# Properties

 Label 1764.2.e.j.1079.12 Level $1764$ Weight $2$ Character 1764.1079 Analytic conductor $14.086$ Analytic rank $0$ Dimension $16$ CM no Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1764 = 2^{2} \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1764.e (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$14.0856109166$$ Analytic rank: $$0$$ Dimension: $$16$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ Defining polynomial: $$x^{16} - 8 x^{14} + 49 x^{12} - 104 x^{10} + 160 x^{8} - 104 x^{6} + 49 x^{4} - 8 x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{14}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 1079.12 Root $$1.11871 + 0.645885i$$ of defining polynomial Character $$\chi$$ $$=$$ 1764.1079 Dual form 1764.2.e.j.1079.9

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.03295 + 0.965926i) q^{2} +(0.133975 + 1.99551i) q^{4} +2.73205i q^{5} +(-1.78912 + 2.19067i) q^{8} +O(q^{10})$$ $$q+(1.03295 + 0.965926i) q^{2} +(0.133975 + 1.99551i) q^{4} +2.73205i q^{5} +(-1.78912 + 2.19067i) q^{8} +(-2.63896 + 2.82207i) q^{10} -5.64415 q^{11} +1.41421 q^{13} +(-3.96410 + 0.534695i) q^{16} -6.19615i q^{17} +4.13180i q^{19} +(-5.45183 + 0.366025i) q^{20} +(-5.83013 - 5.45183i) q^{22} -5.64415 q^{23} -2.46410 q^{25} +(1.46081 + 1.36603i) q^{26} -0.378937i q^{29} +7.15649i q^{31} +(-4.61120 - 3.27671i) q^{32} +(5.98502 - 6.40032i) q^{34} -3.46410 q^{37} +(-3.99102 + 4.26795i) q^{38} +(-5.98502 - 4.88798i) q^{40} -5.26795i q^{41} +5.84325i q^{43} +(-0.756172 - 11.2629i) q^{44} +(-5.83013 - 5.45183i) q^{46} +2.13878 q^{47} +(-2.54530 - 2.38014i) q^{50} +(0.189469 + 2.82207i) q^{52} +0.656339i q^{53} -15.4201i q^{55} +(0.366025 - 0.391424i) q^{58} +13.8253 q^{59} +15.0759 q^{61} +(-6.91264 + 7.39230i) q^{62} +(-1.59808 - 7.83876i) q^{64} +3.86370i q^{65} -7.98203i q^{67} +(12.3645 - 0.830127i) q^{68} -13.9078 q^{71} -13.0053 q^{73} +(-3.57825 - 3.34607i) q^{74} +(-8.24504 + 0.553557i) q^{76} +13.8253i q^{79} +(-1.46081 - 10.8301i) q^{80} +(5.08845 - 5.44153i) q^{82} -10.1208 q^{83} +16.9282 q^{85} +(-5.64415 + 6.03579i) q^{86} +(10.0981 - 12.3645i) q^{88} +5.26795i q^{89} +(-0.756172 - 11.2629i) q^{92} +(2.20925 + 2.06590i) q^{94} -11.2883 q^{95} -9.41902 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q + 16 q^{4} + O(q^{10})$$ $$16 q + 16 q^{4} - 8 q^{16} - 24 q^{22} + 16 q^{25} - 24 q^{46} - 8 q^{58} + 16 q^{64} + 160 q^{85} + 120 q^{88} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$$.

 $$n$$ $$785$$ $$883$$ $$1081$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.03295 + 0.965926i 0.730406 + 0.683013i
$$3$$ 0 0
$$4$$ 0.133975 + 1.99551i 0.0669873 + 0.997754i
$$5$$ 2.73205i 1.22181i 0.791704 + 0.610905i $$0.209194\pi$$
−0.791704 + 0.610905i $$0.790806\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ −1.78912 + 2.19067i −0.632551 + 0.774519i
$$9$$ 0 0
$$10$$ −2.63896 + 2.82207i −0.834512 + 0.892418i
$$11$$ −5.64415 −1.70177 −0.850887 0.525348i $$-0.823935\pi$$
−0.850887 + 0.525348i $$0.823935\pi$$
$$12$$ 0 0
$$13$$ 1.41421 0.392232 0.196116 0.980581i $$-0.437167\pi$$
0.196116 + 0.980581i $$0.437167\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −3.96410 + 0.534695i −0.991025 + 0.133674i
$$17$$ 6.19615i 1.50279i −0.659854 0.751394i $$-0.729382\pi$$
0.659854 0.751394i $$-0.270618\pi$$
$$18$$ 0 0
$$19$$ 4.13180i 0.947901i 0.880552 + 0.473950i $$0.157172\pi$$
−0.880552 + 0.473950i $$0.842828\pi$$
$$20$$ −5.45183 + 0.366025i −1.21907 + 0.0818458i
$$21$$ 0 0
$$22$$ −5.83013 5.45183i −1.24299 1.16233i
$$23$$ −5.64415 −1.17689 −0.588443 0.808539i $$-0.700259\pi$$
−0.588443 + 0.808539i $$0.700259\pi$$
$$24$$ 0 0
$$25$$ −2.46410 −0.492820
$$26$$ 1.46081 + 1.36603i 0.286489 + 0.267900i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 0.378937i 0.0703669i −0.999381 0.0351835i $$-0.988798\pi$$
0.999381 0.0351835i $$-0.0112016\pi$$
$$30$$ 0 0
$$31$$ 7.15649i 1.28534i 0.766141 + 0.642672i $$0.222174\pi$$
−0.766141 + 0.642672i $$0.777826\pi$$
$$32$$ −4.61120 3.27671i −0.815152 0.579247i
$$33$$ 0 0
$$34$$ 5.98502 6.40032i 1.02642 1.09765i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −3.46410 −0.569495 −0.284747 0.958603i $$-0.591910\pi$$
−0.284747 + 0.958603i $$0.591910\pi$$
$$38$$ −3.99102 + 4.26795i −0.647428 + 0.692353i
$$39$$ 0 0
$$40$$ −5.98502 4.88798i −0.946315 0.772857i
$$41$$ 5.26795i 0.822715i −0.911474 0.411358i $$-0.865055\pi$$
0.911474 0.411358i $$-0.134945\pi$$
$$42$$ 0 0
$$43$$ 5.84325i 0.891088i 0.895260 + 0.445544i $$0.146990\pi$$
−0.895260 + 0.445544i $$0.853010\pi$$
$$44$$ −0.756172 11.2629i −0.113997 1.69795i
$$45$$ 0 0
$$46$$ −5.83013 5.45183i −0.859605 0.803828i
$$47$$ 2.13878 0.311973 0.155986 0.987759i $$-0.450144\pi$$
0.155986 + 0.987759i $$0.450144\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ −2.54530 2.38014i −0.359959 0.336603i
$$51$$ 0 0
$$52$$ 0.189469 + 2.82207i 0.0262746 + 0.391351i
$$53$$ 0.656339i 0.0901551i 0.998983 + 0.0450775i $$0.0143535\pi$$
−0.998983 + 0.0450775i $$0.985647\pi$$
$$54$$ 0 0
$$55$$ 15.4201i 2.07925i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0.366025 0.391424i 0.0480615 0.0513964i
$$59$$ 13.8253 1.79990 0.899949 0.435995i $$-0.143603\pi$$
0.899949 + 0.435995i $$0.143603\pi$$
$$60$$ 0 0
$$61$$ 15.0759 1.93027 0.965134 0.261756i $$-0.0843016\pi$$
0.965134 + 0.261756i $$0.0843016\pi$$
$$62$$ −6.91264 + 7.39230i −0.877906 + 0.938824i
$$63$$ 0 0
$$64$$ −1.59808 7.83876i −0.199760 0.979845i
$$65$$ 3.86370i 0.479233i
$$66$$ 0 0
$$67$$ 7.98203i 0.975160i −0.873078 0.487580i $$-0.837880\pi$$
0.873078 0.487580i $$-0.162120\pi$$
$$68$$ 12.3645 0.830127i 1.49941 0.100668i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −13.9078 −1.65055 −0.825273 0.564733i $$-0.808979\pi$$
−0.825273 + 0.564733i $$0.808979\pi$$
$$72$$ 0 0
$$73$$ −13.0053 −1.52216 −0.761079 0.648659i $$-0.775330\pi$$
−0.761079 + 0.648659i $$0.775330\pi$$
$$74$$ −3.57825 3.34607i −0.415963 0.388972i
$$75$$ 0 0
$$76$$ −8.24504 + 0.553557i −0.945771 + 0.0634973i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 13.8253i 1.55547i 0.628595 + 0.777733i $$0.283630\pi$$
−0.628595 + 0.777733i $$0.716370\pi$$
$$80$$ −1.46081 10.8301i −0.163324 1.21085i
$$81$$ 0 0
$$82$$ 5.08845 5.44153i 0.561925 0.600917i
$$83$$ −10.1208 −1.11090 −0.555452 0.831549i $$-0.687455\pi$$
−0.555452 + 0.831549i $$0.687455\pi$$
$$84$$ 0 0
$$85$$ 16.9282 1.83612
$$86$$ −5.64415 + 6.03579i −0.608624 + 0.650856i
$$87$$ 0 0
$$88$$ 10.0981 12.3645i 1.07646 1.31806i
$$89$$ 5.26795i 0.558401i 0.960233 + 0.279201i $$0.0900695\pi$$
−0.960233 + 0.279201i $$0.909931\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −0.756172 11.2629i −0.0788364 1.17424i
$$93$$ 0 0
$$94$$ 2.20925 + 2.06590i 0.227867 + 0.213081i
$$95$$ −11.2883 −1.15815
$$96$$ 0 0
$$97$$ −9.41902 −0.956357 −0.478178 0.878263i $$-0.658703\pi$$
−0.478178 + 0.878263i $$0.658703\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −0.330127 4.91713i −0.0330127 0.491713i
$$101$$ 8.73205i 0.868872i 0.900703 + 0.434436i $$0.143052\pi$$
−0.900703 + 0.434436i $$0.856948\pi$$
$$102$$ 0 0
$$103$$ 12.3954i 1.22136i 0.791879 + 0.610678i $$0.209103\pi$$
−0.791879 + 0.610678i $$0.790897\pi$$
$$104$$ −2.53020 + 3.09808i −0.248107 + 0.303791i
$$105$$ 0 0
$$106$$ −0.633975 + 0.677966i −0.0615771 + 0.0658498i
$$107$$ −2.61946 −0.253233 −0.126616 0.991952i $$-0.540412\pi$$
−0.126616 + 0.991952i $$0.540412\pi$$
$$108$$ 0 0
$$109$$ 6.00000 0.574696 0.287348 0.957826i $$-0.407226\pi$$
0.287348 + 0.957826i $$0.407226\pi$$
$$110$$ 14.8947 15.9282i 1.42015 1.51869i
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 9.14162i 0.859971i 0.902836 + 0.429986i $$0.141481\pi$$
−0.902836 + 0.429986i $$0.858519\pi$$
$$114$$ 0 0
$$115$$ 15.4201i 1.43793i
$$116$$ 0.756172 0.0507680i 0.0702088 0.00471369i
$$117$$ 0 0
$$118$$ 14.2808 + 13.3542i 1.31466 + 1.22935i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 20.8564 1.89604
$$122$$ 15.5726 + 14.5622i 1.40988 + 1.31840i
$$123$$ 0 0
$$124$$ −14.2808 + 0.958788i −1.28246 + 0.0861017i
$$125$$ 6.92820i 0.619677i
$$126$$ 0 0
$$127$$ 3.70447i 0.328719i 0.986401 + 0.164359i $$0.0525557\pi$$
−0.986401 + 0.164359i $$0.947444\pi$$
$$128$$ 5.92093 9.64068i 0.523341 0.852123i
$$129$$ 0 0
$$130$$ −3.73205 + 3.99102i −0.327323 + 0.350035i
$$131$$ −11.6865 −1.02105 −0.510527 0.859862i $$-0.670550\pi$$
−0.510527 + 0.859862i $$0.670550\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 7.71005 8.24504i 0.666047 0.712263i
$$135$$ 0 0
$$136$$ 13.5737 + 11.0857i 1.16394 + 0.950589i
$$137$$ 0.378937i 0.0323748i −0.999869 0.0161874i $$-0.994847\pi$$
0.999869 0.0161874i $$-0.00515284\pi$$
$$138$$ 0 0
$$139$$ 8.26361i 0.700910i −0.936580 0.350455i $$-0.886027\pi$$
0.936580 0.350455i $$-0.113973\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −14.3660 13.4339i −1.20557 1.12734i
$$143$$ −7.98203 −0.667491
$$144$$ 0 0
$$145$$ 1.03528 0.0859750
$$146$$ −13.4339 12.5622i −1.11179 1.03965i
$$147$$ 0 0
$$148$$ −0.464102 6.91264i −0.0381489 0.568216i
$$149$$ 4.24264i 0.347571i −0.984784 0.173785i $$-0.944400\pi$$
0.984784 0.173785i $$-0.0555999\pi$$
$$150$$ 0 0
$$151$$ 5.84325i 0.475517i 0.971324 + 0.237759i $$0.0764127\pi$$
−0.971324 + 0.237759i $$0.923587\pi$$
$$152$$ −9.05142 7.39230i −0.734167 0.599595i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −19.5519 −1.57045
$$156$$ 0 0
$$157$$ 9.41902 0.751720 0.375860 0.926677i $$-0.377347\pi$$
0.375860 + 0.926677i $$0.377347\pi$$
$$158$$ −13.3542 + 14.2808i −1.06240 + 1.13612i
$$159$$ 0 0
$$160$$ 8.95215 12.5980i 0.707730 0.995961i
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 12.2596i 0.960245i −0.877201 0.480123i $$-0.840592\pi$$
0.877201 0.480123i $$-0.159408\pi$$
$$164$$ 10.5122 0.705771i 0.820867 0.0551115i
$$165$$ 0 0
$$166$$ −10.4543 9.77595i −0.811411 0.758761i
$$167$$ −2.13878 −0.165504 −0.0827518 0.996570i $$-0.526371\pi$$
−0.0827518 + 0.996570i $$0.526371\pi$$
$$168$$ 0 0
$$169$$ −11.0000 −0.846154
$$170$$ 17.4860 + 16.3514i 1.34112 + 1.25409i
$$171$$ 0 0
$$172$$ −11.6603 + 0.782847i −0.889086 + 0.0596915i
$$173$$ 7.66025i 0.582398i 0.956662 + 0.291199i $$0.0940542\pi$$
−0.956662 + 0.291199i $$0.905946\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 22.3740 3.01790i 1.68650 0.227482i
$$177$$ 0 0
$$178$$ −5.08845 + 5.44153i −0.381395 + 0.407860i
$$179$$ 8.66884 0.647939 0.323970 0.946067i $$-0.394982\pi$$
0.323970 + 0.946067i $$0.394982\pi$$
$$180$$ 0 0
$$181$$ −14.7985 −1.09996 −0.549981 0.835177i $$-0.685365\pi$$
−0.549981 + 0.835177i $$0.685365\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 10.0981 12.3645i 0.744440 0.911521i
$$185$$ 9.46410i 0.695815i
$$186$$ 0 0
$$187$$ 34.9720i 2.55741i
$$188$$ 0.286542 + 4.26795i 0.0208982 + 0.311272i
$$189$$ 0 0
$$190$$ −11.6603 10.9037i −0.845924 0.791034i
$$191$$ −2.61946 −0.189537 −0.0947687 0.995499i $$-0.530211\pi$$
−0.0947687 + 0.995499i $$0.530211\pi$$
$$192$$ 0 0
$$193$$ 17.8564 1.28533 0.642666 0.766146i $$-0.277828\pi$$
0.642666 + 0.766146i $$0.277828\pi$$
$$194$$ −9.72939 9.09808i −0.698529 0.653204i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 23.8386i 1.69843i 0.528050 + 0.849213i $$0.322923\pi$$
−0.528050 + 0.849213i $$0.677077\pi$$
$$198$$ 0 0
$$199$$ 11.2883i 0.800206i −0.916470 0.400103i $$-0.868974\pi$$
0.916470 0.400103i $$-0.131026\pi$$
$$200$$ 4.40858 5.39804i 0.311734 0.381699i
$$201$$ 0 0
$$202$$ −8.43451 + 9.01978i −0.593450 + 0.634629i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 14.3923 1.00520
$$206$$ −11.9730 + 12.8038i −0.834202 + 0.892086i
$$207$$ 0 0
$$208$$ −5.60609 + 0.756172i −0.388712 + 0.0524311i
$$209$$ 23.3205i 1.61311i
$$210$$ 0 0
$$211$$ 4.27756i 0.294479i −0.989101 0.147240i $$-0.952961\pi$$
0.989101 0.147240i $$-0.0470388\pi$$
$$212$$ −1.30973 + 0.0879327i −0.0899526 + 0.00603924i
$$213$$ 0 0
$$214$$ −2.70577 2.53020i −0.184963 0.172961i
$$215$$ −15.9641 −1.08874
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 6.19770 + 5.79555i 0.419762 + 0.392525i
$$219$$ 0 0
$$220$$ 30.7709 2.06590i 2.07458 0.139283i
$$221$$ 8.76268i 0.589442i
$$222$$ 0 0
$$223$$ 3.02469i 0.202548i 0.994859 + 0.101274i $$0.0322919\pi$$
−0.994859 + 0.101274i $$0.967708\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −8.83013 + 9.44284i −0.587371 + 0.628129i
$$227$$ 2.13878 0.141956 0.0709779 0.997478i $$-0.477388\pi$$
0.0709779 + 0.997478i $$0.477388\pi$$
$$228$$ 0 0
$$229$$ 5.75839 0.380525 0.190263 0.981733i $$-0.439066\pi$$
0.190263 + 0.981733i $$0.439066\pi$$
$$230$$ 14.8947 15.9282i 0.982126 1.05027i
$$231$$ 0 0
$$232$$ 0.830127 + 0.677966i 0.0545005 + 0.0445106i
$$233$$ 28.4601i 1.86449i 0.361833 + 0.932243i $$0.382151\pi$$
−0.361833 + 0.932243i $$0.617849\pi$$
$$234$$ 0 0
$$235$$ 5.84325i 0.381172i
$$236$$ 1.85224 + 27.5885i 0.120570 + 1.79586i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 5.64415 0.365090 0.182545 0.983198i $$-0.441567\pi$$
0.182545 + 0.983198i $$0.441567\pi$$
$$240$$ 0 0
$$241$$ −1.69161 −0.108966 −0.0544832 0.998515i $$-0.517351\pi$$
−0.0544832 + 0.998515i $$0.517351\pi$$
$$242$$ 21.5436 + 20.1457i 1.38488 + 1.29502i
$$243$$ 0 0
$$244$$ 2.01978 + 30.0840i 0.129303 + 1.92593i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 5.84325i 0.371797i
$$248$$ −15.6775 12.8038i −0.995523 0.813045i
$$249$$ 0 0
$$250$$ −6.69213 + 7.15649i −0.423247 + 0.452616i
$$251$$ 23.9461 1.51146 0.755732 0.654881i $$-0.227281\pi$$
0.755732 + 0.654881i $$0.227281\pi$$
$$252$$ 0 0
$$253$$ 31.8564 2.00280
$$254$$ −3.57825 + 3.82654i −0.224519 + 0.240098i
$$255$$ 0 0
$$256$$ 15.4282 4.23917i 0.964263 0.264948i
$$257$$ 23.1244i 1.44246i 0.692697 + 0.721229i $$0.256422\pi$$
−0.692697 + 0.721229i $$0.743578\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ −7.71005 + 0.517638i −0.478157 + 0.0321026i
$$261$$ 0 0
$$262$$ −12.0716 11.2883i −0.745785 0.697393i
$$263$$ 5.64415 0.348033 0.174017 0.984743i $$-0.444325\pi$$
0.174017 + 0.984743i $$0.444325\pi$$
$$264$$ 0 0
$$265$$ −1.79315 −0.110152
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 15.9282 1.06939i 0.972970 0.0653234i
$$269$$ 13.6603i 0.832880i 0.909163 + 0.416440i $$0.136722\pi$$
−0.909163 + 0.416440i $$0.863278\pi$$
$$270$$ 0 0
$$271$$ 18.4448i 1.12044i −0.828343 0.560221i $$-0.810716\pi$$
0.828343 0.560221i $$-0.189284\pi$$
$$272$$ 3.31305 + 24.5622i 0.200883 + 1.48930i
$$273$$ 0 0
$$274$$ 0.366025 0.391424i 0.0221124 0.0236468i
$$275$$ 13.9078 0.838669
$$276$$ 0 0
$$277$$ −20.9282 −1.25745 −0.628727 0.777626i $$-0.716424\pi$$
−0.628727 + 0.777626i $$0.716424\pi$$
$$278$$ 7.98203 8.53590i 0.478730 0.511949i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0.933740i 0.0557023i −0.999612 0.0278511i $$-0.991134\pi$$
0.999612 0.0278511i $$-0.00886644\pi$$
$$282$$ 0 0
$$283$$ 4.13180i 0.245610i −0.992431 0.122805i $$-0.960811\pi$$
0.992431 0.122805i $$-0.0391890\pi$$
$$284$$ −1.86329 27.7530i −0.110566 1.64684i
$$285$$ 0 0
$$286$$ −8.24504 7.71005i −0.487540 0.455905i
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −21.3923 −1.25837
$$290$$ 1.06939 + 1.00000i 0.0627967 + 0.0587220i
$$291$$ 0 0
$$292$$ −1.74238 25.9522i −0.101965 1.51874i
$$293$$ 6.87564i 0.401679i 0.979624 + 0.200840i $$0.0643670\pi$$
−0.979624 + 0.200840i $$0.935633\pi$$
$$294$$ 0 0
$$295$$ 37.7714i 2.19913i
$$296$$ 6.19770 7.58871i 0.360234 0.441085i
$$297$$ 0 0
$$298$$ 4.09808 4.38244i 0.237395 0.253868i
$$299$$ −7.98203 −0.461613
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −5.64415 + 6.03579i −0.324784 + 0.347321i
$$303$$ 0 0
$$304$$ −2.20925 16.3789i −0.126709 0.939394i
$$305$$ 41.1881i 2.35842i
$$306$$ 0 0
$$307$$ 7.15649i 0.408443i 0.978925 + 0.204221i $$0.0654662\pi$$
−0.978925 + 0.204221i $$0.934534\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ −20.1962 18.8857i −1.14706 1.07263i
$$311$$ 25.5118 1.44664 0.723320 0.690513i $$-0.242615\pi$$
0.723320 + 0.690513i $$0.242615\pi$$
$$312$$ 0 0
$$313$$ −0.859411 −0.0485768 −0.0242884 0.999705i $$-0.507732\pi$$
−0.0242884 + 0.999705i $$0.507732\pi$$
$$314$$ 9.72939 + 9.09808i 0.549061 + 0.513434i
$$315$$ 0 0
$$316$$ −27.5885 + 1.85224i −1.55197 + 0.104196i
$$317$$ 4.24264i 0.238290i −0.992877 0.119145i $$-0.961985\pi$$
0.992877 0.119145i $$-0.0380154\pi$$
$$318$$ 0 0
$$319$$ 2.13878i 0.119749i
$$320$$ 21.4159 4.36603i 1.19718 0.244068i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 25.6013 1.42449
$$324$$ 0 0
$$325$$ −3.48477 −0.193300
$$326$$ 11.8419 12.6636i 0.655860 0.701369i
$$327$$ 0 0
$$328$$ 11.5403 + 9.42501i 0.637209 + 0.520409i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 31.9281i 1.75493i 0.479642 + 0.877464i $$0.340766\pi$$
−0.479642 + 0.877464i $$0.659234\pi$$
$$332$$ −1.35593 20.1962i −0.0744164 1.10841i
$$333$$ 0 0
$$334$$ −2.20925 2.06590i −0.120885 0.113041i
$$335$$ 21.8073 1.19146
$$336$$ 0 0
$$337$$ −22.3923 −1.21979 −0.609893 0.792484i $$-0.708788\pi$$
−0.609893 + 0.792484i $$0.708788\pi$$
$$338$$ −11.3625 10.6252i −0.618036 0.577934i
$$339$$ 0 0
$$340$$ 2.26795 + 33.7804i 0.122997 + 1.83200i
$$341$$ 40.3923i 2.18737i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ −12.8006 10.4543i −0.690164 0.563658i
$$345$$ 0 0
$$346$$ −7.39924 + 7.91267i −0.397785 + 0.425388i
$$347$$ 22.1714 1.19022 0.595110 0.803644i $$-0.297108\pi$$
0.595110 + 0.803644i $$0.297108\pi$$
$$348$$ 0 0
$$349$$ 22.8033 1.22063 0.610316 0.792158i $$-0.291043\pi$$
0.610316 + 0.792158i $$0.291043\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 26.0263 + 18.4943i 1.38721 + 0.985748i
$$353$$ 17.8038i 0.947603i −0.880632 0.473802i $$-0.842881\pi$$
0.880632 0.473802i $$-0.157119\pi$$
$$354$$ 0 0
$$355$$ 37.9967i 2.01665i
$$356$$ −10.5122 + 0.705771i −0.557147 + 0.0374058i
$$357$$ 0 0
$$358$$ 8.95448 + 8.37345i 0.473259 + 0.442551i
$$359$$ −13.9078 −0.734023 −0.367012 0.930216i $$-0.619619\pi$$
−0.367012 + 0.930216i $$0.619619\pi$$
$$360$$ 0 0
$$361$$ 1.92820 0.101484
$$362$$ −15.2861 14.2942i −0.803419 0.751288i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 35.5312i 1.85979i
$$366$$ 0 0
$$367$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$368$$ 22.3740 3.01790i 1.16632 0.157319i
$$369$$ 0 0
$$370$$ 9.14162 9.77595i 0.475250 0.508227i
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 3.07180 0.159052 0.0795258 0.996833i $$-0.474659\pi$$
0.0795258 + 0.996833i $$0.474659\pi$$
$$374$$ −33.7804 + 36.1244i −1.74674 + 1.86795i
$$375$$ 0 0
$$376$$ −3.82654 + 4.68536i −0.197339 + 0.241629i
$$377$$ 0.535898i 0.0276002i
$$378$$ 0 0
$$379$$ 20.2416i 1.03974i 0.854245 + 0.519871i $$0.174020\pi$$
−0.854245 + 0.519871i $$0.825980\pi$$
$$380$$ −1.51234 22.5259i −0.0775817 1.15555i
$$381$$ 0 0
$$382$$ −2.70577 2.53020i −0.138439 0.129456i
$$383$$ 4.27756 0.218573 0.109286 0.994010i $$-0.465143\pi$$
0.109286 + 0.994010i $$0.465143\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 18.4448 + 17.2480i 0.938815 + 0.877898i
$$387$$ 0 0
$$388$$ −1.26191 18.7957i −0.0640638 0.954209i
$$389$$ 21.2875i 1.07932i −0.841883 0.539660i $$-0.818553\pi$$
0.841883 0.539660i $$-0.181447\pi$$
$$390$$ 0 0
$$391$$ 34.9720i 1.76861i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ −23.0263 + 24.6241i −1.16005 + 1.24054i
$$395$$ −37.7714 −1.90048
$$396$$ 0 0
$$397$$ 22.2485 1.11662 0.558310 0.829633i $$-0.311450\pi$$
0.558310 + 0.829633i $$0.311450\pi$$
$$398$$ 10.9037 11.6603i 0.546551 0.584476i
$$399$$ 0 0
$$400$$ 9.76795 1.31754i 0.488397 0.0658771i
$$401$$ 15.6307i 0.780559i −0.920696 0.390279i $$-0.872378\pi$$
0.920696 0.390279i $$-0.127622\pi$$
$$402$$ 0 0
$$403$$ 10.1208i 0.504153i
$$404$$ −17.4249 + 1.16987i −0.866920 + 0.0582034i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 19.5519 0.969152
$$408$$ 0 0
$$409$$ −4.52004 −0.223502 −0.111751 0.993736i $$-0.535646\pi$$
−0.111751 + 0.993736i $$0.535646\pi$$
$$410$$ 14.8665 + 13.9019i 0.734206 + 0.686566i
$$411$$ 0 0
$$412$$ −24.7351 + 1.66067i −1.21861 + 0.0818153i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 27.6506i 1.35731i
$$416$$ −6.52122 4.63397i −0.319729 0.227199i
$$417$$ 0 0
$$418$$ 22.5259 24.0889i 1.10178 1.17823i
$$419$$ 12.2596 0.598920 0.299460 0.954109i $$-0.403193\pi$$
0.299460 + 0.954109i $$0.403193\pi$$
$$420$$ 0 0
$$421$$ 25.7128 1.25317 0.626583 0.779355i $$-0.284453\pi$$
0.626583 + 0.779355i $$0.284453\pi$$
$$422$$ 4.13180 4.41851i 0.201133 0.215090i
$$423$$ 0 0
$$424$$ −1.43782 1.17427i −0.0698268 0.0570276i
$$425$$ 15.2679i 0.740604i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −0.350941 5.22715i −0.0169634 0.252664i
$$429$$ 0 0
$$430$$ −16.4901 15.4201i −0.795223 0.743623i
$$431$$ 11.6935 0.563257 0.281629 0.959523i $$-0.409125\pi$$
0.281629 + 0.959523i $$0.409125\pi$$
$$432$$ 0 0
$$433$$ −5.00052 −0.240309 −0.120155 0.992755i $$-0.538339\pi$$
−0.120155 + 0.992755i $$0.538339\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0.803848 + 11.9730i 0.0384973 + 0.573405i
$$437$$ 23.3205i 1.11557i
$$438$$ 0 0
$$439$$ 36.8896i 1.76064i 0.474377 + 0.880322i $$0.342673\pi$$
−0.474377 + 0.880322i $$0.657327\pi$$
$$440$$ 33.7804 + 27.5885i 1.61042 + 1.31523i
$$441$$ 0 0
$$442$$ 8.46410 9.05142i 0.402596 0.430532i
$$443$$ −28.2207 −1.34081 −0.670404 0.741996i $$-0.733879\pi$$
−0.670404 + 0.741996i $$0.733879\pi$$
$$444$$ 0 0
$$445$$ −14.3923 −0.682261
$$446$$ −2.92163 + 3.12436i −0.138343 + 0.147943i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 6.86800i 0.324121i −0.986781 0.162060i $$-0.948186\pi$$
0.986781 0.162060i $$-0.0518139\pi$$
$$450$$ 0 0
$$451$$ 29.7331i 1.40008i
$$452$$ −18.2422 + 1.22474i −0.858040 + 0.0576072i
$$453$$ 0 0
$$454$$ 2.20925 + 2.06590i 0.103685 + 0.0969576i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −9.07180 −0.424361 −0.212180 0.977231i $$-0.568056\pi$$
−0.212180 + 0.977231i $$0.568056\pi$$
$$458$$ 5.94813 + 5.56218i 0.277938 + 0.259904i
$$459$$ 0 0
$$460$$ 30.7709 2.06590i 1.43470 0.0963232i
$$461$$ 12.7321i 0.592991i 0.955034 + 0.296495i $$0.0958179\pi$$
−0.955034 + 0.296495i $$0.904182\pi$$
$$462$$ 0 0
$$463$$ 35.6326i 1.65599i −0.560738 0.827994i $$-0.689482\pi$$
0.560738 0.827994i $$-0.310518\pi$$
$$464$$ 0.202616 + 1.50215i 0.00940620 + 0.0697354i
$$465$$ 0 0
$$466$$ −27.4904 + 29.3979i −1.27347 + 1.36183i
$$467$$ 19.6685 0.910151 0.455076 0.890453i $$-0.349612\pi$$
0.455076 + 0.890453i $$0.349612\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ −5.64415 + 6.03579i −0.260345 + 0.278410i
$$471$$ 0 0
$$472$$ −24.7351 + 30.2866i −1.13853 + 1.39406i
$$473$$ 32.9802i 1.51643i
$$474$$ 0 0
$$475$$ 10.1812i 0.467145i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 5.83013 + 5.45183i 0.266664 + 0.249361i
$$479$$ −19.6685 −0.898678 −0.449339 0.893361i $$-0.648341\pi$$
−0.449339 + 0.893361i $$0.648341\pi$$
$$480$$ 0 0
$$481$$ −4.89898 −0.223374
$$482$$ −1.74735 1.63397i −0.0795898 0.0744255i
$$483$$ 0 0
$$484$$ 2.79423 + 41.6191i 0.127010 + 1.89178i
$$485$$ 25.7332i 1.16849i
$$486$$ 0 0
$$487$$ 10.1208i 0.458618i 0.973354 + 0.229309i $$0.0736466\pi$$
−0.973354 + 0.229309i $$0.926353\pi$$
$$488$$ −26.9726 + 33.0263i −1.22099 + 1.49503i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 2.61946 0.118214 0.0591072 0.998252i $$-0.481175\pi$$
0.0591072 + 0.998252i $$0.481175\pi$$
$$492$$ 0 0
$$493$$ −2.34795 −0.105747
$$494$$ −5.64415 + 6.03579i −0.253942 + 0.271563i
$$495$$ 0 0
$$496$$ −3.82654 28.3691i −0.171817 1.27381i
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 1.56569i 0.0700901i −0.999386 0.0350451i $$-0.988843\pi$$
0.999386 0.0350451i $$-0.0111575\pi$$
$$500$$ −13.8253 + 0.928203i −0.618285 + 0.0415105i
$$501$$ 0 0
$$502$$ 24.7351 + 23.1301i 1.10398 + 1.03235i
$$503$$ 26.0849 1.16307 0.581533 0.813522i $$-0.302453\pi$$
0.581533 + 0.813522i $$0.302453\pi$$
$$504$$ 0 0
$$505$$ −23.8564 −1.06160
$$506$$ 32.9061 + 30.7709i 1.46285 + 1.36793i
$$507$$ 0 0
$$508$$ −7.39230 + 0.496305i −0.327980 + 0.0220200i
$$509$$ 10.3397i 0.458301i −0.973391 0.229151i $$-0.926405\pi$$
0.973391 0.229151i $$-0.0735948\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 20.0313 + 10.5236i 0.885267 + 0.465084i
$$513$$ 0 0
$$514$$ −22.3364 + 23.8863i −0.985217 + 1.05358i
$$515$$ −33.8649 −1.49227
$$516$$ 0 0
$$517$$ −12.0716 −0.530908
$$518$$ 0 0
$$519$$ 0 0
$$520$$ −8.46410 6.91264i −0.371175 0.303139i
$$521$$ 7.66025i 0.335602i −0.985821 0.167801i $$-0.946333\pi$$
0.985821 0.167801i $$-0.0536666\pi$$
$$522$$ 0 0
$$523$$ 30.8402i 1.34855i −0.738481 0.674274i $$-0.764457\pi$$
0.738481 0.674274i $$-0.235543\pi$$
$$524$$ −1.56569 23.3205i −0.0683977 1.01876i
$$525$$ 0 0
$$526$$ 5.83013 + 5.45183i 0.254206 + 0.237711i
$$527$$ 44.3427 1.93160
$$528$$ 0 0
$$529$$ 8.85641 0.385061
$$530$$ −1.85224 1.73205i −0.0804560 0.0752355i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 7.45001i 0.322696i
$$534$$ 0 0
$$535$$ 7.15649i 0.309402i
$$536$$ 17.4860 + 14.2808i 0.755280 + 0.616838i
$$537$$ 0 0
$$538$$ −13.1948 + 14.1104i −0.568868 + 0.608341i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −11.8564 −0.509747 −0.254873 0.966974i $$-0.582034\pi$$
−0.254873 + 0.966974i $$0.582034\pi$$
$$542$$ 17.8163 19.0526i 0.765276 0.818377i
$$543$$ 0 0
$$544$$ −20.3030 + 28.5717i −0.870485 + 1.22500i
$$545$$ 16.3923i 0.702169i
$$546$$ 0 0
$$547$$ 9.54773i 0.408231i −0.978947 0.204116i $$-0.934568\pi$$
0.978947 0.204116i $$-0.0654319\pi$$
$$548$$ 0.756172 0.0507680i 0.0323021 0.00216870i
$$549$$ 0 0
$$550$$ 14.3660 + 13.4339i 0.612569 + 0.572822i
$$551$$ 1.56569 0.0667008
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −21.6178 20.2151i −0.918452 0.858857i
$$555$$ 0 0
$$556$$ 16.4901 1.10711i 0.699336 0.0469521i
$$557$$ 10.4543i 0.442963i 0.975165 + 0.221481i $$0.0710892\pi$$
−0.975165 + 0.221481i $$0.928911\pi$$
$$558$$ 0 0
$$559$$ 8.26361i 0.349513i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0.901924 0.964508i 0.0380454 0.0406853i
$$563$$ −22.3804 −0.943221 −0.471611 0.881807i $$-0.656327\pi$$
−0.471611 + 0.881807i $$0.656327\pi$$
$$564$$ 0 0
$$565$$ −24.9754 −1.05072
$$566$$ 3.99102 4.26795i 0.167755 0.179395i
$$567$$ 0 0
$$568$$ 24.8827 30.4673i 1.04405 1.27838i
$$569$$ 11.6926i 0.490181i 0.969500 + 0.245091i $$0.0788177\pi$$
−0.969500 + 0.245091i $$0.921182\pi$$
$$570$$ 0 0
$$571$$ 29.7893i 1.24665i 0.781965 + 0.623323i $$0.214218\pi$$
−0.781965 + 0.623323i $$0.785782\pi$$
$$572$$ −1.06939 15.9282i −0.0447134 0.665992i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 13.9078 0.579993
$$576$$ 0 0
$$577$$ 21.7680 0.906214 0.453107 0.891456i $$-0.350316\pi$$
0.453107 + 0.891456i $$0.350316\pi$$
$$578$$ −22.0972 20.6634i −0.919122 0.859483i
$$579$$ 0 0
$$580$$ 0.138701 + 2.06590i 0.00575923 + 0.0857819i
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 3.70447i 0.153424i
$$584$$ 23.2681 28.4904i 0.962842 1.17894i
$$585$$ 0 0
$$586$$ −6.64136 + 7.10220i −0.274352 + 0.293389i
$$587$$ −18.1028 −0.747184 −0.373592 0.927593i $$-0.621874\pi$$
−0.373592 + 0.927593i $$0.621874\pi$$
$$588$$ 0 0
$$589$$ −29.5692 −1.21838
$$590$$ −36.4843 + 39.0160i −1.50204 + 1.60626i
$$591$$ 0 0
$$592$$ 13.7321 1.85224i 0.564384 0.0761265i
$$593$$ 17.8038i 0.731116i 0.930788 + 0.365558i $$0.119122\pi$$
−0.930788 + 0.365558i $$0.880878\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 8.46622 0.568406i 0.346790 0.0232828i
$$597$$ 0 0
$$598$$ −8.24504 7.71005i −0.337165 0.315287i
$$599$$ 30.4350 1.24354 0.621770 0.783200i $$-0.286414\pi$$
0.621770 + 0.783200i $$0.286414\pi$$
$$600$$ 0 0
$$601$$ 40.2543 1.64201 0.821004 0.570923i $$-0.193414\pi$$
0.821004 + 0.570923i $$0.193414\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −11.6603 + 0.782847i −0.474449 + 0.0318536i
$$605$$ 56.9808i 2.31660i
$$606$$ 0 0
$$607$$ 39.1038i 1.58717i −0.608456 0.793587i $$-0.708211\pi$$
0.608456 0.793587i $$-0.291789\pi$$
$$608$$ 13.5387 19.0526i 0.549068 0.772683i
$$609$$ 0 0
$$610$$ −39.7846 + 42.5452i −1.61083 + 1.72261i
$$611$$ 3.02469 0.122366
$$612$$ 0 0
$$613$$ −4.39230 −0.177404 −0.0887018 0.996058i $$-0.528272\pi$$
−0.0887018 + 0.996058i $$0.528272\pi$$
$$614$$ −6.91264 + 7.39230i −0.278971 + 0.298329i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 34.8749i 1.40401i 0.712172 + 0.702005i $$0.247711\pi$$
−0.712172 + 0.702005i $$0.752289\pi$$
$$618$$ 0 0
$$619$$ 5.23892i 0.210570i 0.994442 + 0.105285i $$0.0335755\pi$$
−0.994442 + 0.105285i $$0.966425\pi$$
$$620$$ −2.61946 39.0160i −0.105200 1.56692i
$$621$$ 0 0
$$622$$ 26.3524 + 24.6425i 1.05664 + 0.988074i
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −31.2487 −1.24995
$$626$$ −0.887729 0.830127i −0.0354808 0.0331785i
$$627$$ 0 0
$$628$$ 1.26191 + 18.7957i 0.0503557 + 0.750031i
$$629$$ 21.4641i 0.855830i
$$630$$ 0 0
$$631$$ 35.6326i 1.41851i −0.704951 0.709256i $$-0.749031\pi$$
0.704951 0.709256i $$-0.250969\pi$$
$$632$$ −30.2866 24.7351i −1.20474 0.983911i
$$633$$ 0 0
$$634$$ 4.09808 4.38244i 0.162755 0.174049i
$$635$$ −10.1208 −0.401632
$$636$$ 0 0
$$637$$ 0 0
$$638$$ −2.06590 + 2.20925i −0.0817898 + 0.0874652i
$$639$$ 0 0
$$640$$ 26.3388 + 16.1763i 1.04113 + 0.639423i
$$641$$ 18.6622i 0.737112i 0.929606 + 0.368556i $$0.120148\pi$$
−0.929606 + 0.368556i $$0.879852\pi$$
$$642$$ 0 0
$$643$$ 26.7084i 1.05328i 0.850090 + 0.526638i $$0.176548\pi$$
−0.850090 + 0.526638i $$0.823452\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 26.4449 + 24.7289i 1.04046 + 0.972947i
$$647$$ −5.27017 −0.207192 −0.103596 0.994619i $$-0.533035\pi$$
−0.103596 + 0.994619i $$0.533035\pi$$
$$648$$ 0 0
$$649$$ −78.0319 −3.06302
$$650$$ −3.59959 3.36603i −0.141188 0.132026i
$$651$$ 0 0
$$652$$ 24.4641 1.64247i 0.958088 0.0643242i
$$653$$ 34.3201i 1.34305i −0.740983 0.671524i $$-0.765640\pi$$
0.740983 0.671524i $$-0.234360\pi$$
$$654$$ 0 0
$$655$$ 31.9281i 1.24753i
$$656$$ 2.81674 + 20.8827i 0.109975 + 0.815332i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −14.7182 −0.573340 −0.286670 0.958029i $$-0.592548\pi$$
−0.286670 + 0.958029i $$0.592548\pi$$
$$660$$ 0 0
$$661$$ −25.8348 −1.00486 −0.502428 0.864619i $$-0.667560\pi$$
−0.502428 + 0.864619i $$0.667560\pi$$
$$662$$ −30.8402 + 32.9802i −1.19864 + 1.28181i
$$663$$ 0 0
$$664$$ 18.1074 22.1714i 0.702702 0.860416i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 2.13878i 0.0828138i
$$668$$ −0.286542 4.26795i −0.0110866 0.165132i
$$669$$ 0 0
$$670$$ 22.5259 + 21.0642i 0.870251 + 0.813783i
$$671$$ −85.0905 −3.28488
$$672$$ 0 0
$$673$$ −42.0000 −1.61898 −0.809491 0.587133i $$-0.800257\pi$$
−0.809491 + 0.587133i $$0.800257\pi$$
$$674$$ −23.1301 21.6293i −0.890940 0.833130i
$$675$$ 0 0
$$676$$ −1.47372 21.9506i −0.0566816 0.844253i
$$677$$ 49.1244i 1.88800i −0.329942 0.944001i $$-0.607029\pi$$
0.329942 0.944001i $$-0.392971\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ −30.2866 + 37.0841i −1.16144 + 1.42211i
$$681$$ 0 0
$$682$$ 39.0160 41.7233i 1.49400 1.59767i
$$683$$ −10.8831 −0.416429 −0.208214 0.978083i $$-0.566765\pi$$
−0.208214 + 0.978083i $$0.566765\pi$$
$$684$$ 0 0
$$685$$ 1.03528 0.0395559
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −3.12436 23.1632i −0.119115 0.883090i
$$689$$ 0.928203i 0.0353617i
$$690$$ 0 0
$$691$$ 13.5025i 0.513660i −0.966457 0.256830i $$-0.917322\pi$$
0.966457 0.256830i $$-0.0826781\pi$$
$$692$$ −15.2861 + 1.02628i −0.581090 + 0.0390133i
$$693$$ 0 0
$$694$$ 22.9019 + 21.4159i 0.869345 + 0.812936i
$$695$$ 22.5766 0.856379
$$696$$ 0 0
$$697$$ −32.6410 −1.23637
$$698$$ 23.5547 + 22.0263i 0.891557 + 0.833707i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 13.9663i 0.527499i −0.964591 0.263749i $$-0.915041\pi$$
0.964591 0.263749i $$-0.0849592\pi$$
$$702$$ 0 0
$$703$$ 14.3130i 0.539824i
$$704$$ 9.01978 + 44.2431i 0.339946 + 1.66748i
$$705$$ 0 0
$$706$$ 17.1972 18.3905i 0.647225 0.692136i
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 12.9282 0.485529 0.242764 0.970085i $$-0.421946\pi$$
0.242764 + 0.970085i $$0.421946\pi$$
$$710$$ 36.7020 39.2487i 1.37740 1.47298i
$$711$$ 0 0
$$712$$ −11.5403 9.42501i −0.432493 0.353217i
$$713$$ 40.3923i 1.51270i
$$714$$ 0 0
$$715$$ 21.8073i 0.815547i
$$716$$ 1.16140 + 17.2987i 0.0434037 + 0.646484i
$$717$$ 0 0
$$718$$ −14.3660 13.4339i −0.536135 0.501347i
$$719$$ 19.0955 0.712140 0.356070 0.934459i $$-0.384116\pi$$
0.356070 + 0.934459i $$0.384116\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 1.99174 + 1.86250i 0.0741249 + 0.0693151i
$$723$$ 0 0
$$724$$ −1.98262 29.5305i −0.0736835 1.09749i
$$725$$ 0.933740i 0.0346782i
$$726$$ 0 0
$$727$$ 49.2850i 1.82788i −0.405850 0.913939i $$-0.633025\pi$$
0.405850 0.913939i $$-0.366975\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 34.3205 36.7020i 1.27026 1.35840i
$$731$$ 36.2057 1.33912
$$732$$ 0 0
$$733$$ 28.9406 1.06895 0.534473 0.845186i $$-0.320510\pi$$
0.534473 + 0.845186i $$0.320510\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 26.0263 + 18.4943i 0.959341 + 0.681708i
$$737$$ 45.0518i 1.65950i
$$738$$ 0 0
$$739$$ 19.6685i 0.723519i −0.932272 0.361759i $$-0.882176\pi$$
0.932272 0.361759i $$-0.117824\pi$$
$$740$$ 18.8857 1.26795i 0.694252 0.0466107i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −31.2454 −1.14628 −0.573142 0.819456i $$-0.694276\pi$$
−0.573142 + 0.819456i $$0.694276\pi$$
$$744$$ 0 0
$$745$$ 11.5911 0.424665
$$746$$ 3.17301 + 2.96713i 0.116172 + 0.108634i
$$747$$ 0 0
$$748$$ −69.7869 + 4.68536i −2.55166 + 0.171314i
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 36.2057i 1.32116i −0.750754 0.660582i $$-0.770310\pi$$
0.750754 0.660582i $$-0.229690\pi$$
$$752$$ −8.47834 + 1.14359i −0.309173 + 0.0417026i
$$753$$ 0 0
$$754$$ 0.517638 0.553557i 0.0188513 0.0201593i
$$755$$ −15.9641 −0.580992
$$756$$ 0 0
$$757$$ −28.6410 −1.04098 −0.520488 0.853869i $$-0.674250\pi$$
−0.520488 + 0.853869i $$0.674250\pi$$
$$758$$ −19.5519 + 20.9086i −0.710157 + 0.759434i
$$759$$ 0 0
$$760$$ 20.1962 24.7289i 0.732591 0.897013i
$$761$$ 12.8756i 0.466742i 0.972388 + 0.233371i $$0.0749756\pi$$
−0.972388 + 0.233371i $$0.925024\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −0.350941 5.22715i −0.0126966 0.189112i
$$765$$ 0 0
$$766$$ 4.41851 + 4.13180i 0.159647 + 0.149288i
$$767$$ 19.5519 0.705978
$$768$$ 0 0
$$769$$ 16.8690 0.608313 0.304156 0.952622i $$-0.401625\pi$$
0.304156 + 0.952622i $$0.401625\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 2.39230 + 35.6326i 0.0861009 + 1.28245i
$$773$$ 33.5167i 1.20551i 0.797926 + 0.602755i $$0.205930\pi$$
−0.797926 + 0.602755i $$0.794070\pi$$
$$774$$ 0 0
$$775$$ 17.6343i 0.633444i
$$776$$ 16.8518 20.6340i 0.604944 0.740717i
$$777$$ 0 0
$$778$$ 20.5622 21.9890i 0.737190 0.788343i
$$779$$ 21.7661 0.779852
$$780$$ 0 0
$$781$$ 78.4974 2.80886
$$782$$ −33.7804 + 36.1244i −1.20798 + 1.29180i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 25.7332i 0.918459i
$$786$$ 0 0
$$787$$ 36.0791i 1.28608i 0.765832 + 0.643041i $$0.222327\pi$$
−0.765832 + 0.643041i $$0.777673\pi$$
$$788$$ −47.5700 + 3.19376i −1.69461 + 0.113773i
$$789$$ 0 0
$$790$$ −39.0160 36.4843i −1.38813 1.29805i
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 21.3205 0.757113
$$794$$ 22.9816 + 21.4904i 0.815586 + 0.762665i
$$795$$ 0 0
$$796$$ 22.5259 1.51234i 0.798409 0.0536036i
$$797$$