$
0.201066 + 0.979578i $$0.435559\pi$$
$$702$$ 2.35153 + 17.7140i 0.0887526 + 0.668571i
$$703$$ 0.498406 + 0.863265i 0.0187977 + 0.0325587i
$$704$$ 9.53396 + 5.50443i 0.359325 + 0.207456i
$$705$$ 6.54058 0.246333
$$706$$ 13.5117 23.4030i 0.508521 0.880784i
$$707$$ 0 0
$$708$$ −3.78027 2.18254i −0.142071 0.0820248i
$$709$$ 35.2532 20.3535i 1.32396 0.764391i 0.339605 0.940568i $$-0.389707\pi$$
0.984358 + 0.176178i $$0.0563733\pi$$
$$710$$ −47.4833 + 27.4145i −1.78202 + 1.02885i
$$711$$ −3.43472 −0.128812
$$712$$ 22.3237 0.836618
$$713$$ 7.35003 4.24354i 0.275261 0.158922i
$$714$$ 0 0
$$715$$ −10.0273 13.0387i −0.375001 0.487621i
$$716$$ 0.516470 0.894552i 0.0193014 0.0334310i
$$717$$ −15.3648 8.87089i −0.573810 0.331290i
$$718$$ 10.1235 17.5344i 0.377806 0.654380i
$$719$$ 4.88769 + 8.46572i 0.182280 + 0.315718i 0.942657 0.333764i $$-0.108319\pi$$
−0.760377 + 0.649482i $$0.774986\pi$$
$$720$$ 15.3775i 0.573086i
$$721$$ 0 0
$$722$$ 21.0971 + 12.1804i 0.785153 + 0.453308i
$$723$$ −32.3098 18.6541i −1.20161 0.693752i
$$724$$ 2.94881 0.109592
$$725$$ 15.6313 27.0743i 0.580533 1.00551i
$$726$$ 25.8273i 0.958540i
$$727$$ 12.2091 0.452811 0.226406 0.974033i $$-0.427303\pi$$
0.226406 + 0.974033i $$0.427303\pi$$
$$728$$ 0 0
$$729$$ 9.23219 0.341933
$$730$$ 3.65002i 0.135093i
$$731$$ 14.8231 25.6743i 0.548251 0.949598i
$$732$$ −2.97539 −0.109974
$$733$$ 19.3256 + 11.1577i 0.713809 + 0.412118i 0.812470 0.583003i $$-0.198123\pi$$
−0.0986608 + 0.995121i $$0.531456\pi$$
$$734$$ −10.4891 6.05591i −0.387161 0.223528i
$$735$$ 0 0
$$736$$ 1.76768i 0.0651576i
$$737$$ −4.04126 6.99968i −0.148862 0.257836i
$$738$$ −3.39728 + 5.88426i −0.125056 + 0.216603i
$$739$$ −36.6960 21.1865i −1.34989 0.779357i −0.361653 0.932313i $$-0.617787\pi$$
−0.988233 + 0.152956i $$0.951121\pi$$
$$740$$ −0.358637 + 0.621178i −0.0131838 + 0.0228350i
$$741$$ −0.918130 6.91624i −0.0337283 0.254074i
$$742$$ 0 0
$$743$$ −26.8296 + 15.4901i −0.984282 + 0.568276i −0.903560 0.428461i $$-0.859056\pi$$
−0.0807220 + 0.996737i $$0.525723\pi$$
$$744$$ 31.1229 1.14102
$$745$$ −37.3866 −1.36974
$$746$$ 18.8020 10.8553i 0.688390 0.397442i
$$747$$ −2.42192 + 1.39830i −0.0886133 + 0.0511609i
$$748$$ −1.63146 0.941923i −0.0596520 0.0344401i
$$749$$ 0 0
$$750$$ −13.4260 + 23.2545i −0.490248 + 0.849135i
$$751$$ −22.5660 −0.823444 −0.411722 0.911309i $$-0.635073\pi$$
−0.411722 + 0.911309i $$0.635073\pi$$
$$752$$ 2.77475 + 1.60200i 0.101185 + 0.0584190i
$$753$$ 16.2696 + 28.1798i 0.592897 + 1.02693i
$$754$$ 15.5516 11.9598i 0.566356 0.435551i
$$755$$ 16.8187 0.612095
$$756$$ 0 0
$$757$$ −16.1404 27.9560i −0.586633 1.01608i −0.994670 0.103112i $$-0.967120\pi$$
0.408037 0.912965i $$-0.366213\pi$$
$$758$$ 10.5368 + 18.2504i 0.382716 + 0.662883i
$$759$$ 3.73966 2.15909i 0.135741 0.0783701i
$$760$$ 9.92260i 0.359931i
$$761$$ 25.7657 14.8758i 0.934006 0.539249i 0.0459296 0.998945i $$-0.485375\pi$$
0.888076 + 0.459696i $$0.152042\pi$$
$$762$$ 40.5855i 1.47026i
$$763$$ 0 0
$$764$$ −0.451761 0.782473i −0.0163441 0.0283089i
$$765$$ 33.2148i 1.20088i
$$766$$ 16.5684 + 28.6972i 0.598639 + 1.03687i
$$767$$ 5.30687 + 39.9764i 0.191620 + 1.44347i
$$768$$ −4.63947 + 8.03581i −0.167413 + 0.289967i
$$769$$ 36.2090 20.9053i 1.30573 0.753863i 0.324349 0.945938i $$-0.394855\pi$$
0.981380 + 0.192075i $$0.0615215\pi$$
$$770$$ 0 0
$$771$$ −24.9361 + 43.1907i −0.898053 + 1.55547i
$$772$$ 3.46856 + 2.00257i 0.124836 + 0.0720742i
$$773$$ 41.4336i 1.49026i −0.666917 0.745132i $$-0.732387\pi$$
0.666917 0.745132i $$-0.267613\pi$$
$$774$$ 6.19877i 0.222810i
$$775$$ −34.4864 19.9107i −1.23879 0.715215i
$$776$$ 0.705044 1.22117i 0.0253096 0.0438375i
$$777$$ 0 0
$$778$$ −21.9680 + 12.6832i −0.787592 + 0.454716i
$$779$$ −1.98159 + 3.43221i −0.0709978 + 0.122972i
$$780$$ 3.97963 3.06050i 0.142493 0.109583i
$$781$$ −7.30376 12.6505i −0.261349 0.452670i
$$782$$