# Properties

 Label 1512.2.s.n.1297.3 Level $1512$ Weight $2$ Character 1512.1297 Analytic conductor $12.073$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1512 = 2^{3} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1512.s (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$12.0733807856$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ Defining polynomial: $$x^{8} - 3 x^{7} + 4 x^{6} + 28 x^{5} + 14 x^{4} - 52 x^{3} + 306 x^{2} + 1052 x + 1051$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 1297.3 Root $$1.89574 - 2.48951i$$ of defining polynomial Character $$\chi$$ $$=$$ 1512.1297 Dual form 1512.2.s.n.865.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.0144658 + 0.0250554i) q^{5} +(-1.70811 - 2.02048i) q^{7} +O(q^{10})$$ $$q+(-0.0144658 + 0.0250554i) q^{5} +(-1.70811 - 2.02048i) q^{7} +(-1.88127 - 3.25845i) q^{11} -2.97107 q^{13} +(0.708111 + 1.22648i) q^{17} +(-3.81196 + 6.60250i) q^{19} +(-2.98512 + 5.17037i) q^{23} +(2.49958 + 4.32940i) q^{25} +9.99916 q^{29} +(4.27700 + 7.40799i) q^{31} +(0.0753332 - 0.0135696i) q^{35} +(-0.737043 + 1.27660i) q^{37} -4.38729 q^{41} +3.76254 q^{43} +(2.07491 - 3.59386i) q^{47} +(-1.16471 + 6.90242i) q^{49} +(3.60385 + 6.24204i) q^{53} +0.108856 q^{55} +(-6.93027 - 12.0036i) q^{59} +(-5.61831 + 9.73120i) q^{61} +(0.0429788 - 0.0744414i) q^{65} +(-2.77742 - 4.81064i) q^{67} -11.5661 q^{71} +(2.17918 + 3.77445i) q^{73} +(-3.37024 + 9.36688i) q^{77} +(-7.04556 + 12.2033i) q^{79} +6.62475 q^{83} -0.0409735 q^{85} +(2.14423 - 3.71391i) q^{89} +(5.07491 + 6.00300i) q^{91} +(-0.110286 - 0.191020i) q^{95} -6.77458 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 2q^{5} - 4q^{7} + O(q^{10})$$ $$8q - 2q^{5} - 4q^{7} - q^{11} - 20q^{13} - 4q^{17} + q^{19} + 12q^{23} - 14q^{25} + 12q^{29} + 8q^{31} + 9q^{35} - 12q^{41} + 2q^{43} - 9q^{47} + 6q^{49} + 7q^{53} - 36q^{55} - 4q^{59} - 25q^{61} - 28q^{65} - 30q^{67} - 22q^{71} + 4q^{73} - 37q^{77} + 7q^{79} + 58q^{83} + 14q^{85} + 9q^{89} + 15q^{91} - 4q^{95} - 8q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$$.

 $$n$$ $$757$$ $$785$$ $$1081$$ $$1135$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## 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
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −0.0144658 + 0.0250554i −0.00646928 + 0.0112051i −0.869242 0.494387i $$-0.835393\pi$$
0.862773 + 0.505592i $$0.168726\pi$$
$$6$$ 0 0
$$7$$ −1.70811 2.02048i −0.645605 0.763671i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −1.88127 3.25845i −0.567224 0.982461i −0.996839 0.0794487i $$-0.974684\pi$$
0.429615 0.903012i $$-0.358649\pi$$
$$12$$ 0 0
$$13$$ −2.97107 −0.824026 −0.412013 0.911178i $$-0.635174\pi$$
−0.412013 + 0.911178i $$0.635174\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 0.708111 + 1.22648i 0.171742 + 0.297466i 0.939029 0.343838i $$-0.111727\pi$$
−0.767287 + 0.641304i $$0.778394\pi$$
$$18$$ 0 0
$$19$$ −3.81196 + 6.60250i −0.874523 + 1.51472i −0.0172529 + 0.999851i $$0.505492\pi$$
−0.857270 + 0.514867i $$0.827841\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −2.98512 + 5.17037i −0.622440 + 1.07810i 0.366590 + 0.930382i $$0.380525\pi$$
−0.989030 + 0.147715i $$0.952808\pi$$
$$24$$ 0 0
$$25$$ 2.49958 + 4.32940i 0.499916 + 0.865880i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 9.99916 1.85680 0.928399 0.371585i $$-0.121186\pi$$
0.928399 + 0.371585i $$0.121186\pi$$
$$30$$ 0 0
$$31$$ 4.27700 + 7.40799i 0.768173 + 1.33051i 0.938553 + 0.345136i $$0.112167\pi$$
−0.170380 + 0.985378i $$0.554500\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0.0753332 0.0135696i 0.0127336 0.00229368i
$$36$$ 0 0
$$37$$ −0.737043 + 1.27660i −0.121169 + 0.209871i −0.920229 0.391380i $$-0.871998\pi$$
0.799060 + 0.601251i $$0.205331\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −4.38729 −0.685180 −0.342590 0.939485i $$-0.611304\pi$$
−0.342590 + 0.939485i $$0.611304\pi$$
$$42$$ 0 0
$$43$$ 3.76254 0.573782 0.286891 0.957963i $$-0.407378\pi$$
0.286891 + 0.957963i $$0.407378\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 2.07491 3.59386i 0.302657 0.524218i −0.674080 0.738659i $$-0.735460\pi$$
0.976737 + 0.214441i $$0.0687929\pi$$
$$48$$ 0 0
$$49$$ −1.16471 + 6.90242i −0.166388 + 0.986060i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 3.60385 + 6.24204i 0.495026 + 0.857411i 0.999984 0.00573358i $$-0.00182507\pi$$
−0.504957 + 0.863144i $$0.668492\pi$$
$$54$$ 0 0
$$55$$ 0.108856 0.0146781
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −6.93027 12.0036i −0.902244 1.56273i −0.824574 0.565754i $$-0.808585\pi$$
−0.0776699 0.996979i $$-0.524748\pi$$
$$60$$ 0 0
$$61$$ −5.61831 + 9.73120i −0.719351 + 1.24595i 0.241906 + 0.970300i $$0.422227\pi$$
−0.961257 + 0.275653i $$0.911106\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0.0429788 0.0744414i 0.00533086 0.00923332i
$$66$$ 0 0
$$67$$ −2.77742 4.81064i −0.339316 0.587713i 0.644988 0.764193i $$-0.276862\pi$$
−0.984304 + 0.176480i $$0.943529\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −11.5661 −1.37264 −0.686319 0.727301i $$-0.740775\pi$$
−0.686319 + 0.727301i $$0.740775\pi$$
$$72$$ 0 0
$$73$$ 2.17918 + 3.77445i 0.255054 + 0.441766i 0.964910 0.262580i $$-0.0845735\pi$$
−0.709856 + 0.704346i $$0.751240\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −3.37024 + 9.36688i −0.384074 + 1.06745i
$$78$$ 0 0
$$79$$ −7.04556 + 12.2033i −0.792688 + 1.37298i 0.131609 + 0.991302i $$0.457986\pi$$
−0.924297 + 0.381674i $$0.875348\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 6.62475 0.727161 0.363580 0.931563i $$-0.381554\pi$$
0.363580 + 0.931563i $$0.381554\pi$$
$$84$$ 0 0
$$85$$ −0.0409735 −0.00444420
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 2.14423 3.71391i 0.227288 0.393674i −0.729716 0.683751i $$-0.760348\pi$$
0.957003 + 0.290077i $$0.0936809\pi$$
$$90$$ 0 0
$$91$$ 5.07491 + 6.00300i 0.531996 + 0.629285i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −0.110286 0.191020i −0.0113151 0.0195983i
$$96$$ 0 0
$$97$$ −6.77458 −0.687854 −0.343927 0.938996i $$-0.611757\pi$$
−0.343927 + 0.938996i $$0.611757\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 3.37282 + 5.84190i 0.335609 + 0.581291i 0.983602 0.180355i $$-0.0577247\pi$$
−0.647993 + 0.761646i $$0.724391\pi$$
$$102$$ 0 0
$$103$$ −1.38169 + 2.39315i −0.136142 + 0.235804i −0.926033 0.377442i $$-0.876804\pi$$
0.789891 + 0.613247i $$0.210137\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 8.90134 15.4176i 0.860525 1.49047i −0.0108984 0.999941i $$-0.503469\pi$$
0.871423 0.490532i $$-0.163198\pi$$
$$108$$ 0 0
$$109$$ −5.41622 9.38117i −0.518780 0.898553i −0.999762 0.0218227i $$-0.993053\pi$$
0.480982 0.876731i $$-0.340280\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0.879102 0.0826990 0.0413495 0.999145i $$-0.486834\pi$$
0.0413495 + 0.999145i $$0.486834\pi$$
$$114$$ 0 0
$$115$$ −0.0863639 0.149587i −0.00805348 0.0139490i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 1.26856 3.52570i 0.116289 0.323200i
$$120$$ 0 0
$$121$$ −1.57835 + 2.73378i −0.143486 + 0.248526i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −0.289291 −0.0258750
$$126$$ 0 0
$$127$$ −1.27156 −0.112833 −0.0564165 0.998407i $$-0.517967\pi$$
−0.0564165 + 0.998407i $$0.517967\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −8.31998 + 14.4106i −0.726920 + 1.25906i 0.231258 + 0.972892i $$0.425716\pi$$
−0.958179 + 0.286171i $$0.907618\pi$$
$$132$$ 0 0
$$133$$ 19.8515 3.57581i 1.72134 0.310062i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 2.44515 + 4.23513i 0.208904 + 0.361832i 0.951369 0.308052i $$-0.0996772\pi$$
−0.742466 + 0.669884i $$0.766344\pi$$
$$138$$ 0 0
$$139$$ −8.61187 −0.730449 −0.365225 0.930919i $$-0.619008\pi$$
−0.365225 + 0.930919i $$0.619008\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 5.58938 + 9.68109i 0.467407 + 0.809573i
$$144$$ 0 0
$$145$$ −0.144645 + 0.250533i −0.0120122 + 0.0208057i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −4.95920 + 8.58959i −0.406274 + 0.703686i −0.994469 0.105033i $$-0.966505\pi$$
0.588195 + 0.808719i $$0.299839\pi$$
$$150$$ 0 0
$$151$$ −4.73704 8.20480i −0.385495 0.667697i 0.606343 0.795203i $$-0.292636\pi$$
−0.991838 + 0.127506i $$0.959303\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −0.247481 −0.0198781
$$156$$ 0 0
$$157$$ 5.83745 + 10.1108i 0.465880 + 0.806927i 0.999241 0.0389606i $$-0.0124047\pi$$
−0.533361 + 0.845888i $$0.679071\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 15.5456 2.80019i 1.22516 0.220686i
$$162$$ 0 0
$$163$$ −6.36680 + 11.0276i −0.498687 + 0.863750i −0.999999 0.00151597i $$-0.999517\pi$$
0.501312 + 0.865266i $$0.332851\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −19.8597 −1.53679 −0.768395 0.639976i $$-0.778944\pi$$
−0.768395 + 0.639976i $$0.778944\pi$$
$$168$$ 0 0
$$169$$ −4.17275 −0.320981
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 2.55443 4.42440i 0.194210 0.336381i −0.752432 0.658670i $$-0.771119\pi$$
0.946641 + 0.322290i $$0.104452\pi$$
$$174$$ 0 0
$$175$$ 4.47793 12.4455i 0.338499 0.940789i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −8.98470 15.5620i −0.671548 1.16315i −0.977465 0.211097i $$-0.932296\pi$$
0.305917 0.952058i $$-0.401037\pi$$
$$180$$ 0 0
$$181$$ −3.72157 −0.276622 −0.138311 0.990389i $$-0.544167\pi$$
−0.138311 + 0.990389i $$0.544167\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −0.0213238 0.0369338i −0.00156775 0.00271543i
$$186$$ 0 0
$$187$$ 2.66430 4.61469i 0.194833 0.337460i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 2.88127 4.99051i 0.208481 0.361100i −0.742755 0.669563i $$-0.766481\pi$$
0.951236 + 0.308463i $$0.0998146\pi$$
$$192$$ 0 0
$$193$$ −1.80635 3.12870i −0.130024 0.225209i 0.793661 0.608360i $$-0.208172\pi$$
−0.923686 + 0.383151i $$0.874839\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 6.44432 0.459139 0.229569 0.973292i $$-0.426268\pi$$
0.229569 + 0.973292i $$0.426268\pi$$
$$198$$ 0 0
$$199$$ 1.29147 + 2.23689i 0.0915499 + 0.158569i 0.908163 0.418616i $$-0.137485\pi$$
−0.816614 + 0.577185i $$0.804151\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −17.0797 20.2032i −1.19876 1.41798i
$$204$$ 0 0
$$205$$ 0.0634655 0.109925i 0.00443262 0.00767753i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 28.6853 1.98420
$$210$$ 0 0
$$211$$ 19.4162 1.33667 0.668334 0.743861i $$-0.267008\pi$$
0.668334 + 0.743861i $$0.267008\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −0.0544280 + 0.0942720i −0.00371196 + 0.00642930i
$$216$$ 0 0
$$217$$ 7.66213 21.2953i 0.520139 1.44562i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −2.10385 3.64397i −0.141520 0.245120i
$$222$$ 0 0
$$223$$ 11.5074 0.770589 0.385295 0.922794i $$-0.374100\pi$$
0.385295 + 0.922794i $$0.374100\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 1.48595 + 2.57375i 0.0986261 + 0.170826i 0.911116 0.412150i $$-0.135222\pi$$
−0.812490 + 0.582975i $$0.801889\pi$$
$$228$$ 0 0
$$229$$ −11.0775 + 19.1868i −0.732023 + 1.26790i 0.223995 + 0.974590i $$0.428090\pi$$
−0.956017 + 0.293310i $$0.905243\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −10.0056 + 17.3302i −0.655489 + 1.13534i 0.326282 + 0.945272i $$0.394204\pi$$
−0.981771 + 0.190068i $$0.939129\pi$$
$$234$$ 0 0
$$235$$ 0.0600304 + 0.103976i 0.00391595 + 0.00678263i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −23.6930 −1.53257 −0.766286 0.642500i $$-0.777897\pi$$
−0.766286 + 0.642500i $$0.777897\pi$$
$$240$$ 0 0
$$241$$ −5.64983 9.78579i −0.363938 0.630358i 0.624668 0.780891i $$-0.285234\pi$$
−0.988605 + 0.150533i $$0.951901\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −0.156095 0.129031i −0.00997253 0.00824350i
$$246$$ 0 0
$$247$$ 11.3256 19.6165i 0.720630 1.24817i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 4.76254 0.300609 0.150304 0.988640i $$-0.451975\pi$$
0.150304 + 0.988640i $$0.451975\pi$$
$$252$$ 0 0
$$253$$ 22.4632 1.41225
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −12.3230 + 21.3440i −0.768687 + 1.33140i 0.169588 + 0.985515i $$0.445756\pi$$
−0.938275 + 0.345890i $$0.887577\pi$$
$$258$$ 0 0
$$259$$ 3.83829 0.691383i 0.238500 0.0429605i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 5.33787 + 9.24547i 0.329147 + 0.570100i 0.982343 0.187089i $$-0.0599054\pi$$
−0.653196 + 0.757189i $$0.726572\pi$$
$$264$$ 0 0
$$265$$ −0.208530 −0.0128099
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −0.653264 1.13149i −0.0398302 0.0689880i 0.845423 0.534097i $$-0.179348\pi$$
−0.885253 + 0.465109i $$0.846015\pi$$
$$270$$ 0 0
$$271$$ −9.83787 + 17.0397i −0.597608 + 1.03509i 0.395565 + 0.918438i $$0.370549\pi$$
−0.993173 + 0.116650i $$0.962785\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 9.40477 16.2895i 0.567129 0.982296i
$$276$$ 0 0
$$277$$ −14.3774 24.9024i −0.863855 1.49624i −0.868179 0.496250i $$-0.834710\pi$$
0.00432421 0.999991i $$-0.498624\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 9.20853 0.549335 0.274667 0.961539i $$-0.411432\pi$$
0.274667 + 0.961539i $$0.411432\pi$$
$$282$$ 0 0
$$283$$ −11.2613 19.5051i −0.669414 1.15946i −0.978068 0.208285i $$-0.933212\pi$$
0.308654 0.951174i $$-0.400121\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 7.49398 + 8.86445i 0.442356 + 0.523252i
$$288$$ 0 0
$$289$$ 7.49716 12.9855i 0.441009 0.763850i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 3.30534 0.193100 0.0965501 0.995328i $$-0.469219\pi$$
0.0965501 + 0.995328i $$0.469219\pi$$
$$294$$ 0 0
$$295$$ 0.401006 0.0233475
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 8.86898 15.3615i 0.512907 0.888380i
$$300$$ 0 0
$$301$$ −6.42683 7.60215i −0.370437 0.438181i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −0.162546 0.281538i −0.00930737 0.0161208i
$$306$$ 0 0
$$307$$ −14.2358 −0.812479 −0.406240 0.913767i $$-0.633160\pi$$
−0.406240 + 0.913767i $$0.633160\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 14.9694 + 25.9278i 0.848836 + 1.47023i 0.882247 + 0.470786i $$0.156030\pi$$
−0.0334108 + 0.999442i $$0.510637\pi$$
$$312$$ 0 0
$$313$$ −5.47107 + 9.47617i −0.309243 + 0.535625i −0.978197 0.207679i $$-0.933409\pi$$
0.668954 + 0.743304i $$0.266742\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 5.27700 9.14004i 0.296386 0.513356i −0.678920 0.734212i $$-0.737552\pi$$
0.975306 + 0.220856i $$0.0708851\pi$$
$$318$$ 0 0
$$319$$ −18.8111 32.5818i −1.05322 1.82423i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −10.7972 −0.600770
$$324$$ 0 0
$$325$$ −7.42643 12.8630i −0.411944 0.713508i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −10.8055 + 1.94638i −0.595727 + 0.107307i
$$330$$ 0 0
$$331$$ 15.1319 26.2093i 0.831727 1.44059i −0.0649412 0.997889i $$-0.520686\pi$$
0.896668 0.442704i $$-0.145981\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0.160710 0.00878053
$$336$$ 0 0
$$337$$ 26.8428 1.46222 0.731111 0.682259i $$-0.239002\pi$$
0.731111 + 0.682259i $$0.239002\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 16.0924 27.8728i 0.871452 1.50940i
$$342$$ 0 0
$$343$$ 15.9357 9.43682i 0.860447 0.509540i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 9.08938 + 15.7433i 0.487944 + 0.845143i 0.999904 0.0138661i $$-0.00441387\pi$$
−0.511960 + 0.859009i $$0.671081\pi$$
$$348$$ 0 0
$$349$$ 5.15586 0.275987 0.137993 0.990433i $$-0.455935\pi$$
0.137993 + 0.990433i $$0.455935\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −14.1838 24.5670i −0.754926 1.30757i −0.945411 0.325880i $$-0.894339\pi$$
0.190485 0.981690i $$-0.438994\pi$$
$$354$$ 0 0
$$355$$ 0.167312 0.289792i 0.00887998 0.0153806i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −12.9793 + 22.4808i −0.685020 + 1.18649i 0.288411 + 0.957507i $$0.406873\pi$$
−0.973431 + 0.228982i $$0.926460\pi$$
$$360$$ 0 0
$$361$$ −19.5620 33.8824i −1.02958 1.78329i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −0.126094 −0.00660006
$$366$$ 0 0
$$367$$ 9.91062 + 17.1657i 0.517330 + 0.896042i 0.999797 + 0.0201281i $$0.00640740\pi$$
−0.482467 + 0.875914i $$0.660259\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 6.45618 17.9436i 0.335188 0.931586i
$$372$$ 0 0
$$373$$ −4.58294 + 7.93789i −0.237296 + 0.411008i −0.959937 0.280215i $$-0.909594\pi$$
0.722642 + 0.691223i $$0.242928\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −29.7082 −1.53005
$$378$$ 0 0
$$379$$ 6.12575 0.314658 0.157329 0.987546i $$-0.449712\pi$$
0.157329 + 0.987546i $$0.449712\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −4.25795 + 7.37498i −0.217571 + 0.376844i −0.954065 0.299600i $$-0.903147\pi$$
0.736494 + 0.676444i $$0.236480\pi$$
$$384$$ 0 0
$$385$$ −0.185938 0.219942i −0.00947628 0.0112093i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 3.16773 + 5.48667i 0.160610 + 0.278185i 0.935088 0.354416i $$-0.115320\pi$$
−0.774477 + 0.632602i $$0.781987\pi$$
$$390$$ 0 0
$$391$$ −8.45517 −0.427596
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −0.203839 0.353059i −0.0102562 0.0177643i
$$396$$ 0 0
$$397$$ 15.6401 27.0895i 0.784956 1.35958i −0.144070 0.989567i $$-0.546019\pi$$
0.929026 0.370015i $$-0.120648\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 1.31454 2.27686i 0.0656452 0.113701i −0.831335 0.555772i $$-0.812423\pi$$
0.896980 + 0.442071i $$0.145756\pi$$
$$402$$ 0 0
$$403$$ −12.7073 22.0096i −0.632994 1.09638i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 5.54630 0.274920
$$408$$ 0 0
$$409$$ 6.89574 + 11.9438i 0.340972 + 0.590581i 0.984614 0.174746i $$-0.0559105\pi$$
−0.643641 + 0.765327i $$0.722577\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −12.4154 + 34.5059i −0.610921 + 1.69793i
$$414$$ 0 0
$$415$$ −0.0958321 + 0.165986i −0.00470421 + 0.00814793i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 2.84532 0.139003 0.0695016 0.997582i $$-0.477859\pi$$
0.0695016 + 0.997582i $$0.477859\pi$$
$$420$$ 0 0
$$421$$ 29.4374 1.43469 0.717347 0.696716i $$-0.245356\pi$$
0.717347 + 0.696716i $$0.245356\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −3.53996 + 6.13139i −0.171713 + 0.297416i
$$426$$ 0 0
$$427$$ 29.2584 5.27026i 1.41592 0.255046i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 2.36096 + 4.08930i 0.113723 + 0.196975i 0.917269 0.398269i $$-0.130389\pi$$
−0.803545 + 0.595243i $$0.797056\pi$$
$$432$$ 0 0
$$433$$ −3.83813 −0.184449 −0.0922243 0.995738i $$-0.529398\pi$$
−0.0922243 + 0.995738i $$0.529398\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −22.7583 39.4185i −1.08868 1.88564i
$$438$$ 0 0
$$439$$ −9.23018 + 15.9871i −0.440533 + 0.763025i −0.997729 0.0673558i $$-0.978544\pi$$
0.557196 + 0.830381i $$0.311877\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 11.3001 19.5723i 0.536883 0.929908i −0.462187 0.886783i $$-0.652935\pi$$
0.999070 0.0431258i $$-0.0137316\pi$$
$$444$$ 0 0
$$445$$ 0.0620357 + 0.107449i 0.00294078 + 0.00509357i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 20.0043 0.944063 0.472031 0.881582i $$-0.343521\pi$$
0.472031 + 0.881582i $$0.343521\pi$$
$$450$$ 0 0
$$451$$ 8.25368 + 14.2958i 0.388650 + 0.673162i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −0.223820 + 0.0403163i −0.0104929 + 0.00189006i
$$456$$ 0 0
$$457$$ −13.5196 + 23.4167i −0.632423 + 1.09539i 0.354632 + 0.935006i $$0.384606\pi$$
−0.987055 + 0.160382i $$0.948727\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −30.9557 −1.44175 −0.720875 0.693065i $$-0.756260\pi$$
−0.720875 + 0.693065i $$0.756260\pi$$
$$462$$ 0 0
$$463$$ 3.96105 0.184086 0.0920428 0.995755i $$-0.470660\pi$$
0.0920428 + 0.995755i $$0.470660\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 13.5834 23.5271i 0.628563 1.08870i −0.359277 0.933231i $$-0.616977\pi$$
0.987840 0.155472i $$-0.0496899\pi$$
$$468$$ 0 0
$$469$$ −4.97567 + 13.8288i −0.229755 + 0.638557i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −7.07835 12.2601i −0.325463 0.563718i
$$474$$ 0 0
$$475$$ −38.1132 −1.74875
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 8.83788 + 15.3077i 0.403813 + 0.699425i 0.994183 0.107708i $$-0.0343512\pi$$
−0.590369 + 0.807133i $$0.701018\pi$$
$$480$$ 0 0
$$481$$ 2.18980 3.79285i 0.0998465 0.172939i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0.0979995 0.169740i 0.00444993 0.00770750i
$$486$$ 0 0
$$487$$ 6.79665 + 11.7722i 0.307986 + 0.533447i 0.977922 0.208972i $$-0.0670117\pi$$
−0.669936 + 0.742419i $$0.733678\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 21.8256 0.984974 0.492487 0.870320i $$-0.336088\pi$$
0.492487 + 0.870320i $$0.336088\pi$$
$$492$$ 0 0
$$493$$ 7.08052 + 12.2638i 0.318890 + 0.552334i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 19.7561 + 23.3690i 0.886182 + 1.04824i
$$498$$ 0 0
$$499$$ −10.6374 + 18.4245i −0.476194 + 0.824792i −0.999628 0.0272740i $$-0.991317\pi$$
0.523434 + 0.852066i $$0.324651\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 27.2281 1.21404 0.607020 0.794687i $$-0.292365\pi$$
0.607020 + 0.794687i $$0.292365\pi$$
$$504$$ 0 0
$$505$$ −0.195162 −0.00868459
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −9.23879 + 16.0021i −0.409502 + 0.709279i −0.994834 0.101515i $$-0.967631\pi$$
0.585332 + 0.810794i $$0.300964\pi$$
$$510$$ 0 0
$$511$$ 3.90394 10.8502i 0.172700 0.479984i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −0.0399743 0.0692376i −0.00176148 0.00305097i
$$516$$ 0 0
$$517$$ −15.6139 −0.686698
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 2.93913 + 5.09073i 0.128766 + 0.223029i 0.923199 0.384323i $$-0.125565\pi$$
−0.794433 + 0.607352i $$0.792232\pi$$
$$522$$ 0 0
$$523$$ −6.22258 + 10.7778i −0.272094 + 0.471281i −0.969398 0.245495i $$-0.921050\pi$$
0.697304 + 0.716776i $$0.254383\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −6.05719 + 10.4914i −0.263855 + 0.457011i
$$528$$ 0 0
$$529$$ −6.32183 10.9497i −0.274862 0.476075i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 13.0349 0.564606
$$534$$ 0 0
$$535$$ 0.257529 + 0.446054i 0.0111340 + 0.0192846i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 24.6824 9.19015i 1.06314 0.395848i
$$540$$ 0 0
$$541$$ 10.7362 18.5957i 0.461586 0.799490i −0.537455 0.843293i $$-0.680614\pi$$
0.999040 + 0.0438031i $$0.0139474\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0.313399 0.0134245
$$546$$ 0 0
$$547$$ 30.6741 1.31153 0.655764 0.754966i $$-0.272347\pi$$
0.655764 + 0.754966i $$0.272347\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −38.1164 + 66.0195i −1.62381 + 2.81253i
$$552$$ 0 0
$$553$$ 36.6911 6.60910i 1.56027 0.281047i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −20.5857 35.6555i −0.872244 1.51077i −0.859670 0.510850i $$-0.829331\pi$$
−0.0125744 0.999921i $$-0.504003\pi$$
$$558$$ 0 0
$$559$$ −11.1788 −0.472811
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −4.56848 7.91283i −0.192538 0.333486i 0.753552 0.657388i $$-0.228339\pi$$
−0.946091 + 0.323902i $$0.895005\pi$$
$$564$$ 0 0
$$565$$ −0.0127169 + 0.0220263i −0.000535003 + 0.000926653i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −11.7123 + 20.2863i −0.491004 + 0.850445i −0.999946 0.0103562i $$-0.996703\pi$$
0.508942 + 0.860801i $$0.330037\pi$$
$$570$$ 0 0
$$571$$ −9.91580 17.1747i −0.414963 0.718738i 0.580461 0.814288i $$-0.302872\pi$$
−0.995425 + 0.0955501i $$0.969539\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −29.8462 −1.24467
$$576$$ 0 0
$$577$$ 15.2800 + 26.4658i 0.636116 + 1.10178i 0.986278 + 0.165095i $$0.0527932\pi$$
−0.350162 + 0.936689i $$0.613873\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −11.3158 13.3852i −0.469459 0.555312i
$$582$$ 0 0
$$583$$ 13.5596 23.4859i 0.561582 0.972688i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 4.37643 0.180635 0.0903174 0.995913i $$-0.471212\pi$$
0.0903174 + 0.995913i $$0.471212\pi$$
$$588$$ 0 0
$$589$$ −65.2150 −2.68714
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 22.2762 38.5835i 0.914773 1.58443i 0.107539 0.994201i $$-0.465703\pi$$
0.807234 0.590232i $$-0.200964\pi$$
$$594$$ 0 0
$$595$$ 0.0699872 + 0.0827862i 0.00286920 + 0.00339390i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 6.85577 + 11.8745i 0.280119 + 0.485181i 0.971414 0.237392i $$-0.0762926\pi$$
−0.691295 + 0.722573i $$0.742959\pi$$
$$600$$ 0 0
$$601$$ −2.21373 −0.0902997 −0.0451499 0.998980i $$-0.514377\pi$$
−0.0451499 + 0.998980i $$0.514377\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −0.0456641 0.0790925i −0.00185651 0.00321557i
$$606$$ 0 0
$$607$$ 1.58980 2.75361i 0.0645280 0.111766i −0.831957 0.554841i $$-0.812779\pi$$
0.896484 + 0.443075i $$0.146113\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −6.16471 + 10.6776i −0.249398 + 0.431969i
$$612$$ 0 0
$$613$$ −6.15827 10.6664i −0.248730 0.430814i 0.714443 0.699693i $$-0.246680\pi$$
−0.963174 + 0.268880i $$0.913347\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 45.9405 1.84949 0.924747 0.380583i $$-0.124277\pi$$
0.924747 + 0.380583i $$0.124277\pi$$
$$618$$ 0 0
$$619$$ 6.79648 + 11.7718i 0.273174 + 0.473151i 0.969673 0.244407i $$-0.0785933\pi$$
−0.696499 + 0.717558i $$0.745260\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −11.1665 + 2.01139i −0.447375 + 0.0805848i
$$624$$ 0 0
$$625$$ −12.4937 + 21.6398i −0.499749 + 0.865590i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −2.08763 −0.0832393
$$630$$ 0 0
$$631$$ 0.682615 0.0271745 0.0135872 0.999908i $$-0.495675\pi$$
0.0135872 + 0.999908i $$0.495675\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0.0183941 0.0318596i 0.000729949 0.00126431i
$$636$$ 0 0
$$637$$ 3.46044 20.5076i 0.137108 0.812540i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −23.7325 41.1059i −0.937378 1.62359i −0.770337 0.637637i $$-0.779912\pi$$
−0.167042 0.985950i $$-0.553421\pi$$
$$642$$ 0 0
$$643$$ 34.4928 1.36026 0.680132 0.733090i $$-0.261923\pi$$
0.680132 + 0.733090i $$0.261923\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 12.6587 + 21.9255i 0.497665 + 0.861980i 0.999996 0.00269463i $$-0.000857729\pi$$
−0.502332 + 0.864675i $$0.667524\pi$$
$$648$$ 0 0
$$649$$ −26.0754 + 45.1639i −1.02355 + 1.77284i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 4.19122 7.25941i 0.164015 0.284083i −0.772290 0.635270i $$-0.780889\pi$$
0.936305 + 0.351188i $$0.114222\pi$$
$$654$$ 0 0
$$655$$ −0.240710 0.416922i −0.00940531 0.0162905i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −19.4114 −0.756160 −0.378080 0.925773i $$-0.623416\pi$$
−0.378080 + 0.925773i $$0.623416\pi$$
$$660$$ 0 0
$$661$$ 5.39833 + 9.35019i 0.209971 + 0.363680i 0.951705 0.307014i $$-0.0993298\pi$$
−0.741734 + 0.670694i $$0.765996\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −0.197574 + 0.549115i −0.00766158 + 0.0212938i
$$666$$ 0 0
$$667$$ −29.8487 + 51.6994i −1.15574 + 2.00181i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 42.2782 1.63213
$$672$$ 0 0
$$673$$ −5.07074 −0.195463 −0.0977314 0.995213i $$-0.531159\pi$$
−0.0977314 + 0.995213i $$0.531159\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 18.2737 31.6511i 0.702317 1.21645i −0.265334 0.964157i $$-0.585482\pi$$
0.967651 0.252292i $$-0.0811844\pi$$
$$678$$ 0 0
$$679$$ 11.5717 + 13.6879i 0.444082 + 0.525295i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 5.34590 + 9.25937i 0.204555 + 0.354300i 0.949991 0.312278i $$-0.101092\pi$$
−0.745436 + 0.666577i $$0.767759\pi$$
$$684$$ 0 0
$$685$$ −0.141484 −0.00540583
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −10.7073 18.5455i −0.407915 0.706529i
$$690$$ 0 0
$$691$$ −11.4686 + 19.8643i −0.436288 + 0.755673i −0.997400 0.0720673i $$-0.977040\pi$$
0.561112 + 0.827740i $$0.310374\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0.124577 0.215774i 0.00472549 0.00818478i
$$696$$ 0 0
$$697$$ −3.10669 5.38094i −0.117674 0.203818i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −47.9789 −1.81214 −0.906069 0.423129i $$-0.860932\pi$$
−0.906069 + 0.423129i $$0.860932\pi$$
$$702$$ 0 0
$$703$$ −5.61915 9.73265i −0.211930 0.367074i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 6.04232 16.7934i 0.227245 0.631579i
$$708$$ 0 0
$$709$$ −10.3095 + 17.8566i −0.387183 + 0.670620i −0.992069 0.125692i $$-0.959885\pi$$
0.604887 + 0.796312i $$0.293218\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −51.0694 −1.91256
$$714$$ 0 0
$$715$$ −0.323419 −0.0120952
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −2.59498 + 4.49464i −0.0967765 + 0.167622i −0.910349 0.413842i $$-0.864187\pi$$
0.813572 + 0.581464i $$0.197520\pi$$
$$720$$ 0 0
$$721$$ 7.19541 1.29609i 0.267971 0.0482690i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 24.9937 + 43.2904i 0.928244 + 1.60776i
$$726$$ 0 0
$$727$$ −39.9339 −1.48107 −0.740534 0.672019i $$-0.765427\pi$$
−0.740534 + 0.672019i $$0.765427\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 2.66430 + 4.61469i 0.0985425 + 0.170681i
$$732$$ 0 0
$$733$$ −24.6661 + 42.7229i −0.911062 + 1.57800i −0.0984942 + 0.995138i $$0.531403\pi$$
−0.812567 + 0.582867i $$0.801931\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −10.4502 + 18.1002i −0.384937 + 0.666730i
$$738$$ 0 0
$$739$$ −16.5576 28.6786i −0.609081 1.05496i −0.991392 0.130926i $$-0.958205\pi$$
0.382311 0.924034i $$-0.375128\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 23.4157 0.859040 0.429520 0.903057i $$-0.358683\pi$$
0.429520 + 0.903057i $$0.358683\pi$$
$$744$$ 0 0
$$745$$ −0.143477 0.248510i −0.00525660 0.00910470i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −46.3554 + 8.34991i −1.69379 + 0.305099i
$$750$$ 0 0
$$751$$ −9.41364 + 16.3049i −0.343508 + 0.594974i −0.985082 0.172088i $$-0.944949\pi$$
0.641573 + 0.767062i $$0.278282\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0.274100 0.00997551
$$756$$ 0 0
$$757$$ 27.0156 0.981897 0.490949 0.871188i $$-0.336650\pi$$
0.490949 + 0.871188i $$0.336650\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 9.64356 16.7031i 0.349579 0.605488i −0.636596 0.771198i $$-0.719658\pi$$
0.986175 + 0.165709i $$0.0529913\pi$$
$$762$$ 0 0
$$763$$ −9.70300 + 26.9675i −0.351272 + 0.976288i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 20.5903 + 35.6635i 0.743473 + 1.28773i
$$768$$ 0 0
$$769$$ −3.26639 −0.117789 −0.0588946 0.998264i $$-0.518758\pi$$
−0.0588946 + 0.998264i $$0.518758\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 10.9963 + 19.0462i 0.395510 + 0.685044i 0.993166 0.116709i $$-0.0372345\pi$$
−0.597656 + 0.801753i $$0.703901\pi$$
$$774$$ 0 0
$$775$$ −21.3814 + 37.0337i −0.768044 + 1.33029i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 16.7242 28.9671i 0.599205 1.03785i
$$780$$ 0 0
$$781$$ 21.7589 + 37.6875i 0.778593 + 1.34856i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −0.337773 −0.0120556
$$786$$ 0 0
$$787$$ −4.64724 8.04926i −0.165656 0.286925i 0.771232 0.636554i $$-0.219641\pi$$
−0.936888 + 0.349629i $$0.886308\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −1.50160 1.77621i −0.0533909 0.0631548i
$$792$$ 0 0
$$793$$ 16.6924 28.9121i 0.592764 1.02670i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 28.4137 1.00647 0.503233 0.864151i $$-0.332144\pi$$
0.503233 + 0.864151i $$0.332144\pi$$
$$798$$ 0 0
$$799$$ 5.87708 0.207916
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 8.19925 14.2015i 0.289345 0.501161i
$$804$$ 0 0
$$805$$ −0.154718 + 0.430008i −0.00545311 + 0.0151558i