# Properties

 Label 300.2.e.e.251.7 Level $300$ Weight $2$ Character 300.251 Analytic conductor $2.396$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$300 = 2^{2} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 300.e (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.39551206064$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.4521217600.1 Defining polynomial: $$x^{8} + x^{6} - 2 x^{4} + 4 x^{2} + 16$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 251.7 Root $$-1.29437 - 0.569745i$$ of defining polynomial Character $$\chi$$ $$=$$ 300.251 Dual form 300.2.e.e.251.8

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.29437 - 0.569745i) q^{2} +(0.908080 + 1.47492i) q^{3} +(1.35078 - 1.47492i) q^{4} +(2.01572 + 1.39172i) q^{6} -2.50967i q^{7} +(0.908080 - 2.67869i) q^{8} +(-1.35078 + 2.67869i) q^{9} +O(q^{10})$$ $$q+(1.29437 - 0.569745i) q^{2} +(0.908080 + 1.47492i) q^{3} +(1.35078 - 1.47492i) q^{4} +(2.01572 + 1.39172i) q^{6} -2.50967i q^{7} +(0.908080 - 2.67869i) q^{8} +(-1.35078 + 2.67869i) q^{9} +3.36131 q^{11} +(3.40201 + 0.652949i) q^{12} -3.70156 q^{13} +(-1.42987 - 3.24844i) q^{14} +(-0.350781 - 3.98459i) q^{16} +7.63636i q^{17} +(-0.222237 + 4.23682i) q^{18} +0.440172i q^{19} +(3.70156 - 2.27898i) q^{21} +(4.35078 - 1.91509i) q^{22} -5.17748 q^{23} +(4.77547 - 1.09312i) q^{24} +(-4.79119 + 2.10895i) q^{26} +(-5.17748 + 0.440172i) q^{27} +(-3.70156 - 3.39001i) q^{28} +2.27898i q^{29} -3.39001i q^{31} +(-2.72424 - 4.95767i) q^{32} +(3.05234 + 4.95767i) q^{33} +(4.35078 + 9.88427i) q^{34} +(2.12625 + 5.61062i) q^{36} -7.40312 q^{37} +(0.250786 + 0.569745i) q^{38} +(-3.36131 - 5.45951i) q^{39} -3.07840i q^{41} +(3.49275 - 5.05879i) q^{42} -8.40935i q^{43} +(4.54040 - 4.95767i) q^{44} +(-6.70156 + 2.94984i) q^{46} +3.63232 q^{47} +(5.55842 - 4.13570i) q^{48} +0.701562 q^{49} +(-11.2630 + 6.93443i) q^{51} +(-5.00000 + 5.45951i) q^{52} -2.27898i q^{53} +(-6.45078 + 3.51959i) q^{54} +(-6.72263 - 2.27898i) q^{56} +(-0.649219 + 0.399712i) q^{57} +(1.29844 + 2.94984i) q^{58} -5.70156 q^{61} +(-1.93144 - 4.38793i) q^{62} +(6.72263 + 3.39001i) q^{63} +(-6.35078 - 4.86493i) q^{64} +(6.77547 + 4.67800i) q^{66} +5.45951i q^{67} +(11.2630 + 10.3151i) q^{68} +(-4.70156 - 7.63636i) q^{69} +12.4421 q^{71} +(5.94877 + 6.05079i) q^{72} +1.29844 q^{73} +(-9.58237 + 4.21789i) q^{74} +(0.649219 + 0.594576i) q^{76} -8.43579i q^{77} +(-7.46131 - 5.15153i) q^{78} +5.01934i q^{79} +(-5.35078 - 7.23665i) q^{81} +(-1.75391 - 3.98459i) q^{82} +1.81616 q^{83} +(1.63869 - 8.53791i) q^{84} +(-4.79119 - 10.8848i) q^{86} +(-3.36131 + 2.06950i) q^{87} +(3.05234 - 9.00393i) q^{88} +5.35738i q^{89} +9.28970i q^{91} +(-6.99364 + 7.63636i) q^{92} +(5.00000 - 3.07840i) q^{93} +(4.70156 - 2.06950i) q^{94} +(4.83834 - 8.52000i) q^{96} +11.1047 q^{97} +(0.908080 - 0.399712i) q^{98} +(-4.54040 + 9.00393i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 2q^{4} + 3q^{6} + 2q^{9} + O(q^{10})$$ $$8q - 2q^{4} + 3q^{6} + 2q^{9} + 11q^{12} - 4q^{13} + 10q^{16} - 7q^{18} + 4q^{21} + 22q^{22} + 13q^{24} - 4q^{28} - 14q^{33} + 22q^{34} - 21q^{36} - 8q^{37} - 36q^{42} - 28q^{46} + 15q^{48} - 20q^{49} - 40q^{52} - 28q^{54} - 18q^{57} + 36q^{58} - 20q^{61} - 38q^{64} + 29q^{66} - 12q^{69} + 51q^{72} + 36q^{73} + 18q^{76} - 22q^{78} - 30q^{81} + 50q^{82} + 40q^{84} - 14q^{88} + 40q^{93} + 12q^{94} - 39q^{96} + 12q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$151$$ $$277$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.29437 0.569745i 0.915257 0.402871i
$$3$$ 0.908080 + 1.47492i 0.524280 + 0.851546i
$$4$$ 1.35078 1.47492i 0.675391 0.737460i
$$5$$ 0 0
$$6$$ 2.01572 + 1.39172i 0.822914 + 0.568166i
$$7$$ 2.50967i 0.948566i −0.880373 0.474283i $$-0.842707\pi$$
0.880373 0.474283i $$-0.157293\pi$$
$$8$$ 0.908080 2.67869i 0.321055 0.947061i
$$9$$ −1.35078 + 2.67869i −0.450260 + 0.892897i
$$10$$ 0 0
$$11$$ 3.36131 1.01347 0.506737 0.862101i $$-0.330851\pi$$
0.506737 + 0.862101i $$0.330851\pi$$
$$12$$ 3.40201 + 0.652949i 0.982075 + 0.188490i
$$13$$ −3.70156 −1.02663 −0.513314 0.858201i $$-0.671582\pi$$
−0.513314 + 0.858201i $$0.671582\pi$$
$$14$$ −1.42987 3.24844i −0.382149 0.868181i
$$15$$ 0 0
$$16$$ −0.350781 3.98459i −0.0876953 0.996147i
$$17$$ 7.63636i 1.85209i 0.377413 + 0.926045i $$0.376814\pi$$
−0.377413 + 0.926045i $$0.623186\pi$$
$$18$$ −0.222237 + 4.23682i −0.0523818 + 0.998627i
$$19$$ 0.440172i 0.100982i 0.998725 + 0.0504912i $$0.0160787\pi$$
−0.998725 + 0.0504912i $$0.983921\pi$$
$$20$$ 0 0
$$21$$ 3.70156 2.27898i 0.807747 0.497314i
$$22$$ 4.35078 1.91509i 0.927590 0.408299i
$$23$$ −5.17748 −1.07958 −0.539789 0.841800i $$-0.681496\pi$$
−0.539789 + 0.841800i $$0.681496\pi$$
$$24$$ 4.77547 1.09312i 0.974788 0.223132i
$$25$$ 0 0
$$26$$ −4.79119 + 2.10895i −0.939629 + 0.413599i
$$27$$ −5.17748 + 0.440172i −0.996406 + 0.0847112i
$$28$$ −3.70156 3.39001i −0.699529 0.640652i
$$29$$ 2.27898i 0.423196i 0.977357 + 0.211598i $$0.0678668\pi$$
−0.977357 + 0.211598i $$0.932133\pi$$
$$30$$ 0 0
$$31$$ 3.39001i 0.608864i −0.952534 0.304432i $$-0.901533\pi$$
0.952534 0.304432i $$-0.0984667\pi$$
$$32$$ −2.72424 4.95767i −0.481582 0.876401i
$$33$$ 3.05234 + 4.95767i 0.531345 + 0.863020i
$$34$$ 4.35078 + 9.88427i 0.746153 + 1.69514i
$$35$$ 0 0
$$36$$ 2.12625 + 5.61062i 0.354375 + 0.935104i
$$37$$ −7.40312 −1.21707 −0.608533 0.793529i $$-0.708242\pi$$
−0.608533 + 0.793529i $$0.708242\pi$$
$$38$$ 0.250786 + 0.569745i 0.0406828 + 0.0924249i
$$39$$ −3.36131 5.45951i −0.538241 0.874221i
$$40$$ 0 0
$$41$$ 3.07840i 0.480766i −0.970678 0.240383i $$-0.922727\pi$$
0.970678 0.240383i $$-0.0772730\pi$$
$$42$$ 3.49275 5.05879i 0.538943 0.780588i
$$43$$ 8.40935i 1.28241i −0.767368 0.641207i $$-0.778434\pi$$
0.767368 0.641207i $$-0.221566\pi$$
$$44$$ 4.54040 4.95767i 0.684491 0.747397i
$$45$$ 0 0
$$46$$ −6.70156 + 2.94984i −0.988091 + 0.434930i
$$47$$ 3.63232 0.529828 0.264914 0.964272i $$-0.414656\pi$$
0.264914 + 0.964272i $$0.414656\pi$$
$$48$$ 5.55842 4.13570i 0.802288 0.596937i
$$49$$ 0.701562 0.100223
$$50$$ 0 0
$$51$$ −11.2630 + 6.93443i −1.57714 + 0.971014i
$$52$$ −5.00000 + 5.45951i −0.693375 + 0.757098i
$$53$$ 2.27898i 0.313042i −0.987675 0.156521i $$-0.949972\pi$$
0.987675 0.156521i $$-0.0500279\pi$$
$$54$$ −6.45078 + 3.51959i −0.877839 + 0.478955i
$$55$$ 0 0
$$56$$ −6.72263 2.27898i −0.898349 0.304542i
$$57$$ −0.649219 + 0.399712i −0.0859911 + 0.0529431i
$$58$$ 1.29844 + 2.94984i 0.170493 + 0.387333i
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ −5.70156 −0.730010 −0.365005 0.931006i $$-0.618933\pi$$
−0.365005 + 0.931006i $$0.618933\pi$$
$$62$$ −1.93144 4.38793i −0.245294 0.557267i
$$63$$ 6.72263 + 3.39001i 0.846972 + 0.427102i
$$64$$ −6.35078 4.86493i −0.793848 0.608117i
$$65$$ 0 0
$$66$$ 6.77547 + 4.67800i 0.834002 + 0.575822i
$$67$$ 5.45951i 0.666985i 0.942753 + 0.333493i $$0.108227\pi$$
−0.942753 + 0.333493i $$0.891773\pi$$
$$68$$ 11.2630 + 10.3151i 1.36584 + 1.25088i
$$69$$ −4.70156 7.63636i −0.566002 0.919310i
$$70$$ 0 0
$$71$$ 12.4421 1.47661 0.738304 0.674468i $$-0.235627\pi$$
0.738304 + 0.674468i $$0.235627\pi$$
$$72$$ 5.94877 + 6.05079i 0.701070 + 0.713093i
$$73$$ 1.29844 0.151971 0.0759853 0.997109i $$-0.475790\pi$$
0.0759853 + 0.997109i $$0.475790\pi$$
$$74$$ −9.58237 + 4.21789i −1.11393 + 0.490320i
$$75$$ 0 0
$$76$$ 0.649219 + 0.594576i 0.0744705 + 0.0682026i
$$77$$ 8.43579i 0.961347i
$$78$$ −7.46131 5.15153i −0.844827 0.583296i
$$79$$ 5.01934i 0.564720i 0.959309 + 0.282360i $$0.0911172\pi$$
−0.959309 + 0.282360i $$0.908883\pi$$
$$80$$ 0 0
$$81$$ −5.35078 7.23665i −0.594531 0.804073i
$$82$$ −1.75391 3.98459i −0.193686 0.440024i
$$83$$ 1.81616 0.199349 0.0996747 0.995020i $$-0.468220\pi$$
0.0996747 + 0.995020i $$0.468220\pi$$
$$84$$ 1.63869 8.53791i 0.178795 0.931563i
$$85$$ 0 0
$$86$$ −4.79119 10.8848i −0.516647 1.17374i
$$87$$ −3.36131 + 2.06950i −0.360371 + 0.221873i
$$88$$ 3.05234 9.00393i 0.325381 0.959822i
$$89$$ 5.35738i 0.567882i 0.958842 + 0.283941i $$0.0916419\pi$$
−0.958842 + 0.283941i $$0.908358\pi$$
$$90$$ 0 0
$$91$$ 9.28970i 0.973825i
$$92$$ −6.99364 + 7.63636i −0.729137 + 0.796146i
$$93$$ 5.00000 3.07840i 0.518476 0.319216i
$$94$$ 4.70156 2.06950i 0.484929 0.213452i
$$95$$ 0 0
$$96$$ 4.83834 8.52000i 0.493811 0.869569i
$$97$$ 11.1047 1.12751 0.563755 0.825942i $$-0.309356\pi$$
0.563755 + 0.825942i $$0.309356\pi$$
$$98$$ 0.908080 0.399712i 0.0917299 0.0403770i
$$99$$ −4.54040 + 9.00393i −0.456327 + 0.904929i
$$100$$ 0 0
$$101$$ 17.5517i 1.74646i 0.487308 + 0.873230i $$0.337979\pi$$
−0.487308 + 0.873230i $$0.662021\pi$$
$$102$$ −10.6277 + 15.3928i −1.05229 + 1.52411i
$$103$$ 10.9190i 1.07588i 0.842982 + 0.537941i $$0.180798\pi$$
−0.842982 + 0.537941i $$0.819202\pi$$
$$104$$ −3.36131 + 9.91534i −0.329604 + 0.972280i
$$105$$ 0 0
$$106$$ −1.29844 2.94984i −0.126115 0.286514i
$$107$$ 6.45162 0.623702 0.311851 0.950131i $$-0.399051\pi$$
0.311851 + 0.950131i $$0.399051\pi$$
$$108$$ −6.34442 + 8.23094i −0.610492 + 0.792023i
$$109$$ 2.29844 0.220150 0.110075 0.993923i $$-0.464891\pi$$
0.110075 + 0.993923i $$0.464891\pi$$
$$110$$ 0 0
$$111$$ −6.72263 10.9190i −0.638084 1.03639i
$$112$$ −10.0000 + 0.880344i −0.944911 + 0.0831847i
$$113$$ 0.799423i 0.0752034i 0.999293 + 0.0376017i $$0.0119718\pi$$
−0.999293 + 0.0376017i $$0.988028\pi$$
$$114$$ −0.612595 + 0.887263i −0.0573748 + 0.0830998i
$$115$$ 0 0
$$116$$ 3.36131 + 3.07840i 0.312090 + 0.285823i
$$117$$ 5.00000 9.91534i 0.462250 0.916674i
$$118$$ 0 0
$$119$$ 19.1647 1.75683
$$120$$ 0 0
$$121$$ 0.298438 0.0271307
$$122$$ −7.37992 + 3.24844i −0.668147 + 0.294100i
$$123$$ 4.54040 2.79544i 0.409394 0.252056i
$$124$$ −5.00000 4.57917i −0.449013 0.411221i
$$125$$ 0 0
$$126$$ 10.6330 + 0.557742i 0.947263 + 0.0496876i
$$127$$ 12.6797i 1.12514i −0.826749 0.562571i $$-0.809812\pi$$
0.826749 0.562571i $$-0.190188\pi$$
$$128$$ −10.9920 2.67869i −0.971567 0.236765i
$$129$$ 12.4031 7.63636i 1.09203 0.672344i
$$130$$ 0 0
$$131$$ −5.71949 −0.499714 −0.249857 0.968283i $$-0.580384\pi$$
−0.249857 + 0.968283i $$0.580384\pi$$
$$132$$ 11.4352 + 2.19477i 0.995308 + 0.191030i
$$133$$ 1.10469 0.0957885
$$134$$ 3.11053 + 7.06662i 0.268709 + 0.610463i
$$135$$ 0 0
$$136$$ 20.4555 + 6.93443i 1.75404 + 0.594623i
$$137$$ 9.91534i 0.847125i −0.905867 0.423563i $$-0.860779\pi$$
0.905867 0.423563i $$-0.139221\pi$$
$$138$$ −10.4363 7.20558i −0.888400 0.613380i
$$139$$ 2.94984i 0.250202i −0.992144 0.125101i $$-0.960074\pi$$
0.992144 0.125101i $$-0.0399255\pi$$
$$140$$ 0 0
$$141$$ 3.29844 + 5.35738i 0.277779 + 0.451173i
$$142$$ 16.1047 7.08883i 1.35148 0.594882i
$$143$$ −12.4421 −1.04046
$$144$$ 11.1473 + 4.44267i 0.928943 + 0.370223i
$$145$$ 0 0
$$146$$ 1.68066 0.739779i 0.139092 0.0612245i
$$147$$ 0.637075 + 1.03475i 0.0525450 + 0.0853446i
$$148$$ −10.0000 + 10.9190i −0.821995 + 0.897538i
$$149$$ 15.2727i 1.25119i −0.780148 0.625595i $$-0.784856\pi$$
0.780148 0.625595i $$-0.215144\pi$$
$$150$$ 0 0
$$151$$ 19.3284i 1.57292i −0.617641 0.786460i $$-0.711911\pi$$
0.617641 0.786460i $$-0.288089\pi$$
$$152$$ 1.17909 + 0.399712i 0.0956365 + 0.0324209i
$$153$$ −20.4555 10.3151i −1.65373 0.833923i
$$154$$ −4.80625 10.9190i −0.387299 0.879880i
$$155$$ 0 0
$$156$$ −12.5927 2.41693i −1.00823 0.193509i
$$157$$ 11.1047 0.886250 0.443125 0.896460i $$-0.353870\pi$$
0.443125 + 0.896460i $$0.353870\pi$$
$$158$$ 2.85974 + 6.49687i 0.227509 + 0.516864i
$$159$$ 3.36131 2.06950i 0.266570 0.164122i
$$160$$ 0 0
$$161$$ 12.9937i 1.02405i
$$162$$ −11.0489 6.31832i −0.868086 0.496414i
$$163$$ 0.440172i 0.0344769i −0.999851 0.0172385i $$-0.994513\pi$$
0.999851 0.0172385i $$-0.00548745\pi$$
$$164$$ −4.54040 4.15825i −0.354546 0.324705i
$$165$$ 0 0
$$166$$ 2.35078 1.03475i 0.182456 0.0803120i
$$167$$ 15.5324 1.20194 0.600968 0.799273i $$-0.294782\pi$$
0.600968 + 0.799273i $$0.294782\pi$$
$$168$$ −2.74337 11.9848i −0.211656 0.924651i
$$169$$ 0.701562 0.0539663
$$170$$ 0 0
$$171$$ −1.17909 0.594576i −0.0901669 0.0454684i
$$172$$ −12.4031 11.3592i −0.945729 0.866130i
$$173$$ 8.43579i 0.641361i −0.947187 0.320681i $$-0.896088\pi$$
0.947187 0.320681i $$-0.103912\pi$$
$$174$$ −3.17170 + 4.59378i −0.240446 + 0.348254i
$$175$$ 0 0
$$176$$ −1.17909 13.3935i −0.0888769 1.00957i
$$177$$ 0 0
$$178$$ 3.05234 + 6.93443i 0.228783 + 0.519758i
$$179$$ −9.08080 −0.678731 −0.339365 0.940655i $$-0.610212\pi$$
−0.339365 + 0.940655i $$0.610212\pi$$
$$180$$ 0 0
$$181$$ 10.5078 0.781039 0.390520 0.920595i $$-0.372295\pi$$
0.390520 + 0.920595i $$0.372295\pi$$
$$182$$ 5.29276 + 12.0243i 0.392325 + 0.891300i
$$183$$ −5.17748 8.40935i −0.382730 0.621637i
$$184$$ −4.70156 + 13.8689i −0.346604 + 1.02243i
$$185$$ 0 0
$$186$$ 4.71794 6.83331i 0.345936 0.501043i
$$187$$ 25.6682i 1.87705i
$$188$$ 4.90647 5.35738i 0.357841 0.390727i
$$189$$ 1.10469 + 12.9937i 0.0803541 + 0.945156i
$$190$$ 0 0
$$191$$ 12.4421 0.900280 0.450140 0.892958i $$-0.351374\pi$$
0.450140 + 0.892958i $$0.351374\pi$$
$$192$$ 1.40837 13.7846i 0.101641 0.994821i
$$193$$ 19.8062 1.42568 0.712842 0.701324i $$-0.247407\pi$$
0.712842 + 0.701324i $$0.247407\pi$$
$$194$$ 14.3736 6.32684i 1.03196 0.454241i
$$195$$ 0 0
$$196$$ 0.947657 1.03475i 0.0676898 0.0739106i
$$197$$ 10.7148i 0.763396i 0.924287 + 0.381698i $$0.124660\pi$$
−0.924287 + 0.381698i $$0.875340\pi$$
$$198$$ −0.747009 + 14.2413i −0.0530876 + 1.01208i
$$199$$ 21.0891i 1.49496i −0.664282 0.747482i $$-0.731263\pi$$
0.664282 0.747482i $$-0.268737\pi$$
$$200$$ 0 0
$$201$$ −8.05234 + 4.95767i −0.567968 + 0.349687i
$$202$$ 10.0000 + 22.7184i 0.703598 + 1.59846i
$$203$$ 5.71949 0.401429
$$204$$ −4.98615 + 25.9790i −0.349101 + 1.81889i
$$205$$ 0 0
$$206$$ 6.22106 + 14.1332i 0.433442 + 0.984709i
$$207$$ 6.99364 13.8689i 0.486091 0.963952i
$$208$$ 1.29844 + 14.7492i 0.0900305 + 1.02267i
$$209$$ 1.47956i 0.102343i
$$210$$ 0 0
$$211$$ 18.1392i 1.24876i 0.781123 + 0.624378i $$0.214647\pi$$
−0.781123 + 0.624378i $$0.785353\pi$$
$$212$$ −3.36131 3.07840i −0.230856 0.211426i
$$213$$ 11.2984 + 18.3511i 0.774156 + 1.25740i
$$214$$ 8.35078 3.67578i 0.570848 0.251271i
$$215$$ 0 0
$$216$$ −3.52248 + 14.2686i −0.239674 + 0.970853i
$$217$$ −8.50781 −0.577548
$$218$$ 2.97503 1.30952i 0.201494 0.0886921i
$$219$$ 1.17909 + 1.91509i 0.0796752 + 0.129410i
$$220$$ 0 0
$$221$$ 28.2665i 1.90141i
$$222$$ −14.9226 10.3031i −1.00154 0.691496i
$$223$$ 21.0891i 1.41223i 0.708098 + 0.706114i $$0.249553\pi$$
−0.708098 + 0.706114i $$0.750447\pi$$
$$224$$ −12.4421 + 6.83694i −0.831324 + 0.456812i
$$225$$ 0 0
$$226$$ 0.455467 + 1.03475i 0.0302972 + 0.0688304i
$$227$$ −22.2551 −1.47712 −0.738560 0.674188i $$-0.764494\pi$$
−0.738560 + 0.674188i $$0.764494\pi$$
$$228$$ −0.287410 + 1.49747i −0.0190342 + 0.0991723i
$$229$$ 2.29844 0.151885 0.0759425 0.997112i $$-0.475803\pi$$
0.0759425 + 0.997112i $$0.475803\pi$$
$$230$$ 0 0
$$231$$ 12.4421 7.66037i 0.818631 0.504015i
$$232$$ 6.10469 + 2.06950i 0.400792 + 0.135869i
$$233$$ 8.43579i 0.552647i −0.961065 0.276323i $$-0.910884\pi$$
0.961065 0.276323i $$-0.0891161\pi$$
$$234$$ 0.822625 15.6828i 0.0537767 1.02522i
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −7.40312 + 4.55796i −0.480885 + 0.296071i
$$238$$ 24.8062 10.9190i 1.60795 0.707775i
$$239$$ −25.8874 −1.67452 −0.837258 0.546809i $$-0.815842\pi$$
−0.837258 + 0.546809i $$0.815842\pi$$
$$240$$ 0 0
$$241$$ 7.00000 0.450910 0.225455 0.974254i $$-0.427613\pi$$
0.225455 + 0.974254i $$0.427613\pi$$
$$242$$ 0.386289 0.170034i 0.0248316 0.0109302i
$$243$$ 5.81455 14.4634i 0.373004 0.927830i
$$244$$ −7.70156 + 8.40935i −0.493042 + 0.538354i
$$245$$ 0 0
$$246$$ 4.28427 6.20520i 0.273155 0.395629i
$$247$$ 1.62932i 0.103671i
$$248$$ −9.08080 3.07840i −0.576631 0.195479i
$$249$$ 1.64922 + 2.67869i 0.104515 + 0.169755i
$$250$$ 0 0
$$251$$ −22.5261 −1.42183 −0.710916 0.703277i $$-0.751719\pi$$
−0.710916 + 0.703277i $$0.751719\pi$$
$$252$$ 14.0808 5.33618i 0.887007 0.336148i
$$253$$ −17.4031 −1.09413
$$254$$ −7.22420 16.4122i −0.453287 1.02979i
$$255$$ 0 0
$$256$$ −15.7539 + 2.79544i −0.984619 + 0.174715i
$$257$$ 4.55796i 0.284318i 0.989844 + 0.142159i $$0.0454044\pi$$
−0.989844 + 0.142159i $$0.954596\pi$$
$$258$$ 11.7034 16.9509i 0.728624 1.05532i
$$259$$ 18.5794i 1.15447i
$$260$$ 0 0
$$261$$ −6.10469 3.07840i −0.377871 0.190548i
$$262$$ −7.40312 + 3.25865i −0.457367 + 0.201320i
$$263$$ 18.6227 1.14833 0.574164 0.818741i $$-0.305327\pi$$
0.574164 + 0.818741i $$0.305327\pi$$
$$264$$ 16.0518 3.67432i 0.987923 0.226139i
$$265$$ 0 0
$$266$$ 1.42987 0.629390i 0.0876710 0.0385904i
$$267$$ −7.90172 + 4.86493i −0.483577 + 0.297729i
$$268$$ 8.05234 + 7.37460i 0.491875 + 0.450476i
$$269$$ 8.43579i 0.514339i 0.966366 + 0.257170i $$0.0827899\pi$$
−0.966366 + 0.257170i $$0.917210\pi$$
$$270$$ 0 0
$$271$$ 9.15833i 0.556329i 0.960533 + 0.278165i $$0.0897260\pi$$
−0.960533 + 0.278165i $$0.910274\pi$$
$$272$$ 30.4278 2.67869i 1.84495 0.162420i
$$273$$ −13.7016 + 8.43579i −0.829256 + 0.510557i
$$274$$ −5.64922 12.8341i −0.341282 0.775337i
$$275$$ 0 0
$$276$$ −17.6138 3.38063i −1.06023 0.203490i
$$277$$ −8.89531 −0.534468 −0.267234 0.963632i $$-0.586110\pi$$
−0.267234 + 0.963632i $$0.586110\pi$$
$$278$$ −1.68066 3.81818i −0.100799 0.228999i
$$279$$ 9.08080 + 4.57917i 0.543653 + 0.274147i
$$280$$ 0 0
$$281$$ 17.5517i 1.04705i −0.852011 0.523524i $$-0.824617\pi$$
0.852011 0.523524i $$-0.175383\pi$$
$$282$$ 7.32174 + 5.05516i 0.436003 + 0.301030i
$$283$$ 16.3785i 0.973603i −0.873513 0.486801i $$-0.838164\pi$$
0.873513 0.486801i $$-0.161836\pi$$
$$284$$ 16.8066 18.3511i 0.997287 1.08894i
$$285$$ 0 0
$$286$$ −16.1047 + 7.08883i −0.952290 + 0.419172i
$$287$$ −7.72577 −0.456038
$$288$$ 16.9599 0.600671i 0.999373 0.0353949i
$$289$$ −41.3141 −2.43024
$$290$$ 0 0
$$291$$ 10.0839 + 16.3785i 0.591131 + 0.960126i
$$292$$ 1.75391 1.91509i 0.102640 0.112072i
$$293$$ 21.4295i 1.25193i 0.779852 + 0.625963i $$0.215294\pi$$
−0.779852 + 0.625963i $$0.784706\pi$$
$$294$$ 1.41415 + 0.976376i 0.0824750 + 0.0569434i
$$295$$ 0 0
$$296$$ −6.72263 + 19.8307i −0.390745 + 1.15264i
$$297$$ −17.4031 + 1.47956i −1.00983 + 0.0858526i
$$298$$ −8.70156 19.7685i −0.504068 1.14516i
$$299$$ 19.1647 1.10833
$$300$$ 0 0
$$301$$ −21.1047 −1.21645
$$302$$ −11.0122 25.0180i −0.633683 1.43963i
$$303$$ −25.8874 + 15.9384i −1.48719 + 0.915635i
$$304$$ 1.75391 0.154404i 0.100593 0.00885568i
$$305$$ 0 0
$$306$$ −32.3539 1.69708i −1.84955 0.0970159i
$$307$$ 26.4172i 1.50771i −0.657041 0.753855i $$-0.728192\pi$$
0.657041 0.753855i $$-0.271808\pi$$
$$308$$ −12.4421 11.3949i −0.708955 0.649285i
$$309$$ −16.1047 + 9.91534i −0.916164 + 0.564064i
$$310$$ 0 0
$$311$$ −13.4453 −0.762411 −0.381205 0.924490i $$-0.624491\pi$$
−0.381205 + 0.924490i $$0.624491\pi$$
$$312$$ −17.6767 + 4.04625i −1.00075 + 0.229074i
$$313$$ 16.2984 0.921242 0.460621 0.887597i $$-0.347627\pi$$
0.460621 + 0.887597i $$0.347627\pi$$
$$314$$ 14.3736 6.32684i 0.811147 0.357044i
$$315$$ 0 0
$$316$$ 7.40312 + 6.78003i 0.416458 + 0.381406i
$$317$$ 16.8716i 0.947602i 0.880632 + 0.473801i $$0.157118\pi$$
−0.880632 + 0.473801i $$0.842882\pi$$
$$318$$ 3.17170 4.59378i 0.177860 0.257607i
$$319$$ 7.66037i 0.428898i
$$320$$ 0 0
$$321$$ 5.85859 + 9.51563i 0.326995 + 0.531111i
$$322$$ 7.40312 + 16.8187i 0.412560 + 0.937270i
$$323$$ −3.36131 −0.187029
$$324$$ −17.9012 1.88316i −0.994512 0.104620i
$$325$$ 0 0
$$326$$ −0.250786 0.569745i −0.0138897 0.0315553i
$$327$$ 2.08717 + 3.39001i 0.115421 + 0.187468i
$$328$$ −8.24609 2.79544i −0.455314 0.154352i
$$329$$ 9.11592i 0.502577i
$$330$$ 0 0
$$331$$ 17.1275i 0.941413i 0.882290 + 0.470707i $$0.156001\pi$$
−0.882290 + 0.470707i $$0.843999\pi$$
$$332$$ 2.45323 2.67869i 0.134639 0.147012i
$$333$$ 10.0000 19.8307i 0.547997 1.08672i
$$334$$ 20.1047 8.84952i 1.10008 0.484224i
$$335$$ 0 0
$$336$$ −10.3792 13.9498i −0.566234 0.761023i
$$337$$ −12.4031 −0.675641 −0.337821 0.941211i $$-0.609690\pi$$
−0.337821 + 0.941211i $$0.609690\pi$$
$$338$$ 0.908080 0.399712i 0.0493930 0.0217414i
$$339$$ −1.17909 + 0.725940i −0.0640391 + 0.0394277i
$$340$$ 0 0
$$341$$ 11.3949i 0.617069i
$$342$$ −1.86493 0.0978226i −0.100844 0.00528964i
$$343$$ 19.3284i 1.04363i
$$344$$ −22.5261 7.63636i −1.21452 0.411725i
$$345$$ 0 0
$$346$$ −4.80625 10.9190i −0.258386 0.587010i
$$347$$ −19.4358 −1.04337 −0.521683 0.853139i $$-0.674696\pi$$
−0.521683 + 0.853139i $$0.674696\pi$$
$$348$$ −1.48806 + 7.75311i −0.0797682 + 0.415610i
$$349$$ 26.2094 1.40296 0.701478 0.712691i $$-0.252524\pi$$
0.701478 + 0.712691i $$0.252524\pi$$
$$350$$ 0 0
$$351$$ 19.1647 1.62932i 1.02294 0.0869669i
$$352$$ −9.15703 16.6643i −0.488071 0.888210i
$$353$$ 26.6676i 1.41937i 0.704517 + 0.709687i $$0.251164\pi$$
−0.704517 + 0.709687i $$0.748836\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 7.90172 + 7.23665i 0.418790 + 0.383542i
$$357$$ 17.4031 + 28.2665i 0.921071 + 1.49602i
$$358$$ −11.7539 + 5.17374i −0.621213 + 0.273441i
$$359$$ −7.72577 −0.407751 −0.203875 0.978997i $$-0.565354\pi$$
−0.203875 + 0.978997i $$0.565354\pi$$
$$360$$ 0 0
$$361$$ 18.8062 0.989803
$$362$$ 13.6010 5.98677i 0.714852 0.314658i
$$363$$ 0.271006 + 0.440172i 0.0142241 + 0.0231030i
$$364$$ 13.7016 + 12.5483i 0.718157 + 0.657712i
$$365$$ 0 0
$$366$$ −11.4927 7.93496i −0.600736 0.414767i
$$367$$ 2.50967i 0.131004i −0.997852 0.0655018i $$-0.979135\pi$$
0.997852 0.0655018i $$-0.0208648\pi$$
$$368$$ 1.81616 + 20.6301i 0.0946739 + 1.07542i
$$369$$ 8.24609 + 4.15825i 0.429275 + 0.216470i
$$370$$ 0 0
$$371$$ −5.71949 −0.296941
$$372$$ 2.21350 11.5329i 0.114765 0.597951i
$$373$$ −23.7016 −1.22722 −0.613610 0.789609i $$-0.710283\pi$$
−0.613610 + 0.789609i $$0.710283\pi$$
$$374$$ 14.6243 + 33.2241i 0.756207 + 1.71798i
$$375$$ 0 0
$$376$$ 3.29844 9.72987i 0.170104 0.501780i
$$377$$ 8.43579i 0.434465i
$$378$$ 8.83300 + 16.1893i 0.454320 + 0.832688i
$$379$$ 13.1199i 0.673923i −0.941518 0.336961i $$-0.890601\pi$$
0.941518 0.336961i $$-0.109399\pi$$
$$380$$ 0 0
$$381$$ 18.7016 11.5142i 0.958110 0.589890i
$$382$$ 16.1047 7.08883i 0.823987 0.362696i
$$383$$ −7.26464 −0.371206 −0.185603 0.982625i $$-0.559424\pi$$
−0.185603 + 0.982625i $$0.559424\pi$$
$$384$$ −6.03078 18.6448i −0.307757 0.951465i
$$385$$ 0 0
$$386$$ 25.6366 11.2845i 1.30487 0.574367i
$$387$$ 22.5261 + 11.3592i 1.14506 + 0.577420i
$$388$$ 15.0000 16.3785i 0.761510 0.831494i
$$389$$ 37.3824i 1.89536i 0.319218 + 0.947681i $$0.396580\pi$$
−0.319218 + 0.947681i $$0.603420\pi$$
$$390$$ 0 0
$$391$$ 39.5371i 1.99948i
$$392$$ 0.637075 1.87927i 0.0321771 0.0949174i
$$393$$ −5.19375 8.43579i −0.261990 0.425529i
$$394$$ 6.10469 + 13.8689i 0.307550 + 0.698703i
$$395$$ 0 0
$$396$$ 7.14699 + 18.8591i 0.359150 + 0.947704i
$$397$$ −15.9109 −0.798547 −0.399273 0.916832i $$-0.630738\pi$$
−0.399273 + 0.916832i $$0.630738\pi$$
$$398$$ −12.0154 27.2970i −0.602277 1.36828i
$$399$$ 1.00314 + 1.62932i 0.0502200 + 0.0815683i
$$400$$ 0 0
$$401$$ 9.23521i 0.461184i 0.973050 + 0.230592i $$0.0740663\pi$$
−0.973050 + 0.230592i $$0.925934\pi$$
$$402$$ −7.59809 + 11.0048i −0.378958 + 0.548871i
$$403$$ 12.5483i 0.625078i
$$404$$ 25.8874 + 23.7085i 1.28795 + 1.17954i
$$405$$ 0 0
$$406$$ 7.40312 3.25865i 0.367411 0.161724i
$$407$$ −24.8842 −1.23347
$$408$$ 8.34747 + 36.4672i 0.413261 + 1.80540i
$$409$$ 11.2094 0.554268 0.277134 0.960831i $$-0.410615\pi$$
0.277134 + 0.960831i $$0.410615\pi$$
$$410$$ 0 0
$$411$$ 14.6243 9.00393i 0.721366 0.444131i
$$412$$ 16.1047 + 14.7492i 0.793421 + 0.726641i
$$413$$ 0 0
$$414$$ 1.15063 21.9360i 0.0565503 1.07810i
$$415$$ 0 0
$$416$$ 10.0839 + 18.3511i 0.494406 + 0.899738i
$$417$$ 4.35078 2.67869i 0.213059 0.131176i
$$418$$ 0.842970 + 1.91509i 0.0412310 + 0.0936702i
$$419$$ −34.9682 −1.70831 −0.854154 0.520021i $$-0.825924\pi$$
−0.854154 + 0.520021i $$0.825924\pi$$
$$420$$ 0 0
$$421$$ −14.2094 −0.692522 −0.346261 0.938138i $$-0.612549\pi$$
−0.346261 + 0.938138i $$0.612549\pi$$
$$422$$ 10.3347 + 23.4788i 0.503087 + 1.14293i
$$423$$ −4.90647 + 9.72987i −0.238561 + 0.473082i
$$424$$ −6.10469 2.06950i −0.296470 0.100504i
$$425$$ 0 0
$$426$$ 25.0798 + 17.3159i 1.21512 + 0.838958i
$$427$$ 14.3090i 0.692463i
$$428$$ 8.71473 9.51563i 0.421242 0.459955i
$$429$$ −11.2984 18.3511i −0.545494 0.886001i
$$430$$ 0 0
$$431$$ −5.71949 −0.275498 −0.137749 0.990467i $$-0.543987\pi$$
−0.137749 + 0.990467i $$0.543987\pi$$
$$432$$ 3.57007 + 20.4757i 0.171765 + 0.985138i
$$433$$ −7.20937 −0.346460 −0.173230 0.984881i $$-0.555420\pi$$
−0.173230 + 0.984881i $$0.555420\pi$$
$$434$$ −11.0122 + 4.84728i −0.528605 + 0.232677i
$$435$$ 0 0
$$436$$ 3.10469 3.39001i 0.148688 0.162352i
$$437$$ 2.27898i 0.109018i
$$438$$ 2.61729 + 1.80706i 0.125059 + 0.0863446i
$$439$$ 23.4674i 1.12004i −0.828480 0.560018i $$-0.810794\pi$$
0.828480 0.560018i $$-0.189206\pi$$
$$440$$ 0 0
$$441$$ −0.947657 + 1.87927i −0.0451265 + 0.0894890i
$$442$$ −16.1047 36.5872i −0.766022 1.74028i
$$443$$ 29.7907 1.41540 0.707699 0.706514i $$-0.249733\pi$$
0.707699 + 0.706514i $$0.249733\pi$$
$$444$$ −25.1855 4.83386i −1.19525 0.229405i
$$445$$ 0 0
$$446$$ 12.0154 + 27.2970i 0.568945 + 1.29255i
$$447$$ 22.5261 13.8689i 1.06545 0.655975i
$$448$$ −12.2094 + 15.9384i −0.576839 + 0.753017i
$$449$$ 29.7460i 1.40380i −0.712274 0.701901i $$-0.752335\pi$$
0.712274 0.701901i $$-0.247665\pi$$
$$450$$ 0 0
$$451$$ 10.3475i 0.487244i
$$452$$ 1.17909 + 1.07985i 0.0554595 + 0.0507917i
$$453$$ 28.5078 17.5517i 1.33941 0.824651i
$$454$$ −28.8062 + 12.6797i −1.35194 + 0.595088i
$$455$$ 0 0
$$456$$ 0.481161 + 2.10203i 0.0225324 + 0.0984365i
$$457$$ 36.1047 1.68891 0.844453 0.535630i $$-0.179926\pi$$
0.844453 + 0.535630i $$0.179926\pi$$
$$458$$ 2.97503 1.30952i 0.139014 0.0611900i
$$459$$ −3.36131 39.5371i −0.156893 1.84543i
$$460$$ 0 0
$$461$$ 17.5517i 0.817465i 0.912654 + 0.408732i $$0.134029\pi$$
−0.912654 + 0.408732i $$0.865971\pi$$
$$462$$ 11.7402 17.0042i 0.546205 0.791106i
$$463$$ 5.01934i 0.233268i −0.993175 0.116634i $$-0.962789\pi$$
0.993175 0.116634i $$-0.0372105\pi$$
$$464$$ 9.08080 0.799423i 0.421566 0.0371123i
$$465$$ 0 0
$$466$$ −4.80625 10.9190i −0.222645 0.505814i
$$467$$ 29.5197 1.36601 0.683004 0.730414i $$-0.260673\pi$$
0.683004 + 0.730414i $$0.260673\pi$$
$$468$$ −7.87044 20.7681i −0.363811 0.960004i
$$469$$ 13.7016 0.632679
$$470$$ 0 0
$$471$$ 10.0839 + 16.3785i 0.464644 + 0.754683i
$$472$$ 0 0
$$473$$ 28.2665i 1.29969i
$$474$$ −6.98550 + 10.1176i −0.320855 + 0.464716i
$$475$$ 0 0
$$476$$ 25.8874 28.2665i 1.18655 1.29559i
$$477$$ 6.10469 + 3.07840i 0.279514 + 0.140950i
$$478$$ −33.5078 + 14.7492i −1.53261 + 0.674613i
$$479$$ 33.6131 1.53582 0.767912 0.640555i $$-0.221296\pi$$
0.767912 + 0.640555i $$0.221296\pi$$
$$480$$ 0 0
$$481$$ 27.4031 1.24947
$$482$$ 9.06058 3.98822i 0.412698 0.181658i
$$483$$ −19.1647 + 11.7994i −0.872026 + 0.536890i
$$484$$ 0.403124 0.440172i 0.0183238 0.0200078i
$$485$$ 0 0
$$486$$ −0.714301 22.0338i −0.0324013 0.999475i
$$487$$ 0.131364i 0.00595267i −0.999996 0.00297634i $$-0.999053\pi$$
0.999996 0.00297634i $$-0.000947399\pi$$
$$488$$ −5.17748 + 15.2727i −0.234373 + 0.691364i
$$489$$ 0.649219 0.399712i 0.0293587 0.0180756i
$$490$$ 0 0
$$491$$ −13.4453 −0.606776 −0.303388 0.952867i $$-0.598118\pi$$
−0.303388 + 0.952867i $$0.598118\pi$$
$$492$$ 2.01004 10.4728i 0.0906196 0.472148i
$$493$$ −17.4031 −0.783797
$$494$$ −0.928300 2.10895i −0.0417662 0.0948860i
$$495$$ 0 0
$$496$$ −13.5078 + 1.18915i −0.606519 + 0.0533945i
$$497$$ 31.2256i 1.40066i
$$498$$ 3.66087 + 2.52758i 0.164047 + 0.113264i
$$499$$ 40.2861i 1.80345i 0.432308 + 0.901726i $$0.357699\pi$$
−0.432308 + 0.901726i $$0.642301\pi$$
$$500$$ 0 0
$$501$$ 14.1047 + 22.9091i 0.630151 + 1.02350i
$$502$$ −29.1570 + 12.8341i −1.30134 + 0.572814i
$$503$$ 12.9841 0.578934 0.289467 0.957188i $$-0.406522\pi$$
0.289467 + 0.957188i $$0.406522\pi$$
$$504$$ 15.1855 14.9295i 0.676415 0.665011i
$$505$$ 0 0
$$506$$ −22.5261 + 9.91534i −1.00141 + 0.440791i
$$507$$ 0.637075 + 1.03475i 0.0282935 + 0.0459548i
$$508$$ −18.7016 17.1275i −0.829748 0.759910i
$$509$$ 2.95911i 0.131160i −0.997847 0.0655802i $$-0.979110\pi$$
0.997847 0.0655802i $$-0.0208898\pi$$
$$510$$ 0 0
$$511$$ 3.25865i 0.144154i
$$512$$ −18.7987 + 12.5940i −0.830792 + 0.556583i
$$513$$ −0.193752 2.27898i −0.00855434 0.100619i
$$514$$ 2.59688 + 5.89968i 0.114543 + 0.260224i
$$515$$ 0 0
$$516$$ 5.49087 28.6087i 0.241722 1.25943i
$$517$$ 12.2094 0.536968
$$518$$ 10.5855 + 24.0486i 0.465101 + 1.05663i
$$519$$ 12.4421 7.66037i 0.546148 0.336253i
$$520$$ 0 0
$$521$$ 3.07840i 0.134867i 0.997724 + 0.0674337i $$0.0214811\pi$$
−0.997724 + 0.0674337i $$0.978519\pi$$
$$522$$ −9.65562 0.506474i −0.422615 0.0221678i
$$523$$ 14.0002i 0.612187i −0.952001 0.306094i $$-0.900978\pi$$
0.952001 0.306094i $$-0.0990220\pi$$
$$524$$ −7.72577 + 8.43579i −0.337502 + 0.368519i
$$525$$ 0 0
$$526$$ 24.1047 10.6102i 1.05101 0.462627i
$$527$$ 25.8874 1.12767
$$528$$ 18.6836 13.9014i 0.813099 0.604980i
$$529$$ 3.80625 0.165489
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 1.49219 1.62932i 0.0646946 0.0706402i
$$533$$ 11.3949i 0.493568i
$$534$$ −7.45596 + 10.7990i −0.322651 + 0.467318i
$$535$$ 0 0
$$536$$ 14.6243 + 4.95767i 0.631676 + 0.214139i
$$537$$ −8.24609 13.3935i −0.355845 0.577970i
$$538$$ 4.80625 + 10.9190i 0.207212 + 0.470752i
$$539$$ 2.35817 0.101574
$$540$$ 0 0
$$541$$ −25.7016 −1.10500 −0.552498 0.833514i $$-0.686325\pi$$
−0.552498 + 0.833514i $$0.686325\pi$$
$$542$$ 5.21791 + 11.8543i 0.224129 + 0.509184i
$$543$$ 9.54193 + 15.4982i 0.409484 + 0.665091i
$$544$$ 37.8586 20.8033i 1.62317 0.891934i
$$545$$ 0 0
$$546$$ −12.9286 + 18.7254i −0.553294 + 0.801374i
$$547$$ 4.71053i 0.201408i −0.994916 0.100704i $$-0.967891\pi$$
0.994916 0.100704i $$-0.0321095\pi$$
$$548$$ −14.6243 13.3935i −0.624721 0.572140i
$$549$$ 7.70156 15.2727i 0.328695 0.651824i
$$550$$ 0 0
$$551$$ −1.00314 −0.0427354
$$552$$ −24.7249 + 5.65961i −1.05236 + 0.240889i
$$553$$ 12.5969 0.535674
$$554$$ −11.5138 + 5.06806i −0.489175 + 0.215321i
$$555$$ 0 0
$$556$$ −4.35078 3.98459i −0.184514 0.168984i
$$557$$ 36.7023i 1.55512i −0.628806 0.777562i $$-0.716456\pi$$
0.628806 0.777562i $$-0.283544\pi$$
$$558$$ 14.3629 + 0.753387i 0.608028 + 0.0318934i
$$559$$ 31.1277i 1.31656i
$$560$$ 0 0
$$561$$ −37.8586 + 23.3088i −1.59839 + 0.984098i
$$562$$ −10.0000 22.7184i −0.421825 0.958317i
$$563$$ −23.3391 −0.983625 −0.491812 0.870701i $$-0.663665\pi$$
−0.491812 + 0.870701i $$0.663665\pi$$
$$564$$ 12.3572 + 2.37172i 0.520331 + 0.0998674i
$$565$$ 0 0
$$566$$ −9.33159 21.1999i −0.392236 0.891096i
$$567$$ −18.1616 + 13.4287i −0.762716 + 0.563952i
$$568$$ 11.2984 33.3286i 0.474072 1.39844i
$$569$$ 10.5955i 0.444186i 0.975026 + 0.222093i $$0.0712888\pi$$
−0.975026 + 0.222093i $$0.928711\pi$$
$$570$$ 0 0
$$571$$ 16.9501i 0.709338i −0.934992 0.354669i $$-0.884594\pi$$
0.934992 0.354669i $$-0.115406\pi$$
$$572$$ −16.8066 + 18.3511i −0.702718 + 0.767299i
$$573$$ 11.2984 + 18.3511i 0.471999 + 0.766630i
$$574$$ −10.0000 + 4.40172i −0.417392 + 0.183724i
$$575$$ 0 0
$$576$$ 21.6102 10.4403i 0.900424 0.435014i
$$577$$ −12.4031 −0.516349 −0.258174 0.966098i $$-0.583121\pi$$
−0.258174 + 0.966098i $$0.583121\pi$$
$$578$$ −53.4756 + 23.5385i −2.22429 + 0.979072i
$$579$$ 17.9857 + 29.2126i 0.747459 + 1.21404i
$$580$$ 0 0
$$581$$ 4.55796i 0.189096i
$$582$$ 22.3839 + 15.4546i 0.927844 + 0.640613i
$$583$$ 7.66037i 0.317260i
$$584$$ 1.17909 3.47812i 0.0487909 0.143925i
$$585$$ 0 0
$$586$$ 12.2094 + 27.7377i 0.504365 + 1.14583i
$$587$$ −31.3359 −1.29337 −0.646685 0.762758i $$-0.723845\pi$$
−0.646685 + 0.762758i $$0.723845\pi$$
$$588$$ 2.38672 + 0.458084i 0.0984267 + 0.0188911i
$$589$$ 1.49219 0.0614846
$$590$$ 0 0
$$591$$ −15.8034 + 9.72987i −0.650066 + 0.400233i
$$592$$ 2.59688 + 29.4984i 0.106731 + 1.21238i
$$593$$ 10.5955i 0.435104i −0.976049 0.217552i $$-0.930193\pi$$
0.976049 0.217552i $$-0.0698072\pi$$
$$594$$ −21.6831 + 11.8304i −0.889668 + 0.485409i
$$595$$ 0 0
$$596$$ −22.5261 20.6301i −0.922703 0.845042i
$$597$$ 31.1047 19.1506i 1.27303 0.783780i
$$598$$ 24.8062 10.9190i 1.01440 0.446512i
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ −40.0156 −1.63227 −0.816136 0.577860i $$-0.803888\pi$$
−0.816136 + 0.577860i $$0.803888\pi$$
$$602$$ −27.3172 + 12.0243i −1.11337 + 0.490074i
$$603$$ −14.6243 7.37460i −0.595549 0.300317i
$$604$$ −28.5078 26.1084i −1.15997 1.06234i
$$605$$ 0 0
$$606$$ −24.4270 + 35.3793i −0.992279 + 1.43719i
$$607$$ 3.25865i 0.132264i 0.997811 + 0.0661322i $$0.0210659\pi$$
−0.997811 + 0.0661322i $$0.978934\pi$$
$$608$$ 2.18223 1.19913i 0.0885011 0.0486313i
$$609$$ 5.19375 + 8.43579i 0.210461 + 0.341835i
$$610$$ 0 0
$$611$$ −13.4453 −0.543937
$$612$$ −42.8447 + 16.2368i −1.73190 + 0.656334i
$$613$$ 4.80625 0.194123 0.0970613 0.995278i $$-0.469056\pi$$
0.0970613 + 0.995278i $$0.469056\pi$$
$$614$$ −15.0511 34.1936i −0.607412 1.37994i
$$615$$ 0 0
$$616$$ −22.5969 7.66037i −0.910454 0.308645i
$$617$$ 22.1097i 0.890102i 0.895505 + 0.445051i $$0.146814\pi$$
−0.895505 + 0.445051i $$0.853186\pi$$
$$618$$ −15.1962 + 22.0097i −0.611280 + 0.885359i
$$619$$ 5.15070i 0.207024i −0.994628 0.103512i $$-0.966992\pi$$
0.994628 0.103512i $$-0.0330080\pi$$
$$620$$ 0 0
$$621$$ 26.8062 2.27898i 1.07570 0.0914523i
$$622$$ −17.4031 + 7.66037i −0.697802 + 0.307153i
$$623$$ 13.4453 0.538673
$$624$$ −20.5748 + 15.3086i −0.823652 + 0.612833i
$$625$$ 0 0
$$626$$ 21.0962 9.28595i 0.843173 0.371141i
$$627$$ −2.18223 + 1.34356i −0.0871498 + 0.0536565i
$$628$$ 15.0000 16.3785i 0.598565 0.653574i
$$629$$ 56.5330i 2.25412i
$$630$$ 0 0
$$631$$ 42.0468i 1.67385i 0.547314 + 0.836927i $$0.315650\pi$$
−0.547314 + 0.836927i $$0.684350\pi$$
$$632$$ 13.4453 + 4.55796i 0.534824 + 0.181306i
$$633$$ −26.7539 + 16.4719i −1.06337 + 0.654698i
$$634$$ 9.61250 + 21.8380i 0.381761 + 0.867299i
$$635$$ 0 0
$$636$$ 1.48806 7.75311i 0.0590053 0.307431i
$$637$$ −2.59688 −0.102892
$$638$$ 4.36446 + 9.91534i 0.172791 + 0.392552i
$$639$$ −16.8066 + 33.3286i −0.664858 + 1.31846i
$$640$$ 0 0
$$641$$ 12.3136i 0.486359i −0.969981 0.243179i $$-0.921810\pi$$
0.969981 0.243179i $$-0.0781903\pi$$
$$642$$ 13.0047 + 8.97883i 0.513253 + 0.354366i
$$643$$ 24.4791i 0.965360i 0.875797 + 0.482680i $$0.160337\pi$$
−0.875797 + 0.482680i $$0.839663\pi$$
$$644$$ 19.1647 + 17.5517i 0.755197 + 0.691634i
$$645$$ 0 0
$$646$$ −4.35078 + 1.91509i −0.171179 + 0.0753483i
$$647$$ −10.3550 −0.407095 −0.203548 0.979065i $$-0.565247\pi$$
−0.203548 + 0.979065i $$0.565247\pi$$
$$648$$ −24.2437 + 7.76163i −0.952383 + 0.304906i
$$649$$ 0 0
$$650$$ 0 0
$$651$$ −7.72577 12.5483i −0.302797 0.491808i
$$652$$ −0.649219 0.594576i −0.0254254 0.0232854i
$$653$$ 25.9875i 1.01697i −0.861071 0.508485i $$-0.830206\pi$$
0.861071 0.508485i $$-0.169794\pi$$
$$654$$ 4.63301 + 3.19877i 0.181165 + 0.125082i
$$655$$ 0 0
$$656$$ −12.2662 + 1.07985i −0.478914 + 0.0421609i
$$657$$ −1.75391 + 3.47812i −0.0684264 + 0.135694i
$$658$$ −5.19375 11.7994i −0.202474 0.459987i
$$659$$ 16.8066 0.654691 0.327346 0.944905i $$-0.393846\pi$$
0.327346 + 0.944905i $$0.393846\pi$$
$$660$$ 0 0
$$661$$ −18.0000 −0.700119 −0.350059 0.936727i $$-0.613839\pi$$
−0.350059 + 0.936727i $$0.613839\pi$$
$$662$$ 9.75831 + 22.1693i 0.379268 + 0.861635i
$$663$$ 41.6908 25.6682i 1.61914 0.996871i
$$664$$ 1.64922 4.86493i 0.0640021 0.188796i
$$665$$ 0 0
$$666$$ 1.64525 31.3657i 0.0637521 1.21540i
$$667$$ 11.7994i 0.456873i
$$668$$ 20.9809 22.9091i 0.811776 0.886379i
$$669$$ −31.1047 + 19.1506i −1.20258 + 0.740403i
$$670$$ 0 0
$$671$$ −19.1647 −0.739847
$$672$$ −21.3824 12.1426i −0.824843 0.468413i
$$673$$ 24.8062 0.956211 0.478105 0.878303i $$-0.341324\pi$$
0.478105 + 0.878303i $$0.341324\pi$$
$$674$$ −16.0542 + 7.06662i −0.618385 + 0.272196i
$$675$$ 0 0
$$676$$ 0.947657 1.03475i 0.0364483 0.0397980i
$$677$$ 12.9937i 0.499390i −0.968324 0.249695i $$-0.919670\pi$$
0.968324 0.249695i $$-0.0803304\pi$$
$$678$$ −1.11257 + 1.61141i −0.0427280 + 0.0618859i
$$679$$ 27.8691i 1.06952i
$$680$$ 0 0
$$681$$ −20.2094 32.8244i −0.774425 1.25784i
$$682$$ −6.49219 14.7492i −0.248599 0.564776i
$$683$$ 11.6291 0.444975 0.222488 0.974936i $$-0.428582\pi$$
0.222488 + 0.974936i $$0.428582\pi$$
$$684$$ −2.46964 + 0.935915i −0.0944290 + 0.0357856i
$$685$$ 0 0
$$686$$ −11.0122 25.0180i −0.420449 0.955193i
$$687$$ 2.08717 + 3.39001i 0.0796303 + 0.129337i
$$688$$ −33.5078 + 2.94984i −1.27747 + 0.112462i
$$689$$ 8.43579i 0.321378i
$$690$$ 0 0
$$691$$ 1.18915i 0.0452375i 0.999744 + 0.0226187i $$0.00720038\pi$$
−0.999744 + 0.0226187i $$0.992800\pi$$
$$692$$ −12.4421 11.3949i −0.472978 0.433169i
$$693$$ 22.5969 + 11.3949i 0.858384 + 0.432857i
$$694$$ −25.1570 + 11.0734i −0.954948 + 0.420341i
$$695$$ 0 0
$$696$$ 2.49120 + 10.8832i 0.0944287 + 0.412526i
$$697$$ 23.5078 0.890422
$$698$$ 33.9246 14.9327i 1.28406 0.565210i
$$699$$ 12.4421 7.66037i 0.470604 0.289742i
$$700$$ 0 0
$$701$$ 11.3949i 0.430380i 0.976572 + 0.215190i $$0.0690370\pi$$
−0.976572 + 0.215190i $$0.930963\pi$$
$$702$$ 23.8779 13.0280i 0.901215 0.491709i
$$703$$ 3.25865i 0.122902i
$$704$$ −21.3470 16.3526i −0.804544 0.616311i
$$705$$ 0 0
$$706$$ 15.1938 + 34.5177i 0.571824 + 1.29909i
$$707$$ 44.0490 1.65663
$$708$$ 0 0
$$709$$ −17.7016 −0.664796 −0.332398 0.943139i $$-0.607858\pi$$
−0.332398 + 0.943139i $$0.607858\pi$$
$$710$$ 0 0
$$711$$ −13.4453 6.78003i −0.504237 0.254271i
$$712$$ 14.3508 + 4.86493i 0.537818 + 0.182321i
$$713$$ 17.5517i 0.657317i
$$714$$ 38.6307 + 26.6719i 1.44572 + 0.998171i
$$715$$ 0 0
$$716$$ −12.2662 + 13.3935i −0.458408 + 0.500537i
$$717$$ −23.5078 38.1818i −0.877915 1.42593i
$$718$$ −10.0000 + 4.40172i −0.373197 + 0.164271i
$$719$$ −44.0490 −1.64275 −0.821375 0.570389i $$-0.806793\pi$$
−0.821375 + 0.570389i $$0.806793\pi$$
$$720$$ 0 0
$$721$$ 27.4031 1.02055
$$722$$ 24.3422 10.7148i 0.905924 0.398762i
$$723$$ 6.35656 + 10.3244i 0.236403 + 0.383970i
$$724$$ 14.1938 15.4982i 0.527507 0.575986i
$$725$$ 0 0
$$726$$ 0.601567 + 0.415341i 0.0223262 + 0.0154148i
$$727$$ 40.5488i 1.50387i 0.659236 + 0.751936i $$0.270880\pi$$
−0.659236 + 0.751936i $$0.729120\pi$$
$$728$$ 24.8842 + 8.43579i 0.922271 + 0.312651i
$$729$$ 26.6125 4.55796i 0.985648 0.168813i
$$730$$ 0 0
$$731$$ 64.2169 2.37515
$$732$$ −19.3968 3.72283i −0.716925 0.137600i
$$733$$ 4.80625 0.177523 0.0887614 0.996053i $$-0.471709\pi$$
0.0887614 + 0.996053i $$0.471709\pi$$
$$734$$ −1.42987 3.24844i −0.0527775 0.119902i
$$735$$ 0 0
$$736$$ 14.1047 + 25.6682i 0.519906 + 0.946143i
$$737$$ 18.3511i 0.675973i
$$738$$ 13.0426 + 0.684136i 0.480106 + 0.0251834i
$$739$$ 29.2357i 1.07545i −0.843120 0.537726i $$-0.819283\pi$$
0.843120 0.537726i $$-0.180717\pi$$
$$740$$ 0 0
$$741$$ 2.40312 1.47956i 0.0882810 0.0543529i
$$742$$ −7.40312 + 3.25865i −0.271777 + 0.119629i
$$743$$ −40.8778 −1.49966 −0.749830 0.661630i $$-0.769865\pi$$
−0.749830 + 0.661630i $$0.769865\pi$$
$$744$$ −3.70569 16.1889i −0.135857 0.593514i
$$745$$ 0 0
$$746$$ −30.6786 + 13.5038i −1.12322 + 0.494411i
$$747$$ −2.45323 + 4.86493i −0.0897592 + 0.177999i
$$748$$ 37.8586 + 34.6722i 1.38425 + 1.26774i
$$749$$ 16.1914i 0.591622i
$$750$$ 0 0
$$751$$ 36.2784i 1.32382i 0.749584 + 0.661909i $$0.230254\pi$$
−0.749584 + 0.661909i $$0.769746\pi$$
$$752$$ −1.27415 14.4733i −0.0464634 0.527787i
$$753$$ −20.4555 33.2241i −0.745439 1.21076i
$$754$$ −4.80625 10.9190i −0.175033 0.397647i
$$755$$ 0 0
$$756$$ 20.6569 + 15.9224i 0.751285 + 0.579092i
$$757$$ −35.9109 −1.30521 −0.652603 0.757700i $$-0.726323\pi$$
−0.652603 + 0.757700i $$0.726323\pi$$
$$758$$ −7.47499 16.9820i −0.271504 0.616813i
$$759$$ −15.8034 25.6682i −0.573628 0.931698i
$$760$$ 0 0
$$761$$ 20.6301i 0.747841i 0.927461 + 0.373920i $$0.121987\pi$$
−0.927461 + 0.373920i $$0.878013\pi$$
$$762$$ 17.6466 25.5587i 0.639268 0.925895i
$$763$$ 5.76832i 0.208827i
$$764$$ 16.8066 18.3511i 0.608041 0.663921i
$$765$$ 0 0
$$766$$ −9.40312 + 4.13899i −0.339749 + 0.149548i
$$767$$ 0 0
$$768$$ −18.4289 20.6973i −0.664994 0.746849i
$$769$$ −14.1938 −0.511840 −0.255920 0.966698i $$-0.582378\pi$$
−0.255920 + 0.966698i $$0.582378\pi$$
$$770$$ 0 0
$$771$$ −6.72263 + 4.13899i −0.242110 + 0.149062i
$$772$$ 26.7539 29.2126i 0.962894 1.05139i
$$773$$ 2.27898i 0.0819692i −0.999160 0.0409846i $$-0.986951\pi$$
0.999160 0.0409846i $$-0.0130495\pi$$
$$774$$ 35.6289 + 1.86887i 1.28065 + 0.0671752i
$$775$$ 0 0
$$776$$ 10.0839 29.7460i 0.361993 1.06782i
$$777$$ −27.4031 + 16.8716i −0.983082 + 0.605264i
$$778$$ 21.2984 + 48.3866i 0.763586 + 1.73474i
$$779$$ 1.35503 0.0485489
$$780$$ 0 0
$$781$$ 41.8219 1.49650
$$782$$ −22.5261 51.1756i −0.805530 1.83003i
$$783$$ −1.00314 11.7994i −0.0358494 0.421675i
$$784$$ −0.246095 2.79544i −0.00878910 0.0998370i
$$785$$ 0 0
$$786$$ −11.5289 7.95991i −0.411221 0.283920i