# Properties

 Label 300.2.e.c.251.1 Level $300$ Weight $2$ Character 300.251 Analytic conductor $2.396$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Related objects

## Newspace parameters

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

## Newform invariants

 Self dual: no Analytic conductor: $$2.39551206064$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.342102016.5 Defining polynomial: $$x^{8} + x^{6} + 4 x^{4} + 4 x^{2} + 16$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 60) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 251.1 Root $$-1.17915 + 0.780776i$$ of defining polynomial Character $$\chi$$ $$=$$ 300.251 Dual form 300.2.e.c.251.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.17915 - 0.780776i) q^{2} +(1.51022 - 0.848071i) q^{3} +(0.780776 + 1.84130i) q^{4} +(-2.44293 - 0.179147i) q^{6} +3.02045i q^{7} +(0.516994 - 2.78078i) q^{8} +(1.56155 - 2.56155i) q^{9} +O(q^{10})$$ $$q+(-1.17915 - 0.780776i) q^{2} +(1.51022 - 0.848071i) q^{3} +(0.780776 + 1.84130i) q^{4} +(-2.44293 - 0.179147i) q^{6} +3.02045i q^{7} +(0.516994 - 2.78078i) q^{8} +(1.56155 - 2.56155i) q^{9} +1.32431 q^{11} +(2.74070 + 2.11862i) q^{12} +5.12311 q^{13} +(2.35829 - 3.56155i) q^{14} +(-2.78078 + 2.87529i) q^{16} -2.00000i q^{17} +(-3.84130 + 1.80122i) q^{18} +1.32431i q^{19} +(2.56155 + 4.56155i) q^{21} +(-1.56155 - 1.03399i) q^{22} -0.371834 q^{23} +(-1.57752 - 4.63804i) q^{24} +(-6.04090 - 4.00000i) q^{26} +(0.185917 - 5.19283i) q^{27} +(-5.56155 + 2.35829i) q^{28} +3.12311i q^{29} -4.71659i q^{31} +(5.52390 - 1.21922i) q^{32} +(2.00000 - 1.12311i) q^{33} +(-1.56155 + 2.35829i) q^{34} +(5.93581 + 0.875288i) q^{36} -5.12311 q^{37} +(1.03399 - 1.56155i) q^{38} +(7.73704 - 4.34475i) q^{39} -1.12311i q^{41} +(0.541105 - 7.37874i) q^{42} -7.73704i q^{43} +(1.03399 + 2.43845i) q^{44} +(0.438447 + 0.290319i) q^{46} -3.02045 q^{47} +(-1.76115 + 6.70062i) q^{48} -2.12311 q^{49} +(-1.69614 - 3.02045i) q^{51} +(4.00000 + 9.43318i) q^{52} +12.2462i q^{53} +(-4.27366 + 5.97795i) q^{54} +(8.39919 + 1.56155i) q^{56} +(1.12311 + 2.00000i) q^{57} +(2.43845 - 3.68260i) q^{58} -14.1498 q^{59} +3.12311 q^{61} +(-3.68260 + 5.56155i) q^{62} +(7.73704 + 4.71659i) q^{63} +(-7.46543 - 2.87529i) q^{64} +(-3.23519 - 0.237246i) q^{66} +4.34475i q^{67} +(3.68260 - 1.56155i) q^{68} +(-0.561553 + 0.315342i) q^{69} +3.39228 q^{71} +(-6.31579 - 5.66664i) q^{72} -8.24621 q^{73} +(6.04090 + 4.00000i) q^{74} +(-2.43845 + 1.03399i) q^{76} +4.00000i q^{77} +(-12.5154 - 0.917790i) q^{78} +8.10887i q^{79} +(-4.12311 - 8.00000i) q^{81} +(-0.876894 + 1.32431i) q^{82} -15.1022 q^{83} +(-6.39919 + 8.27814i) q^{84} +(-6.04090 + 9.12311i) q^{86} +(2.64861 + 4.71659i) q^{87} +(0.684658 - 3.68260i) q^{88} +10.2462i q^{89} +15.4741i q^{91} +(-0.290319 - 0.684658i) q^{92} +(-4.00000 - 7.12311i) q^{93} +(3.56155 + 2.35829i) q^{94} +(7.30834 - 6.52596i) q^{96} +6.00000 q^{97} +(2.50345 + 1.65767i) q^{98} +(2.06798 - 3.39228i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 2q^{4} - 6q^{6} - 4q^{9} + O(q^{10})$$ $$8q - 2q^{4} - 6q^{6} - 4q^{9} - 4q^{12} + 8q^{13} - 14q^{16} - 16q^{18} + 4q^{21} + 4q^{22} - 2q^{24} - 28q^{28} + 16q^{33} + 4q^{34} + 18q^{36} - 8q^{37} + 12q^{42} + 20q^{46} + 36q^{48} + 16q^{49} + 32q^{52} - 10q^{54} - 24q^{57} + 36q^{58} - 8q^{61} - 2q^{64} - 40q^{66} + 12q^{69} - 24q^{72} - 36q^{76} - 40q^{78} - 40q^{82} + 16q^{84} - 44q^{88} - 32q^{93} + 12q^{94} + 42q^{96} + 48q^{97} + O(q^{100})$$

## Character values

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

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

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.17915 0.780776i −0.833783 0.552092i
$$3$$ 1.51022 0.848071i 0.871928 0.489634i
$$4$$ 0.780776 + 1.84130i 0.390388 + 0.920650i
$$5$$ 0 0
$$6$$ −2.44293 0.179147i −0.997322 0.0731366i
$$7$$ 3.02045i 1.14162i 0.821081 + 0.570811i $$0.193371\pi$$
−0.821081 + 0.570811i $$0.806629\pi$$
$$8$$ 0.516994 2.78078i 0.182785 0.983153i
$$9$$ 1.56155 2.56155i 0.520518 0.853851i
$$10$$ 0 0
$$11$$ 1.32431 0.399294 0.199647 0.979868i $$-0.436021\pi$$
0.199647 + 0.979868i $$0.436021\pi$$
$$12$$ 2.74070 + 2.11862i 0.791172 + 0.611594i
$$13$$ 5.12311 1.42089 0.710447 0.703751i $$-0.248493\pi$$
0.710447 + 0.703751i $$0.248493\pi$$
$$14$$ 2.35829 3.56155i 0.630281 0.951865i
$$15$$ 0 0
$$16$$ −2.78078 + 2.87529i −0.695194 + 0.718822i
$$17$$ 2.00000i 0.485071i −0.970143 0.242536i $$-0.922021\pi$$
0.970143 0.242536i $$-0.0779791\pi$$
$$18$$ −3.84130 + 1.80122i −0.905403 + 0.424553i
$$19$$ 1.32431i 0.303817i 0.988395 + 0.151908i $$0.0485419\pi$$
−0.988395 + 0.151908i $$0.951458\pi$$
$$20$$ 0 0
$$21$$ 2.56155 + 4.56155i 0.558977 + 0.995412i
$$22$$ −1.56155 1.03399i −0.332924 0.220447i
$$23$$ −0.371834 −0.0775328 −0.0387664 0.999248i $$-0.512343\pi$$
−0.0387664 + 0.999248i $$0.512343\pi$$
$$24$$ −1.57752 4.63804i −0.322010 0.946736i
$$25$$ 0 0
$$26$$ −6.04090 4.00000i −1.18472 0.784465i
$$27$$ 0.185917 5.19283i 0.0357798 0.999360i
$$28$$ −5.56155 + 2.35829i −1.05103 + 0.445676i
$$29$$ 3.12311i 0.579946i 0.957035 + 0.289973i $$0.0936464\pi$$
−0.957035 + 0.289973i $$0.906354\pi$$
$$30$$ 0 0
$$31$$ 4.71659i 0.847124i −0.905867 0.423562i $$-0.860780\pi$$
0.905867 0.423562i $$-0.139220\pi$$
$$32$$ 5.52390 1.21922i 0.976497 0.215530i
$$33$$ 2.00000 1.12311i 0.348155 0.195508i
$$34$$ −1.56155 + 2.35829i −0.267804 + 0.404444i
$$35$$ 0 0
$$36$$ 5.93581 + 0.875288i 0.989302 + 0.145881i
$$37$$ −5.12311 −0.842233 −0.421117 0.907006i $$-0.638362\pi$$
−0.421117 + 0.907006i $$0.638362\pi$$
$$38$$ 1.03399 1.56155i 0.167735 0.253317i
$$39$$ 7.73704 4.34475i 1.23892 0.695718i
$$40$$ 0 0
$$41$$ 1.12311i 0.175400i −0.996147 0.0876998i $$-0.972048\pi$$
0.996147 0.0876998i $$-0.0279516\pi$$
$$42$$ 0.541105 7.37874i 0.0834943 1.13856i
$$43$$ 7.73704i 1.17989i −0.807445 0.589944i $$-0.799150\pi$$
0.807445 0.589944i $$-0.200850\pi$$
$$44$$ 1.03399 + 2.43845i 0.155879 + 0.367610i
$$45$$ 0 0
$$46$$ 0.438447 + 0.290319i 0.0646455 + 0.0428052i
$$47$$ −3.02045 −0.440578 −0.220289 0.975435i $$-0.570700\pi$$
−0.220289 + 0.975435i $$0.570700\pi$$
$$48$$ −1.76115 + 6.70062i −0.254200 + 0.967152i
$$49$$ −2.12311 −0.303301
$$50$$ 0 0
$$51$$ −1.69614 3.02045i −0.237507 0.422947i
$$52$$ 4.00000 + 9.43318i 0.554700 + 1.30815i
$$53$$ 12.2462i 1.68215i 0.540921 + 0.841073i $$0.318076\pi$$
−0.540921 + 0.841073i $$0.681924\pi$$
$$54$$ −4.27366 + 5.97795i −0.581571 + 0.813495i
$$55$$ 0 0
$$56$$ 8.39919 + 1.56155i 1.12239 + 0.208671i
$$57$$ 1.12311 + 2.00000i 0.148759 + 0.264906i
$$58$$ 2.43845 3.68260i 0.320184 0.483549i
$$59$$ −14.1498 −1.84214 −0.921071 0.389394i $$-0.872685\pi$$
−0.921071 + 0.389394i $$0.872685\pi$$
$$60$$ 0 0
$$61$$ 3.12311 0.399873 0.199936 0.979809i $$-0.435926\pi$$
0.199936 + 0.979809i $$0.435926\pi$$
$$62$$ −3.68260 + 5.56155i −0.467691 + 0.706318i
$$63$$ 7.73704 + 4.71659i 0.974775 + 0.594234i
$$64$$ −7.46543 2.87529i −0.933179 0.359411i
$$65$$ 0 0
$$66$$ −3.23519 0.237246i −0.398224 0.0292030i
$$67$$ 4.34475i 0.530796i 0.964139 + 0.265398i $$0.0855034\pi$$
−0.964139 + 0.265398i $$0.914497\pi$$
$$68$$ 3.68260 1.56155i 0.446581 0.189366i
$$69$$ −0.561553 + 0.315342i −0.0676030 + 0.0379627i
$$70$$ 0 0
$$71$$ 3.39228 0.402590 0.201295 0.979531i $$-0.435485\pi$$
0.201295 + 0.979531i $$0.435485\pi$$
$$72$$ −6.31579 5.66664i −0.744323 0.667819i
$$73$$ −8.24621 −0.965146 −0.482573 0.875856i $$-0.660298\pi$$
−0.482573 + 0.875856i $$0.660298\pi$$
$$74$$ 6.04090 + 4.00000i 0.702240 + 0.464991i
$$75$$ 0 0
$$76$$ −2.43845 + 1.03399i −0.279709 + 0.118607i
$$77$$ 4.00000i 0.455842i
$$78$$ −12.5154 0.917790i −1.41709 0.103919i
$$79$$ 8.10887i 0.912319i 0.889898 + 0.456160i $$0.150775\pi$$
−0.889898 + 0.456160i $$0.849225\pi$$
$$80$$ 0 0
$$81$$ −4.12311 8.00000i −0.458123 0.888889i
$$82$$ −0.876894 + 1.32431i −0.0968368 + 0.146245i
$$83$$ −15.1022 −1.65769 −0.828843 0.559481i $$-0.811000\pi$$
−0.828843 + 0.559481i $$0.811000\pi$$
$$84$$ −6.39919 + 8.27814i −0.698209 + 0.903219i
$$85$$ 0 0
$$86$$ −6.04090 + 9.12311i −0.651407 + 0.983770i
$$87$$ 2.64861 + 4.71659i 0.283961 + 0.505671i
$$88$$ 0.684658 3.68260i 0.0729848 0.392567i
$$89$$ 10.2462i 1.08610i 0.839702 + 0.543048i $$0.182730\pi$$
−0.839702 + 0.543048i $$0.817270\pi$$
$$90$$ 0 0
$$91$$ 15.4741i 1.62212i
$$92$$ −0.290319 0.684658i −0.0302679 0.0713806i
$$93$$ −4.00000 7.12311i −0.414781 0.738632i
$$94$$ 3.56155 + 2.35829i 0.367346 + 0.243240i
$$95$$ 0 0
$$96$$ 7.30834 6.52596i 0.745904 0.666053i
$$97$$ 6.00000 0.609208 0.304604 0.952479i $$-0.401476\pi$$
0.304604 + 0.952479i $$0.401476\pi$$
$$98$$ 2.50345 + 1.65767i 0.252887 + 0.167450i
$$99$$ 2.06798 3.39228i 0.207839 0.340937i
$$100$$ 0 0
$$101$$ 0.876894i 0.0872543i −0.999048 0.0436271i $$-0.986109\pi$$
0.999048 0.0436271i $$-0.0138914\pi$$
$$102$$ −0.358294 + 4.88586i −0.0354764 + 0.483772i
$$103$$ 9.80501i 0.966117i 0.875588 + 0.483058i $$0.160474\pi$$
−0.875588 + 0.483058i $$0.839526\pi$$
$$104$$ 2.64861 14.2462i 0.259718 1.39696i
$$105$$ 0 0
$$106$$ 9.56155 14.4401i 0.928700 1.40255i
$$107$$ 3.02045 0.291998 0.145999 0.989285i $$-0.453360\pi$$
0.145999 + 0.989285i $$0.453360\pi$$
$$108$$ 9.70671 3.71211i 0.934029 0.357198i
$$109$$ −0.876894 −0.0839912 −0.0419956 0.999118i $$-0.513372\pi$$
−0.0419956 + 0.999118i $$0.513372\pi$$
$$110$$ 0 0
$$111$$ −7.73704 + 4.34475i −0.734367 + 0.412386i
$$112$$ −8.68466 8.39919i −0.820623 0.793649i
$$113$$ 14.0000i 1.31701i −0.752577 0.658505i $$-0.771189\pi$$
0.752577 0.658505i $$-0.228811\pi$$
$$114$$ 0.237246 3.23519i 0.0222201 0.303003i
$$115$$ 0 0
$$116$$ −5.75058 + 2.43845i −0.533928 + 0.226404i
$$117$$ 8.00000 13.1231i 0.739600 1.21323i
$$118$$ 16.6847 + 11.0478i 1.53595 + 1.01703i
$$119$$ 6.04090 0.553768
$$120$$ 0 0
$$121$$ −9.24621 −0.840565
$$122$$ −3.68260 2.43845i −0.333407 0.220767i
$$123$$ −0.952473 1.69614i −0.0858816 0.152936i
$$124$$ 8.68466 3.68260i 0.779905 0.330707i
$$125$$ 0 0
$$126$$ −5.44050 11.6024i −0.484679 1.03363i
$$127$$ 15.1022i 1.34011i −0.742313 0.670054i $$-0.766271\pi$$
0.742313 0.670054i $$-0.233729\pi$$
$$128$$ 6.55789 + 9.21922i 0.579641 + 0.814872i
$$129$$ −6.56155 11.6847i −0.577713 1.02878i
$$130$$ 0 0
$$131$$ 5.46026 0.477065 0.238532 0.971135i $$-0.423334\pi$$
0.238532 + 0.971135i $$0.423334\pi$$
$$132$$ 3.62953 + 2.80571i 0.315910 + 0.244205i
$$133$$ −4.00000 −0.346844
$$134$$ 3.39228 5.12311i 0.293049 0.442569i
$$135$$ 0 0
$$136$$ −5.56155 1.03399i −0.476899 0.0886637i
$$137$$ 8.24621i 0.704521i 0.935902 + 0.352261i $$0.114587\pi$$
−0.935902 + 0.352261i $$0.885413\pi$$
$$138$$ 0.908365 + 0.0666131i 0.0773251 + 0.00567048i
$$139$$ 17.5420i 1.48790i −0.668237 0.743949i $$-0.732951\pi$$
0.668237 0.743949i $$-0.267049\pi$$
$$140$$ 0 0
$$141$$ −4.56155 + 2.56155i −0.384152 + 0.215722i
$$142$$ −4.00000 2.64861i −0.335673 0.222267i
$$143$$ 6.78456 0.567354
$$144$$ 3.02287 + 11.6130i 0.251906 + 0.967752i
$$145$$ 0 0
$$146$$ 9.72350 + 6.43845i 0.804722 + 0.532850i
$$147$$ −3.20636 + 1.80054i −0.264457 + 0.148506i
$$148$$ −4.00000 9.43318i −0.328798 0.775402i
$$149$$ 14.0000i 1.14692i −0.819232 0.573462i $$-0.805600\pi$$
0.819232 0.573462i $$-0.194400\pi$$
$$150$$ 0 0
$$151$$ 7.36520i 0.599372i −0.954038 0.299686i $$-0.903118\pi$$
0.954038 0.299686i $$-0.0968819\pi$$
$$152$$ 3.68260 + 0.684658i 0.298698 + 0.0555331i
$$153$$ −5.12311 3.12311i −0.414179 0.252488i
$$154$$ 3.12311 4.71659i 0.251667 0.380074i
$$155$$ 0 0
$$156$$ 14.0409 + 10.8539i 1.12417 + 0.869010i
$$157$$ 3.36932 0.268901 0.134450 0.990920i $$-0.457073\pi$$
0.134450 + 0.990920i $$0.457073\pi$$
$$158$$ 6.33122 9.56155i 0.503684 0.760676i
$$159$$ 10.3857 + 18.4945i 0.823636 + 1.46671i
$$160$$ 0 0
$$161$$ 1.12311i 0.0885131i
$$162$$ −1.38446 + 12.6524i −0.108774 + 0.994067i
$$163$$ 15.6829i 1.22838i 0.789159 + 0.614189i $$0.210517\pi$$
−0.789159 + 0.614189i $$0.789483\pi$$
$$164$$ 2.06798 0.876894i 0.161482 0.0684739i
$$165$$ 0 0
$$166$$ 17.8078 + 11.7915i 1.38215 + 0.915196i
$$167$$ 9.06134 0.701188 0.350594 0.936528i $$-0.385980\pi$$
0.350594 + 0.936528i $$0.385980\pi$$
$$168$$ 14.0090 4.76481i 1.08082 0.367613i
$$169$$ 13.2462 1.01894
$$170$$ 0 0
$$171$$ 3.39228 + 2.06798i 0.259414 + 0.158142i
$$172$$ 14.2462 6.04090i 1.08626 0.460614i
$$173$$ 2.00000i 0.152057i −0.997106 0.0760286i $$-0.975776\pi$$
0.997106 0.0760286i $$-0.0242240\pi$$
$$174$$ 0.559496 7.62953i 0.0424153 0.578393i
$$175$$ 0 0
$$176$$ −3.68260 + 3.80776i −0.277587 + 0.287021i
$$177$$ −21.3693 + 12.0000i −1.60622 + 0.901975i
$$178$$ 8.00000 12.0818i 0.599625 0.905569i
$$179$$ −10.0138 −0.748468 −0.374234 0.927334i $$-0.622094\pi$$
−0.374234 + 0.927334i $$0.622094\pi$$
$$180$$ 0 0
$$181$$ −12.2462 −0.910254 −0.455127 0.890427i $$-0.650406\pi$$
−0.455127 + 0.890427i $$0.650406\pi$$
$$182$$ 12.0818 18.2462i 0.895562 1.35250i
$$183$$ 4.71659 2.64861i 0.348660 0.195791i
$$184$$ −0.192236 + 1.03399i −0.0141718 + 0.0762266i
$$185$$ 0 0
$$186$$ −0.844964 + 11.5223i −0.0619558 + 0.844856i
$$187$$ 2.64861i 0.193686i
$$188$$ −2.35829 5.56155i −0.171996 0.405618i
$$189$$ 15.6847 + 0.561553i 1.14089 + 0.0408470i
$$190$$ 0 0
$$191$$ −24.9073 −1.80223 −0.901113 0.433585i $$-0.857248\pi$$
−0.901113 + 0.433585i $$0.857248\pi$$
$$192$$ −13.7129 + 1.98889i −0.989645 + 0.143535i
$$193$$ 0.246211 0.0177227 0.00886134 0.999961i $$-0.497179\pi$$
0.00886134 + 0.999961i $$0.497179\pi$$
$$194$$ −7.07488 4.68466i −0.507947 0.336339i
$$195$$ 0 0
$$196$$ −1.65767 3.90928i −0.118405 0.279234i
$$197$$ 4.24621i 0.302530i −0.988493 0.151265i $$-0.951665\pi$$
0.988493 0.151265i $$-0.0483347\pi$$
$$198$$ −5.08706 + 2.38537i −0.361522 + 0.169521i
$$199$$ 5.46026i 0.387067i 0.981094 + 0.193534i $$0.0619949\pi$$
−0.981094 + 0.193534i $$0.938005\pi$$
$$200$$ 0 0
$$201$$ 3.68466 + 6.56155i 0.259896 + 0.462816i
$$202$$ −0.684658 + 1.03399i −0.0481724 + 0.0727511i
$$203$$ −9.43318 −0.662079
$$204$$ 4.23725 5.48140i 0.296667 0.383775i
$$205$$ 0 0
$$206$$ 7.65552 11.5616i 0.533385 0.805532i
$$207$$ −0.580639 + 0.952473i −0.0403572 + 0.0662014i
$$208$$ −14.2462 + 14.7304i −0.987797 + 1.02137i
$$209$$ 1.75379i 0.121312i
$$210$$ 0 0
$$211$$ 16.7984i 1.15645i −0.815878 0.578224i $$-0.803746\pi$$
0.815878 0.578224i $$-0.196254\pi$$
$$212$$ −22.5490 + 9.56155i −1.54867 + 0.656690i
$$213$$ 5.12311 2.87689i 0.351029 0.197122i
$$214$$ −3.56155 2.35829i −0.243463 0.161210i
$$215$$ 0 0
$$216$$ −14.3440 3.20165i −0.975983 0.217845i
$$217$$ 14.2462 0.967096
$$218$$ 1.03399 + 0.684658i 0.0700305 + 0.0463709i
$$219$$ −12.4536 + 6.99337i −0.841538 + 0.472568i
$$220$$ 0 0
$$221$$ 10.2462i 0.689235i
$$222$$ 12.5154 + 0.917790i 0.839978 + 0.0615980i
$$223$$ 8.31768i 0.556993i −0.960437 0.278496i $$-0.910164\pi$$
0.960437 0.278496i $$-0.0898360\pi$$
$$224$$ 3.68260 + 16.6847i 0.246054 + 1.11479i
$$225$$ 0 0
$$226$$ −10.9309 + 16.5081i −0.727111 + 1.09810i
$$227$$ −21.8868 −1.45268 −0.726339 0.687337i $$-0.758780\pi$$
−0.726339 + 0.687337i $$0.758780\pi$$
$$228$$ −2.80571 + 3.62953i −0.185812 + 0.240371i
$$229$$ −16.2462 −1.07358 −0.536790 0.843716i $$-0.680363\pi$$
−0.536790 + 0.843716i $$0.680363\pi$$
$$230$$ 0 0
$$231$$ 3.39228 + 6.04090i 0.223196 + 0.397462i
$$232$$ 8.68466 + 1.61463i 0.570176 + 0.106005i
$$233$$ 10.0000i 0.655122i 0.944830 + 0.327561i $$0.106227\pi$$
−0.944830 + 0.327561i $$0.893773\pi$$
$$234$$ −19.6794 + 9.22786i −1.28648 + 0.603244i
$$235$$ 0 0
$$236$$ −11.0478 26.0540i −0.719151 1.69597i
$$237$$ 6.87689 + 12.2462i 0.446702 + 0.795477i
$$238$$ −7.12311 4.71659i −0.461722 0.305731i
$$239$$ 17.3790 1.12416 0.562078 0.827084i $$-0.310002\pi$$
0.562078 + 0.827084i $$0.310002\pi$$
$$240$$ 0 0
$$241$$ 13.3693 0.861193 0.430597 0.902544i $$-0.358303\pi$$
0.430597 + 0.902544i $$0.358303\pi$$
$$242$$ 10.9026 + 7.21922i 0.700849 + 0.464069i
$$243$$ −13.0114 8.58511i −0.834680 0.550735i
$$244$$ 2.43845 + 5.75058i 0.156106 + 0.368143i
$$245$$ 0 0
$$246$$ −0.201201 + 2.74367i −0.0128281 + 0.174930i
$$247$$ 6.78456i 0.431691i
$$248$$ −13.1158 2.43845i −0.832853 0.154842i
$$249$$ −22.8078 + 12.8078i −1.44538 + 0.811659i
$$250$$ 0 0
$$251$$ 18.7033 1.18054 0.590272 0.807205i $$-0.299021\pi$$
0.590272 + 0.807205i $$0.299021\pi$$
$$252$$ −2.64376 + 17.9288i −0.166541 + 1.12941i
$$253$$ −0.492423 −0.0309583
$$254$$ −11.7915 + 17.8078i −0.739863 + 1.11736i
$$255$$ 0 0
$$256$$ −0.534565 15.9911i −0.0334103 0.999442i
$$257$$ 30.4924i 1.90207i −0.309091 0.951033i $$-0.600025\pi$$
0.309091 0.951033i $$-0.399975\pi$$
$$258$$ −1.38607 + 18.9010i −0.0862929 + 1.17673i
$$259$$ 15.4741i 0.961512i
$$260$$ 0 0
$$261$$ 8.00000 + 4.87689i 0.495188 + 0.301872i
$$262$$ −6.43845 4.26324i −0.397769 0.263384i
$$263$$ 23.7917 1.46706 0.733531 0.679656i $$-0.237871\pi$$
0.733531 + 0.679656i $$0.237871\pi$$
$$264$$ −2.08912 6.14219i −0.128576 0.378026i
$$265$$ 0 0
$$266$$ 4.71659 + 3.12311i 0.289193 + 0.191490i
$$267$$ 8.68951 + 15.4741i 0.531789 + 0.946998i
$$268$$ −8.00000 + 3.39228i −0.488678 + 0.207217i
$$269$$ 14.0000i 0.853595i 0.904347 + 0.426798i $$0.140358\pi$$
−0.904347 + 0.426798i $$0.859642\pi$$
$$270$$ 0 0
$$271$$ 15.3110i 0.930080i 0.885290 + 0.465040i $$0.153960\pi$$
−0.885290 + 0.465040i $$0.846040\pi$$
$$272$$ 5.75058 + 5.56155i 0.348680 + 0.337219i
$$273$$ 13.1231 + 23.3693i 0.794246 + 1.41438i
$$274$$ 6.43845 9.72350i 0.388961 0.587418i
$$275$$ 0 0
$$276$$ −1.01909 0.787776i −0.0613418 0.0474186i
$$277$$ −23.3693 −1.40413 −0.702063 0.712115i $$-0.747738\pi$$
−0.702063 + 0.712115i $$0.747738\pi$$
$$278$$ −13.6964 + 20.6847i −0.821457 + 1.24058i
$$279$$ −12.0818 7.36520i −0.723318 0.440943i
$$280$$ 0 0
$$281$$ 13.6155i 0.812234i 0.913821 + 0.406117i $$0.133118\pi$$
−0.913821 + 0.406117i $$0.866882\pi$$
$$282$$ 7.37874 + 0.541105i 0.439398 + 0.0322223i
$$283$$ 23.2111i 1.37976i −0.723925 0.689879i $$-0.757664\pi$$
0.723925 0.689879i $$-0.242336\pi$$
$$284$$ 2.64861 + 6.24621i 0.157166 + 0.370644i
$$285$$ 0 0
$$286$$ −8.00000 5.29723i −0.473050 0.313232i
$$287$$ 3.39228 0.200240
$$288$$ 5.50276 16.0536i 0.324253 0.945970i
$$289$$ 13.0000 0.764706
$$290$$ 0 0
$$291$$ 9.06134 5.08842i 0.531185 0.298289i
$$292$$ −6.43845 15.1838i −0.376782 0.888562i
$$293$$ 2.49242i 0.145609i −0.997346 0.0728044i $$-0.976805\pi$$
0.997346 0.0728044i $$-0.0231949\pi$$
$$294$$ 5.18660 + 0.380349i 0.302489 + 0.0221824i
$$295$$ 0 0
$$296$$ −2.64861 + 14.2462i −0.153948 + 0.828044i
$$297$$ 0.246211 6.87689i 0.0142866 0.399038i
$$298$$ −10.9309 + 16.5081i −0.633208 + 0.956286i
$$299$$ −1.90495 −0.110166
$$300$$ 0 0
$$301$$ 23.3693 1.34699
$$302$$ −5.75058 + 8.68466i −0.330908 + 0.499746i
$$303$$ −0.743668 1.32431i −0.0427226 0.0760794i
$$304$$ −3.80776 3.68260i −0.218390 0.211212i
$$305$$ 0 0
$$306$$ 3.60245 + 7.68260i 0.205938 + 0.439185i
$$307$$ 11.1293i 0.635184i −0.948227 0.317592i $$-0.897126\pi$$
0.948227 0.317592i $$-0.102874\pi$$
$$308$$ −7.36520 + 3.12311i −0.419671 + 0.177955i
$$309$$ 8.31534 + 14.8078i 0.473043 + 0.842384i
$$310$$ 0 0
$$311$$ 20.7713 1.17783 0.588916 0.808194i $$-0.299555\pi$$
0.588916 + 0.808194i $$0.299555\pi$$
$$312$$ −8.08179 23.7612i −0.457541 1.34521i
$$313$$ 22.4924 1.27135 0.635673 0.771958i $$-0.280722\pi$$
0.635673 + 0.771958i $$0.280722\pi$$
$$314$$ −3.97292 2.63068i −0.224205 0.148458i
$$315$$ 0 0
$$316$$ −14.9309 + 6.33122i −0.839927 + 0.356159i
$$317$$ 16.7386i 0.940135i 0.882630 + 0.470068i $$0.155770\pi$$
−0.882630 + 0.470068i $$0.844230\pi$$
$$318$$ 2.19387 29.9166i 0.123026 1.67764i
$$319$$ 4.13595i 0.231569i
$$320$$ 0 0
$$321$$ 4.56155 2.56155i 0.254601 0.142972i
$$322$$ −0.876894 + 1.32431i −0.0488674 + 0.0738007i
$$323$$ 2.64861 0.147373
$$324$$ 11.5112 13.8381i 0.639510 0.768783i
$$325$$ 0 0
$$326$$ 12.2448 18.4924i 0.678178 1.02420i
$$327$$ −1.32431 + 0.743668i −0.0732343 + 0.0411249i
$$328$$ −3.12311 0.580639i −0.172445 0.0320604i
$$329$$ 9.12311i 0.502973i
$$330$$ 0 0
$$331$$ 3.22925i 0.177496i −0.996054 0.0887479i $$-0.971713\pi$$
0.996054 0.0887479i $$-0.0282865\pi$$
$$332$$ −11.7915 27.8078i −0.647141 1.52615i
$$333$$ −8.00000 + 13.1231i −0.438397 + 0.719142i
$$334$$ −10.6847 7.07488i −0.584638 0.387120i
$$335$$ 0 0
$$336$$ −20.2389 5.31946i −1.10412 0.290200i
$$337$$ 1.50758 0.0821230 0.0410615 0.999157i $$-0.486926\pi$$
0.0410615 + 0.999157i $$0.486926\pi$$
$$338$$ −15.6192 10.3423i −0.849574 0.562549i
$$339$$ −11.8730 21.1431i −0.644852 1.14834i
$$340$$ 0 0
$$341$$ 6.24621i 0.338251i
$$342$$ −2.38537 5.08706i −0.128986 0.275077i
$$343$$ 14.7304i 0.795367i
$$344$$ −21.5150 4.00000i −1.16001 0.215666i
$$345$$ 0 0
$$346$$ −1.56155 + 2.35829i −0.0839496 + 0.126783i
$$347$$ 22.6305 1.21487 0.607434 0.794370i $$-0.292199\pi$$
0.607434 + 0.794370i $$0.292199\pi$$
$$348$$ −6.61668 + 8.55950i −0.354691 + 0.458837i
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 0 0
$$351$$ 0.952473 26.6034i 0.0508392 1.41998i
$$352$$ 7.31534 1.61463i 0.389909 0.0860599i
$$353$$ 20.2462i 1.07760i 0.842435 + 0.538799i $$0.181122\pi$$
−0.842435 + 0.538799i $$0.818878\pi$$
$$354$$ 34.5669 + 2.53489i 1.83721 + 0.134728i
$$355$$ 0 0
$$356$$ −18.8664 + 8.00000i −0.999915 + 0.423999i
$$357$$ 9.12311 5.12311i 0.482846 0.271144i
$$358$$ 11.8078 + 7.81855i 0.624060 + 0.413223i
$$359$$ 21.5150 1.13552 0.567758 0.823195i $$-0.307811\pi$$
0.567758 + 0.823195i $$0.307811\pi$$
$$360$$ 0 0
$$361$$ 17.2462 0.907695
$$362$$ 14.4401 + 9.56155i 0.758954 + 0.502544i
$$363$$ −13.9638 + 7.84144i −0.732912 + 0.411569i
$$364$$ −28.4924 + 12.0818i −1.49341 + 0.633258i
$$365$$ 0 0
$$366$$ −7.62953 0.559496i −0.398802 0.0292453i
$$367$$ 10.9663i 0.572436i 0.958165 + 0.286218i $$0.0923981\pi$$
−0.958165 + 0.286218i $$0.907602\pi$$
$$368$$ 1.03399 1.06913i 0.0539003 0.0557323i
$$369$$ −2.87689 1.75379i −0.149765 0.0912986i
$$370$$ 0 0
$$371$$ −36.9890 −1.92038
$$372$$ 9.99267 12.9268i 0.518096 0.670221i
$$373$$ 9.12311 0.472377 0.236188 0.971707i $$-0.424102\pi$$
0.236188 + 0.971707i $$0.424102\pi$$
$$374$$ −2.06798 + 3.12311i −0.106932 + 0.161492i
$$375$$ 0 0
$$376$$ −1.56155 + 8.39919i −0.0805309 + 0.433155i
$$377$$ 16.0000i 0.824042i
$$378$$ −18.0561 12.9084i −0.928704 0.663935i
$$379$$ 18.7033i 0.960725i 0.877070 + 0.480363i $$0.159495\pi$$
−0.877070 + 0.480363i $$0.840505\pi$$
$$380$$ 0 0
$$381$$ −12.8078 22.8078i −0.656162 1.16848i
$$382$$ 29.3693 + 19.4470i 1.50266 + 0.994995i
$$383$$ 15.1022 0.771688 0.385844 0.922564i $$-0.373910\pi$$
0.385844 + 0.922564i $$0.373910\pi$$
$$384$$ 17.7224 + 8.36154i 0.904394 + 0.426698i
$$385$$ 0 0
$$386$$ −0.290319 0.192236i −0.0147769 0.00978455i
$$387$$ −19.8188 12.0818i −1.00745 0.614152i
$$388$$ 4.68466 + 11.0478i 0.237827 + 0.560867i
$$389$$ 20.7386i 1.05149i −0.850642 0.525745i $$-0.823787\pi$$
0.850642 0.525745i $$-0.176213\pi$$
$$390$$ 0 0
$$391$$ 0.743668i 0.0376089i
$$392$$ −1.09763 + 5.90388i −0.0554388 + 0.298191i
$$393$$ 8.24621 4.63068i 0.415966 0.233587i
$$394$$ −3.31534 + 5.00691i −0.167024 + 0.252244i
$$395$$ 0 0
$$396$$ 7.86084 + 1.15915i 0.395022 + 0.0582495i
$$397$$ −14.8769 −0.746650 −0.373325 0.927701i $$-0.621782\pi$$
−0.373325 + 0.927701i $$0.621782\pi$$
$$398$$ 4.26324 6.43845i 0.213697 0.322730i
$$399$$ −6.04090 + 3.39228i −0.302423 + 0.169827i
$$400$$ 0 0
$$401$$ 24.0000i 1.19850i 0.800561 + 0.599251i $$0.204535\pi$$
−0.800561 + 0.599251i $$0.795465\pi$$
$$402$$ 0.778351 10.6139i 0.0388206 0.529375i
$$403$$ 24.1636i 1.20367i
$$404$$ 1.61463 0.684658i 0.0803307 0.0340630i
$$405$$ 0 0
$$406$$ 11.1231 + 7.36520i 0.552030 + 0.365529i
$$407$$ −6.78456 −0.336298
$$408$$ −9.27608 + 3.15504i −0.459235 + 0.156198i
$$409$$ 25.3693 1.25443 0.627216 0.778845i $$-0.284194\pi$$
0.627216 + 0.778845i $$0.284194\pi$$
$$410$$ 0 0
$$411$$ 6.99337 + 12.4536i 0.344957 + 0.614292i
$$412$$ −18.0540 + 7.65552i −0.889456 + 0.377161i
$$413$$ 42.7386i 2.10303i
$$414$$ 1.42833 0.669757i 0.0701984 0.0329167i
$$415$$ 0 0
$$416$$ 28.2995 6.24621i 1.38750 0.306246i
$$417$$ −14.8769 26.4924i −0.728525 1.29734i
$$418$$ 1.36932 2.06798i 0.0669755 0.101148i
$$419$$ 7.36520 0.359814 0.179907 0.983684i $$-0.442420\pi$$
0.179907 + 0.983684i $$0.442420\pi$$
$$420$$ 0 0
$$421$$ −25.3693 −1.23642 −0.618212 0.786011i $$-0.712143\pi$$
−0.618212 + 0.786011i $$0.712143\pi$$
$$422$$ −13.1158 + 19.8078i −0.638466 + 0.964227i
$$423$$ −4.71659 + 7.73704i −0.229328 + 0.376188i
$$424$$ 34.0540 + 6.33122i 1.65381 + 0.307471i
$$425$$ 0 0
$$426$$ −8.28711 0.607718i −0.401512 0.0294440i
$$427$$ 9.43318i 0.456503i
$$428$$ 2.35829 + 5.56155i 0.113992 + 0.268828i
$$429$$ 10.2462 5.75379i 0.494692 0.277796i
$$430$$ 0 0
$$431$$ −16.6354 −0.801297 −0.400648 0.916232i $$-0.631215\pi$$
−0.400648 + 0.916232i $$0.631215\pi$$
$$432$$ 14.4139 + 14.9747i 0.693488 + 0.720468i
$$433$$ −18.0000 −0.865025 −0.432512 0.901628i $$-0.642373\pi$$
−0.432512 + 0.901628i $$0.642373\pi$$
$$434$$ −16.7984 11.1231i −0.806348 0.533926i
$$435$$ 0 0
$$436$$ −0.684658 1.61463i −0.0327892 0.0773266i
$$437$$ 0.492423i 0.0235558i
$$438$$ 20.1449 + 1.47729i 0.962561 + 0.0705875i
$$439$$ 9.27015i 0.442440i 0.975224 + 0.221220i $$0.0710039\pi$$
−0.975224 + 0.221220i $$0.928996\pi$$
$$440$$ 0 0
$$441$$ −3.31534 + 5.43845i −0.157873 + 0.258974i
$$442$$ −8.00000 + 12.0818i −0.380521 + 0.574672i
$$443$$ 16.5896 0.788195 0.394097 0.919069i $$-0.371057\pi$$
0.394097 + 0.919069i $$0.371057\pi$$
$$444$$ −14.0409 10.8539i −0.666351 0.515105i
$$445$$ 0 0
$$446$$ −6.49424 + 9.80776i −0.307511 + 0.464411i
$$447$$ −11.8730 21.1431i −0.561573 1.00004i
$$448$$ 8.68466 22.5490i 0.410312 1.06534i
$$449$$ 27.3693i 1.29164i −0.763491 0.645819i $$-0.776516\pi$$
0.763491 0.645819i $$-0.223484\pi$$
$$450$$ 0 0
$$451$$ 1.48734i 0.0700359i
$$452$$ 25.7782 10.9309i 1.21250 0.514145i
$$453$$ −6.24621 11.1231i −0.293473 0.522609i
$$454$$ 25.8078 + 17.0887i 1.21122 + 0.802012i
$$455$$ 0 0
$$456$$ 6.14219 2.08912i 0.287634 0.0978319i
$$457$$ 10.0000 0.467780 0.233890 0.972263i $$-0.424854\pi$$
0.233890 + 0.972263i $$0.424854\pi$$
$$458$$ 19.1567 + 12.6847i 0.895133 + 0.592715i
$$459$$ −10.3857 0.371834i −0.484761 0.0173557i
$$460$$ 0 0
$$461$$ 41.8617i 1.94970i 0.222872 + 0.974848i $$0.428457\pi$$
−0.222872 + 0.974848i $$0.571543\pi$$
$$462$$ 0.716589 9.77172i 0.0333387 0.454622i
$$463$$ 3.02045i 0.140372i −0.997534 0.0701861i $$-0.977641\pi$$
0.997534 0.0701861i $$-0.0223593\pi$$
$$464$$ −8.97983 8.68466i −0.416878 0.403175i
$$465$$ 0 0
$$466$$ 7.80776 11.7915i 0.361688 0.546229i
$$467$$ −2.27678 −0.105357 −0.0526784 0.998612i $$-0.516776\pi$$
−0.0526784 + 0.998612i $$0.516776\pi$$
$$468$$ 30.4098 + 4.48419i 1.40569 + 0.207282i
$$469$$ −13.1231 −0.605969
$$470$$ 0 0
$$471$$ 5.08842 2.85742i 0.234462 0.131663i
$$472$$ −7.31534 + 39.3473i −0.336716 + 1.81111i
$$473$$ 10.2462i 0.471121i
$$474$$ 1.45268 19.8094i 0.0667239 0.909876i
$$475$$ 0 0
$$476$$ 4.71659 + 11.1231i 0.216184 + 0.509827i
$$477$$ 31.3693 + 19.1231i 1.43630 + 0.875587i
$$478$$ −20.4924 13.5691i −0.937302 0.620637i
$$479$$ 25.6509 1.17202 0.586010 0.810304i $$-0.300698\pi$$
0.586010 + 0.810304i $$0.300698\pi$$
$$480$$ 0 0
$$481$$ −26.2462 −1.19672
$$482$$ −15.7644 10.4384i −0.718048 0.475458i
$$483$$ −0.952473 1.69614i −0.0433390 0.0771771i
$$484$$ −7.21922 17.0251i −0.328147 0.773866i
$$485$$ 0 0
$$486$$ 8.63928 + 20.2821i 0.391886 + 0.920014i
$$487$$ 25.2791i 1.14550i 0.819728 + 0.572752i $$0.194124\pi$$
−0.819728 + 0.572752i $$0.805876\pi$$
$$488$$ 1.61463 8.68466i 0.0730907 0.393136i
$$489$$ 13.3002 + 23.6847i 0.601455 + 1.07106i
$$490$$ 0 0
$$491$$ 26.9752 1.21737 0.608687 0.793410i $$-0.291696\pi$$
0.608687 + 0.793410i $$0.291696\pi$$
$$492$$ 2.37944 3.07810i 0.107273 0.138771i
$$493$$ 6.24621 0.281315
$$494$$ 5.29723 8.00000i 0.238334 0.359937i
$$495$$ 0 0
$$496$$ 13.5616 + 13.1158i 0.608932 + 0.588916i
$$497$$ 10.2462i 0.459605i
$$498$$ 36.8937 + 2.70552i 1.65325 + 0.121237i
$$499$$ 32.2725i 1.44471i 0.691521 + 0.722357i $$0.256941\pi$$
−0.691521 + 0.722357i $$0.743059\pi$$
$$500$$ 0 0
$$501$$ 13.6847 7.68466i 0.611385 0.343325i
$$502$$ −22.0540 14.6031i −0.984317 0.651769i
$$503$$ −14.3586 −0.640217 −0.320109 0.947381i $$-0.603719\pi$$
−0.320109 + 0.947381i $$0.603719\pi$$
$$504$$ 17.1158 19.0765i 0.762397 0.849736i
$$505$$ 0 0
$$506$$ 0.580639 + 0.384472i 0.0258125 + 0.0170919i
$$507$$ 20.0047 11.2337i 0.888442 0.498907i
$$508$$ 27.8078 11.7915i 1.23377 0.523162i
$$509$$ 11.1231i 0.493023i 0.969140 + 0.246511i $$0.0792843\pi$$
−0.969140 + 0.246511i $$0.920716\pi$$
$$510$$ 0 0
$$511$$ 24.9073i 1.10183i
$$512$$ −11.8551 + 19.2732i −0.523927 + 0.851763i
$$513$$ 6.87689 + 0.246211i 0.303622 + 0.0108705i
$$514$$ −23.8078 + 35.9551i −1.05012 + 1.58591i
$$515$$ 0 0
$$516$$ 16.3919 21.2049i 0.721612 0.933494i
$$517$$ −4.00000 −0.175920
$$518$$ −12.0818 + 18.2462i −0.530843 + 0.801692i
$$519$$ −1.69614 3.02045i −0.0744523 0.132583i
$$520$$ 0 0
$$521$$ 38.2462i 1.67560i −0.545980 0.837798i $$-0.683842\pi$$
0.545980 0.837798i $$-0.316158\pi$$
$$522$$ −5.62541 11.9968i −0.246218 0.525085i
$$523$$ 35.2929i 1.54325i 0.636077 + 0.771625i $$0.280556\pi$$
−0.636077 + 0.771625i $$0.719444\pi$$
$$524$$ 4.26324 + 10.0540i 0.186241 + 0.439210i
$$525$$ 0 0
$$526$$ −28.0540 18.5760i −1.22321 0.809954i
$$527$$ −9.43318 −0.410916
$$528$$ −2.33230 + 8.87368i −0.101500 + 0.386177i
$$529$$ −22.8617 −0.993989
$$530$$ 0 0
$$531$$ −22.0956 + 36.2454i −0.958868 + 1.57292i
$$532$$ −3.12311 7.36520i −0.135404 0.319322i
$$533$$ 5.75379i 0.249224i
$$534$$ 1.83558 25.0308i 0.0794333 1.08319i
$$535$$ 0 0
$$536$$ 12.0818 + 2.24621i 0.521854 + 0.0970215i
$$537$$ −15.1231 + 8.49242i −0.652610 + 0.366475i
$$538$$ 10.9309 16.5081i 0.471263 0.711713i
$$539$$ −2.81164 −0.121106
$$540$$ 0 0
$$541$$ −26.9848 −1.16017 −0.580085 0.814556i $$-0.696980\pi$$
−0.580085 + 0.814556i $$0.696980\pi$$
$$542$$ 11.9545 18.0540i 0.513490 0.775485i
$$543$$ −18.4945 + 10.3857i −0.793676 + 0.445691i
$$544$$ −2.43845 11.0478i −0.104548 0.473671i
$$545$$ 0 0
$$546$$ 2.77214 37.8021i 0.118637 1.61778i
$$547$$ 5.83209i 0.249362i −0.992197 0.124681i $$-0.960209\pi$$
0.992197 0.124681i $$-0.0397908\pi$$
$$548$$ −15.1838 + 6.43845i −0.648618 + 0.275037i
$$549$$ 4.87689 8.00000i 0.208141 0.341432i
$$550$$ 0 0
$$551$$ −4.13595 −0.176197
$$552$$ 0.586575 + 1.72458i 0.0249663 + 0.0734031i
$$553$$ −24.4924 −1.04152
$$554$$ 27.5559 + 18.2462i 1.17074 + 0.775207i
$$555$$ 0 0
$$556$$ 32.3002 13.6964i 1.36983 0.580858i
$$557$$ 36.2462i 1.53580i −0.640569 0.767901i $$-0.721301\pi$$
0.640569 0.767901i $$-0.278699\pi$$
$$558$$ 8.49563 + 18.1178i 0.359649 + 0.766989i
$$559$$ 39.6377i 1.67649i
$$560$$ 0 0
$$561$$ −2.24621 4.00000i −0.0948351 0.168880i
$$562$$ 10.6307 16.0547i 0.448428 0.677227i
$$563$$ 7.90007 0.332948 0.166474 0.986046i $$-0.446762\pi$$
0.166474 + 0.986046i $$0.446762\pi$$
$$564$$ −8.27814 6.39919i −0.348573 0.269455i
$$565$$ 0 0
$$566$$ −18.1227 + 27.3693i −0.761753 + 1.15042i
$$567$$ 24.1636 12.4536i 1.01478 0.523003i
$$568$$ 1.75379 9.43318i 0.0735873 0.395807i
$$569$$ 13.1231i 0.550149i −0.961423 0.275075i $$-0.911297\pi$$
0.961423 0.275075i $$-0.0887026\pi$$
$$570$$ 0 0
$$571$$ 33.0161i 1.38168i 0.723007 + 0.690841i $$0.242759\pi$$
−0.723007 + 0.690841i $$0.757241\pi$$
$$572$$ 5.29723 + 12.4924i 0.221488 + 0.522334i
$$573$$ −37.6155 + 21.1231i −1.57141 + 0.882430i
$$574$$ −4.00000 2.64861i −0.166957 0.110551i
$$575$$ 0 0
$$576$$ −19.0229 + 14.6332i −0.792620 + 0.609716i
$$577$$ 32.2462 1.34243 0.671214 0.741264i $$-0.265773\pi$$
0.671214 + 0.741264i $$0.265773\pi$$
$$578$$ −15.3289 10.1501i −0.637599 0.422188i
$$579$$ 0.371834 0.208805i 0.0154529 0.00867762i
$$580$$ 0 0
$$581$$ 45.6155i 1.89245i
$$582$$ −14.6576 1.07488i −0.607576 0.0445554i
$$583$$ 16.2177i 0.671670i
$$584$$ −4.26324 + 22.9309i −0.176414 + 0.948886i
$$585$$ 0 0
$$586$$ −1.94602 + 2.93893i −0.0803895 + 0.121406i
$$587$$ −1.85917 −0.0767362 −0.0383681 0.999264i $$-0.512216\pi$$
−0.0383681 + 0.999264i $$0.512216\pi$$
$$588$$ −5.81880 4.49806i −0.239963 0.185497i
$$589$$ 6.24621 0.257371
$$590$$ 0 0
$$591$$ −3.60109 6.41273i −0.148129 0.263784i
$$592$$ 14.2462 14.7304i 0.585516 0.605416i
$$593$$ 8.24621i 0.338631i −0.985562 0.169316i $$-0.945844\pi$$
0.985562 0.169316i $$-0.0541557\pi$$
$$594$$ −5.65964 + 7.91664i −0.232218 + 0.324823i
$$595$$ 0 0
$$596$$ 25.7782 10.9309i 1.05592 0.447746i
$$597$$ 4.63068 + 8.24621i 0.189521 + 0.337495i
$$598$$ 2.24621 + 1.48734i 0.0918544 + 0.0608217i
$$599$$ −44.1912 −1.80560 −0.902802 0.430056i $$-0.858494\pi$$
−0.902802 + 0.430056i $$0.858494\pi$$
$$600$$ 0 0
$$601$$ 23.1231 0.943211 0.471606 0.881810i $$-0.343675\pi$$
0.471606 + 0.881810i $$0.343675\pi$$
$$602$$ −27.5559 18.2462i −1.12309 0.743660i
$$603$$ 11.1293 + 6.78456i 0.453221 + 0.276289i
$$604$$ 13.5616 5.75058i 0.551812 0.233988i
$$605$$ 0 0
$$606$$ −0.157093 + 2.14219i −0.00638148 + 0.0870206i
$$607$$ 4.50778i 0.182965i −0.995807 0.0914827i $$-0.970839\pi$$
0.995807 0.0914827i $$-0.0291606\pi$$
$$608$$ 1.61463 + 7.31534i 0.0654817 + 0.296676i
$$609$$ −14.2462 + 8.00000i −0.577286 + 0.324176i
$$610$$ 0 0
$$611$$ −15.4741 −0.626014
$$612$$ 1.75058 11.8716i 0.0707629 0.479882i
$$613$$ −9.12311 −0.368479 −0.184239 0.982881i $$-0.558982\pi$$
−0.184239 + 0.982881i $$0.558982\pi$$
$$614$$ −8.68951 + 13.1231i −0.350680 + 0.529605i
$$615$$ 0 0
$$616$$ 11.1231 + 2.06798i 0.448163 + 0.0833211i
$$617$$ 14.0000i 0.563619i 0.959470 + 0.281809i $$0.0909346\pi$$
−0.959470 + 0.281809i $$0.909065\pi$$
$$618$$ 1.75654 23.9530i 0.0706584 0.963529i
$$619$$ 28.1365i 1.13090i −0.824782 0.565451i $$-0.808702\pi$$
0.824782 0.565451i $$-0.191298\pi$$
$$620$$ 0 0
$$621$$ −0.0691303 + 1.93087i −0.00277410 + 0.0774831i
$$622$$ −24.4924 16.2177i −0.982057 0.650272i
$$623$$ −30.9481 −1.23991
$$624$$ −9.02255 + 34.3280i −0.361191 + 1.37422i
$$625$$ 0 0
$$626$$ −26.5219 17.5616i −1.06003 0.701901i
$$627$$ 1.48734 + 2.64861i 0.0593985 + 0.105775i
$$628$$ 2.63068 + 6.20393i 0.104976 + 0.247564i
$$629$$ 10.2462i 0.408543i
$$630$$ 0 0
$$631$$ 39.8007i 1.58444i 0.610235 + 0.792220i $$0.291075\pi$$
−0.610235 + 0.792220i $$0.708925\pi$$
$$632$$ 22.5490 + 4.19224i 0.896949 + 0.166758i
$$633$$ −14.2462 25.3693i −0.566236 1.00834i
$$634$$ 13.0691 19.7373i 0.519041 0.783869i
$$635$$ 0 0
$$636$$ −25.9451 + 33.5632i −1.02879 + 1.33087i
$$637$$ −10.8769 −0.430958
$$638$$ 3.22925 4.87689i 0.127847 0.193078i
$$639$$ 5.29723 8.68951i 0.209555 0.343752i
$$640$$ 0 0
$$641$$ 6.38447i 0.252171i −0.992019 0.126086i $$-0.959759\pi$$
0.992019 0.126086i $$-0.0402414\pi$$
$$642$$ −7.37874 0.541105i −0.291216 0.0213557i
$$643$$ 3.60109i 0.142013i −0.997476 0.0710065i $$-0.977379\pi$$
0.997476 0.0710065i $$-0.0226211\pi$$
$$644$$ 2.06798 0.876894i 0.0814896 0.0345545i
$$645$$ 0 0
$$646$$ −3.12311 2.06798i −0.122877 0.0813634i
$$647$$ 36.6172 1.43957 0.719786 0.694197i $$-0.244240\pi$$
0.719786 + 0.694197i $$0.244240\pi$$
$$648$$ −24.3778 + 7.32948i −0.957652 + 0.287929i
$$649$$ −18.7386 −0.735556
$$650$$ 0 0
$$651$$ 21.5150 12.0818i 0.843238 0.473523i
$$652$$ −28.8769 + 12.2448i −1.13091 + 0.479544i
$$653$$ 38.9848i 1.52559i 0.646638 + 0.762797i $$0.276175\pi$$
−0.646638 + 0.762797i $$0.723825\pi$$
$$654$$ 2.14219 + 0.157093i 0.0837663 + 0.00614283i
$$655$$ 0 0
$$656$$ 3.22925 + 3.12311i 0.126081 + 0.121937i
$$657$$ −12.8769 + 21.1231i −0.502375 + 0.824091i
$$658$$ −7.12311 + 10.7575i −0.277688 + 0.419370i
$$659$$ 24.7442 0.963898 0.481949 0.876199i $$-0.339929\pi$$
0.481949 + 0.876199i $$0.339929\pi$$
$$660$$ 0 0
$$661$$ 28.1080 1.09327 0.546636 0.837370i $$-0.315908\pi$$
0.546636 + 0.837370i $$0.315908\pi$$
$$662$$ −2.52132 + 3.80776i −0.0979940 + 0.147993i
$$663$$ −8.68951 15.4741i −0.337473 0.600963i
$$664$$ −7.80776 + 41.9960i −0.303000 + 1.62976i
$$665$$ 0 0
$$666$$ 19.6794 9.22786i 0.762561 0.357572i
$$667$$ 1.16128i 0.0449648i
$$668$$ 7.07488 + 16.6847i 0.273735 + 0.645549i
$$669$$ −7.05398 12.5616i −0.272722 0.485658i
$$670$$ 0 0
$$671$$ 4.13595 0.159667
$$672$$ 19.7113 + 22.0745i 0.760381 + 0.851541i
$$673$$ −22.4924 −0.867019 −0.433510 0.901149i $$-0.642725\pi$$
−0.433510 + 0.901149i $$0.642725\pi$$
$$674$$ −1.77766 1.17708i −0.0684727 0.0453395i
$$675$$ 0 0
$$676$$ 10.3423 + 24.3903i 0.397782 + 0.938087i
$$677$$ 1.50758i 0.0579409i −0.999580 0.0289705i $$-0.990777\pi$$
0.999580 0.0289705i $$-0.00922287\pi$$
$$678$$ −2.50806 + 34.2010i −0.0963215 + 1.31348i
$$679$$ 18.1227i 0.695485i
$$680$$ 0 0
$$681$$ −33.0540 + 18.5616i −1.26663 + 0.711280i
$$682$$ −4.87689 + 7.36520i −0.186746 + 0.282028i
$$683$$ −7.90007 −0.302288 −0.151144 0.988512i $$-0.548296\pi$$
−0.151144 + 0.988512i $$0.548296\pi$$
$$684$$ −1.15915 + 7.86084i −0.0443212 + 0.300567i
$$685$$ 0 0
$$686$$ 11.5012 17.3693i 0.439116 0.663164i
$$687$$ −24.5354 + 13.7779i −0.936085 + 0.525661i
$$688$$ 22.2462 + 21.5150i 0.848129 + 0.820251i
$$689$$ 62.7386i 2.39015i
$$690$$ 0 0
$$691$$ 18.2857i 0.695621i −0.937565 0.347811i $$-0.886925\pi$$
0.937565 0.347811i $$-0.113075\pi$$
$$692$$ 3.68260 1.56155i 0.139991 0.0593613i
$$693$$ 10.2462 + 6.24621i 0.389221 + 0.237274i
$$694$$ −26.6847 17.6693i −1.01294 0.670719i
$$695$$ 0 0
$$696$$ 14.4851 4.92676i 0.549056 0.186748i
$$697$$ −2.24621 −0.0850813
$$698$$ 16.5081 + 10.9309i 0.624839 + 0.413740i
$$699$$ 8.48071 + 15.1022i 0.320770 + 0.571219i
$$700$$ 0 0
$$701$$ 17.5076i 0.661252i 0.943762 + 0.330626i $$0.107260\pi$$
−0.943762 + 0.330626i $$0.892740\pi$$
$$702$$ −21.8944 + 30.6256i −0.826351 + 1.15589i
$$703$$ 6.78456i 0.255885i
$$704$$ −9.88653 3.80776i −0.372612 0.143511i
$$705$$ 0 0
$$706$$ 15.8078 23.8733i 0.594933 0.898482i
$$707$$ 2.64861 0.0996114
$$708$$ −38.7803 29.9780i −1.45745 1.12664i
$$709$$ 6.49242 0.243828 0.121914 0.992541i $$-0.461097\pi$$
0.121914 + 0.992541i $$0.461097\pi$$
$$710$$ 0 0
$$711$$ 20.7713 + 12.6624i 0.778985 + 0.474878i
$$712$$ 28.4924 + 5.29723i 1.06780 + 0.198522i
$$713$$ 1.75379i 0.0656799i
$$714$$ −14.7575 1.08221i −0.552285 0.0405007i
$$715$$ 0 0
$$716$$ −7.81855 18.4384i −0.292193 0.689077i
$$717$$ 26.2462 14.7386i 0.980183 0.550424i
$$718$$ −25.3693 16.7984i −0.946774 0.626910i
$$719$$ −30.9481 −1.15417 −0.577086 0.816684i $$-0.695810\pi$$
−0.577086 + 0.816684i $$0.695810\pi$$
$$720$$ 0 0
$$721$$ −29.6155 −1.10294
$$722$$ −20.3358 13.4654i −0.756821 0.501132i
$$723$$ 20.1907 11.3381i 0.750899 0.421669i
$$724$$ −9.56155 22.5490i −0.355352 0.838025i
$$725$$ 0 0
$$726$$ 22.5878 + 1.65643i 0.838314 + 0.0614760i
$$727$$ 10.9663i 0.406717i −0.979104 0.203359i $$-0.934814\pi$$
0.979104 0.203359i $$-0.0651857\pi$$
$$728$$ 43.0299 + 8.00000i 1.59480 + 0.296500i
$$729$$ −26.9309 1.93087i −0.997440 0.0715137i
$$730$$ 0 0
$$731$$ −15.4741 −0.572329
$$732$$ 8.55950 + 6.61668i 0.316368 + 0.244560i
$$733$$ 26.8769 0.992721 0.496360 0.868117i $$-0.334669\pi$$
0.496360 + 0.868117i $$0.334669\pi$$
$$734$$ 8.56222 12.9309i 0.316037 0.477287i
$$735$$ 0 0
$$736$$ −2.05398 + 0.453349i −0.0757105 + 0.0167107i
$$737$$ 5.75379i 0.211944i
$$738$$ 2.02297 + 4.31419i 0.0744664 + 0.158807i
$$739$$ 26.9752i 0.992300i 0.868237 + 0.496150i $$0.165253\pi$$
−0.868237 + 0.496150i $$0.834747\pi$$
$$740$$ 0 0
$$741$$ 5.75379 + 10.2462i 0.211371 + 0.376404i
$$742$$ 43.6155 + 28.8802i 1.60118 + 1.06022i
$$743$$ 9.80501 0.359711 0.179856 0.983693i $$-0.442437\pi$$
0.179856 + 0.983693i $$0.442437\pi$$
$$744$$ −21.8757 + 7.44050i −0.802004 + 0.272782i
$$745$$ 0 0
$$746$$ −10.7575 7.12311i −0.393860 0.260795i
$$747$$ −23.5829 + 38.6852i −0.862855 + 1.41542i
$$748$$ 4.87689 2.06798i 0.178317 0.0756127i
$$749$$ 9.12311i 0.333351i
$$750$$ 0 0
$$751$$ 11.5012i 0.419683i −0.977735 0.209842i $$-0.932705\pi$$
0.977735 0.209842i $$-0.0672948\pi$$
$$752$$ 8.39919 8.68466i 0.306287 0.316697i
$$753$$ 28.2462 15.8617i 1.02935 0.578034i
$$754$$ 12.4924 18.8664i 0.454947 0.687072i
$$755$$ 0 0
$$756$$ 11.2122 + 29.3186i 0.407785 + 1.06631i
$$757$$ −10.8769 −0.395327 −0.197664 0.980270i $$-0.563335\pi$$
−0.197664 + 0.980270i $$0.563335\pi$$
$$758$$ 14.6031 22.0540i 0.530409 0.801036i
$$759$$ −0.743668 + 0.417609i −0.0269934 + 0.0151582i
$$760$$ 0 0
$$761$$ 31.2311i 1.13212i −0.824362 0.566062i $$-0.808466\pi$$
0.824362 0.566062i $$-0.191534\pi$$
$$762$$ −2.70552 + 36.8937i −0.0980108 + 1.33652i
$$763$$ 2.64861i 0.0958863i
$$764$$ −19.4470 45.8617i −0.703568 1.65922i
$$765$$ 0 0
$$766$$ −17.8078 11.7915i −0.643421 0.426043i
$$767$$ −72.4908 −2.61749
$$768$$ −14.3689 23.6967i −0.518492 0.855083i
$$769$$ 38.9848 1.40583 0.702915 0.711274i $$-0.251882\pi$$
0.702915 + 0.711274i $$0.251882\pi$$
$$770$$ 0 0
$$771$$ −25.8597 46.0504i −0.931315 1.65846i
$$772$$ 0.192236 + 0.453349i 0.00691872 + 0.0163164i
$$773$$ 0.246211i 0.00885560i 0.999990 + 0.00442780i $$0.00140942\pi$$
−0.999990 + 0.00442780i $$0.998591\pi$$
$$774$$ 13.9361 + 29.7203i 0.500924 + 1.06827i
$$775$$ 0 0
$$776$$ 3.10196 16.6847i 0.111354 0.598944i
$$777$$ −13.1231 23.3693i −0.470789 0.838370i
$$778$$ −16.1922 + 24.4539i −0.580520 + 0.876715i
$$779$$ 1.48734 0.0532894
$$780$$ 0 0
$$781$$ 4.49242 0.160752
$$782$$ 0.580639 0.876894i 0.0207636 0.0313577i
$$783$$ 16.2177 + 0.580639i 0.579575 + 0.0207503i
$$784$$ 5.90388 6.10454i 0.210853 0.218019i
$$785$$ 0 0