# Properties

 Label 690.2.i.e.47.16 Level $690$ Weight $2$ Character 690.47 Analytic conductor $5.510$ Analytic rank $0$ Dimension $32$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$690 = 2 \cdot 3 \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 690.i (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.50967773947$$ Analytic rank: $$0$$ Dimension: $$32$$ Relative dimension: $$16$$ over $$\Q(i)$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 47.16 Character $$\chi$$ $$=$$ 690.47 Dual form 690.2.i.e.323.16

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.707107 - 0.707107i) q^{2} +(1.66652 - 0.471935i) q^{3} -1.00000i q^{4} +(1.55923 + 1.60274i) q^{5} +(0.844697 - 1.51211i) q^{6} +(-3.44975 - 3.44975i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.55455 - 1.57298i) q^{9} +O(q^{10})$$ $$q+(0.707107 - 0.707107i) q^{2} +(1.66652 - 0.471935i) q^{3} -1.00000i q^{4} +(1.55923 + 1.60274i) q^{5} +(0.844697 - 1.51211i) q^{6} +(-3.44975 - 3.44975i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.55455 - 1.57298i) q^{9} +(2.23586 + 0.0307665i) q^{10} -3.84509i q^{11} +(-0.471935 - 1.66652i) q^{12} +(0.875224 - 0.875224i) q^{13} -4.87868 q^{14} +(3.35488 + 1.93514i) q^{15} -1.00000 q^{16} +(-1.35706 + 1.35706i) q^{17} +(0.694081 - 2.91860i) q^{18} +3.81508i q^{19} +(1.60274 - 1.55923i) q^{20} +(-7.37712 - 4.12100i) q^{21} +(-2.71889 - 2.71889i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(-1.51211 - 0.844697i) q^{24} +(-0.137579 + 4.99811i) q^{25} -1.23775i q^{26} +(3.51487 - 3.82697i) q^{27} +(-3.44975 + 3.44975i) q^{28} +7.78450 q^{29} +(3.74061 - 1.00391i) q^{30} +5.58131 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.81463 - 6.40791i) q^{33} +1.91917i q^{34} +(0.150100 - 10.9080i) q^{35} +(-1.57298 - 2.55455i) q^{36} +(1.86954 + 1.86954i) q^{37} +(2.69767 + 2.69767i) q^{38} +(1.04553 - 1.87162i) q^{39} +(0.0307665 - 2.23586i) q^{40} +4.29759i q^{41} +(-8.13040 + 2.30242i) q^{42} +(0.142657 - 0.142657i) q^{43} -3.84509 q^{44} +(6.50423 + 1.64166i) q^{45} -1.00000 q^{46} +(-3.63185 + 3.63185i) q^{47} +(-1.66652 + 0.471935i) q^{48} +16.8015i q^{49} +(3.43691 + 3.63148i) q^{50} +(-1.62112 + 2.90201i) q^{51} +(-0.875224 - 0.875224i) q^{52} +(3.62512 + 3.62512i) q^{53} +(-0.220693 - 5.19146i) q^{54} +(6.16270 - 5.99540i) q^{55} +4.87868i q^{56} +(1.80047 + 6.35789i) q^{57} +(5.50447 - 5.50447i) q^{58} +3.87315 q^{59} +(1.93514 - 3.35488i) q^{60} -13.5655 q^{61} +(3.94659 - 3.94659i) q^{62} +(-14.2389 - 3.38620i) q^{63} +1.00000i q^{64} +(2.76744 + 0.0380814i) q^{65} +(-5.81422 - 3.24794i) q^{66} +(-2.77087 - 2.77087i) q^{67} +(1.35706 + 1.35706i) q^{68} +(-1.51211 - 0.844697i) q^{69} +(-7.60700 - 7.81928i) q^{70} +6.15174i q^{71} +(-2.91860 - 0.694081i) q^{72} +(-9.60788 + 9.60788i) q^{73} +2.64393 q^{74} +(2.12950 + 8.39436i) q^{75} +3.81508 q^{76} +(-13.2646 + 13.2646i) q^{77} +(-0.584139 - 2.06274i) q^{78} -17.1956i q^{79} +(-1.55923 - 1.60274i) q^{80} +(4.05150 - 8.03650i) q^{81} +(3.03885 + 3.03885i) q^{82} +(2.00448 + 2.00448i) q^{83} +(-4.12100 + 7.37712i) q^{84} +(-4.29100 - 0.0590463i) q^{85} -0.201747i q^{86} +(12.9730 - 3.67378i) q^{87} +(-2.71889 + 2.71889i) q^{88} +12.5987 q^{89} +(5.76001 - 3.43835i) q^{90} -6.03860 q^{91} +(-0.707107 + 0.707107i) q^{92} +(9.30135 - 2.63402i) q^{93} +5.13622i q^{94} +(-6.11459 + 5.94860i) q^{95} +(-0.844697 + 1.51211i) q^{96} +(-3.36602 - 3.36602i) q^{97} +(11.8805 + 11.8805i) q^{98} +(-6.04824 - 9.82250i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$32q + 4q^{3} - 4q^{6} - 8q^{7} + O(q^{10})$$ $$32q + 4q^{3} - 4q^{6} - 8q^{7} - 8q^{10} - 4q^{12} - 4q^{15} - 32q^{16} + 8q^{18} - 32q^{21} - 8q^{22} + 4q^{27} - 8q^{28} + 20q^{30} - 24q^{31} + 20q^{36} - 32q^{37} - 16q^{40} + 8q^{42} + 144q^{43} + 36q^{45} - 32q^{46} - 4q^{48} + 12q^{51} - 64q^{55} + 52q^{57} + 16q^{58} + 4q^{60} - 24q^{61} - 116q^{63} + 12q^{66} - 16q^{67} - 80q^{70} - 8q^{72} + 40q^{73} + 44q^{75} + 24q^{76} - 36q^{78} - 108q^{81} - 32q^{82} - 80q^{85} + 68q^{87} - 8q^{88} + 16q^{90} + 120q^{91} + 12q^{93} + 4q^{96} - 8q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$$.

 $$n$$ $$277$$ $$461$$ $$511$$ $$\chi(n)$$ $$e\left(\frac{1}{4}\right)$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.707107 0.707107i 0.500000 0.500000i
$$3$$ 1.66652 0.471935i 0.962164 0.272472i
$$4$$ 1.00000i 0.500000i
$$5$$ 1.55923 + 1.60274i 0.697311 + 0.716769i
$$6$$ 0.844697 1.51211i 0.344846 0.617318i
$$7$$ −3.44975 3.44975i −1.30388 1.30388i −0.925753 0.378129i $$-0.876568\pi$$
−0.378129 0.925753i $$-0.623432\pi$$
$$8$$ −0.707107 0.707107i −0.250000 0.250000i
$$9$$ 2.55455 1.57298i 0.851518 0.524325i
$$10$$ 2.23586 + 0.0307665i 0.707040 + 0.00972923i
$$11$$ 3.84509i 1.15934i −0.814852 0.579670i $$-0.803182\pi$$
0.814852 0.579670i $$-0.196818\pi$$
$$12$$ −0.471935 1.66652i −0.136236 0.481082i
$$13$$ 0.875224 0.875224i 0.242743 0.242743i −0.575241 0.817984i $$-0.695092\pi$$
0.817984 + 0.575241i $$0.195092\pi$$
$$14$$ −4.87868 −1.30388
$$15$$ 3.35488 + 1.93514i 0.866226 + 0.499652i
$$16$$ −1.00000 −0.250000
$$17$$ −1.35706 + 1.35706i −0.329135 + 0.329135i −0.852258 0.523122i $$-0.824767\pi$$
0.523122 + 0.852258i $$0.324767\pi$$
$$18$$ 0.694081 2.91860i 0.163597 0.687922i
$$19$$ 3.81508i 0.875239i 0.899160 + 0.437619i $$0.144178\pi$$
−0.899160 + 0.437619i $$0.855822\pi$$
$$20$$ 1.60274 1.55923i 0.358385 0.348655i
$$21$$ −7.37712 4.12100i −1.60982 0.899277i
$$22$$ −2.71889 2.71889i −0.579670 0.579670i
$$23$$ −0.707107 0.707107i −0.147442 0.147442i
$$24$$ −1.51211 0.844697i −0.308659 0.172423i
$$25$$ −0.137579 + 4.99811i −0.0275158 + 0.999621i
$$26$$ 1.23775i 0.242743i
$$27$$ 3.51487 3.82697i 0.676436 0.736501i
$$28$$ −3.44975 + 3.44975i −0.651941 + 0.651941i
$$29$$ 7.78450 1.44554 0.722772 0.691086i $$-0.242867\pi$$
0.722772 + 0.691086i $$0.242867\pi$$
$$30$$ 3.74061 1.00391i 0.682939 0.183287i
$$31$$ 5.58131 1.00243 0.501217 0.865322i $$-0.332886\pi$$
0.501217 + 0.865322i $$0.332886\pi$$
$$32$$ −0.707107 + 0.707107i −0.125000 + 0.125000i
$$33$$ −1.81463 6.40791i −0.315887 1.11547i
$$34$$ 1.91917i 0.329135i
$$35$$ 0.150100 10.9080i 0.0253715 1.84379i
$$36$$ −1.57298 2.55455i −0.262163 0.425759i
$$37$$ 1.86954 + 1.86954i 0.307351 + 0.307351i 0.843881 0.536530i $$-0.180265\pi$$
−0.536530 + 0.843881i $$0.680265\pi$$
$$38$$ 2.69767 + 2.69767i 0.437619 + 0.437619i
$$39$$ 1.04553 1.87162i 0.167418 0.299700i
$$40$$ 0.0307665 2.23586i 0.00486461 0.353520i
$$41$$ 4.29759i 0.671170i 0.942010 + 0.335585i $$0.108934\pi$$
−0.942010 + 0.335585i $$0.891066\pi$$
$$42$$ −8.13040 + 2.30242i −1.25455 + 0.355271i
$$43$$ 0.142657 0.142657i 0.0217549 0.0217549i −0.696146 0.717901i $$-0.745103\pi$$
0.717901 + 0.696146i $$0.245103\pi$$
$$44$$ −3.84509 −0.579670
$$45$$ 6.50423 + 1.64166i 0.969593 + 0.244724i
$$46$$ −1.00000 −0.147442
$$47$$ −3.63185 + 3.63185i −0.529760 + 0.529760i −0.920501 0.390741i $$-0.872219\pi$$
0.390741 + 0.920501i $$0.372219\pi$$
$$48$$ −1.66652 + 0.471935i −0.240541 + 0.0681180i
$$49$$ 16.8015i 2.40022i
$$50$$ 3.43691 + 3.63148i 0.486053 + 0.513569i
$$51$$ −1.62112 + 2.90201i −0.227002 + 0.406362i
$$52$$ −0.875224 0.875224i −0.121372 0.121372i
$$53$$ 3.62512 + 3.62512i 0.497949 + 0.497949i 0.910799 0.412850i $$-0.135467\pi$$
−0.412850 + 0.910799i $$0.635467\pi$$
$$54$$ −0.220693 5.19146i −0.0300326 0.706469i
$$55$$ 6.16270 5.99540i 0.830979 0.808420i
$$56$$ 4.87868i 0.651941i
$$57$$ 1.80047 + 6.35789i 0.238478 + 0.842123i
$$58$$ 5.50447 5.50447i 0.722772 0.722772i
$$59$$ 3.87315 0.504241 0.252120 0.967696i $$-0.418872\pi$$
0.252120 + 0.967696i $$0.418872\pi$$
$$60$$ 1.93514 3.35488i 0.249826 0.433113i
$$61$$ −13.5655 −1.73688 −0.868442 0.495791i $$-0.834878\pi$$
−0.868442 + 0.495791i $$0.834878\pi$$
$$62$$ 3.94659 3.94659i 0.501217 0.501217i
$$63$$ −14.2389 3.38620i −1.79394 0.426621i
$$64$$ 1.00000i 0.125000i
$$65$$ 2.76744 + 0.0380814i 0.343259 + 0.00472341i
$$66$$ −5.81422 3.24794i −0.715681 0.399794i
$$67$$ −2.77087 2.77087i −0.338515 0.338515i 0.517293 0.855808i $$-0.326940\pi$$
−0.855808 + 0.517293i $$0.826940\pi$$
$$68$$ 1.35706 + 1.35706i 0.164568 + 0.164568i
$$69$$ −1.51211 0.844697i −0.182037 0.101690i
$$70$$ −7.60700 7.81928i −0.909211 0.934582i
$$71$$ 6.15174i 0.730077i 0.930992 + 0.365039i $$0.118944\pi$$
−0.930992 + 0.365039i $$0.881056\pi$$
$$72$$ −2.91860 0.694081i −0.343961 0.0817983i
$$73$$ −9.60788 + 9.60788i −1.12452 + 1.12452i −0.133463 + 0.991054i $$0.542610\pi$$
−0.991054 + 0.133463i $$0.957390\pi$$
$$74$$ 2.64393 0.307351
$$75$$ 2.12950 + 8.39436i 0.245894 + 0.969297i
$$76$$ 3.81508 0.437619
$$77$$ −13.2646 + 13.2646i −1.51164 + 1.51164i
$$78$$ −0.584139 2.06274i −0.0661408 0.233559i
$$79$$ 17.1956i 1.93466i −0.253525 0.967329i $$-0.581590\pi$$
0.253525 0.967329i $$-0.418410\pi$$
$$80$$ −1.55923 1.60274i −0.174328 0.179192i
$$81$$ 4.05150 8.03650i 0.450166 0.892945i
$$82$$ 3.03885 + 3.03885i 0.335585 + 0.335585i
$$83$$ 2.00448 + 2.00448i 0.220021 + 0.220021i 0.808507 0.588486i $$-0.200276\pi$$
−0.588486 + 0.808507i $$0.700276\pi$$
$$84$$ −4.12100 + 7.37712i −0.449638 + 0.804910i
$$85$$ −4.29100 0.0590463i −0.465424 0.00640447i
$$86$$ 0.201747i 0.0217549i
$$87$$ 12.9730 3.67378i 1.39085 0.393870i
$$88$$ −2.71889 + 2.71889i −0.289835 + 0.289835i
$$89$$ 12.5987 1.33546 0.667728 0.744406i $$-0.267267\pi$$
0.667728 + 0.744406i $$0.267267\pi$$
$$90$$ 5.76001 3.43835i 0.607159 0.362434i
$$91$$ −6.03860 −0.633018
$$92$$ −0.707107 + 0.707107i −0.0737210 + 0.0737210i
$$93$$ 9.30135 2.63402i 0.964505 0.273135i
$$94$$ 5.13622i 0.529760i
$$95$$ −6.11459 + 5.94860i −0.627344 + 0.610313i
$$96$$ −0.844697 + 1.51211i −0.0862115 + 0.154329i
$$97$$ −3.36602 3.36602i −0.341767 0.341767i 0.515264 0.857032i $$-0.327694\pi$$
−0.857032 + 0.515264i $$0.827694\pi$$
$$98$$ 11.8805 + 11.8805i 1.20011 + 1.20011i
$$99$$ −6.04824 9.82250i −0.607871 0.987199i
$$100$$ 4.99811 + 0.137579i 0.499811 + 0.0137579i
$$101$$ 11.2944i 1.12383i −0.827194 0.561916i $$-0.810064\pi$$
0.827194 0.561916i $$-0.189936\pi$$
$$102$$ 0.905725 + 3.19833i 0.0896801 + 0.316682i
$$103$$ −8.36819 + 8.36819i −0.824542 + 0.824542i −0.986756 0.162214i $$-0.948137\pi$$
0.162214 + 0.986756i $$0.448137\pi$$
$$104$$ −1.23775 −0.121372
$$105$$ −4.89774 18.2492i −0.477970 1.78094i
$$106$$ 5.12670 0.497949
$$107$$ −7.21940 + 7.21940i −0.697925 + 0.697925i −0.963963 0.266037i $$-0.914286\pi$$
0.266037 + 0.963963i $$0.414286\pi$$
$$108$$ −3.82697 3.51487i −0.368251 0.338218i
$$109$$ 2.16073i 0.206960i −0.994632 0.103480i $$-0.967002\pi$$
0.994632 0.103480i $$-0.0329978\pi$$
$$110$$ 0.118300 8.59708i 0.0112795 0.819699i
$$111$$ 3.99792 + 2.23332i 0.379466 + 0.211977i
$$112$$ 3.44975 + 3.44975i 0.325971 + 0.325971i
$$113$$ 8.63760 + 8.63760i 0.812557 + 0.812557i 0.985017 0.172459i $$-0.0551713\pi$$
−0.172459 + 0.985017i $$0.555171\pi$$
$$114$$ 5.76883 + 3.22258i 0.540301 + 0.301823i
$$115$$ 0.0307665 2.23586i 0.00286899 0.208495i
$$116$$ 7.78450i 0.722772i
$$117$$ 0.859102 3.61251i 0.0794240 0.333977i
$$118$$ 2.73873 2.73873i 0.252120 0.252120i
$$119$$ 9.36303 0.858308
$$120$$ −1.00391 3.74061i −0.0916437 0.341470i
$$121$$ −3.78475 −0.344068
$$122$$ −9.59226 + 9.59226i −0.868442 + 0.868442i
$$123$$ 2.02818 + 7.16200i 0.182875 + 0.645775i
$$124$$ 5.58131i 0.501217i
$$125$$ −8.22521 + 7.57271i −0.735685 + 0.677324i
$$126$$ −12.4629 + 7.67404i −1.11028 + 0.683658i
$$127$$ −10.4407 10.4407i −0.926462 0.926462i 0.0710131 0.997475i $$-0.477377\pi$$
−0.997475 + 0.0710131i $$0.977377\pi$$
$$128$$ 0.707107 + 0.707107i 0.0625000 + 0.0625000i
$$129$$ 0.170415 0.305064i 0.0150042 0.0268594i
$$130$$ 1.98380 1.92995i 0.173991 0.169268i
$$131$$ 11.2466i 0.982617i 0.870985 + 0.491309i $$0.163481\pi$$
−0.870985 + 0.491309i $$0.836519\pi$$
$$132$$ −6.40791 + 1.81463i −0.557737 + 0.157944i
$$133$$ 13.1611 13.1611i 1.14121 1.14121i
$$134$$ −3.91860 −0.338515
$$135$$ 11.6142 0.333716i 0.999587 0.0287217i
$$136$$ 1.91917 0.164568
$$137$$ 10.4263 10.4263i 0.890776 0.890776i −0.103820 0.994596i $$-0.533107\pi$$
0.994596 + 0.103820i $$0.0331066\pi$$
$$138$$ −1.66652 + 0.471935i −0.141863 + 0.0401738i
$$139$$ 14.6451i 1.24218i 0.783738 + 0.621092i $$0.213311\pi$$
−0.783738 + 0.621092i $$0.786689\pi$$
$$140$$ −10.9080 0.150100i −0.921897 0.0126858i
$$141$$ −4.33854 + 7.76654i −0.365371 + 0.654061i
$$142$$ 4.34994 + 4.34994i 0.365039 + 0.365039i
$$143$$ −3.36532 3.36532i −0.281422 0.281422i
$$144$$ −2.55455 + 1.57298i −0.212880 + 0.131081i
$$145$$ 12.1379 + 12.4766i 1.00799 + 1.03612i
$$146$$ 13.5876i 1.12452i
$$147$$ 7.92922 + 28.0000i 0.653991 + 2.30940i
$$148$$ 1.86954 1.86954i 0.153675 0.153675i
$$149$$ 1.21978 0.0999285 0.0499642 0.998751i $$-0.484089\pi$$
0.0499642 + 0.998751i $$0.484089\pi$$
$$150$$ 7.44149 + 4.42992i 0.607595 + 0.361701i
$$151$$ 6.92084 0.563210 0.281605 0.959530i $$-0.409133\pi$$
0.281605 + 0.959530i $$0.409133\pi$$
$$152$$ 2.69767 2.69767i 0.218810 0.218810i
$$153$$ −1.33206 + 5.60131i −0.107691 + 0.452839i
$$154$$ 18.7590i 1.51164i
$$155$$ 8.70257 + 8.94542i 0.699008 + 0.718513i
$$156$$ −1.87162 1.04553i −0.149850 0.0837091i
$$157$$ 1.67127 + 1.67127i 0.133382 + 0.133382i 0.770646 0.637264i $$-0.219934\pi$$
−0.637264 + 0.770646i $$0.719934\pi$$
$$158$$ −12.1591 12.1591i −0.967329 0.967329i
$$159$$ 7.75215 + 4.33051i 0.614786 + 0.343431i
$$160$$ −2.23586 0.0307665i −0.176760 0.00243231i
$$161$$ 4.87868i 0.384494i
$$162$$ −2.81782 8.54751i −0.221389 0.671556i
$$163$$ 9.29670 9.29670i 0.728173 0.728173i −0.242082 0.970256i $$-0.577830\pi$$
0.970256 + 0.242082i $$0.0778304\pi$$
$$164$$ 4.29759 0.335585
$$165$$ 7.44081 12.8998i 0.579266 1.00425i
$$166$$ 2.83477 0.220021
$$167$$ −10.9776 + 10.9776i −0.849475 + 0.849475i −0.990068 0.140593i $$-0.955099\pi$$
0.140593 + 0.990068i $$0.455099\pi$$
$$168$$ 2.30242 + 8.13040i 0.177636 + 0.627274i
$$169$$ 11.4680i 0.882151i
$$170$$ −3.07594 + 2.99244i −0.235914 + 0.229510i
$$171$$ 6.00102 + 9.74582i 0.458910 + 0.745282i
$$172$$ −0.142657 0.142657i −0.0108775 0.0108775i
$$173$$ −17.3398 17.3398i −1.31832 1.31832i −0.915107 0.403212i $$-0.867894\pi$$
−0.403212 0.915107i $$-0.632106\pi$$
$$174$$ 6.57554 11.7710i 0.498490 0.892361i
$$175$$ 17.7168 16.7676i 1.33927 1.26751i
$$176$$ 3.84509i 0.289835i
$$177$$ 6.45466 1.82787i 0.485162 0.137391i
$$178$$ 8.90860 8.90860i 0.667728 0.667728i
$$179$$ −1.47094 −0.109943 −0.0549715 0.998488i $$-0.517507\pi$$
−0.0549715 + 0.998488i $$0.517507\pi$$
$$180$$ 1.64166 6.50423i 0.122362 0.484796i
$$181$$ −15.6852 −1.16587 −0.582936 0.812518i $$-0.698096\pi$$
−0.582936 + 0.812518i $$0.698096\pi$$
$$182$$ −4.26994 + 4.26994i −0.316509 + 0.316509i
$$183$$ −22.6071 + 6.40203i −1.67117 + 0.473252i
$$184$$ 1.00000i 0.0737210i
$$185$$ −0.0813446 + 5.91145i −0.00598057 + 0.434618i
$$186$$ 4.71452 8.43958i 0.345685 0.618820i
$$187$$ 5.21802 + 5.21802i 0.381580 + 0.381580i
$$188$$ 3.63185 + 3.63185i 0.264880 + 0.264880i
$$189$$ −25.3275 + 1.07669i −1.84230 + 0.0783179i
$$190$$ −0.117377 + 8.52997i −0.00851540 + 0.618829i
$$191$$ 21.7200i 1.57160i −0.618480 0.785800i $$-0.712251\pi$$
0.618480 0.785800i $$-0.287749\pi$$
$$192$$ 0.471935 + 1.66652i 0.0340590 + 0.120270i
$$193$$ 17.8302 17.8302i 1.28345 1.28345i 0.344751 0.938694i $$-0.387963\pi$$
0.938694 0.344751i $$-0.112037\pi$$
$$194$$ −4.76027 −0.341767
$$195$$ 4.62996 1.24259i 0.331558 0.0889836i
$$196$$ 16.8015 1.20011
$$197$$ −0.806128 + 0.806128i −0.0574342 + 0.0574342i −0.735241 0.677806i $$-0.762931\pi$$
0.677806 + 0.735241i $$0.262931\pi$$
$$198$$ −11.2223 2.66881i −0.797535 0.189664i
$$199$$ 18.0493i 1.27948i 0.768590 + 0.639742i $$0.220959\pi$$
−0.768590 + 0.639742i $$0.779041\pi$$
$$200$$ 3.63148 3.43691i 0.256784 0.243026i
$$201$$ −5.92537 3.31003i −0.417943 0.233471i
$$202$$ −7.98633 7.98633i −0.561916 0.561916i
$$203$$ −26.8546 26.8546i −1.88482 1.88482i
$$204$$ 2.90201 + 1.62112i 0.203181 + 0.113501i
$$205$$ −6.88793 + 6.70094i −0.481074 + 0.468014i
$$206$$ 11.8344i 0.824542i
$$207$$ −2.91860 0.694081i −0.202857 0.0482420i
$$208$$ −0.875224 + 0.875224i −0.0606859 + 0.0606859i
$$209$$ 14.6693 1.01470
$$210$$ −16.3674 9.44094i −1.12946 0.651487i
$$211$$ 7.95847 0.547884 0.273942 0.961746i $$-0.411672\pi$$
0.273942 + 0.961746i $$0.411672\pi$$
$$212$$ 3.62512 3.62512i 0.248975 0.248975i
$$213$$ 2.90322 + 10.2520i 0.198925 + 0.702454i
$$214$$ 10.2098i 0.697925i
$$215$$ 0.451077 + 0.00620705i 0.0307632 + 0.000423317i
$$216$$ −5.19146 + 0.220693i −0.353234 + 0.0150163i
$$217$$ −19.2541 19.2541i −1.30706 1.30706i
$$218$$ −1.52786 1.52786i −0.103480 0.103480i
$$219$$ −11.4774 + 20.5460i −0.775570 + 1.38837i
$$220$$ −5.99540 6.16270i −0.404210 0.415489i
$$221$$ 2.37546i 0.159791i
$$222$$ 4.40615 1.24776i 0.295722 0.0837444i
$$223$$ 16.5940 16.5940i 1.11122 1.11122i 0.118233 0.992986i $$-0.462277\pi$$
0.992986 0.118233i $$-0.0377228\pi$$
$$224$$ 4.87868 0.325971
$$225$$ 7.51044 + 12.9843i 0.500696 + 0.865623i
$$226$$ 12.2154 0.812557
$$227$$ 4.89140 4.89140i 0.324653 0.324653i −0.525896 0.850549i $$-0.676270\pi$$
0.850549 + 0.525896i $$0.176270\pi$$
$$228$$ 6.35789 1.80047i 0.421062 0.119239i
$$229$$ 4.39356i 0.290335i −0.989407 0.145167i $$-0.953628\pi$$
0.989407 0.145167i $$-0.0463721\pi$$
$$230$$ −1.55923 1.60274i −0.102813 0.105682i
$$231$$ −15.8456 + 28.3657i −1.04257 + 1.86633i
$$232$$ −5.50447 5.50447i −0.361386 0.361386i
$$233$$ 8.94095 + 8.94095i 0.585741 + 0.585741i 0.936475 0.350734i $$-0.114068\pi$$
−0.350734 + 0.936475i $$0.614068\pi$$
$$234$$ −1.94696 3.16191i −0.127276 0.206700i
$$235$$ −11.4838 0.158024i −0.749123 0.0103083i
$$236$$ 3.87315i 0.252120i
$$237$$ −8.11521 28.6568i −0.527140 1.86146i
$$238$$ 6.62066 6.62066i 0.429154 0.429154i
$$239$$ 7.07155 0.457420 0.228710 0.973495i $$-0.426549\pi$$
0.228710 + 0.973495i $$0.426549\pi$$
$$240$$ −3.35488 1.93514i −0.216557 0.124913i
$$241$$ −4.22605 −0.272224 −0.136112 0.990693i $$-0.543461\pi$$
−0.136112 + 0.990693i $$0.543461\pi$$
$$242$$ −2.67622 + 2.67622i −0.172034 + 0.172034i
$$243$$ 2.95918 15.3050i 0.189832 0.981817i
$$244$$ 13.5655i 0.868442i
$$245$$ −26.9285 + 26.1975i −1.72040 + 1.67370i
$$246$$ 6.49844 + 3.63016i 0.414325 + 0.231450i
$$247$$ 3.33905 + 3.33905i 0.212459 + 0.212459i
$$248$$ −3.94659 3.94659i −0.250608 0.250608i
$$249$$ 4.28649 + 2.39452i 0.271645 + 0.151747i
$$250$$ −0.461381 + 11.1708i −0.0291803 + 0.706504i
$$251$$ 0.318931i 0.0201307i −0.999949 0.0100654i $$-0.996796\pi$$
0.999949 0.0100654i $$-0.00320396\pi$$
$$252$$ −3.38620 + 14.2389i −0.213311 + 0.896969i
$$253$$ −2.71889 + 2.71889i −0.170935 + 0.170935i
$$254$$ −14.7654 −0.926462
$$255$$ −7.17888 + 1.92667i −0.449559 + 0.120653i
$$256$$ 1.00000 0.0625000
$$257$$ −9.89138 + 9.89138i −0.617007 + 0.617007i −0.944763 0.327755i $$-0.893708\pi$$
0.327755 + 0.944763i $$0.393708\pi$$
$$258$$ −0.0952114 0.336214i −0.00592760 0.0209318i
$$259$$ 12.8989i 0.801498i
$$260$$ 0.0380814 2.76744i 0.00236171 0.171629i
$$261$$ 19.8859 12.2448i 1.23091 0.757935i
$$262$$ 7.95253 + 7.95253i 0.491309 + 0.491309i
$$263$$ 6.24409 + 6.24409i 0.385027 + 0.385027i 0.872909 0.487882i $$-0.162231\pi$$
−0.487882 + 0.872909i $$0.662231\pi$$
$$264$$ −3.24794 + 5.81422i −0.199897 + 0.357840i
$$265$$ −0.157731 + 11.4626i −0.00968932 + 0.704140i
$$266$$ 18.6125i 1.14121i
$$267$$ 20.9959 5.94575i 1.28493 0.363874i
$$268$$ −2.77087 + 2.77087i −0.169258 + 0.169258i
$$269$$ 11.4973 0.701002 0.350501 0.936562i $$-0.386011\pi$$
0.350501 + 0.936562i $$0.386011\pi$$
$$270$$ 7.97648 8.44842i 0.485433 0.514155i
$$271$$ 14.4129 0.875519 0.437760 0.899092i $$-0.355772\pi$$
0.437760 + 0.899092i $$0.355772\pi$$
$$272$$ 1.35706 1.35706i 0.0822839 0.0822839i
$$273$$ −10.0634 + 2.84983i −0.609067 + 0.172479i
$$274$$ 14.7450i 0.890776i
$$275$$ 19.2182 + 0.529004i 1.15890 + 0.0319002i
$$276$$ −0.844697 + 1.51211i −0.0508448 + 0.0910185i
$$277$$ −21.8386 21.8386i −1.31215 1.31215i −0.919827 0.392325i $$-0.871671\pi$$
−0.392325 0.919827i $$-0.628329\pi$$
$$278$$ 10.3557 + 10.3557i 0.621092 + 0.621092i
$$279$$ 14.2578 8.77927i 0.853590 0.525601i
$$280$$ −7.81928 + 7.60700i −0.467291 + 0.454605i
$$281$$ 32.5667i 1.94277i 0.237517 + 0.971383i $$0.423666\pi$$
−0.237517 + 0.971383i $$0.576334\pi$$
$$282$$ 2.42396 + 8.55959i 0.144345 + 0.509716i
$$283$$ −18.1562 + 18.1562i −1.07927 + 1.07927i −0.0827000 + 0.996574i $$0.526354\pi$$
−0.996574 + 0.0827000i $$0.973646\pi$$
$$284$$ 6.15174 0.365039
$$285$$ −7.38272 + 12.7991i −0.437315 + 0.758155i
$$286$$ −4.75928 −0.281422
$$287$$ 14.8256 14.8256i 0.875127 0.875127i
$$288$$ −0.694081 + 2.91860i −0.0408991 + 0.171980i
$$289$$ 13.3168i 0.783340i
$$290$$ 17.4050 + 0.239502i 1.02206 + 0.0140640i
$$291$$ −7.19807 4.02098i −0.421958 0.235714i
$$292$$ 9.60788 + 9.60788i 0.562258 + 0.562258i
$$293$$ 9.83546 + 9.83546i 0.574594 + 0.574594i 0.933409 0.358815i $$-0.116819\pi$$
−0.358815 + 0.933409i $$0.616819\pi$$
$$294$$ 25.4058 + 14.1922i 1.48170 + 0.827705i
$$295$$ 6.03914 + 6.20766i 0.351612 + 0.361424i
$$296$$ 2.64393i 0.153675i
$$297$$ −14.7151 13.5150i −0.853855 0.784219i
$$298$$ 0.862517 0.862517i 0.0499642 0.0499642i
$$299$$ −1.23775 −0.0715811
$$300$$ 8.39436 2.12950i 0.484648 0.122947i
$$301$$ −0.984258 −0.0567317
$$302$$ 4.89377 4.89377i 0.281605 0.281605i
$$303$$ −5.33021 18.8223i −0.306213 1.08131i
$$304$$ 3.81508i 0.218810i
$$305$$ −21.1518 21.7420i −1.21115 1.24494i
$$306$$ 3.01881 + 4.90263i 0.172574 + 0.280265i
$$307$$ −16.7681 16.7681i −0.957004 0.957004i 0.0421088 0.999113i $$-0.486592\pi$$
−0.999113 + 0.0421088i $$0.986592\pi$$
$$308$$ 13.2646 + 13.2646i 0.755821 + 0.755821i
$$309$$ −9.99648 + 17.8950i −0.568680 + 1.01801i
$$310$$ 12.4790 + 0.171718i 0.708760 + 0.00975291i
$$311$$ 6.36857i 0.361128i 0.983563 + 0.180564i $$0.0577924\pi$$
−0.983563 + 0.180564i $$0.942208\pi$$
$$312$$ −2.06274 + 0.584139i −0.116779 + 0.0330704i
$$313$$ −16.8425 + 16.8425i −0.951993 + 0.951993i −0.998899 0.0469067i $$-0.985064\pi$$
0.0469067 + 0.998899i $$0.485064\pi$$
$$314$$ 2.36353 0.133382
$$315$$ −16.7746 28.1013i −0.945143 1.58333i
$$316$$ −17.1956 −0.967329
$$317$$ 17.8078 17.8078i 1.00018 1.00018i 0.000184598 1.00000i $$-0.499941\pi$$
1.00000 0.000184598i $$-5.87594e-5\pi$$
$$318$$ 8.54373 2.41947i 0.479108 0.135677i
$$319$$ 29.9321i 1.67588i
$$320$$ −1.60274 + 1.55923i −0.0895961 + 0.0871638i
$$321$$ −8.62416 + 15.4383i −0.481353 + 0.861683i
$$322$$ 3.44975 + 3.44975i 0.192247 + 0.192247i
$$323$$ −5.17729 5.17729i −0.288072 0.288072i
$$324$$ −8.03650 4.05150i −0.446472 0.225083i
$$325$$ 4.25405 + 4.49488i 0.235972 + 0.249331i
$$326$$ 13.1475i 0.728173i
$$327$$ −1.01972 3.60089i −0.0563908 0.199129i
$$328$$ 3.03885 3.03885i 0.167793 0.167793i
$$329$$ 25.0580 1.38149
$$330$$ −3.86011 14.3830i −0.212492 0.791758i
$$331$$ −5.76581 −0.316918 −0.158459 0.987366i $$-0.550653\pi$$
−0.158459 + 0.987366i $$0.550653\pi$$
$$332$$ 2.00448 2.00448i 0.110010 0.110010i
$$333$$ 7.71659 + 1.83510i 0.422866 + 0.100563i
$$334$$ 15.5247i 0.849475i
$$335$$ 0.120562 8.76143i 0.00658699 0.478688i
$$336$$ 7.37712 + 4.12100i 0.402455 + 0.224819i
$$337$$ −11.3239 11.3239i −0.616851 0.616851i 0.327871 0.944722i $$-0.393669\pi$$
−0.944722 + 0.327871i $$0.893669\pi$$
$$338$$ 8.10908 + 8.10908i 0.441076 + 0.441076i
$$339$$ 18.4711 + 10.3183i 1.00321 + 0.560414i
$$340$$ −0.0590463 + 4.29100i −0.00320223 + 0.232712i
$$341$$ 21.4607i 1.16216i
$$342$$ 11.1347 + 2.64797i 0.602096 + 0.143186i
$$343$$ 33.8128 33.8128i 1.82572 1.82572i
$$344$$ −0.201747 −0.0108775
$$345$$ −1.00391 3.74061i −0.0540485 0.201388i
$$346$$ −24.5221 −1.31832
$$347$$ −6.47445 + 6.47445i −0.347567 + 0.347567i −0.859203 0.511636i $$-0.829040\pi$$
0.511636 + 0.859203i $$0.329040\pi$$
$$348$$ −3.67378 12.9730i −0.196935 0.695425i
$$349$$ 11.4593i 0.613401i 0.951806 + 0.306701i $$0.0992251\pi$$
−0.951806 + 0.306701i $$0.900775\pi$$
$$350$$ 0.671204 24.3842i 0.0358774 1.30339i
$$351$$ −0.273164 6.42575i −0.0145804 0.342981i
$$352$$ 2.71889 + 2.71889i 0.144917 + 0.144917i
$$353$$ −14.6045 14.6045i −0.777319 0.777319i 0.202055 0.979374i $$-0.435238\pi$$
−0.979374 + 0.202055i $$0.935238\pi$$
$$354$$ 3.27163 5.85664i 0.173885 0.311277i
$$355$$ −9.85967 + 9.59200i −0.523297 + 0.509091i
$$356$$ 12.5987i 0.667728i
$$357$$ 15.6036 4.41874i 0.825833 0.233865i
$$358$$ −1.04011 + 1.04011i −0.0549715 + 0.0549715i
$$359$$ −3.30519 −0.174441 −0.0872207 0.996189i $$-0.527799\pi$$
−0.0872207 + 0.996189i $$0.527799\pi$$
$$360$$ −3.43835 5.76001i −0.181217 0.303579i
$$361$$ 4.44518 0.233957
$$362$$ −11.0911 + 11.0911i −0.582936 + 0.582936i
$$363$$ −6.30734 + 1.78615i −0.331050 + 0.0937488i
$$364$$ 6.03860i 0.316509i
$$365$$ −30.3799 0.418043i −1.59016 0.0218814i
$$366$$ −11.4587 + 20.5126i −0.598957 + 1.07221i
$$367$$ −12.2911 12.2911i −0.641591 0.641591i 0.309355 0.950946i $$-0.399887\pi$$
−0.950946 + 0.309355i $$0.899887\pi$$
$$368$$ 0.707107 + 0.707107i 0.0368605 + 0.0368605i
$$369$$ 6.75999 + 10.9784i 0.351911 + 0.571513i
$$370$$ 4.12251 + 4.23754i 0.214319 + 0.220299i
$$371$$ 25.0115i 1.29853i
$$372$$ −2.63402 9.30135i −0.136567 0.482253i
$$373$$ 4.21951 4.21951i 0.218478 0.218478i −0.589379 0.807857i $$-0.700627\pi$$
0.807857 + 0.589379i $$0.200627\pi$$
$$374$$ 7.37940 0.381580
$$375$$ −10.1336 + 16.5018i −0.523297 + 0.852150i
$$376$$ 5.13622 0.264880
$$377$$ 6.81318 6.81318i 0.350897 0.350897i
$$378$$ −17.1479 + 18.6706i −0.881993 + 0.960311i
$$379$$ 24.7674i 1.27221i −0.771601 0.636107i $$-0.780544\pi$$
0.771601 0.636107i $$-0.219456\pi$$
$$380$$ 5.94860 + 6.11459i 0.305157 + 0.313672i
$$381$$ −22.3269 12.4723i −1.14384 0.638974i
$$382$$ −15.3583 15.3583i −0.785800 0.785800i
$$383$$ −12.2872 12.2872i −0.627846 0.627846i 0.319680 0.947526i $$-0.396425\pi$$
−0.947526 + 0.319680i $$0.896425\pi$$
$$384$$ 1.51211 + 0.844697i 0.0771647 + 0.0431057i
$$385$$ −41.9424 0.577149i −2.13758 0.0294142i
$$386$$ 25.2157i 1.28345i
$$387$$ 0.140029 0.588819i 0.00711806 0.0299314i
$$388$$ −3.36602 + 3.36602i −0.170884 + 0.170884i
$$389$$ −15.4882 −0.785281 −0.392640 0.919692i $$-0.628438\pi$$
−0.392640 + 0.919692i $$0.628438\pi$$
$$390$$ 2.39523 4.15252i 0.121287 0.210271i
$$391$$ 1.91917 0.0970568
$$392$$ 11.8805 11.8805i 0.600054 0.600054i
$$393$$ 5.30765 + 18.7426i 0.267736 + 0.945439i
$$394$$ 1.14004i 0.0574342i
$$395$$ 27.5602 26.8120i 1.38670 1.34906i
$$396$$ −9.82250 + 6.04824i −0.493599 + 0.303935i
$$397$$ −14.2745 14.2745i −0.716415 0.716415i 0.251454 0.967869i $$-0.419091\pi$$
−0.967869 + 0.251454i $$0.919091\pi$$
$$398$$ 12.7628 + 12.7628i 0.639742 + 0.639742i
$$399$$ 15.7220 28.1443i 0.787082 1.40898i
$$400$$ 0.137579 4.99811i 0.00687895 0.249905i
$$401$$ 3.26739i 0.163166i −0.996667 0.0815829i $$-0.974002\pi$$
0.996667 0.0815829i $$-0.0259975\pi$$
$$402$$ −6.53041 + 1.84932i −0.325707 + 0.0922359i
$$403$$ 4.88490 4.88490i 0.243334 0.243334i
$$404$$ −11.2944 −0.561916
$$405$$ 19.1977 6.03727i 0.953941 0.299994i
$$406$$ −37.9781 −1.88482
$$407$$ 7.18856 7.18856i 0.356324 0.356324i
$$408$$ 3.19833 0.905725i 0.158341 0.0448401i
$$409$$ 33.7644i 1.66954i −0.550596 0.834772i $$-0.685600\pi$$
0.550596 0.834772i $$-0.314400\pi$$
$$410$$ −0.132222 + 9.60878i −0.00652997 + 0.474544i
$$411$$ 12.4550 22.2961i 0.614361 1.09978i
$$412$$ 8.36819 + 8.36819i 0.412271 + 0.412271i
$$413$$ −13.3614 13.3614i −0.657470 0.657470i
$$414$$ −2.55455 + 1.57298i −0.125550 + 0.0773075i
$$415$$ −0.0872160 + 6.33814i −0.00428126 + 0.311127i
$$416$$ 1.23775i 0.0606859i
$$417$$ 6.91155 + 24.4063i 0.338460 + 1.19518i
$$418$$ 10.3728 10.3728i 0.507349 0.507349i
$$419$$ −20.6323 −1.00795 −0.503977 0.863717i $$-0.668130\pi$$
−0.503977 + 0.863717i $$0.668130\pi$$
$$420$$ −18.2492 + 4.89774i −0.890472 + 0.238985i
$$421$$ −33.8481 −1.64966 −0.824828 0.565383i $$-0.808728\pi$$
−0.824828 + 0.565383i $$0.808728\pi$$
$$422$$ 5.62749 5.62749i 0.273942 0.273942i
$$423$$ −3.56495 + 14.9906i −0.173334 + 0.728867i
$$424$$ 5.12670i 0.248975i
$$425$$ −6.59603 6.96944i −0.319954 0.338067i
$$426$$ 9.30213 + 5.19635i 0.450690 + 0.251764i
$$427$$ 46.7975 + 46.7975i 2.26469 + 2.26469i
$$428$$ 7.21940 + 7.21940i 0.348963 + 0.348963i
$$429$$ −7.19657 4.02015i −0.347454 0.194095i
$$430$$ 0.323349 0.314570i 0.0155932 0.0151699i
$$431$$ 11.9724i 0.576690i 0.957527 + 0.288345i $$0.0931051\pi$$
−0.957527 + 0.288345i $$0.906895\pi$$
$$432$$ −3.51487 + 3.82697i −0.169109 + 0.184125i
$$433$$ 13.6433 13.6433i 0.655655 0.655655i −0.298694 0.954349i $$-0.596551\pi$$
0.954349 + 0.298694i $$0.0965511\pi$$
$$434$$ −27.2294 −1.30706
$$435$$ 26.1161 + 15.0641i 1.25217 + 0.722269i
$$436$$ −2.16073 −0.103480
$$437$$ 2.69767 2.69767i 0.129047 0.129047i
$$438$$ 6.41246 + 22.6439i 0.306399 + 1.08197i
$$439$$ 12.4463i 0.594027i −0.954873 0.297014i $$-0.904009\pi$$
0.954873 0.297014i $$-0.0959907\pi$$
$$440$$ −8.59708 0.118300i −0.409850 0.00563974i
$$441$$ 26.4284 + 42.9204i 1.25849 + 2.04383i
$$442$$ 1.67971 + 1.67971i 0.0798955 + 0.0798955i
$$443$$ 8.23721 + 8.23721i 0.391362 + 0.391362i 0.875173 0.483811i $$-0.160748\pi$$
−0.483811 + 0.875173i $$0.660748\pi$$
$$444$$ 2.23332 3.99792i 0.105989 0.189733i
$$445$$ 19.6443 + 20.1924i 0.931227 + 0.957213i
$$446$$ 23.4675i 1.11122i
$$447$$ 2.03279 0.575658i 0.0961476 0.0272277i
$$448$$ 3.44975 3.44975i 0.162985 0.162985i
$$449$$ −16.4715 −0.777340 −0.388670 0.921377i $$-0.627065\pi$$
−0.388670 + 0.921377i $$0.627065\pi$$
$$450$$ 14.4920 + 3.87063i 0.683160 + 0.182463i
$$451$$ 16.5246 0.778114
$$452$$ 8.63760 8.63760i 0.406279 0.406279i
$$453$$ 11.5337 3.26619i 0.541900 0.153459i
$$454$$ 6.91748i 0.324653i
$$455$$ −9.41560 9.67834i −0.441410 0.453728i
$$456$$ 3.22258 5.76883i 0.150911 0.270150i
$$457$$ −8.60752 8.60752i −0.402643 0.402643i 0.476520 0.879163i $$-0.341898\pi$$
−0.879163 + 0.476520i $$0.841898\pi$$
$$458$$ −3.10672 3.10672i −0.145167 0.145167i
$$459$$ 0.423549 + 9.96332i 0.0197696 + 0.465048i
$$460$$ −2.23586 0.0307665i −0.104247 0.00143450i
$$461$$ 37.7905i 1.76008i 0.474898 + 0.880041i $$0.342485\pi$$
−0.474898 + 0.880041i $$0.657515\pi$$
$$462$$ 8.85302 + 31.2622i 0.411880 + 1.45445i
$$463$$ −7.64424 + 7.64424i −0.355258 + 0.355258i −0.862062 0.506804i $$-0.830827\pi$$
0.506804 + 0.862062i $$0.330827\pi$$
$$464$$ −7.78450 −0.361386
$$465$$ 18.7246 + 10.8006i 0.868334 + 0.500868i
$$466$$ 12.6444 0.585741
$$467$$ −5.24131 + 5.24131i −0.242539 + 0.242539i −0.817900 0.575361i $$-0.804862\pi$$
0.575361 + 0.817900i $$0.304862\pi$$
$$468$$ −3.61251 0.859102i −0.166988 0.0397120i
$$469$$ 19.1176i 0.882768i
$$470$$ −8.23204 + 8.00856i −0.379716 + 0.369407i
$$471$$ 3.57393 + 1.99647i 0.164678 + 0.0919923i
$$472$$ −2.73873 2.73873i −0.126060 0.126060i
$$473$$ −0.548528 0.548528i −0.0252213 0.0252213i
$$474$$ −26.0017 14.5251i −1.19430 0.667159i
$$475$$ −19.0682 0.524875i −0.874907 0.0240829i
$$476$$ 9.36303i 0.429154i
$$477$$ 14.9628 + 3.55835i 0.685100 + 0.162926i
$$478$$ 5.00034 5.00034i 0.228710 0.228710i
$$479$$ −26.6043 −1.21558 −0.607790 0.794098i $$-0.707944\pi$$
−0.607790 + 0.794098i $$0.707944\pi$$
$$480$$ −3.74061 + 1.00391i −0.170735 + 0.0458218i
$$481$$ 3.27254 0.149215
$$482$$ −2.98827 + 2.98827i −0.136112 + 0.136112i
$$483$$ 2.30242 + 8.13040i 0.104764 + 0.369946i
$$484$$ 3.78475i 0.172034i
$$485$$ 0.146457 10.6433i 0.00665027 0.483286i
$$486$$ −8.72982 12.9147i −0.395993 0.585824i
$$487$$ −5.61285 5.61285i −0.254342 0.254342i 0.568406 0.822748i $$-0.307560\pi$$
−0.822748 + 0.568406i $$0.807560\pi$$
$$488$$ 9.59226 + 9.59226i 0.434221 + 0.434221i
$$489$$ 11.1057 19.8805i 0.502215 0.899029i
$$490$$ −0.516924 + 37.5658i −0.0233523 + 1.69705i
$$491$$ 35.1263i 1.58523i −0.609724 0.792614i $$-0.708720\pi$$
0.609724 0.792614i $$-0.291280\pi$$
$$492$$ 7.16200 2.02818i 0.322888 0.0914375i
$$493$$ −10.5640 + 10.5640i −0.475780 + 0.475780i
$$494$$ 4.72213 0.212459
$$495$$ 6.31234 25.0094i 0.283719 1.12409i
$$496$$ −5.58131 −0.250608
$$497$$ 21.2219 21.2219i 0.951934 0.951934i
$$498$$ 4.72419 1.33783i 0.211696 0.0599495i
$$499$$ 10.0259i 0.448822i 0.974495 + 0.224411i $$0.0720458\pi$$
−0.974495 + 0.224411i $$0.927954\pi$$
$$500$$ 7.57271 + 8.22521i 0.338662 + 0.367842i
$$501$$ −13.1137 + 23.4751i −0.585876 + 1.04879i
$$502$$ −0.225518 0.225518i −0.0100654 0.0100654i
$$503$$ 14.7345 + 14.7345i 0.656979 + 0.656979i 0.954664 0.297685i $$-0.0962145\pi$$
−0.297685 + 0.954664i $$0.596215\pi$$
$$504$$ 7.67404 + 12.4629i 0.341829 + 0.555140i
$$505$$ 18.1020 17.6106i 0.805528 0.783660i
$$506$$ 3.84509i 0.170935i
$$507$$ 5.41214 + 19.1116i 0.240361 + 0.848774i
$$508$$ −10.4407 + 10.4407i −0.463231 + 0.463231i
$$509$$ −29.8800 −1.32441 −0.662205 0.749323i $$-0.730379\pi$$
−0.662205 + 0.749323i $$0.730379\pi$$
$$510$$ −3.71387 + 6.43860i −0.164453 + 0.285106i
$$511$$ 66.2895 2.93247
$$512$$ 0.707107 0.707107i 0.0312500 0.0312500i
$$513$$ 14.6002 + 13.4095i 0.644615 + 0.592043i
$$514$$ 13.9885i 0.617007i
$$515$$ −26.4600 0.364103i −1.16597 0.0160443i
$$516$$ −0.305064 0.170415i −0.0134297 0.00750209i
$$517$$ 13.9648 + 13.9648i 0.614172 + 0.614172i
$$518$$ −9.12089 9.12089i −0.400749 0.400749i
$$519$$ −37.0803 20.7138i −1.62764 0.909234i
$$520$$ −1.92995 1.98380i −0.0846338 0.0869955i
$$521$$ 1.39433i 0.0610866i 0.999533 + 0.0305433i $$0.00972375\pi$$
−0.999533 + 0.0305433i $$0.990276\pi$$
$$522$$ 5.40308 22.7199i 0.236486 0.994422i
$$523$$ −25.8878 + 25.8878i −1.13199 + 1.13199i −0.142148 + 0.989845i $$0.545401\pi$$
−0.989845 + 0.142148i $$0.954599\pi$$
$$524$$ 11.2466 0.491309
$$525$$ 21.6122 36.3047i 0.943232 1.58447i
$$526$$ 8.83047 0.385027
$$527$$ −7.57418 + 7.57418i −0.329936 + 0.329936i
$$528$$ 1.81463 + 6.40791i 0.0789718 + 0.278869i
$$529$$ 1.00000i 0.0434783i
$$530$$ 7.99372 + 8.21679i 0.347225 + 0.356914i
$$531$$ 9.89417 6.09236i 0.429370 0.264386i
$$532$$ −13.1611 13.1611i −0.570604 0.570604i
$$533$$ 3.76135 + 3.76135i 0.162922 + 0.162922i
$$534$$ 10.6420 19.0506i 0.460526 0.824400i
$$535$$ −22.8276 0.314119i −0.986922 0.0135805i
$$536$$ 3.91860i 0.169258i
$$537$$ −2.45134 + 0.694187i −0.105783 + 0.0299564i
$$538$$ 8.12981 8.12981i 0.350501 0.350501i
$$539$$ 64.6034 2.78267
$$540$$ −0.333716 11.6142i −0.0143608 0.499794i
$$541$$ 18.7230 0.804966 0.402483 0.915427i $$-0.368147\pi$$
0.402483 + 0.915427i $$0.368147\pi$$
$$542$$ 10.1914 10.1914i 0.437760 0.437760i
$$543$$ −26.1396 + 7.40239i −1.12176 + 0.317667i
$$544$$ 1.91917i 0.0822839i
$$545$$ 3.46309 3.36908i 0.148343 0.144315i
$$546$$ −5.10079 + 9.13106i −0.218294 + 0.390773i
$$547$$ 17.9273 + 17.9273i 0.766517 + 0.766517i 0.977492 0.210974i $$-0.0676636\pi$$
−0.210974 + 0.977492i $$0.567664\pi$$
$$548$$ −10.4263 10.4263i −0.445388 0.445388i
$$549$$ −34.6538 + 21.3382i −1.47899 + 0.910692i
$$550$$ 13.9634 13.2152i 0.595400 0.563500i
$$551$$ 29.6985i 1.26520i
$$552$$ 0.471935 + 1.66652i 0.0200869 + 0.0709317i
$$553$$ −59.3205 + 59.3205i −2.52257 + 2.52257i
$$554$$ −30.8844 −1.31215
$$555$$ 2.65426 + 9.88992i 0.112667 + 0.419804i
$$556$$ 14.6451 0.621092
$$557$$ 18.5689 18.5689i 0.786789 0.786789i −0.194178 0.980966i $$-0.562204\pi$$
0.980966 + 0.194178i $$0.0622038\pi$$
$$558$$ 3.87389 16.2896i 0.163995 0.689596i
$$559$$ 0.249713i 0.0105617i
$$560$$ −0.150100 + 10.9080i −0.00634288 + 0.460948i
$$561$$ 11.1585 + 6.23336i 0.471112 + 0.263172i
$$562$$ 23.0281 + 23.0281i 0.971383 + 0.971383i
$$563$$ −9.38961 9.38961i −0.395725 0.395725i 0.480997 0.876722i $$-0.340275\pi$$
−0.876722 + 0.480997i $$0.840275\pi$$
$$564$$ 7.76654 + 4.33854i 0.327030 + 0.182686i
$$565$$ −0.375826 + 27.3119i −0.0158111 + 1.14902i
$$566$$ 25.6768i 1.07927i
$$567$$ −41.7005 + 13.7473i −1.75126 + 0.577330i
$$568$$ 4.34994 4.34994i 0.182519 0.182519i
$$569$$ 9.13075 0.382781 0.191390 0.981514i $$-0.438700\pi$$
0.191390 + 0.981514i $$0.438700\pi$$
$$570$$ 3.82998 + 14.2707i 0.160420 + 0.597735i
$$571$$ 33.9459 1.42059 0.710296 0.703903i $$-0.248561\pi$$
0.710296 + 0.703903i $$0.248561\pi$$
$$572$$ −3.36532 + 3.36532i −0.140711 + 0.140711i
$$573$$ −10.2504 36.1967i −0.428217 1.51214i
$$574$$ 20.9665i 0.875127i
$$575$$ 3.63148 3.43691i 0.151443 0.143329i
$$576$$ 1.57298 + 2.55455i 0.0655406 + 0.106440i
$$577$$ −3.14294 3.14294i −0.130842 0.130842i 0.638653 0.769495i $$-0.279492\pi$$
−0.769495 + 0.638653i $$0.779492\pi$$
$$578$$ 9.41638 + 9.41638i 0.391670 + 0.391670i
$$579$$ 21.2996 38.1290i 0.885182 1.58459i
$$580$$ 12.4766 12.1379i 0.518061 0.503997i
$$581$$ 13.8299i 0.573762i
$$582$$ −7.93307 + 2.24654i −0.328836 + 0.0931220i
$$583$$ 13.9389 13.9389i 0.577292 0.577292i
$$584$$ 13.5876 0.562258
$$585$$ 7.12948 4.25583i 0.294768 0.175957i
$$586$$ 13.9094 0.574594
$$587$$ 15.2589 15.2589i 0.629804 0.629804i −0.318215 0.948019i $$-0.603083\pi$$
0.948019 + 0.318215i $$0.103083\pi$$
$$588$$ 28.0000 7.92922i 1.15470 0.326996i
$$589$$ 21.2931i 0.877369i
$$590$$ 8.65980 + 0.119163i 0.356518 + 0.00490587i
$$591$$ −0.962985 + 1.72387i −0.0396119 + 0.0709103i
$$592$$ −1.86954 1.86954i −0.0768377 0.0768377i
$$593$$ 23.4549 + 23.4549i 0.963176 + 0.963176i 0.999346 0.0361698i $$-0.0115157\pi$$
−0.0361698 + 0.999346i $$0.511516\pi$$
$$594$$ −19.9617 + 0.848587i −0.819037 + 0.0348179i
$$595$$ 14.5992 + 15.0065i 0.598507 + 0.615208i
$$596$$ 1.21978i 0.0499642i
$$597$$ 8.51811 + 30.0795i 0.348623 + 1.23107i
$$598$$ −0.875224 + 0.875224i −0.0357906 + 0.0357906i
$$599$$ −10.6390 −0.434697 −0.217349 0.976094i $$-0.569741\pi$$
−0.217349 + 0.976094i $$0.569741\pi$$
$$600$$ 4.42992 7.44149i 0.180851 0.303798i
$$601$$ −24.4899 −0.998966 −0.499483 0.866324i $$-0.666477\pi$$
−0.499483 + 0.866324i $$0.666477\pi$$
$$602$$ −0.695975 + 0.695975i −0.0283658 + 0.0283658i
$$603$$ −11.4368 2.71983i −0.465744 0.110760i
$$604$$ 6.92084i 0.281605i
$$605$$ −5.90131 6.06598i −0.239922 0.246617i
$$606$$ −17.0784 9.54032i −0.693761 0.387549i
$$607$$ −20.6737 20.6737i −0.839120 0.839120i 0.149623 0.988743i $$-0.452194\pi$$
−0.988743 + 0.149623i $$0.952194\pi$$
$$608$$ −2.69767 2.69767i −0.109405 0.109405i
$$609$$ −57.4272 32.0799i −2.32707 1.29995i
$$610$$ −30.3305 0.417363i −1.22805 0.0168985i
$$611$$ 6.35737i 0.257192i
$$612$$ 5.60131 + 1.33206i 0.226419 + 0.0538454i
$$613$$ 14.6753 14.6753i 0.592731 0.592731i −0.345637 0.938368i $$-0.612337\pi$$
0.938368 + 0.345637i $$0.112337\pi$$
$$614$$ −23.7136 −0.957004
$$615$$ −8.31644 + 14.4179i −0.335351 + 0.581385i
$$616$$ 18.7590 0.755821
$$617$$ 9.12773 9.12773i 0.367469 0.367469i −0.499085 0.866553i $$-0.666330\pi$$
0.866553 + 0.499085i $$0.166330\pi$$
$$618$$ 5.58507 + 19.7222i 0.224664 + 0.793344i
$$619$$ 14.8927i 0.598587i 0.954161 + 0.299294i $$0.0967510\pi$$
−0.954161 + 0.299294i $$0.903249\pi$$
$$620$$ 8.94542 8.70257i 0.359257 0.349504i
$$621$$ −5.19146 + 0.220693i −0.208326 + 0.00885612i
$$622$$ 4.50326 + 4.50326i 0.180564 + 0.180564i
$$623$$ −43.4622 43.4622i −1.74128 1.74128i
$$624$$ −1.04553 + 1.87162i −0.0418546 + 0.0749249i
$$625$$ −24.9621 1.37527i −0.998486 0.0550108i
$$626$$ 23.8188i 0.951993i
$$627$$ 24.4467 6.92297i 0.976307 0.276477i
$$628$$ 1.67127 1.67127i 0.0666909 0.0666909i
$$629$$ −5.07416 −0.202320
$$630$$ −31.7320 8.00914i −1.26423 0.319092i
$$631$$ −5.19423 −0.206779 −0.103390 0.994641i $$-0.532969\pi$$
−0.103390 + 0.994641i $$0.532969\pi$$
$$632$$ −12.1591 + 12.1591i −0.483664 + 0.483664i
$$633$$ 13.2629 3.75588i 0.527154 0.149283i
$$634$$ 25.1840i 1.00018i
$$635$$ 0.454279 33.0133i 0.0180275 1.31009i
$$636$$ 4.33051 7.75215i 0.171716 0.307393i
$$637$$ 14.7051 + 14.7051i 0.582637 + 0.582637i
$$638$$ −21.1652 21.1652i −0.837939 0.837939i
$$639$$ 9.67653 + 15.7150i 0.382798 + 0.621674i
$$640$$ −0.0307665 + 2.23586i −0.00121615 + 0.0883800i
$$641$$ 37.8880i 1.49649i 0.663425 + 0.748243i $$0.269102\pi$$
−0.663425 + 0.748243i $$0.730898\pi$$
$$642$$ 4.81835 + 17.0147i 0.190165 + 0.671518i
$$643$$ −8.06700 + 8.06700i −0.318131 + 0.318131i −0.848049 0.529918i $$-0.822223\pi$$
0.529918 + 0.848049i $$0.322223\pi$$
$$644$$ 4.87868 0.192247
$$645$$ 0.754656 0.202535i 0.0297146 0.00797480i
$$646$$ −7.32179 −0.288072
$$647$$ −19.7436 + 19.7436i −0.776203 + 0.776203i −0.979183 0.202980i $$-0.934937\pi$$
0.202980 + 0.979183i $$0.434937\pi$$
$$648$$ −8.54751 + 2.81782i −0.335778 + 0.110695i
$$649$$ 14.8926i 0.584586i
$$650$$ 6.18643 + 0.170289i 0.242652 + 0.00667928i
$$651$$ −41.1740 23.0006i −1.61374 0.901465i
$$652$$ −9.29670 9.29670i −0.364087 0.364087i
$$653$$ −1.55428 1.55428i −0.0608235 0.0608235i 0.676041 0.736864i $$-0.263694\pi$$
−0.736864 + 0.676041i $$0.763694\pi$$
$$654$$ −3.26726 1.82516i −0.127760 0.0713693i
$$655$$ −18.0254 + 17.5360i −0.704310 + 0.685190i
$$656$$ 4.29759i 0.167793i
$$657$$ −9.43089 + 39.6568i −0.367934 + 1.54716i
$$658$$ 17.7187 17.7187i 0.690745 0.690745i
$$659$$ 10.6771 0.415921 0.207960 0.978137i $$-0.433318\pi$$
0.207960 + 0.978137i $$0.433318\pi$$
$$660$$ −12.8998 7.44081i −0.502125 0.289633i
$$661$$ 40.2271 1.56465 0.782326 0.622869i $$-0.214033\pi$$
0.782326 + 0.622869i $$0.214033\pi$$
$$662$$ −4.07705 + 4.07705i −0.158459 + 0.158459i
$$663$$ 1.12106 + 3.95875i 0.0435385 + 0.153745i
$$664$$ 2.83477i 0.110010i
$$665$$ 41.6150 + 0.572643i 1.61376 + 0.0222062i
$$666$$ 6.75407 4.15884i 0.261715 0.161152i
$$667$$ −5.50447 5.50447i −0.213134 0.213134i
$$668$$ 10.9776 + 10.9776i 0.424738 + 0.424738i
$$669$$ 19.8229 35.4855i 0.766398 1.37195i
$$670$$ −6.11001 6.28051i −0.236050 0.242637i
$$671$$ 52.1606i 2.01364i
$$672$$ 8.13040 2.30242i 0.313637 0.0888178i
$$673$$ −24.3131 + 24.3131i −0.937203 + 0.937203i −0.998142 0.0609388i $$-0.980591\pi$$
0.0609388 + 0.998142i $$0.480591\pi$$
$$674$$ −16.0144 −0.616851
$$675$$ 18.6440 + 18.0942i 0.717610 + 0.696445i
$$676$$ 11.4680 0.441076
$$677$$ −32.4421 + 32.4421i −1.24685 + 1.24685i −0.289749 + 0.957103i $$0.593572\pi$$
−0.957103 + 0.289749i $$0.906428\pi$$
$$678$$ 20.3572 5.76488i 0.781813 0.221399i
$$679$$ 23.2238i 0.891249i
$$680$$ 2.99244 + 3.07594i 0.114755 + 0.117957i
$$681$$ 5.84317 10.4600i 0.223911 0.400829i
$$682$$ −15.1750 15.1750i −0.581080 0.581080i
$$683$$ 30.8958 + 30.8958i 1.18219 + 1.18219i 0.979175 + 0.203020i $$0.0650755\pi$$
0.203020 + 0.979175i $$0.434924\pi$$
$$684$$ 9.74582 6.00102i 0.372641 0.229455i
$$685$$ 32.9676 + 0.453651i 1.25963 + 0.0173331i
$$686$$ 47.8185i 1.82572i
$$687$$ −2.07348 7.32194i −0.0791081 0.279350i
$$688$$ −0.142657 + 0.142657i −0.00543873 + 0.00543873i
$$689$$ 6.34559 0.241748
$$690$$ −3.35488 1.93514i −0.127718 0.0736696i
$$691$$ −4.89262 −0.186124 −0.0930620 0.995660i $$-0.529665\pi$$
−0.0930620 + 0.995660i $$0.529665\pi$$
$$692$$ −17.3398 + 17.3398i −0.659159 + 0.659159i
$$693$$ −13.0203 + 54.7500i −0.494599 + 2.07978i
$$694$$ 9.15626i 0.347567i
$$695$$ −23.4724 + 22.8352i −0.890359 + 0.866188i
$$696$$ −11.7710 6.57554i −0.446180 0.249245i
$$697$$ −5.83208 5.83208i −0.220906 0.220906i
$$698$$ 8.10294 + 8.10294i 0.306701 + 0.306701i
$$699$$ 19.1198 + 10.6807i 0.723177 + 0.403981i
$$700$$ −16.7676 17.7168i −0.633755 0.669633i
$$701$$ 12.6440i 0.477556i −0.971074 0.238778i $$-0.923253\pi$$
0.971074 0.238778i $$-0.0767468\pi$$
$$702$$ −4.73685 4.35054i −0.178781 0.164200i
$$703$$ −7.13245 + 7.13245i −0.269005 + 0.269005i
$$704$$ 3.84509 0.144917
$$705$$ −19.2126 + 5.15628i −0.723588 + 0.194197i
$$706$$ −20.6539 −0.777319
$$707$$ −38.9627 + 38.9627i −1.46534 + 1.46534i
$$708$$ −1.82787 6.45466i −0.0686957 0.242581i
$$709$$ 18.0882i 0.679317i −0.940549 0.339658i $$-0.889689\pi$$
0.940549 0.339658i $$-0.110311\pi$$
$$710$$ −0.189268 + 13.7544i −0.00710309 + 0.516194i
$$711$$ −27.0483 43.9271i −1.01439 1.64740i
$$712$$ −8.90860 8.90860i −0.333864 0.333864i
$$713$$ −3.94659 3.94659i −0.147801 0.147801i
$$714$$ 7.90892 14.1580i 0.295984 0.529849i
$$715$$ 0.146426 10.6411i 0.00547604 0.397953i
$$716$$ 1.47094i 0.0549715i
$$717$$ 11.7849 3.33731i 0.440113 0.124634i
$$718$$ −2.33713 + 2.33713i −0.0872207 + 0.0872207i
$$719$$ 18.9895 0.708188 0.354094 0.935210i $$-0.384789\pi$$
0.354094 + 0.935210i $$0.384789\pi$$
$$720$$ −6.50423 1.64166i −0.242398 0.0611811i
$$721$$ 57.7363 2.15021
$$722$$ 3.14322 3.14322i 0.116978 0.116978i
$$723$$ −7.04278 + 1.99442i −0.261924 + 0.0741733i
$$724$$ 15.6852i 0.582936i
$$725$$ −1.07098 + 38.9078i −0.0397753 + 1.44500i
$$726$$ −3.19696 + 5.72297i −0.118650 + 0.212399i
$$727$$ −2.21531 2.21531i −0.0821613 0.0821613i 0.664832 0.746993i $$-0.268503\pi$$
−0.746993 + 0.664832i $$0.768503\pi$$
$$728$$ 4.26994 + 4.26994i 0.158254 + 0.158254i
$$729$$ −2.29144 26.9026i −0.0848683 0.996392i
$$730$$ −21.7774 + 21.1862i −0.806019 + 0.784138i
$$731$$ 0.387187i 0.0143206i
$$732$$ 6.40203 + 22.6071i 0.236626 + 0.835583i
$$733$$ 23.0122 23.0122i 0.849976 0.849976i −0.140154 0.990130i $$-0.544760\pi$$
0.990130 + 0.140154i $$0.0447597\pi$$
$$734$$ −17.3823 −0.641591
$$735$$ −32.5133 + 56.3671i −1.19927 + 2.07913i
$$736$$ 1.00000 0.0368605
$$737$$ −10.6542 + 10.6542i −0.392454 + 0.392454i
$$738$$ 12.5430 + 2.98287i 0.461712 + 0.109801i
$$739$$ 10.0080i 0.368151i −0.982912 0.184076i $$-0.941071\pi$$
0.982912 0.184076i $$-0.0589291\pi$$
$$740$$ 5.91145 + 0.0813446i 0.217309 + 0.00299029i
$$741$$ 7.14039 + 3.98876i 0.262309 + 0.146531i
$$742$$ −17.6858 17.6858i −0.649267 0.649267i
$$743$$ 23.6306 + 23.6306i 0.866922 + 0.866922i 0.992130 0.125208i $$-0.0399599\pi$$
−0.125208 + 0.992130i $$0.539960\pi$$
$$744$$ −8.43958 4.71452i −0.309410 0.172843i
$$745$$ 1.90193 + 1.95500i 0.0696812 + 0.0716257i
$$746$$ 5.96729i 0.218478i
$$747$$ 8.27357 + 1.96756i 0.302714 + 0.0719893i
$$748$$ 5.21802 5.21802i 0.190790 0.190790i
$$749$$ 49.8102 1.82002
$$750$$ 4.50300 + 18.8341i 0.164426 + 0.687724i
$$751$$ 17.4785 0.637798 0.318899 0.947789i $$-0.396687\pi$$
0.318899 + 0.947789i $$0.396687\pi$$
$$752$$ 3.63185 3.63185i 0.132440 0.132440i
$$753$$ −0.150515 0.531504i −0.00548506 0.0193691i
$$754$$ 9.63529i 0.350897i
$$755$$ 10.7912 + 11.0923i 0.392732 + 0.403691i
$$756$$ 1.07669 + 25.3275i 0.0391589 + 0.921152i
$$757$$ 7.37005 + 7.37005i 0.267869 + 0.267869i 0.828241 0.560372i $$-0.189342\pi$$
−0.560372 + 0.828241i $$0.689342\pi$$
$$758$$ −17.5132 17.5132i −0.636107 0.636107i
$$759$$ −3.24794 + 5.81422i −0.117893 + 0.211043i
$$760$$ 8.52997 + 0.117377i 0.309414 + 0.00425770i
$$761$$ 49.0359i 1.77755i −0.458345 0.888774i $$-0.651558\pi$$
0.458345 0.888774i $$-0.348442\pi$$
$$762$$ −24.6067 + 6.96830i −0.891408 + 0.252435i
$$763$$ −7.45396 + 7.45396i −0.269851 + 0.269851i
$$764$$ −21.7200 −0.785800
$$765$$ −11.0545 + 6.59879i −0.399675 + 0.238580i
$$766$$ −17.3767 −0.627846
$$767$$ 3.38987 3.38987i 0.122401 0.122401i
$$768$$ 1.66652 0.471935i 0.0601352 0.0170295i
$$769$$ 24.0936i 0.868838i −0.900711 0.434419i $$-0.856954\pi$$
0.900711 0.434419i $$-0.143046\pi$$
$$770$$ −30.0659 + 29.2496i −1.08350 + 1.05408i
$$771$$ −11.8161 + 21.1522i −0.425545 + 0.761779i
$$772$$ −17.8302 17.8302i −0.641723 0.641723i
$$773$$ 12.6293 + 12.6293i 0.454243 + 0.454243i 0.896760 0.442517i $$-0.145914\pi$$
−0.442517 + 0.896760i $$0.645914\pi$$
$$774$$ −0.317343 0.515373i −0.0114066 0.0185247i
$$775$$ −0.767872 + 27.8960i −0.0275828 + 1.00205i
$$776$$ 4.76027i 0.170884i
$$777$$ −6.08744 21.4962i −0.218386 0.771172i
\(