Properties

 Label 441.2.w.a.251.5 Level $441$ Weight $2$ Character 441.251 Analytic conductor $3.521$ Analytic rank $0$ Dimension $120$ CM no Inner twists $4$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 441.w (of order $$14$$, degree $$6$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$3.52140272914$$ Analytic rank: $$0$$ Dimension: $$120$$ Relative dimension: $$20$$ over $$\Q(\zeta_{14})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

 Embedding label 251.5 Character $$\chi$$ $$=$$ 441.251 Dual form 441.2.w.a.188.5

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.42590 - 1.13712i) q^{2} +(0.295114 + 1.29298i) q^{4} +(0.0720329 + 0.0346892i) q^{5} +(2.51149 - 0.832121i) q^{7} +(-0.533164 + 1.10713i) q^{8} +O(q^{10})$$ $$q+(-1.42590 - 1.13712i) q^{2} +(0.295114 + 1.29298i) q^{4} +(0.0720329 + 0.0346892i) q^{5} +(2.51149 - 0.832121i) q^{7} +(-0.533164 + 1.10713i) q^{8} +(-0.0632661 - 0.131373i) q^{10} +(0.0489389 + 0.0390274i) q^{11} +(3.06781 + 2.44650i) q^{13} +(-4.52735 - 1.66934i) q^{14} +(4.40896 - 2.12324i) q^{16} +(0.399548 - 1.75053i) q^{17} +5.46553i q^{19} +(-0.0235945 + 0.103374i) q^{20} +(-0.0254032 - 0.111299i) q^{22} +(4.14363 - 0.945756i) q^{23} +(-3.11346 - 3.90416i) q^{25} +(-1.59244 - 6.97692i) q^{26} +(1.81709 + 3.00173i) q^{28} +(8.80774 + 2.01031i) q^{29} -6.38885i q^{31} +(-6.30510 - 1.43910i) q^{32} +(-2.56028 + 2.04175i) q^{34} +(0.209775 + 0.0271815i) q^{35} +(0.385319 - 1.68819i) q^{37} +(6.21495 - 7.79331i) q^{38} +(-0.0768107 + 0.0612545i) q^{40} +(-6.08257 - 2.92921i) q^{41} +(1.79918 - 0.866440i) q^{43} +(-0.0360191 + 0.0747945i) q^{44} +(-6.98384 - 3.36324i) q^{46} +(2.99901 - 3.76064i) q^{47} +(5.61515 - 4.17972i) q^{49} +9.10732i q^{50} +(-2.25792 + 4.68861i) q^{52} +(-0.0985022 + 0.0224825i) q^{53} +(0.00217138 + 0.00450891i) q^{55} +(-0.417772 + 3.22419i) q^{56} +(-10.2730 - 12.8819i) q^{58} +(3.52530 - 1.69769i) q^{59} +(-3.20273 - 0.731001i) q^{61} +(-7.26488 + 9.10987i) q^{62} +(1.25183 + 1.56975i) q^{64} +(0.136116 + 0.282648i) q^{65} -13.0206 q^{67} +2.38132 q^{68} +(-0.268210 - 0.277298i) q^{70} +(2.96758 - 0.677330i) q^{71} +(0.291084 - 0.232132i) q^{73} +(-2.46910 + 1.96904i) q^{74} +(-7.06682 + 1.61296i) q^{76} +(0.155385 + 0.0572939i) q^{77} +10.2856 q^{79} +0.391244 q^{80} +(5.34228 + 11.0934i) q^{82} +(10.5324 + 13.2072i) q^{83} +(0.0895053 - 0.112236i) q^{85} +(-3.55070 - 0.810424i) q^{86} +(-0.0693007 + 0.0333735i) q^{88} +(-3.24641 - 4.07086i) q^{89} +(9.74055 + 3.59156i) q^{91} +(2.44569 + 5.07852i) q^{92} +(-8.55259 + 1.95207i) q^{94} +(-0.189595 + 0.393698i) q^{95} +13.6406i q^{97} +(-12.7595 - 0.425217i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$120 q + 24 q^{4}+O(q^{10})$$ 120 * q + 24 * q^4 $$120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100})$$ 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$$.

 $$n$$ $$199$$ $$344$$ $$\chi(n)$$ $$e\left(\frac{9}{14}\right)$$ $$-1$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.42590 1.13712i −1.00826 0.804064i −0.0275717 0.999620i $$-0.508777\pi$$
−0.980693 + 0.195556i $$0.937349\pi$$
$$3$$ 0 0
$$4$$ 0.295114 + 1.29298i 0.147557 + 0.646490i
$$5$$ 0.0720329 + 0.0346892i 0.0322141 + 0.0155135i 0.449921 0.893068i $$-0.351452\pi$$
−0.417707 + 0.908582i $$0.637166\pi$$
$$6$$ 0 0
$$7$$ 2.51149 0.832121i 0.949253 0.314512i
$$8$$ −0.533164 + 1.10713i −0.188502 + 0.391428i
$$9$$ 0 0
$$10$$ −0.0632661 0.131373i −0.0200065 0.0415439i
$$11$$ 0.0489389 + 0.0390274i 0.0147556 + 0.0117672i 0.630840 0.775913i $$-0.282710\pi$$
−0.616084 + 0.787680i $$0.711282\pi$$
$$12$$ 0 0
$$13$$ 3.06781 + 2.44650i 0.850857 + 0.678536i 0.948532 0.316682i $$-0.102569\pi$$
−0.0976743 + 0.995218i $$0.531140\pi$$
$$14$$ −4.52735 1.66934i −1.20999 0.446149i
$$15$$ 0 0
$$16$$ 4.40896 2.12324i 1.10224 0.530810i
$$17$$ 0.399548 1.75053i 0.0969046 0.424567i −0.903083 0.429465i $$-0.858702\pi$$
0.999988 + 0.00489839i $$0.00155921\pi$$
$$18$$ 0 0
$$19$$ 5.46553i 1.25388i 0.779068 + 0.626939i $$0.215693\pi$$
−0.779068 + 0.626939i $$0.784307\pi$$
$$20$$ −0.0235945 + 0.103374i −0.00527590 + 0.0231152i
$$21$$ 0 0
$$22$$ −0.0254032 0.111299i −0.00541597 0.0237289i
$$23$$ 4.14363 0.945756i 0.864006 0.197204i 0.232520 0.972592i $$-0.425303\pi$$
0.631485 + 0.775388i $$0.282446\pi$$
$$24$$ 0 0
$$25$$ −3.11346 3.90416i −0.622693 0.780832i
$$26$$ −1.59244 6.97692i −0.312303 1.36829i
$$27$$ 0 0
$$28$$ 1.81709 + 3.00173i 0.343398 + 0.567274i
$$29$$ 8.80774 + 2.01031i 1.63556 + 0.373305i 0.938924 0.344124i $$-0.111824\pi$$
0.696632 + 0.717429i $$0.254681\pi$$
$$30$$ 0 0
$$31$$ 6.38885i 1.14747i −0.819040 0.573736i $$-0.805494\pi$$
0.819040 0.573736i $$-0.194506\pi$$
$$32$$ −6.30510 1.43910i −1.11459 0.254399i
$$33$$ 0 0
$$34$$ −2.56028 + 2.04175i −0.439084 + 0.350158i
$$35$$ 0.209775 + 0.0271815i 0.0354585 + 0.00459451i
$$36$$ 0 0
$$37$$ 0.385319 1.68819i 0.0633461 0.277537i −0.933328 0.359024i $$-0.883110\pi$$
0.996674 + 0.0814866i $$0.0259668\pi$$
$$38$$ 6.21495 7.79331i 1.00820 1.26424i
$$39$$ 0 0
$$40$$ −0.0768107 + 0.0612545i −0.0121448 + 0.00968518i
$$41$$ −6.08257 2.92921i −0.949938 0.457466i −0.106274 0.994337i $$-0.533892\pi$$
−0.843664 + 0.536871i $$0.819606\pi$$
$$42$$ 0 0
$$43$$ 1.79918 0.866440i 0.274373 0.132131i −0.291638 0.956529i $$-0.594200\pi$$
0.566011 + 0.824398i $$0.308486\pi$$
$$44$$ −0.0360191 + 0.0747945i −0.00543009 + 0.0112757i
$$45$$ 0 0
$$46$$ −6.98384 3.36324i −1.02971 0.495882i
$$47$$ 2.99901 3.76064i 0.437451 0.548546i −0.513419 0.858138i $$-0.671621\pi$$
0.950869 + 0.309592i $$0.100193\pi$$
$$48$$ 0 0
$$49$$ 5.61515 4.17972i 0.802164 0.597103i
$$50$$ 9.10732i 1.28797i
$$51$$ 0 0
$$52$$ −2.25792 + 4.68861i −0.313117 + 0.650193i
$$53$$ −0.0985022 + 0.0224825i −0.0135303 + 0.00308821i −0.229281 0.973360i $$-0.573637\pi$$
0.215750 + 0.976449i $$0.430780\pi$$
$$54$$ 0 0
$$55$$ 0.00217138 + 0.00450891i 0.000292788 + 0.000607981i
$$56$$ −0.417772 + 3.22419i −0.0558272 + 0.430851i
$$57$$ 0 0
$$58$$ −10.2730 12.8819i −1.34891 1.69148i
$$59$$ 3.52530 1.69769i 0.458955 0.221021i −0.190097 0.981765i $$-0.560880\pi$$
0.649052 + 0.760744i $$0.275166\pi$$
$$60$$ 0 0
$$61$$ −3.20273 0.731001i −0.410067 0.0935951i 0.0125108 0.999922i $$-0.496018\pi$$
−0.422578 + 0.906327i $$0.638875\pi$$
$$62$$ −7.26488 + 9.10987i −0.922641 + 1.15695i
$$63$$ 0 0
$$64$$ 1.25183 + 1.56975i 0.156479 + 0.196219i
$$65$$ 0.136116 + 0.282648i 0.0168831 + 0.0350582i
$$66$$ 0 0
$$67$$ −13.0206 −1.59072 −0.795361 0.606135i $$-0.792719\pi$$
−0.795361 + 0.606135i $$0.792719\pi$$
$$68$$ 2.38132 0.288777
$$69$$ 0 0
$$70$$ −0.268210 0.277298i −0.0320573 0.0331434i
$$71$$ 2.96758 0.677330i 0.352187 0.0803843i −0.0427678 0.999085i $$-0.513618\pi$$
0.394954 + 0.918701i $$0.370760\pi$$
$$72$$ 0 0
$$73$$ 0.291084 0.232132i 0.0340688 0.0271690i −0.606307 0.795230i $$-0.707350\pi$$
0.640376 + 0.768061i $$0.278778\pi$$
$$74$$ −2.46910 + 1.96904i −0.287027 + 0.228897i
$$75$$ 0 0
$$76$$ −7.06682 + 1.61296i −0.810620 + 0.185019i
$$77$$ 0.155385 + 0.0572939i 0.0177078 + 0.00652925i
$$78$$ 0 0
$$79$$ 10.2856 1.15722 0.578609 0.815605i $$-0.303596\pi$$
0.578609 + 0.815605i $$0.303596\pi$$
$$80$$ 0.391244 0.0437424
$$81$$ 0 0
$$82$$ 5.34228 + 11.0934i 0.589957 + 1.22506i
$$83$$ 10.5324 + 13.2072i 1.15608 + 1.44968i 0.871074 + 0.491153i $$0.163424\pi$$
0.285006 + 0.958526i $$0.408004\pi$$
$$84$$ 0 0
$$85$$ 0.0895053 0.112236i 0.00970821 0.0121737i
$$86$$ −3.55070 0.810424i −0.382882 0.0873903i
$$87$$ 0 0
$$88$$ −0.0693007 + 0.0333735i −0.00738748 + 0.00355762i
$$89$$ −3.24641 4.07086i −0.344118 0.431511i 0.579413 0.815034i $$-0.303282\pi$$
−0.923531 + 0.383523i $$0.874711\pi$$
$$90$$ 0 0
$$91$$ 9.74055 + 3.59156i 1.02109 + 0.376498i
$$92$$ 2.44569 + 5.07852i 0.254980 + 0.529472i
$$93$$ 0 0
$$94$$ −8.55259 + 1.95207i −0.882132 + 0.201341i
$$95$$ −0.189595 + 0.393698i −0.0194520 + 0.0403926i
$$96$$ 0 0
$$97$$ 13.6406i 1.38499i 0.721422 + 0.692496i $$0.243489\pi$$
−0.721422 + 0.692496i $$0.756511\pi$$
$$98$$ −12.7595 0.425217i −1.28890 0.0429534i
$$99$$ 0 0
$$100$$ 4.12917 5.17782i 0.412917 0.517782i
$$101$$ 14.6900 + 7.07432i 1.46171 + 0.703921i 0.984584 0.174915i $$-0.0559650\pi$$
0.477124 + 0.878836i $$0.341679\pi$$
$$102$$ 0 0
$$103$$ −6.01021 + 12.4803i −0.592204 + 1.22972i 0.362449 + 0.932004i $$0.381941\pi$$
−0.954653 + 0.297720i $$0.903774\pi$$
$$104$$ −4.34422 + 2.09207i −0.425986 + 0.205144i
$$105$$ 0 0
$$106$$ 0.166020 + 0.0799508i 0.0161252 + 0.00776551i
$$107$$ −4.53315 + 3.61507i −0.438236 + 0.349482i −0.817620 0.575758i $$-0.804707\pi$$
0.379384 + 0.925239i $$0.376136\pi$$
$$108$$ 0 0
$$109$$ −1.20144 + 1.50656i −0.115077 + 0.144302i −0.836034 0.548678i $$-0.815131\pi$$
0.720957 + 0.692980i $$0.243703\pi$$
$$110$$ 0.00203100 0.00889837i 0.000193648 0.000848427i
$$111$$ 0 0
$$112$$ 9.30625 9.00128i 0.879358 0.850541i
$$113$$ −4.97507 + 3.96749i −0.468015 + 0.373230i −0.828915 0.559375i $$-0.811041\pi$$
0.360900 + 0.932605i $$0.382470\pi$$
$$114$$ 0 0
$$115$$ 0.331285 + 0.0756136i 0.0308925 + 0.00705101i
$$116$$ 11.9815i 1.11245i
$$117$$ 0 0
$$118$$ −6.95721 1.58794i −0.640463 0.146181i
$$119$$ −0.453195 4.72892i −0.0415444 0.433499i
$$120$$ 0 0
$$121$$ −2.44686 10.7204i −0.222442 0.974581i
$$122$$ 3.73554 + 4.68421i 0.338200 + 0.424089i
$$123$$ 0 0
$$124$$ 8.26066 1.88544i 0.741829 0.169318i
$$125$$ −0.177793 0.778961i −0.0159023 0.0696724i
$$126$$ 0 0
$$127$$ −2.40561 + 10.5397i −0.213463 + 0.935244i 0.748730 + 0.662876i $$0.230664\pi$$
−0.962193 + 0.272369i $$0.912193\pi$$
$$128$$ 9.27270i 0.819598i
$$129$$ 0 0
$$130$$ 0.127316 0.557808i 0.0111664 0.0489230i
$$131$$ −2.76634 + 1.33220i −0.241697 + 0.116395i −0.550811 0.834630i $$-0.685682\pi$$
0.309115 + 0.951025i $$0.399967\pi$$
$$132$$ 0 0
$$133$$ 4.54798 + 13.7266i 0.394360 + 1.19025i
$$134$$ 18.5661 + 14.8060i 1.60387 + 1.27904i
$$135$$ 0 0
$$136$$ 1.72504 + 1.37567i 0.147921 + 0.117963i
$$137$$ −0.739039 1.53463i −0.0631404 0.131112i 0.867011 0.498290i $$-0.166038\pi$$
−0.930151 + 0.367178i $$0.880324\pi$$
$$138$$ 0 0
$$139$$ −4.50183 + 9.34815i −0.381840 + 0.792900i 0.618136 + 0.786071i $$0.287888\pi$$
−0.999977 + 0.00682869i $$0.997826\pi$$
$$140$$ 0.0267626 + 0.279257i 0.00226185 + 0.0236015i
$$141$$ 0 0
$$142$$ −5.00167 2.40868i −0.419731 0.202132i
$$143$$ 0.0546546 + 0.239458i 0.00457045 + 0.0200244i
$$144$$ 0 0
$$145$$ 0.564711 + 0.450342i 0.0468967 + 0.0373989i
$$146$$ −0.679018 −0.0561959
$$147$$ 0 0
$$148$$ 2.29651 0.188772
$$149$$ −15.6797 12.5041i −1.28453 1.02438i −0.997795 0.0663657i $$-0.978860\pi$$
−0.286732 0.958011i $$-0.592569\pi$$
$$150$$ 0 0
$$151$$ −2.43375 10.6629i −0.198056 0.867738i −0.972093 0.234598i $$-0.924623\pi$$
0.774037 0.633140i $$-0.218234\pi$$
$$152$$ −6.05103 2.91402i −0.490803 0.236358i
$$153$$ 0 0
$$154$$ −0.156414 0.258386i −0.0126042 0.0208214i
$$155$$ 0.221624 0.460208i 0.0178013 0.0369648i
$$156$$ 0 0
$$157$$ 2.34186 + 4.86291i 0.186900 + 0.388103i 0.973273 0.229649i $$-0.0737579\pi$$
−0.786373 + 0.617752i $$0.788044\pi$$
$$158$$ −14.6662 11.6959i −1.16678 0.930476i
$$159$$ 0 0
$$160$$ −0.404253 0.322381i −0.0319590 0.0254865i
$$161$$ 9.61969 5.82325i 0.758137 0.458936i
$$162$$ 0 0
$$163$$ 1.10485 0.532066i 0.0865382 0.0416746i −0.390114 0.920767i $$-0.627564\pi$$
0.476652 + 0.879092i $$0.341850\pi$$
$$164$$ 1.99236 8.72909i 0.155577 0.681628i
$$165$$ 0 0
$$166$$ 30.8087i 2.39122i
$$167$$ −4.81868 + 21.1120i −0.372881 + 1.63370i 0.345764 + 0.938321i $$0.387620\pi$$
−0.718645 + 0.695377i $$0.755237\pi$$
$$168$$ 0 0
$$169$$ 0.533339 + 2.33671i 0.0410260 + 0.179747i
$$170$$ −0.255251 + 0.0582594i −0.0195769 + 0.00446829i
$$171$$ 0 0
$$172$$ 1.65125 + 2.07061i 0.125907 + 0.157882i
$$173$$ −3.33599 14.6159i −0.253630 1.11123i −0.927926 0.372765i $$-0.878410\pi$$
0.674295 0.738462i $$-0.264447\pi$$
$$174$$ 0 0
$$175$$ −11.0682 7.21448i −0.836674 0.545363i
$$176$$ 0.298634 + 0.0681613i 0.0225104 + 0.00513785i
$$177$$ 0 0
$$178$$ 9.49620i 0.711770i
$$179$$ −3.72363 0.849895i −0.278317 0.0635241i 0.0810837 0.996707i $$-0.474162\pi$$
−0.359401 + 0.933183i $$0.617019\pi$$
$$180$$ 0 0
$$181$$ 14.2509 11.3647i 1.05926 0.844730i 0.0709924 0.997477i $$-0.477383\pi$$
0.988265 + 0.152747i $$0.0488120\pi$$
$$182$$ −9.80503 16.1974i −0.726797 1.20063i
$$183$$ 0 0
$$184$$ −1.16216 + 5.09176i −0.0856756 + 0.375369i
$$185$$ 0.0863178 0.108239i 0.00634621 0.00795790i
$$186$$ 0 0
$$187$$ 0.0878723 0.0700758i 0.00642586 0.00512445i
$$188$$ 5.74749 + 2.76784i 0.419178 + 0.201866i
$$189$$ 0 0
$$190$$ 0.718025 0.345783i 0.0520910 0.0250857i
$$191$$ −2.12895 + 4.42080i −0.154045 + 0.319878i −0.963682 0.267054i $$-0.913950\pi$$
0.809637 + 0.586932i $$0.199664\pi$$
$$192$$ 0 0
$$193$$ −0.0963446 0.0463971i −0.00693503 0.00333974i 0.430413 0.902632i $$-0.358368\pi$$
−0.437348 + 0.899292i $$0.644082\pi$$
$$194$$ 15.5110 19.4501i 1.11362 1.39644i
$$195$$ 0 0
$$196$$ 7.06141 + 6.02678i 0.504386 + 0.430484i
$$197$$ 27.0265i 1.92556i −0.270294 0.962778i $$-0.587121\pi$$
0.270294 0.962778i $$-0.412879\pi$$
$$198$$ 0 0
$$199$$ −3.33989 + 6.93534i −0.236758 + 0.491633i −0.985166 0.171606i $$-0.945104\pi$$
0.748408 + 0.663239i $$0.230819\pi$$
$$200$$ 5.98238 1.36544i 0.423018 0.0965512i
$$201$$ 0 0
$$202$$ −12.9021 26.7915i −0.907790 1.88504i
$$203$$ 23.7934 2.28023i 1.66997 0.160041i
$$204$$ 0 0
$$205$$ −0.336533 0.421999i −0.0235045 0.0294737i
$$206$$ 22.7616 10.9614i 1.58587 0.763717i
$$207$$ 0 0
$$208$$ 18.7203 + 4.27280i 1.29802 + 0.296265i
$$209$$ −0.213306 + 0.267477i −0.0147547 + 0.0185018i
$$210$$ 0 0
$$211$$ −10.5551 13.2356i −0.726641 0.911179i 0.272052 0.962283i $$-0.412298\pi$$
−0.998693 + 0.0511032i $$0.983726\pi$$
$$212$$ −0.0581388 0.120726i −0.00399299 0.00829152i
$$213$$ 0 0
$$214$$ 10.5746 0.722863
$$215$$ 0.159656 0.0108885
$$216$$ 0 0
$$217$$ −5.31630 16.0455i −0.360894 1.08924i
$$218$$ 3.42627 0.782023i 0.232056 0.0529653i
$$219$$ 0 0
$$220$$ −0.00518913 + 0.00413819i −0.000349851 + 0.000278997i
$$221$$ 5.50841 4.39281i 0.370536 0.295493i
$$222$$ 0 0
$$223$$ −18.1221 + 4.13624i −1.21354 + 0.276983i −0.780943 0.624602i $$-0.785261\pi$$
−0.432600 + 0.901586i $$0.642404\pi$$
$$224$$ −17.0327 + 1.63233i −1.13804 + 0.109064i
$$225$$ 0 0
$$226$$ 11.6055 0.771983
$$227$$ −10.6354 −0.705899 −0.352950 0.935642i $$-0.614821\pi$$
−0.352950 + 0.935642i $$0.614821\pi$$
$$228$$ 0 0
$$229$$ 6.60218 + 13.7096i 0.436285 + 0.905954i 0.996960 + 0.0779185i $$0.0248274\pi$$
−0.560675 + 0.828036i $$0.689458\pi$$
$$230$$ −0.386398 0.484528i −0.0254783 0.0319488i
$$231$$ 0 0
$$232$$ −6.92163 + 8.67945i −0.454427 + 0.569834i
$$233$$ −27.6145 6.30283i −1.80908 0.412912i −0.821527 0.570169i $$-0.806878\pi$$
−0.987558 + 0.157258i $$0.949735\pi$$
$$234$$ 0 0
$$235$$ 0.346481 0.166857i 0.0226019 0.0108845i
$$236$$ 3.23545 + 4.05713i 0.210610 + 0.264096i
$$237$$ 0 0
$$238$$ −4.73113 + 7.25831i −0.306673 + 0.470486i
$$239$$ −4.08821 8.48926i −0.264444 0.549125i 0.725892 0.687808i $$-0.241427\pi$$
−0.990337 + 0.138684i $$0.955713\pi$$
$$240$$ 0 0
$$241$$ 17.7669 4.05517i 1.14446 0.261216i 0.392074 0.919934i $$-0.371758\pi$$
0.752390 + 0.658717i $$0.228901\pi$$
$$242$$ −8.70137 + 18.0686i −0.559345 + 1.16149i
$$243$$ 0 0
$$244$$ 4.35679i 0.278915i
$$245$$ 0.549467 0.106292i 0.0351042 0.00679078i
$$246$$ 0 0
$$247$$ −13.3714 + 16.7672i −0.850802 + 1.06687i
$$248$$ 7.07326 + 3.40630i 0.449153 + 0.216301i
$$249$$ 0 0
$$250$$ −0.632256 + 1.31289i −0.0399874 + 0.0830347i
$$251$$ 18.9959 9.14794i 1.19901 0.577413i 0.275617 0.961268i $$-0.411118\pi$$
0.923393 + 0.383855i $$0.125404\pi$$
$$252$$ 0 0
$$253$$ 0.239695 + 0.115431i 0.0150695 + 0.00725708i
$$254$$ 15.4150 12.2931i 0.967224 0.771335i
$$255$$ 0 0
$$256$$ 13.0478 16.3614i 0.815489 1.02259i
$$257$$ −4.03415 + 17.6748i −0.251644 + 1.10252i 0.678290 + 0.734794i $$0.262721\pi$$
−0.929933 + 0.367728i $$0.880136\pi$$
$$258$$ 0 0
$$259$$ −0.437056 4.56051i −0.0271574 0.283376i
$$260$$ −0.325289 + 0.259409i −0.0201735 + 0.0160879i
$$261$$ 0 0
$$262$$ 5.45940 + 1.24607i 0.337283 + 0.0769826i
$$263$$ 19.8437i 1.22361i 0.791007 + 0.611807i $$0.209557\pi$$
−0.791007 + 0.611807i $$0.790443\pi$$
$$264$$ 0 0
$$265$$ −0.00787530 0.00179749i −0.000483776 0.000110419i
$$266$$ 9.12382 24.7444i 0.559417 1.51718i
$$267$$ 0 0
$$268$$ −3.84257 16.8354i −0.234722 1.02839i
$$269$$ −12.2821 15.4012i −0.748852 0.939030i 0.250727 0.968058i $$-0.419330\pi$$
−0.999579 + 0.0290276i $$0.990759\pi$$
$$270$$ 0 0
$$271$$ −10.3442 + 2.36100i −0.628365 + 0.143420i −0.524832 0.851206i $$-0.675872\pi$$
−0.103533 + 0.994626i $$0.533015\pi$$
$$272$$ −1.95522 8.56637i −0.118552 0.519412i
$$273$$ 0 0
$$274$$ −0.691259 + 3.02861i −0.0417605 + 0.182965i
$$275$$ 0.312576i 0.0188490i
$$276$$ 0 0
$$277$$ 2.67833 11.7345i 0.160925 0.705059i −0.828497 0.559994i $$-0.810804\pi$$
0.989422 0.145066i $$-0.0463393\pi$$
$$278$$ 17.0491 8.21042i 1.02254 0.492428i
$$279$$ 0 0
$$280$$ −0.141938 + 0.217756i −0.00848242 + 0.0130134i
$$281$$ −12.8009 10.2084i −0.763638 0.608981i 0.162263 0.986748i $$-0.448121\pi$$
−0.925901 + 0.377766i $$0.876692\pi$$
$$282$$ 0 0
$$283$$ 4.21849 + 3.36413i 0.250763 + 0.199977i 0.740802 0.671724i $$-0.234446\pi$$
−0.490038 + 0.871701i $$0.663017\pi$$
$$284$$ 1.75155 + 3.63713i 0.103935 + 0.215824i
$$285$$ 0 0
$$286$$ 0.194359 0.403591i 0.0114927 0.0238649i
$$287$$ −17.7138 2.29525i −1.04561 0.135484i
$$288$$ 0 0
$$289$$ 12.4117 + 5.97718i 0.730102 + 0.351599i
$$290$$ −0.293130 1.28429i −0.0172132 0.0754159i
$$291$$ 0 0
$$292$$ 0.386044 + 0.307860i 0.0225915 + 0.0180162i
$$293$$ −5.02608 −0.293627 −0.146813 0.989164i $$-0.546902\pi$$
−0.146813 + 0.989164i $$0.546902\pi$$
$$294$$ 0 0
$$295$$ 0.312829 0.0182136
$$296$$ 1.66360 + 1.32668i 0.0966951 + 0.0771117i
$$297$$ 0 0
$$298$$ 8.13899 + 35.6592i 0.471479 + 2.06568i
$$299$$ 15.0256 + 7.23597i 0.868955 + 0.418467i
$$300$$ 0 0
$$301$$ 3.79764 3.67319i 0.218892 0.211719i
$$302$$ −8.65475 + 17.9718i −0.498025 + 1.03416i
$$303$$ 0 0
$$304$$ 11.6046 + 24.0973i 0.665572 + 1.38207i
$$305$$ −0.205344 0.163756i −0.0117580 0.00937666i
$$306$$ 0 0
$$307$$ 21.7077 + 17.3113i 1.23892 + 0.988007i 0.999855 + 0.0170033i $$0.00541258\pi$$
0.239066 + 0.971003i $$0.423159\pi$$
$$308$$ −0.0282236 + 0.217818i −0.00160819 + 0.0124113i
$$309$$ 0 0
$$310$$ −0.839325 + 0.404198i −0.0476704 + 0.0229569i
$$311$$ −7.38544 + 32.3577i −0.418790 + 1.83484i 0.120492 + 0.992714i $$0.461553\pi$$
−0.539282 + 0.842125i $$0.681304\pi$$
$$312$$ 0 0
$$313$$ 21.9941i 1.24318i −0.783344 0.621589i $$-0.786488\pi$$
0.783344 0.621589i $$-0.213512\pi$$
$$314$$ 2.19045 9.59700i 0.123614 0.541590i
$$315$$ 0 0
$$316$$ 3.03542 + 13.2990i 0.170756 + 0.748129i
$$317$$ −32.1185 + 7.33084i −1.80395 + 0.411741i −0.986434 0.164159i $$-0.947509\pi$$
−0.817520 + 0.575900i $$0.804652\pi$$
$$318$$ 0 0
$$319$$ 0.352584 + 0.442126i 0.0197409 + 0.0247543i
$$320$$ 0.0357198 + 0.156499i 0.00199680 + 0.00874855i
$$321$$ 0 0
$$322$$ −20.3384 2.63534i −1.13342 0.146862i
$$323$$ 9.56760 + 2.18374i 0.532355 + 0.121507i
$$324$$ 0 0
$$325$$ 19.5943i 1.08690i
$$326$$ −2.18042 0.497667i −0.120762 0.0275632i
$$327$$ 0 0
$$328$$ 6.48601 5.17242i 0.358130 0.285599i
$$329$$ 4.40268 11.9404i 0.242727 0.658293i
$$330$$ 0 0
$$331$$ −6.11936 + 26.8107i −0.336350 + 1.47365i 0.470241 + 0.882538i $$0.344167\pi$$
−0.806591 + 0.591109i $$0.798690\pi$$
$$332$$ −13.9684 + 17.5158i −0.766614 + 0.961304i
$$333$$ 0 0
$$334$$ 30.8778 24.6243i 1.68956 1.34738i
$$335$$ −0.937914 0.451675i −0.0512437 0.0246777i
$$336$$ 0 0
$$337$$ −16.9593 + 8.16718i −0.923834 + 0.444895i −0.834438 0.551101i $$-0.814208\pi$$
−0.0893953 + 0.995996i $$0.528493\pi$$
$$338$$ 1.89663 3.93838i 0.103163 0.214220i
$$339$$ 0 0
$$340$$ 0.171533 + 0.0826060i 0.00930269 + 0.00447994i
$$341$$ 0.249341 0.312663i 0.0135025 0.0169317i
$$342$$ 0 0
$$343$$ 10.6244 15.1698i 0.573661 0.819093i
$$344$$ 2.45388i 0.132304i
$$345$$ 0 0
$$346$$ −11.8632 + 24.6342i −0.637771 + 1.32435i
$$347$$ −6.86589 + 1.56709i −0.368580 + 0.0841260i −0.402799 0.915288i $$-0.631963\pi$$
0.0342191 + 0.999414i $$0.489106\pi$$
$$348$$ 0 0
$$349$$ −12.1607 25.2520i −0.650947 1.35171i −0.921265 0.388935i $$-0.872843\pi$$
0.270318 0.962771i $$-0.412871\pi$$
$$350$$ 7.57839 + 22.8729i 0.405082 + 1.22261i
$$351$$ 0 0
$$352$$ −0.252400 0.316500i −0.0134530 0.0168695i
$$353$$ −22.4618 + 10.8170i −1.19552 + 0.575732i −0.922395 0.386247i $$-0.873771\pi$$
−0.273124 + 0.961979i $$0.588057\pi$$
$$354$$ 0 0
$$355$$ 0.237259 + 0.0541529i 0.0125924 + 0.00287414i
$$356$$ 4.30548 5.39891i 0.228190 0.286141i
$$357$$ 0 0
$$358$$ 4.34310 + 5.44608i 0.229540 + 0.287834i
$$359$$ 4.16953 + 8.65812i 0.220059 + 0.456958i 0.981547 0.191221i $$-0.0612449\pi$$
−0.761487 + 0.648180i $$0.775531\pi$$
$$360$$ 0 0
$$361$$ −10.8720 −0.572212
$$362$$ −33.2433 −1.74723
$$363$$ 0 0
$$364$$ −1.76924 + 13.6543i −0.0927334 + 0.715677i
$$365$$ 0.0290201 0.00662364i 0.00151898 0.000346697i
$$366$$ 0 0
$$367$$ 16.2513 12.9600i 0.848310 0.676505i −0.0996053 0.995027i $$-0.531758\pi$$
0.947915 + 0.318522i $$0.103187\pi$$
$$368$$ 16.2610 12.9677i 0.847663 0.675989i
$$369$$ 0 0
$$370$$ −0.246161 + 0.0561847i −0.0127973 + 0.00292090i
$$371$$ −0.228679 + 0.138430i −0.0118724 + 0.00718694i
$$372$$ 0 0
$$373$$ 23.7079 1.22755 0.613774 0.789482i $$-0.289650\pi$$
0.613774 + 0.789482i $$0.289650\pi$$
$$374$$ −0.204982 −0.0105993
$$375$$ 0 0
$$376$$ 2.56454 + 5.32532i 0.132256 + 0.274633i
$$377$$ 22.1023 + 27.7154i 1.13832 + 1.42741i
$$378$$ 0 0
$$379$$ −17.2796 + 21.6679i −0.887594 + 1.11301i 0.105352 + 0.994435i $$0.466403\pi$$
−0.992945 + 0.118572i $$0.962168\pi$$
$$380$$ −0.564996 0.128957i −0.0289837 0.00661533i
$$381$$ 0 0
$$382$$ 8.06264 3.88276i 0.412521 0.198659i
$$383$$ 22.3799 + 28.0635i 1.14356 + 1.43398i 0.883527 + 0.468380i $$0.155162\pi$$
0.260033 + 0.965600i $$0.416267\pi$$
$$384$$ 0 0
$$385$$ 0.00920535 + 0.00951723i 0.000469148 + 0.000485043i
$$386$$ 0.0846188 + 0.175713i 0.00430699 + 0.00894355i
$$387$$ 0 0
$$388$$ −17.6370 + 4.02553i −0.895384 + 0.204365i
$$389$$ −7.63642 + 15.8572i −0.387182 + 0.803992i 0.612724 + 0.790297i $$0.290074\pi$$
−0.999906 + 0.0136948i $$0.995641\pi$$
$$390$$ 0 0
$$391$$ 7.63143i 0.385938i
$$392$$ 1.63369 + 8.44515i 0.0825136 + 0.426545i
$$393$$ 0 0
$$394$$ −30.7323 + 38.5371i −1.54827 + 1.94147i
$$395$$ 0.740899 + 0.356798i 0.0372787 + 0.0179525i
$$396$$ 0 0
$$397$$ −8.96807 + 18.6224i −0.450094 + 0.934630i 0.545252 + 0.838272i $$0.316434\pi$$
−0.995347 + 0.0963585i $$0.969280\pi$$
$$398$$ 12.6487 6.09127i 0.634020 0.305328i
$$399$$ 0 0
$$400$$ −22.0166 10.6026i −1.10083 0.530132i
$$401$$ 29.6733 23.6636i 1.48181 1.18171i 0.541827 0.840490i $$-0.317733\pi$$
0.939985 0.341216i $$-0.110839\pi$$
$$402$$ 0 0
$$403$$ 15.6303 19.5998i 0.778601 0.976335i
$$404$$ −4.81173 + 21.0816i −0.239393 + 1.04885i
$$405$$ 0 0
$$406$$ −36.5199 23.8045i −1.81245 1.18140i
$$407$$ 0.0847430 0.0675803i 0.00420055 0.00334983i
$$408$$ 0 0
$$409$$ 4.32746 + 0.987715i 0.213979 + 0.0488394i 0.328167 0.944620i $$-0.393569\pi$$
−0.114187 + 0.993459i $$0.536426\pi$$
$$410$$ 0.984407i 0.0486164i
$$411$$ 0 0
$$412$$ −17.9105 4.08796i −0.882388 0.201399i
$$413$$ 7.44106 7.19722i 0.366151 0.354152i
$$414$$ 0 0
$$415$$ 0.300531 + 1.31671i 0.0147525 + 0.0646349i
$$416$$ −15.8221 19.8403i −0.775742 0.972750i
$$417$$ 0 0
$$418$$ 0.608306 0.138842i 0.0297532 0.00679097i
$$419$$ −6.17213 27.0419i −0.301528 1.32108i −0.867820 0.496878i $$-0.834480\pi$$
0.566292 0.824205i $$-0.308377\pi$$
$$420$$ 0 0
$$421$$ 1.22091 5.34915i 0.0595035 0.260702i −0.936423 0.350874i $$-0.885885\pi$$
0.995926 + 0.0901721i $$0.0287417\pi$$
$$422$$ 30.8751i 1.50298i
$$423$$ 0 0
$$424$$ 0.0276269 0.121041i 0.00134168 0.00587828i
$$425$$ −8.07834 + 3.89032i −0.391857 + 0.188708i
$$426$$ 0 0
$$427$$ −8.65189 + 0.829153i −0.418694 + 0.0401255i
$$428$$ −6.01200 4.79441i −0.290601 0.231747i
$$429$$ 0 0
$$430$$ −0.227654 0.181548i −0.0109785 0.00875503i
$$431$$ 9.97595 + 20.7153i 0.480525 + 0.997819i 0.990485 + 0.137622i $$0.0439458\pi$$
−0.509960 + 0.860198i $$0.670340\pi$$
$$432$$ 0 0
$$433$$ −2.52920 + 5.25193i −0.121545 + 0.252392i −0.952860 0.303411i $$-0.901875\pi$$
0.831314 + 0.555802i $$0.187589\pi$$
$$434$$ −10.6652 + 28.9246i −0.511944 + 1.38843i
$$435$$ 0 0
$$436$$ −2.30251 1.10883i −0.110270 0.0531033i
$$437$$ 5.16906 + 22.6471i 0.247270 + 1.08336i
$$438$$ 0 0
$$439$$ −21.0324 16.7728i −1.00382 0.800522i −0.0238631 0.999715i $$-0.507597\pi$$
−0.979960 + 0.199193i $$0.936168\pi$$
$$440$$ −0.00614963 −0.000293172
$$441$$ 0 0
$$442$$ −12.8496 −0.611193
$$443$$ −7.69731 6.13840i −0.365710 0.291644i 0.423342 0.905970i $$-0.360857\pi$$
−0.789053 + 0.614325i $$0.789428\pi$$
$$444$$ 0 0
$$445$$ −0.0926330 0.405851i −0.00439122 0.0192392i
$$446$$ 30.5437 + 14.7091i 1.44628 + 0.696494i
$$447$$ 0 0
$$448$$ 4.45019 + 2.90073i 0.210252 + 0.137047i
$$449$$ 7.61349 15.8096i 0.359303 0.746100i −0.640458 0.767993i $$-0.721255\pi$$
0.999760 + 0.0218939i $$0.00696960\pi$$
$$450$$ 0 0
$$451$$ −0.183354 0.380739i −0.00863383 0.0179283i
$$452$$ −6.59809 5.26180i −0.310348 0.247494i
$$453$$ 0 0
$$454$$ 15.1651 + 12.0938i 0.711733 + 0.567588i
$$455$$ 0.577052 + 0.596603i 0.0270526 + 0.0279692i
$$456$$ 0 0
$$457$$ 15.7239 7.57225i 0.735535 0.354215i −0.0283235 0.999599i $$-0.509017\pi$$
0.763858 + 0.645384i $$0.223303\pi$$
$$458$$ 6.17535 27.0560i 0.288555 1.26424i
$$459$$ 0 0
$$460$$ 0.450659i 0.0210121i
$$461$$ 0.302478 1.32524i 0.0140878 0.0617227i −0.967395 0.253271i $$-0.918494\pi$$
0.981483 + 0.191548i $$0.0613508\pi$$
$$462$$ 0 0
$$463$$ −4.63599 20.3116i −0.215453 0.943961i −0.960791 0.277274i $$-0.910569\pi$$
0.745338 0.666687i $$-0.232288\pi$$
$$464$$ 43.1013 9.83760i 2.00093 0.456699i
$$465$$ 0 0
$$466$$ 32.2085 + 40.3881i 1.49203 + 1.87094i
$$467$$ −4.83052 21.1639i −0.223530 0.979349i −0.954797 0.297258i $$-0.903928\pi$$
0.731267 0.682091i $$-0.238929\pi$$
$$468$$ 0 0
$$469$$ −32.7012 + 10.8347i −1.51000 + 0.500302i
$$470$$ −0.683784 0.156069i −0.0315406 0.00719893i
$$471$$ 0 0
$$472$$ 4.80810i 0.221311i
$$473$$ 0.121865 + 0.0278149i 0.00560335 + 0.00127893i
$$474$$ 0 0
$$475$$ 21.3383 17.0167i 0.979069 0.780781i
$$476$$ 5.98065 1.98154i 0.274123 0.0908239i
$$477$$ 0 0
$$478$$ −3.82390 + 16.7536i −0.174901 + 0.766293i
$$479$$ 0.615662 0.772016i 0.0281303 0.0352743i −0.767567 0.640968i $$-0.778533\pi$$
0.795698 + 0.605694i $$0.207104\pi$$
$$480$$ 0 0
$$481$$ 5.31225 4.23638i 0.242218 0.193162i
$$482$$ −29.9450 14.4207i −1.36396 0.656847i
$$483$$ 0 0
$$484$$ 13.1391 6.32748i 0.597234 0.287613i
$$485$$ −0.473182 + 0.982572i −0.0214861 + 0.0446163i
$$486$$ 0 0
$$487$$ −31.5848 15.2104i −1.43124 0.689251i −0.452016 0.892010i $$-0.649295\pi$$
−0.979229 + 0.202759i $$0.935009\pi$$
$$488$$ 2.51689 3.15608i 0.113934 0.142869i
$$489$$ 0 0
$$490$$ −0.904352 0.473246i −0.0408545 0.0213791i
$$491$$ 11.8176i 0.533321i 0.963791 + 0.266660i $$0.0859202\pi$$
−0.963791 + 0.266660i $$0.914080\pi$$
$$492$$ 0 0
$$493$$ 7.03823 14.6150i 0.316986 0.658228i
$$494$$ 38.1326 8.70352i 1.71567 0.391590i
$$495$$ 0 0
$$496$$ −13.5651 28.1682i −0.609090 1.26479i
$$497$$ 6.88942 4.17049i 0.309033 0.187072i
$$498$$ 0 0
$$499$$ −24.7503 31.0359i −1.10798 1.38936i −0.912711 0.408607i $$-0.866015\pi$$
−0.195265 0.980751i $$-0.562557\pi$$
$$500$$ 0.954712 0.459765i 0.0426960 0.0205613i
$$501$$ 0 0
$$502$$ −37.4886 8.55652i −1.67320 0.381896i
$$503$$ 2.94170 3.68878i 0.131164 0.164474i −0.711912 0.702268i $$-0.752171\pi$$
0.843076 + 0.537794i $$0.180742\pi$$
$$504$$ 0 0
$$505$$ 0.812759 + 1.01917i 0.0361673 + 0.0453524i
$$506$$ −0.210522 0.437154i −0.00935886 0.0194339i
$$507$$ 0 0
$$508$$ −14.3375 −0.636124
$$509$$ 13.6927 0.606918 0.303459 0.952845i $$-0.401858\pi$$
0.303459 + 0.952845i $$0.401858\pi$$
$$510$$ 0 0
$$511$$ 0.537892 0.825213i 0.0237950 0.0365053i
$$512$$ −19.1294 + 4.36616i −0.845407 + 0.192959i
$$513$$ 0 0
$$514$$ 25.8506 20.6152i 1.14022 0.909297i
$$515$$ −0.865866 + 0.690505i −0.0381546 + 0.0304273i
$$516$$ 0 0
$$517$$ 0.293536 0.0669978i 0.0129097 0.00294656i
$$518$$ −4.56264 + 6.99982i −0.200471 + 0.307555i
$$519$$ 0 0
$$520$$ −0.385499 −0.0169053
$$521$$ −33.0259 −1.44689 −0.723446 0.690381i $$-0.757443\pi$$
−0.723446 + 0.690381i $$0.757443\pi$$
$$522$$ 0 0
$$523$$ 1.79046 + 3.71793i 0.0782913 + 0.162574i 0.936440 0.350827i $$-0.114100\pi$$
−0.858149 + 0.513401i $$0.828385\pi$$
$$524$$ −2.53890 3.18368i −0.110912 0.139079i
$$525$$ 0 0
$$526$$ 22.5646 28.2951i 0.983863 1.23373i
$$527$$ −11.1839 2.55265i −0.487179 0.111195i
$$528$$ 0 0
$$529$$ −4.44710 + 2.14161i −0.193352 + 0.0931136i
$$530$$ 0.00918544 + 0.0115182i 0.000398990 + 0.000500318i
$$531$$ 0 0
$$532$$ −16.4061 + 9.93137i −0.711293 + 0.430579i
$$533$$ −11.4939 23.8673i −0.497855 1.03381i
$$534$$ 0 0
$$535$$ −0.451940 + 0.103152i −0.0195391 + 0.00445966i
$$536$$ 6.94213 14.4155i 0.299854 0.622654i
$$537$$ 0 0
$$538$$ 35.9268i 1.54892i
$$539$$ 0.437923 + 0.0145940i 0.0188627 + 0.000628609i
$$540$$ 0 0
$$541$$ −4.69692 + 5.88975i −0.201936 + 0.253220i −0.872480 0.488650i $$-0.837489\pi$$
0.670544 + 0.741870i $$0.266061\pi$$
$$542$$ 17.4345 + 8.39603i 0.748877 + 0.360640i
$$543$$ 0 0
$$544$$ −5.03838 + 10.4623i −0.216019 + 0.448567i
$$545$$ −0.138804 + 0.0668447i −0.00594573 + 0.00286331i
$$546$$ 0 0
$$547$$ 9.81461 + 4.72647i 0.419642 + 0.202089i 0.631775 0.775152i $$-0.282327\pi$$
−0.212133 + 0.977241i $$0.568041\pi$$
$$548$$ 1.76614 1.40845i 0.0754460 0.0601662i
$$549$$ 0 0
$$550$$ −0.355435 + 0.445702i −0.0151558 + 0.0190048i
$$551$$ −10.9874 + 48.1390i −0.468079 + 2.05079i
$$552$$ 0 0
$$553$$ 25.8321 8.55884i 1.09849 0.363959i
$$554$$ −17.1626 + 13.6867i −0.729168 + 0.581492i
$$555$$ 0 0
$$556$$ −13.4155 3.06200i −0.568945 0.129858i
$$557$$ 20.9491i 0.887641i 0.896116 + 0.443821i $$0.146377\pi$$
−0.896116 + 0.443821i $$0.853623\pi$$
$$558$$ 0 0
$$559$$ 7.63929 + 1.74362i 0.323108 + 0.0737472i
$$560$$ 0.982604 0.325562i 0.0415226 0.0137575i
$$561$$ 0 0
$$562$$ 6.64469 + 29.1123i 0.280289 + 1.22803i
$$563$$ −7.84657 9.83929i −0.330694 0.414677i 0.588491 0.808504i $$-0.299722\pi$$
−0.919185 + 0.393827i $$0.871151\pi$$
$$564$$ 0 0
$$565$$ −0.495998 + 0.113208i −0.0208668 + 0.00476271i
$$566$$ −2.18973 9.59384i −0.0920413 0.403259i
$$567$$ 0 0
$$568$$ −0.832315 + 3.64661i −0.0349231 + 0.153008i
$$569$$ 23.8454i 0.999649i 0.866127 + 0.499825i $$0.166602\pi$$
−0.866127 + 0.499825i $$0.833398\pi$$
$$570$$ 0 0
$$571$$ −1.44405 + 6.32680i −0.0604317 + 0.264769i −0.996114 0.0880756i $$-0.971928\pi$$
0.935682 + 0.352844i $$0.114785\pi$$
$$572$$ −0.293484 + 0.141335i −0.0122712 + 0.00590950i
$$573$$ 0 0
$$574$$ 22.6481 + 23.4154i 0.945314 + 0.977342i
$$575$$ −16.5934 13.2328i −0.691993 0.551846i
$$576$$ 0 0
$$577$$ −33.3975 26.6336i −1.39036 1.10877i −0.980477 0.196633i $$-0.936999\pi$$
−0.409880 0.912140i $$-0.634429\pi$$
$$578$$ −10.9012 22.6365i −0.453428 0.941553i
$$579$$ 0 0
$$580$$ −0.415629 + 0.863062i −0.0172580 + 0.0358367i
$$581$$ 37.4420 + 24.4055i 1.55335 + 1.01251i
$$582$$ 0 0
$$583$$ −0.00569802 0.00274402i −0.000235988 0.000113646i
$$584$$ 0.101804 + 0.446031i 0.00421266 + 0.0184569i
$$585$$ 0 0
$$586$$ 7.16670 + 5.71525i 0.296053 + 0.236095i
$$587$$ 15.7350 0.649452 0.324726 0.945808i $$-0.394728\pi$$
0.324726 + 0.945808i $$0.394728\pi$$
$$588$$ 0 0
$$589$$ 34.9185 1.43879
$$590$$ −0.446064 0.355724i −0.0183641 0.0146449i
$$591$$ 0 0
$$592$$ −1.88559 8.26130i −0.0774972 0.339537i
$$593$$ −23.1968 11.1710i −0.952580 0.458738i −0.107990 0.994152i $$-0.534441\pi$$
−0.844590 + 0.535414i $$0.820156\pi$$
$$594$$ 0 0
$$595$$ 0.131397 0.356359i 0.00538677 0.0146093i
$$596$$ 11.5403 23.9636i 0.472708 0.981588i
$$597$$ 0 0
$$598$$ −13.1969 27.4037i −0.539663 1.12062i
$$599$$ −32.7391 26.1085i −1.33768 1.06677i −0.991707 0.128522i $$-0.958977\pi$$
−0.345975 0.938244i $$-0.612452\pi$$
$$600$$ 0 0
$$601$$ 12.1095 + 9.65701i 0.493957 + 0.393918i 0.838542 0.544838i $$-0.183409\pi$$
−0.344584 + 0.938755i $$0.611980\pi$$
$$602$$ −9.59192 + 0.919240i −0.390937 + 0.0374654i
$$603$$ 0 0
$$604$$ 13.0687 6.29357i 0.531759 0.256082i
$$605$$ 0.195628 0.857100i 0.00795339 0.0348461i
$$606$$ 0 0
$$607$$ 6.82644i 0.277077i −0.990357 0.138538i $$-0.955760\pi$$
0.990357 0.138538i $$-0.0442404\pi$$
$$608$$ 7.86543 34.4607i 0.318985 1.39757i
$$609$$ 0 0
$$610$$ 0.106590 + 0.467000i 0.00431569 + 0.0189083i
$$611$$ 18.4008 4.19986i 0.744417 0.169908i
$$612$$ 0 0
$$613$$ 5.74752 + 7.20716i 0.232140 + 0.291095i 0.884234 0.467043i $$-0.154681\pi$$
−0.652094 + 0.758138i $$0.726109\pi$$
$$614$$ −11.2680 49.3683i −0.454739 1.99234i
$$615$$ 0 0
$$616$$ −0.146277 + 0.141484i −0.00589368 + 0.00570054i
$$617$$ −17.3111 3.95114i −0.696918 0.159067i −0.140637 0.990061i $$-0.544915\pi$$
−0.556281 + 0.830994i $$0.687772\pi$$
$$618$$ 0 0
$$619$$ 4.78926i 0.192497i 0.995357 + 0.0962483i $$0.0306843\pi$$
−0.995357 + 0.0962483i $$0.969316\pi$$
$$620$$ 0.660444 + 0.150742i 0.0265241 + 0.00605394i
$$621$$ 0 0
$$622$$ 47.3255 37.7408i 1.89758 1.51327i
$$623$$ −11.5408 7.52253i −0.462371 0.301384i
$$624$$ 0 0
$$625$$ −5.54170 + 24.2798i −0.221668 + 0.971190i
$$626$$ −25.0098 + 31.3613i −0.999594 + 1.25345i
$$627$$ 0 0
$$628$$ −5.59653 + 4.46309i −0.223326 + 0.178097i
$$629$$ −2.80129 1.34903i −0.111695 0.0537893i
$$630$$ 0 0
$$631$$ 18.1773 8.75372i 0.723626 0.348480i −0.0355476 0.999368i $$-0.511318\pi$$
0.759174 + 0.650888i $$0.225603\pi$$
$$632$$ −5.48389 + 11.3874i −0.218138 + 0.452967i
$$633$$ 0 0
$$634$$ 54.1338 + 26.0695i 2.14993 + 1.03535i
$$635$$ −0.538896 + 0.675754i −0.0213854 + 0.0268165i
$$636$$ 0 0
$$637$$ 27.4519 + 0.914849i 1.08768 + 0.0362476i
$$638$$ 1.03136i 0.0408318i
$$639$$ 0 0
$$640$$ −0.321663 + 0.667939i −0.0127148 + 0.0264026i
$$641$$ 40.9493 9.34640i 1.61740 0.369161i 0.684419 0.729089i $$-0.260056\pi$$
0.932980 + 0.359928i $$0.117199\pi$$
$$642$$ 0 0
$$643$$ 19.3615 + 40.2045i 0.763541 + 1.58551i 0.809888 + 0.586585i $$0.199528\pi$$
−0.0463464 + 0.998925i $$0.514758\pi$$
$$644$$ 10.3683 + 10.7195i 0.408566 + 0.422409i
$$645$$ 0 0
$$646$$ −11.1593 13.9933i −0.439056 0.550559i
$$647$$ 23.4669 11.3011i 0.922578 0.444290i 0.0885873 0.996068i $$-0.471765\pi$$
0.833991 + 0.551778i $$0.186051\pi$$
$$648$$ 0 0
$$649$$ 0.238781 + 0.0545002i 0.00937297 + 0.00213932i
$$650$$ −22.2810 + 27.9395i −0.873934 + 1.09588i
$$651$$ 0 0
$$652$$ 1.01401 + 1.27152i 0.0397115 + 0.0497967i
$$653$$ −1.66044 3.44795i −0.0649782 0.134929i 0.865950 0.500130i $$-0.166714\pi$$
−0.930929 + 0.365201i $$0.881000\pi$$
$$654$$ 0 0
$$655$$ −0.245481 −0.00959173
$$656$$ −33.0372 −1.28989
$$657$$ 0 0
$$658$$ −19.8554 + 12.0194i −0.774043 + 0.468565i
$$659$$ 10.8991 2.48764i 0.424567 0.0969047i −0.00489821 0.999988i $$-0.501559\pi$$
0.429465 + 0.903083i $$0.358702\pi$$
$$660$$ 0 0
$$661$$ −25.5622 + 20.3852i −0.994256 + 0.792893i −0.978345 0.206981i $$-0.933636\pi$$
−0.0159108 + 0.999873i $$0.505065\pi$$
$$662$$ 39.2125 31.2709i 1.52404 1.21538i
$$663$$ 0 0
$$664$$ −20.2375 + 4.61908i −0.785368 + 0.179255i
$$665$$ −0.148561 + 1.14653i −0.00576096 + 0.0444607i
$$666$$ 0 0
$$667$$ 38.3972 1.48675
$$668$$ −28.7195 −1.11119
$$669$$ 0 0
$$670$$ 0.823764 + 1.71056i 0.0318248 + 0.0660848i
$$671$$ −0.128209 0.160769i −0.00494944 0.00620640i
$$672$$ 0 0
$$673$$ 26.9597 33.8063i 1.03922 1.30314i 0.0875005 0.996164i $$-0.472112\pi$$
0.951718 0.306974i $$-0.0993165\pi$$
$$674$$ 33.4694 + 7.63917i 1.28919 + 0.294250i
$$675$$ 0 0
$$676$$ −2.86392 + 1.37919i −0.110151 + 0.0530458i
$$677$$ −6.81052 8.54012i −0.261750 0.328224i 0.633539 0.773711i $$-0.281602\pi$$
−0.895288 + 0.445488i $$0.853030\pi$$
$$678$$ 0 0
$$679$$ 11.3506 + 34.2582i 0.435597 + 1.31471i
$$680$$ 0.0765385 + 0.158934i 0.00293512 + 0.00609483i
$$681$$ 0 0
$$682$$ −0.711070 + 0.162297i −0.0272283 + 0.00621468i
$$683$$ 0.211166 0.438491i 0.00808005 0.0167784i −0.896890 0.442254i $$-0.854179\pi$$
0.904970 + 0.425476i $$0.139893\pi$$
$$684$$ 0 0
$$685$$ 0.136181i 0.00520319i
$$686$$ −32.3991 + 9.54951i −1.23700 + 0.364602i
$$687$$ 0 0
$$688$$ 6.09285 7.64020i 0.232288 0.291280i
$$689$$ −0.357189 0.172013i −0.0136078 0.00655318i
$$690$$ 0 0
$$691$$ −13.8343 + 28.7273i −0.526283 + 1.09284i 0.453219 + 0.891399i $$0.350276\pi$$
−0.979501 + 0.201438i $$0.935439\pi$$
$$692$$ 17.9136 8.62672i 0.680972 0.327939i
$$693$$ 0 0
$$694$$ 11.5721 + 5.57281i 0.439269 + 0.211541i
$$695$$ −0.648560 + 0.517209i −0.0246013 + 0.0196189i
$$696$$ 0 0
$$697$$ −7.55796 + 9.47739i −0.286278 + 0.358982i
$$698$$ −11.3745 + 49.8349i −0.430531 + 1.88628i
$$699$$ 0 0
$$700$$ 6.06180 16.4400i 0.229114 0.621374i
$$701$$ 18.2624 14.5638i 0.689762 0.550067i −0.214669 0.976687i $$-0.568867\pi$$
0.904431 + 0.426620i $$0.140296\pi$$
$$702$$ 0 0
$$703$$ 9.22688 + 2.10597i 0.347998 + 0.0794283i
$$704$$ 0.125678i 0.00473666i
$$705$$ 0 0
$$706$$ 44.3285 + 10.1177i 1.66832 + 0.380784i
$$707$$ 42.7804 + 5.54324i 1.60892 + 0.208475i
$$708$$ 0 0
$$709$$ −8.46035 37.0672i −0.317735 1.39209i −0.841514 0.540235i $$-0.818336\pi$$
0.523779 0.851854i $$-0.324522\pi$$
$$710$$ −0.276730 0.347008i −0.0103855 0.0130230i
$$711$$ 0 0
$$712$$ 6.23782 1.42374i 0.233772 0.0533570i
$$713$$ −6.04229 26.4730i −0.226286 0.991422i
$$714$$ 0 0
$$715$$ −0.00436966 + 0.0191447i −0.000163416 + 0.000715973i
$$716$$ 5.06540i 0.189303i
$$717$$ 0 0
$$718$$ 3.89997 17.0869i 0.145545 0.637676i
$$719$$ −26.8474 + 12.9290i −1.00124 + 0.482171i −0.861359 0.507997i $$-0.830386\pi$$
−0.139880 + 0.990168i $$0.544672\pi$$
$$720$$ 0 0
$$721$$ −4.70943 + 36.3454i −0.175389 + 1.35358i
$$722$$ 15.5024 + 12.3628i 0.576941 + 0.460095i
$$723$$ 0 0
$$724$$ 18.8999 + 15.0722i 0.702410 + 0.560154i
$$725$$ −19.5740 40.6458i −0.726960 1.50955i
$$726$$ 0 0
$$727$$ −13.4164 + 27.8594i −0.497586 + 1.03325i 0.489343 + 0.872091i $$0.337237\pi$$
−0.986929 + 0.161156i $$0.948478\pi$$
$$728$$ −9.16962 + 8.86912i −0.339849 + 0.328712i
$$729$$ 0 0
$$730$$ −0.0489116 0.0235546i −0.00181030 0.000871795i
$$731$$ −0.797874 3.49571i −0.0295104 0.129294i
$$732$$ 0 0
$$733$$ −11.7287 9.35330i −0.433208 0.345472i 0.382480 0.923964i $$-0.375070\pi$$
−0.815688 + 0.578492i $$0.803641\pi$$
$$734$$ −37.9097 −1.39927
$$735$$ 0 0
$$736$$ −27.4870 −1.01318
$$737$$ −0.637215 0.508162i −0.0234721 0.0187184i
$$738$$ 0 0
$$739$$ 7.06950 + 30.9735i 0.260056 + 1.13938i 0.921191 + 0.389112i $$0.127218\pi$$
−0.661135 + 0.750267i $$0.729925\pi$$
$$740$$ 0.165425 + 0.0796643i 0.00608113 + 0.00292852i
$$741$$ 0 0
$$742$$ 0.483485 + 0.0626472i 0.0177493 + 0.00229985i
$$743$$ −9.78269 + 20.3140i −0.358892 + 0.745247i −0.999749 0.0224137i $$-0.992865\pi$$
0.640857 + 0.767660i $$0.278579\pi$$
$$744$$ 0 0
$$745$$ −0.695693 1.44462i −0.0254882 0.0529269i
$$746$$ −33.8051 26.9587i −1.23769 0.987027i
$$747$$ 0 0
$$748$$ 0.116539 + 0.0929367i 0.00426109 + 0.00339810i
$$749$$ −8.37678 + 12.8513i −0.306081 + 0.469577i
$$750$$ 0 0
$$751$$ 3.53737 1.70351i 0.129081 0.0621620i −0.368229 0.929735i $$-0.620036\pi$$
0.497309 + 0.867573i $$0.334321\pi$$
$$752$$ 5.23776 22.9481i 0.191002 0.836833i
$$753$$ 0 0
$$754$$ 64.6522i 2.35450i
$$755$$ 0.194579 0.852508i 0.00708147 0.0310259i
$$756$$ 0 0
$$757$$ −2.49190 10.9177i −0.0905696 0.396811i 0.909241 0.416270i $$-0.136663\pi$$
−0.999811 + 0.0194586i $$0.993806\pi$$
$$758$$ 49.2780 11.2474i 1.78986 0.408523i
$$759$$ 0 0
$$760$$ −0.334788 0.419811i −0.0121440 0.0152281i
$$761$$ −0.918025 4.02213i −0.0332784 0.145802i 0.955559 0.294799i $$-0.0952527\pi$$
−0.988838 + 0.148997i $$0.952396\pi$$
$$762$$ 0 0
$$763$$ −1.76376 + 4.78344i −0.0638525 + 0.173172i
$$764$$ −6.34429 1.44804i −0.229528 0.0523883i
$$765$$ 0 0
$$766$$ 65.4644i 2.36533i
$$767$$ 14.9684 + 3.41643i 0.540476 + 0.123360i
$$768$$ 0 0
$$769$$ −33.1561 + 26.4411i −1.19564 + 0.953491i −0.999632 0.0271112i $$-0.991369\pi$$
−0.196008 + 0.980602i $$0.562798\pi$$
$$770$$ −0.00230370 0.0240382i −8.30195e−5 0.000866276i
$$771$$ 0 0
$$772$$ 0.0315579 0.138264i 0.00113579 0.00497623i
$$773$$ −5.38928 + 6.75794i −0.193839 + 0.243066i −0.869247 0.494378i $$-0.835396\pi$$
0.675408 + 0.737444i $$0.263967\pi$$
$$774$$ 0 0
$$775$$ −24.9431 + 19.8915i −0.895983 + 0.714522i
$$776$$ −15.1019 7.27267i −0.542125 0.261074i
$$777$$ 0 0
$$778$$ 28.9203 13.9273i 1.03684 0.499317i
$$779$$ 16.0097 33.2445i 0.573607 1.19111i
$$780$$ 0 0
$$781$$ 0.171664 + 0.0826692i 0.00614263 + 0.00295814i
$$782$$ −8.67784 + 10.8817i −0.310319 + 0.389128i
$$783$$ 0 0
$$784$$ 15.8824 30.3505i 0.567228 1.08395i
$$785$$ 0.431527i 0.0154019i
$$786$$ 0 0
$$787$$ 16.5245 34.3135i 0.589035 1.22314i −0.367090 0.930185i $$-0.619646\pi$$
0.956125 0.292958i $$-0.0946397\pi$$