# Properties

 Label 2268.2.i.n.2053.1 Level $2268$ Weight $2$ Character 2268.2053 Analytic conductor $18.110$ Analytic rank $0$ Dimension $16$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2268 = 2^{2} \cdot 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2268.i (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$18.1100711784$$ Analytic rank: $$0$$ Dimension: $$16$$ Relative dimension: $$8$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ Defining polynomial: $$x^{16} - 9 x^{14} + 31 x^{12} - 282 x^{10} + 1695 x^{8} - 3318 x^{6} + 4606 x^{4} - 4116 x^{2} + 2401$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$3^{7}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 2053.1 Root $$0.817131 + 0.735533i$$ of defining polynomial Character $$\chi$$ $$=$$ 2268.2053 Dual form 2268.2.i.n.865.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.83843 - 3.18426i) q^{5} +(-1.55575 - 2.14001i) q^{7} +O(q^{10})$$ $$q+(-1.83843 - 3.18426i) q^{5} +(-1.55575 - 2.14001i) q^{7} +(-0.301572 + 0.522337i) q^{11} +(2.62851 - 4.55271i) q^{13} +(-2.12557 - 3.68159i) q^{17} +(3.68426 - 6.38133i) q^{19} +(-0.578891 - 1.00267i) q^{23} +(-4.25969 + 7.37799i) q^{25} +(3.98826 + 6.90786i) q^{29} +3.15085 q^{31} +(-3.95419 + 8.88819i) q^{35} +(0.00266923 - 0.00462323i) q^{37} +(2.00937 - 3.48033i) q^{41} +(-3.66193 - 6.34264i) q^{43} -12.2173 q^{47} +(-2.15926 + 6.65865i) q^{49} +(4.64928 + 8.05279i) q^{53} +2.21768 q^{55} -6.61521 q^{59} -1.93850 q^{61} -19.3294 q^{65} +8.63088 q^{67} -1.13815 q^{71} +(-5.33511 - 9.24068i) q^{73} +(1.58698 - 0.167264i) q^{77} +4.14551 q^{79} +(-6.24088 - 10.8095i) q^{83} +(-7.81544 + 13.5367i) q^{85} +(4.09464 - 7.09212i) q^{89} +(-13.8321 + 1.45787i) q^{91} -27.0931 q^{95} +(6.77935 + 11.7422i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q - 6 q^{7} + O(q^{10})$$ $$16 q - 6 q^{7} + 10 q^{13} + 8 q^{19} + 16 q^{31} - 4 q^{37} - 10 q^{43} + 10 q^{49} - 32 q^{55} - 56 q^{61} - 36 q^{67} + 40 q^{79} - 38 q^{85} - 2 q^{91} + 42 q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$1135$$ $$1541$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$5$$ −1.83843 3.18426i −0.822173 1.42405i −0.904061 0.427404i $$-0.859428\pi$$
0.0818877 0.996642i $$-0.473905\pi$$
$$6$$ 0 0
$$7$$ −1.55575 2.14001i −0.588020 0.808846i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −0.301572 + 0.522337i −0.0909273 + 0.157491i −0.907902 0.419183i $$-0.862316\pi$$
0.816974 + 0.576674i $$0.195650\pi$$
$$12$$ 0 0
$$13$$ 2.62851 4.55271i 0.729017 1.26269i −0.228282 0.973595i $$-0.573311\pi$$
0.957299 0.289099i $$-0.0933558\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −2.12557 3.68159i −0.515526 0.892918i −0.999838 0.0180219i $$-0.994263\pi$$
0.484311 0.874896i $$-0.339070\pi$$
$$18$$ 0 0
$$19$$ 3.68426 6.38133i 0.845228 1.46398i −0.0401954 0.999192i $$-0.512798\pi$$
0.885423 0.464786i $$-0.153869\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −0.578891 1.00267i −0.120707 0.209071i 0.799340 0.600880i $$-0.205183\pi$$
−0.920047 + 0.391809i $$0.871850\pi$$
$$24$$ 0 0
$$25$$ −4.25969 + 7.37799i −0.851937 + 1.47560i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 3.98826 + 6.90786i 0.740601 + 1.28276i 0.952222 + 0.305406i $$0.0987922\pi$$
−0.211622 + 0.977352i $$0.567874\pi$$
$$30$$ 0 0
$$31$$ 3.15085 0.565909 0.282954 0.959133i $$-0.408686\pi$$
0.282954 + 0.959133i $$0.408686\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −3.95419 + 8.88819i −0.668380 + 1.50238i
$$36$$ 0 0
$$37$$ 0.00266923 0.00462323i 0.000438818 0.000760055i −0.865806 0.500380i $$-0.833194\pi$$
0.866245 + 0.499620i $$0.166527\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 2.00937 3.48033i 0.313811 0.543537i −0.665373 0.746511i $$-0.731728\pi$$
0.979184 + 0.202974i $$0.0650609\pi$$
$$42$$ 0 0
$$43$$ −3.66193 6.34264i −0.558438 0.967244i −0.997627 0.0688488i $$-0.978067\pi$$
0.439189 0.898395i $$-0.355266\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −12.2173 −1.78207 −0.891036 0.453933i $$-0.850021\pi$$
−0.891036 + 0.453933i $$0.850021\pi$$
$$48$$ 0 0
$$49$$ −2.15926 + 6.65865i −0.308465 + 0.951236i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 4.64928 + 8.05279i 0.638628 + 1.10614i 0.985734 + 0.168310i $$0.0538309\pi$$
−0.347107 + 0.937826i $$0.612836\pi$$
$$54$$ 0 0
$$55$$ 2.21768 0.299032
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −6.61521 −0.861227 −0.430613 0.902537i $$-0.641703\pi$$
−0.430613 + 0.902537i $$0.641703\pi$$
$$60$$ 0 0
$$61$$ −1.93850 −0.248200 −0.124100 0.992270i $$-0.539604\pi$$
−0.124100 + 0.992270i $$0.539604\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −19.3294 −2.39751
$$66$$ 0 0
$$67$$ 8.63088 1.05443 0.527215 0.849732i $$-0.323236\pi$$
0.527215 + 0.849732i $$0.323236\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −1.13815 −0.135074 −0.0675370 0.997717i $$-0.521514\pi$$
−0.0675370 + 0.997717i $$0.521514\pi$$
$$72$$ 0 0
$$73$$ −5.33511 9.24068i −0.624427 1.08154i −0.988651 0.150228i $$-0.951999\pi$$
0.364224 0.931311i $$-0.381334\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 1.58698 0.167264i 0.180853 0.0190614i
$$78$$ 0 0
$$79$$ 4.14551 0.466406 0.233203 0.972428i $$-0.425079\pi$$
0.233203 + 0.972428i $$0.425079\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −6.24088 10.8095i −0.685026 1.18650i −0.973429 0.228990i $$-0.926458\pi$$
0.288403 0.957509i $$-0.406876\pi$$
$$84$$ 0 0
$$85$$ −7.81544 + 13.5367i −0.847703 + 1.46827i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 4.09464 7.09212i 0.434031 0.751764i −0.563185 0.826331i $$-0.690424\pi$$
0.997216 + 0.0745672i $$0.0237575\pi$$
$$90$$ 0 0
$$91$$ −13.8321 + 1.45787i −1.45000 + 0.152827i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −27.0931 −2.77969
$$96$$ 0 0
$$97$$ 6.77935 + 11.7422i 0.688339 + 1.19224i 0.972375 + 0.233425i $$0.0749932\pi$$
−0.284036 + 0.958814i $$0.591673\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −7.66975 + 13.2844i −0.763169 + 1.32185i 0.178041 + 0.984023i $$0.443024\pi$$
−0.941209 + 0.337824i $$0.890309\pi$$
$$102$$ 0 0
$$103$$ 2.48033 + 4.29606i 0.244394 + 0.423303i 0.961961 0.273186i $$-0.0880775\pi$$
−0.717567 + 0.696490i $$0.754744\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −3.41399 + 5.91320i −0.330043 + 0.571651i −0.982520 0.186158i $$-0.940396\pi$$
0.652477 + 0.757808i $$0.273730\pi$$
$$108$$ 0 0
$$109$$ 8.90194 + 15.4186i 0.852651 + 1.47684i 0.878807 + 0.477178i $$0.158340\pi$$
−0.0261554 + 0.999658i $$0.508326\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 4.63946 8.03579i 0.436444 0.755943i −0.560968 0.827837i $$-0.689571\pi$$
0.997412 + 0.0718940i $$0.0229043\pi$$
$$114$$ 0 0
$$115$$ −2.12851 + 3.68668i −0.198484 + 0.343785i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −4.57177 + 10.2764i −0.419093 + 0.942035i
$$120$$ 0 0
$$121$$ 5.31811 + 9.21124i 0.483464 + 0.837385i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 12.9403 1.15741
$$126$$ 0 0
$$127$$ −14.9941 −1.33051 −0.665254 0.746617i $$-0.731677\pi$$
−0.665254 + 0.746617i $$0.731677\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 11.4164 + 19.7737i 0.997452 + 1.72764i 0.560508 + 0.828149i $$0.310606\pi$$
0.436944 + 0.899489i $$0.356061\pi$$
$$132$$ 0 0
$$133$$ −19.3879 + 2.04344i −1.68114 + 0.177188i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0.762784 1.32118i 0.0651690 0.112876i −0.831600 0.555375i $$-0.812575\pi$$
0.896769 + 0.442499i $$0.145908\pi$$
$$138$$ 0 0
$$139$$ −3.31277 + 5.73789i −0.280986 + 0.486681i −0.971628 0.236515i $$-0.923995\pi$$
0.690642 + 0.723197i $$0.257328\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 1.58537 + 2.74594i 0.132575 + 0.229627i
$$144$$ 0 0
$$145$$ 14.6643 25.3993i 1.21780 2.10930i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −8.88746 15.3935i −0.728089 1.26109i −0.957690 0.287802i $$-0.907075\pi$$
0.229601 0.973285i $$-0.426258\pi$$
$$150$$ 0 0
$$151$$ −2.31811 + 4.01508i −0.188645 + 0.326743i −0.944799 0.327651i $$-0.893743\pi$$
0.756154 + 0.654394i $$0.227076\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −5.79262 10.0331i −0.465275 0.805880i
$$156$$ 0 0
$$157$$ 3.41320 0.272403 0.136202 0.990681i $$-0.456511\pi$$
0.136202 + 0.990681i $$0.456511\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −1.24511 + 2.79874i −0.0981281 + 0.220571i
$$162$$ 0 0
$$163$$ 7.55012 13.0772i 0.591371 1.02428i −0.402677 0.915342i $$-0.631920\pi$$
0.994048 0.108942i $$-0.0347464\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 2.85782 4.94988i 0.221144 0.383033i −0.734011 0.679137i $$-0.762354\pi$$
0.955156 + 0.296104i $$0.0956875\pi$$
$$168$$ 0 0
$$169$$ −7.31811 12.6753i −0.562931 0.975026i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −1.89631 −0.144174 −0.0720871 0.997398i $$-0.522966\pi$$
−0.0720871 + 0.997398i $$0.522966\pi$$
$$174$$ 0 0
$$175$$ 22.4160 2.36259i 1.69449 0.178595i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −7.29747 12.6396i −0.545438 0.944727i −0.998579 0.0532881i $$-0.983030\pi$$
0.453141 0.891439i $$-0.350304\pi$$
$$180$$ 0 0
$$181$$ 7.89857 0.587096 0.293548 0.955944i $$-0.405164\pi$$
0.293548 + 0.955944i $$0.405164\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −0.0196288 −0.00144314
$$186$$ 0 0
$$187$$ 2.56405 0.187502
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 8.47340 0.613114 0.306557 0.951852i $$-0.400823\pi$$
0.306557 + 0.951852i $$0.400823\pi$$
$$192$$ 0 0
$$193$$ −6.96600 −0.501424 −0.250712 0.968062i $$-0.580665\pi$$
−0.250712 + 0.968062i $$0.580665\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −16.2371 −1.15685 −0.578424 0.815736i $$-0.696332\pi$$
−0.578424 + 0.815736i $$0.696332\pi$$
$$198$$ 0 0
$$199$$ −7.35153 12.7332i −0.521136 0.902634i −0.999698 0.0245800i $$-0.992175\pi$$
0.478562 0.878054i $$-0.341158\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 8.57812 19.2818i 0.602066 1.35332i
$$204$$ 0 0
$$205$$ −14.7764 −1.03203
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 2.22214 + 3.84886i 0.153709 + 0.266231i
$$210$$ 0 0
$$211$$ 8.41053 14.5675i 0.579005 1.00287i −0.416589 0.909095i $$-0.636775\pi$$
0.995594 0.0937708i $$-0.0298921\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −13.4644 + 23.3211i −0.918266 + 1.59048i
$$216$$ 0 0
$$217$$ −4.90194 6.74283i −0.332766 0.457733i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −22.3483 −1.50331
$$222$$ 0 0
$$223$$ 3.45799 + 5.98942i 0.231564 + 0.401081i 0.958269 0.285869i $$-0.0922823\pi$$
−0.726704 + 0.686950i $$0.758949\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −3.49817 + 6.05900i −0.232182 + 0.402150i −0.958450 0.285261i $$-0.907920\pi$$
0.726268 + 0.687411i $$0.241253\pi$$
$$228$$ 0 0
$$229$$ 1.41350 + 2.44825i 0.0934066 + 0.161785i 0.908942 0.416922i $$-0.136891\pi$$
−0.815536 + 0.578706i $$0.803558\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 11.1679 19.3434i 0.731635 1.26723i −0.224550 0.974463i $$-0.572091\pi$$
0.956184 0.292766i $$-0.0945756\pi$$
$$234$$ 0 0
$$235$$ 22.4606 + 38.9030i 1.46517 + 2.53775i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −0.954829 + 1.65381i −0.0617628 + 0.106976i −0.895253 0.445557i $$-0.853006\pi$$
0.833491 + 0.552534i $$0.186339\pi$$
$$240$$ 0 0
$$241$$ 9.84352 17.0495i 0.634077 1.09825i −0.352633 0.935762i $$-0.614714\pi$$
0.986710 0.162492i $$-0.0519530\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 25.1725 5.36586i 1.60821 0.342812i
$$246$$ 0 0
$$247$$ −19.3682 33.5468i −1.23237 2.13453i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 12.2990 0.776306 0.388153 0.921595i $$-0.373113\pi$$
0.388153 + 0.921595i $$0.373113\pi$$
$$252$$ 0 0
$$253$$ 0.698309 0.0439023
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 5.71210 + 9.89365i 0.356311 + 0.617149i 0.987341 0.158609i $$-0.0507010\pi$$
−0.631030 + 0.775758i $$0.717368\pi$$
$$258$$ 0 0
$$259$$ −0.0140464 + 0.00148046i −0.000872802 + 9.19912e-5i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −9.65544 + 16.7237i −0.595380 + 1.03123i 0.398114 + 0.917336i $$0.369665\pi$$
−0.993493 + 0.113892i $$0.963668\pi$$
$$264$$ 0 0
$$265$$ 17.0948 29.6091i 1.05012 1.81887i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 4.00745 + 6.94110i 0.244338 + 0.423206i 0.961945 0.273242i $$-0.0880959\pi$$
−0.717607 + 0.696448i $$0.754763\pi$$
$$270$$ 0 0
$$271$$ 2.96658 5.13827i 0.180207 0.312128i −0.761744 0.647878i $$-0.775657\pi$$
0.941951 + 0.335750i $$0.108990\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −2.56920 4.44999i −0.154929 0.268344i
$$276$$ 0 0
$$277$$ 6.02768 10.4402i 0.362168 0.627293i −0.626149 0.779703i $$-0.715370\pi$$
0.988317 + 0.152410i $$0.0487034\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 9.73700 + 16.8650i 0.580861 + 1.00608i 0.995378 + 0.0960386i $$0.0306172\pi$$
−0.414517 + 0.910042i $$0.636049\pi$$
$$282$$ 0 0
$$283$$ −28.7036 −1.70625 −0.853127 0.521704i $$-0.825297\pi$$
−0.853127 + 0.521704i $$0.825297\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −10.5740 + 1.11448i −0.624165 + 0.0657854i
$$288$$ 0 0
$$289$$ −0.536086 + 0.928529i −0.0315345 + 0.0546193i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 11.3503 19.6593i 0.663090 1.14851i −0.316709 0.948523i $$-0.602578\pi$$
0.979799 0.199983i $$-0.0640888\pi$$
$$294$$ 0 0
$$295$$ 12.1616 + 21.0646i 0.708077 + 1.22643i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −6.08648 −0.351990
$$300$$ 0 0
$$301$$ −7.87624 + 17.7041i −0.453979 + 1.02045i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 3.56381 + 6.17271i 0.204063 + 0.353448i
$$306$$ 0 0
$$307$$ −27.9486 −1.59511 −0.797555 0.603246i $$-0.793874\pi$$
−0.797555 + 0.603246i $$0.793874\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 15.2982 0.867479 0.433739 0.901038i $$-0.357194\pi$$
0.433739 + 0.901038i $$0.357194\pi$$
$$312$$ 0 0
$$313$$ 3.34103 0.188846 0.0944230 0.995532i $$-0.469899\pi$$
0.0944230 + 0.995532i $$0.469899\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 9.01444 0.506301 0.253151 0.967427i $$-0.418533\pi$$
0.253151 + 0.967427i $$0.418533\pi$$
$$318$$ 0 0
$$319$$ −4.81098 −0.269363
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −31.3246 −1.74295
$$324$$ 0 0
$$325$$ 22.3932 + 38.7862i 1.24215 + 2.15147i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 19.0071 + 26.1450i 1.04789 + 1.44142i
$$330$$ 0 0
$$331$$ 18.2952 1.00559 0.502797 0.864404i $$-0.332304\pi$$
0.502797 + 0.864404i $$0.332304\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −15.8673 27.4830i −0.866924 1.50156i
$$336$$ 0 0
$$337$$ −0.868823 + 1.50485i −0.0473278 + 0.0819741i −0.888719 0.458453i $$-0.848404\pi$$
0.841391 + 0.540427i $$0.181737\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −0.950206 + 1.64580i −0.0514565 + 0.0891253i
$$342$$ 0 0
$$343$$ 17.6088 5.73840i 0.950787 0.309845i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 1.09272 0.0586600 0.0293300 0.999570i $$-0.490663\pi$$
0.0293300 + 0.999570i $$0.490663\pi$$
$$348$$ 0 0
$$349$$ −4.70096 8.14231i −0.251637 0.435848i 0.712340 0.701835i $$-0.247636\pi$$
−0.963977 + 0.265987i $$0.914302\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 9.64549 16.7065i 0.513378 0.889196i −0.486502 0.873680i $$-0.661727\pi$$
0.999880 0.0155167i $$-0.00493933\pi$$
$$354$$ 0 0
$$355$$ 2.09242 + 3.62418i 0.111054 + 0.192352i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 2.94976 5.10914i 0.155682 0.269650i −0.777625 0.628729i $$-0.783576\pi$$
0.933307 + 0.359079i $$0.116909\pi$$
$$360$$ 0 0
$$361$$ −17.6476 30.5665i −0.928820 1.60876i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −19.6165 + 33.9768i −1.02677 + 1.77843i
$$366$$ 0 0
$$367$$ −5.48300 + 9.49684i −0.286210 + 0.495731i −0.972902 0.231218i $$-0.925729\pi$$
0.686692 + 0.726949i $$0.259062\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 9.99988 22.4776i 0.519168 1.16698i
$$372$$ 0 0
$$373$$ 15.9691 + 27.6592i 0.826847 + 1.43214i 0.900500 + 0.434856i $$0.143201\pi$$
−0.0736533 + 0.997284i $$0.523466\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 41.9326 2.15964
$$378$$ 0 0
$$379$$ −14.4354 −0.741495 −0.370747 0.928734i $$-0.620898\pi$$
−0.370747 + 0.928734i $$0.620898\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 8.86006 + 15.3461i 0.452728 + 0.784148i 0.998554 0.0537502i $$-0.0171175\pi$$
−0.545826 + 0.837898i $$0.683784\pi$$
$$384$$ 0 0
$$385$$ −3.45016 4.74585i −0.175837 0.241871i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 9.48751 16.4329i 0.481036 0.833179i −0.518727 0.854940i $$-0.673594\pi$$
0.999763 + 0.0217610i $$0.00692730\pi$$
$$390$$ 0 0
$$391$$ −2.46095 + 4.26249i −0.124455 + 0.215563i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −7.62124 13.2004i −0.383466 0.664183i
$$396$$ 0 0
$$397$$ −10.5889 + 18.3405i −0.531440 + 0.920482i 0.467886 + 0.883789i $$0.345016\pi$$
−0.999327 + 0.0366930i $$0.988318\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 7.39038 + 12.8005i 0.369058 + 0.639227i 0.989419 0.145090i $$-0.0463470\pi$$
−0.620361 + 0.784317i $$0.713014\pi$$
$$402$$ 0 0
$$403$$ 8.28202 14.3449i 0.412557 0.714570i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0.00160993 + 0.00278847i 7.98011e−5 + 0.000138219i
$$408$$ 0 0
$$409$$ −3.73150 −0.184511 −0.0922554 0.995735i $$-0.529408\pi$$
−0.0922554 + 0.995735i $$0.529408\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 10.2916 + 14.1566i 0.506418 + 0.696600i
$$414$$ 0 0
$$415$$ −22.9469 + 39.7452i −1.12642 + 1.95102i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 14.1678 24.5393i 0.692142 1.19883i −0.278993 0.960293i $$-0.590001\pi$$
0.971135 0.238532i $$-0.0766661\pi$$
$$420$$ 0 0
$$421$$ −8.09776 14.0257i −0.394661 0.683572i 0.598397 0.801200i $$-0.295805\pi$$
−0.993058 + 0.117627i $$0.962471\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 36.2170 1.75678
$$426$$ 0 0
$$427$$ 3.01584 + 4.14841i 0.145947 + 0.200756i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −13.5528 23.4741i −0.652815 1.13071i −0.982437 0.186595i $$-0.940255\pi$$
0.329622 0.944113i $$-0.393079\pi$$
$$432$$ 0 0
$$433$$ −11.5028 −0.552789 −0.276394 0.961044i $$-0.589140\pi$$
−0.276394 + 0.961044i $$0.589140\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −8.53115 −0.408100
$$438$$ 0 0
$$439$$ −2.86714 −0.136841 −0.0684205 0.997657i $$-0.521796\pi$$
−0.0684205 + 0.997657i $$0.521796\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 8.84301 0.420144 0.210072 0.977686i $$-0.432630\pi$$
0.210072 + 0.977686i $$0.432630\pi$$
$$444$$ 0 0
$$445$$ −30.1109 −1.42739
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 40.5033 1.91147 0.955735 0.294229i $$-0.0950629\pi$$
0.955735 + 0.294229i $$0.0950629\pi$$
$$450$$ 0 0
$$451$$ 1.21194 + 2.09914i 0.0570680 + 0.0988446i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 30.0717 + 41.3650i 1.40979 + 1.93922i
$$456$$ 0 0
$$457$$ 38.8098 1.81545 0.907723 0.419571i $$-0.137819\pi$$
0.907723 + 0.419571i $$0.137819\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 16.1328 + 27.9428i 0.751378 + 1.30142i 0.947155 + 0.320776i $$0.103944\pi$$
−0.195777 + 0.980648i $$0.562723\pi$$
$$462$$ 0 0
$$463$$ −16.7430 + 28.9997i −0.778112 + 1.34773i 0.154917 + 0.987927i $$0.450489\pi$$
−0.933029 + 0.359802i $$0.882844\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 5.04280 8.73438i 0.233353 0.404179i −0.725440 0.688286i $$-0.758364\pi$$
0.958793 + 0.284107i $$0.0916970\pi$$
$$468$$ 0 0
$$469$$ −13.4275 18.4701i −0.620026 0.852872i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 4.41733 0.203109
$$474$$ 0 0
$$475$$ 31.3876 + 54.3649i 1.44016 + 2.49443i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 4.29759 7.44365i 0.196362 0.340109i −0.750984 0.660320i $$-0.770421\pi$$
0.947346 + 0.320211i $$0.103754\pi$$
$$480$$ 0 0
$$481$$ −0.0140322 0.0243044i −0.000639812 0.00110819i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 24.9268 43.1745i 1.13187 1.96045i
$$486$$ 0 0
$$487$$ −0.298843 0.517612i −0.0135419 0.0234552i 0.859175 0.511682i $$-0.170977\pi$$
−0.872717 + 0.488227i $$0.837644\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −17.1521 + 29.7084i −0.774066 + 1.34072i 0.161253 + 0.986913i $$0.448447\pi$$
−0.935318 + 0.353808i $$0.884887\pi$$
$$492$$ 0 0
$$493$$ 16.9546 29.3663i 0.763598 1.32259i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 1.77069 + 2.43566i 0.0794262 + 0.109254i
$$498$$ 0 0
$$499$$ −15.0247 26.0236i −0.672598 1.16497i −0.977165 0.212483i $$-0.931845\pi$$
0.304566 0.952491i $$-0.401488\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −18.5650 −0.827773 −0.413887 0.910328i $$-0.635829\pi$$
−0.413887 + 0.910328i $$0.635829\pi$$
$$504$$ 0 0
$$505$$ 56.4013 2.50983
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −3.50908 6.07790i −0.155537 0.269398i 0.777717 0.628614i $$-0.216377\pi$$
−0.933254 + 0.359216i $$0.883044\pi$$
$$510$$ 0 0
$$511$$ −11.4750 + 25.7934i −0.507624 + 1.14103i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 9.11986 15.7961i 0.401869 0.696057i
$$516$$ 0 0
$$517$$ 3.68438 6.38154i 0.162039 0.280660i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −15.0742 26.1092i −0.660411 1.14387i −0.980508 0.196481i $$-0.937049\pi$$
0.320096 0.947385i $$-0.396285\pi$$
$$522$$ 0 0
$$523$$ −14.1726 + 24.5476i −0.619724 + 1.07339i 0.369812 + 0.929107i $$0.379422\pi$$
−0.989536 + 0.144287i $$0.953911\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −6.69734 11.6001i −0.291741 0.505310i
$$528$$ 0 0
$$529$$ 10.8298 18.7577i 0.470860 0.815553i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −10.5633 18.2962i −0.457547 0.792495i
$$534$$ 0 0
$$535$$ 25.1056 1.08541
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −2.82689 3.13592i −0.121763 0.135074i
$$540$$ 0 0
$$541$$ −14.5245 + 25.1572i −0.624458 + 1.08159i 0.364187 + 0.931326i $$0.381347\pi$$
−0.988645 + 0.150268i $$0.951986\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 32.7313 56.6922i 1.40205 2.42843i
$$546$$ 0 0
$$547$$ −8.68455 15.0421i −0.371324 0.643153i 0.618445 0.785828i $$-0.287763\pi$$
−0.989770 + 0.142675i $$0.954430\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 58.7751 2.50390
$$552$$ 0 0
$$553$$ −6.44939 8.87141i −0.274256 0.377251i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −19.5927 33.9355i −0.830169 1.43789i −0.897904 0.440191i $$-0.854911\pi$$
0.0677355 0.997703i $$-0.478423\pi$$
$$558$$ 0 0
$$559$$ −38.5016 −1.62844
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −38.4078 −1.61870 −0.809349 0.587328i $$-0.800180\pi$$
−0.809349 + 0.587328i $$0.800180\pi$$
$$564$$ 0 0
$$565$$ −34.1174 −1.43533
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −9.08064 −0.380680 −0.190340 0.981718i $$-0.560959\pi$$
−0.190340 + 0.981718i $$0.560959\pi$$
$$570$$ 0 0
$$571$$ −37.0548 −1.55069 −0.775347 0.631536i $$-0.782425\pi$$
−0.775347 + 0.631536i $$0.782425\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 9.86358 0.411340
$$576$$ 0 0
$$577$$ 1.04241 + 1.80550i 0.0433960 + 0.0751641i 0.886908 0.461947i $$-0.152849\pi$$
−0.843512 + 0.537111i $$0.819516\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −13.4232 + 30.1725i −0.556887 + 1.25177i
$$582$$ 0 0
$$583$$ −5.60836 −0.232275
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −4.75919 8.24316i −0.196433 0.340232i 0.750936 0.660374i $$-0.229602\pi$$
−0.947369 + 0.320143i $$0.896269\pi$$
$$588$$ 0 0
$$589$$ 11.6085 20.1066i 0.478322 0.828477i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −7.63267 + 13.2202i −0.313436 + 0.542887i −0.979104 0.203361i $$-0.934814\pi$$
0.665668 + 0.746248i $$0.268147\pi$$
$$594$$ 0 0
$$595$$ 41.1276 4.33475i 1.68607 0.177707i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 20.1195 0.822059 0.411030 0.911622i $$-0.365169\pi$$
0.411030 + 0.911622i $$0.365169\pi$$
$$600$$ 0 0
$$601$$ −10.1529 17.5854i −0.414146 0.717322i 0.581192 0.813766i $$-0.302586\pi$$
−0.995338 + 0.0964440i $$0.969253\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 19.5540 33.8685i 0.794983 1.37695i
$$606$$ 0 0
$$607$$ 1.03649 + 1.79525i 0.0420698 + 0.0728670i 0.886294 0.463124i $$-0.153271\pi$$
−0.844224 + 0.535991i $$0.819938\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −32.1132 + 55.6217i −1.29916 + 2.25021i
$$612$$ 0 0
$$613$$ −1.10053 1.90618i −0.0444502 0.0769900i 0.842944 0.538001i $$-0.180820\pi$$
−0.887395 + 0.461011i $$0.847487\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 21.1904 36.7029i 0.853095 1.47760i −0.0253061 0.999680i $$-0.508056\pi$$
0.878401 0.477924i $$-0.158611\pi$$
$$618$$ 0 0
$$619$$ −6.93536 + 12.0124i −0.278756 + 0.482819i −0.971076 0.238772i $$-0.923255\pi$$
0.692320 + 0.721590i $$0.256589\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −21.5474 + 2.27105i −0.863280 + 0.0909876i
$$624$$ 0 0
$$625$$ −2.49141 4.31525i −0.0996565 0.172610i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −0.0226945 −0.000904889
$$630$$ 0 0
$$631$$ 45.1845 1.79876 0.899382 0.437163i $$-0.144017\pi$$
0.899382 + 0.437163i $$0.144017\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 27.5656 + 47.7450i 1.09391 + 1.89470i
$$636$$ 0 0
$$637$$ 24.6393 + 27.3328i 0.976244 + 1.08296i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −13.2564 + 22.9608i −0.523597 + 0.906896i 0.476026 + 0.879431i $$0.342077\pi$$
−0.999623 + 0.0274647i $$0.991257\pi$$
$$642$$ 0 0
$$643$$ 24.3184 42.1207i 0.959024 1.66108i 0.234145 0.972202i $$-0.424771\pi$$
0.724879 0.688876i $$-0.241896\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 10.7224 + 18.5717i 0.421540 + 0.730128i 0.996090 0.0883409i $$-0.0281565\pi$$
−0.574551 + 0.818469i $$0.694823\pi$$
$$648$$ 0 0
$$649$$ 1.99496 3.45537i 0.0783090 0.135635i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −1.74496 3.02235i −0.0682854 0.118274i 0.829861 0.557970i $$-0.188420\pi$$
−0.898147 + 0.439696i $$0.855086\pi$$
$$654$$ 0 0
$$655$$ 41.9765 72.7054i 1.64016 2.84083i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 18.2754 + 31.6539i 0.711908 + 1.23306i 0.964140 + 0.265394i $$0.0855021\pi$$
−0.252232 + 0.967667i $$0.581165\pi$$
$$660$$ 0 0
$$661$$ −5.57496 −0.216841 −0.108420 0.994105i $$-0.534579\pi$$
−0.108420 + 0.994105i $$0.534579\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 42.1502 + 57.9794i 1.63452 + 2.24835i
$$666$$ 0 0
$$667$$ 4.61753 7.99780i 0.178792 0.309676i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0.584598 1.01255i 0.0225682 0.0390892i
$$672$$ 0 0
$$673$$ 1.25661 + 2.17652i 0.0484389 + 0.0838986i 0.889228 0.457464i $$-0.151242\pi$$
−0.840789 + 0.541362i $$0.817909\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 31.7213 1.21915 0.609574 0.792729i $$-0.291341\pi$$
0.609574 + 0.792729i $$0.291341\pi$$
$$678$$ 0 0
$$679$$ 14.5813 32.7758i 0.559581 1.25782i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −21.4275 37.1136i −0.819902 1.42011i −0.905754 0.423804i $$-0.860695\pi$$
0.0858521 0.996308i $$-0.472639\pi$$
$$684$$ 0 0
$$685$$ −5.60932 −0.214321
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 48.8827 1.86228
$$690$$ 0 0
$$691$$ −14.7637 −0.561639 −0.280820 0.959761i $$-0.590606\pi$$
−0.280820 + 0.959761i $$0.590606\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 24.3613 0.924075
$$696$$ 0 0
$$697$$ −17.0842 −0.647111
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −19.8352 −0.749167 −0.374583 0.927193i $$-0.622214\pi$$
−0.374583 + 0.927193i $$0.622214\pi$$
$$702$$ 0 0
$$703$$ −0.0196683 0.0340664i −0.000741802 0.00128484i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 40.3609 4.25394i 1.51793 0.159986i
$$708$$ 0 0
$$709$$ 10.2058 0.383288 0.191644 0.981464i $$-0.438618\pi$$
0.191644 + 0.981464i $$0.438618\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −1.82400 3.15926i −0.0683092 0.118315i
$$714$$ 0 0
$$715$$ 5.82919 10.0965i 0.217999 0.377586i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −16.2769 + 28.1924i −0.607025 + 1.05140i 0.384703 + 0.923040i $$0.374304\pi$$
−0.991728 + 0.128358i $$0.959029\pi$$
$$720$$ 0 0
$$721$$ 5.33481 11.9915i 0.198679 0.446588i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −67.9549 −2.52378
$$726$$ 0 0
$$727$$ −7.65095 13.2518i −0.283758 0.491483i 0.688549 0.725190i $$-0.258248\pi$$
−0.972307 + 0.233706i $$0.924915\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −15.5673 + 26.9634i −0.575779 + 0.997279i
$$732$$ 0 0
$$733$$ 4.34677 + 7.52882i 0.160552 + 0.278083i 0.935067 0.354472i $$-0.115339\pi$$
−0.774515 + 0.632555i $$0.782006\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −2.60283 + 4.50823i −0.0958764 + 0.166063i
$$738$$ 0 0
$$739$$ −6.61922 11.4648i −0.243492 0.421740i 0.718215 0.695822i $$-0.244960\pi$$
−0.961707 + 0.274081i $$0.911626\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −10.7693 + 18.6530i −0.395089 + 0.684314i −0.993112 0.117165i $$-0.962619\pi$$
0.598024 + 0.801478i $$0.295953\pi$$
$$744$$ 0 0
$$745$$ −32.6780 + 56.6000i −1.19723 + 2.07366i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 17.9656 1.89353i 0.656449 0.0691881i
$$750$$ 0 0
$$751$$ −19.8241 34.3364i −0.723393 1.25295i −0.959632 0.281258i $$-0.909248\pi$$
0.236239 0.971695i $$-0.424085\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 17.0468 0.620395
$$756$$ 0 0
$$757$$ 13.0719 0.475108 0.237554 0.971374i $$-0.423654\pi$$
0.237554 + 0.971374i $$0.423654\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 9.17145 + 15.8854i 0.332465 + 0.575846i 0.982995 0.183635i $$-0.0587864\pi$$
−0.650530 + 0.759481i $$0.725453\pi$$
$$762$$ 0 0
$$763$$ 19.1467 43.0378i 0.693157 1.55807i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −17.3881 + 30.1171i −0.627849 + 1.08747i
$$768$$ 0 0
$$769$$ 7.46351 12.9272i 0.269141 0.466166i −0.699499 0.714633i $$-0.746594\pi$$
0.968640 + 0.248467i $$0.0799269\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −14.7818 25.6029i −0.531666 0.920873i −0.999317 0.0369592i $$-0.988233\pi$$
0.467651 0.883913i $$-0.345100\pi$$
$$774$$ 0 0
$$775$$ −13.4216 + 23.2469i −0.482118 + 0.835054i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −14.8061 25.6449i −0.530483 0.918824i
$$780$$ 0 0
$$781$$ 0.343235 0.594500i 0.0122819 0.0212729i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −6.27495 10.8685i −0.223962 0.387914i
$$786$$ 0 0
$$787$$ −9.32859 −0.332528 −0.166264 0.986081i $$-0.553170\pi$$
−0.166264 + 0.986081i $$0.553170\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −24.4145 + 2.57323i −0.868080 + 0.0914935i
$$792$$ 0 0
$$793$$ −5.09537 + 8.82545i −0.180942 + 0.313401i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 11.9334 20.6692i 0.422701 0.732140i −0.573502 0.819204i $$-0.694415\pi$$
0.996203 + 0.0870647i $$0.0277487\pi$$
$$798$$ 0 0
$$799$$ 25.9686 + 44.9790i 0.918705 + 1.59124i
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 6.43567 0.227110
$$804$$ 0 0