# Properties

 Label 400.2.u.b.81.1 Level $400$ Weight $2$ Character 400.81 Analytic conductor $3.194$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$400 = 2^{4} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 400.u (of order $$5$$, degree $$4$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.19401608085$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{10})$$ Defining polynomial: $$x^{4} - x^{3} + x^{2} - x + 1$$ x^4 - x^3 + x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 25) Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

## Embedding invariants

 Embedding label 81.1 Root $$-0.309017 + 0.951057i$$ of defining polynomial Character $$\chi$$ $$=$$ 400.81 Dual form 400.2.u.b.321.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.809017 - 0.587785i) q^{3} +(-0.690983 + 2.12663i) q^{5} -0.618034 q^{7} +(-0.618034 + 1.90211i) q^{9} +O(q^{10})$$ $$q+(0.809017 - 0.587785i) q^{3} +(-0.690983 + 2.12663i) q^{5} -0.618034 q^{7} +(-0.618034 + 1.90211i) q^{9} +(1.61803 + 4.97980i) q^{11} +(0.572949 - 1.76336i) q^{13} +(0.690983 + 2.12663i) q^{15} +(4.23607 + 3.07768i) q^{17} +(0.690983 + 0.502029i) q^{19} +(-0.500000 + 0.363271i) q^{21} +(-1.16312 - 3.57971i) q^{23} +(-4.04508 - 2.93893i) q^{25} +(1.54508 + 4.75528i) q^{27} +(2.92705 - 2.12663i) q^{29} +(-2.42705 - 1.76336i) q^{31} +(4.23607 + 3.07768i) q^{33} +(0.427051 - 1.31433i) q^{35} +(-0.0729490 + 0.224514i) q^{37} +(-0.572949 - 1.76336i) q^{39} +(-0.236068 + 0.726543i) q^{41} +4.85410 q^{43} +(-3.61803 - 2.62866i) q^{45} +(0.500000 - 0.363271i) q^{47} -6.61803 q^{49} +5.23607 q^{51} +(2.80902 - 2.04087i) q^{53} -11.7082 q^{55} +0.854102 q^{57} +(3.35410 - 10.3229i) q^{59} +(2.69098 + 8.28199i) q^{61} +(0.381966 - 1.17557i) q^{63} +(3.35410 + 2.43690i) q^{65} +(3.85410 + 2.80017i) q^{67} +(-3.04508 - 2.21238i) q^{69} +(-5.35410 + 3.88998i) q^{71} +(-2.78115 - 8.55951i) q^{73} -5.00000 q^{75} +(-1.00000 - 3.07768i) q^{77} +(-6.54508 + 4.75528i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-5.04508 - 3.66547i) q^{83} +(-9.47214 + 6.88191i) q^{85} +(1.11803 - 3.44095i) q^{87} +(-2.76393 - 8.50651i) q^{89} +(-0.354102 + 1.08981i) q^{91} -3.00000 q^{93} +(-1.54508 + 1.12257i) q^{95} +(3.11803 - 2.26538i) q^{97} -10.4721 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + q^{3} - 5 q^{5} + 2 q^{7} + 2 q^{9}+O(q^{10})$$ 4 * q + q^3 - 5 * q^5 + 2 * q^7 + 2 * q^9 $$4 q + q^{3} - 5 q^{5} + 2 q^{7} + 2 q^{9} + 2 q^{11} + 9 q^{13} + 5 q^{15} + 8 q^{17} + 5 q^{19} - 2 q^{21} + 11 q^{23} - 5 q^{25} - 5 q^{27} + 5 q^{29} - 3 q^{31} + 8 q^{33} - 5 q^{35} - 7 q^{37} - 9 q^{39} + 8 q^{41} + 6 q^{43} - 10 q^{45} + 2 q^{47} - 22 q^{49} + 12 q^{51} + 9 q^{53} - 20 q^{55} - 10 q^{57} + 13 q^{61} + 6 q^{63} + 2 q^{67} - q^{69} - 8 q^{71} + 9 q^{73} - 20 q^{75} - 4 q^{77} - 15 q^{79} - q^{81} - 9 q^{83} - 20 q^{85} - 20 q^{89} + 12 q^{91} - 12 q^{93} + 5 q^{95} + 8 q^{97} - 24 q^{99}+O(q^{100})$$ 4 * q + q^3 - 5 * q^5 + 2 * q^7 + 2 * q^9 + 2 * q^11 + 9 * q^13 + 5 * q^15 + 8 * q^17 + 5 * q^19 - 2 * q^21 + 11 * q^23 - 5 * q^25 - 5 * q^27 + 5 * q^29 - 3 * q^31 + 8 * q^33 - 5 * q^35 - 7 * q^37 - 9 * q^39 + 8 * q^41 + 6 * q^43 - 10 * q^45 + 2 * q^47 - 22 * q^49 + 12 * q^51 + 9 * q^53 - 20 * q^55 - 10 * q^57 + 13 * q^61 + 6 * q^63 + 2 * q^67 - q^69 - 8 * q^71 + 9 * q^73 - 20 * q^75 - 4 * q^77 - 15 * q^79 - q^81 - 9 * q^83 - 20 * q^85 - 20 * q^89 + 12 * q^91 - 12 * q^93 + 5 * q^95 + 8 * q^97 - 24 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$177$$ $$351$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0.809017 0.587785i 0.467086 0.339358i −0.329218 0.944254i $$-0.606785\pi$$
0.796305 + 0.604896i $$0.206785\pi$$
$$4$$ 0 0
$$5$$ −0.690983 + 2.12663i −0.309017 + 0.951057i
$$6$$ 0 0
$$7$$ −0.618034 −0.233595 −0.116797 0.993156i $$-0.537263\pi$$
−0.116797 + 0.993156i $$0.537263\pi$$
$$8$$ 0 0
$$9$$ −0.618034 + 1.90211i −0.206011 + 0.634038i
$$10$$ 0 0
$$11$$ 1.61803 + 4.97980i 0.487856 + 1.50147i 0.827802 + 0.561020i $$0.189591\pi$$
−0.339946 + 0.940445i $$0.610409\pi$$
$$12$$ 0 0
$$13$$ 0.572949 1.76336i 0.158907 0.489067i −0.839628 0.543161i $$-0.817227\pi$$
0.998536 + 0.0540944i $$0.0172272\pi$$
$$14$$ 0 0
$$15$$ 0.690983 + 2.12663i 0.178411 + 0.549093i
$$16$$ 0 0
$$17$$ 4.23607 + 3.07768i 1.02740 + 0.746448i 0.967786 0.251774i $$-0.0810139\pi$$
0.0596113 + 0.998222i $$0.481014\pi$$
$$18$$ 0 0
$$19$$ 0.690983 + 0.502029i 0.158522 + 0.115173i 0.664219 0.747538i $$-0.268764\pi$$
−0.505696 + 0.862712i $$0.668764\pi$$
$$20$$ 0 0
$$21$$ −0.500000 + 0.363271i −0.109109 + 0.0792723i
$$22$$ 0 0
$$23$$ −1.16312 3.57971i −0.242527 0.746422i −0.996033 0.0889808i $$-0.971639\pi$$
0.753506 0.657441i $$-0.228361\pi$$
$$24$$ 0 0
$$25$$ −4.04508 2.93893i −0.809017 0.587785i
$$26$$ 0 0
$$27$$ 1.54508 + 4.75528i 0.297352 + 0.915155i
$$28$$ 0 0
$$29$$ 2.92705 2.12663i 0.543540 0.394905i −0.281858 0.959456i $$-0.590951\pi$$
0.825398 + 0.564551i $$0.190951\pi$$
$$30$$ 0 0
$$31$$ −2.42705 1.76336i −0.435911 0.316708i 0.348097 0.937459i $$-0.386828\pi$$
−0.784008 + 0.620750i $$0.786828\pi$$
$$32$$ 0 0
$$33$$ 4.23607 + 3.07768i 0.737405 + 0.535756i
$$34$$ 0 0
$$35$$ 0.427051 1.31433i 0.0721848 0.222162i
$$36$$ 0 0
$$37$$ −0.0729490 + 0.224514i −0.0119927 + 0.0369099i −0.956874 0.290504i $$-0.906177\pi$$
0.944881 + 0.327414i $$0.106177\pi$$
$$38$$ 0 0
$$39$$ −0.572949 1.76336i −0.0917453 0.282363i
$$40$$ 0 0
$$41$$ −0.236068 + 0.726543i −0.0368676 + 0.113467i −0.967797 0.251733i $$-0.918999\pi$$
0.930929 + 0.365200i $$0.118999\pi$$
$$42$$ 0 0
$$43$$ 4.85410 0.740244 0.370122 0.928983i $$-0.379316\pi$$
0.370122 + 0.928983i $$0.379316\pi$$
$$44$$ 0 0
$$45$$ −3.61803 2.62866i −0.539345 0.391857i
$$46$$ 0 0
$$47$$ 0.500000 0.363271i 0.0729325 0.0529886i −0.550722 0.834689i $$-0.685647\pi$$
0.623654 + 0.781700i $$0.285647\pi$$
$$48$$ 0 0
$$49$$ −6.61803 −0.945433
$$50$$ 0 0
$$51$$ 5.23607 0.733196
$$52$$ 0 0
$$53$$ 2.80902 2.04087i 0.385848 0.280335i −0.377904 0.925845i $$-0.623355\pi$$
0.763752 + 0.645510i $$0.223355\pi$$
$$54$$ 0 0
$$55$$ −11.7082 −1.57873
$$56$$ 0 0
$$57$$ 0.854102 0.113129
$$58$$ 0 0
$$59$$ 3.35410 10.3229i 0.436667 1.34392i −0.454702 0.890644i $$-0.650254\pi$$
0.891369 0.453279i $$-0.149746\pi$$
$$60$$ 0 0
$$61$$ 2.69098 + 8.28199i 0.344545 + 1.06040i 0.961827 + 0.273659i $$0.0882338\pi$$
−0.617282 + 0.786742i $$0.711766\pi$$
$$62$$ 0 0
$$63$$ 0.381966 1.17557i 0.0481232 0.148108i
$$64$$ 0 0
$$65$$ 3.35410 + 2.43690i 0.416025 + 0.302260i
$$66$$ 0 0
$$67$$ 3.85410 + 2.80017i 0.470853 + 0.342095i 0.797774 0.602957i $$-0.206011\pi$$
−0.326920 + 0.945052i $$0.606011\pi$$
$$68$$ 0 0
$$69$$ −3.04508 2.21238i −0.366585 0.266340i
$$70$$ 0 0
$$71$$ −5.35410 + 3.88998i −0.635415 + 0.461656i −0.858272 0.513195i $$-0.828462\pi$$
0.222857 + 0.974851i $$0.428462\pi$$
$$72$$ 0 0
$$73$$ −2.78115 8.55951i −0.325509 1.00181i −0.971210 0.238224i $$-0.923435\pi$$
0.645701 0.763590i $$-0.276565\pi$$
$$74$$ 0 0
$$75$$ −5.00000 −0.577350
$$76$$ 0 0
$$77$$ −1.00000 3.07768i −0.113961 0.350735i
$$78$$ 0 0
$$79$$ −6.54508 + 4.75528i −0.736380 + 0.535011i −0.891575 0.452873i $$-0.850399\pi$$
0.155196 + 0.987884i $$0.450399\pi$$
$$80$$ 0 0
$$81$$ −0.809017 0.587785i −0.0898908 0.0653095i
$$82$$ 0 0
$$83$$ −5.04508 3.66547i −0.553770 0.402337i 0.275404 0.961329i $$-0.411189\pi$$
−0.829174 + 0.558991i $$0.811189\pi$$
$$84$$ 0 0
$$85$$ −9.47214 + 6.88191i −1.02740 + 0.746448i
$$86$$ 0 0
$$87$$ 1.11803 3.44095i 0.119866 0.368909i
$$88$$ 0 0
$$89$$ −2.76393 8.50651i −0.292976 0.901688i −0.983894 0.178754i $$-0.942793\pi$$
0.690918 0.722934i $$-0.257207\pi$$
$$90$$ 0 0
$$91$$ −0.354102 + 1.08981i −0.0371200 + 0.114244i
$$92$$ 0 0
$$93$$ −3.00000 −0.311086
$$94$$ 0 0
$$95$$ −1.54508 + 1.12257i −0.158522 + 0.115173i
$$96$$ 0 0
$$97$$ 3.11803 2.26538i 0.316588 0.230015i −0.418130 0.908387i $$-0.637314\pi$$
0.734718 + 0.678372i $$0.237314\pi$$
$$98$$ 0 0
$$99$$ −10.4721 −1.05249
$$100$$ 0 0
$$101$$ 1.47214 0.146483 0.0732415 0.997314i $$-0.476666\pi$$
0.0732415 + 0.997314i $$0.476666\pi$$
$$102$$ 0 0
$$103$$ 6.92705 5.03280i 0.682543 0.495896i −0.191658 0.981462i $$-0.561386\pi$$
0.874200 + 0.485566i $$0.161386\pi$$
$$104$$ 0 0
$$105$$ −0.427051 1.31433i −0.0416759 0.128265i
$$106$$ 0 0
$$107$$ 16.4164 1.58703 0.793517 0.608548i $$-0.208248\pi$$
0.793517 + 0.608548i $$0.208248\pi$$
$$108$$ 0 0
$$109$$ 3.09017 9.51057i 0.295985 0.910947i −0.686904 0.726748i $$-0.741031\pi$$
0.982889 0.184199i $$-0.0589691\pi$$
$$110$$ 0 0
$$111$$ 0.0729490 + 0.224514i 0.00692401 + 0.0213099i
$$112$$ 0 0
$$113$$ 5.20820 16.0292i 0.489947 1.50790i −0.334740 0.942311i $$-0.608648\pi$$
0.824687 0.565590i $$-0.191352\pi$$
$$114$$ 0 0
$$115$$ 8.41641 0.784834
$$116$$ 0 0
$$117$$ 3.00000 + 2.17963i 0.277350 + 0.201507i
$$118$$ 0 0
$$119$$ −2.61803 1.90211i −0.239995 0.174366i
$$120$$ 0 0
$$121$$ −13.2812 + 9.64932i −1.20738 + 0.877211i
$$122$$ 0 0
$$123$$ 0.236068 + 0.726543i 0.0212855 + 0.0655101i
$$124$$ 0 0
$$125$$ 9.04508 6.57164i 0.809017 0.587785i
$$126$$ 0 0
$$127$$ −6.14590 18.9151i −0.545360 1.67845i −0.720132 0.693837i $$-0.755919\pi$$
0.174772 0.984609i $$-0.444081\pi$$
$$128$$ 0 0
$$129$$ 3.92705 2.85317i 0.345758 0.251208i
$$130$$ 0 0
$$131$$ 5.50000 + 3.99598i 0.480537 + 0.349131i 0.801534 0.597950i $$-0.204018\pi$$
−0.320996 + 0.947080i $$0.604018\pi$$
$$132$$ 0 0
$$133$$ −0.427051 0.310271i −0.0370300 0.0269039i
$$134$$ 0 0
$$135$$ −11.1803 −0.962250
$$136$$ 0 0
$$137$$ −3.69098 + 11.3597i −0.315342 + 0.970523i 0.660271 + 0.751027i $$0.270441\pi$$
−0.975613 + 0.219496i $$0.929559\pi$$
$$138$$ 0 0
$$139$$ −1.54508 4.75528i −0.131052 0.403338i 0.863903 0.503659i $$-0.168013\pi$$
−0.994955 + 0.100321i $$0.968013\pi$$
$$140$$ 0 0
$$141$$ 0.190983 0.587785i 0.0160837 0.0495004i
$$142$$ 0 0
$$143$$ 9.70820 0.811841
$$144$$ 0 0
$$145$$ 2.50000 + 7.69421i 0.207614 + 0.638969i
$$146$$ 0 0
$$147$$ −5.35410 + 3.88998i −0.441599 + 0.320840i
$$148$$ 0 0
$$149$$ −3.94427 −0.323127 −0.161564 0.986862i $$-0.551654\pi$$
−0.161564 + 0.986862i $$0.551654\pi$$
$$150$$ 0 0
$$151$$ −14.5623 −1.18506 −0.592532 0.805547i $$-0.701872\pi$$
−0.592532 + 0.805547i $$0.701872\pi$$
$$152$$ 0 0
$$153$$ −8.47214 + 6.15537i −0.684932 + 0.497632i
$$154$$ 0 0
$$155$$ 5.42705 3.94298i 0.435911 0.316708i
$$156$$ 0 0
$$157$$ 13.1803 1.05191 0.525953 0.850514i $$-0.323709\pi$$
0.525953 + 0.850514i $$0.323709\pi$$
$$158$$ 0 0
$$159$$ 1.07295 3.30220i 0.0850904 0.261881i
$$160$$ 0 0
$$161$$ 0.718847 + 2.21238i 0.0566531 + 0.174360i
$$162$$ 0 0
$$163$$ −3.39919 + 10.4616i −0.266245 + 0.819417i 0.725159 + 0.688581i $$0.241766\pi$$
−0.991404 + 0.130836i $$0.958234\pi$$
$$164$$ 0 0
$$165$$ −9.47214 + 6.88191i −0.737405 + 0.535756i
$$166$$ 0 0
$$167$$ 11.7812 + 8.55951i 0.911653 + 0.662355i 0.941432 0.337202i $$-0.109480\pi$$
−0.0297794 + 0.999556i $$0.509480\pi$$
$$168$$ 0 0
$$169$$ 7.73607 + 5.62058i 0.595082 + 0.432352i
$$170$$ 0 0
$$171$$ −1.38197 + 1.00406i −0.105682 + 0.0767822i
$$172$$ 0 0
$$173$$ 5.83688 + 17.9641i 0.443770 + 1.36578i 0.883827 + 0.467813i $$0.154958\pi$$
−0.440057 + 0.897970i $$0.645042\pi$$
$$174$$ 0 0
$$175$$ 2.50000 + 1.81636i 0.188982 + 0.137304i
$$176$$ 0 0
$$177$$ −3.35410 10.3229i −0.252110 0.775914i
$$178$$ 0 0
$$179$$ −0.427051 + 0.310271i −0.0319193 + 0.0231907i −0.603631 0.797264i $$-0.706280\pi$$
0.571711 + 0.820455i $$0.306280\pi$$
$$180$$ 0 0
$$181$$ −0.236068 0.171513i −0.0175468 0.0127485i 0.578977 0.815344i $$-0.303452\pi$$
−0.596524 + 0.802595i $$0.703452\pi$$
$$182$$ 0 0
$$183$$ 7.04508 + 5.11855i 0.520788 + 0.378374i
$$184$$ 0 0
$$185$$ −0.427051 0.310271i −0.0313974 0.0228116i
$$186$$ 0 0
$$187$$ −8.47214 + 26.0746i −0.619544 + 1.90676i
$$188$$ 0 0
$$189$$ −0.954915 2.93893i −0.0694598 0.213775i
$$190$$ 0 0
$$191$$ 0.562306 1.73060i 0.0406870 0.125222i −0.928650 0.370958i $$-0.879030\pi$$
0.969337 + 0.245736i $$0.0790295\pi$$
$$192$$ 0 0
$$193$$ 7.70820 0.554849 0.277424 0.960747i $$-0.410519\pi$$
0.277424 + 0.960747i $$0.410519\pi$$
$$194$$ 0 0
$$195$$ 4.14590 0.296894
$$196$$ 0 0
$$197$$ −3.00000 + 2.17963i −0.213741 + 0.155292i −0.689505 0.724281i $$-0.742172\pi$$
0.475764 + 0.879573i $$0.342172\pi$$
$$198$$ 0 0
$$199$$ 17.5623 1.24496 0.622479 0.782636i $$-0.286125\pi$$
0.622479 + 0.782636i $$0.286125\pi$$
$$200$$ 0 0
$$201$$ 4.76393 0.336022
$$202$$ 0 0
$$203$$ −1.80902 + 1.31433i −0.126968 + 0.0922477i
$$204$$ 0 0
$$205$$ −1.38197 1.00406i −0.0965207 0.0701264i
$$206$$ 0 0
$$207$$ 7.52786 0.523223
$$208$$ 0 0
$$209$$ −1.38197 + 4.25325i −0.0955926 + 0.294204i
$$210$$ 0 0
$$211$$ 2.83688 + 8.73102i 0.195299 + 0.601068i 0.999973 + 0.00735149i $$0.00234007\pi$$
−0.804674 + 0.593717i $$0.797660\pi$$
$$212$$ 0 0
$$213$$ −2.04508 + 6.29412i −0.140127 + 0.431266i
$$214$$ 0 0
$$215$$ −3.35410 + 10.3229i −0.228748 + 0.704014i
$$216$$ 0 0
$$217$$ 1.50000 + 1.08981i 0.101827 + 0.0739814i
$$218$$ 0 0
$$219$$ −7.28115 5.29007i −0.492015 0.357470i
$$220$$ 0 0
$$221$$ 7.85410 5.70634i 0.528324 0.383850i
$$222$$ 0 0
$$223$$ 0.0557281 + 0.171513i 0.00373183 + 0.0114854i 0.952905 0.303269i $$-0.0980780\pi$$
−0.949173 + 0.314754i $$0.898078\pi$$
$$224$$ 0 0
$$225$$ 8.09017 5.87785i 0.539345 0.391857i
$$226$$ 0 0
$$227$$ −4.56231 14.0413i −0.302811 0.931956i −0.980485 0.196594i $$-0.937012\pi$$
0.677674 0.735362i $$-0.262988\pi$$
$$228$$ 0 0
$$229$$ −17.5623 + 12.7598i −1.16055 + 0.843189i −0.989847 0.142134i $$-0.954604\pi$$
−0.170702 + 0.985323i $$0.554604\pi$$
$$230$$ 0 0
$$231$$ −2.61803 1.90211i −0.172254 0.125150i
$$232$$ 0 0
$$233$$ 2.38197 + 1.73060i 0.156048 + 0.113375i 0.663069 0.748558i $$-0.269254\pi$$
−0.507021 + 0.861933i $$0.669254\pi$$
$$234$$ 0 0
$$235$$ 0.427051 + 1.31433i 0.0278577 + 0.0857373i
$$236$$ 0 0
$$237$$ −2.50000 + 7.69421i −0.162392 + 0.499793i
$$238$$ 0 0
$$239$$ 6.34346 + 19.5232i 0.410324 + 1.26285i 0.916367 + 0.400340i $$0.131108\pi$$
−0.506043 + 0.862508i $$0.668892\pi$$
$$240$$ 0 0
$$241$$ 0.781153 2.40414i 0.0503185 0.154864i −0.922740 0.385423i $$-0.874055\pi$$
0.973058 + 0.230559i $$0.0740554\pi$$
$$242$$ 0 0
$$243$$ −16.0000 −1.02640
$$244$$ 0 0
$$245$$ 4.57295 14.0741i 0.292155 0.899161i
$$246$$ 0 0
$$247$$ 1.28115 0.930812i 0.0815178 0.0592262i
$$248$$ 0 0
$$249$$ −6.23607 −0.395195
$$250$$ 0 0
$$251$$ 29.1803 1.84185 0.920923 0.389744i $$-0.127436\pi$$
0.920923 + 0.389744i $$0.127436\pi$$
$$252$$ 0 0
$$253$$ 15.9443 11.5842i 1.00241 0.728292i
$$254$$ 0 0
$$255$$ −3.61803 + 11.1352i −0.226570 + 0.697311i
$$256$$ 0 0
$$257$$ 22.8541 1.42560 0.712800 0.701367i $$-0.247427\pi$$
0.712800 + 0.701367i $$0.247427\pi$$
$$258$$ 0 0
$$259$$ 0.0450850 0.138757i 0.00280144 0.00862196i
$$260$$ 0 0
$$261$$ 2.23607 + 6.88191i 0.138409 + 0.425980i
$$262$$ 0 0
$$263$$ 3.37132 10.3759i 0.207885 0.639803i −0.791698 0.610913i $$-0.790803\pi$$
0.999583 0.0288905i $$-0.00919740\pi$$
$$264$$ 0 0
$$265$$ 2.39919 + 7.38394i 0.147381 + 0.453592i
$$266$$ 0 0
$$267$$ −7.23607 5.25731i −0.442840 0.321742i
$$268$$ 0 0
$$269$$ 10.3262 + 7.50245i 0.629602 + 0.457433i 0.856262 0.516541i $$-0.172781\pi$$
−0.226660 + 0.973974i $$0.572781\pi$$
$$270$$ 0 0
$$271$$ −6.47214 + 4.70228i −0.393154 + 0.285643i −0.766747 0.641950i $$-0.778126\pi$$
0.373593 + 0.927593i $$0.378126\pi$$
$$272$$ 0 0
$$273$$ 0.354102 + 1.08981i 0.0214312 + 0.0659585i
$$274$$ 0 0
$$275$$ 8.09017 24.8990i 0.487856 1.50147i
$$276$$ 0 0
$$277$$ −7.63525 23.4989i −0.458758 1.41191i −0.866666 0.498889i $$-0.833742\pi$$
0.407908 0.913023i $$-0.366258\pi$$
$$278$$ 0 0
$$279$$ 4.85410 3.52671i 0.290607 0.211139i
$$280$$ 0 0
$$281$$ −8.16312 5.93085i −0.486971 0.353805i 0.317047 0.948410i $$-0.397309\pi$$
−0.804018 + 0.594605i $$0.797309\pi$$
$$282$$ 0 0
$$283$$ −24.1525 17.5478i −1.43572 1.04311i −0.988916 0.148474i $$-0.952564\pi$$
−0.446799 0.894634i $$-0.647436\pi$$
$$284$$ 0 0
$$285$$ −0.590170 + 1.81636i −0.0349587 + 0.107592i
$$286$$ 0 0
$$287$$ 0.145898 0.449028i 0.00861209 0.0265053i
$$288$$ 0 0
$$289$$ 3.21885 + 9.90659i 0.189344 + 0.582741i
$$290$$ 0 0
$$291$$ 1.19098 3.66547i 0.0698167 0.214874i
$$292$$ 0 0
$$293$$ −19.5279 −1.14083 −0.570415 0.821357i $$-0.693218\pi$$
−0.570415 + 0.821357i $$0.693218\pi$$
$$294$$ 0 0
$$295$$ 19.6353 + 14.2658i 1.14321 + 0.830590i
$$296$$ 0 0
$$297$$ −21.1803 + 15.3884i −1.22901 + 0.892927i
$$298$$ 0 0
$$299$$ −6.97871 −0.403589
$$300$$ 0 0
$$301$$ −3.00000 −0.172917
$$302$$ 0 0
$$303$$ 1.19098 0.865300i 0.0684202 0.0497102i
$$304$$ 0 0
$$305$$ −19.4721 −1.11497
$$306$$ 0 0
$$307$$ −9.23607 −0.527130 −0.263565 0.964642i $$-0.584898\pi$$
−0.263565 + 0.964642i $$0.584898\pi$$
$$308$$ 0 0
$$309$$ 2.64590 8.14324i 0.150520 0.463253i
$$310$$ 0 0
$$311$$ −2.62868 8.09024i −0.149059 0.458755i 0.848452 0.529272i $$-0.177535\pi$$
−0.997511 + 0.0705172i $$0.977535\pi$$
$$312$$ 0 0
$$313$$ −5.18034 + 15.9434i −0.292810 + 0.901177i 0.691138 + 0.722723i $$0.257110\pi$$
−0.983948 + 0.178454i $$0.942890\pi$$
$$314$$ 0 0
$$315$$ 2.23607 + 1.62460i 0.125988 + 0.0915358i
$$316$$ 0 0
$$317$$ −6.19098 4.49801i −0.347720 0.252634i 0.400192 0.916431i $$-0.368944\pi$$
−0.747912 + 0.663798i $$0.768944\pi$$
$$318$$ 0 0
$$319$$ 15.3262 + 11.1352i 0.858105 + 0.623449i
$$320$$ 0 0
$$321$$ 13.2812 9.64932i 0.741282 0.538573i
$$322$$ 0 0
$$323$$ 1.38197 + 4.25325i 0.0768946 + 0.236657i
$$324$$ 0 0
$$325$$ −7.50000 + 5.44907i −0.416025 + 0.302260i
$$326$$ 0 0
$$327$$ −3.09017 9.51057i −0.170887 0.525935i
$$328$$ 0 0
$$329$$ −0.309017 + 0.224514i −0.0170367 + 0.0123779i
$$330$$ 0 0
$$331$$ −18.7082 13.5923i −1.02830 0.747101i −0.0603290 0.998179i $$-0.519215\pi$$
−0.967967 + 0.251078i $$0.919215\pi$$
$$332$$ 0 0
$$333$$ −0.381966 0.277515i −0.0209316 0.0152077i
$$334$$ 0 0
$$335$$ −8.61803 + 6.26137i −0.470853 + 0.342095i
$$336$$ 0 0
$$337$$ 2.42705 7.46969i 0.132210 0.406900i −0.862936 0.505314i $$-0.831377\pi$$
0.995146 + 0.0984135i $$0.0313768\pi$$
$$338$$ 0 0
$$339$$ −5.20820 16.0292i −0.282871 0.870587i
$$340$$ 0 0
$$341$$ 4.85410 14.9394i 0.262864 0.809013i
$$342$$ 0 0
$$343$$ 8.41641 0.454443
$$344$$ 0 0
$$345$$ 6.80902 4.94704i 0.366585 0.266340i
$$346$$ 0 0
$$347$$ −16.1074 + 11.7027i −0.864690 + 0.628234i −0.929157 0.369686i $$-0.879465\pi$$
0.0644668 + 0.997920i $$0.479465\pi$$
$$348$$ 0 0
$$349$$ 21.7082 1.16201 0.581007 0.813899i $$-0.302659\pi$$
0.581007 + 0.813899i $$0.302659\pi$$
$$350$$ 0 0
$$351$$ 9.27051 0.494823
$$352$$ 0 0
$$353$$ −10.4443 + 7.58821i −0.555893 + 0.403880i −0.829953 0.557833i $$-0.811633\pi$$
0.274061 + 0.961712i $$0.411633\pi$$
$$354$$ 0 0
$$355$$ −4.57295 14.0741i −0.242707 0.746975i
$$356$$ 0 0
$$357$$ −3.23607 −0.171271
$$358$$ 0 0
$$359$$ −4.24671 + 13.0700i −0.224133 + 0.689810i 0.774246 + 0.632885i $$0.218130\pi$$
−0.998378 + 0.0569247i $$0.981870\pi$$
$$360$$ 0 0
$$361$$ −5.64590 17.3763i −0.297153 0.914541i
$$362$$ 0 0
$$363$$ −5.07295 + 15.6129i −0.266261 + 0.819466i
$$364$$ 0 0
$$365$$ 20.1246 1.05337
$$366$$ 0 0
$$367$$ −20.6803 15.0251i −1.07950 0.784306i −0.101908 0.994794i $$-0.532495\pi$$
−0.977597 + 0.210488i $$0.932495\pi$$
$$368$$ 0 0
$$369$$ −1.23607 0.898056i −0.0643471 0.0467509i
$$370$$ 0 0
$$371$$ −1.73607 + 1.26133i −0.0901322 + 0.0654848i
$$372$$ 0 0
$$373$$ −8.73607 26.8869i −0.452336 1.39215i −0.874234 0.485505i $$-0.838636\pi$$
0.421897 0.906644i $$-0.361364\pi$$
$$374$$ 0 0
$$375$$ 3.45492 10.6331i 0.178411 0.549093i
$$376$$ 0 0
$$377$$ −2.07295 6.37988i −0.106762 0.328581i
$$378$$ 0 0
$$379$$ 11.8090 8.57975i 0.606588 0.440712i −0.241623 0.970370i $$-0.577680\pi$$
0.848211 + 0.529658i $$0.177680\pi$$
$$380$$ 0 0
$$381$$ −16.0902 11.6902i −0.824324 0.598907i
$$382$$ 0 0
$$383$$ 26.9894 + 19.6089i 1.37909 + 1.00197i 0.996964 + 0.0778591i $$0.0248084\pi$$
0.382127 + 0.924110i $$0.375192\pi$$
$$384$$ 0 0
$$385$$ 7.23607 0.368784
$$386$$ 0 0
$$387$$ −3.00000 + 9.23305i −0.152499 + 0.469342i
$$388$$ 0 0
$$389$$ 4.63525 + 14.2658i 0.235017 + 0.723307i 0.997119 + 0.0758507i $$0.0241672\pi$$
−0.762102 + 0.647456i $$0.775833\pi$$
$$390$$ 0 0
$$391$$ 6.09017 18.7436i 0.307993 0.947905i
$$392$$ 0 0
$$393$$ 6.79837 0.342933
$$394$$ 0 0
$$395$$ −5.59017 17.2048i −0.281272 0.865666i
$$396$$ 0 0
$$397$$ −23.4894 + 17.0660i −1.17890 + 0.856519i −0.992047 0.125870i $$-0.959828\pi$$
−0.186850 + 0.982388i $$0.559828\pi$$
$$398$$ 0 0
$$399$$ −0.527864 −0.0264263
$$400$$ 0 0
$$401$$ 26.5967 1.32818 0.664089 0.747653i $$-0.268820\pi$$
0.664089 + 0.747653i $$0.268820\pi$$
$$402$$ 0 0
$$403$$ −4.50000 + 3.26944i −0.224161 + 0.162862i
$$404$$ 0 0
$$405$$ 1.80902 1.31433i 0.0898908 0.0653095i
$$406$$ 0 0
$$407$$ −1.23607 −0.0612696
$$408$$ 0 0
$$409$$ 0.489357 1.50609i 0.0241971 0.0744711i −0.938229 0.346016i $$-0.887534\pi$$
0.962426 + 0.271544i $$0.0875344\pi$$
$$410$$ 0 0
$$411$$ 3.69098 + 11.3597i 0.182063 + 0.560332i
$$412$$ 0 0
$$413$$ −2.07295 + 6.37988i −0.102003 + 0.313933i
$$414$$ 0 0
$$415$$ 11.2812 8.19624i 0.553770 0.402337i
$$416$$ 0 0
$$417$$ −4.04508 2.93893i −0.198089 0.143920i
$$418$$ 0 0
$$419$$ −7.66312 5.56758i −0.374368 0.271994i 0.384652 0.923062i $$-0.374321\pi$$
−0.759020 + 0.651068i $$0.774321\pi$$
$$420$$ 0 0
$$421$$ −25.8885 + 18.8091i −1.26173 + 0.916701i −0.998841 0.0481252i $$-0.984675\pi$$
−0.262889 + 0.964826i $$0.584675\pi$$
$$422$$ 0 0
$$423$$ 0.381966 + 1.17557i 0.0185718 + 0.0571582i
$$424$$ 0 0
$$425$$ −8.09017 24.8990i −0.392431 1.20778i
$$426$$ 0 0
$$427$$ −1.66312 5.11855i −0.0804840 0.247704i
$$428$$ 0 0
$$429$$ 7.85410 5.70634i 0.379200 0.275505i
$$430$$ 0 0
$$431$$ −24.1353 17.5353i −1.16255 0.844645i −0.172456 0.985017i $$-0.555170\pi$$
−0.990099 + 0.140372i $$0.955170\pi$$
$$432$$ 0 0
$$433$$ −21.7254 15.7844i −1.04406 0.758552i −0.0729839 0.997333i $$-0.523252\pi$$
−0.971073 + 0.238781i $$0.923252\pi$$
$$434$$ 0 0
$$435$$ 6.54508 + 4.75528i 0.313813 + 0.227998i
$$436$$ 0 0
$$437$$ 0.993422 3.05744i 0.0475218 0.146257i
$$438$$ 0 0
$$439$$ 12.6631 + 38.9731i 0.604378 + 1.86008i 0.501013 + 0.865440i $$0.332961\pi$$
0.103365 + 0.994644i $$0.467039\pi$$
$$440$$ 0 0
$$441$$ 4.09017 12.5882i 0.194770 0.599440i
$$442$$ 0 0
$$443$$ −29.9443 −1.42270 −0.711348 0.702840i $$-0.751915\pi$$
−0.711348 + 0.702840i $$0.751915\pi$$
$$444$$ 0 0
$$445$$ 20.0000 0.948091
$$446$$ 0 0
$$447$$ −3.19098 + 2.31838i −0.150928 + 0.109656i
$$448$$ 0 0
$$449$$ 4.67376 0.220568 0.110284 0.993900i $$-0.464824\pi$$
0.110284 + 0.993900i $$0.464824\pi$$
$$450$$ 0 0
$$451$$ −4.00000 −0.188353
$$452$$ 0 0
$$453$$ −11.7812 + 8.55951i −0.553527 + 0.402161i
$$454$$ 0 0
$$455$$ −2.07295 1.50609i −0.0971813 0.0706064i
$$456$$ 0 0
$$457$$ −21.4164 −1.00182 −0.500909 0.865500i $$-0.667001\pi$$
−0.500909 + 0.865500i $$0.667001\pi$$
$$458$$ 0 0
$$459$$ −8.09017 + 24.8990i −0.377617 + 1.16218i
$$460$$ 0 0
$$461$$ 0.253289 + 0.779543i 0.0117968 + 0.0363069i 0.956782 0.290807i $$-0.0939238\pi$$
−0.944985 + 0.327114i $$0.893924\pi$$
$$462$$ 0 0
$$463$$ 7.45492 22.9439i 0.346459 1.06629i −0.614339 0.789042i $$-0.710577\pi$$
0.960798 0.277250i $$-0.0894229\pi$$
$$464$$ 0 0
$$465$$ 2.07295 6.37988i 0.0961307 0.295860i
$$466$$ 0 0
$$467$$ 22.2082 + 16.1352i 1.02767 + 0.746648i 0.967842 0.251560i $$-0.0809437\pi$$
0.0598315 + 0.998208i $$0.480944\pi$$
$$468$$ 0 0
$$469$$ −2.38197 1.73060i −0.109989 0.0799117i
$$470$$ 0 0
$$471$$ 10.6631 7.74721i 0.491331 0.356973i
$$472$$ 0 0
$$473$$ 7.85410 + 24.1724i 0.361132 + 1.11145i
$$474$$ 0 0
$$475$$ −1.31966 4.06150i −0.0605502 0.186354i
$$476$$ 0 0
$$477$$ 2.14590 + 6.60440i 0.0982539 + 0.302394i
$$478$$ 0 0
$$479$$ −8.78115 + 6.37988i −0.401221 + 0.291504i −0.770038 0.637998i $$-0.779763\pi$$
0.368817 + 0.929502i $$0.379763\pi$$
$$480$$ 0 0
$$481$$ 0.354102 + 0.257270i 0.0161457 + 0.0117305i
$$482$$ 0 0
$$483$$ 1.88197 + 1.36733i 0.0856324 + 0.0622156i
$$484$$ 0 0
$$485$$ 2.66312 + 8.19624i 0.120926 + 0.372172i
$$486$$ 0 0
$$487$$ 11.2533 34.6341i 0.509935 1.56942i −0.282377 0.959303i $$-0.591123\pi$$
0.792312 0.610116i $$-0.208877\pi$$
$$488$$ 0 0
$$489$$ 3.39919 + 10.4616i 0.153717 + 0.473091i
$$490$$ 0 0
$$491$$ 13.3647 41.1325i 0.603143 1.85628i 0.0940550 0.995567i $$-0.470017\pi$$
0.509088 0.860715i $$-0.329983\pi$$
$$492$$ 0 0
$$493$$ 18.9443 0.853207
$$494$$ 0 0
$$495$$ 7.23607 22.2703i 0.325237 1.00098i
$$496$$ 0 0
$$497$$ 3.30902 2.40414i 0.148430 0.107840i
$$498$$ 0 0
$$499$$ −7.56231 −0.338535 −0.169268 0.985570i $$-0.554140\pi$$
−0.169268 + 0.985570i $$0.554140\pi$$
$$500$$ 0 0
$$501$$ 14.5623 0.650596
$$502$$ 0 0
$$503$$ −30.2705 + 21.9928i −1.34970 + 0.980611i −0.350669 + 0.936500i $$0.614046\pi$$
−0.999027 + 0.0441115i $$0.985954\pi$$
$$504$$ 0 0
$$505$$ −1.01722 + 3.13068i −0.0452657 + 0.139314i
$$506$$ 0 0
$$507$$ 9.56231 0.424677
$$508$$ 0 0
$$509$$ −6.28115 + 19.3314i −0.278407 + 0.856849i 0.709891 + 0.704312i $$0.248744\pi$$
−0.988298 + 0.152537i $$0.951256\pi$$
$$510$$ 0 0
$$511$$ 1.71885 + 5.29007i 0.0760373 + 0.234019i
$$512$$ 0 0
$$513$$ −1.31966 + 4.06150i −0.0582644 + 0.179319i
$$514$$ 0 0
$$515$$ 5.91641 + 18.2088i 0.260708 + 0.802377i
$$516$$ 0 0
$$517$$ 2.61803 + 1.90211i 0.115141 + 0.0836548i
$$518$$ 0 0
$$519$$ 15.2812 + 11.1024i 0.670768 + 0.487342i
$$520$$ 0 0
$$521$$ −23.7533 + 17.2578i −1.04065 + 0.756077i −0.970412 0.241453i $$-0.922376\pi$$
−0.0702381 + 0.997530i $$0.522376\pi$$
$$522$$ 0 0
$$523$$ 4.06231 + 12.5025i 0.177632 + 0.546696i 0.999744 0.0226305i $$-0.00720412\pi$$
−0.822112 + 0.569326i $$0.807204\pi$$
$$524$$ 0 0
$$525$$ 3.09017 0.134866
$$526$$ 0 0
$$527$$ −4.85410 14.9394i −0.211448 0.650770i
$$528$$ 0 0
$$529$$ 7.14590 5.19180i 0.310691 0.225730i
$$530$$ 0 0
$$531$$ 17.5623 + 12.7598i 0.762139 + 0.553727i
$$532$$ 0 0
$$533$$ 1.14590 + 0.832544i 0.0496344 + 0.0360615i
$$534$$ 0 0
$$535$$ −11.3435 + 34.9116i −0.490420 + 1.50936i
$$536$$ 0 0
$$537$$ −0.163119 + 0.502029i −0.00703910 + 0.0216641i
$$538$$ 0 0
$$539$$ −10.7082 32.9565i −0.461235 1.41954i
$$540$$ 0 0
$$541$$ 8.38197 25.7970i 0.360369 1.10910i −0.592462 0.805599i $$-0.701844\pi$$
0.952831 0.303503i $$-0.0981561\pi$$
$$542$$ 0 0
$$543$$ −0.291796 −0.0125222
$$544$$ 0 0
$$545$$ 18.0902 + 13.1433i 0.774898 + 0.562996i
$$546$$ 0 0
$$547$$ −17.2254 + 12.5150i −0.736506 + 0.535103i −0.891615 0.452794i $$-0.850427\pi$$
0.155109 + 0.987897i $$0.450427\pi$$
$$548$$ 0 0
$$549$$ −17.4164 −0.743314
$$550$$ 0 0
$$551$$ 3.09017 0.131646
$$552$$ 0 0
$$553$$ 4.04508 2.93893i 0.172015 0.124976i
$$554$$ 0 0
$$555$$ −0.527864 −0.0224066
$$556$$ 0 0
$$557$$ 4.76393 0.201854 0.100927 0.994894i $$-0.467819\pi$$
0.100927 + 0.994894i $$0.467819\pi$$
$$558$$ 0 0
$$559$$ 2.78115 8.55951i 0.117630 0.362029i
$$560$$ 0 0
$$561$$ 8.47214 + 26.0746i 0.357694 + 1.10087i
$$562$$ 0 0
$$563$$ −2.28115 + 7.02067i −0.0961391 + 0.295886i −0.987549 0.157312i $$-0.949717\pi$$
0.891410 + 0.453198i $$0.149717\pi$$
$$564$$ 0 0
$$565$$ 30.4894 + 22.1518i 1.28270 + 0.931934i
$$566$$ 0 0
$$567$$ 0.500000 + 0.363271i 0.0209980 + 0.0152560i
$$568$$ 0 0
$$569$$ −16.6074 12.0660i −0.696218 0.505832i 0.182480 0.983210i $$-0.441587\pi$$
−0.878698 + 0.477377i $$0.841587\pi$$
$$570$$ 0 0
$$571$$ −6.57295 + 4.77553i −0.275069 + 0.199850i −0.716764 0.697316i $$-0.754377\pi$$
0.441695 + 0.897165i $$0.354377\pi$$
$$572$$ 0 0
$$573$$ −0.562306 1.73060i −0.0234907 0.0722968i
$$574$$ 0 0
$$575$$ −5.81559 + 17.8986i −0.242527 + 0.746422i
$$576$$ 0 0
$$577$$ −10.4377 32.1239i −0.434527 1.33734i −0.893571 0.448923i $$-0.851808\pi$$
0.459044 0.888414i $$-0.348192\pi$$
$$578$$ 0 0
$$579$$ 6.23607 4.53077i 0.259162 0.188292i
$$580$$ 0 0
$$581$$ 3.11803 + 2.26538i 0.129358 + 0.0939840i
$$582$$ 0 0
$$583$$ 14.7082 + 10.6861i 0.609152 + 0.442575i
$$584$$ 0 0
$$585$$ −6.70820 + 4.87380i −0.277350 + 0.201507i
$$586$$ 0 0
$$587$$ −1.63525 + 5.03280i −0.0674942 + 0.207726i −0.979115 0.203306i $$-0.934831\pi$$
0.911621 + 0.411032i $$0.134831\pi$$
$$588$$ 0 0
$$589$$ −0.791796 2.43690i −0.0326254 0.100411i
$$590$$ 0 0
$$591$$ −1.14590 + 3.52671i −0.0471359 + 0.145070i
$$592$$ 0 0
$$593$$ −10.9098 −0.448013 −0.224007 0.974588i $$-0.571914\pi$$
−0.224007 + 0.974588i $$0.571914\pi$$
$$594$$ 0 0
$$595$$ 5.85410 4.25325i 0.239995 0.174366i
$$596$$ 0 0
$$597$$ 14.2082 10.3229i 0.581503 0.422487i
$$598$$ 0 0
$$599$$ 9.47214 0.387021 0.193510 0.981098i $$-0.438013\pi$$
0.193510 + 0.981098i $$0.438013\pi$$
$$600$$ 0 0
$$601$$ 2.72949 0.111338 0.0556691 0.998449i $$-0.482271\pi$$
0.0556691 + 0.998449i $$0.482271\pi$$
$$602$$ 0 0
$$603$$ −7.70820 + 5.60034i −0.313902 + 0.228063i
$$604$$ 0 0
$$605$$ −11.3435 34.9116i −0.461177 1.41936i
$$606$$ 0 0
$$607$$ 35.5623 1.44343 0.721715 0.692191i $$-0.243354\pi$$
0.721715 + 0.692191i $$0.243354\pi$$
$$608$$ 0 0
$$609$$ −0.690983 + 2.12663i −0.0280000 + 0.0861753i
$$610$$ 0 0
$$611$$ −0.354102 1.08981i −0.0143254 0.0440891i
$$612$$ 0 0
$$613$$ −4.62868 + 14.2456i −0.186951 + 0.575374i −0.999977 0.00685287i $$-0.997819\pi$$
0.813026 + 0.582227i $$0.197819\pi$$
$$614$$ 0 0
$$615$$ −1.70820 −0.0688814
$$616$$ 0 0
$$617$$ −11.5172 8.36775i −0.463666 0.336873i 0.331302 0.943525i $$-0.392512\pi$$
−0.794968 + 0.606652i $$0.792512\pi$$
$$618$$ 0 0
$$619$$ 24.6976 + 17.9438i 0.992679 + 0.721223i 0.960506 0.278259i $$-0.0897573\pi$$
0.0321727 + 0.999482i $$0.489757\pi$$
$$620$$ 0 0
$$621$$ 15.2254 11.0619i 0.610975 0.443900i
$$622$$ 0 0
$$623$$ 1.70820 + 5.25731i 0.0684377 + 0.210630i
$$624$$ 0 0
$$625$$ 7.72542 + 23.7764i 0.309017 + 0.951057i
$$626$$ 0 0
$$627$$ 1.38197 + 4.25325i 0.0551904 + 0.169859i
$$628$$ 0 0
$$629$$ −1.00000 + 0.726543i −0.0398726 + 0.0289691i
$$630$$ 0 0
$$631$$ −8.28115 6.01661i −0.329667 0.239517i 0.410622 0.911806i $$-0.365312\pi$$
−0.740290 + 0.672288i $$0.765312\pi$$
$$632$$ 0 0
$$633$$ 7.42705 + 5.39607i 0.295199 + 0.214474i
$$634$$ 0 0
$$635$$ 44.4721 1.76482
$$636$$ 0 0
$$637$$ −3.79180 + 11.6699i −0.150236 + 0.462380i
$$638$$ 0 0
$$639$$ −4.09017 12.5882i −0.161805 0.497983i
$$640$$ 0 0
$$641$$ −0.336881 + 1.03681i −0.0133060 + 0.0409517i −0.957489 0.288470i $$-0.906854\pi$$
0.944183 + 0.329421i $$0.106854\pi$$
$$642$$ 0 0
$$643$$ 30.8328 1.21593 0.607964 0.793965i $$-0.291987\pi$$
0.607964 + 0.793965i $$0.291987\pi$$
$$644$$ 0 0
$$645$$ 3.35410 + 10.3229i 0.132068 + 0.406462i
$$646$$ 0 0
$$647$$ −29.5623 + 21.4783i −1.16221 + 0.844398i −0.990056 0.140671i $$-0.955074\pi$$
−0.172158 + 0.985069i $$0.555074\pi$$
$$648$$ 0 0
$$649$$ 56.8328 2.23088
$$650$$ 0 0
$$651$$ 1.85410 0.0726680
$$652$$ 0 0
$$653$$ −15.4443 + 11.2209i −0.604381 + 0.439109i −0.847431 0.530905i $$-0.821852\pi$$
0.243050 + 0.970014i $$0.421852\pi$$
$$654$$ 0 0
$$655$$ −12.2984 + 8.93529i −0.480537 + 0.349131i
$$656$$ 0 0
$$657$$ 18.0000 0.702247
$$658$$ 0 0
$$659$$ −4.79837 + 14.7679i −0.186918 + 0.575275i −0.999976 0.00690786i $$-0.997801\pi$$
0.813058 + 0.582183i $$0.197801\pi$$
$$660$$ 0 0
$$661$$ 6.08359 + 18.7234i 0.236624 + 0.728255i 0.996902 + 0.0786563i $$0.0250630\pi$$
−0.760277 + 0.649598i $$0.774937\pi$$
$$662$$ 0 0
$$663$$ 3.00000 9.23305i 0.116510 0.358582i
$$664$$ 0 0
$$665$$ 0.954915 0.693786i 0.0370300 0.0269039i
$$666$$ 0 0
$$667$$ −11.0172 8.00448i −0.426588 0.309935i
$$668$$ 0 0
$$669$$ 0.145898 + 0.106001i 0.00564074 + 0.00409824i
$$670$$ 0 0
$$671$$ −36.8885 + 26.8011i −1.42407 + 1.03464i
$$672$$ 0 0
$$673$$ 3.76393 + 11.5842i 0.145089 + 0.446538i 0.997022 0.0771122i $$-0.0245700\pi$$
−0.851934 + 0.523650i $$0.824570\pi$$
$$674$$ 0 0
$$675$$ 7.72542 23.7764i 0.297352 0.915155i
$$676$$ 0 0
$$677$$ 3.28115 + 10.0984i 0.126105 + 0.388111i 0.994101 0.108460i $$-0.0345921\pi$$
−0.867996 + 0.496571i $$0.834592\pi$$
$$678$$ 0 0
$$679$$ −1.92705 + 1.40008i −0.0739534 + 0.0537303i
$$680$$ 0 0
$$681$$ −11.9443 8.67802i −0.457705 0.332543i
$$682$$ 0 0
$$683$$ −10.8992 7.91872i −0.417046 0.303002i 0.359402 0.933183i $$-0.382981\pi$$
−0.776448 + 0.630181i $$0.782981\pi$$
$$684$$ 0 0
$$685$$ −21.6074 15.6987i −0.825576 0.599816i
$$686$$ 0 0
$$687$$ −6.70820 + 20.6457i −0.255934 + 0.787684i
$$688$$ 0 0
$$689$$ −1.98936 6.12261i −0.0757885 0.233253i
$$690$$ 0 0
$$691$$ −11.2082 + 34.4953i −0.426380 + 1.31226i 0.475286 + 0.879831i $$0.342344\pi$$
−0.901667 + 0.432432i $$0.857656\pi$$
$$692$$ 0 0
$$693$$ 6.47214 0.245856
$$694$$ 0 0
$$695$$ 11.1803 0.424094
$$696$$ 0 0
$$697$$ −3.23607 + 2.35114i −0.122575 + 0.0890558i
$$698$$ 0 0
$$699$$ 2.94427 0.111363
$$700$$ 0 0
$$701$$ −41.0132 −1.54905 −0.774523 0.632546i $$-0.782010\pi$$
−0.774523 + 0.632546i $$0.782010\pi$$
$$702$$ 0 0
$$703$$ −0.163119 + 0.118513i −0.00615215 + 0.00446980i
$$704$$ 0 0
$$705$$ 1.11803 + 0.812299i 0.0421076 + 0.0305930i
$$706$$ 0 0
$$707$$ −0.909830 −0.0342177
$$708$$ 0 0
$$709$$ −10.3647 + 31.8994i −0.389256 + 1.19801i 0.544089 + 0.839027i $$0.316875\pi$$
−0.933345 + 0.358980i $$0.883125\pi$$
$$710$$ 0 0
$$711$$ −5.00000 15.3884i −0.187515 0.577111i
$$712$$ 0 0
$$713$$ −3.48936 + 10.7391i −0.130677 + 0.402184i
$$714$$ 0 0
$$715$$ −6.70820 + 20.6457i −0.250873 + 0.772106i
$$716$$ 0 0
$$717$$ 16.6074 + 12.0660i 0.620214 + 0.450612i
$$718$$ 0 0
$$719$$ −18.8435 13.6906i −0.702742 0.510572i 0.178082 0.984016i $$-0.443011\pi$$
−0.880824 + 0.473443i $$0.843011\pi$$
$$720$$ 0 0
$$721$$ −4.28115 + 3.11044i −0.159438 + 0.115839i
$$722$$ 0 0
$$723$$ −0.781153 2.40414i −0.0290514 0.0894110i
$$724$$ 0 0
$$725$$ −18.0902 −0.671852
$$726$$ 0 0
$$727$$ −7.59017 23.3601i −0.281504 0.866380i −0.987425 0.158089i $$-0.949467\pi$$
0.705921 0.708291i $$-0.250533\pi$$
$$728$$ 0 0
$$729$$ −10.5172 + 7.64121i −0.389527 + 0.283008i
$$730$$ 0 0
$$731$$ 20.5623 + 14.9394i 0.760524 + 0.552553i
$$732$$ 0 0
$$733$$ 16.1631 + 11.7432i 0.596998 + 0.433745i 0.844812 0.535063i $$-0.179712\pi$$
−0.247814 + 0.968808i $$0.579712\pi$$
$$734$$ 0 0
$$735$$ −4.57295 14.0741i −0.168676 0.519131i
$$736$$ 0 0
$$737$$ −7.70820 + 23.7234i −0.283935 + 0.873863i
$$738$$ 0 0
$$739$$ −4.93769 15.1967i −0.181636 0.559018i 0.818238 0.574879i $$-0.194951\pi$$
−0.999874 + 0.0158612i $$0.994951\pi$$
$$740$$ 0 0
$$741$$ 0.489357 1.50609i 0.0179770 0.0553274i
$$742$$ 0 0
$$743$$ −28.3607 −1.04045 −0.520226 0.854029i $$-0.674152\pi$$
−0.520226 + 0.854029i $$0.674152\pi$$
$$744$$ 0 0
$$745$$ 2.72542 8.38800i 0.0998518 0.307312i
$$746$$ 0 0
$$747$$ 10.0902 7.33094i 0.369180 0.268225i
$$748$$ 0 0
$$749$$ −10.1459 −0.370723
$$750$$ 0 0
$$751$$ 5.11146 0.186520 0.0932598 0.995642i $$-0.470271\pi$$
0.0932598 + 0.995642i $$0.470271\pi$$
$$752$$ 0 0
$$753$$ 23.6074 17.1518i 0.860301 0.625045i
$$754$$ 0 0
$$755$$ 10.0623 30.9686i 0.366205 1.12706i
$$756$$ 0 0
$$757$$ 30.4164 1.10550 0.552752 0.833346i $$-0.313578\pi$$
0.552752 + 0.833346i $$0.313578\pi$$
$$758$$ 0 0
$$759$$ 6.09017 18.7436i 0.221059 0.680350i
$$760$$ 0 0
$$761$$ −5.70163 17.5478i −0.206684 0.636107i −0.999640 0.0268287i $$-0.991459\pi$$
0.792956 0.609279i $$-0.208541\pi$$
$$762$$ 0 0
$$763$$ −1.90983 + 5.87785i −0.0691405 + 0.212793i
$$764$$ 0 0
$$765$$ −7.23607 22.2703i −0.261621 0.805185i
$$766$$ 0 0
$$767$$ −16.2812 11.8290i −0.587878 0.427119i
$$768$$ 0 0
$$769$$ −10.8541 7.88597i −0.391409 0.284375i 0.374624 0.927177i $$-0.377772\pi$$
−0.766033 + 0.642802i $$0.777772\pi$$
$$770$$ 0 0
$$771$$ 18.4894 13.4333i 0.665878 0.483789i
$$772$$ 0 0
$$773$$ −11.1738 34.3893i −0.401892 1.23690i −0.923462 0.383689i $$-0.874654\pi$$
0.521570 0.853208i $$-0.325346\pi$$
$$774$$ 0 0
$$775$$ 4.63525 + 14.2658i 0.166503 + 0.512444i
$$776$$ 0 0
$$777$$ −0.0450850 0.138757i −0.00161741 0.00497789i
$$778$$ 0 0
$$779$$ −0.527864 + 0.383516i −0.0189127 + 0.0137409i
$$780$$ 0 0
$$781$$ −28.0344 20.3682i −1.00315 0.728832i
$$782$$ 0 0
$$783$$ 14.6353 + 10.6331i 0.523021 + 0.379997i
$$784$$ 0 0
$$785$$ −9.10739 + 28.0297i −0.325057 + 1.00042i
$$786$$ 0 0
$$787$$ 3.65248 11.2412i 0.130197 0.400704i −0.864615 0.502434i $$-0.832438\pi$$
0.994812 + 0.101730i $$0.0324378\pi$$
$$788$$ 0 0
$$789$$ −3.37132 10.3759i −0.120022 0.369391i
$$790$$ 0 0
$$791$$ −3.21885 + 9.90659i −0.114449 + 0.352238i
$$792$$ 0 0
$$793$$ 16.1459