Properties

 Label 840.2.t.e.169.1 Level $840$ Weight $2$ Character 840.169 Analytic conductor $6.707$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$840 = 2^{3} \cdot 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 840.t (of order $$2$$, degree $$1$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$6.70743376979$$ Analytic rank: $$0$$ Dimension: $$6$$ Coefficient field: 6.0.350464.1 Defining polynomial: $$x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2$$ x^6 - 2*x^5 + 2*x^4 + 2*x^3 + 4*x^2 - 4*x + 2 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2^{3}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

 Embedding label 169.1 Root $$-0.854638 - 0.854638i$$ of defining polynomial Character $$\chi$$ $$=$$ 840.169 Dual form 840.2.t.e.169.4

$q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{3} +(-2.17009 + 0.539189i) q^{5} +1.00000i q^{7} -1.00000 q^{9} +O(q^{10})$$ $$q-1.00000i q^{3} +(-2.17009 + 0.539189i) q^{5} +1.00000i q^{7} -1.00000 q^{9} +5.41855 q^{11} -4.34017i q^{13} +(0.539189 + 2.17009i) q^{15} +1.07838i q^{17} -4.34017 q^{19} +1.00000 q^{21} -6.34017i q^{23} +(4.41855 - 2.34017i) q^{25} +1.00000i q^{27} +8.83710 q^{29} -4.34017 q^{31} -5.41855i q^{33} +(-0.539189 - 2.17009i) q^{35} -8.68035i q^{37} -4.34017 q^{39} +8.34017 q^{41} -6.15676i q^{43} +(2.17009 - 0.539189i) q^{45} -6.83710i q^{47} -1.00000 q^{49} +1.07838 q^{51} -6.18342i q^{53} +(-11.7587 + 2.92162i) q^{55} +4.34017i q^{57} +6.83710 q^{59} -4.52359 q^{61} -1.00000i q^{63} +(2.34017 + 9.41855i) q^{65} -6.34017 q^{69} -14.0989 q^{71} +11.1773i q^{73} +(-2.34017 - 4.41855i) q^{75} +5.41855i q^{77} -0.680346 q^{79} +1.00000 q^{81} +6.83710i q^{83} +(-0.581449 - 2.34017i) q^{85} -8.83710i q^{87} -6.49693 q^{89} +4.34017 q^{91} +4.34017i q^{93} +(9.41855 - 2.34017i) q^{95} -10.4969i q^{97} -5.41855 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q - 2 q^{5} - 6 q^{9}+O(q^{10})$$ 6 * q - 2 * q^5 - 6 * q^9 $$6 q - 2 q^{5} - 6 q^{9} + 4 q^{11} - 4 q^{19} + 6 q^{21} - 2 q^{25} - 4 q^{29} - 4 q^{31} - 4 q^{39} + 28 q^{41} + 2 q^{45} - 6 q^{49} - 20 q^{55} - 16 q^{59} + 4 q^{61} - 8 q^{65} - 16 q^{69} - 12 q^{71} + 8 q^{75} + 40 q^{79} + 6 q^{81} - 32 q^{85} - 4 q^{89} + 4 q^{91} + 28 q^{95} - 4 q^{99}+O(q^{100})$$ 6 * q - 2 * q^5 - 6 * q^9 + 4 * q^11 - 4 * q^19 + 6 * q^21 - 2 * q^25 - 4 * q^29 - 4 * q^31 - 4 * q^39 + 28 * q^41 + 2 * q^45 - 6 * q^49 - 20 * q^55 - 16 * q^59 + 4 * q^61 - 8 * q^65 - 16 * q^69 - 12 * q^71 + 8 * q^75 + 40 * q^79 + 6 * q^81 - 32 * q^85 - 4 * q^89 + 4 * q^91 + 28 * q^95 - 4 * q^99

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$$.

 $$n$$ $$241$$ $$281$$ $$337$$ $$421$$ $$631$$ $$\chi(n)$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 1.00000i 0.577350i
$$4$$ 0 0
$$5$$ −2.17009 + 0.539189i −0.970492 + 0.241133i
$$6$$ 0 0
$$7$$ 1.00000i 0.377964i
$$8$$ 0 0
$$9$$ −1.00000 −0.333333
$$10$$ 0 0
$$11$$ 5.41855 1.63375 0.816877 0.576812i $$-0.195703\pi$$
0.816877 + 0.576812i $$0.195703\pi$$
$$12$$ 0 0
$$13$$ 4.34017i 1.20375i −0.798591 0.601874i $$-0.794421\pi$$
0.798591 0.601874i $$-0.205579\pi$$
$$14$$ 0 0
$$15$$ 0.539189 + 2.17009i 0.139218 + 0.560314i
$$16$$ 0 0
$$17$$ 1.07838i 0.261545i 0.991412 + 0.130773i $$0.0417457\pi$$
−0.991412 + 0.130773i $$0.958254\pi$$
$$18$$ 0 0
$$19$$ −4.34017 −0.995704 −0.497852 0.867262i $$-0.665878\pi$$
−0.497852 + 0.867262i $$0.665878\pi$$
$$20$$ 0 0
$$21$$ 1.00000 0.218218
$$22$$ 0 0
$$23$$ 6.34017i 1.32202i −0.750378 0.661009i $$-0.770129\pi$$
0.750378 0.661009i $$-0.229871\pi$$
$$24$$ 0 0
$$25$$ 4.41855 2.34017i 0.883710 0.468035i
$$26$$ 0 0
$$27$$ 1.00000i 0.192450i
$$28$$ 0 0
$$29$$ 8.83710 1.64101 0.820504 0.571640i $$-0.193693\pi$$
0.820504 + 0.571640i $$0.193693\pi$$
$$30$$ 0 0
$$31$$ −4.34017 −0.779518 −0.389759 0.920917i $$-0.627442\pi$$
−0.389759 + 0.920917i $$0.627442\pi$$
$$32$$ 0 0
$$33$$ 5.41855i 0.943249i
$$34$$ 0 0
$$35$$ −0.539189 2.17009i −0.0911396 0.366812i
$$36$$ 0 0
$$37$$ 8.68035i 1.42704i −0.700635 0.713520i $$-0.747100\pi$$
0.700635 0.713520i $$-0.252900\pi$$
$$38$$ 0 0
$$39$$ −4.34017 −0.694984
$$40$$ 0 0
$$41$$ 8.34017 1.30252 0.651258 0.758856i $$-0.274242\pi$$
0.651258 + 0.758856i $$0.274242\pi$$
$$42$$ 0 0
$$43$$ 6.15676i 0.938896i −0.882960 0.469448i $$-0.844453\pi$$
0.882960 0.469448i $$-0.155547\pi$$
$$44$$ 0 0
$$45$$ 2.17009 0.539189i 0.323497 0.0803775i
$$46$$ 0 0
$$47$$ 6.83710i 0.997294i −0.866805 0.498647i $$-0.833830\pi$$
0.866805 0.498647i $$-0.166170\pi$$
$$48$$ 0 0
$$49$$ −1.00000 −0.142857
$$50$$ 0 0
$$51$$ 1.07838 0.151003
$$52$$ 0 0
$$53$$ 6.18342i 0.849358i −0.905344 0.424679i $$-0.860387\pi$$
0.905344 0.424679i $$-0.139613\pi$$
$$54$$ 0 0
$$55$$ −11.7587 + 2.92162i −1.58555 + 0.393951i
$$56$$ 0 0
$$57$$ 4.34017i 0.574870i
$$58$$ 0 0
$$59$$ 6.83710 0.890115 0.445057 0.895502i $$-0.353183\pi$$
0.445057 + 0.895502i $$0.353183\pi$$
$$60$$ 0 0
$$61$$ −4.52359 −0.579186 −0.289593 0.957150i $$-0.593520\pi$$
−0.289593 + 0.957150i $$0.593520\pi$$
$$62$$ 0 0
$$63$$ 1.00000i 0.125988i
$$64$$ 0 0
$$65$$ 2.34017 + 9.41855i 0.290263 + 1.16823i
$$66$$ 0 0
$$67$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$68$$ 0 0
$$69$$ −6.34017 −0.763267
$$70$$ 0 0
$$71$$ −14.0989 −1.67323 −0.836616 0.547790i $$-0.815469\pi$$
−0.836616 + 0.547790i $$0.815469\pi$$
$$72$$ 0 0
$$73$$ 11.1773i 1.30820i 0.756408 + 0.654101i $$0.226953\pi$$
−0.756408 + 0.654101i $$0.773047\pi$$
$$74$$ 0 0
$$75$$ −2.34017 4.41855i −0.270220 0.510210i
$$76$$ 0 0
$$77$$ 5.41855i 0.617501i
$$78$$ 0 0
$$79$$ −0.680346 −0.0765449 −0.0382724 0.999267i $$-0.512185\pi$$
−0.0382724 + 0.999267i $$0.512185\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 6.83710i 0.750469i 0.926930 + 0.375235i $$0.122438\pi$$
−0.926930 + 0.375235i $$0.877562\pi$$
$$84$$ 0 0
$$85$$ −0.581449 2.34017i −0.0630670 0.253827i
$$86$$ 0 0
$$87$$ 8.83710i 0.947437i
$$88$$ 0 0
$$89$$ −6.49693 −0.688673 −0.344337 0.938846i $$-0.611896\pi$$
−0.344337 + 0.938846i $$0.611896\pi$$
$$90$$ 0 0
$$91$$ 4.34017 0.454974
$$92$$ 0 0
$$93$$ 4.34017i 0.450055i
$$94$$ 0 0
$$95$$ 9.41855 2.34017i 0.966323 0.240097i
$$96$$ 0 0
$$97$$ 10.4969i 1.06580i −0.846178 0.532901i $$-0.821102\pi$$
0.846178 0.532901i $$-0.178898\pi$$
$$98$$ 0 0
$$99$$ −5.41855 −0.544585
$$100$$ 0 0
$$101$$ 18.8638 1.87701 0.938507 0.345259i $$-0.112209\pi$$
0.938507 + 0.345259i $$0.112209\pi$$
$$102$$ 0 0
$$103$$ 10.1568i 1.00077i −0.865802 0.500387i $$-0.833191\pi$$
0.865802 0.500387i $$-0.166809\pi$$
$$104$$ 0 0
$$105$$ −2.17009 + 0.539189i −0.211779 + 0.0526194i
$$106$$ 0 0
$$107$$ 14.6537i 1.41663i 0.705899 + 0.708313i $$0.250543\pi$$
−0.705899 + 0.708313i $$0.749457\pi$$
$$108$$ 0 0
$$109$$ 12.8371 1.22957 0.614786 0.788694i $$-0.289243\pi$$
0.614786 + 0.788694i $$0.289243\pi$$
$$110$$ 0 0
$$111$$ −8.68035 −0.823902
$$112$$ 0 0
$$113$$ 1.50307i 0.141397i −0.997498 0.0706985i $$-0.977477\pi$$
0.997498 0.0706985i $$-0.0225228\pi$$
$$114$$ 0 0
$$115$$ 3.41855 + 13.7587i 0.318781 + 1.28301i
$$116$$ 0 0
$$117$$ 4.34017i 0.401249i
$$118$$ 0 0
$$119$$ −1.07838 −0.0988547
$$120$$ 0 0
$$121$$ 18.3607 1.66915
$$122$$ 0 0
$$123$$ 8.34017i 0.752008i
$$124$$ 0 0
$$125$$ −8.32684 + 7.46081i −0.744775 + 0.667315i
$$126$$ 0 0
$$127$$ 19.2039i 1.70407i 0.523482 + 0.852037i $$0.324633\pi$$
−0.523482 + 0.852037i $$0.675367\pi$$
$$128$$ 0 0
$$129$$ −6.15676 −0.542072
$$130$$ 0 0
$$131$$ −4.00000 −0.349482 −0.174741 0.984614i $$-0.555909\pi$$
−0.174741 + 0.984614i $$0.555909\pi$$
$$132$$ 0 0
$$133$$ 4.34017i 0.376341i
$$134$$ 0 0
$$135$$ −0.539189 2.17009i −0.0464060 0.186771i
$$136$$ 0 0
$$137$$ 8.65368i 0.739334i 0.929164 + 0.369667i $$0.120528\pi$$
−0.929164 + 0.369667i $$0.879472\pi$$
$$138$$ 0 0
$$139$$ 6.18342 0.524471 0.262235 0.965004i $$-0.415540\pi$$
0.262235 + 0.965004i $$0.415540\pi$$
$$140$$ 0 0
$$141$$ −6.83710 −0.575788
$$142$$ 0 0
$$143$$ 23.5174i 1.96663i
$$144$$ 0 0
$$145$$ −19.1773 + 4.76487i −1.59259 + 0.395701i
$$146$$ 0 0
$$147$$ 1.00000i 0.0824786i
$$148$$ 0 0
$$149$$ 13.2039 1.08171 0.540854 0.841116i $$-0.318101\pi$$
0.540854 + 0.841116i $$0.318101\pi$$
$$150$$ 0 0
$$151$$ −18.1568 −1.47758 −0.738788 0.673938i $$-0.764601\pi$$
−0.738788 + 0.673938i $$0.764601\pi$$
$$152$$ 0 0
$$153$$ 1.07838i 0.0871817i
$$154$$ 0 0
$$155$$ 9.41855 2.34017i 0.756516 0.187967i
$$156$$ 0 0
$$157$$ 15.1773i 1.21128i 0.795739 + 0.605639i $$0.207083\pi$$
−0.795739 + 0.605639i $$0.792917\pi$$
$$158$$ 0 0
$$159$$ −6.18342 −0.490377
$$160$$ 0 0
$$161$$ 6.34017 0.499676
$$162$$ 0 0
$$163$$ 2.83710i 0.222219i 0.993808 + 0.111109i $$0.0354404\pi$$
−0.993808 + 0.111109i $$0.964560\pi$$
$$164$$ 0 0
$$165$$ 2.92162 + 11.7587i 0.227448 + 0.915415i
$$166$$ 0 0
$$167$$ 13.3607i 1.03388i 0.856021 + 0.516941i $$0.172929\pi$$
−0.856021 + 0.516941i $$0.827071\pi$$
$$168$$ 0 0
$$169$$ −5.83710 −0.449008
$$170$$ 0 0
$$171$$ 4.34017 0.331901
$$172$$ 0 0
$$173$$ 2.55479i 0.194237i −0.995273 0.0971184i $$-0.969037\pi$$
0.995273 0.0971184i $$-0.0309626\pi$$
$$174$$ 0 0
$$175$$ 2.34017 + 4.41855i 0.176900 + 0.334011i
$$176$$ 0 0
$$177$$ 6.83710i 0.513908i
$$178$$ 0 0
$$179$$ 11.9421 0.892598 0.446299 0.894884i $$-0.352742\pi$$
0.446299 + 0.894884i $$0.352742\pi$$
$$180$$ 0 0
$$181$$ 4.15676 0.308969 0.154485 0.987995i $$-0.450628\pi$$
0.154485 + 0.987995i $$0.450628\pi$$
$$182$$ 0 0
$$183$$ 4.52359i 0.334393i
$$184$$ 0 0
$$185$$ 4.68035 + 18.8371i 0.344106 + 1.38493i
$$186$$ 0 0
$$187$$ 5.84324i 0.427300i
$$188$$ 0 0
$$189$$ −1.00000 −0.0727393
$$190$$ 0 0
$$191$$ 6.09890 0.441301 0.220650 0.975353i $$-0.429182\pi$$
0.220650 + 0.975353i $$0.429182\pi$$
$$192$$ 0 0
$$193$$ 12.6803i 0.912751i −0.889787 0.456376i $$-0.849147\pi$$
0.889787 0.456376i $$-0.150853\pi$$
$$194$$ 0 0
$$195$$ 9.41855 2.34017i 0.674476 0.167583i
$$196$$ 0 0
$$197$$ 11.8576i 0.844820i −0.906405 0.422410i $$-0.861184\pi$$
0.906405 0.422410i $$-0.138816\pi$$
$$198$$ 0 0
$$199$$ 5.50307 0.390102 0.195051 0.980793i $$-0.437513\pi$$
0.195051 + 0.980793i $$0.437513\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 8.83710i 0.620243i
$$204$$ 0 0
$$205$$ −18.0989 + 4.49693i −1.26408 + 0.314079i
$$206$$ 0 0
$$207$$ 6.34017i 0.440672i
$$208$$ 0 0
$$209$$ −23.5174 −1.62674
$$210$$ 0 0
$$211$$ −19.1506 −1.31838 −0.659191 0.751975i $$-0.729101\pi$$
−0.659191 + 0.751975i $$0.729101\pi$$
$$212$$ 0 0
$$213$$ 14.0989i 0.966040i
$$214$$ 0 0
$$215$$ 3.31965 + 13.3607i 0.226399 + 0.911192i
$$216$$ 0 0
$$217$$ 4.34017i 0.294630i
$$218$$ 0 0
$$219$$ 11.1773 0.755290
$$220$$ 0 0
$$221$$ 4.68035 0.314834
$$222$$ 0 0
$$223$$ 12.3135i 0.824574i −0.911054 0.412287i $$-0.864730\pi$$
0.911054 0.412287i $$-0.135270\pi$$
$$224$$ 0 0
$$225$$ −4.41855 + 2.34017i −0.294570 + 0.156012i
$$226$$ 0 0
$$227$$ 15.2039i 1.00912i −0.863376 0.504560i $$-0.831655\pi$$
0.863376 0.504560i $$-0.168345\pi$$
$$228$$ 0 0
$$229$$ −5.20394 −0.343886 −0.171943 0.985107i $$-0.555004\pi$$
−0.171943 + 0.985107i $$0.555004\pi$$
$$230$$ 0 0
$$231$$ 5.41855 0.356514
$$232$$ 0 0
$$233$$ 11.6598i 0.763861i −0.924191 0.381930i $$-0.875259\pi$$
0.924191 0.381930i $$-0.124741\pi$$
$$234$$ 0 0
$$235$$ 3.68649 + 14.8371i 0.240480 + 0.967866i
$$236$$ 0 0
$$237$$ 0.680346i 0.0441932i
$$238$$ 0 0
$$239$$ −20.6225 −1.33396 −0.666979 0.745077i $$-0.732413\pi$$
−0.666979 + 0.745077i $$0.732413\pi$$
$$240$$ 0 0
$$241$$ −20.3545 −1.31115 −0.655576 0.755129i $$-0.727574\pi$$
−0.655576 + 0.755129i $$0.727574\pi$$
$$242$$ 0 0
$$243$$ 1.00000i 0.0641500i
$$244$$ 0 0
$$245$$ 2.17009 0.539189i 0.138642 0.0344475i
$$246$$ 0 0
$$247$$ 18.8371i 1.19858i
$$248$$ 0 0
$$249$$ 6.83710 0.433284
$$250$$ 0 0
$$251$$ 10.5236 0.664243 0.332122 0.943237i $$-0.392236\pi$$
0.332122 + 0.943237i $$0.392236\pi$$
$$252$$ 0 0
$$253$$ 34.3545i 2.15985i
$$254$$ 0 0
$$255$$ −2.34017 + 0.581449i −0.146547 + 0.0364118i
$$256$$ 0 0
$$257$$ 22.8059i 1.42259i 0.702892 + 0.711297i $$0.251892\pi$$
−0.702892 + 0.711297i $$0.748108\pi$$
$$258$$ 0 0
$$259$$ 8.68035 0.539370
$$260$$ 0 0
$$261$$ −8.83710 −0.547003
$$262$$ 0 0
$$263$$ 28.0144i 1.72744i 0.503972 + 0.863720i $$0.331872\pi$$
−0.503972 + 0.863720i $$0.668128\pi$$
$$264$$ 0 0
$$265$$ 3.33403 + 13.4186i 0.204808 + 0.824295i
$$266$$ 0 0
$$267$$ 6.49693i 0.397606i
$$268$$ 0 0
$$269$$ −18.4969 −1.12778 −0.563889 0.825851i $$-0.690695\pi$$
−0.563889 + 0.825851i $$0.690695\pi$$
$$270$$ 0 0
$$271$$ −29.0205 −1.76287 −0.881435 0.472304i $$-0.843422\pi$$
−0.881435 + 0.472304i $$0.843422\pi$$
$$272$$ 0 0
$$273$$ 4.34017i 0.262679i
$$274$$ 0 0
$$275$$ 23.9421 12.6803i 1.44377 0.764654i
$$276$$ 0 0
$$277$$ 8.68035i 0.521551i −0.965399 0.260776i $$-0.916022\pi$$
0.965399 0.260776i $$-0.0839783\pi$$
$$278$$ 0 0
$$279$$ 4.34017 0.259839
$$280$$ 0 0
$$281$$ 5.63317 0.336046 0.168023 0.985783i $$-0.446262\pi$$
0.168023 + 0.985783i $$0.446262\pi$$
$$282$$ 0 0
$$283$$ 2.47027i 0.146842i 0.997301 + 0.0734210i $$0.0233917\pi$$
−0.997301 + 0.0734210i $$0.976608\pi$$
$$284$$ 0 0
$$285$$ −2.34017 9.41855i −0.138620 0.557907i
$$286$$ 0 0
$$287$$ 8.34017i 0.492305i
$$288$$ 0 0
$$289$$ 15.8371 0.931594
$$290$$ 0 0
$$291$$ −10.4969 −0.615341
$$292$$ 0 0
$$293$$ 7.60197i 0.444112i 0.975034 + 0.222056i $$0.0712767\pi$$
−0.975034 + 0.222056i $$0.928723\pi$$
$$294$$ 0 0
$$295$$ −14.8371 + 3.68649i −0.863849 + 0.214636i
$$296$$ 0 0
$$297$$ 5.41855i 0.314416i
$$298$$ 0 0
$$299$$ −27.5174 −1.59138
$$300$$ 0 0
$$301$$ 6.15676 0.354869
$$302$$ 0 0
$$303$$ 18.8638i 1.08369i
$$304$$ 0 0
$$305$$ 9.81658 2.43907i 0.562096 0.139661i
$$306$$ 0 0
$$307$$ 6.15676i 0.351385i 0.984445 + 0.175692i $$0.0562164\pi$$
−0.984445 + 0.175692i $$0.943784\pi$$
$$308$$ 0 0
$$309$$ −10.1568 −0.577798
$$310$$ 0 0
$$311$$ −1.52973 −0.0867432 −0.0433716 0.999059i $$-0.513810\pi$$
−0.0433716 + 0.999059i $$0.513810\pi$$
$$312$$ 0 0
$$313$$ 11.9733i 0.676773i −0.941007 0.338387i $$-0.890119\pi$$
0.941007 0.338387i $$-0.109881\pi$$
$$314$$ 0 0
$$315$$ 0.539189 + 2.17009i 0.0303799 + 0.122271i
$$316$$ 0 0
$$317$$ 23.5441i 1.32237i 0.750223 + 0.661184i $$0.229946\pi$$
−0.750223 + 0.661184i $$0.770054\pi$$
$$318$$ 0 0
$$319$$ 47.8843 2.68101
$$320$$ 0 0
$$321$$ 14.6537 0.817889
$$322$$ 0 0
$$323$$ 4.68035i 0.260421i
$$324$$ 0 0
$$325$$ −10.1568 19.1773i −0.563395 1.06376i
$$326$$ 0 0
$$327$$ 12.8371i 0.709893i
$$328$$ 0 0
$$329$$ 6.83710 0.376942
$$330$$ 0 0
$$331$$ −9.16290 −0.503638 −0.251819 0.967774i $$-0.581029\pi$$
−0.251819 + 0.967774i $$0.581029\pi$$
$$332$$ 0 0
$$333$$ 8.68035i 0.475680i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 16.0000i 0.871576i 0.900049 + 0.435788i $$0.143530\pi$$
−0.900049 + 0.435788i $$0.856470\pi$$
$$338$$ 0 0
$$339$$ −1.50307 −0.0816356
$$340$$ 0 0
$$341$$ −23.5174 −1.27354
$$342$$ 0 0
$$343$$ 1.00000i 0.0539949i
$$344$$ 0 0
$$345$$ 13.7587 3.41855i 0.740745 0.184049i
$$346$$ 0 0
$$347$$ 23.0205i 1.23581i −0.786254 0.617903i $$-0.787982\pi$$
0.786254 0.617903i $$-0.212018\pi$$
$$348$$ 0 0
$$349$$ 3.78992 0.202870 0.101435 0.994842i $$-0.467657\pi$$
0.101435 + 0.994842i $$0.467657\pi$$
$$350$$ 0 0
$$351$$ 4.34017 0.231661
$$352$$ 0 0
$$353$$ 28.5958i 1.52200i −0.648751 0.761001i $$-0.724708\pi$$
0.648751 0.761001i $$-0.275292\pi$$
$$354$$ 0 0
$$355$$ 30.5958 7.60197i 1.62386 0.403471i
$$356$$ 0 0
$$357$$ 1.07838i 0.0570738i
$$358$$ 0 0
$$359$$ 11.2618 0.594375 0.297187 0.954819i $$-0.403951\pi$$
0.297187 + 0.954819i $$0.403951\pi$$
$$360$$ 0 0
$$361$$ −0.162899 −0.00857361
$$362$$ 0 0
$$363$$ 18.3607i 0.963686i
$$364$$ 0 0
$$365$$ −6.02666 24.2557i −0.315450 1.26960i
$$366$$ 0 0
$$367$$ 25.3607i 1.32382i −0.749584 0.661909i $$-0.769747\pi$$
0.749584 0.661909i $$-0.230253\pi$$
$$368$$ 0 0
$$369$$ −8.34017 −0.434172
$$370$$ 0 0
$$371$$ 6.18342 0.321027
$$372$$ 0 0
$$373$$ 21.3074i 1.10325i 0.834091 + 0.551627i $$0.185993\pi$$
−0.834091 + 0.551627i $$0.814007\pi$$
$$374$$ 0 0
$$375$$ 7.46081 + 8.32684i 0.385275 + 0.429996i
$$376$$ 0 0
$$377$$ 38.3545i 1.97536i
$$378$$ 0 0
$$379$$ 1.84324 0.0946811 0.0473406 0.998879i $$-0.484925\pi$$
0.0473406 + 0.998879i $$0.484925\pi$$
$$380$$ 0 0
$$381$$ 19.2039 0.983847
$$382$$ 0 0
$$383$$ 4.99386i 0.255174i −0.991827 0.127587i $$-0.959277\pi$$
0.991827 0.127587i $$-0.0407232\pi$$
$$384$$ 0 0
$$385$$ −2.92162 11.7587i −0.148900 0.599280i
$$386$$ 0 0
$$387$$ 6.15676i 0.312965i
$$388$$ 0 0
$$389$$ −16.8371 −0.853675 −0.426837 0.904328i $$-0.640372\pi$$
−0.426837 + 0.904328i $$0.640372\pi$$
$$390$$ 0 0
$$391$$ 6.83710 0.345767
$$392$$ 0 0
$$393$$ 4.00000i 0.201773i
$$394$$ 0 0
$$395$$ 1.47641 0.366835i 0.0742862 0.0184575i
$$396$$ 0 0
$$397$$ 36.8515i 1.84952i −0.380548 0.924761i $$-0.624264\pi$$
0.380548 0.924761i $$-0.375736\pi$$
$$398$$ 0 0
$$399$$ −4.34017 −0.217280
$$400$$ 0 0
$$401$$ −24.3545 −1.21621 −0.608104 0.793857i $$-0.708070\pi$$
−0.608104 + 0.793857i $$0.708070\pi$$
$$402$$ 0 0
$$403$$ 18.8371i 0.938343i
$$404$$ 0 0
$$405$$ −2.17009 + 0.539189i −0.107832 + 0.0267925i
$$406$$ 0 0
$$407$$ 47.0349i 2.33143i
$$408$$ 0 0
$$409$$ 28.0410 1.38654 0.693270 0.720678i $$-0.256169\pi$$
0.693270 + 0.720678i $$0.256169\pi$$
$$410$$ 0 0
$$411$$ 8.65368 0.426855
$$412$$ 0 0
$$413$$ 6.83710i 0.336432i
$$414$$ 0 0
$$415$$ −3.68649 14.8371i −0.180963 0.728325i
$$416$$ 0 0
$$417$$ 6.18342i 0.302803i
$$418$$ 0 0
$$419$$ −0.482553 −0.0235742 −0.0117871 0.999931i $$-0.503752\pi$$
−0.0117871 + 0.999931i $$0.503752\pi$$
$$420$$ 0 0
$$421$$ 21.1506 1.03082 0.515409 0.856944i $$-0.327640\pi$$
0.515409 + 0.856944i $$0.327640\pi$$
$$422$$ 0 0
$$423$$ 6.83710i 0.332431i
$$424$$ 0 0
$$425$$ 2.52359 + 4.76487i 0.122412 + 0.231130i
$$426$$ 0 0
$$427$$ 4.52359i 0.218912i
$$428$$ 0 0
$$429$$ −23.5174 −1.13543
$$430$$ 0 0
$$431$$ −28.7382 −1.38427 −0.692135 0.721768i $$-0.743330\pi$$
−0.692135 + 0.721768i $$0.743330\pi$$
$$432$$ 0 0
$$433$$ 9.02052i 0.433498i −0.976227 0.216749i $$-0.930455\pi$$
0.976227 0.216749i $$-0.0695454\pi$$
$$434$$ 0 0
$$435$$ 4.76487 + 19.1773i 0.228458 + 0.919480i
$$436$$ 0 0
$$437$$ 27.5174i 1.31634i
$$438$$ 0 0
$$439$$ 17.8166 0.850339 0.425170 0.905114i $$-0.360214\pi$$
0.425170 + 0.905114i $$0.360214\pi$$
$$440$$ 0 0
$$441$$ 1.00000 0.0476190
$$442$$ 0 0
$$443$$ 11.7009i 0.555925i −0.960592 0.277962i $$-0.910341\pi$$
0.960592 0.277962i $$-0.0896591\pi$$
$$444$$ 0 0
$$445$$ 14.0989 3.50307i 0.668352 0.166062i
$$446$$ 0 0
$$447$$ 13.2039i 0.624525i
$$448$$ 0 0
$$449$$ −10.7337 −0.506553 −0.253277 0.967394i $$-0.581508\pi$$
−0.253277 + 0.967394i $$0.581508\pi$$
$$450$$ 0 0
$$451$$ 45.1917 2.12799
$$452$$ 0 0
$$453$$ 18.1568i 0.853079i
$$454$$ 0 0
$$455$$ −9.41855 + 2.34017i −0.441548 + 0.109709i
$$456$$ 0 0
$$457$$ 20.9939i 0.982051i 0.871145 + 0.491026i $$0.163378\pi$$
−0.871145 + 0.491026i $$0.836622\pi$$
$$458$$ 0 0
$$459$$ −1.07838 −0.0503344
$$460$$ 0 0
$$461$$ −15.3751 −0.716088 −0.358044 0.933705i $$-0.616556\pi$$
−0.358044 + 0.933705i $$0.616556\pi$$
$$462$$ 0 0
$$463$$ 29.1917i 1.35665i 0.734762 + 0.678326i $$0.237294\pi$$
−0.734762 + 0.678326i $$0.762706\pi$$
$$464$$ 0 0
$$465$$ −2.34017 9.41855i −0.108523 0.436775i
$$466$$ 0 0
$$467$$ 15.2039i 0.703554i 0.936084 + 0.351777i $$0.114423\pi$$
−0.936084 + 0.351777i $$0.885577\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 15.1773 0.699332
$$472$$ 0 0
$$473$$ 33.3607i 1.53393i
$$474$$ 0 0
$$475$$ −19.1773 + 10.1568i −0.879914 + 0.466024i
$$476$$ 0 0
$$477$$ 6.18342i 0.283119i
$$478$$ 0 0
$$479$$ 18.7838 0.858253 0.429126 0.903244i $$-0.358822\pi$$
0.429126 + 0.903244i $$0.358822\pi$$
$$480$$ 0 0
$$481$$ −37.6742 −1.71780
$$482$$ 0 0
$$483$$ 6.34017i 0.288488i
$$484$$ 0 0
$$485$$ 5.65983 + 22.7792i 0.257000 + 1.03435i
$$486$$ 0 0
$$487$$ 16.5113i 0.748199i 0.927389 + 0.374099i $$0.122048\pi$$
−0.927389 + 0.374099i $$0.877952\pi$$
$$488$$ 0 0
$$489$$ 2.83710 0.128298
$$490$$ 0 0
$$491$$ 39.4063 1.77838 0.889190 0.457538i $$-0.151269\pi$$
0.889190 + 0.457538i $$0.151269\pi$$
$$492$$ 0 0
$$493$$ 9.52973i 0.429198i
$$494$$ 0 0
$$495$$ 11.7587 2.92162i 0.528515 0.131317i
$$496$$ 0 0
$$497$$ 14.0989i 0.632422i
$$498$$ 0 0
$$499$$ 31.5174 1.41091 0.705457 0.708752i $$-0.250742\pi$$
0.705457 + 0.708752i $$0.250742\pi$$
$$500$$ 0 0
$$501$$ 13.3607 0.596912
$$502$$ 0 0
$$503$$ 20.3668i 0.908112i 0.890973 + 0.454056i $$0.150023\pi$$
−0.890973 + 0.454056i $$0.849977\pi$$
$$504$$ 0 0
$$505$$ −40.9360 + 10.1711i −1.82163 + 0.452609i
$$506$$ 0 0
$$507$$ 5.83710i 0.259235i
$$508$$ 0 0
$$509$$ −11.1773 −0.495424 −0.247712 0.968834i $$-0.579679\pi$$
−0.247712 + 0.968834i $$0.579679\pi$$
$$510$$ 0 0
$$511$$ −11.1773 −0.494454
$$512$$ 0 0
$$513$$ 4.34017i 0.191623i
$$514$$ 0 0
$$515$$ 5.47641 + 22.0410i 0.241319 + 0.971244i
$$516$$ 0 0
$$517$$ 37.0472i 1.62933i
$$518$$ 0 0
$$519$$ −2.55479 −0.112143
$$520$$ 0 0
$$521$$ 32.6537 1.43058 0.715292 0.698826i $$-0.246294\pi$$
0.715292 + 0.698826i $$0.246294\pi$$
$$522$$ 0 0
$$523$$ 15.6865i 0.685922i −0.939350 0.342961i $$-0.888570\pi$$
0.939350 0.342961i $$-0.111430\pi$$
$$524$$ 0 0
$$525$$ 4.41855 2.34017i 0.192841 0.102134i
$$526$$ 0 0
$$527$$ 4.68035i 0.203879i
$$528$$ 0 0
$$529$$ −17.1978 −0.747730
$$530$$ 0 0
$$531$$ −6.83710 −0.296705
$$532$$ 0 0
$$533$$ 36.1978i 1.56790i
$$534$$ 0 0
$$535$$ −7.90110 31.7998i −0.341594 1.37482i
$$536$$ 0 0
$$537$$ 11.9421i 0.515341i
$$538$$ 0 0
$$539$$ −5.41855 −0.233394
$$540$$ 0 0
$$541$$ 30.1978 1.29830 0.649152 0.760658i $$-0.275124\pi$$
0.649152 + 0.760658i $$0.275124\pi$$
$$542$$ 0 0
$$543$$ 4.15676i 0.178383i
$$544$$ 0 0
$$545$$ −27.8576 + 6.92162i −1.19329 + 0.296490i
$$546$$ 0 0
$$547$$ 9.36069i 0.400234i 0.979772 + 0.200117i $$0.0641323\pi$$
−0.979772 + 0.200117i $$0.935868\pi$$
$$548$$ 0 0
$$549$$ 4.52359 0.193062
$$550$$ 0 0
$$551$$ −38.3545 −1.63396
$$552$$ 0 0
$$553$$ 0.680346i 0.0289313i
$$554$$ 0 0
$$555$$ 18.8371 4.68035i 0.799590 0.198670i
$$556$$ 0 0
$$557$$ 7.49079i 0.317395i −0.987327 0.158697i $$-0.949271\pi$$
0.987327 0.158697i $$-0.0507294\pi$$
$$558$$ 0 0
$$559$$ −26.7214 −1.13019
$$560$$ 0 0
$$561$$ 5.84324 0.246702
$$562$$ 0 0
$$563$$ 31.7152i 1.33664i −0.743875 0.668319i $$-0.767014\pi$$
0.743875 0.668319i $$-0.232986\pi$$
$$564$$ 0 0
$$565$$ 0.810439 + 3.26180i 0.0340954 + 0.137225i
$$566$$ 0 0
$$567$$ 1.00000i 0.0419961i
$$568$$ 0 0
$$569$$ −30.6803 −1.28619 −0.643094 0.765788i $$-0.722349\pi$$
−0.643094 + 0.765788i $$0.722349\pi$$
$$570$$ 0 0
$$571$$ −10.6393 −0.445241 −0.222621 0.974905i $$-0.571461\pi$$
−0.222621 + 0.974905i $$0.571461\pi$$
$$572$$ 0 0
$$573$$ 6.09890i 0.254785i
$$574$$ 0 0
$$575$$ −14.8371 28.0144i −0.618750 1.16828i
$$576$$ 0 0
$$577$$ 30.0677i 1.25173i 0.779930 + 0.625867i $$0.215255\pi$$
−0.779930 + 0.625867i $$0.784745\pi$$
$$578$$ 0 0
$$579$$ −12.6803 −0.526977
$$580$$ 0 0
$$581$$ −6.83710 −0.283651
$$582$$ 0 0
$$583$$ 33.5052i 1.38764i
$$584$$ 0 0
$$585$$ −2.34017 9.41855i −0.0967542 0.389409i
$$586$$ 0 0
$$587$$ 10.0410i 0.414438i 0.978295 + 0.207219i $$0.0664413\pi$$
−0.978295 + 0.207219i $$0.933559\pi$$
$$588$$ 0 0
$$589$$ 18.8371 0.776169
$$590$$ 0 0
$$591$$ −11.8576 −0.487757
$$592$$ 0 0
$$593$$ 24.2823i 0.997155i 0.866845 + 0.498578i $$0.166144\pi$$
−0.866845 + 0.498578i $$0.833856\pi$$
$$594$$ 0 0
$$595$$ 2.34017 0.581449i 0.0959377 0.0238371i
$$596$$ 0 0
$$597$$ 5.50307i 0.225226i
$$598$$ 0 0
$$599$$ 9.90110 0.404548 0.202274 0.979329i $$-0.435167\pi$$
0.202274 + 0.979329i $$0.435167\pi$$
$$600$$ 0 0
$$601$$ 17.6865 0.721447 0.360723 0.932673i $$-0.382530\pi$$
0.360723 + 0.932673i $$0.382530\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −39.8443 + 9.89988i −1.61990 + 0.402487i
$$606$$ 0 0
$$607$$ 28.3135i 1.14921i 0.818431 + 0.574605i $$0.194844\pi$$
−0.818431 + 0.574605i $$0.805156\pi$$
$$608$$ 0 0
$$609$$ 8.83710 0.358097
$$610$$ 0 0
$$611$$ −29.6742 −1.20049
$$612$$ 0 0
$$613$$ 23.6865i 0.956688i 0.878172 + 0.478344i $$0.158763\pi$$
−0.878172 + 0.478344i $$0.841237\pi$$
$$614$$ 0 0
$$615$$ 4.49693 + 18.0989i 0.181334 + 0.729818i
$$616$$ 0 0
$$617$$ 13.7009i 0.551576i −0.961218 0.275788i $$-0.911061\pi$$
0.961218 0.275788i $$-0.0889388\pi$$
$$618$$ 0 0
$$619$$ 2.49693 0.100360 0.0501800 0.998740i $$-0.484020\pi$$
0.0501800 + 0.998740i $$0.484020\pi$$
$$620$$ 0 0
$$621$$ 6.34017 0.254422
$$622$$ 0 0
$$623$$ 6.49693i 0.260294i
$$624$$ 0 0
$$625$$ 14.0472 20.6803i 0.561887 0.827214i
$$626$$ 0 0
$$627$$ 23.5174i 0.939196i
$$628$$ 0 0
$$629$$ 9.36069 0.373235
$$630$$ 0 0
$$631$$ 8.68035 0.345559 0.172780 0.984961i $$-0.444725\pi$$
0.172780 + 0.984961i $$0.444725\pi$$
$$632$$ 0 0
$$633$$ 19.1506i 0.761169i
$$634$$ 0 0
$$635$$ −10.3545 41.6742i −0.410908 1.65379i
$$636$$ 0 0
$$637$$ 4.34017i 0.171964i
$$638$$ 0 0
$$639$$ 14.0989 0.557744
$$640$$ 0 0
$$641$$ 3.30737 0.130633 0.0653166 0.997865i $$-0.479194\pi$$
0.0653166 + 0.997865i $$0.479194\pi$$
$$642$$ 0 0
$$643$$ 6.15676i 0.242799i 0.992604 + 0.121399i $$0.0387382\pi$$
−0.992604 + 0.121399i $$0.961262\pi$$
$$644$$ 0 0
$$645$$ 13.3607 3.31965i 0.526077 0.130711i
$$646$$ 0 0
$$647$$ 6.95282i 0.273344i −0.990616 0.136672i $$-0.956359\pi$$
0.990616 0.136672i $$-0.0436406\pi$$
$$648$$ 0 0
$$649$$ 37.0472 1.45423
$$650$$ 0 0
$$651$$ −4.34017 −0.170105
$$652$$ 0 0
$$653$$ 38.7480i 1.51633i 0.652064 + 0.758164i $$0.273903\pi$$
−0.652064 + 0.758164i $$0.726097\pi$$
$$654$$ 0 0
$$655$$ 8.68035 2.15676i 0.339169 0.0842714i
$$656$$ 0 0
$$657$$ 11.1773i 0.436067i
$$658$$ 0 0
$$659$$ −9.22076 −0.359190 −0.179595 0.983741i $$-0.557479\pi$$
−0.179595 + 0.983741i $$0.557479\pi$$
$$660$$ 0 0
$$661$$ 25.8843 1.00678 0.503391 0.864059i $$-0.332086\pi$$
0.503391 + 0.864059i $$0.332086\pi$$
$$662$$ 0 0
$$663$$ 4.68035i 0.181770i
$$664$$ 0 0
$$665$$ 2.34017 + 9.41855i 0.0907480 + 0.365236i
$$666$$ 0 0
$$667$$ 56.0288i 2.16944i
$$668$$ 0 0
$$669$$ −12.3135 −0.476068
$$670$$ 0 0
$$671$$ −24.5113 −0.946248
$$672$$ 0 0
$$673$$ 40.0821i 1.54505i 0.634984 + 0.772525i $$0.281007\pi$$
−0.634984 + 0.772525i $$0.718993\pi$$
$$674$$ 0 0
$$675$$ 2.34017 + 4.41855i 0.0900733 + 0.170070i
$$676$$ 0 0
$$677$$ 33.5897i 1.29096i 0.763779 + 0.645478i $$0.223342\pi$$
−0.763779 + 0.645478i $$0.776658\pi$$
$$678$$ 0 0
$$679$$ 10.4969 0.402835
$$680$$ 0 0
$$681$$ −15.2039 −0.582616
$$682$$ 0 0
$$683$$ 18.7070i 0.715804i 0.933759 + 0.357902i $$0.116508\pi$$
−0.933759 + 0.357902i $$0.883492\pi$$
$$684$$ 0 0
$$685$$ −4.66597 18.7792i −0.178278 0.717518i
$$686$$ 0 0
$$687$$ 5.20394i 0.198543i
$$688$$ 0 0
$$689$$ −26.8371 −1.02241
$$690$$ 0 0
$$691$$ −19.1773 −0.729538 −0.364769 0.931098i $$-0.618852\pi$$
−0.364769 + 0.931098i $$0.618852\pi$$
$$692$$ 0 0
$$693$$ 5.41855i 0.205834i
$$694$$ 0 0
$$695$$ −13.4186 + 3.33403i −0.508995 + 0.126467i
$$696$$ 0 0
$$697$$ 8.99386i 0.340667i
$$698$$ 0 0
$$699$$ −11.6598 −0.441015
$$700$$ 0 0
$$701$$ 21.4641 0.810689 0.405344 0.914164i $$-0.367152\pi$$
0.405344 + 0.914164i $$0.367152\pi$$
$$702$$ 0 0
$$703$$ 37.6742i 1.42091i
$$704$$ 0 0
$$705$$ 14.8371 3.68649i 0.558798 0.138841i
$$706$$ 0 0
$$707$$ 18.8638i 0.709445i
$$708$$ 0 0
$$709$$ −2.62702 −0.0986599 −0.0493299 0.998783i $$-0.515709\pi$$
−0.0493299 + 0.998783i $$0.515709\pi$$
$$710$$ 0 0
$$711$$ 0.680346 0.0255150
$$712$$ 0 0
$$713$$ 27.5174i 1.03054i
$$714$$ 0 0
$$715$$ 12.6803 + 51.0349i 0.474218 + 1.90860i
$$716$$ 0 0
$$717$$ 20.6225i 0.770161i
$$718$$ 0 0
$$719$$ 4.36683 0.162855 0.0814277 0.996679i $$-0.474052\pi$$
0.0814277 + 0.996679i $$0.474052\pi$$
$$720$$ 0 0
$$721$$ 10.1568 0.378257
$$722$$ 0 0
$$723$$ 20.3545i 0.756994i
$$724$$ 0 0
$$725$$ 39.0472 20.6803i 1.45018 0.768049i
$$726$$ 0 0
$$727$$ 28.1445i 1.04382i −0.853000 0.521910i $$-0.825220\pi$$
0.853000 0.521910i $$-0.174780\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ 6.63931 0.245564
$$732$$ 0 0
$$733$$ 26.7480i 0.987962i −0.869473 0.493981i $$-0.835541\pi$$
0.869473 0.493981i $$-0.164459\pi$$
$$734$$ 0 0
$$735$$ −0.539189 2.17009i −0.0198883 0.0800448i
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −19.0349 −0.700210 −0.350105 0.936710i $$-0.613854\pi$$
−0.350105 + 0.936710i $$0.613854\pi$$
$$740$$ 0 0
$$741$$ 18.8371 0.691998
$$742$$ 0 0
$$743$$ 33.6598i 1.23486i 0.786626 + 0.617430i $$0.211826\pi$$
−0.786626 + 0.617430i $$0.788174\pi$$
$$744$$ 0 0
$$745$$ −28.6537 + 7.11942i −1.04979 + 0.260835i
$$746$$ 0 0
$$747$$ 6.83710i 0.250156i
$$748$$ 0 0
$$749$$ −14.6537 −0.535434
$$750$$ 0 0
$$751$$ −49.8720 −1.81985 −0.909927 0.414767i $$-0.863863\pi$$
−0.909927 + 0.414767i $$0.863863\pi$$
$$752$$ 0 0
$$753$$ 10.5236i 0.383501i
$$754$$ 0 0
$$755$$ 39.4017 9.78992i 1.43398 0.356292i
$$756$$ 0 0
$$757$$ 7.63317i 0.277432i 0.990332 + 0.138716i $$0.0442975\pi$$
−0.990332 + 0.138716i $$0.955702\pi$$
$$758$$ 0 0
$$759$$ −34.3545 −1.24699
$$760$$ 0 0
$$761$$ 19.5974 0.710406 0.355203 0.934789i $$-0.384412\pi$$
0.355203 + 0.934789i $$0.384412\pi$$
$$762$$ 0 0
$$763$$ 12.8371i 0.464734i
$$764$$ 0 0
$$765$$ 0.581449 + 2.34017i 0.0210223 + 0.0846091i
$$766$$ 0 0
$$767$$ 29.6742i 1.07147i
$$768$$ 0 0
$$769$$ 32.4079 1.16866 0.584329 0.811517i $$-0.301358\pi$$
0.584329 + 0.811517i $$0.301358\pi$$
$$770$$ 0 0
$$771$$ 22.8059 0.821335
$$772$$ 0 0
$$773$$ 12.0845i 0.434650i −0.976099 0.217325i $$-0.930267\pi$$
0.976099 0.217325i $$-0.0697331\pi$$
$$774$$ 0 0
$$775$$ −19.1773 + 10.1568i −0.688868 + 0.364841i
$$776$$ 0 0
$$777$$ 8.68035i 0.311406i
$$778$$ 0 0
$$779$$ −36.1978 −1.29692
$$780$$ 0 0
$$781$$ −76.3956 −2.73365
$$782$$ 0 0
$$783$$ 8.83710i 0.315812i
$$784$$ 0 0
$$785$$ −8.18342 32.9360i −0.292079 1.17554i
$$786$$ 0 0
$$787$$ 25.0472i 0.892836i −0.894825 0.446418i $$-0.852700\pi$$
0.894825 0.446418i $$-0.147300\pi$$
$$788$$ 0 0
$$789$$ 28.0144 0.997338
$$790$$ 0 0
$$791$$ 1.50307 0.0534431
$$792$$ 0 0
$$793$$ 19.6332i 0.697194i
$$794$$ 0 0
$$795$$ 13.4186 3.33403i 0.475907 0.118246i
$$796$$ 0 0
$$797$$ 21.2762i 0.753641i 0.926286 + 0.376820i $$0.122983\pi$$
−0.926286 + 0.376820i $$0.877017\pi$$
$$798$$ 0 0
$$799$$ 7.37298 0.260837
$$800$$ 0 0
$$801$$ 6.49693 0.229558
$$802$$ 0