Properties

 Label 637.2.u.g.30.1 Level $637$ Weight $2$ Character 637.30 Analytic conductor $5.086$ Analytic rank $0$ Dimension $12$ CM no Inner twists $2$

Related objects

Newspace parameters

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

Newform invariants

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

Embedding invariants

 Embedding label 30.1 Root $$1.32725 - 0.488273i$$ of defining polynomial Character $$\chi$$ $$=$$ 637.30 Dual form 637.2.u.g.361.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(-2.24179 + 1.29430i) q^{2} -0.518466 q^{3} +(2.35043 - 4.07106i) q^{4} +(-1.39608 - 0.806027i) q^{5} +(1.16229 - 0.671051i) q^{6} +6.99143i q^{8} -2.73119 q^{9} +O(q^{10})$$ $$q+(-2.24179 + 1.29430i) q^{2} -0.518466 q^{3} +(2.35043 - 4.07106i) q^{4} +(-1.39608 - 0.806027i) q^{5} +(1.16229 - 0.671051i) q^{6} +6.99143i q^{8} -2.73119 q^{9} +4.17296 q^{10} +2.70496i q^{11} +(-1.21862 + 2.11070i) q^{12} +(-2.36840 - 2.71858i) q^{13} +(0.723819 + 0.417897i) q^{15} +(-4.34816 - 7.53123i) q^{16} +(-1.56330 + 2.70772i) q^{17} +(6.12277 - 3.53498i) q^{18} +3.68150i q^{19} +(-6.56276 + 3.78901i) q^{20} +(-3.50103 - 6.06396i) q^{22} +(0.993019 + 1.71996i) q^{23} -3.62482i q^{24} +(-1.20064 - 2.07957i) q^{25} +(8.82813 + 3.02907i) q^{26} +2.97143 q^{27} +(2.68636 - 4.65290i) q^{29} -2.16354 q^{30} +(9.07425 - 5.23902i) q^{31} +(7.38583 + 4.26421i) q^{32} -1.40243i q^{33} -8.09354i q^{34} +(-6.41947 + 11.1188i) q^{36} +(5.15585 - 2.97673i) q^{37} +(-4.76497 - 8.25317i) q^{38} +(1.22794 + 1.40949i) q^{39} +(5.63528 - 9.76059i) q^{40} +(6.66970 + 3.85075i) q^{41} +(-1.67800 - 2.90638i) q^{43} +(11.0120 + 6.35780i) q^{44} +(3.81296 + 2.20141i) q^{45} +(-4.45229 - 2.57053i) q^{46} +(0.913730 + 0.527542i) q^{47} +(2.25437 + 3.90469i) q^{48} +(5.38318 + 3.10798i) q^{50} +(0.810520 - 1.40386i) q^{51} +(-16.6343 + 3.25208i) q^{52} +(-3.63284 - 6.29226i) q^{53} +(-6.66133 + 3.84592i) q^{54} +(2.18027 - 3.77633i) q^{55} -1.90873i q^{57} +13.9078i q^{58} +(9.89352 + 5.71203i) q^{59} +(3.40257 - 1.96447i) q^{60} +2.92507 q^{61} +(-13.5617 + 23.4896i) q^{62} -4.68406 q^{64} +(1.11523 + 5.70435i) q^{65} +(1.81516 + 3.14395i) q^{66} +13.5818i q^{67} +(7.34886 + 12.7286i) q^{68} +(-0.514846 - 0.891740i) q^{69} +(1.17009 - 0.675554i) q^{71} -19.0949i q^{72} +(-7.88374 + 4.55168i) q^{73} +(-7.70557 + 13.3464i) q^{74} +(0.622492 + 1.07819i) q^{75} +(14.9876 + 8.65311i) q^{76} +(-4.57708 - 1.57047i) q^{78} +(3.10289 - 5.37436i) q^{79} +14.0189i q^{80} +6.65300 q^{81} -19.9361 q^{82} -2.69672i q^{83} +(4.36499 - 2.52013i) q^{85} +(7.52346 + 4.34367i) q^{86} +(-1.39278 + 2.41237i) q^{87} -18.9115 q^{88} +(-1.52410 + 0.879938i) q^{89} -11.3972 q^{90} +9.33607 q^{92} +(-4.70469 + 2.71625i) q^{93} -2.73119 q^{94} +(2.96739 - 5.13967i) q^{95} +(-3.82930 - 2.21085i) q^{96} +(13.4078 - 7.74102i) q^{97} -7.38776i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12q - 6q^{3} + 4q^{4} - 3q^{5} + 9q^{6} + 2q^{9} + O(q^{10})$$ $$12q - 6q^{3} + 4q^{4} - 3q^{5} + 9q^{6} + 2q^{9} + 24q^{10} + q^{12} + 2q^{13} - 12q^{15} - 8q^{16} - 17q^{17} - 3q^{18} + 3q^{20} - 15q^{22} + 3q^{23} - 5q^{25} + 9q^{26} - 12q^{27} - q^{29} - 22q^{30} + 18q^{31} + 18q^{32} - 13q^{36} + 15q^{37} - 19q^{38} - q^{39} + q^{40} + 6q^{41} + 11q^{43} + 33q^{44} + 9q^{45} - 30q^{46} - 15q^{47} - 19q^{48} + 18q^{50} + 4q^{51} - 47q^{52} - 8q^{53} - 6q^{54} + 15q^{55} - 27q^{59} + 30q^{60} + 10q^{61} - 41q^{62} + 2q^{64} - 3q^{65} + 34q^{66} + 11q^{68} - 7q^{69} + 30q^{71} + 42q^{73} - 33q^{74} - q^{75} + 45q^{76} + 44q^{78} - 35q^{79} - 28q^{81} + 10q^{82} - 21q^{85} + 57q^{86} - 10q^{87} + 28q^{88} - 48q^{89} - 66q^{92} - 81q^{93} + 2q^{94} + 2q^{95} + 21q^{96} + 3q^{97} + O(q^{100})$$

Character values

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

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

Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −2.24179 + 1.29430i −1.58519 + 0.915209i −0.591104 + 0.806596i $$0.701308\pi$$
−0.994084 + 0.108613i $$0.965359\pi$$
$$3$$ −0.518466 −0.299336 −0.149668 0.988736i $$-0.547821\pi$$
−0.149668 + 0.988736i $$0.547821\pi$$
$$4$$ 2.35043 4.07106i 1.17521 2.03553i
$$5$$ −1.39608 0.806027i −0.624346 0.360466i 0.154213 0.988038i $$-0.450716\pi$$
−0.778559 + 0.627571i $$0.784049\pi$$
$$6$$ 1.16229 0.671051i 0.474504 0.273955i
$$7$$ 0 0
$$8$$ 6.99143i 2.47184i
$$9$$ −2.73119 −0.910398
$$10$$ 4.17296 1.31961
$$11$$ 2.70496i 0.815575i 0.913077 + 0.407788i $$0.133700\pi$$
−0.913077 + 0.407788i $$0.866300\pi$$
$$12$$ −1.21862 + 2.11070i −0.351784 + 0.609308i
$$13$$ −2.36840 2.71858i −0.656876 0.753998i
$$14$$ 0 0
$$15$$ 0.723819 + 0.417897i 0.186889 + 0.107901i
$$16$$ −4.34816 7.53123i −1.08704 1.88281i
$$17$$ −1.56330 + 2.70772i −0.379157 + 0.656719i −0.990940 0.134307i $$-0.957119\pi$$
0.611783 + 0.791026i $$0.290453\pi$$
$$18$$ 6.12277 3.53498i 1.44315 0.833204i
$$19$$ 3.68150i 0.844595i 0.906457 + 0.422297i $$0.138776\pi$$
−0.906457 + 0.422297i $$0.861224\pi$$
$$20$$ −6.56276 + 3.78901i −1.46748 + 0.847249i
$$21$$ 0 0
$$22$$ −3.50103 6.06396i −0.746421 1.29284i
$$23$$ 0.993019 + 1.71996i 0.207059 + 0.358636i 0.950787 0.309846i $$-0.100278\pi$$
−0.743728 + 0.668482i $$0.766944\pi$$
$$24$$ 3.62482i 0.739913i
$$25$$ −1.20064 2.07957i −0.240128 0.415914i
$$26$$ 8.82813 + 3.02907i 1.73134 + 0.594050i
$$27$$ 2.97143 0.571852
$$28$$ 0 0
$$29$$ 2.68636 4.65290i 0.498844 0.864023i −0.501155 0.865357i $$-0.667092\pi$$
0.999999 + 0.00133469i $$0.000424845\pi$$
$$30$$ −2.16354 −0.395006
$$31$$ 9.07425 5.23902i 1.62978 0.940956i 0.645627 0.763653i $$-0.276596\pi$$
0.984156 0.177303i $$-0.0567372\pi$$
$$32$$ 7.38583 + 4.26421i 1.30564 + 0.753813i
$$33$$ 1.40243i 0.244131i
$$34$$ 8.09354i 1.38803i
$$35$$ 0 0
$$36$$ −6.41947 + 11.1188i −1.06991 + 1.85314i
$$37$$ 5.15585 2.97673i 0.847616 0.489371i −0.0122297 0.999925i $$-0.503893\pi$$
0.859846 + 0.510554i $$0.170560\pi$$
$$38$$ −4.76497 8.25317i −0.772981 1.33884i
$$39$$ 1.22794 + 1.40949i 0.196627 + 0.225699i
$$40$$ 5.63528 9.76059i 0.891016 1.54329i
$$41$$ 6.66970 + 3.85075i 1.04163 + 0.601386i 0.920295 0.391225i $$-0.127949\pi$$
0.121337 + 0.992611i $$0.461282\pi$$
$$42$$ 0 0
$$43$$ −1.67800 2.90638i −0.255892 0.443219i 0.709245 0.704962i $$-0.249036\pi$$
−0.965138 + 0.261743i $$0.915703\pi$$
$$44$$ 11.0120 + 6.35780i 1.66013 + 0.958475i
$$45$$ 3.81296 + 2.20141i 0.568403 + 0.328168i
$$46$$ −4.45229 2.57053i −0.656454 0.379004i
$$47$$ 0.913730 + 0.527542i 0.133281 + 0.0769500i 0.565158 0.824983i $$-0.308815\pi$$
−0.431877 + 0.901933i $$0.642148\pi$$
$$48$$ 2.25437 + 3.90469i 0.325390 + 0.563593i
$$49$$ 0 0
$$50$$ 5.38318 + 3.10798i 0.761297 + 0.439535i
$$51$$ 0.810520 1.40386i 0.113495 0.196580i
$$52$$ −16.6343 + 3.25208i −2.30676 + 0.450982i
$$53$$ −3.63284 6.29226i −0.499009 0.864308i 0.500991 0.865453i $$-0.332969\pi$$
−0.999999 + 0.00114437i $$0.999636\pi$$
$$54$$ −6.66133 + 3.84592i −0.906492 + 0.523363i
$$55$$ 2.18027 3.77633i 0.293987 0.509201i
$$56$$ 0 0
$$57$$ 1.90873i 0.252818i
$$58$$ 13.9078i 1.82618i
$$59$$ 9.89352 + 5.71203i 1.28803 + 0.743643i 0.978302 0.207183i $$-0.0664297\pi$$
0.309725 + 0.950826i $$0.399763\pi$$
$$60$$ 3.40257 1.96447i 0.439270 0.253613i
$$61$$ 2.92507 0.374517 0.187259 0.982311i $$-0.440040\pi$$
0.187259 + 0.982311i $$0.440040\pi$$
$$62$$ −13.5617 + 23.4896i −1.72234 + 2.98318i
$$63$$ 0 0
$$64$$ −4.68406 −0.585507
$$65$$ 1.11523 + 5.70435i 0.138327 + 0.707537i
$$66$$ 1.81516 + 3.14395i 0.223431 + 0.386994i
$$67$$ 13.5818i 1.65928i 0.558296 + 0.829642i $$0.311455\pi$$
−0.558296 + 0.829642i $$0.688545\pi$$
$$68$$ 7.34886 + 12.7286i 0.891180 + 1.54357i
$$69$$ −0.514846 0.891740i −0.0619802 0.107353i
$$70$$ 0 0
$$71$$ 1.17009 0.675554i 0.138865 0.0801736i −0.428958 0.903324i $$-0.641119\pi$$
0.567823 + 0.823151i $$0.307786\pi$$
$$72$$ 19.0949i 2.25036i
$$73$$ −7.88374 + 4.55168i −0.922721 + 0.532733i −0.884502 0.466536i $$-0.845502\pi$$
−0.0382192 + 0.999269i $$0.512169\pi$$
$$74$$ −7.70557 + 13.3464i −0.895754 + 1.55149i
$$75$$ 0.622492 + 1.07819i 0.0718791 + 0.124498i
$$76$$ 14.9876 + 8.65311i 1.71920 + 0.992579i
$$77$$ 0 0
$$78$$ −4.57708 1.57047i −0.518252 0.177821i
$$79$$ 3.10289 5.37436i 0.349102 0.604663i −0.636988 0.770874i $$-0.719820\pi$$
0.986090 + 0.166211i $$0.0531532\pi$$
$$80$$ 14.0189i 1.56736i
$$81$$ 6.65300 0.739222
$$82$$ −19.9361 −2.20158
$$83$$ 2.69672i 0.296003i −0.988987 0.148002i $$-0.952716\pi$$
0.988987 0.148002i $$-0.0472841\pi$$
$$84$$ 0 0
$$85$$ 4.36499 2.52013i 0.473450 0.273346i
$$86$$ 7.52346 + 4.34367i 0.811275 + 0.468390i
$$87$$ −1.39278 + 2.41237i −0.149322 + 0.258633i
$$88$$ −18.9115 −2.01597
$$89$$ −1.52410 + 0.879938i −0.161554 + 0.0932732i −0.578597 0.815613i $$-0.696400\pi$$
0.417043 + 0.908887i $$0.363066\pi$$
$$90$$ −11.3972 −1.20137
$$91$$ 0 0
$$92$$ 9.33607 0.973353
$$93$$ −4.70469 + 2.71625i −0.487853 + 0.281662i
$$94$$ −2.73119 −0.281701
$$95$$ 2.96739 5.13967i 0.304448 0.527319i
$$96$$ −3.82930 2.21085i −0.390827 0.225644i
$$97$$ 13.4078 7.74102i 1.36136 0.785981i 0.371555 0.928411i $$-0.378825\pi$$
0.989805 + 0.142430i $$0.0454915\pi$$
$$98$$ 0 0
$$99$$ 7.38776i 0.742498i
$$100$$ −11.2881 −1.12881
$$101$$ −1.27930 −0.127295 −0.0636477 0.997972i $$-0.520273\pi$$
−0.0636477 + 0.997972i $$0.520273\pi$$
$$102$$ 4.19622i 0.415488i
$$103$$ 5.73367 9.93101i 0.564956 0.978532i −0.432098 0.901827i $$-0.642227\pi$$
0.997054 0.0767054i $$-0.0244401\pi$$
$$104$$ 19.0068 16.5585i 1.86377 1.62370i
$$105$$ 0 0
$$106$$ 16.2881 + 9.40397i 1.58204 + 0.913394i
$$107$$ 2.56763 + 4.44726i 0.248222 + 0.429933i 0.963033 0.269385i $$-0.0868205\pi$$
−0.714811 + 0.699318i $$0.753487\pi$$
$$108$$ 6.98412 12.0969i 0.672048 1.16402i
$$109$$ −1.49635 + 0.863916i −0.143324 + 0.0827481i −0.569947 0.821681i $$-0.693036\pi$$
0.426623 + 0.904429i $$0.359703\pi$$
$$110$$ 11.2877i 1.07624i
$$111$$ −2.67313 + 1.54333i −0.253722 + 0.146487i
$$112$$ 0 0
$$113$$ 4.29556 + 7.44014i 0.404093 + 0.699909i 0.994215 0.107404i $$-0.0342540\pi$$
−0.590123 + 0.807314i $$0.700921\pi$$
$$114$$ 2.47048 + 4.27899i 0.231381 + 0.400764i
$$115$$ 3.20160i 0.298551i
$$116$$ −12.6282 21.8726i −1.17250 2.03082i
$$117$$ 6.46856 + 7.42497i 0.598019 + 0.686438i
$$118$$ −29.5723 −2.72235
$$119$$ 0 0
$$120$$ −2.92170 + 5.06053i −0.266714 + 0.461961i
$$121$$ 3.68321 0.334837
$$122$$ −6.55741 + 3.78592i −0.593680 + 0.342761i
$$123$$ −3.45801 1.99648i −0.311798 0.180017i
$$124$$ 49.2557i 4.42330i
$$125$$ 11.9313i 1.06716i
$$126$$ 0 0
$$127$$ −1.56206 + 2.70556i −0.138610 + 0.240080i −0.926971 0.375133i $$-0.877597\pi$$
0.788361 + 0.615214i $$0.210930\pi$$
$$128$$ −4.27097 + 2.46585i −0.377504 + 0.217952i
$$129$$ 0.869985 + 1.50686i 0.0765979 + 0.132671i
$$130$$ −9.88325 11.3445i −0.866818 0.994981i
$$131$$ 5.10460 8.84142i 0.445991 0.772479i −0.552130 0.833758i $$-0.686185\pi$$
0.998121 + 0.0612793i $$0.0195180\pi$$
$$132$$ −5.70937 3.29630i −0.496936 0.286906i
$$133$$ 0 0
$$134$$ −17.5790 30.4476i −1.51859 2.63028i
$$135$$ −4.14835 2.39505i −0.357033 0.206133i
$$136$$ −18.9308 10.9297i −1.62331 0.937216i
$$137$$ 8.65385 + 4.99630i 0.739348 + 0.426863i 0.821832 0.569729i $$-0.192952\pi$$
−0.0824839 + 0.996592i $$0.526285\pi$$
$$138$$ 2.30836 + 1.33273i 0.196501 + 0.113450i
$$139$$ −0.832100 1.44124i −0.0705778 0.122244i 0.828577 0.559875i $$-0.189151\pi$$
−0.899155 + 0.437631i $$0.855818\pi$$
$$140$$ 0 0
$$141$$ −0.473738 0.273513i −0.0398959 0.0230339i
$$142$$ −1.74874 + 3.02891i −0.146751 + 0.254180i
$$143$$ 7.35364 6.40642i 0.614942 0.535732i
$$144$$ 11.8757 + 20.5692i 0.989638 + 1.71410i
$$145$$ −7.50073 + 4.33055i −0.622902 + 0.359633i
$$146$$ 11.7825 20.4078i 0.975124 1.68897i
$$147$$ 0 0
$$148$$ 27.9863i 2.30046i
$$149$$ 19.7980i 1.62192i −0.585103 0.810959i $$-0.698946\pi$$
0.585103 0.810959i $$-0.301054\pi$$
$$150$$ −2.79100 1.61138i −0.227884 0.131569i
$$151$$ 6.52544 3.76746i 0.531033 0.306592i −0.210404 0.977614i $$-0.567478\pi$$
0.741437 + 0.671023i $$0.234145\pi$$
$$152$$ −25.7390 −2.08771
$$153$$ 4.26968 7.39531i 0.345183 0.597875i
$$154$$ 0 0
$$155$$ −16.8912 −1.35673
$$156$$ 8.62429 1.68609i 0.690496 0.134995i
$$157$$ 7.00223 + 12.1282i 0.558839 + 0.967938i 0.997594 + 0.0693309i $$0.0220864\pi$$
−0.438755 + 0.898607i $$0.644580\pi$$
$$158$$ 16.0643i 1.27801i
$$159$$ 1.88350 + 3.26232i 0.149371 + 0.258719i
$$160$$ −6.87414 11.9064i −0.543448 0.941280i
$$161$$ 0 0
$$162$$ −14.9146 + 8.61097i −1.17181 + 0.676542i
$$163$$ 7.16995i 0.561594i −0.959767 0.280797i $$-0.909401\pi$$
0.959767 0.280797i $$-0.0905987\pi$$
$$164$$ 31.3533 18.1018i 2.44828 1.41351i
$$165$$ −1.13039 + 1.95790i −0.0880011 + 0.152422i
$$166$$ 3.49036 + 6.04548i 0.270904 + 0.469220i
$$167$$ −15.5716 8.99027i −1.20497 0.695688i −0.243312 0.969948i $$-0.578234\pi$$
−0.961656 + 0.274260i $$0.911567\pi$$
$$168$$ 0 0
$$169$$ −1.78135 + 12.8774i −0.137027 + 0.990567i
$$170$$ −6.52361 + 11.2992i −0.500338 + 0.866611i
$$171$$ 10.0549i 0.768917i
$$172$$ −15.7761 −1.20291
$$173$$ −12.8116 −0.974047 −0.487023 0.873389i $$-0.661917\pi$$
−0.487023 + 0.873389i $$0.661917\pi$$
$$174$$ 7.21072i 0.546643i
$$175$$ 0 0
$$176$$ 20.3717 11.7616i 1.53557 0.886562i
$$177$$ −5.12945 2.96149i −0.385553 0.222599i
$$178$$ 2.27781 3.94528i 0.170729 0.295711i
$$179$$ −1.84022 −0.137545 −0.0687723 0.997632i $$-0.521908\pi$$
−0.0687723 + 0.997632i $$0.521908\pi$$
$$180$$ 17.9242 10.3485i 1.33599 0.771334i
$$181$$ 3.29928 0.245234 0.122617 0.992454i $$-0.460871\pi$$
0.122617 + 0.992454i $$0.460871\pi$$
$$182$$ 0 0
$$183$$ −1.51655 −0.112107
$$184$$ −12.0250 + 6.94262i −0.886493 + 0.511817i
$$185$$ −9.59730 −0.705607
$$186$$ 7.03129 12.1786i 0.515560 0.892975i
$$187$$ −7.32427 4.22867i −0.535604 0.309231i
$$188$$ 4.29531 2.47990i 0.313268 0.180865i
$$189$$ 0 0
$$190$$ 15.3628i 1.11453i
$$191$$ 4.89614 0.354272 0.177136 0.984186i $$-0.443317\pi$$
0.177136 + 0.984186i $$0.443317\pi$$
$$192$$ 2.42852 0.175264
$$193$$ 3.01910i 0.217320i 0.994079 + 0.108660i $$0.0346559\pi$$
−0.994079 + 0.108660i $$0.965344\pi$$
$$194$$ −20.0384 + 34.7075i −1.43867 + 2.49186i
$$195$$ −0.578207 2.95751i −0.0414063 0.211792i
$$196$$ 0 0
$$197$$ 4.02694 + 2.32496i 0.286908 + 0.165646i 0.636546 0.771238i $$-0.280362\pi$$
−0.349639 + 0.936885i $$0.613696\pi$$
$$198$$ 9.56198 + 16.5618i 0.679540 + 1.17700i
$$199$$ −0.205360 + 0.355694i −0.0145576 + 0.0252145i −0.873212 0.487340i $$-0.837967\pi$$
0.858655 + 0.512554i $$0.171301\pi$$
$$200$$ 14.5392 8.39420i 1.02808 0.593560i
$$201$$ 7.04171i 0.496684i
$$202$$ 2.86793 1.65580i 0.201787 0.116502i
$$203$$ 0 0
$$204$$ −3.81013 6.59934i −0.266763 0.462047i
$$205$$ −6.20762 10.7519i −0.433559 0.750946i
$$206$$ 29.6844i 2.06821i
$$207$$ −2.71213 4.69754i −0.188506 0.326502i
$$208$$ −10.1761 + 29.6578i −0.705583 + 2.05640i
$$209$$ −9.95831 −0.688831
$$210$$ 0 0
$$211$$ 3.75800 6.50905i 0.258711 0.448101i −0.707186 0.707028i $$-0.750035\pi$$
0.965897 + 0.258927i $$0.0833688\pi$$
$$212$$ −34.1549 −2.34577
$$213$$ −0.606654 + 0.350252i −0.0415672 + 0.0239989i
$$214$$ −11.5122 6.64656i −0.786956 0.454349i
$$215$$ 5.41005i 0.368962i
$$216$$ 20.7745i 1.41353i
$$217$$ 0 0
$$218$$ 2.23633 3.87344i 0.151464 0.262343i
$$219$$ 4.08745 2.35989i 0.276204 0.159467i
$$220$$ −10.2491 17.7520i −0.690996 1.19684i
$$221$$ 11.0637 2.16300i 0.744224 0.145499i
$$222$$ 3.99507 6.91967i 0.268132 0.464418i
$$223$$ 19.5544 + 11.2897i 1.30946 + 0.756016i 0.982006 0.188852i $$-0.0604766\pi$$
0.327452 + 0.944868i $$0.393810\pi$$
$$224$$ 0 0
$$225$$ 3.27918 + 5.67971i 0.218612 + 0.378648i
$$226$$ −19.2595 11.1195i −1.28113 0.739658i
$$227$$ −11.8401 6.83586i −0.785853 0.453712i 0.0526478 0.998613i $$-0.483234\pi$$
−0.838500 + 0.544901i $$0.816567\pi$$
$$228$$ −7.77057 4.48634i −0.514618 0.297115i
$$229$$ 6.86832 + 3.96543i 0.453872 + 0.262043i 0.709464 0.704742i $$-0.248937\pi$$
−0.255592 + 0.966785i $$0.582270\pi$$
$$230$$ 4.14383 + 7.17733i 0.273236 + 0.473259i
$$231$$ 0 0
$$232$$ 32.5305 + 18.7815i 2.13573 + 1.23306i
$$233$$ −3.28585 + 5.69127i −0.215263 + 0.372847i −0.953354 0.301854i $$-0.902394\pi$$
0.738091 + 0.674702i $$0.235728\pi$$
$$234$$ −24.1113 8.27298i −1.57621 0.540822i
$$235$$ −0.850427 1.47298i −0.0554757 0.0960868i
$$236$$ 46.5080 26.8514i 3.02741 1.74788i
$$237$$ −1.60874 + 2.78642i −0.104499 + 0.180998i
$$238$$ 0 0
$$239$$ 9.39284i 0.607572i 0.952740 + 0.303786i $$0.0982508\pi$$
−0.952740 + 0.303786i $$0.901749\pi$$
$$240$$ 7.26833i 0.469169i
$$241$$ −8.73460 5.04292i −0.562645 0.324843i 0.191562 0.981481i $$-0.438645\pi$$
−0.754206 + 0.656637i $$0.771978\pi$$
$$242$$ −8.25699 + 4.76718i −0.530780 + 0.306446i
$$243$$ −12.3636 −0.793128
$$244$$ 6.87517 11.9081i 0.440137 0.762340i
$$245$$ 0 0
$$246$$ 10.3362 0.659012
$$247$$ 10.0085 8.71928i 0.636823 0.554794i
$$248$$ 36.6282 + 63.4420i 2.32590 + 4.02857i
$$249$$ 1.39816i 0.0886045i
$$250$$ −15.4426 26.7474i −0.976678 1.69166i
$$251$$ 5.17427 + 8.96209i 0.326597 + 0.565682i 0.981834 0.189741i $$-0.0607648\pi$$
−0.655237 + 0.755423i $$0.727431\pi$$
$$252$$ 0 0
$$253$$ −4.65242 + 2.68607i −0.292495 + 0.168872i
$$254$$ 8.08709i 0.507429i
$$255$$ −2.26310 + 1.30660i −0.141721 + 0.0818225i
$$256$$ 11.0672 19.1689i 0.691697 1.19805i
$$257$$ −3.99329 6.91658i −0.249095 0.431445i 0.714180 0.699962i $$-0.246800\pi$$
−0.963275 + 0.268517i $$0.913466\pi$$
$$258$$ −3.90065 2.25204i −0.242844 0.140206i
$$259$$ 0 0
$$260$$ 25.8440 + 8.86749i 1.60278 + 0.549939i
$$261$$ −7.33696 + 12.7080i −0.454146 + 0.786604i
$$262$$ 26.4275i 1.63270i
$$263$$ 5.05934 0.311972 0.155986 0.987759i $$-0.450144\pi$$
0.155986 + 0.987759i $$0.450144\pi$$
$$264$$ 9.80498 0.603455
$$265$$ 11.7127i 0.719503i
$$266$$ 0 0
$$267$$ 0.790192 0.456218i 0.0483590 0.0279201i
$$268$$ 55.2924 + 31.9231i 3.37752 + 1.95001i
$$269$$ 6.94512 12.0293i 0.423451 0.733439i −0.572823 0.819679i $$-0.694152\pi$$
0.996274 + 0.0862400i $$0.0274852\pi$$
$$270$$ 12.3997 0.754619
$$271$$ 7.21158 4.16361i 0.438072 0.252921i −0.264707 0.964329i $$-0.585275\pi$$
0.702780 + 0.711408i $$0.251942\pi$$
$$272$$ 27.1900 1.64863
$$273$$ 0 0
$$274$$ −25.8669 −1.56267
$$275$$ 5.62515 3.24768i 0.339210 0.195843i
$$276$$ −4.84043 −0.291360
$$277$$ −11.6058 + 20.1018i −0.697325 + 1.20780i 0.272066 + 0.962279i $$0.412293\pi$$
−0.969391 + 0.245523i $$0.921040\pi$$
$$278$$ 3.73080 + 2.15398i 0.223758 + 0.129187i
$$279$$ −24.7835 + 14.3088i −1.48375 + 0.856644i
$$280$$ 0 0
$$281$$ 27.1595i 1.62020i 0.586292 + 0.810100i $$0.300587\pi$$
−0.586292 + 0.810100i $$0.699413\pi$$
$$282$$ 1.41603 0.0843234
$$283$$ −16.1513 −0.960092 −0.480046 0.877243i $$-0.659380\pi$$
−0.480046 + 0.877243i $$0.659380\pi$$
$$284$$ 6.35136i 0.376884i
$$285$$ −1.53849 + 2.66474i −0.0911323 + 0.157846i
$$286$$ −8.19351 + 23.8797i −0.484493 + 1.41204i
$$287$$ 0 0
$$288$$ −20.1721 11.6464i −1.18865 0.686270i
$$289$$ 3.61216 + 6.25645i 0.212480 + 0.368027i
$$290$$ 11.2101 19.4164i 0.658278 1.14017i
$$291$$ −6.95151 + 4.01345i −0.407504 + 0.235273i
$$292$$ 42.7935i 2.50430i
$$293$$ 12.6831 7.32260i 0.740956 0.427791i −0.0814609 0.996677i $$-0.525959\pi$$
0.822417 + 0.568885i $$0.192625\pi$$
$$294$$ 0 0
$$295$$ −9.20810 15.9489i −0.536116 0.928580i
$$296$$ 20.8116 + 36.0468i 1.20965 + 2.09517i
$$297$$ 8.03758i 0.466388i
$$298$$ 25.6246 + 44.3831i 1.48439 + 2.57104i
$$299$$ 2.32398 6.77315i 0.134399 0.391702i
$$300$$ 5.85248 0.337893
$$301$$ 0 0
$$302$$ −9.75246 + 16.8918i −0.561191 + 0.972011i
$$303$$ 0.663274 0.0381041
$$304$$ 27.7263 16.0078i 1.59021 0.918108i
$$305$$ −4.08363 2.35769i −0.233828 0.135001i
$$306$$ 22.1050i 1.26366i
$$307$$ 8.97844i 0.512427i 0.966620 + 0.256213i $$0.0824750\pi$$
−0.966620 + 0.256213i $$0.917525\pi$$
$$308$$ 0 0
$$309$$ −2.97271 + 5.14889i −0.169112 + 0.292910i
$$310$$ 37.8665 21.8622i 2.15067 1.24169i
$$311$$ −6.09080 10.5496i −0.345378 0.598212i 0.640045 0.768338i $$-0.278916\pi$$
−0.985422 + 0.170126i $$0.945583\pi$$
$$312$$ −9.85436 + 8.58502i −0.557893 + 0.486031i
$$313$$ 6.56198 11.3657i 0.370905 0.642427i −0.618800 0.785549i $$-0.712381\pi$$
0.989705 + 0.143122i $$0.0457141\pi$$
$$314$$ −31.3951 18.1260i −1.77173 1.02291i
$$315$$ 0 0
$$316$$ −14.5862 25.2641i −0.820540 1.42122i
$$317$$ −14.4761 8.35775i −0.813056 0.469418i 0.0349599 0.999389i $$-0.488870\pi$$
−0.848016 + 0.529971i $$0.822203\pi$$
$$318$$ −8.44485 4.87563i −0.473564 0.273412i
$$319$$ 12.5859 + 7.26648i 0.704675 + 0.406845i
$$320$$ 6.53932 + 3.77548i 0.365559 + 0.211056i
$$321$$ −1.33123 2.30575i −0.0743018 0.128695i
$$322$$ 0 0
$$323$$ −9.96849 5.75531i −0.554661 0.320234i
$$324$$ 15.6374 27.0847i 0.868743 1.50471i
$$325$$ −2.80988 + 8.18930i −0.155864 + 0.454261i
$$326$$ 9.28007 + 16.0736i 0.513976 + 0.890232i
$$327$$ 0.775804 0.447911i 0.0429021 0.0247695i
$$328$$ −26.9223 + 46.6307i −1.48653 + 2.57475i
$$329$$ 0 0
$$330$$ 5.85228i 0.322157i
$$331$$ 3.96665i 0.218027i 0.994040 + 0.109013i $$0.0347691\pi$$
−0.994040 + 0.109013i $$0.965231\pi$$
$$332$$ −10.9785 6.33843i −0.602523 0.347867i
$$333$$ −14.0816 + 8.13002i −0.771668 + 0.445523i
$$334$$ 46.5445 2.54680
$$335$$ 10.9473 18.9613i 0.598116 1.03597i
$$336$$ 0 0
$$337$$ −13.7032 −0.746461 −0.373230 0.927739i $$-0.621750\pi$$
−0.373230 + 0.927739i $$0.621750\pi$$
$$338$$ −12.6738 31.1740i −0.689362 1.69564i
$$339$$ −2.22710 3.85746i −0.120960 0.209508i
$$340$$ 23.6935i 1.28496i
$$341$$ 14.1713 + 24.5455i 0.767420 + 1.32921i
$$342$$ 13.0141 + 22.5410i 0.703720 + 1.21888i
$$343$$ 0 0
$$344$$ 20.3197 11.7316i 1.09557 0.632526i
$$345$$ 1.65992i 0.0893671i
$$346$$ 28.7209 16.5820i 1.54405 0.891456i
$$347$$ 13.1989 22.8612i 0.708556 1.22725i −0.256837 0.966455i $$-0.582680\pi$$
0.965393 0.260800i $$-0.0839863\pi$$
$$348$$ 6.54727 + 11.3402i 0.350971 + 0.607899i
$$349$$ 4.23507 + 2.44512i 0.226698 + 0.130884i 0.609048 0.793133i $$-0.291552\pi$$
−0.382350 + 0.924018i $$0.624885\pi$$
$$350$$ 0 0
$$351$$ −7.03753 8.07806i −0.375636 0.431175i
$$352$$ −11.5345 + 19.9784i −0.614792 + 1.06485i
$$353$$ 13.5577i 0.721605i 0.932642 + 0.360802i $$0.117497\pi$$
−0.932642 + 0.360802i $$0.882503\pi$$
$$354$$ 15.3322 0.814899
$$355$$ −2.17806 −0.115599
$$356$$ 8.27291i 0.438464i
$$357$$ 0 0
$$358$$ 4.12540 2.38180i 0.218034 0.125882i
$$359$$ −7.43541 4.29284i −0.392426 0.226567i 0.290785 0.956789i $$-0.406084\pi$$
−0.683211 + 0.730221i $$0.739417\pi$$
$$360$$ −15.3910 + 26.6581i −0.811179 + 1.40500i
$$361$$ 5.44653 0.286659
$$362$$ −7.39632 + 4.27026i −0.388742 + 0.224440i
$$363$$ −1.90962 −0.100229
$$364$$ 0 0
$$365$$ 14.6751 0.768130
$$366$$ 3.39979 1.96287i 0.177710 0.102601i
$$367$$ 1.66322 0.0868196 0.0434098 0.999057i $$-0.486178\pi$$
0.0434098 + 0.999057i $$0.486178\pi$$
$$368$$ 8.63560 14.9573i 0.450162 0.779703i
$$369$$ −18.2162 10.5171i −0.948299 0.547501i
$$370$$ 21.5152 12.4218i 1.11852 0.645778i
$$371$$ 0 0
$$372$$ 25.5374i 1.32405i
$$373$$ 13.9635 0.723002 0.361501 0.932372i $$-0.382264\pi$$
0.361501 + 0.932372i $$0.382264\pi$$
$$374$$ 21.8927 1.13204
$$375$$ 6.18595i 0.319441i
$$376$$ −3.68828 + 6.38828i −0.190208 + 0.329450i
$$377$$ −19.0117 + 3.71687i −0.979150 + 0.191429i
$$378$$ 0 0
$$379$$ −27.3454 15.7879i −1.40464 0.810969i −0.409775 0.912187i $$-0.634393\pi$$
−0.994864 + 0.101218i $$0.967726\pi$$
$$380$$ −13.9493 24.1608i −0.715582 1.23943i
$$381$$ 0.809874 1.40274i 0.0414911 0.0718647i
$$382$$ −10.9761 + 6.33707i −0.561588 + 0.324233i
$$383$$ 31.9082i 1.63043i −0.579156 0.815217i $$-0.696618\pi$$
0.579156 0.815217i $$-0.303382\pi$$
$$384$$ 2.21435 1.27846i 0.113001 0.0652410i
$$385$$ 0 0
$$386$$ −3.90762 6.76820i −0.198893 0.344492i
$$387$$ 4.58294 + 7.93788i 0.232964 + 0.403505i
$$388$$ 72.7788i 3.69478i
$$389$$ −12.7075 22.0100i −0.644296 1.11595i −0.984464 0.175589i $$-0.943817\pi$$
0.340168 0.940365i $$-0.389516\pi$$
$$390$$ 5.12413 + 5.88175i 0.259470 + 0.297834i
$$391$$ −6.20956 −0.314031
$$392$$ 0 0
$$393$$ −2.64656 + 4.58398i −0.133501 + 0.231231i
$$394$$ −12.0368 −0.606403
$$395$$ −8.66376 + 5.00203i −0.435921 + 0.251679i
$$396$$ −30.0760 17.3644i −1.51138 0.872593i
$$397$$ 4.15897i 0.208733i −0.994539 0.104366i $$-0.966719\pi$$
0.994539 0.104366i $$-0.0332815\pi$$
$$398$$ 1.06319i 0.0532930i
$$399$$ 0 0
$$400$$ −10.4412 + 18.0846i −0.522058 + 0.904231i
$$401$$ −16.9753 + 9.80067i −0.847704 + 0.489422i −0.859875 0.510504i $$-0.829459\pi$$
0.0121716 + 0.999926i $$0.496126\pi$$
$$402$$ 9.11409 + 15.7861i 0.454569 + 0.787337i
$$403$$ −35.7342 12.2610i −1.78005 0.610762i
$$404$$ −3.00691 + 5.20811i −0.149599 + 0.259113i
$$405$$ −9.28811 5.36249i −0.461530 0.266464i
$$406$$ 0 0
$$407$$ 8.05193 + 13.9463i 0.399119 + 0.691295i
$$408$$ 9.81500 + 5.66669i 0.485915 + 0.280543i
$$409$$ 15.2712 + 8.81685i 0.755114 + 0.435965i 0.827539 0.561409i $$-0.189740\pi$$
−0.0724249 + 0.997374i $$0.523074\pi$$
$$410$$ 27.8324 + 16.0690i 1.37454 + 0.793594i
$$411$$ −4.48673 2.59041i −0.221314 0.127776i
$$412$$ −26.9532 46.6842i −1.32789 2.29997i
$$413$$ 0 0
$$414$$ 12.1601 + 7.02061i 0.597634 + 0.345044i
$$415$$ −2.17363 + 3.76483i −0.106699 + 0.184808i
$$416$$ −5.90001 30.1783i −0.289272 1.47962i
$$417$$ 0.431416 + 0.747234i 0.0211265 + 0.0365922i
$$418$$ 22.3245 12.8890i 1.09193 0.630424i
$$419$$ 14.9455 25.8864i 0.730137 1.26463i −0.226688 0.973968i $$-0.572790\pi$$
0.956824 0.290666i $$-0.0938770\pi$$
$$420$$ 0 0
$$421$$ 12.8528i 0.626407i 0.949686 + 0.313203i $$0.101402\pi$$
−0.949686 + 0.313203i $$0.898598\pi$$
$$422$$ 19.4559i 0.947100i
$$423$$ −2.49557 1.44082i −0.121339 0.0700551i
$$424$$ 43.9919 25.3987i 2.13644 1.23347i
$$425$$ 7.50787 0.364185
$$426$$ 0.906662 1.57038i 0.0439279 0.0760854i
$$427$$ 0 0
$$428$$ 24.1401 1.16685
$$429$$ −3.81261 + 3.32151i −0.184075 + 0.160364i
$$430$$ −7.00223 12.1282i −0.337677 0.584874i
$$431$$ 8.97060i 0.432098i 0.976382 + 0.216049i $$0.0693172\pi$$
−0.976382 + 0.216049i $$0.930683\pi$$
$$432$$ −12.9202 22.3785i −0.621625 1.07669i
$$433$$ 1.72531 + 2.98833i 0.0829132 + 0.143610i 0.904500 0.426473i $$-0.140244\pi$$
−0.821587 + 0.570083i $$0.806911\pi$$
$$434$$ 0 0
$$435$$ 3.88887 2.24524i 0.186457 0.107651i
$$436$$ 8.12228i 0.388987i
$$437$$ −6.33204 + 3.65580i −0.302902 + 0.174881i
$$438$$ −6.10881 + 10.5808i −0.291890 + 0.505569i
$$439$$ 19.2572 + 33.3544i 0.919096 + 1.59192i 0.800792 + 0.598943i $$0.204412\pi$$
0.118304 + 0.992977i $$0.462254\pi$$
$$440$$ 26.4020 + 15.2432i 1.25867 + 0.726691i
$$441$$ 0 0
$$442$$ −22.0029 + 19.1687i −1.04657 + 0.911764i
$$443$$ 7.51997 13.0250i 0.357284 0.618835i −0.630222 0.776415i $$-0.717036\pi$$
0.987506 + 0.157580i $$0.0503693\pi$$
$$444$$ 14.5100i 0.688612i
$$445$$ 2.83701 0.134487
$$446$$ −58.4492 −2.76765
$$447$$ 10.2646i 0.485499i
$$448$$ 0 0
$$449$$ 33.7087 19.4617i 1.59081 0.918456i 0.597646 0.801760i $$-0.296103\pi$$
0.993168 0.116696i $$-0.0372304\pi$$
$$450$$ −14.7025 8.48850i −0.693083 0.400152i
$$451$$ −10.4161 + 18.0412i −0.490476 + 0.849529i
$$452$$ 40.3856 1.89958
$$453$$ −3.38322 + 1.95330i −0.158957 + 0.0917741i
$$454$$ 35.3906 1.66097
$$455$$ 0 0
$$456$$ 13.3448 0.624927
$$457$$ −12.0721 + 6.96982i −0.564708 + 0.326034i −0.755033 0.655687i $$-0.772379\pi$$
0.190325 + 0.981721i $$0.439046\pi$$
$$458$$ −20.5298 −0.959295
$$459$$ −4.64524 + 8.04580i −0.216821 + 0.375546i
$$460$$ −13.0339 7.52512i −0.607709 0.350861i
$$461$$ −32.4443 + 18.7317i −1.51108 + 0.872424i −0.511167 + 0.859481i $$0.670787\pi$$
−0.999916 + 0.0129430i $$0.995880\pi$$
$$462$$ 0 0
$$463$$ 6.75275i 0.313827i −0.987612 0.156913i $$-0.949846\pi$$
0.987612 0.156913i $$-0.0501544\pi$$
$$464$$ −46.7228 −2.16905
$$465$$ 8.75749 0.406119
$$466$$ 17.0115i 0.788044i
$$467$$ −2.52516 + 4.37371i −0.116851 + 0.202391i −0.918518 0.395379i $$-0.870613\pi$$
0.801667 + 0.597770i $$0.203947\pi$$
$$468$$ 45.4314 8.88205i 2.10006 0.410573i
$$469$$ 0 0
$$470$$ 3.81296 + 2.20141i 0.175879 + 0.101544i
$$471$$ −3.63042 6.28807i −0.167281 0.289739i
$$472$$ −39.9353 + 69.1699i −1.83817 + 3.18380i
$$473$$ 7.86163 4.53892i 0.361478 0.208700i
$$474$$ 8.32878i 0.382554i
$$475$$ 7.65595 4.42017i 0.351279 0.202811i
$$476$$ 0 0
$$477$$ 9.92198 + 17.1854i 0.454296 + 0.786864i
$$478$$ −12.1572 21.0568i −0.556055 0.963116i
$$479$$ 9.45319i 0.431927i −0.976401 0.215964i $$-0.930711\pi$$
0.976401 0.215964i $$-0.0692892\pi$$
$$480$$ 3.56401 + 6.17304i 0.162674 + 0.281759i
$$481$$ −20.3036 6.96649i −0.925764 0.317645i
$$482$$ 26.1082 1.18920
$$483$$ 0 0
$$484$$ 8.65711 14.9946i 0.393505 0.681571i
$$485$$ −24.9579 −1.13328
$$486$$ 27.7167 16.0023i 1.25726 0.725877i
$$487$$ 34.6407 + 19.9998i 1.56972 + 0.906277i 0.996201 + 0.0870831i $$0.0277546\pi$$
0.573517 + 0.819194i $$0.305579\pi$$
$$488$$ 20.4504i 0.925748i
$$489$$ 3.71737i 0.168105i
$$490$$ 0 0
$$491$$ −3.38049 + 5.85517i −0.152559 + 0.264240i −0.932168 0.362027i $$-0.882085\pi$$
0.779608 + 0.626267i $$0.215418\pi$$
$$492$$ −16.2556 + 9.38518i −0.732859 + 0.423116i
$$493$$ 8.39918 + 14.5478i 0.378280 + 0.655200i
$$494$$ −11.1515 + 32.5008i −0.501732 + 1.46228i
$$495$$ −5.95473 + 10.3139i −0.267645 + 0.463575i
$$496$$ −78.9125 45.5602i −3.54328 2.04571i
$$497$$ 0 0
$$498$$ −1.80963 3.13438i −0.0810916 0.140455i
$$499$$ 9.83591 + 5.67877i 0.440316 + 0.254217i 0.703732 0.710466i $$-0.251516\pi$$
−0.263416 + 0.964682i $$0.584849\pi$$
$$500$$ 48.5729 + 28.0436i 2.17225 + 1.25415i
$$501$$ 8.07335 + 4.66115i 0.360691 + 0.208245i
$$502$$ −23.1993 13.3941i −1.03543 0.597808i
$$503$$ −6.96423 12.0624i −0.310520 0.537836i 0.667955 0.744202i $$-0.267170\pi$$
−0.978475 + 0.206365i $$0.933836\pi$$
$$504$$ 0 0
$$505$$ 1.78601 + 1.03115i 0.0794763 + 0.0458857i
$$506$$ 6.95317 12.0432i 0.309106 0.535388i
$$507$$ 0.923570 6.67648i 0.0410172 0.296513i
$$508$$ 7.34301 + 12.7185i 0.325793 + 0.564290i
$$509$$ −17.1602 + 9.90746i −0.760614 + 0.439141i −0.829516 0.558483i $$-0.811384\pi$$
0.0689022 + 0.997623i $$0.478050\pi$$
$$510$$ 3.38227 5.85826i 0.149769 0.259408i
$$511$$ 0 0
$$512$$ 47.4335i 2.09628i
$$513$$ 10.9393i 0.482983i
$$514$$ 17.9043 + 10.3370i 0.789724 + 0.455947i
$$515$$ −16.0093 + 9.24299i −0.705455 + 0.407295i
$$516$$ 8.17934 0.360076
$$517$$ −1.42698 + 2.47160i −0.0627585 + 0.108701i
$$518$$ 0 0
$$519$$ 6.64237 0.291568
$$520$$ −39.8816 + 7.79704i −1.74892 + 0.341923i
$$521$$ −15.5476 26.9292i −0.681151 1.17979i −0.974630 0.223823i $$-0.928146\pi$$
0.293479 0.955966i $$-0.405187\pi$$
$$522$$ 37.9849i 1.66255i
$$523$$ 11.3601 + 19.6763i 0.496742 + 0.860383i 0.999993 0.00375758i $$-0.00119608\pi$$
−0.503251 + 0.864140i $$0.667863\pi$$
$$524$$ −23.9960 41.5622i −1.04827 1.81565i
$$525$$ 0 0
$$526$$ −11.3420 + 6.54831i −0.494535 + 0.285520i
$$527$$ 32.7607i 1.42708i
$$528$$ −10.5620 + 6.09798i −0.459652 + 0.265380i
$$529$$ 9.52783 16.5027i 0.414253 0.717508i
$$530$$ −15.1597 26.2574i −0.658495 1.14055i
$$531$$ −27.0211 15.6007i −1.17262 0.677011i
$$532$$ 0 0
$$533$$ −5.32794 27.2522i −0.230779 1.18043i
$$534$$ −1.18097 + 2.04549i −0.0511054 + 0.0885171i
$$535$$ 8.27830i 0.357902i
$$536$$ −94.9564 −4.10149
$$537$$ 0.954091 0.0411721
$$538$$ 35.9563i 1.55018i
$$539$$ 0 0
$$540$$ −19.5008 + 11.2588i −0.839180 + 0.484501i
$$541$$ −1.81754 1.04936i −0.0781423 0.0451155i 0.460420 0.887701i $$-0.347699\pi$$
−0.538562 + 0.842586i $$0.681032\pi$$
$$542$$ −10.7779 + 18.6679i −0.462951 + 0.801855i
$$543$$ −1.71057 −0.0734074
$$544$$ −23.0926 + 13.3325i −0.990087 + 0.571627i
$$545$$ 2.78536 0.119312
$$546$$ 0 0
$$547$$ 25.3770 1.08504 0.542521 0.840042i $$-0.317470\pi$$
0.542521 + 0.840042i $$0.317470\pi$$
$$548$$ 40.6805 23.4869i 1.73778 1.00331i
$$549$$ −7.98894 −0.340959
$$550$$ −8.40696 + 14.5613i −0.358474 + 0.620895i
$$551$$ 17.1297 + 9.88983i 0.729749 + 0.421321i
$$552$$ 6.23454 3.59951i 0.265360 0.153205i
$$553$$ 0 0
$$554$$ 60.0855i 2.55279i
$$555$$ 4.97587 0.211214
$$556$$ −7.82316 −0.331776
$$557$$ 44.2503i 1.87495i −0.348058 0.937473i $$-0.613159\pi$$
0.348058 0.937473i $$-0.386841\pi$$
$$558$$ 37.0397 64.1547i 1.56802 2.71588i
$$559$$ −3.92705 + 11.4452i −0.166097 + 0.484082i
$$560$$ 0 0
$$561$$ 3.79738 + 2.19242i 0.160326 + 0.0925641i
$$562$$ −35.1526 60.8860i −1.48282 2.56832i
$$563$$ 19.4453 33.6803i 0.819523 1.41946i −0.0865108 0.996251i $$-0.527572\pi$$
0.906034 0.423205i $$-0.139095\pi$$
$$564$$ −2.22697 + 1.28574i −0.0937725 + 0.0541396i
$$565$$ 13.8494i 0.582647i
$$566$$ 36.2078 20.9046i 1.52193 0.878685i
$$567$$ 0 0
$$568$$ 4.72309 + 8.18063i 0.198177 + 0.343252i
$$569$$ 23.0789 + 39.9739i 0.967520 + 1.67579i 0.702687 + 0.711499i $$0.251983\pi$$
0.264832 + 0.964294i $$0.414683\pi$$
$$570$$ 7.96508i 0.333620i
$$571$$ 10.5684 + 18.3050i 0.442274 + 0.766041i 0.997858 0.0654194i $$-0.0208385\pi$$
−0.555584 + 0.831461i $$0.687505\pi$$
$$572$$ −8.79673 44.9949i −0.367810 1.88133i
$$573$$ −2.53848 −0.106047
$$574$$ 0 0
$$575$$ 2.38452 4.13011i 0.0994413 0.172237i
$$576$$ 12.7931 0.533045
$$577$$ 21.9368 12.6652i 0.913239 0.527259i 0.0317671 0.999495i $$-0.489887\pi$$
0.881472 + 0.472237i $$0.156553\pi$$
$$578$$ −16.1955 9.35045i −0.673642 0.388927i
$$579$$ 1.56530i 0.0650517i
$$580$$ 40.7146i 1.69058i
$$581$$ 0 0
$$582$$ 10.3892 17.9947i 0.430647 0.745903i
$$583$$ 17.0203 9.82667i 0.704908 0.406979i
$$584$$ −31.8227 55.1186i −1.31683 2.28082i
$$585$$ −3.04590 15.5797i −0.125933 0.644140i
$$586$$ −18.9553 + 32.8315i −0.783036 + 1.35626i
$$587$$ −3.08554 1.78144i −0.127354 0.0735278i 0.434970 0.900445i $$-0.356759\pi$$
−0.562324 + 0.826917i $$0.690092\pi$$
$$588$$ 0 0
$$589$$ 19.2875 + 33.4069i 0.794727 + 1.37651i
$$590$$ 41.2853 + 23.8361i 1.69969 + 0.981316i
$$591$$ −2.08783 1.20541i −0.0858819 0.0495839i
$$592$$ −44.8369 25.8866i −1.84278 1.06393i
$$593$$ 21.9568 + 12.6768i 0.901659 + 0.520573i 0.877738 0.479141i $$-0.159052\pi$$
0.0239212 + 0.999714i $$0.492385\pi$$
$$594$$ −10.4030 18.0186i −0.426842 0.739312i
$$595$$ 0 0
$$596$$ −80.5990 46.5338i −3.30146 1.90610i
$$597$$ 0.106472 0.184415i 0.00435762 0.00754762i
$$598$$ 3.55661 + 18.1919i 0.145441 + 0.743924i
$$599$$ −5.46078 9.45835i −0.223122 0.386458i 0.732633 0.680624i $$-0.238291\pi$$
−0.955754 + 0.294166i $$0.904958\pi$$
$$600$$ −7.53807 + 4.35211i −0.307740 + 0.177674i
$$601$$ 12.1282 21.0067i 0.494720 0.856880i −0.505262 0.862966i $$-0.668604\pi$$
0.999981 + 0.00608649i $$0.00193740\pi$$
$$602$$ 0 0
$$603$$ 37.0946i 1.51061i
$$604$$ 35.4206i 1.44124i
$$605$$ −5.14205 2.96876i −0.209054 0.120697i
$$606$$ −1.48692 + 0.858476i −0.0604022 + 0.0348732i
$$607$$ 9.85447 0.399981 0.199990 0.979798i $$-0.435909\pi$$
0.199990 + 0.979798i $$0.435909\pi$$
$$608$$ −15.6987 + 27.1910i −0.636667 + 1.10274i
$$609$$ 0 0
$$610$$ 12.2062 0.494215
$$611$$ −0.729914 3.73348i −0.0295291 0.151040i
$$612$$ −20.0712 34.7643i −0.811328 1.40526i
$$613$$ 3.67688i 0.148508i −0.997239 0.0742540i $$-0.976342\pi$$
0.997239 0.0742540i $$-0.0236575\pi$$
$$614$$ −11.6208 20.1278i −0.468977 0.812293i
$$615$$ 3.21844 + 5.57450i 0.129780 + 0.224785i
$$616$$ 0 0
$$617$$ 16.2352 9.37341i 0.653605 0.377359i −0.136231 0.990677i $$-0.543499\pi$$
0.789836 + 0.613318i $$0.210166\pi$$
$$618$$ 15.3903i 0.619090i
$$619$$ 13.7650 7.94725i 0.553264 0.319427i −0.197174 0.980369i $$-0.563176\pi$$
0.750437 + 0.660942i $$0.229843\pi$$
$$620$$ −39.7014 + 68.7649i −1.59445 + 2.76167i
$$621$$ 2.95068 + 5.11073i 0.118407 + 0.205087i
$$622$$ 27.3086 + 15.7667i 1.09498 + 0.632185i
$$623$$ 0 0
$$624$$ 5.27594 15.3765i 0.211207 0.615555i
$$625$$ 3.61371 6.25913i 0.144549 0.250365i
$$626$$ 33.9727i 1.35782i
$$627$$ 5.16304 0.206192
$$628$$ 65.8330 2.62702
$$629$$ 18.6141i 0.742194i
$$630$$ 0 0
$$631$$ −17.0998 + 9.87255i −0.680731 + 0.393020i −0.800130 0.599826i $$-0.795236\pi$$
0.119400 + 0.992846i $$0.461903\pi$$
$$632$$ 37.5745 + 21.6936i 1.49463 + 0.862927i
$$633$$ −1.94839 + 3.37472i −0.0774417 + 0.134133i
$$634$$ 43.2698 1.71846
$$635$$ 4.36151 2.51812i 0.173081 0.0999286i
$$636$$ 17.7081 0.702173
$$637$$ 0 0
$$638$$ −37.6200 −1.48939
$$639$$ −3.19575 + 1.84507i −0.126422 + 0.0729898i
$$640$$ 7.95016 0.314258
$$641$$ −14.8893 + 25.7890i −0.588092 + 1.01860i 0.406390 + 0.913699i $$0.366787\pi$$
−0.994482 + 0.104905i $$0.966546\pi$$
$$642$$ 5.96867 + 3.44601i 0.235565 + 0.136003i
$$643$$ −10.0220 + 5.78623i −0.395231 + 0.228187i −0.684424 0.729084i $$-0.739946\pi$$
0.289193 + 0.957271i $$0.406613\pi$$
$$644$$ 0 0
$$645$$ 2.80493i 0.110444i
$$646$$ 29.7964 1.17232
$$647$$ 25.5065 1.00276 0.501382 0.865226i $$-0.332825\pi$$
0.501382 + 0.865226i $$0.332825\pi$$
$$648$$ 46.5140i 1.82724i
$$649$$ −15.4508 + 26.7616i −0.606497 + 1.05048i
$$650$$ −4.30024 21.9956i −0.168669 0.862737i
$$651$$ 0 0
$$652$$ −29.1893 16.8524i −1.14314 0.659993i
$$653$$ 22.4146 + 38.8233i 0.877152 + 1.51927i 0.854452 + 0.519530i $$0.173893\pi$$
0.0227004 + 0.999742i $$0.492774\pi$$
$$654$$ −1.15946 + 2.00825i −0.0453386 + 0.0785287i
$$655$$ −14.2529 + 8.22889i −0.556905 + 0.321529i
$$656$$ 66.9747i 2.61492i
$$657$$ 21.5320 12.4315i 0.840043 0.484999i
$$658$$ 0 0
$$659$$ −20.5867 35.6572i −0.801944 1.38901i −0.918335 0.395805i $$-0.870466\pi$$
0.116390 0.993204i $$-0.462868\pi$$
$$660$$ 5.31382 + 9.20380i 0.206840 + 0.358258i
$$661$$ 21.8938i 0.851569i 0.904825 + 0.425785i $$0.140002\pi$$
−0.904825 + 0.425785i $$0.859998\pi$$
$$662$$ −5.13404 8.89241i −0.199540 0.345613i
$$663$$ −5.73614 + 1.12144i −0.222773 + 0.0435533i
$$664$$ 18.8539 0.731673
$$665$$ 0 0
$$666$$ 21.0454 36.4517i 0.815492 1.41247i
$$667$$ 10.6704 0.413160
$$668$$ −73.1999 + 42.2620i −2.83219 + 1.63516i
$$669$$ −10.1383 5.85334i −0.391968 0.226303i
$$670$$ 56.6764i 2.18960i
$$671$$ 7.91219i 0.305447i
$$672$$ 0 0
$$673$$ 17.8344 30.8901i 0.687466 1.19073i −0.285189 0.958471i $$-0.592056\pi$$
0.972655 0.232254i $$-0.0746102\pi$$
$$674$$ 30.7197 17.7361i 1.18328 0.683167i
$$675$$ −3.56762 6.17930i −0.137318 0.237841i
$$676$$ 48.2376 + 37.5193i 1.85529 + 1.44305i
$$677$$ 1.27766 2.21297i 0.0491044 0.0850514i −0.840428 0.541923i $$-0.817697\pi$$
0.889533 + 0.456871i $$0.151030\pi$$
$$678$$ 9.98541 + 5.76508i 0.383488 + 0.221407i
$$679$$ 0 0
$$680$$ 17.6193 + 30.5175i 0.675670 + 1.17029i
$$681$$ 6.13867 + 3.54416i 0.235234 + 0.135813i
$$682$$ −63.5384 36.6839i −2.43301 1.40470i
$$683$$ −30.9517 17.8700i −1.18433 0.683775i −0.227320 0.973820i $$-0.572996\pi$$
−0.957013 + 0.290045i $$0.906330\pi$$
$$684$$ −40.9341 23.6333i −1.56515 0.903642i
$$685$$ −8.05431 13.9505i −0.307739 0.533020i
$$686$$ 0 0
$$687$$ −3.56099 2.05594i −0.135860 0.0784390i
$$688$$ −14.5924 + 25.2748i −0.556330 + 0.963592i
$$689$$ −8.50199 + 24.7788i −0.323900 + 0.943995i
$$690$$ −2.14843 3.72120i −0.0817895 0.141664i
$$691$$ −22.5419 + 13.0146i −0.857536 + 0.495099i −0.863186 0.504885i $$-0.831535\pi$$
0.00565028 + 0.999984i $$0.498201\pi$$
$$692$$ −30.1127 + 52.1567i −1.14471 + 1.98270i
$$693$$ 0 0
$$694$$ 68.3335i 2.59391i
$$695$$ 2.68278i 0.101764i
$$696$$ −16.8659 9.73755i −0.639301 0.369101i
$$697$$ −20.8535 + 12.0398i −0.789884 + 0.456040i
$$698$$ −12.6589 −0.479146
$$699$$ 1.70360 2.95073i 0.0644362 0.111607i
$$700$$ 0 0
$$701$$ −1.12731 −0.0425779 −0.0212890 0.999773i $$-0.506777\pi$$
−0.0212890 + 0.999773i $$0.506777\pi$$
$$702$$ 26.2321 + 9.00067i 0.990068 + 0.339709i
$$703$$ 10.9588 + 18.9813i 0.413321 + 0.715892i
$$704$$ 12.6702i 0.477525i
$$705$$ 0.440917 + 0.763691i 0.0166059 + 0.0287623i
$$706$$ −17.5478 30.3936i −0.660419 1.14388i
$$707$$ 0 0
$$708$$ −24.1128 + 13.9215i −0.906215 + 0.523203i
$$709$$ 6.05031i 0.227224i 0.993525 + 0.113612i $$0.0362421\pi$$
−0.993525 + 0.113612i $$0.963758\pi$$
$$710$$ 4.88276 2.81906i 0.183247 0.105798i
$$711$$ −8.47459 + 14.6784i −0.317822 + 0.550484i
$$712$$ −6.15202 10.6556i −0.230557 0.399336i
$$713$$ 18.0218 + 10.4049i 0.674922 + 0.389666i
$$714$$ 0 0
$$715$$ −15.4300 + 3.01664i −0.577050 + 0.112816i
$$716$$ −4.32530 + 7.49164i −0.161644 + 0.279976i
$$717$$ 4.86986i 0.181868i
$$718$$ 22.2249 0.829425
$$719$$ 47.1177 1.75719 0.878597 0.477563i $$-0.158480\pi$$
0.878597 + 0.477563i $$0.158480\pi$$
$$720$$ 38.2884i 1.42692i
$$721$$ 0 0
$$722$$ −12.2100 + 7.04944i −0.454409 + 0.262353i
$$723$$ 4.52859 + 2.61458i 0.168420 + 0.0972374i
$$724$$ 7.75473 13.4316i 0.288202 0.499181i
$$725$$ −12.9014 −0.479146
$$726$$ 4.28097 2.47162i 0.158882 0.0917303i
$$727$$ −17.9215 −0.664671 −0.332335 0.943161i $$-0.607837\pi$$
−0.332335 + 0.943161i $$0.607837\pi$$
$$728$$ 0 0
$$729$$ −13.5489 −0.501810
$$730$$ −32.8985 + 18.9940i −1.21763 + 0.702999i
$$731$$ 10.4929 0.388093
$$732$$ −3.56454 + 6.17396i −0.131749 + 0.228196i
$$733$$ −39.2037 22.6343i −1.44802 0.836016i −0.449658 0.893201i $$-0.648454\pi$$
−0.998364 + 0.0571848i $$0.981788\pi$$
$$734$$ −3.72861 + 2.15271i −0.137625 + 0.0794581i
$$735$$ 0 0
$$736$$ 16.9378i 0.624335i
$$737$$ −36.7382 −1.35327
$$738$$ 54.4494 2.00431
$$739$$ 19.2613i 0.708539i 0.935143 + 0.354270i $$0.115270\pi$$
−0.935143 + 0.354270i $$0.884730\pi$$
$$740$$ −22.5577 + 39.0712i −0.829239 + 1.43628i
$$741$$ −5.18905 + 4.52065i −0.190624 + 0.166070i
$$742$$ 0 0
$$743$$ 30.2115 + 17.4426i 1.10835 + 0.639908i 0.938402 0.345545i $$-0.112306\pi$$
0.169951 + 0.985453i $$0.445639\pi$$
$$744$$ −18.9905 32.8925i −0.696225 1.20590i
$$745$$ −15.9577 + 27.6396i −0.584647 + 1.01264i
$$746$$ −31.3032 + 18.0729i −1.14609 + 0.661697i
$$747$$ 7.36525i 0.269480i
$$748$$ −34.4303 + 19.8784i −1.25890 + 0.726825i
$$749$$ 0 0
$$750$$ 8.00648 + 13.8676i 0.292355 + 0.506374i
$$751$$ −12.4834 21.6219i −0.455526 0.788993i 0.543193 0.839608i $$-0.317215\pi$$
−0.998718 + 0.0506146i $$0.983882\pi$$
$$752$$ 9.17535i 0.334591i
$$753$$ −2.68268 4.64654i −0.0977623 0.169329i
$$754$$ 37.8095 32.9393i 1.37694 1.19958i
$$755$$ −12.1467 −0.442064
$$756$$ 0 0
$$757$$ 5.30243 9.18408i 0.192720 0.333801i −0.753431 0.657527i $$-0.771602\pi$$
0.946151 + 0.323726i $$0.104936\pi$$
$$758$$ 81.7370 2.96882
$$759$$ 2.41212 1.39264i 0.0875543 0.0505495i
$$760$$ 35.9337 + 20.7463i 1.30345 + 0.752548i
$$761$$ 32.6388i 1.18316i 0.806248 + 0.591578i $$0.201495\pi$$
−0.806248 + 0.591578i $$0.798505\pi$$
$$762$$ 4.19288i 0.151892i
$$763$$ 0 0
$$764$$ 11.5080 19.9325i 0.416345 0.721131i
$$765$$ −11.9216 + 6.88296i −0.431028 + 0.248854i
$$766$$ 41.2988 + 71.5316i 1.49219 + 2.58454i
$$767$$ −7.90323 40.4247i −0.285369 1.45965i
$$768$$ −5.73794 + 9.93841i −0.207050 + 0.358621i
$$769$$ 45.1851 + 26.0876i 1.62942 + 0.940744i 0.984267 + 0.176686i $$0.0565378\pi$$
0.645148 + 0.764057i $$0.276796\pi$$
$$770$$ 0 0
$$771$$ 2.07039 + 3.58601i 0.0745631 + 0.129147i
$$772$$ 12.2909 + 7.09618i 0.442360 + 0.255397i
$$773$$ 30.9221 + 17.8529i 1.11219 + 0.642123i 0.939396 0.342835i $$-0.111387\pi$$
0.172794 + 0.984958i $$0.444721\pi$$
$$774$$ −20.5480 11.8634i −0.738583 0.426421i
$$775$$ −21.7898 12.5804i −0.782714 0.451900i
$$776$$ 54.1208 + 93.7400i 1.94282 + 3.36507i
$$777$$ 0 0
$$778$$ 56.9752 + 32.8947i 2.04266 + 1.17933i
$$779$$ −14.1766 + 24.5545i −0.507928 + 0.879757i
$$780$$ −13.3992 4.59749i −0.479769 0.164617i
$$781$$ 1.82735 + 3.16506i 0.0653876 + 0.113255i