Properties

 Label 1840.2.e.f.369.10 Level $1840$ Weight $2$ Character 1840.369 Analytic conductor $14.692$ Analytic rank $0$ Dimension $12$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$1840 = 2^{4} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1840.e (of order $$2$$, degree $$1$$, not minimal)

Newform invariants

 Self dual: no Analytic conductor: $$14.6924739719$$ Analytic rank: $$0$$ Dimension: $$12$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ Defining polynomial: $$x^{12} + 24 x^{10} + 188 x^{8} + 530 x^{6} + 508 x^{4} + 80 x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{23}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 460) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

 Embedding label 369.10 Root $$1.26443i$$ of defining polynomial Character $$\chi$$ $$=$$ 1840.369 Dual form 1840.2.e.f.369.3

$q$-expansion

 $$f(q)$$ $$=$$ $$q+2.40050i q^{3} +(-0.817027 - 2.08146i) q^{5} +4.41307i q^{7} -2.76241 q^{9} +O(q^{10})$$ $$q+2.40050i q^{3} +(-0.817027 - 2.08146i) q^{5} +4.41307i q^{7} -2.76241 q^{9} -2.29289 q^{11} +6.92936i q^{13} +(4.99655 - 1.96128i) q^{15} -1.51387i q^{17} +2.89920 q^{19} -10.5936 q^{21} -1.00000i q^{23} +(-3.66493 + 3.40122i) q^{25} +0.570328i q^{27} +7.68764 q^{29} -3.85746 q^{31} -5.50408i q^{33} +(9.18562 - 3.60560i) q^{35} -8.62830i q^{37} -16.6340 q^{39} -6.44324 q^{41} +3.48497i q^{43} +(2.25697 + 5.74985i) q^{45} -6.19747i q^{47} -12.4752 q^{49} +3.63405 q^{51} +2.17710i q^{53} +(1.87335 + 4.77255i) q^{55} +6.95953i q^{57} -11.7637 q^{59} -5.11443 q^{61} -12.1907i q^{63} +(14.4232 - 5.66148i) q^{65} +9.94597i q^{67} +2.40050 q^{69} -3.41407 q^{71} -8.95307i q^{73} +(-8.16463 - 8.79768i) q^{75} -10.1187i q^{77} -1.92694 q^{79} -9.65631 q^{81} -8.04131i q^{83} +(-3.15106 + 1.23687i) q^{85} +18.4542i q^{87} +1.09273 q^{89} -30.5798 q^{91} -9.25985i q^{93} +(-2.36872 - 6.03456i) q^{95} +16.9208i q^{97} +6.33390 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q - 20 q^{9} + O(q^{10})$$ $$12 q - 20 q^{9} - 4 q^{11} - 2 q^{15} + 8 q^{19} + 8 q^{25} - 10 q^{29} - 18 q^{31} + 10 q^{35} - 16 q^{39} - 2 q^{41} + 2 q^{45} - 38 q^{49} + 24 q^{51} - 16 q^{55} - 22 q^{59} - 8 q^{61} + 38 q^{65} - 8 q^{69} + 34 q^{71} - 16 q^{75} + 20 q^{79} + 28 q^{81} + 6 q^{85} + 48 q^{89} + 8 q^{91} - 12 q^{95} - 32 q^{99} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times$$.

 $$n$$ $$737$$ $$1151$$ $$1201$$ $$1381$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$ $$1$$

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
$$3$$ 2.40050i 1.38593i 0.720971 + 0.692965i $$0.243696\pi$$
−0.720971 + 0.692965i $$0.756304\pi$$
$$4$$ 0 0
$$5$$ −0.817027 2.08146i −0.365386 0.930856i
$$6$$ 0 0
$$7$$ 4.41307i 1.66798i 0.551777 + 0.833992i $$0.313950\pi$$
−0.551777 + 0.833992i $$0.686050\pi$$
$$8$$ 0 0
$$9$$ −2.76241 −0.920804
$$10$$ 0 0
$$11$$ −2.29289 −0.691332 −0.345666 0.938358i $$-0.612347\pi$$
−0.345666 + 0.938358i $$0.612347\pi$$
$$12$$ 0 0
$$13$$ 6.92936i 1.92186i 0.276792 + 0.960930i $$0.410729\pi$$
−0.276792 + 0.960930i $$0.589271\pi$$
$$14$$ 0 0
$$15$$ 4.99655 1.96128i 1.29010 0.506399i
$$16$$ 0 0
$$17$$ 1.51387i 0.367168i −0.983004 0.183584i $$-0.941230\pi$$
0.983004 0.183584i $$-0.0587699\pi$$
$$18$$ 0 0
$$19$$ 2.89920 0.665121 0.332561 0.943082i $$-0.392087\pi$$
0.332561 + 0.943082i $$0.392087\pi$$
$$20$$ 0 0
$$21$$ −10.5936 −2.31171
$$22$$ 0 0
$$23$$ 1.00000i 0.208514i
$$24$$ 0 0
$$25$$ −3.66493 + 3.40122i −0.732987 + 0.680243i
$$26$$ 0 0
$$27$$ 0.570328i 0.109760i
$$28$$ 0 0
$$29$$ 7.68764 1.42756 0.713779 0.700371i $$-0.246982\pi$$
0.713779 + 0.700371i $$0.246982\pi$$
$$30$$ 0 0
$$31$$ −3.85746 −0.692821 −0.346410 0.938083i $$-0.612599\pi$$
−0.346410 + 0.938083i $$0.612599\pi$$
$$32$$ 0 0
$$33$$ 5.50408i 0.958138i
$$34$$ 0 0
$$35$$ 9.18562 3.60560i 1.55265 0.609457i
$$36$$ 0 0
$$37$$ 8.62830i 1.41848i −0.704965 0.709242i $$-0.749037\pi$$
0.704965 0.709242i $$-0.250963\pi$$
$$38$$ 0 0
$$39$$ −16.6340 −2.66356
$$40$$ 0 0
$$41$$ −6.44324 −1.00626 −0.503132 0.864209i $$-0.667819\pi$$
−0.503132 + 0.864209i $$0.667819\pi$$
$$42$$ 0 0
$$43$$ 3.48497i 0.531453i 0.964048 + 0.265727i $$0.0856119\pi$$
−0.964048 + 0.265727i $$0.914388\pi$$
$$44$$ 0 0
$$45$$ 2.25697 + 5.74985i 0.336449 + 0.857136i
$$46$$ 0 0
$$47$$ 6.19747i 0.903994i −0.892019 0.451997i $$-0.850712\pi$$
0.892019 0.451997i $$-0.149288\pi$$
$$48$$ 0 0
$$49$$ −12.4752 −1.78217
$$50$$ 0 0
$$51$$ 3.63405 0.508869
$$52$$ 0 0
$$53$$ 2.17710i 0.299047i 0.988758 + 0.149524i $$0.0477740\pi$$
−0.988758 + 0.149524i $$0.952226\pi$$
$$54$$ 0 0
$$55$$ 1.87335 + 4.77255i 0.252603 + 0.643530i
$$56$$ 0 0
$$57$$ 6.95953i 0.921812i
$$58$$ 0 0
$$59$$ −11.7637 −1.53150 −0.765750 0.643138i $$-0.777632\pi$$
−0.765750 + 0.643138i $$0.777632\pi$$
$$60$$ 0 0
$$61$$ −5.11443 −0.654835 −0.327418 0.944880i $$-0.606178\pi$$
−0.327418 + 0.944880i $$0.606178\pi$$
$$62$$ 0 0
$$63$$ 12.1907i 1.53589i
$$64$$ 0 0
$$65$$ 14.4232 5.66148i 1.78898 0.702220i
$$66$$ 0 0
$$67$$ 9.94597i 1.21509i 0.794284 + 0.607547i $$0.207846\pi$$
−0.794284 + 0.607547i $$0.792154\pi$$
$$68$$ 0 0
$$69$$ 2.40050 0.288987
$$70$$ 0 0
$$71$$ −3.41407 −0.405175 −0.202588 0.979264i $$-0.564935\pi$$
−0.202588 + 0.979264i $$0.564935\pi$$
$$72$$ 0 0
$$73$$ 8.95307i 1.04788i −0.851756 0.523939i $$-0.824462\pi$$
0.851756 0.523939i $$-0.175538\pi$$
$$74$$ 0 0
$$75$$ −8.16463 8.79768i −0.942770 1.01587i
$$76$$ 0 0
$$77$$ 10.1187i 1.15313i
$$78$$ 0 0
$$79$$ −1.92694 −0.216798 −0.108399 0.994107i $$-0.534572\pi$$
−0.108399 + 0.994107i $$0.534572\pi$$
$$80$$ 0 0
$$81$$ −9.65631 −1.07292
$$82$$ 0 0
$$83$$ 8.04131i 0.882648i −0.897348 0.441324i $$-0.854509\pi$$
0.897348 0.441324i $$-0.145491\pi$$
$$84$$ 0 0
$$85$$ −3.15106 + 1.23687i −0.341781 + 0.134158i
$$86$$ 0 0
$$87$$ 18.4542i 1.97850i
$$88$$ 0 0
$$89$$ 1.09273 0.115829 0.0579147 0.998322i $$-0.481555\pi$$
0.0579147 + 0.998322i $$0.481555\pi$$
$$90$$ 0 0
$$91$$ −30.5798 −3.20563
$$92$$ 0 0
$$93$$ 9.25985i 0.960201i
$$94$$ 0 0
$$95$$ −2.36872 6.03456i −0.243026 0.619132i
$$96$$ 0 0
$$97$$ 16.9208i 1.71805i 0.511933 + 0.859026i $$0.328930\pi$$
−0.511933 + 0.859026i $$0.671070\pi$$
$$98$$ 0 0
$$99$$ 6.33390 0.636581
$$100$$ 0 0
$$101$$ 12.9497 1.28855 0.644274 0.764795i $$-0.277160\pi$$
0.644274 + 0.764795i $$0.277160\pi$$
$$102$$ 0 0
$$103$$ 10.9754i 1.08144i −0.841202 0.540721i $$-0.818152\pi$$
0.841202 0.540721i $$-0.181848\pi$$
$$104$$ 0 0
$$105$$ 8.65525 + 22.0501i 0.844666 + 2.15187i
$$106$$ 0 0
$$107$$ 19.8821i 1.92208i 0.276411 + 0.961040i $$0.410855\pi$$
−0.276411 + 0.961040i $$0.589145\pi$$
$$108$$ 0 0
$$109$$ −0.427249 −0.0409231 −0.0204615 0.999791i $$-0.506514\pi$$
−0.0204615 + 0.999791i $$0.506514\pi$$
$$110$$ 0 0
$$111$$ 20.7123 1.96592
$$112$$ 0 0
$$113$$ 5.38533i 0.506609i −0.967387 0.253304i $$-0.918483\pi$$
0.967387 0.253304i $$-0.0815174\pi$$
$$114$$ 0 0
$$115$$ −2.08146 + 0.817027i −0.194097 + 0.0761882i
$$116$$ 0 0
$$117$$ 19.1418i 1.76966i
$$118$$ 0 0
$$119$$ 6.68082 0.612430
$$120$$ 0 0
$$121$$ −5.74267 −0.522061
$$122$$ 0 0
$$123$$ 15.4670i 1.39461i
$$124$$ 0 0
$$125$$ 10.0738 + 4.84952i 0.901031 + 0.433754i
$$126$$ 0 0
$$127$$ 6.16014i 0.546624i 0.961925 + 0.273312i $$0.0881191\pi$$
−0.961925 + 0.273312i $$0.911881\pi$$
$$128$$ 0 0
$$129$$ −8.36569 −0.736558
$$130$$ 0 0
$$131$$ −14.6325 −1.27845 −0.639225 0.769020i $$-0.720745\pi$$
−0.639225 + 0.769020i $$0.720745\pi$$
$$132$$ 0 0
$$133$$ 12.7944i 1.10941i
$$134$$ 0 0
$$135$$ 1.18711 0.465974i 0.102171 0.0401046i
$$136$$ 0 0
$$137$$ 0.972256i 0.0830654i −0.999137 0.0415327i $$-0.986776\pi$$
0.999137 0.0415327i $$-0.0132241\pi$$
$$138$$ 0 0
$$139$$ 7.74312 0.656763 0.328382 0.944545i $$-0.393497\pi$$
0.328382 + 0.944545i $$0.393497\pi$$
$$140$$ 0 0
$$141$$ 14.8770 1.25287
$$142$$ 0 0
$$143$$ 15.8883i 1.32864i
$$144$$ 0 0
$$145$$ −6.28101 16.0015i −0.521609 1.32885i
$$146$$ 0 0
$$147$$ 29.9467i 2.46996i
$$148$$ 0 0
$$149$$ 17.6823 1.44859 0.724293 0.689492i $$-0.242166\pi$$
0.724293 + 0.689492i $$0.242166\pi$$
$$150$$ 0 0
$$151$$ 2.01286 0.163804 0.0819022 0.996640i $$-0.473900\pi$$
0.0819022 + 0.996640i $$0.473900\pi$$
$$152$$ 0 0
$$153$$ 4.18194i 0.338090i
$$154$$ 0 0
$$155$$ 3.15165 + 8.02914i 0.253147 + 0.644916i
$$156$$ 0 0
$$157$$ 5.82703i 0.465048i 0.972591 + 0.232524i $$0.0746984\pi$$
−0.972591 + 0.232524i $$0.925302\pi$$
$$158$$ 0 0
$$159$$ −5.22612 −0.414459
$$160$$ 0 0
$$161$$ 4.41307 0.347799
$$162$$ 0 0
$$163$$ 6.75147i 0.528816i 0.964411 + 0.264408i $$0.0851765\pi$$
−0.964411 + 0.264408i $$0.914823\pi$$
$$164$$ 0 0
$$165$$ −11.4565 + 4.49698i −0.891889 + 0.350090i
$$166$$ 0 0
$$167$$ 23.4541i 1.81493i −0.420125 0.907466i $$-0.638014\pi$$
0.420125 0.907466i $$-0.361986\pi$$
$$168$$ 0 0
$$169$$ −35.0161 −2.69355
$$170$$ 0 0
$$171$$ −8.00878 −0.612447
$$172$$ 0 0
$$173$$ 8.28850i 0.630163i −0.949065 0.315081i $$-0.897968\pi$$
0.949065 0.315081i $$-0.102032\pi$$
$$174$$ 0 0
$$175$$ −15.0098 16.1736i −1.13463 1.22261i
$$176$$ 0 0
$$177$$ 28.2387i 2.12255i
$$178$$ 0 0
$$179$$ 1.04002 0.0777345 0.0388673 0.999244i $$-0.487625\pi$$
0.0388673 + 0.999244i $$0.487625\pi$$
$$180$$ 0 0
$$181$$ 2.71850 0.202065 0.101032 0.994883i $$-0.467785\pi$$
0.101032 + 0.994883i $$0.467785\pi$$
$$182$$ 0 0
$$183$$ 12.2772i 0.907557i
$$184$$ 0 0
$$185$$ −17.9594 + 7.04956i −1.32040 + 0.518294i
$$186$$ 0 0
$$187$$ 3.47114i 0.253835i
$$188$$ 0 0
$$189$$ −2.51690 −0.183077
$$190$$ 0 0
$$191$$ −8.04858 −0.582375 −0.291187 0.956666i $$-0.594050\pi$$
−0.291187 + 0.956666i $$0.594050\pi$$
$$192$$ 0 0
$$193$$ 16.0276i 1.15370i −0.816852 0.576848i $$-0.804283\pi$$
0.816852 0.576848i $$-0.195717\pi$$
$$194$$ 0 0
$$195$$ 13.5904 + 34.6229i 0.973228 + 2.47940i
$$196$$ 0 0
$$197$$ 4.06316i 0.289488i −0.989469 0.144744i $$-0.953764\pi$$
0.989469 0.144744i $$-0.0462359\pi$$
$$198$$ 0 0
$$199$$ 18.7042 1.32590 0.662952 0.748662i $$-0.269303\pi$$
0.662952 + 0.748662i $$0.269303\pi$$
$$200$$ 0 0
$$201$$ −23.8753 −1.68404
$$202$$ 0 0
$$203$$ 33.9261i 2.38114i
$$204$$ 0 0
$$205$$ 5.26430 + 13.4113i 0.367675 + 0.936688i
$$206$$ 0 0
$$207$$ 2.76241i 0.192001i
$$208$$ 0 0
$$209$$ −6.64753 −0.459819
$$210$$ 0 0
$$211$$ −7.87839 −0.542371 −0.271185 0.962527i $$-0.587416\pi$$
−0.271185 + 0.962527i $$0.587416\pi$$
$$212$$ 0 0
$$213$$ 8.19548i 0.561545i
$$214$$ 0 0
$$215$$ 7.25382 2.84732i 0.494707 0.194185i
$$216$$ 0 0
$$217$$ 17.0232i 1.15561i
$$218$$ 0 0
$$219$$ 21.4919 1.45229
$$220$$ 0 0
$$221$$ 10.4902 0.705645
$$222$$ 0 0
$$223$$ 2.29263i 0.153526i 0.997049 + 0.0767628i $$0.0244584\pi$$
−0.997049 + 0.0767628i $$0.975542\pi$$
$$224$$ 0 0
$$225$$ 10.1241 9.39556i 0.674937 0.626371i
$$226$$ 0 0
$$227$$ 12.8325i 0.851725i 0.904788 + 0.425862i $$0.140029\pi$$
−0.904788 + 0.425862i $$0.859971\pi$$
$$228$$ 0 0
$$229$$ 16.2528 1.07401 0.537007 0.843578i $$-0.319555\pi$$
0.537007 + 0.843578i $$0.319555\pi$$
$$230$$ 0 0
$$231$$ 24.2899 1.59816
$$232$$ 0 0
$$233$$ 21.5410i 1.41120i 0.708613 + 0.705598i $$0.249321\pi$$
−0.708613 + 0.705598i $$0.750679\pi$$
$$234$$ 0 0
$$235$$ −12.8998 + 5.06350i −0.841489 + 0.330307i
$$236$$ 0 0
$$237$$ 4.62563i 0.300467i
$$238$$ 0 0
$$239$$ −11.0622 −0.715555 −0.357778 0.933807i $$-0.616465\pi$$
−0.357778 + 0.933807i $$0.616465\pi$$
$$240$$ 0 0
$$241$$ 18.2164 1.17342 0.586710 0.809797i $$-0.300423\pi$$
0.586710 + 0.809797i $$0.300423\pi$$
$$242$$ 0 0
$$243$$ 21.4690i 1.37724i
$$244$$ 0 0
$$245$$ 10.1926 + 25.9666i 0.651179 + 1.65894i
$$246$$ 0 0
$$247$$ 20.0896i 1.27827i
$$248$$ 0 0
$$249$$ 19.3032 1.22329
$$250$$ 0 0
$$251$$ 10.0182 0.632345 0.316172 0.948702i $$-0.397602\pi$$
0.316172 + 0.948702i $$0.397602\pi$$
$$252$$ 0 0
$$253$$ 2.29289i 0.144153i
$$254$$ 0 0
$$255$$ −2.96912 7.56413i −0.185934 0.473684i
$$256$$ 0 0
$$257$$ 14.3021i 0.892141i 0.894998 + 0.446070i $$0.147177\pi$$
−0.894998 + 0.446070i $$0.852823\pi$$
$$258$$ 0 0
$$259$$ 38.0773 2.36601
$$260$$ 0 0
$$261$$ −21.2364 −1.31450
$$262$$ 0 0
$$263$$ 9.44361i 0.582318i 0.956675 + 0.291159i $$0.0940409\pi$$
−0.956675 + 0.291159i $$0.905959\pi$$
$$264$$ 0 0
$$265$$ 4.53153 1.77875i 0.278370 0.109268i
$$266$$ 0 0
$$267$$ 2.62311i 0.160531i
$$268$$ 0 0
$$269$$ −23.7630 −1.44886 −0.724428 0.689350i $$-0.757896\pi$$
−0.724428 + 0.689350i $$0.757896\pi$$
$$270$$ 0 0
$$271$$ 17.5939 1.06875 0.534375 0.845247i $$-0.320547\pi$$
0.534375 + 0.845247i $$0.320547\pi$$
$$272$$ 0 0
$$273$$ 73.4068i 4.44278i
$$274$$ 0 0
$$275$$ 8.40328 7.79860i 0.506737 0.470273i
$$276$$ 0 0
$$277$$ 29.6582i 1.78199i 0.454014 + 0.890995i $$0.349992\pi$$
−0.454014 + 0.890995i $$0.650008\pi$$
$$278$$ 0 0
$$279$$ 10.6559 0.637952
$$280$$ 0 0
$$281$$ −8.25484 −0.492442 −0.246221 0.969214i $$-0.579189\pi$$
−0.246221 + 0.969214i $$0.579189\pi$$
$$282$$ 0 0
$$283$$ 9.21317i 0.547666i −0.961777 0.273833i $$-0.911708\pi$$
0.961777 0.273833i $$-0.0882916\pi$$
$$284$$ 0 0
$$285$$ 14.4860 5.68613i 0.858075 0.336817i
$$286$$ 0 0
$$287$$ 28.4344i 1.67843i
$$288$$ 0 0
$$289$$ 14.7082 0.865188
$$290$$ 0 0
$$291$$ −40.6185 −2.38110
$$292$$ 0 0
$$293$$ 11.1138i 0.649277i 0.945838 + 0.324639i $$0.105243\pi$$
−0.945838 + 0.324639i $$0.894757\pi$$
$$294$$ 0 0
$$295$$ 9.61125 + 24.4856i 0.559588 + 1.42561i
$$296$$ 0 0
$$297$$ 1.30770i 0.0758804i
$$298$$ 0 0
$$299$$ 6.92936 0.400735
$$300$$ 0 0
$$301$$ −15.3794 −0.886455
$$302$$ 0 0
$$303$$ 31.0859i 1.78584i
$$304$$ 0 0
$$305$$ 4.17863 + 10.6455i 0.239267 + 0.609558i
$$306$$ 0 0
$$307$$ 18.7800i 1.07183i 0.844272 + 0.535916i $$0.180033\pi$$
−0.844272 + 0.535916i $$0.819967\pi$$
$$308$$ 0 0
$$309$$ 26.3465 1.49880
$$310$$ 0 0
$$311$$ −2.51258 −0.142475 −0.0712377 0.997459i $$-0.522695\pi$$
−0.0712377 + 0.997459i $$0.522695\pi$$
$$312$$ 0 0
$$313$$ 19.9278i 1.12638i 0.826326 + 0.563192i $$0.190427\pi$$
−0.826326 + 0.563192i $$0.809573\pi$$
$$314$$ 0 0
$$315$$ −25.3745 + 9.96015i −1.42969 + 0.561191i
$$316$$ 0 0
$$317$$ 27.8849i 1.56617i 0.621912 + 0.783087i $$0.286356\pi$$
−0.621912 + 0.783087i $$0.713644\pi$$
$$318$$ 0 0
$$319$$ −17.6269 −0.986916
$$320$$ 0 0
$$321$$ −47.7271 −2.66387
$$322$$ 0 0
$$323$$ 4.38901i 0.244211i
$$324$$ 0 0
$$325$$ −23.5683 25.3957i −1.30733 1.40870i
$$326$$ 0 0
$$327$$ 1.02561i 0.0567165i
$$328$$ 0 0
$$329$$ 27.3499 1.50785
$$330$$ 0 0
$$331$$ 28.5409 1.56875 0.784375 0.620287i $$-0.212984\pi$$
0.784375 + 0.620287i $$0.212984\pi$$
$$332$$ 0 0
$$333$$ 23.8349i 1.30615i
$$334$$ 0 0
$$335$$ 20.7021 8.12612i 1.13108 0.443978i
$$336$$ 0 0
$$337$$ 3.71371i 0.202298i −0.994871 0.101149i $$-0.967748\pi$$
0.994871 0.101149i $$-0.0322520\pi$$
$$338$$ 0 0
$$339$$ 12.9275 0.702125
$$340$$ 0 0
$$341$$ 8.84472 0.478969
$$342$$ 0 0
$$343$$ 24.1624i 1.30464i
$$344$$ 0 0
$$345$$ −1.96128 4.99655i −0.105592 0.269005i
$$346$$ 0 0
$$347$$ 14.1459i 0.759393i 0.925111 + 0.379696i $$0.123972\pi$$
−0.925111 + 0.379696i $$0.876028\pi$$
$$348$$ 0 0
$$349$$ 21.2802 1.13910 0.569550 0.821957i $$-0.307117\pi$$
0.569550 + 0.821957i $$0.307117\pi$$
$$350$$ 0 0
$$351$$ −3.95201 −0.210943
$$352$$ 0 0
$$353$$ 24.4641i 1.30209i 0.759038 + 0.651046i $$0.225669\pi$$
−0.759038 + 0.651046i $$0.774331\pi$$
$$354$$ 0 0
$$355$$ 2.78939 + 7.10624i 0.148045 + 0.377160i
$$356$$ 0 0
$$357$$ 16.0373i 0.848786i
$$358$$ 0 0
$$359$$ −23.0252 −1.21522 −0.607612 0.794234i $$-0.707872\pi$$
−0.607612 + 0.794234i $$0.707872\pi$$
$$360$$ 0 0
$$361$$ −10.5947 −0.557613
$$362$$ 0 0
$$363$$ 13.7853i 0.723540i
$$364$$ 0 0
$$365$$ −18.6354 + 7.31490i −0.975424 + 0.382880i
$$366$$ 0 0
$$367$$ 0.478057i 0.0249544i 0.999922 + 0.0124772i $$0.00397171\pi$$
−0.999922 + 0.0124772i $$0.996028\pi$$
$$368$$ 0 0
$$369$$ 17.7989 0.926573
$$370$$ 0 0
$$371$$ −9.60767 −0.498806
$$372$$ 0 0
$$373$$ 27.3508i 1.41617i 0.706127 + 0.708085i $$0.250441\pi$$
−0.706127 + 0.708085i $$0.749559\pi$$
$$374$$ 0 0
$$375$$ −11.6413 + 24.1823i −0.601153 + 1.24877i
$$376$$ 0 0
$$377$$ 53.2704i 2.74357i
$$378$$ 0 0
$$379$$ −7.35358 −0.377728 −0.188864 0.982003i $$-0.560481\pi$$
−0.188864 + 0.982003i $$0.560481\pi$$
$$380$$ 0 0
$$381$$ −14.7874 −0.757583
$$382$$ 0 0
$$383$$ 3.34108i 0.170721i 0.996350 + 0.0853606i $$0.0272042\pi$$
−0.996350 + 0.0853606i $$0.972796\pi$$
$$384$$ 0 0
$$385$$ −21.0616 + 8.26723i −1.07340 + 0.421337i
$$386$$ 0 0
$$387$$ 9.62693i 0.489364i
$$388$$ 0 0
$$389$$ −0.366568 −0.0185858 −0.00929288 0.999957i $$-0.502958\pi$$
−0.00929288 + 0.999957i $$0.502958\pi$$
$$390$$ 0 0
$$391$$ −1.51387 −0.0765598
$$392$$ 0 0
$$393$$ 35.1254i 1.77184i
$$394$$ 0 0
$$395$$ 1.57436 + 4.01085i 0.0792148 + 0.201808i
$$396$$ 0 0
$$397$$ 11.3222i 0.568245i 0.958788 + 0.284122i $$0.0917022\pi$$
−0.958788 + 0.284122i $$0.908298\pi$$
$$398$$ 0 0
$$399$$ −30.7129 −1.53757
$$400$$ 0 0
$$401$$ 37.1673 1.85605 0.928024 0.372520i $$-0.121506\pi$$
0.928024 + 0.372520i $$0.121506\pi$$
$$402$$ 0 0
$$403$$ 26.7298i 1.33150i
$$404$$ 0 0
$$405$$ 7.88947 + 20.0992i 0.392031 + 0.998738i
$$406$$ 0 0
$$407$$ 19.7837i 0.980643i
$$408$$ 0 0
$$409$$ 13.7745 0.681107 0.340553 0.940225i $$-0.389386\pi$$
0.340553 + 0.940225i $$0.389386\pi$$
$$410$$ 0 0
$$411$$ 2.33390 0.115123
$$412$$ 0 0
$$413$$ 51.9139i 2.55452i
$$414$$ 0 0
$$415$$ −16.7376 + 6.56997i −0.821619 + 0.322507i
$$416$$ 0 0
$$417$$ 18.5874i 0.910228i
$$418$$ 0 0
$$419$$ 7.50726 0.366753 0.183377 0.983043i $$-0.441297\pi$$
0.183377 + 0.983043i $$0.441297\pi$$
$$420$$ 0 0
$$421$$ −7.65685 −0.373172 −0.186586 0.982439i $$-0.559742\pi$$
−0.186586 + 0.982439i $$0.559742\pi$$
$$422$$ 0 0
$$423$$ 17.1200i 0.832402i
$$424$$ 0 0
$$425$$ 5.14900 + 5.54824i 0.249763 + 0.269129i
$$426$$ 0 0
$$427$$ 22.5703i 1.09225i
$$428$$ 0 0
$$429$$ 38.1398 1.84141
$$430$$ 0 0
$$431$$ −6.22764 −0.299975 −0.149987 0.988688i $$-0.547923\pi$$
−0.149987 + 0.988688i $$0.547923\pi$$
$$432$$ 0 0
$$433$$ 0.704087i 0.0338362i 0.999857 + 0.0169181i $$0.00538546\pi$$
−0.999857 + 0.0169181i $$0.994615\pi$$
$$434$$ 0 0
$$435$$ 38.4116 15.0776i 1.84170 0.722914i
$$436$$ 0 0
$$437$$ 2.89920i 0.138687i
$$438$$ 0 0
$$439$$ −34.8570 −1.66363 −0.831816 0.555052i $$-0.812699\pi$$
−0.831816 + 0.555052i $$0.812699\pi$$
$$440$$ 0 0
$$441$$ 34.4616 1.64103
$$442$$ 0 0
$$443$$ 24.8165i 1.17907i 0.807745 + 0.589533i $$0.200688\pi$$
−0.807745 + 0.589533i $$0.799312\pi$$
$$444$$ 0 0
$$445$$ −0.892792 2.27448i −0.0423224 0.107820i
$$446$$ 0 0
$$447$$ 42.4463i 2.00764i
$$448$$ 0 0
$$449$$ −6.77738 −0.319844 −0.159922 0.987130i $$-0.551124\pi$$
−0.159922 + 0.987130i $$0.551124\pi$$
$$450$$ 0 0
$$451$$ 14.7736 0.695662
$$452$$ 0 0
$$453$$ 4.83188i 0.227021i
$$454$$ 0 0
$$455$$ 24.9845 + 63.6505i 1.17129 + 2.98398i
$$456$$ 0 0
$$457$$ 1.47169i 0.0688429i −0.999407 0.0344214i $$-0.989041\pi$$
0.999407 0.0344214i $$-0.0109588\pi$$
$$458$$ 0 0
$$459$$ 0.863404 0.0403003
$$460$$ 0 0
$$461$$ 25.8037 1.20180 0.600899 0.799325i $$-0.294809\pi$$
0.600899 + 0.799325i $$0.294809\pi$$
$$462$$ 0 0
$$463$$ 15.3469i 0.713231i 0.934251 + 0.356616i $$0.116069\pi$$
−0.934251 + 0.356616i $$0.883931\pi$$
$$464$$ 0 0
$$465$$ −19.2740 + 7.56555i −0.893809 + 0.350844i
$$466$$ 0 0
$$467$$ 10.2933i 0.476315i 0.971227 + 0.238157i $$0.0765434\pi$$
−0.971227 + 0.238157i $$0.923457\pi$$
$$468$$ 0 0
$$469$$ −43.8922 −2.02676
$$470$$ 0 0
$$471$$ −13.9878 −0.644524
$$472$$ 0 0
$$473$$ 7.99065i 0.367410i
$$474$$ 0 0
$$475$$ −10.6254 + 9.86079i −0.487525 + 0.452444i
$$476$$ 0 0
$$477$$ 6.01404i 0.275364i
$$478$$ 0 0
$$479$$ 4.50453 0.205817 0.102909 0.994691i $$-0.467185\pi$$
0.102909 + 0.994691i $$0.467185\pi$$
$$480$$ 0 0
$$481$$ 59.7886 2.72613
$$482$$ 0 0
$$483$$ 10.5936i 0.482025i
$$484$$ 0 0
$$485$$ 35.2200 13.8248i 1.59926 0.627751i
$$486$$ 0 0
$$487$$ 27.2669i 1.23558i −0.786343 0.617790i $$-0.788028\pi$$
0.786343 0.617790i $$-0.211972\pi$$
$$488$$ 0 0
$$489$$ −16.2069 −0.732902
$$490$$ 0 0
$$491$$ −24.4866 −1.10507 −0.552533 0.833491i $$-0.686339\pi$$
−0.552533 + 0.833491i $$0.686339\pi$$
$$492$$ 0 0
$$493$$ 11.6381i 0.524154i
$$494$$ 0 0
$$495$$ −5.17497 13.1838i −0.232598 0.592566i
$$496$$ 0 0
$$497$$ 15.0665i 0.675826i
$$498$$ 0 0
$$499$$ −24.1892 −1.08286 −0.541429 0.840746i $$-0.682117\pi$$
−0.541429 + 0.840746i $$0.682117\pi$$
$$500$$ 0 0
$$501$$ 56.3016 2.51537
$$502$$ 0 0
$$503$$ 30.6230i 1.36541i −0.730693 0.682706i $$-0.760803\pi$$
0.730693 0.682706i $$-0.239197\pi$$
$$504$$ 0 0
$$505$$ −10.5803 26.9543i −0.470817 1.19945i
$$506$$ 0 0
$$507$$ 84.0562i 3.73307i
$$508$$ 0 0
$$509$$ 2.56826 0.113836 0.0569181 0.998379i $$-0.481873\pi$$
0.0569181 + 0.998379i $$0.481873\pi$$
$$510$$ 0 0
$$511$$ 39.5105 1.74784
$$512$$ 0 0
$$513$$ 1.65349i 0.0730035i
$$514$$ 0 0
$$515$$ −22.8449 + 8.96722i −1.00667 + 0.395143i
$$516$$ 0 0
$$517$$ 14.2101i 0.624960i
$$518$$ 0 0
$$519$$ 19.8966 0.873362
$$520$$ 0 0
$$521$$ −44.1355 −1.93361 −0.966807 0.255509i $$-0.917757\pi$$
−0.966807 + 0.255509i $$0.917757\pi$$
$$522$$ 0 0
$$523$$ 42.2884i 1.84914i −0.381008 0.924572i $$-0.624423\pi$$
0.381008 0.924572i $$-0.375577\pi$$
$$524$$ 0 0
$$525$$ 38.8248 36.0311i 1.69445 1.57252i
$$526$$ 0 0
$$527$$ 5.83970i 0.254381i
$$528$$ 0 0
$$529$$ −1.00000 −0.0434783
$$530$$ 0 0
$$531$$ 32.4961 1.41021
$$532$$ 0 0
$$533$$ 44.6475i 1.93390i
$$534$$ 0 0
$$535$$ 41.3838 16.2443i 1.78918 0.702300i
$$536$$ 0 0
$$537$$ 2.49656i 0.107735i
$$538$$ 0 0
$$539$$ 28.6042 1.23207
$$540$$ 0 0
$$541$$ 10.2776 0.441871 0.220935 0.975288i $$-0.429089\pi$$
0.220935 + 0.975288i $$0.429089\pi$$
$$542$$ 0 0
$$543$$ 6.52577i 0.280048i
$$544$$ 0 0
$$545$$ 0.349074 + 0.889302i 0.0149527 + 0.0380935i
$$546$$ 0 0
$$547$$ 3.87305i 0.165600i −0.996566 0.0827998i $$-0.973614\pi$$
0.996566 0.0827998i $$-0.0263862\pi$$
$$548$$ 0 0
$$549$$ 14.1282 0.602975
$$550$$ 0 0
$$551$$ 22.2880 0.949500
$$552$$ 0 0
$$553$$ 8.50373i 0.361615i
$$554$$ 0 0
$$555$$ −16.9225 43.1117i −0.718319 1.82999i
$$556$$ 0 0
$$557$$ 9.62364i 0.407767i 0.978995 + 0.203883i $$0.0653563\pi$$
−0.978995 + 0.203883i $$0.934644\pi$$
$$558$$ 0 0
$$559$$ −24.1486 −1.02138
$$560$$ 0 0
$$561$$ −8.33248 −0.351797
$$562$$ 0 0
$$563$$ 3.35865i 0.141550i −0.997492 0.0707751i $$-0.977453\pi$$
0.997492 0.0707751i $$-0.0225473\pi$$
$$564$$ 0 0
$$565$$ −11.2093 + 4.39996i −0.471580 + 0.185108i
$$566$$ 0 0
$$567$$ 42.6140i 1.78962i
$$568$$ 0 0
$$569$$ 4.26939 0.178982 0.0894910 0.995988i $$-0.471476\pi$$
0.0894910 + 0.995988i $$0.471476\pi$$
$$570$$ 0 0
$$571$$ −16.4567 −0.688689 −0.344345 0.938843i $$-0.611899\pi$$
−0.344345 + 0.938843i $$0.611899\pi$$
$$572$$ 0 0
$$573$$ 19.3206i 0.807131i
$$574$$ 0 0
$$575$$ 3.40122 + 3.66493i 0.141840 + 0.152838i
$$576$$ 0 0
$$577$$ 1.98780i 0.0827530i −0.999144 0.0413765i $$-0.986826\pi$$
0.999144 0.0413765i $$-0.0131743\pi$$
$$578$$ 0 0
$$579$$ 38.4744 1.59894
$$580$$ 0 0
$$581$$ 35.4869 1.47224
$$582$$ 0 0
$$583$$ 4.99184i 0.206741i
$$584$$ 0 0
$$585$$ −39.8428 + 15.6393i −1.64730 + 0.646607i
$$586$$ 0 0
$$587$$ 28.9720i 1.19580i −0.801570 0.597900i $$-0.796002\pi$$
0.801570 0.597900i $$-0.203998\pi$$
$$588$$ 0 0
$$589$$ −11.1835 −0.460810
$$590$$ 0 0
$$591$$ 9.75363 0.401211
$$592$$ 0 0
$$593$$ 19.4799i 0.799944i −0.916527 0.399972i $$-0.869020\pi$$
0.916527 0.399972i $$-0.130980\pi$$
$$594$$ 0 0
$$595$$ −5.45841 13.9059i −0.223773 0.570084i
$$596$$ 0 0
$$597$$ 44.8994i 1.83761i
$$598$$ 0 0
$$599$$ 37.8442 1.54627 0.773136 0.634240i $$-0.218687\pi$$
0.773136 + 0.634240i $$0.218687\pi$$
$$600$$ 0 0
$$601$$ −20.2347 −0.825389 −0.412695 0.910869i $$-0.635412\pi$$
−0.412695 + 0.910869i $$0.635412\pi$$
$$602$$ 0 0
$$603$$ 27.4749i 1.11886i
$$604$$ 0 0
$$605$$ 4.69191 + 11.9531i 0.190753 + 0.485963i
$$606$$ 0 0
$$607$$ 24.4075i 0.990670i 0.868702 + 0.495335i $$0.164955\pi$$
−0.868702 + 0.495335i $$0.835045\pi$$
$$608$$ 0 0
$$609$$ −81.4396 −3.30010
$$610$$ 0 0
$$611$$ 42.9445 1.73735
$$612$$ 0 0
$$613$$ 10.6964i 0.432025i 0.976391 + 0.216012i $$0.0693051\pi$$
−0.976391 + 0.216012i $$0.930695\pi$$
$$614$$ 0 0
$$615$$ −32.1939 + 12.6370i −1.29818 + 0.509572i
$$616$$ 0 0
$$617$$ 27.4738i 1.10605i 0.833164 + 0.553026i $$0.186527\pi$$
−0.833164 + 0.553026i $$0.813473\pi$$
$$618$$ 0 0
$$619$$ −0.389330 −0.0156485 −0.00782425 0.999969i $$-0.502491\pi$$
−0.00782425 + 0.999969i $$0.502491\pi$$
$$620$$ 0 0
$$621$$ 0.570328 0.0228865
$$622$$ 0 0
$$623$$ 4.82230i 0.193201i
$$624$$ 0 0
$$625$$ 1.86347 24.9305i 0.0745389 0.997218i
$$626$$ 0 0
$$627$$ 15.9574i 0.637278i
$$628$$ 0 0
$$629$$ −13.0621 −0.520822
$$630$$ 0 0
$$631$$ 11.9330 0.475047 0.237523 0.971382i $$-0.423664\pi$$
0.237523 + 0.971382i $$0.423664\pi$$
$$632$$ 0 0
$$633$$ 18.9121i 0.751689i
$$634$$ 0 0
$$635$$ 12.8221 5.03300i 0.508828 0.199729i
$$636$$ 0 0
$$637$$ 86.4451i 3.42508i
$$638$$ 0 0
$$639$$ 9.43106 0.373087
$$640$$ 0 0
$$641$$ 22.8525 0.902621 0.451311 0.892367i $$-0.350957\pi$$
0.451311 + 0.892367i $$0.350957\pi$$
$$642$$ 0 0
$$643$$ 34.9279i 1.37742i −0.725036 0.688711i $$-0.758177\pi$$
0.725036 0.688711i $$-0.241823\pi$$
$$644$$ 0 0
$$645$$ 6.83499 + 17.4128i 0.269128 + 0.685629i
$$646$$ 0 0
$$647$$ 26.3738i 1.03686i 0.855120 + 0.518430i $$0.173483\pi$$
−0.855120 + 0.518430i $$0.826517\pi$$
$$648$$ 0 0
$$649$$ 26.9728 1.05877
$$650$$ 0 0
$$651$$ 40.8643 1.60160
$$652$$ 0 0
$$653$$ 2.17022i 0.0849274i −0.999098 0.0424637i $$-0.986479\pi$$
0.999098 0.0424637i $$-0.0135207\pi$$
$$654$$ 0 0
$$655$$ 11.9552 + 30.4570i 0.467127 + 1.19005i
$$656$$ 0 0
$$657$$ 24.7321i 0.964891i
$$658$$ 0 0
$$659$$ 19.7820 0.770596 0.385298 0.922792i $$-0.374099\pi$$
0.385298 + 0.922792i $$0.374099\pi$$
$$660$$ 0 0
$$661$$ 45.7505 1.77949 0.889743 0.456461i $$-0.150883\pi$$
0.889743 + 0.456461i $$0.150883\pi$$
$$662$$ 0 0
$$663$$ 25.1817i 0.977976i
$$664$$ 0 0
$$665$$ 26.6309 10.4533i 1.03270 0.405363i
$$666$$ 0 0
$$667$$ 7.68764i 0.297666i
$$668$$ 0 0
$$669$$ −5.50346 −0.212776
$$670$$ 0 0
$$671$$ 11.7268 0.452708
$$672$$ 0 0
$$673$$ 6.99940i 0.269807i 0.990859 + 0.134904i $$0.0430725\pi$$
−0.990859 + 0.134904i $$0.956928\pi$$
$$674$$ 0 0
$$675$$ −1.93981 2.09021i −0.0746633 0.0804524i
$$676$$ 0 0
$$677$$ 26.7178i 1.02685i −0.858134 0.513425i $$-0.828376\pi$$
0.858134 0.513425i $$-0.171624\pi$$
$$678$$ 0 0
$$679$$ −74.6728 −2.86568
$$680$$ 0 0
$$681$$ −30.8045 −1.18043
$$682$$ 0 0
$$683$$ 19.8947i 0.761248i 0.924730 + 0.380624i $$0.124291\pi$$
−0.924730 + 0.380624i $$0.875709\pi$$
$$684$$ 0 0
$$685$$ −2.02371 + 0.794359i −0.0773219 + 0.0303509i
$$686$$ 0 0
$$687$$ 39.0148i 1.48851i
$$688$$ 0 0
$$689$$ −15.0859 −0.574727
$$690$$ 0 0
$$691$$ −1.24438 −0.0473385 −0.0236693 0.999720i $$-0.507535\pi$$
−0.0236693 + 0.999720i $$0.507535\pi$$
$$692$$ 0 0
$$693$$ 27.9520i 1.06181i
$$694$$ 0 0
$$695$$ −6.32634 16.1170i −0.239972 0.611352i
$$696$$ 0 0
$$697$$ 9.75424i 0.369468i
$$698$$ 0 0
$$699$$ −51.7091 −1.95582
$$700$$ 0 0
$$701$$ −29.8454 −1.12724 −0.563622 0.826033i $$-0.690592\pi$$
−0.563622 + 0.826033i $$0.690592\pi$$
$$702$$ 0 0
$$703$$ 25.0151i 0.943464i
$$704$$ 0 0
$$705$$ −12.1550 30.9660i −0.457782 1.16625i
$$706$$ 0 0
$$707$$ 57.1481i 2.14928i
$$708$$ 0 0
$$709$$ −25.2255 −0.947362 −0.473681 0.880697i $$-0.657075\pi$$
−0.473681 + 0.880697i $$0.657075\pi$$
$$710$$ 0 0
$$711$$ 5.32301 0.199628
$$712$$ 0 0
$$713$$ 3.85746i 0.144463i
$$714$$ 0 0
$$715$$ −33.0707 + 12.9811i −1.23678 + 0.485467i
$$716$$ 0 0
$$717$$ 26.5549i 0.991710i
$$718$$ 0 0
$$719$$ −23.7787 −0.886797 −0.443398 0.896325i $$-0.646227\pi$$
−0.443398 + 0.896325i $$0.646227\pi$$
$$720$$ 0 0
$$721$$ 48.4353 1.80383
$$722$$ 0 0
$$723$$ 43.7285i 1.62628i
$$724$$ 0 0
$$725$$ −28.1747 + 26.1473i −1.04638 + 0.971086i
$$726$$ 0 0
$$727$$ 36.5849i 1.35686i 0.734666 + 0.678429i $$0.237339\pi$$
−0.734666 + 0.678429i $$0.762661\pi$$
$$728$$ 0 0
$$729$$ 22.5675 0.835833
$$730$$ 0 0
$$731$$ 5.27580 0.195133
$$732$$ 0 0
$$733$$ 21.7593i 0.803698i −0.915706 0.401849i $$-0.868368\pi$$
0.915706 0.401849i $$-0.131632\pi$$
$$734$$ 0 0
$$735$$ −62.3328 + 24.4673i −2.29918 + 0.902489i
$$736$$ 0 0
$$737$$ 22.8050i 0.840032i
$$738$$ 0 0
$$739$$ 2.72303 0.100168 0.0500842 0.998745i $$-0.484051\pi$$
0.0500842 + 0.998745i $$0.484051\pi$$
$$740$$ 0 0
$$741$$ −48.2251 −1.77159
$$742$$ 0 0
$$743$$ 32.0161i 1.17456i 0.809385 + 0.587278i $$0.199800\pi$$
−0.809385 + 0.587278i $$0.800200\pi$$
$$744$$ 0 0
$$745$$ −14.4469 36.8049i −0.529293 1.34843i
$$746$$ 0 0
$$747$$ 22.2134i 0.812746i
$$748$$ 0 0
$$749$$ −87.7413 −3.20600
$$750$$ 0 0
$$751$$ 36.0949 1.31712 0.658561 0.752527i $$-0.271165\pi$$
0.658561 + 0.752527i $$0.271165\pi$$
$$752$$ 0 0
$$753$$ 24.0488i 0.876386i
$$754$$ 0 0
$$755$$ −1.64456 4.18969i −0.0598517 0.152478i
$$756$$ 0 0
$$757$$ 46.8188i 1.70166i 0.525442 + 0.850830i $$0.323900\pi$$
−0.525442 + 0.850830i $$0.676100\pi$$
$$758$$ 0 0
$$759$$ −5.50408 −0.199786
$$760$$ 0 0
$$761$$ −28.8182 −1.04466 −0.522330 0.852744i $$-0.674937\pi$$
−0.522330 + 0.852744i $$0.674937\pi$$
$$762$$ 0 0
$$763$$ 1.88548i 0.0682590i
$$764$$ 0 0
$$765$$ 8.70453 3.41676i 0.314713 0.123533i
$$766$$ 0 0
$$767$$ 81.5148i 2.94333i
$$768$$ 0 0
$$769$$ −51.6243 −1.86162 −0.930811 0.365501i $$-0.880898\pi$$
−0.930811 + 0.365501i $$0.880898\pi$$
$$770$$ 0 0
$$771$$ −34.3322 −1.23645
$$772$$ 0 0
$$773$$ 25.9610i 0.933753i 0.884322 + 0.466877i $$0.154621\pi$$
−0.884322 + 0.466877i $$0.845379\pi$$
$$774$$ 0 0
$$775$$ 14.1373 13.1201i 0.507828 0.471286i
$$776$$ 0 0
$$777$$ 91.4046i 3.27912i
$$778$$ 0 0
$$779$$ −18.6802 −0.669288
$$780$$ 0 0
$$781$$ 7.82807 0.280110
$$782$$ 0 0
$$783$$ 4.38448i 0.156688i
$$784$$ 0 0
$$785$$ 12.1287 4.76084i 0.432893 0.169922i
$$786$$ 0 0
$$787$$ 53.2258i 1.89730i 0.316333 + 0.948648i $$0.397548\pi$$
−0.316333 + 0.948648i $$0.602452\pi$$
$$788$$ 0 0
$$789$$ −22.6694 −0.807053
$$790$$ 0 0
$$791$$ 23.7658 0.845015
$$792$$ 0 0
$$793$$ 35.4397i 1.25850i
$$794$$ 0 0
$$795$$ 4.26988 + 10.8780i 0.151437 + 0.385801i
$$796$$ 0 0
$$797$$ 31.1874i 1.10471i −0.833608 0.552357i $$-0.813729\pi$$
0.833608 0.552357i $$-0.186271\pi$$
$$798$$ 0 0
$$799$$ −9.38218 −0.331918
$$800$$ 0 0
$$801$$ −3.01858 −0.106656
$$802$$ 0 0