# Properties

 Label 3024.2.q.l.2881.2 Level $3024$ Weight $2$ Character 3024.2881 Analytic conductor $24.147$ Analytic rank $0$ Dimension $22$ CM no Inner twists $2$

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$3024 = 2^{4} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3024.q (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$24.1467615712$$ Analytic rank: $$0$$ Dimension: $$22$$ Relative dimension: $$11$$ over $$\Q(\zeta_{3})$$ Twist minimal: no (minimal twist has level 504) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 2881.2 Character $$\chi$$ $$=$$ 3024.2881 Dual form 3024.2.q.l.2305.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.89970 + 3.29038i) q^{5} +(0.841809 + 2.50826i) q^{7} +O(q^{10})$$ $$q+(-1.89970 + 3.29038i) q^{5} +(0.841809 + 2.50826i) q^{7} +(-2.25706 - 3.90934i) q^{11} +(0.588451 + 1.01923i) q^{13} +(2.95973 - 5.12641i) q^{17} +(-2.55676 - 4.42844i) q^{19} +(2.09082 - 3.62140i) q^{23} +(-4.71772 - 8.17134i) q^{25} +(-2.11164 + 3.65747i) q^{29} +6.24283 q^{31} +(-9.85230 - 1.99507i) q^{35} +(-3.87179 - 6.70614i) q^{37} +(-0.754693 - 1.30717i) q^{41} +(5.01709 - 8.68986i) q^{43} -2.23665 q^{47} +(-5.58272 + 4.22295i) q^{49} +(-6.49368 + 11.2474i) q^{53} +17.1510 q^{55} +12.3922 q^{59} +1.45834 q^{61} -4.47152 q^{65} -1.62638 q^{67} +8.48517 q^{71} +(3.72984 - 6.46027i) q^{73} +(7.90563 - 8.95221i) q^{77} +1.84185 q^{79} +(-0.307606 + 0.532789i) q^{83} +(11.2452 + 19.4773i) q^{85} +(1.25572 + 2.17496i) q^{89} +(-2.06112 + 2.33398i) q^{91} +19.4283 q^{95} +(2.36751 - 4.10064i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$22q - q^{5} - 5q^{7} + O(q^{10})$$ $$22q - q^{5} - 5q^{7} + 3q^{11} + 7q^{13} + q^{17} - 13q^{19} - 22q^{25} + 7q^{29} + 12q^{31} + 2q^{35} + 6q^{37} - 4q^{41} - 2q^{43} - 34q^{47} - 25q^{49} - q^{53} - 2q^{55} + 42q^{59} - 62q^{61} - 6q^{65} - 52q^{67} - 32q^{71} + 17q^{73} + q^{77} - 32q^{79} - 36q^{83} + 28q^{85} + 2q^{89} - 15q^{91} + 48q^{95} + 19q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$$.

 $$n$$ $$757$$ $$785$$ $$1135$$ $$2593$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$5$$ −1.89970 + 3.29038i −0.849572 + 1.47150i 0.0320189 + 0.999487i $$0.489806\pi$$
−0.881591 + 0.472014i $$0.843527\pi$$
$$6$$ 0 0
$$7$$ 0.841809 + 2.50826i 0.318174 + 0.948032i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −2.25706 3.90934i −0.680529 1.17871i −0.974820 0.222995i $$-0.928417\pi$$
0.294290 0.955716i $$-0.404917\pi$$
$$12$$ 0 0
$$13$$ 0.588451 + 1.01923i 0.163207 + 0.282683i 0.936017 0.351955i $$-0.114483\pi$$
−0.772810 + 0.634637i $$0.781150\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 2.95973 5.12641i 0.717841 1.24334i −0.244012 0.969772i $$-0.578464\pi$$
0.961853 0.273565i $$-0.0882029\pi$$
$$18$$ 0 0
$$19$$ −2.55676 4.42844i −0.586562 1.01595i −0.994679 0.103025i $$-0.967148\pi$$
0.408117 0.912930i $$-0.366185\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 2.09082 3.62140i 0.435966 0.755115i −0.561408 0.827539i $$-0.689740\pi$$
0.997374 + 0.0724243i $$0.0230736\pi$$
$$24$$ 0 0
$$25$$ −4.71772 8.17134i −0.943545 1.63427i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −2.11164 + 3.65747i −0.392122 + 0.679175i −0.992729 0.120369i $$-0.961592\pi$$
0.600607 + 0.799544i $$0.294925\pi$$
$$30$$ 0 0
$$31$$ 6.24283 1.12124 0.560622 0.828072i $$-0.310562\pi$$
0.560622 + 0.828072i $$0.310562\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −9.85230 1.99507i −1.66534 0.337229i
$$36$$ 0 0
$$37$$ −3.87179 6.70614i −0.636519 1.10248i −0.986191 0.165611i $$-0.947040\pi$$
0.349672 0.936872i $$-0.386293\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −0.754693 1.30717i −0.117863 0.204145i 0.801057 0.598587i $$-0.204271\pi$$
−0.918921 + 0.394442i $$0.870938\pi$$
$$42$$ 0 0
$$43$$ 5.01709 8.68986i 0.765099 1.32519i −0.175095 0.984552i $$-0.556023\pi$$
0.940194 0.340639i $$-0.110643\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −2.23665 −0.326248 −0.163124 0.986606i $$-0.552157\pi$$
−0.163124 + 0.986606i $$0.552157\pi$$
$$48$$ 0 0
$$49$$ −5.58272 + 4.22295i −0.797531 + 0.603278i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −6.49368 + 11.2474i −0.891975 + 1.54495i −0.0544716 + 0.998515i $$0.517347\pi$$
−0.837504 + 0.546431i $$0.815986\pi$$
$$54$$ 0 0
$$55$$ 17.1510 2.31263
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 12.3922 1.61332 0.806662 0.591013i $$-0.201272\pi$$
0.806662 + 0.591013i $$0.201272\pi$$
$$60$$ 0 0
$$61$$ 1.45834 0.186722 0.0933608 0.995632i $$-0.470239\pi$$
0.0933608 + 0.995632i $$0.470239\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −4.47152 −0.554624
$$66$$ 0 0
$$67$$ −1.62638 −0.198694 −0.0993472 0.995053i $$-0.531675\pi$$
−0.0993472 + 0.995053i $$0.531675\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 8.48517 1.00700 0.503502 0.863994i $$-0.332045\pi$$
0.503502 + 0.863994i $$0.332045\pi$$
$$72$$ 0 0
$$73$$ 3.72984 6.46027i 0.436544 0.756117i −0.560876 0.827900i $$-0.689535\pi$$
0.997420 + 0.0717827i $$0.0228688\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 7.90563 8.95221i 0.900930 1.02020i
$$78$$ 0 0
$$79$$ 1.84185 0.207224 0.103612 0.994618i $$-0.466960\pi$$
0.103612 + 0.994618i $$0.466960\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −0.307606 + 0.532789i −0.0337641 + 0.0584812i −0.882414 0.470474i $$-0.844083\pi$$
0.848650 + 0.528956i $$0.177416\pi$$
$$84$$ 0 0
$$85$$ 11.2452 + 19.4773i 1.21972 + 2.11261i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 1.25572 + 2.17496i 0.133106 + 0.230546i 0.924872 0.380278i $$-0.124172\pi$$
−0.791767 + 0.610824i $$0.790838\pi$$
$$90$$ 0 0
$$91$$ −2.06112 + 2.33398i −0.216064 + 0.244668i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 19.4283 1.99330
$$96$$ 0 0
$$97$$ 2.36751 4.10064i 0.240384 0.416357i −0.720440 0.693517i $$-0.756060\pi$$
0.960824 + 0.277160i $$0.0893934\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −5.71081 9.89141i −0.568247 0.984232i −0.996739 0.0806872i $$-0.974289\pi$$
0.428493 0.903545i $$-0.359045\pi$$
$$102$$ 0 0
$$103$$ −3.18752 + 5.52095i −0.314076 + 0.543996i −0.979241 0.202701i $$-0.935028\pi$$
0.665165 + 0.746697i $$0.268361\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 1.11999 + 1.93988i 0.108274 + 0.187536i 0.915071 0.403293i $$-0.132134\pi$$
−0.806797 + 0.590828i $$0.798801\pi$$
$$108$$ 0 0
$$109$$ −2.73089 + 4.73005i −0.261572 + 0.453056i −0.966660 0.256064i $$-0.917574\pi$$
0.705088 + 0.709120i $$0.250908\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 4.45456 + 7.71553i 0.419050 + 0.725816i 0.995844 0.0910734i $$-0.0290298\pi$$
−0.576794 + 0.816890i $$0.695696\pi$$
$$114$$ 0 0
$$115$$ 7.94386 + 13.7592i 0.740768 + 1.28305i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 15.3499 + 3.10832i 1.40712 + 0.284939i
$$120$$ 0 0
$$121$$ −4.68864 + 8.12096i −0.426240 + 0.738269i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 16.8520 1.50729
$$126$$ 0 0
$$127$$ −0.434918 −0.0385927 −0.0192964 0.999814i $$-0.506143\pi$$
−0.0192964 + 0.999814i $$0.506143\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 2.67633 4.63553i 0.233832 0.405009i −0.725101 0.688643i $$-0.758207\pi$$
0.958933 + 0.283634i $$0.0915402\pi$$
$$132$$ 0 0
$$133$$ 8.95537 10.1409i 0.776529 0.879329i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 2.95121 + 5.11165i 0.252139 + 0.436718i 0.964115 0.265487i $$-0.0855326\pi$$
−0.711976 + 0.702204i $$0.752199\pi$$
$$138$$ 0 0
$$139$$ −4.33649 7.51102i −0.367816 0.637077i 0.621407 0.783488i $$-0.286561\pi$$
−0.989224 + 0.146411i $$0.953228\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 2.65634 4.60091i 0.222134 0.384747i
$$144$$ 0 0
$$145$$ −8.02297 13.8962i −0.666271 1.15402i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −5.38860 + 9.33333i −0.441451 + 0.764616i −0.997797 0.0663346i $$-0.978870\pi$$
0.556346 + 0.830951i $$0.312203\pi$$
$$150$$ 0 0
$$151$$ −8.41310 14.5719i −0.684648 1.18585i −0.973547 0.228486i $$-0.926622\pi$$
0.288899 0.957360i $$-0.406711\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −11.8595 + 20.5413i −0.952578 + 1.64991i
$$156$$ 0 0
$$157$$ 8.96136 0.715194 0.357597 0.933876i $$-0.383596\pi$$
0.357597 + 0.933876i $$0.383596\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 10.8435 + 2.19578i 0.854586 + 0.173052i
$$162$$ 0 0
$$163$$ 3.71319 + 6.43144i 0.290840 + 0.503749i 0.974009 0.226511i $$-0.0727320\pi$$
−0.683169 + 0.730261i $$0.739399\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −5.13764 8.89866i −0.397563 0.688599i 0.595862 0.803087i $$-0.296811\pi$$
−0.993425 + 0.114488i $$0.963477\pi$$
$$168$$ 0 0
$$169$$ 5.80745 10.0588i 0.446727 0.773754i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 10.2099 0.776246 0.388123 0.921608i $$-0.373124\pi$$
0.388123 + 0.921608i $$0.373124\pi$$
$$174$$ 0 0
$$175$$ 16.5244 18.7120i 1.24913 1.41449i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 9.62985 16.6794i 0.719769 1.24668i −0.241323 0.970445i $$-0.577581\pi$$
0.961091 0.276231i $$-0.0890854\pi$$
$$180$$ 0 0
$$181$$ −1.39163 −0.103439 −0.0517195 0.998662i $$-0.516470\pi$$
−0.0517195 + 0.998662i $$0.516470\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 29.4210 2.16307
$$186$$ 0 0
$$187$$ −26.7212 −1.95405
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −2.71483 −0.196438 −0.0982190 0.995165i $$-0.531315\pi$$
−0.0982190 + 0.995165i $$0.531315\pi$$
$$192$$ 0 0
$$193$$ 1.84169 0.132568 0.0662839 0.997801i $$-0.478886\pi$$
0.0662839 + 0.997801i $$0.478886\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −21.9198 −1.56172 −0.780860 0.624706i $$-0.785219\pi$$
−0.780860 + 0.624706i $$0.785219\pi$$
$$198$$ 0 0
$$199$$ 0.726101 1.25764i 0.0514719 0.0891520i −0.839141 0.543913i $$-0.816942\pi$$
0.890613 + 0.454761i $$0.150275\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −10.9515 2.21765i −0.768643 0.155649i
$$204$$ 0 0
$$205$$ 5.73476 0.400533
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −11.5415 + 19.9905i −0.798344 + 1.38277i
$$210$$ 0 0
$$211$$ −0.771347 1.33601i −0.0531017 0.0919749i 0.838253 0.545282i $$-0.183577\pi$$
−0.891354 + 0.453307i $$0.850244\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 19.0619 + 33.0162i 1.30001 + 2.25169i
$$216$$ 0 0
$$217$$ 5.25527 + 15.6586i 0.356751 + 1.06298i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 6.96663 0.468626
$$222$$ 0 0
$$223$$ 0.346045 0.599368i 0.0231729 0.0401366i −0.854206 0.519934i $$-0.825957\pi$$
0.877379 + 0.479797i $$0.159290\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −9.20797 15.9487i −0.611155 1.05855i −0.991046 0.133520i $$-0.957372\pi$$
0.379892 0.925031i $$-0.375961\pi$$
$$228$$ 0 0
$$229$$ 2.69696 4.67127i 0.178220 0.308686i −0.763051 0.646338i $$-0.776299\pi$$
0.941271 + 0.337652i $$0.109633\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 8.27352 + 14.3302i 0.542016 + 0.938800i 0.998788 + 0.0492161i $$0.0156723\pi$$
−0.456772 + 0.889584i $$0.650994\pi$$
$$234$$ 0 0
$$235$$ 4.24896 7.35941i 0.277171 0.480075i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −1.56724 2.71454i −0.101376 0.175589i 0.810876 0.585219i $$-0.198991\pi$$
−0.912252 + 0.409630i $$0.865658\pi$$
$$240$$ 0 0
$$241$$ 8.23730 + 14.2674i 0.530611 + 0.919046i 0.999362 + 0.0357151i $$0.0113709\pi$$
−0.468751 + 0.883330i $$0.655296\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −3.28960 26.3916i −0.210165 1.68610i
$$246$$ 0 0
$$247$$ 3.00906 5.21184i 0.191462 0.331621i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 12.8939 0.813858 0.406929 0.913460i $$-0.366600\pi$$
0.406929 + 0.913460i $$0.366600\pi$$
$$252$$ 0 0
$$253$$ −18.8764 −1.18675
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 10.3045 17.8478i 0.642774 1.11332i −0.342036 0.939687i $$-0.611117\pi$$
0.984811 0.173631i $$-0.0555501\pi$$
$$258$$ 0 0
$$259$$ 13.5614 15.3567i 0.842666 0.954222i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −4.56616 7.90883i −0.281562 0.487679i 0.690208 0.723611i $$-0.257519\pi$$
−0.971770 + 0.235932i $$0.924186\pi$$
$$264$$ 0 0
$$265$$ −24.6721 42.7333i −1.51559 2.62509i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 12.4387 21.5445i 0.758401 1.31359i −0.185265 0.982689i $$-0.559314\pi$$
0.943666 0.330900i $$-0.107352\pi$$
$$270$$ 0 0
$$271$$ −5.70814 9.88679i −0.346745 0.600580i 0.638924 0.769270i $$-0.279380\pi$$
−0.985669 + 0.168690i $$0.946046\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −21.2964 + 36.8864i −1.28422 + 2.22433i
$$276$$ 0 0
$$277$$ −15.4938 26.8360i −0.930932 1.61242i −0.781732 0.623615i $$-0.785663\pi$$
−0.149200 0.988807i $$-0.547670\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 7.40910 12.8329i 0.441990 0.765549i −0.555847 0.831285i $$-0.687606\pi$$
0.997837 + 0.0657354i $$0.0209393\pi$$
$$282$$ 0 0
$$283$$ −25.7431 −1.53027 −0.765134 0.643872i $$-0.777327\pi$$
−0.765134 + 0.643872i $$0.777327\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 2.64340 2.99335i 0.156035 0.176692i
$$288$$ 0 0
$$289$$ −9.02006 15.6232i −0.530592 0.919012i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −8.41185 14.5697i −0.491425 0.851174i 0.508526 0.861047i $$-0.330191\pi$$
−0.999951 + 0.00987288i $$0.996857\pi$$
$$294$$ 0 0
$$295$$ −23.5414 + 40.7749i −1.37063 + 2.37401i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 4.92137 0.284610
$$300$$ 0 0
$$301$$ 26.0198 + 5.26896i 1.49976 + 0.303698i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −2.77041 + 4.79849i −0.158633 + 0.274761i
$$306$$ 0 0
$$307$$ 28.2972 1.61501 0.807504 0.589862i $$-0.200818\pi$$
0.807504 + 0.589862i $$0.200818\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 19.8695 1.12670 0.563349 0.826219i $$-0.309513\pi$$
0.563349 + 0.826219i $$0.309513\pi$$
$$312$$ 0 0
$$313$$ −18.2859 −1.03358 −0.516789 0.856113i $$-0.672873\pi$$
−0.516789 + 0.856113i $$0.672873\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −13.9480 −0.783399 −0.391700 0.920093i $$-0.628113\pi$$
−0.391700 + 0.920093i $$0.628113\pi$$
$$318$$ 0 0
$$319$$ 19.0644 1.06740
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −30.2694 −1.68423
$$324$$ 0 0
$$325$$ 5.55230 9.61686i 0.307986 0.533447i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −1.88283 5.61009i −0.103804 0.309294i
$$330$$ 0 0
$$331$$ −20.8399 −1.14547 −0.572733 0.819742i $$-0.694117\pi$$
−0.572733 + 0.819742i $$0.694117\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 3.08964 5.35142i 0.168805 0.292379i
$$336$$ 0 0
$$337$$ 15.4376 + 26.7387i 0.840939 + 1.45655i 0.889101 + 0.457710i $$0.151330\pi$$
−0.0481619 + 0.998840i $$0.515336\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −14.0904 24.4054i −0.763040 1.32162i
$$342$$ 0 0
$$343$$ −15.2918 10.4480i −0.825681 0.564138i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −10.2685 −0.551244 −0.275622 0.961266i $$-0.588884\pi$$
−0.275622 + 0.961266i $$0.588884\pi$$
$$348$$ 0 0
$$349$$ 4.61262 7.98930i 0.246908 0.427657i −0.715758 0.698348i $$-0.753919\pi$$
0.962666 + 0.270691i $$0.0872521\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 4.08660 + 7.07820i 0.217508 + 0.376735i 0.954045 0.299662i $$-0.0968739\pi$$
−0.736538 + 0.676397i $$0.763541\pi$$
$$354$$ 0 0
$$355$$ −16.1193 + 27.9194i −0.855522 + 1.48181i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 6.35957 + 11.0151i 0.335645 + 0.581355i 0.983609 0.180317i $$-0.0577123\pi$$
−0.647963 + 0.761672i $$0.724379\pi$$
$$360$$ 0 0
$$361$$ −3.57407 + 6.19047i −0.188109 + 0.325814i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 14.1711 + 24.5452i 0.741752 + 1.28475i
$$366$$ 0 0
$$367$$ −10.9431 18.9540i −0.571224 0.989388i −0.996441 0.0842970i $$-0.973136\pi$$
0.425217 0.905091i $$-0.360198\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −33.6778 6.81968i −1.74846 0.354060i
$$372$$ 0 0
$$373$$ 6.73126 11.6589i 0.348531 0.603674i −0.637457 0.770486i $$-0.720014\pi$$
0.985989 + 0.166811i $$0.0533471\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −4.97038 −0.255988
$$378$$ 0 0
$$379$$ 11.2180 0.576231 0.288115 0.957596i $$-0.406971\pi$$
0.288115 + 0.957596i $$0.406971\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 4.00330 6.93392i 0.204559 0.354307i −0.745433 0.666581i $$-0.767757\pi$$
0.949992 + 0.312274i $$0.101091\pi$$
$$384$$ 0 0
$$385$$ 14.4378 + 43.0190i 0.735819 + 2.19245i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 14.3931 + 24.9296i 0.729759 + 1.26398i 0.956985 + 0.290137i $$0.0937009\pi$$
−0.227226 + 0.973842i $$0.572966\pi$$
$$390$$ 0 0
$$391$$ −12.3765 21.4368i −0.625908 1.08410i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −3.49897 + 6.06039i −0.176052 + 0.304931i
$$396$$ 0 0
$$397$$ 10.8138 + 18.7301i 0.542731 + 0.940037i 0.998746 + 0.0500651i $$0.0159429\pi$$
−0.456015 + 0.889972i $$0.650724\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 13.4966 23.3768i 0.673987 1.16738i −0.302777 0.953062i $$-0.597914\pi$$
0.976764 0.214318i $$-0.0687530\pi$$
$$402$$ 0 0
$$403$$ 3.67360 + 6.36285i 0.182995 + 0.316956i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −17.4777 + 30.2723i −0.866339 + 1.50054i
$$408$$ 0 0
$$409$$ −20.9473 −1.03578 −0.517889 0.855448i $$-0.673282\pi$$
−0.517889 + 0.855448i $$0.673282\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 10.4318 + 31.0828i 0.513317 + 1.52948i
$$414$$ 0 0
$$415$$ −1.16872 2.02428i −0.0573701 0.0993680i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 6.91450 + 11.9763i 0.337795 + 0.585079i 0.984018 0.178070i $$-0.0569855\pi$$
−0.646222 + 0.763149i $$0.723652\pi$$
$$420$$ 0 0
$$421$$ −6.86872 + 11.8970i −0.334761 + 0.579823i −0.983439 0.181240i $$-0.941989\pi$$
0.648678 + 0.761063i $$0.275322\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −55.8529 −2.70926
$$426$$ 0 0
$$427$$ 1.22764 + 3.65790i 0.0594099 + 0.177018i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −9.20392 + 15.9417i −0.443337 + 0.767882i −0.997935 0.0642362i $$-0.979539\pi$$
0.554598 + 0.832119i $$0.312872\pi$$
$$432$$ 0 0
$$433$$ 24.3558 1.17047 0.585233 0.810865i $$-0.301003\pi$$
0.585233 + 0.810865i $$0.301003\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −21.3829 −1.02288
$$438$$ 0 0
$$439$$ 5.83655 0.278564 0.139282 0.990253i $$-0.455521\pi$$
0.139282 + 0.990253i $$0.455521\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 14.8400 0.705071 0.352536 0.935798i $$-0.385320\pi$$
0.352536 + 0.935798i $$0.385320\pi$$
$$444$$ 0 0
$$445$$ −9.54194 −0.452331
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 4.26289 0.201178 0.100589 0.994928i $$-0.467927\pi$$
0.100589 + 0.994928i $$0.467927\pi$$
$$450$$ 0 0
$$451$$ −3.40677 + 5.90070i −0.160419 + 0.277853i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −3.76416 11.2157i −0.176467 0.525801i
$$456$$ 0 0
$$457$$ 39.7459 1.85924 0.929618 0.368525i $$-0.120137\pi$$
0.929618 + 0.368525i $$0.120137\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 2.68671 4.65353i 0.125133 0.216736i −0.796652 0.604438i $$-0.793398\pi$$
0.921785 + 0.387702i $$0.126731\pi$$
$$462$$ 0 0
$$463$$ −19.8205 34.3301i −0.921136 1.59545i −0.797661 0.603106i $$-0.793930\pi$$
−0.123474 0.992348i $$-0.539404\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 9.43069 + 16.3344i 0.436400 + 0.755867i 0.997409 0.0719427i $$-0.0229199\pi$$
−0.561009 + 0.827810i $$0.689587\pi$$
$$468$$ 0 0
$$469$$ −1.36910 4.07939i −0.0632193 0.188369i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −45.2955 −2.08269
$$474$$ 0 0
$$475$$ −24.1242 + 41.7843i −1.10689 + 1.91720i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −9.50287 16.4595i −0.434197 0.752052i 0.563032 0.826435i $$-0.309635\pi$$
−0.997230 + 0.0743830i $$0.976301\pi$$
$$480$$ 0 0
$$481$$ 4.55672 7.89247i 0.207768 0.359866i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 8.99511 + 15.5800i 0.408447 + 0.707451i
$$486$$ 0 0
$$487$$ 5.21626 9.03482i 0.236371 0.409407i −0.723299 0.690535i $$-0.757375\pi$$
0.959670 + 0.281128i $$0.0907085\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −14.3311 24.8221i −0.646752 1.12021i −0.983894 0.178753i $$-0.942794\pi$$
0.337142 0.941454i $$-0.390540\pi$$
$$492$$ 0 0
$$493$$ 12.4998 + 21.6503i 0.562962 + 0.975079i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 7.14289 + 21.2830i 0.320402 + 0.954673i
$$498$$ 0 0
$$499$$ −16.5396 + 28.6475i −0.740416 + 1.28244i 0.211890 + 0.977294i $$0.432038\pi$$
−0.952306 + 0.305145i $$0.901295\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −28.9523 −1.29092 −0.645460 0.763794i $$-0.723334\pi$$
−0.645460 + 0.763794i $$0.723334\pi$$
$$504$$ 0 0
$$505$$ 43.3953 1.93107
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 15.8820 27.5085i 0.703959 1.21929i −0.263107 0.964767i $$-0.584747\pi$$
0.967066 0.254526i $$-0.0819194\pi$$
$$510$$ 0 0
$$511$$ 19.3438 + 3.91709i 0.855721 + 0.173282i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −12.1107 20.9763i −0.533660 0.924327i
$$516$$ 0 0
$$517$$ 5.04825 + 8.74382i 0.222022 + 0.384553i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 2.87897 4.98652i 0.126130 0.218463i −0.796044 0.605239i $$-0.793078\pi$$
0.922174 + 0.386775i $$0.126411\pi$$
$$522$$ 0 0
$$523$$ 22.3123 + 38.6461i 0.975650 + 1.68987i 0.677774 + 0.735270i $$0.262945\pi$$
0.297875 + 0.954605i $$0.403722\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 18.4771 32.0033i 0.804876 1.39409i
$$528$$ 0 0
$$529$$ 2.75696 + 4.77520i 0.119868 + 0.207617i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0.888199 1.53841i 0.0384722 0.0666357i
$$534$$ 0 0
$$535$$ −8.51060 −0.367945
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 29.1095 + 12.2933i 1.25383 + 0.529510i
$$540$$ 0 0
$$541$$ 15.6719 + 27.1445i 0.673786 + 1.16703i 0.976822 + 0.214053i $$0.0686665\pi$$
−0.303036 + 0.952979i $$0.598000\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −10.3758 17.9713i −0.444449 0.769808i
$$546$$ 0 0
$$547$$ −1.37567 + 2.38273i −0.0588195 + 0.101878i −0.893936 0.448195i $$-0.852067\pi$$
0.835116 + 0.550073i $$0.185400\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 21.5959 0.920014
$$552$$ 0 0
$$553$$ 1.55049 + 4.61984i 0.0659334 + 0.196455i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −3.42197 + 5.92703i −0.144994 + 0.251136i −0.929371 0.369148i $$-0.879650\pi$$
0.784377 + 0.620284i $$0.212983\pi$$
$$558$$ 0 0
$$559$$ 11.8092 0.499478
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 15.1001 0.636395 0.318197 0.948025i $$-0.396923\pi$$
0.318197 + 0.948025i $$0.396923\pi$$
$$564$$ 0 0
$$565$$ −33.8494 −1.42405
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 27.5276 1.15402 0.577008 0.816738i $$-0.304220\pi$$
0.577008 + 0.816738i $$0.304220\pi$$
$$570$$ 0 0
$$571$$ 38.8755 1.62689 0.813444 0.581643i $$-0.197590\pi$$
0.813444 + 0.581643i $$0.197590\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −39.4556 −1.64541
$$576$$ 0 0
$$577$$ −9.84330 + 17.0491i −0.409782 + 0.709763i −0.994865 0.101210i $$-0.967729\pi$$
0.585083 + 0.810973i $$0.301062\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −1.59532 0.323049i −0.0661849 0.0134023i
$$582$$ 0 0
$$583$$ 58.6265 2.42806
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 3.14068 5.43982i 0.129630 0.224525i −0.793903 0.608044i $$-0.791954\pi$$
0.923533 + 0.383519i $$0.125288\pi$$
$$588$$ 0 0
$$589$$ −15.9614 27.6460i −0.657679 1.13913i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −7.79280 13.4975i −0.320012 0.554277i 0.660478 0.750845i $$-0.270354\pi$$
−0.980490 + 0.196568i $$0.937020\pi$$
$$594$$ 0 0
$$595$$ −39.3877 + 44.6021i −1.61474 + 1.82851i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 1.05557 0.0431292 0.0215646 0.999767i $$-0.493135\pi$$
0.0215646 + 0.999767i $$0.493135\pi$$
$$600$$ 0 0
$$601$$ −12.1622 + 21.0656i −0.496107 + 0.859283i −0.999990 0.00448941i $$-0.998571\pi$$
0.503883 + 0.863772i $$0.331904\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −17.8140 30.8548i −0.724243 1.25443i
$$606$$ 0 0
$$607$$ 2.16502 3.74993i 0.0878756 0.152205i −0.818737 0.574168i $$-0.805326\pi$$
0.906613 + 0.421963i $$0.138659\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −1.31616 2.27965i −0.0532460 0.0922247i
$$612$$ 0 0
$$613$$ −24.3556 + 42.1852i −0.983714 + 1.70384i −0.336196 + 0.941792i $$0.609140\pi$$
−0.647518 + 0.762050i $$0.724193\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −14.6366 25.3514i −0.589249 1.02061i −0.994331 0.106329i $$-0.966090\pi$$
0.405082 0.914280i $$-0.367243\pi$$
$$618$$ 0 0
$$619$$ −18.2381 31.5893i −0.733050 1.26968i −0.955573 0.294753i $$-0.904763\pi$$
0.222523 0.974927i $$-0.428571\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −4.39830 + 4.98056i −0.176214 + 0.199542i
$$624$$ 0 0
$$625$$ −8.42523 + 14.5929i −0.337009 + 0.583717i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −45.8379 −1.82768
$$630$$ 0 0
$$631$$ −0.501625 −0.0199694 −0.00998468 0.999950i $$-0.503178\pi$$
−0.00998468 + 0.999950i $$0.503178\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0.826214 1.43104i 0.0327873 0.0567893i
$$636$$ 0 0
$$637$$ −7.58929 3.20506i −0.300699 0.126989i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −17.5112 30.3303i −0.691651 1.19797i −0.971297 0.237871i $$-0.923551\pi$$
0.279646 0.960103i $$-0.409783\pi$$
$$642$$ 0 0
$$643$$ −7.29049 12.6275i −0.287509 0.497980i 0.685706 0.727879i $$-0.259494\pi$$
−0.973215 + 0.229899i $$0.926160\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −11.6503 + 20.1790i −0.458022 + 0.793318i −0.998856 0.0478116i $$-0.984775\pi$$
0.540834 + 0.841129i $$0.318109\pi$$
$$648$$ 0 0
$$649$$ −27.9699 48.4453i −1.09791 1.90164i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −4.26780 + 7.39204i −0.167012 + 0.289273i −0.937368 0.348341i $$-0.886745\pi$$
0.770356 + 0.637614i $$0.220078\pi$$
$$654$$ 0 0
$$655$$ 10.1684 + 17.6123i 0.397314 + 0.688168i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −1.81616 + 3.14568i −0.0707476 + 0.122538i −0.899229 0.437478i $$-0.855872\pi$$
0.828482 + 0.560016i $$0.189205\pi$$
$$660$$ 0 0
$$661$$ −31.0231 −1.20666 −0.603330 0.797492i $$-0.706160\pi$$
−0.603330 + 0.797492i $$0.706160\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 16.3549 + 48.7313i 0.634217 + 1.88972i
$$666$$ 0 0
$$667$$ 8.83011 + 15.2942i 0.341903 + 0.592194i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −3.29156 5.70116i −0.127069 0.220091i
$$672$$ 0 0
$$673$$ 0.291838 0.505478i 0.0112495 0.0194848i −0.860346 0.509711i $$-0.829752\pi$$
0.871595 + 0.490226i $$0.163086\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 33.7332 1.29647 0.648237 0.761439i $$-0.275507\pi$$
0.648237 + 0.761439i $$0.275507\pi$$
$$678$$ 0 0
$$679$$ 12.2785 + 2.48636i 0.471204 + 0.0954178i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −1.60312 + 2.77668i −0.0613417 + 0.106247i −0.895065 0.445935i $$-0.852871\pi$$
0.833724 + 0.552182i $$0.186205\pi$$
$$684$$ 0 0
$$685$$ −22.4257 −0.856841
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −15.2848 −0.582306
$$690$$ 0 0
$$691$$ 32.3674 1.23131 0.615657 0.788014i $$-0.288891\pi$$
0.615657 + 0.788014i $$0.288891\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 32.9521 1.24995
$$696$$ 0 0
$$697$$ −8.93476 −0.338428
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −21.2591 −0.802943 −0.401472 0.915871i $$-0.631501\pi$$
−0.401472 + 0.915871i $$0.631501\pi$$
$$702$$ 0 0
$$703$$ −19.7985 + 34.2920i −0.746715 + 1.29335i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 20.0028 22.6509i 0.752283 0.851873i
$$708$$ 0 0
$$709$$ 31.6544 1.18880 0.594402 0.804168i $$-0.297389\pi$$
0.594402 + 0.804168i $$0.297389\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 13.0526 22.6078i 0.488824 0.846669i
$$714$$ 0 0
$$715$$ 10.0925 + 17.4807i 0.377438 + 0.653741i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −14.9776 25.9420i −0.558571 0.967473i −0.997616 0.0690079i $$-0.978017\pi$$
0.439045 0.898465i $$-0.355317\pi$$
$$720$$ 0 0
$$721$$ −16.5313 3.34755i −0.615656 0.124669i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 39.8486 1.47994
$$726$$ 0 0
$$727$$ 13.6310 23.6095i 0.505544 0.875629i −0.494435 0.869215i $$-0.664625\pi$$
0.999979 0.00641398i $$-0.00204165\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −29.6985 51.4393i −1.09844 1.90255i
$$732$$ 0 0
$$733$$ 11.2717 19.5232i 0.416330 0.721105i −0.579237 0.815159i $$-0.696649\pi$$
0.995567 + 0.0940545i $$0.0299828\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 3.67085 + 6.35809i 0.135217 + 0.234203i
$$738$$ 0 0
$$739$$ 8.82742 15.2895i 0.324722 0.562435i −0.656734 0.754122i $$-0.728063\pi$$
0.981456 + 0.191687i $$0.0613960\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −3.31474 5.74130i −0.121606 0.210628i 0.798795 0.601603i $$-0.205471\pi$$
−0.920401 + 0.390975i $$0.872138\pi$$
$$744$$ 0 0
$$745$$ −20.4735 35.4611i −0.750089 1.29919i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −3.92291 + 4.44224i −0.143340 + 0.162316i
$$750$$ 0 0
$$751$$ 3.93721 6.81944i 0.143671 0.248845i −0.785206 0.619235i $$-0.787443\pi$$
0.928876 + 0.370390i $$0.120776\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 63.9295 2.32663
$$756$$ 0 0
$$757$$ −37.1503 −1.35025 −0.675125 0.737703i $$-0.735910\pi$$
−0.675125 + 0.737703i $$0.735910\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −16.2273 + 28.1065i −0.588238 + 1.01886i 0.406225 + 0.913773i $$0.366845\pi$$
−0.994463 + 0.105085i $$0.966488\pi$$
$$762$$ 0 0
$$763$$ −14.1631 2.86799i −0.512737 0.103828i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 7.29218 + 12.6304i 0.263305 + 0.456058i
$$768$$ 0 0
$$769$$ 11.4992 + 19.9172i 0.414671 + 0.718232i 0.995394 0.0958699i $$-0.0305633\pi$$
−0.580723 + 0.814101i $$0.697230\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −13.2117 + 22.8834i −0.475194 + 0.823059i −0.999596 0.0284109i $$-0.990955\pi$$
0.524403 + 0.851470i $$0.324289\pi$$
$$774$$ 0 0
$$775$$ −29.4519 51.0123i −1.05794 1.83241i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −3.85914 + 6.68423i −0.138268 + 0.239487i
$$780$$ 0 0
$$781$$ −19.1515 33.1714i −0.685296 1.18697i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −17.0239 + 29.4862i −0.607609 + 1.05241i
$$786$$ 0 0
$$787$$ 9.11300 0.324843 0.162422 0.986721i $$-0.448069\pi$$
0.162422 + 0.986721i $$0.448069\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −15.6027 + 17.6682i −0.554767 + 0.628209i
$$792$$ 0 0
$$793$$ 0.858162 + 1.48638i 0.0304742 + 0.0527829i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 27.5330 + 47.6886i 0.975270 + 1.68922i 0.679042 + 0.734099i $$0.262395\pi$$
0.296228 + 0.955117i $$0.404271\pi$$