# Properties

 Label 1152.2.w.a.1007.8 Level $1152$ Weight $2$ Character 1152.1007 Analytic conductor $9.199$ Analytic rank $0$ Dimension $32$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1152 = 2^{7} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1152.w (of order $$8$$, degree $$4$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.19876631285$$ Analytic rank: $$0$$ Dimension: $$32$$ Relative dimension: $$8$$ over $$\Q(\zeta_{8})$$ Twist minimal: no (minimal twist has level 288) Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

## Embedding invariants

 Embedding label 1007.8 Character $$\chi$$ $$=$$ 1152.1007 Dual form 1152.2.w.a.143.8

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.39555 + 3.36915i) q^{5} +(1.05755 + 1.05755i) q^{7} +O(q^{10})$$ $$q+(1.39555 + 3.36915i) q^{5} +(1.05755 + 1.05755i) q^{7} +(1.50977 + 3.64490i) q^{11} +(-2.23818 - 0.927086i) q^{13} +7.49610 q^{17} +(-0.818262 + 1.97546i) q^{19} +(-5.80392 - 5.80392i) q^{23} +(-5.86809 + 5.86809i) q^{25} +(-0.326633 - 0.135296i) q^{29} +1.71021i q^{31} +(-2.08718 + 5.03889i) q^{35} +(0.387384 - 0.160460i) q^{37} +(1.50401 - 1.50401i) q^{41} +(-7.40227 + 3.06612i) q^{43} +7.27404i q^{47} -4.76319i q^{49} +(-3.94866 + 1.63559i) q^{53} +(-10.1733 + 10.1733i) q^{55} +(12.7979 - 5.30105i) q^{59} +(-0.579943 + 1.40011i) q^{61} -8.83457i q^{65} +(7.96385 + 3.29874i) q^{67} +(4.75505 - 4.75505i) q^{71} +(-7.99854 - 7.99854i) q^{73} +(-2.25800 + 5.45130i) q^{77} -14.3967 q^{79} +(1.35250 + 0.560224i) q^{83} +(10.4612 + 25.2555i) q^{85} +(4.75638 + 4.75638i) q^{89} +(-1.38655 - 3.34742i) q^{91} -7.79754 q^{95} -1.28856 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$32 q + O(q^{10})$$ $$32 q - 8 q^{11} + 16 q^{29} + 24 q^{35} + 16 q^{53} + 32 q^{55} + 32 q^{59} + 32 q^{61} + 16 q^{67} + 16 q^{71} + 16 q^{77} + 32 q^{79} - 40 q^{83} + 48 q^{91} - 80 q^{95} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$641$$ $$901$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$

## 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
$$5$$ 1.39555 + 3.36915i 0.624108 + 1.50673i 0.846839 + 0.531850i $$0.178503\pi$$
−0.222731 + 0.974880i $$0.571497\pi$$
$$6$$ 0 0
$$7$$ 1.05755 + 1.05755i 0.399715 + 0.399715i 0.878133 0.478417i $$-0.158789\pi$$
−0.478417 + 0.878133i $$0.658789\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 1.50977 + 3.64490i 0.455211 + 1.09898i 0.970314 + 0.241849i $$0.0777539\pi$$
−0.515102 + 0.857129i $$0.672246\pi$$
$$12$$ 0 0
$$13$$ −2.23818 0.927086i −0.620761 0.257127i 0.0500610 0.998746i $$-0.484058\pi$$
−0.670822 + 0.741619i $$0.734058\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 7.49610 1.81807 0.909036 0.416717i $$-0.136820\pi$$
0.909036 + 0.416717i $$0.136820\pi$$
$$18$$ 0 0
$$19$$ −0.818262 + 1.97546i −0.187722 + 0.453201i −0.989520 0.144393i $$-0.953877\pi$$
0.801798 + 0.597595i $$0.203877\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −5.80392 5.80392i −1.21020 1.21020i −0.970960 0.239241i $$-0.923102\pi$$
−0.239241 0.970960i $$-0.576898\pi$$
$$24$$ 0 0
$$25$$ −5.86809 + 5.86809i −1.17362 + 1.17362i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −0.326633 0.135296i −0.0606542 0.0251238i 0.352150 0.935944i $$-0.385451\pi$$
−0.412804 + 0.910820i $$0.635451\pi$$
$$30$$ 0 0
$$31$$ 1.71021i 0.307163i 0.988136 + 0.153582i $$0.0490808\pi$$
−0.988136 + 0.153582i $$0.950919\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −2.08718 + 5.03889i −0.352797 + 0.851728i
$$36$$ 0 0
$$37$$ 0.387384 0.160460i 0.0636856 0.0263794i −0.350613 0.936520i $$-0.614027\pi$$
0.414299 + 0.910141i $$0.364027\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 1.50401 1.50401i 0.234887 0.234887i −0.579842 0.814729i $$-0.696886\pi$$
0.814729 + 0.579842i $$0.196886\pi$$
$$42$$ 0 0
$$43$$ −7.40227 + 3.06612i −1.12884 + 0.467579i −0.867385 0.497638i $$-0.834201\pi$$
−0.261450 + 0.965217i $$0.584201\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 7.27404i 1.06103i 0.847676 + 0.530514i $$0.178001\pi$$
−0.847676 + 0.530514i $$0.821999\pi$$
$$48$$ 0 0
$$49$$ 4.76319i 0.680455i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −3.94866 + 1.63559i −0.542390 + 0.224665i −0.637020 0.770847i $$-0.719833\pi$$
0.0946303 + 0.995512i $$0.469833\pi$$
$$54$$ 0 0
$$55$$ −10.1733 + 10.1733i −1.37176 + 1.37176i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 12.7979 5.30105i 1.66614 0.690138i 0.667619 0.744503i $$-0.267313\pi$$
0.998521 + 0.0543646i $$0.0173133\pi$$
$$60$$ 0 0
$$61$$ −0.579943 + 1.40011i −0.0742542 + 0.179265i −0.956648 0.291245i $$-0.905930\pi$$
0.882394 + 0.470511i $$0.155930\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 8.83457i 1.09579i
$$66$$ 0 0
$$67$$ 7.96385 + 3.29874i 0.972940 + 0.403005i 0.811806 0.583928i $$-0.198485\pi$$
0.161134 + 0.986933i $$0.448485\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 4.75505 4.75505i 0.564320 0.564320i −0.366211 0.930532i $$-0.619345\pi$$
0.930532 + 0.366211i $$0.119345\pi$$
$$72$$ 0 0
$$73$$ −7.99854 7.99854i −0.936158 0.936158i 0.0619229 0.998081i $$-0.480277\pi$$
−0.998081 + 0.0619229i $$0.980277\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −2.25800 + 5.45130i −0.257323 + 0.621233i
$$78$$ 0 0
$$79$$ −14.3967 −1.61975 −0.809877 0.586600i $$-0.800466\pi$$
−0.809877 + 0.586600i $$0.800466\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 1.35250 + 0.560224i 0.148456 + 0.0614926i 0.455674 0.890147i $$-0.349398\pi$$
−0.307218 + 0.951639i $$0.599398\pi$$
$$84$$ 0 0
$$85$$ 10.4612 + 25.2555i 1.13467 + 2.73934i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 4.75638 + 4.75638i 0.504176 + 0.504176i 0.912733 0.408557i $$-0.133968\pi$$
−0.408557 + 0.912733i $$0.633968\pi$$
$$90$$ 0 0
$$91$$ −1.38655 3.34742i −0.145350 0.350905i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −7.79754 −0.800011
$$96$$ 0 0
$$97$$ −1.28856 −0.130834 −0.0654168 0.997858i $$-0.520838\pi$$
−0.0654168 + 0.997858i $$0.520838\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 4.56084 + 11.0109i 0.453821 + 1.09562i 0.970858 + 0.239657i $$0.0770351\pi$$
−0.517037 + 0.855963i $$0.672965\pi$$
$$102$$ 0 0
$$103$$ 8.69287 + 8.69287i 0.856533 + 0.856533i 0.990928 0.134394i $$-0.0429089\pi$$
−0.134394 + 0.990928i $$0.542909\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 6.21290 + 14.9993i 0.600624 + 1.45003i 0.872940 + 0.487827i $$0.162210\pi$$
−0.272316 + 0.962208i $$0.587790\pi$$
$$108$$ 0 0
$$109$$ 1.20531 + 0.499254i 0.115447 + 0.0478198i 0.439659 0.898165i $$-0.355099\pi$$
−0.324212 + 0.945984i $$0.605099\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −4.83947 −0.455259 −0.227630 0.973748i $$-0.573098\pi$$
−0.227630 + 0.973748i $$0.573098\pi$$
$$114$$ 0 0
$$115$$ 11.4546 27.6539i 1.06815 2.57874i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 7.92748 + 7.92748i 0.726711 + 0.726711i
$$120$$ 0 0
$$121$$ −3.22771 + 3.22771i −0.293428 + 0.293428i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −11.1139 4.60353i −0.994059 0.411753i
$$126$$ 0 0
$$127$$ 1.85060i 0.164214i −0.996624 0.0821069i $$-0.973835\pi$$
0.996624 0.0821069i $$-0.0261649\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 2.44102 5.89314i 0.213273 0.514886i −0.780650 0.624969i $$-0.785112\pi$$
0.993922 + 0.110083i $$0.0351116\pi$$
$$132$$ 0 0
$$133$$ −2.95449 + 1.22379i −0.256187 + 0.106116i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −2.65921 + 2.65921i −0.227192 + 0.227192i −0.811519 0.584327i $$-0.801359\pi$$
0.584327 + 0.811519i $$0.301359\pi$$
$$138$$ 0 0
$$139$$ 11.7567 4.86980i 0.997193 0.413051i 0.176426 0.984314i $$-0.443546\pi$$
0.820767 + 0.571263i $$0.193546\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 9.55763i 0.799250i
$$144$$ 0 0
$$145$$ 1.28929i 0.107070i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 8.23656 3.41170i 0.674765 0.279497i −0.0188714 0.999822i $$-0.506007\pi$$
0.693637 + 0.720325i $$0.256007\pi$$
$$150$$ 0 0
$$151$$ 11.9992 11.9992i 0.976478 0.976478i −0.0232512 0.999730i $$-0.507402\pi$$
0.999730 + 0.0232512i $$0.00740175\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −5.76197 + 2.38669i −0.462812 + 0.191703i
$$156$$ 0 0
$$157$$ 5.47915 13.2278i 0.437284 1.05570i −0.539599 0.841922i $$-0.681424\pi$$
0.976883 0.213775i $$-0.0685759\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 12.2758i 0.967471i
$$162$$ 0 0
$$163$$ −10.3137 4.27206i −0.807828 0.334614i −0.0597412 0.998214i $$-0.519028\pi$$
−0.748087 + 0.663600i $$0.769028\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 6.27058 6.27058i 0.485232 0.485232i −0.421566 0.906798i $$-0.638519\pi$$
0.906798 + 0.421566i $$0.138519\pi$$
$$168$$ 0 0
$$169$$ −5.04241 5.04241i −0.387878 0.387878i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −9.58864 + 23.1490i −0.729011 + 1.75999i −0.0831448 + 0.996537i $$0.526496\pi$$
−0.645866 + 0.763451i $$0.723504\pi$$
$$174$$ 0 0
$$175$$ −12.4116 −0.938226
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 6.32195 + 2.61864i 0.472524 + 0.195726i 0.606221 0.795296i $$-0.292685\pi$$
−0.133697 + 0.991022i $$0.542685\pi$$
$$180$$ 0 0
$$181$$ −1.02155 2.46625i −0.0759314 0.183315i 0.881356 0.472453i $$-0.156631\pi$$
−0.957287 + 0.289138i $$0.906631\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 1.08123 + 1.08123i 0.0794934 + 0.0794934i
$$186$$ 0 0
$$187$$ 11.3174 + 27.3225i 0.827607 + 1.99802i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −20.7890 −1.50424 −0.752121 0.659025i $$-0.770969\pi$$
−0.752121 + 0.659025i $$0.770969\pi$$
$$192$$ 0 0
$$193$$ 14.9444 1.07572 0.537861 0.843034i $$-0.319233\pi$$
0.537861 + 0.843034i $$0.319233\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −9.50419 22.9451i −0.677145 1.63477i −0.769191 0.639019i $$-0.779341\pi$$
0.0920460 0.995755i $$-0.470659\pi$$
$$198$$ 0 0
$$199$$ 1.24926 + 1.24926i 0.0885579 + 0.0885579i 0.749998 0.661440i $$-0.230054\pi$$
−0.661440 + 0.749998i $$0.730054\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −0.202348 0.488512i −0.0142021 0.0342868i
$$204$$ 0 0
$$205$$ 7.16615 + 2.96832i 0.500506 + 0.207316i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −8.43573 −0.583512
$$210$$ 0 0
$$211$$ 4.04903 9.77521i 0.278746 0.672953i −0.721055 0.692878i $$-0.756343\pi$$
0.999801 + 0.0199244i $$0.00634254\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −20.6604 20.6604i −1.40903 1.40903i
$$216$$ 0 0
$$217$$ −1.80863 + 1.80863i −0.122778 + 0.122778i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −16.7777 6.94954i −1.12859 0.467476i
$$222$$ 0 0
$$223$$ 19.2531i 1.28928i −0.764485 0.644641i $$-0.777007\pi$$
0.764485 0.644641i $$-0.222993\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 5.98915 14.4591i 0.397514 0.959684i −0.590740 0.806862i $$-0.701164\pi$$
0.988254 0.152822i $$-0.0488361\pi$$
$$228$$ 0 0
$$229$$ −7.93338 + 3.28612i −0.524253 + 0.217153i −0.629084 0.777337i $$-0.716570\pi$$
0.104831 + 0.994490i $$0.466570\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 12.2337 12.2337i 0.801455 0.801455i −0.181868 0.983323i $$-0.558214\pi$$
0.983323 + 0.181868i $$0.0582145\pi$$
$$234$$ 0 0
$$235$$ −24.5073 + 10.1513i −1.59868 + 0.662196i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 10.3650i 0.670459i −0.942137 0.335229i $$-0.891186\pi$$
0.942137 0.335229i $$-0.108814\pi$$
$$240$$ 0 0
$$241$$ 14.1048i 0.908572i 0.890856 + 0.454286i $$0.150106\pi$$
−0.890856 + 0.454286i $$0.849894\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 16.0479 6.64726i 1.02526 0.424678i
$$246$$ 0 0
$$247$$ 3.66284 3.66284i 0.233061 0.233061i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −4.92406 + 2.03961i −0.310804 + 0.128739i −0.532633 0.846346i $$-0.678797\pi$$
0.221829 + 0.975086i $$0.428797\pi$$
$$252$$ 0 0
$$253$$ 12.3921 29.9172i 0.779087 1.88088i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 20.2370i 1.26235i −0.775640 0.631175i $$-0.782573\pi$$
0.775640 0.631175i $$-0.217427\pi$$
$$258$$ 0 0
$$259$$ 0.579371 + 0.239983i 0.0360004 + 0.0149118i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −3.63751 + 3.63751i −0.224299 + 0.224299i −0.810306 0.586007i $$-0.800699\pi$$
0.586007 + 0.810306i $$0.300699\pi$$
$$264$$ 0 0
$$265$$ −11.0211 11.0211i −0.677019 0.677019i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −2.92241 + 7.05531i −0.178182 + 0.430170i −0.987585 0.157083i $$-0.949791\pi$$
0.809403 + 0.587254i $$0.199791\pi$$
$$270$$ 0 0
$$271$$ 7.63925 0.464052 0.232026 0.972710i $$-0.425465\pi$$
0.232026 + 0.972710i $$0.425465\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −30.2480 12.5291i −1.82402 0.755535i
$$276$$ 0 0
$$277$$ −6.85371 16.5463i −0.411799 0.994172i −0.984655 0.174515i $$-0.944164\pi$$
0.572855 0.819657i $$-0.305836\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 13.5776 + 13.5776i 0.809969 + 0.809969i 0.984629 0.174660i $$-0.0558826\pi$$
−0.174660 + 0.984629i $$0.555883\pi$$
$$282$$ 0 0
$$283$$ −7.17080 17.3118i −0.426260 1.02908i −0.980463 0.196701i $$-0.936977\pi$$
0.554204 0.832381i $$-0.313023\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 3.18112 0.187776
$$288$$ 0 0
$$289$$ 39.1916 2.30539
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 1.11909 + 2.70172i 0.0653780 + 0.157836i 0.953192 0.302367i $$-0.0977767\pi$$
−0.887814 + 0.460203i $$0.847777\pi$$
$$294$$ 0 0
$$295$$ 35.7201 + 35.7201i 2.07970 + 2.07970i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 7.60951 + 18.3710i 0.440069 + 1.06242i
$$300$$ 0 0
$$301$$ −11.0708 4.58568i −0.638111 0.264314i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −5.52651 −0.316447
$$306$$ 0 0
$$307$$ −0.597072 + 1.44146i −0.0340767 + 0.0822684i −0.940002 0.341170i $$-0.889177\pi$$
0.905925 + 0.423438i $$0.139177\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 16.3415 + 16.3415i 0.926640 + 0.926640i 0.997487 0.0708472i $$-0.0225703\pi$$
−0.0708472 + 0.997487i $$0.522570\pi$$
$$312$$ 0 0
$$313$$ 11.0100 11.0100i 0.622320 0.622320i −0.323804 0.946124i $$-0.604962\pi$$
0.946124 + 0.323804i $$0.104962\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 6.87945 + 2.84956i 0.386388 + 0.160047i 0.567417 0.823430i $$-0.307943\pi$$
−0.181029 + 0.983478i $$0.557943\pi$$
$$318$$ 0 0
$$319$$ 1.39481i 0.0780943i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −6.13378 + 14.8082i −0.341292 + 0.823953i
$$324$$ 0 0
$$325$$ 18.5741 7.69364i 1.03030 0.426766i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −7.69264 + 7.69264i −0.424109 + 0.424109i
$$330$$ 0 0
$$331$$ −3.18235 + 1.31817i −0.174918 + 0.0724533i −0.468424 0.883504i $$-0.655178\pi$$
0.293506 + 0.955957i $$0.405178\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 31.4350i 1.71748i
$$336$$ 0 0
$$337$$ 33.5837i 1.82942i −0.404110 0.914710i $$-0.632419\pi$$
0.404110 0.914710i $$-0.367581\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −6.23355 + 2.58202i −0.337566 + 0.139824i
$$342$$ 0 0
$$343$$ 12.4401 12.4401i 0.671704 0.671704i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −10.5727 + 4.37938i −0.567575 + 0.235097i −0.647970 0.761666i $$-0.724382\pi$$
0.0803952 + 0.996763i $$0.474382\pi$$
$$348$$ 0 0
$$349$$ −1.93540 + 4.67246i −0.103599 + 0.250111i −0.967176 0.254106i $$-0.918219\pi$$
0.863577 + 0.504217i $$0.168219\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 11.8710i 0.631829i 0.948788 + 0.315915i $$0.102311\pi$$
−0.948788 + 0.315915i $$0.897689\pi$$
$$354$$ 0 0
$$355$$ 22.6564 + 9.38458i 1.20248 + 0.498082i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 7.19895 7.19895i 0.379946 0.379946i −0.491137 0.871083i $$-0.663418\pi$$
0.871083 + 0.491137i $$0.163418\pi$$
$$360$$ 0 0
$$361$$ 10.2021 + 10.2021i 0.536955 + 0.536955i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 15.7859 38.1106i 0.826274 1.99480i
$$366$$ 0 0
$$367$$ −5.49636 −0.286908 −0.143454 0.989657i $$-0.545821\pi$$
−0.143454 + 0.989657i $$0.545821\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −5.90560 2.44618i −0.306603 0.126999i
$$372$$ 0 0
$$373$$ 9.45992 + 22.8383i 0.489816 + 1.18252i 0.954813 + 0.297208i $$0.0960556\pi$$
−0.464996 + 0.885313i $$0.653944\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0.605634 + 0.605634i 0.0311917 + 0.0311917i
$$378$$ 0 0
$$379$$ 5.26808 + 12.7183i 0.270603 + 0.653293i 0.999509 0.0313200i $$-0.00997110\pi$$
−0.728906 + 0.684613i $$0.759971\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0.651517 0.0332910 0.0166455 0.999861i $$-0.494701\pi$$
0.0166455 + 0.999861i $$0.494701\pi$$
$$384$$ 0 0
$$385$$ −21.5174 −1.09663
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 6.58251 + 15.8916i 0.333747 + 0.805736i 0.998288 + 0.0584844i $$0.0186268\pi$$
−0.664542 + 0.747251i $$0.731373\pi$$
$$390$$ 0 0
$$391$$ −43.5068 43.5068i −2.20023 2.20023i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −20.0913 48.5046i −1.01090 2.44053i
$$396$$ 0 0
$$397$$ −23.5792 9.76681i −1.18340 0.490182i −0.297802 0.954628i $$-0.596254\pi$$
−0.885602 + 0.464446i $$0.846254\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 5.64431 0.281864 0.140932 0.990019i $$-0.454990\pi$$
0.140932 + 0.990019i $$0.454990\pi$$
$$402$$ 0 0
$$403$$ 1.58552 3.82777i 0.0789802 0.190675i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 1.16972 + 1.16972i 0.0579808 + 0.0579808i
$$408$$ 0 0
$$409$$ −15.4062 + 15.4062i −0.761790 + 0.761790i −0.976646 0.214856i $$-0.931072\pi$$
0.214856 + 0.976646i $$0.431072\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 19.1405 + 7.92824i 0.941840 + 0.390123i
$$414$$ 0 0
$$415$$ 5.33860i 0.262061i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 9.62264 23.2311i 0.470097 1.13491i −0.494024 0.869449i $$-0.664474\pi$$
0.964120 0.265466i $$-0.0855257\pi$$
$$420$$ 0 0
$$421$$ −2.00854 + 0.831963i −0.0978901 + 0.0405474i −0.431091 0.902308i $$-0.641871\pi$$
0.333201 + 0.942856i $$0.391871\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −43.9878 + 43.9878i −2.13372 + 2.13372i
$$426$$ 0 0
$$427$$ −2.09400 + 0.867362i −0.101336 + 0.0419746i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 16.8804i 0.813100i 0.913628 + 0.406550i $$0.133268\pi$$
−0.913628 + 0.406550i $$0.866732\pi$$
$$432$$ 0 0
$$433$$ 0.162457i 0.00780716i −0.999992 0.00390358i $$-0.998757\pi$$
0.999992 0.00390358i $$-0.00124255\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 16.2145 6.71628i 0.775646 0.321283i
$$438$$ 0 0
$$439$$ 0.853136 0.853136i 0.0407180 0.0407180i −0.686455 0.727173i $$-0.740834\pi$$
0.727173 + 0.686455i $$0.240834\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 22.2491 9.21590i 1.05709 0.437860i 0.214672 0.976686i $$-0.431132\pi$$
0.842417 + 0.538826i $$0.181132\pi$$
$$444$$ 0 0
$$445$$ −9.38721 + 22.6627i −0.444996 + 1.07432i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 23.1544i 1.09272i 0.837549 + 0.546362i $$0.183988\pi$$
−0.837549 + 0.546362i $$0.816012\pi$$
$$450$$ 0 0
$$451$$ 7.75266 + 3.21126i 0.365059 + 0.151212i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 9.34298 9.34298i 0.438006 0.438006i
$$456$$ 0 0
$$457$$ 15.2233 + 15.2233i 0.712114 + 0.712114i 0.966977 0.254863i $$-0.0820304\pi$$
−0.254863 + 0.966977i $$0.582030\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 12.2190 29.4992i 0.569093 1.37391i −0.333227 0.942847i $$-0.608138\pi$$
0.902320 0.431066i $$-0.141862\pi$$
$$462$$ 0 0
$$463$$ −0.577924 −0.0268584 −0.0134292 0.999910i $$-0.504275\pi$$
−0.0134292 + 0.999910i $$0.504275\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −25.0132 10.3608i −1.15747 0.479441i −0.280440 0.959872i $$-0.590480\pi$$
−0.877033 + 0.480431i $$0.840480\pi$$
$$468$$ 0 0
$$469$$ 4.93358 + 11.9107i 0.227812 + 0.549986i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −22.3514 22.3514i −1.02772 1.02772i
$$474$$ 0 0
$$475$$ −6.79053 16.3938i −0.311571 0.752199i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 20.6865 0.945188 0.472594 0.881280i $$-0.343318\pi$$
0.472594 + 0.881280i $$0.343318\pi$$
$$480$$ 0 0
$$481$$ −1.01580 −0.0463164
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −1.79825 4.34136i −0.0816543 0.197131i
$$486$$ 0 0
$$487$$ 17.8979 + 17.8979i 0.811031 + 0.811031i 0.984788 0.173757i $$-0.0555909\pi$$
−0.173757 + 0.984788i $$0.555591\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −0.919341 2.21949i −0.0414893 0.100164i 0.901776 0.432203i $$-0.142264\pi$$
−0.943266 + 0.332039i $$0.892264\pi$$
$$492$$ 0 0
$$493$$ −2.44848 1.01419i −0.110274 0.0456769i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 10.0574 0.451135
$$498$$ 0 0
$$499$$ −8.65228 + 20.8884i −0.387329 + 0.935095i 0.603175 + 0.797609i $$0.293902\pi$$
−0.990504 + 0.137486i $$0.956098\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 9.91458 + 9.91458i 0.442069 + 0.442069i 0.892707 0.450638i $$-0.148803\pi$$
−0.450638 + 0.892707i $$0.648803\pi$$
$$504$$ 0 0
$$505$$ −30.7323 + 30.7323i −1.36757 + 1.36757i
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −8.70757 3.60679i −0.385956 0.159868i 0.181264 0.983434i $$-0.441981\pi$$
−0.567220 + 0.823566i $$0.691981\pi$$
$$510$$ 0 0
$$511$$ 16.9177i 0.748393i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −17.1563 + 41.4189i −0.755995 + 1.82513i
$$516$$ 0 0
$$517$$ −26.5131 + 10.9821i −1.16605 + 0.482992i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −0.843541 + 0.843541i −0.0369562 + 0.0369562i −0.725343 0.688387i $$-0.758319\pi$$
0.688387 + 0.725343i $$0.258319\pi$$
$$522$$ 0 0
$$523$$ −0.0207812 + 0.00860784i −0.000908697 + 0.000376395i −0.383138 0.923691i $$-0.625157\pi$$
0.382229 + 0.924068i $$0.375157\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 12.8199i 0.558445i
$$528$$ 0 0
$$529$$ 44.3710i 1.92917i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −4.76060 + 1.97190i −0.206204 + 0.0854126i
$$534$$ 0 0
$$535$$ −41.8644 + 41.8644i −1.80996 + 1.80996i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 17.3613 7.19130i 0.747805 0.309751i
$$540$$ 0 0
$$541$$ 1.78856 4.31796i 0.0768961 0.185644i −0.880757 0.473569i $$-0.842965\pi$$
0.957653 + 0.287925i $$0.0929655\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 4.75759i 0.203793i
$$546$$ 0 0
$$547$$ −26.9790 11.1751i −1.15354 0.477811i −0.277819 0.960633i $$-0.589612\pi$$
−0.875718 + 0.482823i $$0.839612\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0.534543 0.534543i 0.0227723 0.0227723i
$$552$$ 0 0
$$553$$ −15.2252 15.2252i −0.647440 0.647440i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 2.15147 5.19412i 0.0911609 0.220082i −0.871722 0.490000i $$-0.836997\pi$$
0.962883 + 0.269918i $$0.0869967\pi$$
$$558$$ 0 0
$$559$$ 19.4102 0.820964
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 15.9450 + 6.60465i 0.672003 + 0.278353i 0.692479 0.721438i $$-0.256518\pi$$
−0.0204766 + 0.999790i $$0.506518\pi$$
$$564$$ 0 0
$$565$$ −6.75372 16.3049i −0.284131 0.685953i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 1.67703 + 1.67703i 0.0703046 + 0.0703046i 0.741385 0.671080i $$-0.234169\pi$$
−0.671080 + 0.741385i $$0.734169\pi$$
$$570$$ 0 0
$$571$$ 2.41843 + 5.83861i 0.101208 + 0.244338i 0.966371 0.257154i $$-0.0827847\pi$$
−0.865162 + 0.501492i $$0.832785\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 68.1158 2.84063
$$576$$ 0 0
$$577$$ 10.8983 0.453703 0.226851 0.973929i $$-0.427157\pi$$
0.226851 + 0.973929i $$0.427157\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0.837869 + 2.02280i 0.0347607 + 0.0839197i
$$582$$ 0 0
$$583$$ −11.9231 11.9231i −0.493804 0.493804i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 12.0840 + 29.1734i 0.498760 + 1.20411i 0.950152 + 0.311788i $$0.100928\pi$$
−0.451392 + 0.892326i $$0.649072\pi$$
$$588$$ 0 0
$$589$$ −3.37846 1.39940i −0.139207 0.0576614i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −25.8516 −1.06160 −0.530800 0.847497i $$-0.678108\pi$$
−0.530800 + 0.847497i $$0.678108\pi$$
$$594$$ 0 0
$$595$$ −15.6457 + 37.7721i −0.641411 + 1.54850i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −7.76404 7.76404i −0.317230 0.317230i 0.530472 0.847702i $$-0.322015\pi$$
−0.847702 + 0.530472i $$0.822015\pi$$
$$600$$ 0 0
$$601$$ 27.7695 27.7695i 1.13274 1.13274i 0.143020 0.989720i $$-0.454319\pi$$
0.989720 0.143020i $$-0.0456812\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −15.3790 6.37021i −0.625247 0.258986i
$$606$$ 0 0
$$607$$ 6.83755i 0.277527i −0.990326 0.138764i $$-0.955687\pi$$
0.990326 0.138764i $$-0.0443129\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 6.74366 16.2806i 0.272819 0.658644i
$$612$$ 0 0
$$613$$ 1.88592 0.781173i 0.0761716 0.0315513i −0.344272 0.938870i $$-0.611874\pi$$
0.420444 + 0.907319i $$0.361874\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 16.5582 16.5582i 0.666610 0.666610i −0.290320 0.956930i $$-0.593762\pi$$
0.956930 + 0.290320i $$0.0937617\pi$$
$$618$$ 0 0
$$619$$ −34.0627 + 14.1093i −1.36910 + 0.567099i −0.941544 0.336891i $$-0.890625\pi$$
−0.427554 + 0.903990i $$0.640625\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 10.0602i 0.403053i
$$624$$ 0 0
$$625$$ 2.37526i 0.0950104i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 2.90387 1.20282i 0.115785 0.0479597i
$$630$$ 0 0
$$631$$ 18.8332 18.8332i 0.749737 0.749737i −0.224693 0.974430i $$-0.572138\pi$$
0.974430 + 0.224693i $$0.0721379\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 6.23494 2.58260i 0.247426 0.102487i
$$636$$ 0 0
$$637$$ −4.41589 + 10.6609i −0.174964 + 0.422400i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 34.0636i 1.34543i 0.739900 + 0.672716i $$0.234873\pi$$
−0.739900 + 0.672716i $$0.765127\pi$$
$$642$$ 0 0
$$643$$ −8.14924 3.37552i −0.321374 0.133118i 0.216164 0.976357i $$-0.430646\pi$$
−0.537538 + 0.843239i $$0.680646\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −15.9458 + 15.9458i −0.626894 + 0.626894i −0.947285 0.320391i $$-0.896186\pi$$
0.320391 + 0.947285i $$0.396186\pi$$
$$648$$ 0 0
$$649$$ 38.6436 + 38.6436i 1.51689 + 1.51689i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −10.3560 + 25.0017i −0.405263 + 0.978391i 0.581104 + 0.813829i $$0.302621\pi$$
−0.986367 + 0.164562i $$0.947379\pi$$
$$654$$ 0 0
$$655$$ 23.2614 0.908900
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0.976716 + 0.404569i 0.0380475 + 0.0157598i 0.401626 0.915804i $$-0.368445\pi$$
−0.363579 + 0.931564i $$0.618445\pi$$
$$660$$ 0 0
$$661$$ −10.6003 25.5914i −0.412304 0.995389i −0.984518 0.175285i $$-0.943915\pi$$
0.572214 0.820104i $$-0.306085\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −8.24627 8.24627i −0.319777 0.319777i
$$666$$ 0 0
$$667$$ 1.11051 + 2.68100i 0.0429990 + 0.103809i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −5.97883 −0.230810
$$672$$ 0 0
$$673$$ −17.3400 −0.668409 −0.334205 0.942501i $$-0.608468\pi$$
−0.334205 + 0.942501i $$0.608468\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 1.10411 + 2.66556i 0.0424344 + 0.102446i 0.943676 0.330872i $$-0.107343\pi$$
−0.901241 + 0.433318i $$0.857343\pi$$
$$678$$ 0 0
$$679$$ −1.36271 1.36271i −0.0522962 0.0522962i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −9.51934 22.9817i −0.364247 0.879371i −0.994669 0.103118i $$-0.967118\pi$$
0.630422 0.776253i $$-0.282882\pi$$
$$684$$ 0 0
$$685$$ −12.6703 5.24823i −0.484109 0.200525i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 10.3542 0.394462
$$690$$ 0 0
$$691$$ −8.56212 + 20.6708i −0.325719 + 0.786354i 0.673182 + 0.739477i $$0.264927\pi$$
−0.998901 + 0.0468774i $$0.985073\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 32.8142 + 32.8142i 1.24471 + 1.24471i
$$696$$ 0 0
$$697$$ 11.2742 11.2742i 0.427041 0.427041i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 40.4517 + 16.7556i 1.52784 + 0.632852i 0.979143 0.203171i $$-0.0651247\pi$$
0.548695 + 0.836022i $$0.315125\pi$$
$$702$$ 0 0
$$703$$ 0.896560i 0.0338144i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −6.82119 + 16.4678i −0.256537 + 0.619335i
$$708$$ 0 0
$$709$$ −16.2624 + 6.73611i −0.610748 + 0.252980i −0.666548 0.745462i $$-0.732229\pi$$
0.0558005 + 0.998442i $$0.482229\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 9.92594 9.92594i 0.371730 0.371730i
$$714$$ 0 0
$$715$$ 32.2011 13.3381i 1.20425 0.498818i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 23.5642i 0.878796i −0.898292 0.439398i $$-0.855192\pi$$
0.898292 0.439398i $$-0.144808\pi$$
$$720$$ 0 0
$$721$$ 18.3862i 0.684739i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 2.71064 1.12278i 0.100671 0.0416991i
$$726$$ 0 0
$$727$$ 16.5208 16.5208i 0.612724 0.612724i −0.330931 0.943655i $$-0.607363\pi$$
0.943655 + 0.330931i $$0.107363\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −55.4882 + 22.9840i −2.05230 + 0.850092i
$$732$$ 0 0
$$733$$ −8.74219 + 21.1055i −0.322900 + 0.779550i 0.676183 + 0.736734i $$0.263633\pi$$
−0.999083 + 0.0428159i $$0.986367\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 34.0077i 1.25269i
$$738$$ 0 0
$$739$$ −41.5366 17.2050i −1.52795 0.632897i −0.548785 0.835964i $$-0.684909\pi$$
−0.979165 + 0.203066i $$0.934909\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −19.3232 + 19.3232i −0.708900 + 0.708900i −0.966304 0.257404i $$-0.917133\pi$$
0.257404 + 0.966304i $$0.417133\pi$$
$$744$$ 0 0
$$745$$ 22.9890 + 22.9890i 0.842253 + 0.842253i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −9.29200 + 22.4329i −0.339522 + 0.819679i
$$750$$ 0 0
$$751$$ 9.32371 0.340227 0.170114 0.985424i $$-0.445587\pi$$
0.170114 + 0.985424i $$0.445587\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 57.1724 + 23.6816i 2.08072 + 0.861861i
$$756$$ 0 0
$$757$$ −9.71720 23.4594i −0.353178 0.852647i −0.996224 0.0868193i $$-0.972330\pi$$
0.643046 0.765827i $$-0.277670\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 21.9092 + 21.9092i 0.794207 + 0.794207i 0.982175 0.187968i $$-0.0601902\pi$$
−0.187968 + 0.982175i $$0.560190\pi$$
$$762$$ 0 0
$$763$$ 0.746683 + 1.80265i 0.0270317 + 0.0652604i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −33.5585 −1.21173
$$768$$ 0 0
$$769$$ −11.9106 −0.429508 −0.214754 0.976668i $$-0.568895\pi$$
−0.214754 + 0.976668i $$0.568895\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −3.39696 8.20098i −0.122180 0.294969i 0.850942 0.525260i $$-0.176032\pi$$
−0.973122 + 0.230291i $$0.926032\pi$$
$$774$$ 0 0
$$775$$ −10.0357 10.0357i −0.360492 0.360492i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 1.74044 + 4.20178i 0.0623576 + 0.150545i
$$780$$ 0 0
$$781$$ 24.5107 + 10.1527i 0.877061 + 0.363290i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 52.2130 1.86356
$$786$$ 0 0
$$787$$ −6.32430 + 15.2682i −0.225437 + 0.544253i −0.995612 0.0935798i $$-0.970169\pi$$
0.770175 + 0.637833i $$0.220169\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −5.11797 5.11797i −0.181974 0.181974i
$$792$$ 0 0
$$793$$ 2.59604 2.59604i 0.0921881 0.0921881i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 13.4382 + 5.56628i 0.476005 + 0.197168i 0.607770 0.794113i $$-0.292064\pi$$
−0.131765 + 0.991281i $$0.542064\pi$$
$$798$$ 0 0
$$799$$ 54.5269i 1.92902i
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 17.0779 41.2298i 0.602667 1.45497i
$$804$$ 0 0
$$805$$ 41.3591 17.1315i 1.45772 0.603807i