# Properties

 Label 3024.2.q.g.2881.3 Level $3024$ Weight $2$ Character 3024.2881 Analytic conductor $24.147$ Analytic rank $0$ Dimension $6$ 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: $$6$$ Relative dimension: $$3$$ over $$\Q(\zeta_{3})$$ Coefficient field: 6.0.309123.1 Defining polynomial: $$x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$3$$ Twist minimal: no (minimal twist has level 126) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 2881.3 Root $$0.500000 - 0.224437i$$ of defining polynomial Character $$\chi$$ $$=$$ 3024.2881 Dual form 3024.2.q.g.2305.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.794182 - 1.37556i) q^{5} +(-1.23855 - 2.33795i) q^{7} +O(q^{10})$$ $$q+(0.794182 - 1.37556i) q^{5} +(-1.23855 - 2.33795i) q^{7} +(0.794182 + 1.37556i) q^{11} +(2.40545 + 4.16635i) q^{13} +(2.69963 - 4.67589i) q^{17} +(3.54944 + 6.14781i) q^{19} +(-0.150186 + 0.260130i) q^{23} +(1.23855 + 2.14523i) q^{25} +(-4.13781 + 7.16689i) q^{29} +2.71201 q^{31} +(-4.19963 - 0.153051i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-2.93818 - 5.08907i) q^{41} +(0.833104 - 1.44298i) q^{43} +2.66621 q^{47} +(-3.93199 + 5.79133i) q^{49} +(-2.44437 + 4.23377i) q^{53} +2.52290 q^{55} +6.47710 q^{59} -4.47710 q^{61} +7.64145 q^{65} +10.0531 q^{67} +12.7207 q^{71} +(8.02654 - 13.9024i) q^{73} +(2.23236 - 3.56046i) q^{77} -8.38688 q^{79} +(1.18292 - 2.04887i) q^{83} +(-4.28799 - 7.42702i) q^{85} +(-1.60507 - 2.78007i) q^{89} +(6.76145 - 10.7840i) q^{91} +11.2756 q^{95} +(0.712008 - 1.23323i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6q - q^{5} - 2q^{7} + O(q^{10})$$ $$6q - q^{5} - 2q^{7} - q^{11} + 8q^{13} + 4q^{17} + 3q^{19} - 7q^{23} + 2q^{25} + 5q^{29} + 40q^{31} - 13q^{35} + 3q^{37} + 6q^{43} + 18q^{47} + 12q^{49} - 15q^{53} + 26q^{55} + 28q^{59} - 16q^{61} - 24q^{65} + 2q^{67} + 14q^{71} + 19q^{73} - 10q^{77} + 10q^{79} + 2q^{83} - 2q^{85} + 9q^{89} + 46q^{91} + 8q^{95} + 28q^{97} + O(q^{100})$$

## 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
$$5$$ 0.794182 1.37556i 0.355169 0.615171i −0.631978 0.774986i $$-0.717757\pi$$
0.987147 + 0.159816i $$0.0510900\pi$$
$$6$$ 0 0
$$7$$ −1.23855 2.33795i −0.468128 0.883661i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 0.794182 + 1.37556i 0.239455 + 0.414748i 0.960558 0.278080i $$-0.0896979\pi$$
−0.721103 + 0.692828i $$0.756365\pi$$
$$12$$ 0 0
$$13$$ 2.40545 + 4.16635i 0.667151 + 1.15554i 0.978697 + 0.205308i $$0.0658196\pi$$
−0.311547 + 0.950231i $$0.600847\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 2.69963 4.67589i 0.654756 1.13407i −0.327199 0.944955i $$-0.606105\pi$$
0.981955 0.189115i $$-0.0605620\pi$$
$$18$$ 0 0
$$19$$ 3.54944 + 6.14781i 0.814298 + 1.41041i 0.909831 + 0.414979i $$0.136211\pi$$
−0.0955331 + 0.995426i $$0.530456\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −0.150186 + 0.260130i −0.0313159 + 0.0542408i −0.881259 0.472634i $$-0.843303\pi$$
0.849943 + 0.526875i $$0.176636\pi$$
$$24$$ 0 0
$$25$$ 1.23855 + 2.14523i 0.247710 + 0.429046i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −4.13781 + 7.16689i −0.768371 + 1.33086i 0.170074 + 0.985431i $$0.445599\pi$$
−0.938446 + 0.345427i $$0.887734\pi$$
$$30$$ 0 0
$$31$$ 2.71201 0.487091 0.243545 0.969889i $$-0.421689\pi$$
0.243545 + 0.969889i $$0.421689\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −4.19963 0.153051i −0.709867 0.0258703i
$$36$$ 0 0
$$37$$ 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i $$-0.140472\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −2.93818 5.08907i −0.458866 0.794780i 0.540035 0.841643i $$-0.318411\pi$$
−0.998901 + 0.0468628i $$0.985078\pi$$
$$42$$ 0 0
$$43$$ 0.833104 1.44298i 0.127047 0.220052i −0.795484 0.605974i $$-0.792783\pi$$
0.922531 + 0.385922i $$0.126117\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 2.66621 0.388906 0.194453 0.980912i $$-0.437707\pi$$
0.194453 + 0.980912i $$0.437707\pi$$
$$48$$ 0 0
$$49$$ −3.93199 + 5.79133i −0.561713 + 0.827332i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −2.44437 + 4.23377i −0.335760 + 0.581553i −0.983630 0.180197i $$-0.942326\pi$$
0.647871 + 0.761750i $$0.275660\pi$$
$$54$$ 0 0
$$55$$ 2.52290 0.340188
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 6.47710 0.843247 0.421623 0.906771i $$-0.361460\pi$$
0.421623 + 0.906771i $$0.361460\pi$$
$$60$$ 0 0
$$61$$ −4.47710 −0.573234 −0.286617 0.958045i $$-0.592531\pi$$
−0.286617 + 0.958045i $$0.592531\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 7.64145 0.947805
$$66$$ 0 0
$$67$$ 10.0531 1.22818 0.614090 0.789236i $$-0.289523\pi$$
0.614090 + 0.789236i $$0.289523\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 12.7207 1.50967 0.754833 0.655917i $$-0.227718\pi$$
0.754833 + 0.655917i $$0.227718\pi$$
$$72$$ 0 0
$$73$$ 8.02654 13.9024i 0.939436 1.62715i 0.172909 0.984938i $$-0.444683\pi$$
0.766527 0.642213i $$-0.221983\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 2.23236 3.56046i 0.254401 0.405752i
$$78$$ 0 0
$$79$$ −8.38688 −0.943597 −0.471799 0.881706i $$-0.656395\pi$$
−0.471799 + 0.881706i $$0.656395\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 1.18292 2.04887i 0.129842 0.224893i −0.793773 0.608214i $$-0.791886\pi$$
0.923615 + 0.383321i $$0.125220\pi$$
$$84$$ 0 0
$$85$$ −4.28799 7.42702i −0.465098 0.805573i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −1.60507 2.78007i −0.170138 0.294687i 0.768330 0.640054i $$-0.221088\pi$$
−0.938468 + 0.345367i $$0.887755\pi$$
$$90$$ 0 0
$$91$$ 6.76145 10.7840i 0.708793 1.13047i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 11.2756 1.15685
$$96$$ 0 0
$$97$$ 0.712008 1.23323i 0.0722934 0.125216i −0.827613 0.561300i $$-0.810302\pi$$
0.899906 + 0.436084i $$0.143635\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 6.01671 + 10.4212i 0.598685 + 1.03695i 0.993015 + 0.117984i $$0.0376432\pi$$
−0.394330 + 0.918969i $$0.629023\pi$$
$$102$$ 0 0
$$103$$ −3.04944 + 5.28179i −0.300470 + 0.520430i −0.976243 0.216680i $$-0.930477\pi$$
0.675772 + 0.737111i $$0.263810\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1.54325 2.67299i −0.149192 0.258408i 0.781737 0.623608i $$-0.214334\pi$$
−0.930929 + 0.365200i $$0.881001\pi$$
$$108$$ 0 0
$$109$$ 1.14400 1.98146i 0.109575 0.189789i −0.806023 0.591884i $$-0.798384\pi$$
0.915598 + 0.402095i $$0.131718\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 9.73236 + 16.8569i 0.915543 + 1.58577i 0.806104 + 0.591774i $$0.201572\pi$$
0.109440 + 0.993993i $$0.465094\pi$$
$$114$$ 0 0
$$115$$ 0.238550 + 0.413181i 0.0222449 + 0.0385293i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −14.2756 0.520259i −1.30864 0.0476921i
$$120$$ 0 0
$$121$$ 4.23855 7.34138i 0.385323 0.667399i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 11.8764 1.06225
$$126$$ 0 0
$$127$$ 13.4400 1.19260 0.596302 0.802760i $$-0.296636\pi$$
0.596302 + 0.802760i $$0.296636\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 1.58836 2.75113i 0.138776 0.240367i −0.788258 0.615345i $$-0.789017\pi$$
0.927034 + 0.374978i $$0.122350\pi$$
$$132$$ 0 0
$$133$$ 9.97710 15.9128i 0.865124 1.37981i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −10.6316 18.4145i −0.908320 1.57326i −0.816397 0.577491i $$-0.804032\pi$$
−0.0919231 0.995766i $$-0.529301\pi$$
$$138$$ 0 0
$$139$$ −6.52654 11.3043i −0.553574 0.958818i −0.998013 0.0630092i $$-0.979930\pi$$
0.444439 0.895809i $$-0.353403\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −3.82072 + 6.61769i −0.319505 + 0.553399i
$$144$$ 0 0
$$145$$ 6.57234 + 11.3836i 0.545803 + 0.945359i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 2.60439 4.51093i 0.213360 0.369550i −0.739404 0.673262i $$-0.764893\pi$$
0.952764 + 0.303712i $$0.0982261\pi$$
$$150$$ 0 0
$$151$$ −0.261450 0.452845i −0.0212765 0.0368520i 0.855191 0.518313i $$-0.173440\pi$$
−0.876468 + 0.481461i $$0.840106\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 2.15383 3.73054i 0.173000 0.299644i
$$156$$ 0 0
$$157$$ 8.86398 0.707422 0.353711 0.935355i $$-0.384920\pi$$
0.353711 + 0.935355i $$0.384920\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0.794182 + 0.0289431i 0.0625903 + 0.00228104i
$$162$$ 0 0
$$163$$ −10.9814 19.0204i −0.860132 1.48979i −0.871801 0.489860i $$-0.837048\pi$$
0.0116689 0.999932i $$-0.496286\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 1.65019 + 2.85821i 0.127695 + 0.221175i 0.922783 0.385319i $$-0.125909\pi$$
−0.795088 + 0.606494i $$0.792575\pi$$
$$168$$ 0 0
$$169$$ −5.07234 + 8.78555i −0.390180 + 0.675812i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −19.1075 −1.45272 −0.726360 0.687315i $$-0.758789\pi$$
−0.726360 + 0.687315i $$0.758789\pi$$
$$174$$ 0 0
$$175$$ 3.48143 5.55264i 0.263171 0.419740i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −8.03706 + 13.9206i −0.600718 + 1.04047i 0.391994 + 0.919968i $$0.371785\pi$$
−0.992712 + 0.120507i $$0.961548\pi$$
$$180$$ 0 0
$$181$$ 8.05308 0.598581 0.299291 0.954162i $$-0.403250\pi$$
0.299291 + 0.954162i $$0.403250\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 1.58836 0.116779
$$186$$ 0 0
$$187$$ 8.57598 0.627138
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −23.9629 −1.73389 −0.866946 0.498402i $$-0.833920\pi$$
−0.866946 + 0.498402i $$0.833920\pi$$
$$192$$ 0 0
$$193$$ 9.76509 0.702907 0.351453 0.936205i $$-0.385688\pi$$
0.351453 + 0.936205i $$0.385688\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 18.2436 1.29980 0.649900 0.760020i $$-0.274811\pi$$
0.649900 + 0.760020i $$0.274811\pi$$
$$198$$ 0 0
$$199$$ −9.04944 + 15.6741i −0.641498 + 1.11111i 0.343601 + 0.939116i $$0.388353\pi$$
−0.985098 + 0.171991i $$0.944980\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 21.8807 + 0.797418i 1.53572 + 0.0559678i
$$204$$ 0 0
$$205$$ −9.33379 −0.651900
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −5.63781 + 9.76497i −0.389975 + 0.675457i
$$210$$ 0 0
$$211$$ −0.166208 0.287880i −0.0114422 0.0198185i 0.860248 0.509877i $$-0.170309\pi$$
−0.871690 + 0.490058i $$0.836976\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −1.32327 2.29197i −0.0902464 0.156311i
$$216$$ 0 0
$$217$$ −3.35896 6.34053i −0.228021 0.430423i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 25.9752 1.74728
$$222$$ 0 0
$$223$$ −3.16621 + 5.48403i −0.212025 + 0.367238i −0.952348 0.305013i $$-0.901339\pi$$
0.740323 + 0.672251i $$0.234672\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 11.6545 + 20.1862i 0.773537 + 1.33981i 0.935613 + 0.353028i $$0.114848\pi$$
−0.162075 + 0.986778i $$0.551819\pi$$
$$228$$ 0 0
$$229$$ 2.47710 4.29046i 0.163691 0.283522i −0.772498 0.635017i $$-0.780993\pi$$
0.936190 + 0.351495i $$0.114327\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 7.13781 + 12.3630i 0.467613 + 0.809930i 0.999315 0.0370017i $$-0.0117807\pi$$
−0.531702 + 0.846932i $$0.678447\pi$$
$$234$$ 0 0
$$235$$ 2.11745 3.66754i 0.138127 0.239244i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 2.48762 + 4.30868i 0.160911 + 0.278706i 0.935196 0.354132i $$-0.115224\pi$$
−0.774285 + 0.632837i $$0.781890\pi$$
$$240$$ 0 0
$$241$$ 6.50000 + 11.2583i 0.418702 + 0.725213i 0.995809 0.0914555i $$-0.0291519\pi$$
−0.577107 + 0.816668i $$0.695819\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 4.84362 + 10.0081i 0.309448 + 0.639392i
$$246$$ 0 0
$$247$$ −17.0760 + 29.5765i −1.08652 + 1.88191i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 2.43268 0.153549 0.0767746 0.997048i $$-0.475538\pi$$
0.0767746 + 0.997048i $$0.475538\pi$$
$$252$$ 0 0
$$253$$ −0.477100 −0.0299950
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −0.493810 + 0.855304i −0.0308030 + 0.0533524i −0.881016 0.473087i $$-0.843140\pi$$
0.850213 + 0.526439i $$0.176473\pi$$
$$258$$ 0 0
$$259$$ 1.40545 2.24159i 0.0873302 0.139286i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −8.59269 14.8830i −0.529848 0.917724i −0.999394 0.0348158i $$-0.988916\pi$$
0.469545 0.882908i $$-0.344418\pi$$
$$264$$ 0 0
$$265$$ 3.88255 + 6.72477i 0.238503 + 0.413099i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −11.4523 + 19.8360i −0.698262 + 1.20942i 0.270807 + 0.962634i $$0.412709\pi$$
−0.969069 + 0.246791i $$0.920624\pi$$
$$270$$ 0 0
$$271$$ −7.00364 12.1307i −0.425441 0.736885i 0.571021 0.820936i $$-0.306548\pi$$
−0.996462 + 0.0840504i $$0.973214\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −1.96727 + 3.40741i −0.118631 + 0.205474i
$$276$$ 0 0
$$277$$ −14.1476 24.5044i −0.850049 1.47233i −0.881163 0.472813i $$-0.843239\pi$$
0.0311139 0.999516i $$-0.490095\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 8.79782 15.2383i 0.524834 0.909039i −0.474748 0.880122i $$-0.657461\pi$$
0.999582 0.0289175i $$-0.00920600\pi$$
$$282$$ 0 0
$$283$$ 18.5229 1.10107 0.550536 0.834811i $$-0.314423\pi$$
0.550536 + 0.834811i $$0.314423\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −8.25890 + 13.1724i −0.487508 + 0.777541i
$$288$$ 0 0
$$289$$ −6.07598 10.5239i −0.357411 0.619054i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 7.04256 + 12.1981i 0.411431 + 0.712619i 0.995046 0.0994108i $$-0.0316958\pi$$
−0.583616 + 0.812030i $$0.698362\pi$$
$$294$$ 0 0
$$295$$ 5.14400 8.90966i 0.299495 0.518741i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −1.44506 −0.0835698
$$300$$ 0 0
$$301$$ −4.40545 0.160552i −0.253926 0.00925405i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −3.55563 + 6.15854i −0.203595 + 0.352637i
$$306$$ 0 0
$$307$$ 5.85532 0.334180 0.167090 0.985942i $$-0.446563\pi$$
0.167090 + 0.985942i $$0.446563\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0.810892 0.0459815 0.0229907 0.999736i $$-0.492681\pi$$
0.0229907 + 0.999736i $$0.492681\pi$$
$$312$$ 0 0
$$313$$ 10.5760 0.597790 0.298895 0.954286i $$-0.403382\pi$$
0.298895 + 0.954286i $$0.403382\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −12.1964 −0.685018 −0.342509 0.939515i $$-0.611277\pi$$
−0.342509 + 0.939515i $$0.611277\pi$$
$$318$$ 0 0
$$319$$ −13.1447 −0.735961
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 38.3287 2.13267
$$324$$ 0 0
$$325$$ −5.95853 + 10.3205i −0.330520 + 0.572477i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −3.30223 6.23345i −0.182058 0.343661i
$$330$$ 0 0
$$331$$ 15.6662 0.861093 0.430546 0.902568i $$-0.358321\pi$$
0.430546 + 0.902568i $$0.358321\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 7.98398 13.8287i 0.436211 0.755540i
$$336$$ 0 0
$$337$$ −4.21201 7.29541i −0.229443 0.397406i 0.728200 0.685364i $$-0.240357\pi$$
−0.957643 + 0.287958i $$0.907024\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 2.15383 + 3.73054i 0.116636 + 0.202020i
$$342$$ 0 0
$$343$$ 18.4098 + 2.01993i 0.994035 + 0.109066i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0.567323 0.0304555 0.0152277 0.999884i $$-0.495153\pi$$
0.0152277 + 0.999884i $$0.495153\pi$$
$$348$$ 0 0
$$349$$ −0.00364189 + 0.00630794i −0.000194946 + 0.000337656i −0.866123 0.499831i $$-0.833395\pi$$
0.865928 + 0.500169i $$0.166729\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 3.32691 + 5.76238i 0.177074 + 0.306701i 0.940877 0.338748i $$-0.110004\pi$$
−0.763803 + 0.645449i $$0.776670\pi$$
$$354$$ 0 0
$$355$$ 10.1025 17.4981i 0.536186 0.928702i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −0.398568 0.690339i −0.0210356 0.0364347i 0.855316 0.518107i $$-0.173363\pi$$
−0.876352 + 0.481672i $$0.840030\pi$$
$$360$$ 0 0
$$361$$ −15.6971 + 27.1881i −0.826162 + 1.43095i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −12.7491 22.0820i −0.667317 1.15583i
$$366$$ 0 0
$$367$$ −7.71634 13.3651i −0.402790 0.697652i 0.591272 0.806472i $$-0.298626\pi$$
−0.994061 + 0.108820i $$0.965293\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 12.9258 + 0.471067i 0.671074 + 0.0244566i
$$372$$ 0 0
$$373$$ −5.12110 + 8.87000i −0.265160 + 0.459271i −0.967606 0.252467i $$-0.918758\pi$$
0.702445 + 0.711738i $$0.252092\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −39.8131 −2.05048
$$378$$ 0 0
$$379$$ −25.0087 −1.28461 −0.642304 0.766450i $$-0.722021\pi$$
−0.642304 + 0.766450i $$0.722021\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 3.13348 5.42734i 0.160113 0.277324i −0.774796 0.632211i $$-0.782147\pi$$
0.934909 + 0.354887i $$0.115481\pi$$
$$384$$ 0 0
$$385$$ −3.12474 5.89841i −0.159251 0.300611i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −10.8171 18.7357i −0.548448 0.949940i −0.998381 0.0568774i $$-0.981886\pi$$
0.449933 0.893062i $$-0.351448\pi$$
$$390$$ 0 0
$$391$$ 0.810892 + 1.40451i 0.0410086 + 0.0710290i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −6.66071 + 11.5367i −0.335137 + 0.580473i
$$396$$ 0 0
$$397$$ 2.05308 + 3.55605i 0.103041 + 0.178473i 0.912936 0.408102i $$-0.133809\pi$$
−0.809895 + 0.586575i $$0.800476\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 8.37085 14.4987i 0.418021 0.724033i −0.577720 0.816235i $$-0.696057\pi$$
0.995740 + 0.0922024i $$0.0293907\pi$$
$$402$$ 0 0
$$403$$ 6.52359 + 11.2992i 0.324963 + 0.562853i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −0.794182 + 1.37556i −0.0393661 + 0.0681842i
$$408$$ 0 0
$$409$$ −8.76509 −0.433406 −0.216703 0.976238i $$-0.569530\pi$$
−0.216703 + 0.976238i $$0.569530\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −8.02221 15.1431i −0.394747 0.745144i
$$414$$ 0 0
$$415$$ −1.87890 3.25436i −0.0922318 0.159750i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −0.210149 0.363988i −0.0102664 0.0177820i 0.860847 0.508865i $$-0.169935\pi$$
−0.871113 + 0.491083i $$0.836601\pi$$
$$420$$ 0 0
$$421$$ 3.28799 5.69497i 0.160247 0.277556i −0.774710 0.632316i $$-0.782104\pi$$
0.934957 + 0.354761i $$0.115438\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 13.3745 0.648758
$$426$$ 0 0
$$427$$ 5.54511 + 10.4672i 0.268347 + 0.506544i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 11.0439 19.1287i 0.531968 0.921395i −0.467336 0.884080i $$-0.654786\pi$$
0.999304 0.0373155i $$-0.0118806\pi$$
$$432$$ 0 0
$$433$$ −9.43268 −0.453306 −0.226653 0.973976i $$-0.572778\pi$$
−0.226653 + 0.973976i $$0.572778\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −2.13231 −0.102002
$$438$$ 0 0
$$439$$ 31.2064 1.48940 0.744701 0.667398i $$-0.232592\pi$$
0.744701 + 0.667398i $$0.232592\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 13.0545 0.620236 0.310118 0.950698i $$-0.399631\pi$$
0.310118 + 0.950698i $$0.399631\pi$$
$$444$$ 0 0
$$445$$ −5.09888 −0.241710
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 9.91706 0.468015 0.234008 0.972235i $$-0.424816\pi$$
0.234008 + 0.972235i $$0.424816\pi$$
$$450$$ 0 0
$$451$$ 4.66690 8.08330i 0.219756 0.380628i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −9.46431 17.8653i −0.443694 0.837538i
$$456$$ 0 0
$$457$$ −24.5229 −1.14713 −0.573566 0.819159i $$-0.694441\pi$$
−0.573566 + 0.819159i $$0.694441\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −1.75526 + 3.04020i −0.0817506 + 0.141596i −0.904002 0.427528i $$-0.859384\pi$$
0.822251 + 0.569125i $$0.192718\pi$$
$$462$$ 0 0
$$463$$ −8.69413 15.0587i −0.404050 0.699836i 0.590160 0.807286i $$-0.299065\pi$$
−0.994210 + 0.107451i $$0.965731\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 6.69894 + 11.6029i 0.309990 + 0.536918i 0.978360 0.206911i $$-0.0663410\pi$$
−0.668370 + 0.743829i $$0.733008\pi$$
$$468$$ 0 0
$$469$$ −12.4512 23.5036i −0.574945 1.08529i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 2.64654 0.121688
$$474$$ 0 0
$$475$$ −8.79232 + 15.2287i −0.403419 + 0.698743i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −10.4029 18.0183i −0.475321 0.823279i 0.524280 0.851546i $$-0.324335\pi$$
−0.999600 + 0.0282667i $$0.991001\pi$$
$$480$$ 0 0
$$481$$ −2.40545 + 4.16635i −0.109679 + 0.189969i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −1.13093 1.95882i −0.0513528 0.0889456i
$$486$$ 0 0
$$487$$ −16.2472 + 28.1410i −0.736231 + 1.27519i 0.217950 + 0.975960i $$0.430063\pi$$
−0.954181 + 0.299230i $$0.903270\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −9.66071 16.7328i −0.435982 0.755142i 0.561394 0.827549i $$-0.310265\pi$$
−0.997375 + 0.0724067i $$0.976932\pi$$
$$492$$ 0 0
$$493$$ 22.3411 + 38.6959i 1.00619 + 1.74277i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −15.7552 29.7402i −0.706717 1.33403i
$$498$$ 0 0
$$499$$ −5.57530 + 9.65670i −0.249585 + 0.432293i −0.963411 0.268030i $$-0.913627\pi$$
0.713826 + 0.700323i $$0.246961\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −40.7651 −1.81763 −0.908813 0.417204i $$-0.863010\pi$$
−0.908813 + 0.417204i $$0.863010\pi$$
$$504$$ 0 0
$$505$$ 19.1135 0.850537
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 0.722528 1.25146i 0.0320255 0.0554698i −0.849568 0.527478i $$-0.823138\pi$$
0.881594 + 0.472009i $$0.156471\pi$$
$$510$$ 0 0
$$511$$ −42.4443 1.54684i −1.87762 0.0684280i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 4.84362 + 8.38940i 0.213436 + 0.369681i
$$516$$ 0 0
$$517$$ 2.11745 + 3.66754i 0.0931255 + 0.161298i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −9.64214 + 16.7007i −0.422430 + 0.731670i −0.996177 0.0873630i $$-0.972156\pi$$
0.573747 + 0.819033i $$0.305489\pi$$
$$522$$ 0 0
$$523$$ 18.3454 + 31.7752i 0.802189 + 1.38943i 0.918173 + 0.396180i $$0.129665\pi$$
−0.115984 + 0.993251i $$0.537002\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 7.32141 12.6811i 0.318926 0.552396i
$$528$$ 0 0
$$529$$ 11.4549 + 19.8404i 0.498039 + 0.862628i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 14.1353 24.4830i 0.612266 1.06048i
$$534$$ 0 0
$$535$$ −4.90249 −0.211953
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −11.0891 0.809332i −0.477639 0.0348604i
$$540$$ 0 0
$$541$$ −1.62543 2.81532i −0.0698825 0.121040i 0.828967 0.559298i $$-0.188929\pi$$
−0.898849 + 0.438258i $$0.855596\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −1.81708 3.14728i −0.0778352 0.134815i
$$546$$ 0 0
$$547$$ 2.95853 5.12432i 0.126498 0.219100i −0.795820 0.605534i $$-0.792960\pi$$
0.922317 + 0.386433i $$0.126293\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −58.7476 −2.50273
$$552$$ 0 0
$$553$$ 10.3876 + 19.6081i 0.441724 + 0.833820i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −12.8040 + 22.1772i −0.542523 + 0.939678i 0.456235 + 0.889859i $$0.349198\pi$$
−0.998758 + 0.0498188i $$0.984136\pi$$
$$558$$ 0 0
$$559$$ 8.01594 0.339038
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −46.6377 −1.96555 −0.982773 0.184817i $$-0.940831\pi$$
−0.982773 + 0.184817i $$0.940831\pi$$
$$564$$ 0 0
$$565$$ 30.9171 1.30069
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −31.1978 −1.30788 −0.653939 0.756547i $$-0.726885\pi$$
−0.653939 + 0.756547i $$0.726885\pi$$
$$570$$ 0 0
$$571$$ 15.6762 0.656030 0.328015 0.944672i $$-0.393620\pi$$
0.328015 + 0.944672i $$0.393620\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −0.744051 −0.0310291
$$576$$ 0 0
$$577$$ 6.99567 12.1169i 0.291234 0.504431i −0.682868 0.730542i $$-0.739268\pi$$
0.974102 + 0.226110i $$0.0726010\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −6.25526 0.227966i −0.259512 0.00945763i
$$582$$ 0 0
$$583$$ −7.76509 −0.321597
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 1.44801 2.50803i 0.0597658 0.103517i −0.834594 0.550865i $$-0.814298\pi$$
0.894360 + 0.447348i $$0.147631\pi$$
$$588$$ 0 0
$$589$$ 9.62612 + 16.6729i 0.396637 + 0.686996i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 2.04394 + 3.54021i 0.0839346 + 0.145379i 0.904937 0.425546i $$-0.139918\pi$$
−0.821002 + 0.570925i $$0.806585\pi$$
$$594$$ 0 0
$$595$$ −12.0531 + 19.2238i −0.494128 + 0.788100i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −19.7651 −0.807580 −0.403790 0.914852i $$-0.632307\pi$$
−0.403790 + 0.914852i $$0.632307\pi$$
$$600$$ 0 0
$$601$$ −13.4320 + 23.2649i −0.547902 + 0.948994i 0.450516 + 0.892768i $$0.351240\pi$$
−0.998418 + 0.0562261i $$0.982093\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −6.73236 11.6608i −0.273709 0.474079i
$$606$$ 0 0
$$607$$ −7.62110 + 13.2001i −0.309331 + 0.535777i −0.978216 0.207589i $$-0.933438\pi$$
0.668885 + 0.743366i $$0.266772\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 6.41342 + 11.1084i 0.259459 + 0.449396i
$$612$$ 0 0
$$613$$ −1.36033 + 2.35617i −0.0549434 + 0.0951648i −0.892189 0.451662i $$-0.850831\pi$$
0.837246 + 0.546827i $$0.184165\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 9.21812 + 15.9663i 0.371108 + 0.642777i 0.989736 0.142906i $$-0.0456448\pi$$
−0.618629 + 0.785684i $$0.712311\pi$$
$$618$$ 0 0
$$619$$ 0.0537728 + 0.0931373i 0.00216131 + 0.00374350i 0.867104 0.498127i $$-0.165979\pi$$
−0.864943 + 0.501871i $$0.832645\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −4.51169 + 7.19583i −0.180757 + 0.288295i
$$624$$ 0 0
$$625$$ 3.23924 5.61053i 0.129570 0.224421i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 5.39926 0.215282
$$630$$ 0 0
$$631$$ −35.7266 −1.42225 −0.711126 0.703064i $$-0.751815\pi$$
−0.711126 + 0.703064i $$0.751815\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 10.6738 18.4875i 0.423576 0.733655i
$$636$$ 0 0
$$637$$ −33.5869 2.45133i −1.33076 0.0971254i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 8.65638 + 14.9933i 0.341906 + 0.592199i 0.984787 0.173767i $$-0.0555941\pi$$
−0.642880 + 0.765967i $$0.722261\pi$$
$$642$$ 0 0
$$643$$ −14.4821 25.0838i −0.571119 0.989207i −0.996451 0.0841700i $$-0.973176\pi$$
0.425332 0.905037i $$-0.360157\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 1.27816 2.21384i 0.0502497 0.0870350i −0.839807 0.542886i $$-0.817332\pi$$
0.890056 + 0.455851i $$0.150665\pi$$
$$648$$ 0 0
$$649$$ 5.14400 + 8.90966i 0.201920 + 0.349735i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 14.9883 25.9605i 0.586538 1.01591i −0.408144 0.912918i $$-0.633824\pi$$
0.994682 0.102996i $$-0.0328428\pi$$
$$654$$ 0 0
$$655$$ −2.52290 4.36979i −0.0985779 0.170742i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −7.63162 + 13.2183i −0.297286 + 0.514914i −0.975514 0.219937i $$-0.929415\pi$$
0.678228 + 0.734851i $$0.262748\pi$$
$$660$$ 0 0
$$661$$ −27.2522 −1.05999 −0.529994 0.848001i $$-0.677806\pi$$
−0.529994 + 0.848001i $$0.677806\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −13.9654 26.3618i −0.541555 1.02227i
$$666$$ 0 0
$$667$$ −1.24288 2.15273i −0.0481245 0.0833541i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −3.55563 6.15854i −0.137264 0.237748i
$$672$$ 0 0
$$673$$ 23.2280 40.2320i 0.895372 1.55083i 0.0620280 0.998074i $$-0.480243\pi$$
0.833344 0.552755i $$-0.186423\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −5.09888 −0.195966 −0.0979830 0.995188i $$-0.531239\pi$$
−0.0979830 + 0.995188i $$0.531239\pi$$
$$678$$ 0 0
$$679$$ −3.76509 0.137215i −0.144491 0.00526582i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −7.77197 + 13.4614i −0.297386 + 0.515088i −0.975537 0.219835i $$-0.929448\pi$$
0.678151 + 0.734923i $$0.262782\pi$$
$$684$$ 0 0
$$685$$ −33.7738 −1.29043
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −23.5192 −0.896009
$$690$$ 0 0
$$691$$ −23.2967 −0.886246 −0.443123 0.896461i $$-0.646130\pi$$
−0.443123 + 0.896461i $$0.646130\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −20.7330 −0.786449
$$696$$ 0 0
$$697$$ −31.7280 −1.20178
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 45.6464 1.72404 0.862020 0.506874i $$-0.169199\pi$$
0.862020 + 0.506874i $$0.169199\pi$$
$$702$$ 0 0
$$703$$ −3.54944 + 6.14781i −0.133870 + 0.231869i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 16.9123 26.9740i 0.636053 1.01446i
$$708$$ 0 0
$$709$$ 18.0014 0.676056 0.338028 0.941136i $$-0.390240\pi$$
0.338028 + 0.941136i $$0.390240\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −0.407305 + 0.705474i −0.0152537 + 0.0264202i
$$714$$ 0 0
$$715$$ 6.06870 + 10.5113i 0.226957 + 0.393100i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 18.4389 + 31.9371i 0.687654 + 1.19105i 0.972595 + 0.232506i $$0.0746926\pi$$
−0.284941 + 0.958545i $$0.591974\pi$$
$$720$$ 0 0
$$721$$ 16.1254 + 0.587674i 0.600542 + 0.0218861i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −20.4995 −0.761333
$$726$$ 0 0
$$727$$ −15.2429 + 26.4014i −0.565327 + 0.979175i 0.431692 + 0.902021i $$0.357917\pi$$
−0.997019 + 0.0771543i $$0.975417\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −4.49814 7.79101i −0.166370 0.288161i
$$732$$ 0 0
$$733$$ −3.07530 + 5.32657i −0.113589 + 0.196741i −0.917215 0.398393i $$-0.869568\pi$$
0.803626 + 0.595135i $$0.202901\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 7.98398 + 13.8287i 0.294094 + 0.509385i
$$738$$ 0 0
$$739$$ 20.3912 35.3186i 0.750103 1.29922i −0.197670 0.980269i $$-0.563337\pi$$
0.947772 0.318947i $$-0.103329\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 7.25271 + 12.5621i 0.266076 + 0.460858i 0.967845 0.251547i $$-0.0809394\pi$$
−0.701769 + 0.712405i $$0.747606\pi$$
$$744$$ 0 0
$$745$$ −4.13671 7.16500i −0.151557 0.262505i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −4.33792 + 6.91867i −0.158504 + 0.252803i
$$750$$ 0 0
$$751$$ 2.09455 3.62787i 0.0764314 0.132383i −0.825276 0.564729i $$-0.808981\pi$$
0.901708 + 0.432346i $$0.142314\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −0.830556 −0.0302270
$$756$$ 0 0
$$757$$ 2.38688 0.0867525 0.0433763 0.999059i $$-0.486189\pi$$
0.0433763 + 0.999059i $$0.486189\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 1.81708 3.14728i 0.0658692 0.114089i −0.831210 0.555959i $$-0.812351\pi$$
0.897079 + 0.441870i $$0.145685\pi$$
$$762$$ 0 0
$$763$$ −6.04944 0.220465i −0.219005 0.00798138i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 15.5803 + 26.9859i 0.562573 + 0.974404i
$$768$$ 0 0
$$769$$ −19.9672 34.5842i −0.720035 1.24714i −0.960985 0.276600i $$-0.910792\pi$$
0.240950 0.970538i $$-0.422541\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −18.0698 + 31.2978i −0.649925 + 1.12570i 0.333215 + 0.942851i $$0.391867\pi$$
−0.983140 + 0.182853i $$0.941467\pi$$
$$774$$ 0 0
$$775$$ 3.35896 + 5.81788i 0.120657 + 0.208985i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 20.8578 36.1267i 0.747308 1.29438i
$$780$$ 0 0
$$781$$ 10.1025 + 17.4981i 0.361497 + 0.626131i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 7.03961 12.1930i 0.251254 0.435186i
$$786$$ 0 0
$$787$$ 44.6377 1.59116 0.795582 0.605846i $$-0.207165\pi$$
0.795582 + 0.605846i $$0.207165\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 27.3566 43.6319i 0.972689 1.55137i
$$792$$ 0 0
$$793$$ −10.7694 18.6532i −0.382433 0.662394i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −26.2836 45.5245i −0.931012 1.61256i −0.781595 0.623786i $$-0.785593\pi$$
−0.149418 0.988774i $$-0.547740\pi$$
$$798$$ 0 0
$$799$$ 7.19777 12.4669i 0.254639 0.441047i
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 25.4981 0.899810
$$804$$ 0 0
$$805$$ 0.670538 1.06946i 0.0236334 0.0376936i
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0